Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(64,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.d (of order \(2\), degree \(1\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.84052224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 6x^{3} + 36x^{2} - 36x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.5 | ||
Root | \(2.09148 + 2.09148i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.64 |
Dual form | 105.4.d.a.64.2 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.18296i | 1.12535i | 0.826680 | + | 0.562673i | \(0.190227\pi\) | ||||
−0.826680 | + | 0.562673i | \(0.809773\pi\) | |||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | −2.13122 | −0.266402 | ||||||||
\(5\) | −11.0627 | + | 1.61735i | −0.989481 | + | 0.144660i | ||||
\(6\) | 9.54887 | 0.649718 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 18.6801i | 0.825551i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | −5.14795 | − | 35.2122i | −0.162793 | − | 1.11351i | ||||
\(11\) | −68.7204 | −1.88363 | −0.941817 | − | 0.336127i | \(-0.890883\pi\) | ||||
−0.941817 | + | 0.336127i | \(0.890883\pi\) | |||||||
\(12\) | 6.39365i | 0.153807i | ||||||||
\(13\) | 56.2290i | 1.19962i | 0.800141 | + | 0.599812i | \(0.204758\pi\) | ||||
−0.800141 | + | 0.599812i | \(0.795242\pi\) | |||||||
\(14\) | −22.2807 | −0.425341 | ||||||||
\(15\) | 4.85205 | + | 33.1882i | 0.0835195 | + | 0.571277i | ||||
\(16\) | −76.5076 | −1.19543 | ||||||||
\(17\) | − | 37.9780i | − | 0.541825i | −0.962604 | − | 0.270912i | \(-0.912675\pi\) | ||
0.962604 | − | 0.270912i | \(-0.0873253\pi\) | |||||||
\(18\) | − | 28.6466i | − | 0.375115i | ||||||
\(19\) | 26.0335 | 0.314341 | 0.157171 | − | 0.987571i | \(-0.449763\pi\) | ||||
0.157171 | + | 0.987571i | \(0.449763\pi\) | |||||||
\(20\) | 23.5771 | − | 3.44692i | 0.263600 | − | 0.0385377i | ||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | − | 218.734i | − | 2.11974i | ||||||
\(23\) | 25.5222i | 0.231380i | 0.993285 | + | 0.115690i | \(0.0369079\pi\) | ||||
−0.993285 | + | 0.115690i | \(0.963092\pi\) | |||||||
\(24\) | 56.0403 | 0.476632 | ||||||||
\(25\) | 119.768 | − | 35.7846i | 0.958147 | − | 0.286277i | ||||
\(26\) | −178.974 | −1.34999 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − | 14.9185i | − | 0.100690i | ||||||
\(29\) | −148.336 | −0.949835 | −0.474917 | − | 0.880030i | \(-0.657522\pi\) | ||||
−0.474917 | + | 0.880030i | \(0.657522\pi\) | |||||||
\(30\) | −105.637 | + | 15.4439i | −0.642884 | + | 0.0939883i | ||||
\(31\) | 75.7982 | 0.439153 | 0.219577 | − | 0.975595i | \(-0.429532\pi\) | ||||
0.219577 | + | 0.975595i | \(0.429532\pi\) | |||||||
\(32\) | − | 94.0799i | − | 0.519723i | ||||||
\(33\) | 206.161i | 1.08752i | ||||||||
\(34\) | 120.882 | 0.609740 | ||||||||
\(35\) | −11.3214 | − | 77.4392i | −0.0546764 | − | 0.373989i | ||||
\(36\) | 19.1809 | 0.0888007 | ||||||||
\(37\) | − | 120.199i | − | 0.534070i | −0.963687 | − | 0.267035i | \(-0.913956\pi\) | ||
0.963687 | − | 0.267035i | \(-0.0860439\pi\) | |||||||
\(38\) | 82.8634i | 0.353743i | ||||||||
\(39\) | 168.687 | 0.692603 | ||||||||
\(40\) | −30.2122 | − | 206.653i | −0.119424 | − | 0.816867i | ||||
\(41\) | 345.670 | 1.31670 | 0.658348 | − | 0.752713i | \(-0.271255\pi\) | ||||
0.658348 | + | 0.752713i | \(0.271255\pi\) | |||||||
\(42\) | 66.8421i | 0.245570i | ||||||||
\(43\) | 287.989i | 1.02135i | 0.859774 | + | 0.510674i | \(0.170604\pi\) | ||||
−0.859774 | + | 0.510674i | \(0.829396\pi\) | |||||||
\(44\) | 146.458 | 0.501804 | ||||||||
\(45\) | 99.5646 | − | 14.5561i | 0.329827 | − | 0.0482200i | ||||
\(46\) | −81.2360 | −0.260383 | ||||||||
\(47\) | 528.711i | 1.64086i | 0.571747 | + | 0.820430i | \(0.306266\pi\) | ||||
−0.571747 | + | 0.820430i | \(0.693734\pi\) | |||||||
\(48\) | 229.523i | 0.690183i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 113.901 | + | 381.218i | 0.322160 | + | 1.07825i | ||||
\(51\) | −113.934 | −0.312823 | ||||||||
\(52\) | − | 119.836i | − | 0.319582i | ||||||
\(53\) | 361.728i | 0.937493i | 0.883333 | + | 0.468747i | \(0.155294\pi\) | ||||
−0.883333 | + | 0.468747i | \(0.844706\pi\) | |||||||
\(54\) | −85.9398 | −0.216573 | ||||||||
\(55\) | 760.235 | − | 111.145i | 1.86382 | − | 0.272487i | ||||
\(56\) | −130.761 | −0.312029 | ||||||||
\(57\) | − | 78.1004i | − | 0.181485i | ||||||
\(58\) | − | 472.146i | − | 1.06889i | ||||||
\(59\) | 705.748 | 1.55730 | 0.778649 | − | 0.627460i | \(-0.215905\pi\) | ||||
0.778649 | + | 0.627460i | \(0.215905\pi\) | |||||||
\(60\) | −10.3408 | − | 70.7313i | −0.0222498 | − | 0.152189i | ||||
\(61\) | −393.171 | −0.825253 | −0.412627 | − | 0.910900i | \(-0.635389\pi\) | ||||
−0.412627 | + | 0.910900i | \(0.635389\pi\) | |||||||
\(62\) | 241.262i | 0.494199i | ||||||||
\(63\) | − | 63.0000i | − | 0.125988i | ||||||
\(64\) | −312.609 | −0.610564 | ||||||||
\(65\) | −90.9419 | − | 622.046i | −0.173538 | − | 1.18701i | ||||
\(66\) | −656.202 | −1.22383 | ||||||||
\(67\) | − | 591.202i | − | 1.07801i | −0.842302 | − | 0.539006i | \(-0.818800\pi\) | ||
0.842302 | − | 0.539006i | \(-0.181200\pi\) | |||||||
\(68\) | 80.9393i | 0.144343i | ||||||||
\(69\) | 76.5666 | 0.133587 | ||||||||
\(70\) | 246.486 | − | 36.0357i | 0.420867 | − | 0.0615298i | ||||
\(71\) | −668.829 | −1.11796 | −0.558981 | − | 0.829180i | \(-0.688808\pi\) | ||||
−0.558981 | + | 0.829180i | \(0.688808\pi\) | |||||||
\(72\) | − | 168.121i | − | 0.275184i | ||||||
\(73\) | − | 251.755i | − | 0.403639i | −0.979423 | − | 0.201819i | \(-0.935315\pi\) | ||
0.979423 | − | 0.201819i | \(-0.0646854\pi\) | |||||||
\(74\) | 382.588 | 0.601013 | ||||||||
\(75\) | −107.354 | − | 359.305i | −0.165282 | − | 0.553186i | ||||
\(76\) | −55.4830 | −0.0837412 | ||||||||
\(77\) | − | 481.042i | − | 0.711946i | ||||||
\(78\) | 536.923i | 0.779418i | ||||||||
\(79\) | −295.651 | −0.421054 | −0.210527 | − | 0.977588i | \(-0.567518\pi\) | ||||
−0.210527 | + | 0.977588i | \(0.567518\pi\) | |||||||
\(80\) | 846.384 | − | 123.740i | 1.18286 | − | 0.172931i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1100.25i | 1.48174i | ||||||||
\(83\) | − | 916.511i | − | 1.21205i | −0.795445 | − | 0.606025i | \(-0.792763\pi\) | ||
0.795445 | − | 0.606025i | \(-0.207237\pi\) | |||||||
\(84\) | −44.7555 | −0.0581337 | ||||||||
\(85\) | 61.4237 | + | 420.141i | 0.0783804 | + | 0.536125i | ||||
\(86\) | −916.658 | −1.14937 | ||||||||
\(87\) | 445.007i | 0.548387i | ||||||||
\(88\) | − | 1283.70i | − | 1.55504i | ||||||
\(89\) | 736.838 | 0.877580 | 0.438790 | − | 0.898590i | \(-0.355407\pi\) | ||||
0.438790 | + | 0.898590i | \(0.355407\pi\) | |||||||
\(90\) | 46.3316 | + | 316.910i | 0.0542642 | + | 0.371169i | ||||
\(91\) | −393.603 | −0.453415 | ||||||||
\(92\) | − | 54.3933i | − | 0.0616401i | ||||||
\(93\) | − | 227.395i | − | 0.253545i | ||||||
\(94\) | −1682.86 | −1.84653 | ||||||||
\(95\) | −288.002 | + | 42.1052i | −0.311035 | + | 0.0454727i | ||||
\(96\) | −282.240 | −0.300062 | ||||||||
\(97\) | 142.964i | 0.149647i | 0.997197 | + | 0.0748236i | \(0.0238394\pi\) | ||||
−0.997197 | + | 0.0748236i | \(0.976161\pi\) | |||||||
\(98\) | − | 155.965i | − | 0.160764i | ||||||
\(99\) | 618.483 | 0.627878 | ||||||||
\(100\) | −255.252 | + | 76.2648i | −0.255252 | + | 0.0762648i | ||||
\(101\) | −566.067 | −0.557681 | −0.278840 | − | 0.960337i | \(-0.589950\pi\) | ||||
−0.278840 | + | 0.960337i | \(0.589950\pi\) | |||||||
\(102\) | − | 362.647i | − | 0.352033i | ||||||
\(103\) | 1340.79i | 1.28264i | 0.767275 | + | 0.641318i | \(0.221612\pi\) | ||||
−0.767275 | + | 0.641318i | \(0.778388\pi\) | |||||||
\(104\) | −1050.36 | −0.990351 | ||||||||
\(105\) | −232.318 | + | 33.9643i | −0.215923 | + | 0.0315674i | ||||
\(106\) | −1151.36 | −1.05500 | ||||||||
\(107\) | 1637.85i | 1.47978i | 0.672727 | + | 0.739891i | \(0.265123\pi\) | ||||
−0.672727 | + | 0.739891i | \(0.734877\pi\) | |||||||
\(108\) | − | 57.5428i | − | 0.0512691i | ||||||
\(109\) | 586.693 | 0.515550 | 0.257775 | − | 0.966205i | \(-0.417011\pi\) | ||||
0.257775 | + | 0.966205i | \(0.417011\pi\) | |||||||
\(110\) | 353.769 | + | 2419.80i | 0.306641 | + | 2.09744i | ||||
\(111\) | −360.597 | −0.308345 | ||||||||
\(112\) | − | 535.554i | − | 0.451831i | ||||||
\(113\) | − | 1617.17i | − | 1.34629i | −0.739509 | − | 0.673146i | \(-0.764942\pi\) | ||
0.739509 | − | 0.673146i | \(-0.235058\pi\) | |||||||
\(114\) | 248.590 | 0.204233 | ||||||||
\(115\) | −41.2783 | − | 282.345i | −0.0334715 | − | 0.228946i | ||||
\(116\) | 316.135 | 0.253038 | ||||||||
\(117\) | − | 506.061i | − | 0.399875i | ||||||
\(118\) | 2246.37i | 1.75250i | ||||||||
\(119\) | 265.846 | 0.204790 | ||||||||
\(120\) | −619.959 | + | 90.6367i | −0.471619 | + | 0.0689496i | ||||
\(121\) | 3391.49 | 2.54807 | ||||||||
\(122\) | − | 1251.45i | − | 0.928695i | ||||||
\(123\) | − | 1037.01i | − | 0.760195i | ||||||
\(124\) | −161.542 | −0.116991 | ||||||||
\(125\) | −1267.09 | + | 589.583i | −0.906656 | + | 0.421871i | ||||
\(126\) | 200.526 | 0.141780 | ||||||||
\(127\) | 2042.94i | 1.42741i | 0.700446 | + | 0.713706i | \(0.252985\pi\) | ||||
−0.700446 | + | 0.713706i | \(0.747015\pi\) | |||||||
\(128\) | − | 1747.66i | − | 1.20682i | ||||||
\(129\) | 863.968 | 0.589675 | ||||||||
\(130\) | 1979.95 | − | 289.464i | 1.33579 | − | 0.195290i | ||||
\(131\) | −2631.04 | −1.75477 | −0.877384 | − | 0.479788i | \(-0.840714\pi\) | ||||
−0.877384 | + | 0.479788i | \(0.840714\pi\) | |||||||
\(132\) | − | 439.374i | − | 0.289716i | ||||||
\(133\) | 182.234i | 0.118810i | ||||||||
\(134\) | 1881.77 | 1.21314 | ||||||||
\(135\) | −43.6684 | − | 298.694i | −0.0278398 | − | 0.190426i | ||||
\(136\) | 709.432 | 0.447304 | ||||||||
\(137\) | 1588.54i | 0.990641i | 0.868710 | + | 0.495320i | \(0.164949\pi\) | ||||
−0.868710 | + | 0.495320i | \(0.835051\pi\) | |||||||
\(138\) | 243.708i | 0.150332i | ||||||||
\(139\) | −1733.49 | −1.05779 | −0.528894 | − | 0.848688i | \(-0.677393\pi\) | ||||
−0.528894 | + | 0.848688i | \(0.677393\pi\) | |||||||
\(140\) | 24.1284 | + | 165.040i | 0.0145659 | + | 0.0996314i | ||||
\(141\) | 1586.13 | 0.947351 | ||||||||
\(142\) | − | 2128.85i | − | 1.25809i | ||||||
\(143\) | − | 3864.07i | − | 2.25965i | ||||||
\(144\) | 688.569 | 0.398477 | ||||||||
\(145\) | 1641.00 | − | 239.910i | 0.939844 | − | 0.137403i | ||||
\(146\) | 801.324 | 0.454233 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 256.170i | 0.142277i | ||||||||
\(149\) | 1370.68 | 0.753629 | 0.376815 | − | 0.926289i | \(-0.377019\pi\) | ||||
0.376815 | + | 0.926289i | \(0.377019\pi\) | |||||||
\(150\) | 1143.65 | − | 341.703i | 0.622526 | − | 0.185999i | ||||
\(151\) | −3694.08 | −1.99086 | −0.995429 | − | 0.0955015i | \(-0.969555\pi\) | ||||
−0.995429 | + | 0.0955015i | \(0.969555\pi\) | |||||||
\(152\) | 486.308i | 0.259505i | ||||||||
\(153\) | 341.802i | 0.180608i | ||||||||
\(154\) | 1531.14 | 0.801186 | ||||||||
\(155\) | −838.536 | + | 122.592i | −0.434534 | + | 0.0635280i | ||||
\(156\) | −359.508 | −0.184511 | ||||||||
\(157\) | 1054.56i | 0.536071i | 0.963409 | + | 0.268036i | \(0.0863745\pi\) | ||||
−0.963409 | + | 0.268036i | \(0.913626\pi\) | |||||||
\(158\) | − | 941.044i | − | 0.473832i | ||||||
\(159\) | 1085.18 | 0.541262 | ||||||||
\(160\) | 152.160 | + | 1040.78i | 0.0751831 | + | 0.514256i | ||||
\(161\) | −178.655 | −0.0874535 | ||||||||
\(162\) | 257.820i | 0.125038i | ||||||||
\(163\) | 1380.12i | 0.663185i | 0.943423 | + | 0.331593i | \(0.107586\pi\) | ||||
−0.943423 | + | 0.331593i | \(0.892414\pi\) | |||||||
\(164\) | −736.697 | −0.350771 | ||||||||
\(165\) | −333.434 | − | 2280.71i | −0.157320 | − | 1.07608i | ||||
\(166\) | 2917.22 | 1.36398 | ||||||||
\(167\) | − | 3143.10i | − | 1.45641i | −0.685359 | − | 0.728205i | \(-0.740355\pi\) | ||
0.685359 | − | 0.728205i | \(-0.259645\pi\) | |||||||
\(168\) | 392.282i | 0.180150i | ||||||||
\(169\) | −964.696 | −0.439097 | ||||||||
\(170\) | −1337.29 | + | 195.509i | −0.603326 | + | 0.0882050i | ||||
\(171\) | −234.301 | −0.104780 | ||||||||
\(172\) | − | 613.767i | − | 0.272089i | ||||||
\(173\) | 3306.12i | 1.45295i | 0.687195 | + | 0.726473i | \(0.258842\pi\) | ||||
−0.687195 | + | 0.726473i | \(0.741158\pi\) | |||||||
\(174\) | −1416.44 | −0.617125 | ||||||||
\(175\) | 250.492 | + | 838.379i | 0.108203 | + | 0.362145i | ||||
\(176\) | 5257.63 | 2.25176 | ||||||||
\(177\) | − | 2117.24i | − | 0.899106i | ||||||
\(178\) | 2345.32i | 0.987581i | ||||||||
\(179\) | −2839.60 | −1.18571 | −0.592854 | − | 0.805310i | \(-0.701999\pi\) | ||||
−0.592854 | + | 0.805310i | \(0.701999\pi\) | |||||||
\(180\) | −212.194 | + | 31.0223i | −0.0878666 | + | 0.0128459i | ||||
\(181\) | 741.522 | 0.304513 | 0.152257 | − | 0.988341i | \(-0.451346\pi\) | ||||
0.152257 | + | 0.988341i | \(0.451346\pi\) | |||||||
\(182\) | − | 1252.82i | − | 0.510249i | ||||||
\(183\) | 1179.51i | 0.476460i | ||||||||
\(184\) | −476.757 | −0.191016 | ||||||||
\(185\) | 194.404 | + | 1329.73i | 0.0772586 | + | 0.528452i | ||||
\(186\) | 723.787 | 0.285326 | ||||||||
\(187\) | 2609.86i | 1.02060i | ||||||||
\(188\) | − | 1126.80i | − | 0.437129i | ||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −134.019 | − | 916.696i | −0.0511725 | − | 0.350022i | ||||
\(191\) | 4428.76 | 1.67777 | 0.838885 | − | 0.544309i | \(-0.183208\pi\) | ||||
0.838885 | + | 0.544309i | \(0.183208\pi\) | |||||||
\(192\) | 937.827i | 0.352510i | ||||||||
\(193\) | 815.034i | 0.303976i | 0.988382 | + | 0.151988i | \(0.0485675\pi\) | ||||
−0.988382 | + | 0.151988i | \(0.951432\pi\) | |||||||
\(194\) | −455.048 | −0.168405 | ||||||||
\(195\) | −1866.14 | + | 272.826i | −0.685318 | + | 0.100192i | ||||
\(196\) | 104.430 | 0.0380574 | ||||||||
\(197\) | 1609.61i | 0.582133i | 0.956703 | + | 0.291067i | \(0.0940102\pi\) | ||||
−0.956703 | + | 0.291067i | \(0.905990\pi\) | |||||||
\(198\) | 1968.61i | 0.706579i | ||||||||
\(199\) | 273.622 | 0.0974700 | 0.0487350 | − | 0.998812i | \(-0.484481\pi\) | ||||
0.0487350 | + | 0.998812i | \(0.484481\pi\) | |||||||
\(200\) | 668.460 | + | 2237.28i | 0.236336 | + | 0.790999i | ||||
\(201\) | −1773.60 | −0.622390 | ||||||||
\(202\) | − | 1801.77i | − | 0.627584i | ||||||
\(203\) | − | 1038.35i | − | 0.359004i | ||||||
\(204\) | 242.818 | 0.0833366 | ||||||||
\(205\) | −3824.05 | + | 559.069i | −1.30285 | + | 0.190473i | ||||
\(206\) | −4267.66 | −1.44341 | ||||||||
\(207\) | − | 229.700i | − | 0.0771267i | ||||||
\(208\) | − | 4301.95i | − | 1.43407i | ||||||
\(209\) | −1789.03 | −0.592104 | ||||||||
\(210\) | −108.107 | − | 739.457i | −0.0355242 | − | 0.242987i | ||||
\(211\) | −5157.70 | −1.68280 | −0.841399 | − | 0.540414i | \(-0.818267\pi\) | ||||
−0.841399 | + | 0.540414i | \(0.818267\pi\) | |||||||
\(212\) | − | 770.920i | − | 0.249750i | ||||||
\(213\) | 2006.49i | 0.645456i | ||||||||
\(214\) | −5213.20 | −1.66527 | ||||||||
\(215\) | −465.779 | − | 3185.95i | −0.147748 | − | 1.01060i | ||||
\(216\) | −504.362 | −0.158877 | ||||||||
\(217\) | 530.587i | 0.165984i | ||||||||
\(218\) | 1867.42i | 0.580172i | ||||||||
\(219\) | −755.264 | −0.233041 | ||||||||
\(220\) | −1620.23 | + | 236.874i | −0.496525 | + | 0.0725910i | ||||
\(221\) | 2135.46 | 0.649986 | ||||||||
\(222\) | − | 1147.76i | − | 0.346995i | ||||||
\(223\) | 1444.38i | 0.433733i | 0.976201 | + | 0.216867i | \(0.0695837\pi\) | ||||
−0.976201 | + | 0.216867i | \(0.930416\pi\) | |||||||
\(224\) | 658.559 | 0.196437 | ||||||||
\(225\) | −1077.92 | + | 322.062i | −0.319382 | + | 0.0954257i | ||||
\(226\) | 5147.40 | 1.51504 | ||||||||
\(227\) | − | 1635.20i | − | 0.478114i | −0.971006 | − | 0.239057i | \(-0.923162\pi\) | ||
0.971006 | − | 0.239057i | \(-0.0768383\pi\) | |||||||
\(228\) | 166.449i | 0.0483480i | ||||||||
\(229\) | 2807.34 | 0.810105 | 0.405052 | − | 0.914293i | \(-0.367253\pi\) | ||||
0.405052 | + | 0.914293i | \(0.367253\pi\) | |||||||
\(230\) | 898.693 | − | 131.387i | 0.257644 | − | 0.0376670i | ||||
\(231\) | −1443.13 | −0.411042 | ||||||||
\(232\) | − | 2770.92i | − | 0.784137i | ||||||
\(233\) | 579.805i | 0.163023i | 0.996672 | + | 0.0815113i | \(0.0259747\pi\) | ||||
−0.996672 | + | 0.0815113i | \(0.974025\pi\) | |||||||
\(234\) | 1610.77 | 0.449997 | ||||||||
\(235\) | −855.110 | − | 5848.99i | −0.237367 | − | 1.62360i | ||||
\(236\) | −1504.10 | −0.414867 | ||||||||
\(237\) | 886.952i | 0.243096i | ||||||||
\(238\) | 846.177i | 0.230460i | ||||||||
\(239\) | 1695.51 | 0.458886 | 0.229443 | − | 0.973322i | \(-0.426310\pi\) | ||||
0.229443 | + | 0.973322i | \(0.426310\pi\) | |||||||
\(240\) | −371.219 | − | 2539.15i | −0.0998419 | − | 0.682923i | ||||
\(241\) | −1182.39 | −0.316035 | −0.158018 | − | 0.987436i | \(-0.550510\pi\) | ||||
−0.158018 | + | 0.987436i | \(0.550510\pi\) | |||||||
\(242\) | 10795.0i | 2.86746i | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 837.933 | 0.219849 | ||||||||
\(245\) | 542.074 | − | 79.2501i | 0.141354 | − | 0.0206657i | ||||
\(246\) | 3300.76 | 0.855482 | ||||||||
\(247\) | 1463.84i | 0.377091i | ||||||||
\(248\) | 1415.92i | 0.362544i | ||||||||
\(249\) | −2749.53 | −0.699778 | ||||||||
\(250\) | −1876.62 | − | 4033.09i | −0.474751 | − | 1.02030i | ||||
\(251\) | 2411.68 | 0.606469 | 0.303234 | − | 0.952916i | \(-0.401934\pi\) | ||||
0.303234 | + | 0.952916i | \(0.401934\pi\) | |||||||
\(252\) | 134.267i | 0.0335635i | ||||||||
\(253\) | − | 1753.89i | − | 0.435835i | ||||||
\(254\) | −6502.58 | −1.60633 | ||||||||
\(255\) | 1260.42 | − | 184.271i | 0.309532 | − | 0.0452530i | ||||
\(256\) | 3061.85 | 0.747523 | ||||||||
\(257\) | − | 1054.74i | − | 0.256003i | −0.991774 | − | 0.128002i | \(-0.959144\pi\) | ||
0.991774 | − | 0.128002i | \(-0.0408562\pi\) | |||||||
\(258\) | 2749.97i | 0.663588i | ||||||||
\(259\) | 841.392 | 0.201859 | ||||||||
\(260\) | 193.817 | + | 1325.72i | 0.0462308 | + | 0.316221i | ||||
\(261\) | 1335.02 | 0.316612 | ||||||||
\(262\) | − | 8374.48i | − | 1.97472i | ||||||
\(263\) | − | 3390.76i | − | 0.794993i | −0.917604 | − | 0.397496i | \(-0.869879\pi\) | ||
0.917604 | − | 0.397496i | \(-0.130121\pi\) | |||||||
\(264\) | −3851.11 | −0.897800 | ||||||||
\(265\) | −585.040 | − | 4001.70i | −0.135618 | − | 0.927632i | ||||
\(266\) | −580.044 | −0.133702 | ||||||||
\(267\) | − | 2210.51i | − | 0.506671i | ||||||
\(268\) | 1259.98i | 0.287184i | ||||||||
\(269\) | 8792.06 | 1.99279 | 0.996397 | − | 0.0848151i | \(-0.0270300\pi\) | ||||
0.996397 | + | 0.0848151i | \(0.0270300\pi\) | |||||||
\(270\) | 950.730 | − | 138.995i | 0.214295 | − | 0.0313294i | ||||
\(271\) | 1593.15 | 0.357111 | 0.178556 | − | 0.983930i | \(-0.442858\pi\) | ||||
0.178556 | + | 0.983930i | \(0.442858\pi\) | |||||||
\(272\) | 2905.61i | 0.647715i | ||||||||
\(273\) | 1180.81i | 0.261779i | ||||||||
\(274\) | −5056.24 | −1.11481 | ||||||||
\(275\) | −8230.52 | + | 2459.13i | −1.80480 | + | 0.539241i | ||||
\(276\) | −163.180 | −0.0355880 | ||||||||
\(277\) | 208.765i | 0.0452833i | 0.999744 | + | 0.0226417i | \(0.00720768\pi\) | ||||
−0.999744 | + | 0.0226417i | \(0.992792\pi\) | |||||||
\(278\) | − | 5517.62i | − | 1.19038i | ||||||
\(279\) | −682.184 | −0.146384 | ||||||||
\(280\) | 1446.57 | − | 211.486i | 0.308747 | − | 0.0451381i | ||||
\(281\) | 2445.06 | 0.519075 | 0.259538 | − | 0.965733i | \(-0.416430\pi\) | ||||
0.259538 | + | 0.965733i | \(0.416430\pi\) | |||||||
\(282\) | 5048.59i | 1.06610i | ||||||||
\(283\) | 3894.53i | 0.818042i | 0.912525 | + | 0.409021i | \(0.134130\pi\) | ||||
−0.912525 | + | 0.409021i | \(0.865870\pi\) | |||||||
\(284\) | 1425.42 | 0.297828 | ||||||||
\(285\) | 126.316 | + | 864.005i | 0.0262537 | + | 0.179576i | ||||
\(286\) | 12299.2 | 2.54289 | ||||||||
\(287\) | 2419.69i | 0.497665i | ||||||||
\(288\) | 846.719i | 0.173241i | ||||||||
\(289\) | 3470.67 | 0.706426 | ||||||||
\(290\) | 763.624 | + | 5223.22i | 0.154626 | + | 1.05765i | ||||
\(291\) | 428.892 | 0.0863988 | ||||||||
\(292\) | 536.543i | 0.107530i | ||||||||
\(293\) | − | 5746.21i | − | 1.14572i | −0.819652 | − | 0.572862i | \(-0.805833\pi\) | ||
0.819652 | − | 0.572862i | \(-0.194167\pi\) | |||||||
\(294\) | −467.895 | −0.0928169 | ||||||||
\(295\) | −7807.50 | + | 1141.44i | −1.54092 | + | 0.225279i | ||||
\(296\) | 2245.33 | 0.440902 | ||||||||
\(297\) | − | 1855.45i | − | 0.362505i | ||||||
\(298\) | 4362.83i | 0.848093i | ||||||||
\(299\) | −1435.09 | −0.277569 | ||||||||
\(300\) | 228.794 | + | 765.757i | 0.0440315 | + | 0.147370i | ||||
\(301\) | −2015.93 | −0.386033 | ||||||||
\(302\) | − | 11758.1i | − | 2.24040i | ||||||
\(303\) | 1698.20i | 0.321977i | ||||||||
\(304\) | −1991.76 | −0.375774 | ||||||||
\(305\) | 4349.55 | − | 635.895i | 0.816573 | − | 0.119381i | ||||
\(306\) | −1087.94 | −0.203247 | ||||||||
\(307\) | − | 1979.55i | − | 0.368008i | −0.982925 | − | 0.184004i | \(-0.941094\pi\) | ||
0.982925 | − | 0.184004i | \(-0.0589060\pi\) | |||||||
\(308\) | 1025.21i | 0.189664i | ||||||||
\(309\) | 4022.36 | 0.740531 | ||||||||
\(310\) | −390.206 | − | 2669.02i | −0.0714909 | − | 0.489001i | ||||
\(311\) | 3495.57 | 0.637348 | 0.318674 | − | 0.947864i | \(-0.396762\pi\) | ||||
0.318674 | + | 0.947864i | \(0.396762\pi\) | |||||||
\(312\) | 3151.09i | 0.571779i | ||||||||
\(313\) | − | 1448.68i | − | 0.261611i | −0.991408 | − | 0.130805i | \(-0.958244\pi\) | ||
0.991408 | − | 0.130805i | \(-0.0417563\pi\) | |||||||
\(314\) | −3356.62 | −0.603265 | ||||||||
\(315\) | 101.893 | + | 696.953i | 0.0182255 | + | 0.124663i | ||||
\(316\) | 630.096 | 0.112170 | ||||||||
\(317\) | 9453.34i | 1.67493i | 0.546492 | + | 0.837465i | \(0.315963\pi\) | ||||
−0.546492 | + | 0.837465i | \(0.684037\pi\) | |||||||
\(318\) | 3454.09i | 0.609107i | ||||||||
\(319\) | 10193.7 | 1.78914 | ||||||||
\(320\) | 3458.31 | − | 505.598i | 0.604142 | − | 0.0883243i | ||||
\(321\) | 4913.54 | 0.854353 | ||||||||
\(322\) | − | 568.652i | − | 0.0984154i | ||||||
\(323\) | − | 988.699i | − | 0.170318i | ||||||
\(324\) | −172.629 | −0.0296002 | ||||||||
\(325\) | 2012.13 | + | 6734.45i | 0.343425 | + | 1.14942i | ||||
\(326\) | −4392.86 | −0.746313 | ||||||||
\(327\) | − | 1760.08i | − | 0.297653i | ||||||
\(328\) | 6457.14i | 1.08700i | ||||||||
\(329\) | −3700.98 | −0.620187 | ||||||||
\(330\) | 7259.39 | − | 1061.31i | 1.21096 | − | 0.177040i | ||||
\(331\) | −791.305 | −0.131402 | −0.0657010 | − | 0.997839i | \(-0.520928\pi\) | ||||
−0.0657010 | + | 0.997839i | \(0.520928\pi\) | |||||||
\(332\) | 1953.28i | 0.322893i | ||||||||
\(333\) | 1081.79i | 0.178023i | ||||||||
\(334\) | 10004.4 | 1.63896 | ||||||||
\(335\) | 956.179 | + | 6540.31i | 0.155945 | + | 1.06667i | ||||
\(336\) | −1606.66 | −0.260865 | ||||||||
\(337\) | − | 5959.06i | − | 0.963237i | −0.876381 | − | 0.481618i | \(-0.840049\pi\) | ||
0.876381 | − | 0.481618i | \(-0.159951\pi\) | |||||||
\(338\) | − | 3070.59i | − | 0.494136i | ||||||
\(339\) | −4851.52 | −0.777282 | ||||||||
\(340\) | −130.907 | − | 895.411i | −0.0208807 | − | 0.142825i | ||||
\(341\) | −5208.88 | −0.827204 | ||||||||
\(342\) | − | 745.771i | − | 0.117914i | ||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | −5379.67 | −0.843175 | ||||||||
\(345\) | −847.036 | + | 123.835i | −0.132182 | + | 0.0193248i | ||||
\(346\) | −10523.2 | −1.63507 | ||||||||
\(347\) | 4560.34i | 0.705509i | 0.935716 | + | 0.352755i | \(0.114755\pi\) | ||||
−0.935716 | + | 0.352755i | \(0.885245\pi\) | |||||||
\(348\) | − | 948.405i | − | 0.146092i | ||||||
\(349\) | 9404.92 | 1.44250 | 0.721252 | − | 0.692673i | \(-0.243567\pi\) | ||||
0.721252 | + | 0.692673i | \(0.243567\pi\) | |||||||
\(350\) | −2668.52 | + | 797.306i | −0.407539 | + | 0.121765i | ||||
\(351\) | −1518.18 | −0.230868 | ||||||||
\(352\) | 6465.20i | 0.978967i | ||||||||
\(353\) | 1391.37i | 0.209788i | 0.994483 | + | 0.104894i | \(0.0334503\pi\) | ||||
−0.994483 | + | 0.104894i | \(0.966550\pi\) | |||||||
\(354\) | 6739.10 | 1.01180 | ||||||||
\(355\) | 7399.08 | − | 1081.73i | 1.10620 | − | 0.161725i | ||||
\(356\) | −1570.36 | −0.233789 | ||||||||
\(357\) | − | 797.538i | − | 0.118236i | ||||||
\(358\) | − | 9038.32i | − | 1.33433i | ||||||
\(359\) | −4306.80 | −0.633159 | −0.316579 | − | 0.948566i | \(-0.602534\pi\) | ||||
−0.316579 | + | 0.948566i | \(0.602534\pi\) | |||||||
\(360\) | 271.910 | + | 1859.88i | 0.0398081 | + | 0.272289i | ||||
\(361\) | −6181.26 | −0.901189 | ||||||||
\(362\) | 2360.23i | 0.342682i | ||||||||
\(363\) | − | 10174.5i | − | 1.47113i | ||||||
\(364\) | 838.852 | 0.120791 | ||||||||
\(365\) | 407.175 | + | 2785.09i | 0.0583904 | + | 0.399393i | ||||
\(366\) | −3754.34 | −0.536182 | ||||||||
\(367\) | − | 6405.46i | − | 0.911069i | −0.890218 | − | 0.455534i | \(-0.849448\pi\) | ||
0.890218 | − | 0.455534i | \(-0.150552\pi\) | |||||||
\(368\) | − | 1952.64i | − | 0.276599i | ||||||
\(369\) | −3111.03 | −0.438899 | ||||||||
\(370\) | −4232.47 | + | 618.778i | −0.594691 | + | 0.0869426i | ||||
\(371\) | −2532.09 | −0.354339 | ||||||||
\(372\) | 484.627i | 0.0675450i | ||||||||
\(373\) | − | 10293.2i | − | 1.42885i | −0.699712 | − | 0.714425i | \(-0.746688\pi\) | ||
0.699712 | − | 0.714425i | \(-0.253312\pi\) | |||||||
\(374\) | −8307.08 | −1.14853 | ||||||||
\(375\) | 1768.75 | + | 3801.27i | 0.243568 | + | 0.523458i | ||||
\(376\) | −9876.37 | −1.35461 | ||||||||
\(377\) | − | 8340.75i | − | 1.13944i | ||||||
\(378\) | − | 601.579i | − | 0.0818568i | ||||||
\(379\) | −3832.35 | −0.519405 | −0.259702 | − | 0.965689i | \(-0.583625\pi\) | ||||
−0.259702 | + | 0.965689i | \(0.583625\pi\) | |||||||
\(380\) | 613.793 | − | 89.7353i | 0.0828604 | − | 0.0121140i | ||||
\(381\) | 6128.81 | 0.824116 | ||||||||
\(382\) | 14096.6i | 1.88807i | ||||||||
\(383\) | − | 13514.8i | − | 1.80307i | −0.432705 | − | 0.901536i | \(-0.642441\pi\) | ||
0.432705 | − | 0.901536i | \(-0.357559\pi\) | |||||||
\(384\) | −5242.98 | −0.696757 | ||||||||
\(385\) | 778.014 | + | 5321.65i | 0.102990 | + | 0.704458i | ||||
\(386\) | −2594.22 | −0.342078 | ||||||||
\(387\) | − | 2591.90i | − | 0.340449i | ||||||
\(388\) | − | 304.687i | − | 0.0398663i | ||||||
\(389\) | 6444.44 | 0.839965 | 0.419982 | − | 0.907532i | \(-0.362036\pi\) | ||||
0.419982 | + | 0.907532i | \(0.362036\pi\) | |||||||
\(390\) | −868.392 | − | 5939.84i | −0.112751 | − | 0.771219i | ||||
\(391\) | 969.282 | 0.125367 | ||||||||
\(392\) | − | 915.324i | − | 0.117936i | ||||||
\(393\) | 7893.11i | 1.01312i | ||||||||
\(394\) | −5123.33 | −0.655101 | ||||||||
\(395\) | 3270.71 | − | 478.170i | 0.416626 | − | 0.0609098i | ||||
\(396\) | −1318.12 | −0.167268 | ||||||||
\(397\) | − | 2811.16i | − | 0.355386i | −0.984086 | − | 0.177693i | \(-0.943137\pi\) | ||
0.984086 | − | 0.177693i | \(-0.0568634\pi\) | |||||||
\(398\) | 870.926i | 0.109687i | ||||||||
\(399\) | 546.703 | 0.0685949 | ||||||||
\(400\) | −9163.20 | + | 2737.80i | −1.14540 | + | 0.342225i | ||||
\(401\) | 9918.99 | 1.23524 | 0.617619 | − | 0.786477i | \(-0.288097\pi\) | ||||
0.617619 | + | 0.786477i | \(0.288097\pi\) | |||||||
\(402\) | − | 5645.31i | − | 0.700404i | ||||||
\(403\) | 4262.05i | 0.526819i | ||||||||
\(404\) | 1206.41 | 0.148567 | ||||||||
\(405\) | −896.082 | + | 131.005i | −0.109942 | + | 0.0160733i | ||||
\(406\) | 3305.02 | 0.404003 | ||||||||
\(407\) | 8260.11i | 1.00599i | ||||||||
\(408\) | − | 2128.30i | − | 0.258251i | ||||||
\(409\) | 562.052 | 0.0679504 | 0.0339752 | − | 0.999423i | \(-0.489183\pi\) | ||||
0.0339752 | + | 0.999423i | \(0.489183\pi\) | |||||||
\(410\) | −1779.49 | − | 12171.8i | −0.214348 | − | 1.46615i | ||||
\(411\) | 4765.61 | 0.571947 | ||||||||
\(412\) | − | 2857.50i | − | 0.341697i | ||||||
\(413\) | 4940.24i | 0.588603i | ||||||||
\(414\) | 731.124 | 0.0867942 | ||||||||
\(415\) | 1482.32 | + | 10139.1i | 0.175335 | + | 1.19930i | ||||
\(416\) | 5290.01 | 0.623472 | ||||||||
\(417\) | 5200.46i | 0.610714i | ||||||||
\(418\) | − | 5694.40i | − | 0.666322i | ||||||
\(419\) | −354.260 | −0.0413049 | −0.0206525 | − | 0.999787i | \(-0.506574\pi\) | ||||
−0.0206525 | + | 0.999787i | \(0.506574\pi\) | |||||||
\(420\) | 495.119 | − | 72.3853i | 0.0575222 | − | 0.00840962i | ||||
\(421\) | −2969.20 | −0.343729 | −0.171864 | − | 0.985121i | \(-0.554979\pi\) | ||||
−0.171864 | + | 0.985121i | \(0.554979\pi\) | |||||||
\(422\) | − | 16416.7i | − | 1.89373i | ||||||
\(423\) | − | 4758.40i | − | 0.546954i | ||||||
\(424\) | −6757.11 | −0.773948 | ||||||||
\(425\) | −1359.03 | − | 4548.56i | −0.155112 | − | 0.519148i | ||||
\(426\) | −6386.56 | −0.726361 | ||||||||
\(427\) | − | 2752.20i | − | 0.311916i | ||||||
\(428\) | − | 3490.61i | − | 0.394217i | ||||||
\(429\) | −11592.2 | −1.30461 | ||||||||
\(430\) | 10140.7 | − | 1482.56i | 1.13728 | − | 0.166268i | ||||
\(431\) | −4583.08 | −0.512202 | −0.256101 | − | 0.966650i | \(-0.582438\pi\) | ||||
−0.256101 | + | 0.966650i | \(0.582438\pi\) | |||||||
\(432\) | − | 2065.71i | − | 0.230061i | ||||||
\(433\) | − | 247.808i | − | 0.0275033i | −0.999905 | − | 0.0137516i | \(-0.995623\pi\) | ||
0.999905 | − | 0.0137516i | \(-0.00437742\pi\) | |||||||
\(434\) | −1688.84 | −0.186790 | ||||||||
\(435\) | −719.731 | − | 4922.99i | −0.0793298 | − | 0.542619i | ||||
\(436\) | −1250.37 | −0.137344 | ||||||||
\(437\) | 664.431i | 0.0727324i | ||||||||
\(438\) | − | 2403.97i | − | 0.262252i | ||||||
\(439\) | 3793.19 | 0.412390 | 0.206195 | − | 0.978511i | \(-0.433892\pi\) | ||||
0.206195 | + | 0.978511i | \(0.433892\pi\) | |||||||
\(440\) | 2076.19 | + | 14201.3i | 0.224952 | + | 1.53868i | ||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 6797.09i | 0.731458i | ||||||||
\(443\) | 13157.7i | 1.41115i | 0.708635 | + | 0.705575i | \(0.249311\pi\) | ||||
−0.708635 | + | 0.705575i | \(0.750689\pi\) | |||||||
\(444\) | 768.510 | 0.0821438 | ||||||||
\(445\) | −8151.44 | + | 1191.72i | −0.868349 | + | 0.126951i | ||||
\(446\) | −4597.38 | −0.488100 | ||||||||
\(447\) | − | 4112.05i | − | 0.435108i | ||||||
\(448\) | − | 2188.26i | − | 0.230772i | ||||||
\(449\) | 8705.75 | 0.915033 | 0.457517 | − | 0.889201i | \(-0.348739\pi\) | ||||
0.457517 | + | 0.889201i | \(0.348739\pi\) | |||||||
\(450\) | −1025.11 | − | 3430.96i | −0.107387 | − | 0.359415i | ||||
\(451\) | −23754.6 | −2.48017 | ||||||||
\(452\) | 3446.55i | 0.358655i | ||||||||
\(453\) | 11082.2i | 1.14942i | ||||||||
\(454\) | 5204.76 | 0.538043 | ||||||||
\(455\) | 4354.32 | − | 636.593i | 0.448646 | − | 0.0655911i | ||||
\(456\) | 1458.92 | 0.149825 | ||||||||
\(457\) | 11239.4i | 1.15045i | 0.817994 | + | 0.575227i | \(0.195086\pi\) | ||||
−0.817994 | + | 0.575227i | \(0.804914\pi\) | |||||||
\(458\) | 8935.63i | 0.911648i | ||||||||
\(459\) | 1025.41 | 0.104274 | ||||||||
\(460\) | 87.9729 | + | 601.739i | 0.00891687 | + | 0.0609918i | ||||
\(461\) | −12534.3 | −1.26633 | −0.633167 | − | 0.774015i | \(-0.718246\pi\) | ||||
−0.633167 | + | 0.774015i | \(0.718246\pi\) | |||||||
\(462\) | − | 4593.41i | − | 0.462565i | ||||||
\(463\) | 12563.8i | 1.26110i | 0.776150 | + | 0.630549i | \(0.217170\pi\) | ||||
−0.776150 | + | 0.630549i | \(0.782830\pi\) | |||||||
\(464\) | 11348.8 | 1.13546 | ||||||||
\(465\) | 367.776 | + | 2515.61i | 0.0366779 | + | 0.250878i | ||||
\(466\) | −1845.49 | −0.183457 | ||||||||
\(467\) | 4817.97i | 0.477407i | 0.971093 | + | 0.238703i | \(0.0767223\pi\) | ||||
−0.971093 | + | 0.238703i | \(0.923278\pi\) | |||||||
\(468\) | 1078.52i | 0.106527i | ||||||||
\(469\) | 4138.41 | 0.407450 | ||||||||
\(470\) | 18617.1 | − | 2721.78i | 1.82711 | − | 0.267120i | ||||
\(471\) | 3163.68 | 0.309501 | ||||||||
\(472\) | 13183.4i | 1.28563i | ||||||||
\(473\) | − | 19790.7i | − | 1.92384i | ||||||
\(474\) | −2823.13 | −0.273567 | ||||||||
\(475\) | 3117.99 | − | 931.598i | 0.301185 | − | 0.0899887i | ||||
\(476\) | −566.575 | −0.0545566 | ||||||||
\(477\) | − | 3255.55i | − | 0.312498i | ||||||
\(478\) | 5396.75i | 0.516405i | ||||||||
\(479\) | 7088.81 | 0.676192 | 0.338096 | − | 0.941112i | \(-0.390217\pi\) | ||||
0.338096 | + | 0.941112i | \(0.390217\pi\) | |||||||
\(480\) | 3122.34 | − | 456.480i | 0.296906 | − | 0.0434070i | ||||
\(481\) | 6758.66 | 0.640683 | ||||||||
\(482\) | − | 3763.50i | − | 0.355649i | ||||||
\(483\) | 535.966i | 0.0504913i | ||||||||
\(484\) | −7227.99 | −0.678812 | ||||||||
\(485\) | −231.222 | − | 1581.57i | −0.0216480 | − | 0.148073i | ||||
\(486\) | 773.459 | 0.0721909 | ||||||||
\(487\) | 16131.5i | 1.50101i | 0.660867 | + | 0.750503i | \(0.270189\pi\) | ||||
−0.660867 | + | 0.750503i | \(0.729811\pi\) | |||||||
\(488\) | − | 7344.48i | − | 0.681289i | ||||||
\(489\) | 4140.36 | 0.382890 | ||||||||
\(490\) | 252.250 | + | 1725.40i | 0.0232561 | + | 0.159073i | ||||
\(491\) | −3961.20 | −0.364087 | −0.182043 | − | 0.983290i | \(-0.558271\pi\) | ||||
−0.182043 | + | 0.983290i | \(0.558271\pi\) | |||||||
\(492\) | 2210.09i | 0.202518i | ||||||||
\(493\) | 5633.49i | 0.514644i | ||||||||
\(494\) | −4659.32 | −0.424358 | ||||||||
\(495\) | −6842.12 | + | 1000.30i | −0.621273 | + | 0.0908289i | ||||
\(496\) | −5799.14 | −0.524978 | ||||||||
\(497\) | − | 4681.80i | − | 0.422550i | ||||||
\(498\) | − | 8751.65i | − | 0.787492i | ||||||
\(499\) | 12981.0 | 1.16455 | 0.582274 | − | 0.812992i | \(-0.302163\pi\) | ||||
0.582274 | + | 0.812992i | \(0.302163\pi\) | |||||||
\(500\) | 2700.44 | − | 1256.53i | 0.241535 | − | 0.112387i | ||||
\(501\) | −9429.30 | −0.840859 | ||||||||
\(502\) | 7676.26i | 0.682486i | ||||||||
\(503\) | 9611.24i | 0.851976i | 0.904729 | + | 0.425988i | \(0.140073\pi\) | ||||
−0.904729 | + | 0.425988i | \(0.859927\pi\) | |||||||
\(504\) | 1176.85 | 0.104010 | ||||||||
\(505\) | 6262.25 | − | 915.528i | 0.551815 | − | 0.0806742i | ||||
\(506\) | 5582.57 | 0.490465 | ||||||||
\(507\) | 2894.09i | 0.253513i | ||||||||
\(508\) | − | 4353.94i | − | 0.380265i | ||||||
\(509\) | 2605.16 | 0.226860 | 0.113430 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113430 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(510\) | 586.527 | + | 4011.87i | 0.0509252 | + | 0.348331i | ||||
\(511\) | 1762.28 | 0.152561 | ||||||||
\(512\) | − | 4235.53i | − | 0.365597i | ||||||
\(513\) | 702.904i | 0.0604950i | ||||||||
\(514\) | 3357.19 | 0.288092 | ||||||||
\(515\) | −2168.52 | − | 14832.8i | −0.185546 | − | 1.26915i | ||||
\(516\) | −1841.30 | −0.157091 | ||||||||
\(517\) | − | 36333.2i | − | 3.09078i | ||||||
\(518\) | 2678.12i | 0.227162i | ||||||||
\(519\) | 9918.36 | 0.838858 | ||||||||
\(520\) | 11619.9 | − | 1698.80i | 0.979933 | − | 0.143264i | ||||
\(521\) | −342.674 | −0.0288154 | −0.0144077 | − | 0.999896i | \(-0.504586\pi\) | ||||
−0.0144077 | + | 0.999896i | \(0.504586\pi\) | |||||||
\(522\) | 4249.31i | 0.356297i | ||||||||
\(523\) | 10494.7i | 0.877441i | 0.898624 | + | 0.438720i | \(0.144568\pi\) | ||||
−0.898624 | + | 0.438720i | \(0.855432\pi\) | |||||||
\(524\) | 5607.31 | 0.467474 | ||||||||
\(525\) | 2515.14 | − | 751.477i | 0.209085 | − | 0.0624708i | ||||
\(526\) | 10792.6 | 0.894642 | ||||||||
\(527\) | − | 2878.66i | − | 0.237944i | ||||||
\(528\) | − | 15772.9i | − | 1.30005i | ||||||
\(529\) | 11515.6 | 0.946463 | ||||||||
\(530\) | 12737.2 | − | 1862.16i | 1.04391 | − | 0.152617i | ||||
\(531\) | −6351.73 | −0.519099 | ||||||||
\(532\) | − | 388.381i | − | 0.0316512i | ||||||
\(533\) | 19436.7i | 1.57954i | ||||||||
\(534\) | 7035.97 | 0.570180 | ||||||||
\(535\) | −2648.97 | − | 18119.1i | −0.214065 | − | 1.46422i | ||||
\(536\) | 11043.7 | 0.889953 | ||||||||
\(537\) | 8518.80i | 0.684568i | ||||||||
\(538\) | 27984.8i | 2.24258i | ||||||||
\(539\) | 3367.30 | 0.269090 | ||||||||
\(540\) | 93.0669 | + | 636.581i | 0.00741659 | + | 0.0507298i | ||||
\(541\) | −4026.52 | −0.319988 | −0.159994 | − | 0.987118i | \(-0.551148\pi\) | ||||
−0.159994 | + | 0.987118i | \(0.551148\pi\) | |||||||
\(542\) | 5070.93i | 0.401873i | ||||||||
\(543\) | − | 2224.57i | − | 0.175811i | ||||||
\(544\) | −3572.97 | −0.281599 | ||||||||
\(545\) | −6490.43 | + | 948.887i | −0.510127 | + | 0.0745795i | ||||
\(546\) | −3758.46 | −0.294592 | ||||||||
\(547\) | − | 16182.8i | − | 1.26495i | −0.774581 | − | 0.632475i | \(-0.782039\pi\) | ||
0.774581 | − | 0.632475i | \(-0.217961\pi\) | |||||||
\(548\) | − | 3385.51i | − | 0.263909i | ||||||
\(549\) | 3538.54 | 0.275084 | ||||||||
\(550\) | −7827.31 | − | 26197.4i | −0.606832 | − | 2.03102i | ||||
\(551\) | −3861.69 | −0.298573 | ||||||||
\(552\) | 1430.27i | 0.110283i | ||||||||
\(553\) | − | 2069.55i | − | 0.159144i | ||||||
\(554\) | −664.491 | −0.0509594 | ||||||||
\(555\) | 3989.19 | − | 583.211i | 0.305102 | − | 0.0446053i | ||||
\(556\) | 3694.44 | 0.281797 | ||||||||
\(557\) | − | 10934.3i | − | 0.831779i | −0.909415 | − | 0.415890i | \(-0.863470\pi\) | ||
0.909415 | − | 0.415890i | \(-0.136530\pi\) | |||||||
\(558\) | − | 2171.36i | − | 0.164733i | ||||||
\(559\) | −16193.3 | −1.22523 | ||||||||
\(560\) | 866.177 | + | 5924.69i | 0.0653619 | + | 0.447078i | ||||
\(561\) | 7829.59 | 0.589243 | ||||||||
\(562\) | 7782.52i | 0.584139i | ||||||||
\(563\) | − | 164.542i | − | 0.0123173i | −0.999981 | − | 0.00615863i | \(-0.998040\pi\) | ||
0.999981 | − | 0.00615863i | \(-0.00196037\pi\) | |||||||
\(564\) | −3380.39 | −0.252376 | ||||||||
\(565\) | 2615.54 | + | 17890.4i | 0.194755 | + | 1.33213i | ||||
\(566\) | −12396.1 | −0.920579 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | − | 12493.8i | − | 0.922935i | ||||||
\(569\) | −21924.4 | −1.61532 | −0.807660 | − | 0.589648i | \(-0.799266\pi\) | ||||
−0.807660 | + | 0.589648i | \(0.799266\pi\) | |||||||
\(570\) | −2750.09 | + | 402.057i | −0.202085 | + | 0.0295444i | ||||
\(571\) | −6765.55 | −0.495848 | −0.247924 | − | 0.968779i | \(-0.579748\pi\) | ||||
−0.247924 | + | 0.968779i | \(0.579748\pi\) | |||||||
\(572\) | 8235.18i | 0.601976i | ||||||||
\(573\) | − | 13286.3i | − | 0.968661i | ||||||
\(574\) | −7701.77 | −0.560044 | ||||||||
\(575\) | 913.302 | + | 3056.75i | 0.0662388 | + | 0.221696i | ||||
\(576\) | 2813.48 | 0.203521 | ||||||||
\(577\) | − | 26134.4i | − | 1.88560i | −0.333365 | − | 0.942798i | \(-0.608184\pi\) | ||
0.333365 | − | 0.942798i | \(-0.391816\pi\) | |||||||
\(578\) | 11047.0i | 0.794973i | ||||||||
\(579\) | 2445.10 | 0.175501 | ||||||||
\(580\) | −3497.32 | + | 511.301i | −0.250376 | + | 0.0366045i | ||||
\(581\) | 6415.58 | 0.458112 | ||||||||
\(582\) | 1365.14i | 0.0972285i | ||||||||
\(583\) | − | 24858.1i | − | 1.76589i | ||||||
\(584\) | 4702.80 | 0.333225 | ||||||||
\(585\) | 818.477 | + | 5598.42i | 0.0578459 | + | 0.395668i | ||||
\(586\) | 18289.9 | 1.28933 | ||||||||
\(587\) | 6342.06i | 0.445937i | 0.974826 | + | 0.222968i | \(0.0715747\pi\) | ||||
−0.974826 | + | 0.222968i | \(0.928425\pi\) | |||||||
\(588\) | − | 313.289i | − | 0.0219725i | ||||||
\(589\) | 1973.29 | 0.138044 | ||||||||
\(590\) | −3633.16 | − | 24851.0i | −0.253516 | − | 1.73406i | ||||
\(591\) | 4828.84 | 0.336095 | ||||||||
\(592\) | 9196.14i | 0.638444i | ||||||||
\(593\) | 24801.2i | 1.71748i | 0.512413 | + | 0.858739i | \(0.328752\pi\) | ||||
−0.512413 | + | 0.858739i | \(0.671248\pi\) | |||||||
\(594\) | 5905.82 | 0.407944 | ||||||||
\(595\) | −2940.99 | + | 429.966i | −0.202636 | + | 0.0296250i | ||||
\(596\) | −2921.22 | −0.200768 | ||||||||
\(597\) | − | 820.865i | − | 0.0562743i | ||||||
\(598\) | − | 4567.82i | − | 0.312361i | ||||||
\(599\) | −12339.2 | −0.841681 | −0.420841 | − | 0.907135i | \(-0.638265\pi\) | ||||
−0.420841 | + | 0.907135i | \(0.638265\pi\) | |||||||
\(600\) | 6711.85 | − | 2005.38i | 0.456684 | − | 0.136449i | ||||
\(601\) | 3221.02 | 0.218616 | 0.109308 | − | 0.994008i | \(-0.465137\pi\) | ||||
0.109308 | + | 0.994008i | \(0.465137\pi\) | |||||||
\(602\) | − | 6416.60i | − | 0.434421i | ||||||
\(603\) | 5320.81i | 0.359337i | ||||||||
\(604\) | 7872.87 | 0.530369 | ||||||||
\(605\) | −37519.1 | + | 5485.22i | −2.52127 | + | 0.368605i | ||||
\(606\) | −5405.30 | −0.362336 | ||||||||
\(607\) | 20076.6i | 1.34248i | 0.741241 | + | 0.671239i | \(0.234238\pi\) | ||||
−0.741241 | + | 0.671239i | \(0.765762\pi\) | |||||||
\(608\) | − | 2449.23i | − | 0.163370i | ||||||
\(609\) | −3115.05 | −0.207271 | ||||||||
\(610\) | 2024.03 | + | 13844.4i | 0.134345 | + | 0.918926i | ||||
\(611\) | −29728.9 | −1.96842 | ||||||||
\(612\) | − | 728.454i | − | 0.0481144i | ||||||
\(613\) | − | 7428.07i | − | 0.489424i | −0.969596 | − | 0.244712i | \(-0.921307\pi\) | ||
0.969596 | − | 0.244712i | \(-0.0786934\pi\) | |||||||
\(614\) | 6300.81 | 0.414137 | ||||||||
\(615\) | 1677.21 | + | 11472.2i | 0.109970 | + | 0.752199i | ||||
\(616\) | 8985.92 | 0.587748 | ||||||||
\(617\) | 2200.68i | 0.143592i | 0.997419 | + | 0.0717959i | \(0.0228730\pi\) | ||||
−0.997419 | + | 0.0717959i | \(0.977127\pi\) | |||||||
\(618\) | 12803.0i | 0.833353i | ||||||||
\(619\) | 5674.34 | 0.368451 | 0.184225 | − | 0.982884i | \(-0.441022\pi\) | ||||
0.184225 | + | 0.982884i | \(0.441022\pi\) | |||||||
\(620\) | 1787.10 | − | 261.270i | 0.115761 | − | 0.0169240i | ||||
\(621\) | −689.099 | −0.0445291 | ||||||||
\(622\) | 11126.2i | 0.717237i | ||||||||
\(623\) | 5157.86i | 0.331694i | ||||||||
\(624\) | −12905.8 | −0.827960 | ||||||||
\(625\) | 13063.9 | − | 8571.73i | 0.836091 | − | 0.548591i | ||||
\(626\) | 4611.08 | 0.294403 | ||||||||
\(627\) | 5367.09i | 0.341851i | ||||||||
\(628\) | − | 2247.50i | − | 0.142810i | ||||||
\(629\) | −4564.92 | −0.289372 | ||||||||
\(630\) | −2218.37 | + | 324.321i | −0.140289 | + | 0.0205099i | ||||
\(631\) | −4650.60 | −0.293403 | −0.146701 | − | 0.989181i | \(-0.546866\pi\) | ||||
−0.146701 | + | 0.989181i | \(0.546866\pi\) | |||||||
\(632\) | − | 5522.78i | − | 0.347602i | ||||||
\(633\) | 15473.1i | 0.971564i | ||||||||
\(634\) | −30089.6 | −1.88487 | ||||||||
\(635\) | −3304.14 | − | 22600.5i | −0.206489 | − | 1.41240i | ||||
\(636\) | −2312.76 | −0.144193 | ||||||||
\(637\) | − | 2755.22i | − | 0.171375i | ||||||
\(638\) | 32446.0i | 2.01340i | ||||||||
\(639\) | 6019.46 | 0.372654 | ||||||||
\(640\) | 2826.58 | + | 19333.9i | 0.174578 | + | 1.19412i | ||||
\(641\) | 15808.8 | 0.974119 | 0.487060 | − | 0.873369i | \(-0.338069\pi\) | ||||
0.487060 | + | 0.873369i | \(0.338069\pi\) | |||||||
\(642\) | 15639.6i | 0.961442i | ||||||||
\(643\) | 18829.6i | 1.15485i | 0.816444 | + | 0.577424i | \(0.195942\pi\) | ||||
−0.816444 | + | 0.577424i | \(0.804058\pi\) | |||||||
\(644\) | 380.753 | 0.0232978 | ||||||||
\(645\) | −9557.85 | + | 1397.34i | −0.583473 | + | 0.0853025i | ||||
\(646\) | 3146.99 | 0.191667 | ||||||||
\(647\) | − | 21519.7i | − | 1.30761i | −0.756661 | − | 0.653807i | \(-0.773171\pi\) | ||
0.756661 | − | 0.653807i | \(-0.226829\pi\) | |||||||
\(648\) | 1513.09i | 0.0917279i | ||||||||
\(649\) | −48499.2 | −2.93338 | ||||||||
\(650\) | −21435.5 | + | 6404.53i | −1.29349 | + | 0.386471i | ||||
\(651\) | 1591.76 | 0.0958311 | ||||||||
\(652\) | − | 2941.33i | − | 0.176674i | ||||||
\(653\) | 4298.98i | 0.257629i | 0.991669 | + | 0.128815i | \(0.0411172\pi\) | ||||
−0.991669 | + | 0.128815i | \(0.958883\pi\) | |||||||
\(654\) | 5602.25 | 0.334962 | ||||||||
\(655\) | 29106.5 | − | 4255.30i | 1.73631 | − | 0.253845i | ||||
\(656\) | −26446.4 | −1.57402 | ||||||||
\(657\) | 2265.79i | 0.134546i | ||||||||
\(658\) | − | 11780.1i | − | 0.697925i | ||||||
\(659\) | 1199.37 | 0.0708964 | 0.0354482 | − | 0.999372i | \(-0.488714\pi\) | ||||
0.0354482 | + | 0.999372i | \(0.488714\pi\) | |||||||
\(660\) | 710.621 | + | 4860.68i | 0.0419104 | + | 0.286669i | ||||
\(661\) | 14967.5 | 0.880739 | 0.440369 | − | 0.897817i | \(-0.354847\pi\) | ||||
0.440369 | + | 0.897817i | \(0.354847\pi\) | |||||||
\(662\) | − | 2518.69i | − | 0.147873i | ||||||
\(663\) | − | 6406.39i | − | 0.375269i | ||||||
\(664\) | 17120.5 | 1.00061 | ||||||||
\(665\) | −294.736 | − | 2016.01i | −0.0171871 | − | 0.117560i | ||||
\(666\) | −3443.29 | −0.200338 | ||||||||
\(667\) | − | 3785.85i | − | 0.219773i | ||||||
\(668\) | 6698.63i | 0.387991i | ||||||||
\(669\) | 4333.13 | 0.250416 | ||||||||
\(670\) | −20817.5 | + | 3043.48i | −1.20037 | + | 0.175492i | ||||
\(671\) | 27018.9 | 1.55447 | ||||||||
\(672\) | − | 1975.68i | − | 0.113413i | ||||||
\(673\) | − | 23664.3i | − | 1.35541i | −0.735333 | − | 0.677706i | \(-0.762974\pi\) | ||
0.735333 | − | 0.677706i | \(-0.237026\pi\) | |||||||
\(674\) | 18967.4 | 1.08397 | ||||||||
\(675\) | 966.185 | + | 3233.75i | 0.0550940 | + | 0.184395i | ||||
\(676\) | 2055.98 | 0.116976 | ||||||||
\(677\) | 4413.97i | 0.250580i | 0.992120 | + | 0.125290i | \(0.0399861\pi\) | ||||
−0.992120 | + | 0.125290i | \(0.960014\pi\) | |||||||
\(678\) | − | 15442.2i | − | 0.874711i | ||||||
\(679\) | −1000.75 | −0.0565613 | ||||||||
\(680\) | −7848.27 | + | 1147.40i | −0.442599 | + | 0.0647070i | ||||
\(681\) | −4905.59 | −0.276039 | ||||||||
\(682\) | − | 16579.6i | − | 0.930890i | ||||||
\(683\) | − | 26357.7i | − | 1.47664i | −0.674449 | − | 0.738322i | \(-0.735619\pi\) | ||
0.674449 | − | 0.738322i | \(-0.264381\pi\) | |||||||
\(684\) | 499.347 | 0.0279137 | ||||||||
\(685\) | −2569.22 | − | 17573.6i | −0.143306 | − | 0.980221i | ||||
\(686\) | 1091.75 | 0.0607629 | ||||||||
\(687\) | − | 8422.01i | − | 0.467714i | ||||||
\(688\) | − | 22033.4i | − | 1.22095i | ||||||
\(689\) | −20339.6 | −1.12464 | ||||||||
\(690\) | −394.161 | − | 2696.08i | −0.0217470 | − | 0.148751i | ||||
\(691\) | 19098.2 | 1.05142 | 0.525708 | − | 0.850665i | \(-0.323800\pi\) | ||||
0.525708 | + | 0.850665i | \(0.323800\pi\) | |||||||
\(692\) | − | 7046.05i | − | 0.387068i | ||||||
\(693\) | 4329.38i | 0.237315i | ||||||||
\(694\) | −14515.4 | −0.793942 | ||||||||
\(695\) | 19177.1 | − | 2803.66i | 1.04666 | − | 0.153020i | ||||
\(696\) | −8312.76 | −0.452722 | ||||||||
\(697\) | − | 13127.9i | − | 0.713419i | ||||||
\(698\) | 29935.4i | 1.62331i | ||||||||
\(699\) | 1739.41 | 0.0941211 | ||||||||
\(700\) | −533.853 | − | 1786.77i | −0.0288254 | − | 0.0964763i | ||||
\(701\) | −7008.54 | −0.377616 | −0.188808 | − | 0.982014i | \(-0.560462\pi\) | ||||
−0.188808 | + | 0.982014i | \(0.560462\pi\) | |||||||
\(702\) | − | 4832.31i | − | 0.259806i | ||||||
\(703\) | − | 3129.20i | − | 0.167880i | ||||||
\(704\) | 21482.6 | 1.15008 | ||||||||
\(705\) | −17547.0 | + | 2565.33i | −0.937386 | + | 0.137044i | ||||
\(706\) | −4428.67 | −0.236084 | ||||||||
\(707\) | − | 3962.47i | − | 0.210784i | ||||||
\(708\) | 4512.30i | 0.239524i | ||||||||
\(709\) | −31728.6 | −1.68066 | −0.840332 | − | 0.542071i | \(-0.817640\pi\) | ||||
−0.840332 | + | 0.542071i | \(0.817640\pi\) | |||||||
\(710\) | 3443.10 | + | 23550.9i | 0.181996 | + | 1.24486i | ||||
\(711\) | 2660.86 | 0.140351 | ||||||||
\(712\) | 13764.2i | 0.724487i | ||||||||
\(713\) | 1934.54i | 0.101611i | ||||||||
\(714\) | 2538.53 | 0.133056 | ||||||||
\(715\) | 6249.56 | + | 42747.2i | 0.326881 | + | 2.23588i | ||||
\(716\) | 6051.80 | 0.315875 | ||||||||
\(717\) | − | 5086.54i | − | 0.264938i | ||||||
\(718\) | − | 13708.4i | − | 0.712522i | ||||||
\(719\) | 8033.78 | 0.416703 | 0.208352 | − | 0.978054i | \(-0.433190\pi\) | ||||
0.208352 | + | 0.978054i | \(0.433190\pi\) | |||||||
\(720\) | −7617.46 | + | 1113.66i | −0.394286 | + | 0.0576438i | ||||
\(721\) | −9385.50 | −0.484791 | ||||||||
\(722\) | − | 19674.7i | − | 1.01415i | ||||||
\(723\) | 3547.17i | 0.182463i | ||||||||
\(724\) | −1580.34 | −0.0811229 | ||||||||
\(725\) | −17765.9 | + | 5308.13i | −0.910081 | + | 0.271916i | ||||
\(726\) | 32384.9 | 1.65553 | ||||||||
\(727\) | − | 20514.4i | − | 1.04654i | −0.852166 | − | 0.523272i | \(-0.824711\pi\) | ||
0.852166 | − | 0.523272i | \(-0.175289\pi\) | |||||||
\(728\) | − | 7352.53i | − | 0.374317i | ||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | −8864.84 | + | 1296.02i | −0.449455 | + | 0.0657094i | ||||
\(731\) | 10937.3 | 0.553391 | ||||||||
\(732\) | − | 2513.80i | − | 0.126930i | ||||||
\(733\) | − | 39200.4i | − | 1.97531i | −0.156653 | − | 0.987654i | \(-0.550070\pi\) | ||
0.156653 | − | 0.987654i | \(-0.449930\pi\) | |||||||
\(734\) | 20388.3 | 1.02527 | ||||||||
\(735\) | −237.750 | − | 1626.22i | −0.0119314 | − | 0.0816111i | ||||
\(736\) | 2401.12 | 0.120254 | ||||||||
\(737\) | 40627.6i | 2.03058i | ||||||||
\(738\) | − | 9902.27i | − | 0.493913i | ||||||
\(739\) | 18386.2 | 0.915221 | 0.457611 | − | 0.889153i | \(-0.348705\pi\) | ||||
0.457611 | + | 0.889153i | \(0.348705\pi\) | |||||||
\(740\) | −414.316 | − | 2833.94i | −0.0205818 | − | 0.140781i | ||||
\(741\) | 4391.51 | 0.217714 | ||||||||
\(742\) | − | 8059.55i | − | 0.398754i | ||||||
\(743\) | 10118.8i | 0.499628i | 0.968294 | + | 0.249814i | \(0.0803695\pi\) | ||||
−0.968294 | + | 0.249814i | \(0.919631\pi\) | |||||||
\(744\) | 4247.75 | 0.209315 | ||||||||
\(745\) | −15163.5 | + | 2216.87i | −0.745702 | + | 0.109020i | ||||
\(746\) | 32762.8 | 1.60795 | ||||||||
\(747\) | 8248.60i | 0.404017i | ||||||||
\(748\) | − | 5562.18i | − | 0.271890i | ||||||
\(749\) | −11464.9 | −0.559305 | ||||||||
\(750\) | −12099.3 | + | 5629.85i | −0.589071 | + | 0.274098i | ||||
\(751\) | −16116.3 | −0.783077 | −0.391538 | − | 0.920162i | \(-0.628057\pi\) | ||||
−0.391538 | + | 0.920162i | \(0.628057\pi\) | |||||||
\(752\) | − | 40450.4i | − | 1.96154i | ||||||
\(753\) | − | 7235.03i | − | 0.350145i | ||||||
\(754\) | 26548.3 | 1.28227 | ||||||||
\(755\) | 40866.6 | − | 5974.61i | 1.96992 | − | 0.287998i | ||||
\(756\) | 402.800 | 0.0193779 | ||||||||
\(757\) | 16856.5i | 0.809324i | 0.914466 | + | 0.404662i | \(0.132611\pi\) | ||||
−0.914466 | + | 0.404662i | \(0.867389\pi\) | |||||||
\(758\) | − | 12198.2i | − | 0.584510i | ||||||
\(759\) | −5261.68 | −0.251630 | ||||||||
\(760\) | −786.529 | − | 5379.89i | −0.0375400 | − | 0.256775i | ||||
\(761\) | 19917.5 | 0.948765 | 0.474383 | − | 0.880319i | \(-0.342671\pi\) | ||||
0.474383 | + | 0.880319i | \(0.342671\pi\) | |||||||
\(762\) | 19507.7i | 0.927415i | ||||||||
\(763\) | 4106.85i | 0.194860i | ||||||||
\(764\) | −9438.65 | −0.446961 | ||||||||
\(765\) | −552.813 | − | 3781.27i | −0.0261268 | − | 0.178708i | ||||
\(766\) | 43017.2 | 2.02908 | ||||||||
\(767\) | 39683.5i | 1.86817i | ||||||||
\(768\) | − | 9185.56i | − | 0.431583i | ||||||
\(769\) | −2378.22 | −0.111523 | −0.0557613 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557613 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(770\) | −16938.6 | + | 2476.38i | −0.792758 | + | 0.115900i | ||||
\(771\) | −3164.22 | −0.147803 | ||||||||
\(772\) | − | 1737.01i | − | 0.0809799i | ||||||
\(773\) | − | 7153.02i | − | 0.332828i | −0.986056 | − | 0.166414i | \(-0.946781\pi\) | ||
0.986056 | − | 0.166414i | \(-0.0532188\pi\) | |||||||
\(774\) | 8249.92 | 0.383123 | ||||||||
\(775\) | 9078.23 | − | 2712.41i | 0.420774 | − | 0.125720i | ||||
\(776\) | −2670.58 | −0.123541 | ||||||||
\(777\) | − | 2524.18i | − | 0.116544i | ||||||
\(778\) | 20512.4i | 0.945250i | ||||||||
\(779\) | 8998.99 | 0.413892 | ||||||||
\(780\) | 3977.15 | − | 581.450i | 0.182570 | − | 0.0266914i | ||||
\(781\) | 45962.1 | 2.10583 | ||||||||
\(782\) | 3085.18i | 0.141082i | ||||||||
\(783\) | − | 4005.06i | − | 0.182796i | ||||||
\(784\) | 3748.87 | 0.170776 | ||||||||
\(785\) | −1705.59 | − | 11666.3i | −0.0775481 | − | 0.530432i | ||||
\(786\) | −25123.4 | −1.14011 | ||||||||
\(787\) | 28137.0i | 1.27443i | 0.770687 | + | 0.637214i | \(0.219913\pi\) | ||||
−0.770687 | + | 0.637214i | \(0.780087\pi\) | |||||||
\(788\) | − | 3430.44i | − | 0.155082i | ||||||
\(789\) | −10172.3 | −0.458989 | ||||||||
\(790\) | 1522.00 | + | 10410.5i | 0.0685445 | + | 0.468848i | ||||
\(791\) | 11320.2 | 0.508851 | ||||||||
\(792\) | 11553.3i | 0.518345i | ||||||||
\(793\) | − | 22107.6i | − | 0.989993i | ||||||
\(794\) | 8947.81 | 0.399932 | ||||||||
\(795\) | −12005.1 | + | 1755.12i | −0.535569 | + | 0.0782990i | ||||
\(796\) | −583.147 | −0.0259662 | ||||||||
\(797\) | 40807.1i | 1.81363i | 0.421530 | + | 0.906815i | \(0.361493\pi\) | ||||
−0.421530 | + | 0.906815i | \(0.638507\pi\) | |||||||
\(798\) | 1740.13i | 0.0771930i | ||||||||
\(799\) | 20079.4 | 0.889059 | ||||||||
\(800\) | −3366.61 | − | 11267.8i | −0.148785 | − | 0.497971i | ||||
\(801\) | −6631.54 | −0.292527 | ||||||||
\(802\) | 31571.7i | 1.39007i | ||||||||
\(803\) | 17300.7i | 0.760308i | ||||||||
\(804\) | 3779.93 | 0.165806 | ||||||||
\(805\) | 1976.42 | − | 288.948i | 0.0865336 | − | 0.0126510i | ||||
\(806\) | −13565.9 | −0.592853 | ||||||||
\(807\) | − | 26376.2i | − | 1.15054i | ||||||
\(808\) | − | 10574.2i | − | 0.460394i | ||||||
\(809\) | −15233.3 | −0.662020 | −0.331010 | − | 0.943627i | \(-0.607389\pi\) | ||||
−0.331010 | + | 0.943627i | \(0.607389\pi\) | |||||||
\(810\) | −416.984 | − | 2852.19i | −0.0180881 | − | 0.123723i | ||||
\(811\) | −26847.5 | −1.16245 | −0.581223 | − | 0.813744i | \(-0.697426\pi\) | ||||
−0.581223 | + | 0.813744i | \(0.697426\pi\) | |||||||
\(812\) | 2212.95i | 0.0956393i | ||||||||
\(813\) | − | 4779.46i | − | 0.206178i | ||||||
\(814\) | −26291.6 | −1.13209 | ||||||||
\(815\) | −2232.13 | − | 15267.9i | −0.0959365 | − | 0.656210i | ||||
\(816\) | 8716.82 | 0.373958 | ||||||||
\(817\) | 7497.36i | 0.321052i | ||||||||
\(818\) | 1788.99i | 0.0764676i | ||||||||
\(819\) | 3542.42 | 0.151138 | ||||||||
\(820\) | 8149.89 | − | 1191.50i | 0.347081 | − | 0.0507425i | ||||
\(821\) | 23640.8 | 1.00496 | 0.502479 | − | 0.864590i | \(-0.332422\pi\) | ||||
0.502479 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(822\) | 15168.7i | 0.643638i | ||||||||
\(823\) | 21191.6i | 0.897562i | 0.893642 | + | 0.448781i | \(0.148142\pi\) | ||||
−0.893642 | + | 0.448781i | \(0.851858\pi\) | |||||||
\(824\) | −25046.0 | −1.05888 | ||||||||
\(825\) | 7377.39 | + | 24691.6i | 0.311331 | + | 1.04200i | ||||
\(826\) | −15724.6 | −0.662382 | ||||||||
\(827\) | − | 8177.77i | − | 0.343856i | −0.985110 | − | 0.171928i | \(-0.945000\pi\) | ||
0.985110 | − | 0.171928i | \(-0.0549996\pi\) | |||||||
\(828\) | 489.540i | 0.0205467i | ||||||||
\(829\) | −28931.0 | −1.21208 | −0.606040 | − | 0.795434i | \(-0.707243\pi\) | ||||
−0.606040 | + | 0.795434i | \(0.707243\pi\) | |||||||
\(830\) | −32272.4 | + | 4718.16i | −1.34963 | + | 0.197313i | ||||
\(831\) | 626.296 | 0.0261443 | ||||||||
\(832\) | − | 17577.7i | − | 0.732448i | ||||||
\(833\) | 1860.92i | 0.0774035i | ||||||||
\(834\) | −16552.9 | −0.687264 | ||||||||
\(835\) | 5083.49 | + | 34771.3i | 0.210684 | + | 1.44109i | ||||
\(836\) | 3812.81 | 0.157738 | ||||||||
\(837\) | 2046.55i | 0.0845151i | ||||||||
\(838\) | − | 1127.60i | − | 0.0464823i | ||||||
\(839\) | 41631.2 | 1.71307 | 0.856537 | − | 0.516085i | \(-0.172611\pi\) | ||||
0.856537 | + | 0.516085i | \(0.172611\pi\) | |||||||
\(840\) | −634.457 | − | 4339.71i | −0.0260605 | − | 0.178255i | ||||
\(841\) | −2385.58 | −0.0978137 | ||||||||
\(842\) | − | 9450.83i | − | 0.386814i | ||||||
\(843\) | − | 7335.18i | − | 0.299688i | ||||||
\(844\) | 10992.2 | 0.448301 | ||||||||
\(845\) | 10672.2 | − | 1560.25i | 0.434478 | − | 0.0635198i | ||||
\(846\) | 15145.8 | 0.615512 | ||||||||
\(847\) | 23740.4i | 0.963081i | ||||||||
\(848\) | − | 27674.9i | − | 1.12071i | ||||||
\(849\) | 11683.6 | 0.472297 | ||||||||
\(850\) | 14477.9 | − | 4325.73i | 0.584220 | − | 0.174554i | ||||
\(851\) | 3067.74 | 0.123573 | ||||||||
\(852\) | − | 4276.26i | − | 0.171951i | ||||||
\(853\) | 38242.1i | 1.53503i | 0.641029 | + | 0.767517i | \(0.278508\pi\) | ||||
−0.641029 | + | 0.767517i | \(0.721492\pi\) | |||||||
\(854\) | 8760.13 | 0.351014 | ||||||||
\(855\) | 2592.01 | − | 378.947i | 0.103678 | − | 0.0151576i | ||||
\(856\) | −30595.1 | −1.22164 | ||||||||
\(857\) | 1118.45i | 0.0445805i | 0.999752 | + | 0.0222903i | \(0.00709579\pi\) | ||||
−0.999752 | + | 0.0222903i | \(0.992904\pi\) | |||||||
\(858\) | − | 36897.5i | − | 1.46814i | ||||||
\(859\) | −34103.0 | −1.35458 | −0.677288 | − | 0.735718i | \(-0.736845\pi\) | ||||
−0.677288 | + | 0.735718i | \(0.736845\pi\) | |||||||
\(860\) | 992.676 | + | 6789.95i | 0.0393604 | + | 0.269227i | ||||
\(861\) | 7259.07 | 0.287327 | ||||||||
\(862\) | − | 14587.7i | − | 0.576405i | ||||||
\(863\) | 12332.6i | 0.486450i | 0.969970 | + | 0.243225i | \(0.0782054\pi\) | ||||
−0.969970 | + | 0.243225i | \(0.921795\pi\) | |||||||
\(864\) | 2540.16 | 0.100021 | ||||||||
\(865\) | −5347.15 | − | 36574.7i | −0.210183 | − | 1.43766i | ||||
\(866\) | 788.764 | 0.0309507 | ||||||||
\(867\) | − | 10412.0i | − | 0.407855i | ||||||
\(868\) | − | 1130.80i | − | 0.0442186i | ||||||
\(869\) | 20317.2 | 0.793112 | ||||||||
\(870\) | 15669.7 | − | 2290.87i | 0.610634 | − | 0.0892734i | ||||
\(871\) | 33242.6 | 1.29321 | ||||||||
\(872\) | 10959.5i | 0.425613i | ||||||||
\(873\) | − | 1286.67i | − | 0.0498824i | ||||||
\(874\) | −2114.86 | −0.0818491 | ||||||||
\(875\) | −4127.08 | − | 8869.63i | −0.159452 | − | 0.342684i | ||||
\(876\) | 1609.63 | 0.0620826 | ||||||||
\(877\) | 17287.9i | 0.665644i | 0.942990 | + | 0.332822i | \(0.108001\pi\) | ||||
−0.942990 | + | 0.332822i | \(0.891999\pi\) | |||||||
\(878\) | 12073.6i | 0.464081i | ||||||||
\(879\) | −17238.6 | −0.661484 | ||||||||
\(880\) | −58163.8 | + | 8503.43i | −2.22807 | + | 0.325739i | ||||
\(881\) | −15797.0 | −0.604103 | −0.302052 | − | 0.953292i | \(-0.597671\pi\) | ||||
−0.302052 | + | 0.953292i | \(0.597671\pi\) | |||||||
\(882\) | 1403.68i | 0.0535879i | ||||||||
\(883\) | − | 40601.9i | − | 1.54741i | −0.633545 | − | 0.773706i | \(-0.718401\pi\) | ||
0.633545 | − | 0.773706i | \(-0.281599\pi\) | |||||||
\(884\) | −4551.13 | −0.173157 | ||||||||
\(885\) | 3424.32 | + | 23422.5i | 0.130065 | + | 0.889649i | ||||
\(886\) | −41880.3 | −1.58803 | ||||||||
\(887\) | − | 3654.03i | − | 0.138320i | −0.997606 | − | 0.0691602i | \(-0.977968\pi\) | ||
0.997606 | − | 0.0691602i | \(-0.0220320\pi\) | |||||||
\(888\) | − | 6735.98i | − | 0.254555i | ||||||
\(889\) | −14300.6 | −0.539511 | ||||||||
\(890\) | −3793.21 | − | 25945.7i | −0.142864 | − | 0.977193i | ||||
\(891\) | −5566.35 | −0.209293 | ||||||||
\(892\) | − | 3078.28i | − | 0.115547i | ||||||
\(893\) | 13764.2i | 0.515791i | ||||||||
\(894\) | 13088.5 | 0.489647 | ||||||||
\(895\) | 31413.7 | − | 4592.62i | 1.17324 | − | 0.171524i | ||||
\(896\) | 12233.6 | 0.456135 | ||||||||
\(897\) | 4305.26i | 0.160255i | ||||||||
\(898\) | 27710.0i | 1.02973i | ||||||||
\(899\) | −11243.6 | −0.417123 | ||||||||
\(900\) | 2297.27 | − | 686.383i | 0.0850841 | − | 0.0254216i | ||||
\(901\) | 13737.7 | 0.507957 | ||||||||
\(902\) | − | 75609.7i | − | 2.79105i | ||||||
\(903\) | 6047.78i | 0.222876i | ||||||||
\(904\) | 30209.0 | 1.11143 | ||||||||
\(905\) | −8203.26 | + | 1199.30i | −0.301310 | + | 0.0440509i | ||||
\(906\) | −35274.3 | −1.29350 | ||||||||
\(907\) | − | 8732.15i | − | 0.319676i | −0.987143 | − | 0.159838i | \(-0.948903\pi\) | ||
0.987143 | − | 0.159838i | \(-0.0510972\pi\) | |||||||
\(908\) | 3484.96i | 0.127370i | ||||||||
\(909\) | 5094.60 | 0.185894 | ||||||||
\(910\) | 2026.25 | + | 13859.6i | 0.0738126 | + | 0.504881i | ||||
\(911\) | −29118.5 | −1.05899 | −0.529495 | − | 0.848313i | \(-0.677619\pi\) | ||||
−0.529495 | + | 0.848313i | \(0.677619\pi\) | |||||||
\(912\) | 5975.28i | 0.216953i | ||||||||
\(913\) | 62983.0i | 2.28306i | ||||||||
\(914\) | −35774.6 | −1.29466 | ||||||||
\(915\) | −1907.69 | − | 13048.7i | −0.0689248 | − | 0.471448i | ||||
\(916\) | −5983.04 | −0.215814 | ||||||||
\(917\) | − | 18417.3i | − | 0.663240i | ||||||
\(918\) | 3263.82i | 0.117344i | ||||||||
\(919\) | 36147.4 | 1.29749 | 0.648745 | − | 0.761006i | \(-0.275294\pi\) | ||||
0.648745 | + | 0.761006i | \(0.275294\pi\) | |||||||
\(920\) | 5274.23 | − | 771.082i | 0.189007 | − | 0.0276324i | ||||
\(921\) | −5938.64 | −0.212470 | ||||||||
\(922\) | − | 39896.1i | − | 1.42506i | ||||||
\(923\) | − | 37607.5i | − | 1.34113i | ||||||
\(924\) | 3075.62 | 0.109503 | ||||||||
\(925\) | −4301.27 | − | 14396.0i | −0.152892 | − | 0.511717i | ||||
\(926\) | −39990.0 | −1.41917 | ||||||||
\(927\) | − | 12067.1i | − | 0.427546i | ||||||
\(928\) | 13955.4i | 0.493651i | ||||||||
\(929\) | 380.568 | 0.0134403 | 0.00672015 | − | 0.999977i | \(-0.497861\pi\) | ||||
0.00672015 | + | 0.999977i | \(0.497861\pi\) | |||||||
\(930\) | −8007.07 | + | 1170.62i | −0.282325 | + | 0.0412753i | ||||
\(931\) | −1275.64 | −0.0449059 | ||||||||
\(932\) | − | 1235.69i | − | 0.0434295i | ||||||
\(933\) | − | 10486.7i | − | 0.367973i | ||||||
\(934\) | −15335.4 | −0.537247 | ||||||||
\(935\) | −4221.06 | − | 28872.2i | −0.147640 | − | 1.00986i | ||||
\(936\) | 9453.26 | 0.330117 | ||||||||
\(937\) | 11577.5i | 0.403650i | 0.979422 | + | 0.201825i | \(0.0646872\pi\) | ||||
−0.979422 | + | 0.201825i | \(0.935313\pi\) | |||||||
\(938\) | 13172.4i | 0.458522i | ||||||||
\(939\) | −4346.04 | −0.151041 | ||||||||
\(940\) | 1822.43 | + | 12465.5i | 0.0632351 | + | 0.432531i | ||||
\(941\) | 37835.3 | 1.31073 | 0.655364 | − | 0.755313i | \(-0.272515\pi\) | ||||
0.655364 | + | 0.755313i | \(0.272515\pi\) | |||||||
\(942\) | 10069.9i | 0.348295i | ||||||||
\(943\) | 8822.25i | 0.304657i | ||||||||
\(944\) | −53995.1 | −1.86164 | ||||||||
\(945\) | 2090.86 | − | 305.679i | 0.0719742 | − | 0.0105225i | ||||
\(946\) | 62993.0 | 2.16499 | ||||||||
\(947\) | − | 32719.8i | − | 1.12276i | −0.827559 | − | 0.561379i | \(-0.810271\pi\) | ||
0.827559 | − | 0.561379i | \(-0.189729\pi\) | |||||||
\(948\) | − | 1890.29i | − | 0.0647612i | ||||||
\(949\) | 14155.9 | 0.484215 | ||||||||
\(950\) | 2965.24 | + | 9924.42i | 0.101268 | + | 0.338937i | ||||
\(951\) | 28360.0 | 0.967021 | ||||||||
\(952\) | 4966.03i | 0.169065i | ||||||||
\(953\) | − | 42719.5i | − | 1.45207i | −0.687659 | − | 0.726033i | \(-0.741362\pi\) | ||
0.687659 | − | 0.726033i | \(-0.258638\pi\) | |||||||
\(954\) | 10362.3 | 0.351668 | ||||||||
\(955\) | −48994.3 | + | 7162.86i | −1.66012 | + | 0.242706i | ||||
\(956\) | −3613.51 | −0.122248 | ||||||||
\(957\) | − | 30581.0i | − | 1.03296i | ||||||
\(958\) | 22563.4i | 0.760949i | ||||||||
\(959\) | −11119.8 | −0.374427 | ||||||||
\(960\) | −1516.79 | − | 10374.9i | −0.0509941 | − | 0.348802i | ||||
\(961\) | −24045.6 | −0.807144 | ||||||||
\(962\) | 21512.5i | 0.720989i | ||||||||
\(963\) | − | 14740.6i | − | 0.493261i | ||||||
\(964\) | 2519.93 | 0.0841924 | ||||||||
\(965\) | −1318.19 | − | 9016.50i | −0.0439732 | − | 0.300779i | ||||
\(966\) | −1705.96 | −0.0568201 | ||||||||
\(967\) | 56616.7i | 1.88280i | 0.337286 | + | 0.941402i | \(0.390491\pi\) | ||||
−0.337286 | + | 0.941402i | \(0.609509\pi\) | |||||||
\(968\) | 63353.3i | 2.10357i | ||||||||
\(969\) | −2966.10 | −0.0983331 | ||||||||
\(970\) | 5034.07 | − | 735.971i | 0.166633 | − | 0.0243615i | ||||
\(971\) | −26230.8 | −0.866927 | −0.433463 | − | 0.901171i | \(-0.642709\pi\) | ||||
−0.433463 | + | 0.901171i | \(0.642709\pi\) | |||||||
\(972\) | 517.886i | 0.0170897i | ||||||||
\(973\) | − | 12134.4i | − | 0.399806i | ||||||
\(974\) | −51346.0 | −1.68915 | ||||||||
\(975\) | 20203.4 | − | 6036.40i | 0.663615 | − | 0.198276i | ||||
\(976\) | 30080.6 | 0.986534 | ||||||||
\(977\) | 35339.9i | 1.15724i | 0.815597 | + | 0.578620i | \(0.196409\pi\) | ||||
−0.815597 | + | 0.578620i | \(0.803591\pi\) | |||||||
\(978\) | 13178.6i | 0.430884i | ||||||||
\(979\) | −50635.8 | −1.65304 | ||||||||
\(980\) | −1155.28 | + | 168.899i | −0.0376571 | + | 0.00550539i | ||||
\(981\) | −5280.23 | −0.171850 | ||||||||
\(982\) | − | 12608.3i | − | 0.409723i | ||||||
\(983\) | − | 25377.6i | − | 0.823419i | −0.911315 | − | 0.411710i | \(-0.864932\pi\) | ||
0.911315 | − | 0.411710i | \(-0.135068\pi\) | |||||||
\(984\) | 19371.4 | 0.627580 | ||||||||
\(985\) | −2603.31 | − | 17806.7i | −0.0842115 | − | 0.576010i | ||||
\(986\) | −17931.1 | −0.579152 | ||||||||
\(987\) | 11102.9i | 0.358065i | ||||||||
\(988\) | − | 3119.75i | − | 0.100458i | ||||||
\(989\) | −7350.12 | −0.236320 | ||||||||
\(990\) | −3183.92 | − | 21778.2i | −0.102214 | − | 0.699147i | ||||
\(991\) | −15086.3 | −0.483585 | −0.241792 | − | 0.970328i | \(-0.577735\pi\) | ||||
−0.241792 | + | 0.970328i | \(0.577735\pi\) | |||||||
\(992\) | − | 7131.08i | − | 0.228238i | ||||||
\(993\) | 2373.91i | 0.0758649i | ||||||||
\(994\) | 14902.0 | 0.475515 | ||||||||
\(995\) | −3027.00 | + | 442.542i | −0.0964447 | + | 0.0141000i | ||||
\(996\) | 5859.85 | 0.186422 | ||||||||
\(997\) | 1393.06i | 0.0442513i | 0.999755 | + | 0.0221256i | \(0.00704338\pi\) | ||||
−0.999755 | + | 0.0221256i | \(0.992957\pi\) | |||||||
\(998\) | 41318.0i | 1.31052i | ||||||||
\(999\) | 3245.37 | 0.102782 |
(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 | 105.4.d.a.64.5 | yes | 6 | |
3.2 | odd | 2 | 315.4.d.a.64.2 | 6 | |||
5.2 | odd | 4 | 525.4.a.r.1.1 | 3 | |||
5.3 | odd | 4 | 525.4.a.q.1.3 | 3 | |||
5.4 | even | 2 | inner | 105.4.d.a.64.2 | ✓ | 6 | |
15.2 | even | 4 | 1575.4.a.bc.1.3 | 3 | |||
15.8 | even | 4 | 1575.4.a.bd.1.1 | 3 | |||
15.14 | odd | 2 | 315.4.d.a.64.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.a.64.2 | ✓ | 6 | 5.4 | even | 2 | inner | |
105.4.d.a.64.5 | yes | 6 | 1.1 | even | 1 | trivial | |
315.4.d.a.64.2 | 6 | 3.2 | odd | 2 | |||
315.4.d.a.64.5 | 6 | 15.14 | odd | 2 | |||
525.4.a.q.1.3 | 3 | 5.3 | odd | 4 | |||
525.4.a.r.1.1 | 3 | 5.2 | odd | 4 | |||
1575.4.a.bc.1.3 | 3 | 15.2 | even | 4 | |||
1575.4.a.bd.1.1 | 3 | 15.8 | even | 4 |