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: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.c.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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | + | 2.59808i | −0.530330 | + | 0.918559i | 0.469044 | + | 0.883175i | \(0.344599\pi\) |
−0.999374 | + | 0.0353837i | \(0.988735\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(5\) | 1.50000 | − | 2.59808i | 0.134164 | − | 0.232379i | −0.791114 | − | 0.611669i | \(-0.790498\pi\) |
0.925278 | + | 0.379290i | \(0.123832\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.50000 | + | 7.79423i | 0.142302 | + | 0.246475i | ||||
\(11\) | −7.50000 | − | 12.9904i | −0.205576 | − | 0.356068i | 0.744740 | − | 0.667355i | \(-0.232573\pi\) |
−0.950316 | + | 0.311287i | \(0.899240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 64.0000 | 1.36542 | 0.682708 | − | 0.730691i | \(-0.260802\pi\) | ||||
0.682708 | + | 0.730691i | \(0.260802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 35.5000 | − | 61.4878i | 0.554688 | − | 0.960747i | ||||
\(17\) | −42.0000 | − | 72.7461i | −0.599206 | − | 1.03785i | −0.992939 | − | 0.118630i | \(-0.962150\pi\) |
0.393733 | − | 0.919225i | \(-0.371183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.00000 | + | 13.8564i | −0.0965961 | + | 0.167309i | −0.910274 | − | 0.414007i | \(-0.864129\pi\) |
0.813678 | + | 0.581317i | \(0.197462\pi\) | |||||||
\(20\) | −3.00000 | −0.0335410 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 45.0000 | 0.436092 | ||||||||
\(23\) | −42.0000 | + | 72.7461i | −0.380765 | + | 0.659505i | −0.991172 | − | 0.132583i | \(-0.957673\pi\) |
0.610406 | + | 0.792088i | \(0.291006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 58.0000 | + | 100.459i | 0.464000 | + | 0.803672i | ||||
\(26\) | −96.0000 | + | 166.277i | −0.724121 | + | 1.25421i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 297.000 | 1.90178 | 0.950888 | − | 0.309535i | \(-0.100173\pi\) | ||||
0.950888 | + | 0.309535i | \(0.100173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −126.500 | − | 219.104i | −0.732906 | − | 1.26943i | −0.955636 | − | 0.294550i | \(-0.904830\pi\) |
0.222731 | − | 0.974880i | \(-0.428503\pi\) | |||||||
\(32\) | 22.5000 | + | 38.9711i | 0.124296 | + | 0.215287i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 252.000 | 1.27111 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 158.000 | − | 273.664i | 0.702028 | − | 1.21595i | −0.265725 | − | 0.964049i | \(-0.585611\pi\) |
0.967753 | − | 0.251900i | \(-0.0810553\pi\) | |||||||
\(38\) | −24.0000 | − | 41.5692i | −0.102456 | − | 0.177458i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −31.5000 | + | 54.5596i | −0.124515 | + | 0.215666i | ||||
\(41\) | 360.000 | 1.37128 | 0.685641 | − | 0.727940i | \(-0.259522\pi\) | ||||
0.685641 | + | 0.727940i | \(0.259522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.0000 | 0.0922084 | 0.0461042 | − | 0.998937i | \(-0.485319\pi\) | ||||
0.0461042 | + | 0.998937i | \(0.485319\pi\) | |||||||
\(44\) | −7.50000 | + | 12.9904i | −0.0256970 | + | 0.0445085i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −126.000 | − | 218.238i | −0.403863 | − | 0.699511i | ||||
\(47\) | 15.0000 | − | 25.9808i | 0.0465527 | − | 0.0806316i | −0.841810 | − | 0.539774i | \(-0.818510\pi\) |
0.888363 | + | 0.459142i | \(0.151843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −348.000 | −0.984293 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −32.0000 | − | 55.4256i | −0.0853385 | − | 0.147811i | ||||
\(53\) | 181.500 | + | 314.367i | 0.470395 | + | 0.814748i | 0.999427 | − | 0.0338538i | \(-0.0107781\pi\) |
−0.529032 | + | 0.848602i | \(0.677445\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −45.0000 | −0.110324 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −445.500 | + | 771.629i | −1.00857 | + | 1.74689i | ||||
\(59\) | 7.50000 | + | 12.9904i | 0.0165494 | + | 0.0286645i | 0.874182 | − | 0.485599i | \(-0.161399\pi\) |
−0.857632 | + | 0.514264i | \(0.828065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −59.0000 | + | 102.191i | −0.123839 | + | 0.214495i | −0.921279 | − | 0.388903i | \(-0.872854\pi\) |
0.797440 | + | 0.603399i | \(0.206187\pi\) | |||||||
\(62\) | 759.000 | 1.55473 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 96.0000 | − | 166.277i | 0.183190 | − | 0.317294i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 185.000 | + | 320.429i | 0.337334 | + | 0.584279i | 0.983930 | − | 0.178553i | \(-0.0571417\pi\) |
−0.646597 | + | 0.762832i | \(0.723808\pi\) | |||||||
\(68\) | −42.0000 | + | 72.7461i | −0.0749007 | + | 0.129732i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 342.000 | 0.571661 | 0.285831 | − | 0.958280i | \(-0.407731\pi\) | ||||
0.285831 | + | 0.958280i | \(0.407731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 181.000 | + | 313.501i | 0.290198 | + | 0.502638i | 0.973856 | − | 0.227165i | \(-0.0729455\pi\) |
−0.683658 | + | 0.729802i | \(0.739612\pi\) | |||||||
\(74\) | 474.000 | + | 820.992i | 0.744613 | + | 1.28971i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.0000 | 0.0241490 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −233.500 | + | 404.434i | −0.332542 | + | 0.575979i | −0.983010 | − | 0.183555i | \(-0.941240\pi\) |
0.650468 | + | 0.759534i | \(0.274573\pi\) | |||||||
\(80\) | −106.500 | − | 184.463i | −0.148838 | − | 0.257795i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −540.000 | + | 935.307i | −0.727232 | + | 1.25960i | ||||
\(83\) | 477.000 | 0.630814 | 0.315407 | − | 0.948957i | \(-0.397859\pi\) | ||||
0.315407 | + | 0.948957i | \(0.397859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −252.000 | −0.321568 | ||||||||
\(86\) | −39.0000 | + | 67.5500i | −0.0489009 | + | 0.0846989i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 157.500 | + | 272.798i | 0.190790 | + | 0.330459i | ||||
\(89\) | −453.000 | + | 784.619i | −0.539527 | + | 0.934488i | 0.459402 | + | 0.888228i | \(0.348064\pi\) |
−0.998929 | + | 0.0462600i | \(0.985270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 84.0000 | 0.0951914 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 45.0000 | + | 77.9423i | 0.0493765 | + | 0.0855227i | ||||
\(95\) | 24.0000 | + | 41.5692i | 0.0259195 | + | 0.0448938i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −503.000 | −0.526515 | −0.263257 | − | 0.964726i | \(-0.584797\pi\) | ||||
−0.263257 | + | 0.964726i | \(0.584797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 58.0000 | − | 100.459i | 0.0580000 | − | 0.100459i | ||||
\(101\) | 543.000 | + | 940.504i | 0.534956 | + | 0.926570i | 0.999165 | + | 0.0408451i | \(0.0130050\pi\) |
−0.464210 | + | 0.885725i | \(0.653662\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 868.000 | − | 1503.42i | 0.830355 | − | 1.43822i | −0.0674017 | − | 0.997726i | \(-0.521471\pi\) |
0.897757 | − | 0.440491i | \(-0.145196\pi\) | |||||||
\(104\) | −1344.00 | −1.26721 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1089.00 | −0.997859 | ||||||||
\(107\) | −676.500 | + | 1171.73i | −0.611212 | + | 1.05865i | 0.379824 | + | 0.925059i | \(0.375985\pi\) |
−0.991036 | + | 0.133592i | \(0.957349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 185.000 | + | 320.429i | 0.162567 | + | 0.281574i | 0.935789 | − | 0.352562i | \(-0.114689\pi\) |
−0.773222 | + | 0.634136i | \(0.781356\pi\) | |||||||
\(110\) | 67.5000 | − | 116.913i | 0.0585079 | − | 0.101339i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 648.000 | 0.539458 | 0.269729 | − | 0.962936i | \(-0.413066\pi\) | ||||
0.269729 | + | 0.962936i | \(0.413066\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 126.000 | + | 218.238i | 0.102170 | + | 0.176964i | ||||
\(116\) | −148.500 | − | 257.210i | −0.118861 | − | 0.205873i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −45.0000 | −0.0351067 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 553.000 | − | 957.824i | 0.415477 | − | 0.719627i | ||||
\(122\) | −177.000 | − | 306.573i | −0.131351 | − | 0.227507i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −126.500 | + | 219.104i | −0.0916132 | + | 0.158679i | ||||
\(125\) | 723.000 | 0.517337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 377.000 | 0.263412 | 0.131706 | − | 0.991289i | \(-0.457954\pi\) | ||||
0.131706 | + | 0.991289i | \(0.457954\pi\) | |||||||
\(128\) | −829.500 | + | 1436.74i | −0.572798 | + | 0.992115i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 288.000 | + | 498.831i | 0.194302 | + | 0.336541i | ||||
\(131\) | 325.500 | − | 563.783i | 0.217092 | − | 0.376015i | −0.736826 | − | 0.676083i | \(-0.763676\pi\) |
0.953918 | + | 0.300068i | \(0.0970095\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1110.00 | −0.715593 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 882.000 | + | 1527.67i | 0.556109 | + | 0.963210i | ||||
\(137\) | −885.000 | − | 1532.86i | −0.551903 | − | 0.955923i | −0.998137 | − | 0.0610074i | \(-0.980569\pi\) |
0.446235 | − | 0.894916i | \(-0.352765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1558.00 | 0.950704 | 0.475352 | − | 0.879796i | \(-0.342321\pi\) | ||||
0.475352 | + | 0.879796i | \(0.342321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −513.000 | + | 888.542i | −0.303169 | + | 0.525104i | ||||
\(143\) | −480.000 | − | 831.384i | −0.280697 | − | 0.486181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 445.500 | − | 771.629i | 0.255150 | − | 0.441933i | ||||
\(146\) | −1086.00 | −0.615603 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −316.000 | −0.175507 | ||||||||
\(149\) | 1227.00 | − | 2125.23i | 0.674629 | − | 1.16849i | −0.301948 | − | 0.953324i | \(-0.597637\pi\) |
0.976577 | − | 0.215168i | \(-0.0690298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −629.500 | − | 1090.33i | −0.339258 | − | 0.587612i | 0.645035 | − | 0.764153i | \(-0.276843\pi\) |
−0.984293 | + | 0.176540i | \(0.943509\pi\) | |||||||
\(152\) | 168.000 | − | 290.985i | 0.0896487 | − | 0.155276i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −759.000 | −0.393318 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.0000 | − | 169.741i | −0.0498169 | − | 0.0862854i | 0.840042 | − | 0.542522i | \(-0.182530\pi\) |
−0.889859 | + | 0.456236i | \(0.849197\pi\) | |||||||
\(158\) | −700.500 | − | 1213.30i | −0.352714 | − | 0.610918i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 135.000 | 0.0667043 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 626.000 | − | 1084.26i | 0.300810 | − | 0.521019i | −0.675509 | − | 0.737351i | \(-0.736076\pi\) |
0.976320 | + | 0.216332i | \(0.0694095\pi\) | |||||||
\(164\) | −180.000 | − | 311.769i | −0.0857051 | − | 0.148446i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −715.500 | + | 1239.28i | −0.334540 | + | 0.579440i | ||||
\(167\) | −2646.00 | −1.22607 | −0.613035 | − | 0.790056i | \(-0.710051\pi\) | ||||
−0.613035 | + | 0.790056i | \(0.710051\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1899.00 | 0.864360 | ||||||||
\(170\) | 378.000 | − | 654.715i | 0.170537 | − | 0.295379i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.0000 | − | 22.5167i | −0.00576303 | − | 0.00998186i | ||||
\(173\) | 393.000 | − | 680.696i | 0.172712 | − | 0.299147i | −0.766655 | − | 0.642059i | \(-0.778080\pi\) |
0.939367 | + | 0.342913i | \(0.111414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1065.00 | −0.456122 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1359.00 | − | 2353.86i | −0.572255 | − | 0.991174i | ||||
\(179\) | 1446.00 | + | 2504.55i | 0.603794 | + | 1.04580i | 0.992241 | + | 0.124331i | \(0.0396784\pi\) |
−0.388447 | + | 0.921471i | \(0.626988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1352.00 | −0.555212 | −0.277606 | − | 0.960695i | \(-0.589541\pi\) | ||||
−0.277606 | + | 0.960695i | \(0.589541\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 882.000 | − | 1527.67i | 0.353380 | − | 0.612072i | ||||
\(185\) | −474.000 | − | 820.992i | −0.188374 | − | 0.326273i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −630.000 | + | 1091.19i | −0.246365 | + | 0.426716i | ||||
\(188\) | −30.0000 | −0.0116382 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −144.000 | −0.0549835 | ||||||||
\(191\) | 1956.00 | − | 3387.89i | 0.741001 | − | 1.28345i | −0.211039 | − | 0.977478i | \(-0.567685\pi\) |
0.952040 | − | 0.305974i | \(-0.0989820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −746.500 | − | 1292.98i | −0.278416 | − | 0.482230i | 0.692575 | − | 0.721345i | \(-0.256476\pi\) |
−0.970991 | + | 0.239115i | \(0.923143\pi\) | |||||||
\(194\) | 754.500 | − | 1306.83i | 0.279227 | − | 0.483635i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4086.00 | 1.47774 | 0.738872 | − | 0.673846i | \(-0.235359\pi\) | ||||
0.738872 | + | 0.673846i | \(0.235359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1778.00 | − | 3079.59i | −0.633362 | − | 1.09702i | −0.986860 | − | 0.161580i | \(-0.948341\pi\) |
0.353497 | − | 0.935436i | \(-0.384992\pi\) | |||||||
\(200\) | −1218.00 | − | 2109.64i | −0.430628 | − | 0.745870i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3258.00 | −1.13481 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 540.000 | − | 935.307i | 0.183977 | − | 0.318657i | ||||
\(206\) | 2604.00 | + | 4510.26i | 0.880725 | + | 1.52546i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2272.00 | − | 3935.22i | 0.757379 | − | 1.31182i | ||||
\(209\) | 240.000 | 0.0794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1250.00 | 0.407837 | 0.203918 | − | 0.978988i | \(-0.434632\pi\) | ||||
0.203918 | + | 0.978988i | \(0.434632\pi\) | |||||||
\(212\) | 181.500 | − | 314.367i | 0.0587994 | − | 0.101844i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2029.50 | − | 3515.20i | −0.648289 | − | 1.12287i | ||||
\(215\) | 39.0000 | − | 67.5500i | 0.0123711 | − | 0.0214273i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1110.00 | −0.344856 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.5000 | + | 38.9711i | 0.00689523 | + | 0.0119429i | ||||
\(221\) | −2688.00 | − | 4655.75i | −0.818165 | − | 1.41710i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −425.000 | −0.127624 | −0.0638119 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638119 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −972.000 | + | 1683.55i | −0.286091 | + | 0.495523i | ||||
\(227\) | −1927.50 | − | 3338.53i | −0.563580 | − | 0.976149i | −0.997180 | − | 0.0750439i | \(-0.976090\pi\) |
0.433600 | − | 0.901105i | \(-0.357243\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1094.00 | + | 1894.86i | −0.315692 | + | 0.546795i | −0.979584 | − | 0.201033i | \(-0.935570\pi\) |
0.663892 | + | 0.747828i | \(0.268903\pi\) | |||||||
\(230\) | −756.000 | −0.216735 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6237.00 | −1.76500 | ||||||||
\(233\) | 426.000 | − | 737.854i | 0.119778 | − | 0.207461i | −0.799902 | − | 0.600131i | \(-0.795115\pi\) |
0.919679 | + | 0.392670i | \(0.128449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −45.0000 | − | 77.9423i | −0.0124914 | − | 0.0216357i | ||||
\(236\) | 7.50000 | − | 12.9904i | 0.00206868 | − | 0.00358306i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5508.00 | −1.49072 | −0.745362 | − | 0.666660i | \(-0.767723\pi\) | ||||
−0.745362 | + | 0.666660i | \(0.767723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 395.500 | + | 685.026i | 0.105711 | + | 0.183097i | 0.914029 | − | 0.405650i | \(-0.132955\pi\) |
−0.808317 | + | 0.588747i | \(0.799621\pi\) | |||||||
\(242\) | 1659.00 | + | 2873.47i | 0.440680 | + | 0.763280i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 118.000 | 0.0309597 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −512.000 | + | 886.810i | −0.131894 | + | 0.228447i | ||||
\(248\) | 2656.50 | + | 4601.19i | 0.680193 | + | 1.17813i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1084.50 | + | 1878.41i | −0.274359 | + | 0.475204i | ||||
\(251\) | 5265.00 | 1.32400 | 0.662000 | − | 0.749504i | \(-0.269708\pi\) | ||||
0.662000 | + | 0.749504i | \(0.269708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1260.00 | 0.313105 | ||||||||
\(254\) | −565.500 | + | 979.475i | −0.139695 | + | 0.241959i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −756.500 | − | 1310.30i | −0.184692 | − | 0.319897i | ||||
\(257\) | 3435.00 | − | 5949.59i | 0.833733 | − | 1.44407i | −0.0613246 | − | 0.998118i | \(-0.519532\pi\) |
0.895058 | − | 0.445950i | \(-0.147134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −192.000 | −0.0457974 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 976.500 | + | 1691.35i | 0.230261 | + | 0.398824i | ||||
\(263\) | −111.000 | − | 192.258i | −0.0260249 | − | 0.0450765i | 0.852720 | − | 0.522369i | \(-0.174952\pi\) |
−0.878745 | + | 0.477292i | \(0.841618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1089.00 | 0.252441 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 185.000 | − | 320.429i | 0.0421667 | − | 0.0730349i | ||||
\(269\) | −3925.50 | − | 6799.17i | −0.889747 | − | 1.54109i | −0.840174 | − | 0.542317i | \(-0.817547\pi\) |
−0.0495729 | − | 0.998771i | \(-0.515786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2591.50 | − | 4488.61i | 0.580895 | − | 1.00614i | −0.414479 | − | 0.910059i | \(-0.636036\pi\) |
0.995374 | − | 0.0960800i | \(-0.0306305\pi\) | |||||||
\(272\) | −5964.00 | −1.32949 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5310.00 | 1.17076 | ||||||||
\(275\) | 870.000 | − | 1506.88i | 0.190774 | − | 0.330431i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2480.00 | + | 4295.49i | 0.537938 | + | 0.931736i | 0.999015 | + | 0.0443755i | \(0.0141298\pi\) |
−0.461077 | + | 0.887360i | \(0.652537\pi\) | |||||||
\(278\) | −2337.00 | + | 4047.80i | −0.504187 | + | 0.873277i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 774.000 | 0.164317 | 0.0821583 | − | 0.996619i | \(-0.473819\pi\) | ||||
0.0821583 | + | 0.996619i | \(0.473819\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1849.00 | + | 3202.56i | 0.388380 | + | 0.672695i | 0.992232 | − | 0.124402i | \(-0.0397013\pi\) |
−0.603852 | + | 0.797097i | \(0.706368\pi\) | |||||||
\(284\) | −171.000 | − | 296.181i | −0.0357288 | − | 0.0618841i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2880.00 | 0.595447 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1071.50 | + | 1855.89i | −0.218095 | + | 0.377751i | ||||
\(290\) | 1336.50 | + | 2314.89i | 0.270628 | + | 0.468741i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 181.000 | − | 313.501i | 0.0362747 | − | 0.0628297i | ||||
\(293\) | −6273.00 | −1.25076 | −0.625380 | − | 0.780321i | \(-0.715056\pi\) | ||||
−0.625380 | + | 0.780321i | \(0.715056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.0000 | 0.00888136 | ||||||||
\(296\) | −3318.00 | + | 5746.94i | −0.651537 | + | 1.12849i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3681.00 | + | 6375.68i | 0.715552 | + | 1.23937i | ||||
\(299\) | −2688.00 | + | 4655.75i | −0.519903 | + | 0.900499i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3777.00 | 0.719675 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 568.000 | + | 983.805i | 0.107161 | + | 0.185609i | ||||
\(305\) | 177.000 | + | 306.573i | 0.0332295 | + | 0.0575551i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1684.00 | 0.313065 | 0.156533 | − | 0.987673i | \(-0.449968\pi\) | ||||
0.156533 | + | 0.987673i | \(0.449968\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1138.50 | − | 1971.94i | 0.208589 | − | 0.361286i | ||||
\(311\) | 660.000 | + | 1143.15i | 0.120338 | + | 0.208432i | 0.919901 | − | 0.392151i | \(-0.128269\pi\) |
−0.799563 | + | 0.600582i | \(0.794935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4251.50 | + | 7363.81i | −0.767760 | + | 1.32980i | 0.171014 | + | 0.985269i | \(0.445296\pi\) |
−0.938775 | + | 0.344531i | \(0.888038\pi\) | |||||||
\(314\) | 588.000 | 0.105678 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 467.000 | 0.0831355 | ||||||||
\(317\) | −1288.50 | + | 2231.75i | −0.228295 | + | 0.395418i | −0.957303 | − | 0.289087i | \(-0.906648\pi\) |
0.729008 | + | 0.684505i | \(0.239982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2227.50 | − | 3858.14i | −0.390959 | − | 0.677162i | ||||
\(320\) | 649.500 | − | 1124.97i | 0.113463 | − | 0.196524i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1344.00 | 0.231524 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3712.00 | + | 6429.37i | 0.633553 | + | 1.09735i | ||||
\(326\) | 1878.00 | + | 3252.79i | 0.319058 | + | 0.552624i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7560.00 | −1.27266 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 242.000 | − | 419.156i | 0.0401859 | − | 0.0696040i | −0.845233 | − | 0.534398i | \(-0.820538\pi\) |
0.885419 | + | 0.464794i | \(0.153872\pi\) | |||||||
\(332\) | −238.500 | − | 413.094i | −0.0394259 | − | 0.0682876i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3969.00 | − | 6874.51i | 0.650222 | − | 1.12622i | ||||
\(335\) | 1110.00 | 0.181032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8359.00 | −1.35117 | −0.675584 | − | 0.737283i | \(-0.736109\pi\) | ||||
−0.675584 | + | 0.737283i | \(0.736109\pi\) | |||||||
\(338\) | −2848.50 | + | 4933.75i | −0.458396 | + | 0.793966i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 126.000 | + | 218.238i | 0.0200980 | + | 0.0348107i | ||||
\(341\) | −1897.50 | + | 3286.57i | −0.301335 | + | 0.521928i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −546.000 | −0.0855766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1179.00 | + | 2042.09i | 0.183189 | + | 0.317293i | ||||
\(347\) | −930.000 | − | 1610.81i | −0.143876 | − | 0.249201i | 0.785077 | − | 0.619398i | \(-0.212623\pi\) |
−0.928953 | + | 0.370197i | \(0.879290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1918.00 | 0.294178 | 0.147089 | − | 0.989123i | \(-0.453010\pi\) | ||||
0.147089 | + | 0.989123i | \(0.453010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 337.500 | − | 584.567i | 0.0511046 | − | 0.0885157i | ||||
\(353\) | 1524.00 | + | 2639.65i | 0.229786 | + | 0.398000i | 0.957744 | − | 0.287620i | \(-0.0928642\pi\) |
−0.727959 | + | 0.685621i | \(0.759531\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 513.000 | − | 888.542i | 0.0766964 | − | 0.132842i | ||||
\(356\) | 906.000 | 0.134882 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8676.00 | −1.28084 | ||||||||
\(359\) | −15.0000 | + | 25.9808i | −0.00220521 | + | 0.00381953i | −0.867126 | − | 0.498089i | \(-0.834035\pi\) |
0.864921 | + | 0.501909i | \(0.167369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3301.50 | + | 5718.37i | 0.481338 | + | 0.833703i | ||||
\(362\) | 2028.00 | − | 3512.60i | 0.294446 | − | 0.509995i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1086.00 | 0.155737 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5655.50 | − | 9795.61i | −0.804400 | − | 1.39326i | −0.916696 | − | 0.399586i | \(-0.869154\pi\) |
0.112296 | − | 0.993675i | \(-0.464180\pi\) | |||||||
\(368\) | 2982.00 | + | 5164.98i | 0.422412 | + | 0.731638i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2844.00 | 0.399601 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −604.000 | + | 1046.16i | −0.0838443 | + | 0.145223i | −0.904898 | − | 0.425628i | \(-0.860053\pi\) |
0.821054 | + | 0.570851i | \(0.193387\pi\) | |||||||
\(374\) | −1890.00 | − | 3273.58i | −0.261309 | − | 0.452600i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −315.000 | + | 545.596i | −0.0432045 | + | 0.0748324i | ||||
\(377\) | 19008.0 | 2.59672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7640.00 | 1.03546 | 0.517731 | − | 0.855543i | \(-0.326777\pi\) | ||||
0.517731 | + | 0.855543i | \(0.326777\pi\) | |||||||
\(380\) | 24.0000 | − | 41.5692i | 0.00323993 | − | 0.00561173i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5868.00 | + | 10163.7i | 0.785950 | + | 1.36131i | ||||
\(383\) | −6375.00 | + | 11041.8i | −0.850515 | + | 1.47314i | 0.0302291 | + | 0.999543i | \(0.490376\pi\) |
−0.880744 | + | 0.473592i | \(0.842957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4479.00 | 0.590609 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 251.500 | + | 435.611i | 0.0329072 | + | 0.0569969i | ||||
\(389\) | 1563.00 | + | 2707.20i | 0.203720 | + | 0.352854i | 0.949724 | − | 0.313087i | \(-0.101363\pi\) |
−0.746004 | + | 0.665942i | \(0.768030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7056.00 | 0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6129.00 | + | 10615.7i | −0.783692 | + | 1.35739i | ||||
\(395\) | 700.500 | + | 1213.30i | 0.0892303 | + | 0.154551i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2966.00 | + | 5137.26i | −0.374960 | + | 0.649450i | −0.990321 | − | 0.138795i | \(-0.955677\pi\) |
0.615361 | + | 0.788246i | \(0.289010\pi\) | |||||||
\(398\) | 10668.0 | 1.34356 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8236.00 | 1.02950 | ||||||||
\(401\) | 804.000 | − | 1392.57i | 0.100124 | − | 0.173420i | −0.811611 | − | 0.584198i | \(-0.801409\pi\) |
0.911736 | + | 0.410777i | \(0.134743\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8096.00 | − | 14022.7i | −1.00072 | − | 1.73330i | ||||
\(404\) | 543.000 | − | 940.504i | 0.0668695 | − | 0.115821i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4740.00 | −0.577280 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2232.50 | − | 3866.80i | −0.269902 | − | 0.467484i | 0.698934 | − | 0.715186i | \(-0.253658\pi\) |
−0.968836 | + | 0.247702i | \(0.920325\pi\) | |||||||
\(410\) | 1620.00 | + | 2805.92i | 0.195137 | + | 0.337987i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1736.00 | −0.207589 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 715.500 | − | 1239.28i | 0.0846326 | − | 0.146588i | ||||
\(416\) | 1440.00 | + | 2494.15i | 0.169716 | + | 0.293957i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −360.000 | + | 623.538i | −0.0421248 | + | 0.0729623i | ||||
\(419\) | −1584.00 | −0.184686 | −0.0923430 | − | 0.995727i | \(-0.529436\pi\) | ||||
−0.0923430 | + | 0.995727i | \(0.529436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1330.00 | −0.153967 | −0.0769837 | − | 0.997032i | \(-0.524529\pi\) | ||||
−0.0769837 | + | 0.997032i | \(0.524529\pi\) | |||||||
\(422\) | −1875.00 | + | 3247.60i | −0.216288 | + | 0.374622i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3811.50 | − | 6601.71i | −0.436563 | − | 0.756150i | ||||
\(425\) | 4872.00 | − | 8438.55i | 0.556063 | − | 0.963129i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1353.00 | 0.152803 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 117.000 | + | 202.650i | 0.0131215 | + | 0.0227271i | ||||
\(431\) | 4794.00 | + | 8303.45i | 0.535775 | + | 0.927989i | 0.999125 | + | 0.0418139i | \(0.0133137\pi\) |
−0.463351 | + | 0.886175i | \(0.653353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −494.000 | −0.0548271 | −0.0274135 | − | 0.999624i | \(-0.508727\pi\) | ||||
−0.0274135 | + | 0.999624i | \(0.508727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 185.000 | − | 320.429i | 0.0203209 | − | 0.0351968i | ||||
\(437\) | −672.000 | − | 1163.94i | −0.0735609 | − | 0.127411i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8004.50 | + | 13864.2i | −0.870237 | + | 1.50729i | −0.00848508 | + | 0.999964i | \(0.502701\pi\) |
−0.861752 | + | 0.507330i | \(0.830632\pi\) | |||||||
\(440\) | 945.000 | 0.102389 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16128.0 | 1.73559 | ||||||||
\(443\) | 3886.50 | − | 6731.62i | 0.416824 | − | 0.721961i | −0.578794 | − | 0.815474i | \(-0.696476\pi\) |
0.995618 | + | 0.0935130i | \(0.0298097\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1359.00 | + | 2353.86i | 0.144770 | + | 0.250749i | ||||
\(446\) | 637.500 | − | 1104.18i | 0.0676827 | − | 0.117230i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −864.000 | −0.0908122 | −0.0454061 | − | 0.998969i | \(-0.514458\pi\) | ||||
−0.0454061 | + | 0.998969i | \(0.514458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2700.00 | − | 4676.54i | −0.281903 | − | 0.488269i | ||||
\(452\) | −324.000 | − | 561.184i | −0.0337161 | − | 0.0583980i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11565.0 | 1.19553 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1259.50 | + | 2181.52i | −0.128921 | + | 0.223298i | −0.923259 | − | 0.384179i | \(-0.874485\pi\) |
0.794338 | + | 0.607476i | \(0.207818\pi\) | |||||||
\(458\) | −3282.00 | − | 5684.59i | −0.334842 | − | 0.579964i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 126.000 | − | 218.238i | 0.0127713 | − | 0.0221205i | ||||
\(461\) | −342.000 | −0.0345521 | −0.0172761 | − | 0.999851i | \(-0.505499\pi\) | ||||
−0.0172761 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4336.00 | −0.435229 | −0.217614 | − | 0.976035i | \(-0.569828\pi\) | ||||
−0.217614 | + | 0.976035i | \(0.569828\pi\) | |||||||
\(464\) | 10543.5 | − | 18261.9i | 1.05489 | − | 1.82713i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1278.00 | + | 2213.56i | 0.127043 | + | 0.220046i | ||||
\(467\) | −9318.00 | + | 16139.2i | −0.923310 | + | 1.59922i | −0.129052 | + | 0.991638i | \(0.541194\pi\) |
−0.794257 | + | 0.607581i | \(0.792140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 270.000 | 0.0264982 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −157.500 | − | 272.798i | −0.0153592 | − | 0.0266029i | ||||
\(473\) | −195.000 | − | 337.750i | −0.0189558 | − | 0.0328325i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1856.00 | −0.179282 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8262.00 | − | 14310.2i | 0.790575 | − | 1.36932i | ||||
\(479\) | −7539.00 | − | 13057.9i | −0.719135 | − | 1.24558i | −0.961343 | − | 0.275354i | \(-0.911205\pi\) |
0.242208 | − | 0.970224i | \(-0.422128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10112.0 | − | 17514.5i | 0.958560 | − | 1.66028i | ||||
\(482\) | −2373.00 | −0.224247 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1106.00 | −0.103869 | ||||||||
\(485\) | −754.500 | + | 1306.83i | −0.0706393 | + | 0.122351i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3110.50 | − | 5387.54i | −0.289425 | − | 0.501300i | 0.684247 | − | 0.729250i | \(-0.260131\pi\) |
−0.973673 | + | 0.227950i | \(0.926798\pi\) | |||||||
\(488\) | 1239.00 | − | 2146.01i | 0.114932 | − | 0.199068i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7371.00 | 0.677492 | 0.338746 | − | 0.940878i | \(-0.389997\pi\) | ||||
0.338746 | + | 0.940878i | \(0.389997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12474.0 | − | 21605.6i | −1.13956 | − | 1.97377i | ||||
\(494\) | −1536.00 | − | 2660.43i | −0.139895 | − | 0.242304i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17963.0 | −1.62613 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2137.00 | + | 3701.39i | −0.191714 | + | 0.332058i | −0.945818 | − | 0.324696i | \(-0.894738\pi\) |
0.754104 | + | 0.656755i | \(0.228071\pi\) | |||||||
\(500\) | −361.500 | − | 626.136i | −0.0323335 | − | 0.0560033i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7897.50 | + | 13678.9i | −0.702157 | + | 1.21617i | ||||
\(503\) | −2520.00 | −0.223382 | −0.111691 | − | 0.993743i | \(-0.535627\pi\) | ||||
−0.111691 | + | 0.993743i | \(0.535627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3258.00 | 0.287087 | ||||||||
\(506\) | −1890.00 | + | 3273.58i | −0.166049 | + | 0.287605i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −188.500 | − | 326.492i | −0.0164633 | − | 0.0285152i | ||||
\(509\) | 7138.50 | − | 12364.2i | 0.621628 | − | 1.07669i | −0.367555 | − | 0.930002i | \(-0.619805\pi\) |
0.989183 | − | 0.146689i | \(-0.0468616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10305.0 | + | 17848.8i | 0.884308 | + | 1.53167i | ||||
\(515\) | −2604.00 | − | 4510.26i | −0.222808 | − | 0.385914i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −450.000 | −0.0382804 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2016.00 | + | 3491.81i | −0.170014 | + | 0.294473i | ||||
\(521\) | 3153.00 | + | 5461.16i | 0.265135 | + | 0.459228i | 0.967599 | − | 0.252492i | \(-0.0812501\pi\) |
−0.702464 | + | 0.711719i | \(0.747917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4036.00 | − | 6990.56i | 0.337442 | − | 0.584466i | −0.646509 | − | 0.762906i | \(-0.723772\pi\) |
0.983951 | + | 0.178440i | \(0.0571051\pi\) | |||||||
\(524\) | −651.000 | −0.0542730 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 666.000 | 0.0552072 | ||||||||
\(527\) | −10626.0 | + | 18404.8i | −0.878322 | + | 1.52130i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2555.50 | + | 4426.26i | 0.210035 | + | 0.363792i | ||||
\(530\) | −1633.50 | + | 2829.30i | −0.133877 | + | 0.231881i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23040.0 | 1.87237 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2029.50 | + | 3515.20i | 0.164005 | + | 0.284066i | ||||
\(536\) | −3885.00 | − | 6729.02i | −0.313072 | − | 0.542256i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23553.0 | 1.88744 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11429.0 | − | 19795.6i | 0.908264 | − | 1.57316i | 0.0917903 | − | 0.995778i | \(-0.470741\pi\) |
0.816474 | − | 0.577382i | \(-0.195926\pi\) | |||||||
\(542\) | 7774.50 | + | 13465.8i | 0.616132 | + | 1.06717i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1890.00 | − | 3273.58i | 0.148958 | − | 0.258003i | ||||
\(545\) | 1110.00 | 0.0872425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24724.0 | −1.93258 | −0.966291 | − | 0.257454i | \(-0.917116\pi\) | ||||
−0.966291 | + | 0.257454i | \(0.917116\pi\) | |||||||
\(548\) | −885.000 | + | 1532.86i | −0.0689878 | + | 0.119490i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2610.00 | + | 4520.65i | 0.202347 | + | 0.350475i | ||||
\(551\) | −2376.00 | + | 4115.35i | −0.183704 | + | 0.318185i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14880.0 | −1.14114 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −779.000 | − | 1349.27i | −0.0594190 | − | 0.102917i | ||||
\(557\) | −4921.50 | − | 8524.29i | −0.374382 | − | 0.648448i | 0.615853 | − | 0.787861i | \(-0.288812\pi\) |
−0.990234 | + | 0.139413i | \(0.955478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1664.00 | 0.125903 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1161.00 | + | 2010.91i | −0.0871420 | + | 0.150934i | ||||
\(563\) | 6685.50 | + | 11579.6i | 0.500462 | + | 0.866826i | 1.00000 | 0.000533812i | \(0.000169918\pi\) | |
−0.499538 | + | 0.866292i | \(0.666497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 972.000 | − | 1683.55i | 0.0723758 | − | 0.125359i | ||||
\(566\) | −11094.0 | −0.823879 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7182.00 | −0.530546 | ||||||||
\(569\) | −2616.00 | + | 4531.04i | −0.192739 | + | 0.333834i | −0.946157 | − | 0.323708i | \(-0.895070\pi\) |
0.753418 | + | 0.657542i | \(0.228404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7199.00 | + | 12469.0i | 0.527616 | + | 0.913858i | 0.999482 | + | 0.0321874i | \(0.0102474\pi\) |
−0.471866 | + | 0.881670i | \(0.656419\pi\) | |||||||
\(572\) | −480.000 | + | 831.384i | −0.0350871 | + | 0.0607726i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9744.00 | −0.706701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9935.50 | + | 17208.8i | 0.716846 | + | 1.24161i | 0.962243 | + | 0.272191i | \(0.0877484\pi\) |
−0.245397 | + | 0.969423i | \(0.578918\pi\) | |||||||
\(578\) | −3214.50 | − | 5567.68i | −0.231325 | − | 0.400666i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −891.000 | −0.0637875 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2722.50 | − | 4715.51i | 0.193404 | − | 0.334985i | ||||
\(584\) | −3801.00 | − | 6583.53i | −0.269326 | − | 0.466487i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9409.50 | − | 16297.7i | 0.663315 | − | 1.14890i | ||||
\(587\) | −16137.0 | −1.13466 | −0.567330 | − | 0.823491i | \(-0.692024\pi\) | ||||
−0.567330 | + | 0.823491i | \(0.692024\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4048.00 | 0.283183 | ||||||||
\(590\) | −67.5000 | + | 116.913i | −0.00471005 | + | 0.00815805i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11218.0 | − | 19430.1i | −0.778812 | − | 1.34894i | ||||
\(593\) | 10662.0 | − | 18467.1i | 0.738340 | − | 1.27884i | −0.214902 | − | 0.976636i | \(-0.568943\pi\) |
0.953242 | − | 0.302207i | \(-0.0977235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2454.00 | −0.168657 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8064.00 | − | 13967.3i | −0.551441 | − | 0.955123i | ||||
\(599\) | −4323.00 | − | 7487.66i | −0.294880 | − | 0.510747i | 0.680077 | − | 0.733141i | \(-0.261946\pi\) |
−0.974957 | + | 0.222394i | \(0.928613\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11195.0 | −0.759823 | −0.379911 | − | 0.925023i | \(-0.624046\pi\) | ||||
−0.379911 | + | 0.925023i | \(0.624046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −629.500 | + | 1090.33i | −0.0424073 | + | 0.0734515i | ||||
\(605\) | −1659.00 | − | 2873.47i | −0.111484 | − | 0.193096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4485.50 | + | 7769.11i | −0.299935 | + | 0.519503i | −0.976121 | − | 0.217228i | \(-0.930298\pi\) |
0.676185 | + | 0.736731i | \(0.263632\pi\) | |||||||
\(608\) | −720.000 | −0.0480261 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1062.00 | −0.0704904 | ||||||||
\(611\) | 960.000 | − | 1662.77i | 0.0635637 | − | 0.110096i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6386.00 | + | 11060.9i | 0.420764 | + | 0.728784i | 0.996014 | − | 0.0891932i | \(-0.0284288\pi\) |
−0.575251 | + | 0.817977i | \(0.695096\pi\) | |||||||
\(614\) | −2526.00 | + | 4375.16i | −0.166028 | + | 0.287569i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12762.0 | −0.832705 | −0.416352 | − | 0.909203i | \(-0.636692\pi\) | ||||
−0.416352 | + | 0.909203i | \(0.636692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6421.00 | + | 11121.5i | 0.416933 | + | 0.722150i | 0.995629 | − | 0.0933936i | \(-0.0297715\pi\) |
−0.578696 | + | 0.815543i | \(0.696438\pi\) | |||||||
\(620\) | 379.500 | + | 657.313i | 0.0245824 | + | 0.0425780i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3960.00 | −0.255276 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6165.50 | + | 10679.0i | −0.394592 | + | 0.683453i | ||||
\(626\) | −12754.5 | − | 22091.4i | −0.814333 | − | 1.41047i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −98.0000 | + | 169.741i | −0.00622711 | + | 0.0107857i | ||||
\(629\) | −26544.0 | −1.68264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21365.0 | 1.34790 | 0.673952 | − | 0.738775i | \(-0.264596\pi\) | ||||
0.673952 | + | 0.738775i | \(0.264596\pi\) | |||||||
\(632\) | 4903.50 | − | 8493.11i | 0.308625 | − | 0.534554i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3865.50 | − | 6695.24i | −0.242143 | − | 0.419404i | ||||
\(635\) | 565.500 | − | 979.475i | 0.0353404 | − | 0.0612114i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13365.0 | 0.829350 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2488.50 | + | 4310.21i | 0.153698 | + | 0.266212i | ||||
\(641\) | 4137.00 | + | 7165.49i | 0.254917 | + | 0.441529i | 0.964873 | − | 0.262717i | \(-0.0846186\pi\) |
−0.709956 | + | 0.704246i | \(0.751285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27998.0 | −1.71716 | −0.858580 | − | 0.512680i | \(-0.828653\pi\) | ||||
−0.858580 | + | 0.512680i | \(0.828653\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2016.00 | + | 3491.81i | −0.122784 | + | 0.212668i | ||||
\(647\) | 8733.00 | + | 15126.0i | 0.530649 | + | 0.919110i | 0.999360 | + | 0.0357592i | \(0.0113849\pi\) |
−0.468712 | + | 0.883351i | \(0.655282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 112.500 | − | 194.856i | 0.00680433 | − | 0.0117854i | ||||
\(650\) | −22272.0 | −1.34397 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1252.00 | −0.0752026 | ||||||||
\(653\) | 1078.50 | − | 1868.02i | 0.0646324 | − | 0.111947i | −0.831898 | − | 0.554928i | \(-0.812746\pi\) |
0.896531 | + | 0.442981i | \(0.146079\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −976.500 | − | 1691.35i | −0.0582519 | − | 0.100895i | ||||
\(656\) | 12780.0 | − | 22135.6i | 0.760633 | − | 1.31745i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19944.0 | −1.17892 | −0.589460 | − | 0.807798i | \(-0.700659\pi\) | ||||
−0.589460 | + | 0.807798i | \(0.700659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13753.0 | + | 23820.9i | 0.809273 | + | 1.40170i | 0.913368 | + | 0.407135i | \(0.133472\pi\) |
−0.104095 | + | 0.994567i | \(0.533194\pi\) | |||||||
\(662\) | 726.000 | + | 1257.47i | 0.0426236 | + | 0.0738262i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10017.0 | −0.585444 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12474.0 | + | 21605.6i | −0.724131 | + | 1.25423i | ||||
\(668\) | 1323.00 | + | 2291.50i | 0.0766294 | + | 0.132726i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1665.00 | + | 2883.86i | −0.0960068 | + | 0.166289i | ||||
\(671\) | 1770.00 | 0.101833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19123.0 | −1.09530 | −0.547650 | − | 0.836707i | \(-0.684478\pi\) | ||||
−0.547650 | + | 0.836707i | \(0.684478\pi\) | |||||||
\(674\) | 12538.5 | − | 21717.3i | 0.716565 | − | 1.24113i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −949.500 | − | 1644.58i | −0.0540225 | − | 0.0935698i | ||||
\(677\) | −6928.50 | + | 12000.5i | −0.393329 | + | 0.681266i | −0.992886 | − | 0.119066i | \(-0.962010\pi\) |
0.599557 | + | 0.800332i | \(0.295343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5292.00 | 0.298440 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5692.50 | − | 9859.70i | −0.319615 | − | 0.553589i | ||||
\(683\) | −11122.5 | − | 19264.7i | −0.623120 | − | 1.07927i | −0.988901 | − | 0.148574i | \(-0.952532\pi\) |
0.365782 | − | 0.930701i | \(-0.380802\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5310.00 | −0.296182 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 923.000 | − | 1598.68i | 0.0511469 | − | 0.0885890i | ||||
\(689\) | 11616.0 | + | 20119.5i | 0.642285 | + | 1.11247i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −320.000 | + | 554.256i | −0.0176170 | + | 0.0305136i | −0.874700 | − | 0.484666i | \(-0.838941\pi\) |
0.857082 | + | 0.515179i | \(0.172275\pi\) | |||||||
\(692\) | −786.000 | −0.0431781 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5580.00 | 0.305207 | ||||||||
\(695\) | 2337.00 | − | 4047.80i | 0.127550 | − | 0.220924i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15120.0 | − | 26188.6i | −0.821680 | − | 1.42319i | ||||
\(698\) | −2877.00 | + | 4983.11i | −0.156012 | + | 0.270220i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15561.0 | 0.838418 | 0.419209 | − | 0.907890i | \(-0.362307\pi\) | ||||
0.419209 | + | 0.907890i | \(0.362307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2528.00 | + | 4378.62i | 0.135626 | + | 0.234912i | ||||
\(704\) | −3247.50 | − | 5624.83i | −0.173856 | − | 0.301128i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9144.00 | −0.487449 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2767.00 | + | 4792.58i | −0.146568 | + | 0.253864i | −0.929957 | − | 0.367668i | \(-0.880156\pi\) |
0.783389 | + | 0.621532i | \(0.213489\pi\) | |||||||
\(710\) | 1539.00 | + | 2665.63i | 0.0813488 | + | 0.140900i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9513.00 | − | 16477.0i | 0.500723 | − | 0.867278i | ||||
\(713\) | 21252.0 | 1.11626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2880.00 | −0.150638 | ||||||||
\(716\) | 1446.00 | − | 2504.55i | 0.0754742 | − | 0.130725i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −45.0000 | − | 77.9423i | −0.00233898 | − | 0.00405123i | ||||
\(719\) | 10923.0 | − | 18919.2i | 0.566564 | − | 0.981317i | −0.430339 | − | 0.902667i | \(-0.641606\pi\) |
0.996902 | − | 0.0786494i | \(-0.0250607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −19809.0 | −1.02107 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 676.000 | + | 1170.87i | 0.0347007 | + | 0.0601035i | ||||
\(725\) | 17226.0 | + | 29836.3i | 0.882424 | + | 1.52840i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11089.0 | 0.565706 | 0.282853 | − | 0.959163i | \(-0.408719\pi\) | ||||
0.282853 | + | 0.959163i | \(0.408719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1629.00 | + | 2821.51i | −0.0825918 | + | 0.143053i | ||||
\(731\) | −1092.00 | − | 1891.40i | −0.0552518 | − | 0.0956990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5881.00 | − | 10186.2i | 0.296343 | − | 0.513282i | −0.678953 | − | 0.734182i | \(-0.737566\pi\) |
0.975296 | + | 0.220900i | \(0.0708994\pi\) | |||||||
\(734\) | 33933.0 | 1.70639 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3780.00 | −0.189311 | ||||||||
\(737\) | 2775.00 | − | 4806.44i | 0.138695 | − | 0.240227i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11363.0 | + | 19681.3i | 0.565622 | + | 0.979686i | 0.996992 | + | 0.0775108i | \(0.0246972\pi\) |
−0.431369 | + | 0.902175i | \(0.641969\pi\) | |||||||
\(740\) | −474.000 | + | 820.992i | −0.0235467 | + | 0.0407841i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6678.00 | −0.329734 | −0.164867 | − | 0.986316i | \(-0.552719\pi\) | ||||
−0.164867 | + | 0.986316i | \(0.552719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3681.00 | − | 6375.68i | −0.181022 | − | 0.313539i | ||||
\(746\) | −1812.00 | − | 3138.48i | −0.0889303 | − | 0.154032i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1260.00 | 0.0615911 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9993.50 | − | 17309.2i | 0.485577 | − | 0.841043i | −0.514286 | − | 0.857619i | \(-0.671943\pi\) |
0.999863 | + | 0.0165754i | \(0.00527637\pi\) | |||||||
\(752\) | −1065.00 | − | 1844.63i | −0.0516444 | − | 0.0894506i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28512.0 | + | 49384.2i | −1.37712 | + | 2.38524i | ||||
\(755\) | −3777.00 | −0.182065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 314.000 | 0.0150760 | 0.00753799 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753799 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(758\) | −11460.0 | + | 19849.3i | −0.549137 | + | 0.951133i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −504.000 | − | 872.954i | −0.0240553 | − | 0.0416649i | ||||
\(761\) | 5748.00 | − | 9955.83i | 0.273804 | − | 0.474242i | −0.696029 | − | 0.718014i | \(-0.745051\pi\) |
0.969833 | + | 0.243772i | \(0.0783847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3912.00 | −0.185250 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19125.0 | − | 33125.5i | −0.902107 | − | 1.56250i | ||||
\(767\) | 480.000 | + | 831.384i | 0.0225969 | + | 0.0391389i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2765.00 | −0.129660 | −0.0648299 | − | 0.997896i | \(-0.520650\pi\) | ||||
−0.0648299 | + | 0.997896i | \(0.520650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −746.500 | + | 1292.98i | −0.0348020 | + | 0.0602788i | ||||
\(773\) | 7023.00 | + | 12164.2i | 0.326778 | + | 0.565997i | 0.981871 | − | 0.189552i | \(-0.0607036\pi\) |
−0.655092 | + | 0.755549i | \(0.727370\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14674.0 | − | 25416.1i | 0.680136 | − | 1.17803i | ||||
\(776\) | 10563.0 | 0.488646 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9378.00 | −0.432156 | ||||||||
\(779\) | −2880.00 | + | 4988.31i | −0.132460 | + | 0.229428i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2565.00 | − | 4442.71i | −0.117520 | − | 0.203550i | ||||
\(782\) | −10584.0 | + | 18332.0i | −0.483994 | + | 0.838302i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −588.000 | −0.0267345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9257.00 | − | 16033.6i | −0.419284 | − | 0.726221i | 0.576584 | − | 0.817038i | \(-0.304385\pi\) |
−0.995868 | + | 0.0908171i | \(0.971052\pi\) | |||||||
\(788\) | −2043.00 | − | 3538.58i | −0.0923590 | − | 0.159970i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4203.00 | −0.189286 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3776.00 | + | 6540.22i | −0.169092 | + | 0.292875i | ||||
\(794\) | −8898.00 | − | 15411.8i | −0.397706 | − | 0.688846i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1778.00 | + | 3079.59i | −0.0791703 | + | 0.137127i | ||||
\(797\) | −27495.0 | −1.22199 | −0.610993 | − | 0.791636i | \(-0.709230\pi\) | ||||
−0.610993 | + | 0.791636i | \(0.709230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2520.00 | −0.111578 | ||||||||
\(800\) | −2610.00 | + | 4520.65i | −0.115347 | + | 0.199787i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2412.00 | + | 4177.71i | 0.106198 | + | 0.183940i | ||||
\(803\) | 2715.00 | − | 4702.52i | 0.119315 | − | 0.206660i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 48576.0 | 2.12285 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11403.0 | − | 19750.6i | −0.496480 | − | 0.859929i | ||||
\(809\) | −3972.00 | − | 6879.71i | −0.172618 | − | 0.298983i | 0.766716 | − | 0.641986i | \(-0.221889\pi\) |
−0.939334 | + | 0.343003i | \(0.888556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28942.0 | 1.25313 | 0.626567 | − | 0.779368i | \(-0.284460\pi\) | ||||
0.626567 | + | 0.779368i | \(0.284460\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7110.00 | − | 12314.9i | 0.306149 | − | 0.530266i | ||||
\(815\) | −1878.00 | − | 3252.79i | −0.0807159 | − | 0.139804i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −208.000 | + | 360.267i | −0.00890698 | + | 0.0154273i | ||||
\(818\) | 13395.0 | 0.572549 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1080.00 | −0.0459942 | ||||||||
\(821\) | 4093.50 | − | 7090.15i | 0.174012 | − | 0.301398i | −0.765807 | − | 0.643071i | \(-0.777660\pi\) |
0.939819 | + | 0.341673i | \(0.110993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 140.000 | + | 242.487i | 0.00592964 | + | 0.0102704i | 0.868975 | − | 0.494856i | \(-0.164779\pi\) |
−0.863045 | + | 0.505126i | \(0.831446\pi\) | |||||||
\(824\) | −18228.0 | + | 31571.8i | −0.770634 | + | 1.33478i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25317.0 | −1.06452 | −0.532260 | − | 0.846581i | \(-0.678657\pi\) | ||||
−0.532260 | + | 0.846581i | \(0.678657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7660.00 | + | 13267.5i | 0.320920 | + | 0.555850i | 0.980678 | − | 0.195628i | \(-0.0626746\pi\) |
−0.659758 | + | 0.751478i | \(0.729341\pi\) | |||||||
\(830\) | 2146.50 | + | 3717.85i | 0.0897664 | + | 0.155480i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27712.0 | 1.15474 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3969.00 | + | 6874.51i | −0.164495 | + | 0.284913i | ||||
\(836\) | −120.000 | − | 207.846i | −0.00496446 | − | 0.00859869i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2376.00 | − | 4115.35i | 0.0979446 | − | 0.169645i | ||||
\(839\) | 34092.0 | 1.40284 | 0.701422 | − | 0.712746i | \(-0.252549\pi\) | ||||
0.701422 | + | 0.712746i | \(0.252549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63820.0 | 2.61675 | ||||||||
\(842\) | 1995.00 | − | 3455.44i | 0.0816535 | − | 0.141428i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −625.000 | − | 1082.53i | −0.0254898 | − | 0.0441496i | ||||
\(845\) | 2848.50 | − | 4933.75i | 0.115966 | − | 0.200859i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 25773.0 | 1.04369 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14616.0 | + | 25315.7i | 0.589794 | + | 1.02155i | ||||
\(851\) | 13272.0 | + | 22987.8i | 0.534616 | + | 0.925982i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7378.00 | 0.296152 | 0.148076 | − | 0.988976i | \(-0.452692\pi\) | ||||
0.148076 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14206.5 | − | 24606.4i | 0.567253 | − | 0.982510i | ||||
\(857\) | 7797.00 | + | 13504.8i | 0.310782 | + | 0.538291i | 0.978532 | − | 0.206095i | \(-0.0660757\pi\) |
−0.667750 | + | 0.744386i | \(0.732742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15269.0 | + | 26446.7i | −0.606486 | + | 1.05046i | 0.385329 | + | 0.922779i | \(0.374088\pi\) |
−0.991815 | + | 0.127685i | \(0.959245\pi\) | |||||||
\(860\) | −78.0000 | −0.00309277 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28764.0 | −1.13655 | ||||||||
\(863\) | −411.000 | + | 711.873i | −0.0162116 | + | 0.0280793i | −0.874017 | − | 0.485895i | \(-0.838494\pi\) |
0.857806 | + | 0.513974i | \(0.171827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1179.00 | − | 2042.09i | −0.0463436 | − | 0.0802694i | ||||
\(866\) | 741.000 | − | 1283.45i | 0.0290764 | − | 0.0503619i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7005.00 | 0.273450 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11840.0 | + | 20507.5i | 0.460601 | + | 0.797784i | ||||
\(872\) | −3885.00 | − | 6729.02i | −0.150875 | − | 0.261323i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4032.00 | 0.156046 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20912.0 | − | 36220.6i | 0.805186 | − | 1.39462i | −0.110980 | − | 0.993823i | \(-0.535399\pi\) |
0.916165 | − | 0.400800i | \(-0.131268\pi\) | |||||||
\(878\) | −24013.5 | − | 41592.6i | −0.923025 | − | 1.59873i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1597.50 | + | 2766.95i | −0.0611951 | + | 0.105993i | ||||
\(881\) | −46098.0 | −1.76286 | −0.881431 | − | 0.472313i | \(-0.843419\pi\) | ||||
−0.881431 | + | 0.472313i | \(0.843419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21008.0 | 0.800652 | 0.400326 | − | 0.916373i | \(-0.368897\pi\) | ||||
0.400326 | + | 0.916373i | \(0.368897\pi\) | |||||||
\(884\) | −2688.00 | + | 4655.75i | −0.102271 | + | 0.177138i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11659.5 | + | 20194.8i | 0.442109 | + | 0.765755i | ||||
\(887\) | −12018.0 | + | 20815.8i | −0.454932 | + | 0.787966i | −0.998684 | − | 0.0512801i | \(-0.983670\pi\) |
0.543752 | + | 0.839246i | \(0.317003\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8154.00 | −0.307104 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 212.500 | + | 368.061i | 0.00797649 | + | 0.0138157i | ||||
\(893\) | 240.000 | + | 415.692i | 0.00899361 | + | 0.0155774i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8676.00 | 0.324030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1296.00 | − | 2244.74i | 0.0481604 | − | 0.0834163i | ||||
\(899\) | −37570.5 | − | 65074.0i | −1.39382 | − | 2.41417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15246.0 | − | 26406.8i | 0.563727 | − | 0.976404i | ||||
\(902\) | 16200.0 | 0.598006 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13608.0 | −0.500659 | ||||||||
\(905\) | −2028.00 | + | 3512.60i | −0.0744895 | + | 0.129020i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6646.00 | − | 11511.2i | −0.243304 | − | 0.421415i | 0.718349 | − | 0.695683i | \(-0.244898\pi\) |
−0.961653 | + | 0.274268i | \(0.911565\pi\) | |||||||
\(908\) | −1927.50 | + | 3338.53i | −0.0704475 | + | 0.122019i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9306.00 | 0.338443 | 0.169221 | − | 0.985578i | \(-0.445875\pi\) | ||||
0.169221 | + | 0.985578i | \(0.445875\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3577.50 | − | 6196.41i | −0.129680 | − | 0.224613i | ||||
\(914\) | −3778.50 | − | 6544.55i | −0.136741 | − | 0.236843i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2188.00 | 0.0789231 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8248.00 | + | 14286.0i | −0.296057 | + | 0.512786i | −0.975230 | − | 0.221192i | \(-0.929005\pi\) |
0.679173 | + | 0.733978i | \(0.262339\pi\) | |||||||
\(920\) | −2646.00 | − | 4583.01i | −0.0948218 | − | 0.164236i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 513.000 | − | 888.542i | 0.0183240 | − | 0.0317382i | ||||
\(923\) | 21888.0 | 0.780555 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36656.0 | 1.30296 | ||||||||
\(926\) | 6504.00 | − | 11265.3i | 0.230815 | − | 0.399783i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6682.50 | + | 11574.4i | 0.236383 | + | 0.409428i | ||||
\(929\) | −7077.00 | + | 12257.7i | −0.249934 | + | 0.432899i | −0.963507 | − | 0.267682i | \(-0.913742\pi\) |
0.713573 | + | 0.700581i | \(0.247076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −852.000 | −0.0299444 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27954.0 | − | 48417.7i | −0.979318 | − | 1.69623i | ||||
\(935\) | 1890.00 | + | 3273.58i | 0.0661065 | + | 0.114500i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3781.00 | 0.131825 | 0.0659124 | − | 0.997825i | \(-0.479004\pi\) | ||||
0.0659124 | + | 0.997825i | \(0.479004\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −45.0000 | + | 77.9423i | −0.00156142 | + | 0.00270446i | ||||
\(941\) | 12931.5 | + | 22398.0i | 0.447986 | + | 0.775935i | 0.998255 | − | 0.0590530i | \(-0.0188081\pi\) |
−0.550269 | + | 0.834988i | \(0.685475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15120.0 | + | 26188.6i | −0.522137 | + | 0.904367i | ||||
\(944\) | 1065.00 | 0.0367191 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1170.00 | 0.0402114 | ||||||||
\(947\) | −21192.0 | + | 36705.6i | −0.727188 | + | 1.25953i | 0.230878 | + | 0.972983i | \(0.425840\pi\) |
−0.958067 | + | 0.286545i | \(0.907493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11584.0 | + | 20064.1i | 0.396241 | + | 0.686309i | ||||
\(950\) | 2784.00 | − | 4822.03i | 0.0950788 | − | 0.164681i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10530.0 | −0.357923 | −0.178961 | − | 0.983856i | \(-0.557274\pi\) | ||||
−0.178961 | + | 0.983856i | \(0.557274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5868.00 | − | 10163.7i | −0.198831 | − | 0.344386i | ||||
\(956\) | 2754.00 | + | 4770.07i | 0.0931702 | + | 0.161376i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 45234.0 | 1.52552 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17109.0 | + | 29633.7i | −0.574301 | + | 0.994718i | ||||
\(962\) | 30336.0 | + | 52543.5i | 1.01671 | + | 1.76099i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 395.500 | − | 685.026i | 0.0132139 | − | 0.0228871i | ||||
\(965\) | −4479.00 | −0.149414 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38341.0 | −1.27504 | −0.637520 | − | 0.770434i | \(-0.720040\pi\) | ||||
−0.637520 | + | 0.770434i | \(0.720040\pi\) | |||||||
\(968\) | −11613.0 | + | 20114.3i | −0.385595 | + | 0.667870i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2263.50 | − | 3920.50i | −0.0749243 | − | 0.129773i | ||||
\(971\) | −961.500 | + | 1665.37i | −0.0317776 | + | 0.0550403i | −0.881477 | − | 0.472227i | \(-0.843450\pi\) |
0.849699 | + | 0.527268i | \(0.176783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18663.0 | 0.613964 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4189.00 | + | 7255.56i | 0.137384 | + | 0.237956i | ||||
\(977\) | 28545.0 | + | 49441.4i | 0.934734 | + | 1.61901i | 0.775107 | + | 0.631830i | \(0.217696\pi\) |
0.159627 | + | 0.987177i | \(0.448971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13590.0 | 0.443655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11056.5 | + | 19150.4i | −0.359294 | + | 0.622316i | ||||
\(983\) | −2742.00 | − | 4749.28i | −0.0889687 | − | 0.154098i | 0.818107 | − | 0.575066i | \(-0.195024\pi\) |
−0.907075 | + | 0.420968i | \(0.861690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6129.00 | − | 10615.7i | 0.198260 | − | 0.343397i | ||||
\(986\) | 74844.0 | 2.41736 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1024.00 | 0.0329735 | ||||||||
\(989\) | −1092.00 | + | 1891.40i | −0.0351098 | + | 0.0608119i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11232.5 | + | 19455.3i | 0.360053 | + | 0.623629i | 0.987969 | − | 0.154651i | \(-0.0494254\pi\) |
−0.627917 | + | 0.778281i | \(0.716092\pi\) | |||||||
\(992\) | 5692.50 | − | 9859.70i | 0.182195 | − | 0.315570i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10668.0 | −0.339898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14683.0 | + | 25431.7i | 0.466415 | + | 0.807854i | 0.999264 | − | 0.0383563i | \(-0.0122122\pi\) |
−0.532850 | + | 0.846210i | \(0.678879\pi\) | |||||||
\(998\) | −6411.00 | − | 11104.2i | −0.203343 | − | 0.352201i | ||||
\(999\) | 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.c.226.1 | 2 | ||
3.2 | odd | 2 | 147.4.e.h.79.1 | 2 | |||
7.2 | even | 3 | 441.4.a.k.1.1 | 1 | |||
7.3 | odd | 6 | 63.4.e.a.46.1 | 2 | |||
7.4 | even | 3 | inner | 441.4.e.c.361.1 | 2 | ||
7.5 | odd | 6 | 441.4.a.l.1.1 | 1 | |||
7.6 | odd | 2 | 63.4.e.a.37.1 | 2 | |||
21.2 | odd | 6 | 147.4.a.a.1.1 | 1 | |||
21.5 | even | 6 | 147.4.a.b.1.1 | 1 | |||
21.11 | odd | 6 | 147.4.e.h.67.1 | 2 | |||
21.17 | even | 6 | 21.4.e.a.4.1 | ✓ | 2 | ||
21.20 | even | 2 | 21.4.e.a.16.1 | yes | 2 | ||
84.23 | even | 6 | 2352.4.a.bd.1.1 | 1 | |||
84.47 | odd | 6 | 2352.4.a.i.1.1 | 1 | |||
84.59 | odd | 6 | 336.4.q.e.193.1 | 2 | |||
84.83 | odd | 2 | 336.4.q.e.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.a.4.1 | ✓ | 2 | 21.17 | even | 6 | ||
21.4.e.a.16.1 | yes | 2 | 21.20 | even | 2 | ||
63.4.e.a.37.1 | 2 | 7.6 | odd | 2 | |||
63.4.e.a.46.1 | 2 | 7.3 | odd | 6 | |||
147.4.a.a.1.1 | 1 | 21.2 | odd | 6 | |||
147.4.a.b.1.1 | 1 | 21.5 | even | 6 | |||
147.4.e.h.67.1 | 2 | 21.11 | odd | 6 | |||
147.4.e.h.79.1 | 2 | 3.2 | odd | 2 | |||
336.4.q.e.193.1 | 2 | 84.59 | odd | 6 | |||
336.4.q.e.289.1 | 2 | 84.83 | odd | 2 | |||
441.4.a.k.1.1 | 1 | 7.2 | even | 3 | |||
441.4.a.l.1.1 | 1 | 7.5 | odd | 6 | |||
441.4.e.c.226.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.c.361.1 | 2 | 7.4 | even | 3 | inner | ||
2352.4.a.i.1.1 | 1 | 84.47 | odd | 6 | |||
2352.4.a.bd.1.1 | 1 | 84.23 | even | 6 |