Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1287,2,Mod(298,1287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1287.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1287 = 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1287.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: | \(10.2767467401\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 429) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 298.9 | ||
Root | \(0.584778i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1287.298 |
Dual form | 1287.2.b.c.298.6 |
$q$-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 \(\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(937\) | \(1145\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.584778i | 0.413501i | 0.978394 | + | 0.206750i | \(0.0662888\pi\) | ||||
−0.978394 | + | 0.206750i | \(0.933711\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.65803 | 0.829017 | ||||||||
\(5\) | 1.95350i | 0.873633i | 0.899551 | + | 0.436817i | \(0.143894\pi\) | ||||
−0.899551 | + | 0.436817i | \(0.856106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.51078i | − | 0.571023i | −0.958375 | − | 0.285511i | \(-0.907837\pi\) | ||
0.958375 | − | 0.285511i | \(-0.0921634\pi\) | |||||||
\(8\) | 2.13914i | 0.756300i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.14237 | −0.361248 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.49467 | + | 0.887280i | −0.969248 | + | 0.246087i | ||||
\(14\) | 0.883474 | 0.236118 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.06515 | 0.516286 | ||||||||
\(17\) | 3.44198 | 0.834803 | 0.417401 | − | 0.908722i | \(-0.362941\pi\) | ||||
0.417401 | + | 0.908722i | \(0.362941\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.09587i | 1.16907i | 0.811368 | + | 0.584536i | \(0.198724\pi\) | ||||
−0.811368 | + | 0.584536i | \(0.801276\pi\) | |||||||
\(20\) | 3.23897i | 0.724257i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.584778 | −0.124675 | ||||||||
\(23\) | −0.701611 | −0.146296 | −0.0731480 | − | 0.997321i | \(-0.523305\pi\) | ||||
−0.0731480 | + | 0.997321i | \(0.523305\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.18383 | 0.236765 | ||||||||
\(26\) | −0.518862 | − | 2.04361i | −0.101757 | − | 0.400785i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.50493i | − | 0.473388i | ||||||
\(29\) | −5.04937 | −0.937645 | −0.468822 | − | 0.883292i | \(-0.655322\pi\) | ||||
−0.468822 | + | 0.883292i | \(0.655322\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.26957i | 1.30565i | 0.757507 | + | 0.652827i | \(0.226417\pi\) | ||||
−0.757507 | + | 0.652827i | \(0.773583\pi\) | |||||||
\(32\) | 5.48593i | 0.969785i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.01280i | 0.345192i | ||||||||
\(35\) | 2.95132 | 0.498864 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.08160i | 0.342213i | 0.985253 | + | 0.171106i | \(0.0547342\pi\) | ||||
−0.985253 | + | 0.171106i | \(0.945266\pi\) | |||||||
\(38\) | −2.97995 | −0.483413 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.17882 | −0.660729 | ||||||||
\(41\) | − | 1.03658i | − | 0.161886i | −0.996719 | − | 0.0809430i | \(-0.974207\pi\) | ||
0.996719 | − | 0.0809430i | \(-0.0257932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.48659 | 0.836698 | 0.418349 | − | 0.908286i | \(-0.362609\pi\) | ||||
0.418349 | + | 0.908286i | \(0.362609\pi\) | |||||||
\(44\) | 1.65803i | 0.249958i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 0.410287i | − | 0.0604935i | ||||||
\(47\) | 3.75225i | 0.547322i | 0.961826 | + | 0.273661i | \(0.0882347\pi\) | ||||
−0.961826 | + | 0.273661i | \(0.911765\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.71753 | 0.673933 | ||||||||
\(50\) | 0.692276i | 0.0979026i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.79429 | + | 1.47114i | −0.803523 | + | 0.204010i | ||||
\(53\) | 0.502747 | 0.0690575 | 0.0345288 | − | 0.999404i | \(-0.489007\pi\) | ||||
0.0345288 | + | 0.999404i | \(0.489007\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.95350 | −0.263410 | ||||||||
\(56\) | 3.23178 | 0.431865 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.95276i | − | 0.387717i | ||||||
\(59\) | − | 2.65023i | − | 0.345031i | −0.985007 | − | 0.172515i | \(-0.944811\pi\) | ||
0.985007 | − | 0.172515i | \(-0.0551894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.38195 | −0.689088 | −0.344544 | − | 0.938770i | \(-0.611967\pi\) | ||||
−0.344544 | + | 0.938770i | \(0.611967\pi\) | |||||||
\(62\) | −4.25109 | −0.539889 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.922236 | 0.115279 | ||||||||
\(65\) | −1.73330 | − | 6.82685i | −0.214990 | − | 0.846767i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.47197i | − | 1.03502i | −0.855679 | − | 0.517508i | \(-0.826860\pi\) | ||
0.855679 | − | 0.517508i | \(-0.173140\pi\) | |||||||
\(68\) | 5.70692 | 0.692066 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.72587i | 0.206281i | ||||||||
\(71\) | 2.31533i | 0.274779i | 0.990517 | + | 0.137390i | \(0.0438712\pi\) | ||||
−0.990517 | + | 0.137390i | \(0.956129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.21094i | − | 0.258771i | −0.991594 | − | 0.129385i | \(-0.958700\pi\) | ||
0.991594 | − | 0.129385i | \(-0.0413004\pi\) | |||||||
\(74\) | −1.21727 | −0.141505 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.44913i | 0.969181i | ||||||||
\(77\) | 1.51078 | 0.172170 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.54589 | −0.623961 | −0.311981 | − | 0.950088i | \(-0.600992\pi\) | ||||
−0.311981 | + | 0.950088i | \(0.600992\pi\) | |||||||
\(80\) | 4.03427i | 0.451045i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.606168 | 0.0669400 | ||||||||
\(83\) | − | 14.5137i | − | 1.59308i | −0.604585 | − | 0.796541i | \(-0.706661\pi\) | ||
0.604585 | − | 0.796541i | \(-0.293339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.72392i | 0.729311i | ||||||||
\(86\) | 3.20844i | 0.345975i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.13914 | −0.228033 | ||||||||
\(89\) | − | 1.80966i | − | 0.191824i | −0.995390 | − | 0.0959119i | \(-0.969423\pi\) | ||
0.995390 | − | 0.0959119i | \(-0.0305767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.34049 | + | 5.27970i | 0.140521 | + | 0.553462i | ||||
\(92\) | −1.16330 | −0.121282 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.19424 | −0.226318 | ||||||||
\(95\) | −9.95480 | −1.02134 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5085i | 1.47312i | 0.676372 | + | 0.736560i | \(0.263551\pi\) | ||||
−0.676372 | + | 0.736560i | \(0.736449\pi\) | |||||||
\(98\) | 2.75871i | 0.278672i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.96282 | 0.196282 | ||||||||
\(101\) | 8.63799 | 0.859512 | 0.429756 | − | 0.902945i | \(-0.358600\pi\) | ||||
0.429756 | + | 0.902945i | \(0.358600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.90048 | 0.285792 | 0.142896 | − | 0.989738i | \(-0.454358\pi\) | ||||
0.142896 | + | 0.989738i | \(0.454358\pi\) | |||||||
\(104\) | −1.89802 | − | 7.47559i | −0.186116 | − | 0.733042i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.293995i | 0.0285554i | ||||||||
\(107\) | 2.29234 | 0.221609 | 0.110805 | − | 0.993842i | \(-0.464657\pi\) | ||||
0.110805 | + | 0.993842i | \(0.464657\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8818i | 1.23386i | 0.787019 | + | 0.616929i | \(0.211623\pi\) | ||||
−0.787019 | + | 0.616929i | \(0.788377\pi\) | |||||||
\(110\) | − | 1.14237i | − | 0.108920i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 3.11999i | − | 0.294811i | ||||||
\(113\) | 12.6273 | 1.18788 | 0.593940 | − | 0.804509i | \(-0.297572\pi\) | ||||
0.593940 | + | 0.804509i | \(0.297572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.37060i | − | 0.127809i | ||||||
\(116\) | −8.37203 | −0.777324 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.54980 | 0.142670 | ||||||||
\(119\) | − | 5.20009i | − | 0.476691i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | − | 3.14725i | − | 0.284939i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.0532i | 1.08241i | ||||||||
\(125\) | 12.0801i | 1.08048i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.05085 | −0.448190 | −0.224095 | − | 0.974567i | \(-0.571943\pi\) | ||||
−0.224095 | + | 0.974567i | \(0.571943\pi\) | |||||||
\(128\) | 11.5112i | 1.01745i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.99220 | − | 1.01360i | 0.350139 | − | 0.0888985i | ||||
\(131\) | −15.9772 | −1.39594 | −0.697968 | − | 0.716129i | \(-0.745912\pi\) | ||||
−0.697968 | + | 0.716129i | \(0.745912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.69876 | 0.667567 | ||||||||
\(134\) | 4.95422 | 0.427980 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.36288i | 0.631361i | ||||||||
\(137\) | − | 17.2582i | − | 1.47447i | −0.675639 | − | 0.737233i | \(-0.736132\pi\) | ||
0.675639 | − | 0.737233i | \(-0.263868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.70544 | −0.483929 | −0.241965 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241965 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(140\) | 4.89339 | 0.413567 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.35395 | −0.113621 | ||||||||
\(143\) | −0.887280 | − | 3.49467i | −0.0741981 | − | 0.292239i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.86396i | − | 0.819158i | ||||||
\(146\) | 1.29291 | 0.107002 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.45136i | 0.283700i | ||||||||
\(149\) | 0.161015i | 0.0131908i | 0.999978 | + | 0.00659542i | \(0.00209940\pi\) | ||||
−0.999978 | + | 0.00659542i | \(0.997901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.3107i | − | 1.32734i | −0.748025 | − | 0.663671i | \(-0.768997\pi\) | ||
0.748025 | − | 0.663671i | \(-0.231003\pi\) | |||||||
\(152\) | −10.9008 | −0.884170 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.883474i | 0.0711924i | ||||||||
\(155\) | −14.2011 | −1.14066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2192 | −1.13481 | −0.567407 | − | 0.823437i | \(-0.692053\pi\) | ||||
−0.567407 | + | 0.823437i | \(0.692053\pi\) | |||||||
\(158\) | − | 3.24312i | − | 0.258008i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.7168 | −0.847236 | ||||||||
\(161\) | 1.05998i | 0.0835384i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.0186i | − | 1.01970i | −0.860264 | − | 0.509848i | \(-0.829702\pi\) | ||
0.860264 | − | 0.509848i | \(-0.170298\pi\) | |||||||
\(164\) | − | 1.71868i | − | 0.134206i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.48728 | 0.658740 | ||||||||
\(167\) | 14.0271i | 1.08545i | 0.839911 | + | 0.542724i | \(0.182607\pi\) | ||||
−0.839911 | + | 0.542724i | \(0.817393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4255 | − | 6.20151i | 0.878882 | − | 0.477039i | ||||
\(170\) | −3.93200 | −0.301571 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.09696 | 0.693637 | ||||||||
\(173\) | 17.8674 | 1.35844 | 0.679218 | − | 0.733936i | \(-0.262319\pi\) | ||||
0.679218 | + | 0.733936i | \(0.262319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.78851i | − | 0.135198i | ||||||
\(176\) | 2.06515i | 0.155666i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.05825 | 0.0793193 | ||||||||
\(179\) | 17.2723 | 1.29099 | 0.645495 | − | 0.763764i | \(-0.276651\pi\) | ||||
0.645495 | + | 0.763764i | \(0.276651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.70318 | −0.275255 | −0.137628 | − | 0.990484i | \(-0.543948\pi\) | ||||
−0.137628 | + | 0.990484i | \(0.543948\pi\) | |||||||
\(182\) | −3.08745 | + | 0.783889i | −0.228857 | + | 0.0581057i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.50084i | − | 0.110644i | ||||||
\(185\) | −4.06641 | −0.298969 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.44198i | 0.251703i | ||||||||
\(188\) | 6.22136i | 0.453740i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 5.82135i | − | 0.422325i | ||||||
\(191\) | 20.6259 | 1.49243 | 0.746217 | − | 0.665702i | \(-0.231868\pi\) | ||||
0.746217 | + | 0.665702i | \(0.231868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.8475i | − | 1.35667i | −0.734753 | − | 0.678335i | \(-0.762702\pi\) | ||
0.734753 | − | 0.678335i | \(-0.237298\pi\) | |||||||
\(194\) | −8.48429 | −0.609136 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.82183 | 0.558702 | ||||||||
\(197\) | 7.18370i | 0.511818i | 0.966701 | + | 0.255909i | \(0.0823747\pi\) | ||||
−0.966701 | + | 0.255909i | \(0.917625\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.9591 | 1.34398 | 0.671989 | − | 0.740562i | \(-0.265440\pi\) | ||||
0.671989 | + | 0.740562i | \(0.265440\pi\) | |||||||
\(200\) | 2.53237i | 0.179066i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.05131i | 0.355409i | ||||||||
\(203\) | 7.62851i | 0.535417i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.02496 | 0.141429 | ||||||||
\(206\) | 1.69614i | 0.118175i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.21701 | + | 1.83236i | −0.500409 | + | 0.127051i | ||||
\(209\) | −5.09587 | −0.352489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9916 | −1.37628 | −0.688139 | − | 0.725578i | \(-0.741572\pi\) | ||||
−0.688139 | + | 0.725578i | \(0.741572\pi\) | |||||||
\(212\) | 0.833571 | 0.0572499 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.34051i | 0.0916356i | ||||||||
\(215\) | 10.7181i | 0.730967i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9828 | 0.745558 | ||||||||
\(218\) | −7.53303 | −0.510201 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.23897 | −0.218372 | ||||||||
\(221\) | −12.0286 | + | 3.05400i | −0.809131 | + | 0.205434i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 27.7784i | − | 1.86018i | −0.367330 | − | 0.930091i | \(-0.619728\pi\) | ||
0.367330 | − | 0.930091i | \(-0.380272\pi\) | |||||||
\(224\) | 8.28806 | 0.553769 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.38419i | 0.491189i | ||||||||
\(227\) | − | 28.6524i | − | 1.90173i | −0.309612 | − | 0.950863i | \(-0.600199\pi\) | ||
0.309612 | − | 0.950863i | \(-0.399801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.83459i | − | 0.319479i | −0.987159 | − | 0.159739i | \(-0.948935\pi\) | ||
0.987159 | − | 0.159739i | \(-0.0510654\pi\) | |||||||
\(230\) | 0.801497 | 0.0528491 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 10.8013i | − | 0.709141i | ||||||
\(233\) | 13.6237 | 0.892518 | 0.446259 | − | 0.894904i | \(-0.352756\pi\) | ||||
0.446259 | + | 0.894904i | \(0.352756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.33004 | −0.478159 | ||||||||
\(236\) | − | 4.39417i | − | 0.286036i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.04090 | 0.197112 | ||||||||
\(239\) | 5.99903i | 0.388045i | 0.980997 | + | 0.194023i | \(0.0621535\pi\) | ||||
−0.980997 | + | 0.194023i | \(0.937846\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.9290i | 0.832831i | 0.909174 | + | 0.416416i | \(0.136714\pi\) | ||||
−0.909174 | + | 0.416416i | \(0.863286\pi\) | |||||||
\(242\) | − | 0.584778i | − | 0.0375910i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.92346 | −0.571266 | ||||||||
\(245\) | 9.21571i | 0.588770i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.52146 | − | 17.8084i | −0.287694 | − | 1.13312i | ||||
\(248\) | −15.5506 | −0.987466 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.06420 | −0.446779 | ||||||||
\(251\) | −23.9724 | −1.51313 | −0.756563 | − | 0.653921i | \(-0.773123\pi\) | ||||
−0.756563 | + | 0.653921i | \(0.773123\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.701611i | − | 0.0441099i | ||||||
\(254\) | − | 2.95363i | − | 0.185327i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.88701 | −0.305438 | ||||||||
\(257\) | 16.3441 | 1.01952 | 0.509758 | − | 0.860318i | \(-0.329735\pi\) | ||||
0.509758 | + | 0.860318i | \(0.329735\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.14485 | 0.195411 | ||||||||
\(260\) | −2.87388 | − | 11.3192i | −0.178230 | − | 0.701984i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 9.34313i | − | 0.577220i | ||||||
\(263\) | −10.1510 | −0.625936 | −0.312968 | − | 0.949764i | \(-0.601323\pi\) | ||||
−0.312968 | + | 0.949764i | \(0.601323\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.982117i | 0.0603310i | ||||||||
\(266\) | 4.50207i | 0.276040i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 14.0468i | − | 0.858045i | ||||||
\(269\) | −16.5294 | −1.00781 | −0.503907 | − | 0.863758i | \(-0.668105\pi\) | ||||
−0.503907 | + | 0.863758i | \(0.668105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.8927i | − | 1.26914i | −0.772865 | − | 0.634570i | \(-0.781177\pi\) | ||
0.772865 | − | 0.634570i | \(-0.218823\pi\) | |||||||
\(272\) | 7.10819 | 0.430997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0922 | 0.609693 | ||||||||
\(275\) | 1.18383i | 0.0713874i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.3070 | 1.03988 | 0.519938 | − | 0.854204i | \(-0.325955\pi\) | ||||
0.519938 | + | 0.854204i | \(0.325955\pi\) | |||||||
\(278\) | − | 3.33642i | − | 0.200105i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.31329i | 0.377291i | ||||||||
\(281\) | − | 16.0666i | − | 0.958450i | −0.877692 | − | 0.479225i | \(-0.840918\pi\) | ||
0.877692 | − | 0.479225i | \(-0.159082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.2180 | 1.02350 | 0.511751 | − | 0.859134i | \(-0.328997\pi\) | ||||
0.511751 | + | 0.859134i | \(0.328997\pi\) | |||||||
\(284\) | 3.83890i | 0.227797i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.04361 | − | 0.518862i | 0.120841 | − | 0.0306810i | ||||
\(287\) | −1.56604 | −0.0924406 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.15277 | −0.303104 | ||||||||
\(290\) | 5.76823 | 0.338722 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 3.66581i | − | 0.214525i | ||||||
\(293\) | 5.29670i | 0.309436i | 0.987959 | + | 0.154718i | \(0.0494470\pi\) | ||||
−0.987959 | + | 0.154718i | \(0.950553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.17723 | 0.301430 | ||||||||
\(296\) | −4.45283 | −0.258816 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.0941580 | −0.00545443 | ||||||||
\(299\) | 2.45190 | − | 0.622525i | 0.141797 | − | 0.0360016i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 8.28906i | − | 0.477773i | ||||||
\(302\) | 9.53812 | 0.548857 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.5237i | 0.603576i | ||||||||
\(305\) | − | 10.5137i | − | 0.602010i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.3020i | − | 1.50113i | −0.660794 | − | 0.750567i | \(-0.729780\pi\) | ||
0.660794 | − | 0.750567i | \(-0.270220\pi\) | |||||||
\(308\) | 2.50493 | 0.142732 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 8.30451i | − | 0.471665i | ||||||
\(311\) | 32.8590 | 1.86326 | 0.931632 | − | 0.363403i | \(-0.118385\pi\) | ||||
0.931632 | + | 0.363403i | \(0.118385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.2130 | 1.87731 | 0.938655 | − | 0.344858i | \(-0.112073\pi\) | ||||
0.938655 | + | 0.344858i | \(0.112073\pi\) | |||||||
\(314\) | − | 8.31507i | − | 0.469247i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.19527 | −0.517274 | ||||||||
\(317\) | − | 30.8436i | − | 1.73235i | −0.499740 | − | 0.866175i | \(-0.666571\pi\) | ||
0.499740 | − | 0.866175i | \(-0.333429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.04937i | − | 0.282711i | ||||||
\(320\) | 1.80159i | 0.100712i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.619855 | −0.0345432 | ||||||||
\(323\) | 17.5399i | 0.975945i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.13709 | + | 1.05039i | −0.229484 | + | 0.0582649i | ||||
\(326\) | 7.61300 | 0.421645 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.21738 | 0.122434 | ||||||||
\(329\) | 5.66884 | 0.312534 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.75414i | 0.316276i | 0.987417 | + | 0.158138i | \(0.0505491\pi\) | ||||
−0.987417 | + | 0.158138i | \(0.949451\pi\) | |||||||
\(332\) | − | 24.0641i | − | 1.32069i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.20273 | −0.448833 | ||||||||
\(335\) | 16.5500 | 0.904224 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9245 | −0.595094 | −0.297547 | − | 0.954707i | \(-0.596169\pi\) | ||||
−0.297547 | + | 0.954707i | \(0.596169\pi\) | |||||||
\(338\) | 3.62651 | + | 6.68137i | 0.197256 | + | 0.363419i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.1485i | 0.604612i | ||||||||
\(341\) | −7.26957 | −0.393669 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.7027i | − | 0.955854i | ||||||
\(344\) | 11.7366i | 0.632795i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.4485i | 0.561715i | ||||||||
\(347\) | −16.3474 | −0.877572 | −0.438786 | − | 0.898591i | \(-0.644591\pi\) | ||||
−0.438786 | + | 0.898591i | \(0.644591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.62758i | − | 0.461824i | −0.972975 | − | 0.230912i | \(-0.925829\pi\) | ||
0.972975 | − | 0.230912i | \(-0.0741709\pi\) | |||||||
\(350\) | 1.04588 | 0.0559046 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.48593 | −0.292401 | ||||||||
\(353\) | − | 16.5793i | − | 0.882425i | −0.897403 | − | 0.441212i | \(-0.854549\pi\) | ||
0.897403 | − | 0.441212i | \(-0.145451\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.52300 | −0.240056 | ||||||||
\(356\) | − | 3.00048i | − | 0.159025i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.1005i | 0.533826i | ||||||||
\(359\) | − | 15.5233i | − | 0.819289i | −0.912245 | − | 0.409645i | \(-0.865653\pi\) | ||
0.912245 | − | 0.409645i | \(-0.134347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.96788 | −0.366731 | ||||||||
\(362\) | − | 2.16554i | − | 0.113818i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.22258 | + | 8.75392i | 0.116495 | + | 0.458830i | ||||
\(365\) | 4.31907 | 0.226071 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.4682 | 1.22503 | 0.612514 | − | 0.790460i | \(-0.290158\pi\) | ||||
0.612514 | + | 0.790460i | \(0.290158\pi\) | |||||||
\(368\) | −1.44893 | −0.0755306 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 2.37795i | − | 0.123624i | ||||||
\(371\) | − | 0.759541i | − | 0.0394334i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.3222 | 0.638018 | 0.319009 | − | 0.947752i | \(-0.396650\pi\) | ||||
0.319009 | + | 0.947752i | \(0.396650\pi\) | |||||||
\(374\) | −2.01280 | −0.104079 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.02659 | −0.413940 | ||||||||
\(377\) | 17.6459 | − | 4.48021i | 0.908810 | − | 0.230742i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.8695i | − | 1.17473i | −0.809322 | − | 0.587365i | \(-0.800165\pi\) | ||
0.809322 | − | 0.587365i | \(-0.199835\pi\) | |||||||
\(380\) | −16.5054 | −0.846709 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.0616i | 0.617123i | ||||||||
\(383\) | 35.5259i | 1.81529i | 0.419737 | + | 0.907646i | \(0.362122\pi\) | ||||
−0.419737 | + | 0.907646i | \(0.637878\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.95132i | 0.150413i | ||||||||
\(386\) | 11.0216 | 0.560984 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.0557i | 1.22124i | ||||||||
\(389\) | −2.67074 | −0.135412 | −0.0677060 | − | 0.997705i | \(-0.521568\pi\) | ||||
−0.0677060 | + | 0.997705i | \(0.521568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.41493 | −0.122128 | ||||||||
\(392\) | 10.0915i | 0.509696i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.20087 | −0.211637 | ||||||||
\(395\) | − | 10.8339i | − | 0.545113i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.4406i | 1.82890i | 0.404698 | + | 0.914451i | \(0.367377\pi\) | ||||
−0.404698 | + | 0.914451i | \(0.632623\pi\) | |||||||
\(398\) | 11.0869i | 0.555736i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.44477 | 0.122239 | ||||||||
\(401\) | 13.6597i | 0.682132i | 0.940039 | + | 0.341066i | \(0.110788\pi\) | ||||
−0.940039 | + | 0.341066i | \(0.889212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.45015 | − | 25.4048i | −0.321305 | − | 1.26550i | ||||
\(404\) | 14.3221 | 0.712550 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.46099 | −0.221395 | ||||||||
\(407\) | −2.08160 | −0.103181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8507i | 1.27823i | 0.769110 | + | 0.639117i | \(0.220700\pi\) | ||||
−0.769110 | + | 0.639117i | \(0.779300\pi\) | |||||||
\(410\) | 1.18415i | 0.0584810i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.80909 | 0.236927 | ||||||||
\(413\) | −4.00393 | −0.197020 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.3525 | 1.39177 | ||||||||
\(416\) | −4.86756 | − | 19.1715i | −0.238652 | − | 0.939962i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 2.97995i | − | 0.145754i | ||||||
\(419\) | −22.6067 | −1.10441 | −0.552205 | − | 0.833708i | \(-0.686213\pi\) | ||||
−0.552205 | + | 0.833708i | \(0.686213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.6918i | 1.20341i | 0.798720 | + | 0.601703i | \(0.205511\pi\) | ||||
−0.798720 | + | 0.601703i | \(0.794489\pi\) | |||||||
\(422\) | − | 11.6907i | − | 0.569092i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.07544i | 0.0522282i | ||||||||
\(425\) | 4.07471 | 0.197652 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.13097i | 0.393485i | ||||||||
\(428\) | 3.80079 | 0.183718 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.26770 | −0.302255 | ||||||||
\(431\) | − | 30.1126i | − | 1.45047i | −0.688499 | − | 0.725237i | \(-0.741730\pi\) | ||
0.688499 | − | 0.725237i | \(-0.258270\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.9402 | −1.48689 | −0.743445 | − | 0.668797i | \(-0.766809\pi\) | ||||
−0.743445 | + | 0.668797i | \(0.766809\pi\) | |||||||
\(434\) | 6.42248i | 0.308289i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.3585i | 1.02289i | ||||||||
\(437\) | − | 3.57532i | − | 0.171031i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.02158 | 0.335122 | 0.167561 | − | 0.985862i | \(-0.446411\pi\) | ||||
0.167561 | + | 0.985862i | \(0.446411\pi\) | |||||||
\(440\) | − | 4.17882i | − | 0.199217i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.78591 | − | 7.03406i | −0.0849472 | − | 0.334576i | ||||
\(443\) | 22.5411 | 1.07096 | 0.535480 | − | 0.844548i | \(-0.320131\pi\) | ||||
0.535480 | + | 0.844548i | \(0.320131\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.53518 | 0.167584 | ||||||||
\(446\) | 16.2442 | 0.769187 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 1.39330i | − | 0.0658272i | ||||||
\(449\) | − | 9.41670i | − | 0.444401i | −0.975001 | − | 0.222201i | \(-0.928676\pi\) | ||
0.975001 | − | 0.222201i | \(-0.0713240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.03658 | 0.0488105 | ||||||||
\(452\) | 20.9365 | 0.984772 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.7553 | 0.786365 | ||||||||
\(455\) | −10.3139 | + | 2.61865i | −0.483523 | + | 0.122764i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.48691i | − | 0.163111i | −0.996669 | − | 0.0815554i | \(-0.974011\pi\) | ||
0.996669 | − | 0.0815554i | \(-0.0259887\pi\) | |||||||
\(458\) | 2.82717 | 0.132105 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 2.27250i | − | 0.105956i | ||||||
\(461\) | − | 15.1983i | − | 0.707855i | −0.935273 | − | 0.353928i | \(-0.884846\pi\) | ||
0.935273 | − | 0.353928i | \(-0.115154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.9882i | − | 0.743035i | −0.928426 | − | 0.371518i | \(-0.878838\pi\) | ||
0.928426 | − | 0.371518i | \(-0.121162\pi\) | |||||||
\(464\) | −10.4277 | −0.484093 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.96684i | 0.369057i | ||||||||
\(467\) | 32.9225 | 1.52347 | 0.761736 | − | 0.647888i | \(-0.224348\pi\) | ||||
0.761736 | + | 0.647888i | \(0.224348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7993 | −0.591017 | ||||||||
\(470\) | − | 4.28645i | − | 0.197719i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.66921 | 0.260947 | ||||||||
\(473\) | 5.48659i | 0.252274i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.03262i | 0.276796i | ||||||||
\(476\) | − | 8.62193i | − | 0.395185i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.50811 | −0.160457 | ||||||||
\(479\) | 33.6023i | 1.53533i | 0.640853 | + | 0.767664i | \(0.278581\pi\) | ||||
−0.640853 | + | 0.767664i | \(0.721419\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.84696 | − | 7.27451i | −0.0842142 | − | 0.331689i | ||||
\(482\) | −7.56061 | −0.344376 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.65803 | −0.0753652 | ||||||||
\(485\) | −28.3425 | −1.28697 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.70001i | 0.167663i | 0.996480 | + | 0.0838316i | \(0.0267158\pi\) | ||||
−0.996480 | + | 0.0838316i | \(0.973284\pi\) | |||||||
\(488\) | − | 11.5127i | − | 0.521158i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.38915 | −0.243457 | ||||||||
\(491\) | −10.1397 | −0.457599 | −0.228799 | − | 0.973474i | \(-0.573480\pi\) | ||||
−0.228799 | + | 0.973474i | \(0.573480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.3798 | −0.782749 | ||||||||
\(494\) | 10.4140 | − | 2.64405i | 0.468546 | − | 0.118962i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.0127i | 0.674091i | ||||||||
\(497\) | 3.49796 | 0.156905 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 15.1124i | − | 0.676525i | −0.941052 | − | 0.338263i | \(-0.890161\pi\) | ||
0.941052 | − | 0.338263i | \(-0.109839\pi\) | |||||||
\(500\) | 20.0293i | 0.895736i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 14.0185i | − | 0.625678i | ||||||
\(503\) | −11.9190 | −0.531441 | −0.265721 | − | 0.964050i | \(-0.585610\pi\) | ||||
−0.265721 | + | 0.964050i | \(0.585610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.8743i | 0.750898i | ||||||||
\(506\) | 0.410287 | 0.0182395 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.37448 | −0.371558 | ||||||||
\(509\) | 35.2059i | 1.56047i | 0.625485 | + | 0.780236i | \(0.284901\pi\) | ||||
−0.625485 | + | 0.780236i | \(0.715099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.34025 | −0.147764 | ||||||||
\(512\) | 20.1645i | 0.891154i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.55767i | 0.421571i | ||||||||
\(515\) | 5.66609i | 0.249678i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.75225 | −0.165024 | ||||||||
\(518\) | 1.83904i | 0.0808028i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.6036 | − | 3.70778i | 0.640410 | − | 0.162597i | ||||
\(521\) | 2.84143 | 0.124485 | 0.0622426 | − | 0.998061i | \(-0.480175\pi\) | ||||
0.0622426 | + | 0.998061i | \(0.480175\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.8564 | −0.780804 | −0.390402 | − | 0.920644i | \(-0.627664\pi\) | ||||
−0.390402 | + | 0.920644i | \(0.627664\pi\) | |||||||
\(524\) | −26.4908 | −1.15725 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 5.93607i | − | 0.258825i | ||||||
\(527\) | 25.0217i | 1.08996i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5077 | −0.978597 | ||||||||
\(530\) | −0.574321 | −0.0249469 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.7648 | 0.553424 | ||||||||
\(533\) | 0.919734 | + | 3.62249i | 0.0398381 | + | 0.156908i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.47810i | 0.193605i | ||||||||
\(536\) | 18.1227 | 0.782782 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 9.66602i | − | 0.416732i | ||||||
\(539\) | 4.71753i | 0.203198i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.56883i | 0.153436i | 0.997053 | + | 0.0767179i | \(0.0244441\pi\) | ||||
−0.997053 | + | 0.0767179i | \(0.975556\pi\) | |||||||
\(542\) | 12.2176 | 0.524791 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.8825i | 0.809579i | ||||||||
\(545\) | −25.1647 | −1.07794 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.50639 | 0.149923 | 0.0749613 | − | 0.997186i | \(-0.476117\pi\) | ||||
0.0749613 | + | 0.997186i | \(0.476117\pi\) | |||||||
\(548\) | − | 28.6146i | − | 1.22236i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.692276 | −0.0295188 | ||||||||
\(551\) | − | 25.7309i | − | 1.09617i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.37864i | 0.356296i | ||||||||
\(554\) | 10.1207i | 0.429989i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.45982 | −0.401186 | ||||||||
\(557\) | 7.38164i | 0.312770i | 0.987696 | + | 0.156385i | \(0.0499841\pi\) | ||||
−0.987696 | + | 0.156385i | \(0.950016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.1738 | + | 4.86815i | −0.810967 | + | 0.205901i | ||||
\(560\) | 6.09491 | 0.257557 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.39537 | 0.396320 | ||||||||
\(563\) | −35.5383 | −1.49776 | −0.748879 | − | 0.662706i | \(-0.769408\pi\) | ||||
−0.748879 | + | 0.662706i | \(0.769408\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.6675i | 1.03777i | ||||||||
\(566\) | 10.0687i | 0.423219i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.95281 | −0.207815 | ||||||||
\(569\) | −19.6546 | −0.823966 | −0.411983 | − | 0.911192i | \(-0.635164\pi\) | ||||
−0.411983 | + | 0.911192i | \(0.635164\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.6081 | 0.778726 | 0.389363 | − | 0.921084i | \(-0.372695\pi\) | ||||
0.389363 | + | 0.921084i | \(0.372695\pi\) | |||||||
\(572\) | −1.47114 | − | 5.79429i | −0.0615115 | − | 0.242271i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 0.915788i | − | 0.0382243i | ||||||
\(575\) | −0.830586 | −0.0346378 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5485i | 1.06360i | 0.846871 | + | 0.531799i | \(0.178484\pi\) | ||||
−0.846871 | + | 0.531799i | \(0.821516\pi\) | |||||||
\(578\) | − | 3.01323i | − | 0.125334i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 16.3548i | − | 0.679096i | ||||||
\(581\) | −21.9270 | −0.909686 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.502747i | 0.0208216i | ||||||||
\(584\) | 4.72950 | 0.195708 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.09739 | −0.127952 | ||||||||
\(587\) | − | 2.35936i | − | 0.0973813i | −0.998814 | − | 0.0486907i | \(-0.984495\pi\) | ||
0.998814 | − | 0.0486907i | \(-0.0155049\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.0448 | −1.52640 | ||||||||
\(590\) | 3.02753i | 0.124642i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.29881i | 0.176680i | ||||||||
\(593\) | 11.6707i | 0.479257i | 0.970865 | + | 0.239628i | \(0.0770256\pi\) | ||||
−0.970865 | + | 0.239628i | \(0.922974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.1584 | 0.416453 | ||||||||
\(596\) | 0.266968i | 0.0109354i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.364040 | + | 1.43382i | 0.0148867 | + | 0.0586332i | ||||
\(599\) | −9.12181 | −0.372707 | −0.186354 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186354 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.90316 | 0.281586 | 0.140793 | − | 0.990039i | \(-0.455035\pi\) | ||||
0.140793 | + | 0.990039i | \(0.455035\pi\) | |||||||
\(602\) | 4.84726 | 0.197560 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 27.0436i | − | 1.10039i | ||||||
\(605\) | − | 1.95350i | − | 0.0794212i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5559 | 0.469038 | 0.234519 | − | 0.972112i | \(-0.424648\pi\) | ||||
0.234519 | + | 0.972112i | \(0.424648\pi\) | |||||||
\(608\) | −27.9556 | −1.13375 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.14816 | 0.248932 | ||||||||
\(611\) | −3.32930 | − | 13.1129i | −0.134689 | − | 0.530491i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.7362i | − | 1.52415i | −0.647488 | − | 0.762075i | \(-0.724181\pi\) | ||
0.647488 | − | 0.762075i | \(-0.275819\pi\) | |||||||
\(614\) | 15.3808 | 0.620720 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.23178i | 0.130212i | ||||||||
\(617\) | 28.2159i | 1.13593i | 0.823053 | + | 0.567964i | \(0.192269\pi\) | ||||
−0.823053 | + | 0.567964i | \(0.807731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.4407i | 1.54506i | 0.634978 | + | 0.772530i | \(0.281009\pi\) | ||||
−0.634978 | + | 0.772530i | \(0.718991\pi\) | |||||||
\(620\) | −23.5460 | −0.945628 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.2152i | 0.770461i | ||||||||
\(623\) | −2.73401 | −0.109536 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.6794 | −0.707177 | ||||||||
\(626\) | 19.4222i | 0.776269i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.5759 | −0.940781 | ||||||||
\(629\) | 7.16483i | 0.285680i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16.9688i | − | 0.675519i | −0.941232 | − | 0.337759i | \(-0.890331\pi\) | ||
0.941232 | − | 0.337759i | \(-0.109669\pi\) | |||||||
\(632\) | − | 11.8634i | − | 0.471902i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.0367 | 0.716328 | ||||||||
\(635\) | − | 9.86685i | − | 0.391554i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.4862 | + | 4.18577i | −0.653208 | + | 0.165846i | ||||
\(638\) | 2.95276 | 0.116901 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −22.4871 | −0.888881 | ||||||||
\(641\) | 6.00876 | 0.237332 | 0.118666 | − | 0.992934i | \(-0.462138\pi\) | ||||
0.118666 | + | 0.992934i | \(0.462138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.64269i | − | 0.380270i | −0.981758 | − | 0.190135i | \(-0.939107\pi\) | ||
0.981758 | − | 0.190135i | \(-0.0608927\pi\) | |||||||
\(644\) | 1.75749i | 0.0692547i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.2569 | −0.403554 | ||||||||
\(647\) | −34.1912 | −1.34420 | −0.672098 | − | 0.740463i | \(-0.734606\pi\) | ||||
−0.672098 | + | 0.740463i | \(0.734606\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.65023 | 0.104031 | ||||||||
\(650\) | −0.614243 | − | 2.41928i | −0.0240926 | − | 0.0948919i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 21.5853i | − | 0.845345i | ||||||
\(653\) | 2.32307 | 0.0909086 | 0.0454543 | − | 0.998966i | \(-0.485526\pi\) | ||||
0.0454543 | + | 0.998966i | \(0.485526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 31.2115i | − | 1.21954i | ||||||
\(656\) | − | 2.14068i | − | 0.0835796i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.31502i | 0.129233i | ||||||||
\(659\) | −4.07928 | −0.158906 | −0.0794532 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794532 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.2740i | 1.64427i | 0.569293 | + | 0.822135i | \(0.307217\pi\) | ||||
−0.569293 | + | 0.822135i | \(0.692783\pi\) | |||||||
\(662\) | −3.36489 | −0.130780 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.0467 | 1.20485 | ||||||||
\(665\) | 15.0395i | 0.583209i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.54270 | 0.137174 | ||||||||
\(668\) | 23.2574i | 0.899854i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.67809i | 0.373897i | ||||||||
\(671\) | − | 5.38195i | − | 0.207768i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.6688 | 0.411252 | 0.205626 | − | 0.978631i | \(-0.434077\pi\) | ||||
0.205626 | + | 0.978631i | \(0.434077\pi\) | |||||||
\(674\) | − | 6.38840i | − | 0.246072i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.9438 | − | 10.2823i | 0.728608 | − | 0.395473i | ||||
\(677\) | −24.2174 | −0.930752 | −0.465376 | − | 0.885113i | \(-0.654081\pi\) | ||||
−0.465376 | + | 0.885113i | \(0.654081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.9193 | 0.841185 | ||||||||
\(680\) | −14.3834 | −0.551578 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 4.25109i | − | 0.162783i | ||||||
\(683\) | 37.1698i | 1.42226i | 0.703059 | + | 0.711132i | \(0.251817\pi\) | ||||
−0.703059 | + | 0.711132i | \(0.748183\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.7139 | 1.28814 | ||||||||
\(686\) | 10.3521 | 0.395246 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.3306 | 0.431976 | ||||||||
\(689\) | −1.75693 | + | 0.446077i | −0.0669339 | + | 0.0169942i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 15.9632i | − | 0.607268i | −0.952789 | − | 0.303634i | \(-0.901800\pi\) | ||
0.952789 | − | 0.303634i | \(-0.0981999\pi\) | |||||||
\(692\) | 29.6248 | 1.12617 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 9.55959i | − | 0.362877i | ||||||
\(695\) | − | 11.1456i | − | 0.422777i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.56788i | − | 0.135143i | ||||||
\(698\) | 5.04522 | 0.190965 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 2.96540i | − | 0.112082i | ||||||
\(701\) | −2.01736 | −0.0761947 | −0.0380974 | − | 0.999274i | \(-0.512130\pi\) | ||||
−0.0380974 | + | 0.999274i | \(0.512130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6076 | −0.400072 | ||||||||
\(704\) | 0.922236i | 0.0347581i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.69519 | 0.364883 | ||||||||
\(707\) | − | 13.0501i | − | 0.490801i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.6428i | 1.11326i | 0.830761 | + | 0.556629i | \(0.187905\pi\) | ||||
−0.830761 | + | 0.556629i | \(0.812095\pi\) | |||||||
\(710\) | − | 2.64495i | − | 0.0992634i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.87112 | 0.145076 | ||||||||
\(713\) | − | 5.10041i | − | 0.191012i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.82685 | − | 1.73330i | 0.255310 | − | 0.0648219i | ||||
\(716\) | 28.6380 | 1.07025 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.07770 | 0.338777 | ||||||||
\(719\) | 32.3389 | 1.20604 | 0.603018 | − | 0.797728i | \(-0.293965\pi\) | ||||
0.603018 | + | 0.797728i | \(0.293965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.38199i | − | 0.163194i | ||||||
\(722\) | − | 4.07467i | − | 0.151643i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.13999 | −0.228191 | ||||||||
\(725\) | −5.97758 | −0.222002 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.9325 | −1.40684 | −0.703419 | − | 0.710775i | \(-0.748344\pi\) | ||||
−0.703419 | + | 0.710775i | \(0.748344\pi\) | |||||||
\(728\) | −11.2940 | + | 2.86749i | −0.418584 | + | 0.106276i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.52570i | 0.0934803i | ||||||||
\(731\) | 18.8847 | 0.698478 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.7917i | − | 0.620217i | −0.950701 | − | 0.310109i | \(-0.899635\pi\) | ||
0.950701 | − | 0.310109i | \(-0.100365\pi\) | |||||||
\(734\) | 13.7237i | 0.506550i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.84899i | − | 0.141876i | ||||||
\(737\) | 8.47197 | 0.312069 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4629i | 0.936668i | 0.883551 | + | 0.468334i | \(0.155146\pi\) | ||||
−0.883551 | + | 0.468334i | \(0.844854\pi\) | |||||||
\(740\) | −6.74225 | −0.247850 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.444164 | 0.0163058 | ||||||||
\(743\) | 4.81269i | 0.176560i | 0.996096 | + | 0.0882802i | \(0.0281371\pi\) | ||||
−0.996096 | + | 0.0882802i | \(0.971863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.314543 | −0.0115240 | ||||||||
\(746\) | 7.20574i | 0.263821i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.70692i | 0.208666i | ||||||||
\(749\) | − | 3.46324i | − | 0.126544i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9537 | 0.910574 | 0.455287 | − | 0.890345i | \(-0.349537\pi\) | ||||
0.455287 | + | 0.890345i | \(0.349537\pi\) | |||||||
\(752\) | 7.74895i | 0.282575i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.61993 | + | 10.3189i | 0.0954122 | + | 0.375794i | ||||
\(755\) | 31.8629 | 1.15961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.8373 | −1.22984 | −0.614919 | − | 0.788591i | \(-0.710811\pi\) | ||||
−0.614919 | + | 0.788591i | \(0.710811\pi\) | |||||||
\(758\) | 13.3736 | 0.485752 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 21.2947i | − | 0.772440i | ||||||
\(761\) | 50.5981i | 1.83418i | 0.398679 | + | 0.917091i | \(0.369469\pi\) | ||||
−0.398679 | + | 0.917091i | \(0.630531\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.4617 | 0.704561 | ||||||||
\(764\) | 34.1984 | 1.23725 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.7748 | −0.750624 | ||||||||
\(767\) | 2.35150 | + | 9.26169i | 0.0849076 | + | 0.334420i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 26.1333i | − | 0.942389i | −0.882029 | − | 0.471195i | \(-0.843823\pi\) | ||
0.882029 | − | 0.471195i | \(-0.156177\pi\) | |||||||
\(770\) | −1.72587 | −0.0621960 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 31.2497i | − | 1.12470i | ||||||
\(773\) | − | 0.778578i | − | 0.0280035i | −0.999902 | − | 0.0140018i | \(-0.995543\pi\) | ||
0.999902 | − | 0.0140018i | \(-0.00445704\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.60591i | 0.309133i | ||||||||
\(776\) | −31.0358 | −1.11412 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 1.56179i | − | 0.0559930i | ||||||
\(779\) | 5.28226 | 0.189257 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.31533 | −0.0828490 | ||||||||
\(782\) | − | 1.41220i | − | 0.0505002i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.74239 | 0.347942 | ||||||||
\(785\) | − | 27.7772i | − | 0.991411i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9128i | 1.20886i | 0.796658 | + | 0.604431i | \(0.206599\pi\) | ||||
−0.796658 | + | 0.604431i | \(0.793401\pi\) | |||||||
\(788\) | 11.9108i | 0.424305i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.33544 | 0.225405 | ||||||||
\(791\) | − | 19.0772i | − | 0.678306i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.8082 | − | 4.77530i | 0.667897 | − | 0.169576i | ||||
\(794\) | −21.3097 | −0.756252 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.4349 | 1.11418 | ||||||||
\(797\) | 26.9305 | 0.953928 | 0.476964 | − | 0.878923i | \(-0.341737\pi\) | ||||
0.476964 | + | 0.878923i | \(0.341737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9152i | 0.456906i | ||||||||
\(800\) | 6.49439i | 0.229611i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.98789 | −0.282062 | ||||||||
\(803\) | 2.21094 | 0.0780223 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.07068 | −0.0729819 | ||||||||
\(806\) | 14.8562 | − | 3.77191i | 0.523286 | − | 0.132860i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.4779i | 0.650049i | ||||||||
\(809\) | −52.4814 | −1.84515 | −0.922575 | − | 0.385819i | \(-0.873919\pi\) | ||||
−0.922575 | + | 0.385819i | \(0.873919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.2236i | 0.675033i | 0.941320 | + | 0.337516i | \(0.109587\pi\) | ||||
−0.941320 | + | 0.337516i | \(0.890413\pi\) | |||||||
\(812\) | 12.6483i | 0.443869i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 1.21727i | − | 0.0426655i | ||||||
\(815\) | 25.4319 | 0.890840 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.9590i | 0.978160i | ||||||||
\(818\) | −15.1169 | −0.528551 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.35744 | 0.117247 | ||||||||
\(821\) | − | 30.4099i | − | 1.06131i | −0.847587 | − | 0.530657i | \(-0.821945\pi\) | ||
0.847587 | − | 0.530657i | \(-0.178055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1575 | −0.563216 | −0.281608 | − | 0.959530i | \(-0.590868\pi\) | ||||
−0.281608 | + | 0.959530i | \(0.590868\pi\) | |||||||
\(824\) | 6.20452i | 0.216145i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 2.34141i | − | 0.0814681i | ||||||
\(827\) | − | 47.5066i | − | 1.65197i | −0.563695 | − | 0.825983i | \(-0.690621\pi\) | ||
0.563695 | − | 0.825983i | \(-0.309379\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.6932 | −1.96904 | −0.984519 | − | 0.175278i | \(-0.943917\pi\) | ||||
−0.984519 | + | 0.175278i | \(0.943917\pi\) | |||||||
\(830\) | 16.5799i | 0.575497i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.22291 | + | 0.818281i | −0.111734 | + | 0.0283688i | ||||
\(833\) | 16.2376 | 0.562601 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.4019 | −0.948283 | ||||||||
\(836\) | −8.44913 | −0.292219 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 13.2199i | − | 0.456674i | ||||||
\(839\) | 35.2293i | 1.21625i | 0.793841 | + | 0.608125i | \(0.208078\pi\) | ||||
−0.793841 | + | 0.608125i | \(0.791922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50384 | −0.120822 | ||||||||
\(842\) | −14.4393 | −0.497610 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33.1468 | −1.14096 | ||||||||
\(845\) | 12.1147 | + | 22.3197i | 0.416757 | + | 0.767821i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.51078i | 0.0519112i | ||||||||
\(848\) | 1.03824 | 0.0356535 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.38280i | 0.0817294i | ||||||||
\(851\) | − | 1.46047i | − | 0.0500644i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 18.7185i | − | 0.640909i | −0.947264 | − | 0.320454i | \(-0.896164\pi\) | ||
0.947264 | − | 0.320454i | \(-0.103836\pi\) | |||||||
\(854\) | −4.75482 | −0.162706 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.90365i | 0.167603i | ||||||||
\(857\) | 47.3032 | 1.61585 | 0.807924 | − | 0.589287i | \(-0.200591\pi\) | ||||
0.807924 | + | 0.589287i | \(0.200591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.6908 | −1.38835 | −0.694176 | − | 0.719805i | \(-0.744231\pi\) | ||||
−0.694176 | + | 0.719805i | \(0.744231\pi\) | |||||||
\(860\) | 17.7709i | 0.605984i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.6092 | 0.599772 | ||||||||
\(863\) | 1.42374i | 0.0484647i | 0.999706 | + | 0.0242324i | \(0.00771415\pi\) | ||||
−0.999706 | + | 0.0242324i | \(0.992286\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.9041i | 1.18678i | ||||||||
\(866\) | − | 18.0931i | − | 0.614830i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.2098 | 0.618080 | ||||||||
\(869\) | − | 5.54589i | − | 0.188131i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.51701 | + | 29.6067i | 0.254704 | + | 1.00319i | ||||
\(872\) | −27.5561 | −0.933166 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.09077 | 0.0707213 | ||||||||
\(875\) | 18.2505 | 0.616978 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.1060i | 1.89457i | 0.320397 | + | 0.947283i | \(0.396184\pi\) | ||||
−0.320397 | + | 0.947283i | \(0.603816\pi\) | |||||||
\(878\) | 4.10607i | 0.138573i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.03427 | −0.135995 | ||||||||
\(881\) | 16.2234 | 0.546581 | 0.273290 | − | 0.961932i | \(-0.411888\pi\) | ||||
0.273290 | + | 0.961932i | \(0.411888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.0296 | 1.11153 | 0.555767 | − | 0.831338i | \(-0.312425\pi\) | ||||
0.555767 | + | 0.831338i | \(0.312425\pi\) | |||||||
\(884\) | −19.9438 | + | 5.06364i | −0.670783 | + | 0.170309i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.1815i | 0.442843i | ||||||||
\(887\) | 54.6149 | 1.83379 | 0.916894 | − | 0.399130i | \(-0.130688\pi\) | ||||
0.916894 | + | 0.399130i | \(0.130688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.63074i | 0.255927i | ||||||||
\(890\) | 2.06730i | 0.0692960i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 46.0576i | − | 1.54212i | ||||||
\(893\) | −19.1210 | −0.639860 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.7414i | 1.12785i | ||||||||
\(896\) | 17.3909 | 0.580989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.50668 | 0.183760 | ||||||||
\(899\) | − | 36.7068i | − | 1.22424i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.73044 | 0.0576494 | ||||||||
\(902\) | 0.606168i | 0.0201832i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.0116i | 0.898393i | ||||||||
\(905\) | − | 7.23417i | − | 0.240472i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.1937 | −1.03577 | −0.517884 | − | 0.855451i | \(-0.673280\pi\) | ||||
−0.517884 | + | 0.855451i | \(0.673280\pi\) | |||||||
\(908\) | − | 47.5066i | − | 1.57656i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.53133 | − | 6.03135i | −0.0507631 | − | 0.199937i | ||||
\(911\) | −53.7300 | −1.78015 | −0.890077 | − | 0.455810i | \(-0.849350\pi\) | ||||
−0.890077 | + | 0.455810i | \(0.849350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.5137 | 0.480332 | ||||||||
\(914\) | 2.03907 | 0.0674464 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 8.01592i | − | 0.264853i | ||||||
\(917\) | 24.1381i | 0.797111i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.3202 | 0.538353 | 0.269177 | − | 0.963091i | \(-0.413248\pi\) | ||||
0.269177 | + | 0.963091i | \(0.413248\pi\) | |||||||
\(920\) | 2.93190 | 0.0966620 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.88764 | 0.292699 | ||||||||
\(923\) | −2.05435 | − | 8.09132i | −0.0676196 | − | 0.266329i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.46425i | 0.0810241i | ||||||||
\(926\) | 9.34956 | 0.307246 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 27.7005i | − | 0.909314i | ||||||
\(929\) | − | 56.4975i | − | 1.85362i | −0.375527 | − | 0.926811i | \(-0.622538\pi\) | ||
0.375527 | − | 0.926811i | \(-0.377462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0399i | 0.787877i | ||||||||
\(932\) | 22.5885 | 0.739912 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.2524i | 0.629957i | ||||||||
\(935\) | −6.72392 | −0.219896 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.5328 | 1.71617 | 0.858086 | − | 0.513506i | \(-0.171654\pi\) | ||||
0.858086 | + | 0.513506i | \(0.171654\pi\) | |||||||
\(938\) | − | 7.48476i | − | 0.244386i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.1535 | −0.396402 | ||||||||
\(941\) | − | 24.3963i | − | 0.795296i | −0.917538 | − | 0.397648i | \(-0.869826\pi\) | ||
0.917538 | − | 0.397648i | \(-0.130174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.727273i | 0.0236833i | ||||||||
\(944\) | − | 5.47311i | − | 0.178135i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.20844 | −0.104315 | ||||||||
\(947\) | − | 38.9960i | − | 1.26720i | −0.773661 | − | 0.633600i | \(-0.781577\pi\) | ||
0.773661 | − | 0.633600i | \(-0.218423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.96172 | + | 7.72650i | 0.0636801 | + | 0.250813i | ||||
\(950\) | −3.52775 | −0.114455 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.1237 | 0.360522 | ||||||||
\(953\) | −30.9120 | −1.00134 | −0.500670 | − | 0.865638i | \(-0.666913\pi\) | ||||
−0.500670 | + | 0.865638i | \(0.666913\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.2927i | 1.30384i | ||||||||
\(956\) | 9.94660i | 0.321696i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19.6499 | −0.634859 | ||||||||
\(959\) | −26.0734 | −0.841953 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.8467 | −0.704731 | ||||||||
\(962\) | 4.25398 | − | 1.08006i | 0.137154 | − | 0.0348227i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.4367i | 0.690431i | ||||||||
\(965\) | 36.8186 | 1.18523 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.5859i | − | 1.01573i | −0.861435 | − | 0.507867i | \(-0.830434\pi\) | ||
0.861435 | − | 0.507867i | \(-0.169566\pi\) | |||||||
\(968\) | − | 2.13914i | − | 0.0687546i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 16.5741i | − | 0.532162i | ||||||
\(971\) | 32.5555 | 1.04476 | 0.522378 | − | 0.852714i | \(-0.325045\pi\) | ||||
0.522378 | + | 0.852714i | \(0.325045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.61969i | 0.276335i | ||||||||
\(974\) | −2.16368 | −0.0693289 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.1145 | −0.355767 | ||||||||
\(977\) | 3.54984i | 0.113569i | 0.998386 | + | 0.0567847i | \(0.0180848\pi\) | ||||
−0.998386 | + | 0.0567847i | \(0.981915\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.80966 | 0.0578371 | ||||||||
\(980\) | 15.2800i | 0.488101i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 5.92949i | − | 0.189218i | ||||||
\(983\) | − | 16.6279i | − | 0.530349i | −0.964200 | − | 0.265174i | \(-0.914570\pi\) | ||
0.964200 | − | 0.265174i | \(-0.0854295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0334 | −0.447141 | ||||||||
\(986\) | − | 10.1634i | − | 0.323667i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.49674 | − | 29.5269i | −0.238503 | − | 0.939377i | ||||
\(989\) | −3.84946 | −0.122406 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.4447 | 1.15770 | 0.578852 | − | 0.815433i | \(-0.303501\pi\) | ||||
0.578852 | + | 0.815433i | \(0.303501\pi\) | |||||||
\(992\) | −39.8804 | −1.26620 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.04553i | 0.0648804i | ||||||||
\(995\) | 37.0367i | 1.17414i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.23772 | −0.0708692 | −0.0354346 | − | 0.999372i | \(-0.511282\pi\) | ||||
−0.0354346 | + | 0.999372i | \(0.511282\pi\) | |||||||
\(998\) | 8.83742 | 0.279744 | ||||||||
\(999\) | 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 | 1287.2.b.c.298.9 | 14 | ||
3.2 | odd | 2 | 429.2.b.b.298.6 | ✓ | 14 | ||
13.12 | even | 2 | inner | 1287.2.b.c.298.6 | 14 | ||
39.5 | even | 4 | 5577.2.a.y.1.3 | 7 | |||
39.8 | even | 4 | 5577.2.a.x.1.5 | 7 | |||
39.38 | odd | 2 | 429.2.b.b.298.9 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.6 | ✓ | 14 | 3.2 | odd | 2 | ||
429.2.b.b.298.9 | yes | 14 | 39.38 | odd | 2 | ||
1287.2.b.c.298.6 | 14 | 13.12 | even | 2 | inner | ||
1287.2.b.c.298.9 | 14 | 1.1 | even | 1 | trivial | ||
5577.2.a.x.1.5 | 7 | 39.8 | even | 4 | |||
5577.2.a.y.1.3 | 7 | 39.5 | even | 4 |