Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4129975648\) |
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: | \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.9 | ||
Root | \(0.317290i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.i.1084.8 |
$q$-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 \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.317290i | 0.224358i | 0.993688 | + | 0.112179i | \(0.0357829\pi\) | ||||
−0.993688 | + | 0.112179i | \(0.964217\pi\) | |||||||
\(3\) | 2.04300i | 1.17953i | 0.807576 | + | 0.589763i | \(0.200779\pi\) | ||||
−0.807576 | + | 0.589763i | \(0.799221\pi\) | |||||||
\(4\) | 1.89933 | 0.949664 | ||||||||
\(5\) | −1.85074 | + | 1.25489i | −0.827676 | + | 0.561206i | ||||
\(6\) | −0.648223 | −0.264636 | ||||||||
\(7\) | 3.69961i | 1.39832i | 0.714964 | + | 0.699161i | \(0.246443\pi\) | ||||
−0.714964 | + | 0.699161i | \(0.753557\pi\) | |||||||
\(8\) | 1.23722i | 0.437422i | ||||||||
\(9\) | −1.17385 | −0.391283 | ||||||||
\(10\) | −0.398165 | − | 0.587221i | −0.125911 | − | 0.185695i | ||||
\(11\) | −5.01076 | −1.51080 | −0.755400 | − | 0.655263i | \(-0.772558\pi\) | ||||
−0.755400 | + | 0.655263i | \(0.772558\pi\) | |||||||
\(12\) | 3.88033i | 1.12015i | ||||||||
\(13\) | 4.59159i | 1.27348i | 0.771080 | + | 0.636738i | \(0.219717\pi\) | ||||
−0.771080 | + | 0.636738i | \(0.780283\pi\) | |||||||
\(14\) | −1.17385 | −0.313724 | ||||||||
\(15\) | −2.56375 | − | 3.78106i | −0.661957 | − | 0.976266i | ||||
\(16\) | 3.40610 | 0.851525 | ||||||||
\(17\) | − | 3.21112i | − | 0.778811i | −0.921066 | − | 0.389405i | \(-0.872681\pi\) | ||
0.921066 | − | 0.389405i | \(-0.127319\pi\) | |||||||
\(18\) | − | 0.372450i | − | 0.0877873i | ||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −3.51516 | + | 2.38345i | −0.786014 | + | 0.532957i | ||||
\(21\) | −7.55831 | −1.64936 | ||||||||
\(22\) | − | 1.58986i | − | 0.338960i | ||||||
\(23\) | − | 0.220987i | − | 0.0460789i | −0.999735 | − | 0.0230395i | \(-0.992666\pi\) | ||
0.999735 | − | 0.0230395i | \(-0.00733434\pi\) | |||||||
\(24\) | −2.52763 | −0.515951 | ||||||||
\(25\) | 1.85048 | − | 4.64497i | 0.370096 | − | 0.928993i | ||||
\(26\) | −1.45686 | −0.285714 | ||||||||
\(27\) | 3.73083i | 0.717998i | ||||||||
\(28\) | 7.02678i | 1.32794i | ||||||||
\(29\) | −3.42114 | −0.635289 | −0.317644 | − | 0.948210i | \(-0.602892\pi\) | ||||
−0.317644 | + | 0.948210i | \(0.602892\pi\) | |||||||
\(30\) | 1.19969 | − | 0.813451i | 0.219033 | − | 0.148515i | ||||
\(31\) | 7.89725 | 1.41839 | 0.709194 | − | 0.705013i | \(-0.249059\pi\) | ||||
0.709194 | + | 0.705013i | \(0.249059\pi\) | |||||||
\(32\) | 3.55515i | 0.628468i | ||||||||
\(33\) | − | 10.2370i | − | 1.78203i | ||||||
\(34\) | 1.01885 | 0.174732 | ||||||||
\(35\) | −4.64262 | − | 6.84702i | −0.784747 | − | 1.15736i | ||||
\(36\) | −2.22952 | −0.371587 | ||||||||
\(37\) | 2.98622i | 0.490932i | 0.969405 | + | 0.245466i | \(0.0789410\pi\) | ||||
−0.969405 | + | 0.245466i | \(0.921059\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.38061 | −1.50210 | ||||||||
\(40\) | −1.55258 | − | 2.28977i | −0.245484 | − | 0.362044i | ||||
\(41\) | −0.183247 | −0.0286184 | −0.0143092 | − | 0.999898i | \(-0.504555\pi\) | ||||
−0.0143092 | + | 0.999898i | \(0.504555\pi\) | |||||||
\(42\) | − | 2.39817i | − | 0.370046i | ||||||
\(43\) | − | 7.30424i | − | 1.11389i | −0.830551 | − | 0.556943i | \(-0.811974\pi\) | ||
0.830551 | − | 0.556943i | \(-0.188026\pi\) | |||||||
\(44\) | −9.51707 | −1.43475 | ||||||||
\(45\) | 2.17249 | − | 1.47306i | 0.323856 | − | 0.219590i | ||||
\(46\) | 0.0701168 | 0.0103382 | ||||||||
\(47\) | − | 10.8876i | − | 1.58812i | −0.607840 | − | 0.794060i | \(-0.707964\pi\) | ||
0.607840 | − | 0.794060i | \(-0.292036\pi\) | |||||||
\(48\) | 6.95866i | 1.00440i | ||||||||
\(49\) | −6.68714 | −0.955306 | ||||||||
\(50\) | 1.47380 | + | 0.587138i | 0.208427 | + | 0.0830339i | ||||
\(51\) | 6.56032 | 0.918628 | ||||||||
\(52\) | 8.72092i | 1.20937i | ||||||||
\(53\) | 1.93670i | 0.266026i | 0.991114 | + | 0.133013i | \(0.0424652\pi\) | ||||
−0.991114 | + | 0.133013i | \(0.957535\pi\) | |||||||
\(54\) | −1.18375 | −0.161088 | ||||||||
\(55\) | 9.27362 | − | 6.28797i | 1.25045 | − | 0.847870i | ||||
\(56\) | −4.57722 | −0.611657 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1.08549i | − | 0.142532i | ||||||
\(59\) | 6.15338 | 0.801102 | 0.400551 | − | 0.916275i | \(-0.368819\pi\) | ||||
0.400551 | + | 0.916275i | \(0.368819\pi\) | |||||||
\(60\) | −4.86940 | − | 7.18148i | −0.628637 | − | 0.927125i | ||||
\(61\) | 5.02293 | 0.643121 | 0.321560 | − | 0.946889i | \(-0.395793\pi\) | ||||
0.321560 | + | 0.946889i | \(0.395793\pi\) | |||||||
\(62\) | 2.50572i | 0.318226i | ||||||||
\(63\) | − | 4.34279i | − | 0.547140i | ||||||
\(64\) | 5.68419 | 0.710523 | ||||||||
\(65\) | −5.76195 | − | 8.49783i | −0.714682 | − | 1.05403i | ||||
\(66\) | 3.24809 | 0.399812 | ||||||||
\(67\) | 11.2753i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(68\) | − | 6.09897i | − | 0.739608i | ||||||
\(69\) | 0.451476 | 0.0543513 | ||||||||
\(70\) | 2.17249 | − | 1.47306i | 0.259662 | − | 0.176064i | ||||
\(71\) | 0.851223 | 0.101022 | 0.0505108 | − | 0.998724i | \(-0.483915\pi\) | ||||
0.0505108 | + | 0.998724i | \(0.483915\pi\) | |||||||
\(72\) | − | 1.45230i | − | 0.171156i | ||||||
\(73\) | 5.15625i | 0.603494i | 0.953388 | + | 0.301747i | \(0.0975698\pi\) | ||||
−0.953388 | + | 0.301747i | \(0.902430\pi\) | |||||||
\(74\) | −0.947498 | −0.110144 | ||||||||
\(75\) | 9.48967 | + | 3.78053i | 1.09577 | + | 0.436538i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 18.5379i | − | 2.11259i | ||||||
\(78\) | − | 2.97637i | − | 0.337007i | ||||||
\(79\) | −9.19657 | −1.03469 | −0.517347 | − | 0.855776i | \(-0.673080\pi\) | ||||
−0.517347 | + | 0.855776i | \(0.673080\pi\) | |||||||
\(80\) | −6.30381 | + | 4.27429i | −0.704787 | + | 0.477881i | ||||
\(81\) | −11.1436 | −1.23818 | ||||||||
\(82\) | − | 0.0581424i | − | 0.00642076i | ||||||
\(83\) | 4.53528i | 0.497811i | 0.968528 | + | 0.248906i | \(0.0800709\pi\) | ||||
−0.968528 | + | 0.248906i | \(0.919929\pi\) | |||||||
\(84\) | −14.3557 | −1.56634 | ||||||||
\(85\) | 4.02961 | + | 5.94295i | 0.437073 | + | 0.644603i | ||||
\(86\) | 2.31756 | 0.249909 | ||||||||
\(87\) | − | 6.98938i | − | 0.749340i | ||||||
\(88\) | − | 6.19939i | − | 0.660857i | ||||||
\(89\) | 14.8752 | 1.57677 | 0.788385 | − | 0.615183i | \(-0.210918\pi\) | ||||
0.788385 | + | 0.615183i | \(0.210918\pi\) | |||||||
\(90\) | 0.467385 | + | 0.689308i | 0.0492667 | + | 0.0726595i | ||||
\(91\) | −16.9871 | −1.78073 | ||||||||
\(92\) | − | 0.419726i | − | 0.0437595i | ||||||
\(93\) | 16.1341i | 1.67303i | ||||||||
\(94\) | 3.45452 | 0.356307 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.26317 | −0.741295 | ||||||||
\(97\) | 1.36602i | 0.138698i | 0.997592 | + | 0.0693490i | \(0.0220922\pi\) | ||||
−0.997592 | + | 0.0693490i | \(0.977908\pi\) | |||||||
\(98\) | − | 2.12176i | − | 0.214330i | ||||||
\(99\) | 5.88187 | 0.591151 | ||||||||
\(100\) | 3.51467 | − | 8.82231i | 0.351467 | − | 0.882231i | ||||
\(101\) | −6.08643 | −0.605622 | −0.302811 | − | 0.953051i | \(-0.597925\pi\) | ||||
−0.302811 | + | 0.953051i | \(0.597925\pi\) | |||||||
\(102\) | 2.08152i | 0.206101i | ||||||||
\(103\) | − | 13.7063i | − | 1.35052i | −0.737579 | − | 0.675261i | \(-0.764031\pi\) | ||
0.737579 | − | 0.675261i | \(-0.235969\pi\) | |||||||
\(104\) | −5.68078 | −0.557047 | ||||||||
\(105\) | 13.9885 | − | 9.48488i | 1.36513 | − | 0.925629i | ||||
\(106\) | −0.614494 | −0.0596850 | ||||||||
\(107\) | 17.3036i | 1.67280i | 0.548119 | + | 0.836400i | \(0.315344\pi\) | ||||
−0.548119 | + | 0.836400i | \(0.684656\pi\) | |||||||
\(108\) | 7.08606i | 0.681857i | ||||||||
\(109\) | −13.7511 | −1.31712 | −0.658561 | − | 0.752528i | \(-0.728834\pi\) | ||||
−0.658561 | + | 0.752528i | \(0.728834\pi\) | |||||||
\(110\) | 1.99511 | + | 2.94242i | 0.190226 | + | 0.280549i | ||||
\(111\) | −6.10086 | −0.579068 | ||||||||
\(112\) | 12.6012i | 1.19071i | ||||||||
\(113\) | 4.15573i | 0.390938i | 0.980710 | + | 0.195469i | \(0.0626229\pi\) | ||||
−0.980710 | + | 0.195469i | \(0.937377\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.277315 | + | 0.408989i | 0.0258598 | + | 0.0381384i | ||||
\(116\) | −6.49786 | −0.603311 | ||||||||
\(117\) | − | 5.38983i | − | 0.498290i | ||||||
\(118\) | 1.95240i | 0.179733i | ||||||||
\(119\) | 11.8799 | 1.08903 | ||||||||
\(120\) | 4.67799 | − | 3.17191i | 0.427040 | − | 0.289555i | ||||
\(121\) | 14.1077 | 1.28252 | ||||||||
\(122\) | 1.59372i | 0.144289i | ||||||||
\(123\) | − | 0.374374i | − | 0.0337562i | ||||||
\(124\) | 14.9995 | 1.34699 | ||||||||
\(125\) | 2.40418 | + | 10.9188i | 0.215037 | + | 0.976606i | ||||
\(126\) | 1.37792 | 0.122755 | ||||||||
\(127\) | − | 11.9185i | − | 1.05760i | −0.848747 | − | 0.528799i | \(-0.822643\pi\) | ||
0.848747 | − | 0.528799i | \(-0.177357\pi\) | |||||||
\(128\) | 8.91384i | 0.787879i | ||||||||
\(129\) | 14.9226 | 1.31386 | ||||||||
\(130\) | 2.69627 | − | 1.82821i | 0.236479 | − | 0.160344i | ||||
\(131\) | −7.58093 | −0.662349 | −0.331175 | − | 0.943569i | \(-0.607445\pi\) | ||||
−0.331175 | + | 0.943569i | \(0.607445\pi\) | |||||||
\(132\) | − | 19.4434i | − | 1.69233i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.57755 | −0.309053 | ||||||||
\(135\) | −4.68179 | − | 6.90479i | −0.402945 | − | 0.594270i | ||||
\(136\) | 3.97285 | 0.340669 | ||||||||
\(137\) | 7.98581i | 0.682274i | 0.940014 | + | 0.341137i | \(0.110812\pi\) | ||||
−0.940014 | + | 0.341137i | \(0.889188\pi\) | |||||||
\(138\) | 0.143249i | 0.0121941i | ||||||||
\(139\) | −2.65651 | −0.225322 | −0.112661 | − | 0.993633i | \(-0.535937\pi\) | ||||
−0.112661 | + | 0.993633i | \(0.535937\pi\) | |||||||
\(140\) | −8.81786 | − | 13.0047i | −0.745245 | − | 1.09910i | ||||
\(141\) | 22.2434 | 1.87323 | ||||||||
\(142\) | 0.270084i | 0.0226650i | ||||||||
\(143\) | − | 23.0073i | − | 1.92397i | ||||||
\(144\) | −3.99825 | −0.333187 | ||||||||
\(145\) | 6.33163 | − | 4.29316i | 0.525814 | − | 0.356528i | ||||
\(146\) | −1.63603 | −0.135398 | ||||||||
\(147\) | − | 13.6618i | − | 1.12681i | ||||||
\(148\) | 5.67182i | 0.466221i | ||||||||
\(149\) | −8.35153 | −0.684184 | −0.342092 | − | 0.939666i | \(-0.611135\pi\) | ||||
−0.342092 | + | 0.939666i | \(0.611135\pi\) | |||||||
\(150\) | −1.19952 | + | 3.01097i | −0.0979407 | + | 0.245845i | ||||
\(151\) | 8.56471 | 0.696986 | 0.348493 | − | 0.937311i | \(-0.386694\pi\) | ||||
0.348493 | + | 0.937311i | \(0.386694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.76937i | 0.304735i | ||||||||
\(154\) | 5.88187 | 0.473975 | ||||||||
\(155\) | −14.6158 | + | 9.91022i | −1.17397 | + | 0.796008i | ||||
\(156\) | −17.8168 | −1.42649 | ||||||||
\(157\) | 11.3335i | 0.904510i | 0.891889 | + | 0.452255i | \(0.149380\pi\) | ||||
−0.891889 | + | 0.452255i | \(0.850620\pi\) | |||||||
\(158\) | − | 2.91797i | − | 0.232142i | ||||||
\(159\) | −3.95668 | −0.313785 | ||||||||
\(160\) | −4.46134 | − | 6.57966i | −0.352700 | − | 0.520168i | ||||
\(161\) | 0.817566 | 0.0644332 | ||||||||
\(162\) | − | 3.53576i | − | 0.277795i | ||||||
\(163\) | − | 4.65048i | − | 0.364254i | −0.983275 | − | 0.182127i | \(-0.941702\pi\) | ||
0.983275 | − | 0.182127i | \(-0.0582982\pi\) | |||||||
\(164\) | −0.348046 | −0.0271779 | ||||||||
\(165\) | 12.8463 | + | 18.9460i | 1.00009 | + | 1.47494i | ||||
\(166\) | −1.43900 | −0.111688 | ||||||||
\(167\) | − | 8.89485i | − | 0.688304i | −0.938914 | − | 0.344152i | \(-0.888166\pi\) | ||
0.938914 | − | 0.344152i | \(-0.111834\pi\) | |||||||
\(168\) | − | 9.35126i | − | 0.721466i | ||||||
\(169\) | −8.08265 | −0.621743 | ||||||||
\(170\) | −1.88564 | + | 1.27855i | −0.144622 | + | 0.0980607i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 13.8731i | − | 1.05782i | ||||||
\(173\) | − | 18.6570i | − | 1.41847i | −0.704974 | − | 0.709233i | \(-0.749042\pi\) | ||
0.704974 | − | 0.709233i | \(-0.250958\pi\) | |||||||
\(174\) | 2.21766 | 0.168120 | ||||||||
\(175\) | 17.1846 | + | 6.84606i | 1.29903 | + | 0.517514i | ||||
\(176\) | −17.0671 | −1.28648 | ||||||||
\(177\) | 12.5713i | 0.944921i | ||||||||
\(178\) | 4.71975i | 0.353760i | ||||||||
\(179\) | 0.224791 | 0.0168017 | 0.00840083 | − | 0.999965i | \(-0.497326\pi\) | ||||
0.00840083 | + | 0.999965i | \(0.497326\pi\) | |||||||
\(180\) | 4.12627 | − | 2.79782i | 0.307554 | − | 0.208537i | ||||
\(181\) | −24.8780 | −1.84917 | −0.924583 | − | 0.380981i | \(-0.875586\pi\) | ||||
−0.924583 | + | 0.380981i | \(0.875586\pi\) | |||||||
\(182\) | − | 5.38983i | − | 0.399521i | ||||||
\(183\) | 10.2618i | 0.758578i | ||||||||
\(184\) | 0.273408 | 0.0201559 | ||||||||
\(185\) | −3.74740 | − | 5.52673i | −0.275514 | − | 0.406333i | ||||
\(186\) | −5.11918 | −0.375356 | ||||||||
\(187\) | 16.0901i | 1.17663i | ||||||||
\(188\) | − | 20.6791i | − | 1.50818i | ||||||
\(189\) | −13.8026 | −1.00399 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.43889 | 0.610616 | 0.305308 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(192\) | 11.6128i | 0.838081i | ||||||||
\(193\) | − | 1.60346i | − | 0.115420i | −0.998333 | − | 0.0577098i | \(-0.981620\pi\) | ||
0.998333 | − | 0.0577098i | \(-0.0183798\pi\) | |||||||
\(194\) | −0.433423 | −0.0311180 | ||||||||
\(195\) | 17.3611 | − | 11.7717i | 1.24325 | − | 0.842987i | ||||
\(196\) | −12.7011 | −0.907219 | ||||||||
\(197\) | − | 2.01284i | − | 0.143409i | −0.997426 | − | 0.0717043i | \(-0.977156\pi\) | ||
0.997426 | − | 0.0717043i | \(-0.0228438\pi\) | |||||||
\(198\) | 1.86626i | 0.132629i | ||||||||
\(199\) | −5.03693 | −0.357059 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(200\) | 5.74683 | + | 2.28944i | 0.406362 | + | 0.161888i | ||||
\(201\) | −23.0355 | −1.62480 | ||||||||
\(202\) | − | 1.93116i | − | 0.135876i | ||||||
\(203\) | − | 12.6569i | − | 0.888339i | ||||||
\(204\) | 12.4602 | 0.872388 | ||||||||
\(205\) | 0.339143 | − | 0.229956i | 0.0236868 | − | 0.0160608i | ||||
\(206\) | 4.34886 | 0.303000 | ||||||||
\(207\) | 0.259405i | 0.0180299i | ||||||||
\(208\) | 15.6394i | 1.08440i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.00945 | + | 4.43840i | 0.207672 | + | 0.306278i | ||||
\(211\) | 4.18849 | 0.288348 | 0.144174 | − | 0.989552i | \(-0.453948\pi\) | ||||
0.144174 | + | 0.989552i | \(0.453948\pi\) | |||||||
\(212\) | 3.67842i | 0.252635i | ||||||||
\(213\) | 1.73905i | 0.119158i | ||||||||
\(214\) | −5.49025 | −0.375306 | ||||||||
\(215\) | 9.16604 | + | 13.5182i | 0.625119 | + | 0.921937i | ||||
\(216\) | −4.61584 | −0.314068 | ||||||||
\(217\) | 29.2168i | 1.98336i | ||||||||
\(218\) | − | 4.36310i | − | 0.295506i | ||||||
\(219\) | −10.5342 | −0.711837 | ||||||||
\(220\) | 17.6136 | − | 11.9429i | 1.18751 | − | 0.805192i | ||||
\(221\) | 14.7441 | 0.991797 | ||||||||
\(222\) | − | 1.93574i | − | 0.129918i | ||||||
\(223\) | 5.32967i | 0.356901i | 0.983949 | + | 0.178451i | \(0.0571084\pi\) | ||||
−0.983949 | + | 0.178451i | \(0.942892\pi\) | |||||||
\(224\) | −13.1527 | −0.878801 | ||||||||
\(225\) | −2.17219 | + | 5.45249i | −0.144812 | + | 0.363499i | ||||
\(226\) | −1.31857 | −0.0877099 | ||||||||
\(227\) | 5.17899i | 0.343741i | 0.985120 | + | 0.171871i | \(0.0549811\pi\) | ||||
−0.985120 | + | 0.171871i | \(0.945019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0790 | 1.12861 | 0.564306 | − | 0.825566i | \(-0.309144\pi\) | ||||
0.564306 | + | 0.825566i | \(0.309144\pi\) | |||||||
\(230\) | −0.129768 | + | 0.0879892i | −0.00855665 | + | 0.00580183i | ||||
\(231\) | 37.8729 | 2.49185 | ||||||||
\(232\) | − | 4.23268i | − | 0.277889i | ||||||
\(233\) | 15.8503i | 1.03839i | 0.854656 | + | 0.519195i | \(0.173768\pi\) | ||||
−0.854656 | + | 0.519195i | \(0.826232\pi\) | |||||||
\(234\) | 1.71014 | 0.111795 | ||||||||
\(235\) | 13.6628 | + | 20.1501i | 0.891262 | + | 1.31445i | ||||
\(236\) | 11.6873 | 0.760777 | ||||||||
\(237\) | − | 18.7886i | − | 1.22045i | ||||||
\(238\) | 3.76937i | 0.244332i | ||||||||
\(239\) | 17.7688 | 1.14937 | 0.574685 | − | 0.818375i | \(-0.305125\pi\) | ||||
0.574685 | + | 0.818375i | \(0.305125\pi\) | |||||||
\(240\) | −8.73238 | − | 12.8787i | −0.563673 | − | 0.831315i | ||||
\(241\) | −27.3823 | −1.76385 | −0.881925 | − | 0.471390i | \(-0.843753\pi\) | ||||
−0.881925 | + | 0.471390i | \(0.843753\pi\) | |||||||
\(242\) | 4.47623i | 0.287743i | ||||||||
\(243\) | − | 11.5739i | − | 0.742469i | ||||||
\(244\) | 9.54019 | 0.610748 | ||||||||
\(245\) | 12.3762 | − | 8.39165i | 0.790684 | − | 0.536123i | ||||
\(246\) | 0.118785 | 0.00757345 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.77061i | 0.620434i | ||||||||
\(249\) | −9.26557 | −0.587182 | ||||||||
\(250\) | −3.46442 | + | 0.762822i | −0.219109 | + | 0.0482451i | ||||
\(251\) | −8.50216 | −0.536651 | −0.268326 | − | 0.963328i | \(-0.586470\pi\) | ||||
−0.268326 | + | 0.963328i | \(0.586470\pi\) | |||||||
\(252\) | − | 8.24837i | − | 0.519599i | ||||||
\(253\) | 1.10731i | 0.0696161i | ||||||||
\(254\) | 3.78162 | 0.237280 | ||||||||
\(255\) | −12.1414 | + | 8.23250i | −0.760327 | + | 0.515539i | ||||
\(256\) | 8.54010 | 0.533756 | ||||||||
\(257\) | 20.9865i | 1.30910i | 0.756017 | + | 0.654552i | \(0.227143\pi\) | ||||
−0.756017 | + | 0.654552i | \(0.772857\pi\) | |||||||
\(258\) | 4.73477i | 0.294774i | ||||||||
\(259\) | −11.0479 | −0.686482 | ||||||||
\(260\) | −10.9438 | − | 16.1402i | −0.678708 | − | 1.00097i | ||||
\(261\) | 4.01590 | 0.248578 | ||||||||
\(262\) | − | 2.40535i | − | 0.148603i | ||||||
\(263\) | − | 11.7173i | − | 0.722522i | −0.932465 | − | 0.361261i | \(-0.882346\pi\) | ||
0.932465 | − | 0.361261i | \(-0.117654\pi\) | |||||||
\(264\) | 12.6654 | 0.779499 | ||||||||
\(265\) | −2.43035 | − | 3.58433i | −0.149295 | − | 0.220183i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.3901i | 1.85984i | ||||||||
\(268\) | 21.4156i | 1.30816i | ||||||||
\(269\) | 13.1743 | 0.803253 | 0.401626 | − | 0.915804i | \(-0.368445\pi\) | ||||
0.401626 | + | 0.915804i | \(0.368445\pi\) | |||||||
\(270\) | 2.19082 | − | 1.48548i | 0.133329 | − | 0.0904037i | ||||
\(271\) | −25.7363 | −1.56337 | −0.781683 | − | 0.623676i | \(-0.785639\pi\) | ||||
−0.781683 | + | 0.623676i | \(0.785639\pi\) | |||||||
\(272\) | − | 10.9374i | − | 0.663177i | ||||||
\(273\) | − | 34.7046i | − | 2.10042i | ||||||
\(274\) | −2.53381 | −0.153073 | ||||||||
\(275\) | −9.27232 | + | 23.2748i | −0.559142 | + | 1.40352i | ||||
\(276\) | 0.857501 | 0.0516155 | ||||||||
\(277\) | 5.11697i | 0.307449i | 0.988114 | + | 0.153724i | \(0.0491268\pi\) | ||||
−0.988114 | + | 0.153724i | \(0.950873\pi\) | |||||||
\(278\) | − | 0.842882i | − | 0.0505527i | ||||||
\(279\) | −9.27018 | −0.554991 | ||||||||
\(280\) | 8.47125 | − | 5.74393i | 0.506254 | − | 0.343265i | ||||
\(281\) | −1.80790 | −0.107850 | −0.0539251 | − | 0.998545i | \(-0.517173\pi\) | ||||
−0.0539251 | + | 0.998545i | \(0.517173\pi\) | |||||||
\(282\) | 7.05759i | 0.420273i | ||||||||
\(283\) | − | 18.6741i | − | 1.11006i | −0.831831 | − | 0.555029i | \(-0.812707\pi\) | ||
0.831831 | − | 0.555029i | \(-0.187293\pi\) | |||||||
\(284\) | 1.61675 | 0.0959366 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.29999 | 0.431657 | ||||||||
\(287\) | − | 0.677944i | − | 0.0400178i | ||||||
\(288\) | − | 4.17321i | − | 0.245909i | ||||||
\(289\) | 6.68871 | 0.393454 | ||||||||
\(290\) | 1.36218 | + | 2.00896i | 0.0799897 | + | 0.117970i | ||||
\(291\) | −2.79077 | −0.163598 | ||||||||
\(292\) | 9.79341i | 0.573116i | ||||||||
\(293\) | − | 0.150745i | − | 0.00880664i | −0.999990 | − | 0.00440332i | \(-0.998598\pi\) | ||
0.999990 | − | 0.00440332i | \(-0.00140163\pi\) | |||||||
\(294\) | 4.33475 | 0.252808 | ||||||||
\(295\) | −11.3883 | + | 7.72184i | −0.663053 | + | 0.449583i | ||||
\(296\) | −3.69461 | −0.214745 | ||||||||
\(297\) | − | 18.6943i | − | 1.08475i | ||||||
\(298\) | − | 2.64985i | − | 0.153502i | ||||||
\(299\) | 1.01468 | 0.0586804 | ||||||||
\(300\) | 18.0240 | + | 7.18047i | 1.04062 | + | 0.414565i | ||||
\(301\) | 27.0228 | 1.55757 | ||||||||
\(302\) | 2.71749i | 0.156374i | ||||||||
\(303\) | − | 12.4346i | − | 0.714347i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.29614 | + | 6.30325i | −0.532296 | + | 0.360923i | ||||
\(306\) | −1.19598 | −0.0683697 | ||||||||
\(307\) | 4.94936i | 0.282475i | 0.989976 | + | 0.141237i | \(0.0451081\pi\) | ||||
−0.989976 | + | 0.141237i | \(0.954892\pi\) | |||||||
\(308\) | − | 35.2095i | − | 2.00625i | ||||||
\(309\) | 28.0020 | 1.59298 | ||||||||
\(310\) | −3.14441 | − | 4.63743i | −0.178590 | − | 0.263388i | ||||
\(311\) | −23.6262 | −1.33972 | −0.669859 | − | 0.742489i | \(-0.733645\pi\) | ||||
−0.669859 | + | 0.742489i | \(0.733645\pi\) | |||||||
\(312\) | − | 11.6058i | − | 0.657051i | ||||||
\(313\) | 8.89248i | 0.502632i | 0.967905 | + | 0.251316i | \(0.0808634\pi\) | ||||
−0.967905 | + | 0.251316i | \(0.919137\pi\) | |||||||
\(314\) | −3.59600 | −0.202934 | ||||||||
\(315\) | 5.44974 | + | 8.03737i | 0.307058 | + | 0.452855i | ||||
\(316\) | −17.4673 | −0.982612 | ||||||||
\(317\) | 29.5976i | 1.66237i | 0.555996 | + | 0.831185i | \(0.312337\pi\) | ||||
−0.555996 | + | 0.831185i | \(0.687663\pi\) | |||||||
\(318\) | − | 1.25541i | − | 0.0704000i | ||||||
\(319\) | 17.1425 | 0.959795 | ||||||||
\(320\) | −10.5200 | + | 7.13305i | −0.588083 | + | 0.398750i | ||||
\(321\) | −35.3512 | −1.97311 | ||||||||
\(322\) | 0.259405i | 0.0144561i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −21.1654 | −1.17586 | ||||||||
\(325\) | 21.3278 | + | 8.49664i | 1.18305 | + | 0.471309i | ||||
\(326\) | 1.47555 | 0.0817232 | ||||||||
\(327\) | − | 28.0936i | − | 1.55358i | ||||||
\(328\) | − | 0.226716i | − | 0.0125183i | ||||||
\(329\) | 40.2799 | 2.22070 | ||||||||
\(330\) | −6.01137 | + | 4.07601i | −0.330915 | + | 0.224377i | ||||
\(331\) | 25.8866 | 1.42285 | 0.711427 | − | 0.702760i | \(-0.248049\pi\) | ||||
0.711427 | + | 0.702760i | \(0.248049\pi\) | |||||||
\(332\) | 8.61397i | 0.472753i | ||||||||
\(333\) | − | 3.50538i | − | 0.192093i | ||||||
\(334\) | 2.82224 | 0.154426 | ||||||||
\(335\) | −14.1494 | − | 20.8677i | −0.773062 | − | 1.14013i | ||||
\(336\) | −25.7444 | −1.40447 | ||||||||
\(337\) | 6.08960i | 0.331721i | 0.986149 | + | 0.165861i | \(0.0530402\pi\) | ||||
−0.986149 | + | 0.165861i | \(0.946960\pi\) | |||||||
\(338\) | − | 2.56454i | − | 0.139493i | ||||||
\(339\) | −8.49015 | −0.461122 | ||||||||
\(340\) | 7.65356 | + | 11.2876i | 0.415072 | + | 0.612156i | ||||
\(341\) | −39.5712 | −2.14290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.15747i | 0.0624972i | ||||||||
\(344\) | 9.03692 | 0.487238 | ||||||||
\(345\) | −0.835565 | + | 0.566555i | −0.0449853 | + | 0.0305023i | ||||
\(346\) | 5.91967 | 0.318244 | ||||||||
\(347\) | − | 6.60514i | − | 0.354582i | −0.984158 | − | 0.177291i | \(-0.943267\pi\) | ||
0.984158 | − | 0.177291i | \(-0.0567334\pi\) | |||||||
\(348\) | − | 13.2751i | − | 0.711621i | ||||||
\(349\) | −19.6123 | −1.04982 | −0.524912 | − | 0.851156i | \(-0.675902\pi\) | ||||
−0.524912 | + | 0.851156i | \(0.675902\pi\) | |||||||
\(350\) | −2.17219 | + | 5.45249i | −0.116108 | + | 0.291448i | ||||
\(351\) | −17.1304 | −0.914354 | ||||||||
\(352\) | − | 17.8140i | − | 0.949490i | ||||||
\(353\) | 19.2599i | 1.02510i | 0.858657 | + | 0.512551i | \(0.171299\pi\) | ||||
−0.858657 | + | 0.512551i | \(0.828701\pi\) | |||||||
\(354\) | −3.98876 | −0.212000 | ||||||||
\(355\) | −1.57539 | + | 1.06820i | −0.0836132 | + | 0.0566939i | ||||
\(356\) | 28.2529 | 1.49740 | ||||||||
\(357\) | 24.2706i | 1.28454i | ||||||||
\(358\) | 0.0713238i | 0.00376958i | ||||||||
\(359\) | 35.7362 | 1.88609 | 0.943043 | − | 0.332671i | \(-0.107950\pi\) | ||||
0.943043 | + | 0.332671i | \(0.107950\pi\) | |||||||
\(360\) | 1.82249 | + | 2.68784i | 0.0960536 | + | 0.141662i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | − | 7.89352i | − | 0.414874i | ||||||
\(363\) | 28.8221i | 1.51277i | ||||||||
\(364\) | −32.2640 | −1.69110 | ||||||||
\(365\) | −6.47055 | − | 9.54289i | −0.338684 | − | 0.499498i | ||||
\(366\) | −3.25598 | −0.170193 | ||||||||
\(367\) | 13.8593i | 0.723450i | 0.932285 | + | 0.361725i | \(0.117812\pi\) | ||||
−0.932285 | + | 0.361725i | \(0.882188\pi\) | |||||||
\(368\) | − | 0.752703i | − | 0.0392373i | ||||||
\(369\) | 0.215105 | 0.0111979 | ||||||||
\(370\) | 1.75357 | − | 1.18901i | 0.0911639 | − | 0.0618137i | ||||
\(371\) | −7.16504 | −0.371990 | ||||||||
\(372\) | 30.6439i | 1.58881i | ||||||||
\(373\) | 23.6819i | 1.22620i | 0.790005 | + | 0.613101i | \(0.210078\pi\) | ||||
−0.790005 | + | 0.613101i | \(0.789922\pi\) | |||||||
\(374\) | −5.10524 | −0.263985 | ||||||||
\(375\) | −22.3071 | + | 4.91174i | −1.15193 | + | 0.253641i | ||||
\(376\) | 13.4703 | 0.694678 | ||||||||
\(377\) | − | 15.7084i | − | 0.809026i | ||||||
\(378\) | − | 4.37943i | − | 0.225253i | ||||||
\(379\) | 33.7504 | 1.73364 | 0.866820 | − | 0.498622i | \(-0.166160\pi\) | ||||
0.866820 | + | 0.498622i | \(0.166160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.3495 | 1.24746 | ||||||||
\(382\) | 2.67757i | 0.136996i | ||||||||
\(383\) | 15.9027i | 0.812588i | 0.913742 | + | 0.406294i | \(0.133179\pi\) | ||||
−0.913742 | + | 0.406294i | \(0.866821\pi\) | |||||||
\(384\) | −18.2110 | −0.929325 | ||||||||
\(385\) | 23.2631 | + | 34.3088i | 1.18560 | + | 1.74854i | ||||
\(386\) | 0.508761 | 0.0258953 | ||||||||
\(387\) | 8.57407i | 0.435844i | ||||||||
\(388\) | 2.59451i | 0.131716i | ||||||||
\(389\) | 0.715535 | 0.0362791 | 0.0181395 | − | 0.999835i | \(-0.494226\pi\) | ||||
0.0181395 | + | 0.999835i | \(0.494226\pi\) | |||||||
\(390\) | 3.73503 | + | 5.50849i | 0.189131 | + | 0.278933i | ||||
\(391\) | −0.709615 | −0.0358868 | ||||||||
\(392\) | − | 8.27344i | − | 0.417872i | ||||||
\(393\) | − | 15.4878i | − | 0.781259i | ||||||
\(394\) | 0.638652 | 0.0321748 | ||||||||
\(395\) | 17.0205 | − | 11.5407i | 0.856392 | − | 0.580676i | ||||
\(396\) | 11.1716 | 0.561394 | ||||||||
\(397\) | − | 14.3593i | − | 0.720671i | −0.932823 | − | 0.360336i | \(-0.882662\pi\) | ||
0.932823 | − | 0.360336i | \(-0.117338\pi\) | |||||||
\(398\) | − | 1.59817i | − | 0.0801088i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.30292 | − | 15.8212i | 0.315146 | − | 0.791061i | ||||
\(401\) | −34.5791 | −1.72680 | −0.863398 | − | 0.504524i | \(-0.831668\pi\) | ||||
−0.863398 | + | 0.504524i | \(0.831668\pi\) | |||||||
\(402\) | − | 7.30893i | − | 0.364536i | ||||||
\(403\) | 36.2609i | 1.80628i | ||||||||
\(404\) | −11.5601 | −0.575137 | ||||||||
\(405\) | 20.6240 | − | 13.9841i | 1.02481 | − | 0.694874i | ||||
\(406\) | 4.01590 | 0.199306 | ||||||||
\(407\) | − | 14.9633i | − | 0.741701i | ||||||
\(408\) | 8.11653i | 0.401828i | ||||||||
\(409\) | 18.4355 | 0.911575 | 0.455788 | − | 0.890089i | \(-0.349358\pi\) | ||||
0.455788 | + | 0.890089i | \(0.349358\pi\) | |||||||
\(410\) | 0.0729626 | + | 0.107607i | 0.00360337 | + | 0.00531431i | ||||
\(411\) | −16.3150 | −0.804760 | ||||||||
\(412\) | − | 26.0327i | − | 1.28254i | ||||||
\(413\) | 22.7651i | 1.12020i | ||||||||
\(414\) | −0.0823065 | −0.00404514 | ||||||||
\(415\) | −5.69129 | − | 8.39362i | −0.279375 | − | 0.412027i | ||||
\(416\) | −16.3238 | −0.800339 | ||||||||
\(417\) | − | 5.42725i | − | 0.265773i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.3437 | 1.67780 | 0.838901 | − | 0.544285i | \(-0.183199\pi\) | ||||
0.838901 | + | 0.544285i | \(0.183199\pi\) | |||||||
\(420\) | 26.5687 | − | 18.0149i | 1.29642 | − | 0.879037i | ||||
\(421\) | −0.225020 | −0.0109668 | −0.00548340 | − | 0.999985i | \(-0.501745\pi\) | ||||
−0.00548340 | + | 0.999985i | \(0.501745\pi\) | |||||||
\(422\) | 1.32897i | 0.0646930i | ||||||||
\(423\) | 12.7804i | 0.621404i | ||||||||
\(424\) | −2.39611 | −0.116366 | ||||||||
\(425\) | −14.9155 | − | 5.94211i | −0.723510 | − | 0.288235i | ||||
\(426\) | −0.551782 | −0.0267339 | ||||||||
\(427\) | 18.5829i | 0.899290i | ||||||||
\(428\) | 32.8652i | 1.58860i | ||||||||
\(429\) | 47.0040 | 2.26937 | ||||||||
\(430\) | −4.28920 | + | 2.90829i | −0.206844 | + | 0.140250i | ||||
\(431\) | 13.3531 | 0.643198 | 0.321599 | − | 0.946876i | \(-0.395780\pi\) | ||||
0.321599 | + | 0.946876i | \(0.395780\pi\) | |||||||
\(432\) | 12.7076i | 0.611393i | ||||||||
\(433\) | 21.4161i | 1.02919i | 0.857433 | + | 0.514595i | \(0.172058\pi\) | ||||
−0.857433 | + | 0.514595i | \(0.827942\pi\) | |||||||
\(434\) | −9.27018 | −0.444983 | ||||||||
\(435\) | 8.77093 | + | 12.9355i | 0.420534 | + | 0.620211i | ||||
\(436\) | −26.1179 | −1.25082 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 3.34240i | − | 0.159706i | ||||||
\(439\) | 7.21678 | 0.344438 | 0.172219 | − | 0.985059i | \(-0.444906\pi\) | ||||
0.172219 | + | 0.985059i | \(0.444906\pi\) | |||||||
\(440\) | 7.77958 | + | 11.4735i | 0.370877 | + | 0.546976i | ||||
\(441\) | 7.84969 | 0.373795 | ||||||||
\(442\) | 4.67816i | 0.222517i | ||||||||
\(443\) | 34.6591i | 1.64671i | 0.567530 | + | 0.823353i | \(0.307899\pi\) | ||||
−0.567530 | + | 0.823353i | \(0.692101\pi\) | |||||||
\(444\) | −11.5875 | −0.549920 | ||||||||
\(445\) | −27.5302 | + | 18.6668i | −1.30505 | + | 0.884892i | ||||
\(446\) | −1.69105 | −0.0800735 | ||||||||
\(447\) | − | 17.0622i | − | 0.807013i | ||||||
\(448\) | 21.0293i | 0.993540i | ||||||||
\(449\) | −5.09006 | −0.240215 | −0.120107 | − | 0.992761i | \(-0.538324\pi\) | ||||
−0.120107 | + | 0.992761i | \(0.538324\pi\) | |||||||
\(450\) | −1.73002 | − | 0.689212i | −0.0815538 | − | 0.0324898i | ||||
\(451\) | 0.918208 | 0.0432367 | ||||||||
\(452\) | 7.89309i | 0.371260i | ||||||||
\(453\) | 17.4977i | 0.822113i | ||||||||
\(454\) | −1.64324 | −0.0771210 | ||||||||
\(455\) | 31.4387 | − | 21.3170i | 1.47387 | − | 0.999356i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.9916i | 1.87073i | 0.353686 | + | 0.935364i | \(0.384928\pi\) | ||||
−0.353686 | + | 0.935364i | \(0.615072\pi\) | |||||||
\(458\) | 5.41899i | 0.253213i | ||||||||
\(459\) | 11.9801 | 0.559185 | ||||||||
\(460\) | 0.526712 | + | 0.776804i | 0.0245581 | + | 0.0362187i | ||||
\(461\) | 26.4955 | 1.23402 | 0.617009 | − | 0.786956i | \(-0.288344\pi\) | ||||
0.617009 | + | 0.786956i | \(0.288344\pi\) | |||||||
\(462\) | 12.0167i | 0.559066i | ||||||||
\(463\) | 9.68844i | 0.450260i | 0.974329 | + | 0.225130i | \(0.0722807\pi\) | ||||
−0.974329 | + | 0.225130i | \(0.927719\pi\) | |||||||
\(464\) | −11.6527 | −0.540964 | ||||||||
\(465\) | −20.2466 | − | 29.8600i | −0.938912 | − | 1.38472i | ||||
\(466\) | −5.02915 | −0.232971 | ||||||||
\(467\) | − | 5.78310i | − | 0.267610i | −0.991008 | − | 0.133805i | \(-0.957280\pi\) | ||
0.991008 | − | 0.133805i | \(-0.0427195\pi\) | |||||||
\(468\) | − | 10.2370i | − | 0.473208i | ||||||
\(469\) | −41.7144 | −1.92619 | ||||||||
\(470\) | −6.39342 | + | 4.33506i | −0.294907 | + | 0.199961i | ||||
\(471\) | −23.1543 | −1.06689 | ||||||||
\(472\) | 7.61306i | 0.350419i | ||||||||
\(473\) | 36.5998i | 1.68286i | ||||||||
\(474\) | 5.96142 | 0.273817 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.5638 | 1.03421 | ||||||||
\(477\) | − | 2.27339i | − | 0.104091i | ||||||
\(478\) | 5.63786i | 0.257870i | ||||||||
\(479\) | −1.77194 | −0.0809620 | −0.0404810 | − | 0.999180i | \(-0.512889\pi\) | ||||
−0.0404810 | + | 0.999180i | \(0.512889\pi\) | |||||||
\(480\) | 13.4423 | − | 9.11452i | 0.613552 | − | 0.416019i | ||||
\(481\) | −13.7115 | −0.625191 | ||||||||
\(482\) | − | 8.68812i | − | 0.395733i | ||||||
\(483\) | 1.67029i | 0.0760007i | ||||||||
\(484\) | 26.7952 | 1.21796 | ||||||||
\(485\) | −1.71421 | − | 2.52814i | −0.0778381 | − | 0.114797i | ||||
\(486\) | 3.67229 | 0.166579 | ||||||||
\(487\) | − | 16.2131i | − | 0.734688i | −0.930085 | − | 0.367344i | \(-0.880267\pi\) | ||
0.930085 | − | 0.367344i | \(-0.119733\pi\) | |||||||
\(488\) | 6.21445i | 0.281315i | ||||||||
\(489\) | 9.50094 | 0.429647 | ||||||||
\(490\) | 2.66258 | + | 3.92683i | 0.120283 | + | 0.177396i | ||||
\(491\) | 18.4869 | 0.834300 | 0.417150 | − | 0.908838i | \(-0.363029\pi\) | ||||
0.417150 | + | 0.908838i | \(0.363029\pi\) | |||||||
\(492\) | − | 0.711059i | − | 0.0320570i | ||||||
\(493\) | 10.9857i | 0.494770i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.8858 | + | 7.38113i | −0.489281 | + | 0.331757i | ||||
\(496\) | 26.8988 | 1.20779 | ||||||||
\(497\) | 3.14920i | 0.141261i | ||||||||
\(498\) | − | 2.93987i | − | 0.131739i | ||||||
\(499\) | 17.2843 | 0.773751 | 0.386875 | − | 0.922132i | \(-0.373554\pi\) | ||||
0.386875 | + | 0.922132i | \(0.373554\pi\) | |||||||
\(500\) | 4.56633 | + | 20.7384i | 0.204212 | + | 0.927447i | ||||
\(501\) | 18.1722 | 0.811873 | ||||||||
\(502\) | − | 2.69765i | − | 0.120402i | ||||||
\(503\) | − | 40.7325i | − | 1.81617i | −0.418782 | − | 0.908087i | \(-0.637543\pi\) | ||
0.418782 | − | 0.908087i | \(-0.362457\pi\) | |||||||
\(504\) | 5.37297 | 0.239331 | ||||||||
\(505\) | 11.2644 | − | 7.63782i | 0.501259 | − | 0.339879i | ||||
\(506\) | −0.351338 | −0.0156189 | ||||||||
\(507\) | − | 16.5129i | − | 0.733362i | ||||||
\(508\) | − | 22.6372i | − | 1.00436i | ||||||
\(509\) | −21.2017 | −0.939747 | −0.469873 | − | 0.882734i | \(-0.655700\pi\) | ||||
−0.469873 | + | 0.882734i | \(0.655700\pi\) | |||||||
\(510\) | −2.61209 | − | 3.85235i | −0.115665 | − | 0.170585i | ||||
\(511\) | −19.0761 | −0.843879 | ||||||||
\(512\) | 20.5374i | 0.907632i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.65881 | −0.293707 | ||||||||
\(515\) | 17.1999 | + | 25.3668i | 0.757920 | + | 1.11779i | ||||
\(516\) | 28.3428 | 1.24772 | ||||||||
\(517\) | 54.5551i | 2.39933i | ||||||||
\(518\) | − | 3.50538i | − | 0.154017i | ||||||
\(519\) | 38.1163 | 1.67312 | ||||||||
\(520\) | 10.5137 | − | 7.12878i | 0.461054 | − | 0.312618i | ||||
\(521\) | 19.2704 | 0.844251 | 0.422125 | − | 0.906538i | \(-0.361284\pi\) | ||||
0.422125 | + | 0.906538i | \(0.361284\pi\) | |||||||
\(522\) | 1.27420i | 0.0557703i | ||||||||
\(523\) | − | 24.4971i | − | 1.07118i | −0.844477 | − | 0.535591i | \(-0.820089\pi\) | ||
0.844477 | − | 0.535591i | \(-0.179911\pi\) | |||||||
\(524\) | −14.3987 | −0.629009 | ||||||||
\(525\) | −13.9865 | + | 35.1081i | −0.610421 | + | 1.53224i | ||||
\(526\) | 3.71779 | 0.162103 | ||||||||
\(527\) | − | 25.3590i | − | 1.10466i | ||||||
\(528\) | − | 34.8682i | − | 1.51744i | ||||||
\(529\) | 22.9512 | 0.997877 | ||||||||
\(530\) | 1.13727 | − | 0.771125i | 0.0493998 | − | 0.0334955i | ||||
\(531\) | −7.22313 | −0.313457 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.841395i | − | 0.0364449i | ||||||
\(534\) | −9.64245 | −0.417270 | ||||||||
\(535\) | −21.7142 | − | 32.0244i | −0.938785 | − | 1.38454i | ||||
\(536\) | −13.9500 | −0.602550 | ||||||||
\(537\) | 0.459248i | 0.0198180i | ||||||||
\(538\) | 4.18008i | 0.180216i | ||||||||
\(539\) | 33.5076 | 1.44328 | ||||||||
\(540\) | −8.89226 | − | 13.1145i | −0.382662 | − | 0.564357i | ||||
\(541\) | 30.5029 | 1.31142 | 0.655711 | − | 0.755012i | \(-0.272369\pi\) | ||||
0.655711 | + | 0.755012i | \(0.272369\pi\) | |||||||
\(542\) | − | 8.16585i | − | 0.350753i | ||||||
\(543\) | − | 50.8257i | − | 2.18114i | ||||||
\(544\) | 11.4160 | 0.489458 | ||||||||
\(545\) | 25.4498 | − | 17.2562i | 1.09015 | − | 0.739176i | ||||
\(546\) | 11.0114 | 0.471245 | ||||||||
\(547\) | 3.16224i | 0.135207i | 0.997712 | + | 0.0676037i | \(0.0215354\pi\) | ||||
−0.997712 | + | 0.0676037i | \(0.978465\pi\) | |||||||
\(548\) | 15.1677i | 0.647931i | ||||||||
\(549\) | −5.89616 | −0.251642 | ||||||||
\(550\) | −7.38486 | − | 2.94201i | −0.314891 | − | 0.125448i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.558573i | 0.0237745i | ||||||||
\(553\) | − | 34.0237i | − | 1.44684i | ||||||
\(554\) | −1.62356 | −0.0689785 | ||||||||
\(555\) | 11.2911 | − | 7.65593i | 0.479281 | − | 0.324976i | ||||
\(556\) | −5.04558 | −0.213980 | ||||||||
\(557\) | − | 33.8886i | − | 1.43591i | −0.696092 | − | 0.717953i | \(-0.745079\pi\) | ||
0.696092 | − | 0.717953i | \(-0.254921\pi\) | |||||||
\(558\) | − | 2.94133i | − | 0.124517i | ||||||
\(559\) | 33.5380 | 1.41851 | ||||||||
\(560\) | −15.8132 | − | 23.3216i | −0.668231 | − | 0.985519i | ||||
\(561\) | −32.8722 | −1.38786 | ||||||||
\(562\) | − | 0.573627i | − | 0.0241970i | ||||||
\(563\) | − | 36.5457i | − | 1.54022i | −0.637911 | − | 0.770110i | \(-0.720201\pi\) | ||
0.637911 | − | 0.770110i | \(-0.279799\pi\) | |||||||
\(564\) | 42.2474 | 1.77894 | ||||||||
\(565\) | −5.21500 | − | 7.69117i | −0.219397 | − | 0.323570i | ||||
\(566\) | 5.92509 | 0.249050 | ||||||||
\(567\) | − | 41.2271i | − | 1.73138i | ||||||
\(568\) | 1.05315i | 0.0441891i | ||||||||
\(569\) | 1.31802 | 0.0552543 | 0.0276272 | − | 0.999618i | \(-0.491205\pi\) | ||||
0.0276272 | + | 0.999618i | \(0.491205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0771 | −0.714656 | −0.357328 | − | 0.933979i | \(-0.616312\pi\) | ||||
−0.357328 | + | 0.933979i | \(0.616312\pi\) | |||||||
\(572\) | − | 43.6985i | − | 1.82712i | ||||||
\(573\) | 17.2406i | 0.720238i | ||||||||
\(574\) | 0.215105 | 0.00897829 | ||||||||
\(575\) | −1.02648 | − | 0.408932i | −0.0428070 | − | 0.0170536i | ||||
\(576\) | −6.67237 | −0.278016 | ||||||||
\(577\) | − | 47.2699i | − | 1.96787i | −0.178517 | − | 0.983937i | \(-0.557130\pi\) | ||
0.178517 | − | 0.983937i | \(-0.442870\pi\) | |||||||
\(578\) | 2.12226i | 0.0882744i | ||||||||
\(579\) | 3.27587 | 0.136140 | ||||||||
\(580\) | 12.0258 | − | 8.15412i | 0.499346 | − | 0.338581i | ||||
\(581\) | −16.7788 | −0.696101 | ||||||||
\(582\) | − | 0.885483i | − | 0.0367045i | ||||||
\(583\) | − | 9.70433i | − | 0.401912i | ||||||
\(584\) | −6.37940 | −0.263981 | ||||||||
\(585\) | 6.76366 | + | 9.97517i | 0.279643 | + | 0.412423i | ||||
\(586\) | 0.0478300 | 0.00197584 | ||||||||
\(587\) | 0.620087i | 0.0255937i | 0.999918 | + | 0.0127969i | \(0.00407348\pi\) | ||||
−0.999918 | + | 0.0127969i | \(0.995927\pi\) | |||||||
\(588\) | − | 25.9483i | − | 1.07009i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.45006 | − | 3.61339i | −0.100867 | − | 0.148761i | ||||
\(591\) | 4.11222 | 0.169154 | ||||||||
\(592\) | 10.1714i | 0.418041i | ||||||||
\(593\) | 8.96071i | 0.367972i | 0.982929 | + | 0.183986i | \(0.0589002\pi\) | ||||
−0.982929 | + | 0.183986i | \(0.941100\pi\) | |||||||
\(594\) | 5.93150 | 0.243372 | ||||||||
\(595\) | −21.9866 | + | 14.9080i | −0.901363 | + | 0.611169i | ||||
\(596\) | −15.8623 | −0.649745 | ||||||||
\(597\) | − | 10.2905i | − | 0.421160i | ||||||
\(598\) | 0.321947i | 0.0131654i | ||||||||
\(599\) | −0.338212 | −0.0138190 | −0.00690948 | − | 0.999976i | \(-0.502199\pi\) | ||||
−0.00690948 | + | 0.999976i | \(0.502199\pi\) | |||||||
\(600\) | −4.67734 | + | 11.7408i | −0.190951 | + | 0.479315i | ||||
\(601\) | 39.7523 | 1.62153 | 0.810766 | − | 0.585370i | \(-0.199051\pi\) | ||||
0.810766 | + | 0.585370i | \(0.199051\pi\) | |||||||
\(602\) | 8.57407i | 0.349453i | ||||||||
\(603\) | − | 13.2355i | − | 0.538993i | ||||||
\(604\) | 16.2672 | 0.661902 | ||||||||
\(605\) | −26.1097 | + | 17.7037i | −1.06151 | + | 0.719757i | ||||
\(606\) | 3.94536 | 0.160269 | ||||||||
\(607\) | 22.5614i | 0.915738i | 0.889020 | + | 0.457869i | \(0.151387\pi\) | ||||
−0.889020 | + | 0.457869i | \(0.848613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.8580 | 1.04782 | ||||||||
\(610\) | −1.99996 | − | 2.94957i | −0.0809758 | − | 0.119425i | ||||
\(611\) | 49.9913 | 2.02243 | ||||||||
\(612\) | 7.15926i | 0.289396i | ||||||||
\(613\) | − | 32.5953i | − | 1.31651i | −0.752794 | − | 0.658257i | \(-0.771294\pi\) | ||
0.752794 | − | 0.658257i | \(-0.228706\pi\) | |||||||
\(614\) | −1.57038 | −0.0633754 | ||||||||
\(615\) | 0.469800 | + | 0.692869i | 0.0189442 | + | 0.0279392i | ||||
\(616\) | 22.9354 | 0.924092 | ||||||||
\(617\) | 29.4270i | 1.18469i | 0.805686 | + | 0.592343i | \(0.201797\pi\) | ||||
−0.805686 | + | 0.592343i | \(0.798203\pi\) | |||||||
\(618\) | 8.88473i | 0.357396i | ||||||||
\(619\) | 24.9940 | 1.00459 | 0.502297 | − | 0.864695i | \(-0.332488\pi\) | ||||
0.502297 | + | 0.864695i | \(0.332488\pi\) | |||||||
\(620\) | −27.7601 | + | 18.8227i | −1.11487 | + | 0.755940i | ||||
\(621\) | 0.824463 | 0.0330846 | ||||||||
\(622\) | − | 7.49634i | − | 0.300576i | ||||||
\(623\) | 55.0325i | 2.20483i | ||||||||
\(624\) | −31.9513 | −1.27907 | ||||||||
\(625\) | −18.1514 | − | 17.1908i | −0.726058 | − | 0.687634i | ||||
\(626\) | −2.82149 | −0.112769 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.5260i | 0.858981i | ||||||||
\(629\) | 9.58912 | 0.382343 | ||||||||
\(630\) | −2.55017 | + | 1.72915i | −0.101601 | + | 0.0688908i | ||||
\(631\) | −28.3101 | −1.12701 | −0.563504 | − | 0.826113i | \(-0.690547\pi\) | ||||
−0.563504 | + | 0.826113i | \(0.690547\pi\) | |||||||
\(632\) | − | 11.3781i | − | 0.452598i | ||||||
\(633\) | 8.55709i | 0.340114i | ||||||||
\(634\) | −9.39103 | −0.372965 | ||||||||
\(635\) | 14.9565 | + | 22.0581i | 0.593530 | + | 0.875348i | ||||
\(636\) | −7.51502 | −0.297990 | ||||||||
\(637\) | − | 30.7046i | − | 1.21656i | ||||||
\(638\) | 5.43913i | 0.215337i | ||||||||
\(639\) | −0.999208 | −0.0395280 | ||||||||
\(640\) | −11.1859 | − | 16.4972i | −0.442162 | − | 0.652109i | ||||
\(641\) | −28.7741 | −1.13651 | −0.568254 | − | 0.822853i | \(-0.692381\pi\) | ||||
−0.568254 | + | 0.822853i | \(0.692381\pi\) | |||||||
\(642\) | − | 11.2166i | − | 0.442683i | ||||||
\(643\) | 10.0599i | 0.396722i | 0.980129 | + | 0.198361i | \(0.0635618\pi\) | ||||
−0.980129 | + | 0.198361i | \(0.936438\pi\) | |||||||
\(644\) | 1.55282 | 0.0611899 | ||||||||
\(645\) | −27.6178 | + | 18.7262i | −1.08745 | + | 0.737344i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 18.9903i | − | 0.746586i | −0.927714 | − | 0.373293i | \(-0.878229\pi\) | ||
0.927714 | − | 0.373293i | \(-0.121771\pi\) | |||||||
\(648\) | − | 13.7871i | − | 0.541607i | ||||||
\(649\) | −30.8331 | −1.21030 | ||||||||
\(650\) | −2.69590 | + | 6.76708i | −0.105742 | + | 0.265427i | ||||
\(651\) | −59.6899 | −2.33943 | ||||||||
\(652\) | − | 8.83279i | − | 0.345919i | ||||||
\(653\) | 42.6940i | 1.67074i | 0.549685 | + | 0.835372i | \(0.314748\pi\) | ||||
−0.549685 | + | 0.835372i | \(0.685252\pi\) | |||||||
\(654\) | 8.91381 | 0.348557 | ||||||||
\(655\) | 14.0303 | − | 9.51327i | 0.548211 | − | 0.371714i | ||||
\(656\) | −0.624158 | −0.0243693 | ||||||||
\(657\) | − | 6.05266i | − | 0.236137i | ||||||
\(658\) | 12.7804i | 0.498232i | ||||||||
\(659\) | −14.4043 | −0.561111 | −0.280556 | − | 0.959838i | \(-0.590519\pi\) | ||||
−0.280556 | + | 0.959838i | \(0.590519\pi\) | |||||||
\(660\) | 24.3994 | + | 35.9847i | 0.949745 | + | 1.40070i | ||||
\(661\) | −8.24176 | −0.320567 | −0.160284 | − | 0.987071i | \(-0.551241\pi\) | ||||
−0.160284 | + | 0.987071i | \(0.551241\pi\) | |||||||
\(662\) | 8.21354i | 0.319228i | ||||||||
\(663\) | 30.1222i | 1.16985i | ||||||||
\(664\) | −5.61112 | −0.217754 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.11222 | 0.0430976 | ||||||||
\(667\) | 0.756026i | 0.0292734i | ||||||||
\(668\) | − | 16.8942i | − | 0.653657i | ||||||
\(669\) | −10.8885 | −0.420974 | ||||||||
\(670\) | 6.62111 | − | 4.48944i | 0.255796 | − | 0.173442i | ||||
\(671\) | −25.1687 | −0.971627 | ||||||||
\(672\) | − | 26.8709i | − | 1.03657i | ||||||
\(673\) | 37.9246i | 1.46189i | 0.682438 | + | 0.730944i | \(0.260920\pi\) | ||||
−0.682438 | + | 0.730944i | \(0.739080\pi\) | |||||||
\(674\) | −1.93217 | −0.0744242 | ||||||||
\(675\) | 17.3296 | + | 6.90382i | 0.667015 | + | 0.265728i | ||||
\(676\) | −15.3516 | −0.590446 | ||||||||
\(677\) | − | 8.17207i | − | 0.314078i | −0.987592 | − | 0.157039i | \(-0.949805\pi\) | ||
0.987592 | − | 0.157039i | \(-0.0501949\pi\) | |||||||
\(678\) | − | 2.69384i | − | 0.103456i | ||||||
\(679\) | −5.05374 | −0.193945 | ||||||||
\(680\) | −7.35271 | + | 4.98550i | −0.281964 | + | 0.191185i | ||||
\(681\) | −10.5807 | −0.405452 | ||||||||
\(682\) | − | 12.5555i | − | 0.480777i | ||||||
\(683\) | − | 16.4611i | − | 0.629868i | −0.949114 | − | 0.314934i | \(-0.898018\pi\) | ||
0.949114 | − | 0.314934i | \(-0.101982\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0213 | − | 14.7797i | −0.382896 | − | 0.564702i | ||||
\(686\) | −0.367252 | −0.0140217 | ||||||||
\(687\) | 34.8924i | 1.33123i | ||||||||
\(688\) | − | 24.8789i | − | 0.948501i | ||||||
\(689\) | −8.89252 | −0.338778 | ||||||||
\(690\) | −0.179762 | − | 0.265116i | −0.00684342 | − | 0.0100928i | ||||
\(691\) | 11.9386 | 0.454166 | 0.227083 | − | 0.973875i | \(-0.427081\pi\) | ||||
0.227083 | + | 0.973875i | \(0.427081\pi\) | |||||||
\(692\) | − | 35.4358i | − | 1.34707i | ||||||
\(693\) | 21.7607i | 0.826619i | ||||||||
\(694\) | 2.09574 | 0.0795532 | ||||||||
\(695\) | 4.91651 | − | 3.33364i | 0.186494 | − | 0.126452i | ||||
\(696\) | 8.64737 | 0.327778 | ||||||||
\(697\) | 0.588429i | 0.0222883i | ||||||||
\(698\) | − | 6.22279i | − | 0.235536i | ||||||
\(699\) | −32.3822 | −1.22481 | ||||||||
\(700\) | 32.6391 | + | 13.0029i | 1.23364 | + | 0.491464i | ||||
\(701\) | −15.7112 | −0.593404 | −0.296702 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296702 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(702\) | − | 5.43530i | − | 0.205142i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −28.4821 | −1.07346 | ||||||||
\(705\) | −41.1667 | + | 27.9131i | −1.55043 | + | 1.05127i | ||||
\(706\) | −6.11097 | −0.229989 | ||||||||
\(707\) | − | 22.5174i | − | 0.846855i | ||||||
\(708\) | 23.8771i | 0.897357i | ||||||||
\(709\) | 0.810620 | 0.0304435 | 0.0152217 | − | 0.999884i | \(-0.495155\pi\) | ||||
0.0152217 | + | 0.999884i | \(0.495155\pi\) | |||||||
\(710\) | −0.338927 | − | 0.499856i | −0.0127197 | − | 0.0187593i | ||||
\(711\) | 10.7954 | 0.404858 | ||||||||
\(712\) | 18.4039i | 0.689713i | ||||||||
\(713\) | − | 1.74519i | − | 0.0653578i | ||||||
\(714\) | −7.70082 | −0.288196 | ||||||||
\(715\) | 28.8718 | + | 42.5806i | 1.07974 | + | 1.59242i | ||||
\(716\) | 0.426951 | 0.0159559 | ||||||||
\(717\) | 36.3017i | 1.35571i | ||||||||
\(718\) | 11.3387i | 0.423158i | ||||||||
\(719\) | 13.4593 | 0.501948 | 0.250974 | − | 0.967994i | \(-0.419249\pi\) | ||||
0.250974 | + | 0.967994i | \(0.419249\pi\) | |||||||
\(720\) | 7.39971 | − | 5.01737i | 0.275771 | − | 0.186987i | ||||
\(721\) | 50.7080 | 1.88846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 55.9421i | − | 2.08051i | ||||||
\(724\) | −47.2514 | −1.75609 | ||||||||
\(725\) | −6.33075 | + | 15.8911i | −0.235118 | + | 0.590179i | ||||
\(726\) | −9.14494 | −0.339401 | ||||||||
\(727\) | − | 2.13941i | − | 0.0793464i | −0.999213 | − | 0.0396732i | \(-0.987368\pi\) | ||
0.999213 | − | 0.0396732i | \(-0.0126317\pi\) | |||||||
\(728\) | − | 21.0167i | − | 0.778931i | ||||||
\(729\) | −9.78531 | −0.362419 | ||||||||
\(730\) | 3.02786 | − | 2.05304i | 0.112066 | − | 0.0759864i | ||||
\(731\) | −23.4548 | −0.867506 | ||||||||
\(732\) | 19.4906i | 0.720394i | ||||||||
\(733\) | 0.353890i | 0.0130712i | 0.999979 | + | 0.00653561i | \(0.00208036\pi\) | ||||
−0.999979 | + | 0.00653561i | \(0.997920\pi\) | |||||||
\(734\) | −4.39741 | −0.162311 | ||||||||
\(735\) | 17.1441 | + | 25.2845i | 0.632371 | + | 0.932633i | ||||
\(736\) | 0.785641 | 0.0289591 | ||||||||
\(737\) | − | 56.4980i | − | 2.08113i | ||||||
\(738\) | 0.0682504i | 0.00251233i | ||||||||
\(739\) | −0.530279 | −0.0195066 | −0.00975332 | − | 0.999952i | \(-0.503105\pi\) | ||||
−0.00975332 | + | 0.999952i | \(0.503105\pi\) | |||||||
\(740\) | −7.11753 | − | 10.4971i | −0.261646 | − | 0.385880i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 2.27339i | − | 0.0834588i | ||||||
\(743\) | 10.9210i | 0.400654i | 0.979729 | + | 0.200327i | \(0.0642004\pi\) | ||||
−0.979729 | + | 0.200327i | \(0.935800\pi\) | |||||||
\(744\) | −19.9614 | −0.731819 | ||||||||
\(745\) | 15.4565 | − | 10.4803i | 0.566283 | − | 0.383968i | ||||
\(746\) | −7.51402 | −0.275108 | ||||||||
\(747\) | − | 5.32373i | − | 0.194785i | ||||||
\(748\) | 30.5605i | 1.11740i | ||||||||
\(749\) | −64.0166 | −2.33911 | ||||||||
\(750\) | −1.55845 | − | 7.07780i | −0.0569064 | − | 0.258445i | ||||
\(751\) | −8.00460 | −0.292092 | −0.146046 | − | 0.989278i | \(-0.546655\pi\) | ||||
−0.146046 | + | 0.989278i | \(0.546655\pi\) | |||||||
\(752\) | − | 37.0842i | − | 1.35232i | ||||||
\(753\) | − | 17.3699i | − | 0.632995i | ||||||
\(754\) | 4.98412 | 0.181511 | ||||||||
\(755\) | −15.8510 | + | 10.7478i | −0.576879 | + | 0.391153i | ||||
\(756\) | −26.2157 | −0.953455 | ||||||||
\(757\) | − | 30.1904i | − | 1.09729i | −0.836056 | − | 0.548645i | \(-0.815144\pi\) | ||
0.836056 | − | 0.548645i | \(-0.184856\pi\) | |||||||
\(758\) | 10.7086i | 0.388955i | ||||||||
\(759\) | −2.26224 | −0.0821140 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.399315 | −0.0144751 | −0.00723757 | − | 0.999974i | \(-0.502304\pi\) | ||||
−0.00723757 | + | 0.999974i | \(0.502304\pi\) | |||||||
\(762\) | 7.72585i | 0.279878i | ||||||||
\(763\) | − | 50.8739i | − | 1.84176i | ||||||
\(764\) | 16.0282 | 0.579880 | ||||||||
\(765\) | −4.73016 | − | 6.97612i | −0.171019 | − | 0.252222i | ||||
\(766\) | −5.04575 | −0.182310 | ||||||||
\(767\) | 28.2538i | 1.02018i | ||||||||
\(768\) | 17.4474i | 0.629580i | ||||||||
\(769\) | 6.52791 | 0.235403 | 0.117701 | − | 0.993049i | \(-0.462447\pi\) | ||||
0.117701 | + | 0.993049i | \(0.462447\pi\) | |||||||
\(770\) | −10.8858 | + | 7.38113i | −0.392298 | + | 0.265997i | ||||
\(771\) | −42.8755 | −1.54412 | ||||||||
\(772\) | − | 3.04550i | − | 0.109610i | ||||||
\(773\) | 29.2223i | 1.05105i | 0.850777 | + | 0.525527i | \(0.176132\pi\) | ||||
−0.850777 | + | 0.525527i | \(0.823868\pi\) | |||||||
\(774\) | −2.72046 | −0.0977850 | ||||||||
\(775\) | 14.6137 | − | 36.6825i | 0.524940 | − | 1.31767i | ||||
\(776\) | −1.69006 | −0.0606696 | ||||||||
\(777\) | − | 22.5708i | − | 0.809723i | ||||||
\(778\) | 0.227032i | 0.00813949i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 32.9744 | − | 22.3583i | 1.18067 | − | 0.800554i | ||||
\(781\) | −4.26528 | −0.152624 | ||||||||
\(782\) | − | 0.225153i | − | 0.00805147i | ||||||
\(783\) | − | 12.7637i | − | 0.456136i | ||||||
\(784\) | −22.7771 | −0.813466 | ||||||||
\(785\) | −14.2223 | − | 20.9753i | −0.507616 | − | 0.748642i | ||||
\(786\) | 4.91413 | 0.175281 | ||||||||
\(787\) | − | 43.2638i | − | 1.54219i | −0.636722 | − | 0.771093i | \(-0.719710\pi\) | ||
0.636722 | − | 0.771093i | \(-0.280290\pi\) | |||||||
\(788\) | − | 3.82303i | − | 0.136190i | ||||||
\(789\) | 23.9385 | 0.852234 | ||||||||
\(790\) | 3.66175 | + | 5.40041i | 0.130279 | + | 0.192138i | ||||
\(791\) | −15.3746 | −0.546657 | ||||||||
\(792\) | 7.27715i | 0.258582i | ||||||||
\(793\) | 23.0632i | 0.818999i | ||||||||
\(794\) | 4.55605 | 0.161688 | ||||||||
\(795\) | 7.32278 | − | 4.96521i | 0.259712 | − | 0.176098i | ||||
\(796\) | −9.56678 | −0.339086 | ||||||||
\(797\) | − | 27.5833i | − | 0.977050i | −0.872550 | − | 0.488525i | \(-0.837535\pi\) | ||
0.872550 | − | 0.488525i | \(-0.162465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.9614 | −1.23684 | ||||||||
\(800\) | 16.5136 | + | 6.57874i | 0.583843 | + | 0.232594i | ||||
\(801\) | −17.4613 | −0.616963 | ||||||||
\(802\) | − | 10.9716i | − | 0.387420i | ||||||
\(803\) | − | 25.8368i | − | 0.911759i | ||||||
\(804\) | −43.7520 | −1.54301 | ||||||||
\(805\) | −1.51310 | + | 1.02596i | −0.0533298 | + | 0.0361603i | ||||
\(806\) | −11.5052 | −0.405254 | ||||||||
\(807\) | 26.9151i | 0.947458i | ||||||||
\(808\) | − | 7.53023i | − | 0.264912i | ||||||
\(809\) | −47.2870 | −1.66252 | −0.831262 | − | 0.555881i | \(-0.812381\pi\) | ||||
−0.831262 | + | 0.555881i | \(0.812381\pi\) | |||||||
\(810\) | 4.43700 | + | 6.54377i | 0.155900 | + | 0.229925i | ||||
\(811\) | −35.1587 | −1.23459 | −0.617294 | − | 0.786733i | \(-0.711771\pi\) | ||||
−0.617294 | + | 0.786733i | \(0.711771\pi\) | |||||||
\(812\) | − | 24.0396i | − | 0.843623i | ||||||
\(813\) | − | 52.5792i | − | 1.84403i | ||||||
\(814\) | 4.74769 | 0.166406 | ||||||||
\(815\) | 5.83586 | + | 8.60684i | 0.204421 | + | 0.301484i | ||||
\(816\) | 22.3451 | 0.782234 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 5.84938i | 0.204519i | ||||||||
\(819\) | 19.9403 | 0.696770 | ||||||||
\(820\) | 0.644144 | − | 0.436761i | 0.0224945 | − | 0.0152524i | ||||
\(821\) | 32.1078 | 1.12057 | 0.560285 | − | 0.828300i | \(-0.310692\pi\) | ||||
0.560285 | + | 0.828300i | \(0.310692\pi\) | |||||||
\(822\) | − | 5.17658i | − | 0.180554i | ||||||
\(823\) | − | 24.6481i | − | 0.859180i | −0.903024 | − | 0.429590i | \(-0.858658\pi\) | ||
0.903024 | − | 0.429590i | \(-0.141342\pi\) | |||||||
\(824\) | 16.9576 | 0.590748 | ||||||||
\(825\) | −47.5504 | − | 18.9433i | −1.65549 | − | 0.659523i | ||||
\(826\) | −7.22313 | −0.251325 | ||||||||
\(827\) | − | 4.29867i | − | 0.149479i | −0.997203 | − | 0.0747397i | \(-0.976187\pi\) | ||
0.997203 | − | 0.0747397i | \(-0.0238126\pi\) | |||||||
\(828\) | 0.492695i | 0.0171223i | ||||||||
\(829\) | 11.2729 | 0.391524 | 0.195762 | − | 0.980651i | \(-0.437282\pi\) | ||||
0.195762 | + | 0.980651i | \(0.437282\pi\) | |||||||
\(830\) | 2.66321 | − | 1.80579i | 0.0924413 | − | 0.0626798i | ||||
\(831\) | −10.4540 | −0.362644 | ||||||||
\(832\) | 26.0994i | 0.904835i | ||||||||
\(833\) | 21.4732i | 0.744002i | ||||||||
\(834\) | 1.72201 | 0.0596283 | ||||||||
\(835\) | 11.1621 | + | 16.4621i | 0.386280 | + | 0.569693i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.4633i | 1.01840i | ||||||||
\(838\) | 10.8969i | 0.376427i | ||||||||
\(839\) | 36.5388 | 1.26146 | 0.630730 | − | 0.776003i | \(-0.282756\pi\) | ||||
0.630730 | + | 0.776003i | \(0.282756\pi\) | |||||||
\(840\) | 11.7348 | + | 17.3068i | 0.404891 | + | 0.597140i | ||||
\(841\) | −17.2958 | −0.596408 | ||||||||
\(842\) | − | 0.0713965i | − | 0.00246049i | ||||||
\(843\) | − | 3.69353i | − | 0.127212i | ||||||
\(844\) | 7.95532 | 0.273833 | ||||||||
\(845\) | 14.9589 | − | 10.1429i | 0.514602 | − | 0.348926i | ||||
\(846\) | −4.05509 | −0.139417 | ||||||||
\(847\) | 52.1931i | 1.79338i | ||||||||
\(848\) | 6.59659i | 0.226528i | ||||||||
\(849\) | 38.1511 | 1.30934 | ||||||||
\(850\) | 1.88537 | − | 4.73255i | 0.0646677 | − | 0.162325i | ||||
\(851\) | 0.659916 | 0.0226216 | ||||||||
\(852\) | 3.30302i | 0.113160i | ||||||||
\(853\) | − | 13.5898i | − | 0.465306i | −0.972560 | − | 0.232653i | \(-0.925259\pi\) | ||
0.972560 | − | 0.232653i | \(-0.0747407\pi\) | |||||||
\(854\) | −5.89616 | −0.201763 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.4083 | −0.731720 | ||||||||
\(857\) | 5.85278i | 0.199927i | 0.994991 | + | 0.0999637i | \(0.0318727\pi\) | ||||
−0.994991 | + | 0.0999637i | \(0.968127\pi\) | |||||||
\(858\) | 14.9139i | 0.509151i | ||||||||
\(859\) | 20.2569 | 0.691157 | 0.345579 | − | 0.938390i | \(-0.387683\pi\) | ||||
0.345579 | + | 0.938390i | \(0.387683\pi\) | |||||||
\(860\) | 17.4093 | + | 25.6756i | 0.593653 | + | 0.875530i | ||||
\(861\) | 1.38504 | 0.0472020 | ||||||||
\(862\) | 4.23681i | 0.144306i | ||||||||
\(863\) | − | 5.65447i | − | 0.192481i | −0.995358 | − | 0.0962403i | \(-0.969318\pi\) | ||
0.995358 | − | 0.0962403i | \(-0.0306817\pi\) | |||||||
\(864\) | −13.2637 | −0.451239 | ||||||||
\(865\) | 23.4126 | + | 34.5293i | 0.796051 | + | 1.17403i | ||||
\(866\) | −6.79509 | −0.230907 | ||||||||
\(867\) | 13.6650i | 0.464089i | ||||||||
\(868\) | 55.4922i | 1.88353i | ||||||||
\(869\) | 46.0818 | 1.56322 | ||||||||
\(870\) | −4.10431 | + | 2.78293i | −0.139149 | + | 0.0943500i | ||||
\(871\) | −51.7717 | −1.75422 | ||||||||
\(872\) | − | 17.0131i | − | 0.576138i | ||||||
\(873\) | − | 1.60350i | − | 0.0542702i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.3953 | + | 8.89454i | −1.36561 | + | 0.300690i | ||||
\(876\) | −20.0079 | −0.676006 | ||||||||
\(877\) | − | 57.4540i | − | 1.94008i | −0.242939 | − | 0.970041i | \(-0.578112\pi\) | ||
0.242939 | − | 0.970041i | \(-0.421888\pi\) | |||||||
\(878\) | 2.28981i | 0.0772773i | ||||||||
\(879\) | 0.307973 | 0.0103877 | ||||||||
\(880\) | 31.5869 | − | 21.4175i | 1.06479 | − | 0.721982i | ||||
\(881\) | 8.46121 | 0.285065 | 0.142533 | − | 0.989790i | \(-0.454475\pi\) | ||||
0.142533 | + | 0.989790i | \(0.454475\pi\) | |||||||
\(882\) | 2.49063i | 0.0838637i | ||||||||
\(883\) | − | 12.8839i | − | 0.433578i | −0.976218 | − | 0.216789i | \(-0.930442\pi\) | ||
0.976218 | − | 0.216789i | \(-0.0695584\pi\) | |||||||
\(884\) | 28.0039 | 0.941874 | ||||||||
\(885\) | −15.7757 | − | 23.2663i | −0.530295 | − | 0.782088i | ||||
\(886\) | −10.9970 | −0.369451 | ||||||||
\(887\) | 32.9290i | 1.10565i | 0.833298 | + | 0.552823i | \(0.186450\pi\) | ||||
−0.833298 | + | 0.552823i | \(0.813550\pi\) | |||||||
\(888\) | − | 7.54808i | − | 0.253297i | ||||||
\(889\) | 44.0939 | 1.47886 | ||||||||
\(890\) | −5.92279 | − | 8.73503i | −0.198532 | − | 0.292799i | ||||
\(891\) | 55.8380 | 1.87064 | ||||||||
\(892\) | 10.1228i | 0.338936i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.41365 | 0.181060 | ||||||||
\(895\) | −0.416030 | + | 0.282089i | −0.0139063 | + | 0.00942919i | ||||
\(896\) | −32.9777 | −1.10171 | ||||||||
\(897\) | 2.07299i | 0.0692151i | ||||||||
\(898\) | − | 1.61502i | − | 0.0538940i | ||||||
\(899\) | −27.0176 | −0.901087 | ||||||||
\(900\) | −4.12569 | + | 10.3561i | −0.137523 | + | 0.345202i | ||||
\(901\) | 6.21897 | 0.207184 | ||||||||
\(902\) | 0.291338i | 0.00970049i | ||||||||
\(903\) | 55.2077i | 1.83720i | ||||||||
\(904\) | −5.14153 | −0.171005 | ||||||||
\(905\) | 46.0427 | − | 31.2192i | 1.53051 | − | 1.03776i | ||||
\(906\) | −5.55184 | −0.184447 | ||||||||
\(907\) | − | 34.1251i | − | 1.13311i | −0.824025 | − | 0.566553i | \(-0.808277\pi\) | ||
0.824025 | − | 0.566553i | \(-0.191723\pi\) | |||||||
\(908\) | 9.83659i | 0.326439i | ||||||||
\(909\) | 7.14455 | 0.236970 | ||||||||
\(910\) | 6.76366 | + | 9.97517i | 0.224213 | + | 0.330674i | ||||
\(911\) | −27.5938 | −0.914222 | −0.457111 | − | 0.889410i | \(-0.651116\pi\) | ||||
−0.457111 | + | 0.889410i | \(0.651116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 22.7252i | − | 0.752094i | ||||||
\(914\) | −12.6889 | −0.419712 | ||||||||
\(915\) | −12.8775 | − | 18.9920i | −0.425718 | − | 0.627857i | ||||
\(916\) | 32.4386 | 1.07180 | ||||||||
\(917\) | − | 28.0465i | − | 0.926178i | ||||||
\(918\) | 3.80117i | 0.125457i | ||||||||
\(919\) | −13.1572 | −0.434017 | −0.217009 | − | 0.976170i | \(-0.569630\pi\) | ||||
−0.217009 | + | 0.976170i | \(0.569630\pi\) | |||||||
\(920\) | −0.506008 | + | 0.343099i | −0.0166826 | + | 0.0113116i | ||||
\(921\) | −10.1115 | −0.333186 | ||||||||
\(922\) | 8.40674i | 0.276861i | ||||||||
\(923\) | 3.90846i | 0.128649i | ||||||||
\(924\) | 71.9330 | 2.36642 | ||||||||
\(925\) | 13.8709 | + | 5.52595i | 0.456073 | + | 0.181692i | ||||
\(926\) | −3.07404 | −0.101019 | ||||||||
\(927\) | 16.0891i | 0.528436i | ||||||||
\(928\) | − | 12.1627i | − | 0.399259i | ||||||
\(929\) | 23.5599 | 0.772975 | 0.386487 | − | 0.922295i | \(-0.373688\pi\) | ||||
0.386487 | + | 0.922295i | \(0.373688\pi\) | |||||||
\(930\) | 9.47427 | − | 6.42403i | 0.310674 | − | 0.210652i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.1050i | 0.986121i | ||||||||
\(933\) | − | 48.2683i | − | 1.58023i | ||||||
\(934\) | 1.83492 | 0.0600403 | ||||||||
\(935\) | −20.1914 | − | 29.7787i | −0.660330 | − | 0.973867i | ||||
\(936\) | 6.66838 | 0.217963 | ||||||||
\(937\) | − | 35.9997i | − | 1.17606i | −0.808839 | − | 0.588030i | \(-0.799904\pi\) | ||
0.808839 | − | 0.588030i | \(-0.200096\pi\) | |||||||
\(938\) | − | 13.2355i | − | 0.432156i | ||||||
\(939\) | −18.1673 | −0.592868 | ||||||||
\(940\) | 25.9501 | + | 38.2717i | 0.846399 | + | 1.24828i | ||||
\(941\) | 41.8515 | 1.36432 | 0.682160 | − | 0.731203i | \(-0.261041\pi\) | ||||
0.682160 | + | 0.731203i | \(0.261041\pi\) | |||||||
\(942\) | − | 7.34662i | − | 0.239366i | ||||||
\(943\) | 0.0404952i | 0.00131871i | ||||||||
\(944\) | 20.9590 | 0.682158 | ||||||||
\(945\) | 25.5451 | − | 17.3208i | 0.830981 | − | 0.563446i | ||||
\(946\) | −11.6127 | −0.377562 | ||||||||
\(947\) | 3.63656i | 0.118172i | 0.998253 | + | 0.0590861i | \(0.0188187\pi\) | ||||
−0.998253 | + | 0.0590861i | \(0.981181\pi\) | |||||||
\(948\) | − | 35.6857i | − | 1.15902i | ||||||
\(949\) | −23.6754 | −0.768535 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −60.4680 | −1.96081 | ||||||||
\(952\) | 14.6980i | 0.476365i | ||||||||
\(953\) | 10.7543i | 0.348366i | 0.984713 | + | 0.174183i | \(0.0557284\pi\) | ||||
−0.984713 | + | 0.174183i | \(0.944272\pi\) | |||||||
\(954\) | 0.721324 | 0.0233537 | ||||||||
\(955\) | −15.6182 | + | 10.5899i | −0.505393 | + | 0.342681i | ||||
\(956\) | 33.7488 | 1.09151 | ||||||||
\(957\) | 35.0221i | 1.13210i | ||||||||
\(958\) | − | 0.562218i | − | 0.0181644i | ||||||
\(959\) | −29.5444 | −0.954039 | ||||||||
\(960\) | −14.5728 | − | 21.4923i | −0.470336 | − | 0.693660i | ||||
\(961\) | 31.3666 | 1.01183 | ||||||||
\(962\) | − | 4.35052i | − | 0.140266i | ||||||
\(963\) | − | 20.3118i | − | 0.654538i | ||||||
\(964\) | −52.0080 | −1.67506 | ||||||||
\(965\) | 2.01217 | + | 2.96759i | 0.0647741 | + | 0.0955301i | ||||
\(966\) | −0.529964 | −0.0170513 | ||||||||
\(967\) | 18.7666i | 0.603493i | 0.953388 | + | 0.301747i | \(0.0975696\pi\) | ||||
−0.953388 | + | 0.301747i | \(0.902430\pi\) | |||||||
\(968\) | 17.4543i | 0.561002i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.802154 | − | 0.543900i | 0.0257556 | − | 0.0174636i | ||||
\(971\) | −38.4930 | −1.23530 | −0.617650 | − | 0.786453i | \(-0.711915\pi\) | ||||
−0.617650 | + | 0.786453i | \(0.711915\pi\) | |||||||
\(972\) | − | 21.9827i | − | 0.705096i | ||||||
\(973\) | − | 9.82805i | − | 0.315073i | ||||||
\(974\) | 5.14426 | 0.164833 | ||||||||
\(975\) | −17.3586 | + | 43.5726i | −0.555921 | + | 1.39544i | ||||
\(976\) | 17.1086 | 0.547633 | ||||||||
\(977\) | 21.7651i | 0.696328i | 0.937434 | + | 0.348164i | \(0.113195\pi\) | ||||
−0.937434 | + | 0.348164i | \(0.886805\pi\) | |||||||
\(978\) | 3.01455i | 0.0963946i | ||||||||
\(979\) | −74.5361 | −2.38218 | ||||||||
\(980\) | 23.5064 | − | 15.9385i | 0.750884 | − | 0.509137i | ||||
\(981\) | 16.1418 | 0.515367 | ||||||||
\(982\) | 5.86569i | 0.187182i | ||||||||
\(983\) | − | 32.9796i | − | 1.05189i | −0.850520 | − | 0.525943i | \(-0.823712\pi\) | ||
0.850520 | − | 0.525943i | \(-0.176288\pi\) | |||||||
\(984\) | 0.463182 | 0.0147657 | ||||||||
\(985\) | 2.52590 | + | 3.72524i | 0.0804817 | + | 0.118696i | ||||
\(986\) | −3.48564 | −0.111005 | ||||||||
\(987\) | 82.2918i | 2.61938i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.61414 | −0.0513266 | ||||||||
\(990\) | −2.34196 | − | 3.45396i | −0.0744322 | − | 0.109774i | ||||
\(991\) | −44.9400 | −1.42757 | −0.713783 | − | 0.700367i | \(-0.753020\pi\) | ||||
−0.713783 | + | 0.700367i | \(0.753020\pi\) | |||||||
\(992\) | 28.0759i | 0.891412i | ||||||||
\(993\) | 52.8862i | 1.67829i | ||||||||
\(994\) | −0.999208 | −0.0316929 | ||||||||
\(995\) | 9.32205 | − | 6.32082i | 0.295529 | − | 0.200383i | ||||
\(996\) | −17.5983 | −0.557625 | ||||||||
\(997\) | 1.52970i | 0.0484462i | 0.999707 | + | 0.0242231i | \(0.00771120\pi\) | ||||
−0.999707 | + | 0.0242231i | \(0.992289\pi\) | |||||||
\(998\) | 5.48412i | 0.173597i | ||||||||
\(999\) | −11.1411 | −0.352488 |
(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 | 1805.2.b.i.1084.9 | yes | 16 | |
5.2 | odd | 4 | 9025.2.a.cl.1.8 | 16 | |||
5.3 | odd | 4 | 9025.2.a.cl.1.9 | 16 | |||
5.4 | even | 2 | inner | 1805.2.b.i.1084.8 | ✓ | 16 | |
19.18 | odd | 2 | 1805.2.b.j.1084.8 | yes | 16 | ||
95.18 | even | 4 | 9025.2.a.ck.1.8 | 16 | |||
95.37 | even | 4 | 9025.2.a.ck.1.9 | 16 | |||
95.94 | odd | 2 | 1805.2.b.j.1084.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.i.1084.8 | ✓ | 16 | 5.4 | even | 2 | inner | |
1805.2.b.i.1084.9 | yes | 16 | 1.1 | even | 1 | trivial | |
1805.2.b.j.1084.8 | yes | 16 | 19.18 | odd | 2 | ||
1805.2.b.j.1084.9 | yes | 16 | 95.94 | odd | 2 | ||
9025.2.a.ck.1.8 | 16 | 95.18 | even | 4 | |||
9025.2.a.ck.1.9 | 16 | 95.37 | even | 4 | |||
9025.2.a.cl.1.8 | 16 | 5.2 | odd | 4 | |||
9025.2.a.cl.1.9 | 16 | 5.3 | odd | 4 |