Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + 130215 x^{8} - 239606 x^{7} + 378750 x^{6} - 477124 x^{5} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.10 | ||
Root | \(0.500000 + 3.32851i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.a.2155.7 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 2.46248i | − | 1.10126i | −0.834751 | − | 0.550628i | \(-0.814388\pi\) | ||
0.834751 | − | 0.550628i | \(-0.185612\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.46248 | 0.778705 | ||||||||
\(11\) | 3.20979 | − | 0.834997i | 0.967789 | − | 0.251761i | ||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −1.32035 | −0.366201 | −0.183100 | − | 0.983094i | \(-0.558613\pi\) | ||||
−0.183100 | + | 0.983094i | \(0.558613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.46248 | 0.635810 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.47479 | 1.08529 | 0.542647 | − | 0.839961i | \(-0.317422\pi\) | ||||
0.542647 | + | 0.839961i | \(0.317422\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 4.43177 | 1.01672 | 0.508359 | − | 0.861145i | \(-0.330252\pi\) | ||||
0.508359 | + | 0.861145i | \(0.330252\pi\) | |||||||
\(20\) | 2.46248i | 0.550628i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.834997 | + | 3.20979i | 0.178022 | + | 0.684330i | ||||
\(23\) | −8.28995 | −1.72857 | −0.864287 | − | 0.502999i | \(-0.832230\pi\) | ||||
−0.864287 | + | 0.502999i | \(0.832230\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.06381 | −0.212763 | ||||||||
\(26\) | − | 1.32035i | − | 0.258943i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.44409i | − | 0.268162i | −0.990970 | − | 0.134081i | \(-0.957192\pi\) | ||
0.990970 | − | 0.134081i | \(-0.0428082\pi\) | |||||||
\(30\) | 2.46248i | 0.449585i | ||||||||
\(31\) | − | 2.71125i | − | 0.486955i | −0.969907 | − | 0.243477i | \(-0.921712\pi\) | ||
0.969907 | − | 0.243477i | \(-0.0782881\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.834997 | + | 3.20979i | 0.145354 | + | 0.558753i | ||||
\(34\) | 4.47479i | 0.767419i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.93126 | −0.810695 | −0.405347 | − | 0.914163i | \(-0.632849\pi\) | ||||
−0.405347 | + | 0.914163i | \(0.632849\pi\) | |||||||
\(38\) | 4.43177i | 0.718929i | ||||||||
\(39\) | − | 1.32035i | − | 0.211426i | ||||||
\(40\) | −2.46248 | −0.389352 | ||||||||
\(41\) | −8.18233 | −1.27787 | −0.638933 | − | 0.769263i | \(-0.720624\pi\) | ||||
−0.638933 | + | 0.769263i | \(0.720624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.63797i | − | 1.46978i | −0.678188 | − | 0.734888i | \(-0.737235\pi\) | ||
0.678188 | − | 0.734888i | \(-0.262765\pi\) | |||||||
\(44\) | −3.20979 | + | 0.834997i | −0.483895 | + | 0.125881i | ||||
\(45\) | 2.46248i | 0.367085i | ||||||||
\(46\) | − | 8.28995i | − | 1.22229i | ||||||
\(47\) | − | 0.767488i | − | 0.111950i | −0.998432 | − | 0.0559748i | \(-0.982173\pi\) | ||
0.998432 | − | 0.0559748i | \(-0.0178266\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 1.06381i | − | 0.150446i | ||||||
\(51\) | 4.47479i | 0.626595i | ||||||||
\(52\) | 1.32035 | 0.183100 | ||||||||
\(53\) | −1.89194 | −0.259878 | −0.129939 | − | 0.991522i | \(-0.541478\pi\) | ||||
−0.129939 | + | 0.991522i | \(0.541478\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.05616 | − | 7.90406i | −0.277253 | − | 1.06578i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.43177i | 0.587003i | ||||||||
\(58\) | 1.44409 | 0.189619 | ||||||||
\(59\) | − | 7.78781i | − | 1.01389i | −0.861980 | − | 0.506943i | \(-0.830775\pi\) | ||
0.861980 | − | 0.506943i | \(-0.169225\pi\) | |||||||
\(60\) | −2.46248 | −0.317905 | ||||||||
\(61\) | 4.47886 | 0.573459 | 0.286729 | − | 0.958012i | \(-0.407432\pi\) | ||||
0.286729 | + | 0.958012i | \(0.407432\pi\) | |||||||
\(62\) | 2.71125 | 0.344329 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.25135i | 0.403280i | ||||||||
\(66\) | −3.20979 | + | 0.834997i | −0.395098 | + | 0.102781i | ||||
\(67\) | −1.72369 | −0.210582 | −0.105291 | − | 0.994441i | \(-0.533577\pi\) | ||||
−0.105291 | + | 0.994441i | \(0.533577\pi\) | |||||||
\(68\) | −4.47479 | −0.542647 | ||||||||
\(69\) | − | 8.28995i | − | 0.997992i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3771 | −1.23153 | −0.615766 | − | 0.787929i | \(-0.711153\pi\) | ||||
−0.615766 | + | 0.787929i | \(0.711153\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 11.1724 | 1.30764 | 0.653818 | − | 0.756652i | \(-0.273166\pi\) | ||||
0.653818 | + | 0.756652i | \(0.273166\pi\) | |||||||
\(74\) | − | 4.93126i | − | 0.573248i | ||||||
\(75\) | − | 1.06381i | − | 0.122839i | ||||||
\(76\) | −4.43177 | −0.508359 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.32035 | 0.149501 | ||||||||
\(79\) | 2.92867i | 0.329501i | 0.986335 | + | 0.164750i | \(0.0526819\pi\) | ||||
−0.986335 | + | 0.164750i | \(0.947318\pi\) | |||||||
\(80\) | − | 2.46248i | − | 0.275314i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 8.18233i | − | 0.903587i | ||||||
\(83\) | 10.1118 | 1.10991 | 0.554957 | − | 0.831879i | \(-0.312735\pi\) | ||||
0.554957 | + | 0.831879i | \(0.312735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 11.0191i | − | 1.19519i | ||||||
\(86\) | 9.63797 | 1.03929 | ||||||||
\(87\) | 1.44409 | 0.154823 | ||||||||
\(88\) | −0.834997 | − | 3.20979i | −0.0890110 | − | 0.342165i | ||||
\(89\) | − | 12.6544i | − | 1.34136i | −0.741745 | − | 0.670682i | \(-0.766002\pi\) | ||
0.741745 | − | 0.670682i | \(-0.233998\pi\) | |||||||
\(90\) | −2.46248 | −0.259568 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.28995 | 0.864287 | ||||||||
\(93\) | 2.71125 | 0.281143 | ||||||||
\(94\) | 0.767488 | 0.0791603 | ||||||||
\(95\) | − | 10.9132i | − | 1.11967i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.37808i | 0.139923i | 0.997550 | + | 0.0699613i | \(0.0222876\pi\) | ||||
−0.997550 | + | 0.0699613i | \(0.977712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.20979 | + | 0.834997i | −0.322596 | + | 0.0839204i | ||||
\(100\) | 1.06381 | 0.106381 | ||||||||
\(101\) | 7.56722 | 0.752967 | 0.376483 | − | 0.926423i | \(-0.377133\pi\) | ||||
0.376483 | + | 0.926423i | \(0.377133\pi\) | |||||||
\(102\) | −4.47479 | −0.443070 | ||||||||
\(103\) | 16.4958i | 1.62538i | 0.582697 | + | 0.812690i | \(0.301998\pi\) | ||||
−0.582697 | + | 0.812690i | \(0.698002\pi\) | |||||||
\(104\) | 1.32035i | 0.129471i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 1.89194i | − | 0.183762i | ||||||
\(107\) | − | 5.76864i | − | 0.557675i | −0.960338 | − | 0.278838i | \(-0.910051\pi\) | ||
0.960338 | − | 0.278838i | \(-0.0899492\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | − | 8.63196i | − | 0.826792i | −0.910551 | − | 0.413396i | \(-0.864342\pi\) | ||
0.910551 | − | 0.413396i | \(-0.135658\pi\) | |||||||
\(110\) | 7.90406 | − | 2.05616i | 0.753622 | − | 0.196048i | ||||
\(111\) | − | 4.93126i | − | 0.468055i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.4933 | 1.64563 | 0.822817 | − | 0.568306i | \(-0.192401\pi\) | ||||
0.822817 | + | 0.568306i | \(0.192401\pi\) | |||||||
\(114\) | −4.43177 | −0.415074 | ||||||||
\(115\) | 20.4138i | 1.90360i | ||||||||
\(116\) | 1.44409i | 0.134081i | ||||||||
\(117\) | 1.32035 | 0.122067 | ||||||||
\(118\) | 7.78781 | 0.716926 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 2.46248i | − | 0.224793i | ||||||
\(121\) | 9.60556 | − | 5.36034i | 0.873233 | − | 0.487303i | ||||
\(122\) | 4.47886i | 0.405497i | ||||||||
\(123\) | − | 8.18233i | − | 0.737776i | ||||||
\(124\) | 2.71125i | 0.243477i | ||||||||
\(125\) | − | 9.69279i | − | 0.866949i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.0959i | − | 1.07333i | −0.843794 | − | 0.536667i | \(-0.819683\pi\) | ||
0.843794 | − | 0.536667i | \(-0.180317\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 9.63797 | 0.848576 | ||||||||
\(130\) | −3.25135 | −0.285162 | ||||||||
\(131\) | −17.2415 | −1.50640 | −0.753200 | − | 0.657792i | \(-0.771491\pi\) | ||||
−0.753200 | + | 0.657792i | \(0.771491\pi\) | |||||||
\(132\) | −0.834997 | − | 3.20979i | −0.0726772 | − | 0.279377i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.72369i | − | 0.148904i | ||||||
\(135\) | −2.46248 | −0.211937 | ||||||||
\(136\) | − | 4.47479i | − | 0.383710i | ||||||
\(137\) | 2.50957 | 0.214407 | 0.107204 | − | 0.994237i | \(-0.465810\pi\) | ||||
0.107204 | + | 0.994237i | \(0.465810\pi\) | |||||||
\(138\) | 8.28995 | 0.705687 | ||||||||
\(139\) | 19.9532 | 1.69241 | 0.846206 | − | 0.532856i | \(-0.178881\pi\) | ||||
0.846206 | + | 0.532856i | \(0.178881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.767488 | 0.0646341 | ||||||||
\(142\) | − | 10.3771i | − | 0.870824i | ||||||
\(143\) | −4.23807 | + | 1.10249i | −0.354405 | + | 0.0921951i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −3.55606 | −0.295314 | ||||||||
\(146\) | 11.1724i | 0.924638i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.93126 | 0.405347 | ||||||||
\(149\) | − | 9.78029i | − | 0.801232i | −0.916246 | − | 0.400616i | \(-0.868796\pi\) | ||
0.916246 | − | 0.400616i | \(-0.131204\pi\) | |||||||
\(150\) | 1.06381 | 0.0868600 | ||||||||
\(151\) | − | 2.67337i | − | 0.217556i | −0.994066 | − | 0.108778i | \(-0.965306\pi\) | ||
0.994066 | − | 0.108778i | \(-0.0346937\pi\) | |||||||
\(152\) | − | 4.43177i | − | 0.359464i | ||||||
\(153\) | −4.47479 | −0.361765 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.67640 | −0.536261 | ||||||||
\(156\) | 1.32035i | 0.105713i | ||||||||
\(157\) | − | 15.8345i | − | 1.26373i | −0.775079 | − | 0.631865i | \(-0.782290\pi\) | ||
0.775079 | − | 0.631865i | \(-0.217710\pi\) | |||||||
\(158\) | −2.92867 | −0.232992 | ||||||||
\(159\) | − | 1.89194i | − | 0.150041i | ||||||
\(160\) | 2.46248 | 0.194676 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −20.3615 | −1.59484 | −0.797418 | − | 0.603428i | \(-0.793801\pi\) | ||||
−0.797418 | + | 0.603428i | \(0.793801\pi\) | |||||||
\(164\) | 8.18233 | 0.638933 | ||||||||
\(165\) | 7.90406 | − | 2.05616i | 0.615330 | − | 0.160072i | ||||
\(166\) | 10.1118i | 0.784827i | ||||||||
\(167\) | 16.1119 | 1.24678 | 0.623389 | − | 0.781912i | \(-0.285755\pi\) | ||||
0.623389 | + | 0.781912i | \(0.285755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2567 | −0.865897 | ||||||||
\(170\) | 11.0191 | 0.845124 | ||||||||
\(171\) | −4.43177 | −0.338906 | ||||||||
\(172\) | 9.63797i | 0.734888i | ||||||||
\(173\) | 7.24694 | 0.550975 | 0.275487 | − | 0.961305i | \(-0.411161\pi\) | ||||
0.275487 | + | 0.961305i | \(0.411161\pi\) | |||||||
\(174\) | 1.44409i | 0.109477i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.20979 | − | 0.834997i | 0.241947 | − | 0.0629403i | ||||
\(177\) | 7.78781 | 0.585367 | ||||||||
\(178\) | 12.6544 | 0.948487 | ||||||||
\(179\) | 11.6016 | 0.867141 | 0.433571 | − | 0.901120i | \(-0.357253\pi\) | ||||
0.433571 | + | 0.901120i | \(0.357253\pi\) | |||||||
\(180\) | − | 2.46248i | − | 0.183543i | ||||||
\(181\) | 7.74423i | 0.575624i | 0.957687 | + | 0.287812i | \(0.0929279\pi\) | ||||
−0.957687 | + | 0.287812i | \(0.907072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.47886i | 0.331087i | ||||||||
\(184\) | 8.28995i | 0.611143i | ||||||||
\(185\) | 12.1431i | 0.892782i | ||||||||
\(186\) | 2.71125i | 0.198798i | ||||||||
\(187\) | 14.3631 | − | 3.73643i | 1.05034 | − | 0.273235i | ||||
\(188\) | 0.767488i | 0.0559748i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.9132 | 0.791724 | ||||||||
\(191\) | −21.2314 | −1.53625 | −0.768125 | − | 0.640300i | \(-0.778810\pi\) | ||||
−0.768125 | + | 0.640300i | \(0.778810\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 3.51327i | 0.252891i | 0.991974 | + | 0.126445i | \(0.0403569\pi\) | ||||
−0.991974 | + | 0.126445i | \(0.959643\pi\) | |||||||
\(194\) | −1.37808 | −0.0989402 | ||||||||
\(195\) | −3.25135 | −0.232834 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.9715i | − | 1.56540i | −0.622397 | − | 0.782702i | \(-0.713841\pi\) | ||
0.622397 | − | 0.782702i | \(-0.286159\pi\) | |||||||
\(198\) | −0.834997 | − | 3.20979i | −0.0593407 | − | 0.228110i | ||||
\(199\) | − | 1.44180i | − | 0.102206i | −0.998693 | − | 0.0511032i | \(-0.983726\pi\) | ||
0.998693 | − | 0.0511032i | \(-0.0162737\pi\) | |||||||
\(200\) | 1.06381i | 0.0752229i | ||||||||
\(201\) | − | 1.72369i | − | 0.121580i | ||||||
\(202\) | 7.56722i | 0.532428i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 4.47479i | − | 0.313298i | ||||||
\(205\) | 20.1488i | 1.40726i | ||||||||
\(206\) | −16.4958 | −1.14932 | ||||||||
\(207\) | 8.28995 | 0.576191 | ||||||||
\(208\) | −1.32035 | −0.0915501 | ||||||||
\(209\) | 14.2251 | − | 3.70052i | 0.983970 | − | 0.255970i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.163763i | 0.0112739i | 0.999984 | + | 0.00563697i | \(0.00179431\pi\) | ||||
−0.999984 | + | 0.00563697i | \(0.998206\pi\) | |||||||
\(212\) | 1.89194 | 0.129939 | ||||||||
\(213\) | − | 10.3771i | − | 0.711025i | ||||||
\(214\) | 5.76864 | 0.394336 | ||||||||
\(215\) | −23.7333 | −1.61860 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.63196 | 0.584630 | ||||||||
\(219\) | 11.1724i | 0.754964i | ||||||||
\(220\) | 2.05616 | + | 7.90406i | 0.138627 | + | 0.532891i | ||||
\(221\) | −5.90830 | −0.397436 | ||||||||
\(222\) | 4.93126 | 0.330965 | ||||||||
\(223\) | 27.3847i | 1.83382i | 0.399099 | + | 0.916908i | \(0.369323\pi\) | ||||
−0.399099 | + | 0.916908i | \(0.630677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.06381 | 0.0709209 | ||||||||
\(226\) | 17.4933i | 1.16364i | ||||||||
\(227\) | −3.90255 | −0.259021 | −0.129511 | − | 0.991578i | \(-0.541341\pi\) | ||||
−0.129511 | + | 0.991578i | \(0.541341\pi\) | |||||||
\(228\) | − | 4.43177i | − | 0.293501i | ||||||
\(229\) | − | 5.04055i | − | 0.333089i | −0.986034 | − | 0.166544i | \(-0.946739\pi\) | ||
0.986034 | − | 0.166544i | \(-0.0532609\pi\) | |||||||
\(230\) | −20.4138 | −1.34605 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.44409 | −0.0948095 | ||||||||
\(233\) | − | 21.2457i | − | 1.39185i | −0.718113 | − | 0.695927i | \(-0.754994\pi\) | ||
0.718113 | − | 0.695927i | \(-0.245006\pi\) | |||||||
\(234\) | 1.32035i | 0.0863143i | ||||||||
\(235\) | −1.88992 | −0.123285 | ||||||||
\(236\) | 7.78781i | 0.506943i | ||||||||
\(237\) | −2.92867 | −0.190237 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.64110i | − | 0.364893i | −0.983216 | − | 0.182446i | \(-0.941598\pi\) | ||
0.983216 | − | 0.182446i | \(-0.0584016\pi\) | |||||||
\(240\) | 2.46248 | 0.158952 | ||||||||
\(241\) | −7.77466 | −0.500810 | −0.250405 | − | 0.968141i | \(-0.580564\pi\) | ||||
−0.250405 | + | 0.968141i | \(0.580564\pi\) | |||||||
\(242\) | 5.36034 | + | 9.60556i | 0.344576 | + | 0.617469i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −4.47886 | −0.286729 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.18233 | 0.521686 | ||||||||
\(247\) | −5.85152 | −0.372323 | ||||||||
\(248\) | −2.71125 | −0.172164 | ||||||||
\(249\) | 10.1118i | 0.640809i | ||||||||
\(250\) | 9.69279 | 0.613026 | ||||||||
\(251\) | − | 22.5045i | − | 1.42047i | −0.703963 | − | 0.710236i | \(-0.748588\pi\) | ||
0.703963 | − | 0.710236i | \(-0.251412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.6090 | + | 6.92208i | −1.67290 | + | 0.435188i | ||||
\(254\) | 12.0959 | 0.758962 | ||||||||
\(255\) | 11.0191 | 0.690041 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.01578i | 0.188119i | 0.995567 | + | 0.0940597i | \(0.0299845\pi\) | ||||
−0.995567 | + | 0.0940597i | \(0.970016\pi\) | |||||||
\(258\) | 9.63797i | 0.600034i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 3.25135i | − | 0.201640i | ||||||
\(261\) | 1.44409i | 0.0893872i | ||||||||
\(262\) | − | 17.2415i | − | 1.06519i | ||||||
\(263\) | − | 28.1819i | − | 1.73777i | −0.495011 | − | 0.868887i | \(-0.664836\pi\) | ||
0.495011 | − | 0.868887i | \(-0.335164\pi\) | |||||||
\(264\) | 3.20979 | − | 0.834997i | 0.197549 | − | 0.0513905i | ||||
\(265\) | 4.65887i | 0.286192i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.6544 | 0.774437 | ||||||||
\(268\) | 1.72369 | 0.105291 | ||||||||
\(269\) | 0.604546i | 0.0368598i | 0.999830 | + | 0.0184299i | \(0.00586675\pi\) | ||||
−0.999830 | + | 0.0184299i | \(0.994133\pi\) | |||||||
\(270\) | − | 2.46248i | − | 0.149862i | ||||||
\(271\) | 19.7931 | 1.20234 | 0.601172 | − | 0.799120i | \(-0.294701\pi\) | ||||
0.601172 | + | 0.799120i | \(0.294701\pi\) | |||||||
\(272\) | 4.47479 | 0.271324 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.50957i | 0.151609i | ||||||||
\(275\) | −3.41462 | + | 0.888281i | −0.205909 | + | 0.0535654i | ||||
\(276\) | 8.28995i | 0.498996i | ||||||||
\(277\) | − | 2.16446i | − | 0.130050i | −0.997884 | − | 0.0650249i | \(-0.979287\pi\) | ||
0.997884 | − | 0.0650249i | \(-0.0207127\pi\) | |||||||
\(278\) | 19.9532i | 1.19672i | ||||||||
\(279\) | 2.71125i | 0.162318i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.4916i | 1.75932i | 0.475601 | + | 0.879661i | \(0.342231\pi\) | ||||
−0.475601 | + | 0.879661i | \(0.657769\pi\) | |||||||
\(282\) | 0.767488i | 0.0457032i | ||||||||
\(283\) | 28.3880 | 1.68749 | 0.843745 | − | 0.536744i | \(-0.180346\pi\) | ||||
0.843745 | + | 0.536744i | \(0.180346\pi\) | |||||||
\(284\) | 10.3771 | 0.615766 | ||||||||
\(285\) | 10.9132 | 0.646440 | ||||||||
\(286\) | −1.10249 | − | 4.23807i | −0.0651918 | − | 0.250602i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 3.02370 | 0.177865 | ||||||||
\(290\) | − | 3.55606i | − | 0.208819i | ||||||
\(291\) | −1.37808 | −0.0807843 | ||||||||
\(292\) | −11.1724 | −0.653818 | ||||||||
\(293\) | 9.39403 | 0.548805 | 0.274403 | − | 0.961615i | \(-0.411520\pi\) | ||||
0.274403 | + | 0.961615i | \(0.411520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.1773 | −1.11655 | ||||||||
\(296\) | 4.93126i | 0.286624i | ||||||||
\(297\) | −0.834997 | − | 3.20979i | −0.0484515 | − | 0.186251i | ||||
\(298\) | 9.78029 | 0.566557 | ||||||||
\(299\) | 10.9457 | 0.633005 | ||||||||
\(300\) | 1.06381i | 0.0614193i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.67337 | 0.153835 | ||||||||
\(303\) | 7.56722i | 0.434726i | ||||||||
\(304\) | 4.43177 | 0.254180 | ||||||||
\(305\) | − | 11.0291i | − | 0.631524i | ||||||
\(306\) | − | 4.47479i | − | 0.255806i | ||||||
\(307\) | −26.9732 | −1.53944 | −0.769722 | − | 0.638380i | \(-0.779605\pi\) | ||||
−0.769722 | + | 0.638380i | \(0.779605\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.4958 | −0.938413 | ||||||||
\(310\) | − | 6.67640i | − | 0.379194i | ||||||
\(311\) | − | 0.125330i | − | 0.00710683i | −0.999994 | − | 0.00355342i | \(-0.998869\pi\) | ||
0.999994 | − | 0.00355342i | \(-0.00113109\pi\) | |||||||
\(312\) | −1.32035 | −0.0747504 | ||||||||
\(313\) | − | 7.72987i | − | 0.436918i | −0.975846 | − | 0.218459i | \(-0.929897\pi\) | ||
0.975846 | − | 0.218459i | \(-0.0701030\pi\) | |||||||
\(314\) | 15.8345 | 0.893591 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 2.92867i | − | 0.164750i | ||||||
\(317\) | 24.3802 | 1.36933 | 0.684665 | − | 0.728858i | \(-0.259949\pi\) | ||||
0.684665 | + | 0.728858i | \(0.259949\pi\) | |||||||
\(318\) | 1.89194 | 0.106095 | ||||||||
\(319\) | −1.20582 | − | 4.63525i | −0.0675127 | − | 0.259524i | ||||
\(320\) | 2.46248i | 0.137657i | ||||||||
\(321\) | 5.76864 | 0.321974 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.8312 | 1.10344 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 1.40461 | 0.0779138 | ||||||||
\(326\) | − | 20.3615i | − | 1.12772i | ||||||
\(327\) | 8.63196 | 0.477349 | ||||||||
\(328\) | 8.18233i | 0.451794i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.05616 | + | 7.90406i | 0.113188 | + | 0.435104i | ||||
\(331\) | −21.4532 | −1.17918 | −0.589588 | − | 0.807704i | \(-0.700710\pi\) | ||||
−0.589588 | + | 0.807704i | \(0.700710\pi\) | |||||||
\(332\) | −10.1118 | −0.554957 | ||||||||
\(333\) | 4.93126 | 0.270232 | ||||||||
\(334\) | 16.1119i | 0.881606i | ||||||||
\(335\) | 4.24455i | 0.231905i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.0086i | 1.63467i | 0.576163 | + | 0.817335i | \(0.304549\pi\) | ||||
−0.576163 | + | 0.817335i | \(0.695451\pi\) | |||||||
\(338\) | − | 11.2567i | − | 0.612282i | ||||||
\(339\) | 17.4933i | 0.950108i | ||||||||
\(340\) | 11.0191i | 0.597593i | ||||||||
\(341\) | −2.26388 | − | 8.70255i | −0.122596 | − | 0.471269i | ||||
\(342\) | − | 4.43177i | − | 0.239643i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.63797 | −0.519644 | ||||||||
\(345\) | −20.4138 | −1.09904 | ||||||||
\(346\) | 7.24694i | 0.389598i | ||||||||
\(347\) | 34.5340i | 1.85388i | 0.375205 | + | 0.926942i | \(0.377572\pi\) | ||||
−0.375205 | + | 0.926942i | \(0.622428\pi\) | |||||||
\(348\) | −1.44409 | −0.0774116 | ||||||||
\(349\) | −4.77961 | −0.255847 | −0.127923 | − | 0.991784i | \(-0.540831\pi\) | ||||
−0.127923 | + | 0.991784i | \(0.540831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.32035i | 0.0704753i | ||||||||
\(352\) | 0.834997 | + | 3.20979i | 0.0445055 | + | 0.171083i | ||||
\(353\) | − | 13.5771i | − | 0.722634i | −0.932443 | − | 0.361317i | \(-0.882327\pi\) | ||
0.932443 | − | 0.361317i | \(-0.117673\pi\) | |||||||
\(354\) | 7.78781i | 0.413917i | ||||||||
\(355\) | 25.5533i | 1.35623i | ||||||||
\(356\) | 12.6544i | 0.670682i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.6016i | 0.613161i | ||||||||
\(359\) | − | 1.72779i | − | 0.0911890i | −0.998960 | − | 0.0455945i | \(-0.985482\pi\) | ||
0.998960 | − | 0.0455945i | \(-0.0145182\pi\) | |||||||
\(360\) | 2.46248 | 0.129784 | ||||||||
\(361\) | 0.640626 | 0.0337172 | ||||||||
\(362\) | −7.74423 | −0.407028 | ||||||||
\(363\) | 5.36034 | + | 9.60556i | 0.281345 | + | 0.504161i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 27.5119i | − | 1.44004i | ||||||
\(366\) | −4.47886 | −0.234114 | ||||||||
\(367\) | 25.4861i | 1.33036i | 0.746681 | + | 0.665182i | \(0.231646\pi\) | ||||
−0.746681 | + | 0.665182i | \(0.768354\pi\) | |||||||
\(368\) | −8.28995 | −0.432143 | ||||||||
\(369\) | 8.18233 | 0.425955 | ||||||||
\(370\) | −12.1431 | −0.631292 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.71125 | −0.140572 | ||||||||
\(373\) | 33.3334i | 1.72594i | 0.505258 | + | 0.862968i | \(0.331397\pi\) | ||||
−0.505258 | + | 0.862968i | \(0.668603\pi\) | |||||||
\(374\) | 3.73643 | + | 14.3631i | 0.193206 | + | 0.742700i | ||||
\(375\) | 9.69279 | 0.500533 | ||||||||
\(376\) | −0.767488 | −0.0395801 | ||||||||
\(377\) | 1.90672i | 0.0982010i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.2656 | −0.989610 | −0.494805 | − | 0.869004i | \(-0.664760\pi\) | ||||
−0.494805 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(380\) | 10.9132i | 0.559833i | ||||||||
\(381\) | 12.0959 | 0.619690 | ||||||||
\(382\) | − | 21.2314i | − | 1.08629i | ||||||
\(383\) | 5.15509i | 0.263413i | 0.991289 | + | 0.131706i | \(0.0420456\pi\) | ||||
−0.991289 | + | 0.131706i | \(0.957954\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.51327 | −0.178821 | ||||||||
\(387\) | 9.63797i | 0.489925i | ||||||||
\(388\) | − | 1.37808i | − | 0.0699613i | ||||||
\(389\) | −5.16455 | −0.261853 | −0.130927 | − | 0.991392i | \(-0.541795\pi\) | ||||
−0.130927 | + | 0.991392i | \(0.541795\pi\) | |||||||
\(390\) | − | 3.25135i | − | 0.164638i | ||||||
\(391\) | −37.0957 | −1.87601 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 17.2415i | − | 0.869720i | ||||||
\(394\) | 21.9715 | 1.10691 | ||||||||
\(395\) | 7.21179 | 0.362864 | ||||||||
\(396\) | 3.20979 | − | 0.834997i | 0.161298 | − | 0.0419602i | ||||
\(397\) | 6.34291i | 0.318342i | 0.987251 | + | 0.159171i | \(0.0508821\pi\) | ||||
−0.987251 | + | 0.159171i | \(0.949118\pi\) | |||||||
\(398\) | 1.44180 | 0.0722708 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.06381 | −0.0531907 | ||||||||
\(401\) | 22.0015 | 1.09870 | 0.549351 | − | 0.835591i | \(-0.314875\pi\) | ||||
0.549351 | + | 0.835591i | \(0.314875\pi\) | |||||||
\(402\) | 1.72369 | 0.0859698 | ||||||||
\(403\) | 3.57981i | 0.178323i | ||||||||
\(404\) | −7.56722 | −0.376483 | ||||||||
\(405\) | − | 2.46248i | − | 0.122362i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.8283 | + | 4.11759i | −0.784582 | + | 0.204101i | ||||
\(408\) | 4.47479 | 0.221535 | ||||||||
\(409\) | 14.1189 | 0.698136 | 0.349068 | − | 0.937097i | \(-0.386498\pi\) | ||||
0.349068 | + | 0.937097i | \(0.386498\pi\) | |||||||
\(410\) | −20.1488 | −0.995080 | ||||||||
\(411\) | 2.50957i | 0.123788i | ||||||||
\(412\) | − | 16.4958i | − | 0.812690i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.28995i | 0.407429i | ||||||||
\(415\) | − | 24.9001i | − | 1.22230i | ||||||
\(416\) | − | 1.32035i | − | 0.0647357i | ||||||
\(417\) | 19.9532i | 0.977114i | ||||||||
\(418\) | 3.70052 | + | 14.2251i | 0.180998 | + | 0.695772i | ||||
\(419\) | − | 22.7760i | − | 1.11268i | −0.830955 | − | 0.556340i | \(-0.812205\pi\) | ||
0.830955 | − | 0.556340i | \(-0.187795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.80960 | −0.331880 | −0.165940 | − | 0.986136i | \(-0.553066\pi\) | ||||
−0.165940 | + | 0.986136i | \(0.553066\pi\) | |||||||
\(422\) | −0.163763 | −0.00797188 | ||||||||
\(423\) | 0.767488i | 0.0373165i | ||||||||
\(424\) | 1.89194i | 0.0918808i | ||||||||
\(425\) | −4.76033 | −0.230910 | ||||||||
\(426\) | 10.3771 | 0.502771 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.76864i | 0.278838i | ||||||||
\(429\) | −1.10249 | − | 4.23807i | −0.0532288 | − | 0.204616i | ||||
\(430\) | − | 23.7333i | − | 1.14452i | ||||||
\(431\) | 30.8640i | 1.48667i | 0.668921 | + | 0.743334i | \(0.266757\pi\) | ||||
−0.668921 | + | 0.743334i | \(0.733243\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 32.2967i | − | 1.55208i | −0.630683 | − | 0.776040i | \(-0.717225\pi\) | ||
0.630683 | − | 0.776040i | \(-0.282775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.55606i | − | 0.170500i | ||||||
\(436\) | 8.63196i | 0.413396i | ||||||||
\(437\) | −36.7392 | −1.75747 | ||||||||
\(438\) | −11.1724 | −0.533840 | ||||||||
\(439\) | −28.6715 | −1.36842 | −0.684208 | − | 0.729287i | \(-0.739852\pi\) | ||||
−0.684208 | + | 0.729287i | \(0.739852\pi\) | |||||||
\(440\) | −7.90406 | + | 2.05616i | −0.376811 | + | 0.0980238i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 5.90830i | − | 0.281029i | ||||||
\(443\) | 34.9816 | 1.66203 | 0.831013 | − | 0.556253i | \(-0.187762\pi\) | ||||
0.831013 | + | 0.556253i | \(0.187762\pi\) | |||||||
\(444\) | 4.93126i | 0.234027i | ||||||||
\(445\) | −31.1612 | −1.47718 | ||||||||
\(446\) | −27.3847 | −1.29670 | ||||||||
\(447\) | 9.78029 | 0.462592 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.57926 | −0.168916 | −0.0844579 | − | 0.996427i | \(-0.526916\pi\) | ||||
−0.0844579 | + | 0.996427i | \(0.526916\pi\) | |||||||
\(450\) | 1.06381i | 0.0501486i | ||||||||
\(451\) | −26.2636 | + | 6.83222i | −1.23670 | + | 0.321717i | ||||
\(452\) | −17.4933 | −0.822817 | ||||||||
\(453\) | 2.67337 | 0.125606 | ||||||||
\(454\) | − | 3.90255i | − | 0.183156i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.43177 | 0.207537 | ||||||||
\(457\) | 20.3994i | 0.954242i | 0.878838 | + | 0.477121i | \(0.158320\pi\) | ||||
−0.878838 | + | 0.477121i | \(0.841680\pi\) | |||||||
\(458\) | 5.04055 | 0.235529 | ||||||||
\(459\) | − | 4.47479i | − | 0.208865i | ||||||
\(460\) | − | 20.4138i | − | 0.951800i | ||||||
\(461\) | 13.9967 | 0.651892 | 0.325946 | − | 0.945388i | \(-0.394317\pi\) | ||||
0.325946 | + | 0.945388i | \(0.394317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.6499 | 1.56384 | 0.781922 | − | 0.623376i | \(-0.214239\pi\) | ||||
0.781922 | + | 0.623376i | \(0.214239\pi\) | |||||||
\(464\) | − | 1.44409i | − | 0.0670404i | ||||||
\(465\) | − | 6.67640i | − | 0.309611i | ||||||
\(466\) | 21.2457 | 0.984189 | ||||||||
\(467\) | 9.08969i | 0.420620i | 0.977635 | + | 0.210310i | \(0.0674474\pi\) | ||||
−0.977635 | + | 0.210310i | \(0.932553\pi\) | |||||||
\(468\) | −1.32035 | −0.0610334 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1.88992i | − | 0.0871757i | ||||||
\(471\) | 15.8345 | 0.729614 | ||||||||
\(472\) | −7.78781 | −0.358463 | ||||||||
\(473\) | −8.04768 | − | 30.9359i | −0.370033 | − | 1.42243i | ||||
\(474\) | − | 2.92867i | − | 0.134518i | ||||||
\(475\) | −4.71458 | −0.216320 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.89194 | 0.0866260 | ||||||||
\(478\) | 5.64110 | 0.258018 | ||||||||
\(479\) | −39.5655 | −1.80779 | −0.903897 | − | 0.427751i | \(-0.859306\pi\) | ||||
−0.903897 | + | 0.427751i | \(0.859306\pi\) | |||||||
\(480\) | 2.46248i | 0.112396i | ||||||||
\(481\) | 6.51102 | 0.296877 | ||||||||
\(482\) | − | 7.77466i | − | 0.354126i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.60556 | + | 5.36034i | −0.436616 | + | 0.243652i | ||||
\(485\) | 3.39349 | 0.154090 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −3.20923 | −0.145424 | −0.0727120 | − | 0.997353i | \(-0.523165\pi\) | ||||
−0.0727120 | + | 0.997353i | \(0.523165\pi\) | |||||||
\(488\) | − | 4.47886i | − | 0.202748i | ||||||
\(489\) | − | 20.3615i | − | 0.920779i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.0209i | − | 0.858401i | −0.903209 | − | 0.429200i | \(-0.858795\pi\) | ||
0.903209 | − | 0.429200i | \(-0.141205\pi\) | |||||||
\(492\) | 8.18233i | 0.368888i | ||||||||
\(493\) | − | 6.46201i | − | 0.291034i | ||||||
\(494\) | − | 5.85152i | − | 0.263272i | ||||||
\(495\) | 2.05616 | + | 7.90406i | 0.0924177 | + | 0.355261i | ||||
\(496\) | − | 2.71125i | − | 0.121739i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.1118 | −0.453120 | ||||||||
\(499\) | 25.6082 | 1.14638 | 0.573190 | − | 0.819422i | \(-0.305706\pi\) | ||||
0.573190 | + | 0.819422i | \(0.305706\pi\) | |||||||
\(500\) | 9.69279i | 0.433475i | ||||||||
\(501\) | 16.1119i | 0.719828i | ||||||||
\(502\) | 22.5045 | 1.00443 | ||||||||
\(503\) | −2.73335 | −0.121874 | −0.0609370 | − | 0.998142i | \(-0.519409\pi\) | ||||
−0.0609370 | + | 0.998142i | \(0.519409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.6341i | − | 0.829209i | ||||||
\(506\) | −6.92208 | − | 26.6090i | −0.307724 | − | 1.18292i | ||||
\(507\) | − | 11.2567i | − | 0.499926i | ||||||
\(508\) | 12.0959i | 0.536667i | ||||||||
\(509\) | − | 16.8094i | − | 0.745064i | −0.928019 | − | 0.372532i | \(-0.878490\pi\) | ||
0.928019 | − | 0.372532i | \(-0.121510\pi\) | |||||||
\(510\) | 11.0191i | 0.487933i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 4.43177i | − | 0.195668i | ||||||
\(514\) | −3.01578 | −0.133021 | ||||||||
\(515\) | 40.6206 | 1.78996 | ||||||||
\(516\) | −9.63797 | −0.424288 | ||||||||
\(517\) | −0.640850 | − | 2.46348i | −0.0281845 | − | 0.108344i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.24694i | 0.318105i | ||||||||
\(520\) | 3.25135 | 0.142581 | ||||||||
\(521\) | − | 35.5653i | − | 1.55814i | −0.626936 | − | 0.779071i | \(-0.715691\pi\) | ||
0.626936 | − | 0.779071i | \(-0.284309\pi\) | |||||||
\(522\) | −1.44409 | −0.0632063 | ||||||||
\(523\) | −3.81853 | −0.166973 | −0.0834863 | − | 0.996509i | \(-0.526605\pi\) | ||||
−0.0834863 | + | 0.996509i | \(0.526605\pi\) | |||||||
\(524\) | 17.2415 | 0.753200 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.1819 | 1.22879 | ||||||||
\(527\) | − | 12.1323i | − | 0.528489i | ||||||
\(528\) | 0.834997 | + | 3.20979i | 0.0363386 | + | 0.139688i | ||||
\(529\) | 45.7232 | 1.98797 | ||||||||
\(530\) | −4.65887 | −0.202368 | ||||||||
\(531\) | 7.78781i | 0.337962i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.8036 | 0.467955 | ||||||||
\(534\) | 12.6544i | 0.547609i | ||||||||
\(535\) | −14.2052 | −0.614143 | ||||||||
\(536\) | 1.72369i | 0.0744520i | ||||||||
\(537\) | 11.6016i | 0.500644i | ||||||||
\(538\) | −0.604546 | −0.0260638 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.46248 | 0.105968 | ||||||||
\(541\) | − | 24.8436i | − | 1.06811i | −0.845450 | − | 0.534055i | \(-0.820667\pi\) | ||
0.845450 | − | 0.534055i | \(-0.179333\pi\) | |||||||
\(542\) | 19.7931i | 0.850186i | ||||||||
\(543\) | −7.74423 | −0.332337 | ||||||||
\(544\) | 4.47479i | 0.191855i | ||||||||
\(545\) | −21.2560 | −0.910509 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.4066i | 1.89869i | 0.314237 | + | 0.949345i | \(0.398251\pi\) | ||||
−0.314237 | + | 0.949345i | \(0.601749\pi\) | |||||||
\(548\) | −2.50957 | −0.107204 | ||||||||
\(549\) | −4.47886 | −0.191153 | ||||||||
\(550\) | −0.888281 | − | 3.41462i | −0.0378764 | − | 0.145600i | ||||
\(551\) | − | 6.39990i | − | 0.272645i | ||||||
\(552\) | −8.28995 | −0.352844 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.16446 | 0.0919590 | ||||||||
\(555\) | −12.1431 | −0.515448 | ||||||||
\(556\) | −19.9532 | −0.846206 | ||||||||
\(557\) | 27.6823i | 1.17294i | 0.809972 | + | 0.586469i | \(0.199482\pi\) | ||||
−0.809972 | + | 0.586469i | \(0.800518\pi\) | |||||||
\(558\) | −2.71125 | −0.114776 | ||||||||
\(559\) | 12.7255i | 0.538233i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.73643 | + | 14.3631i | 0.157752 | + | 0.606412i | ||||
\(562\) | −29.4916 | −1.24403 | ||||||||
\(563\) | −11.0353 | −0.465083 | −0.232541 | − | 0.972587i | \(-0.574704\pi\) | ||||
−0.232541 | + | 0.972587i | \(0.574704\pi\) | |||||||
\(564\) | −0.767488 | −0.0323171 | ||||||||
\(565\) | − | 43.0770i | − | 1.81226i | ||||||
\(566\) | 28.3880i | 1.19324i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.3771i | 0.435412i | ||||||||
\(569\) | − | 40.6462i | − | 1.70398i | −0.523559 | − | 0.851989i | \(-0.675396\pi\) | ||
0.523559 | − | 0.851989i | \(-0.324604\pi\) | |||||||
\(570\) | 10.9132i | 0.457102i | ||||||||
\(571\) | 17.7550i | 0.743022i | 0.928429 | + | 0.371511i | \(0.121160\pi\) | ||||
−0.928429 | + | 0.371511i | \(0.878840\pi\) | |||||||
\(572\) | 4.23807 | − | 1.10249i | 0.177203 | − | 0.0460975i | ||||
\(573\) | − | 21.2314i | − | 0.886954i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.81895 | 0.367776 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 1.73555i | 0.0722517i | 0.999347 | + | 0.0361259i | \(0.0115017\pi\) | ||||
−0.999347 | + | 0.0361259i | \(0.988498\pi\) | |||||||
\(578\) | 3.02370i | 0.125769i | ||||||||
\(579\) | −3.51327 | −0.146007 | ||||||||
\(580\) | 3.55606 | 0.147657 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 1.37808i | − | 0.0571231i | ||||||
\(583\) | −6.07274 | + | 1.57977i | −0.251507 | + | 0.0654272i | ||||
\(584\) | − | 11.1724i | − | 0.462319i | ||||||
\(585\) | − | 3.25135i | − | 0.134427i | ||||||
\(586\) | 9.39403i | 0.388064i | ||||||||
\(587\) | 0.837774i | 0.0345786i | 0.999851 | + | 0.0172893i | \(0.00550363\pi\) | ||||
−0.999851 | + | 0.0172893i | \(0.994496\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.0156i | − | 0.495096i | ||||||
\(590\) | − | 19.1773i | − | 0.789518i | ||||||
\(591\) | 21.9715 | 0.903786 | ||||||||
\(592\) | −4.93126 | −0.202674 | ||||||||
\(593\) | −26.0199 | −1.06851 | −0.534255 | − | 0.845323i | \(-0.679408\pi\) | ||||
−0.534255 | + | 0.845323i | \(0.679408\pi\) | |||||||
\(594\) | 3.20979 | − | 0.834997i | 0.131699 | − | 0.0342603i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.78029i | 0.400616i | ||||||||
\(597\) | 1.44180 | 0.0590089 | ||||||||
\(598\) | 10.9457i | 0.447602i | ||||||||
\(599\) | 11.2416 | 0.459320 | 0.229660 | − | 0.973271i | \(-0.426239\pi\) | ||||
0.229660 | + | 0.973271i | \(0.426239\pi\) | |||||||
\(600\) | −1.06381 | −0.0434300 | ||||||||
\(601\) | 11.4274 | 0.466134 | 0.233067 | − | 0.972461i | \(-0.425124\pi\) | ||||
0.233067 | + | 0.972461i | \(0.425124\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.72369 | 0.0701940 | ||||||||
\(604\) | 2.67337i | 0.108778i | ||||||||
\(605\) | −13.1997 | − | 23.6535i | −0.536645 | − | 0.961652i | ||||
\(606\) | −7.56722 | −0.307397 | ||||||||
\(607\) | −10.1805 | −0.413215 | −0.206608 | − | 0.978424i | \(-0.566242\pi\) | ||||
−0.206608 | + | 0.978424i | \(0.566242\pi\) | |||||||
\(608\) | 4.43177i | 0.179732i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.0291 | 0.446555 | ||||||||
\(611\) | 1.01336i | 0.0409960i | ||||||||
\(612\) | 4.47479 | 0.180882 | ||||||||
\(613\) | − | 24.9802i | − | 1.00894i | −0.863429 | − | 0.504471i | \(-0.831687\pi\) | ||
0.863429 | − | 0.504471i | \(-0.168313\pi\) | |||||||
\(614\) | − | 26.9732i | − | 1.08855i | ||||||
\(615\) | −20.1488 | −0.812479 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5114 | −1.14783 | −0.573914 | − | 0.818916i | \(-0.694576\pi\) | ||||
−0.573914 | + | 0.818916i | \(0.694576\pi\) | |||||||
\(618\) | − | 16.4958i | − | 0.663558i | ||||||
\(619\) | 24.3658i | 0.979344i | 0.871907 | + | 0.489672i | \(0.162883\pi\) | ||||
−0.871907 | + | 0.489672i | \(0.837117\pi\) | |||||||
\(620\) | 6.67640 | 0.268131 | ||||||||
\(621\) | 8.28995i | 0.332664i | ||||||||
\(622\) | 0.125330 | 0.00502529 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 1.32035i | − | 0.0528565i | ||||||
\(625\) | −29.1874 | −1.16749 | ||||||||
\(626\) | 7.72987 | 0.308948 | ||||||||
\(627\) | 3.70052 | + | 14.2251i | 0.147785 | + | 0.568095i | ||||
\(628\) | 15.8345i | 0.631865i | ||||||||
\(629\) | −22.0663 | −0.879843 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.2463 | −0.726374 | −0.363187 | − | 0.931716i | \(-0.618311\pi\) | ||||
−0.363187 | + | 0.931716i | \(0.618311\pi\) | |||||||
\(632\) | 2.92867 | 0.116496 | ||||||||
\(633\) | −0.163763 | −0.00650901 | ||||||||
\(634\) | 24.3802i | 0.968262i | ||||||||
\(635\) | −29.7858 | −1.18202 | ||||||||
\(636\) | 1.89194i | 0.0750204i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.63525 | − | 1.20582i | 0.183511 | − | 0.0477387i | ||||
\(639\) | 10.3771 | 0.410511 | ||||||||
\(640\) | −2.46248 | −0.0973381 | ||||||||
\(641\) | −19.3987 | −0.766202 | −0.383101 | − | 0.923706i | \(-0.625144\pi\) | ||||
−0.383101 | + | 0.923706i | \(0.625144\pi\) | |||||||
\(642\) | 5.76864i | 0.227670i | ||||||||
\(643\) | 11.3901i | 0.449182i | 0.974453 | + | 0.224591i | \(0.0721047\pi\) | ||||
−0.974453 | + | 0.224591i | \(0.927895\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 23.7333i | − | 0.934498i | ||||||
\(646\) | 19.8312i | 0.780250i | ||||||||
\(647\) | − | 17.1756i | − | 0.675243i | −0.941282 | − | 0.337621i | \(-0.890378\pi\) | ||
0.941282 | − | 0.337621i | \(-0.109622\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −6.50280 | − | 24.9973i | −0.255257 | − | 0.981228i | ||||
\(650\) | 1.40461i | 0.0550934i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.3615 | 0.797418 | ||||||||
\(653\) | −32.3964 | −1.26777 | −0.633884 | − | 0.773428i | \(-0.718540\pi\) | ||||
−0.633884 | + | 0.773428i | \(0.718540\pi\) | |||||||
\(654\) | 8.63196i | 0.337537i | ||||||||
\(655\) | 42.4569i | 1.65893i | ||||||||
\(656\) | −8.18233 | −0.319466 | ||||||||
\(657\) | −11.1724 | −0.435878 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.52103i | − | 0.331932i | −0.986131 | − | 0.165966i | \(-0.946926\pi\) | ||
0.986131 | − | 0.165966i | \(-0.0530742\pi\) | |||||||
\(660\) | −7.90406 | + | 2.05616i | −0.307665 | + | 0.0800361i | ||||
\(661\) | − | 39.3852i | − | 1.53191i | −0.642897 | − | 0.765953i | \(-0.722268\pi\) | ||
0.642897 | − | 0.765953i | \(-0.277732\pi\) | |||||||
\(662\) | − | 21.4532i | − | 0.833803i | ||||||
\(663\) | − | 5.90830i | − | 0.229460i | ||||||
\(664\) | − | 10.1118i | − | 0.392414i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.93126i | 0.191083i | ||||||||
\(667\) | 11.9715i | 0.463537i | ||||||||
\(668\) | −16.1119 | −0.623389 | ||||||||
\(669\) | −27.3847 | −1.05875 | ||||||||
\(670\) | −4.24455 | −0.163981 | ||||||||
\(671\) | 14.3762 | − | 3.73983i | 0.554987 | − | 0.144375i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.4185i | 0.902716i | 0.892343 | + | 0.451358i | \(0.149060\pi\) | ||||
−0.892343 | + | 0.451358i | \(0.850940\pi\) | |||||||
\(674\) | −30.0086 | −1.15589 | ||||||||
\(675\) | 1.06381i | 0.0409462i | ||||||||
\(676\) | 11.2567 | 0.432949 | ||||||||
\(677\) | −29.6821 | −1.14078 | −0.570388 | − | 0.821376i | \(-0.693207\pi\) | ||||
−0.570388 | + | 0.821376i | \(0.693207\pi\) | |||||||
\(678\) | −17.4933 | −0.671828 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.0191 | −0.422562 | ||||||||
\(681\) | − | 3.90255i | − | 0.149546i | ||||||
\(682\) | 8.70255 | − | 2.26388i | 0.333238 | − | 0.0866886i | ||||
\(683\) | 28.9457 | 1.10757 | 0.553787 | − | 0.832658i | \(-0.313182\pi\) | ||||
0.553787 | + | 0.832658i | \(0.313182\pi\) | |||||||
\(684\) | 4.43177 | 0.169453 | ||||||||
\(685\) | − | 6.17977i | − | 0.236117i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.04055 | 0.192309 | ||||||||
\(688\) | − | 9.63797i | − | 0.367444i | ||||||
\(689\) | 2.49803 | 0.0951675 | ||||||||
\(690\) | − | 20.4138i | − | 0.777142i | ||||||
\(691\) | 27.9501i | 1.06327i | 0.846973 | + | 0.531636i | \(0.178422\pi\) | ||||
−0.846973 | + | 0.531636i | \(0.821578\pi\) | |||||||
\(692\) | −7.24694 | −0.275487 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.5340 | −1.31089 | ||||||||
\(695\) | − | 49.1345i | − | 1.86378i | ||||||
\(696\) | − | 1.44409i | − | 0.0547383i | ||||||
\(697\) | −36.6142 | −1.38686 | ||||||||
\(698\) | − | 4.77961i | − | 0.180911i | ||||||
\(699\) | 21.2457 | 0.803587 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2062i | 0.498793i | 0.968401 | + | 0.249397i | \(0.0802323\pi\) | ||||
−0.968401 | + | 0.249397i | \(0.919768\pi\) | |||||||
\(702\) | −1.32035 | −0.0498336 | ||||||||
\(703\) | −21.8542 | −0.824249 | ||||||||
\(704\) | −3.20979 | + | 0.834997i | −0.120974 | + | 0.0314701i | ||||
\(705\) | − | 1.88992i | − | 0.0711786i | ||||||
\(706\) | 13.5771 | 0.510979 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.78781 | −0.292684 | ||||||||
\(709\) | 14.7808 | 0.555104 | 0.277552 | − | 0.960711i | \(-0.410477\pi\) | ||||
0.277552 | + | 0.960711i | \(0.410477\pi\) | |||||||
\(710\) | −25.5533 | −0.959000 | ||||||||
\(711\) | − | 2.92867i | − | 0.109834i | ||||||
\(712\) | −12.6544 | −0.474244 | ||||||||
\(713\) | 22.4761i | 0.841737i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.71487 | + | 10.4362i | 0.101530 | + | 0.390290i | ||||
\(716\) | −11.6016 | −0.433571 | ||||||||
\(717\) | 5.64110 | 0.210671 | ||||||||
\(718\) | 1.72779 | 0.0644804 | ||||||||
\(719\) | 3.71055i | 0.138380i | 0.997603 | + | 0.0691900i | \(0.0220415\pi\) | ||||
−0.997603 | + | 0.0691900i | \(0.977959\pi\) | |||||||
\(720\) | 2.46248i | 0.0917713i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.640626i | 0.0238416i | ||||||||
\(723\) | − | 7.77466i | − | 0.289143i | ||||||
\(724\) | − | 7.74423i | − | 0.287812i | ||||||
\(725\) | 1.53625i | 0.0570548i | ||||||||
\(726\) | −9.60556 | + | 5.36034i | −0.356496 | + | 0.198941i | ||||
\(727\) | 16.9392i | 0.628241i | 0.949383 | + | 0.314120i | \(0.101710\pi\) | ||||
−0.949383 | + | 0.314120i | \(0.898290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 27.5119 | 1.01826 | ||||||||
\(731\) | − | 43.1278i | − | 1.59514i | ||||||
\(732\) | − | 4.47886i | − | 0.165543i | ||||||
\(733\) | 11.3990 | 0.421032 | 0.210516 | − | 0.977590i | \(-0.432486\pi\) | ||||
0.210516 | + | 0.977590i | \(0.432486\pi\) | |||||||
\(734\) | −25.4861 | −0.940709 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 8.28995i | − | 0.305572i | ||||||
\(737\) | −5.53269 | + | 1.43928i | −0.203799 | + | 0.0530164i | ||||
\(738\) | 8.18233i | 0.301196i | ||||||||
\(739\) | − | 5.65173i | − | 0.207902i | −0.994582 | − | 0.103951i | \(-0.966851\pi\) | ||
0.994582 | − | 0.103951i | \(-0.0331485\pi\) | |||||||
\(740\) | − | 12.1431i | − | 0.446391i | ||||||
\(741\) | − | 5.85152i | − | 0.214961i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.21080i | − | 0.0811065i | −0.999177 | − | 0.0405533i | \(-0.987088\pi\) | ||
0.999177 | − | 0.0405533i | \(-0.0129120\pi\) | |||||||
\(744\) | − | 2.71125i | − | 0.0993992i | ||||||
\(745\) | −24.0838 | −0.882361 | ||||||||
\(746\) | −33.3334 | −1.22042 | ||||||||
\(747\) | −10.1118 | −0.369971 | ||||||||
\(748\) | −14.3631 | + | 3.73643i | −0.525168 | + | 0.136618i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.69279i | 0.353930i | ||||||||
\(751\) | 5.87413 | 0.214350 | 0.107175 | − | 0.994240i | \(-0.465819\pi\) | ||||
0.107175 | + | 0.994240i | \(0.465819\pi\) | |||||||
\(752\) | − | 0.767488i | − | 0.0279874i | ||||||
\(753\) | 22.5045 | 0.820110 | ||||||||
\(754\) | −1.90672 | −0.0694386 | ||||||||
\(755\) | −6.58313 | −0.239585 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3568 | 0.558152 | 0.279076 | − | 0.960269i | \(-0.409972\pi\) | ||||
0.279076 | + | 0.960269i | \(0.409972\pi\) | |||||||
\(758\) | − | 19.2656i | − | 0.699760i | ||||||
\(759\) | −6.92208 | − | 26.6090i | −0.251256 | − | 0.965847i | ||||
\(760\) | −10.9132 | −0.395862 | ||||||||
\(761\) | 22.4927 | 0.815359 | 0.407680 | − | 0.913125i | \(-0.366338\pi\) | ||||
0.407680 | + | 0.913125i | \(0.366338\pi\) | |||||||
\(762\) | 12.0959i | 0.438187i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.2314 | 0.768125 | ||||||||
\(765\) | 11.0191i | 0.398395i | ||||||||
\(766\) | −5.15509 | −0.186261 | ||||||||
\(767\) | 10.2827i | 0.371286i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 39.6302 | 1.42910 | 0.714551 | − | 0.699583i | \(-0.246631\pi\) | ||||
0.714551 | + | 0.699583i | \(0.246631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.01578 | −0.108611 | ||||||||
\(772\) | − | 3.51327i | − | 0.126445i | ||||||
\(773\) | 15.7052i | 0.564877i | 0.959285 | + | 0.282438i | \(0.0911433\pi\) | ||||
−0.959285 | + | 0.282438i | \(0.908857\pi\) | |||||||
\(774\) | −9.63797 | −0.346430 | ||||||||
\(775\) | 2.88426i | 0.103606i | ||||||||
\(776\) | 1.37808 | 0.0494701 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 5.16455i | − | 0.185158i | ||||||
\(779\) | −36.2622 | −1.29923 | ||||||||
\(780\) | 3.25135 | 0.116417 | ||||||||
\(781\) | −33.3083 | + | 8.66483i | −1.19186 | + | 0.310052i | ||||
\(782\) | − | 37.0957i | − | 1.32654i | ||||||
\(783\) | −1.44409 | −0.0516077 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.9921 | −1.39169 | ||||||||
\(786\) | 17.2415 | 0.614985 | ||||||||
\(787\) | 41.3222 | 1.47298 | 0.736488 | − | 0.676450i | \(-0.236483\pi\) | ||||
0.736488 | + | 0.676450i | \(0.236483\pi\) | |||||||
\(788\) | 21.9715i | 0.782702i | ||||||||
\(789\) | 28.1819 | 1.00330 | ||||||||
\(790\) | 7.21179i | 0.256584i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.834997 | + | 3.20979i | 0.0296703 | + | 0.114055i | ||||
\(793\) | −5.91368 | −0.210001 | ||||||||
\(794\) | −6.34291 | −0.225102 | ||||||||
\(795\) | −4.65887 | −0.165233 | ||||||||
\(796\) | 1.44180i | 0.0511032i | ||||||||
\(797\) | 20.2076i | 0.715789i | 0.933762 | + | 0.357894i | \(0.116505\pi\) | ||||
−0.933762 | + | 0.357894i | \(0.883495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.43434i | − | 0.121498i | ||||||
\(800\) | − | 1.06381i | − | 0.0376115i | ||||||
\(801\) | 12.6544i | 0.447121i | ||||||||
\(802\) | 22.0015i | 0.776900i | ||||||||
\(803\) | 35.8612 | − | 9.32896i | 1.26552 | − | 0.329212i | ||||
\(804\) | 1.72369i | 0.0607898i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.57981 | −0.126093 | ||||||||
\(807\) | −0.604546 | −0.0212810 | ||||||||
\(808\) | − | 7.56722i | − | 0.266214i | ||||||
\(809\) | 33.7222i | 1.18561i | 0.805346 | + | 0.592805i | \(0.201980\pi\) | ||||
−0.805346 | + | 0.592805i | \(0.798020\pi\) | |||||||
\(810\) | 2.46248 | 0.0865228 | ||||||||
\(811\) | −9.84154 | −0.345583 | −0.172792 | − | 0.984958i | \(-0.555279\pi\) | ||||
−0.172792 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.7931i | 0.694174i | ||||||||
\(814\) | −4.11759 | − | 15.8283i | −0.144321 | − | 0.554783i | ||||
\(815\) | 50.1398i | 1.75632i | ||||||||
\(816\) | 4.47479i | 0.156649i | ||||||||
\(817\) | − | 42.7133i | − | 1.49435i | ||||||
\(818\) | 14.1189i | 0.493657i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 20.1488i | − | 0.703628i | ||||||
\(821\) | − | 8.79863i | − | 0.307074i | −0.988143 | − | 0.153537i | \(-0.950933\pi\) | ||
0.988143 | − | 0.153537i | \(-0.0490665\pi\) | |||||||
\(822\) | −2.50957 | −0.0875314 | ||||||||
\(823\) | −32.8876 | −1.14639 | −0.573195 | − | 0.819419i | \(-0.694296\pi\) | ||||
−0.573195 | + | 0.819419i | \(0.694296\pi\) | |||||||
\(824\) | 16.4958 | 0.574658 | ||||||||
\(825\) | −0.888281 | − | 3.41462i | −0.0309260 | − | 0.118882i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.5923i | 1.51585i | 0.652339 | + | 0.757927i | \(0.273788\pi\) | ||||
−0.652339 | + | 0.757927i | \(0.726212\pi\) | |||||||
\(828\) | −8.28995 | −0.288096 | ||||||||
\(829\) | 31.6573i | 1.09950i | 0.835328 | + | 0.549752i | \(0.185278\pi\) | ||||
−0.835328 | + | 0.549752i | \(0.814722\pi\) | |||||||
\(830\) | 24.9001 | 0.864295 | ||||||||
\(831\) | 2.16446 | 0.0750842 | ||||||||
\(832\) | 1.32035 | 0.0457751 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −19.9532 | −0.690924 | ||||||||
\(835\) | − | 39.6753i | − | 1.37302i | ||||||
\(836\) | −14.2251 | + | 3.70052i | −0.491985 | + | 0.127985i | ||||
\(837\) | −2.71125 | −0.0937145 | ||||||||
\(838\) | 22.7760 | 0.786784 | ||||||||
\(839\) | 33.1104i | 1.14310i | 0.820568 | + | 0.571549i | \(0.193657\pi\) | ||||
−0.820568 | + | 0.571549i | \(0.806343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.9146 | 0.928089 | ||||||||
\(842\) | − | 6.80960i | − | 0.234674i | ||||||
\(843\) | −29.4916 | −1.01575 | ||||||||
\(844\) | − | 0.163763i | − | 0.00563697i | ||||||
\(845\) | 27.7193i | 0.953574i | ||||||||
\(846\) | −0.767488 | −0.0263868 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.89194 | −0.0649695 | ||||||||
\(849\) | 28.3880i | 0.974273i | ||||||||
\(850\) | − | 4.76033i | − | 0.163278i | ||||||
\(851\) | 40.8799 | 1.40135 | ||||||||
\(852\) | 10.3771i | 0.355513i | ||||||||
\(853\) | 32.8121 | 1.12347 | 0.561733 | − | 0.827318i | \(-0.310135\pi\) | ||||
0.561733 | + | 0.827318i | \(0.310135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.9132i | 0.373222i | ||||||||
\(856\) | −5.76864 | −0.197168 | ||||||||
\(857\) | −11.6763 | −0.398853 | −0.199427 | − | 0.979913i | \(-0.563908\pi\) | ||||
−0.199427 | + | 0.979913i | \(0.563908\pi\) | |||||||
\(858\) | 4.23807 | − | 1.10249i | 0.144685 | − | 0.0376385i | ||||
\(859\) | − | 40.7175i | − | 1.38926i | −0.719366 | − | 0.694631i | \(-0.755568\pi\) | ||
0.719366 | − | 0.694631i | \(-0.244432\pi\) | |||||||
\(860\) | 23.7333 | 0.809299 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.8640 | −1.05123 | ||||||||
\(863\) | −18.0888 | −0.615749 | −0.307874 | − | 0.951427i | \(-0.599618\pi\) | ||||
−0.307874 | + | 0.951427i | \(0.599618\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | − | 17.8455i | − | 0.606764i | ||||||
\(866\) | 32.2967 | 1.09749 | ||||||||
\(867\) | 3.02370i | 0.102690i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.44543 | + | 9.40042i | 0.0829555 | + | 0.318887i | ||||
\(870\) | 3.55606 | 0.120562 | ||||||||
\(871\) | 2.27588 | 0.0771153 | ||||||||
\(872\) | −8.63196 | −0.292315 | ||||||||
\(873\) | − | 1.37808i | − | 0.0466408i | ||||||
\(874\) | − | 36.7392i | − | 1.24272i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 11.1724i | − | 0.377482i | ||||||
\(877\) | 6.62096i | 0.223574i | 0.993732 | + | 0.111787i | \(0.0356574\pi\) | ||||
−0.993732 | + | 0.111787i | \(0.964343\pi\) | |||||||
\(878\) | − | 28.6715i | − | 0.967616i | ||||||
\(879\) | 9.39403i | 0.316853i | ||||||||
\(880\) | −2.05616 | − | 7.90406i | −0.0693133 | − | 0.266446i | ||||
\(881\) | − | 16.5800i | − | 0.558594i | −0.960205 | − | 0.279297i | \(-0.909899\pi\) | ||
0.960205 | − | 0.279297i | \(-0.0901014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.3526 | 1.49258 | 0.746292 | − | 0.665619i | \(-0.231832\pi\) | ||||
0.746292 | + | 0.665619i | \(0.231832\pi\) | |||||||
\(884\) | 5.90830 | 0.198718 | ||||||||
\(885\) | − | 19.1773i | − | 0.644639i | ||||||
\(886\) | 34.9816i | 1.17523i | ||||||||
\(887\) | −32.5838 | −1.09406 | −0.547028 | − | 0.837114i | \(-0.684241\pi\) | ||||
−0.547028 | + | 0.837114i | \(0.684241\pi\) | |||||||
\(888\) | −4.93126 | −0.165482 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 31.1612i | − | 1.04453i | ||||||
\(891\) | 3.20979 | − | 0.834997i | 0.107532 | − | 0.0279735i | ||||
\(892\) | − | 27.3847i | − | 0.916908i | ||||||
\(893\) | − | 3.40133i | − | 0.113821i | ||||||
\(894\) | 9.78029i | 0.327102i | ||||||||
\(895\) | − | 28.5686i | − | 0.954944i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.9457i | 0.365465i | ||||||||
\(898\) | − | 3.57926i | − | 0.119441i | ||||||
\(899\) | −3.91530 | −0.130583 | ||||||||
\(900\) | −1.06381 | −0.0354604 | ||||||||
\(901\) | −8.46603 | −0.282044 | ||||||||
\(902\) | −6.83222 | − | 26.2636i | −0.227488 | − | 0.874482i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 17.4933i | − | 0.581820i | ||||||
\(905\) | 19.0700 | 0.633909 | ||||||||
\(906\) | 2.67337i | 0.0888168i | ||||||||
\(907\) | −41.0943 | −1.36451 | −0.682257 | − | 0.731112i | \(-0.739002\pi\) | ||||
−0.682257 | + | 0.731112i | \(0.739002\pi\) | |||||||
\(908\) | 3.90255 | 0.129511 | ||||||||
\(909\) | −7.56722 | −0.250989 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.2471 | 0.935868 | 0.467934 | − | 0.883764i | \(-0.344999\pi\) | ||||
0.467934 | + | 0.883764i | \(0.344999\pi\) | |||||||
\(912\) | 4.43177i | 0.146751i | ||||||||
\(913\) | 32.4568 | − | 8.44332i | 1.07416 | − | 0.279433i | ||||
\(914\) | −20.3994 | −0.674751 | ||||||||
\(915\) | 11.0291 | 0.364611 | ||||||||
\(916\) | 5.04055i | 0.166544i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.47479 | 0.147690 | ||||||||
\(919\) | 39.1121i | 1.29019i | 0.764102 | + | 0.645095i | \(0.223182\pi\) | ||||
−0.764102 | + | 0.645095i | \(0.776818\pi\) | |||||||
\(920\) | 20.4138 | 0.673024 | ||||||||
\(921\) | − | 26.9732i | − | 0.888798i | ||||||
\(922\) | 13.9967i | 0.460957i | ||||||||
\(923\) | 13.7014 | 0.450988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.24594 | 0.172486 | ||||||||
\(926\) | 33.6499i | 1.10581i | ||||||||
\(927\) | − | 16.4958i | − | 0.541793i | ||||||
\(928\) | 1.44409 | 0.0474047 | ||||||||
\(929\) | 24.6597i | 0.809058i | 0.914525 | + | 0.404529i | \(0.132565\pi\) | ||||
−0.914525 | + | 0.404529i | \(0.867435\pi\) | |||||||
\(930\) | 6.67640 | 0.218928 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.2457i | 0.695927i | ||||||||
\(933\) | 0.125330 | 0.00410313 | ||||||||
\(934\) | −9.08969 | −0.297424 | ||||||||
\(935\) | −9.20090 | − | 35.3690i | −0.300901 | − | 1.15669i | ||||
\(936\) | − | 1.32035i | − | 0.0431572i | ||||||
\(937\) | 10.7483 | 0.351133 | 0.175566 | − | 0.984468i | \(-0.443824\pi\) | ||||
0.175566 | + | 0.984468i | \(0.443824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.72987 | 0.252255 | ||||||||
\(940\) | 1.88992 | 0.0616425 | ||||||||
\(941\) | −33.8736 | −1.10425 | −0.552125 | − | 0.833762i | \(-0.686183\pi\) | ||||
−0.552125 | + | 0.833762i | \(0.686183\pi\) | |||||||
\(942\) | 15.8345i | 0.515915i | ||||||||
\(943\) | 67.8311 | 2.20888 | ||||||||
\(944\) | − | 7.78781i | − | 0.253471i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.9359 | − | 8.04768i | 1.00581 | − | 0.261652i | ||||
\(947\) | 20.7718 | 0.674994 | 0.337497 | − | 0.941327i | \(-0.390420\pi\) | ||||
0.337497 | + | 0.941327i | \(0.390420\pi\) | |||||||
\(948\) | 2.92867 | 0.0951187 | ||||||||
\(949\) | −14.7516 | −0.478857 | ||||||||
\(950\) | − | 4.71458i | − | 0.152961i | ||||||
\(951\) | 24.3802i | 0.790583i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.28486i | 0.0416205i | 0.999783 | + | 0.0208103i | \(0.00662459\pi\) | ||||
−0.999783 | + | 0.0208103i | \(0.993375\pi\) | |||||||
\(954\) | 1.89194i | 0.0612539i | ||||||||
\(955\) | 52.2819i | 1.69180i | ||||||||
\(956\) | 5.64110i | 0.182446i | ||||||||
\(957\) | 4.63525 | − | 1.20582i | 0.149836 | − | 0.0389785i | ||||
\(958\) | − | 39.5655i | − | 1.27830i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.46248 | −0.0794762 | ||||||||
\(961\) | 23.6491 | 0.762875 | ||||||||
\(962\) | 6.51102i | 0.209924i | ||||||||
\(963\) | 5.76864i | 0.185892i | ||||||||
\(964\) | 7.77466 | 0.250405 | ||||||||
\(965\) | 8.65137 | 0.278497 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.2584i | 1.42325i | 0.702558 | + | 0.711627i | \(0.252041\pi\) | ||||
−0.702558 | + | 0.711627i | \(0.747959\pi\) | |||||||
\(968\) | −5.36034 | − | 9.60556i | −0.172288 | − | 0.308734i | ||||
\(969\) | 19.8312i | 0.637071i | ||||||||
\(970\) | 3.39349i | 0.108958i | ||||||||
\(971\) | − | 39.8945i | − | 1.28028i | −0.768260 | − | 0.640138i | \(-0.778877\pi\) | ||
0.768260 | − | 0.640138i | \(-0.221123\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 3.20923i | − | 0.102830i | ||||||
\(975\) | 1.40461i | 0.0449835i | ||||||||
\(976\) | 4.47886 | 0.143365 | ||||||||
\(977\) | −1.60685 | −0.0514076 | −0.0257038 | − | 0.999670i | \(-0.508183\pi\) | ||||
−0.0257038 | + | 0.999670i | \(0.508183\pi\) | |||||||
\(978\) | 20.3615 | 0.651089 | ||||||||
\(979\) | −10.5664 | − | 40.6180i | −0.337703 | − | 1.29816i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.63196i | 0.275597i | ||||||||
\(982\) | 19.0209 | 0.606981 | ||||||||
\(983\) | − | 1.13364i | − | 0.0361574i | −0.999837 | − | 0.0180787i | \(-0.994245\pi\) | ||
0.999837 | − | 0.0180787i | \(-0.00575494\pi\) | |||||||
\(984\) | −8.18233 | −0.260843 | ||||||||
\(985\) | −54.1044 | −1.72391 | ||||||||
\(986\) | 6.46201 | 0.205792 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.85152 | 0.186162 | ||||||||
\(989\) | 79.8982i | 2.54062i | ||||||||
\(990\) | −7.90406 | + | 2.05616i | −0.251207 | + | 0.0653492i | ||||
\(991\) | −5.28668 | −0.167937 | −0.0839684 | − | 0.996468i | \(-0.526759\pi\) | ||||
−0.0839684 | + | 0.996468i | \(0.526759\pi\) | |||||||
\(992\) | 2.71125 | 0.0860822 | ||||||||
\(993\) | − | 21.4532i | − | 0.680798i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.55040 | −0.112555 | ||||||||
\(996\) | − | 10.1118i | − | 0.320404i | ||||||
\(997\) | 1.09038 | 0.0345327 | 0.0172663 | − | 0.999851i | \(-0.494504\pi\) | ||||
0.0172663 | + | 0.999851i | \(0.494504\pi\) | |||||||
\(998\) | 25.6082i | 0.810613i | ||||||||
\(999\) | 4.93126i | 0.156018i |
(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 | 3234.2.e.a.2155.10 | 16 | ||
7.2 | even | 3 | 462.2.p.a.241.5 | ✓ | 16 | ||
7.3 | odd | 6 | 462.2.p.b.439.1 | yes | 16 | ||
7.6 | odd | 2 | 3234.2.e.b.2155.15 | 16 | |||
11.10 | odd | 2 | 3234.2.e.b.2155.2 | 16 | |||
21.2 | odd | 6 | 1386.2.bk.a.703.4 | 16 | |||
21.17 | even | 6 | 1386.2.bk.b.901.8 | 16 | |||
77.10 | even | 6 | 462.2.p.a.439.5 | yes | 16 | ||
77.65 | odd | 6 | 462.2.p.b.241.1 | yes | 16 | ||
77.76 | even | 2 | inner | 3234.2.e.a.2155.7 | 16 | ||
231.65 | even | 6 | 1386.2.bk.b.703.8 | 16 | |||
231.164 | odd | 6 | 1386.2.bk.a.901.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.5 | ✓ | 16 | 7.2 | even | 3 | ||
462.2.p.a.439.5 | yes | 16 | 77.10 | even | 6 | ||
462.2.p.b.241.1 | yes | 16 | 77.65 | odd | 6 | ||
462.2.p.b.439.1 | yes | 16 | 7.3 | odd | 6 | ||
1386.2.bk.a.703.4 | 16 | 21.2 | odd | 6 | |||
1386.2.bk.a.901.4 | 16 | 231.164 | odd | 6 | |||
1386.2.bk.b.703.8 | 16 | 231.65 | even | 6 | |||
1386.2.bk.b.901.8 | 16 | 21.17 | even | 6 | |||
3234.2.e.a.2155.7 | 16 | 77.76 | even | 2 | inner | ||
3234.2.e.a.2155.10 | 16 | 1.1 | even | 1 | trivial | ||
3234.2.e.b.2155.2 | 16 | 11.10 | odd | 2 | |||
3234.2.e.b.2155.15 | 16 | 7.6 | odd | 2 |