Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 124x^{6} + 4272x^{4} + 28129x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.5 | ||
Root | \(-7.12571i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.4.b.o.599.4 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 10.1257i | − 1.94869i | −0.225050 | − | 0.974347i | \(-0.572255\pi\) | ||||
0.225050 | − | 0.974347i | \(-0.427745\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 20.2514 | 1.37794 | ||||||||
\(7\) | − 24.6431i | − 1.33060i | −0.746575 | − | 0.665301i | \(-0.768303\pi\) | ||||
0.746575 | − | 0.665301i | \(-0.231697\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | −75.5301 | −2.79741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.3867 | −0.476572 | −0.238286 | − | 0.971195i | \(-0.576586\pi\) | ||||
−0.238286 | + | 0.971195i | \(0.576586\pi\) | |||||||
\(12\) | 40.5029i | 0.974347i | ||||||||
\(13\) | − 4.00699i | − 0.0854876i | −0.999086 | − | 0.0427438i | \(-0.986390\pi\) | ||||
0.999086 | − | 0.0427438i | \(-0.0136099\pi\) | |||||||
\(14\) | 49.2862 | 0.940877 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 48.2740i | 0.688716i | 0.938838 | + | 0.344358i | \(0.111903\pi\) | ||||
−0.938838 | + | 0.344358i | \(0.888097\pi\) | |||||||
\(18\) | − 151.060i | − 1.97807i | ||||||||
\(19\) | −79.3172 | −0.957717 | −0.478859 | − | 0.877892i | \(-0.658949\pi\) | ||||
−0.478859 | + | 0.877892i | \(0.658949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −249.529 | −2.59294 | ||||||||
\(22\) | − 34.7734i | − 0.336987i | ||||||||
\(23\) | 23.0000i | 0.208514i | ||||||||
\(24\) | −81.0057 | −0.688968 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.01398 | 0.0604488 | ||||||||
\(27\) | 491.402i | 3.50260i | ||||||||
\(28\) | 98.5723i | 0.665301i | ||||||||
\(29\) | 254.267 | 1.62815 | 0.814074 | − | 0.580761i | \(-0.197245\pi\) | ||||
0.814074 | + | 0.580761i | \(0.197245\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −220.696 | −1.27865 | −0.639325 | − | 0.768937i | \(-0.720786\pi\) | ||||
−0.639325 | + | 0.768937i | \(0.720786\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 176.053i | 0.928693i | ||||||||
\(34\) | −96.5480 | −0.486996 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 302.120 | 1.39870 | ||||||||
\(37\) | − 422.904i | − 1.87905i | −0.342476 | − | 0.939527i | \(-0.611265\pi\) | ||||
0.342476 | − | 0.939527i | \(-0.388735\pi\) | |||||||
\(38\) | − 158.634i | − 0.677208i | ||||||||
\(39\) | −40.5736 | −0.166589 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −170.251 | −0.648505 | −0.324252 | − | 0.945971i | \(-0.605113\pi\) | ||||
−0.324252 | + | 0.945971i | \(0.605113\pi\) | |||||||
\(42\) | − 499.058i | − 1.83348i | ||||||||
\(43\) | 228.920i | 0.811860i | 0.913904 | + | 0.405930i | \(0.133052\pi\) | ||||
−0.913904 | + | 0.405930i | \(0.866948\pi\) | |||||||
\(44\) | 69.5468 | 0.238286 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 580.087i | 1.80031i | 0.435572 | + | 0.900154i | \(0.356546\pi\) | ||||
−0.435572 | + | 0.900154i | \(0.643454\pi\) | |||||||
\(48\) | − 162.011i | − 0.487174i | ||||||||
\(49\) | −264.282 | −0.770500 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 488.809 | 1.34210 | ||||||||
\(52\) | 16.0280i | 0.0427438i | ||||||||
\(53\) | 260.354i | 0.674762i | 0.941368 | + | 0.337381i | \(0.109541\pi\) | ||||
−0.941368 | + | 0.337381i | \(0.890459\pi\) | |||||||
\(54\) | −982.803 | −2.47671 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −197.145 | −0.470439 | ||||||||
\(57\) | 803.144i | 1.86630i | ||||||||
\(58\) | 508.535i | 1.15127i | ||||||||
\(59\) | −353.130 | −0.779215 | −0.389607 | − | 0.920981i | \(-0.627389\pi\) | ||||
−0.389607 | + | 0.920981i | \(0.627389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −80.6108 | −0.169199 | −0.0845996 | − | 0.996415i | \(-0.526961\pi\) | ||||
−0.0845996 | + | 0.996415i | \(0.526961\pi\) | |||||||
\(62\) | − 441.392i | − 0.904142i | ||||||||
\(63\) | 1861.29i | 3.72224i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −352.106 | −0.656685 | ||||||||
\(67\) | − 820.011i | − 1.49523i | −0.664133 | − | 0.747614i | \(-0.731199\pi\) | ||||
0.664133 | − | 0.747614i | \(-0.268801\pi\) | |||||||
\(68\) | − 193.096i | − 0.344358i | ||||||||
\(69\) | 232.891 | 0.406331 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 614.845 | 1.02773 | 0.513864 | − | 0.857872i | \(-0.328214\pi\) | ||||
0.513864 | + | 0.857872i | \(0.328214\pi\) | |||||||
\(72\) | 604.241i | 0.989034i | ||||||||
\(73\) | − 511.586i | − 0.820228i | −0.912034 | − | 0.410114i | \(-0.865489\pi\) | ||||
0.912034 | − | 0.410114i | \(-0.134511\pi\) | |||||||
\(74\) | 845.808 | 1.32869 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 317.269 | 0.478859 | ||||||||
\(77\) | 428.462i | 0.634127i | ||||||||
\(78\) | − 81.1472i | − 0.117796i | ||||||||
\(79\) | −160.464 | −0.228526 | −0.114263 | − | 0.993451i | \(-0.536451\pi\) | ||||
−0.114263 | + | 0.993451i | \(0.536451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2936.48 | 4.02809 | ||||||||
\(82\) | − 340.502i | − 0.458562i | ||||||||
\(83\) | 32.5646i | 0.0430654i | 0.999768 | + | 0.0215327i | \(0.00685460\pi\) | ||||
−0.999768 | + | 0.0215327i | \(0.993145\pi\) | |||||||
\(84\) | 998.115 | 1.29647 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −457.840 | −0.574072 | ||||||||
\(87\) | − 2574.64i | − 3.17276i | ||||||||
\(88\) | 139.094i | 0.168494i | ||||||||
\(89\) | 25.0375 | 0.0298199 | 0.0149100 | − | 0.999889i | \(-0.495254\pi\) | ||||
0.0149100 | + | 0.999889i | \(0.495254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −98.7445 | −0.113750 | ||||||||
\(92\) | − 92.0000i | − 0.104257i | ||||||||
\(93\) | 2234.70i | 2.49170i | ||||||||
\(94\) | −1160.17 | −1.27301 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 324.023 | 0.344484 | ||||||||
\(97\) | − 249.798i | − 0.261476i | −0.991417 | − | 0.130738i | \(-0.958265\pi\) | ||||
0.991417 | − | 0.130738i | \(-0.0417347\pi\) | |||||||
\(98\) | − 528.563i | − 0.544826i | ||||||||
\(99\) | 1313.22 | 1.33317 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 620.493 | 0.611300 | 0.305650 | − | 0.952144i | \(-0.401126\pi\) | ||||
0.305650 | + | 0.952144i | \(0.401126\pi\) | |||||||
\(102\) | 977.618i | 0.949006i | ||||||||
\(103\) | − 1473.24i | − 1.40935i | −0.709532 | − | 0.704673i | \(-0.751094\pi\) | ||||
0.709532 | − | 0.704673i | \(-0.248906\pi\) | |||||||
\(104\) | −32.0559 | −0.0302244 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −520.708 | −0.477129 | ||||||||
\(107\) | − 940.141i | − 0.849410i | −0.905332 | − | 0.424705i | \(-0.860378\pi\) | ||||
0.905332 | − | 0.424705i | \(-0.139622\pi\) | |||||||
\(108\) | − 1965.61i | − 1.75130i | ||||||||
\(109\) | 636.264 | 0.559111 | 0.279555 | − | 0.960130i | \(-0.409813\pi\) | ||||
0.279555 | + | 0.960130i | \(0.409813\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4282.20 | −3.66170 | ||||||||
\(112\) | − 394.289i | − 0.332650i | ||||||||
\(113\) | − 832.451i | − 0.693013i | −0.938048 | − | 0.346506i | \(-0.887368\pi\) | ||||
0.938048 | − | 0.346506i | \(-0.112632\pi\) | |||||||
\(114\) | −1606.29 | −1.31967 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1017.07 | −0.814074 | ||||||||
\(117\) | 302.648i | 0.239144i | ||||||||
\(118\) | − 706.261i | − 0.550988i | ||||||||
\(119\) | 1189.62 | 0.916406 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1028.70 | −0.772879 | ||||||||
\(122\) | − 161.222i | − 0.119642i | ||||||||
\(123\) | 1723.91i | 1.26374i | ||||||||
\(124\) | 882.783 | 0.639325 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3722.59 | −2.63202 | ||||||||
\(127\) | 1614.60i | 1.12813i | 0.825729 | + | 0.564067i | \(0.190764\pi\) | ||||
−0.825729 | + | 0.564067i | \(0.809236\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 2317.98 | 1.58207 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1974.56 | −1.31693 | −0.658464 | − | 0.752612i | \(-0.728794\pi\) | ||||
−0.658464 | + | 0.752612i | \(0.728794\pi\) | |||||||
\(132\) | − 704.211i | − 0.464346i | ||||||||
\(133\) | 1954.62i | 1.27434i | ||||||||
\(134\) | 1640.02 | 1.05729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 386.192 | 0.243498 | ||||||||
\(137\) | 753.805i | 0.470087i | 0.971985 | + | 0.235044i | \(0.0755233\pi\) | ||||
−0.971985 | + | 0.235044i | \(0.924477\pi\) | |||||||
\(138\) | 465.783i | 0.287319i | ||||||||
\(139\) | −1014.10 | −0.618810 | −0.309405 | − | 0.950930i | \(-0.600130\pi\) | ||||
−0.309405 | + | 0.950930i | \(0.600130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5873.80 | 3.50825 | ||||||||
\(142\) | 1229.69i | 0.726714i | ||||||||
\(143\) | 69.6683i | 0.0407410i | ||||||||
\(144\) | −1208.48 | −0.699352 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1023.17 | 0.579989 | ||||||||
\(147\) | 2676.04i | 1.50147i | ||||||||
\(148\) | 1691.62i | 0.939527i | ||||||||
\(149\) | 2771.80 | 1.52399 | 0.761995 | − | 0.647583i | \(-0.224220\pi\) | ||||
0.761995 | + | 0.647583i | \(0.224220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3108.62 | 1.67534 | 0.837668 | − | 0.546180i | \(-0.183918\pi\) | ||||
0.837668 | + | 0.546180i | \(0.183918\pi\) | |||||||
\(152\) | 634.538i | 0.338604i | ||||||||
\(153\) | − 3646.14i | − 1.92662i | ||||||||
\(154\) | −856.924 | −0.448396 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 162.294 | 0.0832946 | ||||||||
\(157\) | 3712.87i | 1.88739i | 0.330822 | + | 0.943693i | \(0.392674\pi\) | ||||
−0.330822 | + | 0.943693i | \(0.607326\pi\) | |||||||
\(158\) | − 320.928i | − 0.161593i | ||||||||
\(159\) | 2636.27 | 1.31490 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 566.791 | 0.277450 | ||||||||
\(162\) | 5872.96i | 2.84829i | ||||||||
\(163\) | − 915.791i | − 0.440063i | −0.975493 | − | 0.220032i | \(-0.929384\pi\) | ||||
0.975493 | − | 0.220032i | \(-0.0706161\pi\) | |||||||
\(164\) | 681.003 | 0.324252 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −65.1292 | −0.0304518 | ||||||||
\(167\) | 1432.32i | 0.663688i | 0.943334 | + | 0.331844i | \(0.107671\pi\) | ||||
−0.943334 | + | 0.331844i | \(0.892329\pi\) | |||||||
\(168\) | 1996.23i | 0.916741i | ||||||||
\(169\) | 2180.94 | 0.992692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5990.84 | 2.67913 | ||||||||
\(172\) | − 915.680i | − 0.405930i | ||||||||
\(173\) | 3479.54i | 1.52916i | 0.644529 | + | 0.764580i | \(0.277054\pi\) | ||||
−0.644529 | + | 0.764580i | \(0.722946\pi\) | |||||||
\(174\) | 5149.28 | 2.24348 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −278.187 | −0.119143 | ||||||||
\(177\) | 3575.70i | 1.51845i | ||||||||
\(178\) | 50.0751i | 0.0210859i | ||||||||
\(179\) | −3642.71 | −1.52105 | −0.760527 | − | 0.649307i | \(-0.775059\pi\) | ||||
−0.760527 | + | 0.649307i | \(0.775059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2409.15 | 0.989342 | 0.494671 | − | 0.869080i | \(-0.335289\pi\) | ||||
0.494671 | + | 0.869080i | \(0.335289\pi\) | |||||||
\(182\) | − 197.489i | − 0.0804333i | ||||||||
\(183\) | 816.241i | 0.329717i | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4469.41 | −1.76190 | ||||||||
\(187\) | − 839.326i | − 0.328223i | ||||||||
\(188\) | − 2320.35i | − 0.900154i | ||||||||
\(189\) | 12109.6 | 4.66057 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −189.608 | −0.0718299 | −0.0359150 | − | 0.999355i | \(-0.511435\pi\) | ||||
−0.0359150 | + | 0.999355i | \(0.511435\pi\) | |||||||
\(192\) | 648.046i | 0.243587i | ||||||||
\(193\) | 1855.45i | 0.692012i | 0.938232 | + | 0.346006i | \(0.112462\pi\) | ||||
−0.938232 | + | 0.346006i | \(0.887538\pi\) | |||||||
\(194\) | 499.597 | 0.184891 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1057.13 | 0.385250 | ||||||||
\(197\) | 2429.85i | 0.878779i | 0.898297 | + | 0.439390i | \(0.144805\pi\) | ||||
−0.898297 | + | 0.439390i | \(0.855195\pi\) | |||||||
\(198\) | 2626.44i | 0.942691i | ||||||||
\(199\) | −4333.49 | −1.54368 | −0.771842 | − | 0.635815i | \(-0.780664\pi\) | ||||
−0.771842 | + | 0.635815i | \(0.780664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8303.20 | −2.91374 | ||||||||
\(202\) | 1240.99i | 0.432255i | ||||||||
\(203\) | − 6265.94i | − 2.16642i | ||||||||
\(204\) | −1955.24 | −0.671048 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2946.48 | 0.996558 | ||||||||
\(207\) | − 1737.19i | − 0.583300i | ||||||||
\(208\) | − 64.1118i | − 0.0213719i | ||||||||
\(209\) | 1379.07 | 0.456421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −816.788 | −0.266493 | −0.133247 | − | 0.991083i | \(-0.542540\pi\) | ||||
−0.133247 | + | 0.991083i | \(0.542540\pi\) | |||||||
\(212\) | − 1041.42i | − 0.337381i | ||||||||
\(213\) | − 6225.75i | − 2.00273i | ||||||||
\(214\) | 1880.28 | 0.600624 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3931.21 | 1.23836 | ||||||||
\(217\) | 5438.63i | 1.70137i | ||||||||
\(218\) | 1272.53i | 0.395351i | ||||||||
\(219\) | −5180.18 | −1.59837 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 193.433 | 0.0588767 | ||||||||
\(222\) | − 8564.41i | − 2.58921i | ||||||||
\(223\) | 4513.80i | 1.35546i | 0.735313 | + | 0.677728i | \(0.237035\pi\) | ||||
−0.735313 | + | 0.677728i | \(0.762965\pi\) | |||||||
\(224\) | 788.579 | 0.235219 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1664.90 | 0.490034 | ||||||||
\(227\) | 2792.85i | 0.816599i | 0.912848 | + | 0.408300i | \(0.133878\pi\) | ||||
−0.912848 | + | 0.408300i | \(0.866122\pi\) | |||||||
\(228\) | − 3212.57i | − 0.933149i | ||||||||
\(229\) | −1404.50 | −0.405292 | −0.202646 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202646 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4338.48 | 1.23572 | ||||||||
\(232\) | − 2034.14i | − 0.575637i | ||||||||
\(233\) | − 1073.79i | − 0.301916i | −0.988540 | − | 0.150958i | \(-0.951764\pi\) | ||||
0.988540 | − | 0.150958i | \(-0.0482359\pi\) | |||||||
\(234\) | −605.296 | −0.169100 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1412.52 | 0.389607 | ||||||||
\(237\) | 1624.81i | 0.445328i | ||||||||
\(238\) | 2379.24i | 0.647997i | ||||||||
\(239\) | 2573.18 | 0.696423 | 0.348212 | − | 0.937416i | \(-0.386789\pi\) | ||||
0.348212 | + | 0.937416i | \(0.386789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −696.127 | −0.186064 | −0.0930321 | − | 0.995663i | \(-0.529656\pi\) | ||||
−0.0930321 | + | 0.995663i | \(0.529656\pi\) | |||||||
\(242\) | − 2057.40i | − 0.546508i | ||||||||
\(243\) | − 16466.1i | − 4.34692i | ||||||||
\(244\) | 322.443 | 0.0845996 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3447.82 | −0.893598 | ||||||||
\(247\) | 317.823i | 0.0818729i | ||||||||
\(248\) | 1765.57i | 0.452071i | ||||||||
\(249\) | 329.740 | 0.0839213 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6467.81 | 1.62647 | 0.813236 | − | 0.581934i | \(-0.197704\pi\) | ||||
0.813236 | + | 0.581934i | \(0.197704\pi\) | |||||||
\(252\) | − 7445.18i | − 1.86112i | ||||||||
\(253\) | − 399.894i | − 0.0993721i | ||||||||
\(254\) | −3229.21 | −0.797711 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5332.72i | 1.29434i | 0.762344 | + | 0.647172i | \(0.224048\pi\) | ||||
−0.762344 | + | 0.647172i | \(0.775952\pi\) | |||||||
\(258\) | 4635.96i | 1.11869i | ||||||||
\(259\) | −10421.7 | −2.50027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19204.8 | −4.55460 | ||||||||
\(262\) | − 3949.11i | − 0.931209i | ||||||||
\(263\) | 6872.85i | 1.61140i | 0.592325 | + | 0.805699i | \(0.298210\pi\) | ||||
−0.592325 | + | 0.805699i | \(0.701790\pi\) | |||||||
\(264\) | 1408.42 | 0.328342 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3909.24 | −0.901094 | ||||||||
\(267\) | − 253.523i | − 0.0581099i | ||||||||
\(268\) | 3280.04i | 0.747614i | ||||||||
\(269\) | 1926.13 | 0.436572 | 0.218286 | − | 0.975885i | \(-0.429953\pi\) | ||||
0.218286 | + | 0.975885i | \(0.429953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3653.06 | −0.818847 | −0.409423 | − | 0.912344i | \(-0.634270\pi\) | ||||
−0.409423 | + | 0.912344i | \(0.634270\pi\) | |||||||
\(272\) | 772.384i | 0.172179i | ||||||||
\(273\) | 999.859i | 0.221664i | ||||||||
\(274\) | −1507.61 | −0.332402 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −931.566 | −0.203165 | ||||||||
\(277\) | − 1047.37i | − 0.227185i | −0.993527 | − | 0.113592i | \(-0.963764\pi\) | ||||
0.993527 | − | 0.113592i | \(-0.0362358\pi\) | |||||||
\(278\) | − 2028.19i | − 0.437565i | ||||||||
\(279\) | 16669.2 | 3.57691 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2758.90 | −0.585701 | −0.292851 | − | 0.956158i | \(-0.594604\pi\) | ||||
−0.292851 | + | 0.956158i | \(0.594604\pi\) | |||||||
\(282\) | 11747.6i | 2.48071i | ||||||||
\(283\) | − 3355.58i | − 0.704837i | −0.935843 | − | 0.352418i | \(-0.885359\pi\) | ||||
0.935843 | − | 0.352418i | \(-0.114641\pi\) | |||||||
\(284\) | −2459.38 | −0.513864 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −139.337 | −0.0288082 | ||||||||
\(287\) | 4195.50i | 0.862902i | ||||||||
\(288\) | − 2416.96i | − 0.494517i | ||||||||
\(289\) | 2582.62 | 0.525670 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2529.39 | −0.509537 | ||||||||
\(292\) | 2046.35i | 0.410114i | ||||||||
\(293\) | − 419.625i | − 0.0836681i | −0.999125 | − | 0.0418341i | \(-0.986680\pi\) | ||||
0.999125 | − | 0.0418341i | \(-0.0133201\pi\) | |||||||
\(294\) | −5352.08 | −1.06170 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3383.23 | −0.664346 | ||||||||
\(297\) | − 8543.85i | − 1.66924i | ||||||||
\(298\) | 5543.59i | 1.07762i | ||||||||
\(299\) | 92.1607 | 0.0178254 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5641.30 | 1.08026 | ||||||||
\(302\) | 6217.24i | 1.18464i | ||||||||
\(303\) | − 6282.93i | − 1.19124i | ||||||||
\(304\) | −1269.08 | −0.239429 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7292.28 | 1.36233 | ||||||||
\(307\) | − 4133.41i | − 0.768425i | −0.923245 | − | 0.384212i | \(-0.874473\pi\) | ||||
0.923245 | − | 0.384212i | \(-0.125527\pi\) | |||||||
\(308\) | − 1713.85i | − 0.317064i | ||||||||
\(309\) | −14917.6 | −2.74639 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6991.03 | −1.27468 | −0.637339 | − | 0.770584i | \(-0.719965\pi\) | ||||
−0.637339 | + | 0.770584i | \(0.719965\pi\) | |||||||
\(312\) | 324.589i | 0.0588982i | ||||||||
\(313\) | − 9380.53i | − 1.69399i | −0.531600 | − | 0.846996i | \(-0.678409\pi\) | ||||
0.531600 | − | 0.846996i | \(-0.321591\pi\) | |||||||
\(314\) | −7425.75 | −1.33458 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 641.855 | 0.114263 | ||||||||
\(317\) | − 7995.35i | − 1.41660i | −0.705910 | − | 0.708302i | \(-0.749462\pi\) | ||||
0.705910 | − | 0.708302i | \(-0.250538\pi\) | |||||||
\(318\) | 5272.54i | 0.929778i | ||||||||
\(319\) | −4420.87 | −0.775929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9519.60 | −1.65524 | ||||||||
\(322\) | 1133.58i | 0.196186i | ||||||||
\(323\) | − 3828.96i | − 0.659595i | ||||||||
\(324\) | −11745.9 | −2.01405 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1831.58 | 0.311172 | ||||||||
\(327\) | − 6442.63i | − 1.08954i | ||||||||
\(328\) | 1362.01i | 0.229281i | ||||||||
\(329\) | 14295.1 | 2.39549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4798.86 | −0.796886 | −0.398443 | − | 0.917193i | \(-0.630449\pi\) | ||||
−0.398443 | + | 0.917193i | \(0.630449\pi\) | |||||||
\(332\) | − 130.258i | − 0.0215327i | ||||||||
\(333\) | 31942.0i | 5.25648i | ||||||||
\(334\) | −2864.63 | −0.469298 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3992.46 | −0.648234 | ||||||||
\(337\) | 6895.51i | 1.11461i | 0.830309 | + | 0.557303i | \(0.188164\pi\) | ||||
−0.830309 | + | 0.557303i | \(0.811836\pi\) | |||||||
\(338\) | 4361.89i | 0.701939i | ||||||||
\(339\) | −8429.16 | −1.35047 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3837.17 | 0.609368 | ||||||||
\(342\) | 11981.7i | 1.89443i | ||||||||
\(343\) | − 1939.86i | − 0.305372i | ||||||||
\(344\) | 1831.36 | 0.287036 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6959.08 | −1.08128 | ||||||||
\(347\) | − 8744.17i | − 1.35277i | −0.736548 | − | 0.676386i | \(-0.763545\pi\) | ||||
0.736548 | − | 0.676386i | \(-0.236455\pi\) | |||||||
\(348\) | 10298.6i | 1.58638i | ||||||||
\(349\) | 6387.08 | 0.979635 | 0.489818 | − | 0.871825i | \(-0.337063\pi\) | ||||
0.489818 | + | 0.871825i | \(0.337063\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1969.04 | 0.299429 | ||||||||
\(352\) | − 556.375i | − 0.0842468i | ||||||||
\(353\) | 589.384i | 0.0888661i | 0.999012 | + | 0.0444331i | \(0.0141481\pi\) | ||||
−0.999012 | + | 0.0444331i | \(0.985852\pi\) | |||||||
\(354\) | −7151.39 | −1.07371 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −100.150 | −0.0149100 | ||||||||
\(357\) | − 12045.8i | − 1.78580i | ||||||||
\(358\) | − 7285.41i | − 1.07555i | ||||||||
\(359\) | −7214.13 | −1.06058 | −0.530289 | − | 0.847817i | \(-0.677917\pi\) | ||||
−0.530289 | + | 0.847817i | \(0.677917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −567.774 | −0.0827780 | ||||||||
\(362\) | 4818.30i | 0.699570i | ||||||||
\(363\) | 10416.3i | 1.50611i | ||||||||
\(364\) | 394.978 | 0.0568749 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1632.48 | −0.233145 | ||||||||
\(367\) | 12356.4i | 1.75750i | 0.477286 | + | 0.878748i | \(0.341621\pi\) | ||||
−0.477286 | + | 0.878748i | \(0.658379\pi\) | |||||||
\(368\) | 368.000i | 0.0521286i | ||||||||
\(369\) | 12859.1 | 1.81413 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6415.92 | 0.897839 | ||||||||
\(372\) | − 8938.81i | − 1.24585i | ||||||||
\(373\) | − 7145.98i | − 0.991969i | −0.868331 | − | 0.495985i | \(-0.834807\pi\) | ||||
0.868331 | − | 0.495985i | \(-0.165193\pi\) | |||||||
\(374\) | 1678.65 | 0.232088 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4640.70 | 0.636505 | ||||||||
\(377\) | − 1018.85i | − 0.139186i | ||||||||
\(378\) | 24219.3i | 3.29552i | ||||||||
\(379\) | −2170.69 | −0.294197 | −0.147099 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147099 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16349.0 | 2.19839 | ||||||||
\(382\) | − 379.215i | − 0.0507914i | ||||||||
\(383\) | 7967.21i | 1.06294i | 0.847078 | + | 0.531469i | \(0.178360\pi\) | ||||
−0.847078 | + | 0.531469i | \(0.821640\pi\) | |||||||
\(384\) | −1296.09 | −0.172242 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3710.90 | −0.489326 | ||||||||
\(387\) | − 17290.3i | − 2.27111i | ||||||||
\(388\) | 999.193i | 0.130738i | ||||||||
\(389\) | 568.951 | 0.0741567 | 0.0370783 | − | 0.999312i | \(-0.488195\pi\) | ||||
0.0370783 | + | 0.999312i | \(0.488195\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1110.30 | −0.143607 | ||||||||
\(392\) | 2114.25i | 0.272413i | ||||||||
\(393\) | 19993.8i | 2.56629i | ||||||||
\(394\) | −4859.70 | −0.621391 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5252.88 | −0.666583 | ||||||||
\(397\) | 8564.88i | 1.08277i | 0.840775 | + | 0.541384i | \(0.182100\pi\) | ||||
−0.840775 | + | 0.541384i | \(0.817900\pi\) | |||||||
\(398\) | − 8666.98i | − 1.09155i | ||||||||
\(399\) | 19791.9 | 2.48330 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12455.6 | −1.55113 | −0.775563 | − | 0.631270i | \(-0.782534\pi\) | ||||
−0.775563 | + | 0.631270i | \(0.782534\pi\) | |||||||
\(402\) | − 16606.4i | − 2.06033i | ||||||||
\(403\) | 884.325i | 0.109309i | ||||||||
\(404\) | −2481.97 | −0.305650 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12531.9 | 1.53189 | ||||||||
\(407\) | 7352.91i | 0.895504i | ||||||||
\(408\) | − 3910.47i | − 0.474503i | ||||||||
\(409\) | −11838.9 | −1.43129 | −0.715645 | − | 0.698465i | \(-0.753867\pi\) | ||||
−0.715645 | + | 0.698465i | \(0.753867\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7632.82 | 0.916056 | ||||||||
\(412\) | 5892.96i | 0.704673i | ||||||||
\(413\) | 8702.22i | 1.03682i | ||||||||
\(414\) | 3474.38 | 0.412456 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 128.224 | 0.0151122 | ||||||||
\(417\) | 10268.5i | 1.20587i | ||||||||
\(418\) | 2758.13i | 0.322738i | ||||||||
\(419\) | 1531.77 | 0.178596 | 0.0892981 | − | 0.996005i | \(-0.471538\pi\) | ||||
0.0892981 | + | 0.996005i | \(0.471538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9985.06 | −1.15592 | −0.577959 | − | 0.816066i | \(-0.696151\pi\) | ||||
−0.577959 | + | 0.816066i | \(0.696151\pi\) | |||||||
\(422\) | − 1633.58i | − 0.188439i | ||||||||
\(423\) | − 43814.0i | − 5.03620i | ||||||||
\(424\) | 2082.83 | 0.238564 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12451.5 | 1.41614 | ||||||||
\(427\) | 1986.50i | 0.225137i | ||||||||
\(428\) | 3760.56i | 0.424705i | ||||||||
\(429\) | 705.441 | 0.0793917 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13786.7 | −1.54079 | −0.770396 | − | 0.637566i | \(-0.779941\pi\) | ||||
−0.770396 | + | 0.637566i | \(0.779941\pi\) | |||||||
\(432\) | 7862.42i | 0.875651i | ||||||||
\(433\) | 2621.92i | 0.290996i | 0.989359 | + | 0.145498i | \(0.0464784\pi\) | ||||
−0.989359 | + | 0.145498i | \(0.953522\pi\) | |||||||
\(434\) | −10877.3 | −1.20305 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2545.06 | −0.279555 | ||||||||
\(437\) | − 1824.30i | − 0.199698i | ||||||||
\(438\) | − 10360.4i | − 1.13022i | ||||||||
\(439\) | −12062.7 | −1.31143 | −0.655717 | − | 0.755007i | \(-0.727633\pi\) | ||||
−0.655717 | + | 0.755007i | \(0.727633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19961.2 | 2.15541 | ||||||||
\(442\) | 386.867i | 0.0416321i | ||||||||
\(443\) | − 3659.26i | − 0.392453i | −0.980559 | − | 0.196227i | \(-0.937131\pi\) | ||||
0.980559 | − | 0.196227i | \(-0.0628689\pi\) | |||||||
\(444\) | 17128.8 | 1.83085 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9027.60 | −0.958452 | ||||||||
\(447\) | − 28066.4i | − 2.96979i | ||||||||
\(448\) | 1577.16i | 0.166325i | ||||||||
\(449\) | 10529.6 | 1.10674 | 0.553368 | − | 0.832937i | \(-0.313342\pi\) | ||||
0.553368 | + | 0.832937i | \(0.313342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2960.10 | 0.309059 | ||||||||
\(452\) | 3329.81i | 0.346506i | ||||||||
\(453\) | − 31477.0i | − 3.26472i | ||||||||
\(454\) | −5585.70 | −0.577423 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6425.15 | 0.659836 | ||||||||
\(457\) | 6443.23i | 0.659522i | 0.944064 | + | 0.329761i | \(0.106968\pi\) | ||||
−0.944064 | + | 0.329761i | \(0.893032\pi\) | |||||||
\(458\) | − 2809.00i | − 0.286585i | ||||||||
\(459\) | −23721.9 | −2.41230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3263.86 | −0.329747 | −0.164873 | − | 0.986315i | \(-0.552722\pi\) | ||||
−0.164873 | + | 0.986315i | \(0.552722\pi\) | |||||||
\(462\) | 8676.97i | 0.873786i | ||||||||
\(463\) | − 9518.12i | − 0.955388i | −0.878526 | − | 0.477694i | \(-0.841473\pi\) | ||||
0.878526 | − | 0.477694i | \(-0.158527\pi\) | |||||||
\(464\) | 4068.28 | 0.407037 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2147.59 | 0.213487 | ||||||||
\(467\) | 19092.6i | 1.89187i | 0.324360 | + | 0.945934i | \(0.394851\pi\) | ||||
−0.324360 | + | 0.945934i | \(0.605149\pi\) | |||||||
\(468\) | − 1210.59i | − 0.119572i | ||||||||
\(469\) | −20207.6 | −1.98955 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37595.5 | 3.67794 | ||||||||
\(472\) | 2825.04i | 0.275494i | ||||||||
\(473\) | − 3980.17i | − 0.386910i | ||||||||
\(474\) | −3249.62 | −0.314895 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4758.48 | −0.458203 | ||||||||
\(477\) | − 19664.6i | − 1.88758i | ||||||||
\(478\) | 5146.36i | 0.492446i | ||||||||
\(479\) | 6324.81 | 0.603315 | 0.301658 | − | 0.953416i | \(-0.402460\pi\) | ||||
0.301658 | + | 0.953416i | \(0.402460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1694.57 | −0.160636 | ||||||||
\(482\) | − 1392.25i | − 0.131567i | ||||||||
\(483\) | − 5739.16i | − 0.540664i | ||||||||
\(484\) | 4114.81 | 0.386440 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 32932.2 | 3.07373 | ||||||||
\(487\) | − 7873.07i | − 0.732573i | −0.930502 | − | 0.366286i | \(-0.880629\pi\) | ||||
0.930502 | − | 0.366286i | \(-0.119371\pi\) | |||||||
\(488\) | 644.886i | 0.0598209i | ||||||||
\(489\) | −9273.04 | −0.857549 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3556.82 | −0.326918 | −0.163459 | − | 0.986550i | \(-0.552265\pi\) | ||||
−0.163459 | + | 0.986550i | \(0.552265\pi\) | |||||||
\(492\) | − 6895.64i | − 0.631869i | ||||||||
\(493\) | 12274.5i | 1.12133i | ||||||||
\(494\) | −635.646 | −0.0578929 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3531.13 | −0.319662 | ||||||||
\(497\) | − 15151.7i | − 1.36750i | ||||||||
\(498\) | 659.479i | 0.0593413i | ||||||||
\(499\) | 1933.37 | 0.173446 | 0.0867231 | − | 0.996232i | \(-0.472360\pi\) | ||||
0.0867231 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14503.2 | 1.29332 | ||||||||
\(502\) | 12935.6i | 1.15009i | ||||||||
\(503\) | − 2114.36i | − 0.187425i | −0.995599 | − | 0.0937123i | \(-0.970127\pi\) | ||||
0.995599 | − | 0.0937123i | \(-0.0298734\pi\) | |||||||
\(504\) | 14890.4 | 1.31601 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 799.789 | 0.0702667 | ||||||||
\(507\) | − 22083.6i | − 1.93445i | ||||||||
\(508\) | − 6458.42i | − 0.564067i | ||||||||
\(509\) | 316.452 | 0.0275570 | 0.0137785 | − | 0.999905i | \(-0.495614\pi\) | ||||
0.0137785 | + | 0.999905i | \(0.495614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12607.1 | −1.09140 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | − 38976.6i | − 3.35450i | ||||||||
\(514\) | −10665.4 | −0.915239 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9271.92 | −0.791034 | ||||||||
\(517\) | − 10085.8i | − 0.857976i | ||||||||
\(518\) | − 20843.3i | − 1.76796i | ||||||||
\(519\) | 35232.8 | 2.97987 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −309.041 | −0.0259872 | −0.0129936 | − | 0.999916i | \(-0.504136\pi\) | ||||
−0.0129936 | + | 0.999916i | \(0.504136\pi\) | |||||||
\(522\) | − 38409.7i | − 3.22059i | ||||||||
\(523\) | 5892.46i | 0.492656i | 0.969186 | + | 0.246328i | \(0.0792241\pi\) | ||||
−0.969186 | + | 0.246328i | \(0.920776\pi\) | |||||||
\(524\) | 7898.22 | 0.658464 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13745.7 | −1.13943 | ||||||||
\(527\) | − 10653.9i | − 0.880626i | ||||||||
\(528\) | 2816.84i | 0.232173i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26672.0 | 2.17978 | ||||||||
\(532\) | − 7818.49i | − 0.637170i | ||||||||
\(533\) | 682.193i | 0.0554391i | ||||||||
\(534\) | 507.046 | 0.0410899 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6560.09 | −0.528643 | ||||||||
\(537\) | 36885.0i | 2.96407i | ||||||||
\(538\) | 3852.25i | 0.308703i | ||||||||
\(539\) | 4594.99 | 0.367199 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1560.55 | 0.124017 | 0.0620085 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620085 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(542\) | − 7306.12i | − 0.579012i | ||||||||
\(543\) | − 24394.4i | − 1.92792i | ||||||||
\(544\) | −1544.77 | −0.121749 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1999.72 | −0.156740 | ||||||||
\(547\) | 17756.3i | 1.38795i | 0.720001 | + | 0.693973i | \(0.244141\pi\) | ||||
−0.720001 | + | 0.693973i | \(0.755859\pi\) | |||||||
\(548\) | − 3015.22i | − 0.235044i | ||||||||
\(549\) | 6088.54 | 0.473319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20167.8 | −1.55930 | ||||||||
\(552\) | − 1863.13i | − 0.143660i | ||||||||
\(553\) | 3954.32i | 0.304078i | ||||||||
\(554\) | 2094.73 | 0.160644 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4056.39 | 0.309405 | ||||||||
\(557\) | 1212.77i | 0.0922559i | 0.998936 | + | 0.0461280i | \(0.0146882\pi\) | ||||
−0.998936 | + | 0.0461280i | \(0.985312\pi\) | |||||||
\(558\) | 33338.3i | 2.52926i | ||||||||
\(559\) | 917.280 | 0.0694040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8498.78 | −0.639605 | ||||||||
\(562\) | − 5517.80i | − 0.414153i | ||||||||
\(563\) | − 12558.2i | − 0.940078i | −0.882646 | − | 0.470039i | \(-0.844240\pi\) | ||||
0.882646 | − | 0.470039i | \(-0.155760\pi\) | |||||||
\(564\) | −23495.2 | −1.75412 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6711.17 | 0.498395 | ||||||||
\(567\) | − 72363.9i | − 5.35978i | ||||||||
\(568\) | − 4918.76i | − 0.363357i | ||||||||
\(569\) | −9776.72 | −0.720319 | −0.360159 | − | 0.932891i | \(-0.617278\pi\) | ||||
−0.360159 | + | 0.932891i | \(0.617278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18733.9 | −1.37301 | −0.686505 | − | 0.727125i | \(-0.740856\pi\) | ||||
−0.686505 | + | 0.727125i | \(0.740856\pi\) | |||||||
\(572\) | − 278.673i | − 0.0203705i | ||||||||
\(573\) | 1919.91i | 0.139975i | ||||||||
\(574\) | −8391.01 | −0.610164 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4833.92 | 0.349676 | ||||||||
\(577\) | 5113.58i | 0.368944i | 0.982838 | + | 0.184472i | \(0.0590576\pi\) | ||||
−0.982838 | + | 0.184472i | \(0.940942\pi\) | |||||||
\(578\) | 5165.24i | 0.371705i | ||||||||
\(579\) | 18787.8 | 1.34852 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 802.492 | 0.0573029 | ||||||||
\(582\) | − 5058.77i | − 0.360297i | ||||||||
\(583\) | − 4526.70i | − 0.321572i | ||||||||
\(584\) | −4092.69 | −0.289995 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 839.250 | 0.0591623 | ||||||||
\(587\) | − 5379.95i | − 0.378287i | −0.981949 | − | 0.189143i | \(-0.939429\pi\) | ||||
0.981949 | − | 0.189143i | \(-0.0605711\pi\) | |||||||
\(588\) | − 10704.2i | − 0.750735i | ||||||||
\(589\) | 17505.0 | 1.22458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24603.9 | 1.71247 | ||||||||
\(592\) | − 6766.46i | − 0.469763i | ||||||||
\(593\) | 15060.3i | 1.04292i | 0.853275 | + | 0.521461i | \(0.174613\pi\) | ||||
−0.853275 | + | 0.521461i | \(0.825387\pi\) | |||||||
\(594\) | 17087.7 | 1.18033 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11087.2 | −0.761995 | ||||||||
\(597\) | 43879.7i | 3.00817i | ||||||||
\(598\) | 184.321i | 0.0126045i | ||||||||
\(599\) | 3772.04 | 0.257298 | 0.128649 | − | 0.991690i | \(-0.458936\pi\) | ||||
0.128649 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14663.9 | −0.995261 | −0.497631 | − | 0.867389i | \(-0.665796\pi\) | ||||
−0.497631 | + | 0.867389i | \(0.665796\pi\) | |||||||
\(602\) | 11282.6i | 0.763861i | ||||||||
\(603\) | 61935.5i | 4.18277i | ||||||||
\(604\) | −12434.5 | −0.837668 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12565.9 | 0.842332 | ||||||||
\(607\) | − 24514.5i | − 1.63923i | −0.572915 | − | 0.819614i | \(-0.694188\pi\) | ||||
0.572915 | − | 0.819614i | \(-0.305812\pi\) | |||||||
\(608\) | − 2538.15i | − 0.169302i | ||||||||
\(609\) | −63447.1 | −4.22168 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2324.40 | 0.153904 | ||||||||
\(612\) | 14584.6i | 0.963310i | ||||||||
\(613\) | − 14451.2i | − 0.952167i | −0.879400 | − | 0.476084i | \(-0.842056\pi\) | ||||
0.879400 | − | 0.476084i | \(-0.157944\pi\) | |||||||
\(614\) | 8266.83 | 0.543358 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3427.70 | 0.224198 | ||||||||
\(617\) | 3292.19i | 0.214811i | 0.994215 | + | 0.107406i | \(0.0342544\pi\) | ||||
−0.994215 | + | 0.107406i | \(0.965746\pi\) | |||||||
\(618\) | − 29835.2i | − 1.94199i | ||||||||
\(619\) | 12595.5 | 0.817858 | 0.408929 | − | 0.912566i | \(-0.365902\pi\) | ||||
0.408929 | + | 0.912566i | \(0.365902\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11302.2 | −0.730343 | ||||||||
\(622\) | − 13982.1i | − 0.901333i | ||||||||
\(623\) | − 617.002i | − 0.0396785i | ||||||||
\(624\) | −649.178 | −0.0416473 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18761.1 | 1.19783 | ||||||||
\(627\) | − 13964.0i | − 0.889425i | ||||||||
\(628\) | − 14851.5i | − 0.943693i | ||||||||
\(629\) | 20415.3 | 1.29413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19889.3 | 1.25480 | 0.627401 | − | 0.778697i | \(-0.284119\pi\) | ||||
0.627401 | + | 0.778697i | \(0.284119\pi\) | |||||||
\(632\) | 1283.71i | 0.0807963i | ||||||||
\(633\) | 8270.56i | 0.519313i | ||||||||
\(634\) | 15990.7 | 1.00169 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10545.1 | −0.657452 | ||||||||
\(637\) | 1058.97i | 0.0658682i | ||||||||
\(638\) | − 8841.75i | − 0.548665i | ||||||||
\(639\) | −46439.3 | −2.87498 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19276.0 | −1.18776 | −0.593880 | − | 0.804553i | \(-0.702405\pi\) | ||||
−0.593880 | + | 0.804553i | \(0.702405\pi\) | |||||||
\(642\) | − 19039.2i | − 1.17043i | ||||||||
\(643\) | 10219.2i | 0.626758i | 0.949628 | + | 0.313379i | \(0.101461\pi\) | ||||
−0.949628 | + | 0.313379i | \(0.898539\pi\) | |||||||
\(644\) | −2267.16 | −0.138725 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7657.93 | 0.466404 | ||||||||
\(647\) | 20818.4i | 1.26500i | 0.774560 | + | 0.632500i | \(0.217971\pi\) | ||||
−0.774560 | + | 0.632500i | \(0.782029\pi\) | |||||||
\(648\) | − 23491.8i | − 1.42415i | ||||||||
\(649\) | 6139.77 | 0.371352 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 55070.0 | 3.31546 | ||||||||
\(652\) | 3663.17i | 0.220032i | ||||||||
\(653\) | 15135.3i | 0.907031i | 0.891248 | + | 0.453516i | \(0.149830\pi\) | ||||
−0.891248 | + | 0.453516i | \(0.850170\pi\) | |||||||
\(654\) | 12885.3 | 0.770418 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2724.01 | −0.162126 | ||||||||
\(657\) | 38640.2i | 2.29451i | ||||||||
\(658\) | 28590.3i | 1.69387i | ||||||||
\(659\) | 13207.9 | 0.780737 | 0.390369 | − | 0.920659i | \(-0.372348\pi\) | ||||
0.390369 | + | 0.920659i | \(0.372348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6671.34 | 0.392564 | 0.196282 | − | 0.980547i | \(-0.437113\pi\) | ||||
0.196282 | + | 0.980547i | \(0.437113\pi\) | |||||||
\(662\) | − 9597.72i | − 0.563484i | ||||||||
\(663\) | − 1958.65i | − 0.114733i | ||||||||
\(664\) | 260.517 | 0.0152259 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −63883.9 | −3.71689 | ||||||||
\(667\) | 5848.15i | 0.339492i | ||||||||
\(668\) | − 5729.26i | − 0.331844i | ||||||||
\(669\) | 45705.5 | 2.64137 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1401.56 | 0.0806355 | ||||||||
\(672\) | − 7984.92i | − 0.458371i | ||||||||
\(673\) | 9534.41i | 0.546099i | 0.962000 | + | 0.273049i | \(0.0880322\pi\) | ||||
−0.962000 | + | 0.273049i | \(0.911968\pi\) | |||||||
\(674\) | −13791.0 | −0.788146 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8723.78 | −0.496346 | ||||||||
\(677\) | 17748.4i | 1.00757i | 0.863828 | + | 0.503787i | \(0.168060\pi\) | ||||
−0.863828 | + | 0.503787i | \(0.831940\pi\) | |||||||
\(678\) | − 16858.3i | − 0.954927i | ||||||||
\(679\) | −6155.80 | −0.347920 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28279.6 | 1.59130 | ||||||||
\(682\) | 7674.35i | 0.430888i | ||||||||
\(683\) | − 9583.57i | − 0.536904i | −0.963293 | − | 0.268452i | \(-0.913488\pi\) | ||||
0.963293 | − | 0.268452i | \(-0.0865120\pi\) | |||||||
\(684\) | −23963.3 | −1.33956 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3879.73 | 0.215931 | ||||||||
\(687\) | 14221.5i | 0.789790i | ||||||||
\(688\) | 3662.72i | 0.202965i | ||||||||
\(689\) | 1043.24 | 0.0576837 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9410.74 | 0.518092 | 0.259046 | − | 0.965865i | \(-0.416592\pi\) | ||||
0.259046 | + | 0.965865i | \(0.416592\pi\) | |||||||
\(692\) | − 13918.2i | − 0.764580i | ||||||||
\(693\) | − 32361.8i | − 1.77391i | ||||||||
\(694\) | 17488.3 | 0.956554 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −20597.1 | −1.12174 | ||||||||
\(697\) | − 8218.69i | − 0.446636i | ||||||||
\(698\) | 12774.2i | 0.692707i | ||||||||
\(699\) | −10872.9 | −0.588343 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19517.9 | −1.05161 | −0.525806 | − | 0.850605i | \(-0.676236\pi\) | ||||
−0.525806 | + | 0.850605i | \(0.676236\pi\) | |||||||
\(702\) | 3938.08i | 0.211728i | ||||||||
\(703\) | 33543.6i | 1.79960i | ||||||||
\(704\) | 1112.75 | 0.0595715 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1178.77 | −0.0628378 | ||||||||
\(707\) | − 15290.9i | − 0.813397i | ||||||||
\(708\) | − 14302.8i | − 0.759225i | ||||||||
\(709\) | 28430.7 | 1.50598 | 0.752990 | − | 0.658033i | \(-0.228611\pi\) | ||||
0.752990 | + | 0.658033i | \(0.228611\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12119.8 | 0.639282 | ||||||||
\(712\) | − 200.300i | − 0.0105429i | ||||||||
\(713\) | − 5076.00i | − 0.266617i | ||||||||
\(714\) | 24091.5 | 1.26275 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14570.8 | 0.760527 | ||||||||
\(717\) | − 26055.3i | − 1.35712i | ||||||||
\(718\) | − 14428.3i | − 0.749942i | ||||||||
\(719\) | −18716.0 | −0.970779 | −0.485390 | − | 0.874298i | \(-0.661322\pi\) | ||||
−0.485390 | + | 0.874298i | \(0.661322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36305.2 | −1.87528 | ||||||||
\(722\) | − 1135.55i | − 0.0585329i | ||||||||
\(723\) | 7048.78i | 0.362582i | ||||||||
\(724\) | −9636.61 | −0.494671 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −20832.7 | −1.06498 | ||||||||
\(727\) | 18419.5i | 0.939670i | 0.882754 | + | 0.469835i | \(0.155687\pi\) | ||||
−0.882754 | + | 0.469835i | \(0.844313\pi\) | |||||||
\(728\) | 789.956i | 0.0402167i | ||||||||
\(729\) | −87446.1 | −4.44272 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11050.9 | −0.559141 | ||||||||
\(732\) | − 3264.97i | − 0.164859i | ||||||||
\(733\) | 21548.4i | 1.08582i | 0.839790 | + | 0.542912i | \(0.182678\pi\) | ||||
−0.839790 | + | 0.542912i | \(0.817322\pi\) | |||||||
\(734\) | −24712.9 | −1.24274 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 14257.3i | 0.712584i | ||||||||
\(738\) | 25718.1i | 1.28279i | ||||||||
\(739\) | −12066.4 | −0.600636 | −0.300318 | − | 0.953839i | \(-0.597093\pi\) | ||||
−0.300318 | + | 0.953839i | \(0.597093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3218.19 | 0.159545 | ||||||||
\(742\) | 12831.8i | 0.634868i | ||||||||
\(743\) | 21951.0i | 1.08385i | 0.840426 | + | 0.541926i | \(0.182305\pi\) | ||||
−0.840426 | + | 0.541926i | \(0.817695\pi\) | |||||||
\(744\) | 17877.6 | 0.880948 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14292.0 | 0.701428 | ||||||||
\(747\) | − 2459.61i | − 0.120472i | ||||||||
\(748\) | 3357.31i | 0.164111i | ||||||||
\(749\) | −23168.0 | −1.13023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3112.43 | −0.151230 | −0.0756152 | − | 0.997137i | \(-0.524092\pi\) | ||||
−0.0756152 | + | 0.997137i | \(0.524092\pi\) | |||||||
\(752\) | 9281.40i | 0.450077i | ||||||||
\(753\) | − 65491.2i | − 3.16950i | ||||||||
\(754\) | 2037.69 | 0.0984197 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −48438.6 | −2.33028 | ||||||||
\(757\) | − 7684.64i | − 0.368960i | −0.982836 | − | 0.184480i | \(-0.940940\pi\) | ||||
0.982836 | − | 0.184480i | \(-0.0590602\pi\) | |||||||
\(758\) | − 4341.38i | − 0.208029i | ||||||||
\(759\) | −4049.21 | −0.193646 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36484.6 | −1.73793 | −0.868965 | − | 0.494874i | \(-0.835214\pi\) | ||||
−0.868965 | + | 0.494874i | \(0.835214\pi\) | |||||||
\(762\) | 32698.0i | 1.55450i | ||||||||
\(763\) | − 15679.5i | − 0.743954i | ||||||||
\(764\) | 758.430 | 0.0359150 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15934.4 | −0.751611 | ||||||||
\(767\) | 1414.99i | 0.0666132i | ||||||||
\(768\) | − 2592.18i | − 0.121793i | ||||||||
\(769\) | −2004.39 | −0.0939925 | −0.0469962 | − | 0.998895i | \(-0.514965\pi\) | ||||
−0.0469962 | + | 0.998895i | \(0.514965\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53997.6 | 2.52228 | ||||||||
\(772\) | − 7421.81i | − 0.346006i | ||||||||
\(773\) | − 7716.17i | − 0.359031i | −0.983755 | − | 0.179516i | \(-0.942547\pi\) | ||||
0.983755 | − | 0.179516i | \(-0.0574531\pi\) | |||||||
\(774\) | 34580.7 | 1.60591 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1998.39 | −0.0924457 | ||||||||
\(777\) | 105527.i | 4.87226i | ||||||||
\(778\) | 1137.90i | 0.0524367i | ||||||||
\(779\) | 13503.8 | 0.621084 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10690.1 | −0.489786 | ||||||||
\(782\) | − 2220.61i | − 0.101546i | ||||||||
\(783\) | 124947.i | 5.70275i | ||||||||
\(784\) | −4228.51 | −0.192625 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −39987.6 | −1.81464 | ||||||||
\(787\) | − 57.0149i | − 0.00258241i | −0.999999 | − | 0.00129121i | \(-0.999589\pi\) | ||||
0.999999 | − | 0.00129121i | \(-0.000411004\pi\) | |||||||
\(788\) | − 9719.39i | − 0.439390i | ||||||||
\(789\) | 69592.5 | 3.14012 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20514.2 | −0.922124 | ||||||||
\(792\) | − 10505.8i | − 0.471346i | ||||||||
\(793\) | 323.006i | 0.0144644i | ||||||||
\(794\) | −17129.8 | −0.765633 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17334.0 | 0.771842 | ||||||||
\(797\) | − 15184.7i | − 0.674870i | −0.941349 | − | 0.337435i | \(-0.890441\pi\) | ||||
0.941349 | − | 0.337435i | \(-0.109559\pi\) | |||||||
\(798\) | 39583.9i | 1.75596i | ||||||||
\(799\) | −28003.2 | −1.23990 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1891.09 | −0.0834186 | ||||||||
\(802\) | − 24911.1i | − 1.09681i | ||||||||
\(803\) | 8894.80i | 0.390898i | ||||||||
\(804\) | 33212.8 | 1.45687 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1768.65 | −0.0772929 | ||||||||
\(807\) | − 19503.4i | − 0.850746i | ||||||||
\(808\) | − 4963.94i | − 0.216127i | ||||||||
\(809\) | 30286.4 | 1.31621 | 0.658105 | − | 0.752926i | \(-0.271358\pi\) | ||||
0.658105 | + | 0.752926i | \(0.271358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43936.2 | −1.90235 | −0.951176 | − | 0.308650i | \(-0.900123\pi\) | ||||
−0.951176 | + | 0.308650i | \(0.900123\pi\) | |||||||
\(812\) | 25063.7i | 1.08321i | ||||||||
\(813\) | 36989.8i | 1.59568i | ||||||||
\(814\) | −14705.8 | −0.633217 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7820.94 | 0.335524 | ||||||||
\(817\) | − 18157.3i | − 0.777532i | ||||||||
\(818\) | − 23677.9i | − 1.01207i | ||||||||
\(819\) | 7458.18 | 0.318205 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5245.69 | −0.222991 | −0.111496 | − | 0.993765i | \(-0.535564\pi\) | ||||
−0.111496 | + | 0.993765i | \(0.535564\pi\) | |||||||
\(822\) | 15265.6i | 0.647750i | ||||||||
\(823\) | − 10678.0i | − 0.452260i | −0.974097 | − | 0.226130i | \(-0.927393\pi\) | ||||
0.974097 | − | 0.226130i | \(-0.0726074\pi\) | |||||||
\(824\) | −11785.9 | −0.498279 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17404.4 | −0.733145 | ||||||||
\(827\) | 3393.69i | 0.142697i | 0.997451 | + | 0.0713484i | \(0.0227302\pi\) | ||||
−0.997451 | + | 0.0713484i | \(0.977270\pi\) | |||||||
\(828\) | 6948.77i | 0.291650i | ||||||||
\(829\) | −9601.74 | −0.402270 | −0.201135 | − | 0.979564i | \(-0.564463\pi\) | ||||
−0.201135 | + | 0.979564i | \(0.564463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10605.3 | −0.442713 | ||||||||
\(832\) | 256.447i | 0.0106859i | ||||||||
\(833\) | − 12757.9i | − 0.530656i | ||||||||
\(834\) | −20536.9 | −0.852680 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5516.26 | −0.228210 | ||||||||
\(837\) | − 108450.i | − 4.47860i | ||||||||
\(838\) | 3063.54i | 0.126287i | ||||||||
\(839\) | −11992.8 | −0.493489 | −0.246744 | − | 0.969081i | \(-0.579361\pi\) | ||||
−0.246744 | + | 0.969081i | \(0.579361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40263.0 | 1.65087 | ||||||||
\(842\) | − 19970.1i | − 0.817358i | ||||||||
\(843\) | 27935.8i | 1.14135i | ||||||||
\(844\) | 3267.15 | 0.133247 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 87628.1 | 3.56113 | ||||||||
\(847\) | 25350.4i | 1.02839i | ||||||||
\(848\) | 4165.66i | 0.168690i | ||||||||
\(849\) | −33977.7 | −1.37351 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9726.79 | 0.391810 | ||||||||
\(852\) | 24903.0i | 1.00136i | ||||||||
\(853\) | 15441.5i | 0.619821i | 0.950766 | + | 0.309911i | \(0.100299\pi\) | ||||
−0.950766 | + | 0.309911i | \(0.899701\pi\) | |||||||
\(854\) | −3973.00 | −0.159196 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7521.13 | −0.300312 | ||||||||
\(857\) | − 44572.4i | − 1.77662i | −0.459244 | − | 0.888310i | \(-0.651880\pi\) | ||||
0.459244 | − | 0.888310i | \(-0.348120\pi\) | |||||||
\(858\) | 1410.88i | 0.0561384i | ||||||||
\(859\) | −2519.56 | −0.100077 | −0.0500386 | − | 0.998747i | \(-0.515934\pi\) | ||||
−0.0500386 | + | 0.998747i | \(0.515934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42482.5 | 1.68153 | ||||||||
\(862\) | − 27573.4i | − 1.08950i | ||||||||
\(863\) | − 28980.1i | − 1.14310i | −0.820568 | − | 0.571548i | \(-0.806343\pi\) | ||||
0.820568 | − | 0.571548i | \(-0.193657\pi\) | |||||||
\(864\) | −15724.8 | −0.619178 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5243.83 | −0.205765 | ||||||||
\(867\) | − 26150.9i | − 1.02437i | ||||||||
\(868\) | − 21754.5i | − 0.850687i | ||||||||
\(869\) | 2789.94 | 0.108909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3285.77 | −0.127823 | ||||||||
\(872\) | − 5090.11i | − 0.197675i | ||||||||
\(873\) | 18867.3i | 0.731455i | ||||||||
\(874\) | 3648.59 | 0.141208 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20720.7 | 0.799187 | ||||||||
\(877\) | − 7955.28i | − 0.306307i | −0.988202 | − | 0.153153i | \(-0.951057\pi\) | ||||
0.988202 | − | 0.153153i | \(-0.0489428\pi\) | |||||||
\(878\) | − 24125.3i | − 0.927323i | ||||||||
\(879\) | −4249.00 | −0.163044 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29722.0 | 1.13662 | 0.568309 | − | 0.822815i | \(-0.307598\pi\) | ||||
0.568309 | + | 0.822815i | \(0.307598\pi\) | |||||||
\(882\) | 39922.4i | 1.52410i | ||||||||
\(883\) | 19379.7i | 0.738596i | 0.929311 | + | 0.369298i | \(0.120402\pi\) | ||||
−0.929311 | + | 0.369298i | \(0.879598\pi\) | |||||||
\(884\) | −773.734 | −0.0294383 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7318.53 | 0.277507 | ||||||||
\(887\) | 22901.7i | 0.866925i | 0.901172 | + | 0.433463i | \(0.142708\pi\) | ||||
−0.901172 | + | 0.433463i | \(0.857292\pi\) | |||||||
\(888\) | 34257.6i | 1.29461i | ||||||||
\(889\) | 39788.8 | 1.50110 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −51055.7 | −1.91967 | ||||||||
\(892\) | − 18055.2i | − 0.677728i | ||||||||
\(893\) | − 46010.9i | − 1.72419i | ||||||||
\(894\) | 56132.9 | 2.09996 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3154.31 | −0.117610 | ||||||||
\(897\) | − 933.193i | − 0.0347362i | ||||||||
\(898\) | 21059.3i | 0.782581i | ||||||||
\(899\) | −56115.8 | −2.08183 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12568.3 | −0.464719 | ||||||||
\(902\) | 5920.20i | 0.218538i | ||||||||
\(903\) | − 57122.2i | − 2.10510i | ||||||||
\(904\) | −6659.61 | −0.245017 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 62953.9 | 2.30850 | ||||||||
\(907\) | 42542.2i | 1.55743i | 0.627376 | + | 0.778716i | \(0.284129\pi\) | ||||
−0.627376 | + | 0.778716i | \(0.715871\pi\) | |||||||
\(908\) | − 11171.4i | − 0.408300i | ||||||||
\(909\) | −46865.9 | −1.71006 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 220.864 | 0.00803243 | 0.00401622 | − | 0.999992i | \(-0.498722\pi\) | ||||
0.00401622 | + | 0.999992i | \(0.498722\pi\) | |||||||
\(912\) | 12850.3i | 0.466574i | ||||||||
\(913\) | − 566.191i | − 0.0205237i | ||||||||
\(914\) | −12886.5 | −0.466352 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5617.99 | 0.202646 | ||||||||
\(917\) | 48659.1i | 1.75231i | ||||||||
\(918\) | − 47443.9i | − 1.70575i | ||||||||
\(919\) | −27835.4 | −0.999135 | −0.499567 | − | 0.866275i | \(-0.666508\pi\) | ||||
−0.499567 | + | 0.866275i | \(0.666508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41853.8 | −1.49743 | ||||||||
\(922\) | − 6527.72i | − 0.233166i | ||||||||
\(923\) | − 2463.68i | − 0.0878580i | ||||||||
\(924\) | −17353.9 | −0.617860 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19036.2 | 0.675562 | ||||||||
\(927\) | 111274.i | 3.94252i | ||||||||
\(928\) | 8136.56i | 0.287819i | ||||||||
\(929\) | 2172.71 | 0.0767323 | 0.0383661 | − | 0.999264i | \(-0.487785\pi\) | ||||
0.0383661 | + | 0.999264i | \(0.487785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20962.1 | 0.737921 | ||||||||
\(932\) | 4295.17i | 0.150958i | ||||||||
\(933\) | 70789.1i | 2.48396i | ||||||||
\(934\) | −38185.3 | −1.33775 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2421.18 | 0.0845501 | ||||||||
\(937\) | 54906.5i | 1.91432i | 0.289560 | + | 0.957160i | \(0.406491\pi\) | ||||
−0.289560 | + | 0.957160i | \(0.593509\pi\) | |||||||
\(938\) | − 40415.2i | − 1.40683i | ||||||||
\(939\) | −94984.6 | −3.30107 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5980.06 | 0.207167 | 0.103584 | − | 0.994621i | \(-0.466969\pi\) | ||||
0.103584 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(942\) | 75191.0i | 2.60070i | ||||||||
\(943\) | − 3915.77i | − 0.135223i | ||||||||
\(944\) | −5650.09 | −0.194804 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7960.33 | 0.273586 | ||||||||
\(947\) | − 20268.6i | − 0.695504i | −0.937587 | − | 0.347752i | \(-0.886945\pi\) | ||||
0.937587 | − | 0.347752i | \(-0.113055\pi\) | |||||||
\(948\) | − 6499.24i | − 0.222664i | ||||||||
\(949\) | −2049.92 | −0.0701193 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −80958.6 | −2.76053 | ||||||||
\(952\) | − 9516.97i | − 0.323999i | ||||||||
\(953\) | 21797.9i | 0.740925i | 0.928847 | + | 0.370463i | \(0.120801\pi\) | ||||
−0.928847 | + | 0.370463i | \(0.879199\pi\) | |||||||
\(954\) | 39329.1 | 1.33472 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10292.7 | −0.348212 | ||||||||
\(957\) | 44764.5i | 1.51205i | ||||||||
\(958\) | 12649.6i | 0.426608i | ||||||||
\(959\) | 18576.1 | 0.625499 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18915.6 | 0.634945 | ||||||||
\(962\) | − 3389.14i | − 0.113587i | ||||||||
\(963\) | 71008.9i | 2.37615i | ||||||||
\(964\) | 2784.51 | 0.0930321 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 11478.3 | 0.382308 | ||||||||
\(967\) | 48950.6i | 1.62786i | 0.580960 | + | 0.813932i | \(0.302677\pi\) | ||||
−0.580960 | + | 0.813932i | \(0.697323\pi\) | |||||||
\(968\) | 8229.62i | 0.273254i | ||||||||
\(969\) | −38771.0 | −1.28535 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26426.2 | −0.873386 | −0.436693 | − | 0.899611i | \(-0.643850\pi\) | ||||
−0.436693 | + | 0.899611i | \(0.643850\pi\) | |||||||
\(972\) | 65864.4i | 2.17346i | ||||||||
\(973\) | 24990.5i | 0.823389i | ||||||||
\(974\) | 15746.1 | 0.518007 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1289.77 | −0.0422998 | ||||||||
\(977\) | 5770.09i | 0.188947i | 0.995527 | + | 0.0944736i | \(0.0301168\pi\) | ||||
−0.995527 | + | 0.0944736i | \(0.969883\pi\) | |||||||
\(978\) | − 18546.1i | − 0.606379i | ||||||||
\(979\) | −435.320 | −0.0142113 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48057.1 | −1.56406 | ||||||||
\(982\) | − 7113.64i | − 0.231166i | ||||||||
\(983\) | 484.532i | 0.0157214i | 0.999969 | + | 0.00786071i | \(0.00250217\pi\) | ||||
−0.999969 | + | 0.00786071i | \(0.997498\pi\) | |||||||
\(984\) | 13791.3 | 0.446799 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24549.0 | −0.792901 | ||||||||
\(987\) | − 144749.i | − 4.66808i | ||||||||
\(988\) | − 1271.29i | − 0.0409365i | ||||||||
\(989\) | −5265.16 | −0.169285 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26511.5 | −0.849813 | −0.424907 | − | 0.905237i | \(-0.639693\pi\) | ||||
−0.424907 | + | 0.905237i | \(0.639693\pi\) | |||||||
\(992\) | − 7062.27i | − 0.226035i | ||||||||
\(993\) | 48591.9i | 1.55289i | ||||||||
\(994\) | 30303.4 | 0.966966 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1318.96 | −0.0419606 | ||||||||
\(997\) | − 4628.20i | − 0.147018i | −0.997295 | − | 0.0735088i | \(-0.976580\pi\) | ||||
0.997295 | − | 0.0735088i | \(-0.0234197\pi\) | |||||||
\(998\) | 3866.74i | 0.122645i | ||||||||
\(999\) | 207816. | 6.58158 |
(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 | 1150.4.b.o.599.5 | 8 | ||
5.2 | odd | 4 | 1150.4.a.n.1.1 | 4 | |||
5.3 | odd | 4 | 230.4.a.j.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1150.4.b.o.599.4 | 8 | ||
15.8 | even | 4 | 2070.4.a.bg.1.1 | 4 | |||
20.3 | even | 4 | 1840.4.a.k.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.j.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
1150.4.a.n.1.1 | 4 | 5.2 | odd | 4 | |||
1150.4.b.o.599.4 | 8 | 5.4 | even | 2 | inner | ||
1150.4.b.o.599.5 | 8 | 1.1 | even | 1 | trivial | ||
1840.4.a.k.1.1 | 4 | 20.3 | even | 4 | |||
2070.4.a.bg.1.1 | 4 | 15.8 | even | 4 |