Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1709,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2394.1709");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 10x^{6} + 30x^{4} + 24x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1709.5 | ||
Root | \(1.08784i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1709 |
Dual form | 2394.2.b.i.1709.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.15484i | 0.516459i | 0.966084 | + | 0.258230i | \(0.0831392\pi\) | ||||
−0.966084 | + | 0.258230i | \(0.916861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.15484i | − | 0.365192i | ||||||
\(11\) | − | 2.90624i | − | 0.876265i | −0.898910 | − | 0.438133i | \(-0.855640\pi\) | ||
0.898910 | − | 0.438133i | \(-0.144360\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.38329i | − | 0.383656i | −0.981429 | − | 0.191828i | \(-0.938558\pi\) | ||
0.981429 | − | 0.191828i | \(-0.0614416\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.90624i | − | 0.704868i | −0.935837 | − | 0.352434i | \(-0.885354\pi\) | ||
0.935837 | − | 0.352434i | \(-0.114646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.79473 | − | 2.14477i | 0.870571 | − | 0.492043i | ||||
\(20\) | 1.15484i | 0.258230i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.90624i | 0.619613i | ||||||||
\(23\) | 7.14888i | 1.49065i | 0.666704 | + | 0.745323i | \(0.267705\pi\) | ||||
−0.666704 | + | 0.745323i | \(0.732295\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.66635 | 0.733270 | ||||||||
\(26\) | 1.38329i | 0.271286i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −4.66635 | −0.866519 | −0.433260 | − | 0.901269i | \(-0.642637\pi\) | ||||
−0.433260 | + | 0.901269i | \(0.642637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.06108i | 0.729392i | 0.931127 | + | 0.364696i | \(0.118827\pi\) | ||||
−0.931127 | + | 0.364696i | \(0.881173\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.90624i | 0.498417i | ||||||||
\(35\) | − | 1.15484i | − | 0.195203i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.55232i | − | 1.07719i | −0.842563 | − | 0.538597i | \(-0.818954\pi\) | ||
0.842563 | − | 0.538597i | \(-0.181046\pi\) | |||||||
\(38\) | −3.79473 | + | 2.14477i | −0.615586 | + | 0.347927i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1.15484i | − | 0.182596i | ||||||
\(41\) | −11.1869 | −1.74711 | −0.873553 | − | 0.486729i | \(-0.838190\pi\) | ||||
−0.873553 | + | 0.486729i | \(0.838190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.04373 | −0.311666 | −0.155833 | − | 0.987783i | \(-0.549806\pi\) | ||||
−0.155833 | + | 0.987783i | \(0.549806\pi\) | |||||||
\(44\) | − | 2.90624i | − | 0.438133i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 7.14888i | − | 1.05405i | ||||||
\(47\) | − | 2.76658i | − | 0.403548i | −0.979432 | − | 0.201774i | \(-0.935329\pi\) | ||
0.979432 | − | 0.201774i | \(-0.0646706\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.66635 | −0.518500 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.38329i | − | 0.191828i | ||||||
\(53\) | −7.39997 | −1.01646 | −0.508232 | − | 0.861220i | \(-0.669701\pi\) | ||||
−0.508232 | + | 0.861220i | \(0.669701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.35624 | 0.452556 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.66635 | 0.612722 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.29954 | −1.06265 | −0.531323 | − | 0.847169i | \(-0.678305\pi\) | ||||
−0.531323 | + | 0.847169i | \(0.678305\pi\) | |||||||
\(62\) | − | 4.06108i | − | 0.515758i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.59748 | 0.198143 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.91547i | − | 1.21137i | −0.795706 | − | 0.605684i | \(-0.792900\pi\) | ||
0.795706 | − | 0.605684i | \(-0.207100\pi\) | |||||||
\(68\) | − | 2.90624i | − | 0.352434i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.15484i | 0.138030i | ||||||||
\(71\) | −6.06632 | −0.719940 | −0.359970 | − | 0.932964i | \(-0.617213\pi\) | ||||
−0.359970 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.37643 | 1.09743 | 0.548714 | − | 0.836010i | \(-0.315118\pi\) | ||||
0.548714 | + | 0.836010i | \(0.315118\pi\) | |||||||
\(74\) | 6.55232i | 0.761691i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.79473 | − | 2.14477i | 0.435285 | − | 0.246022i | ||||
\(77\) | 2.90624i | 0.331197i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.1783i | − | 1.37016i | −0.728468 | − | 0.685080i | \(-0.759767\pi\) | ||
0.728468 | − | 0.685080i | \(-0.240233\pi\) | |||||||
\(80\) | 1.15484i | 0.129115i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.1869 | 1.23539 | ||||||||
\(83\) | − | 14.5262i | − | 1.59446i | −0.603676 | − | 0.797230i | \(-0.706298\pi\) | ||
0.603676 | − | 0.797230i | \(-0.293702\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.35624 | 0.364036 | ||||||||
\(86\) | 2.04373 | 0.220381 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.90624i | 0.309807i | ||||||||
\(89\) | 17.2533 | 1.82884 | 0.914421 | − | 0.404765i | \(-0.132647\pi\) | ||||
0.914421 | + | 0.404765i | \(0.132647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.38329i | 0.145008i | ||||||||
\(92\) | 7.14888i | 0.745323i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.76658i | 0.285351i | ||||||||
\(95\) | 2.47686 | + | 4.38230i | 0.254121 | + | 0.449614i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.92142i | − | 0.398160i | −0.979983 | − | 0.199080i | \(-0.936205\pi\) | ||
0.979983 | − | 0.199080i | \(-0.0637954\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.66635 | 0.366635 | ||||||||
\(101\) | 1.61175i | 0.160375i | 0.996780 | + | 0.0801873i | \(0.0255519\pi\) | ||||
−0.996780 | + | 0.0801873i | \(0.974448\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.6603i | − | 1.05039i | −0.850982 | − | 0.525195i | \(-0.823992\pi\) | ||
0.850982 | − | 0.525195i | \(-0.176008\pi\) | |||||||
\(104\) | 1.38329i | 0.135643i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.39997 | 0.718749 | ||||||||
\(107\) | −11.2226 | −1.08493 | −0.542467 | − | 0.840077i | \(-0.682510\pi\) | ||||
−0.542467 | + | 0.840077i | \(0.682510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.91282i | 0.374780i | 0.982286 | + | 0.187390i | \(0.0600029\pi\) | ||||
−0.982286 | + | 0.187390i | \(0.939997\pi\) | |||||||
\(110\) | −3.35624 | −0.320005 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 11.4202 | 1.07432 | 0.537159 | − | 0.843481i | \(-0.319498\pi\) | ||||
0.537159 | + | 0.843481i | \(0.319498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.25581 | −0.769858 | ||||||||
\(116\) | −4.66635 | −0.433260 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.90624i | 0.266415i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.55375 | 0.232159 | ||||||||
\(122\) | 8.29954 | 0.751405 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.06108i | 0.364696i | ||||||||
\(125\) | 10.0082i | 0.895164i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.9145i | − | 1.14597i | −0.819564 | − | 0.572987i | \(-0.805784\pi\) | ||
0.819564 | − | 0.572987i | \(-0.194216\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.59748 | −0.140108 | ||||||||
\(131\) | − | 11.8101i | − | 1.03186i | −0.856632 | − | 0.515928i | \(-0.827447\pi\) | ||
0.856632 | − | 0.515928i | \(-0.172553\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.79473 | + | 2.14477i | −0.329045 | + | 0.185975i | ||||
\(134\) | 9.91547i | 0.856566i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.90624i | 0.249208i | ||||||||
\(137\) | − | 10.0551i | − | 0.859068i | −0.903051 | − | 0.429534i | \(-0.858678\pi\) | ||
0.903051 | − | 0.429534i | \(-0.141322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8663 | −1.43058 | −0.715289 | − | 0.698829i | \(-0.753705\pi\) | ||||
−0.715289 | + | 0.698829i | \(0.753705\pi\) | |||||||
\(140\) | − | 1.15484i | − | 0.0976017i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.06632 | 0.509074 | ||||||||
\(143\) | −4.02018 | −0.336185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.38888i | − | 0.447522i | ||||||
\(146\) | −9.37643 | −0.775998 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.55232i | − | 0.538597i | ||||||
\(149\) | − | 14.2978i | − | 1.17132i | −0.810557 | − | 0.585659i | \(-0.800836\pi\) | ||
0.810557 | − | 0.585659i | \(-0.199164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.64508i | 0.540769i | 0.962752 | + | 0.270385i | \(0.0871508\pi\) | ||||
−0.962752 | + | 0.270385i | \(0.912849\pi\) | |||||||
\(152\) | −3.79473 | + | 2.14477i | −0.307793 | + | 0.173964i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 2.90624i | − | 0.234192i | ||||||
\(155\) | −4.68989 | −0.376701 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.8201 | 1.34239 | 0.671196 | − | 0.741280i | \(-0.265781\pi\) | ||||
0.671196 | + | 0.741280i | \(0.265781\pi\) | |||||||
\(158\) | 12.1783i | 0.968850i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.15484i | − | 0.0912980i | ||||||
\(161\) | − | 7.14888i | − | 0.563411i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.9100 | 0.854536 | 0.427268 | − | 0.904125i | \(-0.359476\pi\) | ||||
0.427268 | + | 0.904125i | \(0.359476\pi\) | |||||||
\(164\) | −11.1869 | −0.873553 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5262i | 1.12745i | ||||||||
\(167\) | 5.31251 | 0.411095 | 0.205547 | − | 0.978647i | \(-0.434103\pi\) | ||||
0.205547 | + | 0.978647i | \(0.434103\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0865 | 0.852808 | ||||||||
\(170\) | −3.35624 | −0.257412 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.04373 | −0.155833 | ||||||||
\(173\) | −11.2226 | −0.853242 | −0.426621 | − | 0.904430i | \(-0.640296\pi\) | ||||
−0.426621 | + | 0.904430i | \(0.640296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.66635 | −0.277150 | ||||||||
\(176\) | − | 2.90624i | − | 0.219066i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.2533 | −1.29319 | ||||||||
\(179\) | 15.3990 | 1.15098 | 0.575488 | − | 0.817810i | \(-0.304812\pi\) | ||||
0.575488 | + | 0.817810i | \(0.304812\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6276i | 1.31025i | 0.755520 | + | 0.655125i | \(0.227384\pi\) | ||||
−0.755520 | + | 0.655125i | \(0.772616\pi\) | |||||||
\(182\) | − | 1.38329i | − | 0.102536i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 7.14888i | − | 0.527023i | ||||||
\(185\) | 7.56687 | 0.556327 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.44625 | −0.617651 | ||||||||
\(188\) | − | 2.76658i | − | 0.201774i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.47686 | − | 4.38230i | −0.179690 | − | 0.317925i | ||||
\(191\) | − | 18.8244i | − | 1.36208i | −0.732245 | − | 0.681041i | \(-0.761527\pi\) | ||
0.732245 | − | 0.681041i | \(-0.238473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.27201i | − | 0.667414i | −0.942677 | − | 0.333707i | \(-0.891700\pi\) | ||
0.942677 | − | 0.333707i | \(-0.108300\pi\) | |||||||
\(194\) | 3.92142i | 0.281542i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 2.76658i | 0.197111i | 0.995132 | + | 0.0985555i | \(0.0314222\pi\) | ||||
−0.995132 | + | 0.0985555i | \(0.968578\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.9302 | −1.05837 | −0.529186 | − | 0.848506i | \(-0.677503\pi\) | ||||
−0.529186 | + | 0.848506i | \(0.677503\pi\) | |||||||
\(200\) | −3.66635 | −0.259250 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 1.61175i | − | 0.113402i | ||||||
\(203\) | 4.66635 | 0.327513 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 12.9191i | − | 0.902310i | ||||||
\(206\) | 10.6603i | 0.742738i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.38329i | − | 0.0959141i | ||||||
\(209\) | −6.23322 | − | 11.0284i | −0.431161 | − | 0.762851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.85935i | 0.196846i | 0.995145 | + | 0.0984228i | \(0.0313798\pi\) | ||||
−0.995145 | + | 0.0984228i | \(0.968620\pi\) | |||||||
\(212\) | −7.39997 | −0.508232 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.2226 | 0.767164 | ||||||||
\(215\) | − | 2.36018i | − | 0.160963i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.06108i | − | 0.275684i | ||||||
\(218\) | − | 3.91282i | − | 0.265010i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.35624 | 0.226278 | ||||||||
\(221\) | −4.02018 | −0.270427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.9297i | − | 1.13370i | −0.823822 | − | 0.566848i | \(-0.808163\pi\) | ||
0.823822 | − | 0.566848i | \(-0.191837\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.4202 | −0.759657 | ||||||||
\(227\) | 12.6889 | 0.842194 | 0.421097 | − | 0.907016i | \(-0.361645\pi\) | ||||
0.421097 | + | 0.907016i | \(0.361645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.55375 | −0.367002 | −0.183501 | − | 0.983020i | \(-0.558743\pi\) | ||||
−0.183501 | + | 0.983020i | \(0.558743\pi\) | |||||||
\(230\) | 8.25581 | 0.544372 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.66635 | 0.306361 | ||||||||
\(233\) | − | 13.6084i | − | 0.891518i | −0.895153 | − | 0.445759i | \(-0.852934\pi\) | ||
0.895153 | − | 0.445759i | \(-0.147066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.19496 | 0.208416 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.90624i | − | 0.188384i | ||||||
\(239\) | 21.7765i | 1.40860i | 0.709901 | + | 0.704301i | \(0.248740\pi\) | ||||
−0.709901 | + | 0.704301i | \(0.751260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9379i | 1.54197i | 0.636850 | + | 0.770987i | \(0.280237\pi\) | ||||
−0.636850 | + | 0.770987i | \(0.719763\pi\) | |||||||
\(242\) | −2.55375 | −0.164161 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.29954 | −0.531323 | ||||||||
\(245\) | 1.15484i | 0.0737799i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.96684 | − | 5.24922i | −0.188776 | − | 0.334000i | ||||
\(248\) | − | 4.06108i | − | 0.257879i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 10.0082i | − | 0.632976i | ||||||
\(251\) | − | 10.6936i | − | 0.674974i | −0.941330 | − | 0.337487i | \(-0.890423\pi\) | ||
0.941330 | − | 0.337487i | \(-0.109577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7764 | 1.30620 | ||||||||
\(254\) | 12.9145i | 0.810326i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.3407 | −0.832171 | −0.416086 | − | 0.909325i | \(-0.636598\pi\) | ||||
−0.416086 | + | 0.909325i | \(0.636598\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.55232i | 0.407141i | ||||||||
\(260\) | 1.59748 | 0.0990714 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.8101i | 0.729633i | ||||||||
\(263\) | − | 30.3555i | − | 1.87180i | −0.352262 | − | 0.935901i | \(-0.614587\pi\) | ||
0.352262 | − | 0.935901i | \(-0.385413\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.54577i | − | 0.524963i | ||||||
\(266\) | 3.79473 | − | 2.14477i | 0.232670 | − | 0.131504i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 9.91547i | − | 0.605684i | ||||||
\(269\) | −6.84367 | −0.417266 | −0.208633 | − | 0.977994i | \(-0.566901\pi\) | ||||
−0.208633 | + | 0.977994i | \(0.566901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.4865 | −1.66968 | −0.834842 | − | 0.550489i | \(-0.814441\pi\) | ||||
−0.834842 | + | 0.550489i | \(0.814441\pi\) | |||||||
\(272\) | − | 2.90624i | − | 0.176217i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0551i | 0.607452i | ||||||||
\(275\) | − | 10.6553i | − | 0.642539i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.6191 | −1.53930 | −0.769652 | − | 0.638464i | \(-0.779570\pi\) | ||||
−0.769652 | + | 0.638464i | \(0.779570\pi\) | |||||||
\(278\) | 16.8663 | 1.01157 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.15484i | 0.0690148i | ||||||||
\(281\) | 8.79994 | 0.524961 | 0.262480 | − | 0.964937i | \(-0.415460\pi\) | ||||
0.262480 | + | 0.964937i | \(0.415460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.47686 | −0.385009 | −0.192505 | − | 0.981296i | \(-0.561661\pi\) | ||||
−0.192505 | + | 0.981296i | \(0.561661\pi\) | |||||||
\(284\) | −6.06632 | −0.359970 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.02018 | 0.237718 | ||||||||
\(287\) | 11.1869 | 0.660344 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.55375 | 0.503162 | ||||||||
\(290\) | 5.38888i | 0.316446i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.37643 | 0.548714 | ||||||||
\(293\) | 4.64280 | 0.271235 | 0.135618 | − | 0.990761i | \(-0.456698\pi\) | ||||
0.135618 | + | 0.990761i | \(0.456698\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.55232i | 0.380846i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.2978i | 0.828247i | ||||||||
\(299\) | 9.88900 | 0.571895 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.04373 | 0.117799 | ||||||||
\(302\) | − | 6.64508i | − | 0.382382i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.79473 | − | 2.14477i | 0.217643 | − | 0.123011i | ||||
\(305\) | − | 9.58462i | − | 0.548814i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.3684i | − | 0.705902i | −0.935642 | − | 0.352951i | \(-0.885178\pi\) | ||
0.935642 | − | 0.352951i | \(-0.114822\pi\) | |||||||
\(308\) | 2.90624i | 0.165599i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.68989 | 0.266368 | ||||||||
\(311\) | 4.71314i | 0.267258i | 0.991031 | + | 0.133629i | \(0.0426630\pi\) | ||||
−0.991031 | + | 0.133629i | \(0.957337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.17892 | −0.518823 | −0.259412 | − | 0.965767i | \(-0.583529\pi\) | ||||
−0.259412 | + | 0.965767i | \(0.583529\pi\) | |||||||
\(314\) | −16.8201 | −0.949215 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 12.1783i | − | 0.685080i | ||||||
\(317\) | −25.7117 | −1.44411 | −0.722056 | − | 0.691835i | \(-0.756803\pi\) | ||||
−0.722056 | + | 0.691835i | \(0.756803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5615i | 0.759301i | ||||||||
\(320\) | 1.15484i | 0.0645574i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.14888i | 0.398392i | ||||||||
\(323\) | −6.23322 | − | 11.0284i | −0.346825 | − | 0.613637i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.07163i | − | 0.281323i | ||||||
\(326\) | −10.9100 | −0.604249 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.1869 | 0.617695 | ||||||||
\(329\) | 2.76658i | 0.152527i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.3473i | − | 1.11839i | −0.829036 | − | 0.559195i | \(-0.811110\pi\) | ||
0.829036 | − | 0.559195i | \(-0.188890\pi\) | |||||||
\(332\) | − | 14.5262i | − | 0.797230i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.31251 | −0.290688 | ||||||||
\(335\) | 11.4508 | 0.625622 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.8316i | 1.89740i | 0.316178 | + | 0.948700i | \(0.397600\pi\) | ||||
−0.316178 | + | 0.948700i | \(0.602400\pi\) | |||||||
\(338\) | −11.0865 | −0.603026 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.35624 | 0.182018 | ||||||||
\(341\) | 11.8025 | 0.639141 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.04373 | 0.110191 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.2226 | 0.603333 | ||||||||
\(347\) | − | 12.9650i | − | 0.695996i | −0.937495 | − | 0.347998i | \(-0.886862\pi\) | ||
0.937495 | − | 0.347998i | \(-0.113138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.12062 | −0.488216 | −0.244108 | − | 0.969748i | \(-0.578495\pi\) | ||||
−0.244108 | + | 0.969748i | \(0.578495\pi\) | |||||||
\(350\) | 3.66635 | 0.195975 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.90624i | 0.154903i | ||||||||
\(353\) | 22.1865i | 1.18087i | 0.807086 | + | 0.590434i | \(0.201043\pi\) | ||||
−0.807086 | + | 0.590434i | \(0.798957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.00562i | − | 0.371820i | ||||||
\(356\) | 17.2533 | 0.914421 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.3990 | −0.813863 | ||||||||
\(359\) | − | 5.29611i | − | 0.279518i | −0.990186 | − | 0.139759i | \(-0.955367\pi\) | ||
0.990186 | − | 0.139759i | \(-0.0446328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.79994 | − | 16.2776i | 0.515786 | − | 0.856717i | ||||
\(362\) | − | 17.6276i | − | 0.926487i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.38329i | 0.0725042i | ||||||||
\(365\) | 10.8283i | 0.566777i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3527 | −1.27120 | −0.635601 | − | 0.772018i | \(-0.719248\pi\) | ||||
−0.635601 | + | 0.772018i | \(0.719248\pi\) | |||||||
\(368\) | 7.14888i | 0.372661i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.56687 | −0.393383 | ||||||||
\(371\) | 7.39997 | 0.384187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.4235i | − | 1.16105i | −0.814244 | − | 0.580523i | \(-0.802848\pi\) | ||
0.814244 | − | 0.580523i | \(-0.197152\pi\) | |||||||
\(374\) | 8.44625 | 0.436745 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.76658i | 0.142676i | ||||||||
\(377\) | 6.45492i | 0.332445i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.49186i | 0.487564i | 0.969830 | + | 0.243782i | \(0.0783882\pi\) | ||||
−0.969830 | + | 0.243782i | \(0.921612\pi\) | |||||||
\(380\) | 2.47686 | + | 4.38230i | 0.127060 | + | 0.224807i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.8244i | 0.963138i | ||||||||
\(383\) | 24.4086 | 1.24722 | 0.623611 | − | 0.781735i | \(-0.285665\pi\) | ||||
0.623611 | + | 0.781735i | \(0.285665\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.35624 | −0.171050 | ||||||||
\(386\) | 9.27201i | 0.471933i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 3.92142i | − | 0.199080i | ||||||
\(389\) | 33.7656i | 1.71198i | 0.516990 | + | 0.855992i | \(0.327053\pi\) | ||||
−0.516990 | + | 0.855992i | \(0.672947\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7764 | 1.05071 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 2.76658i | − | 0.139379i | ||||||
\(395\) | 14.0639 | 0.707632 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.46629 | −0.274345 | −0.137173 | − | 0.990547i | \(-0.543802\pi\) | ||||
−0.137173 | + | 0.990547i | \(0.543802\pi\) | |||||||
\(398\) | 14.9302 | 0.748382 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.66635 | 0.183317 | ||||||||
\(401\) | 36.2417 | 1.80983 | 0.904913 | − | 0.425597i | \(-0.139936\pi\) | ||||
0.904913 | + | 0.425597i | \(0.139936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.61766 | 0.279836 | ||||||||
\(404\) | 1.61175i | 0.0801873i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.66635 | −0.231587 | ||||||||
\(407\) | −19.0426 | −0.943908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8128i | 0.880785i | 0.897805 | + | 0.440393i | \(0.145161\pi\) | ||||
−0.897805 | + | 0.440393i | \(0.854839\pi\) | |||||||
\(410\) | 12.9191i | 0.638029i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 10.6603i | − | 0.525195i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.7754 | 0.823474 | ||||||||
\(416\) | 1.38329i | 0.0678215i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.23322 | + | 11.0284i | 0.304877 | + | 0.539417i | ||||
\(419\) | − | 4.75402i | − | 0.232249i | −0.993235 | − | 0.116124i | \(-0.962953\pi\) | ||
0.993235 | − | 0.116124i | \(-0.0370472\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.7821i | − | 1.25654i | −0.777995 | − | 0.628270i | \(-0.783763\pi\) | ||
0.777995 | − | 0.628270i | \(-0.216237\pi\) | |||||||
\(422\) | − | 2.85935i | − | 0.139191i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.39997 | 0.359374 | ||||||||
\(425\) | − | 10.6553i | − | 0.516858i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.29954 | 0.401643 | ||||||||
\(428\) | −11.2226 | −0.542467 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.36018i | 0.113818i | ||||||||
\(431\) | −14.4839 | −0.697666 | −0.348833 | − | 0.937185i | \(-0.613422\pi\) | ||||
−0.348833 | + | 0.937185i | \(0.613422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.77419i | 0.277490i | 0.990328 | + | 0.138745i | \(0.0443068\pi\) | ||||
−0.990328 | + | 0.138745i | \(0.955693\pi\) | |||||||
\(434\) | 4.06108i | 0.194938i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.91282i | 0.187390i | ||||||||
\(437\) | 15.3327 | + | 27.1281i | 0.733462 | + | 1.29771i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.6814i | 1.32116i | 0.750756 | + | 0.660580i | \(0.229689\pi\) | ||||
−0.750756 | + | 0.660580i | \(0.770311\pi\) | |||||||
\(440\) | −3.35624 | −0.160003 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.02018 | 0.191221 | ||||||||
\(443\) | − | 10.2922i | − | 0.488996i | −0.969650 | − | 0.244498i | \(-0.921377\pi\) | ||
0.969650 | − | 0.244498i | \(-0.0786232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.9247i | 0.944523i | ||||||||
\(446\) | 16.9297i | 0.801644i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −29.6191 | −1.39781 | −0.698906 | − | 0.715213i | \(-0.746330\pi\) | ||||
−0.698906 | + | 0.715213i | \(0.746330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.5120i | 1.53093i | ||||||||
\(452\) | 11.4202 | 0.537159 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.6889 | −0.595521 | ||||||||
\(455\) | −1.59748 | −0.0748910 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8664 | −0.835755 | −0.417878 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417878 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(458\) | 5.55375 | 0.259510 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.25581 | −0.384929 | ||||||||
\(461\) | 14.3533i | 0.668498i | 0.942485 | + | 0.334249i | \(0.108483\pi\) | ||||
−0.942485 | + | 0.334249i | \(0.891517\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6840 | −1.00774 | −0.503870 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503870 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(464\) | −4.66635 | −0.216630 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.6084i | 0.630399i | ||||||||
\(467\) | − | 10.1096i | − | 0.467816i | −0.972259 | − | 0.233908i | \(-0.924848\pi\) | ||
0.972259 | − | 0.233908i | \(-0.0751515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.91547i | 0.457854i | ||||||||
\(470\) | −3.19496 | −0.147372 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.93958i | 0.273102i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.9128 | − | 7.86346i | 0.638363 | − | 0.360801i | ||||
\(476\) | 2.90624i | 0.133207i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 21.7765i | − | 0.996033i | ||||||
\(479\) | 17.0644i | 0.779690i | 0.920880 | + | 0.389845i | \(0.127471\pi\) | ||||
−0.920880 | + | 0.389845i | \(0.872529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.06377 | −0.413272 | ||||||||
\(482\) | − | 23.9379i | − | 1.09034i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.55375 | 0.116080 | ||||||||
\(485\) | 4.52861 | 0.205634 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5642i | 0.886538i | 0.896389 | + | 0.443269i | \(0.146181\pi\) | ||||
−0.896389 | + | 0.443269i | \(0.853819\pi\) | |||||||
\(488\) | 8.29954 | 0.375702 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 1.15484i | − | 0.0521703i | ||||||
\(491\) | 6.86596i | 0.309856i | 0.987926 | + | 0.154928i | \(0.0495146\pi\) | ||||
−0.987926 | + | 0.154928i | \(0.950485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5615i | 0.610781i | ||||||||
\(494\) | 2.96684 | + | 5.24922i | 0.133484 | + | 0.236174i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.06108i | 0.182348i | ||||||||
\(497\) | 6.06632 | 0.272112 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7529 | −0.481364 | −0.240682 | − | 0.970604i | \(-0.577371\pi\) | ||||
−0.240682 | + | 0.970604i | \(0.577371\pi\) | |||||||
\(500\) | 10.0082i | 0.447582i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.6936i | 0.477278i | ||||||||
\(503\) | − | 9.00268i | − | 0.401410i | −0.979652 | − | 0.200705i | \(-0.935677\pi\) | ||
0.979652 | − | 0.200705i | \(-0.0643232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.86131 | −0.0828270 | ||||||||
\(506\) | −20.7764 | −0.923623 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 12.9145i | − | 0.572987i | ||||||
\(509\) | 31.1126 | 1.37904 | 0.689521 | − | 0.724266i | \(-0.257821\pi\) | ||||
0.689521 | + | 0.724266i | \(0.257821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.37643 | −0.414789 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.3407 | 0.588434 | ||||||||
\(515\) | 12.3109 | 0.542484 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.04037 | −0.353615 | ||||||||
\(518\) | − | 6.55232i | − | 0.287892i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.59748 | −0.0700541 | ||||||||
\(521\) | −5.82094 | −0.255020 | −0.127510 | − | 0.991837i | \(-0.540698\pi\) | ||||
−0.127510 | + | 0.991837i | \(0.540698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.1010i | 1.53486i | 0.641134 | + | 0.767429i | \(0.278464\pi\) | ||||
−0.641134 | + | 0.767429i | \(0.721536\pi\) | |||||||
\(524\) | − | 11.8101i | − | 0.515928i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30.3555i | 1.32356i | ||||||||
\(527\) | 11.8025 | 0.514125 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.1065 | −1.22202 | ||||||||
\(530\) | 8.54577i | 0.371205i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.79473 | + | 2.14477i | −0.164522 | + | 0.0929875i | ||||
\(533\) | 15.4748i | 0.670288i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 12.9603i | − | 0.560325i | ||||||
\(536\) | 9.91547i | 0.428283i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.84367 | 0.295052 | ||||||||
\(539\) | − | 2.90624i | − | 0.125181i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.04359 | −0.130854 | −0.0654270 | − | 0.997857i | \(-0.520841\pi\) | ||||
−0.0654270 | + | 0.997857i | \(0.520841\pi\) | |||||||
\(542\) | 27.4865 | 1.18065 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.90624i | 0.124604i | ||||||||
\(545\) | −4.51868 | −0.193559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.47609i | − | 0.191384i | −0.995411 | − | 0.0956919i | \(-0.969494\pi\) | ||
0.995411 | − | 0.0956919i | \(-0.0305064\pi\) | |||||||
\(548\) | − | 10.0551i | − | 0.429534i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.6553i | 0.454343i | ||||||||
\(551\) | −17.7075 | + | 10.0082i | −0.754366 | + | 0.426365i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1783i | 0.517872i | ||||||||
\(554\) | 25.6191 | 1.08845 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.8663 | −0.715289 | ||||||||
\(557\) | 0.185529i | 0.00786110i | 0.999992 | + | 0.00393055i | \(0.00125114\pi\) | ||||
−0.999992 | + | 0.00393055i | \(0.998749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.82707i | 0.119573i | ||||||||
\(560\) | − | 1.15484i | − | 0.0488008i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.79994 | −0.371203 | ||||||||
\(563\) | −2.62021 | −0.110429 | −0.0552144 | − | 0.998475i | \(-0.517584\pi\) | ||||
−0.0552144 | + | 0.998475i | \(0.517584\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.1884i | 0.554842i | ||||||||
\(566\) | 6.47686 | 0.272243 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.06632 | 0.254537 | ||||||||
\(569\) | −25.1974 | −1.05633 | −0.528164 | − | 0.849142i | \(-0.677119\pi\) | ||||
−0.528164 | + | 0.849142i | \(0.677119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.2890 | −1.14201 | −0.571004 | − | 0.820947i | \(-0.693446\pi\) | ||||
−0.571004 | + | 0.820947i | \(0.693446\pi\) | |||||||
\(572\) | −4.02018 | −0.168092 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.1869 | −0.466934 | ||||||||
\(575\) | 26.2103i | 1.09304i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.11515 | 0.337838 | 0.168919 | − | 0.985630i | \(-0.445972\pi\) | ||||
0.168919 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(578\) | −8.55375 | −0.355789 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 5.38888i | − | 0.223761i | ||||||
\(581\) | 14.5262i | 0.602649i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.5061i | 0.890692i | ||||||||
\(584\) | −9.37643 | −0.387999 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.64280 | −0.191792 | ||||||||
\(587\) | − | 5.49024i | − | 0.226607i | −0.993560 | − | 0.113303i | \(-0.963857\pi\) | ||
0.993560 | − | 0.113303i | \(-0.0361432\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.71008 | + | 15.4107i | 0.358892 | + | 0.634987i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 6.55232i | − | 0.269299i | ||||||
\(593\) | 43.4133i | 1.78277i | 0.453247 | + | 0.891385i | \(0.350266\pi\) | ||||
−0.453247 | + | 0.891385i | \(0.649734\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.35624 | −0.137592 | ||||||||
\(596\) | − | 14.2978i | − | 0.585659i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.88900 | −0.404391 | ||||||||
\(599\) | 36.7317 | 1.50082 | 0.750409 | − | 0.660974i | \(-0.229857\pi\) | ||||
0.750409 | + | 0.660974i | \(0.229857\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.2991i | − | 1.48067i | −0.672238 | − | 0.740335i | \(-0.734667\pi\) | ||
0.672238 | − | 0.740335i | \(-0.265333\pi\) | |||||||
\(602\) | −2.04373 | −0.0832962 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.64508i | 0.270385i | ||||||||
\(605\) | 2.94917i | 0.119901i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4176i | 1.15343i | 0.816944 | + | 0.576717i | \(0.195666\pi\) | ||||
−0.816944 | + | 0.576717i | \(0.804334\pi\) | |||||||
\(608\) | −3.79473 | + | 2.14477i | −0.153897 | + | 0.0869818i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.58462i | 0.388070i | ||||||||
\(611\) | −3.82699 | −0.154824 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.46133 | −0.341750 | −0.170875 | − | 0.985293i | \(-0.554659\pi\) | ||||
−0.170875 | + | 0.985293i | \(0.554659\pi\) | |||||||
\(614\) | 12.3684i | 0.499148i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 2.90624i | − | 0.117096i | ||||||
\(617\) | 21.6873i | 0.873098i | 0.899680 | + | 0.436549i | \(0.143800\pi\) | ||||
−0.899680 | + | 0.436549i | \(0.856200\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.7075 | 1.35482 | 0.677410 | − | 0.735606i | \(-0.263102\pi\) | ||||
0.677410 | + | 0.735606i | \(0.263102\pi\) | |||||||
\(620\) | −4.68989 | −0.188351 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 4.71314i | − | 0.188980i | ||||||
\(623\) | −17.2533 | −0.691237 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.77385 | 0.270954 | ||||||||
\(626\) | 9.17892 | 0.366863 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.8201 | 0.671196 | ||||||||
\(629\) | −19.0426 | −0.759279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.7780 | 1.42430 | 0.712150 | − | 0.702028i | \(-0.247722\pi\) | ||||
0.712150 | + | 0.702028i | \(0.247722\pi\) | |||||||
\(632\) | 12.1783i | 0.484425i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.7117 | 1.02114 | ||||||||
\(635\) | 14.9141 | 0.591849 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.38329i | − | 0.0548080i | ||||||
\(638\) | − | 13.5615i | − | 0.536907i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 1.15484i | − | 0.0456490i | ||||||
\(641\) | 43.1267 | 1.70340 | 0.851702 | − | 0.524027i | \(-0.175571\pi\) | ||||
0.851702 | + | 0.524027i | \(0.175571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.24028 | 0.324965 | 0.162482 | − | 0.986711i | \(-0.448050\pi\) | ||||
0.162482 | + | 0.986711i | \(0.448050\pi\) | |||||||
\(644\) | − | 7.14888i | − | 0.281705i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.23322 | + | 11.0284i | 0.245243 | + | 0.433907i | ||||
\(647\) | 8.02837i | 0.315628i | 0.987469 | + | 0.157814i | \(0.0504446\pi\) | ||||
−0.987469 | + | 0.157814i | \(0.949555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.07163i | 0.198926i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.9100 | 0.427268 | ||||||||
\(653\) | − | 11.9881i | − | 0.469130i | −0.972100 | − | 0.234565i | \(-0.924633\pi\) | ||
0.972100 | − | 0.234565i | \(-0.0753666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.6388 | 0.532912 | ||||||||
\(656\) | −11.1869 | −0.436777 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 2.76658i | − | 0.107853i | ||||||
\(659\) | 14.6688 | 0.571414 | 0.285707 | − | 0.958317i | \(-0.407772\pi\) | ||||
0.285707 | + | 0.958317i | \(0.407772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.6876i | 1.62146i | 0.585420 | + | 0.810730i | \(0.300929\pi\) | ||||
−0.585420 | + | 0.810730i | \(0.699071\pi\) | |||||||
\(662\) | 20.3473i | 0.790821i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.5262i | 0.563727i | ||||||||
\(665\) | −2.47686 | − | 4.38230i | −0.0960485 | − | 0.169938i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 33.3592i | − | 1.29167i | ||||||
\(668\) | 5.31251 | 0.205547 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.4508 | −0.442382 | ||||||||
\(671\) | 24.1205i | 0.931160i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20.0337i | − | 0.772241i | −0.922448 | − | 0.386121i | \(-0.873815\pi\) | ||
0.922448 | − | 0.386121i | \(-0.126185\pi\) | |||||||
\(674\) | − | 34.8316i | − | 1.34166i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0865 | 0.426404 | ||||||||
\(677\) | −0.202607 | −0.00778682 | −0.00389341 | − | 0.999992i | \(-0.501239\pi\) | ||||
−0.00389341 | + | 0.999992i | \(0.501239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.92142i | 0.150490i | ||||||||
\(680\) | −3.35624 | −0.128706 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.8025 | −0.451941 | ||||||||
\(683\) | 36.3965 | 1.39267 | 0.696336 | − | 0.717716i | \(-0.254812\pi\) | ||||
0.696336 | + | 0.717716i | \(0.254812\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.6120 | 0.443674 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.04373 | −0.0779165 | ||||||||
\(689\) | 10.2363i | 0.389973i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.8443 | −1.59183 | −0.795916 | − | 0.605407i | \(-0.793010\pi\) | ||||
−0.795916 | + | 0.605407i | \(0.793010\pi\) | |||||||
\(692\) | −11.2226 | −0.426621 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.9650i | 0.492144i | ||||||||
\(695\) | − | 19.4778i | − | 0.738835i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.5120i | 1.23148i | ||||||||
\(698\) | 9.12062 | 0.345221 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.66635 | −0.138575 | ||||||||
\(701\) | − | 37.6920i | − | 1.42361i | −0.702378 | − | 0.711804i | \(-0.747879\pi\) | ||
0.702378 | − | 0.711804i | \(-0.252121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0532 | − | 24.8643i | −0.530026 | − | 0.937774i | ||||
\(704\) | − | 2.90624i | − | 0.109533i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 22.1865i | − | 0.834999i | ||||||
\(707\) | − | 1.61175i | − | 0.0606159i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.5081 | 1.33353 | 0.666767 | − | 0.745266i | \(-0.267677\pi\) | ||||
0.666767 | + | 0.745266i | \(0.267677\pi\) | |||||||
\(710\) | 7.00562i | 0.262916i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.2533 | −0.646593 | ||||||||
\(713\) | −29.0322 | −1.08726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.64266i | − | 0.173626i | ||||||
\(716\) | 15.3990 | 0.575488 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.29611i | 0.197649i | ||||||||
\(719\) | − | 28.6288i | − | 1.06768i | −0.845587 | − | 0.533838i | \(-0.820749\pi\) | ||
0.845587 | − | 0.533838i | \(-0.179251\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6603i | 0.397010i | ||||||||
\(722\) | −9.79994 | + | 16.2776i | −0.364716 | + | 0.605791i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.6276i | 0.655125i | ||||||||
\(725\) | −17.1085 | −0.635392 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.7117 | −0.656890 | −0.328445 | − | 0.944523i | \(-0.606524\pi\) | ||||
−0.328445 | + | 0.944523i | \(0.606524\pi\) | |||||||
\(728\) | − | 1.38329i | − | 0.0512682i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 10.8283i | − | 0.400772i | ||||||
\(731\) | 5.93958i | 0.219683i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.9197 | 0.846560 | 0.423280 | − | 0.905999i | \(-0.360879\pi\) | ||||
0.423280 | + | 0.905999i | \(0.360879\pi\) | |||||||
\(734\) | 24.3527 | 0.898876 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.14888i | − | 0.263511i | ||||||
\(737\) | −28.8168 | −1.06148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.0215 | −1.80328 | −0.901642 | − | 0.432482i | \(-0.857638\pi\) | ||||
−0.901642 | + | 0.432482i | \(0.857638\pi\) | |||||||
\(740\) | 7.56687 | 0.278164 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.39997 | −0.271661 | ||||||||
\(743\) | −15.1301 | −0.555069 | −0.277535 | − | 0.960716i | \(-0.589517\pi\) | ||||
−0.277535 | + | 0.960716i | \(0.589517\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.5116 | 0.604939 | ||||||||
\(746\) | 22.4235i | 0.820984i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.44625 | −0.308826 | ||||||||
\(749\) | 11.2226 | 0.410067 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 42.9079i | − | 1.56573i | −0.622190 | − | 0.782866i | \(-0.713757\pi\) | ||
0.622190 | − | 0.782866i | \(-0.286243\pi\) | |||||||
\(752\) | − | 2.76658i | − | 0.100887i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 6.45492i | − | 0.235074i | ||||||
\(755\) | −7.67400 | −0.279285 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.4916 | 0.563051 | 0.281525 | − | 0.959554i | \(-0.409160\pi\) | ||||
0.281525 | + | 0.959554i | \(0.409160\pi\) | |||||||
\(758\) | − | 9.49186i | − | 0.344760i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.47686 | − | 4.38230i | −0.0898452 | − | 0.158963i | ||||
\(761\) | − | 1.98244i | − | 0.0718633i | −0.999354 | − | 0.0359317i | \(-0.988560\pi\) | ||
0.999354 | − | 0.0359317i | \(-0.0114399\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.91282i | − | 0.141654i | ||||||
\(764\) | − | 18.8244i | − | 0.681041i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.4086 | −0.881920 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.8443 | 1.29258 | 0.646289 | − | 0.763092i | \(-0.276320\pi\) | ||||
0.646289 | + | 0.763092i | \(0.276320\pi\) | |||||||
\(770\) | 3.35624 | 0.120951 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 9.27201i | − | 0.333707i | ||||||
\(773\) | −23.0864 | −0.830359 | −0.415179 | − | 0.909740i | \(-0.636281\pi\) | ||||
−0.415179 | + | 0.909740i | \(0.636281\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.8893i | 0.534841i | ||||||||
\(776\) | 3.92142i | 0.140771i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 33.7656i | − | 1.21055i | ||||||
\(779\) | −42.4514 | + | 23.9934i | −1.52098 | + | 0.859652i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.6302i | 0.630858i | ||||||||
\(782\) | −20.7764 | −0.742962 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 19.4245i | 0.693291i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.57646i | 0.198779i | 0.995049 | + | 0.0993896i | \(0.0316890\pi\) | ||||
−0.995049 | + | 0.0993896i | \(0.968311\pi\) | |||||||
\(788\) | 2.76658i | 0.0985555i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.0639 | −0.500372 | ||||||||
\(791\) | −11.4202 | −0.406054 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4807i | 0.407691i | ||||||||
\(794\) | 5.46629 | 0.193991 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.9302 | −0.529186 | ||||||||
\(797\) | 26.0404 | 0.922397 | 0.461199 | − | 0.887297i | \(-0.347420\pi\) | ||||
0.461199 | + | 0.887297i | \(0.347420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.04037 | −0.284448 | ||||||||
\(800\) | −3.66635 | −0.129625 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.2417 | −1.27974 | ||||||||
\(803\) | − | 27.2502i | − | 0.961638i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.25581 | 0.290979 | ||||||||
\(806\) | −5.61766 | −0.197874 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 1.61175i | − | 0.0567010i | ||||||
\(809\) | 43.3033i | 1.52246i | 0.648480 | + | 0.761232i | \(0.275405\pi\) | ||||
−0.648480 | + | 0.761232i | \(0.724595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.3961i | 1.62919i | 0.580032 | + | 0.814594i | \(0.303040\pi\) | ||||
−0.580032 | + | 0.814594i | \(0.696960\pi\) | |||||||
\(812\) | 4.66635 | 0.163757 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.0426 | 0.667444 | ||||||||
\(815\) | 12.5993i | 0.441333i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.75540 | + | 4.38333i | −0.271327 | + | 0.153353i | ||||
\(818\) | − | 17.8128i | − | 0.622809i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 12.9191i | − | 0.451155i | ||||||
\(821\) | − | 22.1839i | − | 0.774224i | −0.922033 | − | 0.387112i | \(-0.873473\pi\) | ||
0.922033 | − | 0.387112i | \(-0.126527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1341 | 1.39899 | 0.699493 | − | 0.714639i | \(-0.253409\pi\) | ||||
0.699493 | + | 0.714639i | \(0.253409\pi\) | |||||||
\(824\) | 10.6603i | 0.371369i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.979960 | −0.0340765 | −0.0170383 | − | 0.999855i | \(-0.505424\pi\) | ||||
−0.0170383 | + | 0.999855i | \(0.505424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5623i | 1.09620i | 0.836412 | + | 0.548101i | \(0.184649\pi\) | ||||
−0.836412 | + | 0.548101i | \(0.815351\pi\) | |||||||
\(830\) | −16.7754 | −0.582284 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.38329i | − | 0.0479570i | ||||||
\(833\) | − | 2.90624i | − | 0.100695i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.13509i | 0.212314i | ||||||||
\(836\) | −6.23322 | − | 11.0284i | −0.215580 | − | 0.381425i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.75402i | 0.164225i | ||||||||
\(839\) | −26.4548 | −0.913320 | −0.456660 | − | 0.889641i | \(-0.650954\pi\) | ||||
−0.456660 | + | 0.889641i | \(0.650954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.22520 | −0.249145 | ||||||||
\(842\) | 25.7821i | 0.888508i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.85935i | 0.0984228i | ||||||||
\(845\) | 12.8031i | 0.440441i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.55375 | −0.0877479 | ||||||||
\(848\) | −7.39997 | −0.254116 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.6553i | 0.365474i | ||||||||
\(851\) | 46.8418 | 1.60571 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.20101 | −0.178079 | −0.0890397 | − | 0.996028i | \(-0.528380\pi\) | ||||
−0.0890397 | + | 0.996028i | \(0.528380\pi\) | |||||||
\(854\) | −8.29954 | −0.284004 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.2226 | 0.383582 | ||||||||
\(857\) | −18.8935 | −0.645390 | −0.322695 | − | 0.946503i | \(-0.604589\pi\) | ||||
−0.322695 | + | 0.946503i | \(0.604589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3548 | 0.455660 | 0.227830 | − | 0.973701i | \(-0.426837\pi\) | ||||
0.227830 | + | 0.973701i | \(0.426837\pi\) | |||||||
\(860\) | − | 2.36018i | − | 0.0804814i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.4839 | 0.493324 | ||||||||
\(863\) | −57.6872 | −1.96369 | −0.981847 | − | 0.189674i | \(-0.939257\pi\) | ||||
−0.981847 | + | 0.189674i | \(0.939257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 12.9603i | − | 0.440665i | ||||||
\(866\) | − | 5.77419i | − | 0.196215i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 4.06108i | − | 0.137842i | ||||||
\(869\) | −35.3930 | −1.20062 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.7160 | −0.464749 | ||||||||
\(872\) | − | 3.91282i | − | 0.132505i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.3327 | − | 27.1281i | −0.518636 | − | 0.917621i | ||||
\(875\) | − | 10.0082i | − | 0.338340i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27.0762i | − | 0.914298i | −0.889390 | − | 0.457149i | \(-0.848871\pi\) | ||
0.889390 | − | 0.457149i | \(-0.151129\pi\) | |||||||
\(878\) | − | 27.6814i | − | 0.934201i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.35624 | 0.113139 | ||||||||
\(881\) | 1.23900i | 0.0417430i | 0.999782 | + | 0.0208715i | \(0.00664409\pi\) | ||||
−0.999782 | + | 0.0208715i | \(0.993356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.53357 | 0.118914 | 0.0594570 | − | 0.998231i | \(-0.481063\pi\) | ||||
0.0594570 | + | 0.998231i | \(0.481063\pi\) | |||||||
\(884\) | −4.02018 | −0.135213 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.2922i | 0.345773i | ||||||||
\(887\) | 58.7825 | 1.97372 | 0.986862 | − | 0.161567i | \(-0.0516549\pi\) | ||||
0.986862 | + | 0.161567i | \(0.0516549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.9145i | 0.433138i | ||||||||
\(890\) | − | 19.9247i | − | 0.667878i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 16.9297i | − | 0.566848i | ||||||
\(893\) | −5.93368 | − | 10.4984i | −0.198563 | − | 0.351317i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.7834i | 0.594433i | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.6191 | 0.988403 | ||||||||
\(899\) | − | 18.9504i | − | 0.632032i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.5061i | 0.716473i | ||||||||
\(902\) | − | 32.5120i | − | 1.08253i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.4202 | −0.379829 | ||||||||
\(905\) | −20.3571 | −0.676691 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 21.9135i | − | 0.727627i | −0.931472 | − | 0.363814i | \(-0.881474\pi\) | ||
0.931472 | − | 0.363814i | \(-0.118526\pi\) | |||||||
\(908\) | 12.6889 | 0.421097 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.59748 | 0.0529559 | ||||||||
\(911\) | 17.4202 | 0.577155 | 0.288578 | − | 0.957456i | \(-0.406818\pi\) | ||||
0.288578 | + | 0.957456i | \(0.406818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.2167 | −1.39717 | ||||||||
\(914\) | 17.8664 | 0.590968 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.55375 | −0.183501 | ||||||||
\(917\) | 11.8101i | 0.390005i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.7351 | 0.815935 | 0.407967 | − | 0.912996i | \(-0.366238\pi\) | ||||
0.407967 | + | 0.912996i | \(0.366238\pi\) | |||||||
\(920\) | 8.25581 | 0.272186 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 14.3533i | − | 0.472700i | ||||||
\(923\) | 8.39149i | 0.276209i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 24.0231i | − | 0.789874i | ||||||
\(926\) | 21.6840 | 0.712580 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.66635 | 0.153180 | ||||||||
\(929\) | − | 0.325188i | − | 0.0106691i | −0.999986 | − | 0.00533453i | \(-0.998302\pi\) | ||
0.999986 | − | 0.00533453i | \(-0.00169804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.79473 | − | 2.14477i | 0.124367 | − | 0.0702919i | ||||
\(932\) | − | 13.6084i | − | 0.445759i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.1096i | 0.330796i | ||||||||
\(935\) | − | 9.75406i | − | 0.318992i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.6417 | 1.88307 | 0.941536 | − | 0.336912i | \(-0.109382\pi\) | ||||
0.941536 | + | 0.336912i | \(0.109382\pi\) | |||||||
\(938\) | − | 9.91547i | − | 0.323752i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.19496 | 0.104208 | ||||||||
\(941\) | 26.2201 | 0.854751 | 0.427375 | − | 0.904074i | \(-0.359438\pi\) | ||||
0.427375 | + | 0.904074i | \(0.359438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 79.9741i | − | 2.60432i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 5.93958i | − | 0.193112i | ||||||
\(947\) | − | 8.80253i | − | 0.286044i | −0.989720 | − | 0.143022i | \(-0.954318\pi\) | ||
0.989720 | − | 0.143022i | \(-0.0456819\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.9703i | − | 0.421035i | ||||||
\(950\) | −13.9128 | + | 7.86346i | −0.451391 | + | 0.255124i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 2.90624i | − | 0.0941919i | ||||||
\(953\) | −30.0714 | −0.974109 | −0.487054 | − | 0.873372i | \(-0.661929\pi\) | ||||
−0.487054 | + | 0.873372i | \(0.661929\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.7391 | 0.703461 | ||||||||
\(956\) | 21.7765i | 0.704301i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 17.0644i | − | 0.551324i | ||||||
\(959\) | 10.0551i | 0.324697i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5076 | 0.467988 | ||||||||
\(962\) | 9.06377 | 0.292228 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.9379i | 0.770987i | ||||||||
\(965\) | 10.7077 | 0.344692 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8217 | 0.508792 | 0.254396 | − | 0.967100i | \(-0.418123\pi\) | ||||
0.254396 | + | 0.967100i | \(0.418123\pi\) | |||||||
\(968\) | −2.55375 | −0.0820806 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.52861 | −0.145405 | ||||||||
\(971\) | 21.4226 | 0.687483 | 0.343741 | − | 0.939064i | \(-0.388306\pi\) | ||||
0.343741 | + | 0.939064i | \(0.388306\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.8663 | 0.540708 | ||||||||
\(974\) | − | 19.5642i | − | 0.626877i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.29954 | −0.265662 | ||||||||
\(977\) | −11.6427 | −0.372482 | −0.186241 | − | 0.982504i | \(-0.559630\pi\) | ||||
−0.186241 | + | 0.982504i | \(0.559630\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 50.1422i | − | 1.60255i | ||||||
\(980\) | 1.15484i | 0.0368900i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 6.86596i | − | 0.219102i | ||||||
\(983\) | 42.6297 | 1.35968 | 0.679838 | − | 0.733362i | \(-0.262050\pi\) | ||||
0.679838 | + | 0.733362i | \(0.262050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.19496 | −0.101800 | ||||||||
\(986\) | − | 13.5615i | − | 0.431888i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.96684 | − | 5.24922i | −0.0943878 | − | 0.167000i | ||||
\(989\) | − | 14.6104i | − | 0.464583i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.6332i | − | 0.591902i | −0.955203 | − | 0.295951i | \(-0.904363\pi\) | ||
0.955203 | − | 0.295951i | \(-0.0956366\pi\) | |||||||
\(992\) | − | 4.06108i | − | 0.128939i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.06632 | −0.192412 | ||||||||
\(995\) | − | 17.2419i | − | 0.546606i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.02610 | 0.0324968 | 0.0162484 | − | 0.999868i | \(-0.494828\pi\) | ||||
0.0162484 | + | 0.999868i | \(0.494828\pi\) | |||||||
\(998\) | 10.7529 | 0.340376 | ||||||||
\(999\) | 0 | 0 |
(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 | 2394.2.b.i.1709.5 | yes | 8 | |
3.2 | odd | 2 | 2394.2.b.j.1709.4 | yes | 8 | ||
19.18 | odd | 2 | 2394.2.b.j.1709.5 | yes | 8 | ||
57.56 | even | 2 | inner | 2394.2.b.i.1709.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.b.i.1709.4 | ✓ | 8 | 57.56 | even | 2 | inner | |
2394.2.b.i.1709.5 | yes | 8 | 1.1 | even | 1 | trivial | |
2394.2.b.j.1709.4 | yes | 8 | 3.2 | odd | 2 | ||
2394.2.b.j.1709.5 | yes | 8 | 19.18 | odd | 2 |