Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(417,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.417");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.14584320320.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 4x^{6} + 11x^{5} - 11x^{4} + 32x^{3} + 44x^{2} - 18x + 46 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 417.8 | ||
Root | \(0.274776 + 0.839339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.417 |
Dual form | 418.2.b.c.417.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.37171i | 1.94666i | 0.229410 | + | 0.973330i | \(0.426320\pi\) | ||||
−0.229410 | + | 0.973330i | \(0.573680\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.549551 | 0.245767 | 0.122883 | − | 0.992421i | \(-0.460786\pi\) | ||||
0.122883 | + | 0.992421i | \(0.460786\pi\) | |||||||
\(6\) | − | 3.37171i | − | 1.37650i | ||||||
\(7\) | − | 2.61555i | − | 0.988587i | −0.869295 | − | 0.494293i | \(-0.835427\pi\) | ||
0.869295 | − | 0.494293i | \(-0.164573\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −8.36845 | −2.78948 | ||||||||
\(10\) | −0.549551 | −0.173783 | ||||||||
\(11\) | −2.53057 | + | 2.14388i | −0.762994 | + | 0.646405i | ||||
\(12\) | 3.37171i | 0.973330i | ||||||||
\(13\) | −3.98957 | −1.10651 | −0.553253 | − | 0.833013i | \(-0.686614\pi\) | ||||
−0.553253 | + | 0.833013i | \(0.686614\pi\) | |||||||
\(14\) | 2.61555i | 0.699036i | ||||||||
\(15\) | 1.85293i | 0.478424i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.05039i | 1.22490i | 0.790509 | + | 0.612450i | \(0.209816\pi\) | ||||
−0.790509 | + | 0.612450i | \(0.790184\pi\) | |||||||
\(18\) | 8.36845 | 1.97246 | ||||||||
\(19\) | −4.14844 | − | 1.33807i | −0.951718 | − | 0.306974i | ||||
\(20\) | 0.549551 | 0.122883 | ||||||||
\(21\) | 8.81890 | 1.92444 | ||||||||
\(22\) | 2.53057 | − | 2.14388i | 0.539518 | − | 0.457077i | ||||
\(23\) | 3.67046 | 0.765343 | 0.382672 | − | 0.923884i | \(-0.375004\pi\) | ||||
0.382672 | + | 0.923884i | \(0.375004\pi\) | |||||||
\(24\) | − | 3.37171i | − | 0.688248i | ||||||
\(25\) | −4.69799 | −0.939599 | ||||||||
\(26\) | 3.98957 | 0.782418 | ||||||||
\(27\) | − | 18.1009i | − | 3.48351i | ||||||
\(28\) | − | 2.61555i | − | 0.494293i | ||||||
\(29\) | −4.22001 | −0.783636 | −0.391818 | − | 0.920043i | \(-0.628154\pi\) | ||||
−0.391818 | + | 0.920043i | \(0.628154\pi\) | |||||||
\(30\) | − | 1.85293i | − | 0.338297i | ||||||
\(31\) | 4.52906i | 0.813444i | 0.913552 | + | 0.406722i | \(0.133328\pi\) | ||||
−0.913552 | + | 0.406722i | \(0.866672\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.22856 | − | 8.53234i | −1.25833 | − | 1.48529i | ||||
\(34\) | − | 5.05039i | − | 0.866135i | ||||||
\(35\) | − | 1.43738i | − | 0.242962i | ||||||
\(36\) | −8.36845 | −1.39474 | ||||||||
\(37\) | 8.93697i | 1.46923i | 0.678485 | + | 0.734614i | \(0.262637\pi\) | ||||
−0.678485 | + | 0.734614i | \(0.737363\pi\) | |||||||
\(38\) | 4.14844 | + | 1.33807i | 0.672966 | + | 0.217063i | ||||
\(39\) | − | 13.4517i | − | 2.15399i | ||||||
\(40\) | −0.549551 | −0.0868917 | ||||||||
\(41\) | 10.7591 | 1.68029 | 0.840147 | − | 0.542359i | \(-0.182469\pi\) | ||||
0.840147 | + | 0.542359i | \(0.182469\pi\) | |||||||
\(42\) | −8.81890 | −1.36079 | ||||||||
\(43\) | − | 2.26059i | − | 0.344736i | −0.985033 | − | 0.172368i | \(-0.944858\pi\) | ||
0.985033 | − | 0.172368i | \(-0.0551419\pi\) | |||||||
\(44\) | −2.53057 | + | 2.14388i | −0.381497 | + | 0.323203i | ||||
\(45\) | −4.59889 | −0.685562 | ||||||||
\(46\) | −3.67046 | −0.541179 | ||||||||
\(47\) | 7.34091 | 1.07078 | 0.535391 | − | 0.844604i | \(-0.320164\pi\) | ||||
0.535391 | + | 0.844604i | \(0.320164\pi\) | |||||||
\(48\) | 3.37171i | 0.486665i | ||||||||
\(49\) | 0.158876 | 0.0226965 | ||||||||
\(50\) | 4.69799 | 0.664397 | ||||||||
\(51\) | −17.0285 | −2.38446 | ||||||||
\(52\) | −3.98957 | −0.553253 | ||||||||
\(53\) | − | 2.63638i | − | 0.362134i | −0.983471 | − | 0.181067i | \(-0.942045\pi\) | ||
0.983471 | − | 0.181067i | \(-0.0579551\pi\) | |||||||
\(54\) | 18.1009i | 2.46322i | ||||||||
\(55\) | −1.39068 | + | 1.17817i | −0.187519 | + | 0.158865i | ||||
\(56\) | 2.61555i | 0.349518i | ||||||||
\(57\) | 4.51158 | − | 13.9874i | 0.597573 | − | 1.85267i | ||||
\(58\) | 4.22001 | 0.554114 | ||||||||
\(59\) | 5.14971i | 0.670434i | 0.942141 | + | 0.335217i | \(0.108810\pi\) | ||||
−0.942141 | + | 0.335217i | \(0.891190\pi\) | |||||||
\(60\) | 1.85293i | 0.239212i | ||||||||
\(61\) | 11.7124i | 1.49962i | 0.661653 | + | 0.749811i | \(0.269855\pi\) | ||||
−0.661653 | + | 0.749811i | \(0.730145\pi\) | |||||||
\(62\) | − | 4.52906i | − | 0.575192i | ||||||
\(63\) | 21.8881i | 2.75765i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.19247 | −0.271943 | ||||||||
\(66\) | 7.22856 | + | 8.53234i | 0.889774 | + | 1.05026i | ||||
\(67\) | − | 9.09686i | − | 1.11136i | −0.831397 | − | 0.555679i | \(-0.812458\pi\) | ||
0.831397 | − | 0.555679i | \(-0.187542\pi\) | |||||||
\(68\) | 5.05039i | 0.612450i | ||||||||
\(69\) | 12.3757i | 1.48986i | ||||||||
\(70\) | 1.43738i | 0.171800i | ||||||||
\(71\) | − | 2.28930i | − | 0.271690i | −0.990730 | − | 0.135845i | \(-0.956625\pi\) | ||
0.990730 | − | 0.135845i | \(-0.0433749\pi\) | |||||||
\(72\) | 8.36845 | 0.986231 | ||||||||
\(73\) | 4.68896i | 0.548801i | 0.961615 | + | 0.274401i | \(0.0884794\pi\) | ||||
−0.961615 | + | 0.274401i | \(0.911521\pi\) | |||||||
\(74\) | − | 8.93697i | − | 1.03890i | ||||||
\(75\) | − | 15.8403i | − | 1.82908i | ||||||
\(76\) | −4.14844 | − | 1.33807i | −0.475859 | − | 0.153487i | ||||
\(77\) | 5.60744 | + | 6.61883i | 0.639027 | + | 0.754286i | ||||
\(78\) | 13.4517i | 1.52310i | ||||||||
\(79\) | −10.5767 | −1.18997 | −0.594984 | − | 0.803738i | \(-0.702842\pi\) | ||||
−0.594984 | + | 0.803738i | \(0.702842\pi\) | |||||||
\(80\) | 0.549551 | 0.0614417 | ||||||||
\(81\) | 35.9256 | 3.99173 | ||||||||
\(82\) | −10.7591 | −1.18815 | ||||||||
\(83\) | 0.876294i | 0.0961858i | 0.998843 | + | 0.0480929i | \(0.0153144\pi\) | ||||
−0.998843 | + | 0.0480929i | \(0.984686\pi\) | |||||||
\(84\) | 8.81890 | 0.962221 | ||||||||
\(85\) | 2.77545i | 0.301040i | ||||||||
\(86\) | 2.26059i | 0.243765i | ||||||||
\(87\) | − | 14.2287i | − | 1.52547i | ||||||
\(88\) | 2.53057 | − | 2.14388i | 0.269759 | − | 0.228539i | ||||
\(89\) | 11.2646i | 1.19405i | 0.802224 | + | 0.597023i | \(0.203650\pi\) | ||||
−0.802224 | + | 0.597023i | \(0.796350\pi\) | |||||||
\(90\) | 4.59889 | 0.484766 | ||||||||
\(91\) | 10.4349i | 1.09388i | ||||||||
\(92\) | 3.67046 | 0.382672 | ||||||||
\(93\) | −15.2707 | −1.58350 | ||||||||
\(94\) | −7.34091 | −0.757157 | ||||||||
\(95\) | −2.27978 | − | 0.735337i | −0.233901 | − | 0.0754440i | ||||
\(96\) | − | 3.37171i | − | 0.344124i | ||||||
\(97\) | − | 2.77545i | − | 0.281804i | −0.990024 | − | 0.140902i | \(-0.955000\pi\) | ||
0.990024 | − | 0.140902i | \(-0.0450003\pi\) | |||||||
\(98\) | −0.158876 | −0.0160489 | ||||||||
\(99\) | 21.1769 | − | 17.9410i | 2.12836 | − | 1.80314i | ||||
\(100\) | −4.69799 | −0.469799 | ||||||||
\(101\) | 11.2646i | 1.12087i | 0.828198 | + | 0.560435i | \(0.189366\pi\) | ||||
−0.828198 | + | 0.560435i | \(0.810634\pi\) | |||||||
\(102\) | 17.0285 | 1.68607 | ||||||||
\(103\) | − | 5.86713i | − | 0.578106i | −0.957313 | − | 0.289053i | \(-0.906660\pi\) | ||
0.957313 | − | 0.289053i | \(-0.0933403\pi\) | |||||||
\(104\) | 3.98957 | 0.391209 | ||||||||
\(105\) | 4.84644 | 0.472964 | ||||||||
\(106\) | 2.63638i | 0.256068i | ||||||||
\(107\) | −8.14844 | −0.787740 | −0.393870 | − | 0.919166i | \(-0.628864\pi\) | ||||
−0.393870 | + | 0.919166i | \(0.628864\pi\) | |||||||
\(108\) | − | 18.1009i | − | 1.74176i | ||||||
\(109\) | 7.10441 | 0.680479 | 0.340240 | − | 0.940339i | \(-0.389492\pi\) | ||||
0.340240 | + | 0.940339i | \(0.389492\pi\) | |||||||
\(110\) | 1.39068 | − | 1.17817i | 0.132596 | − | 0.112334i | ||||
\(111\) | −30.1329 | −2.86009 | ||||||||
\(112\) | − | 2.61555i | − | 0.247147i | ||||||
\(113\) | − | 5.80008i | − | 0.545626i | −0.962067 | − | 0.272813i | \(-0.912046\pi\) | ||
0.962067 | − | 0.272813i | \(-0.0879540\pi\) | |||||||
\(114\) | −4.51158 | + | 13.9874i | −0.422548 | + | 1.31004i | ||||
\(115\) | 2.01710 | 0.188096 | ||||||||
\(116\) | −4.22001 | −0.391818 | ||||||||
\(117\) | 33.3865 | 3.08658 | ||||||||
\(118\) | − | 5.14971i | − | 0.474069i | ||||||
\(119\) | 13.2096 | 1.21092 | ||||||||
\(120\) | − | 1.85293i | − | 0.169148i | ||||||
\(121\) | 1.80753 | − | 10.8505i | 0.164321 | − | 0.986407i | ||||
\(122\) | − | 11.7124i | − | 1.06039i | ||||||
\(123\) | 36.2767i | 3.27096i | ||||||||
\(124\) | 4.52906i | 0.406722i | ||||||||
\(125\) | −5.32954 | −0.476689 | ||||||||
\(126\) | − | 21.8881i | − | 1.94995i | ||||||
\(127\) | 12.3785 | 1.09841 | 0.549205 | − | 0.835687i | \(-0.314930\pi\) | ||||
0.549205 | + | 0.835687i | \(0.314930\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.62205 | 0.671084 | ||||||||
\(130\) | 2.19247 | 0.192292 | ||||||||
\(131\) | 6.73554i | 0.588487i | 0.955731 | + | 0.294243i | \(0.0950676\pi\) | ||||
−0.955731 | + | 0.294243i | \(0.904932\pi\) | |||||||
\(132\) | −7.22856 | − | 8.53234i | −0.629165 | − | 0.742645i | ||||
\(133\) | −3.49979 | + | 10.8505i | −0.303470 | + | 0.940856i | ||||
\(134\) | 9.09686i | 0.785849i | ||||||||
\(135\) | − | 9.94736i | − | 0.856132i | ||||||
\(136\) | − | 5.05039i | − | 0.433068i | ||||||
\(137\) | −2.29021 | −0.195666 | −0.0978331 | − | 0.995203i | \(-0.531191\pi\) | ||||
−0.0978331 | + | 0.995203i | \(0.531191\pi\) | |||||||
\(138\) | − | 12.3757i | − | 1.05349i | ||||||
\(139\) | − | 3.06983i | − | 0.260380i | −0.991489 | − | 0.130190i | \(-0.958441\pi\) | ||
0.991489 | − | 0.130190i | \(-0.0415587\pi\) | |||||||
\(140\) | − | 1.43738i | − | 0.121481i | ||||||
\(141\) | 24.7515i | 2.08445i | ||||||||
\(142\) | 2.28930i | 0.192114i | ||||||||
\(143\) | 10.0959 | − | 8.55317i | 0.844258 | − | 0.715252i | ||||
\(144\) | −8.36845 | −0.697371 | ||||||||
\(145\) | −2.31911 | −0.192592 | ||||||||
\(146\) | − | 4.68896i | − | 0.388061i | ||||||
\(147\) | 0.535683i | 0.0441824i | ||||||||
\(148\) | 8.93697i | 0.734614i | ||||||||
\(149\) | 21.4518i | 1.75740i | 0.477377 | + | 0.878699i | \(0.341588\pi\) | ||||
−0.477377 | + | 0.878699i | \(0.658412\pi\) | |||||||
\(150\) | 15.8403i | 1.29335i | ||||||||
\(151\) | 7.23575 | 0.588837 | 0.294419 | − | 0.955677i | \(-0.404874\pi\) | ||||
0.294419 | + | 0.955677i | \(0.404874\pi\) | |||||||
\(152\) | 4.14844 | + | 1.33807i | 0.336483 | + | 0.108532i | ||||
\(153\) | − | 42.2640i | − | 3.41684i | ||||||
\(154\) | −5.60744 | − | 6.61883i | −0.451861 | − | 0.533361i | ||||
\(155\) | 2.48895i | 0.199917i | ||||||||
\(156\) | − | 13.4517i | − | 1.07700i | ||||||
\(157\) | −16.7849 | −1.33958 | −0.669790 | − | 0.742551i | \(-0.733616\pi\) | ||||
−0.669790 | + | 0.742551i | \(0.733616\pi\) | |||||||
\(158\) | 10.5767 | 0.841434 | ||||||||
\(159\) | 8.88911 | 0.704952 | ||||||||
\(160\) | −0.549551 | −0.0434458 | ||||||||
\(161\) | − | 9.60028i | − | 0.756608i | ||||||
\(162\) | −35.9256 | −2.82258 | ||||||||
\(163\) | −17.6549 | −1.38284 | −0.691419 | − | 0.722454i | \(-0.743014\pi\) | ||||
−0.691419 | + | 0.722454i | \(0.743014\pi\) | |||||||
\(164\) | 10.7591 | 0.840147 | ||||||||
\(165\) | −3.97246 | − | 4.68896i | −0.309256 | − | 0.365035i | ||||
\(166\) | − | 0.876294i | − | 0.0680136i | ||||||
\(167\) | 8.10516 | 0.627196 | 0.313598 | − | 0.949556i | \(-0.398466\pi\) | ||||
0.313598 | + | 0.949556i | \(0.398466\pi\) | |||||||
\(168\) | −8.81890 | −0.680393 | ||||||||
\(169\) | 2.91664 | 0.224357 | ||||||||
\(170\) | − | 2.77545i | − | 0.212867i | ||||||
\(171\) | 34.7160 | + | 11.1976i | 2.65480 | + | 0.856298i | ||||
\(172\) | − | 2.26059i | − | 0.172368i | ||||||
\(173\) | −7.70936 | −0.586132 | −0.293066 | − | 0.956092i | \(-0.594676\pi\) | ||||
−0.293066 | + | 0.956092i | \(0.594676\pi\) | |||||||
\(174\) | 14.2287i | 1.07867i | ||||||||
\(175\) | 12.2879i | 0.928875i | ||||||||
\(176\) | −2.53057 | + | 2.14388i | −0.190749 | + | 0.161601i | ||||
\(177\) | −17.3633 | −1.30511 | ||||||||
\(178\) | − | 11.2646i | − | 0.844318i | ||||||
\(179\) | 7.66595i | 0.572980i | 0.958083 | + | 0.286490i | \(0.0924885\pi\) | ||||
−0.958083 | + | 0.286490i | \(0.907512\pi\) | |||||||
\(180\) | −4.59889 | −0.342781 | ||||||||
\(181\) | − | 0.440951i | − | 0.0327757i | −0.999866 | − | 0.0163878i | \(-0.994783\pi\) | ||
0.999866 | − | 0.0163878i | \(-0.00521664\pi\) | |||||||
\(182\) | − | 10.4349i | − | 0.773488i | ||||||
\(183\) | −39.4909 | −2.91925 | ||||||||
\(184\) | −3.67046 | −0.270590 | ||||||||
\(185\) | 4.91132i | 0.361087i | ||||||||
\(186\) | 15.2707 | 1.11970 | ||||||||
\(187\) | −10.8275 | − | 12.7804i | −0.791782 | − | 0.934592i | ||||
\(188\) | 7.34091 | 0.535391 | ||||||||
\(189\) | −47.3438 | −3.44376 | ||||||||
\(190\) | 2.27978 | + | 0.735337i | 0.165393 | + | 0.0533469i | ||||
\(191\) | 0.305959 | 0.0221384 | 0.0110692 | − | 0.999939i | \(-0.496476\pi\) | ||||
0.0110692 | + | 0.999939i | \(0.496476\pi\) | |||||||
\(192\) | 3.37171i | 0.243332i | ||||||||
\(193\) | −17.8024 | −1.28145 | −0.640723 | − | 0.767772i | \(-0.721365\pi\) | ||||
−0.640723 | + | 0.767772i | \(0.721365\pi\) | |||||||
\(194\) | 2.77545i | 0.199266i | ||||||||
\(195\) | − | 7.39238i | − | 0.529380i | ||||||
\(196\) | 0.158876 | 0.0113483 | ||||||||
\(197\) | − | 13.4869i | − | 0.960898i | −0.877023 | − | 0.480449i | \(-0.840474\pi\) | ||
0.877023 | − | 0.480449i | \(-0.159526\pi\) | |||||||
\(198\) | −21.1769 | + | 17.9410i | −1.50498 | + | 1.27501i | ||||
\(199\) | −6.72511 | −0.476730 | −0.238365 | − | 0.971176i | \(-0.576612\pi\) | ||||
−0.238365 | + | 0.971176i | \(0.576612\pi\) | |||||||
\(200\) | 4.69799 | 0.332198 | ||||||||
\(201\) | 30.6720 | 2.16344 | ||||||||
\(202\) | − | 11.2646i | − | 0.792575i | ||||||
\(203\) | 11.0377i | 0.774692i | ||||||||
\(204\) | −17.0285 | −1.19223 | ||||||||
\(205\) | 5.91269 | 0.412960 | ||||||||
\(206\) | 5.86713i | 0.408782i | ||||||||
\(207\) | −30.7160 | −2.13491 | ||||||||
\(208\) | −3.98957 | −0.276627 | ||||||||
\(209\) | 13.3666 | − | 5.50771i | 0.924585 | − | 0.380976i | ||||
\(210\) | −4.84644 | −0.334436 | ||||||||
\(211\) | 14.0080 | 0.964352 | 0.482176 | − | 0.876074i | \(-0.339846\pi\) | ||||
0.482176 | + | 0.876074i | \(0.339846\pi\) | |||||||
\(212\) | − | 2.63638i | − | 0.181067i | ||||||
\(213\) | 7.71886 | 0.528888 | ||||||||
\(214\) | 8.14844 | 0.557016 | ||||||||
\(215\) | − | 1.24231i | − | 0.0847247i | ||||||
\(216\) | 18.1009i | 1.23161i | ||||||||
\(217\) | 11.8460 | 0.804160 | ||||||||
\(218\) | −7.10441 | −0.481172 | ||||||||
\(219\) | −15.8098 | −1.06833 | ||||||||
\(220\) | −1.39068 | + | 1.17817i | −0.0937593 | + | 0.0794324i | ||||
\(221\) | − | 20.1489i | − | 1.35536i | ||||||
\(222\) | 30.1329 | 2.02239 | ||||||||
\(223\) | − | 4.40001i | − | 0.294647i | −0.989088 | − | 0.147323i | \(-0.952934\pi\) | ||
0.989088 | − | 0.147323i | \(-0.0470658\pi\) | |||||||
\(224\) | 2.61555i | 0.174759i | ||||||||
\(225\) | 39.3149 | 2.62100 | ||||||||
\(226\) | 5.80008i | 0.385816i | ||||||||
\(227\) | 2.32306 | 0.154187 | 0.0770936 | − | 0.997024i | \(-0.475436\pi\) | ||||
0.0770936 | + | 0.997024i | \(0.475436\pi\) | |||||||
\(228\) | 4.51158 | − | 13.9874i | 0.298787 | − | 0.926335i | ||||
\(229\) | 11.6600 | 0.770516 | 0.385258 | − | 0.922809i | \(-0.374112\pi\) | ||||
0.385258 | + | 0.922809i | \(0.374112\pi\) | |||||||
\(230\) | −2.01710 | −0.133004 | ||||||||
\(231\) | −22.3168 | + | 18.9067i | −1.46834 | + | 1.24397i | ||||
\(232\) | 4.22001 | 0.277057 | ||||||||
\(233\) | 7.57452i | 0.496223i | 0.968731 | + | 0.248112i | \(0.0798100\pi\) | ||||
−0.968731 | + | 0.248112i | \(0.920190\pi\) | |||||||
\(234\) | −33.3865 | −2.18254 | ||||||||
\(235\) | 4.03421 | 0.263163 | ||||||||
\(236\) | 5.14971i | 0.335217i | ||||||||
\(237\) | − | 35.6615i | − | 2.31646i | ||||||
\(238\) | −13.2096 | −0.856250 | ||||||||
\(239\) | 6.81545i | 0.440855i | 0.975403 | + | 0.220427i | \(0.0707452\pi\) | ||||
−0.975403 | + | 0.220427i | \(0.929255\pi\) | |||||||
\(240\) | 1.85293i | 0.119606i | ||||||||
\(241\) | −14.8529 | −0.956760 | −0.478380 | − | 0.878153i | \(-0.658776\pi\) | ||||
−0.478380 | + | 0.878153i | \(0.658776\pi\) | |||||||
\(242\) | −1.80753 | + | 10.8505i | −0.116192 | + | 0.697495i | ||||
\(243\) | 66.8282i | 4.28703i | ||||||||
\(244\) | 11.7124i | 0.749811i | ||||||||
\(245\) | 0.0873103 | 0.00557805 | ||||||||
\(246\) | − | 36.2767i | − | 2.31292i | ||||||
\(247\) | 16.5505 | + | 5.33831i | 1.05308 | + | 0.339669i | ||||
\(248\) | − | 4.52906i | − | 0.287596i | ||||||
\(249\) | −2.95461 | −0.187241 | ||||||||
\(250\) | 5.32954 | 0.337070 | ||||||||
\(251\) | −15.7137 | −0.991842 | −0.495921 | − | 0.868368i | \(-0.665170\pi\) | ||||
−0.495921 | + | 0.868368i | \(0.665170\pi\) | |||||||
\(252\) | 21.8881i | 1.37882i | ||||||||
\(253\) | −9.28833 | + | 7.86903i | −0.583952 | + | 0.494722i | ||||
\(254\) | −12.3785 | −0.776694 | ||||||||
\(255\) | −9.35802 | −0.586022 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 15.1780i | − | 0.946778i | −0.880854 | − | 0.473389i | \(-0.843031\pi\) | ||
0.880854 | − | 0.473389i | \(-0.156969\pi\) | |||||||
\(258\) | −7.62205 | −0.474528 | ||||||||
\(259\) | 23.3751 | 1.45246 | ||||||||
\(260\) | −2.19247 | −0.135971 | ||||||||
\(261\) | 35.3149 | 2.18594 | ||||||||
\(262\) | − | 6.73554i | − | 0.416123i | ||||||
\(263\) | 17.3014i | 1.06685i | 0.845847 | + | 0.533425i | \(0.179095\pi\) | ||||
−0.845847 | + | 0.533425i | \(0.820905\pi\) | |||||||
\(264\) | 7.22856 | + | 8.53234i | 0.444887 | + | 0.525129i | ||||
\(265\) | − | 1.44882i | − | 0.0890005i | ||||||
\(266\) | 3.49979 | − | 10.8505i | 0.214586 | − | 0.665285i | ||||
\(267\) | −37.9810 | −2.32440 | ||||||||
\(268\) | − | 9.09686i | − | 0.555679i | ||||||
\(269\) | − | 2.68907i | − | 0.163955i | −0.996634 | − | 0.0819777i | \(-0.973876\pi\) | ||
0.996634 | − | 0.0819777i | \(-0.0261236\pi\) | |||||||
\(270\) | 9.94736i | 0.605377i | ||||||||
\(271\) | − | 14.9386i | − | 0.907455i | −0.891141 | − | 0.453727i | \(-0.850094\pi\) | ||
0.891141 | − | 0.453727i | \(-0.149906\pi\) | |||||||
\(272\) | 5.05039i | 0.306225i | ||||||||
\(273\) | −35.1836 | −2.12941 | ||||||||
\(274\) | 2.29021 | 0.138357 | ||||||||
\(275\) | 11.8886 | − | 10.0719i | 0.716909 | − | 0.607361i | ||||
\(276\) | 12.3757i | 0.744931i | ||||||||
\(277\) | − | 10.7978i | − | 0.648776i | −0.945924 | − | 0.324388i | \(-0.894842\pi\) | ||
0.945924 | − | 0.324388i | \(-0.105158\pi\) | |||||||
\(278\) | 3.06983i | 0.184116i | ||||||||
\(279\) | − | 37.9013i | − | 2.26909i | ||||||
\(280\) | 1.43738i | 0.0858999i | ||||||||
\(281\) | −6.80575 | −0.405997 | −0.202998 | − | 0.979179i | \(-0.565069\pi\) | ||||
−0.202998 | + | 0.979179i | \(0.565069\pi\) | |||||||
\(282\) | − | 24.7515i | − | 1.47393i | ||||||
\(283\) | − | 32.3915i | − | 1.92548i | −0.270434 | − | 0.962738i | \(-0.587167\pi\) | ||
0.270434 | − | 0.962738i | \(-0.412833\pi\) | |||||||
\(284\) | − | 2.28930i | − | 0.135845i | ||||||
\(285\) | 2.47934 | − | 7.68677i | 0.146864 | − | 0.455325i | ||||
\(286\) | −10.0959 | + | 8.55317i | −0.596981 | + | 0.505759i | ||||
\(287\) | − | 28.1411i | − | 1.66112i | ||||||
\(288\) | 8.36845 | 0.493116 | ||||||||
\(289\) | −8.50646 | −0.500380 | ||||||||
\(290\) | 2.31911 | 0.136183 | ||||||||
\(291\) | 9.35802 | 0.548577 | ||||||||
\(292\) | 4.68896i | 0.274401i | ||||||||
\(293\) | 27.9451 | 1.63257 | 0.816286 | − | 0.577649i | \(-0.196030\pi\) | ||||
0.816286 | + | 0.577649i | \(0.196030\pi\) | |||||||
\(294\) | − | 0.535683i | − | 0.0312417i | ||||||
\(295\) | 2.83003i | 0.164770i | ||||||||
\(296\) | − | 8.93697i | − | 0.519451i | ||||||
\(297\) | 38.8062 | + | 45.8055i | 2.25176 | + | 2.65790i | ||||
\(298\) | − | 21.4518i | − | 1.24267i | ||||||
\(299\) | −14.6435 | −0.846857 | ||||||||
\(300\) | − | 15.8403i | − | 0.914539i | ||||||
\(301\) | −5.91269 | −0.340802 | ||||||||
\(302\) | −7.23575 | −0.416371 | ||||||||
\(303\) | −37.9810 | −2.18195 | ||||||||
\(304\) | −4.14844 | − | 1.33807i | −0.237929 | − | 0.0767435i | ||||
\(305\) | 6.43657i | 0.368557i | ||||||||
\(306\) | 42.2640i | 2.41607i | ||||||||
\(307\) | 8.48362 | 0.484186 | 0.242093 | − | 0.970253i | \(-0.422166\pi\) | ||||
0.242093 | + | 0.970253i | \(0.422166\pi\) | |||||||
\(308\) | 5.60744 | + | 6.61883i | 0.319514 | + | 0.377143i | ||||
\(309\) | 19.7823 | 1.12538 | ||||||||
\(310\) | − | 2.48895i | − | 0.141363i | ||||||
\(311\) | 10.6492 | 0.603859 | 0.301929 | − | 0.953330i | \(-0.402369\pi\) | ||||
0.301929 | + | 0.953330i | \(0.402369\pi\) | |||||||
\(312\) | 13.4517i | 0.761551i | ||||||||
\(313\) | 24.2599 | 1.37125 | 0.685624 | − | 0.727956i | \(-0.259529\pi\) | ||||
0.685624 | + | 0.727956i | \(0.259529\pi\) | |||||||
\(314\) | 16.7849 | 0.947226 | ||||||||
\(315\) | 12.0286i | 0.677738i | ||||||||
\(316\) | −10.5767 | −0.594984 | ||||||||
\(317\) | 6.10196i | 0.342720i | 0.985208 | + | 0.171360i | \(0.0548162\pi\) | ||||
−0.985208 | + | 0.171360i | \(0.945184\pi\) | |||||||
\(318\) | −8.88911 | −0.498476 | ||||||||
\(319\) | 10.6790 | − | 9.04720i | 0.597910 | − | 0.506546i | ||||
\(320\) | 0.549551 | 0.0307208 | ||||||||
\(321\) | − | 27.4742i | − | 1.53346i | ||||||
\(322\) | 9.60028i | 0.535003i | ||||||||
\(323\) | 6.75777 | − | 20.9513i | 0.376012 | − | 1.16576i | ||||
\(324\) | 35.9256 | 1.99587 | ||||||||
\(325\) | 18.7430 | 1.03967 | ||||||||
\(326\) | 17.6549 | 0.977815 | ||||||||
\(327\) | 23.9540i | 1.32466i | ||||||||
\(328\) | −10.7591 | −0.594073 | ||||||||
\(329\) | − | 19.2006i | − | 1.05856i | ||||||
\(330\) | 3.97246 | + | 4.68896i | 0.218677 | + | 0.258119i | ||||
\(331\) | − | 13.5012i | − | 0.742094i | −0.928614 | − | 0.371047i | \(-0.878999\pi\) | ||
0.928614 | − | 0.371047i | \(-0.121001\pi\) | |||||||
\(332\) | 0.876294i | 0.0480929i | ||||||||
\(333\) | − | 74.7886i | − | 4.09839i | ||||||
\(334\) | −8.10516 | −0.443495 | ||||||||
\(335\) | − | 4.99919i | − | 0.273135i | ||||||
\(336\) | 8.81890 | 0.481110 | ||||||||
\(337\) | 11.2371 | 0.612124 | 0.306062 | − | 0.952012i | \(-0.400988\pi\) | ||||
0.306062 | + | 0.952012i | \(0.400988\pi\) | |||||||
\(338\) | −2.91664 | −0.158644 | ||||||||
\(339\) | 19.5562 | 1.06215 | ||||||||
\(340\) | 2.77545i | 0.150520i | ||||||||
\(341\) | −9.70979 | − | 11.4611i | −0.525814 | − | 0.620653i | ||||
\(342\) | −34.7160 | − | 11.1976i | −1.87723 | − | 0.605494i | ||||
\(343\) | − | 18.7244i | − | 1.01102i | ||||||
\(344\) | 2.26059i | 0.121883i | ||||||||
\(345\) | 6.80109i | 0.366159i | ||||||||
\(346\) | 7.70936 | 0.414458 | ||||||||
\(347\) | 5.20240i | 0.279279i | 0.990202 | + | 0.139640i | \(0.0445944\pi\) | ||||
−0.990202 | + | 0.139640i | \(0.955406\pi\) | |||||||
\(348\) | − | 14.2287i | − | 0.762736i | ||||||
\(349\) | 4.91132i | 0.262897i | 0.991323 | + | 0.131448i | \(0.0419628\pi\) | ||||
−0.991323 | + | 0.131448i | \(0.958037\pi\) | |||||||
\(350\) | − | 12.2879i | − | 0.656814i | ||||||
\(351\) | 72.2146i | 3.85453i | ||||||||
\(352\) | 2.53057 | − | 2.14388i | 0.134880 | − | 0.114269i | ||||
\(353\) | −8.82463 | −0.469688 | −0.234844 | − | 0.972033i | \(-0.575458\pi\) | ||||
−0.234844 | + | 0.972033i | \(0.575458\pi\) | |||||||
\(354\) | 17.3633 | 0.922851 | ||||||||
\(355\) | − | 1.25809i | − | 0.0667723i | ||||||
\(356\) | 11.2646i | 0.597023i | ||||||||
\(357\) | 44.5389i | 2.35725i | ||||||||
\(358\) | − | 7.66595i | − | 0.405158i | ||||||
\(359\) | 13.2564i | 0.699644i | 0.936816 | + | 0.349822i | \(0.113758\pi\) | ||||
−0.936816 | + | 0.349822i | \(0.886242\pi\) | |||||||
\(360\) | 4.59889 | 0.242383 | ||||||||
\(361\) | 15.4191 | + | 11.1018i | 0.811534 | + | 0.584305i | ||||
\(362\) | 0.440951i | 0.0231759i | ||||||||
\(363\) | 36.5847 | + | 6.09447i | 1.92020 | + | 0.319877i | ||||
\(364\) | 10.4349i | 0.546939i | ||||||||
\(365\) | 2.57682i | 0.134877i | ||||||||
\(366\) | 39.4909 | 2.06422 | ||||||||
\(367\) | 21.5733 | 1.12612 | 0.563059 | − | 0.826417i | \(-0.309624\pi\) | ||||
0.563059 | + | 0.826417i | \(0.309624\pi\) | |||||||
\(368\) | 3.67046 | 0.191336 | ||||||||
\(369\) | −90.0372 | −4.68715 | ||||||||
\(370\) | − | 4.91132i | − | 0.255327i | ||||||
\(371\) | −6.89559 | −0.358001 | ||||||||
\(372\) | −15.2707 | −0.791749 | ||||||||
\(373\) | 5.97820 | 0.309539 | 0.154770 | − | 0.987951i | \(-0.450536\pi\) | ||||
0.154770 | + | 0.987951i | \(0.450536\pi\) | |||||||
\(374\) | 10.8275 | + | 12.7804i | 0.559874 | + | 0.660856i | ||||
\(375\) | − | 17.9697i | − | 0.927951i | ||||||
\(376\) | −7.34091 | −0.378579 | ||||||||
\(377\) | 16.8360 | 0.867098 | ||||||||
\(378\) | 47.3438 | 2.43510 | ||||||||
\(379\) | 24.1506i | 1.24053i | 0.784391 | + | 0.620267i | \(0.212976\pi\) | ||||
−0.784391 | + | 0.620267i | \(0.787024\pi\) | |||||||
\(380\) | −2.27978 | − | 0.735337i | −0.116950 | − | 0.0377220i | ||||
\(381\) | 41.7366i | 2.13823i | ||||||||
\(382\) | −0.305959 | −0.0156542 | ||||||||
\(383\) | 12.1325i | 0.619944i | 0.950746 | + | 0.309972i | \(0.100320\pi\) | ||||
−0.950746 | + | 0.309972i | \(0.899680\pi\) | |||||||
\(384\) | − | 3.37171i | − | 0.172062i | ||||||
\(385\) | 3.08158 | + | 3.63739i | 0.157052 | + | 0.185378i | ||||
\(386\) | 17.8024 | 0.906119 | ||||||||
\(387\) | 18.9176i | 0.961636i | ||||||||
\(388\) | − | 2.77545i | − | 0.140902i | ||||||
\(389\) | −30.9307 | −1.56825 | −0.784125 | − | 0.620603i | \(-0.786888\pi\) | ||||
−0.784125 | + | 0.620603i | \(0.786888\pi\) | |||||||
\(390\) | 7.39238i | 0.374328i | ||||||||
\(391\) | 18.5372i | 0.937469i | ||||||||
\(392\) | −0.158876 | −0.00802443 | ||||||||
\(393\) | −22.7103 | −1.14558 | ||||||||
\(394\) | 13.4869i | 0.679458i | ||||||||
\(395\) | −5.81242 | −0.292455 | ||||||||
\(396\) | 21.1769 | − | 17.9410i | 1.06418 | − | 0.901568i | ||||
\(397\) | −34.3210 | −1.72252 | −0.861260 | − | 0.508164i | \(-0.830324\pi\) | ||||
−0.861260 | + | 0.508164i | \(0.830324\pi\) | |||||||
\(398\) | 6.72511 | 0.337099 | ||||||||
\(399\) | −36.5847 | − | 11.8003i | −1.83153 | − | 0.590753i | ||||
\(400\) | −4.69799 | −0.234900 | ||||||||
\(401\) | 28.5279i | 1.42462i | 0.701867 | + | 0.712308i | \(0.252350\pi\) | ||||
−0.701867 | + | 0.712308i | \(0.747650\pi\) | |||||||
\(402\) | −30.6720 | −1.52978 | ||||||||
\(403\) | − | 18.0690i | − | 0.900081i | ||||||
\(404\) | 11.2646i | 0.560435i | ||||||||
\(405\) | 19.7430 | 0.981036 | ||||||||
\(406\) | − | 11.0377i | − | 0.547790i | ||||||
\(407\) | −19.1598 | − | 22.6156i | −0.949717 | − | 1.12101i | ||||
\(408\) | 17.0285 | 0.843035 | ||||||||
\(409\) | 17.6593 | 0.873195 | 0.436598 | − | 0.899657i | \(-0.356183\pi\) | ||||
0.436598 | + | 0.899657i | \(0.356183\pi\) | |||||||
\(410\) | −5.91269 | −0.292007 | ||||||||
\(411\) | − | 7.72195i | − | 0.380896i | ||||||
\(412\) | − | 5.86713i | − | 0.289053i | ||||||
\(413\) | 13.4693 | 0.662783 | ||||||||
\(414\) | 30.7160 | 1.50961 | ||||||||
\(415\) | 0.481568i | 0.0236393i | ||||||||
\(416\) | 3.98957 | 0.195605 | ||||||||
\(417\) | 10.3506 | 0.506871 | ||||||||
\(418\) | −13.3666 | + | 5.50771i | −0.653780 | + | 0.269391i | ||||
\(419\) | −14.3376 | −0.700436 | −0.350218 | − | 0.936668i | \(-0.613893\pi\) | ||||
−0.350218 | + | 0.936668i | \(0.613893\pi\) | |||||||
\(420\) | 4.84644 | 0.236482 | ||||||||
\(421\) | 17.9266i | 0.873690i | 0.899537 | + | 0.436845i | \(0.143904\pi\) | ||||
−0.899537 | + | 0.436845i | \(0.856096\pi\) | |||||||
\(422\) | −14.0080 | −0.681900 | ||||||||
\(423\) | −61.4321 | −2.98693 | ||||||||
\(424\) | 2.63638i | 0.128034i | ||||||||
\(425\) | − | 23.7267i | − | 1.15091i | ||||||
\(426\) | −7.71886 | −0.373980 | ||||||||
\(427\) | 30.6345 | 1.48251 | ||||||||
\(428\) | −8.14844 | −0.393870 | ||||||||
\(429\) | 28.8388 | + | 34.0404i | 1.39235 | + | 1.64348i | ||||
\(430\) | 1.24231i | 0.0599094i | ||||||||
\(431\) | −29.0015 | −1.39695 | −0.698475 | − | 0.715634i | \(-0.746138\pi\) | ||||
−0.698475 | + | 0.715634i | \(0.746138\pi\) | |||||||
\(432\) | − | 18.1009i | − | 0.870879i | ||||||
\(433\) | − | 19.6742i | − | 0.945483i | −0.881201 | − | 0.472742i | \(-0.843264\pi\) | ||
0.881201 | − | 0.472742i | \(-0.156736\pi\) | |||||||
\(434\) | −11.8460 | −0.568627 | ||||||||
\(435\) | − | 7.81937i | − | 0.374910i | ||||||
\(436\) | 7.10441 | 0.340240 | ||||||||
\(437\) | −15.2267 | − | 4.91132i | −0.728391 | − | 0.234940i | ||||
\(438\) | 15.8098 | 0.755423 | ||||||||
\(439\) | 21.3057 | 1.01686 | 0.508432 | − | 0.861102i | \(-0.330225\pi\) | ||||
0.508432 | + | 0.861102i | \(0.330225\pi\) | |||||||
\(440\) | 1.39068 | − | 1.17817i | 0.0662979 | − | 0.0561672i | ||||
\(441\) | −1.32954 | −0.0633116 | ||||||||
\(442\) | 20.1489i | 0.958384i | ||||||||
\(443\) | 38.0569 | 1.80814 | 0.904070 | − | 0.427384i | \(-0.140565\pi\) | ||||
0.904070 | + | 0.427384i | \(0.140565\pi\) | |||||||
\(444\) | −30.1329 | −1.43004 | ||||||||
\(445\) | 6.19047i | 0.293457i | ||||||||
\(446\) | 4.40001i | 0.208347i | ||||||||
\(447\) | −72.3292 | −3.42105 | ||||||||
\(448\) | − | 2.61555i | − | 0.123573i | ||||||
\(449\) | 7.29947i | 0.344483i | 0.985055 | + | 0.172242i | \(0.0551010\pi\) | ||||
−0.985055 | + | 0.172242i | \(0.944899\pi\) | |||||||
\(450\) | −39.3149 | −1.85332 | ||||||||
\(451\) | −27.2267 | + | 23.0663i | −1.28205 | + | 1.08615i | ||||
\(452\) | − | 5.80008i | − | 0.272813i | ||||||
\(453\) | 24.3969i | 1.14627i | ||||||||
\(454\) | −2.32306 | −0.109027 | ||||||||
\(455\) | 5.73453i | 0.268839i | ||||||||
\(456\) | −4.51158 | + | 13.9874i | −0.211274 | + | 0.655018i | ||||
\(457\) | 42.2044i | 1.97424i | 0.159986 | + | 0.987119i | \(0.448855\pi\) | ||||
−0.159986 | + | 0.987119i | \(0.551145\pi\) | |||||||
\(458\) | −11.6600 | −0.544837 | ||||||||
\(459\) | 91.4165 | 4.26696 | ||||||||
\(460\) | 2.01710 | 0.0940479 | ||||||||
\(461\) | 34.1868i | 1.59224i | 0.605140 | + | 0.796119i | \(0.293117\pi\) | ||||
−0.605140 | + | 0.796119i | \(0.706883\pi\) | |||||||
\(462\) | 22.3168 | − | 18.9067i | 1.03827 | − | 0.879619i | ||||
\(463\) | 23.9347 | 1.11234 | 0.556170 | − | 0.831069i | \(-0.312271\pi\) | ||||
0.556170 | + | 0.831069i | \(0.312271\pi\) | |||||||
\(464\) | −4.22001 | −0.195909 | ||||||||
\(465\) | −8.39203 | −0.389171 | ||||||||
\(466\) | − | 7.57452i | − | 0.350883i | ||||||
\(467\) | 17.6443 | 0.816480 | 0.408240 | − | 0.912875i | \(-0.366143\pi\) | ||||
0.408240 | + | 0.912875i | \(0.366143\pi\) | |||||||
\(468\) | 33.3865 | 1.54329 | ||||||||
\(469\) | −23.7933 | −1.09867 | ||||||||
\(470\) | −4.03421 | −0.186084 | ||||||||
\(471\) | − | 56.5938i | − | 2.60771i | ||||||
\(472\) | − | 5.14971i | − | 0.237034i | ||||||
\(473\) | 4.84644 | + | 5.72057i | 0.222839 | + | 0.263032i | ||||
\(474\) | 35.6615i | 1.63799i | ||||||||
\(475\) | 19.4894 | + | 6.28623i | 0.894233 | + | 0.288432i | ||||
\(476\) | 13.2096 | 0.605460 | ||||||||
\(477\) | 22.0624i | 1.01017i | ||||||||
\(478\) | − | 6.81545i | − | 0.311731i | ||||||
\(479\) | − | 32.9775i | − | 1.50678i | −0.657575 | − | 0.753389i | \(-0.728418\pi\) | ||
0.657575 | − | 0.753389i | \(-0.271582\pi\) | |||||||
\(480\) | − | 1.85293i | − | 0.0845742i | ||||||
\(481\) | − | 35.6546i | − | 1.62571i | ||||||
\(482\) | 14.8529 | 0.676532 | ||||||||
\(483\) | 32.3694 | 1.47286 | ||||||||
\(484\) | 1.80753 | − | 10.8505i | 0.0821604 | − | 0.493203i | ||||
\(485\) | − | 1.52525i | − | 0.0692581i | ||||||
\(486\) | − | 66.8282i | − | 3.03139i | ||||||
\(487\) | 38.0849i | 1.72579i | 0.505383 | + | 0.862895i | \(0.331351\pi\) | ||||
−0.505383 | + | 0.862895i | \(0.668649\pi\) | |||||||
\(488\) | − | 11.7124i | − | 0.530196i | ||||||
\(489\) | − | 59.5273i | − | 2.69192i | ||||||
\(490\) | −0.0873103 | −0.00394428 | ||||||||
\(491\) | − | 30.3390i | − | 1.36918i | −0.728929 | − | 0.684589i | \(-0.759982\pi\) | ||
0.728929 | − | 0.684589i | \(-0.240018\pi\) | |||||||
\(492\) | 36.2767i | 1.63548i | ||||||||
\(493\) | − | 21.3127i | − | 0.959875i | ||||||
\(494\) | −16.5505 | − | 5.33831i | −0.744642 | − | 0.240182i | ||||
\(495\) | 11.6378 | − | 9.85949i | 0.523080 | − | 0.443151i | ||||
\(496\) | 4.52906i | 0.203361i | ||||||||
\(497\) | −5.98779 | −0.268589 | ||||||||
\(498\) | 2.95461 | 0.132399 | ||||||||
\(499\) | −13.8596 | −0.620440 | −0.310220 | − | 0.950665i | \(-0.600403\pi\) | ||||
−0.310220 | + | 0.950665i | \(0.600403\pi\) | |||||||
\(500\) | −5.32954 | −0.238344 | ||||||||
\(501\) | 27.3283i | 1.22094i | ||||||||
\(502\) | 15.7137 | 0.701338 | ||||||||
\(503\) | − | 17.0503i | − | 0.760237i | −0.924938 | − | 0.380118i | \(-0.875883\pi\) | ||
0.924938 | − | 0.380118i | \(-0.124117\pi\) | |||||||
\(504\) | − | 21.8881i | − | 0.974975i | ||||||
\(505\) | 6.19047i | 0.275473i | ||||||||
\(506\) | 9.28833 | − | 7.86903i | 0.412917 | − | 0.349821i | ||||
\(507\) | 9.83408i | 0.436747i | ||||||||
\(508\) | 12.3785 | 0.549205 | ||||||||
\(509\) | 12.6845i | 0.562229i | 0.959674 | + | 0.281115i | \(0.0907041\pi\) | ||||
−0.959674 | + | 0.281115i | \(0.909296\pi\) | |||||||
\(510\) | 9.35802 | 0.414380 | ||||||||
\(511\) | 12.2642 | 0.542537 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −24.2202 | + | 75.0904i | −1.06935 | + | 3.31532i | ||||
\(514\) | 15.1780i | 0.669473i | ||||||||
\(515\) | − | 3.22429i | − | 0.142079i | ||||||
\(516\) | 7.62205 | 0.335542 | ||||||||
\(517\) | −18.5767 | + | 15.7381i | −0.817001 | + | 0.692159i | ||||
\(518\) | −23.3751 | −1.02704 | ||||||||
\(519\) | − | 25.9938i | − | 1.14100i | ||||||
\(520\) | 2.19247 | 0.0961462 | ||||||||
\(521\) | − | 37.5513i | − | 1.64515i | −0.568656 | − | 0.822575i | \(-0.692537\pi\) | ||
0.568656 | − | 0.822575i | \(-0.307463\pi\) | |||||||
\(522\) | −35.3149 | −1.54569 | ||||||||
\(523\) | 1.00489 | 0.0439408 | 0.0219704 | − | 0.999759i | \(-0.493006\pi\) | ||||
0.0219704 | + | 0.999759i | \(0.493006\pi\) | |||||||
\(524\) | 6.73554i | 0.294243i | ||||||||
\(525\) | −41.4311 | −1.80820 | ||||||||
\(526\) | − | 17.3014i | − | 0.754377i | ||||||
\(527\) | −22.8736 | −0.996388 | ||||||||
\(528\) | −7.22856 | − | 8.53234i | −0.314583 | − | 0.371323i | ||||
\(529\) | −9.52775 | −0.414250 | ||||||||
\(530\) | 1.44882i | 0.0629329i | ||||||||
\(531\) | − | 43.0951i | − | 1.87017i | ||||||
\(532\) | −3.49979 | + | 10.8505i | −0.151735 | + | 0.470428i | ||||
\(533\) | −42.9242 | −1.85926 | ||||||||
\(534\) | 37.9810 | 1.64360 | ||||||||
\(535\) | −4.47799 | −0.193600 | ||||||||
\(536\) | 9.09686i | 0.392925i | ||||||||
\(537\) | −25.8474 | −1.11540 | ||||||||
\(538\) | 2.68907i | 0.115934i | ||||||||
\(539\) | −0.402045 | + | 0.340611i | −0.0173173 | + | 0.0146712i | ||||
\(540\) | − | 9.94736i | − | 0.428066i | ||||||
\(541\) | − | 32.1921i | − | 1.38405i | −0.721875 | − | 0.692024i | \(-0.756719\pi\) | ||
0.721875 | − | 0.692024i | \(-0.243281\pi\) | |||||||
\(542\) | 14.9386i | 0.641667i | ||||||||
\(543\) | 1.48676 | 0.0638030 | ||||||||
\(544\) | − | 5.05039i | − | 0.216534i | ||||||
\(545\) | 3.90424 | 0.167239 | ||||||||
\(546\) | 35.1836 | 1.50572 | ||||||||
\(547\) | −7.40623 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(548\) | −2.29021 | −0.0978331 | ||||||||
\(549\) | − | 98.0148i | − | 4.18317i | ||||||
\(550\) | −11.8886 | + | 10.0719i | −0.506931 | + | 0.429469i | ||||
\(551\) | 17.5065 | + | 5.64666i | 0.745800 | + | 0.240556i | ||||
\(552\) | − | 12.3757i | − | 0.526746i | ||||||
\(553\) | 27.6638i | 1.17639i | ||||||||
\(554\) | 10.7978i | 0.458754i | ||||||||
\(555\) | −16.5596 | −0.702914 | ||||||||
\(556\) | − | 3.06983i | − | 0.130190i | ||||||
\(557\) | 14.1333i | 0.598847i | 0.954120 | + | 0.299423i | \(0.0967943\pi\) | ||||
−0.954120 | + | 0.299423i | \(0.903206\pi\) | |||||||
\(558\) | 37.9013i | 1.60449i | ||||||||
\(559\) | 9.01877i | 0.381453i | ||||||||
\(560\) | − | 1.43738i | − | 0.0607404i | ||||||
\(561\) | 43.0917 | − | 36.5071i | 1.81933 | − | 1.54133i | ||||
\(562\) | 6.80575 | 0.287083 | ||||||||
\(563\) | 36.0797 | 1.52058 | 0.760289 | − | 0.649585i | \(-0.225057\pi\) | ||||
0.760289 | + | 0.649585i | \(0.225057\pi\) | |||||||
\(564\) | 24.7515i | 1.04222i | ||||||||
\(565\) | − | 3.18744i | − | 0.134097i | ||||||
\(566\) | 32.3915i | 1.36152i | ||||||||
\(567\) | − | 93.9654i | − | 3.94618i | ||||||
\(568\) | 2.28930i | 0.0960569i | ||||||||
\(569\) | 5.05706 | 0.212003 | 0.106001 | − | 0.994366i | \(-0.466195\pi\) | ||||
0.106001 | + | 0.994366i | \(0.466195\pi\) | |||||||
\(570\) | −2.47934 | + | 7.68677i | −0.103848 | + | 0.321963i | ||||
\(571\) | 17.4759i | 0.731344i | 0.930744 | + | 0.365672i | \(0.119161\pi\) | ||||
−0.930744 | + | 0.365672i | \(0.880839\pi\) | |||||||
\(572\) | 10.0959 | − | 8.55317i | 0.422129 | − | 0.357626i | ||||
\(573\) | 1.03161i | 0.0430960i | ||||||||
\(574\) | 28.1411i | 1.17459i | ||||||||
\(575\) | −17.2438 | −0.719115 | ||||||||
\(576\) | −8.36845 | −0.348685 | ||||||||
\(577\) | −34.5036 | −1.43641 | −0.718203 | − | 0.695834i | \(-0.755035\pi\) | ||||
−0.718203 | + | 0.695834i | \(0.755035\pi\) | |||||||
\(578\) | 8.50646 | 0.353822 | ||||||||
\(579\) | − | 60.0246i | − | 2.49454i | ||||||
\(580\) | −2.31911 | −0.0962958 | ||||||||
\(581\) | 2.29200 | 0.0950880 | ||||||||
\(582\) | −9.35802 | −0.387902 | ||||||||
\(583\) | 5.65208 | + | 6.67153i | 0.234085 | + | 0.276306i | ||||
\(584\) | − | 4.68896i | − | 0.194030i | ||||||
\(585\) | 18.3476 | 0.758579 | ||||||||
\(586\) | −27.9451 | −1.15440 | ||||||||
\(587\) | −3.35154 | −0.138333 | −0.0691664 | − | 0.997605i | \(-0.522034\pi\) | ||||
−0.0691664 | + | 0.997605i | \(0.522034\pi\) | |||||||
\(588\) | 0.535683i | 0.0220912i | ||||||||
\(589\) | 6.06020 | − | 18.7886i | 0.249706 | − | 0.774169i | ||||
\(590\) | − | 2.83003i | − | 0.116510i | ||||||
\(591\) | 45.4738 | 1.87054 | ||||||||
\(592\) | 8.93697i | 0.367307i | ||||||||
\(593\) | 14.0111i | 0.575367i | 0.957726 | + | 0.287683i | \(0.0928851\pi\) | ||||
−0.957726 | + | 0.287683i | \(0.907115\pi\) | |||||||
\(594\) | −38.8062 | − | 45.8055i | −1.59224 | − | 1.87942i | ||||
\(595\) | 7.25934 | 0.297604 | ||||||||
\(596\) | 21.4518i | 0.878699i | ||||||||
\(597\) | − | 22.6751i | − | 0.928032i | ||||||
\(598\) | 14.6435 | 0.598819 | ||||||||
\(599\) | 15.1874i | 0.620540i | 0.950649 | + | 0.310270i | \(0.100419\pi\) | ||||
−0.950649 | + | 0.310270i | \(0.899581\pi\) | |||||||
\(600\) | 15.8403i | 0.646677i | ||||||||
\(601\) | −39.7522 | −1.62153 | −0.810764 | − | 0.585374i | \(-0.800948\pi\) | ||||
−0.810764 | + | 0.585374i | \(0.800948\pi\) | |||||||
\(602\) | 5.91269 | 0.240983 | ||||||||
\(603\) | 76.1266i | 3.10012i | ||||||||
\(604\) | 7.23575 | 0.294419 | ||||||||
\(605\) | 0.993330 | − | 5.96289i | 0.0403846 | − | 0.242426i | ||||
\(606\) | 37.9810 | 1.54287 | ||||||||
\(607\) | 10.3196 | 0.418861 | 0.209430 | − | 0.977824i | \(-0.432839\pi\) | ||||
0.209430 | + | 0.977824i | \(0.432839\pi\) | |||||||
\(608\) | 4.14844 | + | 1.33807i | 0.168242 | + | 0.0542658i | ||||
\(609\) | −37.2158 | −1.50806 | ||||||||
\(610\) | − | 6.43657i | − | 0.260609i | ||||||
\(611\) | −29.2871 | −1.18483 | ||||||||
\(612\) | − | 42.2640i | − | 1.70842i | ||||||
\(613\) | 3.01777i | 0.121887i | 0.998141 | + | 0.0609434i | \(0.0194109\pi\) | ||||
−0.998141 | + | 0.0609434i | \(0.980589\pi\) | |||||||
\(614\) | −8.48362 | −0.342371 | ||||||||
\(615\) | 19.9359i | 0.803893i | ||||||||
\(616\) | −5.60744 | − | 6.61883i | −0.225930 | − | 0.266680i | ||||
\(617\) | 20.9072 | 0.841694 | 0.420847 | − | 0.907132i | \(-0.361733\pi\) | ||||
0.420847 | + | 0.907132i | \(0.361733\pi\) | |||||||
\(618\) | −19.7823 | −0.795760 | ||||||||
\(619\) | −4.43082 | −0.178090 | −0.0890448 | − | 0.996028i | \(-0.528381\pi\) | ||||
−0.0890448 | + | 0.996028i | \(0.528381\pi\) | |||||||
\(620\) | 2.48895i | 0.0999587i | ||||||||
\(621\) | − | 66.4385i | − | 2.66608i | ||||||
\(622\) | −10.6492 | −0.426993 | ||||||||
\(623\) | 29.4632 | 1.18042 | ||||||||
\(624\) | − | 13.4517i | − | 0.538498i | ||||||
\(625\) | 20.5611 | 0.822444 | ||||||||
\(626\) | −24.2599 | −0.969619 | ||||||||
\(627\) | 18.5704 | + | 45.0682i | 0.741631 | + | 1.79985i | ||||
\(628\) | −16.7849 | −0.669790 | ||||||||
\(629\) | −45.1352 | −1.79966 | ||||||||
\(630\) | − | 12.0286i | − | 0.479233i | ||||||
\(631\) | 39.6614 | 1.57889 | 0.789447 | − | 0.613818i | \(-0.210367\pi\) | ||||
0.789447 | + | 0.613818i | \(0.210367\pi\) | |||||||
\(632\) | 10.5767 | 0.420717 | ||||||||
\(633\) | 47.2311i | 1.87727i | ||||||||
\(634\) | − | 6.10196i | − | 0.242340i | ||||||
\(635\) | 6.80260 | 0.269953 | ||||||||
\(636\) | 8.88911 | 0.352476 | ||||||||
\(637\) | −0.633845 | −0.0251139 | ||||||||
\(638\) | −10.6790 | + | 9.04720i | −0.422786 | + | 0.358182i | ||||
\(639\) | 19.1579i | 0.757874i | ||||||||
\(640\) | −0.549551 | −0.0217229 | ||||||||
\(641\) | 33.9734i | 1.34187i | 0.741516 | + | 0.670935i | \(0.234107\pi\) | ||||
−0.741516 | + | 0.670935i | \(0.765893\pi\) | |||||||
\(642\) | 27.4742i | 1.08432i | ||||||||
\(643\) | 2.27414 | 0.0896835 | 0.0448418 | − | 0.998994i | \(-0.485722\pi\) | ||||
0.0448418 | + | 0.998994i | \(0.485722\pi\) | |||||||
\(644\) | − | 9.60028i | − | 0.378304i | ||||||
\(645\) | 4.18871 | 0.164930 | ||||||||
\(646\) | −6.75777 | + | 20.9513i | −0.265881 | + | 0.824316i | ||||
\(647\) | −44.2461 | −1.73949 | −0.869746 | − | 0.493499i | \(-0.835718\pi\) | ||||
−0.869746 | + | 0.493499i | \(0.835718\pi\) | |||||||
\(648\) | −35.9256 | −1.41129 | ||||||||
\(649\) | −11.0404 | − | 13.0317i | −0.433372 | − | 0.511538i | ||||
\(650\) | −18.7430 | −0.735159 | ||||||||
\(651\) | 39.9414i | 1.56543i | ||||||||
\(652\) | −17.6549 | −0.691419 | ||||||||
\(653\) | 31.5131 | 1.23320 | 0.616602 | − | 0.787275i | \(-0.288509\pi\) | ||||
0.616602 | + | 0.787275i | \(0.288509\pi\) | |||||||
\(654\) | − | 23.9540i | − | 0.936677i | ||||||
\(655\) | 3.70152i | 0.144630i | ||||||||
\(656\) | 10.7591 | 0.420073 | ||||||||
\(657\) | − | 39.2393i | − | 1.53087i | ||||||
\(658\) | 19.2006i | 0.748516i | ||||||||
\(659\) | −12.0612 | −0.469839 | −0.234919 | − | 0.972015i | \(-0.575483\pi\) | ||||
−0.234919 | + | 0.972015i | \(0.575483\pi\) | |||||||
\(660\) | −3.97246 | − | 4.68896i | −0.154628 | − | 0.182517i | ||||
\(661\) | − | 21.7536i | − | 0.846119i | −0.906102 | − | 0.423059i | \(-0.860956\pi\) | ||
0.906102 | − | 0.423059i | \(-0.139044\pi\) | |||||||
\(662\) | 13.5012i | 0.524739i | ||||||||
\(663\) | 67.9362 | 2.63842 | ||||||||
\(664\) | − | 0.876294i | − | 0.0340068i | ||||||
\(665\) | −1.92331 | + | 5.96289i | −0.0745829 | + | 0.231231i | ||||
\(666\) | 74.7886i | 2.89800i | ||||||||
\(667\) | −15.4894 | −0.599750 | ||||||||
\(668\) | 8.10516 | 0.313598 | ||||||||
\(669\) | 14.8356 | 0.573577 | ||||||||
\(670\) | 4.99919i | 0.193136i | ||||||||
\(671\) | −25.1101 | − | 29.6390i | −0.969363 | − | 1.14420i | ||||
\(672\) | −8.81890 | −0.340196 | ||||||||
\(673\) | −0.138009 | −0.00531986 | −0.00265993 | − | 0.999996i | \(-0.500847\pi\) | ||||
−0.00265993 | + | 0.999996i | \(0.500847\pi\) | |||||||
\(674\) | −11.2371 | −0.432837 | ||||||||
\(675\) | 85.0378i | 3.27311i | ||||||||
\(676\) | 2.91664 | 0.112179 | ||||||||
\(677\) | 26.2333 | 1.00823 | 0.504115 | − | 0.863637i | \(-0.331819\pi\) | ||||
0.504115 | + | 0.863637i | \(0.331819\pi\) | |||||||
\(678\) | −19.5562 | −0.751052 | ||||||||
\(679\) | −7.25934 | −0.278588 | ||||||||
\(680\) | − | 2.77545i | − | 0.106434i | ||||||
\(681\) | 7.83270i | 0.300150i | ||||||||
\(682\) | 9.70979 | + | 11.4611i | 0.371807 | + | 0.438868i | ||||
\(683\) | − | 21.9562i | − | 0.840131i | −0.907494 | − | 0.420066i | \(-0.862007\pi\) | ||
0.907494 | − | 0.420066i | \(-0.137993\pi\) | |||||||
\(684\) | 34.7160 | + | 11.1976i | 1.32740 | + | 0.428149i | ||||
\(685\) | −1.25859 | −0.0480883 | ||||||||
\(686\) | 18.7244i | 0.714902i | ||||||||
\(687\) | 39.3143i | 1.49993i | ||||||||
\(688\) | − | 2.26059i | − | 0.0861841i | ||||||
\(689\) | 10.5180i | 0.400704i | ||||||||
\(690\) | − | 6.80109i | − | 0.258913i | ||||||
\(691\) | 18.1093 | 0.688910 | 0.344455 | − | 0.938803i | \(-0.388064\pi\) | ||||
0.344455 | + | 0.938803i | \(0.388064\pi\) | |||||||
\(692\) | −7.70936 | −0.293066 | ||||||||
\(693\) | −46.9256 | − | 55.3894i | −1.78256 | − | 2.10407i | ||||
\(694\) | − | 5.20240i | − | 0.197480i | ||||||
\(695\) | − | 1.68703i | − | 0.0639927i | ||||||
\(696\) | 14.2287i | 0.539336i | ||||||||
\(697\) | 54.3378i | 2.05819i | ||||||||
\(698\) | − | 4.91132i | − | 0.185896i | ||||||
\(699\) | −25.5391 | −0.965978 | ||||||||
\(700\) | 12.2879i | 0.464437i | ||||||||
\(701\) | − | 11.1851i | − | 0.422455i | −0.977437 | − | 0.211227i | \(-0.932254\pi\) | ||
0.977437 | − | 0.211227i | \(-0.0677461\pi\) | |||||||
\(702\) | − | 72.2146i | − | 2.72557i | ||||||
\(703\) | 11.9583 | − | 37.0745i | 0.451015 | − | 1.39829i | ||||
\(704\) | −2.53057 | + | 2.14388i | −0.0953743 | + | 0.0808006i | ||||
\(705\) | 13.6022i | 0.512288i | ||||||||
\(706\) | 8.82463 | 0.332119 | ||||||||
\(707\) | 29.4632 | 1.10808 | ||||||||
\(708\) | −17.3633 | −0.652554 | ||||||||
\(709\) | 46.8540 | 1.75964 | 0.879820 | − | 0.475307i | \(-0.157663\pi\) | ||||
0.879820 | + | 0.475307i | \(0.157663\pi\) | |||||||
\(710\) | 1.25809i | 0.0472152i | ||||||||
\(711\) | 88.5103 | 3.31940 | ||||||||
\(712\) | − | 11.2646i | − | 0.422159i | ||||||
\(713\) | 16.6237i | 0.622564i | ||||||||
\(714\) | − | 44.5389i | − | 1.66683i | ||||||
\(715\) | 5.54819 | − | 4.70040i | 0.207491 | − | 0.175785i | ||||
\(716\) | 7.66595i | 0.286490i | ||||||||
\(717\) | −22.9797 | −0.858194 | ||||||||
\(718\) | − | 13.2564i | − | 0.494723i | ||||||
\(719\) | −41.2438 | −1.53813 | −0.769067 | − | 0.639168i | \(-0.779279\pi\) | ||||
−0.769067 | + | 0.639168i | \(0.779279\pi\) | |||||||
\(720\) | −4.59889 | −0.171391 | ||||||||
\(721\) | −15.3458 | −0.571508 | ||||||||
\(722\) | −15.4191 | − | 11.1018i | −0.573841 | − | 0.413166i | ||||
\(723\) | − | 50.0798i | − | 1.86249i | ||||||
\(724\) | − | 0.440951i | − | 0.0163878i | ||||||
\(725\) | 19.8256 | 0.736303 | ||||||||
\(726\) | −36.5847 | − | 6.09447i | −1.35779 | − | 0.226187i | ||||
\(727\) | 18.5148 | 0.686675 | 0.343338 | − | 0.939212i | \(-0.388442\pi\) | ||||
0.343338 | + | 0.939212i | \(0.388442\pi\) | |||||||
\(728\) | − | 10.4349i | − | 0.386744i | ||||||
\(729\) | −117.549 | −4.35366 | ||||||||
\(730\) | − | 2.57682i | − | 0.0953725i | ||||||
\(731\) | 11.4169 | 0.422268 | ||||||||
\(732\) | −39.4909 | −1.45963 | ||||||||
\(733\) | 44.8982i | 1.65835i | 0.558987 | + | 0.829176i | \(0.311190\pi\) | ||||
−0.558987 | + | 0.829176i | \(0.688810\pi\) | |||||||
\(734\) | −21.5733 | −0.796286 | ||||||||
\(735\) | 0.294385i | 0.0108586i | ||||||||
\(736\) | −3.67046 | −0.135295 | ||||||||
\(737\) | 19.5026 | + | 23.0202i | 0.718388 | + | 0.847960i | ||||
\(738\) | 90.0372 | 3.31432 | ||||||||
\(739\) | − | 7.30885i | − | 0.268860i | −0.990923 | − | 0.134430i | \(-0.957080\pi\) | ||
0.990923 | − | 0.134430i | \(-0.0429204\pi\) | |||||||
\(740\) | 4.91132i | 0.180544i | ||||||||
\(741\) | −17.9993 | + | 55.8035i | −0.661219 | + | 2.04999i | ||||
\(742\) | 6.89559 | 0.253145 | ||||||||
\(743\) | −39.0601 | −1.43298 | −0.716488 | − | 0.697600i | \(-0.754251\pi\) | ||||
−0.716488 | + | 0.697600i | \(0.754251\pi\) | |||||||
\(744\) | 15.2707 | 0.559851 | ||||||||
\(745\) | 11.7888i | 0.431910i | ||||||||
\(746\) | −5.97820 | −0.218877 | ||||||||
\(747\) | − | 7.33322i | − | 0.268309i | ||||||
\(748\) | −10.8275 | − | 12.7804i | −0.395891 | − | 0.467296i | ||||
\(749\) | 21.3127i | 0.778749i | ||||||||
\(750\) | 17.9697i | 0.656160i | ||||||||
\(751\) | 29.3174i | 1.06981i | 0.844914 | + | 0.534903i | \(0.179652\pi\) | ||||
−0.844914 | + | 0.534903i | \(0.820348\pi\) | |||||||
\(752\) | 7.34091 | 0.267696 | ||||||||
\(753\) | − | 52.9822i | − | 1.93078i | ||||||
\(754\) | −16.8360 | −0.613131 | ||||||||
\(755\) | 3.97642 | 0.144717 | ||||||||
\(756\) | −47.3438 | −1.72188 | ||||||||
\(757\) | 0.123922 | 0.00450401 | 0.00225201 | − | 0.999997i | \(-0.499283\pi\) | ||||
0.00225201 | + | 0.999997i | \(0.499283\pi\) | |||||||
\(758\) | − | 24.1506i | − | 0.877190i | ||||||
\(759\) | −26.5321 | − | 31.3176i | −0.963055 | − | 1.13676i | ||||
\(760\) | 2.27978 | + | 0.735337i | 0.0826964 | + | 0.0266735i | ||||
\(761\) | − | 39.6344i | − | 1.43675i | −0.695657 | − | 0.718374i | \(-0.744887\pi\) | ||
0.695657 | − | 0.718374i | \(-0.255113\pi\) | |||||||
\(762\) | − | 41.7366i | − | 1.51196i | ||||||
\(763\) | − | 18.5820i | − | 0.672713i | ||||||
\(764\) | 0.305959 | 0.0110692 | ||||||||
\(765\) | − | 23.2262i | − | 0.839745i | ||||||
\(766\) | − | 12.1325i | − | 0.438367i | ||||||
\(767\) | − | 20.5451i | − | 0.741840i | ||||||
\(768\) | 3.37171i | 0.121666i | ||||||||
\(769\) | 48.0946i | 1.73434i | 0.498015 | + | 0.867168i | \(0.334062\pi\) | ||||
−0.498015 | + | 0.867168i | \(0.665938\pi\) | |||||||
\(770\) | −3.08158 | − | 3.63739i | −0.111052 | − | 0.131082i | ||||
\(771\) | 51.1759 | 1.84305 | ||||||||
\(772\) | −17.8024 | −0.640723 | ||||||||
\(773\) | 45.0990i | 1.62210i | 0.584979 | + | 0.811048i | \(0.301103\pi\) | ||||
−0.584979 | + | 0.811048i | \(0.698897\pi\) | |||||||
\(774\) | − | 18.9176i | − | 0.679980i | ||||||
\(775\) | − | 21.2775i | − | 0.764311i | ||||||
\(776\) | 2.77545i | 0.0996328i | ||||||||
\(777\) | 78.8142i | 2.82744i | ||||||||
\(778\) | 30.9307 | 1.10892 | ||||||||
\(779\) | −44.6336 | − | 14.3964i | −1.59917 | − | 0.515806i | ||||
\(780\) | − | 7.39238i | − | 0.264690i | ||||||
\(781\) | 4.90799 | + | 5.79322i | 0.175622 | + | 0.207298i | ||||
\(782\) | − | 18.5372i | − | 0.662891i | ||||||
\(783\) | 76.3858i | 2.72981i | ||||||||
\(784\) | 0.158876 | 0.00567413 | ||||||||
\(785\) | −9.22415 | −0.329224 | ||||||||
\(786\) | 22.7103 | 0.810050 | ||||||||
\(787\) | −10.3124 | −0.367599 | −0.183799 | − | 0.982964i | \(-0.558840\pi\) | ||||
−0.183799 | + | 0.982964i | \(0.558840\pi\) | |||||||
\(788\) | − | 13.4869i | − | 0.480449i | ||||||
\(789\) | −58.3354 | −2.07679 | ||||||||
\(790\) | 5.81242 | 0.206797 | ||||||||
\(791\) | −15.1704 | −0.539399 | ||||||||
\(792\) | −21.1769 | + | 17.9410i | −0.752489 | + | 0.637505i | ||||
\(793\) | − | 46.7275i | − | 1.65934i | ||||||
\(794\) | 34.3210 | 1.21801 | ||||||||
\(795\) | 4.88502 | 0.173254 | ||||||||
\(796\) | −6.72511 | −0.238365 | ||||||||
\(797\) | 23.3363i | 0.826615i | 0.910592 | + | 0.413307i | \(0.135627\pi\) | ||||
−0.910592 | + | 0.413307i | \(0.864373\pi\) | |||||||
\(798\) | 36.5847 | + | 11.8003i | 1.29508 | + | 0.417726i | ||||
\(799\) | 37.0745i | 1.31160i | ||||||||
\(800\) | 4.69799 | 0.166099 | ||||||||
\(801\) | − | 94.2673i | − | 3.33077i | ||||||
\(802\) | − | 28.5279i | − | 1.00736i | ||||||
\(803\) | −10.0526 | − | 11.8657i | −0.354748 | − | 0.418732i | ||||
\(804\) | 30.6720 | 1.08172 | ||||||||
\(805\) | − | 5.27584i | − | 0.185949i | ||||||
\(806\) | 18.0690i | 0.636454i | ||||||||
\(807\) | 9.06677 | 0.319165 | ||||||||
\(808\) | − | 11.2646i | − | 0.396287i | ||||||
\(809\) | 31.6627i | 1.11320i | 0.830781 | + | 0.556600i | \(0.187894\pi\) | ||||
−0.830781 | + | 0.556600i | \(0.812106\pi\) | |||||||
\(810\) | −19.7430 | −0.693697 | ||||||||
\(811\) | 0.563001 | 0.0197696 | 0.00988481 | − | 0.999951i | \(-0.496854\pi\) | ||||
0.00988481 | + | 0.999951i | \(0.496854\pi\) | |||||||
\(812\) | 11.0377i | 0.387346i | ||||||||
\(813\) | 50.3686 | 1.76651 | ||||||||
\(814\) | 19.1598 | + | 22.6156i | 0.671551 | + | 0.792676i | ||||
\(815\) | −9.70227 | −0.339856 | ||||||||
\(816\) | −17.0285 | −0.596116 | ||||||||
\(817\) | −3.02482 | + | 9.37792i | −0.105825 | + | 0.328092i | ||||
\(818\) | −17.6593 | −0.617442 | ||||||||
\(819\) | − | 87.3242i | − | 3.05135i | ||||||
\(820\) | 5.91269 | 0.206480 | ||||||||
\(821\) | − | 12.2039i | − | 0.425920i | −0.977061 | − | 0.212960i | \(-0.931690\pi\) | ||
0.977061 | − | 0.212960i | \(-0.0683104\pi\) | |||||||
\(822\) | 7.72195i | 0.269334i | ||||||||
\(823\) | −0.691745 | −0.0241127 | −0.0120564 | − | 0.999927i | \(-0.503838\pi\) | ||||
−0.0120564 | + | 0.999927i | \(0.503838\pi\) | |||||||
\(824\) | 5.86713i | 0.204391i | ||||||||
\(825\) | 33.9597 | + | 40.0849i | 1.18233 | + | 1.39558i | ||||
\(826\) | −13.4693 | −0.468658 | ||||||||
\(827\) | −5.10441 | −0.177498 | −0.0887489 | − | 0.996054i | \(-0.528287\pi\) | ||||
−0.0887489 | + | 0.996054i | \(0.528287\pi\) | |||||||
\(828\) | −30.7160 | −1.06746 | ||||||||
\(829\) | − | 41.3515i | − | 1.43620i | −0.695942 | − | 0.718098i | \(-0.745013\pi\) | ||
0.695942 | − | 0.718098i | \(-0.254987\pi\) | |||||||
\(830\) | − | 0.481568i | − | 0.0167155i | ||||||
\(831\) | 36.4070 | 1.26295 | ||||||||
\(832\) | −3.98957 | −0.138313 | ||||||||
\(833\) | 0.802385i | 0.0278010i | ||||||||
\(834\) | −10.3506 | −0.358412 | ||||||||
\(835\) | 4.45420 | 0.154144 | ||||||||
\(836\) | 13.3666 | − | 5.50771i | 0.462292 | − | 0.190488i | ||||
\(837\) | 81.9800 | 2.83364 | ||||||||
\(838\) | 14.3376 | 0.495283 | ||||||||
\(839\) | 20.6329i | 0.712327i | 0.934424 | + | 0.356163i | \(0.115915\pi\) | ||||
−0.934424 | + | 0.356163i | \(0.884085\pi\) | |||||||
\(840\) | −4.84644 | −0.167218 | ||||||||
\(841\) | −11.1915 | −0.385915 | ||||||||
\(842\) | − | 17.9266i | − | 0.617792i | ||||||
\(843\) | − | 22.9470i | − | 0.790338i | ||||||
\(844\) | 14.0080 | 0.482176 | ||||||||
\(845\) | 1.60284 | 0.0551395 | ||||||||
\(846\) | 61.4321 | 2.11208 | ||||||||
\(847\) | −28.3800 | − | 4.72769i | −0.975149 | − | 0.162445i | ||||
\(848\) | − | 2.63638i | − | 0.0905335i | ||||||
\(849\) | 109.215 | 3.74825 | ||||||||
\(850\) | 23.7267i | 0.813819i | ||||||||
\(851\) | 32.8027i | 1.12446i | ||||||||
\(852\) | 7.71886 | 0.264444 | ||||||||
\(853\) | 12.7678i | 0.437160i | 0.975819 | + | 0.218580i | \(0.0701424\pi\) | ||||
−0.975819 | + | 0.218580i | \(0.929858\pi\) | |||||||
\(854\) | −30.6345 | −1.04829 | ||||||||
\(855\) | 19.0782 | + | 6.15363i | 0.652462 | + | 0.210450i | ||||
\(856\) | 8.14844 | 0.278508 | ||||||||
\(857\) | −37.8401 | −1.29259 | −0.646296 | − | 0.763087i | \(-0.723683\pi\) | ||||
−0.646296 | + | 0.763087i | \(0.723683\pi\) | |||||||
\(858\) | −28.8388 | − | 34.0404i | −0.984541 | − | 1.16212i | ||||
\(859\) | −12.3728 | −0.422155 | −0.211078 | − | 0.977469i | \(-0.567697\pi\) | ||||
−0.211078 | + | 0.977469i | \(0.567697\pi\) | |||||||
\(860\) | − | 1.24231i | − | 0.0423624i | ||||||
\(861\) | 94.8836 | 3.23363 | ||||||||
\(862\) | 29.0015 | 0.987793 | ||||||||
\(863\) | − | 57.3000i | − | 1.95051i | −0.221075 | − | 0.975257i | \(-0.570956\pi\) | ||
0.221075 | − | 0.975257i | \(-0.429044\pi\) | |||||||
\(864\) | 18.1009i | 0.615804i | ||||||||
\(865\) | −4.23669 | −0.144052 | ||||||||
\(866\) | 19.6742i | 0.668558i | ||||||||
\(867\) | − | 28.6813i | − | 0.974069i | ||||||
\(868\) | 11.8460 | 0.402080 | ||||||||
\(869\) | 26.7650 | − | 22.6751i | 0.907939 | − | 0.769201i | ||||
\(870\) | 7.81937i | 0.265102i | ||||||||
\(871\) | 36.2925i | 1.22973i | ||||||||
\(872\) | −7.10441 | −0.240586 | ||||||||
\(873\) | 23.2262i | 0.786088i | ||||||||
\(874\) | 15.2267 | + | 4.91132i | 0.515050 | + | 0.166128i | ||||
\(875\) | 13.9397i | 0.471248i | ||||||||
\(876\) | −15.8098 | −0.534164 | ||||||||
\(877\) | −17.2974 | −0.584092 | −0.292046 | − | 0.956404i | \(-0.594336\pi\) | ||||
−0.292046 | + | 0.956404i | \(0.594336\pi\) | |||||||
\(878\) | −21.3057 | −0.719031 | ||||||||
\(879\) | 94.2229i | 3.17806i | ||||||||
\(880\) | −1.39068 | + | 1.17817i | −0.0468797 | + | 0.0397162i | ||||
\(881\) | −4.50293 | −0.151708 | −0.0758538 | − | 0.997119i | \(-0.524168\pi\) | ||||
−0.0758538 | + | 0.997119i | \(0.524168\pi\) | |||||||
\(882\) | 1.32954 | 0.0447681 | ||||||||
\(883\) | −14.9153 | −0.501939 | −0.250970 | − | 0.967995i | \(-0.580749\pi\) | ||||
−0.250970 | + | 0.967995i | \(0.580749\pi\) | |||||||
\(884\) | − | 20.1489i | − | 0.677680i | ||||||
\(885\) | −9.54204 | −0.320752 | ||||||||
\(886\) | −38.0569 | −1.27855 | ||||||||
\(887\) | 7.21760 | 0.242343 | 0.121172 | − | 0.992632i | \(-0.461335\pi\) | ||||
0.121172 | + | 0.992632i | \(0.461335\pi\) | |||||||
\(888\) | 30.1329 | 1.01119 | ||||||||
\(889\) | − | 32.3765i | − | 1.08587i | ||||||
\(890\) | − | 6.19047i | − | 0.207505i | ||||||
\(891\) | −90.9121 | + | 77.0203i | −3.04567 | + | 2.58028i | ||||
\(892\) | − | 4.40001i | − | 0.147323i | ||||||
\(893\) | −30.4534 | − | 9.82264i | −1.01908 | − | 0.328702i | ||||
\(894\) | 72.3292 | 2.41905 | ||||||||
\(895\) | 4.21283i | 0.140819i | ||||||||
\(896\) | 2.61555i | 0.0873795i | ||||||||
\(897\) | − | 49.3738i | − | 1.64854i | ||||||
\(898\) | − | 7.29947i | − | 0.243586i | ||||||
\(899\) | − | 19.1127i | − | 0.637444i | ||||||
\(900\) | 39.3149 | 1.31050 | ||||||||
\(901\) | 13.3147 | 0.443578 | ||||||||
\(902\) | 27.2267 | − | 23.0663i | 0.906549 | − | 0.768024i | ||||
\(903\) | − | 19.9359i | − | 0.663425i | ||||||
\(904\) | 5.80008i | 0.192908i | ||||||||
\(905\) | − | 0.242325i | − | 0.00805517i | ||||||
\(906\) | − | 24.3969i | − | 0.810532i | ||||||
\(907\) | 20.9068i | 0.694198i | 0.937829 | + | 0.347099i | \(0.112833\pi\) | ||||
−0.937829 | + | 0.347099i | \(0.887167\pi\) | |||||||
\(908\) | 2.32306 | 0.0770936 | ||||||||
\(909\) | − | 94.2673i | − | 3.12665i | ||||||
\(910\) | − | 5.73453i | − | 0.190098i | ||||||
\(911\) | − | 8.14065i | − | 0.269712i | −0.990865 | − | 0.134856i | \(-0.956943\pi\) | ||
0.990865 | − | 0.134856i | \(-0.0430572\pi\) | |||||||
\(912\) | 4.51158 | − | 13.9874i | 0.149393 | − | 0.463168i | ||||
\(913\) | −1.87867 | − | 2.21752i | −0.0621750 | − | 0.0733892i | ||||
\(914\) | − | 42.2044i | − | 1.39600i | ||||||
\(915\) | −21.7023 | −0.717455 | ||||||||
\(916\) | 11.6600 | 0.385258 | ||||||||
\(917\) | 17.6172 | 0.581770 | ||||||||
\(918\) | −91.4165 | −3.01719 | ||||||||
\(919\) | − | 40.9735i | − | 1.35159i | −0.737089 | − | 0.675796i | \(-0.763800\pi\) | ||
0.737089 | − | 0.675796i | \(-0.236200\pi\) | |||||||
\(920\) | −2.01710 | −0.0665019 | ||||||||
\(921\) | 28.6043i | 0.942545i | ||||||||
\(922\) | − | 34.1868i | − | 1.12588i | ||||||
\(923\) | 9.13331i | 0.300627i | ||||||||
\(924\) | −22.3168 | + | 18.9067i | −0.734169 | + | 0.621984i | ||||
\(925\) | − | 41.9858i | − | 1.38048i | ||||||
\(926\) | −23.9347 | −0.786542 | ||||||||
\(927\) | 49.0988i | 1.61262i | ||||||||
\(928\) | 4.22001 | 0.138529 | ||||||||
\(929\) | 7.14938 | 0.234564 | 0.117282 | − | 0.993099i | \(-0.462582\pi\) | ||||
0.117282 | + | 0.993099i | \(0.462582\pi\) | |||||||
\(930\) | 8.39203 | 0.275186 | ||||||||
\(931\) | −0.659087 | − | 0.212586i | −0.0216007 | − | 0.00696724i | ||||
\(932\) | 7.57452i | 0.248112i | ||||||||
\(933\) | 35.9059i | 1.17551i | ||||||||
\(934\) | −17.6443 | −0.577338 | ||||||||
\(935\) | −5.95024 | − | 7.02346i | −0.194594 | − | 0.229692i | ||||
\(936\) | −33.3865 | −1.09127 | ||||||||
\(937\) | − | 26.4991i | − | 0.865687i | −0.901469 | − | 0.432843i | \(-0.857510\pi\) | ||
0.901469 | − | 0.432843i | \(-0.142490\pi\) | |||||||
\(938\) | 23.7933 | 0.776880 | ||||||||
\(939\) | 81.7973i | 2.66935i | ||||||||
\(940\) | 4.03421 | 0.131581 | ||||||||
\(941\) | 32.4157 | 1.05672 | 0.528361 | − | 0.849020i | \(-0.322807\pi\) | ||||
0.528361 | + | 0.849020i | \(0.322807\pi\) | |||||||
\(942\) | 56.5938i | 1.84393i | ||||||||
\(943\) | 39.4909 | 1.28600 | ||||||||
\(944\) | 5.14971i | 0.167609i | ||||||||
\(945\) | −26.0179 | −0.846361 | ||||||||
\(946\) | −4.84644 | − | 5.72057i | −0.157571 | − | 0.185992i | ||||
\(947\) | −21.1899 | −0.688578 | −0.344289 | − | 0.938864i | \(-0.611880\pi\) | ||||
−0.344289 | + | 0.938864i | \(0.611880\pi\) | |||||||
\(948\) | − | 35.6615i | − | 1.15823i | ||||||
\(949\) | − | 18.7069i | − | 0.607252i | ||||||
\(950\) | −19.4894 | − | 6.28623i | −0.632318 | − | 0.203952i | ||||
\(951\) | −20.5741 | −0.667160 | ||||||||
\(952\) | −13.2096 | −0.428125 | ||||||||
\(953\) | 33.9745 | 1.10054 | 0.550271 | − | 0.834986i | \(-0.314524\pi\) | ||||
0.550271 | + | 0.834986i | \(0.314524\pi\) | |||||||
\(954\) | − | 22.0624i | − | 0.714296i | ||||||
\(955\) | 0.168140 | 0.00544089 | ||||||||
\(956\) | 6.81545i | 0.220427i | ||||||||
\(957\) | 30.5046 | + | 36.0066i | 0.986073 | + | 1.16393i | ||||
\(958\) | 32.9775i | 1.06545i | ||||||||
\(959\) | 5.99018i | 0.193433i | ||||||||
\(960\) | 1.85293i | 0.0598030i | ||||||||
\(961\) | 10.4876 | 0.338309 | ||||||||
\(962\) | 35.6546i | 1.14955i | ||||||||
\(963\) | 68.1898 | 2.19739 | ||||||||
\(964\) | −14.8529 | −0.478380 | ||||||||
\(965\) | −9.78333 | −0.314937 | ||||||||
\(966\) | −32.3694 | −1.04147 | ||||||||
\(967\) | − | 38.6701i | − | 1.24355i | −0.783197 | − | 0.621773i | \(-0.786413\pi\) | ||
0.783197 | − | 0.621773i | \(-0.213587\pi\) | |||||||
\(968\) | −1.80753 | + | 10.8505i | −0.0580962 | + | 0.348748i | ||||
\(969\) | 70.6416 | + | 22.7853i | 2.26934 | + | 0.731968i | ||||
\(970\) | 1.52525i | 0.0489729i | ||||||||
\(971\) | − | 13.6334i | − | 0.437517i | −0.975779 | − | 0.218759i | \(-0.929799\pi\) | ||
0.975779 | − | 0.218759i | \(-0.0702007\pi\) | |||||||
\(972\) | 66.8282i | 2.14352i | ||||||||
\(973\) | −8.02932 | −0.257408 | ||||||||
\(974\) | − | 38.0849i | − | 1.22032i | ||||||
\(975\) | 63.1959i | 2.02389i | ||||||||
\(976\) | 11.7124i | 0.374905i | ||||||||
\(977\) | 39.4021i | 1.26059i | 0.776357 | + | 0.630293i | \(0.217065\pi\) | ||||
−0.776357 | + | 0.630293i | \(0.782935\pi\) | |||||||
\(978\) | 59.5273i | 1.90347i | ||||||||
\(979\) | −24.1500 | − | 28.5058i | −0.771837 | − | 0.911050i | ||||
\(980\) | 0.0873103 | 0.00278903 | ||||||||
\(981\) | −59.4529 | −1.89819 | ||||||||
\(982\) | 30.3390i | 0.968155i | ||||||||
\(983\) | 2.35737i | 0.0751886i | 0.999293 | + | 0.0375943i | \(0.0119695\pi\) | ||||
−0.999293 | + | 0.0375943i | \(0.988031\pi\) | |||||||
\(984\) | − | 36.2767i | − | 1.15646i | ||||||
\(985\) | − | 7.41172i | − | 0.236157i | ||||||
\(986\) | 21.3127i | 0.678734i | ||||||||
\(987\) | 64.7388 | 2.06066 | ||||||||
\(988\) | 16.5505 | + | 5.33831i | 0.526541 | + | 0.169834i | ||||
\(989\) | − | 8.29739i | − | 0.263842i | ||||||
\(990\) | −11.6378 | + | 9.85949i | −0.369874 | + | 0.313355i | ||||
\(991\) | 44.4844i | 1.41309i | 0.707667 | + | 0.706547i | \(0.249748\pi\) | ||||
−0.707667 | + | 0.706547i | \(0.750252\pi\) | |||||||
\(992\) | − | 4.52906i | − | 0.143798i | ||||||
\(993\) | 45.5222 | 1.44460 | ||||||||
\(994\) | 5.98779 | 0.189921 | ||||||||
\(995\) | −3.69579 | −0.117164 | ||||||||
\(996\) | −2.95461 | −0.0936205 | ||||||||
\(997\) | − | 8.70938i | − | 0.275829i | −0.990444 | − | 0.137914i | \(-0.955960\pi\) | ||
0.990444 | − | 0.137914i | \(-0.0440399\pi\) | |||||||
\(998\) | 13.8596 | 0.438718 | ||||||||
\(999\) | 161.767 | 5.11808 |
(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 | 418.2.b.c.417.8 | yes | 8 | |
3.2 | odd | 2 | 3762.2.g.h.2089.5 | 8 | |||
11.10 | odd | 2 | 418.2.b.d.417.8 | yes | 8 | ||
19.18 | odd | 2 | 418.2.b.d.417.1 | yes | 8 | ||
33.32 | even | 2 | 3762.2.g.g.2089.6 | 8 | |||
57.56 | even | 2 | 3762.2.g.g.2089.5 | 8 | |||
209.208 | even | 2 | inner | 418.2.b.c.417.1 | ✓ | 8 | |
627.626 | odd | 2 | 3762.2.g.h.2089.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.b.c.417.1 | ✓ | 8 | 209.208 | even | 2 | inner | |
418.2.b.c.417.8 | yes | 8 | 1.1 | even | 1 | trivial | |
418.2.b.d.417.1 | yes | 8 | 19.18 | odd | 2 | ||
418.2.b.d.417.8 | yes | 8 | 11.10 | odd | 2 | ||
3762.2.g.g.2089.5 | 8 | 57.56 | even | 2 | |||
3762.2.g.g.2089.6 | 8 | 33.32 | even | 2 | |||
3762.2.g.h.2089.5 | 8 | 3.2 | odd | 2 | |||
3762.2.g.h.2089.6 | 8 | 627.626 | odd | 2 |