Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), degree \(2\), not 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(2.13746 - 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.q.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63746 | + | 4.56821i | −0.932482 | + | 1.61511i | −0.153420 | + | 0.988161i | \(0.549029\pi\) |
−0.779063 | + | 0.626946i | \(0.784305\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −9.91238 | − | 17.1687i | −1.23905 | − | 2.14609i | ||||
\(5\) | 5.27492 | − | 9.13642i | 0.471803 | − | 0.817187i | −0.527677 | − | 0.849445i | \(-0.676937\pi\) |
0.999480 | + | 0.0322587i | \(0.0102700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 62.3746 | 2.75659 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 27.8248 | + | 48.1939i | 0.879896 | + | 1.52402i | ||||
\(11\) | 17.3746 | + | 30.0937i | 0.476240 | + | 0.824871i | 0.999629 | − | 0.0272223i | \(-0.00866619\pi\) |
−0.523390 | + | 0.852093i | \(0.675333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.2990 | −0.795760 | −0.397880 | − | 0.917437i | \(-0.630254\pi\) | ||||
−0.397880 | + | 0.917437i | \(0.630254\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −85.2114 | + | 147.590i | −1.33143 | + | 2.30610i | ||||
\(17\) | −5.27492 | − | 9.13642i | −0.0752562 | − | 0.130348i | 0.825941 | − | 0.563756i | \(-0.190644\pi\) |
−0.901198 | + | 0.433408i | \(0.857311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.2990 | − | 50.7474i | 0.353771 | − | 0.612750i | −0.633136 | − | 0.774041i | \(-0.718232\pi\) |
0.986907 | + | 0.161291i | \(0.0515658\pi\) | |||||||
\(20\) | −209.148 | −2.33834 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −183.299 | −1.77634 | ||||||||
\(23\) | −62.6736 | + | 108.554i | −0.568189 | + | 0.984132i | 0.428556 | + | 0.903515i | \(0.359022\pi\) |
−0.996745 | + | 0.0806171i | \(0.974311\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.85050 | + | 11.8654i | 0.0548040 | + | 0.0949233i | ||||
\(26\) | 98.3746 | − | 170.390i | 0.742032 | − | 1.28524i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.4020 | 0.226689 | 0.113345 | − | 0.993556i | \(-0.463844\pi\) | ||||
0.113345 | + | 0.993556i | \(0.463844\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −145.897 | − | 252.701i | −0.845286 | − | 1.46408i | −0.885372 | − | 0.464883i | \(-0.846096\pi\) |
0.0400859 | − | 0.999196i | \(-0.487237\pi\) | |||||||
\(32\) | −199.985 | − | 346.384i | −1.10477 | − | 1.91352i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 55.6495 | 0.280700 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 129.949 | − | 225.077i | 0.577389 | − | 1.00007i | −0.418388 | − | 0.908268i | \(-0.637405\pi\) |
0.995778 | − | 0.0917993i | \(-0.0292618\pi\) | |||||||
\(38\) | 154.550 | + | 267.688i | 0.659771 | + | 1.14276i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 329.021 | − | 569.881i | 1.30057 | − | 2.25265i | ||||
\(41\) | 338.248 | 1.28842 | 0.644212 | − | 0.764847i | \(-0.277185\pi\) | ||||
0.644212 | + | 0.764847i | \(0.277185\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.80397 | 0.0241301 | 0.0120651 | − | 0.999927i | \(-0.496159\pi\) | ||||
0.0120651 | + | 0.999927i | \(0.496159\pi\) | |||||||
\(44\) | 344.447 | − | 596.599i | 1.18017 | − | 2.04411i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −330.598 | − | 572.613i | −1.05965 | − | 1.83537i | ||||
\(47\) | 125.347 | − | 217.108i | 0.389016 | − | 0.673796i | −0.603301 | − | 0.797513i | \(-0.706148\pi\) |
0.992317 | + | 0.123717i | \(0.0394816\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −72.2716 | −0.204415 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 369.722 | + | 640.377i | 0.985984 | + | 1.70777i | ||||
\(53\) | −268.450 | − | 464.969i | −0.695745 | − | 1.20507i | −0.969929 | − | 0.243388i | \(-0.921741\pi\) |
0.274184 | − | 0.961677i | \(-0.411592\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 366.598 | 0.898765 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −93.3713 | + | 161.724i | −0.211384 | + | 0.366127i | ||||
\(59\) | −17.9452 | − | 31.0820i | −0.0395977 | − | 0.0685853i | 0.845547 | − | 0.533900i | \(-0.179274\pi\) |
−0.885145 | + | 0.465315i | \(0.845941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.8970 | + | 50.0511i | −0.0606538 | + | 0.105056i | −0.894758 | − | 0.446552i | \(-0.852652\pi\) |
0.834104 | + | 0.551607i | \(0.185985\pi\) | |||||||
\(62\) | 1539.19 | 3.15286 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 746.423 | 1.45786 | ||||||||
\(65\) | −196.749 | + | 340.780i | −0.375442 | + | 0.650285i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −240.846 | − | 417.157i | −0.439164 | − | 0.760654i | 0.558462 | − | 0.829530i | \(-0.311392\pi\) |
−0.997625 | + | 0.0688767i | \(0.978059\pi\) | |||||||
\(68\) | −104.574 | + | 181.127i | −0.186492 | + | 0.323013i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −363.752 | −0.608021 | −0.304010 | − | 0.952669i | \(-0.598326\pi\) | ||||
−0.304010 | + | 0.952669i | \(0.598326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −290.650 | − | 503.420i | −0.465999 | − | 0.807135i | 0.533247 | − | 0.845960i | \(-0.320972\pi\) |
−0.999246 | + | 0.0388253i | \(0.987638\pi\) | |||||||
\(74\) | 685.468 | + | 1187.26i | 1.07681 | + | 1.86509i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1161.69 | −1.75336 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 346.846 | − | 600.754i | 0.493964 | − | 0.855571i | −0.506012 | − | 0.862527i | \(-0.668881\pi\) |
0.999976 | + | 0.00695559i | \(0.00221405\pi\) | |||||||
\(80\) | 898.966 | + | 1557.05i | 1.25634 | + | 2.17605i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −892.114 | + | 1545.19i | −1.20143 | + | 2.08094i | ||||
\(83\) | −1334.39 | −1.76468 | −0.882341 | − | 0.470611i | \(-0.844033\pi\) | ||||
−0.882341 | + | 0.470611i | \(0.844033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −111.299 | −0.142024 | ||||||||
\(86\) | −17.9452 | + | 31.0820i | −0.0225009 | + | 0.0389728i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1083.73 | + | 1877.08i | 1.31280 | + | 2.27383i | ||||
\(89\) | −176.519 | + | 305.740i | −0.210236 | + | 0.364139i | −0.951788 | − | 0.306756i | \(-0.900757\pi\) |
0.741552 | + | 0.670895i | \(0.234090\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2484.98 | 2.81605 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 661.196 | + | 1145.23i | 0.725502 | + | 1.25661i | ||||
\(95\) | −309.100 | − | 535.376i | −0.333821 | − | 0.578194i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1445.88 | 1.51347 | 0.756735 | − | 0.653722i | \(-0.226793\pi\) | ||||
0.756735 | + | 0.653722i | \(0.226793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 135.809 | − | 235.229i | 0.135809 | − | 0.235229i | ||||
\(101\) | 237.426 | + | 411.234i | 0.233909 | + | 0.405142i | 0.958955 | − | 0.283558i | \(-0.0915150\pi\) |
−0.725046 | + | 0.688700i | \(0.758182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 999.794 | − | 1731.69i | 0.956433 | − | 1.65659i | 0.225380 | − | 0.974271i | \(-0.427638\pi\) |
0.731053 | − | 0.682320i | \(-0.239029\pi\) | |||||||
\(104\) | −2326.51 | −2.19359 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2832.10 | 2.59508 | ||||||||
\(107\) | 583.368 | − | 1010.42i | 0.527068 | − | 0.912909i | −0.472434 | − | 0.881366i | \(-0.656625\pi\) |
0.999502 | − | 0.0315431i | \(-0.0100421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 668.588 | + | 1158.03i | 0.587515 | + | 1.01761i | 0.994557 | + | 0.104196i | \(0.0332270\pi\) |
−0.407042 | + | 0.913410i | \(0.633440\pi\) | |||||||
\(110\) | −966.887 | + | 1674.70i | −0.838082 | + | 1.45160i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −906.578 | −0.754723 | −0.377361 | − | 0.926066i | \(-0.623169\pi\) | ||||
−0.377361 | + | 0.926066i | \(0.623169\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 661.196 | + | 1145.23i | 0.536146 | + | 0.928633i | ||||
\(116\) | −350.918 | − | 607.807i | −0.280878 | − | 0.486496i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 189.319 | 0.147697 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 61.7475 | − | 106.950i | 0.0463918 | − | 0.0803530i | ||||
\(122\) | −152.429 | − | 264.015i | −0.113117 | − | 0.195925i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2892.37 | + | 5009.74i | −2.09470 | + | 3.62813i | ||||
\(125\) | 1463.27 | 1.04703 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1714.89 | −1.19820 | −0.599101 | − | 0.800674i | \(-0.704475\pi\) | ||||
−0.599101 | + | 0.800674i | \(0.704475\pi\) | |||||||
\(128\) | −368.782 | + | 638.749i | −0.254656 | + | 0.441078i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1037.84 | − | 1797.58i | −0.700186 | − | 1.21276i | ||||
\(131\) | 235.306 | − | 407.561i | 0.156937 | − | 0.271823i | −0.776826 | − | 0.629716i | \(-0.783171\pi\) |
0.933763 | + | 0.357893i | \(0.116505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2540.88 | 1.63805 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −329.021 | − | 569.881i | −0.207451 | − | 0.359315i | ||||
\(137\) | −221.955 | − | 384.438i | −0.138415 | − | 0.239742i | 0.788482 | − | 0.615058i | \(-0.210868\pi\) |
−0.926897 | + | 0.375316i | \(0.877534\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1669.98 | 1.01904 | 0.509518 | − | 0.860460i | \(-0.329824\pi\) | ||||
0.509518 | + | 0.860460i | \(0.329824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 959.382 | − | 1661.70i | 0.566969 | − | 0.982019i | ||||
\(143\) | −648.055 | − | 1122.46i | −0.378972 | − | 0.656400i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 186.743 | − | 323.448i | 0.106953 | − | 0.185247i | ||||
\(146\) | 3066.30 | 1.73814 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5152.39 | −2.86165 | ||||||||
\(149\) | 371.935 | − | 644.211i | 0.204497 | − | 0.354200i | −0.745475 | − | 0.666534i | \(-0.767777\pi\) |
0.949973 | + | 0.312334i | \(0.101111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −303.382 | − | 525.473i | −0.163503 | − | 0.283195i | 0.772620 | − | 0.634869i | \(-0.218946\pi\) |
−0.936123 | + | 0.351674i | \(0.885613\pi\) | |||||||
\(152\) | 1827.51 | − | 3165.35i | 0.975203 | − | 1.68910i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3078.38 | −1.59523 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1557.39 | − | 2697.48i | −0.791678 | − | 1.37123i | −0.924927 | − | 0.380144i | \(-0.875875\pi\) |
0.133250 | − | 0.991083i | \(-0.457459\pi\) | |||||||
\(158\) | 1829.58 | + | 3168.93i | 0.921226 | + | 1.59561i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4219.61 | −2.08493 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1206.54 | + | 2089.78i | −0.579774 | + | 1.00420i | 0.415730 | + | 0.909488i | \(0.363526\pi\) |
−0.995505 | + | 0.0947109i | \(0.969807\pi\) | |||||||
\(164\) | −3352.84 | − | 5807.28i | −1.59642 | − | 2.76508i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3519.40 | − | 6095.79i | 1.64553 | − | 2.85015i | ||||
\(167\) | 610.475 | 0.282874 | 0.141437 | − | 0.989947i | \(-0.454828\pi\) | ||||
0.141437 | + | 0.989947i | \(0.454828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −805.784 | −0.366766 | ||||||||
\(170\) | 293.547 | − | 508.437i | 0.132435 | − | 0.229385i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −67.4435 | − | 116.816i | −0.0298984 | − | 0.0517855i | ||||
\(173\) | 1896.90 | − | 3285.54i | 0.833636 | − | 1.44390i | −0.0615006 | − | 0.998107i | \(-0.519589\pi\) |
0.895136 | − | 0.445792i | \(-0.147078\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5922.05 | −2.53631 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −931.124 | − | 1612.75i | −0.392082 | − | 0.679107i | ||||
\(179\) | −1402.34 | − | 2428.92i | −0.585562 | − | 1.01422i | −0.994805 | − | 0.101798i | \(-0.967540\pi\) |
0.409243 | − | 0.912426i | \(-0.365793\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3106.04 | 1.27553 | 0.637763 | − | 0.770232i | \(-0.279860\pi\) | ||||
0.637763 | + | 0.770232i | \(0.279860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3909.24 | + | 6771.00i | −1.56627 | + | 2.71285i | ||||
\(185\) | −1370.94 | − | 2374.53i | −0.544828 | − | 0.943670i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 183.299 | − | 317.483i | 0.0716800 | − | 0.124153i | ||||
\(188\) | −4969.95 | −1.92804 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3260.95 | 1.24513 | ||||||||
\(191\) | 130.976 | − | 226.857i | 0.0496182 | − | 0.0859413i | −0.840150 | − | 0.542355i | \(-0.817533\pi\) |
0.889768 | + | 0.456413i | \(0.150866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2025.54 | − | 3508.33i | −0.755447 | − | 1.30847i | −0.945152 | − | 0.326632i | \(-0.894086\pi\) |
0.189704 | − | 0.981841i | \(-0.439247\pi\) | |||||||
\(194\) | −3813.44 | + | 6605.07i | −1.41128 | + | 2.44442i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2874.83 | 1.03971 | 0.519855 | − | 0.854254i | \(-0.325986\pi\) | ||||
0.519855 | + | 0.854254i | \(0.325986\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1533.49 | + | 2656.07i | 0.546261 | + | 0.946151i | 0.998526 | + | 0.0542680i | \(0.0172825\pi\) |
−0.452266 | + | 0.891883i | \(0.649384\pi\) | |||||||
\(200\) | 427.297 | + | 740.100i | 0.151072 | + | 0.261665i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2504.81 | −0.872463 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1784.23 | − | 3090.37i | 0.607882 | − | 1.05288i | ||||
\(206\) | 5273.83 | + | 9134.54i | 1.78371 | + | 3.08948i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3178.30 | − | 5504.98i | 1.05950 | − | 1.83510i | ||||
\(209\) | 2036.23 | 0.673919 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 595.422 | 0.194268 | 0.0971340 | − | 0.995271i | \(-0.469032\pi\) | ||||
0.0971340 | + | 0.995271i | \(0.469032\pi\) | |||||||
\(212\) | −5321.96 | + | 9217.90i | −1.72412 | + | 2.98626i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3077.22 | + | 5329.90i | 0.982964 | + | 1.70254i | ||||
\(215\) | 35.8904 | − | 62.1640i | 0.0113847 | − | 0.0197188i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7053.49 | −2.19139 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3633.86 | − | 6294.03i | −1.11361 | − | 1.92883i | ||||
\(221\) | 196.749 | + | 340.780i | 0.0598859 | + | 0.103725i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3779.79 | −1.13504 | −0.567520 | − | 0.823360i | \(-0.692097\pi\) | ||||
−0.567520 | + | 0.823360i | \(0.692097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2391.06 | − | 4141.44i | 0.703766 | − | 1.21896i | ||||
\(227\) | 913.809 | + | 1582.76i | 0.267188 | + | 0.462783i | 0.968135 | − | 0.250431i | \(-0.0805722\pi\) |
−0.700947 | + | 0.713214i | \(0.747239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 425.125 | − | 736.338i | 0.122677 | − | 0.212483i | −0.798146 | − | 0.602465i | \(-0.794185\pi\) |
0.920823 | + | 0.389982i | \(0.127519\pi\) | |||||||
\(230\) | −6975.51 | −1.99979 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2208.18 | 0.624890 | ||||||||
\(233\) | −3295.55 | + | 5708.06i | −0.926604 | + | 1.60492i | −0.137642 | + | 0.990482i | \(0.543952\pi\) |
−0.788962 | + | 0.614443i | \(0.789381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1322.39 | − | 2290.45i | −0.367078 | − | 0.635798i | ||||
\(236\) | −355.759 | + | 616.193i | −0.0981269 | + | 0.169961i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 182.556 | 0.0494083 | 0.0247042 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247042 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −761.949 | − | 1319.73i | −0.203657 | − | 0.352745i | 0.746047 | − | 0.665894i | \(-0.231950\pi\) |
−0.949704 | + | 0.313149i | \(0.898616\pi\) | |||||||
\(242\) | 325.713 | + | 564.152i | 0.0865191 | + | 0.149856i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1145.75 | 0.300612 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1092.82 | + | 1892.83i | −0.281517 | + | 0.487602i | ||||
\(248\) | −9100.27 | − | 15762.1i | −2.33011 | − | 4.03587i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3859.32 | + | 6684.54i | −0.976339 | + | 1.69107i | ||||
\(251\) | −2357.73 | −0.592903 | −0.296451 | − | 0.955048i | \(-0.595803\pi\) | ||||
−0.296451 | + | 0.955048i | \(0.595803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4355.71 | −1.08238 | ||||||||
\(254\) | 4522.94 | − | 7833.97i | 1.11730 | − | 1.93522i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1040.40 | + | 1802.02i | 0.254003 | + | 0.439946i | ||||
\(257\) | 1391.27 | − | 2409.76i | 0.337686 | − | 0.584890i | −0.646311 | − | 0.763074i | \(-0.723689\pi\) |
0.983997 | + | 0.178185i | \(0.0570224\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7801.01 | 1.86076 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1241.22 | + | 2149.85i | 0.292682 | + | 0.506940i | ||||
\(263\) | 1021.89 | + | 1769.97i | 0.239591 | + | 0.414984i | 0.960597 | − | 0.277945i | \(-0.0896532\pi\) |
−0.721006 | + | 0.692929i | \(0.756320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5664.21 | −1.31302 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4774.70 | + | 8270.03i | −1.08829 | + | 1.88497i | ||||
\(269\) | 1726.42 | + | 2990.24i | 0.391307 | + | 0.677763i | 0.992622 | − | 0.121248i | \(-0.0386898\pi\) |
−0.601315 | + | 0.799012i | \(0.705356\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1322.15 | + | 2290.02i | −0.296364 | + | 0.513318i | −0.975301 | − | 0.220879i | \(-0.929108\pi\) |
0.678937 | + | 0.734196i | \(0.262441\pi\) | |||||||
\(272\) | 1797.93 | 0.400793 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2341.59 | 0.516280 | ||||||||
\(275\) | −238.049 | + | 412.313i | −0.0521996 | + | 0.0904124i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1339.74 | − | 2320.50i | −0.290604 | − | 0.503341i | 0.683349 | − | 0.730092i | \(-0.260523\pi\) |
−0.973953 | + | 0.226751i | \(0.927190\pi\) | |||||||
\(278\) | −4404.50 | + | 7628.82i | −0.950232 | + | 1.64585i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1019.69 | 0.216476 | 0.108238 | − | 0.994125i | \(-0.465479\pi\) | ||||
0.108238 | + | 0.994125i | \(0.465479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −216.103 | − | 374.301i | −0.0453922 | − | 0.0786216i | 0.842437 | − | 0.538795i | \(-0.181120\pi\) |
−0.887829 | + | 0.460174i | \(0.847787\pi\) | |||||||
\(284\) | 3605.65 | + | 6245.17i | 0.753366 | + | 1.30487i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6836.87 | 1.41354 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2400.85 | − | 4158.40i | 0.488673 | − | 0.846406i | ||||
\(290\) | 985.051 | + | 1706.16i | 0.199463 | + | 0.345480i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5762.05 | + | 9980.17i | −1.15479 | + | 2.00016i | ||||
\(293\) | 2245.92 | 0.447809 | 0.223904 | − | 0.974611i | \(-0.428120\pi\) | ||||
0.223904 | + | 0.974611i | \(0.428120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −378.638 | −0.0747293 | ||||||||
\(296\) | 8105.48 | − | 14039.1i | 1.59163 | − | 2.75678i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1961.93 | + | 3398.16i | 0.381381 | + | 0.660571i | ||||
\(299\) | 2337.66 | − | 4048.95i | 0.452142 | − | 0.783133i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3200.63 | 0.609853 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4993.22 | + | 8648.51i | 0.942042 | + | 1.63166i | ||||
\(305\) | 304.859 | + | 528.031i | 0.0572333 | + | 0.0991310i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3197.08 | −0.594354 | −0.297177 | − | 0.954822i | \(-0.596045\pi\) | ||||
−0.297177 | + | 0.954822i | \(0.596045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8119.10 | − | 14062.7i | 1.48753 | − | 2.57647i | ||||
\(311\) | −1677.80 | − | 2906.04i | −0.305915 | − | 0.529860i | 0.671550 | − | 0.740959i | \(-0.265629\pi\) |
−0.977465 | + | 0.211100i | \(0.932296\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1128.20 | − | 1954.09i | 0.203736 | − | 0.352881i | −0.745993 | − | 0.665954i | \(-0.768025\pi\) |
0.949729 | + | 0.313072i | \(0.101358\pi\) | |||||||
\(314\) | 16430.2 | 2.95290 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13752.3 | −2.44818 | ||||||||
\(317\) | −3069.59 | + | 5316.69i | −0.543866 | + | 0.942004i | 0.454811 | + | 0.890588i | \(0.349707\pi\) |
−0.998677 | + | 0.0514158i | \(0.983627\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 615.095 | + | 1065.38i | 0.107958 | + | 0.186989i | ||||
\(320\) | 3937.32 | − | 6819.64i | 0.687821 | − | 1.19134i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −618.199 | −0.106494 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −255.517 | − | 442.568i | −0.0436108 | − | 0.0755362i | ||||
\(326\) | −6364.38 | − | 11023.4i | −1.08126 | − | 1.87280i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 21098.0 | 3.55166 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3514.91 | + | 6088.00i | −0.583676 | + | 1.01096i | 0.411363 | + | 0.911472i | \(0.365053\pi\) |
−0.995039 | + | 0.0994849i | \(0.968280\pi\) | |||||||
\(332\) | 13227.0 | + | 22909.8i | 2.18652 | + | 3.78717i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1610.10 | + | 2788.78i | −0.263775 | + | 0.456872i | ||||
\(335\) | −5081.76 | −0.828795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10328.4 | 1.66951 | 0.834757 | − | 0.550619i | \(-0.185608\pi\) | ||||
0.834757 | + | 0.550619i | \(0.185608\pi\) | |||||||
\(338\) | 2125.22 | − | 3680.99i | 0.342003 | − | 0.592366i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1103.24 | + | 1910.86i | 0.175975 | + | 0.304797i | ||||
\(341\) | 5069.80 | − | 8781.15i | 0.805118 | − | 1.39450i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 424.395 | 0.0665170 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10006.0 | + | 17330.9i | 1.55470 | + | 2.69282i | ||||
\(347\) | 983.768 | + | 1703.94i | 0.152194 | + | 0.263608i | 0.932034 | − | 0.362371i | \(-0.118033\pi\) |
−0.779840 | + | 0.625980i | \(0.784699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4365.46 | −0.669564 | −0.334782 | − | 0.942296i | \(-0.608663\pi\) | ||||
−0.334782 | + | 0.942296i | \(0.608663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6949.30 | − | 12036.5i | 1.05227 | − | 1.82258i | ||||
\(353\) | −3035.79 | − | 5258.15i | −0.457731 | − | 0.792813i | 0.541110 | − | 0.840952i | \(-0.318004\pi\) |
−0.998841 | + | 0.0481389i | \(0.984671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1918.76 | + | 3323.40i | −0.286866 | + | 0.496866i | ||||
\(356\) | 6998.90 | 1.04197 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14794.4 | 2.18411 | ||||||||
\(359\) | 4819.02 | − | 8346.79i | 0.708463 | − | 1.22709i | −0.256965 | − | 0.966421i | \(-0.582722\pi\) |
0.965427 | − | 0.260673i | \(-0.0839443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1712.64 | + | 2966.37i | 0.249692 | + | 0.432479i | ||||
\(362\) | −8192.06 | + | 14189.1i | −1.18941 | + | 2.06011i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6132.61 | −0.879439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −261.362 | − | 452.693i | −0.0371744 | − | 0.0643879i | 0.846840 | − | 0.531848i | \(-0.178502\pi\) |
−0.884014 | + | 0.467460i | \(0.845169\pi\) | |||||||
\(368\) | −10681.0 | − | 18500.0i | −1.51301 | − | 2.62060i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14463.1 | 2.03217 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1614.92 | + | 2797.12i | −0.224175 | + | 0.388283i | −0.956072 | − | 0.293133i | \(-0.905302\pi\) |
0.731896 | + | 0.681416i | \(0.238636\pi\) | |||||||
\(374\) | 966.887 | + | 1674.70i | 0.133681 | + | 0.231542i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7818.48 | − | 13542.0i | 1.07236 | − | 1.85738i | ||||
\(377\) | −1320.46 | −0.180390 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6639.71 | 0.899892 | 0.449946 | − | 0.893056i | \(-0.351443\pi\) | ||||
0.449946 | + | 0.893056i | \(0.351443\pi\) | |||||||
\(380\) | −6127.82 | + | 10613.7i | −0.827239 | + | 1.43282i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 690.887 | + | 1196.65i | 0.0925363 | + | 0.160278i | ||||
\(383\) | −7112.22 | + | 12318.7i | −0.948871 | + | 1.64349i | −0.201063 | + | 0.979578i | \(0.564439\pi\) |
−0.747809 | + | 0.663914i | \(0.768894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21369.1 | 2.81777 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14332.1 | − | 24823.9i | −1.87526 | − | 3.24805i | ||||
\(389\) | 1460.91 | + | 2530.37i | 0.190414 | + | 0.329807i | 0.945388 | − | 0.325948i | \(-0.105684\pi\) |
−0.754973 | + | 0.655755i | \(0.772350\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1322.39 | 0.171039 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7582.24 | + | 13132.8i | −0.969512 | + | 1.67924i | ||||
\(395\) | −3659.16 | − | 6337.86i | −0.466108 | − | 0.807322i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −405.970 | + | 703.161i | −0.0513226 | + | 0.0888933i | −0.890545 | − | 0.454894i | \(-0.849677\pi\) |
0.839223 | + | 0.543788i | \(0.183010\pi\) | |||||||
\(398\) | −16178.0 | −2.03751 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2334.96 | −0.291870 | ||||||||
\(401\) | 1169.32 | − | 2025.32i | 0.145618 | − | 0.252218i | −0.783985 | − | 0.620780i | \(-0.786816\pi\) |
0.929603 | + | 0.368561i | \(0.120150\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5441.81 | + | 9425.50i | 0.672645 | + | 1.16506i | ||||
\(404\) | 4706.91 | − | 8152.61i | 0.579648 | − | 1.00398i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9031.21 | 1.09990 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1363.79 | + | 2362.15i | 0.164877 | + | 0.285576i | 0.936612 | − | 0.350369i | \(-0.113944\pi\) |
−0.771734 | + | 0.635945i | \(0.780610\pi\) | |||||||
\(410\) | 9411.65 | + | 16301.5i | 1.13368 | + | 1.96359i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −39641.3 | −4.74026 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7038.81 | + | 12191.6i | −0.832582 | + | 1.44207i | ||||
\(416\) | 7459.23 | + | 12919.8i | 0.879132 | + | 1.52270i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5370.48 | + | 9301.94i | −0.628418 | + | 1.08845i | ||||
\(419\) | −13306.3 | −1.55144 | −0.775721 | − | 0.631076i | \(-0.782614\pi\) | ||||
−0.775721 | + | 0.631076i | \(0.782614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11007.5 | −1.27428 | −0.637138 | − | 0.770750i | \(-0.719882\pi\) | ||||
−0.637138 | + | 0.770750i | \(0.719882\pi\) | |||||||
\(422\) | −1570.40 | + | 2720.01i | −0.181151 | + | 0.313763i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16744.5 | − | 29002.3i | −1.91789 | − | 3.32187i | ||||
\(425\) | 72.2716 | − | 125.178i | 0.00824868 | − | 0.0142871i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −23130.2 | −2.61225 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 189.319 | + | 327.910i | 0.0212320 | + | 0.0367749i | ||||
\(431\) | −3262.81 | − | 5651.36i | −0.364650 | − | 0.631592i | 0.624070 | − | 0.781368i | \(-0.285478\pi\) |
−0.988720 | + | 0.149776i | \(0.952145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11716.3 | −1.30034 | −0.650171 | − | 0.759788i | \(-0.725303\pi\) | ||||
−0.650171 | + | 0.759788i | \(0.725303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13254.6 | − | 22957.6i | 1.45592 | − | 2.52172i | ||||
\(437\) | 3672.55 | + | 6361.04i | 0.402018 | + | 0.696315i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7305.69 | − | 12653.8i | 0.794264 | − | 1.37571i | −0.129042 | − | 0.991639i | \(-0.541190\pi\) |
0.923306 | − | 0.384066i | \(-0.125476\pi\) | |||||||
\(440\) | 22866.4 | 2.47753 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2075.67 | −0.223370 | ||||||||
\(443\) | −7619.89 | + | 13198.0i | −0.817228 | + | 1.41548i | 0.0904888 | + | 0.995897i | \(0.471157\pi\) |
−0.907717 | + | 0.419583i | \(0.862176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1862.25 | + | 3225.51i | 0.198380 | + | 0.343604i | ||||
\(446\) | 9969.05 | − | 17266.9i | 1.05840 | − | 1.83321i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10678.8 | −1.12241 | −0.561206 | − | 0.827676i | \(-0.689662\pi\) | ||||
−0.561206 | + | 0.827676i | \(0.689662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5876.91 | + | 10179.1i | 0.613598 | + | 1.06278i | ||||
\(452\) | 8986.34 | + | 15564.8i | 0.935137 | + | 1.61971i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9640.53 | −0.996592 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2114.12 | + | 3661.76i | −0.216399 | + | 0.374814i | −0.953704 | − | 0.300746i | \(-0.902764\pi\) |
0.737306 | + | 0.675559i | \(0.236098\pi\) | |||||||
\(458\) | 2242.50 | + | 3884.12i | 0.228788 | + | 0.396273i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13108.0 | − | 22703.8i | 1.32862 | − | 2.30124i | ||||
\(461\) | −910.121 | −0.0919492 | −0.0459746 | − | 0.998943i | \(-0.514639\pi\) | ||||
−0.0459746 | + | 0.998943i | \(0.514639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4456.16 | 0.447290 | 0.223645 | − | 0.974671i | \(-0.428204\pi\) | ||||
0.223645 | + | 0.974671i | \(0.428204\pi\) | |||||||
\(464\) | −3016.65 | + | 5224.99i | −0.301820 | + | 0.522768i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17383.8 | − | 30109.5i | −1.72808 | − | 2.99313i | ||||
\(467\) | −2214.71 | + | 3835.99i | −0.219453 | + | 0.380104i | −0.954641 | − | 0.297759i | \(-0.903761\pi\) |
0.735188 | + | 0.677864i | \(0.237094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13951.0 | 1.36918 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1119.32 | − | 1938.73i | −0.109155 | − | 0.189062i | ||||
\(473\) | 118.216 | + | 204.757i | 0.0114917 | + | 0.0199043i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 802.851 | 0.0775523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −481.485 | + | 833.957i | −0.0460724 | + | 0.0797998i | ||||
\(479\) | 1376.43 | + | 2384.04i | 0.131296 | + | 0.227411i | 0.924176 | − | 0.381966i | \(-0.124753\pi\) |
−0.792881 | + | 0.609377i | \(0.791420\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4846.95 | + | 8395.16i | −0.459463 | + | 0.795814i | ||||
\(482\) | 8038.43 | 0.759628 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2448.26 | −0.229927 | ||||||||
\(485\) | 7626.88 | − | 13210.1i | 0.714060 | − | 1.23679i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 335.299 | + | 580.755i | 0.0311989 | + | 0.0540380i | 0.881203 | − | 0.472738i | \(-0.156734\pi\) |
−0.850004 | + | 0.526776i | \(0.823401\pi\) | |||||||
\(488\) | −1802.44 | + | 3121.92i | −0.167198 | + | 0.289595i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8244.70 | 0.757797 | 0.378898 | − | 0.925438i | \(-0.376303\pi\) | ||||
0.378898 | + | 0.925438i | \(0.376303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −186.743 | − | 323.448i | −0.0170598 | − | 0.0295484i | ||||
\(494\) | −5764.56 | − | 9984.50i | −0.525019 | − | 0.909360i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 49728.3 | 4.50175 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4082.46 | + | 7071.02i | −0.366244 | + | 0.634353i | −0.988975 | − | 0.148083i | \(-0.952690\pi\) |
0.622731 | + | 0.782436i | \(0.286023\pi\) | |||||||
\(500\) | −14504.5 | − | 25122.5i | −1.29732 | − | 2.24703i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6218.42 | − | 10770.6i | 0.552872 | − | 0.957602i | ||||
\(503\) | −8175.59 | −0.724715 | −0.362357 | − | 0.932039i | \(-0.618028\pi\) | ||||
−0.362357 | + | 0.932039i | \(0.618028\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5009.61 | 0.441435 | ||||||||
\(506\) | 11488.0 | − | 19897.8i | 1.00930 | − | 1.74815i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16998.6 | + | 29442.4i | 1.48463 | + | 2.57145i | ||||
\(509\) | −439.224 | + | 760.758i | −0.0382480 | + | 0.0662475i | −0.884516 | − | 0.466510i | \(-0.845511\pi\) |
0.846268 | + | 0.532758i | \(0.178844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16876.5 | −1.45673 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7338.86 | + | 12711.3i | 0.629773 | + | 1.09080i | ||||
\(515\) | −10547.7 | − | 18269.1i | −0.902496 | − | 1.56317i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8711.42 | 0.741060 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12272.1 | + | 21256.0i | −1.03494 | + | 1.79257i | ||||
\(521\) | 5856.30 | + | 10143.4i | 0.492455 | + | 0.852957i | 0.999962 | − | 0.00869048i | \(-0.00276630\pi\) |
−0.507507 | + | 0.861647i | \(0.669433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3670.91 | − | 6358.20i | 0.306917 | − | 0.531596i | −0.670769 | − | 0.741666i | \(-0.734036\pi\) |
0.977686 | + | 0.210070i | \(0.0673692\pi\) | |||||||
\(524\) | −9329.75 | −0.777809 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10780.8 | −0.893659 | ||||||||
\(527\) | −1539.19 | + | 2665.95i | −0.127226 | + | 0.220362i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1772.46 | − | 3069.99i | −0.145678 | − | 0.252321i | ||||
\(530\) | 14939.1 | − | 25875.3i | 1.22437 | − | 2.12066i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12616.3 | −1.02528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6154.44 | − | 10659.8i | −0.497345 | − | 0.861426i | ||||
\(536\) | −15022.6 | − | 26020.0i | −1.21060 | − | 2.09681i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18213.4 | −1.45955 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7934.36 | − | 13742.7i | 0.630545 | − | 1.09214i | −0.356895 | − | 0.934144i | \(-0.616165\pi\) |
0.987440 | − | 0.157992i | \(-0.0505020\pi\) | |||||||
\(542\) | −6974.21 | − | 12079.7i | −0.552709 | − | 0.957319i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2109.80 | + | 3654.29i | −0.166282 | + | 0.288008i | ||||
\(545\) | 14107.0 | 1.10877 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2315.26 | 0.180975 | 0.0904875 | − | 0.995898i | \(-0.471157\pi\) | ||||
0.0904875 | + | 0.995898i | \(0.471157\pi\) | |||||||
\(548\) | −4400.21 | + | 7621.38i | −0.343006 | + | 0.594104i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1255.69 | − | 2174.92i | −0.0973505 | − | 0.168616i | ||||
\(551\) | 1037.24 | − | 1796.56i | 0.0801961 | − | 0.138904i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14134.1 | 1.08393 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16553.5 | − | 28671.5i | −1.26263 | − | 2.18694i | ||||
\(557\) | −2409.52 | − | 4173.42i | −0.183294 | − | 0.317475i | 0.759706 | − | 0.650266i | \(-0.225343\pi\) |
−0.943000 | + | 0.332792i | \(0.892009\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −253.781 | −0.0192018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2689.39 | + | 4658.17i | −0.201860 | + | 0.349631i | ||||
\(563\) | 1270.43 | + | 2200.45i | 0.0951017 | + | 0.164721i | 0.909651 | − | 0.415373i | \(-0.136349\pi\) |
−0.814549 | + | 0.580094i | \(0.803016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4782.12 | + | 8282.88i | −0.356081 | + | 0.616750i | ||||
\(566\) | 2279.85 | 0.169310 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22688.9 | −1.67607 | ||||||||
\(569\) | −12110.0 | + | 20975.1i | −0.892227 | + | 1.54538i | −0.0550275 | + | 0.998485i | \(0.517525\pi\) |
−0.837200 | + | 0.546898i | \(0.815809\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5886.04 | + | 10194.9i | 0.431389 | + | 0.747188i | 0.996993 | − | 0.0774891i | \(-0.0246903\pi\) |
−0.565604 | + | 0.824677i | \(0.691357\pi\) | |||||||
\(572\) | −12847.5 | + | 22252.6i | −0.939129 | + | 1.62662i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1717.38 | −0.124556 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5292.13 | − | 9166.24i | −0.381827 | − | 0.661344i | 0.609496 | − | 0.792789i | \(-0.291372\pi\) |
−0.991324 | + | 0.131445i | \(0.958038\pi\) | |||||||
\(578\) | 12664.3 | + | 21935.2i | 0.911358 | + | 1.57852i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7404.25 | −0.530077 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9328.42 | − | 16157.3i | 0.662682 | − | 1.14780i | ||||
\(584\) | −18129.1 | − | 31400.6i | −1.28457 | − | 2.22494i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5923.52 | + | 10259.8i | −0.417574 | + | 0.723259i | ||||
\(587\) | 8712.63 | 0.612621 | 0.306311 | − | 0.951932i | \(-0.400905\pi\) | ||||
0.306311 | + | 0.951932i | \(0.400905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17098.6 | −1.19615 | ||||||||
\(590\) | 998.641 | − | 1729.70i | 0.0696838 | − | 0.120696i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22146.2 | + | 38358.3i | 1.53750 | + | 2.66304i | ||||
\(593\) | −7681.43 | + | 13304.6i | −0.531937 | + | 0.921341i | 0.467368 | + | 0.884063i | \(0.345202\pi\) |
−0.999305 | + | 0.0372786i | \(0.988131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14747.0 | −1.01353 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12331.0 | + | 21357.9i | 0.843229 | + | 1.46052i | ||||
\(599\) | 13001.9 | + | 22519.9i | 0.886883 | + | 1.53613i | 0.843540 | + | 0.537066i | \(0.180467\pi\) |
0.0433430 | + | 0.999060i | \(0.486199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20567.7 | 1.39596 | 0.697982 | − | 0.716115i | \(-0.254082\pi\) | ||||
0.697982 | + | 0.716115i | \(0.254082\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6014.48 | + | 10417.4i | −0.405175 | + | 0.701783i | ||||
\(605\) | −651.426 | − | 1128.30i | −0.0437756 | − | 0.0758216i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9821.04 | + | 17010.5i | −0.656711 | + | 1.13746i | 0.324751 | + | 0.945800i | \(0.394720\pi\) |
−0.981462 | + | 0.191657i | \(0.938614\pi\) | |||||||
\(608\) | −23437.4 | −1.56334 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3216.21 | −0.213476 | ||||||||
\(611\) | −4675.33 | + | 8097.90i | −0.309564 | + | 0.536180i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4227.29 | − | 7321.89i | −0.278530 | − | 0.482428i | 0.692490 | − | 0.721428i | \(-0.256514\pi\) |
−0.971020 | + | 0.239000i | \(0.923180\pi\) | |||||||
\(614\) | 8432.16 | − | 14604.9i | 0.554225 | − | 0.959946i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24168.4 | 1.57696 | 0.788479 | − | 0.615061i | \(-0.210869\pi\) | ||||
0.788479 | + | 0.615061i | \(0.210869\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1018.78 | + | 1764.58i | 0.0661523 | + | 0.114579i | 0.897205 | − | 0.441615i | \(-0.145594\pi\) |
−0.831052 | + | 0.556194i | \(0.812261\pi\) | |||||||
\(620\) | 30514.0 | + | 52851.9i | 1.97657 | + | 3.42352i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17700.5 | 1.14104 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6862.33 | − | 11885.9i | 0.439189 | − | 0.760698i | ||||
\(626\) | 5951.14 | + | 10307.7i | 0.379961 | + | 0.658111i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30874.9 | + | 53476.9i | −1.96185 | + | 3.39803i | ||||
\(629\) | −2741.87 | −0.173808 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12339.5 | 0.778489 | 0.389244 | − | 0.921135i | \(-0.372736\pi\) | ||||
0.389244 | + | 0.921135i | \(0.372736\pi\) | |||||||
\(632\) | 21634.3 | − | 37471.8i | 1.36166 | − | 2.35846i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16191.9 | − | 28045.1i | −1.01429 | − | 1.75680i | ||||
\(635\) | −9045.89 | + | 15667.9i | −0.565315 | + | 0.979154i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6489.15 | −0.402677 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3890.59 | + | 6738.70i | 0.240295 | + | 0.416204i | ||||
\(641\) | −5111.32 | − | 8853.06i | −0.314953 | − | 0.545515i | 0.664474 | − | 0.747311i | \(-0.268655\pi\) |
−0.979428 | + | 0.201796i | \(0.935322\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1211.75 | −0.0743187 | −0.0371594 | − | 0.999309i | \(-0.511831\pi\) | ||||
−0.0371594 | + | 0.999309i | \(0.511831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1630.48 | − | 2824.07i | 0.0993037 | − | 0.171999i | ||||
\(647\) | −1408.61 | − | 2439.78i | −0.0855922 | − | 0.148250i | 0.820051 | − | 0.572290i | \(-0.193945\pi\) |
−0.905643 | + | 0.424040i | \(0.860612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 623.581 | − | 1080.07i | 0.0377160 | − | 0.0653260i | ||||
\(650\) | 2695.66 | 0.162665 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 47838.6 | 2.87347 | ||||||||
\(653\) | 10493.1 | − | 18174.6i | 0.628831 | − | 1.08917i | −0.358956 | − | 0.933355i | \(-0.616867\pi\) |
0.987787 | − | 0.155812i | \(-0.0497995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2482.44 | − | 4299.70i | −0.148087 | − | 0.256494i | ||||
\(656\) | −28822.5 | + | 49922.1i | −1.71544 | + | 2.97124i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2384.09 | 0.140927 | 0.0704635 | − | 0.997514i | \(-0.477552\pi\) | ||||
0.0704635 | + | 0.997514i | \(0.477552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3788.55 | + | 6561.96i | 0.222931 | + | 0.386128i | 0.955697 | − | 0.294353i | \(-0.0951042\pi\) |
−0.732766 | + | 0.680481i | \(0.761771\pi\) | |||||||
\(662\) | −18540.8 | − | 32113.7i | −1.08854 | − | 1.88540i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −83232.2 | −4.86451 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2218.77 | + | 3843.02i | −0.128802 | + | 0.223092i | ||||
\(668\) | −6051.26 | − | 10481.1i | −0.350494 | − | 0.607074i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13402.9 | − | 23214.6i | 0.772837 | − | 1.33859i | ||||
\(671\) | −2008.30 | −0.115543 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11724.6 | 0.671547 | 0.335774 | − | 0.941943i | \(-0.391002\pi\) | ||||
0.335774 | + | 0.941943i | \(0.391002\pi\) | |||||||
\(674\) | −27240.8 | + | 47182.5i | −1.55679 | + | 2.69644i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7987.23 | + | 13834.3i | 0.454440 | + | 0.787113i | ||||
\(677\) | 16152.1 | − | 27976.3i | 0.916952 | − | 1.58821i | 0.112935 | − | 0.993602i | \(-0.463975\pi\) |
0.804018 | − | 0.594606i | \(-0.202692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6942.23 | −0.391503 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26742.8 | + | 46319.9i | 1.50152 | + | 2.60070i | ||||
\(683\) | 16683.6 | + | 28896.8i | 0.934669 | + | 1.61889i | 0.775223 | + | 0.631687i | \(0.217637\pi\) |
0.159446 | + | 0.987207i | \(0.449029\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4683.18 | −0.261219 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −579.776 | + | 1004.20i | −0.0321275 | + | 0.0556465i | ||||
\(689\) | 10012.9 | + | 17342.9i | 0.553646 | + | 0.958943i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 521.837 | − | 903.849i | 0.0287288 | − | 0.0497598i | −0.851304 | − | 0.524674i | \(-0.824187\pi\) |
0.880032 | + | 0.474914i | \(0.157521\pi\) | |||||||
\(692\) | −75211.3 | −4.13166 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10378.6 | −0.567674 | ||||||||
\(695\) | 8809.01 | − | 15257.6i | 0.480784 | − | 0.832742i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1784.23 | − | 3090.37i | −0.0969619 | − | 0.167943i | ||||
\(698\) | 11513.7 | − | 19942.4i | 0.624357 | − | 1.08142i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11305.7 | 0.609143 | 0.304572 | − | 0.952489i | \(-0.401487\pi\) | ||||
0.304572 | + | 0.952489i | \(0.401487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7614.72 | − | 13189.1i | −0.408527 | − | 0.707590i | ||||
\(704\) | 12968.8 | + | 22462.6i | 0.694289 | + | 1.20254i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32027.1 | 1.70730 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6653.38 | − | 11524.0i | 0.352430 | − | 0.610427i | −0.634245 | − | 0.773132i | \(-0.718689\pi\) |
0.986675 | + | 0.162706i | \(0.0520221\pi\) | |||||||
\(710\) | −10121.3 | − | 17530.6i | −0.534995 | − | 0.926639i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11010.3 | + | 19070.4i | −0.579535 | + | 1.00378i | ||||
\(713\) | 36575.6 | 1.92113 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13673.7 | −0.715201 | ||||||||
\(716\) | −27801.0 | + | 48152.8i | −1.45108 | + | 2.51334i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25419.9 | + | 44028.6i | 1.32126 | + | 2.28849i | ||||
\(719\) | 5350.62 | − | 9267.55i | 0.277531 | − | 0.480697i | −0.693240 | − | 0.720707i | \(-0.743817\pi\) |
0.970770 | + | 0.240010i | \(0.0771506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18068.0 | −0.931333 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −30788.3 | − | 53326.8i | −1.58044 | − | 2.73740i | ||||
\(725\) | 242.521 | + | 420.059i | 0.0124235 | + | 0.0215181i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2121.14 | −0.108210 | −0.0541051 | − | 0.998535i | \(-0.517231\pi\) | ||||
−0.0541051 | + | 0.998535i | \(0.517231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16174.5 | − | 28015.1i | 0.820062 | − | 1.42039i | ||||
\(731\) | −35.8904 | − | 62.1640i | −0.00181594 | − | 0.00314531i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10792.0 | − | 18692.3i | 0.543809 | − | 0.941906i | −0.454871 | − | 0.890557i | \(-0.650315\pi\) |
0.998681 | − | 0.0513484i | \(-0.0163519\pi\) | |||||||
\(734\) | 2757.33 | 0.138658 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 50135.0 | 2.51087 | ||||||||
\(737\) | 8369.18 | − | 14495.8i | 0.418294 | − | 0.724507i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4972.61 | + | 8612.81i | 0.247524 | + | 0.428724i | 0.962838 | − | 0.270079i | \(-0.0870497\pi\) |
−0.715314 | + | 0.698803i | \(0.753716\pi\) | |||||||
\(740\) | −27178.5 | + | 47074.5i | −1.35013 | + | 2.33850i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2867.01 | −0.141562 | −0.0707808 | − | 0.997492i | \(-0.522549\pi\) | ||||
−0.0707808 | + | 0.997492i | \(0.522549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3923.86 | − | 6796.32i | −0.192965 | − | 0.334225i | ||||
\(746\) | −8518.57 | − | 14754.6i | −0.418079 | − | 0.724134i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7267.71 | −0.355259 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5412.05 | − | 9373.94i | 0.262967 | − | 0.455473i | −0.704062 | − | 0.710139i | \(-0.748632\pi\) |
0.967029 | + | 0.254666i | \(0.0819655\pi\) | |||||||
\(752\) | 21362.0 | + | 37000.1i | 1.03589 | + | 1.79422i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3482.66 | − | 6032.14i | 0.168211 | − | 0.291349i | ||||
\(755\) | −6401.26 | −0.308564 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14512.0 | −0.696761 | −0.348381 | − | 0.937353i | \(-0.613268\pi\) | ||||
−0.348381 | + | 0.937353i | \(0.613268\pi\) | |||||||
\(758\) | −17512.0 | + | 30331.6i | −0.839134 | + | 1.45342i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19280.0 | − | 33393.9i | −0.920208 | − | 1.59385i | ||||
\(761\) | −16537.9 | + | 28644.5i | −0.787778 | + | 1.36447i | 0.139547 | + | 0.990215i | \(0.455435\pi\) |
−0.927325 | + | 0.374256i | \(0.877898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5193.13 | −0.245917 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37516.4 | − | 64980.3i | −1.76961 | − | 3.06506i | ||||
\(767\) | 669.338 | + | 1159.33i | 0.0315103 | + | 0.0545774i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6728.44 | 0.315518 | 0.157759 | − | 0.987478i | \(-0.449573\pi\) | ||||
0.157759 | + | 0.987478i | \(0.449573\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −40155.8 | + | 69551.8i | −1.87207 | + | 3.24252i | ||||
\(773\) | −12116.6 | − | 20986.6i | −0.563784 | − | 0.976503i | −0.997162 | − | 0.0752907i | \(-0.976012\pi\) |
0.433377 | − | 0.901213i | \(-0.357322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1998.93 | − | 3462.26i | 0.0926501 | − | 0.160475i | ||||
\(776\) | 90186.0 | 4.17202 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15412.4 | −0.710231 | ||||||||
\(779\) | 9910.32 | − | 17165.2i | 0.455807 | − | 0.789481i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6320.05 | − | 10946.6i | −0.289564 | − | 0.501539i | ||||
\(782\) | −3487.75 | + | 6040.97i | −0.159491 | + | 0.276246i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32860.5 | −1.49406 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8600.19 | + | 14896.0i | 0.389535 | + | 0.674694i | 0.992387 | − | 0.123159i | \(-0.0393026\pi\) |
−0.602852 | + | 0.797853i | \(0.705969\pi\) | |||||||
\(788\) | −28496.4 | − | 49357.2i | −1.28825 | − | 2.23131i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 38603.6 | 1.73855 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1077.83 | − | 1866.86i | 0.0482659 | − | 0.0835990i | ||||
\(794\) | −2141.46 | − | 3709.12i | −0.0957148 | − | 0.165783i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30401.0 | − | 52656.0i | 1.35369 | − | 2.34465i | ||||
\(797\) | 4208.87 | 0.187059 | 0.0935295 | − | 0.995617i | \(-0.470185\pi\) | ||||
0.0935295 | + | 0.995617i | \(0.470185\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2644.78 | −0.117104 | ||||||||
\(800\) | 2739.99 | − | 4745.80i | 0.121092 | − | 0.209737i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6168.05 | + | 10683.4i | 0.271573 | + | 0.470378i | ||||
\(803\) | 10099.8 | − | 17493.4i | 0.443855 | − | 0.768779i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −57410.2 | −2.50892 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14809.4 | + | 25650.6i | 0.644791 | + | 1.11681i | ||||
\(809\) | −11816.1 | − | 20466.0i | −0.513511 | − | 0.889428i | −0.999877 | − | 0.0156725i | \(-0.995011\pi\) |
0.486366 | − | 0.873755i | \(-0.338322\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28425.1 | 1.23075 | 0.615377 | − | 0.788233i | \(-0.289004\pi\) | ||||
0.615377 | + | 0.788233i | \(0.289004\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23819.4 | + | 41256.5i | −1.02564 | + | 1.77646i | ||||
\(815\) | 12728.8 | + | 22046.9i | 0.547079 | + | 0.947568i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 199.350 | − | 345.284i | 0.00853655 | − | 0.0147857i | ||||
\(818\) | −14387.7 | −0.614981 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −70743.7 | −3.01278 | ||||||||
\(821\) | 19704.8 | − | 34129.7i | 0.837640 | − | 1.45083i | −0.0542229 | − | 0.998529i | \(-0.517268\pi\) |
0.891863 | − | 0.452306i | \(-0.149399\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8173.28 | − | 14156.5i | −0.346176 | − | 0.599594i | 0.639391 | − | 0.768882i | \(-0.279187\pi\) |
−0.985567 | + | 0.169288i | \(0.945853\pi\) | |||||||
\(824\) | 62361.7 | − | 108014.i | 2.63650 | − | 4.56655i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3738.87 | 0.157211 | 0.0786054 | − | 0.996906i | \(-0.474953\pi\) | ||||
0.0786054 | + | 0.996906i | \(0.474953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22598.1 | + | 39141.1i | 0.946761 | + | 1.63984i | 0.752186 | + | 0.658951i | \(0.228999\pi\) |
0.194575 | + | 0.980888i | \(0.437667\pi\) | |||||||
\(830\) | −37129.1 | − | 64309.5i | −1.55274 | − | 2.68942i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27840.8 | −1.16010 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3220.21 | − | 5577.56i | 0.133461 | − | 0.231161i | ||||
\(836\) | −20183.9 | − | 34959.5i | −0.835018 | − | 1.44629i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35094.8 | − | 60785.9i | 1.44669 | − | 2.50574i | ||||
\(839\) | −15899.7 | −0.654254 | −0.327127 | − | 0.944980i | \(-0.606080\pi\) | ||||
−0.327127 | + | 0.944980i | \(0.606080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23135.7 | −0.948612 | ||||||||
\(842\) | 29031.7 | − | 50284.4i | 1.18824 | − | 2.05809i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5902.05 | − | 10222.6i | −0.240707 | − | 0.416917i | ||||
\(845\) | −4250.44 | + | 7361.99i | −0.173041 | + | 0.299716i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 91500.0 | 3.70534 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 381.227 | + | 660.304i | 0.0153835 | + | 0.0266450i | ||||
\(851\) | 16288.7 | + | 28212.8i | 0.656133 | + | 1.13645i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33926.7 | 1.36182 | 0.680908 | − | 0.732369i | \(-0.261585\pi\) | ||||
0.680908 | + | 0.732369i | \(0.261585\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36387.3 | − | 63024.7i | 1.45291 | − | 2.51652i | ||||
\(857\) | −17716.2 | − | 30685.4i | −0.706154 | − | 1.22310i | −0.966273 | − | 0.257519i | \(-0.917095\pi\) |
0.260119 | − | 0.965577i | \(-0.416238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3390.09 | − | 5871.80i | 0.134655 | − | 0.233229i | −0.790811 | − | 0.612061i | \(-0.790341\pi\) |
0.925465 | + | 0.378832i | \(0.123674\pi\) | |||||||
\(860\) | −1423.04 | −0.0564246 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34422.1 | 1.36012 | ||||||||
\(863\) | −15337.5 | + | 26565.4i | −0.604977 | + | 1.04785i | 0.387078 | + | 0.922047i | \(0.373485\pi\) |
−0.992055 | + | 0.125805i | \(0.959849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20012.0 | − | 34661.9i | −0.786624 | − | 1.36247i | ||||
\(866\) | 30901.2 | − | 53522.5i | 1.21255 | − | 2.10019i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24105.2 | 0.940981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8983.30 | + | 15559.5i | 0.349469 | + | 0.605298i | ||||
\(872\) | 41702.9 | + | 72231.5i | 1.61954 | + | 2.80512i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −38744.8 | −1.49950 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20430.6 | + | 35386.9i | −0.786652 | + | 1.36252i | 0.141355 | + | 0.989959i | \(0.454854\pi\) |
−0.928007 | + | 0.372562i | \(0.878479\pi\) | |||||||
\(878\) | 38536.9 | + | 66747.9i | 1.48127 | + | 2.56564i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −31238.3 | + | 54106.4i | −1.19664 | + | 2.07264i | ||||
\(881\) | 43839.0 | 1.67647 | 0.838236 | − | 0.545308i | \(-0.183587\pi\) | ||||
0.838236 | + | 0.545308i | \(0.183587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44625.1 | 1.70074 | 0.850371 | − | 0.526183i | \(-0.176377\pi\) | ||||
0.850371 | + | 0.526183i | \(0.176377\pi\) | |||||||
\(884\) | 3900.50 | − | 6755.87i | 0.148403 | − | 0.257041i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40194.3 | − | 69618.6i | −1.52410 | − | 2.63982i | ||||
\(887\) | −21983.7 | + | 38076.9i | −0.832178 | + | 1.44137i | 0.0641300 | + | 0.997942i | \(0.479573\pi\) |
−0.896308 | + | 0.443433i | \(0.853761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19646.4 | −0.739943 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 37466.7 | + | 64894.3i | 1.40637 | + | 2.43590i | ||||
\(893\) | −7345.10 | − | 12722.1i | −0.275246 | − | 0.476739i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29588.9 | −1.10508 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28164.9 | − | 48783.0i | 1.04663 | − | 1.81282i | ||||
\(899\) | −5165.04 | − | 8946.12i | −0.191617 | − | 0.331891i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2832.10 | + | 4905.35i | −0.104718 | + | 0.181377i | ||||
\(902\) | −62000.4 | −2.28868 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −56547.4 | −2.08046 | ||||||||
\(905\) | 16384.1 | − | 28378.1i | 0.601797 | − | 1.04234i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6792.15 | + | 11764.3i | 0.248654 | + | 0.430682i | 0.963153 | − | 0.268955i | \(-0.0866783\pi\) |
−0.714498 | + | 0.699637i | \(0.753345\pi\) | |||||||
\(908\) | 18116.0 | − | 31377.9i | 0.662117 | − | 1.14682i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16421.6 | 0.597226 | 0.298613 | − | 0.954374i | \(-0.403476\pi\) | ||||
0.298613 | + | 0.954374i | \(0.403476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23184.5 | − | 40156.7i | −0.840411 | − | 1.45563i | ||||
\(914\) | −11151.8 | − | 19315.5i | −0.403576 | − | 0.699014i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16856.0 | −0.608010 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14743.6 | − | 25536.7i | 0.529214 | − | 0.916625i | −0.470206 | − | 0.882557i | \(-0.655820\pi\) |
0.999420 | − | 0.0340684i | \(-0.0108464\pi\) | |||||||
\(920\) | 41241.8 | + | 71432.9i | 1.47794 | + | 2.55986i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2400.41 | − | 4157.63i | 0.0857410 | − | 0.148508i | ||||
\(923\) | 13567.6 | 0.483839 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3560.85 | 0.126573 | ||||||||
\(926\) | −11752.9 | + | 20356.7i | −0.417090 | + | 0.722422i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7079.85 | − | 12262.7i | −0.250439 | − | 0.433773i | ||||
\(929\) | 1720.93 | − | 2980.73i | 0.0607769 | − | 0.105269i | −0.834036 | − | 0.551710i | \(-0.813976\pi\) |
0.894813 | + | 0.446441i | \(0.147309\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 130667. | 4.59242 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11682.4 | − | 20234.6i | −0.409273 | − | 0.708881i | ||||
\(935\) | −1933.77 | − | 3349.40i | −0.0676376 | − | 0.117152i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5646.60 | 0.196869 | 0.0984346 | − | 0.995144i | \(-0.468616\pi\) | ||||
0.0984346 | + | 0.995144i | \(0.468616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26216.1 | + | 45407.6i | −0.909654 | + | 1.57557i | ||||
\(941\) | −22340.1 | − | 38694.1i | −0.773927 | − | 1.34048i | −0.935396 | − | 0.353603i | \(-0.884956\pi\) |
0.161469 | − | 0.986878i | \(-0.448377\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21199.2 | + | 36718.1i | −0.732068 | + | 1.26798i | ||||
\(944\) | 6116.54 | 0.210886 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1247.16 | −0.0428633 | ||||||||
\(947\) | −24462.3 | + | 42369.9i | −0.839406 | + | 1.45389i | 0.0509860 | + | 0.998699i | \(0.483764\pi\) |
−0.890392 | + | 0.455195i | \(0.849570\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10840.9 | + | 18777.1i | 0.370824 | + | 0.642286i | ||||
\(950\) | −2117.49 | + | 3667.59i | −0.0723161 | + | 0.125255i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52014.3 | −1.76801 | −0.884003 | − | 0.467482i | \(-0.845161\pi\) | ||||
−0.884003 | + | 0.467482i | \(0.845161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1381.77 | − | 2393.30i | −0.0468201 | − | 0.0810947i | ||||
\(956\) | −1809.57 | − | 3134.26i | −0.0612193 | − | 0.106035i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14521.1 | −0.489723 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27676.4 | + | 47936.9i | −0.929018 | + | 1.60911i | ||||
\(962\) | −25567.3 | − | 44283.8i | −0.856883 | − | 1.48417i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15105.4 | + | 26163.4i | −0.504682 | + | 0.874135i | ||||
\(965\) | −42738.2 | −1.42569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47117.7 | −1.56691 | −0.783456 | − | 0.621448i | \(-0.786545\pi\) | ||||
−0.783456 | + | 0.621448i | \(0.786545\pi\) | |||||||
\(968\) | 3851.48 | − | 6670.95i | 0.127883 | − | 0.221501i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 40231.2 | + | 69682.4i | 1.33170 | + | 2.30657i | ||||
\(971\) | −4097.52 | + | 7097.12i | −0.135423 | + | 0.234560i | −0.925759 | − | 0.378114i | \(-0.876573\pi\) |
0.790336 | + | 0.612674i | \(0.209906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3537.35 | −0.116370 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4924.71 | − | 8529.85i | −0.161512 | − | 0.279748i | ||||
\(977\) | 2321.76 | + | 4021.40i | 0.0760282 | + | 0.131685i | 0.901533 | − | 0.432710i | \(-0.142443\pi\) |
−0.825505 | + | 0.564395i | \(0.809109\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12267.8 | −0.400490 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21745.1 | + | 37663.6i | −0.706632 | + | 1.22392i | ||||
\(983\) | 21993.3 | + | 38093.4i | 0.713607 | + | 1.23600i | 0.963494 | + | 0.267729i | \(0.0862732\pi\) |
−0.249887 | + | 0.968275i | \(0.580393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15164.5 | − | 26265.6i | 0.490538 | − | 0.849638i | ||||
\(986\) | 1970.10 | 0.0636317 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 43329.9 | 1.39525 | ||||||||
\(989\) | −426.429 | + | 738.598i | −0.0137105 | + | 0.0237473i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −797.604 | − | 1381.49i | −0.0255668 | − | 0.0442831i | 0.852959 | − | 0.521978i | \(-0.174806\pi\) |
−0.878526 | + | 0.477695i | \(0.841472\pi\) | |||||||
\(992\) | −58354.3 | + | 101073.i | −1.86769 | + | 3.23494i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32356.0 | 1.03091 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10750.6 | − | 18620.6i | −0.341499 | − | 0.591494i | 0.643212 | − | 0.765688i | \(-0.277601\pi\) |
−0.984711 | + | 0.174194i | \(0.944268\pi\) | |||||||
\(998\) | −21534.6 | − | 37299.0i | −0.683032 | − | 1.18305i | ||||
\(999\) | 0 | 0 |
(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 | 441.4.e.q.226.1 | 4 | ||
3.2 | odd | 2 | 147.4.e.l.79.2 | 4 | |||
7.2 | even | 3 | 63.4.a.e.1.2 | 2 | |||
7.3 | odd | 6 | 441.4.e.p.361.1 | 4 | |||
7.4 | even | 3 | inner | 441.4.e.q.361.1 | 4 | ||
7.5 | odd | 6 | 441.4.a.r.1.2 | 2 | |||
7.6 | odd | 2 | 441.4.e.p.226.1 | 4 | |||
21.2 | odd | 6 | 21.4.a.c.1.1 | ✓ | 2 | ||
21.5 | even | 6 | 147.4.a.i.1.1 | 2 | |||
21.11 | odd | 6 | 147.4.e.l.67.2 | 4 | |||
21.17 | even | 6 | 147.4.e.m.67.2 | 4 | |||
21.20 | even | 2 | 147.4.e.m.79.2 | 4 | |||
28.23 | odd | 6 | 1008.4.a.ba.1.1 | 2 | |||
35.9 | even | 6 | 1575.4.a.p.1.1 | 2 | |||
84.23 | even | 6 | 336.4.a.m.1.2 | 2 | |||
84.47 | odd | 6 | 2352.4.a.bz.1.1 | 2 | |||
105.2 | even | 12 | 525.4.d.g.274.1 | 4 | |||
105.23 | even | 12 | 525.4.d.g.274.4 | 4 | |||
105.44 | odd | 6 | 525.4.a.n.1.2 | 2 | |||
168.107 | even | 6 | 1344.4.a.bo.1.1 | 2 | |||
168.149 | odd | 6 | 1344.4.a.bg.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.c.1.1 | ✓ | 2 | 21.2 | odd | 6 | ||
63.4.a.e.1.2 | 2 | 7.2 | even | 3 | |||
147.4.a.i.1.1 | 2 | 21.5 | even | 6 | |||
147.4.e.l.67.2 | 4 | 21.11 | odd | 6 | |||
147.4.e.l.79.2 | 4 | 3.2 | odd | 2 | |||
147.4.e.m.67.2 | 4 | 21.17 | even | 6 | |||
147.4.e.m.79.2 | 4 | 21.20 | even | 2 | |||
336.4.a.m.1.2 | 2 | 84.23 | even | 6 | |||
441.4.a.r.1.2 | 2 | 7.5 | odd | 6 | |||
441.4.e.p.226.1 | 4 | 7.6 | odd | 2 | |||
441.4.e.p.361.1 | 4 | 7.3 | odd | 6 | |||
441.4.e.q.226.1 | 4 | 1.1 | even | 1 | trivial | ||
441.4.e.q.361.1 | 4 | 7.4 | even | 3 | inner | ||
525.4.a.n.1.2 | 2 | 105.44 | odd | 6 | |||
525.4.d.g.274.1 | 4 | 105.2 | even | 12 | |||
525.4.d.g.274.4 | 4 | 105.23 | even | 12 | |||
1008.4.a.ba.1.1 | 2 | 28.23 | odd | 6 | |||
1344.4.a.bg.1.1 | 2 | 168.149 | odd | 6 | |||
1344.4.a.bo.1.1 | 2 | 168.107 | even | 6 | |||
1575.4.a.p.1.1 | 2 | 35.9 | even | 6 | |||
2352.4.a.bz.1.1 | 2 | 84.47 | odd | 6 |