Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.c (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.18 | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.j.337.7 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35819i | 0.960385i | 0.877163 | + | 0.480192i | \(0.159433\pi\) | ||||
−0.877163 | + | 0.480192i | \(0.840567\pi\) | |||||||
\(3\) | 3.39737 | 1.96147 | 0.980737 | − | 0.195331i | \(-0.0625782\pi\) | ||||
0.980737 | + | 0.195331i | \(0.0625782\pi\) | |||||||
\(4\) | 0.155322 | 0.0776609 | ||||||||
\(5\) | 0.772491i | 0.345468i | 0.984968 | + | 0.172734i | \(0.0552602\pi\) | ||||
−0.984968 | + | 0.172734i | \(0.944740\pi\) | |||||||
\(6\) | 4.61428i | 1.88377i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.92733i | 1.03497i | ||||||||
\(9\) | 8.54215 | 2.84738 | ||||||||
\(10\) | −1.04919 | −0.331783 | ||||||||
\(11\) | − 2.11612i | − 0.638034i | −0.947749 | − | 0.319017i | \(-0.896647\pi\) | ||||
0.947749 | − | 0.319017i | \(-0.103353\pi\) | |||||||
\(12\) | 0.527686 | 0.152330 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.35819 | −0.362991 | ||||||||
\(15\) | 2.62444i | 0.677627i | ||||||||
\(16\) | −3.66523 | −0.916308 | ||||||||
\(17\) | −5.63627 | −1.36700 | −0.683498 | − | 0.729952i | \(-0.739542\pi\) | ||||
−0.683498 | + | 0.729952i | \(0.739542\pi\) | |||||||
\(18\) | 11.6019i | 2.73458i | ||||||||
\(19\) | − 2.99988i | − 0.688219i | −0.938930 | − | 0.344110i | \(-0.888181\pi\) | ||||
0.938930 | − | 0.344110i | \(-0.111819\pi\) | |||||||
\(20\) | 0.119985i | 0.0268294i | ||||||||
\(21\) | 3.39737i | 0.741368i | ||||||||
\(22\) | 2.87409 | 0.612759 | ||||||||
\(23\) | −1.24177 | −0.258927 | −0.129464 | − | 0.991584i | \(-0.541326\pi\) | ||||
−0.129464 | + | 0.991584i | \(0.541326\pi\) | |||||||
\(24\) | 9.94525i | 2.03007i | ||||||||
\(25\) | 4.40326 | 0.880652 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.8288 | 3.62359 | ||||||||
\(28\) | 0.155322i | 0.0293530i | ||||||||
\(29\) | −7.96564 | −1.47918 | −0.739591 | − | 0.673057i | \(-0.764981\pi\) | ||||
−0.739591 | + | 0.673057i | \(0.764981\pi\) | |||||||
\(30\) | −3.56449 | −0.650783 | ||||||||
\(31\) | − 1.26728i | − 0.227609i | −0.993503 | − | 0.113805i | \(-0.963696\pi\) | ||||
0.993503 | − | 0.113805i | \(-0.0363038\pi\) | |||||||
\(32\) | 0.876591i | 0.154961i | ||||||||
\(33\) | − 7.18925i | − 1.25149i | ||||||||
\(34\) | − 7.65512i | − 1.31284i | ||||||||
\(35\) | −0.772491 | −0.130575 | ||||||||
\(36\) | 1.32678 | 0.221130 | ||||||||
\(37\) | − 4.54251i | − 0.746784i | −0.927674 | − | 0.373392i | \(-0.878195\pi\) | ||||
0.927674 | − | 0.373392i | \(-0.121805\pi\) | |||||||
\(38\) | 4.07440 | 0.660955 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.26134 | −0.357549 | ||||||||
\(41\) | − 9.82390i | − 1.53424i | −0.641506 | − | 0.767118i | \(-0.721690\pi\) | ||||
0.641506 | − | 0.767118i | \(-0.278310\pi\) | |||||||
\(42\) | −4.61428 | −0.711998 | ||||||||
\(43\) | −2.64573 | −0.403470 | −0.201735 | − | 0.979440i | \(-0.564658\pi\) | ||||
−0.201735 | + | 0.979440i | \(0.564658\pi\) | |||||||
\(44\) | − 0.328679i | − 0.0495503i | ||||||||
\(45\) | 6.59873i | 0.983681i | ||||||||
\(46\) | − 1.68656i | − 0.248670i | ||||||||
\(47\) | 7.68703i | 1.12127i | 0.828064 | + | 0.560634i | \(0.189443\pi\) | ||||
−0.828064 | + | 0.560634i | \(0.810557\pi\) | |||||||
\(48\) | −12.4522 | −1.79731 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 5.98046i | 0.845764i | ||||||||
\(51\) | −19.1485 | −2.68133 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.350895 | −0.0481991 | −0.0240995 | − | 0.999710i | \(-0.507672\pi\) | ||||
−0.0240995 | + | 0.999710i | \(0.507672\pi\) | |||||||
\(54\) | 25.5730i | 3.48005i | ||||||||
\(55\) | 1.63468 | 0.220421 | ||||||||
\(56\) | −2.92733 | −0.391182 | ||||||||
\(57\) | − 10.1917i | − 1.34992i | ||||||||
\(58\) | − 10.8188i | − 1.42058i | ||||||||
\(59\) | − 5.00519i | − 0.651621i | −0.945435 | − | 0.325810i | \(-0.894363\pi\) | ||||
0.945435 | − | 0.325810i | \(-0.105637\pi\) | |||||||
\(60\) | 0.407633i | 0.0526251i | ||||||||
\(61\) | 4.24504 | 0.543522 | 0.271761 | − | 0.962365i | \(-0.412394\pi\) | ||||
0.271761 | + | 0.962365i | \(0.412394\pi\) | |||||||
\(62\) | 1.72120 | 0.218593 | ||||||||
\(63\) | 8.54215i | 1.07621i | ||||||||
\(64\) | −8.52104 | −1.06513 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.76437 | 1.20191 | ||||||||
\(67\) | 11.3053i | 1.38117i | 0.723253 | + | 0.690583i | \(0.242646\pi\) | ||||
−0.723253 | + | 0.690583i | \(0.757354\pi\) | |||||||
\(68\) | −0.875435 | −0.106162 | ||||||||
\(69\) | −4.21876 | −0.507879 | ||||||||
\(70\) | − 1.04919i | − 0.125402i | ||||||||
\(71\) | − 11.8975i | − 1.41198i | −0.708223 | − | 0.705989i | \(-0.750503\pi\) | ||||
0.708223 | − | 0.705989i | \(-0.249497\pi\) | |||||||
\(72\) | 25.0057i | 2.94695i | ||||||||
\(73\) | 8.99347i | 1.05261i | 0.850297 | + | 0.526303i | \(0.176422\pi\) | ||||
−0.850297 | + | 0.526303i | \(0.823578\pi\) | |||||||
\(74\) | 6.16959 | 0.717200 | ||||||||
\(75\) | 14.9595 | 1.72738 | ||||||||
\(76\) | − 0.465946i | − 0.0534477i | ||||||||
\(77\) | 2.11612 | 0.241154 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.30010 | −0.708817 | −0.354408 | − | 0.935091i | \(-0.615318\pi\) | ||||
−0.354408 | + | 0.935091i | \(0.615318\pi\) | |||||||
\(80\) | − 2.83136i | − 0.316555i | ||||||||
\(81\) | 38.3419 | 4.26021 | ||||||||
\(82\) | 13.3427 | 1.47346 | ||||||||
\(83\) | − 2.92778i | − 0.321366i | −0.987006 | − | 0.160683i | \(-0.948630\pi\) | ||||
0.987006 | − | 0.160683i | \(-0.0513697\pi\) | |||||||
\(84\) | 0.527686i | 0.0575753i | ||||||||
\(85\) | − 4.35397i | − 0.472254i | ||||||||
\(86\) | − 3.59340i | − 0.387487i | ||||||||
\(87\) | −27.0622 | −2.90138 | ||||||||
\(88\) | 6.19459 | 0.660346 | ||||||||
\(89\) | − 1.97181i | − 0.209012i | −0.994524 | − | 0.104506i | \(-0.966674\pi\) | ||||
0.994524 | − | 0.104506i | \(-0.0333261\pi\) | |||||||
\(90\) | −8.96233 | −0.944712 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.192874 | −0.0201085 | ||||||||
\(93\) | − 4.30541i | − 0.446450i | ||||||||
\(94\) | −10.4404 | −1.07685 | ||||||||
\(95\) | 2.31738 | 0.237758 | ||||||||
\(96\) | 2.97811i | 0.303952i | ||||||||
\(97\) | − 7.88255i | − 0.800352i | −0.916438 | − | 0.400176i | \(-0.868949\pi\) | ||||
0.916438 | − | 0.400176i | \(-0.131051\pi\) | |||||||
\(98\) | − 1.35819i | − 0.137198i | ||||||||
\(99\) | − 18.0762i | − 1.81673i | ||||||||
\(100\) | 0.683922 | 0.0683922 | ||||||||
\(101\) | −1.76856 | −0.175978 | −0.0879890 | − | 0.996121i | \(-0.528044\pi\) | ||||
−0.0879890 | + | 0.996121i | \(0.528044\pi\) | |||||||
\(102\) | − 26.0073i | − 2.57511i | ||||||||
\(103\) | 11.4598 | 1.12917 | 0.564586 | − | 0.825375i | \(-0.309036\pi\) | ||||
0.564586 | + | 0.825375i | \(0.309036\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.62444 | −0.256119 | ||||||||
\(106\) | − 0.476581i | − 0.0462897i | ||||||||
\(107\) | −3.29566 | −0.318603 | −0.159302 | − | 0.987230i | \(-0.550924\pi\) | ||||
−0.159302 | + | 0.987230i | \(0.550924\pi\) | |||||||
\(108\) | 2.92451 | 0.281412 | ||||||||
\(109\) | 13.1559i | 1.26011i | 0.776551 | + | 0.630055i | \(0.216968\pi\) | ||||
−0.776551 | + | 0.630055i | \(0.783032\pi\) | |||||||
\(110\) | 2.22021i | 0.211689i | ||||||||
\(111\) | − 15.4326i | − 1.46480i | ||||||||
\(112\) | − 3.66523i | − 0.346332i | ||||||||
\(113\) | 1.44552 | 0.135984 | 0.0679918 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679918 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(114\) | 13.8423 | 1.29645 | ||||||||
\(115\) | − 0.959257i | − 0.0894512i | ||||||||
\(116\) | −1.23724 | −0.114875 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.79800 | 0.625807 | ||||||||
\(119\) | − 5.63627i | − 0.516676i | ||||||||
\(120\) | −7.68261 | −0.701324 | ||||||||
\(121\) | 6.52203 | 0.592912 | ||||||||
\(122\) | 5.76557i | 0.521990i | ||||||||
\(123\) | − 33.3755i | − 3.00936i | ||||||||
\(124\) | − 0.196835i | − 0.0176763i | ||||||||
\(125\) | 7.26393i | 0.649706i | ||||||||
\(126\) | −11.6019 | −1.03358 | ||||||||
\(127\) | 10.9224 | 0.969209 | 0.484605 | − | 0.874733i | \(-0.338963\pi\) | ||||
0.484605 | + | 0.874733i | \(0.338963\pi\) | |||||||
\(128\) | − 9.82000i | − 0.867974i | ||||||||
\(129\) | −8.98854 | −0.791397 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.24077 | −0.195777 | −0.0978886 | − | 0.995197i | \(-0.531209\pi\) | ||||
−0.0978886 | + | 0.995197i | \(0.531209\pi\) | |||||||
\(132\) | − 1.11665i | − 0.0971917i | ||||||||
\(133\) | 2.99988 | 0.260122 | ||||||||
\(134\) | −15.3548 | −1.32645 | ||||||||
\(135\) | 14.5450i | 1.25184i | ||||||||
\(136\) | − 16.4993i | − 1.41480i | ||||||||
\(137\) | 7.48827i | 0.639766i | 0.947457 | + | 0.319883i | \(0.103644\pi\) | ||||
−0.947457 | + | 0.319883i | \(0.896356\pi\) | |||||||
\(138\) | − 5.72988i | − 0.487759i | ||||||||
\(139\) | 3.17757 | 0.269518 | 0.134759 | − | 0.990878i | \(-0.456974\pi\) | ||||
0.134759 | + | 0.990878i | \(0.456974\pi\) | |||||||
\(140\) | −0.119985 | −0.0101405 | ||||||||
\(141\) | 26.1157i | 2.19934i | ||||||||
\(142\) | 16.1591 | 1.35604 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −31.3090 | −2.60908 | ||||||||
\(145\) | − 6.15338i | − 0.511010i | ||||||||
\(146\) | −12.2148 | −1.01091 | ||||||||
\(147\) | −3.39737 | −0.280211 | ||||||||
\(148\) | − 0.705550i | − 0.0579959i | ||||||||
\(149\) | 15.6423i | 1.28147i | 0.767762 | + | 0.640735i | \(0.221370\pi\) | ||||
−0.767762 | + | 0.640735i | \(0.778630\pi\) | |||||||
\(150\) | 20.3179i | 1.65895i | ||||||||
\(151\) | 15.2282i | 1.23925i | 0.784897 | + | 0.619626i | \(0.212716\pi\) | ||||
−0.784897 | + | 0.619626i | \(0.787284\pi\) | |||||||
\(152\) | 8.78165 | 0.712286 | ||||||||
\(153\) | −48.1459 | −3.89236 | ||||||||
\(154\) | 2.87409i | 0.231601i | ||||||||
\(155\) | 0.978959 | 0.0786318 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4128 | −1.15027 | −0.575134 | − | 0.818059i | \(-0.695050\pi\) | ||||
−0.575134 | + | 0.818059i | \(0.695050\pi\) | |||||||
\(158\) | − 8.55673i | − 0.680737i | ||||||||
\(159\) | −1.19212 | −0.0945413 | ||||||||
\(160\) | −0.677159 | −0.0535341 | ||||||||
\(161\) | − 1.24177i | − 0.0978653i | ||||||||
\(162\) | 52.0755i | 4.09144i | ||||||||
\(163\) | − 10.6875i | − 0.837113i | −0.908191 | − | 0.418556i | \(-0.862536\pi\) | ||||
0.908191 | − | 0.418556i | \(-0.137464\pi\) | |||||||
\(164\) | − 1.52587i | − 0.119150i | ||||||||
\(165\) | 5.55363 | 0.432350 | ||||||||
\(166\) | 3.97648 | 0.308635 | ||||||||
\(167\) | 5.89574i | 0.456226i | 0.973635 | + | 0.228113i | \(0.0732555\pi\) | ||||
−0.973635 | + | 0.228113i | \(0.926744\pi\) | |||||||
\(168\) | −9.94525 | −0.767293 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5.91351 | 0.453546 | ||||||||
\(171\) | − 25.6254i | − 1.95962i | ||||||||
\(172\) | −0.410940 | −0.0313338 | ||||||||
\(173\) | −5.63112 | −0.428126 | −0.214063 | − | 0.976820i | \(-0.568670\pi\) | ||||
−0.214063 | + | 0.976820i | \(0.568670\pi\) | |||||||
\(174\) | − 36.7557i | − 2.78644i | ||||||||
\(175\) | 4.40326i | 0.332855i | ||||||||
\(176\) | 7.75607i | 0.584636i | ||||||||
\(177\) | − 17.0045i | − 1.27814i | ||||||||
\(178\) | 2.67810 | 0.200732 | ||||||||
\(179\) | −7.18084 | −0.536721 | −0.268361 | − | 0.963318i | \(-0.586482\pi\) | ||||
−0.268361 | + | 0.963318i | \(0.586482\pi\) | |||||||
\(180\) | 1.02493i | 0.0763935i | ||||||||
\(181\) | 0.567427 | 0.0421765 | 0.0210883 | − | 0.999778i | \(-0.493287\pi\) | ||||
0.0210883 | + | 0.999778i | \(0.493287\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.4220 | 1.06611 | ||||||||
\(184\) | − 3.63508i | − 0.267982i | ||||||||
\(185\) | 3.50905 | 0.257990 | ||||||||
\(186\) | 5.84756 | 0.428764 | ||||||||
\(187\) | 11.9270i | 0.872191i | ||||||||
\(188\) | 1.19396i | 0.0870787i | ||||||||
\(189\) | 18.8288i | 1.36959i | ||||||||
\(190\) | 3.14744i | 0.228339i | ||||||||
\(191\) | −7.95163 | −0.575360 | −0.287680 | − | 0.957727i | \(-0.592884\pi\) | ||||
−0.287680 | + | 0.957727i | \(0.592884\pi\) | |||||||
\(192\) | −28.9492 | −2.08923 | ||||||||
\(193\) | − 20.5748i | − 1.48100i | −0.672054 | − | 0.740502i | \(-0.734588\pi\) | ||||
0.672054 | − | 0.740502i | \(-0.265412\pi\) | |||||||
\(194\) | 10.7060 | 0.768646 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.155322 | −0.0110944 | ||||||||
\(197\) | − 1.52219i | − 0.108451i | −0.998529 | − | 0.0542256i | \(-0.982731\pi\) | ||||
0.998529 | − | 0.0542256i | \(-0.0172690\pi\) | |||||||
\(198\) | 24.5509 | 1.74476 | ||||||||
\(199\) | −25.3123 | −1.79434 | −0.897172 | − | 0.441681i | \(-0.854382\pi\) | ||||
−0.897172 | + | 0.441681i | \(0.854382\pi\) | |||||||
\(200\) | 12.8898i | 0.911447i | ||||||||
\(201\) | 38.4084i | 2.70912i | ||||||||
\(202\) | − 2.40204i | − 0.169007i | ||||||||
\(203\) | − 7.96564i | − 0.559078i | ||||||||
\(204\) | −2.97418 | −0.208234 | ||||||||
\(205\) | 7.58887 | 0.530030 | ||||||||
\(206\) | 15.5646i | 1.08444i | ||||||||
\(207\) | −10.6074 | −0.737265 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.34810 | −0.439107 | ||||||||
\(210\) | − 3.56449i | − 0.245973i | ||||||||
\(211\) | 5.54406 | 0.381669 | 0.190834 | − | 0.981622i | \(-0.438881\pi\) | ||||
0.190834 | + | 0.981622i | \(0.438881\pi\) | |||||||
\(212\) | −0.0545016 | −0.00374318 | ||||||||
\(213\) | − 40.4204i | − 2.76956i | ||||||||
\(214\) | − 4.47612i | − 0.305982i | ||||||||
\(215\) | − 2.04380i | − 0.139386i | ||||||||
\(216\) | 55.1181i | 3.75031i | ||||||||
\(217\) | 1.26728 | 0.0860283 | ||||||||
\(218\) | −17.8682 | −1.21019 | ||||||||
\(219\) | 30.5542i | 2.06466i | ||||||||
\(220\) | 0.253902 | 0.0171181 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 20.9604 | 1.40677 | ||||||||
\(223\) | 6.89711i | 0.461865i | 0.972970 | + | 0.230932i | \(0.0741776\pi\) | ||||
−0.972970 | + | 0.230932i | \(0.925822\pi\) | |||||||
\(224\) | −0.876591 | −0.0585697 | ||||||||
\(225\) | 37.6133 | 2.50755 | ||||||||
\(226\) | 1.96330i | 0.130597i | ||||||||
\(227\) | 3.16626i | 0.210152i | 0.994464 | + | 0.105076i | \(0.0335086\pi\) | ||||
−0.994464 | + | 0.105076i | \(0.966491\pi\) | |||||||
\(228\) | − 1.58299i | − 0.104836i | ||||||||
\(229\) | − 23.3695i | − 1.54430i | −0.635442 | − | 0.772148i | \(-0.719182\pi\) | ||||
0.635442 | − | 0.772148i | \(-0.280818\pi\) | |||||||
\(230\) | 1.30285 | 0.0859075 | ||||||||
\(231\) | 7.18925 | 0.473018 | ||||||||
\(232\) | − 23.3181i | − 1.53091i | ||||||||
\(233\) | 9.65245 | 0.632353 | 0.316177 | − | 0.948700i | \(-0.397601\pi\) | ||||
0.316177 | + | 0.948700i | \(0.397601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.93816 | −0.387363 | ||||||||
\(236\) | − 0.777415i | − 0.0506054i | ||||||||
\(237\) | −21.4038 | −1.39033 | ||||||||
\(238\) | 7.65512 | 0.496208 | ||||||||
\(239\) | 6.98215i | 0.451638i | 0.974169 | + | 0.225819i | \(0.0725058\pi\) | ||||
−0.974169 | + | 0.225819i | \(0.927494\pi\) | |||||||
\(240\) | − 9.61918i | − 0.620915i | ||||||||
\(241\) | − 18.5592i | − 1.19550i | −0.801681 | − | 0.597751i | \(-0.796061\pi\) | ||||
0.801681 | − | 0.597751i | \(-0.203939\pi\) | |||||||
\(242\) | 8.85816i | 0.569424i | ||||||||
\(243\) | 73.7754 | 4.73269 | ||||||||
\(244\) | 0.659348 | 0.0422104 | ||||||||
\(245\) | − 0.772491i | − 0.0493526i | ||||||||
\(246\) | 45.3302 | 2.89015 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.70974 | 0.235569 | ||||||||
\(249\) | − 9.94677i | − 0.630351i | ||||||||
\(250\) | −9.86579 | −0.623967 | ||||||||
\(251\) | −16.6573 | −1.05140 | −0.525699 | − | 0.850671i | \(-0.676196\pi\) | ||||
−0.525699 | + | 0.850671i | \(0.676196\pi\) | |||||||
\(252\) | 1.32678i | 0.0835794i | ||||||||
\(253\) | 2.62774i | 0.165204i | ||||||||
\(254\) | 14.8347i | 0.930814i | ||||||||
\(255\) | − 14.7921i | − 0.926314i | ||||||||
\(256\) | −3.70466 | −0.231541 | ||||||||
\(257\) | −7.63652 | −0.476353 | −0.238177 | − | 0.971222i | \(-0.576550\pi\) | ||||
−0.238177 | + | 0.971222i | \(0.576550\pi\) | |||||||
\(258\) | − 12.2081i | − 0.760045i | ||||||||
\(259\) | 4.54251 | 0.282258 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −68.0436 | −4.21180 | ||||||||
\(262\) | − 3.04339i | − 0.188022i | ||||||||
\(263\) | −18.6358 | −1.14913 | −0.574567 | − | 0.818458i | \(-0.694830\pi\) | ||||
−0.574567 | + | 0.818458i | \(0.694830\pi\) | |||||||
\(264\) | 21.0453 | 1.29525 | ||||||||
\(265\) | − 0.271063i | − 0.0166513i | ||||||||
\(266\) | 4.07440i | 0.249818i | ||||||||
\(267\) | − 6.69899i | − 0.409971i | ||||||||
\(268\) | 1.75596i | 0.107263i | ||||||||
\(269\) | 24.8582 | 1.51563 | 0.757817 | − | 0.652467i | \(-0.226266\pi\) | ||||
0.757817 | + | 0.652467i | \(0.226266\pi\) | |||||||
\(270\) | −19.7549 | −1.20225 | ||||||||
\(271\) | − 22.0518i | − 1.33955i | −0.742562 | − | 0.669777i | \(-0.766390\pi\) | ||||
0.742562 | − | 0.669777i | \(-0.233610\pi\) | |||||||
\(272\) | 20.6582 | 1.25259 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1705 | −0.614421 | ||||||||
\(275\) | − 9.31782i | − 0.561886i | ||||||||
\(276\) | −0.655265 | −0.0394423 | ||||||||
\(277\) | 19.7139 | 1.18449 | 0.592245 | − | 0.805758i | \(-0.298242\pi\) | ||||
0.592245 | + | 0.805758i | \(0.298242\pi\) | |||||||
\(278\) | 4.31574i | 0.258841i | ||||||||
\(279\) | − 10.8253i | − 0.648091i | ||||||||
\(280\) | − 2.26134i | − 0.135141i | ||||||||
\(281\) | 4.42005i | 0.263678i | 0.991271 | + | 0.131839i | \(0.0420882\pi\) | ||||
−0.991271 | + | 0.131839i | \(0.957912\pi\) | |||||||
\(282\) | −35.4701 | −2.11221 | ||||||||
\(283\) | 31.9312 | 1.89811 | 0.949057 | − | 0.315106i | \(-0.102040\pi\) | ||||
0.949057 | + | 0.315106i | \(0.102040\pi\) | |||||||
\(284\) | − 1.84795i | − 0.109655i | ||||||||
\(285\) | 7.87300 | 0.466356 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.82390 | 0.579887 | ||||||||
\(288\) | 7.48797i | 0.441233i | ||||||||
\(289\) | 14.7675 | 0.868679 | ||||||||
\(290\) | 8.35746 | 0.490767 | ||||||||
\(291\) | − 26.7800i | − 1.56987i | ||||||||
\(292\) | 1.39688i | 0.0817463i | ||||||||
\(293\) | − 16.2471i | − 0.949169i | −0.880210 | − | 0.474584i | \(-0.842598\pi\) | ||||
0.880210 | − | 0.474584i | \(-0.157402\pi\) | |||||||
\(294\) | − 4.61428i | − 0.269110i | ||||||||
\(295\) | 3.86647 | 0.225114 | ||||||||
\(296\) | 13.2974 | 0.772898 | ||||||||
\(297\) | − 39.8439i | − 2.31198i | ||||||||
\(298\) | −21.2453 | −1.23071 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.32354 | 0.134150 | ||||||||
\(301\) | − 2.64573i | − 0.152497i | ||||||||
\(302\) | −20.6828 | −1.19016 | ||||||||
\(303\) | −6.00845 | −0.345176 | ||||||||
\(304\) | 10.9952i | 0.630621i | ||||||||
\(305\) | 3.27926i | 0.187770i | ||||||||
\(306\) | − 65.3912i | − 3.73817i | ||||||||
\(307\) | − 13.5052i | − 0.770782i | −0.922753 | − | 0.385391i | \(-0.874067\pi\) | ||||
0.922753 | − | 0.385391i | \(-0.125933\pi\) | |||||||
\(308\) | 0.328679 | 0.0187283 | ||||||||
\(309\) | 38.9333 | 2.21484 | ||||||||
\(310\) | 1.32961i | 0.0755168i | ||||||||
\(311\) | −2.26442 | −0.128404 | −0.0642018 | − | 0.997937i | \(-0.520450\pi\) | ||||
−0.0642018 | + | 0.997937i | \(0.520450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1386 | 1.13830 | 0.569151 | − | 0.822233i | \(-0.307272\pi\) | ||||
0.569151 | + | 0.822233i | \(0.307272\pi\) | |||||||
\(314\) | − 19.5753i | − 1.10470i | ||||||||
\(315\) | −6.59873 | −0.371796 | ||||||||
\(316\) | −0.978543 | −0.0550473 | ||||||||
\(317\) | 31.3079i | 1.75843i | 0.476429 | + | 0.879213i | \(0.341931\pi\) | ||||
−0.476429 | + | 0.879213i | \(0.658069\pi\) | |||||||
\(318\) | − 1.61913i | − 0.0907960i | ||||||||
\(319\) | 16.8562i | 0.943769i | ||||||||
\(320\) | − 6.58243i | − 0.367969i | ||||||||
\(321\) | −11.1966 | −0.624932 | ||||||||
\(322\) | 1.68656 | 0.0939883 | ||||||||
\(323\) | 16.9081i | 0.940793i | ||||||||
\(324\) | 5.95532 | 0.330851 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.5157 | 0.803950 | ||||||||
\(327\) | 44.6956i | 2.47167i | ||||||||
\(328\) | 28.7578 | 1.58789 | ||||||||
\(329\) | −7.68703 | −0.423800 | ||||||||
\(330\) | 7.54288i | 0.415222i | ||||||||
\(331\) | 5.86072i | 0.322134i | 0.986943 | + | 0.161067i | \(0.0514936\pi\) | ||||
−0.986943 | + | 0.161067i | \(0.948506\pi\) | |||||||
\(332\) | − 0.454748i | − 0.0249576i | ||||||||
\(333\) | − 38.8028i | − 2.12638i | ||||||||
\(334\) | −8.00753 | −0.438152 | ||||||||
\(335\) | −8.73327 | −0.477149 | ||||||||
\(336\) | − 12.4522i | − 0.679321i | ||||||||
\(337\) | −14.0167 | −0.763539 | −0.381769 | − | 0.924258i | \(-0.624685\pi\) | ||||
−0.381769 | + | 0.924258i | \(0.624685\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.91099 | 0.266728 | ||||||||
\(340\) | − 0.676266i | − 0.0366757i | ||||||||
\(341\) | −2.68171 | −0.145223 | ||||||||
\(342\) | 34.8041 | 1.88199 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | − 7.74494i | − 0.417579i | ||||||||
\(345\) | − 3.25895i | − 0.175456i | ||||||||
\(346\) | − 7.64813i | − 0.411166i | ||||||||
\(347\) | −18.4346 | −0.989622 | −0.494811 | − | 0.869001i | \(-0.664763\pi\) | ||||
−0.494811 | + | 0.869001i | \(0.664763\pi\) | |||||||
\(348\) | −4.20335 | −0.225323 | ||||||||
\(349\) | 0.841480i | 0.0450434i | 0.999746 | + | 0.0225217i | \(0.00716948\pi\) | ||||
−0.999746 | + | 0.0225217i | \(0.992831\pi\) | |||||||
\(350\) | −5.98046 | −0.319669 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.85497 | 0.0988704 | ||||||||
\(353\) | 4.32366i | 0.230125i | 0.993358 | + | 0.115063i | \(0.0367069\pi\) | ||||
−0.993358 | + | 0.115063i | \(0.963293\pi\) | |||||||
\(354\) | 23.0953 | 1.22750 | ||||||||
\(355\) | 9.19074 | 0.487794 | ||||||||
\(356\) | − 0.306265i | − 0.0162320i | ||||||||
\(357\) | − 19.1485i | − 1.01345i | ||||||||
\(358\) | − 9.75295i | − 0.515459i | ||||||||
\(359\) | 12.0924i | 0.638213i | 0.947719 | + | 0.319107i | \(0.103383\pi\) | ||||
−0.947719 | + | 0.319107i | \(0.896617\pi\) | |||||||
\(360\) | −19.3167 | −1.01808 | ||||||||
\(361\) | 10.0007 | 0.526355 | ||||||||
\(362\) | 0.770673i | 0.0405057i | ||||||||
\(363\) | 22.1578 | 1.16298 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.94737 | −0.363642 | ||||||||
\(366\) | 19.5878i | 1.02387i | ||||||||
\(367\) | −9.05715 | −0.472779 | −0.236390 | − | 0.971658i | \(-0.575964\pi\) | ||||
−0.236390 | + | 0.971658i | \(0.575964\pi\) | |||||||
\(368\) | 4.55138 | 0.237257 | ||||||||
\(369\) | − 83.9172i | − 4.36856i | ||||||||
\(370\) | 4.76595i | 0.247770i | ||||||||
\(371\) | − 0.350895i | − 0.0182175i | ||||||||
\(372\) | − 0.668724i | − 0.0346717i | ||||||||
\(373\) | −23.0254 | −1.19221 | −0.596104 | − | 0.802907i | \(-0.703285\pi\) | ||||
−0.596104 | + | 0.802907i | \(0.703285\pi\) | |||||||
\(374\) | −16.1992 | −0.837639 | ||||||||
\(375\) | 24.6783i | 1.27438i | ||||||||
\(376\) | −22.5025 | −1.16048 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −25.5730 | −1.31533 | ||||||||
\(379\) | 29.5778i | 1.51931i | 0.650326 | + | 0.759655i | \(0.274632\pi\) | ||||
−0.650326 | + | 0.759655i | \(0.725368\pi\) | |||||||
\(380\) | 0.359939 | 0.0184645 | ||||||||
\(381\) | 37.1076 | 1.90108 | ||||||||
\(382\) | − 10.7998i | − 0.552567i | ||||||||
\(383\) | 19.0793i | 0.974906i | 0.873149 | + | 0.487453i | \(0.162074\pi\) | ||||
−0.873149 | + | 0.487453i | \(0.837926\pi\) | |||||||
\(384\) | − 33.3622i | − 1.70251i | ||||||||
\(385\) | 1.63468i | 0.0833112i | ||||||||
\(386\) | 27.9444 | 1.42233 | ||||||||
\(387\) | −22.6002 | −1.14883 | ||||||||
\(388\) | − 1.22433i | − 0.0621560i | ||||||||
\(389\) | 11.3977 | 0.577885 | 0.288942 | − | 0.957347i | \(-0.406696\pi\) | ||||
0.288942 | + | 0.957347i | \(0.406696\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.99896 | 0.353953 | ||||||||
\(392\) | − 2.92733i | − 0.147853i | ||||||||
\(393\) | −7.61274 | −0.384012 | ||||||||
\(394\) | 2.06742 | 0.104155 | ||||||||
\(395\) | − 4.86677i | − 0.244874i | ||||||||
\(396\) | − 2.80763i | − 0.141089i | ||||||||
\(397\) | 29.1687i | 1.46394i | 0.681339 | + | 0.731968i | \(0.261398\pi\) | ||||
−0.681339 | + | 0.731968i | \(0.738602\pi\) | |||||||
\(398\) | − 34.3790i | − 1.72326i | ||||||||
\(399\) | 10.1917 | 0.510223 | ||||||||
\(400\) | −16.1390 | −0.806948 | ||||||||
\(401\) | 17.0352i | 0.850697i | 0.905030 | + | 0.425349i | \(0.139849\pi\) | ||||
−0.905030 | + | 0.425349i | \(0.860151\pi\) | |||||||
\(402\) | −52.1659 | −2.60180 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.274695 | −0.0136666 | ||||||||
\(405\) | 29.6187i | 1.47177i | ||||||||
\(406\) | 10.8188 | 0.536930 | ||||||||
\(407\) | −9.61250 | −0.476474 | ||||||||
\(408\) | − 56.0541i | − 2.77509i | ||||||||
\(409\) | − 7.21000i | − 0.356511i | −0.983984 | − | 0.178256i | \(-0.942955\pi\) | ||||
0.983984 | − | 0.178256i | \(-0.0570454\pi\) | |||||||
\(410\) | 10.3071i | 0.509033i | ||||||||
\(411\) | 25.4404i | 1.25488i | ||||||||
\(412\) | 1.77996 | 0.0876924 | ||||||||
\(413\) | 5.00519 | 0.246289 | ||||||||
\(414\) | − 14.4069i | − 0.708058i | ||||||||
\(415\) | 2.26169 | 0.111022 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.7954 | 0.528653 | ||||||||
\(418\) | − 8.62192i | − 0.421712i | ||||||||
\(419\) | 34.1903 | 1.67030 | 0.835152 | − | 0.550019i | \(-0.185379\pi\) | ||||
0.835152 | + | 0.550019i | \(0.185379\pi\) | |||||||
\(420\) | −0.407633 | −0.0198904 | ||||||||
\(421\) | − 33.3533i | − 1.62554i | −0.582585 | − | 0.812770i | \(-0.697959\pi\) | ||||
0.582585 | − | 0.812770i | \(-0.302041\pi\) | |||||||
\(422\) | 7.52989i | 0.366549i | ||||||||
\(423\) | 65.6638i | 3.19268i | ||||||||
\(424\) | − 1.02719i | − 0.0498846i | ||||||||
\(425\) | −24.8180 | −1.20385 | ||||||||
\(426\) | 54.8985 | 2.65984 | ||||||||
\(427\) | 4.24504i | 0.205432i | ||||||||
\(428\) | −0.511887 | −0.0247430 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.77587 | 0.133864 | ||||||||
\(431\) | − 31.8622i | − 1.53475i | −0.641200 | − | 0.767374i | \(-0.721563\pi\) | ||||
0.641200 | − | 0.767374i | \(-0.278437\pi\) | |||||||
\(432\) | −69.0117 | −3.32033 | ||||||||
\(433\) | −2.69773 | −0.129645 | −0.0648223 | − | 0.997897i | \(-0.520648\pi\) | ||||
−0.0648223 | + | 0.997897i | \(0.520648\pi\) | |||||||
\(434\) | 1.72120i | 0.0826202i | ||||||||
\(435\) | − 20.9053i | − 1.00233i | ||||||||
\(436\) | 2.04340i | 0.0978612i | ||||||||
\(437\) | 3.72516i | 0.178199i | ||||||||
\(438\) | −41.4983 | −1.98287 | ||||||||
\(439\) | 21.5226 | 1.02722 | 0.513609 | − | 0.858024i | \(-0.328308\pi\) | ||||
0.513609 | + | 0.858024i | \(0.328308\pi\) | |||||||
\(440\) | 4.78527i | 0.228129i | ||||||||
\(441\) | −8.54215 | −0.406769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.74835 | 0.320624 | 0.160312 | − | 0.987066i | \(-0.448750\pi\) | ||||
0.160312 | + | 0.987066i | \(0.448750\pi\) | |||||||
\(444\) | − 2.39702i | − 0.113757i | ||||||||
\(445\) | 1.52321 | 0.0722069 | ||||||||
\(446\) | −9.36759 | −0.443568 | ||||||||
\(447\) | 53.1429i | 2.51357i | ||||||||
\(448\) | − 8.52104i | − 0.402581i | ||||||||
\(449\) | − 32.3984i | − 1.52898i | −0.644638 | − | 0.764488i | \(-0.722992\pi\) | ||||
0.644638 | − | 0.764488i | \(-0.277008\pi\) | |||||||
\(450\) | 51.0860i | 2.40822i | ||||||||
\(451\) | −20.7886 | −0.978895 | ||||||||
\(452\) | 0.224521 | 0.0105606 | ||||||||
\(453\) | 51.7359i | 2.43076i | ||||||||
\(454\) | −4.30038 | −0.201827 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 29.8345 | 1.39713 | ||||||||
\(457\) | − 5.27900i | − 0.246941i | −0.992348 | − | 0.123471i | \(-0.960598\pi\) | ||||
0.992348 | − | 0.123471i | \(-0.0394025\pi\) | |||||||
\(458\) | 31.7401 | 1.48312 | ||||||||
\(459\) | −106.124 | −4.95344 | ||||||||
\(460\) | − 0.148993i | − 0.00694685i | ||||||||
\(461\) | 39.9387i | 1.86013i | 0.367396 | + | 0.930065i | \(0.380250\pi\) | ||||
−0.367396 | + | 0.930065i | \(0.619750\pi\) | |||||||
\(462\) | 9.76437i | 0.454279i | ||||||||
\(463\) | 7.02805i | 0.326621i | 0.986575 | + | 0.163311i | \(0.0522173\pi\) | ||||
−0.986575 | + | 0.163311i | \(0.947783\pi\) | |||||||
\(464\) | 29.1959 | 1.35539 | ||||||||
\(465\) | 3.32589 | 0.154234 | ||||||||
\(466\) | 13.1099i | 0.607302i | ||||||||
\(467\) | 12.7122 | 0.588252 | 0.294126 | − | 0.955767i | \(-0.404971\pi\) | ||||
0.294126 | + | 0.955767i | \(0.404971\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.3053 | −0.522032 | ||||||||
\(470\) | − 8.06515i | − 0.372017i | ||||||||
\(471\) | −48.9657 | −2.25622 | ||||||||
\(472\) | 14.6519 | 0.674407 | ||||||||
\(473\) | 5.59869i | 0.257428i | ||||||||
\(474\) | − 29.0704i | − 1.33525i | ||||||||
\(475\) | − 13.2092i | − 0.606081i | ||||||||
\(476\) | − 0.875435i | − 0.0401255i | ||||||||
\(477\) | −2.99739 | −0.137241 | ||||||||
\(478\) | −9.48309 | −0.433746 | ||||||||
\(479\) | − 23.9405i | − 1.09387i | −0.837175 | − | 0.546935i | \(-0.815794\pi\) | ||||
0.837175 | − | 0.546935i | \(-0.184206\pi\) | |||||||
\(480\) | −2.30056 | −0.105006 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 25.2069 | 1.14814 | ||||||||
\(483\) | − 4.21876i | − 0.191960i | ||||||||
\(484\) | 1.01301 | 0.0460461 | ||||||||
\(485\) | 6.08920 | 0.276496 | ||||||||
\(486\) | 100.201i | 4.54521i | ||||||||
\(487\) | 10.6960i | 0.484683i | 0.970191 | + | 0.242342i | \(0.0779155\pi\) | ||||
−0.970191 | + | 0.242342i | \(0.922084\pi\) | |||||||
\(488\) | 12.4267i | 0.562529i | ||||||||
\(489\) | − 36.3096i | − 1.64198i | ||||||||
\(490\) | 1.04919 | 0.0473975 | ||||||||
\(491\) | −13.8352 | −0.624373 | −0.312187 | − | 0.950021i | \(-0.601061\pi\) | ||||
−0.312187 | + | 0.950021i | \(0.601061\pi\) | |||||||
\(492\) | − 5.18393i | − 0.233710i | ||||||||
\(493\) | 44.8965 | 2.02204 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.9637 | 0.627622 | ||||||||
\(496\) | 4.64486i | 0.208560i | ||||||||
\(497\) | 11.8975 | 0.533677 | ||||||||
\(498\) | 13.5096 | 0.605380 | ||||||||
\(499\) | 14.6054i | 0.653827i | 0.945054 | + | 0.326913i | \(0.106009\pi\) | ||||
−0.945054 | + | 0.326913i | \(0.893991\pi\) | |||||||
\(500\) | 1.12825i | 0.0504567i | ||||||||
\(501\) | 20.0300i | 0.894875i | ||||||||
\(502\) | − 22.6237i | − 1.00975i | ||||||||
\(503\) | 9.63765 | 0.429721 | 0.214861 | − | 0.976645i | \(-0.431070\pi\) | ||||
0.214861 | + | 0.976645i | \(0.431070\pi\) | |||||||
\(504\) | −25.0057 | −1.11384 | ||||||||
\(505\) | − 1.36619i | − 0.0607948i | ||||||||
\(506\) | −3.56897 | −0.158660 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.69649 | 0.0752696 | ||||||||
\(509\) | − 6.16582i | − 0.273295i | −0.990620 | − | 0.136648i | \(-0.956367\pi\) | ||||
0.990620 | − | 0.136648i | \(-0.0436328\pi\) | |||||||
\(510\) | 20.0904 | 0.889618 | ||||||||
\(511\) | −8.99347 | −0.397848 | ||||||||
\(512\) | − 24.6716i | − 1.09034i | ||||||||
\(513\) | − 56.4839i | − 2.49383i | ||||||||
\(514\) | − 10.3718i | − 0.457482i | ||||||||
\(515\) | 8.85262i | 0.390093i | ||||||||
\(516\) | −1.39612 | −0.0614606 | ||||||||
\(517\) | 16.2667 | 0.715408 | ||||||||
\(518\) | 6.16959i | 0.271076i | ||||||||
\(519\) | −19.1310 | −0.839759 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1162 | −1.31942 | −0.659708 | − | 0.751522i | \(-0.729320\pi\) | ||||
−0.659708 | + | 0.751522i | \(0.729320\pi\) | |||||||
\(522\) | − 92.4162i | − 4.04495i | ||||||||
\(523\) | 6.30225 | 0.275578 | 0.137789 | − | 0.990462i | \(-0.456000\pi\) | ||||
0.137789 | + | 0.990462i | \(0.456000\pi\) | |||||||
\(524\) | −0.348041 | −0.0152042 | ||||||||
\(525\) | 14.9595i | 0.652887i | ||||||||
\(526\) | − 25.3110i | − 1.10361i | ||||||||
\(527\) | 7.14271i | 0.311141i | ||||||||
\(528\) | 26.3503i | 1.14675i | ||||||||
\(529\) | −21.4580 | −0.932957 | ||||||||
\(530\) | 0.368155 | 0.0159916 | ||||||||
\(531\) | − 42.7551i | − 1.85541i | ||||||||
\(532\) | 0.465946 | 0.0202013 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.09849 | 0.393730 | ||||||||
\(535\) | − 2.54586i | − 0.110067i | ||||||||
\(536\) | −33.0945 | −1.42946 | ||||||||
\(537\) | −24.3960 | −1.05277 | ||||||||
\(538\) | 33.7622i | 1.45559i | ||||||||
\(539\) | 2.11612i | 0.0911478i | ||||||||
\(540\) | 2.25916i | 0.0972188i | ||||||||
\(541\) | − 1.95419i | − 0.0840171i | −0.999117 | − | 0.0420086i | \(-0.986624\pi\) | ||||
0.999117 | − | 0.0420086i | \(-0.0133757\pi\) | |||||||
\(542\) | 29.9506 | 1.28649 | ||||||||
\(543\) | 1.92776 | 0.0827282 | ||||||||
\(544\) | − 4.94071i | − 0.211831i | ||||||||
\(545\) | −10.1628 | −0.435328 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.2888 | −1.93641 | −0.968204 | − | 0.250162i | \(-0.919516\pi\) | ||||
−0.968204 | + | 0.250162i | \(0.919516\pi\) | |||||||
\(548\) | 1.16309i | 0.0496848i | ||||||||
\(549\) | 36.2618 | 1.54762 | ||||||||
\(550\) | 12.6554 | 0.539627 | ||||||||
\(551\) | 23.8959i | 1.01800i | ||||||||
\(552\) | − 12.3497i | − 0.525639i | ||||||||
\(553\) | − 6.30010i | − 0.267908i | ||||||||
\(554\) | 26.7751i | 1.13757i | ||||||||
\(555\) | 11.9215 | 0.506041 | ||||||||
\(556\) | 0.493546 | 0.0209310 | ||||||||
\(557\) | 4.02083i | 0.170368i | 0.996365 | + | 0.0851841i | \(0.0271478\pi\) | ||||
−0.996365 | + | 0.0851841i | \(0.972852\pi\) | |||||||
\(558\) | 14.7027 | 0.622417 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.83136 | 0.119647 | ||||||||
\(561\) | 40.5206i | 1.71078i | ||||||||
\(562\) | −6.00326 | −0.253232 | ||||||||
\(563\) | −14.4667 | −0.609700 | −0.304850 | − | 0.952400i | \(-0.598606\pi\) | ||||
−0.304850 | + | 0.952400i | \(0.598606\pi\) | |||||||
\(564\) | 4.05634i | 0.170803i | ||||||||
\(565\) | 1.11665i | 0.0469780i | ||||||||
\(566\) | 43.3686i | 1.82292i | ||||||||
\(567\) | 38.3419i | 1.61021i | ||||||||
\(568\) | 34.8281 | 1.46135 | ||||||||
\(569\) | −39.0095 | −1.63536 | −0.817682 | − | 0.575670i | \(-0.804741\pi\) | ||||
−0.817682 | + | 0.575670i | \(0.804741\pi\) | |||||||
\(570\) | 10.6930i | 0.447881i | ||||||||
\(571\) | 13.5719 | 0.567966 | 0.283983 | − | 0.958829i | \(-0.408344\pi\) | ||||
0.283983 | + | 0.958829i | \(0.408344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.0147 | −1.12855 | ||||||||
\(574\) | 13.3427i | 0.556914i | ||||||||
\(575\) | −5.46784 | −0.228025 | ||||||||
\(576\) | −72.7880 | −3.03283 | ||||||||
\(577\) | − 8.39100i | − 0.349322i | −0.984629 | − | 0.174661i | \(-0.944117\pi\) | ||||
0.984629 | − | 0.174661i | \(-0.0558829\pi\) | |||||||
\(578\) | 20.0571i | 0.834266i | ||||||||
\(579\) | − 69.9002i | − 2.90495i | ||||||||
\(580\) | − 0.955754i | − 0.0396855i | ||||||||
\(581\) | 2.92778 | 0.121465 | ||||||||
\(582\) | 36.3723 | 1.50768 | ||||||||
\(583\) | 0.742535i | 0.0307527i | ||||||||
\(584\) | −26.3269 | −1.08941 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.0667 | 0.911567 | ||||||||
\(587\) | 22.1640i | 0.914808i | 0.889259 | + | 0.457404i | \(0.151221\pi\) | ||||
−0.889259 | + | 0.457404i | \(0.848779\pi\) | |||||||
\(588\) | −0.527686 | −0.0217614 | ||||||||
\(589\) | −3.80167 | −0.156645 | ||||||||
\(590\) | 5.25139i | 0.216196i | ||||||||
\(591\) | − 5.17143i | − 0.212724i | ||||||||
\(592\) | 16.6494i | 0.684284i | ||||||||
\(593\) | 39.0195i | 1.60234i | 0.598437 | + | 0.801170i | \(0.295789\pi\) | ||||
−0.598437 | + | 0.801170i | \(0.704211\pi\) | |||||||
\(594\) | 54.1156 | 2.22039 | ||||||||
\(595\) | 4.35397 | 0.178495 | ||||||||
\(596\) | 2.42960i | 0.0995201i | ||||||||
\(597\) | −85.9955 | −3.51956 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.3114 | 1.27935 | 0.639674 | − | 0.768646i | \(-0.279069\pi\) | ||||
0.639674 | + | 0.768646i | \(0.279069\pi\) | |||||||
\(600\) | 43.7915i | 1.78778i | ||||||||
\(601\) | 24.7669 | 1.01026 | 0.505132 | − | 0.863042i | \(-0.331444\pi\) | ||||
0.505132 | + | 0.863042i | \(0.331444\pi\) | |||||||
\(602\) | 3.59340 | 0.146456 | ||||||||
\(603\) | 96.5718i | 3.93271i | ||||||||
\(604\) | 2.36527i | 0.0962415i | ||||||||
\(605\) | 5.03821i | 0.204832i | ||||||||
\(606\) | − 8.16061i | − 0.331502i | ||||||||
\(607\) | 4.33301 | 0.175871 | 0.0879357 | − | 0.996126i | \(-0.471973\pi\) | ||||
0.0879357 | + | 0.996126i | \(0.471973\pi\) | |||||||
\(608\) | 2.62967 | 0.106647 | ||||||||
\(609\) | − 27.0622i | − 1.09662i | ||||||||
\(610\) | −4.45385 | −0.180331 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.47810 | −0.302284 | ||||||||
\(613\) | 45.9015i | 1.85394i | 0.375131 | + | 0.926972i | \(0.377598\pi\) | ||||
−0.375131 | + | 0.926972i | \(0.622402\pi\) | |||||||
\(614\) | 18.3426 | 0.740247 | ||||||||
\(615\) | 25.7822 | 1.03964 | ||||||||
\(616\) | 6.19459i | 0.249587i | ||||||||
\(617\) | 29.0145i | 1.16808i | 0.811725 | + | 0.584040i | \(0.198529\pi\) | ||||
−0.811725 | + | 0.584040i | \(0.801471\pi\) | |||||||
\(618\) | 52.8789i | 2.12710i | ||||||||
\(619\) | − 8.57642i | − 0.344715i | −0.985034 | − | 0.172358i | \(-0.944861\pi\) | ||||
0.985034 | − | 0.172358i | \(-0.0551385\pi\) | |||||||
\(620\) | 0.152054 | 0.00610662 | ||||||||
\(621\) | −23.3810 | −0.938247 | ||||||||
\(622\) | − 3.07551i | − 0.123317i | ||||||||
\(623\) | 1.97181 | 0.0789990 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.4050 | 0.656199 | ||||||||
\(626\) | 27.3521i | 1.09321i | ||||||||
\(627\) | −21.5669 | −0.861298 | ||||||||
\(628\) | −2.23862 | −0.0893308 | ||||||||
\(629\) | 25.6028i | 1.02085i | ||||||||
\(630\) | − 8.96233i | − 0.357068i | ||||||||
\(631\) | 31.4081i | 1.25034i | 0.780490 | + | 0.625168i | \(0.214970\pi\) | ||||
−0.780490 | + | 0.625168i | \(0.785030\pi\) | |||||||
\(632\) | − 18.4425i | − 0.733604i | ||||||||
\(633\) | 18.8353 | 0.748634 | ||||||||
\(634\) | −42.5220 | −1.68877 | ||||||||
\(635\) | 8.43748i | 0.334831i | ||||||||
\(636\) | −0.185162 | −0.00734216 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.8940 | −0.906381 | ||||||||
\(639\) | − 101.631i | − 4.02044i | ||||||||
\(640\) | 7.58586 | 0.299858 | ||||||||
\(641\) | −7.67208 | −0.303029 | −0.151514 | − | 0.988455i | \(-0.548415\pi\) | ||||
−0.151514 | + | 0.988455i | \(0.548415\pi\) | |||||||
\(642\) | − 15.2071i | − 0.600175i | ||||||||
\(643\) | − 7.48239i | − 0.295076i | −0.989056 | − | 0.147538i | \(-0.952865\pi\) | ||||
0.989056 | − | 0.147538i | \(-0.0471350\pi\) | |||||||
\(644\) | − 0.192874i | − 0.00760030i | ||||||||
\(645\) | − 6.94356i | − 0.273403i | ||||||||
\(646\) | −22.9644 | −0.903523 | ||||||||
\(647\) | −23.9406 | −0.941201 | −0.470600 | − | 0.882346i | \(-0.655963\pi\) | ||||
−0.470600 | + | 0.882346i | \(0.655963\pi\) | |||||||
\(648\) | 112.239i | 4.40918i | ||||||||
\(649\) | −10.5916 | −0.415756 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.30541 | 0.168742 | ||||||||
\(652\) | − 1.66001i | − 0.0650109i | ||||||||
\(653\) | 34.2885 | 1.34181 | 0.670907 | − | 0.741541i | \(-0.265905\pi\) | ||||
0.670907 | + | 0.741541i | \(0.265905\pi\) | |||||||
\(654\) | −60.7051 | −2.37376 | ||||||||
\(655\) | − 1.73098i | − 0.0676349i | ||||||||
\(656\) | 36.0069i | 1.40583i | ||||||||
\(657\) | 76.8235i | 2.99717i | ||||||||
\(658\) | − 10.4404i | − 0.407011i | ||||||||
\(659\) | −8.82716 | −0.343857 | −0.171929 | − | 0.985109i | \(-0.555000\pi\) | ||||
−0.171929 | + | 0.985109i | \(0.555000\pi\) | |||||||
\(660\) | 0.862600 | 0.0335766 | ||||||||
\(661\) | 33.3881i | 1.29865i | 0.760512 | + | 0.649324i | \(0.224948\pi\) | ||||
−0.760512 | + | 0.649324i | \(0.775052\pi\) | |||||||
\(662\) | −7.95997 | −0.309373 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.57060 | 0.332604 | ||||||||
\(665\) | 2.31738i | 0.0898640i | ||||||||
\(666\) | 52.7015 | 2.04214 | ||||||||
\(667\) | 9.89150 | 0.383000 | ||||||||
\(668\) | 0.915736i | 0.0354309i | ||||||||
\(669\) | 23.4321i | 0.905936i | ||||||||
\(670\) | − 11.8614i | − 0.458247i | ||||||||
\(671\) | − 8.98302i | − 0.346786i | ||||||||
\(672\) | −2.97811 | −0.114883 | ||||||||
\(673\) | −33.1395 | −1.27743 | −0.638717 | − | 0.769442i | \(-0.720534\pi\) | ||||
−0.638717 | + | 0.769442i | \(0.720534\pi\) | |||||||
\(674\) | − 19.0373i | − 0.733291i | ||||||||
\(675\) | 82.9079 | 3.19112 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8217 | 1.10771 | 0.553854 | − | 0.832614i | \(-0.313157\pi\) | ||||
0.553854 | + | 0.832614i | \(0.313157\pi\) | |||||||
\(678\) | 6.67005i | 0.256162i | ||||||||
\(679\) | 7.88255 | 0.302505 | ||||||||
\(680\) | 12.7455 | 0.488768 | ||||||||
\(681\) | 10.7570i | 0.412207i | ||||||||
\(682\) | − 3.64227i | − 0.139470i | ||||||||
\(683\) | 17.0467i | 0.652274i | 0.945323 | + | 0.326137i | \(0.105747\pi\) | ||||
−0.945323 | + | 0.326137i | \(0.894253\pi\) | |||||||
\(684\) | − 3.98018i | − 0.152186i | ||||||||
\(685\) | −5.78462 | −0.221019 | ||||||||
\(686\) | 1.35819 | 0.0518559 | ||||||||
\(687\) | − 79.3948i | − 3.02910i | ||||||||
\(688\) | 9.69722 | 0.369703 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.42628 | 0.168505 | ||||||||
\(691\) | − 3.56418i | − 0.135588i | −0.997699 | − | 0.0677939i | \(-0.978404\pi\) | ||||
0.997699 | − | 0.0677939i | \(-0.0215960\pi\) | |||||||
\(692\) | −0.874636 | −0.0332487 | ||||||||
\(693\) | 18.0762 | 0.686659 | ||||||||
\(694\) | − 25.0377i | − 0.950418i | ||||||||
\(695\) | 2.45464i | 0.0931099i | ||||||||
\(696\) | − 79.2203i | − 3.00284i | ||||||||
\(697\) | 55.3702i | 2.09729i | ||||||||
\(698\) | −1.14289 | −0.0432590 | ||||||||
\(699\) | 32.7930 | 1.24034 | ||||||||
\(700\) | 0.683922i | 0.0258498i | ||||||||
\(701\) | −5.75672 | −0.217428 | −0.108714 | − | 0.994073i | \(-0.534673\pi\) | ||||
−0.108714 | + | 0.994073i | \(0.534673\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.6270 | −0.513951 | ||||||||
\(704\) | 18.0315i | 0.679590i | ||||||||
\(705\) | −20.1741 | −0.759802 | ||||||||
\(706\) | −5.87235 | −0.221009 | ||||||||
\(707\) | − 1.76856i | − 0.0665134i | ||||||||
\(708\) | − 2.64117i | − 0.0992613i | ||||||||
\(709\) | − 5.47541i | − 0.205633i | −0.994700 | − | 0.102817i | \(-0.967214\pi\) | ||||
0.994700 | − | 0.102817i | \(-0.0327855\pi\) | |||||||
\(710\) | 12.4828i | 0.468470i | ||||||||
\(711\) | −53.8164 | −2.01827 | ||||||||
\(712\) | 5.77216 | 0.216321 | ||||||||
\(713\) | 1.57367i | 0.0589343i | ||||||||
\(714\) | 26.0073 | 0.973299 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.11534 | −0.0416823 | ||||||||
\(717\) | 23.7210i | 0.885876i | ||||||||
\(718\) | −16.4238 | −0.612930 | ||||||||
\(719\) | 45.1042 | 1.68210 | 0.841051 | − | 0.540955i | \(-0.181937\pi\) | ||||
0.841051 | + | 0.540955i | \(0.181937\pi\) | |||||||
\(720\) | − 24.1859i | − 0.901354i | ||||||||
\(721\) | 11.4598i | 0.426787i | ||||||||
\(722\) | 13.5829i | 0.505503i | ||||||||
\(723\) | − 63.0525i | − 2.34495i | ||||||||
\(724\) | 0.0881337 | 0.00327546 | ||||||||
\(725\) | −35.0748 | −1.30264 | ||||||||
\(726\) | 30.0945i | 1.11691i | ||||||||
\(727\) | −35.7464 | −1.32576 | −0.662880 | − | 0.748725i | \(-0.730666\pi\) | ||||
−0.662880 | + | 0.748725i | \(0.730666\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 135.617 | 5.02285 | ||||||||
\(730\) | − 9.43584i | − 0.349236i | ||||||||
\(731\) | 14.9121 | 0.551542 | ||||||||
\(732\) | 2.24005 | 0.0827946 | ||||||||
\(733\) | − 30.7972i | − 1.13752i | −0.822503 | − | 0.568761i | \(-0.807423\pi\) | ||||
0.822503 | − | 0.568761i | \(-0.192577\pi\) | |||||||
\(734\) | − 12.3013i | − 0.454050i | ||||||||
\(735\) | − 2.62444i | − 0.0968039i | ||||||||
\(736\) | − 1.08853i | − 0.0401236i | ||||||||
\(737\) | 23.9234 | 0.881231 | ||||||||
\(738\) | 113.975 | 4.19550 | ||||||||
\(739\) | 38.1399i | 1.40300i | 0.712670 | + | 0.701499i | \(0.247486\pi\) | ||||
−0.712670 | + | 0.701499i | \(0.752514\pi\) | |||||||
\(740\) | 0.545031 | 0.0200357 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.476581 | 0.0174959 | ||||||||
\(743\) | − 19.8187i | − 0.727079i | −0.931579 | − | 0.363539i | \(-0.881568\pi\) | ||||
0.931579 | − | 0.363539i | \(-0.118432\pi\) | |||||||
\(744\) | 12.6034 | 0.462062 | ||||||||
\(745\) | −12.0836 | −0.442708 | ||||||||
\(746\) | − 31.2728i | − 1.14498i | ||||||||
\(747\) | − 25.0096i | − 0.915052i | ||||||||
\(748\) | 1.85253i | 0.0677351i | ||||||||
\(749\) | − 3.29566i | − 0.120421i | ||||||||
\(750\) | −33.5178 | −1.22390 | ||||||||
\(751\) | −11.0353 | −0.402683 | −0.201341 | − | 0.979521i | \(-0.564530\pi\) | ||||
−0.201341 | + | 0.979521i | \(0.564530\pi\) | |||||||
\(752\) | − 28.1747i | − 1.02743i | ||||||||
\(753\) | −56.5910 | −2.06229 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.7636 | −0.428123 | ||||||||
\(756\) | 2.92451i | 0.106364i | ||||||||
\(757\) | −5.63273 | −0.204725 | −0.102363 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102363 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(758\) | −40.1723 | −1.45912 | ||||||||
\(759\) | 8.92741i | 0.324044i | ||||||||
\(760\) | 6.78374i | 0.246072i | ||||||||
\(761\) | − 6.45648i | − 0.234047i | −0.993129 | − | 0.117024i | \(-0.962665\pi\) | ||||
0.993129 | − | 0.117024i | \(-0.0373353\pi\) | |||||||
\(762\) | 50.3991i | 1.82577i | ||||||||
\(763\) | −13.1559 | −0.476277 | ||||||||
\(764\) | −1.23506 | −0.0446830 | ||||||||
\(765\) | − 37.1922i | − 1.34469i | ||||||||
\(766\) | −25.9133 | −0.936285 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.5861 | −0.454162 | ||||||||
\(769\) | 8.81720i | 0.317956i | 0.987282 | + | 0.158978i | \(0.0508199\pi\) | ||||
−0.987282 | + | 0.158978i | \(0.949180\pi\) | |||||||
\(770\) | −2.22021 | −0.0800108 | ||||||||
\(771\) | −25.9441 | −0.934355 | ||||||||
\(772\) | − 3.19571i | − 0.115016i | ||||||||
\(773\) | − 46.0758i | − 1.65723i | −0.559818 | − | 0.828616i | \(-0.689129\pi\) | ||||
0.559818 | − | 0.828616i | \(-0.310871\pi\) | |||||||
\(774\) | − 30.6954i | − 1.10332i | ||||||||
\(775\) | − 5.58014i | − 0.200445i | ||||||||
\(776\) | 23.0749 | 0.828340 | ||||||||
\(777\) | 15.4326 | 0.553642 | ||||||||
\(778\) | 15.4802i | 0.554992i | ||||||||
\(779\) | −29.4705 | −1.05589 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.1766 | −0.900890 | ||||||||
\(782\) | 9.50591i | 0.339931i | ||||||||
\(783\) | −149.983 | −5.35995 | ||||||||
\(784\) | 3.66523 | 0.130901 | ||||||||
\(785\) | − 11.1338i | − 0.397381i | ||||||||
\(786\) | − 10.3395i | − 0.368799i | ||||||||
\(787\) | 2.92457i | 0.104250i | 0.998641 | + | 0.0521248i | \(0.0165994\pi\) | ||||
−0.998641 | + | 0.0521248i | \(0.983401\pi\) | |||||||
\(788\) | − 0.236429i | − 0.00842242i | ||||||||
\(789\) | −63.3129 | −2.25400 | ||||||||
\(790\) | 6.61000 | 0.235173 | ||||||||
\(791\) | 1.44552i | 0.0513970i | ||||||||
\(792\) | 52.9151 | 1.88026 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −39.6166 | −1.40594 | ||||||||
\(795\) | − 0.920902i | − 0.0326610i | ||||||||
\(796\) | −3.93156 | −0.139350 | ||||||||
\(797\) | −34.7197 | −1.22984 | −0.614918 | − | 0.788591i | \(-0.710811\pi\) | ||||
−0.614918 | + | 0.788591i | \(0.710811\pi\) | |||||||
\(798\) | 13.8423i | 0.490011i | ||||||||
\(799\) | − 43.3262i | − 1.53277i | ||||||||
\(800\) | 3.85986i | 0.136467i | ||||||||
\(801\) | − 16.8435i | − 0.595136i | ||||||||
\(802\) | −23.1370 | −0.816997 | ||||||||
\(803\) | 19.0313 | 0.671599 | ||||||||
\(804\) | 5.96567i | 0.210393i | ||||||||
\(805\) | 0.959257 | 0.0338094 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 84.4528 | 2.97288 | ||||||||
\(808\) | − 5.17716i | − 0.182132i | ||||||||
\(809\) | −36.7435 | −1.29183 | −0.645917 | − | 0.763407i | \(-0.723525\pi\) | ||||
−0.645917 | + | 0.763407i | \(0.723525\pi\) | |||||||
\(810\) | −40.2278 | −1.41346 | ||||||||
\(811\) | − 49.5717i | − 1.74070i | −0.492437 | − | 0.870348i | \(-0.663894\pi\) | ||||
0.492437 | − | 0.870348i | \(-0.336106\pi\) | |||||||
\(812\) | − 1.23724i | − 0.0434185i | ||||||||
\(813\) | − 74.9183i | − 2.62750i | ||||||||
\(814\) | − 13.0556i | − 0.457598i | ||||||||
\(815\) | 8.25603 | 0.289196 | ||||||||
\(816\) | 70.1838 | 2.45692 | ||||||||
\(817\) | 7.93687i | 0.277676i | ||||||||
\(818\) | 9.79254 | 0.342388 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.17872 | 0.0411626 | ||||||||
\(821\) | 31.7074i | 1.10660i | 0.832983 | + | 0.553299i | \(0.186631\pi\) | ||||
−0.832983 | + | 0.553299i | \(0.813369\pi\) | |||||||
\(822\) | −34.5529 | −1.20517 | ||||||||
\(823\) | 28.7128 | 1.00086 | 0.500432 | − | 0.865776i | \(-0.333174\pi\) | ||||
0.500432 | + | 0.865776i | \(0.333174\pi\) | |||||||
\(824\) | 33.5468i | 1.16866i | ||||||||
\(825\) | − 31.6561i | − 1.10213i | ||||||||
\(826\) | 6.79800i | 0.236533i | ||||||||
\(827\) | 30.8034i | 1.07114i | 0.844491 | + | 0.535569i | \(0.179903\pi\) | ||||
−0.844491 | + | 0.535569i | \(0.820097\pi\) | |||||||
\(828\) | −1.64756 | −0.0572566 | ||||||||
\(829\) | −30.9789 | −1.07594 | −0.537970 | − | 0.842964i | \(-0.680809\pi\) | ||||
−0.537970 | + | 0.842964i | \(0.680809\pi\) | |||||||
\(830\) | 3.07180i | 0.106624i | ||||||||
\(831\) | 66.9753 | 2.32335 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.63627 | 0.195285 | ||||||||
\(834\) | 14.6622i | 0.507710i | ||||||||
\(835\) | −4.55440 | −0.157612 | ||||||||
\(836\) | −0.985998 | −0.0341015 | ||||||||
\(837\) | − 23.8612i | − 0.824764i | ||||||||
\(838\) | 46.4369i | 1.60414i | ||||||||
\(839\) | − 48.0432i | − 1.65863i | −0.558778 | − | 0.829317i | \(-0.688730\pi\) | ||||
0.558778 | − | 0.829317i | \(-0.311270\pi\) | |||||||
\(840\) | − 7.68261i | − 0.265075i | ||||||||
\(841\) | 34.4514 | 1.18798 | ||||||||
\(842\) | 45.3001 | 1.56114 | ||||||||
\(843\) | 15.0166i | 0.517198i | ||||||||
\(844\) | 0.861113 | 0.0296407 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −89.1838 | −3.06620 | ||||||||
\(847\) | 6.52203i | 0.224100i | ||||||||
\(848\) | 1.28611 | 0.0441652 | ||||||||
\(849\) | 108.482 | 3.72310 | ||||||||
\(850\) | − 33.7075i | − 1.15616i | ||||||||
\(851\) | 5.64076i | 0.193363i | ||||||||
\(852\) | − 6.27816i | − 0.215086i | ||||||||
\(853\) | − 10.1693i | − 0.348189i | −0.984729 | − | 0.174095i | \(-0.944300\pi\) | ||||
0.984729 | − | 0.174095i | \(-0.0556998\pi\) | |||||||
\(854\) | −5.76557 | −0.197294 | ||||||||
\(855\) | 19.7954 | 0.676988 | ||||||||
\(856\) | − 9.64749i | − 0.329744i | ||||||||
\(857\) | 4.52581 | 0.154599 | 0.0772993 | − | 0.997008i | \(-0.475370\pi\) | ||||
0.0772993 | + | 0.997008i | \(0.475370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8293 | 1.01776 | 0.508881 | − | 0.860837i | \(-0.330059\pi\) | ||||
0.508881 | + | 0.860837i | \(0.330059\pi\) | |||||||
\(860\) | − 0.317447i | − 0.0108249i | ||||||||
\(861\) | 33.3755 | 1.13743 | ||||||||
\(862\) | 43.2749 | 1.47395 | ||||||||
\(863\) | − 34.3352i | − 1.16879i | −0.811471 | − | 0.584393i | \(-0.801333\pi\) | ||||
0.811471 | − | 0.584393i | \(-0.198667\pi\) | |||||||
\(864\) | 16.5051i | 0.561516i | ||||||||
\(865\) | − 4.34999i | − 0.147904i | ||||||||
\(866\) | − 3.66403i | − 0.124509i | ||||||||
\(867\) | 50.1709 | 1.70389 | ||||||||
\(868\) | 0.196835 | 0.00668103 | ||||||||
\(869\) | 13.3318i | 0.452249i | ||||||||
\(870\) | 28.3934 | 0.962626 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −38.5118 | −1.30417 | ||||||||
\(873\) | − 67.3340i | − 2.27891i | ||||||||
\(874\) | −5.05947 | −0.171139 | ||||||||
\(875\) | −7.26393 | −0.245566 | ||||||||
\(876\) | 4.74573i | 0.160343i | ||||||||
\(877\) | 29.0504i | 0.980963i | 0.871452 | + | 0.490481i | \(0.163179\pi\) | ||||
−0.871452 | + | 0.490481i | \(0.836821\pi\) | |||||||
\(878\) | 29.2318i | 0.986524i | ||||||||
\(879\) | − 55.1976i | − 1.86177i | ||||||||
\(880\) | −5.99149 | −0.201973 | ||||||||
\(881\) | −18.4225 | −0.620669 | −0.310335 | − | 0.950627i | \(-0.600441\pi\) | ||||
−0.310335 | + | 0.950627i | \(0.600441\pi\) | |||||||
\(882\) | − 11.6019i | − 0.390655i | ||||||||
\(883\) | −33.6175 | −1.13132 | −0.565659 | − | 0.824639i | \(-0.691378\pi\) | ||||
−0.565659 | + | 0.824639i | \(0.691378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.1358 | 0.441556 | ||||||||
\(886\) | 9.16554i | 0.307922i | ||||||||
\(887\) | 35.9829 | 1.20819 | 0.604094 | − | 0.796913i | \(-0.293535\pi\) | ||||
0.604094 | + | 0.796913i | \(0.293535\pi\) | |||||||
\(888\) | 45.1764 | 1.51602 | ||||||||
\(889\) | 10.9224i | 0.366327i | ||||||||
\(890\) | 2.06880i | 0.0693465i | ||||||||
\(891\) | − 81.1360i | − 2.71816i | ||||||||
\(892\) | 1.07127i | 0.0358688i | ||||||||
\(893\) | 23.0601 | 0.771678 | ||||||||
\(894\) | −72.1781 | −2.41400 | ||||||||
\(895\) | − 5.54714i | − 0.185420i | ||||||||
\(896\) | 9.82000 | 0.328063 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 44.0032 | 1.46841 | ||||||||
\(899\) | 10.0947i | 0.336676i | ||||||||
\(900\) | 5.84216 | 0.194739 | ||||||||
\(901\) | 1.97774 | 0.0658880 | ||||||||
\(902\) | − 28.2348i | − 0.940116i | ||||||||
\(903\) | − 8.98854i | − 0.299120i | ||||||||
\(904\) | 4.23154i | 0.140739i | ||||||||
\(905\) | 0.438332i | 0.0145706i | ||||||||
\(906\) | −70.2671 | −2.33447 | ||||||||
\(907\) | 26.2877 | 0.872868 | 0.436434 | − | 0.899736i | \(-0.356241\pi\) | ||||
0.436434 | + | 0.899736i | \(0.356241\pi\) | |||||||
\(908\) | 0.491788i | 0.0163206i | ||||||||
\(909\) | −15.1073 | −0.501077 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.8689 | −1.32092 | −0.660458 | − | 0.750863i | \(-0.729638\pi\) | ||||
−0.660458 | + | 0.750863i | \(0.729638\pi\) | |||||||
\(912\) | 37.3550i | 1.23695i | ||||||||
\(913\) | −6.19554 | −0.205043 | ||||||||
\(914\) | 7.16989 | 0.237159 | ||||||||
\(915\) | 11.1409i | 0.368306i | ||||||||
\(916\) | − 3.62978i | − 0.119931i | ||||||||
\(917\) | − 2.24077i | − 0.0739969i | ||||||||
\(918\) | − 144.136i | − 4.75721i | ||||||||
\(919\) | −27.5349 | −0.908292 | −0.454146 | − | 0.890927i | \(-0.650056\pi\) | ||||
−0.454146 | + | 0.890927i | \(0.650056\pi\) | |||||||
\(920\) | 2.80807 | 0.0925792 | ||||||||
\(921\) | − 45.8822i | − 1.51187i | ||||||||
\(922\) | −54.2443 | −1.78644 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.11665 | 0.0367350 | ||||||||
\(925\) | − 20.0018i | − 0.657657i | ||||||||
\(926\) | −9.54542 | −0.313682 | ||||||||
\(927\) | 97.8916 | 3.21518 | ||||||||
\(928\) | − 6.98261i | − 0.229215i | ||||||||
\(929\) | − 14.5572i | − 0.477607i | −0.971068 | − | 0.238804i | \(-0.923245\pi\) | ||||
0.971068 | − | 0.238804i | \(-0.0767552\pi\) | |||||||
\(930\) | 4.51719i | 0.148124i | ||||||||
\(931\) | 2.99988i | 0.0983170i | ||||||||
\(932\) | 1.49924 | 0.0491091 | ||||||||
\(933\) | −7.69308 | −0.251860 | ||||||||
\(934\) | 17.2656i | 0.564949i | ||||||||
\(935\) | −9.21352 | −0.301314 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.11811 | −0.0365270 | −0.0182635 | − | 0.999833i | \(-0.505814\pi\) | ||||
−0.0182635 | + | 0.999833i | \(0.505814\pi\) | |||||||
\(938\) | − 15.3548i | − 0.501351i | ||||||||
\(939\) | 68.4184 | 2.23275 | ||||||||
\(940\) | −0.922325 | −0.0300829 | ||||||||
\(941\) | 30.8810i | 1.00669i | 0.864085 | + | 0.503346i | \(0.167898\pi\) | ||||
−0.864085 | + | 0.503346i | \(0.832102\pi\) | |||||||
\(942\) | − 66.5047i | − 2.16684i | ||||||||
\(943\) | 12.1990i | 0.397255i | ||||||||
\(944\) | 18.3452i | 0.597085i | ||||||||
\(945\) | −14.5450 | −0.473150 | ||||||||
\(946\) | −7.60408 | −0.247230 | ||||||||
\(947\) | − 20.2675i | − 0.658604i | −0.944225 | − | 0.329302i | \(-0.893187\pi\) | ||||
0.944225 | − | 0.329302i | \(-0.106813\pi\) | |||||||
\(948\) | −3.32448 | −0.107974 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 17.9406 | 0.582071 | ||||||||
\(951\) | 106.365i | 3.44911i | ||||||||
\(952\) | 16.4993 | 0.534744 | ||||||||
\(953\) | −30.7177 | −0.995043 | −0.497522 | − | 0.867452i | \(-0.665757\pi\) | ||||
−0.497522 | + | 0.867452i | \(0.665757\pi\) | |||||||
\(954\) | − 4.07103i | − 0.131804i | ||||||||
\(955\) | − 6.14256i | − 0.198769i | ||||||||
\(956\) | 1.08448i | 0.0350746i | ||||||||
\(957\) | 57.2670i | 1.85118i | ||||||||
\(958\) | 32.5158 | 1.05054 | ||||||||
\(959\) | −7.48827 | −0.241809 | ||||||||
\(960\) | − 22.3630i | − 0.721761i | ||||||||
\(961\) | 29.3940 | 0.948194 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.1520 | −0.907185 | ||||||||
\(964\) | − 2.88265i | − 0.0928438i | ||||||||
\(965\) | 15.8938 | 0.511640 | ||||||||
\(966\) | 5.72988 | 0.184356 | ||||||||
\(967\) | − 20.0281i | − 0.644060i | −0.946729 | − | 0.322030i | \(-0.895635\pi\) | ||||
0.946729 | − | 0.322030i | \(-0.104365\pi\) | |||||||
\(968\) | 19.0922i | 0.613646i | ||||||||
\(969\) | 57.4432i | 1.84534i | ||||||||
\(970\) | 8.27029i | 0.265543i | ||||||||
\(971\) | −9.01006 | −0.289146 | −0.144573 | − | 0.989494i | \(-0.546181\pi\) | ||||
−0.144573 | + | 0.989494i | \(0.546181\pi\) | |||||||
\(972\) | 11.4589 | 0.367545 | ||||||||
\(973\) | 3.17757i | 0.101868i | ||||||||
\(974\) | −14.5272 | −0.465483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.5591 | −0.498034 | ||||||||
\(977\) | 15.4962i | 0.495766i | 0.968790 | + | 0.247883i | \(0.0797349\pi\) | ||||
−0.968790 | + | 0.247883i | \(0.920265\pi\) | |||||||
\(978\) | 49.3153 | 1.57693 | ||||||||
\(979\) | −4.17259 | −0.133357 | ||||||||
\(980\) | − 0.119985i | − 0.00383277i | ||||||||
\(981\) | 112.380i | 3.58801i | ||||||||
\(982\) | − 18.7908i | − 0.599639i | ||||||||
\(983\) | 45.8307i | 1.46177i | 0.682499 | + | 0.730886i | \(0.260893\pi\) | ||||
−0.682499 | + | 0.730886i | \(0.739107\pi\) | |||||||
\(984\) | 97.7012 | 3.11460 | ||||||||
\(985\) | 1.17587 | 0.0374665 | ||||||||
\(986\) | 60.9779i | 1.94193i | ||||||||
\(987\) | −26.1157 | −0.831272 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.28539 | 0.104469 | ||||||||
\(990\) | 18.9654i | 0.602759i | ||||||||
\(991\) | 5.91658 | 0.187946 | 0.0939731 | − | 0.995575i | \(-0.470043\pi\) | ||||
0.0939731 | + | 0.995575i | \(0.470043\pi\) | |||||||
\(992\) | 1.11088 | 0.0352706 | ||||||||
\(993\) | 19.9111i | 0.631858i | ||||||||
\(994\) | 16.1591i | 0.512536i | ||||||||
\(995\) | − 19.5536i | − 0.619889i | ||||||||
\(996\) | − 1.54495i | − 0.0489536i | ||||||||
\(997\) | 27.0852 | 0.857798 | 0.428899 | − | 0.903352i | \(-0.358902\pi\) | ||||
0.428899 | + | 0.903352i | \(0.358902\pi\) | |||||||
\(998\) | −19.8369 | −0.627925 | ||||||||
\(999\) | − 85.5298i | − 2.70604i |
(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 | 1183.2.c.j.337.18 | 24 | ||
13.5 | odd | 4 | 1183.2.a.q.1.10 | ✓ | 12 | ||
13.8 | odd | 4 | 1183.2.a.r.1.3 | yes | 12 | ||
13.12 | even | 2 | inner | 1183.2.c.j.337.7 | 24 | ||
91.34 | even | 4 | 8281.2.a.cq.1.3 | 12 | |||
91.83 | even | 4 | 8281.2.a.cn.1.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.q.1.10 | ✓ | 12 | 13.5 | odd | 4 | ||
1183.2.a.r.1.3 | yes | 12 | 13.8 | odd | 4 | ||
1183.2.c.j.337.7 | 24 | 13.12 | even | 2 | inner | ||
1183.2.c.j.337.18 | 24 | 1.1 | even | 1 | trivial | ||
8281.2.a.cn.1.10 | 12 | 91.83 | even | 4 | |||
8281.2.a.cq.1.3 | 12 | 91.34 | even | 4 |