Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + 599392 x^{8} - 1089732 x^{7} + 4808401 x^{6} - 7939134 x^{5} + \cdots + 21307456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.5 | ||
Root | \(0.403686 - 0.699204i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.b.22.5 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.403686 | + | 0.699204i | −0.142725 | + | 0.247206i | −0.928522 | − | 0.371278i | \(-0.878920\pi\) |
0.785797 | + | 0.618484i | \(0.212253\pi\) | |||||||
\(3\) | −0.172376 | − | 5.19329i | −0.0331738 | − | 0.999450i | ||||
\(4\) | 3.67408 | + | 6.36369i | 0.459259 | + | 0.795461i | ||||
\(5\) | −9.11444 | − | 15.7867i | −0.815220 | − | 1.41200i | −0.909170 | − | 0.416426i | \(-0.863283\pi\) |
0.0939497 | − | 0.995577i | \(-0.470051\pi\) | |||||||
\(6\) | 3.70076 | + | 1.97593i | 0.251805 | + | 0.134445i | ||||
\(7\) | 3.50000 | − | 6.06218i | 0.188982 | − | 0.327327i | ||||
\(8\) | −12.3917 | −0.547639 | ||||||||
\(9\) | −26.9406 | + | 1.79040i | −0.997799 | + | 0.0663110i | ||||
\(10\) | 14.7175 | 0.465408 | ||||||||
\(11\) | 24.7147 | − | 42.8070i | 0.677432 | − | 1.17335i | −0.298320 | − | 0.954466i | \(-0.596426\pi\) |
0.975752 | − | 0.218880i | \(-0.0702404\pi\) | |||||||
\(12\) | 32.4152 | − | 20.1775i | 0.779787 | − | 0.485395i | ||||
\(13\) | −22.2430 | − | 38.5260i | −0.474546 | − | 0.821937i | 0.525030 | − | 0.851084i | \(-0.324054\pi\) |
−0.999575 | + | 0.0291470i | \(0.990721\pi\) | |||||||
\(14\) | 2.82580 | + | 4.89443i | 0.0539448 | + | 0.0934351i | ||||
\(15\) | −80.4137 | + | 50.0552i | −1.38418 | + | 0.861613i | ||||
\(16\) | −24.3903 | + | 42.2452i | −0.381098 | + | 0.660081i | ||||
\(17\) | 47.2301 | 0.673822 | 0.336911 | − | 0.941536i | \(-0.390618\pi\) | ||||
0.336911 | + | 0.941536i | \(0.390618\pi\) | |||||||
\(18\) | 9.62367 | − | 19.5597i | 0.126018 | − | 0.256126i | ||||
\(19\) | 56.7545 | 0.685283 | 0.342641 | − | 0.939466i | \(-0.388678\pi\) | ||||
0.342641 | + | 0.939466i | \(0.388678\pi\) | |||||||
\(20\) | 66.9743 | − | 116.003i | 0.748795 | − | 1.29695i | ||||
\(21\) | −32.0860 | − | 17.1315i | −0.333416 | − | 0.178020i | ||||
\(22\) | 19.9539 | + | 34.5612i | 0.193372 | + | 0.334930i | ||||
\(23\) | 27.7116 | + | 47.9979i | 0.251229 | + | 0.435142i | 0.963864 | − | 0.266393i | \(-0.0858319\pi\) |
−0.712635 | + | 0.701535i | \(0.752499\pi\) | |||||||
\(24\) | 2.13603 | + | 64.3535i | 0.0181673 | + | 0.547338i | ||||
\(25\) | −103.646 | + | 179.520i | −0.829168 | + | 1.43616i | ||||
\(26\) | 35.9167 | 0.270917 | ||||||||
\(27\) | 13.9420 | + | 139.602i | 0.0993753 | + | 0.995050i | ||||
\(28\) | 51.4371 | 0.347167 | ||||||||
\(29\) | −75.1405 | + | 130.147i | −0.481146 | + | 0.833370i | −0.999766 | − | 0.0216352i | \(-0.993113\pi\) |
0.518620 | + | 0.855005i | \(0.326446\pi\) | |||||||
\(30\) | −2.53694 | − | 76.4322i | −0.0154393 | − | 0.465151i | ||||
\(31\) | 83.7746 | + | 145.102i | 0.485367 | + | 0.840680i | 0.999859 | − | 0.0168154i | \(-0.00535276\pi\) |
−0.514492 | + | 0.857495i | \(0.672019\pi\) | |||||||
\(32\) | −69.2587 | − | 119.960i | −0.382604 | − | 0.662689i | ||||
\(33\) | −226.570 | − | 120.972i | −1.19517 | − | 0.638135i | ||||
\(34\) | −19.0661 | + | 33.0235i | −0.0961710 | + | 0.166573i | ||||
\(35\) | −127.602 | −0.616248 | ||||||||
\(36\) | −110.375 | − | 164.863i | −0.510996 | − | 0.763256i | ||||
\(37\) | 331.480 | 1.47284 | 0.736419 | − | 0.676526i | \(-0.236515\pi\) | ||||
0.736419 | + | 0.676526i | \(0.236515\pi\) | |||||||
\(38\) | −22.9110 | + | 39.6830i | −0.0978066 | + | 0.169406i | ||||
\(39\) | −196.242 | + | 122.155i | −0.805742 | + | 0.501551i | ||||
\(40\) | 112.943 | + | 195.623i | 0.446447 | + | 0.773268i | ||||
\(41\) | −147.716 | − | 255.852i | −0.562667 | − | 0.974568i | −0.997263 | − | 0.0739423i | \(-0.976442\pi\) |
0.434595 | − | 0.900626i | \(-0.356891\pi\) | |||||||
\(42\) | 24.9311 | − | 15.5189i | 0.0915941 | − | 0.0570147i | ||||
\(43\) | 158.894 | − | 275.213i | 0.563514 | − | 0.976036i | −0.433672 | − | 0.901071i | \(-0.642782\pi\) |
0.997186 | − | 0.0749648i | \(-0.0238844\pi\) | |||||||
\(44\) | 363.214 | 1.24447 | ||||||||
\(45\) | 273.813 | + | 408.983i | 0.907057 | + | 1.35484i | ||||
\(46\) | −44.7471 | −0.143426 | ||||||||
\(47\) | 68.9395 | − | 119.407i | 0.213955 | − | 0.370580i | −0.738994 | − | 0.673712i | \(-0.764699\pi\) |
0.952949 | + | 0.303132i | \(0.0980322\pi\) | |||||||
\(48\) | 223.596 | + | 119.384i | 0.672360 | + | 0.358991i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −83.6808 | − | 144.939i | −0.236685 | − | 0.409951i | ||||
\(51\) | −8.14133 | − | 245.280i | −0.0223532 | − | 0.673452i | ||||
\(52\) | 163.445 | − | 283.095i | 0.435879 | − | 0.754965i | ||||
\(53\) | 411.775 | 1.06720 | 0.533600 | − | 0.845737i | \(-0.320839\pi\) | ||||
0.533600 | + | 0.845737i | \(0.320839\pi\) | |||||||
\(54\) | −103.238 | − | 46.6069i | −0.260166 | − | 0.117452i | ||||
\(55\) | −901.041 | −2.20902 | ||||||||
\(56\) | −43.3708 | + | 75.1205i | −0.103494 | + | 0.179257i | ||||
\(57\) | −9.78311 | − | 294.743i | −0.0227334 | − | 0.684905i | ||||
\(58\) | −60.6663 | − | 105.077i | −0.137343 | − | 0.237885i | ||||
\(59\) | −106.152 | − | 183.861i | −0.234235 | − | 0.405707i | 0.724815 | − | 0.688944i | \(-0.241925\pi\) |
−0.959050 | + | 0.283236i | \(0.908592\pi\) | |||||||
\(60\) | −613.981 | − | 327.821i | −1.32108 | − | 0.705358i | ||||
\(61\) | 26.1785 | − | 45.3424i | 0.0549477 | − | 0.0951722i | −0.837243 | − | 0.546831i | \(-0.815834\pi\) |
0.892191 | + | 0.451659i | \(0.149167\pi\) | |||||||
\(62\) | −135.275 | −0.277095 | ||||||||
\(63\) | −83.4383 | + | 169.585i | −0.166861 | + | 0.339138i | ||||
\(64\) | −278.409 | −0.543768 | ||||||||
\(65\) | −405.464 | + | 702.285i | −0.773718 | + | 1.34012i | ||||
\(66\) | 176.047 | − | 109.584i | 0.328331 | − | 0.204377i | ||||
\(67\) | −353.386 | − | 612.082i | −0.644372 | − | 1.11609i | −0.984446 | − | 0.175687i | \(-0.943785\pi\) |
0.340074 | − | 0.940399i | \(-0.389548\pi\) | |||||||
\(68\) | 173.527 | + | 300.557i | 0.309459 | + | 0.535999i | ||||
\(69\) | 244.490 | − | 152.188i | 0.426568 | − | 0.265526i | ||||
\(70\) | 51.5112 | − | 89.2200i | 0.0879538 | − | 0.152340i | ||||
\(71\) | −78.7569 | −0.131644 | −0.0658220 | − | 0.997831i | \(-0.520967\pi\) | ||||
−0.0658220 | + | 0.997831i | \(0.520967\pi\) | |||||||
\(72\) | 333.839 | − | 22.1860i | 0.546434 | − | 0.0363145i | ||||
\(73\) | 839.292 | 1.34564 | 0.672820 | − | 0.739806i | \(-0.265083\pi\) | ||||
0.672820 | + | 0.739806i | \(0.265083\pi\) | |||||||
\(74\) | −133.814 | + | 231.772i | −0.210210 | + | 0.364094i | ||||
\(75\) | 950.166 | + | 507.319i | 1.46288 | + | 0.781068i | ||||
\(76\) | 208.520 | + | 361.168i | 0.314722 | + | 0.545115i | ||||
\(77\) | −173.003 | − | 299.649i | −0.256045 | − | 0.443483i | ||||
\(78\) | −6.19118 | − | 186.526i | −0.00898734 | − | 0.270768i | ||||
\(79\) | −507.663 | + | 879.298i | −0.722994 | + | 1.25226i | 0.236800 | + | 0.971558i | \(0.423901\pi\) |
−0.959794 | + | 0.280705i | \(0.909432\pi\) | |||||||
\(80\) | 889.214 | 1.24271 | ||||||||
\(81\) | 722.589 | − | 96.4687i | 0.991206 | − | 0.132330i | ||||
\(82\) | 238.523 | 0.321226 | ||||||||
\(83\) | −543.305 | + | 941.032i | −0.718500 | + | 1.24448i | 0.243094 | + | 0.970003i | \(0.421837\pi\) |
−0.961594 | + | 0.274475i | \(0.911496\pi\) | |||||||
\(84\) | −8.86651 | − | 267.128i | −0.0115169 | − | 0.346976i | ||||
\(85\) | −430.476 | − | 745.606i | −0.549314 | − | 0.951439i | ||||
\(86\) | 128.287 | + | 222.199i | 0.160855 | + | 0.278608i | ||||
\(87\) | 688.845 | + | 367.792i | 0.848873 | + | 0.453235i | ||||
\(88\) | −306.256 | + | 530.450i | −0.370988 | + | 0.642570i | ||||
\(89\) | −762.726 | −0.908414 | −0.454207 | − | 0.890896i | \(-0.650077\pi\) | ||||
−0.454207 | + | 0.890896i | \(0.650077\pi\) | |||||||
\(90\) | −396.497 | + | 26.3501i | −0.464383 | + | 0.0308617i | ||||
\(91\) | −311.402 | −0.358723 | ||||||||
\(92\) | −203.629 | + | 352.696i | −0.230759 | + | 0.399686i | ||||
\(93\) | 739.116 | − | 460.078i | 0.824116 | − | 0.512988i | ||||
\(94\) | 55.6598 | + | 96.4056i | 0.0610731 | + | 0.105782i | ||||
\(95\) | −517.285 | − | 895.964i | −0.558656 | − | 0.967621i | ||||
\(96\) | −611.046 | + | 380.359i | −0.649632 | + | 0.404377i | ||||
\(97\) | 671.315 | − | 1162.75i | 0.702698 | − | 1.21711i | −0.264818 | − | 0.964298i | \(-0.585312\pi\) |
0.967516 | − | 0.252810i | \(-0.0813548\pi\) | |||||||
\(98\) | 39.5612 | 0.0407784 | ||||||||
\(99\) | −589.185 | + | 1197.50i | −0.598135 | + | 1.21568i | ||||
\(100\) | −1523.21 | −1.52321 | ||||||||
\(101\) | −353.491 | + | 612.265i | −0.348254 | + | 0.603194i | −0.985939 | − | 0.167103i | \(-0.946559\pi\) |
0.637685 | + | 0.770297i | \(0.279892\pi\) | |||||||
\(102\) | 174.787 | + | 93.3235i | 0.169672 | + | 0.0905922i | ||||
\(103\) | −257.488 | − | 445.983i | −0.246321 | − | 0.426640i | 0.716181 | − | 0.697914i | \(-0.245888\pi\) |
−0.962502 | + | 0.271274i | \(0.912555\pi\) | |||||||
\(104\) | 275.627 | + | 477.401i | 0.259880 | + | 0.450125i | ||||
\(105\) | 21.9955 | + | 662.675i | 0.0204433 | + | 0.615909i | ||||
\(106\) | −166.228 | + | 287.915i | −0.152316 | + | 0.263818i | ||||
\(107\) | 1186.50 | 1.07199 | 0.535997 | − | 0.844220i | \(-0.319936\pi\) | ||||
0.535997 | + | 0.844220i | \(0.319936\pi\) | |||||||
\(108\) | −837.157 | + | 601.629i | −0.745884 | + | 0.536035i | ||||
\(109\) | 1909.52 | 1.67797 | 0.838987 | − | 0.544151i | \(-0.183148\pi\) | ||||
0.838987 | + | 0.544151i | \(0.183148\pi\) | |||||||
\(110\) | 363.737 | − | 630.012i | 0.315282 | − | 0.546084i | ||||
\(111\) | −57.1392 | − | 1721.47i | −0.0488596 | − | 1.47203i | ||||
\(112\) | 170.732 | + | 295.716i | 0.144041 | + | 0.249487i | ||||
\(113\) | 470.970 | + | 815.743i | 0.392080 | + | 0.679103i | 0.992724 | − | 0.120414i | \(-0.0384222\pi\) |
−0.600643 | + | 0.799517i | \(0.705089\pi\) | |||||||
\(114\) | 210.035 | + | 112.143i | 0.172557 | + | 0.0921329i | ||||
\(115\) | 505.151 | − | 874.948i | 0.409614 | − | 0.709472i | ||||
\(116\) | −1104.29 | −0.883884 | ||||||||
\(117\) | 668.215 | + | 998.088i | 0.528005 | + | 0.788660i | ||||
\(118\) | 171.409 | 0.133724 | ||||||||
\(119\) | 165.305 | − | 286.317i | 0.127340 | − | 0.220560i | ||||
\(120\) | 996.459 | − | 620.267i | 0.758032 | − | 0.471853i | ||||
\(121\) | −556.128 | − | 963.242i | −0.417827 | − | 0.723698i | ||||
\(122\) | 21.1358 | + | 36.6082i | 0.0156848 | + | 0.0271668i | ||||
\(123\) | −1303.25 | + | 811.235i | −0.955366 | + | 0.594688i | ||||
\(124\) | −615.589 | + | 1066.23i | −0.445818 | + | 0.772180i | ||||
\(125\) | 1500.09 | 1.07338 | ||||||||
\(126\) | −84.8917 | − | 126.799i | −0.0600218 | − | 0.0896523i | ||||
\(127\) | −1584.85 | −1.10734 | −0.553672 | − | 0.832735i | \(-0.686774\pi\) | ||||
−0.553672 | + | 0.832735i | \(0.686774\pi\) | |||||||
\(128\) | 666.459 | − | 1154.34i | 0.460213 | − | 0.797112i | ||||
\(129\) | −1456.65 | − | 777.743i | −0.994192 | − | 0.530826i | ||||
\(130\) | −327.361 | − | 567.005i | −0.220857 | − | 0.382536i | ||||
\(131\) | −1086.93 | − | 1882.61i | −0.724926 | − | 1.25561i | −0.959005 | − | 0.283391i | \(-0.908541\pi\) |
0.234079 | − | 0.972218i | \(-0.424793\pi\) | |||||||
\(132\) | −62.6094 | − | 1886.28i | −0.0412837 | − | 1.24378i | ||||
\(133\) | 198.641 | − | 344.056i | 0.129506 | − | 0.224311i | ||||
\(134\) | 570.628 | 0.367871 | ||||||||
\(135\) | 2076.77 | − | 1492.49i | 1.32400 | − | 0.951503i | ||||
\(136\) | −585.259 | −0.369012 | ||||||||
\(137\) | −1047.25 | + | 1813.90i | −0.653087 | + | 1.13118i | 0.329283 | + | 0.944231i | \(0.393193\pi\) |
−0.982370 | + | 0.186948i | \(0.940140\pi\) | |||||||
\(138\) | 7.71333 | + | 232.385i | 0.00475799 | + | 0.143347i | ||||
\(139\) | 656.661 | + | 1137.37i | 0.400700 | + | 0.694033i | 0.993811 | − | 0.111088i | \(-0.0354337\pi\) |
−0.593111 | + | 0.805121i | \(0.702100\pi\) | |||||||
\(140\) | −468.820 | − | 812.020i | −0.283018 | − | 0.490201i | ||||
\(141\) | −631.998 | − | 337.440i | −0.377474 | − | 0.201543i | ||||
\(142\) | 31.7930 | − | 55.0671i | 0.0187888 | − | 0.0325432i | ||||
\(143\) | −2198.91 | −1.28589 | ||||||||
\(144\) | 581.452 | − | 1181.78i | 0.336488 | − | 0.683899i | ||||
\(145\) | 2739.45 | 1.56896 | ||||||||
\(146\) | −338.810 | + | 586.837i | −0.192056 | + | 0.332650i | ||||
\(147\) | −216.155 | + | 134.550i | −0.121280 | + | 0.0754934i | ||||
\(148\) | 1217.88 | + | 2109.43i | 0.676414 | + | 1.17158i | ||||
\(149\) | 743.727 | + | 1288.17i | 0.408916 | + | 0.708264i | 0.994769 | − | 0.102154i | \(-0.0325735\pi\) |
−0.585852 | + | 0.810418i | \(0.699240\pi\) | |||||||
\(150\) | −738.288 | + | 459.563i | −0.401873 | + | 0.250154i | ||||
\(151\) | 1101.85 | − | 1908.45i | 0.593821 | − | 1.02853i | −0.399891 | − | 0.916562i | \(-0.630952\pi\) |
0.993712 | − | 0.111965i | \(-0.0357145\pi\) | |||||||
\(152\) | −703.282 | −0.375288 | ||||||||
\(153\) | −1272.41 | + | 84.5607i | −0.672339 | + | 0.0446819i | ||||
\(154\) | 279.355 | 0.146176 | ||||||||
\(155\) | 1527.12 | − | 2645.04i | 0.791361 | − | 1.37068i | ||||
\(156\) | −1498.37 | − | 800.018i | −0.769009 | − | 0.410594i | ||||
\(157\) | 1722.67 | + | 2983.76i | 0.875696 | + | 1.51675i | 0.856020 | + | 0.516943i | \(0.172930\pi\) |
0.0196759 | + | 0.999806i | \(0.493737\pi\) | |||||||
\(158\) | −409.873 | − | 709.921i | −0.206378 | − | 0.357457i | ||||
\(159\) | −70.9801 | − | 2138.47i | −0.0354031 | − | 1.06661i | ||||
\(160\) | −1262.51 | + | 2186.73i | −0.623812 | + | 1.08047i | ||||
\(161\) | 387.963 | 0.189911 | ||||||||
\(162\) | −224.248 | + | 544.180i | −0.108757 | + | 0.263919i | ||||
\(163\) | −2723.83 | −1.30888 | −0.654439 | − | 0.756115i | \(-0.727095\pi\) | ||||
−0.654439 | + | 0.756115i | \(0.727095\pi\) | |||||||
\(164\) | 1085.44 | − | 1880.04i | 0.516820 | − | 0.895159i | ||||
\(165\) | 155.318 | + | 4679.37i | 0.0732817 | + | 2.20781i | ||||
\(166\) | −438.649 | − | 759.763i | −0.205095 | − | 0.355235i | ||||
\(167\) | 506.393 | + | 877.098i | 0.234646 | + | 0.406419i | 0.959170 | − | 0.282831i | \(-0.0912736\pi\) |
−0.724524 | + | 0.689250i | \(0.757940\pi\) | |||||||
\(168\) | 397.599 | + | 212.288i | 0.182592 | + | 0.0974905i | ||||
\(169\) | 109.000 | − | 188.793i | 0.0496131 | − | 0.0859323i | ||||
\(170\) | 695.108 | 0.313602 | ||||||||
\(171\) | −1529.00 | + | 101.613i | −0.683774 | + | 0.0454418i | ||||
\(172\) | 2335.16 | 1.03520 | ||||||||
\(173\) | 747.910 | − | 1295.42i | 0.328685 | − | 0.569300i | −0.653566 | − | 0.756870i | \(-0.726728\pi\) |
0.982251 | + | 0.187570i | \(0.0600611\pi\) | |||||||
\(174\) | −535.239 | + | 333.171i | −0.233197 | + | 0.145159i | ||||
\(175\) | 725.522 | + | 1256.64i | 0.313396 | + | 0.542818i | ||||
\(176\) | 1205.59 | + | 2088.15i | 0.516336 | + | 0.894319i | ||||
\(177\) | −936.548 | + | 582.974i | −0.397713 | + | 0.247565i | ||||
\(178\) | 307.902 | − | 533.301i | 0.129653 | − | 0.224565i | ||||
\(179\) | 1989.77 | 0.830851 | 0.415425 | − | 0.909627i | \(-0.363633\pi\) | ||||
0.415425 | + | 0.909627i | \(0.363633\pi\) | |||||||
\(180\) | −1596.63 | + | 3245.09i | −0.661145 | + | 1.34375i | ||||
\(181\) | −2790.78 | −1.14606 | −0.573031 | − | 0.819534i | \(-0.694232\pi\) | ||||
−0.573031 | + | 0.819534i | \(0.694232\pi\) | |||||||
\(182\) | 125.708 | − | 217.733i | 0.0511985 | − | 0.0886784i | ||||
\(183\) | −239.989 | − | 128.136i | −0.0969426 | − | 0.0517602i | ||||
\(184\) | −343.393 | − | 594.774i | −0.137583 | − | 0.238301i | ||||
\(185\) | −3021.25 | − | 5232.97i | −1.20069 | − | 2.07965i | ||||
\(186\) | 23.3181 | + | 702.520i | 0.00919228 | + | 0.276942i | ||||
\(187\) | 1167.28 | − | 2021.78i | 0.456469 | − | 0.790627i | ||||
\(188\) | 1013.16 | 0.393043 | ||||||||
\(189\) | 895.087 | + | 404.087i | 0.344487 | + | 0.155519i | ||||
\(190\) | 835.283 | 0.318936 | ||||||||
\(191\) | −2167.85 | + | 3754.82i | −0.821256 | + | 1.42246i | 0.0834912 | + | 0.996509i | \(0.473393\pi\) |
−0.904747 | + | 0.425949i | \(0.859940\pi\) | |||||||
\(192\) | 47.9911 | + | 1445.86i | 0.0180388 | + | 0.543469i | ||||
\(193\) | 1214.95 | + | 2104.36i | 0.453130 | + | 0.784844i | 0.998579 | − | 0.0533002i | \(-0.0169740\pi\) |
−0.545449 | + | 0.838144i | \(0.683641\pi\) | |||||||
\(194\) | 542.001 | + | 938.773i | 0.200584 | + | 0.347422i | ||||
\(195\) | 3717.06 | + | 1984.64i | 1.36505 | + | 0.728835i | ||||
\(196\) | 180.030 | − | 311.821i | 0.0656085 | − | 0.113637i | ||||
\(197\) | 273.113 | 0.0987742 | 0.0493871 | − | 0.998780i | \(-0.484273\pi\) | ||||
0.0493871 | + | 0.998780i | \(0.484273\pi\) | |||||||
\(198\) | −599.448 | − | 895.373i | −0.215156 | − | 0.321371i | ||||
\(199\) | 648.752 | 0.231100 | 0.115550 | − | 0.993302i | \(-0.463137\pi\) | ||||
0.115550 | + | 0.993302i | \(0.463137\pi\) | |||||||
\(200\) | 1284.35 | − | 2224.55i | 0.454085 | − | 0.786498i | ||||
\(201\) | −3117.81 | + | 1940.74i | −1.09410 | + | 0.681043i | ||||
\(202\) | −285.399 | − | 494.325i | −0.0994088 | − | 0.172181i | ||||
\(203\) | 525.984 | + | 911.030i | 0.181856 | + | 0.314984i | ||||
\(204\) | 1530.97 | − | 952.985i | 0.525438 | − | 0.327070i | ||||
\(205\) | −2692.70 | + | 4663.89i | −0.917395 | + | 1.58897i | ||||
\(206\) | 415.777 | 0.140624 | ||||||||
\(207\) | −832.502 | − | 1243.48i | −0.279531 | − | 0.417525i | ||||
\(208\) | 2170.05 | 0.723393 | ||||||||
\(209\) | 1402.67 | − | 2429.49i | 0.464232 | − | 0.804074i | ||||
\(210\) | −472.225 | − | 252.133i | −0.155174 | − | 0.0828516i | ||||
\(211\) | −121.543 | − | 210.518i | −0.0396557 | − | 0.0686857i | 0.845516 | − | 0.533950i | \(-0.179293\pi\) |
−0.885172 | + | 0.465264i | \(0.845959\pi\) | |||||||
\(212\) | 1512.89 | + | 2620.40i | 0.490122 | + | 0.848916i | ||||
\(213\) | 13.5758 | + | 409.007i | 0.00436713 | + | 0.131571i | ||||
\(214\) | −478.973 | + | 829.606i | −0.153000 | + | 0.265003i | ||||
\(215\) | −5792.92 | −1.83755 | ||||||||
\(216\) | −172.764 | − | 1729.90i | −0.0544218 | − | 0.544929i | ||||
\(217\) | 1172.84 | 0.366903 | ||||||||
\(218\) | −770.848 | + | 1335.15i | −0.239488 | + | 0.414806i | ||||
\(219\) | −144.674 | − | 4358.69i | −0.0446399 | − | 1.34490i | ||||
\(220\) | −3310.49 | − | 5733.94i | −1.01451 | − | 1.75719i | ||||
\(221\) | −1050.54 | − | 1819.59i | −0.319759 | − | 0.553840i | ||||
\(222\) | 1226.73 | + | 654.982i | 0.370867 | + | 0.198016i | ||||
\(223\) | −910.318 | + | 1576.72i | −0.273361 | + | 0.473474i | −0.969720 | − | 0.244219i | \(-0.921469\pi\) |
0.696360 | + | 0.717693i | \(0.254802\pi\) | |||||||
\(224\) | −969.621 | −0.289221 | ||||||||
\(225\) | 2470.87 | − | 5021.94i | 0.732109 | − | 1.48798i | ||||
\(226\) | −760.495 | −0.223838 | ||||||||
\(227\) | −850.099 | + | 1472.41i | −0.248560 | + | 0.430518i | −0.963126 | − | 0.269049i | \(-0.913291\pi\) |
0.714567 | + | 0.699567i | \(0.246624\pi\) | |||||||
\(228\) | 1839.70 | − | 1145.16i | 0.534375 | − | 0.332633i | ||||
\(229\) | −94.4886 | − | 163.659i | −0.0272663 | − | 0.0472266i | 0.852070 | − | 0.523427i | \(-0.175347\pi\) |
−0.879337 | + | 0.476201i | \(0.842014\pi\) | |||||||
\(230\) | 407.845 | + | 706.408i | 0.116924 | + | 0.202518i | ||||
\(231\) | −1526.34 | + | 950.105i | −0.434745 | + | 0.270616i | ||||
\(232\) | 931.116 | − | 1612.74i | 0.263495 | − | 0.456386i | ||||
\(233\) | −647.185 | −0.181968 | −0.0909840 | − | 0.995852i | \(-0.529001\pi\) | ||||
−0.0909840 | + | 0.995852i | \(0.529001\pi\) | |||||||
\(234\) | −967.617 | + | 64.3052i | −0.270321 | + | 0.0179648i | ||||
\(235\) | −2513.38 | −0.697680 | ||||||||
\(236\) | 780.024 | − | 1351.04i | 0.215149 | − | 0.372650i | ||||
\(237\) | 4653.96 | + | 2484.87i | 1.27556 | + | 0.681054i | ||||
\(238\) | 133.463 | + | 231.164i | 0.0363492 | + | 0.0629587i | ||||
\(239\) | 1760.61 | + | 3049.46i | 0.476503 | + | 0.825328i | 0.999638 | − | 0.0269226i | \(-0.00857078\pi\) |
−0.523134 | + | 0.852250i | \(0.675237\pi\) | |||||||
\(240\) | −153.279 | − | 4617.95i | −0.0412255 | − | 1.24203i | ||||
\(241\) | −162.250 | + | 281.026i | −0.0433671 | + | 0.0751140i | −0.886894 | − | 0.461973i | \(-0.847142\pi\) |
0.843527 | + | 0.537087i | \(0.180475\pi\) | |||||||
\(242\) | 898.004 | 0.238537 | ||||||||
\(243\) | −625.547 | − | 3735.99i | −0.165139 | − | 0.986270i | ||||
\(244\) | 384.727 | 0.100941 | ||||||||
\(245\) | −446.607 | + | 773.547i | −0.116460 | + | 0.201715i | ||||
\(246\) | −41.1157 | − | 1238.72i | −0.0106563 | − | 0.321049i | ||||
\(247\) | −1262.39 | − | 2186.52i | −0.325198 | − | 0.563259i | ||||
\(248\) | −1038.11 | − | 1798.05i | −0.265806 | − | 0.460389i | ||||
\(249\) | 4980.71 | + | 2659.33i | 1.26763 | + | 0.676820i | ||||
\(250\) | −605.565 | + | 1048.87i | −0.153197 | + | 0.265345i | ||||
\(251\) | 3501.08 | 0.880424 | 0.440212 | − | 0.897894i | \(-0.354903\pi\) | ||||
0.440212 | + | 0.897894i | \(0.354903\pi\) | |||||||
\(252\) | −1385.74 | + | 92.0928i | −0.346403 | + | 0.0230210i | ||||
\(253\) | 2739.53 | 0.680762 | ||||||||
\(254\) | 639.782 | − | 1108.13i | 0.158045 | − | 0.273742i | ||||
\(255\) | −3797.95 | + | 2364.11i | −0.932692 | + | 0.580574i | ||||
\(256\) | −575.557 | − | 996.893i | −0.140517 | − | 0.243382i | ||||
\(257\) | 919.514 | + | 1592.64i | 0.223182 | + | 0.386562i | 0.955772 | − | 0.294107i | \(-0.0950223\pi\) |
−0.732591 | + | 0.680669i | \(0.761689\pi\) | |||||||
\(258\) | 1131.83 | − | 704.532i | 0.273119 | − | 0.170009i | ||||
\(259\) | 1160.18 | − | 2009.49i | 0.278340 | − | 0.482099i | ||||
\(260\) | −5958.83 | −1.42135 | ||||||||
\(261\) | 1791.31 | − | 3640.77i | 0.424826 | − | 0.863441i | ||||
\(262\) | 1755.11 | 0.413859 | ||||||||
\(263\) | −55.6729 | + | 96.4283i | −0.0130530 | + | 0.0226085i | −0.872478 | − | 0.488653i | \(-0.837488\pi\) |
0.859425 | + | 0.511262i | \(0.170822\pi\) | |||||||
\(264\) | 2807.58 | + | 1499.04i | 0.654524 | + | 0.349468i | ||||
\(265\) | −3753.10 | − | 6500.55i | −0.870003 | − | 1.50689i | ||||
\(266\) | 160.377 | + | 277.781i | 0.0369674 | + | 0.0640295i | ||||
\(267\) | 131.476 | + | 3961.06i | 0.0301355 | + | 0.907914i | ||||
\(268\) | 2596.73 | − | 4497.67i | 0.591868 | − | 1.02515i | ||||
\(269\) | −2355.30 | −0.533848 | −0.266924 | − | 0.963718i | \(-0.586007\pi\) | ||||
−0.266924 | + | 0.963718i | \(0.586007\pi\) | |||||||
\(270\) | 205.191 | + | 2054.58i | 0.0462500 | + | 0.463104i | ||||
\(271\) | −3281.29 | −0.735514 | −0.367757 | − | 0.929922i | \(-0.619874\pi\) | ||||
−0.367757 | + | 0.929922i | \(0.619874\pi\) | |||||||
\(272\) | −1151.95 | + | 1995.24i | −0.256792 | + | 0.444777i | ||||
\(273\) | 53.6782 | + | 1617.20i | 0.0119002 | + | 0.358525i | ||||
\(274\) | −845.522 | − | 1464.49i | −0.186423 | − | 0.322894i | ||||
\(275\) | 5123.15 | + | 8873.55i | 1.12341 | + | 1.94580i | ||||
\(276\) | 1866.75 | + | 996.709i | 0.407121 | + | 0.217373i | ||||
\(277\) | −1110.42 | + | 1923.30i | −0.240861 | + | 0.417183i | −0.960960 | − | 0.276688i | \(-0.910763\pi\) |
0.720099 | + | 0.693871i | \(0.244096\pi\) | |||||||
\(278\) | −1060.34 | −0.228759 | ||||||||
\(279\) | −2516.73 | − | 3759.14i | −0.540045 | − | 0.806644i | ||||
\(280\) | 1581.20 | 0.337482 | ||||||||
\(281\) | 594.751 | − | 1030.14i | 0.126263 | − | 0.218694i | −0.795963 | − | 0.605345i | \(-0.793035\pi\) |
0.922226 | + | 0.386652i | \(0.126368\pi\) | |||||||
\(282\) | 491.068 | − | 305.676i | 0.103697 | − | 0.0645487i | ||||
\(283\) | −579.806 | − | 1004.25i | −0.121788 | − | 0.210942i | 0.798685 | − | 0.601749i | \(-0.205529\pi\) |
−0.920473 | + | 0.390807i | \(0.872196\pi\) | |||||||
\(284\) | −289.359 | − | 501.184i | −0.0604587 | − | 0.104718i | ||||
\(285\) | −4563.84 | + | 2840.86i | −0.948555 | + | 0.590448i | ||||
\(286\) | 887.669 | − | 1537.49i | 0.183528 | − | 0.317880i | ||||
\(287\) | −2068.02 | −0.425336 | ||||||||
\(288\) | 2080.64 | + | 3107.78i | 0.425705 | + | 0.635860i | ||||
\(289\) | −2682.32 | −0.545963 | ||||||||
\(290\) | −1105.88 | + | 1915.44i | −0.223929 | + | 0.387857i | ||||
\(291\) | −6154.23 | − | 3285.90i | −1.23975 | − | 0.661935i | ||||
\(292\) | 3083.62 | + | 5340.99i | 0.617998 | + | 1.07040i | ||||
\(293\) | −268.645 | − | 465.307i | −0.0535645 | − | 0.0927765i | 0.838000 | − | 0.545670i | \(-0.183725\pi\) |
−0.891564 | + | 0.452894i | \(0.850392\pi\) | |||||||
\(294\) | −6.81940 | − | 205.453i | −0.00135277 | − | 0.0407560i | ||||
\(295\) | −1935.04 | + | 3351.59i | −0.381906 | + | 0.661481i | ||||
\(296\) | −4107.59 | −0.806584 | ||||||||
\(297\) | 6320.50 | + | 2853.39i | 1.23486 | + | 0.557477i | ||||
\(298\) | −1200.93 | −0.233450 | ||||||||
\(299\) | 1232.78 | − | 2135.23i | 0.238439 | − | 0.412989i | ||||
\(300\) | 262.565 | + | 7910.49i | 0.0505307 | + | 1.52237i | ||||
\(301\) | −1112.26 | − | 1926.49i | −0.212988 | − | 0.368907i | ||||
\(302\) | 889.599 | + | 1540.83i | 0.169506 | + | 0.293592i | ||||
\(303\) | 3240.60 | + | 1730.24i | 0.614415 | + | 0.328052i | ||||
\(304\) | −1384.26 | + | 2397.60i | −0.261160 | + | 0.452342i | ||||
\(305\) | −954.408 | −0.179178 | ||||||||
\(306\) | 454.527 | − | 923.808i | 0.0849137 | − | 0.172584i | ||||
\(307\) | −1740.18 | −0.323510 | −0.161755 | − | 0.986831i | \(-0.551715\pi\) | ||||
−0.161755 | + | 0.986831i | \(0.551715\pi\) | |||||||
\(308\) | 1271.25 | − | 2201.87i | 0.235182 | − | 0.407348i | ||||
\(309\) | −2271.73 | + | 1414.09i | −0.418234 | + | 0.260339i | ||||
\(310\) | 1232.95 | + | 2135.53i | 0.225893 | + | 0.391259i | ||||
\(311\) | 1958.95 | + | 3393.00i | 0.357177 | + | 0.618648i | 0.987488 | − | 0.157694i | \(-0.0504061\pi\) |
−0.630311 | + | 0.776343i | \(0.717073\pi\) | |||||||
\(312\) | 2431.77 | − | 1513.71i | 0.441256 | − | 0.274669i | ||||
\(313\) | 4742.77 | − | 8214.72i | 0.856477 | − | 1.48346i | −0.0187903 | − | 0.999823i | \(-0.505981\pi\) |
0.875268 | − | 0.483639i | \(-0.160685\pi\) | |||||||
\(314\) | −2781.67 | −0.499933 | ||||||||
\(315\) | 3437.67 | − | 228.459i | 0.614892 | − | 0.0408641i | ||||
\(316\) | −7460.77 | −1.32817 | ||||||||
\(317\) | 2837.18 | − | 4914.15i | 0.502688 | − | 0.870681i | −0.497307 | − | 0.867575i | \(-0.665678\pi\) |
0.999995 | − | 0.00310684i | \(-0.000988941\pi\) | |||||||
\(318\) | 1523.88 | + | 813.639i | 0.268726 | + | 0.143480i | ||||
\(319\) | 3714.14 | + | 6433.09i | 0.651888 | + | 1.12910i | ||||
\(320\) | 2537.54 | + | 4395.15i | 0.443291 | + | 0.767802i | ||||
\(321\) | −204.524 | − | 6161.84i | −0.0355621 | − | 1.07140i | ||||
\(322\) | −156.615 | + | 271.265i | −0.0271050 | + | 0.0469472i | ||||
\(323\) | 2680.52 | 0.461759 | ||||||||
\(324\) | 3268.74 | + | 4243.90i | 0.560484 | + | 0.727691i | ||||
\(325\) | 9221.58 | 1.57391 | ||||||||
\(326\) | 1099.57 | − | 1904.52i | 0.186809 | − | 0.323563i | ||||
\(327\) | −329.156 | − | 9916.72i | −0.0556648 | − | 1.67705i | ||||
\(328\) | 1830.45 | + | 3170.43i | 0.308139 | + | 0.533712i | ||||
\(329\) | −482.577 | − | 835.847i | −0.0808672 | − | 0.140066i | ||||
\(330\) | −3334.53 | − | 1780.40i | −0.556243 | − | 0.296993i | ||||
\(331\) | −2366.29 | + | 4098.54i | −0.392940 | + | 0.680593i | −0.992836 | − | 0.119486i | \(-0.961875\pi\) |
0.599896 | + | 0.800078i | \(0.295209\pi\) | |||||||
\(332\) | −7984.57 | −1.31991 | ||||||||
\(333\) | −8930.26 | + | 593.481i | −1.46960 | + | 0.0976654i | ||||
\(334\) | −817.695 | −0.133959 | ||||||||
\(335\) | −6441.83 | + | 11157.6i | −1.05061 | + | 1.81971i | ||||
\(336\) | 1506.31 | − | 937.635i | 0.244571 | − | 0.152239i | ||||
\(337\) | 2021.65 | + | 3501.59i | 0.326783 | + | 0.566006i | 0.981872 | − | 0.189547i | \(-0.0607019\pi\) |
−0.655088 | + | 0.755552i | \(0.727369\pi\) | |||||||
\(338\) | 88.0034 | + | 152.426i | 0.0141620 | + | 0.0245293i | ||||
\(339\) | 4155.21 | − | 2586.50i | 0.665723 | − | 0.414393i | ||||
\(340\) | 3163.20 | − | 5478.82i | 0.504555 | − | 0.873915i | ||||
\(341\) | 8281.84 | 1.31521 | ||||||||
\(342\) | 546.187 | − | 1110.10i | 0.0863579 | − | 0.175519i | ||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −1968.96 | + | 3410.34i | −0.308603 | + | 0.534516i | ||||
\(345\) | −4630.94 | − | 2472.58i | −0.722670 | − | 0.385853i | ||||
\(346\) | 603.841 | + | 1045.88i | 0.0938229 | + | 0.162506i | ||||
\(347\) | 1946.93 | + | 3372.19i | 0.301201 | + | 0.521696i | 0.976408 | − | 0.215933i | \(-0.0692791\pi\) |
−0.675207 | + | 0.737628i | \(0.735946\pi\) | |||||||
\(348\) | 190.353 | + | 5734.89i | 0.0293218 | + | 0.883397i | ||||
\(349\) | 472.304 | − | 818.054i | 0.0724408 | − | 0.125471i | −0.827530 | − | 0.561422i | \(-0.810254\pi\) |
0.899971 | + | 0.435951i | \(0.143588\pi\) | |||||||
\(350\) | −1171.53 | −0.178917 | ||||||||
\(351\) | 5068.18 | − | 3642.28i | 0.770710 | − | 0.553877i | ||||
\(352\) | −6846.82 | −1.03675 | ||||||||
\(353\) | 4699.26 | − | 8139.35i | 0.708545 | − | 1.22724i | −0.256852 | − | 0.966451i | \(-0.582685\pi\) |
0.965397 | − | 0.260785i | \(-0.0839813\pi\) | |||||||
\(354\) | −29.5468 | − | 890.177i | −0.00443614 | − | 0.133651i | ||||
\(355\) | 717.825 | + | 1243.31i | 0.107319 | + | 0.185882i | ||||
\(356\) | −2802.31 | − | 4853.75i | −0.417198 | − | 0.722607i | ||||
\(357\) | −1515.42 | − | 809.125i | −0.224663 | − | 0.119954i | ||||
\(358\) | −803.241 | + | 1391.25i | −0.118583 | + | 0.205391i | ||||
\(359\) | 6522.25 | 0.958861 | 0.479430 | − | 0.877580i | \(-0.340843\pi\) | ||||
0.479430 | + | 0.877580i | \(0.340843\pi\) | |||||||
\(360\) | −3392.99 | − | 5067.99i | −0.496740 | − | 0.741962i | ||||
\(361\) | −3637.93 | −0.530388 | ||||||||
\(362\) | 1126.60 | − | 1951.33i | 0.163571 | − | 0.283313i | ||||
\(363\) | −4906.54 | + | 3054.18i | −0.709439 | + | 0.441605i | ||||
\(364\) | −1144.11 | − | 1981.66i | −0.164747 | − | 0.285350i | ||||
\(365\) | −7649.67 | − | 13249.6i | −1.09699 | − | 1.90005i | ||||
\(366\) | 186.474 | − | 116.075i | 0.0266315 | − | 0.0165774i | ||||
\(367\) | −2368.17 | + | 4101.80i | −0.336833 | + | 0.583412i | −0.983835 | − | 0.179076i | \(-0.942689\pi\) |
0.647002 | + | 0.762488i | \(0.276022\pi\) | |||||||
\(368\) | −2703.57 | −0.382972 | ||||||||
\(369\) | 4437.63 | + | 6628.32i | 0.626053 | + | 0.935112i | ||||
\(370\) | 4878.55 | 0.685470 | ||||||||
\(371\) | 1441.21 | − | 2496.25i | 0.201682 | − | 0.349323i | ||||
\(372\) | 5643.36 | + | 3013.14i | 0.786545 | + | 0.419957i | ||||
\(373\) | −2863.01 | − | 4958.87i | −0.397429 | − | 0.688366i | 0.595979 | − | 0.803000i | \(-0.296764\pi\) |
−0.993408 | + | 0.114633i | \(0.963431\pi\) | |||||||
\(374\) | 942.425 | + | 1632.33i | 0.130299 | + | 0.225684i | ||||
\(375\) | −258.579 | − | 7790.40i | −0.0356079 | − | 1.07279i | ||||
\(376\) | −854.275 | + | 1479.65i | −0.117170 | + | 0.202944i | ||||
\(377\) | 6685.39 | 0.913303 | ||||||||
\(378\) | −643.873 | + | 462.725i | −0.0876118 | + | 0.0629629i | ||||
\(379\) | −2131.56 | −0.288894 | −0.144447 | − | 0.989513i | \(-0.546140\pi\) | ||||
−0.144447 | + | 0.989513i | \(0.546140\pi\) | |||||||
\(380\) | 3801.09 | − | 6583.68i | 0.513136 | − | 0.888778i | ||||
\(381\) | 273.190 | + | 8230.59i | 0.0367348 | + | 1.10673i | ||||
\(382\) | −1750.26 | − | 3031.54i | −0.234427 | − | 0.406039i | ||||
\(383\) | −5095.30 | − | 8825.32i | −0.679785 | − | 1.17742i | −0.975045 | − | 0.222005i | \(-0.928740\pi\) |
0.295260 | − | 0.955417i | \(-0.404594\pi\) | |||||||
\(384\) | −6109.71 | − | 3262.14i | −0.811940 | − | 0.433516i | ||||
\(385\) | −3153.64 | + | 5462.27i | −0.417466 | + | 0.723073i | ||||
\(386\) | −1961.83 | −0.258691 | ||||||||
\(387\) | −3787.96 | + | 7698.87i | −0.497552 | + | 1.01125i | ||||
\(388\) | 9865.85 | 1.29088 | ||||||||
\(389\) | −2374.73 | + | 4113.15i | −0.309521 | + | 0.536106i | −0.978258 | − | 0.207393i | \(-0.933502\pi\) |
0.668737 | + | 0.743499i | \(0.266835\pi\) | |||||||
\(390\) | −2888.19 | + | 1797.82i | −0.374998 | + | 0.233426i | ||||
\(391\) | 1308.82 | + | 2266.95i | 0.169284 | + | 0.293208i | ||||
\(392\) | 303.596 | + | 525.843i | 0.0391171 | + | 0.0677528i | ||||
\(393\) | −9589.60 | + | 5969.25i | −1.23087 | + | 0.766180i | ||||
\(394\) | −110.252 | + | 190.962i | −0.0140975 | + | 0.0244176i | ||||
\(395\) | 18508.3 | 2.35760 | ||||||||
\(396\) | −9785.19 | + | 650.298i | −1.24173 | + | 0.0825219i | ||||
\(397\) | −4178.89 | −0.528294 | −0.264147 | − | 0.964482i | \(-0.585090\pi\) | ||||
−0.264147 | + | 0.964482i | \(0.585090\pi\) | |||||||
\(398\) | −261.892 | + | 453.611i | −0.0329836 | + | 0.0571293i | ||||
\(399\) | −1821.02 | − | 972.292i | −0.228484 | − | 0.121994i | ||||
\(400\) | −5055.90 | − | 8757.08i | −0.631988 | − | 1.09464i | ||||
\(401\) | −1769.54 | − | 3064.94i | −0.220366 | − | 0.381685i | 0.734553 | − | 0.678551i | \(-0.237392\pi\) |
−0.954919 | + | 0.296866i | \(0.904058\pi\) | |||||||
\(402\) | −98.3625 | − | 2963.44i | −0.0122037 | − | 0.367668i | ||||
\(403\) | 3726.79 | − | 6455.00i | 0.460657 | − | 0.797882i | ||||
\(404\) | −5195.01 | −0.639756 | ||||||||
\(405\) | −8108.91 | − | 10528.0i | −0.994901 | − | 1.29171i | ||||
\(406\) | −849.329 | −0.103821 | ||||||||
\(407\) | 8192.41 | − | 14189.7i | 0.997747 | − | 1.72815i | ||||
\(408\) | 100.885 | + | 3039.42i | 0.0122415 | + | 0.368809i | ||||
\(409\) | 2984.72 | + | 5169.68i | 0.360843 | + | 0.624998i | 0.988100 | − | 0.153814i | \(-0.0491557\pi\) |
−0.627257 | + | 0.778812i | \(0.715822\pi\) | |||||||
\(410\) | −2174.01 | − | 3765.49i | −0.261870 | − | 0.453571i | ||||
\(411\) | 9600.61 | + | 5126.02i | 1.15222 | + | 0.615202i | ||||
\(412\) | 1892.06 | − | 3277.15i | 0.226250 | − | 0.391877i | ||||
\(413\) | −1486.13 | −0.177065 | ||||||||
\(414\) | 1205.51 | − | 80.1152i | 0.143111 | − | 0.00951074i | ||||
\(415\) | 19807.7 | 2.34294 | ||||||||
\(416\) | −3081.04 | + | 5336.51i | −0.363126 | + | 0.628952i | ||||
\(417\) | 5793.51 | − | 3606.29i | 0.680358 | − | 0.423503i | ||||
\(418\) | 1132.47 | + | 1961.50i | 0.132515 | + | 0.229522i | ||||
\(419\) | −5774.52 | − | 10001.8i | −0.673279 | − | 1.16615i | −0.976969 | − | 0.213382i | \(-0.931552\pi\) |
0.303690 | − | 0.952771i | \(-0.401781\pi\) | |||||||
\(420\) | −4136.24 | + | 2574.69i | −0.480543 | + | 0.299124i | ||||
\(421\) | −1347.49 | + | 2333.92i | −0.155992 | + | 0.270187i | −0.933420 | − | 0.358786i | \(-0.883191\pi\) |
0.777428 | + | 0.628972i | \(0.216524\pi\) | |||||||
\(422\) | 196.260 | 0.0226394 | ||||||||
\(423\) | −1643.48 | + | 3340.32i | −0.188910 | + | 0.383952i | ||||
\(424\) | −5102.57 | −0.584441 | ||||||||
\(425\) | −4895.21 | + | 8478.75i | −0.558712 | + | 0.967717i | ||||
\(426\) | −291.460 | − | 155.618i | −0.0331486 | − | 0.0176989i | ||||
\(427\) | −183.249 | − | 317.397i | −0.0207683 | − | 0.0359717i | ||||
\(428\) | 4359.29 | + | 7550.51i | 0.492323 | + | 0.852729i | ||||
\(429\) | 379.039 | + | 11419.6i | 0.0426578 | + | 1.28518i | ||||
\(430\) | 2338.52 | − | 4050.44i | 0.262264 | − | 0.454254i | ||||
\(431\) | 2267.88 | 0.253457 | 0.126729 | − | 0.991937i | \(-0.459552\pi\) | ||||
0.126729 | + | 0.991937i | \(0.459552\pi\) | |||||||
\(432\) | −6237.54 | − | 2815.94i | −0.694685 | − | 0.313616i | ||||
\(433\) | 11979.8 | 1.32958 | 0.664792 | − | 0.747028i | \(-0.268520\pi\) | ||||
0.664792 | + | 0.747028i | \(0.268520\pi\) | |||||||
\(434\) | −473.461 | + | 820.058i | −0.0523660 | + | 0.0907006i | ||||
\(435\) | −472.216 | − | 14226.8i | −0.0520483 | − | 1.56810i | ||||
\(436\) | 7015.74 | + | 12151.6i | 0.770626 | + | 1.33476i | ||||
\(437\) | 1572.76 | + | 2724.10i | 0.172163 | + | 0.298195i | ||||
\(438\) | 3106.02 | + | 1658.38i | 0.338838 | + | 0.180915i | ||||
\(439\) | −5450.29 | + | 9440.17i | −0.592547 | + | 1.02632i | 0.401341 | + | 0.915928i | \(0.368544\pi\) |
−0.993888 | + | 0.110392i | \(0.964789\pi\) | |||||||
\(440\) | 11165.4 | 1.20975 | ||||||||
\(441\) | 736.020 | + | 1099.37i | 0.0794752 | + | 0.118709i | ||||
\(442\) | 1696.35 | 0.182550 | ||||||||
\(443\) | 184.244 | − | 319.121i | 0.0197601 | − | 0.0342255i | −0.855976 | − | 0.517015i | \(-0.827043\pi\) |
0.875736 | + | 0.482790i | \(0.160376\pi\) | |||||||
\(444\) | 10745.0 | − | 6688.44i | 1.14850 | − | 0.714908i | ||||
\(445\) | 6951.82 | + | 12040.9i | 0.740557 | + | 1.28268i | ||||
\(446\) | −734.965 | − | 1273.00i | −0.0780305 | − | 0.135153i | ||||
\(447\) | 6561.66 | − | 4084.44i | 0.694309 | − | 0.432187i | ||||
\(448\) | −974.432 | + | 1687.77i | −0.102763 | + | 0.177990i | ||||
\(449\) | −10077.9 | −1.05925 | −0.529625 | − | 0.848232i | \(-0.677667\pi\) | ||||
−0.529625 | + | 0.848232i | \(0.677667\pi\) | |||||||
\(450\) | 2513.91 | + | 3754.93i | 0.263348 | + | 0.393353i | ||||
\(451\) | −14603.0 | −1.52467 | ||||||||
\(452\) | −3460.76 | + | 5994.20i | −0.360133 | + | 0.623769i | ||||
\(453\) | −10101.1 | − | 5393.23i | −1.04766 | − | 0.559374i | ||||
\(454\) | −686.346 | − | 1188.79i | −0.0709511 | − | 0.122891i | ||||
\(455\) | 2838.25 | + | 4916.00i | 0.292438 | + | 0.506517i | ||||
\(456\) | 121.229 | + | 3652.35i | 0.0124497 | + | 0.375081i | ||||
\(457\) | 1092.37 | − | 1892.03i | 0.111813 | − | 0.193666i | −0.804688 | − | 0.593698i | \(-0.797667\pi\) |
0.916501 | + | 0.400031i | \(0.131001\pi\) | |||||||
\(458\) | 152.575 | 0.0155663 | ||||||||
\(459\) | 658.480 | + | 6593.40i | 0.0669613 | + | 0.670487i | ||||
\(460\) | 7423.86 | 0.752476 | ||||||||
\(461\) | −8301.22 | + | 14378.1i | −0.838669 | + | 1.45262i | 0.0523384 | + | 0.998629i | \(0.483333\pi\) |
−0.891008 | + | 0.453988i | \(0.850001\pi\) | |||||||
\(462\) | −48.1541 | − | 1450.77i | −0.00484920 | − | 0.146095i | ||||
\(463\) | 1918.36 | + | 3322.69i | 0.192557 | + | 0.333518i | 0.946097 | − | 0.323884i | \(-0.104989\pi\) |
−0.753540 | + | 0.657402i | \(0.771655\pi\) | |||||||
\(464\) | −3665.39 | − | 6348.65i | −0.366728 | − | 0.635191i | ||||
\(465\) | −13999.7 | − | 7474.82i | −1.39618 | − | 0.745455i | ||||
\(466\) | 261.260 | − | 452.515i | 0.0259713 | − | 0.0449836i | ||||
\(467\) | 9751.89 | 0.966304 | 0.483152 | − | 0.875537i | \(-0.339492\pi\) | ||||
0.483152 | + | 0.875537i | \(0.339492\pi\) | |||||||
\(468\) | −3896.44 | + | 7919.36i | −0.384857 | + | 0.782207i | ||||
\(469\) | −4947.40 | −0.487100 | ||||||||
\(470\) | 1014.62 | − | 1757.37i | 0.0995761 | − | 0.172471i | ||||
\(471\) | 15198.6 | − | 9460.67i | 1.48686 | − | 0.925530i | ||||
\(472\) | 1315.41 | + | 2278.35i | 0.128276 | + | 0.222181i | ||||
\(473\) | −7854.03 | − | 13603.6i | −0.763485 | − | 1.32240i | ||||
\(474\) | −3616.17 | + | 2250.96i | −0.350414 | + | 0.218123i | ||||
\(475\) | −5882.37 | + | 10188.6i | −0.568214 | + | 0.984176i | ||||
\(476\) | 2429.38 | 0.233929 | ||||||||
\(477\) | −11093.4 | + | 737.241i | −1.06485 | + | 0.0707671i | ||||
\(478\) | −2842.93 | −0.272035 | ||||||||
\(479\) | −3519.95 | + | 6096.73i | −0.335763 | + | 0.581558i | −0.983631 | − | 0.180194i | \(-0.942327\pi\) |
0.647868 | + | 0.761752i | \(0.275661\pi\) | |||||||
\(480\) | 11573.9 | + | 6179.63i | 1.10057 | + | 0.587626i | ||||
\(481\) | −7373.10 | − | 12770.6i | −0.698928 | − | 1.21058i | ||||
\(482\) | −130.996 | − | 226.892i | −0.0123791 | − | 0.0214412i | ||||
\(483\) | −66.8754 | − | 2014.80i | −0.00630008 | − | 0.189807i | ||||
\(484\) | 4086.51 | − | 7078.05i | 0.383782 | − | 0.664730i | ||||
\(485\) | −24474.6 | −2.29141 | ||||||||
\(486\) | 2864.74 | + | 1070.78i | 0.267381 | + | 0.0999415i | ||||
\(487\) | −8005.18 | −0.744865 | −0.372433 | − | 0.928059i | \(-0.621476\pi\) | ||||
−0.372433 | + | 0.928059i | \(0.621476\pi\) | |||||||
\(488\) | −324.395 | + | 561.868i | −0.0300915 | + | 0.0521200i | ||||
\(489\) | 469.523 | + | 14145.7i | 0.0434204 | + | 1.30816i | ||||
\(490\) | −360.578 | − | 624.540i | −0.0332434 | − | 0.0575793i | ||||
\(491\) | 3946.98 | + | 6836.37i | 0.362779 | + | 0.628352i | 0.988417 | − | 0.151761i | \(-0.0484945\pi\) |
−0.625638 | + | 0.780114i | \(0.715161\pi\) | |||||||
\(492\) | −9950.68 | − | 5312.93i | −0.911811 | − | 0.486840i | ||||
\(493\) | −3548.89 | + | 6146.86i | −0.324207 | + | 0.561543i | ||||
\(494\) | 2038.43 | 0.185655 | ||||||||
\(495\) | 24274.6 | − | 1613.22i | 2.20416 | − | 0.146483i | ||||
\(496\) | −8173.14 | −0.739889 | ||||||||
\(497\) | −275.649 | + | 477.438i | −0.0248784 | + | 0.0430906i | ||||
\(498\) | −3870.06 | + | 2409.00i | −0.348236 | + | 0.216767i | ||||
\(499\) | −1370.23 | − | 2373.31i | −0.122926 | − | 0.212914i | 0.797994 | − | 0.602665i | \(-0.205894\pi\) |
−0.920920 | + | 0.389751i | \(0.872561\pi\) | |||||||
\(500\) | 5511.44 | + | 9546.09i | 0.492958 | + | 0.853828i | ||||
\(501\) | 4467.74 | − | 2781.04i | 0.398411 | − | 0.247999i | ||||
\(502\) | −1413.34 | + | 2447.97i | −0.125658 | + | 0.217646i | ||||
\(503\) | 5275.06 | 0.467601 | 0.233801 | − | 0.972285i | \(-0.424884\pi\) | ||||
0.233801 | + | 0.972285i | \(0.424884\pi\) | |||||||
\(504\) | 1033.94 | − | 2101.44i | 0.0913796 | − | 0.185725i | ||||
\(505\) | 12887.5 | 1.13562 | ||||||||
\(506\) | −1105.91 | + | 1915.49i | −0.0971615 | + | 0.168289i | ||||
\(507\) | −999.248 | − | 533.525i | −0.0875309 | − | 0.0467351i | ||||
\(508\) | −5822.86 | − | 10085.5i | −0.508558 | − | 0.880849i | ||||
\(509\) | 7851.04 | + | 13598.4i | 0.683676 | + | 1.18416i | 0.973851 | + | 0.227188i | \(0.0729531\pi\) |
−0.290175 | + | 0.956974i | \(0.593714\pi\) | |||||||
\(510\) | −119.820 | − | 3609.90i | −0.0104034 | − | 0.313429i | ||||
\(511\) | 2937.52 | − | 5087.94i | 0.254302 | − | 0.440464i | ||||
\(512\) | 11592.7 | 1.00065 | ||||||||
\(513\) | 791.269 | + | 7923.02i | 0.0681002 | + | 0.681890i | ||||
\(514\) | −1484.78 | −0.127414 | ||||||||
\(515\) | −4693.72 | + | 8129.76i | −0.401612 | + | 0.695612i | ||||
\(516\) | −402.525 | − | 12127.1i | −0.0343414 | − | 1.03463i | ||||
\(517\) | −3407.63 | − | 5902.19i | −0.289879 | − | 0.502085i | ||||
\(518\) | 936.697 | + | 1622.41i | 0.0794519 | + | 0.137615i | ||||
\(519\) | −6856.41 | − | 3660.82i | −0.579890 | − | 0.309619i | ||||
\(520\) | 5024.38 | − | 8702.48i | 0.423718 | − | 0.733902i | ||||
\(521\) | 17171.3 | 1.44393 | 0.721966 | − | 0.691928i | \(-0.243238\pi\) | ||||
0.721966 | + | 0.691928i | \(0.243238\pi\) | |||||||
\(522\) | 1822.52 | + | 2722.22i | 0.152815 | + | 0.228254i | ||||
\(523\) | −8658.40 | −0.723911 | −0.361955 | − | 0.932195i | \(-0.617891\pi\) | ||||
−0.361955 | + | 0.932195i | \(0.617891\pi\) | |||||||
\(524\) | 7986.91 | − | 13833.7i | 0.665858 | − | 1.15330i | ||||
\(525\) | 6401.04 | − | 3984.46i | 0.532122 | − | 0.331231i | ||||
\(526\) | −44.9487 | − | 77.8535i | −0.00372597 | − | 0.00645356i | ||||
\(527\) | 3956.68 | + | 6853.18i | 0.327051 | + | 0.566469i | ||||
\(528\) | 10636.6 | − | 6620.95i | 0.876698 | − | 0.545719i | ||||
\(529\) | 4547.63 | − | 7876.73i | 0.373768 | − | 0.647385i | ||||
\(530\) | 6060.29 | 0.496683 | ||||||||
\(531\) | 3188.99 | + | 4763.28i | 0.260622 | + | 0.389282i | ||||
\(532\) | 2919.28 | 0.237908 | ||||||||
\(533\) | −6571.28 | + | 11381.8i | −0.534022 | + | 0.924954i | ||||
\(534\) | −2822.67 | − | 1507.10i | −0.228743 | − | 0.122132i | ||||
\(535\) | −10814.3 | − | 18730.9i | −0.873911 | − | 1.51366i | ||||
\(536\) | 4379.04 | + | 7584.72i | 0.352884 | + | 0.611212i | ||||
\(537\) | −342.988 | − | 10333.4i | −0.0275624 | − | 0.830393i | ||||
\(538\) | 950.801 | − | 1646.84i | 0.0761932 | − | 0.131970i | ||||
\(539\) | −2422.04 | −0.193552 | ||||||||
\(540\) | 17127.9 | + | 7732.41i | 1.36494 | + | 0.616204i | ||||
\(541\) | 11733.7 | 0.932480 | 0.466240 | − | 0.884658i | \(-0.345608\pi\) | ||||
0.466240 | + | 0.884658i | \(0.345608\pi\) | |||||||
\(542\) | 1324.61 | − | 2294.29i | 0.104976 | − | 0.181824i | ||||
\(543\) | 481.064 | + | 14493.3i | 0.0380192 | + | 1.14543i | ||||
\(544\) | −3271.09 | − | 5665.70i | −0.257807 | − | 0.446535i | ||||
\(545\) | −17404.2 | − | 30145.0i | −1.36792 | − | 2.36930i | ||||
\(546\) | −1152.42 | − | 615.309i | −0.0903281 | − | 0.0482285i | ||||
\(547\) | −1267.05 | + | 2194.60i | −0.0990408 | + | 0.171544i | −0.911288 | − | 0.411770i | \(-0.864911\pi\) |
0.812247 | + | 0.583314i | \(0.198244\pi\) | |||||||
\(548\) | −15390.7 | −1.19974 | ||||||||
\(549\) | −624.082 | + | 1268.42i | −0.0485158 | + | 0.0986064i | ||||
\(550\) | −8272.57 | −0.641352 | ||||||||
\(551\) | −4264.56 | + | 7386.43i | −0.329721 | + | 0.571094i | ||||
\(552\) | −3029.64 | + | 1885.86i | −0.233605 | + | 0.145413i | ||||
\(553\) | 3553.64 | + | 6155.09i | 0.273266 | + | 0.473311i | ||||
\(554\) | −896.519 | − | 1552.82i | −0.0687535 | − | 0.119085i | ||||
\(555\) | −26655.5 | + | 16592.3i | −2.03867 | + | 1.26902i | ||||
\(556\) | −4825.25 | + | 8357.57i | −0.368050 | + | 0.637482i | ||||
\(557\) | 2697.62 | 0.205210 | 0.102605 | − | 0.994722i | \(-0.467282\pi\) | ||||
0.102605 | + | 0.994722i | \(0.467282\pi\) | |||||||
\(558\) | 3644.37 | − | 242.195i | 0.276485 | − | 0.0183744i | ||||
\(559\) | −14137.1 | −1.06965 | ||||||||
\(560\) | 3112.25 | − | 5390.57i | 0.234851 | − | 0.406774i | ||||
\(561\) | −10700.9 | − | 5713.50i | −0.805334 | − | 0.429989i | ||||
\(562\) | 480.185 | + | 831.705i | 0.0360416 | + | 0.0624259i | ||||
\(563\) | −8699.80 | − | 15068.5i | −0.651249 | − | 1.12800i | −0.982820 | − | 0.184566i | \(-0.940912\pi\) |
0.331571 | − | 0.943430i | \(-0.392421\pi\) | |||||||
\(564\) | −174.644 | − | 5261.62i | −0.0130387 | − | 0.392826i | ||||
\(565\) | 8585.24 | − | 14870.1i | 0.639264 | − | 1.10724i | ||||
\(566\) | 936.238 | 0.0695283 | ||||||||
\(567\) | 1944.25 | − | 4718.10i | 0.144005 | − | 0.349456i | ||||
\(568\) | 975.929 | 0.0720934 | ||||||||
\(569\) | 5178.36 | − | 8969.18i | 0.381526 | − | 0.660822i | −0.609755 | − | 0.792590i | \(-0.708732\pi\) |
0.991281 | + | 0.131768i | \(0.0420654\pi\) | |||||||
\(570\) | −143.983 | − | 4337.87i | −0.0105803 | − | 0.318760i | ||||
\(571\) | −7692.04 | − | 13323.0i | −0.563751 | − | 0.976446i | −0.997165 | − | 0.0752505i | \(-0.976024\pi\) |
0.433414 | − | 0.901195i | \(-0.357309\pi\) | |||||||
\(572\) | −8078.96 | − | 13993.2i | −0.590557 | − | 1.02287i | ||||
\(573\) | 19873.6 | + | 10611.0i | 1.44892 | + | 0.773616i | ||||
\(574\) | 834.832 | − | 1445.97i | 0.0607059 | − | 0.105146i | ||||
\(575\) | −11488.8 | −0.833244 | ||||||||
\(576\) | 7500.50 | − | 498.463i | 0.542571 | − | 0.0360578i | ||||
\(577\) | −25346.5 | −1.82875 | −0.914375 | − | 0.404868i | \(-0.867318\pi\) | ||||
−0.914375 | + | 0.404868i | \(0.867318\pi\) | |||||||
\(578\) | 1082.81 | − | 1875.49i | 0.0779224 | − | 0.134965i | ||||
\(579\) | 10719.1 | − | 6672.34i | 0.769380 | − | 0.478917i | ||||
\(580\) | 10065.0 | + | 17433.0i | 0.720560 | + | 1.24805i | ||||
\(581\) | 3803.13 | + | 6587.22i | 0.271567 | + | 0.470368i | ||||
\(582\) | 4781.89 | − | 2976.59i | 0.340577 | − | 0.211999i | ||||
\(583\) | 10176.9 | − | 17626.9i | 0.722955 | − | 1.25220i | ||||
\(584\) | −10400.2 | −0.736925 | ||||||||
\(585\) | 9666.08 | − | 19645.9i | 0.683150 | − | 1.38848i | ||||
\(586\) | 433.793 | 0.0305799 | ||||||||
\(587\) | −3879.66 | + | 6719.77i | −0.272795 | + | 0.472495i | −0.969576 | − | 0.244789i | \(-0.921281\pi\) |
0.696781 | + | 0.717284i | \(0.254615\pi\) | |||||||
\(588\) | −1650.41 | − | 881.196i | −0.115751 | − | 0.0618026i | ||||
\(589\) | 4754.58 | + | 8235.18i | 0.332613 | + | 0.576103i | ||||
\(590\) | −1562.30 | − | 2705.98i | −0.109015 | − | 0.188819i | ||||
\(591\) | −47.0782 | − | 1418.36i | −0.00327671 | − | 0.0987198i | ||||
\(592\) | −8084.88 | + | 14003.4i | −0.561295 | + | 0.972192i | ||||
\(593\) | −16418.8 | −1.13700 | −0.568500 | − | 0.822684i | \(-0.692476\pi\) | ||||
−0.568500 | + | 0.822684i | \(0.692476\pi\) | |||||||
\(594\) | −4546.60 | + | 3267.45i | −0.314056 | + | 0.225699i | ||||
\(595\) | −6026.66 | −0.415242 | ||||||||
\(596\) | −5465.02 | + | 9465.70i | −0.375597 | + | 0.650554i | ||||
\(597\) | −111.829 | − | 3369.16i | −0.00766645 | − | 0.230972i | ||||
\(598\) | 995.310 | + | 1723.93i | 0.0680623 | + | 0.117887i | ||||
\(599\) | 12824.4 | + | 22212.6i | 0.874779 | + | 1.51516i | 0.856998 | + | 0.515319i | \(0.172327\pi\) |
0.0177803 | + | 0.999842i | \(0.494340\pi\) | |||||||
\(600\) | −11774.1 | − | 6286.52i | −0.801129 | − | 0.427744i | ||||
\(601\) | 3109.62 | − | 5386.01i | 0.211055 | − | 0.365558i | −0.740990 | − | 0.671516i | \(-0.765643\pi\) |
0.952045 | + | 0.305958i | \(0.0989768\pi\) | |||||||
\(602\) | 1796.01 | 0.121595 | ||||||||
\(603\) | 10616.3 | + | 15857.1i | 0.716963 | + | 1.07090i | ||||
\(604\) | 16193.1 | 1.09087 | ||||||||
\(605\) | −10137.6 | + | 17558.8i | −0.681243 | + | 1.17995i | ||||
\(606\) | −2517.98 | + | 1567.37i | −0.168789 | + | 0.105066i | ||||
\(607\) | 4779.12 | + | 8277.67i | 0.319569 | + | 0.553510i | 0.980398 | − | 0.197027i | \(-0.0631286\pi\) |
−0.660829 | + | 0.750536i | \(0.729795\pi\) | |||||||
\(608\) | −3930.74 | − | 6808.24i | −0.262192 | − | 0.454129i | ||||
\(609\) | 4640.58 | − | 2888.63i | 0.308778 | − | 0.192205i | ||||
\(610\) | 385.281 | − | 667.326i | 0.0255731 | − | 0.0442939i | ||||
\(611\) | −6133.68 | −0.406125 | ||||||||
\(612\) | −5213.03 | − | 7786.51i | −0.344321 | − | 0.514299i | ||||
\(613\) | 23697.2 | 1.56137 | 0.780685 | − | 0.624925i | \(-0.214870\pi\) | ||||
0.780685 | + | 0.624925i | \(0.214870\pi\) | |||||||
\(614\) | 702.487 | − | 1216.74i | 0.0461728 | − | 0.0799736i | ||||
\(615\) | 24685.1 | + | 13180.0i | 1.61853 | + | 0.864178i | ||||
\(616\) | 2143.79 | + | 3713.15i | 0.140220 | + | 0.242869i | ||||
\(617\) | 5182.35 | + | 8976.10i | 0.338142 | + | 0.585679i | 0.984083 | − | 0.177708i | \(-0.0568682\pi\) |
−0.645941 | + | 0.763387i | \(0.723535\pi\) | |||||||
\(618\) | −71.6700 | − | 2159.25i | −0.00466503 | − | 0.140547i | ||||
\(619\) | 5909.25 | − | 10235.1i | 0.383704 | − | 0.664595i | −0.607884 | − | 0.794025i | \(-0.707982\pi\) |
0.991588 | + | 0.129431i | \(0.0413150\pi\) | |||||||
\(620\) | 22443.0 | 1.45376 | ||||||||
\(621\) | −6314.23 | + | 4537.77i | −0.408022 | + | 0.293228i | ||||
\(622\) | −3163.20 | −0.203911 | ||||||||
\(623\) | −2669.54 | + | 4623.78i | −0.171674 | + | 0.297348i | ||||
\(624\) | −374.064 | − | 11269.7i | −0.0239977 | − | 0.722995i | ||||
\(625\) | −716.721 | − | 1241.40i | −0.0458701 | − | 0.0794494i | ||||
\(626\) | 3829.18 | + | 6632.34i | 0.244481 | + | 0.423453i | ||||
\(627\) | −12858.8 | − | 6865.67i | −0.819031 | − | 0.437302i | ||||
\(628\) | −12658.5 | + | 21925.1i | −0.804343 | + | 1.39316i | ||||
\(629\) | 15655.8 | 0.992431 | ||||||||
\(630\) | −1228.00 | + | 2495.86i | −0.0776583 | + | 0.157837i | ||||
\(631\) | 16150.5 | 1.01892 | 0.509462 | − | 0.860493i | \(-0.329845\pi\) | ||||
0.509462 | + | 0.860493i | \(0.329845\pi\) | |||||||
\(632\) | 6290.79 | − | 10896.0i | 0.395940 | − | 0.685789i | ||||
\(633\) | −1072.33 | + | 667.496i | −0.0673324 | + | 0.0419124i | ||||
\(634\) | 2290.66 | + | 3967.54i | 0.143492 | + | 0.248535i | ||||
\(635\) | 14445.0 | + | 25019.5i | 0.902729 | + | 1.56357i | ||||
\(636\) | 13347.7 | − | 8308.58i | 0.832189 | − | 0.518014i | ||||
\(637\) | −1089.91 | + | 1887.77i | −0.0677922 | + | 0.117420i | ||||
\(638\) | −5997.39 | −0.372161 | ||||||||
\(639\) | 2121.76 | − | 141.006i | 0.131354 | − | 0.00872945i | ||||
\(640\) | −24297.6 | −1.50070 | ||||||||
\(641\) | 5905.98 | − | 10229.4i | 0.363919 | − | 0.630326i | −0.624683 | − | 0.780878i | \(-0.714772\pi\) |
0.988602 | + | 0.150552i | \(0.0481052\pi\) | |||||||
\(642\) | 4390.95 | + | 2344.44i | 0.269933 | + | 0.144124i | ||||
\(643\) | −3098.97 | − | 5367.57i | −0.190064 | − | 0.329201i | 0.755207 | − | 0.655486i | \(-0.227536\pi\) |
−0.945271 | + | 0.326285i | \(0.894203\pi\) | |||||||
\(644\) | 1425.40 | + | 2468.87i | 0.0872186 | + | 0.151067i | ||||
\(645\) | 998.561 | + | 30084.3i | 0.0609586 | + | 1.83654i | ||||
\(646\) | −1082.09 | + | 1874.23i | −0.0659043 | + | 0.114150i | ||||
\(647\) | −4568.63 | −0.277606 | −0.138803 | − | 0.990320i | \(-0.544326\pi\) | ||||
−0.138803 | + | 0.990320i | \(0.544326\pi\) | |||||||
\(648\) | −8954.08 | + | 1195.41i | −0.542823 | + | 0.0724692i | ||||
\(649\) | −10494.1 | −0.634713 | ||||||||
\(650\) | −3722.62 | + | 6447.77i | −0.224636 | + | 0.389080i | ||||
\(651\) | −202.170 | − | 6090.93i | −0.0121715 | − | 0.366701i | ||||
\(652\) | −10007.6 | − | 17333.6i | −0.601114 | − | 1.04116i | ||||
\(653\) | −13537.8 | − | 23448.1i | −0.811294 | − | 1.40520i | −0.911959 | − | 0.410281i | \(-0.865430\pi\) |
0.100665 | − | 0.994920i | \(-0.467903\pi\) | |||||||
\(654\) | 7066.69 | + | 3773.09i | 0.422522 | + | 0.225596i | ||||
\(655\) | −19813.5 | + | 34317.9i | −1.18195 | + | 2.04719i | ||||
\(656\) | 14411.3 | 0.857725 | ||||||||
\(657\) | −22611.0 | + | 1502.67i | −1.34268 | + | 0.0892308i | ||||
\(658\) | 779.238 | 0.0461669 | ||||||||
\(659\) | 9021.56 | − | 15625.8i | 0.533278 | − | 0.923664i | −0.465967 | − | 0.884802i | \(-0.654293\pi\) |
0.999245 | − | 0.0388620i | \(-0.0123733\pi\) | |||||||
\(660\) | −29207.4 | + | 18180.7i | −1.72257 | + | 1.07225i | ||||
\(661\) | 4091.02 | + | 7085.86i | 0.240730 | + | 0.416956i | 0.960922 | − | 0.276818i | \(-0.0892799\pi\) |
−0.720193 | + | 0.693774i | \(0.755947\pi\) | |||||||
\(662\) | −1910.48 | − | 3309.05i | −0.112164 | − | 0.194275i | ||||
\(663\) | −9268.55 | + | 5769.40i | −0.542927 | + | 0.337956i | ||||
\(664\) | 6732.45 | − | 11660.9i | 0.393479 | − | 0.681525i | ||||
\(665\) | −7241.99 | −0.422304 | ||||||||
\(666\) | 3190.06 | − | 6483.66i | 0.185604 | − | 0.377232i | ||||
\(667\) | −8329.06 | −0.483512 | ||||||||
\(668\) | −3721.05 | + | 6445.05i | −0.215527 | + | 0.373303i | ||||
\(669\) | 8345.27 | + | 4455.76i | 0.482282 | + | 0.257503i | ||||
\(670\) | −5200.95 | − | 9008.31i | −0.299896 | − | 0.519435i | ||||
\(671\) | −1293.98 | − | 2241.25i | −0.0744466 | − | 0.128945i | ||||
\(672\) | 167.139 | + | 5035.53i | 0.00959456 | + | 0.289062i | ||||
\(673\) | 9551.45 | − | 16543.6i | 0.547075 | − | 0.947561i | −0.451398 | − | 0.892322i | \(-0.649075\pi\) |
0.998473 | − | 0.0552387i | \(-0.0175920\pi\) | |||||||
\(674\) | −3264.44 | −0.186560 | ||||||||
\(675\) | −26506.3 | − | 11966.3i | −1.51145 | − | 0.682344i | ||||
\(676\) | 1601.90 | 0.0911411 | ||||||||
\(677\) | −4081.39 | + | 7069.17i | −0.231699 | + | 0.401315i | −0.958308 | − | 0.285736i | \(-0.907762\pi\) |
0.726609 | + | 0.687051i | \(0.241095\pi\) | |||||||
\(678\) | 131.091 | + | 3949.47i | 0.00742555 | + | 0.223715i | ||||
\(679\) | −4699.20 | − | 8139.26i | −0.265595 | − | 0.460024i | ||||
\(680\) | 5334.31 | + | 9239.30i | 0.300826 | + | 0.521045i | ||||
\(681\) | 7793.21 | + | 4161.00i | 0.438527 | + | 0.234141i | ||||
\(682\) | −3343.26 | + | 5790.70i | −0.187713 | + | 0.325128i | ||||
\(683\) | 15581.2 | 0.872909 | 0.436454 | − | 0.899726i | \(-0.356234\pi\) | ||||
0.436454 | + | 0.899726i | \(0.356234\pi\) | |||||||
\(684\) | −6264.29 | − | 9356.73i | −0.350177 | − | 0.523046i | ||||
\(685\) | 38180.5 | 2.12964 | ||||||||
\(686\) | 138.464 | − | 239.827i | 0.00770640 | − | 0.0133479i | ||||
\(687\) | −833.642 | + | 518.918i | −0.0462961 | + | 0.0288180i | ||||
\(688\) | 7750.94 | + | 13425.0i | 0.429508 | + | 0.743930i | ||||
\(689\) | −9159.10 | − | 15864.0i | −0.506435 | − | 0.877171i | ||||
\(690\) | 3598.28 | − | 2239.83i | 0.198528 | − | 0.123578i | ||||
\(691\) | −11866.9 | + | 20554.0i | −0.653310 | + | 1.13157i | 0.329005 | + | 0.944328i | \(0.393287\pi\) |
−0.982315 | + | 0.187238i | \(0.940046\pi\) | |||||||
\(692\) | 10991.5 | 0.603807 | ||||||||
\(693\) | 5197.28 | + | 7762.98i | 0.284889 | + | 0.425528i | ||||
\(694\) | −3143.80 | −0.171955 | ||||||||
\(695\) | 11970.2 | − | 20733.0i | 0.653317 | − | 1.13158i | ||||
\(696\) | −8535.93 | − | 4557.56i | −0.464876 | − | 0.248210i | ||||
\(697\) | −6976.64 | − | 12083.9i | −0.379138 | − | 0.656686i | ||||
\(698\) | 381.325 | + | 660.474i | 0.0206782 | + | 0.0358156i | ||||
\(699\) | 111.559 | + | 3361.02i | 0.00603656 | + | 0.181868i | ||||
\(700\) | −5331.24 | + | 9233.98i | −0.287860 | + | 0.498588i | ||||
\(701\) | 32518.0 | 1.75205 | 0.876025 | − | 0.482266i | \(-0.160186\pi\) | ||||
0.876025 | + | 0.482266i | \(0.160186\pi\) | |||||||
\(702\) | 500.750 | + | 5014.03i | 0.0269225 | + | 0.269576i | ||||
\(703\) | 18813.0 | 1.00931 | ||||||||
\(704\) | −6880.79 | + | 11917.9i | −0.368366 | + | 0.638028i | ||||
\(705\) | 433.246 | + | 13052.7i | 0.0231447 | + | 0.697296i | ||||
\(706\) | 3794.05 | + | 6571.49i | 0.202253 | + | 0.350313i | ||||
\(707\) | 2474.44 | + | 4285.85i | 0.131628 | + | 0.227986i | ||||
\(708\) | −7150.81 | − | 3818.01i | −0.379582 | − | 0.202669i | ||||
\(709\) | −6957.97 | + | 12051.6i | −0.368564 | + | 0.638372i | −0.989341 | − | 0.145615i | \(-0.953484\pi\) |
0.620777 | + | 0.783987i | \(0.286817\pi\) | |||||||
\(710\) | −1159.10 | −0.0612681 | ||||||||
\(711\) | 12102.4 | − | 24597.7i | 0.638364 | − | 1.29745i | ||||
\(712\) | 9451.45 | 0.497483 | ||||||||
\(713\) | −4643.06 | + | 8042.02i | −0.243877 | + | 0.422407i | ||||
\(714\) | 1177.50 | − | 732.959i | 0.0617182 | − | 0.0384178i | ||||
\(715\) | 20041.8 | + | 34713.5i | 1.04828 | + | 1.81568i | ||||
\(716\) | 7310.56 | + | 12662.3i | 0.381576 | + | 0.660909i | ||||
\(717\) | 15533.3 | − | 9669.00i | 0.809066 | − | 0.503620i | ||||
\(718\) | −2632.94 | + | 4560.38i | −0.136853 | + | 0.237036i | ||||
\(719\) | −20884.8 | −1.08327 | −0.541635 | − | 0.840614i | \(-0.682194\pi\) | ||||
−0.541635 | + | 0.840614i | \(0.682194\pi\) | |||||||
\(720\) | −23955.9 | + | 1592.05i | −1.23998 | + | 0.0824057i | ||||
\(721\) | −3604.83 | −0.186201 | ||||||||
\(722\) | 1468.58 | − | 2543.66i | 0.0756993 | − | 0.131115i | ||||
\(723\) | 1487.42 | + | 794.171i | 0.0765113 | + | 0.0408514i | ||||
\(724\) | −10253.5 | − | 17759.6i | −0.526339 | − | 0.911647i | ||||
\(725\) | −15576.0 | − | 26978.5i | −0.797902 | − | 1.38201i | ||||
\(726\) | −154.794 | − | 4663.60i | −0.00791317 | − | 0.238406i | ||||
\(727\) | 10445.4 | − | 18092.0i | 0.532875 | − | 0.922967i | −0.466388 | − | 0.884580i | \(-0.654445\pi\) |
0.999263 | − | 0.0383863i | \(-0.0122218\pi\) | |||||||
\(728\) | 3858.78 | 0.196451 | ||||||||
\(729\) | −19294.2 | + | 3892.64i | −0.980249 | + | 0.197767i | ||||
\(730\) | 12352.3 | 0.626271 | ||||||||
\(731\) | 7504.58 | − | 12998.3i | 0.379709 | − | 0.657675i | ||||
\(732\) | −66.3176 | − | 1998.00i | −0.00334859 | − | 0.100885i | ||||
\(733\) | 4126.43 | + | 7147.19i | 0.207931 | + | 0.360147i | 0.951063 | − | 0.308998i | \(-0.0999938\pi\) |
−0.743132 | + | 0.669145i | \(0.766660\pi\) | |||||||
\(734\) | −1912.00 | − | 3311.67i | −0.0961486 | − | 0.166534i | ||||
\(735\) | 4094.24 | + | 2186.02i | 0.205467 | + | 0.109704i | ||||
\(736\) | 3838.54 | − | 6648.54i | 0.192242 | − | 0.332974i | ||||
\(737\) | −34935.2 | −1.74607 | ||||||||
\(738\) | −6425.96 | + | 427.052i | −0.320519 | + | 0.0213008i | ||||
\(739\) | 29252.3 | 1.45611 | 0.728054 | − | 0.685520i | \(-0.240425\pi\) | ||||
0.728054 | + | 0.685520i | \(0.240425\pi\) | |||||||
\(740\) | 22200.6 | − | 38452.6i | 1.10285 | − | 1.91020i | ||||
\(741\) | −11137.6 | + | 6932.86i | −0.552161 | + | 0.343704i | ||||
\(742\) | 1163.59 | + | 2015.40i | 0.0575699 | + | 0.0997140i | ||||
\(743\) | −13701.6 | − | 23731.9i | −0.676532 | − | 1.17179i | −0.976018 | − | 0.217688i | \(-0.930149\pi\) |
0.299486 | − | 0.954101i | \(-0.403185\pi\) | |||||||
\(744\) | −9158.88 | + | 5701.13i | −0.451318 | + | 0.280932i | ||||
\(745\) | 13557.3 | − | 23482.0i | 0.666714 | − | 1.15478i | ||||
\(746\) | 4623.02 | 0.226891 | ||||||||
\(747\) | 12952.1 | − | 26324.7i | 0.634396 | − | 1.28938i | ||||
\(748\) | 17154.6 | 0.838550 | ||||||||
\(749\) | 4152.75 | − | 7192.78i | 0.202588 | − | 0.350892i | ||||
\(750\) | 5551.47 | + | 2964.07i | 0.270281 | + | 0.144310i | ||||
\(751\) | −9515.80 | − | 16481.9i | −0.462366 | − | 0.800841i | 0.536713 | − | 0.843765i | \(-0.319666\pi\) |
−0.999078 | + | 0.0429244i | \(0.986333\pi\) | |||||||
\(752\) | 3362.91 | + | 5824.72i | 0.163075 | + | 0.282455i | ||||
\(753\) | −603.503 | − | 18182.2i | −0.0292070 | − | 0.879940i | ||||
\(754\) | −2698.80 | + | 4674.46i | −0.130351 | + | 0.225774i | ||||
\(755\) | −40170.8 | −1.93638 | ||||||||
\(756\) | 717.134 | + | 7180.70i | 0.0344999 | + | 0.345449i | ||||
\(757\) | −15036.1 | −0.721926 | −0.360963 | − | 0.932580i | \(-0.617552\pi\) | ||||
−0.360963 | + | 0.932580i | \(0.617552\pi\) | |||||||
\(758\) | 860.481 | − | 1490.40i | 0.0412323 | − | 0.0714164i | ||||
\(759\) | −472.229 | − | 14227.2i | −0.0225835 | − | 0.680388i | ||||
\(760\) | 6410.02 | + | 11102.5i | 0.305942 | + | 0.529907i | ||||
\(761\) | 10108.5 | + | 17508.4i | 0.481513 | + | 0.834004i | 0.999775 | − | 0.0212174i | \(-0.00675422\pi\) |
−0.518262 | + | 0.855222i | \(0.673421\pi\) | |||||||
\(762\) | −5865.15 | − | 3131.56i | −0.278835 | − | 0.148877i | ||||
\(763\) | 6683.33 | − | 11575.9i | 0.317107 | − | 0.549246i | ||||
\(764\) | −31859.3 | −1.50868 | ||||||||
\(765\) | 12932.2 | + | 19316.3i | 0.611195 | + | 0.912919i | ||||
\(766\) | 8227.60 | 0.388088 | ||||||||
\(767\) | −4722.29 | + | 8179.25i | −0.222310 | + | 0.385053i | ||||
\(768\) | −5077.95 | + | 3160.87i | −0.238587 | + | 0.148513i | ||||
\(769\) | 6078.16 | + | 10527.7i | 0.285025 | + | 0.493677i | 0.972615 | − | 0.232421i | \(-0.0746649\pi\) |
−0.687590 | + | 0.726099i | \(0.741332\pi\) | |||||||
\(770\) | −2546.16 | − | 4410.08i | −0.119165 | − | 0.206400i | ||||
\(771\) | 8112.57 | − | 5049.84i | 0.378946 | − | 0.235883i | ||||
\(772\) | −8927.64 | + | 15463.1i | −0.416208 | + | 0.720894i | ||||
\(773\) | 2842.00 | 0.132237 | 0.0661187 | − | 0.997812i | \(-0.478938\pi\) | ||||
0.0661187 | + | 0.997812i | \(0.478938\pi\) | |||||||
\(774\) | −3853.94 | − | 5756.48i | −0.178975 | − | 0.267329i | ||||
\(775\) | −34731.6 | −1.60980 | ||||||||
\(776\) | −8318.71 | + | 14408.4i | −0.384825 | + | 0.666536i | ||||
\(777\) | −10635.9 | − | 5678.77i | −0.491067 | − | 0.262194i | ||||
\(778\) | −1917.29 | − | 3320.84i | −0.0883524 | − | 0.153031i | ||||
\(779\) | −8383.54 | − | 14520.7i | −0.385586 | − | 0.667854i | ||||
\(780\) | 1027.16 | + | 30945.9i | 0.0471515 | + | 1.42057i | ||||
\(781\) | −1946.45 | + | 3371.35i | −0.0891798 | + | 0.154464i | ||||
\(782\) | −2113.41 | −0.0966438 | ||||||||
\(783\) | −19216.4 | − | 8675.23i | −0.877059 | − | 0.395948i | ||||
\(784\) | 2390.25 | 0.108885 | ||||||||
\(785\) | 31402.4 | − | 54390.5i | 1.42777 | − | 2.47297i | ||||
\(786\) | −302.539 | − | 9114.79i | −0.0137293 | − | 0.413631i | ||||
\(787\) | 14085.2 | + | 24396.2i | 0.637970 | + | 1.10500i | 0.985878 | + | 0.167467i | \(0.0535589\pi\) |
−0.347908 | + | 0.937529i | \(0.613108\pi\) | |||||||
\(788\) | 1003.44 | + | 1738.01i | 0.0453630 | + | 0.0785710i | ||||
\(789\) | 510.377 | + | 272.504i | 0.0230290 | + | 0.0122958i | ||||
\(790\) | −7471.52 | + | 12941.1i | −0.336487 | + | 0.582813i | ||||
\(791\) | 6593.57 | 0.296385 | ||||||||
\(792\) | 7300.99 | − | 14839.0i | 0.327562 | − | 0.665757i | ||||
\(793\) | −2329.15 | −0.104301 | ||||||||
\(794\) | 1686.96 | − | 2921.90i | 0.0754005 | − | 0.130597i | ||||
\(795\) | −33112.3 | + | 20611.5i | −1.47720 | + | 0.919513i | ||||
\(796\) | 2383.57 | + | 4128.46i | 0.106135 | + | 0.183831i | ||||
\(797\) | 16188.6 | + | 28039.5i | 0.719486 | + | 1.24619i | 0.961204 | + | 0.275840i | \(0.0889559\pi\) |
−0.241718 | + | 0.970347i | \(0.577711\pi\) | |||||||
\(798\) | 1414.95 | − | 880.767i | 0.0627679 | − | 0.0390712i | ||||
\(799\) | 3256.02 | − | 5639.59i | 0.144167 | − | 0.249705i | ||||
\(800\) | 28713.5 | 1.26897 | ||||||||
\(801\) | 20548.3 | − | 1365.58i | 0.906414 | − | 0.0602378i | ||||
\(802\) | 2857.36 | 0.125806 | ||||||||
\(803\) | 20742.8 | − | 35927.6i | 0.911579 | − | 1.57890i | ||||
\(804\) | −23805.3 | − | 12710.3i | −1.04422 | − | 0.557535i | ||||
\(805\) | −3536.06 | − | 6124.64i | −0.154820 | − | 0.268155i | ||||
\(806\) | 3008.91 | + | 5211.58i | 0.131494 | + | 0.227755i | ||||
\(807\) | 405.997 | + | 12231.8i | 0.0177098 | + | 0.533554i | ||||
\(808\) | 4380.34 | − | 7586.98i | 0.190718 | − | 0.330333i | ||||
\(809\) | 11154.6 | 0.484764 | 0.242382 | − | 0.970181i | \(-0.422071\pi\) | ||||
0.242382 | + | 0.970181i | \(0.422071\pi\) | |||||||
\(810\) | 10634.7 | − | 1419.78i | 0.461315 | − | 0.0615875i | ||||
\(811\) | −21528.0 | −0.932122 | −0.466061 | − | 0.884753i | \(-0.654327\pi\) | ||||
−0.466061 | + | 0.884753i | \(0.654327\pi\) | |||||||
\(812\) | −3865.01 | + | 6694.39i | −0.167038 | + | 0.289319i | ||||
\(813\) | 565.616 | + | 17040.7i | 0.0243998 | + | 0.735109i | ||||
\(814\) | 6614.32 | + | 11456.3i | 0.284806 | + | 0.493298i | ||||
\(815\) | 24826.2 | + | 43000.2i | 1.06702 | + | 1.84814i | ||||
\(816\) | 10560.5 | + | 5638.50i | 0.453051 | + | 0.241896i | ||||
\(817\) | 9017.95 | − | 15619.5i | 0.386167 | − | 0.668860i | ||||
\(818\) | −4819.55 | −0.206005 | ||||||||
\(819\) | 8389.34 | − | 557.533i | 0.357933 | − | 0.0237873i | ||||
\(820\) | −39572.7 | −1.68529 | ||||||||
\(821\) | −3315.61 | + | 5742.80i | −0.140945 | + | 0.244123i | −0.927853 | − | 0.372947i | \(-0.878347\pi\) |
0.786908 | + | 0.617070i | \(0.211681\pi\) | |||||||
\(822\) | −7459.77 | + | 4643.49i | −0.316532 | + | 0.197032i | ||||
\(823\) | −10791.9 | − | 18692.0i | −0.457084 | − | 0.791693i | 0.541721 | − | 0.840558i | \(-0.317773\pi\) |
−0.998805 | + | 0.0488650i | \(0.984440\pi\) | |||||||
\(824\) | 3190.71 | + | 5526.47i | 0.134895 | + | 0.233645i | ||||
\(825\) | 45199.8 | − | 28135.6i | 1.90746 | − | 1.18734i | ||||
\(826\) | 599.931 | − | 1039.11i | 0.0252715 | − | 0.0437716i | ||||
\(827\) | −39987.3 | −1.68137 | −0.840686 | − | 0.541523i | \(-0.817848\pi\) | ||||
−0.840686 | + | 0.541523i | \(0.817848\pi\) | |||||||
\(828\) | 4854.42 | − | 9866.41i | 0.203747 | − | 0.414108i | ||||
\(829\) | −28422.3 | −1.19077 | −0.595384 | − | 0.803442i | \(-0.703000\pi\) | ||||
−0.595384 | + | 0.803442i | \(0.703000\pi\) | |||||||
\(830\) | −7996.08 | + | 13849.6i | −0.334395 | + | 0.579189i | ||||
\(831\) | 10179.7 | + | 5435.19i | 0.424944 | + | 0.226889i | ||||
\(832\) | 6192.65 | + | 10726.0i | 0.258043 | + | 0.446943i | ||||
\(833\) | −1157.14 | − | 2004.22i | −0.0481302 | − | 0.0833639i | ||||
\(834\) | 182.777 | + | 5506.65i | 0.00758879 | + | 0.228633i | ||||
\(835\) | 9230.97 | − | 15988.5i | 0.382576 | − | 0.662641i | ||||
\(836\) | 20614.0 | 0.852812 | ||||||||
\(837\) | −19088.5 | + | 13718.1i | −0.788285 | + | 0.566507i | ||||
\(838\) | 9324.37 | 0.384374 | ||||||||
\(839\) | −11230.9 | + | 19452.5i | −0.462138 | + | 0.800446i | −0.999067 | − | 0.0431811i | \(-0.986251\pi\) |
0.536930 | + | 0.843627i | \(0.319584\pi\) | |||||||
\(840\) | −272.561 | − | 8211.65i | −0.0111955 | − | 0.337296i | ||||
\(841\) | 902.307 | + | 1562.84i | 0.0369965 | + | 0.0640798i | ||||
\(842\) | −1087.93 | − | 1884.34i | −0.0445278 | − | 0.0771245i | ||||
\(843\) | −5452.33 | − | 2911.14i | −0.222762 | − | 0.118938i | ||||
\(844\) | 893.115 | − | 1546.92i | 0.0364245 | − | 0.0630891i | ||||
\(845\) | −3973.89 | −0.161782 | ||||||||
\(846\) | −1672.11 | − | 2497.57i | −0.0679532 | − | 0.101499i | ||||
\(847\) | −7785.80 | −0.315848 | ||||||||
\(848\) | −10043.3 | + | 17395.5i | −0.406708 | + | 0.704438i | ||||
\(849\) | −5115.44 | + | 3184.21i | −0.206786 | + | 0.128718i | ||||
\(850\) | −3952.25 | − | 6845.50i | −0.159484 | − | 0.276234i | ||||
\(851\) | 9185.84 | + | 15910.3i | 0.370020 | + | 0.640893i | ||||
\(852\) | −2552.92 | + | 1589.12i | −0.102654 | + | 0.0638993i | ||||
\(853\) | 5581.97 | − | 9668.25i | 0.224060 | − | 0.388083i | −0.731977 | − | 0.681329i | \(-0.761402\pi\) |
0.956037 | + | 0.293246i | \(0.0947356\pi\) | |||||||
\(854\) | 295.901 | 0.0118566 | ||||||||
\(855\) | 15540.1 | + | 23211.6i | 0.621590 | + | 0.928446i | ||||
\(856\) | −14702.7 | −0.587066 | ||||||||
\(857\) | −1516.63 | + | 2626.87i | −0.0604515 | + | 0.104705i | −0.894667 | − | 0.446733i | \(-0.852587\pi\) |
0.834216 | + | 0.551438i | \(0.185921\pi\) | |||||||
\(858\) | −8137.64 | − | 4344.90i | −0.323793 | − | 0.172882i | ||||
\(859\) | −1723.64 | − | 2985.43i | −0.0684632 | − | 0.118582i | 0.829762 | − | 0.558118i | \(-0.188476\pi\) |
−0.898225 | + | 0.439536i | \(0.855143\pi\) | |||||||
\(860\) | −21283.6 | − | 36864.3i | −0.843914 | − | 1.46170i | ||||
\(861\) | 356.478 | + | 10739.8i | 0.0141100 | + | 0.425102i | ||||
\(862\) | −915.513 | + | 1585.72i | −0.0361746 | + | 0.0626562i | ||||
\(863\) | 15012.0 | 0.592135 | 0.296068 | − | 0.955167i | \(-0.404325\pi\) | ||||
0.296068 | + | 0.955167i | \(0.404325\pi\) | |||||||
\(864\) | 15780.9 | − | 11341.1i | 0.621387 | − | 0.446565i | ||||
\(865\) | −27267.1 | −1.07180 | ||||||||
\(866\) | −4836.06 | + | 8376.30i | −0.189764 | + | 0.328681i | ||||
\(867\) | 462.367 | + | 13930.1i | 0.0181117 | + | 0.545663i | ||||
\(868\) | 4309.12 | + | 7463.62i | 0.168504 | + | 0.291857i | ||||
\(869\) | 25093.4 | + | 43463.1i | 0.979559 | + | 1.69665i | ||||
\(870\) | 10138.1 | + | 5412.98i | 0.395072 | + | 0.210939i | ||||
\(871\) | −15720.7 | + | 27229.1i | −0.611568 | + | 1.05927i | ||||
\(872\) | −23662.2 | −0.918925 | ||||||||
\(873\) | −16003.8 | + | 32527.1i | −0.620444 | + | 1.26103i | ||||
\(874\) | −2539.60 | −0.0982875 | ||||||||
\(875\) | 5250.31 | − | 9093.80i | 0.202849 | − | 0.351345i | ||||
\(876\) | 27205.8 | − | 16934.8i | 1.04931 | − | 0.653167i | ||||
\(877\) | 2829.30 | + | 4900.49i | 0.108938 | + | 0.188686i | 0.915340 | − | 0.402681i | \(-0.131922\pi\) |
−0.806402 | + | 0.591367i | \(0.798588\pi\) | |||||||
\(878\) | −4400.41 | − | 7621.73i | −0.169142 | − | 0.292962i | ||||
\(879\) | −2370.17 | + | 1475.36i | −0.0909485 | + | 0.0566128i | ||||
\(880\) | 21976.6 | − | 38064.6i | 0.841854 | − | 1.45813i | ||||
\(881\) | 38874.9 | 1.48664 | 0.743320 | − | 0.668936i | \(-0.233250\pi\) | ||||
0.743320 | + | 0.668936i | \(0.233250\pi\) | |||||||
\(882\) | −1065.80 | + | 70.8303i | −0.0406887 | + | 0.00270406i | ||||
\(883\) | 13946.0 | 0.531507 | 0.265753 | − | 0.964041i | \(-0.414379\pi\) | ||||
0.265753 | + | 0.964041i | \(0.414379\pi\) | |||||||
\(884\) | 7719.51 | − | 13370.6i | 0.293705 | − | 0.508712i | ||||
\(885\) | 17739.3 | + | 9471.49i | 0.673786 | + | 0.359752i | ||||
\(886\) | 148.754 | + | 257.649i | 0.00564050 | + | 0.00976963i | ||||
\(887\) | 10064.3 | + | 17431.8i | 0.380975 | + | 0.659869i | 0.991202 | − | 0.132358i | \(-0.0422549\pi\) |
−0.610226 | + | 0.792227i | \(0.708922\pi\) | |||||||
\(888\) | 708.050 | + | 21331.9i | 0.0267574 | + | 0.806140i | ||||
\(889\) | −5546.98 | + | 9607.64i | −0.209268 | + | 0.362463i | ||||
\(890\) | −11225.4 | −0.422783 | ||||||||
\(891\) | 13729.0 | − | 33316.1i | 0.516205 | − | 1.25267i | ||||
\(892\) | −13378.3 | −0.502174 | ||||||||
\(893\) | 3912.63 | − | 6776.87i | 0.146619 | − | 0.253952i | ||||
\(894\) | 207.011 | + | 6236.78i | 0.00774440 | + | 0.233321i | ||||
\(895\) | −18135.6 | − | 31411.8i | −0.677326 | − | 1.17316i | ||||
\(896\) | −4665.21 | − | 8080.39i | −0.173944 | − | 0.301280i | ||||
\(897\) | −11301.4 | − | 6034.11i | −0.420672 | − | 0.224608i | ||||
\(898\) | 4068.29 | − | 7046.48i | 0.151181 | − | 0.261853i | ||||
\(899\) | −25179.5 | −0.934130 | ||||||||
\(900\) | 41036.2 | − | 2727.16i | 1.51986 | − | 0.101006i | ||||
\(901\) | 19448.2 | 0.719103 | ||||||||
\(902\) | 5895.02 | − | 10210.5i | 0.217608 | − | 0.376909i | ||||
\(903\) | −9813.09 | + | 6108.37i | −0.361638 | + | 0.225109i | ||||
\(904\) | −5836.10 | − | 10108.4i | −0.214719 | − | 0.371904i | ||||
\(905\) | 25436.4 | + | 44057.1i | 0.934292 | + | 1.61824i | ||||
\(906\) | 7848.64 | − | 4885.55i | 0.287807 | − | 0.179152i | ||||
\(907\) | 8385.50 | − | 14524.1i | 0.306986 | − | 0.531715i | −0.670716 | − | 0.741714i | \(-0.734013\pi\) |
0.977701 | + | 0.210000i | \(0.0673463\pi\) | |||||||
\(908\) | −12493.3 | −0.456613 | ||||||||
\(909\) | 8427.06 | − | 17127.6i | 0.307489 | − | 0.624960i | ||||
\(910\) | −4583.05 | −0.166952 | ||||||||
\(911\) | −3313.33 | + | 5738.86i | −0.120500 | + | 0.208712i | −0.919965 | − | 0.392001i | \(-0.871783\pi\) |
0.799465 | + | 0.600713i | \(0.205116\pi\) | |||||||
\(912\) | 12690.1 | + | 6775.56i | 0.460757 | + | 0.246010i | ||||
\(913\) | 26855.2 | + | 46514.6i | 0.973469 | + | 1.68610i | ||||
\(914\) | 881.945 | + | 1527.57i | 0.0319170 | + | 0.0552819i | ||||
\(915\) | 164.517 | + | 4956.52i | 0.00594401 | + | 0.179079i | ||||
\(916\) | 694.316 | − | 1202.59i | 0.0250446 | − | 0.0433785i | ||||
\(917\) | −15217.0 | −0.547992 | ||||||||
\(918\) | −4875.95 | − | 2201.25i | −0.175305 | − | 0.0791417i | ||||
\(919\) | 23808.0 | 0.854573 | 0.427287 | − | 0.904116i | \(-0.359469\pi\) | ||||
0.427287 | + | 0.904116i | \(0.359469\pi\) | |||||||
\(920\) | −6259.67 | + | 10842.1i | −0.224321 | + | 0.388535i | ||||
\(921\) | 299.966 | + | 9037.28i | 0.0107320 | + | 0.323332i | ||||
\(922\) | −6702.17 | − | 11608.5i | −0.239397 | − | 0.414648i | ||||
\(923\) | 1751.79 | + | 3034.18i | 0.0624710 | + | 0.108203i | ||||
\(924\) | −11654.1 | − | 6222.42i | −0.414925 | − | 0.221540i | ||||
\(925\) | −34356.6 | + | 59507.3i | −1.22123 | + | 2.11523i | ||||
\(926\) | −3097.66 | −0.109930 | ||||||||
\(927\) | 7735.36 | + | 11554.0i | 0.274070 | + | 0.409368i | ||||
\(928\) | 20816.5 | 0.736353 | ||||||||
\(929\) | −26028.8 | + | 45083.2i | −0.919243 | + | 1.59218i | −0.118676 | + | 0.992933i | \(0.537865\pi\) |
−0.800567 | + | 0.599243i | \(0.795468\pi\) | |||||||
\(930\) | 10877.9 | − | 6771.19i | 0.383550 | − | 0.238749i | ||||
\(931\) | −1390.48 | − | 2408.39i | −0.0489488 | − | 0.0847817i | ||||
\(932\) | −2377.81 | − | 4118.48i | −0.0835705 | − | 0.144748i | ||||
\(933\) | 17283.2 | − | 10758.3i | 0.606459 | − | 0.377503i | ||||
\(934\) | −3936.70 | + | 6818.57i | −0.137915 | + | 0.238876i | ||||
\(935\) | −42556.2 | −1.48849 | ||||||||
\(936\) | −8280.30 | − | 12368.0i | −0.289156 | − | 0.431901i | ||||
\(937\) | −23455.8 | −0.817789 | −0.408895 | − | 0.912582i | \(-0.634086\pi\) | ||||
−0.408895 | + | 0.912582i | \(0.634086\pi\) | |||||||
\(938\) | 1997.20 | − | 3459.25i | 0.0695211 | − | 0.120414i | ||||
\(939\) | −43479.0 | − | 23214.6i | −1.51106 | − | 0.806794i | ||||
\(940\) | −9234.35 | − | 15994.4i | −0.320416 | − | 0.554977i | ||||
\(941\) | −20051.3 | − | 34729.8i | −0.694636 | − | 1.20314i | −0.970303 | − | 0.241891i | \(-0.922232\pi\) |
0.275668 | − | 0.961253i | \(-0.411101\pi\) | |||||||
\(942\) | 479.494 | + | 14446.0i | 0.0165847 | + | 0.499658i | ||||
\(943\) | 8186.89 | − | 14180.1i | 0.282717 | − | 0.489680i | ||||
\(944\) | 10356.3 | 0.357066 | ||||||||
\(945\) | −1779.02 | − | 17813.5i | −0.0612399 | − | 0.613198i | ||||
\(946\) | 12682.2 | 0.435872 | ||||||||
\(947\) | −21106.6 | + | 36557.7i | −0.724259 | + | 1.25445i | 0.235020 | + | 0.971991i | \(0.424484\pi\) |
−0.959278 | + | 0.282462i | \(0.908849\pi\) | |||||||
\(948\) | 1286.06 | + | 38746.0i | 0.0440604 | + | 1.32744i | ||||
\(949\) | −18668.4 | − | 32334.5i | −0.638567 | − | 1.10603i | ||||
\(950\) | −4749.26 | − | 8225.96i | −0.162196 | − | 0.280932i | ||||
\(951\) | −26009.7 | − | 13887.2i | −0.886878 | − | 0.473528i | ||||
\(952\) | −2048.41 | + | 3547.95i | −0.0697366 | + | 0.120787i | ||||
\(953\) | −26903.6 | −0.914475 | −0.457237 | − | 0.889345i | \(-0.651161\pi\) | ||||
−0.457237 | + | 0.889345i | \(0.651161\pi\) | |||||||
\(954\) | 3962.79 | − | 8054.20i | 0.134486 | − | 0.273338i | ||||
\(955\) | 79034.8 | 2.67802 | ||||||||
\(956\) | −12937.2 | + | 22407.9i | −0.437677 | + | 0.758079i | ||||
\(957\) | 32768.7 | − | 20397.5i | 1.10686 | − | 0.688985i | ||||
\(958\) | −2841.91 | − | 4922.32i | −0.0958432 | − | 0.166005i | ||||
\(959\) | 7330.77 | + | 12697.3i | 0.246844 | + | 0.427546i | ||||
\(960\) | 22387.9 | − | 13935.8i | 0.752674 | − | 0.468518i | ||||
\(961\) | 859.121 | − | 1488.04i | 0.0288383 | − | 0.0499494i | ||||
\(962\) | 11905.7 | 0.399017 | ||||||||
\(963\) | −31965.0 | + | 2124.31i | −1.06963 | + | 0.0710850i | ||||
\(964\) | −2384.48 | −0.0796669 | ||||||||
\(965\) | 22147.2 | − | 38360.1i | 0.738801 | − | 1.27964i | ||||
\(966\) | 1435.76 | + | 766.588i | 0.0478206 | + | 0.0255327i | ||||
\(967\) | −23891.7 | − | 41381.7i | −0.794525 | − | 1.37616i | −0.923140 | − | 0.384463i | \(-0.874387\pi\) |
0.128615 | − | 0.991695i | \(-0.458947\pi\) | |||||||
\(968\) | 6891.35 | + | 11936.2i | 0.228819 | + | 0.396326i | ||||
\(969\) | −462.057 | − | 13920.7i | −0.0153183 | − | 0.461505i | ||||
\(970\) | 9880.06 | − | 17112.8i | 0.327041 | − | 0.566451i | ||||
\(971\) | −35958.5 | −1.18843 | −0.594214 | − | 0.804307i | \(-0.702537\pi\) | ||||
−0.594214 | + | 0.804307i | \(0.702537\pi\) | |||||||
\(972\) | 21476.3 | − | 17707.1i | 0.708697 | − | 0.584316i | ||||
\(973\) | 9193.26 | 0.302901 | ||||||||
\(974\) | 3231.58 | − | 5597.26i | 0.106311 | − | 0.184135i | ||||
\(975\) | −1589.58 | − | 47890.3i | −0.0522126 | − | 1.57304i | ||||
\(976\) | 1277.00 | + | 2211.83i | 0.0418809 | + | 0.0725398i | ||||
\(977\) | −16602.3 | − | 28756.0i | −0.543659 | − | 0.941644i | −0.998690 | − | 0.0511688i | \(-0.983705\pi\) |
0.455032 | − | 0.890475i | \(-0.349628\pi\) | |||||||
\(978\) | −10080.2 | − | 5382.11i | −0.329582 | − | 0.175972i | ||||
\(979\) | −18850.5 | + | 32650.0i | −0.615388 | + | 1.06588i | ||||
\(980\) | −6563.48 | −0.213941 | ||||||||
\(981\) | −51443.7 | + | 3418.81i | −1.67428 | + | 0.111268i | ||||
\(982\) | −6373.36 | −0.207110 | ||||||||
\(983\) | 8108.41 | − | 14044.2i | 0.263091 | − | 0.455687i | −0.703971 | − | 0.710229i | \(-0.748591\pi\) |
0.967062 | + | 0.254542i | \(0.0819248\pi\) | |||||||
\(984\) | 16149.4 | − | 10052.5i | 0.523196 | − | 0.325674i | ||||
\(985\) | −2489.27 | − | 4311.55i | −0.0805227 | − | 0.139469i | ||||
\(986\) | −2865.28 | − | 4962.80i | −0.0925446 | − | 0.160292i | ||||
\(987\) | −4257.61 | + | 2650.24i | −0.137306 | + | 0.0854692i | ||||
\(988\) | 9276.22 | − | 16066.9i | 0.298700 | − | 0.517364i | ||||
\(989\) | 17612.8 | 0.566285 | ||||||||
\(990\) | −8671.32 | + | 17624.1i | −0.278376 | + | 0.565789i | ||||
\(991\) | −45661.6 | −1.46366 | −0.731830 | − | 0.681487i | \(-0.761334\pi\) | ||||
−0.731830 | + | 0.681487i | \(0.761334\pi\) | |||||||
\(992\) | 11604.2 | − | 20099.1i | 0.371406 | − | 0.643294i | ||||
\(993\) | 21692.8 | + | 11582.4i | 0.693254 | + | 0.370146i | ||||
\(994\) | −222.551 | − | 385.470i | −0.00710151 | − | 0.0123002i | ||||
\(995\) | −5913.01 | − | 10241.6i | −0.188397 | − | 0.326313i | ||||
\(996\) | 1376.35 | + | 41466.2i | 0.0437864 | + | 1.31918i | ||||
\(997\) | 8241.78 | − | 14275.2i | 0.261805 | − | 0.453460i | −0.704917 | − | 0.709290i | \(-0.749016\pi\) |
0.966722 | + | 0.255830i | \(0.0823489\pi\) | |||||||
\(998\) | 2212.58 | 0.0701782 | ||||||||
\(999\) | 4621.48 | + | 46275.2i | 0.146364 | + | 1.46555i |
(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 | 63.4.f.b.43.5 | yes | 16 | |
3.2 | odd | 2 | 189.4.f.b.127.4 | 16 | |||
9.2 | odd | 6 | 567.4.a.g.1.5 | 8 | |||
9.4 | even | 3 | inner | 63.4.f.b.22.5 | ✓ | 16 | |
9.5 | odd | 6 | 189.4.f.b.64.4 | 16 | |||
9.7 | even | 3 | 567.4.a.i.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.5 | ✓ | 16 | 9.4 | even | 3 | inner | |
63.4.f.b.43.5 | yes | 16 | 1.1 | even | 1 | trivial | |
189.4.f.b.64.4 | 16 | 9.5 | odd | 6 | |||
189.4.f.b.127.4 | 16 | 3.2 | odd | 2 | |||
567.4.a.g.1.5 | 8 | 9.2 | odd | 6 | |||
567.4.a.i.1.4 | 8 | 9.7 | even | 3 |