Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 103 x^{10} + 14 x^{9} + 7600 x^{8} + 1474 x^{7} + 229961 x^{6} + 442438 x^{5} + \cdots + 69739201 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.2 | ||
Root | \(4.23503 + 7.33529i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.d.601.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 2.03595 | − | 6.69738i | 0.290849 | − | 0.956769i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.30397 | −0.482179 | −0.241090 | − | 0.970503i | \(-0.577505\pi\) | ||||
−0.241090 | + | 0.970503i | \(0.577505\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | − | 15.0546i | − | 1.15805i | −0.815311 | − | 0.579023i | \(-0.803434\pi\) | ||
0.815311 | − | 0.579023i | \(-0.196566\pi\) | |||||||
\(14\) | −2.87926 | + | 9.47153i | −0.205662 | + | 0.676538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 1.80427i | 0.106133i | 0.998591 | + | 0.0530667i | \(0.0168996\pi\) | ||||
−0.998591 | + | 0.0530667i | \(0.983100\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | − | 7.35835i | − | 0.387282i | −0.981073 | − | 0.193641i | \(-0.937970\pi\) | ||
0.981073 | − | 0.193641i | \(-0.0620296\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.6002 | − | 3.52636i | −0.552391 | − | 0.167922i | ||||
\(22\) | 7.50095 | 0.340952 | ||||||||
\(23\) | 15.8246 | 0.688024 | 0.344012 | − | 0.938965i | \(-0.388214\pi\) | ||||
0.344012 | + | 0.938965i | \(0.388214\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 21.2904i | 0.818862i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 4.07189 | − | 13.3948i | 0.145425 | − | 0.478384i | ||||
\(29\) | −44.3922 | −1.53077 | −0.765384 | − | 0.643574i | \(-0.777451\pi\) | ||||
−0.765384 | + | 0.643574i | \(0.777451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.10279i | − | 0.196864i | −0.995144 | − | 0.0984322i | \(-0.968617\pi\) | ||
0.995144 | − | 0.0984322i | \(-0.0313827\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 9.18674i | 0.278386i | ||||||||
\(34\) | − | 2.55162i | − | 0.0750477i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −36.0606 | −0.974611 | −0.487305 | − | 0.873232i | \(-0.662020\pi\) | ||||
−0.487305 | + | 0.873232i | \(0.662020\pi\) | |||||||
\(38\) | 10.4063i | 0.273849i | ||||||||
\(39\) | −26.0753 | −0.668598 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.8619i | 0.460047i | 0.973185 | + | 0.230024i | \(0.0738803\pi\) | ||||
−0.973185 | + | 0.230024i | \(0.926120\pi\) | |||||||
\(42\) | 16.4052 | + | 4.98703i | 0.390599 | + | 0.118739i | ||||
\(43\) | 36.0186 | 0.837641 | 0.418820 | − | 0.908069i | \(-0.362444\pi\) | ||||
0.418820 | + | 0.908069i | \(0.362444\pi\) | |||||||
\(44\) | −10.6079 | −0.241090 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22.3793 | −0.486506 | ||||||||
\(47\) | − | 26.7314i | − | 0.568753i | −0.958713 | − | 0.284376i | \(-0.908213\pi\) | ||
0.958713 | − | 0.284376i | \(-0.0917866\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | −40.7099 | − | 27.2710i | −0.830813 | − | 0.556551i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.12509 | 0.0612762 | ||||||||
\(52\) | − | 30.1092i | − | 0.579023i | ||||||
\(53\) | 80.7350 | 1.52330 | 0.761651 | − | 0.647987i | \(-0.224389\pi\) | ||||
0.761651 | + | 0.647987i | \(0.224389\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.75852 | + | 18.9431i | −0.102831 | + | 0.338269i | ||||
\(57\) | −12.7450 | −0.223597 | ||||||||
\(58\) | 62.7801 | 1.08242 | ||||||||
\(59\) | 38.7017i | 0.655961i | 0.944684 | + | 0.327981i | \(0.106368\pi\) | ||||
−0.944684 | + | 0.327981i | \(0.893632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25.5365i | 0.418630i | 0.977848 | + | 0.209315i | \(0.0671235\pi\) | ||||
−0.977848 | + | 0.209315i | \(0.932877\pi\) | |||||||
\(62\) | 8.63065i | 0.139204i | ||||||||
\(63\) | −6.10784 | + | 20.0921i | −0.0969498 | + | 0.318923i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 12.9920i | − | 0.196849i | ||||||
\(67\) | −90.4318 | −1.34973 | −0.674864 | − | 0.737942i | \(-0.735798\pi\) | ||||
−0.674864 | + | 0.737942i | \(0.735798\pi\) | |||||||
\(68\) | 3.60854i | 0.0530667i | ||||||||
\(69\) | − | 27.4089i | − | 0.397231i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −41.4375 | −0.583626 | −0.291813 | − | 0.956475i | \(-0.594259\pi\) | ||||
−0.291813 | + | 0.956475i | \(0.594259\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | − | 106.712i | − | 1.46181i | −0.682481 | − | 0.730903i | \(-0.739099\pi\) | ||
0.682481 | − | 0.730903i | \(-0.260901\pi\) | |||||||
\(74\) | 50.9974 | 0.689154 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 14.7167i | − | 0.193641i | ||||||
\(77\) | −10.7986 | + | 35.5227i | −0.140241 | + | 0.461334i | ||||
\(78\) | 36.8761 | 0.472770 | ||||||||
\(79\) | −16.1960 | −0.205013 | −0.102507 | − | 0.994732i | \(-0.532686\pi\) | ||||
−0.102507 | + | 0.994732i | \(0.532686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 26.6748i | − | 0.325302i | ||||||
\(83\) | 34.7857i | 0.419105i | 0.977797 | + | 0.209552i | \(0.0672006\pi\) | ||||
−0.977797 | + | 0.209552i | \(0.932799\pi\) | |||||||
\(84\) | −23.2004 | − | 7.05272i | −0.276195 | − | 0.0839610i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −50.9379 | −0.592302 | ||||||||
\(87\) | 76.8896i | 0.883789i | ||||||||
\(88\) | 15.0019 | 0.170476 | ||||||||
\(89\) | 58.7705i | 0.660342i | 0.943921 | + | 0.330171i | \(0.107106\pi\) | ||||
−0.943921 | + | 0.330171i | \(0.892894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −100.826 | − | 30.6503i | −1.10798 | − | 0.336817i | ||||
\(92\) | 31.6491 | 0.344012 | ||||||||
\(93\) | −10.5703 | −0.113660 | ||||||||
\(94\) | 37.8039i | 0.402169i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 140.734i | 1.45087i | 0.688293 | + | 0.725433i | \(0.258360\pi\) | ||||
−0.688293 | + | 0.725433i | \(0.741640\pi\) | |||||||
\(98\) | 57.5724 | + | 38.5670i | 0.587474 | + | 0.393541i | ||||
\(99\) | 15.9119 | 0.160726 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 96.7964i | − | 0.958380i | −0.877711 | − | 0.479190i | \(-0.840930\pi\) | ||
0.877711 | − | 0.479190i | \(-0.159070\pi\) | |||||||
\(102\) | −4.41954 | −0.0433288 | ||||||||
\(103\) | − | 102.523i | − | 0.995374i | −0.867357 | − | 0.497687i | \(-0.834183\pi\) | ||
0.867357 | − | 0.497687i | \(-0.165817\pi\) | |||||||
\(104\) | 42.5808i | 0.409431i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −114.177 | −1.07714 | ||||||||
\(107\) | −139.632 | −1.30497 | −0.652487 | − | 0.757800i | \(-0.726274\pi\) | ||||
−0.652487 | + | 0.757800i | \(0.726274\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | −27.3238 | −0.250677 | −0.125338 | − | 0.992114i | \(-0.540002\pi\) | ||||
−0.125338 | + | 0.992114i | \(0.540002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 62.4588i | 0.562692i | ||||||||
\(112\) | 8.14378 | − | 26.7895i | 0.0727123 | − | 0.239192i | ||||
\(113\) | 46.4392 | 0.410966 | 0.205483 | − | 0.978661i | \(-0.434123\pi\) | ||||
0.205483 | + | 0.978661i | \(0.434123\pi\) | |||||||
\(114\) | 18.0242 | 0.158107 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −88.7845 | −0.765384 | ||||||||
\(117\) | 45.1638i | 0.386015i | ||||||||
\(118\) | − | 54.7325i | − | 0.463835i | ||||||
\(119\) | 12.0839 | + | 3.67339i | 0.101545 | + | 0.0308688i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −92.8679 | −0.767503 | ||||||||
\(122\) | − | 36.1140i | − | 0.296016i | ||||||
\(123\) | 32.6698 | 0.265608 | ||||||||
\(124\) | − | 12.2056i | − | 0.0984322i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.63779 | − | 28.4146i | 0.0685538 | − | 0.225513i | ||||
\(127\) | −60.7189 | −0.478101 | −0.239051 | − | 0.971007i | \(-0.576836\pi\) | ||||
−0.239051 | + | 0.971007i | \(0.576836\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − | 62.3860i | − | 0.483612i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 202.250i | 1.54389i | 0.635688 | + | 0.771946i | \(0.280717\pi\) | ||||
−0.635688 | + | 0.771946i | \(0.719283\pi\) | |||||||
\(132\) | 18.3735i | 0.139193i | ||||||||
\(133\) | −49.2817 | − | 14.9812i | −0.370539 | − | 0.112641i | ||||
\(134\) | 127.890 | 0.954402 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.10324i | − | 0.0375238i | ||||||
\(137\) | −118.169 | −0.862548 | −0.431274 | − | 0.902221i | \(-0.641936\pi\) | ||||
−0.431274 | + | 0.902221i | \(0.641936\pi\) | |||||||
\(138\) | 38.7621i | 0.280885i | ||||||||
\(139\) | 256.027i | 1.84192i | 0.389658 | + | 0.920959i | \(0.372593\pi\) | ||||
−0.389658 | + | 0.920959i | \(0.627407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −46.3001 | −0.328370 | ||||||||
\(142\) | 58.6014 | 0.412686 | ||||||||
\(143\) | 79.8491i | 0.558385i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 150.913i | 1.03365i | ||||||||
\(147\) | −47.2348 | + | 70.5115i | −0.321325 | + | 0.479670i | ||||
\(148\) | −72.1212 | −0.487305 | ||||||||
\(149\) | −264.538 | −1.77543 | −0.887713 | − | 0.460398i | \(-0.847707\pi\) | ||||
−0.887713 | + | 0.460398i | \(0.847707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8709 | 0.0852377 | 0.0426188 | − | 0.999091i | \(-0.486430\pi\) | ||||
0.0426188 | + | 0.999091i | \(0.486430\pi\) | |||||||
\(152\) | 20.8126i | 0.136925i | ||||||||
\(153\) | − | 5.41281i | − | 0.0353778i | ||||||
\(154\) | 15.2715 | − | 50.2367i | 0.0991657 | − | 0.326212i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −52.1507 | −0.334299 | ||||||||
\(157\) | − | 203.635i | − | 1.29704i | −0.761200 | − | 0.648518i | \(-0.775389\pi\) | ||
0.761200 | − | 0.648518i | \(-0.224611\pi\) | |||||||
\(158\) | 22.9047 | 0.144966 | ||||||||
\(159\) | − | 139.837i | − | 0.879479i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.2179 | − | 105.983i | 0.200111 | − | 0.658280i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −261.841 | −1.60639 | −0.803194 | − | 0.595718i | \(-0.796868\pi\) | ||||
−0.803194 | + | 0.595718i | \(0.796868\pi\) | |||||||
\(164\) | 37.7239i | 0.230024i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 49.1944i | − | 0.296352i | ||||||
\(167\) | 90.7037i | 0.543136i | 0.962419 | + | 0.271568i | \(0.0875422\pi\) | ||||
−0.962419 | + | 0.271568i | \(0.912458\pi\) | |||||||
\(168\) | 32.8103 | + | 9.97405i | 0.195300 | + | 0.0593694i | ||||
\(169\) | −57.6409 | −0.341070 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.0750i | 0.129094i | ||||||||
\(172\) | 72.0371 | 0.418820 | ||||||||
\(173\) | 248.626i | 1.43714i | 0.695452 | + | 0.718572i | \(0.255204\pi\) | ||||
−0.695452 | + | 0.718572i | \(0.744796\pi\) | |||||||
\(174\) | − | 108.738i | − | 0.624933i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −21.2159 | −0.120545 | ||||||||
\(177\) | 67.0333 | 0.378719 | ||||||||
\(178\) | − | 83.1140i | − | 0.466933i | ||||||
\(179\) | 138.861 | 0.775761 | 0.387880 | − | 0.921710i | \(-0.373207\pi\) | ||||
0.387880 | + | 0.921710i | \(0.373207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 148.488i | − | 0.820375i | −0.912001 | − | 0.410187i | \(-0.865463\pi\) | ||
0.912001 | − | 0.410187i | \(-0.134537\pi\) | |||||||
\(182\) | 142.590 | + | 43.3461i | 0.783462 | + | 0.238166i | ||||
\(183\) | 44.2304 | 0.241696 | ||||||||
\(184\) | −44.7586 | −0.243253 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.9487 | 0.0803695 | ||||||||
\(187\) | − | 9.56979i | − | 0.0511753i | ||||||
\(188\) | − | 53.4628i | − | 0.284376i | ||||||
\(189\) | 34.8006 | + | 10.5791i | 0.184130 | + | 0.0559740i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −46.0781 | −0.241247 | −0.120623 | − | 0.992698i | \(-0.538489\pi\) | ||||
−0.120623 | + | 0.992698i | \(0.538489\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | −26.4406 | −0.136998 | −0.0684991 | − | 0.997651i | \(-0.521821\pi\) | ||||
−0.0684991 | + | 0.997651i | \(0.521821\pi\) | |||||||
\(194\) | − | 199.028i | − | 1.02592i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −81.4197 | − | 54.5420i | −0.415407 | − | 0.278276i | ||||
\(197\) | −286.547 | −1.45455 | −0.727277 | − | 0.686345i | \(-0.759214\pi\) | ||||
−0.727277 | + | 0.686345i | \(0.759214\pi\) | |||||||
\(198\) | −22.5028 | −0.113651 | ||||||||
\(199\) | − | 34.4563i | − | 0.173147i | −0.996245 | − | 0.0865737i | \(-0.972408\pi\) | ||
0.996245 | − | 0.0865737i | \(-0.0275918\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 156.632i | 0.779266i | ||||||||
\(202\) | 136.891i | 0.677677i | ||||||||
\(203\) | −90.3802 | + | 297.312i | −0.445223 | + | 1.46459i | ||||
\(204\) | 6.25017 | 0.0306381 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 144.990i | 0.703835i | ||||||||
\(207\) | −47.4737 | −0.229341 | ||||||||
\(208\) | − | 60.2184i | − | 0.289511i | ||||||
\(209\) | 39.0285i | 0.186739i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 121.627 | 0.576432 | 0.288216 | − | 0.957565i | \(-0.406938\pi\) | ||||
0.288216 | + | 0.957565i | \(0.406938\pi\) | |||||||
\(212\) | 161.470 | 0.761651 | ||||||||
\(213\) | 71.7718i | 0.336957i | ||||||||
\(214\) | 197.470 | 0.922756 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −40.8727 | − | 12.4250i | −0.188354 | − | 0.0572579i | ||||
\(218\) | 38.6416 | 0.177255 | ||||||||
\(219\) | −184.830 | −0.843974 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.1625 | 0.122907 | ||||||||
\(222\) | − | 88.3301i | − | 0.397883i | ||||||
\(223\) | − | 302.025i | − | 1.35437i | −0.735811 | − | 0.677187i | \(-0.763199\pi\) | ||
0.735811 | − | 0.677187i | \(-0.236801\pi\) | |||||||
\(224\) | −11.5170 | + | 37.8861i | −0.0514154 | + | 0.169134i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −65.6749 | −0.290597 | ||||||||
\(227\) | − | 159.784i | − | 0.703892i | −0.936020 | − | 0.351946i | \(-0.885520\pi\) | ||
0.936020 | − | 0.351946i | \(-0.114480\pi\) | |||||||
\(228\) | −25.4901 | −0.111799 | ||||||||
\(229\) | 46.0123i | 0.200927i | 0.994941 | + | 0.100463i | \(0.0320325\pi\) | ||||
−0.994941 | + | 0.100463i | \(0.967967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 61.5271 | + | 18.7037i | 0.266351 | + | 0.0809684i | ||||
\(232\) | 125.560 | 0.541208 | ||||||||
\(233\) | 97.3113 | 0.417645 | 0.208822 | − | 0.977954i | \(-0.433037\pi\) | ||||
0.208822 | + | 0.977954i | \(0.433037\pi\) | |||||||
\(234\) | − | 63.8712i | − | 0.272954i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 77.4034i | 0.327981i | ||||||||
\(237\) | 28.0524i | 0.118364i | ||||||||
\(238\) | −17.0892 | − | 5.19496i | −0.0718033 | − | 0.0218276i | ||||
\(239\) | 124.280 | 0.520000 | 0.260000 | − | 0.965609i | \(-0.416278\pi\) | ||||
0.260000 | + | 0.965609i | \(0.416278\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 332.949i | − | 1.38153i | −0.723078 | − | 0.690766i | \(-0.757273\pi\) | ||
0.723078 | − | 0.690766i | \(-0.242727\pi\) | |||||||
\(242\) | 131.335 | 0.542707 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 51.0729i | 0.209315i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −46.2021 | −0.187813 | ||||||||
\(247\) | −110.777 | −0.448490 | ||||||||
\(248\) | 17.2613i | 0.0696020i | ||||||||
\(249\) | 60.2506 | 0.241970 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 154.118i | 0.614018i | 0.951707 | + | 0.307009i | \(0.0993281\pi\) | ||||
−0.951707 | + | 0.307009i | \(0.900672\pi\) | |||||||
\(252\) | −12.2157 | + | 40.1843i | −0.0484749 | + | 0.159461i | ||||
\(253\) | −83.9329 | −0.331751 | ||||||||
\(254\) | 85.8695 | 0.338069 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 410.364i | − | 1.59675i | −0.602164 | − | 0.798373i | \(-0.705694\pi\) | ||
0.602164 | − | 0.798373i | \(-0.294306\pi\) | |||||||
\(258\) | 88.2271i | 0.341965i | ||||||||
\(259\) | −73.4174 | + | 241.512i | −0.283465 | + | 0.932477i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 133.177 | 0.510256 | ||||||||
\(262\) | − | 286.025i | − | 1.09170i | ||||||
\(263\) | −342.998 | −1.30418 | −0.652088 | − | 0.758143i | \(-0.726107\pi\) | ||||
−0.652088 | + | 0.758143i | \(0.726107\pi\) | |||||||
\(264\) | − | 25.9840i | − | 0.0984244i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 69.6948 | + | 21.1866i | 0.262011 | + | 0.0796489i | ||||
\(267\) | 101.793 | 0.381249 | ||||||||
\(268\) | −180.864 | −0.674864 | ||||||||
\(269\) | − | 238.076i | − | 0.885042i | −0.896758 | − | 0.442521i | \(-0.854084\pi\) | ||
0.896758 | − | 0.442521i | \(-0.145916\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.6454i | 0.120463i | 0.998184 | + | 0.0602313i | \(0.0191838\pi\) | ||||
−0.998184 | + | 0.0602313i | \(0.980816\pi\) | |||||||
\(272\) | 7.21707i | 0.0265334i | ||||||||
\(273\) | −53.0879 | + | 174.636i | −0.194461 | + | 0.639694i | ||||
\(274\) | 167.116 | 0.609914 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 54.8179i | − | 0.198615i | ||||||
\(277\) | −230.271 | −0.831301 | −0.415651 | − | 0.909524i | \(-0.636446\pi\) | ||||
−0.415651 | + | 0.909524i | \(0.636446\pi\) | |||||||
\(278\) | − | 362.076i | − | 1.30243i | ||||||
\(279\) | 18.3084i | 0.0656214i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 486.859 | 1.73260 | 0.866298 | − | 0.499528i | \(-0.166493\pi\) | ||||
0.866298 | + | 0.499528i | \(0.166493\pi\) | |||||||
\(282\) | 65.4783 | 0.232192 | ||||||||
\(283\) | − | 324.645i | − | 1.14716i | −0.819151 | − | 0.573578i | \(-0.805555\pi\) | ||
0.819151 | − | 0.573578i | \(-0.194445\pi\) | |||||||
\(284\) | −82.8749 | −0.291813 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 112.924i | − | 0.394838i | ||||||
\(287\) | 126.326 | + | 38.4019i | 0.440159 | + | 0.133804i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 285.745 | 0.988736 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 243.758 | 0.837658 | ||||||||
\(292\) | − | 213.424i | − | 0.730903i | ||||||
\(293\) | 128.334i | 0.438000i | 0.975725 | + | 0.219000i | \(0.0702795\pi\) | ||||
−0.975725 | + | 0.219000i | \(0.929721\pi\) | |||||||
\(294\) | 66.8001 | − | 99.7184i | 0.227211 | − | 0.339178i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 101.995 | 0.344577 | ||||||||
\(297\) | − | 27.5602i | − | 0.0927954i | ||||||
\(298\) | 374.114 | 1.25542 | ||||||||
\(299\) | − | 238.232i | − | 0.796763i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 73.3318 | − | 241.230i | 0.243627 | − | 0.801429i | ||||
\(302\) | −18.2022 | −0.0602721 | ||||||||
\(303\) | −167.656 | −0.553321 | ||||||||
\(304\) | − | 29.4334i | − | 0.0968204i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.65486i | 0.0250159i | ||||||||
\(307\) | 290.110i | 0.944983i | 0.881335 | + | 0.472492i | \(0.156645\pi\) | ||||
−0.881335 | + | 0.472492i | \(0.843355\pi\) | |||||||
\(308\) | −21.5972 | + | 71.0454i | −0.0701207 | + | 0.230667i | ||||
\(309\) | −177.576 | −0.574679 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 76.1670i | − | 0.244910i | −0.992474 | − | 0.122455i | \(-0.960923\pi\) | ||
0.992474 | − | 0.122455i | \(-0.0390767\pi\) | |||||||
\(312\) | 73.7522 | 0.236385 | ||||||||
\(313\) | − | 527.145i | − | 1.68417i | −0.539344 | − | 0.842085i | \(-0.681328\pi\) | ||
0.539344 | − | 0.842085i | \(-0.318672\pi\) | |||||||
\(314\) | 287.983i | 0.917142i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −32.3921 | −0.102507 | ||||||||
\(317\) | 488.328 | 1.54047 | 0.770233 | − | 0.637763i | \(-0.220140\pi\) | ||||
0.770233 | + | 0.637763i | \(0.220140\pi\) | |||||||
\(318\) | 197.760i | 0.621886i | ||||||||
\(319\) | 235.455 | 0.738104 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 241.850i | 0.753427i | ||||||||
\(322\) | −45.5630 | + | 149.883i | −0.141500 | + | 0.465474i | ||||
\(323\) | 13.2764 | 0.0411035 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 370.299 | 1.13589 | ||||||||
\(327\) | 47.3261i | 0.144728i | ||||||||
\(328\) | − | 53.3496i | − | 0.162651i | ||||||
\(329\) | −179.030 | − | 54.4236i | −0.544165 | − | 0.165421i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 519.849 | 1.57054 | 0.785271 | − | 0.619152i | \(-0.212524\pi\) | ||||
0.785271 | + | 0.619152i | \(0.212524\pi\) | |||||||
\(332\) | 69.5714i | 0.209552i | ||||||||
\(333\) | 108.182 | 0.324870 | ||||||||
\(334\) | − | 128.274i | − | 0.384055i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −46.4008 | − | 14.1054i | −0.138098 | − | 0.0419805i | ||||
\(337\) | 460.233 | 1.36568 | 0.682838 | − | 0.730570i | \(-0.260745\pi\) | ||||
0.682838 | + | 0.730570i | \(0.260745\pi\) | |||||||
\(338\) | 81.5165 | 0.241173 | ||||||||
\(339\) | − | 80.4350i | − | 0.237271i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.3690i | 0.0949238i | ||||||||
\(342\) | − | 31.2188i | − | 0.0912831i | ||||||
\(343\) | −265.527 | + | 217.127i | −0.774132 | + | 0.633024i | ||||
\(344\) | −101.876 | −0.296151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 351.610i | − | 1.01621i | ||||||
\(347\) | −5.51518 | −0.0158939 | −0.00794695 | − | 0.999968i | \(-0.502530\pi\) | ||||
−0.00794695 | + | 0.999968i | \(0.502530\pi\) | |||||||
\(348\) | 153.779i | 0.441894i | ||||||||
\(349\) | 563.892i | 1.61574i | 0.589364 | + | 0.807868i | \(0.299378\pi\) | ||||
−0.589364 | + | 0.807868i | \(0.700622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 78.2260 | 0.222866 | ||||||||
\(352\) | 30.0038 | 0.0852380 | ||||||||
\(353\) | 274.152i | 0.776633i | 0.921526 | + | 0.388317i | \(0.126943\pi\) | ||||
−0.921526 | + | 0.388317i | \(0.873057\pi\) | |||||||
\(354\) | −94.7994 | −0.267795 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 117.541i | 0.330171i | ||||||||
\(357\) | 6.36250 | − | 20.9299i | 0.0178221 | − | 0.0586271i | ||||
\(358\) | −196.379 | −0.548546 | ||||||||
\(359\) | −65.4883 | −0.182419 | −0.0912093 | − | 0.995832i | \(-0.529073\pi\) | ||||
−0.0912093 | + | 0.995832i | \(0.529073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 306.855 | 0.850013 | ||||||||
\(362\) | 209.993i | 0.580092i | ||||||||
\(363\) | 160.852i | 0.443118i | ||||||||
\(364\) | −201.653 | − | 61.3007i | −0.553991 | − | 0.168408i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −62.5513 | −0.170905 | ||||||||
\(367\) | 159.838i | 0.435526i | 0.976002 | + | 0.217763i | \(0.0698760\pi\) | ||||
−0.976002 | + | 0.217763i | \(0.930124\pi\) | |||||||
\(368\) | 63.2982 | 0.172006 | ||||||||
\(369\) | − | 56.5858i | − | 0.153349i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 164.372 | − | 540.713i | 0.443051 | − | 1.45745i | ||||
\(372\) | −21.1407 | −0.0568298 | ||||||||
\(373\) | 470.755 | 1.26208 | 0.631039 | − | 0.775751i | \(-0.282629\pi\) | ||||
0.631039 | + | 0.775751i | \(0.282629\pi\) | |||||||
\(374\) | 13.5337i | 0.0361864i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 75.6078i | 0.201085i | ||||||||
\(377\) | 668.307i | 1.77270i | ||||||||
\(378\) | −49.2155 | − | 14.9611i | −0.130200 | − | 0.0395796i | ||||
\(379\) | 61.4701 | 0.162190 | 0.0810951 | − | 0.996706i | \(-0.474158\pi\) | ||||
0.0810951 | + | 0.996706i | \(0.474158\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 105.168i | 0.276032i | ||||||||
\(382\) | 65.1643 | 0.170587 | ||||||||
\(383\) | 120.113i | 0.313611i | 0.987629 | + | 0.156806i | \(0.0501196\pi\) | ||||
−0.987629 | + | 0.156806i | \(0.949880\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 37.3927 | 0.0968723 | ||||||||
\(387\) | −108.056 | −0.279214 | ||||||||
\(388\) | 281.468i | 0.725433i | ||||||||
\(389\) | 309.597 | 0.795879 | 0.397939 | − | 0.917412i | \(-0.369725\pi\) | ||||
0.397939 | + | 0.917412i | \(0.369725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.5517i | 0.0730224i | ||||||||
\(392\) | 115.145 | + | 77.1341i | 0.293737 | + | 0.196771i | ||||
\(393\) | 350.307 | 0.891367 | ||||||||
\(394\) | 405.239 | 1.02852 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 31.8238 | 0.0803632 | ||||||||
\(397\) | − | 754.188i | − | 1.89972i | −0.312680 | − | 0.949858i | \(-0.601227\pi\) | ||
0.312680 | − | 0.949858i | \(-0.398773\pi\) | |||||||
\(398\) | 48.7286i | 0.122434i | ||||||||
\(399\) | −25.9482 | + | 85.3584i | −0.0650331 | + | 0.213931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 235.697 | 0.587774 | 0.293887 | − | 0.955840i | \(-0.405051\pi\) | ||||
0.293887 | + | 0.955840i | \(0.405051\pi\) | |||||||
\(402\) | − | 221.512i | − | 0.551024i | ||||||
\(403\) | −91.8751 | −0.227978 | ||||||||
\(404\) | − | 193.593i | − | 0.479190i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 127.817 | − | 420.462i | 0.314820 | − | 1.03562i | ||||
\(407\) | 191.264 | 0.469937 | ||||||||
\(408\) | −8.83908 | −0.0216644 | ||||||||
\(409\) | − | 81.3407i | − | 0.198877i | −0.995044 | − | 0.0994385i | \(-0.968295\pi\) | ||
0.995044 | − | 0.0994385i | \(-0.0317047\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 204.675i | 0.497993i | ||||||||
\(412\) | − | 205.047i | − | 0.497687i | ||||||
\(413\) | 259.200 | + | 78.7946i | 0.627603 | + | 0.190786i | ||||
\(414\) | 67.1379 | 0.162169 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 85.1617i | 0.204716i | ||||||||
\(417\) | 443.451 | 1.06343 | ||||||||
\(418\) | − | 55.1946i | − | 0.132044i | ||||||
\(419\) | − | 213.030i | − | 0.508424i | −0.967149 | − | 0.254212i | \(-0.918184\pi\) | ||
0.967149 | − | 0.254212i | \(-0.0818161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 416.836 | 0.990108 | 0.495054 | − | 0.868862i | \(-0.335148\pi\) | ||||
0.495054 | + | 0.868862i | \(0.335148\pi\) | |||||||
\(422\) | −172.007 | −0.407599 | ||||||||
\(423\) | 80.1942i | 0.189584i | ||||||||
\(424\) | −228.353 | −0.538569 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 101.501i | − | 0.238264i | ||||||
\(427\) | 171.027 | + | 51.9908i | 0.400533 | + | 0.121758i | ||||
\(428\) | −279.265 | −0.652487 | ||||||||
\(429\) | 138.303 | 0.322384 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −331.912 | −0.770096 | −0.385048 | − | 0.922896i | \(-0.625815\pi\) | ||||
−0.385048 | + | 0.922896i | \(0.625815\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | − | 304.120i | − | 0.702356i | −0.936309 | − | 0.351178i | \(-0.885781\pi\) | ||
0.936309 | − | 0.351178i | \(-0.114219\pi\) | |||||||
\(434\) | 57.8028 | + | 17.5715i | 0.133186 | + | 0.0404874i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −54.6475 | −0.125338 | ||||||||
\(437\) | − | 116.443i | − | 0.266459i | ||||||
\(438\) | 261.390 | 0.596780 | ||||||||
\(439\) | − | 24.3758i | − | 0.0555258i | −0.999615 | − | 0.0277629i | \(-0.991162\pi\) | ||
0.999615 | − | 0.0277629i | \(-0.00883834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 122.130 | + | 81.8130i | 0.276938 | + | 0.185517i | ||||
\(442\) | −38.4136 | −0.0869087 | ||||||||
\(443\) | 30.3119 | 0.0684241 | 0.0342121 | − | 0.999415i | \(-0.489108\pi\) | ||||
0.0342121 | + | 0.999415i | \(0.489108\pi\) | |||||||
\(444\) | 124.918i | 0.281346i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 427.128i | 0.957687i | ||||||||
\(447\) | 458.194i | 1.02504i | ||||||||
\(448\) | 16.2876 | − | 53.5791i | 0.0363562 | − | 0.119596i | ||||
\(449\) | −550.099 | −1.22517 | −0.612583 | − | 0.790407i | \(-0.709869\pi\) | ||||
−0.612583 | + | 0.790407i | \(0.709869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 100.043i | − | 0.221825i | ||||||
\(452\) | 92.8783 | 0.205483 | ||||||||
\(453\) | − | 22.2930i | − | 0.0492120i | ||||||
\(454\) | 225.968i | 0.497727i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 36.0484 | 0.0790535 | ||||||||
\(457\) | 477.234 | 1.04428 | 0.522138 | − | 0.852861i | \(-0.325135\pi\) | ||||
0.522138 | + | 0.852861i | \(0.325135\pi\) | |||||||
\(458\) | − | 65.0712i | − | 0.142077i | ||||||
\(459\) | −9.37526 | −0.0204254 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 860.755i | − | 1.86715i | −0.358386 | − | 0.933574i | \(-0.616673\pi\) | ||
0.358386 | − | 0.933574i | \(-0.383327\pi\) | |||||||
\(462\) | −87.0125 | − | 26.4510i | −0.188339 | − | 0.0572533i | ||||
\(463\) | −774.505 | −1.67280 | −0.836398 | − | 0.548122i | \(-0.815343\pi\) | ||||
−0.836398 | + | 0.548122i | \(0.815343\pi\) | |||||||
\(464\) | −177.569 | −0.382692 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −137.619 | −0.295320 | ||||||||
\(467\) | − | 769.862i | − | 1.64853i | −0.566207 | − | 0.824263i | \(-0.691590\pi\) | ||
0.566207 | − | 0.824263i | \(-0.308410\pi\) | |||||||
\(468\) | 90.3276i | 0.193008i | ||||||||
\(469\) | −184.114 | + | 605.656i | −0.392568 | + | 1.29138i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −352.705 | −0.748844 | ||||||||
\(472\) | − | 109.465i | − | 0.231917i | ||||||
\(473\) | −191.041 | −0.403893 | ||||||||
\(474\) | − | 39.6720i | − | 0.0836962i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.1678 | + | 7.34679i | 0.0507726 | + | 0.0154344i | ||||
\(477\) | −242.205 | −0.507767 | ||||||||
\(478\) | −175.758 | −0.367695 | ||||||||
\(479\) | − | 724.734i | − | 1.51302i | −0.653985 | − | 0.756508i | \(-0.726904\pi\) | ||
0.653985 | − | 0.756508i | \(-0.273096\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 542.878i | 1.12864i | ||||||||
\(482\) | 470.861i | 0.976891i | ||||||||
\(483\) | −183.568 | − | 55.8031i | −0.380058 | − | 0.115534i | ||||
\(484\) | −185.736 | −0.383752 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −58.9904 | −0.121130 | −0.0605651 | − | 0.998164i | \(-0.519290\pi\) | ||||
−0.0605651 | + | 0.998164i | \(0.519290\pi\) | |||||||
\(488\) | − | 72.2280i | − | 0.148008i | ||||||
\(489\) | 453.522i | 0.927448i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −574.652 | −1.17037 | −0.585185 | − | 0.810900i | \(-0.698978\pi\) | ||||
−0.585185 | + | 0.810900i | \(0.698978\pi\) | |||||||
\(492\) | 65.3396 | 0.132804 | ||||||||
\(493\) | − | 80.0955i | − | 0.162466i | ||||||
\(494\) | 156.662 | 0.317130 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 24.4112i | − | 0.0492161i | ||||||
\(497\) | −84.3644 | + | 277.523i | −0.169747 | + | 0.558396i | ||||
\(498\) | −85.2072 | −0.171099 | ||||||||
\(499\) | 282.439 | 0.566010 | 0.283005 | − | 0.959118i | \(-0.408669\pi\) | ||||
0.283005 | + | 0.959118i | \(0.408669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 157.103 | 0.313580 | ||||||||
\(502\) | − | 217.956i | − | 0.434176i | ||||||
\(503\) | 87.4043i | 0.173766i | 0.996219 | + | 0.0868830i | \(0.0276906\pi\) | ||||
−0.996219 | + | 0.0868830i | \(0.972309\pi\) | |||||||
\(504\) | 17.2756 | − | 56.8292i | 0.0342769 | − | 0.112756i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 118.699 | 0.234583 | ||||||||
\(507\) | 99.8370i | 0.196917i | ||||||||
\(508\) | −121.438 | −0.239051 | ||||||||
\(509\) | − | 632.350i | − | 1.24234i | −0.783677 | − | 0.621169i | \(-0.786658\pi\) | ||
0.783677 | − | 0.621169i | \(-0.213342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −714.690 | − | 217.260i | −1.39861 | − | 0.425165i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 38.2351 | 0.0745324 | ||||||||
\(514\) | 580.342i | 1.12907i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 124.772i | − | 0.241806i | ||||||
\(517\) | 141.782i | 0.274241i | ||||||||
\(518\) | 103.828 | − | 341.549i | 0.200440 | − | 0.659361i | ||||
\(519\) | 430.633 | 0.829736 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 637.695i | − | 1.22398i | −0.790864 | − | 0.611992i | \(-0.790369\pi\) | ||
0.790864 | − | 0.611992i | \(-0.209631\pi\) | |||||||
\(522\) | −188.340 | −0.360805 | ||||||||
\(523\) | − | 315.243i | − | 0.602759i | −0.953504 | − | 0.301380i | \(-0.902553\pi\) | ||
0.953504 | − | 0.301380i | \(-0.0974471\pi\) | |||||||
\(524\) | 404.500i | 0.771946i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 485.073 | 0.922192 | ||||||||
\(527\) | 11.0111 | 0.0208939 | ||||||||
\(528\) | 36.7470i | 0.0695965i | ||||||||
\(529\) | −278.584 | −0.526623 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 116.105i | − | 0.218654i | ||||||
\(532\) | −98.5634 | − | 29.9624i | −0.185269 | − | 0.0563203i | ||||
\(533\) | 283.959 | 0.532756 | ||||||||
\(534\) | −143.958 | −0.269584 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 255.780 | 0.477201 | ||||||||
\(537\) | − | 240.515i | − | 0.447886i | ||||||
\(538\) | 336.691i | 0.625819i | ||||||||
\(539\) | 215.924 | + | 144.645i | 0.400601 | + | 0.268357i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −273.034 | −0.504684 | −0.252342 | − | 0.967638i | \(-0.581201\pi\) | ||||
−0.252342 | + | 0.967638i | \(0.581201\pi\) | |||||||
\(542\) | − | 46.1675i | − | 0.0851800i | ||||||
\(543\) | −257.188 | −0.473644 | ||||||||
\(544\) | − | 10.2065i | − | 0.0187619i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 75.0777 | − | 246.973i | 0.137505 | − | 0.452332i | ||||
\(547\) | 31.9994 | 0.0584998 | 0.0292499 | − | 0.999572i | \(-0.490688\pi\) | ||||
0.0292499 | + | 0.999572i | \(0.490688\pi\) | |||||||
\(548\) | −236.338 | −0.431274 | ||||||||
\(549\) | − | 76.6094i | − | 0.139543i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 326.654i | 0.592838i | ||||||||
\(552\) | 77.5242i | 0.140442i | ||||||||
\(553\) | −32.9742 | + | 108.471i | −0.0596279 | + | 0.196150i | ||||
\(554\) | 325.652 | 0.587819 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 512.053i | 0.920959i | ||||||||
\(557\) | 134.429 | 0.241344 | 0.120672 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120672 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(558\) | − | 25.8920i | − | 0.0464014i | ||||||
\(559\) | − | 542.245i | − | 0.970027i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.5754 | −0.0295461 | ||||||||
\(562\) | −688.523 | −1.22513 | ||||||||
\(563\) | 138.895i | 0.246706i | 0.992363 | + | 0.123353i | \(0.0393647\pi\) | ||||
−0.992363 | + | 0.123353i | \(0.960635\pi\) | |||||||
\(564\) | −92.6002 | −0.164185 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 459.118i | 0.811162i | ||||||||
\(567\) | 18.3235 | − | 60.2764i | 0.0323166 | − | 0.106308i | ||||
\(568\) | 117.203 | 0.206343 | ||||||||
\(569\) | −247.938 | −0.435744 | −0.217872 | − | 0.975977i | \(-0.569912\pi\) | ||||
−0.217872 | + | 0.975977i | \(0.569912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1085.67 | −1.90134 | −0.950672 | − | 0.310197i | \(-0.899605\pi\) | ||||
−0.950672 | + | 0.310197i | \(0.899605\pi\) | |||||||
\(572\) | 159.698i | 0.279193i | ||||||||
\(573\) | 79.8096i | 0.139284i | ||||||||
\(574\) | −178.651 | − | 54.3084i | −0.311239 | − | 0.0946140i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | − | 155.146i | − | 0.268884i | −0.990921 | − | 0.134442i | \(-0.957076\pi\) | ||
0.990921 | − | 0.134442i | \(-0.0429242\pi\) | |||||||
\(578\) | −404.104 | −0.699142 | ||||||||
\(579\) | 45.7965i | 0.0790959i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 232.973 | + | 70.8217i | 0.400986 | + | 0.121896i | ||||
\(582\) | −344.726 | −0.592313 | ||||||||
\(583\) | −428.216 | −0.734504 | ||||||||
\(584\) | 301.827i | 0.516827i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 181.492i | − | 0.309713i | ||||||
\(587\) | 938.218i | 1.59833i | 0.601113 | + | 0.799164i | \(0.294724\pi\) | ||||
−0.601113 | + | 0.799164i | \(0.705276\pi\) | |||||||
\(588\) | −94.4695 | + | 141.023i | −0.160662 | + | 0.239835i | ||||
\(589\) | −44.9065 | −0.0762419 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 496.314i | 0.839787i | ||||||||
\(592\) | −144.242 | −0.243653 | ||||||||
\(593\) | − | 736.439i | − | 1.24189i | −0.783856 | − | 0.620943i | \(-0.786750\pi\) | ||
0.783856 | − | 0.620943i | \(-0.213250\pi\) | |||||||
\(594\) | 38.9761i | 0.0656163i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −529.077 | −0.887713 | ||||||||
\(597\) | −59.6801 | −0.0999667 | ||||||||
\(598\) | 336.911i | 0.563397i | ||||||||
\(599\) | 385.386 | 0.643383 | 0.321692 | − | 0.946845i | \(-0.395749\pi\) | ||||
0.321692 | + | 0.946845i | \(0.395749\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 965.914i | 1.60718i | 0.595184 | + | 0.803589i | \(0.297079\pi\) | ||||
−0.595184 | + | 0.803589i | \(0.702921\pi\) | |||||||
\(602\) | −103.707 | + | 341.151i | −0.172271 | + | 0.566696i | ||||
\(603\) | 271.295 | 0.449909 | ||||||||
\(604\) | 25.7418 | 0.0426188 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 237.102 | 0.391257 | ||||||||
\(607\) | − | 1162.16i | − | 1.91460i | −0.289103 | − | 0.957298i | \(-0.593357\pi\) | ||
0.289103 | − | 0.957298i | \(-0.406643\pi\) | |||||||
\(608\) | 41.6251i | 0.0684623i | ||||||||
\(609\) | 514.959 | + | 156.543i | 0.845582 | + | 0.257049i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −402.430 | −0.658642 | ||||||||
\(612\) | − | 10.8256i | − | 0.0176889i | ||||||
\(613\) | 709.805 | 1.15792 | 0.578960 | − | 0.815356i | \(-0.303459\pi\) | ||||
0.578960 | + | 0.815356i | \(0.303459\pi\) | |||||||
\(614\) | − | 410.277i | − | 0.668204i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 30.5430 | − | 100.473i | 0.0495828 | − | 0.163106i | ||||
\(617\) | −326.387 | −0.528990 | −0.264495 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264495 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(618\) | 251.130 | 0.406360 | ||||||||
\(619\) | − | 340.928i | − | 0.550772i | −0.961334 | − | 0.275386i | \(-0.911194\pi\) | ||
0.961334 | − | 0.275386i | \(-0.0888056\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 82.2268i | 0.132410i | ||||||||
\(622\) | 107.716i | 0.173177i | ||||||||
\(623\) | 393.608 | + | 119.653i | 0.631795 | + | 0.192060i | ||||
\(624\) | −104.301 | −0.167150 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 745.496i | 1.19089i | ||||||||
\(627\) | 67.5993 | 0.107814 | ||||||||
\(628\) | − | 407.269i | − | 0.648518i | ||||||
\(629\) | − | 65.0630i | − | 0.103439i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −64.3589 | −0.101995 | −0.0509975 | − | 0.998699i | \(-0.516240\pi\) | ||||
−0.0509975 | + | 0.998699i | \(0.516240\pi\) | |||||||
\(632\) | 45.8093 | 0.0724831 | ||||||||
\(633\) | − | 210.664i | − | 0.332803i | ||||||
\(634\) | −690.600 | −1.08927 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 279.674i | − | 0.439739i | ||||||
\(637\) | −410.554 | + | 612.870i | −0.644512 | + | 0.962120i | ||||
\(638\) | −332.984 | −0.521918 | ||||||||
\(639\) | 124.312 | 0.194542 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −621.739 | −0.969952 | −0.484976 | − | 0.874527i | \(-0.661172\pi\) | ||||
−0.484976 | + | 0.874527i | \(0.661172\pi\) | |||||||
\(642\) | − | 342.028i | − | 0.532754i | ||||||
\(643\) | 396.767i | 0.617056i | 0.951215 | + | 0.308528i | \(0.0998363\pi\) | ||||
−0.951215 | + | 0.308528i | \(0.900164\pi\) | |||||||
\(644\) | 64.4358 | − | 211.966i | 0.100056 | − | 0.329140i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.7757 | −0.0290646 | ||||||||
\(647\) | − | 564.262i | − | 0.872121i | −0.899917 | − | 0.436060i | \(-0.856373\pi\) | ||
0.899917 | − | 0.436060i | \(-0.143627\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | − | 205.273i | − | 0.316291i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.5207 | + | 70.7937i | −0.0330578 | + | 0.108746i | ||||
\(652\) | −523.682 | −0.803194 | ||||||||
\(653\) | 804.359 | 1.23179 | 0.615895 | − | 0.787828i | \(-0.288794\pi\) | ||||
0.615895 | + | 0.787828i | \(0.288794\pi\) | |||||||
\(654\) | − | 66.9293i | − | 0.102338i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 75.4477i | 0.115012i | ||||||||
\(657\) | 320.136i | 0.487269i | ||||||||
\(658\) | 253.187 | + | 76.9667i | 0.384783 | + | 0.116971i | ||||
\(659\) | 229.717 | 0.348584 | 0.174292 | − | 0.984694i | \(-0.444236\pi\) | ||||
0.174292 | + | 0.984694i | \(0.444236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 411.750i | 0.622920i | 0.950259 | + | 0.311460i | \(0.100818\pi\) | ||||
−0.950259 | + | 0.311460i | \(0.899182\pi\) | |||||||
\(662\) | −735.178 | −1.11054 | ||||||||
\(663\) | − | 47.0469i | − | 0.0709606i | ||||||
\(664\) | − | 98.3888i | − | 0.148176i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −152.992 | −0.229718 | ||||||||
\(667\) | −702.487 | −1.05320 | ||||||||
\(668\) | 181.407i | 0.271568i | ||||||||
\(669\) | −523.123 | −0.781948 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 135.445i | − | 0.201855i | ||||||
\(672\) | 65.6207 | + | 19.9481i | 0.0976498 | + | 0.0296847i | ||||
\(673\) | 905.399 | 1.34532 | 0.672659 | − | 0.739952i | \(-0.265152\pi\) | ||||
0.672659 | + | 0.739952i | \(0.265152\pi\) | |||||||
\(674\) | −650.868 | −0.965679 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −115.282 | −0.170535 | ||||||||
\(677\) | − | 632.507i | − | 0.934279i | −0.884184 | − | 0.467139i | \(-0.845285\pi\) | ||
0.884184 | − | 0.467139i | \(-0.154715\pi\) | |||||||
\(678\) | 113.752i | 0.167776i | ||||||||
\(679\) | 942.549 | + | 286.527i | 1.38814 | + | 0.421983i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −276.753 | −0.406392 | ||||||||
\(682\) | − | 45.7767i | − | 0.0671213i | ||||||
\(683\) | −1050.88 | −1.53862 | −0.769310 | − | 0.638876i | \(-0.779400\pi\) | ||||
−0.769310 | + | 0.638876i | \(0.779400\pi\) | |||||||
\(684\) | 44.1501i | 0.0645469i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 375.512 | − | 307.064i | 0.547394 | − | 0.447615i | ||||
\(687\) | 79.6956 | 0.116005 | ||||||||
\(688\) | 144.074 | 0.209410 | ||||||||
\(689\) | − | 1215.43i | − | 1.76405i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1353.15i | 1.95825i | 0.203270 | + | 0.979123i | \(0.434843\pi\) | ||||
−0.203270 | + | 0.979123i | \(0.565157\pi\) | |||||||
\(692\) | 497.252i | 0.718572i | ||||||||
\(693\) | 32.3958 | − | 106.568i | 0.0467472 | − | 0.153778i | ||||
\(694\) | 7.79965 | 0.0112387 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 217.477i | − | 0.312467i | ||||||
\(697\) | −34.0320 | −0.0488264 | ||||||||
\(698\) | − | 797.463i | − | 1.14250i | ||||||
\(699\) | − | 168.548i | − | 0.241127i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1124.26 | −1.60379 | −0.801897 | − | 0.597462i | \(-0.796176\pi\) | ||||
−0.801897 | + | 0.597462i | \(0.796176\pi\) | |||||||
\(702\) | −110.628 | −0.157590 | ||||||||
\(703\) | 265.347i | 0.377449i | ||||||||
\(704\) | −42.4318 | −0.0602724 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 387.709i | − | 0.549163i | ||||||
\(707\) | −648.283 | − | 197.072i | −0.916949 | − | 0.278744i | ||||
\(708\) | 134.067 | 0.189360 | ||||||||
\(709\) | 270.618 | 0.381689 | 0.190845 | − | 0.981620i | \(-0.438877\pi\) | ||||
0.190845 | + | 0.981620i | \(0.438877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.5881 | 0.0683377 | ||||||||
\(712\) | − | 166.228i | − | 0.233466i | ||||||
\(713\) | − | 96.5740i | − | 0.135447i | ||||||
\(714\) | −8.99794 | + | 29.5993i | −0.0126022 | + | 0.0414556i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 277.722 | 0.387880 | ||||||||
\(717\) | − | 215.259i | − | 0.300222i | ||||||
\(718\) | 92.6144 | 0.128989 | ||||||||
\(719\) | 865.721i | 1.20406i | 0.798473 | + | 0.602031i | \(0.205642\pi\) | ||||
−0.798473 | + | 0.602031i | \(0.794358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −686.639 | − | 208.732i | −0.952342 | − | 0.289504i | ||||
\(722\) | −433.958 | −0.601050 | ||||||||
\(723\) | −576.685 | −0.797628 | ||||||||
\(724\) | − | 296.976i | − | 0.410187i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 227.479i | − | 0.313332i | ||||||
\(727\) | 747.526i | 1.02823i | 0.857720 | + | 0.514117i | \(0.171880\pi\) | ||||
−0.857720 | + | 0.514117i | \(0.828120\pi\) | |||||||
\(728\) | 285.180 | + | 86.6922i | 0.391731 | + | 0.119083i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 64.9872i | 0.0889017i | ||||||||
\(732\) | 88.4609 | 0.120848 | ||||||||
\(733\) | 506.845i | 0.691467i | 0.938333 | + | 0.345733i | \(0.112370\pi\) | ||||
−0.938333 | + | 0.345733i | \(0.887630\pi\) | |||||||
\(734\) | − | 226.045i | − | 0.307963i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −89.5172 | −0.121627 | ||||||||
\(737\) | 479.647 | 0.650811 | ||||||||
\(738\) | 80.0244i | 0.108434i | ||||||||
\(739\) | −350.632 | −0.474468 | −0.237234 | − | 0.971453i | \(-0.576241\pi\) | ||||
−0.237234 | + | 0.971453i | \(0.576241\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 191.871i | 0.258936i | ||||||||
\(742\) | −232.457 | + | 764.684i | −0.313285 | + | 1.03057i | ||||
\(743\) | 958.163 | 1.28959 | 0.644793 | − | 0.764357i | \(-0.276944\pi\) | ||||
0.644793 | + | 0.764357i | \(0.276944\pi\) | |||||||
\(744\) | 29.8975 | 0.0401848 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −665.749 | −0.892424 | ||||||||
\(747\) | − | 104.357i | − | 0.139702i | ||||||
\(748\) | − | 19.1396i | − | 0.0255877i | ||||||
\(749\) | −284.284 | + | 935.171i | −0.379551 | + | 1.24856i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −457.638 | −0.609371 | −0.304686 | − | 0.952453i | \(-0.598551\pi\) | ||||
−0.304686 | + | 0.952453i | \(0.598551\pi\) | |||||||
\(752\) | − | 106.926i | − | 0.142188i | ||||||
\(753\) | 266.941 | 0.354503 | ||||||||
\(754\) | − | 945.129i | − | 1.25349i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 69.6012 | + | 21.1582i | 0.0920651 | + | 0.0279870i | ||||
\(757\) | 1273.11 | 1.68179 | 0.840893 | − | 0.541201i | \(-0.182030\pi\) | ||||
0.840893 | + | 0.541201i | \(0.182030\pi\) | |||||||
\(758\) | −86.9319 | −0.114686 | ||||||||
\(759\) | 145.376i | 0.191536i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 103.915i | 0.136551i | 0.997667 | + | 0.0682754i | \(0.0217496\pi\) | ||||
−0.997667 | + | 0.0682754i | \(0.978250\pi\) | |||||||
\(762\) | − | 148.730i | − | 0.195184i | ||||||
\(763\) | −55.6297 | + | 182.998i | −0.0729091 | + | 0.239840i | ||||
\(764\) | −92.1562 | −0.120623 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 169.866i | − | 0.221757i | ||||||
\(767\) | 582.639 | 0.759633 | ||||||||
\(768\) | − | 27.7128i | − | 0.0360844i | ||||||
\(769\) | 433.921i | 0.564266i | 0.959375 | + | 0.282133i | \(0.0910420\pi\) | ||||
−0.959375 | + | 0.282133i | \(0.908958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −710.771 | −0.921881 | ||||||||
\(772\) | −52.8813 | −0.0684991 | ||||||||
\(773\) | − | 1220.86i | − | 1.57937i | −0.613510 | − | 0.789687i | \(-0.710243\pi\) | ||
0.613510 | − | 0.789687i | \(-0.289757\pi\) | |||||||
\(774\) | 152.814 | 0.197434 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 398.056i | − | 0.512958i | ||||||
\(777\) | 418.310 | + | 127.163i | 0.538366 | + | 0.163659i | ||||
\(778\) | −437.836 | −0.562771 | ||||||||
\(779\) | 138.793 | 0.178168 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 219.783 | 0.281412 | ||||||||
\(782\) | − | 40.3783i | − | 0.0516346i | ||||||
\(783\) | − | 230.669i | − | 0.294596i | ||||||
\(784\) | −162.839 | − | 109.084i | −0.207703 | − | 0.139138i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −495.409 | −0.630292 | ||||||||
\(787\) | 866.849i | 1.10146i | 0.834683 | + | 0.550730i | \(0.185651\pi\) | ||||
−0.834683 | + | 0.550730i | \(0.814349\pi\) | |||||||
\(788\) | −573.094 | −0.727277 | ||||||||
\(789\) | 594.091i | 0.752967i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 94.5476 | − | 311.021i | 0.119529 | − | 0.393199i | ||||
\(792\) | −45.0057 | −0.0568253 | ||||||||
\(793\) | 384.441 | 0.484793 | ||||||||
\(794\) | 1066.58i | 1.34330i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 68.9127i | − | 0.0865737i | ||||||
\(797\) | − | 915.806i | − | 1.14907i | −0.818481 | − | 0.574533i | \(-0.805184\pi\) | ||
0.818481 | − | 0.574533i | \(-0.194816\pi\) | |||||||
\(798\) | 36.6963 | − | 120.715i | 0.0459853 | − | 0.151272i | ||||
\(799\) | 48.2306 | 0.0603637 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 176.311i | − | 0.220114i | ||||||
\(802\) | −333.326 | −0.415619 | ||||||||
\(803\) | 565.996i | 0.704852i | ||||||||
\(804\) | 313.265i | 0.389633i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 129.931 | 0.161205 | ||||||||
\(807\) | −412.360 | −0.510979 | ||||||||
\(808\) | 273.782i | 0.338839i | ||||||||
\(809\) | −693.212 | −0.856875 | −0.428437 | − | 0.903571i | \(-0.640936\pi\) | ||||
−0.428437 | + | 0.903571i | \(0.640936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1165.31i | − | 1.43688i | −0.695591 | − | 0.718438i | \(-0.744857\pi\) | ||
0.695591 | − | 0.718438i | \(-0.255143\pi\) | |||||||
\(812\) | −180.760 | + | 594.624i | −0.222611 | + | 0.732295i | ||||
\(813\) | 56.5435 | 0.0695492 | ||||||||
\(814\) | −270.489 | −0.332296 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.5003 | 0.0153190 | ||||||||
\(817\) | − | 265.037i | − | 0.324403i | ||||||
\(818\) | 115.033i | 0.140627i | ||||||||
\(819\) | 302.479 | + | 91.9510i | 0.369327 | + | 0.112272i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −392.977 | −0.478657 | −0.239329 | − | 0.970939i | \(-0.576927\pi\) | ||||
−0.239329 | + | 0.970939i | \(0.576927\pi\) | |||||||
\(822\) | − | 289.454i | − | 0.352134i | ||||||
\(823\) | 1430.26 | 1.73786 | 0.868932 | − | 0.494931i | \(-0.164807\pi\) | ||||
0.868932 | + | 0.494931i | \(0.164807\pi\) | |||||||
\(824\) | 289.980i | 0.351918i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −366.564 | − | 111.432i | −0.443782 | − | 0.134906i | ||||
\(827\) | −667.082 | −0.806629 | −0.403314 | − | 0.915062i | \(-0.632142\pi\) | ||||
−0.403314 | + | 0.915062i | \(0.632142\pi\) | |||||||
\(828\) | −94.9473 | −0.114671 | ||||||||
\(829\) | − | 851.079i | − | 1.02663i | −0.858199 | − | 0.513317i | \(-0.828417\pi\) | ||
0.858199 | − | 0.513317i | \(-0.171583\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 398.840i | 0.479952i | ||||||||
\(832\) | − | 120.437i | − | 0.144756i | ||||||
\(833\) | 49.2042 | − | 73.4515i | 0.0590687 | − | 0.0881771i | ||||
\(834\) | −627.135 | −0.751960 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 78.0569i | 0.0933695i | ||||||||
\(837\) | 31.7110 | 0.0378866 | ||||||||
\(838\) | 301.269i | 0.359510i | ||||||||
\(839\) | 1401.61i | 1.67057i | 0.549815 | + | 0.835287i | \(0.314698\pi\) | ||||
−0.549815 | + | 0.835287i | \(0.685302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1129.67 | 1.34325 | ||||||||
\(842\) | −589.494 | −0.700112 | ||||||||
\(843\) | − | 843.265i | − | 1.00031i | ||||||
\(844\) | 243.254 | 0.288216 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 113.412i | − | 0.134056i | ||||||
\(847\) | −189.074 | + | 621.972i | −0.223228 | + | 0.734323i | ||||
\(848\) | 322.940 | 0.380826 | ||||||||
\(849\) | −562.302 | −0.662311 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −570.643 | −0.670556 | ||||||||
\(852\) | 143.544i | 0.168478i | ||||||||
\(853\) | 390.367i | 0.457640i | 0.973469 | + | 0.228820i | \(0.0734867\pi\) | ||||
−0.973469 | + | 0.228820i | \(0.926513\pi\) | |||||||
\(854\) | −241.869 | − | 73.5261i | −0.283219 | − | 0.0860962i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 394.940 | 0.461378 | ||||||||
\(857\) | 1123.67i | 1.31117i | 0.755124 | + | 0.655583i | \(0.227577\pi\) | ||||
−0.755124 | + | 0.655583i | \(0.772423\pi\) | |||||||
\(858\) | −195.590 | −0.227960 | ||||||||
\(859\) | − | 774.660i | − | 0.901816i | −0.892571 | − | 0.450908i | \(-0.851100\pi\) | ||
0.892571 | − | 0.450908i | \(-0.148900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 66.5140 | − | 218.802i | 0.0772520 | − | 0.254126i | ||||
\(862\) | 469.394 | 0.544540 | ||||||||
\(863\) | 596.376 | 0.691050 | 0.345525 | − | 0.938409i | \(-0.387701\pi\) | ||||
0.345525 | + | 0.938409i | \(0.387701\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 430.091i | 0.496641i | ||||||||
\(867\) | − | 494.924i | − | 0.570847i | ||||||
\(868\) | −81.7455 | − | 24.8499i | −0.0941768 | − | 0.0286289i | ||||
\(869\) | 85.9033 | 0.0988530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1361.41i | 1.56305i | ||||||||
\(872\) | 77.2832 | 0.0886276 | ||||||||
\(873\) | − | 422.202i | − | 0.483622i | ||||||
\(874\) | 164.675i | 0.188415i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −369.661 | −0.421987 | ||||||||
\(877\) | −481.187 | −0.548674 | −0.274337 | − | 0.961634i | \(-0.588458\pi\) | ||||
−0.274337 | + | 0.961634i | \(0.588458\pi\) | |||||||
\(878\) | 34.4726i | 0.0392627i | ||||||||
\(879\) | 222.281 | 0.252879 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1098.21i | − | 1.24655i | −0.782004 | − | 0.623273i | \(-0.785803\pi\) | ||
0.782004 | − | 0.623273i | \(-0.214197\pi\) | |||||||
\(882\) | −172.717 | − | 115.701i | −0.195825 | − | 0.131180i | ||||
\(883\) | −930.631 | −1.05394 | −0.526971 | − | 0.849883i | \(-0.676672\pi\) | ||||
−0.526971 | + | 0.849883i | \(0.676672\pi\) | |||||||
\(884\) | 54.3251 | 0.0614537 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −42.8675 | −0.0483832 | ||||||||
\(887\) | − | 1762.36i | − | 1.98688i | −0.114343 | − | 0.993441i | \(-0.536476\pi\) | ||
0.114343 | − | 0.993441i | \(-0.463524\pi\) | |||||||
\(888\) | − | 176.660i | − | 0.198942i | ||||||
\(889\) | −123.620 | + | 406.657i | −0.139055 | + | 0.457432i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −47.7357 | −0.0535754 | ||||||||
\(892\) | − | 604.051i | − | 0.677187i | ||||||
\(893\) | −196.699 | −0.220268 | ||||||||
\(894\) | − | 647.984i | − | 0.724814i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −23.0341 | + | 75.7722i | −0.0257077 | + | 0.0845672i | ||||
\(897\) | −412.630 | −0.460012 | ||||||||
\(898\) | 777.958 | 0.866323 | ||||||||
\(899\) | 270.917i | 0.301353i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 145.668i | 0.161673i | ||||||||
\(902\) | 141.482i | 0.156854i | ||||||||
\(903\) | −417.823 | − | 127.014i | −0.462705 | − | 0.140658i | ||||
\(904\) | −131.350 | −0.145298 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 31.5271i | 0.0347981i | ||||||||
\(907\) | 135.202 | 0.149065 | 0.0745327 | − | 0.997219i | \(-0.476253\pi\) | ||||
0.0745327 | + | 0.997219i | \(0.476253\pi\) | |||||||
\(908\) | − | 319.567i | − | 0.351946i | ||||||
\(909\) | 290.389i | 0.319460i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −995.115 | −1.09233 | −0.546166 | − | 0.837677i | \(-0.683913\pi\) | ||||
−0.546166 | + | 0.837677i | \(0.683913\pi\) | |||||||
\(912\) | −50.9801 | −0.0558993 | ||||||||
\(913\) | − | 184.502i | − | 0.202083i | ||||||
\(914\) | −674.911 | −0.738414 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 92.0245i | 0.100463i | ||||||||
\(917\) | 1354.55 | + | 411.770i | 1.47715 | + | 0.449040i | ||||
\(918\) | 13.2586 | 0.0144429 | ||||||||
\(919\) | 514.989 | 0.560380 | 0.280190 | − | 0.959945i | \(-0.409603\pi\) | ||||
0.280190 | + | 0.959945i | \(0.409603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 502.485 | 0.545586 | ||||||||
\(922\) | 1217.29i | 1.32027i | ||||||||
\(923\) | 623.824i | 0.675866i | ||||||||
\(924\) | 123.054 | + | 37.4074i | 0.133176 | + | 0.0404842i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1095.32 | 1.18285 | ||||||||
\(927\) | 307.570i | 0.331791i | ||||||||
\(928\) | 251.120 | 0.270604 | ||||||||
\(929\) | − | 865.807i | − | 0.931977i | −0.884791 | − | 0.465989i | \(-0.845699\pi\) | ||
0.884791 | − | 0.465989i | \(-0.154301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −200.670 | + | 299.557i | −0.215542 | + | 0.321759i | ||||
\(932\) | 194.623 | 0.208822 | ||||||||
\(933\) | −131.925 | −0.141399 | ||||||||
\(934\) | 1088.75i | 1.16568i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 127.742i | − | 0.136477i | ||||||
\(937\) | 1000.06i | 1.06730i | 0.845706 | + | 0.533649i | \(0.179180\pi\) | ||||
−0.845706 | + | 0.533649i | \(0.820820\pi\) | |||||||
\(938\) | 260.377 | − | 856.527i | 0.277587 | − | 0.913142i | ||||
\(939\) | −913.043 | −0.972356 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 776.370i | 0.825048i | 0.910947 | + | 0.412524i | \(0.135353\pi\) | ||||
−0.910947 | + | 0.412524i | \(0.864647\pi\) | |||||||
\(942\) | 498.801 | 0.529512 | ||||||||
\(943\) | 298.482i | 0.316523i | ||||||||
\(944\) | 154.807i | 0.163990i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 270.173 | 0.285595 | ||||||||
\(947\) | −472.690 | −0.499144 | −0.249572 | − | 0.968356i | \(-0.580290\pi\) | ||||
−0.249572 | + | 0.968356i | \(0.580290\pi\) | |||||||
\(948\) | 56.1047i | 0.0591822i | ||||||||
\(949\) | −1606.50 | −1.69284 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 845.808i | − | 0.889388i | ||||||
\(952\) | −34.1784 | − | 10.3899i | −0.0359016 | − | 0.0109138i | ||||
\(953\) | 104.665 | 0.109827 | 0.0549133 | − | 0.998491i | \(-0.482512\pi\) | ||||
0.0549133 | + | 0.998491i | \(0.482512\pi\) | |||||||
\(954\) | 342.530 | 0.359046 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 248.560 | 0.260000 | ||||||||
\(957\) | − | 407.820i | − | 0.426144i | ||||||
\(958\) | 1024.93i | 1.06986i | ||||||||
\(959\) | −240.586 | + | 791.424i | −0.250872 | + | 0.825259i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 923.756 | 0.961244 | ||||||||
\(962\) | − | 767.745i | − | 0.798072i | ||||||
\(963\) | 418.897 | 0.434992 | ||||||||
\(964\) | − | 665.899i | − | 0.690766i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 259.604 | + | 78.9175i | 0.268742 | + | 0.0816951i | ||||
\(967\) | 1463.91 | 1.51386 | 0.756931 | − | 0.653495i | \(-0.226698\pi\) | ||||
0.756931 | + | 0.653495i | \(0.226698\pi\) | |||||||
\(968\) | 262.670 | 0.271353 | ||||||||
\(969\) | − | 22.9955i | − | 0.0237311i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 101.826i | − | 0.104867i | −0.998624 | − | 0.0524333i | \(-0.983302\pi\) | ||
0.998624 | − | 0.0524333i | \(-0.0166977\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | 1714.71 | + | 521.256i | 1.76229 | + | 0.535721i | ||||
\(974\) | 83.4250 | 0.0856520 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 102.146i | 0.104658i | ||||||||
\(977\) | 69.4893 | 0.0711252 | 0.0355626 | − | 0.999367i | \(-0.488678\pi\) | ||||
0.0355626 | + | 0.999367i | \(0.488678\pi\) | |||||||
\(978\) | − | 641.377i | − | 0.655805i | ||||||
\(979\) | − | 311.717i | − | 0.318403i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 81.9713 | 0.0835589 | ||||||||
\(982\) | 812.681 | 0.827577 | ||||||||
\(983\) | 166.731i | 0.169614i | 0.996397 | + | 0.0848070i | \(0.0270274\pi\) | ||||
−0.996397 | + | 0.0848070i | \(0.972973\pi\) | |||||||
\(984\) | −92.4042 | −0.0939067 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 113.272i | 0.114881i | ||||||||
\(987\) | −94.2645 | + | 310.090i | −0.0955061 | + | 0.314174i | ||||
\(988\) | −221.554 | −0.224245 | ||||||||
\(989\) | 569.978 | 0.576317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −990.392 | −0.999387 | −0.499693 | − | 0.866202i | \(-0.666554\pi\) | ||||
−0.499693 | + | 0.866202i | \(0.666554\pi\) | |||||||
\(992\) | 34.5226i | 0.0348010i | ||||||||
\(993\) | − | 900.405i | − | 0.906753i | ||||||
\(994\) | 119.309 | − | 392.476i | 0.120030 | − | 0.394845i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 120.501 | 0.120985 | ||||||||
\(997\) | 567.448i | 0.569156i | 0.958653 | + | 0.284578i | \(0.0918534\pi\) | ||||
−0.958653 | + | 0.284578i | \(0.908147\pi\) | |||||||
\(998\) | −399.429 | −0.400230 | ||||||||
\(999\) | − | 187.376i | − | 0.187564i |
(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 | 1050.3.f.d.601.2 | yes | 12 | |
5.2 | odd | 4 | 1050.3.h.c.349.7 | 24 | |||
5.3 | odd | 4 | 1050.3.h.c.349.20 | 24 | |||
5.4 | even | 2 | 1050.3.f.c.601.11 | yes | 12 | ||
7.6 | odd | 2 | inner | 1050.3.f.d.601.5 | yes | 12 | |
35.13 | even | 4 | 1050.3.h.c.349.8 | 24 | |||
35.27 | even | 4 | 1050.3.h.c.349.19 | 24 | |||
35.34 | odd | 2 | 1050.3.f.c.601.8 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.f.c.601.8 | ✓ | 12 | 35.34 | odd | 2 | ||
1050.3.f.c.601.11 | yes | 12 | 5.4 | even | 2 | ||
1050.3.f.d.601.2 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.3.f.d.601.5 | yes | 12 | 7.6 | odd | 2 | inner | |
1050.3.h.c.349.7 | 24 | 5.2 | odd | 4 | |||
1050.3.h.c.349.8 | 24 | 35.13 | even | 4 | |||
1050.3.h.c.349.19 | 24 | 35.27 | even | 4 | |||
1050.3.h.c.349.20 | 24 | 5.3 | odd | 4 |