Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (of order \(6\), degree \(2\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.121721 + 0.507075i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.67 |
Dual form | 392.3.k.l.275.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78207 | − | 0.907869i | −0.891035 | − | 0.453934i | ||||
\(3\) | −1.99052 | + | 3.44767i | −0.663505 | + | 1.14922i | 0.316183 | + | 0.948698i | \(0.397599\pi\) |
−0.979688 | + | 0.200526i | \(0.935735\pi\) | |||||||
\(4\) | 2.35155 | + | 3.23577i | 0.587887 | + | 0.808943i | ||||
\(5\) | −1.63031 | + | 0.941260i | −0.326062 | + | 0.188252i | −0.654091 | − | 0.756416i | \(-0.726949\pi\) |
0.328029 | + | 0.944668i | \(0.393616\pi\) | |||||||
\(6\) | 6.67727 | − | 4.33687i | 1.11288 | − | 0.722812i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.25297 | − | 7.90127i | −0.156621 | − | 0.987659i | ||||
\(9\) | −3.42430 | − | 5.93106i | −0.380478 | − | 0.659007i | ||||
\(10\) | 3.75987 | − | 0.197284i | 0.375987 | − | 0.0197284i | ||||
\(11\) | 3.93973 | − | 6.82381i | 0.358157 | − | 0.620346i | −0.629496 | − | 0.777004i | \(-0.716739\pi\) |
0.987653 | + | 0.156658i | \(0.0500719\pi\) | |||||||
\(12\) | −15.8367 | + | 1.66652i | −1.31972 | + | 0.138877i | ||||
\(13\) | − | 11.4863i | − | 0.883564i | −0.897122 | − | 0.441782i | \(-0.854346\pi\) | ||
0.897122 | − | 0.441782i | \(-0.145654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.49437i | − | 0.499625i | ||||||
\(16\) | −4.94043 | + | 15.2182i | −0.308777 | + | 0.951134i | ||||
\(17\) | −1.44921 | + | 2.51011i | −0.0852478 | + | 0.147654i | −0.905497 | − | 0.424353i | \(-0.860502\pi\) |
0.820249 | + | 0.572007i | \(0.193835\pi\) | |||||||
\(18\) | 0.717719 | + | 13.6784i | 0.0398733 | + | 0.759910i | ||||
\(19\) | −15.0223 | − | 26.0194i | −0.790649 | − | 1.36944i | −0.925566 | − | 0.378587i | \(-0.876410\pi\) |
0.134916 | − | 0.990857i | \(-0.456923\pi\) | |||||||
\(20\) | −6.87946 | − | 3.06189i | −0.343973 | − | 0.153095i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −13.2160 | + | 8.58375i | −0.600727 | + | 0.390171i | ||||
\(23\) | 33.3838 | − | 19.2741i | 1.45147 | − | 0.838006i | 0.452904 | − | 0.891559i | \(-0.350388\pi\) |
0.998565 | + | 0.0535530i | \(0.0170546\pi\) | |||||||
\(24\) | 29.7351 | + | 11.4078i | 1.23896 | + | 0.475323i | ||||
\(25\) | −10.7281 | + | 18.5815i | −0.429122 | + | 0.743262i | ||||
\(26\) | −10.4281 | + | 20.4695i | −0.401080 | + | 0.787287i | ||||
\(27\) | −8.56478 | −0.317214 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.8701i | 0.961039i | 0.876984 | + | 0.480519i | \(0.159552\pi\) | ||||
−0.876984 | + | 0.480519i | \(0.840448\pi\) | |||||||
\(30\) | −6.80390 | + | 13.3555i | −0.226797 | + | 0.445183i | ||||
\(31\) | 19.4709 | + | 11.2416i | 0.628095 | + | 0.362631i | 0.780014 | − | 0.625762i | \(-0.215212\pi\) |
−0.151919 | + | 0.988393i | \(0.548545\pi\) | |||||||
\(32\) | 22.6203 | − | 22.6346i | 0.706884 | − | 0.707330i | ||||
\(33\) | 15.6842 | + | 27.1658i | 0.475278 | + | 0.823206i | ||||
\(34\) | 4.86145 | − | 3.15750i | 0.142984 | − | 0.0928676i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11.1392 | − | 25.0274i | 0.309421 | − | 0.695207i | ||||
\(37\) | 39.4520 | − | 22.7776i | 1.06627 | − | 0.615611i | 0.139109 | − | 0.990277i | \(-0.455576\pi\) |
0.927160 | + | 0.374666i | \(0.122243\pi\) | |||||||
\(38\) | 3.14862 | + | 60.0068i | 0.0828584 | + | 1.57913i | ||||
\(39\) | 39.6011 | + | 22.8637i | 1.01541 | + | 0.586249i | ||||
\(40\) | 9.47988 | + | 11.7021i | 0.236997 | + | 0.292554i | ||||
\(41\) | 40.6313 | 0.991007 | 0.495503 | − | 0.868606i | \(-0.334984\pi\) | ||||
0.495503 | + | 0.868606i | \(0.334984\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −47.2806 | −1.09955 | −0.549774 | − | 0.835313i | \(-0.685286\pi\) | ||||
−0.549774 | + | 0.835313i | \(0.685286\pi\) | |||||||
\(44\) | 31.3448 | − | 3.29846i | 0.712381 | − | 0.0749651i | ||||
\(45\) | 11.1653 | + | 6.44632i | 0.248119 | + | 0.143251i | ||||
\(46\) | −76.9907 | + | 4.03978i | −1.67371 | + | 0.0878213i | ||||
\(47\) | 71.5172 | − | 41.2905i | 1.52164 | − | 0.878520i | 0.521968 | − | 0.852965i | \(-0.325198\pi\) |
0.999673 | − | 0.0255554i | \(-0.00813541\pi\) | |||||||
\(48\) | −42.6332 | − | 47.3250i | −0.888192 | − | 0.985937i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 35.9878 | − | 23.3739i | 0.719755 | − | 0.467479i | ||||
\(51\) | −5.76936 | − | 9.99283i | −0.113125 | − | 0.195938i | ||||
\(52\) | 37.1672 | − | 27.0107i | 0.714753 | − | 0.519436i | ||||
\(53\) | 23.2823 | + | 13.4420i | 0.439288 | + | 0.253623i | 0.703296 | − | 0.710897i | \(-0.251711\pi\) |
−0.264007 | + | 0.964521i | \(0.585044\pi\) | |||||||
\(54\) | 15.2630 | + | 7.77569i | 0.282649 | + | 0.143994i | ||||
\(55\) | 14.8332i | 0.269695i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 119.609 | 2.09840 | ||||||||
\(58\) | 25.3024 | − | 49.6665i | 0.436249 | − | 0.856320i | ||||
\(59\) | −5.20555 | + | 9.01627i | −0.0882296 | + | 0.152818i | −0.906763 | − | 0.421641i | \(-0.861454\pi\) |
0.818533 | + | 0.574459i | \(0.194788\pi\) | |||||||
\(60\) | 24.2501 | − | 17.6234i | 0.404168 | − | 0.293723i | ||||
\(61\) | −19.1932 | + | 11.0812i | −0.314642 | + | 0.181659i | −0.649002 | − | 0.760787i | \(-0.724813\pi\) |
0.334360 | + | 0.942446i | \(0.391480\pi\) | |||||||
\(62\) | −24.4927 | − | 37.7103i | −0.395044 | − | 0.608231i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −60.8601 | + | 19.8001i | −0.950939 | + | 0.309377i | ||||
\(65\) | 10.8116 | + | 18.7263i | 0.166333 | + | 0.288097i | ||||
\(66\) | −3.28734 | − | 62.6505i | −0.0498082 | − | 0.949250i | ||||
\(67\) | 29.6549 | − | 51.3639i | 0.442611 | − | 0.766625i | −0.555271 | − | 0.831669i | \(-0.687386\pi\) |
0.997882 | + | 0.0650444i | \(0.0207189\pi\) | |||||||
\(68\) | −11.5300 | + | 1.21333i | −0.169559 | + | 0.0178430i | ||||
\(69\) | 153.462i | 2.22409i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 38.2541i | − | 0.538791i | −0.963030 | − | 0.269395i | \(-0.913176\pi\) | ||
0.963030 | − | 0.269395i | \(-0.0868238\pi\) | |||||||
\(72\) | −42.5724 | + | 34.4878i | −0.591283 | + | 0.478997i | ||||
\(73\) | 6.98890 | − | 12.1051i | 0.0957383 | − | 0.165824i | −0.814178 | − | 0.580615i | \(-0.802812\pi\) |
0.909917 | + | 0.414791i | \(0.136145\pi\) | |||||||
\(74\) | −90.9852 | + | 4.77409i | −1.22953 | + | 0.0645147i | ||||
\(75\) | −42.7087 | − | 73.9737i | −0.569450 | − | 0.986316i | ||||
\(76\) | 48.8672 | − | 109.795i | 0.642990 | − | 1.44467i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −49.8147 | − | 76.6974i | −0.638651 | − | 0.983300i | ||||
\(79\) | −44.3314 | + | 25.5948i | −0.561157 | + | 0.323984i | −0.753610 | − | 0.657322i | \(-0.771689\pi\) |
0.192453 | + | 0.981306i | \(0.438356\pi\) | |||||||
\(80\) | −6.26980 | − | 29.4605i | −0.0783725 | − | 0.368257i | ||||
\(81\) | 47.8670 | − | 82.9081i | 0.590951 | − | 1.02356i | ||||
\(82\) | −72.4078 | − | 36.8879i | −0.883022 | − | 0.449852i | ||||
\(83\) | 89.4458 | 1.07766 | 0.538830 | − | 0.842414i | \(-0.318866\pi\) | ||||
0.538830 | + | 0.842414i | \(0.318866\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.45635i | − | 0.0641923i | ||||||
\(86\) | 84.2573 | + | 42.9246i | 0.979737 | + | 0.499123i | ||||
\(87\) | −96.0871 | − | 55.4759i | −1.10445 | − | 0.637654i | ||||
\(88\) | −58.8531 | − | 22.5788i | −0.668786 | − | 0.256578i | ||||
\(89\) | 52.6288 | + | 91.1558i | 0.591335 | + | 1.02422i | 0.994053 | + | 0.108898i | \(0.0347323\pi\) |
−0.402718 | + | 0.915324i | \(0.631934\pi\) | |||||||
\(90\) | −14.0450 | − | 21.6245i | −0.156056 | − | 0.240272i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 140.870 | + | 62.6982i | 1.53120 | + | 0.681502i | ||||
\(93\) | −77.5144 | + | 44.7530i | −0.833488 | + | 0.481215i | ||||
\(94\) | −164.935 | + | 8.65431i | −1.75463 | + | 0.0920671i | ||||
\(95\) | 48.9821 | + | 28.2798i | 0.515601 | + | 0.297683i | ||||
\(96\) | 33.0105 | + | 123.042i | 0.343860 | + | 1.28168i | ||||
\(97\) | −55.3301 | −0.570413 | −0.285206 | − | 0.958466i | \(-0.592062\pi\) | ||||
−0.285206 | + | 0.958466i | \(0.592062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −53.9633 | −0.545084 | ||||||||
\(100\) | −85.3532 | + | 8.98187i | −0.853532 | + | 0.0898187i | ||||
\(101\) | 27.2216 | + | 15.7164i | 0.269521 | + | 0.155608i | 0.628670 | − | 0.777672i | \(-0.283600\pi\) |
−0.359149 | + | 0.933280i | \(0.616933\pi\) | |||||||
\(102\) | 1.20923 | + | 23.0457i | 0.0118552 | + | 0.225939i | ||||
\(103\) | 69.2701 | − | 39.9931i | 0.672525 | − | 0.388283i | −0.124508 | − | 0.992219i | \(-0.539735\pi\) |
0.797033 | + | 0.603936i | \(0.206402\pi\) | |||||||
\(104\) | −90.7566 | + | 14.3920i | −0.872660 | + | 0.138385i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.2871 | − | 45.0919i | −0.276293 | − | 0.425395i | ||||
\(107\) | −24.3817 | − | 42.2303i | −0.227866 | − | 0.394676i | 0.729309 | − | 0.684184i | \(-0.239842\pi\) |
−0.957175 | + | 0.289508i | \(0.906508\pi\) | |||||||
\(108\) | −20.1405 | − | 27.7137i | −0.186486 | − | 0.256608i | ||||
\(109\) | 99.6528 | + | 57.5346i | 0.914246 | + | 0.527840i | 0.881795 | − | 0.471633i | \(-0.156335\pi\) |
0.0324509 | + | 0.999473i | \(0.489669\pi\) | |||||||
\(110\) | 13.4666 | − | 26.4339i | 0.122424 | − | 0.240308i | ||||
\(111\) | 181.357i | 1.63384i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −55.7570 | −0.493425 | −0.246712 | − | 0.969089i | \(-0.579350\pi\) | ||||
−0.246712 | + | 0.969089i | \(0.579350\pi\) | |||||||
\(114\) | −213.151 | − | 108.589i | −1.86975 | − | 0.952535i | ||||
\(115\) | −36.2840 | + | 62.8457i | −0.315513 | + | 0.546484i | ||||
\(116\) | −90.1814 | + | 65.5380i | −0.777426 | + | 0.564983i | ||||
\(117\) | −68.1262 | + | 39.3327i | −0.582275 | + | 0.336177i | ||||
\(118\) | 17.4622 | − | 11.3417i | 0.147985 | − | 0.0961159i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −59.2150 | + | 9.39023i | −0.493459 | + | 0.0782519i | ||||
\(121\) | 29.4571 | + | 51.0212i | 0.243447 | + | 0.421663i | ||||
\(122\) | 44.2639 | − | 2.32257i | 0.362819 | − | 0.0190375i | ||||
\(123\) | −80.8772 | + | 140.083i | −0.657538 | + | 1.13889i | ||||
\(124\) | 9.41178 | + | 89.4386i | 0.0759015 | + | 0.721279i | ||||
\(125\) | − | 87.4546i | − | 0.699637i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 35.6964i | 0.281074i | 0.990075 | + | 0.140537i | \(0.0448828\pi\) | ||||
−0.990075 | + | 0.140537i | \(0.955117\pi\) | |||||||
\(128\) | 126.433 | + | 19.9678i | 0.987757 | + | 0.155998i | ||||
\(129\) | 94.1127 | − | 163.008i | 0.729556 | − | 1.26363i | ||||
\(130\) | −2.26607 | − | 43.1871i | −0.0174313 | − | 0.332208i | ||||
\(131\) | −60.6462 | − | 105.042i | −0.462948 | − | 0.801849i | 0.536158 | − | 0.844117i | \(-0.319875\pi\) |
−0.999106 | + | 0.0422680i | \(0.986542\pi\) | |||||||
\(132\) | −51.0202 | + | 114.632i | −0.386516 | + | 0.868425i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −99.4788 | + | 64.6112i | −0.742379 | + | 0.482173i | ||||
\(135\) | 13.9632 | − | 8.06168i | 0.103431 | − | 0.0597162i | ||||
\(136\) | 21.6489 | + | 8.30553i | 0.159183 | + | 0.0610701i | ||||
\(137\) | 4.24835 | − | 7.35836i | 0.0310099 | − | 0.0537107i | −0.850104 | − | 0.526615i | \(-0.823461\pi\) |
0.881114 | + | 0.472904i | \(0.156794\pi\) | |||||||
\(138\) | 139.323 | − | 273.480i | 1.00959 | − | 1.98174i | ||||
\(139\) | 3.05942 | 0.0220102 | 0.0110051 | − | 0.999939i | \(-0.496497\pi\) | ||||
0.0110051 | + | 0.999939i | \(0.496497\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 328.757i | 2.33161i | ||||||||
\(142\) | −34.7297 | + | 68.1716i | −0.244576 | + | 0.480081i | ||||
\(143\) | −78.3806 | − | 45.2530i | −0.548116 | − | 0.316455i | ||||
\(144\) | 107.177 | − | 22.8095i | 0.744287 | − | 0.158399i | ||||
\(145\) | −26.2330 | − | 45.4370i | −0.180918 | − | 0.313358i | ||||
\(146\) | −23.4446 | + | 15.2272i | −0.160579 | + | 0.104296i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 166.476 | + | 74.0949i | 1.12484 | + | 0.500641i | ||||
\(149\) | −27.4740 | + | 15.8621i | −0.184389 | + | 0.106457i | −0.589353 | − | 0.807876i | \(-0.700617\pi\) |
0.404964 | + | 0.914333i | \(0.367284\pi\) | |||||||
\(150\) | 8.95157 | + | 170.600i | 0.0596771 | + | 1.13733i | ||||
\(151\) | −219.621 | − | 126.798i | −1.45444 | − | 0.839723i | −0.455713 | − | 0.890127i | \(-0.650616\pi\) |
−0.998729 | + | 0.0504039i | \(0.983949\pi\) | |||||||
\(152\) | −186.764 | + | 151.297i | −1.22871 | + | 0.995376i | ||||
\(153\) | 19.8502 | 0.129740 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −42.3249 | −0.273064 | ||||||||
\(156\) | 19.1422 | + | 181.905i | 0.122707 | + | 1.16606i | ||||
\(157\) | −42.7187 | − | 24.6636i | −0.272093 | − | 0.157093i | 0.357745 | − | 0.933819i | \(-0.383546\pi\) |
−0.629839 | + | 0.776726i | \(0.716879\pi\) | |||||||
\(158\) | 102.238 | − | 5.36455i | 0.647078 | − | 0.0339529i | ||||
\(159\) | −92.6875 | + | 53.5132i | −0.582940 | + | 0.336561i | ||||
\(160\) | −15.5731 | + | 58.1929i | −0.0973317 | + | 0.363706i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −160.572 | + | 104.291i | −0.991186 | + | 0.643773i | ||||
\(163\) | −57.8597 | − | 100.216i | −0.354967 | − | 0.614821i | 0.632145 | − | 0.774850i | \(-0.282175\pi\) |
−0.987112 | + | 0.160029i | \(0.948841\pi\) | |||||||
\(164\) | 95.5465 | + | 131.474i | 0.582600 | + | 0.801668i | ||||
\(165\) | −51.1401 | − | 29.5258i | −0.309940 | − | 0.178944i | ||||
\(166\) | −159.399 | − | 81.2050i | −0.960233 | − | 0.489187i | ||||
\(167\) | − | 32.3859i | − | 0.193928i | −0.995288 | − | 0.0969639i | \(-0.969087\pi\) | ||
0.995288 | − | 0.0969639i | \(-0.0309131\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.0641 | 0.219314 | ||||||||
\(170\) | −4.95364 | + | 9.72359i | −0.0291391 | + | 0.0571976i | ||||
\(171\) | −102.882 | + | 178.197i | −0.601649 | + | 1.04209i | ||||
\(172\) | −111.183 | − | 152.989i | −0.646411 | − | 0.889472i | ||||
\(173\) | 179.479 | − | 103.622i | 1.03745 | − | 0.598973i | 0.118341 | − | 0.992973i | \(-0.462242\pi\) |
0.919110 | + | 0.394000i | \(0.128909\pi\) | |||||||
\(174\) | 120.869 | + | 186.096i | 0.694650 | + | 1.06952i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 84.3818 | + | 93.6679i | 0.479442 | + | 0.532204i | ||||
\(177\) | −20.7234 | − | 35.8941i | −0.117082 | − | 0.202791i | ||||
\(178\) | −11.0308 | − | 210.226i | −0.0619707 | − | 1.18105i | ||||
\(179\) | −87.0837 | + | 150.833i | −0.486501 | + | 0.842644i | −0.999880 | − | 0.0155178i | \(-0.995060\pi\) |
0.513379 | + | 0.858162i | \(0.328394\pi\) | |||||||
\(180\) | 5.39706 | + | 51.2873i | 0.0299837 | + | 0.284930i | ||||
\(181\) | − | 204.244i | − | 1.12842i | −0.825632 | − | 0.564209i | \(-0.809181\pi\) | ||
0.825632 | − | 0.564209i | \(-0.190819\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 88.2291i | − | 0.482126i | ||||||
\(184\) | −194.119 | − | 239.624i | −1.05500 | − | 1.30231i | ||||
\(185\) | −42.8793 | + | 74.2691i | −0.231780 | + | 0.401455i | ||||
\(186\) | 178.766 | − | 9.38003i | 0.961107 | − | 0.0504303i | ||||
\(187\) | 11.4190 | + | 19.7783i | 0.0610642 | + | 0.105766i | ||||
\(188\) | 301.783 | + | 134.317i | 1.60523 | + | 0.714450i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −61.6152 | − | 94.8660i | −0.324291 | − | 0.499295i | ||||
\(191\) | 258.518 | − | 149.255i | 1.35350 | − | 0.781442i | 0.364759 | − | 0.931102i | \(-0.381151\pi\) |
0.988737 | + | 0.149660i | \(0.0478180\pi\) | |||||||
\(192\) | 52.8786 | − | 249.238i | 0.275410 | − | 1.29812i | ||||
\(193\) | 165.381 | − | 286.448i | 0.856896 | − | 1.48419i | −0.0179791 | − | 0.999838i | \(-0.505723\pi\) |
0.874875 | − | 0.484349i | \(-0.160943\pi\) | |||||||
\(194\) | 98.6021 | + | 50.2324i | 0.508258 | + | 0.258930i | ||||
\(195\) | −86.0828 | −0.441450 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 327.309i | − | 1.66146i | −0.556672 | − | 0.830732i | \(-0.687922\pi\) | ||
0.556672 | − | 0.830732i | \(-0.312078\pi\) | |||||||
\(198\) | 96.1663 | + | 48.9916i | 0.485689 | + | 0.247432i | ||||
\(199\) | 11.0295 | + | 6.36789i | 0.0554246 | + | 0.0319994i | 0.527456 | − | 0.849582i | \(-0.323146\pi\) |
−0.472032 | + | 0.881582i | \(0.656479\pi\) | |||||||
\(200\) | 160.260 | + | 61.4832i | 0.801299 | + | 0.307416i | ||||
\(201\) | 118.057 | + | 204.481i | 0.587349 | + | 1.01732i | ||||
\(202\) | −34.2424 | − | 52.7214i | −0.169517 | − | 0.260997i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 18.7676 | − | 42.1670i | 0.0919979 | − | 0.206701i | ||||
\(205\) | −66.2416 | + | 38.2446i | −0.323130 | + | 0.186559i | ||||
\(206\) | −159.753 | + | 8.38239i | −0.775498 | + | 0.0406912i | ||||
\(207\) | −228.632 | − | 132.001i | −1.10450 | − | 0.637686i | ||||
\(208\) | 174.801 | + | 56.7475i | 0.840388 | + | 0.272824i | ||||
\(209\) | −236.736 | −1.13271 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 120.455 | 0.570875 | 0.285437 | − | 0.958397i | \(-0.407861\pi\) | ||||
0.285437 | + | 0.958397i | \(0.407861\pi\) | |||||||
\(212\) | 11.2541 | + | 106.946i | 0.0530854 | + | 0.504461i | ||||
\(213\) | 131.888 | + | 76.1454i | 0.619191 | + | 0.357490i | ||||
\(214\) | 5.11030 | + | 97.3927i | 0.0238799 | + | 0.455106i | ||||
\(215\) | 77.0820 | − | 44.5033i | 0.358521 | − | 0.206992i | ||||
\(216\) | 10.7314 | + | 67.6726i | 0.0496825 | + | 0.313299i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −125.354 | − | 193.002i | −0.575020 | − | 0.885331i | ||||
\(219\) | 27.8230 | + | 48.1909i | 0.127046 | + | 0.220050i | ||||
\(220\) | −47.9970 | + | 34.8811i | −0.218168 | + | 0.158550i | ||||
\(221\) | 28.8320 | + | 16.6461i | 0.130461 | + | 0.0753219i | ||||
\(222\) | 164.648 | − | 323.190i | 0.741657 | − | 1.45581i | ||||
\(223\) | − | 372.958i | − | 1.67246i | −0.548382 | − | 0.836228i | \(-0.684756\pi\) | ||
0.548382 | − | 0.836228i | \(-0.315244\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 146.944 | 0.653086 | ||||||||
\(226\) | 99.3629 | + | 50.6200i | 0.439659 | + | 0.223982i | ||||
\(227\) | 36.7128 | − | 63.5885i | 0.161730 | − | 0.280125i | −0.773759 | − | 0.633480i | \(-0.781626\pi\) |
0.935489 | + | 0.353355i | \(0.114959\pi\) | |||||||
\(228\) | 281.266 | + | 387.026i | 1.23362 | + | 1.69748i | ||||
\(229\) | −367.587 | + | 212.226i | −1.60518 | + | 0.926752i | −0.614755 | + | 0.788718i | \(0.710745\pi\) |
−0.990428 | + | 0.138034i | \(0.955922\pi\) | |||||||
\(230\) | 121.716 | − | 79.0543i | 0.529201 | − | 0.343714i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 220.209 | − | 34.9205i | 0.949179 | − | 0.150519i | ||||
\(233\) | 41.7070 | + | 72.2386i | 0.179000 | + | 0.310037i | 0.941538 | − | 0.336906i | \(-0.109380\pi\) |
−0.762538 | + | 0.646943i | \(0.776047\pi\) | |||||||
\(234\) | 157.115 | − | 8.24396i | 0.671430 | − | 0.0352306i | ||||
\(235\) | −77.7301 | + | 134.632i | −0.330766 | + | 0.572904i | ||||
\(236\) | −41.4157 | + | 4.35825i | −0.175490 | + | 0.0184672i | ||||
\(237\) | − | 203.787i | − | 0.859861i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 112.561i | − | 0.470967i | −0.971878 | − | 0.235484i | \(-0.924333\pi\) | ||
0.971878 | − | 0.235484i | \(-0.0756674\pi\) | |||||||
\(240\) | 114.050 | + | 37.0254i | 0.475210 | + | 0.154273i | ||||
\(241\) | 140.216 | − | 242.861i | 0.581809 | − | 1.00772i | −0.413455 | − | 0.910524i | \(-0.635678\pi\) |
0.995265 | − | 0.0971992i | \(-0.0309884\pi\) | |||||||
\(242\) | −6.17408 | − | 117.666i | −0.0255127 | − | 0.486225i | ||||
\(243\) | 152.019 | + | 263.304i | 0.625591 | + | 1.08356i | ||||
\(244\) | −80.9899 | − | 36.0468i | −0.331926 | − | 0.147733i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 271.306 | − | 176.213i | 1.10287 | − | 0.716311i | ||||
\(247\) | −298.868 | + | 172.552i | −1.20999 | + | 0.698589i | ||||
\(248\) | 64.4260 | − | 167.931i | 0.259782 | − | 0.677139i | ||||
\(249\) | −178.043 | + | 308.380i | −0.715033 | + | 1.23847i | ||||
\(250\) | −79.3973 | + | 155.850i | −0.317589 | + | 0.623401i | ||||
\(251\) | 32.9560 | 0.131299 | 0.0656493 | − | 0.997843i | \(-0.479088\pi\) | ||||
0.0656493 | + | 0.997843i | \(0.479088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 303.740i | − | 1.20055i | ||||||
\(254\) | 32.4076 | − | 63.6134i | 0.127589 | − | 0.250446i | ||||
\(255\) | 18.8117 | + | 10.8609i | 0.0737714 | + | 0.0425919i | ||||
\(256\) | −207.184 | − | 150.368i | −0.809314 | − | 0.587377i | ||||
\(257\) | −112.109 | − | 194.179i | −0.436223 | − | 0.755561i | 0.561172 | − | 0.827700i | \(-0.310351\pi\) |
−0.997395 | + | 0.0721390i | \(0.977017\pi\) | |||||||
\(258\) | −315.705 | + | 205.050i | −1.22366 | + | 0.794767i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −35.1699 | + | 79.0197i | −0.135269 | + | 0.303922i | ||||
\(261\) | 165.300 | − | 95.4357i | 0.633332 | − | 0.365654i | ||||
\(262\) | 12.7112 | + | 242.252i | 0.0485160 | + | 0.924624i | ||||
\(263\) | 147.190 | + | 84.9804i | 0.559659 | + | 0.323119i | 0.753009 | − | 0.658011i | \(-0.228602\pi\) |
−0.193350 | + | 0.981130i | \(0.561935\pi\) | |||||||
\(264\) | 194.992 | − | 157.963i | 0.738608 | − | 0.598344i | ||||
\(265\) | −50.6098 | −0.190980 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −419.034 | −1.56942 | ||||||||
\(268\) | 235.937 | − | 24.8280i | 0.880361 | − | 0.0926420i | ||||
\(269\) | 93.9863 | + | 54.2630i | 0.349391 | + | 0.201721i | 0.664417 | − | 0.747362i | \(-0.268680\pi\) |
−0.315026 | + | 0.949083i | \(0.602013\pi\) | |||||||
\(270\) | −32.2024 | + | 1.68969i | −0.119268 | + | 0.00625813i | ||||
\(271\) | 16.7690 | − | 9.68157i | 0.0618781 | − | 0.0357253i | −0.468742 | − | 0.883335i | \(-0.655293\pi\) |
0.530620 | + | 0.847610i | \(0.321959\pi\) | |||||||
\(272\) | −31.0395 | − | 34.4554i | −0.114116 | − | 0.126674i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.2513 | + | 9.25617i | −0.0520120 | + | 0.0337817i | ||||
\(275\) | 84.5313 | + | 146.412i | 0.307386 | + | 0.532409i | ||||
\(276\) | −496.568 | + | 360.873i | −1.79916 | + | 1.30751i | ||||
\(277\) | −112.104 | − | 64.7231i | −0.404707 | − | 0.233658i | 0.283806 | − | 0.958882i | \(-0.408403\pi\) |
−0.688513 | + | 0.725224i | \(0.741736\pi\) | |||||||
\(278\) | −5.45210 | − | 2.77755i | −0.0196119 | − | 0.00999120i | ||||
\(279\) | − | 153.978i | − | 0.551892i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 83.3608 | 0.296658 | 0.148329 | − | 0.988938i | \(-0.452611\pi\) | ||||
0.148329 | + | 0.988938i | \(0.452611\pi\) | |||||||
\(282\) | 298.468 | − | 585.868i | 1.05840 | − | 2.07755i | ||||
\(283\) | 14.4646 | − | 25.0535i | 0.0511118 | − | 0.0885282i | −0.839338 | − | 0.543611i | \(-0.817057\pi\) |
0.890449 | + | 0.455082i | \(0.150390\pi\) | |||||||
\(284\) | 123.782 | − | 89.9565i | 0.435851 | − | 0.316748i | ||||
\(285\) | −194.999 | + | 112.583i | −0.684208 | + | 0.395028i | ||||
\(286\) | 98.5959 | + | 151.803i | 0.344741 | + | 0.530781i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −211.706 | − | 56.6548i | −0.735089 | − | 0.196718i | ||||
\(289\) | 140.300 | + | 243.006i | 0.485466 | + | 0.840851i | ||||
\(290\) | 5.49833 | + | 104.788i | 0.0189598 | + | 0.361338i | ||||
\(291\) | 110.135 | − | 190.760i | 0.378472 | − | 0.655533i | ||||
\(292\) | 55.6042 | − | 5.85133i | 0.190425 | − | 0.0200388i | ||||
\(293\) | 214.613i | 0.732468i | 0.930523 | + | 0.366234i | \(0.119353\pi\) | ||||
−0.930523 | + | 0.366234i | \(0.880647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 19.5991i | − | 0.0664376i | ||||||
\(296\) | −229.404 | − | 283.181i | −0.775014 | − | 0.956692i | ||||
\(297\) | −33.7429 | + | 58.4444i | −0.113612 | + | 0.196783i | ||||
\(298\) | 63.3612 | − | 3.32463i | 0.212622 | − | 0.0111565i | ||||
\(299\) | −221.389 | − | 383.457i | −0.740432 | − | 1.28247i | ||||
\(300\) | 138.930 | − | 312.148i | 0.463101 | − | 1.04049i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 276.264 | + | 425.350i | 0.914780 | + | 1.40844i | ||||
\(303\) | −108.370 | + | 62.5675i | −0.357657 | + | 0.206493i | ||||
\(304\) | 470.185 | − | 100.065i | 1.54666 | − | 0.329161i | ||||
\(305\) | 20.8606 | − | 36.1316i | 0.0683953 | − | 0.118464i | ||||
\(306\) | −35.3744 | − | 18.0213i | −0.115603 | − | 0.0588933i | ||||
\(307\) | 120.542 | 0.392644 | 0.196322 | − | 0.980539i | \(-0.437100\pi\) | ||||
0.196322 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 318.427i | 1.03051i | ||||||||
\(310\) | 75.4259 | + | 38.4254i | 0.243309 | + | 0.123953i | ||||
\(311\) | 281.771 | + | 162.681i | 0.906016 | + | 0.523089i | 0.879147 | − | 0.476550i | \(-0.158113\pi\) |
0.0268689 | + | 0.999639i | \(0.491446\pi\) | |||||||
\(312\) | 131.033 | − | 341.547i | 0.419979 | − | 1.09470i | ||||
\(313\) | 228.378 | + | 395.562i | 0.729642 | + | 1.26378i | 0.957034 | + | 0.289974i | \(0.0936467\pi\) |
−0.227392 | + | 0.973803i | \(0.573020\pi\) | |||||||
\(314\) | 53.7363 | + | 82.7353i | 0.171135 | + | 0.263488i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −187.066 | − | 83.2590i | −0.591982 | − | 0.263478i | ||||
\(317\) | −104.980 | + | 60.6102i | −0.331167 | + | 0.191199i | −0.656359 | − | 0.754449i | \(-0.727904\pi\) |
0.325192 | + | 0.945648i | \(0.394571\pi\) | |||||||
\(318\) | 213.759 | − | 11.2161i | 0.672197 | − | 0.0352709i | ||||
\(319\) | 190.180 | + | 109.801i | 0.596177 | + | 0.344203i | ||||
\(320\) | 80.5838 | − | 89.5655i | 0.251824 | − | 0.279892i | ||||
\(321\) | 194.128 | 0.604761 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 87.0822 | 0.269604 | ||||||||
\(324\) | 380.833 | − | 40.0758i | 1.17541 | − | 0.123691i | ||||
\(325\) | 213.434 | + | 123.226i | 0.656719 | + | 0.379157i | ||||
\(326\) | 12.1271 | + | 231.121i | 0.0371998 | + | 0.708959i | ||||
\(327\) | −396.721 | + | 229.047i | −1.21321 | + | 0.700449i | ||||
\(328\) | −50.9098 | − | 321.039i | −0.155213 | − | 0.978777i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 64.3298 | + | 99.0455i | 0.194939 | + | 0.300138i | ||||
\(331\) | −60.5842 | − | 104.935i | −0.183034 | − | 0.317024i | 0.759878 | − | 0.650065i | \(-0.225258\pi\) |
−0.942912 | + | 0.333041i | \(0.891925\pi\) | |||||||
\(332\) | 210.336 | + | 289.426i | 0.633543 | + | 0.871766i | ||||
\(333\) | −270.191 | − | 155.995i | −0.811384 | − | 0.468453i | ||||
\(334\) | −29.4022 | + | 57.7140i | −0.0880305 | + | 0.172797i | ||||
\(335\) | 111.652i | 0.333290i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −464.021 | −1.37692 | −0.688459 | − | 0.725275i | \(-0.741713\pi\) | ||||
−0.688459 | + | 0.725275i | \(0.741713\pi\) | |||||||
\(338\) | −66.0509 | − | 33.6494i | −0.195417 | − | 0.0995543i | ||||
\(339\) | 110.985 | − | 192.232i | 0.327390 | − | 0.567056i | ||||
\(340\) | 17.6555 | − | 12.8309i | 0.0519279 | − | 0.0377378i | ||||
\(341\) | 153.420 | − | 88.5773i | 0.449913 | − | 0.259758i | ||||
\(342\) | 345.122 | − | 224.156i | 1.00913 | − | 0.655427i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 59.2412 | + | 373.577i | 0.172213 | + | 1.08598i | ||||
\(345\) | −144.448 | − | 250.190i | −0.418688 | − | 0.725190i | ||||
\(346\) | −413.920 | + | 21.7188i | −1.19630 | + | 0.0627711i | ||||
\(347\) | 185.593 | − | 321.457i | 0.534851 | − | 0.926388i | −0.464320 | − | 0.885667i | \(-0.653701\pi\) |
0.999171 | − | 0.0407208i | \(-0.0129654\pi\) | |||||||
\(348\) | −46.4462 | − | 441.370i | −0.133466 | − | 1.26831i | ||||
\(349\) | − | 207.871i | − | 0.595619i | −0.954625 | − | 0.297809i | \(-0.903744\pi\) | ||
0.954625 | − | 0.297809i | \(-0.0962560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 98.3779i | 0.280279i | ||||||||
\(352\) | −65.3361 | − | 243.530i | −0.185614 | − | 0.691848i | ||||
\(353\) | −307.007 | + | 531.751i | −0.869708 | + | 1.50638i | −0.00741211 | + | 0.999973i | \(0.502359\pi\) |
−0.862296 | + | 0.506405i | \(0.830974\pi\) | |||||||
\(354\) | 4.34355 | + | 82.7799i | 0.0122699 | + | 0.233841i | ||||
\(355\) | 36.0071 | + | 62.3661i | 0.101428 | + | 0.175679i | ||||
\(356\) | −171.200 | + | 384.652i | −0.480899 | + | 1.08048i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 292.126 | − | 189.735i | 0.815995 | − | 0.529986i | ||||
\(359\) | 93.5930 | − | 54.0359i | 0.260705 | − | 0.150518i | −0.363951 | − | 0.931418i | \(-0.618573\pi\) |
0.624656 | + | 0.780900i | \(0.285239\pi\) | |||||||
\(360\) | 36.9442 | − | 96.2975i | 0.102623 | − | 0.267493i | ||||
\(361\) | −270.841 | + | 469.110i | −0.750252 | + | 1.29947i | ||||
\(362\) | −185.427 | + | 363.977i | −0.512228 | + | 1.00546i | ||||
\(363\) | −234.539 | −0.646113 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.3135i | 0.0720917i | ||||||||
\(366\) | −80.1005 | + | 157.231i | −0.218854 | + | 0.429592i | ||||
\(367\) | 393.881 | + | 227.407i | 1.07325 | + | 0.619639i | 0.929067 | − | 0.369913i | \(-0.120612\pi\) |
0.144179 | + | 0.989552i | \(0.453946\pi\) | |||||||
\(368\) | 128.386 | + | 603.262i | 0.348876 | + | 1.63930i | ||||
\(369\) | −139.134 | − | 240.987i | −0.377056 | − | 0.653081i | ||||
\(370\) | 143.840 | − | 93.4240i | 0.388758 | − | 0.252497i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −327.089 | − | 145.580i | −0.879272 | − | 0.391344i | ||||
\(373\) | −235.344 | + | 135.876i | −0.630949 | + | 0.364279i | −0.781119 | − | 0.624382i | \(-0.785351\pi\) |
0.150171 | + | 0.988660i | \(0.452018\pi\) | |||||||
\(374\) | −2.39338 | − | 45.6133i | −0.00639940 | − | 0.121961i | ||||
\(375\) | 301.515 | + | 174.080i | 0.804039 | + | 0.464212i | ||||
\(376\) | −415.856 | − | 513.341i | −1.10600 | − | 1.36527i | ||||
\(377\) | 320.126 | 0.849140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 268.351 | 0.708051 | 0.354026 | − | 0.935236i | \(-0.384813\pi\) | ||||
0.354026 | + | 0.935236i | \(0.384813\pi\) | |||||||
\(380\) | 23.6768 | + | 224.996i | 0.0623073 | + | 0.592096i | ||||
\(381\) | −123.069 | − | 71.0541i | −0.323017 | − | 0.186494i | ||||
\(382\) | −596.201 | + | 31.2833i | −1.56074 | + | 0.0818934i | ||||
\(383\) | 283.718 | − | 163.805i | 0.740779 | − | 0.427689i | −0.0815738 | − | 0.996667i | \(-0.525995\pi\) |
0.822352 | + | 0.568979i | \(0.192661\pi\) | |||||||
\(384\) | −320.509 | + | 396.153i | −0.834659 | + | 1.03165i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −554.778 | + | 360.327i | −1.43725 | + | 0.933489i | ||||
\(387\) | 161.903 | + | 280.424i | 0.418354 | + | 0.724610i | ||||
\(388\) | −130.111 | − | 179.035i | −0.335339 | − | 0.461431i | ||||
\(389\) | 109.380 | + | 63.1506i | 0.281183 | + | 0.162341i | 0.633959 | − | 0.773367i | \(-0.281429\pi\) |
−0.352776 | + | 0.935708i | \(0.614762\pi\) | |||||||
\(390\) | 153.406 | + | 78.1519i | 0.393348 | + | 0.200389i | ||||
\(391\) | 111.729i | 0.285753i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 482.869 | 1.22867 | ||||||||
\(394\) | −297.153 | + | 583.287i | −0.754196 | + | 1.48042i | ||||
\(395\) | 48.1826 | − | 83.4548i | 0.121981 | − | 0.211278i | ||||
\(396\) | −126.897 | − | 174.613i | −0.320448 | − | 0.440941i | ||||
\(397\) | −110.110 | + | 63.5720i | −0.277355 | + | 0.160131i | −0.632225 | − | 0.774784i | \(-0.717858\pi\) |
0.354870 | + | 0.934916i | \(0.384525\pi\) | |||||||
\(398\) | −13.8741 | − | 21.3614i | −0.0348597 | − | 0.0536718i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −229.775 | − | 255.062i | −0.574439 | − | 0.637655i | ||||
\(401\) | −30.0751 | − | 52.0916i | −0.0750003 | − | 0.129904i | 0.826086 | − | 0.563544i | \(-0.190562\pi\) |
−0.901086 | + | 0.433640i | \(0.857229\pi\) | |||||||
\(402\) | −24.7443 | − | 471.580i | −0.0615530 | − | 1.17308i | ||||
\(403\) | 129.124 | − | 223.650i | 0.320408 | − | 0.554962i | ||||
\(404\) | 13.1583 | + | 125.041i | 0.0325700 | + | 0.309507i | ||||
\(405\) | 180.221i | 0.444991i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 358.950i | − | 0.881941i | ||||||
\(408\) | −71.7272 | + | 58.1060i | −0.175802 | + | 0.142417i | ||||
\(409\) | −34.8873 | + | 60.4267i | −0.0852991 | + | 0.147742i | −0.905519 | − | 0.424306i | \(-0.860518\pi\) |
0.820220 | + | 0.572049i | \(0.193851\pi\) | |||||||
\(410\) | 152.768 | − | 8.01591i | 0.372605 | − | 0.0195510i | ||||
\(411\) | 16.9128 | + | 29.2939i | 0.0411504 | + | 0.0712746i | ||||
\(412\) | 292.301 | + | 130.096i | 0.709467 | + | 0.315768i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 287.599 | + | 442.803i | 0.694685 | + | 1.06957i | ||||
\(415\) | −145.824 | + | 84.1918i | −0.351384 | + | 0.202872i | ||||
\(416\) | −259.988 | − | 259.824i | −0.624971 | − | 0.624577i | ||||
\(417\) | −6.08982 | + | 10.5479i | −0.0146039 | + | 0.0252947i | ||||
\(418\) | 421.880 | + | 214.925i | 1.00928 | + | 0.514174i | ||||
\(419\) | −714.794 | −1.70595 | −0.852976 | − | 0.521950i | \(-0.825205\pi\) | ||||
−0.852976 | + | 0.521950i | \(0.825205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 303.440i | 0.720759i | 0.932806 | + | 0.360380i | \(0.117353\pi\) | ||||
−0.932806 | + | 0.360380i | \(0.882647\pi\) | |||||||
\(422\) | −214.658 | − | 109.357i | −0.508669 | − | 0.259140i | ||||
\(423\) | −489.793 | − | 282.782i | −1.15790 | − | 0.668515i | ||||
\(424\) | 77.0371 | − | 200.802i | 0.181691 | − | 0.473590i | ||||
\(425\) | −31.0945 | − | 53.8572i | −0.0731635 | − | 0.126723i | ||||
\(426\) | −165.903 | − | 255.433i | −0.389444 | − | 0.599609i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 79.3129 | − | 178.200i | 0.185310 | − | 0.416356i | ||||
\(429\) | 312.035 | − | 180.154i | 0.727355 | − | 0.419939i | ||||
\(430\) | −177.769 | + | 9.32771i | −0.413416 | + | 0.0216924i | ||||
\(431\) | −373.685 | − | 215.747i | −0.867019 | − | 0.500574i | −0.000662591 | − | 1.00000i | \(-0.500211\pi\) |
−0.866357 | + | 0.499426i | \(0.833544\pi\) | |||||||
\(432\) | 42.3137 | − | 130.340i | 0.0979484 | − | 0.301713i | ||||
\(433\) | −194.875 | −0.450057 | −0.225029 | − | 0.974352i | \(-0.572248\pi\) | ||||
−0.225029 | + | 0.974352i | \(0.572248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 208.869 | 0.480159 | ||||||||
\(436\) | 48.1697 | + | 457.749i | 0.110481 | + | 1.04988i | ||||
\(437\) | −1003.00 | − | 579.085i | −2.29521 | − | 1.32514i | ||||
\(438\) | −5.83159 | − | 111.139i | −0.0133141 | − | 0.253742i | ||||
\(439\) | −264.977 | + | 152.985i | −0.603593 | + | 0.348485i | −0.770454 | − | 0.637496i | \(-0.779970\pi\) |
0.166861 | + | 0.985980i | \(0.446637\pi\) | |||||||
\(440\) | 117.201 | − | 18.5856i | 0.266367 | − | 0.0422400i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.2681 | − | 55.8402i | −0.0820545 | − | 0.126335i | ||||
\(443\) | −125.099 | − | 216.677i | −0.282390 | − | 0.489113i | 0.689583 | − | 0.724206i | \(-0.257794\pi\) |
−0.971973 | + | 0.235093i | \(0.924460\pi\) | |||||||
\(444\) | −586.828 | + | 426.469i | −1.32169 | + | 0.960516i | ||||
\(445\) | −171.603 | − | 99.0748i | −0.385624 | − | 0.222640i | ||||
\(446\) | −338.597 | + | 664.637i | −0.759185 | + | 1.49022i | ||||
\(447\) | − | 126.295i | − | 0.282539i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −688.681 | −1.53381 | −0.766905 | − | 0.641761i | \(-0.778204\pi\) | ||||
−0.766905 | + | 0.641761i | \(0.778204\pi\) | |||||||
\(450\) | −261.865 | − | 133.406i | −0.581923 | − | 0.296458i | ||||
\(451\) | 160.076 | − | 277.260i | 0.354936 | − | 0.614768i | ||||
\(452\) | −131.115 | − | 180.417i | −0.290078 | − | 0.399152i | ||||
\(453\) | 874.317 | − | 504.787i | 1.93006 | − | 1.11432i | ||||
\(454\) | −123.155 | + | 79.9887i | −0.271266 | + | 0.176187i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −149.866 | − | 945.061i | −0.328654 | − | 2.07250i | ||||
\(457\) | −402.259 | − | 696.733i | −0.880217 | − | 1.52458i | −0.851100 | − | 0.525004i | \(-0.824064\pi\) |
−0.0291166 | − | 0.999576i | \(-0.509269\pi\) | |||||||
\(458\) | 847.739 | − | 44.4817i | 1.85096 | − | 0.0971217i | ||||
\(459\) | 12.4122 | − | 21.4985i | 0.0270418 | − | 0.0468378i | ||||
\(460\) | −288.678 | + | 30.3781i | −0.627560 | + | 0.0660393i | ||||
\(461\) | 693.657i | 1.50468i | 0.658776 | + | 0.752339i | \(0.271074\pi\) | ||||
−0.658776 | + | 0.752339i | \(0.728926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 321.194i | 0.693724i | 0.937916 | + | 0.346862i | \(0.112753\pi\) | ||||
−0.937916 | + | 0.346862i | \(0.887247\pi\) | |||||||
\(464\) | −424.132 | − | 137.690i | −0.914077 | − | 0.296747i | ||||
\(465\) | 84.2484 | − | 145.922i | 0.181179 | − | 0.313812i | ||||
\(466\) | −8.74161 | − | 166.599i | −0.0187588 | − | 0.357508i | ||||
\(467\) | 375.937 | + | 651.142i | 0.805005 | + | 1.39431i | 0.916288 | + | 0.400521i | \(0.131171\pi\) |
−0.111283 | + | 0.993789i | \(0.535496\pi\) | |||||||
\(468\) | −287.474 | − | 127.948i | −0.614260 | − | 0.273393i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 260.749 | − | 169.356i | 0.554785 | − | 0.360332i | ||||
\(471\) | 170.064 | − | 98.1867i | 0.361071 | − | 0.208464i | ||||
\(472\) | 77.7624 | + | 29.8333i | 0.164751 | + | 0.0632062i | ||||
\(473\) | −186.273 | + | 322.634i | −0.393811 | + | 0.682101i | ||||
\(474\) | −185.012 | + | 363.163i | −0.390320 | + | 0.766166i | ||||
\(475\) | 644.642 | 1.35714 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 184.118i | − | 0.385992i | ||||||
\(478\) | −102.191 | + | 200.592i | −0.213788 | + | 0.419648i | ||||
\(479\) | −625.392 | − | 361.070i | −1.30562 | − | 0.753800i | −0.324257 | − | 0.945969i | \(-0.605114\pi\) |
−0.981362 | + | 0.192169i | \(0.938448\pi\) | |||||||
\(480\) | −169.632 | − | 169.525i | −0.353399 | − | 0.353176i | ||||
\(481\) | −261.631 | − | 453.158i | −0.543932 | − | 0.942117i | ||||
\(482\) | −470.361 | + | 305.498i | −0.975853 | + | 0.633814i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −95.8230 | + | 215.295i | −0.197981 | + | 0.444825i | ||||
\(485\) | 90.2052 | − | 52.0800i | 0.185990 | − | 0.107381i | ||||
\(486\) | −31.8625 | − | 607.239i | −0.0655606 | − | 1.24946i | ||||
\(487\) | 41.4211 | + | 23.9145i | 0.0850536 | + | 0.0491057i | 0.541924 | − | 0.840428i | \(-0.317696\pi\) |
−0.456870 | + | 0.889533i | \(0.651030\pi\) | |||||||
\(488\) | 111.604 | + | 137.766i | 0.228697 | + | 0.282308i | ||||
\(489\) | 460.682 | 0.942090 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 44.4724 | 0.0905752 | 0.0452876 | − | 0.998974i | \(-0.485580\pi\) | ||||
0.0452876 | + | 0.998974i | \(0.485580\pi\) | |||||||
\(492\) | −643.465 | + | 67.7129i | −1.30785 | + | 0.137628i | ||||
\(493\) | −69.9571 | − | 40.3898i | −0.141901 | − | 0.0819265i | ||||
\(494\) | 689.258 | − | 36.1661i | 1.39526 | − | 0.0732107i | ||||
\(495\) | 87.9769 | − | 50.7935i | 0.177731 | − | 0.102613i | ||||
\(496\) | −267.271 | + | 240.774i | −0.538852 | + | 0.485431i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 597.254 | − | 387.915i | 1.19931 | − | 0.778945i | ||||
\(499\) | 250.786 | + | 434.374i | 0.502577 | + | 0.870489i | 0.999996 | + | 0.00297862i | \(0.000948124\pi\) |
−0.497418 | + | 0.867511i | \(0.665719\pi\) | |||||||
\(500\) | 282.983 | − | 205.654i | 0.565966 | − | 0.411307i | ||||
\(501\) | 111.656 | + | 64.4647i | 0.222867 | + | 0.128672i | ||||
\(502\) | −58.7298 | − | 29.9197i | −0.116992 | − | 0.0596010i | ||||
\(503\) | 462.733i | 0.919946i | 0.887933 | + | 0.459973i | \(0.152141\pi\) | ||||
−0.887933 | + | 0.459973i | \(0.847859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −59.1729 | −0.117174 | ||||||||
\(506\) | −275.756 | + | 541.285i | −0.544971 | + | 1.06973i | ||||
\(507\) | −73.7767 | + | 127.785i | −0.145516 | + | 0.252041i | ||||
\(508\) | −115.505 | + | 83.9417i | −0.227372 | + | 0.165240i | ||||
\(509\) | 408.751 | − | 235.992i | 0.803046 | − | 0.463639i | −0.0414889 | − | 0.999139i | \(-0.513210\pi\) |
0.844535 | + | 0.535500i | \(0.179877\pi\) | |||||||
\(510\) | −23.6635 | − | 36.4335i | −0.0463989 | − | 0.0714382i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 232.702 | + | 456.063i | 0.454496 | + | 0.890749i | ||||
\(513\) | 128.663 | + | 222.851i | 0.250805 | + | 0.434407i | ||||
\(514\) | 23.4976 | + | 447.821i | 0.0457153 | + | 0.871248i | ||||
\(515\) | −75.2878 | + | 130.402i | −0.146190 | + | 0.253208i | ||||
\(516\) | 748.767 | − | 78.7941i | 1.45110 | − | 0.152702i | ||||
\(517\) | − | 650.693i | − | 1.25859i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 825.047i | 1.58969i | ||||||||
\(520\) | 134.415 | − | 108.889i | 0.258490 | − | 0.209402i | ||||
\(521\) | −45.3709 | + | 78.5848i | −0.0870843 | + | 0.150834i | −0.906277 | − | 0.422683i | \(-0.861088\pi\) |
0.819193 | + | 0.573518i | \(0.194422\pi\) | |||||||
\(522\) | −381.218 | + | 20.0029i | −0.730304 | + | 0.0383198i | ||||
\(523\) | −180.256 | − | 312.213i | −0.344658 | − | 0.596965i | 0.640634 | − | 0.767847i | \(-0.278672\pi\) |
−0.985292 | + | 0.170882i | \(0.945338\pi\) | |||||||
\(524\) | 197.280 | − | 443.249i | 0.376489 | − | 0.845896i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −185.152 | − | 285.070i | −0.352001 | − | 0.541959i | ||||
\(527\) | −56.4351 | + | 32.5828i | −0.107087 | + | 0.0618270i | ||||
\(528\) | −490.900 | + | 104.473i | −0.929734 | + | 0.197866i | ||||
\(529\) | 478.485 | − | 828.760i | 0.904509 | − | 1.56665i | ||||
\(530\) | 90.1902 | + | 45.9470i | 0.170170 | + | 0.0866925i | ||||
\(531\) | 71.3014 | 0.134278 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 466.705i | − | 0.875618i | ||||||
\(534\) | 746.748 | + | 380.428i | 1.39840 | + | 0.712412i | ||||
\(535\) | 79.4994 | + | 45.8990i | 0.148597 | + | 0.0857925i | ||||
\(536\) | −442.997 | − | 169.954i | −0.826486 | − | 0.317079i | ||||
\(537\) | −346.683 | − | 600.472i | −0.645592 | − | 1.11820i | ||||
\(538\) | −118.226 | − | 182.028i | −0.219752 | − | 0.338341i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 58.9210 | + | 26.2244i | 0.109113 | + | 0.0485637i | ||||
\(541\) | 485.969 | − | 280.574i | 0.898278 | − | 0.518621i | 0.0216371 | − | 0.999766i | \(-0.493112\pi\) |
0.876641 | + | 0.481145i | \(0.159779\pi\) | |||||||
\(542\) | −38.6731 | + | 2.02922i | −0.0713525 | + | 0.00374394i | ||||
\(543\) | 704.166 | + | 406.550i | 1.29681 | + | 0.748712i | ||||
\(544\) | 24.0336 | + | 89.5817i | 0.0441795 | + | 0.164672i | ||||
\(545\) | −216.620 | −0.397468 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1043.62 | 1.90790 | 0.953952 | − | 0.299960i | \(-0.0969733\pi\) | ||||
0.953952 | + | 0.299960i | \(0.0969733\pi\) | |||||||
\(548\) | 33.8002 | − | 3.55685i | 0.0616792 | − | 0.00649061i | ||||
\(549\) | 131.447 | + | 75.8907i | 0.239429 | + | 0.138234i | ||||
\(550\) | −17.7174 | − | 337.661i | −0.0322135 | − | 0.613928i | ||||
\(551\) | 725.165 | − | 418.674i | 1.31609 | − | 0.759845i | ||||
\(552\) | 1212.54 | − | 192.283i | 2.19664 | − | 0.348339i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 141.017 | + | 217.117i | 0.254543 | + | 0.391907i | ||||
\(555\) | −170.704 | − | 295.667i | −0.307574 | − | 0.532734i | ||||
\(556\) | 7.19438 | + | 9.89959i | 0.0129395 | + | 0.0178050i | ||||
\(557\) | −42.1273 | − | 24.3222i | −0.0756324 | − | 0.0436664i | 0.461707 | − | 0.887033i | \(-0.347237\pi\) |
−0.537339 | + | 0.843366i | \(0.680571\pi\) | |||||||
\(558\) | −139.792 | + | 274.399i | −0.250523 | + | 0.491755i | ||||
\(559\) | 543.081i | 0.971522i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −90.9189 | −0.162066 | ||||||||
\(562\) | −148.555 | − | 75.6807i | −0.264332 | − | 0.134663i | ||||
\(563\) | 363.015 | − | 628.761i | 0.644787 | − | 1.11680i | −0.339563 | − | 0.940583i | \(-0.610279\pi\) |
0.984351 | − | 0.176221i | \(-0.0563874\pi\) | |||||||
\(564\) | −1063.78 | + | 773.088i | −1.88614 | + | 1.37072i | ||||
\(565\) | 90.9012 | − | 52.4818i | 0.160887 | − | 0.0928882i | ||||
\(566\) | −48.5223 | + | 31.5151i | −0.0857284 | + | 0.0556804i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −302.256 | + | 47.9313i | −0.532141 | + | 0.0843861i | ||||
\(569\) | 240.696 | + | 416.898i | 0.423016 | + | 0.732685i | 0.996233 | − | 0.0867185i | \(-0.0276381\pi\) |
−0.573217 | + | 0.819404i | \(0.694305\pi\) | |||||||
\(570\) | 449.713 | − | 23.5969i | 0.788970 | − | 0.0413981i | ||||
\(571\) | −55.0633 | + | 95.3724i | −0.0964331 | + | 0.167027i | −0.910206 | − | 0.414156i | \(-0.864077\pi\) |
0.813773 | + | 0.581183i | \(0.197410\pi\) | |||||||
\(572\) | −37.8873 | − | 360.036i | −0.0662365 | − | 0.629434i | ||||
\(573\) | 1188.38i | 2.07396i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 827.097i | 1.43843i | ||||||||
\(576\) | 325.839 | + | 293.164i | 0.565693 | + | 0.508965i | ||||
\(577\) | −101.168 | + | 175.228i | −0.175335 | + | 0.303688i | −0.940277 | − | 0.340410i | \(-0.889434\pi\) |
0.764942 | + | 0.644099i | \(0.222767\pi\) | |||||||
\(578\) | −29.4062 | − | 560.427i | −0.0508758 | − | 0.969597i | ||||
\(579\) | 658.386 | + | 1140.36i | 1.13711 | + | 1.96953i | ||||
\(580\) | 85.3353 | − | 191.731i | 0.147130 | − | 0.330571i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −369.454 | + | 239.959i | −0.634800 | + | 0.412301i | ||||
\(583\) | 183.452 | − | 105.916i | 0.314669 | − | 0.181674i | ||||
\(584\) | −104.403 | − | 40.0538i | −0.178772 | − | 0.0685853i | ||||
\(585\) | 74.0445 | − | 128.249i | 0.126572 | − | 0.219229i | ||||
\(586\) | 194.841 | − | 382.456i | 0.332492 | − | 0.652655i | ||||
\(587\) | 568.689 | 0.968805 | 0.484403 | − | 0.874845i | \(-0.339037\pi\) | ||||
0.484403 | + | 0.874845i | \(0.339037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 675.497i | − | 1.14685i | ||||||
\(590\) | −17.7934 | + | 34.9270i | −0.0301583 | + | 0.0591982i | ||||
\(591\) | 1128.45 | + | 651.513i | 1.90940 | + | 1.10239i | ||||
\(592\) | 151.723 | + | 712.917i | 0.256289 | + | 1.20425i | ||||
\(593\) | −342.686 | − | 593.550i | −0.577886 | − | 1.00093i | −0.995721 | − | 0.0924054i | \(-0.970544\pi\) |
0.417835 | − | 0.908523i | \(-0.362789\pi\) | |||||||
\(594\) | 113.192 | − | 73.5179i | 0.190559 | − | 0.123768i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −115.932 | − | 51.5989i | −0.194518 | − | 0.0865754i | ||||
\(597\) | −43.9088 | + | 25.3507i | −0.0735491 | + | 0.0424636i | ||||
\(598\) | 46.4023 | + | 884.340i | 0.0775957 | + | 1.47883i | ||||
\(599\) | −318.077 | − | 183.642i | −0.531013 | − | 0.306580i | 0.210416 | − | 0.977612i | \(-0.432518\pi\) |
−0.741429 | + | 0.671032i | \(0.765851\pi\) | |||||||
\(600\) | −530.973 | + | 430.140i | −0.884955 | + | 0.716900i | ||||
\(601\) | −412.344 | −0.686097 | −0.343049 | − | 0.939318i | \(-0.611460\pi\) | ||||
−0.343049 | + | 0.939318i | \(0.611460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −406.190 | −0.673615 | ||||||||
\(604\) | −106.159 | − | 1008.81i | −0.175761 | − | 1.67022i | ||||
\(605\) | −96.0484 | − | 55.4535i | −0.158758 | − | 0.0916588i | ||||
\(606\) | 249.926 | − | 13.1139i | 0.412420 | − | 0.0216401i | ||||
\(607\) | −1010.46 | + | 583.389i | −1.66468 | + | 0.961102i | −0.694241 | + | 0.719743i | \(0.744260\pi\) |
−0.970436 | + | 0.241359i | \(0.922407\pi\) | |||||||
\(608\) | −928.748 | − | 248.543i | −1.52755 | − | 0.408788i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −69.9777 | + | 45.4503i | −0.114718 | + | 0.0745087i | ||||
\(611\) | −474.276 | − | 821.470i | −0.776229 | − | 1.34447i | ||||
\(612\) | 46.6787 | + | 64.2306i | 0.0762723 | + | 0.104952i | ||||
\(613\) | 373.900 | + | 215.871i | 0.609951 | + | 0.352155i | 0.772946 | − | 0.634471i | \(-0.218782\pi\) |
−0.162995 | + | 0.986627i | \(0.552115\pi\) | |||||||
\(614\) | −214.814 | − | 109.436i | −0.349860 | − | 0.178235i | ||||
\(615\) | − | 304.506i | − | 0.495131i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −333.751 | −0.540926 | −0.270463 | − | 0.962730i | \(-0.587177\pi\) | ||||
−0.270463 | + | 0.962730i | \(0.587177\pi\) | |||||||
\(618\) | 289.090 | − | 567.460i | 0.467784 | − | 0.918220i | ||||
\(619\) | −488.158 | + | 845.514i | −0.788624 | + | 1.36594i | 0.138187 | + | 0.990406i | \(0.455873\pi\) |
−0.926810 | + | 0.375530i | \(0.877461\pi\) | |||||||
\(620\) | −99.5291 | − | 136.954i | −0.160531 | − | 0.220893i | ||||
\(621\) | −285.925 | + | 165.079i | −0.460426 | + | 0.265827i | ||||
\(622\) | −354.443 | − | 545.719i | −0.569844 | − | 0.877362i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −543.590 | + | 489.699i | −0.871138 | + | 0.784775i | ||||
\(625\) | −185.884 | − | 321.961i | −0.297414 | − | 0.515137i | ||||
\(626\) | −47.8671 | − | 912.257i | −0.0764650 | − | 1.45728i | ||||
\(627\) | 471.226 | − | 816.187i | 0.751556 | − | 1.30173i | ||||
\(628\) | −20.6492 | − | 196.226i | −0.0328808 | − | 0.312461i | ||||
\(629\) | 132.038i | 0.209918i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 639.885i | 1.01408i | 0.861922 | + | 0.507040i | \(0.169261\pi\) | ||||
−0.861922 | + | 0.507040i | \(0.830739\pi\) | |||||||
\(632\) | 257.777 | + | 318.205i | 0.407875 | + | 0.503489i | ||||
\(633\) | −239.767 | + | 415.288i | −0.378778 | + | 0.656063i | ||||
\(634\) | 242.108 | − | 12.7036i | 0.381873 | − | 0.0200373i | ||||
\(635\) | −33.5995 | − | 58.1961i | −0.0529127 | − | 0.0916474i | ||||
\(636\) | −391.116 | − | 174.077i | −0.614962 | − | 0.273706i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −239.230 | − | 368.332i | −0.374969 | − | 0.577322i | ||||
\(639\) | −226.888 | + | 130.994i | −0.355067 | + | 0.204998i | ||||
\(640\) | −224.920 | + | 86.4526i | −0.351437 | + | 0.135082i | ||||
\(641\) | −10.4295 | + | 18.0645i | −0.0162707 | + | 0.0281817i | −0.874046 | − | 0.485843i | \(-0.838513\pi\) |
0.857775 | + | 0.514025i | \(0.171846\pi\) | |||||||
\(642\) | −345.950 | − | 176.243i | −0.538864 | − | 0.274522i | ||||
\(643\) | 69.1348 | 0.107519 | 0.0537596 | − | 0.998554i | \(-0.482880\pi\) | ||||
0.0537596 | + | 0.998554i | \(0.482880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 354.338i | 0.549362i | ||||||||
\(646\) | −155.187 | − | 79.0592i | −0.240227 | − | 0.122383i | ||||
\(647\) | 310.868 | + | 179.480i | 0.480476 | + | 0.277403i | 0.720615 | − | 0.693336i | \(-0.243860\pi\) |
−0.240139 | + | 0.970739i | \(0.577193\pi\) | |||||||
\(648\) | −715.056 | − | 274.329i | −1.10348 | − | 0.423347i | ||||
\(649\) | 41.0169 | + | 71.0433i | 0.0632001 | + | 0.109466i | ||||
\(650\) | −268.481 | − | 413.367i | −0.413048 | − | 0.635950i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 188.216 | − | 422.883i | 0.288675 | − | 0.648594i | ||||
\(653\) | −32.1227 | + | 18.5460i | −0.0491925 | + | 0.0284013i | −0.524395 | − | 0.851475i | \(-0.675708\pi\) |
0.475202 | + | 0.879877i | \(0.342375\pi\) | |||||||
\(654\) | 914.929 | − | 48.0073i | 1.39897 | − | 0.0734056i | ||||
\(655\) | 197.744 | + | 114.168i | 0.301900 | + | 0.174302i | ||||
\(656\) | −200.736 | + | 618.333i | −0.306000 | + | 0.942581i | ||||
\(657\) | −95.7284 | −0.145705 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 197.302 | 0.299396 | 0.149698 | − | 0.988732i | \(-0.452170\pi\) | ||||
0.149698 | + | 0.988732i | \(0.452170\pi\) | |||||||
\(660\) | −24.7199 | − | 234.909i | −0.0374544 | − | 0.355923i | ||||
\(661\) | 938.626 | + | 541.916i | 1.42001 | + | 0.819843i | 0.996299 | − | 0.0859554i | \(-0.0273942\pi\) |
0.423710 | + | 0.905798i | \(0.360728\pi\) | |||||||
\(662\) | 12.6982 | + | 242.004i | 0.0191816 | + | 0.365565i | ||||
\(663\) | −114.781 | + | 66.2688i | −0.173124 | + | 0.0999530i | ||||
\(664\) | −112.073 | − | 706.735i | −0.168785 | − | 1.06436i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 339.876 | + | 523.291i | 0.510325 | + | 0.785723i | ||||
\(667\) | 537.173 | + | 930.411i | 0.805357 | + | 1.39492i | ||||
\(668\) | 104.794 | − | 76.1571i | 0.156877 | − | 0.114008i | ||||
\(669\) | 1285.84 | + | 742.378i | 1.92203 | + | 1.10968i | ||||
\(670\) | 101.365 | − | 198.972i | 0.151292 | − | 0.296973i | ||||
\(671\) | 174.628i | 0.260250i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −286.066 | −0.425061 | −0.212530 | − | 0.977154i | \(-0.568170\pi\) | ||||
−0.212530 | + | 0.977154i | \(0.568170\pi\) | |||||||
\(674\) | 826.919 | + | 421.270i | 1.22688 | + | 0.625030i | ||||
\(675\) | 91.8834 | − | 159.147i | 0.136124 | − | 0.235773i | ||||
\(676\) | 87.1581 | + | 119.931i | 0.128932 | + | 0.177413i | ||||
\(677\) | 433.324 | − | 250.180i | 0.640065 | − | 0.369542i | −0.144575 | − | 0.989494i | \(-0.546181\pi\) |
0.784640 | + | 0.619952i | \(0.212848\pi\) | |||||||
\(678\) | −372.305 | + | 241.811i | −0.549122 | + | 0.356653i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −43.1121 | + | 6.83664i | −0.0634001 | + | 0.0100539i | ||||
\(681\) | 146.155 | + | 253.148i | 0.214618 | + | 0.371729i | ||||
\(682\) | −353.823 | + | 18.5654i | −0.518801 | + | 0.0272221i | ||||
\(683\) | −473.225 | + | 819.650i | −0.692862 | + | 1.20007i | 0.278034 | + | 0.960571i | \(0.410317\pi\) |
−0.970896 | + | 0.239501i | \(0.923016\pi\) | |||||||
\(684\) | −818.536 | + | 86.1360i | −1.19669 | + | 0.125930i | ||||
\(685\) | 15.9952i | 0.0233507i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1689.76i | − | 2.45962i | ||||||
\(688\) | 233.587 | − | 719.523i | 0.339515 | − | 1.04582i | ||||
\(689\) | 154.400 | − | 267.428i | 0.224092 | − | 0.388140i | ||||
\(690\) | 30.2756 | + | 576.996i | 0.0438777 | + | 0.836227i | ||||
\(691\) | 151.632 | + | 262.634i | 0.219439 | + | 0.380079i | 0.954636 | − | 0.297774i | \(-0.0962441\pi\) |
−0.735198 | + | 0.677853i | \(0.762911\pi\) | |||||||
\(692\) | 757.352 | + | 337.080i | 1.09444 | + | 0.487111i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −622.580 | + | 404.364i | −0.897090 | + | 0.582658i | ||||
\(695\) | −4.98781 | + | 2.87971i | −0.00717670 | + | 0.00414347i | ||||
\(696\) | −317.936 | + | 828.720i | −0.456804 | + | 1.19069i | ||||
\(697\) | −58.8834 | + | 101.989i | −0.0844812 | + | 0.146326i | ||||
\(698\) | −188.720 | + | 370.441i | −0.270372 | + | 0.530717i | ||||
\(699\) | −332.074 | −0.475069 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 390.864i | − | 0.557580i | −0.960352 | − | 0.278790i | \(-0.910067\pi\) | ||
0.960352 | − | 0.278790i | \(-0.0899333\pi\) | |||||||
\(702\) | 89.3142 | − | 175.316i | 0.127228 | − | 0.249738i | ||||
\(703\) | −1185.32 | − | 684.345i | −1.68609 | − | 0.973464i | ||||
\(704\) | −104.660 | + | 493.305i | −0.148665 | + | 0.700717i | ||||
\(705\) | −309.446 | − | 535.976i | −0.438930 | − | 0.760250i | ||||
\(706\) | 1029.87 | − | 668.897i | 1.45874 | − | 0.947446i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 67.4128 | − | 151.463i | 0.0952158 | − | 0.213931i | ||||
\(709\) | −832.393 | + | 480.582i | −1.17404 | + | 0.677831i | −0.954628 | − | 0.297801i | \(-0.903747\pi\) |
−0.219410 | + | 0.975633i | \(0.570413\pi\) | |||||||
\(710\) | −7.54693 | − | 143.830i | −0.0106295 | − | 0.202578i | ||||
\(711\) | 303.608 | + | 175.288i | 0.427016 | + | 0.246538i | ||||
\(712\) | 654.304 | − | 530.050i | 0.918967 | − | 0.744453i | ||||
\(713\) | 866.685 | 1.21555 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 170.379 | 0.238293 | ||||||||
\(716\) | −692.844 | + | 72.9092i | −0.967659 | + | 0.101828i | ||||
\(717\) | 388.074 | + | 224.055i | 0.541247 | + | 0.312489i | ||||
\(718\) | −215.847 | + | 11.3257i | −0.300622 | + | 0.0157740i | ||||
\(719\) | −454.773 | + | 262.563i | −0.632507 | + | 0.365178i | −0.781722 | − | 0.623627i | \(-0.785659\pi\) |
0.149215 | + | 0.988805i | \(0.452325\pi\) | |||||||
\(720\) | −153.263 | + | 138.068i | −0.212865 | + | 0.191762i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 908.548 | − | 590.100i | 1.25838 | − | 0.817312i | ||||
\(723\) | 558.204 | + | 966.838i | 0.772067 | + | 1.33726i | ||||
\(724\) | 660.886 | − | 480.289i | 0.912826 | − | 0.663383i | ||||
\(725\) | −517.870 | − | 298.992i | −0.714304 | − | 0.412403i | ||||
\(726\) | 417.965 | + | 212.931i | 0.575710 | + | 0.293293i | ||||
\(727\) | 108.633i | 0.149426i | 0.997205 | + | 0.0747131i | \(0.0238041\pi\) | ||||
−0.997205 | + | 0.0747131i | \(0.976196\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −348.775 | −0.478429 | ||||||||
\(730\) | 23.8892 | − | 46.8925i | 0.0327249 | − | 0.0642363i | ||||
\(731\) | 68.5197 | − | 118.680i | 0.0937341 | − | 0.162352i | ||||
\(732\) | 285.489 | − | 207.475i | 0.390013 | − | 0.283436i | ||||
\(733\) | 34.8609 | − | 20.1270i | 0.0475593 | − | 0.0274584i | −0.476032 | − | 0.879428i | \(-0.657925\pi\) |
0.523591 | + | 0.851970i | \(0.324592\pi\) | |||||||
\(734\) | −495.468 | − | 762.849i | −0.675025 | − | 1.03930i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 318.889 | − | 1191.61i | 0.433273 | − | 1.61904i | ||||
\(737\) | −233.665 | − | 404.719i | −0.317049 | − | 0.549144i | ||||
\(738\) | 29.1619 | + | 555.770i | 0.0395147 | + | 0.753077i | ||||
\(739\) | −498.602 | + | 863.603i | −0.674698 | + | 1.16861i | 0.301859 | + | 0.953352i | \(0.402393\pi\) |
−0.976557 | + | 0.215258i | \(0.930941\pi\) | |||||||
\(740\) | −341.151 | + | 35.8999i | −0.461014 | + | 0.0485134i | ||||
\(741\) | − | 1373.87i | − | 1.85407i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 476.575i | − | 0.641420i | −0.947177 | − | 0.320710i | \(-0.896078\pi\) | ||
0.947177 | − | 0.320710i | \(-0.103922\pi\) | |||||||
\(744\) | 450.729 | + | 556.388i | 0.605818 | + | 0.747833i | ||||
\(745\) | 29.8607 | − | 51.7203i | 0.0400815 | − | 0.0694232i | ||||
\(746\) | 542.757 | − | 28.4790i | 0.727556 | − | 0.0381756i | ||||
\(747\) | −306.289 | − | 530.509i | −0.410026 | − | 0.710186i | ||||
\(748\) | −37.1457 | + | 83.4590i | −0.0496600 | + | 0.111576i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −379.279 | − | 583.958i | −0.505706 | − | 0.778611i | ||||
\(751\) | 457.691 | − | 264.248i | 0.609442 | − | 0.351862i | −0.163305 | − | 0.986576i | \(-0.552215\pi\) |
0.772747 | + | 0.634714i | \(0.218882\pi\) | |||||||
\(752\) | 275.039 | + | 1292.35i | 0.365743 | + | 1.71855i | ||||
\(753\) | −65.5993 | + | 113.621i | −0.0871173 | + | 0.150892i | ||||
\(754\) | −570.486 | − | 290.632i | −0.756613 | − | 0.385454i | ||||
\(755\) | 477.400 | 0.632318 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 455.964i | 0.602331i | 0.953572 | + | 0.301165i | \(0.0973756\pi\) | ||||
−0.953572 | + | 0.301165i | \(0.902624\pi\) | |||||||
\(758\) | −478.221 | − | 243.628i | −0.630898 | − | 0.321409i | ||||
\(759\) | 1047.19 | + | 604.598i | 1.37970 | + | 0.796572i | ||||
\(760\) | 162.073 | − | 422.455i | 0.213255 | − | 0.555862i | ||||
\(761\) | 238.325 | + | 412.791i | 0.313174 | + | 0.542433i | 0.979048 | − | 0.203632i | \(-0.0652745\pi\) |
−0.665874 | + | 0.746064i | \(0.731941\pi\) | |||||||
\(762\) | 154.810 | + | 238.354i | 0.203163 | + | 0.312801i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1090.87 | + | 485.523i | 1.42784 | + | 0.635502i | ||||
\(765\) | −32.3619 | + | 18.6842i | −0.0423032 | + | 0.0244238i | ||||
\(766\) | −654.319 | + | 34.3328i | −0.854202 | + | 0.0448209i | ||||
\(767\) | 103.564 | + | 59.7927i | 0.135025 | + | 0.0779565i | ||||
\(768\) | 930.825 | − | 414.993i | 1.21201 | − | 0.540355i | ||||
\(769\) | 568.246 | 0.738941 | 0.369471 | − | 0.929242i | \(-0.379539\pi\) | ||||
0.369471 | + | 0.929242i | \(0.379539\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 892.621 | 1.15774 | ||||||||
\(772\) | 1315.78 | − | 138.462i | 1.70438 | − | 0.179355i | ||||
\(773\) | −1036.66 | − | 598.515i | −1.34108 | − | 0.774275i | −0.354118 | − | 0.935201i | \(-0.615219\pi\) |
−0.986967 | + | 0.160925i | \(0.948552\pi\) | |||||||
\(774\) | −33.9342 | − | 646.722i | −0.0438426 | − | 0.835559i | ||||
\(775\) | −417.771 | + | 241.200i | −0.539059 | + | 0.311226i | ||||
\(776\) | 69.3270 | + | 437.178i | 0.0893389 | + | 0.563373i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −137.590 | − | 211.842i | −0.176852 | − | 0.272290i | ||||
\(779\) | −610.377 | − | 1057.20i | −0.783539 | − | 1.35713i | ||||
\(780\) | −202.428 | − | 278.544i | −0.259523 | − | 0.357108i | ||||
\(781\) | −261.039 | − | 150.711i | −0.334237 | − | 0.192972i | ||||
\(782\) | 101.436 | − | 199.110i | 0.129713 | − | 0.254616i | ||||
\(783\) | − | 238.701i | − | 0.304855i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 92.8596 | 0.118292 | ||||||||
\(786\) | −860.506 | − | 438.381i | −1.09479 | − | 0.557737i | ||||
\(787\) | 226.134 | − | 391.676i | 0.287337 | − | 0.497682i | −0.685836 | − | 0.727756i | \(-0.740563\pi\) |
0.973173 | + | 0.230074i | \(0.0738967\pi\) | |||||||
\(788\) | 1059.10 | − | 769.682i | 1.34403 | − | 0.976754i | ||||
\(789\) | −585.969 | + | 338.309i | −0.742673 | + | 0.428783i | ||||
\(790\) | −161.631 | + | 104.979i | −0.204596 | + | 0.132885i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 67.6144 | + | 426.378i | 0.0853717 | + | 0.538356i | ||||
\(793\) | 127.282 | + | 220.459i | 0.160507 | + | 0.278007i | ||||
\(794\) | 253.939 | − | 13.3244i | 0.319822 | − | 0.0167814i | ||||
\(795\) | 100.740 | − | 174.486i | 0.126716 | − | 0.219479i | ||||
\(796\) | 5.33139 | + | 50.6633i | 0.00669773 | + | 0.0636474i | ||||
\(797\) | − | 1047.47i | − | 1.31426i | −0.753777 | − | 0.657130i | \(-0.771770\pi\) | ||
0.753777 | − | 0.657130i | \(-0.228230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 239.355i | 0.299568i | ||||||||
\(800\) | 177.913 | + | 663.145i | 0.222392 | + | 0.828931i | ||||
\(801\) | 360.434 | − | 624.290i | 0.449980 | − | 0.779388i | ||||
\(802\) | 6.30362 | + | 120.135i | 0.00785987 | + | 0.149794i | ||||
\(803\) | −55.0687 | − | 95.3818i | −0.0685787 | − | 0.118782i | ||||
\(804\) | −384.037 | + | 862.854i | −0.477658 | + | 1.07320i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −433.153 | + | 281.332i | −0.537411 | + | 0.349047i | ||||
\(807\) | −374.162 | + | 216.023i | −0.463646 | + | 0.267686i | ||||
\(808\) | 90.0717 | − | 234.778i | 0.111475 | − | 0.290566i | ||||
\(809\) | 149.332 | − | 258.651i | 0.184589 | − | 0.319717i | −0.758849 | − | 0.651267i | \(-0.774238\pi\) |
0.943438 | + | 0.331549i | \(0.107571\pi\) | |||||||
\(810\) | 163.617 | − | 321.167i | 0.201997 | − | 0.396502i | ||||
\(811\) | −633.054 | −0.780584 | −0.390292 | − | 0.920691i | \(-0.627626\pi\) | ||||
−0.390292 | + | 0.920691i | \(0.627626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 77.0852i | 0.0948158i | ||||||||
\(814\) | −325.880 | + | 639.674i | −0.400343 | + | 0.785841i | ||||
\(815\) | 188.658 | + | 108.922i | 0.231483 | + | 0.133647i | ||||
\(816\) | 180.575 | − | 38.4301i | 0.221293 | − | 0.0470957i | ||||
\(817\) | 710.265 | + | 1230.21i | 0.869357 | + | 1.50577i | ||||
\(818\) | 117.031 | − | 76.0114i | 0.143070 | − | 0.0929235i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −279.521 | − | 124.409i | −0.340879 | − | 0.151718i | ||||
\(821\) | 1083.83 | − | 625.749i | 1.32013 | − | 0.762178i | 0.336382 | − | 0.941725i | \(-0.390797\pi\) |
0.983749 | + | 0.179547i | \(0.0574632\pi\) | |||||||
\(822\) | −3.54486 | − | 67.5583i | −0.00431248 | − | 0.0821878i | ||||
\(823\) | −1062.45 | − | 613.409i | −1.29095 | − | 0.745332i | −0.312130 | − | 0.950039i | \(-0.601043\pi\) |
−0.978823 | + | 0.204707i | \(0.934376\pi\) | |||||||
\(824\) | −402.790 | − | 497.211i | −0.488822 | − | 0.603412i | ||||
\(825\) | −673.043 | −0.815810 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1438.26 | −1.73913 | −0.869566 | − | 0.493816i | \(-0.835602\pi\) | ||||
−0.869566 | + | 0.493816i | \(0.835602\pi\) | |||||||
\(828\) | −110.515 | − | 1050.21i | −0.133473 | − | 1.26837i | ||||
\(829\) | 542.554 | + | 313.244i | 0.654468 | + | 0.377858i | 0.790166 | − | 0.612893i | \(-0.209994\pi\) |
−0.135698 | + | 0.990750i | \(0.543328\pi\) | |||||||
\(830\) | 336.304 | − | 17.6462i | 0.405186 | − | 0.0212605i | ||||
\(831\) | 446.289 | − | 257.665i | 0.537050 | − | 0.310066i | ||||
\(832\) | 227.431 | + | 699.060i | 0.273354 | + | 0.840216i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.4286 | − | 13.2683i | 0.0244947 | − | 0.0159092i | ||||
\(835\) | 30.4836 | + | 52.7991i | 0.0365073 | + | 0.0632325i | ||||
\(836\) | −556.696 | − | 766.022i | −0.665904 | − | 0.916295i | ||||
\(837\) | −166.764 | − | 96.2814i | −0.199240 | − | 0.115032i | ||||
\(838\) | 1273.81 | + | 648.939i | 1.52006 | + | 0.774390i | ||||
\(839\) | − | 1062.37i | − | 1.26624i | −0.774055 | − | 0.633118i | \(-0.781775\pi\) | ||
0.774055 | − | 0.633118i | \(-0.218225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.2558 | 0.0764041 | ||||||||
\(842\) | 275.483 | − | 540.751i | 0.327177 | − | 0.642222i | ||||
\(843\) | −165.931 | + | 287.401i | −0.196834 | + | 0.340926i | ||||
\(844\) | 283.255 | + | 389.763i | 0.335610 | + | 0.461805i | ||||
\(845\) | −60.4260 | + | 34.8870i | −0.0715101 | + | 0.0412864i | ||||
\(846\) | 616.116 | + | 948.605i | 0.728270 | + | 1.12128i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −319.588 | + | 287.904i | −0.376872 | + | 0.339509i | ||||
\(849\) | 57.5842 | + | 99.7387i | 0.0678259 | + | 0.117478i | ||||
\(850\) | 6.51727 | + | 124.207i | 0.00766738 | + | 0.146126i | ||||
\(851\) | 878.037 | − | 1520.80i | 1.03177 | − | 1.78708i | ||||
\(852\) | 63.7514 | + | 605.818i | 0.0748255 | + | 0.711054i | ||||
\(853\) | 698.388i | 0.818743i | 0.912368 | + | 0.409372i | \(0.134252\pi\) | ||||
−0.912368 | + | 0.409372i | \(0.865748\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 387.355i | − | 0.453047i | ||||||
\(856\) | −303.123 | + | 245.560i | −0.354116 | + | 0.286869i | ||||
\(857\) | −365.162 | + | 632.479i | −0.426094 | + | 0.738016i | −0.996522 | − | 0.0833317i | \(-0.973444\pi\) |
0.570428 | + | 0.821347i | \(0.306777\pi\) | |||||||
\(858\) | −719.625 | + | 37.7595i | −0.838724 | + | 0.0440087i | ||||
\(859\) | −483.130 | − | 836.805i | −0.562433 | − | 0.974162i | −0.997283 | − | 0.0736593i | \(-0.976532\pi\) |
0.434851 | − | 0.900502i | \(-0.356801\pi\) | |||||||
\(860\) | 325.265 | + | 144.768i | 0.378215 | + | 0.168335i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 470.063 | + | 723.734i | 0.545317 | + | 0.839598i | ||||
\(863\) | 255.023 | − | 147.237i | 0.295507 | − | 0.170611i | −0.344916 | − | 0.938634i | \(-0.612093\pi\) |
0.640423 | + | 0.768023i | \(0.278759\pi\) | |||||||
\(864\) | −193.738 | + | 193.860i | −0.224233 | + | 0.224375i | ||||
\(865\) | −195.071 | + | 337.873i | −0.225516 | + | 0.390605i | ||||
\(866\) | 347.281 | + | 176.921i | 0.401017 | + | 0.204296i | ||||
\(867\) | −1117.07 | −1.28844 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 403.346i | 0.464149i | ||||||||
\(870\) | −372.219 | − | 189.626i | −0.427838 | − | 0.217961i | ||||
\(871\) | −589.983 | − | 340.627i | −0.677362 | − | 0.391075i | ||||
\(872\) | 329.734 | − | 859.473i | 0.378135 | − | 0.985634i | ||||
\(873\) | 189.467 | + | 328.166i | 0.217030 | + | 0.375906i | ||||
\(874\) | 1261.69 | + | 1942.57i | 1.44358 | + | 2.22262i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −90.5075 | + | 203.352i | −0.103319 | + | 0.232137i | ||||
\(877\) | 818.300 | − | 472.446i | 0.933067 | − | 0.538706i | 0.0452867 | − | 0.998974i | \(-0.485580\pi\) |
0.887780 | + | 0.460268i | \(0.152247\pi\) | |||||||
\(878\) | 611.098 | − | 32.0650i | 0.696012 | − | 0.0365205i | ||||
\(879\) | −739.916 | − | 427.191i | −0.841770 | − | 0.485996i | ||||
\(880\) | −225.734 | − | 73.2826i | −0.256516 | − | 0.0832757i | ||||
\(881\) | −744.098 | −0.844606 | −0.422303 | − | 0.906455i | \(-0.638778\pi\) | ||||
−0.422303 | + | 0.906455i | \(0.638778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.9032 | 0.0270704 | 0.0135352 | − | 0.999908i | \(-0.495691\pi\) | ||||
0.0135352 | + | 0.999908i | \(0.495691\pi\) | |||||||
\(884\) | 13.9367 | + | 132.438i | 0.0157655 | + | 0.149817i | ||||
\(885\) | 67.5713 | + | 39.0123i | 0.0763517 | + | 0.0440817i | ||||
\(886\) | 26.2201 | + | 499.707i | 0.0295938 | + | 0.564003i | ||||
\(887\) | 820.397 | − | 473.656i | 0.924912 | − | 0.533998i | 0.0397129 | − | 0.999211i | \(-0.487356\pi\) |
0.885199 | + | 0.465213i | \(0.154022\pi\) | |||||||
\(888\) | 1432.95 | − | 227.235i | 1.61368 | − | 0.255895i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 215.861 | + | 332.351i | 0.242541 | + | 0.373428i | ||||
\(891\) | −377.166 | − | 653.271i | −0.423307 | − | 0.733189i | ||||
\(892\) | 1206.81 | − | 877.029i | 1.35292 | − | 0.983216i | ||||
\(893\) | −2148.71 | − | 1240.56i | −2.40617 | − | 1.38920i | ||||
\(894\) | −114.659 | + | 225.067i | −0.128254 | + | 0.251752i | ||||
\(895\) | − | 327.874i | − | 0.366339i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1762.71 | 1.96512 | ||||||||
\(898\) | 1227.28 | + | 625.232i | 1.36668 | + | 0.696249i | ||||
\(899\) | −313.304 | + | 542.658i | −0.348502 | + | 0.603624i | ||||
\(900\) | 345.547 | + | 475.479i | 0.383941 | + | 0.528310i | ||||
\(901\) | −67.4820 | + | 38.9607i | −0.0748968 | + | 0.0432417i | ||||
\(902\) | −536.983 | + | 348.769i | −0.595325 | + | 0.386662i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 69.8619 | + | 440.551i | 0.0772809 | + | 0.487335i | ||||
\(905\) | 192.247 | + | 332.981i | 0.212427 | + | 0.367935i | ||||
\(906\) | −2016.37 | + | 105.801i | −2.22558 | + | 0.116778i | ||||
\(907\) | −275.512 | + | 477.200i | −0.303761 | + | 0.526130i | −0.976985 | − | 0.213309i | \(-0.931576\pi\) |
0.673223 | + | 0.739439i | \(0.264909\pi\) | |||||||
\(908\) | 292.090 | − | 30.7371i | 0.321685 | − | 0.0338515i | ||||
\(909\) | − | 215.271i | − | 0.236822i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 827.652i | − | 0.908509i | −0.890872 | − | 0.454254i | \(-0.849906\pi\) | ||
0.890872 | − | 0.454254i | \(-0.150094\pi\) | |||||||
\(912\) | −590.919 | + | 1820.22i | −0.647937 | + | 1.99586i | ||||
\(913\) | 352.392 | − | 610.361i | 0.385972 | − | 0.668523i | ||||
\(914\) | 84.3118 | + | 1606.83i | 0.0922448 | + | 1.75801i | ||||
\(915\) | 83.0466 | + | 143.841i | 0.0907613 | + | 0.157203i | ||||
\(916\) | −1551.11 | − | 690.366i | −1.69336 | − | 0.753675i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −41.6372 | + | 27.0433i | −0.0453565 | + | 0.0294589i | ||||
\(919\) | 309.165 | − | 178.497i | 0.336415 | − | 0.194229i | −0.322271 | − | 0.946648i | \(-0.604446\pi\) |
0.658685 | + | 0.752418i | \(0.271113\pi\) | |||||||
\(920\) | 542.023 | + | 207.946i | 0.589156 | + | 0.226028i | ||||
\(921\) | −239.940 | + | 415.588i | −0.260521 | + | 0.451236i | ||||
\(922\) | 629.749 | − | 1236.14i | 0.683025 | − | 1.34072i | ||||
\(923\) | −439.400 | −0.476056 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 977.438i | 1.05669i | ||||||||
\(926\) | 291.602 | − | 572.390i | 0.314905 | − | 0.618132i | ||||
\(927\) | −474.403 | − | 273.897i | −0.511762 | − | 0.295466i | ||||
\(928\) | 630.828 | + | 630.430i | 0.679771 | + | 0.679343i | ||||
\(929\) | 484.873 | + | 839.824i | 0.521930 | + | 0.904009i | 0.999675 | + | 0.0255102i | \(0.00812102\pi\) |
−0.477745 | + | 0.878499i | \(0.658546\pi\) | |||||||
\(930\) | −282.615 | + | 183.558i | −0.303887 | + | 0.197374i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −135.672 | + | 304.827i | −0.145570 | + | 0.327068i | ||||
\(933\) | −1121.74 | + | 647.636i | −1.20229 | + | 0.694144i | ||||
\(934\) | −78.7949 | − | 1501.68i | −0.0843628 | − | 1.60780i | ||||
\(935\) | −37.2331 | − | 21.4965i | −0.0398215 | − | 0.0229909i | ||||
\(936\) | 396.138 | + | 489.001i | 0.423225 | + | 0.522437i | ||||
\(937\) | −1287.55 | −1.37412 | −0.687061 | − | 0.726600i | \(-0.741099\pi\) | ||||
−0.687061 | + | 0.726600i | \(0.741099\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1818.36 | −1.93649 | ||||||||
\(940\) | −618.426 | + | 65.0781i | −0.657900 | + | 0.0692320i | ||||
\(941\) | −395.597 | − | 228.398i | −0.420400 | − | 0.242718i | 0.274848 | − | 0.961488i | \(-0.411372\pi\) |
−0.695249 | + | 0.718769i | \(0.744706\pi\) | |||||||
\(942\) | −392.207 | + | 20.5795i | −0.416356 | + | 0.0218466i | ||||
\(943\) | 1356.43 | − | 783.133i | 1.43842 | − | 0.830470i | ||||
\(944\) | −111.493 | − | 123.763i | −0.118107 | − | 0.131105i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 624.860 | − | 405.845i | 0.660529 | − | 0.429012i | ||||
\(947\) | 573.925 | + | 994.067i | 0.606045 | + | 1.04970i | 0.991885 | + | 0.127135i | \(0.0405782\pi\) |
−0.385840 | + | 0.922566i | \(0.626088\pi\) | |||||||
\(948\) | 659.408 | − | 479.215i | 0.695578 | − | 0.505501i | ||||
\(949\) | −139.044 | − | 80.2768i | −0.146516 | − | 0.0845910i | ||||
\(950\) | −1148.80 | − | 585.250i | −1.20926 | − | 0.616053i | ||||
\(951\) | − | 482.582i | − | 0.507447i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 873.170 | 0.916232 | 0.458116 | − | 0.888892i | \(-0.348524\pi\) | ||||
0.458116 | + | 0.888892i | \(0.348524\pi\) | |||||||
\(954\) | −167.155 | + | 328.112i | −0.175215 | + | 0.343933i | ||||
\(955\) | −280.976 | + | 486.665i | −0.294216 | + | 0.509597i | ||||
\(956\) | 364.222 | − | 264.693i | 0.380986 | − | 0.276876i | ||||
\(957\) | −757.114 | + | 437.120i | −0.791133 | + | 0.456761i | ||||
\(958\) | 786.688 | + | 1211.23i | 0.821177 | + | 1.26433i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 148.389 | + | 456.108i | 0.154572 | + | 0.475113i | ||||
\(961\) | −227.755 | − | 394.483i | −0.236998 | − | 0.410492i | ||||
\(962\) | 54.8368 | + | 1045.09i | 0.0570029 | + | 1.08637i | ||||
\(963\) | −166.980 | + | 289.219i | −0.173396 | + | 0.300331i | ||||
\(964\) | 1115.57 | − | 117.393i | 1.15723 | − | 0.121777i | ||||
\(965\) | 622.666i | 0.645249i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 449.047i | 0.464372i | 0.972671 | + | 0.232186i | \(0.0745878\pi\) | ||||
−0.972671 | + | 0.232186i | \(0.925412\pi\) | |||||||
\(968\) | 366.223 | − | 296.676i | 0.378330 | − | 0.306484i | ||||
\(969\) | −173.339 | + | 300.231i | −0.178884 | + | 0.309836i | ||||
\(970\) | −208.034 | + | 10.9157i | −0.214468 | + | 0.0112533i | ||||
\(971\) | −618.929 | − | 1072.02i | −0.637414 | − | 1.10403i | −0.985998 | − | 0.166756i | \(-0.946671\pi\) |
0.348584 | − | 0.937278i | \(-0.386663\pi\) | |||||||
\(972\) | −494.512 | + | 1111.07i | −0.508757 | + | 1.14308i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −52.1041 | − | 80.2222i | −0.0534950 | − | 0.0823636i | ||||
\(975\) | −849.687 | + | 490.567i | −0.871473 | + | 0.503145i | ||||
\(976\) | −73.8126 | − | 346.831i | −0.0756277 | − | 0.355359i | ||||
\(977\) | −853.445 | + | 1478.21i | −0.873536 | + | 1.51301i | −0.0152219 | + | 0.999884i | \(0.504845\pi\) |
−0.858314 | + | 0.513125i | \(0.828488\pi\) | |||||||
\(978\) | −820.968 | − | 418.239i | −0.839435 | − | 0.427647i | ||||
\(979\) | 829.373 | 0.847164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 788.063i | − | 0.803326i | ||||||
\(982\) | −79.2530 | − | 40.3751i | −0.0807057 | − | 0.0411152i | ||||
\(983\) | −997.793 | − | 576.076i | −1.01505 | − | 0.586039i | −0.102383 | − | 0.994745i | \(-0.532647\pi\) |
−0.912666 | + | 0.408706i | \(0.865980\pi\) | |||||||
\(984\) | 1208.17 | + | 463.512i | 1.22782 | + | 0.471049i | ||||
\(985\) | 308.082 | + | 533.614i | 0.312774 | + | 0.541741i | ||||
\(986\) | 87.9999 | + | 135.489i | 0.0892494 | + | 0.137413i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1261.14 | − | 561.305i | −1.27646 | − | 0.568123i | ||||
\(989\) | −1578.41 | + | 911.293i | −1.59596 | + | 0.921429i | ||||
\(990\) | −202.895 | + | 10.6461i | −0.204944 | + | 0.0107536i | ||||
\(991\) | 357.511 | + | 206.409i | 0.360758 | + | 0.208283i | 0.669413 | − | 0.742890i | \(-0.266546\pi\) |
−0.308655 | + | 0.951174i | \(0.599879\pi\) | |||||||
\(992\) | 694.886 | − | 186.429i | 0.700490 | − | 0.187932i | ||||
\(993\) | 482.375 | 0.485776 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.9753 | −0.0240958 | ||||||||
\(996\) | −1416.52 | + | 149.063i | −1.42221 | + | 0.149662i | ||||
\(997\) | 260.805 | + | 150.576i | 0.261590 | + | 0.151029i | 0.625060 | − | 0.780577i | \(-0.285075\pi\) |
−0.363470 | + | 0.931606i | \(0.618408\pi\) | |||||||
\(998\) | −52.5637 | − | 1001.77i | −0.0526691 | − | 1.00377i | ||||
\(999\) | −337.897 | + | 195.085i | −0.338235 | + | 0.195280i |
(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 | 392.3.k.l.67.1 | 12 | ||
7.2 | even | 3 | inner | 392.3.k.l.275.3 | 12 | ||
7.3 | odd | 6 | 392.3.g.j.99.5 | 6 | |||
7.4 | even | 3 | 392.3.g.i.99.5 | 6 | |||
7.5 | odd | 6 | 56.3.k.d.51.3 | yes | 12 | ||
7.6 | odd | 2 | 56.3.k.d.11.1 | ✓ | 12 | ||
8.3 | odd | 2 | inner | 392.3.k.l.67.3 | 12 | ||
28.3 | even | 6 | 1568.3.g.j.687.6 | 6 | |||
28.11 | odd | 6 | 1568.3.g.l.687.1 | 6 | |||
28.19 | even | 6 | 224.3.o.d.79.1 | 12 | |||
28.27 | even | 2 | 224.3.o.d.207.2 | 12 | |||
56.3 | even | 6 | 392.3.g.j.99.6 | 6 | |||
56.5 | odd | 6 | 224.3.o.d.79.2 | 12 | |||
56.11 | odd | 6 | 392.3.g.i.99.6 | 6 | |||
56.13 | odd | 2 | 224.3.o.d.207.1 | 12 | |||
56.19 | even | 6 | 56.3.k.d.51.1 | yes | 12 | ||
56.27 | even | 2 | 56.3.k.d.11.3 | yes | 12 | ||
56.45 | odd | 6 | 1568.3.g.j.687.5 | 6 | |||
56.51 | odd | 6 | inner | 392.3.k.l.275.1 | 12 | ||
56.53 | even | 6 | 1568.3.g.l.687.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.d.11.1 | ✓ | 12 | 7.6 | odd | 2 | ||
56.3.k.d.11.3 | yes | 12 | 56.27 | even | 2 | ||
56.3.k.d.51.1 | yes | 12 | 56.19 | even | 6 | ||
56.3.k.d.51.3 | yes | 12 | 7.5 | odd | 6 | ||
224.3.o.d.79.1 | 12 | 28.19 | even | 6 | |||
224.3.o.d.79.2 | 12 | 56.5 | odd | 6 | |||
224.3.o.d.207.1 | 12 | 56.13 | odd | 2 | |||
224.3.o.d.207.2 | 12 | 28.27 | even | 2 | |||
392.3.g.i.99.5 | 6 | 7.4 | even | 3 | |||
392.3.g.i.99.6 | 6 | 56.11 | odd | 6 | |||
392.3.g.j.99.5 | 6 | 7.3 | odd | 6 | |||
392.3.g.j.99.6 | 6 | 56.3 | even | 6 | |||
392.3.k.l.67.1 | 12 | 1.1 | even | 1 | trivial | ||
392.3.k.l.67.3 | 12 | 8.3 | odd | 2 | inner | ||
392.3.k.l.275.1 | 12 | 56.51 | odd | 6 | inner | ||
392.3.k.l.275.3 | 12 | 7.2 | even | 3 | inner | ||
1568.3.g.j.687.5 | 6 | 56.45 | odd | 6 | |||
1568.3.g.j.687.6 | 6 | 28.3 | even | 6 | |||
1568.3.g.l.687.1 | 6 | 28.11 | odd | 6 | |||
1568.3.g.l.687.2 | 6 | 56.53 | even | 6 |