Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.7 | ||
Character | \(\chi\) | \(=\) | 225.151 |
Dual form | 225.4.e.e.76.7 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.238017 | − | 0.412258i | 0.0841519 | − | 0.145755i | −0.820878 | − | 0.571104i | \(-0.806515\pi\) |
0.905030 | + | 0.425349i | \(0.139849\pi\) | |||||||
\(3\) | −3.09012 | − | 4.17746i | −0.594694 | − | 0.803953i | ||||
\(4\) | 3.88670 | + | 6.73195i | 0.485837 | + | 0.841494i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.45769 | + | 0.279619i | −0.167225 | + | 0.0190256i | ||||
\(7\) | 6.34045 | − | 10.9820i | 0.342352 | − | 0.592971i | −0.642517 | − | 0.766271i | \(-0.722110\pi\) |
0.984869 | + | 0.173300i | \(0.0554431\pi\) | |||||||
\(8\) | 7.50869 | 0.331840 | ||||||||
\(9\) | −7.90234 | + | 25.8177i | −0.292679 | + | 0.956211i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.794994 | − | 1.37697i | 0.0217909 | − | 0.0377429i | −0.854924 | − | 0.518753i | \(-0.826397\pi\) |
0.876715 | + | 0.481010i | \(0.159730\pi\) | |||||||
\(12\) | 16.1121 | − | 37.0390i | 0.387597 | − | 0.891021i | ||||
\(13\) | 5.36718 | + | 9.29622i | 0.114507 | + | 0.198331i | 0.917582 | − | 0.397546i | \(-0.130138\pi\) |
−0.803076 | + | 0.595877i | \(0.796805\pi\) | |||||||
\(14\) | −3.01828 | − | 5.22781i | −0.0576191 | − | 0.0997993i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −29.3064 | + | 50.7601i | −0.457912 | + | 0.793127i | ||||
\(17\) | 69.7787 | 0.995519 | 0.497760 | − | 0.867315i | \(-0.334156\pi\) | ||||
0.497760 | + | 0.867315i | \(0.334156\pi\) | |||||||
\(18\) | 8.76266 | + | 9.40287i | 0.114743 | + | 0.123127i | ||||
\(19\) | 98.5661 | 1.19014 | 0.595069 | − | 0.803675i | \(-0.297125\pi\) | ||||
0.595069 | + | 0.803675i | \(0.297125\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −65.4695 | + | 7.44864i | −0.680315 | + | 0.0774013i | ||||
\(22\) | −0.378445 | − | 0.655486i | −0.00366749 | − | 0.00635227i | ||||
\(23\) | −15.7777 | − | 27.3278i | −0.143038 | − | 0.247750i | 0.785601 | − | 0.618734i | \(-0.212354\pi\) |
−0.928639 | + | 0.370984i | \(0.879021\pi\) | |||||||
\(24\) | −23.2027 | − | 31.3672i | −0.197343 | − | 0.266784i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.10993 | 0.0385438 | ||||||||
\(27\) | 132.272 | − | 46.7680i | 0.942802 | − | 0.333352i | ||||
\(28\) | 98.5736 | 0.665309 | ||||||||
\(29\) | 150.627 | − | 260.893i | 0.964507 | − | 1.67058i | 0.253574 | − | 0.967316i | \(-0.418394\pi\) |
0.710933 | − | 0.703260i | \(-0.248273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58.6364 | + | 101.561i | 0.339723 | + | 0.588417i | 0.984380 | − | 0.176054i | \(-0.0563334\pi\) |
−0.644658 | + | 0.764471i | \(0.723000\pi\) | |||||||
\(32\) | 43.9856 | + | 76.1853i | 0.242988 | + | 0.420868i | ||||
\(33\) | −8.20886 | + | 0.933944i | −0.0433024 | + | 0.00492663i | ||||
\(34\) | 16.6086 | − | 28.7669i | 0.0837748 | − | 0.145102i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −204.517 | + | 47.1473i | −0.946840 | + | 0.218275i | ||||
\(37\) | 169.562 | 0.753402 | 0.376701 | − | 0.926335i | \(-0.377059\pi\) | ||||
0.376701 | + | 0.926335i | \(0.377059\pi\) | |||||||
\(38\) | 23.4605 | − | 40.6347i | 0.100152 | − | 0.173469i | ||||
\(39\) | 22.2494 | − | 51.1476i | 0.0913526 | − | 0.210004i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70.9376 | − | 122.868i | −0.270210 | − | 0.468017i | 0.698706 | − | 0.715409i | \(-0.253760\pi\) |
−0.968915 | + | 0.247392i | \(0.920426\pi\) | |||||||
\(42\) | −12.5121 | + | 28.7633i | −0.0459682 | + | 0.105673i | ||||
\(43\) | 150.121 | − | 260.018i | 0.532402 | − | 0.922147i | −0.466882 | − | 0.884319i | \(-0.654623\pi\) |
0.999284 | − | 0.0378277i | \(-0.0120438\pi\) | |||||||
\(44\) | 12.3596 | 0.0423472 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.0215 | −0.0481478 | ||||||||
\(47\) | 243.712 | − | 422.122i | 0.756364 | − | 1.31006i | −0.188330 | − | 0.982106i | \(-0.560307\pi\) |
0.944694 | − | 0.327954i | \(-0.106359\pi\) | |||||||
\(48\) | 302.608 | − | 34.4286i | 0.909953 | − | 0.103528i | ||||
\(49\) | 91.0974 | + | 157.785i | 0.265590 | + | 0.460016i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −215.625 | − | 291.498i | −0.592029 | − | 0.800350i | ||||
\(52\) | −41.7212 | + | 72.2632i | −0.111263 | + | 0.192713i | ||||
\(53\) | −459.166 | −1.19002 | −0.595012 | − | 0.803717i | \(-0.702853\pi\) | ||||
−0.595012 | + | 0.803717i | \(0.702853\pi\) | |||||||
\(54\) | 12.2024 | − | 65.6616i | 0.0307508 | − | 0.165471i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 47.6084 | − | 82.4602i | 0.113606 | − | 0.196772i | ||||
\(57\) | −304.581 | − | 411.756i | −0.707767 | − | 0.956814i | ||||
\(58\) | −71.7037 | − | 124.194i | −0.162330 | − | 0.281164i | ||||
\(59\) | 250.099 | + | 433.185i | 0.551867 | + | 0.955862i | 0.998140 | + | 0.0609650i | \(0.0194178\pi\) |
−0.446273 | + | 0.894897i | \(0.647249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −290.915 | + | 503.880i | −0.610621 | + | 1.05763i | 0.380515 | + | 0.924775i | \(0.375747\pi\) |
−0.991136 | + | 0.132852i | \(0.957587\pi\) | |||||||
\(62\) | 55.8259 | 0.114353 | ||||||||
\(63\) | 233.425 | + | 250.479i | 0.466806 | + | 0.500911i | ||||
\(64\) | −427.024 | −0.834032 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.56883 | + | 3.60647i | −0.00292589 | + | 0.00672614i | ||||
\(67\) | 250.468 | + | 433.823i | 0.456709 | + | 0.791044i | 0.998785 | − | 0.0492862i | \(-0.0156946\pi\) |
−0.542075 | + | 0.840330i | \(0.682361\pi\) | |||||||
\(68\) | 271.209 | + | 469.747i | 0.483660 | + | 0.837724i | ||||
\(69\) | −65.4059 | + | 150.357i | −0.114115 | + | 0.262331i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1066.69 | 1.78299 | 0.891495 | − | 0.453031i | \(-0.149657\pi\) | ||||
0.891495 | + | 0.453031i | \(0.149657\pi\) | |||||||
\(72\) | −59.3362 | + | 193.857i | −0.0971227 | + | 0.317309i | ||||
\(73\) | −435.288 | −0.697899 | −0.348950 | − | 0.937141i | \(-0.613462\pi\) | ||||
−0.348950 | + | 0.937141i | \(0.613462\pi\) | |||||||
\(74\) | 40.3588 | − | 69.9034i | 0.0634002 | − | 0.109812i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 383.096 | + | 663.542i | 0.578213 | + | 1.00149i | ||||
\(77\) | −10.0812 | − | 17.4612i | −0.0149203 | − | 0.0258427i | ||||
\(78\) | −15.7903 | − | 21.3465i | −0.0229218 | − | 0.0309874i | ||||
\(79\) | −187.644 | + | 325.009i | −0.267236 | + | 0.462866i | −0.968147 | − | 0.250383i | \(-0.919444\pi\) |
0.700911 | + | 0.713248i | \(0.252777\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −604.106 | − | 408.040i | −0.828678 | − | 0.559726i | ||||
\(82\) | −67.5375 | −0.0909546 | ||||||||
\(83\) | −646.617 | + | 1119.97i | −0.855126 | + | 1.48112i | 0.0214014 | + | 0.999771i | \(0.493187\pi\) |
−0.876528 | + | 0.481351i | \(0.840146\pi\) | |||||||
\(84\) | −304.604 | − | 411.787i | −0.395655 | − | 0.534877i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −71.4630 | − | 123.778i | −0.0896053 | − | 0.155201i | ||||
\(87\) | −1555.33 | + | 176.954i | −1.91665 | + | 0.218062i | ||||
\(88\) | 5.96936 | − | 10.3392i | 0.00723109 | − | 0.0125246i | ||||
\(89\) | −403.296 | −0.480330 | −0.240165 | − | 0.970732i | \(-0.577201\pi\) | ||||
−0.240165 | + | 0.970732i | \(0.577201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 136.121 | 0.156806 | ||||||||
\(92\) | 122.646 | − | 212.430i | 0.138987 | − | 0.240732i | ||||
\(93\) | 243.074 | − | 558.787i | 0.271028 | − | 0.623049i | ||||
\(94\) | −116.016 | − | 200.945i | −0.127299 | − | 0.220488i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 182.340 | − | 419.170i | 0.193854 | − | 0.445639i | ||||
\(97\) | −790.735 | + | 1369.59i | −0.827700 | + | 1.43362i | 0.0721373 | + | 0.997395i | \(0.477018\pi\) |
−0.899838 | + | 0.436225i | \(0.856315\pi\) | |||||||
\(98\) | 86.7311 | 0.0893996 | ||||||||
\(99\) | 29.2679 | + | 31.4062i | 0.0297124 | + | 0.0318832i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 577.422 | − | 1000.12i | 0.568867 | − | 0.985307i | −0.427811 | − | 0.903868i | \(-0.640715\pi\) |
0.996678 | − | 0.0814388i | \(-0.0259515\pi\) | |||||||
\(102\) | −171.495 | + | 19.5114i | −0.166476 | + | 0.0189404i | ||||
\(103\) | −725.615 | − | 1256.80i | −0.694145 | − | 1.20229i | −0.970468 | − | 0.241230i | \(-0.922449\pi\) |
0.276323 | − | 0.961065i | \(-0.410884\pi\) | |||||||
\(104\) | 40.3004 | + | 69.8024i | 0.0379979 | + | 0.0658143i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −109.290 | + | 189.295i | −0.100143 | + | 0.173452i | ||||
\(107\) | −136.728 | −0.123533 | −0.0617664 | − | 0.998091i | \(-0.519673\pi\) | ||||
−0.0617664 | + | 0.998091i | \(0.519673\pi\) | |||||||
\(108\) | 828.939 | + | 708.673i | 0.738562 | + | 0.631408i | ||||
\(109\) | 40.1176 | 0.0352529 | 0.0176265 | − | 0.999845i | \(-0.494389\pi\) | ||||
0.0176265 | + | 0.999845i | \(0.494389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −523.967 | − | 708.339i | −0.448043 | − | 0.605699i | ||||
\(112\) | 371.631 | + | 643.684i | 0.313534 | + | 0.543057i | ||||
\(113\) | −989.231 | − | 1713.40i | −0.823531 | − | 1.42640i | −0.903037 | − | 0.429564i | \(-0.858667\pi\) |
0.0795054 | − | 0.996834i | \(-0.474666\pi\) | |||||||
\(114\) | −242.245 | + | 27.5609i | −0.199021 | + | 0.0226431i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2341.76 | 1.87437 | ||||||||
\(117\) | −282.420 | + | 65.1062i | −0.223160 | + | 0.0514450i | ||||
\(118\) | 238.112 | 0.185763 | ||||||||
\(119\) | 442.428 | − | 766.309i | 0.340818 | − | 0.590314i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 664.236 | + | 1150.49i | 0.499050 | + | 0.864381i | ||||
\(122\) | 138.486 | + | 239.865i | 0.102770 | + | 0.178003i | ||||
\(123\) | −294.069 | + | 676.014i | −0.215571 | + | 0.495562i | ||||
\(124\) | −455.804 | + | 789.475i | −0.330100 | + | 0.571750i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 158.821 | − | 36.6130i | 0.112293 | − | 0.0258869i | ||||
\(127\) | −1318.35 | −0.921142 | −0.460571 | − | 0.887623i | \(-0.652355\pi\) | ||||
−0.460571 | + | 0.887623i | \(0.652355\pi\) | |||||||
\(128\) | −453.524 | + | 785.527i | −0.313174 | + | 0.542433i | ||||
\(129\) | −1550.11 | + | 176.360i | −1.05798 | + | 0.120369i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −792.463 | − | 1372.59i | −0.528533 | − | 0.915446i | −0.999447 | − | 0.0332667i | \(-0.989409\pi\) |
0.470913 | − | 0.882179i | \(-0.343924\pi\) | |||||||
\(132\) | −38.1926 | − | 51.6317i | −0.0251836 | − | 0.0340452i | ||||
\(133\) | 624.953 | − | 1082.45i | 0.407446 | − | 0.705717i | ||||
\(134\) | 238.463 | 0.153732 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 523.947 | 0.330353 | ||||||||
\(137\) | 190.760 | − | 330.406i | 0.118961 | − | 0.206047i | −0.800395 | − | 0.599473i | \(-0.795377\pi\) |
0.919356 | + | 0.393426i | \(0.128710\pi\) | |||||||
\(138\) | 46.4182 | + | 62.7517i | 0.0286332 | + | 0.0387086i | ||||
\(139\) | 1231.19 | + | 2132.49i | 0.751283 | + | 1.30126i | 0.947201 | + | 0.320641i | \(0.103898\pi\) |
−0.195918 | + | 0.980620i | \(0.562769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2516.50 | + | 286.309i | −1.50303 | + | 0.171004i | ||||
\(142\) | 253.890 | − | 439.750i | 0.150042 | − | 0.259880i | ||||
\(143\) | 17.0675 | 0.00998080 | ||||||||
\(144\) | −1078.92 | − | 1157.75i | −0.624375 | − | 0.669992i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −103.606 | + | 179.451i | −0.0587295 | + | 0.101723i | ||||
\(147\) | 377.640 | − | 868.131i | 0.211886 | − | 0.487090i | ||||
\(148\) | 659.037 | + | 1141.48i | 0.366030 | + | 0.633983i | ||||
\(149\) | −192.172 | − | 332.852i | −0.105660 | − | 0.183008i | 0.808348 | − | 0.588705i | \(-0.200362\pi\) |
−0.914008 | + | 0.405697i | \(0.867029\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −398.550 | + | 690.308i | −0.214792 | + | 0.372030i | −0.953208 | − | 0.302315i | \(-0.902241\pi\) |
0.738417 | + | 0.674345i | \(0.235574\pi\) | |||||||
\(152\) | 740.102 | 0.394935 | ||||||||
\(153\) | −551.415 | + | 1801.53i | −0.291368 | + | 0.951926i | ||||
\(154\) | −9.59804 | −0.00502229 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 430.800 | − | 49.0133i | 0.221100 | − | 0.0251551i | ||||
\(157\) | −435.496 | − | 754.300i | −0.221378 | − | 0.383438i | 0.733849 | − | 0.679313i | \(-0.237722\pi\) |
−0.955227 | + | 0.295875i | \(0.904389\pi\) | |||||||
\(158\) | 89.3252 | + | 154.716i | 0.0449768 | + | 0.0779021i | ||||
\(159\) | 1418.88 | + | 1918.15i | 0.707700 | + | 0.956723i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −400.152 | −0.195878 | ||||||||
\(162\) | −312.006 | + | 151.927i | −0.151318 | + | 0.0736822i | ||||
\(163\) | 31.2604 | 0.0150215 | 0.00751074 | − | 0.999972i | \(-0.497609\pi\) | ||||
0.00751074 | + | 0.999972i | \(0.497609\pi\) | |||||||
\(164\) | 551.426 | − | 955.097i | 0.262556 | − | 0.454759i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 307.813 | + | 533.147i | 0.143921 | + | 0.249278i | ||||
\(167\) | −18.6415 | − | 32.2881i | −0.00863787 | − | 0.0149612i | 0.861674 | − | 0.507462i | \(-0.169416\pi\) |
−0.870312 | + | 0.492501i | \(0.836083\pi\) | |||||||
\(168\) | −491.590 | + | 55.9295i | −0.225756 | + | 0.0256849i | ||||
\(169\) | 1040.89 | − | 1802.87i | 0.473776 | − | 0.820605i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −778.903 | + | 2544.75i | −0.348329 | + | 1.13802i | ||||
\(172\) | 2333.90 | 1.03464 | ||||||||
\(173\) | −590.590 | + | 1022.93i | −0.259548 | + | 0.449550i | −0.966121 | − | 0.258090i | \(-0.916907\pi\) |
0.706573 | + | 0.707640i | \(0.250240\pi\) | |||||||
\(174\) | −297.244 | + | 683.315i | −0.129506 | + | 0.297712i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 46.5967 | + | 80.7079i | 0.0199566 | + | 0.0345658i | ||||
\(177\) | 1036.78 | − | 2383.37i | 0.440276 | − | 1.01212i | ||||
\(178\) | −95.9916 | + | 166.262i | −0.0404206 | + | 0.0700106i | ||||
\(179\) | −429.484 | −0.179336 | −0.0896680 | − | 0.995972i | \(-0.528581\pi\) | ||||
−0.0896680 | + | 0.995972i | \(0.528581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1787.97 | −0.734246 | −0.367123 | − | 0.930172i | \(-0.619657\pi\) | ||||
−0.367123 | + | 0.930172i | \(0.619657\pi\) | |||||||
\(182\) | 32.3992 | − | 56.1171i | 0.0131956 | − | 0.0228554i | ||||
\(183\) | 3003.90 | − | 341.762i | 1.21341 | − | 0.138053i | ||||
\(184\) | −118.470 | − | 205.196i | −0.0474659 | − | 0.0822134i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −172.509 | − | 233.211i | −0.0680051 | − | 0.0919346i | ||||
\(187\) | 55.4736 | − | 96.0832i | 0.0216932 | − | 0.0375738i | ||||
\(188\) | 3788.94 | 1.46988 | ||||||||
\(189\) | 325.056 | − | 1749.13i | 0.125102 | − | 0.673178i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −392.583 | + | 679.974i | −0.148724 | + | 0.257598i | −0.930756 | − | 0.365640i | \(-0.880850\pi\) |
0.782032 | + | 0.623238i | \(0.214183\pi\) | |||||||
\(192\) | 1319.56 | + | 1783.88i | 0.495994 | + | 0.670522i | ||||
\(193\) | −238.539 | − | 413.162i | −0.0889659 | − | 0.154093i | 0.818108 | − | 0.575064i | \(-0.195023\pi\) |
−0.907074 | + | 0.420971i | \(0.861690\pi\) | |||||||
\(194\) | 376.417 | + | 651.974i | 0.139305 | + | 0.241284i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −708.136 | + | 1226.53i | −0.258067 | + | 0.446985i | ||||
\(197\) | 4628.37 | 1.67390 | 0.836949 | − | 0.547281i | \(-0.184337\pi\) | ||||
0.836949 | + | 0.547281i | \(0.184337\pi\) | |||||||
\(198\) | 19.9137 | − | 4.59070i | 0.00714751 | − | 0.00164771i | ||||
\(199\) | 2533.85 | 0.902611 | 0.451305 | − | 0.892370i | \(-0.350958\pi\) | ||||
0.451305 | + | 0.892370i | \(0.350958\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1038.30 | − | 2386.88i | 0.364359 | − | 0.837601i | ||||
\(202\) | −274.873 | − | 476.094i | −0.0957425 | − | 0.165831i | ||||
\(203\) | −1910.08 | − | 3308.36i | −0.660402 | − | 1.14385i | ||||
\(204\) | 1124.28 | − | 2584.54i | 0.385861 | − | 0.887029i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −690.836 | −0.233654 | ||||||||
\(207\) | 830.222 | − | 191.391i | 0.278765 | − | 0.0642636i | ||||
\(208\) | −629.170 | −0.209736 | ||||||||
\(209\) | 78.3594 | − | 135.722i | 0.0259341 | − | 0.0449192i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1382.70 | − | 2394.90i | −0.451131 | − | 0.781382i | 0.547325 | − | 0.836920i | \(-0.315646\pi\) |
−0.998457 | + | 0.0555378i | \(0.982313\pi\) | |||||||
\(212\) | −1784.64 | − | 3091.08i | −0.578158 | − | 1.00140i | ||||
\(213\) | −3296.18 | − | 4456.03i | −1.06033 | − | 1.43344i | ||||
\(214\) | −32.5437 | + | 56.3673i | −0.0103955 | + | 0.0180056i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 993.185 | − | 351.166i | 0.312860 | − | 0.110620i | ||||
\(217\) | 1487.12 | 0.465219 | ||||||||
\(218\) | 9.54869 | − | 16.5388i | 0.00296660 | − | 0.00513830i | ||||
\(219\) | 1345.09 | + | 1818.40i | 0.415036 | + | 0.561078i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 374.515 | + | 648.679i | 0.113994 | + | 0.197443i | ||||
\(222\) | −416.732 | + | 47.4128i | −0.125988 | + | 0.0143339i | ||||
\(223\) | 234.694 | − | 406.502i | 0.0704767 | − | 0.122069i | −0.828634 | − | 0.559791i | \(-0.810881\pi\) |
0.899110 | + | 0.437722i | \(0.144215\pi\) | |||||||
\(224\) | 1115.55 | 0.332750 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −941.817 | −0.277207 | ||||||||
\(227\) | −2143.99 | + | 3713.50i | −0.626879 | + | 1.08579i | 0.361295 | + | 0.932452i | \(0.382335\pi\) |
−0.988174 | + | 0.153335i | \(0.950999\pi\) | |||||||
\(228\) | 1588.11 | − | 3650.79i | 0.461294 | − | 1.06044i | ||||
\(229\) | −2052.30 | − | 3554.69i | −0.592227 | − | 1.02577i | −0.993932 | − | 0.109998i | \(-0.964916\pi\) |
0.401705 | − | 0.915769i | \(-0.368418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −41.7913 | + | 96.0711i | −0.0119033 | + | 0.0273637i | ||||
\(232\) | 1131.01 | − | 1958.97i | 0.320062 | − | 0.554364i | ||||
\(233\) | 4272.57 | 1.20131 | 0.600656 | − | 0.799508i | \(-0.294906\pi\) | ||||
0.600656 | + | 0.799508i | \(0.294906\pi\) | |||||||
\(234\) | −40.3804 | + | 131.927i | −0.0112810 | + | 0.0368560i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1944.12 | + | 3367.31i | −0.536235 | + | 0.928786i | ||||
\(237\) | 1937.56 | − | 220.441i | 0.531045 | − | 0.0604185i | ||||
\(238\) | −210.611 | − | 364.790i | −0.0573610 | − | 0.0993521i | ||||
\(239\) | 780.619 | + | 1352.07i | 0.211272 | + | 0.365934i | 0.952113 | − | 0.305747i | \(-0.0989061\pi\) |
−0.740841 | + | 0.671681i | \(0.765573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2410.77 | − | 4175.58i | 0.644362 | − | 1.11607i | −0.340086 | − | 0.940394i | \(-0.610456\pi\) |
0.984448 | − | 0.175674i | \(-0.0562105\pi\) | |||||||
\(242\) | 632.399 | 0.167984 | ||||||||
\(243\) | 162.187 | + | 3784.52i | 0.0428161 | + | 0.999083i | ||||
\(244\) | −4522.80 | −1.18665 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 208.699 | + | 282.135i | 0.0540901 | + | 0.0731232i | ||||
\(247\) | 529.021 | + | 916.292i | 0.136279 | + | 0.236042i | ||||
\(248\) | 440.282 | + | 762.591i | 0.112734 | + | 0.195260i | ||||
\(249\) | 6676.77 | − | 759.634i | 1.69929 | − | 0.193333i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3487.72 | −0.877063 | −0.438532 | − | 0.898716i | \(-0.644501\pi\) | ||||
−0.438532 | + | 0.898716i | \(0.644501\pi\) | |||||||
\(252\) | −778.962 | + | 2544.94i | −0.194722 | + | 0.636176i | ||||
\(253\) | −50.1728 | −0.0124677 | ||||||||
\(254\) | −313.791 | + | 543.503i | −0.0775158 | + | 0.134261i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1492.20 | − | 2584.57i | −0.364308 | − | 0.631000i | ||||
\(257\) | −2460.87 | − | 4262.35i | −0.597295 | − | 1.03454i | −0.993219 | − | 0.116261i | \(-0.962909\pi\) |
0.395924 | − | 0.918283i | \(-0.370424\pi\) | |||||||
\(258\) | −296.247 | + | 681.021i | −0.0714865 | + | 0.164335i | ||||
\(259\) | 1075.10 | − | 1862.13i | 0.257929 | − | 0.446745i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5545.36 | + | 5950.51i | 1.31513 | + | 1.41121i | ||||
\(262\) | −754.480 | −0.177908 | ||||||||
\(263\) | −2758.58 | + | 4777.99i | −0.646772 | + | 1.12024i | 0.337117 | + | 0.941463i | \(0.390548\pi\) |
−0.983889 | + | 0.178780i | \(0.942785\pi\) | |||||||
\(264\) | −61.6377 | + | 7.01269i | −0.0143695 | + | 0.00163485i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −297.500 | − | 515.284i | −0.0685747 | − | 0.118775i | ||||
\(267\) | 1246.23 | + | 1684.75i | 0.285649 | + | 0.386162i | ||||
\(268\) | −1946.98 | + | 3372.28i | −0.443772 | + | 0.768636i | ||||
\(269\) | −7844.13 | −1.77794 | −0.888969 | − | 0.457968i | \(-0.848577\pi\) | ||||
−0.888969 | + | 0.457968i | \(0.848577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4301.35 | 0.964164 | 0.482082 | − | 0.876126i | \(-0.339881\pi\) | ||||
0.482082 | + | 0.876126i | \(0.339881\pi\) | |||||||
\(272\) | −2044.96 | + | 3541.98i | −0.455860 | + | 0.789573i | ||||
\(273\) | −420.631 | − | 568.641i | −0.0932517 | − | 0.126065i | ||||
\(274\) | −90.8083 | − | 157.285i | −0.0200216 | − | 0.0346785i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1266.41 | + | 144.083i | −0.276192 | + | 0.0314231i | ||||
\(277\) | 925.922 | − | 1603.74i | 0.200842 | − | 0.347869i | −0.747958 | − | 0.663746i | \(-0.768966\pi\) |
0.948800 | + | 0.315877i | \(0.102299\pi\) | |||||||
\(278\) | 1172.18 | 0.252888 | ||||||||
\(279\) | −3085.44 | + | 711.285i | −0.662081 | + | 0.152629i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3470.93 | + | 6011.82i | −0.736862 | + | 1.27628i | 0.217040 | + | 0.976163i | \(0.430360\pi\) |
−0.953902 | + | 0.300119i | \(0.902974\pi\) | |||||||
\(282\) | −480.937 | + | 1105.59i | −0.101558 | + | 0.233465i | ||||
\(283\) | 3216.21 | + | 5570.64i | 0.675562 | + | 1.17011i | 0.976304 | + | 0.216402i | \(0.0694321\pi\) |
−0.300743 | + | 0.953705i | \(0.597235\pi\) | |||||||
\(284\) | 4145.88 | + | 7180.87i | 0.866242 | + | 1.50038i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.06236 | − | 7.03621i | 0.000839903 | − | 0.00145476i | ||||
\(287\) | −1799.10 | −0.370027 | ||||||||
\(288\) | −2314.52 | + | 533.564i | −0.473556 | + | 0.109169i | ||||
\(289\) | −43.9287 | −0.00894133 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8164.88 | − | 928.941i | 1.64479 | − | 0.187132i | ||||
\(292\) | −1691.83 | − | 2930.34i | −0.339065 | − | 0.587278i | ||||
\(293\) | −3820.89 | − | 6617.98i | −0.761840 | − | 1.31955i | −0.941901 | − | 0.335890i | \(-0.890963\pi\) |
0.180062 | − | 0.983655i | \(-0.442370\pi\) | |||||||
\(294\) | −268.009 | − | 362.316i | −0.0531654 | − | 0.0718731i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1273.19 | 0.250009 | ||||||||
\(297\) | 40.7569 | − | 219.314i | 0.00796281 | − | 0.0428481i | ||||
\(298\) | −182.961 | −0.0355660 | ||||||||
\(299\) | 169.364 | − | 293.347i | 0.0327577 | − | 0.0567380i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1903.67 | − | 3297.26i | −0.364538 | − | 0.631398i | ||||
\(302\) | 189.724 | + | 328.611i | 0.0361502 | + | 0.0626140i | ||||
\(303\) | −5962.28 | + | 678.344i | −1.13044 | + | 0.128613i | ||||
\(304\) | −2888.61 | + | 5003.23i | −0.544978 | + | 0.943930i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 611.448 | + | 656.120i | 0.114229 | + | 0.122575i | ||||
\(307\) | −4517.66 | −0.839857 | −0.419929 | − | 0.907557i | \(-0.637945\pi\) | ||||
−0.419929 | + | 0.907557i | \(0.637945\pi\) | |||||||
\(308\) | 78.3654 | − | 135.733i | 0.0144977 | − | 0.0251107i | ||||
\(309\) | −3008.00 | + | 6914.89i | −0.553784 | + | 1.27306i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1966.54 | − | 3406.15i | −0.358560 | − | 0.621044i | 0.629160 | − | 0.777275i | \(-0.283399\pi\) |
−0.987721 | + | 0.156231i | \(0.950066\pi\) | |||||||
\(312\) | 167.064 | − | 384.051i | 0.0303145 | − | 0.0696879i | ||||
\(313\) | −1583.09 | + | 2742.00i | −0.285884 | + | 0.495165i | −0.972823 | − | 0.231549i | \(-0.925620\pi\) |
0.686939 | + | 0.726715i | \(0.258954\pi\) | |||||||
\(314\) | −414.622 | −0.0745175 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2917.26 | −0.519332 | ||||||||
\(317\) | −3920.86 | + | 6791.13i | −0.694692 | + | 1.20324i | 0.275592 | + | 0.961275i | \(0.411126\pi\) |
−0.970284 | + | 0.241967i | \(0.922207\pi\) | |||||||
\(318\) | 1128.49 | − | 128.391i | 0.199002 | − | 0.0226410i | ||||
\(319\) | −239.495 | − | 414.817i | −0.0420349 | − | 0.0728066i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 422.506 | + | 571.176i | 0.0734641 | + | 0.0993145i | ||||
\(322\) | −95.2431 | + | 164.966i | −0.0164835 | + | 0.0285503i | ||||
\(323\) | 6877.82 | 1.18480 | ||||||||
\(324\) | 398.932 | − | 5652.74i | 0.0684040 | − | 0.969263i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.44051 | − | 12.8873i | 0.00126409 | − | 0.00218946i | ||||
\(327\) | −123.968 | − | 167.590i | −0.0209647 | − | 0.0283417i | ||||
\(328\) | −532.648 | − | 922.574i | −0.0896664 | − | 0.155307i | ||||
\(329\) | −3090.49 | − | 5352.89i | −0.517885 | − | 0.897004i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5426.53 | − | 9399.03i | 0.901115 | − | 1.56078i | 0.0750663 | − | 0.997179i | \(-0.476083\pi\) |
0.826049 | − | 0.563599i | \(-0.190584\pi\) | |||||||
\(332\) | −10052.8 | −1.66181 | ||||||||
\(333\) | −1339.94 | + | 4377.70i | −0.220505 | + | 0.720411i | ||||
\(334\) | −17.7480 | −0.00290757 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1540.58 | − | 3541.53i | 0.250135 | − | 0.575019i | ||||
\(337\) | −3258.64 | − | 5644.13i | −0.526735 | − | 0.912331i | −0.999515 | − | 0.0311507i | \(-0.990083\pi\) |
0.472780 | − | 0.881180i | \(-0.343251\pi\) | |||||||
\(338\) | −495.499 | − | 858.229i | −0.0797384 | − | 0.138111i | ||||
\(339\) | −4100.81 | + | 9427.08i | −0.657008 | + | 1.51035i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 186.462 | 0.0296114 | ||||||||
\(342\) | 863.701 | + | 926.804i | 0.136560 | + | 0.146537i | ||||
\(343\) | 6659.94 | 1.04841 | ||||||||
\(344\) | 1127.21 | − | 1952.39i | 0.176672 | − | 0.306005i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 281.142 | + | 486.952i | 0.0436829 | + | 0.0756609i | ||||
\(347\) | 2969.27 | + | 5142.93i | 0.459363 | + | 0.795640i | 0.998927 | − | 0.0463041i | \(-0.0147443\pi\) |
−0.539564 | + | 0.841944i | \(0.681411\pi\) | |||||||
\(348\) | −7236.33 | − | 9782.62i | −1.11468 | − | 1.50691i | ||||
\(349\) | 3648.27 | − | 6318.99i | 0.559563 | − | 0.969192i | −0.437970 | − | 0.898990i | \(-0.644302\pi\) |
0.997533 | − | 0.0702022i | \(-0.0223644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1144.69 | + | 978.613i | 0.174071 | + | 0.148816i | ||||
\(352\) | 139.873 | 0.0211797 | ||||||||
\(353\) | 625.356 | − | 1083.15i | 0.0942900 | − | 0.163315i | −0.815022 | − | 0.579430i | \(-0.803275\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(354\) | −735.795 | − | 994.704i | −0.110472 | − | 0.149344i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1567.49 | − | 2714.97i | −0.233362 | − | 0.404195i | ||||
\(357\) | −4568.38 | + | 519.757i | −0.677267 | + | 0.0770545i | ||||
\(358\) | −102.225 | + | 177.058i | −0.0150915 | + | 0.0261392i | ||||
\(359\) | −10928.3 | −1.60661 | −0.803303 | − | 0.595570i | \(-0.796926\pi\) | ||||
−0.803303 | + | 0.595570i | \(0.796926\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2856.27 | 0.416427 | ||||||||
\(362\) | −425.567 | + | 737.104i | −0.0617882 | + | 0.107020i | ||||
\(363\) | 2753.56 | − | 6329.97i | 0.398139 | − | 0.915254i | ||||
\(364\) | 529.062 | + | 916.362i | 0.0761823 | + | 0.131952i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 574.087 | − | 1319.73i | 0.0819891 | − | 0.188479i | ||||
\(367\) | −3215.66 | + | 5569.68i | −0.457373 | + | 0.792194i | −0.998821 | − | 0.0485405i | \(-0.984543\pi\) |
0.541448 | + | 0.840734i | \(0.317876\pi\) | |||||||
\(368\) | 1849.55 | 0.261996 | ||||||||
\(369\) | 3732.73 | − | 860.504i | 0.526607 | − | 0.121398i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2911.32 | + | 5042.55i | −0.407407 | + | 0.705650i | ||||
\(372\) | 4706.49 | − | 535.470i | 0.655968 | − | 0.0746312i | ||||
\(373\) | 2455.85 | + | 4253.66i | 0.340909 | + | 0.590472i | 0.984602 | − | 0.174812i | \(-0.0559317\pi\) |
−0.643693 | + | 0.765284i | \(0.722598\pi\) | |||||||
\(374\) | −26.4074 | − | 45.7389i | −0.00365105 | − | 0.00632381i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1829.96 | − | 3169.58i | 0.250992 | − | 0.434731i | ||||
\(377\) | 3233.76 | 0.441770 | ||||||||
\(378\) | −643.726 | − | 550.331i | −0.0875918 | − | 0.0748836i | ||||
\(379\) | 4805.81 | 0.651340 | 0.325670 | − | 0.945483i | \(-0.394410\pi\) | ||||
0.325670 | + | 0.945483i | \(0.394410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4073.87 | + | 5507.37i | 0.547797 | + | 0.740554i | ||||
\(382\) | 186.883 | + | 323.691i | 0.0250308 | + | 0.0433547i | ||||
\(383\) | −2116.08 | − | 3665.15i | −0.282314 | − | 0.488983i | 0.689640 | − | 0.724152i | \(-0.257769\pi\) |
−0.971954 | + | 0.235170i | \(0.924435\pi\) | |||||||
\(384\) | 4682.95 | − | 532.792i | 0.622333 | − | 0.0708045i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −227.106 | −0.0299466 | ||||||||
\(387\) | 5526.75 | + | 5930.53i | 0.725944 | + | 0.778982i | ||||
\(388\) | −12293.4 | −1.60851 | ||||||||
\(389\) | 1758.54 | − | 3045.89i | 0.229208 | − | 0.396999i | −0.728366 | − | 0.685188i | \(-0.759720\pi\) |
0.957573 | + | 0.288189i | \(0.0930532\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1100.95 | − | 1906.90i | −0.142398 | − | 0.246640i | ||||
\(392\) | 684.022 | + | 1184.76i | 0.0881335 | + | 0.152652i | ||||
\(393\) | −3285.12 | + | 7551.94i | −0.421660 | + | 0.969325i | ||||
\(394\) | 1101.63 | − | 1908.09i | 0.140862 | − | 0.243980i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −97.6697 | + | 319.096i | −0.0123942 | + | 0.0404929i | ||||
\(397\) | −3925.05 | −0.496203 | −0.248101 | − | 0.968734i | \(-0.579807\pi\) | ||||
−0.248101 | + | 0.968734i | \(0.579807\pi\) | |||||||
\(398\) | 603.100 | − | 1044.60i | 0.0759564 | − | 0.131560i | ||||
\(399\) | −6453.07 | + | 734.184i | −0.809669 | + | 0.0921182i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −403.676 | − | 699.188i | −0.0502709 | − | 0.0870718i | 0.839795 | − | 0.542904i | \(-0.182675\pi\) |
−0.890066 | + | 0.455832i | \(0.849342\pi\) | |||||||
\(402\) | −736.879 | − | 996.169i | −0.0914233 | − | 0.123593i | ||||
\(403\) | −629.424 | + | 1090.19i | −0.0778011 | + | 0.134755i | ||||
\(404\) | 8977.05 | 1.10551 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1818.53 | −0.222296 | ||||||||
\(407\) | 134.801 | − | 233.482i | 0.0164173 | − | 0.0284356i | ||||
\(408\) | −1619.06 | − | 2188.77i | −0.196459 | − | 0.265588i | ||||
\(409\) | −404.224 | − | 700.137i | −0.0488694 | − | 0.0846444i | 0.840556 | − | 0.541725i | \(-0.182228\pi\) |
−0.889425 | + | 0.457080i | \(0.848895\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1969.73 | + | 224.101i | −0.236398 | + | 0.0268956i | ||||
\(412\) | 5640.49 | − | 9769.61i | 0.674482 | − | 1.16824i | ||||
\(413\) | 6342.97 | 0.755732 | ||||||||
\(414\) | 118.705 | − | 387.821i | 0.0140919 | − | 0.0460395i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −472.157 | + | 817.800i | −0.0556476 | + | 0.0963844i | ||||
\(417\) | 5103.85 | − | 11732.9i | 0.599369 | − | 1.37785i | ||||
\(418\) | −37.3018 | − | 64.6086i | −0.00436481 | − | 0.00756008i | ||||
\(419\) | −880.089 | − | 1524.36i | −0.102614 | − | 0.177732i | 0.810147 | − | 0.586227i | \(-0.199387\pi\) |
−0.912761 | + | 0.408495i | \(0.866054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7287.86 | + | 12622.9i | −0.843678 | + | 1.46129i | 0.0430868 | + | 0.999071i | \(0.486281\pi\) |
−0.886765 | + | 0.462221i | \(0.847053\pi\) | |||||||
\(422\) | −1316.42 | −0.151854 | ||||||||
\(423\) | 8972.32 | + | 9627.84i | 1.03132 | + | 1.10667i | ||||
\(424\) | −3447.73 | −0.394898 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2621.59 | + | 298.265i | −0.298160 | + | 0.0339225i | ||||
\(427\) | 3689.07 | + | 6389.65i | 0.418095 | + | 0.724161i | ||||
\(428\) | −531.421 | − | 920.447i | −0.0600168 | − | 0.103952i | ||||
\(429\) | −52.7405 | − | 71.2987i | −0.00593552 | − | 0.00802409i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5715.34 | 0.638743 | 0.319371 | − | 0.947630i | \(-0.396528\pi\) | ||||
0.319371 | + | 0.947630i | \(0.396528\pi\) | |||||||
\(432\) | −1502.45 | + | 8084.72i | −0.167330 | + | 0.900408i | ||||
\(433\) | 12751.4 | 1.41523 | 0.707614 | − | 0.706599i | \(-0.249772\pi\) | ||||
0.707614 | + | 0.706599i | \(0.249772\pi\) | |||||||
\(434\) | 353.962 | − | 613.079i | 0.0391491 | − | 0.0678082i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 155.925 | + | 270.070i | 0.0171272 | + | 0.0296651i | ||||
\(437\) | −1555.15 | − | 2693.60i | −0.170235 | − | 0.294856i | ||||
\(438\) | 1069.81 | − | 121.715i | 0.116706 | − | 0.0132780i | ||||
\(439\) | −2420.51 | + | 4192.44i | −0.263154 | + | 0.455796i | −0.967078 | − | 0.254479i | \(-0.918096\pi\) |
0.703924 | + | 0.710275i | \(0.251429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4793.54 | + | 1105.05i | −0.517605 | + | 0.119323i | ||||
\(442\) | 356.564 | 0.0383711 | ||||||||
\(443\) | −4472.98 | + | 7747.43i | −0.479724 | + | 0.830907i | −0.999730 | − | 0.0232564i | \(-0.992597\pi\) |
0.520005 | + | 0.854163i | \(0.325930\pi\) | |||||||
\(444\) | 2732.01 | − | 6280.42i | 0.292016 | − | 0.671297i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −111.723 | − | 193.509i | −0.0118615 | − | 0.0205447i | ||||
\(447\) | −796.640 | + | 1831.34i | −0.0842948 | + | 0.193780i | ||||
\(448\) | −2707.53 | + | 4689.57i | −0.285533 | + | 0.494557i | ||||
\(449\) | −2743.57 | −0.288367 | −0.144184 | − | 0.989551i | \(-0.546056\pi\) | ||||
−0.144184 | + | 0.989551i | \(0.546056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −225.580 | −0.0235524 | ||||||||
\(452\) | 7689.68 | − | 13318.9i | 0.800204 | − | 1.38599i | ||||
\(453\) | 4115.30 | − | 468.209i | 0.426829 | − | 0.0485615i | ||||
\(454\) | 1020.61 | + | 1767.76i | 0.105506 | + | 0.182742i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2287.00 | − | 3091.75i | −0.234865 | − | 0.317509i | ||||
\(457\) | 2806.35 | − | 4860.74i | 0.287255 | − | 0.497540i | −0.685899 | − | 0.727697i | \(-0.740591\pi\) |
0.973153 | + | 0.230157i | \(0.0739240\pi\) | |||||||
\(458\) | −1953.93 | −0.199348 | ||||||||
\(459\) | 9229.74 | − | 3263.41i | 0.938578 | − | 0.331858i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6273.50 | + | 10866.0i | −0.633809 | + | 1.09779i | 0.352957 | + | 0.935640i | \(0.385176\pi\) |
−0.986766 | + | 0.162150i | \(0.948157\pi\) | |||||||
\(462\) | 29.6591 | + | 40.0954i | 0.00298672 | + | 0.00403768i | ||||
\(463\) | −5361.12 | − | 9285.74i | −0.538126 | − | 0.932062i | −0.999005 | − | 0.0445990i | \(-0.985799\pi\) |
0.460879 | − | 0.887463i | \(-0.347534\pi\) | |||||||
\(464\) | 8828.65 | + | 15291.7i | 0.883319 | + | 1.52995i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1016.95 | − | 1761.40i | 0.101093 | − | 0.175098i | ||||
\(467\) | 12798.4 | 1.26818 | 0.634089 | − | 0.773260i | \(-0.281375\pi\) | ||||
0.634089 | + | 0.773260i | \(0.281375\pi\) | |||||||
\(468\) | −1535.97 | − | 1648.19i | −0.151710 | − | 0.162794i | ||||
\(469\) | 6352.31 | 0.625421 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1805.33 | + | 4150.14i | −0.176614 | + | 0.406005i | ||||
\(472\) | 1877.92 | + | 3252.65i | 0.183132 | + | 0.317193i | ||||
\(473\) | −238.691 | − | 413.425i | −0.0232030 | − | 0.0401888i | ||||
\(474\) | 370.293 | − | 851.242i | 0.0358822 | − | 0.0824870i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6878.34 | 0.662328 | ||||||||
\(477\) | 3628.49 | − | 11854.6i | 0.348296 | − | 1.13791i | ||||
\(478\) | 743.203 | 0.0711158 | ||||||||
\(479\) | −1207.38 | + | 2091.25i | −0.115171 | + | 0.199481i | −0.917848 | − | 0.396932i | \(-0.870075\pi\) |
0.802677 | + | 0.596413i | \(0.203408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 910.070 | + | 1576.29i | 0.0862695 | + | 0.149423i | ||||
\(482\) | −1147.61 | − | 1987.72i | −0.108449 | − | 0.187839i | ||||
\(483\) | 1236.52 | + | 1671.62i | 0.116487 | + | 0.157477i | ||||
\(484\) | −5163.37 | + | 8943.21i | −0.484914 | + | 0.839896i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1598.80 | + | 833.919i | 0.149225 | + | 0.0778340i | ||||
\(487\) | 16386.9 | 1.52477 | 0.762384 | − | 0.647125i | \(-0.224029\pi\) | ||||
0.762384 | + | 0.647125i | \(0.224029\pi\) | |||||||
\(488\) | −2184.39 | + | 3783.48i | −0.202629 | + | 0.350963i | ||||
\(489\) | −96.5982 | − | 130.589i | −0.00893317 | − | 0.0120766i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7935.54 | − | 13744.8i | −0.729381 | − | 1.26332i | −0.957145 | − | 0.289609i | \(-0.906475\pi\) |
0.227764 | − | 0.973716i | \(-0.426858\pi\) | |||||||
\(492\) | −5693.85 | + | 647.805i | −0.521745 | + | 0.0593604i | ||||
\(493\) | 10510.6 | − | 18204.8i | 0.960186 | − | 1.66309i | ||||
\(494\) | 503.665 | 0.0458724 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6873.68 | −0.622252 | ||||||||
\(497\) | 6763.26 | − | 11714.3i | 0.610410 | − | 1.05726i | ||||
\(498\) | 1276.02 | − | 2933.36i | 0.114819 | − | 0.263950i | ||||
\(499\) | −5730.39 | − | 9925.33i | −0.514083 | − | 0.890419i | −0.999867 | − | 0.0163392i | \(-0.994799\pi\) |
0.485783 | − | 0.874079i | \(-0.338534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −77.2776 | + | 177.648i | −0.00689123 | + | 0.0158418i | ||||
\(502\) | −830.138 | + | 1437.84i | −0.0738065 | + | 0.127837i | ||||
\(503\) | −1038.52 | −0.0920585 | −0.0460293 | − | 0.998940i | \(-0.514657\pi\) | ||||
−0.0460293 | + | 0.998940i | \(0.514657\pi\) | |||||||
\(504\) | 1752.71 | + | 1880.77i | 0.154905 | + | 0.166222i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.9420 | + | 20.6841i | −0.00104918 | + | 0.00181724i | ||||
\(507\) | −10747.9 | + | 1222.81i | −0.941479 | + | 0.107115i | ||||
\(508\) | −5124.04 | − | 8875.10i | −0.447525 | − | 0.775135i | ||||
\(509\) | 2514.44 | + | 4355.14i | 0.218960 | + | 0.379249i | 0.954490 | − | 0.298242i | \(-0.0964003\pi\) |
−0.735530 | + | 0.677492i | \(0.763067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2759.92 | + | 4780.33i | −0.238927 | + | 0.413834i | ||||
\(512\) | −8677.07 | −0.748976 | ||||||||
\(513\) | 13037.5 | − | 4609.74i | 1.12206 | − | 0.396735i | ||||
\(514\) | −2342.92 | −0.201054 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7212.04 | − | 9749.79i | −0.615295 | − | 0.831803i | ||||
\(517\) | −387.499 | − | 671.169i | −0.0329636 | − | 0.0570947i | ||||
\(518\) | −511.785 | − | 886.438i | −0.0434104 | − | 0.0751889i | ||||
\(519\) | 6098.25 | − | 693.815i | 0.515768 | − | 0.0586803i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7057.78 | 0.593487 | 0.296744 | − | 0.954957i | \(-0.404099\pi\) | ||||
0.296744 | + | 0.954957i | \(0.404099\pi\) | |||||||
\(522\) | 3773.04 | − | 869.797i | 0.316363 | − | 0.0729310i | ||||
\(523\) | −14453.5 | −1.20843 | −0.604215 | − | 0.796821i | \(-0.706513\pi\) | ||||
−0.604215 | + | 0.796821i | \(0.706513\pi\) | |||||||
\(524\) | 6160.13 | − | 10669.7i | 0.513562 | − | 0.889515i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1313.18 | + | 2274.49i | 0.108854 | + | 0.188541i | ||||
\(527\) | 4091.57 | + | 7086.81i | 0.338201 | + | 0.585781i | ||||
\(528\) | 193.165 | − | 444.053i | 0.0159212 | − | 0.0366002i | ||||
\(529\) | 5585.63 | − | 9674.59i | 0.459080 | − | 0.795150i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13160.2 | + | 3033.81i | −1.07553 | + | 0.247940i | ||||
\(532\) | 9716.01 | 0.791809 | ||||||||
\(533\) | 761.469 | − | 1318.90i | 0.0618816 | − | 0.107182i | ||||
\(534\) | 991.180 | − | 112.769i | 0.0803231 | − | 0.00913858i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1880.68 | + | 3257.44i | 0.151554 | + | 0.262500i | ||||
\(537\) | 1327.16 | + | 1794.15i | 0.106650 | + | 0.144178i | ||||
\(538\) | −1867.04 | + | 3233.81i | −0.149617 | + | 0.259144i | ||||
\(539\) | 289.687 | 0.0231498 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4101.59 | 0.325954 | 0.162977 | − | 0.986630i | \(-0.447890\pi\) | ||||
0.162977 | + | 0.986630i | \(0.447890\pi\) | |||||||
\(542\) | 1023.80 | − | 1773.27i | 0.0811362 | − | 0.140532i | ||||
\(543\) | 5525.03 | + | 7469.16i | 0.436651 | + | 0.590299i | ||||
\(544\) | 3069.26 | + | 5316.11i | 0.241900 | + | 0.418982i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −334.544 | + | 38.0620i | −0.0262219 | + | 0.00298334i | ||||
\(547\) | −8410.52 | + | 14567.4i | −0.657418 | + | 1.13868i | 0.323863 | + | 0.946104i | \(0.395018\pi\) |
−0.981282 | + | 0.192578i | \(0.938315\pi\) | |||||||
\(548\) | 2965.70 | 0.231183 | ||||||||
\(549\) | −10710.1 | − | 11492.6i | −0.832598 | − | 0.893428i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14846.7 | − | 25715.2i | 1.14790 | − | 1.98821i | ||||
\(552\) | −491.112 | + | 1128.98i | −0.0378680 | + | 0.0870521i | ||||
\(553\) | 2379.50 | + | 4121.41i | 0.182977 | + | 0.316926i | ||||
\(554\) | −440.771 | − | 763.438i | −0.0338025 | − | 0.0585476i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9570.54 | + | 16576.7i | −0.730002 | + | 1.26440i | ||||
\(557\) | 12248.8 | 0.931771 | 0.465885 | − | 0.884845i | \(-0.345736\pi\) | ||||
0.465885 | + | 0.884845i | \(0.345736\pi\) | |||||||
\(558\) | −441.156 | + | 1441.30i | −0.0334688 | + | 0.109346i | ||||
\(559\) | 3222.91 | 0.243854 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −572.804 | + | 65.1694i | −0.0431084 | + | 0.00490455i | ||||
\(562\) | 1652.28 | + | 2861.84i | 0.124017 | + | 0.214803i | ||||
\(563\) | 4422.86 | + | 7660.62i | 0.331086 | + | 0.573457i | 0.982725 | − | 0.185072i | \(-0.0592517\pi\) |
−0.651639 | + | 0.758529i | \(0.725918\pi\) | |||||||
\(564\) | −11708.3 | − | 15828.1i | −0.874127 | − | 1.18171i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3062.06 | 0.227399 | ||||||||
\(567\) | −8311.39 | + | 4047.12i | −0.615601 | + | 0.299759i | ||||
\(568\) | 8009.40 | 0.591667 | ||||||||
\(569\) | 4049.35 | − | 7013.68i | 0.298344 | − | 0.516747i | −0.677413 | − | 0.735603i | \(-0.736899\pi\) |
0.975757 | + | 0.218856i | \(0.0702325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8189.02 | + | 14183.8i | 0.600175 | + | 1.03953i | 0.992794 | + | 0.119832i | \(0.0382356\pi\) |
−0.392619 | + | 0.919701i | \(0.628431\pi\) | |||||||
\(572\) | 66.3361 | + | 114.897i | 0.00484904 | + | 0.00839879i | ||||
\(573\) | 4053.69 | − | 461.200i | 0.295542 | − | 0.0336246i | ||||
\(574\) | −428.218 | + | 741.696i | −0.0311385 | + | 0.0539334i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3374.49 | − | 11024.8i | 0.244104 | − | 0.797510i | ||||
\(577\) | −24920.9 | −1.79804 | −0.899020 | − | 0.437907i | \(-0.855720\pi\) | ||||
−0.899020 | + | 0.437907i | \(0.855720\pi\) | |||||||
\(578\) | −10.4558 | + | 18.1100i | −0.000752430 | + | 0.00130325i | ||||
\(579\) | −988.853 | + | 2273.21i | −0.0709764 | + | 0.163163i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8199.69 | + | 14202.3i | 0.585509 | + | 1.01413i | ||||
\(582\) | 1560.42 | − | 3587.15i | 0.111137 | − | 0.255484i | ||||
\(583\) | −365.034 | + | 632.257i | −0.0259317 | + | 0.0449150i | ||||
\(584\) | −3268.44 | −0.231591 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3637.76 | −0.256441 | ||||||||
\(587\) | −4182.25 | + | 7243.86i | −0.294071 | + | 0.509346i | −0.974768 | − | 0.223219i | \(-0.928344\pi\) |
0.680697 | + | 0.732565i | \(0.261677\pi\) | |||||||
\(588\) | 7311.99 | − | 831.905i | 0.512826 | − | 0.0583456i | ||||
\(589\) | 5779.56 | + | 10010.5i | 0.404317 | + | 0.700297i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14302.2 | − | 19334.8i | −0.995456 | − | 1.34573i | ||||
\(592\) | −4969.25 | + | 8607.00i | −0.344992 | + | 0.597543i | ||||
\(593\) | −27169.7 | −1.88150 | −0.940749 | − | 0.339105i | \(-0.889876\pi\) | ||||
−0.940749 | + | 0.339105i | \(0.889876\pi\) | |||||||
\(594\) | −80.7132 | − | 69.0030i | −0.00557526 | − | 0.00476637i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1493.83 | − | 2587.39i | 0.102667 | − | 0.177825i | ||||
\(597\) | −7829.88 | − | 10585.0i | −0.536777 | − | 0.725656i | ||||
\(598\) | −80.6231 | − | 139.643i | −0.00551325 | − | 0.00954923i | ||||
\(599\) | −10666.2 | − | 18474.4i | −0.727560 | − | 1.26017i | −0.957911 | − | 0.287064i | \(-0.907321\pi\) |
0.230351 | − | 0.973108i | \(-0.426013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −292.016 | + | 505.786i | −0.0198196 | + | 0.0343285i | −0.875765 | − | 0.482738i | \(-0.839643\pi\) |
0.855946 | + | 0.517066i | \(0.172976\pi\) | |||||||
\(602\) | −1812.43 | −0.122706 | ||||||||
\(603\) | −13179.6 | + | 3038.28i | −0.890074 | + | 0.205188i | ||||
\(604\) | −6196.17 | −0.417415 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1139.47 | + | 2619.46i | −0.0763827 | + | 0.175591i | ||||
\(607\) | 5635.12 | + | 9760.32i | 0.376808 | + | 0.652651i | 0.990596 | − | 0.136820i | \(-0.0436883\pi\) |
−0.613788 | + | 0.789471i | \(0.710355\pi\) | |||||||
\(608\) | 4335.49 | + | 7509.29i | 0.289190 | + | 0.500891i | ||||
\(609\) | −7918.17 | + | 18202.5i | −0.526864 | + | 1.21117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5232.19 | 0.346435 | ||||||||
\(612\) | −14271.0 | + | 3289.88i | −0.942598 | + | 0.217297i | ||||
\(613\) | −4271.02 | −0.281411 | −0.140706 | − | 0.990051i | \(-0.544937\pi\) | ||||
−0.140706 | + | 0.990051i | \(0.544937\pi\) | |||||||
\(614\) | −1075.28 | + | 1862.44i | −0.0706756 | + | 0.122414i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −75.6968 | − | 131.111i | −0.00495115 | − | 0.00857565i | ||||
\(617\) | −3598.08 | − | 6232.06i | −0.234770 | − | 0.406634i | 0.724436 | − | 0.689342i | \(-0.242100\pi\) |
−0.959206 | + | 0.282708i | \(0.908767\pi\) | |||||||
\(618\) | 2134.76 | + | 2885.94i | 0.138953 | + | 0.187847i | ||||
\(619\) | −5128.24 | + | 8882.36i | −0.332991 | + | 0.576757i | −0.983097 | − | 0.183087i | \(-0.941391\pi\) |
0.650106 | + | 0.759843i | \(0.274724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3365.01 | − | 2876.80i | −0.217445 | − | 0.185897i | ||||
\(622\) | −1872.28 | −0.120694 | ||||||||
\(623\) | −2557.08 | + | 4428.99i | −0.164442 | + | 0.284822i | ||||
\(624\) | 1944.21 | + | 2628.33i | 0.124729 | + | 0.168618i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 753.607 | + | 1305.29i | 0.0481153 | + | 0.0833382i | ||||
\(627\) | −809.115 | + | 92.0552i | −0.0515358 | + | 0.00586337i | ||||
\(628\) | 3385.28 | − | 5863.47i | 0.215107 | − | 0.372576i | ||||
\(629\) | 11831.8 | 0.750026 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15187.7 | 0.958183 | 0.479091 | − | 0.877765i | \(-0.340966\pi\) | ||||
0.479091 | + | 0.877765i | \(0.340966\pi\) | |||||||
\(632\) | −1408.96 | + | 2440.39i | −0.0886795 | + | 0.153597i | ||||
\(633\) | −5731.90 | + | 13176.7i | −0.359909 | + | 0.827371i | ||||
\(634\) | 1866.47 | + | 3232.81i | 0.116919 | + | 0.202510i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7398.14 | + | 17007.1i | −0.461250 | + | 1.06034i | ||||
\(637\) | −977.872 | + | 1693.72i | −0.0608237 | + | 0.105350i | ||||
\(638\) | −228.016 | −0.0141493 | ||||||||
\(639\) | −8429.31 | + | 27539.3i | −0.521844 | + | 1.70491i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14196.7 | − | 24589.4i | 0.874783 | − | 1.51517i | 0.0177891 | − | 0.999842i | \(-0.494337\pi\) |
0.856994 | − | 0.515327i | \(-0.172329\pi\) | |||||||
\(642\) | 336.036 | − | 38.2317i | 0.0206578 | − | 0.00235029i | ||||
\(643\) | −5844.00 | − | 10122.1i | −0.358421 | − | 0.620804i | 0.629276 | − | 0.777182i | \(-0.283351\pi\) |
−0.987697 | + | 0.156378i | \(0.950018\pi\) | |||||||
\(644\) | −1555.27 | − | 2693.80i | −0.0951648 | − | 0.164830i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1637.04 | − | 2835.44i | 0.0997036 | − | 0.172692i | ||||
\(647\) | 12800.8 | 0.777822 | 0.388911 | − | 0.921275i | \(-0.372851\pi\) | ||||
0.388911 | + | 0.921275i | \(0.372851\pi\) | |||||||
\(648\) | −4536.04 | − | 3063.85i | −0.274989 | − | 0.185740i | ||||
\(649\) | 795.310 | 0.0481027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4595.39 | − | 6212.40i | −0.276663 | − | 0.374014i | ||||
\(652\) | 121.500 | + | 210.443i | 0.00729799 | + | 0.0126405i | ||||
\(653\) | −3079.46 | − | 5333.78i | −0.184546 | − | 0.319643i | 0.758877 | − | 0.651233i | \(-0.225748\pi\) |
−0.943423 | + | 0.331590i | \(0.892415\pi\) | |||||||
\(654\) | −98.5968 | + | 11.2176i | −0.00589517 | + | 0.000670709i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8315.69 | 0.494929 | ||||||||
\(657\) | 3439.80 | − | 11238.1i | 0.204261 | − | 0.667339i | ||||
\(658\) | −2942.36 | −0.174324 | ||||||||
\(659\) | −8289.10 | + | 14357.1i | −0.489981 | + | 0.848672i | −0.999934 | − | 0.0115307i | \(-0.996330\pi\) |
0.509953 | + | 0.860202i | \(0.329663\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11469.8 | + | 19866.4i | 0.674925 | + | 1.16900i | 0.976491 | + | 0.215559i | \(0.0691573\pi\) |
−0.301566 | + | 0.953445i | \(0.597509\pi\) | |||||||
\(662\) | −2583.22 | − | 4474.27i | −0.151661 | − | 0.262685i | ||||
\(663\) | 1552.53 | − | 3569.01i | 0.0909433 | − | 0.209063i | ||||
\(664\) | −4855.25 | + | 8409.53i | −0.283765 | + | 0.491496i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1485.82 | + | 1594.37i | 0.0864478 | + | 0.0927637i | ||||
\(667\) | −9506.20 | −0.551847 | ||||||||
\(668\) | 144.908 | − | 250.988i | 0.00839319 | − | 0.0145374i | ||||
\(669\) | −2423.38 | + | 275.715i | −0.140050 | + | 0.0159338i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 462.552 | + | 801.163i | 0.0266119 | + | 0.0460932i | ||||
\(672\) | −3447.19 | − | 4660.18i | −0.197884 | − | 0.267515i | ||||
\(673\) | 1181.62 | − | 2046.62i | 0.0676790 | − | 0.117223i | −0.830200 | − | 0.557465i | \(-0.811774\pi\) |
0.897879 | + | 0.440242i | \(0.145107\pi\) | |||||||
\(674\) | −3102.46 | −0.177303 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16182.4 | 0.920712 | ||||||||
\(677\) | −7824.09 | + | 13551.7i | −0.444172 | + | 0.769328i | −0.997994 | − | 0.0633068i | \(-0.979835\pi\) |
0.553822 | + | 0.832635i | \(0.313169\pi\) | |||||||
\(678\) | 2910.33 | + | 3934.40i | 0.164853 | + | 0.222861i | ||||
\(679\) | 10027.2 | + | 17367.7i | 0.566730 | + | 0.981605i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22138.2 | − | 2518.72i | 1.24572 | − | 0.141729i | ||||
\(682\) | 44.3813 | − | 76.8706i | 0.00249186 | − | 0.00431602i | ||||
\(683\) | −19626.7 | −1.09955 | −0.549777 | − | 0.835311i | \(-0.685287\pi\) | ||||
−0.549777 | + | 0.835311i | \(0.685287\pi\) | |||||||
\(684\) | −20158.5 | + | 4647.12i | −1.12687 | + | 0.259777i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1585.18 | − | 2745.62i | 0.0882253 | − | 0.152811i | ||||
\(687\) | −8507.72 | + | 19557.8i | −0.472474 | + | 1.08614i | ||||
\(688\) | 8799.02 | + | 15240.3i | 0.487586 | + | 0.844524i | ||||
\(689\) | −2464.42 | − | 4268.51i | −0.136266 | − | 0.236019i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.5955 | − | 89.3660i | 0.00284050 | − | 0.00491989i | −0.864602 | − | 0.502458i | \(-0.832429\pi\) |
0.867442 | + | 0.497538i | \(0.165763\pi\) | |||||||
\(692\) | −9181.78 | −0.504391 | ||||||||
\(693\) | 530.473 | − | 122.290i | 0.0290779 | − | 0.00670332i | ||||
\(694\) | 2826.96 | 0.154625 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11678.5 | + | 1328.69i | −0.636021 | + | 0.0723619i | ||||
\(697\) | −4949.93 | − | 8573.54i | −0.268999 | − | 0.465920i | ||||
\(698\) | −1736.71 | − | 3008.06i | −0.0941766 | − | 0.163119i | ||||
\(699\) | −13202.8 | − | 17848.5i | −0.714412 | − | 0.965797i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17977.8 | −0.968631 | −0.484316 | − | 0.874893i | \(-0.660931\pi\) | ||||
−0.484316 | + | 0.874893i | \(0.660931\pi\) | |||||||
\(702\) | 675.898 | − | 238.981i | 0.0363392 | − | 0.0128487i | ||||
\(703\) | 16713.1 | 0.896651 | ||||||||
\(704\) | −339.482 | + | 588.000i | −0.0181743 | + | 0.0314788i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −297.692 | − | 515.617i | −0.0158694 | − | 0.0274865i | ||||
\(707\) | −7322.22 | − | 12682.5i | −0.389506 | − | 0.674644i | ||||
\(708\) | 20074.4 | − | 2283.92i | 1.06560 | − | 0.121236i | ||||
\(709\) | −5385.10 | + | 9327.26i | −0.285249 | + | 0.494066i | −0.972670 | − | 0.232194i | \(-0.925410\pi\) |
0.687421 | + | 0.726260i | \(0.258743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6908.16 | − | 7412.87i | −0.364383 | − | 0.391005i | ||||
\(712\) | −3028.23 | −0.159393 | ||||||||
\(713\) | 1850.30 | − | 3204.81i | 0.0971868 | − | 0.168333i | ||||
\(714\) | −873.080 | + | 2007.06i | −0.0457622 | + | 0.105200i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1669.27 | − | 2891.27i | −0.0871280 | − | 0.150910i | ||||
\(717\) | 3236.02 | − | 7439.06i | 0.168551 | − | 0.387471i | ||||
\(718\) | −2601.12 | + | 4505.27i | −0.135199 | + | 0.234171i | ||||
\(719\) | 24138.7 | 1.25205 | 0.626023 | − | 0.779804i | \(-0.284681\pi\) | ||||
0.626023 | + | 0.779804i | \(0.284681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18402.9 | −0.950568 | ||||||||
\(722\) | 679.843 | − | 1177.52i | 0.0350431 | − | 0.0606964i | ||||
\(723\) | −24892.9 | + | 2832.13i | −1.28046 | + | 0.145682i | ||||
\(724\) | −6949.28 | − | 12036.5i | −0.356724 | − | 0.617864i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1954.19 | − | 2641.82i | −0.0998991 | − | 0.135051i | ||||
\(727\) | −5395.46 | + | 9345.20i | −0.275250 | + | 0.476746i | −0.970198 | − | 0.242313i | \(-0.922094\pi\) |
0.694949 | + | 0.719059i | \(0.255427\pi\) | |||||||
\(728\) | 1022.09 | 0.0520347 | ||||||||
\(729\) | 15308.5 | − | 12372.1i | 0.777753 | − | 0.628570i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10475.3 | − | 18143.7i | 0.530016 | − | 0.918015i | ||||
\(732\) | 13976.0 | + | 18893.8i | 0.705692 | + | 0.954009i | ||||
\(733\) | −10492.9 | − | 18174.3i | −0.528738 | − | 0.915801i | −0.999438 | − | 0.0335082i | \(-0.989332\pi\) |
0.470700 | − | 0.882293i | \(-0.344001\pi\) | |||||||
\(734\) | 1530.77 | + | 2651.36i | 0.0769776 | + | 0.133329i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1387.99 | − | 2404.06i | 0.0695134 | − | 0.120401i | ||||
\(737\) | 796.481 | 0.0398084 | ||||||||
\(738\) | 533.705 | − | 1743.66i | 0.0266205 | − | 0.0869717i | ||||
\(739\) | 1773.47 | 0.0882790 | 0.0441395 | − | 0.999025i | \(-0.485945\pi\) | ||||
0.0441395 | + | 0.999025i | \(0.485945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2193.03 | − | 5041.42i | 0.108722 | − | 0.249934i | ||||
\(742\) | 1385.89 | + | 2400.43i | 0.0685682 | + | 0.118764i | ||||
\(743\) | −2640.39 | − | 4573.28i | −0.130372 | − | 0.225811i | 0.793448 | − | 0.608638i | \(-0.208284\pi\) |
−0.923820 | + | 0.382827i | \(0.874950\pi\) | |||||||
\(744\) | 1825.17 | − | 4195.76i | 0.0899381 | − | 0.206753i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2338.14 | 0.114753 | ||||||||
\(747\) | −23805.4 | − | 25544.6i | −1.16599 | − | 1.25117i | ||||
\(748\) | 862.437 | 0.0421575 | ||||||||
\(749\) | −866.918 | + | 1501.55i | −0.0422917 | + | 0.0732514i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5514.51 | − | 9551.40i | −0.267946 | − | 0.464095i | 0.700386 | − | 0.713765i | \(-0.253011\pi\) |
−0.968331 | + | 0.249669i | \(0.919678\pi\) | |||||||
\(752\) | 14284.6 | + | 24741.7i | 0.692696 | + | 1.19978i | ||||
\(753\) | 10777.5 | + | 14569.8i | 0.521584 | + | 0.705117i | ||||
\(754\) | 769.692 | − | 1333.15i | 0.0371758 | − | 0.0643904i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 13038.5 | − | 4610.09i | 0.627255 | − | 0.221782i | ||||
\(757\) | 19897.2 | 0.955318 | 0.477659 | − | 0.878545i | \(-0.341486\pi\) | ||||
0.477659 | + | 0.878545i | \(0.341486\pi\) | |||||||
\(758\) | 1143.87 | − | 1981.24i | 0.0548115 | − | 0.0949363i | ||||
\(759\) | 155.040 | + | 209.595i | 0.00741448 | + | 0.0100235i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12636.2 | + | 21886.5i | 0.601920 | + | 1.04256i | 0.992530 | + | 0.122000i | \(0.0389307\pi\) |
−0.390610 | + | 0.920556i | \(0.627736\pi\) | |||||||
\(762\) | 3240.11 | − | 368.636i | 0.154038 | − | 0.0175253i | ||||
\(763\) | 254.364 | − | 440.571i | 0.0120689 | − | 0.0209040i | ||||
\(764\) | −6103.40 | −0.289023 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2014.65 | −0.0950292 | ||||||||
\(767\) | −2684.65 | + | 4649.96i | −0.126385 | + | 0.218905i | ||||
\(768\) | −6185.87 | + | 14220.3i | −0.290642 | + | 0.668137i | ||||
\(769\) | −15167.1 | − | 26270.1i | −0.711233 | − | 1.23189i | −0.964395 | − | 0.264467i | \(-0.914804\pi\) |
0.253162 | − | 0.967424i | \(-0.418529\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10201.4 | + | 23451.3i | −0.476517 | + | 1.09543i | ||||
\(772\) | 1854.26 | − | 3211.67i | 0.0864458 | − | 0.149729i | ||||
\(773\) | −6671.36 | −0.310417 | −0.155208 | − | 0.987882i | \(-0.549605\pi\) | ||||
−0.155208 | + | 0.987882i | \(0.549605\pi\) | |||||||
\(774\) | 3760.37 | − | 866.877i | 0.174630 | − | 0.0402574i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5937.38 | + | 10283.8i | −0.274664 | + | 0.475732i | ||||
\(777\) | −11101.2 | + | 1263.01i | −0.512551 | + | 0.0583143i | ||||
\(778\) | −837.129 | − | 1449.95i | −0.0385765 | − | 0.0668165i | ||||
\(779\) | −6992.04 | − | 12110.6i | −0.321586 | − | 0.557004i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 848.008 | − | 1468.79i | 0.0388529 | − | 0.0672952i | ||||
\(782\) | −1048.18 | −0.0479321 | ||||||||
\(783\) | 7722.18 | − | 41553.3i | 0.352450 | − | 1.89654i | ||||
\(784\) | −10678.9 | −0.486468 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2331.43 | + | 3151.81i | 0.105801 | + | 0.143030i | ||||
\(787\) | 10503.1 | + | 18192.0i | 0.475726 | + | 0.823981i | 0.999613 | − | 0.0278064i | \(-0.00885218\pi\) |
−0.523888 | + | 0.851787i | \(0.675519\pi\) | |||||||
\(788\) | 17989.1 | + | 31158.0i | 0.813241 | + | 1.40858i | ||||
\(789\) | 28484.2 | − | 3240.73i | 1.28525 | − | 0.146227i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25088.7 | −1.12775 | ||||||||
\(792\) | 219.763 | + | 235.819i | 0.00985978 | + | 0.0105801i | ||||
\(793\) | −6245.57 | −0.279681 | ||||||||
\(794\) | −934.230 | + | 1618.13i | −0.0417564 | + | 0.0723242i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9848.29 | + | 17057.7i | 0.438522 | + | 0.759542i | ||||
\(797\) | −4566.27 | − | 7909.00i | −0.202943 | − | 0.351507i | 0.746533 | − | 0.665349i | \(-0.231717\pi\) |
−0.949475 | + | 0.313842i | \(0.898384\pi\) | |||||||
\(798\) | −1233.27 | + | 2835.08i | −0.0547084 | + | 0.125765i | ||||
\(799\) | 17005.9 | − | 29455.1i | 0.752975 | − | 1.30419i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3186.99 | − | 10412.2i | 0.140583 | − | 0.459296i | ||||
\(802\) | −384.328 | −0.0169216 | ||||||||
\(803\) | −346.051 | + | 599.379i | −0.0152078 | + | 0.0263407i | ||||
\(804\) | 20104.0 | − | 2287.28i | 0.881856 | − | 0.100331i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 299.628 | + | 518.970i | 0.0130942 | + | 0.0226798i | ||||
\(807\) | 24239.3 | + | 32768.5i | 1.05733 | + | 1.42938i | ||||
\(808\) | 4335.68 | − | 7509.61i | 0.188773 | − | 0.326964i | ||||
\(809\) | 17687.6 | 0.768681 | 0.384341 | − | 0.923191i | \(-0.374429\pi\) | ||||
0.384341 | + | 0.923191i | \(0.374429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7211.00 | −0.312223 | −0.156111 | − | 0.987739i | \(-0.549896\pi\) | ||||
−0.156111 | + | 0.987739i | \(0.549896\pi\) | |||||||
\(812\) | 14847.8 | − | 25717.2i | 0.641695 | − | 1.11145i | ||||
\(813\) | −13291.7 | − | 17968.7i | −0.573382 | − | 0.775142i | ||||
\(814\) | −64.1699 | − | 111.146i | −0.00276309 | − | 0.00478581i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 21115.6 | − | 2402.38i | 0.905876 | − | 0.103064i | ||||
\(817\) | 14796.9 | − | 25628.9i | 0.633631 | − | 1.09748i | ||||
\(818\) | −384.850 | −0.0164498 | ||||||||
\(819\) | −1075.68 | + | 3514.34i | −0.0458940 | + | 0.149940i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21037.2 | + | 36437.6i | −0.894281 | + | 1.54894i | −0.0595894 | + | 0.998223i | \(0.518979\pi\) |
−0.834692 | + | 0.550717i | \(0.814354\pi\) | |||||||
\(822\) | −376.442 | + | 865.376i | −0.0159731 | + | 0.0367195i | ||||
\(823\) | 10437.6 | + | 18078.5i | 0.442081 | + | 0.765707i | 0.997844 | − | 0.0656341i | \(-0.0209070\pi\) |
−0.555763 | + | 0.831341i | \(0.687574\pi\) | |||||||
\(824\) | −5448.41 | − | 9436.93i | −0.230345 | − | 0.398970i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1509.74 | − | 2614.94i | 0.0635962 | − | 0.110152i | ||||
\(827\) | −3128.34 | −0.131540 | −0.0657698 | − | 0.997835i | \(-0.520950\pi\) | ||||
−0.0657698 | + | 0.997835i | \(0.520950\pi\) | |||||||
\(828\) | 4515.26 | + | 4845.14i | 0.189512 | + | 0.203358i | ||||
\(829\) | −6854.35 | −0.287167 | −0.143583 | − | 0.989638i | \(-0.545863\pi\) | ||||
−0.143583 | + | 0.989638i | \(0.545863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9560.78 | + | 1087.76i | −0.399109 | + | 0.0454078i | ||||
\(832\) | −2291.92 | − | 3969.71i | −0.0955022 | − | 0.165415i | ||||
\(833\) | 6356.66 | + | 11010.1i | 0.264400 | + | 0.457954i | ||||
\(834\) | −3622.18 | − | 4896.74i | −0.150391 | − | 0.203310i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1218.24 | 0.0503990 | ||||||||
\(837\) | 12505.7 | + | 10691.3i | 0.516442 | + | 0.441514i | ||||
\(838\) | −837.906 | −0.0345405 | ||||||||
\(839\) | −20793.2 | + | 36014.9i | −0.855615 | + | 1.48197i | 0.0204588 | + | 0.999791i | \(0.493487\pi\) |
−0.876074 | + | 0.482178i | \(0.839846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33182.4 | − | 57473.6i | −1.36055 | − | 2.35654i | ||||
\(842\) | 3469.27 | + | 6008.96i | 0.141994 | + | 0.245941i | ||||
\(843\) | 35839.7 | − | 4077.58i | 1.46428 | − | 0.166595i | ||||
\(844\) | 10748.2 | − | 18616.5i | 0.438352 | − | 0.759249i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6104.73 | − | 1407.32i | 0.248091 | − | 0.0571922i | ||||
\(847\) | 16846.2 | 0.683404 | ||||||||
\(848\) | 13456.5 | − | 23307.3i | 0.544926 | − | 0.943840i | ||||
\(849\) | 13332.7 | − | 30649.5i | 0.538958 | − | 1.23897i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2675.31 | − | 4633.77i | −0.107765 | − | 0.186655i | ||||
\(852\) | 17186.6 | − | 39509.0i | 0.691082 | − | 1.58868i | ||||
\(853\) | −9160.28 | + | 15866.1i | −0.367693 | + | 0.636863i | −0.989204 | − | 0.146542i | \(-0.953186\pi\) |
0.621512 | + | 0.783405i | \(0.286519\pi\) | |||||||
\(854\) | 3512.25 | 0.140734 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1026.65 | −0.0409931 | ||||||||
\(857\) | 6189.48 | − | 10720.5i | 0.246708 | − | 0.427310i | −0.715903 | − | 0.698200i | \(-0.753985\pi\) |
0.962610 | + | 0.270890i | \(0.0873179\pi\) | |||||||
\(858\) | −41.9467 | + | 4.77239i | −0.00166904 | + | 0.000189891i | ||||
\(859\) | 14758.5 | + | 25562.5i | 0.586210 | + | 1.01534i | 0.994723 | + | 0.102593i | \(0.0327139\pi\) |
−0.408514 | + | 0.912752i | \(0.633953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5559.45 | + | 7515.69i | 0.220053 | + | 0.297484i | ||||
\(862\) | 1360.35 | − | 2356.19i | 0.0537514 | − | 0.0931001i | ||||
\(863\) | 41307.0 | 1.62932 | 0.814661 | − | 0.579937i | \(-0.196923\pi\) | ||||
0.814661 | + | 0.579937i | \(0.196923\pi\) | |||||||
\(864\) | 9381.08 | + | 8020.03i | 0.369387 | + | 0.315795i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3035.06 | − | 5256.88i | 0.119094 | − | 0.206277i | ||||
\(867\) | 135.745 | + | 183.511i | 0.00531735 | + | 0.00718840i | ||||
\(868\) | 5780.00 | + | 10011.3i | 0.226021 | + | 0.391479i | ||||
\(869\) | 298.352 | + | 516.760i | 0.0116466 | + | 0.0201725i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2688.61 | + | 4656.81i | −0.104593 | + | 0.181160i | ||||
\(872\) | 301.230 | 0.0116983 | ||||||||
\(873\) | −29111.1 | − | 31237.9i | −1.12859 | − | 1.21105i | ||||
\(874\) | −1480.61 | −0.0573025 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7013.42 | + | 16122.7i | −0.270504 | + | 0.621843i | ||||
\(877\) | −19153.4 | − | 33174.7i | −0.737475 | − | 1.27734i | −0.953629 | − | 0.300984i | \(-0.902685\pi\) |
0.216155 | − | 0.976359i | \(-0.430648\pi\) | |||||||
\(878\) | 1152.25 | + | 1995.75i | 0.0442898 | + | 0.0767122i | ||||
\(879\) | −15839.3 | + | 36412.0i | −0.607790 | + | 1.39721i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47903.1 | −1.83189 | −0.915946 | − | 0.401301i | \(-0.868558\pi\) | ||||
−0.915946 | + | 0.401301i | \(0.868558\pi\) | |||||||
\(882\) | −685.379 | + | 2239.20i | −0.0261654 | + | 0.0854849i | ||||
\(883\) | −39098.9 | −1.49013 | −0.745064 | − | 0.666993i | \(-0.767581\pi\) | ||||
−0.745064 | + | 0.666993i | \(0.767581\pi\) | |||||||
\(884\) | −2911.25 | + | 5042.43i | −0.110765 | + | 0.191850i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2129.30 | + | 3688.05i | 0.0807394 | + | 0.139845i | ||||
\(887\) | −14117.0 | − | 24451.4i | −0.534389 | − | 0.925590i | −0.999193 | − | 0.0401756i | \(-0.987208\pi\) |
0.464803 | − | 0.885414i | \(-0.346125\pi\) | |||||||
\(888\) | −3934.31 | − | 5318.70i | −0.148679 | − | 0.200995i | ||||
\(889\) | −8358.96 | + | 14478.1i | −0.315355 | + | 0.546211i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1042.12 | + | 507.446i | −0.0391833 | + | 0.0190798i | ||||
\(892\) | 3648.74 | 0.136961 | ||||||||
\(893\) | 24021.8 | − | 41606.9i | 0.900177 | − | 1.55915i | ||||
\(894\) | 565.371 | + | 764.313i | 0.0211508 | + | 0.0285933i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5751.09 | + | 9961.18i | 0.214431 | + | 0.371406i | ||||
\(897\) | −1748.80 | + | 198.965i | −0.0650955 | + | 0.00740609i | ||||
\(898\) | −653.016 | + | 1131.06i | −0.0242666 | + | 0.0420311i | ||||
\(899\) | 35328.9 | 1.31066 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32040.0 | −1.18469 | ||||||||
\(902\) | −53.6919 | + | 92.9971i | −0.00198198 | + | 0.00343289i | ||||
\(903\) | −7891.59 | + | 18141.4i | −0.290826 | + | 0.668559i | ||||
\(904\) | −7427.83 | − | 12865.4i | −0.273281 | − | 0.473336i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 786.491 | − | 1808.01i | 0.0288404 | − | 0.0662992i | ||||
\(907\) | 9530.28 | − | 16506.9i | 0.348895 | − | 0.604304i | −0.637159 | − | 0.770733i | \(-0.719890\pi\) |
0.986053 | + | 0.166429i | \(0.0532237\pi\) | |||||||
\(908\) | −33332.1 | −1.21824 | ||||||||
\(909\) | 21257.9 | + | 22811.0i | 0.775665 | + | 0.832336i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 727.041 | − | 1259.27i | 0.0264412 | − | 0.0457975i | −0.852502 | − | 0.522724i | \(-0.824916\pi\) |
0.878943 | + | 0.476926i | \(0.158249\pi\) | |||||||
\(912\) | 29826.9 | − | 3393.49i | 1.08297 | − | 0.123212i | ||||
\(913\) | 1028.11 | + | 1780.74i | 0.0372679 | + | 0.0645499i | ||||
\(914\) | −1335.92 | − | 2313.88i | −0.0483461 | − | 0.0837379i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15953.3 | − | 27632.0i | 0.575451 | − | 0.996711i | ||||
\(917\) | −20098.3 | −0.723778 | ||||||||
\(918\) | 851.470 | − | 4581.79i | 0.0306130 | − | 0.164729i | ||||
\(919\) | −6383.04 | −0.229115 | −0.114558 | − | 0.993417i | \(-0.536545\pi\) | ||||
−0.114558 | + | 0.993417i | \(0.536545\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13960.1 | + | 18872.3i | 0.499458 | + | 0.675205i | ||||
\(922\) | 2986.41 | + | 5172.61i | 0.106673 | + | 0.184762i | ||||
\(923\) | 5725.09 | + | 9916.14i | 0.204164 | + | 0.353623i | ||||
\(924\) | −809.176 | + | 92.0622i | −0.0288095 | + | 0.00327773i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5104.16 | −0.181137 | ||||||||
\(927\) | 38181.8 | − | 8802.02i | 1.35281 | − | 0.311862i | ||||
\(928\) | 26501.7 | 0.937456 | ||||||||
\(929\) | −14466.9 | + | 25057.5i | −0.510920 | + | 0.884939i | 0.489000 | + | 0.872284i | \(0.337362\pi\) |
−0.999920 | + | 0.0126553i | \(0.995972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8979.11 | + | 15552.3i | 0.316089 | + | 0.547482i | ||||
\(932\) | 16606.2 | + | 28762.8i | 0.583641 | + | 1.01090i | ||||
\(933\) | −8152.20 | + | 18740.5i | −0.286057 | + | 0.657596i | ||||
\(934\) | 3046.24 | − | 5276.25i | 0.106720 | − | 0.184844i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2120.60 | + | 488.862i | −0.0740536 | + | 0.0170715i | ||||
\(937\) | 8282.43 | 0.288768 | 0.144384 | − | 0.989522i | \(-0.453880\pi\) | ||||
0.144384 | + | 0.989522i | \(0.453880\pi\) | |||||||
\(938\) | 1511.96 | − | 2618.80i | 0.0526304 | − | 0.0911585i | ||||
\(939\) | 16346.5 | − | 1859.79i | 0.568103 | − | 0.0646346i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18408.2 | + | 31883.9i | 0.637715 | + | 1.10455i | 0.985933 | + | 0.167141i | \(0.0534534\pi\) |
−0.348219 | + | 0.937413i | \(0.613213\pi\) | |||||||
\(942\) | 1281.23 | + | 1732.07i | 0.0443151 | + | 0.0599085i | ||||
\(943\) | −2238.47 | + | 3877.14i | −0.0773007 | + | 0.133889i | ||||
\(944\) | −29318.0 | −1.01083 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −227.250 | −0.00781031 | ||||||||
\(947\) | 465.404 | − | 806.104i | 0.0159700 | − | 0.0276609i | −0.857930 | − | 0.513767i | \(-0.828250\pi\) |
0.873900 | + | 0.486106i | \(0.161583\pi\) | |||||||
\(948\) | 9014.69 | + | 12186.7i | 0.308843 | + | 0.417518i | ||||
\(949\) | −2336.27 | − | 4046.54i | −0.0799141 | − | 0.138415i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40485.6 | − | 4606.15i | 1.38048 | − | 0.157061i | ||||
\(952\) | 3322.06 | − | 5753.97i | 0.113097 | − | 0.195890i | ||||
\(953\) | −11327.1 | −0.385016 | −0.192508 | − | 0.981295i | \(-0.561662\pi\) | ||||
−0.192508 | + | 0.981295i | \(0.561662\pi\) | |||||||
\(954\) | −4023.52 | − | 4317.48i | −0.136547 | − | 0.146524i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6068.05 | + | 10510.2i | −0.205287 | + | 0.355568i | ||||
\(957\) | −992.815 | + | 2282.31i | −0.0335352 | + | 0.0770917i | ||||
\(958\) | 574.756 | + | 995.507i | 0.0193836 | + | 0.0335734i | ||||
\(959\) | −2419.00 | − | 4189.84i | −0.0814533 | − | 0.141081i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8019.05 | − | 13889.4i | 0.269177 | − | 0.466228i | ||||
\(962\) | 866.451 | 0.0290390 | ||||||||
\(963\) | 1080.47 | − | 3530.00i | 0.0361555 | − | 0.118123i | ||||
\(964\) | 37479.7 | 1.25222 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 983.451 | − | 111.890i | 0.0327557 | − | 0.00372670i | ||||
\(967\) | −20908.9 | − | 36215.3i | −0.695330 | − | 1.20435i | −0.970069 | − | 0.242829i | \(-0.921925\pi\) |
0.274739 | − | 0.961519i | \(-0.411409\pi\) | |||||||
\(968\) | 4987.54 | + | 8638.67i | 0.165605 | + | 0.286836i | ||||
\(969\) | −21253.3 | − | 28731.8i | −0.704596 | − | 0.952527i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40444.6 | −1.33669 | −0.668346 | − | 0.743850i | \(-0.732997\pi\) | ||||
−0.668346 | + | 0.743850i | \(0.732997\pi\) | |||||||
\(972\) | −24846.9 | + | 15801.1i | −0.819921 | + | 0.521421i | ||||
\(973\) | 31225.3 | 1.02881 | ||||||||
\(974\) | 3900.37 | − | 6755.64i | 0.128312 | − | 0.222243i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17051.3 | − | 29533.8i | −0.559221 | − | 0.968600i | ||||
\(977\) | 21271.4 | + | 36843.1i | 0.696553 | + | 1.20646i | 0.969655 | + | 0.244479i | \(0.0786170\pi\) |
−0.273102 | + | 0.961985i | \(0.588050\pi\) | |||||||
\(978\) | −76.8284 | + | 8.74098i | −0.00251197 | + | 0.000285793i | ||||
\(979\) | −320.618 | + | 555.327i | −0.0104668 | + | 0.0181290i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −317.023 | + | 1035.74i | −0.0103178 | + | 0.0337092i | ||||
\(982\) | −7555.19 | −0.245515 | ||||||||
\(983\) | 8943.52 | − | 15490.6i | 0.290187 | − | 0.502619i | −0.683667 | − | 0.729794i | \(-0.739616\pi\) |
0.973854 | + | 0.227175i | \(0.0729491\pi\) | |||||||
\(984\) | −2208.07 | + | 5075.98i | −0.0715352 | + | 0.164447i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5003.39 | − | 8666.13i | −0.161603 | − | 0.279904i | ||||
\(987\) | −12811.5 | + | 29451.5i | −0.413165 | + | 0.949797i | ||||
\(988\) | −4112.29 | + | 7122.70i | −0.132418 | + | 0.229355i | ||||
\(989\) | −9474.29 | −0.304616 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41046.0 | 1.31571 | 0.657856 | − | 0.753144i | \(-0.271464\pi\) | ||||
0.657856 | + | 0.753144i | \(0.271464\pi\) | |||||||
\(992\) | −5158.31 | + | 8934.46i | −0.165097 | + | 0.285957i | ||||
\(993\) | −56032.7 | + | 6374.99i | −1.79068 | + | 0.203730i | ||||
\(994\) | −3219.55 | − | 5576.42i | −0.102734 | − | 0.177941i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 31064.4 | + | 41995.3i | 0.988266 | + | 1.33601i | ||||
\(997\) | −12415.4 | + | 21504.2i | −0.394384 | + | 0.683093i | −0.993022 | − | 0.117926i | \(-0.962375\pi\) |
0.598638 | + | 0.801019i | \(0.295709\pi\) | |||||||
\(998\) | −5455.74 | −0.173044 | ||||||||
\(999\) | 22428.3 | − | 7930.09i | 0.710309 | − | 0.251148i |
(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 | 225.4.e.e.151.7 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.124.13 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.124.12 | 48 | |||
5.4 | even | 2 | 225.4.e.f.151.6 | yes | 24 | ||
9.2 | odd | 6 | 2025.4.a.be.1.7 | 12 | |||
9.4 | even | 3 | inner | 225.4.e.e.76.7 | ✓ | 24 | |
9.7 | even | 3 | 2025.4.a.bi.1.6 | 12 | |||
45.4 | even | 6 | 225.4.e.f.76.6 | yes | 24 | ||
45.13 | odd | 12 | 225.4.k.e.49.13 | 48 | |||
45.22 | odd | 12 | 225.4.k.e.49.12 | 48 | |||
45.29 | odd | 6 | 2025.4.a.bj.1.6 | 12 | |||
45.34 | even | 6 | 2025.4.a.bf.1.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.7 | ✓ | 24 | 9.4 | even | 3 | inner | |
225.4.e.e.151.7 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.e.f.76.6 | yes | 24 | 45.4 | even | 6 | ||
225.4.e.f.151.6 | yes | 24 | 5.4 | even | 2 | ||
225.4.k.e.49.12 | 48 | 45.22 | odd | 12 | |||
225.4.k.e.49.13 | 48 | 45.13 | odd | 12 | |||
225.4.k.e.124.12 | 48 | 5.3 | odd | 4 | |||
225.4.k.e.124.13 | 48 | 5.2 | odd | 4 | |||
2025.4.a.be.1.7 | 12 | 9.2 | odd | 6 | |||
2025.4.a.bf.1.7 | 12 | 45.34 | even | 6 | |||
2025.4.a.bi.1.6 | 12 | 9.7 | even | 3 | |||
2025.4.a.bj.1.6 | 12 | 45.29 | odd | 6 |