Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.17 | ||
Root | \(2.28323i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.f.694.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.28323i | 1.61449i | 0.590217 | + | 0.807244i | \(0.299042\pi\) | ||||
−0.590217 | + | 0.807244i | \(0.700958\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −3.21315 | −1.60657 | ||||||||
\(5\) | −2.23363 | + | 0.104355i | −0.998910 | + | 0.0466690i | ||||
\(6\) | −2.28323 | −0.932125 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 2.76990i | − | 0.979307i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.238267 | − | 5.09990i | −0.0753466 | − | 1.61273i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − | 3.21315i | − | 0.927556i | ||||||
\(13\) | − | 4.08903i | − | 1.13409i | −0.823686 | − | 0.567047i | \(-0.808086\pi\) | ||
0.823686 | − | 0.567047i | \(-0.191914\pi\) | |||||||
\(14\) | −2.28323 | −0.610219 | ||||||||
\(15\) | −0.104355 | − | 2.23363i | −0.0269444 | − | 0.576721i | ||||
\(16\) | −0.101977 | −0.0254944 | ||||||||
\(17\) | − | 0.333296i | − | 0.0808362i | −0.999183 | − | 0.0404181i | \(-0.987131\pi\) | ||
0.999183 | − | 0.0404181i | \(-0.0128690\pi\) | |||||||
\(18\) | − | 2.28323i | − | 0.538163i | ||||||
\(19\) | −4.72571 | −1.08415 | −0.542076 | − | 0.840330i | \(-0.682361\pi\) | ||||
−0.542076 | + | 0.840330i | \(0.682361\pi\) | |||||||
\(20\) | 7.17699 | − | 0.335308i | 1.60482 | − | 0.0749772i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.28323i | 0.486787i | ||||||||
\(23\) | − | 7.98665i | − | 1.66533i | −0.553776 | − | 0.832666i | \(-0.686814\pi\) | ||
0.553776 | − | 0.832666i | \(-0.313186\pi\) | |||||||
\(24\) | 2.76990 | 0.565403 | ||||||||
\(25\) | 4.97822 | − | 0.466182i | 0.995644 | − | 0.0932363i | ||||
\(26\) | 9.33621 | 1.83098 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 3.21315i | − | 0.607228i | ||||||
\(29\) | 0.373782 | 0.0694096 | 0.0347048 | − | 0.999398i | \(-0.488951\pi\) | ||||
0.0347048 | + | 0.999398i | \(0.488951\pi\) | |||||||
\(30\) | 5.09990 | − | 0.238267i | 0.931110 | − | 0.0435014i | ||||
\(31\) | −9.24196 | −1.65990 | −0.829952 | − | 0.557835i | \(-0.811632\pi\) | ||||
−0.829952 | + | 0.557835i | \(0.811632\pi\) | |||||||
\(32\) | − | 5.77263i | − | 1.02047i | ||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 0.760993 | 0.130509 | ||||||||
\(35\) | −0.104355 | − | 2.23363i | −0.0176392 | − | 0.377553i | ||||
\(36\) | 3.21315 | 0.535525 | ||||||||
\(37\) | − | 3.51370i | − | 0.577649i | −0.957382 | − | 0.288825i | \(-0.906736\pi\) | ||
0.957382 | − | 0.288825i | \(-0.0932645\pi\) | |||||||
\(38\) | − | 10.7899i | − | 1.75035i | ||||||
\(39\) | 4.08903 | 0.654769 | ||||||||
\(40\) | 0.289053 | + | 6.18693i | 0.0457033 | + | 0.978240i | ||||
\(41\) | 7.35561 | 1.14875 | 0.574377 | − | 0.818591i | \(-0.305244\pi\) | ||||
0.574377 | + | 0.818591i | \(0.305244\pi\) | |||||||
\(42\) | − | 2.28323i | − | 0.352310i | ||||||
\(43\) | 2.50440i | 0.381917i | 0.981598 | + | 0.190959i | \(0.0611596\pi\) | ||||
−0.981598 | + | 0.190959i | \(0.938840\pi\) | |||||||
\(44\) | −3.21315 | −0.484400 | ||||||||
\(45\) | 2.23363 | − | 0.104355i | 0.332970 | − | 0.0155563i | ||||
\(46\) | 18.2354 | 2.68866 | ||||||||
\(47\) | 11.9625i | 1.74490i | 0.488699 | + | 0.872452i | \(0.337471\pi\) | ||||
−0.488699 | + | 0.872452i | \(0.662529\pi\) | |||||||
\(48\) | − | 0.101977i | − | 0.0147192i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.06440 | + | 11.3664i | 0.150529 | + | 1.60746i | ||||
\(51\) | 0.333296 | 0.0466708 | ||||||||
\(52\) | 13.1387i | 1.82200i | ||||||||
\(53\) | 12.8762i | 1.76868i | 0.466842 | + | 0.884341i | \(0.345392\pi\) | ||||
−0.466842 | + | 0.884341i | \(0.654608\pi\) | |||||||
\(54\) | 2.28323 | 0.310708 | ||||||||
\(55\) | −2.23363 | + | 0.104355i | −0.301183 | + | 0.0140712i | ||||
\(56\) | 2.76990 | 0.370143 | ||||||||
\(57\) | − | 4.72571i | − | 0.625935i | ||||||
\(58\) | 0.853432i | 0.112061i | ||||||||
\(59\) | 2.46158 | 0.320470 | 0.160235 | − | 0.987079i | \(-0.448775\pi\) | ||||
0.160235 | + | 0.987079i | \(0.448775\pi\) | |||||||
\(60\) | 0.335308 | + | 7.17699i | 0.0432881 | + | 0.926545i | ||||
\(61\) | −8.83037 | −1.13061 | −0.565306 | − | 0.824881i | \(-0.691242\pi\) | ||||
−0.565306 | + | 0.824881i | \(0.691242\pi\) | |||||||
\(62\) | − | 21.1015i | − | 2.67990i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 12.9763 | 1.62204 | ||||||||
\(65\) | 0.426711 | + | 9.13339i | 0.0529270 | + | 1.13286i | ||||
\(66\) | −2.28323 | −0.281046 | ||||||||
\(67\) | − | 11.1473i | − | 1.36186i | −0.732350 | − | 0.680929i | \(-0.761576\pi\) | ||
0.732350 | − | 0.680929i | \(-0.238424\pi\) | |||||||
\(68\) | 1.07093i | 0.129869i | ||||||||
\(69\) | 7.98665 | 0.961480 | ||||||||
\(70\) | 5.09990 | − | 0.238267i | 0.609554 | − | 0.0284783i | ||||
\(71\) | 13.7980 | 1.63752 | 0.818761 | − | 0.574134i | \(-0.194661\pi\) | ||||
0.818761 | + | 0.574134i | \(0.194661\pi\) | |||||||
\(72\) | 2.76990i | 0.326436i | ||||||||
\(73\) | − | 8.53510i | − | 0.998958i | −0.866326 | − | 0.499479i | \(-0.833525\pi\) | ||
0.866326 | − | 0.499479i | \(-0.166475\pi\) | |||||||
\(74\) | 8.02260 | 0.932608 | ||||||||
\(75\) | 0.466182 | + | 4.97822i | 0.0538300 | + | 0.574835i | ||||
\(76\) | 15.1844 | 1.74177 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 9.33621i | 1.05712i | ||||||||
\(79\) | −6.95125 | −0.782077 | −0.391039 | − | 0.920374i | \(-0.627884\pi\) | ||||
−0.391039 | + | 0.920374i | \(0.627884\pi\) | |||||||
\(80\) | 0.227780 | − | 0.0106419i | 0.0254666 | − | 0.00118980i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.7946i | 1.85465i | ||||||||
\(83\) | − | 9.02465i | − | 0.990584i | −0.868727 | − | 0.495292i | \(-0.835061\pi\) | ||
0.868727 | − | 0.495292i | \(-0.164939\pi\) | |||||||
\(84\) | 3.21315 | 0.350583 | ||||||||
\(85\) | 0.0347812 | + | 0.744461i | 0.00377255 | + | 0.0807482i | ||||
\(86\) | −5.71812 | −0.616601 | ||||||||
\(87\) | 0.373782i | 0.0400737i | ||||||||
\(88\) | − | 2.76990i | − | 0.295272i | ||||||
\(89\) | −17.9041 | −1.89783 | −0.948915 | − | 0.315531i | \(-0.897817\pi\) | ||||
−0.948915 | + | 0.315531i | \(0.897817\pi\) | |||||||
\(90\) | 0.238267 | + | 5.09990i | 0.0251155 | + | 0.537577i | ||||
\(91\) | 4.08903 | 0.428647 | ||||||||
\(92\) | 25.6623i | 2.67548i | ||||||||
\(93\) | − | 9.24196i | − | 0.958346i | ||||||
\(94\) | −27.3131 | −2.81713 | ||||||||
\(95\) | 10.5555 | − | 0.493152i | 1.08297 | − | 0.0505963i | ||||
\(96\) | 5.77263 | 0.589167 | ||||||||
\(97\) | 7.95736i | 0.807948i | 0.914771 | + | 0.403974i | \(0.132371\pi\) | ||||
−0.914771 | + | 0.403974i | \(0.867629\pi\) | |||||||
\(98\) | − | 2.28323i | − | 0.230641i | ||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −15.9958 | + | 1.49791i | −1.59958 | + | 0.149791i | ||||
\(101\) | 7.33584 | 0.729943 | 0.364972 | − | 0.931019i | \(-0.381079\pi\) | ||||
0.364972 | + | 0.931019i | \(0.381079\pi\) | |||||||
\(102\) | 0.760993i | 0.0753495i | ||||||||
\(103\) | − | 16.6422i | − | 1.63980i | −0.572505 | − | 0.819901i | \(-0.694028\pi\) | ||
0.572505 | − | 0.819901i | \(-0.305972\pi\) | |||||||
\(104\) | −11.3262 | −1.11063 | ||||||||
\(105\) | 2.23363 | − | 0.104355i | 0.217980 | − | 0.0101840i | ||||
\(106\) | −29.3993 | −2.85552 | ||||||||
\(107\) | − | 17.7684i | − | 1.71774i | −0.512196 | − | 0.858869i | \(-0.671168\pi\) | ||
0.512196 | − | 0.858869i | \(-0.328832\pi\) | |||||||
\(108\) | 3.21315i | 0.309185i | ||||||||
\(109\) | −14.9455 | −1.43152 | −0.715760 | − | 0.698347i | \(-0.753919\pi\) | ||||
−0.715760 | + | 0.698347i | \(0.753919\pi\) | |||||||
\(110\) | −0.238267 | − | 5.09990i | −0.0227179 | − | 0.486256i | ||||
\(111\) | 3.51370 | 0.333506 | ||||||||
\(112\) | − | 0.101977i | − | 0.00963596i | ||||||
\(113\) | − | 4.90620i | − | 0.461537i | −0.973009 | − | 0.230768i | \(-0.925876\pi\) | ||
0.973009 | − | 0.230768i | \(-0.0741240\pi\) | |||||||
\(114\) | 10.7899 | 1.01057 | ||||||||
\(115\) | 0.833447 | + | 17.8392i | 0.0777194 | + | 1.66352i | ||||
\(116\) | −1.20102 | −0.111512 | ||||||||
\(117\) | 4.08903i | 0.378031i | ||||||||
\(118\) | 5.62036i | 0.517396i | ||||||||
\(119\) | 0.333296 | 0.0305532 | ||||||||
\(120\) | −6.18693 | + | 0.289053i | −0.564787 | + | 0.0263868i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 20.1618i | − | 1.82536i | ||||||
\(123\) | 7.35561i | 0.663233i | ||||||||
\(124\) | 29.6958 | 2.66676 | ||||||||
\(125\) | −11.0709 | + | 1.56078i | −0.990208 | + | 0.139600i | ||||
\(126\) | 2.28323 | 0.203406 | ||||||||
\(127\) | 6.50360i | 0.577101i | 0.957465 | + | 0.288551i | \(0.0931734\pi\) | ||||
−0.957465 | + | 0.288551i | \(0.906827\pi\) | |||||||
\(128\) | 18.0826i | 1.59830i | ||||||||
\(129\) | −2.50440 | −0.220500 | ||||||||
\(130\) | −20.8537 | + | 0.974281i | −1.82899 | + | 0.0854501i | ||||
\(131\) | −8.42573 | −0.736159 | −0.368080 | − | 0.929794i | \(-0.619985\pi\) | ||||
−0.368080 | + | 0.929794i | \(0.619985\pi\) | |||||||
\(132\) | − | 3.21315i | − | 0.279669i | ||||||
\(133\) | − | 4.72571i | − | 0.409771i | ||||||
\(134\) | 25.4518 | 2.19870 | ||||||||
\(135\) | 0.104355 | + | 2.23363i | 0.00898145 | + | 0.192240i | ||||
\(136\) | −0.923197 | −0.0791635 | ||||||||
\(137\) | − | 13.5898i | − | 1.16106i | −0.814240 | − | 0.580529i | \(-0.802846\pi\) | ||
0.814240 | − | 0.580529i | \(-0.197154\pi\) | |||||||
\(138\) | 18.2354i | 1.55230i | ||||||||
\(139\) | −11.0612 | −0.938196 | −0.469098 | − | 0.883146i | \(-0.655421\pi\) | ||||
−0.469098 | + | 0.883146i | \(0.655421\pi\) | |||||||
\(140\) | 0.335308 | + | 7.17699i | 0.0283387 | + | 0.606566i | ||||
\(141\) | −11.9625 | −1.00742 | ||||||||
\(142\) | 31.5041i | 2.64376i | ||||||||
\(143\) | − | 4.08903i | − | 0.341942i | ||||||
\(144\) | 0.101977 | 0.00849812 | ||||||||
\(145\) | −0.834892 | + | 0.0390061i | −0.0693340 | + | 0.00323928i | ||||
\(146\) | 19.4876 | 1.61281 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 11.2900i | 0.928036i | ||||||||
\(149\) | −18.5727 | −1.52153 | −0.760766 | − | 0.649026i | \(-0.775177\pi\) | ||||
−0.760766 | + | 0.649026i | \(0.775177\pi\) | |||||||
\(150\) | −11.3664 | + | 1.06440i | −0.928065 | + | 0.0869079i | ||||
\(151\) | −3.07826 | −0.250505 | −0.125253 | − | 0.992125i | \(-0.539974\pi\) | ||||
−0.125253 | + | 0.992125i | \(0.539974\pi\) | |||||||
\(152\) | 13.0897i | 1.06172i | ||||||||
\(153\) | 0.333296i | 0.0269454i | ||||||||
\(154\) | −2.28323 | −0.183988 | ||||||||
\(155\) | 20.6431 | − | 0.964445i | 1.65810 | − | 0.0774661i | ||||
\(156\) | −13.1387 | −1.05194 | ||||||||
\(157\) | − | 4.25537i | − | 0.339616i | −0.985477 | − | 0.169808i | \(-0.945685\pi\) | ||
0.985477 | − | 0.169808i | \(-0.0543147\pi\) | |||||||
\(158\) | − | 15.8713i | − | 1.26265i | ||||||
\(159\) | −12.8762 | −1.02115 | ||||||||
\(160\) | 0.602404 | + | 12.8939i | 0.0476242 | + | 1.01936i | ||||
\(161\) | 7.98665 | 0.629436 | ||||||||
\(162\) | 2.28323i | 0.179388i | ||||||||
\(163\) | − | 13.7375i | − | 1.07601i | −0.842943 | − | 0.538003i | \(-0.819179\pi\) | ||
0.842943 | − | 0.538003i | \(-0.180821\pi\) | |||||||
\(164\) | −23.6347 | −1.84556 | ||||||||
\(165\) | −0.104355 | − | 2.23363i | −0.00812403 | − | 0.173888i | ||||
\(166\) | 20.6054 | 1.59929 | ||||||||
\(167\) | − | 10.1244i | − | 0.783447i | −0.920083 | − | 0.391724i | \(-0.871879\pi\) | ||
0.920083 | − | 0.391724i | \(-0.128121\pi\) | |||||||
\(168\) | 2.76990i | 0.213702i | ||||||||
\(169\) | −3.72018 | −0.286168 | ||||||||
\(170\) | −1.69978 | + | 0.0794135i | −0.130367 | + | 0.00609073i | ||||
\(171\) | 4.72571 | 0.361384 | ||||||||
\(172\) | − | 8.04700i | − | 0.613578i | ||||||
\(173\) | 24.2008i | 1.83995i | 0.391977 | + | 0.919975i | \(0.371791\pi\) | ||||
−0.391977 | + | 0.919975i | \(0.628209\pi\) | |||||||
\(174\) | −0.853432 | −0.0646985 | ||||||||
\(175\) | 0.466182 | + | 4.97822i | 0.0352400 | + | 0.376318i | ||||
\(176\) | −0.101977 | −0.00768684 | ||||||||
\(177\) | 2.46158i | 0.185024i | ||||||||
\(178\) | − | 40.8792i | − | 3.06403i | ||||||
\(179\) | 3.90862 | 0.292144 | 0.146072 | − | 0.989274i | \(-0.453337\pi\) | ||||
0.146072 | + | 0.989274i | \(0.453337\pi\) | |||||||
\(180\) | −7.17699 | + | 0.335308i | −0.534941 | + | 0.0249924i | ||||
\(181\) | −7.76620 | −0.577257 | −0.288628 | − | 0.957441i | \(-0.593199\pi\) | ||||
−0.288628 | + | 0.957441i | \(0.593199\pi\) | |||||||
\(182\) | 9.33621i | 0.692046i | ||||||||
\(183\) | − | 8.83037i | − | 0.652759i | ||||||
\(184\) | −22.1222 | −1.63087 | ||||||||
\(185\) | 0.366673 | + | 7.84832i | 0.0269583 | + | 0.577020i | ||||
\(186\) | 21.1015 | 1.54724 | ||||||||
\(187\) | − | 0.333296i | − | 0.0243730i | ||||||
\(188\) | − | 38.4372i | − | 2.80332i | ||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.12598 | + | 24.1006i | 0.0816871 | + | 1.74844i | ||||
\(191\) | −6.99980 | −0.506488 | −0.253244 | − | 0.967402i | \(-0.581498\pi\) | ||||
−0.253244 | + | 0.967402i | \(0.581498\pi\) | |||||||
\(192\) | 12.9763i | 0.936484i | ||||||||
\(193\) | 8.84126i | 0.636408i | 0.948022 | + | 0.318204i | \(0.103080\pi\) | ||||
−0.948022 | + | 0.318204i | \(0.896920\pi\) | |||||||
\(194\) | −18.1685 | −1.30442 | ||||||||
\(195\) | −9.13339 | + | 0.426711i | −0.654056 | + | 0.0305574i | ||||
\(196\) | 3.21315 | 0.229511 | ||||||||
\(197\) | 7.51103i | 0.535139i | 0.963539 | + | 0.267569i | \(0.0862204\pi\) | ||||
−0.963539 | + | 0.267569i | \(0.913780\pi\) | |||||||
\(198\) | − | 2.28323i | − | 0.162262i | ||||||
\(199\) | −21.5564 | −1.52810 | −0.764048 | − | 0.645160i | \(-0.776791\pi\) | ||||
−0.764048 | + | 0.645160i | \(0.776791\pi\) | |||||||
\(200\) | −1.29128 | − | 13.7892i | −0.0913069 | − | 0.975041i | ||||
\(201\) | 11.1473 | 0.786269 | ||||||||
\(202\) | 16.7494i | 1.17849i | ||||||||
\(203\) | 0.373782i | 0.0262344i | ||||||||
\(204\) | −1.07093 | −0.0749801 | ||||||||
\(205\) | −16.4297 | + | 0.767595i | −1.14750 | + | 0.0536112i | ||||
\(206\) | 37.9980 | 2.64744 | ||||||||
\(207\) | 7.98665i | 0.555111i | ||||||||
\(208\) | 0.416989i | 0.0289130i | ||||||||
\(209\) | −4.72571 | −0.326884 | ||||||||
\(210\) | 0.238267 | + | 5.09990i | 0.0164420 | + | 0.351926i | ||||
\(211\) | 4.98337 | 0.343069 | 0.171535 | − | 0.985178i | \(-0.445127\pi\) | ||||
0.171535 | + | 0.985178i | \(0.445127\pi\) | |||||||
\(212\) | − | 41.3731i | − | 2.84152i | ||||||
\(213\) | 13.7980i | 0.945424i | ||||||||
\(214\) | 40.5694 | 2.77327 | ||||||||
\(215\) | −0.261347 | − | 5.59390i | −0.0178237 | − | 0.381501i | ||||
\(216\) | −2.76990 | −0.188468 | ||||||||
\(217\) | − | 9.24196i | − | 0.627385i | ||||||
\(218\) | − | 34.1240i | − | 2.31117i | ||||||
\(219\) | 8.53510 | 0.576749 | ||||||||
\(220\) | 7.17699 | − | 0.335308i | 0.483872 | − | 0.0226065i | ||||
\(221\) | −1.36286 | −0.0916759 | ||||||||
\(222\) | 8.02260i | 0.538442i | ||||||||
\(223\) | − | 1.31258i | − | 0.0878967i | −0.999034 | − | 0.0439484i | \(-0.986006\pi\) | ||
0.999034 | − | 0.0439484i | \(-0.0139937\pi\) | |||||||
\(224\) | 5.77263 | 0.385700 | ||||||||
\(225\) | −4.97822 | + | 0.466182i | −0.331881 | + | 0.0310788i | ||||
\(226\) | 11.2020 | 0.745146 | ||||||||
\(227\) | − | 24.4941i | − | 1.62573i | −0.582451 | − | 0.812866i | \(-0.697906\pi\) | ||
0.582451 | − | 0.812866i | \(-0.302094\pi\) | |||||||
\(228\) | 15.1844i | 1.00561i | ||||||||
\(229\) | 17.6904 | 1.16901 | 0.584506 | − | 0.811390i | \(-0.301288\pi\) | ||||
0.584506 | + | 0.811390i | \(0.301288\pi\) | |||||||
\(230\) | −40.7311 | + | 1.90295i | −2.68573 | + | 0.125477i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | − | 1.03534i | − | 0.0679733i | ||||||
\(233\) | 15.2475i | 0.998898i | 0.866343 | + | 0.499449i | \(0.166464\pi\) | ||||
−0.866343 | + | 0.499449i | \(0.833536\pi\) | |||||||
\(234\) | −9.33621 | −0.610327 | ||||||||
\(235\) | −1.24834 | − | 26.7197i | −0.0814330 | − | 1.74300i | ||||
\(236\) | −7.90942 | −0.514859 | ||||||||
\(237\) | − | 6.95125i | − | 0.451532i | ||||||
\(238\) | 0.760993i | 0.0493278i | ||||||||
\(239\) | 6.67755 | 0.431935 | 0.215967 | − | 0.976401i | \(-0.430710\pi\) | ||||
0.215967 | + | 0.976401i | \(0.430710\pi\) | |||||||
\(240\) | 0.0106419 | + | 0.227780i | 0.000686930 | + | 0.0147031i | ||||
\(241\) | 4.97410 | 0.320410 | 0.160205 | − | 0.987084i | \(-0.448785\pi\) | ||||
0.160205 | + | 0.987084i | \(0.448785\pi\) | |||||||
\(242\) | 2.28323i | 0.146772i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 28.3733 | 1.81641 | ||||||||
\(245\) | 2.23363 | − | 0.104355i | 0.142701 | − | 0.00666700i | ||||
\(246\) | −16.7946 | −1.07078 | ||||||||
\(247\) | 19.3236i | 1.22953i | ||||||||
\(248\) | 25.5993i | 1.62556i | ||||||||
\(249\) | 9.02465 | 0.571914 | ||||||||
\(250\) | −3.56362 | − | 25.2773i | −0.225383 | − | 1.59868i | ||||
\(251\) | −10.7702 | −0.679810 | −0.339905 | − | 0.940460i | \(-0.610395\pi\) | ||||
−0.339905 | + | 0.940460i | \(0.610395\pi\) | |||||||
\(252\) | 3.21315i | 0.202409i | ||||||||
\(253\) | − | 7.98665i | − | 0.502116i | ||||||
\(254\) | −14.8492 | −0.931724 | ||||||||
\(255\) | −0.744461 | + | 0.0347812i | −0.0466200 | + | 0.00217808i | ||||
\(256\) | −15.3343 | −0.958391 | ||||||||
\(257\) | − | 3.36008i | − | 0.209596i | −0.994494 | − | 0.104798i | \(-0.966580\pi\) | ||
0.994494 | − | 0.104798i | \(-0.0334196\pi\) | |||||||
\(258\) | − | 5.71812i | − | 0.355995i | ||||||
\(259\) | 3.51370 | 0.218331 | ||||||||
\(260\) | −1.37109 | − | 29.3469i | −0.0850312 | − | 1.82002i | ||||
\(261\) | −0.373782 | −0.0231365 | ||||||||
\(262\) | − | 19.2379i | − | 1.18852i | ||||||
\(263\) | 16.8761i | 1.04063i | 0.853975 | + | 0.520313i | \(0.174185\pi\) | ||||
−0.853975 | + | 0.520313i | \(0.825815\pi\) | |||||||
\(264\) | 2.76990 | 0.170475 | ||||||||
\(265\) | −1.34370 | − | 28.7607i | −0.0825426 | − | 1.76675i | ||||
\(266\) | 10.7899 | 0.661570 | ||||||||
\(267\) | − | 17.9041i | − | 1.09571i | ||||||
\(268\) | 35.8179i | 2.18792i | ||||||||
\(269\) | −13.5808 | −0.828039 | −0.414019 | − | 0.910268i | \(-0.635875\pi\) | ||||
−0.414019 | + | 0.910268i | \(0.635875\pi\) | |||||||
\(270\) | −5.09990 | + | 0.238267i | −0.310370 | + | 0.0145005i | ||||
\(271\) | 5.53292 | 0.336101 | 0.168050 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168050 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(272\) | 0.0339887i | 0.00206087i | ||||||||
\(273\) | 4.08903i | 0.247479i | ||||||||
\(274\) | 31.0287 | 1.87451 | ||||||||
\(275\) | 4.97822 | − | 0.466182i | 0.300198 | − | 0.0281118i | ||||
\(276\) | −25.6623 | −1.54469 | ||||||||
\(277\) | 6.03226i | 0.362444i | 0.983442 | + | 0.181222i | \(0.0580052\pi\) | ||||
−0.983442 | + | 0.181222i | \(0.941995\pi\) | |||||||
\(278\) | − | 25.2552i | − | 1.51471i | ||||||
\(279\) | 9.24196 | 0.553301 | ||||||||
\(280\) | −6.18693 | + | 0.289053i | −0.369740 | + | 0.0172742i | ||||
\(281\) | 9.15740 | 0.546285 | 0.273142 | − | 0.961974i | \(-0.411937\pi\) | ||||
0.273142 | + | 0.961974i | \(0.411937\pi\) | |||||||
\(282\) | − | 27.3131i | − | 1.62647i | ||||||
\(283\) | 6.85266i | 0.407348i | 0.979039 | + | 0.203674i | \(0.0652883\pi\) | ||||
−0.979039 | + | 0.203674i | \(0.934712\pi\) | |||||||
\(284\) | −44.3351 | −2.63080 | ||||||||
\(285\) | 0.493152 | + | 10.5555i | 0.0292118 | + | 0.625253i | ||||
\(286\) | 9.33621 | 0.552062 | ||||||||
\(287\) | 7.35561i | 0.434188i | ||||||||
\(288\) | 5.77263i | 0.340156i | ||||||||
\(289\) | 16.8889 | 0.993466 | ||||||||
\(290\) | −0.0890599 | − | 1.90625i | −0.00522978 | − | 0.111939i | ||||
\(291\) | −7.95736 | −0.466469 | ||||||||
\(292\) | 27.4245i | 1.60490i | ||||||||
\(293\) | − | 8.34763i | − | 0.487674i | −0.969816 | − | 0.243837i | \(-0.921594\pi\) | ||
0.969816 | − | 0.243837i | \(-0.0784061\pi\) | |||||||
\(294\) | 2.28323 | 0.133161 | ||||||||
\(295\) | −5.49826 | + | 0.256878i | −0.320121 | + | 0.0149560i | ||||
\(296\) | −9.73260 | −0.565696 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | − | 42.4057i | − | 2.45650i | ||||||
\(299\) | −32.6577 | −1.88864 | ||||||||
\(300\) | −1.49791 | − | 15.9958i | −0.0864819 | − | 0.923515i | ||||
\(301\) | −2.50440 | −0.144351 | ||||||||
\(302\) | − | 7.02838i | − | 0.404438i | ||||||
\(303\) | 7.33584i | 0.421433i | ||||||||
\(304\) | 0.481916 | 0.0276398 | ||||||||
\(305\) | 19.7238 | − | 0.921493i | 1.12938 | − | 0.0527646i | ||||
\(306\) | −0.760993 | −0.0435031 | ||||||||
\(307\) | − | 4.85539i | − | 0.277112i | −0.990355 | − | 0.138556i | \(-0.955754\pi\) | ||
0.990355 | − | 0.138556i | \(-0.0442461\pi\) | |||||||
\(308\) | − | 3.21315i | − | 0.183086i | ||||||
\(309\) | 16.6422 | 0.946741 | ||||||||
\(310\) | 2.20205 | + | 47.1330i | 0.125068 | + | 2.67698i | ||||
\(311\) | −31.3660 | −1.77861 | −0.889303 | − | 0.457319i | \(-0.848810\pi\) | ||||
−0.889303 | + | 0.457319i | \(0.848810\pi\) | |||||||
\(312\) | − | 11.3262i | − | 0.641220i | ||||||
\(313\) | − | 10.7766i | − | 0.609129i | −0.952492 | − | 0.304564i | \(-0.901489\pi\) | ||
0.952492 | − | 0.304564i | \(-0.0985109\pi\) | |||||||
\(314\) | 9.71600 | 0.548306 | ||||||||
\(315\) | 0.104355 | + | 2.23363i | 0.00587974 | + | 0.125851i | ||||
\(316\) | 22.3354 | 1.25646 | ||||||||
\(317\) | − | 8.66340i | − | 0.486585i | −0.969953 | − | 0.243293i | \(-0.921772\pi\) | ||
0.969953 | − | 0.243293i | \(-0.0782275\pi\) | |||||||
\(318\) | − | 29.3993i | − | 1.64863i | ||||||
\(319\) | 0.373782 | 0.0209278 | ||||||||
\(320\) | −28.9843 | + | 1.35414i | −1.62027 | + | 0.0756989i | ||||
\(321\) | 17.7684 | 0.991736 | ||||||||
\(322\) | 18.2354i | 1.01622i | ||||||||
\(323\) | 1.57506i | 0.0876388i | ||||||||
\(324\) | −3.21315 | −0.178508 | ||||||||
\(325\) | −1.90623 | − | 20.3561i | −0.105739 | − | 1.12915i | ||||
\(326\) | 31.3660 | 1.73720 | ||||||||
\(327\) | − | 14.9455i | − | 0.826488i | ||||||
\(328\) | − | 20.3743i | − | 1.12498i | ||||||
\(329\) | −11.9625 | −0.659512 | ||||||||
\(330\) | 5.09990 | − | 0.238267i | 0.280740 | − | 0.0131162i | ||||
\(331\) | 2.72257 | 0.149646 | 0.0748230 | − | 0.997197i | \(-0.476161\pi\) | ||||
0.0748230 | + | 0.997197i | \(0.476161\pi\) | |||||||
\(332\) | 28.9975i | 1.59145i | ||||||||
\(333\) | 3.51370i | 0.192550i | ||||||||
\(334\) | 23.1163 | 1.26487 | ||||||||
\(335\) | 1.16328 | + | 24.8989i | 0.0635565 | + | 1.36037i | ||||
\(336\) | 0.101977 | 0.00556333 | ||||||||
\(337\) | 10.2202i | 0.556727i | 0.960476 | + | 0.278364i | \(0.0897920\pi\) | ||||
−0.960476 | + | 0.278364i | \(0.910208\pi\) | |||||||
\(338\) | − | 8.49404i | − | 0.462015i | ||||||
\(339\) | 4.90620 | 0.266468 | ||||||||
\(340\) | −0.111757 | − | 2.39206i | −0.00606088 | − | 0.129728i | ||||
\(341\) | −9.24196 | −0.500480 | ||||||||
\(342\) | 10.7899i | 0.583450i | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 6.93692 | 0.374014 | ||||||||
\(345\) | −17.8392 | + | 0.833447i | −0.960432 | + | 0.0448713i | ||||
\(346\) | −55.2559 | −2.97058 | ||||||||
\(347\) | − | 5.99829i | − | 0.322005i | −0.986954 | − | 0.161002i | \(-0.948527\pi\) | ||
0.986954 | − | 0.161002i | \(-0.0514727\pi\) | |||||||
\(348\) | − | 1.20102i | − | 0.0643813i | ||||||
\(349\) | −11.4244 | −0.611533 | −0.305767 | − | 0.952106i | \(-0.598913\pi\) | ||||
−0.305767 | + | 0.952106i | \(0.598913\pi\) | |||||||
\(350\) | −11.3664 | + | 1.06440i | −0.607561 | + | 0.0568946i | ||||
\(351\) | −4.08903 | −0.218256 | ||||||||
\(352\) | − | 5.77263i | − | 0.307682i | ||||||
\(353\) | − | 3.54554i | − | 0.188710i | −0.995539 | − | 0.0943551i | \(-0.969921\pi\) | ||
0.995539 | − | 0.0943551i | \(-0.0300789\pi\) | |||||||
\(354\) | −5.62036 | −0.298719 | ||||||||
\(355\) | −30.8197 | + | 1.43989i | −1.63574 | + | 0.0764216i | ||||
\(356\) | 57.5285 | 3.04900 | ||||||||
\(357\) | 0.333296i | 0.0176399i | ||||||||
\(358\) | 8.92429i | 0.471664i | ||||||||
\(359\) | 26.3556 | 1.39099 | 0.695497 | − | 0.718529i | \(-0.255184\pi\) | ||||
0.695497 | + | 0.718529i | \(0.255184\pi\) | |||||||
\(360\) | −0.289053 | − | 6.18693i | −0.0152344 | − | 0.326080i | ||||
\(361\) | 3.33232 | 0.175385 | ||||||||
\(362\) | − | 17.7320i | − | 0.931975i | ||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −13.1387 | −0.688653 | ||||||||
\(365\) | 0.890681 | + | 19.0643i | 0.0466204 | + | 0.997869i | ||||
\(366\) | 20.1618 | 1.05387 | ||||||||
\(367\) | 18.6763i | 0.974897i | 0.873152 | + | 0.487449i | \(0.162072\pi\) | ||||
−0.873152 | + | 0.487449i | \(0.837928\pi\) | |||||||
\(368\) | 0.814458i | 0.0424566i | ||||||||
\(369\) | −7.35561 | −0.382918 | ||||||||
\(370\) | −17.9195 | + | 0.837199i | −0.931592 | + | 0.0435239i | ||||
\(371\) | −12.8762 | −0.668499 | ||||||||
\(372\) | 29.6958i | 1.53965i | ||||||||
\(373\) | 23.4194i | 1.21261i | 0.795231 | + | 0.606307i | \(0.207350\pi\) | ||||
−0.795231 | + | 0.606307i | \(0.792650\pi\) | |||||||
\(374\) | 0.760993 | 0.0393500 | ||||||||
\(375\) | −1.56078 | − | 11.0709i | −0.0805984 | − | 0.571697i | ||||
\(376\) | 33.1348 | 1.70880 | ||||||||
\(377\) | − | 1.52841i | − | 0.0787170i | ||||||
\(378\) | 2.28323i | 0.117437i | ||||||||
\(379\) | −29.5437 | −1.51756 | −0.758779 | − | 0.651349i | \(-0.774204\pi\) | ||||
−0.758779 | + | 0.651349i | \(0.774204\pi\) | |||||||
\(380\) | −33.9164 | + | 1.58457i | −1.73987 | + | 0.0812867i | ||||
\(381\) | −6.50360 | −0.333190 | ||||||||
\(382\) | − | 15.9822i | − | 0.817719i | ||||||
\(383\) | 6.00131i | 0.306652i | 0.988176 | + | 0.153326i | \(0.0489985\pi\) | ||||
−0.988176 | + | 0.153326i | \(0.951001\pi\) | |||||||
\(384\) | −18.0826 | −0.922776 | ||||||||
\(385\) | −0.104355 | − | 2.23363i | −0.00531843 | − | 0.113836i | ||||
\(386\) | −20.1866 | −1.02747 | ||||||||
\(387\) | − | 2.50440i | − | 0.127306i | ||||||
\(388\) | − | 25.5682i | − | 1.29803i | ||||||
\(389\) | 22.6232 | 1.14704 | 0.573520 | − | 0.819192i | \(-0.305577\pi\) | ||||
0.573520 | + | 0.819192i | \(0.305577\pi\) | |||||||
\(390\) | −0.974281 | − | 20.8537i | −0.0493346 | − | 1.05597i | ||||
\(391\) | −2.66192 | −0.134619 | ||||||||
\(392\) | 2.76990i | 0.139901i | ||||||||
\(393\) | − | 8.42573i | − | 0.425022i | ||||||
\(394\) | −17.1494 | −0.863975 | ||||||||
\(395\) | 15.5265 | − | 0.725398i | 0.781225 | − | 0.0364988i | ||||
\(396\) | 3.21315 | 0.161467 | ||||||||
\(397\) | − | 12.0631i | − | 0.605428i | −0.953081 | − | 0.302714i | \(-0.902107\pi\) | ||
0.953081 | − | 0.302714i | \(-0.0978927\pi\) | |||||||
\(398\) | − | 49.2183i | − | 2.46709i | ||||||
\(399\) | 4.72571 | 0.236581 | ||||||||
\(400\) | −0.507666 | + | 0.0475400i | −0.0253833 | + | 0.00237700i | ||||
\(401\) | 1.19718 | 0.0597842 | 0.0298921 | − | 0.999553i | \(-0.490484\pi\) | ||||
0.0298921 | + | 0.999553i | \(0.490484\pi\) | |||||||
\(402\) | 25.4518i | 1.26942i | ||||||||
\(403\) | 37.7907i | 1.88249i | ||||||||
\(404\) | −23.5711 | −1.17271 | ||||||||
\(405\) | −2.23363 | + | 0.104355i | −0.110990 | + | 0.00518545i | ||||
\(406\) | −0.853432 | −0.0423551 | ||||||||
\(407\) | − | 3.51370i | − | 0.174168i | ||||||
\(408\) | − | 0.923197i | − | 0.0457050i | ||||||
\(409\) | 9.52123 | 0.470795 | 0.235397 | − | 0.971899i | \(-0.424361\pi\) | ||||
0.235397 | + | 0.971899i | \(0.424361\pi\) | |||||||
\(410\) | −1.75260 | − | 37.5129i | −0.0865547 | − | 1.85263i | ||||
\(411\) | 13.5898 | 0.670337 | ||||||||
\(412\) | 53.4738i | 2.63446i | ||||||||
\(413\) | 2.46158i | 0.121126i | ||||||||
\(414\) | −18.2354 | −0.896220 | ||||||||
\(415\) | 0.941768 | + | 20.1577i | 0.0462296 | + | 0.989505i | ||||
\(416\) | −23.6045 | −1.15730 | ||||||||
\(417\) | − | 11.0612i | − | 0.541668i | ||||||
\(418\) | − | 10.7899i | − | 0.527751i | ||||||
\(419\) | −22.1761 | −1.08338 | −0.541688 | − | 0.840580i | \(-0.682215\pi\) | ||||
−0.541688 | + | 0.840580i | \(0.682215\pi\) | |||||||
\(420\) | −7.17699 | + | 0.335308i | −0.350201 | + | 0.0163614i | ||||
\(421\) | 10.7062 | 0.521789 | 0.260895 | − | 0.965367i | \(-0.415983\pi\) | ||||
0.260895 | + | 0.965367i | \(0.415983\pi\) | |||||||
\(422\) | 11.3782i | 0.553881i | ||||||||
\(423\) | − | 11.9625i | − | 0.581635i | ||||||
\(424\) | 35.6657 | 1.73208 | ||||||||
\(425\) | −0.155377 | − | 1.65922i | −0.00753687 | − | 0.0804841i | ||||
\(426\) | −31.5041 | −1.52638 | ||||||||
\(427\) | − | 8.83037i | − | 0.427331i | ||||||
\(428\) | 57.0925i | 2.75967i | ||||||||
\(429\) | 4.08903 | 0.197420 | ||||||||
\(430\) | 12.7722 | − | 0.596715i | 0.615929 | − | 0.0287761i | ||||
\(431\) | −23.5902 | −1.13630 | −0.568151 | − | 0.822924i | \(-0.692341\pi\) | ||||
−0.568151 | + | 0.822924i | \(0.692341\pi\) | |||||||
\(432\) | 0.101977i | 0.00490639i | ||||||||
\(433\) | − | 30.0656i | − | 1.44486i | −0.691445 | − | 0.722429i | \(-0.743025\pi\) | ||
0.691445 | − | 0.722429i | \(-0.256975\pi\) | |||||||
\(434\) | 21.1015 | 1.01291 | ||||||||
\(435\) | −0.0390061 | − | 0.834892i | −0.00187020 | − | 0.0400300i | ||||
\(436\) | 48.0221 | 2.29984 | ||||||||
\(437\) | 37.7426i | 1.80547i | ||||||||
\(438\) | 19.4876i | 0.931154i | ||||||||
\(439\) | −15.7721 | −0.752764 | −0.376382 | − | 0.926465i | \(-0.622832\pi\) | ||||
−0.376382 | + | 0.926465i | \(0.622832\pi\) | |||||||
\(440\) | 0.289053 | + | 6.18693i | 0.0137801 | + | 0.294950i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − | 3.11172i | − | 0.148010i | ||||||
\(443\) | 30.7895i | 1.46285i | 0.681919 | + | 0.731427i | \(0.261145\pi\) | ||||
−0.681919 | + | 0.731427i | \(0.738855\pi\) | |||||||
\(444\) | −11.2900 | −0.535802 | ||||||||
\(445\) | 39.9912 | − | 1.86838i | 1.89576 | − | 0.0885699i | ||||
\(446\) | 2.99692 | 0.141908 | ||||||||
\(447\) | − | 18.5727i | − | 0.878457i | ||||||
\(448\) | 12.9763i | 0.613073i | ||||||||
\(449\) | 18.8430 | 0.889257 | 0.444628 | − | 0.895715i | \(-0.353336\pi\) | ||||
0.444628 | + | 0.895715i | \(0.353336\pi\) | |||||||
\(450\) | −1.06440 | − | 11.3664i | −0.0501763 | − | 0.535819i | ||||
\(451\) | 7.35561 | 0.346362 | ||||||||
\(452\) | 15.7644i | 0.741493i | ||||||||
\(453\) | − | 3.07826i | − | 0.144629i | ||||||
\(454\) | 55.9258 | 2.62473 | ||||||||
\(455\) | −9.13339 | + | 0.426711i | −0.428180 | + | 0.0200045i | ||||
\(456\) | −13.0897 | −0.612983 | ||||||||
\(457\) | 6.78391i | 0.317338i | 0.987332 | + | 0.158669i | \(0.0507203\pi\) | ||||
−0.987332 | + | 0.158669i | \(0.949280\pi\) | |||||||
\(458\) | 40.3912i | 1.88736i | ||||||||
\(459\) | −0.333296 | −0.0155569 | ||||||||
\(460\) | −2.67799 | − | 57.3201i | −0.124862 | − | 2.67256i | ||||
\(461\) | 3.24599 | 0.151181 | 0.0755905 | − | 0.997139i | \(-0.475916\pi\) | ||||
0.0755905 | + | 0.997139i | \(0.475916\pi\) | |||||||
\(462\) | − | 2.28323i | − | 0.106226i | ||||||
\(463\) | − | 2.48973i | − | 0.115708i | −0.998325 | − | 0.0578538i | \(-0.981574\pi\) | ||
0.998325 | − | 0.0578538i | \(-0.0184257\pi\) | |||||||
\(464\) | −0.0381174 | −0.00176955 | ||||||||
\(465\) | 0.964445 | + | 20.6431i | 0.0447251 | + | 0.957302i | ||||
\(466\) | −34.8136 | −1.61271 | ||||||||
\(467\) | − | 11.1908i | − | 0.517847i | −0.965898 | − | 0.258923i | \(-0.916632\pi\) | ||
0.965898 | − | 0.258923i | \(-0.0833677\pi\) | |||||||
\(468\) | − | 13.1387i | − | 0.607335i | ||||||
\(469\) | 11.1473 | 0.514734 | ||||||||
\(470\) | 61.0073 | − | 2.85026i | 2.81406 | − | 0.131473i | ||||
\(471\) | 4.25537 | 0.196077 | ||||||||
\(472\) | − | 6.81832i | − | 0.313839i | ||||||
\(473\) | 2.50440i | 0.115152i | ||||||||
\(474\) | 15.8713 | 0.728994 | ||||||||
\(475\) | −23.5256 | + | 2.20304i | −1.07943 | + | 0.101082i | ||||
\(476\) | −1.07093 | −0.0490860 | ||||||||
\(477\) | − | 12.8762i | − | 0.589560i | ||||||
\(478\) | 15.2464i | 0.697354i | ||||||||
\(479\) | 24.2516 | 1.10808 | 0.554042 | − | 0.832489i | \(-0.313085\pi\) | ||||
0.554042 | + | 0.832489i | \(0.313085\pi\) | |||||||
\(480\) | −12.8939 | + | 0.602404i | −0.588525 | + | 0.0274958i | ||||
\(481\) | −14.3676 | −0.655108 | ||||||||
\(482\) | 11.3570i | 0.517298i | ||||||||
\(483\) | 7.98665i | 0.363405i | ||||||||
\(484\) | −3.21315 | −0.146052 | ||||||||
\(485\) | −0.830391 | − | 17.7738i | −0.0377061 | − | 0.807067i | ||||
\(486\) | −2.28323 | −0.103569 | ||||||||
\(487\) | − | 17.1527i | − | 0.777264i | −0.921393 | − | 0.388632i | \(-0.872948\pi\) | ||
0.921393 | − | 0.388632i | \(-0.127052\pi\) | |||||||
\(488\) | 24.4592i | 1.10722i | ||||||||
\(489\) | 13.7375 | 0.621232 | ||||||||
\(490\) | 0.238267 | + | 5.09990i | 0.0107638 | + | 0.230390i | ||||
\(491\) | −31.9038 | −1.43980 | −0.719899 | − | 0.694079i | \(-0.755812\pi\) | ||||
−0.719899 | + | 0.694079i | \(0.755812\pi\) | |||||||
\(492\) | − | 23.6347i | − | 1.06553i | ||||||
\(493\) | − | 0.124580i | − | 0.00561081i | ||||||
\(494\) | −44.1202 | −1.98506 | ||||||||
\(495\) | 2.23363 | − | 0.104355i | 0.100394 | − | 0.00469041i | ||||
\(496\) | 0.942471 | 0.0423182 | ||||||||
\(497\) | 13.7980i | 0.618925i | ||||||||
\(498\) | 20.6054i | 0.923348i | ||||||||
\(499\) | 21.3522 | 0.955858 | 0.477929 | − | 0.878399i | \(-0.341388\pi\) | ||||
0.477929 | + | 0.878399i | \(0.341388\pi\) | |||||||
\(500\) | 35.5723 | − | 5.01502i | 1.59084 | − | 0.224278i | ||||
\(501\) | 10.1244 | 0.452323 | ||||||||
\(502\) | − | 24.5909i | − | 1.09755i | ||||||
\(503\) | 28.7233i | 1.28071i | 0.768079 | + | 0.640355i | \(0.221213\pi\) | ||||
−0.768079 | + | 0.640355i | \(0.778787\pi\) | |||||||
\(504\) | −2.76990 | −0.123381 | ||||||||
\(505\) | −16.3856 | + | 0.765532i | −0.729148 | + | 0.0340657i | ||||
\(506\) | 18.2354 | 0.810661 | ||||||||
\(507\) | − | 3.72018i | − | 0.165219i | ||||||
\(508\) | − | 20.8970i | − | 0.927156i | ||||||
\(509\) | −27.9961 | −1.24091 | −0.620453 | − | 0.784244i | \(-0.713051\pi\) | ||||
−0.620453 | + | 0.784244i | \(0.713051\pi\) | |||||||
\(510\) | −0.0794135 | − | 1.69978i | −0.00351649 | − | 0.0752674i | ||||
\(511\) | 8.53510 | 0.377571 | ||||||||
\(512\) | 1.15361i | 0.0509830i | ||||||||
\(513\) | 4.72571i | 0.208645i | ||||||||
\(514\) | 7.67183 | 0.338390 | ||||||||
\(515\) | 1.73670 | + | 37.1725i | 0.0765280 | + | 1.63802i | ||||
\(516\) | 8.04700 | 0.354249 | ||||||||
\(517\) | 11.9625i | 0.526108i | ||||||||
\(518\) | 8.02260i | 0.352493i | ||||||||
\(519\) | −24.2008 | −1.06230 | ||||||||
\(520\) | 25.2986 | − | 1.18195i | 1.10942 | − | 0.0518318i | ||||
\(521\) | 31.1067 | 1.36281 | 0.681405 | − | 0.731907i | \(-0.261369\pi\) | ||||
0.681405 | + | 0.731907i | \(0.261369\pi\) | |||||||
\(522\) | − | 0.853432i | − | 0.0373537i | ||||||
\(523\) | 2.20540i | 0.0964354i | 0.998837 | + | 0.0482177i | \(0.0153541\pi\) | ||||
−0.998837 | + | 0.0482177i | \(0.984646\pi\) | |||||||
\(524\) | 27.0731 | 1.18269 | ||||||||
\(525\) | −4.97822 | + | 0.466182i | −0.217267 | + | 0.0203458i | ||||
\(526\) | −38.5321 | −1.68008 | ||||||||
\(527\) | 3.08031i | 0.134180i | ||||||||
\(528\) | − | 0.101977i | − | 0.00443800i | ||||||
\(529\) | −40.7866 | −1.77333 | ||||||||
\(530\) | 65.6673 | − | 3.06797i | 2.85240 | − | 0.133264i | ||||
\(531\) | −2.46158 | −0.106823 | ||||||||
\(532\) | 15.1844i | 0.658327i | ||||||||
\(533\) | − | 30.0773i | − | 1.30279i | ||||||
\(534\) | 40.8792 | 1.76902 | ||||||||
\(535\) | 1.85422 | + | 39.6881i | 0.0801651 | + | 1.71587i | ||||
\(536\) | −30.8768 | −1.33368 | ||||||||
\(537\) | 3.90862i | 0.168670i | ||||||||
\(538\) | − | 31.0082i | − | 1.33686i | ||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | −0.335308 | − | 7.17699i | −0.0144294 | − | 0.308848i | ||||
\(541\) | −7.33898 | −0.315527 | −0.157764 | − | 0.987477i | \(-0.550428\pi\) | ||||
−0.157764 | + | 0.987477i | \(0.550428\pi\) | |||||||
\(542\) | 12.6329i | 0.542631i | ||||||||
\(543\) | − | 7.76620i | − | 0.333279i | ||||||
\(544\) | −1.92400 | −0.0824907 | ||||||||
\(545\) | 33.3827 | − | 1.55964i | 1.42996 | − | 0.0668076i | ||||
\(546\) | −9.33621 | −0.399553 | ||||||||
\(547\) | − | 19.4589i | − | 0.832001i | −0.909364 | − | 0.416001i | \(-0.863431\pi\) | ||
0.909364 | − | 0.416001i | \(-0.136569\pi\) | |||||||
\(548\) | 43.6661i | 1.86532i | ||||||||
\(549\) | 8.83037 | 0.376871 | ||||||||
\(550\) | 1.06440 | + | 11.3664i | 0.0453862 | + | 0.484666i | ||||
\(551\) | −1.76639 | −0.0752506 | ||||||||
\(552\) | − | 22.1222i | − | 0.941583i | ||||||
\(553\) | − | 6.95125i | − | 0.295597i | ||||||
\(554\) | −13.7731 | −0.585161 | ||||||||
\(555\) | −7.84832 | + | 0.366673i | −0.333143 | + | 0.0155644i | ||||
\(556\) | 35.5412 | 1.50728 | ||||||||
\(557\) | − | 4.79104i | − | 0.203003i | −0.994835 | − | 0.101501i | \(-0.967635\pi\) | ||
0.994835 | − | 0.101501i | \(-0.0323646\pi\) | |||||||
\(558\) | 21.1015i | 0.893299i | ||||||||
\(559\) | 10.2406 | 0.433130 | ||||||||
\(560\) | 0.0106419 | + | 0.227780i | 0.000449701 | + | 0.00962547i | ||||
\(561\) | 0.333296 | 0.0140718 | ||||||||
\(562\) | 20.9085i | 0.881970i | ||||||||
\(563\) | 33.4653i | 1.41040i | 0.709010 | + | 0.705198i | \(0.249142\pi\) | ||||
−0.709010 | + | 0.705198i | \(0.750858\pi\) | |||||||
\(564\) | 38.4372 | 1.61850 | ||||||||
\(565\) | 0.511987 | + | 10.9586i | 0.0215395 | + | 0.461034i | ||||
\(566\) | −15.6462 | −0.657659 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | − | 38.2191i | − | 1.60364i | ||||||
\(569\) | −9.03326 | −0.378694 | −0.189347 | − | 0.981910i | \(-0.560637\pi\) | ||||
−0.189347 | + | 0.981910i | \(0.560637\pi\) | |||||||
\(570\) | −24.1006 | + | 1.12598i | −1.00946 | + | 0.0471621i | ||||
\(571\) | 34.8782 | 1.45961 | 0.729803 | − | 0.683658i | \(-0.239612\pi\) | ||||
0.729803 | + | 0.683658i | \(0.239612\pi\) | |||||||
\(572\) | 13.1387i | 0.549355i | ||||||||
\(573\) | − | 6.99980i | − | 0.292421i | ||||||
\(574\) | −16.7946 | −0.700992 | ||||||||
\(575\) | −3.72323 | − | 39.7593i | −0.155269 | − | 1.65808i | ||||
\(576\) | −12.9763 | −0.540679 | ||||||||
\(577\) | 11.0507i | 0.460049i | 0.973185 | + | 0.230024i | \(0.0738806\pi\) | ||||
−0.973185 | + | 0.230024i | \(0.926119\pi\) | |||||||
\(578\) | 38.5613i | 1.60394i | ||||||||
\(579\) | −8.84126 | −0.367430 | ||||||||
\(580\) | 2.68263 | − | 0.125332i | 0.111390 | − | 0.00520414i | ||||
\(581\) | 9.02465 | 0.374406 | ||||||||
\(582\) | − | 18.1685i | − | 0.753109i | ||||||
\(583\) | 12.8762i | 0.533278i | ||||||||
\(584\) | −23.6413 | −0.978286 | ||||||||
\(585\) | −0.426711 | − | 9.13339i | −0.0176423 | − | 0.377619i | ||||
\(586\) | 19.0596 | 0.787344 | ||||||||
\(587\) | − | 12.0202i | − | 0.496127i | −0.968744 | − | 0.248064i | \(-0.920206\pi\) | ||
0.968744 | − | 0.248064i | \(-0.0797942\pi\) | |||||||
\(588\) | 3.21315i | 0.132508i | ||||||||
\(589\) | 43.6748 | 1.79959 | ||||||||
\(590\) | −0.586513 | − | 12.5538i | −0.0241464 | − | 0.516832i | ||||
\(591\) | −7.51103 | −0.308962 | ||||||||
\(592\) | 0.358319i | 0.0147268i | ||||||||
\(593\) | 33.1150i | 1.35987i | 0.733272 | + | 0.679936i | \(0.237992\pi\) | ||||
−0.733272 | + | 0.679936i | \(0.762008\pi\) | |||||||
\(594\) | 2.28323 | 0.0936821 | ||||||||
\(595\) | −0.744461 | + | 0.0347812i | −0.0305199 | + | 0.00142589i | ||||
\(596\) | 59.6768 | 2.44445 | ||||||||
\(597\) | − | 21.5564i | − | 0.882246i | ||||||
\(598\) | − | 74.5650i | − | 3.04919i | ||||||
\(599\) | −24.4768 | −1.00009 | −0.500047 | − | 0.865999i | \(-0.666684\pi\) | ||||
−0.500047 | + | 0.865999i | \(0.666684\pi\) | |||||||
\(600\) | 13.7892 | − | 1.29128i | 0.562940 | − | 0.0527161i | ||||
\(601\) | 4.80295 | 0.195917 | 0.0979583 | − | 0.995191i | \(-0.468769\pi\) | ||||
0.0979583 | + | 0.995191i | \(0.468769\pi\) | |||||||
\(602\) | − | 5.71812i | − | 0.233053i | ||||||
\(603\) | 11.1473i | 0.453953i | ||||||||
\(604\) | 9.89091 | 0.402455 | ||||||||
\(605\) | −2.23363 | + | 0.104355i | −0.0908100 | + | 0.00424264i | ||||
\(606\) | −16.7494 | −0.680399 | ||||||||
\(607\) | − | 14.0235i | − | 0.569196i | −0.958647 | − | 0.284598i | \(-0.908140\pi\) | ||
0.958647 | − | 0.284598i | \(-0.0918601\pi\) | |||||||
\(608\) | 27.2798i | 1.10634i | ||||||||
\(609\) | −0.373782 | −0.0151464 | ||||||||
\(610\) | 2.10398 | + | 45.0340i | 0.0851878 | + | 1.82337i | ||||
\(611\) | 48.9149 | 1.97888 | ||||||||
\(612\) | − | 1.07093i | − | 0.0432898i | ||||||
\(613\) | 36.7612i | 1.48477i | 0.669974 | + | 0.742385i | \(0.266305\pi\) | ||||
−0.669974 | + | 0.742385i | \(0.733695\pi\) | |||||||
\(614\) | 11.0860 | 0.447394 | ||||||||
\(615\) | −0.767595 | − | 16.4297i | −0.0309524 | − | 0.662510i | ||||
\(616\) | 2.76990 | 0.111602 | ||||||||
\(617\) | 13.0689i | 0.526135i | 0.964777 | + | 0.263068i | \(0.0847343\pi\) | ||||
−0.964777 | + | 0.263068i | \(0.915266\pi\) | |||||||
\(618\) | 37.9980i | 1.52850i | ||||||||
\(619\) | −7.47221 | −0.300334 | −0.150167 | − | 0.988661i | \(-0.547981\pi\) | ||||
−0.150167 | + | 0.988661i | \(0.547981\pi\) | |||||||
\(620\) | −66.3294 | + | 3.09890i | −2.66385 | + | 0.124455i | ||||
\(621\) | −7.98665 | −0.320493 | ||||||||
\(622\) | − | 71.6160i | − | 2.87154i | ||||||
\(623\) | − | 17.9041i | − | 0.717312i | ||||||
\(624\) | −0.416989 | −0.0166929 | ||||||||
\(625\) | 24.5653 | − | 4.64151i | 0.982614 | − | 0.185660i | ||||
\(626\) | 24.6055 | 0.983432 | ||||||||
\(627\) | − | 4.72571i | − | 0.188727i | ||||||
\(628\) | 13.6731i | 0.545618i | ||||||||
\(629\) | −1.17110 | −0.0466950 | ||||||||
\(630\) | −5.09990 | + | 0.238267i | −0.203185 | + | 0.00949278i | ||||
\(631\) | −35.9123 | −1.42965 | −0.714824 | − | 0.699305i | \(-0.753493\pi\) | ||||
−0.714824 | + | 0.699305i | \(0.753493\pi\) | |||||||
\(632\) | 19.2543i | 0.765893i | ||||||||
\(633\) | 4.98337i | 0.198071i | ||||||||
\(634\) | 19.7806 | 0.785586 | ||||||||
\(635\) | −0.678684 | − | 14.5267i | −0.0269327 | − | 0.576473i | ||||
\(636\) | 41.3731 | 1.64055 | ||||||||
\(637\) | 4.08903i | 0.162013i | ||||||||
\(638\) | 0.853432i | 0.0337877i | ||||||||
\(639\) | −13.7980 | −0.545841 | ||||||||
\(640\) | −1.88702 | − | 40.3900i | −0.0745909 | − | 1.59655i | ||||
\(641\) | −5.22403 | −0.206337 | −0.103168 | − | 0.994664i | \(-0.532898\pi\) | ||||
−0.103168 | + | 0.994664i | \(0.532898\pi\) | |||||||
\(642\) | 40.5694i | 1.60115i | ||||||||
\(643\) | − | 4.17844i | − | 0.164782i | −0.996600 | − | 0.0823908i | \(-0.973744\pi\) | ||
0.996600 | − | 0.0823908i | \(-0.0262556\pi\) | |||||||
\(644\) | −25.6623 | −1.01124 | ||||||||
\(645\) | 5.59390 | − | 0.261347i | 0.220260 | − | 0.0102905i | ||||
\(646\) | −3.59623 | −0.141492 | ||||||||
\(647\) | − | 10.7576i | − | 0.422923i | −0.977386 | − | 0.211462i | \(-0.932178\pi\) | ||
0.977386 | − | 0.211462i | \(-0.0678224\pi\) | |||||||
\(648\) | − | 2.76990i | − | 0.108812i | ||||||
\(649\) | 2.46158 | 0.0966255 | ||||||||
\(650\) | 46.4777 | − | 4.35237i | 1.82301 | − | 0.170714i | ||||
\(651\) | 9.24196 | 0.362221 | ||||||||
\(652\) | 44.1407i | 1.72868i | ||||||||
\(653\) | − | 0.714816i | − | 0.0279729i | −0.999902 | − | 0.0139864i | \(-0.995548\pi\) | ||
0.999902 | − | 0.0139864i | \(-0.00445217\pi\) | |||||||
\(654\) | 34.1240 | 1.33436 | ||||||||
\(655\) | 18.8200 | − | 0.879268i | 0.735357 | − | 0.0343558i | ||||
\(656\) | −0.750107 | −0.0292867 | ||||||||
\(657\) | 8.53510i | 0.332986i | ||||||||
\(658\) | − | 27.3131i | − | 1.06477i | ||||||
\(659\) | −40.6003 | −1.58156 | −0.790782 | − | 0.612098i | \(-0.790326\pi\) | ||||
−0.790782 | + | 0.612098i | \(0.790326\pi\) | |||||||
\(660\) | 0.335308 | + | 7.17699i | 0.0130519 | + | 0.279364i | ||||
\(661\) | 5.98602 | 0.232829 | 0.116415 | − | 0.993201i | \(-0.462860\pi\) | ||||
0.116415 | + | 0.993201i | \(0.462860\pi\) | |||||||
\(662\) | 6.21626i | 0.241602i | ||||||||
\(663\) | − | 1.36286i | − | 0.0529291i | ||||||
\(664\) | −24.9973 | −0.970085 | ||||||||
\(665\) | 0.493152 | + | 10.5555i | 0.0191236 | + | 0.409324i | ||||
\(666\) | −8.02260 | −0.310869 | ||||||||
\(667\) | − | 2.98527i | − | 0.115590i | ||||||
\(668\) | 32.5311i | 1.25867i | ||||||||
\(669\) | 1.31258 | 0.0507472 | ||||||||
\(670\) | −56.8500 | + | 2.65603i | −2.19631 | + | 0.102611i | ||||
\(671\) | −8.83037 | −0.340892 | ||||||||
\(672\) | 5.77263i | 0.222684i | ||||||||
\(673\) | 25.8542i | 0.996608i | 0.867002 | + | 0.498304i | \(0.166044\pi\) | ||||
−0.867002 | + | 0.498304i | \(0.833956\pi\) | |||||||
\(674\) | −23.3350 | −0.898830 | ||||||||
\(675\) | −0.466182 | − | 4.97822i | −0.0179433 | − | 0.191612i | ||||
\(676\) | 11.9535 | 0.459750 | ||||||||
\(677\) | 32.9500i | 1.26637i | 0.774000 | + | 0.633186i | \(0.218253\pi\) | ||||
−0.774000 | + | 0.633186i | \(0.781747\pi\) | |||||||
\(678\) | 11.2020i | 0.430210i | ||||||||
\(679\) | −7.95736 | −0.305376 | ||||||||
\(680\) | 2.06208 | − | 0.0963403i | 0.0790772 | − | 0.00369448i | ||||
\(681\) | 24.4941 | 0.938617 | ||||||||
\(682\) | − | 21.1015i | − | 0.808019i | ||||||
\(683\) | 19.2301i | 0.735818i | 0.929862 | + | 0.367909i | \(0.119926\pi\) | ||||
−0.929862 | + | 0.367909i | \(0.880074\pi\) | |||||||
\(684\) | −15.1844 | −0.580590 | ||||||||
\(685\) | 1.41817 | + | 30.3547i | 0.0541854 | + | 1.15979i | ||||
\(686\) | 2.28323 | 0.0871742 | ||||||||
\(687\) | 17.6904i | 0.674929i | ||||||||
\(688\) | − | 0.255392i | − | 0.00973673i | ||||||
\(689\) | 52.6512 | 2.00585 | ||||||||
\(690\) | −1.90295 | − | 40.7311i | −0.0724442 | − | 1.55061i | ||||
\(691\) | 31.5635 | 1.20073 | 0.600366 | − | 0.799725i | \(-0.295021\pi\) | ||||
0.600366 | + | 0.799725i | \(0.295021\pi\) | |||||||
\(692\) | − | 77.7606i | − | 2.95602i | ||||||
\(693\) | − | 1.00000i | − | 0.0379869i | ||||||
\(694\) | 13.6955 | 0.519873 | ||||||||
\(695\) | 24.7066 | − | 1.15429i | 0.937174 | − | 0.0437847i | ||||
\(696\) | 1.03534 | 0.0392444 | ||||||||
\(697\) | − | 2.45160i | − | 0.0928609i | ||||||
\(698\) | − | 26.0845i | − | 0.987314i | ||||||
\(699\) | −15.2475 | −0.576714 | ||||||||
\(700\) | −1.49791 | − | 15.9958i | −0.0566157 | − | 0.604583i | ||||
\(701\) | −29.5304 | −1.11535 | −0.557675 | − | 0.830060i | \(-0.688306\pi\) | ||||
−0.557675 | + | 0.830060i | \(0.688306\pi\) | |||||||
\(702\) | − | 9.33621i | − | 0.352372i | ||||||
\(703\) | 16.6047i | 0.626260i | ||||||||
\(704\) | 12.9763 | 0.489063 | ||||||||
\(705\) | 26.7197 | − | 1.24834i | 1.00632 | − | 0.0470153i | ||||
\(706\) | 8.09530 | 0.304671 | ||||||||
\(707\) | 7.33584i | 0.275893i | ||||||||
\(708\) | − | 7.90942i | − | 0.297254i | ||||||
\(709\) | −11.1002 | −0.416877 | −0.208438 | − | 0.978035i | \(-0.566838\pi\) | ||||
−0.208438 | + | 0.978035i | \(0.566838\pi\) | |||||||
\(710\) | −3.28761 | − | 70.3685i | −0.123382 | − | 2.64088i | ||||
\(711\) | 6.95125 | 0.260692 | ||||||||
\(712\) | 49.5925i | 1.85856i | ||||||||
\(713\) | 73.8123i | 2.76429i | ||||||||
\(714\) | −0.760993 | −0.0284794 | ||||||||
\(715\) | 0.426711 | + | 9.13339i | 0.0159581 | + | 0.341569i | ||||
\(716\) | −12.5590 | −0.469351 | ||||||||
\(717\) | 6.67755i | 0.249378i | ||||||||
\(718\) | 60.1759i | 2.24574i | ||||||||
\(719\) | 32.6862 | 1.21899 | 0.609495 | − | 0.792790i | \(-0.291372\pi\) | ||||
0.609495 | + | 0.792790i | \(0.291372\pi\) | |||||||
\(720\) | −0.227780 | + | 0.0106419i | −0.00848886 | + | 0.000396599i | ||||
\(721\) | 16.6422 | 0.619787 | ||||||||
\(722\) | 7.60846i | 0.283157i | ||||||||
\(723\) | 4.97410i | 0.184989i | ||||||||
\(724\) | 24.9539 | 0.927406 | ||||||||
\(725\) | 1.86077 | − | 0.174250i | 0.0691073 | − | 0.00647150i | ||||
\(726\) | −2.28323 | −0.0847387 | ||||||||
\(727\) | − | 39.4688i | − | 1.46382i | −0.681404 | − | 0.731908i | \(-0.738630\pi\) | ||
0.681404 | − | 0.731908i | \(-0.261370\pi\) | |||||||
\(728\) | − | 11.3262i | − | 0.419777i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −43.5281 | + | 2.03363i | −1.61105 | + | 0.0752681i | ||||
\(731\) | 0.834706 | 0.0308727 | ||||||||
\(732\) | 28.3733i | 1.04871i | ||||||||
\(733\) | 26.7103i | 0.986569i | 0.869868 | + | 0.493284i | \(0.164204\pi\) | ||||
−0.869868 | + | 0.493284i | \(0.835796\pi\) | |||||||
\(734\) | −42.6424 | −1.57396 | ||||||||
\(735\) | 0.104355 | + | 2.23363i | 0.00384919 | + | 0.0823887i | ||||
\(736\) | −46.1040 | −1.69942 | ||||||||
\(737\) | − | 11.1473i | − | 0.410616i | ||||||
\(738\) | − | 16.7946i | − | 0.618216i | ||||||
\(739\) | 3.88131 | 0.142776 | 0.0713882 | − | 0.997449i | \(-0.477257\pi\) | ||||
0.0713882 | + | 0.997449i | \(0.477257\pi\) | |||||||
\(740\) | −1.17817 | − | 25.2178i | −0.0433105 | − | 0.927025i | ||||
\(741\) | −19.3236 | −0.709869 | ||||||||
\(742\) | − | 29.3993i | − | 1.07928i | ||||||
\(743\) | − | 10.7320i | − | 0.393717i | −0.980432 | − | 0.196859i | \(-0.936926\pi\) | ||
0.980432 | − | 0.196859i | \(-0.0630740\pi\) | |||||||
\(744\) | −25.5993 | −0.938515 | ||||||||
\(745\) | 41.4845 | − | 1.93815i | 1.51988 | − | 0.0710084i | ||||
\(746\) | −53.4720 | −1.95775 | ||||||||
\(747\) | 9.02465i | 0.330195i | ||||||||
\(748\) | 1.07093i | 0.0391571i | ||||||||
\(749\) | 17.7684 | 0.649244 | ||||||||
\(750\) | 25.2773 | − | 3.56362i | 0.922998 | − | 0.130125i | ||||
\(751\) | 9.05305 | 0.330351 | 0.165175 | − | 0.986264i | \(-0.447181\pi\) | ||||
0.165175 | + | 0.986264i | \(0.447181\pi\) | |||||||
\(752\) | − | 1.21990i | − | 0.0444852i | ||||||
\(753\) | − | 10.7702i | − | 0.392488i | ||||||
\(754\) | 3.48971 | 0.127088 | ||||||||
\(755\) | 6.87570 | − | 0.321232i | 0.250232 | − | 0.0116908i | ||||
\(756\) | −3.21315 | −0.116861 | ||||||||
\(757\) | − | 50.2974i | − | 1.82809i | −0.405612 | − | 0.914045i | \(-0.632942\pi\) | ||
0.405612 | − | 0.914045i | \(-0.367058\pi\) | |||||||
\(758\) | − | 67.4551i | − | 2.45008i | ||||||
\(759\) | 7.98665 | 0.289897 | ||||||||
\(760\) | −1.36598 | − | 29.2376i | −0.0495493 | − | 1.06056i | ||||
\(761\) | 46.5455 | 1.68727 | 0.843637 | − | 0.536914i | \(-0.180410\pi\) | ||||
0.843637 | + | 0.536914i | \(0.180410\pi\) | |||||||
\(762\) | − | 14.8492i | − | 0.537931i | ||||||
\(763\) | − | 14.9455i | − | 0.541063i | ||||||
\(764\) | 22.4914 | 0.813710 | ||||||||
\(765\) | −0.0347812 | − | 0.744461i | −0.00125752 | − | 0.0269161i | ||||
\(766\) | −13.7024 | −0.495087 | ||||||||
\(767\) | − | 10.0655i | − | 0.363443i | ||||||
\(768\) | − | 15.3343i | − | 0.553328i | ||||||
\(769\) | −10.6989 | −0.385813 | −0.192907 | − | 0.981217i | \(-0.561791\pi\) | ||||
−0.192907 | + | 0.981217i | \(0.561791\pi\) | |||||||
\(770\) | 5.09990 | − | 0.238267i | 0.183788 | − | 0.00858654i | ||||
\(771\) | 3.36008 | 0.121010 | ||||||||
\(772\) | − | 28.4083i | − | 1.02244i | ||||||
\(773\) | − | 13.3630i | − | 0.480634i | −0.970694 | − | 0.240317i | \(-0.922749\pi\) | ||
0.970694 | − | 0.240317i | \(-0.0772514\pi\) | |||||||
\(774\) | 5.71812 | 0.205534 | ||||||||
\(775\) | −46.0085 | + | 4.30843i | −1.65267 | + | 0.154763i | ||||
\(776\) | 22.0411 | 0.791228 | ||||||||
\(777\) | 3.51370i | 0.126053i | ||||||||
\(778\) | 51.6539i | 1.85188i | ||||||||
\(779\) | −34.7605 | −1.24542 | ||||||||
\(780\) | 29.3469 | − | 1.37109i | 1.05079 | − | 0.0490928i | ||||
\(781\) | 13.7980 | 0.493732 | ||||||||
\(782\) | − | 6.07778i | − | 0.217341i | ||||||
\(783\) | − | 0.373782i | − | 0.0133579i | ||||||
\(784\) | 0.101977 | 0.00364205 | ||||||||
\(785\) | 0.444070 | + | 9.50493i | 0.0158495 | + | 0.339246i | ||||
\(786\) | 19.2379 | 0.686193 | ||||||||
\(787\) | − | 15.3830i | − | 0.548345i | −0.961681 | − | 0.274172i | \(-0.911596\pi\) | ||
0.961681 | − | 0.274172i | \(-0.0884039\pi\) | |||||||
\(788\) | − | 24.1340i | − | 0.859740i | ||||||
\(789\) | −16.8761 | −0.600806 | ||||||||
\(790\) | 1.65625 | + | 35.4507i | 0.0589268 | + | 1.26128i | ||||
\(791\) | 4.90620 | 0.174444 | ||||||||
\(792\) | 2.76990i | 0.0984240i | ||||||||
\(793\) | 36.1076i | 1.28222i | ||||||||
\(794\) | 27.5428 | 0.977457 | ||||||||
\(795\) | 28.7607 | − | 1.34370i | 1.02004 | − | 0.0476560i | ||||
\(796\) | 69.2640 | 2.45500 | ||||||||
\(797\) | − | 9.55195i | − | 0.338348i | −0.985586 | − | 0.169174i | \(-0.945890\pi\) | ||
0.985586 | − | 0.169174i | \(-0.0541099\pi\) | |||||||
\(798\) | 10.7899i | 0.381958i | ||||||||
\(799\) | 3.98704 | 0.141052 | ||||||||
\(800\) | −2.69110 | − | 28.7374i | −0.0951446 | − | 1.01602i | ||||
\(801\) | 17.9041 | 0.632610 | ||||||||
\(802\) | 2.73344i | 0.0965210i | ||||||||
\(803\) | − | 8.53510i | − | 0.301197i | ||||||
\(804\) | −35.8179 | −1.26320 | ||||||||
\(805\) | −17.8392 | + | 0.833447i | −0.628750 | + | 0.0293752i | ||||
\(806\) | −86.2848 | −3.03925 | ||||||||
\(807\) | − | 13.5808i | − | 0.478068i | ||||||
\(808\) | − | 20.3195i | − | 0.714838i | ||||||
\(809\) | 45.5218 | 1.60046 | 0.800230 | − | 0.599693i | \(-0.204711\pi\) | ||||
0.800230 | + | 0.599693i | \(0.204711\pi\) | |||||||
\(810\) | −0.238267 | − | 5.09990i | −0.00837184 | − | 0.179192i | ||||
\(811\) | 3.34608 | 0.117497 | 0.0587484 | − | 0.998273i | \(-0.481289\pi\) | ||||
0.0587484 | + | 0.998273i | \(0.481289\pi\) | |||||||
\(812\) | − | 1.20102i | − | 0.0421475i | ||||||
\(813\) | 5.53292i | 0.194048i | ||||||||
\(814\) | 8.02260 | 0.281192 | ||||||||
\(815\) | 1.43358 | + | 30.6846i | 0.0502161 | + | 1.07483i | ||||
\(816\) | −0.0339887 | −0.00118984 | ||||||||
\(817\) | − | 11.8351i | − | 0.414056i | ||||||
\(818\) | 21.7392i | 0.760093i | ||||||||
\(819\) | −4.08903 | −0.142882 | ||||||||
\(820\) | 52.7911 | − | 2.46640i | 1.84355 | − | 0.0861303i | ||||
\(821\) | 29.5150 | 1.03008 | 0.515040 | − | 0.857166i | \(-0.327777\pi\) | ||||
0.515040 | + | 0.857166i | \(0.327777\pi\) | |||||||
\(822\) | 31.0287i | 1.08225i | ||||||||
\(823\) | 3.27997i | 0.114333i | 0.998365 | + | 0.0571664i | \(0.0182065\pi\) | ||||
−0.998365 | + | 0.0571664i | \(0.981793\pi\) | |||||||
\(824\) | −46.0971 | −1.60587 | ||||||||
\(825\) | 0.466182 | + | 4.97822i | 0.0162304 | + | 0.173319i | ||||
\(826\) | −5.62036 | −0.195557 | ||||||||
\(827\) | 40.6064i | 1.41202i | 0.708200 | + | 0.706012i | \(0.249507\pi\) | ||||
−0.708200 | + | 0.706012i | \(0.750493\pi\) | |||||||
\(828\) | − | 25.6623i | − | 0.891826i | ||||||
\(829\) | −47.2963 | −1.64267 | −0.821335 | − | 0.570446i | \(-0.806770\pi\) | ||||
−0.821335 | + | 0.570446i | \(0.806770\pi\) | |||||||
\(830\) | −46.0248 | + | 2.15027i | −1.59754 | + | 0.0746371i | ||||
\(831\) | −6.03226 | −0.209257 | ||||||||
\(832\) | − | 53.0605i | − | 1.83954i | ||||||
\(833\) | 0.333296i | 0.0115480i | ||||||||
\(834\) | 25.2552 | 0.874516 | ||||||||
\(835\) | 1.05653 | + | 22.6141i | 0.0365627 | + | 0.782593i | ||||
\(836\) | 15.1844 | 0.525163 | ||||||||
\(837\) | 9.24196i | 0.319449i | ||||||||
\(838\) | − | 50.6333i | − | 1.74910i | ||||||
\(839\) | 6.46419 | 0.223169 | 0.111584 | − | 0.993755i | \(-0.464408\pi\) | ||||
0.111584 | + | 0.993755i | \(0.464408\pi\) | |||||||
\(840\) | −0.289053 | − | 6.18693i | −0.00997327 | − | 0.213469i | ||||
\(841\) | −28.8603 | −0.995182 | ||||||||
\(842\) | 24.4448i | 0.842423i | ||||||||
\(843\) | 9.15740i | 0.315398i | ||||||||
\(844\) | −16.0123 | −0.551166 | ||||||||
\(845\) | 8.30952 | − | 0.388220i | 0.285856 | − | 0.0133552i | ||||
\(846\) | 27.3131 | 0.939043 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | − | 1.31308i | − | 0.0450914i | ||||||
\(849\) | −6.85266 | −0.235183 | ||||||||
\(850\) | 3.78839 | − | 0.354761i | 0.129941 | − | 0.0121682i | ||||
\(851\) | −28.0627 | −0.961978 | ||||||||
\(852\) | − | 44.3351i | − | 1.51889i | ||||||
\(853\) | − | 26.2091i | − | 0.897384i | −0.893687 | − | 0.448692i | \(-0.851890\pi\) | ||
0.893687 | − | 0.448692i | \(-0.148110\pi\) | |||||||
\(854\) | 20.1618 | 0.689922 | ||||||||
\(855\) | −10.5555 | + | 0.493152i | −0.360990 | + | 0.0168654i | ||||
\(856\) | −49.2167 | −1.68219 | ||||||||
\(857\) | 5.66404i | 0.193480i | 0.995310 | + | 0.0967400i | \(0.0308415\pi\) | ||||
−0.995310 | + | 0.0967400i | \(0.969158\pi\) | |||||||
\(858\) | 9.33621i | 0.318733i | ||||||||
\(859\) | −30.3158 | −1.03436 | −0.517181 | − | 0.855876i | \(-0.673019\pi\) | ||||
−0.517181 | + | 0.855876i | \(0.673019\pi\) | |||||||
\(860\) | 0.839745 | + | 17.9740i | 0.0286351 | + | 0.612909i | ||||
\(861\) | −7.35561 | −0.250679 | ||||||||
\(862\) | − | 53.8620i | − | 1.83455i | ||||||
\(863\) | − | 22.5684i | − | 0.768238i | −0.923284 | − | 0.384119i | \(-0.874505\pi\) | ||
0.923284 | − | 0.384119i | \(-0.125495\pi\) | |||||||
\(864\) | −5.77263 | −0.196389 | ||||||||
\(865\) | −2.52547 | − | 54.0556i | −0.0858686 | − | 1.83794i | ||||
\(866\) | 68.6467 | 2.33271 | ||||||||
\(867\) | 16.8889i | 0.573578i | ||||||||
\(868\) | 29.6958i | 1.00794i | ||||||||
\(869\) | −6.95125 | −0.235805 | ||||||||
\(870\) | 1.90625 | − | 0.0890599i | 0.0646280 | − | 0.00301941i | ||||
\(871\) | −45.5816 | −1.54447 | ||||||||
\(872\) | 41.3975i | 1.40190i | ||||||||
\(873\) | − | 7.95736i | − | 0.269316i | ||||||
\(874\) | −86.1751 | −2.91491 | ||||||||
\(875\) | −1.56078 | − | 11.0709i | −0.0527640 | − | 0.374263i | ||||
\(876\) | −27.4245 | −0.926589 | ||||||||
\(877\) | − | 23.0829i | − | 0.779453i | −0.920931 | − | 0.389727i | \(-0.872570\pi\) | ||
0.920931 | − | 0.389727i | \(-0.127430\pi\) | |||||||
\(878\) | − | 36.0115i | − | 1.21533i | ||||||
\(879\) | 8.34763 | 0.281559 | ||||||||
\(880\) | 0.227780 | − | 0.0106419i | 0.00767847 | − | 0.000358737i | ||||
\(881\) | −16.2468 | −0.547368 | −0.273684 | − | 0.961820i | \(-0.588242\pi\) | ||||
−0.273684 | + | 0.961820i | \(0.588242\pi\) | |||||||
\(882\) | 2.28323i | 0.0768804i | ||||||||
\(883\) | 40.6837i | 1.36912i | 0.728958 | + | 0.684558i | \(0.240005\pi\) | ||||
−0.728958 | + | 0.684558i | \(0.759995\pi\) | |||||||
\(884\) | 4.37907 | 0.147284 | ||||||||
\(885\) | −0.256878 | − | 5.49826i | −0.00863487 | − | 0.184822i | ||||
\(886\) | −70.2996 | −2.36176 | ||||||||
\(887\) | 6.41283i | 0.215322i | 0.994188 | + | 0.107661i | \(0.0343361\pi\) | ||||
−0.994188 | + | 0.107661i | \(0.965664\pi\) | |||||||
\(888\) | − | 9.73260i | − | 0.326605i | ||||||
\(889\) | −6.50360 | −0.218124 | ||||||||
\(890\) | 4.26595 | + | 91.3091i | 0.142995 | + | 3.06069i | ||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 4.21751i | 0.141213i | ||||||||
\(893\) | − | 56.5311i | − | 1.89174i | ||||||
\(894\) | 42.4057 | 1.41826 | ||||||||
\(895\) | −8.73043 | + | 0.407885i | −0.291826 | + | 0.0136341i | ||||
\(896\) | −18.0826 | −0.604099 | ||||||||
\(897\) | − | 32.6577i | − | 1.09041i | ||||||
\(898\) | 43.0230i | 1.43569i | ||||||||
\(899\) | −3.45448 | −0.115213 | ||||||||
\(900\) | 15.9958 | − | 1.49791i | 0.533192 | − | 0.0499303i | ||||
\(901\) | 4.29159 | 0.142974 | ||||||||
\(902\) | 16.7946i | 0.559198i | ||||||||
\(903\) | − | 2.50440i | − | 0.0833411i | ||||||
\(904\) | −13.5897 | −0.451986 | ||||||||
\(905\) | 17.3468 | − | 0.810442i | 0.576628 | − | 0.0269400i | ||||
\(906\) | 7.02838 | 0.233502 | ||||||||
\(907\) | − | 31.8085i | − | 1.05619i | −0.849187 | − | 0.528093i | \(-0.822907\pi\) | ||
0.849187 | − | 0.528093i | \(-0.177093\pi\) | |||||||
\(908\) | 78.7032i | 2.61186i | ||||||||
\(909\) | −7.33584 | −0.243314 | ||||||||
\(910\) | −0.974281 | − | 20.8537i | −0.0322971 | − | 0.691292i | ||||
\(911\) | −5.87685 | −0.194709 | −0.0973544 | − | 0.995250i | \(-0.531038\pi\) | ||||
−0.0973544 | + | 0.995250i | \(0.531038\pi\) | |||||||
\(912\) | 0.481916i | 0.0159578i | ||||||||
\(913\) | − | 9.02465i | − | 0.298672i | ||||||
\(914\) | −15.4893 | −0.512339 | ||||||||
\(915\) | 0.921493 | + | 19.7238i | 0.0304636 | + | 0.652048i | ||||
\(916\) | −56.8417 | −1.87810 | ||||||||
\(917\) | − | 8.42573i | − | 0.278242i | ||||||
\(918\) | − | 0.760993i | − | 0.0251165i | ||||||
\(919\) | −43.6491 | −1.43985 | −0.719925 | − | 0.694052i | \(-0.755824\pi\) | ||||
−0.719925 | + | 0.694052i | \(0.755824\pi\) | |||||||
\(920\) | 49.4128 | − | 2.30856i | 1.62909 | − | 0.0761111i | ||||
\(921\) | 4.85539 | 0.159991 | ||||||||
\(922\) | 7.41135i | 0.244080i | ||||||||
\(923\) | − | 56.4205i | − | 1.85710i | ||||||
\(924\) | 3.21315 | 0.105705 | ||||||||
\(925\) | −1.63802 | − | 17.4920i | −0.0538579 | − | 0.575133i | ||||
\(926\) | 5.68463 | 0.186808 | ||||||||
\(927\) | 16.6422i | 0.546601i | ||||||||
\(928\) | − | 2.15771i | − | 0.0708302i | ||||||
\(929\) | −53.2435 | −1.74686 | −0.873432 | − | 0.486946i | \(-0.838111\pi\) | ||||
−0.873432 | + | 0.486946i | \(0.838111\pi\) | |||||||
\(930\) | −47.1330 | + | 2.20205i | −1.54555 | + | 0.0722081i | ||||
\(931\) | 4.72571 | 0.154879 | ||||||||
\(932\) | − | 48.9925i | − | 1.60480i | ||||||
\(933\) | − | 31.3660i | − | 1.02688i | ||||||
\(934\) | 25.5511 | 0.836058 | ||||||||
\(935\) | 0.0347812 | + | 0.744461i | 0.00113747 | + | 0.0243465i | ||||
\(936\) | 11.3262 | 0.370208 | ||||||||
\(937\) | − | 1.30555i | − | 0.0426505i | −0.999773 | − | 0.0213253i | \(-0.993211\pi\) | ||
0.999773 | − | 0.0213253i | \(-0.00678855\pi\) | |||||||
\(938\) | 25.4518i | 0.831032i | ||||||||
\(939\) | 10.7766 | 0.351681 | ||||||||
\(940\) | 4.01111 | + | 85.8544i | 0.130828 | + | 2.80026i | ||||
\(941\) | −12.3370 | −0.402176 | −0.201088 | − | 0.979573i | \(-0.564448\pi\) | ||||
−0.201088 | + | 0.979573i | \(0.564448\pi\) | |||||||
\(942\) | 9.71600i | 0.316564i | ||||||||
\(943\) | − | 58.7467i | − | 1.91306i | ||||||
\(944\) | −0.251026 | −0.00817019 | ||||||||
\(945\) | −2.23363 | + | 0.104355i | −0.0726600 | + | 0.00339467i | ||||
\(946\) | −5.71812 | −0.185912 | ||||||||
\(947\) | − | 55.9077i | − | 1.81676i | −0.418149 | − | 0.908379i | \(-0.637321\pi\) | ||
0.418149 | − | 0.908379i | \(-0.362679\pi\) | |||||||
\(948\) | 22.3354i | 0.725420i | ||||||||
\(949\) | −34.9003 | −1.13291 | ||||||||
\(950\) | −5.03005 | − | 53.7144i | −0.163196 | − | 1.74273i | ||||
\(951\) | 8.66340 | 0.280930 | ||||||||
\(952\) | − | 0.923197i | − | 0.0299210i | ||||||
\(953\) | 45.8913i | 1.48656i | 0.668978 | + | 0.743282i | \(0.266732\pi\) | ||||
−0.668978 | + | 0.743282i | \(0.733268\pi\) | |||||||
\(954\) | 29.3993 | 0.951839 | ||||||||
\(955\) | 15.6350 | − | 0.730465i | 0.505936 | − | 0.0236373i | ||||
\(956\) | −21.4559 | −0.693935 | ||||||||
\(957\) | 0.373782i | 0.0120827i | ||||||||
\(958\) | 55.3721i | 1.78899i | ||||||||
\(959\) | 13.5898 | 0.438839 | ||||||||
\(960\) | −1.35414 | − | 28.9843i | −0.0437048 | − | 0.935464i | ||||
\(961\) | 54.4137 | 1.75528 | ||||||||
\(962\) | − | 32.8047i | − | 1.05766i | ||||||
\(963\) | 17.7684i | 0.572579i | ||||||||
\(964\) | −15.9825 | −0.514762 | ||||||||
\(965\) | −0.922630 | − | 19.7481i | −0.0297005 | − | 0.635714i | ||||
\(966\) | −18.2354 | −0.586714 | ||||||||
\(967\) | 21.9288i | 0.705182i | 0.935778 | + | 0.352591i | \(0.114699\pi\) | ||||
−0.935778 | + | 0.352591i | \(0.885301\pi\) | |||||||
\(968\) | − | 2.76990i | − | 0.0890279i | ||||||
\(969\) | −1.57506 | −0.0505983 | ||||||||
\(970\) | 40.5817 | − | 1.89598i | 1.30300 | − | 0.0608761i | ||||
\(971\) | −45.1675 | −1.44949 | −0.724746 | − | 0.689016i | \(-0.758043\pi\) | ||||
−0.724746 | + | 0.689016i | \(0.758043\pi\) | |||||||
\(972\) | − | 3.21315i | − | 0.103062i | ||||||
\(973\) | − | 11.0612i | − | 0.354605i | ||||||
\(974\) | 39.1637 | 1.25488 | ||||||||
\(975\) | 20.3561 | − | 1.90623i | 0.651917 | − | 0.0610483i | ||||
\(976\) | 0.900498 | 0.0288242 | ||||||||
\(977\) | − | 9.57855i | − | 0.306445i | −0.988192 | − | 0.153223i | \(-0.951035\pi\) | ||
0.988192 | − | 0.153223i | \(-0.0489651\pi\) | |||||||
\(978\) | 31.3660i | 1.00297i | ||||||||
\(979\) | −17.9041 | −0.572217 | ||||||||
\(980\) | −7.17699 | + | 0.335308i | −0.229260 | + | 0.0107110i | ||||
\(981\) | 14.9455 | 0.477173 | ||||||||
\(982\) | − | 72.8438i | − | 2.32454i | ||||||
\(983\) | 29.0482i | 0.926493i | 0.886229 | + | 0.463247i | \(0.153316\pi\) | ||||
−0.886229 | + | 0.463247i | \(0.846684\pi\) | |||||||
\(984\) | 20.3743 | 0.649509 | ||||||||
\(985\) | −0.783814 | − | 16.7769i | −0.0249744 | − | 0.534555i | ||||
\(986\) | 0.284446 | 0.00905859 | ||||||||
\(987\) | − | 11.9625i | − | 0.380769i | ||||||
\(988\) | − | 62.0895i | − | 1.97533i | ||||||
\(989\) | 20.0017 | 0.636018 | ||||||||
\(990\) | 0.238267 | + | 5.09990i | 0.00757262 | + | 0.162085i | ||||
\(991\) | 4.77270 | 0.151610 | 0.0758049 | − | 0.997123i | \(-0.475847\pi\) | ||||
0.0758049 | + | 0.997123i | \(0.475847\pi\) | |||||||
\(992\) | 53.3504i | 1.69388i | ||||||||
\(993\) | 2.72257i | 0.0863981i | ||||||||
\(994\) | −31.5041 | −0.999248 | ||||||||
\(995\) | 48.1491 | − | 2.24952i | 1.52643 | − | 0.0713147i | ||||
\(996\) | −28.9975 | −0.918822 | ||||||||
\(997\) | 15.4478i | 0.489236i | 0.969620 | + | 0.244618i | \(0.0786625\pi\) | ||||
−0.969620 | + | 0.244618i | \(0.921337\pi\) | |||||||
\(998\) | 48.7521i | 1.54322i | ||||||||
\(999\) | −3.51370 | −0.111169 |
(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 | 1155.2.c.f.694.17 | yes | 20 | |
5.2 | odd | 4 | 5775.2.a.co.1.2 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cn.1.9 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.f.694.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.f.694.4 | ✓ | 20 | 5.4 | even | 2 | inner | |
1155.2.c.f.694.17 | yes | 20 | 1.1 | even | 1 | trivial | |
5775.2.a.cn.1.9 | 10 | 5.3 | odd | 4 | |||
5775.2.a.co.1.2 | 10 | 5.2 | odd | 4 |