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 | 831.2 | ||
Root | \(-0.335868 + 0.0442178i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.831 |
Dual form | 896.2.q.c.703.2 |
$q$-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 | −0.604787 | − | 0.796387i | \(-0.706742\pi\) |
0.992085 | + | 0.125567i | \(0.0400750\pi\) | |||||||
\(6\) | 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 | \(-0.806064\pi\) | ||||
−0.820068 | + | 0.572267i | \(0.806064\pi\) | |||||||
\(14\) | 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 | 0.683834 | − | 0.729637i | \(-0.260311\pi\) |
−0.289967 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(24\) | 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 | \(0.241683\pi\) | ||||
−0.725338 | + | 0.688392i | \(0.758317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.03865 | − | 6.99514i | −0.725362 | − | 1.25636i | −0.958825 | − | 0.283998i | \(-0.908339\pi\) |
0.233463 | − | 0.972366i | \(-0.424994\pi\) | |||||||
\(32\) | 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 | 0.585844 | − | 0.810424i | \(-0.300763\pi\) |
−0.408925 | + | 0.912568i | \(0.634096\pi\) | |||||||
\(38\) | 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 | \(0.398313\pi\) |
−0.979236 | + | 0.202724i | \(0.935021\pi\) | |||||||
\(48\) | 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 | −0.402705 | − | 0.915330i | \(-0.631930\pi\) |
0.591346 | + | 0.806418i | \(0.298597\pi\) | |||||||
\(54\) | 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 | −0.926659 | − | 0.375903i | \(-0.877333\pi\) |
0.788871 | + | 0.614559i | \(0.210666\pi\) | |||||||
\(62\) | 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 | \(0.173214\pi\) | ||||
−0.855558 | + | 0.517707i | \(0.826786\pi\) | |||||||
\(72\) | 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 | 0.848211 | − | 0.529659i | \(-0.177680\pi\) |
−0.0345928 | + | 0.999401i | \(0.511013\pi\) | |||||||
\(80\) | 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 | 0.592588 | − | 0.805505i | \(-0.298106\pi\) |
−0.993882 | + | 0.110444i | \(0.964773\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.93214 | − | 5.07862i | 0.288913 | − | 0.500411i | −0.684638 | − | 0.728883i | \(-0.740040\pi\) |
0.973550 | + | 0.228472i | \(0.0733730\pi\) | |||||||
\(104\) | 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 | −0.619238 | − | 0.785203i | \(-0.712558\pi\) |
0.370387 | + | 0.928877i | \(0.379225\pi\) | |||||||
\(110\) | 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 | \(0.384167\pi\) | ||||
−0.355921 | + | 0.934516i | \(0.615833\pi\) | |||||||
\(128\) | 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 | 0.671194 | − | 0.741282i | \(-0.265782\pi\) |
−0.306372 | + | 0.951912i | \(0.599115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.99542 | − | 1.72941i | 0.243764 | − | 0.140737i | −0.373141 | − | 0.927774i | \(-0.621719\pi\) |
0.616906 | + | 0.787037i | \(0.288386\pi\) | |||||||
\(152\) | 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 | 0.991917 | − | 0.126889i | \(-0.0404993\pi\) |
−0.605848 | + | 0.795581i | \(0.707166\pi\) | |||||||
\(158\) | 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 | \(-0.134164\pi\) | ||||
0.912481 | + | 0.409120i | \(0.134164\pi\) | |||||||
\(168\) | 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 | \(0.365952\pi\) |
−0.994754 | + | 0.102294i | \(0.967382\pi\) | |||||||
\(174\) | 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 | \(-0.391973\pi\) | ||||
0.332900 | + | 0.942962i | \(0.391973\pi\) | |||||||
\(182\) | 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 | −0.0846597 | − | 0.996410i | \(-0.526980\pi\) |
−0.905246 | + | 0.424888i | \(0.860314\pi\) | |||||||
\(192\) | 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 | \(-0.845825\pi\) | ||
0.884976 | − | 0.465638i | \(-0.154175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.260805 | − | 0.451728i | −0.0184880 | − | 0.0320222i | 0.856633 | − | 0.515926i | \(-0.172552\pi\) |
−0.875121 | + | 0.483903i | \(0.839219\pi\) | |||||||
\(200\) | 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 | \(-0.511121\pi\) | ||||
−0.0349296 | + | 0.999390i | \(0.511121\pi\) | |||||||
\(224\) | 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 | −0.979206 | − | 0.202867i | \(-0.934974\pi\) |
0.665291 | + | 0.746584i | \(0.268307\pi\) | |||||||
\(230\) | 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 | \(-0.903251\pi\) | ||
0.954163 | − | 0.299289i | \(-0.0967494\pi\) | |||||||
\(240\) | 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 | −0.848804 | − | 0.528708i | \(-0.822677\pi\) |
0.0334730 | + | 0.999440i | \(0.489343\pi\) | |||||||
\(264\) | 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 | 0.624355 | − | 0.781141i | \(-0.285362\pi\) |
−0.988665 | + | 0.150137i | \(0.952029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.93214 | − | 5.07862i | 0.178115 | − | 0.308504i | −0.763120 | − | 0.646257i | \(-0.776333\pi\) |
0.941235 | + | 0.337753i | \(0.109667\pi\) | |||||||
\(272\) | 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 | 0.444770 | − | 0.895645i | \(-0.353285\pi\) |
0.998036 | + | 0.0626400i | \(0.0199520\pi\) | |||||||
\(278\) | 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 | \(-0.647388\pi\) | ||||
−0.446663 | + | 0.894702i | \(0.647388\pi\) | |||||||
\(294\) | 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 | \(0.0860070\pi\) |
−0.250697 | + | 0.968066i | \(0.580660\pi\) | |||||||
\(312\) | 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 | 0.205116 | − | 0.978738i | \(-0.434243\pi\) |
−0.745054 | + | 0.667004i | \(0.767576\pi\) | |||||||
\(318\) | 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 | \(-0.861316\pi\) | ||||
−0.906579 | + | 0.422036i | \(0.861316\pi\) | |||||||
\(350\) | 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 | 0.461773 | − | 0.886998i | \(-0.347214\pi\) |
−0.537277 | + | 0.843406i | \(0.680547\pi\) | |||||||
\(360\) | 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 | \(0.00748787\pi\) |
−0.479491 | + | 0.877547i | \(0.659179\pi\) | |||||||
\(368\) | 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 | 0.389531 | − | 0.921014i | \(-0.372637\pi\) |
−0.602856 | + | 0.797850i | \(0.705971\pi\) | |||||||
\(374\) | 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 | \(-0.482570\pi\) |
0.837361 | − | 0.546650i | \(-0.184097\pi\) | |||||||
\(384\) | 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 | −0.496228 | − | 0.868192i | \(-0.665282\pi\) |
0.503762 | + | 0.863842i | \(0.331949\pi\) | |||||||
\(390\) | 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 | −0.960260 | − | 0.279108i | \(-0.909961\pi\) |
0.721844 | + | 0.692055i | \(0.243295\pi\) | |||||||
\(398\) | 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 | \(0.129536\pi\) | ||||
−0.918333 | + | 0.395809i | \(0.870464\pi\) | |||||||
\(422\) | 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 | −0.791888 | − | 0.610666i | \(-0.790902\pi\) |
0.132909 | + | 0.991128i | \(0.457568\pi\) | |||||||
\(432\) | 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 | −0.999996 | − | 0.00284264i | \(-0.999095\pi\) |
0.502460 | + | 0.864601i | \(0.332428\pi\) | |||||||
\(440\) | 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 | \(-0.352653\pi\) | ||||
0.446550 | + | 0.894759i | \(0.352653\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.36227i | 0.202732i | 0.994849 | + | 0.101366i | \(0.0323213\pi\) | ||||
−0.994849 | + | 0.101366i | \(0.967679\pi\) | |||||||
\(464\) | 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 | 0.592039 | − | 0.805910i | \(-0.298323\pi\) |
−0.993958 | + | 0.109766i | \(0.964990\pi\) | |||||||
\(480\) | 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 | −0.857694 | − | 0.514160i | \(-0.828104\pi\) |
0.0164286 | + | 0.999865i | \(0.494770\pi\) | |||||||
\(488\) | 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 | \(-0.477773\pi\) | ||||
0.0697724 | + | 0.997563i | \(0.477773\pi\) | |||||||
\(504\) | 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 | −0.934915 | − | 0.354872i | \(-0.884525\pi\) |
0.774785 | + | 0.632224i | \(0.217858\pi\) | |||||||
\(510\) | 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 | 0.0552031 | − | 0.998475i | \(-0.482419\pi\) |
−0.837103 | + | 0.547045i | \(0.815753\pi\) | |||||||
\(542\) | 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 | 0.0941107 | − | 0.995562i | \(-0.469999\pi\) |
0.909237 | + | 0.416279i | \(0.136666\pi\) | |||||||
\(558\) | 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 | −0.920055 | − | 0.391789i | \(-0.871856\pi\) |
−0.120728 | + | 0.992686i | \(0.538523\pi\) | |||||||
\(600\) | 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 | −0.991173 | − | 0.132572i | \(-0.957676\pi\) |
0.610397 | + | 0.792095i | \(0.291010\pi\) | |||||||
\(608\) | 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 | −0.609591 | − | 0.792716i | \(-0.708666\pi\) |
0.381717 | + | 0.924279i | \(0.375333\pi\) | |||||||
\(614\) | 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 | \(-0.960814\pi\) | ||
0.992432 | − | 0.122796i | \(-0.0391860\pi\) | |||||||
\(632\) | 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 | 0.900765 | − | 0.434307i | \(-0.143007\pi\) |
−0.826504 | + | 0.562931i | \(0.809674\pi\) | |||||||
\(648\) | 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 | 0.858571 | − | 0.512695i | \(-0.171353\pi\) |
−0.0147219 | + | 0.999892i | \(0.504686\pi\) | |||||||
\(654\) | 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 | 0.921957 | − | 0.387293i | \(-0.126590\pi\) |
−0.796384 | + | 0.604792i | \(0.793256\pi\) | |||||||
\(662\) | 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 | −0.992934 | − | 0.118667i | \(-0.962138\pi\) |
0.599236 | + | 0.800572i | \(0.295471\pi\) | |||||||
\(678\) | 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 | \(-0.913944\pi\) | ||
0.963677 | − | 0.267071i | \(-0.0860557\pi\) | |||||||
\(702\) | 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 | 0.288061 | − | 0.957612i | \(-0.406990\pi\) |
−0.685286 | + | 0.728274i | \(0.740323\pi\) | |||||||
\(710\) | 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 | −0.828651 | − | 0.559765i | \(-0.810891\pi\) |
0.899096 | + | 0.437751i | \(0.144225\pi\) | |||||||
\(720\) | 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 | \(-0.303133\pi\) | ||||
0.579795 | + | 0.814762i | \(0.303133\pi\) | |||||||
\(728\) | 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 | −0.998392 | − | 0.0566949i | \(-0.981944\pi\) |
0.548295 | + | 0.836285i | \(0.315277\pi\) | |||||||
\(734\) | 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 | \(0.435648\pi\) | ||||
−0.200793 | + | 0.979634i | \(0.564352\pi\) | |||||||
\(744\) | 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 | −0.275369 | − | 0.961339i | \(-0.588800\pi\) |
−0.970228 | + | 0.242193i | \(0.922133\pi\) | |||||||
\(752\) | 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 | \(0.380790\pi\) | ||||
−0.365815 | + | 0.930688i | \(0.619210\pi\) | |||||||
\(758\) | 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 | 0.815513 | − | 0.578739i | \(-0.196455\pi\) |
−0.908959 | + | 0.416885i | \(0.863122\pi\) | |||||||
\(774\) | 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 | \(-0.564753\pi\) | ||||
−0.202027 | + | 0.979380i | \(0.564753\pi\) | |||||||
\(798\) | 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 | 0.996708 | − | 0.0810768i | \(-0.0258359\pi\) |
0.428139 | + | 0.903713i | \(0.359169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1391 | − | 8.16321i | 0.492858 | − | 0.284552i | −0.232901 | − | 0.972500i | \(-0.574822\pi\) |
0.725759 | + | 0.687949i | \(0.241489\pi\) | |||||||
\(824\) | 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 | \(0.0384370\pi\) |
−0.392037 | + | 0.919949i | \(0.628230\pi\) | |||||||
\(830\) | 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 | \(-0.250430\pi\) | ||||
0.706152 | + | 0.708061i | \(0.250430\pi\) | |||||||
\(840\) | 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 | \(-0.532281\pi\) | ||||
−0.101239 | + | 0.994862i | \(0.532281\pi\) | |||||||
\(854\) | 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 | 0.383746 | − | 0.923439i | \(-0.374634\pi\) |
−0.607848 | + | 0.794053i | \(0.707967\pi\) | |||||||
\(864\) | 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 | −0.0260658 | − | 0.999660i | \(-0.508298\pi\) |
−0.878764 | + | 0.477256i | \(0.841631\pi\) | |||||||
\(878\) | 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 | \(0.396326\pi\) |
−0.980482 | + | 0.196608i | \(0.937007\pi\) | |||||||
\(888\) | 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 | \(0.311646\pi\) | ||||
−0.557799 | + | 0.829976i | \(0.688354\pi\) | |||||||
\(912\) | 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 | 0.00708041 | − | 0.999975i | \(-0.497746\pi\) |
−0.862463 | + | 0.506119i | \(0.831080\pi\) | |||||||
\(920\) | 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 | \(-0.843899\pi\) |
0.0331867 | − | 0.999449i | \(-0.489434\pi\) | |||||||
\(942\) | 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 | \(0.0130822\pi\) | ||||
−0.999156 | + | 0.0410874i | \(0.986918\pi\) | |||||||
\(968\) | 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 | 0.853278 | − | 0.521456i | \(-0.174611\pi\) |
−0.878233 | + | 0.478232i | \(0.841278\pi\) | |||||||
\(984\) | 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 | −0.0240142 | − | 0.999712i | \(-0.507645\pi\) |
0.853769 | + | 0.520653i | \(0.174311\pi\) | |||||||
\(992\) | 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 | \(0.00824447\pi\) |
−0.477404 | + | 0.878684i | \(0.658422\pi\) | |||||||
\(998\) | 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.831.2 | yes | 16 | |
4.3 | odd | 2 | inner | 896.2.q.c.831.8 | yes | 16 | |
7.3 | odd | 6 | inner | 896.2.q.c.703.1 | ✓ | 16 | |
8.3 | odd | 2 | inner | 896.2.q.c.831.1 | yes | 16 | |
8.5 | even | 2 | inner | 896.2.q.c.831.7 | yes | 16 | |
28.3 | even | 6 | inner | 896.2.q.c.703.7 | yes | 16 | |
56.3 | even | 6 | inner | 896.2.q.c.703.2 | yes | 16 | |
56.45 | odd | 6 | inner | 896.2.q.c.703.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.q.c.703.1 | ✓ | 16 | 7.3 | odd | 6 | inner | |
896.2.q.c.703.2 | yes | 16 | 56.3 | even | 6 | inner | |
896.2.q.c.703.7 | yes | 16 | 28.3 | even | 6 | inner | |
896.2.q.c.703.8 | yes | 16 | 56.45 | odd | 6 | inner | |
896.2.q.c.831.1 | yes | 16 | 8.3 | odd | 2 | inner | |
896.2.q.c.831.2 | yes | 16 | 1.1 | even | 1 | trivial | |
896.2.q.c.831.7 | yes | 16 | 8.5 | even | 2 | inner | |
896.2.q.c.831.8 | yes | 16 | 4.3 | odd | 2 | inner |