Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(81,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.u (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 321.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.321 |
Dual form | 400.2.u.b.81.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | 0.796305 | − | 0.604896i | \(-0.206785\pi\) |
−0.329218 | + | 0.944254i | \(0.606785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.690983 | − | 2.12663i | −0.309017 | − | 0.951057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.618034 | −0.233595 | −0.116797 | − | 0.993156i | \(-0.537263\pi\) | ||||
−0.116797 | + | 0.993156i | \(0.537263\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.618034 | − | 1.90211i | −0.206011 | − | 0.634038i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.61803 | − | 4.97980i | 0.487856 | − | 1.50147i | −0.339946 | − | 0.940445i | \(-0.610409\pi\) |
0.827802 | − | 0.561020i | \(-0.189591\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.572949 | + | 1.76336i | 0.158907 | + | 0.489067i | 0.998536 | − | 0.0540944i | \(-0.0172272\pi\) |
−0.839628 | + | 0.543161i | \(0.817227\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.690983 | − | 2.12663i | 0.178411 | − | 0.549093i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.23607 | − | 3.07768i | 1.02740 | − | 0.746448i | 0.0596113 | − | 0.998222i | \(-0.481014\pi\) |
0.967786 | + | 0.251774i | \(0.0810139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.690983 | − | 0.502029i | 0.158522 | − | 0.115173i | −0.505696 | − | 0.862712i | \(-0.668764\pi\) |
0.664219 | + | 0.747538i | \(0.268764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | − | 0.363271i | −0.109109 | − | 0.0792723i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.16312 | + | 3.57971i | −0.242527 | + | 0.746422i | 0.753506 | + | 0.657441i | \(0.228361\pi\) |
−0.996033 | + | 0.0889808i | \(0.971639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | + | 2.93893i | −0.809017 | + | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.54508 | − | 4.75528i | 0.297352 | − | 0.915155i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.92705 | + | 2.12663i | 0.543540 | + | 0.394905i | 0.825398 | − | 0.564551i | \(-0.190951\pi\) |
−0.281858 | + | 0.959456i | \(0.590951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.42705 | + | 1.76336i | −0.435911 | + | 0.316708i | −0.784008 | − | 0.620750i | \(-0.786828\pi\) |
0.348097 | + | 0.937459i | \(0.386828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.23607 | − | 3.07768i | 0.737405 | − | 0.535756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.427051 | + | 1.31433i | 0.0721848 | + | 0.222162i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0729490 | − | 0.224514i | −0.0119927 | − | 0.0369099i | 0.944881 | − | 0.327414i | \(-0.106177\pi\) |
−0.956874 | + | 0.290504i | \(0.906177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.572949 | + | 1.76336i | −0.0917453 | + | 0.282363i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.236068 | − | 0.726543i | −0.0368676 | − | 0.113467i | 0.930929 | − | 0.365200i | \(-0.118999\pi\) |
−0.967797 | + | 0.251733i | \(0.918999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.85410 | 0.740244 | 0.370122 | − | 0.928983i | \(-0.379316\pi\) | ||||
0.370122 | + | 0.928983i | \(0.379316\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.61803 | + | 2.62866i | −0.539345 | + | 0.391857i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.500000 | + | 0.363271i | 0.0729325 | + | 0.0529886i | 0.623654 | − | 0.781700i | \(-0.285647\pi\) |
−0.550722 | + | 0.834689i | \(0.685647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23607 | 0.733196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.80902 | + | 2.04087i | 0.385848 | + | 0.280335i | 0.763752 | − | 0.645510i | \(-0.223355\pi\) |
−0.377904 | + | 0.925845i | \(0.623355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.7082 | −1.57873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.854102 | 0.113129 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.35410 | + | 10.3229i | 0.436667 | + | 1.34392i | 0.891369 | + | 0.453279i | \(0.149746\pi\) |
−0.454702 | + | 0.890644i | \(0.650254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69098 | − | 8.28199i | 0.344545 | − | 1.06040i | −0.617282 | − | 0.786742i | \(-0.711766\pi\) |
0.961827 | − | 0.273659i | \(-0.0882338\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.381966 | + | 1.17557i | 0.0481232 | + | 0.148108i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.35410 | − | 2.43690i | 0.416025 | − | 0.302260i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.85410 | − | 2.80017i | 0.470853 | − | 0.342095i | −0.326920 | − | 0.945052i | \(-0.606011\pi\) |
0.797774 | + | 0.602957i | \(0.206011\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.04508 | + | 2.21238i | −0.366585 | + | 0.266340i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.35410 | − | 3.88998i | −0.635415 | − | 0.461656i | 0.222857 | − | 0.974851i | \(-0.428462\pi\) |
−0.858272 | + | 0.513195i | \(0.828462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.78115 | + | 8.55951i | −0.325509 | + | 1.00181i | 0.645701 | + | 0.763590i | \(0.276565\pi\) |
−0.971210 | + | 0.238224i | \(0.923435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00000 | −0.577350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | + | 3.07768i | −0.113961 | + | 0.350735i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.54508 | − | 4.75528i | −0.736380 | − | 0.535011i | 0.155196 | − | 0.987884i | \(-0.450399\pi\) |
−0.891575 | + | 0.452873i | \(0.850399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.04508 | + | 3.66547i | −0.553770 | + | 0.402337i | −0.829174 | − | 0.558991i | \(-0.811189\pi\) |
0.275404 | + | 0.961329i | \(0.411189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.47214 | − | 6.88191i | −1.02740 | − | 0.746448i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.11803 | + | 3.44095i | 0.119866 | + | 0.368909i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.76393 | + | 8.50651i | −0.292976 | + | 0.901688i | 0.690918 | + | 0.722934i | \(0.257207\pi\) |
−0.983894 | + | 0.178754i | \(0.942793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.354102 | − | 1.08981i | −0.0371200 | − | 0.114244i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.00000 | −0.311086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.54508 | − | 1.12257i | −0.158522 | − | 0.115173i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.11803 | + | 2.26538i | 0.316588 | + | 0.230015i | 0.734718 | − | 0.678372i | \(-0.237314\pi\) |
−0.418130 | + | 0.908387i | \(0.637314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.4721 | −1.05249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.47214 | 0.146483 | 0.0732415 | − | 0.997314i | \(-0.476666\pi\) | ||||
0.0732415 | + | 0.997314i | \(0.476666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92705 | + | 5.03280i | 0.682543 | + | 0.495896i | 0.874200 | − | 0.485566i | \(-0.161386\pi\) |
−0.191658 | + | 0.981462i | \(0.561386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.427051 | + | 1.31433i | −0.0416759 | + | 0.128265i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4164 | 1.58703 | 0.793517 | − | 0.608548i | \(-0.208248\pi\) | ||||
0.793517 | + | 0.608548i | \(0.208248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.09017 | + | 9.51057i | 0.295985 | + | 0.910947i | 0.982889 | + | 0.184199i | \(0.0589691\pi\) |
−0.686904 | + | 0.726748i | \(0.741031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0729490 | − | 0.224514i | 0.00692401 | − | 0.0213099i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.20820 | + | 16.0292i | 0.489947 | + | 1.50790i | 0.824687 | + | 0.565590i | \(0.191352\pi\) |
−0.334740 | + | 0.942311i | \(0.608648\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.41641 | 0.784834 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | − | 2.17963i | 0.277350 | − | 0.201507i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.61803 | + | 1.90211i | −0.239995 | + | 0.174366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.2812 | − | 9.64932i | −1.20738 | − | 0.877211i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.236068 | − | 0.726543i | 0.0212855 | − | 0.0655101i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.04508 | + | 6.57164i | 0.809017 | + | 0.587785i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.14590 | + | 18.9151i | −0.545360 | + | 1.67845i | 0.174772 | + | 0.984609i | \(0.444081\pi\) |
−0.720132 | + | 0.693837i | \(0.755919\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.92705 | + | 2.85317i | 0.345758 | + | 0.251208i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.50000 | − | 3.99598i | 0.480537 | − | 0.349131i | −0.320996 | − | 0.947080i | \(-0.604018\pi\) |
0.801534 | + | 0.597950i | \(0.204018\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.427051 | + | 0.310271i | −0.0370300 | + | 0.0269039i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.1803 | −0.962250 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.69098 | − | 11.3597i | −0.315342 | − | 0.970523i | −0.975613 | − | 0.219496i | \(-0.929559\pi\) |
0.660271 | − | 0.751027i | \(-0.270441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.54508 | + | 4.75528i | −0.131052 | + | 0.403338i | −0.994955 | − | 0.100321i | \(-0.968013\pi\) |
0.863903 | + | 0.503659i | \(0.168013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.190983 | + | 0.587785i | 0.0160837 | + | 0.0495004i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.70820 | 0.811841 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | − | 7.69421i | 0.207614 | − | 0.638969i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.35410 | − | 3.88998i | −0.441599 | − | 0.320840i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.94427 | −0.323127 | −0.161564 | − | 0.986862i | \(-0.551654\pi\) | ||||
−0.161564 | + | 0.986862i | \(0.551654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5623 | −1.18506 | −0.592532 | − | 0.805547i | \(-0.701872\pi\) | ||||
−0.592532 | + | 0.805547i | \(0.701872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.47214 | − | 6.15537i | −0.684932 | − | 0.497632i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.42705 | + | 3.94298i | 0.435911 | + | 0.316708i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1803 | 1.05191 | 0.525953 | − | 0.850514i | \(-0.323709\pi\) | ||||
0.525953 | + | 0.850514i | \(0.323709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.07295 | + | 3.30220i | 0.0850904 | + | 0.261881i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.718847 | − | 2.21238i | 0.0566531 | − | 0.174360i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.39919 | − | 10.4616i | −0.266245 | − | 0.819417i | −0.991404 | − | 0.130836i | \(-0.958234\pi\) |
0.725159 | − | 0.688581i | \(-0.241766\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.47214 | − | 6.88191i | −0.737405 | − | 0.535756i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.7812 | − | 8.55951i | 0.911653 | − | 0.662355i | −0.0297794 | − | 0.999556i | \(-0.509480\pi\) |
0.941432 | + | 0.337202i | \(0.109480\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.73607 | − | 5.62058i | 0.595082 | − | 0.432352i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.38197 | − | 1.00406i | −0.105682 | − | 0.0767822i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.83688 | − | 17.9641i | 0.443770 | − | 1.36578i | −0.440057 | − | 0.897970i | \(-0.645042\pi\) |
0.883827 | − | 0.467813i | \(-0.154958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | − | 1.81636i | 0.188982 | − | 0.137304i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.35410 | + | 10.3229i | −0.252110 | + | 0.775914i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.427051 | − | 0.310271i | −0.0319193 | − | 0.0231907i | 0.571711 | − | 0.820455i | \(-0.306280\pi\) |
−0.603631 | + | 0.797264i | \(0.706280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.236068 | + | 0.171513i | −0.0175468 | + | 0.0127485i | −0.596524 | − | 0.802595i | \(-0.703452\pi\) |
0.578977 | + | 0.815344i | \(0.303452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.04508 | − | 5.11855i | 0.520788 | − | 0.378374i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.427051 | + | 0.310271i | −0.0313974 | + | 0.0228116i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.47214 | − | 26.0746i | −0.619544 | − | 1.90676i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.954915 | + | 2.93893i | −0.0694598 | + | 0.213775i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.562306 | + | 1.73060i | 0.0406870 | + | 0.125222i | 0.969337 | − | 0.245736i | \(-0.0790295\pi\) |
−0.928650 | + | 0.370958i | \(0.879030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.70820 | 0.554849 | 0.277424 | − | 0.960747i | \(-0.410519\pi\) | ||||
0.277424 | + | 0.960747i | \(0.410519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.14590 | 0.296894 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | − | 2.17963i | −0.213741 | − | 0.155292i | 0.475764 | − | 0.879573i | \(-0.342172\pi\) |
−0.689505 | + | 0.724281i | \(0.742172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.5623 | 1.24496 | 0.622479 | − | 0.782636i | \(-0.286125\pi\) | ||||
0.622479 | + | 0.782636i | \(0.286125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.76393 | 0.336022 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.80902 | − | 1.31433i | −0.126968 | − | 0.0922477i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.38197 | + | 1.00406i | −0.0965207 | + | 0.0701264i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.52786 | 0.523223 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.38197 | − | 4.25325i | −0.0955926 | − | 0.294204i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.83688 | − | 8.73102i | 0.195299 | − | 0.601068i | −0.804674 | − | 0.593717i | \(-0.797660\pi\) |
0.999973 | − | 0.00735149i | \(-0.00234007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.04508 | − | 6.29412i | −0.140127 | − | 0.431266i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.35410 | − | 10.3229i | −0.228748 | − | 0.704014i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50000 | − | 1.08981i | 0.101827 | − | 0.0739814i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.28115 | + | 5.29007i | −0.492015 | + | 0.357470i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.85410 | + | 5.70634i | 0.528324 | + | 0.383850i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0557281 | − | 0.171513i | 0.00373183 | − | 0.0114854i | −0.949173 | − | 0.314754i | \(-0.898078\pi\) |
0.952905 | + | 0.303269i | \(0.0980780\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.09017 | + | 5.87785i | 0.539345 | + | 0.391857i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.56231 | + | 14.0413i | −0.302811 | + | 0.931956i | 0.677674 | + | 0.735362i | \(0.262988\pi\) |
−0.980485 | + | 0.196594i | \(0.937012\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5623 | − | 12.7598i | −1.16055 | − | 0.843189i | −0.170702 | − | 0.985323i | \(-0.554604\pi\) |
−0.989847 | + | 0.142134i | \(0.954604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.61803 | + | 1.90211i | −0.172254 | + | 0.125150i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.38197 | − | 1.73060i | 0.156048 | − | 0.113375i | −0.507021 | − | 0.861933i | \(-0.669254\pi\) |
0.663069 | + | 0.748558i | \(0.269254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.427051 | − | 1.31433i | 0.0278577 | − | 0.0857373i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.50000 | − | 7.69421i | −0.162392 | − | 0.499793i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.34346 | − | 19.5232i | 0.410324 | − | 1.26285i | −0.506043 | − | 0.862508i | \(-0.668892\pi\) |
0.916367 | − | 0.400340i | \(-0.131108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.781153 | + | 2.40414i | 0.0503185 | + | 0.154864i | 0.973058 | − | 0.230559i | \(-0.0740554\pi\) |
−0.922740 | + | 0.385423i | \(0.874055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.57295 | + | 14.0741i | 0.292155 | + | 0.899161i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.28115 | + | 0.930812i | 0.0815178 | + | 0.0592262i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.23607 | −0.395195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.1803 | 1.84185 | 0.920923 | − | 0.389744i | \(-0.127436\pi\) | ||||
0.920923 | + | 0.389744i | \(0.127436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.9443 | + | 11.5842i | 1.00241 | + | 0.728292i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.61803 | − | 11.1352i | −0.226570 | − | 0.697311i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.8541 | 1.42560 | 0.712800 | − | 0.701367i | \(-0.247427\pi\) | ||||
0.712800 | + | 0.701367i | \(0.247427\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0450850 | + | 0.138757i | 0.00280144 | + | 0.00862196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23607 | − | 6.88191i | 0.138409 | − | 0.425980i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.37132 | + | 10.3759i | 0.207885 | + | 0.639803i | 0.999583 | + | 0.0288905i | \(0.00919740\pi\) |
−0.791698 | + | 0.610913i | \(0.790803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.39919 | − | 7.38394i | 0.147381 | − | 0.453592i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.23607 | + | 5.25731i | −0.442840 | + | 0.321742i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3262 | − | 7.50245i | 0.629602 | − | 0.457433i | −0.226660 | − | 0.973974i | \(-0.572781\pi\) |
0.856262 | + | 0.516541i | \(0.172781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.47214 | − | 4.70228i | −0.393154 | − | 0.285643i | 0.373593 | − | 0.927593i | \(-0.378126\pi\) |
−0.766747 | + | 0.641950i | \(0.778126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.354102 | − | 1.08981i | 0.0214312 | − | 0.0659585i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.09017 | + | 24.8990i | 0.487856 | + | 1.50147i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.63525 | + | 23.4989i | −0.458758 | + | 1.41191i | 0.407908 | + | 0.913023i | \(0.366258\pi\) |
−0.866666 | + | 0.498889i | \(0.833742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.85410 | + | 3.52671i | 0.290607 | + | 0.211139i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.16312 | + | 5.93085i | −0.486971 | + | 0.353805i | −0.804018 | − | 0.594605i | \(-0.797309\pi\) |
0.317047 | + | 0.948410i | \(0.397309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.1525 | + | 17.5478i | −1.43572 | + | 1.04311i | −0.446799 | + | 0.894634i | \(0.647436\pi\) |
−0.988916 | + | 0.148474i | \(0.952564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.590170 | − | 1.81636i | −0.0349587 | − | 0.107592i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.145898 | + | 0.449028i | 0.00861209 | + | 0.0265053i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.21885 | − | 9.90659i | 0.189344 | − | 0.582741i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.19098 | + | 3.66547i | 0.0698167 | + | 0.214874i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5279 | −1.14083 | −0.570415 | − | 0.821357i | \(-0.693218\pi\) | ||||
−0.570415 | + | 0.821357i | \(0.693218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.6353 | − | 14.2658i | 1.14321 | − | 0.830590i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.1803 | − | 15.3884i | −1.22901 | − | 0.892927i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.97871 | −0.403589 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.19098 | + | 0.865300i | 0.0684202 | + | 0.0497102i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.4721 | −1.11497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.23607 | −0.527130 | −0.263565 | − | 0.964642i | \(-0.584898\pi\) | ||||
−0.263565 | + | 0.964642i | \(0.584898\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.64590 | + | 8.14324i | 0.150520 | + | 0.463253i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.62868 | + | 8.09024i | −0.149059 | + | 0.458755i | −0.997511 | − | 0.0705172i | \(-0.977535\pi\) |
0.848452 | + | 0.529272i | \(0.177535\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.18034 | − | 15.9434i | −0.292810 | − | 0.901177i | −0.983948 | − | 0.178454i | \(-0.942890\pi\) |
0.691138 | − | 0.722723i | \(-0.257110\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.23607 | − | 1.62460i | 0.125988 | − | 0.0915358i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.19098 | + | 4.49801i | −0.347720 | + | 0.252634i | −0.747912 | − | 0.663798i | \(-0.768944\pi\) |
0.400192 | + | 0.916431i | \(0.368944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.3262 | − | 11.1352i | 0.858105 | − | 0.623449i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.2812 | + | 9.64932i | 0.741282 | + | 0.538573i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.38197 | − | 4.25325i | 0.0768946 | − | 0.236657i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.50000 | − | 5.44907i | −0.416025 | − | 0.302260i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.09017 | + | 9.51057i | −0.170887 | + | 0.525935i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.309017 | − | 0.224514i | −0.0170367 | − | 0.0123779i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7082 | + | 13.5923i | −1.02830 | + | 0.747101i | −0.967967 | − | 0.251078i | \(-0.919215\pi\) |
−0.0603290 | + | 0.998179i | \(0.519215\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.381966 | + | 0.277515i | −0.0209316 | + | 0.0152077i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.61803 | − | 6.26137i | −0.470853 | − | 0.342095i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.42705 | + | 7.46969i | 0.132210 | + | 0.406900i | 0.995146 | − | 0.0984135i | \(-0.0313768\pi\) |
−0.862936 | + | 0.505314i | \(0.831377\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.20820 | + | 16.0292i | −0.282871 | + | 0.870587i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.85410 | + | 14.9394i | 0.262864 | + | 0.809013i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.41641 | 0.454443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.80902 | + | 4.94704i | 0.366585 | + | 0.266340i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.1074 | − | 11.7027i | −0.864690 | − | 0.628234i | 0.0644668 | − | 0.997920i | \(-0.479465\pi\) |
−0.929157 | + | 0.369686i | \(0.879465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7082 | 1.16201 | 0.581007 | − | 0.813899i | \(-0.302659\pi\) | ||||
0.581007 | + | 0.813899i | \(0.302659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.27051 | 0.494823 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4443 | − | 7.58821i | −0.555893 | − | 0.403880i | 0.274061 | − | 0.961712i | \(-0.411633\pi\) |
−0.829953 | + | 0.557833i | \(0.811633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.57295 | + | 14.0741i | −0.242707 | + | 0.746975i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.23607 | −0.171271 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.24671 | − | 13.0700i | −0.224133 | − | 0.689810i | −0.998378 | − | 0.0569247i | \(-0.981870\pi\) |
0.774246 | − | 0.632885i | \(-0.218130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.64590 | + | 17.3763i | −0.297153 | + | 0.914541i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.07295 | − | 15.6129i | −0.266261 | − | 0.819466i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.1246 | 1.05337 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.6803 | + | 15.0251i | −1.07950 | + | 0.784306i | −0.977597 | − | 0.210488i | \(-0.932495\pi\) |
−0.101908 | + | 0.994794i | \(0.532495\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.23607 | + | 0.898056i | −0.0643471 | + | 0.0467509i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.73607 | − | 1.26133i | −0.0901322 | − | 0.0654848i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.73607 | + | 26.8869i | −0.452336 | + | 1.39215i | 0.421897 | + | 0.906644i | \(0.361364\pi\) |
−0.874234 | + | 0.485505i | \(0.838636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.45492 | + | 10.6331i | 0.178411 | + | 0.549093i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.07295 | + | 6.37988i | −0.106762 | + | 0.328581i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8090 | + | 8.57975i | 0.606588 | + | 0.440712i | 0.848211 | − | 0.529658i | \(-0.177680\pi\) |
−0.241623 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0902 | + | 11.6902i | −0.824324 | + | 0.598907i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.9894 | − | 19.6089i | 1.37909 | − | 1.00197i | 0.382127 | − | 0.924110i | \(-0.375192\pi\) |
0.996964 | − | 0.0778591i | \(-0.0248084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.23607 | 0.368784 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | − | 9.23305i | −0.152499 | − | 0.469342i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.63525 | − | 14.2658i | 0.235017 | − | 0.723307i | −0.762102 | − | 0.647456i | \(-0.775833\pi\) |
0.997119 | − | 0.0758507i | \(-0.0241672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.09017 | + | 18.7436i | 0.307993 | + | 0.947905i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.79837 | 0.342933 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.59017 | + | 17.2048i | −0.281272 | + | 0.865666i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.4894 | − | 17.0660i | −1.17890 | − | 0.856519i | −0.186850 | − | 0.982388i | \(-0.559828\pi\) |
−0.992047 | + | 0.125870i | \(0.959828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.527864 | −0.0264263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5967 | 1.32818 | 0.664089 | − | 0.747653i | \(-0.268820\pi\) | ||||
0.664089 | + | 0.747653i | \(0.268820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | − | 3.26944i | −0.224161 | − | 0.162862i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.80902 | + | 1.31433i | 0.0898908 | + | 0.0653095i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.23607 | −0.0612696 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.489357 | + | 1.50609i | 0.0241971 | + | 0.0744711i | 0.962426 | − | 0.271544i | \(-0.0875344\pi\) |
−0.938229 | + | 0.346016i | \(0.887534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.69098 | − | 11.3597i | 0.182063 | − | 0.560332i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.07295 | − | 6.37988i | −0.102003 | − | 0.313933i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2812 | + | 8.19624i | 0.553770 | + | 0.402337i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.04508 | + | 2.93893i | −0.198089 | + | 0.143920i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.66312 | + | 5.56758i | −0.374368 | + | 0.271994i | −0.759020 | − | 0.651068i | \(-0.774321\pi\) |
0.384652 | + | 0.923062i | \(0.374321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8885 | − | 18.8091i | −1.26173 | − | 0.916701i | −0.262889 | − | 0.964826i | \(-0.584675\pi\) |
−0.998841 | + | 0.0481252i | \(0.984675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.381966 | − | 1.17557i | 0.0185718 | − | 0.0571582i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.09017 | + | 24.8990i | −0.392431 | + | 1.20778i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.66312 | + | 5.11855i | −0.0804840 | + | 0.247704i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.85410 | + | 5.70634i | 0.379200 | + | 0.275505i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.1353 | + | 17.5353i | −1.16255 | + | 0.844645i | −0.990099 | − | 0.140372i | \(-0.955170\pi\) |
−0.172456 | + | 0.985017i | \(0.555170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.7254 | + | 15.7844i | −1.04406 | + | 0.758552i | −0.971073 | − | 0.238781i | \(-0.923252\pi\) |
−0.0729839 | + | 0.997333i | \(0.523252\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.54508 | − | 4.75528i | 0.313813 | − | 0.227998i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.993422 | + | 3.05744i | 0.0475218 | + | 0.146257i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6631 | − | 38.9731i | 0.604378 | − | 1.86008i | 0.103365 | − | 0.994644i | \(-0.467039\pi\) |
0.501013 | − | 0.865440i | \(-0.332961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.09017 | + | 12.5882i | 0.194770 | + | 0.599440i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.9443 | −1.42270 | −0.711348 | − | 0.702840i | \(-0.751915\pi\) | ||||
−0.711348 | + | 0.702840i | \(0.751915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.0000 | 0.948091 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.19098 | − | 2.31838i | −0.150928 | − | 0.109656i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.67376 | 0.220568 | 0.110284 | − | 0.993900i | \(-0.464824\pi\) | ||||
0.110284 | + | 0.993900i | \(0.464824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | −0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.7812 | − | 8.55951i | −0.553527 | − | 0.402161i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.07295 | + | 1.50609i | −0.0971813 | + | 0.0706064i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.4164 | −1.00182 | −0.500909 | − | 0.865500i | \(-0.667001\pi\) | ||||
−0.500909 | + | 0.865500i | \(0.667001\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.09017 | − | 24.8990i | −0.377617 | − | 1.16218i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.253289 | − | 0.779543i | 0.0117968 | − | 0.0363069i | −0.944985 | − | 0.327114i | \(-0.893924\pi\) |
0.956782 | + | 0.290807i | \(0.0939238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.45492 | + | 22.9439i | 0.346459 | + | 1.06629i | 0.960798 | + | 0.277250i | \(0.0894229\pi\) |
−0.614339 | + | 0.789042i | \(0.710577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.07295 | + | 6.37988i | 0.0961307 | + | 0.295860i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.2082 | − | 16.1352i | 1.02767 | − | 0.746648i | 0.0598315 | − | 0.998208i | \(-0.480944\pi\) |
0.967842 | + | 0.251560i | \(0.0809437\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.38197 | + | 1.73060i | −0.109989 | + | 0.0799117i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.6631 | + | 7.74721i | 0.491331 | + | 0.356973i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.85410 | − | 24.1724i | 0.361132 | − | 1.11145i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.31966 | + | 4.06150i | −0.0605502 | + | 0.186354i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.14590 | − | 6.60440i | 0.0982539 | − | 0.302394i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.78115 | − | 6.37988i | −0.401221 | − | 0.291504i | 0.368817 | − | 0.929502i | \(-0.379763\pi\) |
−0.770038 | + | 0.637998i | \(0.779763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.354102 | − | 0.257270i | 0.0161457 | − | 0.0117305i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.88197 | − | 1.36733i | 0.0856324 | − | 0.0622156i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.66312 | − | 8.19624i | 0.120926 | − | 0.372172i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.2533 | + | 34.6341i | 0.509935 | + | 1.56942i | 0.792312 | + | 0.610116i | \(0.208877\pi\) |
−0.282377 | + | 0.959303i | \(0.591123\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.39919 | − | 10.4616i | 0.153717 | − | 0.473091i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.3647 | + | 41.1325i | 0.603143 | + | 1.85628i | 0.509088 | + | 0.860715i | \(0.329983\pi\) |
0.0940550 | + | 0.995567i | \(0.470017\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.9443 | 0.853207 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.23607 | + | 22.2703i | 0.325237 | + | 1.00098i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.30902 | + | 2.40414i | 0.148430 | + | 0.107840i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.56231 | −0.338535 | −0.169268 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169268 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5623 | 0.650596 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.2705 | − | 21.9928i | −1.34970 | − | 0.980611i | −0.999027 | − | 0.0441115i | \(-0.985954\pi\) |
−0.350669 | − | 0.936500i | \(-0.614046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.01722 | − | 3.13068i | −0.0452657 | − | 0.139314i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.56231 | 0.424677 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.28115 | − | 19.3314i | −0.278407 | − | 0.856849i | −0.988298 | − | 0.152537i | \(-0.951256\pi\) |
0.709891 | − | 0.704312i | \(-0.248744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.71885 | − | 5.29007i | 0.0760373 | − | 0.234019i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.31966 | − | 4.06150i | −0.0582644 | − | 0.179319i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.91641 | − | 18.2088i | 0.260708 | − | 0.802377i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.61803 | − | 1.90211i | 0.115141 | − | 0.0836548i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.2812 | − | 11.1024i | 0.670768 | − | 0.487342i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7533 | − | 17.2578i | −1.04065 | − | 0.756077i | −0.0702381 | − | 0.997530i | \(-0.522376\pi\) |
−0.970412 | + | 0.241453i | \(0.922376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.06231 | − | 12.5025i | 0.177632 | − | 0.546696i | −0.822112 | − | 0.569326i | \(-0.807204\pi\) |
0.999744 | + | 0.0226305i | \(0.00720412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.09017 | 0.134866 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.85410 | + | 14.9394i | −0.211448 | + | 0.650770i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.14590 | + | 5.19180i | 0.310691 | + | 0.225730i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.5623 | − | 12.7598i | 0.762139 | − | 0.553727i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.14590 | − | 0.832544i | 0.0496344 | − | 0.0360615i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3435 | − | 34.9116i | −0.490420 | − | 1.50936i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.163119 | − | 0.502029i | −0.00703910 | − | 0.0216641i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.7082 | + | 32.9565i | −0.461235 | + | 1.41954i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.38197 | + | 25.7970i | 0.360369 | + | 1.10910i | 0.952831 | + | 0.303503i | \(0.0981561\pi\) |
−0.592462 | + | 0.805599i | \(0.701844\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.291796 | −0.0125222 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.0902 | − | 13.1433i | 0.774898 | − | 0.562996i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.2254 | − | 12.5150i | −0.736506 | − | 0.535103i | 0.155109 | − | 0.987897i | \(-0.450427\pi\) |
−0.891615 | + | 0.452794i | \(0.850427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.4164 | −0.743314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.09017 | 0.131646 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.04508 | + | 2.93893i | 0.172015 | + | 0.124976i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.527864 | −0.0224066 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.76393 | 0.201854 | 0.100927 | − | 0.994894i | \(-0.467819\pi\) | ||||
0.100927 | + | 0.994894i | \(0.467819\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.78115 | + | 8.55951i | 0.117630 | + | 0.362029i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.47214 | − | 26.0746i | 0.357694 | − | 1.10087i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.28115 | − | 7.02067i | −0.0961391 | − | 0.295886i | 0.891410 | − | 0.453198i | \(-0.149717\pi\) |
−0.987549 | + | 0.157312i | \(0.949717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.4894 | − | 22.1518i | 1.28270 | − | 0.931934i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.500000 | − | 0.363271i | 0.0209980 | − | 0.0152560i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6074 | + | 12.0660i | −0.696218 | + | 0.505832i | −0.878698 | − | 0.477377i | \(-0.841587\pi\) |
0.182480 | + | 0.983210i | \(0.441587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.57295 | − | 4.77553i | −0.275069 | − | 0.199850i | 0.441695 | − | 0.897165i | \(-0.354377\pi\) |
−0.716764 | + | 0.697316i | \(0.754377\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.562306 | + | 1.73060i | −0.0234907 | + | 0.0722968i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.81559 | − | 17.8986i | −0.242527 | − | 0.746422i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.4377 | + | 32.1239i | −0.434527 | + | 1.33734i | 0.459044 | + | 0.888414i | \(0.348192\pi\) |
−0.893571 | + | 0.448923i | \(0.851808\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.23607 | + | 4.53077i | 0.259162 | + | 0.188292i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.11803 | − | 2.26538i | 0.129358 | − | 0.0939840i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.7082 | − | 10.6861i | 0.609152 | − | 0.442575i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.70820 | − | 4.87380i | −0.277350 | − | 0.201507i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.63525 | − | 5.03280i | −0.0674942 | − | 0.207726i | 0.911621 | − | 0.411032i | \(-0.134831\pi\) |
−0.979115 | + | 0.203306i | \(0.934831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.791796 | + | 2.43690i | −0.0326254 | + | 0.100411i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.14590 | − | 3.52671i | −0.0471359 | − | 0.145070i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.9098 | −0.448013 | −0.224007 | − | 0.974588i | \(-0.571914\pi\) | ||||
−0.224007 | + | 0.974588i | \(0.571914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.85410 | + | 4.25325i | 0.239995 | + | 0.174366i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2082 | + | 10.3229i | 0.581503 | + | 0.422487i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.47214 | 0.387021 | 0.193510 | − | 0.981098i | \(-0.438013\pi\) | ||||
0.193510 | + | 0.981098i | \(0.438013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.72949 | 0.111338 | 0.0556691 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556691 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.70820 | − | 5.60034i | −0.313902 | − | 0.228063i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.3435 | + | 34.9116i | −0.461177 | + | 1.41936i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.5623 | 1.44343 | 0.721715 | − | 0.692191i | \(-0.243354\pi\) | ||||
0.721715 | + | 0.692191i | \(0.243354\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.690983 | − | 2.12663i | −0.0280000 | − | 0.0861753i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.354102 | + | 1.08981i | −0.0143254 | + | 0.0440891i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.62868 | − | 14.2456i | −0.186951 | − | 0.575374i | 0.813026 | − | 0.582227i | \(-0.197819\pi\) |
−0.999977 | + | 0.00685287i | \(0.997819\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.70820 | −0.0688814 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5172 | + | 8.36775i | −0.463666 | + | 0.336873i | −0.794968 | − | 0.606652i | \(-0.792512\pi\) |
0.331302 | + | 0.943525i | \(0.392512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.6976 | − | 17.9438i | 0.992679 | − | 0.721223i | 0.0321727 | − | 0.999482i | \(-0.489757\pi\) |
0.960506 | + | 0.278259i | \(0.0897573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.2254 | + | 11.0619i | 0.610975 | + | 0.443900i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.70820 | − | 5.25731i | 0.0684377 | − | 0.210630i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | − | 23.7764i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.38197 | − | 4.25325i | 0.0551904 | − | 0.169859i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.00000 | − | 0.726543i | −0.0398726 | − | 0.0289691i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.28115 | + | 6.01661i | −0.329667 | + | 0.239517i | −0.740290 | − | 0.672288i | \(-0.765312\pi\) |
0.410622 | + | 0.911806i | \(0.365312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.42705 | − | 5.39607i | 0.295199 | − | 0.214474i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 44.4721 | 1.76482 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.79180 | − | 11.6699i | −0.150236 | − | 0.462380i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.09017 | + | 12.5882i | −0.161805 | + | 0.497983i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.336881 | − | 1.03681i | −0.0133060 | − | 0.0409517i | 0.944183 | − | 0.329421i | \(-0.106854\pi\) |
−0.957489 | + | 0.288470i | \(0.906854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.8328 | 1.21593 | 0.607964 | − | 0.793965i | \(-0.291987\pi\) | ||||
0.607964 | + | 0.793965i | \(0.291987\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.35410 | − | 10.3229i | 0.132068 | − | 0.406462i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.5623 | − | 21.4783i | −1.16221 | − | 0.844398i | −0.172158 | − | 0.985069i | \(-0.555074\pi\) |
−0.990056 | + | 0.140671i | \(0.955074\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.8328 | 2.23088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.85410 | 0.0726680 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.4443 | − | 11.2209i | −0.604381 | − | 0.439109i | 0.243050 | − | 0.970014i | \(-0.421852\pi\) |
−0.847431 | + | 0.530905i | \(0.821852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.2984 | − | 8.93529i | −0.480537 | − | 0.349131i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.0000 | 0.702247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.79837 | − | 14.7679i | −0.186918 | − | 0.575275i | 0.813058 | − | 0.582183i | \(-0.197801\pi\) |
−0.999976 | + | 0.00690786i | \(0.997801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.08359 | − | 18.7234i | 0.236624 | − | 0.728255i | −0.760277 | − | 0.649598i | \(-0.774937\pi\) |
0.996902 | − | 0.0786563i | \(-0.0250630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00000 | + | 9.23305i | 0.116510 | + | 0.358582i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.954915 | + | 0.693786i | 0.0370300 | + | 0.0269039i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0172 | + | 8.00448i | −0.426588 | + | 0.309935i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.145898 | − | 0.106001i | 0.00564074 | − | 0.00409824i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.8885 | − | 26.8011i | −1.42407 | − | 1.03464i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.76393 | − | 11.5842i | 0.145089 | − | 0.446538i | −0.851934 | − | 0.523650i | \(-0.824570\pi\) |
0.997022 | + | 0.0771122i | \(0.0245700\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.72542 | + | 23.7764i | 0.297352 | + | 0.915155i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.28115 | − | 10.0984i | 0.126105 | − | 0.388111i | −0.867996 | − | 0.496571i | \(-0.834592\pi\) |
0.994101 | + | 0.108460i | \(0.0345921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.92705 | − | 1.40008i | −0.0739534 | − | 0.0537303i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.9443 | + | 8.67802i | −0.457705 | + | 0.332543i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.8992 | + | 7.91872i | −0.417046 | + | 0.303002i | −0.776448 | − | 0.630181i | \(-0.782981\pi\) |
0.359402 | + | 0.933183i | \(0.382981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.6074 | + | 15.6987i | −0.825576 | + | 0.599816i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.70820 | − | 20.6457i | −0.255934 | − | 0.787684i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.98936 | + | 6.12261i | −0.0757885 | + | 0.233253i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.2082 | − | 34.4953i | −0.426380 | − | 1.31226i | −0.901667 | − | 0.432432i | \(-0.857656\pi\) |
0.475286 | − | 0.879831i | \(-0.342344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.47214 | 0.245856 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.1803 | 0.424094 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.23607 | − | 2.35114i | −0.122575 | − | 0.0890558i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.94427 | 0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.0132 | −1.54905 | −0.774523 | − | 0.632546i | \(-0.782010\pi\) | ||||
−0.774523 | + | 0.632546i | \(0.782010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.163119 | − | 0.118513i | −0.00615215 | − | 0.00446980i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.11803 | − | 0.812299i | 0.0421076 | − | 0.0305930i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.909830 | −0.0342177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.3647 | − | 31.8994i | −0.389256 | − | 1.19801i | −0.933345 | − | 0.358980i | \(-0.883125\pi\) |
0.544089 | − | 0.839027i | \(-0.316875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.00000 | + | 15.3884i | −0.187515 | + | 0.577111i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.48936 | − | 10.7391i | −0.130677 | − | 0.402184i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.70820 | − | 20.6457i | −0.250873 | − | 0.772106i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.6074 | − | 12.0660i | 0.620214 | − | 0.450612i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.8435 | + | 13.6906i | −0.702742 | + | 0.510572i | −0.880824 | − | 0.473443i | \(-0.843011\pi\) |
0.178082 | + | 0.984016i | \(0.443011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.28115 | − | 3.11044i | −0.159438 | − | 0.115839i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.781153 | + | 2.40414i | −0.0290514 | + | 0.0894110i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0902 | −0.671852 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.59017 | + | 23.3601i | −0.281504 | + | 0.866380i | 0.705921 | + | 0.708291i | \(0.250533\pi\) |
−0.987425 | + | 0.158089i | \(0.949467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.5172 | − | 7.64121i | −0.389527 | − | 0.283008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.5623 | − | 14.9394i | 0.760524 | − | 0.552553i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.1631 | − | 11.7432i | 0.596998 | − | 0.433745i | −0.247814 | − | 0.968808i | \(-0.579712\pi\) |
0.844812 | + | 0.535063i | \(0.179712\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.57295 | + | 14.0741i | −0.168676 | + | 0.519131i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.70820 | − | 23.7234i | −0.283935 | − | 0.873863i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.93769 | + | 15.1967i | −0.181636 | + | 0.559018i | −0.999874 | − | 0.0158612i | \(-0.994951\pi\) |
0.818238 | + | 0.574879i | \(0.194951\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.489357 | + | 1.50609i | 0.0179770 | + | 0.0553274i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.3607 | −1.04045 | −0.520226 | − | 0.854029i | \(-0.674152\pi\) | ||||
−0.520226 | + | 0.854029i | \(0.674152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.72542 | + | 8.38800i | 0.0998518 | + | 0.307312i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.0902 | + | 7.33094i | 0.369180 | + | 0.268225i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1459 | −0.370723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.11146 | 0.186520 | 0.0932598 | − | 0.995642i | \(-0.470271\pi\) | ||||
0.0932598 | + | 0.995642i | \(0.470271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.6074 | + | 17.1518i | 0.860301 | + | 0.625045i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0623 | + | 30.9686i | 0.366205 | + | 1.12706i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.4164 | 1.10550 | 0.552752 | − | 0.833346i | \(-0.313578\pi\) | ||||
0.552752 | + | 0.833346i | \(0.313578\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.09017 | + | 18.7436i | 0.221059 | + | 0.680350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.70163 | + | 17.5478i | −0.206684 | + | 0.636107i | 0.792956 | + | 0.609279i | \(0.208541\pi\) |
−0.999640 | + | 0.0268287i | \(0.991459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.90983 | − | 5.87785i | −0.0691405 | − | 0.212793i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.23607 | + | 22.2703i | −0.261621 | + | 0.805185i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.2812 | + | 11.8290i | −0.587878 | + | 0.427119i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.8541 | + | 7.88597i | −0.391409 | + | 0.284375i | −0.766033 | − | 0.642802i | \(-0.777772\pi\) |
0.374624 | + | 0.927177i | \(0.377772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.4894 | + | 13.4333i | 0.665878 | + | 0.483789i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.1738 | + | 34.3893i | −0.401892 | + | 1.23690i | 0.521570 | + | 0.853208i | \(0.325346\pi\) |
−0.923462 | + | 0.383689i | \(0.874654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.63525 | − | 14.2658i | 0.166503 | − | 0.512444i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.0450850 | + | 0.138757i | −0.00161741 | + | 0.00497789i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.527864 | − | 0.383516i | −0.0189127 | − | 0.0137409i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0344 | + | 20.3682i | −1.00315 | + | 0.728832i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.6353 | − | 10.6331i | 0.523021 | − | 0.379997i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.10739 | − | 28.0297i | −0.325057 | − | 1.00042i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.65248 | + | 11.2412i | 0.130197 | + | 0.400704i | 0.994812 | − | 0.101730i | \(-0.0324378\pi\) |
−0.864615 | + | 0.502434i | \(0.832438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.37132 | + | 10.3759i | −0.120022 | + | 0.369391i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.21885 | − | 9.90659i | −0.114449 | − | 0.352238i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1459 | 0.573358 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.28115 | − | 4.56352i | 0.222770 | − | 0.161852i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.89919 | − | 5.73910i | −0.279804 | − | 0.203289i | 0.439028 | − | 0.898473i | \(-0.355323\pi\) |
−0.718832 | + | 0.695184i | \(0.755323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.23607 | 0.114484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8885 | 0.632061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.1246 | + | 27.6992i | 1.34539 | + | 0.977482i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.20163 | −0.183333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.7639 | 0.449312 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.57295 | + | 29.4625i | 0.336567 | + | 1.03585i | 0.965945 | + | 0.258747i | \(0.0833097\pi\) |
−0.629378 | + | 0.777099i | \(0.716690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.54508 | − | 13.9883i | 0.159600 | − | 0.491197i | −0.838998 | − | 0.544134i | \(-0.816858\pi\) |
0.998598 | + | 0.0529372i | \(0.0168583\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.47214 | − | 7.60845i | −0.0867016 | − | 0.266840i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.8992 | + | 14.4576i | −0.697038 | + | 0.506428i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.35410 | − | 2.43690i | 0.117345 | − | 0.0852563i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.85410 | + | 1.34708i | −0.0647876 | + | 0.0470709i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.9164 | + | 23.9152i | 1.14879 | + | 0.834645i | 0.988320 | − | 0.152395i | \(-0.0486987\pi\) |
0.160471 | + | 0.987041i | \(0.448699\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.7426 | + | 45.3732i | −0.513896 | + | 1.58161i | 0.271385 | + | 0.962471i | \(0.412518\pi\) |
−0.785281 | + | 0.619139i | \(0.787482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.09017 | + | 24.8990i | −0.281664 | + | 0.866871i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.298374 | − | 0.918300i | 0.0103755 | − | 0.0319324i | −0.945735 | − | 0.324940i | \(-0.894656\pi\) |
0.956110 | + | 0.293007i | \(0.0946560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.0066 | + | 21.0745i | 1.00744 | + | 0.731948i | 0.963671 | − | 0.267094i | \(-0.0860633\pi\) |
0.0437695 | + | 0.999042i | \(0.486063\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.9894 | + | 14.5231i | −0.693423 | + | 0.503801i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.0344 | + | 20.3682i | −0.971336 | + | 0.705717i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.3435 | − | 19.1396i | −0.911653 | − | 0.662355i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.63525 | + | 14.2658i | 0.160218 | + | 0.493100i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.35410 | + | 10.3229i | −0.115796 | + | 0.356385i | −0.992112 | − | 0.125352i | \(-0.959994\pi\) |
0.876316 | + | 0.481737i | \(0.159994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.91641 | − | 15.1311i | −0.169531 | − | 0.521764i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.0902 | −0.347524 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.2984 | − | 12.5680i | −0.595082 | − | 0.432352i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.20820 | + | 5.96361i | 0.282037 | + | 0.204912i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.8541 | −1.02459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.888544 | 0.0304589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.3820 | + | 8.99602i | 0.423950 | + | 0.308018i | 0.779225 | − | 0.626744i | \(-0.215613\pi\) |
−0.355275 | + | 0.934762i | \(0.615613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.18034 | + | 3.63271i | −0.0403668 | + | 0.124236i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.6869 | 0.672492 | 0.336246 | − | 0.941774i | \(-0.390843\pi\) | ||||
0.336246 | + | 0.941774i | \(0.390843\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.489357 | + | 1.50609i | 0.0166966 | + | 0.0513870i | 0.959058 | − | 0.283211i | \(-0.0913996\pi\) |
−0.942361 | + | 0.334598i | \(0.891400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.145898 | + | 0.449028i | −0.00497219 | + | 0.0153028i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.62461 | + | 20.3885i | 0.225504 | + | 0.694031i | 0.998240 | + | 0.0593032i | \(0.0188879\pi\) |
−0.772736 | + | 0.634728i | \(0.781112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.2361 | −1.43607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.42705 | − | 6.12261i | 0.286198 | − | 0.207935i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.2705 | + | 24.8990i | −1.16255 | + | 0.844640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.14590 | + | 5.19180i | 0.242130 | + | 0.175917i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.38197 | − | 7.33094i | 0.0806173 | − | 0.248115i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.59017 | − | 4.06150i | −0.188982 | − | 0.137304i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.2918 | + | 34.7526i | −0.381297 | + | 1.17351i | 0.557834 | + | 0.829952i | \(0.311632\pi\) |
−0.939131 | + | 0.343559i | \(0.888368\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.7984 | − | 11.4782i | −0.532866 | − | 0.387150i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.6525 | − | 23.7234i | 1.10009 | − | 0.799262i | 0.119015 | − | 0.992892i | \(-0.462026\pi\) |
0.981075 | + | 0.193630i | \(0.0620262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.6525 | + | 12.0987i | −0.560400 | + | 0.407155i | −0.831605 | − | 0.555367i | \(-0.812578\pi\) |
0.271205 | + | 0.962522i | \(0.412578\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.2705 | 0.815844 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.23607 | − | 28.4257i | −0.310117 | − | 0.954441i | −0.977718 | − | 0.209922i | \(-0.932679\pi\) |
0.667601 | − | 0.744519i | \(-0.267321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.79837 | − | 11.6902i | 0.127393 | − | 0.392076i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.61803 | + | 4.97980i | 0.0542062 | + | 0.166829i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.527864 | 0.0176643 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.364745 | + | 1.12257i | −0.0121921 | + | 0.0375234i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.64590 | − | 4.10199i | −0.188511 | − | 0.136961i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.8541 | −0.362005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1803 | 0.605675 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.42705 | − | 1.76336i | −0.0807672 | − | 0.0586808i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.527864 | + | 0.383516i | 0.0175468 | + | 0.0127485i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.2492 | 1.10402 | 0.552011 | − | 0.833837i | \(-0.313861\pi\) | ||||
0.552011 | + | 0.833837i | \(0.313861\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.909830 | − | 2.80017i | −0.0301772 | − | 0.0928757i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.4336 | − | 38.2668i | 0.411944 | − | 1.26783i | −0.503011 | − | 0.864280i | \(-0.667774\pi\) |
0.914955 | − | 0.403555i | \(-0.132226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0902 | + | 31.0543i | 0.333936 | + | 1.02775i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.7533 | − | 11.4454i | −0.520788 | − | 0.378374i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.39919 | + | 2.46965i | −0.112251 | + | 0.0815552i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.0517 | + | 31.2789i | −1.42014 | + | 1.03179i | −0.428395 | + | 0.903591i | \(0.640921\pi\) |
−0.991748 | + | 0.128203i | \(0.959079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.47214 | − | 5.42882i | −0.246215 | − | 0.178886i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.79180 | − | 11.6699i | 0.124808 | − | 0.384121i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.954915 | + | 0.693786i | 0.0313974 | + | 0.0228116i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.29180 | − | 16.2865i | 0.173805 | − | 0.534918i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.6803 | − | 24.4702i | −1.10502 | − | 0.802841i | −0.123145 | − | 0.992389i | \(-0.539298\pi\) |
−0.981872 | + | 0.189548i | \(0.939298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.57295 | + | 3.32244i | −0.149872 | + | 0.108889i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.88197 | + | 5.00004i | −0.225305 | + | 0.163694i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −49.5967 | + | 36.0341i | −1.62199 | + | 1.17844i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.47871 | + | 16.8617i | 0.178982 | + | 0.550849i | 0.999793 | − | 0.0203504i | \(-0.00647819\pi\) |
−0.820811 | + | 0.571200i | \(0.806478\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.18034 | − | 15.9434i | 0.169054 | − | 0.520295i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.3435 | − | 44.1446i | −0.467583 | − | 1.43907i | −0.855704 | − | 0.517465i | \(-0.826876\pi\) |
0.388121 | − | 0.921608i | \(-0.373124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.87539 | 0.0936355 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.90983 | 0.224777 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.14590 | + | 1.55909i | 0.0697323 | + | 0.0506635i | 0.622105 | − | 0.782934i | \(-0.286278\pi\) |
−0.552373 | + | 0.833597i | \(0.686278\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.6869 | −0.541680 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.65248 | −0.248149 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.26393 | + | 4.55101i | 0.202909 | + | 0.147422i | 0.684599 | − | 0.728919i | \(-0.259977\pi\) |
−0.481691 | + | 0.876341i | \(0.659977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.29180 | − | 2.39163i | 0.106520 | − | 0.0773913i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.9443 | 0.612381 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.28115 | + | 7.02067i | 0.0736623 | + | 0.226709i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.79837 | + | 20.9232i | −0.219302 | + | 0.674943i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.1459 | − | 31.2259i | −0.326947 | − | 1.00624i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.32624 | − | 16.3925i | −0.171458 | − | 0.527692i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.32624 | − | 2.41665i | 0.106965 | − | 0.0777143i | −0.533017 | − | 0.846104i | \(-0.678942\pi\) |
0.639982 | + | 0.768390i | \(0.278942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.61803 | − | 2.62866i | 0.116228 | − | 0.0844446i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.54508 | + | 3.30220i | 0.145859 | + | 0.105973i | 0.658321 | − | 0.752737i | \(-0.271267\pi\) |
−0.512463 | + | 0.858709i | \(0.671267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.954915 | − | 2.93893i | 0.0306132 | − | 0.0942177i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.86475 | − | 8.81678i | −0.0917453 | − | 0.282363i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.725425 | + | 2.23263i | −0.0232084 | + | 0.0714281i | −0.961990 | − | 0.273085i | \(-0.911956\pi\) |
0.938782 | + | 0.344513i | \(0.111956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.8885 | + | 27.5276i | 1.21092 | + | 0.879787i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1803 | − | 11.7557i | 0.516598 | − | 0.375331i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.78115 | − | 5.65334i | 0.248180 | − | 0.180313i | −0.456740 | − | 0.889600i | \(-0.650983\pi\) |
0.704920 | + | 0.709287i | \(0.250983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.56231 | + | 7.88597i | −0.0816419 | + | 0.251268i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.118034 | − | 0.363271i | −0.00375706 | − | 0.0115631i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.64590 | + | 17.3763i | −0.179529 | + | 0.552534i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.74671 | + | 14.6089i | 0.150784 | + | 0.464066i | 0.997709 | − | 0.0676459i | \(-0.0215488\pi\) |
−0.846925 | + | 0.531712i | \(0.821549\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.1246 | −0.733837 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.1353 | − | 37.3485i | −0.384713 | − | 1.18403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.1353 | − | 14.6291i | −0.637690 | − | 0.463309i | 0.221366 | − | 0.975191i | \(-0.428949\pi\) |
−0.859056 | + | 0.511882i | \(0.828949\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.18034 | −0.0373443 |
(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 | 400.2.u.b.321.1 | 4 | ||
4.3 | odd | 2 | 25.2.d.a.21.1 | yes | 4 | ||
12.11 | even | 2 | 225.2.h.b.46.1 | 4 | |||
20.3 | even | 4 | 125.2.e.a.24.2 | 8 | |||
20.7 | even | 4 | 125.2.e.a.24.1 | 8 | |||
20.19 | odd | 2 | 125.2.d.a.101.1 | 4 | |||
25.6 | even | 5 | inner | 400.2.u.b.81.1 | 4 | ||
25.9 | even | 10 | 10000.2.a.l.1.2 | 2 | |||
25.16 | even | 5 | 10000.2.a.c.1.1 | 2 | |||
100.3 | even | 20 | 625.2.e.c.374.1 | 8 | |||
100.11 | odd | 10 | 625.2.d.h.376.1 | 4 | |||
100.19 | odd | 10 | 125.2.d.a.26.1 | 4 | |||
100.23 | even | 20 | 625.2.e.c.249.2 | 8 | |||
100.27 | even | 20 | 625.2.e.c.249.1 | 8 | |||
100.31 | odd | 10 | 25.2.d.a.6.1 | ✓ | 4 | ||
100.39 | odd | 10 | 625.2.d.b.376.1 | 4 | |||
100.47 | even | 20 | 625.2.e.c.374.2 | 8 | |||
100.59 | odd | 10 | 625.2.a.c.1.2 | 2 | |||
100.63 | even | 20 | 625.2.b.a.624.4 | 4 | |||
100.67 | even | 20 | 125.2.e.a.99.2 | 8 | |||
100.71 | odd | 10 | 625.2.d.h.251.1 | 4 | |||
100.79 | odd | 10 | 625.2.d.b.251.1 | 4 | |||
100.83 | even | 20 | 125.2.e.a.99.1 | 8 | |||
100.87 | even | 20 | 625.2.b.a.624.1 | 4 | |||
100.91 | odd | 10 | 625.2.a.b.1.1 | 2 | |||
300.59 | even | 10 | 5625.2.a.d.1.1 | 2 | |||
300.131 | even | 10 | 225.2.h.b.181.1 | 4 | |||
300.191 | even | 10 | 5625.2.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.6.1 | ✓ | 4 | 100.31 | odd | 10 | ||
25.2.d.a.21.1 | yes | 4 | 4.3 | odd | 2 | ||
125.2.d.a.26.1 | 4 | 100.19 | odd | 10 | |||
125.2.d.a.101.1 | 4 | 20.19 | odd | 2 | |||
125.2.e.a.24.1 | 8 | 20.7 | even | 4 | |||
125.2.e.a.24.2 | 8 | 20.3 | even | 4 | |||
125.2.e.a.99.1 | 8 | 100.83 | even | 20 | |||
125.2.e.a.99.2 | 8 | 100.67 | even | 20 | |||
225.2.h.b.46.1 | 4 | 12.11 | even | 2 | |||
225.2.h.b.181.1 | 4 | 300.131 | even | 10 | |||
400.2.u.b.81.1 | 4 | 25.6 | even | 5 | inner | ||
400.2.u.b.321.1 | 4 | 1.1 | even | 1 | trivial | ||
625.2.a.b.1.1 | 2 | 100.91 | odd | 10 | |||
625.2.a.c.1.2 | 2 | 100.59 | odd | 10 | |||
625.2.b.a.624.1 | 4 | 100.87 | even | 20 | |||
625.2.b.a.624.4 | 4 | 100.63 | even | 20 | |||
625.2.d.b.251.1 | 4 | 100.79 | odd | 10 | |||
625.2.d.b.376.1 | 4 | 100.39 | odd | 10 | |||
625.2.d.h.251.1 | 4 | 100.71 | odd | 10 | |||
625.2.d.h.376.1 | 4 | 100.11 | odd | 10 | |||
625.2.e.c.249.1 | 8 | 100.27 | even | 20 | |||
625.2.e.c.249.2 | 8 | 100.23 | even | 20 | |||
625.2.e.c.374.1 | 8 | 100.3 | even | 20 | |||
625.2.e.c.374.2 | 8 | 100.47 | even | 20 | |||
5625.2.a.d.1.1 | 2 | 300.59 | even | 10 | |||
5625.2.a.f.1.2 | 2 | 300.191 | even | 10 | |||
10000.2.a.c.1.1 | 2 | 25.16 | even | 5 | |||
10000.2.a.l.1.2 | 2 | 25.9 | even | 10 |