Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,4,Mod(559,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.559");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(54.8717763053\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + \cdots + 34\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.19 | ||
Root | \(22.4343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.559 |
Dual form | 930.4.d.c.559.9 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 10.6574 | − | 3.37922i | 0.953230 | − | 0.302247i | ||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 22.4343i | 1.21134i | 0.795716 | + | 0.605670i | \(0.207095\pi\) | ||||
−0.795716 | + | 0.605670i | \(0.792905\pi\) | |||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 6.75844 | + | 21.3149i | 0.213721 | + | 0.674035i | ||||
\(11\) | −57.5594 | −1.57771 | −0.788855 | − | 0.614580i | \(-0.789326\pi\) | ||||
−0.788855 | + | 0.614580i | \(0.789326\pi\) | |||||||
\(12\) | 12.0000i | 0.288675i | ||||||||
\(13\) | − | 41.6653i | − | 0.888914i | −0.895800 | − | 0.444457i | \(-0.853397\pi\) | ||
0.895800 | − | 0.444457i | \(-0.146603\pi\) | |||||||
\(14\) | −44.8686 | −0.856546 | ||||||||
\(15\) | −10.1377 | − | 31.9723i | −0.174502 | − | 0.550347i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 41.4957i | − | 0.592011i | −0.955186 | − | 0.296005i | \(-0.904345\pi\) | ||
0.955186 | − | 0.296005i | \(-0.0956546\pi\) | |||||||
\(18\) | − | 18.0000i | − | 0.235702i | ||||||
\(19\) | 55.8008 | 0.673768 | 0.336884 | − | 0.941546i | \(-0.390627\pi\) | ||||
0.336884 | + | 0.941546i | \(0.390627\pi\) | |||||||
\(20\) | −42.6297 | + | 13.5169i | −0.476615 | + | 0.151123i | ||||
\(21\) | 67.3030 | 0.699367 | ||||||||
\(22\) | − | 115.119i | − | 1.11561i | ||||||
\(23\) | 115.808i | 1.04990i | 0.851134 | + | 0.524948i | \(0.175915\pi\) | ||||
−0.851134 | + | 0.524948i | \(0.824085\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 102.162 | − | 72.0276i | 0.817294 | − | 0.576221i | ||||
\(26\) | 83.3306 | 0.628557 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − | 89.7373i | − | 0.605670i | ||||||
\(29\) | 220.538 | 1.41217 | 0.706083 | − | 0.708129i | \(-0.250460\pi\) | ||||
0.706083 | + | 0.708129i | \(0.250460\pi\) | |||||||
\(30\) | 63.9446 | − | 20.2753i | 0.389154 | − | 0.123392i | ||||
\(31\) | −31.0000 | −0.179605 | ||||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 172.678i | 0.910891i | ||||||||
\(34\) | 82.9914 | 0.418615 | ||||||||
\(35\) | 75.8105 | + | 239.092i | 0.366123 | + | 1.15468i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | − | 40.0489i | − | 0.177946i | −0.996034 | − | 0.0889729i | \(-0.971642\pi\) | ||
0.996034 | − | 0.0889729i | \(-0.0283584\pi\) | |||||||
\(38\) | 111.602i | 0.476426i | ||||||||
\(39\) | −124.996 | −0.513215 | ||||||||
\(40\) | −27.0338 | − | 85.2595i | −0.106860 | − | 0.337018i | ||||
\(41\) | 236.222 | 0.899797 | 0.449898 | − | 0.893080i | \(-0.351460\pi\) | ||||
0.449898 | + | 0.893080i | \(0.351460\pi\) | |||||||
\(42\) | 134.606i | 0.494527i | ||||||||
\(43\) | − | 52.3815i | − | 0.185770i | −0.995677 | − | 0.0928849i | \(-0.970391\pi\) | ||
0.995677 | − | 0.0928849i | \(-0.0296089\pi\) | |||||||
\(44\) | 230.238 | 0.788855 | ||||||||
\(45\) | −95.9169 | + | 30.4130i | −0.317743 | + | 0.100749i | ||||
\(46\) | −231.616 | −0.742388 | ||||||||
\(47\) | 3.59556i | 0.0111588i | 0.999984 | + | 0.00557942i | \(0.00177599\pi\) | ||||
−0.999984 | + | 0.00557942i | \(0.998224\pi\) | |||||||
\(48\) | − | 48.0000i | − | 0.144338i | ||||||
\(49\) | −160.299 | −0.467343 | ||||||||
\(50\) | 144.055 | + | 204.323i | 0.407450 | + | 0.577914i | ||||
\(51\) | −124.487 | −0.341798 | ||||||||
\(52\) | 166.661i | 0.444457i | ||||||||
\(53\) | − | 263.196i | − | 0.682127i | −0.940040 | − | 0.341063i | \(-0.889213\pi\) | ||
0.940040 | − | 0.341063i | \(-0.110787\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −613.435 | + | 194.506i | −1.50392 | + | 0.476858i | ||||
\(56\) | 179.475 | 0.428273 | ||||||||
\(57\) | − | 167.402i | − | 0.389000i | ||||||
\(58\) | 441.075i | 0.998552i | ||||||||
\(59\) | 212.525 | 0.468957 | 0.234478 | − | 0.972121i | \(-0.424662\pi\) | ||||
0.234478 | + | 0.972121i | \(0.424662\pi\) | |||||||
\(60\) | 40.5507 | + | 127.889i | 0.0872511 | + | 0.275174i | ||||
\(61\) | 678.688 | 1.42454 | 0.712271 | − | 0.701904i | \(-0.247667\pi\) | ||||
0.712271 | + | 0.701904i | \(0.247667\pi\) | |||||||
\(62\) | − | 62.0000i | − | 0.127000i | ||||||
\(63\) | − | 201.909i | − | 0.403780i | ||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −140.796 | − | 444.045i | −0.268671 | − | 0.847339i | ||||
\(66\) | −345.356 | −0.644097 | ||||||||
\(67\) | − | 736.794i | − | 1.34349i | −0.740783 | − | 0.671744i | \(-0.765545\pi\) | ||
0.740783 | − | 0.671744i | \(-0.234455\pi\) | |||||||
\(68\) | 165.983i | 0.296005i | ||||||||
\(69\) | 347.423 | 0.606158 | ||||||||
\(70\) | −478.184 | + | 151.621i | −0.816485 | + | 0.258888i | ||||
\(71\) | −379.090 | −0.633658 | −0.316829 | − | 0.948483i | \(-0.602618\pi\) | ||||
−0.316829 | + | 0.948483i | \(0.602618\pi\) | |||||||
\(72\) | 72.0000i | 0.117851i | ||||||||
\(73\) | 1076.93i | 1.72665i | 0.504652 | + | 0.863323i | \(0.331621\pi\) | ||||
−0.504652 | + | 0.863323i | \(0.668379\pi\) | |||||||
\(74\) | 80.0977 | 0.125827 | ||||||||
\(75\) | −216.083 | − | 306.485i | −0.332681 | − | 0.471865i | ||||
\(76\) | −223.203 | −0.336884 | ||||||||
\(77\) | − | 1291.31i | − | 1.91114i | ||||||
\(78\) | − | 249.992i | − | 0.362898i | ||||||
\(79\) | 288.554 | 0.410947 | 0.205473 | − | 0.978663i | \(-0.434127\pi\) | ||||
0.205473 | + | 0.978663i | \(0.434127\pi\) | |||||||
\(80\) | 170.519 | − | 54.0675i | 0.238307 | − | 0.0755617i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 472.444i | 0.636253i | ||||||||
\(83\) | 876.288i | 1.15886i | 0.815023 | + | 0.579428i | \(0.196724\pi\) | ||||
−0.815023 | + | 0.579428i | \(0.803276\pi\) | |||||||
\(84\) | −269.212 | −0.349684 | ||||||||
\(85\) | −140.223 | − | 442.238i | −0.178933 | − | 0.564322i | ||||
\(86\) | 104.763 | 0.131359 | ||||||||
\(87\) | − | 661.613i | − | 0.815315i | ||||||
\(88\) | 460.475i | 0.557805i | ||||||||
\(89\) | 1116.75 | 1.33006 | 0.665032 | − | 0.746814i | \(-0.268418\pi\) | ||||
0.665032 | + | 0.746814i | \(0.268418\pi\) | |||||||
\(90\) | −60.8260 | − | 191.834i | −0.0712402 | − | 0.224678i | ||||
\(91\) | 934.733 | 1.07678 | ||||||||
\(92\) | − | 463.231i | − | 0.524948i | ||||||
\(93\) | 93.0000i | 0.103695i | ||||||||
\(94\) | −7.19111 | −0.00789050 | ||||||||
\(95\) | 594.693 | − | 188.563i | 0.642255 | − | 0.203644i | ||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | − | 1308.93i | − | 1.37012i | −0.728488 | − | 0.685058i | \(-0.759777\pi\) | ||
0.728488 | − | 0.685058i | \(-0.240223\pi\) | |||||||
\(98\) | − | 320.597i | − | 0.330461i | ||||||
\(99\) | 518.034 | 0.525903 | ||||||||
\(100\) | −408.647 | + | 288.111i | −0.408647 | + | 0.288111i | ||||
\(101\) | 450.901 | 0.444221 | 0.222110 | − | 0.975022i | \(-0.428705\pi\) | ||||
0.222110 | + | 0.975022i | \(0.428705\pi\) | |||||||
\(102\) | − | 248.974i | − | 0.241687i | ||||||
\(103\) | 212.078i | 0.202880i | 0.994842 | + | 0.101440i | \(0.0323450\pi\) | ||||
−0.994842 | + | 0.101440i | \(0.967655\pi\) | |||||||
\(104\) | −333.323 | −0.314279 | ||||||||
\(105\) | 717.277 | − | 227.432i | 0.666657 | − | 0.211381i | ||||
\(106\) | 526.391 | 0.482336 | ||||||||
\(107\) | − | 1111.74i | − | 1.00445i | −0.864737 | − | 0.502224i | \(-0.832515\pi\) | ||
0.864737 | − | 0.502224i | \(-0.167485\pi\) | |||||||
\(108\) | − | 108.000i | − | 0.0962250i | ||||||
\(109\) | 1200.10 | 1.05458 | 0.527288 | − | 0.849687i | \(-0.323209\pi\) | ||||
0.527288 | + | 0.849687i | \(0.323209\pi\) | |||||||
\(110\) | −389.012 | − | 1226.87i | −0.337189 | − | 1.06343i | ||||
\(111\) | −120.147 | −0.102737 | ||||||||
\(112\) | 358.949i | 0.302835i | ||||||||
\(113\) | 771.438i | 0.642219i | 0.947042 | + | 0.321109i | \(0.104056\pi\) | ||||
−0.947042 | + | 0.321109i | \(0.895944\pi\) | |||||||
\(114\) | 334.805 | 0.275064 | ||||||||
\(115\) | 391.340 | + | 1234.21i | 0.317328 | + | 1.00079i | ||||
\(116\) | −882.151 | −0.706083 | ||||||||
\(117\) | 374.988i | 0.296305i | ||||||||
\(118\) | 425.051i | 0.331603i | ||||||||
\(119\) | 930.928 | 0.717126 | ||||||||
\(120\) | −255.778 | + | 81.1013i | −0.194577 | + | 0.0616959i | ||||
\(121\) | 1982.08 | 1.48917 | ||||||||
\(122\) | 1357.38i | 1.00730i | ||||||||
\(123\) | − | 708.666i | − | 0.519498i | ||||||
\(124\) | 124.000 | 0.0898027 | ||||||||
\(125\) | 845.384 | − | 1112.86i | 0.604908 | − | 0.796296i | ||||
\(126\) | 403.818 | 0.285515 | ||||||||
\(127\) | 2103.35i | 1.46962i | 0.678272 | + | 0.734811i | \(0.262729\pi\) | ||||
−0.678272 | + | 0.734811i | \(0.737271\pi\) | |||||||
\(128\) | − | 128.000i | − | 0.0883883i | ||||||
\(129\) | −157.144 | −0.107254 | ||||||||
\(130\) | 888.091 | − | 281.593i | 0.599159 | − | 0.189979i | ||||
\(131\) | 1698.77 | 1.13299 | 0.566497 | − | 0.824064i | \(-0.308298\pi\) | ||||
0.566497 | + | 0.824064i | \(0.308298\pi\) | |||||||
\(132\) | − | 690.713i | − | 0.455446i | ||||||
\(133\) | 1251.85i | 0.816161i | ||||||||
\(134\) | 1473.59 | 0.949990 | ||||||||
\(135\) | 91.2390 | + | 287.751i | 0.0581674 | + | 0.183449i | ||||
\(136\) | −331.966 | −0.209307 | ||||||||
\(137\) | 1289.18i | 0.803955i | 0.915650 | + | 0.401978i | \(0.131677\pi\) | ||||
−0.915650 | + | 0.401978i | \(0.868323\pi\) | |||||||
\(138\) | 694.847i | 0.428618i | ||||||||
\(139\) | −724.171 | −0.441895 | −0.220947 | − | 0.975286i | \(-0.570915\pi\) | ||||
−0.220947 | + | 0.975286i | \(0.570915\pi\) | |||||||
\(140\) | −303.242 | − | 956.369i | −0.183062 | − | 0.577342i | ||||
\(141\) | 10.7867 | 0.00644256 | ||||||||
\(142\) | − | 758.180i | − | 0.448064i | ||||||
\(143\) | 2398.23i | 1.40245i | ||||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | 2350.37 | − | 745.246i | 1.34612 | − | 0.426823i | ||||
\(146\) | −2153.86 | −1.22092 | ||||||||
\(147\) | 480.896i | 0.269821i | ||||||||
\(148\) | 160.195i | 0.0889729i | ||||||||
\(149\) | −5.97522 | −0.00328529 | −0.00164265 | − | 0.999999i | \(-0.500523\pi\) | ||||
−0.00164265 | + | 0.999999i | \(0.500523\pi\) | |||||||
\(150\) | 612.970 | − | 432.166i | 0.333659 | − | 0.235241i | ||||
\(151\) | 959.441 | 0.517074 | 0.258537 | − | 0.966001i | \(-0.416760\pi\) | ||||
0.258537 | + | 0.966001i | \(0.416760\pi\) | |||||||
\(152\) | − | 446.406i | − | 0.238213i | ||||||
\(153\) | 373.461i | 0.197337i | ||||||||
\(154\) | 2582.61 | 1.35138 | ||||||||
\(155\) | −330.380 | + | 104.756i | −0.171205 | + | 0.0542851i | ||||
\(156\) | 499.984 | 0.256607 | ||||||||
\(157\) | − | 2298.66i | − | 1.16849i | −0.811577 | − | 0.584246i | \(-0.801390\pi\) | ||
0.811577 | − | 0.584246i | \(-0.198610\pi\) | |||||||
\(158\) | 577.107i | 0.290583i | ||||||||
\(159\) | −789.587 | −0.393826 | ||||||||
\(160\) | 108.135 | + | 341.038i | 0.0534302 | + | 0.168509i | ||||
\(161\) | −2598.07 | −1.27178 | ||||||||
\(162\) | 162.000i | 0.0785674i | ||||||||
\(163\) | − | 4055.96i | − | 1.94900i | −0.224386 | − | 0.974500i | \(-0.572038\pi\) | ||
0.224386 | − | 0.974500i | \(-0.427962\pi\) | |||||||
\(164\) | −944.888 | −0.449898 | ||||||||
\(165\) | 583.518 | + | 1840.31i | 0.275314 | + | 0.868288i | ||||
\(166\) | −1752.58 | −0.819436 | ||||||||
\(167\) | − | 430.521i | − | 0.199489i | −0.995013 | − | 0.0997446i | \(-0.968197\pi\) | ||
0.995013 | − | 0.0997446i | \(-0.0318026\pi\) | |||||||
\(168\) | − | 538.424i | − | 0.247264i | ||||||
\(169\) | 461.001 | 0.209832 | ||||||||
\(170\) | 884.475 | − | 280.446i | 0.399036 | − | 0.126525i | ||||
\(171\) | −502.207 | −0.224589 | ||||||||
\(172\) | 209.526i | 0.0928849i | ||||||||
\(173\) | 2264.40i | 0.995141i | 0.867423 | + | 0.497571i | \(0.165774\pi\) | ||||
−0.867423 | + | 0.497571i | \(0.834226\pi\) | |||||||
\(174\) | 1323.23 | 0.576514 | ||||||||
\(175\) | 1615.89 | + | 2291.93i | 0.697999 | + | 0.990020i | ||||
\(176\) | −920.950 | −0.394427 | ||||||||
\(177\) | − | 637.576i | − | 0.270752i | ||||||
\(178\) | 2233.51i | 0.940498i | ||||||||
\(179\) | 480.399 | 0.200596 | 0.100298 | − | 0.994957i | \(-0.468020\pi\) | ||||
0.100298 | + | 0.994957i | \(0.468020\pi\) | |||||||
\(180\) | 383.668 | − | 121.652i | 0.158872 | − | 0.0503745i | ||||
\(181\) | 2389.42 | 0.981239 | 0.490619 | − | 0.871374i | \(-0.336771\pi\) | ||||
0.490619 | + | 0.871374i | \(0.336771\pi\) | |||||||
\(182\) | 1869.47i | 0.761396i | ||||||||
\(183\) | − | 2036.06i | − | 0.822460i | ||||||
\(184\) | 926.463 | 0.371194 | ||||||||
\(185\) | −135.334 | − | 426.818i | −0.0537835 | − | 0.169623i | ||||
\(186\) | −186.000 | −0.0733236 | ||||||||
\(187\) | 2388.47i | 0.934021i | ||||||||
\(188\) | − | 14.3822i | − | 0.00557942i | ||||||
\(189\) | −605.727 | −0.233122 | ||||||||
\(190\) | 377.127 | + | 1189.39i | 0.143998 | + | 0.454143i | ||||
\(191\) | −386.040 | −0.146246 | −0.0731228 | − | 0.997323i | \(-0.523296\pi\) | ||||
−0.0731228 | + | 0.997323i | \(0.523296\pi\) | |||||||
\(192\) | 192.000i | 0.0721688i | ||||||||
\(193\) | − | 2832.74i | − | 1.05650i | −0.849088 | − | 0.528251i | \(-0.822848\pi\) | ||
0.849088 | − | 0.528251i | \(-0.177152\pi\) | |||||||
\(194\) | 2617.85 | 0.968819 | ||||||||
\(195\) | −1332.14 | + | 422.389i | −0.489211 | + | 0.155117i | ||||
\(196\) | 641.194 | 0.233671 | ||||||||
\(197\) | − | 95.0624i | − | 0.0343803i | −0.999852 | − | 0.0171901i | \(-0.994528\pi\) | ||
0.999852 | − | 0.0171901i | \(-0.00547206\pi\) | |||||||
\(198\) | 1036.07i | 0.371870i | ||||||||
\(199\) | −424.470 | −0.151205 | −0.0756027 | − | 0.997138i | \(-0.524088\pi\) | ||||
−0.0756027 | + | 0.997138i | \(0.524088\pi\) | |||||||
\(200\) | −576.221 | − | 817.294i | −0.203725 | − | 0.288957i | ||||
\(201\) | −2210.38 | −0.775663 | ||||||||
\(202\) | 901.801i | 0.314111i | ||||||||
\(203\) | 4947.61i | 1.71061i | ||||||||
\(204\) | 497.948 | 0.170899 | ||||||||
\(205\) | 2517.52 | − | 798.246i | 0.857713 | − | 0.271961i | ||||
\(206\) | −424.156 | −0.143458 | ||||||||
\(207\) | − | 1042.27i | − | 0.349965i | ||||||
\(208\) | − | 666.645i | − | 0.222228i | ||||||
\(209\) | −3211.86 | −1.06301 | ||||||||
\(210\) | 454.863 | + | 1434.55i | 0.149469 | + | 0.471398i | ||||
\(211\) | −4889.26 | −1.59522 | −0.797608 | − | 0.603176i | \(-0.793902\pi\) | ||||
−0.797608 | + | 0.603176i | \(0.793902\pi\) | |||||||
\(212\) | 1052.78i | 0.341063i | ||||||||
\(213\) | 1137.27i | 0.365843i | ||||||||
\(214\) | 2223.48 | 0.710252 | ||||||||
\(215\) | −177.009 | − | 558.252i | −0.0561483 | − | 0.177081i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | − | 695.464i | − | 0.217563i | ||||||
\(218\) | 2400.20i | 0.745698i | ||||||||
\(219\) | 3230.79 | 0.996879 | ||||||||
\(220\) | 2453.74 | − | 778.023i | 0.751960 | − | 0.238429i | ||||
\(221\) | −1728.93 | −0.526247 | ||||||||
\(222\) | − | 240.293i | − | 0.0726461i | ||||||
\(223\) | 233.543i | 0.0701309i | 0.999385 | + | 0.0350655i | \(0.0111640\pi\) | ||||
−0.999385 | + | 0.0350655i | \(0.988836\pi\) | |||||||
\(224\) | −717.898 | −0.214137 | ||||||||
\(225\) | −919.456 | + | 648.249i | −0.272431 | + | 0.192074i | ||||
\(226\) | −1542.88 | −0.454117 | ||||||||
\(227\) | 1432.11i | 0.418734i | 0.977837 | + | 0.209367i | \(0.0671403\pi\) | ||||
−0.977837 | + | 0.209367i | \(0.932860\pi\) | |||||||
\(228\) | 669.610i | 0.194500i | ||||||||
\(229\) | 1142.48 | 0.329683 | 0.164842 | − | 0.986320i | \(-0.447289\pi\) | ||||
0.164842 | + | 0.986320i | \(0.447289\pi\) | |||||||
\(230\) | −2468.43 | + | 782.681i | −0.707667 | + | 0.224384i | ||||
\(231\) | −3873.92 | −1.10340 | ||||||||
\(232\) | − | 1764.30i | − | 0.499276i | ||||||
\(233\) | − | 1546.92i | − | 0.434943i | −0.976067 | − | 0.217472i | \(-0.930219\pi\) | ||
0.976067 | − | 0.217472i | \(-0.0697810\pi\) | |||||||
\(234\) | −749.976 | −0.209519 | ||||||||
\(235\) | 12.1502 | + | 38.3194i | 0.00337273 | + | 0.0106369i | ||||
\(236\) | −850.102 | −0.234478 | ||||||||
\(237\) | − | 865.661i | − | 0.237260i | ||||||
\(238\) | 1861.86i | 0.507085i | ||||||||
\(239\) | −822.195 | −0.222525 | −0.111262 | − | 0.993791i | \(-0.535489\pi\) | ||||
−0.111262 | + | 0.993791i | \(0.535489\pi\) | |||||||
\(240\) | −162.203 | − | 511.557i | −0.0436256 | − | 0.137587i | ||||
\(241\) | 3862.11 | 1.03228 | 0.516142 | − | 0.856503i | \(-0.327368\pi\) | ||||
0.516142 | + | 0.856503i | \(0.327368\pi\) | |||||||
\(242\) | 3964.16i | 1.05300i | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | −2714.75 | −0.712271 | ||||||||
\(245\) | −1708.37 | + | 541.685i | −0.445485 | + | 0.141253i | ||||
\(246\) | 1417.33 | 0.367341 | ||||||||
\(247\) | − | 2324.96i | − | 0.598921i | ||||||
\(248\) | 248.000i | 0.0635001i | ||||||||
\(249\) | 2628.86 | 0.669066 | ||||||||
\(250\) | 2225.71 | + | 1690.77i | 0.563066 | + | 0.427734i | ||||
\(251\) | 2133.84 | 0.536602 | 0.268301 | − | 0.963335i | \(-0.413538\pi\) | ||||
0.268301 | + | 0.963335i | \(0.413538\pi\) | |||||||
\(252\) | 807.635i | 0.201890i | ||||||||
\(253\) | − | 6665.83i | − | 1.65643i | ||||||
\(254\) | −4206.70 | −1.03918 | ||||||||
\(255\) | −1326.71 | + | 420.669i | −0.325812 | + | 0.103307i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 3083.52i | − | 0.748423i | −0.927343 | − | 0.374212i | \(-0.877913\pi\) | ||
0.927343 | − | 0.374212i | \(-0.122087\pi\) | |||||||
\(258\) | − | 314.289i | − | 0.0758402i | ||||||
\(259\) | 898.469 | 0.215553 | ||||||||
\(260\) | 563.185 | + | 1776.18i | 0.134336 | + | 0.423670i | ||||
\(261\) | −1984.84 | −0.470722 | ||||||||
\(262\) | 3397.54i | 0.801147i | ||||||||
\(263\) | 3582.39i | 0.839922i | 0.907542 | + | 0.419961i | \(0.137956\pi\) | ||||
−0.907542 | + | 0.419961i | \(0.862044\pi\) | |||||||
\(264\) | 1381.43 | 0.322049 | ||||||||
\(265\) | −889.397 | − | 2804.99i | −0.206171 | − | 0.650223i | ||||
\(266\) | −2503.71 | −0.577113 | ||||||||
\(267\) | − | 3350.26i | − | 0.767913i | ||||||
\(268\) | 2947.18i | 0.671744i | ||||||||
\(269\) | −2132.95 | −0.483450 | −0.241725 | − | 0.970345i | \(-0.577713\pi\) | ||||
−0.241725 | + | 0.970345i | \(0.577713\pi\) | |||||||
\(270\) | −575.501 | + | 182.478i | −0.129718 | + | 0.0411306i | ||||
\(271\) | 4909.37 | 1.10045 | 0.550227 | − | 0.835015i | \(-0.314541\pi\) | ||||
0.550227 | + | 0.835015i | \(0.314541\pi\) | |||||||
\(272\) | − | 663.931i | − | 0.148003i | ||||||
\(273\) | − | 2804.20i | − | 0.621677i | ||||||
\(274\) | −2578.35 | −0.568482 | ||||||||
\(275\) | −5880.37 | + | 4145.87i | −1.28945 | + | 0.909110i | ||||
\(276\) | −1389.69 | −0.303079 | ||||||||
\(277\) | 2781.01i | 0.603231i | 0.953430 | + | 0.301615i | \(0.0975258\pi\) | ||||
−0.953430 | + | 0.301615i | \(0.902474\pi\) | |||||||
\(278\) | − | 1448.34i | − | 0.312467i | ||||||
\(279\) | 279.000 | 0.0598684 | ||||||||
\(280\) | 1912.74 | − | 606.484i | 0.408243 | − | 0.129444i | ||||
\(281\) | −4183.11 | −0.888054 | −0.444027 | − | 0.896013i | \(-0.646451\pi\) | ||||
−0.444027 | + | 0.896013i | \(0.646451\pi\) | |||||||
\(282\) | 21.5733i | 0.00455558i | ||||||||
\(283\) | − | 5911.48i | − | 1.24170i | −0.783929 | − | 0.620850i | \(-0.786788\pi\) | ||
0.783929 | − | 0.620850i | \(-0.213212\pi\) | |||||||
\(284\) | 1516.36 | 0.316829 | ||||||||
\(285\) | −565.690 | − | 1784.08i | −0.117574 | − | 0.370806i | ||||
\(286\) | −4796.46 | −0.991680 | ||||||||
\(287\) | 5299.48i | 1.08996i | ||||||||
\(288\) | − | 288.000i | − | 0.0589256i | ||||||
\(289\) | 3191.11 | 0.649523 | ||||||||
\(290\) | 1490.49 | + | 4700.73i | 0.301809 | + | 0.951850i | ||||
\(291\) | −3926.78 | −0.791037 | ||||||||
\(292\) | − | 4307.72i | − | 0.863323i | ||||||
\(293\) | 9034.01i | 1.80127i | 0.434576 | + | 0.900635i | \(0.356898\pi\) | ||||
−0.434576 | + | 0.900635i | \(0.643102\pi\) | |||||||
\(294\) | −961.792 | −0.190792 | ||||||||
\(295\) | 2264.98 | − | 718.171i | 0.447024 | − | 0.141741i | ||||
\(296\) | −320.391 | −0.0629133 | ||||||||
\(297\) | − | 1554.10i | − | 0.303630i | ||||||
\(298\) | − | 11.9504i | − | 0.00232305i | ||||||
\(299\) | 4825.17 | 0.933267 | ||||||||
\(300\) | 864.332 | + | 1225.94i | 0.166341 | + | 0.235932i | ||||
\(301\) | 1175.14 | 0.225030 | ||||||||
\(302\) | 1918.88i | 0.365627i | ||||||||
\(303\) | − | 1352.70i | − | 0.256471i | ||||||
\(304\) | 892.813 | 0.168442 | ||||||||
\(305\) | 7233.07 | − | 2293.44i | 1.35792 | − | 0.430563i | ||||
\(306\) | −746.923 | −0.139538 | ||||||||
\(307\) | − | 6256.30i | − | 1.16308i | −0.813517 | − | 0.581541i | \(-0.802450\pi\) | ||
0.813517 | − | 0.581541i | \(-0.197550\pi\) | |||||||
\(308\) | 5165.22i | 0.955571i | ||||||||
\(309\) | 636.234 | 0.117133 | ||||||||
\(310\) | −209.512 | − | 660.761i | −0.0383854 | − | 0.121060i | ||||
\(311\) | 635.997 | 0.115962 | 0.0579809 | − | 0.998318i | \(-0.481534\pi\) | ||||
0.0579809 | + | 0.998318i | \(0.481534\pi\) | |||||||
\(312\) | 999.968i | 0.181449i | ||||||||
\(313\) | 3035.48i | 0.548164i | 0.961706 | + | 0.274082i | \(0.0883740\pi\) | ||||
−0.961706 | + | 0.274082i | \(0.911626\pi\) | |||||||
\(314\) | 4597.33 | 0.826249 | ||||||||
\(315\) | −682.295 | − | 2151.83i | −0.122041 | − | 0.384895i | ||||
\(316\) | −1154.21 | −0.205473 | ||||||||
\(317\) | − | 6984.39i | − | 1.23748i | −0.785594 | − | 0.618742i | \(-0.787643\pi\) | ||
0.785594 | − | 0.618742i | \(-0.212357\pi\) | |||||||
\(318\) | − | 1579.17i | − | 0.278477i | ||||||
\(319\) | −12694.0 | −2.22799 | ||||||||
\(320\) | −682.076 | + | 216.270i | −0.119154 | + | 0.0377808i | ||||
\(321\) | −3335.22 | −0.579919 | ||||||||
\(322\) | − | 5196.14i | − | 0.899284i | ||||||
\(323\) | − | 2315.49i | − | 0.398878i | ||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | −3001.05 | − | 4256.60i | −0.512211 | − | 0.726504i | ||||
\(326\) | 8111.91 | 1.37815 | ||||||||
\(327\) | − | 3600.30i | − | 0.608860i | ||||||
\(328\) | − | 1889.78i | − | 0.318126i | ||||||
\(329\) | −80.6639 | −0.0135171 | ||||||||
\(330\) | −3680.61 | + | 1167.04i | −0.613973 | + | 0.194676i | ||||
\(331\) | 6327.31 | 1.05070 | 0.525348 | − | 0.850887i | \(-0.323935\pi\) | ||||
0.525348 | + | 0.850887i | \(0.323935\pi\) | |||||||
\(332\) | − | 3505.15i | − | 0.579428i | ||||||
\(333\) | 360.440i | 0.0593153i | ||||||||
\(334\) | 861.041 | 0.141060 | ||||||||
\(335\) | −2489.79 | − | 7852.33i | −0.406065 | − | 1.28065i | ||||
\(336\) | 1076.85 | 0.174842 | ||||||||
\(337\) | 501.049i | 0.0809907i | 0.999180 | + | 0.0404954i | \(0.0128936\pi\) | ||||
−0.999180 | + | 0.0404954i | \(0.987106\pi\) | |||||||
\(338\) | 922.002i | 0.148374i | ||||||||
\(339\) | 2314.31 | 0.370785 | ||||||||
\(340\) | 560.893 | + | 1768.95i | 0.0894667 | + | 0.282161i | ||||
\(341\) | 1784.34 | 0.283365 | ||||||||
\(342\) | − | 1004.41i | − | 0.158809i | ||||||
\(343\) | 4098.78i | 0.645228i | ||||||||
\(344\) | −419.052 | −0.0656795 | ||||||||
\(345\) | 3702.64 | − | 1174.02i | 0.577807 | − | 0.183209i | ||||
\(346\) | −4528.81 | −0.703671 | ||||||||
\(347\) | − | 1157.28i | − | 0.179038i | −0.995985 | − | 0.0895191i | \(-0.971467\pi\) | ||
0.995985 | − | 0.0895191i | \(-0.0285330\pi\) | |||||||
\(348\) | 2646.45i | 0.407657i | ||||||||
\(349\) | −3980.30 | −0.610489 | −0.305245 | − | 0.952274i | \(-0.598738\pi\) | ||||
−0.305245 | + | 0.952274i | \(0.598738\pi\) | |||||||
\(350\) | −4583.86 | + | 3231.78i | −0.700050 | + | 0.493560i | ||||
\(351\) | 1124.96 | 0.171072 | ||||||||
\(352\) | − | 1841.90i | − | 0.278902i | ||||||
\(353\) | 4029.24i | 0.607521i | 0.952748 | + | 0.303761i | \(0.0982423\pi\) | ||||
−0.952748 | + | 0.303761i | \(0.901758\pi\) | |||||||
\(354\) | 1275.15 | 0.191451 | ||||||||
\(355\) | −4040.13 | + | 1281.03i | −0.604021 | + | 0.191521i | ||||
\(356\) | −4467.02 | −0.665032 | ||||||||
\(357\) | − | 2792.78i | − | 0.414033i | ||||||
\(358\) | 960.798i | 0.141843i | ||||||||
\(359\) | 2100.54 | 0.308809 | 0.154404 | − | 0.988008i | \(-0.450654\pi\) | ||||
0.154404 | + | 0.988008i | \(0.450654\pi\) | |||||||
\(360\) | 243.304 | + | 767.335i | 0.0356201 | + | 0.112339i | ||||
\(361\) | −3745.27 | −0.546037 | ||||||||
\(362\) | 4778.84i | 0.693840i | ||||||||
\(363\) | − | 5946.25i | − | 0.859771i | ||||||
\(364\) | −3738.93 | −0.538388 | ||||||||
\(365\) | 3639.19 | + | 11477.3i | 0.521873 | + | 1.64589i | ||||
\(366\) | 4072.13 | 0.581567 | ||||||||
\(367\) | 6519.16i | 0.927241i | 0.886034 | + | 0.463620i | \(0.153450\pi\) | ||||
−0.886034 | + | 0.463620i | \(0.846550\pi\) | |||||||
\(368\) | 1852.93i | 0.262474i | ||||||||
\(369\) | −2126.00 | −0.299932 | ||||||||
\(370\) | 853.636 | − | 270.668i | 0.119942 | − | 0.0380307i | ||||
\(371\) | 5904.62 | 0.826287 | ||||||||
\(372\) | − | 372.000i | − | 0.0518476i | ||||||
\(373\) | − | 157.218i | − | 0.0218242i | −0.999940 | − | 0.0109121i | \(-0.996527\pi\) | ||
0.999940 | − | 0.0109121i | \(-0.00347350\pi\) | |||||||
\(374\) | −4776.93 | −0.660453 | ||||||||
\(375\) | −3338.57 | − | 2536.15i | −0.459741 | − | 0.349244i | ||||
\(376\) | 28.7644 | 0.00394525 | ||||||||
\(377\) | − | 9188.77i | − | 1.25529i | ||||||
\(378\) | − | 1211.45i | − | 0.164842i | ||||||
\(379\) | 10091.4 | 1.36770 | 0.683851 | − | 0.729622i | \(-0.260304\pi\) | ||||
0.683851 | + | 0.729622i | \(0.260304\pi\) | |||||||
\(380\) | −2378.77 | + | 754.253i | −0.321128 | + | 0.101822i | ||||
\(381\) | 6310.04 | 0.848487 | ||||||||
\(382\) | − | 772.081i | − | 0.103411i | ||||||
\(383\) | − | 186.982i | − | 0.0249460i | −0.999922 | − | 0.0124730i | \(-0.996030\pi\) | ||
0.999922 | − | 0.0124730i | \(-0.00397039\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −4363.61 | − | 13762.0i | −0.577636 | − | 1.82176i | ||||
\(386\) | 5665.48 | 0.747060 | ||||||||
\(387\) | 471.433i | 0.0619233i | ||||||||
\(388\) | 5235.71i | 0.685058i | ||||||||
\(389\) | −8164.80 | −1.06419 | −0.532097 | − | 0.846683i | \(-0.678596\pi\) | ||||
−0.532097 | + | 0.846683i | \(0.678596\pi\) | |||||||
\(390\) | −844.778 | − | 2664.27i | −0.109685 | − | 0.345925i | ||||
\(391\) | 4805.53 | 0.621550 | ||||||||
\(392\) | 1282.39i | 0.165231i | ||||||||
\(393\) | − | 5096.31i | − | 0.654134i | ||||||
\(394\) | 190.125 | 0.0243105 | ||||||||
\(395\) | 3075.24 | − | 975.086i | 0.391727 | − | 0.124207i | ||||
\(396\) | −2072.14 | −0.262952 | ||||||||
\(397\) | 3031.44i | 0.383233i | 0.981470 | + | 0.191617i | \(0.0613730\pi\) | ||||
−0.981470 | + | 0.191617i | \(0.938627\pi\) | |||||||
\(398\) | − | 848.940i | − | 0.106918i | ||||||
\(399\) | 3755.56 | 0.471211 | ||||||||
\(400\) | 1634.59 | − | 1152.44i | 0.204323 | − | 0.144055i | ||||
\(401\) | −14669.2 | −1.82679 | −0.913395 | − | 0.407075i | \(-0.866549\pi\) | ||||
−0.913395 | + | 0.407075i | \(0.866549\pi\) | |||||||
\(402\) | − | 4420.76i | − | 0.548477i | ||||||
\(403\) | 1291.62i | 0.159654i | ||||||||
\(404\) | −1803.60 | −0.222110 | ||||||||
\(405\) | 863.252 | − | 273.717i | 0.105914 | − | 0.0335830i | ||||
\(406\) | −9895.23 | −1.20959 | ||||||||
\(407\) | 2305.19i | 0.280747i | ||||||||
\(408\) | 995.897i | 0.120844i | ||||||||
\(409\) | −10988.9 | −1.32852 | −0.664260 | − | 0.747502i | \(-0.731253\pi\) | ||||
−0.664260 | + | 0.747502i | \(0.731253\pi\) | |||||||
\(410\) | 1596.49 | + | 5035.04i | 0.192305 | + | 0.606495i | ||||
\(411\) | 3867.53 | 0.464164 | ||||||||
\(412\) | − | 848.312i | − | 0.101440i | ||||||
\(413\) | 4767.86i | 0.568066i | ||||||||
\(414\) | 2084.54 | 0.247463 | ||||||||
\(415\) | 2961.17 | + | 9338.98i | 0.350261 | + | 1.10466i | ||||
\(416\) | 1333.29 | 0.157139 | ||||||||
\(417\) | 2172.51i | 0.255128i | ||||||||
\(418\) | − | 6423.72i | − | 0.751661i | ||||||
\(419\) | 4258.01 | 0.496462 | 0.248231 | − | 0.968701i | \(-0.420151\pi\) | ||||
0.248231 | + | 0.968701i | \(0.420151\pi\) | |||||||
\(420\) | −2869.11 | + | 909.726i | −0.333329 | + | 0.105691i | ||||
\(421\) | 1538.19 | 0.178068 | 0.0890339 | − | 0.996029i | \(-0.471622\pi\) | ||||
0.0890339 | + | 0.996029i | \(0.471622\pi\) | |||||||
\(422\) | − | 9778.52i | − | 1.12799i | ||||||
\(423\) | − | 32.3600i | − | 0.00371962i | ||||||
\(424\) | −2105.57 | −0.241168 | ||||||||
\(425\) | −2988.84 | − | 4239.27i | −0.341129 | − | 0.483847i | ||||
\(426\) | −2274.54 | −0.258690 | ||||||||
\(427\) | 15225.9i | 1.72560i | ||||||||
\(428\) | 4446.96i | 0.502224i | ||||||||
\(429\) | 7194.69 | 0.809704 | ||||||||
\(430\) | 1116.50 | − | 354.017i | 0.125215 | − | 0.0397028i | ||||
\(431\) | −3432.85 | −0.383653 | −0.191826 | − | 0.981429i | \(-0.561441\pi\) | ||||
−0.191826 | + | 0.981429i | \(0.561441\pi\) | |||||||
\(432\) | 432.000i | 0.0481125i | ||||||||
\(433\) | − | 4646.46i | − | 0.515692i | −0.966186 | − | 0.257846i | \(-0.916987\pi\) | ||
0.966186 | − | 0.257846i | \(-0.0830128\pi\) | |||||||
\(434\) | 1390.93 | 0.153840 | ||||||||
\(435\) | −2235.74 | − | 7051.10i | −0.246426 | − | 0.777182i | ||||
\(436\) | −4800.40 | −0.527288 | ||||||||
\(437\) | 6462.17i | 0.707386i | ||||||||
\(438\) | 6461.58i | 0.704900i | ||||||||
\(439\) | 3080.19 | 0.334873 | 0.167437 | − | 0.985883i | \(-0.446451\pi\) | ||||
0.167437 | + | 0.985883i | \(0.446451\pi\) | |||||||
\(440\) | 1556.05 | + | 4907.48i | 0.168595 | + | 0.531716i | ||||
\(441\) | 1442.69 | 0.155781 | ||||||||
\(442\) | − | 3457.86i | − | 0.372113i | ||||||
\(443\) | − | 10840.0i | − | 1.16259i | −0.813695 | − | 0.581293i | \(-0.802547\pi\) | ||
0.813695 | − | 0.581293i | \(-0.197453\pi\) | |||||||
\(444\) | 480.586 | 0.0513685 | ||||||||
\(445\) | 11901.7 | − | 3773.76i | 1.26786 | − | 0.402008i | ||||
\(446\) | −467.086 | −0.0495901 | ||||||||
\(447\) | 17.9256i | 0.00189676i | ||||||||
\(448\) | − | 1435.80i | − | 0.151417i | ||||||
\(449\) | −9724.20 | −1.02208 | −0.511039 | − | 0.859557i | \(-0.670739\pi\) | ||||
−0.511039 | + | 0.859557i | \(0.670739\pi\) | |||||||
\(450\) | −1296.50 | − | 1838.91i | −0.135817 | − | 0.192638i | ||||
\(451\) | −13596.8 | −1.41962 | ||||||||
\(452\) | − | 3085.75i | − | 0.321109i | ||||||
\(453\) | − | 2878.32i | − | 0.298533i | ||||||
\(454\) | −2864.22 | −0.296090 | ||||||||
\(455\) | 9961.85 | − | 3158.67i | 1.02642 | − | 0.325452i | ||||
\(456\) | −1339.22 | −0.137532 | ||||||||
\(457\) | − | 15252.2i | − | 1.56120i | −0.625030 | − | 0.780601i | \(-0.714913\pi\) | ||
0.625030 | − | 0.780601i | \(-0.285087\pi\) | |||||||
\(458\) | 2284.97i | 0.233121i | ||||||||
\(459\) | 1120.38 | 0.113933 | ||||||||
\(460\) | −1565.36 | − | 4936.86i | −0.158664 | − | 0.500396i | ||||
\(461\) | −18790.6 | −1.89841 | −0.949203 | − | 0.314663i | \(-0.898108\pi\) | ||||
−0.949203 | + | 0.314663i | \(0.898108\pi\) | |||||||
\(462\) | − | 7747.83i | − | 0.780220i | ||||||
\(463\) | − | 6086.94i | − | 0.610980i | −0.952195 | − | 0.305490i | \(-0.901180\pi\) | ||
0.952195 | − | 0.305490i | \(-0.0988203\pi\) | |||||||
\(464\) | 3528.60 | 0.353042 | ||||||||
\(465\) | 314.268 | + | 991.141i | 0.0313415 | + | 0.0988453i | ||||
\(466\) | 3093.83 | 0.307551 | ||||||||
\(467\) | − | 981.191i | − | 0.0972250i | −0.998818 | − | 0.0486125i | \(-0.984520\pi\) | ||
0.998818 | − | 0.0486125i | \(-0.0154799\pi\) | |||||||
\(468\) | − | 1499.95i | − | 0.148152i | ||||||
\(469\) | 16529.5 | 1.62742 | ||||||||
\(470\) | −76.6388 | + | 24.3004i | −0.00752146 | + | 0.00238488i | ||||
\(471\) | −6895.99 | −0.674629 | ||||||||
\(472\) | − | 1700.20i | − | 0.165801i | ||||||
\(473\) | 3015.04i | 0.293091i | ||||||||
\(474\) | 1731.32 | 0.167768 | ||||||||
\(475\) | 5700.71 | − | 4019.20i | 0.550666 | − | 0.388239i | ||||
\(476\) | −3723.71 | −0.358563 | ||||||||
\(477\) | 2368.76i | 0.227376i | ||||||||
\(478\) | − | 1644.39i | − | 0.157349i | ||||||
\(479\) | −20392.2 | −1.94519 | −0.972593 | − | 0.232513i | \(-0.925305\pi\) | ||||
−0.972593 | + | 0.232513i | \(0.925305\pi\) | |||||||
\(480\) | 1023.11 | − | 324.405i | 0.0972886 | − | 0.0308479i | ||||
\(481\) | −1668.65 | −0.158178 | ||||||||
\(482\) | 7724.23i | 0.729936i | ||||||||
\(483\) | 7794.21i | 0.734262i | ||||||||
\(484\) | −7928.33 | −0.744584 | ||||||||
\(485\) | −4423.15 | − | 13949.8i | −0.414113 | − | 1.30604i | ||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 8755.86i | 0.814714i | 0.913269 | + | 0.407357i | \(0.133550\pi\) | ||||
−0.913269 | + | 0.407357i | \(0.866450\pi\) | |||||||
\(488\) | − | 5429.50i | − | 0.503652i | ||||||
\(489\) | −12167.9 | −1.12526 | ||||||||
\(490\) | −1083.37 | − | 3416.74i | −0.0998809 | − | 0.315006i | ||||
\(491\) | −9788.68 | −0.899709 | −0.449855 | − | 0.893102i | \(-0.648524\pi\) | ||||
−0.449855 | + | 0.893102i | \(0.648524\pi\) | |||||||
\(492\) | 2834.66i | 0.259749i | ||||||||
\(493\) | − | 9151.37i | − | 0.836018i | ||||||
\(494\) | 4649.92 | 0.423501 | ||||||||
\(495\) | 5520.92 | − | 1750.55i | 0.501307 | − | 0.158953i | ||||
\(496\) | −496.000 | −0.0449013 | ||||||||
\(497\) | − | 8504.63i | − | 0.767575i | ||||||
\(498\) | 5257.73i | 0.473101i | ||||||||
\(499\) | 9506.90 | 0.852880 | 0.426440 | − | 0.904516i | \(-0.359768\pi\) | ||||
0.426440 | + | 0.904516i | \(0.359768\pi\) | |||||||
\(500\) | −3381.54 | + | 4451.43i | −0.302454 | + | 0.398148i | ||||
\(501\) | −1291.56 | −0.115175 | ||||||||
\(502\) | 4267.69i | 0.379435i | ||||||||
\(503\) | 3358.96i | 0.297751i | 0.988856 | + | 0.148875i | \(0.0475654\pi\) | ||||
−0.988856 | + | 0.148875i | \(0.952435\pi\) | |||||||
\(504\) | −1615.27 | −0.142758 | ||||||||
\(505\) | 4805.44 | − | 1523.69i | 0.423444 | − | 0.134264i | ||||
\(506\) | 13331.7 | 1.17127 | ||||||||
\(507\) | − | 1383.00i | − | 0.121147i | ||||||
\(508\) | − | 8413.39i | − | 0.734811i | ||||||
\(509\) | −22834.6 | −1.98846 | −0.994230 | − | 0.107274i | \(-0.965788\pi\) | ||||
−0.994230 | + | 0.107274i | \(0.965788\pi\) | |||||||
\(510\) | −841.339 | − | 2653.43i | −0.0730492 | − | 0.230384i | ||||
\(511\) | −24160.2 | −2.09155 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 1506.62i | 0.129667i | ||||||||
\(514\) | 6167.04 | 0.529215 | ||||||||
\(515\) | 716.659 | + | 2260.21i | 0.0613199 | + | 0.193392i | ||||
\(516\) | 628.578 | 0.0536271 | ||||||||
\(517\) | − | 206.958i | − | 0.0176054i | ||||||
\(518\) | 1796.94i | 0.152419i | ||||||||
\(519\) | 6793.21 | 0.574545 | ||||||||
\(520\) | −3552.36 | + | 1126.37i | −0.299580 | + | 0.0949897i | ||||
\(521\) | −18524.1 | −1.55769 | −0.778845 | − | 0.627217i | \(-0.784194\pi\) | ||||
−0.778845 | + | 0.627217i | \(0.784194\pi\) | |||||||
\(522\) | − | 3969.68i | − | 0.332851i | ||||||
\(523\) | − | 5652.88i | − | 0.472626i | −0.971677 | − | 0.236313i | \(-0.924061\pi\) | ||
0.971677 | − | 0.236313i | \(-0.0759391\pi\) | |||||||
\(524\) | −6795.08 | −0.566497 | ||||||||
\(525\) | 6875.79 | − | 4847.67i | 0.571588 | − | 0.402990i | ||||
\(526\) | −7164.77 | −0.593914 | ||||||||
\(527\) | 1286.37i | 0.106328i | ||||||||
\(528\) | 2762.85i | 0.227723i | ||||||||
\(529\) | −1244.45 | −0.102281 | ||||||||
\(530\) | 5609.98 | − | 1778.79i | 0.459777 | − | 0.145785i | ||||
\(531\) | −1912.73 | −0.156319 | ||||||||
\(532\) | − | 5007.41i | − | 0.408081i | ||||||
\(533\) | − | 9842.26i | − | 0.799842i | ||||||
\(534\) | 6700.53 | 0.542997 | ||||||||
\(535\) | −3756.82 | − | 11848.3i | −0.303591 | − | 0.957470i | ||||
\(536\) | −5894.35 | −0.474995 | ||||||||
\(537\) | − | 1441.20i | − | 0.115814i | ||||||
\(538\) | − | 4265.89i | − | 0.341851i | ||||||
\(539\) | 9226.69 | 0.737331 | ||||||||
\(540\) | −364.956 | − | 1151.00i | −0.0290837 | − | 0.0917246i | ||||
\(541\) | 14341.3 | 1.13970 | 0.569852 | − | 0.821748i | \(-0.307001\pi\) | ||||
0.569852 | + | 0.821748i | \(0.307001\pi\) | |||||||
\(542\) | 9818.74i | 0.778138i | ||||||||
\(543\) | − | 7168.26i | − | 0.566518i | ||||||
\(544\) | 1327.86 | 0.104654 | ||||||||
\(545\) | 12790.0 | − | 4055.40i | 1.00525 | − | 0.318742i | ||||
\(546\) | 5608.40 | 0.439592 | ||||||||
\(547\) | 3284.64i | 0.256747i | 0.991726 | + | 0.128374i | \(0.0409757\pi\) | ||||
−0.991726 | + | 0.128374i | \(0.959024\pi\) | |||||||
\(548\) | − | 5156.71i | − | 0.401978i | ||||||
\(549\) | −6108.19 | −0.474848 | ||||||||
\(550\) | −8291.73 | − | 11760.7i | −0.642838 | − | 0.911780i | ||||
\(551\) | 12306.2 | 0.951472 | ||||||||
\(552\) | − | 2779.39i | − | 0.214309i | ||||||
\(553\) | 6473.50i | 0.497796i | ||||||||
\(554\) | −5562.03 | −0.426548 | ||||||||
\(555\) | −1280.45 | + | 406.002i | −0.0979320 | + | 0.0310519i | ||||
\(556\) | 2896.68 | 0.220947 | ||||||||
\(557\) | − | 2529.86i | − | 0.192448i | −0.995360 | − | 0.0962240i | \(-0.969323\pi\) | ||
0.995360 | − | 0.0962240i | \(-0.0306765\pi\) | |||||||
\(558\) | 558.000i | 0.0423334i | ||||||||
\(559\) | −2182.49 | −0.165133 | ||||||||
\(560\) | 1212.97 | + | 3825.48i | 0.0915308 | + | 0.288671i | ||||
\(561\) | 7165.40 | 0.539257 | ||||||||
\(562\) | − | 8366.22i | − | 0.627949i | ||||||
\(563\) | 1728.05i | 0.129358i | 0.997906 | + | 0.0646792i | \(0.0206024\pi\) | ||||
−0.997906 | + | 0.0646792i | \(0.979398\pi\) | |||||||
\(564\) | −43.1467 | −0.00322128 | ||||||||
\(565\) | 2606.86 | + | 8221.54i | 0.194109 | + | 0.612182i | ||||
\(566\) | 11823.0 | 0.878015 | ||||||||
\(567\) | 1817.18i | 0.134593i | ||||||||
\(568\) | 3032.72i | 0.224032i | ||||||||
\(569\) | 7481.61 | 0.551222 | 0.275611 | − | 0.961269i | \(-0.411120\pi\) | ||||
0.275611 | + | 0.961269i | \(0.411120\pi\) | |||||||
\(570\) | 3568.16 | − | 1131.38i | 0.262200 | − | 0.0831373i | ||||
\(571\) | −14370.7 | −1.05323 | −0.526616 | − | 0.850103i | \(-0.676539\pi\) | ||||
−0.526616 | + | 0.850103i | \(0.676539\pi\) | |||||||
\(572\) | − | 9592.92i | − | 0.701224i | ||||||
\(573\) | 1158.12i | 0.0844349i | ||||||||
\(574\) | −10599.0 | −0.770718 | ||||||||
\(575\) | 8341.37 | + | 11831.1i | 0.604972 | + | 0.858073i | ||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | − | 19900.0i | − | 1.43578i | −0.696155 | − | 0.717891i | \(-0.745108\pi\) | ||
0.696155 | − | 0.717891i | \(-0.254892\pi\) | |||||||
\(578\) | 6382.21i | 0.459282i | ||||||||
\(579\) | −8498.21 | −0.609972 | ||||||||
\(580\) | −9401.46 | + | 2980.98i | −0.673059 | + | 0.213411i | ||||
\(581\) | −19658.9 | −1.40377 | ||||||||
\(582\) | − | 7853.56i | − | 0.559348i | ||||||
\(583\) | 15149.4i | 1.07620i | ||||||||
\(584\) | 8615.44 | 0.610462 | ||||||||
\(585\) | 1267.17 | + | 3996.41i | 0.0895571 | + | 0.282446i | ||||
\(586\) | −18068.0 | −1.27369 | ||||||||
\(587\) | 11044.9i | 0.776614i | 0.921530 | + | 0.388307i | \(0.126940\pi\) | ||||
−0.921530 | + | 0.388307i | \(0.873060\pi\) | |||||||
\(588\) | − | 1923.58i | − | 0.134910i | ||||||
\(589\) | −1729.82 | −0.121012 | ||||||||
\(590\) | 1436.34 | + | 4529.95i | 0.100226 | + | 0.316093i | ||||
\(591\) | −285.187 | −0.0198495 | ||||||||
\(592\) | − | 640.782i | − | 0.0444864i | ||||||
\(593\) | 5730.49i | 0.396835i | 0.980118 | + | 0.198417i | \(0.0635801\pi\) | ||||
−0.980118 | + | 0.198417i | \(0.936420\pi\) | |||||||
\(594\) | 3108.21 | 0.214699 | ||||||||
\(595\) | 9921.30 | − | 3145.81i | 0.683586 | − | 0.216749i | ||||
\(596\) | 23.9009 | 0.00164265 | ||||||||
\(597\) | 1273.41i | 0.0872985i | ||||||||
\(598\) | 9650.34i | 0.659919i | ||||||||
\(599\) | −18192.0 | −1.24091 | −0.620456 | − | 0.784241i | \(-0.713053\pi\) | ||||
−0.620456 | + | 0.784241i | \(0.713053\pi\) | |||||||
\(600\) | −2451.88 | + | 1728.66i | −0.166829 | + | 0.117621i | ||||
\(601\) | −27821.7 | −1.88831 | −0.944154 | − | 0.329506i | \(-0.893118\pi\) | ||||
−0.944154 | + | 0.329506i | \(0.893118\pi\) | |||||||
\(602\) | 2350.29i | 0.159120i | ||||||||
\(603\) | 6631.15i | 0.447829i | ||||||||
\(604\) | −3837.76 | −0.258537 | ||||||||
\(605\) | 21123.9 | − | 6697.89i | 1.41952 | − | 0.450096i | ||||
\(606\) | 2705.40 | 0.181352 | ||||||||
\(607\) | 20709.7i | 1.38481i | 0.721509 | + | 0.692405i | \(0.243449\pi\) | ||||
−0.721509 | + | 0.692405i | \(0.756551\pi\) | |||||||
\(608\) | 1785.63i | 0.119106i | ||||||||
\(609\) | 14842.8 | 0.987623 | ||||||||
\(610\) | 4586.87 | + | 14466.1i | 0.304454 | + | 0.960192i | ||||
\(611\) | 149.810 | 0.00991925 | ||||||||
\(612\) | − | 1493.85i | − | 0.0986685i | ||||||
\(613\) | 21571.2i | 1.42129i | 0.703550 | + | 0.710646i | \(0.251597\pi\) | ||||
−0.703550 | + | 0.710646i | \(0.748403\pi\) | |||||||
\(614\) | 12512.6 | 0.822423 | ||||||||
\(615\) | −2394.74 | − | 7552.56i | −0.157017 | − | 0.495201i | ||||
\(616\) | −10330.4 | −0.675691 | ||||||||
\(617\) | − | 15924.1i | − | 1.03903i | −0.854461 | − | 0.519515i | \(-0.826113\pi\) | ||
0.854461 | − | 0.519515i | \(-0.173887\pi\) | |||||||
\(618\) | 1272.47i | 0.0828255i | ||||||||
\(619\) | −21362.2 | −1.38711 | −0.693554 | − | 0.720405i | \(-0.743956\pi\) | ||||
−0.693554 | + | 0.720405i | \(0.743956\pi\) | |||||||
\(620\) | 1321.52 | − | 419.023i | 0.0856026 | − | 0.0271426i | ||||
\(621\) | −3126.81 | −0.202053 | ||||||||
\(622\) | 1271.99i | 0.0819973i | ||||||||
\(623\) | 25053.6i | 1.61116i | ||||||||
\(624\) | −1999.94 | −0.128304 | ||||||||
\(625\) | 5249.04 | − | 14716.9i | 0.335938 | − | 0.941884i | ||||
\(626\) | −6070.96 | −0.387611 | ||||||||
\(627\) | 9635.58i | 0.613729i | ||||||||
\(628\) | 9194.65i | 0.584246i | ||||||||
\(629\) | −1661.86 | −0.105346 | ||||||||
\(630\) | 4303.66 | − | 1364.59i | 0.272162 | − | 0.0862961i | ||||
\(631\) | 29763.6 | 1.87777 | 0.938883 | − | 0.344237i | \(-0.111862\pi\) | ||||
0.938883 | + | 0.344237i | \(0.111862\pi\) | |||||||
\(632\) | − | 2308.43i | − | 0.145292i | ||||||
\(633\) | 14667.8i | 0.920999i | ||||||||
\(634\) | 13968.8 | 0.875033 | ||||||||
\(635\) | 7107.68 | + | 22416.3i | 0.444188 | + | 1.40089i | ||||
\(636\) | 3158.35 | 0.196913 | ||||||||
\(637\) | 6678.89i | 0.415428i | ||||||||
\(638\) | − | 25388.0i | − | 1.57543i | ||||||
\(639\) | 3411.81 | 0.211219 | ||||||||
\(640\) | −432.540 | − | 1364.15i | −0.0267151 | − | 0.0842544i | ||||
\(641\) | 20950.0 | 1.29091 | 0.645456 | − | 0.763797i | \(-0.276667\pi\) | ||||
0.645456 | + | 0.763797i | \(0.276667\pi\) | |||||||
\(642\) | − | 6670.44i | − | 0.410064i | ||||||
\(643\) | − | 21161.2i | − | 1.29785i | −0.760853 | − | 0.648925i | \(-0.775219\pi\) | ||
0.760853 | − | 0.648925i | \(-0.224781\pi\) | |||||||
\(644\) | 10392.3 | 0.635890 | ||||||||
\(645\) | −1674.76 | + | 531.026i | −0.102238 | + | 0.0324172i | ||||
\(646\) | 4630.99 | 0.282049 | ||||||||
\(647\) | 27929.0i | 1.69707i | 0.529140 | + | 0.848535i | \(0.322515\pi\) | ||||
−0.529140 | + | 0.848535i | \(0.677485\pi\) | |||||||
\(648\) | − | 648.000i | − | 0.0392837i | ||||||
\(649\) | −12232.8 | −0.739878 | ||||||||
\(650\) | 8513.20 | − | 6002.11i | 0.513716 | − | 0.362188i | ||||
\(651\) | −2086.39 | −0.125610 | ||||||||
\(652\) | 16223.8i | 0.974500i | ||||||||
\(653\) | 24990.7i | 1.49764i | 0.662772 | + | 0.748821i | \(0.269380\pi\) | ||||
−0.662772 | + | 0.748821i | \(0.730620\pi\) | |||||||
\(654\) | 7200.60 | 0.430529 | ||||||||
\(655\) | 18104.5 | − | 5740.52i | 1.08000 | − | 0.342444i | ||||
\(656\) | 3779.55 | 0.224949 | ||||||||
\(657\) | − | 9692.37i | − | 0.575549i | ||||||
\(658\) | − | 161.328i | − | 0.00955807i | ||||||
\(659\) | 31126.7 | 1.83995 | 0.919973 | − | 0.391983i | \(-0.128211\pi\) | ||||
0.919973 | + | 0.391983i | \(0.128211\pi\) | |||||||
\(660\) | −2334.07 | − | 7361.22i | −0.137657 | − | 0.434144i | ||||
\(661\) | −14724.6 | −0.866446 | −0.433223 | − | 0.901287i | \(-0.642624\pi\) | ||||
−0.433223 | + | 0.901287i | \(0.642624\pi\) | |||||||
\(662\) | 12654.6i | 0.742955i | ||||||||
\(663\) | 5186.79i | 0.303829i | ||||||||
\(664\) | 7010.31 | 0.409718 | ||||||||
\(665\) | 4230.29 | + | 13341.5i | 0.246682 | + | 0.777989i | ||||
\(666\) | −720.880 | −0.0419422 | ||||||||
\(667\) | 25540.0i | 1.48263i | ||||||||
\(668\) | 1722.08i | 0.0997446i | ||||||||
\(669\) | 700.629 | 0.0404901 | ||||||||
\(670\) | 15704.7 | − | 4979.58i | 0.905559 | − | 0.287131i | ||||
\(671\) | −39064.9 | −2.24751 | ||||||||
\(672\) | 2153.69i | 0.123632i | ||||||||
\(673\) | 29919.4i | 1.71368i | 0.515581 | + | 0.856841i | \(0.327576\pi\) | ||||
−0.515581 | + | 0.856841i | \(0.672424\pi\) | |||||||
\(674\) | −1002.10 | −0.0572691 | ||||||||
\(675\) | 1944.75 | + | 2758.37i | 0.110894 | + | 0.157288i | ||||
\(676\) | −1844.00 | −0.104916 | ||||||||
\(677\) | 14987.8i | 0.850856i | 0.904992 | + | 0.425428i | \(0.139876\pi\) | ||||
−0.904992 | + | 0.425428i | \(0.860124\pi\) | |||||||
\(678\) | 4628.63i | 0.262185i | ||||||||
\(679\) | 29364.9 | 1.65968 | ||||||||
\(680\) | −3537.90 | + | 1121.79i | −0.199518 | + | 0.0632625i | ||||
\(681\) | 4296.33 | 0.241756 | ||||||||
\(682\) | 3568.68i | 0.200369i | ||||||||
\(683\) | 18606.8i | 1.04242i | 0.853429 | + | 0.521208i | \(0.174519\pi\) | ||||
−0.853429 | + | 0.521208i | \(0.825481\pi\) | |||||||
\(684\) | 2008.83 | 0.112295 | ||||||||
\(685\) | 4356.42 | + | 13739.3i | 0.242993 | + | 0.766354i | ||||
\(686\) | −8197.56 | −0.456245 | ||||||||
\(687\) | − | 3427.45i | − | 0.190343i | ||||||
\(688\) | − | 838.104i | − | 0.0464424i | ||||||
\(689\) | −10966.1 | −0.606352 | ||||||||
\(690\) | 2348.04 | + | 7405.28i | 0.129548 | + | 0.408572i | ||||
\(691\) | −18534.0 | −1.02036 | −0.510178 | − | 0.860069i | \(-0.670421\pi\) | ||||
−0.510178 | + | 0.860069i | \(0.670421\pi\) | |||||||
\(692\) | − | 9057.62i | − | 0.497571i | ||||||
\(693\) | 11621.7i | 0.637047i | ||||||||
\(694\) | 2314.57 | 0.126599 | ||||||||
\(695\) | −7717.80 | + | 2447.13i | −0.421227 | + | 0.133561i | ||||
\(696\) | −5292.90 | −0.288257 | ||||||||
\(697\) | − | 9802.19i | − | 0.532690i | ||||||
\(698\) | − | 7960.60i | − | 0.431681i | ||||||
\(699\) | −4640.75 | −0.251115 | ||||||||
\(700\) | −6463.56 | − | 9167.71i | −0.349000 | − | 0.495010i | ||||
\(701\) | −18960.0 | −1.02156 | −0.510778 | − | 0.859713i | \(-0.670642\pi\) | ||||
−0.510778 | + | 0.859713i | \(0.670642\pi\) | |||||||
\(702\) | 2249.93i | 0.120966i | ||||||||
\(703\) | − | 2234.76i | − | 0.119894i | ||||||
\(704\) | 3683.80 | 0.197214 | ||||||||
\(705\) | 114.958 | − | 36.4505i | 0.00614124 | − | 0.00194724i | ||||
\(706\) | −8058.49 | −0.429582 | ||||||||
\(707\) | 10115.6i | 0.538102i | ||||||||
\(708\) | 2550.31i | 0.135376i | ||||||||
\(709\) | 28218.1 | 1.49472 | 0.747358 | − | 0.664422i | \(-0.231322\pi\) | ||||
0.747358 | + | 0.664422i | \(0.231322\pi\) | |||||||
\(710\) | −2562.06 | − | 8080.25i | −0.135426 | − | 0.427108i | ||||
\(711\) | −2596.98 | −0.136982 | ||||||||
\(712\) | − | 8934.04i | − | 0.470249i | ||||||
\(713\) | − | 3590.04i | − | 0.188567i | ||||||
\(714\) | 5585.57 | 0.292765 | ||||||||
\(715\) | 8104.15 | + | 25559.0i | 0.423885 | + | 1.33686i | ||||
\(716\) | −1921.60 | −0.100298 | ||||||||
\(717\) | 2466.59i | 0.128475i | ||||||||
\(718\) | 4201.09i | 0.218361i | ||||||||
\(719\) | 12392.6 | 0.642792 | 0.321396 | − | 0.946945i | \(-0.395848\pi\) | ||||
0.321396 | + | 0.946945i | \(0.395848\pi\) | |||||||
\(720\) | −1534.67 | + | 486.608i | −0.0794358 | + | 0.0251872i | ||||
\(721\) | −4757.83 | −0.245757 | ||||||||
\(722\) | − | 7490.54i | − | 0.386107i | ||||||
\(723\) | − | 11586.3i | − | 0.595990i | ||||||
\(724\) | −9557.68 | −0.490619 | ||||||||
\(725\) | 22530.5 | − | 15884.8i | 1.15415 | − | 0.813720i | ||||
\(726\) | 11892.5 | 0.607950 | ||||||||
\(727\) | − | 31895.4i | − | 1.62714i | −0.581464 | − | 0.813572i | \(-0.697520\pi\) | ||
0.581464 | − | 0.813572i | \(-0.302480\pi\) | |||||||
\(728\) | − | 7477.86i | − | 0.380698i | ||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | −22954.6 | + | 7278.37i | −1.16382 | + | 0.369020i | ||||
\(731\) | −2173.61 | −0.109978 | ||||||||
\(732\) | 8144.26i | 0.411230i | ||||||||
\(733\) | − | 24622.5i | − | 1.24073i | −0.784315 | − | 0.620363i | \(-0.786985\pi\) | ||
0.784315 | − | 0.620363i | \(-0.213015\pi\) | |||||||
\(734\) | −13038.3 | −0.655658 | ||||||||
\(735\) | 1625.05 | + | 5125.12i | 0.0815524 | + | 0.257201i | ||||
\(736\) | −3705.85 | −0.185597 | ||||||||
\(737\) | 42409.4i | 2.11963i | ||||||||
\(738\) | − | 4252.00i | − | 0.212084i | ||||||
\(739\) | 33118.3 | 1.64855 | 0.824274 | − | 0.566191i | \(-0.191584\pi\) | ||||
0.824274 | + | 0.566191i | \(0.191584\pi\) | |||||||
\(740\) | 541.336 | + | 1707.27i | 0.0268918 | + | 0.0848116i | ||||
\(741\) | −6974.88 | −0.345787 | ||||||||
\(742\) | 11809.2i | 0.584273i | ||||||||
\(743\) | − | 3339.76i | − | 0.164905i | −0.996595 | − | 0.0824523i | \(-0.973725\pi\) | ||
0.996595 | − | 0.0824523i | \(-0.0262752\pi\) | |||||||
\(744\) | 744.000 | 0.0366618 | ||||||||
\(745\) | −63.6805 | + | 20.1916i | −0.00313164 | + | 0.000992969i | ||||
\(746\) | 314.435 | 0.0154320 | ||||||||
\(747\) | − | 7886.59i | − | 0.386286i | ||||||
\(748\) | − | 9553.87i | − | 0.467011i | ||||||
\(749\) | 24941.1 | 1.21673 | ||||||||
\(750\) | 5072.31 | − | 6677.14i | 0.246953 | − | 0.325086i | ||||
\(751\) | −28779.3 | −1.39837 | −0.699183 | − | 0.714943i | \(-0.746453\pi\) | ||||
−0.699183 | + | 0.714943i | \(0.746453\pi\) | |||||||
\(752\) | 57.5289i | 0.00278971i | ||||||||
\(753\) | − | 6401.53i | − | 0.309807i | ||||||
\(754\) | 18377.5 | 0.887627 | ||||||||
\(755\) | 10225.2 | − | 3242.16i | 0.492890 | − | 0.156284i | ||||
\(756\) | 2422.91 | 0.116561 | ||||||||
\(757\) | 518.139i | 0.0248772i | 0.999923 | + | 0.0124386i | \(0.00395944\pi\) | ||||
−0.999923 | + | 0.0124386i | \(0.996041\pi\) | |||||||
\(758\) | 20182.7i | 0.967111i | ||||||||
\(759\) | −19997.5 | −0.956341 | ||||||||
\(760\) | −1508.51 | − | 4757.55i | −0.0719990 | − | 0.227072i | ||||
\(761\) | 33119.3 | 1.57762 | 0.788812 | − | 0.614634i | \(-0.210696\pi\) | ||||
0.788812 | + | 0.614634i | \(0.210696\pi\) | |||||||
\(762\) | 12620.1i | 0.599971i | ||||||||
\(763\) | 26923.4i | 1.27745i | ||||||||
\(764\) | 1544.16 | 0.0731228 | ||||||||
\(765\) | 1262.01 | + | 3980.14i | 0.0596445 | + | 0.188107i | ||||
\(766\) | 373.964 | 0.0176395 | ||||||||
\(767\) | − | 8854.94i | − | 0.416862i | ||||||
\(768\) | − | 768.000i | − | 0.0360844i | ||||||
\(769\) | 6074.22 | 0.284840 | 0.142420 | − | 0.989806i | \(-0.454512\pi\) | ||||
0.142420 | + | 0.989806i | \(0.454512\pi\) | |||||||
\(770\) | 27524.0 | − | 8727.21i | 1.28818 | − | 0.408451i | ||||
\(771\) | −9250.57 | −0.432102 | ||||||||
\(772\) | 11331.0i | 0.528251i | ||||||||
\(773\) | − | 2650.10i | − | 0.123309i | −0.998098 | − | 0.0616544i | \(-0.980362\pi\) | ||
0.998098 | − | 0.0616544i | \(-0.0196376\pi\) | |||||||
\(774\) | −942.866 | −0.0437864 | ||||||||
\(775\) | −3167.01 | + | 2232.86i | −0.146790 | + | 0.103492i | ||||
\(776\) | −10471.4 | −0.484409 | ||||||||
\(777\) | − | 2695.41i | − | 0.124449i | ||||||
\(778\) | − | 16329.6i | − | 0.752499i | ||||||
\(779\) | 13181.4 | 0.606254 | ||||||||
\(780\) | 5328.54 | − | 1689.56i | 0.244606 | − | 0.0775587i | ||||
\(781\) | 21820.2 | 0.999728 | ||||||||
\(782\) | 9611.05i | 0.439502i | ||||||||
\(783\) | 5954.52i | 0.271772i | ||||||||
\(784\) | −2564.78 | −0.116836 | ||||||||
\(785\) | −7767.69 | − | 24497.8i | −0.353173 | − | 1.11384i | ||||
\(786\) | 10192.6 | 0.462543 | ||||||||
\(787\) | 12990.2i | 0.588376i | 0.955748 | + | 0.294188i | \(0.0950492\pi\) | ||||
−0.955748 | + | 0.294188i | \(0.904951\pi\) | |||||||
\(788\) | 380.249i | 0.0171901i | ||||||||
\(789\) | 10747.2 | 0.484929 | ||||||||
\(790\) | 1950.17 | + | 6150.48i | 0.0878279 | + | 0.276993i | ||||
\(791\) | −17306.7 | −0.777945 | ||||||||
\(792\) | − | 4144.28i | − | 0.185935i | ||||||
\(793\) | − | 28277.8i | − | 1.26630i | ||||||
\(794\) | −6062.88 | −0.270987 | ||||||||
\(795\) | −8414.97 | + | 2668.19i | −0.375407 | + | 0.119033i | ||||
\(796\) | 1697.88 | 0.0756027 | ||||||||
\(797\) | 22872.5i | 1.01654i | 0.861197 | + | 0.508272i | \(0.169715\pi\) | ||||
−0.861197 | + | 0.508272i | \(0.830285\pi\) | |||||||
\(798\) | 7511.12i | 0.333196i | ||||||||
\(799\) | 149.200 | 0.00660616 | ||||||||
\(800\) | 2304.88 | + | 3269.18i | 0.101862 | + | 0.144478i | ||||
\(801\) | −10050.8 | −0.443355 | ||||||||
\(802\) | − | 29338.3i | − | 1.29173i | ||||||
\(803\) | − | 61987.4i | − | 2.72415i | ||||||
\(804\) | 8841.53 | 0.387832 | ||||||||
\(805\) | −27688.8 | + | 8779.45i | −1.21230 | + | 0.384391i | ||||
\(806\) | −2583.25 | −0.112892 | ||||||||
\(807\) | 6398.84i | 0.279120i | ||||||||
\(808\) | − | 3607.20i | − | 0.157056i | ||||||
\(809\) | 10880.8 | 0.472866 | 0.236433 | − | 0.971648i | \(-0.424022\pi\) | ||||
0.236433 | + | 0.971648i | \(0.424022\pi\) | |||||||
\(810\) | 547.434 | + | 1726.50i | 0.0237467 | + | 0.0748928i | ||||
\(811\) | 44284.1 | 1.91742 | 0.958709 | − | 0.284388i | \(-0.0917903\pi\) | ||||
0.958709 | + | 0.284388i | \(0.0917903\pi\) | |||||||
\(812\) | − | 19790.5i | − | 0.855306i | ||||||
\(813\) | − | 14728.1i | − | 0.635347i | ||||||
\(814\) | −4610.38 | −0.198518 | ||||||||
\(815\) | −13706.0 | − | 43226.1i | −0.589079 | − | 1.85785i | ||||
\(816\) | −1991.79 | −0.0854494 | ||||||||
\(817\) | − | 2922.93i | − | 0.125166i | ||||||
\(818\) | − | 21977.7i | − | 0.939405i | ||||||
\(819\) | −8412.60 | −0.358925 | ||||||||
\(820\) | −10070.1 | + | 3192.99i | −0.428857 | + | 0.135980i | ||||
\(821\) | 20401.3 | 0.867249 | 0.433624 | − | 0.901094i | \(-0.357234\pi\) | ||||
0.433624 | + | 0.901094i | \(0.357234\pi\) | |||||||
\(822\) | 7735.06i | 0.328213i | ||||||||
\(823\) | − | 31905.5i | − | 1.35134i | −0.737203 | − | 0.675671i | \(-0.763854\pi\) | ||
0.737203 | − | 0.675671i | \(-0.236146\pi\) | |||||||
\(824\) | 1696.62 | 0.0717290 | ||||||||
\(825\) | 12437.6 | + | 17641.1i | 0.524875 | + | 0.744466i | ||||
\(826\) | −9535.73 | −0.401683 | ||||||||
\(827\) | 11424.3i | 0.480364i | 0.970728 | + | 0.240182i | \(0.0772072\pi\) | ||||
−0.970728 | + | 0.240182i | \(0.922793\pi\) | |||||||
\(828\) | 4169.08i | 0.174983i | ||||||||
\(829\) | 21995.0 | 0.921494 | 0.460747 | − | 0.887532i | \(-0.347582\pi\) | ||||
0.460747 | + | 0.887532i | \(0.347582\pi\) | |||||||
\(830\) | −18678.0 | + | 5922.34i | −0.781110 | + | 0.247672i | ||||
\(831\) | 8343.04 | 0.348275 | ||||||||
\(832\) | 2666.58i | 0.111114i | ||||||||
\(833\) | 6651.70i | 0.276672i | ||||||||
\(834\) | −4345.03 | −0.180403 | ||||||||
\(835\) | −1454.82 | − | 4588.25i | −0.0602950 | − | 0.190159i | ||||
\(836\) | 12847.4 | 0.531505 | ||||||||
\(837\) | − | 837.000i | − | 0.0345651i | ||||||
\(838\) | 8516.03i | 0.351052i | ||||||||
\(839\) | −17674.3 | −0.727278 | −0.363639 | − | 0.931540i | \(-0.618466\pi\) | ||||
−0.363639 | + | 0.931540i | \(0.618466\pi\) | |||||||
\(840\) | −1819.45 | − | 5738.21i | −0.0747346 | − | 0.235699i | ||||
\(841\) | 24247.9 | 0.994214 | ||||||||
\(842\) | 3076.37i | 0.125913i | ||||||||
\(843\) | 12549.3i | 0.512718i | ||||||||
\(844\) | 19557.0 | 0.797608 | ||||||||
\(845\) | 4913.09 | − | 1557.82i | 0.200018 | − | 0.0634211i | ||||
\(846\) | 64.7200 | 0.00263017 | ||||||||
\(847\) | 44466.7i | 1.80389i | ||||||||
\(848\) | − | 4211.13i | − | 0.170532i | ||||||
\(849\) | −17734.5 | −0.716896 | ||||||||
\(850\) | 8478.54 | − | 5977.67i | 0.342131 | − | 0.241215i | ||||
\(851\) | 4637.97 | 0.186825 | ||||||||
\(852\) | − | 4549.08i | − | 0.182921i | ||||||
\(853\) | − | 36566.9i | − | 1.46779i | −0.679262 | − | 0.733896i | \(-0.737700\pi\) | ||
0.679262 | − | 0.733896i | \(-0.262300\pi\) | |||||||
\(854\) | −30451.8 | −1.22019 | ||||||||
\(855\) | −5352.24 | + | 1697.07i | −0.214085 | + | 0.0678813i | ||||
\(856\) | −8893.92 | −0.355126 | ||||||||
\(857\) | − | 10794.9i | − | 0.430278i | −0.976583 | − | 0.215139i | \(-0.930980\pi\) | ||
0.976583 | − | 0.215139i | \(-0.0690204\pi\) | |||||||
\(858\) | 14389.4i | 0.572547i | ||||||||
\(859\) | 31664.1 | 1.25770 | 0.628851 | − | 0.777526i | \(-0.283526\pi\) | ||||
0.628851 | + | 0.777526i | \(0.283526\pi\) | |||||||
\(860\) | 708.034 | + | 2233.01i | 0.0280742 | + | 0.0885406i | ||||
\(861\) | 15898.4 | 0.629288 | ||||||||
\(862\) | − | 6865.69i | − | 0.271283i | ||||||
\(863\) | 26769.7i | 1.05591i | 0.849273 | + | 0.527955i | \(0.177041\pi\) | ||||
−0.849273 | + | 0.527955i | \(0.822959\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 7651.92 | + | 24132.7i | 0.300778 | + | 0.948598i | ||||
\(866\) | 9292.93 | 0.364650 | ||||||||
\(867\) | − | 9573.32i | − | 0.375002i | ||||||
\(868\) | 2781.86i | 0.108781i | ||||||||
\(869\) | −16609.0 | −0.648355 | ||||||||
\(870\) | 14102.2 | − | 4471.47i | 0.549551 | − | 0.174250i | ||||
\(871\) | −30698.8 | −1.19425 | ||||||||
\(872\) | − | 9600.80i | − | 0.372849i | ||||||
\(873\) | 11780.3i | 0.456706i | ||||||||
\(874\) | −12924.3 | −0.500197 | ||||||||
\(875\) | 24966.2 | + | 18965.6i | 0.964584 | + | 0.732749i | ||||
\(876\) | −12923.2 | −0.498440 | ||||||||
\(877\) | 29225.9i | 1.12530i | 0.826695 | + | 0.562650i | \(0.190218\pi\) | ||||
−0.826695 | + | 0.562650i | \(0.809782\pi\) | |||||||
\(878\) | 6160.38i | 0.236791i | ||||||||
\(879\) | 27102.0 | 1.03996 | ||||||||
\(880\) | −9814.96 | + | 3112.09i | −0.375980 | + | 0.119214i | ||||
\(881\) | 7606.81 | 0.290897 | 0.145448 | − | 0.989366i | \(-0.453538\pi\) | ||||
0.145448 | + | 0.989366i | \(0.453538\pi\) | |||||||
\(882\) | 2885.38i | 0.110154i | ||||||||
\(883\) | − | 49912.4i | − | 1.90225i | −0.308806 | − | 0.951125i | \(-0.599929\pi\) | ||
0.308806 | − | 0.951125i | \(-0.400071\pi\) | |||||||
\(884\) | 6915.73 | 0.263123 | ||||||||
\(885\) | −2154.51 | − | 6794.93i | −0.0818340 | − | 0.258089i | ||||
\(886\) | 21680.1 | 0.822072 | ||||||||
\(887\) | − | 5775.46i | − | 0.218626i | −0.994007 | − | 0.109313i | \(-0.965135\pi\) | ||
0.994007 | − | 0.109313i | \(-0.0348651\pi\) | |||||||
\(888\) | 961.173i | 0.0363230i | ||||||||
\(889\) | −47187.2 | −1.78021 | ||||||||
\(890\) | 7547.52 | + | 23803.5i | 0.284262 | + | 0.896511i | ||||
\(891\) | −4662.31 | −0.175301 | ||||||||
\(892\) | − | 934.172i | − | 0.0350655i | ||||||
\(893\) | 200.635i | 0.00751847i | ||||||||
\(894\) | −35.8513 | −0.00134122 | ||||||||
\(895\) | 5119.82 | − | 1623.38i | 0.191214 | − | 0.0606296i | ||||
\(896\) | 2871.59 | 0.107068 | ||||||||
\(897\) | − | 14475.5i | − | 0.538822i | ||||||
\(898\) | − | 19448.4i | − | 0.722719i | ||||||
\(899\) | −6836.67 | −0.253633 | ||||||||
\(900\) | 3677.82 | − | 2593.00i | 0.136216 | − | 0.0960369i | ||||
\(901\) | −10921.5 | −0.403826 | ||||||||
\(902\) | − | 27193.6i | − | 1.00382i | ||||||
\(903\) | − | 3525.43i | − | 0.129921i | ||||||
\(904\) | 6171.50 | 0.227059 | ||||||||
\(905\) | 25465.1 | − | 8074.38i | 0.935346 | − | 0.296576i | ||||
\(906\) | 5756.65 | 0.211095 | ||||||||
\(907\) | − | 34185.5i | − | 1.25150i | −0.780024 | − | 0.625750i | \(-0.784793\pi\) | ||
0.780024 | − | 0.625750i | \(-0.215207\pi\) | |||||||
\(908\) | − | 5728.45i | − | 0.209367i | ||||||
\(909\) | −4058.11 | −0.148074 | ||||||||
\(910\) | 6317.34 | + | 19923.7i | 0.230129 | + | 0.725785i | ||||
\(911\) | 17367.6 | 0.631629 | 0.315814 | − | 0.948821i | \(-0.397722\pi\) | ||||
0.315814 | + | 0.948821i | \(0.397722\pi\) | |||||||
\(912\) | − | 2678.44i | − | 0.0972500i | ||||||
\(913\) | − | 50438.6i | − | 1.82834i | ||||||
\(914\) | 30504.5 | 1.10394 | ||||||||
\(915\) | −6880.31 | − | 21699.2i | −0.248586 | − | 0.783993i | ||||
\(916\) | −4569.93 | −0.164842 | ||||||||
\(917\) | 38110.7i | 1.37244i | ||||||||
\(918\) | 2240.77i | 0.0805625i | ||||||||
\(919\) | 38445.5 | 1.37998 | 0.689989 | − | 0.723820i | \(-0.257615\pi\) | ||||
0.689989 | + | 0.723820i | \(0.257615\pi\) | |||||||
\(920\) | 9873.71 | − | 3130.72i | 0.353833 | − | 0.112192i | ||||
\(921\) | −18768.9 | −0.671506 | ||||||||
\(922\) | − | 37581.2i | − | 1.34238i | ||||||
\(923\) | 15794.9i | 0.563267i | ||||||||
\(924\) | 15495.7 | 0.551699 | ||||||||
\(925\) | −2884.63 | − | 4091.46i | −0.102536 | − | 0.145434i | ||||
\(926\) | 12173.9 | 0.432028 | ||||||||
\(927\) | − | 1908.70i | − | 0.0676268i | ||||||
\(928\) | 7057.21i | 0.249638i | ||||||||
\(929\) | −44008.6 | −1.55422 | −0.777112 | − | 0.629362i | \(-0.783316\pi\) | ||||
−0.777112 | + | 0.629362i | \(0.783316\pi\) | |||||||
\(930\) | −1982.28 | + | 628.535i | −0.0698942 | + | 0.0221618i | ||||
\(931\) | −8944.79 | −0.314880 | ||||||||
\(932\) | 6187.66i | 0.217472i | ||||||||
\(933\) | − | 1907.99i | − | 0.0669506i | ||||||
\(934\) | 1962.38 | 0.0687485 | ||||||||
\(935\) | 8071.16 | + | 25454.9i | 0.282305 | + | 0.890337i | ||||
\(936\) | 2999.90 | 0.104760 | ||||||||
\(937\) | 56605.9i | 1.97357i | 0.162037 | + | 0.986785i | \(0.448194\pi\) | ||||
−0.162037 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(938\) | 33058.9i | 1.15076i | ||||||||
\(939\) | 9106.44 | 0.316483 | ||||||||
\(940\) | −48.6007 | − | 153.278i | −0.00168636 | − | 0.00531847i | ||||
\(941\) | 48627.9 | 1.68462 | 0.842309 | − | 0.538995i | \(-0.181196\pi\) | ||||
0.842309 | + | 0.538995i | \(0.181196\pi\) | |||||||
\(942\) | − | 13792.0i | − | 0.477035i | ||||||
\(943\) | 27356.4i | 0.944693i | ||||||||
\(944\) | 3400.41 | 0.117239 | ||||||||
\(945\) | −6455.49 | + | 2046.88i | −0.222219 | + | 0.0704605i | ||||
\(946\) | −6030.09 | −0.207246 | ||||||||
\(947\) | − | 34717.9i | − | 1.19132i | −0.803237 | − | 0.595659i | \(-0.796891\pi\) | ||
0.803237 | − | 0.595659i | \(-0.203109\pi\) | |||||||
\(948\) | 3462.64i | 0.118630i | ||||||||
\(949\) | 44870.6 | 1.53484 | ||||||||
\(950\) | 8038.40 | + | 11401.4i | 0.274527 | + | 0.389380i | ||||
\(951\) | −20953.2 | −0.714461 | ||||||||
\(952\) | − | 7447.42i | − | 0.253542i | ||||||
\(953\) | − | 27703.8i | − | 0.941674i | −0.882220 | − | 0.470837i | \(-0.843952\pi\) | ||
0.882220 | − | 0.470837i | \(-0.156048\pi\) | |||||||
\(954\) | −4737.52 | −0.160779 | ||||||||
\(955\) | −4114.20 | + | 1304.52i | −0.139406 | + | 0.0442022i | ||||
\(956\) | 3288.78 | 0.111262 | ||||||||
\(957\) | 38082.0i | 1.28633i | ||||||||
\(958\) | − | 40784.4i | − | 1.37545i | ||||||
\(959\) | −28921.8 | −0.973862 | ||||||||
\(960\) | 648.811 | + | 2046.23i | 0.0218128 | + | 0.0687934i | ||||
\(961\) | 961.000 | 0.0322581 | ||||||||
\(962\) | − | 3337.30i | − | 0.111849i | ||||||
\(963\) | 10005.7i | 0.334816i | ||||||||
\(964\) | −15448.5 | −0.516142 | ||||||||
\(965\) | −9572.45 | − | 30189.7i | −0.319324 | − | 1.00709i | ||||
\(966\) | −15588.4 | −0.519202 | ||||||||
\(967\) | 42653.7i | 1.41846i | 0.704977 | + | 0.709230i | \(0.250957\pi\) | ||||
−0.704977 | + | 0.709230i | \(0.749043\pi\) | |||||||
\(968\) | − | 15856.7i | − | 0.526500i | ||||||
\(969\) | −6946.48 | −0.230292 | ||||||||
\(970\) | 27899.6 | − | 8846.30i | 0.923507 | − | 0.292822i | ||||
\(971\) | −22521.7 | −0.744343 | −0.372172 | − | 0.928164i | \(-0.621387\pi\) | ||||
−0.372172 | + | 0.928164i | \(0.621387\pi\) | |||||||
\(972\) | 972.000i | 0.0320750i | ||||||||
\(973\) | − | 16246.3i | − | 0.535285i | ||||||
\(974\) | −17511.7 | −0.576090 | ||||||||
\(975\) | −12769.8 | + | 9003.16i | −0.419447 | + | 0.295725i | ||||
\(976\) | 10859.0 | 0.356136 | ||||||||
\(977\) | 5033.46i | 0.164826i | 0.996598 | + | 0.0824128i | \(0.0262626\pi\) | ||||
−0.996598 | + | 0.0824128i | \(0.973737\pi\) | |||||||
\(978\) | − | 24335.7i | − | 0.795676i | ||||||
\(979\) | −64279.7 | −2.09846 | ||||||||
\(980\) | 6833.49 | − | 2166.74i | 0.222743 | − | 0.0706264i | ||||
\(981\) | −10800.9 | −0.351525 | ||||||||
\(982\) | − | 19577.4i | − | 0.636190i | ||||||
\(983\) | − | 11793.2i | − | 0.382649i | −0.981527 | − | 0.191325i | \(-0.938722\pi\) | ||
0.981527 | − | 0.191325i | \(-0.0612783\pi\) | |||||||
\(984\) | −5669.33 | −0.183670 | ||||||||
\(985\) | −321.237 | − | 1013.12i | −0.0103913 | − | 0.0327723i | ||||
\(986\) | 18302.7 | 0.591154 | ||||||||
\(987\) | 241.992i | 0.00780413i | ||||||||
\(988\) | 9299.83i | 0.299461i | ||||||||
\(989\) | 6066.18 | 0.195039 | ||||||||
\(990\) | 3501.11 | + | 11041.8i | 0.112396 | + | 0.354477i | ||||
\(991\) | 38245.7 | 1.22595 | 0.612974 | − | 0.790103i | \(-0.289973\pi\) | ||||
0.612974 | + | 0.790103i | \(0.289973\pi\) | |||||||
\(992\) | − | 992.000i | − | 0.0317500i | ||||||
\(993\) | − | 18981.9i | − | 0.606620i | ||||||
\(994\) | 17009.3 | 0.542757 | ||||||||
\(995\) | −4523.76 | + | 1434.38i | −0.144134 | + | 0.0457013i | ||||
\(996\) | −10515.5 | −0.334533 | ||||||||
\(997\) | 6791.48i | 0.215736i | 0.994165 | + | 0.107868i | \(0.0344023\pi\) | ||||
−0.994165 | + | 0.107868i | \(0.965598\pi\) | |||||||
\(998\) | 19013.8i | 0.603077i | ||||||||
\(999\) | 1081.32 | 0.0342457 |
(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 | 930.4.d.c.559.19 | yes | 20 | |
5.4 | even | 2 | inner | 930.4.d.c.559.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.4.d.c.559.9 | ✓ | 20 | 5.4 | even | 2 | inner | |
930.4.d.c.559.19 | yes | 20 | 1.1 | even | 1 | trivial |