Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,2,Mod(349,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1450.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.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: | \(11.5783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.24681024.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 12x^{4} + 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 290) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.3 | ||
Root | \(2.14510i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.349 |
Dual form | 1450.2.b.l.349.4 |
$q$-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 \(\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 3.14510i | 1.81583i | 0.419159 | + | 0.907913i | \(0.362325\pi\) | ||||
−0.419159 | + | 0.907913i | \(0.637675\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.14510 | 1.28398 | ||||||||
\(7\) | 3.89167i | 1.47091i | 0.677572 | + | 0.735457i | \(0.263032\pi\) | ||||
−0.677572 | + | 0.735457i | \(0.736968\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −6.89167 | −2.29722 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.29021 | −1.29355 | −0.646773 | − | 0.762683i | \(-0.723882\pi\) | ||||
−0.646773 | + | 0.762683i | \(0.723882\pi\) | |||||||
\(12\) | − 3.14510i | − 0.907913i | ||||||||
\(13\) | 4.34803i | 1.20593i | 0.797769 | + | 0.602964i | \(0.206014\pi\) | ||||
−0.797769 | + | 0.602964i | \(0.793986\pi\) | |||||||
\(14\) | 3.89167 | 1.04009 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 1.60147i | − 0.388412i | −0.980961 | − | 0.194206i | \(-0.937787\pi\) | ||||
0.980961 | − | 0.194206i | \(-0.0622131\pi\) | |||||||
\(18\) | 6.89167i | 1.62438i | ||||||||
\(19\) | 1.20293 | 0.275971 | 0.137986 | − | 0.990434i | \(-0.455937\pi\) | ||||
0.137986 | + | 0.990434i | \(0.455937\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.2397 | −2.67092 | ||||||||
\(22\) | 4.29021i | 0.914675i | ||||||||
\(23\) | − 8.34803i | − 1.74069i | −0.492447 | − | 0.870343i | \(-0.663897\pi\) | ||||
0.492447 | − | 0.870343i | \(-0.336103\pi\) | |||||||
\(24\) | −3.14510 | −0.641991 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.34803 | 0.852720 | ||||||||
\(27\) | − 12.2397i | − 2.35553i | ||||||||
\(28\) | − 3.89167i | − 0.735457i | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.39853 | −0.430790 | −0.215395 | − | 0.976527i | \(-0.569104\pi\) | ||||
−0.215395 | + | 0.976527i | \(0.569104\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 13.4931i | − 2.34885i | ||||||||
\(34\) | −1.60147 | −0.274649 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.89167 | 1.14861 | ||||||||
\(37\) | 9.78334i | 1.60837i | 0.594378 | + | 0.804186i | \(0.297398\pi\) | ||||
−0.594378 | + | 0.804186i | \(0.702602\pi\) | |||||||
\(38\) | − 1.20293i | − 0.195141i | ||||||||
\(39\) | −13.6750 | −2.18975 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.78334 | 0.903206 | 0.451603 | − | 0.892219i | \(-0.350852\pi\) | ||||
0.451603 | + | 0.892219i | \(0.350852\pi\) | |||||||
\(42\) | 12.2397i | 1.88863i | ||||||||
\(43\) | 3.60147i | 0.549218i | 0.961556 | + | 0.274609i | \(0.0885485\pi\) | ||||
−0.961556 | + | 0.274609i | \(0.911452\pi\) | |||||||
\(44\) | 4.29021 | 0.646773 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.34803 | −1.23085 | ||||||||
\(47\) | − 8.58041i | − 1.25158i | −0.779991 | − | 0.625791i | \(-0.784776\pi\) | ||||
0.779991 | − | 0.625791i | \(-0.215224\pi\) | |||||||
\(48\) | 3.14510i | 0.453956i | ||||||||
\(49\) | −8.14510 | −1.16359 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.03677 | 0.705289 | ||||||||
\(52\) | − 4.34803i | − 0.602964i | ||||||||
\(53\) | 4.80440i | 0.659935i | 0.943992 | + | 0.329967i | \(0.107038\pi\) | ||||
−0.943992 | + | 0.329967i | \(0.892962\pi\) | |||||||
\(54\) | −12.2397 | −1.66561 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.89167 | −0.520046 | ||||||||
\(57\) | 3.78334i | 0.501116i | ||||||||
\(58\) | − 1.00000i | − 0.131306i | ||||||||
\(59\) | 4.05783 | 0.528284 | 0.264142 | − | 0.964484i | \(-0.414911\pi\) | ||||
0.264142 | + | 0.964484i | \(0.414911\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4353 | 1.46414 | 0.732071 | − | 0.681229i | \(-0.238554\pi\) | ||||
0.732071 | + | 0.681229i | \(0.238554\pi\) | |||||||
\(62\) | 2.39853i | 0.304614i | ||||||||
\(63\) | − 26.8201i | − 3.37902i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.4931 | −1.66089 | ||||||||
\(67\) | − 9.08727i | − 1.11019i | −0.831788 | − | 0.555094i | \(-0.812682\pi\) | ||||
0.831788 | − | 0.555094i | \(-0.187318\pi\) | |||||||
\(68\) | 1.60147i | 0.194206i | ||||||||
\(69\) | 26.2554 | 3.16078 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | − 6.89167i | − 0.812191i | ||||||||
\(73\) | − 2.39853i | − 0.280727i | −0.990100 | − | 0.140364i | \(-0.955173\pi\) | ||||
0.990100 | − | 0.140364i | \(-0.0448272\pi\) | |||||||
\(74\) | 9.78334 | 1.13729 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.20293 | −0.137986 | ||||||||
\(77\) | − 16.6961i | − 1.90269i | ||||||||
\(78\) | 13.6750i | 1.54839i | ||||||||
\(79\) | −7.55096 | −0.849550 | −0.424775 | − | 0.905299i | \(-0.639647\pi\) | ||||
−0.424775 | + | 0.905299i | \(0.639647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.8201 | 1.98001 | ||||||||
\(82\) | − 5.78334i | − 0.638663i | ||||||||
\(83\) | 2.79707i | 0.307018i | 0.988147 | + | 0.153509i | \(0.0490574\pi\) | ||||
−0.988147 | + | 0.153509i | \(0.950943\pi\) | |||||||
\(84\) | 12.2397 | 1.33546 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.60147 | 0.388356 | ||||||||
\(87\) | 3.14510i | 0.337190i | ||||||||
\(88\) | − 4.29021i | − 0.457337i | ||||||||
\(89\) | 4.29021 | 0.454761 | 0.227380 | − | 0.973806i | \(-0.426984\pi\) | ||||
0.227380 | + | 0.973806i | \(0.426984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.9211 | −1.77382 | ||||||||
\(92\) | 8.34803i | 0.870343i | ||||||||
\(93\) | − 7.54364i | − 0.782239i | ||||||||
\(94\) | −8.58041 | −0.885002 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.14510 | 0.320996 | ||||||||
\(97\) | 0.348034i | 0.0353375i | 0.999844 | + | 0.0176687i | \(0.00562443\pi\) | ||||
−0.999844 | + | 0.0176687i | \(0.994376\pi\) | |||||||
\(98\) | 8.14510i | 0.822780i | ||||||||
\(99\) | 29.5667 | 2.97156 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.4216 | −1.83302 | −0.916508 | − | 0.400017i | \(-0.869004\pi\) | ||||
−0.916508 | + | 0.400017i | \(0.869004\pi\) | |||||||
\(102\) | − 5.03677i | − 0.498715i | ||||||||
\(103\) | 12.0735i | 1.18964i | 0.803858 | + | 0.594821i | \(0.202777\pi\) | ||||
−0.803858 | + | 0.594821i | \(0.797223\pi\) | |||||||
\(104\) | −4.34803 | −0.426360 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.80440 | 0.466644 | ||||||||
\(107\) | 5.78334i | 0.559097i | 0.960132 | + | 0.279548i | \(0.0901847\pi\) | ||||
−0.960132 | + | 0.279548i | \(0.909815\pi\) | |||||||
\(108\) | 12.2397i | 1.17777i | ||||||||
\(109\) | −10.7971 | −1.03417 | −0.517086 | − | 0.855934i | \(-0.672983\pi\) | ||||
−0.517086 | + | 0.855934i | \(0.672983\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.7696 | −2.92052 | ||||||||
\(112\) | 3.89167i | 0.367728i | ||||||||
\(113\) | 12.2324i | 1.15073i | 0.817898 | + | 0.575363i | \(0.195139\pi\) | ||||
−0.817898 | + | 0.575363i | \(0.804861\pi\) | |||||||
\(114\) | 3.78334 | 0.354342 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | − 29.9652i | − 2.77029i | ||||||||
\(118\) | − 4.05783i | − 0.373553i | ||||||||
\(119\) | 6.23238 | 0.571321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.40586 | 0.673260 | ||||||||
\(122\) | − 11.4353i | − 1.03530i | ||||||||
\(123\) | 18.1892i | 1.64007i | ||||||||
\(124\) | 2.39853 | 0.215395 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −26.8201 | −2.38933 | ||||||||
\(127\) | − 8.00000i | − 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −11.3270 | −0.997285 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.9863 | −1.83358 | −0.916790 | − | 0.399371i | \(-0.869229\pi\) | ||||
−0.916790 | + | 0.399371i | \(0.869229\pi\) | |||||||
\(132\) | 13.4931i | 1.17443i | ||||||||
\(133\) | 4.68141i | 0.405930i | ||||||||
\(134\) | −9.08727 | −0.785021 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.60147 | 0.137325 | ||||||||
\(137\) | − 3.65197i | − 0.312009i | −0.987756 | − | 0.156004i | \(-0.950139\pi\) | ||||
0.987756 | − | 0.156004i | \(-0.0498614\pi\) | |||||||
\(138\) | − 26.2554i | − 2.23501i | ||||||||
\(139\) | −13.6750 | −1.15990 | −0.579950 | − | 0.814652i | \(-0.696928\pi\) | ||||
−0.579950 | + | 0.814652i | \(0.696928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.9863 | 2.27265 | ||||||||
\(142\) | 12.0000i | 1.00702i | ||||||||
\(143\) | − 18.6540i | − 1.55992i | ||||||||
\(144\) | −6.89167 | −0.574306 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.39853 | −0.198504 | ||||||||
\(147\) | − 25.6172i | − 2.11287i | ||||||||
\(148\) | − 9.78334i | − 0.804186i | ||||||||
\(149\) | −7.27648 | −0.596112 | −0.298056 | − | 0.954548i | \(-0.596338\pi\) | ||||
−0.298056 | + | 0.954548i | \(0.596338\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.69607 | −0.707676 | −0.353838 | − | 0.935307i | \(-0.615124\pi\) | ||||
−0.353838 | + | 0.935307i | \(0.615124\pi\) | |||||||
\(152\) | 1.20293i | 0.0975706i | ||||||||
\(153\) | 11.0368i | 0.892270i | ||||||||
\(154\) | −16.6961 | −1.34541 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.6750 | 1.09488 | ||||||||
\(157\) | 10.0000i | 0.798087i | 0.916932 | + | 0.399043i | \(0.130658\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(158\) | 7.55096i | 0.600723i | ||||||||
\(159\) | −15.1103 | −1.19833 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.4878 | 2.56040 | ||||||||
\(162\) | − 17.8201i | − 1.40008i | ||||||||
\(163\) | − 0.580411i | − 0.0454613i | −0.999742 | − | 0.0227306i | \(-0.992764\pi\) | ||||
0.999742 | − | 0.0227306i | \(-0.00723601\pi\) | |||||||
\(164\) | −5.78334 | −0.451603 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.79707 | 0.217095 | ||||||||
\(167\) | − 20.2554i | − 1.56741i | −0.621132 | − | 0.783706i | \(-0.713327\pi\) | ||||
0.621132 | − | 0.783706i | \(-0.286673\pi\) | |||||||
\(168\) | − 12.2397i | − 0.944314i | ||||||||
\(169\) | −5.90540 | −0.454261 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.29021 | −0.633968 | ||||||||
\(172\) | − 3.60147i | − 0.274609i | ||||||||
\(173\) | − 1.94217i | − 0.147661i | −0.997271 | − | 0.0738303i | \(-0.976478\pi\) | ||||
0.997271 | − | 0.0738303i | \(-0.0235223\pi\) | |||||||
\(174\) | 3.14510 | 0.238430 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.29021 | −0.323386 | ||||||||
\(177\) | 12.7623i | 0.959272i | ||||||||
\(178\) | − 4.29021i | − 0.321564i | ||||||||
\(179\) | 10.9284 | 0.816830 | 0.408415 | − | 0.912796i | \(-0.366082\pi\) | ||||
0.408415 | + | 0.912796i | \(0.366082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.20293 | −0.0894132 | −0.0447066 | − | 0.999000i | \(-0.514235\pi\) | ||||
−0.0447066 | + | 0.999000i | \(0.514235\pi\) | |||||||
\(182\) | 16.9211i | 1.25428i | ||||||||
\(183\) | 35.9652i | 2.65863i | ||||||||
\(184\) | 8.34803 | 0.615425 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.54364 | −0.553126 | ||||||||
\(187\) | 6.87062i | 0.502429i | ||||||||
\(188\) | 8.58041i | 0.625791i | ||||||||
\(189\) | 47.6329 | 3.46478 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.7760 | −1.14151 | −0.570756 | − | 0.821120i | \(-0.693350\pi\) | ||||
−0.570756 | + | 0.821120i | \(0.693350\pi\) | |||||||
\(192\) | − 3.14510i | − 0.226978i | ||||||||
\(193\) | 9.94217i | 0.715653i | 0.933788 | + | 0.357827i | \(0.116482\pi\) | ||||
−0.933788 | + | 0.357827i | \(0.883518\pi\) | |||||||
\(194\) | 0.348034 | 0.0249874 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.14510 | 0.581793 | ||||||||
\(197\) | 25.1681i | 1.79316i | 0.442885 | + | 0.896578i | \(0.353955\pi\) | ||||
−0.442885 | + | 0.896578i | \(0.646045\pi\) | |||||||
\(198\) | − 29.5667i | − 2.10121i | ||||||||
\(199\) | 18.7696 | 1.33054 | 0.665271 | − | 0.746602i | \(-0.268316\pi\) | ||||
0.665271 | + | 0.746602i | \(0.268316\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.5804 | 2.01591 | ||||||||
\(202\) | 18.4216i | 1.29614i | ||||||||
\(203\) | 3.89167i | 0.273142i | ||||||||
\(204\) | −5.03677 | −0.352645 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.0735 | 0.841204 | ||||||||
\(207\) | 57.5319i | 3.99874i | ||||||||
\(208\) | 4.34803i | 0.301482i | ||||||||
\(209\) | −5.16082 | −0.356981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2902 | 0.846093 | 0.423046 | − | 0.906108i | \(-0.360961\pi\) | ||||
0.423046 | + | 0.906108i | \(0.360961\pi\) | |||||||
\(212\) | − 4.80440i | − 0.329967i | ||||||||
\(213\) | − 37.7412i | − 2.58599i | ||||||||
\(214\) | 5.78334 | 0.395341 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.2397 | 0.832806 | ||||||||
\(217\) | − 9.33431i | − 0.633654i | ||||||||
\(218\) | 10.7971i | 0.731270i | ||||||||
\(219\) | 7.54364 | 0.509752 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.96323 | 0.468397 | ||||||||
\(222\) | 30.7696i | 2.06512i | ||||||||
\(223\) | 20.2324i | 1.35486i | 0.735587 | + | 0.677430i | \(0.236906\pi\) | ||||
−0.735587 | + | 0.677430i | \(0.763094\pi\) | |||||||
\(224\) | 3.89167 | 0.260023 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.2324 | 0.813686 | ||||||||
\(227\) | − 8.98627i | − 0.596440i | −0.954497 | − | 0.298220i | \(-0.903607\pi\) | ||||
0.954497 | − | 0.298220i | \(-0.0963929\pi\) | |||||||
\(228\) | − 3.78334i | − 0.250558i | ||||||||
\(229\) | 21.2692 | 1.40551 | 0.702753 | − | 0.711434i | \(-0.251954\pi\) | ||||
0.702753 | + | 0.711434i | \(0.251954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 52.5108 | 3.45496 | ||||||||
\(232\) | 1.00000i | 0.0656532i | ||||||||
\(233\) | 11.1608i | 0.731170i | 0.930778 | + | 0.365585i | \(0.119131\pi\) | ||||
−0.930778 | + | 0.365585i | \(0.880869\pi\) | |||||||
\(234\) | −29.9652 | −1.95889 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.05783 | −0.264142 | ||||||||
\(237\) | − 23.7486i | − 1.54263i | ||||||||
\(238\) | − 6.23238i | − 0.403985i | ||||||||
\(239\) | 1.92645 | 0.124612 | 0.0623059 | − | 0.998057i | \(-0.480155\pi\) | ||||
0.0623059 | + | 0.998057i | \(0.480155\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7255 | −1.14180 | −0.570900 | − | 0.821019i | \(-0.693406\pi\) | ||||
−0.570900 | + | 0.821019i | \(0.693406\pi\) | |||||||
\(242\) | − 7.40586i | − 0.476067i | ||||||||
\(243\) | 19.3270i | 1.23983i | ||||||||
\(244\) | −11.4353 | −0.732071 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.1892 | 1.15970 | ||||||||
\(247\) | 5.23039i | 0.332801i | ||||||||
\(248\) | − 2.39853i | − 0.152307i | ||||||||
\(249\) | −8.79707 | −0.557492 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.3638 | −0.906632 | −0.453316 | − | 0.891350i | \(-0.649759\pi\) | ||||
−0.453316 | + | 0.891350i | \(0.649759\pi\) | |||||||
\(252\) | 26.8201i | 1.68951i | ||||||||
\(253\) | 35.8148i | 2.25166i | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.3638i | 0.895986i | 0.894037 | + | 0.447993i | \(0.147861\pi\) | ||||
−0.894037 | + | 0.447993i | \(0.852139\pi\) | |||||||
\(258\) | 11.3270i | 0.705187i | ||||||||
\(259\) | −38.0735 | −2.36578 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.89167 | −0.426584 | ||||||||
\(262\) | 20.9863i | 1.29654i | ||||||||
\(263\) | − 12.0000i | − 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(264\) | 13.4931 | 0.830445 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.68141 | 0.287036 | ||||||||
\(267\) | 13.4931i | 0.825767i | ||||||||
\(268\) | 9.08727i | 0.555094i | ||||||||
\(269\) | 12.1083 | 0.738258 | 0.369129 | − | 0.929378i | \(-0.379656\pi\) | ||||
0.369129 | + | 0.929378i | \(0.379656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.49314 | 0.212193 | 0.106096 | − | 0.994356i | \(-0.466165\pi\) | ||||
0.106096 | + | 0.994356i | \(0.466165\pi\) | |||||||
\(272\) | − 1.60147i | − 0.0971031i | ||||||||
\(273\) | − 53.2186i | − 3.22094i | ||||||||
\(274\) | −3.65197 | −0.220623 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −26.2554 | −1.58039 | ||||||||
\(277\) | − 22.1471i | − 1.33069i | −0.746536 | − | 0.665345i | \(-0.768284\pi\) | ||||
0.746536 | − | 0.665345i | \(-0.231716\pi\) | |||||||
\(278\) | 13.6750i | 0.820173i | ||||||||
\(279\) | 16.5299 | 0.989620 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.8779 | −0.887544 | −0.443772 | − | 0.896140i | \(-0.646360\pi\) | ||||
−0.443772 | + | 0.896140i | \(0.646360\pi\) | |||||||
\(282\) | − 26.9863i | − 1.60701i | ||||||||
\(283\) | 5.20293i | 0.309282i | 0.987971 | + | 0.154641i | \(0.0494221\pi\) | ||||
−0.987971 | + | 0.154641i | \(0.950578\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.6540 | −1.10303 | ||||||||
\(287\) | 22.5069i | 1.32854i | ||||||||
\(288\) | 6.89167i | 0.406096i | ||||||||
\(289\) | 14.4353 | 0.849136 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.09460 | −0.0641667 | ||||||||
\(292\) | 2.39853i | 0.140364i | ||||||||
\(293\) | 17.7833i | 1.03891i | 0.854497 | + | 0.519457i | \(0.173866\pi\) | ||||
−0.854497 | + | 0.519457i | \(0.826134\pi\) | |||||||
\(294\) | −25.6172 | −1.49402 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.78334 | −0.568645 | ||||||||
\(297\) | 52.5108i | 3.04699i | ||||||||
\(298\) | 7.27648i | 0.421515i | ||||||||
\(299\) | 36.2975 | 2.09914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0157 | −0.807853 | ||||||||
\(302\) | 8.69607i | 0.500402i | ||||||||
\(303\) | − 57.9378i | − 3.32844i | ||||||||
\(304\) | 1.20293 | 0.0689928 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.0368 | 0.630930 | ||||||||
\(307\) | − 2.40586i | − 0.137310i | −0.997640 | − | 0.0686549i | \(-0.978129\pi\) | ||||
0.997640 | − | 0.0686549i | \(-0.0218707\pi\) | |||||||
\(308\) | 16.6961i | 0.951347i | ||||||||
\(309\) | −37.9725 | −2.16018 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.2470 | 0.921285 | 0.460642 | − | 0.887586i | \(-0.347619\pi\) | ||||
0.460642 | + | 0.887586i | \(0.347619\pi\) | |||||||
\(312\) | − 13.6750i | − 0.774195i | ||||||||
\(313\) | − 12.1745i | − 0.688146i | −0.938943 | − | 0.344073i | \(-0.888193\pi\) | ||||
0.938943 | − | 0.344073i | \(-0.111807\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.55096 | 0.424775 | ||||||||
\(317\) | 13.6823i | 0.768477i | 0.923234 | + | 0.384238i | \(0.125536\pi\) | ||||
−0.923234 | + | 0.384238i | \(0.874464\pi\) | |||||||
\(318\) | 15.1103i | 0.847345i | ||||||||
\(319\) | −4.29021 | −0.240205 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.1892 | −1.01522 | ||||||||
\(322\) | − 32.4878i | − 1.81047i | ||||||||
\(323\) | − 1.92645i | − 0.107191i | ||||||||
\(324\) | −17.8201 | −0.990006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.580411 | −0.0321460 | ||||||||
\(327\) | − 33.9579i | − 1.87788i | ||||||||
\(328\) | 5.78334i | 0.319332i | ||||||||
\(329\) | 33.3921 | 1.84097 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.87062 | 0.487573 | 0.243787 | − | 0.969829i | \(-0.421610\pi\) | ||||
0.243787 | + | 0.969829i | \(0.421610\pi\) | |||||||
\(332\) | − 2.79707i | − 0.153509i | ||||||||
\(333\) | − 67.4236i | − 3.69479i | ||||||||
\(334\) | −20.2554 | −1.10833 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.2397 | −0.667731 | ||||||||
\(337\) | 14.1819i | 0.772536i | 0.922387 | + | 0.386268i | \(0.126236\pi\) | ||||
−0.922387 | + | 0.386268i | \(0.873764\pi\) | |||||||
\(338\) | 5.90540i | 0.321211i | ||||||||
\(339\) | −38.4721 | −2.08952 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2902 | 0.557246 | ||||||||
\(342\) | 8.29021i | 0.448283i | ||||||||
\(343\) | − 4.45636i | − 0.240621i | ||||||||
\(344\) | −3.60147 | −0.194178 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.94217 | −0.104412 | ||||||||
\(347\) | 27.1755i | 1.45886i | 0.684058 | + | 0.729428i | \(0.260214\pi\) | ||||
−0.684058 | + | 0.729428i | \(0.739786\pi\) | |||||||
\(348\) | − 3.14510i | − 0.168595i | ||||||||
\(349\) | −1.31859 | −0.0705824 | −0.0352912 | − | 0.999377i | \(-0.511236\pi\) | ||||
−0.0352912 | + | 0.999377i | \(0.511236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 53.2186 | 2.84060 | ||||||||
\(352\) | 4.29021i | 0.228669i | ||||||||
\(353\) | 13.8990i | 0.739769i | 0.929078 | + | 0.369885i | \(0.120603\pi\) | ||||
−0.929078 | + | 0.369885i | \(0.879397\pi\) | |||||||
\(354\) | 12.7623 | 0.678308 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.29021 | −0.227380 | ||||||||
\(357\) | 19.6015i | 1.03742i | ||||||||
\(358\) | − 10.9284i | − 0.577586i | ||||||||
\(359\) | −1.26076 | −0.0665403 | −0.0332702 | − | 0.999446i | \(-0.510592\pi\) | ||||
−0.0332702 | + | 0.999446i | \(0.510592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5530 | −0.923840 | ||||||||
\(362\) | 1.20293i | 0.0632247i | ||||||||
\(363\) | 23.2922i | 1.22252i | ||||||||
\(364\) | 16.9211 | 0.886908 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 35.9652 | 1.87993 | ||||||||
\(367\) | 17.2765i | 0.901825i | 0.892568 | + | 0.450912i | \(0.148901\pi\) | ||||
−0.892568 | + | 0.450912i | \(0.851099\pi\) | |||||||
\(368\) | − 8.34803i | − 0.435171i | ||||||||
\(369\) | −39.8569 | −2.07487 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.6971 | −0.970707 | ||||||||
\(372\) | 7.54364i | 0.391119i | ||||||||
\(373\) | 32.9515i | 1.70616i | 0.521777 | + | 0.853082i | \(0.325269\pi\) | ||||
−0.521777 | + | 0.853082i | \(0.674731\pi\) | |||||||
\(374\) | 6.87062 | 0.355271 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.58041 | 0.442501 | ||||||||
\(377\) | 4.34803i | 0.223935i | ||||||||
\(378\) | − 47.6329i | − 2.44997i | ||||||||
\(379\) | 4.87062 | 0.250187 | 0.125093 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125093 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.1608 | 1.28903 | ||||||||
\(382\) | 15.7760i | 0.807171i | ||||||||
\(383\) | − 2.06622i | − 0.105579i | −0.998606 | − | 0.0527894i | \(-0.983189\pi\) | ||||
0.998606 | − | 0.0527894i | \(-0.0168112\pi\) | |||||||
\(384\) | −3.14510 | −0.160498 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.94217 | 0.506043 | ||||||||
\(387\) | − 24.8201i | − 1.26168i | ||||||||
\(388\) | − 0.348034i | − 0.0176687i | ||||||||
\(389\) | −23.9725 | −1.21546 | −0.607728 | − | 0.794145i | \(-0.707919\pi\) | ||||
−0.607728 | + | 0.794145i | \(0.707919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.3691 | −0.676104 | ||||||||
\(392\) | − 8.14510i | − 0.411390i | ||||||||
\(393\) | − 66.0040i | − 3.32946i | ||||||||
\(394\) | 25.1681 | 1.26795 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −29.5667 | −1.48578 | ||||||||
\(397\) | − 24.1544i | − 1.21228i | −0.795360 | − | 0.606138i | \(-0.792718\pi\) | ||||
0.795360 | − | 0.606138i | \(-0.207282\pi\) | |||||||
\(398\) | − 18.7696i | − 0.940836i | ||||||||
\(399\) | −14.7235 | −0.737098 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.2470 | 0.811338 | 0.405669 | − | 0.914020i | \(-0.367039\pi\) | ||||
0.405669 | + | 0.914020i | \(0.367039\pi\) | |||||||
\(402\) | − 28.5804i | − 1.42546i | ||||||||
\(403\) | − 10.4289i | − 0.519501i | ||||||||
\(404\) | 18.4216 | 0.916508 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.89167 | 0.193140 | ||||||||
\(407\) | − 41.9725i | − 2.08050i | ||||||||
\(408\) | 5.03677i | 0.249357i | ||||||||
\(409\) | −9.08727 | −0.449337 | −0.224668 | − | 0.974435i | \(-0.572130\pi\) | ||||
−0.224668 | + | 0.974435i | \(0.572130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.4858 | 0.566553 | ||||||||
\(412\) | − 12.0735i | − 0.594821i | ||||||||
\(413\) | 15.7917i | 0.777060i | ||||||||
\(414\) | 57.5319 | 2.82754 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.34803 | 0.213180 | ||||||||
\(417\) | − 43.0093i | − 2.10618i | ||||||||
\(418\) | 5.16082i | 0.252424i | ||||||||
\(419\) | −32.4446 | −1.58502 | −0.792512 | − | 0.609856i | \(-0.791227\pi\) | ||||
−0.792512 | + | 0.609856i | \(0.791227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.5667 | 1.24604 | 0.623022 | − | 0.782204i | \(-0.285905\pi\) | ||||
0.623022 | + | 0.782204i | \(0.285905\pi\) | |||||||
\(422\) | − 12.2902i | − 0.598278i | ||||||||
\(423\) | 59.1334i | 2.87516i | ||||||||
\(424\) | −4.80440 | −0.233322 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −37.7412 | −1.82857 | ||||||||
\(427\) | 44.5025i | 2.15362i | ||||||||
\(428\) | − 5.78334i | − 0.279548i | ||||||||
\(429\) | 58.6686 | 2.83255 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.70979 | −0.0823579 | −0.0411790 | − | 0.999152i | \(-0.513111\pi\) | ||||
−0.0411790 | + | 0.999152i | \(0.513111\pi\) | |||||||
\(432\) | − 12.2397i | − 0.588883i | ||||||||
\(433\) | − 23.7412i | − 1.14093i | −0.821322 | − | 0.570465i | \(-0.806763\pi\) | ||||
0.821322 | − | 0.570465i | \(-0.193237\pi\) | |||||||
\(434\) | −9.33431 | −0.448061 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.7971 | 0.517086 | ||||||||
\(437\) | − 10.0421i | − 0.480379i | ||||||||
\(438\) | − 7.54364i | − 0.360449i | ||||||||
\(439\) | 8.47941 | 0.404700 | 0.202350 | − | 0.979313i | \(-0.435142\pi\) | ||||
0.202350 | + | 0.979313i | \(0.435142\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 56.1334 | 2.67302 | ||||||||
\(442\) | − 6.96323i | − 0.331207i | ||||||||
\(443\) | 18.4490i | 0.876540i | 0.898843 | + | 0.438270i | \(0.144409\pi\) | ||||
−0.898843 | + | 0.438270i | \(0.855591\pi\) | |||||||
\(444\) | 30.7696 | 1.46026 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.2324 | 0.958031 | ||||||||
\(447\) | − 22.8853i | − 1.08244i | ||||||||
\(448\) | − 3.89167i | − 0.183864i | ||||||||
\(449\) | 11.3775 | 0.536936 | 0.268468 | − | 0.963289i | \(-0.413483\pi\) | ||||
0.268468 | + | 0.963289i | \(0.413483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.8117 | −1.16834 | ||||||||
\(452\) | − 12.2324i | − 0.575363i | ||||||||
\(453\) | − 27.3500i | − 1.28502i | ||||||||
\(454\) | −8.98627 | −0.421747 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.78334 | −0.177171 | ||||||||
\(457\) | 4.40586i | 0.206098i | 0.994676 | + | 0.103049i | \(0.0328598\pi\) | ||||
−0.994676 | + | 0.103049i | \(0.967140\pi\) | |||||||
\(458\) | − 21.2692i | − 0.993842i | ||||||||
\(459\) | −19.6015 | −0.914918 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.3113 | 0.713116 | 0.356558 | − | 0.934273i | \(-0.383950\pi\) | ||||
0.356558 | + | 0.934273i | \(0.383950\pi\) | |||||||
\(462\) | − 52.5108i | − 2.44303i | ||||||||
\(463\) | − 17.0873i | − 0.794113i | −0.917794 | − | 0.397056i | \(-0.870032\pi\) | ||||
0.917794 | − | 0.397056i | \(-0.129968\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.1608 | 0.517015 | ||||||||
\(467\) | 22.3711i | 1.03521i | 0.855620 | + | 0.517605i | \(0.173176\pi\) | ||||
−0.855620 | + | 0.517605i | \(0.826824\pi\) | |||||||
\(468\) | 29.9652i | 1.38514i | ||||||||
\(469\) | 35.3647 | 1.63299 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.4510 | −1.44919 | ||||||||
\(472\) | 4.05783i | 0.186777i | ||||||||
\(473\) | − 15.4510i | − 0.710439i | ||||||||
\(474\) | −23.7486 | −1.09081 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.23238 | −0.285661 | ||||||||
\(477\) | − 33.1103i | − 1.51602i | ||||||||
\(478\) | − 1.92645i | − 0.0881139i | ||||||||
\(479\) | 8.00733 | 0.365864 | 0.182932 | − | 0.983126i | \(-0.441441\pi\) | ||||
0.182932 | + | 0.983126i | \(0.441441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.5383 | −1.93958 | ||||||||
\(482\) | 17.7255i | 0.807375i | ||||||||
\(483\) | 102.177i | 4.64924i | ||||||||
\(484\) | −7.40586 | −0.336630 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.3270 | 0.876690 | ||||||||
\(487\) | 17.0441i | 0.772342i | 0.922427 | + | 0.386171i | \(0.126203\pi\) | ||||
−0.922427 | + | 0.386171i | \(0.873797\pi\) | |||||||
\(488\) | 11.4353i | 0.517652i | ||||||||
\(489\) | 1.82545 | 0.0825498 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.0873 | 1.67373 | 0.836863 | − | 0.547413i | \(-0.184387\pi\) | ||||
0.836863 | + | 0.547413i | \(0.184387\pi\) | |||||||
\(492\) | − 18.1892i | − 0.820033i | ||||||||
\(493\) | − 1.60147i | − 0.0721264i | ||||||||
\(494\) | 5.23039 | 0.235326 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.39853 | −0.107697 | ||||||||
\(497\) | − 46.7001i | − 2.09478i | ||||||||
\(498\) | 8.79707i | 0.394206i | ||||||||
\(499\) | 23.5089 | 1.05240 | 0.526200 | − | 0.850361i | \(-0.323616\pi\) | ||||
0.526200 | + | 0.850361i | \(0.323616\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 63.7054 | 2.84615 | ||||||||
\(502\) | 14.3638i | 0.641086i | ||||||||
\(503\) | 17.1608i | 0.765163i | 0.923922 | + | 0.382582i | \(0.124965\pi\) | ||||
−0.923922 | + | 0.382582i | \(0.875035\pi\) | |||||||
\(504\) | 26.8201 | 1.19466 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 35.8148 | 1.59216 | ||||||||
\(507\) | − 18.5731i | − 0.824860i | ||||||||
\(508\) | 8.00000i | 0.354943i | ||||||||
\(509\) | 14.3638 | 0.636662 | 0.318331 | − | 0.947980i | \(-0.396878\pi\) | ||||
0.318331 | + | 0.947980i | \(0.396878\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.33431 | 0.412925 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 14.7235i | − 0.650059i | ||||||||
\(514\) | 14.3638 | 0.633558 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 11.3270 | 0.498642 | ||||||||
\(517\) | 36.8117i | 1.61898i | ||||||||
\(518\) | 38.0735i | 1.67286i | ||||||||
\(519\) | 6.10833 | 0.268126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.0388 | −1.40364 | −0.701822 | − | 0.712352i | \(-0.747630\pi\) | ||||
−0.701822 | + | 0.712352i | \(0.747630\pi\) | |||||||
\(522\) | 6.89167i | 0.301640i | ||||||||
\(523\) | − 26.9442i | − 1.17819i | −0.808065 | − | 0.589093i | \(-0.799485\pi\) | ||||
0.808065 | − | 0.589093i | \(-0.200515\pi\) | |||||||
\(524\) | 20.9863 | 0.916790 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | 3.84117i | 0.167324i | ||||||||
\(528\) | − 13.4931i | − 0.587213i | ||||||||
\(529\) | −46.6897 | −2.02999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.9652 | −1.21359 | ||||||||
\(532\) | − 4.68141i | − 0.202965i | ||||||||
\(533\) | 25.1462i | 1.08920i | ||||||||
\(534\) | 13.4931 | 0.583905 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.08727 | 0.392510 | ||||||||
\(537\) | 34.3711i | 1.48322i | ||||||||
\(538\) | − 12.1083i | − 0.522027i | ||||||||
\(539\) | 34.9442 | 1.50515 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5005 | −0.580430 | −0.290215 | − | 0.956961i | \(-0.593727\pi\) | ||||
−0.290215 | + | 0.956961i | \(0.593727\pi\) | |||||||
\(542\) | − 3.49314i | − 0.150043i | ||||||||
\(543\) | − 3.78334i | − 0.162359i | ||||||||
\(544\) | −1.60147 | −0.0686623 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −53.2186 | −2.27755 | ||||||||
\(547\) | − 35.1755i | − 1.50399i | −0.659166 | − | 0.751997i | \(-0.729091\pi\) | ||||
0.659166 | − | 0.751997i | \(-0.270909\pi\) | |||||||
\(548\) | 3.65197i | 0.156004i | ||||||||
\(549\) | −78.8084 | −3.36346 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.20293 | 0.0512466 | ||||||||
\(552\) | 26.2554i | 1.11751i | ||||||||
\(553\) | − 29.3859i | − 1.24961i | ||||||||
\(554\) | −22.1471 | −0.940940 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.6750 | 0.579950 | ||||||||
\(557\) | − 18.6382i | − 0.789728i | −0.918740 | − | 0.394864i | \(-0.870792\pi\) | ||||
0.918740 | − | 0.394864i | \(-0.129208\pi\) | |||||||
\(558\) | − 16.5299i | − 0.699767i | ||||||||
\(559\) | −15.6593 | −0.662318 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.6088 | −0.912324 | ||||||||
\(562\) | 14.8779i | 0.627588i | ||||||||
\(563\) | − 0.421581i | − 0.0177675i | −0.999961 | − | 0.00888376i | \(-0.997172\pi\) | ||||
0.999961 | − | 0.00888376i | \(-0.00282783\pi\) | |||||||
\(564\) | −26.9863 | −1.13633 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.20293 | 0.218696 | ||||||||
\(567\) | 69.3500i | 2.91243i | ||||||||
\(568\) | − 12.0000i | − 0.503509i | ||||||||
\(569\) | −7.49314 | −0.314129 | −0.157064 | − | 0.987588i | \(-0.550203\pi\) | ||||
−0.157064 | + | 0.987588i | \(0.550203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.46369 | 0.270497 | 0.135249 | − | 0.990812i | \(-0.456817\pi\) | ||||
0.135249 | + | 0.990812i | \(0.456817\pi\) | |||||||
\(572\) | 18.6540i | 0.779961i | ||||||||
\(573\) | − 49.6172i | − 2.07279i | ||||||||
\(574\) | 22.5069 | 0.939418 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.89167 | 0.287153 | ||||||||
\(577\) | 31.5594i | 1.31383i | 0.753963 | + | 0.656917i | \(0.228140\pi\) | ||||
−0.753963 | + | 0.656917i | \(0.771860\pi\) | |||||||
\(578\) | − 14.4353i | − 0.600430i | ||||||||
\(579\) | −31.2692 | −1.29950 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.8853 | −0.451597 | ||||||||
\(582\) | 1.09460i | 0.0453727i | ||||||||
\(583\) | − 20.6118i | − 0.853656i | ||||||||
\(584\) | 2.39853 | 0.0992521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.7833 | 0.734623 | ||||||||
\(587\) | 11.5941i | 0.478541i | 0.970953 | + | 0.239271i | \(0.0769083\pi\) | ||||
−0.970953 | + | 0.239271i | \(0.923092\pi\) | |||||||
\(588\) | 25.6172i | 1.05643i | ||||||||
\(589\) | −2.88527 | −0.118886 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −79.1564 | −3.25606 | ||||||||
\(592\) | 9.78334i | 0.402093i | ||||||||
\(593\) | − 18.4648i | − 0.758257i | −0.925344 | − | 0.379128i | \(-0.876224\pi\) | ||||
0.925344 | − | 0.379128i | \(-0.123776\pi\) | |||||||
\(594\) | 52.5108 | 2.15455 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.27648 | 0.298056 | ||||||||
\(597\) | 59.0324i | 2.41603i | ||||||||
\(598\) | − 36.2975i | − 1.48432i | ||||||||
\(599\) | 28.3711 | 1.15921 | 0.579605 | − | 0.814897i | \(-0.303207\pi\) | ||||
0.579605 | + | 0.814897i | \(0.303207\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.4648 | −1.40585 | −0.702923 | − | 0.711266i | \(-0.748122\pi\) | ||||
−0.702923 | + | 0.711266i | \(0.748122\pi\) | |||||||
\(602\) | 14.0157i | 0.571238i | ||||||||
\(603\) | 62.6265i | 2.55035i | ||||||||
\(604\) | 8.69607 | 0.353838 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −57.9378 | −2.35356 | ||||||||
\(607\) | − 36.7275i | − 1.49072i | −0.666660 | − | 0.745362i | \(-0.732277\pi\) | ||||
0.666660 | − | 0.745362i | \(-0.267723\pi\) | |||||||
\(608\) | − 1.20293i | − 0.0487853i | ||||||||
\(609\) | −12.2397 | −0.495978 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.3079 | 1.50932 | ||||||||
\(612\) | − 11.0368i | − 0.446135i | ||||||||
\(613\) | 8.95149i | 0.361547i | 0.983525 | + | 0.180774i | \(0.0578601\pi\) | ||||
−0.983525 | + | 0.180774i | \(0.942140\pi\) | |||||||
\(614\) | −2.40586 | −0.0970927 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.6961 | 0.672704 | ||||||||
\(617\) | − 22.3985i | − 0.901731i | −0.892592 | − | 0.450866i | \(-0.851115\pi\) | ||||
0.892592 | − | 0.450866i | \(-0.148885\pi\) | |||||||
\(618\) | 37.9725i | 1.52748i | ||||||||
\(619\) | −31.5392 | −1.26767 | −0.633834 | − | 0.773469i | \(-0.718520\pi\) | ||||
−0.633834 | + | 0.773469i | \(0.718520\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −102.177 | −4.10024 | ||||||||
\(622\) | − 16.2470i | − 0.651447i | ||||||||
\(623\) | 16.6961i | 0.668914i | ||||||||
\(624\) | −13.6750 | −0.547439 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.1745 | −0.486593 | ||||||||
\(627\) | − 16.2313i | − 0.648216i | ||||||||
\(628\) | − 10.0000i | − 0.399043i | ||||||||
\(629\) | 15.6677 | 0.624712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.0598 | −1.63457 | −0.817283 | − | 0.576237i | \(-0.804521\pi\) | ||||
−0.817283 | + | 0.576237i | \(0.804521\pi\) | |||||||
\(632\) | − 7.55096i | − 0.300361i | ||||||||
\(633\) | 38.6540i | 1.53636i | ||||||||
\(634\) | 13.6823 | 0.543395 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.1103 | 0.599163 | ||||||||
\(637\) | − 35.4152i | − 1.40320i | ||||||||
\(638\) | 4.29021i | 0.169851i | ||||||||
\(639\) | 82.7001 | 3.27156 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.5383 | 1.60117 | 0.800583 | − | 0.599221i | \(-0.204523\pi\) | ||||
0.800583 | + | 0.599221i | \(0.204523\pi\) | |||||||
\(642\) | 18.1892i | 0.717871i | ||||||||
\(643\) | − 35.2765i | − 1.39117i | −0.718445 | − | 0.695584i | \(-0.755146\pi\) | ||||
0.718445 | − | 0.695584i | \(-0.244854\pi\) | |||||||
\(644\) | −32.4878 | −1.28020 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.92645 | −0.0757953 | ||||||||
\(647\) | 3.69514i | 0.145271i | 0.997359 | + | 0.0726355i | \(0.0231410\pi\) | ||||
−0.997359 | + | 0.0726355i | \(0.976859\pi\) | |||||||
\(648\) | 17.8201i | 0.700040i | ||||||||
\(649\) | −17.4089 | −0.683360 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.3574 | 1.15061 | ||||||||
\(652\) | 0.580411i | 0.0227306i | ||||||||
\(653\) | − 8.52152i | − 0.333473i | −0.986002 | − | 0.166736i | \(-0.946677\pi\) | ||||
0.986002 | − | 0.166736i | \(-0.0533229\pi\) | |||||||
\(654\) | −33.9579 | −1.32786 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.78334 | 0.225802 | ||||||||
\(657\) | 16.5299i | 0.644893i | ||||||||
\(658\) | − 33.3921i | − 1.30176i | ||||||||
\(659\) | 5.10193 | 0.198743 | 0.0993715 | − | 0.995050i | \(-0.468317\pi\) | ||||
0.0993715 | + | 0.995050i | \(0.468317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6961 | −0.571611 | −0.285805 | − | 0.958288i | \(-0.592261\pi\) | ||||
−0.285805 | + | 0.958288i | \(0.592261\pi\) | |||||||
\(662\) | − 8.87062i | − 0.344766i | ||||||||
\(663\) | 21.9001i | 0.850528i | ||||||||
\(664\) | −2.79707 | −0.108547 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −67.4236 | −2.61261 | ||||||||
\(667\) | − 8.34803i | − 0.323237i | ||||||||
\(668\) | 20.2554i | 0.783706i | ||||||||
\(669\) | −63.6329 | −2.46019 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.0598 | −1.89393 | ||||||||
\(672\) | 12.2397i | 0.472157i | ||||||||
\(673\) | − 25.5813i | − 0.986088i | −0.870004 | − | 0.493044i | \(-0.835884\pi\) | ||||
0.870004 | − | 0.493044i | \(-0.164116\pi\) | |||||||
\(674\) | 14.1819 | 0.546265 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.90540 | 0.227131 | ||||||||
\(677\) | 21.2344i | 0.816103i | 0.912959 | + | 0.408052i | \(0.133792\pi\) | ||||
−0.912959 | + | 0.408052i | \(0.866208\pi\) | |||||||
\(678\) | 38.4721i | 1.47751i | ||||||||
\(679\) | −1.35443 | −0.0519784 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.2628 | 1.08303 | ||||||||
\(682\) | − 10.2902i | − 0.394032i | ||||||||
\(683\) | − 22.1324i | − 0.846874i | −0.905925 | − | 0.423437i | \(-0.860823\pi\) | ||||
0.905925 | − | 0.423437i | \(-0.139177\pi\) | |||||||
\(684\) | 8.29021 | 0.316984 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.45636 | −0.170145 | ||||||||
\(687\) | 66.8937i | 2.55215i | ||||||||
\(688\) | 3.60147i | 0.137305i | ||||||||
\(689\) | −20.8897 | −0.795833 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.08088 | 0.307411 | 0.153705 | − | 0.988117i | \(-0.450879\pi\) | ||||
0.153705 | + | 0.988117i | \(0.450879\pi\) | |||||||
\(692\) | 1.94217i | 0.0738303i | ||||||||
\(693\) | 115.064i | 4.37091i | ||||||||
\(694\) | 27.1755 | 1.03157 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.14510 | −0.119215 | ||||||||
\(697\) | − 9.26182i | − 0.350817i | ||||||||
\(698\) | 1.31859i | 0.0499093i | ||||||||
\(699\) | −35.1019 | −1.32768 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.2902 | 1.06851 | 0.534253 | − | 0.845325i | \(-0.320593\pi\) | ||||
0.534253 | + | 0.845325i | \(0.320593\pi\) | |||||||
\(702\) | − 53.2186i | − 2.00861i | ||||||||
\(703\) | 11.7687i | 0.443864i | ||||||||
\(704\) | 4.29021 | 0.161693 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.8990 | 0.523096 | ||||||||
\(707\) | − 71.6907i | − 2.69621i | ||||||||
\(708\) | − 12.7623i | − 0.479636i | ||||||||
\(709\) | −52.2060 | −1.96064 | −0.980318 | − | 0.197423i | \(-0.936743\pi\) | ||||
−0.980318 | + | 0.197423i | \(0.936743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 52.0388 | 1.95161 | ||||||||
\(712\) | 4.29021i | 0.160782i | ||||||||
\(713\) | 20.0230i | 0.749869i | ||||||||
\(714\) | 19.6015 | 0.733566 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.9284 | −0.408415 | ||||||||
\(717\) | 6.05889i | 0.226273i | ||||||||
\(718\) | 1.26076i | 0.0470511i | ||||||||
\(719\) | −27.0177 | −1.00759 | −0.503795 | − | 0.863823i | \(-0.668063\pi\) | ||||
−0.503795 | + | 0.863823i | \(0.668063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46.9863 | −1.74986 | ||||||||
\(722\) | 17.5530i | 0.653253i | ||||||||
\(723\) | − 55.7486i | − 2.07331i | ||||||||
\(724\) | 1.20293 | 0.0447066 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.2922 | 0.864455 | ||||||||
\(727\) | 33.7559i | 1.25194i | 0.779849 | + | 0.625968i | \(0.215296\pi\) | ||||
−0.779849 | + | 0.625968i | \(0.784704\pi\) | |||||||
\(728\) | − 16.9211i | − 0.627138i | ||||||||
\(729\) | −7.32499 | −0.271296 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.76762 | 0.213323 | ||||||||
\(732\) | − 35.9652i | − 1.32931i | ||||||||
\(733\) | 9.52059i | 0.351651i | 0.984421 | + | 0.175826i | \(0.0562595\pi\) | ||||
−0.984421 | + | 0.175826i | \(0.943741\pi\) | |||||||
\(734\) | 17.2765 | 0.637686 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.34803 | −0.307713 | ||||||||
\(737\) | 38.9863i | 1.43608i | ||||||||
\(738\) | 39.8569i | 1.46715i | ||||||||
\(739\) | −0.0735473 | −0.00270548 | −0.00135274 | − | 0.999999i | \(-0.500431\pi\) | ||||
−0.00135274 | + | 0.999999i | \(0.500431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.4501 | −0.604309 | ||||||||
\(742\) | 18.6971i | 0.686393i | ||||||||
\(743\) | 27.4196i | 1.00593i | 0.864308 | + | 0.502964i | \(0.167757\pi\) | ||||
−0.864308 | + | 0.502964i | \(0.832243\pi\) | |||||||
\(744\) | 7.54364 | 0.276563 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.9515 | 1.20644 | ||||||||
\(747\) | − 19.2765i | − 0.705289i | ||||||||
\(748\) | − 6.87062i | − 0.251215i | ||||||||
\(749\) | −22.5069 | −0.822383 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.0873 | −0.623523 | −0.311762 | − | 0.950160i | \(-0.600919\pi\) | ||||
−0.311762 | + | 0.950160i | \(0.600919\pi\) | |||||||
\(752\) | − 8.58041i | − 0.312895i | ||||||||
\(753\) | − 45.1755i | − 1.64629i | ||||||||
\(754\) | 4.34803 | 0.158346 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −47.6329 | −1.73239 | ||||||||
\(757\) | − 25.7833i | − 0.937111i | −0.883434 | − | 0.468556i | \(-0.844775\pi\) | ||||
0.883434 | − | 0.468556i | \(-0.155225\pi\) | |||||||
\(758\) | − 4.87062i | − 0.176909i | ||||||||
\(759\) | −112.641 | −4.08862 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.28381 | 0.336538 | 0.168269 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168269 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(762\) | − 25.1608i | − 0.911480i | ||||||||
\(763\) | − 42.0186i | − 1.52118i | ||||||||
\(764\) | 15.7760 | 0.570756 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.06622 | −0.0746555 | ||||||||
\(767\) | 17.6436i | 0.637073i | ||||||||
\(768\) | 3.14510i | 0.113489i | ||||||||
\(769\) | 33.1019 | 1.19369 | 0.596843 | − | 0.802358i | \(-0.296421\pi\) | ||||
0.596843 | + | 0.802358i | \(0.296421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.1755 | −1.62696 | ||||||||
\(772\) | − 9.94217i | − 0.357827i | ||||||||
\(773\) | 25.7687i | 0.926835i | 0.886140 | + | 0.463418i | \(0.153377\pi\) | ||||
−0.886140 | + | 0.463418i | \(0.846623\pi\) | |||||||
\(774\) | −24.8201 | −0.892141 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.348034 | −0.0124937 | ||||||||
\(777\) | − 119.745i | − 4.29584i | ||||||||
\(778\) | 23.9725i | 0.859457i | ||||||||
\(779\) | 6.95696 | 0.249259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.4825 | 1.84219 | ||||||||
\(782\) | 13.3691i | 0.478078i | ||||||||
\(783\) | − 12.2397i | − 0.437411i | ||||||||
\(784\) | −8.14510 | −0.290897 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −66.0040 | −2.35428 | ||||||||
\(787\) | 33.3500i | 1.18880i | 0.804170 | + | 0.594400i | \(0.202610\pi\) | ||||
−0.804170 | + | 0.594400i | \(0.797390\pi\) | |||||||
\(788\) | − 25.1681i | − 0.896578i | ||||||||
\(789\) | 37.7412 | 1.34362 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.6044 | −1.69262 | ||||||||
\(792\) | 29.5667i | 1.05061i | ||||||||
\(793\) | 49.7211i | 1.76565i | ||||||||
\(794\) | −24.1544 | −0.857208 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.7696 | −0.665271 | ||||||||
\(797\) | 7.05982i | 0.250072i | 0.992152 | + | 0.125036i | \(0.0399046\pi\) | ||||
−0.992152 | + | 0.125036i | \(0.960095\pi\) | |||||||
\(798\) | 14.7235i | 0.521207i | ||||||||
\(799\) | −13.7412 | −0.486130 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.5667 | −1.04469 | ||||||||
\(802\) | − 16.2470i | − 0.573703i | ||||||||
\(803\) | 10.2902i | 0.363133i | ||||||||
\(804\) | −28.5804 | −1.00795 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.4289 | −0.367343 | ||||||||
\(807\) | 38.0819i | 1.34055i | ||||||||
\(808\) | − 18.4216i | − 0.648069i | ||||||||
\(809\) | −18.6814 | −0.656803 | −0.328402 | − | 0.944538i | \(-0.606510\pi\) | ||||
−0.328402 | + | 0.944538i | \(0.606510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.2133 | 1.27162 | 0.635811 | − | 0.771845i | \(-0.280666\pi\) | ||||
0.635811 | + | 0.771845i | \(0.280666\pi\) | |||||||
\(812\) | − 3.89167i | − 0.136571i | ||||||||
\(813\) | 10.9863i | 0.385305i | ||||||||
\(814\) | −41.9725 | −1.47114 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.03677 | 0.176322 | ||||||||
\(817\) | 4.33231i | 0.151569i | ||||||||
\(818\) | 9.08727i | 0.317729i | ||||||||
\(819\) | 116.615 | 4.07485 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.8706 | −1.28679 | −0.643397 | − | 0.765533i | \(-0.722475\pi\) | ||||
−0.643397 | + | 0.765533i | \(0.722475\pi\) | |||||||
\(822\) | − 11.4858i | − 0.400614i | ||||||||
\(823\) | 39.0324i | 1.36058i | 0.732942 | + | 0.680291i | \(0.238147\pi\) | ||||
−0.732942 | + | 0.680291i | \(0.761853\pi\) | |||||||
\(824\) | −12.0735 | −0.420602 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.7917 | 0.549465 | ||||||||
\(827\) | − 17.2103i | − 0.598459i | −0.954181 | − | 0.299230i | \(-0.903270\pi\) | ||||
0.954181 | − | 0.299230i | \(-0.0967297\pi\) | |||||||
\(828\) | − 57.5319i | − 1.99937i | ||||||||
\(829\) | −32.7034 | −1.13584 | −0.567918 | − | 0.823085i | \(-0.692251\pi\) | ||||
−0.567918 | + | 0.823085i | \(0.692251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69.6549 | 2.41630 | ||||||||
\(832\) | − 4.34803i | − 0.150741i | ||||||||
\(833\) | 13.0441i | 0.451951i | ||||||||
\(834\) | −43.0093 | −1.48929 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.16082 | 0.178491 | ||||||||
\(837\) | 29.3574i | 1.01474i | ||||||||
\(838\) | 32.4446i | 1.12078i | ||||||||
\(839\) | 32.3049 | 1.11529 | 0.557644 | − | 0.830080i | \(-0.311706\pi\) | ||||
0.557644 | + | 0.830080i | \(0.311706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − 25.5667i | − 0.881086i | ||||||||
\(843\) | − 46.7927i | − 1.61162i | ||||||||
\(844\) | −12.2902 | −0.423046 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 59.1334 | 2.03305 | ||||||||
\(847\) | 28.8212i | 0.990307i | ||||||||
\(848\) | 4.80440i | 0.164984i | ||||||||
\(849\) | −16.3638 | −0.561603 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 81.6717 | 2.79967 | ||||||||
\(852\) | 37.7412i | 1.29299i | ||||||||
\(853\) | 46.7422i | 1.60042i | 0.599719 | + | 0.800211i | \(0.295279\pi\) | ||||
−0.599719 | + | 0.800211i | \(0.704721\pi\) | |||||||
\(854\) | 44.5025 | 1.52284 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.78334 | −0.197671 | ||||||||
\(857\) | − 30.4648i | − 1.04066i | −0.853966 | − | 0.520328i | \(-0.825810\pi\) | ||||
0.853966 | − | 0.520328i | \(-0.174190\pi\) | |||||||
\(858\) | − 58.6686i | − 2.00291i | ||||||||
\(859\) | 30.7971 | 1.05078 | 0.525391 | − | 0.850861i | \(-0.323919\pi\) | ||||
0.525391 | + | 0.850861i | \(0.323919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −70.7864 | −2.41239 | ||||||||
\(862\) | 1.70979i | 0.0582358i | ||||||||
\(863\) | 34.9010i | 1.18804i | 0.804449 | + | 0.594022i | \(0.202461\pi\) | ||||
−0.804449 | + | 0.594022i | \(0.797539\pi\) | |||||||
\(864\) | −12.2397 | −0.416403 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.7412 | −0.806760 | ||||||||
\(867\) | 45.4005i | 1.54188i | ||||||||
\(868\) | 9.33431i | 0.316827i | ||||||||
\(869\) | 32.3952 | 1.09893 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.5118 | 1.33881 | ||||||||
\(872\) | − 10.7971i | − 0.365635i | ||||||||
\(873\) | − 2.39853i | − 0.0811781i | ||||||||
\(874\) | −10.0421 | −0.339679 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.54364 | −0.254876 | ||||||||
\(877\) | − 36.9599i | − 1.24805i | −0.781406 | − | 0.624023i | \(-0.785497\pi\) | ||||
0.781406 | − | 0.624023i | \(-0.214503\pi\) | |||||||
\(878\) | − 8.47941i | − 0.286166i | ||||||||
\(879\) | −55.9304 | −1.88649 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0009 | 0.842303 | 0.421151 | − | 0.906990i | \(-0.361626\pi\) | ||||
0.421151 | + | 0.906990i | \(0.361626\pi\) | |||||||
\(882\) | − 56.1334i | − 1.89011i | ||||||||
\(883\) | 52.7696i | 1.77584i | 0.459999 | + | 0.887919i | \(0.347850\pi\) | ||||
−0.459999 | + | 0.887919i | \(0.652150\pi\) | |||||||
\(884\) | −6.96323 | −0.234199 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.4490 | 0.619807 | ||||||||
\(887\) | 23.5667i | 0.791292i | 0.918403 | + | 0.395646i | \(0.129479\pi\) | ||||
−0.918403 | + | 0.395646i | \(0.870521\pi\) | |||||||
\(888\) | − 30.7696i | − 1.03256i | ||||||||
\(889\) | 31.1334 | 1.04418 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −76.4520 | −2.56124 | ||||||||
\(892\) | − 20.2324i | − 0.677430i | ||||||||
\(893\) | − 10.3216i | − 0.345401i | ||||||||
\(894\) | −22.8853 | −0.765398 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.89167 | −0.130012 | ||||||||
\(897\) | 114.159i | 3.81167i | ||||||||
\(898\) | − 11.3775i | − 0.379671i | ||||||||
\(899\) | −2.39853 | −0.0799956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.69408 | 0.256327 | ||||||||
\(902\) | 24.8117i | 0.826140i | ||||||||
\(903\) | − 44.0809i | − 1.46692i | ||||||||
\(904\) | −12.2324 | −0.406843 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −27.3500 | −0.908644 | ||||||||
\(907\) | − 25.2103i | − 0.837093i | −0.908195 | − | 0.418546i | \(-0.862540\pi\) | ||||
0.908195 | − | 0.418546i | \(-0.137460\pi\) | |||||||
\(908\) | 8.98627i | 0.298220i | ||||||||
\(909\) | 126.955 | 4.21085 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.5961 | 1.07996 | 0.539979 | − | 0.841679i | \(-0.318432\pi\) | ||||
0.539979 | + | 0.841679i | \(0.318432\pi\) | |||||||
\(912\) | 3.78334i | 0.125279i | ||||||||
\(913\) | − 12.0000i | − 0.397142i | ||||||||
\(914\) | 4.40586 | 0.145733 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.2692 | −0.702753 | ||||||||
\(917\) | − 81.6717i | − 2.69704i | ||||||||
\(918\) | 19.6015i | 0.646945i | ||||||||
\(919\) | −44.0000 | −1.45143 | −0.725713 | − | 0.687998i | \(-0.758490\pi\) | ||||
−0.725713 | + | 0.687998i | \(0.758490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.56668 | 0.249331 | ||||||||
\(922\) | − 15.3113i | − 0.504249i | ||||||||
\(923\) | − 52.1764i | − 1.71741i | ||||||||
\(924\) | −52.5108 | −1.72748 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.0873 | −0.561523 | ||||||||
\(927\) | − 83.2069i | − 2.73287i | ||||||||
\(928\) | − 1.00000i | − 0.0328266i | ||||||||
\(929\) | −5.05249 | −0.165767 | −0.0828835 | − | 0.996559i | \(-0.526413\pi\) | ||||
−0.0828835 | + | 0.996559i | \(0.526413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.79800 | −0.321116 | ||||||||
\(932\) | − 11.1608i | − 0.365585i | ||||||||
\(933\) | 51.0986i | 1.67289i | ||||||||
\(934\) | 22.3711 | 0.732004 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 29.9652 | 0.979444 | ||||||||
\(937\) | 19.6088i | 0.640591i | 0.947318 | + | 0.320296i | \(0.103782\pi\) | ||||
−0.947318 | + | 0.320296i | \(0.896218\pi\) | |||||||
\(938\) | − 35.3647i | − 1.15470i | ||||||||
\(939\) | 38.2902 | 1.24955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.68141 | 0.217808 | 0.108904 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108904 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(942\) | 31.4510i | 1.02473i | ||||||||
\(943\) | − 48.2795i | − 1.57220i | ||||||||
\(944\) | 4.05783 | 0.132071 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.4510 | −0.502356 | ||||||||
\(947\) | − 33.4667i | − 1.08752i | −0.839240 | − | 0.543762i | \(-0.817000\pi\) | ||||
0.839240 | − | 0.543762i | \(-0.183000\pi\) | |||||||
\(948\) | 23.7486i | 0.771317i | ||||||||
\(949\) | 10.4289 | 0.338537 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −43.0324 | −1.39542 | ||||||||
\(952\) | 6.23238i | 0.201992i | ||||||||
\(953\) | − 43.7412i | − 1.41692i | −0.705752 | − | 0.708459i | \(-0.749391\pi\) | ||||
0.705752 | − | 0.708459i | \(-0.250609\pi\) | |||||||
\(954\) | −33.1103 | −1.07199 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.92645 | −0.0623059 | ||||||||
\(957\) | − 13.4931i | − 0.436171i | ||||||||
\(958\) | − 8.00733i | − 0.258705i | ||||||||
\(959\) | 14.2123 | 0.458938 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.2470 | −0.814420 | ||||||||
\(962\) | 42.5383i | 1.37149i | ||||||||
\(963\) | − 39.8569i | − 1.28437i | ||||||||
\(964\) | 17.7255 | 0.570900 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 102.177 | 3.28751 | ||||||||
\(967\) | 35.9304i | 1.15544i | 0.816233 | + | 0.577722i | \(0.196058\pi\) | ||||
−0.816233 | + | 0.577722i | \(0.803942\pi\) | |||||||
\(968\) | 7.40586i | 0.238033i | ||||||||
\(969\) | 6.05889 | 0.194640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.7971 | 0.859959 | 0.429979 | − | 0.902839i | \(-0.358521\pi\) | ||||
0.429979 | + | 0.902839i | \(0.358521\pi\) | |||||||
\(972\) | − 19.3270i | − 0.619913i | ||||||||
\(973\) | − 53.2186i | − 1.70611i | ||||||||
\(974\) | 17.0441 | 0.546128 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.4353 | 0.366035 | ||||||||
\(977\) | 21.4510i | 0.686279i | 0.939284 | + | 0.343140i | \(0.111490\pi\) | ||||
−0.939284 | + | 0.343140i | \(0.888510\pi\) | |||||||
\(978\) | − 1.82545i | − 0.0583715i | ||||||||
\(979\) | −18.4059 | −0.588254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 74.4098 | 2.37572 | ||||||||
\(982\) | − 37.0873i | − 1.18350i | ||||||||
\(983\) | 49.8715i | 1.59066i | 0.606180 | + | 0.795328i | \(0.292701\pi\) | ||||
−0.606180 | + | 0.795328i | \(0.707299\pi\) | |||||||
\(984\) | −18.1892 | −0.579851 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.60147 | −0.0510011 | ||||||||
\(987\) | 105.022i | 3.34288i | ||||||||
\(988\) | − 5.23039i | − 0.166401i | ||||||||
\(989\) | 30.0652 | 0.956016 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.2167 | −0.515139 | −0.257570 | − | 0.966260i | \(-0.582922\pi\) | ||||
−0.257570 | + | 0.966260i | \(0.582922\pi\) | |||||||
\(992\) | 2.39853i | 0.0761535i | ||||||||
\(993\) | 27.8990i | 0.885348i | ||||||||
\(994\) | −46.7001 | −1.48124 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.79707 | 0.278746 | ||||||||
\(997\) | − 6.31766i | − 0.200082i | −0.994983 | − | 0.100041i | \(-0.968103\pi\) | ||||
0.994983 | − | 0.100041i | \(-0.0318974\pi\) | |||||||
\(998\) | − 23.5089i | − 0.744160i | ||||||||
\(999\) | 119.745 | 3.78857 |
(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 | 1450.2.b.l.349.3 | 6 | ||
5.2 | odd | 4 | 290.2.a.e.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 1450.2.a.p.1.1 | 3 | |||
5.4 | even | 2 | inner | 1450.2.b.l.349.4 | 6 | ||
15.2 | even | 4 | 2610.2.a.x.1.1 | 3 | |||
20.7 | even | 4 | 2320.2.a.l.1.1 | 3 | |||
40.27 | even | 4 | 9280.2.a.by.1.3 | 3 | |||
40.37 | odd | 4 | 9280.2.a.bf.1.1 | 3 | |||
145.57 | odd | 4 | 8410.2.a.v.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
290.2.a.e.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
1450.2.a.p.1.1 | 3 | 5.3 | odd | 4 | |||
1450.2.b.l.349.3 | 6 | 1.1 | even | 1 | trivial | ||
1450.2.b.l.349.4 | 6 | 5.4 | even | 2 | inner | ||
2320.2.a.l.1.1 | 3 | 20.7 | even | 4 | |||
2610.2.a.x.1.1 | 3 | 15.2 | even | 4 | |||
8410.2.a.v.1.1 | 3 | 145.57 | odd | 4 | |||
9280.2.a.bf.1.1 | 3 | 40.37 | odd | 4 | |||
9280.2.a.by.1.3 | 3 | 40.27 | even | 4 |