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 | 76.6 | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.f.151.6 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | \(-0.193485\pi\) |
−0.905030 | + | 0.425349i | \(0.860151\pi\) | |||||||
\(3\) | 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 | \(-0.277890\pi\) |
−0.984869 | + | 0.173300i | \(0.944557\pi\) | |||||||
\(8\) | −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 | 0.876715 | − | 0.481010i | \(-0.159730\pi\) |
−0.854924 | + | 0.518753i | \(0.826397\pi\) | |||||||
\(12\) | −16.1121 | − | 37.0390i | −0.387597 | − | 0.891021i | ||||
\(13\) | −5.36718 | + | 9.29622i | −0.114507 | + | 0.198331i | −0.917582 | − | 0.397546i | \(-0.869862\pi\) |
0.803076 | + | 0.595877i | \(0.203195\pi\) | |||||||
\(14\) | −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 | \(-0.665844\pi\) | ||||
−0.497760 | + | 0.867315i | \(0.665844\pi\) | |||||||
\(18\) | −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 | \(-0.787646\pi\) |
0.928639 | + | 0.370984i | \(0.120979\pi\) | |||||||
\(24\) | −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 | 0.710933 | + | 0.703260i | \(0.248273\pi\) |
0.253574 | + | 0.967316i | \(0.418394\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58.6364 | − | 101.561i | 0.339723 | − | 0.588417i | −0.644658 | − | 0.764471i | \(-0.723000\pi\) |
0.984380 | + | 0.176054i | \(0.0563334\pi\) | |||||||
\(32\) | −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 | \(-0.622941\pi\) | ||||
−0.376701 | + | 0.926335i | \(0.622941\pi\) | |||||||
\(38\) | −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 | −0.968915 | − | 0.247392i | \(-0.920426\pi\) |
0.698706 | + | 0.715409i | \(0.253760\pi\) | |||||||
\(42\) | 12.5121 | + | 28.7633i | 0.0459682 | + | 0.105673i | ||||
\(43\) | −150.121 | − | 260.018i | −0.532402 | − | 0.922147i | −0.999284 | − | 0.0378277i | \(-0.987956\pi\) |
0.466882 | − | 0.884319i | \(-0.345377\pi\) | |||||||
\(44\) | 12.3596 | 0.0423472 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.0215 | −0.0481478 | ||||||||
\(47\) | −243.712 | − | 422.122i | −0.756364 | − | 1.31006i | −0.944694 | − | 0.327954i | \(-0.893641\pi\) |
0.188330 | − | 0.982106i | \(-0.439693\pi\) | |||||||
\(48\) | −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 | \(-0.297147\pi\) | ||||
0.595012 | + | 0.803717i | \(0.297147\pi\) | |||||||
\(54\) | 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 | −0.446273 | − | 0.894897i | \(-0.647249\pi\) |
0.998140 | − | 0.0609650i | \(-0.0194178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −290.915 | − | 503.880i | −0.610621 | − | 1.05763i | −0.991136 | − | 0.132852i | \(-0.957587\pi\) |
0.380515 | − | 0.924775i | \(-0.375747\pi\) | |||||||
\(62\) | −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 | \(-0.984305\pi\) |
0.542075 | + | 0.840330i | \(0.317639\pi\) | |||||||
\(68\) | −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 | \(-0.386538\pi\) | ||||
0.348950 | + | 0.937141i | \(0.386538\pi\) | |||||||
\(74\) | 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 | 0.700911 | − | 0.713248i | \(-0.252777\pi\) |
−0.968147 | + | 0.250383i | \(0.919444\pi\) | |||||||
\(80\) | 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 | 0.876528 | + | 0.481351i | \(0.159854\pi\) |
−0.0214014 | + | 0.999771i | \(0.506813\pi\) | |||||||
\(84\) | −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 | 0.899838 | + | 0.436225i | \(0.143685\pi\) |
−0.0721373 | + | 0.997395i | \(0.522982\pi\) | |||||||
\(98\) | −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 | 0.996678 | + | 0.0814388i | \(0.0259515\pi\) |
−0.427811 | + | 0.903868i | \(0.640715\pi\) | |||||||
\(102\) | 171.495 | + | 19.5114i | 0.166476 | + | 0.0189404i | ||||
\(103\) | 725.615 | − | 1256.80i | 0.694145 | − | 1.20229i | −0.276323 | − | 0.961065i | \(-0.589116\pi\) |
0.970468 | − | 0.241230i | \(-0.0775507\pi\) | |||||||
\(104\) | 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 | \(-0.480327\pi\) | ||||
0.0617664 | + | 0.998091i | \(0.480327\pi\) | |||||||
\(108\) | −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 | −0.0795054 | − | 0.996834i | \(-0.525334\pi\) |
0.903037 | − | 0.429564i | \(-0.141333\pi\) | |||||||
\(114\) | −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 | \(-0.347645\pi\) | ||||
0.460571 | + | 0.887623i | \(0.347645\pi\) | |||||||
\(128\) | 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 | 0.470913 | + | 0.882179i | \(0.343924\pi\) |
−0.999447 | + | 0.0332667i | \(0.989409\pi\) | |||||||
\(132\) | 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 | \(-0.204623\pi\) |
−0.919356 | + | 0.393426i | \(0.871290\pi\) | |||||||
\(138\) | −46.4182 | + | 62.7517i | −0.0286332 | + | 0.0387086i | ||||
\(139\) | 1231.19 | − | 2132.49i | 0.751283 | − | 1.30126i | −0.195918 | − | 0.980620i | \(-0.562769\pi\) |
0.947201 | − | 0.320641i | \(-0.103898\pi\) | |||||||
\(140\) | 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 | −0.914008 | − | 0.405697i | \(-0.867029\pi\) |
0.808348 | + | 0.588705i | \(0.200362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −398.550 | − | 690.308i | −0.214792 | − | 0.372030i | 0.738417 | − | 0.674345i | \(-0.235574\pi\) |
−0.953208 | + | 0.302315i | \(0.902241\pi\) | |||||||
\(152\) | −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 | \(-0.762278\pi\) |
0.955227 | + | 0.295875i | \(0.0956112\pi\) | |||||||
\(158\) | −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 | \(-0.502391\pi\) | ||||
−0.00751074 | + | 0.999972i | \(0.502391\pi\) | |||||||
\(164\) | 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 | \(-0.830584\pi\) |
0.870312 | + | 0.492501i | \(0.163917\pi\) | |||||||
\(168\) | 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 | \(-0.0830932\pi\) |
−0.706573 | + | 0.707640i | \(0.749760\pi\) | |||||||
\(174\) | −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 | 0.782032 | − | 0.623238i | \(-0.214183\pi\) |
−0.930756 | + | 0.365640i | \(0.880850\pi\) | |||||||
\(192\) | −1319.56 | + | 1783.88i | −0.495994 | + | 0.670522i | ||||
\(193\) | 238.539 | − | 413.162i | 0.0889659 | − | 0.154093i | −0.818108 | − | 0.575064i | \(-0.804977\pi\) |
0.907074 | + | 0.420971i | \(0.138310\pi\) | |||||||
\(194\) | 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 | \(-0.815663\pi\) | ||||
−0.836949 | + | 0.547281i | \(0.815663\pi\) | |||||||
\(198\) | −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 | −0.998457 | − | 0.0555378i | \(-0.982313\pi\) |
0.547325 | + | 0.836920i | \(0.315646\pi\) | |||||||
\(212\) | 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 | \(-0.189119\pi\) |
−0.899110 | + | 0.437722i | \(0.855785\pi\) | |||||||
\(224\) | 1115.55 | 0.332750 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −941.817 | −0.277207 | ||||||||
\(227\) | 2143.99 | + | 3713.50i | 0.626879 | + | 1.08579i | 0.988174 | + | 0.153335i | \(0.0490015\pi\) |
−0.361295 | + | 0.932452i | \(0.617665\pi\) | |||||||
\(228\) | −1588.11 | − | 3650.79i | −0.461294 | − | 1.06044i | ||||
\(229\) | −2052.30 | + | 3554.69i | −0.592227 | + | 1.02577i | 0.401705 | + | 0.915769i | \(0.368418\pi\) |
−0.993932 | + | 0.109998i | \(0.964916\pi\) | |||||||
\(230\) | 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 | \(-0.705094\pi\) | ||||
−0.600656 | + | 0.799508i | \(0.705094\pi\) | |||||||
\(234\) | −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 | −0.740841 | − | 0.671681i | \(-0.765573\pi\) |
0.952113 | + | 0.305747i | \(0.0989061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2410.77 | + | 4175.58i | 0.644362 | + | 1.11607i | 0.984448 | + | 0.175674i | \(0.0562105\pi\) |
−0.340086 | + | 0.940394i | \(0.610456\pi\) | |||||||
\(242\) | −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 | −0.395924 | − | 0.918283i | \(-0.629576\pi\) |
0.993219 | − | 0.116261i | \(-0.0370910\pi\) | |||||||
\(258\) | 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 | 0.983889 | + | 0.178780i | \(0.0572149\pi\) |
−0.337117 | + | 0.941463i | \(0.609452\pi\) | |||||||
\(264\) | −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 | \(-0.231034\pi\) |
−0.948800 | + | 0.315877i | \(0.897701\pi\) | |||||||
\(278\) | −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 | −0.953902 | − | 0.300119i | \(-0.902974\pi\) |
0.217040 | − | 0.976163i | \(-0.430360\pi\) | |||||||
\(282\) | 480.937 | + | 1105.59i | 0.101558 | + | 0.233465i | ||||
\(283\) | −3216.21 | + | 5570.64i | −0.675562 | + | 1.17011i | 0.300743 | + | 0.953705i | \(0.402765\pi\) |
−0.976304 | + | 0.216402i | \(0.930568\pi\) | |||||||
\(284\) | 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 | −0.180062 | − | 0.983655i | \(-0.557630\pi\) |
0.941901 | − | 0.335890i | \(-0.109037\pi\) | |||||||
\(294\) | −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 | \(-0.362055\pi\) | ||||
0.419929 | + | 0.907557i | \(0.362055\pi\) | |||||||
\(308\) | −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 | −0.987721 | − | 0.156231i | \(-0.950066\pi\) |
0.629160 | + | 0.777275i | \(0.283399\pi\) | |||||||
\(312\) | −167.064 | − | 384.051i | −0.0303145 | − | 0.0696879i | ||||
\(313\) | 1583.09 | + | 2742.00i | 0.285884 | + | 0.495165i | 0.972823 | − | 0.231549i | \(-0.0743795\pi\) |
−0.686939 | + | 0.726715i | \(0.741046\pi\) | |||||||
\(314\) | −414.622 | −0.0745175 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2917.26 | −0.519332 | ||||||||
\(317\) | 3920.86 | + | 6791.13i | 0.694692 | + | 1.20324i | 0.970284 | + | 0.241967i | \(0.0777927\pi\) |
−0.275592 | + | 0.961275i | \(0.588874\pi\) | |||||||
\(318\) | −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 | 0.826049 | + | 0.563599i | \(0.190584\pi\) |
0.0750663 | + | 0.997179i | \(0.476083\pi\) | |||||||
\(332\) | 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 | −0.472780 | − | 0.881180i | \(-0.656749\pi\) |
0.999515 | − | 0.0311507i | \(-0.00991719\pi\) | |||||||
\(338\) | 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 | \(-0.985256\pi\) |
0.539564 | + | 0.841944i | \(0.318589\pi\) | |||||||
\(348\) | 7236.33 | − | 9782.62i | 1.11468 | − | 1.50691i | ||||
\(349\) | 3648.27 | + | 6318.99i | 0.559563 | + | 0.969192i | 0.997533 | + | 0.0702022i | \(0.0223644\pi\) |
−0.437970 | + | 0.898990i | \(0.644302\pi\) | |||||||
\(350\) | 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 | \(-0.196725\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(354\) | −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 | \(-0.0154570\pi\) |
−0.541448 | + | 0.840734i | \(0.682124\pi\) | |||||||
\(368\) | −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 | \(-0.944068\pi\) |
0.643693 | + | 0.765284i | \(0.277402\pi\) | |||||||
\(374\) | −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 | \(-0.742231\pi\) |
0.971954 | + | 0.235170i | \(0.0755645\pi\) | |||||||
\(384\) | 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 | 0.957573 | − | 0.288189i | \(-0.0930532\pi\) |
−0.728366 | + | 0.685188i | \(0.759720\pi\) | |||||||
\(390\) | 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 | \(-0.420193\pi\) | ||||
0.248101 | + | 0.968734i | \(0.420193\pi\) | |||||||
\(398\) | −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 | −0.890066 | − | 0.455832i | \(-0.849342\pi\) |
0.839795 | + | 0.542904i | \(0.182675\pi\) | |||||||
\(402\) | 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 | −0.889425 | − | 0.457080i | \(-0.848895\pi\) |
0.840556 | + | 0.541725i | \(0.182228\pi\) | |||||||
\(410\) | 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 | −0.912761 | − | 0.408495i | \(-0.866054\pi\) |
0.810147 | + | 0.586227i | \(0.199387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7287.86 | − | 12622.9i | −0.843678 | − | 1.46129i | −0.886765 | − | 0.462221i | \(-0.847053\pi\) |
0.0430868 | − | 0.999071i | \(-0.486281\pi\) | |||||||
\(422\) | 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 | \(-0.750228\pi\) | ||||
−0.707614 | + | 0.706599i | \(0.750228\pi\) | |||||||
\(434\) | 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 | 0.703924 | − | 0.710275i | \(-0.251429\pi\) |
−0.967078 | + | 0.254479i | \(0.918096\pi\) | |||||||
\(440\) | 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 | \(-0.00740339\pi\) |
−0.520005 | + | 0.854163i | \(0.674070\pi\) | |||||||
\(444\) | 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 | \(-0.259409\pi\) |
−0.973153 | + | 0.230157i | \(0.926076\pi\) | |||||||
\(458\) | 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 | −0.986766 | − | 0.162150i | \(-0.948157\pi\) |
0.352957 | − | 0.935640i | \(-0.385176\pi\) | |||||||
\(462\) | −29.6591 | + | 40.0954i | −0.00298672 | + | 0.00403768i | ||||
\(463\) | 5361.12 | − | 9285.74i | 0.538126 | − | 0.932062i | −0.460879 | − | 0.887463i | \(-0.652466\pi\) |
0.999005 | − | 0.0445990i | \(-0.0142010\pi\) | |||||||
\(464\) | 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 | \(-0.718625\pi\) | ||||
−0.634089 | + | 0.773260i | \(0.718625\pi\) | |||||||
\(468\) | 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 | 0.802677 | − | 0.596413i | \(-0.203408\pi\) |
−0.917848 | + | 0.396932i | \(0.870075\pi\) | |||||||
\(480\) | 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 | \(-0.775971\pi\) | ||||
−0.762384 | + | 0.647125i | \(0.775971\pi\) | |||||||
\(488\) | 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 | 0.227764 | + | 0.973716i | \(0.426858\pi\) |
−0.957145 | + | 0.289609i | \(0.906475\pi\) | |||||||
\(492\) | 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 | 0.485783 | + | 0.874079i | \(0.338534\pi\) |
−0.999867 | + | 0.0163392i | \(0.994799\pi\) | |||||||
\(500\) | 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 | \(-0.485343\pi\) | ||||
0.0460293 | + | 0.998940i | \(0.485343\pi\) | |||||||
\(504\) | 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 | −0.735530 | − | 0.677492i | \(-0.763067\pi\) |
0.954490 | + | 0.298242i | \(0.0964003\pi\) | |||||||
\(510\) | 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 | \(-0.293487\pi\) | ||||
0.604215 | + | 0.796821i | \(0.293487\pi\) | |||||||
\(524\) | 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 | 0.981282 | + | 0.192578i | \(0.0616848\pi\) |
−0.323863 | + | 0.946104i | \(0.604982\pi\) | |||||||
\(548\) | −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 | \(-0.654264\pi\) | ||||
−0.465885 | + | 0.884845i | \(0.654264\pi\) | |||||||
\(558\) | 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 | \(-0.940748\pi\) |
0.651639 | + | 0.758529i | \(0.274082\pi\) | |||||||
\(564\) | −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 | 0.975757 | − | 0.218856i | \(-0.0702325\pi\) |
−0.677413 | + | 0.735603i | \(0.736899\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8189.02 | − | 14183.8i | 0.600175 | − | 1.03953i | −0.392619 | − | 0.919701i | \(-0.628431\pi\) |
0.992794 | − | 0.119832i | \(-0.0382356\pi\) | |||||||
\(572\) | −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 | \(-0.144280\pi\) | ||||
0.899020 | + | 0.437907i | \(0.144280\pi\) | |||||||
\(578\) | 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 | \(-0.0716564\pi\) |
−0.680697 | + | 0.732565i | \(0.738323\pi\) | |||||||
\(588\) | −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 | \(-0.110124\pi\) | ||||
0.940749 | + | 0.339105i | \(0.110124\pi\) | |||||||
\(594\) | −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 | 0.230351 | + | 0.973108i | \(0.426013\pi\) |
−0.957911 | + | 0.287064i | \(0.907321\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −292.016 | − | 505.786i | −0.0198196 | − | 0.0343285i | 0.855946 | − | 0.517066i | \(-0.172976\pi\) |
−0.875765 | + | 0.482738i | \(0.839643\pi\) | |||||||
\(602\) | 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 | \(-0.956312\pi\) |
0.613788 | + | 0.789471i | \(0.289645\pi\) | |||||||
\(608\) | −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 | \(-0.455063\pi\) | ||||
0.140706 | + | 0.990051i | \(0.455063\pi\) | |||||||
\(614\) | −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 | \(-0.757900\pi\) |
0.959206 | + | 0.282708i | \(0.0912329\pi\) | |||||||
\(618\) | −2134.76 | + | 2885.94i | −0.138953 | + | 0.187847i | ||||
\(619\) | −5128.24 | − | 8882.36i | −0.332991 | − | 0.576757i | 0.650106 | − | 0.759843i | \(-0.274724\pi\) |
−0.983097 | + | 0.183087i | \(0.941391\pi\) | |||||||
\(620\) | 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 | 0.856994 | + | 0.515327i | \(0.172329\pi\) |
0.0177891 | + | 0.999842i | \(0.494337\pi\) | |||||||
\(642\) | −336.036 | − | 38.2317i | −0.0206578 | − | 0.00235029i | ||||
\(643\) | 5844.00 | − | 10122.1i | 0.358421 | − | 0.620804i | −0.629276 | − | 0.777182i | \(-0.716649\pi\) |
0.987697 | + | 0.156378i | \(0.0499818\pi\) | |||||||
\(644\) | −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 | \(-0.627149\pi\) | ||||
−0.388911 | + | 0.921275i | \(0.627149\pi\) | |||||||
\(648\) | 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 | \(-0.774252\pi\) |
0.943423 | + | 0.331590i | \(0.107585\pi\) | |||||||
\(654\) | −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 | 0.509953 | − | 0.860202i | \(-0.329663\pi\) |
−0.999934 | + | 0.0115307i | \(0.996330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11469.8 | − | 19866.4i | 0.674925 | − | 1.16900i | −0.301566 | − | 0.953445i | \(-0.597509\pi\) |
0.976491 | − | 0.215559i | \(-0.0691573\pi\) | |||||||
\(662\) | 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 | \(-0.188226\pi\) |
−0.897879 | + | 0.440242i | \(0.854893\pi\) | |||||||
\(674\) | −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 | \(-0.0201647\pi\) |
−0.553822 | + | 0.832635i | \(0.686831\pi\) | |||||||
\(678\) | −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 | \(-0.314713\pi\) | ||||
0.549777 | + | 0.835311i | \(0.314713\pi\) | |||||||
\(684\) | −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 | 0.867442 | − | 0.497538i | \(-0.165763\pi\) |
−0.864602 | + | 0.502458i | \(0.832429\pi\) | |||||||
\(692\) | 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 | 0.687421 | − | 0.726260i | \(-0.258743\pi\) |
−0.972670 | + | 0.232194i | \(0.925410\pi\) | |||||||
\(710\) | 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 | \(-0.0779062\pi\) |
−0.694949 | + | 0.719059i | \(0.744573\pi\) | |||||||
\(728\) | −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 | −0.470700 | − | 0.882293i | \(-0.655999\pi\) |
0.999438 | − | 0.0335082i | \(-0.0106680\pi\) | |||||||
\(734\) | 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 | \(-0.791716\pi\) |
0.923820 | + | 0.382827i | \(0.125050\pi\) | |||||||
\(744\) | 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 | −0.968331 | − | 0.249669i | \(-0.919678\pi\) |
0.700386 | + | 0.713765i | \(0.253011\pi\) | |||||||
\(752\) | −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 | \(-0.658514\pi\) | ||||
−0.477659 | + | 0.878545i | \(0.658514\pi\) | |||||||
\(758\) | −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 | −0.390610 | − | 0.920556i | \(-0.627736\pi\) |
0.992530 | − | 0.122000i | \(-0.0389307\pi\) | |||||||
\(762\) | −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 | 0.253162 | + | 0.967424i | \(0.418529\pi\) |
−0.964395 | + | 0.264467i | \(0.914804\pi\) | |||||||
\(770\) | 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 | \(-0.450395\pi\) | ||||
0.155208 | + | 0.987882i | \(0.450395\pi\) | |||||||
\(774\) | 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 | \(-0.991148\pi\) |
0.523888 | + | 0.851787i | \(0.324481\pi\) | |||||||
\(788\) | −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 | \(-0.768283\pi\) |
0.949475 | + | 0.313842i | \(0.101616\pi\) | |||||||
\(798\) | 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 | −0.834692 | − | 0.550717i | \(-0.814354\pi\) |
−0.0595894 | − | 0.998223i | \(-0.518979\pi\) | |||||||
\(822\) | 376.442 | + | 865.376i | 0.0159731 | + | 0.0367195i | ||||
\(823\) | −10437.6 | + | 18078.5i | −0.442081 | + | 0.765707i | −0.997844 | − | 0.0656341i | \(-0.979093\pi\) |
0.555763 | + | 0.831341i | \(0.312426\pi\) | |||||||
\(824\) | −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 | \(-0.479050\pi\) | ||||
0.0657698 | + | 0.997835i | \(0.479050\pi\) | |||||||
\(828\) | −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 | −0.876074 | − | 0.482178i | \(-0.839846\pi\) |
0.0204588 | − | 0.999791i | \(-0.493487\pi\) | |||||||
\(840\) | 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 | \(-0.0468145\pi\) |
−0.621512 | + | 0.783405i | \(0.713481\pi\) | |||||||
\(854\) | 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 | \(-0.246015\pi\) |
−0.962610 | + | 0.270890i | \(0.912682\pi\) | |||||||
\(858\) | 41.9467 | + | 4.77239i | 0.00166904 | + | 0.000189891i | ||||
\(859\) | 14758.5 | − | 25562.5i | 0.586210 | − | 1.01534i | −0.408514 | − | 0.912752i | \(-0.633953\pi\) |
0.994723 | − | 0.102593i | \(-0.0327139\pi\) | |||||||
\(860\) | 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 | \(-0.803077\pi\) | ||||
−0.814661 | + | 0.579937i | \(0.803077\pi\) | |||||||
\(864\) | 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 | −0.216155 | − | 0.976359i | \(-0.569352\pi\) |
0.953629 | − | 0.300984i | \(-0.0973152\pi\) | |||||||
\(878\) | −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 | \(-0.232419\pi\) | ||||
0.745064 | + | 0.666993i | \(0.232419\pi\) | |||||||
\(884\) | −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 | −0.464803 | − | 0.885414i | \(-0.653875\pi\) |
0.999193 | − | 0.0401756i | \(-0.0127917\pi\) | |||||||
\(888\) | 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 | \(-0.280110\pi\) |
−0.986053 | + | 0.166429i | \(0.946776\pi\) | |||||||
\(908\) | 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 | 0.878943 | − | 0.476926i | \(-0.158249\pi\) |
−0.852502 | + | 0.522724i | \(0.824916\pi\) | |||||||
\(912\) | −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 | −0.999920 | − | 0.0126553i | \(-0.995972\pi\) |
0.489000 | − | 0.872284i | \(-0.337362\pi\) | |||||||
\(930\) | 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 | \(-0.546120\pi\) | ||||
−0.144384 | + | 0.989522i | \(0.546120\pi\) | |||||||
\(938\) | −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 | −0.348219 | − | 0.937413i | \(-0.613213\pi\) |
0.985933 | − | 0.167141i | \(-0.0534534\pi\) | |||||||
\(942\) | −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 | \(-0.171750\pi\) |
−0.873900 | + | 0.486106i | \(0.838417\pi\) | |||||||
\(948\) | −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 | \(-0.438338\pi\) | ||||
0.192508 | + | 0.981295i | \(0.438338\pi\) | |||||||
\(954\) | −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 | −0.274739 | − | 0.961519i | \(-0.588591\pi\) |
0.970069 | − | 0.242829i | \(-0.0780752\pi\) | |||||||
\(968\) | −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 | 0.273102 | + | 0.961985i | \(0.411950\pi\) |
−0.969655 | + | 0.244479i | \(0.921383\pi\) | |||||||
\(978\) | 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 | \(-0.260384\pi\) |
−0.973854 | + | 0.227175i | \(0.927051\pi\) | |||||||
\(984\) | −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 | \(-0.0376247\pi\) |
−0.598638 | + | 0.801019i | \(0.704291\pi\) | |||||||
\(998\) | 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.f.76.6 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.49.13 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.49.12 | 48 | |||
5.4 | even | 2 | 225.4.e.e.76.7 | ✓ | 24 | ||
9.4 | even | 3 | 2025.4.a.bf.1.7 | 12 | |||
9.5 | odd | 6 | 2025.4.a.bj.1.6 | 12 | |||
9.7 | even | 3 | inner | 225.4.e.f.151.6 | yes | 24 | |
45.4 | even | 6 | 2025.4.a.bi.1.6 | 12 | |||
45.7 | odd | 12 | 225.4.k.e.124.12 | 48 | |||
45.14 | odd | 6 | 2025.4.a.be.1.7 | 12 | |||
45.34 | even | 6 | 225.4.e.e.151.7 | yes | 24 | ||
45.43 | odd | 12 | 225.4.k.e.124.13 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.7 | ✓ | 24 | 5.4 | even | 2 | ||
225.4.e.e.151.7 | yes | 24 | 45.34 | even | 6 | ||
225.4.e.f.76.6 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.e.f.151.6 | yes | 24 | 9.7 | even | 3 | inner | |
225.4.k.e.49.12 | 48 | 5.3 | odd | 4 | |||
225.4.k.e.49.13 | 48 | 5.2 | odd | 4 | |||
225.4.k.e.124.12 | 48 | 45.7 | odd | 12 | |||
225.4.k.e.124.13 | 48 | 45.43 | odd | 12 | |||
2025.4.a.be.1.7 | 12 | 45.14 | odd | 6 | |||
2025.4.a.bf.1.7 | 12 | 9.4 | even | 3 | |||
2025.4.a.bi.1.6 | 12 | 45.4 | even | 6 | |||
2025.4.a.bj.1.6 | 12 | 9.5 | odd | 6 |