Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,4,Mod(3,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.c (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.13923111069\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 11) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(0.535233 + 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 121.3 |
Dual form | 121.4.c.c.81.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21028 | + | 1.60586i | −0.781450 | + | 0.567757i | −0.905414 | − | 0.424530i | \(-0.860439\pi\) |
0.123964 | + | 0.992287i | \(0.460439\pi\) | |||||||
\(3\) | −2.44995 | − | 7.54017i | −0.471493 | − | 1.45111i | −0.850630 | − | 0.525766i | \(-0.823779\pi\) |
0.379137 | − | 0.925341i | \(-0.376221\pi\) | |||||||
\(4\) | −0.165602 | + | 0.509670i | −0.0207002 | + | 0.0637087i | ||||
\(5\) | −12.0191 | − | 8.73238i | −1.07502 | − | 0.781048i | −0.0982119 | − | 0.995166i | \(-0.531312\pi\) |
−0.976808 | + | 0.214118i | \(0.931312\pi\) | |||||||
\(6\) | 17.5235 | + | 12.7316i | 1.19232 | + | 0.866274i | ||||
\(7\) | 0.949237 | − | 2.92145i | 0.0512540 | − | 0.157744i | −0.922153 | − | 0.386824i | \(-0.873572\pi\) |
0.973407 | + | 0.229081i | \(0.0735720\pi\) | |||||||
\(8\) | −7.20643 | − | 22.1791i | −0.318482 | − | 0.980188i | ||||
\(9\) | −29.0084 | + | 21.0759i | −1.07439 | + | 0.780588i | ||||
\(10\) | 40.5885 | 1.28352 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 4.24871 | 0.102208 | ||||||||
\(13\) | −4.33551 | + | 3.14993i | −0.0924964 | + | 0.0672026i | −0.633072 | − | 0.774093i | \(-0.718206\pi\) |
0.540576 | + | 0.841295i | \(0.318206\pi\) | |||||||
\(14\) | 2.59336 | + | 7.98156i | 0.0495076 | + | 0.152369i | ||||
\(15\) | −36.3974 | + | 112.020i | −0.626519 | + | 1.92823i | ||||
\(16\) | 48.0763 | + | 34.9295i | 0.751193 | + | 0.545774i | ||||
\(17\) | 33.3440 | + | 24.2258i | 0.475712 | + | 0.345625i | 0.799663 | − | 0.600449i | \(-0.205011\pi\) |
−0.323951 | + | 0.946074i | \(0.605011\pi\) | |||||||
\(18\) | 30.2718 | − | 93.1669i | 0.396396 | − | 1.21998i | ||||
\(19\) | 43.2386 | + | 133.075i | 0.522085 | + | 1.60681i | 0.770009 | + | 0.638033i | \(0.220252\pi\) |
−0.247924 | + | 0.968779i | \(0.579748\pi\) | |||||||
\(20\) | 6.44101 | − | 4.67967i | 0.0720127 | − | 0.0523203i | ||||
\(21\) | −24.3538 | −0.253069 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −111.354 | −1.00952 | −0.504758 | − | 0.863261i | \(-0.668418\pi\) | ||||
−0.504758 | + | 0.863261i | \(0.668418\pi\) | |||||||
\(24\) | −149.579 | + | 108.675i | −1.27219 | + | 0.924304i | ||||
\(25\) | 29.5769 | + | 91.0283i | 0.236615 | + | 0.728226i | ||||
\(26\) | 4.52432 | − | 13.9244i | 0.0341266 | − | 0.105031i | ||||
\(27\) | 56.8054 | + | 41.2716i | 0.404897 | + | 0.294175i | ||||
\(28\) | 1.33178 | + | 0.967595i | 0.00898867 | + | 0.00653065i | ||||
\(29\) | −7.72383 | + | 23.7715i | −0.0494579 | + | 0.152216i | −0.972735 | − | 0.231918i | \(-0.925500\pi\) |
0.923277 | + | 0.384134i | \(0.125500\pi\) | |||||||
\(30\) | −99.4397 | − | 306.044i | −0.605171 | − | 1.86252i | ||||
\(31\) | −25.4820 | + | 18.5137i | −0.147635 | + | 0.107263i | −0.659151 | − | 0.752011i | \(-0.729084\pi\) |
0.511516 | + | 0.859274i | \(0.329084\pi\) | |||||||
\(32\) | 24.2102 | 0.133744 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −112.603 | −0.567976 | ||||||||
\(35\) | −36.9202 | + | 26.8241i | −0.178304 | + | 0.129546i | ||||
\(36\) | −5.93788 | − | 18.2749i | −0.0274902 | − | 0.0846061i | ||||
\(37\) | 4.06159 | − | 12.5003i | 0.0180465 | − | 0.0555415i | −0.941628 | − | 0.336656i | \(-0.890704\pi\) |
0.959674 | + | 0.281114i | \(0.0907041\pi\) | |||||||
\(38\) | −309.268 | − | 224.697i | −1.32026 | − | 0.959227i | ||||
\(39\) | 34.3728 | + | 24.9733i | 0.141130 | + | 0.102537i | ||||
\(40\) | −107.062 | + | 329.502i | −0.423199 | + | 1.30247i | ||||
\(41\) | 80.6756 | + | 248.294i | 0.307303 | + | 0.945781i | 0.978808 | + | 0.204781i | \(0.0656482\pi\) |
−0.671505 | + | 0.741000i | \(0.734352\pi\) | |||||||
\(42\) | 53.8287 | − | 39.1088i | 0.197761 | − | 0.143681i | ||||
\(43\) | −57.7128 | −0.204677 | −0.102339 | − | 0.994750i | \(-0.532633\pi\) | ||||
−0.102339 | + | 0.994750i | \(0.532633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 532.697 | 1.76466 | ||||||||
\(46\) | 246.123 | − | 178.819i | 0.788887 | − | 0.573160i | ||||
\(47\) | −106.254 | − | 327.017i | −0.329761 | − | 1.01490i | −0.969245 | − | 0.246097i | \(-0.920852\pi\) |
0.639484 | − | 0.768804i | \(-0.279148\pi\) | |||||||
\(48\) | 145.590 | − | 448.079i | 0.437793 | − | 1.34739i | ||||
\(49\) | 269.859 | + | 196.064i | 0.786761 | + | 0.571615i | ||||
\(50\) | −211.552 | − | 153.701i | −0.598359 | − | 0.434733i | ||||
\(51\) | 100.976 | − | 310.771i | 0.277243 | − | 0.853268i | ||||
\(52\) | −0.887457 | − | 2.73131i | −0.00236669 | − | 0.00728394i | ||||
\(53\) | 277.489 | − | 201.607i | 0.719170 | − | 0.522507i | −0.166949 | − | 0.985966i | \(-0.553392\pi\) |
0.886119 | + | 0.463458i | \(0.153392\pi\) | |||||||
\(54\) | −191.832 | −0.483426 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −71.6359 | −0.170942 | ||||||||
\(57\) | 897.474 | − | 652.053i | 2.08550 | − | 1.51520i | ||||
\(58\) | −21.1019 | − | 64.9450i | −0.0477727 | − | 0.147029i | ||||
\(59\) | 27.3076 | − | 84.0442i | 0.0602568 | − | 0.185451i | −0.916397 | − | 0.400270i | \(-0.868916\pi\) |
0.976654 | + | 0.214819i | \(0.0689162\pi\) | |||||||
\(60\) | −51.0656 | − | 37.1013i | −0.109876 | − | 0.0798294i | ||||
\(61\) | −597.619 | − | 434.195i | −1.25438 | − | 0.911361i | −0.255913 | − | 0.966700i | \(-0.582376\pi\) |
−0.998468 | + | 0.0553387i | \(0.982376\pi\) | |||||||
\(62\) | 26.5917 | − | 81.8408i | 0.0544702 | − | 0.167642i | ||||
\(63\) | 34.0362 | + | 104.753i | 0.0680661 | + | 0.209486i | ||||
\(64\) | −438.122 | + | 318.314i | −0.855707 | + | 0.621708i | ||||
\(65\) | 79.6152 | 0.151924 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 342.359 | 0.624266 | 0.312133 | − | 0.950038i | \(-0.398957\pi\) | ||||
0.312133 | + | 0.950038i | \(0.398957\pi\) | |||||||
\(68\) | −17.8690 | + | 12.9826i | −0.0318666 | + | 0.0231525i | ||||
\(69\) | 272.811 | + | 839.627i | 0.475980 | + | 1.46492i | ||||
\(70\) | 38.5281 | − | 118.577i | 0.0657855 | − | 0.202467i | ||||
\(71\) | 167.761 | + | 121.886i | 0.280417 | + | 0.203735i | 0.719099 | − | 0.694908i | \(-0.244555\pi\) |
−0.438682 | + | 0.898642i | \(0.644555\pi\) | |||||||
\(72\) | 676.492 | + | 491.500i | 1.10730 | + | 0.804498i | ||||
\(73\) | −312.293 | + | 961.138i | −0.500700 | + | 1.54100i | 0.307182 | + | 0.951651i | \(0.400614\pi\) |
−0.807882 | + | 0.589344i | \(0.799386\pi\) | |||||||
\(74\) | 11.0965 | + | 34.1515i | 0.0174316 | + | 0.0536490i | ||||
\(75\) | 613.907 | − | 446.029i | 0.945171 | − | 0.686707i | ||||
\(76\) | −74.9845 | −0.113175 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −116.077 | −0.168502 | ||||||||
\(79\) | −1047.05 | + | 760.727i | −1.49117 | + | 1.08340i | −0.517432 | + | 0.855725i | \(0.673112\pi\) |
−0.973738 | + | 0.227673i | \(0.926888\pi\) | |||||||
\(80\) | −272.816 | − | 839.641i | −0.381272 | − | 1.17343i | ||||
\(81\) | −127.142 | + | 391.304i | −0.174406 | + | 0.536768i | ||||
\(82\) | −577.041 | − | 419.245i | −0.777116 | − | 0.564607i | ||||
\(83\) | −357.461 | − | 259.711i | −0.472728 | − | 0.343457i | 0.325775 | − | 0.945447i | \(-0.394375\pi\) |
−0.798504 | + | 0.601990i | \(0.794375\pi\) | |||||||
\(84\) | 4.03304 | − | 12.4124i | 0.00523857 | − | 0.0161227i | ||||
\(85\) | −189.215 | − | 582.344i | −0.241450 | − | 0.743107i | ||||
\(86\) | 127.561 | − | 92.6787i | 0.159945 | − | 0.116207i | ||||
\(87\) | 198.164 | 0.244200 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1489.11 | −1.77355 | −0.886773 | − | 0.462205i | \(-0.847058\pi\) | ||||
−0.886773 | + | 0.462205i | \(0.847058\pi\) | |||||||
\(90\) | −1177.41 | + | 855.437i | −1.37900 | + | 1.00190i | ||||
\(91\) | 5.08695 | + | 15.6560i | 0.00585997 | + | 0.0180351i | ||||
\(92\) | 18.4404 | − | 56.7537i | 0.0208972 | − | 0.0643150i | ||||
\(93\) | 202.026 | + | 146.781i | 0.225259 | + | 0.163661i | ||||
\(94\) | 759.995 | + | 552.168i | 0.833909 | + | 0.605870i | ||||
\(95\) | 642.370 | − | 1977.01i | 0.693745 | − | 2.13513i | ||||
\(96\) | −59.3139 | − | 182.549i | −0.0630593 | − | 0.194077i | ||||
\(97\) | −1089.27 | + | 791.403i | −1.14019 | + | 0.828400i | −0.987146 | − | 0.159819i | \(-0.948909\pi\) |
−0.153048 | + | 0.988219i | \(0.548909\pi\) | |||||||
\(98\) | −911.314 | −0.939353 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −51.2923 | −0.0512923 | ||||||||
\(101\) | 130.625 | − | 94.9046i | 0.128690 | − | 0.0934986i | −0.521578 | − | 0.853203i | \(-0.674657\pi\) |
0.650268 | + | 0.759705i | \(0.274657\pi\) | |||||||
\(102\) | 275.871 | + | 849.042i | 0.267797 | + | 0.824193i | ||||
\(103\) | −10.7412 | + | 33.0580i | −0.0102753 | + | 0.0316243i | −0.956063 | − | 0.293162i | \(-0.905292\pi\) |
0.945787 | + | 0.324786i | \(0.105292\pi\) | |||||||
\(104\) | 101.106 | + | 73.4580i | 0.0953297 | + | 0.0692611i | ||||
\(105\) | 292.711 | + | 212.667i | 0.272054 | + | 0.197659i | ||||
\(106\) | −289.573 | + | 891.215i | −0.265338 | + | 0.816627i | ||||
\(107\) | 257.158 | + | 791.450i | 0.232340 | + | 0.715068i | 0.997463 | + | 0.0711847i | \(0.0226780\pi\) |
−0.765123 | + | 0.643884i | \(0.777322\pi\) | |||||||
\(108\) | −30.4419 | + | 22.1174i | −0.0271229 | + | 0.0197060i | ||||
\(109\) | 1044.26 | 0.917629 | 0.458815 | − | 0.888532i | \(-0.348274\pi\) | ||||
0.458815 | + | 0.888532i | \(0.348274\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −104.205 | −0.0891055 | ||||||||
\(112\) | 147.681 | − | 107.296i | 0.124594 | − | 0.0905228i | ||||
\(113\) | 91.1853 | + | 280.639i | 0.0759114 | + | 0.233631i | 0.981811 | − | 0.189861i | \(-0.0608039\pi\) |
−0.905899 | + | 0.423493i | \(0.860804\pi\) | |||||||
\(114\) | −936.559 | + | 2882.43i | −0.769446 | + | 2.36811i | ||||
\(115\) | 1338.37 | + | 972.384i | 1.08525 | + | 0.788480i | ||||
\(116\) | −10.8365 | − | 7.87321i | −0.00867368 | − | 0.00630180i | ||||
\(117\) | 59.3788 | − | 182.749i | 0.0469194 | − | 0.144403i | ||||
\(118\) | 74.6058 | + | 229.613i | 0.0582036 | + | 0.179132i | ||||
\(119\) | 102.426 | − | 74.4167i | 0.0789022 | − | 0.0573258i | ||||
\(120\) | 2746.80 | 2.08956 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2018.16 | 1.49767 | ||||||||
\(123\) | 1674.53 | − | 1216.62i | 1.22754 | − | 0.891858i | ||||
\(124\) | −5.21603 | − | 16.0533i | −0.00377752 | − | 0.0116260i | ||||
\(125\) | −134.454 | + | 413.807i | −0.0962075 | + | 0.296096i | ||||
\(126\) | −243.448 | − | 176.875i | −0.172127 | − | 0.125058i | ||||
\(127\) | 1065.96 | + | 774.469i | 0.744796 | + | 0.541126i | 0.894209 | − | 0.447649i | \(-0.147739\pi\) |
−0.149414 | + | 0.988775i | \(0.547739\pi\) | |||||||
\(128\) | 397.351 | − | 1222.92i | 0.274385 | − | 0.844469i | ||||
\(129\) | 141.393 | + | 435.164i | 0.0965039 | + | 0.297008i | ||||
\(130\) | −175.972 | + | 127.851i | −0.118721 | + | 0.0862559i | ||||
\(131\) | −1600.71 | −1.06759 | −0.533797 | − | 0.845612i | \(-0.679235\pi\) | ||||
−0.533797 | + | 0.845612i | \(0.679235\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 429.815 | 0.280223 | ||||||||
\(134\) | −756.708 | + | 549.780i | −0.487833 | + | 0.354431i | ||||
\(135\) | −322.351 | − | 992.093i | −0.205508 | − | 0.632487i | ||||
\(136\) | 297.016 | − | 914.121i | 0.187271 | − | 0.576362i | ||||
\(137\) | −1303.87 | − | 947.320i | −0.813120 | − | 0.590766i | 0.101613 | − | 0.994824i | \(-0.467600\pi\) |
−0.914734 | + | 0.404058i | \(0.867600\pi\) | |||||||
\(138\) | −1951.31 | − | 1417.71i | −1.20367 | − | 0.874518i | ||||
\(139\) | −9.84588 | + | 30.3025i | −0.00600803 | + | 0.0184908i | −0.954016 | − | 0.299757i | \(-0.903094\pi\) |
0.948008 | + | 0.318248i | \(0.103094\pi\) | |||||||
\(140\) | −7.55738 | − | 23.2592i | −0.00456225 | − | 0.0140412i | ||||
\(141\) | −2205.45 | + | 1602.35i | −1.31725 | + | 0.957037i | ||||
\(142\) | −566.529 | −0.334803 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2130.79 | −1.23310 | ||||||||
\(145\) | 300.415 | − | 218.264i | 0.172056 | − | 0.125006i | ||||
\(146\) | −853.199 | − | 2625.88i | −0.483639 | − | 1.48849i | ||||
\(147\) | 817.215 | − | 2515.13i | 0.458522 | − | 1.41119i | ||||
\(148\) | 5.69842 | + | 4.14014i | 0.00316491 | + | 0.00229944i | ||||
\(149\) | 1964.57 | + | 1427.34i | 1.08016 | + | 0.784782i | 0.977711 | − | 0.209956i | \(-0.0673320\pi\) |
0.102449 | + | 0.994738i | \(0.467332\pi\) | |||||||
\(150\) | −640.643 | + | 1971.70i | −0.348722 | + | 1.07326i | ||||
\(151\) | −796.237 | − | 2450.57i | −0.429118 | − | 1.32069i | −0.898995 | − | 0.437958i | \(-0.855702\pi\) |
0.469877 | − | 0.882732i | \(-0.344298\pi\) | |||||||
\(152\) | 2639.88 | − | 1917.99i | 1.40870 | − | 1.02348i | ||||
\(153\) | −1477.84 | −0.780889 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 467.939 | 0.242489 | ||||||||
\(156\) | −18.4203 | + | 13.3832i | −0.00945389 | + | 0.00686865i | ||||
\(157\) | 765.109 | + | 2354.76i | 0.388932 | + | 1.19701i | 0.933587 | + | 0.358350i | \(0.116660\pi\) |
−0.544656 | + | 0.838660i | \(0.683340\pi\) | |||||||
\(158\) | 1092.65 | − | 3362.83i | 0.550168 | − | 1.69324i | ||||
\(159\) | −2199.99 | − | 1598.38i | −1.09730 | − | 0.797233i | ||||
\(160\) | −290.985 | − | 211.413i | −0.143777 | − | 0.104460i | ||||
\(161\) | −105.701 | + | 325.315i | −0.0517418 | + | 0.159245i | ||||
\(162\) | −347.359 | − | 1069.06i | −0.168464 | − | 0.518478i | ||||
\(163\) | 2204.66 | − | 1601.78i | 1.05940 | − | 0.769699i | 0.0854225 | − | 0.996345i | \(-0.472776\pi\) |
0.973977 | + | 0.226646i | \(0.0727760\pi\) | |||||||
\(164\) | −139.908 | −0.0666157 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1207.15 | 0.564414 | ||||||||
\(167\) | −2214.52 | + | 1608.94i | −1.02614 | + | 0.745531i | −0.967532 | − | 0.252750i | \(-0.918665\pi\) |
−0.0586043 | + | 0.998281i | \(0.518665\pi\) | |||||||
\(168\) | 175.504 | + | 540.147i | 0.0805979 | + | 0.248055i | ||||
\(169\) | −670.036 | + | 2062.16i | −0.304978 | + | 0.938625i | ||||
\(170\) | 1353.38 | + | 983.288i | 0.610585 | + | 0.443616i | ||||
\(171\) | −4058.95 | − | 2949.00i | −1.81518 | − | 1.31880i | ||||
\(172\) | 9.55734 | − | 29.4145i | 0.00423686 | − | 0.0130397i | ||||
\(173\) | 713.031 | + | 2194.48i | 0.313357 | + | 0.964413i | 0.976426 | + | 0.215854i | \(0.0692536\pi\) |
−0.663069 | + | 0.748558i | \(0.730746\pi\) | |||||||
\(174\) | −437.998 | + | 318.224i | −0.190830 | + | 0.138646i | ||||
\(175\) | 294.010 | 0.127001 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −700.610 | −0.297520 | ||||||||
\(178\) | 3291.35 | − | 2391.31i | 1.38594 | − | 1.00694i | ||||
\(179\) | −405.478 | − | 1247.93i | −0.169312 | − | 0.521089i | 0.830016 | − | 0.557739i | \(-0.188331\pi\) |
−0.999328 | + | 0.0366506i | \(0.988331\pi\) | |||||||
\(180\) | −88.2156 | + | 271.500i | −0.0365289 | + | 0.112424i | ||||
\(181\) | 649.781 | + | 472.094i | 0.266839 | + | 0.193870i | 0.713157 | − | 0.701005i | \(-0.247265\pi\) |
−0.446318 | + | 0.894875i | \(0.647265\pi\) | |||||||
\(182\) | −36.3849 | − | 26.4352i | −0.0148188 | − | 0.0107665i | ||||
\(183\) | −1809.77 | + | 5569.90i | −0.731050 | + | 2.24994i | ||||
\(184\) | 802.464 | + | 2469.73i | 0.321513 | + | 0.989516i | ||||
\(185\) | −157.974 | + | 114.775i | −0.0627810 | + | 0.0456130i | ||||
\(186\) | −682.242 | −0.268949 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 184.267 | 0.0714842 | ||||||||
\(189\) | 174.495 | − | 126.778i | 0.0671568 | − | 0.0487922i | ||||
\(190\) | 1754.99 | + | 5401.30i | 0.670106 | + | 2.06238i | ||||
\(191\) | 530.967 | − | 1634.15i | 0.201149 | − | 0.619073i | −0.798701 | − | 0.601729i | \(-0.794479\pi\) |
0.999850 | − | 0.0173442i | \(-0.00552110\pi\) | |||||||
\(192\) | 3473.52 | + | 2523.66i | 1.30562 | + | 0.948591i | ||||
\(193\) | −1084.23 | − | 787.740i | −0.404377 | − | 0.293797i | 0.366945 | − | 0.930243i | \(-0.380404\pi\) |
−0.771321 | + | 0.636446i | \(0.780404\pi\) | |||||||
\(194\) | 1136.71 | − | 3498.44i | 0.420676 | − | 1.29471i | ||||
\(195\) | −195.053 | − | 600.312i | −0.0716311 | − | 0.220458i | ||||
\(196\) | −144.617 | + | 105.070i | −0.0527030 | + | 0.0382910i | ||||
\(197\) | −3518.33 | −1.27244 | −0.636220 | − | 0.771508i | \(-0.719503\pi\) | ||||
−0.636220 | + | 0.771508i | \(0.719503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 823.692 | 0.293417 | 0.146709 | − | 0.989180i | \(-0.453132\pi\) | ||||
0.146709 | + | 0.989180i | \(0.453132\pi\) | |||||||
\(200\) | 1805.78 | − | 1311.98i | 0.638441 | − | 0.463855i | ||||
\(201\) | −838.762 | − | 2581.44i | −0.294337 | − | 0.905876i | ||||
\(202\) | −136.314 | + | 419.531i | −0.0474802 | + | 0.146129i | ||||
\(203\) | 62.1156 | + | 45.1296i | 0.0214762 | + | 0.0156033i | ||||
\(204\) | 141.669 | + | 102.928i | 0.0486216 | + | 0.0353256i | ||||
\(205\) | 1198.55 | − | 3688.76i | 0.408343 | − | 1.25675i | ||||
\(206\) | −29.3455 | − | 90.3161i | −0.00992522 | − | 0.0305467i | ||||
\(207\) | 3230.20 | − | 2346.88i | 1.08461 | − | 0.788016i | ||||
\(208\) | −318.461 | −0.106160 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −988.484 | −0.324819 | ||||||||
\(211\) | 86.8424 | − | 63.0947i | 0.0283340 | − | 0.0205859i | −0.573528 | − | 0.819186i | \(-0.694426\pi\) |
0.601862 | + | 0.798600i | \(0.294426\pi\) | |||||||
\(212\) | 56.8005 | + | 174.814i | 0.0184013 | + | 0.0566334i | ||||
\(213\) | 508.032 | − | 1563.56i | 0.163426 | − | 0.502974i | ||||
\(214\) | −1839.35 | − | 1336.36i | −0.587547 | − | 0.426878i | ||||
\(215\) | 693.655 | + | 503.970i | 0.220032 | + | 0.159863i | ||||
\(216\) | 506.003 | − | 1557.32i | 0.159394 | − | 0.490564i | ||||
\(217\) | 29.8985 | + | 92.0182i | 0.00935320 | + | 0.0287862i | ||||
\(218\) | −2308.09 | + | 1676.93i | −0.717082 | + | 0.520990i | ||||
\(219\) | 8012.24 | 2.47222 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −220.873 | −0.0672285 | ||||||||
\(222\) | 230.322 | − | 167.339i | 0.0696315 | − | 0.0505903i | ||||
\(223\) | −1215.57 | − | 3741.15i | −0.365026 | − | 1.12344i | −0.949965 | − | 0.312358i | \(-0.898881\pi\) |
0.584938 | − | 0.811078i | \(-0.301119\pi\) | |||||||
\(224\) | 22.9813 | − | 70.7290i | 0.00685491 | − | 0.0210972i | ||||
\(225\) | −2776.48 | − | 2017.23i | −0.822661 | − | 0.597698i | ||||
\(226\) | −652.212 | − | 473.860i | −0.191967 | − | 0.139472i | ||||
\(227\) | −547.548 | + | 1685.18i | −0.160097 | + | 0.492728i | −0.998642 | − | 0.0521050i | \(-0.983407\pi\) |
0.838545 | + | 0.544833i | \(0.183407\pi\) | |||||||
\(228\) | 183.708 | + | 565.396i | 0.0533613 | + | 0.164229i | ||||
\(229\) | −1549.57 | + | 1125.83i | −0.447154 | + | 0.324876i | −0.788471 | − | 0.615072i | \(-0.789127\pi\) |
0.341317 | + | 0.939948i | \(0.389127\pi\) | |||||||
\(230\) | −4519.68 | −1.29573 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 582.892 | 0.164952 | ||||||||
\(233\) | −3556.70 | + | 2584.09i | −1.00003 | + | 0.726564i | −0.962095 | − | 0.272716i | \(-0.912078\pi\) |
−0.0379350 | + | 0.999280i | \(0.512078\pi\) | |||||||
\(234\) | 162.226 | + | 499.280i | 0.0453207 | + | 0.139483i | ||||
\(235\) | −1578.56 | + | 4858.30i | −0.438186 | + | 1.34860i | ||||
\(236\) | 38.3126 | + | 27.8357i | 0.0105675 | + | 0.00767776i | ||||
\(237\) | 8301.23 | + | 6031.19i | 2.27520 | + | 1.65303i | ||||
\(238\) | −106.887 | + | 328.963i | −0.0291110 | + | 0.0895945i | ||||
\(239\) | −1262.18 | − | 3884.58i | −0.341604 | − | 1.05135i | −0.963377 | − | 0.268152i | \(-0.913587\pi\) |
0.621772 | − | 0.783198i | \(-0.286413\pi\) | |||||||
\(240\) | −5662.65 | + | 4114.16i | −1.52301 | + | 1.10653i | ||||
\(241\) | 3908.58 | 1.04471 | 0.522353 | − | 0.852730i | \(-0.325054\pi\) | ||||
0.522353 | + | 0.852730i | \(0.325054\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5157.80 | 1.36162 | ||||||||
\(244\) | 320.263 | − | 232.685i | 0.0840276 | − | 0.0610496i | ||||
\(245\) | −1531.35 | − | 4713.02i | −0.399325 | − | 1.22900i | ||||
\(246\) | −1747.45 | + | 5378.11i | −0.452901 | + | 1.39389i | ||||
\(247\) | −606.638 | − | 440.748i | −0.156273 | − | 0.113539i | ||||
\(248\) | 594.252 | + | 431.749i | 0.152157 | + | 0.110549i | ||||
\(249\) | −1082.50 | + | 3331.59i | −0.275505 | + | 0.847917i | ||||
\(250\) | −367.335 | − | 1130.54i | −0.0929293 | − | 0.286007i | ||||
\(251\) | −885.786 | + | 643.561i | −0.222750 | + | 0.161838i | −0.693564 | − | 0.720395i | \(-0.743960\pi\) |
0.470813 | + | 0.882233i | \(0.343960\pi\) | |||||||
\(252\) | −59.0258 | −0.0147551 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3599.76 | −0.889249 | ||||||||
\(255\) | −3927.40 | + | 2853.43i | −0.964485 | + | 0.700739i | ||||
\(256\) | −253.197 | − | 779.261i | −0.0618158 | − | 0.190249i | ||||
\(257\) | 242.016 | − | 744.847i | 0.0587413 | − | 0.180787i | −0.917380 | − | 0.398012i | \(-0.869700\pi\) |
0.976122 | + | 0.217224i | \(0.0697004\pi\) | |||||||
\(258\) | −1011.33 | − | 734.775i | −0.244042 | − | 0.177307i | ||||
\(259\) | −32.6636 | − | 23.7315i | −0.00783636 | − | 0.00569345i | ||||
\(260\) | −13.1844 | + | 40.5775i | −0.00314486 | + | 0.00967888i | ||||
\(261\) | −276.949 | − | 852.361i | −0.0656809 | − | 0.202145i | ||||
\(262\) | 3538.02 | − | 2570.52i | 0.834272 | − | 0.606134i | ||||
\(263\) | 6180.06 | 1.44897 | 0.724484 | − | 0.689292i | \(-0.242078\pi\) | ||||
0.724484 | + | 0.689292i | \(0.242078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5095.67 | −1.18122 | ||||||||
\(266\) | −950.010 | + | 690.223i | −0.218981 | + | 0.159099i | ||||
\(267\) | 3648.25 | + | 11228.2i | 0.836215 | + | 2.57360i | ||||
\(268\) | −56.6952 | + | 174.490i | −0.0129224 | + | 0.0397712i | ||||
\(269\) | −798.471 | − | 580.123i | −0.180980 | − | 0.131490i | 0.493607 | − | 0.869685i | \(-0.335678\pi\) |
−0.674587 | + | 0.738195i | \(0.735678\pi\) | |||||||
\(270\) | 2305.65 | + | 1675.15i | 0.519693 | + | 0.377579i | ||||
\(271\) | 1414.37 | − | 4352.98i | 0.317036 | − | 0.975736i | −0.657873 | − | 0.753129i | \(-0.728543\pi\) |
0.974908 | − | 0.222607i | \(-0.0714565\pi\) | |||||||
\(272\) | 756.860 | + | 2329.38i | 0.168718 | + | 0.519262i | ||||
\(273\) | 105.586 | − | 76.7129i | 0.0234079 | − | 0.0170069i | ||||
\(274\) | 4403.18 | 0.970825 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −473.110 | −0.103181 | ||||||||
\(277\) | −459.389 | + | 333.766i | −0.0996462 | + | 0.0723972i | −0.636493 | − | 0.771283i | \(-0.719615\pi\) |
0.536846 | + | 0.843680i | \(0.319615\pi\) | |||||||
\(278\) | −26.8994 | − | 82.7880i | −0.00580331 | − | 0.0178608i | ||||
\(279\) | 348.999 | − | 1074.11i | 0.0748890 | − | 0.230485i | ||||
\(280\) | 860.998 | + | 625.551i | 0.183766 | + | 0.133514i | ||||
\(281\) | −4296.70 | − | 3121.74i | −0.912170 | − | 0.662730i | 0.0293930 | − | 0.999568i | \(-0.490643\pi\) |
−0.941563 | + | 0.336838i | \(0.890643\pi\) | |||||||
\(282\) | 2301.49 | − | 7083.27i | 0.486000 | − | 1.49575i | ||||
\(283\) | −1461.17 | − | 4497.01i | −0.306917 | − | 0.944593i | −0.978955 | − | 0.204076i | \(-0.934581\pi\) |
0.672038 | − | 0.740517i | \(-0.265419\pi\) | |||||||
\(284\) | −89.9029 | + | 65.3183i | −0.0187844 | + | 0.0136476i | ||||
\(285\) | −16480.8 | −3.42539 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 801.960 | 0.164941 | ||||||||
\(288\) | −702.301 | + | 510.252i | −0.143693 | + | 0.104399i | ||||
\(289\) | −993.271 | − | 3056.97i | −0.202172 | − | 0.622221i | ||||
\(290\) | −313.498 | + | 964.849i | −0.0634802 | + | 0.195372i | ||||
\(291\) | 8635.98 | + | 6274.40i | 1.73969 | + | 1.26396i | ||||
\(292\) | −438.146 | − | 318.332i | −0.0878102 | − | 0.0637979i | ||||
\(293\) | 719.675 | − | 2214.93i | 0.143494 | − | 0.441630i | −0.853320 | − | 0.521388i | \(-0.825415\pi\) |
0.996814 | + | 0.0797574i | \(0.0254146\pi\) | |||||||
\(294\) | 2232.67 | + | 6871.46i | 0.442898 | + | 1.36310i | ||||
\(295\) | −1062.12 | + | 771.674i | −0.209623 | + | 0.152300i | ||||
\(296\) | −306.515 | −0.0601886 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6634.36 | −1.28966 | ||||||||
\(299\) | 482.776 | − | 350.757i | 0.0933767 | − | 0.0678421i | ||||
\(300\) | 125.664 | + | 386.753i | 0.0241840 | + | 0.0744306i | ||||
\(301\) | −54.7832 | + | 168.605i | −0.0104905 | + | 0.0322865i | ||||
\(302\) | 5695.17 | + | 4137.78i | 1.08517 | + | 0.788419i | ||||
\(303\) | −1035.62 | − | 752.423i | −0.196353 | − | 0.142659i | ||||
\(304\) | −2569.48 | + | 7908.05i | −0.484769 | + | 1.49197i | ||||
\(305\) | 3391.27 | + | 10437.3i | 0.636668 | + | 1.95946i | ||||
\(306\) | 3266.42 | − | 2373.20i | 0.610226 | − | 0.443355i | ||||
\(307\) | −1678.07 | −0.311962 | −0.155981 | − | 0.987760i | \(-0.549854\pi\) | ||||
−0.155981 | + | 0.987760i | \(0.549854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 275.578 | 0.0507349 | ||||||||
\(310\) | −1034.27 | + | 751.443i | −0.189493 | + | 0.137675i | ||||
\(311\) | 1104.03 | + | 3397.85i | 0.201298 | + | 0.619531i | 0.999845 | + | 0.0175989i | \(0.00560221\pi\) |
−0.798547 | + | 0.601932i | \(0.794398\pi\) | |||||||
\(312\) | 306.181 | − | 942.327i | 0.0555579 | − | 0.170990i | ||||
\(313\) | −5812.27 | − | 4222.86i | −1.04961 | − | 0.762589i | −0.0774746 | − | 0.996994i | \(-0.524686\pi\) |
−0.972139 | + | 0.234405i | \(0.924686\pi\) | |||||||
\(314\) | −5472.52 | − | 3976.02i | −0.983541 | − | 0.714585i | ||||
\(315\) | 505.656 | − | 1556.25i | 0.0904460 | − | 0.278364i | ||||
\(316\) | −214.326 | − | 659.627i | −0.0381544 | − | 0.117427i | ||||
\(317\) | 12.7078 | − | 9.23273i | 0.00225154 | − | 0.00163584i | −0.586659 | − | 0.809834i | \(-0.699557\pi\) |
0.588910 | + | 0.808198i | \(0.299557\pi\) | |||||||
\(318\) | 7429.36 | 1.31012 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8045.47 | 1.40549 | ||||||||
\(321\) | 5337.64 | − | 3878.02i | 0.928094 | − | 0.674299i | ||||
\(322\) | −288.781 | − | 888.777i | −0.0499787 | − | 0.153819i | ||||
\(323\) | −1782.10 | + | 5484.73i | −0.306992 | + | 0.944825i | ||||
\(324\) | −178.381 | − | 129.601i | −0.0305865 | − | 0.0222224i | ||||
\(325\) | −414.964 | − | 301.489i | −0.0708248 | − | 0.0514572i | ||||
\(326\) | −2300.67 | + | 7080.74i | −0.390866 | + | 1.20296i | ||||
\(327\) | −2558.38 | − | 7873.87i | −0.432656 | − | 1.33158i | ||||
\(328\) | 4925.56 | − | 3578.63i | 0.829172 | − | 0.602429i | ||||
\(329\) | −1056.23 | −0.176996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1318.95 | −0.219022 | −0.109511 | − | 0.993986i | \(-0.534928\pi\) | ||||
−0.109511 | + | 0.993986i | \(0.534928\pi\) | |||||||
\(332\) | 191.563 | − | 139.179i | 0.0316668 | − | 0.0230073i | ||||
\(333\) | 145.634 | + | 448.216i | 0.0239661 | + | 0.0737600i | ||||
\(334\) | 2310.96 | − | 7112.41i | 0.378594 | − | 1.16519i | ||||
\(335\) | −4114.84 | − | 2989.61i | −0.671098 | − | 0.487581i | ||||
\(336\) | −1170.84 | − | 850.667i | −0.190103 | − | 0.138118i | ||||
\(337\) | −73.9116 | + | 227.477i | −0.0119472 | + | 0.0367698i | −0.956852 | − | 0.290574i | \(-0.906154\pi\) |
0.944905 | + | 0.327344i | \(0.106154\pi\) | |||||||
\(338\) | −1830.57 | − | 5633.92i | −0.294586 | − | 0.906642i | ||||
\(339\) | 1892.67 | − | 1375.10i | 0.303232 | − | 0.220311i | ||||
\(340\) | 328.137 | 0.0523404 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 13707.1 | 2.16723 | ||||||||
\(343\) | 1681.35 | − | 1221.57i | 0.264678 | − | 0.192300i | ||||
\(344\) | 415.904 | + | 1280.02i | 0.0651861 | + | 0.200622i | ||||
\(345\) | 4052.99 | − | 12473.8i | 0.632481 | − | 1.94658i | ||||
\(346\) | −5100.02 | − | 3705.38i | −0.792425 | − | 0.575730i | ||||
\(347\) | 4743.10 | + | 3446.06i | 0.733784 | + | 0.533125i | 0.890758 | − | 0.454478i | \(-0.150174\pi\) |
−0.156975 | + | 0.987603i | \(0.550174\pi\) | |||||||
\(348\) | −32.8163 | + | 100.998i | −0.00505500 | + | 0.0155577i | ||||
\(349\) | 1079.00 | + | 3320.83i | 0.165495 | + | 0.509341i | 0.999072 | − | 0.0430615i | \(-0.0137111\pi\) |
−0.833577 | + | 0.552403i | \(0.813711\pi\) | |||||||
\(350\) | −649.844 | + | 472.139i | −0.0992446 | + | 0.0721054i | ||||
\(351\) | −376.283 | −0.0572208 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10916.7 | −1.64600 | −0.822999 | − | 0.568043i | \(-0.807701\pi\) | ||||
−0.822999 | + | 0.568043i | \(0.807701\pi\) | |||||||
\(354\) | 1548.54 | − | 1125.08i | 0.232497 | − | 0.168919i | ||||
\(355\) | −951.984 | − | 2929.91i | −0.142327 | − | 0.438037i | ||||
\(356\) | 246.600 | − | 758.956i | 0.0367128 | − | 0.112990i | ||||
\(357\) | −812.053 | − | 589.991i | −0.120388 | − | 0.0874668i | ||||
\(358\) | 2900.22 | + | 2107.13i | 0.428161 | + | 0.311077i | ||||
\(359\) | −3553.92 | + | 10937.8i | −0.522476 | + | 1.60802i | 0.246778 | + | 0.969072i | \(0.420628\pi\) |
−0.769254 | + | 0.638943i | \(0.779372\pi\) | |||||||
\(360\) | −3838.85 | − | 11814.8i | −0.562014 | − | 1.72970i | ||||
\(361\) | −10290.3 | + | 7476.31i | −1.50026 | + | 1.09000i | ||||
\(362\) | −2194.31 | −0.318592 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.82180 | −0.00127030 | ||||||||
\(365\) | 12146.5 | − | 8824.94i | 1.74185 | − | 1.26553i | ||||
\(366\) | −4944.39 | − | 15217.3i | −0.706140 | − | 2.17328i | ||||
\(367\) | 2091.12 | − | 6435.80i | 0.297427 | − | 0.915385i | −0.684969 | − | 0.728572i | \(-0.740184\pi\) |
0.982396 | − | 0.186813i | \(-0.0598157\pi\) | |||||||
\(368\) | −5353.48 | − | 3889.53i | −0.758342 | − | 0.550967i | ||||
\(369\) | −7573.29 | − | 5502.31i | −1.06843 | − | 0.776258i | ||||
\(370\) | 164.854 | − | 507.368i | 0.0231631 | − | 0.0712887i | ||||
\(371\) | −325.584 | − | 1002.04i | −0.0455619 | − | 0.140225i | ||||
\(372\) | −108.265 | + | 78.6595i | −0.0150895 | + | 0.0109632i | ||||
\(373\) | −5310.22 | −0.737139 | −0.368569 | − | 0.929600i | \(-0.620152\pi\) | ||||
−0.368569 | + | 0.929600i | \(0.620152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3449.58 | 0.475028 | ||||||||
\(376\) | −6487.24 | + | 4713.25i | −0.889770 | + | 0.646456i | ||||
\(377\) | −41.3919 | − | 127.391i | −0.00565462 | − | 0.0174031i | ||||
\(378\) | −182.094 | + | 560.428i | −0.0247775 | + | 0.0762574i | ||||
\(379\) | 678.172 | + | 492.721i | 0.0919139 | + | 0.0667794i | 0.632793 | − | 0.774321i | \(-0.281908\pi\) |
−0.540879 | + | 0.841100i | \(0.681908\pi\) | |||||||
\(380\) | 901.246 | + | 654.793i | 0.121666 | + | 0.0883952i | ||||
\(381\) | 3228.07 | − | 9934.96i | 0.434065 | − | 1.33592i | ||||
\(382\) | 1450.63 | + | 4464.58i | 0.194295 | + | 0.597978i | ||||
\(383\) | 2291.27 | − | 1664.70i | 0.305688 | − | 0.222095i | −0.424356 | − | 0.905495i | \(-0.639500\pi\) |
0.730044 | + | 0.683400i | \(0.239500\pi\) | |||||||
\(384\) | −10194.5 | −1.35479 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3661.45 | 0.482806 | ||||||||
\(387\) | 1674.16 | − | 1216.35i | 0.219903 | − | 0.159769i | ||||
\(388\) | −222.969 | − | 686.227i | −0.0291740 | − | 0.0897884i | ||||
\(389\) | 961.431 | − | 2958.98i | 0.125312 | − | 0.385671i | −0.868646 | − | 0.495434i | \(-0.835009\pi\) |
0.993958 | + | 0.109763i | \(0.0350090\pi\) | |||||||
\(390\) | 1395.14 | + | 1013.63i | 0.181143 | + | 0.131608i | ||||
\(391\) | −3712.98 | − | 2697.64i | −0.480239 | − | 0.348914i | ||||
\(392\) | 2403.81 | − | 7398.16i | 0.309721 | − | 0.953223i | ||||
\(393\) | 3921.66 | + | 12069.6i | 0.503363 | + | 1.54919i | ||||
\(394\) | 7776.48 | − | 5649.94i | 0.994348 | − | 0.722436i | ||||
\(395\) | 19227.5 | 2.44922 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14208.7 | 1.79626 | 0.898131 | − | 0.439728i | \(-0.144925\pi\) | ||||
0.898131 | + | 0.439728i | \(0.144925\pi\) | |||||||
\(398\) | −1820.59 | + | 1322.73i | −0.229291 | + | 0.166590i | ||||
\(399\) | −1053.03 | − | 3240.88i | −0.132123 | − | 0.406634i | ||||
\(400\) | −1757.62 | + | 5409.41i | −0.219703 | + | 0.676177i | ||||
\(401\) | 5065.81 | + | 3680.52i | 0.630859 | + | 0.458346i | 0.856698 | − | 0.515819i | \(-0.172512\pi\) |
−0.225839 | + | 0.974165i | \(0.572512\pi\) | |||||||
\(402\) | 5999.33 | + | 4358.77i | 0.744327 | + | 0.540785i | ||||
\(403\) | 52.1603 | − | 160.533i | 0.00644737 | − | 0.0198429i | ||||
\(404\) | 26.7383 | + | 82.2919i | 0.00329277 | + | 0.0101341i | ||||
\(405\) | 4945.15 | − | 3592.86i | 0.606732 | − | 0.440816i | ||||
\(406\) | −209.764 | −0.0256415 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7620.30 | −0.924660 | ||||||||
\(409\) | 3391.80 | − | 2464.29i | 0.410059 | − | 0.297925i | −0.363567 | − | 0.931568i | \(-0.618441\pi\) |
0.773625 | + | 0.633643i | \(0.218441\pi\) | |||||||
\(410\) | 3274.50 | + | 10077.9i | 0.394429 | + | 1.21393i | ||||
\(411\) | −3948.53 | + | 12152.3i | −0.473884 | + | 1.45847i | ||||
\(412\) | −15.0699 | − | 10.9489i | −0.00180204 | − | 0.00130926i | ||||
\(413\) | −219.610 | − | 159.556i | −0.0261653 | − | 0.0190102i | ||||
\(414\) | −3370.88 | + | 10374.5i | −0.400168 | + | 1.23159i | ||||
\(415\) | 2028.46 | + | 6242.97i | 0.239936 | + | 0.738446i | ||||
\(416\) | −104.964 | + | 76.2606i | −0.0123708 | + | 0.00898794i | ||||
\(417\) | 252.608 | 0.0296649 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9287.15 | −1.08283 | −0.541416 | − | 0.840755i | \(-0.682112\pi\) | ||||
−0.541416 | + | 0.840755i | \(0.682112\pi\) | |||||||
\(420\) | −156.863 | + | 113.968i | −0.0182241 | + | 0.0132406i | ||||
\(421\) | 4062.34 | + | 12502.6i | 0.470276 | + | 1.44736i | 0.852224 | + | 0.523178i | \(0.175254\pi\) |
−0.381947 | + | 0.924184i | \(0.624746\pi\) | |||||||
\(422\) | −90.6245 | + | 278.913i | −0.0104539 | + | 0.0321737i | ||||
\(423\) | 9974.44 | + | 7246.85i | 1.14651 | + | 0.832988i | ||||
\(424\) | −6471.18 | − | 4701.58i | −0.741198 | − | 0.538512i | ||||
\(425\) | −1219.02 | + | 3751.77i | −0.139132 | + | 0.428206i | ||||
\(426\) | 1387.97 | + | 4271.73i | 0.157857 | + | 0.485835i | ||||
\(427\) | −1835.76 | + | 1333.76i | −0.208053 | + | 0.151160i | ||||
\(428\) | −445.964 | −0.0503656 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2342.47 | −0.262707 | ||||||||
\(431\) | −3972.00 | + | 2885.83i | −0.443909 | + | 0.322519i | −0.787186 | − | 0.616715i | \(-0.788463\pi\) |
0.343277 | + | 0.939234i | \(0.388463\pi\) | |||||||
\(432\) | 1289.40 | + | 3968.37i | 0.143603 | + | 0.441964i | ||||
\(433\) | −3628.88 | + | 11168.5i | −0.402755 | + | 1.23955i | 0.520000 | + | 0.854166i | \(0.325932\pi\) |
−0.922755 | + | 0.385386i | \(0.874068\pi\) | |||||||
\(434\) | −213.852 | − | 155.373i | −0.0236526 | − | 0.0171846i | ||||
\(435\) | −2381.75 | − | 1730.44i | −0.262520 | − | 0.190732i | ||||
\(436\) | −172.931 | + | 532.226i | −0.0189951 | + | 0.0584610i | ||||
\(437\) | −4814.78 | − | 14818.4i | −0.527053 | − | 1.62210i | ||||
\(438\) | −17709.3 | + | 12866.5i | −1.93192 | + | 1.40362i | ||||
\(439\) | −11824.2 | −1.28551 | −0.642754 | − | 0.766073i | \(-0.722208\pi\) | ||||
−0.642754 | + | 0.766073i | \(0.722208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11960.4 | −1.29148 | ||||||||
\(442\) | 488.189 | − | 354.690i | 0.0525357 | − | 0.0381695i | ||||
\(443\) | 3121.72 | + | 9607.68i | 0.334803 | + | 1.03042i | 0.966819 | + | 0.255462i | \(0.0822275\pi\) |
−0.632016 | + | 0.774955i | \(0.717772\pi\) | |||||||
\(444\) | 17.2565 | − | 53.1102i | 0.00184450 | − | 0.00567680i | ||||
\(445\) | 17897.8 | + | 13003.5i | 1.90660 | + | 1.38522i | ||||
\(446\) | 8694.52 | + | 6316.94i | 0.923088 | + | 0.670663i | ||||
\(447\) | 5949.32 | − | 18310.1i | 0.629515 | − | 1.93745i | ||||
\(448\) | 514.058 | + | 1582.11i | 0.0542120 | + | 0.166847i | ||||
\(449\) | 279.316 | − | 202.935i | 0.0293580 | − | 0.0213299i | −0.573009 | − | 0.819549i | \(-0.694224\pi\) |
0.602368 | + | 0.798219i | \(0.294224\pi\) | |||||||
\(450\) | 9376.17 | 0.982216 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −158.134 | −0.0164557 | ||||||||
\(453\) | −16526.9 | + | 12007.5i | −1.71414 | + | 1.24539i | ||||
\(454\) | −1495.93 | − | 4603.99i | −0.154642 | − | 0.475939i | ||||
\(455\) | 75.5738 | − | 232.592i | 0.00778671 | − | 0.0239650i | ||||
\(456\) | −20929.5 | − | 15206.2i | −2.14938 | − | 1.56161i | ||||
\(457\) | 8549.00 | + | 6211.21i | 0.875067 | + | 0.635773i | 0.931942 | − | 0.362608i | \(-0.118114\pi\) |
−0.0568749 | + | 0.998381i | \(0.518114\pi\) | |||||||
\(458\) | 1617.05 | − | 4976.77i | 0.164978 | − | 0.507749i | ||||
\(459\) | 894.281 | + | 2752.31i | 0.0909400 | + | 0.279885i | ||||
\(460\) | −717.231 | + | 521.099i | −0.0726980 | + | 0.0528182i | ||||
\(461\) | 4733.96 | 0.478270 | 0.239135 | − | 0.970986i | \(-0.423136\pi\) | ||||
0.239135 | + | 0.970986i | \(0.423136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3431.20 | 0.344409 | 0.172204 | − | 0.985061i | \(-0.444911\pi\) | ||||
0.172204 | + | 0.985061i | \(0.444911\pi\) | |||||||
\(464\) | −1201.66 | + | 873.058i | −0.120228 | + | 0.0873506i | ||||
\(465\) | −1146.43 | − | 3528.34i | −0.114332 | − | 0.351877i | ||||
\(466\) | 3711.59 | − | 11423.1i | 0.368962 | − | 1.13555i | ||||
\(467\) | −4139.71 | − | 3007.67i | −0.410199 | − | 0.298027i | 0.363483 | − | 0.931601i | \(-0.381587\pi\) |
−0.773682 | + | 0.633574i | \(0.781587\pi\) | |||||||
\(468\) | 83.3085 | + | 60.5272i | 0.00822850 | + | 0.00597835i | ||||
\(469\) | 324.980 | − | 1000.19i | 0.0319961 | − | 0.0984739i | ||||
\(470\) | −4312.70 | − | 13273.1i | −0.423255 | − | 1.30265i | ||||
\(471\) | 15880.8 | − | 11538.1i | 1.55361 | − | 1.12876i | ||||
\(472\) | −2060.82 | −0.200968 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −28033.2 | −2.71648 | ||||||||
\(475\) | −10834.7 | + | 7871.87i | −1.04659 | + | 0.760392i | ||||
\(476\) | 20.9661 | + | 64.5269i | 0.00201886 | + | 0.00621341i | ||||
\(477\) | −3800.46 | + | 11696.6i | −0.364804 | + | 1.12275i | ||||
\(478\) | 9027.85 | + | 6559.12i | 0.863858 | + | 0.627630i | ||||
\(479\) | −9357.81 | − | 6798.85i | −0.892629 | − | 0.648533i | 0.0439333 | − | 0.999034i | \(-0.486011\pi\) |
−0.936562 | + | 0.350502i | \(0.886011\pi\) | |||||||
\(480\) | −881.191 | + | 2712.03i | −0.0837931 | + | 0.257889i | ||||
\(481\) | 21.7660 | + | 66.9889i | 0.00206329 | + | 0.00635017i | ||||
\(482\) | −8639.05 | + | 6276.64i | −0.816386 | + | 0.593139i | ||||
\(483\) | 2711.89 | 0.255477 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20002.9 | 1.87275 | ||||||||
\(486\) | −11400.2 | + | 8282.71i | −1.06404 | + | 0.773068i | ||||
\(487\) | −5663.21 | − | 17429.6i | −0.526950 | − | 1.62179i | −0.760427 | − | 0.649423i | \(-0.775010\pi\) |
0.233477 | − | 0.972362i | \(-0.424990\pi\) | |||||||
\(488\) | −5323.37 | + | 16383.7i | −0.493807 | + | 1.51978i | ||||
\(489\) | −17479.0 | − | 12699.2i | −1.61641 | − | 1.17439i | ||||
\(490\) | 10953.2 | + | 7957.94i | 1.00982 | + | 0.733679i | ||||
\(491\) | −2353.96 | + | 7244.75i | −0.216360 | + | 0.665888i | 0.782694 | + | 0.622407i | \(0.213845\pi\) |
−0.999054 | + | 0.0434814i | \(0.986155\pi\) | |||||||
\(492\) | 342.767 | + | 1054.93i | 0.0314088 | + | 0.0966665i | ||||
\(493\) | −833.427 | + | 605.520i | −0.0761372 | + | 0.0553169i | ||||
\(494\) | 2048.62 | 0.186582 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1871.75 | −0.169444 | ||||||||
\(497\) | 515.328 | − | 374.408i | 0.0465103 | − | 0.0337917i | ||||
\(498\) | −2957.45 | − | 9102.09i | −0.266117 | − | 0.819024i | ||||
\(499\) | 3989.14 | − | 12277.3i | 0.357872 | − | 1.10142i | −0.596453 | − | 0.802648i | \(-0.703424\pi\) |
0.954325 | − | 0.298770i | \(-0.0965763\pi\) | |||||||
\(500\) | −188.639 | − | 137.054i | −0.0168724 | − | 0.0122585i | ||||
\(501\) | 17557.2 | + | 12756.0i | 1.56566 | + | 1.13752i | ||||
\(502\) | 924.363 | − | 2844.90i | 0.0821839 | − | 0.252936i | ||||
\(503\) | 3141.36 | + | 9668.11i | 0.278462 | + | 0.857017i | 0.988283 | + | 0.152635i | \(0.0487759\pi\) |
−0.709821 | + | 0.704382i | \(0.751224\pi\) | |||||||
\(504\) | 2078.04 | − | 1509.79i | 0.183658 | − | 0.133435i | ||||
\(505\) | −2398.74 | −0.211371 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17190.6 | 1.50584 | ||||||||
\(508\) | −571.249 | + | 415.037i | −0.0498919 | + | 0.0362486i | ||||
\(509\) | 1993.14 | + | 6134.25i | 0.173564 | + | 0.534177i | 0.999565 | − | 0.0294928i | \(-0.00938922\pi\) |
−0.826001 | + | 0.563669i | \(0.809389\pi\) | |||||||
\(510\) | 4098.44 | − | 12613.7i | 0.355847 | − | 1.09519i | ||||
\(511\) | 2511.48 | + | 1824.70i | 0.217419 | + | 0.157964i | ||||
\(512\) | 10133.3 | + | 7362.24i | 0.874670 | + | 0.635485i | ||||
\(513\) | −3036.02 | + | 9343.89i | −0.261293 | + | 0.804177i | ||||
\(514\) | 661.199 | + | 2034.96i | 0.0567398 | + | 0.174627i | ||||
\(515\) | 417.774 | − | 303.530i | 0.0357462 | − | 0.0259712i | ||||
\(516\) | −245.205 | −0.0209197 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 110.305 | 0.00935623 | ||||||||
\(519\) | 14799.9 | − | 10752.7i | 1.25172 | − | 0.909428i | ||||
\(520\) | −573.742 | − | 1765.80i | −0.0483851 | − | 0.148914i | ||||
\(521\) | −5972.50 | + | 18381.5i | −0.502227 | + | 1.54569i | 0.303157 | + | 0.952941i | \(0.401959\pi\) |
−0.805383 | + | 0.592754i | \(0.798041\pi\) | |||||||
\(522\) | 1980.90 | + | 1439.21i | 0.166096 | + | 0.120675i | ||||
\(523\) | −5063.71 | − | 3679.00i | −0.423367 | − | 0.307594i | 0.355624 | − | 0.934629i | \(-0.384268\pi\) |
−0.778991 | + | 0.627035i | \(0.784268\pi\) | |||||||
\(524\) | 265.081 | − | 815.835i | 0.0220994 | − | 0.0680151i | ||||
\(525\) | −720.310 | − | 2216.89i | −0.0598799 | − | 0.184291i | ||||
\(526\) | −13659.6 | + | 9924.30i | −1.13230 | + | 0.822662i | ||||
\(527\) | −1298.18 | −0.107305 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 232.675 | 0.0191235 | ||||||||
\(530\) | 11262.8 | − | 8182.93i | 0.923069 | − | 0.670649i | ||||
\(531\) | 979.153 | + | 3013.52i | 0.0800219 | + | 0.246282i | ||||
\(532\) | −71.1781 | + | 219.064i | −0.00580068 | + | 0.0178527i | ||||
\(533\) | −1131.88 | − | 822.358i | −0.0919834 | − | 0.0668298i | ||||
\(534\) | −26094.5 | − | 18958.8i | −2.11464 | − | 1.53638i | ||||
\(535\) | 3820.44 | − | 11758.1i | 0.308733 | − | 0.950181i | ||||
\(536\) | −2467.19 | − | 7593.22i | −0.198818 | − | 0.611898i | ||||
\(537\) | −8416.22 | + | 6114.75i | −0.676326 | + | 0.491379i | ||||
\(538\) | 2696.44 | 0.216081 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 559.022 | 0.0445490 | ||||||||
\(541\) | 11332.8 | − | 8233.79i | 0.900623 | − | 0.654341i | −0.0380030 | − | 0.999278i | \(-0.512100\pi\) |
0.938626 | + | 0.344937i | \(0.112100\pi\) | |||||||
\(542\) | 3864.12 | + | 11892.6i | 0.306233 | + | 0.942489i | ||||
\(543\) | 1967.74 | − | 6056.07i | 0.155513 | − | 0.478620i | ||||
\(544\) | 807.265 | + | 586.512i | 0.0636235 | + | 0.0462252i | ||||
\(545\) | −12551.0 | − | 9118.84i | −0.986470 | − | 0.716712i | ||||
\(546\) | −110.185 | + | 339.113i | −0.00863638 | + | 0.0265801i | ||||
\(547\) | −1529.46 | − | 4707.20i | −0.119552 | − | 0.367944i | 0.873317 | − | 0.487152i | \(-0.161964\pi\) |
−0.992869 | + | 0.119208i | \(0.961964\pi\) | |||||||
\(548\) | 698.744 | − | 507.667i | 0.0544687 | − | 0.0395738i | ||||
\(549\) | 26487.0 | 2.05909 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3497.35 | −0.270404 | ||||||||
\(552\) | 16656.2 | − | 12101.4i | 1.28430 | − | 0.933100i | ||||
\(553\) | 1228.53 | + | 3781.02i | 0.0944707 | + | 0.290751i | ||||
\(554\) | 479.395 | − | 1475.43i | 0.0367645 | − | 0.113150i | ||||
\(555\) | 1252.45 | + | 909.958i | 0.0957901 | + | 0.0695956i | ||||
\(556\) | −13.8138 | − | 10.0363i | −0.00105366 | − | 0.000765528i | ||||
\(557\) | −1174.75 | + | 3615.51i | −0.0893641 | + | 0.275034i | −0.985744 | − | 0.168252i | \(-0.946188\pi\) |
0.896380 | + | 0.443287i | \(0.146188\pi\) | |||||||
\(558\) | 953.483 | + | 2934.52i | 0.0723372 | + | 0.222631i | ||||
\(559\) | 250.214 | − | 181.791i | 0.0189319 | − | 0.0137548i | ||||
\(560\) | −2711.94 | −0.204644 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14510.0 | 1.08908 | ||||||||
\(563\) | 8009.36 | − | 5819.14i | 0.599564 | − | 0.435608i | −0.246160 | − | 0.969229i | \(-0.579169\pi\) |
0.845724 | + | 0.533621i | \(0.179169\pi\) | |||||||
\(564\) | −451.444 | − | 1389.40i | −0.0337043 | − | 0.103731i | ||||
\(565\) | 1354.69 | − | 4169.29i | 0.100871 | − | 0.310449i | ||||
\(566\) | 10451.2 | + | 7593.21i | 0.776139 | + | 0.563898i | ||||
\(567\) | 1022.49 | + | 742.880i | 0.0757327 | + | 0.0550230i | ||||
\(568\) | 1494.36 | − | 4599.15i | 0.110390 | − | 0.339747i | ||||
\(569\) | 1646.80 | + | 5068.33i | 0.121331 | + | 0.373419i | 0.993215 | − | 0.116294i | \(-0.0371015\pi\) |
−0.871884 | + | 0.489713i | \(0.837102\pi\) | |||||||
\(570\) | 36427.1 | − | 26465.8i | 2.67678 | − | 1.94479i | ||||
\(571\) | −16962.6 | −1.24319 | −0.621597 | − | 0.783337i | \(-0.713516\pi\) | ||||
−0.621597 | + | 0.783337i | \(0.713516\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13622.6 | −0.993181 | ||||||||
\(574\) | −1772.55 | + | 1287.83i | −0.128893 | + | 0.0936466i | ||||
\(575\) | −3293.50 | − | 10136.3i | −0.238867 | − | 0.735156i | ||||
\(576\) | 6000.49 | − | 18467.6i | 0.434063 | − | 1.33591i | ||||
\(577\) | 12529.2 | + | 9103.01i | 0.903983 | + | 0.656782i | 0.939486 | − | 0.342587i | \(-0.111303\pi\) |
−0.0355028 | + | 0.999370i | \(0.511303\pi\) | |||||||
\(578\) | 7104.47 | + | 5161.70i | 0.511258 | + | 0.371451i | ||||
\(579\) | −3283.38 | + | 10105.2i | −0.235670 | + | 0.725317i | ||||
\(580\) | 61.4935 | + | 189.257i | 0.00440238 | + | 0.0135491i | ||||
\(581\) | −1098.05 | + | 797.778i | −0.0784074 | + | 0.0569663i | ||||
\(582\) | −29163.7 | −2.07710 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 23567.7 | 1.66993 | ||||||||
\(585\) | −2309.51 | + | 1677.96i | −0.163225 | + | 0.118590i | ||||
\(586\) | 1966.19 | + | 6051.30i | 0.138605 | + | 0.426582i | ||||
\(587\) | 3425.19 | − | 10541.7i | 0.240839 | − | 0.741228i | −0.755453 | − | 0.655202i | \(-0.772583\pi\) |
0.996293 | − | 0.0860254i | \(-0.0274166\pi\) | |||||||
\(588\) | 1146.55 | + | 833.019i | 0.0804133 | + | 0.0584237i | ||||
\(589\) | −3565.51 | − | 2590.50i | −0.249430 | − | 0.181222i | ||||
\(590\) | 1108.37 | − | 3411.22i | 0.0773407 | − | 0.238030i | ||||
\(591\) | 8619.73 | + | 26528.8i | 0.599946 | + | 1.84644i | ||||
\(592\) | 631.896 | − | 459.099i | 0.0438695 | − | 0.0318731i | ||||
\(593\) | 4349.68 | 0.301214 | 0.150607 | − | 0.988594i | \(-0.451877\pi\) | ||||
0.150607 | + | 0.988594i | \(0.451877\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1880.90 | −0.129596 | ||||||||
\(596\) | −1052.81 | + | 764.911i | −0.0723570 | + | 0.0525705i | ||||
\(597\) | −2018.00 | − | 6210.78i | −0.138344 | − | 0.425779i | ||||
\(598\) | −503.801 | + | 1550.54i | −0.0344514 | + | 0.106031i | ||||
\(599\) | −10666.0 | − | 7749.31i | −0.727548 | − | 0.528595i | 0.161239 | − | 0.986915i | \(-0.448451\pi\) |
−0.888787 | + | 0.458321i | \(0.848451\pi\) | |||||||
\(600\) | −14316.6 | − | 10401.6i | −0.974123 | − | 0.707742i | ||||
\(601\) | −5798.71 | + | 17846.6i | −0.393568 | + | 1.21128i | 0.536503 | + | 0.843898i | \(0.319745\pi\) |
−0.930071 | + | 0.367379i | \(0.880255\pi\) | |||||||
\(602\) | −149.670 | − | 460.638i | −0.0101331 | − | 0.0311864i | ||||
\(603\) | −9931.30 | + | 7215.51i | −0.670703 | + | 0.487294i | ||||
\(604\) | 1380.84 | 0.0930223 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3497.29 | 0.234435 | ||||||||
\(607\) | −17694.3 | + | 12855.7i | −1.18318 | + | 0.859629i | −0.992527 | − | 0.122028i | \(-0.961060\pi\) |
−0.190652 | + | 0.981658i | \(0.561060\pi\) | |||||||
\(608\) | 1046.82 | + | 3221.77i | 0.0698257 | + | 0.214901i | ||||
\(609\) | 188.105 | − | 578.927i | 0.0125162 | − | 0.0385210i | ||||
\(610\) | −24256.4 | − | 17623.3i | −1.61002 | − | 1.16975i | ||||
\(611\) | 1490.75 | + | 1083.09i | 0.0987057 | + | 0.0717139i | ||||
\(612\) | 244.732 | − | 753.208i | 0.0161646 | − | 0.0497494i | ||||
\(613\) | −1090.17 | − | 3355.19i | −0.0718294 | − | 0.221068i | 0.908697 | − | 0.417457i | \(-0.137079\pi\) |
−0.980526 | + | 0.196389i | \(0.937079\pi\) | |||||||
\(614\) | 3708.99 | − | 2694.74i | 0.243783 | − | 0.177119i | ||||
\(615\) | −30750.2 | −2.01621 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22728.1 | −1.48298 | −0.741490 | − | 0.670963i | \(-0.765881\pi\) | ||||
−0.741490 | + | 0.670963i | \(0.765881\pi\) | |||||||
\(618\) | −609.103 | + | 442.540i | −0.0396468 | + | 0.0288051i | ||||
\(619\) | −6626.35 | − | 20393.8i | −0.430267 | − | 1.32423i | −0.897860 | − | 0.440282i | \(-0.854879\pi\) |
0.467592 | − | 0.883944i | \(-0.345121\pi\) | |||||||
\(620\) | −77.4914 | + | 238.494i | −0.00501956 | + | 0.0154486i | ||||
\(621\) | −6325.50 | − | 4595.75i | −0.408750 | − | 0.296974i | ||||
\(622\) | −7896.67 | − | 5737.26i | −0.509047 | − | 0.369845i | ||||
\(623\) | −1413.52 | + | 4350.37i | −0.0909013 | + | 0.279766i | ||||
\(624\) | 780.213 | + | 2401.25i | 0.0500537 | + | 0.154050i | ||||
\(625\) | 14908.7 | − | 10831.8i | 0.954156 | − | 0.693235i | ||||
\(626\) | 19628.0 | 1.25319 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1326.85 | −0.0843109 | ||||||||
\(629\) | 438.259 | − | 318.414i | 0.0277815 | − | 0.0201844i | ||||
\(630\) | 1381.48 | + | 4251.75i | 0.0873642 | + | 0.268879i | ||||
\(631\) | 6653.74 | − | 20478.1i | 0.419780 | − | 1.29195i | −0.488124 | − | 0.872774i | \(-0.662319\pi\) |
0.907905 | − | 0.419177i | \(-0.137681\pi\) | |||||||
\(632\) | 24417.7 | + | 17740.5i | 1.53684 | + | 1.11658i | ||||
\(633\) | −688.504 | − | 500.228i | −0.0432316 | − | 0.0314096i | ||||
\(634\) | −13.2612 | + | 40.8138i | −0.000830709 | + | 0.00255666i | ||||
\(635\) | −6048.97 | − | 18616.8i | −0.378025 | − | 1.16344i | ||||
\(636\) | 1178.97 | − | 856.571i | 0.0735050 | − | 0.0534045i | ||||
\(637\) | −1787.56 | −0.111187 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7435.33 | −0.460309 | ||||||||
\(640\) | −15454.8 | + | 11228.6i | −0.954540 | + | 0.693514i | ||||
\(641\) | 6226.16 | + | 19162.1i | 0.383648 | + | 1.18075i | 0.937456 | + | 0.348103i | \(0.113174\pi\) |
−0.553808 | + | 0.832644i | \(0.686826\pi\) | |||||||
\(642\) | −5570.10 | + | 17143.0i | −0.342421 | + | 1.05386i | ||||
\(643\) | −23356.1 | − | 16969.2i | −1.43246 | − | 1.04074i | −0.989552 | − | 0.144179i | \(-0.953946\pi\) |
−0.442911 | − | 0.896566i | \(-0.646054\pi\) | |||||||
\(644\) | −148.299 | − | 107.745i | −0.00907421 | − | 0.00659280i | ||||
\(645\) | 2100.60 | − | 6464.98i | 0.128234 | − | 0.394664i | ||||
\(646\) | −4868.78 | − | 14984.6i | −0.296532 | − | 0.912631i | ||||
\(647\) | 1286.35 | − | 934.591i | 0.0781636 | − | 0.0567891i | −0.548017 | − | 0.836467i | \(-0.684617\pi\) |
0.626181 | + | 0.779678i | \(0.284617\pi\) | |||||||
\(648\) | 9595.02 | 0.581679 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1401.33 | 0.0845612 | ||||||||
\(651\) | 620.583 | − | 450.880i | 0.0373619 | − | 0.0271450i | ||||
\(652\) | 451.282 | + | 1388.90i | 0.0271067 | + | 0.0834259i | ||||
\(653\) | 6189.01 | − | 19047.8i | 0.370896 | − | 1.14150i | −0.575311 | − | 0.817935i | \(-0.695119\pi\) |
0.946206 | − | 0.323564i | \(-0.104881\pi\) | |||||||
\(654\) | 18299.0 | + | 13295.0i | 1.09411 | + | 0.794919i | ||||
\(655\) | 19239.1 | + | 13978.0i | 1.14769 | + | 0.833842i | ||||
\(656\) | −4794.20 | + | 14755.0i | −0.285338 | + | 0.878182i | ||||
\(657\) | −11197.7 | − | 34462.9i | −0.664937 | − | 2.04646i | ||||
\(658\) | 2334.55 | − | 1696.15i | 0.138313 | − | 0.100491i | ||||
\(659\) | −10520.7 | −0.621897 | −0.310948 | − | 0.950427i | \(-0.600647\pi\) | ||||
−0.310948 | + | 0.950427i | \(0.600647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3295.83 | 0.193938 | 0.0969690 | − | 0.995287i | \(-0.469085\pi\) | ||||
0.0969690 | + | 0.995287i | \(0.469085\pi\) | |||||||
\(662\) | 2915.25 | − | 2118.05i | 0.171155 | − | 0.124351i | ||||
\(663\) | 541.127 | + | 1665.42i | 0.0316978 | + | 0.0975557i | ||||
\(664\) | −3184.13 | + | 9799.76i | −0.186097 | + | 0.572748i | ||||
\(665\) | −5165.99 | − | 3753.31i | −0.301246 | − | 0.218868i | ||||
\(666\) | −1041.66 | − | 756.813i | −0.0606060 | − | 0.0440329i | ||||
\(667\) | 860.078 | − | 2647.05i | 0.0499286 | − | 0.153664i | ||||
\(668\) | −453.301 | − | 1395.12i | −0.0262556 | − | 0.0808064i | ||||
\(669\) | −25230.8 | + | 18331.3i | −1.45812 | + | 1.05938i | ||||
\(670\) | 13895.8 | 0.801257 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −589.612 | −0.0338464 | ||||||||
\(673\) | 960.819 | − | 698.076i | 0.0550325 | − | 0.0399834i | −0.559929 | − | 0.828541i | \(-0.689172\pi\) |
0.614961 | + | 0.788557i | \(0.289172\pi\) | |||||||
\(674\) | −201.930 | − | 621.477i | −0.0115402 | − | 0.0355169i | ||||
\(675\) | −2076.75 | + | 6391.59i | −0.118421 | + | 0.364463i | ||||
\(676\) | −940.060 | − | 682.994i | −0.0534855 | − | 0.0388595i | ||||
\(677\) | −10696.3 | − | 7771.33i | −0.607227 | − | 0.441177i | 0.241210 | − | 0.970473i | \(-0.422456\pi\) |
−0.848437 | + | 0.529297i | \(0.822456\pi\) | |||||||
\(678\) | −1975.10 | + | 6078.72i | −0.111878 | + | 0.344324i | ||||
\(679\) | 1278.07 | + | 3933.49i | 0.0722353 | + | 0.222317i | ||||
\(680\) | −11552.3 | + | 8393.24i | −0.651487 | + | 0.473333i | ||||
\(681\) | 14048.0 | 0.790485 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13831.4 | −0.774882 | −0.387441 | − | 0.921894i | \(-0.626641\pi\) | ||||
−0.387441 | + | 0.921894i | \(0.626641\pi\) | |||||||
\(684\) | 2175.18 | − | 1580.36i | 0.121594 | − | 0.0883432i | ||||
\(685\) | 7399.02 | + | 22771.8i | 0.412704 | + | 1.27017i | ||||
\(686\) | −1754.58 | + | 5400.03i | −0.0976532 | + | 0.300546i | ||||
\(687\) | 12285.3 | + | 8925.78i | 0.682260 | + | 0.495691i | ||||
\(688\) | −2774.62 | − | 2015.88i | −0.153752 | − | 0.111707i | ||||
\(689\) | −568.005 | + | 1748.14i | −0.0314068 | + | 0.0966602i | ||||
\(690\) | 11073.0 | + | 34079.2i | 0.610930 | + | 1.88025i | ||||
\(691\) | 7942.18 | − | 5770.33i | 0.437243 | − | 0.317675i | −0.347296 | − | 0.937756i | \(-0.612900\pi\) |
0.784538 | + | 0.620080i | \(0.212900\pi\) | |||||||
\(692\) | −1236.54 | −0.0679280 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16017.4 | −0.876101 | ||||||||
\(695\) | 382.951 | − | 278.230i | 0.0209010 | − | 0.0151854i | ||||
\(696\) | −1428.06 | − | 4395.11i | −0.0777735 | − | 0.239362i | ||||
\(697\) | −3325.08 | + | 10233.5i | −0.180698 | + | 0.556130i | ||||
\(698\) | −7717.68 | − | 5607.22i | −0.418508 | − | 0.304064i | ||||
\(699\) | 28198.2 | + | 20487.2i | 1.52583 | + | 1.10858i | ||||
\(700\) | −48.6886 | + | 149.848i | −0.00262894 | + | 0.00809104i | ||||
\(701\) | 9254.98 | + | 28483.9i | 0.498653 | + | 1.53470i | 0.811185 | + | 0.584789i | \(0.198823\pi\) |
−0.312532 | + | 0.949907i | \(0.601177\pi\) | |||||||
\(702\) | 831.689 | − | 604.258i | 0.0447152 | − | 0.0324875i | ||||
\(703\) | 1839.09 | 0.0986667 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40499.8 | 2.16356 | ||||||||
\(706\) | 24128.9 | − | 17530.7i | 1.28627 | − | 0.934527i | ||||
\(707\) | −153.265 | − | 471.702i | −0.00815294 | − | 0.0250922i | ||||
\(708\) | 116.022 | − | 357.080i | 0.00615873 | − | 0.0189546i | ||||
\(709\) | −9147.95 | − | 6646.38i | −0.484568 | − | 0.352059i | 0.318524 | − | 0.947915i | \(-0.396813\pi\) |
−0.803091 | + | 0.595856i | \(0.796813\pi\) | |||||||
\(710\) | 6809.16 | + | 4947.15i | 0.359920 | + | 0.261497i | ||||
\(711\) | 14340.3 | − | 44135.0i | 0.756405 | − | 2.32798i | ||||
\(712\) | 10731.2 | + | 33027.2i | 0.564843 | + | 1.73841i | ||||
\(713\) | 2837.51 | − | 2061.57i | 0.149040 | − | 0.108284i | ||||
\(714\) | 2742.30 | 0.143737 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 703.181 | 0.0367027 | ||||||||
\(717\) | −26198.1 | + | 19034.1i | −1.36456 | + | 0.991409i | ||||
\(718\) | −9709.49 | − | 29882.8i | −0.504673 | − | 1.55322i | ||||
\(719\) | −10081.2 | + | 31026.7i | −0.522900 | + | 1.60932i | 0.245531 | + | 0.969389i | \(0.421038\pi\) |
−0.768431 | + | 0.639933i | \(0.778962\pi\) | |||||||
\(720\) | 25610.1 | + | 18606.9i | 1.32560 | + | 0.963106i | ||||
\(721\) | 86.3813 | + | 62.7597i | 0.00446187 | + | 0.00324174i | ||||
\(722\) | 10738.4 | − | 33049.4i | 0.553521 | − | 1.70356i | ||||
\(723\) | −9575.83 | − | 29471.4i | −0.492571 | − | 1.51598i | ||||
\(724\) | −348.217 | + | 252.994i | −0.0178748 | + | 0.0129868i | ||||
\(725\) | −2392.33 | −0.122550 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −502.545 | −0.0256373 | −0.0128187 | − | 0.999918i | \(-0.504080\pi\) | ||||
−0.0128187 | + | 0.999918i | \(0.504080\pi\) | |||||||
\(728\) | 310.578 | − | 225.648i | 0.0158115 | − | 0.0114877i | ||||
\(729\) | −9203.52 | − | 28325.5i | −0.467587 | − | 1.43909i | ||||
\(730\) | −12675.5 | + | 39011.1i | −0.642658 | + | 1.97790i | ||||
\(731\) | −1924.37 | − | 1398.14i | −0.0973673 | − | 0.0707415i | ||||
\(732\) | −2539.11 | − | 1844.77i | −0.128208 | − | 0.0931485i | ||||
\(733\) | 2667.24 | − | 8208.93i | 0.134402 | − | 0.413647i | −0.861094 | − | 0.508445i | \(-0.830220\pi\) |
0.995497 | + | 0.0947978i | \(0.0302204\pi\) | |||||||
\(734\) | 5713.05 | + | 17582.9i | 0.287292 | + | 0.884194i | ||||
\(735\) | −31785.2 | + | 23093.3i | −1.59512 | + | 1.15893i | ||||
\(736\) | −2695.90 | −0.135017 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 25575.0 | 1.27565 | ||||||||
\(739\) | 14851.5 | − | 10790.3i | 0.739273 | − | 0.537113i | −0.153210 | − | 0.988194i | \(-0.548961\pi\) |
0.892483 | + | 0.451080i | \(0.148961\pi\) | |||||||
\(740\) | −32.3365 | − | 99.5214i | −0.00160637 | − | 0.00494389i | ||||
\(741\) | −1837.08 | + | 5653.96i | −0.0910755 | + | 0.280302i | ||||
\(742\) | 2328.77 | + | 1691.95i | 0.115218 | + | 0.0837108i | ||||
\(743\) | −9046.95 | − | 6572.99i | −0.446703 | − | 0.324549i | 0.341590 | − | 0.939849i | \(-0.389035\pi\) |
−0.788293 | + | 0.615300i | \(0.789035\pi\) | |||||||
\(744\) | 1799.58 | − | 5538.53i | 0.0886770 | − | 0.272920i | ||||
\(745\) | −11148.2 | − | 34310.7i | −0.548241 | − | 1.68731i | ||||
\(746\) | 11737.0 | − | 8527.47i | 0.576037 | − | 0.418516i | ||||
\(747\) | 15843.0 | 0.775991 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2556.29 | 0.124706 | ||||||||
\(750\) | −7624.52 | + | 5539.54i | −0.371211 | + | 0.269701i | ||||
\(751\) | 5170.90 | + | 15914.4i | 0.251250 | + | 0.773269i | 0.994545 | + | 0.104305i | \(0.0332618\pi\) |
−0.743295 | + | 0.668964i | \(0.766738\pi\) | |||||||
\(752\) | 6314.23 | − | 19433.2i | 0.306192 | − | 0.942361i | ||||
\(753\) | 7022.69 | + | 5102.29i | 0.339869 | + | 0.246929i | ||||
\(754\) | 296.060 | + | 215.100i | 0.0142995 | + | 0.0103892i | ||||
\(755\) | −11829.2 | + | 36406.6i | −0.570211 | + | 1.75493i | ||||
\(756\) | 35.7182 | + | 109.929i | 0.00171833 | + | 0.00528848i | ||||
\(757\) | 19742.0 | − | 14343.4i | 0.947865 | − | 0.688664i | −0.00243609 | − | 0.999997i | \(-0.500775\pi\) |
0.950301 | + | 0.311333i | \(0.100775\pi\) | |||||||
\(758\) | −2290.19 | −0.109741 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −48477.6 | −2.31377 | ||||||||
\(761\) | −6851.83 | + | 4978.15i | −0.326385 | + | 0.237132i | −0.738895 | − | 0.673821i | \(-0.764652\pi\) |
0.412510 | + | 0.910953i | \(0.364652\pi\) | |||||||
\(762\) | 8819.24 | + | 27142.8i | 0.419275 | + | 1.29039i | ||||
\(763\) | 991.247 | − | 3050.74i | 0.0470322 | − | 0.144750i | ||||
\(764\) | 744.947 | + | 541.236i | 0.0352765 | + | 0.0256299i | ||||
\(765\) | 17762.2 | + | 12905.0i | 0.839471 | + | 0.609911i | ||||
\(766\) | −2391.06 | + | 7358.91i | −0.112784 | + | 0.347113i | ||||
\(767\) | 146.341 | + | 450.391i | 0.00688927 | + | 0.0212030i | ||||
\(768\) | −5255.44 | + | 3818.30i | −0.246926 | + | 0.179402i | ||||
\(769\) | 32834.7 | 1.53973 | 0.769864 | − | 0.638208i | \(-0.220324\pi\) | ||||
0.769864 | + | 0.638208i | \(0.220324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6209.20 | −0.290038 | ||||||||
\(772\) | 581.038 | − | 422.149i | 0.0270881 | − | 0.0196807i | ||||
\(773\) | −10992.2 | − | 33830.4i | −0.511463 | − | 1.57412i | −0.789627 | − | 0.613587i | \(-0.789726\pi\) |
0.278164 | − | 0.960533i | \(-0.410274\pi\) | |||||||
\(774\) | −1747.07 | + | 5376.93i | −0.0811332 | + | 0.249702i | ||||
\(775\) | −2438.95 | − | 1772.00i | −0.113045 | − | 0.0821318i | ||||
\(776\) | 25402.4 | + | 18455.9i | 1.17512 | + | 0.853774i | ||||
\(777\) | −98.9154 | + | 304.430i | −0.00456701 | + | 0.0140558i | ||||
\(778\) | 2626.68 | + | 8084.08i | 0.121042 | + | 0.372530i | ||||
\(779\) | −29553.4 | + | 21471.8i | −1.35925 | + | 0.987556i | ||||
\(780\) | 338.262 | 0.0155279 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12538.7 | 0.573381 | ||||||||
\(783\) | −1419.84 | + | 1031.58i | −0.0648034 | + | 0.0470824i | ||||
\(784\) | 6125.41 | + | 18852.1i | 0.279037 | + | 0.858787i | ||||
\(785\) | 11366.8 | − | 34983.3i | 0.516812 | − | 1.59058i | ||||
\(786\) | −28050.1 | − | 20379.6i | −1.27292 | − | 0.924830i | ||||
\(787\) | −12725.5 | − | 9245.63i | −0.576386 | − | 0.418769i | 0.261033 | − | 0.965330i | \(-0.415937\pi\) |
−0.837419 | + | 0.546561i | \(0.815937\pi\) | |||||||
\(788\) | 582.641 | − | 1793.19i | 0.0263398 | − | 0.0810655i | ||||
\(789\) | −15140.8 | − | 46598.7i | −0.683178 | − | 2.10261i | ||||
\(790\) | −42498.2 | + | 30876.7i | −1.91394 | + | 1.39056i | ||||
\(791\) | 906.431 | 0.0407446 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3958.67 | 0.177272 | ||||||||
\(794\) | −31405.2 | + | 22817.2i | −1.40369 | + | 1.01984i | ||||
\(795\) | 12484.1 | + | 38422.2i | 0.556939 | + | 1.71408i | ||||
\(796\) | −136.405 | + | 419.811i | −0.00607380 | + | 0.0186932i | ||||
\(797\) | −6381.58 | − | 4636.49i | −0.283623 | − | 0.206064i | 0.436873 | − | 0.899523i | \(-0.356086\pi\) |
−0.720496 | + | 0.693459i | \(0.756086\pi\) | |||||||
\(798\) | 7531.87 | + | 5472.23i | 0.334117 | + | 0.242750i | ||||
\(799\) | 4379.31 | − | 13478.1i | 0.193904 | − | 0.596774i | ||||
\(800\) | 716.063 | + | 2203.82i | 0.0316458 | + | 0.0973958i | ||||
\(801\) | 43196.8 | − | 31384.3i | 1.90547 | − | 1.38441i | ||||
\(802\) | −17107.2 | −0.753214 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1454.58 | 0.0638050 | ||||||||
\(805\) | 4111.20 | − | 2986.96i | 0.180001 | − | 0.130778i | ||||
\(806\) | 142.505 | + | 438.584i | 0.00622768 | + | 0.0191668i | ||||
\(807\) | −2418.01 | + | 7441.88i | −0.105475 | + | 0.324618i | ||||
\(808\) | −3046.24 | − | 2213.22i | −0.132632 | − | 0.0963625i | ||||
\(809\) | −4770.75 | − | 3466.15i | −0.207331 | − | 0.150635i | 0.479274 | − | 0.877665i | \(-0.340900\pi\) |
−0.686605 | + | 0.727030i | \(0.740900\pi\) | |||||||
\(810\) | −5160.51 | + | 15882.4i | −0.223854 | + | 0.688952i | ||||
\(811\) | 4387.41 | + | 13503.0i | 0.189966 | + | 0.584656i | 0.999999 | − | 0.00172932i | \(-0.000550460\pi\) |
−0.810032 | + | 0.586385i | \(0.800550\pi\) | |||||||
\(812\) | −33.2876 | + | 24.1849i | −0.00143863 | + | 0.00104523i | ||||
\(813\) | −36287.3 | −1.56538 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40485.3 | −1.74005 | ||||||||
\(816\) | 15709.6 | − | 11413.7i | 0.673954 | − | 0.489656i | ||||
\(817\) | −2495.42 | − | 7680.12i | −0.106859 | − | 0.328878i | ||||
\(818\) | −3539.52 | + | 10893.5i | −0.151291 | + | 0.465627i | ||||
\(819\) | −477.529 | − | 346.945i | −0.0203739 | − | 0.0148025i | ||||
\(820\) | 1681.57 | + | 1221.73i | 0.0716132 | + | 0.0520300i | ||||
\(821\) | −6131.42 | + | 18870.6i | −0.260643 | + | 0.802177i | 0.732022 | + | 0.681281i | \(0.238577\pi\) |
−0.992665 | + | 0.120896i | \(0.961423\pi\) | |||||||
\(822\) | −10787.6 | − | 33200.7i | −0.457737 | − | 1.40877i | ||||
\(823\) | 22816.0 | − | 16576.8i | 0.966364 | − | 0.702104i | 0.0117439 | − | 0.999931i | \(-0.496262\pi\) |
0.954620 | + | 0.297827i | \(0.0962617\pi\) | |||||||
\(824\) | 810.602 | 0.0342702 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 741.622 | 0.0312401 | ||||||||
\(827\) | −27531.7 | + | 20002.9i | −1.15764 | + | 0.841076i | −0.989478 | − | 0.144683i | \(-0.953784\pi\) |
−0.168164 | + | 0.985759i | \(0.553784\pi\) | |||||||
\(828\) | 661.206 | + | 2034.98i | 0.0277518 | + | 0.0854113i | ||||
\(829\) | 1523.93 | − | 4690.19i | 0.0638461 | − | 0.196498i | −0.914045 | − | 0.405613i | \(-0.867058\pi\) |
0.977891 | + | 0.209115i | \(0.0670582\pi\) | |||||||
\(830\) | −14508.8 | − | 10541.3i | −0.606756 | − | 0.440834i | ||||
\(831\) | 3642.13 | + | 2646.16i | 0.152039 | + | 0.110462i | ||||
\(832\) | 896.814 | − | 2760.11i | 0.0373695 | − | 0.115011i | ||||
\(833\) | 4248.36 | + | 13075.1i | 0.176707 | + | 0.543848i | ||||
\(834\) | −558.333 | + | 405.653i | −0.0231816 | + | 0.0168424i | ||||
\(835\) | 40666.4 | 1.68541 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2211.60 | −0.0913312 | ||||||||
\(838\) | 20527.2 | − | 14913.9i | 0.846180 | − | 0.614786i | ||||
\(839\) | −11801.3 | − | 36320.6i | −0.485609 | − | 1.49455i | −0.831097 | − | 0.556127i | \(-0.812287\pi\) |
0.345489 | − | 0.938423i | \(-0.387713\pi\) | |||||||
\(840\) | 2607.36 | − | 8024.64i | 0.107098 | − | 0.329615i | ||||
\(841\) | 19225.7 | + | 13968.3i | 0.788293 | + | 0.572729i | ||||
\(842\) | −29056.3 | − | 21110.6i | −1.18925 | − | 0.864039i | ||||
\(843\) | −13011.7 | + | 40045.9i | −0.531610 | + | 1.63613i | ||||
\(844\) | 17.7762 | + | 54.7095i | 0.000724979 | + | 0.00223126i | ||||
\(845\) | 26060.8 | − | 18934.2i | 1.06097 | − | 0.770838i | ||||
\(846\) | −33683.7 | −1.36888 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20382.7 | 0.825406 | ||||||||
\(849\) | −30328.5 | + | 22034.9i | −1.22600 | + | 0.890738i | ||||
\(850\) | −3330.43 | − | 10250.0i | −0.134392 | − | 0.413615i | ||||
\(851\) | −452.274 | + | 1391.96i | −0.0182183 | + | 0.0560701i | ||||
\(852\) | 712.769 | + | 517.857i | 0.0286609 | + | 0.0208233i | ||||
\(853\) | −34760.9 | − | 25255.3i | −1.39530 | − | 1.01374i | −0.995260 | − | 0.0972464i | \(-0.968997\pi\) |
−0.400039 | − | 0.916498i | \(-0.631003\pi\) | |||||||
\(854\) | 1915.71 | − | 5895.95i | 0.0767615 | − | 0.236248i | ||||
\(855\) | 23033.1 | + | 70888.6i | 0.921304 | + | 2.83548i | ||||
\(856\) | 15700.5 | − | 11407.1i | 0.626905 | − | 0.455473i | ||||
\(857\) | −17281.5 | −0.688828 | −0.344414 | − | 0.938818i | \(-0.611922\pi\) | ||||
−0.344414 | + | 0.938818i | \(0.611922\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9316.75 | 0.370062 | 0.185031 | − | 0.982733i | \(-0.440761\pi\) | ||||
0.185031 | + | 0.982733i | \(0.440761\pi\) | |||||||
\(860\) | −371.729 | + | 270.077i | −0.0147394 | + | 0.0107088i | ||||
\(861\) | −1964.76 | − | 6046.91i | −0.0777687 | − | 0.239347i | ||||
\(862\) | 4144.99 | − | 12757.0i | 0.163780 | − | 0.504065i | ||||
\(863\) | 7805.11 | + | 5670.75i | 0.307867 | + | 0.223678i | 0.730981 | − | 0.682398i | \(-0.239063\pi\) |
−0.423114 | + | 0.906077i | \(0.639063\pi\) | |||||||
\(864\) | 1375.27 | + | 999.194i | 0.0541525 | + | 0.0393441i | ||||
\(865\) | 10593.1 | − | 32602.1i | 0.416388 | − | 1.28151i | ||||
\(866\) | −9914.29 | − | 30513.0i | −0.389031 | − | 1.19732i | ||||
\(867\) | −20616.6 | + | 14978.9i | −0.807586 | + | 0.586746i | ||||
\(868\) | −51.8501 | −0.00202754 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 8043.18 | 0.313436 | ||||||||
\(871\) | −1484.30 | + | 1078.41i | −0.0577424 | + | 0.0419523i | ||||
\(872\) | −7525.36 | − | 23160.7i | −0.292249 | − | 0.899449i | ||||
\(873\) | 14918.6 | − | 45914.7i | 0.578371 | − | 1.78004i | ||||
\(874\) | 34438.2 | + | 25020.8i | 1.33283 | + | 0.968355i | ||||
\(875\) | 1081.29 | + | 785.602i | 0.0417763 | + | 0.0303522i | ||||
\(876\) | −1326.84 | + | 4083.60i | −0.0511756 | + | 0.157502i | ||||
\(877\) | 6096.50 | + | 18763.1i | 0.234737 | + | 0.722445i | 0.997156 | + | 0.0753623i | \(0.0240113\pi\) |
−0.762419 | + | 0.647083i | \(0.775989\pi\) | |||||||
\(878\) | 26134.7 | − | 18988.0i | 1.00456 | − | 0.729856i | ||||
\(879\) | −18464.1 | −0.708509 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19473.9 | 0.744712 | 0.372356 | − | 0.928090i | \(-0.378550\pi\) | ||||
0.372356 | + | 0.928090i | \(0.378550\pi\) | |||||||
\(882\) | 26435.8 | − | 19206.7i | 1.00923 | − | 0.733248i | ||||
\(883\) | 15170.4 | + | 46689.7i | 0.578170 | + | 1.77943i | 0.625121 | + | 0.780528i | \(0.285050\pi\) |
−0.0469507 | + | 0.998897i | \(0.514950\pi\) | |||||||
\(884\) | 36.5769 | − | 112.572i | 0.00139164 | − | 0.00428304i | ||||
\(885\) | 8420.69 | + | 6117.99i | 0.319840 | + | 0.232377i | ||||
\(886\) | −22328.5 | − | 16222.6i | −0.846658 | − | 0.615133i | ||||
\(887\) | 2871.65 | − | 8838.03i | 0.108704 | − | 0.334557i | −0.881878 | − | 0.471478i | \(-0.843721\pi\) |
0.990582 | + | 0.136921i | \(0.0437207\pi\) | |||||||
\(888\) | 750.947 | + | 2311.18i | 0.0283785 | + | 0.0873401i | ||||
\(889\) | 3274.43 | − | 2379.01i | 0.123533 | − | 0.0897519i | ||||
\(890\) | −60440.8 | −2.27638 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2108.05 | 0.0791288 | ||||||||
\(893\) | 38923.4 | − | 28279.5i | 1.45859 | − | 1.05973i | ||||
\(894\) | 16253.8 | + | 50024.2i | 0.608064 | + | 1.87143i | ||||
\(895\) | −6023.95 | + | 18539.8i | −0.224981 | + | 0.692421i | ||||
\(896\) | −3195.53 | − | 2321.69i | −0.119146 | − | 0.0865649i | ||||
\(897\) | −3827.54 | − | 2780.87i | −0.142473 | − | 0.103512i | ||||
\(898\) | −291.481 | + | 897.086i | −0.0108317 | + | 0.0333365i | ||||
\(899\) | −243.281 | − | 748.741i | −0.00902544 | − | 0.0277774i | ||||
\(900\) | 1487.91 | − | 1081.03i | 0.0551078 | − | 0.0400382i | ||||
\(901\) | 14136.7 | 0.522709 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1405.53 | 0.0517974 | ||||||||
\(904\) | 5567.21 | − | 4044.82i | 0.204826 | − | 0.148815i | ||||
\(905\) | −3687.28 | − | 11348.3i | −0.135436 | − | 0.416828i | ||||
\(906\) | 17246.7 | − | 53079.9i | 0.632432 | − | 1.94642i | ||||
\(907\) | −30490.8 | − | 22152.9i | −1.11624 | − | 0.810997i | −0.132606 | − | 0.991169i | \(-0.542335\pi\) |
−0.983635 | + | 0.180172i | \(0.942335\pi\) | |||||||
\(908\) | −768.210 | − | 558.137i | −0.0280770 | − | 0.0203991i | ||||
\(909\) | −1789.03 | + | 5506.07i | −0.0652788 | + | 0.200907i | ||||
\(910\) | 206.471 | + | 635.454i | 0.00752138 | + | 0.0231484i | ||||
\(911\) | −26737.7 | + | 19426.1i | −0.972404 | + | 0.706493i | −0.955998 | − | 0.293372i | \(-0.905222\pi\) |
−0.0164061 | + | 0.999865i | \(0.505222\pi\) | |||||||
\(912\) | 65923.1 | 2.39357 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −28870.0 | −1.04479 | ||||||||
\(915\) | 70390.3 | − | 51141.5i | 2.54320 | − | 1.84775i | ||||
\(916\) | −317.188 | − | 976.206i | −0.0114413 | − | 0.0352126i | ||||
\(917\) | −1519.46 | + | 4676.41i | −0.0547185 | + | 0.168406i | ||||
\(918\) | −6396.44 | − | 4647.28i | −0.229972 | − | 0.167084i | ||||
\(919\) | 18727.1 | + | 13606.0i | 0.672198 | + | 0.488381i | 0.870760 | − | 0.491708i | \(-0.163627\pi\) |
−0.198562 | + | 0.980088i | \(0.563627\pi\) | |||||||
\(920\) | 11921.7 | − | 36691.3i | 0.427226 | − | 1.31487i | ||||
\(921\) | 4111.18 | + | 12652.9i | 0.147088 | + | 0.452690i | ||||
\(922\) | −10463.4 | + | 7602.07i | −0.373744 | + | 0.271541i | ||||
\(923\) | −1111.26 | −0.0396290 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1258.01 | 0.0447169 | ||||||||
\(926\) | −7583.89 | + | 5510.02i | −0.269138 | + | 0.195541i | ||||
\(927\) | −385.140 | − | 1185.34i | −0.0136458 | − | 0.0419975i | ||||
\(928\) | −186.996 | + | 575.514i | −0.00661470 | + | 0.0203579i | ||||
\(929\) | 18751.3 | + | 13623.6i | 0.662230 | + | 0.481138i | 0.867415 | − | 0.497585i | \(-0.165780\pi\) |
−0.205186 | + | 0.978723i | \(0.565780\pi\) | |||||||
\(930\) | 8199.93 | + | 5957.60i | 0.289125 | + | 0.210062i | ||||
\(931\) | −14422.8 | + | 44388.9i | −0.507722 | + | 1.56261i | ||||
\(932\) | −728.038 | − | 2240.67i | −0.0255876 | − | 0.0787506i | ||||
\(933\) | 22915.5 | − | 16649.1i | 0.804095 | − | 0.584209i | ||||
\(934\) | 13979.8 | 0.489757 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4481.13 | −0.156485 | ||||||||
\(937\) | 27971.5 | − | 20322.5i | 0.975228 | − | 0.708545i | 0.0185910 | − | 0.999827i | \(-0.494082\pi\) |
0.956637 | + | 0.291283i | \(0.0940820\pi\) | |||||||
\(938\) | 887.862 | + | 2732.56i | 0.0309059 | + | 0.0951185i | ||||
\(939\) | −17601.3 | + | 54171.3i | −0.611712 | + | 1.88266i | ||||
\(940\) | −2214.72 | − | 1609.09i | −0.0768469 | − | 0.0558325i | ||||
\(941\) | −33842.1 | − | 24587.7i | −1.17239 | − | 0.851793i | −0.181099 | − | 0.983465i | \(-0.557966\pi\) |
−0.991293 | + | 0.131672i | \(0.957966\pi\) | |||||||
\(942\) | −16572.4 | + | 51004.7i | −0.573205 | + | 1.76414i | ||||
\(943\) | −8983.54 | − | 27648.5i | −0.310227 | − | 0.954781i | ||||
\(944\) | 4248.47 | − | 3086.70i | 0.146479 | − | 0.106423i | ||||
\(945\) | −3204.34 | −0.110304 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27231.2 | 0.934419 | 0.467209 | − | 0.884147i | \(-0.345259\pi\) | ||||
0.467209 | + | 0.884147i | \(0.345259\pi\) | |||||||
\(948\) | −4448.61 | + | 3232.11i | −0.152410 | + | 0.110732i | ||||
\(949\) | −1673.57 | − | 5150.72i | −0.0572459 | − | 0.176185i | ||||
\(950\) | 11306.6 | − | 34798.0i | 0.386140 | − | 1.18842i | ||||
\(951\) | −100.750 | − | 73.1990i | −0.00343537 | − | 0.00249594i | ||||
\(952\) | −2388.62 | − | 1735.44i | −0.0813190 | − | 0.0590817i | ||||
\(953\) | 12651.0 | − | 38935.7i | 0.430016 | − | 1.32345i | −0.468092 | − | 0.883680i | \(-0.655058\pi\) |
0.898108 | − | 0.439774i | \(-0.144942\pi\) | |||||||
\(954\) | −10383.1 | − | 31955.8i | −0.352373 | − | 1.08449i | ||||
\(955\) | −20651.7 | + | 15004.4i | −0.699764 | + | 0.508409i | ||||
\(956\) | 2188.87 | 0.0740515 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31601.3 | 1.06575 | ||||||||
\(959\) | −4005.24 | + | 2909.97i | −0.134865 | + | 0.0979854i | ||||
\(960\) | −19711.0 | − | 60664.2i | −0.662676 | − | 2.03951i | ||||
\(961\) | −8899.35 | + | 27389.4i | −0.298726 | + | 0.919385i | ||||
\(962\) | −155.684 | − | 113.111i | −0.00521772 | − | 0.00379089i | ||||
\(963\) | −24140.2 | − | 17538.9i | −0.807796 | − | 0.586898i | ||||
\(964\) | −647.268 | + | 1992.09i | −0.0216256 | + | 0.0665568i | ||||
\(965\) | 6152.63 | + | 18935.8i | 0.205244 | + | 0.631675i | ||||
\(966\) | −5994.03 | + | 4354.92i | −0.199643 | + | 0.145049i | ||||
\(967\) | −46173.1 | −1.53550 | −0.767750 | − | 0.640750i | \(-0.778624\pi\) | ||||
−0.767750 | + | 0.640750i | \(0.778624\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45721.8 | 1.51579 | ||||||||
\(970\) | −44211.9 | + | 32121.8i | −1.46346 | + | 1.06327i | ||||
\(971\) | −1592.65 | − | 4901.66i | −0.0526369 | − | 0.162000i | 0.921282 | − | 0.388894i | \(-0.127143\pi\) |
−0.973919 | + | 0.226894i | \(0.927143\pi\) | |||||||
\(972\) | −854.141 | + | 2628.78i | −0.0281858 | + | 0.0867470i | ||||
\(973\) | 79.1812 | + | 57.5285i | 0.00260887 | + | 0.00189546i | ||||
\(974\) | 40506.7 | + | 29429.8i | 1.33257 | + | 0.968165i | ||||
\(975\) | −1256.64 | + | 3867.53i | −0.0412765 | + | 0.127036i | ||||
\(976\) | −13565.1 | − | 41749.1i | −0.444885 | − | 1.36922i | ||||
\(977\) | −7841.10 | + | 5696.89i | −0.256765 | + | 0.186550i | −0.708719 | − | 0.705490i | \(-0.750727\pi\) |
0.451955 | + | 0.892041i | \(0.350727\pi\) | |||||||
\(978\) | 59026.5 | 1.92992 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2655.68 | 0.0865638 | ||||||||
\(981\) | −30292.2 | + | 22008.6i | −0.985889 | + | 0.716290i | ||||
\(982\) | −6431.14 | − | 19793.0i | −0.208988 | − | 0.643198i | ||||
\(983\) | 10171.5 | − | 31304.7i | 0.330031 | − | 1.01573i | −0.639087 | − | 0.769135i | \(-0.720687\pi\) |
0.969118 | − | 0.246597i | \(-0.0793125\pi\) | |||||||
\(984\) | −39050.8 | − | 28372.1i | −1.26514 | − | 0.919176i | ||||
\(985\) | 42287.1 | + | 30723.4i | 1.36790 | + | 0.993835i | ||||
\(986\) | 869.723 | − | 2676.73i | 0.0280909 | − | 0.0864549i | ||||
\(987\) | 2587.70 | + | 7964.12i | 0.0834522 | + | 0.256840i | ||||
\(988\) | 325.096 | − | 236.196i | 0.0104683 | − | 0.00760567i | ||||
\(989\) | 6426.54 | 0.206625 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29477.9 | 0.944901 | 0.472451 | − | 0.881357i | \(-0.343370\pi\) | ||||
0.472451 | + | 0.881357i | \(0.343370\pi\) | |||||||
\(992\) | −616.924 | + | 448.222i | −0.0197453 | + | 0.0143458i | ||||
\(993\) | 3231.37 | + | 9945.13i | 0.103267 | + | 0.317824i | ||||
\(994\) | −537.771 | + | 1655.09i | −0.0171600 | + | 0.0528131i | ||||
\(995\) | −9900.03 | − | 7192.79i | −0.315429 | − | 0.229173i | ||||
\(996\) | −1518.75 | − | 1103.44i | −0.0483167 | − | 0.0351041i | ||||
\(997\) | −9871.35 | + | 30380.9i | −0.313570 | + | 0.965068i | 0.662770 | + | 0.748823i | \(0.269381\pi\) |
−0.976339 | + | 0.216245i | \(0.930619\pi\) | |||||||
\(998\) | 10898.5 | + | 33542.2i | 0.345678 | + | 1.06389i | ||||
\(999\) | 746.628 | − | 542.457i | 0.0236459 | − | 0.0171798i |
(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 | 121.4.c.c.3.1 | 8 | ||
11.2 | odd | 10 | 121.4.a.c.1.1 | 2 | |||
11.3 | even | 5 | inner | 121.4.c.c.27.2 | 8 | ||
11.4 | even | 5 | inner | 121.4.c.c.81.1 | 8 | ||
11.5 | even | 5 | inner | 121.4.c.c.9.2 | 8 | ||
11.6 | odd | 10 | 121.4.c.f.9.1 | 8 | |||
11.7 | odd | 10 | 121.4.c.f.81.2 | 8 | |||
11.8 | odd | 10 | 121.4.c.f.27.1 | 8 | |||
11.9 | even | 5 | 11.4.a.a.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 121.4.c.f.3.2 | 8 | |||
33.2 | even | 10 | 1089.4.a.v.1.2 | 2 | |||
33.20 | odd | 10 | 99.4.a.c.1.1 | 2 | |||
44.31 | odd | 10 | 176.4.a.i.1.2 | 2 | |||
44.35 | even | 10 | 1936.4.a.w.1.2 | 2 | |||
55.9 | even | 10 | 275.4.a.b.1.1 | 2 | |||
55.42 | odd | 20 | 275.4.b.c.199.4 | 4 | |||
55.53 | odd | 20 | 275.4.b.c.199.1 | 4 | |||
77.20 | odd | 10 | 539.4.a.e.1.2 | 2 | |||
88.53 | even | 10 | 704.4.a.p.1.2 | 2 | |||
88.75 | odd | 10 | 704.4.a.n.1.1 | 2 | |||
132.119 | even | 10 | 1584.4.a.bc.1.1 | 2 | |||
143.64 | even | 10 | 1859.4.a.a.1.1 | 2 | |||
165.119 | odd | 10 | 2475.4.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.4.a.a.1.2 | ✓ | 2 | 11.9 | even | 5 | ||
99.4.a.c.1.1 | 2 | 33.20 | odd | 10 | |||
121.4.a.c.1.1 | 2 | 11.2 | odd | 10 | |||
121.4.c.c.3.1 | 8 | 1.1 | even | 1 | trivial | ||
121.4.c.c.9.2 | 8 | 11.5 | even | 5 | inner | ||
121.4.c.c.27.2 | 8 | 11.3 | even | 5 | inner | ||
121.4.c.c.81.1 | 8 | 11.4 | even | 5 | inner | ||
121.4.c.f.3.2 | 8 | 11.10 | odd | 2 | |||
121.4.c.f.9.1 | 8 | 11.6 | odd | 10 | |||
121.4.c.f.27.1 | 8 | 11.8 | odd | 10 | |||
121.4.c.f.81.2 | 8 | 11.7 | odd | 10 | |||
176.4.a.i.1.2 | 2 | 44.31 | odd | 10 | |||
275.4.a.b.1.1 | 2 | 55.9 | even | 10 | |||
275.4.b.c.199.1 | 4 | 55.53 | odd | 20 | |||
275.4.b.c.199.4 | 4 | 55.42 | odd | 20 | |||
539.4.a.e.1.2 | 2 | 77.20 | odd | 10 | |||
704.4.a.n.1.1 | 2 | 88.75 | odd | 10 | |||
704.4.a.p.1.2 | 2 | 88.53 | even | 10 | |||
1089.4.a.v.1.2 | 2 | 33.2 | even | 10 | |||
1584.4.a.bc.1.1 | 2 | 132.119 | even | 10 | |||
1859.4.a.a.1.1 | 2 | 143.64 | even | 10 | |||
1936.4.a.w.1.2 | 2 | 44.35 | even | 10 | |||
2475.4.a.q.1.2 | 2 | 165.119 | odd | 10 |