Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,5,Mod(5,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.d (of order \(4\), 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: | \(1.34380952009\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | 6.0.53039932416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} - 12x^{3} + 529x^{2} - 1334x + 1682 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(1.30633 - 1.30633i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.5 |
Dual form | 13.5.d.a.8.2 |
$q$-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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30633 | + | 1.30633i | −0.326581 | + | 0.326581i | −0.851285 | − | 0.524704i | \(-0.824176\pi\) |
0.524704 | + | 0.851285i | \(0.324176\pi\) | |||||||
\(3\) | 9.97438 | 1.10826 | 0.554132 | − | 0.832429i | \(-0.313050\pi\) | ||||
0.554132 | + | 0.832429i | \(0.313050\pi\) | |||||||
\(4\) | 12.5870i | 0.786689i | ||||||||
\(5\) | 9.28070 | − | 9.28070i | 0.371228 | − | 0.371228i | −0.496696 | − | 0.867924i | \(-0.665454\pi\) |
0.867924 | + | 0.496696i | \(0.165454\pi\) | |||||||
\(6\) | −13.0298 | + | 13.0298i | −0.361938 | + | 0.361938i | ||||
\(7\) | −46.1782 | − | 46.1782i | −0.942413 | − | 0.942413i | 0.0560172 | − | 0.998430i | \(-0.482160\pi\) |
−0.998430 | + | 0.0560172i | \(0.982160\pi\) | |||||||
\(8\) | −37.3440 | − | 37.3440i | −0.583499 | − | 0.583499i | ||||
\(9\) | 18.4882 | 0.228250 | ||||||||
\(10\) | 24.2472i | 0.242472i | ||||||||
\(11\) | 90.5598 | + | 90.5598i | 0.748428 | + | 0.748428i | 0.974184 | − | 0.225756i | \(-0.0724851\pi\) |
−0.225756 | + | 0.974184i | \(0.572485\pi\) | |||||||
\(12\) | 125.548i | 0.871860i | ||||||||
\(13\) | −37.9467 | − | 164.685i | −0.224537 | − | 0.974466i | ||||
\(14\) | 120.648 | 0.615549 | ||||||||
\(15\) | 92.5693 | − | 92.5693i | 0.411419 | − | 0.411419i | ||||
\(16\) | −103.826 | −0.405569 | ||||||||
\(17\) | 298.690i | 1.03353i | 0.856127 | + | 0.516766i | \(0.172864\pi\) | ||||
−0.856127 | + | 0.516766i | \(0.827136\pi\) | |||||||
\(18\) | −24.1516 | + | 24.1516i | −0.0745421 | + | 0.0745421i | ||||
\(19\) | 145.723 | − | 145.723i | 0.403665 | − | 0.403665i | −0.475858 | − | 0.879522i | \(-0.657862\pi\) |
0.879522 | + | 0.475858i | \(0.157862\pi\) | |||||||
\(20\) | 116.816 | + | 116.816i | 0.292041 | + | 0.292041i | ||||
\(21\) | −460.599 | − | 460.599i | −1.04444 | − | 1.04444i | ||||
\(22\) | −236.601 | −0.488845 | ||||||||
\(23\) | 72.2918i | 0.136657i | 0.997663 | + | 0.0683287i | \(0.0217667\pi\) | ||||
−0.997663 | + | 0.0683287i | \(0.978233\pi\) | |||||||
\(24\) | −372.483 | − | 372.483i | −0.646671 | − | 0.646671i | ||||
\(25\) | 452.737i | 0.724379i | ||||||||
\(26\) | 264.702 | + | 165.561i | 0.391572 | + | 0.244913i | ||||
\(27\) | −623.516 | −0.855303 | ||||||||
\(28\) | 581.247 | − | 581.247i | 0.741386 | − | 0.741386i | ||||
\(29\) | 1458.98 | 1.73481 | 0.867407 | − | 0.497600i | \(-0.165785\pi\) | ||||
0.867407 | + | 0.497600i | \(0.165785\pi\) | |||||||
\(30\) | 241.851i | 0.268723i | ||||||||
\(31\) | −974.947 | + | 974.947i | −1.01451 | + | 1.01451i | −0.0146199 | + | 0.999893i | \(0.504654\pi\) |
−0.999893 | + | 0.0146199i | \(0.995346\pi\) | |||||||
\(32\) | 733.134 | − | 733.134i | 0.715951 | − | 0.715951i | ||||
\(33\) | 903.278 | + | 903.278i | 0.829456 | + | 0.829456i | ||||
\(34\) | −390.187 | − | 390.187i | −0.337532 | − | 0.337532i | ||||
\(35\) | −857.133 | −0.699700 | ||||||||
\(36\) | 232.712i | 0.179562i | ||||||||
\(37\) | 345.648 | + | 345.648i | 0.252482 | + | 0.252482i | 0.821988 | − | 0.569505i | \(-0.192865\pi\) |
−0.569505 | + | 0.821988i | \(0.692865\pi\) | |||||||
\(38\) | 380.723i | 0.263659i | ||||||||
\(39\) | −378.495 | − | 1642.63i | −0.248846 | − | 1.07997i | ||||
\(40\) | −693.156 | −0.433223 | ||||||||
\(41\) | −546.990 | + | 546.990i | −0.325396 | + | 0.325396i | −0.850833 | − | 0.525437i | \(-0.823902\pi\) |
0.525437 | + | 0.850833i | \(0.323902\pi\) | |||||||
\(42\) | 1203.38 | 0.682191 | ||||||||
\(43\) | − | 2284.35i | − | 1.23545i | −0.786393 | − | 0.617726i | \(-0.788054\pi\) | ||
0.786393 | − | 0.617726i | \(-0.211946\pi\) | |||||||
\(44\) | −1139.88 | + | 1139.88i | −0.588780 | + | 0.588780i | ||||
\(45\) | 171.584 | − | 171.584i | 0.0847327 | − | 0.0847327i | ||||
\(46\) | −94.4365 | − | 94.4365i | −0.0446297 | − | 0.0446297i | ||||
\(47\) | −1932.68 | − | 1932.68i | −0.874910 | − | 0.874910i | 0.118093 | − | 0.993003i | \(-0.462322\pi\) |
−0.993003 | + | 0.118093i | \(0.962322\pi\) | |||||||
\(48\) | −1035.60 | −0.449478 | ||||||||
\(49\) | 1863.86i | 0.776283i | ||||||||
\(50\) | −591.422 | − | 591.422i | −0.236569 | − | 0.236569i | ||||
\(51\) | 2979.25i | 1.14543i | ||||||||
\(52\) | 2072.89 | − | 477.636i | 0.766602 | − | 0.176641i | ||||
\(53\) | 4356.45 | 1.55089 | 0.775445 | − | 0.631415i | \(-0.217526\pi\) | ||||
0.775445 | + | 0.631415i | \(0.217526\pi\) | |||||||
\(54\) | 814.515 | − | 814.515i | 0.279326 | − | 0.279326i | ||||
\(55\) | 1680.92 | 0.555675 | ||||||||
\(56\) | 3448.95i | 1.09979i | ||||||||
\(57\) | 1453.50 | − | 1453.50i | 0.447367 | − | 0.447367i | ||||
\(58\) | −1905.90 | + | 1905.90i | −0.566558 | + | 0.566558i | ||||
\(59\) | −1548.85 | − | 1548.85i | −0.444945 | − | 0.444945i | 0.448725 | − | 0.893670i | \(-0.351878\pi\) |
−0.893670 | + | 0.448725i | \(0.851878\pi\) | |||||||
\(60\) | 1165.17 | + | 1165.17i | 0.323659 | + | 0.323659i | ||||
\(61\) | −897.748 | −0.241265 | −0.120633 | − | 0.992697i | \(-0.538492\pi\) | ||||
−0.120633 | + | 0.992697i | \(0.538492\pi\) | |||||||
\(62\) | − | 2547.20i | − | 0.662642i | ||||||
\(63\) | −853.754 | − | 853.754i | −0.215105 | − | 0.215105i | ||||
\(64\) | 254.209i | 0.0620628i | ||||||||
\(65\) | −1880.56 | − | 1176.22i | −0.445103 | − | 0.278395i | ||||
\(66\) | −2359.95 | −0.541770 | ||||||||
\(67\) | 2232.99 | − | 2232.99i | 0.497435 | − | 0.497435i | −0.413204 | − | 0.910639i | \(-0.635590\pi\) |
0.910639 | + | 0.413204i | \(0.135590\pi\) | |||||||
\(68\) | −3759.63 | −0.813068 | ||||||||
\(69\) | 721.065i | 0.151453i | ||||||||
\(70\) | 1119.69 | − | 1119.69i | 0.228509 | − | 0.228509i | ||||
\(71\) | −1218.01 | + | 1218.01i | −0.241620 | + | 0.241620i | −0.817520 | − | 0.575900i | \(-0.804652\pi\) |
0.575900 | + | 0.817520i | \(0.304652\pi\) | |||||||
\(72\) | −690.424 | − | 690.424i | −0.133184 | − | 0.133184i | ||||
\(73\) | 1615.47 | + | 1615.47i | 0.303147 | + | 0.303147i | 0.842244 | − | 0.539097i | \(-0.181234\pi\) |
−0.539097 | + | 0.842244i | \(0.681234\pi\) | |||||||
\(74\) | −903.058 | −0.164912 | ||||||||
\(75\) | 4515.77i | 0.802804i | ||||||||
\(76\) | 1834.22 | + | 1834.22i | 0.317559 | + | 0.317559i | ||||
\(77\) | − | 8363.78i | − | 1.41066i | ||||||
\(78\) | 2640.24 | + | 1651.37i | 0.433965 | + | 0.271428i | ||||
\(79\) | −1235.04 | −0.197891 | −0.0989455 | − | 0.995093i | \(-0.531547\pi\) | ||||
−0.0989455 | + | 0.995093i | \(0.531547\pi\) | |||||||
\(80\) | −963.576 | + | 963.576i | −0.150559 | + | 0.150559i | ||||
\(81\) | −7716.73 | −1.17615 | ||||||||
\(82\) | − | 1429.09i | − | 0.212536i | ||||||
\(83\) | −2620.61 | + | 2620.61i | −0.380406 | + | 0.380406i | −0.871248 | − | 0.490843i | \(-0.836689\pi\) |
0.490843 | + | 0.871248i | \(0.336689\pi\) | |||||||
\(84\) | 5797.57 | − | 5797.57i | 0.821652 | − | 0.821652i | ||||
\(85\) | 2772.06 | + | 2772.06i | 0.383676 | + | 0.383676i | ||||
\(86\) | 2984.10 | + | 2984.10i | 0.403475 | + | 0.403475i | ||||
\(87\) | 14552.4 | 1.92263 | ||||||||
\(88\) | − | 6763.72i | − | 0.873415i | ||||||
\(89\) | 2845.64 | + | 2845.64i | 0.359253 | + | 0.359253i | 0.863538 | − | 0.504285i | \(-0.168244\pi\) |
−0.504285 | + | 0.863538i | \(0.668244\pi\) | |||||||
\(90\) | 448.288i | 0.0553443i | ||||||||
\(91\) | −5852.54 | + | 9357.16i | −0.706743 | + | 1.12995i | ||||
\(92\) | −909.938 | −0.107507 | ||||||||
\(93\) | −9724.49 | + | 9724.49i | −1.12435 | + | 1.12435i | ||||
\(94\) | 5049.40 | 0.571458 | ||||||||
\(95\) | − | 2704.82i | − | 0.299703i | ||||||
\(96\) | 7312.55 | − | 7312.55i | 0.793463 | − | 0.793463i | ||||
\(97\) | −4189.00 | + | 4189.00i | −0.445212 | + | 0.445212i | −0.893759 | − | 0.448547i | \(-0.851942\pi\) |
0.448547 | + | 0.893759i | \(0.351942\pi\) | |||||||
\(98\) | −2434.80 | − | 2434.80i | −0.253520 | − | 0.253520i | ||||
\(99\) | 1674.29 | + | 1674.29i | 0.170829 | + | 0.170829i | ||||
\(100\) | −5698.61 | −0.569861 | ||||||||
\(101\) | − | 10674.4i | − | 1.04641i | −0.852206 | − | 0.523206i | \(-0.824736\pi\) | ||
0.852206 | − | 0.523206i | \(-0.175264\pi\) | |||||||
\(102\) | −3891.87 | − | 3891.87i | −0.374075 | − | 0.374075i | ||||
\(103\) | − | 13211.9i | − | 1.24535i | −0.782482 | − | 0.622673i | \(-0.786047\pi\) | ||
0.782482 | − | 0.622673i | \(-0.213953\pi\) | |||||||
\(104\) | −4732.90 | + | 7567.06i | −0.437583 | + | 0.699617i | ||||
\(105\) | −8549.37 | −0.775453 | ||||||||
\(106\) | −5690.94 | + | 5690.94i | −0.506492 | + | 0.506492i | ||||
\(107\) | −5048.88 | −0.440988 | −0.220494 | − | 0.975388i | \(-0.570767\pi\) | ||||
−0.220494 | + | 0.975388i | \(0.570767\pi\) | |||||||
\(108\) | − | 7848.21i | − | 0.672858i | ||||||
\(109\) | 6220.78 | − | 6220.78i | 0.523591 | − | 0.523591i | −0.395063 | − | 0.918654i | \(-0.629277\pi\) |
0.918654 | + | 0.395063i | \(0.129277\pi\) | |||||||
\(110\) | −2195.82 | + | 2195.82i | −0.181473 | + | 0.181473i | ||||
\(111\) | 3447.63 | + | 3447.63i | 0.279817 | + | 0.279817i | ||||
\(112\) | 4794.49 | + | 4794.49i | 0.382214 | + | 0.382214i | ||||
\(113\) | 11006.7 | 0.861984 | 0.430992 | − | 0.902356i | \(-0.358164\pi\) | ||||
0.430992 | + | 0.902356i | \(0.358164\pi\) | |||||||
\(114\) | 3797.48i | 0.292204i | ||||||||
\(115\) | 670.918 | + | 670.918i | 0.0507311 | + | 0.0507311i | ||||
\(116\) | 18364.2i | 1.36476i | ||||||||
\(117\) | −701.567 | − | 3044.73i | −0.0512504 | − | 0.222422i | ||||
\(118\) | 4046.62 | 0.290622 | ||||||||
\(119\) | 13793.0 | − | 13793.0i | 0.974013 | − | 0.974013i | ||||
\(120\) | −6913.80 | −0.480125 | ||||||||
\(121\) | 1761.16i | 0.120289i | ||||||||
\(122\) | 1172.75 | − | 1172.75i | 0.0787927 | − | 0.0787927i | ||||
\(123\) | −5455.89 | + | 5455.89i | −0.360625 | + | 0.360625i | ||||
\(124\) | −12271.7 | − | 12271.7i | −0.798107 | − | 0.798107i | ||||
\(125\) | 10002.2 | + | 10002.2i | 0.640138 | + | 0.640138i | ||||
\(126\) | 2230.56 | 0.140499 | ||||||||
\(127\) | 16682.3i | 1.03431i | 0.855893 | + | 0.517153i | \(0.173008\pi\) | ||||
−0.855893 | + | 0.517153i | \(0.826992\pi\) | |||||||
\(128\) | 11398.1 | + | 11398.1i | 0.695682 | + | 0.695682i | ||||
\(129\) | − | 22785.0i | − | 1.36921i | ||||||
\(130\) | 3993.15 | − | 920.102i | 0.236281 | − | 0.0544439i | ||||
\(131\) | 21766.7 | 1.26838 | 0.634190 | − | 0.773177i | \(-0.281334\pi\) | ||||
0.634190 | + | 0.773177i | \(0.281334\pi\) | |||||||
\(132\) | −11369.6 | + | 11369.6i | −0.652524 | + | 0.652524i | ||||
\(133\) | −13458.5 | −0.760838 | ||||||||
\(134\) | 5834.01i | 0.324906i | ||||||||
\(135\) | −5786.67 | + | 5786.67i | −0.317513 | + | 0.317513i | ||||
\(136\) | 11154.3 | − | 11154.3i | 0.603065 | − | 0.603065i | ||||
\(137\) | 833.609 | + | 833.609i | 0.0444142 | + | 0.0444142i | 0.728965 | − | 0.684551i | \(-0.240002\pi\) |
−0.684551 | + | 0.728965i | \(0.740002\pi\) | |||||||
\(138\) | −941.946 | − | 941.946i | −0.0494616 | − | 0.0494616i | ||||
\(139\) | −21688.2 | −1.12252 | −0.561261 | − | 0.827639i | \(-0.689683\pi\) | ||||
−0.561261 | + | 0.827639i | \(0.689683\pi\) | |||||||
\(140\) | − | 10788.8i | − | 0.550447i | ||||||
\(141\) | −19277.2 | − | 19277.2i | −0.969631 | − | 0.969631i | ||||
\(142\) | − | 3182.23i | − | 0.157817i | ||||||
\(143\) | 11477.4 | − | 18350.3i | 0.561268 | − | 0.897367i | ||||
\(144\) | −1919.55 | −0.0925711 | ||||||||
\(145\) | 13540.3 | − | 13540.3i | 0.644012 | − | 0.644012i | ||||
\(146\) | −4220.66 | −0.198004 | ||||||||
\(147\) | 18590.8i | 0.860327i | ||||||||
\(148\) | −4350.69 | + | 4350.69i | −0.198625 | + | 0.198625i | ||||
\(149\) | −28179.1 | + | 28179.1i | −1.26927 | + | 1.26927i | −0.322807 | + | 0.946465i | \(0.604627\pi\) |
−0.946465 | + | 0.322807i | \(0.895373\pi\) | |||||||
\(150\) | −5899.07 | − | 5899.07i | −0.262181 | − | 0.262181i | ||||
\(151\) | −15225.9 | − | 15225.9i | −0.667773 | − | 0.667773i | 0.289427 | − | 0.957200i | \(-0.406535\pi\) |
−0.957200 | + | 0.289427i | \(0.906535\pi\) | |||||||
\(152\) | −10883.7 | −0.471076 | ||||||||
\(153\) | 5522.26i | 0.235903i | ||||||||
\(154\) | 10925.8 | + | 10925.8i | 0.460694 | + | 0.460694i | ||||
\(155\) | 18096.4i | 0.753232i | ||||||||
\(156\) | 20675.8 | − | 4764.12i | 0.849597 | − | 0.195764i | ||||
\(157\) | −5638.66 | −0.228758 | −0.114379 | − | 0.993437i | \(-0.536488\pi\) | ||||
−0.114379 | + | 0.993437i | \(0.536488\pi\) | |||||||
\(158\) | 1613.36 | − | 1613.36i | 0.0646275 | − | 0.0646275i | ||||
\(159\) | 43452.9 | 1.71880 | ||||||||
\(160\) | − | 13608.0i | − | 0.531562i | ||||||
\(161\) | 3338.30 | − | 3338.30i | 0.128788 | − | 0.128788i | ||||
\(162\) | 10080.6 | − | 10080.6i | 0.384109 | − | 0.384109i | ||||
\(163\) | 22791.6 | + | 22791.6i | 0.857826 | + | 0.857826i | 0.991082 | − | 0.133255i | \(-0.0425431\pi\) |
−0.133255 | + | 0.991082i | \(0.542543\pi\) | |||||||
\(164\) | −6884.98 | − | 6884.98i | −0.255985 | − | 0.255985i | ||||
\(165\) | 16766.1 | 0.615835 | ||||||||
\(166\) | − | 6846.75i | − | 0.248467i | ||||||
\(167\) | −11597.7 | − | 11597.7i | −0.415852 | − | 0.415852i | 0.467919 | − | 0.883771i | \(-0.345004\pi\) |
−0.883771 | + | 0.467919i | \(0.845004\pi\) | |||||||
\(168\) | 34401.2i | 1.21886i | ||||||||
\(169\) | −25681.1 | + | 12498.5i | −0.899167 | + | 0.437606i | ||||
\(170\) | −7242.42 | −0.250603 | ||||||||
\(171\) | 2694.16 | − | 2694.16i | 0.0921364 | − | 0.0921364i | ||||
\(172\) | 28753.2 | 0.971917 | ||||||||
\(173\) | − | 7266.07i | − | 0.242777i | −0.992605 | − | 0.121388i | \(-0.961265\pi\) | ||
0.992605 | − | 0.121388i | \(-0.0387347\pi\) | |||||||
\(174\) | −19010.2 | + | 19010.2i | −0.627896 | + | 0.627896i | ||||
\(175\) | 20906.6 | − | 20906.6i | 0.682664 | − | 0.682664i | ||||
\(176\) | −9402.44 | − | 9402.44i | −0.303540 | − | 0.303540i | ||||
\(177\) | −15448.9 | − | 15448.9i | −0.493117 | − | 0.493117i | ||||
\(178\) | −7434.67 | −0.234651 | ||||||||
\(179\) | 18706.0i | 0.583816i | 0.956446 | + | 0.291908i | \(0.0942900\pi\) | ||||
−0.956446 | + | 0.291908i | \(0.905710\pi\) | |||||||
\(180\) | 2159.73 | + | 2159.73i | 0.0666583 | + | 0.0666583i | ||||
\(181\) | 14931.3i | 0.455765i | 0.973689 | + | 0.227882i | \(0.0731802\pi\) | ||||
−0.973689 | + | 0.227882i | \(0.926820\pi\) | |||||||
\(182\) | −4578.17 | − | 19868.8i | −0.138213 | − | 0.599831i | ||||
\(183\) | −8954.48 | −0.267386 | ||||||||
\(184\) | 2699.66 | − | 2699.66i | 0.0797395 | − | 0.0797395i | ||||
\(185\) | 6415.72 | 0.187457 | ||||||||
\(186\) | − | 25406.7i | − | 0.734382i | ||||||
\(187\) | −27049.4 | + | 27049.4i | −0.773524 | + | 0.773524i | ||||
\(188\) | 24326.6 | − | 24326.6i | 0.688282 | − | 0.688282i | ||||
\(189\) | 28792.9 | + | 28792.9i | 0.806049 | + | 0.806049i | ||||
\(190\) | 3533.38 | + | 3533.38i | 0.0978775 | + | 0.0978775i | ||||
\(191\) | −34297.6 | −0.940150 | −0.470075 | − | 0.882626i | \(-0.655773\pi\) | ||||
−0.470075 | + | 0.882626i | \(0.655773\pi\) | |||||||
\(192\) | 2535.58i | 0.0687820i | ||||||||
\(193\) | −5043.50 | − | 5043.50i | −0.135400 | − | 0.135400i | 0.636159 | − | 0.771558i | \(-0.280522\pi\) |
−0.771558 | + | 0.636159i | \(0.780522\pi\) | |||||||
\(194\) | − | 10944.4i | − | 0.290796i | ||||||
\(195\) | −18757.4 | − | 11732.0i | −0.493292 | − | 0.308535i | ||||
\(196\) | −23460.4 | −0.610694 | ||||||||
\(197\) | −9293.04 | + | 9293.04i | −0.239456 | + | 0.239456i | −0.816625 | − | 0.577169i | \(-0.804157\pi\) |
0.577169 | + | 0.816625i | \(0.304157\pi\) | |||||||
\(198\) | −4374.34 | −0.111579 | ||||||||
\(199\) | 9337.31i | 0.235785i | 0.993026 | + | 0.117892i | \(0.0376138\pi\) | ||||
−0.993026 | + | 0.117892i | \(0.962386\pi\) | |||||||
\(200\) | 16907.0 | − | 16907.0i | 0.422675 | − | 0.422675i | ||||
\(201\) | 22272.7 | − | 22272.7i | 0.551290 | − | 0.551290i | ||||
\(202\) | 13944.3 | + | 13944.3i | 0.341739 | + | 0.341739i | ||||
\(203\) | −67373.0 | − | 67373.0i | −1.63491 | − | 1.63491i | ||||
\(204\) | −37499.9 | −0.901094 | ||||||||
\(205\) | 10152.9i | 0.241592i | ||||||||
\(206\) | 17259.0 | + | 17259.0i | 0.406707 | + | 0.406707i | ||||
\(207\) | 1336.55i | 0.0311920i | ||||||||
\(208\) | 3939.84 | + | 17098.5i | 0.0910652 | + | 0.395213i | ||||
\(209\) | 26393.3 | 0.604228 | ||||||||
\(210\) | 11168.3 | − | 11168.3i | 0.253248 | − | 0.253248i | ||||
\(211\) | 53816.1 | 1.20878 | 0.604390 | − | 0.796689i | \(-0.293417\pi\) | ||||
0.604390 | + | 0.796689i | \(0.293417\pi\) | |||||||
\(212\) | 54834.8i | 1.22007i | ||||||||
\(213\) | −12148.9 | + | 12148.9i | −0.267779 | + | 0.267779i | ||||
\(214\) | 6595.47 | − | 6595.47i | 0.144019 | − | 0.144019i | ||||
\(215\) | −21200.4 | − | 21200.4i | −0.458635 | − | 0.458635i | ||||
\(216\) | 23284.6 | + | 23284.6i | 0.499069 | + | 0.499069i | ||||
\(217\) | 90042.6 | 1.91218 | ||||||||
\(218\) | 16252.7i | 0.341990i | ||||||||
\(219\) | 16113.3 | + | 16113.3i | 0.335967 | + | 0.335967i | ||||
\(220\) | 21157.8i | 0.437144i | ||||||||
\(221\) | 49189.8 | − | 11334.3i | 1.00714 | − | 0.232066i | ||||
\(222\) | −9007.44 | −0.182766 | ||||||||
\(223\) | 27165.3 | − | 27165.3i | 0.546266 | − | 0.546266i | −0.379093 | − | 0.925359i | \(-0.623764\pi\) |
0.925359 | + | 0.379093i | \(0.123764\pi\) | |||||||
\(224\) | −67709.6 | −1.34944 | ||||||||
\(225\) | 8370.31i | 0.165339i | ||||||||
\(226\) | −14378.3 | + | 14378.3i | −0.281508 | + | 0.281508i | ||||
\(227\) | −63491.1 | + | 63491.1i | −1.23214 | + | 1.23214i | −0.269003 | + | 0.963139i | \(0.586694\pi\) |
−0.963139 | + | 0.269003i | \(0.913306\pi\) | |||||||
\(228\) | 18295.2 | + | 18295.2i | 0.351939 | + | 0.351939i | ||||
\(229\) | 21248.1 | + | 21248.1i | 0.405180 | + | 0.405180i | 0.880054 | − | 0.474874i | \(-0.157506\pi\) |
−0.474874 | + | 0.880054i | \(0.657506\pi\) | |||||||
\(230\) | −1752.88 | −0.0331356 | ||||||||
\(231\) | − | 83423.5i | − | 1.56338i | ||||||
\(232\) | −54484.0 | − | 54484.0i | −1.01226 | − | 1.01226i | ||||
\(233\) | − | 7414.27i | − | 0.136570i | −0.997666 | − | 0.0682852i | \(-0.978247\pi\) | ||
0.997666 | − | 0.0682852i | \(-0.0217528\pi\) | |||||||
\(234\) | 4893.88 | + | 3060.93i | 0.0893762 | + | 0.0559013i | ||||
\(235\) | −35873.2 | −0.649582 | ||||||||
\(236\) | 19495.5 | − | 19495.5i | 0.350034 | − | 0.350034i | ||||
\(237\) | −12318.7 | −0.219316 | ||||||||
\(238\) | 36036.3i | 0.636189i | ||||||||
\(239\) | 40406.7 | − | 40406.7i | 0.707388 | − | 0.707388i | −0.258597 | − | 0.965985i | \(-0.583260\pi\) |
0.965985 | + | 0.258597i | \(0.0832603\pi\) | |||||||
\(240\) | −9611.07 | + | 9611.07i | −0.166859 | + | 0.166859i | ||||
\(241\) | −65853.8 | − | 65853.8i | −1.13383 | − | 1.13383i | −0.989535 | − | 0.144291i | \(-0.953910\pi\) |
−0.144291 | − | 0.989535i | \(-0.546090\pi\) | |||||||
\(242\) | −2300.64 | − | 2300.64i | −0.0392843 | − | 0.0392843i | ||||
\(243\) | −26464.8 | −0.448184 | ||||||||
\(244\) | − | 11300.0i | − | 0.189801i | ||||||
\(245\) | 17297.9 | + | 17297.9i | 0.288178 | + | 0.288178i | ||||
\(246\) | − | 14254.3i | − | 0.235546i | ||||||
\(247\) | −29528.1 | − | 18468.6i | −0.483995 | − | 0.302720i | ||||
\(248\) | 72816.8 | 1.18394 | ||||||||
\(249\) | −26139.0 | + | 26139.0i | −0.421590 | + | 0.421590i | ||||
\(250\) | −26132.1 | −0.418114 | ||||||||
\(251\) | 11580.7i | 0.183817i | 0.995767 | + | 0.0919086i | \(0.0292968\pi\) | ||||
−0.995767 | + | 0.0919086i | \(0.970703\pi\) | |||||||
\(252\) | 10746.2 | − | 10746.2i | 0.169221 | − | 0.169221i | ||||
\(253\) | −6546.73 | + | 6546.73i | −0.102278 | + | 0.102278i | ||||
\(254\) | −21792.5 | − | 21792.5i | −0.337785 | − | 0.337785i | ||||
\(255\) | 27649.6 | + | 27649.6i | 0.425214 | + | 0.425214i | ||||
\(256\) | −33846.5 | −0.516456 | ||||||||
\(257\) | 112157.i | 1.69808i | 0.528325 | + | 0.849042i | \(0.322820\pi\) | ||||
−0.528325 | + | 0.849042i | \(0.677180\pi\) | |||||||
\(258\) | 29764.6 | + | 29764.6i | 0.447157 | + | 0.447157i | ||||
\(259\) | − | 31922.8i | − | 0.475885i | ||||||
\(260\) | 14805.1 | − | 23670.7i | 0.219010 | − | 0.350158i | ||||
\(261\) | 26973.9 | 0.395971 | ||||||||
\(262\) | −28434.4 | + | 28434.4i | −0.414229 | + | 0.414229i | ||||
\(263\) | −49442.1 | −0.714802 | −0.357401 | − | 0.933951i | \(-0.616337\pi\) | ||||
−0.357401 | + | 0.933951i | \(0.616337\pi\) | |||||||
\(264\) | − | 67463.9i | − | 0.967974i | ||||||
\(265\) | 40430.9 | − | 40430.9i | 0.575734 | − | 0.575734i | ||||
\(266\) | 17581.1 | − | 17581.1i | 0.248475 | − | 0.248475i | ||||
\(267\) | 28383.5 | + | 28383.5i | 0.398147 | + | 0.398147i | ||||
\(268\) | 28106.7 | + | 28106.7i | 0.391327 | + | 0.391327i | ||||
\(269\) | 48335.1 | 0.667972 | 0.333986 | − | 0.942578i | \(-0.391606\pi\) | ||||
0.333986 | + | 0.942578i | \(0.391606\pi\) | |||||||
\(270\) | − | 15118.5i | − | 0.207387i | ||||||
\(271\) | 29110.8 | + | 29110.8i | 0.396383 | + | 0.396383i | 0.876955 | − | 0.480572i | \(-0.159571\pi\) |
−0.480572 | + | 0.876955i | \(0.659571\pi\) | |||||||
\(272\) | − | 31011.8i | − | 0.419169i | ||||||
\(273\) | −58375.4 | + | 93331.8i | −0.783258 | + | 1.25229i | ||||
\(274\) | −2177.93 | −0.0290097 | ||||||||
\(275\) | −40999.8 | + | 40999.8i | −0.542146 | + | 0.542146i | ||||
\(276\) | −9076.07 | −0.119146 | ||||||||
\(277\) | − | 122108.i | − | 1.59142i | −0.605679 | − | 0.795709i | \(-0.707098\pi\) | ||
0.605679 | − | 0.795709i | \(-0.292902\pi\) | |||||||
\(278\) | 28331.9 | − | 28331.9i | 0.366594 | − | 0.366594i | ||||
\(279\) | −18025.0 | + | 18025.0i | −0.231562 | + | 0.231562i | ||||
\(280\) | 32008.7 | + | 32008.7i | 0.408275 | + | 0.408275i | ||||
\(281\) | 91868.7 | + | 91868.7i | 1.16347 | + | 1.16347i | 0.983711 | + | 0.179759i | \(0.0575318\pi\) |
0.179759 | + | 0.983711i | \(0.442468\pi\) | |||||||
\(282\) | 50364.7 | 0.633327 | ||||||||
\(283\) | − | 19341.5i | − | 0.241500i | −0.992683 | − | 0.120750i | \(-0.961470\pi\) | ||
0.992683 | − | 0.120750i | \(-0.0385299\pi\) | |||||||
\(284\) | −15331.1 | − | 15331.1i | −0.190080 | − | 0.190080i | ||||
\(285\) | − | 26978.9i | − | 0.332151i | ||||||
\(286\) | 8978.23 | + | 38964.6i | 0.109764 | + | 0.476363i | ||||
\(287\) | 50518.1 | 0.613314 | ||||||||
\(288\) | 13554.3 | − | 13554.3i | 0.163416 | − | 0.163416i | ||||
\(289\) | −5695.00 | −0.0681865 | ||||||||
\(290\) | 35376.2i | 0.420644i | ||||||||
\(291\) | −41782.6 | + | 41782.6i | −0.493412 | + | 0.493412i | ||||
\(292\) | −20334.0 | + | 20334.0i | −0.238483 | + | 0.238483i | ||||
\(293\) | −73142.2 | − | 73142.2i | −0.851986 | − | 0.851986i | 0.138391 | − | 0.990378i | \(-0.455807\pi\) |
−0.990378 | + | 0.138391i | \(0.955807\pi\) | |||||||
\(294\) | −24285.6 | − | 24285.6i | −0.280967 | − | 0.280967i | ||||
\(295\) | −28748.9 | −0.330352 | ||||||||
\(296\) | − | 25815.8i | − | 0.294647i | ||||||
\(297\) | −56465.5 | − | 56465.5i | −0.640133 | − | 0.640133i | ||||
\(298\) | − | 73622.2i | − | 0.829041i | ||||||
\(299\) | 11905.3 | − | 2743.23i | 0.133168 | − | 0.0306846i | ||||
\(300\) | −56840.1 | −0.631557 | ||||||||
\(301\) | −105487. | + | 105487.i | −1.16431 | + | 1.16431i | ||||
\(302\) | 39779.9 | 0.436164 | ||||||||
\(303\) | − | 106471.i | − | 1.15970i | ||||||
\(304\) | −15129.8 | + | 15129.8i | −0.163714 | + | 0.163714i | ||||
\(305\) | −8331.74 | + | 8331.74i | −0.0895645 | + | 0.0895645i | ||||
\(306\) | −7213.87 | − | 7213.87i | −0.0770416 | − | 0.0770416i | ||||
\(307\) | 48488.0 | + | 48488.0i | 0.514467 | + | 0.514467i | 0.915892 | − | 0.401425i | \(-0.131485\pi\) |
−0.401425 | + | 0.915892i | \(0.631485\pi\) | |||||||
\(308\) | 105275. | 1.10975 | ||||||||
\(309\) | − | 131780.i | − | 1.38017i | ||||||
\(310\) | −23639.8 | − | 23639.8i | −0.245991 | − | 0.245991i | ||||
\(311\) | 77566.8i | 0.801965i | 0.916086 | + | 0.400982i | \(0.131331\pi\) | ||||
−0.916086 | + | 0.400982i | \(0.868669\pi\) | |||||||
\(312\) | −47207.7 | + | 75476.7i | −0.484958 | + | 0.775361i | ||||
\(313\) | −154244. | −1.57441 | −0.787206 | − | 0.616690i | \(-0.788473\pi\) | ||||
−0.787206 | + | 0.616690i | \(0.788473\pi\) | |||||||
\(314\) | 7365.93 | − | 7365.93i | 0.0747082 | − | 0.0747082i | ||||
\(315\) | −15846.9 | −0.159706 | ||||||||
\(316\) | − | 15545.5i | − | 0.155679i | ||||||
\(317\) | 81584.8 | − | 81584.8i | 0.811878 | − | 0.811878i | −0.173038 | − | 0.984915i | \(-0.555358\pi\) |
0.984915 | + | 0.173038i | \(0.0553582\pi\) | |||||||
\(318\) | −56763.6 | + | 56763.6i | −0.561327 | + | 0.561327i | ||||
\(319\) | 132125. | + | 132125.i | 1.29838 | + | 1.29838i | ||||
\(320\) | 2359.24 | + | 2359.24i | 0.0230395 | + | 0.0230395i | ||||
\(321\) | −50359.4 | −0.488732 | ||||||||
\(322\) | 8721.82i | 0.0841193i | ||||||||
\(323\) | 43526.1 | + | 43526.1i | 0.417200 | + | 0.417200i | ||||
\(324\) | − | 97130.7i | − | 0.925266i | ||||||
\(325\) | 74558.9 | − | 17179.9i | 0.705883 | − | 0.162650i | ||||
\(326\) | −59546.4 | −0.560300 | ||||||||
\(327\) | 62048.4 | − | 62048.4i | 0.580277 | − | 0.580277i | ||||
\(328\) | 40853.6 | 0.379736 | ||||||||
\(329\) | 178495.i | 1.64905i | ||||||||
\(330\) | −21902.0 | + | 21902.0i | −0.201120 | + | 0.201120i | ||||
\(331\) | 117644. | − | 117644.i | 1.07378 | − | 1.07378i | 0.0767231 | − | 0.997052i | \(-0.475554\pi\) |
0.997052 | − | 0.0767231i | \(-0.0244458\pi\) | |||||||
\(332\) | −32985.8 | − | 32985.8i | −0.299261 | − | 0.299261i | ||||
\(333\) | 6390.43 | + | 6390.43i | 0.0576290 | + | 0.0576290i | ||||
\(334\) | 30300.7 | 0.271619 | ||||||||
\(335\) | − | 41447.4i | − | 0.369324i | ||||||
\(336\) | 47822.0 | + | 47822.0i | 0.423594 | + | 0.423594i | ||||
\(337\) | − | 75439.4i | − | 0.664260i | −0.943234 | − | 0.332130i | \(-0.892233\pi\) | ||
0.943234 | − | 0.332130i | \(-0.107767\pi\) | |||||||
\(338\) | 17220.8 | − | 49874.9i | 0.150737 | − | 0.436565i | ||||
\(339\) | 109785. | 0.955306 | ||||||||
\(340\) | −34892.0 | + | 34892.0i | −0.301834 | + | 0.301834i | ||||
\(341\) | −176582. | −1.51858 | ||||||||
\(342\) | 7038.90i | 0.0601800i | ||||||||
\(343\) | −24804.4 | + | 24804.4i | −0.210834 | + | 0.210834i | ||||
\(344\) | −85306.7 | + | 85306.7i | −0.720885 | + | 0.720885i | ||||
\(345\) | 6691.99 | + | 6691.99i | 0.0562234 | + | 0.0562234i | ||||
\(346\) | 9491.85 | + | 9491.85i | 0.0792864 | + | 0.0792864i | ||||
\(347\) | −20140.8 | −0.167270 | −0.0836349 | − | 0.996496i | \(-0.526653\pi\) | ||||
−0.0836349 | + | 0.996496i | \(0.526653\pi\) | |||||||
\(348\) | 183171.i | 1.51251i | ||||||||
\(349\) | −39641.5 | − | 39641.5i | −0.325461 | − | 0.325461i | 0.525396 | − | 0.850858i | \(-0.323917\pi\) |
−0.850858 | + | 0.525396i | \(0.823917\pi\) | |||||||
\(350\) | 54621.6i | 0.445891i | ||||||||
\(351\) | 23660.4 | + | 102684.i | 0.192047 | + | 0.833464i | ||||
\(352\) | 132785. | 1.07168 | ||||||||
\(353\) | 109698. | − | 109698.i | 0.880337 | − | 0.880337i | −0.113232 | − | 0.993569i | \(-0.536120\pi\) |
0.993569 | + | 0.113232i | \(0.0361202\pi\) | |||||||
\(354\) | 40362.5 | 0.322086 | ||||||||
\(355\) | 22607.9i | 0.179393i | ||||||||
\(356\) | −35818.2 | + | 35818.2i | −0.282620 | + | 0.282620i | ||||
\(357\) | 137577. | − | 137577.i | 1.07946 | − | 1.07946i | ||||
\(358\) | −24436.2 | − | 24436.2i | −0.190663 | − | 0.190663i | ||||
\(359\) | −64675.4 | − | 64675.4i | −0.501823 | − | 0.501823i | 0.410181 | − | 0.912004i | \(-0.365465\pi\) |
−0.912004 | + | 0.410181i | \(0.865465\pi\) | |||||||
\(360\) | −12815.2 | −0.0988830 | ||||||||
\(361\) | 87850.6i | 0.674109i | ||||||||
\(362\) | −19505.2 | − | 19505.2i | −0.148844 | − | 0.148844i | ||||
\(363\) | 17566.4i | 0.133312i | ||||||||
\(364\) | −117779. | − | 73666.0i | −0.888923 | − | 0.555987i | ||||
\(365\) | 29985.4 | 0.225074 | ||||||||
\(366\) | 11697.5 | − | 11697.5i | 0.0873232 | − | 0.0873232i | ||||
\(367\) | −76091.9 | −0.564945 | −0.282473 | − | 0.959275i | \(-0.591155\pi\) | ||||
−0.282473 | + | 0.959275i | \(0.591155\pi\) | |||||||
\(368\) | − | 7505.75i | − | 0.0554241i | ||||||
\(369\) | −10112.9 | + | 10112.9i | −0.0742715 | + | 0.0742715i | ||||
\(370\) | −8381.02 | + | 8381.02i | −0.0612200 | + | 0.0612200i | ||||
\(371\) | −201173. | − | 201173.i | −1.46158 | − | 1.46158i | ||||
\(372\) | −122402. | − | 122402.i | −0.884513 | − | 0.884513i | ||||
\(373\) | −71517.3 | −0.514036 | −0.257018 | − | 0.966407i | \(-0.582740\pi\) | ||||
−0.257018 | + | 0.966407i | \(0.582740\pi\) | |||||||
\(374\) | − | 70670.5i | − | 0.505237i | ||||||
\(375\) | 99765.3 | + | 99765.3i | 0.709442 | + | 0.709442i | ||||
\(376\) | 144347.i | 1.02102i | ||||||||
\(377\) | −55363.4 | − | 240271.i | −0.389529 | − | 1.69052i | ||||
\(378\) | −75225.7 | −0.526481 | ||||||||
\(379\) | 28771.4 | − | 28771.4i | 0.200301 | − | 0.200301i | −0.599828 | − | 0.800129i | \(-0.704764\pi\) |
0.800129 | + | 0.599828i | \(0.204764\pi\) | |||||||
\(380\) | 34045.7 | 0.235774 | ||||||||
\(381\) | 166396.i | 1.14628i | ||||||||
\(382\) | 44803.8 | − | 44803.8i | 0.307035 | − | 0.307035i | ||||
\(383\) | −64468.1 | + | 64468.1i | −0.439488 | + | 0.439488i | −0.891840 | − | 0.452352i | \(-0.850585\pi\) |
0.452352 | + | 0.891840i | \(0.350585\pi\) | |||||||
\(384\) | 113689. | + | 113689.i | 0.771000 | + | 0.771000i | ||||
\(385\) | −77621.8 | − | 77621.8i | −0.523675 | − | 0.523675i | ||||
\(386\) | 13176.9 | 0.0884379 | ||||||||
\(387\) | − | 42233.6i | − | 0.281992i | ||||||
\(388\) | −52727.0 | − | 52727.0i | −0.350243 | − | 0.350243i | ||||
\(389\) | 220659.i | 1.45822i | 0.684397 | + | 0.729110i | \(0.260066\pi\) | ||||
−0.684397 | + | 0.729110i | \(0.739934\pi\) | |||||||
\(390\) | 39829.2 | − | 9177.45i | 0.261862 | − | 0.0603382i | ||||
\(391\) | −21592.9 | −0.141240 | ||||||||
\(392\) | 69603.7 | − | 69603.7i | 0.452961 | − | 0.452961i | ||||
\(393\) | 217109. | 1.40570 | ||||||||
\(394\) | − | 24279.5i | − | 0.156404i | ||||||
\(395\) | −11462.0 | + | 11462.0i | −0.0734627 | + | 0.0734627i | ||||
\(396\) | −21074.3 | + | 21074.3i | −0.134389 | + | 0.134389i | ||||
\(397\) | 96072.7 | + | 96072.7i | 0.609563 | + | 0.609563i | 0.942832 | − | 0.333269i | \(-0.108152\pi\) |
−0.333269 | + | 0.942832i | \(0.608152\pi\) | |||||||
\(398\) | −12197.6 | − | 12197.6i | −0.0770029 | − | 0.0770029i | ||||
\(399\) | −134240. | −0.843209 | ||||||||
\(400\) | − | 47005.8i | − | 0.293786i | ||||||
\(401\) | −3174.38 | − | 3174.38i | −0.0197410 | − | 0.0197410i | 0.697167 | − | 0.716908i | \(-0.254443\pi\) |
−0.716908 | + | 0.697167i | \(0.754443\pi\) | |||||||
\(402\) | 58190.7i | 0.360082i | ||||||||
\(403\) | 197555. | + | 123563.i | 1.21640 | + | 0.760813i | ||||
\(404\) | 134360. | 0.823201 | ||||||||
\(405\) | −71616.7 | + | 71616.7i | −0.436621 | + | 0.436621i | ||||
\(406\) | 176022. | 1.06786 | ||||||||
\(407\) | 62603.7i | 0.377930i | ||||||||
\(408\) | 111257. | − | 111257.i | 0.668355 | − | 0.668355i | ||||
\(409\) | 46288.7 | − | 46288.7i | 0.276712 | − | 0.276712i | −0.555083 | − | 0.831795i | \(-0.687313\pi\) |
0.831795 | + | 0.555083i | \(0.187313\pi\) | |||||||
\(410\) | −13263.0 | − | 13263.0i | −0.0788995 | − | 0.0788995i | ||||
\(411\) | 8314.73 | + | 8314.73i | 0.0492226 | + | 0.0492226i | ||||
\(412\) | 166298. | 0.979701 | ||||||||
\(413\) | 143047.i | 0.838644i | ||||||||
\(414\) | −1745.96 | − | 1745.96i | −0.0101867 | − | 0.0101867i | ||||
\(415\) | 48642.3i | 0.282435i | ||||||||
\(416\) | −148556. | − | 92915.9i | −0.858426 | − | 0.536912i | ||||
\(417\) | −216327. | −1.24405 | ||||||||
\(418\) | −34478.2 | + | 34478.2i | −0.197330 | + | 0.197330i | ||||
\(419\) | 67972.5 | 0.387173 | 0.193586 | − | 0.981083i | \(-0.437988\pi\) | ||||
0.193586 | + | 0.981083i | \(0.437988\pi\) | |||||||
\(420\) | − | 107611.i | − | 0.610040i | ||||||
\(421\) | −187465. | + | 187465.i | −1.05768 | + | 1.05768i | −0.0594522 | + | 0.998231i | \(0.518935\pi\) |
−0.998231 | + | 0.0594522i | \(0.981065\pi\) | |||||||
\(422\) | −70301.3 | + | 70301.3i | −0.394765 | + | 0.394765i | ||||
\(423\) | −35731.7 | − | 35731.7i | −0.199698 | − | 0.199698i | ||||
\(424\) | −162687. | − | 162687.i | −0.904943 | − | 0.904943i | ||||
\(425\) | −135228. | −0.748669 | ||||||||
\(426\) | − | 31740.8i | − | 0.174903i | ||||||
\(427\) | 41456.4 | + | 41456.4i | 0.227371 | + | 0.227371i | ||||
\(428\) | − | 63550.4i | − | 0.346921i | ||||||
\(429\) | 114480. | − | 183032.i | 0.622033 | − | 0.994520i | ||||
\(430\) | 55389.2 | 0.299563 | ||||||||
\(431\) | 66845.4 | − | 66845.4i | 0.359846 | − | 0.359846i | −0.503910 | − | 0.863756i | \(-0.668106\pi\) |
0.863756 | + | 0.503910i | \(0.168106\pi\) | |||||||
\(432\) | 64737.0 | 0.346885 | ||||||||
\(433\) | − | 186395.i | − | 0.994166i | −0.867703 | − | 0.497083i | \(-0.834404\pi\) | ||
0.867703 | − | 0.497083i | \(-0.165596\pi\) | |||||||
\(434\) | −117625. | + | 117625.i | −0.624482 | + | 0.624482i | ||||
\(435\) | 135057. | − | 135057.i | 0.713735 | − | 0.713735i | ||||
\(436\) | 78301.1 | + | 78301.1i | 0.411903 | + | 0.411903i | ||||
\(437\) | 10534.6 | + | 10534.6i | 0.0551638 | + | 0.0551638i | ||||
\(438\) | −42098.5 | −0.219441 | ||||||||
\(439\) | − | 106639.i | − | 0.553333i | −0.960966 | − | 0.276667i | \(-0.910770\pi\) | ||
0.960966 | − | 0.276667i | \(-0.0892297\pi\) | |||||||
\(440\) | −62772.1 | − | 62772.1i | −0.324236 | − | 0.324236i | ||||
\(441\) | 34459.4i | 0.177186i | ||||||||
\(442\) | −49451.5 | + | 79064.1i | −0.253125 | + | 0.404702i | ||||
\(443\) | 90694.5 | 0.462140 | 0.231070 | − | 0.972937i | \(-0.425777\pi\) | ||||
0.231070 | + | 0.972937i | \(0.425777\pi\) | |||||||
\(444\) | −43395.4 | + | 43395.4i | −0.220129 | + | 0.220129i | ||||
\(445\) | 52819.1 | 0.266730 | ||||||||
\(446\) | 70973.3i | 0.356800i | ||||||||
\(447\) | −281069. | + | 281069.i | −1.40669 | + | 1.40669i | ||||
\(448\) | 11738.9 | − | 11738.9i | 0.0584888 | − | 0.0584888i | ||||
\(449\) | 53532.0 | + | 53532.0i | 0.265534 | + | 0.265534i | 0.827298 | − | 0.561764i | \(-0.189877\pi\) |
−0.561764 | + | 0.827298i | \(0.689877\pi\) | |||||||
\(450\) | −10934.3 | − | 10934.3i | −0.0539968 | − | 0.0539968i | ||||
\(451\) | −99070.7 | −0.487071 | ||||||||
\(452\) | 138541.i | 0.678114i | ||||||||
\(453\) | −151869. | − | 151869.i | −0.740069 | − | 0.740069i | ||||
\(454\) | − | 165880.i | − | 0.804789i | ||||||
\(455\) | 32525.3 | + | 141157.i | 0.157108 | + | 0.681834i | ||||
\(456\) | −108559. | −0.522077 | ||||||||
\(457\) | 21404.9 | − | 21404.9i | 0.102490 | − | 0.102490i | −0.654003 | − | 0.756492i | \(-0.726911\pi\) |
0.756492 | + | 0.654003i | \(0.226911\pi\) | |||||||
\(458\) | −55513.8 | −0.264649 | ||||||||
\(459\) | − | 186238.i | − | 0.883982i | ||||||
\(460\) | −8444.87 | + | 8444.87i | −0.0399096 | + | 0.0399096i | ||||
\(461\) | 225398. | − | 225398.i | 1.06059 | − | 1.06059i | 0.0625486 | − | 0.998042i | \(-0.480077\pi\) |
0.998042 | − | 0.0625486i | \(-0.0199228\pi\) | |||||||
\(462\) | 108978. | + | 108978.i | 0.510571 | + | 0.510571i | ||||
\(463\) | 1729.47 | + | 1729.47i | 0.00806774 | + | 0.00806774i | 0.711129 | − | 0.703061i | \(-0.248184\pi\) |
−0.703061 | + | 0.711129i | \(0.748184\pi\) | |||||||
\(464\) | −151480. | −0.703587 | ||||||||
\(465\) | 180500.i | 0.834780i | ||||||||
\(466\) | 9685.45 | + | 9685.45i | 0.0446014 | + | 0.0446014i | ||||
\(467\) | − | 131914.i | − | 0.604864i | −0.953171 | − | 0.302432i | \(-0.902201\pi\) | ||
0.953171 | − | 0.302432i | \(-0.0977985\pi\) | |||||||
\(468\) | 38324.1 | − | 8830.64i | 0.174977 | − | 0.0403182i | ||||
\(469\) | −206231. | −0.937578 | ||||||||
\(470\) | 46862.0 | − | 46862.0i | 0.212141 | − | 0.212141i | ||||
\(471\) | −56242.2 | −0.253525 | ||||||||
\(472\) | 115681.i | 0.519251i | ||||||||
\(473\) | 206870. | − | 206870.i | 0.924647 | − | 0.924647i | ||||
\(474\) | 16092.3 | − | 16092.3i | 0.0716243 | − | 0.0716243i | ||||
\(475\) | 65974.2 | + | 65974.2i | 0.292406 | + | 0.292406i | ||||
\(476\) | 173613. | + | 173613.i | 0.766245 | + | 0.766245i | ||||
\(477\) | 80543.0 | 0.353990 | ||||||||
\(478\) | 105569.i | 0.462039i | ||||||||
\(479\) | 113839. | + | 113839.i | 0.496158 | + | 0.496158i | 0.910240 | − | 0.414082i | \(-0.135897\pi\) |
−0.414082 | + | 0.910240i | \(0.635897\pi\) | |||||||
\(480\) | − | 135731.i | − | 0.589111i | ||||||
\(481\) | 43806.8 | − | 70039.2i | 0.189344 | − | 0.302727i | ||||
\(482\) | 172053. | 0.740573 | ||||||||
\(483\) | 33297.5 | − | 33297.5i | 0.142731 | − | 0.142731i | ||||
\(484\) | −22167.7 | −0.0946304 | ||||||||
\(485\) | 77753.7i | 0.330550i | ||||||||
\(486\) | 34571.6 | − | 34571.6i | 0.146368 | − | 0.146368i | ||||
\(487\) | −252418. | + | 252418.i | −1.06430 | + | 1.06430i | −0.0665104 | + | 0.997786i | \(0.521187\pi\) |
−0.997786 | + | 0.0665104i | \(0.978813\pi\) | |||||||
\(488\) | 33525.5 | + | 33525.5i | 0.140778 | + | 0.140778i | ||||
\(489\) | 227332. | + | 227332.i | 0.950698 | + | 0.950698i | ||||
\(490\) | −45193.3 | −0.188227 | ||||||||
\(491\) | − | 336665.i | − | 1.39648i | −0.715864 | − | 0.698240i | \(-0.753967\pi\) | ||
0.715864 | − | 0.698240i | \(-0.246033\pi\) | |||||||
\(492\) | −68673.4 | − | 68673.4i | −0.283699 | − | 0.283699i | ||||
\(493\) | 435783.i | 1.79298i | ||||||||
\(494\) | 62699.3 | − | 14447.2i | 0.256926 | − | 0.0592010i | ||||
\(495\) | 31077.2 | 0.126833 | ||||||||
\(496\) | 101225. | − | 101225.i | 0.411455 | − | 0.411455i | ||||
\(497\) | 112491. | 0.455412 | ||||||||
\(498\) | − | 68292.1i | − | 0.275367i | ||||||
\(499\) | 239050. | − | 239050.i | 0.960036 | − | 0.960036i | −0.0391952 | − | 0.999232i | \(-0.512479\pi\) |
0.999232 | + | 0.0391952i | \(0.0124794\pi\) | |||||||
\(500\) | −125897. | + | 125897.i | −0.503590 | + | 0.503590i | ||||
\(501\) | −115680. | − | 115680.i | −0.460874 | − | 0.460874i | ||||
\(502\) | −15128.1 | − | 15128.1i | −0.0600313 | − | 0.0600313i | ||||
\(503\) | 27136.5 | 0.107255 | 0.0536276 | − | 0.998561i | \(-0.482922\pi\) | ||||
0.0536276 | + | 0.998561i | \(0.482922\pi\) | |||||||
\(504\) | 63765.1i | 0.251028i | ||||||||
\(505\) | −99066.4 | − | 99066.4i | −0.388458 | − | 0.388458i | ||||
\(506\) | − | 17104.3i | − | 0.0668043i | ||||||
\(507\) | −256153. | + | 124665.i | −0.996514 | + | 0.484984i | ||||
\(508\) | −209981. | −0.813677 | ||||||||
\(509\) | −193359. | + | 193359.i | −0.746325 | + | 0.746325i | −0.973787 | − | 0.227462i | \(-0.926957\pi\) |
0.227462 | + | 0.973787i | \(0.426957\pi\) | |||||||
\(510\) | −72238.6 | −0.277734 | ||||||||
\(511\) | − | 149199.i | − | 0.571380i | ||||||
\(512\) | −138154. | + | 138154.i | −0.527017 | + | 0.527017i | ||||
\(513\) | −90860.6 | + | 90860.6i | −0.345256 | + | 0.345256i | ||||
\(514\) | −146513. | − | 146513.i | −0.554563 | − | 0.554563i | ||||
\(515\) | −122616. | − | 122616.i | −0.462308 | − | 0.462308i | ||||
\(516\) | 286795. | 1.07714 | ||||||||
\(517\) | − | 350045.i | − | 1.30961i | ||||||
\(518\) | 41701.6 | + | 41701.6i | 0.155415 | + | 0.155415i | ||||
\(519\) | − | 72474.5i | − | 0.269061i | ||||||
\(520\) | 26303.0 | + | 114152.i | 0.0972744 | + | 0.422161i | ||||
\(521\) | 436420. | 1.60779 | 0.803895 | − | 0.594772i | \(-0.202758\pi\) | ||||
0.803895 | + | 0.594772i | \(0.202758\pi\) | |||||||
\(522\) | −35236.7 | + | 35236.7i | −0.129317 | + | 0.129317i | ||||
\(523\) | −405280. | −1.48167 | −0.740835 | − | 0.671687i | \(-0.765570\pi\) | ||||
−0.740835 | + | 0.671687i | \(0.765570\pi\) | |||||||
\(524\) | 273978.i | 0.997821i | ||||||||
\(525\) | 208530. | − | 208530.i | 0.756572 | − | 0.756572i | ||||
\(526\) | 64587.5 | − | 64587.5i | 0.233441 | − | 0.233441i | ||||
\(527\) | −291207. | − | 291207.i | −1.04853 | − | 1.04853i | ||||
\(528\) | −93783.5 | − | 93783.5i | −0.336402 | − | 0.336402i | ||||
\(529\) | 274615. | 0.981325 | ||||||||
\(530\) | 105632.i | 0.376048i | ||||||||
\(531\) | −28635.6 | − | 28635.6i | −0.101559 | − | 0.101559i | ||||
\(532\) | − | 169402.i | − | 0.598543i | ||||||
\(533\) | 110837. | + | 69324.5i | 0.390150 | + | 0.244024i | ||||
\(534\) | −74156.2 | −0.260055 | ||||||||
\(535\) | −46857.1 | + | 46857.1i | −0.163707 | + | 0.163707i | ||||
\(536\) | −166777. | −0.580506 | ||||||||
\(537\) | 186581.i | 0.647022i | ||||||||
\(538\) | −63141.4 | + | 63141.4i | −0.218147 | + | 0.218147i | ||||
\(539\) | −168790. | + | 168790.i | −0.580992 | + | 0.580992i | ||||
\(540\) | −72837.0 | − | 72837.0i | −0.249784 | − | 0.249784i | ||||
\(541\) | −16926.3 | − | 16926.3i | −0.0578320 | − | 0.0578320i | 0.677599 | − | 0.735431i | \(-0.263020\pi\) |
−0.735431 | + | 0.677599i | \(0.763020\pi\) | |||||||
\(542\) | −76056.2 | −0.258902 | ||||||||
\(543\) | 148931.i | 0.505108i | ||||||||
\(544\) | 218980. | + | 218980.i | 0.739957 | + | 0.739957i | ||||
\(545\) | − | 115466.i | − | 0.388743i | ||||||
\(546\) | −45664.4 | − | 198179.i | −0.153177 | − | 0.664771i | ||||
\(547\) | 249610. | 0.834234 | 0.417117 | − | 0.908853i | \(-0.363041\pi\) | ||||
0.417117 | + | 0.908853i | \(0.363041\pi\) | |||||||
\(548\) | −10492.7 | + | 10492.7i | −0.0349401 | + | 0.0349401i | ||||
\(549\) | −16597.8 | −0.0550688 | ||||||||
\(550\) | − | 107118.i | − | 0.354109i | ||||||
\(551\) | 212607. | − | 212607.i | 0.700283 | − | 0.700283i | ||||
\(552\) | 26927.4 | − | 26927.4i | 0.0883724 | − | 0.0883724i | ||||
\(553\) | 57031.8 | + | 57031.8i | 0.186495 | + | 0.186495i | ||||
\(554\) | 159513. | + | 159513.i | 0.519728 | + | 0.519728i | ||||
\(555\) | 63992.8 | 0.207752 | ||||||||
\(556\) | − | 272990.i | − | 0.883075i | ||||||
\(557\) | 294084. | + | 294084.i | 0.947896 | + | 0.947896i | 0.998708 | − | 0.0508124i | \(-0.0161811\pi\) |
−0.0508124 | + | 0.998708i | \(0.516181\pi\) | |||||||
\(558\) | − | 47093.1i | − | 0.151248i | ||||||
\(559\) | −376198. | + | 86683.5i | −1.20391 | + | 0.277404i | ||||
\(560\) | 88992.5 | 0.283777 | ||||||||
\(561\) | −269800. | + | 269800.i | −0.857269 | + | 0.857269i | ||||
\(562\) | −240021. | −0.759935 | ||||||||
\(563\) | − | 196107.i | − | 0.618694i | −0.950949 | − | 0.309347i | \(-0.899890\pi\) | ||
0.950949 | − | 0.309347i | \(-0.100110\pi\) | |||||||
\(564\) | 242643. | − | 242643.i | 0.762798 | − | 0.762798i | ||||
\(565\) | 102150. | − | 102150.i | 0.319993 | − | 0.319993i | ||||
\(566\) | 25266.3 | + | 25266.3i | 0.0788693 | + | 0.0788693i | ||||
\(567\) | 356345. | + | 356345.i | 1.10842 | + | 1.10842i | ||||
\(568\) | 90970.5 | 0.281971 | ||||||||
\(569\) | 446515.i | 1.37915i | 0.724215 | + | 0.689575i | \(0.242202\pi\) | ||||
−0.724215 | + | 0.689575i | \(0.757798\pi\) | |||||||
\(570\) | 35243.3 | + | 35243.3i | 0.108474 | + | 0.108474i | ||||
\(571\) | − | 337194.i | − | 1.03421i | −0.855922 | − | 0.517104i | \(-0.827010\pi\) | ||
0.855922 | − | 0.517104i | \(-0.172990\pi\) | |||||||
\(572\) | 230975. | + | 144466.i | 0.705949 | + | 0.441544i | ||||
\(573\) | −342097. | −1.04194 | ||||||||
\(574\) | −65993.0 | + | 65993.0i | −0.200297 | + | 0.200297i | ||||
\(575\) | −32729.2 | −0.0989918 | ||||||||
\(576\) | 4699.88i | 0.0141658i | ||||||||
\(577\) | −111217. | + | 111217.i | −0.334055 | + | 0.334055i | −0.854124 | − | 0.520069i | \(-0.825906\pi\) |
0.520069 | + | 0.854124i | \(0.325906\pi\) | |||||||
\(578\) | 7439.52 | − | 7439.52i | 0.0222684 | − | 0.0222684i | ||||
\(579\) | −50305.8 | − | 50305.8i | −0.150058 | − | 0.150058i | ||||
\(580\) | 170433. | + | 170433.i | 0.506637 | + | 0.506637i | ||||
\(581\) | 242031. | 0.716998 | ||||||||
\(582\) | − | 109163.i | − | 0.322278i | ||||||
\(583\) | 394519. | + | 394519.i | 1.16073 | + | 1.16073i | ||||
\(584\) | − | 120656.i | − | 0.353772i | ||||||
\(585\) | −34768.3 | − | 21746.2i | −0.101595 | − | 0.0635435i | ||||
\(586\) | 191095. | 0.556486 | ||||||||
\(587\) | 36868.8 | − | 36868.8i | 0.107000 | − | 0.107000i | −0.651580 | − | 0.758580i | \(-0.725894\pi\) |
0.758580 | + | 0.651580i | \(0.225894\pi\) | |||||||
\(588\) | −234003. | −0.676810 | ||||||||
\(589\) | 284144.i | 0.819046i | ||||||||
\(590\) | 37555.4 | − | 37555.4i | 0.107887 | − | 0.107887i | ||||
\(591\) | −92692.3 | + | 92692.3i | −0.265380 | + | 0.265380i | ||||
\(592\) | −35887.2 | − | 35887.2i | −0.102399 | − | 0.102399i | ||||
\(593\) | −404224. | − | 404224.i | −1.14951 | − | 1.14951i | −0.986649 | − | 0.162862i | \(-0.947928\pi\) |
−0.162862 | − | 0.986649i | \(-0.552072\pi\) | |||||||
\(594\) | 147525. | 0.418111 | ||||||||
\(595\) | − | 256017.i | − | 0.723162i | ||||||
\(596\) | −354691. | − | 354691.i | −0.998523 | − | 0.998523i | ||||
\(597\) | 93133.9i | 0.261312i | ||||||||
\(598\) | −11968.7 | + | 19135.8i | −0.0334691 | + | 0.0535112i | ||||
\(599\) | −593378. | −1.65378 | −0.826890 | − | 0.562363i | \(-0.809892\pi\) | ||||
−0.826890 | + | 0.562363i | \(0.809892\pi\) | |||||||
\(600\) | 168637. | − | 168637.i | 0.468435 | − | 0.468435i | ||||
\(601\) | 213129. | 0.590057 | 0.295029 | − | 0.955488i | \(-0.404671\pi\) | ||||
0.295029 | + | 0.955488i | \(0.404671\pi\) | |||||||
\(602\) | − | 275601.i | − | 0.760481i | ||||||
\(603\) | 41284.0 | − | 41284.0i | 0.113539 | − | 0.113539i | ||||
\(604\) | 191649. | − | 191649.i | 0.525330 | − | 0.525330i | ||||
\(605\) | 16344.8 | + | 16344.8i | 0.0446548 | + | 0.0446548i | ||||
\(606\) | 139086. | + | 139086.i | 0.378737 | + | 0.378737i | ||||
\(607\) | −342979. | −0.930871 | −0.465436 | − | 0.885082i | \(-0.654102\pi\) | ||||
−0.465436 | + | 0.885082i | \(0.654102\pi\) | |||||||
\(608\) | − | 213669.i | − | 0.578008i | ||||||
\(609\) | −672004. | − | 672004.i | −1.81191 | − | 1.81191i | ||||
\(610\) | − | 21767.9i | − | 0.0585002i | ||||||
\(611\) | −244943. | + | 391621.i | −0.656120 | + | 1.04902i | ||||
\(612\) | −69508.8 | −0.185583 | ||||||||
\(613\) | 48611.1 | − | 48611.1i | 0.129364 | − | 0.129364i | −0.639460 | − | 0.768824i | \(-0.720842\pi\) |
0.768824 | + | 0.639460i | \(0.220842\pi\) | |||||||
\(614\) | −126682. | −0.336031 | ||||||||
\(615\) | 101269.i | 0.267748i | ||||||||
\(616\) | −312337. | + | 312337.i | −0.823117 | + | 0.823117i | ||||
\(617\) | −1700.28 | + | 1700.28i | −0.00446632 | + | 0.00446632i | −0.709336 | − | 0.704870i | \(-0.751005\pi\) |
0.704870 | + | 0.709336i | \(0.251005\pi\) | |||||||
\(618\) | 172148. | + | 172148.i | 0.450739 | + | 0.450739i | ||||
\(619\) | 332782. | + | 332782.i | 0.868518 | + | 0.868518i | 0.992308 | − | 0.123790i | \(-0.0395051\pi\) |
−0.123790 | + | 0.992308i | \(0.539505\pi\) | |||||||
\(620\) | −227780. | −0.592559 | ||||||||
\(621\) | − | 45075.1i | − | 0.116884i | ||||||
\(622\) | −101328. | − | 101328.i | −0.261907 | − | 0.261907i | ||||
\(623\) | − | 262813.i | − | 0.677129i | ||||||
\(624\) | 39297.5 | + | 170547.i | 0.100924 | + | 0.438001i | ||||
\(625\) | −97306.5 | −0.249105 | ||||||||
\(626\) | 201492. | − | 201492.i | 0.514173 | − | 0.514173i | ||||
\(627\) | 263257. | 0.669645 | ||||||||
\(628\) | − | 70974.0i | − | 0.179962i | ||||||
\(629\) | −103242. | + | 103242.i | −0.260948 | + | 0.260948i | ||||
\(630\) | 20701.2 | − | 20701.2i | 0.0521571 | − | 0.0521571i | ||||
\(631\) | 282632. | + | 282632.i | 0.709845 | + | 0.709845i | 0.966502 | − | 0.256658i | \(-0.0826213\pi\) |
−0.256658 | + | 0.966502i | \(0.582621\pi\) | |||||||
\(632\) | 46121.2 | + | 46121.2i | 0.115469 | + | 0.115469i | ||||
\(633\) | 536782. | 1.33965 | ||||||||
\(634\) | 213152.i | 0.530288i | ||||||||
\(635\) | 154824. | + | 154824.i | 0.383963 | + | 0.383963i | ||||
\(636\) | 546943.i | 1.35216i | ||||||||
\(637\) | 306949. | − | 70727.1i | 0.756461 | − | 0.174304i | ||||
\(638\) | −345196. | −0.848055 | ||||||||
\(639\) | −22518.8 | + | 22518.8i | −0.0551498 | + | 0.0551498i | ||||
\(640\) | 211564. | 0.516514 | ||||||||
\(641\) | − | 396296.i | − | 0.964502i | −0.876033 | − | 0.482251i | \(-0.839819\pi\) | ||
0.876033 | − | 0.482251i | \(-0.160181\pi\) | |||||||
\(642\) | 65785.8 | − | 65785.8i | 0.159611 | − | 0.159611i | ||||
\(643\) | −269894. | + | 269894.i | −0.652787 | + | 0.652787i | −0.953663 | − | 0.300876i | \(-0.902721\pi\) |
0.300876 | + | 0.953663i | \(0.402721\pi\) | |||||||
\(644\) | 42019.3 | + | 42019.3i | 0.101316 | + | 0.101316i | ||||
\(645\) | −211461. | − | 211461.i | −0.508288 | − | 0.508288i | ||||
\(646\) | −113718. | −0.272500 | ||||||||
\(647\) | − | 420499.i | − | 1.00451i | −0.864718 | − | 0.502257i | \(-0.832503\pi\) | ||
0.864718 | − | 0.502257i | \(-0.167497\pi\) | |||||||
\(648\) | 288173. | + | 288173.i | 0.686284 | + | 0.686284i | ||||
\(649\) | − | 280528.i | − | 0.666019i | ||||||
\(650\) | −74955.6 | + | 119841.i | −0.177410 | + | 0.283646i | ||||
\(651\) | 898119. | 2.11920 | ||||||||
\(652\) | −286878. | + | 286878.i | −0.674843 | + | 0.674843i | ||||
\(653\) | 22664.5 | 0.0531519 | 0.0265760 | − | 0.999647i | \(-0.491540\pi\) | ||||
0.0265760 | + | 0.999647i | \(0.491540\pi\) | |||||||
\(654\) | 162111.i | 0.379015i | ||||||||
\(655\) | 202010. | − | 202010.i | 0.470858 | − | 0.470858i | ||||
\(656\) | 56791.7 | − | 56791.7i | 0.131971 | − | 0.131971i | ||||
\(657\) | 29867.2 | + | 29867.2i | 0.0691933 | + | 0.0691933i | ||||
\(658\) | −233173. | − | 233173.i | −0.538549 | − | 0.538549i | ||||
\(659\) | −298784. | −0.687998 | −0.343999 | − | 0.938970i | \(-0.611782\pi\) | ||||
−0.343999 | + | 0.938970i | \(0.611782\pi\) | |||||||
\(660\) | 211035.i | 0.484471i | ||||||||
\(661\) | −451526. | − | 451526.i | −1.03343 | − | 1.03343i | −0.999422 | − | 0.0340055i | \(-0.989174\pi\) |
−0.0340055 | − | 0.999422i | \(-0.510826\pi\) | |||||||
\(662\) | 307362.i | 0.701350i | ||||||||
\(663\) | 490637. | − | 113053.i | 1.11618 | − | 0.257190i | ||||
\(664\) | 195728. | 0.443933 | ||||||||
\(665\) | −124904. | + | 124904.i | −0.282444 | + | 0.282444i | ||||
\(666\) | −16695.9 | −0.0376411 | ||||||||
\(667\) | 105472.i | 0.237075i | ||||||||
\(668\) | 145981. | − | 145981.i | 0.327146 | − | 0.327146i | ||||
\(669\) | 270957. | − | 270957.i | 0.605407 | − | 0.605407i | ||||
\(670\) | 54143.7 | + | 54143.7i | 0.120614 | + | 0.120614i | ||||
\(671\) | −81299.9 | − | 81299.9i | −0.180570 | − | 0.180570i | ||||
\(672\) | −675361. | −1.49554 | ||||||||
\(673\) | 740886.i | 1.63577i | 0.575384 | + | 0.817883i | \(0.304852\pi\) | ||||
−0.575384 | + | 0.817883i | \(0.695148\pi\) | |||||||
\(674\) | 98548.4 | + | 98548.4i | 0.216935 | + | 0.216935i | ||||
\(675\) | − | 282289.i | − | 0.619564i | ||||||
\(676\) | −157319. | − | 323249.i | −0.344260 | − | 0.707365i | ||||
\(677\) | −220043. | −0.480099 | −0.240050 | − | 0.970761i | \(-0.577164\pi\) | ||||
−0.240050 | + | 0.970761i | \(0.577164\pi\) | |||||||
\(678\) | −143415. | + | 143415.i | −0.311985 | + | 0.311985i | ||||
\(679\) | 386881. | 0.839146 | ||||||||
\(680\) | − | 207039.i | − | 0.447749i | ||||||
\(681\) | −633284. | + | 633284.i | −1.36554 | + | 1.36554i | ||||
\(682\) | 230674. | − | 230674.i | 0.495940 | − | 0.495940i | ||||
\(683\) | 472955. | + | 472955.i | 1.01386 | + | 1.01386i | 0.999903 | + | 0.0139589i | \(0.00444341\pi\) |
0.0139589 | + | 0.999903i | \(0.495557\pi\) | |||||||
\(684\) | 33911.5 | + | 33911.5i | 0.0724827 | + | 0.0724827i | ||||
\(685\) | 15473.0 | 0.0329756 | ||||||||
\(686\) | − | 64805.1i | − | 0.137709i | ||||||
\(687\) | 211936. | + | 211936.i | 0.449047 | + | 0.449047i | ||||
\(688\) | 237174.i | 0.501062i | ||||||||
\(689\) | −165313. | − | 717441.i | −0.348231 | − | 1.51129i | ||||
\(690\) | −17483.8 | −0.0367230 | ||||||||
\(691\) | 423991. | − | 423991.i | 0.887974 | − | 0.887974i | −0.106354 | − | 0.994328i | \(-0.533918\pi\) |
0.994328 | + | 0.106354i | \(0.0339176\pi\) | |||||||
\(692\) | 91458.2 | 0.190990 | ||||||||
\(693\) | − | 154632.i | − | 0.321982i | ||||||
\(694\) | 26310.4 | − | 26310.4i | 0.0546272 | − | 0.0546272i | ||||
\(695\) | −201282. | + | 201282.i | −0.416711 | + | 0.416711i | ||||
\(696\) | −543444. | − | 543444.i | −1.12185 | − | 1.12185i | ||||
\(697\) | −163381. | − | 163381.i | −0.336307 | − | 0.336307i | ||||
\(698\) | 103569. | 0.212579 | ||||||||
\(699\) | − | 73952.8i | − | 0.151356i | ||||||
\(700\) | 263152. | + | 263152.i | 0.537045 | + | 0.537045i | ||||
\(701\) | 298102.i | 0.606637i | 0.952889 | + | 0.303318i | \(0.0980946\pi\) | ||||
−0.952889 | + | 0.303318i | \(0.901905\pi\) | |||||||
\(702\) | −165046. | − | 103230.i | −0.334913 | − | 0.209475i | ||||
\(703\) | 100738. | 0.203836 | ||||||||
\(704\) | −23021.1 | + | 23021.1i | −0.0464495 | + | 0.0464495i | ||||
\(705\) | −357813. | −0.719909 | ||||||||
\(706\) | 286602.i | 0.575003i | ||||||||
\(707\) | −492927. | + | 492927.i | −0.986152 | + | 0.986152i | ||||
\(708\) | 194455. | − | 194455.i | 0.387930 | − | 0.387930i | ||||
\(709\) | −605423. | − | 605423.i | −1.20439 | − | 1.20439i | −0.972818 | − | 0.231570i | \(-0.925614\pi\) |
−0.231570 | − | 0.972818i | \(-0.574386\pi\) | |||||||
\(710\) | −29533.3 | − | 29533.3i | −0.0585862 | − | 0.0585862i | ||||
\(711\) | −22833.7 | −0.0451686 | ||||||||
\(712\) | − | 212535.i | − | 0.419248i | ||||||
\(713\) | −70480.6 | − | 70480.6i | −0.138641 | − | 0.138641i | ||||
\(714\) | 359439.i | 0.705065i | ||||||||
\(715\) | −63785.2 | − | 276821.i | −0.124769 | − | 0.541486i | ||||
\(716\) | −235453. | −0.459281 | ||||||||
\(717\) | 403032. | − | 403032.i | 0.783973 | − | 0.783973i | ||||
\(718\) | 168974. | 0.327772 | ||||||||
\(719\) | − | 9526.58i | − | 0.0184281i | −0.999958 | − | 0.00921403i | \(-0.997067\pi\) | ||
0.999958 | − | 0.00921403i | \(-0.00293296\pi\) | |||||||
\(720\) | −17814.8 | + | 17814.8i | −0.0343650 | + | 0.0343650i | ||||
\(721\) | −610101. | + | 610101.i | −1.17363 | + | 1.17363i | ||||
\(722\) | −114761. | − | 114761.i | −0.220152 | − | 0.220152i | ||||
\(723\) | −656850. | − | 656850.i | −1.25658 | − | 1.25658i | ||||
\(724\) | −187941. | −0.358545 | ||||||||
\(725\) | 660533.i | 1.25666i | ||||||||
\(726\) | −22947.5 | − | 22947.5i | −0.0435373 | − | 0.0435373i | ||||
\(727\) | 502918.i | 0.951543i | 0.879569 | + | 0.475771i | \(0.157831\pi\) | ||||
−0.879569 | + | 0.475771i | \(0.842169\pi\) | |||||||
\(728\) | 567990. | − | 130876.i | 1.07171 | − | 0.246944i | ||||
\(729\) | 361085. | 0.679446 | ||||||||
\(730\) | −39170.7 | + | 39170.7i | −0.0735048 | + | 0.0735048i | ||||
\(731\) | 682314. | 1.27688 | ||||||||
\(732\) | − | 112710.i | − | 0.210350i | ||||||
\(733\) | 400336. | − | 400336.i | 0.745103 | − | 0.745103i | −0.228452 | − | 0.973555i | \(-0.573366\pi\) |
0.973555 | + | 0.228452i | \(0.0733664\pi\) | |||||||
\(734\) | 99400.8 | − | 99400.8i | 0.184501 | − | 0.184501i | ||||
\(735\) | 172536. | + | 172536.i | 0.319378 | + | 0.319378i | ||||
\(736\) | 52999.5 | + | 52999.5i | 0.0978400 | + | 0.0978400i | ||||
\(737\) | 404438. | 0.744589 | ||||||||
\(738\) | − | 26421.4i | − | 0.0485114i | ||||||
\(739\) | −111403. | − | 111403.i | −0.203990 | − | 0.203990i | 0.597717 | − | 0.801707i | \(-0.296075\pi\) |
−0.801707 | + | 0.597717i | \(0.796075\pi\) | |||||||
\(740\) | 80754.8i | 0.147471i | ||||||||
\(741\) | −294524. | − | 184213.i | −0.536394 | − | 0.335494i | ||||
\(742\) | 525595. | 0.954648 | ||||||||
\(743\) | 255155. | − | 255155.i | 0.462196 | − | 0.462196i | −0.437179 | − | 0.899375i | \(-0.644022\pi\) |
0.899375 | + | 0.437179i | \(0.144022\pi\) | |||||||
\(744\) | 726302. | 1.31211 | ||||||||
\(745\) | 523044.i | 0.942379i | ||||||||
\(746\) | 93424.9 | − | 93424.9i | 0.167875 | − | 0.167875i | ||||
\(747\) | −48450.5 | + | 48450.5i | −0.0868275 | + | 0.0868275i | ||||
\(748\) | −340471. | − | 340471.i | −0.608523 | − | 0.608523i | ||||
\(749\) | 233148. | + | 233148.i | 0.415593 | + | 0.415593i | ||||
\(750\) | −260652. | −0.463381 | ||||||||
\(751\) | 272472.i | 0.483106i | 0.970388 | + | 0.241553i | \(0.0776568\pi\) | ||||
−0.970388 | + | 0.241553i | \(0.922343\pi\) | |||||||
\(752\) | 200661. | + | 200661.i | 0.354837 | + | 0.354837i | ||||
\(753\) | 115510.i | 0.203718i | ||||||||
\(754\) | 386195. | + | 241550.i | 0.679304 | + | 0.424878i | ||||
\(755\) | −282614. | −0.495792 | ||||||||
\(756\) | −362417. | + | 362417.i | −0.634110 | + | 0.634110i | ||||
\(757\) | −136228. | −0.237725 | −0.118862 | − | 0.992911i | \(-0.537925\pi\) | ||||
−0.118862 | + | 0.992911i | \(0.537925\pi\) | |||||||
\(758\) | 75169.7i | 0.130829i | ||||||||
\(759\) | −65299.5 | + | 65299.5i | −0.113351 | + | 0.113351i | ||||
\(760\) | −101009. | + | 101009.i | −0.174877 | + | 0.174877i | ||||
\(761\) | 815054. | + | 815054.i | 1.40740 | + | 1.40740i | 0.773033 | + | 0.634366i | \(0.218739\pi\) |
0.634366 | + | 0.773033i | \(0.281261\pi\) | |||||||
\(762\) | −217367. | − | 217367.i | −0.374355 | − | 0.374355i | ||||
\(763\) | −574529. | −0.986877 | ||||||||
\(764\) | − | 431705.i | − | 0.739606i | ||||||
\(765\) | 51250.4 | + | 51250.4i | 0.0875739 | + | 0.0875739i | ||||
\(766\) | − | 168433.i | − | 0.287057i | ||||||
\(767\) | −196299. | + | 313847.i | −0.333677 | + | 0.533490i | ||||
\(768\) | −337598. | −0.572370 | ||||||||
\(769\) | 494798. | − | 494798.i | 0.836710 | − | 0.836710i | −0.151714 | − | 0.988424i | \(-0.548479\pi\) |
0.988424 | + | 0.151714i | \(0.0484793\pi\) | |||||||
\(770\) | 202799. | 0.342045 | ||||||||
\(771\) | 1.11869e6i | 1.88193i | ||||||||
\(772\) | 63482.6 | − | 63482.6i | 0.106517 | − | 0.106517i | ||||
\(773\) | 536178. | − | 536178.i | 0.897325 | − | 0.897325i | −0.0978738 | − | 0.995199i | \(-0.531204\pi\) |
0.995199 | + | 0.0978738i | \(0.0312042\pi\) | |||||||
\(774\) | 55170.8 | + | 55170.8i | 0.0920932 | + | 0.0920932i | ||||
\(775\) | −441395. | − | 441395.i | −0.734892 | − | 0.734892i | ||||
\(776\) | 312867. | 0.519561 | ||||||||
\(777\) | − | 318411.i | − | 0.527406i | ||||||
\(778\) | −288253. | − | 288253.i | −0.476227 | − | 0.476227i | ||||
\(779\) | 159418.i | 0.262702i | ||||||||
\(780\) | 147672. | − | 236100.i | 0.242721 | − | 0.388068i | ||||
\(781\) | −220605. | −0.361671 | ||||||||
\(782\) | 28207.3 | − | 28207.3i | 0.0461262 | − | 0.0461262i | ||||
\(783\) | −909696. | −1.48379 | ||||||||
\(784\) | − | 193516.i | − | 0.314837i | ||||||
\(785\) | −52330.8 | + | 52330.8i | −0.0849215 | + | 0.0849215i | ||||
\(786\) | −283615. | + | 283615.i | −0.459075 | + | 0.459075i | ||||
\(787\) | −108003. | − | 108003.i | −0.174376 | − | 0.174376i | 0.614523 | − | 0.788899i | \(-0.289349\pi\) |
−0.788899 | + | 0.614523i | \(0.789349\pi\) | |||||||
\(788\) | −116972. | − | 116972.i | −0.188377 | − | 0.188377i | ||||
\(789\) | −493154. | −0.792189 | ||||||||
\(790\) | − | 29946.2i | − | 0.0479831i | ||||||
\(791\) | −508269. | − | 508269.i | −0.812345 | − | 0.812345i | ||||
\(792\) | − | 125049.i | − | 0.199357i | ||||||
\(793\) | 34066.6 | + | 147845.i | 0.0541729 | + | 0.235105i | ||||
\(794\) | −251004. | −0.398144 | ||||||||
\(795\) | 403273. | − | 403273.i | 0.638065 | − | 0.638065i | ||||
\(796\) | −117529. | −0.185489 | ||||||||
\(797\) | − | 196692.i | − | 0.309649i | −0.987942 | − | 0.154824i | \(-0.950519\pi\) | ||
0.987942 | − | 0.154824i | \(-0.0494812\pi\) | |||||||
\(798\) | 175361. | − | 175361.i | 0.275376 | − | 0.275376i | ||||
\(799\) | 577272. | − | 577272.i | 0.904246 | − | 0.904246i | ||||
\(800\) | 331917. | + | 331917.i | 0.518620 | + | 0.518620i | ||||
\(801\) | 52610.9 | + | 52610.9i | 0.0819994 | + | 0.0819994i | ||||
\(802\) | 8293.53 | 0.0128941 | ||||||||
\(803\) | 292594.i | 0.453768i | ||||||||
\(804\) | 280347. | + | 280347.i | 0.433694 | + | 0.433694i | ||||
\(805\) | − | 61963.6i | − | 0.0956192i | ||||||
\(806\) | −419484. | + | 96657.6i | −0.645722 | + | 0.148787i | ||||
\(807\) | 482113. | 0.740290 | ||||||||
\(808\) | −398626. | + | 398626.i | −0.610581 | + | 0.610581i | ||||
\(809\) | −171772. | −0.262455 | −0.131228 | − | 0.991352i | \(-0.541892\pi\) | ||||
−0.131228 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(810\) | − | 187109.i | − | 0.285184i | ||||||
\(811\) | −801579. | + | 801579.i | −1.21872 | + | 1.21872i | −0.250642 | + | 0.968080i | \(0.580642\pi\) |
−0.968080 | + | 0.250642i | \(0.919358\pi\) | |||||||
\(812\) | 848026. | − | 848026.i | 1.28617 | − | 1.28617i | ||||
\(813\) | 290362. | + | 290362.i | 0.439297 | + | 0.439297i | ||||
\(814\) | −81780.8 | − | 81780.8i | −0.123425 | − | 0.123425i | ||||
\(815\) | 423044. | 0.636899 | ||||||||
\(816\) | − | 309323.i | − | 0.464550i | ||||||
\(817\) | −332882. | − | 332882.i | −0.498708 | − | 0.498708i | ||||
\(818\) | 120936.i | 0.180738i | ||||||||
\(819\) | −108203. | + | 172997.i | −0.161314 | + | 0.257912i | ||||
\(820\) | −127795. | −0.190058 | ||||||||
\(821\) | −840896. | + | 840896.i | −1.24754 | + | 1.24754i | −0.290742 | + | 0.956801i | \(0.593902\pi\) |
−0.956801 | + | 0.290742i | \(0.906098\pi\) | |||||||
\(822\) | −21723.5 | −0.0321504 | ||||||||
\(823\) | − | 1.00240e6i | − | 1.47993i | −0.672646 | − | 0.739964i | \(-0.734842\pi\) | ||
0.672646 | − | 0.739964i | \(-0.265158\pi\) | |||||||
\(824\) | −493384. | + | 493384.i | −0.726659 | + | 0.726659i | ||||
\(825\) | −408947. | + | 408947.i | −0.600841 | + | 0.600841i | ||||
\(826\) | −186865. | − | 186865.i | −0.273885 | − | 0.273885i | ||||
\(827\) | 238471. | + | 238471.i | 0.348679 | + | 0.348679i | 0.859617 | − | 0.510939i | \(-0.170702\pi\) |
−0.510939 | + | 0.859617i | \(0.670702\pi\) | |||||||
\(828\) | −16823.2 | −0.0245384 | ||||||||
\(829\) | 188792.i | 0.274711i | 0.990522 | + | 0.137355i | \(0.0438602\pi\) | ||||
−0.990522 | + | 0.137355i | \(0.956140\pi\) | |||||||
\(830\) | −63542.7 | − | 63542.7i | −0.0922379 | − | 0.0922379i | ||||
\(831\) | − | 1.21795e6i | − | 1.76371i | ||||||
\(832\) | 41864.4 | − | 9646.40i | 0.0604781 | − | 0.0139354i | ||||
\(833\) | −556716. | −0.802313 | ||||||||
\(834\) | 282593. | − | 282593.i | 0.406283 | − | 0.406283i | ||||
\(835\) | −215270. | −0.308752 | ||||||||
\(836\) | 332213.i | 0.475340i | ||||||||
\(837\) | 607895. | − | 607895.i | 0.867716 | − | 0.867716i | ||||
\(838\) | −88794.1 | + | 88794.1i | −0.126443 | + | 0.126443i | ||||
\(839\) | 380475. | + | 380475.i | 0.540508 | + | 0.540508i | 0.923678 | − | 0.383170i | \(-0.125168\pi\) |
−0.383170 | + | 0.923678i | \(0.625168\pi\) | |||||||
\(840\) | 319267. | + | 319267.i | 0.452476 | + | 0.452476i | ||||
\(841\) | 1.42134e6 | 2.00958 | ||||||||
\(842\) | − | 489780.i | − | 0.690839i | ||||||
\(843\) | 916334. | + | 916334.i | 1.28943 | + | 1.28943i | ||||
\(844\) | 677384.i | 0.950934i | ||||||||
\(845\) | −122344. | + | 354333.i | −0.171344 | + | 0.496248i | ||||
\(846\) | 93354.6 | 0.130435 | ||||||||
\(847\) | 81327.1 | − | 81327.1i | 0.113362 | − | 0.113362i | ||||
\(848\) | −452312. | −0.628993 | ||||||||
\(849\) | − | 192919.i | − | 0.267646i | ||||||
\(850\) | 176652. | − | 176652.i | 0.244501 | − | 0.244501i | ||||
\(851\) | −24987.5 | + | 24987.5i | −0.0345036 | + | 0.0345036i | ||||
\(852\) | −152918. | − | 152918.i | −0.210659 | − | 0.210659i | ||||
\(853\) | 904173. | + | 904173.i | 1.24266 | + | 1.24266i | 0.958892 | + | 0.283771i | \(0.0915856\pi\) |
0.283771 | + | 0.958892i | \(0.408414\pi\) | |||||||
\(854\) | −108311. | −0.148511 | ||||||||
\(855\) | − | 50007.4i | − | 0.0684073i | ||||||
\(856\) | 188545. | + | 188545.i | 0.257316 | + | 0.257316i | ||||
\(857\) | − | 544039.i | − | 0.740744i | −0.928883 | − | 0.370372i | \(-0.879230\pi\) | ||
0.928883 | − | 0.370372i | \(-0.120770\pi\) | |||||||
\(858\) | 89552.2 | + | 388647.i | 0.121647 | + | 0.527936i | ||||
\(859\) | −265582. | −0.359925 | −0.179963 | − | 0.983673i | \(-0.557598\pi\) | ||||
−0.179963 | + | 0.983673i | \(0.557598\pi\) | |||||||
\(860\) | 266850. | − | 266850.i | 0.360803 | − | 0.360803i | ||||
\(861\) | 503886. | 0.679714 | ||||||||
\(862\) | 174644.i | 0.235038i | ||||||||
\(863\) | 412705. | − | 412705.i | 0.554139 | − | 0.554139i | −0.373494 | − | 0.927633i | \(-0.621840\pi\) |
0.927633 | + | 0.373494i | \(0.121840\pi\) | |||||||
\(864\) | −457121. | + | 457121.i | −0.612355 | + | 0.612355i | ||||
\(865\) | −67434.2 | − | 67434.2i | −0.0901256 | − | 0.0901256i | ||||
\(866\) | 243493. | + | 243493.i | 0.324676 | + | 0.324676i | ||||
\(867\) | −56804.1 | −0.0755686 | ||||||||
\(868\) | 1.13337e6i | 1.50429i | ||||||||
\(869\) | −111845. | − | 111845.i | −0.148107 | − | 0.148107i | ||||
\(870\) | 352855.i | 0.466185i | ||||||||
\(871\) | −452473. | − | 283004.i | −0.596426 | − | 0.373041i | ||||
\(872\) | −464617. | −0.611029 | ||||||||
\(873\) | −77447.1 | + | 77447.1i | −0.101619 | + | 0.101619i | ||||
\(874\) | −27523.2 | −0.0360309 | ||||||||
\(875\) | − | 923764.i | − | 1.20655i | ||||||
\(876\) | −202819. | + | 202819.i | −0.264302 | + | 0.264302i | ||||
\(877\) | 163839. | − | 163839.i | 0.213018 | − | 0.213018i | −0.592530 | − | 0.805548i | \(-0.701871\pi\) |
0.805548 | + | 0.592530i | \(0.201871\pi\) | |||||||
\(878\) | 139305. | + | 139305.i | 0.180708 | + | 0.180708i | ||||
\(879\) | −729548. | − | 729548.i | −0.944226 | − | 0.944226i | ||||
\(880\) | −174523. | −0.225365 | ||||||||
\(881\) | − | 852288.i | − | 1.09808i | −0.835796 | − | 0.549041i | \(-0.814993\pi\) | ||
0.835796 | − | 0.549041i | \(-0.185007\pi\) | |||||||
\(882\) | −45015.2 | − | 45015.2i | −0.0578658 | − | 0.0578658i | ||||
\(883\) | − | 470317.i | − | 0.603211i | −0.953433 | − | 0.301606i | \(-0.902477\pi\) | ||
0.953433 | − | 0.301606i | \(-0.0975226\pi\) | |||||||
\(884\) | 142665. | + | 619153.i | 0.182563 | + | 0.792307i | ||||
\(885\) | −286753. | −0.366118 | ||||||||
\(886\) | −118477. | + | 118477.i | −0.150926 | + | 0.150926i | ||||
\(887\) | 699651. | 0.889271 | 0.444635 | − | 0.895712i | \(-0.353333\pi\) | ||||
0.444635 | + | 0.895712i | \(0.353333\pi\) | |||||||
\(888\) | − | 257496.i | − | 0.326546i | ||||||
\(889\) | 770359. | − | 770359.i | 0.974743 | − | 0.974743i | ||||
\(890\) | −68999.0 | + | 68999.0i | −0.0871089 | + | 0.0871089i | ||||
\(891\) | −698826. | − | 698826.i | −0.880265 | − | 0.880265i | ||||
\(892\) | 341930. | + | 341930.i | 0.429742 | + | 0.429742i | ||||
\(893\) | −563270. | −0.706340 | ||||||||
\(894\) | − | 734335.i | − | 0.918797i | ||||||
\(895\) | 173605. | + | 173605.i | 0.216729 | + | 0.216729i | ||||
\(896\) | − | 1.05268e6i | − | 1.31124i | ||||||
\(897\) | 118748. | − | 27362.0i | 0.147585 | − | 0.0340066i | ||||
\(898\) | −139860. | −0.173437 | ||||||||
\(899\) | −1.42243e6 | + | 1.42243e6i | −1.75999 | + | 1.75999i | ||||
\(900\) | −105357. | −0.130071 | ||||||||
\(901\) | 1.30123e6i | 1.60289i | ||||||||
\(902\) | 129419. | − | 129419.i | 0.159068 | − | 0.159068i | ||||
\(903\) | −1.05217e6 | + | 1.05217e6i | −1.29036 | + | 1.29036i | ||||
\(904\) | −411033. | − | 411033.i | −0.502967 | − | 0.502967i | ||||
\(905\) | 138573. | + | 138573.i | 0.169193 | + | 0.169193i | ||||
\(906\) | 396780. | 0.483385 | ||||||||
\(907\) | − | 299763.i | − | 0.364387i | −0.983263 | − | 0.182194i | \(-0.941680\pi\) | ||
0.983263 | − | 0.182194i | \(-0.0583198\pi\) | |||||||
\(908\) | −799164. | − | 799164.i | −0.969313 | − | 0.969313i | ||||
\(909\) | − | 197352.i | − | 0.238843i | ||||||
\(910\) | −226885. | − | 141908.i | −0.273983 | − | 0.171366i | ||||
\(911\) | 1.46063e6 | 1.75996 | 0.879980 | − | 0.475010i | \(-0.157556\pi\) | ||||
0.879980 | + | 0.475010i | \(0.157556\pi\) | |||||||
\(912\) | −150910. | + | 150910.i | −0.181438 | + | 0.181438i | ||||
\(913\) | −474645. | −0.569413 | ||||||||
\(914\) | 55923.5i | 0.0669425i | ||||||||
\(915\) | −83103.9 | + | 83103.9i | −0.0992611 | + | 0.0992611i | ||||
\(916\) | −267450. | + | 267450.i | −0.318751 | + | 0.318751i | ||||
\(917\) | −1.00515e6 | − | 1.00515e6i | −1.19534 | − | 1.19534i | ||||
\(918\) | 243288. | + | 243288.i | 0.288692 | + | 0.288692i | ||||
\(919\) | 386349. | 0.457456 | 0.228728 | − | 0.973490i | \(-0.426543\pi\) | ||||
0.228728 | + | 0.973490i | \(0.426543\pi\) | |||||||
\(920\) | − | 50109.5i | − | 0.0592031i | ||||||
\(921\) | 483638. | + | 483638.i | 0.570165 | + | 0.570165i | ||||
\(922\) | 588886.i | 0.692738i | ||||||||
\(923\) | 246807. | + | 154368.i | 0.289703 | + | 0.181198i | ||||
\(924\) | 1.05005e6 | 1.22989 | ||||||||
\(925\) | −156488. | + | 156488.i | −0.182893 | + | 0.182893i | ||||
\(926\) | −4518.51 | −0.00526955 | ||||||||
\(927\) | − | 244264.i | − | 0.284250i | ||||||
\(928\) | 1.06963e6 | − | 1.06963e6i | 1.24204 | − | 1.24204i | ||||
\(929\) | −59576.2 | + | 59576.2i | −0.0690306 | + | 0.0690306i | −0.740779 | − | 0.671749i | \(-0.765544\pi\) |
0.671749 | + | 0.740779i | \(0.265544\pi\) | |||||||
\(930\) | −235792. | − | 235792.i | −0.272623 | − | 0.272623i | ||||
\(931\) | 271607. | + | 271607.i | 0.313358 | + | 0.313358i | ||||
\(932\) | 93323.7 | 0.107439 | ||||||||
\(933\) | 773681.i | 0.888789i | ||||||||
\(934\) | 172323. | + | 172323.i | 0.197537 | + | 0.197537i | ||||
\(935\) | 502074.i | 0.574308i | ||||||||
\(936\) | −87502.9 | + | 139902.i | −0.0998782 | + | 0.159687i | ||||
\(937\) | 507904. | 0.578499 | 0.289250 | − | 0.957254i | \(-0.406594\pi\) | ||||
0.289250 | + | 0.957254i | \(0.406594\pi\) | |||||||
\(938\) | 269404. | − | 269404.i | 0.306196 | − | 0.306196i | ||||
\(939\) | −1.53848e6 | −1.74486 | ||||||||
\(940\) | − | 451537.i | − | 0.511019i | ||||||
\(941\) | −494292. | + | 494292.i | −0.558219 | + | 0.558219i | −0.928800 | − | 0.370581i | \(-0.879159\pi\) |
0.370581 | + | 0.928800i | \(0.379159\pi\) | |||||||
\(942\) | 73470.6 | − | 73470.6i | 0.0827964 | − | 0.0827964i | ||||
\(943\) | −39542.9 | − | 39542.9i | −0.0444677 | − | 0.0444677i | ||||
\(944\) | 160811. | + | 160811.i | 0.180456 | + | 0.180456i | ||||
\(945\) | 534436. | 0.598456 | ||||||||
\(946\) | 540480.i | 0.603945i | ||||||||
\(947\) | −472638. | − | 472638.i | −0.527022 | − | 0.527022i | 0.392661 | − | 0.919683i | \(-0.371555\pi\) |
−0.919683 | + | 0.392661i | \(0.871555\pi\) | |||||||
\(948\) | − | 155056.i | − | 0.172533i | ||||||
\(949\) | 204742. | − | 327345.i | 0.227339 | − | 0.363474i | ||||
\(950\) | −172368. | −0.190989 | ||||||||
\(951\) | 813757. | − | 813757.i | 0.899775 | − | 0.899775i | ||||
\(952\) | −1.03017e6 | −1.13667 | ||||||||
\(953\) | − | 926281.i | − | 1.01990i | −0.860204 | − | 0.509949i | \(-0.829664\pi\) | ||
0.860204 | − | 0.509949i | \(-0.170336\pi\) | |||||||
\(954\) | −105215. | + | 105215.i | −0.115607 | + | 0.115607i | ||||
\(955\) | −318306. | + | 318306.i | −0.349010 | + | 0.349010i | ||||
\(956\) | 508600. | + | 508600.i | 0.556494 | + | 0.556494i | ||||
\(957\) | 1.31786e6 | + | 1.31786e6i | 1.43895 | + | 1.43895i | ||||
\(958\) | −297422. | −0.324072 | ||||||||
\(959\) | − | 76989.2i | − | 0.0837129i | ||||||
\(960\) | 23532.0 | + | 23532.0i | 0.0255338 | + | 0.0255338i | ||||
\(961\) | − | 977522.i | − | 1.05847i | ||||||
\(962\) | 34268.1 | + | 148720.i | 0.0370288 | + | 0.160701i | ||||
\(963\) | −93344.8 | −0.100656 | ||||||||
\(964\) | 828903. | − | 828903.i | 0.891969 | − | 0.891969i | ||||
\(965\) | −93614.4 | −0.100528 | ||||||||
\(966\) | 86994.8i | 0.0932264i | ||||||||
\(967\) | −123341. | + | 123341.i | −0.131903 | + | 0.131903i | −0.769976 | − | 0.638073i | \(-0.779732\pi\) |
0.638073 | + | 0.769976i | \(0.279732\pi\) | |||||||
\(968\) | 65768.6 | − | 65768.6i | 0.0701888 | − | 0.0701888i | ||||
\(969\) | 434146. | + | 434146.i | 0.462368 | + | 0.462368i | ||||
\(970\) | −101572. | − | 101572.i | −0.107952 | − | 0.107952i | ||||
\(971\) | 134660. | 0.142824 | 0.0714120 | − | 0.997447i | \(-0.477249\pi\) | ||||
0.0714120 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(972\) | − | 333113.i | − | 0.352581i | ||||||
\(973\) | 1.00152e6 | + | 1.00152e6i | 1.05788 | + | 1.05788i | ||||
\(974\) | − | 659480.i | − | 0.695158i | ||||||
\(975\) | 743678. | − | 171359.i | 0.782305 | − | 0.180259i | ||||
\(976\) | 93209.4 | 0.0978498 | ||||||||
\(977\) | −1.21699e6 | + | 1.21699e6i | −1.27497 | + | 1.27497i | −0.331518 | + | 0.943449i | \(0.607561\pi\) |
−0.943449 | + | 0.331518i | \(0.892439\pi\) | |||||||
\(978\) | −593939. | −0.620961 | ||||||||
\(979\) | 515402.i | 0.537750i | ||||||||
\(980\) | −217729. | + | 217729.i | −0.226707 | + | 0.226707i | ||||
\(981\) | 115011. | − | 115011.i | 0.119509 | − | 0.119509i | ||||
\(982\) | 439794. | + | 439794.i | 0.456064 | + | 0.456064i | ||||
\(983\) | −330188. | − | 330188.i | −0.341708 | − | 0.341708i | 0.515301 | − | 0.857009i | \(-0.327680\pi\) |
−0.857009 | + | 0.515301i | \(0.827680\pi\) | |||||||
\(984\) | 407489. | 0.420848 | ||||||||
\(985\) | 172492.i | 0.177785i | ||||||||
\(986\) | −569274. | − | 569274.i | −0.585555 | − | 0.585555i | ||||
\(987\) | 1.78038e6i | 1.82759i | ||||||||
\(988\) | 232465. | − | 371670.i | 0.238147 | − | 0.380754i | ||||
\(989\) | 165140. | 0.168834 | ||||||||
\(990\) | −40596.9 | + | 40596.9i | −0.0414212 | + | 0.0414212i | ||||
\(991\) | 131994. | 0.134402 | 0.0672010 | − | 0.997739i | \(-0.478593\pi\) | ||||
0.0672010 | + | 0.997739i | \(0.478593\pi\) | |||||||
\(992\) | 1.42953e6i | 1.45268i | ||||||||
\(993\) | 1.17343e6 | − | 1.17343e6i | 1.19003 | − | 1.19003i | ||||
\(994\) | −146950. | + | 146950.i | −0.148729 | + | 0.148729i | ||||
\(995\) | 86656.8 | + | 86656.8i | 0.0875299 | + | 0.0875299i | ||||
\(996\) | −329012. | − | 329012.i | −0.331660 | − | 0.331660i | ||||
\(997\) | −981116. | −0.987029 | −0.493514 | − | 0.869738i | \(-0.664288\pi\) | ||||
−0.493514 | + | 0.869738i | \(0.664288\pi\) | |||||||
\(998\) | 624554.i | 0.627060i | ||||||||
\(999\) | −215517. | − | 215517.i | −0.215949 | − | 0.215949i |
(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 | 13.5.d.a.5.2 | ✓ | 6 | |
3.2 | odd | 2 | 117.5.j.a.109.2 | 6 | |||
4.3 | odd | 2 | 208.5.t.c.161.1 | 6 | |||
13.5 | odd | 4 | 169.5.d.a.99.2 | 6 | |||
13.8 | odd | 4 | inner | 13.5.d.a.8.2 | yes | 6 | |
13.12 | even | 2 | 169.5.d.a.70.2 | 6 | |||
39.8 | even | 4 | 117.5.j.a.73.2 | 6 | |||
52.47 | even | 4 | 208.5.t.c.177.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.5.d.a.5.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
13.5.d.a.8.2 | yes | 6 | 13.8 | odd | 4 | inner | |
117.5.j.a.73.2 | 6 | 39.8 | even | 4 | |||
117.5.j.a.109.2 | 6 | 3.2 | odd | 2 | |||
169.5.d.a.70.2 | 6 | 13.12 | even | 2 | |||
169.5.d.a.99.2 | 6 | 13.5 | odd | 4 | |||
208.5.t.c.161.1 | 6 | 4.3 | odd | 2 | |||
208.5.t.c.177.1 | 6 | 52.47 | even | 4 |