Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(14,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.14");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.h (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: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 14.1 | ||
Root | \(1.44078 + 0.961330i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.14 |
Dual form | 45.3.h.a.29.1 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84364 | − | 3.19328i | −0.921819 | − | 1.59664i | −0.796599 | − | 0.604509i | \(-0.793369\pi\) |
−0.125221 | − | 0.992129i | \(-0.539964\pi\) | |||||||
\(3\) | −1.66507 | + | 2.49550i | −0.555024 | + | 0.831834i | ||||
\(4\) | −4.79800 | + | 8.31039i | −1.19950 | + | 2.07760i | ||||
\(5\) | −4.90060 | − | 0.992036i | −0.980120 | − | 0.198407i | ||||
\(6\) | 11.0386 | + | 0.716233i | 1.83977 | + | 0.119372i | ||||
\(7\) | −2.22343 | + | 1.28370i | −0.317633 | + | 0.183385i | −0.650337 | − | 0.759646i | \(-0.725372\pi\) |
0.332704 | + | 0.943031i | \(0.392039\pi\) | |||||||
\(8\) | 20.6340 | 2.57925 | ||||||||
\(9\) | −3.45506 | − | 8.31039i | −0.383896 | − | 0.923376i | ||||
\(10\) | 5.86709 | + | 17.4779i | 0.586709 | + | 1.74779i | ||||
\(11\) | −8.51311 | + | 4.91505i | −0.773919 | + | 0.446823i | −0.834271 | − | 0.551355i | \(-0.814111\pi\) |
0.0603516 | + | 0.998177i | \(0.480778\pi\) | |||||||
\(12\) | −12.7496 | − | 25.8108i | −1.06246 | − | 2.15090i | ||||
\(13\) | −10.4471 | − | 6.03166i | −0.803626 | − | 0.463974i | 0.0411114 | − | 0.999155i | \(-0.486910\pi\) |
−0.844738 | + | 0.535181i | \(0.820243\pi\) | |||||||
\(14\) | 8.19840 | + | 4.73335i | 0.585600 | + | 0.338096i | ||||
\(15\) | 10.6355 | − | 10.5776i | 0.709032 | − | 0.705176i | ||||
\(16\) | −18.8497 | − | 32.6486i | −1.17810 | − | 2.04054i | ||||
\(17\) | −4.28451 | −0.252030 | −0.126015 | − | 0.992028i | \(-0.540219\pi\) | ||||
−0.126015 | + | 0.992028i | \(0.540219\pi\) | |||||||
\(18\) | −20.1675 | + | 26.3543i | −1.12041 | + | 1.46413i | ||||
\(19\) | 7.16698 | 0.377210 | 0.188605 | − | 0.982053i | \(-0.439603\pi\) | ||||
0.188605 | + | 0.982053i | \(0.439603\pi\) | |||||||
\(20\) | 31.7573 | − | 35.9661i | 1.58786 | − | 1.79830i | ||||
\(21\) | 0.498702 | − | 7.68602i | 0.0237477 | − | 0.366001i | ||||
\(22\) | 31.3902 | + | 18.1231i | 1.42683 | + | 0.823779i | ||||
\(23\) | 0.255270 | − | 0.442140i | 0.0110987 | − | 0.0192235i | −0.860423 | − | 0.509581i | \(-0.829800\pi\) |
0.871521 | + | 0.490357i | \(0.163134\pi\) | |||||||
\(24\) | −34.3572 | + | 51.4923i | −1.43155 | + | 2.14551i | ||||
\(25\) | 23.0317 | + | 9.72314i | 0.921269 | + | 0.388926i | ||||
\(26\) | 44.4808i | 1.71080i | ||||||||
\(27\) | 26.4915 | + | 5.21528i | 0.981168 | + | 0.193159i | ||||
\(28\) | − | 24.6367i | − | 0.879884i | ||||||
\(29\) | −26.4589 | + | 15.2761i | −0.912376 | + | 0.526760i | −0.881195 | − | 0.472753i | \(-0.843260\pi\) |
−0.0311810 | + | 0.999514i | \(0.509927\pi\) | |||||||
\(30\) | −53.3853 | − | 14.4607i | −1.77951 | − | 0.482023i | ||||
\(31\) | 9.61361 | − | 16.6513i | 0.310116 | − | 0.537137i | −0.668271 | − | 0.743918i | \(-0.732965\pi\) |
0.978387 | + | 0.206781i | \(0.0662986\pi\) | |||||||
\(32\) | −28.2359 | + | 48.9060i | −0.882372 | + | 1.52831i | ||||
\(33\) | 1.90944 | − | 29.4284i | 0.0578618 | − | 0.891770i | ||||
\(34\) | 7.89910 | + | 13.6816i | 0.232326 | + | 0.402401i | ||||
\(35\) | 12.1696 | − | 4.08516i | 0.347703 | − | 0.116719i | ||||
\(36\) | 85.6399 | + | 11.1604i | 2.37889 | + | 0.310010i | ||||
\(37\) | 1.31851i | 0.0356355i | 0.999841 | + | 0.0178177i | \(0.00567186\pi\) | ||||
−0.999841 | + | 0.0178177i | \(0.994328\pi\) | |||||||
\(38\) | −13.2133 | − | 22.8862i | −0.347719 | − | 0.602267i | ||||
\(39\) | 32.4473 | − | 16.0277i | 0.831981 | − | 0.410967i | ||||
\(40\) | −101.119 | − | 20.4697i | −2.52798 | − | 0.511743i | ||||
\(41\) | −29.9735 | − | 17.3052i | −0.731061 | − | 0.422078i | 0.0877493 | − | 0.996143i | \(-0.472033\pi\) |
−0.818810 | + | 0.574064i | \(0.805366\pi\) | |||||||
\(42\) | −25.4630 | + | 12.5778i | −0.606262 | + | 0.299470i | ||||
\(43\) | −44.9872 | + | 25.9734i | −1.04621 | + | 0.604032i | −0.921587 | − | 0.388172i | \(-0.873107\pi\) |
−0.124627 | + | 0.992204i | \(0.539773\pi\) | |||||||
\(44\) | − | 94.3297i | − | 2.14386i | ||||||
\(45\) | 8.68767 | + | 44.1534i | 0.193059 | + | 0.981187i | ||||
\(46\) | −1.88250 | −0.0409239 | ||||||||
\(47\) | 25.4656 | + | 44.1078i | 0.541822 | + | 0.938463i | 0.998800 | + | 0.0489851i | \(0.0155987\pi\) |
−0.456977 | + | 0.889478i | \(0.651068\pi\) | |||||||
\(48\) | 112.861 | + | 7.32289i | 2.35126 | + | 0.152560i | ||||
\(49\) | −21.2042 | + | 36.7268i | −0.432740 | + | 0.749527i | ||||
\(50\) | −11.4135 | − | 91.4726i | −0.228270 | − | 1.82945i | ||||
\(51\) | 7.13403 | − | 10.6920i | 0.139883 | − | 0.209647i | ||||
\(52\) | 100.251 | − | 57.8799i | 1.92790 | − | 1.11307i | ||||
\(53\) | −86.6349 | −1.63462 | −0.817311 | − | 0.576197i | \(-0.804536\pi\) | ||||
−0.817311 | + | 0.576197i | \(0.804536\pi\) | |||||||
\(54\) | −32.1870 | − | 94.2098i | −0.596055 | − | 1.74463i | ||||
\(55\) | 46.5953 | − | 15.6414i | 0.847186 | − | 0.284388i | ||||
\(56\) | −45.8783 | + | 26.4879i | −0.819255 | + | 0.472997i | ||||
\(57\) | −11.9336 | + | 17.8852i | −0.209361 | + | 0.313776i | ||||
\(58\) | 97.5613 | + | 56.3270i | 1.68209 | + | 0.971156i | ||||
\(59\) | 91.7656 | + | 52.9809i | 1.55535 | + | 0.897982i | 0.997691 | + | 0.0679111i | \(0.0216334\pi\) |
0.557658 | + | 0.830071i | \(0.311700\pi\) | |||||||
\(60\) | 36.8752 | + | 139.137i | 0.614587 | + | 2.31894i | ||||
\(61\) | −15.6600 | − | 27.1239i | −0.256721 | − | 0.444655i | 0.708640 | − | 0.705570i | \(-0.249309\pi\) |
−0.965362 | + | 0.260915i | \(0.915976\pi\) | |||||||
\(62\) | −70.8961 | −1.14348 | ||||||||
\(63\) | 18.3501 | + | 14.0423i | 0.291272 | + | 0.222894i | ||||
\(64\) | 57.4297 | 0.897339 | ||||||||
\(65\) | 45.2136 | + | 39.9227i | 0.695594 | + | 0.614195i | ||||
\(66\) | −97.4933 | + | 48.1580i | −1.47717 | + | 0.729666i | ||||
\(67\) | −67.5968 | − | 39.0271i | −1.00891 | − | 0.582493i | −0.0980363 | − | 0.995183i | \(-0.531256\pi\) |
−0.910872 | + | 0.412689i | \(0.864589\pi\) | |||||||
\(68\) | 20.5571 | − | 35.6060i | 0.302311 | − | 0.523617i | ||||
\(69\) | 0.678318 | + | 1.37322i | 0.00983070 | + | 0.0199017i | ||||
\(70\) | −35.4814 | − | 31.3293i | −0.506877 | − | 0.447562i | ||||
\(71\) | − | 72.6762i | − | 1.02361i | −0.859102 | − | 0.511804i | \(-0.828977\pi\) | ||
0.859102 | − | 0.511804i | \(-0.171023\pi\) | |||||||
\(72\) | −71.2919 | − | 171.477i | −0.990165 | − | 2.38162i | ||||
\(73\) | − | 30.3097i | − | 0.415201i | −0.978214 | − | 0.207601i | \(-0.933435\pi\) | ||
0.978214 | − | 0.207601i | \(-0.0665654\pi\) | |||||||
\(74\) | 4.21037 | − | 2.43086i | 0.0568969 | − | 0.0328494i | ||||
\(75\) | −62.6136 | + | 41.2860i | −0.834848 | + | 0.550480i | ||||
\(76\) | −34.3872 | + | 59.5604i | −0.452463 | + | 0.783690i | ||||
\(77\) | 12.6189 | − | 21.8565i | 0.163881 | − | 0.283851i | ||||
\(78\) | −111.002 | − | 74.0638i | −1.42310 | − | 0.949535i | ||||
\(79\) | −57.6398 | − | 99.8350i | −0.729617 | − | 1.26373i | −0.957045 | − | 0.289940i | \(-0.906365\pi\) |
0.227428 | − | 0.973795i | \(-0.426969\pi\) | |||||||
\(80\) | 59.9861 | + | 178.697i | 0.749826 | + | 2.23371i | ||||
\(81\) | −57.1251 | + | 57.4258i | −0.705248 | + | 0.708961i | ||||
\(82\) | 127.618i | 1.55632i | ||||||||
\(83\) | 30.0069 | + | 51.9734i | 0.361529 | + | 0.626186i | 0.988213 | − | 0.153087i | \(-0.0489216\pi\) |
−0.626684 | + | 0.779274i | \(0.715588\pi\) | |||||||
\(84\) | 61.4810 | + | 41.0220i | 0.731917 | + | 0.488357i | ||||
\(85\) | 20.9967 | + | 4.25039i | 0.247020 | + | 0.0500046i | ||||
\(86\) | 165.880 | + | 95.7710i | 1.92884 | + | 1.11362i | ||||
\(87\) | 5.93457 | − | 91.4640i | 0.0682135 | − | 1.05131i | ||||
\(88\) | −175.660 | + | 101.417i | −1.99613 | + | 1.15247i | ||||
\(89\) | 71.2992i | 0.801115i | 0.916272 | + | 0.400558i | \(0.131184\pi\) | ||||
−0.916272 | + | 0.400558i | \(0.868816\pi\) | |||||||
\(90\) | 124.977 | − | 109.145i | 1.38863 | − | 1.21272i | ||||
\(91\) | 30.9713 | 0.340344 | ||||||||
\(92\) | 2.44957 | + | 4.24278i | 0.0266257 | + | 0.0461171i | ||||
\(93\) | 25.5459 | + | 51.7163i | 0.274687 | + | 0.556090i | ||||
\(94\) | 93.8989 | − | 162.638i | 0.998924 | − | 1.73019i | ||||
\(95\) | −35.1225 | − | 7.10991i | −0.369711 | − | 0.0748412i | ||||
\(96\) | −75.0302 | − | 151.895i | −0.781565 | − | 1.58224i | ||||
\(97\) | 110.820 | − | 63.9819i | 1.14247 | − | 0.659607i | 0.195431 | − | 0.980717i | \(-0.437389\pi\) |
0.947042 | + | 0.321111i | \(0.104056\pi\) | |||||||
\(98\) | 156.372 | 1.59563 | ||||||||
\(99\) | 70.2593 | + | 53.7655i | 0.709690 | + | 0.543085i | ||||
\(100\) | −191.309 | + | 144.751i | −1.91309 | + | 1.44751i | ||||
\(101\) | 74.5445 | − | 43.0383i | 0.738065 | − | 0.426122i | −0.0833005 | − | 0.996524i | \(-0.526546\pi\) |
0.821365 | + | 0.570403i | \(0.193213\pi\) | |||||||
\(102\) | −47.2951 | − | 3.06871i | −0.463678 | − | 0.0300854i | ||||
\(103\) | 35.4060 | + | 20.4416i | 0.343747 | + | 0.198463i | 0.661928 | − | 0.749568i | \(-0.269739\pi\) |
−0.318181 | + | 0.948030i | \(0.603072\pi\) | |||||||
\(104\) | −215.567 | − | 124.457i | −2.07276 | − | 1.19671i | ||||
\(105\) | −10.0688 | + | 37.1714i | −0.0958929 | + | 0.354013i | ||||
\(106\) | 159.723 | + | 276.649i | 1.50683 | + | 2.60990i | ||||
\(107\) | −1.66026 | −0.0155165 | −0.00775823 | − | 0.999970i | \(-0.502470\pi\) | ||||
−0.00775823 | + | 0.999970i | \(0.502470\pi\) | |||||||
\(108\) | −170.447 | + | 195.132i | −1.57822 | + | 1.80678i | ||||
\(109\) | −148.641 | −1.36368 | −0.681839 | − | 0.731502i | \(-0.738820\pi\) | ||||
−0.681839 | + | 0.731502i | \(0.738820\pi\) | |||||||
\(110\) | −135.852 | − | 119.954i | −1.23502 | − | 1.09050i | ||||
\(111\) | −3.29035 | − | 2.19542i | −0.0296428 | − | 0.0197785i | ||||
\(112\) | 83.8218 | + | 48.3946i | 0.748409 | + | 0.432094i | ||||
\(113\) | 65.7284 | − | 113.845i | 0.581667 | − | 1.00748i | −0.413615 | − | 0.910452i | \(-0.635734\pi\) |
0.995282 | − | 0.0970249i | \(-0.0309326\pi\) | |||||||
\(114\) | 79.1136 | + | 5.13323i | 0.693979 | + | 0.0450283i | ||||
\(115\) | −1.68959 | + | 1.91351i | −0.0146921 | + | 0.0166392i | ||||
\(116\) | − | 293.178i | − | 2.52740i | ||||||
\(117\) | −14.0299 | + | 107.660i | −0.119914 | + | 0.920167i | ||||
\(118\) | − | 390.711i | − | 3.31111i | ||||||
\(119\) | 9.52631 | − | 5.50002i | 0.0800531 | − | 0.0462187i | ||||
\(120\) | 219.453 | − | 218.259i | 1.82877 | − | 1.81883i | ||||
\(121\) | −12.1846 | + | 21.1044i | −0.100699 | + | 0.174416i | ||||
\(122\) | −57.7428 | + | 100.013i | −0.473301 | + | 0.819782i | ||||
\(123\) | 93.0932 | − | 45.9845i | 0.756856 | − | 0.373858i | ||||
\(124\) | 92.2523 | + | 159.786i | 0.743970 | + | 1.28859i | ||||
\(125\) | −103.224 | − | 70.4975i | −0.825788 | − | 0.563980i | ||||
\(126\) | 11.0100 | − | 84.4859i | 0.0873806 | − | 0.670523i | ||||
\(127\) | 101.150i | 0.796460i | 0.917286 | + | 0.398230i | \(0.130375\pi\) | ||||
−0.917286 | + | 0.398230i | \(0.869625\pi\) | |||||||
\(128\) | 7.06394 | + | 12.2351i | 0.0551870 | + | 0.0955867i | ||||
\(129\) | 10.0904 | − | 155.513i | 0.0782198 | − | 1.20553i | ||||
\(130\) | 44.1266 | − | 217.982i | 0.339435 | − | 1.67679i | ||||
\(131\) | −74.3023 | − | 42.8985i | −0.567193 | − | 0.327469i | 0.188834 | − | 0.982009i | \(-0.439529\pi\) |
−0.756028 | + | 0.654540i | \(0.772862\pi\) | |||||||
\(132\) | 235.400 | + | 157.066i | 1.78333 | + | 1.18989i | ||||
\(133\) | −15.9353 | + | 9.20024i | −0.119814 | + | 0.0691747i | ||||
\(134\) | 287.807i | 2.14781i | ||||||||
\(135\) | −124.651 | − | 51.8386i | −0.923338 | − | 0.383989i | ||||
\(136\) | −88.4068 | −0.650050 | ||||||||
\(137\) | −34.8631 | − | 60.3847i | −0.254475 | − | 0.440764i | 0.710278 | − | 0.703922i | \(-0.248569\pi\) |
−0.964753 | + | 0.263158i | \(0.915236\pi\) | |||||||
\(138\) | 3.13450 | − | 4.69778i | 0.0227138 | − | 0.0340419i | ||||
\(139\) | −69.4587 | + | 120.306i | −0.499703 | + | 0.865511i | −1.00000 | 0.000342926i | \(-0.999891\pi\) | |
0.500297 | + | 0.865854i | \(0.333224\pi\) | |||||||
\(140\) | −24.4405 | + | 120.735i | −0.174575 | + | 0.862391i | ||||
\(141\) | −152.473 | − | 9.89312i | −1.08137 | − | 0.0701639i | ||||
\(142\) | −232.075 | + | 133.989i | −1.63433 | + | 0.943582i | ||||
\(143\) | 118.584 | 0.829256 | ||||||||
\(144\) | −206.196 | + | 269.451i | −1.43191 | + | 1.87119i | ||||
\(145\) | 144.819 | − | 48.6136i | 0.998751 | − | 0.335266i | ||||
\(146\) | −96.7872 | + | 55.8801i | −0.662926 | + | 0.382740i | ||||
\(147\) | −56.3453 | − | 114.068i | −0.383301 | − | 0.775973i | ||||
\(148\) | −10.9573 | − | 6.32622i | −0.0740361 | − | 0.0427448i | ||||
\(149\) | 41.3586 | + | 23.8784i | 0.277574 | + | 0.160258i | 0.632325 | − | 0.774703i | \(-0.282101\pi\) |
−0.354750 | + | 0.934961i | \(0.615434\pi\) | |||||||
\(150\) | 247.274 | + | 123.826i | 1.64850 | + | 0.825508i | ||||
\(151\) | −27.7457 | − | 48.0569i | −0.183746 | − | 0.318258i | 0.759407 | − | 0.650616i | \(-0.225489\pi\) |
−0.943153 | + | 0.332358i | \(0.892156\pi\) | |||||||
\(152\) | 147.884 | 0.972920 | ||||||||
\(153\) | 14.8033 | + | 35.6060i | 0.0967534 | + | 0.232719i | ||||
\(154\) | −93.0585 | −0.604276 | ||||||||
\(155\) | −63.6311 | + | 72.0641i | −0.410523 | + | 0.464929i | ||||
\(156\) | −22.4857 | + | 346.550i | −0.144139 | + | 2.22148i | ||||
\(157\) | −9.58875 | − | 5.53607i | −0.0610749 | − | 0.0352616i | 0.469152 | − | 0.883118i | \(-0.344560\pi\) |
−0.530226 | + | 0.847856i | \(0.677893\pi\) | |||||||
\(158\) | −212.534 | + | 368.119i | −1.34515 | + | 2.32987i | ||||
\(159\) | 144.254 | − | 216.198i | 0.907255 | − | 1.35973i | ||||
\(160\) | 186.889 | − | 211.658i | 1.16806 | − | 1.32286i | ||||
\(161\) | 1.31076i | 0.00814134i | ||||||||
\(162\) | 288.694 | + | 76.5436i | 1.78206 | + | 0.472491i | ||||
\(163\) | 216.230i | 1.32656i | 0.748370 | + | 0.663282i | \(0.230837\pi\) | ||||
−0.748370 | + | 0.663282i | \(0.769163\pi\) | |||||||
\(164\) | 287.626 | − | 166.061i | 1.75382 | − | 1.01257i | ||||
\(165\) | −38.5515 | + | 142.323i | −0.233645 | + | 0.862561i | ||||
\(166\) | 110.644 | − | 191.640i | 0.666528 | − | 1.15446i | ||||
\(167\) | −30.9734 | + | 53.6475i | −0.185469 | + | 0.321242i | −0.943735 | − | 0.330704i | \(-0.892714\pi\) |
0.758265 | + | 0.651946i | \(0.226047\pi\) | |||||||
\(168\) | 10.2902 | − | 158.594i | 0.0612514 | − | 0.944010i | ||||
\(169\) | −11.7382 | − | 20.3311i | −0.0694567 | − | 0.120302i | ||||
\(170\) | −25.1376 | − | 74.8844i | −0.147868 | − | 0.440496i | ||||
\(171\) | −24.7624 | − | 59.5604i | −0.144809 | − | 0.348307i | ||||
\(172\) | − | 498.481i | − | 2.89815i | ||||||
\(173\) | −166.735 | − | 288.794i | −0.963788 | − | 1.66933i | −0.712837 | − | 0.701330i | \(-0.752590\pi\) |
−0.250951 | − | 0.968000i | \(-0.580743\pi\) | |||||||
\(174\) | −303.011 | + | 149.676i | −1.74144 | + | 0.860206i | ||||
\(175\) | −63.6910 | + | 7.94705i | −0.363948 | + | 0.0454117i | ||||
\(176\) | 320.939 | + | 185.294i | 1.82352 | + | 1.05281i | ||||
\(177\) | −285.010 | + | 140.784i | −1.61023 | + | 0.795391i | ||||
\(178\) | 227.678 | − | 131.450i | 1.27909 | − | 0.738483i | ||||
\(179\) | 193.521i | 1.08112i | 0.841304 | + | 0.540562i | \(0.181788\pi\) | ||||
−0.841304 | + | 0.540562i | \(0.818212\pi\) | |||||||
\(180\) | −408.615 | − | 139.650i | −2.27009 | − | 0.775835i | ||||
\(181\) | 243.865 | 1.34732 | 0.673661 | − | 0.739041i | \(-0.264721\pi\) | ||||
0.673661 | + | 0.739041i | \(0.264721\pi\) | |||||||
\(182\) | −57.0999 | − | 98.8999i | −0.313736 | − | 0.543406i | ||||
\(183\) | 93.7629 | + | 6.08374i | 0.512365 | + | 0.0332445i | ||||
\(184\) | 5.26724 | − | 9.12313i | 0.0286263 | − | 0.0495822i | ||||
\(185\) | 1.30801 | − | 6.46150i | 0.00707033 | − | 0.0349270i | ||||
\(186\) | 118.047 | − | 176.921i | 0.634662 | − | 0.951190i | ||||
\(187\) | 36.4746 | − | 21.0586i | 0.195051 | − | 0.112613i | ||||
\(188\) | −488.737 | −2.59966 | ||||||||
\(189\) | −65.5969 | + | 22.4113i | −0.347073 | + | 0.118578i | ||||
\(190\) | 42.0493 | + | 125.264i | 0.221312 | + | 0.659284i | ||||
\(191\) | −122.599 | + | 70.7825i | −0.641879 | + | 0.370589i | −0.785338 | − | 0.619067i | \(-0.787511\pi\) |
0.143459 | + | 0.989656i | \(0.454177\pi\) | |||||||
\(192\) | −95.6247 | + | 143.316i | −0.498045 | + | 0.746438i | ||||
\(193\) | 191.757 | + | 110.711i | 0.993561 | + | 0.573633i | 0.906337 | − | 0.422556i | \(-0.138867\pi\) |
0.0872244 | + | 0.996189i | \(0.472200\pi\) | |||||||
\(194\) | −408.623 | − | 235.919i | −2.10631 | − | 1.21608i | ||||
\(195\) | −174.911 | + | 46.3565i | −0.896980 | + | 0.237726i | ||||
\(196\) | −203.476 | − | 352.431i | −1.03814 | − | 1.79812i | ||||
\(197\) | 28.4424 | 0.144378 | 0.0721889 | − | 0.997391i | \(-0.477002\pi\) | ||||
0.0721889 | + | 0.997391i | \(0.477002\pi\) | |||||||
\(198\) | 42.1552 | − | 323.481i | 0.212905 | − | 1.63374i | ||||
\(199\) | 153.875 | 0.773244 | 0.386622 | − | 0.922238i | \(-0.373642\pi\) | ||||
0.386622 | + | 0.922238i | \(0.373642\pi\) | |||||||
\(200\) | 475.237 | + | 200.628i | 2.37619 | + | 1.00314i | ||||
\(201\) | 209.946 | − | 103.705i | 1.04451 | − | 0.515946i | ||||
\(202\) | −274.866 | − | 158.694i | −1.36072 | − | 0.785615i | ||||
\(203\) | 39.2197 | − | 67.9304i | 0.193200 | − | 0.334633i | ||||
\(204\) | 54.6257 | + | 110.587i | 0.267773 | + | 0.542093i | ||||
\(205\) | 129.721 | + | 114.541i | 0.632784 | + | 0.558735i | ||||
\(206\) | − | 150.748i | − | 0.731786i | ||||||
\(207\) | −4.55632 | − | 0.593767i | −0.0220112 | − | 0.00286844i | ||||
\(208\) | 454.779i | 2.18644i | ||||||||
\(209\) | −61.0133 | + | 35.2261i | −0.291930 | + | 0.168546i | ||||
\(210\) | 137.262 | − | 36.3783i | 0.653627 | − | 0.173230i | ||||
\(211\) | −90.0891 | + | 156.039i | −0.426962 | + | 0.739521i | −0.996601 | − | 0.0823744i | \(-0.973750\pi\) |
0.569639 | + | 0.821895i | \(0.307083\pi\) | |||||||
\(212\) | 415.675 | − | 719.970i | 1.96073 | − | 3.39608i | ||||
\(213\) | 181.364 | + | 121.011i | 0.851472 | + | 0.568127i | ||||
\(214\) | 3.06092 | + | 5.30167i | 0.0143034 | + | 0.0247742i | ||||
\(215\) | 246.231 | − | 82.6561i | 1.14526 | − | 0.384447i | ||||
\(216\) | 546.627 | + | 107.612i | 2.53068 | + | 0.498205i | ||||
\(217\) | 49.3638i | 0.227483i | ||||||||
\(218\) | 274.040 | + | 474.651i | 1.25706 | + | 2.17730i | ||||
\(219\) | 75.6379 | + | 50.4679i | 0.345379 | + | 0.230447i | ||||
\(220\) | −93.5785 | + | 462.272i | −0.425357 | + | 2.10124i | ||||
\(221\) | 44.7609 | + | 25.8427i | 0.202538 | + | 0.116935i | ||||
\(222\) | −0.944361 | + | 14.5545i | −0.00425388 | + | 0.0655610i | ||||
\(223\) | −186.544 | + | 107.701i | −0.836521 | + | 0.482966i | −0.856080 | − | 0.516843i | \(-0.827107\pi\) |
0.0195592 | + | 0.999809i | \(0.493774\pi\) | |||||||
\(224\) | − | 144.985i | − | 0.647256i | ||||||
\(225\) | 1.22701 | − | 224.997i | 0.00545336 | − | 0.999985i | ||||
\(226\) | −484.717 | −2.14477 | ||||||||
\(227\) | 25.2080 | + | 43.6615i | 0.111048 | + | 0.192341i | 0.916193 | − | 0.400737i | \(-0.131246\pi\) |
−0.805145 | + | 0.593078i | \(0.797912\pi\) | |||||||
\(228\) | −91.3759 | − | 184.986i | −0.400772 | − | 0.811341i | ||||
\(229\) | 3.08352 | − | 5.34081i | 0.0134652 | − | 0.0233223i | −0.859214 | − | 0.511616i | \(-0.829047\pi\) |
0.872679 | + | 0.488294i | \(0.162380\pi\) | |||||||
\(230\) | 9.22537 | + | 1.86751i | 0.0401103 | + | 0.00811960i | ||||
\(231\) | 33.5317 | + | 67.8831i | 0.145159 | + | 0.293866i | ||||
\(232\) | −545.954 | + | 315.207i | −2.35325 | + | 1.35865i | ||||
\(233\) | −52.5336 | −0.225466 | −0.112733 | − | 0.993625i | \(-0.535960\pi\) | ||||
−0.112733 | + | 0.993625i | \(0.535960\pi\) | |||||||
\(234\) | 369.653 | − | 153.684i | 1.57971 | − | 0.656769i | ||||
\(235\) | −81.0403 | − | 241.417i | −0.344853 | − | 1.02731i | ||||
\(236\) | −880.584 | + | 508.405i | −3.73129 | + | 2.15426i | ||||
\(237\) | 345.113 | + | 22.3924i | 1.45617 | + | 0.0944827i | ||||
\(238\) | −35.1262 | − | 20.2801i | −0.147589 | − | 0.0852105i | ||||
\(239\) | 84.5102 | + | 48.7920i | 0.353599 | + | 0.204151i | 0.666269 | − | 0.745711i | \(-0.267890\pi\) |
−0.312670 | + | 0.949862i | \(0.601223\pi\) | |||||||
\(240\) | −545.820 | − | 147.848i | −2.27425 | − | 0.616035i | ||||
\(241\) | 71.3647 | + | 123.607i | 0.296119 | + | 0.512893i | 0.975245 | − | 0.221129i | \(-0.0709742\pi\) |
−0.679126 | + | 0.734022i | \(0.737641\pi\) | |||||||
\(242\) | 89.8560 | 0.371306 | ||||||||
\(243\) | −48.1889 | − | 238.174i | −0.198308 | − | 0.980140i | ||||
\(244\) | 300.547 | 1.23175 | ||||||||
\(245\) | 140.348 | − | 158.948i | 0.572848 | − | 0.648767i | ||||
\(246\) | −318.471 | − | 212.494i | −1.29460 | − | 0.863795i | ||||
\(247\) | −74.8745 | − | 43.2288i | −0.303136 | − | 0.175015i | ||||
\(248\) | 198.367 | − | 343.583i | 0.799869 | − | 1.38541i | ||||
\(249\) | −179.663 | − | 11.6573i | −0.721540 | − | 0.0468166i | ||||
\(250\) | −34.8112 | + | 459.593i | −0.139245 | + | 1.83837i | ||||
\(251\) | 254.631i | 1.01447i | 0.861809 | + | 0.507233i | \(0.169332\pi\) | ||||
−0.861809 | + | 0.507233i | \(0.830668\pi\) | |||||||
\(252\) | −204.741 | + | 85.1215i | −0.812464 | + | 0.337784i | ||||
\(253\) | 5.01865i | 0.0198366i | ||||||||
\(254\) | 323.001 | − | 186.485i | 1.27166 | − | 0.734192i | ||||
\(255\) | −45.5679 | + | 45.3201i | −0.178698 | + | 0.177726i | ||||
\(256\) | 140.906 | − | 244.057i | 0.550415 | − | 0.953346i | ||||
\(257\) | −71.3682 | + | 123.613i | −0.277697 | + | 0.480986i | −0.970812 | − | 0.239841i | \(-0.922905\pi\) |
0.693115 | + | 0.720827i | \(0.256238\pi\) | |||||||
\(258\) | −515.199 | + | 254.489i | −1.99690 | + | 0.986390i | ||||
\(259\) | −1.69257 | − | 2.93162i | −0.00653502 | − | 0.0113190i | ||||
\(260\) | −548.708 | + | 184.193i | −2.11042 | + | 0.708436i | ||||
\(261\) | 218.367 | + | 167.104i | 0.836656 | + | 0.640245i | ||||
\(262\) | 316.357i | 1.20747i | ||||||||
\(263\) | −126.234 | − | 218.644i | −0.479979 | − | 0.831347i | 0.519758 | − | 0.854314i | \(-0.326022\pi\) |
−0.999736 | + | 0.0229665i | \(0.992689\pi\) | |||||||
\(264\) | 39.3995 | − | 607.227i | 0.149240 | − | 2.30010i | ||||
\(265\) | 424.563 | + | 85.9450i | 1.60212 | + | 0.324321i | ||||
\(266\) | 58.7578 | + | 33.9238i | 0.220894 | + | 0.127533i | ||||
\(267\) | −177.927 | − | 118.718i | −0.666395 | − | 0.444638i | ||||
\(268\) | 648.660 | − | 374.504i | 2.42037 | − | 1.39740i | ||||
\(269\) | − | 388.672i | − | 1.44488i | −0.691435 | − | 0.722439i | \(-0.743021\pi\) | ||
0.691435 | − | 0.722439i | \(-0.256979\pi\) | |||||||
\(270\) | 64.2758 | + | 493.615i | 0.238058 | + | 1.82820i | ||||
\(271\) | −163.253 | −0.602410 | −0.301205 | − | 0.953559i | \(-0.597389\pi\) | ||||
−0.301205 | + | 0.953559i | \(0.597389\pi\) | |||||||
\(272\) | 80.7617 | + | 139.883i | 0.296918 | + | 0.514277i | ||||
\(273\) | −51.5695 | + | 77.2889i | −0.188899 | + | 0.283110i | ||||
\(274\) | −128.550 | + | 222.655i | −0.469160 | + | 0.812610i | ||||
\(275\) | −243.861 | + | 30.4278i | −0.886769 | + | 0.110647i | ||||
\(276\) | −14.6666 | − | 0.951630i | −0.0531397 | − | 0.00344793i | ||||
\(277\) | 419.003 | − | 241.912i | 1.51265 | − | 0.873328i | 0.512757 | − | 0.858534i | \(-0.328624\pi\) |
0.999891 | − | 0.0147939i | \(-0.00470921\pi\) | |||||||
\(278\) | 512.227 | 1.84254 | ||||||||
\(279\) | −171.594 | − | 22.3616i | −0.615032 | − | 0.0801493i | ||||
\(280\) | 251.108 | − | 84.2934i | 0.896814 | − | 0.301048i | ||||
\(281\) | 231.798 | − | 133.829i | 0.824906 | − | 0.476260i | −0.0271995 | − | 0.999630i | \(-0.508659\pi\) |
0.852105 | + | 0.523371i | \(0.175326\pi\) | |||||||
\(282\) | 249.514 | + | 505.128i | 0.884802 | + | 1.79124i | ||||
\(283\) | −425.908 | − | 245.898i | −1.50498 | − | 0.868898i | −0.999983 | − | 0.00577475i | \(-0.998162\pi\) |
−0.504993 | − | 0.863124i | \(-0.668505\pi\) | |||||||
\(284\) | 603.967 | + | 348.701i | 2.12664 | + | 1.22782i | ||||
\(285\) | 76.2243 | − | 75.8098i | 0.267454 | − | 0.265999i | ||||
\(286\) | −218.625 | − | 378.670i | −0.764424 | − | 1.32402i | ||||
\(287\) | 88.8586 | 0.309612 | ||||||||
\(288\) | 503.985 | + | 65.6779i | 1.74995 | + | 0.228048i | ||||
\(289\) | −270.643 | −0.936481 | ||||||||
\(290\) | −422.230 | − | 372.820i | −1.45597 | − | 1.28559i | ||||
\(291\) | −24.8562 | + | 383.086i | −0.0854166 | + | 1.31645i | ||||
\(292\) | 251.885 | + | 145.426i | 0.862621 | + | 0.498034i | ||||
\(293\) | −161.073 | + | 278.986i | −0.549737 | + | 0.952172i | 0.448555 | + | 0.893755i | \(0.351939\pi\) |
−0.998292 | + | 0.0584171i | \(0.981395\pi\) | |||||||
\(294\) | −260.370 | + | 390.226i | −0.885614 | + | 1.32730i | ||||
\(295\) | −397.148 | − | 350.673i | −1.34626 | − | 1.18872i | ||||
\(296\) | 27.2062i | 0.0919129i | ||||||||
\(297\) | −251.159 | + | 85.8088i | −0.845652 | + | 0.288919i | ||||
\(298\) | − | 176.092i | − | 0.590914i | ||||||
\(299\) | −5.33367 | + | 3.07940i | −0.0178384 | + | 0.0102990i | ||||
\(300\) | −42.6820 | − | 718.434i | −0.142273 | − | 2.39478i | ||||
\(301\) | 66.6839 | − | 115.500i | 0.221541 | − | 0.383720i | ||||
\(302\) | −102.306 | + | 177.199i | −0.338762 | + | 0.586752i | ||||
\(303\) | −16.7199 | + | 257.688i | −0.0551812 | + | 0.850455i | ||||
\(304\) | −135.095 | − | 233.992i | −0.444392 | − | 0.769710i | ||||
\(305\) | 49.8355 | + | 148.459i | 0.163395 | + | 0.486750i | ||||
\(306\) | 86.4078 | − | 112.915i | 0.282378 | − | 0.369005i | ||||
\(307\) | 426.031i | 1.38772i | 0.720109 | + | 0.693861i | \(0.244092\pi\) | ||||
−0.720109 | + | 0.693861i | \(0.755908\pi\) | |||||||
\(308\) | 121.091 | + | 209.735i | 0.393152 | + | 0.680959i | ||||
\(309\) | −109.966 | + | 54.3188i | −0.355876 | + | 0.175789i | ||||
\(310\) | 347.433 | + | 70.3315i | 1.12075 | + | 0.226876i | ||||
\(311\) | −1.01150 | − | 0.583987i | −0.00325240 | − | 0.00187777i | 0.498373 | − | 0.866963i | \(-0.333931\pi\) |
−0.501625 | + | 0.865085i | \(0.667264\pi\) | |||||||
\(312\) | 669.518 | − | 330.716i | 2.14589 | − | 1.05999i | ||||
\(313\) | −225.989 | + | 130.475i | −0.722009 | + | 0.416852i | −0.815492 | − | 0.578769i | \(-0.803533\pi\) |
0.0934824 | + | 0.995621i | \(0.470200\pi\) | |||||||
\(314\) | 40.8260i | 0.130019i | ||||||||
\(315\) | −75.9960 | − | 87.0196i | −0.241257 | − | 0.276253i | ||||
\(316\) | 1106.22 | 3.50071 | ||||||||
\(317\) | 65.5178 | + | 113.480i | 0.206681 | + | 0.357981i | 0.950667 | − | 0.310213i | \(-0.100401\pi\) |
−0.743986 | + | 0.668195i | \(0.767067\pi\) | |||||||
\(318\) | −956.330 | − | 62.0508i | −3.00733 | − | 0.195128i | ||||
\(319\) | 150.165 | − | 260.094i | 0.470737 | − | 0.815340i | ||||
\(320\) | −281.440 | − | 56.9724i | −0.879500 | − | 0.178039i | ||||
\(321\) | 2.76446 | − | 4.14318i | 0.00861201 | − | 0.0129071i | ||||
\(322\) | 4.18560 | − | 2.41656i | 0.0129988 | − | 0.00750484i | ||||
\(323\) | −30.7071 | −0.0950683 | ||||||||
\(324\) | −203.145 | − | 750.261i | −0.626989 | − | 2.31562i | ||||
\(325\) | −181.969 | − | 240.499i | −0.559905 | − | 0.739996i | ||||
\(326\) | 690.482 | − | 398.650i | 2.11804 | − | 1.22285i | ||||
\(327\) | 247.498 | − | 370.934i | 0.756874 | − | 1.13435i | ||||
\(328\) | −618.474 | − | 357.076i | −1.88559 | − | 1.08865i | ||||
\(329\) | −113.242 | − | 65.3803i | −0.344201 | − | 0.198724i | ||||
\(330\) | 525.550 | − | 139.286i | 1.59258 | − | 0.422079i | ||||
\(331\) | −96.7419 | − | 167.562i | −0.292272 | − | 0.506229i | 0.682075 | − | 0.731282i | \(-0.261078\pi\) |
−0.974347 | + | 0.225053i | \(0.927745\pi\) | |||||||
\(332\) | −575.893 | −1.73462 | ||||||||
\(333\) | 10.9573 | − | 4.55554i | 0.0329049 | − | 0.0136803i | ||||
\(334\) | 228.415 | 0.683877 | ||||||||
\(335\) | 292.549 | + | 258.314i | 0.873280 | + | 0.771088i | ||||
\(336\) | −260.338 | + | 128.597i | −0.774816 | + | 0.382729i | ||||
\(337\) | −401.485 | − | 231.798i | −1.19135 | − | 0.687827i | −0.232738 | − | 0.972539i | \(-0.574769\pi\) |
−0.958613 | + | 0.284712i | \(0.908102\pi\) | |||||||
\(338\) | −43.2819 | + | 74.9664i | −0.128053 | + | 0.221794i | ||||
\(339\) | 174.658 | + | 353.585i | 0.515214 | + | 1.04302i | ||||
\(340\) | −136.065 | + | 154.097i | −0.400190 | + | 0.453227i | ||||
\(341\) | 189.005i | 0.554268i | ||||||||
\(342\) | −144.540 | + | 188.881i | −0.422631 | + | 0.552284i | ||||
\(343\) | − | 234.682i | − | 0.684203i | ||||||
\(344\) | −928.267 | + | 535.935i | −2.69845 | + | 1.55795i | ||||
\(345\) | −1.96188 | − | 7.40252i | −0.00568661 | − | 0.0214566i | ||||
\(346\) | −614.799 | + | 1064.86i | −1.77688 | + | 3.07764i | ||||
\(347\) | −4.85934 | + | 8.41662i | −0.0140039 | + | 0.0242554i | −0.872942 | − | 0.487823i | \(-0.837791\pi\) |
0.858939 | + | 0.512079i | \(0.171124\pi\) | |||||||
\(348\) | 731.627 | + | 488.163i | 2.10238 | + | 1.40277i | ||||
\(349\) | 24.6679 | + | 42.7260i | 0.0706816 | + | 0.122424i | 0.899200 | − | 0.437537i | \(-0.144149\pi\) |
−0.828519 | + | 0.559962i | \(0.810816\pi\) | |||||||
\(350\) | 142.800 | + | 188.731i | 0.408001 | + | 0.539232i | ||||
\(351\) | −245.304 | − | 214.273i | −0.698871 | − | 0.610463i | ||||
\(352\) | − | 555.123i | − | 1.57705i | ||||||
\(353\) | −47.6810 | − | 82.5859i | −0.135074 | − | 0.233954i | 0.790552 | − | 0.612395i | \(-0.209794\pi\) |
−0.925626 | + | 0.378441i | \(0.876460\pi\) | |||||||
\(354\) | 975.019 | + | 650.562i | 2.75429 | + | 1.83774i | ||||
\(355\) | −72.0974 | + | 356.157i | −0.203091 | + | 1.00326i | ||||
\(356\) | −592.524 | − | 342.094i | −1.66439 | − | 0.960938i | ||||
\(357\) | −2.13670 | + | 32.9309i | −0.00598514 | + | 0.0922433i | ||||
\(358\) | 617.966 | − | 356.783i | 1.72616 | − | 0.996600i | ||||
\(359\) | − | 539.284i | − | 1.50219i | −0.660197 | − | 0.751093i | \(-0.729527\pi\) | ||
0.660197 | − | 0.751093i | \(-0.270473\pi\) | |||||||
\(360\) | 179.262 | + | 911.063i | 0.497949 | + | 2.53073i | ||||
\(361\) | −309.634 | −0.857713 | ||||||||
\(362\) | −449.599 | − | 778.729i | −1.24199 | − | 2.15118i | ||||
\(363\) | −32.3777 | − | 65.5470i | −0.0891948 | − | 0.180570i | ||||
\(364\) | −148.600 | + | 257.383i | −0.408243 | + | 0.707098i | ||||
\(365\) | −30.0683 | + | 148.536i | −0.0823790 | + | 0.406947i | ||||
\(366\) | −153.438 | − | 310.627i | −0.419229 | − | 0.848707i | ||||
\(367\) | 262.482 | − | 151.544i | 0.715211 | − | 0.412927i | −0.0977766 | − | 0.995208i | \(-0.531173\pi\) |
0.812987 | + | 0.582281i | \(0.197840\pi\) | |||||||
\(368\) | −19.2470 | −0.0523016 | ||||||||
\(369\) | −40.2526 | + | 308.882i | −0.109086 | + | 0.837078i | ||||
\(370\) | −23.0448 | + | 7.73582i | −0.0622833 | + | 0.0209076i | ||||
\(371\) | 192.627 | − | 111.213i | 0.519209 | − | 0.299766i | ||||
\(372\) | −552.352 | − | 35.8390i | −1.48482 | − | 0.0963413i | ||||
\(373\) | 113.159 | + | 65.3325i | 0.303376 | + | 0.175154i | 0.643959 | − | 0.765060i | \(-0.277291\pi\) |
−0.340582 | + | 0.940215i | \(0.610624\pi\) | |||||||
\(374\) | −134.492 | − | 77.6489i | −0.359604 | − | 0.207617i | ||||
\(375\) | 347.801 | − | 140.211i | 0.927471 | − | 0.373896i | ||||
\(376\) | 525.459 | + | 910.121i | 1.39750 | + | 2.42054i | ||||
\(377\) | 368.560 | 0.977612 | ||||||||
\(378\) | 192.502 | + | 168.151i | 0.509265 | + | 0.444843i | ||||
\(379\) | 545.141 | 1.43837 | 0.719183 | − | 0.694821i | \(-0.244516\pi\) | ||||
0.719183 | + | 0.694821i | \(0.244516\pi\) | |||||||
\(380\) | 227.604 | − | 257.768i | 0.598958 | − | 0.678338i | ||||
\(381\) | −252.421 | − | 168.423i | −0.662522 | − | 0.442054i | ||||
\(382\) | 452.056 | + | 260.995i | 1.18339 | + | 0.683232i | ||||
\(383\) | 0.623248 | − | 1.07950i | 0.00162728 | − | 0.00281853i | −0.865211 | − | 0.501409i | \(-0.832815\pi\) |
0.866838 | + | 0.498590i | \(0.166149\pi\) | |||||||
\(384\) | −42.2947 | − | 2.74426i | −0.110142 | − | 0.00714651i | ||||
\(385\) | −83.5225 | + | 94.5917i | −0.216941 | + | 0.245693i | ||||
\(386\) | − | 816.445i | − | 2.11514i | ||||||
\(387\) | 371.282 | + | 284.121i | 0.959386 | + | 0.734163i | ||||
\(388\) | 1227.94i | 3.16480i | ||||||||
\(389\) | −345.001 | + | 199.187i | −0.886893 | + | 0.512048i | −0.872925 | − | 0.487855i | \(-0.837780\pi\) |
−0.0139679 | + | 0.999902i | \(0.504446\pi\) | |||||||
\(390\) | 470.502 | + | 473.075i | 1.20642 | + | 1.21301i | ||||
\(391\) | −1.09371 | + | 1.89435i | −0.00279720 | + | 0.00484490i | ||||
\(392\) | −437.529 | + | 757.822i | −1.11615 | + | 1.93322i | ||||
\(393\) | 230.772 | − | 113.993i | 0.587206 | − | 0.290057i | ||||
\(394\) | −52.4376 | − | 90.8245i | −0.133090 | − | 0.230519i | ||||
\(395\) | 183.429 | + | 546.432i | 0.464378 | + | 1.38337i | ||||
\(396\) | −783.916 | + | 325.915i | −1.97959 | + | 0.823018i | ||||
\(397\) | − | 685.998i | − | 1.72795i | −0.503531 | − | 0.863977i | \(-0.667966\pi\) | ||
0.503531 | − | 0.863977i | \(-0.332034\pi\) | |||||||
\(398\) | −283.691 | − | 491.367i | −0.712791 | − | 1.23459i | ||||
\(399\) | 3.57419 | − | 55.0856i | 0.00895787 | − | 0.138059i | ||||
\(400\) | −116.694 | − | 935.232i | −0.291734 | − | 2.33808i | ||||
\(401\) | 44.9212 | + | 25.9353i | 0.112023 | + | 0.0646764i | 0.554965 | − | 0.831874i | \(-0.312732\pi\) |
−0.442942 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(402\) | −718.223 | − | 479.220i | −1.78663 | − | 1.19209i | ||||
\(403\) | −200.869 | + | 115.972i | −0.498435 | + | 0.287772i | ||||
\(404\) | 825.992i | 2.04453i | ||||||||
\(405\) | 336.916 | − | 224.751i | 0.831890 | − | 0.554940i | ||||
\(406\) | −289.227 | −0.712383 | ||||||||
\(407\) | −6.48055 | − | 11.2246i | −0.0159227 | − | 0.0275790i | ||||
\(408\) | 147.204 | − | 220.619i | 0.360794 | − | 0.540734i | ||||
\(409\) | 135.648 | − | 234.950i | 0.331658 | − | 0.574449i | −0.651179 | − | 0.758924i | \(-0.725725\pi\) |
0.982837 | + | 0.184475i | \(0.0590586\pi\) | |||||||
\(410\) | 126.602 | − | 625.405i | 0.308785 | − | 1.52538i | ||||
\(411\) | 208.740 | + | 13.5439i | 0.507883 | + | 0.0329536i | ||||
\(412\) | −339.756 | + | 196.158i | −0.824650 | + | 0.476112i | ||||
\(413\) | −272.046 | −0.658707 | ||||||||
\(414\) | 6.50415 | + | 15.6443i | 0.0157105 | + | 0.0377881i | ||||
\(415\) | −95.4921 | − | 284.469i | −0.230101 | − | 0.685467i | ||||
\(416\) | 589.969 | − | 340.619i | 1.41819 | − | 0.818795i | ||||
\(417\) | −184.570 | − | 373.653i | −0.442614 | − | 0.896050i | ||||
\(418\) | 224.973 | + | 129.888i | 0.538213 | + | 0.310738i | ||||
\(419\) | 23.9467 | + | 13.8256i | 0.0571520 | + | 0.0329967i | 0.528304 | − | 0.849055i | \(-0.322828\pi\) |
−0.471152 | + | 0.882052i | \(0.656162\pi\) | |||||||
\(420\) | −260.599 | − | 262.024i | −0.620473 | − | 0.623866i | ||||
\(421\) | 218.613 | + | 378.649i | 0.519271 | + | 0.899403i | 0.999749 | + | 0.0223967i | \(0.00712970\pi\) |
−0.480478 | + | 0.877007i | \(0.659537\pi\) | |||||||
\(422\) | 664.367 | 1.57433 | ||||||||
\(423\) | 278.567 | − | 364.025i | 0.658552 | − | 0.860578i | ||||
\(424\) | −1787.63 | −4.21610 | ||||||||
\(425\) | −98.6798 | − | 41.6590i | −0.232188 | − | 0.0980211i | ||||
\(426\) | 52.0531 | − | 802.245i | 0.122190 | − | 1.88320i | ||||
\(427\) | 69.6378 | + | 40.2054i | 0.163086 | + | 0.0941579i | ||||
\(428\) | 7.96594 | − | 13.7974i | 0.0186120 | − | 0.0322369i | ||||
\(429\) | −197.450 | + | 295.926i | −0.460257 | + | 0.689803i | ||||
\(430\) | −717.904 | − | 633.894i | −1.66954 | − | 1.47417i | ||||
\(431\) | 54.3602i | 0.126126i | 0.998010 | + | 0.0630629i | \(0.0200869\pi\) | ||||
−0.998010 | + | 0.0630629i | \(0.979913\pi\) | |||||||
\(432\) | −329.085 | − | 963.217i | −0.761771 | − | 2.22967i | ||||
\(433\) | 526.426i | 1.21576i | 0.794028 | + | 0.607882i | \(0.207981\pi\) | ||||
−0.794028 | + | 0.607882i | \(0.792019\pi\) | |||||||
\(434\) | 157.632 | − | 91.0091i | 0.363208 | − | 0.209698i | ||||
\(435\) | −119.819 | + | 442.341i | −0.275445 | + | 1.01688i | ||||
\(436\) | 713.180 | − | 1235.26i | 1.63573 | − | 2.83317i | ||||
\(437\) | 1.82951 | − | 3.16881i | 0.00418653 | − | 0.00725128i | ||||
\(438\) | 21.7088 | − | 334.577i | 0.0495635 | − | 0.763875i | ||||
\(439\) | 208.124 | + | 360.481i | 0.474087 | + | 0.821142i | 0.999560 | − | 0.0296681i | \(-0.00944503\pi\) |
−0.525473 | + | 0.850810i | \(0.676112\pi\) | |||||||
\(440\) | 961.448 | − | 322.744i | 2.18511 | − | 0.733510i | ||||
\(441\) | 378.476 | + | 49.3219i | 0.858223 | + | 0.111841i | ||||
\(442\) | − | 190.579i | − | 0.431173i | ||||||
\(443\) | 213.582 | + | 369.935i | 0.482127 | + | 0.835069i | 0.999790 | − | 0.0205163i | \(-0.00653100\pi\) |
−0.517662 | + | 0.855585i | \(0.673198\pi\) | |||||||
\(444\) | 34.0319 | − | 16.8104i | 0.0766484 | − | 0.0378614i | ||||
\(445\) | 70.7314 | − | 349.409i | 0.158947 | − | 0.785189i | ||||
\(446\) | 687.840 | + | 397.125i | 1.54224 | + | 0.890414i | ||||
\(447\) | −128.454 | + | 63.4512i | −0.287368 | + | 0.141949i | ||||
\(448\) | −127.691 | + | 73.7224i | −0.285024 | + | 0.164559i | ||||
\(449\) | − | 236.730i | − | 0.527239i | −0.964627 | − | 0.263620i | \(-0.915084\pi\) | ||
0.964627 | − | 0.263620i | \(-0.0849164\pi\) | |||||||
\(450\) | −720.738 | + | 410.894i | −1.60164 | + | 0.913098i | ||||
\(451\) | 340.224 | 0.754376 | ||||||||
\(452\) | 630.730 | + | 1092.46i | 1.39542 | + | 2.41694i | ||||
\(453\) | 166.125 | + | 10.7789i | 0.366721 | + | 0.0237945i | ||||
\(454\) | 92.9488 | − | 160.992i | 0.204733 | − | 0.354608i | ||||
\(455\) | −151.778 | − | 30.7247i | −0.333578 | − | 0.0675267i | ||||
\(456\) | −246.237 | + | 369.044i | −0.539994 | + | 0.809308i | ||||
\(457\) | −604.296 | + | 348.891i | −1.32231 | + | 0.763437i | −0.984097 | − | 0.177633i | \(-0.943156\pi\) |
−0.338214 | + | 0.941069i | \(0.609823\pi\) | |||||||
\(458\) | −22.7396 | −0.0496497 | ||||||||
\(459\) | −113.503 | − | 22.3450i | −0.247284 | − | 0.0486818i | ||||
\(460\) | −7.79536 | − | 23.2222i | −0.0169464 | − | 0.0504831i | ||||
\(461\) | −332.339 | + | 191.876i | −0.720910 | + | 0.416217i | −0.815087 | − | 0.579338i | \(-0.803311\pi\) |
0.0941777 | + | 0.995555i | \(0.469978\pi\) | |||||||
\(462\) | 154.949 | − | 232.228i | 0.335388 | − | 0.502657i | ||||
\(463\) | 233.924 | + | 135.056i | 0.505235 | + | 0.291698i | 0.730873 | − | 0.682514i | \(-0.239113\pi\) |
−0.225638 | + | 0.974211i | \(0.572447\pi\) | |||||||
\(464\) | 997.483 | + | 575.897i | 2.14975 | + | 1.24116i | ||||
\(465\) | −73.8857 | − | 278.783i | −0.158894 | − | 0.599534i | ||||
\(466\) | 96.8529 | + | 167.754i | 0.207839 | + | 0.359987i | ||||
\(467\) | −777.952 | −1.66585 | −0.832926 | − | 0.553385i | \(-0.813336\pi\) | ||||
−0.832926 | + | 0.553385i | \(0.813336\pi\) | |||||||
\(468\) | −827.377 | − | 633.145i | −1.76790 | − | 1.35287i | ||||
\(469\) | 200.396 | 0.427283 | ||||||||
\(470\) | −621.503 | + | 703.870i | −1.32235 | + | 1.49760i | ||||
\(471\) | 29.7812 | − | 14.7108i | 0.0632298 | − | 0.0312331i | ||||
\(472\) | 1893.50 | + | 1093.21i | 4.01164 | + | 2.31612i | ||||
\(473\) | 255.321 | − | 442.228i | 0.539790 | − | 0.934943i | ||||
\(474\) | −564.758 | − | 1143.32i | −1.19147 | − | 2.41208i | ||||
\(475\) | 165.068 | + | 69.6856i | 0.347512 | + | 0.146707i | ||||
\(476\) | 105.556i | 0.221757i | ||||||||
\(477\) | 299.329 | + | 719.970i | 0.627525 | + | 1.50937i | ||||
\(478\) | − | 359.819i | − | 0.752760i | ||||||
\(479\) | 62.8429 | − | 36.2824i | 0.131196 | − | 0.0757460i | −0.432966 | − | 0.901410i | \(-0.642533\pi\) |
0.564162 | + | 0.825664i | \(0.309200\pi\) | |||||||
\(480\) | 217.008 | + | 818.808i | 0.452100 | + | 1.70585i | ||||
\(481\) | 7.95281 | − | 13.7747i | 0.0165339 | − | 0.0286376i | ||||
\(482\) | 263.141 | − | 455.774i | 0.545936 | − | 0.945590i | ||||
\(483\) | −3.27099 | − | 2.18250i | −0.00677224 | − | 0.00451864i | ||||
\(484\) | −116.924 | − | 202.518i | −0.241578 | − | 0.418425i | ||||
\(485\) | −606.556 | + | 203.612i | −1.25063 | + | 0.419819i | ||||
\(486\) | −671.712 | + | 592.987i | −1.38212 | + | 1.22014i | ||||
\(487\) | 729.487i | 1.49792i | 0.662616 | + | 0.748959i | \(0.269446\pi\) | ||||
−0.662616 | + | 0.748959i | \(0.730554\pi\) | |||||||
\(488\) | −323.129 | − | 559.676i | −0.662150 | − | 1.14688i | ||||
\(489\) | −539.602 | − | 360.039i | −1.10348 | − | 0.736275i | ||||
\(490\) | −766.315 | − | 155.127i | −1.56391 | − | 0.316585i | ||||
\(491\) | 3.30449 | + | 1.90785i | 0.00673012 | + | 0.00388564i | 0.503361 | − | 0.864076i | \(-0.332096\pi\) |
−0.496631 | + | 0.867962i | \(0.665430\pi\) | |||||||
\(492\) | −64.5128 | + | 994.275i | −0.131124 | + | 2.02088i | ||||
\(493\) | 113.364 | − | 65.4505i | 0.229946 | − | 0.132760i | ||||
\(494\) | 318.793i | 0.645330i | ||||||||
\(495\) | −290.975 | − | 333.183i | −0.587829 | − | 0.673096i | ||||
\(496\) | −724.853 | −1.46140 | ||||||||
\(497\) | 93.2942 | + | 161.590i | 0.187715 | + | 0.325131i | ||||
\(498\) | 294.009 | + | 595.207i | 0.590380 | + | 1.19519i | ||||
\(499\) | −102.651 | + | 177.797i | −0.205714 | + | 0.356307i | −0.950360 | − | 0.311152i | \(-0.899285\pi\) |
0.744646 | + | 0.667460i | \(0.232618\pi\) | |||||||
\(500\) | 1081.13 | − | 519.580i | 2.16226 | − | 1.03916i | ||||
\(501\) | −82.3044 | − | 166.621i | −0.164280 | − | 0.332577i | ||||
\(502\) | 813.107 | − | 469.448i | 1.61974 | − | 0.935155i | ||||
\(503\) | −224.016 | −0.445360 | −0.222680 | − | 0.974892i | \(-0.571481\pi\) | ||||
−0.222680 | + | 0.974892i | \(0.571481\pi\) | |||||||
\(504\) | 378.637 | + | 289.749i | 0.751263 | + | 0.574899i | ||||
\(505\) | −408.008 | + | 136.963i | −0.807937 | + | 0.271213i | ||||
\(506\) | 16.0259 | − | 9.25257i | 0.0316718 | − | 0.0182857i | ||||
\(507\) | 70.2813 | + | 4.56015i | 0.138622 | + | 0.00899438i | ||||
\(508\) | −840.599 | − | 485.320i | −1.65472 | − | 0.955354i | ||||
\(509\) | −399.073 | − | 230.405i | −0.784033 | − | 0.452662i | 0.0538245 | − | 0.998550i | \(-0.482859\pi\) |
−0.837858 | + | 0.545889i | \(0.816192\pi\) | |||||||
\(510\) | 228.730 | + | 61.9570i | 0.448490 | + | 0.121484i | ||||
\(511\) | 38.9085 | + | 67.3915i | 0.0761418 | + | 0.131882i | ||||
\(512\) | −982.608 | −1.91916 | ||||||||
\(513\) | 189.864 | + | 37.3778i | 0.370106 | + | 0.0728613i | ||||
\(514\) | 526.309 | 1.02395 | ||||||||
\(515\) | −153.232 | − | 135.300i | −0.297537 | − | 0.262719i | ||||
\(516\) | 1243.96 | + | 830.007i | 2.41078 | + | 1.60854i | ||||
\(517\) | −433.584 | − | 250.330i | −0.838653 | − | 0.484197i | ||||
\(518\) | −6.24097 | + | 10.8097i | −0.0120482 | + | 0.0208681i | ||||
\(519\) | 998.313 | + | 64.7748i | 1.92353 | + | 0.124807i | ||||
\(520\) | 932.939 | + | 823.766i | 1.79411 | + | 1.58417i | ||||
\(521\) | 182.438i | 0.350168i | 0.984554 | + | 0.175084i | \(0.0560197\pi\) | ||||
−0.984554 | + | 0.175084i | \(0.943980\pi\) | |||||||
\(522\) | 131.019 | − | 1005.39i | 0.250994 | − | 1.92603i | ||||
\(523\) | − | 431.339i | − | 0.824741i | −0.911016 | − | 0.412370i | \(-0.864701\pi\) | ||
0.911016 | − | 0.412370i | \(-0.135299\pi\) | |||||||
\(524\) | 713.006 | − | 411.654i | 1.36070 | − | 0.785599i | ||||
\(525\) | 86.2183 | − | 172.173i | 0.164225 | − | 0.327949i | ||||
\(526\) | −465.461 | + | 806.202i | −0.884907 | + | 1.53270i | ||||
\(527\) | −41.1896 | + | 71.3426i | −0.0781587 | + | 0.135375i | ||||
\(528\) | −996.788 | + | 492.375i | −1.88786 | + | 0.932529i | ||||
\(529\) | 264.370 | + | 457.902i | 0.499754 | + | 0.865599i | ||||
\(530\) | −508.295 | − | 1514.20i | −0.959046 | − | 2.85698i | ||||
\(531\) | 123.236 | − | 945.660i | 0.232083 | − | 1.78090i | ||||
\(532\) | − | 176.571i | − | 0.331901i | ||||||
\(533\) | 208.758 | + | 361.580i | 0.391666 | + | 0.678386i | ||||
\(534\) | −51.0669 | + | 787.045i | −0.0956308 | + | 1.47387i | ||||
\(535\) | 8.13627 | + | 1.64704i | 0.0152080 | + | 0.00307858i | ||||
\(536\) | −1394.80 | − | 805.285i | −2.60223 | − | 1.50240i | ||||
\(537\) | −482.932 | − | 322.227i | −0.899315 | − | 0.600050i | ||||
\(538\) | −1241.14 | + | 716.571i | −2.30695 | + | 1.33192i | ||||
\(539\) | − | 416.879i | − | 0.773431i | ||||||
\(540\) | 1028.87 | − | 787.173i | 1.90532 | − | 1.45773i | ||||
\(541\) | −649.924 | −1.20134 | −0.600669 | − | 0.799498i | \(-0.705099\pi\) | ||||
−0.600669 | + | 0.799498i | \(0.705099\pi\) | |||||||
\(542\) | 300.980 | + | 521.312i | 0.555313 | + | 0.961830i | ||||
\(543\) | −406.053 | + | 608.566i | −0.747796 | + | 1.12075i | ||||
\(544\) | 120.977 | − | 209.539i | 0.222384 | − | 0.385181i | ||||
\(545\) | 728.429 | + | 147.457i | 1.33657 | + | 0.270564i | ||||
\(546\) | 341.880 | + | 22.1827i | 0.626154 | + | 0.0406276i | ||||
\(547\) | 368.334 | − | 212.658i | 0.673371 | − | 0.388771i | −0.123982 | − | 0.992285i | \(-0.539566\pi\) |
0.797353 | + | 0.603513i | \(0.206233\pi\) | |||||||
\(548\) | 669.094 | 1.22097 | ||||||||
\(549\) | −171.304 | + | 223.856i | −0.312029 | + | 0.407752i | ||||
\(550\) | 546.757 | + | 722.619i | 0.994103 | + | 1.31385i | ||||
\(551\) | −189.631 | + | 109.483i | −0.344157 | + | 0.198699i | ||||
\(552\) | 13.9964 | + | 28.3351i | 0.0253559 | + | 0.0513317i | ||||
\(553\) | 256.316 | + | 147.984i | 0.463501 | + | 0.267602i | ||||
\(554\) | −1544.98 | − | 891.995i | −2.78878 | − | 1.61010i | ||||
\(555\) | 13.9467 | + | 14.0230i | 0.0251293 | + | 0.0252667i | ||||
\(556\) | −666.526 | − | 1154.46i | −1.19879 | − | 2.07636i | ||||
\(557\) | 325.885 | 0.585073 | 0.292536 | − | 0.956254i | \(-0.405501\pi\) | ||||
0.292536 | + | 0.956254i | \(0.405501\pi\) | |||||||
\(558\) | 244.950 | + | 589.174i | 0.438979 | + | 1.05587i | ||||
\(559\) | 626.650 | 1.12102 | ||||||||
\(560\) | −362.768 | − | 320.317i | −0.647800 | − | 0.571994i | ||||
\(561\) | −8.18103 | + | 126.086i | −0.0145829 | + | 0.224753i | ||||
\(562\) | −854.705 | − | 493.464i | −1.52083 | − | 0.878050i | ||||
\(563\) | 353.382 | − | 612.075i | 0.627676 | − | 1.08717i | −0.360341 | − | 0.932821i | \(-0.617340\pi\) |
0.988017 | − | 0.154346i | \(-0.0493270\pi\) | |||||||
\(564\) | 813.783 | − | 1219.64i | 1.44288 | − | 2.16249i | ||||
\(565\) | −435.047 | + | 492.703i | −0.769994 | + | 0.872041i | ||||
\(566\) | 1813.39i | 3.20387i | ||||||||
\(567\) | 53.2962 | − | 201.014i | 0.0939967 | − | 0.354521i | ||||
\(568\) | − | 1499.60i | − | 2.64015i | ||||||
\(569\) | −485.178 | + | 280.118i | −0.852686 | + | 0.492299i | −0.861556 | − | 0.507662i | \(-0.830510\pi\) |
0.00887015 | + | 0.999961i | \(0.497177\pi\) | |||||||
\(570\) | −382.612 | − | 103.639i | −0.671248 | − | 0.181824i | ||||
\(571\) | 105.346 | − | 182.465i | 0.184494 | − | 0.319553i | −0.758912 | − | 0.651193i | \(-0.774269\pi\) |
0.943406 | + | 0.331640i | \(0.107602\pi\) | |||||||
\(572\) | −568.965 | + | 985.475i | −0.994693 | + | 1.72286i | ||||
\(573\) | 27.4982 | − | 423.804i | 0.0479899 | − | 0.739623i | ||||
\(574\) | −163.823 | − | 283.750i | −0.285406 | − | 0.494338i | ||||
\(575\) | 10.1783 | − | 7.70122i | 0.0177014 | − | 0.0133934i | ||||
\(576\) | −198.423 | − | 477.263i | −0.344485 | − | 0.828582i | ||||
\(577\) | 502.258i | 0.870464i | 0.900318 | + | 0.435232i | \(0.143334\pi\) | ||||
−0.900318 | + | 0.435232i | \(0.856666\pi\) | |||||||
\(578\) | 498.968 | + | 864.237i | 0.863266 | + | 1.49522i | ||||
\(579\) | −595.570 | + | 294.189i | −1.02862 | + | 0.508098i | ||||
\(580\) | −290.844 | + | 1436.75i | −0.501454 | + | 2.47715i | ||||
\(581\) | −133.436 | − | 77.0395i | −0.229667 | − | 0.132598i | ||||
\(582\) | 1269.12 | − | 626.899i | 2.18063 | − | 1.07715i | ||||
\(583\) | 737.533 | − | 425.815i | 1.26507 | − | 0.730386i | ||||
\(584\) | − | 625.411i | − | 1.07091i | ||||||
\(585\) | 175.557 | − | 513.678i | 0.300098 | − | 0.878082i | ||||
\(586\) | 1187.84 | 2.02703 | ||||||||
\(587\) | −204.886 | − | 354.873i | −0.349040 | − | 0.604554i | 0.637040 | − | 0.770831i | \(-0.280159\pi\) |
−0.986079 | + | 0.166277i | \(0.946825\pi\) | |||||||
\(588\) | 1218.29 | + | 79.0482i | 2.07193 | + | 0.134436i | ||||
\(589\) | 68.9006 | − | 119.339i | 0.116979 | − | 0.202613i | ||||
\(590\) | −387.599 | + | 1914.72i | −0.656948 | + | 3.24528i | ||||
\(591\) | −47.3587 | + | 70.9782i | −0.0801332 | + | 0.120098i | ||||
\(592\) | 43.0476 | − | 24.8535i | 0.0727155 | − | 0.0419823i | ||||
\(593\) | 944.139 | 1.59214 | 0.796070 | − | 0.605204i | \(-0.206908\pi\) | ||||
0.796070 | + | 0.605204i | \(0.206908\pi\) | |||||||
\(594\) | 737.057 | + | 643.818i | 1.24084 | + | 1.08387i | ||||
\(595\) | −52.1409 | + | 17.5029i | −0.0876317 | + | 0.0294167i | ||||
\(596\) | −396.877 | + | 229.137i | −0.665902 | + | 0.384458i | ||||
\(597\) | −256.214 | + | 383.997i | −0.429169 | + | 0.643210i | ||||
\(598\) | 19.6667 | + | 11.3546i | 0.0328875 | + | 0.0189876i | ||||
\(599\) | 461.021 | + | 266.171i | 0.769652 | + | 0.444359i | 0.832750 | − | 0.553649i | \(-0.186765\pi\) |
−0.0630986 | + | 0.998007i | \(0.520098\pi\) | |||||||
\(600\) | −1291.97 | + | 851.896i | −2.15329 | + | 1.41983i | ||||
\(601\) | −257.783 | − | 446.493i | −0.428923 | − | 0.742917i | 0.567855 | − | 0.823129i | \(-0.307774\pi\) |
−0.996778 | + | 0.0802121i | \(0.974440\pi\) | |||||||
\(602\) | −491.764 | −0.816883 | ||||||||
\(603\) | −90.7785 | + | 696.597i | −0.150545 | + | 1.15522i | ||||
\(604\) | 532.496 | 0.881615 | ||||||||
\(605\) | 80.6481 | − | 91.3364i | 0.133303 | − | 0.150969i | ||||
\(606\) | 853.694 | − | 421.692i | 1.40874 | − | 0.695862i | ||||
\(607\) | 148.223 | + | 85.5764i | 0.244189 | + | 0.140983i | 0.617101 | − | 0.786884i | \(-0.288307\pi\) |
−0.372912 | + | 0.927867i | \(0.621640\pi\) | |||||||
\(608\) | −202.366 | + | 350.509i | −0.332839 | + | 0.576494i | ||||
\(609\) | 104.217 | + | 210.982i | 0.171128 | + | 0.346440i | ||||
\(610\) | 382.191 | − | 432.843i | 0.626543 | − | 0.709578i | ||||
\(611\) | − | 614.400i | − | 1.00557i | ||||||
\(612\) | −366.926 | − | 47.8167i | −0.599552 | − | 0.0781319i | ||||
\(613\) | − | 875.826i | − | 1.42875i | −0.699761 | − | 0.714377i | \(-0.746710\pi\) | ||
0.699761 | − | 0.714377i | \(-0.253290\pi\) | |||||||
\(614\) | 1360.43 | − | 785.447i | 2.21569 | − | 1.27923i | ||||
\(615\) | −501.831 | + | 133.000i | −0.815985 | + | 0.216260i | ||||
\(616\) | 260.378 | − | 450.988i | 0.422692 | − | 0.732124i | ||||
\(617\) | 565.874 | − | 980.122i | 0.917137 | − | 1.58853i | 0.113396 | − | 0.993550i | \(-0.463827\pi\) |
0.803742 | − | 0.594978i | \(-0.202839\pi\) | |||||||
\(618\) | 376.192 | + | 251.006i | 0.608725 | + | 0.406159i | ||||
\(619\) | −260.187 | − | 450.658i | −0.420335 | − | 0.728042i | 0.575637 | − | 0.817705i | \(-0.304754\pi\) |
−0.995972 | + | 0.0896637i | \(0.971421\pi\) | |||||||
\(620\) | −293.578 | − | 874.563i | −0.473513 | − | 1.41058i | ||||
\(621\) | 9.06836 | − | 10.3817i | 0.0146028 | − | 0.0167176i | ||||
\(622\) | 4.30664i | 0.00692386i | ||||||||
\(623\) | −91.5266 | − | 158.529i | −0.146913 | − | 0.254460i | ||||
\(624\) | −1134.90 | − | 757.241i | −1.81875 | − | 1.21353i | ||||
\(625\) | 435.921 | + | 447.882i | 0.697474 | + | 0.716611i | ||||
\(626\) | 833.284 | + | 481.097i | 1.33112 | + | 0.768525i | ||||
\(627\) | 13.6849 | − | 210.913i | 0.0218261 | − | 0.336384i | ||||
\(628\) | 92.0138 | − | 53.1242i | 0.146519 | − | 0.0845926i | ||||
\(629\) | − | 5.64918i | − | 0.00898121i | ||||||
\(630\) | −137.768 | + | 403.109i | −0.218680 | + | 0.639856i | ||||
\(631\) | −607.475 | −0.962718 | −0.481359 | − | 0.876523i | \(-0.659857\pi\) | ||||
−0.481359 | + | 0.876523i | \(0.659857\pi\) | |||||||
\(632\) | −1189.34 | − | 2060.00i | −1.88187 | − | 3.25949i | ||||
\(633\) | −239.390 | − | 484.633i | −0.378184 | − | 0.765614i | ||||
\(634\) | 241.582 | − | 418.433i | 0.381044 | − | 0.659988i | ||||
\(635\) | 100.345 | − | 495.697i | 0.158023 | − | 0.780626i | ||||
\(636\) | 1104.56 | + | 2236.12i | 1.73673 | + | 3.51591i | ||||
\(637\) | 443.047 | − | 255.794i | 0.695522 | − | 0.401560i | ||||
\(638\) | −1107.40 | −1.73574 | ||||||||
\(639\) | −603.967 | + | 251.101i | −0.945176 | + | 0.392959i | ||||
\(640\) | −22.4799 | − | 66.9670i | −0.0351248 | − | 0.104636i | ||||
\(641\) | 161.252 | − | 93.0990i | 0.251564 | − | 0.145240i | −0.368916 | − | 0.929463i | \(-0.620271\pi\) |
0.620480 | + | 0.784222i | \(0.286938\pi\) | |||||||
\(642\) | −18.3270 | − | 1.18913i | −0.0285467 | − | 0.00185223i | ||||
\(643\) | 690.674 | + | 398.761i | 1.07414 | + | 0.620157i | 0.929311 | − | 0.369299i | \(-0.120402\pi\) |
0.144833 | + | 0.989456i | \(0.453736\pi\) | |||||||
\(644\) | −10.8929 | − | 6.28901i | −0.0169144 | − | 0.00976554i | ||||
\(645\) | −203.723 | + | 752.097i | −0.315850 | + | 1.16604i | ||||
\(646\) | 56.6127 | + | 98.0561i | 0.0876357 | + | 0.151790i | ||||
\(647\) | −849.489 | −1.31297 | −0.656483 | − | 0.754341i | \(-0.727957\pi\) | ||||
−0.656483 | + | 0.754341i | \(0.727957\pi\) | |||||||
\(648\) | −1178.72 | + | 1184.93i | −1.81901 | + | 1.82859i | ||||
\(649\) | −1041.61 | −1.60495 | ||||||||
\(650\) | −432.493 | + | 1024.47i | −0.665374 | + | 1.57611i | ||||
\(651\) | −123.188 | − | 82.1944i | −0.189228 | − | 0.126259i | ||||
\(652\) | −1796.95 | − | 1037.47i | −2.75607 | − | 1.59122i | ||||
\(653\) | −520.594 | + | 901.696i | −0.797235 | + | 1.38085i | 0.124175 | + | 0.992260i | \(0.460371\pi\) |
−0.921410 | + | 0.388591i | \(0.872962\pi\) | |||||||
\(654\) | −1640.79 | − | 106.461i | −2.50885 | − | 0.162785i | ||||
\(655\) | 321.569 | + | 283.939i | 0.490945 | + | 0.433494i | ||||
\(656\) | 1304.79i | 1.98901i | ||||||||
\(657\) | −251.885 | + | 104.722i | −0.383387 | + | 0.159394i | ||||
\(658\) | 482.151i | 0.732752i | ||||||||
\(659\) | 556.318 | − | 321.190i | 0.844185 | − | 0.487390i | −0.0144997 | − | 0.999895i | \(-0.504616\pi\) |
0.858685 | + | 0.512505i | \(0.171282\pi\) | |||||||
\(660\) | −997.786 | − | 1003.24i | −1.51180 | − | 1.52006i | ||||
\(661\) | 394.759 | − | 683.742i | 0.597214 | − | 1.03441i | −0.396016 | − | 0.918244i | \(-0.629608\pi\) |
0.993230 | − | 0.116162i | \(-0.0370591\pi\) | |||||||
\(662\) | −356.714 | + | 617.847i | −0.538843 | + | 0.933304i | ||||
\(663\) | −139.021 | + | 68.6710i | −0.209684 | + | 0.103576i | ||||
\(664\) | 619.163 | + | 1072.42i | 0.932474 | + | 1.61509i | ||||
\(665\) | 87.2194 | − | 29.2783i | 0.131157 | − | 0.0440275i | ||||
\(666\) | −34.7485 | − | 26.5910i | −0.0521749 | − | 0.0399265i | ||||
\(667\) | 15.5980i | 0.0233854i | ||||||||
\(668\) | −297.221 | − | 514.802i | −0.444941 | − | 0.770661i | ||||
\(669\) | 41.8408 | − | 644.852i | 0.0625422 | − | 0.963904i | ||||
\(670\) | 285.515 | − | 1410.43i | 0.426142 | − | 2.10511i | ||||
\(671\) | 266.631 | + | 153.939i | 0.397363 | + | 0.229418i | ||||
\(672\) | 361.811 | + | 241.411i | 0.538410 | + | 0.359243i | ||||
\(673\) | −879.824 | + | 507.967i | −1.30732 | + | 0.754780i | −0.981648 | − | 0.190704i | \(-0.938923\pi\) |
−0.325669 | + | 0.945484i | \(0.605590\pi\) | |||||||
\(674\) | 1709.40i | 2.53621i | ||||||||
\(675\) | 559.437 | + | 377.698i | 0.828795 | + | 0.559552i | ||||
\(676\) | 225.279 | 0.333253 | ||||||||
\(677\) | 371.811 | + | 643.996i | 0.549204 | + | 0.951249i | 0.998329 | + | 0.0577802i | \(0.0184023\pi\) |
−0.449126 | + | 0.893469i | \(0.648264\pi\) | |||||||
\(678\) | 807.090 | − | 1209.61i | 1.19040 | − | 1.78409i | ||||
\(679\) | −164.267 | + | 284.518i | −0.241924 | + | 0.419025i | ||||
\(680\) | 433.246 | + | 87.7028i | 0.637127 | + | 0.128975i | ||||
\(681\) | −150.930 | − | 9.79301i | −0.221631 | − | 0.0143803i | ||||
\(682\) | 603.546 | − | 348.458i | 0.884965 | − | 0.510935i | ||||
\(683\) | −152.482 | −0.223254 | −0.111627 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111627 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(684\) | 613.780 | + | 79.9861i | 0.897339 | + | 0.116939i | ||||
\(685\) | 110.946 | + | 330.507i | 0.161965 | + | 0.482491i | ||||
\(686\) | −749.403 | + | 432.668i | −1.09242 | + | 0.630711i | ||||
\(687\) | 8.19373 | + | 16.5878i | 0.0119268 | + | 0.0241452i | ||||
\(688\) | 1695.99 | + | 979.179i | 2.46510 | + | 1.42322i | ||||
\(689\) | 905.087 | + | 522.552i | 1.31362 | + | 0.758422i | ||||
\(690\) | −20.0213 | + | 19.9124i | −0.0290163 | + | 0.0288585i | ||||
\(691\) | −388.586 | − | 673.050i | −0.562353 | − | 0.974023i | −0.997291 | − | 0.0735628i | \(-0.976563\pi\) |
0.434938 | − | 0.900460i | \(-0.356770\pi\) | |||||||
\(692\) | 3199.99 | 4.62426 | ||||||||
\(693\) | −225.235 | − | 29.3520i | −0.325015 | − | 0.0423550i | ||||
\(694\) | 35.8355 | 0.0516361 | ||||||||
\(695\) | 459.737 | − | 520.666i | 0.661492 | − | 0.749160i | ||||
\(696\) | 122.454 | − | 1887.27i | 0.175940 | − | 2.71160i | ||||
\(697\) | 128.422 | + | 74.1444i | 0.184249 | + | 0.106376i | ||||
\(698\) | 90.9573 | − | 157.543i | 0.130311 | − | 0.225706i | ||||
\(699\) | 87.4722 | − | 131.098i | 0.125139 | − | 0.187550i | ||||
\(700\) | 239.547 | − | 567.427i | 0.342209 | − | 0.810610i | ||||
\(701\) | − | 461.657i | − | 0.658569i | −0.944231 | − | 0.329284i | \(-0.893192\pi\) | ||
0.944231 | − | 0.329284i | \(-0.106808\pi\) | |||||||
\(702\) | −231.980 | + | 1178.36i | −0.330456 | + | 1.67858i | ||||
\(703\) | 9.44975i | 0.0134420i | ||||||||
\(704\) | −488.906 | + | 282.270i | −0.694468 | + | 0.400952i | ||||
\(705\) | 737.396 | + | 199.741i | 1.04595 | + | 0.283321i | ||||
\(706\) | −175.813 | + | 304.517i | −0.249027 | + | 0.431327i | ||||
\(707\) | −110.496 | + | 191.385i | −0.156289 | + | 0.270701i | ||||
\(708\) | 197.510 | − | 3044.03i | 0.278969 | − | 4.29948i | ||||
\(709\) | 179.227 | + | 310.431i | 0.252789 | + | 0.437843i | 0.964293 | − | 0.264839i | \(-0.0853189\pi\) |
−0.711504 | + | 0.702682i | \(0.751986\pi\) | |||||||
\(710\) | 1270.23 | − | 426.397i | 1.78905 | − | 0.600560i | ||||
\(711\) | −630.519 | + | 823.945i | −0.886805 | + | 1.15885i | ||||
\(712\) | 1471.19i | 2.06628i | ||||||||
\(713\) | −4.90812 | − | 8.50112i | −0.00688376 | − | 0.0119230i | ||||
\(714\) | 109.097 | − | 53.8896i | 0.152796 | − | 0.0754756i | ||||
\(715\) | −581.130 | − | 117.639i | −0.812770 | − | 0.164530i | ||||
\(716\) | −1608.24 | − | 928.515i | −2.24614 | − | 1.29681i | ||||
\(717\) | −262.476 | + | 129.653i | −0.366076 | + | 0.180827i | ||||
\(718\) | −1722.08 | + | 994.245i | −2.39845 | + | 1.38474i | ||||
\(719\) | 283.414i | 0.394178i | 0.980386 | + | 0.197089i | \(0.0631488\pi\) | ||||
−0.980386 | + | 0.197089i | \(0.936851\pi\) | |||||||
\(720\) | 1277.79 | − | 1115.92i | 1.77470 | − | 1.54989i | ||||
\(721\) | −104.964 | −0.145580 | ||||||||
\(722\) | 570.854 | + | 988.748i | 0.790656 | + | 1.36946i | ||||
\(723\) | −427.290 | − | 27.7244i | −0.590995 | − | 0.0383463i | ||||
\(724\) | −1170.07 | + | 2026.61i | −1.61611 | + | 2.79919i | ||||
\(725\) | −757.925 | + | 94.5702i | −1.04541 | + | 0.130442i | ||||
\(726\) | −149.617 | + | 224.236i | −0.206084 | + | 0.308865i | ||||
\(727\) | −134.545 | + | 77.6796i | −0.185069 | + | 0.106850i | −0.589672 | − | 0.807643i | \(-0.700743\pi\) |
0.404603 | + | 0.914492i | \(0.367410\pi\) | |||||||
\(728\) | 639.063 | 0.877833 | ||||||||
\(729\) | 674.602 | + | 276.322i | 0.925380 | + | 0.379042i | ||||
\(730\) | 529.750 | − | 177.830i | 0.725685 | − | 0.243602i | ||||
\(731\) | 192.748 | − | 111.283i | 0.263677 | − | 0.152234i | ||||
\(732\) | −500.433 | + | 750.016i | −0.683652 | + | 1.02461i | ||||
\(733\) | −90.8735 | − | 52.4658i | −0.123975 | − | 0.0715768i | 0.436730 | − | 0.899593i | \(-0.356136\pi\) |
−0.560705 | + | 0.828016i | \(0.689470\pi\) | |||||||
\(734\) | −967.845 | − | 558.786i | −1.31859 | − | 0.761288i | ||||
\(735\) | 162.966 | + | 614.898i | 0.221722 | + | 0.836596i | ||||
\(736\) | 14.4155 | + | 24.9684i | 0.0195863 | + | 0.0339245i | ||||
\(737\) | 767.279 | 1.04108 | ||||||||
\(738\) | 1060.56 | − | 440.929i | 1.43707 | − | 0.597465i | ||||
\(739\) | −627.375 | −0.848951 | −0.424476 | − | 0.905439i | \(-0.639542\pi\) | ||||
−0.424476 | + | 0.905439i | \(0.639542\pi\) | |||||||
\(740\) | 47.4217 | + | 41.8724i | 0.0640834 | + | 0.0565843i | ||||
\(741\) | 232.549 | − | 114.870i | 0.313831 | − | 0.155021i | ||||
\(742\) | −710.268 | − | 410.073i | −0.957234 | − | 0.552659i | ||||
\(743\) | −193.295 | + | 334.797i | −0.260155 | + | 0.450602i | −0.966283 | − | 0.257483i | \(-0.917107\pi\) |
0.706128 | + | 0.708084i | \(0.250440\pi\) | |||||||
\(744\) | 527.115 | + | 1067.12i | 0.708488 | + | 1.43430i | ||||
\(745\) | −178.994 | − | 158.048i | −0.240260 | − | 0.212144i | ||||
\(746\) | − | 481.798i | − | 0.645842i | ||||||
\(747\) | 328.244 | − | 428.940i | 0.439416 | − | 0.574217i | ||||
\(748\) | 404.157i | 0.540317i | ||||||||
\(749\) | 3.69147 | − | 2.13127i | 0.00492853 | − | 0.00284549i | ||||
\(750\) | −1088.95 | − | 852.127i | −1.45194 | − | 1.13617i | ||||
\(751\) | −452.601 | + | 783.928i | −0.602665 | + | 1.04385i | 0.389751 | + | 0.920920i | \(0.372561\pi\) |
−0.992416 | + | 0.122926i | \(0.960772\pi\) | |||||||
\(752\) | 960.038 | − | 1662.83i | 1.27665 | − | 2.21122i | ||||
\(753\) | −635.433 | − | 423.979i | −0.843868 | − | 0.563054i | ||||
\(754\) | −679.491 | − | 1176.91i | −0.901182 | − | 1.56089i | ||||
\(755\) | 88.2962 | + | 263.032i | 0.116949 | + | 0.348387i | ||||
\(756\) | 128.488 | − | 652.665i | 0.169957 | − | 0.863313i | ||||
\(757\) | − | 332.222i | − | 0.438867i | −0.975627 | − | 0.219433i | \(-0.929579\pi\) | ||
0.975627 | − | 0.219433i | \(-0.0704209\pi\) | |||||||
\(758\) | −1005.04 | − | 1740.78i | −1.32591 | − | 2.29655i | ||||
\(759\) | −12.5240 | − | 8.35641i | −0.0165007 | − | 0.0110098i | ||||
\(760\) | −724.719 | − | 146.706i | −0.953578 | − | 0.193034i | ||||
\(761\) | −396.726 | − | 229.050i | −0.521322 | − | 0.300986i | 0.216153 | − | 0.976359i | \(-0.430649\pi\) |
−0.737475 | + | 0.675374i | \(0.763982\pi\) | |||||||
\(762\) | −72.4472 | + | 1116.56i | −0.0950751 | + | 1.46530i | ||||
\(763\) | 330.492 | − | 190.810i | 0.433149 | − | 0.250079i | ||||
\(764\) | − | 1358.46i | − | 1.77809i | ||||||
\(765\) | −37.2225 | − | 189.176i | −0.0486568 | − | 0.247289i | ||||
\(766\) | −4.59618 | −0.00600023 | ||||||||
\(767\) | −639.126 | − | 1107.00i | −0.833280 | − | 1.44328i | ||||
\(768\) | 374.425 | + | 758.004i | 0.487532 | + | 0.986984i | ||||
\(769\) | 458.196 | − | 793.618i | 0.595833 | − | 1.03201i | −0.397595 | − | 0.917561i | \(-0.630155\pi\) |
0.993429 | − | 0.114453i | \(-0.0365115\pi\) | |||||||
\(770\) | 456.042 | + | 92.3174i | 0.592263 | + | 0.119893i | ||||
\(771\) | −189.644 | − | 383.925i | −0.245972 | − | 0.497957i | ||||
\(772\) | −1840.11 | + | 1062.39i | −2.38356 | + | 1.37615i | ||||
\(773\) | −1186.06 | −1.53436 | −0.767178 | − | 0.641434i | \(-0.778340\pi\) | ||||
−0.767178 | + | 0.641434i | \(0.778340\pi\) | |||||||
\(774\) | 222.767 | − | 1709.42i | 0.287813 | − | 2.20856i | ||||
\(775\) | 383.321 | − | 290.033i | 0.494607 | − | 0.374236i | ||||
\(776\) | 2286.66 | − | 1320.20i | 2.94673 | − | 1.70129i | ||||
\(777\) | 10.1341 | + | 0.657544i | 0.0130426 | + | 0.000846261i | ||||
\(778\) | 1272.12 | + | 734.456i | 1.63511 | + | 0.944031i | ||||
\(779\) | −214.820 | − | 124.026i | −0.275763 | − | 0.159212i | ||||
\(780\) | 453.984 | − | 1676.00i | 0.582031 | − | 2.14872i | ||||
\(781\) | 357.207 | + | 618.701i | 0.457371 | + | 0.792190i | ||||
\(782\) | 8.06559 | 0.0103141 | ||||||||
\(783\) | −780.605 | + | 266.695i | −0.996942 | + | 0.340607i | ||||
\(784\) | 1598.77 | 2.03925 | ||||||||
\(785\) | 41.4986 | + | 36.6424i | 0.0528645 | + | 0.0466783i | ||||
\(786\) | −789.470 | − | 526.757i | −1.00441 | − | 0.670175i | ||||
\(787\) | 764.249 | + | 441.240i | 0.971092 | + | 0.560660i | 0.899569 | − | 0.436779i | \(-0.143881\pi\) |
0.0715229 | + | 0.997439i | \(0.477214\pi\) | |||||||
\(788\) | −136.467 | + | 236.368i | −0.173181 | + | 0.299959i | ||||
\(789\) | 755.817 | + | 49.0406i | 0.957943 | + | 0.0621554i | ||||
\(790\) | 1406.73 | − | 1593.16i | 1.78067 | − | 2.01666i | ||||
\(791\) | 337.501i | 0.426677i | ||||||||
\(792\) | 1449.73 | + | 1109.40i | 1.83047 | + | 1.40076i | ||||
\(793\) | 377.823i | 0.476448i | ||||||||
\(794\) | −2190.58 | + | 1264.73i | −2.75892 | + | 1.59286i | ||||
\(795\) | −921.404 | + | 916.393i | −1.15900 | + | 1.15270i | ||||
\(796\) | −738.295 | + | 1278.76i | −0.927507 | + | 1.60649i | ||||
\(797\) | −71.9016 | + | 124.537i | −0.0902153 | + | 0.156258i | −0.907602 | − | 0.419832i | \(-0.862089\pi\) |
0.817386 | + | 0.576090i | \(0.195422\pi\) | |||||||
\(798\) | −182.493 | + | 90.1446i | −0.228688 | + | 0.112963i | ||||
\(799\) | −109.108 | − | 188.980i | −0.136556 | − | 0.236521i | ||||
\(800\) | −1125.84 | + | 851.848i | −1.40730 | + | 1.06481i | ||||
\(801\) | 592.524 | − | 246.343i | 0.739731 | − | 0.307545i | ||||
\(802\) | − | 191.261i | − | 0.238480i | ||||||
\(803\) | 148.974 | + | 258.030i | 0.185521 | + | 0.321332i | ||||
\(804\) | −145.491 | + | 2242.31i | −0.180958 | + | 2.78894i | ||||
\(805\) | 1.30032 | − | 6.42348i | 0.00161530 | − | 0.00797948i | ||||
\(806\) | 740.661 | + | 427.621i | 0.918934 | + | 0.530547i | ||||
\(807\) | 969.932 | + | 647.167i | 1.20190 | + | 0.801942i | ||||
\(808\) | 1538.15 | − | 888.054i | 1.90366 | − | 1.09908i | ||||
\(809\) | 52.3078i | 0.0646574i | 0.999477 | + | 0.0323287i | \(0.0102923\pi\) | ||||
−0.999477 | + | 0.0323287i | \(0.989708\pi\) | |||||||
\(810\) | −1338.84 | − | 661.505i | −1.65289 | − | 0.816673i | ||||
\(811\) | 1518.65 | 1.87256 | 0.936281 | − | 0.351253i | \(-0.114244\pi\) | ||||
0.936281 | + | 0.351253i | \(0.114244\pi\) | |||||||
\(812\) | 376.352 | + | 651.861i | 0.463488 | + | 0.802785i | ||||
\(813\) | 271.828 | − | 407.398i | 0.334352 | − | 0.501105i | ||||
\(814\) | −23.8956 | + | 41.3883i | −0.0293557 | + | 0.0508456i | ||||
\(815\) | 214.508 | − | 1059.66i | 0.263200 | − | 1.30019i | ||||
\(816\) | −483.553 | − | 31.3750i | −0.592590 | − | 0.0384498i | ||||
\(817\) | −322.422 | + | 186.151i | −0.394642 | + | 0.227847i | ||||
\(818\) | −1000.35 | −1.22292 | ||||||||
\(819\) | −107.008 | − | 257.383i | −0.130657 | − | 0.314266i | ||||
\(820\) | −1574.28 | + | 528.462i | −1.91985 | + | 0.644466i | ||||
\(821\) | 950.059 | − | 548.517i | 1.15720 | − | 0.668108i | 0.206567 | − | 0.978432i | \(-0.433771\pi\) |
0.950631 | + | 0.310324i | \(0.100438\pi\) | |||||||
\(822\) | −341.591 | − | 691.534i | −0.415561 | − | 0.841282i | ||||
\(823\) | −828.873 | − | 478.550i | −1.00714 | − | 0.581470i | −0.0967841 | − | 0.995305i | \(-0.530856\pi\) |
−0.910352 | + | 0.413835i | \(0.864189\pi\) | |||||||
\(824\) | 730.568 | + | 421.793i | 0.886611 | + | 0.511885i | ||||
\(825\) | 330.114 | − | 659.221i | 0.400139 | − | 0.799056i | ||||
\(826\) | 501.554 | + | 868.717i | 0.607208 | + | 1.05172i | ||||
\(827\) | 171.626 | 0.207529 | 0.103764 | − | 0.994602i | \(-0.466911\pi\) | ||||
0.103764 | + | 0.994602i | \(0.466911\pi\) | |||||||
\(828\) | 26.7957 | − | 35.0159i | 0.0323620 | − | 0.0422898i | ||||
\(829\) | 203.896 | 0.245954 | 0.122977 | − | 0.992410i | \(-0.460756\pi\) | ||||
0.122977 | + | 0.992410i | \(0.460756\pi\) | |||||||
\(830\) | −732.334 | + | 829.390i | −0.882331 | + | 0.999265i | ||||
\(831\) | −93.9800 | + | 1448.42i | −0.113093 | + | 1.74299i | ||||
\(832\) | −599.976 | − | 346.397i | −0.721126 | − | 0.416342i | ||||
\(833\) | 90.8499 | − | 157.357i | 0.109063 | − | 0.188904i | ||||
\(834\) | −852.895 | + | 1278.26i | −1.02266 | + | 1.53269i | ||||
\(835\) | 205.008 | − | 232.178i | 0.245519 | − | 0.278057i | ||||
\(836\) | − | 676.059i | − | 0.808683i | ||||||
\(837\) | 341.520 | − | 390.979i | 0.408029 | − | 0.467120i | ||||
\(838\) | − | 101.958i | − | 0.121668i | ||||||
\(839\) | −1348.10 | + | 778.323i | −1.60679 | + | 0.927680i | −0.616705 | + | 0.787194i | \(0.711533\pi\) |
−0.990083 | + | 0.140486i | \(0.955134\pi\) | |||||||
\(840\) | −207.759 | + | 766.995i | −0.247332 | + | 0.913090i | ||||
\(841\) | 46.2156 | − | 80.0477i | 0.0549531 | − | 0.0951816i | ||||
\(842\) | 806.087 | − | 1396.18i | 0.957347 | − | 1.65817i | ||||
\(843\) | −51.9910 | + | 801.289i | −0.0616738 | + | 0.950520i | ||||
\(844\) | −864.495 | − | 1497.35i | −1.02428 | − | 1.77411i | ||||
\(845\) | 37.3549 | + | 111.279i | 0.0442069 | + | 0.131692i | ||||
\(846\) | −1676.01 | − | 218.413i | −1.98110 | − | 0.258171i | ||||
\(847\) | − | 62.5654i | − | 0.0738670i | ||||||
\(848\) | 1633.04 | + | 2828.51i | 1.92576 | + | 3.33551i | ||||
\(849\) | 1322.81 | − | 653.416i | 1.55808 | − | 0.769631i | ||||
\(850\) | 48.9013 | + | 391.916i | 0.0575310 | + | 0.461077i | ||||
\(851\) | 0.582966 | + | 0.336576i | 0.000685037 | + | 0.000395506i | ||||
\(852\) | −1875.83 | + | 926.589i | −2.20168 | + | 1.08755i | ||||
\(853\) | 488.377 | − | 281.964i | 0.572540 | − | 0.330556i | −0.185623 | − | 0.982621i | \(-0.559430\pi\) |
0.758163 | + | 0.652065i | \(0.226097\pi\) | |||||||
\(854\) | − | 296.497i | − | 0.347186i | ||||||
\(855\) | 62.2644 | + | 316.447i | 0.0728239 | + | 0.370113i | ||||
\(856\) | −34.2579 | −0.0400209 | ||||||||
\(857\) | 476.953 | + | 826.107i | 0.556538 | + | 0.963952i | 0.997782 | + | 0.0665649i | \(0.0212039\pi\) |
−0.441244 | + | 0.897387i | \(0.645463\pi\) | |||||||
\(858\) | 1309.00 | + | 84.9334i | 1.52564 | + | 0.0989900i | ||||
\(859\) | −422.728 | + | 732.186i | −0.492116 | + | 0.852371i | −0.999959 | − | 0.00907936i | \(-0.997110\pi\) |
0.507842 | + | 0.861450i | \(0.330443\pi\) | |||||||
\(860\) | −494.511 | + | 2442.86i | −0.575013 | + | 2.84053i | ||||
\(861\) | −147.956 | + | 221.747i | −0.171842 | + | 0.257546i | ||||
\(862\) | 173.587 | − | 100.221i | 0.201377 | − | 0.116265i | ||||
\(863\) | 1109.42 | 1.28554 | 0.642768 | − | 0.766061i | \(-0.277786\pi\) | ||||
0.642768 | + | 0.766061i | \(0.277786\pi\) | |||||||
\(864\) | −1003.07 | + | 1148.34i | −1.16096 | + | 1.32909i | ||||
\(865\) | 530.609 | + | 1580.67i | 0.613420 | + | 1.82737i | ||||
\(866\) | 1681.02 | − | 970.538i | 1.94113 | − | 1.12071i | ||||
\(867\) | 450.640 | − | 675.390i | 0.519770 | − | 0.778997i | ||||
\(868\) | −410.233 | − | 236.848i | −0.472618 | − | 0.272866i | ||||
\(869\) | 981.388 | + | 566.605i | 1.12933 | + | 0.652019i | ||||
\(870\) | 1633.42 | − | 432.903i | 1.87749 | − | 0.497590i | ||||
\(871\) | 470.796 | + | 815.442i | 0.540523 | + | 0.936214i | ||||
\(872\) | −3067.06 | −3.51727 | ||||||||
\(873\) | −914.604 | − | 699.894i | −1.04766 | − | 0.801712i | ||||
\(874\) | −13.4918 | −0.0154369 | ||||||||
\(875\) | 320.008 | + | 24.2385i | 0.365723 | + | 0.0277011i | ||||
\(876\) | −782.318 | + | 386.435i | −0.893058 | + | 0.441136i | ||||
\(877\) | −878.724 | − | 507.331i | −1.00197 | − | 0.578485i | −0.0931364 | − | 0.995653i | \(-0.529689\pi\) |
−0.908829 | + | 0.417168i | \(0.863023\pi\) | |||||||
\(878\) | 767.411 | − | 1329.19i | 0.874044 | − | 1.51389i | ||||
\(879\) | −428.013 | − | 866.491i | −0.486932 | − | 0.985769i | ||||
\(880\) | −1388.97 | − | 1226.43i | −1.57838 | − | 1.39368i | ||||
\(881\) | 1226.86i | 1.39257i | 0.717764 | + | 0.696287i | \(0.245166\pi\) | ||||
−0.717764 | + | 0.696287i | \(0.754834\pi\) | |||||||
\(882\) | −540.275 | − | 1299.51i | −0.612556 | − | 1.47337i | ||||
\(883\) | − | 659.407i | − | 0.746780i | −0.927674 | − | 0.373390i | \(-0.878195\pi\) | ||
0.927674 | − | 0.373390i | \(-0.121805\pi\) | |||||||
\(884\) | −429.526 | + | 247.987i | −0.485889 | + | 0.280528i | ||||
\(885\) | 1536.39 | − | 407.186i | 1.73603 | − | 0.460098i | ||||
\(886\) | 787.537 | − | 1364.05i | 0.888868 | − | 1.53956i | ||||
\(887\) | −385.984 | + | 668.543i | −0.435156 | + | 0.753713i | −0.997308 | − | 0.0733209i | \(-0.976640\pi\) |
0.562152 | + | 0.827034i | \(0.309974\pi\) | |||||||
\(888\) | −67.8932 | − | 45.3003i | −0.0764563 | − | 0.0510139i | ||||
\(889\) | −129.846 | − | 224.901i | −0.146059 | − | 0.252982i | ||||
\(890\) | −1246.16 | + | 418.319i | −1.40018 | + | 0.470021i | ||||
\(891\) | 204.061 | − | 769.645i | 0.229025 | − | 0.863799i | ||||
\(892\) | − | 2067.01i | − | 2.31727i | ||||||
\(893\) | 182.512 | + | 316.120i | 0.204381 | + | 0.353998i | ||||
\(894\) | 439.439 | + | 293.207i | 0.491543 | + | 0.327972i | ||||
\(895\) | 191.980 | − | 948.369i | 0.214503 | − | 1.05963i | ||||
\(896\) | −31.4123 | − | 18.1359i | −0.0350584 | − | 0.0202410i | ||||
\(897\) | 1.19631 | − | 18.4376i | 0.00133368 | − | 0.0205548i | ||||
\(898\) | −755.945 | + | 436.445i | −0.841810 | + | 0.486019i | ||||
\(899\) | 587.432i | 0.653428i | ||||||||
\(900\) | 1863.92 | + | 1089.73i | 2.07102 | + | 1.21081i | ||||
\(901\) | 371.189 | 0.411974 | ||||||||
\(902\) | −627.249 | − | 1086.43i | −0.695398 | − | 1.20447i | ||||
\(903\) | 177.197 | + | 358.725i | 0.196231 | + | 0.397260i | ||||
\(904\) | 1356.24 | − | 2349.08i | 1.50027 | − | 2.59854i | ||||
\(905\) | −1195.09 | − | 241.923i | −1.32054 | − | 0.267318i | ||||
\(906\) | −271.854 | − | 550.355i | −0.300060 | − | 0.607455i | ||||
\(907\) | −105.197 | + | 60.7354i | −0.115983 | + | 0.0669629i | −0.556869 | − | 0.830600i | \(-0.687998\pi\) |
0.440886 | + | 0.897563i | \(0.354664\pi\) | |||||||
\(908\) | −483.792 | −0.532810 | ||||||||
\(909\) | −615.221 | − | 470.794i | −0.676811 | − | 0.517925i | ||||
\(910\) | 181.711 | + | 541.314i | 0.199683 | + | 0.594850i | ||||
\(911\) | −1000.46 | + | 577.616i | −1.09820 | + | 0.634046i | −0.935748 | − | 0.352670i | \(-0.885274\pi\) |
−0.162453 | + | 0.986716i | \(0.551940\pi\) | |||||||
\(912\) | 808.871 | + | 52.4830i | 0.886920 | + | 0.0575472i | ||||
\(913\) | −510.904 | − | 294.971i | −0.559588 | − | 0.323078i | ||||
\(914\) | 2228.21 | + | 1286.46i | 2.43786 | + | 1.40750i | ||||
\(915\) | −453.459 | − | 122.830i | −0.495584 | − | 0.134241i | ||||
\(916\) | 29.5895 | + | 51.2505i | 0.0323029 | + | 0.0559503i | ||||
\(917\) | 220.275 | 0.240212 | ||||||||
\(918\) | 137.905 | + | 403.643i | 0.150224 | + | 0.439699i | ||||
\(919\) | −994.576 | −1.08224 | −0.541119 | − | 0.840946i | \(-0.681999\pi\) | ||||
−0.541119 | + | 0.840946i | \(0.681999\pi\) | |||||||
\(920\) | −34.8631 | + | 39.4835i | −0.0378947 | + | 0.0429168i | ||||
\(921\) | −1063.16 | − | 709.372i | −1.15436 | − | 0.770220i | ||||
\(922\) | 1225.43 | + | 707.501i | 1.32910 | + | 0.767354i | ||||
\(923\) | −438.358 | + | 759.258i | −0.474927 | + | 0.822598i | ||||
\(924\) | −725.020 | − | 47.0424i | −0.784654 | − | 0.0509117i | ||||
\(925\) | −12.8201 | + | 30.3676i | −0.0138595 | + | 0.0328298i | ||||
\(926\) | − | 995.977i | − | 1.07557i | ||||||
\(927\) | 47.5481 | − | 364.864i | 0.0512924 | − | 0.393597i | ||||
\(928\) | − | 1725.33i | − | 1.85919i | ||||||
\(929\) | 140.236 | − | 80.9655i | 0.150954 | − | 0.0871534i | −0.422620 | − | 0.906307i | \(-0.638890\pi\) |
0.573575 | + | 0.819153i | \(0.305556\pi\) | |||||||
\(930\) | −754.014 | + | 749.913i | −0.810768 | + | 0.806358i | ||||
\(931\) | −151.970 | + | 263.221i | −0.163234 | + | 0.282729i | ||||
\(932\) | 252.056 | − | 436.574i | 0.270447 | − | 0.468427i | ||||
\(933\) | 3.14155 | − | 1.55181i | 0.00336715 | − | 0.00166324i | ||||
\(934\) | 1434.26 | + | 2484.22i | 1.53561 | + | 2.65976i | ||||
\(935\) | −199.638 | + | 67.0156i | −0.213517 | + | 0.0716745i | ||||
\(936\) | −289.493 | + | 2221.45i | −0.309288 | + | 2.37334i | ||||
\(937\) | − | 660.489i | − | 0.704898i | −0.935831 | − | 0.352449i | \(-0.885349\pi\) | ||
0.935831 | − | 0.352449i | \(-0.114651\pi\) | |||||||
\(938\) | −369.457 | − | 639.919i | −0.393878 | − | 0.682216i | ||||
\(939\) | 50.6880 | − | 781.206i | 0.0539808 | − | 0.831955i | ||||
\(940\) | 2395.10 | + | 484.845i | 2.54798 | + | 0.515792i | ||||
\(941\) | −1378.06 | − | 795.624i | −1.46446 | − | 0.845509i | −0.465252 | − | 0.885179i | \(-0.654036\pi\) |
−0.999213 | + | 0.0396696i | \(0.987369\pi\) | |||||||
\(942\) | −101.881 | − | 67.9783i | −0.108154 | − | 0.0721638i | ||||
\(943\) | −15.3026 | + | 8.83498i | −0.0162276 | + | 0.00936902i | ||||
\(944\) | − | 3994.69i | − | 4.23167i | ||||||
\(945\) | 343.697 | − | 44.7542i | 0.363700 | − | 0.0473590i | ||||
\(946\) | −1882.88 | −1.99035 | ||||||||
\(947\) | −781.678 | − | 1353.91i | −0.825426 | − | 1.42968i | −0.901594 | − | 0.432584i | \(-0.857602\pi\) |
0.0761680 | − | 0.997095i | \(-0.475731\pi\) | |||||||
\(948\) | −1841.94 | + | 2760.58i | −1.94298 | + | 2.91201i | ||||
\(949\) | −182.818 | + | 316.650i | −0.192643 | + | 0.333667i | ||||
\(950\) | −81.8004 | − | 655.583i | −0.0861057 | − | 0.690087i | ||||
\(951\) | −392.282 | − | 25.4529i | −0.412494 | − | 0.0267644i | ||||
\(952\) | 196.566 | − | 113.488i | 0.206477 | − | 0.119210i | ||||
\(953\) | 996.612 | 1.04576 | 0.522881 | − | 0.852405i | \(-0.324857\pi\) | ||||
0.522881 | + | 0.852405i | \(0.324857\pi\) | |||||||
\(954\) | 1747.21 | − | 2283.20i | 1.83145 | − | 2.39330i | ||||
\(955\) | 671.027 | − | 225.254i | 0.702646 | − | 0.235868i | ||||
\(956\) | −810.961 | + | 468.209i | −0.848285 | + | 0.489758i | ||||
\(957\) | 399.028 | + | 807.812i | 0.416957 | + | 0.844109i | ||||
\(958\) | −231.719 | − | 133.783i | −0.241878 | − | 0.139648i | ||||
\(959\) | 155.031 | + | 89.5074i | 0.161659 | + | 0.0933341i | ||||
\(960\) | 610.793 | − | 607.471i | 0.636243 | − | 0.632782i | ||||
\(961\) | 295.657 | + | 512.093i | 0.307656 | + | 0.532875i | ||||
\(962\) | −58.6484 | −0.0609651 | ||||||||
\(963\) | 5.73631 | + | 13.7974i | 0.00595670 | + | 0.0143275i | ||||
\(964\) | −1369.63 | −1.42078 | ||||||||
\(965\) | −829.896 | − | 732.781i | −0.859996 | − | 0.759359i | ||||
\(966\) | −0.938806 | + | 14.4689i | −0.000971849 | + | 0.0149782i | ||||
\(967\) | 562.916 | + | 325.000i | 0.582126 | + | 0.336091i | 0.761978 | − | 0.647603i | \(-0.224229\pi\) |
−0.179852 | + | 0.983694i | \(0.557562\pi\) | |||||||
\(968\) | −251.418 | + | 435.468i | −0.259729 | + | 0.449864i | ||||
\(969\) | 51.1295 | − | 76.6295i | 0.0527652 | − | 0.0790810i | ||||
\(970\) | 1768.46 | + | 1561.51i | 1.82315 | + | 1.60981i | ||||
\(971\) | − | 1717.75i | − | 1.76905i | −0.466495 | − | 0.884524i | \(-0.654483\pi\) | ||
0.466495 | − | 0.884524i | \(-0.345517\pi\) | |||||||
\(972\) | 2210.53 | + | 742.291i | 2.27421 | + | 0.763674i | ||||
\(973\) | − | 356.656i | − | 0.366553i | ||||||
\(974\) | 2329.45 | − | 1344.91i | 2.39163 | − | 1.38081i | ||||
\(975\) | 903.156 | − | 53.6564i | 0.926314 | − | 0.0550322i | ||||
\(976\) | −590.372 | + | 1022.55i | −0.604889 | + | 1.04770i | ||||
\(977\) | −141.061 | + | 244.324i | −0.144381 | + | 0.250076i | −0.929142 | − | 0.369723i | \(-0.879453\pi\) |
0.784761 | + | 0.619799i | \(0.212786\pi\) | |||||||
\(978\) | −154.871 | + | 2386.88i | −0.158355 | + | 2.44057i | ||||
\(979\) | −350.439 | − | 606.979i | −0.357956 | − | 0.619998i | ||||
\(980\) | 647.530 | + | 1928.98i | 0.660745 | + | 1.96834i | ||||
\(981\) | 513.564 | + | 1235.26i | 0.523510 | + | 1.25919i | ||||
\(982\) | − | 14.0695i | − | 0.0143274i | ||||||
\(983\) | 192.267 | + | 333.017i | 0.195592 | + | 0.338776i | 0.947095 | − | 0.320955i | \(-0.104004\pi\) |
−0.751502 | + | 0.659731i | \(0.770670\pi\) | |||||||
\(984\) | 1920.89 | − | 948.846i | 1.95212 | − | 0.964274i | ||||
\(985\) | −139.385 | − | 28.2159i | −0.141508 | − | 0.0286456i | ||||
\(986\) | −418.003 | − | 241.334i | −0.423938 | − | 0.244761i | ||||
\(987\) | 351.713 | − | 173.733i | 0.356346 | − | 0.176021i | ||||
\(988\) | 718.496 | − | 414.824i | 0.727223 | − | 0.419862i | ||||
\(989\) | 26.5208i | 0.0268158i | ||||||||
\(990\) | −527.491 | + | 1543.43i | −0.532819 | + | 1.55902i | ||||
\(991\) | 399.250 | 0.402876 | 0.201438 | − | 0.979501i | \(-0.435439\pi\) | ||||
0.201438 | + | 0.979501i | \(0.435439\pi\) | |||||||
\(992\) | 542.898 | + | 940.326i | 0.547276 | + | 0.947910i | ||||
\(993\) | 579.234 | + | 37.5832i | 0.583317 | + | 0.0378481i | ||||
\(994\) | 344.002 | − | 595.828i | 0.346078 | − | 0.599425i | ||||
\(995\) | −754.082 | − | 152.650i | −0.757871 | − | 0.153417i | ||||
\(996\) | 958.903 | − | 1437.14i | 0.962754 | − | 1.44291i | ||||
\(997\) | −1257.62 | + | 726.087i | −1.26140 | + | 0.728272i | −0.973346 | − | 0.229341i | \(-0.926343\pi\) |
−0.288058 | + | 0.957613i | \(0.593009\pi\) | |||||||
\(998\) | 757.008 | 0.758525 | ||||||||
\(999\) | −6.87641 | + | 34.9294i | −0.00688329 | + | 0.0349643i |
(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 | 45.3.h.a.14.1 | ✓ | 20 | |
3.2 | odd | 2 | 135.3.h.a.44.10 | 20 | |||
5.2 | odd | 4 | 225.3.j.e.176.10 | 20 | |||
5.3 | odd | 4 | 225.3.j.e.176.1 | 20 | |||
5.4 | even | 2 | inner | 45.3.h.a.14.10 | yes | 20 | |
9.2 | odd | 6 | inner | 45.3.h.a.29.10 | yes | 20 | |
9.4 | even | 3 | 405.3.d.a.404.20 | 20 | |||
9.5 | odd | 6 | 405.3.d.a.404.1 | 20 | |||
9.7 | even | 3 | 135.3.h.a.89.1 | 20 | |||
15.2 | even | 4 | 675.3.j.e.476.1 | 20 | |||
15.8 | even | 4 | 675.3.j.e.476.10 | 20 | |||
15.14 | odd | 2 | 135.3.h.a.44.1 | 20 | |||
45.2 | even | 12 | 225.3.j.e.101.10 | 20 | |||
45.4 | even | 6 | 405.3.d.a.404.2 | 20 | |||
45.7 | odd | 12 | 675.3.j.e.251.1 | 20 | |||
45.14 | odd | 6 | 405.3.d.a.404.19 | 20 | |||
45.29 | odd | 6 | inner | 45.3.h.a.29.1 | yes | 20 | |
45.34 | even | 6 | 135.3.h.a.89.10 | 20 | |||
45.38 | even | 12 | 225.3.j.e.101.1 | 20 | |||
45.43 | odd | 12 | 675.3.j.e.251.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.h.a.14.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
45.3.h.a.14.10 | yes | 20 | 5.4 | even | 2 | inner | |
45.3.h.a.29.1 | yes | 20 | 45.29 | odd | 6 | inner | |
45.3.h.a.29.10 | yes | 20 | 9.2 | odd | 6 | inner | |
135.3.h.a.44.1 | 20 | 15.14 | odd | 2 | |||
135.3.h.a.44.10 | 20 | 3.2 | odd | 2 | |||
135.3.h.a.89.1 | 20 | 9.7 | even | 3 | |||
135.3.h.a.89.10 | 20 | 45.34 | even | 6 | |||
225.3.j.e.101.1 | 20 | 45.38 | even | 12 | |||
225.3.j.e.101.10 | 20 | 45.2 | even | 12 | |||
225.3.j.e.176.1 | 20 | 5.3 | odd | 4 | |||
225.3.j.e.176.10 | 20 | 5.2 | odd | 4 | |||
405.3.d.a.404.1 | 20 | 9.5 | odd | 6 | |||
405.3.d.a.404.2 | 20 | 45.4 | even | 6 | |||
405.3.d.a.404.19 | 20 | 45.14 | odd | 6 | |||
405.3.d.a.404.20 | 20 | 9.4 | even | 3 | |||
675.3.j.e.251.1 | 20 | 45.7 | odd | 12 | |||
675.3.j.e.251.10 | 20 | 45.43 | odd | 12 | |||
675.3.j.e.476.1 | 20 | 15.2 | even | 4 | |||
675.3.j.e.476.10 | 20 | 15.8 | even | 4 |