Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,3,Mod(43,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.96185790339\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Character | \(\chi\) | \(=\) | 72.67 |
Dual form | 72.3.p.b.43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99054 | − | 0.194264i | −0.995272 | − | 0.0971320i | ||||
\(3\) | −0.136174 | − | 2.99691i | −0.0453914 | − | 0.998969i | ||||
\(4\) | 3.92452 | + | 0.773382i | 0.981131 | + | 0.193345i | ||||
\(5\) | −3.84571 | − | 2.22032i | −0.769141 | − | 0.444064i | 0.0634270 | − | 0.997986i | \(-0.479797\pi\) |
−0.832568 | + | 0.553923i | \(0.813130\pi\) | |||||||
\(6\) | −0.311131 | + | 5.99193i | −0.0518551 | + | 0.998655i | ||||
\(7\) | −0.704321 | + | 0.406640i | −0.100617 | + | 0.0580915i | −0.549464 | − | 0.835517i | \(-0.685168\pi\) |
0.448847 | + | 0.893609i | \(0.351835\pi\) | |||||||
\(8\) | −7.66169 | − | 2.30184i | −0.957711 | − | 0.287730i | ||||
\(9\) | −8.96291 | + | 0.816203i | −0.995879 | + | 0.0906893i | ||||
\(10\) | 7.22371 | + | 5.16672i | 0.722371 | + | 0.516672i | ||||
\(11\) | −3.72022 | − | 6.44360i | −0.338201 | − | 0.585782i | 0.645893 | − | 0.763428i | \(-0.276485\pi\) |
−0.984094 | + | 0.177646i | \(0.943152\pi\) | |||||||
\(12\) | 1.78333 | − | 11.8667i | 0.148611 | − | 0.988896i | ||||
\(13\) | −18.0943 | − | 10.4468i | −1.39187 | − | 0.803598i | −0.398349 | − | 0.917234i | \(-0.630417\pi\) |
−0.993522 | + | 0.113636i | \(0.963750\pi\) | |||||||
\(14\) | 1.48098 | − | 0.672610i | 0.105784 | − | 0.0480436i | ||||
\(15\) | −6.13041 | + | 11.8276i | −0.408694 | + | 0.788505i | ||||
\(16\) | 14.8038 | + | 6.07031i | 0.925235 | + | 0.379394i | ||||
\(17\) | 1.74716 | 0.102774 | 0.0513869 | − | 0.998679i | \(-0.483636\pi\) | ||||
0.0513869 | + | 0.998679i | \(0.483636\pi\) | |||||||
\(18\) | 17.9996 | + | 0.116483i | 0.999979 | + | 0.00647129i | ||||
\(19\) | 31.7920 | 1.67326 | 0.836631 | − | 0.547767i | \(-0.184522\pi\) | ||||
0.836631 | + | 0.547767i | \(0.184522\pi\) | |||||||
\(20\) | −13.3754 | − | 11.6879i | −0.668770 | − | 0.584395i | ||||
\(21\) | 1.31457 | + | 2.05541i | 0.0625987 | + | 0.0978768i | ||||
\(22\) | 6.15349 | + | 13.5490i | 0.279704 | + | 0.615862i | ||||
\(23\) | 6.44927 | + | 3.72348i | 0.280403 | + | 0.161891i | 0.633606 | − | 0.773656i | \(-0.281574\pi\) |
−0.353203 | + | 0.935547i | \(0.614907\pi\) | |||||||
\(24\) | −5.85509 | + | 23.2748i | −0.243962 | + | 0.969785i | ||||
\(25\) | −2.64036 | − | 4.57325i | −0.105615 | − | 0.182930i | ||||
\(26\) | 33.9881 | + | 24.3098i | 1.30724 | + | 0.934993i | ||||
\(27\) | 3.66660 | + | 26.7499i | 0.135800 | + | 0.990736i | ||||
\(28\) | −3.07861 | + | 1.05116i | −0.109950 | + | 0.0375414i | ||||
\(29\) | 26.9672 | − | 15.5695i | 0.929904 | − | 0.536880i | 0.0431225 | − | 0.999070i | \(-0.486269\pi\) |
0.886781 | + | 0.462190i | \(0.152936\pi\) | |||||||
\(30\) | 14.5005 | − | 22.3524i | 0.483350 | − | 0.745079i | ||||
\(31\) | 4.91458 | + | 2.83744i | 0.158535 | + | 0.0915302i | 0.577169 | − | 0.816625i | \(-0.304158\pi\) |
−0.418634 | + | 0.908155i | \(0.637491\pi\) | |||||||
\(32\) | −28.2883 | − | 14.9590i | −0.884009 | − | 0.467470i | ||||
\(33\) | −18.8043 | + | 12.0266i | −0.569827 | + | 0.364442i | ||||
\(34\) | −3.47779 | − | 0.339410i | −0.102288 | − | 0.00998263i | ||||
\(35\) | 3.61148 | 0.103185 | ||||||||
\(36\) | −35.8064 | − | 3.72854i | −0.994622 | − | 0.103571i | ||||
\(37\) | − | 62.0787i | − | 1.67780i | −0.544283 | − | 0.838902i | \(-0.683198\pi\) | ||
0.544283 | − | 0.838902i | \(-0.316802\pi\) | |||||||
\(38\) | −63.2833 | − | 6.17604i | −1.66535 | − | 0.162527i | ||||
\(39\) | −28.8440 | + | 55.6496i | −0.739590 | + | 1.42691i | ||||
\(40\) | 24.3538 | + | 25.8636i | 0.608845 | + | 0.646590i | ||||
\(41\) | 2.74032 | − | 4.74637i | 0.0668370 | − | 0.115765i | −0.830670 | − | 0.556765i | \(-0.812043\pi\) |
0.897507 | + | 0.440999i | \(0.145376\pi\) | |||||||
\(42\) | −2.21742 | − | 4.34676i | −0.0527958 | − | 0.103494i | ||||
\(43\) | −22.3782 | − | 38.7602i | −0.520424 | − | 0.901401i | −0.999718 | − | 0.0237465i | \(-0.992441\pi\) |
0.479294 | − | 0.877654i | \(-0.340893\pi\) | |||||||
\(44\) | −9.61671 | − | 28.1652i | −0.218562 | − | 0.640119i | ||||
\(45\) | 36.2810 | + | 16.7617i | 0.806244 | + | 0.372481i | ||||
\(46\) | −12.1142 | − | 8.66462i | −0.263352 | − | 0.188361i | ||||
\(47\) | 71.1253 | − | 41.0642i | 1.51330 | − | 0.873707i | 0.513425 | − | 0.858134i | \(-0.328376\pi\) |
0.999879 | − | 0.0155723i | \(-0.00495702\pi\) | |||||||
\(48\) | 16.1763 | − | 45.1921i | 0.337005 | − | 0.941503i | ||||
\(49\) | −24.1693 | + | 41.8624i | −0.493251 | + | 0.854335i | ||||
\(50\) | 4.36734 | + | 9.61617i | 0.0873469 | + | 0.192323i | ||||
\(51\) | −0.237918 | − | 5.23607i | −0.00466505 | − | 0.102668i | ||||
\(52\) | −62.9323 | − | 54.9924i | −1.21024 | − | 1.05755i | ||||
\(53\) | 85.0348i | 1.60443i | 0.597035 | + | 0.802215i | \(0.296345\pi\) | ||||
−0.597035 | + | 0.802215i | \(0.703655\pi\) | |||||||
\(54\) | −2.10200 | − | 53.9591i | −0.0389258 | − | 0.999242i | ||||
\(55\) | 33.0403i | 0.600732i | ||||||||
\(56\) | 6.33232 | − | 1.49431i | 0.113077 | − | 0.0266842i | ||||
\(57\) | −4.32925 | − | 95.2776i | −0.0759517 | − | 1.67154i | ||||
\(58\) | −56.7040 | + | 25.7530i | −0.977655 | + | 0.444018i | ||||
\(59\) | −21.8641 | + | 37.8697i | −0.370578 | + | 0.641860i | −0.989655 | − | 0.143471i | \(-0.954174\pi\) |
0.619077 | + | 0.785331i | \(0.287507\pi\) | |||||||
\(60\) | −33.2061 | + | 41.6765i | −0.553436 | + | 0.694608i | ||||
\(61\) | −61.1107 | + | 35.2823i | −1.00182 | + | 0.578398i | −0.908785 | − | 0.417265i | \(-0.862989\pi\) |
−0.0930305 | + | 0.995663i | \(0.529655\pi\) | |||||||
\(62\) | −9.23148 | − | 6.60276i | −0.148895 | − | 0.106496i | ||||
\(63\) | 5.98087 | − | 4.21955i | 0.0949345 | − | 0.0669770i | ||||
\(64\) | 53.4030 | + | 35.2720i | 0.834422 | + | 0.551125i | ||||
\(65\) | 46.3903 | + | 80.3504i | 0.713697 | + | 1.23616i | ||||
\(66\) | 39.7671 | − | 20.2865i | 0.602531 | − | 0.307371i | ||||
\(67\) | 9.91758 | − | 17.1778i | 0.148024 | − | 0.256384i | −0.782473 | − | 0.622684i | \(-0.786042\pi\) |
0.930497 | + | 0.366300i | \(0.119376\pi\) | |||||||
\(68\) | 6.85675 | + | 1.35122i | 0.100835 | + | 0.0198709i | ||||
\(69\) | 10.2807 | − | 19.8349i | 0.148996 | − | 0.287462i | ||||
\(70\) | −7.18881 | − | 0.701581i | −0.102697 | − | 0.0100226i | ||||
\(71\) | − | 69.3125i | − | 0.976232i | −0.872779 | − | 0.488116i | \(-0.837684\pi\) | ||
0.872779 | − | 0.488116i | \(-0.162316\pi\) | |||||||
\(72\) | 70.5498 | + | 14.3777i | 0.979859 | + | 0.199691i | ||||
\(73\) | −21.7177 | −0.297502 | −0.148751 | − | 0.988875i | \(-0.547525\pi\) | ||||
−0.148751 | + | 0.988875i | \(0.547525\pi\) | |||||||
\(74\) | −12.0597 | + | 123.570i | −0.162968 | + | 1.66987i | ||||
\(75\) | −13.3460 | + | 8.53569i | −0.177947 | + | 0.113809i | ||||
\(76\) | 124.768 | + | 24.5873i | 1.64169 | + | 0.323518i | ||||
\(77\) | 5.24046 | + | 3.02558i | 0.0680579 | + | 0.0392932i | ||||
\(78\) | 68.2260 | − | 105.170i | 0.874692 | − | 1.34833i | ||||
\(79\) | 37.1475 | − | 21.4471i | 0.470221 | − | 0.271482i | −0.246111 | − | 0.969242i | \(-0.579153\pi\) |
0.716332 | + | 0.697759i | \(0.245820\pi\) | |||||||
\(80\) | −43.4529 | − | 56.2137i | −0.543161 | − | 0.702671i | ||||
\(81\) | 79.6676 | − | 14.6311i | 0.983551 | − | 0.180631i | ||||
\(82\) | −6.37677 | + | 8.91551i | −0.0777655 | + | 0.108726i | ||||
\(83\) | −3.53270 | − | 6.11881i | −0.0425626 | − | 0.0737206i | 0.843959 | − | 0.536407i | \(-0.180219\pi\) |
−0.886522 | + | 0.462687i | \(0.846886\pi\) | |||||||
\(84\) | 3.56946 | + | 9.08318i | 0.0424935 | + | 0.108133i | ||||
\(85\) | −6.71905 | − | 3.87924i | −0.0790476 | − | 0.0456382i | ||||
\(86\) | 37.0151 | + | 81.5012i | 0.430408 | + | 0.947689i | ||||
\(87\) | −50.3327 | − | 78.6981i | −0.578536 | − | 0.904575i | ||||
\(88\) | 13.6710 | + | 57.9323i | 0.155352 | + | 0.658321i | ||||
\(89\) | 37.1192 | 0.417070 | 0.208535 | − | 0.978015i | \(-0.433130\pi\) | ||||
0.208535 | + | 0.978015i | \(0.433130\pi\) | |||||||
\(90\) | −68.9626 | − | 40.4129i | −0.766251 | − | 0.449032i | ||||
\(91\) | 16.9923 | 0.186729 | ||||||||
\(92\) | 22.4306 | + | 19.6006i | 0.243811 | + | 0.213050i | ||||
\(93\) | 7.83429 | − | 15.1149i | 0.0842397 | − | 0.162526i | ||||
\(94\) | −149.555 | + | 67.9230i | −1.59101 | + | 0.722585i | ||||
\(95\) | −122.263 | − | 70.5883i | −1.28697 | − | 0.743035i | ||||
\(96\) | −40.9788 | + | 86.8144i | −0.426862 | + | 0.904317i | ||||
\(97\) | 9.38806 | + | 16.2606i | 0.0967841 | + | 0.167635i | 0.910352 | − | 0.413835i | \(-0.135811\pi\) |
−0.813568 | + | 0.581470i | \(0.802478\pi\) | |||||||
\(98\) | 56.2424 | − | 78.6338i | 0.573902 | − | 0.802385i | ||||
\(99\) | 38.6033 | + | 54.7170i | 0.389932 | + | 0.552697i | ||||
\(100\) | −6.82531 | − | 19.9898i | −0.0682531 | − | 0.199898i | ||||
\(101\) | −70.1044 | + | 40.4748i | −0.694103 | + | 0.400740i | −0.805147 | − | 0.593075i | \(-0.797914\pi\) |
0.111044 | + | 0.993815i | \(0.464580\pi\) | |||||||
\(102\) | −0.543594 | + | 10.4688i | −0.00532935 | + | 0.102636i | ||||
\(103\) | 28.0494 | + | 16.1943i | 0.272324 | + | 0.157226i | 0.629943 | − | 0.776641i | \(-0.283078\pi\) |
−0.357619 | + | 0.933867i | \(0.616411\pi\) | |||||||
\(104\) | 114.586 | + | 121.690i | 1.10179 | + | 1.17010i | ||||
\(105\) | −0.491791 | − | 10.8233i | −0.00468373 | − | 0.103079i | ||||
\(106\) | 16.5192 | − | 169.265i | 0.155842 | − | 1.59684i | ||||
\(107\) | −182.822 | −1.70862 | −0.854309 | − | 0.519765i | \(-0.826019\pi\) | ||||
−0.854309 | + | 0.519765i | \(0.826019\pi\) | |||||||
\(108\) | −6.29819 | + | 107.816i | −0.0583166 | + | 0.998298i | ||||
\(109\) | − | 7.30063i | − | 0.0669782i | −0.999439 | − | 0.0334891i | \(-0.989338\pi\) | ||
0.999439 | − | 0.0334891i | \(-0.0106619\pi\) | |||||||
\(110\) | 6.41853 | − | 65.7681i | 0.0583503 | − | 0.597892i | ||||
\(111\) | −186.044 | + | 8.45352i | −1.67607 | + | 0.0761579i | ||||
\(112\) | −12.8950 | + | 1.74436i | −0.115134 | + | 0.0155746i | ||||
\(113\) | 70.9810 | − | 122.943i | 0.628151 | − | 1.08799i | −0.359772 | − | 0.933040i | \(-0.617145\pi\) |
0.987923 | − | 0.154949i | \(-0.0495212\pi\) | |||||||
\(114\) | −9.89146 | + | 190.495i | −0.0867672 | + | 1.67101i | ||||
\(115\) | −16.5347 | − | 28.6389i | −0.143780 | − | 0.249034i | ||||
\(116\) | 117.875 | − | 40.2470i | 1.01616 | − | 0.346957i | ||||
\(117\) | 170.705 | + | 78.8648i | 1.45901 | + | 0.674058i | ||||
\(118\) | 50.8781 | − | 71.1339i | 0.431171 | − | 0.602830i | ||||
\(119\) | −1.23056 | + | 0.710464i | −0.0103408 | + | 0.00597028i | ||||
\(120\) | 74.1945 | − | 76.5080i | 0.618288 | − | 0.637567i | ||||
\(121\) | 32.8200 | − | 56.8459i | 0.271240 | − | 0.469801i | ||||
\(122\) | 128.498 | − | 58.3593i | 1.05326 | − | 0.478355i | ||||
\(123\) | −14.5976 | − | 7.56615i | −0.118680 | − | 0.0615134i | ||||
\(124\) | 17.0930 | + | 14.9364i | 0.137847 | + | 0.120455i | ||||
\(125\) | 134.466i | 1.07573i | ||||||||
\(126\) | −12.7249 | + | 7.23733i | −0.100991 | + | 0.0574391i | ||||
\(127\) | 113.378i | 0.892740i | 0.894849 | + | 0.446370i | \(0.147283\pi\) | ||||
−0.894849 | + | 0.446370i | \(0.852717\pi\) | |||||||
\(128\) | −99.4490 | − | 80.5848i | −0.776945 | − | 0.629568i | ||||
\(129\) | −113.114 | + | 72.3437i | −0.876849 | + | 0.560804i | ||||
\(130\) | −76.7327 | − | 168.953i | −0.590252 | − | 1.29964i | ||||
\(131\) | 77.7152 | − | 134.607i | 0.593245 | − | 1.02753i | −0.400546 | − | 0.916276i | \(-0.631180\pi\) |
0.993792 | − | 0.111255i | \(-0.0354870\pi\) | |||||||
\(132\) | −83.0990 | + | 32.6558i | −0.629538 | + | 0.247392i | ||||
\(133\) | −22.3918 | + | 12.9279i | −0.168359 | + | 0.0972022i | ||||
\(134\) | −23.0784 | + | 32.2664i | −0.172227 | + | 0.240794i | ||||
\(135\) | 45.2926 | − | 111.013i | 0.335501 | − | 0.822320i | ||||
\(136\) | −13.3862 | − | 4.02168i | −0.0984277 | − | 0.0295712i | ||||
\(137\) | −30.9899 | − | 53.6760i | −0.226203 | − | 0.391796i | 0.730476 | − | 0.682938i | \(-0.239298\pi\) |
−0.956680 | + | 0.291142i | \(0.905965\pi\) | |||||||
\(138\) | −24.3174 | + | 37.4850i | −0.176213 | + | 0.271631i | ||||
\(139\) | −67.1343 | + | 116.280i | −0.482981 | + | 0.836547i | −0.999809 | − | 0.0195419i | \(-0.993779\pi\) |
0.516828 | + | 0.856089i | \(0.327113\pi\) | |||||||
\(140\) | 14.1734 | + | 2.79306i | 0.101238 | + | 0.0199504i | ||||
\(141\) | −132.751 | − | 207.564i | −0.941497 | − | 1.47209i | ||||
\(142\) | −13.4649 | + | 137.970i | −0.0948234 | + | 0.971616i | ||||
\(143\) | 155.457i | 1.08711i | ||||||||
\(144\) | −137.639 | − | 42.3248i | −0.955829 | − | 0.293922i | ||||
\(145\) | −138.277 | −0.953636 | ||||||||
\(146\) | 43.2299 | + | 4.21896i | 0.296095 | + | 0.0288970i | ||||
\(147\) | 128.749 | + | 66.7325i | 0.875844 | + | 0.453963i | ||||
\(148\) | 48.0105 | − | 243.629i | 0.324396 | − | 1.64614i | ||||
\(149\) | −137.914 | − | 79.6250i | −0.925600 | − | 0.534396i | −0.0401830 | − | 0.999192i | \(-0.512794\pi\) |
−0.885417 | + | 0.464797i | \(0.846127\pi\) | |||||||
\(150\) | 28.2241 | − | 14.3980i | 0.188160 | − | 0.0959867i | ||||
\(151\) | 170.069 | − | 98.1895i | 1.12629 | − | 0.650261i | 0.183288 | − | 0.983059i | \(-0.441326\pi\) |
0.942998 | + | 0.332798i | \(0.107993\pi\) | |||||||
\(152\) | −243.580 | − | 73.1801i | −1.60250 | − | 0.481448i | ||||
\(153\) | −15.6596 | + | 1.42603i | −0.102350 | + | 0.00932049i | ||||
\(154\) | −9.84359 | − | 7.04058i | −0.0639194 | − | 0.0457180i | ||||
\(155\) | −12.6000 | − | 21.8239i | −0.0812905 | − | 0.140799i | ||||
\(156\) | −156.237 | + | 196.091i | −1.00152 | + | 1.25699i | ||||
\(157\) | 179.848 | + | 103.835i | 1.14553 | + | 0.661371i | 0.947794 | − | 0.318884i | \(-0.103308\pi\) |
0.197735 | + | 0.980256i | \(0.436642\pi\) | |||||||
\(158\) | −78.1100 | + | 35.4750i | −0.494367 | + | 0.224525i | ||||
\(159\) | 254.841 | − | 11.5796i | 1.60278 | − | 0.0728274i | ||||
\(160\) | 75.5745 | + | 120.337i | 0.472341 | + | 0.752107i | ||||
\(161\) | −6.05647 | −0.0376179 | ||||||||
\(162\) | −161.424 | + | 13.6473i | −0.996445 | + | 0.0842427i | ||||
\(163\) | 194.579 | 1.19373 | 0.596867 | − | 0.802340i | \(-0.296412\pi\) | ||||
0.596867 | + | 0.802340i | \(0.296412\pi\) | |||||||
\(164\) | 14.4252 | − | 16.5079i | 0.0879585 | − | 0.100658i | ||||
\(165\) | 99.0186 | − | 4.49923i | 0.600113 | − | 0.0272681i | ||||
\(166\) | 5.84332 | + | 12.8660i | 0.0352007 | + | 0.0775063i | ||||
\(167\) | −40.2285 | − | 23.2259i | −0.240889 | − | 0.139077i | 0.374696 | − | 0.927148i | \(-0.377747\pi\) |
−0.615585 | + | 0.788070i | \(0.711080\pi\) | |||||||
\(168\) | −5.34062 | − | 18.7739i | −0.0317894 | − | 0.111749i | ||||
\(169\) | 133.770 | + | 231.696i | 0.791538 | + | 1.37098i | ||||
\(170\) | 12.6210 | + | 9.02707i | 0.0742409 | + | 0.0531004i | ||||
\(171\) | −284.949 | + | 25.9487i | −1.66637 | + | 0.151747i | ||||
\(172\) | −57.8474 | − | 169.422i | −0.336322 | − | 0.985014i | ||||
\(173\) | 52.2672 | − | 30.1765i | 0.302123 | − | 0.174431i | −0.341273 | − | 0.939964i | \(-0.610858\pi\) |
0.643396 | + | 0.765533i | \(0.277525\pi\) | |||||||
\(174\) | 84.9011 | + | 166.430i | 0.487938 | + | 0.956492i | ||||
\(175\) | 3.71933 | + | 2.14736i | 0.0212533 | + | 0.0122706i | ||||
\(176\) | −15.9585 | − | 117.972i | −0.0906735 | − | 0.670298i | ||||
\(177\) | 116.469 | + | 60.3678i | 0.658019 | + | 0.341061i | ||||
\(178\) | −73.8874 | − | 7.21093i | −0.415098 | − | 0.0405108i | ||||
\(179\) | 123.945 | 0.692427 | 0.346214 | − | 0.938156i | \(-0.387467\pi\) | ||||
0.346214 | + | 0.938156i | \(0.387467\pi\) | |||||||
\(180\) | 129.422 | + | 93.8405i | 0.719013 | + | 0.521336i | ||||
\(181\) | − | 114.095i | − | 0.630359i | −0.949032 | − | 0.315179i | \(-0.897935\pi\) | ||
0.949032 | − | 0.315179i | \(-0.102065\pi\) | |||||||
\(182\) | −33.8239 | − | 3.30099i | −0.185846 | − | 0.0181373i | ||||
\(183\) | 114.060 | + | 178.339i | 0.623276 | + | 0.974528i | ||||
\(184\) | −40.8414 | − | 43.3734i | −0.221964 | − | 0.235725i | ||||
\(185\) | −137.835 | + | 238.736i | −0.745052 | + | 1.29047i | ||||
\(186\) | −18.5308 | + | 28.5650i | −0.0996279 | + | 0.153575i | ||||
\(187\) | −6.49980 | − | 11.2580i | −0.0347583 | − | 0.0602031i | ||||
\(188\) | 310.891 | − | 106.150i | 1.65368 | − | 0.564630i | ||||
\(189\) | −13.4600 | − | 17.3495i | −0.0712172 | − | 0.0917964i | ||||
\(190\) | 229.656 | + | 164.260i | 1.20872 | + | 0.864528i | ||||
\(191\) | 12.0842 | − | 6.97684i | 0.0632683 | − | 0.0365280i | −0.468032 | − | 0.883711i | \(-0.655037\pi\) |
0.531300 | + | 0.847183i | \(0.321704\pi\) | |||||||
\(192\) | 98.4349 | − | 164.847i | 0.512682 | − | 0.858579i | ||||
\(193\) | 30.2654 | − | 52.4212i | 0.156816 | − | 0.271613i | −0.776903 | − | 0.629620i | \(-0.783210\pi\) |
0.933719 | + | 0.358008i | \(0.116544\pi\) | |||||||
\(194\) | −15.5285 | − | 34.1912i | −0.0800437 | − | 0.176243i | ||||
\(195\) | 234.486 | − | 149.969i | 1.20249 | − | 0.769073i | ||||
\(196\) | −127.229 | + | 145.598i | −0.649125 | + | 0.742847i | ||||
\(197\) | − | 154.506i | − | 0.784296i | −0.919902 | − | 0.392148i | \(-0.871732\pi\) | ||
0.919902 | − | 0.392148i | \(-0.128268\pi\) | |||||||
\(198\) | −66.2119 | − | 116.416i | −0.334404 | − | 0.587958i | ||||
\(199\) | 268.439i | 1.34894i | 0.738301 | + | 0.674471i | \(0.235628\pi\) | ||||
−0.738301 | + | 0.674471i | \(0.764372\pi\) | |||||||
\(200\) | 9.70277 | + | 41.1165i | 0.0485138 | + | 0.205583i | ||||
\(201\) | −52.8307 | − | 27.3829i | −0.262839 | − | 0.136233i | ||||
\(202\) | 147.409 | − | 66.9480i | 0.729745 | − | 0.331426i | ||||
\(203\) | −12.6624 | + | 21.9319i | −0.0623763 | + | 0.108039i | ||||
\(204\) | 3.11576 | − | 20.7331i | 0.0152734 | − | 0.101633i | ||||
\(205\) | −21.0769 | + | 12.1688i | −0.102814 | + | 0.0593598i | ||||
\(206\) | −52.6875 | − | 37.6845i | −0.255765 | − | 0.182934i | ||||
\(207\) | −60.8433 | − | 28.1094i | −0.293929 | − | 0.135794i | ||||
\(208\) | −204.449 | − | 264.490i | −0.982928 | − | 1.27158i | ||||
\(209\) | −118.273 | − | 204.855i | −0.565900 | − | 0.980167i | ||||
\(210\) | −1.12364 | + | 21.6398i | −0.00535068 | + | 0.103046i | ||||
\(211\) | 59.5357 | − | 103.119i | 0.282159 | − | 0.488715i | −0.689757 | − | 0.724041i | \(-0.742283\pi\) |
0.971916 | + | 0.235326i | \(0.0756159\pi\) | |||||||
\(212\) | −65.7644 | + | 333.721i | −0.310209 | + | 1.57416i | ||||
\(213\) | −207.723 | + | 9.43858i | −0.975226 | + | 0.0443126i | ||||
\(214\) | 363.915 | + | 35.5158i | 1.70054 | + | 0.165962i | ||||
\(215\) | 198.747i | 0.924406i | ||||||||
\(216\) | 33.4816 | − | 213.389i | 0.155008 | − | 0.987913i | ||||
\(217\) | −4.61526 | −0.0212685 | ||||||||
\(218\) | −1.41825 | + | 14.5322i | −0.00650573 | + | 0.0666615i | ||||
\(219\) | 2.95739 | + | 65.0858i | 0.0135040 | + | 0.297196i | ||||
\(220\) | −25.5527 | + | 129.667i | −0.116149 | + | 0.589397i | ||||
\(221\) | −31.6136 | − | 18.2521i | −0.143048 | − | 0.0825888i | ||||
\(222\) | 371.971 | + | 19.3146i | 1.67555 | + | 0.0870026i | ||||
\(223\) | −93.8558 | + | 54.1876i | −0.420878 | + | 0.242994i | −0.695453 | − | 0.718572i | \(-0.744796\pi\) |
0.274575 | + | 0.961566i | \(0.411463\pi\) | |||||||
\(224\) | 26.0070 | − | 0.967174i | 0.116103 | − | 0.00431774i | ||||
\(225\) | 27.3981 | + | 38.8345i | 0.121769 | + | 0.172598i | ||||
\(226\) | −165.174 | + | 230.934i | −0.730859 | + | 1.02183i | ||||
\(227\) | 135.060 | + | 233.930i | 0.594977 | + | 1.03053i | 0.993550 | + | 0.113394i | \(0.0361721\pi\) |
−0.398573 | + | 0.917136i | \(0.630495\pi\) | |||||||
\(228\) | 56.6957 | − | 377.267i | 0.248666 | − | 1.65468i | ||||
\(229\) | 92.7803 | + | 53.5667i | 0.405154 | + | 0.233916i | 0.688705 | − | 0.725041i | \(-0.258179\pi\) |
−0.283551 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(230\) | 27.3494 | + | 60.2190i | 0.118911 | + | 0.261822i | ||||
\(231\) | 8.35376 | − | 16.1172i | 0.0361635 | − | 0.0697713i | ||||
\(232\) | −242.453 | + | 57.2146i | −1.04506 | + | 0.246615i | ||||
\(233\) | −224.925 | −0.965344 | −0.482672 | − | 0.875801i | \(-0.660334\pi\) | ||||
−0.482672 | + | 0.875801i | \(0.660334\pi\) | |||||||
\(234\) | −324.474 | − | 190.146i | −1.38664 | − | 0.812588i | ||||
\(235\) | −364.703 | −1.55193 | ||||||||
\(236\) | −115.094 | + | 131.711i | −0.487686 | + | 0.558099i | ||||
\(237\) | −69.3335 | − | 108.407i | −0.292546 | − | 0.457413i | ||||
\(238\) | 2.58750 | − | 1.17516i | 0.0108718 | − | 0.00493763i | ||||
\(239\) | 77.4022 | + | 44.6882i | 0.323859 | + | 0.186980i | 0.653111 | − | 0.757262i | \(-0.273463\pi\) |
−0.329253 | + | 0.944242i | \(0.606797\pi\) | |||||||
\(240\) | −162.550 | + | 137.879i | −0.677292 | + | 0.574497i | ||||
\(241\) | −135.051 | − | 233.915i | −0.560377 | − | 0.970602i | −0.997463 | − | 0.0711821i | \(-0.977323\pi\) |
0.437086 | − | 0.899420i | \(-0.356010\pi\) | |||||||
\(242\) | −76.3727 | + | 106.778i | −0.315590 | + | 0.441233i | ||||
\(243\) | −54.6968 | − | 236.764i | −0.225090 | − | 0.974338i | ||||
\(244\) | −267.117 | + | 91.2043i | −1.09474 | + | 0.373788i | ||||
\(245\) | 185.896 | − | 107.327i | 0.758759 | − | 0.438070i | ||||
\(246\) | 27.5873 | + | 17.8965i | 0.112144 | + | 0.0727501i | ||||
\(247\) | −575.255 | − | 332.123i | −2.32897 | − | 1.34463i | ||||
\(248\) | −31.1227 | − | 33.0522i | −0.125495 | − | 0.133275i | ||||
\(249\) | −17.8565 | + | 11.4204i | −0.0717127 | + | 0.0458650i | ||||
\(250\) | 26.1219 | − | 267.660i | 0.104487 | − | 1.07064i | ||||
\(251\) | 247.901 | 0.987654 | 0.493827 | − | 0.869560i | \(-0.335598\pi\) | ||||
0.493827 | + | 0.869560i | \(0.335598\pi\) | |||||||
\(252\) | 26.7354 | − | 11.9342i | 0.106093 | − | 0.0473580i | ||||
\(253\) | − | 55.4087i | − | 0.219007i | ||||||
\(254\) | 22.0253 | − | 225.684i | 0.0867136 | − | 0.888518i | ||||
\(255\) | −10.7108 | + | 20.6646i | −0.0420030 | + | 0.0810377i | ||||
\(256\) | 182.303 | + | 179.727i | 0.712120 | + | 0.702058i | ||||
\(257\) | 43.2996 | − | 74.9972i | 0.168481 | − | 0.291818i | −0.769405 | − | 0.638761i | \(-0.779447\pi\) |
0.937886 | + | 0.346944i | \(0.112780\pi\) | |||||||
\(258\) | 239.211 | − | 122.029i | 0.927175 | − | 0.472982i | ||||
\(259\) | 25.2437 | + | 43.7234i | 0.0974660 | + | 0.168816i | ||||
\(260\) | 119.918 | + | 351.214i | 0.461224 | + | 1.35082i | ||||
\(261\) | −228.997 | + | 161.559i | −0.877382 | + | 0.619000i | ||||
\(262\) | −180.845 | + | 252.843i | −0.690247 | + | 0.965050i | ||||
\(263\) | −36.7606 | + | 21.2237i | −0.139774 | + | 0.0806986i | −0.568256 | − | 0.822852i | \(-0.692382\pi\) |
0.428482 | + | 0.903550i | \(0.359048\pi\) | |||||||
\(264\) | 171.756 | − | 48.8596i | 0.650591 | − | 0.185074i | ||||
\(265\) | 188.804 | − | 327.019i | 0.712470 | − | 1.23403i | ||||
\(266\) | 47.0832 | − | 21.3836i | 0.177005 | − | 0.0803895i | ||||
\(267\) | −5.05468 | − | 111.243i | −0.0189314 | − | 0.416640i | ||||
\(268\) | 52.2067 | − | 59.7444i | 0.194801 | − | 0.222927i | ||||
\(269\) | − | 329.459i | − | 1.22475i | −0.790566 | − | 0.612377i | \(-0.790214\pi\) | ||
0.790566 | − | 0.612377i | \(-0.209786\pi\) | |||||||
\(270\) | −111.723 | + | 212.178i | −0.413788 | + | 0.785844i | ||||
\(271\) | − | 369.325i | − | 1.36282i | −0.731901 | − | 0.681411i | \(-0.761367\pi\) | ||
0.731901 | − | 0.681411i | \(-0.238633\pi\) | |||||||
\(272\) | 25.8645 | + | 10.6058i | 0.0950900 | + | 0.0389918i | ||||
\(273\) | −2.31391 | − | 50.9244i | −0.00847588 | − | 0.186536i | ||||
\(274\) | 51.2594 | + | 112.865i | 0.187078 | + | 0.411915i | ||||
\(275\) | −19.6455 | + | 34.0269i | −0.0714380 | + | 0.123734i | ||||
\(276\) | 55.6869 | − | 69.8916i | 0.201764 | − | 0.253230i | ||||
\(277\) | −159.324 | + | 91.9857i | −0.575177 | + | 0.332078i | −0.759214 | − | 0.650841i | \(-0.774417\pi\) |
0.184038 | + | 0.982919i | \(0.441083\pi\) | |||||||
\(278\) | 156.223 | − | 218.419i | 0.561952 | − | 0.785679i | ||||
\(279\) | −46.3649 | − | 21.4204i | −0.166182 | − | 0.0767756i | ||||
\(280\) | −27.6701 | − | 8.31307i | −0.0988217 | − | 0.0296895i | ||||
\(281\) | 197.079 | + | 341.350i | 0.701348 | + | 1.21477i | 0.967993 | + | 0.250976i | \(0.0807514\pi\) |
−0.266646 | + | 0.963795i | \(0.585915\pi\) | |||||||
\(282\) | 223.925 | + | 438.954i | 0.794059 | + | 1.55657i | ||||
\(283\) | −147.257 | + | 255.057i | −0.520344 | + | 0.901262i | 0.479377 | + | 0.877609i | \(0.340863\pi\) |
−0.999720 | + | 0.0236524i | \(0.992471\pi\) | |||||||
\(284\) | 53.6050 | − | 272.019i | 0.188750 | − | 0.957812i | ||||
\(285\) | −194.898 | + | 376.022i | −0.683852 | + | 1.31938i | ||||
\(286\) | 30.1997 | − | 309.444i | 0.105593 | − | 1.08197i | ||||
\(287\) | 4.45729i | 0.0155306i | ||||||||
\(288\) | 265.755 | + | 110.988i | 0.922761 | + | 0.385374i | ||||
\(289\) | −285.947 | −0.989438 | ||||||||
\(290\) | 275.247 | + | 26.8623i | 0.949127 | + | 0.0926286i | ||||
\(291\) | 47.4531 | − | 30.3494i | 0.163069 | − | 0.104294i | ||||
\(292\) | −85.2314 | − | 16.7960i | −0.291889 | − | 0.0575207i | ||||
\(293\) | 230.417 | + | 133.031i | 0.786406 | + | 0.454032i | 0.838696 | − | 0.544600i | \(-0.183319\pi\) |
−0.0522899 | + | 0.998632i | \(0.516652\pi\) | |||||||
\(294\) | −243.317 | − | 157.845i | −0.827608 | − | 0.536889i | ||||
\(295\) | 168.166 | − | 97.0905i | 0.570053 | − | 0.329120i | ||||
\(296\) | −142.895 | + | 475.628i | −0.482755 | + | 1.60685i | ||||
\(297\) | 158.725 | − | 123.141i | 0.534428 | − | 0.414618i | ||||
\(298\) | 259.056 | + | 185.289i | 0.869317 | + | 0.621774i | ||||
\(299\) | −77.7968 | − | 134.748i | −0.260190 | − | 0.450662i | ||||
\(300\) | −58.9782 | + | 23.1769i | −0.196594 | + | 0.0772564i | ||||
\(301\) | 31.5229 | + | 18.1998i | 0.104727 | + | 0.0604644i | ||||
\(302\) | −357.605 | + | 162.412i | −1.18412 | + | 0.537788i | ||||
\(303\) | 130.846 | + | 204.585i | 0.431834 | + | 0.675197i | ||||
\(304\) | 470.641 | + | 192.987i | 1.54816 | + | 0.634826i | ||||
\(305\) | 313.352 | 1.02738 | ||||||||
\(306\) | 31.4482 | + | 0.203514i | 0.102772 | + | 0.000665080i | ||||
\(307\) | 104.646 | 0.340865 | 0.170433 | − | 0.985369i | \(-0.445483\pi\) | ||||
0.170433 | + | 0.985369i | \(0.445483\pi\) | |||||||
\(308\) | 18.2264 | + | 15.9268i | 0.0591765 | + | 0.0517105i | ||||
\(309\) | 44.7133 | − | 86.2667i | 0.144703 | − | 0.279180i | ||||
\(310\) | 20.8413 | + | 45.8891i | 0.0672300 | + | 0.148029i | ||||
\(311\) | 268.616 | + | 155.085i | 0.863716 | + | 0.498667i | 0.865255 | − | 0.501332i | \(-0.167157\pi\) |
−0.00153895 | + | 0.999999i | \(0.500490\pi\) | |||||||
\(312\) | 349.091 | − | 359.976i | 1.11888 | − | 1.15377i | ||||
\(313\) | 201.331 | + | 348.715i | 0.643229 | + | 1.11411i | 0.984708 | + | 0.174216i | \(0.0557390\pi\) |
−0.341479 | + | 0.939890i | \(0.610928\pi\) | |||||||
\(314\) | −337.824 | − | 241.627i | −1.07587 | − | 0.769511i | ||||
\(315\) | −32.3694 | + | 2.94771i | −0.102760 | + | 0.00935780i | ||||
\(316\) | 162.373 | − | 55.4405i | 0.513838 | − | 0.175444i | ||||
\(317\) | 162.167 | − | 93.6269i | 0.511566 | − | 0.295353i | −0.221911 | − | 0.975067i | \(-0.571229\pi\) |
0.733477 | + | 0.679714i | \(0.237896\pi\) | |||||||
\(318\) | −509.522 | − | 26.4569i | −1.60227 | − | 0.0831979i | ||||
\(319\) | −200.648 | − | 115.844i | −0.628989 | − | 0.363147i | ||||
\(320\) | −127.057 | − | 254.218i | −0.397054 | − | 0.794430i | ||||
\(321\) | 24.8957 | + | 547.901i | 0.0775566 | + | 1.70686i | ||||
\(322\) | 12.0557 | + | 1.17655i | 0.0374400 | + | 0.00365390i | ||||
\(323\) | 55.5456 | 0.171968 | ||||||||
\(324\) | 323.973 | + | 4.19331i | 0.999916 | + | 0.0129423i | ||||
\(325\) | 110.333i | 0.339487i | ||||||||
\(326\) | −387.317 | − | 37.7996i | −1.18809 | − | 0.115950i | ||||
\(327\) | −21.8793 | + | 0.994158i | −0.0669092 | + | 0.00304024i | ||||
\(328\) | −31.9209 | + | 30.0574i | −0.0973197 | + | 0.0916386i | ||||
\(329\) | −33.3967 | + | 57.8448i | −0.101510 | + | 0.175820i | ||||
\(330\) | −197.975 | − | 10.2798i | −0.599924 | − | 0.0311510i | ||||
\(331\) | −77.0344 | − | 133.427i | −0.232732 | − | 0.403104i | 0.725879 | − | 0.687822i | \(-0.241433\pi\) |
−0.958611 | + | 0.284718i | \(0.908100\pi\) | |||||||
\(332\) | −9.13198 | − | 26.7455i | −0.0275060 | − | 0.0805589i | ||||
\(333\) | 50.6689 | + | 556.406i | 0.152159 | + | 1.67089i | ||||
\(334\) | 75.5646 | + | 54.0472i | 0.226241 | + | 0.161818i | ||||
\(335\) | −76.2802 | + | 44.0404i | −0.227702 | + | 0.131464i | ||||
\(336\) | 6.98365 | + | 38.4077i | 0.0207847 | + | 0.114309i | ||||
\(337\) | 199.096 | − | 344.845i | 0.590790 | − | 1.02328i | −0.403336 | − | 0.915052i | \(-0.632150\pi\) |
0.994126 | − | 0.108226i | \(-0.0345171\pi\) | |||||||
\(338\) | −221.265 | − | 487.188i | −0.654629 | − | 1.44139i | ||||
\(339\) | −378.114 | − | 195.982i | −1.11538 | − | 0.578118i | ||||
\(340\) | −23.3689 | − | 20.4206i | −0.0687321 | − | 0.0600605i | ||||
\(341\) | − | 42.2235i | − | 0.123823i | ||||||
\(342\) | 572.244 | + | 3.70323i | 1.67323 | + | 0.0108282i | ||||
\(343\) | − | 79.1635i | − | 0.230798i | ||||||
\(344\) | 82.2352 | + | 348.480i | 0.239056 | + | 1.01302i | ||||
\(345\) | −83.5764 | + | 53.4527i | −0.242250 | + | 0.154935i | ||||
\(346\) | −109.902 | + | 49.9140i | −0.317637 | + | 0.144260i | ||||
\(347\) | −211.923 | + | 367.061i | −0.610729 | + | 1.05781i | 0.380389 | + | 0.924827i | \(0.375790\pi\) |
−0.991118 | + | 0.132987i | \(0.957543\pi\) | |||||||
\(348\) | −136.668 | − | 347.779i | −0.392724 | − | 0.999364i | ||||
\(349\) | −140.567 | + | 81.1564i | −0.402771 | + | 0.232540i | −0.687679 | − | 0.726015i | \(-0.741370\pi\) |
0.284908 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(350\) | −6.98633 | − | 4.99694i | −0.0199610 | − | 0.0142770i | ||||
\(351\) | 213.105 | − | 522.325i | 0.607137 | − | 1.48811i | ||||
\(352\) | 8.84836 | + | 237.929i | 0.0251374 | + | 0.675936i | ||||
\(353\) | −162.240 | − | 281.009i | −0.459605 | − | 0.796059i | 0.539335 | − | 0.842091i | \(-0.318676\pi\) |
−0.998940 | + | 0.0460324i | \(0.985342\pi\) | |||||||
\(354\) | −220.110 | − | 142.791i | −0.621780 | − | 0.403363i | ||||
\(355\) | −153.896 | + | 266.555i | −0.433510 | + | 0.750861i | ||||
\(356\) | 145.675 | + | 28.7073i | 0.409200 | + | 0.0806386i | ||||
\(357\) | 2.29677 | + | 3.59113i | 0.00643352 | + | 0.0100592i | ||||
\(358\) | −246.717 | − | 24.0780i | −0.689153 | − | 0.0672569i | ||||
\(359\) | − | 344.963i | − | 0.960899i | −0.877022 | − | 0.480449i | \(-0.840474\pi\) | ||
0.877022 | − | 0.480449i | \(-0.159526\pi\) | |||||||
\(360\) | −239.391 | − | 211.936i | −0.664975 | − | 0.588710i | ||||
\(361\) | 649.730 | 1.79981 | ||||||||
\(362\) | −22.1645 | + | 227.111i | −0.0612280 | + | 0.627378i | ||||
\(363\) | −174.831 | − | 90.6175i | −0.481628 | − | 0.249635i | ||||
\(364\) | 66.6867 | + | 13.1415i | 0.183205 | + | 0.0361031i | ||||
\(365\) | 83.5197 | + | 48.2201i | 0.228821 | + | 0.132110i | ||||
\(366\) | −192.396 | − | 377.149i | −0.525671 | − | 1.03046i | ||||
\(367\) | 16.3628 | − | 9.44709i | 0.0445854 | − | 0.0257414i | −0.477542 | − | 0.878609i | \(-0.658472\pi\) |
0.522127 | + | 0.852868i | \(0.325139\pi\) | |||||||
\(368\) | 72.8707 | + | 94.2706i | 0.198018 | + | 0.256170i | ||||
\(369\) | −20.6872 | + | 44.7780i | −0.0560630 | + | 0.121350i | ||||
\(370\) | 320.744 | − | 448.439i | 0.866874 | − | 1.21200i | ||||
\(371\) | −34.5786 | − | 59.8918i | −0.0932037 | − | 0.161434i | ||||
\(372\) | 42.4355 | − | 53.2600i | 0.114074 | − | 0.143172i | ||||
\(373\) | 465.036 | + | 268.489i | 1.24675 | + | 0.719809i | 0.970459 | − | 0.241267i | \(-0.0775628\pi\) |
0.276286 | + | 0.961075i | \(0.410896\pi\) | |||||||
\(374\) | 10.7511 | + | 23.6722i | 0.0287463 | + | 0.0632946i | ||||
\(375\) | 402.982 | − | 18.3108i | 1.07462 | − | 0.0488287i | ||||
\(376\) | −639.463 | + | 150.902i | −1.70070 | + | 0.401335i | ||||
\(377\) | −650.605 | −1.72574 | ||||||||
\(378\) | 23.4224 | + | 37.1498i | 0.0619640 | + | 0.0982798i | ||||
\(379\) | 439.491 | 1.15961 | 0.579804 | − | 0.814756i | \(-0.303129\pi\) | ||||
0.579804 | + | 0.814756i | \(0.303129\pi\) | |||||||
\(380\) | −425.231 | − | 371.581i | −1.11903 | − | 0.977845i | ||||
\(381\) | 339.783 | − | 15.4392i | 0.891820 | − | 0.0405227i | ||||
\(382\) | −25.4096 | + | 11.5402i | −0.0665172 | + | 0.0302099i | ||||
\(383\) | 225.692 | + | 130.303i | 0.589275 | + | 0.340218i | 0.764811 | − | 0.644255i | \(-0.222833\pi\) |
−0.175536 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(384\) | −227.963 | + | 309.013i | −0.593653 | + | 0.804721i | ||||
\(385\) | −13.4355 | − | 23.2710i | −0.0348974 | − | 0.0604441i | ||||
\(386\) | −70.4282 | + | 98.4672i | −0.182456 | + | 0.255096i | ||||
\(387\) | 232.210 | + | 329.139i | 0.600027 | + | 0.850490i | ||||
\(388\) | 24.2680 | + | 71.0756i | 0.0625464 | + | 0.183185i | ||||
\(389\) | −166.109 | + | 95.9029i | −0.427015 | + | 0.246537i | −0.698074 | − | 0.716026i | \(-0.745959\pi\) |
0.271059 | + | 0.962563i | \(0.412626\pi\) | |||||||
\(390\) | −495.887 | + | 252.968i | −1.27151 | + | 0.648636i | ||||
\(391\) | 11.2679 | + | 6.50551i | 0.0288181 | + | 0.0166381i | ||||
\(392\) | 281.538 | − | 265.103i | 0.718210 | − | 0.676284i | ||||
\(393\) | −413.986 | − | 214.575i | −1.05340 | − | 0.545993i | ||||
\(394\) | −30.0150 | + | 307.551i | −0.0761802 | + | 0.780587i | ||||
\(395\) | −190.478 | −0.482222 | ||||||||
\(396\) | 109.182 | + | 244.593i | 0.275713 | + | 0.617660i | ||||
\(397\) | − | 154.843i | − | 0.390032i | −0.980800 | − | 0.195016i | \(-0.937524\pi\) | ||
0.980800 | − | 0.195016i | \(-0.0624760\pi\) | |||||||
\(398\) | 52.1481 | − | 534.340i | 0.131025 | − | 1.34256i | ||||
\(399\) | 41.7929 | + | 65.3456i | 0.104744 | + | 0.163774i | ||||
\(400\) | −11.3263 | − | 83.7291i | −0.0283158 | − | 0.209323i | ||||
\(401\) | 185.704 | − | 321.649i | 0.463103 | − | 0.802118i | −0.536010 | − | 0.844211i | \(-0.680069\pi\) |
0.999114 | + | 0.0420930i | \(0.0134026\pi\) | |||||||
\(402\) | 99.8422 | + | 64.7699i | 0.248364 | + | 0.161119i | ||||
\(403\) | −59.2841 | − | 102.683i | −0.147107 | − | 0.254797i | ||||
\(404\) | −306.429 | + | 104.627i | −0.758487 | + | 0.258977i | ||||
\(405\) | −338.864 | − | 120.621i | −0.836701 | − | 0.297829i | ||||
\(406\) | 29.4656 | − | 41.1965i | 0.0725754 | − | 0.101469i | ||||
\(407\) | −400.011 | + | 230.946i | −0.982827 | + | 0.567435i | ||||
\(408\) | −10.2297 | + | 40.6648i | −0.0250729 | + | 0.0996686i | ||||
\(409\) | −95.0595 | + | 164.648i | −0.232419 | + | 0.402562i | −0.958520 | − | 0.285027i | \(-0.907997\pi\) |
0.726100 | + | 0.687589i | \(0.241331\pi\) | |||||||
\(410\) | 44.3185 | − | 20.1280i | 0.108094 | − | 0.0490926i | ||||
\(411\) | −156.642 | + | 100.183i | −0.381124 | + | 0.243754i | ||||
\(412\) | 97.5561 | + | 85.2479i | 0.236787 | + | 0.206912i | ||||
\(413\) | − | 35.5633i | − | 0.0861096i | ||||||
\(414\) | 115.651 | + | 67.7726i | 0.279349 | + | 0.163702i | ||||
\(415\) | 31.3749i | 0.0756021i | ||||||||
\(416\) | 355.584 | + | 566.195i | 0.854769 | + | 1.36105i | ||||
\(417\) | 357.623 | + | 185.361i | 0.857608 | + | 0.444511i | ||||
\(418\) | 195.632 | + | 430.749i | 0.468018 | + | 1.03050i | ||||
\(419\) | 311.307 | − | 539.200i | 0.742976 | − | 1.28687i | −0.208158 | − | 0.978095i | \(-0.566747\pi\) |
0.951134 | − | 0.308778i | \(-0.0999199\pi\) | |||||||
\(420\) | 6.44048 | − | 42.8566i | 0.0153345 | − | 0.102039i | ||||
\(421\) | 202.420 | − | 116.867i | 0.480808 | − | 0.277595i | −0.239945 | − | 0.970786i | \(-0.577129\pi\) |
0.720753 | + | 0.693192i | \(0.243796\pi\) | |||||||
\(422\) | −138.541 | + | 193.697i | −0.328295 | + | 0.458997i | ||||
\(423\) | −603.973 | + | 426.108i | −1.42783 | + | 1.00735i | ||||
\(424\) | 195.737 | − | 651.510i | 0.461643 | − | 1.53658i | ||||
\(425\) | −4.61313 | − | 7.99018i | −0.0108544 | − | 0.0188004i | ||||
\(426\) | 415.315 | + | 21.5652i | 0.974919 | + | 0.0506226i | ||||
\(427\) | 28.6944 | − | 49.7002i | 0.0672000 | − | 0.116394i | ||||
\(428\) | −717.490 | − | 141.391i | −1.67638 | − | 0.330354i | ||||
\(429\) | 465.890 | − | 21.1692i | 1.08599 | − | 0.0493455i | ||||
\(430\) | 38.6094 | − | 395.615i | 0.0897894 | − | 0.920035i | ||||
\(431\) | − | 458.401i | − | 1.06358i | −0.846878 | − | 0.531788i | \(-0.821520\pi\) | ||
0.846878 | − | 0.531788i | \(-0.178480\pi\) | |||||||
\(432\) | −108.100 | + | 418.256i | −0.250233 | + | 0.968186i | ||||
\(433\) | −281.824 | −0.650864 | −0.325432 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325432 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(434\) | 9.18688 | + | 0.896579i | 0.0211679 | + | 0.00206585i | ||||
\(435\) | 18.8298 | + | 414.404i | 0.0432869 | + | 0.952653i | ||||
\(436\) | 5.64617 | − | 28.6515i | 0.0129499 | − | 0.0657144i | ||||
\(437\) | 205.035 | + | 118.377i | 0.469187 | + | 0.270885i | ||||
\(438\) | 6.75703 | − | 130.131i | 0.0154270 | − | 0.297102i | ||||
\(439\) | −148.016 | + | 85.4568i | −0.337165 | + | 0.194662i | −0.659018 | − | 0.752127i | \(-0.729028\pi\) |
0.321853 | + | 0.946790i | \(0.395694\pi\) | |||||||
\(440\) | 76.0535 | − | 253.144i | 0.172849 | − | 0.575328i | ||||
\(441\) | 182.459 | − | 394.936i | 0.413739 | − | 0.895547i | ||||
\(442\) | 59.3825 | + | 42.4730i | 0.134350 | + | 0.0960929i | ||||
\(443\) | −14.6968 | − | 25.4556i | −0.0331756 | − | 0.0574618i | 0.848961 | − | 0.528456i | \(-0.177229\pi\) |
−0.882136 | + | 0.470994i | \(0.843895\pi\) | |||||||
\(444\) | −736.673 | − | 110.707i | −1.65917 | − | 0.249340i | ||||
\(445\) | −142.750 | − | 82.4165i | −0.320786 | − | 0.185206i | ||||
\(446\) | 197.351 | − | 89.6300i | 0.442490 | − | 0.200964i | ||||
\(447\) | −219.848 | + | 424.160i | −0.491831 | + | 0.948903i | ||||
\(448\) | −51.9559 | − | 3.12702i | −0.115973 | − | 0.00697996i | ||||
\(449\) | 426.134 | 0.949074 | 0.474537 | − | 0.880236i | \(-0.342616\pi\) | ||||
0.474537 | + | 0.880236i | \(0.342616\pi\) | |||||||
\(450\) | −46.9929 | − | 82.6243i | −0.104429 | − | 0.183609i | ||||
\(451\) | −40.7783 | −0.0904175 | ||||||||
\(452\) | 373.648 | − | 427.596i | 0.826656 | − | 0.946009i | ||||
\(453\) | −317.424 | − | 496.311i | −0.700715 | − | 1.09561i | ||||
\(454\) | −223.398 | − | 491.886i | −0.492066 | − | 1.08345i | ||||
\(455\) | −65.3474 | − | 37.7283i | −0.143621 | − | 0.0829194i | ||||
\(456\) | −186.145 | + | 739.953i | −0.408212 | + | 1.62270i | ||||
\(457\) | −178.504 | − | 309.178i | −0.390600 | − | 0.676539i | 0.601929 | − | 0.798550i | \(-0.294399\pi\) |
−0.992529 | + | 0.122011i | \(0.961066\pi\) | |||||||
\(458\) | −174.277 | − | 124.651i | −0.380517 | − | 0.272163i | ||||
\(459\) | 6.40613 | + | 46.7362i | 0.0139567 | + | 0.101822i | ||||
\(460\) | −42.7419 | − | 125.181i | −0.0929171 | − | 0.272134i | ||||
\(461\) | −724.146 | + | 418.086i | −1.57082 | + | 0.906911i | −0.574746 | + | 0.818332i | \(0.694899\pi\) |
−0.996069 | + | 0.0885790i | \(0.971767\pi\) | |||||||
\(462\) | −19.7595 | + | 30.4591i | −0.0427695 | + | 0.0659287i | ||||
\(463\) | 401.085 | + | 231.566i | 0.866274 | + | 0.500143i | 0.866108 | − | 0.499857i | \(-0.166614\pi\) |
0.000165490 | 1.00000i | \(0.499947\pi\) | ||||||||
\(464\) | 493.728 | − | 66.7883i | 1.06407 | − | 0.143940i | ||||
\(465\) | −63.6884 | + | 40.7330i | −0.136964 | + | 0.0875978i | ||||
\(466\) | 447.723 | + | 43.6949i | 0.960779 | + | 0.0937658i | ||||
\(467\) | 221.217 | 0.473698 | 0.236849 | − | 0.971546i | \(-0.423885\pi\) | ||||
0.236849 | + | 0.971546i | \(0.423885\pi\) | |||||||
\(468\) | 608.942 | + | 441.527i | 1.30116 | + | 0.943433i | ||||
\(469\) | 16.1315i | 0.0343956i | ||||||||
\(470\) | 725.956 | + | 70.8486i | 1.54459 | + | 0.150742i | ||||
\(471\) | 286.694 | − | 553.127i | 0.608692 | − | 1.17437i | ||||
\(472\) | 254.686 | − | 239.818i | 0.539589 | − | 0.508090i | ||||
\(473\) | −166.504 | + | 288.393i | −0.352016 | + | 0.609710i | ||||
\(474\) | 116.952 | + | 229.258i | 0.246734 | + | 0.483666i | ||||
\(475\) | −83.9424 | − | 145.393i | −0.176721 | − | 0.306090i | ||||
\(476\) | −5.37882 | + | 1.83654i | −0.0113000 | + | 0.00385828i | ||||
\(477\) | −69.4057 | − | 762.160i | −0.145505 | − | 1.59782i | ||||
\(478\) | −145.391 | − | 103.990i | −0.304166 | − | 0.217553i | ||||
\(479\) | −496.351 | + | 286.569i | −1.03622 | + | 0.598264i | −0.918761 | − | 0.394813i | \(-0.870809\pi\) |
−0.117463 | + | 0.993077i | \(0.537476\pi\) | |||||||
\(480\) | 350.348 | − | 242.877i | 0.729892 | − | 0.505993i | ||||
\(481\) | −648.522 | + | 1123.27i | −1.34828 | + | 2.33529i | ||||
\(482\) | 223.383 | + | 491.853i | 0.463451 | + | 1.02044i | ||||
\(483\) | 0.824736 | + | 18.1507i | 0.00170753 | + | 0.0375791i | ||||
\(484\) | 172.766 | − | 197.711i | 0.356955 | − | 0.408493i | ||||
\(485\) | − | 83.3779i | − | 0.171913i | ||||||
\(486\) | 62.8816 | + | 481.915i | 0.129386 | + | 0.991594i | ||||
\(487\) | 391.908i | 0.804739i | 0.915477 | + | 0.402369i | \(0.131813\pi\) | ||||
−0.915477 | + | 0.402369i | \(0.868187\pi\) | |||||||
\(488\) | 549.426 | − | 129.655i | 1.12587 | − | 0.265686i | ||||
\(489\) | −26.4966 | − | 583.134i | −0.0541853 | − | 1.19250i | ||||
\(490\) | −390.884 | + | 177.526i | −0.797722 | + | 0.362298i | ||||
\(491\) | −58.8904 | + | 102.001i | −0.119940 | + | 0.207742i | −0.919744 | − | 0.392520i | \(-0.871603\pi\) |
0.799804 | + | 0.600261i | \(0.204937\pi\) | |||||||
\(492\) | −51.4371 | − | 40.9830i | −0.104547 | − | 0.0832989i | ||||
\(493\) | 47.1159 | − | 27.2024i | 0.0955698 | − | 0.0551773i | ||||
\(494\) | 1080.55 | + | 772.857i | 2.18735 | + | 1.56449i | ||||
\(495\) | −26.9676 | − | 296.137i | −0.0544800 | − | 0.598257i | ||||
\(496\) | 55.5302 | + | 71.8378i | 0.111956 | + | 0.144834i | ||||
\(497\) | 28.1852 | + | 48.8183i | 0.0567108 | + | 0.0982259i | ||||
\(498\) | 37.7626 | − | 19.2639i | 0.0758286 | − | 0.0386826i | ||||
\(499\) | 30.7207 | − | 53.2099i | 0.0615646 | − | 0.106633i | −0.833600 | − | 0.552368i | \(-0.813724\pi\) |
0.895165 | + | 0.445735i | \(0.147058\pi\) | |||||||
\(500\) | −103.993 | + | 527.714i | −0.207987 | + | 1.05543i | ||||
\(501\) | −64.1279 | + | 123.724i | −0.128000 | + | 0.246954i | ||||
\(502\) | −493.458 | − | 48.1583i | −0.982984 | − | 0.0959328i | ||||
\(503\) | 284.541i | 0.565688i | 0.959166 | + | 0.282844i | \(0.0912779\pi\) | ||||
−0.959166 | + | 0.282844i | \(0.908722\pi\) | |||||||
\(504\) | −55.5363 | + | 18.5619i | −0.110191 | + | 0.0368291i | ||||
\(505\) | 359.468 | 0.711817 | ||||||||
\(506\) | −10.7639 | + | 110.293i | −0.0212725 | + | 0.217971i | ||||
\(507\) | 676.157 | − | 432.447i | 1.33364 | − | 0.852953i | ||||
\(508\) | −87.6844 | + | 444.954i | −0.172607 | + | 0.875894i | ||||
\(509\) | −445.430 | − | 257.169i | −0.875109 | − | 0.505244i | −0.00606608 | − | 0.999982i | \(-0.501931\pi\) |
−0.869043 | + | 0.494737i | \(0.835264\pi\) | |||||||
\(510\) | 25.3347 | − | 39.0531i | 0.0496758 | − | 0.0765747i | ||||
\(511\) | 15.2962 | − | 8.83127i | 0.0299339 | − | 0.0172823i | ||||
\(512\) | −327.967 | − | 393.169i | −0.640560 | − | 0.767908i | ||||
\(513\) | 116.569 | + | 850.432i | 0.227229 | + | 1.65776i | ||||
\(514\) | −100.759 | + | 140.874i | −0.196029 | + | 0.274073i | ||||
\(515\) | −71.9131 | − | 124.557i | −0.139637 | − | 0.241859i | ||||
\(516\) | −499.866 | + | 196.434i | −0.968732 | + | 0.380687i | ||||
\(517\) | −529.203 | − | 305.535i | −1.02360 | − | 0.590978i | ||||
\(518\) | −41.7548 | − | 91.9372i | −0.0806077 | − | 0.177485i | ||||
\(519\) | −97.5536 | − | 152.531i | −0.187965 | − | 0.293894i | ||||
\(520\) | −170.474 | − | 722.403i | −0.327835 | − | 1.38924i | ||||
\(521\) | 208.517 | 0.400224 | 0.200112 | − | 0.979773i | \(-0.435869\pi\) | ||||
0.200112 | + | 0.979773i | \(0.435869\pi\) | |||||||
\(522\) | 487.213 | − | 277.104i | 0.933358 | − | 0.530851i | ||||
\(523\) | −17.5861 | −0.0336254 | −0.0168127 | − | 0.999859i | \(-0.505352\pi\) | ||||
−0.0168127 | + | 0.999859i | \(0.505352\pi\) | |||||||
\(524\) | 409.097 | − | 468.163i | 0.780720 | − | 0.893441i | ||||
\(525\) | 5.92895 | − | 11.4389i | 0.0112932 | − | 0.0217884i | ||||
\(526\) | 77.2965 | − | 35.1055i | 0.146952 | − | 0.0667405i | ||||
\(527\) | 8.58654 | + | 4.95744i | 0.0162933 | + | 0.00940691i | ||||
\(528\) | −351.379 | + | 63.8911i | −0.665491 | + | 0.121006i | ||||
\(529\) | −236.771 | − | 410.100i | −0.447583 | − | 0.775236i | ||||
\(530\) | −439.351 | + | 614.267i | −0.828965 | + | 1.15899i | ||||
\(531\) | 165.057 | − | 357.269i | 0.310841 | − | 0.672822i | ||||
\(532\) | −97.8752 | + | 33.4184i | −0.183976 | + | 0.0628166i | ||||
\(533\) | −99.1685 | + | 57.2549i | −0.186057 | + | 0.107420i | ||||
\(534\) | −11.5489 | + | 222.416i | −0.0216272 | + | 0.416509i | ||||
\(535\) | 703.080 | + | 405.924i | 1.31417 | + | 0.758736i | ||||
\(536\) | −115.526 | + | 108.782i | −0.215533 | + | 0.202951i | ||||
\(537\) | −16.8781 | − | 371.450i | −0.0314303 | − | 0.691714i | ||||
\(538\) | −64.0020 | + | 655.802i | −0.118963 | + | 1.21896i | ||||
\(539\) | 359.660 | 0.667273 | ||||||||
\(540\) | 263.607 | − | 400.645i | 0.488162 | − | 0.741936i | ||||
\(541\) | − | 476.226i | − | 0.880271i | −0.897931 | − | 0.440135i | \(-0.854930\pi\) | ||
0.897931 | − | 0.440135i | \(-0.145070\pi\) | |||||||
\(542\) | −71.7465 | + | 735.156i | −0.132374 | + | 1.35638i | ||||
\(543\) | −341.932 | + | 15.5368i | −0.629709 | + | 0.0286129i | ||||
\(544\) | −49.4240 | − | 26.1358i | −0.0908530 | − | 0.0480437i | ||||
\(545\) | −16.2097 | + | 28.0761i | −0.0297426 | + | 0.0515157i | ||||
\(546\) | −5.28682 | + | 101.817i | −0.00968283 | + | 0.186477i | ||||
\(547\) | −64.5016 | − | 111.720i | −0.117919 | − | 0.204241i | 0.801024 | − | 0.598632i | \(-0.204289\pi\) |
−0.918943 | + | 0.394391i | \(0.870956\pi\) | |||||||
\(548\) | −80.1084 | − | 234.620i | −0.146183 | − | 0.428138i | ||||
\(549\) | 518.933 | − | 366.111i | 0.945233 | − | 0.666869i | ||||
\(550\) | 45.7153 | − | 63.9157i | 0.0831188 | − | 0.116210i | ||||
\(551\) | 857.341 | − | 494.986i | 1.55597 | − | 0.898341i | ||||
\(552\) | −124.425 | + | 128.304i | −0.225407 | + | 0.232435i | ||||
\(553\) | −17.4425 | + | 30.2113i | −0.0315416 | + | 0.0546316i | ||||
\(554\) | 335.011 | − | 152.151i | 0.604712 | − | 0.274640i | ||||
\(555\) | 734.241 | + | 380.568i | 1.32296 | + | 0.685708i | ||||
\(556\) | −353.399 | + | 404.423i | −0.635610 | + | 0.727380i | ||||
\(557\) | 325.840i | 0.584991i | 0.956267 | + | 0.292495i | \(0.0944856\pi\) | ||||
−0.956267 | + | 0.292495i | \(0.905514\pi\) | |||||||
\(558\) | 88.1301 | + | 51.6452i | 0.157939 | + | 0.0925542i | ||||
\(559\) | 935.121i | 1.67285i | ||||||||
\(560\) | 53.4635 | + | 21.9228i | 0.0954706 | + | 0.0391479i | ||||
\(561\) | −32.8540 | + | 21.0123i | −0.0585633 | + | 0.0374552i | ||||
\(562\) | −325.982 | − | 717.758i | −0.580039 | − | 1.27715i | ||||
\(563\) | −372.114 | + | 644.521i | −0.660949 | + | 1.14480i | 0.319418 | + | 0.947614i | \(0.396513\pi\) |
−0.980367 | + | 0.197183i | \(0.936821\pi\) | |||||||
\(564\) | −360.458 | − | 917.257i | −0.639111 | − | 1.62634i | ||||
\(565\) | −545.944 | + | 315.201i | −0.966273 | + | 0.557878i | ||||
\(566\) | 342.670 | − | 479.095i | 0.605425 | − | 0.846458i | ||||
\(567\) | −50.1620 | + | 42.7011i | −0.0884692 | + | 0.0753105i | ||||
\(568\) | −159.546 | + | 531.051i | −0.280892 | + | 0.934949i | ||||
\(569\) | −128.890 | − | 223.244i | −0.226520 | − | 0.392344i | 0.730255 | − | 0.683175i | \(-0.239401\pi\) |
−0.956774 | + | 0.290831i | \(0.906068\pi\) | |||||||
\(570\) | 461.000 | − | 710.626i | 0.808772 | − | 1.24671i | ||||
\(571\) | 300.850 | − | 521.087i | 0.526883 | − | 0.912587i | −0.472627 | − | 0.881263i | \(-0.656694\pi\) |
0.999509 | − | 0.0313247i | \(-0.00997259\pi\) | |||||||
\(572\) | −120.228 | + | 610.094i | −0.210188 | + | 1.06660i | ||||
\(573\) | −22.5545 | − | 35.2653i | −0.0393621 | − | 0.0615450i | ||||
\(574\) | 0.865892 | − | 8.87244i | 0.00150852 | − | 0.0154572i | ||||
\(575\) | − | 39.3254i | − | 0.0683921i | ||||||
\(576\) | −507.436 | − | 272.552i | −0.880965 | − | 0.473181i | ||||
\(577\) | −1095.59 | −1.89878 | −0.949388 | − | 0.314105i | \(-0.898296\pi\) | ||||
−0.949388 | + | 0.314105i | \(0.898296\pi\) | |||||||
\(578\) | 569.191 | + | 55.5493i | 0.984759 | + | 0.0961060i | ||||
\(579\) | −161.223 | − | 83.5642i | −0.278451 | − | 0.144325i | ||||
\(580\) | −542.672 | − | 106.941i | −0.935642 | − | 0.184381i | ||||
\(581\) | 4.97631 | + | 2.87307i | 0.00856508 | + | 0.00494505i | ||||
\(582\) | −100.353 | + | 51.1934i | −0.172428 | + | 0.0879611i | ||||
\(583\) | 547.931 | − | 316.348i | 0.939847 | − | 0.542621i | ||||
\(584\) | 166.394 | + | 49.9906i | 0.284921 | + | 0.0856004i | ||||
\(585\) | −481.375 | − | 682.310i | −0.822863 | − | 1.16634i | ||||
\(586\) | −432.812 | − | 309.566i | −0.738586 | − | 0.528270i | ||||
\(587\) | −229.342 | − | 397.231i | −0.390701 | − | 0.676714i | 0.601841 | − | 0.798616i | \(-0.294434\pi\) |
−0.992542 | + | 0.121902i | \(0.961101\pi\) | |||||||
\(588\) | 453.669 | + | 361.466i | 0.771546 | + | 0.614737i | ||||
\(589\) | 156.244 | + | 90.2077i | 0.265270 | + | 0.153154i | ||||
\(590\) | −353.602 | + | 160.594i | −0.599326 | + | 0.272194i | ||||
\(591\) | −463.041 | + | 21.0398i | −0.783487 | + | 0.0356003i | ||||
\(592\) | 376.837 | − | 918.999i | 0.636549 | − | 1.55236i | ||||
\(593\) | 660.704 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(594\) | −339.871 | + | 214.284i | −0.572173 | + | 0.360747i | ||||
\(595\) | 6.30983 | 0.0106048 | ||||||||
\(596\) | −479.668 | − | 419.150i | −0.804812 | − | 0.703273i | ||||
\(597\) | 804.488 | − | 36.5545i | 1.34755 | − | 0.0612304i | ||||
\(598\) | 128.681 | + | 283.335i | 0.215186 | + | 0.473804i | ||||
\(599\) | −787.521 | − | 454.676i | −1.31473 | − | 0.759058i | −0.331852 | − | 0.943332i | \(-0.607673\pi\) |
−0.982875 | + | 0.184274i | \(0.941007\pi\) | |||||||
\(600\) | 121.901 | − | 34.6773i | 0.203169 | − | 0.0577955i | ||||
\(601\) | 177.135 | + | 306.806i | 0.294733 | + | 0.510493i | 0.974923 | − | 0.222543i | \(-0.0714358\pi\) |
−0.680189 | + | 0.733036i | \(0.738103\pi\) | |||||||
\(602\) | −59.2122 | − | 42.3512i | −0.0983592 | − | 0.0703509i | ||||
\(603\) | −74.8699 | + | 162.057i | −0.124162 | + | 0.268752i | ||||
\(604\) | 743.378 | − | 253.819i | 1.23076 | − | 0.420229i | ||||
\(605\) | −252.432 | + | 145.742i | −0.417243 | + | 0.240895i | ||||
\(606\) | −220.710 | − | 432.653i | −0.364208 | − | 0.713949i | ||||
\(607\) | 452.946 | + | 261.509i | 0.746205 | + | 0.430822i | 0.824321 | − | 0.566123i | \(-0.191557\pi\) |
−0.0781160 | + | 0.996944i | \(0.524890\pi\) | |||||||
\(608\) | −899.341 | − | 475.578i | −1.47918 | − | 0.782200i | ||||
\(609\) | 67.4522 | + | 34.9614i | 0.110759 | + | 0.0574080i | ||||
\(610\) | −623.740 | − | 60.8730i | −1.02253 | − | 0.0997918i | ||||
\(611\) | −1715.95 | −2.80843 | ||||||||
\(612\) | −62.5594 | − | 6.51435i | −0.102221 | − | 0.0106444i | ||||
\(613\) | 642.493i | 1.04811i | 0.851684 | + | 0.524056i | \(0.175582\pi\) | ||||
−0.851684 | + | 0.524056i | \(0.824418\pi\) | |||||||
\(614\) | −208.302 | − | 20.3289i | −0.339254 | − | 0.0331089i | ||||
\(615\) | 39.3388 | + | 61.5085i | 0.0639655 | + | 0.100014i | ||||
\(616\) | −33.1863 | − | 35.2438i | −0.0538739 | − | 0.0572139i | ||||
\(617\) | −489.218 | + | 847.351i | −0.792899 | + | 1.37334i | 0.131266 | + | 0.991347i | \(0.458096\pi\) |
−0.924165 | + | 0.381994i | \(0.875238\pi\) | |||||||
\(618\) | −105.762 | + | 163.031i | −0.171136 | + | 0.263805i | ||||
\(619\) | 297.240 | + | 514.836i | 0.480195 | + | 0.831721i | 0.999742 | − | 0.0227203i | \(-0.00723273\pi\) |
−0.519547 | + | 0.854442i | \(0.673899\pi\) | |||||||
\(620\) | −32.5709 | − | 95.3930i | −0.0525337 | − | 0.153860i | ||||
\(621\) | −75.9559 | + | 186.170i | −0.122312 | + | 0.299790i | ||||
\(622\) | −504.564 | − | 360.886i | −0.811195 | − | 0.580203i | ||||
\(623\) | −26.1439 | + | 15.0942i | −0.0419645 | + | 0.0242282i | ||||
\(624\) | −764.810 | + | 648.732i | −1.22566 | + | 1.03963i | ||||
\(625\) | 232.548 | − | 402.785i | 0.372077 | − | 0.644455i | ||||
\(626\) | −333.015 | − | 733.243i | −0.531972 | − | 1.17132i | ||||
\(627\) | −597.826 | + | 382.349i | −0.953470 | + | 0.609808i | ||||
\(628\) | 625.513 | + | 546.595i | 0.996040 | + | 0.870374i | ||||
\(629\) | − | 108.461i | − | 0.172434i | ||||||
\(630\) | 65.0054 | + | 0.420677i | 0.103183 | + | 0.000667742i | ||||
\(631\) | − | 259.788i | − | 0.411709i | −0.978583 | − | 0.205854i | \(-0.934003\pi\) | ||
0.978583 | − | 0.205854i | \(-0.0659973\pi\) | |||||||
\(632\) | −333.980 | + | 78.8134i | −0.528450 | + | 0.124705i | ||||
\(633\) | −317.145 | − | 164.381i | −0.501018 | − | 0.259685i | ||||
\(634\) | −340.988 | + | 154.865i | −0.537836 | + | 0.244267i | ||||
\(635\) | 251.735 | − | 436.018i | 0.396433 | − | 0.686643i | ||||
\(636\) | 1009.09 | + | 151.646i | 1.58661 | + | 0.238436i | ||||
\(637\) | 874.654 | − | 504.982i | 1.37308 | − | 0.792750i | ||||
\(638\) | 376.893 | + | 269.571i | 0.590742 | + | 0.422525i | ||||
\(639\) | 56.5731 | + | 621.242i | 0.0885338 | + | 0.972210i | ||||
\(640\) | 203.528 | + | 530.714i | 0.318012 | + | 0.829240i | ||||
\(641\) | 308.536 | + | 534.401i | 0.481336 | + | 0.833698i | 0.999771 | − | 0.0214189i | \(-0.00681837\pi\) |
−0.518435 | + | 0.855117i | \(0.673485\pi\) | |||||||
\(642\) | 56.8816 | − | 1095.46i | 0.0886006 | − | 1.70632i | ||||
\(643\) | −79.5086 | + | 137.713i | −0.123653 | + | 0.214172i | −0.921205 | − | 0.389077i | \(-0.872794\pi\) |
0.797553 | + | 0.603249i | \(0.206127\pi\) | |||||||
\(644\) | −23.7688 | − | 4.68397i | −0.0369080 | − | 0.00727324i | ||||
\(645\) | 595.627 | − | 27.0643i | 0.923453 | − | 0.0419601i | ||||
\(646\) | −110.566 | − | 10.7905i | −0.171155 | − | 0.0167036i | ||||
\(647\) | 53.2623i | 0.0823219i | 0.999153 | + | 0.0411610i | \(0.0131056\pi\) | ||||
−0.999153 | + | 0.0411610i | \(0.986894\pi\) | |||||||
\(648\) | −644.067 | − | 71.2832i | −0.993931 | − | 0.110005i | ||||
\(649\) | 325.357 | 0.501320 | ||||||||
\(650\) | 21.4338 | − | 219.623i | 0.0329750 | − | 0.337881i | ||||
\(651\) | 0.628480 | + | 13.8315i | 0.000965407 | + | 0.0212466i | ||||
\(652\) | 763.628 | + | 150.484i | 1.17121 | + | 0.230803i | ||||
\(653\) | 971.623 | + | 560.967i | 1.48794 | + | 0.859061i | 0.999905 | − | 0.0137652i | \(-0.00438174\pi\) |
0.488032 | + | 0.872826i | \(0.337715\pi\) | |||||||
\(654\) | 43.7448 | + | 2.27145i | 0.0668881 | + | 0.00347316i | ||||
\(655\) | −597.739 | + | 345.105i | −0.912579 | + | 0.526878i | ||||
\(656\) | 69.3790 | − | 53.6296i | 0.105761 | − | 0.0817524i | ||||
\(657\) | 194.653 | − | 17.7260i | 0.296276 | − | 0.0269803i | ||||
\(658\) | 77.7148 | − | 108.655i | 0.118108 | − | 0.165129i | ||||
\(659\) | 225.540 | + | 390.647i | 0.342246 | + | 0.592788i | 0.984850 | − | 0.173411i | \(-0.0554789\pi\) |
−0.642603 | + | 0.766199i | \(0.722146\pi\) | |||||||
\(660\) | 392.081 | + | 58.9219i | 0.594061 | + | 0.0892755i | ||||
\(661\) | −593.593 | − | 342.711i | −0.898023 | − | 0.518474i | −0.0214650 | − | 0.999770i | \(-0.506833\pi\) |
−0.876558 | + | 0.481296i | \(0.840166\pi\) | |||||||
\(662\) | 127.420 | + | 280.558i | 0.192477 | + | 0.423804i | ||||
\(663\) | −50.3950 | + | 97.2286i | −0.0760106 | + | 0.146649i | ||||
\(664\) | 12.9819 | + | 55.0122i | 0.0195511 | + | 0.0828497i | ||||
\(665\) | 114.816 | 0.172656 | ||||||||
\(666\) | 7.23113 | − | 1117.39i | 0.0108576 | − | 1.67777i | ||||
\(667\) | 231.892 | 0.347663 | ||||||||
\(668\) | −139.915 | − | 122.263i | −0.209454 | − | 0.183028i | ||||
\(669\) | 175.176 | + | 273.898i | 0.261848 | + | 0.409414i | ||||
\(670\) | 160.394 | − | 72.8458i | 0.239395 | − | 0.108725i | ||||
\(671\) | 454.690 | + | 262.516i | 0.677631 | + | 0.391230i | ||||
\(672\) | −6.44002 | − | 77.8089i | −0.00958336 | − | 0.115787i | ||||
\(673\) | 218.694 | + | 378.790i | 0.324954 | + | 0.562838i | 0.981503 | − | 0.191446i | \(-0.0613177\pi\) |
−0.656549 | + | 0.754284i | \(0.727984\pi\) | |||||||
\(674\) | −463.300 | + | 647.751i | −0.687389 | + | 0.961055i | ||||
\(675\) | 112.653 | − | 87.3977i | 0.166893 | − | 0.129478i | ||||
\(676\) | 345.794 | + | 1012.75i | 0.511529 | + | 1.49816i | ||||
\(677\) | 326.939 | − | 188.758i | 0.482923 | − | 0.278815i | −0.238711 | − | 0.971091i | \(-0.576725\pi\) |
0.721634 | + | 0.692275i | \(0.243392\pi\) | |||||||
\(678\) | 714.580 | + | 463.564i | 1.05395 | + | 0.683723i | ||||
\(679\) | −13.2244 | − | 7.63512i | −0.0194763 | − | 0.0112447i | ||||
\(680\) | 42.5499 | + | 45.1878i | 0.0625733 | + | 0.0664526i | ||||
\(681\) | 682.676 | − | 436.617i | 1.00246 | − | 0.641141i | ||||
\(682\) | −8.20250 | + | 84.0477i | −0.0120271 | + | 0.123237i | ||||
\(683\) | 1023.64 | 1.49874 | 0.749371 | − | 0.662151i | \(-0.230356\pi\) | ||||
0.749371 | + | 0.662151i | \(0.230356\pi\) | |||||||
\(684\) | −1138.36 | − | 118.538i | −1.66426 | − | 0.173301i | ||||
\(685\) | 275.230i | 0.401795i | ||||||||
\(686\) | −15.3786 | + | 157.578i | −0.0224178 | + | 0.229706i | ||||
\(687\) | 147.900 | − | 285.348i | 0.215284 | − | 0.415354i | ||||
\(688\) | −95.9955 | − | 709.640i | −0.139528 | − | 1.03145i | ||||
\(689\) | 888.339 | − | 1538.65i | 1.28932 | − | 2.23316i | ||||
\(690\) | 176.746 | − | 90.1640i | 0.256154 | − | 0.130672i | ||||
\(691\) | 134.426 | + | 232.833i | 0.194539 | + | 0.336951i | 0.946749 | − | 0.321972i | \(-0.104346\pi\) |
−0.752210 | + | 0.658923i | \(0.771012\pi\) | |||||||
\(692\) | 228.462 | − | 78.0058i | 0.330147 | − | 0.112725i | ||||
\(693\) | −49.4392 | − | 22.8407i | −0.0713409 | − | 0.0329592i | ||||
\(694\) | 493.149 | − | 689.483i | 0.710589 | − | 0.993491i | ||||
\(695\) | 516.358 | − | 298.119i | 0.742961 | − | 0.428949i | ||||
\(696\) | 204.483 | + | 718.818i | 0.293797 | + | 1.03278i | ||||
\(697\) | 4.78776 | − | 8.29265i | 0.00686910 | − | 0.0118976i | ||||
\(698\) | 295.570 | − | 134.238i | 0.423453 | − | 0.192318i | ||||
\(699\) | 30.6290 | + | 674.080i | 0.0438183 | + | 0.964349i | ||||
\(700\) | 12.9359 | + | 11.3038i | 0.0184798 | + | 0.0161483i | ||||
\(701\) | 888.158i | 1.26699i | 0.773748 | + | 0.633494i | \(0.218380\pi\) | ||||
−0.773748 | + | 0.633494i | \(0.781620\pi\) | |||||||
\(702\) | −525.664 | + | 998.313i | −0.748809 | + | 1.42210i | ||||
\(703\) | − | 1973.61i | − | 2.80740i | ||||||
\(704\) | 28.6081 | − | 475.328i | 0.0406365 | − | 0.675181i | ||||
\(705\) | 49.6631 | + | 1092.98i | 0.0704441 | + | 1.55033i | ||||
\(706\) | 268.357 | + | 590.878i | 0.380109 | + | 0.836937i | ||||
\(707\) | 32.9173 | − | 57.0145i | 0.0465592 | − | 0.0806429i | ||||
\(708\) | 410.399 | + | 326.990i | 0.579660 | + | 0.461850i | ||||
\(709\) | 158.288 | − | 91.3877i | 0.223256 | − | 0.128897i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(710\) | 358.119 | − | 500.694i | 0.504392 | − | 0.705202i | ||||
\(711\) | −315.444 | + | 222.548i | −0.443663 | + | 0.313008i | ||||
\(712\) | −284.396 | − | 85.4426i | −0.399433 | − | 0.120004i | ||||
\(713\) | 21.1303 | + | 36.5987i | 0.0296358 | + | 0.0513306i | ||||
\(714\) | −3.87418 | − | 7.59447i | −0.00542603 | − | 0.0106365i | ||||
\(715\) | 345.164 | − | 597.842i | 0.482747 | − | 0.836142i | ||||
\(716\) | 486.423 | + | 95.8564i | 0.679362 | + | 0.133878i | ||||
\(717\) | 123.386 | − | 238.053i | 0.172087 | − | 0.332012i | ||||
\(718\) | −67.0138 | + | 686.663i | −0.0933340 | + | 0.956355i | ||||
\(719\) | − | 1086.03i | − | 1.51047i | −0.655454 | − | 0.755235i | \(-0.727523\pi\) | ||
0.655454 | − | 0.755235i | \(-0.272477\pi\) | |||||||
\(720\) | 435.346 | + | 468.372i | 0.604648 | + | 0.650517i | ||||
\(721\) | −26.3410 | −0.0365340 | ||||||||
\(722\) | −1293.32 | − | 126.219i | −1.79130 | − | 0.174819i | ||||
\(723\) | −682.631 | + | 436.588i | −0.944165 | + | 0.603857i | ||||
\(724\) | 88.2389 | − | 447.768i | 0.121877 | − | 0.618464i | ||||
\(725\) | −142.407 | − | 82.2184i | −0.196423 | − | 0.113405i | ||||
\(726\) | 330.405 | + | 214.341i | 0.455103 | + | 0.295236i | ||||
\(727\) | −672.535 | + | 388.288i | −0.925082 | + | 0.534096i | −0.885253 | − | 0.465110i | \(-0.846015\pi\) |
−0.0398294 | + | 0.999206i | \(0.512681\pi\) | |||||||
\(728\) | −130.190 | − | 39.1136i | −0.178832 | − | 0.0537275i | ||||
\(729\) | −702.112 | + | 196.162i | −0.963117 | + | 0.269084i | ||||
\(730\) | −156.882 | − | 112.209i | −0.214907 | − | 0.153711i | ||||
\(731\) | −39.0983 | − | 67.7202i | −0.0534860 | − | 0.0926405i | ||||
\(732\) | 309.705 | + | 788.106i | 0.423095 | + | 1.07665i | ||||
\(733\) | −1046.17 | − | 604.007i | −1.42724 | − | 0.824020i | −0.430342 | − | 0.902666i | \(-0.641607\pi\) |
−0.996903 | + | 0.0786463i | \(0.974940\pi\) | |||||||
\(734\) | −34.4062 | + | 15.6261i | −0.0468749 | + | 0.0212890i | ||||
\(735\) | −346.964 | − | 542.498i | −0.472059 | − | 0.738092i | ||||
\(736\) | −126.739 | − | 201.806i | −0.172200 | − | 0.274193i | ||||
\(737\) | −147.582 | −0.200247 | ||||||||
\(738\) | 49.8776 | − | 85.1137i | 0.0675848 | − | 0.115330i | ||||
\(739\) | −1269.30 | −1.71759 | −0.858794 | − | 0.512322i | \(-0.828786\pi\) | ||||
−0.858794 | + | 0.512322i | \(0.828786\pi\) | |||||||
\(740\) | −725.569 | + | 830.328i | −0.980499 | + | 1.12207i | ||||
\(741\) | −917.009 | + | 1769.21i | −1.23753 | + | 2.38760i | ||||
\(742\) | 57.1953 | + | 125.935i | 0.0770826 | + | 0.169723i | ||||
\(743\) | −49.1224 | − | 28.3609i | −0.0661136 | − | 0.0381707i | 0.466579 | − | 0.884480i | \(-0.345486\pi\) |
−0.532692 | + | 0.846309i | \(0.678820\pi\) | |||||||
\(744\) | −94.8162 | + | 97.7727i | −0.127441 | + | 0.131415i | ||||
\(745\) | 353.586 | + | 612.428i | 0.474612 | + | 0.822051i | ||||
\(746\) | −873.516 | − | 624.778i | −1.17093 | − | 0.837504i | ||||
\(747\) | 36.6575 | + | 51.9590i | 0.0490729 | + | 0.0695569i | ||||
\(748\) | −16.8019 | − | 49.2090i | −0.0224624 | − | 0.0657875i | ||||
\(749\) | 128.766 | − | 74.3428i | 0.171917 | − | 0.0992561i | ||||
\(750\) | −805.709 | − | 41.8364i | −1.07428 | − | 0.0557819i | ||||
\(751\) | 79.1677 | + | 45.7075i | 0.105416 | + | 0.0608622i | 0.551781 | − | 0.833989i | \(-0.313948\pi\) |
−0.446365 | + | 0.894851i | \(0.647282\pi\) | |||||||
\(752\) | 1302.19 | − | 176.152i | 1.73164 | − | 0.234245i | ||||
\(753\) | −33.7578 | − | 742.937i | −0.0448310 | − | 0.986636i | ||||
\(754\) | 1295.06 | + | 126.389i | 1.71758 | + | 0.167625i | ||||
\(755\) | −872.048 | −1.15503 | ||||||||
\(756\) | −39.4064 | − | 78.4984i | −0.0521249 | − | 0.103834i | ||||
\(757\) | − | 883.777i | − | 1.16747i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) | ||
0.811943 | − | 0.583736i | \(-0.198410\pi\) | |||||||
\(758\) | −874.826 | − | 85.3773i | −1.15412 | − | 0.112635i | ||||
\(759\) | −166.055 | + | 7.54524i | −0.218781 | + | 0.00994102i | ||||
\(760\) | 774.255 | + | 822.255i | 1.01876 | + | 1.08192i | ||||
\(761\) | −210.778 | + | 365.078i | −0.276975 | + | 0.479734i | −0.970631 | − | 0.240571i | \(-0.922665\pi\) |
0.693657 | + | 0.720306i | \(0.255999\pi\) | |||||||
\(762\) | −679.352 | − | 35.2753i | −0.891539 | − | 0.0462931i | ||||
\(763\) | 2.96873 | + | 5.14199i | 0.00389086 | + | 0.00673917i | ||||
\(764\) | 52.8206 | − | 18.0350i | 0.0691370 | − | 0.0236061i | ||||
\(765\) | 63.3885 | + | 29.2852i | 0.0828608 | + | 0.0382813i | ||||
\(766\) | −423.937 | − | 303.218i | −0.553442 | − | 0.395847i | ||||
\(767\) | 791.232 | − | 456.818i | 1.03159 | − | 0.595591i | ||||
\(768\) | 513.800 | − | 570.819i | 0.669010 | − | 0.743253i | ||||
\(769\) | −37.4028 | + | 64.7836i | −0.0486383 | + | 0.0842440i | −0.889320 | − | 0.457286i | \(-0.848821\pi\) |
0.840681 | + | 0.541530i | \(0.182155\pi\) | |||||||
\(770\) | 22.2232 | + | 48.9319i | 0.0288613 | + | 0.0635479i | ||||
\(771\) | −230.656 | − | 119.552i | −0.299165 | − | 0.155061i | ||||
\(772\) | 159.319 | − | 182.322i | 0.206372 | − | 0.236168i | ||||
\(773\) | 723.612i | 0.936108i | 0.883700 | + | 0.468054i | \(0.155045\pi\) | ||||
−0.883700 | + | 0.468054i | \(0.844955\pi\) | |||||||
\(774\) | −398.285 | − | 700.276i | −0.514580 | − | 0.904750i | ||||
\(775\) | − | 29.9675i | − | 0.0386677i | ||||||
\(776\) | −34.4991 | − | 146.193i | −0.0444576 | − | 0.188394i | ||||
\(777\) | 127.597 | − | 81.6070i | 0.164218 | − | 0.105028i | ||||
\(778\) | 349.277 | − | 158.630i | 0.448942 | − | 0.203894i | ||||
\(779\) | 87.1202 | − | 150.897i | 0.111836 | − | 0.193705i | ||||
\(780\) | 1036.23 | − | 407.211i | 1.32850 | − | 0.522065i | ||||
\(781\) | −446.622 | + | 257.857i | −0.571859 | + | 0.330163i | ||||
\(782\) | −21.1654 | − | 15.1384i | −0.0270657 | − | 0.0193586i | ||||
\(783\) | 515.361 | + | 664.282i | 0.658188 | + | 0.848381i | ||||
\(784\) | −611.914 | + | 473.006i | −0.780503 | + | 0.603325i | ||||
\(785\) | −461.095 | − | 798.640i | −0.587382 | − | 1.01738i | ||||
\(786\) | 782.373 | + | 507.544i | 0.995386 | + | 0.645730i | ||||
\(787\) | 608.548 | − | 1054.04i | 0.773251 | − | 1.33931i | −0.162522 | − | 0.986705i | \(-0.551963\pi\) |
0.935773 | − | 0.352604i | \(-0.114704\pi\) | |||||||
\(788\) | 119.492 | − | 606.363i | 0.151640 | − | 0.769496i | ||||
\(789\) | 68.6114 | + | 107.278i | 0.0869600 | + | 0.135967i | ||||
\(790\) | 379.154 | + | 37.0029i | 0.479942 | + | 0.0468392i | ||||
\(791\) | 115.455i | 0.145961i | ||||||||
\(792\) | −169.816 | − | 508.083i | −0.214415 | − | 0.641520i | ||||
\(793\) | 1474.34 | 1.85920 | ||||||||
\(794\) | −30.0804 | + | 308.221i | −0.0378846 | + | 0.388188i | ||||
\(795\) | −1005.76 | − | 521.298i | −1.26510 | − | 0.655721i | ||||
\(796\) | −207.606 | + | 1053.50i | −0.260812 | + | 1.32349i | ||||
\(797\) | −571.321 | − | 329.853i | −0.716840 | − | 0.413868i | 0.0967485 | − | 0.995309i | \(-0.469156\pi\) |
−0.813588 | + | 0.581441i | \(0.802489\pi\) | |||||||
\(798\) | −70.4963 | − | 138.192i | −0.0883412 | − | 0.173173i | ||||
\(799\) | 124.267 | − | 71.7456i | 0.155528 | − | 0.0897942i | ||||
\(800\) | 6.27998 | + | 168.867i | 0.00784998 | + | 0.211083i | ||||
\(801\) | −332.696 | + | 30.2968i | −0.415351 | + | 0.0378238i | ||||
\(802\) | −432.137 | + | 604.181i | −0.538825 | + | 0.753343i | ||||
\(803\) | 80.7944 | + | 139.940i | 0.100616 | + | 0.174271i | ||||
\(804\) | −186.158 | − | 148.323i | −0.231539 | − | 0.184481i | ||||
\(805\) | 23.2914 | + | 13.4473i | 0.0289334 | + | 0.0167047i | ||||
\(806\) | 98.0599 | + | 215.912i | 0.121662 | + | 0.267881i | ||||
\(807\) | −987.358 | + | 44.8638i | −1.22349 | + | 0.0555933i | ||||
\(808\) | 630.285 | − | 148.736i | 0.780055 | − | 0.184079i | ||||
\(809\) | −409.864 | −0.506631 | −0.253315 | − | 0.967384i | \(-0.581521\pi\) | ||||
−0.253315 | + | 0.967384i | \(0.581521\pi\) | |||||||
\(810\) | 651.091 | + | 305.930i | 0.803816 | + | 0.377691i | ||||
\(811\) | 283.012 | 0.348967 | 0.174483 | − | 0.984660i | \(-0.444174\pi\) | ||||
0.174483 | + | 0.984660i | \(0.444174\pi\) | |||||||
\(812\) | −66.6556 | + | 76.2794i | −0.0820881 | + | 0.0939401i | ||||
\(813\) | −1106.83 | + | 50.2925i | −1.36142 | + | 0.0618604i | ||||
\(814\) | 841.103 | − | 382.001i | 1.03330 | − | 0.469288i | ||||
\(815\) | −748.292 | − | 432.027i | −0.918150 | − | 0.530094i | ||||
\(816\) | 28.2625 | − | 78.9577i | 0.0346354 | − | 0.0967619i | ||||
\(817\) | −711.448 | − | 1232.26i | −0.870806 | − | 1.50828i | ||||
\(818\) | 221.205 | − | 309.272i | 0.270422 | − | 0.378083i | ||||
\(819\) | −152.301 | + | 13.8692i | −0.185959 | + | 0.0169343i | ||||
\(820\) | −92.1279 | + | 31.4561i | −0.112351 | + | 0.0383611i | ||||
\(821\) | −14.8260 | + | 8.55980i | −0.0180585 | + | 0.0104261i | −0.509002 | − | 0.860765i | \(-0.669985\pi\) |
0.490944 | + | 0.871191i | \(0.336652\pi\) | |||||||
\(822\) | 331.265 | − | 168.989i | 0.402999 | − | 0.205583i | ||||
\(823\) | −1015.98 | − | 586.577i | −1.23449 | − | 0.712731i | −0.266524 | − | 0.963828i | \(-0.585875\pi\) |
−0.967962 | + | 0.251098i | \(0.919208\pi\) | |||||||
\(824\) | −177.629 | − | 188.641i | −0.215569 | − | 0.228933i | ||||
\(825\) | 104.651 | + | 54.2420i | 0.126849 | + | 0.0657479i | ||||
\(826\) | −6.90866 | + | 70.7902i | −0.00836400 | + | 0.0857025i | ||||
\(827\) | 219.406 | 0.265304 | 0.132652 | − | 0.991163i | \(-0.457651\pi\) | ||||
0.132652 | + | 0.991163i | \(0.457651\pi\) | |||||||
\(828\) | −217.042 | − | 157.371i | −0.262128 | − | 0.190062i | ||||
\(829\) | 1596.80i | 1.92618i | 0.269180 | + | 0.963090i | \(0.413247\pi\) | ||||
−0.269180 | + | 0.963090i | \(0.586753\pi\) | |||||||
\(830\) | 6.09501 | − | 62.4530i | 0.00734338 | − | 0.0752446i | ||||
\(831\) | 297.369 | + | 464.953i | 0.357844 | + | 0.559510i | ||||
\(832\) | −597.814 | − | 1196.11i | −0.718526 | − | 1.43764i | ||||
\(833\) | −42.2275 | + | 73.1402i | −0.0506933 | + | 0.0878034i | ||||
\(834\) | −675.854 | − | 438.442i | −0.810377 | − | 0.525710i | ||||
\(835\) | 103.138 | + | 178.640i | 0.123519 | + | 0.213940i | ||||
\(836\) | −305.734 | − | 895.428i | −0.365711 | − | 1.07109i | ||||
\(837\) | −57.8812 | + | 141.868i | −0.0691532 | + | 0.169496i | ||||
\(838\) | −724.417 | + | 1012.82i | −0.864460 | + | 1.20862i | ||||
\(839\) | −774.395 | + | 447.097i | −0.922997 | + | 0.532893i | −0.884590 | − | 0.466370i | \(-0.845562\pi\) |
−0.0384071 | + | 0.999262i | \(0.512228\pi\) | |||||||
\(840\) | −21.1455 | + | 84.0567i | −0.0251733 | + | 0.100067i | ||||
\(841\) | 64.3200 | − | 111.406i | 0.0764804 | − | 0.132468i | ||||
\(842\) | −425.629 | + | 193.307i | −0.505498 | + | 0.229580i | ||||
\(843\) | 996.159 | − | 637.110i | 1.18168 | − | 0.755765i | ||||
\(844\) | 313.399 | − | 358.648i | 0.371326 | − | 0.424939i | ||||
\(845\) | − | 1188.05i | − | 1.40597i | ||||||
\(846\) | 1285.01 | − | 730.855i | 1.51893 | − | 0.863895i | ||||
\(847\) | 53.3837i | 0.0630268i | ||||||||
\(848\) | −516.187 | + | 1258.84i | −0.608712 | + | 1.48448i | ||||
\(849\) | 784.435 | + | 406.584i | 0.923952 | + | 0.478898i | ||||
\(850\) | 7.63043 | + | 16.8010i | 0.00897698 | + | 0.0197658i | ||||
\(851\) | 231.149 | − | 400.362i | 0.271621 | − | 0.470461i | ||||
\(852\) | −822.514 | − | 123.607i | −0.965392 | − | 0.145079i | ||||
\(853\) | 997.466 | − | 575.887i | 1.16936 | − | 0.675132i | 0.215833 | − | 0.976430i | \(-0.430753\pi\) |
0.953530 | + | 0.301298i | \(0.0974201\pi\) | |||||||
\(854\) | −66.7724 | + | 93.3560i | −0.0781878 | + | 0.109316i | ||||
\(855\) | 1153.44 | + | 532.886i | 1.34906 | + | 0.623259i | ||||
\(856\) | 1400.73 | + | 420.828i | 1.63636 | + | 0.491621i | ||||
\(857\) | 548.214 | + | 949.534i | 0.639689 | + | 1.10797i | 0.985501 | + | 0.169670i | \(0.0542702\pi\) |
−0.345812 | + | 0.938304i | \(0.612396\pi\) | |||||||
\(858\) | −931.487 | − | 48.3674i | −1.08565 | − | 0.0563723i | ||||
\(859\) | −3.03512 | + | 5.25698i | −0.00353332 | + | 0.00611989i | −0.867787 | − | 0.496937i | \(-0.834458\pi\) |
0.864253 | + | 0.503057i | \(0.167791\pi\) | |||||||
\(860\) | −153.708 | + | 779.988i | −0.178730 | + | 0.906963i | ||||
\(861\) | 13.3581 | − | 0.606969i | 0.0155146 | − | 0.000704958i | ||||
\(862\) | −89.0508 | + | 912.467i | −0.103307 | + | 1.05855i | ||||
\(863\) | 1246.70i | 1.44461i | 0.691573 | + | 0.722306i | \(0.256918\pi\) | ||||
−0.691573 | + | 0.722306i | \(0.743082\pi\) | |||||||
\(864\) | 296.431 | − | 811.557i | 0.343091 | − | 0.939302i | ||||
\(865\) | −268.006 | −0.309833 | ||||||||
\(866\) | 560.983 | + | 54.7483i | 0.647786 | + | 0.0632197i | ||||
\(867\) | 38.9387 | + | 856.958i | 0.0449120 | + | 0.988418i | ||||
\(868\) | −18.1127 | − | 3.56936i | −0.0208672 | − | 0.00411216i | ||||
\(869\) | −276.393 | − | 159.576i | −0.318059 | − | 0.183631i | ||||
\(870\) | 43.0223 | − | 828.547i | 0.0494509 | − | 0.952353i | ||||
\(871\) | −358.904 | + | 207.213i | −0.412060 | + | 0.237903i | ||||
\(872\) | −16.8049 | + | 55.9352i | −0.0192717 | + | 0.0641458i | ||||
\(873\) | −97.4163 | − | 138.080i | −0.111588 | − | 0.158167i | ||||
\(874\) | −385.134 | − | 275.465i | −0.440657 | − | 0.315178i | ||||
\(875\) | −54.6792 | − | 94.7071i | −0.0624905 | − | 0.108237i | ||||
\(876\) | −38.7298 | + | 257.718i | −0.0442122 | + | 0.294199i | ||||
\(877\) | −73.4991 | − | 42.4347i | −0.0838074 | − | 0.0483862i | 0.457511 | − | 0.889204i | \(-0.348741\pi\) |
−0.541318 | + | 0.840818i | \(0.682074\pi\) | |||||||
\(878\) | 311.232 | − | 141.351i | 0.354479 | − | 0.160992i | ||||
\(879\) | 367.306 | − | 708.654i | 0.417868 | − | 0.806204i | ||||
\(880\) | −200.565 | + | 489.120i | −0.227914 | + | 0.555818i | ||||
\(881\) | −377.451 | −0.428434 | −0.214217 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214217 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(882\) | −439.914 | + | 750.693i | −0.498769 | + | 0.851126i | ||||
\(883\) | −586.966 | −0.664741 | −0.332370 | − | 0.943149i | \(-0.607848\pi\) | ||||
−0.332370 | + | 0.943149i | \(0.607848\pi\) | |||||||
\(884\) | −109.953 | − | 96.0803i | −0.124381 | − | 0.108688i | ||||
\(885\) | −313.871 | − | 490.756i | −0.354657 | − | 0.554527i | ||||
\(886\) | 24.3095 | + | 53.5255i | 0.0274374 | + | 0.0604126i | ||||
\(887\) | 955.774 | + | 551.816i | 1.07754 | + | 0.622115i | 0.930230 | − | 0.366976i | \(-0.119607\pi\) |
0.147305 | + | 0.989091i | \(0.452940\pi\) | |||||||
\(888\) | 1444.87 | + | 363.476i | 1.62711 | + | 0.409320i | ||||
\(889\) | −46.1040 | − | 79.8545i | −0.0518605 | − | 0.0898251i | ||||
\(890\) | 268.139 | + | 191.785i | 0.301279 | + | 0.215488i | ||||
\(891\) | −390.658 | − | 458.916i | −0.438449 | − | 0.515057i | ||||
\(892\) | −410.247 | + | 140.074i | −0.459918 | + | 0.157034i | ||||
\(893\) | 2261.21 | − | 1305.51i | 2.53215 | − | 1.46194i | ||||
\(894\) | 520.016 | − | 801.600i | 0.581674 | − | 0.896644i | ||||
\(895\) | −476.654 | − | 275.196i | −0.532574 | − | 0.307482i | ||||
\(896\) | 102.813 | + | 16.3176i | 0.114747 | + | 0.0182116i | ||||
\(897\) | −393.233 | + | 251.499i | −0.438387 | + | 0.280378i | ||||
\(898\) | −848.238 | − | 82.7825i | −0.944586 | − | 0.0921854i | ||||
\(899\) | 176.710 | 0.196563 | ||||||||
\(900\) | 77.4904 | + | 173.596i | 0.0861004 | + | 0.192885i | ||||
\(901\) | 148.569i | 0.164894i | ||||||||
\(902\) | 81.1710 | + | 7.92176i | 0.0899900 | + | 0.00878244i | ||||
\(903\) | 50.2504 | − | 96.9497i | 0.0556483 | − | 0.107364i | ||||
\(904\) | −826.830 | + | 778.562i | −0.914635 | + | 0.861241i | ||||
\(905\) | −253.327 | + | 438.776i | −0.279920 | + | 0.484835i | ||||
\(906\) | 535.431 | + | 1049.59i | 0.590983 | + | 1.15849i | ||||
\(907\) | 616.897 | + | 1068.50i | 0.680151 | + | 1.17806i | 0.974934 | + | 0.222493i | \(0.0714193\pi\) |
−0.294783 | + | 0.955564i | \(0.595247\pi\) | |||||||
\(908\) | 349.128 | + | 1022.52i | 0.384502 | + | 1.12612i | ||||
\(909\) | 595.304 | − | 419.991i | 0.654900 | − | 0.462037i | ||||
\(910\) | 122.748 | + | 87.7945i | 0.134887 | + | 0.0964775i | ||||
\(911\) | 430.671 | − | 248.648i | 0.472746 | − | 0.272940i | −0.244643 | − | 0.969613i | \(-0.578671\pi\) |
0.717388 | + | 0.696673i | \(0.245337\pi\) | |||||||
\(912\) | 514.275 | − | 1436.75i | 0.563898 | − | 1.57538i | ||||
\(913\) | −26.2848 | + | 45.5266i | −0.0287895 | + | 0.0498649i | ||||
\(914\) | 295.258 | + | 650.110i | 0.323040 | + | 0.711280i | ||||
\(915\) | −42.6705 | − | 939.087i | −0.0466344 | − | 1.02632i | ||||
\(916\) | 322.691 | + | 281.978i | 0.352282 | + | 0.307837i | ||||
\(917\) | 126.408i | 0.137850i | ||||||||
\(918\) | −3.67251 | − | 94.2749i | −0.00400056 | − | 0.102696i | ||||
\(919\) | − | 222.255i | − | 0.241845i | −0.992662 | − | 0.120922i | \(-0.961415\pi\) | ||
0.992662 | − | 0.120922i | \(-0.0385852\pi\) | |||||||
\(920\) | 60.7612 | + | 257.482i | 0.0660448 | + | 0.279872i | ||||
\(921\) | −14.2500 | − | 313.613i | −0.0154724 | − | 0.340514i | ||||
\(922\) | 1522.66 | − | 691.542i | 1.65148 | − | 0.750046i | ||||
\(923\) | −724.092 | + | 1254.16i | −0.784498 | + | 1.35879i | ||||
\(924\) | 45.2493 | − | 56.7916i | 0.0489711 | − | 0.0614627i | ||||
\(925\) | −283.901 | + | 163.910i | −0.306920 | + | 0.177201i | ||||
\(926\) | −753.391 | − | 538.859i | −0.813598 | − | 0.581921i | ||||
\(927\) | −264.622 | − | 122.254i | −0.285461 | − | 0.131882i | ||||
\(928\) | −995.761 | + | 37.0314i | −1.07302 | + | 0.0399045i | ||||
\(929\) | 481.758 | + | 834.429i | 0.518577 | + | 0.898201i | 0.999767 | + | 0.0215848i | \(0.00687120\pi\) |
−0.481190 | + | 0.876616i | \(0.659795\pi\) | |||||||
\(930\) | 134.687 | − | 68.7084i | 0.144825 | − | 0.0738800i | ||||
\(931\) | −768.390 | + | 1330.89i | −0.825338 | + | 1.42953i | ||||
\(932\) | −882.724 | − | 173.953i | −0.947129 | − | 0.186645i | ||||
\(933\) | 428.198 | − | 826.135i | 0.458947 | − | 0.885461i | ||||
\(934\) | −440.342 | − | 42.9745i | −0.471459 | − | 0.0460113i | ||||
\(935\) | 57.7265i | 0.0617396i | ||||||||
\(936\) | −1126.35 | − | 997.173i | −1.20337 | − | 1.06536i | ||||
\(937\) | 7.75413 | 0.00827549 | 0.00413774 | − | 0.999991i | \(-0.498683\pi\) | ||||
0.00413774 | + | 0.999991i | \(0.498683\pi\) | |||||||
\(938\) | 3.13378 | − | 32.1105i | 0.00334091 | − | 0.0342330i | ||||
\(939\) | 1017.65 | − | 650.855i | 1.08376 | − | 0.693137i | ||||
\(940\) | −1431.28 | − | 282.054i | −1.52264 | − | 0.300058i | ||||
\(941\) | −407.216 | − | 235.106i | −0.432748 | − | 0.249847i | 0.267768 | − | 0.963483i | \(-0.413714\pi\) |
−0.700517 | + | 0.713636i | \(0.747047\pi\) | |||||||
\(942\) | −678.130 | + | 1045.33i | −0.719883 | + | 1.10969i | ||||
\(943\) | 35.3461 | − | 20.4071i | 0.0374826 | − | 0.0216406i | ||||
\(944\) | −553.552 | + | 427.893i | −0.586390 | + | 0.453276i | ||||
\(945\) | 13.2419 | + | 96.6068i | 0.0140126 | + | 0.102229i | ||||
\(946\) | 387.457 | − | 541.713i | 0.409574 | − | 0.572635i | ||||
\(947\) | 881.063 | + | 1526.05i | 0.930372 | + | 1.61145i | 0.782685 | + | 0.622418i | \(0.213850\pi\) |
0.147687 | + | 0.989034i | \(0.452817\pi\) | |||||||
\(948\) | −188.261 | − | 479.067i | −0.198587 | − | 0.505345i | ||||
\(949\) | 392.967 | + | 226.879i | 0.414085 | + | 0.239072i | ||||
\(950\) | 138.846 | + | 305.717i | 0.146154 | + | 0.321807i | ||||
\(951\) | −302.674 | − | 473.249i | −0.318269 | − | 0.497633i | ||||
\(952\) | 11.0635 | − | 2.61080i | 0.0116214 | − | 0.00274244i | ||||
\(953\) | −1271.02 | −1.33371 | −0.666854 | − | 0.745188i | \(-0.732360\pi\) | ||||
−0.666854 | + | 0.745188i | \(0.732360\pi\) | |||||||
\(954\) | −9.90513 | + | 1530.59i | −0.0103827 | + | 1.60440i | ||||
\(955\) | −61.9632 | −0.0648830 | ||||||||
\(956\) | 269.206 | + | 235.241i | 0.281596 | + | 0.246068i | ||||
\(957\) | −319.851 | + | 617.097i | −0.334222 | + | 0.644825i | ||||
\(958\) | 1043.68 | − | 474.004i | 1.08943 | − | 0.494785i | ||||
\(959\) | 43.6537 | + | 25.2035i | 0.0455200 | + | 0.0262810i | ||||
\(960\) | −744.565 | + | 415.397i | −0.775588 | + | 0.432705i | ||||
\(961\) | −464.398 | − | 804.361i | −0.483244 | − | 0.837004i | ||||
\(962\) | 1509.12 | − | 2109.94i | 1.56873 | − | 2.19328i | ||||
\(963\) | 1638.62 | − | 149.220i | 1.70158 | − | 0.154953i | ||||
\(964\) | −349.105 | − | 1022.45i | −0.362142 | − | 1.06063i | ||||
\(965\) | −232.784 | + | 134.398i | −0.241227 | + | 0.139272i | ||||
\(966\) | 1.88435 | − | 36.2900i | 0.00195068 | − | 0.0375672i | ||||
\(967\) | 1466.93 | + | 846.934i | 1.51699 | + | 0.875836i | 0.999801 | + | 0.0199668i | \(0.00635606\pi\) |
0.517192 | + | 0.855869i | \(0.326977\pi\) | |||||||
\(968\) | −382.307 | + | 359.989i | −0.394945 | + | 0.371890i | ||||
\(969\) | −7.56387 | − | 166.465i | −0.00780586 | − | 0.171790i | ||||
\(970\) | −16.1973 | + | 165.967i | −0.0166983 | + | 0.171100i | ||||
\(971\) | 1414.92 | 1.45717 | 0.728587 | − | 0.684953i | \(-0.240177\pi\) | ||||
0.728587 | + | 0.684953i | \(0.240177\pi\) | |||||||
\(972\) | −31.5498 | − | 971.488i | −0.0324586 | − | 0.999473i | ||||
\(973\) | − | 109.198i | − | 0.112228i | ||||||
\(974\) | 76.1335 | − | 780.109i | 0.0781659 | − | 0.800933i | ||||
\(975\) | 330.658 | − | 15.0245i | 0.339137 | − | 0.0154098i | ||||
\(976\) | −1118.84 | + | 151.350i | −1.14636 | + | 0.155071i | ||||
\(977\) | 717.018 | − | 1241.91i | 0.733897 | − | 1.27115i | −0.221308 | − | 0.975204i | \(-0.571033\pi\) |
0.955205 | − | 0.295944i | \(-0.0956341\pi\) | |||||||
\(978\) | −60.5393 | + | 1165.90i | −0.0619012 | + | 1.19213i | ||||
\(979\) | −138.092 | − | 239.182i | −0.141054 | − | 0.244312i | ||||
\(980\) | 812.558 | − | 277.439i | 0.829140 | − | 0.283101i | ||||
\(981\) | 5.95880 | + | 65.4349i | 0.00607421 | + | 0.0667022i | ||||
\(982\) | 137.039 | − | 191.597i | 0.139551 | − | 0.195109i | ||||
\(983\) | −702.617 | + | 405.656i | −0.714768 | + | 0.412672i | −0.812824 | − | 0.582509i | \(-0.802071\pi\) |
0.0980558 | + | 0.995181i | \(0.468738\pi\) | |||||||
\(984\) | 94.4262 | + | 91.5709i | 0.0959616 | + | 0.0930598i | ||||
\(985\) | −343.053 | + | 594.185i | −0.348277 | + | 0.603234i | ||||
\(986\) | −99.0707 | + | 44.9946i | −0.100477 | + | 0.0456335i | ||||
\(987\) | 177.903 | + | 92.2099i | 0.180247 | + | 0.0934244i | ||||
\(988\) | −2000.74 | − | 1748.32i | −2.02504 | − | 1.76955i | ||||
\(989\) | − | 333.300i | − | 0.337007i | ||||||
\(990\) | −3.84864 | + | 594.712i | −0.00388751 | + | 0.600720i | ||||
\(991\) | 1111.56i | 1.12166i | 0.827931 | + | 0.560829i | \(0.189518\pi\) | ||||
−0.827931 | + | 0.560829i | \(0.810482\pi\) | |||||||
\(992\) | −96.5798 | − | 153.784i | −0.0973586 | − | 0.155024i | ||||
\(993\) | −389.380 | + | 249.034i | −0.392125 | + | 0.250790i | ||||
\(994\) | −46.6203 | − | 102.650i | −0.0469017 | − | 0.103270i | ||||
\(995\) | 596.021 | − | 1032.34i | 0.599016 | − | 1.03753i | ||||
\(996\) | −78.9104 | + | 31.0098i | −0.0792273 | + | 0.0311343i | ||||
\(997\) | 1017.90 | − | 587.682i | 1.02096 | − | 0.589451i | 0.106577 | − | 0.994304i | \(-0.466011\pi\) |
0.914381 | + | 0.404854i | \(0.132678\pi\) | |||||||
\(998\) | −71.4877 | + | 99.9486i | −0.0716310 | + | 0.100149i | ||||
\(999\) | 1660.60 | − | 227.618i | 1.66226 | − | 0.227846i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 72.3.p.b.67.1 | yes | 40 | |
3.2 | odd | 2 | 216.3.p.b.91.20 | 40 | |||
4.3 | odd | 2 | 288.3.t.b.175.11 | 40 | |||
8.3 | odd | 2 | inner | 72.3.p.b.67.14 | yes | 40 | |
8.5 | even | 2 | 288.3.t.b.175.12 | 40 | |||
9.2 | odd | 6 | 216.3.p.b.19.7 | 40 | |||
9.4 | even | 3 | 648.3.b.f.163.13 | 20 | |||
9.5 | odd | 6 | 648.3.b.e.163.8 | 20 | |||
9.7 | even | 3 | inner | 72.3.p.b.43.14 | yes | 40 | |
12.11 | even | 2 | 864.3.t.b.847.14 | 40 | |||
24.5 | odd | 2 | 864.3.t.b.847.7 | 40 | |||
24.11 | even | 2 | 216.3.p.b.91.7 | 40 | |||
36.7 | odd | 6 | 288.3.t.b.79.12 | 40 | |||
36.11 | even | 6 | 864.3.t.b.559.7 | 40 | |||
36.23 | even | 6 | 2592.3.b.f.1135.7 | 20 | |||
36.31 | odd | 6 | 2592.3.b.e.1135.14 | 20 | |||
72.5 | odd | 6 | 2592.3.b.f.1135.14 | 20 | |||
72.11 | even | 6 | 216.3.p.b.19.20 | 40 | |||
72.13 | even | 6 | 2592.3.b.e.1135.7 | 20 | |||
72.29 | odd | 6 | 864.3.t.b.559.14 | 40 | |||
72.43 | odd | 6 | inner | 72.3.p.b.43.1 | ✓ | 40 | |
72.59 | even | 6 | 648.3.b.e.163.7 | 20 | |||
72.61 | even | 6 | 288.3.t.b.79.11 | 40 | |||
72.67 | odd | 6 | 648.3.b.f.163.14 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.p.b.43.1 | ✓ | 40 | 72.43 | odd | 6 | inner | |
72.3.p.b.43.14 | yes | 40 | 9.7 | even | 3 | inner | |
72.3.p.b.67.1 | yes | 40 | 1.1 | even | 1 | trivial | |
72.3.p.b.67.14 | yes | 40 | 8.3 | odd | 2 | inner | |
216.3.p.b.19.7 | 40 | 9.2 | odd | 6 | |||
216.3.p.b.19.20 | 40 | 72.11 | even | 6 | |||
216.3.p.b.91.7 | 40 | 24.11 | even | 2 | |||
216.3.p.b.91.20 | 40 | 3.2 | odd | 2 | |||
288.3.t.b.79.11 | 40 | 72.61 | even | 6 | |||
288.3.t.b.79.12 | 40 | 36.7 | odd | 6 | |||
288.3.t.b.175.11 | 40 | 4.3 | odd | 2 | |||
288.3.t.b.175.12 | 40 | 8.5 | even | 2 | |||
648.3.b.e.163.7 | 20 | 72.59 | even | 6 | |||
648.3.b.e.163.8 | 20 | 9.5 | odd | 6 | |||
648.3.b.f.163.13 | 20 | 9.4 | even | 3 | |||
648.3.b.f.163.14 | 20 | 72.67 | odd | 6 | |||
864.3.t.b.559.7 | 40 | 36.11 | even | 6 | |||
864.3.t.b.559.14 | 40 | 72.29 | odd | 6 | |||
864.3.t.b.847.7 | 40 | 24.5 | odd | 2 | |||
864.3.t.b.847.14 | 40 | 12.11 | even | 2 | |||
2592.3.b.e.1135.7 | 20 | 72.13 | even | 6 | |||
2592.3.b.e.1135.14 | 20 | 36.31 | odd | 6 | |||
2592.3.b.f.1135.7 | 20 | 36.23 | even | 6 | |||
2592.3.b.f.1135.14 | 20 | 72.5 | odd | 6 |