Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [198,4,Mod(37,198)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(198, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("198.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.f (of order \(5\), degree \(4\), 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: | \(11.6823781811\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 651x^{10} + 154866x^{8} + 16636791x^{6} + 828488506x^{4} + 17109953235x^{2} + 84670385805 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Root | \(2.64944i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 198.37 |
Dual form | 198.4.f.h.91.3 |
$q$-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 \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(155\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | + | 1.17557i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.23607 | + | 3.80423i | 0.154508 | + | 0.475528i | ||||
\(5\) | 3.70247 | − | 2.69000i | 0.331159 | − | 0.240601i | −0.409763 | − | 0.912192i | \(-0.634389\pi\) |
0.740922 | + | 0.671591i | \(0.234389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.17534 | − | 6.69500i | −0.117457 | − | 0.361496i | 0.874994 | − | 0.484133i | \(-0.160865\pi\) |
−0.992452 | + | 0.122637i | \(0.960865\pi\) | |||||||
\(8\) | −2.47214 | + | 7.60845i | −0.109254 | + | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.15301 | 0.289444 | ||||||||
\(11\) | 19.7086 | + | 30.7013i | 0.540216 | + | 0.841526i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.3928 | + | 52.5964i | 1.54447 | + | 1.12212i | 0.947452 | + | 0.319899i | \(0.103649\pi\) |
0.597020 | + | 0.802226i | \(0.296351\pi\) | |||||||
\(14\) | 4.35067 | − | 13.3900i | 0.0830547 | − | 0.255616i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.9443 | + | 9.40456i | −0.202254 | + | 0.146946i | ||||
\(17\) | 83.4632 | − | 60.6396i | 1.19075 | − | 0.865133i | 0.197410 | − | 0.980321i | \(-0.436747\pi\) |
0.993344 | + | 0.115188i | \(0.0367471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.51500 | + | 20.0511i | −0.0786655 | + | 0.242107i | −0.982654 | − | 0.185450i | \(-0.940626\pi\) |
0.903988 | + | 0.427557i | \(0.140626\pi\) | |||||||
\(20\) | 14.8099 | + | 10.7600i | 0.165580 | + | 0.120301i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.20231 | + | 72.8446i | −0.0407244 | + | 0.705933i | ||||
\(23\) | −89.9033 | −0.815050 | −0.407525 | − | 0.913194i | \(-0.633608\pi\) | ||||
−0.407525 | + | 0.913194i | \(0.633608\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −32.1549 | + | 98.9628i | −0.257240 | + | 0.791702i | ||||
\(26\) | 55.3031 | + | 170.206i | 0.417148 | + | 1.28385i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 22.7804 | − | 16.5509i | 0.153753 | − | 0.111708i | ||||
\(29\) | −48.5558 | − | 149.439i | −0.310917 | − | 0.956903i | −0.977403 | − | 0.211386i | \(-0.932202\pi\) |
0.666486 | − | 0.745518i | \(-0.267798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 182.900 | + | 132.885i | 1.05967 | + | 0.769896i | 0.974027 | − | 0.226430i | \(-0.0727055\pi\) |
0.0856433 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 206.332 | 1.04076 | ||||||||
\(35\) | −26.0637 | − | 18.9364i | −0.125873 | − | 0.0914523i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 54.0050 | + | 166.210i | 0.239956 | + | 0.738508i | 0.996425 | + | 0.0844788i | \(0.0269225\pi\) |
−0.756470 | + | 0.654029i | \(0.773077\pi\) | |||||||
\(38\) | −34.1130 | + | 24.7845i | −0.145628 | + | 0.105805i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.3137 | + | 34.8201i | 0.0447215 | + | 0.137639i | ||||
\(41\) | −28.3857 | + | 87.3621i | −0.108124 | + | 0.332772i | −0.990451 | − | 0.137865i | \(-0.955976\pi\) |
0.882327 | + | 0.470637i | \(0.155976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.8603 | −0.0420622 | −0.0210311 | − | 0.999779i | \(-0.506695\pi\) | ||||
−0.0210311 | + | 0.999779i | \(0.506695\pi\) | |||||||
\(44\) | −92.4335 | + | 112.925i | −0.316702 | + | 0.386911i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −145.467 | − | 105.688i | −0.466258 | − | 0.338757i | ||||
\(47\) | 90.9895 | − | 280.037i | 0.282387 | − | 0.869097i | −0.704783 | − | 0.709423i | \(-0.748956\pi\) |
0.987170 | − | 0.159674i | \(-0.0510444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 237.402 | − | 172.483i | 0.692134 | − | 0.502865i | ||||
\(50\) | −168.365 | + | 122.325i | −0.476210 | + | 0.345986i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −110.606 | + | 340.411i | −0.294968 | + | 0.907818i | ||||
\(53\) | −406.416 | − | 295.278i | −1.05331 | − | 0.765276i | −0.0804721 | − | 0.996757i | \(-0.525643\pi\) |
−0.972839 | + | 0.231481i | \(0.925643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 155.557 | + | 60.6544i | 0.381370 | + | 0.148703i | ||||
\(56\) | 56.3163 | 0.134385 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 97.1116 | − | 298.879i | 0.219851 | − | 0.676633i | ||||
\(59\) | −144.288 | − | 444.073i | −0.318385 | − | 0.979888i | −0.974339 | − | 0.225087i | \(-0.927733\pi\) |
0.655954 | − | 0.754801i | \(-0.272267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −99.4965 | + | 72.2884i | −0.208840 | + | 0.151731i | −0.687289 | − | 0.726385i | \(-0.741199\pi\) |
0.478449 | + | 0.878115i | \(0.341199\pi\) | |||||||
\(62\) | 139.723 | + | 430.023i | 0.286207 | + | 0.880855i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −51.7771 | − | 37.6183i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 409.517 | 0.781450 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −874.971 | −1.59544 | −0.797722 | − | 0.603026i | \(-0.793962\pi\) | ||||
−0.797722 | + | 0.603026i | \(0.793962\pi\) | |||||||
\(68\) | 333.853 | + | 242.558i | 0.595377 | + | 0.432566i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −19.9109 | − | 61.2794i | −0.0339972 | − | 0.104633i | ||||
\(71\) | 90.0102 | − | 65.3962i | 0.150454 | − | 0.109311i | −0.510012 | − | 0.860168i | \(-0.670359\pi\) |
0.660466 | + | 0.750856i | \(0.270359\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −251.479 | − | 773.974i | −0.403198 | − | 1.24092i | −0.922391 | − | 0.386258i | \(-0.873767\pi\) |
0.519193 | − | 0.854657i | \(-0.326233\pi\) | |||||||
\(74\) | −108.010 | + | 332.420i | −0.169674 | + | 0.522204i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −84.3320 | −0.127283 | ||||||||
\(77\) | 162.672 | − | 198.735i | 0.240756 | − | 0.294129i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −352.670 | − | 256.230i | −0.502259 | − | 0.364912i | 0.307620 | − | 0.951509i | \(-0.400467\pi\) |
−0.809879 | + | 0.586597i | \(0.800467\pi\) | |||||||
\(80\) | −22.6275 | + | 69.6403i | −0.0316229 | + | 0.0973252i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −148.629 | + | 107.985i | −0.200163 | + | 0.145427i | ||||
\(83\) | −536.956 | + | 390.121i | −0.710103 | + | 0.515920i | −0.883207 | − | 0.468984i | \(-0.844620\pi\) |
0.173104 | + | 0.984904i | \(0.444620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 145.900 | − | 449.033i | 0.186177 | − | 0.572993i | ||||
\(86\) | −19.1903 | − | 13.9426i | −0.0240622 | − | 0.0174822i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −282.312 | + | 74.0544i | −0.341983 | + | 0.0897071i | ||||
\(89\) | 1288.31 | 1.53439 | 0.767195 | − | 0.641414i | \(-0.221652\pi\) | ||||
0.767195 | + | 0.641414i | \(0.221652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 194.654 | − | 599.084i | 0.224234 | − | 0.690122i | ||||
\(92\) | −111.127 | − | 342.013i | −0.125932 | − | 0.387579i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 476.427 | − | 346.145i | 0.522763 | − | 0.379809i | ||||
\(95\) | 29.8159 | + | 91.7640i | 0.0322005 | + | 0.0991031i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 165.625 | + | 120.334i | 0.173368 | + | 0.125959i | 0.671085 | − | 0.741380i | \(-0.265828\pi\) |
−0.497718 | + | 0.867339i | \(0.665828\pi\) | |||||||
\(98\) | 586.890 | 0.604947 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −416.222 | −0.416222 | ||||||||
\(101\) | −85.6474 | − | 62.2265i | −0.0843786 | − | 0.0613046i | 0.544796 | − | 0.838569i | \(-0.316607\pi\) |
−0.629175 | + | 0.777264i | \(0.716607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −148.999 | − | 458.571i | −0.142537 | − | 0.438683i | 0.854149 | − | 0.520028i | \(-0.174078\pi\) |
−0.996686 | + | 0.0813452i | \(0.974078\pi\) | |||||||
\(104\) | −579.142 | + | 420.771i | −0.546053 | + | 0.396731i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −310.474 | − | 955.541i | −0.284490 | − | 0.875569i | ||||
\(107\) | −138.975 | + | 427.722i | −0.125563 | + | 0.386443i | −0.994003 | − | 0.109351i | \(-0.965123\pi\) |
0.868440 | + | 0.495794i | \(0.165123\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1214.86 | −1.06754 | −0.533772 | − | 0.845629i | \(-0.679226\pi\) | ||||
−0.533772 | + | 0.845629i | \(0.679226\pi\) | |||||||
\(110\) | 180.393 | + | 281.009i | 0.156362 | + | 0.243574i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 91.1217 | + | 66.2038i | 0.0768767 | + | 0.0558542i | ||||
\(113\) | 483.559 | − | 1488.24i | 0.402561 | − | 1.23895i | −0.520354 | − | 0.853951i | \(-0.674200\pi\) |
0.922915 | − | 0.385004i | \(-0.125800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −332.865 | + | 241.840i | −0.269911 | + | 0.196102i | ||||
\(116\) | 508.483 | − | 369.434i | 0.406995 | − | 0.295699i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 288.576 | − | 888.146i | 0.225132 | − | 0.692885i | ||||
\(119\) | −587.542 | − | 426.875i | −0.452604 | − | 0.328836i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −554.140 | + | 1210.16i | −0.416333 | + | 0.909212i | ||||
\(122\) | −245.969 | −0.182533 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −279.446 | + | 860.047i | −0.202379 | + | 0.622859i | ||||
\(125\) | 323.935 | + | 996.968i | 0.231789 | + | 0.713372i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1983.67 | − | 1441.22i | 1.38600 | − | 1.00699i | 0.389715 | − | 0.920936i | \(-0.372574\pi\) |
0.996290 | − | 0.0860558i | \(-0.0274263\pi\) | |||||||
\(128\) | −39.5542 | − | 121.735i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 662.612 | + | 481.416i | 0.447038 | + | 0.324792i | ||||
\(131\) | −2460.67 | −1.64114 | −0.820572 | − | 0.571543i | \(-0.806345\pi\) | ||||
−0.820572 | + | 0.571543i | \(0.806345\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 148.414 | 0.0967606 | ||||||||
\(134\) | −1415.73 | − | 1028.59i | −0.912692 | − | 0.663109i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 255.041 | + | 784.935i | 0.160806 | + | 0.494909i | ||||
\(137\) | −505.998 | + | 367.629i | −0.315550 | + | 0.229260i | −0.734274 | − | 0.678853i | \(-0.762477\pi\) |
0.418724 | + | 0.908113i | \(0.362477\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 361.676 | + | 1113.12i | 0.220698 | + | 0.679238i | 0.998700 | + | 0.0509760i | \(0.0162332\pi\) |
−0.778002 | + | 0.628262i | \(0.783767\pi\) | |||||||
\(140\) | 39.8218 | − | 122.559i | 0.0240397 | − | 0.0739865i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 222.517 | 0.131502 | ||||||||
\(143\) | −188.016 | + | 3259.16i | −0.109949 | + | 1.90590i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −581.769 | − | 422.680i | −0.333195 | − | 0.242080i | ||||
\(146\) | 502.959 | − | 1547.95i | 0.285104 | − | 0.877460i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −565.547 | + | 410.894i | −0.314106 | + | 0.228211i | ||||
\(149\) | 1602.19 | − | 1164.06i | 0.880919 | − | 0.640025i | −0.0525757 | − | 0.998617i | \(-0.516743\pi\) |
0.933494 | + | 0.358592i | \(0.116743\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −788.343 | + | 2426.27i | −0.424864 | + | 1.30760i | 0.478261 | + | 0.878218i | \(0.341267\pi\) |
−0.903125 | + | 0.429378i | \(0.858733\pi\) | |||||||
\(152\) | −136.452 | − | 99.1382i | −0.0728139 | − | 0.0529024i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 496.836 | − | 130.327i | 0.259975 | − | 0.0681952i | ||||
\(155\) | 1034.64 | 0.536157 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 699.558 | − | 2153.02i | 0.355610 | − | 1.09446i | −0.600045 | − | 0.799967i | \(-0.704850\pi\) |
0.955655 | − | 0.294489i | \(-0.0951495\pi\) | |||||||
\(158\) | −269.416 | − | 829.177i | −0.135656 | − | 0.417505i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −118.479 | + | 86.0801i | −0.0585412 | + | 0.0425327i | ||||
\(161\) | 195.570 | + | 601.903i | 0.0957334 | + | 0.294637i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 399.068 | + | 289.940i | 0.191763 | + | 0.139324i | 0.679524 | − | 0.733653i | \(-0.262186\pi\) |
−0.487761 | + | 0.872977i | \(0.662186\pi\) | |||||||
\(164\) | −367.432 | −0.174949 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1327.43 | −0.620653 | ||||||||
\(167\) | −1898.37 | − | 1379.25i | −0.879644 | − | 0.639099i | 0.0535135 | − | 0.998567i | \(-0.482958\pi\) |
−0.933157 | + | 0.359469i | \(0.882958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1795.42 | + | 5525.73i | 0.817213 | + | 2.51512i | ||||
\(170\) | 763.940 | − | 555.035i | 0.344656 | − | 0.250407i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.6601 | − | 45.1192i | −0.00649897 | − | 0.0200018i | ||||
\(173\) | −915.293 | + | 2816.98i | −0.402245 | + | 1.23798i | 0.520928 | + | 0.853601i | \(0.325586\pi\) |
−0.923174 | + | 0.384383i | \(0.874414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 732.503 | 0.316412 | ||||||||
\(176\) | −543.846 | − | 212.055i | −0.232920 | − | 0.0908196i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2084.53 | + | 1514.50i | 0.877765 | + | 0.637734i | ||||
\(179\) | −461.215 | + | 1419.47i | −0.192586 | + | 0.592718i | 0.807411 | + | 0.589990i | \(0.200868\pi\) |
−0.999996 | + | 0.00272778i | \(0.999132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1250.62 | − | 908.630i | 0.513580 | − | 0.373138i | −0.300600 | − | 0.953750i | \(-0.597187\pi\) |
0.814180 | + | 0.580613i | \(0.197187\pi\) | |||||||
\(182\) | 1019.22 | − | 740.509i | 0.415109 | − | 0.301594i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 222.253 | − | 684.025i | 0.0890474 | − | 0.274060i | ||||
\(185\) | 647.058 | + | 470.115i | 0.257149 | + | 0.186830i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3506.66 | + | 1367.31i | 1.37130 | + | 0.534692i | ||||
\(188\) | 1177.79 | 0.456911 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −59.6319 | + | 183.528i | −0.0227692 | + | 0.0700765i | ||||
\(191\) | −358.846 | − | 1104.41i | −0.135943 | − | 0.418391i | 0.859792 | − | 0.510644i | \(-0.170593\pi\) |
−0.995736 | + | 0.0922534i | \(0.970593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 580.247 | − | 421.574i | 0.216410 | − | 0.157231i | −0.474299 | − | 0.880364i | \(-0.657298\pi\) |
0.690709 | + | 0.723133i | \(0.257298\pi\) | |||||||
\(194\) | 126.526 | + | 389.407i | 0.0468250 | + | 0.144113i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 949.608 | + | 689.930i | 0.346067 | + | 0.251432i | ||||
\(197\) | 3628.45 | 1.31227 | 0.656133 | − | 0.754645i | \(-0.272191\pi\) | ||||
0.656133 | + | 0.754645i | \(0.272191\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1276.68 | −0.454782 | −0.227391 | − | 0.973804i | \(-0.573020\pi\) | ||||
−0.227391 | + | 0.973804i | \(0.573020\pi\) | |||||||
\(200\) | −673.462 | − | 489.299i | −0.238105 | − | 0.172993i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −65.4288 | − | 201.369i | −0.0227899 | − | 0.0701400i | ||||
\(203\) | −894.871 | + | 650.162i | −0.309397 | + | 0.224790i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 129.907 | + | 399.813i | 0.0442591 | + | 0.136215i | ||||
\(206\) | 297.997 | − | 917.141i | 0.100789 | − | 0.310195i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1431.72 | −0.477268 | ||||||||
\(209\) | −743.997 | + | 195.161i | −0.246236 | + | 0.0645912i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2612.70 | − | 1898.24i | −0.852443 | − | 0.619336i | 0.0733755 | − | 0.997304i | \(-0.476623\pi\) |
−0.925819 | + | 0.377968i | \(0.876623\pi\) | |||||||
\(212\) | 620.948 | − | 1911.08i | 0.201165 | − | 0.619121i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −727.684 | + | 528.693i | −0.232446 | + | 0.168882i | ||||
\(215\) | −43.9124 | + | 31.9042i | −0.0139293 | + | 0.0101202i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 491.793 | − | 1513.58i | 0.153848 | − | 0.473496i | ||||
\(218\) | −1965.68 | − | 1428.15i | −0.610700 | − | 0.443700i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −38.4638 | + | 666.748i | −0.0117874 | + | 0.204328i | ||||
\(221\) | 9231.56 | 2.80987 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1015.74 | + | 3126.13i | −0.305018 | + | 0.938750i | 0.674652 | + | 0.738136i | \(0.264294\pi\) |
−0.979670 | + | 0.200614i | \(0.935706\pi\) | |||||||
\(224\) | 69.6108 | + | 214.240i | 0.0207637 | + | 0.0639040i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2531.95 | − | 1839.57i | 0.745232 | − | 0.541443i | ||||
\(227\) | 1943.90 | + | 5982.70i | 0.568374 | + | 1.74928i | 0.657706 | + | 0.753275i | \(0.271527\pi\) |
−0.0893318 | + | 0.996002i | \(0.528473\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 862.762 | + | 626.833i | 0.248965 | + | 0.180883i | 0.705268 | − | 0.708941i | \(-0.250827\pi\) |
−0.456303 | + | 0.889824i | \(0.650827\pi\) | |||||||
\(230\) | −822.886 | −0.235911 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1257.04 | 0.355727 | ||||||||
\(233\) | −2984.89 | − | 2168.65i | −0.839257 | − | 0.609756i | 0.0829060 | − | 0.996557i | \(-0.473580\pi\) |
−0.922163 | + | 0.386801i | \(0.873580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −416.414 | − | 1281.59i | −0.115591 | − | 0.355752i | ||||
\(236\) | 1511.00 | − | 1097.81i | 0.416771 | − | 0.302802i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −448.842 | − | 1381.40i | −0.122244 | − | 0.376229i | ||||
\(239\) | −2203.64 | + | 6782.10i | −0.596408 | + | 1.83556i | −0.0488199 | + | 0.998808i | \(0.515546\pi\) |
−0.547588 | + | 0.836748i | \(0.684454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3210.60 | −0.858146 | −0.429073 | − | 0.903270i | \(-0.641160\pi\) | ||||
−0.429073 | + | 0.903270i | \(0.641160\pi\) | |||||||
\(242\) | −2319.25 | + | 1306.65i | −0.616061 | + | 0.347086i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −397.986 | − | 289.154i | −0.104420 | − | 0.0758654i | ||||
\(245\) | 414.995 | − | 1277.22i | 0.108217 | − | 0.333056i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1526.26 | + | 1108.89i | −0.393171 | + | 0.285656i | ||||
\(248\) | −1463.20 | + | 1063.08i | −0.374650 | + | 0.272199i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −647.869 | + | 1993.94i | −0.163899 | + | 0.504430i | ||||
\(251\) | −5529.55 | − | 4017.45i | −1.39053 | − | 1.01028i | −0.995807 | − | 0.0914745i | \(-0.970842\pi\) |
−0.394719 | − | 0.918802i | \(-0.629158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1771.87 | − | 2760.15i | −0.440303 | − | 0.685886i | ||||
\(254\) | 4903.91 | 1.21141 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 79.1084 | − | 243.470i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −1707.99 | − | 5256.64i | −0.414558 | − | 1.27588i | −0.912646 | − | 0.408751i | \(-0.865965\pi\) |
0.498088 | − | 0.867126i | \(-0.334035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 995.298 | − | 723.126i | 0.238783 | − | 0.173486i | ||||
\(260\) | 506.190 | + | 1557.89i | 0.120741 | + | 0.371602i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3981.45 | − | 2892.69i | −0.938836 | − | 0.682104i | ||||
\(263\) | −3472.45 | −0.814147 | −0.407073 | − | 0.913395i | \(-0.633451\pi\) | ||||
−0.407073 | + | 0.913395i | \(0.633451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2299.04 | −0.532940 | ||||||||
\(266\) | 240.140 | + | 174.472i | 0.0553530 | + | 0.0402163i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1081.52 | − | 3328.59i | −0.246510 | − | 0.758679i | ||||
\(269\) | 3555.78 | − | 2583.42i | 0.805946 | − | 0.585554i | −0.106706 | − | 0.994291i | \(-0.534030\pi\) |
0.912652 | + | 0.408736i | \(0.134030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1824.70 | − | 5615.85i | −0.409014 | − | 1.25882i | −0.917497 | − | 0.397743i | \(-0.869794\pi\) |
0.508483 | − | 0.861072i | \(-0.330206\pi\) | |||||||
\(272\) | −510.082 | + | 1569.87i | −0.113707 | + | 0.349954i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1250.90 | −0.275801 | ||||||||
\(275\) | −3672.02 | + | 963.222i | −0.805203 | + | 0.211216i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 185.944 | + | 135.097i | 0.0403333 | + | 0.0293038i | 0.607769 | − | 0.794114i | \(-0.292065\pi\) |
−0.567436 | + | 0.823418i | \(0.692065\pi\) | |||||||
\(278\) | −723.352 | + | 2226.25i | −0.156057 | + | 0.480293i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 208.509 | − | 151.491i | 0.0445029 | − | 0.0323333i | ||||
\(281\) | 3228.10 | − | 2345.35i | 0.685311 | − | 0.497907i | −0.189805 | − | 0.981822i | \(-0.560785\pi\) |
0.875115 | + | 0.483915i | \(0.160785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 626.599 | − | 1928.47i | 0.131616 | − | 0.405073i | −0.863432 | − | 0.504465i | \(-0.831690\pi\) |
0.995048 | + | 0.0993917i | \(0.0316897\pi\) | |||||||
\(284\) | 360.041 | + | 261.585i | 0.0752271 | + | 0.0546557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4135.58 | + | 5052.40i | −0.855043 | + | 1.04460i | ||||
\(287\) | 646.637 | 0.132996 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1770.75 | − | 5449.81i | 0.360422 | − | 1.10926i | ||||
\(290\) | −444.432 | − | 1367.82i | −0.0899929 | − | 0.276970i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2633.53 | − | 1913.37i | 0.527793 | − | 0.383464i | ||||
\(293\) | 888.434 | + | 2734.32i | 0.177143 | + | 0.545190i | 0.999725 | − | 0.0234567i | \(-0.00746718\pi\) |
−0.822582 | + | 0.568647i | \(0.807467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1728.78 | − | 1256.03i | −0.341198 | − | 0.247895i | ||||
\(296\) | −1398.11 | −0.274539 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3960.84 | 0.769951 | ||||||||
\(299\) | −6508.35 | − | 4728.59i | −1.25882 | − | 0.914587i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.8001 | + | 79.4046i | 0.00494051 | + | 0.0152053i | ||||
\(302\) | −4127.82 | + | 2999.03i | −0.786520 | + | 0.571440i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −104.240 | − | 320.818i | −0.0196664 | − | 0.0605269i | ||||
\(305\) | −173.927 | + | 535.292i | −0.0326525 | + | 0.100494i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 841.144 | 0.156373 | 0.0781867 | − | 0.996939i | \(-0.475087\pi\) | ||||
0.0781867 | + | 0.996939i | \(0.475087\pi\) | |||||||
\(308\) | 957.106 | + | 373.192i | 0.177066 | + | 0.0690409i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1674.08 | + | 1216.29i | 0.306715 | + | 0.222841i | ||||
\(311\) | 2835.09 | − | 8725.51i | 0.516924 | − | 1.59093i | −0.262831 | − | 0.964842i | \(-0.584656\pi\) |
0.779755 | − | 0.626085i | \(-0.215344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2356.13 | − | 1711.83i | 0.425483 | − | 0.309132i | −0.354357 | − | 0.935110i | \(-0.615300\pi\) |
0.779840 | + | 0.625978i | \(0.215300\pi\) | |||||||
\(314\) | 3662.93 | − | 2661.28i | 0.658316 | − | 0.478295i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 538.832 | − | 1658.35i | 0.0959229 | − | 0.295220i | ||||
\(317\) | −1479.67 | − | 1075.04i | −0.262165 | − | 0.190474i | 0.448936 | − | 0.893564i | \(-0.351803\pi\) |
−0.711101 | + | 0.703090i | \(0.751803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3631.01 | − | 4435.97i | 0.637297 | − | 0.778579i | ||||
\(320\) | −292.896 | −0.0511669 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −391.140 | + | 1203.81i | −0.0676937 | + | 0.208340i | ||||
\(323\) | 672.128 | + | 2068.60i | 0.115784 | + | 0.356346i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7532.87 | + | 5472.95i | −1.28569 | + | 0.934107i | ||||
\(326\) | 304.861 | + | 938.266i | 0.0517935 | + | 0.159404i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −594.517 | − | 431.942i | −0.100081 | − | 0.0727134i | ||||
\(329\) | −2072.78 | −0.347343 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6235.51 | −1.03545 | −0.517726 | − | 0.855547i | \(-0.673221\pi\) | ||||
−0.517726 | + | 0.855547i | \(0.673221\pi\) | |||||||
\(332\) | −2147.82 | − | 1560.48i | −0.355051 | − | 0.257960i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1450.23 | − | 4463.34i | −0.237584 | − | 0.731207i | ||||
\(335\) | −3239.55 | + | 2353.67i | −0.528346 | + | 0.383866i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 304.894 | + | 938.367i | 0.0492838 | + | 0.151680i | 0.972670 | − | 0.232193i | \(-0.0745901\pi\) |
−0.923386 | + | 0.383873i | \(0.874590\pi\) | |||||||
\(338\) | −3590.84 | + | 11051.5i | −0.577857 | + | 1.77846i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1888.56 | 0.301240 | ||||||||
\(341\) | −475.022 | + | 8234.24i | −0.0754367 | + | 1.30765i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3624.62 | − | 2633.44i | −0.570586 | − | 0.414555i | ||||
\(344\) | 29.3202 | − | 90.2384i | 0.00459547 | − | 0.0141434i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4792.54 | + | 3481.98i | −0.744649 | + | 0.541019i | ||||
\(347\) | 9289.28 | − | 6749.06i | 1.43710 | − | 1.04412i | 0.448465 | − | 0.893801i | \(-0.351971\pi\) |
0.988638 | − | 0.150316i | \(-0.0480290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −989.860 | + | 3046.48i | −0.151822 | + | 0.467261i | −0.997825 | − | 0.0659175i | \(-0.979003\pi\) |
0.846003 | + | 0.533179i | \(0.179003\pi\) | |||||||
\(350\) | 1185.21 | + | 861.109i | 0.181007 | + | 0.131509i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −630.676 | − | 982.442i | −0.0954976 | − | 0.148762i | ||||
\(353\) | 8669.58 | 1.30718 | 0.653591 | − | 0.756848i | \(-0.273262\pi\) | ||||
0.653591 | + | 0.756848i | \(0.273262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 157.344 | − | 484.255i | 0.0235238 | − | 0.0723989i | ||||
\(356\) | 1592.44 | + | 4901.03i | 0.237076 | + | 0.729646i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2414.95 | + | 1754.57i | −0.356520 | + | 0.259027i | ||||
\(359\) | −1327.01 | − | 4084.11i | −0.195089 | − | 0.600421i | −0.999976 | − | 0.00699304i | \(-0.997774\pi\) |
0.804887 | − | 0.593428i | \(-0.202226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5189.45 | + | 3770.35i | 0.756589 | + | 0.549694i | ||||
\(362\) | 3091.71 | 0.448885 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2519.66 | 0.362818 | ||||||||
\(365\) | −3013.09 | − | 2189.14i | −0.432088 | − | 0.313930i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2814.23 | + | 8661.31i | 0.400277 | + | 1.23193i | 0.924775 | + | 0.380514i | \(0.124253\pi\) |
−0.524498 | + | 0.851412i | \(0.675747\pi\) | |||||||
\(368\) | 1163.73 | − | 845.502i | 0.164847 | − | 0.119769i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 494.308 | + | 1521.32i | 0.0694536 | + | 0.213756i | ||||
\(371\) | −1092.80 | + | 3363.28i | −0.152925 | + | 0.470655i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7648.04 | 1.06166 | 0.530831 | − | 0.847477i | \(-0.321880\pi\) | ||||
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(374\) | 4066.53 | + | 6334.67i | 0.562233 | + | 0.875824i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1905.71 | + | 1384.58i | 0.261381 | + | 0.189905i | ||||
\(377\) | 4344.89 | − | 13372.2i | 0.593563 | − | 1.82680i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7525.63 | − | 5467.69i | 1.01996 | − | 0.741046i | 0.0536869 | − | 0.998558i | \(-0.482903\pi\) |
0.966275 | + | 0.257512i | \(0.0829027\pi\) | |||||||
\(380\) | −312.237 | + | 226.853i | −0.0421511 | + | 0.0306245i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 717.692 | − | 2208.83i | 0.0961265 | − | 0.295847i | ||||
\(383\) | 319.946 | + | 232.454i | 0.0426853 | + | 0.0310127i | 0.608923 | − | 0.793229i | \(-0.291602\pi\) |
−0.566238 | + | 0.824242i | \(0.691602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 67.6918 | − | 1173.40i | 0.00896077 | − | 0.155330i | ||||
\(386\) | 1434.45 | 0.189149 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −253.052 | + | 778.815i | −0.0331103 | + | 0.101903i | ||||
\(389\) | −745.903 | − | 2295.65i | −0.0972206 | − | 0.299214i | 0.890605 | − | 0.454777i | \(-0.150281\pi\) |
−0.987826 | + | 0.155563i | \(0.950281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7503.62 | + | 5451.70i | −0.970523 | + | 0.705126i | ||||
\(392\) | 725.436 | + | 2232.66i | 0.0934695 | + | 0.287670i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5870.96 | + | 4265.50i | 0.750697 | + | 0.545413i | ||||
\(395\) | −1995.01 | −0.254126 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4882.03 | 0.617185 | 0.308592 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308592 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(398\) | −2065.72 | − | 1500.83i | −0.260163 | − | 0.189020i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −514.479 | − | 1583.40i | −0.0643099 | − | 0.197926i | ||||
\(401\) | 1414.86 | − | 1027.95i | 0.176196 | − | 0.128014i | −0.496192 | − | 0.868213i | \(-0.665269\pi\) |
0.672388 | + | 0.740199i | \(0.265269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6251.38 | + | 19239.8i | 0.772713 | + | 2.37817i | ||||
\(404\) | 130.858 | − | 402.738i | 0.0161149 | − | 0.0495965i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2212.24 | −0.270423 | ||||||||
\(407\) | −4038.50 | + | 4933.80i | −0.491846 | + | 0.600883i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4019.59 | − | 2920.40i | −0.485956 | − | 0.353068i | 0.317671 | − | 0.948201i | \(-0.397099\pi\) |
−0.803627 | + | 0.595133i | \(0.797099\pi\) | |||||||
\(410\) | −259.814 | + | 799.626i | −0.0312959 | + | 0.0963188i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1560.33 | − | 1133.65i | 0.186583 | − | 0.135560i | ||||
\(413\) | −2659.19 | + | 1932.02i | −0.316829 | + | 0.230190i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −938.636 | + | 2888.82i | −0.111026 | + | 0.341703i | ||||
\(416\) | −2316.57 | − | 1683.09i | −0.273027 | − | 0.198365i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1433.24 | − | 558.844i | −0.167708 | − | 0.0653922i | ||||
\(419\) | 11763.3 | 1.37154 | 0.685770 | − | 0.727819i | \(-0.259466\pi\) | ||||
0.685770 | + | 0.727819i | \(0.259466\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1350.16 | + | 4155.37i | −0.156301 | + | 0.481046i | −0.998290 | − | 0.0584485i | \(-0.981385\pi\) |
0.841989 | + | 0.539495i | \(0.181385\pi\) | |||||||
\(422\) | −1995.92 | − | 6142.82i | −0.230237 | − | 0.708597i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3251.33 | − | 2362.23i | 0.372402 | − | 0.270566i | ||||
\(425\) | 3317.30 | + | 10209.6i | 0.378619 | + | 1.16527i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 700.409 | + | 508.877i | 0.0793798 | + | 0.0576728i | ||||
\(428\) | −1798.93 | −0.203165 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −108.557 | −0.0121746 | ||||||||
\(431\) | −2576.48 | − | 1871.92i | −0.287946 | − | 0.209205i | 0.434430 | − | 0.900706i | \(-0.356950\pi\) |
−0.722376 | + | 0.691501i | \(0.756950\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1711.52 | − | 5267.53i | −0.189955 | − | 0.584622i | 0.810043 | − | 0.586370i | \(-0.199444\pi\) |
−0.999998 | + | 0.00174800i | \(0.999444\pi\) | |||||||
\(434\) | 2575.06 | − | 1870.89i | 0.284808 | − | 0.206925i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1501.65 | − | 4621.59i | −0.164944 | − | 0.507647i | ||||
\(437\) | 585.720 | − | 1802.66i | 0.0641163 | − | 0.197330i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8450.31 | 0.918704 | 0.459352 | − | 0.888254i | \(-0.348082\pi\) | ||||
0.459352 | + | 0.888254i | \(0.348082\pi\) | |||||||
\(440\) | −846.045 | + | 1033.60i | −0.0916673 | + | 0.111989i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14937.0 | + | 10852.3i | 1.60742 | + | 1.16786i | ||||
\(443\) | 490.145 | − | 1508.51i | 0.0525677 | − | 0.161787i | −0.921326 | − | 0.388791i | \(-0.872893\pi\) |
0.973894 | + | 0.227004i | \(0.0728930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4769.94 | − | 3465.56i | 0.508127 | − | 0.369176i | ||||
\(446\) | −5318.49 | + | 3864.11i | −0.564659 | + | 0.410249i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −139.222 | + | 428.480i | −0.0146821 | + | 0.0451870i | ||||
\(449\) | −11534.2 | − | 8380.07i | −1.21232 | − | 0.880802i | −0.216880 | − | 0.976198i | \(-0.569588\pi\) |
−0.995439 | + | 0.0953968i | \(0.969588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3241.57 | + | 850.310i | −0.338447 | + | 0.0887795i | ||||
\(452\) | 6259.31 | 0.651357 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3887.79 | + | 11965.4i | −0.401901 | + | 1.23693i | ||||
\(455\) | −890.836 | − | 2741.71i | −0.0917869 | − | 0.282491i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −710.920 | + | 516.514i | −0.0727690 | + | 0.0528698i | −0.623575 | − | 0.781764i | \(-0.714320\pi\) |
0.550806 | + | 0.834633i | \(0.314320\pi\) | |||||||
\(458\) | 659.091 | + | 2028.47i | 0.0672430 | + | 0.206953i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1331.46 | − | 967.361i | −0.134956 | − | 0.0980509i | ||||
\(461\) | 4936.37 | 0.498719 | 0.249360 | − | 0.968411i | \(-0.419780\pi\) | ||||
0.249360 | + | 0.968411i | \(0.419780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16955.6 | 1.70193 | 0.850964 | − | 0.525224i | \(-0.176019\pi\) | ||||
0.850964 | + | 0.525224i | \(0.176019\pi\) | |||||||
\(464\) | 2033.93 | + | 1477.74i | 0.203498 | + | 0.147850i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2280.26 | − | 7017.91i | −0.226676 | − | 0.697636i | ||||
\(467\) | −7796.52 | + | 5664.50i | −0.772548 | + | 0.561289i | −0.902733 | − | 0.430201i | \(-0.858443\pi\) |
0.130185 | + | 0.991490i | \(0.458443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1903.36 | + | 5857.93i | 0.187396 | + | 0.576746i | ||||
\(470\) | 832.828 | − | 2563.18i | 0.0817351 | − | 0.251555i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3735.41 | 0.364271 | ||||||||
\(473\) | −233.750 | − | 364.126i | −0.0227227 | − | 0.0353965i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1774.82 | − | 1289.49i | −0.171441 | − | 0.124559i | ||||
\(476\) | 897.685 | − | 2762.79i | 0.0864397 | − | 0.266034i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11538.4 | + | 8383.14i | −1.10409 | + | 0.802167i | ||||
\(479\) | −10129.9 | + | 7359.82i | −0.966279 | + | 0.702043i | −0.954601 | − | 0.297889i | \(-0.903718\pi\) |
−0.0116787 | + | 0.999932i | \(0.503718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4832.49 | + | 14872.9i | −0.458093 | + | 1.40986i | ||||
\(482\) | −5194.87 | − | 3774.29i | −0.490912 | − | 0.356669i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5288.68 | − | 612.232i | −0.496683 | − | 0.0574973i | ||||
\(485\) | 936.919 | 0.0877181 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3886.11 | − | 11960.2i | 0.361594 | − | 1.11287i | −0.590492 | − | 0.807043i | \(-0.701066\pi\) |
0.952086 | − | 0.305829i | \(-0.0989337\pi\) | |||||||
\(488\) | −304.034 | − | 935.721i | −0.0282028 | − | 0.0867994i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2172.94 | − | 1578.74i | 0.200334 | − | 0.145551i | ||||
\(491\) | −609.139 | − | 1874.74i | −0.0559879 | − | 0.172313i | 0.919152 | − | 0.393903i | \(-0.128875\pi\) |
−0.975140 | + | 0.221590i | \(0.928875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13114.6 | − | 9528.29i | −1.19807 | − | 0.870451i | ||||
\(494\) | −3773.11 | −0.343644 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3617.23 | −0.327456 | ||||||||
\(497\) | −633.630 | − | 460.359i | −0.0571875 | − | 0.0415491i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2278.94 | − | 7013.86i | −0.204448 | − | 0.629225i | −0.999736 | − | 0.0229933i | \(-0.992680\pi\) |
0.795288 | − | 0.606232i | \(-0.207320\pi\) | |||||||
\(500\) | −3392.29 | + | 2464.64i | −0.303415 | + | 0.220444i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4224.20 | − | 13000.8i | −0.375568 | − | 1.15588i | ||||
\(503\) | −3766.54 | + | 11592.2i | −0.333880 | + | 1.02758i | 0.633391 | + | 0.773832i | \(0.281662\pi\) |
−0.967271 | + | 0.253745i | \(0.918338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −484.497 | −0.0426927 | ||||||||
\(506\) | 377.802 | − | 6548.98i | 0.0331924 | − | 0.575371i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7934.70 | + | 5764.89i | 0.693002 | + | 0.503496i | ||||
\(509\) | −2283.20 | + | 7026.95i | −0.198823 | + | 0.611914i | 0.801088 | + | 0.598547i | \(0.204255\pi\) |
−0.999911 | + | 0.0133671i | \(0.995745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4634.70 | + | 3367.31i | −0.401227 | + | 0.291509i | ||||
\(512\) | 414.217 | − | 300.946i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3415.97 | − | 10513.3i | 0.293136 | − | 0.902181i | ||||
\(515\) | −1785.22 | − | 1297.04i | −0.152750 | − | 0.110979i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10390.8 | − | 2725.65i | 0.883918 | − | 0.231864i | ||||
\(518\) | 2460.51 | 0.208704 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1012.38 | + | 3115.79i | −0.0853766 | + | 0.262762i | ||||
\(521\) | −4180.77 | − | 12867.1i | −0.351560 | − | 1.08199i | −0.957977 | − | 0.286844i | \(-0.907394\pi\) |
0.606417 | − | 0.795147i | \(-0.292606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15309.4 | + | 11123.0i | −1.27999 | + | 0.929967i | −0.999553 | − | 0.0299056i | \(-0.990479\pi\) |
−0.280437 | + | 0.959872i | \(0.590479\pi\) | |||||||
\(524\) | −3041.56 | − | 9360.96i | −0.253571 | − | 0.780411i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5618.55 | − | 4082.11i | −0.465742 | − | 0.338381i | ||||
\(527\) | 23323.5 | 1.92787 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4084.39 | −0.335694 | ||||||||
\(530\) | −3719.93 | − | 2702.69i | −0.304874 | − | 0.221504i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 183.450 | + | 564.602i | 0.0149503 | + | 0.0460124i | ||||
\(533\) | −6649.85 | + | 4831.40i | −0.540407 | + | 0.392629i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 636.021 | + | 1957.47i | 0.0513973 | + | 0.158185i | ||||
\(536\) | 2163.05 | − | 6657.18i | 0.174309 | − | 0.536467i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8790.36 | 0.704423 | ||||||||
\(539\) | 9974.31 | + | 3889.15i | 0.797076 | + | 0.310793i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10238.2 | − | 7438.52i | −0.813635 | − | 0.591140i | 0.101247 | − | 0.994861i | \(-0.467717\pi\) |
−0.914882 | + | 0.403721i | \(0.867717\pi\) | |||||||
\(542\) | 3649.40 | − | 11231.7i | 0.289216 | − | 0.890117i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2670.82 | + | 1940.47i | −0.210497 | + | 0.152935i | ||||
\(545\) | −4497.97 | + | 3267.97i | −0.353527 | + | 0.256852i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7240.20 | − | 22283.0i | 0.565939 | − | 1.74178i | −0.0992069 | − | 0.995067i | \(-0.531631\pi\) |
0.665146 | − | 0.746714i | \(-0.268369\pi\) | |||||||
\(548\) | −2023.99 | − | 1470.52i | −0.157775 | − | 0.114630i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7073.78 | − | 2758.19i | −0.548413 | − | 0.213835i | ||||
\(551\) | 3312.77 | 0.256132 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −948.281 | + | 2918.51i | −0.0729205 | + | 0.224426i | ||||
\(554\) | 142.049 | + | 437.182i | 0.0108936 | + | 0.0335272i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3787.52 | + | 2751.80i | −0.288897 | + | 0.209896i | ||||
\(557\) | 7027.95 | + | 21629.8i | 0.534621 | + | 1.64539i | 0.744467 | + | 0.667659i | \(0.232704\pi\) |
−0.209846 | + | 0.977734i | \(0.567296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −858.599 | − | 623.808i | −0.0649640 | − | 0.0471991i | ||||
\(560\) | 515.464 | 0.0388970 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7980.30 | 0.598983 | ||||||||
\(563\) | −1939.45 | − | 1409.09i | −0.145183 | − | 0.105482i | 0.512823 | − | 0.858494i | \(-0.328600\pi\) |
−0.658006 | + | 0.753013i | \(0.728600\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2213.01 | − | 6810.94i | −0.164782 | − | 0.507148i | ||||
\(566\) | 3280.91 | − | 2383.72i | 0.243652 | − | 0.177024i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 275.047 | + | 846.506i | 0.0203181 | + | 0.0625328i | ||||
\(569\) | −3845.29 | + | 11834.6i | −0.283309 | + | 0.871936i | 0.703591 | + | 0.710605i | \(0.251579\pi\) |
−0.986900 | + | 0.161331i | \(0.948421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25337.2 | −1.85697 | −0.928485 | − | 0.371370i | \(-0.878888\pi\) | ||||
−0.928485 | + | 0.371370i | \(0.878888\pi\) | |||||||
\(572\) | −12631.0 | + | 3313.28i | −0.923299 | + | 0.242194i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1046.28 | + | 760.168i | 0.0760817 | + | 0.0552766i | ||||
\(575\) | 2890.84 | − | 8897.08i | 0.209663 | − | 0.645277i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13308.7 | − | 9669.33i | 0.960222 | − | 0.697642i | 0.00702003 | − | 0.999975i | \(-0.497765\pi\) |
0.953202 | + | 0.302333i | \(0.0977654\pi\) | |||||||
\(578\) | 9271.77 | − | 6736.34i | 0.667223 | − | 0.484766i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 888.863 | − | 2735.64i | 0.0636346 | − | 0.195847i | ||||
\(581\) | 3779.92 | + | 2746.27i | 0.269910 | + | 0.196101i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1055.53 | − | 18297.0i | 0.0749840 | − | 1.29980i | ||||
\(584\) | 6510.44 | 0.461308 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1776.87 | + | 5468.64i | −0.125259 | + | 0.385508i | ||||
\(587\) | 4916.48 | + | 15131.4i | 0.345698 | + | 1.06395i | 0.961209 | + | 0.275821i | \(0.0889498\pi\) |
−0.615511 | + | 0.788129i | \(0.711050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3856.08 | + | 2801.60i | −0.269757 | + | 0.195990i | ||||
\(590\) | −1320.67 | − | 4064.61i | −0.0921545 | − | 0.283622i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2262.19 | − | 1643.58i | −0.157053 | − | 0.114106i | ||||
\(593\) | −26361.5 | −1.82552 | −0.912762 | − | 0.408492i | \(-0.866055\pi\) | ||||
−0.912762 | + | 0.408492i | \(0.866055\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3323.65 | −0.229002 | ||||||||
\(596\) | 6408.78 | + | 4656.25i | 0.440459 | + | 0.320012i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4971.94 | − | 15302.1i | −0.339996 | − | 1.04640i | ||||
\(599\) | 12603.2 | − | 9156.74i | 0.859685 | − | 0.624598i | −0.0681140 | − | 0.997678i | \(-0.521698\pi\) |
0.927799 | + | 0.373080i | \(0.121698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 818.084 | + | 2517.80i | 0.0555247 | + | 0.170887i | 0.974973 | − | 0.222324i | \(-0.0713642\pi\) |
−0.919448 | + | 0.393211i | \(0.871364\pi\) | |||||||
\(602\) | −51.6002 | + | 158.809i | −0.00349347 | + | 0.0107518i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10204.5 | −0.687444 | ||||||||
\(605\) | 1203.65 | + | 5971.22i | 0.0808849 | + | 0.401264i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14232.0 | − | 10340.2i | −0.951663 | − | 0.691424i | −0.000463413 | − | 1.00000i | \(-0.500148\pi\) |
−0.951200 | + | 0.308576i | \(0.900148\pi\) | |||||||
\(608\) | 208.480 | − | 641.636i | 0.0139062 | − | 0.0427990i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −910.692 | + | 661.657i | −0.0604473 | + | 0.0439175i | ||||
\(611\) | 21315.9 | − | 15486.9i | 1.41137 | − | 1.02542i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4092.77 | + | 12596.3i | −0.269666 | + | 0.829948i | 0.720915 | + | 0.693023i | \(0.243722\pi\) |
−0.990582 | + | 0.136924i | \(0.956278\pi\) | |||||||
\(614\) | 1361.00 | + | 988.825i | 0.0894552 | + | 0.0649930i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1109.92 | + | 1728.98i | 0.0725971 | + | 0.113089i | ||||
\(617\) | −20902.5 | −1.36386 | −0.681930 | − | 0.731417i | \(-0.738859\pi\) | ||||
−0.681930 | + | 0.731417i | \(0.738859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2153.70 | − | 6628.40i | 0.139846 | − | 0.430401i | −0.856467 | − | 0.516202i | \(-0.827345\pi\) |
0.996312 | + | 0.0858018i | \(0.0273452\pi\) | |||||||
\(620\) | 1278.89 | + | 3936.01i | 0.0828409 | + | 0.254958i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14844.7 | − | 10785.3i | 0.956944 | − | 0.695261i | ||||
\(623\) | −2802.51 | − | 8625.24i | −0.180225 | − | 0.554676i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6641.64 | − | 4825.43i | −0.425065 | − | 0.308828i | ||||
\(626\) | 5824.67 | 0.371886 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9055.27 | 0.575390 | ||||||||
\(629\) | 14586.3 | + | 10597.6i | 0.924635 | + | 0.671787i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9423.94 | + | 29003.9i | 0.594550 | + | 1.82984i | 0.556954 | + | 0.830543i | \(0.311970\pi\) |
0.0375960 | + | 0.999293i | \(0.488030\pi\) | |||||||
\(632\) | 2821.36 | − | 2049.84i | 0.177575 | − | 0.129016i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1130.37 | − | 3478.91i | −0.0708085 | − | 0.217926i | ||||
\(635\) | 3467.60 | − | 10672.2i | 0.216705 | − | 0.666949i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26258.1 | 1.63326 | ||||||||
\(638\) | 11089.9 | − | 2909.04i | 0.688172 | − | 0.180517i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −473.916 | − | 344.320i | −0.0292706 | − | 0.0212663i | ||||
\(641\) | −4499.66 | + | 13848.5i | −0.277264 | + | 0.853330i | 0.711348 | + | 0.702840i | \(0.248085\pi\) |
−0.988612 | + | 0.150490i | \(0.951915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15693.4 | − | 11401.9i | 0.962497 | − | 0.699295i | 0.00876768 | − | 0.999962i | \(-0.497209\pi\) |
0.953729 | + | 0.300667i | \(0.0972091\pi\) | |||||||
\(644\) | −2048.04 | + | 1487.98i | −0.125317 | + | 0.0910479i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1344.26 | + | 4137.20i | −0.0818716 | + | 0.251975i | ||||
\(647\) | 24183.7 | + | 17570.5i | 1.46949 | + | 1.06765i | 0.980761 | + | 0.195211i | \(0.0625392\pi\) |
0.488729 | + | 0.872436i | \(0.337461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10789.9 | − | 13181.9i | 0.652605 | − | 0.797280i | ||||
\(650\) | −18622.3 | −1.12373 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −609.722 | + | 1876.53i | −0.0366236 | + | 0.112716i | ||||
\(653\) | 6980.91 | + | 21485.0i | 0.418352 | + | 1.28756i | 0.909218 | + | 0.416321i | \(0.136681\pi\) |
−0.490865 | + | 0.871236i | \(0.663319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9110.57 | + | 6619.22i | −0.543480 | + | 0.394861i | ||||
\(656\) | −454.171 | − | 1397.79i | −0.0270311 | − | 0.0831931i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3353.83 | − | 2436.70i | −0.198702 | − | 0.144365i | ||||
\(659\) | −12824.3 | −0.758061 | −0.379030 | − | 0.925384i | \(-0.623742\pi\) | ||||
−0.379030 | + | 0.925384i | \(0.623742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28829.4 | −1.69642 | −0.848209 | − | 0.529662i | \(-0.822319\pi\) | ||||
−0.848209 | + | 0.529662i | \(0.822319\pi\) | |||||||
\(662\) | −10089.3 | − | 7330.28i | −0.592342 | − | 0.430361i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1640.79 | − | 5049.83i | −0.0958961 | − | 0.295138i | ||||
\(665\) | 549.500 | − | 399.235i | 0.0320432 | − | 0.0232807i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4365.33 | + | 13435.1i | 0.253413 | + | 0.779924i | ||||
\(668\) | 2900.46 | − | 8926.68i | 0.167997 | − | 0.517042i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8008.62 | −0.461791 | ||||||||
\(671\) | −4180.29 | − | 1629.97i | −0.240504 | − | 0.0937766i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8198.04 | − | 5956.22i | −0.469556 | − | 0.341152i | 0.327712 | − | 0.944778i | \(-0.393722\pi\) |
−0.797268 | + | 0.603625i | \(0.793722\pi\) | |||||||
\(674\) | −609.788 | + | 1876.73i | −0.0348489 | + | 0.107254i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18801.9 | + | 13660.3i | −1.06975 | + | 0.777216i | ||||
\(677\) | −4086.40 | + | 2968.94i | −0.231984 | + | 0.168546i | −0.697704 | − | 0.716386i | \(-0.745795\pi\) |
0.465721 | + | 0.884932i | \(0.345795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 445.343 | − | 1370.62i | 0.0251704 | − | 0.0774664i | ||||
\(680\) | 3055.76 | + | 2220.14i | 0.172328 | + | 0.125204i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10448.5 | + | 12764.9i | −0.586649 | + | 0.716703i | ||||
\(683\) | −5966.92 | −0.334287 | −0.167144 | − | 0.985933i | \(-0.553454\pi\) | ||||
−0.167144 | + | 0.985933i | \(0.553454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −884.520 | + | 2722.27i | −0.0493369 | + | 0.151843i | ||||
\(686\) | −2768.96 | − | 8521.99i | −0.154110 | − | 0.474302i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 153.523 | − | 111.541i | 0.00850727 | − | 0.00618089i | ||||
\(689\) | −13891.0 | − | 42752.0i | −0.768076 | − | 2.36389i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4875.68 | − | 3542.39i | −0.268422 | − | 0.195020i | 0.445430 | − | 0.895317i | \(-0.353051\pi\) |
−0.713852 | + | 0.700297i | \(0.753051\pi\) | |||||||
\(692\) | −11847.8 | −0.650847 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22964.4 | 1.25607 | ||||||||
\(695\) | 4333.40 | + | 3148.40i | 0.236511 | + | 0.171836i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2928.44 | + | 9012.82i | 0.159143 | + | 0.489792i | ||||
\(698\) | −5182.97 | + | 3765.65i | −0.281058 | + | 0.204201i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 905.424 | + | 2786.61i | 0.0488883 | + | 0.150463i | ||||
\(701\) | −2956.72 | + | 9099.85i | −0.159306 | + | 0.490295i | −0.998572 | − | 0.0534275i | \(-0.982985\pi\) |
0.839265 | + | 0.543722i | \(0.182985\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3684.54 | −0.197674 | ||||||||
\(704\) | 134.474 | − | 2331.03i | 0.00719912 | − | 0.124793i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14027.7 | + | 10191.7i | 0.747789 | + | 0.543300i | ||||
\(707\) | −230.294 | + | 708.773i | −0.0122505 | + | 0.0377032i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4172.92 | − | 3031.80i | 0.221040 | − | 0.160595i | −0.471755 | − | 0.881730i | \(-0.656379\pi\) |
0.692795 | + | 0.721135i | \(0.256379\pi\) | |||||||
\(710\) | 823.864 | − | 598.572i | 0.0435480 | − | 0.0316395i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3184.88 | + | 9802.06i | −0.167638 | + | 0.515938i | ||||
\(713\) | −16443.3 | − | 11946.8i | −0.863684 | − | 0.627503i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8071.01 | + | 12572.7i | 0.422152 | + | 0.657611i | ||||
\(716\) | −5970.09 | −0.311610 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2654.02 | − | 8168.23i | 0.137949 | − | 0.424562i | ||||
\(719\) | −2171.59 | − | 6683.47i | −0.112638 | − | 0.346664i | 0.878809 | − | 0.477173i | \(-0.158339\pi\) |
−0.991447 | + | 0.130510i | \(0.958339\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2746.01 | + | 1995.09i | −0.141840 | + | 0.103053i | ||||
\(722\) | 3964.38 | + | 12201.1i | 0.204348 | + | 0.628918i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5002.49 | + | 3634.52i | 0.256790 | + | 0.186569i | ||||
\(725\) | 16350.2 | 0.837562 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9911.22 | 0.505621 | 0.252811 | − | 0.967516i | \(-0.418645\pi\) | ||||
0.252811 | + | 0.967516i | \(0.418645\pi\) | |||||||
\(728\) | 4076.89 | + | 2962.03i | 0.207554 | + | 0.150797i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2301.79 | − | 7084.19i | −0.116703 | − | 0.359175i | ||||
\(731\) | −989.898 | + | 719.203i | −0.0500858 | + | 0.0363894i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4564.03 | + | 14046.6i | 0.229981 | + | 0.707810i | 0.997748 | + | 0.0670797i | \(0.0213682\pi\) |
−0.767766 | + | 0.640730i | \(0.778632\pi\) | |||||||
\(734\) | −5628.46 | + | 17322.6i | −0.283039 | + | 0.871103i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2876.91 | 0.144082 | ||||||||
\(737\) | −17244.5 | − | 26862.7i | −0.861884 | − | 1.34261i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24816.4 | + | 18030.2i | 1.23530 | + | 0.897497i | 0.997276 | − | 0.0737622i | \(-0.0235006\pi\) |
0.238023 | + | 0.971259i | \(0.423501\pi\) | |||||||
\(740\) | −988.616 | + | 3042.65i | −0.0491111 | + | 0.151149i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5721.96 | + | 4157.25i | −0.283099 | + | 0.205684i | ||||
\(743\) | −4848.48 | + | 3522.63i | −0.239399 | + | 0.173934i | −0.701015 | − | 0.713146i | \(-0.747270\pi\) |
0.461617 | + | 0.887080i | \(0.347270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2800.75 | − | 8619.81i | 0.137733 | − | 0.423900i | ||||
\(746\) | 12374.8 | + | 8990.80i | 0.607336 | + | 0.441256i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −867.073 | + | 15030.2i | −0.0423841 | + | 0.734705i | ||||
\(749\) | 3165.91 | 0.154446 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −819.025 | + | 2520.70i | −0.0397958 | + | 0.122479i | −0.968981 | − | 0.247136i | \(-0.920510\pi\) |
0.929185 | + | 0.369615i | \(0.120510\pi\) | |||||||
\(752\) | 1455.83 | + | 4480.59i | 0.0705967 | + | 0.217274i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22750.1 | − | 16528.9i | 1.09882 | − | 0.798340i | ||||
\(755\) | 3607.85 | + | 11103.8i | 0.173912 | + | 0.535245i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24133.2 | + | 17533.8i | 1.15870 | + | 0.841847i | 0.989613 | − | 0.143754i | \(-0.0459174\pi\) |
0.169089 | + | 0.985601i | \(0.445917\pi\) | |||||||
\(758\) | 18604.4 | 0.891479 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −771.891 | −0.0368414 | ||||||||
\(761\) | −16777.4 | − | 12189.5i | −0.799186 | − | 0.580643i | 0.111489 | − | 0.993766i | \(-0.464438\pi\) |
−0.910675 | + | 0.413123i | \(0.864438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2642.72 | + | 8133.46i | 0.125391 | + | 0.385912i | ||||
\(764\) | 3757.88 | − | 2730.26i | 0.177952 | − | 0.129290i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 244.417 | + | 752.238i | 0.0115289 | + | 0.0354823i | ||||
\(767\) | 12911.2 | − | 39736.7i | 0.607820 | − | 1.87068i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20601.9 | 0.966092 | 0.483046 | − | 0.875595i | \(-0.339530\pi\) | ||||
0.483046 | + | 0.875595i | \(0.339530\pi\) | |||||||
\(770\) | 1488.94 | − | 1819.02i | 0.0696853 | − | 0.0851338i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2320.99 | + | 1686.30i | 0.108205 | + | 0.0786155i | ||||
\(773\) | −8697.88 | + | 26769.3i | −0.404710 | + | 1.24557i | 0.516426 | + | 0.856332i | \(0.327262\pi\) |
−0.921137 | + | 0.389239i | \(0.872738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19031.8 | + | 13827.4i | −0.882117 | + | 0.640896i | ||||
\(776\) | −1325.00 | + | 962.668i | −0.0612947 | + | 0.0445332i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1491.81 | − | 4591.31i | 0.0687453 | − | 0.211576i | ||||
\(779\) | −1566.77 | − | 1138.33i | −0.0720610 | − | 0.0523554i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3781.73 | + | 1474.56i | 0.173266 | + | 0.0675594i | ||||
\(782\) | −18550.0 | −0.848268 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1450.87 | + | 4465.32i | −0.0660929 | + | 0.203413i | ||||
\(785\) | −3201.53 | − | 9853.30i | −0.145564 | − | 0.447999i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4186.83 | − | 3041.91i | 0.189637 | − | 0.137779i | −0.488916 | − | 0.872331i | \(-0.662607\pi\) |
0.678553 | + | 0.734552i | \(0.262607\pi\) | |||||||
\(788\) | 4485.01 | + | 13803.5i | 0.202756 | + | 0.624020i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3227.99 | − | 2345.27i | −0.145376 | − | 0.105622i | ||||
\(791\) | −11015.7 | −0.495160 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11004.9 | −0.492808 | ||||||||
\(794\) | 7899.30 | + | 5739.18i | 0.353067 | + | 0.256519i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1578.07 | − | 4856.79i | −0.0702677 | − | 0.216262i | ||||
\(797\) | 1776.57 | − | 1290.76i | 0.0789578 | − | 0.0573662i | −0.547606 | − | 0.836736i | \(-0.684461\pi\) |
0.626564 | + | 0.779370i | \(0.284461\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9387.04 | − | 28890.3i | −0.415632 | − | 1.27918i | ||||
\(800\) | 1028.96 | − | 3166.81i | 0.0454740 | − | 0.139954i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3497.72 | 0.154001 | ||||||||
\(803\) | 18805.7 | − | 22974.7i | 0.826449 | − | 1.00966i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2343.21 | + | 1702.44i | 0.102593 | + | 0.0745382i | ||||
\(806\) | −12502.8 | + | 38479.5i | −0.546390 | + | 1.68162i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 685.179 | − | 497.812i | 0.0298323 | − | 0.0216745i | ||||
\(809\) | −25063.3 | + | 18209.5i | −1.08922 | + | 0.791364i | −0.979267 | − | 0.202573i | \(-0.935070\pi\) |
−0.109952 | + | 0.993937i | \(0.535070\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3139.90 | + | 9663.62i | −0.135952 | + | 0.418416i | −0.995737 | − | 0.0922396i | \(-0.970597\pi\) |
0.859785 | + | 0.510656i | \(0.170597\pi\) | |||||||
\(812\) | −3579.48 | − | 2600.65i | −0.154699 | − | 0.112395i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12334.5 | + | 3235.50i | −0.531109 | + | 0.139317i | ||||
\(815\) | 2257.48 | 0.0970258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 77.2698 | − | 237.812i | 0.00330885 | − | 0.0101836i | ||||
\(818\) | −3070.69 | − | 9450.62i | −0.131252 | − | 0.403953i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1360.41 | + | 988.392i | −0.0579359 | + | 0.0420929i | ||||
\(821\) | 664.158 | + | 2044.07i | 0.0282330 | + | 0.0868921i | 0.964180 | − | 0.265248i | \(-0.0854539\pi\) |
−0.935947 | + | 0.352140i | \(0.885454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35937.5 | + | 26110.1i | 1.52212 | + | 1.10588i | 0.960425 | + | 0.278538i | \(0.0898499\pi\) |
0.561693 | + | 0.827345i | \(0.310150\pi\) | |||||||
\(824\) | 3857.36 | 0.163079 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6573.89 | −0.276919 | ||||||||
\(827\) | 32751.9 | + | 23795.7i | 1.37714 | + | 1.00055i | 0.997141 | + | 0.0755668i | \(0.0240766\pi\) |
0.380002 | + | 0.924986i | \(0.375923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6726.09 | + | 20700.8i | 0.281794 | + | 0.867271i | 0.987341 | + | 0.158609i | \(0.0507010\pi\) |
−0.705548 | + | 0.708662i | \(0.749299\pi\) | |||||||
\(830\) | −4914.76 | + | 3570.78i | −0.205535 | + | 0.149330i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1769.70 | − | 5446.58i | −0.0737420 | − | 0.226954i | ||||
\(833\) | 9355.06 | − | 28791.9i | 0.389116 | − | 1.19758i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10738.9 | −0.445070 | ||||||||
\(836\) | −1662.07 | − | 2589.10i | −0.0687605 | − | 0.107112i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19033.4 | + | 13828.6i | 0.784605 | + | 0.570049i | ||||
\(839\) | −7886.61 | + | 24272.5i | −0.324525 | + | 0.998784i | 0.647130 | + | 0.762379i | \(0.275969\pi\) |
−0.971655 | + | 0.236404i | \(0.924031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −243.344 | + | 176.800i | −0.00997761 | + | 0.00724916i | ||||
\(842\) | −7069.54 | + | 5136.32i | −0.289350 | + | 0.210225i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3991.85 | − | 12285.6i | 0.162802 | − | 0.501053i | ||||
\(845\) | 21511.7 | + | 15629.2i | 0.875769 | + | 0.636284i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9307.46 | + | 1077.46i | 0.377578 | + | 0.0437094i | ||||
\(848\) | 8037.72 | 0.325491 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6634.61 | + | 20419.2i | −0.267724 | + | 0.823969i | ||||
\(851\) | −4855.23 | − | 14942.9i | −0.195576 | − | 0.601920i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16902.3 | − | 12280.2i | 0.678456 | − | 0.492927i | −0.194389 | − | 0.980925i | \(-0.562272\pi\) |
0.872845 | + | 0.487997i | \(0.162272\pi\) | |||||||
\(854\) | 535.065 | + | 1646.76i | 0.0214397 | + | 0.0659847i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2910.73 | − | 2114.77i | −0.116223 | − | 0.0844409i | ||||
\(857\) | 4786.08 | 0.190769 | 0.0953847 | − | 0.995440i | \(-0.469592\pi\) | ||||
0.0953847 | + | 0.995440i | \(0.469592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13013.8 | −0.516911 | −0.258455 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258455 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(860\) | −175.649 | − | 127.617i | −0.00696465 | − | 0.00506011i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1968.26 | − | 6057.67i | −0.0777716 | − | 0.239356i | ||||
\(863\) | 40121.7 | − | 29150.1i | 1.58257 | − | 1.14980i | 0.668896 | − | 0.743356i | \(-0.266767\pi\) |
0.913674 | − | 0.406449i | \(-0.133233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4188.84 | + | 12891.9i | 0.164653 | + | 0.506750i | ||||
\(866\) | 3423.05 | − | 10535.1i | 0.134319 | − | 0.413390i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6365.90 | 0.248932 | ||||||||
\(869\) | 915.944 | − | 15877.4i | 0.0357552 | − | 0.619796i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −63341.6 | − | 46020.3i | −2.46412 | − | 1.79029i | ||||
\(872\) | 3003.29 | − | 9243.18i | 0.116633 | − | 0.358961i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3066.87 | − | 2228.21i | 0.118694 | − | 0.0862362i | ||||
\(875\) | 5970.03 | − | 4337.48i | 0.230656 | − | 0.167581i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7469.00 | + | 22987.2i | −0.287583 | + | 0.885089i | 0.698030 | + | 0.716069i | \(0.254060\pi\) |
−0.985613 | + | 0.169020i | \(0.945940\pi\) | |||||||
\(878\) | 13672.9 | + | 9933.93i | 0.525555 | + | 0.381838i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2584.00 | + | 677.821i | −0.0989849 | + | 0.0259651i | ||||
\(881\) | −31630.8 | −1.20961 | −0.604806 | − | 0.796373i | \(-0.706749\pi\) | ||||
−0.604806 | + | 0.796373i | \(0.706749\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6918.75 | − | 21293.7i | 0.263686 | − | 0.811541i | −0.728307 | − | 0.685251i | \(-0.759693\pi\) |
0.991993 | − | 0.126291i | \(-0.0403073\pi\) | |||||||
\(884\) | 11410.8 | + | 35118.9i | 0.434149 | + | 1.33617i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2566.43 | − | 1864.62i | 0.0973150 | − | 0.0707035i | ||||
\(887\) | −4958.10 | − | 15259.5i | −0.187685 | − | 0.577636i | 0.812299 | − | 0.583241i | \(-0.198216\pi\) |
−0.999984 | + | 0.00560528i | \(0.998216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13964.1 | − | 10145.5i | −0.526819 | − | 0.382757i | ||||
\(890\) | 11791.9 | 0.444120 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13148.0 | −0.493530 | ||||||||
\(893\) | 5022.25 | + | 3648.88i | 0.188201 | + | 0.136736i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2110.75 | + | 6496.23i | 0.0788321 | + | 0.242620i | ||||
\(896\) | −728.973 | + | 529.630i | −0.0271800 | + | 0.0197474i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8811.33 | − | 27118.5i | −0.327436 | − | 1.00775i | ||||
\(899\) | 10977.3 | − | 33784.8i | 0.407247 | − | 1.25338i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51826.3 | −1.91630 | ||||||||
\(902\) | −6244.57 | − | 2434.87i | −0.230512 | − | 0.0898804i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10127.8 | + | 7358.26i | 0.372616 | + | 0.270721i | ||||
\(905\) | 2186.17 | − | 6728.35i | 0.0802993 | − | 0.247136i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41220.1 | − | 29948.1i | 1.50903 | − | 1.09637i | 0.542425 | − | 0.840104i | \(-0.317506\pi\) |
0.966605 | − | 0.256271i | \(-0.0824939\pi\) | |||||||
\(908\) | −20356.8 | + | 14790.0i | −0.744012 | + | 0.540556i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1781.67 | − | 5483.42i | 0.0649031 | − | 0.199751i | ||||
\(911\) | 6331.44 | + | 4600.06i | 0.230264 | + | 0.167296i | 0.696935 | − | 0.717135i | \(-0.254547\pi\) |
−0.466671 | + | 0.884431i | \(0.654547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22559.9 | − | 8796.49i | −0.817769 | − | 0.318862i | ||||
\(914\) | −1757.49 | −0.0636024 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1318.18 | + | 4056.95i | −0.0475480 | + | 0.146338i | ||||
\(917\) | 5352.79 | + | 16474.2i | 0.192764 | + | 0.593267i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9538.92 | + | 6930.43i | −0.342394 | + | 0.248764i | −0.745671 | − | 0.666314i | \(-0.767871\pi\) |
0.403277 | + | 0.915078i | \(0.367871\pi\) | |||||||
\(920\) | −1017.14 | − | 3130.45i | −0.0364502 | − | 0.112182i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7987.21 | + | 5803.05i | 0.285298 | + | 0.207281i | ||||
\(923\) | 9955.69 | 0.355033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18185.1 | −0.646404 | ||||||||
\(926\) | 27434.7 | + | 19932.5i | 0.973607 | + | 0.707367i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1553.79 | + | 4782.06i | 0.0549628 | + | 0.169158i | ||||
\(929\) | −23048.6 | + | 16745.8i | −0.813994 | + | 0.591401i | −0.914986 | − | 0.403486i | \(-0.867798\pi\) |
0.100992 | + | 0.994887i | \(0.467798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1911.79 | + | 5883.90i | 0.0673002 | + | 0.207129i | ||||
\(932\) | 4560.51 | − | 14035.8i | 0.160284 | − | 0.493303i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19274.1 | −0.675232 | ||||||||
\(935\) | 16661.4 | − | 4370.51i | 0.582765 | − | 0.152867i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16174.4 | − | 11751.4i | −0.563923 | − | 0.409714i | 0.268970 | − | 0.963149i | \(-0.413317\pi\) |
−0.832892 | + | 0.553435i | \(0.813317\pi\) | |||||||
\(938\) | −3806.71 | + | 11715.9i | −0.132509 | + | 0.407821i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4360.74 | − | 3168.27i | 0.151310 | − | 0.109933i | ||||
\(941\) | −10986.0 | + | 7981.79i | −0.380588 | + | 0.276513i | −0.761588 | − | 0.648062i | \(-0.775580\pi\) |
0.381000 | + | 0.924575i | \(0.375580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2551.97 | − | 7854.14i | 0.0881267 | − | 0.271226i | ||||
\(944\) | 6044.02 | + | 4391.24i | 0.208386 | + | 0.151401i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.8406 | − | 863.958i | 0.00171296 | − | 0.0296931i | ||||
\(947\) | −54932.1 | −1.88496 | −0.942478 | − | 0.334269i | \(-0.891511\pi\) | ||||
−0.942478 | + | 0.334269i | \(0.891511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22503.0 | − | 69257.0i | 0.769734 | − | 2.36900i | ||||
\(950\) | −1355.84 | − | 4172.86i | −0.0463046 | − | 0.142511i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4700.34 | − | 3415.00i | 0.160020 | − | 0.116261i | ||||
\(953\) | −10537.2 | − | 32430.2i | −0.358167 | − | 1.10233i | −0.954150 | − | 0.299329i | \(-0.903237\pi\) |
0.595983 | − | 0.802997i | \(-0.296763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4299.49 | − | 3123.77i | −0.145684 | − | 0.105846i | ||||
\(956\) | −28524.5 | −0.965009 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25042.5 | −0.844559 | ||||||||
\(959\) | 3561.99 | + | 2587.94i | 0.119940 | + | 0.0871417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6588.14 | + | 20276.2i | 0.221145 | + | 0.680616i | ||||
\(962\) | −25303.3 | + | 18383.9i | −0.848035 | + | 0.616133i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3968.52 | − | 12213.9i | −0.132591 | − | 0.408073i | ||||
\(965\) | 1014.31 | − | 3121.73i | 0.0338362 | − | 0.104137i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33962.8 | 1.12944 | 0.564721 | − | 0.825282i | \(-0.308984\pi\) | ||||
0.564721 | + | 0.825282i | \(0.308984\pi\) | |||||||
\(968\) | −7837.54 | − | 7207.83i | −0.260236 | − | 0.239327i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1515.97 | + | 1101.41i | 0.0501802 | + | 0.0364580i | ||||
\(971\) | −8903.01 | + | 27400.7i | −0.294244 | + | 0.905591i | 0.689230 | + | 0.724543i | \(0.257949\pi\) |
−0.983474 | + | 0.181048i | \(0.942051\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6665.60 | − | 4842.84i | 0.219619 | − | 0.159563i | ||||
\(974\) | 20347.9 | − | 14783.6i | 0.669394 | − | 0.486343i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 608.068 | − | 1871.44i | 0.0199424 | − | 0.0613764i | ||||
\(977\) | 34031.5 | + | 24725.3i | 1.11439 | + | 0.809655i | 0.983350 | − | 0.181722i | \(-0.0581671\pi\) |
0.131044 | + | 0.991377i | \(0.458167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25390.9 | + | 39552.8i | 0.828902 | + | 1.29123i | ||||
\(980\) | 5371.81 | 0.175098 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1218.28 | − | 3749.48i | 0.0395894 | − | 0.121844i | ||||
\(983\) | 6739.22 | + | 20741.2i | 0.218665 | + | 0.672982i | 0.998873 | + | 0.0474618i | \(0.0151132\pi\) |
−0.780208 | + | 0.625520i | \(0.784887\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13434.2 | − | 9760.55i | 0.434569 | − | 0.315733i | ||||
\(986\) | −10018.6 | − | 30834.2i | −0.323589 | − | 0.995903i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6105.02 | − | 4435.56i | −0.196586 | − | 0.142828i | ||||
\(989\) | 1066.28 | 0.0342828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11621.1 | 0.372508 | 0.186254 | − | 0.982502i | \(-0.440365\pi\) | ||||
0.186254 | + | 0.982502i | \(0.440365\pi\) | |||||||
\(992\) | −5852.80 | − | 4252.31i | −0.187325 | − | 0.136100i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −484.050 | − | 1489.75i | −0.0154458 | − | 0.0475373i | ||||
\(995\) | −4726.88 | + | 3434.28i | −0.150605 | + | 0.109421i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16964.3 | − | 52210.7i | −0.538881 | − | 1.65850i | −0.735111 | − | 0.677947i | \(-0.762870\pi\) |
0.196230 | − | 0.980558i | \(-0.437130\pi\) | |||||||
\(998\) | 4557.88 | − | 14027.7i | 0.144566 | − | 0.444929i | ||||
\(999\) | 0 | 0 |
(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 | 198.4.f.h.37.3 | yes | 12 | |
3.2 | odd | 2 | 198.4.f.g.37.1 | ✓ | 12 | ||
11.3 | even | 5 | inner | 198.4.f.h.91.3 | yes | 12 | |
11.5 | even | 5 | 2178.4.a.ce.1.2 | 6 | |||
11.6 | odd | 10 | 2178.4.a.cg.1.2 | 6 | |||
33.5 | odd | 10 | 2178.4.a.cf.1.5 | 6 | |||
33.14 | odd | 10 | 198.4.f.g.91.1 | yes | 12 | ||
33.17 | even | 10 | 2178.4.a.cd.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
198.4.f.g.37.1 | ✓ | 12 | 3.2 | odd | 2 | ||
198.4.f.g.91.1 | yes | 12 | 33.14 | odd | 10 | ||
198.4.f.h.37.3 | yes | 12 | 1.1 | even | 1 | trivial | |
198.4.f.h.91.3 | yes | 12 | 11.3 | even | 5 | inner | |
2178.4.a.cd.1.5 | 6 | 33.17 | even | 10 | |||
2178.4.a.ce.1.2 | 6 | 11.5 | even | 5 | |||
2178.4.a.cf.1.5 | 6 | 33.5 | odd | 10 | |||
2178.4.a.cg.1.2 | 6 | 11.6 | odd | 10 |