Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(703,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.q (of order \(6\), degree \(2\), 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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} - 24 x^{13} + 104 x^{12} - 196 x^{11} + 312 x^{10} - 236 x^{9} + 31 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 831.1 | ||
Root | \(-1.79700 + 2.34189i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.831 |
Dual form | 896.2.q.c.703.1 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −2.63287 | + | 1.52009i | −1.52009 | + | 0.877622i | −0.520366 | + | 0.853943i | \(0.674204\pi\) |
−0.999720 | + | 0.0236785i | \(0.992462\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.866025 | + | 1.50000i | −0.387298 | + | 0.670820i | −0.992085 | − | 0.125567i | \(-0.959925\pi\) |
0.604787 | + | 0.796387i | \(0.293258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.14973 | + | 1.54230i | 0.812520 | + | 0.582933i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.12132 | − | 5.40629i | 1.04044 | − | 1.80210i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09057 | + | 1.88892i | 0.328819 | + | 0.569531i | 0.982278 | − | 0.187431i | \(-0.0600161\pi\) |
−0.653459 | + | 0.756962i | \(0.726683\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.91359 | 1.64014 | 0.820068 | − | 0.572267i | \(-0.193936\pi\) | ||||
0.820068 | + | 0.572267i | \(0.193936\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.26573i | − | 1.35961i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.62132 | − | 2.09077i | 0.878299 | − | 0.507086i | 0.00820195 | − | 0.999966i | \(-0.497389\pi\) |
0.870097 | + | 0.492880i | \(0.164056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.27171 | + | 1.88892i | 0.750581 | + | 0.433348i | 0.825904 | − | 0.563811i | \(-0.190665\pi\) |
−0.0753229 | + | 0.997159i | \(0.523999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.00436 | − | 0.792893i | −1.74669 | − | 0.173023i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.88892 | − | 1.09057i | −0.393867 | − | 0.227399i | 0.289967 | − | 0.957037i | \(-0.406356\pi\) |
−0.683834 | + | 0.729637i | \(0.739689\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 1.73205i | 0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.85818i | 1.89721i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.41421i | − | 1.37678i | −0.725338 | − | 0.688392i | \(-0.758317\pi\) | ||
0.725338 | − | 0.688392i | \(-0.241683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.03865 | + | 6.99514i | 0.725362 | + | 1.25636i | 0.958825 | + | 0.283998i | \(0.0916610\pi\) |
−0.233463 | + | 0.972366i | \(0.575006\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.74264 | − | 3.31552i | −0.999665 | − | 0.577157i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.17516 | + | 1.88892i | −0.705731 | + | 0.319286i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.07616 | − | 0.621320i | −0.176919 | − | 0.102144i | 0.408925 | − | 0.912568i | \(-0.365904\pi\) |
−0.585844 | + | 0.810424i | \(0.699237\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.5697 | + | 8.98916i | −2.49315 | + | 1.43942i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.34847i | 1.14764i | 0.818982 | + | 0.573819i | \(0.194539\pi\) | ||||
−0.818982 | + | 0.573819i | \(0.805461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.16919 | −0.940792 | −0.470396 | − | 0.882455i | \(-0.655889\pi\) | ||||
−0.470396 | + | 0.882455i | \(0.655889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.40629 | + | 9.36396i | 0.805921 | + | 1.39590i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.56026 | − | 7.89860i | 0.665182 | − | 1.15213i | −0.314054 | − | 0.949405i | \(-0.601687\pi\) |
0.979236 | − | 0.202724i | \(-0.0649793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.24264 | + | 6.63103i | 0.320377 | + | 0.947290i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.35630 | + | 11.0094i | −0.890060 | + | 1.54163i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.37333 | + | 0.792893i | −0.188642 | + | 0.108912i | −0.591346 | − | 0.806418i | \(-0.701403\pi\) |
0.402705 | + | 0.915330i | \(0.368070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.77784 | −0.509404 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.4853 | −1.52126 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.63287 | + | 1.52009i | −0.342770 | + | 0.197898i | −0.661496 | − | 0.749948i | \(-0.730078\pi\) |
0.318726 | + | 0.947847i | \(0.396745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.07616 | − | 1.86396i | 0.137788 | − | 0.238656i | −0.788871 | − | 0.614559i | \(-0.789334\pi\) |
0.926659 | + | 0.375903i | \(0.122667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.0481 | − | 6.80803i | 1.89588 | − | 0.857731i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.12132 | + | 8.87039i | −0.635222 | + | 1.10024i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.81400 | + | 8.33810i | 0.588124 | + | 1.01866i | 0.994478 | + | 0.104945i | \(0.0334666\pi\) |
−0.406354 | + | 0.913716i | \(0.633200\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.63103 | 0.798282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.72455i | − | 1.03541i | −0.855558 | − | 0.517707i | \(-0.826786\pi\) | ||
0.855558 | − | 0.517707i | \(-0.173214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7426 | + | 6.77962i | −1.37437 | + | 0.793494i | −0.991475 | − | 0.130297i | \(-0.958407\pi\) |
−0.382897 | + | 0.923791i | \(0.625074\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.26573 | − | 3.04017i | −0.608034 | − | 0.351049i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.568852 | + | 5.74264i | −0.0648268 | + | 0.654435i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.23159 | − | 4.17516i | −0.813618 | − | 0.469742i | 0.0345928 | − | 0.999401i | \(-0.488987\pi\) |
−0.848211 | + | 0.529659i | \(0.822320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.62132 | − | 9.73641i | −0.624591 | − | 1.08182i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.1607i | − | 1.33481i | −0.744696 | − | 0.667404i | \(-0.767405\pi\) | ||
0.744696 | − | 0.667404i | \(-0.232595\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.24264i | 0.785575i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.2702 | + | 19.5206i | 1.20830 | + | 2.09283i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.98528 | + | 5.76500i | 1.05844 | + | 0.611089i | 0.925000 | − | 0.379968i | \(-0.124065\pi\) |
0.133438 | + | 0.991057i | \(0.457398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.7126 | + | 9.12051i | 1.33264 | + | 0.956090i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.2664 | − | 12.2782i | −2.20523 | − | 1.27319i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.66676 | + | 3.27171i | −0.581397 | + | 0.335670i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.91359i | 0.600434i | 0.953871 | + | 0.300217i | \(0.0970591\pi\) | ||||
−0.953871 | + | 0.300217i | \(0.902941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.6161 | 1.36847 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.03295 | + | 6.98528i | 0.401294 | + | 0.695061i | 0.993882 | − | 0.110444i | \(-0.0352273\pi\) |
−0.592588 | + | 0.805505i | \(0.701894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.93214 | + | 5.07862i | −0.288913 | + | 0.500411i | −0.973550 | − | 0.228472i | \(-0.926627\pi\) |
0.684638 | + | 0.728883i | \(0.259960\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.12132 | − | 11.3199i | 0.792560 | − | 1.10471i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.17516 | − | 7.23159i | 0.403628 | − | 0.699105i | −0.590533 | − | 0.807014i | \(-0.701082\pi\) |
0.994161 | + | 0.107909i | \(0.0344156\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.59808 | − | 1.50000i | 0.248851 | − | 0.143674i | −0.370387 | − | 0.928877i | \(-0.620775\pi\) |
0.619238 | + | 0.785203i | \(0.287442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.77784 | 0.358577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.27171 | − | 1.88892i | 0.305088 | − | 0.176143i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.4582 | − | 31.9706i | 1.70646 | − | 2.95568i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.0094 | + | 1.09057i | 1.00923 | + | 0.0999723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.12132 | − | 5.40629i | 0.283756 | − | 0.491480i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.1703 | − | 19.3475i | −1.00719 | − | 1.74451i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 21.0629i | − | 1.86903i | −0.355921 | − | 0.934516i | \(-0.615833\pi\) | ||
0.355921 | − | 0.934516i | \(-0.384167\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.2426 | − | 9.37769i | 1.43008 | − | 0.825660i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.91055 | − | 2.25775i | −0.341666 | − | 0.197261i | 0.319343 | − | 0.947639i | \(-0.396538\pi\) |
−0.661009 | + | 0.750378i | \(0.729871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.11999 | + | 9.10660i | 0.357249 | + | 0.789643i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.7873 | − | 8.53744i | −1.27269 | − | 0.734786i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.37868 | + | 4.11999i | 0.203224 | + | 0.351995i | 0.949566 | − | 0.313569i | \(-0.101525\pi\) |
−0.746341 | + | 0.665564i | \(0.768191\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6853i | 0.906319i | 0.891429 | + | 0.453160i | \(0.149703\pi\) | ||||
−0.891429 | + | 0.453160i | \(0.850297\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.7279i | 2.33511i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.44918 | + | 11.1703i | 0.539307 | + | 0.934108i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.1213 | + | 6.42090i | 0.923575 | + | 0.533226i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.9843 | − | 14.0496i | −1.31836 | − | 1.15879i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.45322 | − | 2.57107i | −0.364822 | − | 0.210630i | 0.306372 | − | 0.951912i | \(-0.400885\pi\) |
−0.671194 | + | 0.741282i | \(0.734218\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.99542 | + | 1.72941i | −0.243764 | + | 0.140737i | −0.616906 | − | 0.787037i | \(-0.711614\pi\) |
0.373141 | + | 0.927774i | \(0.378281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 26.1039i | − | 2.11037i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.9903 | −1.12373 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.83743 | − | 8.37868i | −0.386069 | − | 0.668691i | 0.605848 | − | 0.795581i | \(-0.292834\pi\) |
−0.991917 | + | 0.126889i | \(0.959501\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.41053 | − | 4.17516i | 0.191168 | − | 0.331112i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.37868 | − | 5.25770i | −0.187466 | − | 0.414365i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.72941 | − | 2.99542i | 0.135458 | − | 0.234620i | −0.790314 | − | 0.612701i | \(-0.790083\pi\) |
0.925772 | + | 0.378082i | \(0.123416\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.94655 | − | 5.74264i | 0.774338 | − | 0.447064i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.5837 | −1.82496 | −0.912481 | − | 0.409120i | \(-0.865836\pi\) | ||||
−0.912481 | + | 0.409120i | \(0.865836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.9706 | 1.69004 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.4241 | − | 11.7919i | 1.56187 | − | 0.901745i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.70719 | − | 13.3492i | 0.585967 | − | 1.01492i | −0.408787 | − | 0.912630i | \(-0.634048\pi\) |
0.994754 | − | 0.102294i | \(-0.0326184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.521611 | + | 5.26573i | −0.0394301 | + | 0.398052i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.62132 | − | 8.00436i | 0.347360 | − | 0.601645i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.187112 | − | 0.324087i | −0.0139854 | − | 0.0242234i | 0.858948 | − | 0.512063i | \(-0.171119\pi\) |
−0.872933 | + | 0.487839i | \(0.837785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.95743 | −0.665800 | −0.332900 | − | 0.942962i | \(-0.608027\pi\) | ||||
−0.332900 | + | 0.942962i | \(0.608027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.54341i | 0.483703i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.86396 | − | 1.07616i | 0.137041 | − | 0.0791207i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.89860 | + | 4.56026i | 0.577603 | + | 0.333479i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.2042 | + | 21.1924i | −1.10595 | + | 1.54152i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6808 | + | 7.89860i | 0.989906 | + | 0.571522i | 0.905246 | − | 0.424888i | \(-0.139686\pi\) |
0.0846597 | + | 0.996410i | \(0.473020\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.37868 | − | 7.58410i | −0.315184 | − | 0.545915i | 0.664292 | − | 0.747473i | \(-0.268733\pi\) |
−0.979477 | + | 0.201558i | \(0.935400\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 31.1394i | − | 2.22994i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0711i | 0.931275i | 0.884976 | + | 0.465638i | \(0.154175\pi\) | ||||
−0.884976 | + | 0.465638i | \(0.845825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.260805 | + | 0.451728i | 0.0184880 | + | 0.0320222i | 0.875121 | − | 0.483903i | \(-0.160781\pi\) |
−0.856633 | + | 0.515926i | \(0.827448\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.3492 | − | 14.6354i | −1.78800 | − | 1.03230i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4349 | − | 15.9385i | 0.802574 | − | 1.11867i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.0227 | − | 6.36396i | −0.769859 | − | 0.444478i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.7919 | + | 6.80803i | −0.819590 | + | 0.473191i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.23999i | 0.569972i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.4252 | 1.75034 | 0.875171 | − | 0.483813i | \(-0.160749\pi\) | ||||
0.875171 | + | 0.483813i | \(0.160749\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.2621 | + | 22.9706i | 0.908701 | + | 1.57392i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.34267 | − | 9.25378i | 0.364367 | − | 0.631103i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.10660 | + | 21.2664i | −0.143005 | + | 1.44366i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.6112 | − | 35.6996i | 1.39278 | − | 2.41236i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.4150 | − | 12.3640i | 1.44053 | − | 0.831690i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.04322 | 0.0698593 | 0.0349296 | − | 0.999390i | \(-0.488879\pi\) | ||||
0.0349296 | + | 0.999390i | \(0.488879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.4853 | 0.832352 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0808 | + | 8.70693i | −1.00095 | + | 0.577899i | −0.908530 | − | 0.417821i | \(-0.862794\pi\) |
−0.0924215 | + | 0.995720i | \(0.529461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.75039 | − | 8.22792i | 0.313915 | − | 0.543716i | −0.665291 | − | 0.746584i | \(-0.731693\pi\) |
0.979206 | + | 0.202867i | \(0.0650260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.23159 | − | 15.9843i | −0.475804 | − | 1.05169i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.10660 | + | 15.7731i | −0.596593 | + | 1.03333i | 0.396727 | + | 0.917937i | \(0.370146\pi\) |
−0.993320 | + | 0.115393i | \(0.963187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.89860 | + | 13.6808i | 0.515248 | + | 0.892435i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.3864 | 1.64902 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.25378i | 0.598577i | 0.954163 | + | 0.299289i | \(0.0967494\pi\) | ||||
−0.954163 | + | 0.299289i | \(0.903251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2279 | + | 6.48244i | −0.723254 | + | 0.417571i | −0.815949 | − | 0.578124i | \(-0.803785\pi\) |
0.0926951 | + | 0.995695i | \(0.470452\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.98805 | + | 2.30250i | 0.255834 | + | 0.147706i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.8887 | − | 2.37868i | −0.759543 | − | 0.151968i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.3475 | + | 11.1703i | 1.23105 | + | 0.710749i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.4853 | + | 32.0174i | 1.17146 | + | 2.02902i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.737669i | − | 0.0465613i | −0.999729 | − | 0.0232806i | \(-0.992589\pi\) | ||
0.999729 | − | 0.0232806i | \(-0.00741113\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.75736i | − | 0.299093i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.0094 | − | 19.0689i | −0.689437 | − | 1.19414i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.86396 | + | 1.07616i | 0.116271 | + | 0.0671289i | 0.557008 | − | 0.830507i | \(-0.311949\pi\) |
−0.440737 | + | 0.897636i | \(0.645283\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.35518 | − | 2.99542i | −0.0842071 | − | 0.186127i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.0834 | − | 23.1421i | −2.48110 | − | 1.43246i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2224 | − | 7.63398i | 0.815331 | − | 0.470731i | −0.0334730 | − | 0.999440i | \(-0.510657\pi\) |
0.848804 | + | 0.528708i | \(0.177323\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.74666i | − | 0.168726i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.0532 | −2.14522 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.97514 | + | 10.3492i | 0.364311 | + | 0.631004i | 0.988665 | − | 0.150137i | \(-0.0479713\pi\) |
−0.624355 | + | 0.781141i | \(0.714638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.93214 | + | 5.07862i | −0.178115 | + | 0.308504i | −0.941235 | − | 0.337753i | \(-0.890333\pi\) |
0.763120 | + | 0.646257i | \(0.223667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −47.3345 | − | 4.68885i | −2.86482 | − | 0.283782i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.18114 | + | 3.77784i | −0.131528 | + | 0.227812i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.0131 | + | 13.8640i | −1.44281 | + | 0.833005i | −0.998036 | − | 0.0626400i | \(-0.980048\pi\) |
−0.444770 | + | 0.895645i | \(0.646715\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 50.4236 | 3.01878 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.2426 | −0.968955 | −0.484477 | − | 0.874804i | \(-0.660990\pi\) | ||||
−0.484477 | + | 0.874804i | \(0.660990\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.98208 | + | 3.45375i | −0.355597 | + | 0.205304i | −0.667148 | − | 0.744925i | \(-0.732485\pi\) |
0.311550 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.94655 | − | 17.2279i | 0.589183 | − | 1.02049i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3335 | + | 15.7972i | −0.668997 | + | 0.932479i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.242641 | − | 0.420266i | 0.0142730 | − | 0.0247215i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.98916 | − | 15.5697i | −0.526954 | − | 0.912711i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.2913 | 0.893326 | 0.446663 | − | 0.894702i | \(-0.352612\pi\) | ||||
0.446663 | + | 0.894702i | \(0.352612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.26573i | − | 0.306583i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.6213 | + | 10.7510i | −1.08052 | + | 0.623838i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.1703 | − | 6.44918i | −0.645995 | − | 0.372966i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.2621 | − | 9.51472i | −0.764412 | − | 0.548419i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.2365 | − | 12.2609i | −1.22000 | − | 0.704369i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.86396 | + | 3.22848i | 0.106730 | + | 0.184862i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.55568i | 0.431225i | 0.976479 | + | 0.215613i | \(0.0691749\pi\) | ||||
−0.976479 | + | 0.215613i | \(0.930825\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 17.8284i | − | 1.01422i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.5743 | − | 21.7793i | −0.713021 | − | 1.23499i | −0.963718 | − | 0.266923i | \(-0.913993\pi\) |
0.250697 | − | 0.968066i | \(-0.419340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7426 | − | 10.2437i | −1.00287 | − | 0.579009i | −0.0937762 | − | 0.995593i | \(-0.529894\pi\) |
−0.909097 | + | 0.416584i | \(0.863227\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.81998 | + | 28.4680i | −0.158888 | + | 1.60399i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.61332 | + | 5.55025i | 0.539938 | + | 0.311733i | 0.745054 | − | 0.667004i | \(-0.232424\pi\) |
−0.205116 | + | 0.978738i | \(0.565757\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0049 | − | 8.08571i | 0.784121 | − | 0.452713i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.3864i | 1.41693i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.7972 | 0.878979 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.91359 | + | 10.2426i | 0.328027 | + | 0.568159i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.56026 | + | 7.89860i | −0.252183 | + | 0.436793i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.9853 | − | 9.94655i | 1.21209 | − | 0.548371i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9832 | + | 19.0234i | −0.603691 | + | 1.04562i | 0.388566 | + | 0.921421i | \(0.372970\pi\) |
−0.992257 | + | 0.124202i | \(0.960363\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.71807 | + | 3.87868i | −0.368148 | + | 0.212550i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.6762 | −0.911118 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.24264 | 0.122164 | 0.0610822 | − | 0.998133i | \(-0.480545\pi\) | ||||
0.0610822 | + | 0.998133i | \(0.480545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.1703 | − | 6.44918i | 0.606688 | − | 0.350271i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.80884 | + | 15.2574i | −0.477025 | + | 0.826232i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.40596 | + | 17.7137i | −0.291894 | + | 0.956451i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.74264 | + | 9.94655i | −0.309173 | + | 0.535504i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0678 | − | 24.3661i | −0.755198 | − | 1.30804i | −0.945276 | − | 0.326273i | \(-0.894207\pi\) |
0.190078 | − | 0.981769i | \(-0.439126\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.8726 | 1.81316 | 0.906579 | − | 0.422036i | \(-0.138684\pi\) | ||||
0.906579 | + | 0.422036i | \(0.138684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 58.2973i | 3.11168i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.65076 | − | 0.953065i | 0.0878610 | − | 0.0507265i | −0.455426 | − | 0.890274i | \(-0.650513\pi\) |
0.543287 | + | 0.839547i | \(0.317180\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.0868 | + | 7.55568i | 0.694576 | + | 0.401014i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −30.6441 | + | 13.8640i | −1.62186 | + | 0.733759i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.43059 | + | 0.825952i | 0.0755037 | + | 0.0435921i | 0.537277 | − | 0.843406i | \(-0.319453\pi\) |
−0.461773 | + | 0.886998i | \(0.652786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.36396 | − | 4.09450i | −0.124419 | − | 0.215500i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.9787i | 0.996123i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 23.4853i | − | 1.22928i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.96621 | − | 17.2620i | −0.520232 | − | 0.901068i | −0.999723 | − | 0.0235217i | \(-0.992512\pi\) |
0.479491 | − | 0.877547i | \(-0.340821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 39.7279 | + | 22.9369i | 2.06815 | + | 1.19405i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.17516 | − | 0.413582i | −0.216764 | − | 0.0214721i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.11999 | + | 2.37868i | 0.213325 | + | 0.123163i | 0.602856 | − | 0.797850i | \(-0.294029\pi\) |
−0.389531 | + | 0.921014i | \(0.627363\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.9218 | − | 18.4301i | 1.64843 | − | 0.951724i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 43.8446i | − | 2.25811i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.4274 | 1.81978 | 0.909892 | − | 0.414844i | \(-0.136164\pi\) | ||||
0.909892 | + | 0.414844i | \(0.136164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.0174 | + | 55.4558i | 1.64030 | + | 2.84109i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.4586 | + | 30.2392i | −0.892093 | + | 1.54515i | −0.0547321 | + | 0.998501i | \(0.517430\pi\) |
−0.837361 | + | 0.546650i | \(0.815903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.12132 | − | 5.82655i | −0.413901 | − | 0.296949i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.2560 | + | 33.3524i | −0.978838 | + | 1.69540i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.148586 | + | 0.0857864i | −0.00753363 | + | 0.00434955i | −0.503762 | − | 0.863842i | \(-0.668051\pi\) |
0.496228 | + | 0.868192i | \(0.334718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.12051 | −0.461244 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.7279 | 0.692482 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.5255 | − | 7.23159i | 0.630226 | − | 0.363861i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.75039 | − | 8.22792i | 0.238415 | − | 0.412948i | −0.721844 | − | 0.692055i | \(-0.756705\pi\) |
0.960260 | + | 0.279108i | \(0.0900387\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −24.6902 | − | 17.7137i | −1.23606 | − | 0.886795i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.37868 | − | 4.11999i | 0.118786 | − | 0.205743i | −0.800501 | − | 0.599331i | \(-0.795433\pi\) |
0.919287 | + | 0.393589i | \(0.128767\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.8829 | + | 41.3664i | 1.18969 | + | 2.06061i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.4728 | 0.967612 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.71037i | − | 0.134348i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3492 | − | 5.97514i | 0.511737 | − | 0.295452i | −0.221810 | − | 0.975090i | \(-0.571197\pi\) |
0.733547 | + | 0.679638i | \(0.237863\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.5255 | − | 7.23159i | −0.617837 | − | 0.356708i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00436 | − | 0.792893i | −0.393869 | − | 0.0390157i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.2410 | + | 10.5315i | 0.895417 | + | 0.516969i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.2426 | − | 28.1331i | −0.795406 | − | 1.37768i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.08034i | 0.297044i | 0.988909 | + | 0.148522i | \(0.0474516\pi\) | ||||
−0.988909 | + | 0.148522i | \(0.952548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16.2426i | − | 0.791618i | −0.918333 | − | 0.395809i | \(-0.870464\pi\) | ||
0.918333 | − | 0.395809i | \(-0.129536\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.4680 | − | 49.3081i | −1.38416 | − | 2.39744i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.24264 | + | 4.18154i | 0.351320 | + | 0.202835i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.18823 | − | 2.34725i | 0.251076 | − | 0.113591i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33.9596 | − | 19.6066i | −1.63959 | − | 0.946616i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.6808 | − | 7.89860i | 0.658980 | − | 0.380462i | −0.132909 | − | 0.991128i | \(-0.542432\pi\) |
0.791888 | + | 0.610666i | \(0.209098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.6823i | − | 0.657531i | −0.944412 | − | 0.328765i | \(-0.893367\pi\) | ||
0.944412 | − | 0.328765i | \(-0.106633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −39.0413 | −1.87188 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.11999 | − | 7.13604i | −0.197086 | − | 0.341363i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4245 | − | 18.0558i | 0.497536 | − | 0.861758i | −0.502460 | − | 0.864601i | \(-0.667572\pi\) |
0.999996 | + | 0.00284264i | \(0.000904841\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 42.8492 | + | 8.57321i | 2.04044 | + | 0.408248i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.53744 | + | 14.7873i | −0.405626 | + | 0.702565i | −0.994394 | − | 0.105737i | \(-0.966280\pi\) |
0.588768 | + | 0.808302i | \(0.299613\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.2950 | + | 9.98528i | −0.819862 | + | 0.473348i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.6330 | 0.739414 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7574 | 0.649250 | 0.324625 | − | 0.945843i | \(-0.394762\pi\) | ||||
0.324625 | + | 0.945843i | \(0.394762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8807 | + | 8.01401i | −0.653615 | + | 0.377365i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.25770 | − | 9.10660i | 0.247028 | − | 0.427865i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.6902 | + | 11.1703i | −1.15749 | + | 0.523672i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.74264 | − | 16.8747i | 0.455742 | − | 0.789367i | −0.542989 | − | 0.839740i | \(-0.682707\pi\) |
0.998731 | + | 0.0503724i | \(0.0160408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.6112 | + | 35.6996i | 0.962048 | + | 1.66632i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.1757 | −0.893099 | −0.446550 | − | 0.894759i | \(-0.647347\pi\) | ||||
−0.446550 | + | 0.894759i | \(0.647347\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.36227i | − | 0.202732i | −0.994849 | − | 0.101366i | \(-0.967679\pi\) | ||
0.994849 | − | 0.101366i | \(-0.0323213\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.8345 | − | 21.2664i | 1.70816 | − | 0.986207i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.6838 | − | 15.9833i | −1.28106 | − | 0.739618i | −0.304014 | − | 0.952668i | \(-0.598327\pi\) |
−0.977041 | + | 0.213050i | \(0.931660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51104 | + | 25.3492i | −0.115949 | + | 1.17052i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.4726 | + | 14.7066i | 1.17372 | + | 0.677645i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.72792 | − | 11.6531i | −0.309350 | − | 0.535810i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.55568i | 0.346678i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.89949i | 0.453267i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.79643 | + | 15.2359i | 0.401919 | + | 0.696144i | 0.993958 | − | 0.109766i | \(-0.0350100\pi\) |
−0.592039 | + | 0.805910i | \(0.701677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.36396 | − | 3.67423i | −0.290172 | − | 0.167531i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.2549 | + | 10.2270i | 0.648620 | + | 0.465345i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.87039 | − | 5.12132i | −0.402784 | − | 0.232547i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5651 | − | 10.7186i | 0.841266 | − | 0.485705i | −0.0164286 | − | 0.999865i | \(-0.505230\pi\) |
0.857694 | + | 0.514160i | \(0.171896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.5154i | 0.475523i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.1475 | −1.08976 | −0.544881 | − | 0.838513i | \(-0.683425\pi\) | ||||
−0.544881 | + | 0.838513i | \(0.683425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.5014 | − | 26.8492i | −0.698149 | − | 1.20923i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.7919 | + | 20.4241i | −0.530004 | + | 0.917994i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.4558 | − | 18.7554i | 0.603577 | − | 0.841294i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.35518 | + | 2.34725i | −0.0606664 | + | 0.105077i | −0.894763 | − | 0.446540i | \(-0.852656\pi\) |
0.834097 | + | 0.551618i | \(0.185989\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 62.0927 | − | 35.8492i | 2.77410 | − | 1.60163i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.12967 | −0.139545 | −0.0697724 | − | 0.997563i | \(-0.522227\pi\) | ||||
−0.0697724 | + | 0.997563i | \(0.522227\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.9706 | −0.621682 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −57.8455 | + | 33.3971i | −2.56901 | + | 1.48322i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.61269 | − | 6.25736i | 0.160130 | − | 0.277353i | −0.774785 | − | 0.632224i | \(-0.782142\pi\) |
0.934915 | + | 0.354872i | \(0.115475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.6996 | − | 3.53632i | −1.57926 | − | 0.156438i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.6213 | + | 32.2531i | −0.822151 | + | 1.42401i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.07862 | − | 8.79643i | −0.223791 | − | 0.387617i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.8931 | 0.874897 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.8623i | 2.05703i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.7426 | + | 11.9758i | −0.908752 | + | 0.524668i | −0.880029 | − | 0.474919i | \(-0.842477\pi\) |
−0.0287223 | + | 0.999587i | \(0.509144\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.6123 | + | 14.7873i | 1.11995 | + | 0.646602i | 0.941388 | − | 0.337327i | \(-0.109523\pi\) |
0.178560 | + | 0.983929i | \(0.442856\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.63103 | − | 14.6569i | −0.289402 | − | 0.639678i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.2505 | + | 16.8878i | 1.27417 | + | 0.735642i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.12132 | − | 15.7986i | −0.396579 | − | 0.686895i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.9787i | 0.823605i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.4558i | 1.88228i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.23159 | + | 12.5255i | 0.312649 | + | 0.541524i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.985281 | + | 0.568852i | 0.0425180 | + | 0.0245478i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.0797 | + | 11.4678i | −0.434165 | + | 0.493952i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.1865 | + | 10.5000i | 0.781900 | + | 0.451430i | 0.837103 | − | 0.547045i | \(-0.184247\pi\) |
−0.0552031 | + | 0.998475i | \(0.517581\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.5837 | − | 13.6161i | 1.01207 | − | 0.584321i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.19615i | 0.222579i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.25378 | −0.395663 | −0.197832 | − | 0.980236i | \(-0.563390\pi\) | ||||
−0.197832 | + | 0.980236i | \(0.563390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.71807 | − | 11.6360i | −0.286720 | − | 0.496614i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0049 | − | 24.2571i | 0.596627 | − | 1.03339i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.10660 | − | 20.1287i | −0.387252 | − | 0.855960i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.27171 | + | 5.66676i | −0.138876 | + | 0.240541i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.6799 | + | 13.6716i | −1.00335 | + | 0.579283i | −0.909237 | − | 0.416279i | \(-0.863334\pi\) |
−0.0941107 | + | 0.995562i | \(0.530001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.4821 | −1.54303 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.7279 | −1.17067 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.1643 | − | 7.60043i | 0.554810 | − | 0.320320i | −0.196250 | − | 0.980554i | \(-0.562876\pi\) |
0.751060 | + | 0.660234i | \(0.229543\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.67423 | − | 6.36396i | 0.154576 | − | 0.267734i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.93214 | − | 29.6004i | 0.123138 | − | 1.24310i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.74264 | − | 9.94655i | 0.240744 | − | 0.416981i | −0.720182 | − | 0.693785i | \(-0.755942\pi\) |
0.960926 | + | 0.276804i | \(0.0892752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.44089 | − | 16.3521i | −0.395089 | − | 0.684314i | 0.598023 | − | 0.801479i | \(-0.295953\pi\) |
−0.993113 | + | 0.117164i | \(0.962620\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −48.0262 | −2.00632 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.36227i | − | 0.181919i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5000 | − | 14.7224i | 1.06158 | − | 0.612903i | 0.135710 | − | 0.990749i | \(-0.456668\pi\) |
0.925869 | + | 0.377846i | \(0.123335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.0569 | + | 13.3119i | 0.958214 | + | 0.553225i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.7554 | − | 26.1421i | 0.778105 | − | 1.08456i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.99542 | − | 1.72941i | −0.124058 | − | 0.0716248i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.9706 | + | 55.3746i | 1.32182 | + | 2.28946i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.65433i | − | 0.0682814i | −0.999417 | − | 0.0341407i | \(-0.989131\pi\) | ||
0.999417 | − | 0.0341407i | \(-0.0108694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.5147i | 1.25734i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8691 | − | 34.4144i | −0.817307 | − | 1.41562i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.86396 | − | 1.07616i | −0.0765437 | − | 0.0441925i | 0.461240 | − | 0.887276i | \(-0.347405\pi\) |
−0.537783 | + | 0.843083i | \(0.680738\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.1703 | + | 15.5697i | −0.457938 | + | 0.638295i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.37333 | − | 0.792893i | −0.0562067 | − | 0.0324510i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4726 | − | 14.7066i | 1.04078 | − | 0.600896i | 0.120728 | − | 0.992686i | \(-0.461477\pi\) |
0.920055 | + | 0.391789i | \(0.128144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.4511i | 0.875007i | 0.899217 | + | 0.437504i | \(0.144137\pi\) | ||||
−0.899217 | + | 0.437504i | \(0.855863\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 60.1042 | 2.44763 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.40629 | + | 9.36396i | 0.219797 | + | 0.380699i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.38132 | − | 16.2489i | 0.380776 | − | 0.659523i | −0.610397 | − | 0.792095i | \(-0.708990\pi\) |
0.991173 | + | 0.132572i | \(0.0423236\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.87868 | + | 59.3460i | −0.238216 | + | 2.40482i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.9675 | − | 46.7091i | 1.09099 | − | 1.88965i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.64191 | − | 3.25736i | 0.227875 | − | 0.131564i | −0.381717 | − | 0.924279i | \(-0.624667\pi\) |
0.609591 | + | 0.792716i | \(0.291334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.6951 | 1.56034 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.2132 | −1.57866 | −0.789332 | − | 0.613967i | \(-0.789573\pi\) | ||||
−0.789332 | + | 0.613967i | \(0.789573\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.7826 | − | 21.2365i | 1.47842 | − | 0.853565i | 0.478716 | − | 0.877970i | \(-0.341102\pi\) |
0.999702 | + | 0.0244049i | \(0.00776908\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.7510 | − | 18.6213i | 0.431424 | − | 0.747248i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.5743 | + | 27.7934i | 0.503777 | + | 1.11352i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.5255 | − | 21.6948i | −0.500220 | − | 0.866406i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.19615 | −0.207184 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.16919i | 0.245591i | 0.992432 | + | 0.122796i | \(0.0391860\pi\) | ||||
−0.992432 | + | 0.122796i | \(0.960814\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −66.9411 | + | 38.6485i | −2.66067 | + | 1.53614i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.5944 | + | 18.2410i | 1.25378 | + | 0.723873i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.2621 | + | 39.2132i | 0.525462 | + | 1.55368i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −47.1674 | − | 27.2321i | −1.86591 | − | 1.07729i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9853 | − | 38.0796i | −0.868366 | − | 1.50405i | −0.863665 | − | 0.504066i | \(-0.831837\pi\) |
−0.00470114 | − | 0.999989i | \(-0.501496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.9264i | 1.14074i | 0.821386 | + | 0.570372i | \(0.193201\pi\) | ||||
−0.821386 | + | 0.570372i | \(0.806799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.4853i | 1.27911i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.88892 | − | 3.27171i | −0.0742611 | − | 0.128624i | 0.826504 | − | 0.562931i | \(-0.190326\pi\) |
−0.900765 | + | 0.434307i | \(0.856993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.74264 | − | 3.31552i | −0.225418 | − | 0.130145i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.7804 | − | 59.1938i | −1.04961 | − | 2.31999i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.5636 | − | 12.4497i | −0.843849 | − | 0.487196i | 0.0147219 | − | 0.999892i | \(-0.495314\pi\) |
−0.858571 | + | 0.512695i | \(0.828647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.77326 | − | 3.91055i | 0.264653 | − | 0.152798i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 84.6454i | 3.30233i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.2560 | −0.750108 | −0.375054 | − | 0.927003i | \(-0.622376\pi\) | ||||
−0.375054 | + | 0.927003i | \(0.622376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.22848 | − | 5.59188i | −0.125573 | − | 0.217499i | 0.796384 | − | 0.604792i | \(-0.206744\pi\) |
−0.921957 | + | 0.387293i | \(0.873410\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37.5886 | + | 65.1053i | −1.45982 | + | 2.52848i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.2279 | − | 1.70656i | −0.668070 | − | 0.0661775i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.08571 | + | 14.0049i | −0.313080 | + | 0.542270i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.74666 | + | 1.58579i | −0.106192 | + | 0.0613100i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.69450 | 0.181229 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.24264 | −0.0864474 | −0.0432237 | − | 0.999065i | \(-0.513763\pi\) | ||||
−0.0432237 | + | 0.999065i | \(0.513763\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.0749 | + | 9.85818i | −0.657212 | + | 0.379442i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.2437 | − | 17.7426i | 0.393698 | − | 0.681905i | −0.599236 | − | 0.800572i | \(-0.704529\pi\) |
0.992934 | + | 0.118667i | \(0.0378622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.12051 | + | 12.7126i | −0.350013 | + | 0.487865i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.4706 | − | 45.8484i | 1.01435 | − | 1.75691i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.2478 | + | 19.4818i | 0.430385 | + | 0.745449i | 0.996906 | − | 0.0785980i | \(-0.0250443\pi\) |
−0.566521 | + | 0.824047i | \(0.691711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.23999 | −0.314834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.8840i | 1.10199i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.12132 | + | 4.68885i | −0.309398 | + | 0.178631i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.89860 | + | 4.56026i | 0.300477 | + | 0.173480i | 0.642657 | − | 0.766154i | \(-0.277832\pi\) |
−0.342180 | + | 0.939634i | \(0.611165\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.2708 | + | 21.0000i | 1.11191 | + | 0.797724i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0280 | − | 9.25378i | −0.607977 | − | 0.351016i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.3640 | + | 26.6112i | 0.581952 | + | 1.00797i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 55.3713i | − | 2.09433i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.1421i | 0.534141i | 0.963677 | + | 0.267071i | \(0.0860557\pi\) | ||||
−0.963677 | + | 0.267071i | \(0.913944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.34725 | − | 4.06555i | −0.0885282 | − | 0.153335i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.5919 | − | 24.0131i | −1.56644 | − | 0.904385i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.10363 | + | 21.2365i | −0.0791153 | + | 0.798679i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.5769 | + | 6.10660i | 0.397225 | + | 0.229338i | 0.685286 | − | 0.728274i | \(-0.259677\pi\) |
−0.288061 | + | 0.957612i | \(0.593010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −45.1442 | + | 26.0640i | −1.69304 | + | 0.977478i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 17.6177i | − | 0.659787i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.3406 | −0.835491 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.0665 | − | 24.3640i | −0.525325 | − | 0.909889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.88892 | + | 3.27171i | −0.0704448 | + | 0.122014i | −0.899096 | − | 0.437751i | \(-0.855775\pi\) |
0.828651 | + | 0.559765i | \(0.189109\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1360 | + | 6.39540i | −0.526454 | + | 0.238177i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.7077 | − | 34.1348i | 0.732939 | − | 1.26949i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.8418 | − | 7.41421i | 0.476932 | − | 0.275357i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.2659 | −1.15959 | −0.579795 | − | 0.814762i | \(-0.696867\pi\) | ||||
−0.579795 | + | 0.814762i | \(0.696867\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.7279 | 0.730664 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.3406 | + | 12.8984i | −0.826297 | + | 0.477063i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1859 | − | 21.1066i | 0.450097 | − | 0.779590i | −0.548295 | − | 0.836285i | \(-0.684723\pi\) |
0.998392 | + | 0.0566949i | \(0.0180562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.9172 | − | 11.8091i | 1.28794 | − | 0.435587i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5000 | + | 18.1865i | −0.386772 | + | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.81512 | − | 17.0003i | −0.361055 | − | 0.625365i | 0.627080 | − | 0.778955i | \(-0.284250\pi\) |
−0.988135 | + | 0.153590i | \(0.950917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −67.9193 | −2.49508 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 53.4058i | − | 1.95927i | −0.200793 | − | 0.979634i | \(-0.564352\pi\) | ||
0.200793 | − | 0.979634i | \(-0.435648\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.71320 | − | 4.45322i | 0.282590 | − | 0.163153i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −65.7441 | − | 37.9574i | −2.40545 | − | 1.38879i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.1287 | − | 9.10660i | 0.735487 | − | 0.332748i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.1348 | + | 19.7077i | 1.24560 | + | 0.719146i | 0.970228 | − | 0.242193i | \(-0.0778668\pi\) |
0.275369 | + | 0.961339i | \(0.411200\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.12132 | + | 1.94218i | 0.0408632 | + | 0.0707771i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.99085i | − | 0.218029i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 51.2132i | − | 1.86138i | −0.365815 | − | 0.930688i | \(-0.619210\pi\) | ||
0.365815 | − | 0.930688i | \(-0.380790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.23159 | + | 12.5255i | 0.262490 | + | 0.454646i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.106602 | + | 0.0615465i | 0.00386431 | + | 0.00223106i | 0.501931 | − | 0.864908i | \(-0.332623\pi\) |
−0.498067 | + | 0.867139i | \(0.665956\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.89860 | + | 0.782416i | 0.285948 | + | 0.0283254i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 39.1558 | + | 22.6066i | 1.41568 | + | 0.817343i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.5697 | + | 8.98916i | −0.562189 | + | 0.324580i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 19.1757i | − | 0.691492i | −0.938328 | − | 0.345746i | \(-0.887626\pi\) | ||
0.938328 | − | 0.345746i | \(-0.112374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.54341 | −0.235655 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.59808 | + | 4.50000i | 0.0934463 | + | 0.161854i | 0.908959 | − | 0.416885i | \(-0.136878\pi\) |
−0.815513 | + | 0.578739i | \(0.803545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.07729 | + | 13.9903i | −0.290145 | + | 0.502546i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.12132 | + | 5.82655i | 0.291351 | + | 0.209026i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.8807 | + | 24.0420i | −0.497327 | + | 0.861395i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.4800 | − | 9.51472i | 0.589700 | − | 0.340463i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 73.0907 | 2.61205 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.7574 | 0.598096 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.4062 | − | 15.2456i | 0.941278 | − | 0.543447i | 0.0509172 | − | 0.998703i | \(-0.483786\pi\) |
0.890361 | + | 0.455256i | \(0.150452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.2086 | + | 40.1985i | −0.826248 | + | 1.43110i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.12051 | − | 6.54341i | −0.324288 | − | 0.232657i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.36396 | − | 11.0227i | 0.225991 | − | 0.391428i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.17516 | + | 7.23159i | 0.148078 | + | 0.256478i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.4069 | 0.404054 | 0.202027 | − | 0.979380i | \(-0.435247\pi\) | ||||
0.202027 | + | 0.979380i | \(0.435247\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 38.1378i | − | 1.34922i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 62.3345 | − | 35.9889i | 2.20248 | − | 1.27160i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.6123 | − | 14.7873i | −0.903839 | − | 0.521832i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.94655 | + | 0.985281i | 0.350570 | + | 0.0347266i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.4635 | − | 18.1654i | −1.10757 | − | 0.639454i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.22792 | − | 9.05503i | −0.183804 | − | 0.318358i | 0.759369 | − | 0.650660i | \(-0.225508\pi\) |
−0.943173 | + | 0.332303i | \(0.892174\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.3524i | − | 1.17116i | −0.810614 | − | 0.585580i | \(-0.800867\pi\) | ||
0.810614 | − | 0.585580i | \(-0.199133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 17.8284i | − | 0.625270i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.99542 | + | 5.18823i | 0.104925 | + | 0.181736i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.1838 | − | 11.6531i | −0.706141 | − | 0.407690i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 88.9882 | − | 40.2599i | 3.10950 | − | 1.40679i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.8263 | − | 23.5711i | −1.42485 | − | 0.822636i | −0.428139 | − | 0.903713i | \(-0.640831\pi\) |
−0.996708 | + | 0.0810768i | \(0.974164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1391 | + | 8.16321i | −0.492858 | + | 0.284552i | −0.725759 | − | 0.687949i | \(-0.758511\pi\) |
0.232901 | + | 0.972500i | \(0.425178\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 13.2621i | − | 0.461726i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.5705 | 1.37600 | 0.688000 | − | 0.725710i | \(-0.258489\pi\) | ||||
0.688000 | + | 0.725710i | \(0.258489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.2950 | − | 29.9558i | −0.600681 | − | 1.04041i | −0.992718 | − | 0.120460i | \(-0.961563\pi\) |
0.392037 | − | 0.919949i | \(-0.371770\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.1488 | − | 73.0039i | 1.46213 | − | 2.53248i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.9853 | + | 19.3242i | 0.761745 | + | 0.669545i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.4241 | − | 35.3756i | 0.706805 | − | 1.22422i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −68.9594 | + | 39.8137i | −2.38358 | + | 1.37616i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.9081 | −1.41230 | −0.706152 | − | 0.708061i | \(-0.749570\pi\) | ||||
−0.706152 | + | 0.708061i | \(0.749570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9706 | −0.895537 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.7647 | − | 24.6902i | 1.47289 | − | 0.850376i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.0271 | + | 32.9558i | −0.654551 | + | 1.13372i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.0481 | − | 6.80803i | 0.517058 | − | 0.233927i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.5000 | − | 18.1865i | 0.360359 | − | 0.624160i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.35518 | + | 2.34725i | 0.0464551 | + | 0.0804627i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.91359 | 0.202478 | 0.101239 | − | 0.994862i | \(-0.467719\pi\) | ||||
0.101239 | + | 0.994862i | \(0.467719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40.8482i | 1.39698i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.7426 | − | 11.9758i | 0.708555 | − | 0.409084i | −0.101971 | − | 0.994787i | \(-0.532515\pi\) |
0.810526 | + | 0.585703i | \(0.199181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.2359 | + | 8.79643i | 0.519841 | + | 0.300130i | 0.736869 | − | 0.676035i | \(-0.236303\pi\) |
−0.217029 | + | 0.976165i | \(0.569637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.82655 | − | 58.8198i | 0.198568 | − | 2.00457i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.58342 | + | 3.80094i | 0.224102 | + | 0.129385i | 0.607848 | − | 0.794053i | \(-0.292033\pi\) |
−0.383746 | + | 0.923439i | \(0.625366\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3492 | + | 23.1216i | 0.453888 | + | 0.786157i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.47534i | 0.0501051i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 18.2132i | − | 0.617841i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.4680 | + | 49.3081i | 0.964603 | + | 1.67074i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.9706 | + | 18.4582i | 1.08204 | + | 0.624716i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.0640 | − | 18.6994i | −0.881125 | − | 0.632154i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7958 | + | 15.4706i | 0.904830 | + | 0.522404i | 0.878764 | − | 0.477256i | \(-0.158369\pi\) |
0.0260658 | + | 0.999660i | \(0.491702\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.2599 | + | 23.2441i | −1.35793 | + | 0.784003i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 0.246186i | − | 0.00829422i | −0.999991 | − | 0.00414711i | \(-0.998680\pi\) | ||
0.999991 | − | 0.00414711i | \(-0.00132007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.4252 | −0.855626 | −0.427813 | − | 0.903867i | \(-0.640716\pi\) | ||||
−0.427813 | + | 0.903867i | \(0.640716\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.00436 | + | 13.8640i | 0.269064 | + | 0.466032i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.6716 | − | 34.0722i | 0.660508 | − | 1.14403i | −0.319974 | − | 0.947426i | \(-0.603674\pi\) |
0.980482 | − | 0.196608i | \(-0.0629925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.4853 | − | 45.2795i | 1.08952 | − | 1.51863i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.2609 | − | 21.2365i | 0.410755 | − | 0.711448i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.8396 | − | 17.2279i | 0.998545 | − | 0.576510i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.648175 | 0.0216661 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 39.2132 | 1.30929 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 51.8635 | − | 29.9434i | 1.72974 | − | 0.998668i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.31552 | + | 5.74264i | −0.110456 | + | 0.191315i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 49.3804 | + | 4.89151i | 1.64328 | + | 0.162779i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.75736 | − | 13.4361i | 0.257863 | − | 0.446632i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.89860 | − | 13.6808i | −0.262269 | − | 0.454263i | 0.704576 | − | 0.709629i | \(-0.251137\pi\) |
−0.966844 | + | 0.255366i | \(0.917804\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50.3526 | 1.67009 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 50.1019i | − | 1.65995i | −0.557799 | − | 0.829976i | \(-0.688354\pi\) | ||
0.557799 | − | 0.829976i | \(-0.311646\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.9706 | − | 13.2621i | 0.760215 | − | 0.438910i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.81512 | − | 5.66676i | −0.324478 | − | 0.187337i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.92447 | − | 10.8848i | −0.162620 | − | 0.359447i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.9309 | + | 14.9712i | 0.855383 | + | 0.493856i | 0.862463 | − | 0.506119i | \(-0.168920\pi\) |
−0.00708041 | + | 0.999975i | \(0.502254\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4853 | − | 19.8931i | −0.378453 | − | 0.655500i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 51.5934i | − | 1.69822i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.48528i | − | 0.0817155i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.3043 | + | 31.7040i | 0.601192 | + | 1.04130i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.9558 | + | 6.90271i | 0.392259 | + | 0.226471i | 0.683138 | − | 0.730289i | \(-0.260615\pi\) |
−0.290880 | + | 0.956760i | \(0.593948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.18823 | + | 25.9309i | −0.170037 | + | 0.849853i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 66.2127 | + | 38.2279i | 2.16771 | + | 1.25153i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.6808 | + | 7.89860i | −0.447409 | + | 0.258312i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24.4949i | − | 0.800213i | −0.916469 | − | 0.400107i | \(-0.868973\pi\) | ||
0.916469 | − | 0.400107i | \(-0.131027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.2853 | 2.03260 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0423 | + | 45.1066i | 0.848955 | + | 1.47043i | 0.882142 | + | 0.470984i | \(0.156101\pi\) |
−0.0331867 | + | 0.999449i | \(0.510566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.01401 | − | 13.8807i | 0.260972 | − | 0.452017i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.6213 | − | 41.1595i | −0.605752 | − | 1.33892i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.9008 | + | 31.0051i | −0.581699 | + | 1.00753i | 0.413580 | + | 0.910468i | \(0.364278\pi\) |
−0.995278 | + | 0.0970636i | \(0.969055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −69.4412 | + | 40.0919i | −2.25416 | + | 1.30144i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.7474 | −1.09434 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.1838 | 1.62561 | 0.812806 | − | 0.582535i | \(-0.197939\pi\) | ||||
0.812806 | + | 0.582535i | \(0.197939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.6958 | + | 13.6808i | −0.766778 | + | 0.442699i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.5819 | + | 42.5772i | −0.794621 | + | 1.37632i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.24075 | + | 12.5255i | −0.0400658 | + | 0.404469i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.1213 | + | 29.6550i | −0.552301 | + | 0.956613i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.0640 | − | 45.1442i | −0.839902 | − | 1.45475i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.1682 | 0.488281 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.55536i | − | 0.0821749i | −0.999156 | − | 0.0410874i | \(-0.986918\pi\) | ||
0.999156 | − | 0.0410874i | \(-0.0130822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −41.5919 | + | 24.0131i | −1.33612 | + | 0.771411i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.9615 | + | 16.7209i | 0.929419 | + | 0.536601i | 0.886628 | − | 0.462483i | \(-0.153042\pi\) |
0.0427915 | + | 0.999084i | \(0.486375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.4800 | + | 22.9706i | −0.528324 | + | 0.736402i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −31.1394 | − | 17.9783i | −0.997258 | − | 0.575767i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.3492 | − | 43.9062i | −0.810994 | − | 1.40468i | −0.912169 | − | 0.409814i | \(-0.865593\pi\) |
0.101175 | − | 0.994869i | \(-0.467740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.1485i | 0.803751i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 18.7279i | − | 0.597937i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.782416 | + | 1.35518i | 0.0249552 | + | 0.0432237i | 0.878233 | − | 0.478232i | \(-0.158722\pi\) |
−0.853278 | + | 0.521456i | \(0.825389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.6066 | − | 11.3199i | −0.624718 | − | 0.360681i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −42.7647 | + | 59.6074i | −1.36122 | + | 1.89733i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.6531 | + | 6.72792i | 0.370547 | + | 0.213935i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.1208 | + | 15.0808i | −0.829754 | + | 0.479059i | −0.853769 | − | 0.520653i | \(-0.825689\pi\) |
0.0240142 | + | 0.999712i | \(0.492355\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 66.7816i | − | 2.11925i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.903457 | −0.0286415 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4905 | − | 28.5624i | −0.522261 | − | 0.904582i | −0.999665 | − | 0.0258979i | \(-0.991756\pi\) |
0.477404 | − | 0.878684i | \(-0.341578\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.12509 | − | 10.6090i | 0.193789 | − | 0.335653i |
(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 | 896.2.q.c.831.1 | yes | 16 | |
4.3 | odd | 2 | inner | 896.2.q.c.831.7 | yes | 16 | |
7.3 | odd | 6 | inner | 896.2.q.c.703.2 | yes | 16 | |
8.3 | odd | 2 | inner | 896.2.q.c.831.2 | yes | 16 | |
8.5 | even | 2 | inner | 896.2.q.c.831.8 | yes | 16 | |
28.3 | even | 6 | inner | 896.2.q.c.703.8 | yes | 16 | |
56.3 | even | 6 | inner | 896.2.q.c.703.1 | ✓ | 16 | |
56.45 | odd | 6 | inner | 896.2.q.c.703.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.q.c.703.1 | ✓ | 16 | 56.3 | even | 6 | inner | |
896.2.q.c.703.2 | yes | 16 | 7.3 | odd | 6 | inner | |
896.2.q.c.703.7 | yes | 16 | 56.45 | odd | 6 | inner | |
896.2.q.c.703.8 | yes | 16 | 28.3 | even | 6 | inner | |
896.2.q.c.831.1 | yes | 16 | 1.1 | even | 1 | trivial | |
896.2.q.c.831.2 | yes | 16 | 8.3 | odd | 2 | inner | |
896.2.q.c.831.7 | yes | 16 | 4.3 | odd | 2 | inner | |
896.2.q.c.831.8 | yes | 16 | 8.5 | even | 2 | inner |