Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.5 | ||
Root | \(2.35083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.h.1249.12 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.35083i | − 0.955181i | −0.878583 | − | 0.477590i | \(-0.841510\pi\) | ||||
0.878583 | − | 0.477590i | \(-0.158490\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.175259 | 0.0876296 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.35083 | 0.551474 | ||||||||
\(7\) | 1.59580i | 0.603155i | 0.953442 | + | 0.301577i | \(0.0975131\pi\) | ||||
−0.953442 | + | 0.301577i | \(0.902487\pi\) | |||||||
\(8\) | − 2.93840i | − 1.03888i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.33277 | 1.00487 | 0.502434 | − | 0.864616i | \(-0.332438\pi\) | ||||
0.502434 | + | 0.864616i | \(0.332438\pi\) | |||||||
\(12\) | 0.175259i | 0.0505930i | ||||||||
\(13\) | − 7.05132i | − 1.95568i | −0.209345 | − | 0.977842i | \(-0.567133\pi\) | ||||
0.209345 | − | 0.977842i | \(-0.432867\pi\) | |||||||
\(14\) | 2.15565 | 0.576122 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.61877 | −0.904691 | ||||||||
\(17\) | 4.09625i | 0.993486i | 0.867898 | + | 0.496743i | \(0.165471\pi\) | ||||
−0.867898 | + | 0.496743i | \(0.834529\pi\) | |||||||
\(18\) | 1.35083i | 0.318394i | ||||||||
\(19\) | −0.567535 | −0.130201 | −0.0651007 | − | 0.997879i | \(-0.520737\pi\) | ||||
−0.0651007 | + | 0.997879i | \(0.520737\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.59580 | −0.348231 | ||||||||
\(22\) | − 4.50200i | − 0.959830i | ||||||||
\(23\) | − 6.30400i | − 1.31448i | −0.753683 | − | 0.657238i | \(-0.771725\pi\) | ||||
0.753683 | − | 0.657238i | \(-0.228275\pi\) | |||||||
\(24\) | 2.93840 | 0.599799 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.52513 | −1.86803 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0.279678i | 0.0528542i | ||||||||
\(29\) | 2.78357 | 0.516897 | 0.258448 | − | 0.966025i | \(-0.416789\pi\) | ||||
0.258448 | + | 0.966025i | \(0.416789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.995824 | −0.178855 | −0.0894276 | − | 0.995993i | \(-0.528504\pi\) | ||||
−0.0894276 | + | 0.995993i | \(0.528504\pi\) | |||||||
\(32\) | − 0.988473i | − 0.174739i | ||||||||
\(33\) | 3.33277i | 0.580161i | ||||||||
\(34\) | 5.53333 | 0.948959 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.175259 | −0.0292099 | ||||||||
\(37\) | − 3.55334i | − 0.584165i | −0.956393 | − | 0.292083i | \(-0.905652\pi\) | ||||
0.956393 | − | 0.292083i | \(-0.0943483\pi\) | |||||||
\(38\) | 0.766643i | 0.124366i | ||||||||
\(39\) | 7.05132 | 1.12911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.16293 | 0.181618 | 0.0908092 | − | 0.995868i | \(-0.471055\pi\) | ||||
0.0908092 | + | 0.995868i | \(0.471055\pi\) | |||||||
\(42\) | 2.15565i | 0.332624i | ||||||||
\(43\) | − 0.117022i | − 0.0178456i | −0.999960 | − | 0.00892281i | \(-0.997160\pi\) | ||||
0.999960 | − | 0.00892281i | \(-0.00284026\pi\) | |||||||
\(44\) | 0.584098 | 0.0880561 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.51563 | −1.25556 | ||||||||
\(47\) | 7.64173i | 1.11466i | 0.830291 | + | 0.557331i | \(0.188174\pi\) | ||||
−0.830291 | + | 0.557331i | \(0.811826\pi\) | |||||||
\(48\) | − 3.61877i | − 0.522324i | ||||||||
\(49\) | 4.45343 | 0.636205 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.09625 | −0.573589 | ||||||||
\(52\) | − 1.23581i | − 0.171376i | ||||||||
\(53\) | − 0.523635i | − 0.0719268i | −0.999353 | − | 0.0359634i | \(-0.988550\pi\) | ||||
0.999353 | − | 0.0359634i | \(-0.0114500\pi\) | |||||||
\(54\) | −1.35083 | −0.183825 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.68910 | 0.626607 | ||||||||
\(57\) | − 0.567535i | − 0.0751718i | ||||||||
\(58\) | − 3.76013i | − 0.493730i | ||||||||
\(59\) | −0.983998 | −0.128106 | −0.0640528 | − | 0.997947i | \(-0.520403\pi\) | ||||
−0.0640528 | + | 0.997947i | \(0.520403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6137 | 1.35895 | 0.679473 | − | 0.733701i | \(-0.262208\pi\) | ||||
0.679473 | + | 0.733701i | \(0.262208\pi\) | |||||||
\(62\) | 1.34519i | 0.170839i | ||||||||
\(63\) | − 1.59580i | − 0.201052i | ||||||||
\(64\) | −8.57279 | −1.07160 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.50200 | 0.554158 | ||||||||
\(67\) | − 15.2159i | − 1.85892i | −0.368920 | − | 0.929461i | \(-0.620272\pi\) | ||||
0.368920 | − | 0.929461i | \(-0.379728\pi\) | |||||||
\(68\) | 0.717905i | 0.0870588i | ||||||||
\(69\) | 6.30400 | 0.758913 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6639 | −1.26558 | −0.632788 | − | 0.774325i | \(-0.718090\pi\) | ||||
−0.632788 | + | 0.774325i | \(0.718090\pi\) | |||||||
\(72\) | 2.93840i | 0.346294i | ||||||||
\(73\) | − 5.55832i | − 0.650552i | −0.945619 | − | 0.325276i | \(-0.894543\pi\) | ||||
0.945619 | − | 0.325276i | \(-0.105457\pi\) | |||||||
\(74\) | −4.79996 | −0.557984 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0994657 | −0.0114095 | ||||||||
\(77\) | 5.31842i | 0.606090i | ||||||||
\(78\) | − 9.52513i | − 1.07851i | ||||||||
\(79\) | 14.5969 | 1.64227 | 0.821137 | − | 0.570731i | \(-0.193340\pi\) | ||||
0.821137 | + | 0.570731i | \(0.193340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 1.57091i | − 0.173478i | ||||||||
\(83\) | − 5.02398i | − 0.551453i | −0.961236 | − | 0.275727i | \(-0.911082\pi\) | ||||
0.961236 | − | 0.275727i | \(-0.0889184\pi\) | |||||||
\(84\) | −0.279678 | −0.0305154 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.158076 | −0.0170458 | ||||||||
\(87\) | 2.78357i | 0.298430i | ||||||||
\(88\) | − 9.79302i | − 1.04394i | ||||||||
\(89\) | −2.82350 | −0.299291 | −0.149645 | − | 0.988740i | \(-0.547813\pi\) | ||||
−0.149645 | + | 0.988740i | \(0.547813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.2525 | 1.17958 | ||||||||
\(92\) | − 1.10483i | − 0.115187i | ||||||||
\(93\) | − 0.995824i | − 0.103262i | ||||||||
\(94\) | 10.3227 | 1.06470 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.988473 | 0.100886 | ||||||||
\(97\) | − 1.70592i | − 0.173210i | −0.996243 | − | 0.0866049i | \(-0.972398\pi\) | ||||
0.996243 | − | 0.0866049i | \(-0.0276018\pi\) | |||||||
\(98\) | − 6.01583i | − 0.607690i | ||||||||
\(99\) | −3.33277 | −0.334956 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1747 | 1.31093 | 0.655464 | − | 0.755226i | \(-0.272473\pi\) | ||||
0.655464 | + | 0.755226i | \(0.272473\pi\) | |||||||
\(102\) | 5.53333i | 0.547882i | ||||||||
\(103\) | − 10.8720i | − 1.07125i | −0.844456 | − | 0.535624i | \(-0.820076\pi\) | ||||
0.844456 | − | 0.535624i | \(-0.179924\pi\) | |||||||
\(104\) | −20.7196 | −2.03173 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.707341 | −0.0687031 | ||||||||
\(107\) | 9.37236i | 0.906060i | 0.891495 | + | 0.453030i | \(0.149657\pi\) | ||||
−0.891495 | + | 0.453030i | \(0.850343\pi\) | |||||||
\(108\) | − 0.175259i | − 0.0168643i | ||||||||
\(109\) | 15.5899 | 1.49324 | 0.746622 | − | 0.665249i | \(-0.231674\pi\) | ||||
0.746622 | + | 0.665249i | \(0.231674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.55334 | 0.337268 | ||||||||
\(112\) | − 5.77482i | − 0.545669i | ||||||||
\(113\) | 10.0481i | 0.945243i | 0.881265 | + | 0.472622i | \(0.156692\pi\) | ||||
−0.881265 | + | 0.472622i | \(0.843308\pi\) | |||||||
\(114\) | −0.766643 | −0.0718027 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.487847 | 0.0452954 | ||||||||
\(117\) | 7.05132i | 0.651895i | ||||||||
\(118\) | 1.32921i | 0.122364i | ||||||||
\(119\) | −6.53678 | −0.599226 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.107347 | 0.00975880 | ||||||||
\(122\) | − 14.3373i | − 1.29804i | ||||||||
\(123\) | 1.16293i | 0.104857i | ||||||||
\(124\) | −0.174527 | −0.0156730 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.15565 | −0.192041 | ||||||||
\(127\) | 0.976784i | 0.0866756i | 0.999060 | + | 0.0433378i | \(0.0137992\pi\) | ||||
−0.999060 | + | 0.0433378i | \(0.986201\pi\) | |||||||
\(128\) | 9.60343i | 0.848832i | ||||||||
\(129\) | 0.117022 | 0.0103032 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0616 | 0.879086 | 0.439543 | − | 0.898221i | \(-0.355140\pi\) | ||||
0.439543 | + | 0.898221i | \(0.355140\pi\) | |||||||
\(132\) | 0.584098i | 0.0508392i | ||||||||
\(133\) | − 0.905670i | − 0.0785316i | ||||||||
\(134\) | −20.5541 | −1.77561 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0364 | 1.03212 | ||||||||
\(137\) | 4.87244i | 0.416281i | 0.978099 | + | 0.208140i | \(0.0667411\pi\) | ||||
−0.978099 | + | 0.208140i | \(0.933259\pi\) | |||||||
\(138\) | − 8.51563i | − 0.724899i | ||||||||
\(139\) | −0.185784 | −0.0157580 | −0.00787898 | − | 0.999969i | \(-0.502508\pi\) | ||||
−0.00787898 | + | 0.999969i | \(0.502508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.64173 | −0.643550 | ||||||||
\(142\) | 14.4052i | 1.20885i | ||||||||
\(143\) | − 23.5004i | − 1.96520i | ||||||||
\(144\) | 3.61877 | 0.301564 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.50834 | −0.621395 | ||||||||
\(147\) | 4.45343i | 0.367313i | ||||||||
\(148\) | − 0.622755i | − 0.0511902i | ||||||||
\(149\) | −3.88889 | −0.318590 | −0.159295 | − | 0.987231i | \(-0.550922\pi\) | ||||
−0.159295 | + | 0.987231i | \(0.550922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.1146 | −1.79966 | −0.899829 | − | 0.436242i | \(-0.856309\pi\) | ||||
−0.899829 | + | 0.436242i | \(0.856309\pi\) | |||||||
\(152\) | 1.66765i | 0.135264i | ||||||||
\(153\) | − 4.09625i | − 0.331162i | ||||||||
\(154\) | 7.18428 | 0.578926 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.23581 | 0.0989438 | ||||||||
\(157\) | − 13.6058i | − 1.08586i | −0.839777 | − | 0.542931i | \(-0.817314\pi\) | ||||
0.839777 | − | 0.542931i | \(-0.182686\pi\) | |||||||
\(158\) | − 19.7179i | − 1.56867i | ||||||||
\(159\) | 0.523635 | 0.0415269 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0599 | 0.792832 | ||||||||
\(162\) | − 1.35083i | − 0.106131i | ||||||||
\(163\) | 8.62895i | 0.675871i | 0.941169 | + | 0.337936i | \(0.109729\pi\) | ||||
−0.941169 | + | 0.337936i | \(0.890271\pi\) | |||||||
\(164\) | 0.203813 | 0.0159151 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.78654 | −0.526737 | ||||||||
\(167\) | − 6.59891i | − 0.510639i | −0.966857 | − | 0.255319i | \(-0.917819\pi\) | ||||
0.966857 | − | 0.255319i | \(-0.0821806\pi\) | |||||||
\(168\) | 4.68910i | 0.361772i | ||||||||
\(169\) | −36.7211 | −2.82470 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.567535 | 0.0434005 | ||||||||
\(172\) | − 0.0205091i | − 0.00156381i | ||||||||
\(173\) | 13.6595i | 1.03851i | 0.854618 | + | 0.519257i | \(0.173791\pi\) | ||||
−0.854618 | + | 0.519257i | \(0.826209\pi\) | |||||||
\(174\) | 3.76013 | 0.285055 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0605 | −0.909095 | ||||||||
\(177\) | − 0.983998i | − 0.0739618i | ||||||||
\(178\) | 3.81407i | 0.285877i | ||||||||
\(179\) | −9.82880 | −0.734639 | −0.367320 | − | 0.930095i | \(-0.619724\pi\) | ||||
−0.367320 | + | 0.930095i | \(0.619724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8687 | 1.32817 | 0.664085 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(182\) | − 15.2002i | − 1.12671i | ||||||||
\(183\) | 10.6137i | 0.784588i | ||||||||
\(184\) | −18.5237 | −1.36559 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.34519 | −0.0986340 | ||||||||
\(187\) | 13.6518i | 0.998322i | ||||||||
\(188\) | 1.33928i | 0.0976773i | ||||||||
\(189\) | 1.59580 | 0.116077 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.325813 | 0.0235750 | 0.0117875 | − | 0.999931i | \(-0.496248\pi\) | ||||
0.0117875 | + | 0.999931i | \(0.496248\pi\) | |||||||
\(192\) | − 8.57279i | − 0.618688i | ||||||||
\(193\) | − 2.90187i | − 0.208881i | −0.994531 | − | 0.104441i | \(-0.966695\pi\) | ||||
0.994531 | − | 0.104441i | \(-0.0333052\pi\) | |||||||
\(194\) | −2.30441 | −0.165447 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.780505 | 0.0557503 | ||||||||
\(197\) | 18.1220i | 1.29114i | 0.763702 | + | 0.645568i | \(0.223380\pi\) | ||||
−0.763702 | + | 0.645568i | \(0.776620\pi\) | |||||||
\(198\) | 4.50200i | 0.319943i | ||||||||
\(199\) | −1.53256 | −0.108640 | −0.0543201 | − | 0.998524i | \(-0.517299\pi\) | ||||
−0.0543201 | + | 0.998524i | \(0.517299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.2159 | 1.07325 | ||||||||
\(202\) | − 17.7967i | − 1.25217i | ||||||||
\(203\) | 4.44202i | 0.311769i | ||||||||
\(204\) | −0.717905 | −0.0502634 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.6862 | −1.02324 | ||||||||
\(207\) | 6.30400i | 0.438158i | ||||||||
\(208\) | 25.5171i | 1.76929i | ||||||||
\(209\) | −1.89146 | −0.130835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3698 | −0.782727 | −0.391363 | − | 0.920236i | \(-0.627996\pi\) | ||||
−0.391363 | + | 0.920236i | \(0.627996\pi\) | |||||||
\(212\) | − 0.0917718i | − 0.00630291i | ||||||||
\(213\) | − 10.6639i | − 0.730681i | ||||||||
\(214\) | 12.6605 | 0.865451 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.93840 | −0.199933 | ||||||||
\(217\) | − 1.58913i | − 0.107877i | ||||||||
\(218\) | − 21.0593i | − 1.42632i | ||||||||
\(219\) | 5.55832 | 0.375596 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.8839 | 1.94294 | ||||||||
\(222\) | − 4.79996i | − 0.322152i | ||||||||
\(223\) | 16.9507i | 1.13510i | 0.823339 | + | 0.567550i | \(0.192109\pi\) | ||||
−0.823339 | + | 0.567550i | \(0.807891\pi\) | |||||||
\(224\) | 1.57740 | 0.105395 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.5732 | 0.902878 | ||||||||
\(227\) | − 14.1117i | − 0.936627i | −0.883562 | − | 0.468314i | \(-0.844862\pi\) | ||||
0.883562 | − | 0.468314i | \(-0.155138\pi\) | |||||||
\(228\) | − 0.0994657i | − 0.00658728i | ||||||||
\(229\) | −0.0619945 | −0.00409671 | −0.00204835 | − | 0.999998i | \(-0.500652\pi\) | ||||
−0.00204835 | + | 0.999998i | \(0.500652\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.31842 | −0.349926 | ||||||||
\(232\) | − 8.17927i | − 0.536995i | ||||||||
\(233\) | − 26.0191i | − 1.70457i | −0.523081 | − | 0.852283i | \(-0.675218\pi\) | ||||
0.523081 | − | 0.852283i | \(-0.324782\pi\) | |||||||
\(234\) | 9.52513 | 0.622677 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.172455 | −0.0112258 | ||||||||
\(237\) | 14.5969i | 0.948168i | ||||||||
\(238\) | 8.83008i | 0.572369i | ||||||||
\(239\) | −19.4970 | −1.26116 | −0.630579 | − | 0.776125i | \(-0.717183\pi\) | ||||
−0.630579 | + | 0.776125i | \(0.717183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.09860 | −0.264014 | −0.132007 | − | 0.991249i | \(-0.542142\pi\) | ||||
−0.132007 | + | 0.991249i | \(0.542142\pi\) | |||||||
\(242\) | − 0.145007i | − 0.00932141i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 1.86015 | 0.119084 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.57091 | 0.100158 | ||||||||
\(247\) | 4.00187i | 0.254633i | ||||||||
\(248\) | 2.92613i | 0.185810i | ||||||||
\(249\) | 5.02398 | 0.318382 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.02933 | −0.0649704 | −0.0324852 | − | 0.999472i | \(-0.510342\pi\) | ||||
−0.0324852 | + | 0.999472i | \(0.510342\pi\) | |||||||
\(252\) | − 0.279678i | − 0.0176181i | ||||||||
\(253\) | − 21.0098i | − 1.32087i | ||||||||
\(254\) | 1.31947 | 0.0827909 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.17298 | −0.260811 | ||||||||
\(257\) | 18.5597i | 1.15772i | 0.815426 | + | 0.578862i | \(0.196503\pi\) | ||||
−0.815426 | + | 0.578862i | \(0.803497\pi\) | |||||||
\(258\) | − 0.158076i | − 0.00984140i | ||||||||
\(259\) | 5.67041 | 0.352342 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.78357 | −0.172299 | ||||||||
\(262\) | − 13.5915i | − 0.839686i | ||||||||
\(263\) | 12.3938i | 0.764231i | 0.924114 | + | 0.382116i | \(0.124804\pi\) | ||||
−0.924114 | + | 0.382116i | \(0.875196\pi\) | |||||||
\(264\) | 9.79302 | 0.602719 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.22341 | −0.0750119 | ||||||||
\(267\) | − 2.82350i | − 0.172796i | ||||||||
\(268\) | − 2.66673i | − 0.162897i | ||||||||
\(269\) | 5.30032 | 0.323166 | 0.161583 | − | 0.986859i | \(-0.448340\pi\) | ||||
0.161583 | + | 0.986859i | \(0.448340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.797428 | 0.0484403 | 0.0242201 | − | 0.999707i | \(-0.492290\pi\) | ||||
0.0242201 | + | 0.999707i | \(0.492290\pi\) | |||||||
\(272\) | − 14.8234i | − 0.898798i | ||||||||
\(273\) | 11.2525i | 0.681031i | ||||||||
\(274\) | 6.58184 | 0.397624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.10483 | 0.0665032 | ||||||||
\(277\) | 4.74425i | 0.285054i | 0.989791 | + | 0.142527i | \(0.0455228\pi\) | ||||
−0.989791 | + | 0.142527i | \(0.954477\pi\) | |||||||
\(278\) | 0.250962i | 0.0150517i | ||||||||
\(279\) | 0.995824 | 0.0596184 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7398 | −1.11792 | −0.558961 | − | 0.829194i | \(-0.688800\pi\) | ||||
−0.558961 | + | 0.829194i | \(0.688800\pi\) | |||||||
\(282\) | 10.3227i | 0.614707i | ||||||||
\(283\) | 11.7612i | 0.699130i | 0.936912 | + | 0.349565i | \(0.113671\pi\) | ||||
−0.936912 | + | 0.349565i | \(0.886329\pi\) | |||||||
\(284\) | −1.86895 | −0.110902 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.7451 | −1.87712 | ||||||||
\(287\) | 1.85579i | 0.109544i | ||||||||
\(288\) | 0.988473i | 0.0582463i | ||||||||
\(289\) | 0.220750 | 0.0129853 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.70592 | 0.100003 | ||||||||
\(292\) | − 0.974146i | − 0.0570076i | ||||||||
\(293\) | 22.2819i | 1.30172i | 0.759198 | + | 0.650860i | \(0.225592\pi\) | ||||
−0.759198 | + | 0.650860i | \(0.774408\pi\) | |||||||
\(294\) | 6.01583 | 0.350850 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.4411 | −0.606879 | ||||||||
\(297\) | − 3.33277i | − 0.193387i | ||||||||
\(298\) | 5.25322i | 0.304311i | ||||||||
\(299\) | −44.4515 | −2.57070 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.186743 | 0.0107637 | ||||||||
\(302\) | 29.8730i | 1.71900i | ||||||||
\(303\) | 13.1747i | 0.756865i | ||||||||
\(304\) | 2.05378 | 0.117792 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.53333 | −0.316320 | ||||||||
\(307\) | 15.3063i | 0.873574i | 0.899565 | + | 0.436787i | \(0.143884\pi\) | ||||
−0.899565 | + | 0.436787i | \(0.856116\pi\) | |||||||
\(308\) | 0.932102i | 0.0531115i | ||||||||
\(309\) | 10.8720 | 0.618486 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8545 | −0.728913 | −0.364456 | − | 0.931220i | \(-0.618745\pi\) | ||||
−0.364456 | + | 0.931220i | \(0.618745\pi\) | |||||||
\(312\) | − 20.7196i | − 1.17302i | ||||||||
\(313\) | − 10.5072i | − 0.593901i | −0.954893 | − | 0.296951i | \(-0.904030\pi\) | ||||
0.954893 | − | 0.296951i | \(-0.0959697\pi\) | |||||||
\(314\) | −18.3791 | −1.03720 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.55823 | 0.143912 | ||||||||
\(317\) | 19.4806i | 1.09414i | 0.837086 | + | 0.547071i | \(0.184257\pi\) | ||||
−0.837086 | + | 0.547071i | \(0.815743\pi\) | |||||||
\(318\) | − 0.707341i | − 0.0396657i | ||||||||
\(319\) | 9.27701 | 0.519413 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.37236 | −0.523114 | ||||||||
\(322\) | − 13.5892i | − 0.757298i | ||||||||
\(323\) | − 2.32476i | − 0.129353i | ||||||||
\(324\) | 0.175259 | 0.00973662 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.6562 | 0.645579 | ||||||||
\(327\) | 15.5899i | 0.862125i | ||||||||
\(328\) | − 3.41714i | − 0.188680i | ||||||||
\(329\) | −12.1947 | −0.672313 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4925 | −0.796579 | −0.398289 | − | 0.917260i | \(-0.630396\pi\) | ||||
−0.398289 | + | 0.917260i | \(0.630396\pi\) | |||||||
\(332\) | − 0.880498i | − 0.0483236i | ||||||||
\(333\) | 3.55334i | 0.194722i | ||||||||
\(334\) | −8.91400 | −0.487753 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.77482 | 0.315042 | ||||||||
\(337\) | − 9.33225i | − 0.508360i | −0.967157 | − | 0.254180i | \(-0.918194\pi\) | ||||
0.967157 | − | 0.254180i | \(-0.0818056\pi\) | |||||||
\(338\) | 49.6039i | 2.69810i | ||||||||
\(339\) | −10.0481 | −0.545737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.31885 | −0.179726 | ||||||||
\(342\) | − 0.766643i | − 0.0414553i | ||||||||
\(343\) | 18.2774i | 0.986884i | ||||||||
\(344\) | −0.343857 | −0.0185395 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.4517 | 0.991968 | ||||||||
\(347\) | 1.05341i | 0.0565499i | 0.999600 | + | 0.0282750i | \(0.00900140\pi\) | ||||
−0.999600 | + | 0.0282750i | \(0.990999\pi\) | |||||||
\(348\) | 0.487847i | 0.0261513i | ||||||||
\(349\) | 13.0715 | 0.699700 | 0.349850 | − | 0.936806i | \(-0.386233\pi\) | ||||
0.349850 | + | 0.936806i | \(0.386233\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.05132 | −0.376371 | ||||||||
\(352\) | − 3.29435i | − 0.175590i | ||||||||
\(353\) | 33.9473i | 1.80683i | 0.428767 | + | 0.903415i | \(0.358948\pi\) | ||||
−0.428767 | + | 0.903415i | \(0.641052\pi\) | |||||||
\(354\) | −1.32921 | −0.0706469 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.494845 | −0.0262267 | ||||||||
\(357\) | − 6.53678i | − 0.345963i | ||||||||
\(358\) | 13.2770i | 0.701713i | ||||||||
\(359\) | 6.09450 | 0.321656 | 0.160828 | − | 0.986982i | \(-0.448584\pi\) | ||||
0.160828 | + | 0.986982i | \(0.448584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6779 | −0.983048 | ||||||||
\(362\) | − 24.1376i | − 1.26864i | ||||||||
\(363\) | 0.107347i | 0.00563424i | ||||||||
\(364\) | 1.97210 | 0.103366 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.3373 | 0.749423 | ||||||||
\(367\) | 21.8636i | 1.14127i | 0.821203 | + | 0.570636i | \(0.193303\pi\) | ||||
−0.821203 | + | 0.570636i | \(0.806697\pi\) | |||||||
\(368\) | 22.8127i | 1.18919i | ||||||||
\(369\) | −1.16293 | −0.0605395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.835615 | 0.0433830 | ||||||||
\(372\) | − 0.174527i | − 0.00904882i | ||||||||
\(373\) | − 24.4559i | − 1.26628i | −0.774037 | − | 0.633140i | \(-0.781766\pi\) | ||||
0.774037 | − | 0.633140i | \(-0.218234\pi\) | |||||||
\(374\) | 18.4413 | 0.953578 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.4545 | 1.15800 | ||||||||
\(377\) | − 19.6279i | − 1.01089i | ||||||||
\(378\) | − 2.15565i | − 0.110875i | ||||||||
\(379\) | 6.27821 | 0.322490 | 0.161245 | − | 0.986914i | \(-0.448449\pi\) | ||||
0.161245 | + | 0.986914i | \(0.448449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.976784 | −0.0500422 | ||||||||
\(382\) | − 0.440118i | − 0.0225184i | ||||||||
\(383\) | 24.6876i | 1.26148i | 0.775996 | + | 0.630738i | \(0.217248\pi\) | ||||
−0.775996 | + | 0.630738i | \(0.782752\pi\) | |||||||
\(384\) | −9.60343 | −0.490073 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.91993 | −0.199519 | ||||||||
\(387\) | 0.117022i | 0.00594854i | ||||||||
\(388\) | − 0.298978i | − 0.0151783i | ||||||||
\(389\) | 12.9236 | 0.655251 | 0.327626 | − | 0.944808i | \(-0.393752\pi\) | ||||
0.327626 | + | 0.944808i | \(0.393752\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.8228 | 1.30591 | ||||||||
\(392\) | − 13.0860i | − 0.660942i | ||||||||
\(393\) | 10.0616i | 0.507541i | ||||||||
\(394\) | 24.4797 | 1.23327 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.584098 | −0.0293520 | ||||||||
\(397\) | 29.0214i | 1.45654i | 0.685288 | + | 0.728272i | \(0.259676\pi\) | ||||
−0.685288 | + | 0.728272i | \(0.740324\pi\) | |||||||
\(398\) | 2.07022i | 0.103771i | ||||||||
\(399\) | 0.905670 | 0.0453402 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.3926 | 1.16817 | 0.584084 | − | 0.811693i | \(-0.301454\pi\) | ||||
0.584084 | + | 0.811693i | \(0.301454\pi\) | |||||||
\(402\) | − 20.5541i | − 1.02515i | ||||||||
\(403\) | 7.02187i | 0.349784i | ||||||||
\(404\) | 2.30898 | 0.114876 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00041 | 0.297795 | ||||||||
\(407\) | − 11.8425i | − 0.587009i | ||||||||
\(408\) | 12.0364i | 0.595892i | ||||||||
\(409\) | 15.9918 | 0.790742 | 0.395371 | − | 0.918521i | \(-0.370616\pi\) | ||||
0.395371 | + | 0.918521i | \(0.370616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.87244 | −0.240340 | ||||||||
\(412\) | − 1.90542i | − 0.0938731i | ||||||||
\(413\) | − 1.57026i | − 0.0772675i | ||||||||
\(414\) | 8.51563 | 0.418521 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.97004 | −0.341734 | ||||||||
\(417\) | − 0.185784i | − 0.00909787i | ||||||||
\(418\) | 2.55504i | 0.124971i | ||||||||
\(419\) | −32.3769 | −1.58172 | −0.790858 | − | 0.611999i | \(-0.790366\pi\) | ||||
−0.790858 | + | 0.611999i | \(0.790366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0520 | 0.879801 | 0.439900 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439900 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(422\) | 15.3586i | 0.747646i | ||||||||
\(423\) | − 7.64173i | − 0.371554i | ||||||||
\(424\) | −1.53865 | −0.0747235 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4052 | −0.697932 | ||||||||
\(427\) | 16.9373i | 0.819654i | ||||||||
\(428\) | 1.64259i | 0.0793977i | ||||||||
\(429\) | 23.5004 | 1.13461 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.1353 | 1.59607 | 0.798035 | − | 0.602612i | \(-0.205873\pi\) | ||||
0.798035 | + | 0.602612i | \(0.205873\pi\) | |||||||
\(432\) | 3.61877i | 0.174108i | ||||||||
\(433\) | − 22.6653i | − 1.08922i | −0.838688 | − | 0.544612i | \(-0.816677\pi\) | ||||
0.838688 | − | 0.544612i | \(-0.183323\pi\) | |||||||
\(434\) | −2.14665 | −0.103042 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.73228 | 0.130852 | ||||||||
\(437\) | 3.57774i | 0.171147i | ||||||||
\(438\) | − 7.50834i | − 0.358762i | ||||||||
\(439\) | 8.50436 | 0.405891 | 0.202945 | − | 0.979190i | \(-0.434949\pi\) | ||||
0.202945 | + | 0.979190i | \(0.434949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.45343 | −0.212068 | ||||||||
\(442\) | − 39.0173i | − 1.85586i | ||||||||
\(443\) | 6.35768i | 0.302063i | 0.988529 | + | 0.151031i | \(0.0482594\pi\) | ||||
−0.988529 | + | 0.151031i | \(0.951741\pi\) | |||||||
\(444\) | 0.622755 | 0.0295547 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.8975 | 1.08423 | ||||||||
\(447\) | − 3.88889i | − 0.183938i | ||||||||
\(448\) | − 13.6804i | − 0.646340i | ||||||||
\(449\) | 6.25726 | 0.295298 | 0.147649 | − | 0.989040i | \(-0.452829\pi\) | ||||
0.147649 | + | 0.989040i | \(0.452829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.87576 | 0.182502 | ||||||||
\(452\) | 1.76102i | 0.0828313i | ||||||||
\(453\) | − 22.1146i | − 1.03903i | ||||||||
\(454\) | −19.0625 | −0.894648 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.66765 | −0.0780947 | ||||||||
\(457\) | 11.0441i | 0.516620i | 0.966062 | + | 0.258310i | \(0.0831657\pi\) | ||||
−0.966062 | + | 0.258310i | \(0.916834\pi\) | |||||||
\(458\) | 0.0837440i | 0.00391310i | ||||||||
\(459\) | 4.09625 | 0.191196 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.6622 | −1.10206 | −0.551029 | − | 0.834486i | \(-0.685765\pi\) | ||||
−0.551029 | + | 0.834486i | \(0.685765\pi\) | |||||||
\(462\) | 7.18428i | 0.334243i | ||||||||
\(463\) | − 6.22442i | − 0.289273i | −0.989485 | − | 0.144637i | \(-0.953799\pi\) | ||||
0.989485 | − | 0.144637i | \(-0.0462013\pi\) | |||||||
\(464\) | −10.0731 | −0.467632 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.1473 | −1.62817 | ||||||||
\(467\) | − 4.94679i | − 0.228910i | −0.993428 | − | 0.114455i | \(-0.963488\pi\) | ||||
0.993428 | − | 0.114455i | \(-0.0365122\pi\) | |||||||
\(468\) | 1.23581i | 0.0571252i | ||||||||
\(469\) | 24.2815 | 1.12122 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.6058 | 0.626923 | ||||||||
\(472\) | 2.89138i | 0.133087i | ||||||||
\(473\) | − 0.390006i | − 0.0179325i | ||||||||
\(474\) | 19.7179 | 0.905671 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.14563 | −0.0525099 | ||||||||
\(477\) | 0.523635i | 0.0239756i | ||||||||
\(478\) | 26.3372i | 1.20463i | ||||||||
\(479\) | 30.0898 | 1.37484 | 0.687419 | − | 0.726261i | \(-0.258744\pi\) | ||||
0.687419 | + | 0.726261i | \(0.258744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.0557 | −1.14244 | ||||||||
\(482\) | 5.53651i | 0.252181i | ||||||||
\(483\) | 10.0599i | 0.457742i | ||||||||
\(484\) | 0.0188135 | 0.000855159 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.35083 | 0.0612749 | ||||||||
\(487\) | 34.2499i | 1.55201i | 0.630726 | + | 0.776006i | \(0.282757\pi\) | ||||
−0.630726 | + | 0.776006i | \(0.717243\pi\) | |||||||
\(488\) | − 31.1874i | − 1.41179i | ||||||||
\(489\) | −8.62895 | −0.390215 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.4193 | −0.470218 | −0.235109 | − | 0.971969i | \(-0.575545\pi\) | ||||
−0.235109 | + | 0.971969i | \(0.575545\pi\) | |||||||
\(492\) | 0.203813i | 0.00918861i | ||||||||
\(493\) | 11.4022i | 0.513530i | ||||||||
\(494\) | 5.40584 | 0.243220 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.60365 | 0.161809 | ||||||||
\(497\) | − 17.0175i | − 0.763338i | ||||||||
\(498\) | − 6.78654i | − 0.304112i | ||||||||
\(499\) | −8.83514 | −0.395515 | −0.197757 | − | 0.980251i | \(-0.563366\pi\) | ||||
−0.197757 | + | 0.980251i | \(0.563366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.59891 | 0.294818 | ||||||||
\(502\) | 1.39044i | 0.0620585i | ||||||||
\(503\) | 21.3734i | 0.952994i | 0.879176 | + | 0.476497i | \(0.158094\pi\) | ||||
−0.879176 | + | 0.476497i | \(0.841906\pi\) | |||||||
\(504\) | −4.68910 | −0.208869 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −28.3806 | −1.26167 | ||||||||
\(507\) | − 36.7211i | − 1.63084i | ||||||||
\(508\) | 0.171190i | 0.00759535i | ||||||||
\(509\) | 16.7800 | 0.743759 | 0.371879 | − | 0.928281i | \(-0.378714\pi\) | ||||
0.371879 | + | 0.928281i | \(0.378714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.86994 | 0.392383 | ||||||||
\(512\) | 24.8438i | 1.09795i | ||||||||
\(513\) | 0.567535i | 0.0250573i | ||||||||
\(514\) | 25.0710 | 1.10584 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0205091 | 0.000902863 0 | ||||||||
\(517\) | 25.4681i | 1.12009i | ||||||||
\(518\) | − 7.65976i | − 0.336550i | ||||||||
\(519\) | −13.6595 | −0.599586 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.60508 | −0.201752 | −0.100876 | − | 0.994899i | \(-0.532165\pi\) | ||||
−0.100876 | + | 0.994899i | \(0.532165\pi\) | |||||||
\(522\) | 3.76013i | 0.164577i | ||||||||
\(523\) | 12.9634i | 0.566852i | 0.958994 | + | 0.283426i | \(0.0914710\pi\) | ||||
−0.958994 | + | 0.283426i | \(0.908529\pi\) | |||||||
\(524\) | 1.76339 | 0.0770340 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.7418 | 0.729979 | ||||||||
\(527\) | − 4.07914i | − 0.177690i | ||||||||
\(528\) | − 12.0605i | − 0.524866i | ||||||||
\(529\) | −16.7405 | −0.727846 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.983998 | 0.0427019 | ||||||||
\(532\) | − 0.158727i | − 0.00688169i | ||||||||
\(533\) | − 8.20015i | − 0.355188i | ||||||||
\(534\) | −3.81407 | −0.165051 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −44.7106 | −1.93120 | ||||||||
\(537\) | − 9.82880i | − 0.424144i | ||||||||
\(538\) | − 7.15983i | − 0.308682i | ||||||||
\(539\) | 14.8423 | 0.639301 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.3641 | −1.17647 | −0.588237 | − | 0.808688i | \(-0.700178\pi\) | ||||
−0.588237 | + | 0.808688i | \(0.700178\pi\) | |||||||
\(542\) | − 1.07719i | − 0.0462692i | ||||||||
\(543\) | 17.8687i | 0.766819i | ||||||||
\(544\) | 4.04903 | 0.173601 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.2002 | 0.650507 | ||||||||
\(547\) | − 27.6453i | − 1.18203i | −0.806661 | − | 0.591015i | \(-0.798728\pi\) | ||||
0.806661 | − | 0.591015i | \(-0.201272\pi\) | |||||||
\(548\) | 0.853941i | 0.0364785i | ||||||||
\(549\) | −10.6137 | −0.452982 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57978 | −0.0673007 | ||||||||
\(552\) | − 18.5237i | − 0.788422i | ||||||||
\(553\) | 23.2936i | 0.990545i | ||||||||
\(554\) | 6.40868 | 0.272279 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0325603 | −0.00138086 | ||||||||
\(557\) | 6.17333i | 0.261572i | 0.991411 | + | 0.130786i | \(0.0417501\pi\) | ||||
−0.991411 | + | 0.130786i | \(0.958250\pi\) | |||||||
\(558\) | − 1.34519i | − 0.0569464i | ||||||||
\(559\) | −0.825156 | −0.0349004 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6518 | −0.576381 | ||||||||
\(562\) | 25.3143i | 1.06782i | ||||||||
\(563\) | 5.69934i | 0.240198i | 0.992762 | + | 0.120099i | \(0.0383213\pi\) | ||||
−0.992762 | + | 0.120099i | \(0.961679\pi\) | |||||||
\(564\) | −1.33928 | −0.0563940 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.8874 | 0.667796 | ||||||||
\(567\) | 1.59580i | 0.0670172i | ||||||||
\(568\) | 31.3350i | 1.31479i | ||||||||
\(569\) | −20.1708 | −0.845605 | −0.422802 | − | 0.906222i | \(-0.638954\pi\) | ||||
−0.422802 | + | 0.906222i | \(0.638954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7554 | −0.659341 | −0.329671 | − | 0.944096i | \(-0.606938\pi\) | ||||
−0.329671 | + | 0.944096i | \(0.606938\pi\) | |||||||
\(572\) | − 4.11866i | − 0.172210i | ||||||||
\(573\) | 0.325813i | 0.0136111i | ||||||||
\(574\) | 2.50686 | 0.104634 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.57279 | 0.357200 | ||||||||
\(577\) | 16.1062i | 0.670509i | 0.942128 | + | 0.335255i | \(0.108822\pi\) | ||||
−0.942128 | + | 0.335255i | \(0.891178\pi\) | |||||||
\(578\) | − 0.298195i | − 0.0124033i | ||||||||
\(579\) | 2.90187 | 0.120598 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.01725 | 0.332611 | ||||||||
\(582\) | − 2.30441i | − 0.0955207i | ||||||||
\(583\) | − 1.74515i | − 0.0722769i | ||||||||
\(584\) | −16.3326 | −0.675847 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0990 | 1.24338 | ||||||||
\(587\) | − 2.00072i | − 0.0825786i | −0.999147 | − | 0.0412893i | \(-0.986853\pi\) | ||||
0.999147 | − | 0.0412893i | \(-0.0131465\pi\) | |||||||
\(588\) | 0.780505i | 0.0321875i | ||||||||
\(589\) | 0.565165 | 0.0232872 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.1220 | −0.745438 | ||||||||
\(592\) | 12.8587i | 0.528489i | ||||||||
\(593\) | − 26.8231i | − 1.10149i | −0.834672 | − | 0.550747i | \(-0.814343\pi\) | ||||
0.834672 | − | 0.550747i | \(-0.185657\pi\) | |||||||
\(594\) | −4.50200 | −0.184719 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.681563 | −0.0279179 | ||||||||
\(597\) | − 1.53256i | − 0.0627234i | ||||||||
\(598\) | 60.0464i | 2.45548i | ||||||||
\(599\) | 44.8025 | 1.83058 | 0.915290 | − | 0.402796i | \(-0.131962\pi\) | ||||
0.915290 | + | 0.402796i | \(0.131962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.2298 | −0.580446 | −0.290223 | − | 0.956959i | \(-0.593729\pi\) | ||||
−0.290223 | + | 0.956959i | \(0.593729\pi\) | |||||||
\(602\) | − 0.252258i | − 0.0102813i | ||||||||
\(603\) | 15.2159i | 0.619641i | ||||||||
\(604\) | −3.87578 | −0.157703 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 17.7967 | 0.722943 | ||||||||
\(607\) | 20.3346i | 0.825356i | 0.910877 | + | 0.412678i | \(0.135406\pi\) | ||||
−0.910877 | + | 0.412678i | \(0.864594\pi\) | |||||||
\(608\) | 0.560993i | 0.0227513i | ||||||||
\(609\) | −4.44202 | −0.180000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.8843 | 2.17993 | ||||||||
\(612\) | − 0.717905i | − 0.0290196i | ||||||||
\(613\) | − 20.7921i | − 0.839783i | −0.907574 | − | 0.419892i | \(-0.862068\pi\) | ||||
0.907574 | − | 0.419892i | \(-0.137932\pi\) | |||||||
\(614\) | 20.6761 | 0.834421 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.6277 | 0.629657 | ||||||||
\(617\) | − 4.94634i | − 0.199132i | −0.995031 | − | 0.0995660i | \(-0.968255\pi\) | ||||
0.995031 | − | 0.0995660i | \(-0.0317454\pi\) | |||||||
\(618\) | − 14.6862i | − 0.590766i | ||||||||
\(619\) | 45.9527 | 1.84700 | 0.923498 | − | 0.383603i | \(-0.125317\pi\) | ||||
0.923498 | + | 0.383603i | \(0.125317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.30400 | −0.252971 | ||||||||
\(622\) | 17.3643i | 0.696243i | ||||||||
\(623\) | − 4.50574i | − 0.180519i | ||||||||
\(624\) | −25.5171 | −1.02150 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.1934 | −0.567283 | ||||||||
\(627\) | − 1.89146i | − 0.0755377i | ||||||||
\(628\) | − 2.38454i | − 0.0951537i | ||||||||
\(629\) | 14.5554 | 0.580360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6636 | −0.862414 | −0.431207 | − | 0.902253i | \(-0.641912\pi\) | ||||
−0.431207 | + | 0.902253i | \(0.641912\pi\) | |||||||
\(632\) | − 42.8915i | − 1.70613i | ||||||||
\(633\) | − 11.3698i | − 0.451908i | ||||||||
\(634\) | 26.3150 | 1.04510 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0917718 | 0.00363899 | ||||||||
\(637\) | − 31.4026i | − 1.24421i | ||||||||
\(638\) | − 12.5317i | − 0.496133i | ||||||||
\(639\) | 10.6639 | 0.421859 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.3870 | 1.43720 | 0.718600 | − | 0.695424i | \(-0.244783\pi\) | ||||
0.718600 | + | 0.695424i | \(0.244783\pi\) | |||||||
\(642\) | 12.6605i | 0.499668i | ||||||||
\(643\) | − 1.01349i | − 0.0399682i | −0.999800 | − | 0.0199841i | \(-0.993638\pi\) | ||||
0.999800 | − | 0.0199841i | \(-0.00636156\pi\) | |||||||
\(644\) | 1.76309 | 0.0694755 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.14036 | −0.123556 | ||||||||
\(647\) | − 13.7007i | − 0.538629i | −0.963052 | − | 0.269315i | \(-0.913203\pi\) | ||||
0.963052 | − | 0.269315i | \(-0.0867972\pi\) | |||||||
\(648\) | − 2.93840i | − 0.115431i | ||||||||
\(649\) | −3.27944 | −0.128729 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.58913 | 0.0622830 | ||||||||
\(652\) | 1.51230i | 0.0592263i | ||||||||
\(653\) | − 23.8372i | − 0.932822i | −0.884568 | − | 0.466411i | \(-0.845547\pi\) | ||||
0.884568 | − | 0.466411i | \(-0.154453\pi\) | |||||||
\(654\) | 21.0593 | 0.823485 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.20835 | −0.164309 | ||||||||
\(657\) | 5.55832i | 0.216851i | ||||||||
\(658\) | 16.4729i | 0.642181i | ||||||||
\(659\) | −14.7758 | −0.575583 | −0.287791 | − | 0.957693i | \(-0.592921\pi\) | ||||
−0.287791 | + | 0.957693i | \(0.592921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.55471 | 0.293844 | 0.146922 | − | 0.989148i | \(-0.453063\pi\) | ||||
0.146922 | + | 0.989148i | \(0.453063\pi\) | |||||||
\(662\) | 19.5769i | 0.760877i | ||||||||
\(663\) | 28.8839i | 1.12176i | ||||||||
\(664\) | −14.7625 | −0.572895 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.79996 | 0.185995 | ||||||||
\(667\) | − 17.5477i | − 0.679448i | ||||||||
\(668\) | − 1.15652i | − 0.0447471i | ||||||||
\(669\) | −16.9507 | −0.655351 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.3730 | 1.36556 | ||||||||
\(672\) | 1.57740i | 0.0608496i | ||||||||
\(673\) | − 12.1947i | − 0.470069i | −0.971987 | − | 0.235035i | \(-0.924480\pi\) | ||||
0.971987 | − | 0.235035i | \(-0.0755204\pi\) | |||||||
\(674\) | −12.6063 | −0.485576 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.43571 | −0.247527 | ||||||||
\(677\) | − 17.9507i | − 0.689900i | −0.938621 | − | 0.344950i | \(-0.887896\pi\) | ||||
0.938621 | − | 0.344950i | \(-0.112104\pi\) | |||||||
\(678\) | 13.5732i | 0.521277i | ||||||||
\(679\) | 2.72230 | 0.104472 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.1117 | 0.540762 | ||||||||
\(682\) | 4.48320i | 0.171671i | ||||||||
\(683\) | 10.0273i | 0.383685i | 0.981426 | + | 0.191842i | \(0.0614462\pi\) | ||||
−0.981426 | + | 0.191842i | \(0.938554\pi\) | |||||||
\(684\) | 0.0994657 | 0.00380317 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.6896 | 0.942653 | ||||||||
\(687\) | − 0.0619945i | − 0.00236524i | ||||||||
\(688\) | 0.423474i | 0.0161448i | ||||||||
\(689\) | −3.69231 | −0.140666 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1296 | 0.727722 | 0.363861 | − | 0.931453i | \(-0.381458\pi\) | ||||
0.363861 | + | 0.931453i | \(0.381458\pi\) | |||||||
\(692\) | 2.39396i | 0.0910045i | ||||||||
\(693\) | − 5.31842i | − 0.202030i | ||||||||
\(694\) | 1.42297 | 0.0540154 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.17927 | 0.310034 | ||||||||
\(697\) | 4.76363i | 0.180435i | ||||||||
\(698\) | − 17.6573i | − 0.668340i | ||||||||
\(699\) | 26.0191 | 0.984131 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.81920 | −0.144249 | −0.0721246 | − | 0.997396i | \(-0.522978\pi\) | ||||
−0.0721246 | + | 0.997396i | \(0.522978\pi\) | |||||||
\(702\) | 9.52513i | 0.359503i | ||||||||
\(703\) | 2.01664i | 0.0760592i | ||||||||
\(704\) | −28.5711 | −1.07681 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.8570 | 1.72585 | ||||||||
\(707\) | 21.0241i | 0.790692i | ||||||||
\(708\) | − 0.172455i | − 0.00648124i | ||||||||
\(709\) | −38.0535 | −1.42913 | −0.714565 | − | 0.699569i | \(-0.753375\pi\) | ||||
−0.714565 | + | 0.699569i | \(0.753375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.5969 | −0.547425 | ||||||||
\(712\) | 8.29660i | 0.310928i | ||||||||
\(713\) | 6.27768i | 0.235101i | ||||||||
\(714\) | −8.83008 | −0.330457 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.72259 | −0.0643761 | ||||||||
\(717\) | − 19.4970i | − 0.728130i | ||||||||
\(718\) | − 8.23264i | − 0.307239i | ||||||||
\(719\) | −19.4340 | −0.724766 | −0.362383 | − | 0.932029i | \(-0.618037\pi\) | ||||
−0.362383 | + | 0.932029i | \(0.618037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.3495 | 0.646129 | ||||||||
\(722\) | 25.2307i | 0.938988i | ||||||||
\(723\) | − 4.09860i | − 0.152429i | ||||||||
\(724\) | 3.13165 | 0.116387 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.145007 | 0.00538172 | ||||||||
\(727\) | 38.0739i | 1.41208i | 0.708170 | + | 0.706042i | \(0.249521\pi\) | ||||
−0.708170 | + | 0.706042i | \(0.750479\pi\) | |||||||
\(728\) | − 33.0643i | − 1.22544i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.479350 | 0.0177294 | ||||||||
\(732\) | 1.86015i | 0.0687531i | ||||||||
\(733\) | 16.9591i | 0.626400i | 0.949687 | + | 0.313200i | \(0.101401\pi\) | ||||
−0.949687 | + | 0.313200i | \(0.898599\pi\) | |||||||
\(734\) | 29.5341 | 1.09012 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.23134 | −0.229690 | ||||||||
\(737\) | − 50.7112i | − 1.86797i | ||||||||
\(738\) | 1.57091i | 0.0578261i | ||||||||
\(739\) | −13.2040 | −0.485716 | −0.242858 | − | 0.970062i | \(-0.578085\pi\) | ||||
−0.242858 | + | 0.970062i | \(0.578085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.00187 | −0.147012 | ||||||||
\(742\) | − 1.12877i | − 0.0414386i | ||||||||
\(743\) | 42.2364i | 1.54950i | 0.632265 | + | 0.774752i | \(0.282125\pi\) | ||||
−0.632265 | + | 0.774752i | \(0.717875\pi\) | |||||||
\(744\) | −2.92613 | −0.107277 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −33.0358 | −1.20953 | ||||||||
\(747\) | 5.02398i | 0.183818i | ||||||||
\(748\) | 2.39261i | 0.0874825i | ||||||||
\(749\) | −14.9564 | −0.546494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.04801 | −0.0382426 | −0.0191213 | − | 0.999817i | \(-0.506087\pi\) | ||||
−0.0191213 | + | 0.999817i | \(0.506087\pi\) | |||||||
\(752\) | − 27.6536i | − 1.00842i | ||||||||
\(753\) | − 1.02933i | − 0.0375107i | ||||||||
\(754\) | −26.5139 | −0.965579 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.279678 | 0.0101718 | ||||||||
\(757\) | − 17.0074i | − 0.618146i | −0.951038 | − | 0.309073i | \(-0.899981\pi\) | ||||
0.951038 | − | 0.309073i | \(-0.100019\pi\) | |||||||
\(758\) | − 8.48079i | − 0.308036i | ||||||||
\(759\) | 21.0098 | 0.762607 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1244 | −0.874508 | −0.437254 | − | 0.899338i | \(-0.644049\pi\) | ||||
−0.437254 | + | 0.899338i | \(0.644049\pi\) | |||||||
\(762\) | 1.31947i | 0.0477993i | ||||||||
\(763\) | 24.8783i | 0.900657i | ||||||||
\(764\) | 0.0571018 | 0.00206587 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.3487 | 1.20494 | ||||||||
\(767\) | 6.93848i | 0.250534i | ||||||||
\(768\) | − 4.17298i | − 0.150579i | ||||||||
\(769\) | −49.7819 | −1.79518 | −0.897591 | − | 0.440830i | \(-0.854684\pi\) | ||||
−0.897591 | + | 0.440830i | \(0.854684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.5597 | −0.668412 | ||||||||
\(772\) | − 0.508580i | − 0.0183042i | ||||||||
\(773\) | − 31.4743i | − 1.13205i | −0.824388 | − | 0.566025i | \(-0.808480\pi\) | ||||
0.824388 | − | 0.566025i | \(-0.191520\pi\) | |||||||
\(774\) | 0.158076 | 0.00568193 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.01268 | −0.179945 | ||||||||
\(777\) | 5.67041i | 0.203425i | ||||||||
\(778\) | − 17.4575i | − 0.625883i | ||||||||
\(779\) | −0.660001 | −0.0236470 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.5404 | −1.27174 | ||||||||
\(782\) | − 34.8822i | − 1.24738i | ||||||||
\(783\) | − 2.78357i | − 0.0994768i | ||||||||
\(784\) | −16.1159 | −0.575569 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.5915 | 0.484793 | ||||||||
\(787\) | 19.1415i | 0.682321i | 0.940005 | + | 0.341161i | \(0.110820\pi\) | ||||
−0.940005 | + | 0.341161i | \(0.889180\pi\) | |||||||
\(788\) | 3.17604i | 0.113142i | ||||||||
\(789\) | −12.3938 | −0.441229 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.0347 | −0.570128 | ||||||||
\(792\) | 9.79302i | 0.347980i | ||||||||
\(793\) | − 74.8406i | − 2.65767i | ||||||||
\(794\) | 39.2030 | 1.39126 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.268595 | −0.00952009 | ||||||||
\(797\) | 7.21437i | 0.255546i | 0.991803 | + | 0.127773i | \(0.0407829\pi\) | ||||
−0.991803 | + | 0.127773i | \(0.959217\pi\) | |||||||
\(798\) | − 1.22341i | − 0.0433081i | ||||||||
\(799\) | −31.3024 | −1.10740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.82350 | 0.0997636 | ||||||||
\(802\) | − 31.5994i | − 1.11581i | ||||||||
\(803\) | − 18.5246i | − 0.653718i | ||||||||
\(804\) | 2.66673 | 0.0940484 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.48535 | 0.334107 | ||||||||
\(807\) | 5.30032i | 0.186580i | ||||||||
\(808\) | − 38.7125i | − 1.36190i | ||||||||
\(809\) | −1.05941 | −0.0372469 | −0.0186234 | − | 0.999827i | \(-0.505928\pi\) | ||||
−0.0186234 | + | 0.999827i | \(0.505928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.6400 | 0.759883 | 0.379941 | − | 0.925011i | \(-0.375944\pi\) | ||||
0.379941 | + | 0.925011i | \(0.375944\pi\) | |||||||
\(812\) | 0.778504i | 0.0273202i | ||||||||
\(813\) | 0.797428i | 0.0279670i | ||||||||
\(814\) | −15.9971 | −0.560700 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 14.8234 | 0.518922 | ||||||||
\(817\) | 0.0664138i | 0.00232353i | ||||||||
\(818\) | − 21.6022i | − 0.755302i | ||||||||
\(819\) | −11.2525 | −0.393193 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.1828 | −0.809085 | −0.404543 | − | 0.914519i | \(-0.632569\pi\) | ||||
−0.404543 | + | 0.914519i | \(0.632569\pi\) | |||||||
\(822\) | 6.58184i | 0.229568i | ||||||||
\(823\) | − 27.9769i | − 0.975214i | −0.873063 | − | 0.487607i | \(-0.837870\pi\) | ||||
0.873063 | − | 0.487607i | \(-0.162130\pi\) | |||||||
\(824\) | −31.9463 | −1.11290 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.12116 | −0.0738044 | ||||||||
\(827\) | 41.3045i | 1.43630i | 0.695889 | + | 0.718150i | \(0.255011\pi\) | ||||
−0.695889 | + | 0.718150i | \(0.744989\pi\) | |||||||
\(828\) | 1.10483i | 0.0383956i | ||||||||
\(829\) | −47.5687 | −1.65213 | −0.826064 | − | 0.563577i | \(-0.809425\pi\) | ||||
−0.826064 | + | 0.563577i | \(0.809425\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.74425 | −0.164576 | ||||||||
\(832\) | 60.4495i | 2.09571i | ||||||||
\(833\) | 18.2424i | 0.632060i | ||||||||
\(834\) | −0.250962 | −0.00869011 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.331496 | −0.0114650 | ||||||||
\(837\) | 0.995824i | 0.0344207i | ||||||||
\(838\) | 43.7357i | 1.51083i | ||||||||
\(839\) | −49.0322 | −1.69278 | −0.846389 | − | 0.532565i | \(-0.821228\pi\) | ||||
−0.846389 | + | 0.532565i | \(0.821228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.2517 | −0.732818 | ||||||||
\(842\) | − 24.3852i | − 0.840369i | ||||||||
\(843\) | − 18.7398i | − 0.645433i | ||||||||
\(844\) | −1.99266 | −0.0685900 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.3227 | −0.354901 | ||||||||
\(847\) | 0.171304i | 0.00588606i | ||||||||
\(848\) | 1.89491i | 0.0650715i | ||||||||
\(849\) | −11.7612 | −0.403643 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.4003 | −0.767871 | ||||||||
\(852\) | − 1.86895i | − 0.0640293i | ||||||||
\(853\) | − 32.5376i | − 1.11407i | −0.830490 | − | 0.557033i | \(-0.811939\pi\) | ||||
0.830490 | − | 0.557033i | \(-0.188061\pi\) | |||||||
\(854\) | 22.8794 | 0.782918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.5398 | 0.941290 | ||||||||
\(857\) | 30.4813i | 1.04122i | 0.853794 | + | 0.520610i | \(0.174296\pi\) | ||||
−0.853794 | + | 0.520610i | \(0.825704\pi\) | |||||||
\(858\) | − 31.7451i | − 1.08376i | ||||||||
\(859\) | −4.12215 | −0.140646 | −0.0703231 | − | 0.997524i | \(-0.522403\pi\) | ||||
−0.0703231 | + | 0.997524i | \(0.522403\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.85579 | −0.0632452 | ||||||||
\(862\) | − 44.7601i | − 1.52453i | ||||||||
\(863\) | − 18.4184i | − 0.626969i | −0.949593 | − | 0.313485i | \(-0.898504\pi\) | ||||
0.949593 | − | 0.313485i | \(-0.101496\pi\) | |||||||
\(864\) | −0.988473 | −0.0336285 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.6169 | −1.04041 | ||||||||
\(867\) | 0.220750i | 0.00749705i | ||||||||
\(868\) | − 0.278510i | − 0.00945325i | ||||||||
\(869\) | 48.6479 | 1.65027 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −107.292 | −3.63546 | ||||||||
\(872\) | − 45.8095i | − 1.55131i | ||||||||
\(873\) | 1.70592i | 0.0577366i | ||||||||
\(874\) | 4.83292 | 0.163476 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.974146 | 0.0329133 | ||||||||
\(877\) | 18.9126i | 0.638634i | 0.947648 | + | 0.319317i | \(0.103453\pi\) | ||||
−0.947648 | + | 0.319317i | \(0.896547\pi\) | |||||||
\(878\) | − 11.4879i | − 0.387699i | ||||||||
\(879\) | −22.2819 | −0.751548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.6336 | 1.16684 | 0.583418 | − | 0.812172i | \(-0.301715\pi\) | ||||
0.583418 | + | 0.812172i | \(0.301715\pi\) | |||||||
\(882\) | 6.01583i | 0.202563i | ||||||||
\(883\) | − 32.6874i | − 1.10002i | −0.835158 | − | 0.550009i | \(-0.814624\pi\) | ||||
0.835158 | − | 0.550009i | \(-0.185376\pi\) | |||||||
\(884\) | 5.06218 | 0.170259 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.58814 | 0.288524 | ||||||||
\(887\) | − 48.7918i | − 1.63827i | −0.573602 | − | 0.819134i | \(-0.694455\pi\) | ||||
0.573602 | − | 0.819134i | \(-0.305545\pi\) | |||||||
\(888\) | − 10.4411i | − 0.350382i | ||||||||
\(889\) | −1.55875 | −0.0522788 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.33277 | 0.111652 | ||||||||
\(892\) | 2.97076i | 0.0994684i | ||||||||
\(893\) | − 4.33695i | − 0.145131i | ||||||||
\(894\) | −5.25322 | −0.175694 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −15.3251 | −0.511977 | ||||||||
\(897\) | − 44.4515i | − 1.48419i | ||||||||
\(898\) | − 8.45249i | − 0.282063i | ||||||||
\(899\) | −2.77195 | −0.0924497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.14494 | 0.0714582 | ||||||||
\(902\) | − 5.23549i | − 0.174323i | ||||||||
\(903\) | 0.186743i | 0.00621441i | ||||||||
\(904\) | 29.5253 | 0.981997 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −29.8730 | −0.992465 | ||||||||
\(907\) | − 45.0367i | − 1.49542i | −0.664025 | − | 0.747710i | \(-0.731153\pi\) | ||||
0.664025 | − | 0.747710i | \(-0.268847\pi\) | |||||||
\(908\) | − 2.47321i | − 0.0820762i | ||||||||
\(909\) | −13.1747 | −0.436976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.9449 | 0.428882 | 0.214441 | − | 0.976737i | \(-0.431207\pi\) | ||||
0.214441 | + | 0.976737i | \(0.431207\pi\) | |||||||
\(912\) | 2.05378i | 0.0680073i | ||||||||
\(913\) | − 16.7438i | − 0.554137i | ||||||||
\(914\) | 14.9187 | 0.493466 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0108651 | −0.000358993 0 | ||||||||
\(917\) | 16.0563i | 0.530225i | ||||||||
\(918\) | − 5.53333i | − 0.182627i | ||||||||
\(919\) | −14.5719 | −0.480682 | −0.240341 | − | 0.970689i | \(-0.577259\pi\) | ||||
−0.240341 | + | 0.970689i | \(0.577259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3063 | −0.504358 | ||||||||
\(922\) | 31.9636i | 1.05266i | ||||||||
\(923\) | 75.1948i | 2.47507i | ||||||||
\(924\) | −0.932102 | −0.0306639 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.40813 | −0.276308 | ||||||||
\(927\) | 10.8720i | 0.357083i | ||||||||
\(928\) | − 2.75149i | − 0.0903220i | ||||||||
\(929\) | 31.3591 | 1.02886 | 0.514430 | − | 0.857532i | \(-0.328004\pi\) | ||||
0.514430 | + | 0.857532i | \(0.328004\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.52748 | −0.0828347 | ||||||||
\(932\) | − 4.56008i | − 0.149370i | ||||||||
\(933\) | − 12.8545i | − 0.420838i | ||||||||
\(934\) | −6.68227 | −0.218651 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.7196 | 0.677242 | ||||||||
\(937\) | 48.7726i | 1.59333i | 0.604420 | + | 0.796666i | \(0.293405\pi\) | ||||
−0.604420 | + | 0.796666i | \(0.706595\pi\) | |||||||
\(938\) | − 32.8002i | − 1.07097i | ||||||||
\(939\) | 10.5072 | 0.342889 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.2359 | −1.05086 | −0.525431 | − | 0.850836i | \(-0.676096\pi\) | ||||
−0.525431 | + | 0.850836i | \(0.676096\pi\) | |||||||
\(942\) | − 18.3791i | − 0.598825i | ||||||||
\(943\) | − 7.33108i | − 0.238733i | ||||||||
\(944\) | 3.56086 | 0.115896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.526832 | −0.0171288 | ||||||||
\(947\) | 51.9235i | 1.68729i | 0.536903 | + | 0.843644i | \(0.319594\pi\) | ||||
−0.536903 | + | 0.843644i | \(0.680406\pi\) | |||||||
\(948\) | 2.55823i | 0.0830875i | ||||||||
\(949\) | −39.1935 | −1.27227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.4806 | −0.631703 | ||||||||
\(952\) | 19.2077i | 0.622525i | ||||||||
\(953\) | − 39.7788i | − 1.28856i | −0.764789 | − | 0.644281i | \(-0.777157\pi\) | ||||
0.764789 | − | 0.644281i | \(-0.222843\pi\) | |||||||
\(954\) | 0.707341 | 0.0229010 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.41703 | −0.110515 | ||||||||
\(957\) | 9.27701i | 0.299883i | ||||||||
\(958\) | − 40.6462i | − 1.31322i | ||||||||
\(959\) | −7.77543 | −0.251082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0083 | −0.968011 | ||||||||
\(962\) | 33.8460i | 1.09124i | ||||||||
\(963\) | − 9.37236i | − 0.302020i | ||||||||
\(964\) | −0.718317 | −0.0231354 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.5892 | 0.437226 | ||||||||
\(967\) | 19.8817i | 0.639353i | 0.947527 | + | 0.319677i | \(0.103574\pi\) | ||||
−0.947527 | + | 0.319677i | \(0.896426\pi\) | |||||||
\(968\) | − 0.315428i | − 0.0101382i | ||||||||
\(969\) | 2.32476 | 0.0746822 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.3841 | −1.32808 | −0.664039 | − | 0.747698i | \(-0.731159\pi\) | ||||
−0.664039 | + | 0.747698i | \(0.731159\pi\) | |||||||
\(972\) | 0.175259i | 0.00562144i | ||||||||
\(973\) | − 0.296473i | − 0.00950449i | ||||||||
\(974\) | 46.2658 | 1.48245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.4085 | −1.22943 | ||||||||
\(977\) | 3.61991i | 0.115811i | 0.998322 | + | 0.0579056i | \(0.0184422\pi\) | ||||
−0.998322 | + | 0.0579056i | \(0.981558\pi\) | |||||||
\(978\) | 11.6562i | 0.372725i | ||||||||
\(979\) | −9.41009 | −0.300748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.5899 | −0.497748 | ||||||||
\(982\) | 14.0747i | 0.449143i | ||||||||
\(983\) | 20.1099i | 0.641405i | 0.947180 | + | 0.320702i | \(0.103919\pi\) | ||||
−0.947180 | + | 0.320702i | \(0.896081\pi\) | |||||||
\(984\) | 3.41714 | 0.108935 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.4024 | 0.490514 | ||||||||
\(987\) | − 12.1947i | − 0.388160i | ||||||||
\(988\) | 0.701364i | 0.0223134i | ||||||||
\(989\) | −0.737705 | −0.0234576 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.43990 | 0.236336 | 0.118168 | − | 0.992994i | \(-0.462298\pi\) | ||||
0.118168 | + | 0.992994i | \(0.462298\pi\) | |||||||
\(992\) | 0.984345i | 0.0312530i | ||||||||
\(993\) | − 14.4925i | − 0.459905i | ||||||||
\(994\) | −22.9877 | −0.729126 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.880498 | 0.0278996 | ||||||||
\(997\) | − 46.1472i | − 1.46150i | −0.682648 | − | 0.730748i | \(-0.739172\pi\) | ||||
0.682648 | − | 0.730748i | \(-0.260828\pi\) | |||||||
\(998\) | 11.9348i | 0.377788i | ||||||||
\(999\) | −3.55334 | −0.112423 |
(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 | 1875.2.b.h.1249.5 | 16 | ||
5.2 | odd | 4 | 1875.2.a.m.1.7 | 8 | |||
5.3 | odd | 4 | 1875.2.a.p.1.2 | 8 | |||
5.4 | even | 2 | inner | 1875.2.b.h.1249.12 | 16 | ||
15.2 | even | 4 | 5625.2.a.bd.1.2 | 8 | |||
15.8 | even | 4 | 5625.2.a.t.1.7 | 8 | |||
25.2 | odd | 20 | 375.2.g.e.226.4 | 16 | |||
25.9 | even | 10 | 375.2.i.c.349.2 | 16 | |||
25.11 | even | 5 | 375.2.i.c.274.2 | 16 | |||
25.12 | odd | 20 | 375.2.g.e.151.4 | 16 | |||
25.13 | odd | 20 | 375.2.g.d.151.1 | 16 | |||
25.14 | even | 10 | 75.2.i.a.4.3 | ✓ | 16 | ||
25.16 | even | 5 | 75.2.i.a.19.3 | yes | 16 | ||
25.23 | odd | 20 | 375.2.g.d.226.1 | 16 | |||
75.14 | odd | 10 | 225.2.m.b.154.2 | 16 | |||
75.41 | odd | 10 | 225.2.m.b.19.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.3 | ✓ | 16 | 25.14 | even | 10 | ||
75.2.i.a.19.3 | yes | 16 | 25.16 | even | 5 | ||
225.2.m.b.19.2 | 16 | 75.41 | odd | 10 | |||
225.2.m.b.154.2 | 16 | 75.14 | odd | 10 | |||
375.2.g.d.151.1 | 16 | 25.13 | odd | 20 | |||
375.2.g.d.226.1 | 16 | 25.23 | odd | 20 | |||
375.2.g.e.151.4 | 16 | 25.12 | odd | 20 | |||
375.2.g.e.226.4 | 16 | 25.2 | odd | 20 | |||
375.2.i.c.274.2 | 16 | 25.11 | even | 5 | |||
375.2.i.c.349.2 | 16 | 25.9 | even | 10 | |||
1875.2.a.m.1.7 | 8 | 5.2 | odd | 4 | |||
1875.2.a.p.1.2 | 8 | 5.3 | odd | 4 | |||
1875.2.b.h.1249.5 | 16 | 1.1 | even | 1 | trivial | ||
1875.2.b.h.1249.12 | 16 | 5.4 | even | 2 | inner | ||
5625.2.a.t.1.7 | 8 | 15.8 | even | 4 | |||
5625.2.a.bd.1.2 | 8 | 15.2 | even | 4 |