Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,4,Mod(293,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.293");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.3465615417\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 293.20 | ||
Character | \(\chi\) | \(=\) | 294.293 |
Dual form | 294.4.d.b.293.19 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 4.92023 | + | 1.67071i | 0.946900 | + | 0.321529i | ||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −21.7262 | −1.94325 | −0.971626 | − | 0.236521i | \(-0.923993\pi\) | ||||
−0.971626 | + | 0.236521i | \(0.923993\pi\) | |||||||
\(6\) | −3.34143 | + | 9.84047i | −0.227355 | + | 0.669559i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | 21.4174 | + | 16.4406i | 0.793238 | + | 0.608912i | ||||
\(10\) | − | 43.4525i | − | 1.37409i | ||||||
\(11\) | − | 48.6690i | − | 1.33402i | −0.745048 | − | 0.667011i | \(-0.767573\pi\) | ||
0.745048 | − | 0.667011i | \(-0.232427\pi\) | |||||||
\(12\) | −19.6809 | − | 6.68286i | −0.473450 | − | 0.160765i | ||||
\(13\) | − | 13.5281i | − | 0.288618i | −0.989533 | − | 0.144309i | \(-0.953904\pi\) | ||
0.989533 | − | 0.144309i | \(-0.0460959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −106.898 | − | 36.2983i | −1.84007 | − | 0.624813i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 61.2540 | 0.873898 | 0.436949 | − | 0.899486i | \(-0.356059\pi\) | ||||
0.436949 | + | 0.899486i | \(0.356059\pi\) | |||||||
\(18\) | −32.8812 | + | 42.8348i | −0.430566 | + | 0.560904i | ||||
\(19\) | 27.4217i | 0.331104i | 0.986201 | + | 0.165552i | \(0.0529405\pi\) | ||||
−0.986201 | + | 0.165552i | \(0.947060\pi\) | |||||||
\(20\) | 86.9049 | 0.971626 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 97.3380 | 0.943297 | ||||||||
\(23\) | − | 139.599i | − | 1.26558i | −0.774324 | − | 0.632789i | \(-0.781910\pi\) | ||
0.774324 | − | 0.632789i | \(-0.218090\pi\) | |||||||
\(24\) | 13.3657 | − | 39.3619i | 0.113678 | − | 0.334780i | ||||
\(25\) | 347.029 | 2.77623 | ||||||||
\(26\) | 27.0563 | 0.204084 | ||||||||
\(27\) | 77.9112 | + | 116.674i | 0.555334 | + | 0.831628i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 82.4366i | − | 0.527865i | −0.964541 | − | 0.263933i | \(-0.914980\pi\) | ||
0.964541 | − | 0.263933i | \(-0.0850197\pi\) | |||||||
\(30\) | 72.5967 | − | 213.796i | 0.441809 | − | 1.30112i | ||||
\(31\) | − | 123.758i | − | 0.717017i | −0.933526 | − | 0.358509i | \(-0.883285\pi\) | ||
0.933526 | − | 0.358509i | \(-0.116715\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 81.3120 | − | 239.463i | 0.428927 | − | 1.26319i | ||||
\(34\) | 122.508i | 0.617940i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −85.6697 | − | 65.7625i | −0.396619 | − | 0.304456i | ||||
\(37\) | 44.9998 | 0.199944 | 0.0999718 | − | 0.994990i | \(-0.468125\pi\) | ||||
0.0999718 | + | 0.994990i | \(0.468125\pi\) | |||||||
\(38\) | −54.8434 | −0.234126 | ||||||||
\(39\) | 22.6017 | − | 66.5617i | 0.0927991 | − | 0.273292i | ||||
\(40\) | 173.810i | 0.687044i | ||||||||
\(41\) | −418.462 | −1.59397 | −0.796986 | − | 0.603998i | \(-0.793574\pi\) | ||||
−0.796986 | + | 0.603998i | \(0.793574\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 223.323 | 0.792012 | 0.396006 | − | 0.918248i | \(-0.370396\pi\) | ||||
0.396006 | + | 0.918248i | \(0.370396\pi\) | |||||||
\(44\) | 194.676i | 0.667011i | ||||||||
\(45\) | −465.320 | − | 357.193i | −1.54146 | − | 1.18327i | ||||
\(46\) | 279.197 | 0.894899 | ||||||||
\(47\) | −282.148 | −0.875650 | −0.437825 | − | 0.899060i | \(-0.644251\pi\) | ||||
−0.437825 | + | 0.899060i | \(0.644251\pi\) | |||||||
\(48\) | 78.7238 | + | 26.7314i | 0.236725 | + | 0.0803823i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 694.058i | 1.96309i | ||||||||
\(51\) | 301.384 | + | 102.338i | 0.827494 | + | 0.280984i | ||||
\(52\) | 54.1126i | 0.144309i | ||||||||
\(53\) | − | 648.059i | − | 1.67958i | −0.542912 | − | 0.839790i | \(-0.682678\pi\) | ||
0.542912 | − | 0.839790i | \(-0.317322\pi\) | |||||||
\(54\) | −233.348 | + | 155.822i | −0.588049 | + | 0.392680i | ||||
\(55\) | 1057.39i | 2.59234i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −45.8138 | + | 134.921i | −0.106459 | + | 0.313522i | ||||
\(58\) | 164.873 | 0.373257 | ||||||||
\(59\) | −190.334 | −0.419990 | −0.209995 | − | 0.977702i | \(-0.567345\pi\) | ||||
−0.209995 | + | 0.977702i | \(0.567345\pi\) | |||||||
\(60\) | 427.593 | + | 145.193i | 0.920033 | + | 0.312406i | ||||
\(61\) | − | 674.695i | − | 1.41616i | −0.706132 | − | 0.708080i | \(-0.749562\pi\) | ||
0.706132 | − | 0.708080i | \(-0.250438\pi\) | |||||||
\(62\) | 247.515 | 0.507008 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 293.916i | 0.560858i | ||||||||
\(66\) | 478.926 | + | 162.624i | 0.893207 | + | 0.303297i | ||||
\(67\) | −204.894 | −0.373609 | −0.186804 | − | 0.982397i | \(-0.559813\pi\) | ||||
−0.186804 | + | 0.982397i | \(0.559813\pi\) | |||||||
\(68\) | −245.016 | −0.436949 | ||||||||
\(69\) | 233.229 | − | 686.858i | 0.406920 | − | 1.19838i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 688.830i | − | 1.15140i | −0.817663 | − | 0.575698i | \(-0.804730\pi\) | ||
0.817663 | − | 0.575698i | \(-0.195270\pi\) | |||||||
\(72\) | 131.525 | − | 171.339i | 0.215283 | − | 0.280452i | ||||
\(73\) | 201.684i | 0.323361i | 0.986843 | + | 0.161680i | \(0.0516914\pi\) | ||||
−0.986843 | + | 0.161680i | \(0.948309\pi\) | |||||||
\(74\) | 89.9995i | 0.141381i | ||||||||
\(75\) | 1707.46 | + | 579.786i | 2.62881 | + | 0.892640i | ||||
\(76\) | − | 109.687i | − | 0.165552i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 133.123 | + | 45.2034i | 0.193247 | + | 0.0656189i | ||||
\(79\) | 317.046 | 0.451524 | 0.225762 | − | 0.974182i | \(-0.427513\pi\) | ||||
0.225762 | + | 0.974182i | \(0.427513\pi\) | |||||||
\(80\) | −347.620 | −0.485813 | ||||||||
\(81\) | 188.412 | + | 704.231i | 0.258453 | + | 0.966024i | ||||
\(82\) | − | 836.925i | − | 1.12711i | ||||||
\(83\) | 360.449 | 0.476680 | 0.238340 | − | 0.971182i | \(-0.423397\pi\) | ||||
0.238340 | + | 0.971182i | \(0.423397\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1330.82 | −1.69821 | ||||||||
\(86\) | 446.647i | 0.560037i | ||||||||
\(87\) | 137.728 | − | 405.608i | 0.169724 | − | 0.499836i | ||||
\(88\) | −389.352 | −0.471648 | ||||||||
\(89\) | 203.018 | 0.241797 | 0.120898 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(90\) | 714.385 | − | 930.640i | 0.836698 | − | 1.08998i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 558.394i | 0.632789i | ||||||||
\(93\) | 206.764 | − | 608.917i | 0.230542 | − | 0.678943i | ||||
\(94\) | − | 564.296i | − | 0.619178i | ||||||
\(95\) | − | 595.770i | − | 0.643418i | ||||||
\(96\) | −53.4629 | + | 157.448i | −0.0568389 | + | 0.167390i | ||||
\(97\) | − | 361.361i | − | 0.378254i | −0.981953 | − | 0.189127i | \(-0.939434\pi\) | ||
0.981953 | − | 0.189127i | \(-0.0605658\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 800.148 | − | 1042.36i | 0.812302 | − | 1.05820i | ||||
\(100\) | −1388.12 | −1.38812 | ||||||||
\(101\) | 404.006 | 0.398021 | 0.199011 | − | 0.979997i | \(-0.436227\pi\) | ||||
0.199011 | + | 0.979997i | \(0.436227\pi\) | |||||||
\(102\) | −204.676 | + | 602.768i | −0.198686 | + | 0.585127i | ||||
\(103\) | 1232.70i | 1.17924i | 0.807681 | + | 0.589620i | \(0.200722\pi\) | ||||
−0.807681 | + | 0.589620i | \(0.799278\pi\) | |||||||
\(104\) | −108.225 | −0.102042 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1296.12 | 1.18764 | ||||||||
\(107\) | 1088.36i | 0.983328i | 0.870785 | + | 0.491664i | \(0.163611\pi\) | ||||
−0.870785 | + | 0.491664i | \(0.836389\pi\) | |||||||
\(108\) | −311.645 | − | 466.696i | −0.277667 | − | 0.415814i | ||||
\(109\) | −793.844 | −0.697582 | −0.348791 | − | 0.937201i | \(-0.613408\pi\) | ||||
−0.348791 | + | 0.937201i | \(0.613408\pi\) | |||||||
\(110\) | −2114.79 | −1.83306 | ||||||||
\(111\) | 221.409 | + | 75.1818i | 0.189327 | + | 0.0642877i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 584.946i | − | 0.486966i | −0.969905 | − | 0.243483i | \(-0.921710\pi\) | ||
0.969905 | − | 0.243483i | \(-0.0782900\pi\) | |||||||
\(114\) | −269.842 | − | 91.6277i | −0.221693 | − | 0.0752782i | ||||
\(115\) | 3032.95i | 2.45934i | ||||||||
\(116\) | 329.747i | 0.263933i | ||||||||
\(117\) | 222.411 | − | 289.738i | 0.175743 | − | 0.228943i | ||||
\(118\) | − | 380.668i | − | 0.296978i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −290.387 | + | 855.185i | −0.220905 | + | 0.650561i | ||||
\(121\) | −1037.67 | −0.779617 | ||||||||
\(122\) | 1349.39 | 1.00138 | ||||||||
\(123\) | −2058.93 | − | 699.131i | −1.50933 | − | 0.512509i | ||||
\(124\) | 495.031i | 0.358509i | ||||||||
\(125\) | −4823.85 | −3.45167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 447.085 | 0.312381 | 0.156190 | − | 0.987727i | \(-0.450079\pi\) | ||||
0.156190 | + | 0.987727i | \(0.450079\pi\) | |||||||
\(128\) | − | 128.000i | − | 0.0883883i | ||||||
\(129\) | 1098.80 | + | 373.110i | 0.749956 | + | 0.254655i | ||||
\(130\) | −587.831 | −0.396586 | ||||||||
\(131\) | −2202.28 | −1.46881 | −0.734405 | − | 0.678711i | \(-0.762539\pi\) | ||||
−0.734405 | + | 0.678711i | \(0.762539\pi\) | |||||||
\(132\) | −325.248 | + | 957.851i | −0.214464 | + | 0.631593i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 409.788i | − | 0.264181i | ||||||
\(135\) | −1692.72 | − | 2534.89i | −1.07915 | − | 1.61606i | ||||
\(136\) | − | 490.032i | − | 0.308970i | ||||||
\(137\) | − | 355.722i | − | 0.221835i | −0.993830 | − | 0.110917i | \(-0.964621\pi\) | ||
0.993830 | − | 0.110917i | \(-0.0353789\pi\) | |||||||
\(138\) | 1373.72 | + | 466.459i | 0.847380 | + | 0.287736i | ||||
\(139\) | − | 1857.98i | − | 1.13376i | −0.823802 | − | 0.566878i | \(-0.808151\pi\) | ||
0.823802 | − | 0.566878i | \(-0.191849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1388.23 | − | 471.389i | −0.829152 | − | 0.281547i | ||||
\(142\) | 1377.66 | 0.814160 | ||||||||
\(143\) | −658.401 | −0.385023 | ||||||||
\(144\) | 342.679 | + | 263.050i | 0.198309 | + | 0.152228i | ||||
\(145\) | 1791.04i | 1.02578i | ||||||||
\(146\) | −403.368 | −0.228651 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −179.999 | −0.0999718 | ||||||||
\(149\) | 1412.62i | 0.776686i | 0.921515 | + | 0.388343i | \(0.126952\pi\) | ||||
−0.921515 | + | 0.388343i | \(0.873048\pi\) | |||||||
\(150\) | −1159.57 | + | 3414.93i | −0.631192 | + | 1.85885i | ||||
\(151\) | −169.505 | −0.0913519 | −0.0456760 | − | 0.998956i | \(-0.514544\pi\) | ||||
−0.0456760 | + | 0.998956i | \(0.514544\pi\) | |||||||
\(152\) | 219.374 | 0.117063 | ||||||||
\(153\) | 1311.90 | + | 1007.05i | 0.693209 | + | 0.532127i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2688.79i | 1.39335i | ||||||||
\(156\) | −90.4067 | + | 266.247i | −0.0463995 | + | 0.136646i | ||||
\(157\) | − | 1736.20i | − | 0.882573i | −0.897366 | − | 0.441286i | \(-0.854522\pi\) | ||
0.897366 | − | 0.441286i | \(-0.145478\pi\) | |||||||
\(158\) | 634.092i | 0.319276i | ||||||||
\(159\) | 1082.72 | − | 3188.60i | 0.540034 | − | 1.59039i | ||||
\(160\) | − | 695.239i | − | 0.343522i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1408.46 | + | 376.824i | −0.683082 | + | 0.182754i | ||||
\(163\) | −2991.62 | −1.43756 | −0.718778 | − | 0.695240i | \(-0.755298\pi\) | ||||
−0.718778 | + | 0.695240i | \(0.755298\pi\) | |||||||
\(164\) | 1673.85 | 0.796986 | ||||||||
\(165\) | −1766.60 | + | 5202.62i | −0.833514 | + | 2.45469i | ||||
\(166\) | 720.899i | 0.337064i | ||||||||
\(167\) | 2158.27 | 1.00007 | 0.500036 | − | 0.866004i | \(-0.333320\pi\) | ||||
0.500036 | + | 0.866004i | \(0.333320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2013.99 | 0.916700 | ||||||||
\(170\) | − | 2661.64i | − | 1.20081i | ||||||
\(171\) | −450.830 | + | 587.302i | −0.201613 | + | 0.262644i | ||||
\(172\) | −893.294 | −0.396006 | ||||||||
\(173\) | 1626.35 | 0.714735 | 0.357367 | − | 0.933964i | \(-0.383674\pi\) | ||||
0.357367 | + | 0.933964i | \(0.383674\pi\) | |||||||
\(174\) | 811.215 | + | 275.456i | 0.353437 | + | 0.120013i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 778.704i | − | 0.333506i | ||||||
\(177\) | −936.489 | − | 317.994i | −0.397688 | − | 0.135039i | ||||
\(178\) | 406.037i | 0.170976i | ||||||||
\(179\) | − | 1967.54i | − | 0.821570i | −0.911732 | − | 0.410785i | \(-0.865255\pi\) | ||
0.911732 | − | 0.410785i | \(-0.134745\pi\) | |||||||
\(180\) | 1861.28 | + | 1428.77i | 0.770731 | + | 0.591635i | ||||
\(181\) | − | 2783.32i | − | 1.14300i | −0.820603 | − | 0.571499i | \(-0.806362\pi\) | ||
0.820603 | − | 0.571499i | \(-0.193638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1127.22 | − | 3319.66i | 0.455337 | − | 1.34096i | ||||
\(184\) | −1116.79 | −0.447450 | ||||||||
\(185\) | −977.675 | −0.388541 | ||||||||
\(186\) | 1217.83 | + | 413.527i | 0.480085 | + | 0.163018i | ||||
\(187\) | − | 2981.17i | − | 1.16580i | ||||||
\(188\) | 1128.59 | 0.437825 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1191.54 | 0.454965 | ||||||||
\(191\) | 2821.24i | 1.06878i | 0.845237 | + | 0.534392i | \(0.179459\pi\) | ||||
−0.845237 | + | 0.534392i | \(0.820541\pi\) | |||||||
\(192\) | −314.895 | − | 106.926i | −0.118362 | − | 0.0401912i | ||||
\(193\) | 1214.08 | 0.452804 | 0.226402 | − | 0.974034i | \(-0.427304\pi\) | ||||
0.226402 | + | 0.974034i | \(0.427304\pi\) | |||||||
\(194\) | 722.722 | 0.267466 | ||||||||
\(195\) | −491.049 | + | 1446.13i | −0.180332 | + | 0.531076i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.68871i | 0.00205738i | 0.999999 | + | 0.00102869i | \(0.000327442\pi\) | ||||
−0.999999 | + | 0.00102869i | \(0.999673\pi\) | |||||||
\(198\) | 2084.73 | + | 1600.30i | 0.748259 | + | 0.574384i | ||||
\(199\) | − | 1137.21i | − | 0.405098i | −0.979272 | − | 0.202549i | \(-0.935077\pi\) | ||
0.979272 | − | 0.202549i | \(-0.0649225\pi\) | |||||||
\(200\) | − | 2776.23i | − | 0.981546i | ||||||
\(201\) | −1008.13 | − | 342.320i | −0.353770 | − | 0.120126i | ||||
\(202\) | 808.012i | 0.281443i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1205.54 | − | 409.352i | −0.413747 | − | 0.140492i | ||||
\(205\) | 9091.61 | 3.09749 | ||||||||
\(206\) | −2465.40 | −0.833849 | ||||||||
\(207\) | 2295.09 | − | 2989.84i | 0.770626 | − | 1.00390i | ||||
\(208\) | − | 216.450i | − | 0.0721545i | ||||||
\(209\) | 1334.59 | 0.441700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5612.13 | −1.83107 | −0.915533 | − | 0.402243i | \(-0.868231\pi\) | ||||
−0.915533 | + | 0.402243i | \(0.868231\pi\) | |||||||
\(212\) | 2592.23i | 0.839790i | ||||||||
\(213\) | 1150.84 | − | 3389.21i | 0.370207 | − | 1.09026i | ||||
\(214\) | −2176.73 | −0.695318 | ||||||||
\(215\) | −4851.98 | −1.53908 | ||||||||
\(216\) | 933.393 | − | 623.289i | 0.294025 | − | 0.196340i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 1587.69i | − | 0.493265i | ||||||
\(219\) | −336.957 | + | 992.333i | −0.103970 | + | 0.306190i | ||||
\(220\) | − | 4229.57i | − | 1.29617i | ||||||
\(221\) | − | 828.653i | − | 0.252223i | ||||||
\(222\) | −150.364 | + | 442.819i | −0.0454583 | + | 0.133874i | ||||
\(223\) | − | 1737.80i | − | 0.521846i | −0.965360 | − | 0.260923i | \(-0.915973\pi\) | ||
0.965360 | − | 0.260923i | \(-0.0840268\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7432.47 | + | 5705.37i | 2.20221 | + | 1.69048i | ||||
\(226\) | 1169.89 | 0.344337 | ||||||||
\(227\) | 2305.05 | 0.673972 | 0.336986 | − | 0.941510i | \(-0.390592\pi\) | ||||
0.336986 | + | 0.941510i | \(0.390592\pi\) | |||||||
\(228\) | 183.255 | − | 539.685i | 0.0532297 | − | 0.156761i | ||||
\(229\) | 5434.63i | 1.56826i | 0.620599 | + | 0.784128i | \(0.286889\pi\) | ||||
−0.620599 | + | 0.784128i | \(0.713111\pi\) | |||||||
\(230\) | −6065.90 | −1.73902 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −659.493 | −0.186629 | ||||||||
\(233\) | 3847.42i | 1.08177i | 0.841096 | + | 0.540885i | \(0.181911\pi\) | ||||
−0.841096 | + | 0.540885i | \(0.818089\pi\) | |||||||
\(234\) | 579.476 | + | 444.822i | 0.161887 | + | 0.124269i | ||||
\(235\) | 6130.01 | 1.70161 | ||||||||
\(236\) | 761.336 | 0.209995 | ||||||||
\(237\) | 1559.94 | + | 529.693i | 0.427548 | + | 0.145178i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6913.12i | 1.87101i | 0.353308 | + | 0.935507i | \(0.385057\pi\) | ||||
−0.353308 | + | 0.935507i | \(0.614943\pi\) | |||||||
\(240\) | −1710.37 | − | 580.773i | −0.460016 | − | 0.156203i | ||||
\(241\) | 5125.57i | 1.36999i | 0.728548 | + | 0.684994i | \(0.240195\pi\) | ||||
−0.728548 | + | 0.684994i | \(0.759805\pi\) | |||||||
\(242\) | − | 2075.34i | − | 0.551272i | ||||||
\(243\) | −249.538 | + | 3779.77i | −0.0658761 | + | 0.997828i | ||||
\(244\) | 2698.78i | 0.708080i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1398.26 | − | 4117.87i | 0.362398 | − | 1.06726i | ||||
\(247\) | 370.965 | 0.0955624 | ||||||||
\(248\) | −990.061 | −0.253504 | ||||||||
\(249\) | 1773.50 | + | 602.208i | 0.451368 | + | 0.153267i | ||||
\(250\) | − | 9647.70i | − | 2.44070i | ||||||
\(251\) | 4752.99 | 1.19524 | 0.597622 | − | 0.801778i | \(-0.296112\pi\) | ||||
0.597622 | + | 0.801778i | \(0.296112\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6794.12 | −1.68831 | ||||||||
\(254\) | 894.170i | 0.220887i | ||||||||
\(255\) | −6547.94 | − | 2223.42i | −1.60803 | − | 0.546023i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2684.79 | 0.651644 | 0.325822 | − | 0.945431i | \(-0.394359\pi\) | ||||
0.325822 | + | 0.945431i | \(0.394359\pi\) | |||||||
\(258\) | −746.220 | + | 2197.61i | −0.180068 | + | 0.530299i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1175.66i | − | 0.280429i | ||||||
\(261\) | 1355.31 | − | 1765.58i | 0.321424 | − | 0.418723i | ||||
\(262\) | − | 4404.56i | − | 1.03861i | ||||||
\(263\) | 1936.11i | 0.453937i | 0.973902 | + | 0.226968i | \(0.0728814\pi\) | ||||
−0.973902 | + | 0.226968i | \(0.927119\pi\) | |||||||
\(264\) | −1915.70 | − | 650.496i | −0.446604 | − | 0.151649i | ||||
\(265\) | 14079.9i | 3.26385i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 998.898 | + | 339.186i | 0.228957 | + | 0.0777447i | ||||
\(268\) | 819.577 | 0.186804 | ||||||||
\(269\) | 2558.15 | 0.579826 | 0.289913 | − | 0.957053i | \(-0.406374\pi\) | ||||
0.289913 | + | 0.957053i | \(0.406374\pi\) | |||||||
\(270\) | 5069.78 | − | 3385.43i | 1.14273 | − | 0.763077i | ||||
\(271\) | − | 1869.65i | − | 0.419090i | −0.977799 | − | 0.209545i | \(-0.932802\pi\) | ||
0.977799 | − | 0.209545i | \(-0.0671983\pi\) | |||||||
\(272\) | 980.064 | 0.218475 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 711.444 | 0.156861 | ||||||||
\(275\) | − | 16889.5i | − | 3.70356i | ||||||
\(276\) | −932.917 | + | 2747.43i | −0.203460 | + | 0.599188i | ||||
\(277\) | 3239.48 | 0.702677 | 0.351338 | − | 0.936249i | \(-0.385727\pi\) | ||||
0.351338 | + | 0.936249i | \(0.385727\pi\) | |||||||
\(278\) | 3715.96 | 0.801686 | ||||||||
\(279\) | 2034.65 | − | 2650.57i | 0.436600 | − | 0.568765i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7733.03i | − | 1.64169i | −0.571153 | − | 0.820843i | \(-0.693504\pi\) | ||
0.571153 | − | 0.820843i | \(-0.306496\pi\) | |||||||
\(282\) | 942.778 | − | 2776.47i | 0.199084 | − | 0.586299i | ||||
\(283\) | − | 1550.02i | − | 0.325580i | −0.986661 | − | 0.162790i | \(-0.947951\pi\) | ||
0.986661 | − | 0.162790i | \(-0.0520493\pi\) | |||||||
\(284\) | 2755.32i | 0.575698i | ||||||||
\(285\) | 995.362 | − | 2931.33i | 0.206878 | − | 0.609252i | ||||
\(286\) | − | 1316.80i | − | 0.272252i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −526.100 | + | 685.358i | −0.107641 | + | 0.140226i | ||||
\(289\) | −1160.95 | −0.236301 | ||||||||
\(290\) | −3582.07 | −0.725333 | ||||||||
\(291\) | 603.731 | − | 1777.98i | 0.121620 | − | 0.358169i | ||||
\(292\) | − | 806.736i | − | 0.161680i | ||||||
\(293\) | −1754.65 | −0.349856 | −0.174928 | − | 0.984581i | \(-0.555969\pi\) | ||||
−0.174928 | + | 0.984581i | \(0.555969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4135.24 | 0.816146 | ||||||||
\(296\) | − | 359.998i | − | 0.0706907i | ||||||
\(297\) | 5678.41 | − | 3791.86i | 1.10941 | − | 0.740828i | ||||
\(298\) | −2825.24 | −0.549200 | ||||||||
\(299\) | −1888.51 | −0.365269 | ||||||||
\(300\) | −6829.86 | − | 2319.15i | −1.31441 | − | 0.446320i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 339.011i | − | 0.0645956i | ||||||
\(303\) | 1987.81 | + | 674.979i | 0.376886 | + | 0.127975i | ||||
\(304\) | 438.747i | 0.0827759i | ||||||||
\(305\) | 14658.6i | 2.75196i | ||||||||
\(306\) | −2014.11 | + | 2623.81i | −0.376271 | + | 0.490173i | ||||
\(307\) | − | 3328.40i | − | 0.618768i | −0.950937 | − | 0.309384i | \(-0.899877\pi\) | ||
0.950937 | − | 0.309384i | \(-0.100123\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2059.49 | + | 6065.18i | −0.379160 | + | 1.11662i | ||||
\(310\) | −5377.57 | −0.985244 | ||||||||
\(311\) | −6516.09 | −1.18808 | −0.594041 | − | 0.804435i | \(-0.702468\pi\) | ||||
−0.594041 | + | 0.804435i | \(0.702468\pi\) | |||||||
\(312\) | −532.493 | − | 180.813i | −0.0966234 | − | 0.0328094i | ||||
\(313\) | − | 2138.94i | − | 0.386262i | −0.981173 | − | 0.193131i | \(-0.938136\pi\) | ||
0.981173 | − | 0.193131i | \(-0.0618642\pi\) | |||||||
\(314\) | 3472.40 | 0.624073 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1268.18 | −0.225762 | ||||||||
\(317\) | − | 2800.51i | − | 0.496190i | −0.968736 | − | 0.248095i | \(-0.920195\pi\) | ||
0.968736 | − | 0.248095i | \(-0.0798045\pi\) | |||||||
\(318\) | 6377.20 | + | 2165.44i | 1.12458 | + | 0.381862i | ||||
\(319\) | −4012.11 | −0.704184 | ||||||||
\(320\) | 1390.48 | 0.242907 | ||||||||
\(321\) | −1818.34 | + | 5355.00i | −0.316169 | + | 0.931113i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1679.69i | 0.289351i | ||||||||
\(324\) | −753.648 | − | 2816.93i | −0.129226 | − | 0.483012i | ||||
\(325\) | − | 4694.66i | − | 0.801270i | ||||||
\(326\) | − | 5983.24i | − | 1.01651i | ||||||
\(327\) | −3905.90 | − | 1326.29i | −0.660540 | − | 0.224293i | ||||
\(328\) | 3347.70i | 0.563554i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10405.2 | − | 3533.21i | −1.73573 | − | 0.589384i | ||||
\(331\) | 3547.29 | 0.589054 | 0.294527 | − | 0.955643i | \(-0.404838\pi\) | ||||
0.294527 | + | 0.955643i | \(0.404838\pi\) | |||||||
\(332\) | −1441.80 | −0.238340 | ||||||||
\(333\) | 963.779 | + | 739.824i | 0.158603 | + | 0.121748i | ||||
\(334\) | 4316.54i | 0.707158i | ||||||||
\(335\) | 4451.58 | 0.726017 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9536.10 | 1.54144 | 0.770719 | − | 0.637175i | \(-0.219897\pi\) | ||||
0.770719 | + | 0.637175i | \(0.219897\pi\) | |||||||
\(338\) | 4027.98i | 0.648205i | ||||||||
\(339\) | 977.278 | − | 2878.07i | 0.156574 | − | 0.461108i | ||||
\(340\) | 5323.27 | 0.849103 | ||||||||
\(341\) | −6023.16 | −0.956517 | ||||||||
\(342\) | −1174.60 | − | 901.659i | −0.185717 | − | 0.142562i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1786.59i | − | 0.280018i | ||||||
\(345\) | −5067.19 | + | 14922.8i | −0.790749 | + | 2.32875i | ||||
\(346\) | 3252.70i | 0.505394i | ||||||||
\(347\) | − | 11462.9i | − | 1.77338i | −0.462368 | − | 0.886688i | \(-0.653000\pi\) | ||
0.462368 | − | 0.886688i | \(-0.347000\pi\) | |||||||
\(348\) | −550.912 | + | 1622.43i | −0.0848621 | + | 0.249918i | ||||
\(349\) | − | 6414.25i | − | 0.983802i | −0.870651 | − | 0.491901i | \(-0.836302\pi\) | ||
0.870651 | − | 0.491901i | \(-0.163698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1578.38 | − | 1053.99i | 0.240023 | − | 0.160279i | ||||
\(352\) | 1557.41 | 0.235824 | ||||||||
\(353\) | 9432.88 | 1.42227 | 0.711135 | − | 0.703055i | \(-0.248181\pi\) | ||||
0.711135 | + | 0.703055i | \(0.248181\pi\) | |||||||
\(354\) | 635.988 | − | 1872.98i | 0.0954870 | − | 0.281208i | ||||
\(355\) | 14965.7i | 2.23745i | ||||||||
\(356\) | −812.073 | −0.120898 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3935.09 | 0.580938 | ||||||||
\(359\) | − | 2187.42i | − | 0.321582i | −0.986988 | − | 0.160791i | \(-0.948596\pi\) | ||
0.986988 | − | 0.160791i | \(-0.0514045\pi\) | |||||||
\(360\) | −2857.54 | + | 3722.56i | −0.418349 | + | 0.544989i | ||||
\(361\) | 6107.05 | 0.890370 | ||||||||
\(362\) | 5566.65 | 0.808222 | ||||||||
\(363\) | −5105.58 | − | 1733.65i | −0.738219 | − | 0.250670i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4381.83i | − | 0.628372i | ||||||
\(366\) | 6639.31 | + | 2254.44i | 0.948203 | + | 0.321972i | ||||
\(367\) | 6596.58i | 0.938253i | 0.883131 | + | 0.469127i | \(0.155431\pi\) | ||||
−0.883131 | + | 0.469127i | \(0.844569\pi\) | |||||||
\(368\) | − | 2233.58i | − | 0.316395i | ||||||
\(369\) | −8962.39 | − | 6879.78i | −1.26440 | − | 0.970588i | ||||
\(370\) | − | 1955.35i | − | 0.274740i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −827.055 | + | 2435.67i | −0.115271 | + | 0.339472i | ||||
\(373\) | −9102.50 | −1.26356 | −0.631782 | − | 0.775146i | \(-0.717676\pi\) | ||||
−0.631782 | + | 0.775146i | \(0.717676\pi\) | |||||||
\(374\) | 5962.34 | 0.824345 | ||||||||
\(375\) | −23734.5 | − | 8059.28i | −3.26838 | − | 1.10981i | ||||
\(376\) | 2257.18i | 0.309589i | ||||||||
\(377\) | −1115.21 | −0.152351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2129.23 | −0.288578 | −0.144289 | − | 0.989536i | \(-0.546090\pi\) | ||||
−0.144289 | + | 0.989536i | \(0.546090\pi\) | |||||||
\(380\) | 2383.08i | 0.321709i | ||||||||
\(381\) | 2199.76 | + | 746.951i | 0.295793 | + | 0.100440i | ||||
\(382\) | −5642.48 | −0.755745 | ||||||||
\(383\) | 8599.66 | 1.14732 | 0.573658 | − | 0.819095i | \(-0.305524\pi\) | ||||
0.573658 | + | 0.819095i | \(0.305524\pi\) | |||||||
\(384\) | 213.852 | − | 629.790i | 0.0284194 | − | 0.0836949i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2428.16i | 0.320181i | ||||||||
\(387\) | 4783.01 | + | 3671.58i | 0.628254 | + | 0.482265i | ||||
\(388\) | 1445.44i | 0.189127i | ||||||||
\(389\) | 8528.65i | 1.11162i | 0.831310 | + | 0.555809i | \(0.187591\pi\) | ||||
−0.831310 | + | 0.555809i | \(0.812409\pi\) | |||||||
\(390\) | −2892.27 | − | 982.098i | −0.375527 | − | 0.127514i | ||||
\(391\) | − | 8550.97i | − | 1.10599i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10835.7 | − | 3679.38i | −1.39082 | − | 0.472265i | ||||
\(394\) | −11.3774 | −0.00145479 | ||||||||
\(395\) | −6888.21 | −0.877426 | ||||||||
\(396\) | −3200.59 | + | 4169.46i | −0.406151 | + | 0.529099i | ||||
\(397\) | − | 3008.62i | − | 0.380349i | −0.981750 | − | 0.190174i | \(-0.939095\pi\) | ||
0.981750 | − | 0.190174i | \(-0.0609053\pi\) | |||||||
\(398\) | 2274.42 | 0.286448 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5552.46 | 0.694058 | ||||||||
\(401\) | 8292.05i | 1.03263i | 0.856398 | + | 0.516316i | \(0.172697\pi\) | ||||
−0.856398 | + | 0.516316i | \(0.827303\pi\) | |||||||
\(402\) | 684.639 | − | 2016.25i | 0.0849421 | − | 0.250153i | ||||
\(403\) | −1674.21 | −0.206944 | ||||||||
\(404\) | −1616.02 | −0.199011 | ||||||||
\(405\) | −4093.48 | − | 15300.3i | −0.502239 | − | 1.87723i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2190.09i | − | 0.266729i | ||||||
\(408\) | 818.704 | − | 2411.07i | 0.0993428 | − | 0.292563i | ||||
\(409\) | 11599.6i | 1.40236i | 0.712984 | + | 0.701180i | \(0.247343\pi\) | ||||
−0.712984 | + | 0.701180i | \(0.752657\pi\) | |||||||
\(410\) | 18183.2i | 2.19026i | ||||||||
\(411\) | 594.310 | − | 1750.24i | 0.0713264 | − | 0.210055i | ||||
\(412\) | − | 4930.81i | − | 0.589620i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5979.68 | + | 4590.17i | 0.709868 | + | 0.544915i | ||||
\(415\) | −7831.20 | −0.926310 | ||||||||
\(416\) | 432.901 | 0.0510209 | ||||||||
\(417\) | 3104.16 | − | 9141.71i | 0.364535 | − | 1.07355i | ||||
\(418\) | 2669.17i | 0.312329i | ||||||||
\(419\) | 11271.3 | 1.31417 | 0.657085 | − | 0.753816i | \(-0.271789\pi\) | ||||
0.657085 | + | 0.753816i | \(0.271789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1344.95 | 0.155697 | 0.0778487 | − | 0.996965i | \(-0.475195\pi\) | ||||
0.0778487 | + | 0.996965i | \(0.475195\pi\) | |||||||
\(422\) | − | 11224.3i | − | 1.29476i | ||||||
\(423\) | −6042.89 | − | 4638.69i | −0.694598 | − | 0.533193i | ||||
\(424\) | −5184.47 | −0.593821 | ||||||||
\(425\) | 21256.9 | 2.42614 | ||||||||
\(426\) | 6778.41 | + | 2301.68i | 0.770927 | + | 0.261776i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 4353.45i | − | 0.491664i | ||||||
\(429\) | −3239.49 | − | 1100.00i | −0.364578 | − | 0.123796i | ||||
\(430\) | − | 9703.95i | − | 1.08829i | ||||||
\(431\) | 15201.0i | 1.69885i | 0.527707 | + | 0.849427i | \(0.323052\pi\) | ||||
−0.527707 | + | 0.849427i | \(0.676948\pi\) | |||||||
\(432\) | 1246.58 | + | 1866.79i | 0.138833 | + | 0.207907i | ||||
\(433\) | − | 953.542i | − | 0.105830i | −0.998599 | − | 0.0529149i | \(-0.983149\pi\) | ||
0.998599 | − | 0.0529149i | \(-0.0168512\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2992.31 | + | 8812.32i | −0.329817 | + | 0.971307i | ||||
\(436\) | 3175.37 | 0.348791 | ||||||||
\(437\) | 3828.03 | 0.419038 | ||||||||
\(438\) | −1984.67 | − | 673.913i | −0.216509 | − | 0.0735179i | ||||
\(439\) | − | 7267.08i | − | 0.790066i | −0.918667 | − | 0.395033i | \(-0.870733\pi\) | ||
0.918667 | − | 0.395033i | \(-0.129267\pi\) | |||||||
\(440\) | 8459.15 | 0.916532 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1657.31 | 0.178348 | ||||||||
\(443\) | 158.197i | 0.0169665i | 0.999964 | + | 0.00848326i | \(0.00270034\pi\) | ||||
−0.999964 | + | 0.00848326i | \(0.997300\pi\) | |||||||
\(444\) | −885.637 | − | 300.727i | −0.0946633 | − | 0.0321439i | ||||
\(445\) | −4410.82 | −0.469872 | ||||||||
\(446\) | 3475.60 | 0.369001 | ||||||||
\(447\) | −2360.08 | + | 6950.42i | −0.249727 | + | 0.735444i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5856.97i | 0.615606i | 0.951450 | + | 0.307803i | \(0.0995938\pi\) | ||||
−0.951450 | + | 0.307803i | \(0.900406\pi\) | |||||||
\(450\) | −11410.7 | + | 14864.9i | −1.19535 | + | 1.55720i | ||||
\(451\) | 20366.1i | 2.12639i | ||||||||
\(452\) | 2339.79i | 0.243483i | ||||||||
\(453\) | −834.006 | − | 283.195i | −0.0865011 | − | 0.0293723i | ||||
\(454\) | 4610.10i | 0.476570i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1079.37 | + | 366.511i | 0.110847 | + | 0.0376391i | ||||
\(457\) | −9973.38 | −1.02086 | −0.510432 | − | 0.859918i | \(-0.670515\pi\) | ||||
−0.510432 | + | 0.859918i | \(0.670515\pi\) | |||||||
\(458\) | −10869.3 | −1.10892 | ||||||||
\(459\) | 4772.37 | + | 7146.76i | 0.485305 | + | 0.726758i | ||||
\(460\) | − | 12131.8i | − | 1.22967i | ||||||
\(461\) | −12159.0 | −1.22842 | −0.614209 | − | 0.789144i | \(-0.710525\pi\) | ||||
−0.614209 | + | 0.789144i | \(0.710525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5686.12 | −0.570748 | −0.285374 | − | 0.958416i | \(-0.592118\pi\) | ||||
−0.285374 | + | 0.958416i | \(0.592118\pi\) | |||||||
\(464\) | − | 1318.99i | − | 0.131966i | ||||||
\(465\) | −4492.20 | + | 13229.5i | −0.448001 | + | 1.31936i | ||||
\(466\) | −7694.83 | −0.764928 | ||||||||
\(467\) | 13467.8 | 1.33451 | 0.667254 | − | 0.744830i | \(-0.267469\pi\) | ||||
0.667254 | + | 0.744830i | \(0.267469\pi\) | |||||||
\(468\) | −889.644 | + | 1158.95i | −0.0878714 | + | 0.114471i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12260.0i | 1.20322i | ||||||||
\(471\) | 2900.70 | − | 8542.52i | 0.283773 | − | 0.835708i | ||||
\(472\) | 1522.67i | 0.148489i | ||||||||
\(473\) | − | 10868.9i | − | 1.05656i | ||||||
\(474\) | −1059.39 | + | 3119.88i | −0.102657 | + | 0.302322i | ||||
\(475\) | 9516.12i | 0.919220i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10654.5 | − | 13879.7i | 1.02272 | − | 1.33231i | ||||
\(478\) | −13826.2 | −1.32301 | ||||||||
\(479\) | 902.528 | 0.0860910 | 0.0430455 | − | 0.999073i | \(-0.486294\pi\) | ||||
0.0430455 | + | 0.999073i | \(0.486294\pi\) | |||||||
\(480\) | 1161.55 | − | 3420.74i | 0.110452 | − | 0.325281i | ||||
\(481\) | − | 608.763i | − | 0.0577073i | ||||||
\(482\) | −10251.1 | −0.968728 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4150.68 | 0.389808 | ||||||||
\(485\) | 7851.01i | 0.735044i | ||||||||
\(486\) | −7559.53 | − | 499.076i | −0.705571 | − | 0.0465814i | ||||
\(487\) | −10707.8 | −0.996341 | −0.498170 | − | 0.867079i | \(-0.665995\pi\) | ||||
−0.498170 | + | 0.867079i | \(0.665995\pi\) | |||||||
\(488\) | −5397.56 | −0.500688 | ||||||||
\(489\) | −14719.5 | − | 4998.14i | −1.36122 | − | 0.462216i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4248.26i | − | 0.390471i | −0.980756 | − | 0.195236i | \(-0.937453\pi\) | ||
0.980756 | − | 0.195236i | \(-0.0625472\pi\) | |||||||
\(492\) | 8235.73 | + | 2796.53i | 0.754666 | + | 0.256254i | ||||
\(493\) | − | 5049.57i | − | 0.461301i | ||||||
\(494\) | 741.929i | 0.0675728i | ||||||||
\(495\) | −17384.2 | + | 22646.6i | −1.57851 | + | 2.05635i | ||||
\(496\) | − | 1980.12i | − | 0.179254i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1204.42 | + | 3546.99i | −0.108376 | + | 0.319166i | ||||
\(499\) | 13120.7 | 1.17708 | 0.588542 | − | 0.808467i | \(-0.299702\pi\) | ||||
0.588542 | + | 0.808467i | \(0.299702\pi\) | |||||||
\(500\) | 19295.4 | 1.72583 | ||||||||
\(501\) | 10619.2 | + | 3605.86i | 0.946968 | + | 0.321553i | ||||
\(502\) | 9505.99i | 0.845165i | ||||||||
\(503\) | −12220.6 | −1.08328 | −0.541639 | − | 0.840611i | \(-0.682196\pi\) | ||||
−0.541639 | + | 0.840611i | \(0.682196\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8777.53 | −0.773456 | ||||||||
\(506\) | − | 13588.2i | − | 1.19382i | ||||||
\(507\) | 9909.30 | + | 3364.80i | 0.868023 | + | 0.294746i | ||||
\(508\) | −1788.34 | −0.156190 | ||||||||
\(509\) | −4376.04 | −0.381070 | −0.190535 | − | 0.981680i | \(-0.561022\pi\) | ||||
−0.190535 | + | 0.981680i | \(0.561022\pi\) | |||||||
\(510\) | 4446.84 | − | 13095.9i | 0.386096 | − | 1.13705i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | −3199.40 | + | 2136.46i | −0.275355 | + | 0.183873i | ||||
\(514\) | 5369.57i | 0.460782i | ||||||||
\(515\) | − | 26782.0i | − | 2.29156i | ||||||
\(516\) | −4395.21 | − | 1492.44i | −0.374978 | − | 0.127327i | ||||
\(517\) | 13731.9i | 1.16814i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8002.02 | + | 2717.17i | 0.676782 | + | 0.229808i | ||||
\(520\) | 2351.32 | 0.198293 | ||||||||
\(521\) | −10723.9 | −0.901772 | −0.450886 | − | 0.892582i | \(-0.648892\pi\) | ||||
−0.450886 | + | 0.892582i | \(0.648892\pi\) | |||||||
\(522\) | 3531.16 | + | 2710.62i | 0.296082 | + | 0.227281i | ||||
\(523\) | − | 9119.08i | − | 0.762427i | −0.924487 | − | 0.381214i | \(-0.875506\pi\) | ||
0.924487 | − | 0.381214i | \(-0.124494\pi\) | |||||||
\(524\) | 8809.12 | 0.734405 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3872.21 | −0.320982 | ||||||||
\(527\) | − | 7580.65i | − | 0.626600i | ||||||
\(528\) | 1300.99 | − | 3831.41i | 0.107232 | − | 0.315796i | ||||
\(529\) | −7320.75 | −0.601689 | ||||||||
\(530\) | −28159.7 | −2.30789 | ||||||||
\(531\) | −4076.47 | − | 3129.21i | −0.333152 | − | 0.255737i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5661.02i | 0.460049i | ||||||||
\(534\) | −678.371 | + | 1997.80i | −0.0549738 | + | 0.161897i | ||||
\(535\) | − | 23646.0i | − | 1.91085i | ||||||
\(536\) | 1639.15i | 0.132091i | ||||||||
\(537\) | 3287.20 | − | 9680.77i | 0.264159 | − | 0.777944i | ||||
\(538\) | 5116.30i | 0.409999i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6770.86 | + | 10139.6i | 0.539577 | + | 0.808031i | ||||
\(541\) | 19220.5 | 1.52746 | 0.763728 | − | 0.645539i | \(-0.223367\pi\) | ||||
0.763728 | + | 0.645539i | \(0.223367\pi\) | |||||||
\(542\) | 3739.31 | 0.296341 | ||||||||
\(543\) | 4650.14 | − | 13694.6i | 0.367507 | − | 1.08231i | ||||
\(544\) | 1960.13i | 0.154485i | ||||||||
\(545\) | 17247.2 | 1.35558 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10042.0 | −0.784946 | −0.392473 | − | 0.919764i | \(-0.628380\pi\) | ||||
−0.392473 | + | 0.919764i | \(0.628380\pi\) | |||||||
\(548\) | 1422.89i | 0.110917i | ||||||||
\(549\) | 11092.4 | − | 14450.2i | 0.862317 | − | 1.12335i | ||||
\(550\) | 33779.1 | 2.61881 | ||||||||
\(551\) | 2260.55 | 0.174778 | ||||||||
\(552\) | −5494.86 | − | 1865.83i | −0.423690 | − | 0.143868i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6478.96i | 0.496868i | ||||||||
\(555\) | −4810.39 | − | 1633.42i | −0.367909 | − | 0.124927i | ||||
\(556\) | 7431.93i | 0.566878i | ||||||||
\(557\) | 17628.0i | 1.34098i | 0.741920 | + | 0.670488i | \(0.233915\pi\) | ||||
−0.741920 | + | 0.670488i | \(0.766085\pi\) | |||||||
\(558\) | 5301.14 | + | 4069.30i | 0.402178 | + | 0.308723i | ||||
\(559\) | − | 3021.15i | − | 0.228589i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4980.68 | − | 14668.1i | 0.374839 | − | 1.10390i | ||||
\(562\) | 15466.1 | 1.16085 | ||||||||
\(563\) | −19043.6 | −1.42556 | −0.712782 | − | 0.701386i | \(-0.752565\pi\) | ||||
−0.712782 | + | 0.701386i | \(0.752565\pi\) | |||||||
\(564\) | 5552.94 | + | 1885.56i | 0.414576 | + | 0.140773i | ||||
\(565\) | 12708.7i | 0.946297i | ||||||||
\(566\) | 3100.04 | 0.230220 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5510.64 | −0.407080 | ||||||||
\(569\) | − | 8296.20i | − | 0.611239i | −0.952154 | − | 0.305619i | \(-0.901136\pi\) | ||
0.952154 | − | 0.305619i | \(-0.0988635\pi\) | |||||||
\(570\) | 5862.66 | + | 1990.72i | 0.430806 | + | 0.146285i | ||||
\(571\) | −1386.13 | −0.101589 | −0.0507947 | − | 0.998709i | \(-0.516175\pi\) | ||||
−0.0507947 | + | 0.998709i | \(0.516175\pi\) | |||||||
\(572\) | 2633.60 | 0.192511 | ||||||||
\(573\) | −4713.49 | + | 13881.2i | −0.343645 | + | 1.01203i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 48444.7i | − | 3.51354i | ||||||
\(576\) | −1370.72 | − | 1052.20i | −0.0991547 | − | 0.0761140i | ||||
\(577\) | − | 14971.8i | − | 1.08022i | −0.841595 | − | 0.540108i | \(-0.818383\pi\) | ||
0.841595 | − | 0.540108i | \(-0.181617\pi\) | |||||||
\(578\) | − | 2321.90i | − | 0.167090i | ||||||
\(579\) | 5973.55 | + | 2028.38i | 0.428760 | + | 0.145590i | ||||
\(580\) | − | 7164.15i | − | 0.512888i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3555.96 | + | 1207.46i | 0.253264 | + | 0.0859982i | ||||
\(583\) | −31540.4 | −2.24060 | ||||||||
\(584\) | 1613.47 | 0.114325 | ||||||||
\(585\) | −4832.15 | + | 6294.92i | −0.341513 | + | 0.444894i | ||||
\(586\) | − | 3509.30i | − | 0.247386i | ||||||
\(587\) | 4416.35 | 0.310532 | 0.155266 | − | 0.987873i | \(-0.450377\pi\) | ||||
0.155266 | + | 0.987873i | \(0.450377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3393.64 | 0.237407 | ||||||||
\(590\) | 8270.48i | 0.577102i | ||||||||
\(591\) | −9.50422 | + | 27.9898i | −0.000661508 | + | 0.00194813i | ||||
\(592\) | 719.996 | 0.0499859 | ||||||||
\(593\) | 5548.49 | 0.384231 | 0.192116 | − | 0.981372i | \(-0.438465\pi\) | ||||
0.192116 | + | 0.981372i | \(0.438465\pi\) | |||||||
\(594\) | 7583.71 | + | 11356.8i | 0.523844 | + | 0.784471i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5650.47i | − | 0.388343i | ||||||
\(597\) | 1899.95 | − | 5595.33i | 0.130251 | − | 0.383587i | ||||
\(598\) | − | 3777.02i | − | 0.258284i | ||||||
\(599\) | − | 2016.74i | − | 0.137566i | −0.997632 | − | 0.0687829i | \(-0.978088\pi\) | ||
0.997632 | − | 0.0687829i | \(-0.0219116\pi\) | |||||||
\(600\) | 4638.29 | − | 13659.7i | 0.315596 | − | 0.929426i | ||||
\(601\) | 5439.16i | 0.369165i | 0.982817 | + | 0.184582i | \(0.0590933\pi\) | ||||
−0.982817 | + | 0.184582i | \(0.940907\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4388.30 | − | 3368.59i | −0.296361 | − | 0.227495i | ||||
\(604\) | 678.021 | 0.0456760 | ||||||||
\(605\) | 22544.6 | 1.51499 | ||||||||
\(606\) | −1349.96 | + | 3975.61i | −0.0904923 | + | 0.266499i | ||||
\(607\) | − | 22433.8i | − | 1.50010i | −0.661381 | − | 0.750050i | \(-0.730029\pi\) | ||
0.661381 | − | 0.750050i | \(-0.269971\pi\) | |||||||
\(608\) | −877.494 | −0.0585314 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29317.1 | −1.94593 | ||||||||
\(611\) | 3816.94i | 0.252728i | ||||||||
\(612\) | −5247.61 | − | 4028.21i | −0.346605 | − | 0.266064i | ||||
\(613\) | 3599.69 | 0.237178 | 0.118589 | − | 0.992943i | \(-0.462163\pi\) | ||||
0.118589 | + | 0.992943i | \(0.462163\pi\) | |||||||
\(614\) | 6656.79 | 0.437535 | ||||||||
\(615\) | 44732.9 | + | 15189.5i | 2.93301 | + | 0.995934i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21419.4i | 1.39759i | 0.715321 | + | 0.698796i | \(0.246280\pi\) | ||||
−0.715321 | + | 0.698796i | \(0.753720\pi\) | |||||||
\(618\) | −12130.4 | − | 4118.99i | −0.789571 | − | 0.268107i | ||||
\(619\) | − | 18366.9i | − | 1.19262i | −0.802756 | − | 0.596308i | \(-0.796634\pi\) | ||
0.802756 | − | 0.596308i | \(-0.203366\pi\) | |||||||
\(620\) | − | 10755.1i | − | 0.696673i | ||||||
\(621\) | 16287.5 | − | 10876.3i | 1.05249 | − | 0.702818i | ||||
\(622\) | − | 13032.2i | − | 0.840101i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 361.627 | − | 1064.99i | 0.0231998 | − | 0.0683231i | ||||
\(625\) | 61425.5 | 3.93123 | ||||||||
\(626\) | 4277.88 | 0.273128 | ||||||||
\(627\) | 6566.48 | + | 2229.71i | 0.418245 | + | 0.142019i | ||||
\(628\) | 6944.80i | 0.441286i | ||||||||
\(629\) | 2756.41 | 0.174730 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21152.9 | 1.33452 | 0.667262 | − | 0.744823i | \(-0.267466\pi\) | ||||
0.667262 | + | 0.744823i | \(0.267466\pi\) | |||||||
\(632\) | − | 2536.37i | − | 0.159638i | ||||||
\(633\) | −27613.0 | − | 9376.27i | −1.73384 | − | 0.588741i | ||||
\(634\) | 5601.02 | 0.350859 | ||||||||
\(635\) | −9713.47 | −0.607035 | ||||||||
\(636\) | −4330.88 | + | 12754.4i | −0.270017 | + | 0.795197i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 8024.21i | − | 0.497934i | ||||||
\(639\) | 11324.8 | − | 14753.0i | 0.701098 | − | 0.913331i | ||||
\(640\) | 2780.96i | 0.171761i | ||||||||
\(641\) | 2450.79i | 0.151014i | 0.997145 | + | 0.0755072i | \(0.0240576\pi\) | ||||
−0.997145 | + | 0.0755072i | \(0.975942\pi\) | |||||||
\(642\) | −10710.0 | − | 3636.69i | −0.658396 | − | 0.223565i | ||||
\(643\) | − | 15343.8i | − | 0.941056i | −0.882385 | − | 0.470528i | \(-0.844063\pi\) | ||
0.882385 | − | 0.470528i | \(-0.155937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23872.9 | − | 8106.27i | −1.45735 | − | 0.494859i | ||||
\(646\) | −3359.38 | −0.204602 | ||||||||
\(647\) | −5712.58 | −0.347117 | −0.173558 | − | 0.984824i | \(-0.555527\pi\) | ||||
−0.173558 | + | 0.984824i | \(0.555527\pi\) | |||||||
\(648\) | 5633.85 | − | 1507.30i | 0.341541 | − | 0.0913769i | ||||
\(649\) | 9263.37i | 0.560276i | ||||||||
\(650\) | 9389.32 | 0.566584 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11966.5 | 0.718778 | ||||||||
\(653\) | − | 15033.5i | − | 0.900930i | −0.892794 | − | 0.450465i | \(-0.851258\pi\) | ||
0.892794 | − | 0.450465i | \(-0.148742\pi\) | |||||||
\(654\) | 2652.57 | − | 7811.79i | 0.158599 | − | 0.467072i | ||||
\(655\) | 47847.2 | 2.85427 | ||||||||
\(656\) | −6695.40 | −0.398493 | ||||||||
\(657\) | −3315.81 | + | 4319.55i | −0.196898 | + | 0.256502i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24135.6i | 1.42669i | 0.700813 | + | 0.713345i | \(0.252821\pi\) | ||||
−0.700813 | + | 0.713345i | \(0.747179\pi\) | |||||||
\(660\) | 7066.41 | − | 20810.5i | 0.416757 | − | 1.22734i | ||||
\(661\) | − | 3739.96i | − | 0.220072i | −0.993928 | − | 0.110036i | \(-0.964903\pi\) | ||
0.993928 | − | 0.110036i | \(-0.0350966\pi\) | |||||||
\(662\) | 7094.59i | 0.416524i | ||||||||
\(663\) | 1384.44 | − | 4077.17i | 0.0810970 | − | 0.238830i | ||||
\(664\) | − | 2883.59i | − | 0.168532i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1479.65 | + | 1927.56i | −0.0860889 | + | 0.112149i | ||||
\(667\) | −11508.0 | −0.668055 | ||||||||
\(668\) | −8633.09 | −0.500036 | ||||||||
\(669\) | 2903.37 | − | 8550.38i | 0.167789 | − | 0.494136i | ||||
\(670\) | 8903.15i | 0.513371i | ||||||||
\(671\) | −32836.7 | −1.88919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11803.0 | −0.676037 | −0.338018 | − | 0.941140i | \(-0.609757\pi\) | ||||
−0.338018 | + | 0.941140i | \(0.609757\pi\) | |||||||
\(674\) | 19072.2i | 1.08996i | ||||||||
\(675\) | 27037.4 | + | 40489.3i | 1.54174 | + | 2.30879i | ||||
\(676\) | −8055.96 | −0.458350 | ||||||||
\(677\) | −30670.1 | −1.74113 | −0.870567 | − | 0.492050i | \(-0.836248\pi\) | ||||
−0.870567 | + | 0.492050i | \(0.836248\pi\) | |||||||
\(678\) | 5756.15 | + | 1954.56i | 0.326052 | + | 0.110714i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10646.5i | 0.600406i | ||||||||
\(681\) | 11341.4 | + | 3851.08i | 0.638184 | + | 0.216702i | ||||
\(682\) | − | 12046.3i | − | 0.676360i | ||||||
\(683\) | − | 14007.5i | − | 0.784747i | −0.919806 | − | 0.392374i | \(-0.871654\pi\) | ||
0.919806 | − | 0.392374i | \(-0.128346\pi\) | |||||||
\(684\) | 1803.32 | − | 2349.21i | 0.100806 | − | 0.131322i | ||||
\(685\) | 7728.49i | 0.431081i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9079.72 | + | 26739.7i | −0.504240 | + | 1.48498i | ||||
\(688\) | 3573.17 | 0.198003 | ||||||||
\(689\) | −8767.03 | −0.484757 | ||||||||
\(690\) | −29845.6 | − | 10134.4i | −1.64667 | − | 0.559144i | ||||
\(691\) | − | 9461.83i | − | 0.520905i | −0.965487 | − | 0.260452i | \(-0.916128\pi\) | ||
0.965487 | − | 0.260452i | \(-0.0838717\pi\) | |||||||
\(692\) | −6505.40 | −0.357367 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22925.8 | 1.25397 | ||||||||
\(695\) | 40366.9i | 2.20317i | ||||||||
\(696\) | −3244.86 | − | 1101.82i | −0.176719 | − | 0.0600066i | ||||
\(697\) | −25632.5 | −1.39297 | ||||||||
\(698\) | 12828.5 | 0.695653 | ||||||||
\(699\) | −6427.94 | + | 18930.2i | −0.347821 | + | 1.02433i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8147.43i | − | 0.438979i | −0.975615 | − | 0.219489i | \(-0.929561\pi\) | ||
0.975615 | − | 0.219489i | \(-0.0704391\pi\) | |||||||
\(702\) | 2107.99 | + | 3156.77i | 0.113335 | + | 0.169722i | ||||
\(703\) | 1233.97i | 0.0662020i | ||||||||
\(704\) | 3114.81i | 0.166753i | ||||||||
\(705\) | 30161.1 | + | 10241.5i | 1.61125 | + | 0.547117i | ||||
\(706\) | 18865.8i | 1.00570i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3745.95 | + | 1271.98i | 0.198844 | + | 0.0675195i | ||||
\(709\) | −28097.3 | −1.48831 | −0.744157 | − | 0.668005i | \(-0.767149\pi\) | ||||
−0.744157 | + | 0.668005i | \(0.767149\pi\) | |||||||
\(710\) | −29931.4 | −1.58212 | ||||||||
\(711\) | 6790.30 | + | 5212.43i | 0.358166 | + | 0.274939i | ||||
\(712\) | − | 1624.15i | − | 0.0854880i | ||||||
\(713\) | −17276.4 | −0.907441 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14304.6 | 0.748197 | ||||||||
\(716\) | 7870.17i | 0.410785i | ||||||||
\(717\) | −11549.8 | + | 34014.2i | −0.601586 | + | 1.77166i | ||||
\(718\) | 4374.85 | 0.227393 | ||||||||
\(719\) | −21857.1 | −1.13370 | −0.566851 | − | 0.823821i | \(-0.691838\pi\) | ||||
−0.566851 | + | 0.823821i | \(0.691838\pi\) | |||||||
\(720\) | −7445.12 | − | 5715.08i | −0.385365 | − | 0.295817i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12214.1i | 0.629587i | ||||||||
\(723\) | −8563.37 | + | 25219.0i | −0.440491 | + | 1.29724i | ||||
\(724\) | 11133.3i | 0.571499i | ||||||||
\(725\) | − | 28607.9i | − | 1.46548i | ||||||
\(726\) | 3467.30 | − | 10211.2i | 0.177250 | − | 0.521999i | ||||
\(727\) | 29.7842i | 0.00151944i | 1.00000 | 0.000759722i | \(0.000241827\pi\) | |||||
−1.00000 | 0.000759722i | \(0.999758\pi\) | ||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7542.70 | + | 18180.4i | −0.383209 | + | 0.923662i | ||||
\(730\) | 8763.67 | 0.444326 | ||||||||
\(731\) | 13679.5 | 0.692138 | ||||||||
\(732\) | −4508.89 | + | 13278.6i | −0.227668 | + | 0.670481i | ||||
\(733\) | 33848.6i | 1.70563i | 0.522213 | + | 0.852815i | \(0.325107\pi\) | ||||
−0.522213 | + | 0.852815i | \(0.674893\pi\) | |||||||
\(734\) | −13193.2 | −0.663445 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4467.15 | 0.223725 | ||||||||
\(737\) | 9971.99i | 0.498403i | ||||||||
\(738\) | 13759.6 | − | 17924.8i | 0.686310 | − | 0.894065i | ||||
\(739\) | 25275.2 | 1.25814 | 0.629068 | − | 0.777350i | \(-0.283437\pi\) | ||||
0.629068 | + | 0.777350i | \(0.283437\pi\) | |||||||
\(740\) | 3910.70 | 0.194270 | ||||||||
\(741\) | 1825.23 | + | 619.776i | 0.0904880 | + | 0.0307261i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9958.69i | 0.491721i | 0.969305 | + | 0.245861i | \(0.0790705\pi\) | ||||
−0.969305 | + | 0.245861i | \(0.920929\pi\) | |||||||
\(744\) | −4871.33 | − | 1654.11i | −0.240043 | − | 0.0815089i | ||||
\(745\) | − | 30690.9i | − | 1.50930i | ||||||
\(746\) | − | 18205.0i | − | 0.893475i | ||||||
\(747\) | 7719.89 | + | 5926.01i | 0.378121 | + | 0.290256i | ||||
\(748\) | 11924.7i | 0.582900i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 16118.6 | − | 47469.0i | 0.784756 | − | 2.31110i | ||||
\(751\) | 13112.3 | 0.637119 | 0.318559 | − | 0.947903i | \(-0.396801\pi\) | ||||
0.318559 | + | 0.947903i | \(0.396801\pi\) | |||||||
\(752\) | −4514.37 | −0.218912 | ||||||||
\(753\) | 23385.8 | + | 7940.90i | 1.13178 | + | 0.384306i | ||||
\(754\) | − | 2230.43i | − | 0.107729i | ||||||
\(755\) | 3682.71 | 0.177520 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28844.1 | 1.38488 | 0.692442 | − | 0.721473i | \(-0.256535\pi\) | ||||
0.692442 | + | 0.721473i | \(0.256535\pi\) | |||||||
\(758\) | − | 4258.46i | − | 0.204056i | ||||||
\(759\) | −33428.7 | − | 11351.0i | −1.59866 | − | 0.542841i | ||||
\(760\) | −4766.16 | −0.227483 | ||||||||
\(761\) | −17175.4 | −0.818144 | −0.409072 | − | 0.912502i | \(-0.634147\pi\) | ||||
−0.409072 | + | 0.912502i | \(0.634147\pi\) | |||||||
\(762\) | −1493.90 | + | 4399.53i | −0.0710215 | + | 0.209157i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 11285.0i | − | 0.534392i | ||||||
\(765\) | −28502.7 | − | 21879.5i | −1.34708 | − | 1.03406i | ||||
\(766\) | 17199.3i | 0.811275i | ||||||||
\(767\) | 2574.87i | 0.121217i | ||||||||
\(768\) | 1259.58 | + | 427.703i | 0.0591812 | + | 0.0200956i | ||||
\(769\) | − | 34779.8i | − | 1.63094i | −0.578800 | − | 0.815470i | \(-0.696479\pi\) | ||
0.578800 | − | 0.815470i | \(-0.303521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13209.8 | + | 4485.51i | 0.617041 | + | 0.209522i | ||||
\(772\) | −4856.31 | −0.226402 | ||||||||
\(773\) | −16923.2 | −0.787432 | −0.393716 | − | 0.919232i | \(-0.628811\pi\) | ||||
−0.393716 | + | 0.919232i | \(0.628811\pi\) | |||||||
\(774\) | −7343.15 | + | 9566.02i | −0.341013 | + | 0.444242i | ||||
\(775\) | − | 42947.5i | − | 1.99061i | ||||||
\(776\) | −2890.89 | −0.133733 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17057.3 | −0.786033 | ||||||||
\(779\) | − | 11474.9i | − | 0.527770i | ||||||
\(780\) | 1964.20 | − | 5784.54i | 0.0901661 | − | 0.265538i | ||||
\(781\) | −33524.7 | −1.53599 | ||||||||
\(782\) | 17101.9 | 0.782051 | ||||||||
\(783\) | 9618.22 | − | 6422.73i | 0.438987 | − | 0.293141i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37721.1i | 1.71506i | ||||||||
\(786\) | 7358.76 | − | 21671.5i | 0.333942 | − | 0.983455i | ||||
\(787\) | 39489.6i | 1.78863i | 0.447436 | + | 0.894316i | \(0.352337\pi\) | ||||
−0.447436 | + | 0.894316i | \(0.647663\pi\) | |||||||
\(788\) | − | 22.7548i | − | 0.00102869i | ||||||
\(789\) | −3234.68 | + | 9526.09i | −0.145954 | + | 0.429833i | ||||
\(790\) | − | 13776.4i | − | 0.620434i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8338.91 | − | 6401.19i | −0.374129 | − | 0.287192i | ||||
\(793\) | −9127.37 | −0.408729 | ||||||||
\(794\) | 6017.24 | 0.268947 | ||||||||
\(795\) | −23523.4 | + | 69276.3i | −1.04942 | + | 3.09054i | ||||
\(796\) | 4548.83i | 0.202549i | ||||||||
\(797\) | 32760.9 | 1.45602 | 0.728012 | − | 0.685565i | \(-0.240445\pi\) | ||||
0.728012 | + | 0.685565i | \(0.240445\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17282.7 | −0.765229 | ||||||||
\(800\) | 11104.9i | 0.490773i | ||||||||
\(801\) | 4348.13 | + | 3337.75i | 0.191802 | + | 0.147233i | ||||
\(802\) | −16584.1 | −0.730180 | ||||||||
\(803\) | 9815.76 | 0.431371 | ||||||||
\(804\) | 4032.51 | + | 1369.28i | 0.176885 | + | 0.0600631i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3348.42i | − | 0.146331i | ||||||
\(807\) | 12586.7 | + | 4273.94i | 0.549037 | + | 0.186431i | ||||
\(808\) | − | 3232.05i | − | 0.140722i | ||||||
\(809\) | 24216.1i | 1.05240i | 0.850360 | + | 0.526201i | \(0.176384\pi\) | ||||
−0.850360 | + | 0.526201i | \(0.823616\pi\) | |||||||
\(810\) | 30600.6 | − | 8186.97i | 1.32740 | − | 0.355137i | ||||
\(811\) | − | 27676.9i | − | 1.19836i | −0.800615 | − | 0.599179i | \(-0.795494\pi\) | ||
0.800615 | − | 0.599179i | \(-0.204506\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3123.66 | − | 9199.13i | 0.134750 | − | 0.396836i | ||||
\(814\) | 4380.18 | 0.188606 | ||||||||
\(815\) | 64996.6 | 2.79353 | ||||||||
\(816\) | 4822.14 | + | 1637.41i | 0.206874 | + | 0.0702460i | ||||
\(817\) | 6123.91i | 0.262238i | ||||||||
\(818\) | −23199.3 | −0.991618 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36366.4 | −1.54875 | ||||||||
\(821\) | − | 36666.3i | − | 1.55866i | −0.626612 | − | 0.779331i | \(-0.715559\pi\) | ||
0.626612 | − | 0.779331i | \(-0.284441\pi\) | |||||||
\(822\) | 3500.47 | + | 1188.62i | 0.148532 | + | 0.0504354i | ||||
\(823\) | −39504.0 | −1.67318 | −0.836588 | − | 0.547833i | \(-0.815453\pi\) | ||||
−0.836588 | + | 0.547833i | \(0.815453\pi\) | |||||||
\(824\) | 9861.61 | 0.416924 | ||||||||
\(825\) | 28217.6 | − | 83100.5i | 1.19080 | − | 3.50690i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36665.1i | − | 1.54168i | −0.637029 | − | 0.770840i | \(-0.719837\pi\) | ||
0.637029 | − | 0.770840i | \(-0.280163\pi\) | |||||||
\(828\) | −9180.35 | + | 11959.4i | −0.385313 | + | 0.501952i | ||||
\(829\) | 17217.1i | 0.721320i | 0.932697 | + | 0.360660i | \(0.117449\pi\) | ||||
−0.932697 | + | 0.360660i | \(0.882551\pi\) | |||||||
\(830\) | − | 15662.4i | − | 0.655000i | ||||||
\(831\) | 15939.0 | + | 5412.25i | 0.665365 | + | 0.225931i | ||||
\(832\) | 865.801i | 0.0360772i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18283.4 | + | 6208.32i | 0.759116 | + | 0.257766i | ||||
\(835\) | −46891.1 | −1.94339 | ||||||||
\(836\) | −5338.34 | −0.220850 | ||||||||
\(837\) | 14439.3 | − | 9642.10i | 0.596291 | − | 0.398184i | ||||
\(838\) | 22542.5i | 0.929259i | ||||||||
\(839\) | −8274.08 | −0.340468 | −0.170234 | − | 0.985404i | \(-0.554452\pi\) | ||||
−0.170234 | + | 0.985404i | \(0.554452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17593.2 | 0.721358 | ||||||||
\(842\) | 2689.89i | 0.110095i | ||||||||
\(843\) | 12919.7 | − | 38048.3i | 0.527850 | − | 1.55451i | ||||
\(844\) | 22448.5 | 0.915533 | ||||||||
\(845\) | −43756.4 | −1.78138 | ||||||||
\(846\) | 9277.38 | − | 12085.8i | 0.377025 | − | 0.491155i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 10368.9i | − | 0.419895i | ||||||
\(849\) | 2589.64 | − | 7626.46i | 0.104683 | − | 0.308292i | ||||
\(850\) | 42513.8i | 1.71554i | ||||||||
\(851\) | − | 6281.90i | − | 0.253044i | ||||||
\(852\) | −4603.35 | + | 13556.8i | −0.185104 | + | 0.545128i | ||||
\(853\) | 45421.2i | 1.82320i | 0.411075 | + | 0.911601i | \(0.365153\pi\) | ||||
−0.411075 | + | 0.911601i | \(0.634847\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9794.83 | − | 12759.9i | 0.391785 | − | 0.510383i | ||||
\(856\) | 8706.91 | 0.347659 | ||||||||
\(857\) | 3995.75 | 0.159267 | 0.0796337 | − | 0.996824i | \(-0.474625\pi\) | ||||
0.0796337 | + | 0.996824i | \(0.474625\pi\) | |||||||
\(858\) | 2200.00 | − | 6478.98i | 0.0875371 | − | 0.257796i | ||||
\(859\) | − | 8676.84i | − | 0.344645i | −0.985041 | − | 0.172323i | \(-0.944873\pi\) | ||
0.985041 | − | 0.172323i | \(-0.0551271\pi\) | |||||||
\(860\) | 19407.9 | 0.769540 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30402.0 | −1.20127 | ||||||||
\(863\) | 32022.9i | 1.26312i | 0.775328 | + | 0.631559i | \(0.217585\pi\) | ||||
−0.775328 | + | 0.631559i | \(0.782415\pi\) | |||||||
\(864\) | −3733.57 | + | 2493.16i | −0.147012 | + | 0.0981701i | ||||
\(865\) | −35334.5 | −1.38891 | ||||||||
\(866\) | 1907.08 | 0.0748330 | ||||||||
\(867\) | −5712.14 | − | 1939.61i | −0.223754 | − | 0.0759778i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 15430.3i | − | 0.602344i | ||||||
\(870\) | −17624.6 | − | 5984.62i | −0.686818 | − | 0.233216i | ||||
\(871\) | 2771.84i | 0.107830i | ||||||||
\(872\) | 6350.75i | 0.246632i | ||||||||
\(873\) | 5941.00 | − | 7739.42i | 0.230323 | − | 0.300046i | ||||
\(874\) | 7656.06i | 0.296304i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1347.83 | − | 3969.33i | 0.0519850 | − | 0.153095i | ||||
\(877\) | −14787.5 | −0.569372 | −0.284686 | − | 0.958621i | \(-0.591889\pi\) | ||||
−0.284686 | + | 0.958621i | \(0.591889\pi\) | |||||||
\(878\) | 14534.2 | 0.558661 | ||||||||
\(879\) | −8633.30 | − | 2931.52i | −0.331279 | − | 0.112489i | ||||
\(880\) | 16918.3i | 0.648086i | ||||||||
\(881\) | −10308.3 | −0.394206 | −0.197103 | − | 0.980383i | \(-0.563153\pi\) | ||||
−0.197103 | + | 0.980383i | \(0.563153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30917.7 | −1.17833 | −0.589165 | − | 0.808013i | \(-0.700543\pi\) | ||||
−0.589165 | + | 0.808013i | \(0.700543\pi\) | |||||||
\(884\) | 3314.61i | 0.126111i | ||||||||
\(885\) | 20346.4 | + | 6908.81i | 0.772808 | + | 0.262415i | ||||
\(886\) | −316.394 | −0.0119971 | ||||||||
\(887\) | −7802.14 | −0.295344 | −0.147672 | − | 0.989036i | \(-0.547178\pi\) | ||||
−0.147672 | + | 0.989036i | \(0.547178\pi\) | |||||||
\(888\) | 601.454 | − | 1771.27i | 0.0227291 | − | 0.0669370i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 8821.64i | − | 0.332250i | ||||||
\(891\) | 34274.2 | − | 9169.82i | 1.28870 | − | 0.344782i | ||||
\(892\) | 6951.19i | 0.260923i | ||||||||
\(893\) | − | 7736.98i | − | 0.289931i | ||||||
\(894\) | −13900.8 | − | 4720.17i | −0.520037 | − | 0.176584i | ||||
\(895\) | 42747.3i | 1.59652i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9291.91 | − | 3155.16i | −0.345873 | − | 0.117445i | ||||
\(898\) | −11713.9 | −0.435299 | ||||||||
\(899\) | −10202.2 | −0.378489 | ||||||||
\(900\) | −29729.9 | − | 22821.5i | −1.10111 | − | 0.845240i | ||||
\(901\) | − | 39696.2i | − | 1.46778i | ||||||
\(902\) | −40732.3 | −1.50359 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4679.57 | −0.172168 | ||||||||
\(905\) | 60471.1i | 2.22114i | ||||||||
\(906\) | 566.390 | − | 1668.01i | 0.0207694 | − | 0.0611655i | ||||
\(907\) | −27721.8 | −1.01487 | −0.507435 | − | 0.861690i | \(-0.669406\pi\) | ||||
−0.507435 | + | 0.861690i | \(0.669406\pi\) | |||||||
\(908\) | −9220.21 | −0.336986 | ||||||||
\(909\) | 8652.77 | + | 6642.11i | 0.315725 | + | 0.242360i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49080.0i | 1.78495i | 0.451094 | + | 0.892476i | \(0.351034\pi\) | ||||
−0.451094 | + | 0.892476i | \(0.648966\pi\) | |||||||
\(912\) | −733.021 | + | 2158.74i | −0.0266149 | + | 0.0783805i | ||||
\(913\) | − | 17542.7i | − | 0.635902i | ||||||
\(914\) | − | 19946.8i | − | 0.721860i | ||||||
\(915\) | −24490.3 | + | 72123.6i | −0.884835 | + | 2.60583i | ||||
\(916\) | − | 21738.5i | − | 0.784128i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −14293.5 | + | 9544.74i | −0.513896 | + | 0.343163i | ||||
\(919\) | 7603.45 | 0.272921 | 0.136461 | − | 0.990645i | \(-0.456427\pi\) | ||||
0.136461 | + | 0.990645i | \(0.456427\pi\) | |||||||
\(920\) | 24263.6 | 0.869508 | ||||||||
\(921\) | 5560.80 | − | 16376.5i | 0.198952 | − | 0.585911i | ||||
\(922\) | − | 24318.0i | − | 0.868622i | ||||||
\(923\) | −9318.59 | −0.332313 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15616.2 | 0.555090 | ||||||||
\(926\) | − | 11372.2i | − | 0.403580i | ||||||
\(927\) | −20266.4 | + | 26401.3i | −0.718053 | + | 0.935418i | ||||
\(928\) | 2637.97 | 0.0933143 | ||||||||
\(929\) | −4956.43 | −0.175043 | −0.0875216 | − | 0.996163i | \(-0.527895\pi\) | ||||
−0.0875216 | + | 0.996163i | \(0.527895\pi\) | |||||||
\(930\) | −26458.9 | − | 8984.39i | −0.932927 | − | 0.316785i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 15389.7i | − | 0.540885i | ||||||
\(933\) | −32060.7 | − | 10886.5i | −1.12499 | − | 0.382003i | ||||
\(934\) | 26935.6i | 0.943640i | ||||||||
\(935\) | 64769.6i | 2.26545i | ||||||||
\(936\) | −2317.90 | − | 1779.29i | −0.0809435 | − | 0.0621345i | ||||
\(937\) | − | 30085.4i | − | 1.04893i | −0.851433 | − | 0.524464i | \(-0.824266\pi\) | ||
0.851433 | − | 0.524464i | \(-0.175734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3573.56 | − | 10524.1i | 0.124194 | − | 0.365751i | ||||
\(940\) | −24520.1 | −0.850804 | ||||||||
\(941\) | 35955.2 | 1.24560 | 0.622799 | − | 0.782382i | \(-0.285996\pi\) | ||||
0.622799 | + | 0.782382i | \(0.285996\pi\) | |||||||
\(942\) | 17085.0 | + | 5801.39i | 0.590935 | + | 0.200658i | ||||
\(943\) | 58416.7i | 2.01730i | ||||||||
\(944\) | −3045.35 | −0.104997 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21737.8 | 0.747102 | ||||||||
\(947\) | − | 21321.7i | − | 0.731639i | −0.930686 | − | 0.365819i | \(-0.880789\pi\) | ||
0.930686 | − | 0.365819i | \(-0.119211\pi\) | |||||||
\(948\) | −6239.76 | − | 2118.77i | −0.213774 | − | 0.0725892i | ||||
\(949\) | 2728.41 | 0.0933277 | ||||||||
\(950\) | −19032.2 | −0.649987 | ||||||||
\(951\) | 4678.85 | − | 13779.2i | 0.159540 | − | 0.469842i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25987.9i | 0.883347i | 0.897176 | + | 0.441674i | \(0.145615\pi\) | ||||
−0.897176 | + | 0.441674i | \(0.854385\pi\) | |||||||
\(954\) | 27759.5 | + | 21309.0i | 0.942083 | + | 0.723169i | ||||
\(955\) | − | 61294.9i | − | 2.07692i | ||||||
\(956\) | − | 27652.5i | − | 0.935507i | ||||||
\(957\) | −19740.5 | − | 6703.09i | −0.666792 | − | 0.226416i | ||||
\(958\) | 1805.06i | 0.0608755i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6841.48 | + | 2323.09i | 0.230008 | + | 0.0781016i | ||||
\(961\) | 14475.0 | 0.485886 | ||||||||
\(962\) | 1217.53 | 0.0408052 | ||||||||
\(963\) | −17893.4 | + | 23309.9i | −0.598760 | + | 0.780013i | ||||
\(964\) | − | 20502.3i | − | 0.684994i | ||||||
\(965\) | −26377.3 | −0.879913 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44652.9 | 1.48494 | 0.742471 | − | 0.669878i | \(-0.233653\pi\) | ||||
0.742471 | + | 0.669878i | \(0.233653\pi\) | |||||||
\(968\) | 8301.36i | 0.275636i | ||||||||
\(969\) | −2806.28 | + | 8264.46i | −0.0930348 | + | 0.273986i | ||||
\(970\) | −15702.0 | −0.519754 | ||||||||
\(971\) | −26384.2 | −0.871997 | −0.435998 | − | 0.899947i | \(-0.643605\pi\) | ||||
−0.435998 | + | 0.899947i | \(0.643605\pi\) | |||||||
\(972\) | 998.153 | − | 15119.1i | 0.0329380 | − | 0.498914i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 21415.7i | − | 0.704519i | ||||||
\(975\) | 7843.44 | − | 23098.8i | 0.257632 | − | 0.758723i | ||||
\(976\) | − | 10795.1i | − | 0.354040i | ||||||
\(977\) | − | 30645.4i | − | 1.00351i | −0.865009 | − | 0.501756i | \(-0.832687\pi\) | ||
0.865009 | − | 0.501756i | \(-0.167313\pi\) | |||||||
\(978\) | 9996.28 | − | 29438.9i | 0.326836 | − | 0.962529i | ||||
\(979\) | − | 9880.69i | − | 0.322562i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17002.1 | − | 13051.3i | −0.553348 | − | 0.424766i | ||||
\(982\) | 8496.53 | 0.276105 | ||||||||
\(983\) | 546.210 | 0.0177227 | 0.00886134 | − | 0.999961i | \(-0.497179\pi\) | ||||
0.00886134 | + | 0.999961i | \(0.497179\pi\) | |||||||
\(984\) | −5593.05 | + | 16471.5i | −0.181199 | + | 0.533629i | ||||
\(985\) | − | 123.594i | − | 0.00399801i | ||||||
\(986\) | 10099.1 | 0.326189 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1483.86 | −0.0477812 | ||||||||
\(989\) | − | 31175.6i | − | 1.00235i | ||||||
\(990\) | −45293.3 | − | 34768.4i | −1.45406 | − | 1.11617i | ||||
\(991\) | 15440.5 | 0.494938 | 0.247469 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247469 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(992\) | 3960.24 | 0.126752 | ||||||||
\(993\) | 17453.5 | + | 5926.52i | 0.557775 | + | 0.189398i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24707.2i | 0.787208i | ||||||||
\(996\) | −7093.98 | − | 2408.83i | −0.225684 | − | 0.0766333i | ||||
\(997\) | 53069.1i | 1.68577i | 0.538092 | + | 0.842886i | \(0.319145\pi\) | ||||
−0.538092 | + | 0.842886i | \(0.680855\pi\) | |||||||
\(998\) | 26241.5i | 0.832324i | ||||||||
\(999\) | 3505.98 | + | 5250.31i | 0.111035 | + | 0.166279i |
(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 | 294.4.d.b.293.20 | yes | 24 | |
3.2 | odd | 2 | inner | 294.4.d.b.293.5 | ✓ | 24 | |
7.2 | even | 3 | 294.4.f.c.227.13 | 48 | |||
7.3 | odd | 6 | 294.4.f.c.215.12 | 48 | |||
7.4 | even | 3 | 294.4.f.c.215.10 | 48 | |||
7.5 | odd | 6 | 294.4.f.c.227.15 | 48 | |||
7.6 | odd | 2 | inner | 294.4.d.b.293.6 | yes | 24 | |
21.2 | odd | 6 | 294.4.f.c.227.12 | 48 | |||
21.5 | even | 6 | 294.4.f.c.227.10 | 48 | |||
21.11 | odd | 6 | 294.4.f.c.215.15 | 48 | |||
21.17 | even | 6 | 294.4.f.c.215.13 | 48 | |||
21.20 | even | 2 | inner | 294.4.d.b.293.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.d.b.293.5 | ✓ | 24 | 3.2 | odd | 2 | inner | |
294.4.d.b.293.6 | yes | 24 | 7.6 | odd | 2 | inner | |
294.4.d.b.293.19 | yes | 24 | 21.20 | even | 2 | inner | |
294.4.d.b.293.20 | yes | 24 | 1.1 | even | 1 | trivial | |
294.4.f.c.215.10 | 48 | 7.4 | even | 3 | |||
294.4.f.c.215.12 | 48 | 7.3 | odd | 6 | |||
294.4.f.c.215.13 | 48 | 21.17 | even | 6 | |||
294.4.f.c.215.15 | 48 | 21.11 | odd | 6 | |||
294.4.f.c.227.10 | 48 | 21.5 | even | 6 | |||
294.4.f.c.227.12 | 48 | 21.2 | odd | 6 | |||
294.4.f.c.227.13 | 48 | 7.2 | even | 3 | |||
294.4.f.c.227.15 | 48 | 7.5 | odd | 6 |