Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,3,Mod(29,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("201.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.g (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: | \(5.47685331364\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Relative dimension: | \(42\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 29.17 | ||
Character | \(\chi\) | \(=\) | 201.29 |
Dual form | 201.3.g.b.104.17 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.922015 | − | 0.532326i | −0.461008 | − | 0.266163i | 0.251460 | − | 0.967868i | \(-0.419089\pi\) |
−0.712468 | + | 0.701705i | \(0.752423\pi\) | |||||||
\(3\) | −0.226863 | − | 2.99141i | −0.0756209 | − | 0.997137i | ||||
\(4\) | −1.43326 | − | 2.48248i | −0.358315 | − | 0.620619i | ||||
\(5\) | 3.49902i | 0.699805i | 0.936786 | + | 0.349902i | \(0.113785\pi\) | ||||
−0.936786 | + | 0.349902i | \(0.886215\pi\) | |||||||
\(6\) | −1.38323 | + | 2.87889i | −0.230539 | + | 0.479815i | ||||
\(7\) | −3.66463 | − | 6.34732i | −0.523518 | − | 0.906761i | −0.999625 | − | 0.0273731i | \(-0.991286\pi\) |
0.476107 | − | 0.879387i | \(-0.342048\pi\) | |||||||
\(8\) | 7.31045i | 0.913806i | ||||||||
\(9\) | −8.89707 | + | 1.35728i | −0.988563 | + | 0.150809i | ||||
\(10\) | 1.86262 | − | 3.22615i | 0.186262 | − | 0.322615i | ||||
\(11\) | −7.57038 | + | 4.37076i | −0.688217 | + | 0.397342i | −0.802944 | − | 0.596055i | \(-0.796734\pi\) |
0.114727 | + | 0.993397i | \(0.463401\pi\) | |||||||
\(12\) | −7.10095 | + | 4.85065i | −0.591746 | + | 0.404221i | ||||
\(13\) | 7.80551 | − | 13.5195i | 0.600424 | − | 1.03996i | −0.392333 | − | 0.919823i | \(-0.628332\pi\) |
0.992757 | − | 0.120141i | \(-0.0383348\pi\) | |||||||
\(14\) | 7.80310i | 0.557365i | ||||||||
\(15\) | 10.4670 | − | 0.793798i | 0.697801 | − | 0.0529199i | ||||
\(16\) | −1.84150 | + | 3.18957i | −0.115094 | + | 0.199348i | ||||
\(17\) | 5.61889 | + | 3.24407i | 0.330523 | + | 0.190827i | 0.656073 | − | 0.754697i | \(-0.272216\pi\) |
−0.325550 | + | 0.945525i | \(0.605550\pi\) | |||||||
\(18\) | 8.92574 | + | 3.48470i | 0.495875 | + | 0.193595i | ||||
\(19\) | −17.6375 | + | 30.5490i | −0.928289 | + | 1.60784i | −0.142105 | + | 0.989852i | \(0.545387\pi\) |
−0.786184 | + | 0.617992i | \(0.787946\pi\) | |||||||
\(20\) | 8.68624 | − | 5.01501i | 0.434312 | − | 0.250750i | ||||
\(21\) | −18.1561 | + | 12.4024i | −0.864575 | + | 0.590589i | ||||
\(22\) | 9.30668 | 0.423031 | ||||||||
\(23\) | 1.47866 | + | 0.853704i | 0.0642895 | + | 0.0371176i | 0.531800 | − | 0.846870i | \(-0.321516\pi\) |
−0.467511 | + | 0.883987i | \(0.654849\pi\) | |||||||
\(24\) | 21.8685 | − | 1.65847i | 0.911189 | − | 0.0691029i | ||||
\(25\) | 12.7568 | 0.510274 | ||||||||
\(26\) | −14.3936 | + | 8.31015i | −0.553600 | + | 0.319621i | ||||
\(27\) | 6.07859 | + | 26.3069i | 0.225133 | + | 0.974328i | ||||
\(28\) | −10.5047 | + | 18.1947i | −0.375169 | + | 0.649811i | ||||
\(29\) | −38.8478 | + | 22.4288i | −1.33958 | + | 0.773406i | −0.986745 | − | 0.162281i | \(-0.948115\pi\) |
−0.352833 | + | 0.935686i | \(0.614782\pi\) | |||||||
\(30\) | −10.0733 | − | 4.83996i | −0.335777 | − | 0.161332i | ||||
\(31\) | −22.3841 | − | 38.7704i | −0.722068 | − | 1.25066i | −0.960170 | − | 0.279418i | \(-0.909859\pi\) |
0.238102 | − | 0.971240i | \(-0.423475\pi\) | |||||||
\(32\) | 28.7199 | − | 16.5814i | 0.897497 | − | 0.518170i | ||||
\(33\) | 14.7922 | + | 21.6546i | 0.448248 | + | 0.656199i | ||||
\(34\) | −3.45380 | − | 5.98215i | −0.101582 | − | 0.175946i | ||||
\(35\) | 22.2094 | − | 12.8226i | 0.634555 | − | 0.366361i | ||||
\(36\) | 16.1212 | + | 20.1414i | 0.447811 | + | 0.559484i | ||||
\(37\) | 2.74210 | − | 4.74945i | 0.0741107 | − | 0.128363i | −0.826589 | − | 0.562807i | \(-0.809722\pi\) |
0.900699 | + | 0.434443i | \(0.143055\pi\) | |||||||
\(38\) | 32.5241 | − | 18.7778i | 0.855897 | − | 0.494152i | ||||
\(39\) | −42.2133 | − | 20.2824i | −1.08239 | − | 0.520062i | ||||
\(40\) | −25.5794 | −0.639486 | ||||||||
\(41\) | 7.37884 | − | 4.26018i | 0.179972 | − | 0.103907i | −0.407308 | − | 0.913291i | \(-0.633532\pi\) |
0.587279 | + | 0.809384i | \(0.300199\pi\) | |||||||
\(42\) | 23.3423 | − | 1.77023i | 0.555769 | − | 0.0421484i | ||||
\(43\) | −61.0618 | −1.42004 | −0.710021 | − | 0.704181i | \(-0.751314\pi\) | ||||
−0.710021 | + | 0.704181i | \(0.751314\pi\) | |||||||
\(44\) | 21.7006 | + | 12.5289i | 0.493196 | + | 0.284747i | ||||
\(45\) | −4.74915 | − | 31.1310i | −0.105537 | − | 0.691801i | ||||
\(46\) | −0.908897 | − | 1.57426i | −0.0197586 | − | 0.0342230i | ||||
\(47\) | −61.2387 | + | 35.3562i | −1.30295 | + | 0.752259i | −0.980909 | − | 0.194466i | \(-0.937703\pi\) |
−0.322042 | + | 0.946725i | \(0.604369\pi\) | |||||||
\(48\) | 9.95907 | + | 4.78508i | 0.207481 | + | 0.0996891i | ||||
\(49\) | −2.35901 | + | 4.08593i | −0.0481431 | + | 0.0833863i | ||||
\(50\) | −11.7620 | − | 6.79079i | −0.235240 | − | 0.135816i | ||||
\(51\) | 8.42961 | − | 17.5443i | 0.165287 | − | 0.344007i | ||||
\(52\) | −44.7493 | −0.860563 | ||||||||
\(53\) | − | 103.769i | − | 1.95790i | −0.204096 | − | 0.978951i | \(-0.565426\pi\) | ||
0.204096 | − | 0.978951i | \(-0.434574\pi\) | |||||||
\(54\) | 8.39926 | − | 27.4911i | 0.155542 | − | 0.509095i | ||||
\(55\) | −15.2934 | − | 26.4889i | −0.278062 | − | 0.481617i | ||||
\(56\) | 46.4018 | − | 26.7901i | 0.828603 | − | 0.478394i | ||||
\(57\) | 95.3860 | + | 45.8305i | 1.67344 | + | 0.804044i | ||||
\(58\) | 47.7576 | 0.823407 | ||||||||
\(59\) | − | 32.6824i | − | 0.553940i | −0.960879 | − | 0.276970i | \(-0.910670\pi\) | ||
0.960879 | − | 0.276970i | \(-0.0893302\pi\) | |||||||
\(60\) | −16.9725 | − | 24.8464i | −0.282875 | − | 0.414107i | ||||
\(61\) | 19.3186 | − | 33.4609i | 0.316699 | − | 0.548539i | −0.663098 | − | 0.748532i | \(-0.730759\pi\) |
0.979797 | + | 0.199994i | \(0.0640922\pi\) | |||||||
\(62\) | 47.6625i | 0.768750i | ||||||||
\(63\) | 41.2195 | + | 51.4986i | 0.654278 | + | 0.817439i | ||||
\(64\) | −20.5749 | −0.321483 | ||||||||
\(65\) | 47.3052 | + | 27.3117i | 0.727772 | + | 0.420179i | ||||
\(66\) | −2.11134 | − | 27.8401i | −0.0319900 | − | 0.421820i | ||||
\(67\) | −30.1071 | + | 59.8545i | −0.449360 | + | 0.893351i | ||||
\(68\) | − | 18.5983i | − | 0.273505i | ||||||
\(69\) | 2.21833 | − | 4.61695i | 0.0321497 | − | 0.0669123i | ||||
\(70\) | −27.3032 | −0.390046 | ||||||||
\(71\) | −25.8373 | + | 14.9172i | −0.363906 | + | 0.210101i | −0.670793 | − | 0.741645i | \(-0.734046\pi\) |
0.306887 | + | 0.951746i | \(0.400713\pi\) | |||||||
\(72\) | −9.92232 | − | 65.0415i | −0.137810 | − | 0.903355i | ||||
\(73\) | 44.7274 | − | 77.4701i | 0.612704 | − | 1.06123i | −0.378078 | − | 0.925774i | \(-0.623415\pi\) |
0.990783 | − | 0.135461i | \(-0.0432516\pi\) | |||||||
\(74\) | −5.05651 | + | 2.91938i | −0.0683312 | + | 0.0394510i | ||||
\(75\) | −2.89405 | − | 38.1609i | −0.0385874 | − | 0.508812i | ||||
\(76\) | 101.116 | 1.33048 | ||||||||
\(77\) | 55.4853 | + | 32.0345i | 0.720588 | + | 0.416032i | ||||
\(78\) | 28.1244 | + | 41.1719i | 0.360570 | + | 0.527845i | ||||
\(79\) | 5.54828 | + | 9.60990i | 0.0702313 | + | 0.121644i | 0.899003 | − | 0.437943i | \(-0.144293\pi\) |
−0.828771 | + | 0.559587i | \(0.810960\pi\) | |||||||
\(80\) | −11.1604 | − | 6.44344i | −0.139505 | − | 0.0805430i | ||||
\(81\) | 77.3156 | − | 24.1516i | 0.954513 | − | 0.298168i | ||||
\(82\) | −9.07120 | −0.110624 | ||||||||
\(83\) | −113.146 | − | 65.3246i | −1.36320 | − | 0.787044i | −0.373152 | − | 0.927770i | \(-0.621723\pi\) |
−0.990049 | + | 0.140726i | \(0.955056\pi\) | |||||||
\(84\) | 56.8110 | + | 27.2962i | 0.676321 | + | 0.324955i | ||||
\(85\) | −11.3511 | + | 19.6606i | −0.133542 | + | 0.231301i | ||||
\(86\) | 56.2999 | + | 32.5048i | 0.654650 | + | 0.377962i | ||||
\(87\) | 75.9067 | + | 111.121i | 0.872491 | + | 1.27726i | ||||
\(88\) | −31.9522 | − | 55.3429i | −0.363094 | − | 0.628896i | ||||
\(89\) | − | 105.058i | − | 1.18043i | −0.807247 | − | 0.590213i | \(-0.799044\pi\) | ||
0.807247 | − | 0.590213i | \(-0.200956\pi\) | |||||||
\(90\) | −12.1931 | + | 31.2314i | −0.135478 | + | 0.347015i | ||||
\(91\) | −114.417 | −1.25733 | ||||||||
\(92\) | − | 4.89432i | − | 0.0531991i | ||||||
\(93\) | −110.900 | + | 75.7556i | −1.19247 | + | 0.814576i | ||||
\(94\) | 75.2840 | 0.800894 | ||||||||
\(95\) | −106.892 | − | 61.7140i | −1.12518 | − | 0.649621i | ||||
\(96\) | −56.1174 | − | 82.1513i | −0.584556 | − | 0.855743i | ||||
\(97\) | 33.7046 | − | 58.3781i | 0.347470 | − | 0.601836i | −0.638329 | − | 0.769764i | \(-0.720374\pi\) |
0.985799 | + | 0.167927i | \(0.0537074\pi\) | |||||||
\(98\) | 4.35009 | − | 2.51153i | 0.0443887 | − | 0.0256278i | ||||
\(99\) | 61.4219 | − | 49.1621i | 0.620423 | − | 0.496587i | ||||
\(100\) | −18.2839 | − | 31.6686i | −0.182839 | − | 0.316686i | ||||
\(101\) | −80.3871 | + | 46.4115i | −0.795912 | + | 0.459520i | −0.842040 | − | 0.539415i | \(-0.818645\pi\) |
0.0461275 | + | 0.998936i | \(0.485312\pi\) | |||||||
\(102\) | −17.1115 | + | 11.6889i | −0.167760 | + | 0.114597i | ||||
\(103\) | 20.7632 | + | 35.9630i | 0.201585 | + | 0.349155i | 0.949039 | − | 0.315158i | \(-0.102057\pi\) |
−0.747454 | + | 0.664313i | \(0.768724\pi\) | |||||||
\(104\) | 98.8339 | + | 57.0618i | 0.950326 | + | 0.548671i | ||||
\(105\) | −43.3962 | − | 63.5285i | −0.413297 | − | 0.605034i | ||||
\(106\) | −55.2388 | + | 95.6764i | −0.521121 | + | 0.902607i | ||||
\(107\) | 37.0884i | 0.346621i | 0.984867 | + | 0.173310i | \(0.0554464\pi\) | ||||
−0.984867 | + | 0.173310i | \(0.944554\pi\) | |||||||
\(108\) | 56.5940 | − | 52.7945i | 0.524018 | − | 0.488838i | ||||
\(109\) | −76.9467 | −0.705933 | −0.352966 | − | 0.935636i | \(-0.614827\pi\) | ||||
−0.352966 | + | 0.935636i | \(0.614827\pi\) | |||||||
\(110\) | 32.5643i | 0.296039i | ||||||||
\(111\) | −14.8296 | − | 7.12526i | −0.133600 | − | 0.0641915i | ||||
\(112\) | 26.9936 | 0.241014 | ||||||||
\(113\) | −53.5363 | + | 30.9092i | −0.473773 | + | 0.273533i | −0.717818 | − | 0.696231i | \(-0.754859\pi\) |
0.244045 | + | 0.969764i | \(0.421526\pi\) | |||||||
\(114\) | −63.5505 | − | 93.0328i | −0.557461 | − | 0.816078i | ||||
\(115\) | −2.98713 | + | 5.17386i | −0.0259750 | + | 0.0449901i | ||||
\(116\) | 111.358 | + | 64.2924i | 0.959981 | + | 0.554245i | ||||
\(117\) | −51.0963 | + | 130.878i | −0.436721 | + | 1.11862i | ||||
\(118\) | −17.3977 | + | 30.1337i | −0.147438 | + | 0.255370i | ||||
\(119\) | − | 47.5532i | − | 0.399607i | ||||||
\(120\) | 5.80302 | + | 76.5185i | 0.0483585 | + | 0.637654i | ||||
\(121\) | −22.2929 | + | 38.6124i | −0.184238 | + | 0.319110i | ||||
\(122\) | −35.6241 | + | 20.5676i | −0.292001 | + | 0.168587i | ||||
\(123\) | −14.4179 | − | 21.1067i | −0.117219 | − | 0.171599i | ||||
\(124\) | −64.1644 | + | 111.136i | −0.517455 | + | 0.896258i | ||||
\(125\) | 132.112i | 1.05690i | ||||||||
\(126\) | −10.5910 | − | 69.4247i | −0.0840555 | − | 0.550990i | ||||
\(127\) | −11.9491 | − | 20.6964i | −0.0940871 | − | 0.162964i | 0.815140 | − | 0.579264i | \(-0.196660\pi\) |
−0.909227 | + | 0.416300i | \(0.863327\pi\) | |||||||
\(128\) | −95.9092 | − | 55.3732i | −0.749291 | − | 0.432603i | ||||
\(129\) | 13.8526 | + | 182.661i | 0.107385 | + | 1.41598i | ||||
\(130\) | −29.0774 | − | 50.3635i | −0.223672 | − | 0.387412i | ||||
\(131\) | − | 48.1582i | − | 0.367620i | −0.982962 | − | 0.183810i | \(-0.941157\pi\) | ||
0.982962 | − | 0.183810i | \(-0.0588430\pi\) | |||||||
\(132\) | 32.5559 | − | 67.7578i | 0.246636 | − | 0.513317i | ||||
\(133\) | 258.539 | 1.94391 | ||||||||
\(134\) | 59.6213 | − | 39.1600i | 0.444935 | − | 0.292239i | ||||
\(135\) | −92.0483 | + | 21.2691i | −0.681839 | + | 0.157549i | ||||
\(136\) | −23.7156 | + | 41.0766i | −0.174379 | + | 0.302034i | ||||
\(137\) | 256.618i | 1.87312i | 0.350501 | + | 0.936562i | \(0.386011\pi\) | ||||
−0.350501 | + | 0.936562i | \(0.613989\pi\) | |||||||
\(138\) | −4.50305 | + | 3.07602i | −0.0326308 | + | 0.0222900i | ||||
\(139\) | 122.839 | 0.883735 | 0.441867 | − | 0.897080i | \(-0.354316\pi\) | ||||
0.441867 | + | 0.897080i | \(0.354316\pi\) | |||||||
\(140\) | −63.6637 | − | 36.7563i | −0.454741 | − | 0.262545i | ||||
\(141\) | 119.658 | + | 175.169i | 0.848636 | + | 1.24233i | ||||
\(142\) | 31.7632 | 0.223684 | ||||||||
\(143\) | 136.464i | 0.954295i | ||||||||
\(144\) | 12.0548 | − | 30.8772i | 0.0837138 | − | 0.214425i | ||||
\(145\) | −78.4787 | − | 135.929i | −0.541233 | − | 0.937443i | ||||
\(146\) | −82.4787 | + | 47.6191i | −0.564922 | + | 0.326158i | ||||
\(147\) | 12.7579 | + | 6.12983i | 0.0867882 | + | 0.0416995i | ||||
\(148\) | −15.7205 | −0.106220 | ||||||||
\(149\) | 35.1770i | 0.236087i | 0.993008 | + | 0.118044i | \(0.0376623\pi\) | ||||
−0.993008 | + | 0.118044i | \(0.962338\pi\) | |||||||
\(150\) | −17.6457 | + | 36.7255i | −0.117638 | + | 0.244837i | ||||
\(151\) | 53.4378 | − | 92.5570i | 0.353893 | − | 0.612960i | −0.633035 | − | 0.774123i | \(-0.718191\pi\) |
0.986928 | + | 0.161163i | \(0.0515244\pi\) | |||||||
\(152\) | −223.327 | − | 128.938i | −1.46926 | − | 0.848276i | ||||
\(153\) | −54.3947 | − | 21.2363i | −0.355521 | − | 0.138799i | ||||
\(154\) | −34.1055 | − | 59.0725i | −0.221464 | − | 0.383588i | ||||
\(155\) | 135.659 | − | 78.3225i | 0.875216 | − | 0.505306i | ||||
\(156\) | 10.1519 | + | 133.863i | 0.0650766 | + | 0.858099i | ||||
\(157\) | 68.8127 | − | 119.187i | 0.438297 | − | 0.759153i | −0.559261 | − | 0.828992i | \(-0.688915\pi\) |
0.997558 | + | 0.0698384i | \(0.0222484\pi\) | |||||||
\(158\) | − | 11.8140i | − | 0.0747719i | ||||||
\(159\) | −310.415 | + | 23.5413i | −1.95230 | + | 0.148058i | ||||
\(160\) | 58.0189 | + | 100.492i | 0.362618 | + | 0.628073i | ||||
\(161\) | − | 12.5140i | − | 0.0777269i | ||||||
\(162\) | −84.1427 | − | 18.8889i | −0.519399 | − | 0.116598i | ||||
\(163\) | 127.665 | + | 221.122i | 0.783221 | + | 1.35658i | 0.930056 | + | 0.367418i | \(0.119758\pi\) |
−0.146835 | + | 0.989161i | \(0.546909\pi\) | |||||||
\(164\) | −21.1516 | − | 12.2119i | −0.128973 | − | 0.0744626i | ||||
\(165\) | −75.7698 | + | 51.7582i | −0.459211 | + | 0.313686i | ||||
\(166\) | 69.5480 | + | 120.461i | 0.418964 | + | 0.725666i | ||||
\(167\) | 0.664259 | − | 0.383510i | 0.00397760 | − | 0.00229647i | −0.498010 | − | 0.867171i | \(-0.665936\pi\) |
0.501987 | + | 0.864875i | \(0.332602\pi\) | |||||||
\(168\) | −90.6669 | − | 132.729i | −0.539684 | − | 0.790054i | ||||
\(169\) | −37.3520 | − | 64.6955i | −0.221018 | − | 0.382814i | ||||
\(170\) | 20.9317 | − | 12.0849i | 0.123128 | − | 0.0710878i | ||||
\(171\) | 115.458 | − | 295.736i | 0.675195 | − | 1.72945i | ||||
\(172\) | 87.5173 | + | 151.584i | 0.508822 | + | 0.881305i | ||||
\(173\) | 17.7375 | + | 10.2407i | 0.102529 | + | 0.0591949i | 0.550388 | − | 0.834909i | \(-0.314480\pi\) |
−0.447859 | + | 0.894104i | \(0.647813\pi\) | |||||||
\(174\) | −10.8344 | − | 142.863i | −0.0622668 | − | 0.821050i | ||||
\(175\) | −46.7491 | − | 80.9718i | −0.267138 | − | 0.462696i | ||||
\(176\) | − | 32.1950i | − | 0.182926i | ||||||
\(177\) | −97.7666 | + | 7.41443i | −0.552353 | + | 0.0418894i | ||||
\(178\) | −55.9251 | + | 96.8650i | −0.314186 | + | 0.544186i | ||||
\(179\) | − | 189.671i | − | 1.05961i | −0.848118 | − | 0.529807i | \(-0.822264\pi\) | ||
0.848118 | − | 0.529807i | \(-0.177736\pi\) | |||||||
\(180\) | −70.4753 | + | 56.4085i | −0.391530 | + | 0.313381i | ||||
\(181\) | −101.194 | − | 175.273i | −0.559082 | − | 0.968359i | −0.997573 | − | 0.0696232i | \(-0.977820\pi\) |
0.438491 | − | 0.898735i | \(-0.355513\pi\) | |||||||
\(182\) | 105.494 | + | 60.9072i | 0.579639 | + | 0.334655i | ||||
\(183\) | −104.478 | − | 50.1989i | −0.570917 | − | 0.274311i | ||||
\(184\) | −6.24096 | + | 10.8097i | −0.0339182 | + | 0.0587481i | ||||
\(185\) | 16.6184 | + | 9.59465i | 0.0898293 | + | 0.0518630i | ||||
\(186\) | 142.578 | − | 10.8129i | 0.766549 | − | 0.0581336i | ||||
\(187\) | −56.7162 | −0.303295 | ||||||||
\(188\) | 175.542 | + | 101.349i | 0.933733 | + | 0.539091i | ||||
\(189\) | 144.702 | − | 134.988i | 0.765621 | − | 0.714220i | ||||
\(190\) | 65.7039 | + | 113.802i | 0.345810 | + | 0.598960i | ||||
\(191\) | 27.4349 | + | 15.8396i | 0.143638 | + | 0.0829296i | 0.570097 | − | 0.821577i | \(-0.306906\pi\) |
−0.426459 | + | 0.904507i | \(0.640239\pi\) | |||||||
\(192\) | 4.66769 | + | 61.5481i | 0.0243109 | + | 0.320563i | ||||
\(193\) | 52.2310 | 0.270627 | 0.135314 | − | 0.990803i | \(-0.456796\pi\) | ||||
0.135314 | + | 0.990803i | \(0.456796\pi\) | |||||||
\(194\) | −62.1523 | + | 35.8837i | −0.320373 | + | 0.184967i | ||||
\(195\) | 70.9686 | − | 147.705i | 0.363941 | − | 0.757462i | ||||
\(196\) | 13.5243 | 0.0690016 | ||||||||
\(197\) | 178.120 | − | 102.837i | 0.904160 | − | 0.522017i | 0.0256125 | − | 0.999672i | \(-0.491846\pi\) |
0.878548 | + | 0.477655i | \(0.158513\pi\) | |||||||
\(198\) | −82.8021 | + | 12.6318i | −0.418193 | + | 0.0637968i | ||||
\(199\) | 28.3985 | − | 49.1876i | 0.142706 | − | 0.247174i | −0.785809 | − | 0.618470i | \(-0.787753\pi\) |
0.928515 | + | 0.371296i | \(0.121086\pi\) | |||||||
\(200\) | 93.2582i | 0.466291i | ||||||||
\(201\) | 185.880 | + | 76.4839i | 0.924774 | + | 0.380517i | ||||
\(202\) | 98.8242 | 0.489229 | ||||||||
\(203\) | 284.725 | + | 164.386i | 1.40259 | + | 0.809784i | ||||
\(204\) | −55.6353 | + | 4.21927i | −0.272722 | + | 0.0206827i | ||||
\(205\) | 14.9065 | + | 25.8187i | 0.0727144 | + | 0.125945i | ||||
\(206\) | − | 44.2112i | − | 0.214618i | ||||||
\(207\) | −14.3144 | − | 5.58851i | −0.0691519 | − | 0.0269976i | ||||
\(208\) | 28.7476 | + | 49.7924i | 0.138210 | + | 0.239386i | ||||
\(209\) | − | 308.357i | − | 1.47539i | ||||||
\(210\) | 6.19409 | + | 81.6752i | 0.0294957 | + | 0.388929i | ||||
\(211\) | 37.0172 | − | 64.1157i | 0.175437 | − | 0.303866i | −0.764875 | − | 0.644178i | \(-0.777200\pi\) |
0.940312 | + | 0.340312i | \(0.110533\pi\) | |||||||
\(212\) | −257.604 | + | 148.728i | −1.21511 | + | 0.701545i | ||||
\(213\) | 50.4849 | + | 73.9058i | 0.237018 | + | 0.346976i | ||||
\(214\) | 19.7431 | − | 34.1961i | 0.0922576 | − | 0.159795i | ||||
\(215\) | − | 213.657i | − | 0.993752i | ||||||
\(216\) | −192.315 | + | 44.4372i | −0.890347 | + | 0.205728i | ||||
\(217\) | −164.059 | + | 284.158i | −0.756032 | + | 1.30949i | ||||
\(218\) | 70.9460 | + | 40.9607i | 0.325440 | + | 0.187893i | ||||
\(219\) | −241.892 | − | 116.223i | −1.10453 | − | 0.530698i | ||||
\(220\) | −43.8388 | + | 75.9310i | −0.199267 | + | 0.345141i | ||||
\(221\) | 87.7165 | − | 50.6432i | 0.396907 | − | 0.229155i | ||||
\(222\) | 9.88018 | + | 14.4638i | 0.0445053 | + | 0.0651522i | ||||
\(223\) | 310.836 | 1.39388 | 0.696941 | − | 0.717128i | \(-0.254544\pi\) | ||||
0.696941 | + | 0.717128i | \(0.254544\pi\) | |||||||
\(224\) | −210.496 | − | 121.530i | −0.939713 | − | 0.542543i | ||||
\(225\) | −113.498 | + | 17.3146i | −0.504438 | + | 0.0769537i | ||||
\(226\) | 65.8150 | 0.291217 | ||||||||
\(227\) | −257.878 | + | 148.886i | −1.13603 | + | 0.655885i | −0.945443 | − | 0.325787i | \(-0.894371\pi\) |
−0.190582 | + | 0.981671i | \(0.561038\pi\) | |||||||
\(228\) | −22.9395 | − | 302.481i | −0.100612 | − | 1.32667i | ||||
\(229\) | −12.8588 | + | 22.2721i | −0.0561519 | + | 0.0972579i | −0.892735 | − | 0.450582i | \(-0.851216\pi\) |
0.836583 | + | 0.547840i | \(0.184550\pi\) | |||||||
\(230\) | 5.50836 | − | 3.18025i | 0.0239494 | − | 0.0138272i | ||||
\(231\) | 83.2406 | − | 173.247i | 0.360349 | − | 0.749986i | ||||
\(232\) | −163.964 | − | 283.994i | −0.706743 | − | 1.22411i | ||||
\(233\) | −0.274420 | + | 0.158436i | −0.00117777 | + | 0.000679985i | −0.500589 | − | 0.865685i | \(-0.666883\pi\) |
0.499411 | + | 0.866365i | \(0.333550\pi\) | |||||||
\(234\) | 116.782 | − | 93.4721i | 0.499067 | − | 0.399453i | ||||
\(235\) | −123.712 | − | 214.276i | −0.526434 | − | 0.911811i | ||||
\(236\) | −81.1334 | + | 46.8424i | −0.343786 | + | 0.198485i | ||||
\(237\) | 27.4884 | − | 18.7773i | 0.115985 | − | 0.0792291i | ||||
\(238\) | −25.3138 | + | 43.8448i | −0.106360 | + | 0.184222i | ||||
\(239\) | 341.120 | − | 196.946i | 1.42728 | − | 0.824040i | 0.430374 | − | 0.902651i | \(-0.358382\pi\) |
0.996905 | + | 0.0786104i | \(0.0250483\pi\) | |||||||
\(240\) | −16.7431 | + | 34.8470i | −0.0697629 | + | 0.145196i | ||||
\(241\) | −351.412 | −1.45814 | −0.729071 | − | 0.684438i | \(-0.760048\pi\) | ||||
−0.729071 | + | 0.684438i | \(0.760048\pi\) | |||||||
\(242\) | 41.1087 | − | 23.7341i | 0.169871 | − | 0.0980749i | ||||
\(243\) | −89.7874 | − | 225.804i | −0.369495 | − | 0.929233i | ||||
\(244\) | −110.754 | −0.453911 | ||||||||
\(245\) | −14.2968 | − | 8.25424i | −0.0583541 | − | 0.0336908i | ||||
\(246\) | 2.05792 | + | 27.1357i | 0.00836552 | + | 0.110308i | ||||
\(247\) | 275.339 | + | 476.902i | 1.11473 | + | 1.93078i | ||||
\(248\) | 283.429 | − | 163.638i | 1.14286 | − | 0.659830i | ||||
\(249\) | −169.744 | + | 353.285i | −0.681704 | + | 1.41881i | ||||
\(250\) | 70.3266 | − | 121.809i | 0.281307 | − | 0.487237i | ||||
\(251\) | 227.364 | + | 131.268i | 0.905831 | + | 0.522982i | 0.879087 | − | 0.476661i | \(-0.158153\pi\) |
0.0267434 | + | 0.999642i | \(0.491486\pi\) | |||||||
\(252\) | 68.7659 | − | 176.137i | 0.272881 | − | 0.698958i | ||||
\(253\) | −14.9254 | −0.0589935 | ||||||||
\(254\) | 25.4432i | 0.100170i | ||||||||
\(255\) | 61.3881 | + | 29.4954i | 0.240738 | + | 0.115668i | ||||
\(256\) | 100.103 | + | 173.384i | 0.391028 | + | 0.677280i | ||||
\(257\) | −92.6308 | + | 53.4804i | −0.360431 | + | 0.208095i | −0.669270 | − | 0.743019i | \(-0.733393\pi\) |
0.308839 | + | 0.951114i | \(0.400060\pi\) | |||||||
\(258\) | 84.4627 | − | 175.790i | 0.327375 | − | 0.681357i | ||||
\(259\) | −40.1950 | −0.155193 | ||||||||
\(260\) | − | 156.579i | − | 0.602226i | ||||||
\(261\) | 315.189 | − | 252.277i | 1.20762 | − | 0.966580i | ||||
\(262\) | −25.6358 | + | 44.4026i | −0.0978467 | + | 0.169475i | ||||
\(263\) | − | 391.796i | − | 1.48972i | −0.667222 | − | 0.744859i | \(-0.732517\pi\) | ||
0.667222 | − | 0.744859i | \(-0.267483\pi\) | |||||||
\(264\) | −158.305 | + | 108.137i | −0.599638 | + | 0.409612i | ||||
\(265\) | 363.089 | 1.37015 | ||||||||
\(266\) | −238.377 | − | 137.627i | −0.896155 | − | 0.517395i | ||||
\(267\) | −314.271 | + | 23.8337i | −1.17705 | + | 0.0892650i | ||||
\(268\) | 191.739 | − | 11.0468i | 0.715443 | − | 0.0412194i | ||||
\(269\) | 228.018i | 0.847649i | 0.905744 | + | 0.423824i | \(0.139313\pi\) | ||||
−0.905744 | + | 0.423824i | \(0.860687\pi\) | |||||||
\(270\) | 96.1920 | + | 29.3892i | 0.356267 | + | 0.108849i | ||||
\(271\) | −119.513 | −0.441009 | −0.220504 | − | 0.975386i | \(-0.570770\pi\) | ||||
−0.220504 | + | 0.975386i | \(0.570770\pi\) | |||||||
\(272\) | −20.6943 | + | 11.9479i | −0.0760821 | + | 0.0439260i | ||||
\(273\) | 25.9570 | + | 342.269i | 0.0950806 | + | 1.25373i | ||||
\(274\) | 136.604 | − | 236.606i | 0.498556 | − | 0.863525i | ||||
\(275\) | −96.5742 | + | 55.7571i | −0.351179 | + | 0.202753i | ||||
\(276\) | −14.6409 | + | 1.11034i | −0.0530467 | + | 0.00402296i | ||||
\(277\) | 333.903 | 1.20543 | 0.602713 | − | 0.797958i | \(-0.294086\pi\) | ||||
0.602713 | + | 0.797958i | \(0.294086\pi\) | |||||||
\(278\) | −113.260 | − | 65.3904i | −0.407408 | − | 0.235217i | ||||
\(279\) | 251.775 | + | 314.561i | 0.902420 | + | 1.12746i | ||||
\(280\) | 93.7391 | + | 162.361i | 0.334782 | + | 0.579860i | ||||
\(281\) | 183.796 | + | 106.115i | 0.654078 | + | 0.377632i | 0.790017 | − | 0.613085i | \(-0.210072\pi\) |
−0.135939 | + | 0.990717i | \(0.543405\pi\) | |||||||
\(282\) | −17.0791 | − | 225.205i | −0.0605643 | − | 0.798601i | ||||
\(283\) | −116.411 | −0.411347 | −0.205674 | − | 0.978621i | \(-0.565938\pi\) | ||||
−0.205674 | + | 0.978621i | \(0.565938\pi\) | |||||||
\(284\) | 74.0631 | + | 42.7603i | 0.260786 | + | 0.150565i | ||||
\(285\) | −160.362 | + | 333.758i | −0.562674 | + | 1.17108i | ||||
\(286\) | 72.6434 | − | 125.822i | 0.253998 | − | 0.439937i | ||||
\(287\) | −54.0814 | − | 31.2239i | −0.188437 | − | 0.108794i | ||||
\(288\) | −233.017 | + | 186.507i | −0.809088 | + | 0.647594i | ||||
\(289\) | −123.452 | − | 213.825i | −0.427170 | − | 0.739880i | ||||
\(290\) | 167.105i | 0.576224i | ||||||||
\(291\) | −182.279 | − | 87.5805i | −0.626389 | − | 0.300964i | ||||
\(292\) | −256.424 | −0.878164 | ||||||||
\(293\) | 25.2338i | 0.0861221i | 0.999072 | + | 0.0430610i | \(0.0137110\pi\) | ||||
−0.999072 | + | 0.0430610i | \(0.986289\pi\) | |||||||
\(294\) | −8.49988 | − | 12.4431i | −0.0289112 | − | 0.0423236i | ||||
\(295\) | 114.357 | 0.387649 | ||||||||
\(296\) | 34.7206 | + | 20.0459i | 0.117299 | + | 0.0677228i | ||||
\(297\) | −160.998 | − | 172.585i | −0.542082 | − | 0.581094i | ||||
\(298\) | 18.7256 | − | 32.4337i | 0.0628376 | − | 0.108838i | ||||
\(299\) | 23.0834 | − | 13.3272i | 0.0772019 | − | 0.0445725i | ||||
\(300\) | −90.5857 | + | 61.8789i | −0.301952 | + | 0.206263i | ||||
\(301\) | 223.769 | + | 387.579i | 0.743418 | + | 1.28764i | ||||
\(302\) | −98.5410 | + | 56.8927i | −0.326295 | + | 0.188386i | ||||
\(303\) | 157.073 | + | 229.942i | 0.518392 | + | 0.758884i | ||||
\(304\) | −64.9588 | − | 112.512i | −0.213680 | − | 0.370105i | ||||
\(305\) | 117.080 | + | 67.5963i | 0.383870 | + | 0.221627i | ||||
\(306\) | 38.8481 | + | 48.5359i | 0.126955 | + | 0.158614i | ||||
\(307\) | −15.2405 | + | 26.3972i | −0.0496432 | + | 0.0859845i | −0.889779 | − | 0.456391i | \(-0.849142\pi\) |
0.840136 | + | 0.542376i | \(0.182475\pi\) | |||||||
\(308\) | − | 183.655i | − | 0.596281i | ||||||
\(309\) | 102.870 | − | 70.2700i | 0.332911 | − | 0.227411i | ||||
\(310\) | −166.772 | −0.537975 | ||||||||
\(311\) | 98.5812i | 0.316981i | 0.987360 | + | 0.158491i | \(0.0506628\pi\) | ||||
−0.987360 | + | 0.158491i | \(0.949337\pi\) | |||||||
\(312\) | 148.273 | − | 308.598i | 0.475235 | − | 0.989096i | ||||
\(313\) | −70.6652 | −0.225767 | −0.112884 | − | 0.993608i | \(-0.536009\pi\) | ||||
−0.112884 | + | 0.993608i | \(0.536009\pi\) | |||||||
\(314\) | −126.893 | + | 73.2615i | −0.404117 | + | 0.233317i | ||||
\(315\) | −180.195 | + | 144.228i | −0.572047 | + | 0.457867i | ||||
\(316\) | 15.9042 | − | 27.5469i | 0.0503298 | − | 0.0871738i | ||||
\(317\) | −351.005 | − | 202.653i | −1.10727 | − | 0.639283i | −0.169149 | − | 0.985591i | \(-0.554102\pi\) |
−0.938121 | + | 0.346308i | \(0.887435\pi\) | |||||||
\(318\) | 298.739 | + | 143.536i | 0.939431 | + | 0.451372i | ||||
\(319\) | 196.062 | − | 339.589i | 0.614613 | − | 1.06454i | ||||
\(320\) | − | 71.9922i | − | 0.224976i | ||||||
\(321\) | 110.947 | − | 8.41398i | 0.345628 | − | 0.0262118i | ||||
\(322\) | −6.66154 | + | 11.5381i | −0.0206880 | + | 0.0358327i | ||||
\(323\) | −198.206 | + | 114.434i | −0.613641 | + | 0.354286i | ||||
\(324\) | −170.769 | − | 157.319i | −0.527065 | − | 0.485551i | ||||
\(325\) | 99.5736 | − | 172.467i | 0.306380 | − | 0.530666i | ||||
\(326\) | − | 271.838i | − | 0.833857i | ||||||
\(327\) | 17.4563 | + | 230.179i | 0.0533833 | + | 0.703911i | ||||
\(328\) | 31.1438 | + | 53.9426i | 0.0949506 | + | 0.164459i | ||||
\(329\) | 448.834 | + | 259.135i | 1.36424 | + | 0.787643i | ||||
\(330\) | 97.4131 | − | 7.38762i | 0.295191 | − | 0.0223867i | ||||
\(331\) | −83.8706 | − | 145.268i | −0.253386 | − | 0.438877i | 0.711070 | − | 0.703121i | \(-0.248211\pi\) |
−0.964456 | + | 0.264244i | \(0.914877\pi\) | |||||||
\(332\) | 374.509i | 1.12804i | ||||||||
\(333\) | −17.9503 | + | 45.9779i | −0.0539047 | + | 0.138072i | ||||
\(334\) | −0.816609 | −0.00244494 | ||||||||
\(335\) | −209.432 | − | 105.345i | −0.625171 | − | 0.314464i | ||||
\(336\) | −6.12385 | − | 80.7490i | −0.0182257 | − | 0.240324i | ||||
\(337\) | −158.869 | + | 275.170i | −0.471422 | + | 0.816527i | −0.999466 | − | 0.0326900i | \(-0.989593\pi\) |
0.528043 | + | 0.849218i | \(0.322926\pi\) | |||||||
\(338\) | 79.5336i | 0.235307i | ||||||||
\(339\) | 104.607 | + | 153.137i | 0.308577 | + | 0.451731i | ||||
\(340\) | 65.0760 | 0.191400 | ||||||||
\(341\) | 338.912 | + | 195.671i | 0.993878 | + | 0.573816i | ||||
\(342\) | −263.882 | + | 211.211i | −0.771585 | + | 0.617577i | ||||
\(343\) | −324.554 | −0.946222 | ||||||||
\(344\) | − | 446.389i | − | 1.29764i | ||||||
\(345\) | 16.1548 | + | 7.76197i | 0.0468255 | + | 0.0224985i | ||||
\(346\) | −10.9028 | − | 18.8842i | −0.0315110 | − | 0.0545786i | ||||
\(347\) | −301.912 | + | 174.309i | −0.870063 | + | 0.502331i | −0.867369 | − | 0.497665i | \(-0.834191\pi\) |
−0.00269406 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(348\) | 167.062 | − | 347.702i | 0.480064 | − | 0.999145i | ||||
\(349\) | −263.699 | −0.755584 | −0.377792 | − | 0.925890i | \(-0.623317\pi\) | ||||
−0.377792 | + | 0.925890i | \(0.623317\pi\) | |||||||
\(350\) | 99.5429i | 0.284408i | ||||||||
\(351\) | 403.103 | + | 123.159i | 1.14844 | + | 0.350879i | ||||
\(352\) | −144.947 | + | 251.056i | −0.411782 | + | 0.713227i | ||||
\(353\) | 24.1915 | + | 13.9670i | 0.0685311 | + | 0.0395664i | 0.533874 | − | 0.845564i | \(-0.320736\pi\) |
−0.465343 | + | 0.885130i | \(0.654069\pi\) | |||||||
\(354\) | 94.0891 | + | 45.2074i | 0.265788 | + | 0.127705i | ||||
\(355\) | −52.1955 | − | 90.4053i | −0.147030 | − | 0.254663i | ||||
\(356\) | −260.804 | + | 150.575i | −0.732596 | + | 0.422964i | ||||
\(357\) | −142.251 | + | 10.7880i | −0.398462 | + | 0.0302186i | ||||
\(358\) | −100.967 | + | 174.879i | −0.282030 | + | 0.488490i | ||||
\(359\) | − | 512.479i | − | 1.42752i | −0.700391 | − | 0.713760i | \(-0.746991\pi\) | ||
0.700391 | − | 0.713760i | \(-0.253009\pi\) | |||||||
\(360\) | 227.582 | − | 34.7184i | 0.632172 | − | 0.0964400i | ||||
\(361\) | −441.662 | − | 764.982i | −1.22344 | − | 2.11906i | ||||
\(362\) | 215.472i | 0.595228i | ||||||||
\(363\) | 120.563 | + | 57.9274i | 0.332129 | + | 0.159580i | ||||
\(364\) | 163.989 | + | 284.038i | 0.450520 | + | 0.780324i | ||||
\(365\) | 271.070 | + | 156.502i | 0.742657 | + | 0.428773i | ||||
\(366\) | 69.6079 | + | 101.900i | 0.190186 | + | 0.278416i | ||||
\(367\) | −182.779 | − | 316.583i | −0.498037 | − | 0.862625i | 0.501961 | − | 0.864890i | \(-0.332612\pi\) |
−0.999997 | + | 0.00226548i | \(0.999279\pi\) | |||||||
\(368\) | −5.44589 | + | 3.14419i | −0.0147986 | + | 0.00854398i | ||||
\(369\) | −59.8678 | + | 47.9182i | −0.162243 | + | 0.129860i | ||||
\(370\) | −10.2150 | − | 17.6928i | −0.0276080 | − | 0.0478185i | ||||
\(371\) | −658.654 | + | 380.274i | −1.77535 | + | 1.02500i | ||||
\(372\) | 347.010 | + | 166.729i | 0.932822 | + | 0.448197i | ||||
\(373\) | −69.8619 | − | 121.004i | −0.187297 | − | 0.324409i | 0.757051 | − | 0.653356i | \(-0.226639\pi\) |
−0.944348 | + | 0.328947i | \(0.893306\pi\) | |||||||
\(374\) | 52.2932 | + | 30.1915i | 0.139821 | + | 0.0807259i | ||||
\(375\) | 395.201 | − | 29.9713i | 1.05387 | − | 0.0799235i | ||||
\(376\) | −258.470 | − | 447.682i | −0.687419 | − | 1.19064i | ||||
\(377\) | 700.272i | 1.85748i | ||||||||
\(378\) | −205.275 | + | 47.4319i | −0.543056 | + | 0.125481i | ||||
\(379\) | −133.778 | + | 231.710i | −0.352976 | + | 0.611373i | −0.986769 | − | 0.162130i | \(-0.948164\pi\) |
0.633793 | + | 0.773503i | \(0.281497\pi\) | |||||||
\(380\) | 353.808i | 0.931075i | ||||||||
\(381\) | −59.2006 | + | 40.4398i | −0.155382 | + | 0.106141i | ||||
\(382\) | −16.8636 | − | 29.2086i | −0.0441456 | − | 0.0764624i | ||||
\(383\) | −46.1988 | − | 26.6729i | −0.120624 | − | 0.0696420i | 0.438474 | − | 0.898744i | \(-0.355519\pi\) |
−0.559098 | + | 0.829102i | \(0.688852\pi\) | |||||||
\(384\) | −143.886 | + | 299.466i | −0.374702 | + | 0.779859i | ||||
\(385\) | −112.089 | + | 194.144i | −0.291141 | + | 0.504271i | ||||
\(386\) | −48.1578 | − | 27.8039i | −0.124761 | − | 0.0720309i | ||||
\(387\) | 543.271 | − | 82.8779i | 1.40380 | − | 0.214155i | ||||
\(388\) | −193.230 | −0.498015 | ||||||||
\(389\) | −228.037 | − | 131.657i | −0.586213 | − | 0.338450i | 0.177386 | − | 0.984141i | \(-0.443236\pi\) |
−0.763599 | + | 0.645691i | \(0.776569\pi\) | |||||||
\(390\) | −144.061 | + | 98.4080i | −0.369388 | + | 0.252328i | ||||
\(391\) | 5.53894 | + | 9.59373i | 0.0141661 | + | 0.0245364i | ||||
\(392\) | −29.8700 | − | 17.2454i | −0.0761989 | − | 0.0439935i | ||||
\(393\) | −144.061 | + | 10.9253i | −0.366567 | + | 0.0277997i | ||||
\(394\) | −218.972 | −0.555766 | ||||||||
\(395\) | −33.6252 | + | 19.4135i | −0.0851272 | + | 0.0491482i | ||||
\(396\) | −210.077 | − | 82.0164i | −0.530498 | − | 0.207112i | ||||
\(397\) | 189.072 | 0.476252 | 0.238126 | − | 0.971234i | \(-0.423467\pi\) | ||||
0.238126 | + | 0.971234i | \(0.423467\pi\) | |||||||
\(398\) | −52.3676 | + | 30.2345i | −0.131577 | + | 0.0759660i | ||||
\(399\) | −58.6530 | − | 773.398i | −0.147000 | − | 1.93834i | ||||
\(400\) | −23.4917 | + | 40.6888i | −0.0587292 | + | 0.101722i | ||||
\(401\) | − | 544.149i | − | 1.35698i | −0.734610 | − | 0.678490i | \(-0.762635\pi\) | ||
0.734610 | − | 0.678490i | \(-0.237365\pi\) | |||||||
\(402\) | −130.669 | − | 169.468i | −0.325048 | − | 0.421562i | ||||
\(403\) | −698.877 | −1.73419 | ||||||||
\(404\) | 230.431 | + | 133.039i | 0.570374 | + | 0.329306i | ||||
\(405\) | 84.5070 | + | 270.529i | 0.208659 | + | 0.667973i | ||||
\(406\) | −175.014 | − | 303.133i | −0.431069 | − | 0.746633i | ||||
\(407\) | 47.9402i | 0.117789i | ||||||||
\(408\) | 128.257 | + | 61.6242i | 0.314355 | + | 0.151040i | ||||
\(409\) | 397.545 | + | 688.568i | 0.971993 | + | 1.68354i | 0.689522 | + | 0.724265i | \(0.257821\pi\) |
0.282471 | + | 0.959276i | \(0.408846\pi\) | |||||||
\(410\) | − | 31.7403i | − | 0.0774155i | ||||||
\(411\) | 767.650 | − | 58.2171i | 1.86776 | − | 0.141647i | ||||
\(412\) | 59.5182 | − | 103.089i | 0.144462 | − | 0.250215i | ||||
\(413\) | −207.446 | + | 119.769i | −0.502291 | + | 0.289998i | ||||
\(414\) | 10.2232 | + | 12.7726i | 0.0246938 | + | 0.0308518i | ||||
\(415\) | 228.572 | − | 395.899i | 0.550777 | − | 0.953974i | ||||
\(416\) | − | 517.707i | − | 1.24449i | ||||||
\(417\) | −27.8676 | − | 367.462i | −0.0668288 | − | 0.881204i | ||||
\(418\) | −164.146 | + | 284.310i | −0.392695 | + | 0.680168i | ||||
\(419\) | 84.4576 | + | 48.7616i | 0.201569 | + | 0.116376i | 0.597387 | − | 0.801953i | \(-0.296206\pi\) |
−0.395818 | + | 0.918329i | \(0.629539\pi\) | |||||||
\(420\) | −95.5101 | + | 198.783i | −0.227405 | + | 0.473293i | ||||
\(421\) | −149.078 | + | 258.211i | −0.354104 | + | 0.613327i | −0.986964 | − | 0.160940i | \(-0.948548\pi\) |
0.632860 | + | 0.774266i | \(0.281881\pi\) | |||||||
\(422\) | −68.2608 | + | 39.4104i | −0.161756 | + | 0.0933896i | ||||
\(423\) | 496.857 | − | 397.684i | 1.17460 | − | 0.940152i | ||||
\(424\) | 758.596 | 1.78914 | ||||||||
\(425\) | 71.6792 | + | 41.3840i | 0.168657 | + | 0.0973742i | ||||
\(426\) | −7.20588 | − | 95.0167i | −0.0169152 | − | 0.223044i | ||||
\(427\) | −283.182 | −0.663191 | ||||||||
\(428\) | 92.0711 | − | 53.1573i | 0.215120 | − | 0.124199i | ||||
\(429\) | 408.220 | − | 30.9586i | 0.951562 | − | 0.0721647i | ||||
\(430\) | −113.735 | + | 196.995i | −0.264500 | + | 0.458127i | ||||
\(431\) | −500.706 | + | 289.083i | −1.16173 | + | 0.670726i | −0.951718 | − | 0.306973i | \(-0.900684\pi\) |
−0.210013 | + | 0.977699i | \(0.567351\pi\) | |||||||
\(432\) | −95.1012 | − | 29.0559i | −0.220142 | − | 0.0672591i | ||||
\(433\) | −389.708 | − | 674.995i | −0.900019 | − | 1.55888i | −0.827467 | − | 0.561514i | \(-0.810219\pi\) |
−0.0725523 | − | 0.997365i | \(-0.523114\pi\) | |||||||
\(434\) | 302.529 | − | 174.665i | 0.697073 | − | 0.402455i | ||||
\(435\) | −388.816 | + | 265.599i | −0.893830 | + | 0.610573i | ||||
\(436\) | 110.284 | + | 191.018i | 0.252946 | + | 0.438115i | ||||
\(437\) | −52.1597 | + | 30.1144i | −0.119359 | + | 0.0689117i | ||||
\(438\) | 161.160 | + | 235.925i | 0.367944 | + | 0.538641i | ||||
\(439\) | −55.3872 | + | 95.9335i | −0.126167 | + | 0.218527i | −0.922188 | − | 0.386741i | \(-0.873601\pi\) |
0.796022 | + | 0.605268i | \(0.206934\pi\) | |||||||
\(440\) | 193.646 | − | 111.802i | 0.440105 | − | 0.254095i | ||||
\(441\) | 15.4425 | − | 39.5546i | 0.0350171 | − | 0.0896930i | ||||
\(442\) | −107.835 | −0.243970 | ||||||||
\(443\) | 287.978 | − | 166.264i | 0.650064 | − | 0.375315i | −0.138417 | − | 0.990374i | \(-0.544201\pi\) |
0.788481 | + | 0.615060i | \(0.210868\pi\) | |||||||
\(444\) | 3.56640 | + | 47.0265i | 0.00803244 | + | 0.105916i | ||||
\(445\) | 367.600 | 0.826068 | ||||||||
\(446\) | −286.595 | − | 165.466i | −0.642590 | − | 0.371000i | ||||
\(447\) | 105.229 | − | 7.98035i | 0.235411 | − | 0.0178531i | ||||
\(448\) | 75.3995 | + | 130.596i | 0.168303 | + | 0.291509i | ||||
\(449\) | −572.363 | + | 330.454i | −1.27475 | + | 0.735977i | −0.975878 | − | 0.218316i | \(-0.929944\pi\) |
−0.298872 | + | 0.954293i | \(0.596610\pi\) | |||||||
\(450\) | 113.864 | + | 44.4538i | 0.253032 | + | 0.0987863i | ||||
\(451\) | −37.2404 | + | 64.5023i | −0.0825730 | + | 0.143021i | ||||
\(452\) | 153.463 | + | 88.6018i | 0.339519 | + | 0.196022i | ||||
\(453\) | −288.999 | − | 138.857i | −0.637967 | − | 0.306527i | ||||
\(454\) | 317.023 | 0.698289 | ||||||||
\(455\) | − | 400.348i | − | 0.879887i | ||||||
\(456\) | −335.042 | + | 697.314i | −0.734741 | + | 1.52920i | ||||
\(457\) | 390.886 | + | 677.035i | 0.855331 | + | 1.48148i | 0.876337 | + | 0.481698i | \(0.159980\pi\) |
−0.0210063 | + | 0.999779i | \(0.506687\pi\) | |||||||
\(458\) | 23.7120 | − | 13.6901i | 0.0517729 | − | 0.0298911i | ||||
\(459\) | −51.1862 | + | 167.535i | −0.111517 | + | 0.364999i | ||||
\(460\) | 17.1253 | 0.0372290 | ||||||||
\(461\) | 490.543i | 1.06409i | 0.846718 | + | 0.532043i | \(0.178575\pi\) | ||||
−0.846718 | + | 0.532043i | \(0.821425\pi\) | |||||||
\(462\) | −168.973 | + | 115.425i | −0.365742 | + | 0.249838i | ||||
\(463\) | 263.098 | − | 455.699i | 0.568246 | − | 0.984231i | −0.428494 | − | 0.903545i | \(-0.640956\pi\) |
0.996740 | − | 0.0806859i | \(-0.0257111\pi\) | |||||||
\(464\) | − | 165.210i | − | 0.356056i | ||||||
\(465\) | −265.071 | − | 388.042i | −0.570044 | − | 0.834498i | ||||
\(466\) | 0.337359 | 0.000723947 | ||||||||
\(467\) | −167.537 | − | 96.7278i | −0.358752 | − | 0.207126i | 0.309781 | − | 0.950808i | \(-0.399744\pi\) |
−0.668533 | + | 0.743682i | \(0.733078\pi\) | |||||||
\(468\) | 398.137 | − | 60.7372i | 0.850720 | − | 0.129780i | ||||
\(469\) | 490.247 | − | 28.2450i | 1.04530 | − | 0.0602240i | ||||
\(470\) | 263.420i | 0.560469i | ||||||||
\(471\) | −372.148 | − | 178.808i | −0.790124 | − | 0.379634i | ||||
\(472\) | 238.923 | 0.506193 | ||||||||
\(473\) | 462.261 | − | 266.887i | 0.977296 | − | 0.564242i | ||||
\(474\) | −35.3404 | + | 2.68015i | −0.0745578 | + | 0.00565432i | ||||
\(475\) | −224.999 | + | 389.709i | −0.473681 | + | 0.820440i | ||||
\(476\) | −118.050 | + | 68.1560i | −0.248004 | + | 0.143185i | ||||
\(477\) | 140.843 | + | 923.238i | 0.295269 | + | 1.93551i | ||||
\(478\) | −419.357 | −0.877315 | ||||||||
\(479\) | 751.774 | + | 434.037i | 1.56947 | + | 0.906132i | 0.996231 | + | 0.0867414i | \(0.0276454\pi\) |
0.573236 | + | 0.819391i | \(0.305688\pi\) | |||||||
\(480\) | 287.449 | − | 196.356i | 0.598853 | − | 0.409075i | ||||
\(481\) | −42.8069 | − | 74.1437i | −0.0889956 | − | 0.154145i | ||||
\(482\) | 324.007 | + | 187.066i | 0.672214 | + | 0.388103i | ||||
\(483\) | −37.4346 | + | 2.83897i | −0.0775044 | + | 0.00587778i | ||||
\(484\) | 127.806 | 0.264061 | ||||||||
\(485\) | 204.266 | + | 117.933i | 0.421168 | + | 0.243161i | ||||
\(486\) | −37.4157 | + | 255.990i | −0.0769870 | + | 0.526729i | ||||
\(487\) | −66.2305 | + | 114.715i | −0.135997 | + | 0.235554i | −0.925978 | − | 0.377578i | \(-0.876757\pi\) |
0.789981 | + | 0.613131i | \(0.210090\pi\) | |||||||
\(488\) | 244.614 | + | 141.228i | 0.501258 | + | 0.289401i | ||||
\(489\) | 632.505 | − | 432.063i | 1.29347 | − | 0.883564i | ||||
\(490\) | 8.78789 | + | 15.2211i | 0.0179345 | + | 0.0310634i | ||||
\(491\) | − | 600.161i | − | 1.22232i | −0.791506 | − | 0.611162i | \(-0.790702\pi\) | ||
0.791506 | − | 0.611162i | \(-0.209298\pi\) | |||||||
\(492\) | −31.7322 | + | 66.0434i | −0.0644963 | + | 0.134235i | ||||
\(493\) | −291.041 | −0.590348 | ||||||||
\(494\) | − | 586.281i | − | 1.18680i | ||||||
\(495\) | 172.019 | + | 214.917i | 0.347514 | + | 0.434175i | ||||
\(496\) | 164.881 | 0.332421 | ||||||||
\(497\) | 189.368 | + | 109.332i | 0.381023 | + | 0.219984i | ||||
\(498\) | 344.569 | − | 235.375i | 0.691906 | − | 0.472640i | ||||
\(499\) | 313.823 | − | 543.558i | 0.628905 | − | 1.08929i | −0.358867 | − | 0.933389i | \(-0.616837\pi\) |
0.987772 | − | 0.155906i | \(-0.0498298\pi\) | |||||||
\(500\) | 327.965 | − | 189.351i | 0.655930 | − | 0.378701i | ||||
\(501\) | −1.29793 | − | 1.90007i | −0.00259068 | − | 0.00379255i | ||||
\(502\) | −139.755 | − | 242.063i | −0.278397 | − | 0.482197i | ||||
\(503\) | 606.698 | − | 350.277i | 1.20616 | − | 0.696377i | 0.244242 | − | 0.969714i | \(-0.421461\pi\) |
0.961918 | + | 0.273338i | \(0.0881276\pi\) | |||||||
\(504\) | −376.478 | + | 301.333i | −0.746980 | + | 0.597883i | ||||
\(505\) | −162.395 | − | 281.276i | −0.321574 | − | 0.556983i | ||||
\(506\) | 13.7614 | + | 7.94515i | 0.0271964 | + | 0.0157019i | ||||
\(507\) | −185.057 | + | 126.412i | −0.365004 | + | 0.249333i | ||||
\(508\) | −34.2522 | + | 59.3266i | −0.0674256 | + | 0.116785i | ||||
\(509\) | − | 234.115i | − | 0.459950i | −0.973197 | − | 0.229975i | \(-0.926136\pi\) | ||
0.973197 | − | 0.229975i | \(-0.0738645\pi\) | |||||||
\(510\) | −40.8996 | − | 59.8737i | −0.0801952 | − | 0.117399i | ||||
\(511\) | −655.637 | −1.28305 | ||||||||
\(512\) | 229.836i | 0.448899i | ||||||||
\(513\) | −910.860 | − | 278.292i | −1.77556 | − | 0.542479i | ||||
\(514\) | 113.876 | 0.221549 | ||||||||
\(515\) | −125.835 | + | 72.6511i | −0.244340 | + | 0.141070i | ||||
\(516\) | 433.597 | − | 296.189i | 0.840304 | − | 0.574010i | ||||
\(517\) | 309.067 | − | 535.320i | 0.597809 | − | 1.03543i | ||||
\(518\) | 37.0604 | + | 21.3969i | 0.0715452 | + | 0.0413067i | ||||
\(519\) | 26.6102 | − | 55.3832i | 0.0512721 | − | 0.106711i | ||||
\(520\) | −199.660 | + | 345.822i | −0.383962 | + | 0.665042i | ||||
\(521\) | − | 963.753i | − | 1.84981i | −0.380194 | − | 0.924907i | \(-0.624143\pi\) | ||
0.380194 | − | 0.924907i | \(-0.375857\pi\) | |||||||
\(522\) | −424.903 | + | 64.8204i | −0.813990 | + | 0.124177i | ||||
\(523\) | 413.249 | − | 715.768i | 0.790151 | − | 1.36858i | −0.135722 | − | 0.990747i | \(-0.543335\pi\) |
0.925873 | − | 0.377835i | \(-0.123331\pi\) | |||||||
\(524\) | −119.552 | + | 69.0231i | −0.228152 | + | 0.131723i | ||||
\(525\) | −231.614 | + | 158.215i | −0.441170 | + | 0.301362i | ||||
\(526\) | −208.563 | + | 361.242i | −0.396508 | + | 0.686771i | ||||
\(527\) | − | 290.462i | − | 0.551161i | ||||||
\(528\) | −96.3084 | + | 7.30385i | −0.182402 | + | 0.0138330i | ||||
\(529\) | −263.042 | − | 455.603i | −0.497245 | − | 0.861253i | ||||
\(530\) | −334.774 | − | 193.282i | −0.631649 | − | 0.364683i | ||||
\(531\) | 44.3592 | + | 290.778i | 0.0835390 | + | 0.547604i | ||||
\(532\) | −370.554 | − | 641.818i | −0.696530 | − | 1.20643i | ||||
\(533\) | − | 133.011i | − | 0.249552i | ||||||
\(534\) | 302.450 | + | 145.320i | 0.566386 | + | 0.272134i | ||||
\(535\) | −129.773 | −0.242567 | ||||||||
\(536\) | −437.563 | − | 220.096i | −0.816349 | − | 0.410628i | ||||
\(537\) | −567.383 | + | 43.0293i | −1.05658 | + | 0.0801290i | ||||
\(538\) | 121.380 | − | 210.236i | 0.225613 | − | 0.390772i | ||||
\(539\) | − | 41.2428i | − | 0.0765172i | ||||||
\(540\) | 184.729 | + | 198.024i | 0.342091 | + | 0.366710i | ||||
\(541\) | −321.404 | −0.594093 | −0.297046 | − | 0.954863i | \(-0.596002\pi\) | ||||
−0.297046 | + | 0.954863i | \(0.596002\pi\) | |||||||
\(542\) | 110.193 | + | 63.6200i | 0.203308 | + | 0.117380i | ||||
\(543\) | −501.356 | + | 342.475i | −0.923308 | + | 0.630709i | ||||
\(544\) | 215.165 | 0.395524 | ||||||||
\(545\) | − | 269.238i | − | 0.494015i | ||||||
\(546\) | 158.266 | − | 329.395i | 0.289864 | − | 0.603287i | ||||
\(547\) | 11.8406 | + | 20.5086i | 0.0216465 | + | 0.0374928i | 0.876646 | − | 0.481136i | \(-0.159776\pi\) |
−0.854999 | + | 0.518629i | \(0.826443\pi\) | |||||||
\(548\) | 637.048 | − | 367.800i | 1.16250 | − | 0.671168i | ||||
\(549\) | −126.463 | + | 323.924i | −0.230352 | + | 0.590026i | ||||
\(550\) | 118.724 | 0.215861 | ||||||||
\(551\) | − | 1582.35i | − | 2.87178i | ||||||
\(552\) | 33.7520 | + | 16.2170i | 0.0611448 | + | 0.0293785i | ||||
\(553\) | 40.6647 | − | 70.4334i | 0.0735348 | − | 0.127366i | ||||
\(554\) | −307.864 | − | 177.745i | −0.555711 | − | 0.320840i | ||||
\(555\) | 24.9314 | − | 51.8892i | 0.0449215 | − | 0.0934940i | ||||
\(556\) | −176.060 | − | 304.945i | −0.316655 | − | 0.548463i | ||||
\(557\) | −425.153 | + | 245.462i | −0.763291 | + | 0.440686i | −0.830476 | − | 0.557054i | \(-0.811932\pi\) |
0.0671849 | + | 0.997741i | \(0.478598\pi\) | |||||||
\(558\) | −64.6914 | − | 424.057i | −0.115934 | − | 0.759958i | ||||
\(559\) | −476.618 | + | 825.527i | −0.852627 | + | 1.47679i | ||||
\(560\) | 94.4513i | 0.168663i | ||||||||
\(561\) | 12.8668 | + | 169.661i | 0.0229355 | + | 0.302427i | ||||
\(562\) | −112.975 | − | 195.678i | −0.201023 | − | 0.348182i | ||||
\(563\) | 601.353i | 1.06812i | 0.845446 | + | 0.534061i | \(0.179335\pi\) | ||||
−0.845446 | + | 0.534061i | \(0.820665\pi\) | |||||||
\(564\) | 263.353 | − | 548.110i | 0.466938 | − | 0.971826i | ||||
\(565\) | −108.152 | − | 187.325i | −0.191419 | − | 0.331548i | ||||
\(566\) | 107.333 | + | 61.9687i | 0.189634 | + | 0.109485i | ||||
\(567\) | −436.631 | − | 402.240i | −0.770072 | − | 0.709419i | ||||
\(568\) | −109.051 | − | 188.882i | −0.191992 | − | 0.332539i | ||||
\(569\) | −325.936 | + | 188.179i | −0.572823 | + | 0.330719i | −0.758276 | − | 0.651934i | \(-0.773958\pi\) |
0.185453 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(570\) | 325.524 | − | 222.365i | 0.571095 | − | 0.390114i | ||||
\(571\) | −31.4877 | − | 54.5383i | −0.0551448 | − | 0.0955136i | 0.837135 | − | 0.546996i | \(-0.184229\pi\) |
−0.892280 | + | 0.451482i | \(0.850895\pi\) | |||||||
\(572\) | 338.769 | − | 195.588i | 0.592254 | − | 0.341938i | ||||
\(573\) | 41.1586 | − | 85.6625i | 0.0718301 | − | 0.149498i | ||||
\(574\) | 33.2426 | + | 57.5779i | 0.0579139 | + | 0.100310i | ||||
\(575\) | 18.8630 | + | 10.8906i | 0.0328052 | + | 0.0189401i | ||||
\(576\) | 183.057 | − | 27.9259i | 0.317807 | − | 0.0484825i | ||||
\(577\) | 389.743 | + | 675.054i | 0.675464 | + | 1.16994i | 0.976333 | + | 0.216273i | \(0.0693900\pi\) |
−0.300869 | + | 0.953666i | \(0.597277\pi\) | |||||||
\(578\) | 262.867i | 0.454787i | ||||||||
\(579\) | −11.8493 | − | 156.244i | −0.0204651 | − | 0.269852i | ||||
\(580\) | −224.961 | + | 389.643i | −0.387863 | + | 0.671799i | ||||
\(581\) | 957.562i | 1.64813i | ||||||||
\(582\) | 121.443 | + | 177.782i | 0.208665 | + | 0.305468i | ||||
\(583\) | 453.549 | + | 785.570i | 0.777957 | + | 1.34746i | ||||
\(584\) | 566.341 | + | 326.977i | 0.969763 | + | 0.559893i | ||||
\(585\) | −457.947 | − | 178.787i | −0.782815 | − | 0.305619i | ||||
\(586\) | 13.4326 | − | 23.2659i | 0.0229225 | − | 0.0397029i | ||||
\(587\) | 218.603 | + | 126.210i | 0.372407 | + | 0.215009i | 0.674509 | − | 0.738266i | \(-0.264355\pi\) |
−0.302103 | + | 0.953275i | \(0.597688\pi\) | |||||||
\(588\) | −3.06816 | − | 40.4567i | −0.00521796 | − | 0.0688040i | ||||
\(589\) | 1579.20 | 2.68115 | ||||||||
\(590\) | −105.438 | − | 60.8749i | −0.178709 | − | 0.103178i | ||||
\(591\) | −348.037 | − | 509.499i | −0.588896 | − | 0.862096i | ||||
\(592\) | 10.0991 | + | 17.4922i | 0.0170593 | + | 0.0295476i | ||||
\(593\) | 45.1074 | + | 26.0427i | 0.0760664 | + | 0.0439169i | 0.537551 | − | 0.843231i | \(-0.319350\pi\) |
−0.461484 | + | 0.887148i | \(0.652683\pi\) | |||||||
\(594\) | 56.5715 | + | 244.829i | 0.0952382 | + | 0.412171i | ||||
\(595\) | 166.390 | 0.279647 | ||||||||
\(596\) | 87.3261 | − | 50.4177i | 0.146520 | − | 0.0845935i | ||||
\(597\) | −153.583 | − | 73.7927i | −0.257258 | − | 0.123606i | ||||
\(598\) | −28.3776 | −0.0474542 | ||||||||
\(599\) | 19.2844 | − | 11.1339i | 0.0321943 | − | 0.0185874i | −0.483816 | − | 0.875169i | \(-0.660750\pi\) |
0.516011 | + | 0.856582i | \(0.327416\pi\) | |||||||
\(600\) | 278.973 | − | 21.1568i | 0.464956 | − | 0.0352614i | ||||
\(601\) | 221.789 | − | 384.151i | 0.369034 | − | 0.639186i | −0.620381 | − | 0.784301i | \(-0.713022\pi\) |
0.989415 | + | 0.145115i | \(0.0463552\pi\) | |||||||
\(602\) | − | 476.471i | − | 0.791481i | ||||||
\(603\) | 186.626 | − | 573.393i | 0.309495 | − | 0.950901i | ||||
\(604\) | −306.361 | −0.507220 | ||||||||
\(605\) | −135.106 | − | 78.0032i | −0.223315 | − | 0.128931i | ||||
\(606\) | −22.4195 | − | 295.624i | −0.0369959 | − | 0.487828i | ||||
\(607\) | 370.650 | + | 641.985i | 0.610626 | + | 1.05764i | 0.991135 | + | 0.132859i | \(0.0424156\pi\) |
−0.380509 | + | 0.924777i | \(0.624251\pi\) | |||||||
\(608\) | 1169.82i | 1.92405i | ||||||||
\(609\) | 427.153 | − | 889.023i | 0.701400 | − | 1.45981i | ||||
\(610\) | −71.9665 | − | 124.650i | −0.117978 | − | 0.204344i | ||||
\(611\) | 1103.89i | 1.80670i | ||||||||
\(612\) | 25.2431 | + | 165.471i | 0.0412470 | + | 0.270377i | ||||
\(613\) | −319.697 | + | 553.732i | −0.521529 | + | 0.903314i | 0.478158 | + | 0.878274i | \(0.341305\pi\) |
−0.999686 | + | 0.0250403i | \(0.992029\pi\) | |||||||
\(614\) | 28.1039 | − | 16.2258i | 0.0457718 | − | 0.0264263i | ||||
\(615\) | 73.8527 | − | 50.4486i | 0.120086 | − | 0.0820303i | ||||
\(616\) | −234.186 | + | 405.622i | −0.380172 | + | 0.658478i | ||||
\(617\) | 153.362i | 0.248561i | 0.992247 | + | 0.124281i | \(0.0396623\pi\) | ||||
−0.992247 | + | 0.124281i | \(0.960338\pi\) | |||||||
\(618\) | −132.254 | + | 10.0299i | −0.214003 | + | 0.0162296i | ||||
\(619\) | −484.552 | + | 839.269i | −0.782798 | + | 1.35585i | 0.147507 | + | 0.989061i | \(0.452875\pi\) |
−0.930305 | + | 0.366786i | \(0.880458\pi\) | |||||||
\(620\) | −388.868 | − | 224.513i | −0.627206 | − | 0.362117i | ||||
\(621\) | −13.4701 | + | 44.0882i | −0.0216910 | + | 0.0709955i | ||||
\(622\) | 52.4773 | − | 90.8934i | 0.0843687 | − | 0.146131i | ||||
\(623\) | −666.837 | + | 384.999i | −1.07036 | + | 0.617975i | ||||
\(624\) | 142.428 | − | 97.2920i | 0.228249 | − | 0.155917i | ||||
\(625\) | −143.342 | −0.229347 | ||||||||
\(626\) | 65.1543 | + | 37.6169i | 0.104080 | + | 0.0600909i | ||||
\(627\) | −922.423 | + | 69.9548i | −1.47117 | + | 0.111571i | ||||
\(628\) | −394.506 | −0.628194 | ||||||||
\(629\) | 30.8150 | − | 17.7911i | 0.0489905 | − | 0.0282847i | ||||
\(630\) | 242.919 | − | 37.0581i | 0.385585 | − | 0.0588224i | ||||
\(631\) | −66.0443 | + | 114.392i | −0.104666 | + | 0.181287i | −0.913602 | − | 0.406610i | \(-0.866711\pi\) |
0.808936 | + | 0.587897i | \(0.200044\pi\) | |||||||
\(632\) | −70.2526 | + | 40.5604i | −0.111159 | + | 0.0641778i | ||||
\(633\) | −200.194 | − | 96.1882i | −0.316262 | − | 0.151956i | ||||
\(634\) | 215.754 | + | 373.697i | 0.340306 | + | 0.589428i | ||||
\(635\) | 72.4171 | − | 41.8101i | 0.114043 | − | 0.0658426i | ||||
\(636\) | 503.346 | + | 736.857i | 0.791424 | + | 1.15858i | ||||
\(637\) | 36.8266 | + | 63.7855i | 0.0578126 | + | 0.100134i | ||||
\(638\) | −361.544 | + | 208.737i | −0.566683 | + | 0.327174i | ||||
\(639\) | 209.629 | − | 167.788i | 0.328059 | − | 0.262578i | ||||
\(640\) | 193.752 | − | 335.589i | 0.302738 | − | 0.524357i | ||||
\(641\) | 760.362 | − | 438.995i | 1.18621 | − | 0.684859i | 0.228768 | − | 0.973481i | \(-0.426530\pi\) |
0.957443 | + | 0.288621i | \(0.0931969\pi\) | |||||||
\(642\) | −106.773 | − | 51.3019i | −0.166314 | − | 0.0799096i | ||||
\(643\) | 390.141 | 0.606751 | 0.303375 | − | 0.952871i | \(-0.401886\pi\) | ||||
0.303375 | + | 0.952871i | \(0.401886\pi\) | |||||||
\(644\) | −31.0658 | + | 17.9358i | −0.0482388 | + | 0.0278507i | ||||
\(645\) | −639.134 | + | 48.4707i | −0.990906 | + | 0.0751484i | ||||
\(646\) | 243.665 | 0.377191 | ||||||||
\(647\) | 319.328 | + | 184.364i | 0.493552 | + | 0.284952i | 0.726047 | − | 0.687645i | \(-0.241356\pi\) |
−0.232495 | + | 0.972598i | \(0.574689\pi\) | |||||||
\(648\) | 176.559 | + | 565.211i | 0.272468 | + | 0.872240i | ||||
\(649\) | 142.847 | + | 247.419i | 0.220104 | + | 0.381230i | ||||
\(650\) | −183.617 | + | 106.011i | −0.282487 | + | 0.163094i | ||||
\(651\) | 887.253 | + | 426.302i | 1.36291 | + | 0.654842i | ||||
\(652\) | 365.954 | − | 633.851i | 0.561279 | − | 0.972164i | ||||
\(653\) | 51.4118 | + | 29.6826i | 0.0787317 | + | 0.0454558i | 0.538849 | − | 0.842402i | \(-0.318859\pi\) |
−0.460117 | + | 0.887858i | \(0.652193\pi\) | |||||||
\(654\) | 106.435 | − | 221.521i | 0.162745 | − | 0.338717i | ||||
\(655\) | 168.507 | 0.257262 | ||||||||
\(656\) | 31.3804i | 0.0478360i | ||||||||
\(657\) | −292.794 | + | 749.965i | −0.445653 | + | 1.14150i | ||||
\(658\) | −275.888 | − | 477.852i | −0.419283 | − | 0.726219i | ||||
\(659\) | −523.913 | + | 302.481i | −0.795012 | + | 0.459000i | −0.841724 | − | 0.539908i | \(-0.818459\pi\) |
0.0467122 | + | 0.998908i | \(0.485126\pi\) | |||||||
\(660\) | 237.086 | + | 113.914i | 0.359222 | + | 0.172597i | ||||
\(661\) | 831.325 | 1.25768 | 0.628839 | − | 0.777536i | \(-0.283531\pi\) | ||||
0.628839 | + | 0.777536i | \(0.283531\pi\) | |||||||
\(662\) | 178.586i | 0.269767i | ||||||||
\(663\) | −171.394 | − | 250.907i | −0.258513 | − | 0.378442i | ||||
\(664\) | 477.552 | − | 827.145i | 0.719205 | − | 1.24570i | ||||
\(665\) | 904.636i | 1.36035i | ||||||||
\(666\) | 41.0257 | − | 32.8370i | 0.0616001 | − | 0.0493048i | ||||
\(667\) | −76.5901 | −0.114828 | ||||||||
\(668\) | −1.90411 | − | 1.09934i | −0.00285046 | − | 0.00164572i | ||||
\(669\) | −70.5171 | − | 929.837i | −0.105407 | − | 1.38989i | ||||
\(670\) | 137.022 | + | 208.616i | 0.204510 | + | 0.311368i | ||||
\(671\) | 337.749i | 0.503351i | ||||||||
\(672\) | −315.792 | + | 657.249i | −0.469928 | + | 0.978049i | ||||
\(673\) | −36.6995 | −0.0545312 | −0.0272656 | − | 0.999628i | \(-0.508680\pi\) | ||||
−0.0272656 | + | 0.999628i | \(0.508680\pi\) | |||||||
\(674\) | 292.960 | − | 169.140i | 0.434659 | − | 0.250950i | ||||
\(675\) | 77.5436 | + | 335.592i | 0.114879 | + | 0.497174i | ||||
\(676\) | −107.070 | + | 185.451i | −0.158388 | + | 0.274335i | ||||
\(677\) | −341.830 | + | 197.356i | −0.504919 | + | 0.291515i | −0.730743 | − | 0.682653i | \(-0.760826\pi\) |
0.225823 | + | 0.974168i | \(0.427493\pi\) | |||||||
\(678\) | −14.9310 | − | 196.880i | −0.0220221 | − | 0.290383i | ||||
\(679\) | −494.060 | −0.727628 | ||||||||
\(680\) | −143.728 | − | 82.9813i | −0.211364 | − | 0.122031i | ||||
\(681\) | 503.881 | + | 737.642i | 0.739914 | + | 1.08317i | ||||
\(682\) | −208.322 | − | 360.824i | −0.305457 | − | 0.529067i | ||||
\(683\) | −932.720 | − | 538.506i | −1.36562 | − | 0.788442i | −0.375256 | − | 0.926921i | \(-0.622445\pi\) |
−0.990365 | + | 0.138479i | \(0.955779\pi\) | |||||||
\(684\) | −899.639 | + | 137.243i | −1.31526 | + | 0.200648i | ||||
\(685\) | −897.913 | −1.31082 | ||||||||
\(686\) | 299.244 | + | 172.768i | 0.436215 | + | 0.251849i | ||||
\(687\) | 69.5421 | + | 33.4132i | 0.101226 | + | 0.0486364i | ||||
\(688\) | 112.445 | − | 194.761i | 0.163438 | − | 0.283082i | ||||
\(689\) | −1402.91 | − | 809.968i | −2.03615 | − | 1.17557i | ||||
\(690\) | −10.7631 | − | 15.7563i | −0.0155987 | − | 0.0228352i | ||||
\(691\) | 364.082 | + | 630.609i | 0.526891 | + | 0.912603i | 0.999509 | + | 0.0313351i | \(0.00997592\pi\) |
−0.472617 | + | 0.881268i | \(0.656691\pi\) | |||||||
\(692\) | − | 58.7104i | − | 0.0848417i | ||||||
\(693\) | −537.136 | − | 209.704i | −0.775088 | − | 0.302603i | ||||
\(694\) | 371.157 | 0.534808 | ||||||||
\(695\) | 429.817i | 0.618441i | ||||||||
\(696\) | −812.346 | + | 554.912i | −1.16716 | + | 0.797288i | ||||
\(697\) | 55.2811 | 0.0793130 | ||||||||
\(698\) | 243.134 | + | 140.374i | 0.348330 | + | 0.201108i | ||||
\(699\) | 0.536204 | + | 0.784959i | 0.000767102 | + | 0.00112297i | ||||
\(700\) | −134.007 | + | 232.107i | −0.191439 | + | 0.331582i | ||||
\(701\) | 87.2945 | − | 50.3995i | 0.124528 | − | 0.0718965i | −0.436442 | − | 0.899732i | \(-0.643762\pi\) |
0.560970 | + | 0.827836i | \(0.310428\pi\) | |||||||
\(702\) | −306.107 | − | 328.136i | −0.436049 | − | 0.467431i | ||||
\(703\) | 96.7274 | + | 167.537i | 0.137592 | + | 0.238317i | ||||
\(704\) | 155.760 | − | 89.9282i | 0.221250 | − | 0.127739i | ||||
\(705\) | −612.921 | + | 418.685i | −0.869391 | + | 0.593879i | ||||
\(706\) | −14.8699 | − | 25.7555i | −0.0210622 | − | 0.0364809i | ||||
\(707\) | 589.178 | + | 340.162i | 0.833350 | + | 0.481135i | ||||
\(708\) | 158.531 | + | 232.076i | 0.223914 | + | 0.327792i | ||||
\(709\) | 125.673 | − | 217.671i | 0.177253 | − | 0.307012i | −0.763685 | − | 0.645589i | \(-0.776612\pi\) |
0.940939 | + | 0.338577i | \(0.109945\pi\) | |||||||
\(710\) | 111.140i | 0.156535i | ||||||||
\(711\) | −62.4067 | − | 77.9693i | −0.0877731 | − | 0.109661i | ||||
\(712\) | 768.021 | 1.07868 | ||||||||
\(713\) | − | 76.4376i | − | 0.107206i | ||||||
\(714\) | 136.900 | + | 65.7771i | 0.191737 | + | 0.0921249i | ||||
\(715\) | −477.491 | −0.667820 | ||||||||
\(716\) | −470.854 | + | 271.848i | −0.657617 | + | 0.379675i | ||||
\(717\) | −666.532 | − | 975.750i | −0.929613 | − | 1.36088i | ||||
\(718\) | −272.806 | + | 472.514i | −0.379953 | + | 0.658097i | ||||
\(719\) | −333.541 | − | 192.570i | −0.463895 | − | 0.267830i | 0.249785 | − | 0.968301i | \(-0.419640\pi\) |
−0.713681 | + | 0.700471i | \(0.752973\pi\) | |||||||
\(720\) | 108.040 | + | 42.1800i | 0.150056 | + | 0.0585833i | ||||
\(721\) | 152.179 | − | 263.582i | 0.211067 | − | 0.365578i | ||||
\(722\) | 940.433i | 1.30254i | ||||||||
\(723\) | 79.7223 | + | 1051.22i | 0.110266 | + | 1.45397i | ||||
\(724\) | −290.074 | + | 502.423i | −0.400655 | + | 0.693954i | ||||
\(725\) | −495.575 | + | 286.120i | −0.683551 | + | 0.394648i | ||||
\(726\) | −80.3245 | − | 117.589i | −0.110640 | − | 0.161968i | ||||
\(727\) | 325.341 | − | 563.507i | 0.447511 | − | 0.775113i | −0.550712 | − | 0.834695i | \(-0.685644\pi\) |
0.998223 | + | 0.0595829i | \(0.0189771\pi\) | |||||||
\(728\) | − | 836.441i | − | 1.14896i | ||||||
\(729\) | −655.101 | + | 319.817i | −0.898630 | + | 0.438707i | ||||
\(730\) | −166.620 | − | 288.595i | −0.228247 | − | 0.395335i | ||||
\(731\) | −343.099 | − | 198.088i | −0.469356 | − | 0.270983i | ||||
\(732\) | 25.1261 | + | 331.312i | 0.0343252 | + | 0.452612i | ||||
\(733\) | 489.009 | + | 846.989i | 0.667134 | + | 1.15551i | 0.978702 | + | 0.205287i | \(0.0658126\pi\) |
−0.311568 | + | 0.950224i | \(0.600854\pi\) | |||||||
\(734\) | 389.193i | 0.530235i | ||||||||
\(735\) | −21.4484 | + | 44.6401i | −0.0291815 | + | 0.0607348i | ||||
\(736\) | 56.6226 | 0.0769329 | ||||||||
\(737\) | −33.6876 | − | 584.713i | −0.0457090 | − | 0.793369i | ||||
\(738\) | 80.7071 | − | 12.3122i | 0.109359 | − | 0.0166831i | ||||
\(739\) | −425.788 | + | 737.486i | −0.576168 | + | 0.997952i | 0.419746 | + | 0.907642i | \(0.362119\pi\) |
−0.995914 | + | 0.0903101i | \(0.971214\pi\) | |||||||
\(740\) | − | 55.0065i | − | 0.0743331i | ||||||
\(741\) | 1364.14 | − | 931.844i | 1.84095 | − | 1.25755i | ||||
\(742\) | 809.719 | 1.09127 | ||||||||
\(743\) | −207.273 | − | 119.669i | −0.278968 | − | 0.161062i | 0.353988 | − | 0.935250i | \(-0.384825\pi\) |
−0.632956 | + | 0.774188i | \(0.718159\pi\) | |||||||
\(744\) | −553.807 | − | 810.729i | −0.744364 | − | 1.08969i | ||||
\(745\) | −123.085 | −0.165215 | ||||||||
\(746\) | 148.757i | 0.199406i | ||||||||
\(747\) | 1095.33 | + | 427.628i | 1.46630 | + | 0.572460i | ||||
\(748\) | 81.2889 | + | 140.797i | 0.108675 | + | 0.188231i | ||||
\(749\) | 235.412 | − | 135.915i | 0.314302 | − | 0.181462i | ||||
\(750\) | −380.336 | − | 182.742i | −0.507115 | − | 0.243656i | ||||
\(751\) | −662.294 | −0.881883 | −0.440941 | − | 0.897536i | \(-0.645355\pi\) | ||||
−0.440941 | + | 0.897536i | \(0.645355\pi\) | |||||||
\(752\) | − | 260.433i | − | 0.346321i | ||||||
\(753\) | 341.097 | − | 709.917i | 0.452984 | − | 0.942785i | ||||
\(754\) | 372.773 | − | 645.661i | 0.494393 | − | 0.856314i | ||||
\(755\) | 323.859 | + | 186.980i | 0.428953 | + | 0.247656i | ||||
\(756\) | −542.500 | − | 165.748i | −0.717592 | − | 0.219243i | ||||
\(757\) | 352.447 | + | 610.455i | 0.465583 | + | 0.806414i | 0.999228 | − | 0.0392950i | \(-0.0125112\pi\) |
−0.533644 | + | 0.845709i | \(0.679178\pi\) | |||||||
\(758\) | 246.691 | − | 142.427i | 0.325450 | − | 0.187898i | ||||
\(759\) | 3.38601 | + | 44.6478i | 0.00446114 | + | 0.0588246i | ||||
\(760\) | 451.157 | − | 781.427i | 0.593627 | − | 1.02819i | ||||
\(761\) | − | 1060.15i | − | 1.39310i | −0.717506 | − | 0.696552i | \(-0.754716\pi\) | ||
0.717506 | − | 0.696552i | \(-0.245284\pi\) | |||||||
\(762\) | 76.1110 | − | 5.77211i | 0.0998832 | − | 0.00757495i | ||||
\(763\) | 281.981 | + | 488.405i | 0.369569 | + | 0.640112i | ||||
\(764\) | − | 90.8087i | − | 0.118860i | ||||||
\(765\) | 74.3062 | − | 190.328i | 0.0971323 | − | 0.248795i | ||||
\(766\) | 28.3973 | + | 49.1856i | 0.0370722 | + | 0.0642110i | ||||
\(767\) | −441.851 | − | 255.103i | −0.576077 | − | 0.332598i | ||||
\(768\) | 495.952 | − | 338.784i | 0.645770 | − | 0.441124i | ||||
\(769\) | 189.494 | + | 328.213i | 0.246416 | + | 0.426805i | 0.962529 | − | 0.271180i | \(-0.0874138\pi\) |
−0.716113 | + | 0.697984i | \(0.754080\pi\) | |||||||
\(770\) | 206.696 | − | 119.336i | 0.268436 | − | 0.154982i | ||||
\(771\) | 180.996 | + | 264.964i | 0.234755 | + | 0.343663i | ||||
\(772\) | −74.8606 | − | 129.662i | −0.0969697 | − | 0.167956i | ||||
\(773\) | 1234.85 | − | 712.939i | 1.59747 | − | 0.922301i | 0.605501 | − | 0.795845i | \(-0.292973\pi\) |
0.991972 | − | 0.126456i | \(-0.0403604\pi\) | |||||||
\(774\) | −545.022 | − | 212.782i | −0.704163 | − | 0.274913i | ||||
\(775\) | −285.550 | − | 494.588i | −0.368452 | − | 0.638178i | ||||
\(776\) | 426.770 | + | 246.396i | 0.549961 | + | 0.317520i | ||||
\(777\) | 9.11876 | + | 120.240i | 0.0117359 | + | 0.154749i | ||||
\(778\) | 140.169 | + | 242.780i | 0.180166 | + | 0.312056i | ||||
\(779\) | 300.555i | 0.385822i | ||||||||
\(780\) | −468.391 | + | 35.5219i | −0.600501 | + | 0.0455409i | ||||
\(781\) | 130.399 | − | 225.857i | 0.166964 | − | 0.289190i | ||||
\(782\) | − | 11.7941i | − | 0.0150820i | ||||||
\(783\) | −826.170 | − | 885.627i | −1.05513 | − | 1.13107i | ||||
\(784\) | −8.68823 | − | 15.0485i | −0.0110819 | − | 0.0191945i | ||||
\(785\) | 417.038 | + | 240.777i | 0.531259 | + | 0.306722i | ||||
\(786\) | 138.642 | + | 66.6140i | 0.176389 | + | 0.0847506i | ||||
\(787\) | −342.283 | + | 592.852i | −0.434922 | + | 0.753307i | −0.997289 | − | 0.0735808i | \(-0.976557\pi\) |
0.562367 | + | 0.826887i | \(0.309891\pi\) | |||||||
\(788\) | −510.583 | − | 294.785i | −0.647948 | − | 0.374093i | ||||
\(789\) | −1172.02 | + | 88.8839i | −1.48545 | + | 0.112654i | ||||
\(790\) | 41.3373 | 0.0523257 | ||||||||
\(791\) | 392.381 | + | 226.542i | 0.496057 | + | 0.286399i | ||||
\(792\) | 359.397 | + | 449.021i | 0.453784 | + | 0.566946i | ||||
\(793\) | −301.584 | − | 522.358i | −0.380307 | − | 0.658711i | ||||
\(794\) | −174.327 | − | 100.648i | −0.219556 | − | 0.126761i | ||||
\(795\) | −82.3715 | − | 1086.15i | −0.103612 | − | 1.36623i | ||||
\(796\) | −162.809 | −0.204535 | ||||||||
\(797\) | −1038.03 | + | 599.306i | −1.30242 | + | 0.751953i | −0.980819 | − | 0.194923i | \(-0.937554\pi\) |
−0.321601 | + | 0.946875i | \(0.604221\pi\) | |||||||
\(798\) | −357.620 | + | 744.307i | −0.448146 | + | 0.932715i | ||||
\(799\) | −458.791 | −0.574207 | ||||||||
\(800\) | 366.375 | − | 211.527i | 0.457969 | − | 0.264409i | ||||
\(801\) | 142.593 | + | 934.708i | 0.178019 | + | 1.16693i | ||||
\(802\) | −289.664 | + | 501.713i | −0.361177 | + | 0.625578i | ||||
\(803\) | 781.972i | 0.973813i | ||||||||
\(804\) | −76.5439 | − | 571.063i | −0.0952039 | − | 0.710277i | ||||
\(805\) | 43.7869 | 0.0543937 | ||||||||
\(806\) | 644.375 | + | 372.030i | 0.799473 | + | 0.461576i | ||||
\(807\) | 682.094 | − | 51.7287i | 0.845222 | − | 0.0641000i | ||||
\(808\) | −339.289 | − | 587.666i | −0.419912 | − | 0.727309i | ||||
\(809\) | − | 39.0854i | − | 0.0483132i | −0.999708 | − | 0.0241566i | \(-0.992310\pi\) | ||
0.999708 | − | 0.0241566i | \(-0.00769003\pi\) | |||||||
\(810\) | 66.0928 | − | 294.417i | 0.0815960 | − | 0.363478i | ||||
\(811\) | −30.7515 | − | 53.2631i | −0.0379180 | − | 0.0656759i | 0.846444 | − | 0.532478i | \(-0.178739\pi\) |
−0.884362 | + | 0.466802i | \(0.845406\pi\) | |||||||
\(812\) | − | 942.432i | − | 1.16063i | ||||||
\(813\) | 27.1131 | + | 357.513i | 0.0333495 | + | 0.439746i | ||||
\(814\) | 25.5198 | − | 44.2016i | 0.0313511 | − | 0.0543017i | ||||
\(815\) | −773.712 | + | 446.703i | −0.949340 | + | 0.548102i | ||||
\(816\) | 40.4358 | + | 59.1947i | 0.0495536 | + | 0.0725425i | ||||
\(817\) | 1076.98 | − | 1865.38i | 1.31821 | − | 2.28321i | ||||
\(818\) | − | 846.494i | − | 1.03483i | ||||||
\(819\) | 1017.98 | − | 155.296i | 1.24295 | − | 0.189617i | ||||
\(820\) | 42.7296 | − | 74.0098i | 0.0521093 | − | 0.0902559i | ||||
\(821\) | 1303.07 | + | 752.328i | 1.58717 | + | 0.916356i | 0.993770 | + | 0.111452i | \(0.0355501\pi\) |
0.593405 | + | 0.804904i | \(0.297783\pi\) | |||||||
\(822\) | −738.775 | − | 354.963i | −0.898753 | − | 0.431828i | ||||
\(823\) | −543.813 | + | 941.911i | −0.660769 | + | 1.14449i | 0.319645 | + | 0.947537i | \(0.396436\pi\) |
−0.980414 | + | 0.196948i | \(0.936897\pi\) | |||||||
\(824\) | −262.906 | + | 151.789i | −0.319060 | + | 0.184209i | ||||
\(825\) | 188.702 | + | 276.244i | 0.228729 | + | 0.334841i | ||||
\(826\) | 255.024 | 0.308746 | ||||||||
\(827\) | −1141.79 | − | 659.212i | −1.38064 | − | 0.797113i | −0.388405 | − | 0.921489i | \(-0.626974\pi\) |
−0.992235 | + | 0.124376i | \(0.960307\pi\) | |||||||
\(828\) | 6.64295 | + | 43.5450i | 0.00802289 | + | 0.0525906i | ||||
\(829\) | 241.393 | 0.291186 | 0.145593 | − | 0.989345i | \(-0.453491\pi\) | ||||
0.145593 | + | 0.989345i | \(0.453491\pi\) | |||||||
\(830\) | −421.494 | + | 243.350i | −0.507825 | + | 0.293193i | ||||
\(831\) | −75.7502 | − | 998.841i | −0.0911555 | − | 1.20197i | ||||
\(832\) | −160.598 | + | 278.164i | −0.193026 | + | 0.334331i | ||||
\(833\) | −26.5100 | + | 15.3056i | −0.0318248 | + | 0.0183741i | ||||
\(834\) | −169.915 | + | 353.640i | −0.203735 | + | 0.424029i | ||||
\(835\) | 1.34191 | + | 2.32426i | 0.00160708 | + | 0.00278354i | ||||
\(836\) | −765.490 | + | 441.956i | −0.915658 | + | 0.528655i | ||||
\(837\) | 883.864 | − | 824.525i | 1.05599 | − | 0.985095i | ||||
\(838\) | −51.9141 | − | 89.9178i | −0.0619500 | − | 0.107301i | ||||
\(839\) | 701.075 | − | 404.766i | 0.835607 | − | 0.482438i | −0.0201613 | − | 0.999797i | \(-0.506418\pi\) |
0.855769 | + | 0.517359i | \(0.173085\pi\) | |||||||
\(840\) | 464.422 | − | 317.246i | 0.552883 | − | 0.377673i | ||||
\(841\) | 585.599 | − | 1014.29i | 0.696312 | − | 1.20605i | ||||
\(842\) | 274.904 | − | 158.716i | 0.326490 | − | 0.188499i | ||||
\(843\) | 275.736 | − | 573.882i | 0.327089 | − | 0.680762i | ||||
\(844\) | −212.221 | −0.251447 | ||||||||
\(845\) | 226.371 | − | 130.695i | 0.267895 | − | 0.154669i | ||||
\(846\) | −669.807 | + | 102.181i | −0.791734 | + | 0.120782i | ||||
\(847\) | 326.780 | 0.385809 | ||||||||
\(848\) | 330.977 | + | 191.090i | 0.390304 | + | 0.225342i | ||||
\(849\) | 26.4094 | + | 348.234i | 0.0311064 | + | 0.410169i | ||||
\(850\) | −44.0595 | − | 76.3134i | −0.0518348 | − | 0.0897804i | ||||
\(851\) | 8.10925 | − | 4.68187i | 0.00952908 | − | 0.00550162i | ||||
\(852\) | 111.112 | − | 231.254i | 0.130413 | − | 0.271425i | ||||
\(853\) | −275.856 | + | 477.797i | −0.323395 | + | 0.560137i | −0.981186 | − | 0.193063i | \(-0.938158\pi\) |
0.657791 | + | 0.753201i | \(0.271491\pi\) | |||||||
\(854\) | 261.099 | + | 150.745i | 0.305736 | + | 0.176517i | ||||
\(855\) | 1034.79 | + | 403.992i | 1.21028 | + | 0.472505i | ||||
\(856\) | −271.133 | −0.316744 | ||||||||
\(857\) | 313.636i | 0.365969i | 0.983116 | + | 0.182985i | \(0.0585758\pi\) | ||||
−0.983116 | + | 0.182985i | \(0.941424\pi\) | |||||||
\(858\) | −392.865 | − | 188.762i | −0.457885 | − | 0.220002i | ||||
\(859\) | −332.548 | − | 575.990i | −0.387134 | − | 0.670535i | 0.604929 | − | 0.796279i | \(-0.293201\pi\) |
−0.992063 | + | 0.125744i | \(0.959868\pi\) | |||||||
\(860\) | −530.398 | + | 306.225i | −0.616741 | + | 0.356076i | ||||
\(861\) | −81.1345 | + | 168.863i | −0.0942329 | + | 0.196125i | ||||
\(862\) | 615.545 | 0.714089 | ||||||||
\(863\) | − | 1175.87i | − | 1.36254i | −0.732033 | − | 0.681269i | \(-0.761428\pi\) | ||
0.732033 | − | 0.681269i | \(-0.238572\pi\) | |||||||
\(864\) | 610.782 | + | 654.739i | 0.706924 | + | 0.757799i | ||||
\(865\) | −35.8325 | + | 62.0637i | −0.0414249 | + | 0.0717500i | ||||
\(866\) | 829.807i | 0.958207i | ||||||||
\(867\) | −611.632 | + | 417.805i | −0.705458 | + | 0.481897i | ||||
\(868\) | 940.555 | 1.08359 | ||||||||
\(869\) | −84.0052 | − | 48.5004i | −0.0966688 | − | 0.0558117i | ||||
\(870\) | 499.880 | − | 37.9099i | 0.574574 | − | 0.0435746i | ||||
\(871\) | 574.204 | + | 874.229i | 0.659247 | + | 1.00371i | ||||
\(872\) | − | 562.515i | − | 0.645086i | ||||||
\(873\) | −220.637 | + | 565.140i | −0.252734 | + | 0.647354i | ||||
\(874\) | 64.1227 | 0.0733669 | ||||||||
\(875\) | 838.558 | − | 484.142i | 0.958352 | − | 0.553305i | ||||
\(876\) | 58.1730 | + | 767.069i | 0.0664076 | + | 0.875649i | ||||
\(877\) | −711.872 | + | 1233.00i | −0.811713 | + | 1.40593i | 0.0999510 | + | 0.994992i | \(0.468131\pi\) |
−0.911664 | + | 0.410936i | \(0.865202\pi\) | |||||||
\(878\) | 102.136 | − | 58.9681i | 0.116328 | − | 0.0671618i | ||||
\(879\) | 75.4846 | − | 5.72460i | 0.0858755 | − | 0.00651263i | ||||
\(880\) | 112.651 | 0.128012 | ||||||||
\(881\) | −535.757 | − | 309.320i | −0.608124 | − | 0.351101i | 0.164107 | − | 0.986443i | \(-0.447526\pi\) |
−0.772231 | + | 0.635342i | \(0.780859\pi\) | |||||||
\(882\) | −35.2942 | + | 28.2495i | −0.0400161 | + | 0.0320289i | ||||
\(883\) | 342.094 | + | 592.525i | 0.387423 | + | 0.671036i | 0.992102 | − | 0.125433i | \(-0.0400320\pi\) |
−0.604679 | + | 0.796469i | \(0.706699\pi\) | |||||||
\(884\) | −251.441 | − | 145.170i | −0.284436 | − | 0.164219i | ||||
\(885\) | −25.9433 | − | 342.087i | −0.0293144 | − | 0.386539i | ||||
\(886\) | −354.027 | −0.399579 | ||||||||
\(887\) | 203.804 | + | 117.666i | 0.229767 | + | 0.132656i | 0.610465 | − | 0.792043i | \(-0.290983\pi\) |
−0.380697 | + | 0.924700i | \(0.624316\pi\) | |||||||
\(888\) | 52.0888 | − | 108.411i | 0.0586586 | − | 0.122085i | ||||
\(889\) | −87.5778 | + | 151.689i | −0.0985127 | + | 0.170629i | ||||
\(890\) | −338.933 | − | 195.683i | −0.380824 | − | 0.219869i | ||||
\(891\) | −479.748 | + | 520.765i | −0.538437 | + | 0.584473i | ||||
\(892\) | −445.508 | − | 771.643i | −0.499448 | − | 0.865070i | ||||
\(893\) | − | 2494.38i | − | 2.79326i | ||||||
\(894\) | −101.271 | − | 48.6580i | −0.113278 | − | 0.0544273i | ||||
\(895\) | 663.663 | 0.741523 | ||||||||
\(896\) | 811.689i | 0.905903i | ||||||||
\(897\) | −45.1038 | − | 66.0284i | −0.0502830 | − | 0.0736102i | ||||
\(898\) | 703.636 | 0.783559 | ||||||||
\(899\) | 1739.14 | + | 1004.10i | 1.93453 | + | 1.11690i | ||||
\(900\) | 205.656 | + | 256.941i | 0.228506 | + | 0.285490i | ||||
\(901\) | 336.633 | − | 583.065i | 0.373621 | − | 0.647131i | ||||
\(902\) | 68.6725 | − | 39.6481i | 0.0761336 | − | 0.0439557i | ||||
\(903\) | 1108.64 | − | 757.311i | 1.22773 | − | 0.838662i | ||||
\(904\) | −225.960 | − | 391.374i | −0.249956 | − | 0.432936i | ||||
\(905\) | 613.284 | − | 354.080i | 0.677662 | − | 0.391248i | ||||
\(906\) | 192.545 | + | 281.870i | 0.212522 | + | 0.311114i | ||||
\(907\) | −485.244 | − | 840.467i | −0.534999 | − | 0.926645i | −0.999163 | − | 0.0408958i | \(-0.986979\pi\) |
0.464165 | − | 0.885749i | \(-0.346355\pi\) | |||||||
\(908\) | 739.211 | + | 426.784i | 0.814109 | + | 0.470026i | ||||
\(909\) | 652.216 | − | 522.034i | 0.717510 | − | 0.574295i | ||||
\(910\) | −213.116 | + | 369.127i | −0.234193 | + | 0.405634i | ||||
\(911\) | − | 1570.90i | − | 1.72436i | −0.506598 | − | 0.862182i | \(-0.669097\pi\) | ||
0.506598 | − | 0.862182i | \(-0.330903\pi\) | |||||||
\(912\) | −321.832 | + | 219.843i | −0.352886 | + | 0.241056i | ||||
\(913\) | 1142.07 | 1.25090 | ||||||||
\(914\) | − | 832.315i | − | 0.910629i | ||||||
\(915\) | 175.647 | − | 365.570i | 0.191964 | − | 0.399530i | ||||
\(916\) | 73.7199 | 0.0804802 | ||||||||
\(917\) | −305.675 | + | 176.482i | −0.333343 | + | 0.192456i | ||||
\(918\) | 136.377 | − | 127.222i | 0.148559 | − | 0.138586i | ||||
\(919\) | −231.732 | + | 401.372i | −0.252157 | + | 0.436748i | −0.964119 | − | 0.265469i | \(-0.914473\pi\) |
0.711963 | + | 0.702217i | \(0.247807\pi\) | |||||||
\(920\) | −37.8232 | − | 21.8373i | −0.0411122 | − | 0.0237361i | ||||
\(921\) | 82.4225 | + | 39.6019i | 0.0894924 | + | 0.0429988i | ||||
\(922\) | 261.129 | − | 452.288i | 0.283220 | − | 0.490551i | ||||
\(923\) | 465.745i | 0.504599i | ||||||||
\(924\) | −549.386 | + | 41.6644i | −0.594574 | + | 0.0450914i | ||||
\(925\) | 34.9805 | − | 60.5879i | 0.0378167 | − | 0.0655005i | ||||
\(926\) | −485.160 | + | 280.107i | −0.523931 | + | 0.302492i | ||||
\(927\) | −233.544 | − | 291.784i | −0.251935 | − | 0.314761i | ||||
\(928\) | −743.803 | + | 1288.30i | −0.801511 | + | 1.38826i | ||||
\(929\) | 802.955i | 0.864322i | 0.901796 | + | 0.432161i | \(0.142249\pi\) | ||||
−0.901796 | + | 0.432161i | \(0.857751\pi\) | |||||||
\(930\) | 37.8344 | + | 498.884i | 0.0406822 | + | 0.536435i | ||||
\(931\) | −83.2142 | − | 144.131i | −0.0893815 | − | 0.154813i | ||||
\(932\) | 0.786630 | + | 0.454161i | 0.000844023 | + | 0.000487297i | ||||
\(933\) | 294.897 | − | 22.3644i | 0.316074 | − | 0.0239704i | ||||
\(934\) | 102.981 | + | 178.369i | 0.110258 | + | 0.190973i | ||||
\(935\) | − | 198.451i | − | 0.212247i | ||||||
\(936\) | −956.780 | − | 373.537i | −1.02220 | − | 0.399078i | ||||
\(937\) | −731.336 | −0.780508 | −0.390254 | − | 0.920707i | \(-0.627613\pi\) | ||||
−0.390254 | + | 0.920707i | \(0.627613\pi\) | |||||||
\(938\) | −467.051 | − | 234.929i | −0.497922 | − | 0.250457i | ||||
\(939\) | 16.0313 | + | 211.388i | 0.0170727 | + | 0.225121i | ||||
\(940\) | −354.623 | + | 614.225i | −0.377258 | + | 0.653431i | ||||
\(941\) | 1606.75i | 1.70749i | 0.520688 | + | 0.853747i | \(0.325676\pi\) | ||||
−0.520688 | + | 0.853747i | \(0.674324\pi\) | |||||||
\(942\) | 247.942 | + | 362.968i | 0.263209 | + | 0.385316i | ||||
\(943\) | 14.5477 | 0.0154271 | ||||||||
\(944\) | 104.243 | + | 60.1846i | 0.110427 | + | 0.0637549i | ||||
\(945\) | 472.325 | + | 506.317i | 0.499815 | + | 0.535785i | ||||
\(946\) | −568.282 | −0.600721 | ||||||||
\(947\) | − | 1389.67i | − | 1.46745i | −0.679449 | − | 0.733723i | \(-0.737781\pi\) | ||
0.679449 | − | 0.733723i | \(-0.262219\pi\) | |||||||
\(948\) | −86.0123 | − | 41.3267i | −0.0907302 | − | 0.0435936i | ||||
\(949\) | −698.240 | − | 1209.39i | −0.735764 | − | 1.27438i | ||||
\(950\) | 414.904 | − | 239.545i | 0.436741 | − | 0.252153i | ||||
\(951\) | −526.587 | + | 1095.97i | −0.553719 | + | 1.15244i | ||||
\(952\) | 347.635 | 0.365163 | ||||||||
\(953\) | − | 210.833i | − | 0.221231i | −0.993863 | − | 0.110616i | \(-0.964718\pi\) | ||
0.993863 | − | 0.110616i | \(-0.0352822\pi\) | |||||||
\(954\) | 361.604 | − | 926.214i | 0.379039 | − | 0.970874i | ||||
\(955\) | −55.4230 | + | 95.9954i | −0.0580345 | + | 0.100519i | ||||
\(956\) | −977.826 | − | 564.548i | −1.02283 | − | 0.590531i | ||||
\(957\) | −1060.33 | − | 509.461i | −1.10797 | − | 0.532352i | ||||
\(958\) | −462.098 | − | 800.378i | −0.482357 | − | 0.835467i | ||||
\(959\) | 1628.84 | − | 940.410i | 1.69848 | − | 0.980615i | ||||
\(960\) | −215.358 | + | 16.3323i | −0.224331 | + | 0.0170129i | ||||
\(961\) | −521.596 | + | 903.431i | −0.542764 | + | 0.940094i | ||||
\(962\) | 91.1488i | 0.0947493i | ||||||||
\(963\) | −50.3393 | − | 329.978i | −0.0522735 | − | 0.342656i | ||||
\(964\) | 503.665 | + | 872.373i | 0.522474 | + | 0.904951i | ||||
\(965\) | 182.758i | 0.189386i | ||||||||
\(966\) | 36.0265 | + | 17.3098i | 0.0372945 | + | 0.0179191i | ||||
\(967\) | −411.360 | − | 712.496i | −0.425398 | − | 0.736811i | 0.571060 | − | 0.820909i | \(-0.306532\pi\) |
−0.996457 | + | 0.0840980i | \(0.973199\pi\) | |||||||
\(968\) | −282.274 | − | 162.971i | −0.291605 | − | 0.168358i | ||||
\(969\) | 387.286 | + | 566.955i | 0.399676 | + | 0.585093i | ||||
\(970\) | −125.558 | − | 217.472i | −0.129441 | − | 0.224198i | ||||
\(971\) | −1473.64 | + | 850.805i | −1.51765 | + | 0.876215i | −0.517864 | + | 0.855463i | \(0.673273\pi\) |
−0.999785 | + | 0.0207517i | \(0.993394\pi\) | |||||||
\(972\) | −431.863 | + | 546.530i | −0.444304 | + | 0.562274i | ||||
\(973\) | −450.160 | − | 779.700i | −0.462651 | − | 0.801336i | ||||
\(974\) | 122.131 | − | 70.5124i | 0.125391 | − | 0.0723947i | ||||
\(975\) | −538.508 | − | 258.739i | −0.552316 | − | 0.265374i | ||||
\(976\) | 71.1504 | + | 123.236i | 0.0729000 | + | 0.126267i | ||||
\(977\) | −786.461 | − | 454.064i | −0.804976 | − | 0.464753i | 0.0402322 | − | 0.999190i | \(-0.487190\pi\) |
−0.845208 | + | 0.534437i | \(0.820524\pi\) | |||||||
\(978\) | −813.177 | + | 61.6698i | −0.831470 | + | 0.0630571i | ||||
\(979\) | 459.184 | + | 795.329i | 0.469033 | + | 0.812389i | ||||
\(980\) | 47.3219i | 0.0482876i | ||||||||
\(981\) | 684.600 | − | 104.438i | 0.697859 | − | 0.106461i | ||||
\(982\) | −319.481 | + | 553.358i | −0.325337 | + | 0.563501i | ||||
\(983\) | 1440.01i | 1.46491i | 0.680814 | + | 0.732456i | \(0.261626\pi\) | ||||
−0.680814 | + | 0.732456i | \(0.738374\pi\) | |||||||
\(984\) | 154.299 | − | 105.401i | 0.156808 | − | 0.107115i | ||||
\(985\) | 359.830 | + | 623.244i | 0.365310 | + | 0.632735i | ||||
\(986\) | 268.345 | + | 154.929i | 0.272155 | + | 0.157129i | ||||
\(987\) | 673.354 | − | 1401.44i | 0.682223 | − | 1.41989i | ||||
\(988\) | 789.265 | − | 1367.05i | 0.798851 | − | 1.38365i | ||||
\(989\) | −90.2895 | − | 52.1287i | −0.0912938 | − | 0.0527085i | ||||
\(990\) | −44.1988 | − | 289.727i | −0.0446453 | − | 0.292653i | ||||
\(991\) | −709.114 | −0.715554 | −0.357777 | − | 0.933807i | \(-0.616465\pi\) | ||||
−0.357777 | + | 0.933807i | \(0.616465\pi\) | |||||||
\(992\) | −1285.74 | − | 742.322i | −1.29611 | − | 0.748308i | ||||
\(993\) | −415.530 | + | 283.847i | −0.418459 | + | 0.285848i | ||||
\(994\) | −116.400 | − | 201.611i | −0.117103 | − | 0.202828i | ||||
\(995\) | 172.109 | + | 99.3669i | 0.172973 | + | 0.0998663i | ||||
\(996\) | 1120.31 | − | 84.9621i | 1.12481 | − | 0.0853033i | ||||
\(997\) | 759.121 | 0.761405 | 0.380702 | − | 0.924698i | \(-0.375682\pi\) | ||||
0.380702 | + | 0.924698i | \(0.375682\pi\) | |||||||
\(998\) | −578.700 | + | 334.113i | −0.579860 | + | 0.334782i | ||||
\(999\) | 141.611 | + | 43.2659i | 0.141753 | + | 0.0433093i |
(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 | 201.3.g.b.29.17 | ✓ | 84 | |
3.2 | odd | 2 | inner | 201.3.g.b.29.26 | yes | 84 | |
67.37 | even | 3 | inner | 201.3.g.b.104.26 | yes | 84 | |
201.104 | odd | 6 | inner | 201.3.g.b.104.17 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.3.g.b.29.17 | ✓ | 84 | 1.1 | even | 1 | trivial | |
201.3.g.b.29.26 | yes | 84 | 3.2 | odd | 2 | inner | |
201.3.g.b.104.17 | yes | 84 | 201.104 | odd | 6 | inner | |
201.3.g.b.104.26 | yes | 84 | 67.37 | even | 3 | inner |