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 | 64.2 | ||
Root | \(2.09148 - 2.09148i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.64 |
Dual form | 105.4.d.a.64.5 |
$q$-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 | \(-0.809773\pi\) | ||
0.826680 | − | 0.562673i | \(-0.190227\pi\) | |||||||
\(3\) | 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 | \(-0.795242\pi\) | ||
0.800141 | − | 0.599812i | \(-0.204758\pi\) | |||||||
\(14\) | −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 | \(0.0873253\pi\) | ||||
−0.962604 | + | 0.270912i | \(0.912675\pi\) | |||||||
\(18\) | 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 | \(-0.963092\pi\) | ||
0.993285 | − | 0.115690i | \(-0.0369079\pi\) | |||||||
\(24\) | 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 | \(0.0860439\pi\) | ||||
−0.963687 | + | 0.267035i | \(0.913956\pi\) | |||||||
\(38\) | − | 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 | \(-0.829396\pi\) | ||
0.859774 | − | 0.510674i | \(-0.170604\pi\) | |||||||
\(44\) | 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 | \(-0.693734\pi\) | ||
0.571747 | − | 0.820430i | \(-0.306266\pi\) | |||||||
\(48\) | − | 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 | \(-0.844706\pi\) | ||
0.883333 | − | 0.468747i | \(-0.155294\pi\) | |||||||
\(54\) | −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 | \(0.181200\pi\) | ||||
−0.842302 | + | 0.539006i | \(0.818800\pi\) | |||||||
\(68\) | − | 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 | \(0.0646854\pi\) | ||||
−0.979423 | + | 0.201819i | \(0.935315\pi\) | |||||||
\(74\) | 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 | \(0.207237\pi\) | ||||
−0.795445 | + | 0.606025i | \(0.792763\pi\) | |||||||
\(84\) | −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 | \(-0.976161\pi\) | ||
0.997197 | − | 0.0748236i | \(-0.0238394\pi\) | |||||||
\(98\) | 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 | \(-0.778388\pi\) | ||
0.767275 | − | 0.641318i | \(-0.221612\pi\) | |||||||
\(104\) | −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 | \(-0.734877\pi\) | ||
0.672727 | − | 0.739891i | \(-0.265123\pi\) | |||||||
\(108\) | 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 | \(0.235058\pi\) | ||||
−0.739509 | + | 0.673146i | \(0.764942\pi\) | |||||||
\(114\) | 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 | \(-0.747015\pi\) | ||
0.700446 | − | 0.713706i | \(-0.252985\pi\) | |||||||
\(128\) | 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 | \(-0.835051\pi\) | ||
0.868710 | − | 0.495320i | \(-0.164949\pi\) | |||||||
\(138\) | − | 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 | \(-0.913626\pi\) | ||
0.963409 | − | 0.268036i | \(-0.0863745\pi\) | |||||||
\(158\) | 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 | \(-0.892414\pi\) | ||
0.943423 | − | 0.331593i | \(-0.107586\pi\) | |||||||
\(164\) | −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 | \(0.259645\pi\) | ||||
−0.685359 | + | 0.728205i | \(0.740355\pi\) | |||||||
\(168\) | − | 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 | \(-0.741158\pi\) | ||
0.687195 | − | 0.726473i | \(-0.258842\pi\) | |||||||
\(174\) | −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 | \(-0.951432\pi\) | ||
0.988382 | − | 0.151988i | \(-0.0485675\pi\) | |||||||
\(194\) | −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 | \(-0.905990\pi\) | ||
0.956703 | − | 0.291067i | \(-0.0940102\pi\) | |||||||
\(198\) | − | 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 | \(-0.930416\pi\) | ||
0.976201 | − | 0.216867i | \(-0.0695837\pi\) | |||||||
\(224\) | 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 | \(0.0768383\pi\) | ||||
−0.971006 | + | 0.239057i | \(0.923162\pi\) | |||||||
\(228\) | − | 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 | \(-0.974025\pi\) | ||
0.996672 | − | 0.0815113i | \(-0.0259747\pi\) | |||||||
\(234\) | 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 | \(0.0408562\pi\) | ||||
−0.991774 | + | 0.128002i | \(0.959144\pi\) | |||||||
\(258\) | − | 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 | \(0.130121\pi\) | ||||
−0.917604 | + | 0.397496i | \(0.869879\pi\) | |||||||
\(264\) | −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 | \(-0.992792\pi\) | ||
0.999744 | − | 0.0226417i | \(-0.00720768\pi\) | |||||||
\(278\) | 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 | \(-0.865870\pi\) | ||
0.912525 | − | 0.409021i | \(-0.134130\pi\) | |||||||
\(284\) | 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 | \(0.194167\pi\) | ||||
−0.819652 | + | 0.572862i | \(0.805833\pi\) | |||||||
\(294\) | −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 | \(0.0589060\pi\) | ||||
−0.982925 | + | 0.184004i | \(0.941094\pi\) | |||||||
\(308\) | − | 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 | \(0.0417563\pi\) | ||||
−0.991408 | + | 0.130805i | \(0.958244\pi\) | |||||||
\(314\) | −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 | \(-0.684037\pi\) | ||
0.546492 | − | 0.837465i | \(-0.315963\pi\) | |||||||
\(318\) | − | 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 | \(0.159951\pi\) | ||||
−0.876381 | + | 0.481618i | \(0.840049\pi\) | |||||||
\(338\) | 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 | \(-0.885245\pi\) | ||
0.935716 | − | 0.352755i | \(-0.114755\pi\) | |||||||
\(348\) | 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 | \(-0.966550\pi\) | ||
0.994483 | − | 0.104894i | \(-0.0334503\pi\) | |||||||
\(354\) | 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 | \(0.150552\pi\) | ||||
−0.890218 | + | 0.455534i | \(0.849448\pi\) | |||||||
\(368\) | 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 | \(0.253312\pi\) | ||||
−0.699712 | + | 0.714425i | \(0.746688\pi\) | |||||||
\(374\) | −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 | \(0.357559\pi\) | ||||
−0.432705 | + | 0.901536i | \(0.642441\pi\) | |||||||
\(384\) | −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 | \(0.0568634\pi\) | ||||
−0.984086 | + | 0.177693i | \(0.943137\pi\) | |||||||
\(398\) | − | 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 | \(0.00437742\pi\) | ||||
−0.999905 | + | 0.0137516i | \(0.995623\pi\) | |||||||
\(434\) | −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 | \(-0.750689\pi\) | ||
0.708635 | − | 0.705575i | \(-0.249311\pi\) | |||||||
\(444\) | 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 | \(-0.804914\pi\) | ||
0.817994 | − | 0.575227i | \(-0.195086\pi\) | |||||||
\(458\) | − | 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 | \(-0.782830\pi\) | ||
0.776150 | − | 0.630549i | \(-0.217170\pi\) | |||||||
\(464\) | 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 | \(-0.923278\pi\) | ||
0.971093 | − | 0.238703i | \(-0.0767223\pi\) | |||||||
\(468\) | − | 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 | \(-0.729811\pi\) | ||
0.660867 | − | 0.750503i | \(-0.270189\pi\) | |||||||
\(488\) | 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 | \(-0.859927\pi\) | ||
0.904729 | − | 0.425988i | \(-0.140073\pi\) | |||||||
\(504\) | 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 | \(-0.855432\pi\) | ||
0.898624 | − | 0.438720i | \(-0.144568\pi\) | |||||||
\(524\) | 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 | \(0.217961\pi\) | ||||
−0.774581 | + | 0.632475i | \(0.782039\pi\) | |||||||
\(548\) | 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 | \(0.136530\pi\) | ||||
−0.909415 | + | 0.415890i | \(0.863470\pi\) | |||||||
\(558\) | 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 | \(0.00196037\pi\) | ||||
−0.999981 | + | 0.00615863i | \(0.998040\pi\) | |||||||
\(564\) | −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 | \(0.391816\pi\) | ||||
−0.333365 | + | 0.942798i | \(0.608184\pi\) | |||||||
\(578\) | − | 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 | \(-0.928425\pi\) | ||
0.974826 | − | 0.222968i | \(-0.0715747\pi\) | |||||||
\(588\) | 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 | \(-0.671248\pi\) | ||
0.512413 | − | 0.858739i | \(-0.328752\pi\) | |||||||
\(594\) | 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 | \(-0.765762\pi\) | ||
0.741241 | − | 0.671239i | \(-0.234238\pi\) | |||||||
\(608\) | 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 | \(0.0786934\pi\) | ||||
−0.969596 | + | 0.244712i | \(0.921307\pi\) | |||||||
\(614\) | 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 | \(-0.977127\pi\) | ||
0.997419 | − | 0.0717959i | \(-0.0228730\pi\) | |||||||
\(618\) | − | 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 | \(-0.804058\pi\) | ||
0.816444 | − | 0.577424i | \(-0.195942\pi\) | |||||||
\(644\) | 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 | \(0.226829\pi\) | ||||
−0.756661 | + | 0.653807i | \(0.773171\pi\) | |||||||
\(648\) | − | 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 | \(-0.958883\pi\) | ||
0.991669 | − | 0.128815i | \(-0.0411172\pi\) | |||||||
\(654\) | 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 | \(0.237026\pi\) | ||||
−0.735333 | + | 0.677706i | \(0.762974\pi\) | |||||||
\(674\) | 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 | \(-0.960014\pi\) | ||
0.992120 | − | 0.125290i | \(-0.0399861\pi\) | |||||||
\(678\) | 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 | \(0.264381\pi\) | ||||
−0.674449 | + | 0.738322i | \(0.735619\pi\) | |||||||
\(684\) | 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 | \(0.175289\pi\) | ||||
−0.852166 | + | 0.523272i | \(0.824711\pi\) | |||||||
\(728\) | 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 | \(0.449930\pi\) | ||||
−0.156653 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(734\) | 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 | \(-0.919631\pi\) | ||
0.968294 | − | 0.249814i | \(-0.0803695\pi\) | |||||||
\(744\) | 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 | \(-0.867389\pi\) | ||
0.914466 | − | 0.404662i | \(-0.132611\pi\) | |||||||
\(758\) | 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 | \(0.0532188\pi\) | ||||
−0.986056 | + | 0.166414i | \(0.946781\pi\) | |||||||
\(774\) | 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 | \(-0.780087\pi\) | ||
0.770687 | − | 0.637214i | \(-0.219913\pi\) | |||||||
\(788\) | 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 | \(-0.638507\pi\) | ||
0.421530 | − | 0.906815i | \(-0.361493\pi\) | |||||||
\(798\) | − | 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 | \(-0.851858\pi\) | ||
0.893642 | − | 0.448781i | \(-0.148142\pi\) | |||||||
\(824\) | −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 | \(0.0549996\pi\) | ||||
−0.985110 | + | 0.171928i | \(0.945000\pi\) | |||||||
\(828\) | − | 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 | \(-0.721492\pi\) | ||
0.641029 | − | 0.767517i | \(-0.278508\pi\) | |||||||
\(854\) | 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 | \(-0.992904\pi\) | ||
0.999752 | − | 0.0222903i | \(-0.00709579\pi\) | |||||||
\(858\) | 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 | \(-0.921795\pi\) | ||
0.969970 | − | 0.243225i | \(-0.0782054\pi\) | |||||||
\(864\) | 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 | \(-0.891999\pi\) | ||
0.942990 | − | 0.332822i | \(-0.108001\pi\) | |||||||
\(878\) | − | 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 | \(0.281599\pi\) | ||||
−0.633545 | + | 0.773706i | \(0.718401\pi\) | |||||||
\(884\) | −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 | \(0.0220320\pi\) | ||||
−0.997606 | + | 0.0691602i | \(0.977968\pi\) | |||||||
\(888\) | 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 | \(0.0510972\pi\) | ||||
−0.987143 | + | 0.159838i | \(0.948903\pi\) | |||||||
\(908\) | − | 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 | \(-0.935313\pi\) | ||
0.979422 | − | 0.201825i | \(-0.0646872\pi\) | |||||||
\(938\) | − | 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 | \(0.189729\pi\) | ||||
−0.827559 | + | 0.561379i | \(0.810271\pi\) | |||||||
\(948\) | 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 | \(0.258638\pi\) | ||||
−0.687659 | + | 0.726033i | \(0.741362\pi\) | |||||||
\(954\) | 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 | \(-0.609509\pi\) | ||
0.337286 | − | 0.941402i | \(-0.390491\pi\) | |||||||
\(968\) | − | 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 | \(-0.803591\pi\) | ||
0.815597 | − | 0.578620i | \(-0.196409\pi\) | |||||||
\(978\) | − | 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 | \(0.135068\pi\) | ||||
−0.911315 | + | 0.411710i | \(0.864932\pi\) | |||||||
\(984\) | 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 | \(-0.992957\pi\) | ||
0.999755 | − | 0.0221256i | \(-0.00704338\pi\) | |||||||
\(998\) | − | 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.64.2 | ✓ | 6 | |
3.2 | odd | 2 | 315.4.d.a.64.5 | 6 | |||
5.2 | odd | 4 | 525.4.a.q.1.3 | 3 | |||
5.3 | odd | 4 | 525.4.a.r.1.1 | 3 | |||
5.4 | even | 2 | inner | 105.4.d.a.64.5 | yes | 6 | |
15.2 | even | 4 | 1575.4.a.bd.1.1 | 3 | |||
15.8 | even | 4 | 1575.4.a.bc.1.3 | 3 | |||
15.14 | odd | 2 | 315.4.d.a.64.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.a.64.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
105.4.d.a.64.5 | yes | 6 | 5.4 | even | 2 | inner | |
315.4.d.a.64.2 | 6 | 15.14 | odd | 2 | |||
315.4.d.a.64.5 | 6 | 3.2 | odd | 2 | |||
525.4.a.q.1.3 | 3 | 5.2 | odd | 4 | |||
525.4.a.r.1.1 | 3 | 5.3 | odd | 4 | |||
1575.4.a.bc.1.3 | 3 | 15.8 | even | 4 | |||
1575.4.a.bd.1.1 | 3 | 15.2 | even | 4 |