Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,2,Mod(139,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.83655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.11574317056.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 45x^{4} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.8 | ||
Root | \(1.83051 + 1.83051i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.139 |
Dual form | 230.2.b.b.139.1 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 2.40815i | 1.39034i | 0.718843 | + | 0.695172i | \(0.244672\pi\) | ||||
−0.718843 | + | 0.695172i | \(0.755328\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.83051 | + | 1.28422i | 0.818631 | + | 0.574320i | ||||
\(6\) | −2.40815 | −0.983122 | ||||||||
\(7\) | 0.706585i | 0.267064i | 0.991044 | + | 0.133532i | \(0.0426319\pi\) | ||||
−0.991044 | + | 0.133532i | \(0.957368\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.79917 | −0.933058 | ||||||||
\(10\) | −1.28422 | + | 1.83051i | −0.406106 | + | 0.578859i | ||||
\(11\) | 0.747120 | 0.225265 | 0.112633 | − | 0.993637i | \(-0.464072\pi\) | ||||
0.112633 | + | 0.993637i | \(0.464072\pi\) | |||||||
\(12\) | − | 2.40815i | − | 0.695172i | ||||||
\(13\) | − | 1.29341i | − | 0.358729i | −0.983783 | − | 0.179364i | \(-0.942596\pi\) | ||
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(14\) | −0.706585 | −0.188843 | ||||||||
\(15\) | −3.09259 | + | 4.40815i | −0.798503 | + | 1.13818i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.50074i | − | 1.33412i | −0.745002 | − | 0.667062i | \(-0.767551\pi\) | ||
0.745002 | − | 0.667062i | \(-0.232449\pi\) | |||||||
\(18\) | − | 2.79917i | − | 0.659772i | ||||||
\(19\) | −2.44868 | −0.561766 | −0.280883 | − | 0.959742i | \(-0.590627\pi\) | ||||
−0.280883 | + | 0.959742i | \(0.590627\pi\) | |||||||
\(20\) | −1.83051 | − | 1.28422i | −0.409315 | − | 0.287160i | ||||
\(21\) | −1.70156 | −0.371311 | ||||||||
\(22\) | 0.747120i | 0.159286i | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 2.40815 | 0.491561 | ||||||||
\(25\) | 1.70156 | + | 4.70156i | 0.340312 | + | 0.940312i | ||||
\(26\) | 1.29341 | 0.253659 | ||||||||
\(27\) | 0.483617i | 0.0930721i | ||||||||
\(28\) | − | 0.706585i | − | 0.133532i | ||||||
\(29\) | −5.72371 | −1.06287 | −0.531433 | − | 0.847100i | \(-0.678346\pi\) | ||||
−0.531433 | + | 0.847100i | \(0.678346\pi\) | |||||||
\(30\) | −4.40815 | − | 3.09259i | −0.804814 | − | 0.564627i | ||||
\(31\) | 7.52288 | 1.35115 | 0.675575 | − | 0.737292i | \(-0.263896\pi\) | ||||
0.675575 | + | 0.737292i | \(0.263896\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.79917i | 0.313196i | ||||||||
\(34\) | 5.50074 | 0.943369 | ||||||||
\(35\) | −0.907411 | + | 1.29341i | −0.153380 | + | 0.218627i | ||||
\(36\) | 2.79917 | 0.466529 | ||||||||
\(37\) | − | 5.07420i | − | 0.834193i | −0.908862 | − | 0.417097i | \(-0.863048\pi\) | ||
0.908862 | − | 0.417097i | \(-0.136952\pi\) | |||||||
\(38\) | − | 2.44868i | − | 0.397229i | ||||||
\(39\) | 3.11473 | 0.498756 | ||||||||
\(40\) | 1.28422 | − | 1.83051i | 0.203053 | − | 0.289430i | ||||
\(41\) | 10.0876 | 1.57541 | 0.787707 | − | 0.616051i | \(-0.211268\pi\) | ||||
0.787707 | + | 0.616051i | \(0.211268\pi\) | |||||||
\(42\) | − | 1.70156i | − | 0.262557i | ||||||
\(43\) | 5.34045i | 0.814410i | 0.913337 | + | 0.407205i | \(0.133497\pi\) | ||||
−0.913337 | + | 0.407205i | \(0.866503\pi\) | |||||||
\(44\) | −0.747120 | −0.112633 | ||||||||
\(45\) | −5.12393 | − | 3.59475i | −0.763830 | − | 0.535874i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 7.90888i | 1.15363i | 0.816875 | + | 0.576815i | \(0.195705\pi\) | ||||
−0.816875 | + | 0.576815i | \(0.804295\pi\) | |||||||
\(48\) | 2.40815i | 0.347586i | ||||||||
\(49\) | 6.50074 | 0.928677 | ||||||||
\(50\) | −4.70156 | + | 1.70156i | −0.664901 | + | 0.240637i | ||||
\(51\) | 13.2466 | 1.85489 | ||||||||
\(52\) | 1.29341i | 0.179364i | ||||||||
\(53\) | − | 5.84621i | − | 0.803038i | −0.915851 | − | 0.401519i | \(-0.868482\pi\) | ||
0.915851 | − | 0.401519i | \(-0.131518\pi\) | |||||||
\(54\) | −0.483617 | −0.0658119 | ||||||||
\(55\) | 1.36761 | + | 0.959466i | 0.184409 | + | 0.129374i | ||||
\(56\) | 0.706585 | 0.0944215 | ||||||||
\(57\) | − | 5.89679i | − | 0.781049i | ||||||
\(58\) | − | 5.72371i | − | 0.751559i | ||||||
\(59\) | −12.4146 | −1.61625 | −0.808125 | − | 0.589012i | \(-0.799517\pi\) | ||||
−0.808125 | + | 0.589012i | \(0.799517\pi\) | |||||||
\(60\) | 3.09259 | − | 4.40815i | 0.399252 | − | 0.569089i | ||||
\(61\) | 1.57346 | 0.201461 | 0.100731 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100731 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(62\) | 7.52288i | 0.955407i | ||||||||
\(63\) | − | 1.97786i | − | 0.249186i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.66103 | − | 2.36761i | 0.206025 | − | 0.293666i | ||||
\(66\) | −1.79917 | −0.221463 | ||||||||
\(67\) | 5.25938i | 0.642535i | 0.946988 | + | 0.321268i | \(0.104109\pi\) | ||||
−0.946988 | + | 0.321268i | \(0.895891\pi\) | |||||||
\(68\) | 5.50074i | 0.667062i | ||||||||
\(69\) | 2.40815 | 0.289907 | ||||||||
\(70\) | −1.29341 | − | 0.907411i | −0.154593 | − | 0.108456i | ||||
\(71\) | 2.68444 | 0.318585 | 0.159292 | − | 0.987231i | \(-0.449079\pi\) | ||||
0.159292 | + | 0.987231i | \(0.449079\pi\) | |||||||
\(72\) | 2.79917i | 0.329886i | ||||||||
\(73\) | − | 10.4589i | − | 1.22413i | −0.790809 | − | 0.612063i | \(-0.790340\pi\) | ||
0.790809 | − | 0.612063i | \(-0.209660\pi\) | |||||||
\(74\) | 5.07420 | 0.589864 | ||||||||
\(75\) | −11.3221 | + | 4.09761i | −1.30736 | + | 0.473152i | ||||
\(76\) | 2.44868 | 0.280883 | ||||||||
\(77\) | 0.527904i | 0.0601602i | ||||||||
\(78\) | 3.11473i | 0.352674i | ||||||||
\(79\) | 6.55005 | 0.736938 | 0.368469 | − | 0.929640i | \(-0.379882\pi\) | ||||
0.368469 | + | 0.929640i | \(0.379882\pi\) | |||||||
\(80\) | 1.83051 | + | 1.28422i | 0.204658 | + | 0.143580i | ||||
\(81\) | −9.56214 | −1.06246 | ||||||||
\(82\) | 10.0876i | 1.11399i | ||||||||
\(83\) | − | 12.7068i | − | 1.39475i | −0.716706 | − | 0.697376i | \(-0.754351\pi\) | ||
0.716706 | − | 0.697376i | \(-0.245649\pi\) | |||||||
\(84\) | 1.70156 | 0.185656 | ||||||||
\(85\) | 7.06415 | − | 10.0692i | 0.766215 | − | 1.09216i | ||||
\(86\) | −5.34045 | −0.575875 | ||||||||
\(87\) | − | 13.7835i | − | 1.47775i | ||||||
\(88\) | − | 0.747120i | − | 0.0796432i | ||||||
\(89\) | −13.6426 | −1.44612 | −0.723058 | − | 0.690787i | \(-0.757264\pi\) | ||||
−0.723058 | + | 0.690787i | \(0.757264\pi\) | |||||||
\(90\) | 3.59475 | − | 5.12393i | 0.378920 | − | 0.540109i | ||||
\(91\) | 0.913908 | 0.0958036 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 18.1162i | 1.87856i | ||||||||
\(94\) | −7.90888 | −0.815739 | ||||||||
\(95\) | −4.48235 | − | 3.14464i | −0.459879 | − | 0.322634i | ||||
\(96\) | −2.40815 | −0.245781 | ||||||||
\(97\) | 1.50074i | 0.152377i | 0.997093 | + | 0.0761884i | \(0.0242750\pi\) | ||||
−0.997093 | + | 0.0761884i | \(0.975725\pi\) | |||||||
\(98\) | 6.50074i | 0.656674i | ||||||||
\(99\) | −2.09132 | −0.210185 | ||||||||
\(100\) | −1.70156 | − | 4.70156i | −0.170156 | − | 0.470156i | ||||
\(101\) | −16.0472 | −1.59676 | −0.798380 | − | 0.602154i | \(-0.794309\pi\) | ||||
−0.798380 | + | 0.602154i | \(0.794309\pi\) | |||||||
\(102\) | 13.2466i | 1.31161i | ||||||||
\(103\) | − | 9.49069i | − | 0.935145i | −0.883955 | − | 0.467573i | \(-0.845129\pi\) | ||
0.883955 | − | 0.467573i | \(-0.154871\pi\) | |||||||
\(104\) | −1.29341 | −0.126830 | ||||||||
\(105\) | −3.11473 | − | 2.18518i | −0.303967 | − | 0.213252i | ||||
\(106\) | 5.84621 | 0.567834 | ||||||||
\(107\) | 1.38473i | 0.133867i | 0.997757 | + | 0.0669336i | \(0.0213216\pi\) | ||||
−0.997757 | + | 0.0669336i | \(0.978678\pi\) | |||||||
\(108\) | − | 0.483617i | − | 0.0465360i | ||||||
\(109\) | 14.0370 | 1.34450 | 0.672250 | − | 0.740325i | \(-0.265328\pi\) | ||||
0.672250 | + | 0.740325i | \(0.265328\pi\) | |||||||
\(110\) | −0.959466 | + | 1.36761i | −0.0914815 | + | 0.130397i | ||||
\(111\) | 12.2194 | 1.15982 | ||||||||
\(112\) | 0.706585i | 0.0667661i | ||||||||
\(113\) | 16.3105i | 1.53437i | 0.641428 | + | 0.767183i | \(0.278342\pi\) | ||||
−0.641428 | + | 0.767183i | \(0.721658\pi\) | |||||||
\(114\) | 5.89679 | 0.552285 | ||||||||
\(115\) | 1.28422 | − | 1.83051i | 0.119754 | − | 0.170696i | ||||
\(116\) | 5.72371 | 0.531433 | ||||||||
\(117\) | 3.62049i | 0.334715i | ||||||||
\(118\) | − | 12.4146i | − | 1.14286i | ||||||
\(119\) | 3.88674 | 0.356297 | ||||||||
\(120\) | 4.40815 | + | 3.09259i | 0.402407 | + | 0.282313i | ||||
\(121\) | −10.4418 | −0.949256 | ||||||||
\(122\) | 1.57346i | 0.142455i | ||||||||
\(123\) | 24.2923i | 2.19037i | ||||||||
\(124\) | −7.52288 | −0.675575 | ||||||||
\(125\) | −2.92310 | + | 10.7915i | −0.261450 | + | 0.965217i | ||||
\(126\) | 1.97786 | 0.176201 | ||||||||
\(127\) | − | 2.73523i | − | 0.242712i | −0.992609 | − | 0.121356i | \(-0.961276\pi\) | ||
0.992609 | − | 0.121356i | \(-0.0387243\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −12.8606 | −1.13231 | ||||||||
\(130\) | 2.36761 | + | 1.66103i | 0.207653 | + | 0.145682i | ||||
\(131\) | −8.21942 | −0.718134 | −0.359067 | − | 0.933312i | \(-0.616905\pi\) | ||||
−0.359067 | + | 0.933312i | \(0.616905\pi\) | |||||||
\(132\) | − | 1.79917i | − | 0.156598i | ||||||
\(133\) | − | 1.73020i | − | 0.150028i | ||||||
\(134\) | −5.25938 | −0.454341 | ||||||||
\(135\) | −0.621070 | + | 0.885267i | −0.0534532 | + | 0.0761916i | ||||
\(136\) | −5.50074 | −0.471684 | ||||||||
\(137\) | − | 22.8449i | − | 1.95177i | −0.218275 | − | 0.975887i | \(-0.570043\pi\) | ||
0.218275 | − | 0.975887i | \(-0.429957\pi\) | |||||||
\(138\) | 2.40815i | 0.204995i | ||||||||
\(139\) | −3.76049 | −0.318960 | −0.159480 | − | 0.987201i | \(-0.550982\pi\) | ||||
−0.159480 | + | 0.987201i | \(0.550982\pi\) | |||||||
\(140\) | 0.907411 | − | 1.29341i | 0.0766902 | − | 0.109313i | ||||
\(141\) | −19.0458 | −1.60394 | ||||||||
\(142\) | 2.68444i | 0.225273i | ||||||||
\(143\) | − | 0.966336i | − | 0.0808090i | ||||||
\(144\) | −2.79917 | −0.233265 | ||||||||
\(145\) | −10.4773 | − | 7.35049i | −0.870094 | − | 0.610425i | ||||
\(146\) | 10.4589 | 0.865587 | ||||||||
\(147\) | 15.6547i | 1.29118i | ||||||||
\(148\) | 5.07420i | 0.417097i | ||||||||
\(149\) | 1.90614 | 0.156157 | 0.0780785 | − | 0.996947i | \(-0.475122\pi\) | ||||
0.0780785 | + | 0.996947i | \(0.475122\pi\) | |||||||
\(150\) | −4.09761 | − | 11.3221i | −0.334569 | − | 0.924442i | ||||
\(151\) | −9.41967 | −0.766562 | −0.383281 | − | 0.923632i | \(-0.625206\pi\) | ||||
−0.383281 | + | 0.923632i | \(0.625206\pi\) | |||||||
\(152\) | 2.44868i | 0.198614i | ||||||||
\(153\) | 15.3975i | 1.24482i | ||||||||
\(154\) | −0.527904 | −0.0425397 | ||||||||
\(155\) | 13.7707 | + | 9.66103i | 1.10609 | + | 0.775992i | ||||
\(156\) | −3.11473 | −0.249378 | ||||||||
\(157\) | 4.43304i | 0.353795i | 0.984229 | + | 0.176897i | \(0.0566061\pi\) | ||||
−0.984229 | + | 0.176897i | \(0.943394\pi\) | |||||||
\(158\) | 6.55005i | 0.521094i | ||||||||
\(159\) | 14.0785 | 1.11650 | ||||||||
\(160\) | −1.28422 | + | 1.83051i | −0.101526 | + | 0.144715i | ||||
\(161\) | 0.706585 | 0.0556867 | ||||||||
\(162\) | − | 9.56214i | − | 0.751273i | ||||||
\(163\) | − | 9.92453i | − | 0.777349i | −0.921375 | − | 0.388675i | \(-0.872933\pi\) | ||
0.921375 | − | 0.388675i | \(-0.127067\pi\) | |||||||
\(164\) | −10.0876 | −0.787707 | ||||||||
\(165\) | −2.31053 | + | 3.29341i | −0.179875 | + | 0.256392i | ||||
\(166\) | 12.7068 | 0.986238 | ||||||||
\(167\) | − | 11.9089i | − | 0.921537i | −0.887520 | − | 0.460769i | \(-0.847574\pi\) | ||
0.887520 | − | 0.460769i | \(-0.152426\pi\) | |||||||
\(168\) | 1.70156i | 0.131278i | ||||||||
\(169\) | 11.3271 | 0.871314 | ||||||||
\(170\) | 10.0692 | + | 7.06415i | 0.772270 | + | 0.541796i | ||||
\(171\) | 6.85429 | 0.524161 | ||||||||
\(172\) | − | 5.34045i | − | 0.407205i | ||||||
\(173\) | − | 2.91391i | − | 0.221540i | −0.993846 | − | 0.110770i | \(-0.964668\pi\) | ||
0.993846 | − | 0.110770i | \(-0.0353317\pi\) | |||||||
\(174\) | 13.7835 | 1.04493 | ||||||||
\(175\) | −3.32206 | + | 1.20230i | −0.251124 | + | 0.0908853i | ||||
\(176\) | 0.747120 | 0.0563163 | ||||||||
\(177\) | − | 29.8963i | − | 2.24714i | ||||||
\(178\) | − | 13.6426i | − | 1.02256i | ||||||
\(179\) | −19.3663 | −1.44751 | −0.723754 | − | 0.690058i | \(-0.757585\pi\) | ||||
−0.723754 | + | 0.690058i | \(0.757585\pi\) | |||||||
\(180\) | 5.12393 | + | 3.59475i | 0.381915 | + | 0.267937i | ||||
\(181\) | 17.5986 | 1.30809 | 0.654045 | − | 0.756456i | \(-0.273071\pi\) | ||||
0.654045 | + | 0.756456i | \(0.273071\pi\) | |||||||
\(182\) | 0.913908i | 0.0677434i | ||||||||
\(183\) | 3.78913i | 0.280100i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 6.51638 | − | 9.28839i | 0.479094 | − | 0.682896i | ||||
\(186\) | −18.1162 | −1.32834 | ||||||||
\(187\) | − | 4.10971i | − | 0.300532i | ||||||
\(188\) | − | 7.90888i | − | 0.576815i | ||||||
\(189\) | −0.341716 | −0.0248562 | ||||||||
\(190\) | 3.14464 | − | 4.48235i | 0.228136 | − | 0.325184i | ||||
\(191\) | 20.3578 | 1.47304 | 0.736518 | − | 0.676418i | \(-0.236469\pi\) | ||||
0.736518 | + | 0.676418i | \(0.236469\pi\) | |||||||
\(192\) | − | 2.40815i | − | 0.173793i | ||||||
\(193\) | 1.41317i | 0.101722i | 0.998706 | + | 0.0508611i | \(0.0161966\pi\) | ||||
−0.998706 | + | 0.0508611i | \(0.983803\pi\) | |||||||
\(194\) | −1.50074 | −0.107747 | ||||||||
\(195\) | 5.70156 | + | 4.00000i | 0.408297 | + | 0.286446i | ||||
\(196\) | −6.50074 | −0.464338 | ||||||||
\(197\) | 4.92395i | 0.350817i | 0.984496 | + | 0.175409i | \(0.0561247\pi\) | ||||
−0.984496 | + | 0.175409i | \(0.943875\pi\) | |||||||
\(198\) | − | 2.09132i | − | 0.148624i | ||||||
\(199\) | 10.3105 | 0.730894 | 0.365447 | − | 0.930832i | \(-0.380916\pi\) | ||||
0.365447 | + | 0.930832i | \(0.380916\pi\) | |||||||
\(200\) | 4.70156 | − | 1.70156i | 0.332451 | − | 0.120319i | ||||
\(201\) | −12.6654 | −0.893345 | ||||||||
\(202\) | − | 16.0472i | − | 1.12908i | ||||||
\(203\) | − | 4.04429i | − | 0.283853i | ||||||
\(204\) | −13.2466 | −0.927447 | ||||||||
\(205\) | 18.4654 | + | 12.9546i | 1.28968 | + | 0.904792i | ||||
\(206\) | 9.49069 | 0.661248 | ||||||||
\(207\) | 2.79917i | 0.194556i | ||||||||
\(208\) | − | 1.29341i | − | 0.0896822i | ||||||
\(209\) | −1.82946 | −0.126546 | ||||||||
\(210\) | 2.18518 | − | 3.11473i | 0.150792 | − | 0.214937i | ||||
\(211\) | 11.4161 | 0.785918 | 0.392959 | − | 0.919556i | \(-0.371451\pi\) | ||||
0.392959 | + | 0.919556i | \(0.371451\pi\) | |||||||
\(212\) | 5.84621i | 0.401519i | ||||||||
\(213\) | 6.46453i | 0.442942i | ||||||||
\(214\) | −1.38473 | −0.0946584 | ||||||||
\(215\) | −6.85830 | + | 9.77576i | −0.467732 | + | 0.666701i | ||||
\(216\) | 0.483617 | 0.0329059 | ||||||||
\(217\) | 5.31556i | 0.360844i | ||||||||
\(218\) | 14.0370i | 0.950705i | ||||||||
\(219\) | 25.1867 | 1.70196 | ||||||||
\(220\) | −1.36761 | − | 0.959466i | −0.0922045 | − | 0.0646872i | ||||
\(221\) | −7.11473 | −0.478589 | ||||||||
\(222\) | 12.2194i | 0.820114i | ||||||||
\(223\) | 18.2094i | 1.21939i | 0.792636 | + | 0.609695i | \(0.208708\pi\) | ||||
−0.792636 | + | 0.609695i | \(0.791292\pi\) | |||||||
\(224\) | −0.706585 | −0.0472107 | ||||||||
\(225\) | −4.76297 | − | 13.1605i | −0.317531 | − | 0.877366i | ||||
\(226\) | −16.3105 | −1.08496 | ||||||||
\(227\) | − | 18.9363i | − | 1.25684i | −0.777873 | − | 0.628422i | \(-0.783701\pi\) | ||
0.777873 | − | 0.628422i | \(-0.216299\pi\) | |||||||
\(228\) | 5.89679i | 0.390524i | ||||||||
\(229\) | 8.46433 | 0.559339 | 0.279669 | − | 0.960096i | \(-0.409775\pi\) | ||||
0.279669 | + | 0.960096i | \(0.409775\pi\) | |||||||
\(230\) | 1.83051 | + | 1.28422i | 0.120701 | + | 0.0846789i | ||||
\(231\) | −1.27127 | −0.0836435 | ||||||||
\(232\) | 5.72371i | 0.375780i | ||||||||
\(233\) | − | 16.6341i | − | 1.08973i | −0.838523 | − | 0.544867i | \(-0.816580\pi\) | ||
0.838523 | − | 0.544867i | \(-0.183420\pi\) | |||||||
\(234\) | −3.62049 | −0.236679 | ||||||||
\(235\) | −10.1567 | + | 14.4773i | −0.662553 | + | 0.944396i | ||||
\(236\) | 12.4146 | 0.808125 | ||||||||
\(237\) | 15.7735i | 1.02460i | ||||||||
\(238\) | 3.88674i | 0.251940i | ||||||||
\(239\) | 16.0840 | 1.04039 | 0.520194 | − | 0.854048i | \(-0.325860\pi\) | ||||
0.520194 | + | 0.854048i | \(0.325860\pi\) | |||||||
\(240\) | −3.09259 | + | 4.40815i | −0.199626 | + | 0.284545i | ||||
\(241\) | −28.1283 | −1.81190 | −0.905952 | − | 0.423381i | \(-0.860843\pi\) | ||||
−0.905952 | + | 0.423381i | \(0.860843\pi\) | |||||||
\(242\) | − | 10.4418i | − | 0.671225i | ||||||
\(243\) | − | 21.5762i | − | 1.38411i | ||||||
\(244\) | −1.57346 | −0.100731 | ||||||||
\(245\) | 11.8997 | + | 8.34837i | 0.760243 | + | 0.533358i | ||||
\(246\) | −24.2923 | −1.54882 | ||||||||
\(247\) | 3.16716i | 0.201522i | ||||||||
\(248\) | − | 7.52288i | − | 0.477703i | ||||||
\(249\) | 30.5998 | 1.93919 | ||||||||
\(250\) | −10.7915 | − | 2.92310i | −0.682511 | − | 0.184873i | ||||
\(251\) | −20.5770 | −1.29881 | −0.649404 | − | 0.760444i | \(-0.724982\pi\) | ||||
−0.649404 | + | 0.760444i | \(0.724982\pi\) | |||||||
\(252\) | 1.97786i | 0.124593i | ||||||||
\(253\) | − | 0.747120i | − | 0.0469710i | ||||||
\(254\) | 2.73523 | 0.171623 | ||||||||
\(255\) | 24.2481 | + | 17.0115i | 1.51847 | + | 1.06530i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.8505i | 1.05111i | 0.850760 | + | 0.525554i | \(0.176142\pi\) | ||||
−0.850760 | + | 0.525554i | \(0.823858\pi\) | |||||||
\(258\) | − | 12.8606i | − | 0.800665i | ||||||
\(259\) | 3.58536 | 0.222783 | ||||||||
\(260\) | −1.66103 | + | 2.36761i | −0.103013 | + | 0.146833i | ||||
\(261\) | 16.0217 | 0.991715 | ||||||||
\(262\) | − | 8.21942i | − | 0.507797i | ||||||
\(263\) | − | 24.7630i | − | 1.52695i | −0.645837 | − | 0.763475i | \(-0.723492\pi\) | ||
0.645837 | − | 0.763475i | \(-0.276508\pi\) | |||||||
\(264\) | 1.79917 | 0.110732 | ||||||||
\(265\) | 7.50781 | − | 10.7016i | 0.461201 | − | 0.657392i | ||||
\(266\) | 1.73020 | 0.106086 | ||||||||
\(267\) | − | 32.8535i | − | 2.01060i | ||||||
\(268\) | − | 5.25938i | − | 0.321268i | ||||||
\(269\) | 3.55152 | 0.216540 | 0.108270 | − | 0.994122i | \(-0.465469\pi\) | ||||
0.108270 | + | 0.994122i | \(0.465469\pi\) | |||||||
\(270\) | −0.885267 | − | 0.621070i | −0.0538756 | − | 0.0377971i | ||||
\(271\) | −27.4761 | −1.66905 | −0.834526 | − | 0.550969i | \(-0.814258\pi\) | ||||
−0.834526 | + | 0.550969i | \(0.814258\pi\) | |||||||
\(272\) | − | 5.50074i | − | 0.333531i | ||||||
\(273\) | 2.20083i | 0.133200i | ||||||||
\(274\) | 22.8449 | 1.38011 | ||||||||
\(275\) | 1.27127 | + | 3.51263i | 0.0766605 | + | 0.211820i | ||||
\(276\) | −2.40815 | −0.144953 | ||||||||
\(277\) | 11.1001i | 0.666940i | 0.942761 | + | 0.333470i | \(0.108220\pi\) | ||||
−0.942761 | + | 0.333470i | \(0.891780\pi\) | |||||||
\(278\) | − | 3.76049i | − | 0.225539i | ||||||
\(279\) | −21.0579 | −1.26070 | ||||||||
\(280\) | 1.29341 | + | 0.907411i | 0.0772963 | + | 0.0542282i | ||||
\(281\) | 13.0458 | 0.778245 | 0.389122 | − | 0.921186i | \(-0.372778\pi\) | ||||
0.389122 | + | 0.921186i | \(0.372778\pi\) | |||||||
\(282\) | − | 19.0458i | − | 1.13416i | ||||||
\(283\) | 3.35049i | 0.199166i | 0.995029 | + | 0.0995831i | \(0.0317509\pi\) | ||||
−0.995029 | + | 0.0995831i | \(0.968249\pi\) | |||||||
\(284\) | −2.68444 | −0.159292 | ||||||||
\(285\) | 7.57277 | − | 10.7942i | 0.448572 | − | 0.639390i | ||||
\(286\) | 0.966336 | 0.0571406 | ||||||||
\(287\) | 7.12773i | 0.420736i | ||||||||
\(288\) | − | 2.79917i | − | 0.164943i | ||||||
\(289\) | −13.2581 | −0.779889 | ||||||||
\(290\) | 7.35049 | − | 10.4773i | 0.431636 | − | 0.615250i | ||||
\(291\) | −3.61400 | −0.211856 | ||||||||
\(292\) | 10.4589i | 0.612063i | ||||||||
\(293\) | 8.89197i | 0.519474i | 0.965679 | + | 0.259737i | \(0.0836359\pi\) | ||||
−0.965679 | + | 0.259737i | \(0.916364\pi\) | |||||||
\(294\) | −15.6547 | −0.913003 | ||||||||
\(295\) | −22.7252 | − | 15.9431i | −1.32311 | − | 0.928245i | ||||
\(296\) | −5.07420 | −0.294932 | ||||||||
\(297\) | 0.361320i | 0.0209659i | ||||||||
\(298\) | 1.90614i | 0.110420i | ||||||||
\(299\) | −1.29341 | −0.0748001 | ||||||||
\(300\) | 11.3221 | − | 4.09761i | 0.653679 | − | 0.236576i | ||||
\(301\) | −3.77348 | −0.217500 | ||||||||
\(302\) | − | 9.41967i | − | 0.542041i | ||||||
\(303\) | − | 38.6441i | − | 2.22005i | ||||||
\(304\) | −2.44868 | −0.140442 | ||||||||
\(305\) | 2.88024 | + | 2.02067i | 0.164922 | + | 0.115703i | ||||
\(306\) | −15.3975 | −0.880218 | ||||||||
\(307\) | 28.4111i | 1.62151i | 0.585388 | + | 0.810753i | \(0.300942\pi\) | ||||
−0.585388 | + | 0.810753i | \(0.699058\pi\) | |||||||
\(308\) | − | 0.527904i | − | 0.0300801i | ||||||
\(309\) | 22.8550 | 1.30017 | ||||||||
\(310\) | −9.66103 | + | 13.7707i | −0.548710 | + | 0.782125i | ||||
\(311\) | −28.0105 | −1.58833 | −0.794164 | − | 0.607704i | \(-0.792091\pi\) | ||||
−0.794164 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(312\) | − | 3.11473i | − | 0.176337i | ||||||
\(313\) | 7.42882i | 0.419902i | 0.977712 | + | 0.209951i | \(0.0673304\pi\) | ||||
−0.977712 | + | 0.209951i | \(0.932670\pi\) | |||||||
\(314\) | −4.43304 | −0.250171 | ||||||||
\(315\) | 2.54000 | − | 3.62049i | 0.143113 | − | 0.203992i | ||||
\(316\) | −6.55005 | −0.368469 | ||||||||
\(317\) | 13.1480i | 0.738463i | 0.929337 | + | 0.369232i | \(0.120379\pi\) | ||||
−0.929337 | + | 0.369232i | \(0.879621\pi\) | |||||||
\(318\) | 14.0785i | 0.789485i | ||||||||
\(319\) | −4.27629 | −0.239427 | ||||||||
\(320\) | −1.83051 | − | 1.28422i | −0.102329 | − | 0.0717900i | ||||
\(321\) | −3.33464 | −0.186122 | ||||||||
\(322\) | 0.706585i | 0.0393765i | ||||||||
\(323\) | 13.4696i | 0.749466i | ||||||||
\(324\) | 9.56214 | 0.531230 | ||||||||
\(325\) | 6.08107 | − | 2.20083i | 0.337317 | − | 0.122080i | ||||
\(326\) | 9.92453 | 0.549669 | ||||||||
\(327\) | 33.8031i | 1.86932i | ||||||||
\(328\) | − | 10.0876i | − | 0.556993i | ||||||
\(329\) | −5.58830 | −0.308093 | ||||||||
\(330\) | −3.29341 | − | 2.31053i | −0.181297 | − | 0.127191i | ||||
\(331\) | −15.6225 | −0.858693 | −0.429346 | − | 0.903140i | \(-0.641256\pi\) | ||||
−0.429346 | + | 0.903140i | \(0.641256\pi\) | |||||||
\(332\) | 12.7068i | 0.697376i | ||||||||
\(333\) | 14.2036i | 0.778351i | ||||||||
\(334\) | 11.9089 | 0.651625 | ||||||||
\(335\) | −6.75419 | + | 9.62736i | −0.369021 | + | 0.525999i | ||||
\(336\) | −1.70156 | −0.0928278 | ||||||||
\(337\) | − | 16.6965i | − | 0.909518i | −0.890614 | − | 0.454759i | \(-0.849725\pi\) | ||
0.890614 | − | 0.454759i | \(-0.150275\pi\) | |||||||
\(338\) | 11.3271i | 0.616112i | ||||||||
\(339\) | −39.2782 | −2.13330 | ||||||||
\(340\) | −7.06415 | + | 10.0692i | −0.383107 | + | 0.546078i | ||||
\(341\) | 5.62049 | 0.304367 | ||||||||
\(342\) | 6.85429i | 0.370637i | ||||||||
\(343\) | 9.53942i | 0.515081i | ||||||||
\(344\) | 5.34045 | 0.287938 | ||||||||
\(345\) | 4.40815 | + | 3.09259i | 0.237327 | + | 0.166499i | ||||
\(346\) | 2.91391 | 0.156653 | ||||||||
\(347\) | 16.3981i | 0.880296i | 0.897925 | + | 0.440148i | \(0.145074\pi\) | ||||
−0.897925 | + | 0.440148i | \(0.854926\pi\) | |||||||
\(348\) | 13.7835i | 0.738875i | ||||||||
\(349\) | 1.86165 | 0.0996518 | 0.0498259 | − | 0.998758i | \(-0.484133\pi\) | ||||
0.0498259 | + | 0.998758i | \(0.484133\pi\) | |||||||
\(350\) | −1.20230 | − | 3.32206i | −0.0642656 | − | 0.177571i | ||||
\(351\) | 0.625517 | 0.0333876 | ||||||||
\(352\) | 0.747120i | 0.0398216i | ||||||||
\(353\) | 25.8408i | 1.37537i | 0.726010 | + | 0.687684i | \(0.241372\pi\) | ||||
−0.726010 | + | 0.687684i | \(0.758628\pi\) | |||||||
\(354\) | 29.8963 | 1.58897 | ||||||||
\(355\) | 4.91391 | + | 3.44741i | 0.260803 | + | 0.182970i | ||||
\(356\) | 13.6426 | 0.723058 | ||||||||
\(357\) | 9.35985i | 0.495376i | ||||||||
\(358\) | − | 19.3663i | − | 1.02354i | ||||||
\(359\) | −8.72223 | −0.460342 | −0.230171 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230171 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(360\) | −3.59475 | + | 5.12393i | −0.189460 | + | 0.270055i | ||||
\(361\) | −13.0040 | −0.684419 | ||||||||
\(362\) | 17.5986i | 0.924959i | ||||||||
\(363\) | − | 25.1454i | − | 1.31979i | ||||||
\(364\) | −0.913908 | −0.0479018 | ||||||||
\(365\) | 13.4316 | − | 19.1452i | 0.703040 | − | 1.00211i | ||||
\(366\) | −3.78913 | −0.198061 | ||||||||
\(367\) | 25.5958i | 1.33609i | 0.744121 | + | 0.668045i | \(0.232869\pi\) | ||||
−0.744121 | + | 0.668045i | \(0.767131\pi\) | |||||||
\(368\) | − | 1.00000i | − | 0.0521286i | ||||||
\(369\) | −28.2369 | −1.46995 | ||||||||
\(370\) | 9.28839 | + | 6.51638i | 0.482880 | + | 0.338771i | ||||
\(371\) | 4.13084 | 0.214463 | ||||||||
\(372\) | − | 18.1162i | − | 0.939282i | ||||||
\(373\) | 17.2125i | 0.891232i | 0.895224 | + | 0.445616i | \(0.147015\pi\) | ||||
−0.895224 | + | 0.445616i | \(0.852985\pi\) | |||||||
\(374\) | 4.10971 | 0.212508 | ||||||||
\(375\) | −25.9874 | − | 7.03926i | −1.34198 | − | 0.363506i | ||||
\(376\) | 7.90888 | 0.407870 | ||||||||
\(377\) | 7.40312i | 0.381280i | ||||||||
\(378\) | − | 0.341716i | − | 0.0175760i | ||||||
\(379\) | −23.0339 | −1.18317 | −0.591585 | − | 0.806243i | \(-0.701498\pi\) | ||||
−0.591585 | + | 0.806243i | \(0.701498\pi\) | |||||||
\(380\) | 4.48235 | + | 3.14464i | 0.229940 | + | 0.161317i | ||||
\(381\) | 6.58683 | 0.337453 | ||||||||
\(382\) | 20.3578i | 1.04159i | ||||||||
\(383\) | − | 3.81777i | − | 0.195079i | −0.995232 | − | 0.0975394i | \(-0.968903\pi\) | ||
0.995232 | − | 0.0975394i | \(-0.0310972\pi\) | |||||||
\(384\) | 2.40815 | 0.122890 | ||||||||
\(385\) | −0.677944 | + | 0.966336i | −0.0345513 | + | 0.0492490i | ||||
\(386\) | −1.41317 | −0.0719285 | ||||||||
\(387\) | − | 14.9488i | − | 0.759892i | ||||||
\(388\) | − | 1.50074i | − | 0.0761884i | ||||||
\(389\) | 8.25435 | 0.418512 | 0.209256 | − | 0.977861i | \(-0.432896\pi\) | ||||
0.209256 | + | 0.977861i | \(0.432896\pi\) | |||||||
\(390\) | −4.00000 | + | 5.70156i | −0.202548 | + | 0.288710i | ||||
\(391\) | −5.50074 | −0.278184 | ||||||||
\(392\) | − | 6.50074i | − | 0.328337i | ||||||
\(393\) | − | 19.7936i | − | 0.998454i | ||||||
\(394\) | −4.92395 | −0.248065 | ||||||||
\(395\) | 11.9900 | + | 8.41170i | 0.603280 | + | 0.423238i | ||||
\(396\) | 2.09132 | 0.105093 | ||||||||
\(397\) | 12.4967i | 0.627193i | 0.949556 | + | 0.313596i | \(0.101534\pi\) | ||||
−0.949556 | + | 0.313596i | \(0.898466\pi\) | |||||||
\(398\) | 10.3105i | 0.516820i | ||||||||
\(399\) | 4.16658 | 0.208590 | ||||||||
\(400\) | 1.70156 | + | 4.70156i | 0.0850781 | + | 0.235078i | ||||
\(401\) | 34.5660 | 1.72614 | 0.863072 | − | 0.505082i | \(-0.168538\pi\) | ||||
0.863072 | + | 0.505082i | \(0.168538\pi\) | |||||||
\(402\) | − | 12.6654i | − | 0.631691i | ||||||
\(403\) | − | 9.73020i | − | 0.484696i | ||||||
\(404\) | 16.0472 | 0.798380 | ||||||||
\(405\) | −17.5036 | − | 12.2799i | −0.869763 | − | 0.610193i | ||||
\(406\) | 4.04429 | 0.200715 | ||||||||
\(407\) | − | 3.79103i | − | 0.187915i | ||||||
\(408\) | − | 13.2466i | − | 0.655804i | ||||||
\(409\) | −12.0499 | −0.595829 | −0.297914 | − | 0.954593i | \(-0.596291\pi\) | ||||
−0.297914 | + | 0.954593i | \(0.596291\pi\) | |||||||
\(410\) | −12.9546 | + | 18.4654i | −0.639784 | + | 0.911943i | ||||
\(411\) | 55.0140 | 2.71364 | ||||||||
\(412\) | 9.49069i | 0.467573i | ||||||||
\(413\) | − | 8.77201i | − | 0.431642i | ||||||
\(414\) | −2.79917 | −0.137572 | ||||||||
\(415\) | 16.3183 | − | 23.2600i | 0.801034 | − | 1.14179i | ||||
\(416\) | 1.29341 | 0.0634149 | ||||||||
\(417\) | − | 9.05581i | − | 0.443465i | ||||||
\(418\) | − | 1.82946i | − | 0.0894818i | ||||||
\(419\) | −38.6157 | −1.88650 | −0.943250 | − | 0.332085i | \(-0.892248\pi\) | ||||
−0.943250 | + | 0.332085i | \(0.892248\pi\) | |||||||
\(420\) | 3.11473 | + | 2.18518i | 0.151983 | + | 0.106626i | ||||
\(421\) | 32.7384 | 1.59557 | 0.797785 | − | 0.602941i | \(-0.206005\pi\) | ||||
0.797785 | + | 0.602941i | \(0.206005\pi\) | |||||||
\(422\) | 11.4161i | 0.555728i | ||||||||
\(423\) | − | 22.1384i | − | 1.07640i | ||||||
\(424\) | −5.84621 | −0.283917 | ||||||||
\(425\) | 25.8621 | − | 9.35985i | 1.25449 | − | 0.454019i | ||||
\(426\) | −6.46453 | −0.313208 | ||||||||
\(427\) | 1.11179i | 0.0538031i | ||||||||
\(428\) | − | 1.38473i | − | 0.0669336i | ||||||
\(429\) | 2.32708 | 0.112352 | ||||||||
\(430\) | −9.77576 | − | 6.85830i | −0.471429 | − | 0.330737i | ||||
\(431\) | −35.7739 | −1.72317 | −0.861584 | − | 0.507615i | \(-0.830527\pi\) | ||||
−0.861584 | + | 0.507615i | \(0.830527\pi\) | |||||||
\(432\) | 0.483617i | 0.0232680i | ||||||||
\(433\) | 10.5682i | 0.507877i | 0.967220 | + | 0.253938i | \(0.0817261\pi\) | ||||
−0.967220 | + | 0.253938i | \(0.918274\pi\) | |||||||
\(434\) | −5.31556 | −0.255155 | ||||||||
\(435\) | 17.7011 | − | 25.2309i | 0.848701 | − | 1.20973i | ||||
\(436\) | −14.0370 | −0.672250 | ||||||||
\(437\) | 2.44868i | 0.117136i | ||||||||
\(438\) | 25.1867i | 1.20346i | ||||||||
\(439\) | 27.6642 | 1.32034 | 0.660170 | − | 0.751117i | \(-0.270484\pi\) | ||||
0.660170 | + | 0.751117i | \(0.270484\pi\) | |||||||
\(440\) | 0.959466 | − | 1.36761i | 0.0457407 | − | 0.0651984i | ||||
\(441\) | −18.1967 | −0.866509 | ||||||||
\(442\) | − | 7.11473i | − | 0.338413i | ||||||
\(443\) | − | 36.8082i | − | 1.74881i | −0.485198 | − | 0.874404i | \(-0.661253\pi\) | ||
0.485198 | − | 0.874404i | \(-0.338747\pi\) | |||||||
\(444\) | −12.2194 | −0.579908 | ||||||||
\(445\) | −24.9730 | − | 17.5201i | −1.18384 | − | 0.830534i | ||||
\(446\) | −18.2094 | −0.862239 | ||||||||
\(447\) | 4.59027i | 0.217112i | ||||||||
\(448\) | − | 0.706585i | − | 0.0333830i | ||||||
\(449\) | −18.2711 | −0.862267 | −0.431133 | − | 0.902288i | \(-0.641886\pi\) | ||||
−0.431133 | + | 0.902288i | \(0.641886\pi\) | |||||||
\(450\) | 13.1605 | − | 4.76297i | 0.620392 | − | 0.224529i | ||||
\(451\) | 7.53662 | 0.354886 | ||||||||
\(452\) | − | 16.3105i | − | 0.767183i | ||||||
\(453\) | − | 22.6840i | − | 1.06579i | ||||||
\(454\) | 18.9363 | 0.888722 | ||||||||
\(455\) | 1.67292 | + | 1.17366i | 0.0784278 | + | 0.0550219i | ||||
\(456\) | −5.89679 | −0.276142 | ||||||||
\(457\) | − | 27.6326i | − | 1.29260i | −0.763084 | − | 0.646299i | \(-0.776316\pi\) | ||
0.763084 | − | 0.646299i | \(-0.223684\pi\) | |||||||
\(458\) | 8.46433i | 0.395512i | ||||||||
\(459\) | 2.66025 | 0.124170 | ||||||||
\(460\) | −1.28422 | + | 1.83051i | −0.0598770 | + | 0.0853481i | ||||
\(461\) | 35.5515 | 1.65580 | 0.827900 | − | 0.560876i | \(-0.189536\pi\) | ||||
0.827900 | + | 0.560876i | \(0.189536\pi\) | |||||||
\(462\) | − | 1.27127i | − | 0.0591449i | ||||||
\(463\) | 23.9331i | 1.11226i | 0.831094 | + | 0.556132i | \(0.187715\pi\) | ||||
−0.831094 | + | 0.556132i | \(0.812285\pi\) | |||||||
\(464\) | −5.72371 | −0.265716 | ||||||||
\(465\) | −23.2652 | + | 33.1620i | −1.07890 | + | 1.53785i | ||||
\(466\) | 16.6341 | 0.770558 | ||||||||
\(467\) | − | 19.9035i | − | 0.921024i | −0.887654 | − | 0.460512i | \(-0.847666\pi\) | ||
0.887654 | − | 0.460512i | \(-0.152334\pi\) | |||||||
\(468\) | − | 3.62049i | − | 0.167357i | ||||||
\(469\) | −3.71620 | −0.171598 | ||||||||
\(470\) | −14.4773 | − | 10.1567i | −0.667789 | − | 0.468496i | ||||
\(471\) | −10.6754 | −0.491897 | ||||||||
\(472\) | 12.4146i | 0.571430i | ||||||||
\(473\) | 3.98995i | 0.183458i | ||||||||
\(474\) | −15.7735 | −0.724500 | ||||||||
\(475\) | −4.16658 | − | 11.5126i | −0.191176 | − | 0.528236i | ||||
\(476\) | −3.88674 | −0.178148 | ||||||||
\(477\) | 16.3646i | 0.749281i | ||||||||
\(478\) | 16.0840i | 0.735666i | ||||||||
\(479\) | 3.86206 | 0.176462 | 0.0882309 | − | 0.996100i | \(-0.471879\pi\) | ||||
0.0882309 | + | 0.996100i | \(0.471879\pi\) | |||||||
\(480\) | −4.40815 | − | 3.09259i | −0.201203 | − | 0.141157i | ||||
\(481\) | −6.56304 | −0.299249 | ||||||||
\(482\) | − | 28.1283i | − | 1.28121i | ||||||
\(483\) | 1.70156i | 0.0774238i | ||||||||
\(484\) | 10.4418 | 0.474628 | ||||||||
\(485\) | −1.92728 | + | 2.74712i | −0.0875131 | + | 0.124740i | ||||
\(486\) | 21.5762 | 0.978717 | ||||||||
\(487\) | − | 15.1499i | − | 0.686506i | −0.939243 | − | 0.343253i | \(-0.888471\pi\) | ||
0.939243 | − | 0.343253i | \(-0.111529\pi\) | |||||||
\(488\) | − | 1.57346i | − | 0.0712273i | ||||||
\(489\) | 23.8997 | 1.08078 | ||||||||
\(490\) | −8.34837 | + | 11.8997i | −0.377141 | + | 0.537573i | ||||
\(491\) | −6.86312 | −0.309728 | −0.154864 | − | 0.987936i | \(-0.549494\pi\) | ||||
−0.154864 | + | 0.987936i | \(0.549494\pi\) | |||||||
\(492\) | − | 24.2923i | − | 1.09518i | ||||||
\(493\) | 31.4846i | 1.41800i | ||||||||
\(494\) | −3.16716 | −0.142497 | ||||||||
\(495\) | −3.82819 | − | 2.68571i | −0.172064 | − | 0.120714i | ||||
\(496\) | 7.52288 | 0.337787 | ||||||||
\(497\) | 1.89679i | 0.0850826i | ||||||||
\(498\) | 30.5998i | 1.37121i | ||||||||
\(499\) | 18.6809 | 0.836272 | 0.418136 | − | 0.908385i | \(-0.362684\pi\) | ||||
0.418136 | + | 0.908385i | \(0.362684\pi\) | |||||||
\(500\) | 2.92310 | − | 10.7915i | 0.130725 | − | 0.482608i | ||||
\(501\) | 28.6784 | 1.28125 | ||||||||
\(502\) | − | 20.5770i | − | 0.918396i | ||||||
\(503\) | − | 23.1886i | − | 1.03393i | −0.856008 | − | 0.516963i | \(-0.827062\pi\) | ||
0.856008 | − | 0.516963i | \(-0.172938\pi\) | |||||||
\(504\) | −1.97786 | −0.0881007 | ||||||||
\(505\) | −29.3747 | − | 20.6082i | −1.30716 | − | 0.917051i | ||||
\(506\) | 0.747120 | 0.0332135 | ||||||||
\(507\) | 27.2773i | 1.21143i | ||||||||
\(508\) | 2.73523i | 0.121356i | ||||||||
\(509\) | −11.5385 | −0.511436 | −0.255718 | − | 0.966751i | \(-0.582312\pi\) | ||||
−0.255718 | + | 0.966751i | \(0.582312\pi\) | |||||||
\(510\) | −17.0115 | + | 24.2481i | −0.753283 | + | 1.07372i | ||||
\(511\) | 7.39013 | 0.326920 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 1.18422i | − | 0.0522847i | ||||||
\(514\) | −16.8505 | −0.743245 | ||||||||
\(515\) | 12.1881 | − | 17.3728i | 0.537073 | − | 0.765539i | ||||
\(516\) | 12.8606 | 0.566156 | ||||||||
\(517\) | 5.90888i | 0.259872i | ||||||||
\(518\) | 3.58536i | 0.157531i | ||||||||
\(519\) | 7.01712 | 0.308017 | ||||||||
\(520\) | −2.36761 | − | 1.66103i | −0.103827 | − | 0.0728409i | ||||
\(521\) | −16.2792 | −0.713207 | −0.356603 | − | 0.934256i | \(-0.616065\pi\) | ||||
−0.356603 | + | 0.934256i | \(0.616065\pi\) | |||||||
\(522\) | 16.0217i | 0.701249i | ||||||||
\(523\) | − | 30.8347i | − | 1.34831i | −0.738591 | − | 0.674153i | \(-0.764509\pi\) | ||
0.738591 | − | 0.674153i | \(-0.235491\pi\) | |||||||
\(524\) | 8.21942 | 0.359067 | ||||||||
\(525\) | −2.89531 | − | 8.00000i | −0.126362 | − | 0.349149i | ||||
\(526\) | 24.7630 | 1.07972 | ||||||||
\(527\) | − | 41.3814i | − | 1.80260i | ||||||
\(528\) | 1.79917i | 0.0782990i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 10.7016 | + | 7.50781i | 0.464846 | + | 0.326118i | ||||
\(531\) | 34.7508 | 1.50805 | ||||||||
\(532\) | 1.73020i | 0.0750138i | ||||||||
\(533\) | − | 13.0474i | − | 0.565146i | ||||||
\(534\) | 32.8535 | 1.42171 | ||||||||
\(535\) | −1.77830 | + | 2.53477i | −0.0768827 | + | 0.109588i | ||||
\(536\) | 5.25938 | 0.227171 | ||||||||
\(537\) | − | 46.6370i | − | 2.01254i | ||||||
\(538\) | 3.55152i | 0.153117i | ||||||||
\(539\) | 4.85683 | 0.209198 | ||||||||
\(540\) | 0.621070 | − | 0.885267i | 0.0267266 | − | 0.0380958i | ||||
\(541\) | −30.5199 | −1.31215 | −0.656077 | − | 0.754694i | \(-0.727785\pi\) | ||||
−0.656077 | + | 0.754694i | \(0.727785\pi\) | |||||||
\(542\) | − | 27.4761i | − | 1.18020i | ||||||
\(543\) | 42.3799i | 1.81870i | ||||||||
\(544\) | 5.50074 | 0.235842 | ||||||||
\(545\) | 25.6949 | + | 18.0266i | 1.10065 | + | 0.772173i | ||||
\(546\) | −2.20083 | −0.0941866 | ||||||||
\(547\) | 28.0416i | 1.19897i | 0.800385 | + | 0.599487i | \(0.204629\pi\) | ||||
−0.800385 | + | 0.599487i | \(0.795371\pi\) | |||||||
\(548\) | 22.8449i | 0.975887i | ||||||||
\(549\) | −4.40439 | −0.187975 | ||||||||
\(550\) | −3.51263 | + | 1.27127i | −0.149779 | + | 0.0542072i | ||||
\(551\) | 14.0155 | 0.597082 | ||||||||
\(552\) | − | 2.40815i | − | 0.102498i | ||||||
\(553\) | 4.62817i | 0.196810i | ||||||||
\(554\) | −11.1001 | −0.471598 | ||||||||
\(555\) | 22.3678 | + | 15.6924i | 0.949461 | + | 0.666106i | ||||
\(556\) | 3.76049 | 0.159480 | ||||||||
\(557\) | − | 4.15674i | − | 0.176127i | −0.996115 | − | 0.0880634i | \(-0.971932\pi\) | ||
0.996115 | − | 0.0880634i | \(-0.0280678\pi\) | |||||||
\(558\) | − | 21.0579i | − | 0.891450i | ||||||
\(559\) | 6.90741 | 0.292152 | ||||||||
\(560\) | −0.907411 | + | 1.29341i | −0.0383451 | + | 0.0546567i | ||||
\(561\) | 9.89679 | 0.417843 | ||||||||
\(562\) | 13.0458i | 0.550302i | ||||||||
\(563\) | 21.3480i | 0.899709i | 0.893102 | + | 0.449854i | \(0.148524\pi\) | ||||
−0.893102 | + | 0.449854i | \(0.851476\pi\) | |||||||
\(564\) | 19.0458 | 0.801971 | ||||||||
\(565\) | −20.9463 | + | 29.8567i | −0.881218 | + | 1.25608i | ||||
\(566\) | −3.35049 | −0.140832 | ||||||||
\(567\) | − | 6.75647i | − | 0.283745i | ||||||
\(568\) | − | 2.68444i | − | 0.112637i | ||||||
\(569\) | 25.6430 | 1.07501 | 0.537506 | − | 0.843260i | \(-0.319366\pi\) | ||||
0.537506 | + | 0.843260i | \(0.319366\pi\) | |||||||
\(570\) | 10.7942 | + | 7.57277i | 0.452117 | + | 0.317188i | ||||
\(571\) | −7.10743 | −0.297437 | −0.148718 | − | 0.988880i | \(-0.547515\pi\) | ||||
−0.148718 | + | 0.988880i | \(0.547515\pi\) | |||||||
\(572\) | 0.966336i | 0.0404045i | ||||||||
\(573\) | 49.0245i | 2.04803i | ||||||||
\(574\) | −7.12773 | −0.297506 | ||||||||
\(575\) | 4.70156 | − | 1.70156i | 0.196069 | − | 0.0709600i | ||||
\(576\) | 2.79917 | 0.116632 | ||||||||
\(577\) | − | 22.7226i | − | 0.945956i | −0.881074 | − | 0.472978i | \(-0.843179\pi\) | ||
0.881074 | − | 0.472978i | \(-0.156821\pi\) | |||||||
\(578\) | − | 13.2581i | − | 0.551465i | ||||||
\(579\) | −3.40312 | −0.141429 | ||||||||
\(580\) | 10.4773 | + | 7.35049i | 0.435047 | + | 0.305213i | ||||
\(581\) | 8.97843 | 0.372488 | ||||||||
\(582\) | − | 3.61400i | − | 0.149805i | ||||||
\(583\) | − | 4.36782i | − | 0.180896i | ||||||
\(584\) | −10.4589 | −0.432794 | ||||||||
\(585\) | −4.64951 | + | 6.62736i | −0.192233 | + | 0.274008i | ||||
\(586\) | −8.89197 | −0.367324 | ||||||||
\(587\) | − | 7.06600i | − | 0.291645i | −0.989311 | − | 0.145822i | \(-0.953417\pi\) | ||
0.989311 | − | 0.145822i | \(-0.0465828\pi\) | |||||||
\(588\) | − | 15.6547i | − | 0.645590i | ||||||
\(589\) | −18.4211 | −0.759030 | ||||||||
\(590\) | 15.9431 | − | 22.7252i | 0.656368 | − | 0.935581i | ||||
\(591\) | −11.8576 | −0.487757 | ||||||||
\(592\) | − | 5.07420i | − | 0.208548i | ||||||
\(593\) | 14.9914i | 0.615624i | 0.951447 | + | 0.307812i | \(0.0995968\pi\) | ||||
−0.951447 | + | 0.307812i | \(0.900403\pi\) | |||||||
\(594\) | −0.361320 | −0.0148251 | ||||||||
\(595\) | 7.11473 | + | 4.99143i | 0.291676 | + | 0.204629i | ||||
\(596\) | −1.90614 | −0.0780785 | ||||||||
\(597\) | 24.8293i | 1.01620i | ||||||||
\(598\) | − | 1.29341i | − | 0.0528917i | ||||||
\(599\) | 4.03069 | 0.164690 | 0.0823448 | − | 0.996604i | \(-0.473759\pi\) | ||||
0.0823448 | + | 0.996604i | \(0.473759\pi\) | |||||||
\(600\) | 4.09761 | + | 11.3221i | 0.167284 | + | 0.462221i | ||||
\(601\) | 13.9320 | 0.568300 | 0.284150 | − | 0.958780i | \(-0.408289\pi\) | ||||
0.284150 | + | 0.958780i | \(0.408289\pi\) | |||||||
\(602\) | − | 3.77348i | − | 0.153796i | ||||||
\(603\) | − | 14.7219i | − | 0.599523i | ||||||
\(604\) | 9.41967 | 0.383281 | ||||||||
\(605\) | −19.1139 | − | 13.4096i | −0.777090 | − | 0.545177i | ||||
\(606\) | 38.6441 | 1.56981 | ||||||||
\(607\) | 31.0588i | 1.26064i | 0.776337 | + | 0.630318i | \(0.217075\pi\) | ||||
−0.776337 | + | 0.630318i | \(0.782925\pi\) | |||||||
\(608\) | − | 2.44868i | − | 0.0993072i | ||||||
\(609\) | 9.73924 | 0.394654 | ||||||||
\(610\) | −2.02067 | + | 2.88024i | −0.0818145 | + | 0.116618i | ||||
\(611\) | 10.2295 | 0.413840 | ||||||||
\(612\) | − | 15.3975i | − | 0.622408i | ||||||
\(613\) | 19.6722i | 0.794554i | 0.917699 | + | 0.397277i | \(0.130045\pi\) | ||||
−0.917699 | + | 0.397277i | \(0.869955\pi\) | |||||||
\(614\) | −28.4111 | −1.14658 | ||||||||
\(615\) | −31.1967 | + | 44.4675i | −1.25797 | + | 1.79310i | ||||
\(616\) | 0.527904 | 0.0212699 | ||||||||
\(617\) | 40.9043i | 1.64674i | 0.567502 | + | 0.823372i | \(0.307910\pi\) | ||||
−0.567502 | + | 0.823372i | \(0.692090\pi\) | |||||||
\(618\) | 22.8550i | 0.919362i | ||||||||
\(619\) | 3.58556 | 0.144116 | 0.0720579 | − | 0.997400i | \(-0.477043\pi\) | ||||
0.0720579 | + | 0.997400i | \(0.477043\pi\) | |||||||
\(620\) | −13.7707 | − | 9.66103i | −0.553046 | − | 0.387996i | ||||
\(621\) | 0.483617 | 0.0194069 | ||||||||
\(622\) | − | 28.0105i | − | 1.12312i | ||||||
\(623\) | − | 9.63969i | − | 0.386206i | ||||||
\(624\) | 3.11473 | 0.124689 | ||||||||
\(625\) | −19.2094 | + | 16.0000i | −0.768375 | + | 0.640000i | ||||
\(626\) | −7.42882 | −0.296915 | ||||||||
\(627\) | − | 4.40561i | − | 0.175943i | ||||||
\(628\) | − | 4.43304i | − | 0.176897i | ||||||
\(629\) | −27.9118 | −1.11292 | ||||||||
\(630\) | 3.62049 | + | 2.54000i | 0.144244 | + | 0.101196i | ||||
\(631\) | −7.19670 | −0.286496 | −0.143248 | − | 0.989687i | \(-0.545755\pi\) | ||||
−0.143248 | + | 0.989687i | \(0.545755\pi\) | |||||||
\(632\) | − | 6.55005i | − | 0.260547i | ||||||
\(633\) | 27.4917i | 1.09270i | ||||||||
\(634\) | −13.1480 | −0.522172 | ||||||||
\(635\) | 3.51263 | − | 5.00687i | 0.139394 | − | 0.198692i | ||||
\(636\) | −14.0785 | −0.558250 | ||||||||
\(637\) | − | 8.40815i | − | 0.333143i | ||||||
\(638\) | − | 4.27629i | − | 0.169300i | ||||||
\(639\) | −7.51422 | −0.297258 | ||||||||
\(640\) | 1.28422 | − | 1.83051i | 0.0507632 | − | 0.0723574i | ||||
\(641\) | −16.3436 | −0.645534 | −0.322767 | − | 0.946478i | \(-0.604613\pi\) | ||||
−0.322767 | + | 0.946478i | \(0.604613\pi\) | |||||||
\(642\) | − | 3.33464i | − | 0.131608i | ||||||
\(643\) | − | 6.55839i | − | 0.258638i | −0.991603 | − | 0.129319i | \(-0.958721\pi\) | ||
0.991603 | − | 0.129319i | \(-0.0412791\pi\) | |||||||
\(644\) | −0.706585 | −0.0278434 | ||||||||
\(645\) | −23.5415 | − | 16.5158i | −0.926945 | − | 0.650309i | ||||
\(646\) | −13.4696 | −0.529953 | ||||||||
\(647\) | − | 16.5455i | − | 0.650470i | −0.945633 | − | 0.325235i | \(-0.894557\pi\) | ||
0.945633 | − | 0.325235i | \(-0.105443\pi\) | |||||||
\(648\) | 9.56214i | 0.375637i | ||||||||
\(649\) | −9.27523 | −0.364085 | ||||||||
\(650\) | 2.20083 | + | 6.08107i | 0.0863235 | + | 0.238519i | ||||
\(651\) | −12.8006 | −0.501697 | ||||||||
\(652\) | 9.92453i | 0.388675i | ||||||||
\(653\) | − | 12.7408i | − | 0.498587i | −0.968428 | − | 0.249294i | \(-0.919802\pi\) | ||
0.968428 | − | 0.249294i | \(-0.0801984\pi\) | |||||||
\(654\) | −33.8031 | −1.32181 | ||||||||
\(655\) | −15.0458 | − | 10.5555i | −0.587887 | − | 0.412439i | ||||
\(656\) | 10.0876 | 0.393853 | ||||||||
\(657\) | 29.2764i | 1.14218i | ||||||||
\(658\) | − | 5.58830i | − | 0.217855i | ||||||
\(659\) | 23.8094 | 0.927484 | 0.463742 | − | 0.885970i | \(-0.346507\pi\) | ||||
0.463742 | + | 0.885970i | \(0.346507\pi\) | |||||||
\(660\) | 2.31053 | − | 3.29341i | 0.0899374 | − | 0.128196i | ||||
\(661\) | 24.9323 | 0.969754 | 0.484877 | − | 0.874582i | \(-0.338864\pi\) | ||||
0.484877 | + | 0.874582i | \(0.338864\pi\) | |||||||
\(662\) | − | 15.6225i | − | 0.607187i | ||||||
\(663\) | − | 17.1333i | − | 0.665403i | ||||||
\(664\) | −12.7068 | −0.493119 | ||||||||
\(665\) | 2.22196 | − | 3.16716i | 0.0861639 | − | 0.122817i | ||||
\(666\) | −14.2036 | −0.550377 | ||||||||
\(667\) | 5.72371i | 0.221623i | ||||||||
\(668\) | 11.9089i | 0.460769i | ||||||||
\(669\) | −43.8509 | −1.69537 | ||||||||
\(670\) | −9.62736 | − | 6.75419i | −0.371937 | − | 0.260937i | ||||
\(671\) | 1.17556 | 0.0453822 | ||||||||
\(672\) | − | 1.70156i | − | 0.0656392i | ||||||
\(673\) | 5.48050i | 0.211258i | 0.994406 | + | 0.105629i | \(0.0336856\pi\) | ||||
−0.994406 | + | 0.105629i | \(0.966314\pi\) | |||||||
\(674\) | 16.6965 | 0.643127 | ||||||||
\(675\) | −2.27375 | + | 0.822904i | −0.0875168 | + | 0.0316736i | ||||
\(676\) | −11.3271 | −0.435657 | ||||||||
\(677\) | − | 1.75255i | − | 0.0673560i | −0.999433 | − | 0.0336780i | \(-0.989278\pi\) | ||
0.999433 | − | 0.0336780i | \(-0.0107221\pi\) | |||||||
\(678\) | − | 39.2782i | − | 1.50847i | ||||||
\(679\) | −1.06040 | −0.0406944 | ||||||||
\(680\) | −10.0692 | − | 7.06415i | −0.386135 | − | 0.270898i | ||||
\(681\) | 45.6013 | 1.74745 | ||||||||
\(682\) | 5.62049i | 0.215220i | ||||||||
\(683\) | 23.5091i | 0.899552i | 0.893141 | + | 0.449776i | \(0.148496\pi\) | ||||
−0.893141 | + | 0.449776i | \(0.851504\pi\) | |||||||
\(684\) | −6.85429 | −0.262080 | ||||||||
\(685\) | 29.3379 | − | 41.8180i | 1.12094 | − | 1.59778i | ||||
\(686\) | −9.53942 | −0.364217 | ||||||||
\(687\) | 20.3834i | 0.777673i | ||||||||
\(688\) | 5.34045i | 0.203603i | ||||||||
\(689\) | −7.56157 | −0.288073 | ||||||||
\(690\) | −3.09259 | + | 4.40815i | −0.117733 | + | 0.167815i | ||||
\(691\) | −21.4834 | −0.817269 | −0.408634 | − | 0.912698i | \(-0.633995\pi\) | ||||
−0.408634 | + | 0.912698i | \(0.633995\pi\) | |||||||
\(692\) | 2.91391i | 0.110770i | ||||||||
\(693\) | − | 1.47770i | − | 0.0561330i | ||||||
\(694\) | −16.3981 | −0.622463 | ||||||||
\(695\) | −6.88362 | − | 4.82929i | −0.261111 | − | 0.183185i | ||||
\(696\) | −13.7835 | −0.522463 | ||||||||
\(697\) | − | 55.4890i | − | 2.10180i | ||||||
\(698\) | 1.86165i | 0.0704645i | ||||||||
\(699\) | 40.0573 | 1.51511 | ||||||||
\(700\) | 3.32206 | − | 1.20230i | 0.125562 | − | 0.0454426i | ||||
\(701\) | 9.62985 | 0.363714 | 0.181857 | − | 0.983325i | \(-0.441789\pi\) | ||||
0.181857 | + | 0.983325i | \(0.441789\pi\) | |||||||
\(702\) | 0.625517i | 0.0236086i | ||||||||
\(703\) | 12.4251i | 0.468621i | ||||||||
\(704\) | −0.747120 | −0.0281581 | ||||||||
\(705\) | −34.8635 | − | 24.4589i | −1.31304 | − | 0.921177i | ||||
\(706\) | −25.8408 | −0.972532 | ||||||||
\(707\) | − | 11.3387i | − | 0.426437i | ||||||
\(708\) | 29.8963i | 1.12357i | ||||||||
\(709\) | −11.8970 | −0.446801 | −0.223400 | − | 0.974727i | \(-0.571716\pi\) | ||||
−0.223400 | + | 0.974727i | \(0.571716\pi\) | |||||||
\(710\) | −3.44741 | + | 4.91391i | −0.129379 | + | 0.184416i | ||||
\(711\) | −18.3347 | −0.687606 | ||||||||
\(712\) | 13.6426i | 0.511279i | ||||||||
\(713\) | − | 7.52288i | − | 0.281734i | ||||||
\(714\) | −9.35985 | −0.350283 | ||||||||
\(715\) | 1.24099 | − | 1.76889i | 0.0464103 | − | 0.0661528i | ||||
\(716\) | 19.3663 | 0.723754 | ||||||||
\(717\) | 38.7327i | 1.44650i | ||||||||
\(718\) | − | 8.72223i | − | 0.325511i | ||||||
\(719\) | −24.2949 | −0.906046 | −0.453023 | − | 0.891499i | \(-0.649655\pi\) | ||||
−0.453023 | + | 0.891499i | \(0.649655\pi\) | |||||||
\(720\) | −5.12393 | − | 3.59475i | −0.190958 | − | 0.133969i | ||||
\(721\) | 6.70598 | 0.249744 | ||||||||
\(722\) | − | 13.0040i | − | 0.483957i | ||||||
\(723\) | − | 67.7371i | − | 2.51917i | ||||||
\(724\) | −17.5986 | −0.654045 | ||||||||
\(725\) | −9.73924 | − | 26.9104i | −0.361706 | − | 0.999426i | ||||
\(726\) | 25.1454 | 0.933234 | ||||||||
\(727\) | 6.25721i | 0.232067i | 0.993245 | + | 0.116034i | \(0.0370180\pi\) | ||||
−0.993245 | + | 0.116034i | \(0.962982\pi\) | |||||||
\(728\) | − | 0.913908i | − | 0.0338717i | ||||||
\(729\) | 23.2723 | 0.861935 | ||||||||
\(730\) | 19.1452 | + | 13.4316i | 0.708596 | + | 0.497124i | ||||
\(731\) | 29.3764 | 1.08653 | ||||||||
\(732\) | − | 3.78913i | − | 0.140050i | ||||||
\(733\) | 37.3304i | 1.37883i | 0.724367 | + | 0.689415i | \(0.242132\pi\) | ||||
−0.724367 | + | 0.689415i | \(0.757868\pi\) | |||||||
\(734\) | −25.5958 | −0.944759 | ||||||||
\(735\) | −20.1041 | + | 28.6562i | −0.741551 | + | 1.05700i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 3.92939i | 0.144741i | ||||||||
\(738\) | − | 28.2369i | − | 1.03941i | ||||||
\(739\) | 26.9889 | 0.992802 | 0.496401 | − | 0.868093i | \(-0.334655\pi\) | ||||
0.496401 | + | 0.868093i | \(0.334655\pi\) | |||||||
\(740\) | −6.51638 | + | 9.28839i | −0.239547 | + | 0.341448i | ||||
\(741\) | −7.62699 | −0.280185 | ||||||||
\(742\) | 4.13084i | 0.151648i | ||||||||
\(743\) | 32.1544i | 1.17963i | 0.807538 | + | 0.589815i | \(0.200799\pi\) | ||||
−0.807538 | + | 0.589815i | \(0.799201\pi\) | |||||||
\(744\) | 18.1162 | 0.664172 | ||||||||
\(745\) | 3.48922 | + | 2.44790i | 0.127835 | + | 0.0896842i | ||||
\(746\) | −17.2125 | −0.630196 | ||||||||
\(747\) | 35.5685i | 1.30138i | ||||||||
\(748\) | 4.10971i | 0.150266i | ||||||||
\(749\) | −0.978433 | −0.0357512 | ||||||||
\(750\) | 7.03926 | − | 25.9874i | 0.257038 | − | 0.948926i | ||||
\(751\) | 39.7865 | 1.45183 | 0.725915 | − | 0.687785i | \(-0.241417\pi\) | ||||
0.725915 | + | 0.687785i | \(0.241417\pi\) | |||||||
\(752\) | 7.90888i | 0.288407i | ||||||||
\(753\) | − | 49.5524i | − | 1.80579i | ||||||
\(754\) | −7.40312 | −0.269606 | ||||||||
\(755\) | −17.2428 | − | 12.0969i | −0.627531 | − | 0.440252i | ||||
\(756\) | 0.341716 | 0.0124281 | ||||||||
\(757\) | − | 26.9961i | − | 0.981189i | −0.871388 | − | 0.490595i | \(-0.836780\pi\) | ||
0.871388 | − | 0.490595i | \(-0.163220\pi\) | |||||||
\(758\) | − | 23.0339i | − | 0.836628i | ||||||
\(759\) | 1.79917 | 0.0653059 | ||||||||
\(760\) | −3.14464 | + | 4.48235i | −0.114068 | + | 0.162592i | ||||
\(761\) | −7.21529 | −0.261554 | −0.130777 | − | 0.991412i | \(-0.541747\pi\) | ||||
−0.130777 | + | 0.991412i | \(0.541747\pi\) | |||||||
\(762\) | 6.58683i | 0.238616i | ||||||||
\(763\) | 9.91833i | 0.359068i | ||||||||
\(764\) | −20.3578 | −0.736518 | ||||||||
\(765\) | −19.7738 | + | 28.1854i | −0.714923 | + | 1.01904i | ||||
\(766\) | 3.81777 | 0.137942 | ||||||||
\(767\) | 16.0573i | 0.579795i | ||||||||
\(768\) | 2.40815i | 0.0868965i | ||||||||
\(769\) | −6.40916 | −0.231120 | −0.115560 | − | 0.993300i | \(-0.536866\pi\) | ||||
−0.115560 | + | 0.993300i | \(0.536866\pi\) | |||||||
\(770\) | −0.966336 | − | 0.677944i | −0.0348243 | − | 0.0244314i | ||||
\(771\) | −40.5786 | −1.46140 | ||||||||
\(772\) | − | 1.41317i | − | 0.0508611i | ||||||
\(773\) | 50.2483i | 1.80730i | 0.428267 | + | 0.903652i | \(0.359124\pi\) | ||||
−0.428267 | + | 0.903652i | \(0.640876\pi\) | |||||||
\(774\) | 14.9488 | 0.537325 | ||||||||
\(775\) | 12.8006 | + | 35.3693i | 0.459813 | + | 1.27050i | ||||
\(776\) | 1.50074 | 0.0538733 | ||||||||
\(777\) | 8.63406i | 0.309745i | ||||||||
\(778\) | 8.25435i | 0.295933i | ||||||||
\(779\) | −24.7012 | −0.885014 | ||||||||
\(780\) | −5.70156 | − | 4.00000i | −0.204149 | − | 0.143223i | ||||
\(781\) | 2.00560 | 0.0717660 | ||||||||
\(782\) | − | 5.50074i | − | 0.196706i | ||||||
\(783\) | − | 2.76808i | − | 0.0989231i | ||||||
\(784\) | 6.50074 | 0.232169 | ||||||||
\(785\) | −5.69299 | + | 8.11473i | −0.203192 | + | 0.289627i | ||||
\(786\) | 19.7936 | 0.706013 | ||||||||
\(787\) | − | 2.70933i | − | 0.0965772i | −0.998833 | − | 0.0482886i | \(-0.984623\pi\) | ||
0.998833 | − | 0.0482886i | \(-0.0153767\pi\) | |||||||
\(788\) | − | 4.92395i | − | 0.175409i | ||||||
\(789\) | 59.6329 | 2.12299 | ||||||||
\(790\) | −8.41170 | + | 11.9900i | −0.299275 | + | 0.426583i | ||||
\(791\) | −11.5248 | −0.409774 | ||||||||
\(792\) | 2.09132i | 0.0743118i | ||||||||
\(793\) | − | 2.03514i | − | 0.0722699i | ||||||
\(794\) | −12.4967 | −0.443492 | ||||||||
\(795\) | 25.7709 | + | 18.0799i | 0.914001 | + | 0.641229i | ||||
\(796\) | −10.3105 | −0.365447 | ||||||||
\(797\) | 15.1452i | 0.536471i | 0.963353 | + | 0.268236i | \(0.0864406\pi\) | ||||
−0.963353 | + | 0.268236i | \(0.913559\pi\) | |||||||
\(798\) | 4.16658i | 0.147495i | ||||||||
\(799\) | 43.5047 | 1.53909 | ||||||||
\(800\) | −4.70156 | + | 1.70156i | −0.166225 | + | 0.0601593i | ||||
\(801\) | 38.1881 | 1.34931 | ||||||||
\(802\) | 34.5660i | 1.22057i | ||||||||
\(803\) | − | 7.81408i | − | 0.275753i | ||||||
\(804\) | 12.6654 | 0.446673 | ||||||||
\(805\) | 1.29341 | + | 0.907411i | 0.0455869 | + | 0.0319820i | ||||
\(806\) | 9.73020 | 0.342732 | ||||||||
\(807\) | 8.55259i | 0.301065i | ||||||||
\(808\) | 16.0472i | 0.564540i | ||||||||
\(809\) | 3.94373 | 0.138654 | 0.0693270 | − | 0.997594i | \(-0.477915\pi\) | ||||
0.0693270 | + | 0.997594i | \(0.477915\pi\) | |||||||
\(810\) | 12.2799 | − | 17.5036i | 0.431471 | − | 0.615015i | ||||
\(811\) | −14.1521 | −0.496947 | −0.248474 | − | 0.968639i | \(-0.579929\pi\) | ||||
−0.248474 | + | 0.968639i | \(0.579929\pi\) | |||||||
\(812\) | 4.04429i | 0.141927i | ||||||||
\(813\) | − | 66.1664i | − | 2.32056i | ||||||
\(814\) | 3.79103 | 0.132876 | ||||||||
\(815\) | 12.7453 | − | 18.1670i | 0.446447 | − | 0.636362i | ||||
\(816\) | 13.2466 | 0.463723 | ||||||||
\(817\) | − | 13.0771i | − | 0.457508i | ||||||
\(818\) | − | 12.0499i | − | 0.421314i | ||||||
\(819\) | −2.55819 | −0.0893903 | ||||||||
\(820\) | −18.4654 | − | 12.9546i | −0.644841 | − | 0.452396i | ||||
\(821\) | 37.0094 | 1.29164 | 0.645818 | − | 0.763491i | \(-0.276516\pi\) | ||||
0.645818 | + | 0.763491i | \(0.276516\pi\) | |||||||
\(822\) | 55.0140i | 1.91883i | ||||||||
\(823\) | − | 18.1208i | − | 0.631651i | −0.948817 | − | 0.315826i | \(-0.897719\pi\) | ||
0.948817 | − | 0.315826i | \(-0.102281\pi\) | |||||||
\(824\) | −9.49069 | −0.330624 | ||||||||
\(825\) | −8.45893 | + | 3.06141i | −0.294502 | + | 0.106585i | ||||
\(826\) | 8.77201 | 0.305217 | ||||||||
\(827\) | 41.5398i | 1.44448i | 0.691643 | + | 0.722240i | \(0.256887\pi\) | ||||
−0.691643 | + | 0.722240i | \(0.743113\pi\) | |||||||
\(828\) | − | 2.79917i | − | 0.0972781i | ||||||
\(829\) | −21.3976 | −0.743171 | −0.371585 | − | 0.928399i | \(-0.621186\pi\) | ||||
−0.371585 | + | 0.928399i | \(0.621186\pi\) | |||||||
\(830\) | 23.2600 | + | 16.3183i | 0.807365 | + | 0.566417i | ||||
\(831\) | −26.7307 | −0.927277 | ||||||||
\(832\) | 1.29341i | 0.0448411i | ||||||||
\(833\) | − | 35.7588i | − | 1.23897i | ||||||
\(834\) | 9.05581 | 0.313577 | ||||||||
\(835\) | 15.2936 | − | 21.7994i | 0.529257 | − | 0.754399i | ||||
\(836\) | 1.82946 | 0.0632732 | ||||||||
\(837\) | 3.63819i | 0.125754i | ||||||||
\(838\) | − | 38.6157i | − | 1.33396i | ||||||
\(839\) | 41.3437 | 1.42734 | 0.713672 | − | 0.700480i | \(-0.247031\pi\) | ||||
0.713672 | + | 0.700480i | \(0.247031\pi\) | |||||||
\(840\) | −2.18518 | + | 3.11473i | −0.0753958 | + | 0.107469i | ||||
\(841\) | 3.76081 | 0.129683 | ||||||||
\(842\) | 32.7384i | 1.12824i | ||||||||
\(843\) | 31.4161i | 1.08203i | ||||||||
\(844\) | −11.4161 | −0.392959 | ||||||||
\(845\) | 20.7344 | + | 14.5465i | 0.713284 | + | 0.500413i | ||||
\(846\) | 22.1384 | 0.761132 | ||||||||
\(847\) | − | 7.37803i | − | 0.253512i | ||||||
\(848\) | − | 5.84621i | − | 0.200760i | ||||||
\(849\) | −8.06848 | −0.276910 | ||||||||
\(850\) | 9.35985 | + | 25.8621i | 0.321040 | + | 0.887061i | ||||
\(851\) | −5.07420 | −0.173941 | ||||||||
\(852\) | − | 6.46453i | − | 0.221471i | ||||||
\(853\) | − | 56.0373i | − | 1.91868i | −0.282252 | − | 0.959340i | \(-0.591081\pi\) | ||
0.282252 | − | 0.959340i | \(-0.408919\pi\) | |||||||
\(854\) | −1.11179 | −0.0380445 | ||||||||
\(855\) | 12.5469 | + | 8.80241i | 0.429094 | + | 0.301036i | ||||
\(856\) | 1.38473 | 0.0473292 | ||||||||
\(857\) | 43.4734i | 1.48502i | 0.669833 | + | 0.742512i | \(0.266366\pi\) | ||||
−0.669833 | + | 0.742512i | \(0.733634\pi\) | |||||||
\(858\) | 2.32708i | 0.0794452i | ||||||||
\(859\) | −11.1599 | −0.380771 | −0.190386 | − | 0.981709i | \(-0.560974\pi\) | ||||
−0.190386 | + | 0.981709i | \(0.560974\pi\) | |||||||
\(860\) | 6.85830 | − | 9.77576i | 0.233866 | − | 0.333351i | ||||
\(861\) | −17.1646 | −0.584969 | ||||||||
\(862\) | − | 35.7739i | − | 1.21846i | ||||||
\(863\) | 32.2767i | 1.09871i | 0.835589 | + | 0.549356i | \(0.185127\pi\) | ||||
−0.835589 | + | 0.549356i | \(0.814873\pi\) | |||||||
\(864\) | −0.483617 | −0.0164530 | ||||||||
\(865\) | 3.74210 | − | 5.33395i | 0.127235 | − | 0.181360i | ||||
\(866\) | −10.5682 | −0.359123 | ||||||||
\(867\) | − | 31.9275i | − | 1.08431i | ||||||
\(868\) | − | 5.31556i | − | 0.180422i | ||||||
\(869\) | 4.89367 | 0.166006 | ||||||||
\(870\) | 25.2309 | + | 17.7011i | 0.855409 | + | 0.600123i | ||||
\(871\) | 6.80256 | 0.230496 | ||||||||
\(872\) | − | 14.0370i | − | 0.475352i | ||||||
\(873\) | − | 4.20083i | − | 0.142176i | ||||||
\(874\) | −2.44868 | −0.0828279 | ||||||||
\(875\) | −7.62508 | − | 2.06542i | −0.257775 | − | 0.0698240i | ||||
\(876\) | −25.1867 | −0.850978 | ||||||||
\(877\) | 9.52493i | 0.321634i | 0.986984 | + | 0.160817i | \(0.0514129\pi\) | ||||
−0.986984 | + | 0.160817i | \(0.948587\pi\) | |||||||
\(878\) | 27.6642i | 0.933621i | ||||||||
\(879\) | −21.4132 | −0.722248 | ||||||||
\(880\) | 1.36761 | + | 0.959466i | 0.0461022 | + | 0.0323436i | ||||
\(881\) | 49.1585 | 1.65619 | 0.828096 | − | 0.560586i | \(-0.189424\pi\) | ||||
0.828096 | + | 0.560586i | \(0.189424\pi\) | |||||||
\(882\) | − | 18.1967i | − | 0.612715i | ||||||
\(883\) | 33.1379i | 1.11518i | 0.830117 | + | 0.557590i | \(0.188274\pi\) | ||||
−0.830117 | + | 0.557590i | \(0.811726\pi\) | |||||||
\(884\) | 7.11473 | 0.239294 | ||||||||
\(885\) | 38.3934 | − | 54.7256i | 1.29058 | − | 1.83958i | ||||
\(886\) | 36.8082 | 1.23659 | ||||||||
\(887\) | 1.59084i | 0.0534153i | 0.999643 | + | 0.0267076i | \(0.00850232\pi\) | ||||
−0.999643 | + | 0.0267076i | \(0.991498\pi\) | |||||||
\(888\) | − | 12.2194i | − | 0.410057i | ||||||
\(889\) | 1.93267 | 0.0648197 | ||||||||
\(890\) | 17.5201 | − | 24.9730i | 0.587276 | − | 0.837098i | ||||
\(891\) | −7.14407 | −0.239335 | ||||||||
\(892\) | − | 18.2094i | − | 0.609695i | ||||||
\(893\) | − | 19.3663i | − | 0.648070i | ||||||
\(894\) | −4.59027 | −0.153522 | ||||||||
\(895\) | −35.4504 | − | 24.8706i | −1.18497 | − | 0.831333i | ||||
\(896\) | 0.706585 | 0.0236054 | ||||||||
\(897\) | − | 3.11473i | − | 0.103998i | ||||||
\(898\) | − | 18.2711i | − | 0.609715i | ||||||
\(899\) | −43.0588 | −1.43609 | ||||||||
\(900\) | 4.76297 | + | 13.1605i | 0.158766 | + | 0.438683i | ||||
\(901\) | −32.1584 | −1.07135 | ||||||||
\(902\) | 7.53662i | 0.250942i | ||||||||
\(903\) | − | 9.08710i | − | 0.302400i | ||||||
\(904\) | 16.3105 | 0.542480 | ||||||||
\(905\) | 32.2144 | + | 22.6004i | 1.07084 | + | 0.751263i | ||||
\(906\) | 22.6840 | 0.753624 | ||||||||
\(907\) | − | 17.4658i | − | 0.579942i | −0.957035 | − | 0.289971i | \(-0.906354\pi\) | ||
0.957035 | − | 0.289971i | \(-0.0936457\pi\) | |||||||
\(908\) | 18.9363i | 0.628422i | ||||||||
\(909\) | 44.9190 | 1.48987 | ||||||||
\(910\) | −1.17366 | + | 1.67292i | −0.0389064 | + | 0.0554568i | ||||
\(911\) | −21.6050 | −0.715805 | −0.357903 | − | 0.933759i | \(-0.616508\pi\) | ||||
−0.357903 | + | 0.933759i | \(0.616508\pi\) | |||||||
\(912\) | − | 5.89679i | − | 0.195262i | ||||||
\(913\) | − | 9.49349i | − | 0.314189i | ||||||
\(914\) | 27.6326 | 0.914005 | ||||||||
\(915\) | −4.86607 | + | 6.93605i | −0.160867 | + | 0.229299i | ||||
\(916\) | −8.46433 | −0.279669 | ||||||||
\(917\) | − | 5.80772i | − | 0.191788i | ||||||
\(918\) | 2.66025i | 0.0878013i | ||||||||
\(919\) | 41.7396 | 1.37686 | 0.688432 | − | 0.725301i | \(-0.258299\pi\) | ||||
0.688432 | + | 0.725301i | \(0.258299\pi\) | |||||||
\(920\) | −1.83051 | − | 1.28422i | −0.0603503 | − | 0.0423395i | ||||
\(921\) | −68.4181 | −2.25445 | ||||||||
\(922\) | 35.5515i | 1.17083i | ||||||||
\(923\) | − | 3.47210i | − | 0.114285i | ||||||
\(924\) | 1.27127 | 0.0418217 | ||||||||
\(925\) | 23.8567 | − | 8.63406i | 0.784402 | − | 0.283886i | ||||
\(926\) | −23.9331 | −0.786490 | ||||||||
\(927\) | 26.5661i | 0.872545i | ||||||||
\(928\) | − | 5.72371i | − | 0.187890i | ||||||
\(929\) | −38.8505 | −1.27464 | −0.637322 | − | 0.770597i | \(-0.719958\pi\) | ||||
−0.637322 | + | 0.770597i | \(0.719958\pi\) | |||||||
\(930\) | −33.1620 | − | 23.2652i | −1.08742 | − | 0.762895i | ||||
\(931\) | −15.9182 | −0.521699 | ||||||||
\(932\) | 16.6341i | 0.544867i | ||||||||
\(933\) | − | 67.4533i | − | 2.20832i | ||||||
\(934\) | 19.9035 | 0.651262 | ||||||||
\(935\) | 5.27777 | − | 7.52288i | 0.172601 | − | 0.246025i | ||||
\(936\) | 3.62049 | 0.118340 | ||||||||
\(937\) | − | 33.1555i | − | 1.08314i | −0.840655 | − | 0.541571i | \(-0.817830\pi\) | ||
0.840655 | − | 0.541571i | \(-0.182170\pi\) | |||||||
\(938\) | − | 3.71620i | − | 0.121338i | ||||||
\(939\) | −17.8897 | −0.583808 | ||||||||
\(940\) | 10.1567 | − | 14.4773i | 0.331276 | − | 0.472198i | ||||
\(941\) | −33.8004 | −1.10186 | −0.550931 | − | 0.834551i | \(-0.685727\pi\) | ||||
−0.550931 | + | 0.834551i | \(0.685727\pi\) | |||||||
\(942\) | − | 10.6754i | − | 0.347823i | ||||||
\(943\) | − | 10.0876i | − | 0.328496i | ||||||
\(944\) | −12.4146 | −0.404062 | ||||||||
\(945\) | −0.625517 | − | 0.438839i | −0.0203481 | − | 0.0142754i | ||||
\(946\) | −3.98995 | −0.129725 | ||||||||
\(947\) | 20.2406i | 0.657730i | 0.944377 | + | 0.328865i | \(0.106666\pi\) | ||||
−0.944377 | + | 0.328865i | \(0.893334\pi\) | |||||||
\(948\) | − | 15.7735i | − | 0.512299i | ||||||
\(949\) | −13.5277 | −0.439129 | ||||||||
\(950\) | 11.5126 | − | 4.16658i | 0.373519 | − | 0.135182i | ||||
\(951\) | −31.6622 | −1.02672 | ||||||||
\(952\) | − | 3.88674i | − | 0.125970i | ||||||
\(953\) | 28.3885i | 0.919592i | 0.888024 | + | 0.459796i | \(0.152078\pi\) | ||||
−0.888024 | + | 0.459796i | \(0.847922\pi\) | |||||||
\(954\) | −16.3646 | −0.529822 | ||||||||
\(955\) | 37.2652 | + | 26.1438i | 1.20587 | + | 0.845995i | ||||
\(956\) | −16.0840 | −0.520194 | ||||||||
\(957\) | − | 10.2979i | − | 0.332885i | ||||||
\(958\) | 3.86206i | 0.124777i | ||||||||
\(959\) | 16.1419 | 0.521249 | ||||||||
\(960\) | 3.09259 | − | 4.40815i | 0.0998129 | − | 0.142272i | ||||
\(961\) | 25.5937 | 0.825604 | ||||||||
\(962\) | − | 6.56304i | − | 0.211601i | ||||||
\(963\) | − | 3.87611i | − | 0.124906i | ||||||
\(964\) | 28.1283 | 0.905952 | ||||||||
\(965\) | −1.81482 | + | 2.58683i | −0.0584212 | + | 0.0832730i | ||||
\(966\) | −1.70156 | −0.0547469 | ||||||||
\(967\) | − | 57.6163i | − | 1.85282i | −0.376522 | − | 0.926408i | \(-0.622880\pi\) | ||
0.376522 | − | 0.926408i | \(-0.377120\pi\) | |||||||
\(968\) | 10.4418i | 0.335613i | ||||||||
\(969\) | −32.4367 | −1.04202 | ||||||||
\(970\) | −2.74712 | − | 1.92728i | −0.0882047 | − | 0.0618811i | ||||
\(971\) | −1.47686 | −0.0473946 | −0.0236973 | − | 0.999719i | \(-0.507544\pi\) | ||||
−0.0236973 | + | 0.999719i | \(0.507544\pi\) | |||||||
\(972\) | 21.5762i | 0.692057i | ||||||||
\(973\) | − | 2.65711i | − | 0.0851829i | ||||||
\(974\) | 15.1499 | 0.485433 | ||||||||
\(975\) | 5.29991 | + | 14.6441i | 0.169733 | + | 0.468987i | ||||
\(976\) | 1.57346 | 0.0503653 | ||||||||
\(977\) | − | 11.5709i | − | 0.370185i | −0.982721 | − | 0.185092i | \(-0.940742\pi\) | ||
0.982721 | − | 0.185092i | \(-0.0592584\pi\) | |||||||
\(978\) | 23.8997i | 0.764229i | ||||||||
\(979\) | −10.1927 | −0.325760 | ||||||||
\(980\) | −11.8997 | − | 8.34837i | −0.380122 | − | 0.266679i | ||||
\(981\) | −39.2920 | −1.25450 | ||||||||
\(982\) | − | 6.86312i | − | 0.219011i | ||||||
\(983\) | − | 37.5275i | − | 1.19694i | −0.801145 | − | 0.598470i | \(-0.795775\pi\) | ||
0.801145 | − | 0.598470i | \(-0.204225\pi\) | |||||||
\(984\) | 24.2923 | 0.774412 | ||||||||
\(985\) | −6.32344 | + | 9.01337i | −0.201481 | + | 0.287190i | ||||
\(986\) | −31.4846 | −1.00267 | ||||||||
\(987\) | − | 13.4575i | − | 0.428356i | ||||||
\(988\) | − | 3.16716i | − | 0.100761i | ||||||
\(989\) | 5.34045 | 0.169816 | ||||||||
\(990\) | 2.68571 | − | 3.82819i | 0.0853575 | − | 0.121668i | ||||
\(991\) | 9.87860 | 0.313804 | 0.156902 | − | 0.987614i | \(-0.449849\pi\) | ||||
0.156902 | + | 0.987614i | \(0.449849\pi\) | |||||||
\(992\) | 7.52288i | 0.238852i | ||||||||
\(993\) | − | 37.6214i | − | 1.19388i | ||||||
\(994\) | −1.89679 | −0.0601624 | ||||||||
\(995\) | 18.8736 | + | 13.2410i | 0.598333 | + | 0.419768i | ||||
\(996\) | −30.5998 | −0.969593 | ||||||||
\(997\) | − | 53.6506i | − | 1.69913i | −0.527484 | − | 0.849565i | \(-0.676865\pi\) | ||
0.527484 | − | 0.849565i | \(-0.323135\pi\) | |||||||
\(998\) | 18.6809i | 0.591333i | ||||||||
\(999\) | 2.45397 | 0.0776401 |
(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 | 230.2.b.b.139.8 | yes | 8 | |
3.2 | odd | 2 | 2070.2.d.f.829.1 | 8 | |||
4.3 | odd | 2 | 1840.2.e.e.369.2 | 8 | |||
5.2 | odd | 4 | 1150.2.a.r.1.4 | 4 | |||
5.3 | odd | 4 | 1150.2.a.s.1.1 | 4 | |||
5.4 | even | 2 | inner | 230.2.b.b.139.1 | ✓ | 8 | |
15.14 | odd | 2 | 2070.2.d.f.829.5 | 8 | |||
20.3 | even | 4 | 9200.2.a.cj.1.4 | 4 | |||
20.7 | even | 4 | 9200.2.a.cr.1.1 | 4 | |||
20.19 | odd | 2 | 1840.2.e.e.369.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.b.139.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
230.2.b.b.139.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1150.2.a.r.1.4 | 4 | 5.2 | odd | 4 | |||
1150.2.a.s.1.1 | 4 | 5.3 | odd | 4 | |||
1840.2.e.e.369.2 | 8 | 4.3 | odd | 2 | |||
1840.2.e.e.369.7 | 8 | 20.19 | odd | 2 | |||
2070.2.d.f.829.1 | 8 | 3.2 | odd | 2 | |||
2070.2.d.f.829.5 | 8 | 15.14 | odd | 2 | |||
9200.2.a.cj.1.4 | 4 | 20.3 | even | 4 | |||
9200.2.a.cr.1.1 | 4 | 20.7 | even | 4 |