Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.5 | ||
Character | \(\chi\) | \(=\) | 225.91 |
Dual form | 225.4.h.a.136.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.08389 | + | 0.787491i | 0.383212 | + | 0.278420i | 0.762668 | − | 0.646790i | \(-0.223889\pi\) |
−0.379456 | + | 0.925210i | \(0.623889\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.91746 | − | 5.90135i | −0.239683 | − | 0.737669i | ||||
\(5\) | 3.83217 | − | 10.5031i | 0.342760 | − | 0.939423i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.2101 | −0.659284 | −0.329642 | − | 0.944106i | \(-0.606928\pi\) | ||||
−0.329642 | + | 0.944106i | \(0.606928\pi\) | |||||||
\(8\) | 5.88101 | − | 18.0999i | 0.259906 | − | 0.799909i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 12.4247 | − | 8.36635i | 0.392904 | − | 0.264567i | ||||
\(11\) | −2.00821 | − | 1.45905i | −0.0550454 | − | 0.0399928i | 0.559922 | − | 0.828545i | \(-0.310831\pi\) |
−0.614968 | + | 0.788552i | \(0.710831\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −69.2682 | + | 50.3263i | −1.47781 | + | 1.07369i | −0.499557 | + | 0.866281i | \(0.666504\pi\) |
−0.978254 | + | 0.207411i | \(0.933496\pi\) | |||||||
\(14\) | −13.2344 | − | 9.61535i | −0.252646 | − | 0.183558i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.5320 | + | 14.1909i | −0.305188 | + | 0.221732i | ||||
\(17\) | 1.71458 | − | 5.27694i | 0.0244616 | − | 0.0752850i | −0.938080 | − | 0.346417i | \(-0.887398\pi\) |
0.962542 | + | 0.271132i | \(0.0873981\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.45887 | + | 22.9561i | −0.0900623 | + | 0.277183i | −0.985935 | − | 0.167127i | \(-0.946551\pi\) |
0.895873 | + | 0.444310i | \(0.146551\pi\) | |||||||
\(20\) | −69.3303 | − | 2.47571i | −0.775137 | − | 0.0276793i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.02769 | − | 3.16290i | −0.00995927 | − | 0.0306515i | ||||
\(23\) | −83.6143 | − | 60.7493i | −0.758034 | − | 0.550744i | 0.140273 | − | 0.990113i | \(-0.455202\pi\) |
−0.898307 | + | 0.439369i | \(0.855202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −95.6289 | − | 80.4991i | −0.765031 | − | 0.643993i | ||||
\(26\) | −114.710 | −0.865253 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 23.4124 | + | 72.0561i | 0.158019 | + | 0.486333i | ||||
\(29\) | 35.3035 | + | 108.653i | 0.226059 | + | 0.695737i | 0.998182 | + | 0.0602646i | \(0.0191945\pi\) |
−0.772124 | + | 0.635472i | \(0.780806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.5487 | − | 146.340i | 0.275484 | − | 0.847852i | −0.713607 | − | 0.700546i | \(-0.752940\pi\) |
0.989091 | − | 0.147306i | \(-0.0470602\pi\) | |||||||
\(32\) | −184.596 | −1.01976 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.01395 | − | 4.36939i | 0.0303348 | − | 0.0220395i | ||||
\(35\) | −46.7912 | + | 128.244i | −0.225976 | + | 0.619346i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 277.229 | − | 201.419i | 1.23179 | − | 0.894948i | 0.234767 | − | 0.972052i | \(-0.424567\pi\) |
0.997023 | + | 0.0771043i | \(0.0245674\pi\) | |||||||
\(38\) | −26.1623 | + | 19.0080i | −0.111686 | + | 0.0811449i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −167.567 | − | 131.130i | −0.662368 | − | 0.518339i | ||||
\(41\) | 28.0530 | − | 20.3817i | 0.106857 | − | 0.0776363i | −0.533073 | − | 0.846069i | \(-0.678963\pi\) |
0.639931 | + | 0.768433i | \(0.278963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −154.740 | −0.548783 | −0.274391 | − | 0.961618i | \(-0.588476\pi\) | ||||
−0.274391 | + | 0.961618i | \(0.588476\pi\) | |||||||
\(44\) | −4.75970 | + | 14.6489i | −0.0163080 | + | 0.0501908i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −42.7890 | − | 131.691i | −0.137150 | − | 0.422104i | ||||
\(47\) | −104.613 | − | 321.965i | −0.324666 | − | 0.999221i | −0.971591 | − | 0.236667i | \(-0.923945\pi\) |
0.646924 | − | 0.762554i | \(-0.276055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −193.913 | −0.565345 | ||||||||
\(50\) | −40.2588 | − | 162.559i | −0.113869 | − | 0.459786i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 429.812 | + | 312.277i | 1.14624 | + | 0.832789i | ||||
\(53\) | −199.512 | − | 614.036i | −0.517078 | − | 1.59140i | −0.779469 | − | 0.626441i | \(-0.784511\pi\) |
0.262390 | − | 0.964962i | \(-0.415489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −23.0204 | + | 15.5011i | −0.0564375 | + | 0.0380030i | ||||
\(56\) | −71.8077 | + | 221.001i | −0.171352 | + | 0.527367i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −47.2982 | + | 145.569i | −0.107079 | + | 0.329554i | ||||
\(59\) | 536.260 | − | 389.616i | 1.18331 | − | 0.859724i | 0.190767 | − | 0.981635i | \(-0.438903\pi\) |
0.992541 | + | 0.121912i | \(0.0389025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 289.370 | + | 210.239i | 0.607377 | + | 0.441285i | 0.848490 | − | 0.529212i | \(-0.177512\pi\) |
−0.241113 | + | 0.970497i | \(0.577512\pi\) | |||||||
\(62\) | 166.779 | − | 121.172i | 0.341628 | − | 0.248207i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −43.8256 | − | 31.8411i | −0.0855968 | − | 0.0621897i | ||||
\(65\) | 263.133 | + | 920.387i | 0.502117 | + | 1.75631i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −164.205 | + | 505.370i | −0.299415 | + | 0.921504i | 0.682288 | + | 0.731083i | \(0.260985\pi\) |
−0.981703 | + | 0.190420i | \(0.939015\pi\) | |||||||
\(68\) | −34.4287 | −0.0613984 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −151.707 | + | 102.154i | −0.259035 | + | 0.174425i | ||||
\(71\) | 196.164 | + | 603.732i | 0.327893 | + | 1.00915i | 0.970118 | + | 0.242635i | \(0.0780118\pi\) |
−0.642224 | + | 0.766517i | \(0.721988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −779.001 | − | 565.977i | −1.24897 | − | 0.907433i | −0.250812 | − | 0.968036i | \(-0.580698\pi\) |
−0.998162 | + | 0.0606028i | \(0.980698\pi\) | |||||||
\(74\) | 459.101 | 0.721208 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 149.774 | 0.226056 | ||||||||
\(77\) | 24.5205 | + | 17.8152i | 0.0362905 | + | 0.0263666i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 175.752 | + | 540.908i | 0.250299 | + | 0.770340i | 0.994720 | + | 0.102630i | \(0.0327257\pi\) |
−0.744421 | + | 0.667711i | \(0.767274\pi\) | |||||||
\(80\) | 74.1975 | + | 259.528i | 0.103694 | + | 0.362702i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 46.4568 | 0.0625645 | ||||||||
\(83\) | 98.8352 | − | 304.184i | 0.130706 | − | 0.402271i | −0.864192 | − | 0.503163i | \(-0.832170\pi\) |
0.994897 | + | 0.100892i | \(0.0321696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −48.8535 | − | 38.2305i | −0.0623400 | − | 0.0487844i | ||||
\(86\) | −167.721 | − | 121.856i | −0.210300 | − | 0.152792i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −38.2190 | + | 27.7677i | −0.0462973 | + | 0.0336369i | ||||
\(89\) | −1079.81 | − | 784.525i | −1.28606 | − | 0.934376i | −0.286341 | − | 0.958128i | \(-0.592439\pi\) |
−0.999718 | + | 0.0237515i | \(0.992439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 845.772 | − | 614.489i | 0.974296 | − | 0.707868i | ||||
\(92\) | −198.176 | + | 609.922i | −0.224579 | + | 0.691182i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 140.156 | − | 431.355i | 0.153787 | − | 0.473307i | ||||
\(95\) | 212.525 | + | 166.313i | 0.229523 | + | 0.179614i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 123.390 | + | 379.754i | 0.129158 | + | 0.397507i | 0.994636 | − | 0.103440i | \(-0.0329850\pi\) |
−0.865478 | + | 0.500947i | \(0.832985\pi\) | |||||||
\(98\) | −210.180 | − | 152.705i | −0.216647 | − | 0.157403i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −291.688 | + | 718.694i | −0.291688 | + | 0.718694i | ||||
\(101\) | 131.408 | 0.129461 | 0.0647307 | − | 0.997903i | \(-0.479381\pi\) | ||||
0.0647307 | + | 0.997903i | \(0.479381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.82218 | + | 17.9188i | 0.00556967 | + | 0.0171417i | 0.953803 | − | 0.300434i | \(-0.0971314\pi\) |
−0.948233 | + | 0.317575i | \(0.897131\pi\) | |||||||
\(104\) | 503.533 | + | 1549.72i | 0.474764 | + | 1.46117i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 267.299 | − | 822.661i | 0.244928 | − | 0.753810i | ||||
\(107\) | 1832.09 | 1.65528 | 0.827640 | − | 0.561259i | \(-0.189683\pi\) | ||||
0.827640 | + | 0.561259i | \(0.189683\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1082.18 | − | 786.250i | 0.950954 | − | 0.690909i | −7.79623e−5 | − | 1.00000i | \(-0.500025\pi\) |
0.951032 | + | 0.309091i | \(0.100025\pi\) | |||||||
\(110\) | −37.1584 | − | 1.32689i | −0.0322083 | − | 0.00115013i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 238.488 | − | 173.272i | 0.201206 | − | 0.146184i | ||||
\(113\) | 29.3061 | − | 21.2921i | 0.0243972 | − | 0.0177256i | −0.575520 | − | 0.817788i | \(-0.695200\pi\) |
0.599917 | + | 0.800062i | \(0.295200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −958.478 | + | 645.405i | −0.777205 | + | 0.523342i | ||||
\(116\) | 573.506 | − | 416.677i | 0.459041 | − | 0.333513i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 888.065 | 0.692822 | ||||||||
\(119\) | −20.9352 | + | 64.4319i | −0.0161271 | + | 0.0496342i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −409.398 | − | 1260.00i | −0.307586 | − | 0.946654i | ||||
\(122\) | 148.083 | + | 455.752i | 0.109892 | + | 0.338212i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −954.776 | −0.691463 | ||||||||
\(125\) | −1211.95 | + | 695.911i | −0.867204 | + | 0.497953i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1130.69 | + | 821.496i | 0.790021 | + | 0.573984i | 0.907970 | − | 0.419036i | \(-0.137632\pi\) |
−0.117949 | + | 0.993020i | \(0.537632\pi\) | |||||||
\(128\) | 433.920 | + | 1335.47i | 0.299637 | + | 0.922187i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −439.590 | + | 1204.81i | −0.296574 | + | 0.812838i | ||||
\(131\) | 877.005 | − | 2699.14i | 0.584918 | − | 1.80019i | −0.0146799 | − | 0.999892i | \(-0.504673\pi\) |
0.599598 | − | 0.800301i | \(-0.295327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 91.0736 | − | 280.296i | 0.0593766 | − | 0.182742i | ||||
\(134\) | −575.953 | + | 418.455i | −0.371304 | + | 0.269768i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −85.4284 | − | 62.0674i | −0.0538634 | − | 0.0391341i | ||||
\(137\) | −655.541 | + | 476.279i | −0.408808 | + | 0.297016i | −0.773119 | − | 0.634261i | \(-0.781304\pi\) |
0.364311 | + | 0.931277i | \(0.381304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2540.67 | + | 1845.91i | 1.55034 | + | 1.12639i | 0.943410 | + | 0.331628i | \(0.107598\pi\) |
0.606927 | + | 0.794758i | \(0.292402\pi\) | |||||||
\(140\) | 846.530 | + | 30.2287i | 0.511035 | + | 0.0182485i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −262.813 | + | 808.855i | −0.155315 | + | 0.478012i | ||||
\(143\) | 212.534 | 0.124287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1276.48 | + | 45.5818i | 0.731075 | + | 0.0261059i | ||||
\(146\) | −398.648 | − | 1226.91i | −0.225975 | − | 0.695479i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1720.22 | − | 1249.81i | −0.955414 | − | 0.694149i | ||||
\(149\) | 1008.26 | 0.554362 | 0.277181 | − | 0.960818i | \(-0.410600\pi\) | ||||
0.277181 | + | 0.960818i | \(0.410600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2162.97 | −1.16570 | −0.582848 | − | 0.812581i | \(-0.698062\pi\) | ||||
−0.582848 | + | 0.812581i | \(0.698062\pi\) | |||||||
\(152\) | 371.636 | + | 270.009i | 0.198314 | + | 0.144083i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.5482 | + | 38.6193i | 0.00656598 | + | 0.0202080i | ||||
\(155\) | −1354.80 | − | 1060.21i | −0.702067 | − | 0.549406i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2618.64 | −1.33115 | −0.665575 | − | 0.746331i | \(-0.731814\pi\) | ||||
−0.665575 | + | 0.746331i | \(0.731814\pi\) | |||||||
\(158\) | −235.465 | + | 724.686i | −0.118561 | + | 0.364892i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −707.405 | + | 1938.83i | −0.349533 | + | 0.957987i | ||||
\(161\) | 1020.94 | + | 741.756i | 0.499759 | + | 0.363096i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 261.518 | − | 190.004i | 0.125667 | − | 0.0913022i | −0.523176 | − | 0.852224i | \(-0.675253\pi\) |
0.648843 | + | 0.760922i | \(0.275253\pi\) | |||||||
\(164\) | −174.070 | − | 126.469i | −0.0828818 | − | 0.0602171i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 346.668 | − | 251.869i | 0.162088 | − | 0.117764i | ||||
\(167\) | −49.1296 | + | 151.205i | −0.0227650 | + | 0.0700636i | −0.961794 | − | 0.273775i | \(-0.911727\pi\) |
0.939029 | + | 0.343839i | \(0.111727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1586.44 | − | 4882.55i | 0.722092 | − | 2.22237i | ||||
\(170\) | −22.8455 | − | 79.9092i | −0.0103069 | − | 0.0360515i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 296.709 | + | 913.176i | 0.131534 | + | 0.404820i | ||||
\(173\) | −2663.82 | − | 1935.38i | −1.17067 | − | 0.850545i | −0.179585 | − | 0.983743i | \(-0.557475\pi\) |
−0.991089 | + | 0.133198i | \(0.957475\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1167.64 | + | 982.903i | 0.504373 | + | 0.424574i | ||||
\(176\) | 59.9297 | 0.0256669 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −552.583 | − | 1700.67i | −0.232684 | − | 0.716129i | ||||
\(179\) | −871.102 | − | 2680.98i | −0.363739 | − | 1.11947i | −0.950767 | − | 0.309906i | \(-0.899702\pi\) |
0.587028 | − | 0.809566i | \(-0.300298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 129.046 | − | 397.161i | 0.0529938 | − | 0.163098i | −0.921057 | − | 0.389428i | \(-0.872673\pi\) |
0.974051 | + | 0.226330i | \(0.0726727\pi\) | |||||||
\(182\) | 1400.63 | 0.570447 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1591.29 | + | 1156.14i | −0.637563 | + | 0.463217i | ||||
\(185\) | −1053.13 | − | 3683.63i | −0.418526 | − | 1.46392i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.1426 | + | 8.09555i | −0.00435736 | + | 0.00316580i | ||||
\(188\) | −1699.43 | + | 1234.71i | −0.659277 | + | 0.478992i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 99.3841 | + | 347.626i | 0.0379478 | + | 0.132734i | ||||
\(191\) | 421.982 | − | 306.588i | 0.159861 | − | 0.116146i | −0.504979 | − | 0.863132i | \(-0.668500\pi\) |
0.664840 | + | 0.746986i | \(0.268500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4528.65 | −1.68901 | −0.844506 | − | 0.535547i | \(-0.820106\pi\) | ||||
−0.844506 | + | 0.535547i | \(0.820106\pi\) | |||||||
\(194\) | −165.312 | + | 508.779i | −0.0611791 | + | 0.188290i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 371.822 | + | 1144.35i | 0.135504 | + | 0.417037i | ||||
\(197\) | 859.280 | + | 2644.59i | 0.310767 | + | 0.956444i | 0.977462 | + | 0.211112i | \(0.0677086\pi\) |
−0.666694 | + | 0.745331i | \(0.732291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4988.03 | 1.77685 | 0.888423 | − | 0.459026i | \(-0.151801\pi\) | ||||
0.888423 | + | 0.459026i | \(0.151801\pi\) | |||||||
\(200\) | −2019.42 | + | 1257.46i | −0.713972 | + | 0.444578i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 142.432 | + | 103.483i | 0.0496112 | + | 0.0360446i | ||||
\(203\) | −431.060 | − | 1326.67i | −0.149037 | − | 0.458688i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −106.567 | − | 372.749i | −0.0363070 | − | 0.126995i | ||||
\(206\) | −7.80032 | + | 24.0069i | −0.00263822 | + | 0.00811961i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 638.776 | − | 1965.95i | 0.212938 | − | 0.655356i | ||||
\(209\) | 48.4731 | − | 35.2178i | 0.0160428 | − | 0.0116558i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3035.52 | − | 2205.44i | −0.990398 | − | 0.719566i | −0.0303898 | − | 0.999538i | \(-0.509675\pi\) |
−0.960008 | + | 0.279972i | \(0.909675\pi\) | |||||||
\(212\) | −3241.08 | + | 2354.79i | −1.04999 | + | 0.762865i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1985.78 | + | 1442.76i | 0.634324 | + | 0.460863i | ||||
\(215\) | −592.991 | + | 1625.25i | −0.188101 | + | 0.515539i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −580.575 | + | 1786.83i | −0.181622 | + | 0.558975i | ||||
\(218\) | 1792.13 | 0.556780 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 135.618 | + | 106.128i | 0.0415607 | + | 0.0325235i | ||||
\(221\) | 146.803 | + | 451.812i | 0.0446833 | + | 0.137521i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1324.82 | − | 962.540i | −0.397833 | − | 0.289042i | 0.370825 | − | 0.928703i | \(-0.379075\pi\) |
−0.768658 | + | 0.639660i | \(0.779075\pi\) | |||||||
\(224\) | 2253.94 | 0.672312 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 48.5319 | 0.0142845 | ||||||||
\(227\) | −3068.69 | − | 2229.54i | −0.897252 | − | 0.651892i | 0.0405064 | − | 0.999179i | \(-0.487103\pi\) |
−0.937759 | + | 0.347287i | \(0.887103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.8795 | + | 85.8041i | 0.00804509 | + | 0.0247603i | 0.954998 | − | 0.296611i | \(-0.0958564\pi\) |
−0.946953 | + | 0.321371i | \(0.895856\pi\) | |||||||
\(230\) | −1547.13 | − | 55.2465i | −0.443543 | − | 0.0158385i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2174.23 | 0.615280 | ||||||||
\(233\) | −1118.15 | + | 3441.31i | −0.314388 | + | 0.967587i | 0.661617 | + | 0.749842i | \(0.269870\pi\) |
−0.976006 | + | 0.217746i | \(0.930130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3782.51 | − | 135.070i | −1.04997 | − | 0.0374935i | ||||
\(236\) | −3327.52 | − | 2417.59i | −0.917810 | − | 0.666828i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −73.4310 | + | 53.3507i | −0.0199993 | + | 0.0145303i | ||||
\(239\) | −1189.87 | − | 864.489i | −0.322034 | − | 0.233971i | 0.415009 | − | 0.909817i | \(-0.363778\pi\) |
−0.737043 | + | 0.675846i | \(0.763778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3192.76 | − | 2319.68i | 0.853377 | − | 0.620014i | −0.0726983 | − | 0.997354i | \(-0.523161\pi\) |
0.926075 | + | 0.377340i | \(0.123161\pi\) | |||||||
\(242\) | 548.494 | − | 1688.09i | 0.145696 | − | 0.448408i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 685.840 | − | 2110.80i | 0.179944 | − | 0.553811i | ||||
\(245\) | −743.109 | + | 2036.69i | −0.193778 | + | 0.531098i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −638.630 | − | 1965.50i | −0.164514 | − | 0.506323i | ||||
\(248\) | −2369.10 | − | 1721.25i | −0.606605 | − | 0.440724i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1861.65 | − | 200.113i | −0.470963 | − | 0.0506251i | ||||
\(251\) | −3410.52 | −0.857649 | −0.428825 | − | 0.903388i | \(-0.641072\pi\) | ||||
−0.428825 | + | 0.903388i | \(0.641072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 79.2789 | + | 243.995i | 0.0197005 | + | 0.0606318i | ||||
\(254\) | 578.623 | + | 1780.82i | 0.142937 | + | 0.439915i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −715.268 | + | 2201.37i | −0.174626 | + | 0.537443i | ||||
\(257\) | 6919.87 | 1.67957 | 0.839785 | − | 0.542918i | \(-0.182681\pi\) | ||||
0.839785 | + | 0.542918i | \(0.182681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3385.00 | + | 2459.35i | −0.812099 | + | 0.590024i | ||||
\(260\) | 4926.98 | − | 3317.65i | 1.17522 | − | 0.791353i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3076.13 | − | 2234.94i | 0.725358 | − | 0.527003i | ||||
\(263\) | 3081.19 | − | 2238.62i | 0.722413 | − | 0.524863i | −0.164742 | − | 0.986337i | \(-0.552679\pi\) |
0.887154 | + | 0.461473i | \(0.152679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7213.83 | − | 257.598i | −1.67223 | − | 0.0597138i | ||||
\(266\) | 319.444 | − | 232.090i | 0.0736330 | − | 0.0534975i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3297.22 | 0.751529 | ||||||||
\(269\) | −799.222 | + | 2459.75i | −0.181150 | + | 0.557523i | −0.999861 | − | 0.0166834i | \(-0.994689\pi\) |
0.818711 | + | 0.574206i | \(0.194689\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 329.230 | + | 1013.27i | 0.0737981 | + | 0.227127i | 0.981151 | − | 0.193242i | \(-0.0619004\pi\) |
−0.907353 | + | 0.420370i | \(0.861900\pi\) | |||||||
\(272\) | 41.3950 | + | 127.401i | 0.00922772 | + | 0.0284000i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1085.60 | −0.239356 | ||||||||
\(275\) | 74.5909 | + | 301.187i | 0.0163564 | + | 0.0660446i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1996.88 | + | 1450.82i | 0.433144 | + | 0.314698i | 0.782905 | − | 0.622141i | \(-0.213737\pi\) |
−0.349761 | + | 0.936839i | \(0.613737\pi\) | |||||||
\(278\) | 1300.17 | + | 4001.51i | 0.280500 | + | 0.863290i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2046.01 | + | 1601.12i | 0.436688 | + | 0.341732i | ||||
\(281\) | −960.683 | + | 2956.68i | −0.203948 | + | 0.627689i | 0.795806 | + | 0.605551i | \(0.207047\pi\) |
−0.999755 | + | 0.0221378i | \(0.992953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1994.41 | + | 6138.15i | −0.418923 | + | 1.28931i | 0.489772 | + | 0.871851i | \(0.337080\pi\) |
−0.908695 | + | 0.417461i | \(0.862920\pi\) | |||||||
\(284\) | 3186.69 | − | 2315.27i | 0.665829 | − | 0.483753i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 230.363 | + | 167.369i | 0.0476282 | + | 0.0346039i | ||||
\(287\) | −342.530 | + | 248.863i | −0.0704493 | + | 0.0511844i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3949.79 | + | 2869.69i | 0.803948 | + | 0.584102i | ||||
\(290\) | 1347.67 | + | 1054.62i | 0.272888 | + | 0.213550i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1846.32 | + | 5682.39i | −0.370027 | + | 1.13883i | ||||
\(293\) | −835.063 | −0.166501 | −0.0832507 | − | 0.996529i | \(-0.526530\pi\) | ||||
−0.0832507 | + | 0.996529i | \(0.526530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2037.12 | − | 7125.46i | −0.402054 | − | 1.40631i | ||||
\(296\) | −2015.27 | − | 6202.36i | −0.395727 | − | 1.21792i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1092.84 | + | 793.996i | 0.212438 | + | 0.154346i | ||||
\(299\) | 8849.10 | 1.71156 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1889.39 | 0.361803 | ||||||||
\(302\) | −2344.42 | − | 1703.32i | −0.446709 | − | 0.324553i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −180.079 | − | 554.227i | −0.0339745 | − | 0.104563i | ||||
\(305\) | 3317.07 | − | 2233.60i | 0.622738 | − | 0.419329i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2681.88 | 0.498577 | 0.249289 | − | 0.968429i | \(-0.419803\pi\) | ||||
0.249289 | + | 0.968429i | \(0.419803\pi\) | |||||||
\(308\) | 58.1164 | − | 178.864i | 0.0107516 | − | 0.0330900i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −633.552 | − | 2216.04i | −0.116075 | − | 0.406009i | ||||
\(311\) | 6580.24 | + | 4780.83i | 1.19978 | + | 0.871691i | 0.994263 | − | 0.106963i | \(-0.0341126\pi\) |
0.205516 | + | 0.978654i | \(0.434113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6248.59 | + | 4539.87i | −1.12841 | + | 0.819835i | −0.985462 | − | 0.169895i | \(-0.945657\pi\) |
−0.142944 | + | 0.989731i | \(0.545657\pi\) | |||||||
\(314\) | −2838.32 | − | 2062.16i | −0.510113 | − | 0.370619i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2855.09 | − | 2074.34i | 0.508263 | − | 0.369275i | ||||
\(317\) | −995.186 | + | 3062.87i | −0.176326 | + | 0.542674i | −0.999692 | − | 0.0248365i | \(-0.992093\pi\) |
0.823366 | + | 0.567511i | \(0.192093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 87.6335 | − | 269.708i | 0.0153810 | − | 0.0473378i | ||||
\(320\) | −502.377 | + | 338.282i | −0.0877616 | + | 0.0590955i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 522.458 | + | 1607.96i | 0.0904206 | + | 0.278286i | ||||
\(323\) | 108.349 | + | 78.7200i | 0.0186647 | + | 0.0135607i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10675.3 | + | 763.379i | 1.82202 | + | 0.130291i | ||||
\(326\) | 433.083 | 0.0735774 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −203.927 | − | 627.622i | −0.0343292 | − | 0.105654i | ||||
\(329\) | 1277.33 | + | 3931.22i | 0.214047 | + | 0.658770i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1297.25 | − | 3992.52i | 0.215417 | − | 0.662987i | −0.783706 | − | 0.621132i | \(-0.786673\pi\) |
0.999124 | − | 0.0418550i | \(-0.0133268\pi\) | |||||||
\(332\) | −1984.61 | −0.328071 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −172.324 | + | 125.201i | −0.0282309 | + | 0.0205110i | ||||
\(335\) | 4678.67 | + | 3661.31i | 0.763054 | + | 0.597131i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1039.69 | + | 755.378i | −0.168058 | + | 0.122101i | −0.668635 | − | 0.743591i | \(-0.733121\pi\) |
0.500577 | + | 0.865692i | \(0.333121\pi\) | |||||||
\(338\) | 5564.48 | − | 4042.83i | 0.895467 | − | 0.650595i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −131.937 | + | 361.607i | −0.0210449 | + | 0.0576791i | ||||
\(341\) | −309.006 | + | 224.506i | −0.0490721 | + | 0.0356530i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6555.77 | 1.03201 | ||||||||
\(344\) | −910.028 | + | 2800.78i | −0.142632 | + | 0.438976i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1363.19 | − | 4195.47i | −0.211808 | − | 0.651878i | ||||
\(347\) | 96.1696 | + | 295.980i | 0.0148780 | + | 0.0457897i | 0.958220 | − | 0.286033i | \(-0.0923366\pi\) |
−0.943342 | + | 0.331822i | \(0.892337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3853.76 | −0.591081 | −0.295540 | − | 0.955330i | \(-0.595500\pi\) | ||||
−0.295540 | + | 0.955330i | \(0.595500\pi\) | |||||||
\(350\) | 491.564 | + | 1984.86i | 0.0750719 | + | 0.303129i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 370.709 | + | 269.336i | 0.0561331 | + | 0.0407831i | ||||
\(353\) | −371.671 | − | 1143.89i | −0.0560398 | − | 0.172473i | 0.919119 | − | 0.393980i | \(-0.128902\pi\) |
−0.975159 | + | 0.221508i | \(0.928902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7092.77 | + | 253.276i | 1.06041 | + | 0.0378661i | ||||
\(356\) | −2559.27 | + | 7876.61i | −0.381014 | + | 1.17264i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1167.07 | − | 3591.86i | 0.172295 | − | 0.530268i | ||||
\(359\) | 8830.61 | − | 6415.81i | 1.29822 | − | 0.943213i | 0.298285 | − | 0.954477i | \(-0.403585\pi\) |
0.999937 | + | 0.0112636i | \(0.00358538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5077.70 | + | 3689.17i | 0.740298 | + | 0.537858i | ||||
\(362\) | 452.632 | − | 328.856i | 0.0657177 | − | 0.0477467i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5248.05 | − | 3812.93i | −0.755694 | − | 0.549044i | ||||
\(365\) | −8929.76 | + | 6012.98i | −1.28056 | + | 0.862284i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −44.8963 | + | 138.177i | −0.00638575 | + | 0.0196533i | −0.954199 | − | 0.299174i | \(-0.903289\pi\) |
0.947813 | + | 0.318827i | \(0.103289\pi\) | |||||||
\(368\) | 2495.24 | 0.353461 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1759.35 | − | 4821.97i | 0.247201 | − | 0.677520i | ||||
\(371\) | 2436.07 | + | 7497.45i | 0.340901 | + | 1.04919i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2847.26 | + | 2068.66i | 0.395243 | + | 0.287161i | 0.767601 | − | 0.640929i | \(-0.221451\pi\) |
−0.372358 | + | 0.928089i | \(0.621451\pi\) | |||||||
\(374\) | −18.4525 | −0.00255122 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6442.75 | −0.883669 | ||||||||
\(377\) | −7913.51 | − | 5749.50i | −1.08108 | − | 0.785450i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −124.955 | − | 384.571i | −0.0169354 | − | 0.0521217i | 0.942232 | − | 0.334962i | \(-0.108723\pi\) |
−0.959167 | + | 0.282840i | \(0.908723\pi\) | |||||||
\(380\) | 573.959 | − | 1573.08i | 0.0774828 | − | 0.212362i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 698.816 | 0.0935982 | ||||||||
\(383\) | 1292.81 | − | 3978.86i | 0.172479 | − | 0.530836i | −0.827030 | − | 0.562158i | \(-0.809971\pi\) |
0.999509 | + | 0.0313212i | \(0.00997146\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 281.081 | − | 189.270i | 0.0372083 | − | 0.0250547i | ||||
\(386\) | −4908.55 | − | 3566.27i | −0.647250 | − | 0.470255i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2004.47 | − | 1456.33i | 0.262272 | − | 0.190551i | ||||
\(389\) | −8299.40 | − | 6029.87i | −1.08174 | − | 0.785929i | −0.103754 | − | 0.994603i | \(-0.533085\pi\) |
−0.977985 | + | 0.208674i | \(0.933085\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −463.934 | + | 337.067i | −0.0600054 | + | 0.0435965i | ||||
\(392\) | −1140.41 | + | 3509.81i | −0.146937 | + | 0.452225i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1151.23 | + | 3543.12i | −0.147203 | + | 0.453045i | ||||
\(395\) | 6354.70 | + | 226.920i | 0.809468 | + | 0.0289053i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3149.37 | − | 9692.75i | −0.398142 | − | 1.22535i | −0.926488 | − | 0.376325i | \(-0.877188\pi\) |
0.528346 | − | 0.849029i | \(-0.322812\pi\) | |||||||
\(398\) | 5406.47 | + | 3928.03i | 0.680909 | + | 0.494710i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3010.18 | + | 215.255i | 0.376273 | + | 0.0269069i | ||||
\(401\) | −5912.32 | −0.736277 | −0.368139 | − | 0.929771i | \(-0.620005\pi\) | ||||
−0.368139 | + | 0.929771i | \(0.620005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4071.13 | + | 12529.6i | 0.503219 | + | 1.54875i | ||||
\(404\) | −251.970 | − | 775.485i | −0.0310297 | − | 0.0954996i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 577.516 | − | 1777.41i | 0.0705952 | − | 0.217270i | ||||
\(407\) | −850.616 | −0.103596 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4576.30 | + | 3324.88i | −0.553260 | + | 0.401967i | −0.828986 | − | 0.559269i | \(-0.811082\pi\) |
0.275726 | + | 0.961236i | \(0.411082\pi\) | |||||||
\(410\) | 178.030 | − | 487.939i | 0.0214446 | − | 0.0587746i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 94.5814 | − | 68.7174i | 0.0113099 | − | 0.00821714i | ||||
\(413\) | −6547.80 | + | 4757.25i | −0.780136 | + | 0.566802i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2816.11 | − | 2203.76i | −0.333102 | − | 0.260670i | ||||
\(416\) | 12786.7 | − | 9290.05i | 1.50701 | − | 1.09491i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 80.2731 | 0.00939303 | ||||||||
\(419\) | −4234.75 | + | 13033.2i | −0.493749 | + | 1.51960i | 0.325148 | + | 0.945663i | \(0.394586\pi\) |
−0.818897 | + | 0.573940i | \(0.805414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2847.48 | + | 8763.66i | 0.329639 | + | 1.01452i | 0.969303 | + | 0.245869i | \(0.0790734\pi\) |
−0.639664 | + | 0.768654i | \(0.720927\pi\) | |||||||
\(422\) | −1553.41 | − | 4780.89i | −0.179191 | − | 0.551493i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12287.3 | −1.40737 | ||||||||
\(425\) | −588.752 | + | 366.606i | −0.0671969 | + | 0.0418423i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3533.23 | − | 2567.04i | −0.400434 | − | 0.290932i | ||||
\(428\) | −3512.97 | − | 10811.8i | −0.396743 | − | 1.22105i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1922.60 | + | 1294.61i | −0.215619 | + | 0.145190i | ||||
\(431\) | −2337.94 | + | 7195.44i | −0.261287 | + | 0.804158i | 0.731239 | + | 0.682121i | \(0.238942\pi\) |
−0.992526 | + | 0.122036i | \(0.961058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1250.50 | − | 3848.63i | 0.138788 | − | 0.427144i | −0.857372 | − | 0.514697i | \(-0.827905\pi\) |
0.996160 | + | 0.0875525i | \(0.0279046\pi\) | |||||||
\(434\) | −2036.39 | + | 1479.52i | −0.225230 | + | 0.163639i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6714.97 | − | 4878.71i | −0.737589 | − | 0.535890i | ||||
\(437\) | 2018.23 | − | 1466.33i | 0.220927 | − | 0.160513i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3157.92 | − | 2294.36i | −0.343324 | − | 0.249440i | 0.402739 | − | 0.915315i | \(-0.368058\pi\) |
−0.746063 | + | 0.665875i | \(0.768058\pi\) | |||||||
\(440\) | 145.185 | + | 507.828i | 0.0157305 | + | 0.0550221i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −196.680 | + | 605.320i | −0.0211654 | + | 0.0651405i | ||||
\(443\) | −2288.91 | −0.245484 | −0.122742 | − | 0.992439i | \(-0.539169\pi\) | ||||
−0.122742 | + | 0.992439i | \(0.539169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12377.9 | + | 8334.84i | −1.31858 | + | 0.887887i | ||||
\(446\) | −677.968 | − | 2086.57i | −0.0719792 | − | 0.221529i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 535.115 | + | 388.784i | 0.0564326 | + | 0.0410007i | ||||
\(449\) | −10025.3 | −1.05373 | −0.526863 | − | 0.849950i | \(-0.676632\pi\) | ||||
−0.526863 | + | 0.849950i | \(0.676632\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −86.0745 | −0.00898690 | ||||||||
\(452\) | −181.846 | − | 132.119i | −0.0189232 | − | 0.0137485i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1570.38 | − | 4833.13i | −0.162338 | − | 0.499626i | ||||
\(455\) | −3212.88 | − | 11238.0i | −0.331038 | − | 1.15791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3293.06 | −0.337075 | −0.168537 | − | 0.985695i | \(-0.553904\pi\) | ||||
−0.168537 | + | 0.985695i | \(0.553904\pi\) | |||||||
\(458\) | −37.3518 | + | 114.957i | −0.00381077 | + | 0.0117283i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5646.61 | + | 4418.77i | 0.572336 | + | 0.447884i | ||||
\(461\) | −672.561 | − | 488.644i | −0.0679486 | − | 0.0493676i | 0.553292 | − | 0.832987i | \(-0.313371\pi\) |
−0.621241 | + | 0.783620i | \(0.713371\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7302.69 | − | 5305.71i | 0.733012 | − | 0.532565i | −0.157503 | − | 0.987519i | \(-0.550344\pi\) |
0.890515 | + | 0.454954i | \(0.150344\pi\) | |||||||
\(464\) | −2231.43 | − | 1621.23i | −0.223258 | − | 0.162206i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3921.95 | + | 2849.46i | −0.389873 | + | 0.283259i | ||||
\(467\) | −406.581 | + | 1251.33i | −0.0402876 | + | 0.123992i | −0.969177 | − | 0.246364i | \(-0.920764\pi\) |
0.928890 | + | 0.370356i | \(0.120764\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2004.95 | − | 6170.62i | 0.197399 | − | 0.607532i | ||||
\(470\) | −3993.45 | − | 3125.09i | −0.391924 | − | 0.306702i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3898.25 | − | 11997.6i | −0.380152 | − | 1.16999i | ||||
\(473\) | 310.751 | + | 225.774i | 0.0302080 | + | 0.0219474i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2561.23 | − | 1594.83i | 0.247404 | − | 0.154054i | ||||
\(476\) | 420.378 | 0.0404790 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −608.906 | − | 1874.02i | −0.0582651 | − | 0.179321i | ||||
\(479\) | −2883.48 | − | 8874.45i | −0.275052 | − | 0.846522i | −0.989206 | − | 0.146533i | \(-0.953188\pi\) |
0.714154 | − | 0.699989i | \(-0.246812\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9066.51 | + | 27903.8i | −0.859454 | + | 2.64513i | ||||
\(482\) | 5287.32 | 0.499649 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6650.67 | + | 4831.99i | −0.624593 | + | 0.453794i | ||||
\(485\) | 4461.43 | + | 159.313i | 0.417698 | + | 0.0149155i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1662.91 | − | 1208.18i | 0.154731 | − | 0.112418i | −0.507726 | − | 0.861519i | \(-0.669514\pi\) |
0.662457 | + | 0.749100i | \(0.269514\pi\) | |||||||
\(488\) | 5507.09 | − | 4001.14i | 0.510849 | − | 0.371154i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2409.32 | + | 1622.35i | −0.222126 | + | 0.149572i | ||||
\(491\) | 2888.29 | − | 2098.47i | 0.265472 | − | 0.192877i | −0.447084 | − | 0.894492i | \(-0.647537\pi\) |
0.712556 | + | 0.701615i | \(0.247537\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 633.886 | 0.0579083 | ||||||||
\(494\) | 855.611 | − | 2633.30i | 0.0779266 | − | 0.239833i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1147.97 | + | 3533.07i | 0.103922 | + | 0.319838i | ||||
\(497\) | −2395.19 | − | 7371.63i | −0.216175 | − | 0.665317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −316.957 | −0.0284347 | −0.0142174 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142174 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(500\) | 6430.69 | + | 5817.78i | 0.575179 | + | 0.520358i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3696.62 | − | 2685.75i | −0.328662 | − | 0.238787i | ||||
\(503\) | 3270.63 | + | 10066.0i | 0.289921 | + | 0.892285i | 0.984880 | + | 0.173236i | \(0.0554223\pi\) |
−0.694959 | + | 0.719049i | \(0.744578\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 503.578 | − | 1380.19i | 0.0443741 | − | 0.121619i | ||||
\(506\) | −106.215 | + | 326.895i | −0.00933165 | + | 0.0287199i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2679.87 | − | 8247.79i | 0.234055 | − | 0.720348i | ||||
\(509\) | −11989.3 | + | 8710.74i | −1.04404 | + | 0.758540i | −0.971070 | − | 0.238794i | \(-0.923248\pi\) |
−0.0729705 | + | 0.997334i | \(0.523248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9511.68 | + | 6910.64i | 0.823428 | + | 0.598256i | ||||
\(512\) | 6579.32 | − | 4780.15i | 0.567905 | − | 0.412607i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7500.37 | + | 5449.34i | 0.643632 | + | 0.467626i | ||||
\(515\) | 210.514 | + | 7.51724i | 0.0180124 | + | 0.000643202i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −259.679 | + | 799.209i | −0.0220903 | + | 0.0679868i | ||||
\(518\) | −5605.67 | −0.475481 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18206.4 | + | 650.131i | 1.53539 | + | 0.0548272i | ||||
\(521\) | −1266.26 | − | 3897.16i | −0.106480 | − | 0.327711i | 0.883595 | − | 0.468252i | \(-0.155116\pi\) |
−0.990075 | + | 0.140541i | \(0.955116\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4884.26 | − | 3548.62i | −0.408363 | − | 0.296693i | 0.364576 | − | 0.931174i | \(-0.381214\pi\) |
−0.772939 | + | 0.634481i | \(0.781214\pi\) | |||||||
\(524\) | −17610.2 | −1.46814 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5102.56 | 0.422970 | ||||||||
\(527\) | −690.700 | − | 501.823i | −0.0570918 | − | 0.0414796i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −458.945 | − | 1412.49i | −0.0377204 | − | 0.116092i | ||||
\(530\) | −7616.13 | − | 5960.03i | −0.624195 | − | 0.488467i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1828.75 | −0.149035 | ||||||||
\(533\) | −917.446 | + | 2823.61i | −0.0745573 | + | 0.229464i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7020.89 | − | 19242.6i | 0.567364 | − | 1.55501i | ||||
\(536\) | 8181.44 | + | 5944.17i | 0.659300 | + | 0.479009i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2803.30 | + | 2036.72i | −0.224645 | + | 0.163214i | ||||
\(539\) | 389.419 | + | 282.930i | 0.0311196 | + | 0.0226097i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3971.18 | + | 2885.23i | −0.315590 | + | 0.229290i | −0.734291 | − | 0.678834i | \(-0.762485\pi\) |
0.418701 | + | 0.908124i | \(0.362485\pi\) | |||||||
\(542\) | −441.089 | + | 1357.53i | −0.0349564 | + | 0.107585i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −316.505 | + | 974.104i | −0.0249450 | + | 0.0767727i | ||||
\(545\) | −4110.94 | − | 14379.3i | −0.323107 | − | 1.13016i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5430.58 | − | 16713.6i | −0.424488 | − | 1.30644i | −0.903484 | − | 0.428623i | \(-0.858999\pi\) |
0.478995 | − | 0.877817i | \(-0.341001\pi\) | |||||||
\(548\) | 4067.66 | + | 2955.33i | 0.317084 | + | 0.230375i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −156.334 | + | 385.193i | −0.0121202 | + | 0.0298630i | ||||
\(551\) | −2757.57 | −0.213206 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2145.95 | − | 6604.54i | −0.165018 | − | 0.507873i | ||||
\(554\) | 1021.89 | + | 3145.05i | 0.0783680 | + | 0.241192i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6021.68 | − | 18532.8i | 0.459310 | − | 1.41361i | ||||
\(557\) | 23625.5 | 1.79721 | 0.898603 | − | 0.438764i | \(-0.144583\pi\) | ||||
0.898603 | + | 0.438764i | \(0.144583\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10718.6 | − | 7787.50i | 0.810997 | − | 0.589224i | ||||
\(560\) | −905.959 | − | 3168.87i | −0.0683638 | − | 0.239123i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3369.63 | + | 2448.18i | −0.252917 | + | 0.183755i | ||||
\(563\) | −18736.1 | + | 13612.6i | −1.40254 | + | 1.01901i | −0.408188 | + | 0.912898i | \(0.633839\pi\) |
−0.994355 | + | 0.106109i | \(0.966161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −111.327 | − | 389.399i | −0.00828947 | − | 0.0289950i | ||||
\(566\) | −6995.45 | + | 5082.49i | −0.519507 | + | 0.377444i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12081.1 | 0.892452 | ||||||||
\(569\) | 2625.00 | − | 8078.93i | 0.193402 | − | 0.595231i | −0.806589 | − | 0.591112i | \(-0.798689\pi\) |
0.999992 | − | 0.00411844i | \(-0.00131094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4777.92 | + | 14704.9i | 0.350174 | + | 1.07773i | 0.958755 | + | 0.284234i | \(0.0917393\pi\) |
−0.608580 | + | 0.793492i | \(0.708261\pi\) | |||||||
\(572\) | −407.526 | − | 1254.24i | −0.0297894 | − | 0.0916823i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −567.242 | −0.0412478 | ||||||||
\(575\) | 3105.68 | + | 12540.3i | 0.225245 | + | 0.909505i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21389.0 | − | 15540.0i | −1.54322 | − | 1.12121i | −0.948278 | − | 0.317440i | \(-0.897177\pi\) |
−0.594937 | − | 0.803772i | \(-0.702823\pi\) | |||||||
\(578\) | 2021.28 | + | 6220.85i | 0.145457 | + | 0.447670i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2178.61 | − | 7620.35i | −0.155969 | − | 0.545548i | ||||
\(581\) | −1206.79 | + | 3714.11i | −0.0861722 | + | 0.265211i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −495.248 | + | 1524.22i | −0.0351819 | + | 0.108279i | ||||
\(584\) | −14825.4 | + | 10771.3i | −1.05048 | + | 0.763219i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −905.115 | − | 657.605i | −0.0638054 | − | 0.0463573i | ||||
\(587\) | −4812.71 | + | 3496.64i | −0.338402 | + | 0.245863i | −0.743987 | − | 0.668194i | \(-0.767068\pi\) |
0.405585 | + | 0.914057i | \(0.367068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3004.73 | + | 2183.06i | 0.210200 | + | 0.152719i | ||||
\(590\) | 3403.22 | − | 9327.41i | 0.237472 | − | 0.650853i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2556.55 | + | 7868.24i | −0.177489 | + | 0.546255i | ||||
\(593\) | 11755.3 | 0.814054 | 0.407027 | − | 0.913416i | \(-0.366566\pi\) | ||||
0.407027 | + | 0.913416i | \(0.366566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 596.506 | + | 466.798i | 0.0410998 | + | 0.0321628i | ||||
\(596\) | −1933.30 | − | 5950.10i | −0.132871 | − | 0.408936i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9591.43 | + | 6968.58i | 0.655891 | + | 0.476533i | ||||
\(599\) | 10184.4 | 0.694698 | 0.347349 | − | 0.937736i | \(-0.387082\pi\) | ||||
0.347349 | + | 0.937736i | \(0.387082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16384.2 | −1.11202 | −0.556012 | − | 0.831174i | \(-0.687669\pi\) | ||||
−0.556012 | + | 0.831174i | \(0.687669\pi\) | |||||||
\(602\) | 2047.89 | + | 1487.88i | 0.138648 | + | 0.100733i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4147.42 | + | 12764.4i | 0.279398 | + | 0.859897i | ||||
\(605\) | −14802.7 | − | 528.589i | −0.994737 | − | 0.0355210i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20161.1 | 1.34813 | 0.674066 | − | 0.738672i | \(-0.264547\pi\) | ||||
0.674066 | + | 0.738672i | \(0.264547\pi\) | |||||||
\(608\) | 1376.88 | − | 4237.61i | 0.0918420 | − | 0.282661i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5354.27 | + | 191.195i | 0.355390 | + | 0.0126906i | ||||
\(611\) | 23449.6 | + | 17037.1i | 1.55265 | + | 1.12807i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2555.01 | − | 1856.32i | 0.168346 | − | 0.122310i | −0.500422 | − | 0.865781i | \(-0.666822\pi\) |
0.668768 | + | 0.743471i | \(0.266822\pi\) | |||||||
\(614\) | 2906.86 | + | 2111.96i | 0.191061 | + | 0.138814i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 466.658 | − | 339.047i | 0.0305230 | − | 0.0221763i | ||||
\(617\) | −2032.29 | + | 6254.74i | −0.132604 | + | 0.408114i | −0.995210 | − | 0.0977634i | \(-0.968831\pi\) |
0.862605 | + | 0.505877i | \(0.168831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6522.15 | + | 20073.1i | −0.423502 | + | 1.30340i | 0.480920 | + | 0.876764i | \(0.340303\pi\) |
−0.904422 | + | 0.426639i | \(0.859697\pi\) | |||||||
\(620\) | −3658.86 | + | 10028.1i | −0.237006 | + | 0.649576i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3367.39 | + | 10363.8i | 0.217074 | + | 0.668085i | ||||
\(623\) | 13184.5 | + | 9579.13i | 0.847877 | + | 0.616019i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2664.79 | + | 15396.1i | 0.170546 | + | 0.985350i | ||||
\(626\) | −10347.9 | −0.660678 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5021.16 | + | 15453.5i | 0.319054 | + | 0.981947i | ||||
\(629\) | −587.542 | − | 1808.27i | −0.0372446 | − | 0.114627i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8297.74 | + | 25537.8i | −0.523499 | + | 1.61116i | 0.243765 | + | 0.969834i | \(0.421617\pi\) |
−0.767265 | + | 0.641331i | \(0.778383\pi\) | |||||||
\(632\) | 10824.0 | 0.681257 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3490.65 | + | 2536.11i | −0.218662 | + | 0.158867i | ||||
\(635\) | 12961.2 | − | 8727.62i | 0.810001 | − | 0.545425i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13432.0 | − | 9758.94i | 0.835473 | − | 0.607007i | ||||
\(638\) | 307.378 | − | 223.323i | 0.0190740 | − | 0.0138581i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15689.4 | + | 560.251i | 0.969027 | + | 0.0346029i | ||||
\(641\) | 20566.4 | − | 14942.4i | 1.26728 | − | 0.920732i | 0.268188 | − | 0.963367i | \(-0.413575\pi\) |
0.999091 | + | 0.0426350i | \(0.0135753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10481.7 | −0.642856 | −0.321428 | − | 0.946934i | \(-0.604163\pi\) | ||||
−0.321428 | + | 0.946934i | \(0.604163\pi\) | |||||||
\(644\) | 2419.74 | − | 7447.21i | 0.148061 | − | 0.455685i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 55.4467 | + | 170.647i | 0.00337697 | + | 0.0103932i | ||||
\(647\) | −5847.14 | − | 17995.7i | −0.355294 | − | 1.09348i | −0.955839 | − | 0.293891i | \(-0.905050\pi\) |
0.600545 | − | 0.799591i | \(-0.294950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1645.40 | −0.0995184 | ||||||||
\(650\) | 10969.6 | + | 9234.09i | 0.661946 | + | 0.557217i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1622.73 | − | 1178.98i | −0.0974710 | − | 0.0708168i | ||||
\(653\) | 3911.37 | + | 12037.9i | 0.234401 | + | 0.721411i | 0.997200 | + | 0.0747761i | \(0.0238242\pi\) |
−0.762800 | + | 0.646635i | \(0.776176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24988.5 | − | 19554.8i | −1.49066 | − | 1.16652i | ||||
\(656\) | −258.699 | + | 796.193i | −0.0153971 | + | 0.0473874i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1711.32 | + | 5266.89i | −0.101389 | + | 0.312044i | ||||
\(659\) | 9820.27 | − | 7134.84i | 0.580491 | − | 0.421751i | −0.258410 | − | 0.966035i | \(-0.583199\pi\) |
0.838901 | + | 0.544284i | \(0.183199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3379.82 | − | 2455.59i | −0.198880 | − | 0.144495i | 0.483888 | − | 0.875130i | \(-0.339224\pi\) |
−0.682768 | + | 0.730635i | \(0.739224\pi\) | |||||||
\(662\) | 4550.14 | − | 3305.87i | 0.267139 | − | 0.194088i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4924.44 | − | 3577.81i | −0.287809 | − | 0.209105i | ||||
\(665\) | −2594.96 | − | 2030.69i | −0.151320 | − | 0.118416i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3648.72 | − | 11229.6i | 0.211813 | − | 0.651892i | ||||
\(668\) | 986.519 | 0.0571401 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2187.91 | + | 7652.87i | 0.126159 | + | 0.441278i | ||||
\(671\) | −274.366 | − | 844.411i | −0.0157851 | − | 0.0485814i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6124.43 | − | 4449.66i | −0.350787 | − | 0.254862i | 0.398412 | − | 0.917206i | \(-0.369561\pi\) |
−0.749199 | + | 0.662345i | \(0.769561\pi\) | |||||||
\(674\) | −1721.76 | −0.0983972 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −31855.6 | −1.81245 | ||||||||
\(677\) | −26966.3 | − | 19592.1i | −1.53087 | − | 1.11224i | −0.955754 | − | 0.294168i | \(-0.904958\pi\) |
−0.575114 | − | 0.818073i | \(-0.695042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1506.60 | − | 4636.84i | −0.0851517 | − | 0.262070i | ||||
\(680\) | −979.275 | + | 659.408i | −0.0552257 | + | 0.0371870i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −511.724 | −0.0287315 | ||||||||
\(683\) | 10789.5 | − | 33206.6i | 0.604463 | − | 1.86035i | 0.104023 | − | 0.994575i | \(-0.466828\pi\) |
0.500440 | − | 0.865771i | \(-0.333172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2490.24 | + | 8710.38i | 0.138901 | + | 0.485849i | ||||
\(686\) | 7105.72 | + | 5162.61i | 0.395478 | + | 0.287331i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3022.39 | − | 2195.90i | 0.167482 | − | 0.121683i | ||||
\(689\) | 44722.0 | + | 32492.5i | 2.47282 | + | 1.79661i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27262.3 | − | 19807.2i | 1.50088 | − | 1.09045i | 0.530846 | − | 0.847468i | \(-0.321874\pi\) |
0.970031 | − | 0.242982i | \(-0.0781257\pi\) | |||||||
\(692\) | −6313.57 | + | 19431.2i | −0.346829 | + | 1.06743i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −128.844 | + | 396.542i | −0.00704735 | + | 0.0216895i | ||||
\(695\) | 29124.0 | − | 19611.0i | 1.58955 | − | 1.07034i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.4539 | − | 182.980i | −0.00323095 | − | 0.00994386i | ||||
\(698\) | −4177.05 | − | 3034.80i | −0.226510 | − | 0.164569i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3561.54 | − | 8775.33i | 0.192305 | − | 0.473823i | ||||
\(701\) | −23077.6 | −1.24341 | −0.621704 | − | 0.783252i | \(-0.713559\pi\) | ||||
−0.621704 | + | 0.783252i | \(0.713559\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2555.96 | + | 7866.45i | 0.137127 | + | 0.422032i | ||||
\(704\) | 41.5532 | + | 127.888i | 0.00222457 | + | 0.00684651i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 497.950 | − | 1532.53i | 0.0265447 | − | 0.0816963i | ||||
\(707\) | −1604.51 | −0.0853518 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15178.3 | − | 11027.7i | 0.803997 | − | 0.584138i | −0.108087 | − | 0.994141i | \(-0.534472\pi\) |
0.912084 | + | 0.410003i | \(0.134472\pi\) | |||||||
\(710\) | 7488.32 | + | 5860.02i | 0.395819 | + | 0.309750i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20550.2 | + | 14930.6i | −1.08167 | + | 0.785880i | ||||
\(713\) | −12865.8 | + | 9347.55i | −0.675776 | + | 0.490980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 814.467 | − | 2232.26i | 0.0426005 | − | 0.116758i | ||||
\(716\) | −14151.1 | + | 10281.4i | −0.738618 | + | 0.536637i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14623.8 | 0.760104 | ||||||||
\(719\) | 4136.61 | − | 12731.2i | 0.214561 | − | 0.660351i | −0.784623 | − | 0.619973i | \(-0.787144\pi\) |
0.999184 | − | 0.0403783i | \(-0.0128563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −71.0894 | − | 218.791i | −0.00367199 | − | 0.0113012i | ||||
\(722\) | 2598.48 | + | 7997.29i | 0.133941 | + | 0.412227i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2591.23 | −0.133014 | ||||||||
\(725\) | 5370.44 | − | 13232.3i | 0.275108 | − | 0.677841i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8138.17 | + | 5912.73i | 0.415169 | + | 0.301638i | 0.775691 | − | 0.631113i | \(-0.217401\pi\) |
−0.360522 | + | 0.932751i | \(0.617401\pi\) | |||||||
\(728\) | −6148.19 | − | 18922.2i | −0.313004 | − | 0.963328i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14414.0 | − | 514.710i | −0.730804 | − | 0.0260963i | ||||
\(731\) | −265.314 | + | 816.554i | −0.0134241 | + | 0.0413151i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −884.238 | + | 2721.40i | −0.0445567 | + | 0.137131i | −0.970860 | − | 0.239647i | \(-0.922968\pi\) |
0.926303 | + | 0.376779i | \(0.122968\pi\) | |||||||
\(734\) | −157.475 | + | 114.413i | −0.00791897 | + | 0.00575347i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15434.9 | + | 11214.1i | 0.773013 | + | 0.561627i | ||||
\(737\) | 1067.12 | − | 775.307i | 0.0533349 | − | 0.0387501i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24379.0 | − | 17712.4i | −1.21353 | − | 0.881680i | −0.217982 | − | 0.975953i | \(-0.569947\pi\) |
−0.995546 | + | 0.0942726i | \(0.969947\pi\) | |||||||
\(740\) | −19719.1 | + | 13278.1i | −0.979577 | + | 0.659611i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3263.75 | + | 10044.8i | −0.161477 | + | 0.496975i | ||||
\(743\) | −1183.79 | −0.0584508 | −0.0292254 | − | 0.999573i | \(-0.509304\pi\) | ||||
−0.0292254 | + | 0.999573i | \(0.509304\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3863.83 | − | 10589.8i | 0.190013 | − | 0.520781i | ||||
\(746\) | 1457.06 | + | 4484.38i | 0.0715106 | + | 0.220087i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 69.1401 | + | 50.2333i | 0.00337970 | + | 0.00245549i | ||||
\(749\) | −22370.0 | −1.09130 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33092.2 | 1.60793 | 0.803964 | − | 0.594679i | \(-0.202721\pi\) | ||||
0.803964 | + | 0.594679i | \(0.202721\pi\) | |||||||
\(752\) | 6612.26 | + | 4804.08i | 0.320644 | + | 0.232961i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4049.68 | − | 12463.6i | −0.195598 | − | 0.601988i | ||||
\(755\) | −8288.88 | + | 22717.8i | −0.399554 | + | 1.09508i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14001.4 | 0.672246 | 0.336123 | − | 0.941818i | \(-0.390884\pi\) | ||||
0.336123 | + | 0.941818i | \(0.390884\pi\) | |||||||
\(758\) | 167.409 | − | 515.233i | 0.00802188 | − | 0.0246888i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4260.10 | − | 2868.60i | 0.203329 | − | 0.136914i | ||||
\(761\) | −13651.0 | − | 9918.02i | −0.650260 | − | 0.472441i | 0.213100 | − | 0.977030i | \(-0.431644\pi\) |
−0.863360 | + | 0.504589i | \(0.831644\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13213.5 | + | 9600.19i | −0.626949 | + | 0.455505i | ||||
\(764\) | −2618.41 | − | 1902.39i | −0.123993 | − | 0.0900864i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4534.58 | − | 3294.56i | 0.213892 | − | 0.155401i | ||||
\(767\) | −17537.9 | + | 53976.0i | −0.825627 | + | 2.54102i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2146.67 | − | 6606.78i | 0.100665 | − | 0.309813i | −0.888024 | − | 0.459797i | \(-0.847922\pi\) |
0.988688 | + | 0.149984i | \(0.0479221\pi\) | |||||||
\(770\) | 453.708 | + | 16.2015i | 0.0212344 | + | 0.000758260i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8683.52 | + | 26725.1i | 0.404827 | + | 1.24593i | ||||
\(773\) | −6808.98 | − | 4947.01i | −0.316820 | − | 0.230183i | 0.417997 | − | 0.908448i | \(-0.362732\pi\) |
−0.734817 | + | 0.678265i | \(0.762732\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16327.3 | + | 10166.7i | −0.756765 | + | 0.471224i | ||||
\(776\) | 7599.16 | 0.351539 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4247.16 | − | 13071.4i | −0.195717 | − | 0.602356i | ||||
\(779\) | 258.640 | + | 796.012i | 0.0118957 | + | 0.0366111i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 486.937 | − | 1498.64i | 0.0223098 | − | 0.0686625i | ||||
\(782\) | −768.290 | −0.0351330 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3787.52 | − | 2751.80i | 0.172537 | − | 0.125355i | ||||
\(785\) | −10035.1 | + | 27503.8i | −0.456265 | + | 1.25051i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10033.4 | − | 7289.66i | 0.454448 | − | 0.330176i | −0.336901 | − | 0.941540i | \(-0.609379\pi\) |
0.791349 | + | 0.611364i | \(0.209379\pi\) | |||||||
\(788\) | 13959.0 | − | 10141.8i | 0.631053 | − | 0.458487i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6709.09 | + | 5250.23i | 0.302150 | + | 0.236449i | ||||
\(791\) | −357.831 | + | 259.979i | −0.0160847 | + | 0.0116862i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30624.7 | −1.37139 | ||||||||
\(794\) | 4219.39 | − | 12986.0i | 0.188590 | − | 0.580421i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9564.38 | − | 29436.1i | −0.425880 | − | 1.31072i | ||||
\(797\) | −10310.5 | − | 31732.5i | −0.458240 | − | 1.41032i | −0.867289 | − | 0.497806i | \(-0.834139\pi\) |
0.409048 | − | 0.912513i | \(-0.365861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1878.35 | −0.0831682 | ||||||||
\(800\) | 17652.8 | + | 14859.9i | 0.780149 | + | 0.656719i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6408.29 | − | 4655.90i | −0.282151 | − | 0.204994i | ||||
\(803\) | 738.609 | + | 2273.21i | 0.0324595 | + | 0.0999000i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11703.1 | − | 7880.46i | 0.512399 | − | 0.345031i | ||||
\(806\) | −5454.33 | + | 16786.7i | −0.238363 | + | 0.733607i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 772.812 | − | 2378.47i | 0.0336478 | − | 0.103557i | ||||
\(809\) | 11812.8 | − | 8582.52i | 0.513371 | − | 0.372986i | −0.300730 | − | 0.953709i | \(-0.597230\pi\) |
0.814101 | + | 0.580724i | \(0.197230\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4741.12 | − | 3444.63i | −0.205282 | − | 0.149146i | 0.480395 | − | 0.877052i | \(-0.340493\pi\) |
−0.685676 | + | 0.727907i | \(0.740493\pi\) | |||||||
\(812\) | −7002.57 | + | 5087.67i | −0.302638 | + | 0.219879i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −921.973 | − | 669.853i | −0.0396992 | − | 0.0288431i | ||||
\(815\) | −993.444 | − | 3474.87i | −0.0426979 | − | 0.149349i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1154.19 | − | 3552.22i | 0.0494246 | − | 0.152113i | ||||
\(818\) | −7578.50 | −0.323932 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1995.39 | + | 1343.62i | −0.0849779 | + | 0.0572210i | ||||
\(821\) | −4761.16 | − | 14653.3i | −0.202394 | − | 0.622905i | −0.999810 | − | 0.0194753i | \(-0.993800\pi\) |
0.797416 | − | 0.603430i | \(-0.206200\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33713.6 | + | 24494.3i | 1.42792 | + | 1.03745i | 0.990399 | + | 0.138241i | \(0.0441447\pi\) |
0.437525 | + | 0.899206i | \(0.355855\pi\) | |||||||
\(824\) | 358.569 | 0.0151594 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10843.4 | −0.456767 | ||||||||
\(827\) | −12428.2 | − | 9029.60i | −0.522576 | − | 0.379673i | 0.294998 | − | 0.955498i | \(-0.404681\pi\) |
−0.817573 | + | 0.575825i | \(0.804681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4586.20 | + | 14114.9i | 0.192142 | + | 0.591351i | 0.999998 | + | 0.00197177i | \(0.000627633\pi\) |
−0.807856 | + | 0.589379i | \(0.799372\pi\) | |||||||
\(830\) | −1316.91 | − | 4606.28i | −0.0550729 | − | 0.192634i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4638.16 | 0.193268 | ||||||||
\(833\) | −332.480 | + | 1023.27i | −0.0138292 | + | 0.0425620i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1399.85 | + | 1095.46i | 0.0580164 | + | 0.0454010i | ||||
\(836\) | −300.778 | − | 218.528i | −0.0124433 | − | 0.00904060i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14853.5 | + | 10791.7i | −0.612299 | + | 0.444861i | ||||
\(839\) | 3570.89 | + | 2594.40i | 0.146938 | + | 0.106757i | 0.658825 | − | 0.752296i | \(-0.271054\pi\) |
−0.511888 | + | 0.859052i | \(0.671054\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9171.97 | − | 6663.83i | 0.376070 | − | 0.273231i | ||||
\(842\) | −3814.94 | + | 11741.2i | −0.156142 | + | 0.480556i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7194.54 | + | 22142.5i | −0.293420 | + | 0.903053i | ||||
\(845\) | −45202.3 | − | 35373.2i | −1.84024 | − | 1.44009i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4998.79 | + | 15384.7i | 0.202787 | + | 0.624113i | ||||
\(848\) | 12610.6 | + | 9162.13i | 0.510672 | + | 0.371025i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −926.840 | − | 66.2775i | −0.0374004 | − | 0.00267447i | ||||
\(851\) | −35416.4 | −1.42663 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1784.63 | − | 5492.53i | −0.0716350 | − | 0.220470i | 0.908829 | − | 0.417169i | \(-0.136978\pi\) |
−0.980464 | + | 0.196699i | \(0.936978\pi\) | |||||||
\(854\) | −1808.11 | − | 5564.78i | −0.0724498 | − | 0.222977i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10774.5 | − | 33160.7i | 0.430218 | − | 1.32407i | ||||
\(857\) | 4100.45 | 0.163441 | 0.0817203 | − | 0.996655i | \(-0.473959\pi\) | ||||
0.0817203 | + | 0.996655i | \(0.473959\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7956.07 | − | 5780.42i | 0.316016 | − | 0.229599i | −0.418458 | − | 0.908236i | \(-0.637429\pi\) |
0.734473 | + | 0.678637i | \(0.237429\pi\) | |||||||
\(860\) | 10728.2 | + | 383.092i | 0.425381 | + | 0.0151899i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8200.41 | + | 5957.94i | −0.324022 | + | 0.235416i | ||||
\(863\) | 13882.1 | − | 10086.0i | 0.547571 | − | 0.397834i | −0.279318 | − | 0.960199i | \(-0.590108\pi\) |
0.826889 | + | 0.562365i | \(0.190108\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30535.7 | + | 20561.6i | −1.20028 | + | 0.808226i | ||||
\(866\) | 4386.16 | − | 3186.73i | 0.172111 | − | 0.125046i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11657.9 | 0.455870 | ||||||||
\(869\) | 436.266 | − | 1342.69i | 0.0170303 | − | 0.0524138i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14059.2 | − | 43269.8i | −0.546933 | − | 1.68329i | ||||
\(872\) | −7866.72 | − | 24211.3i | −0.305505 | − | 0.940249i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3342.26 | 0.129352 | ||||||||
\(875\) | 14798.1 | − | 8497.15i | 0.571733 | − | 0.328293i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7136.71 | + | 5185.12i | 0.274789 | + | 0.199646i | 0.716641 | − | 0.697442i | \(-0.245679\pi\) |
−0.441853 | + | 0.897088i | \(0.645679\pi\) | |||||||
\(878\) | −1616.04 | − | 4973.67i | −0.0621171 | − | 0.191177i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 229.661 | − | 629.446i | 0.00879758 | − | 0.0241121i | ||||
\(881\) | 9227.88 | − | 28400.5i | 0.352889 | − | 1.08608i | −0.604335 | − | 0.796731i | \(-0.706561\pi\) |
0.957223 | − | 0.289350i | \(-0.0934391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2159.26 | − | 6645.52i | 0.0822932 | − | 0.253272i | −0.901441 | − | 0.432902i | \(-0.857490\pi\) |
0.983734 | + | 0.179629i | \(0.0574898\pi\) | |||||||
\(884\) | 2384.81 | − | 1732.67i | 0.0907352 | − | 0.0659230i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2480.92 | − | 1802.49i | −0.0940723 | − | 0.0683476i | ||||
\(887\) | 35503.0 | − | 25794.4i | 1.34394 | − | 0.976428i | 0.344648 | − | 0.938732i | \(-0.387998\pi\) |
0.999289 | − | 0.0376958i | \(-0.0120018\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13805.9 | − | 10030.5i | −0.520848 | − | 0.378418i | ||||
\(890\) | −19979.9 | − | 713.461i | −0.752503 | − | 0.0268711i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3139.98 | + | 9663.87i | −0.117864 | + | 0.362747i | ||||
\(893\) | 8171.33 | 0.306207 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31496.7 | − | 1124.71i | −1.17633 | − | 0.0420057i | ||||
\(896\) | −5298.21 | − | 16306.2i | −0.197546 | − | 0.607983i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10866.3 | − | 7894.83i | −0.403801 | − | 0.293379i | ||||
\(899\) | 17578.9 | 0.652157 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3582.31 | −0.132457 | ||||||||
\(902\) | −93.2951 | − | 67.7829i | −0.00344389 | − | 0.00250213i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −213.036 | − | 655.657i | −0.00783790 | − | 0.0241226i | ||||
\(905\) | −3676.89 | − | 2877.36i | −0.135054 | − | 0.105687i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20572.4 | 0.753138 | 0.376569 | − | 0.926389i | \(-0.377104\pi\) | ||||
0.376569 | + | 0.926389i | \(0.377104\pi\) | |||||||
\(908\) | −7273.16 | + | 22384.5i | −0.265824 | + | 0.818122i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5367.44 | − | 14710.9i | 0.195526 | − | 0.535891i | ||||
\(911\) | −5933.73 | − | 4311.11i | −0.215799 | − | 0.156787i | 0.474634 | − | 0.880183i | \(-0.342580\pi\) |
−0.690434 | + | 0.723396i | \(0.742580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −642.302 | + | 466.660i | −0.0232827 | + | 0.0169159i | ||||
\(914\) | −3569.31 | − | 2593.26i | −0.129171 | − | 0.0938483i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 452.902 | − | 329.053i | 0.0163366 | − | 0.0118692i | ||||
\(917\) | −10708.3 | + | 32956.8i | −0.385627 | + | 1.18684i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12333.6 | + | 37958.9i | −0.442707 | + | 1.36251i | 0.442271 | + | 0.896882i | \(0.354173\pi\) |
−0.884978 | + | 0.465632i | \(0.845827\pi\) | |||||||
\(920\) | 6044.93 | + | 21144.0i | 0.216625 | + | 0.757713i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −344.178 | − | 1059.27i | −0.0122938 | − | 0.0378365i | ||||
\(923\) | −43971.5 | − | 31947.2i | −1.56808 | − | 1.13928i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42725.2 | − | 3055.24i | −1.51870 | − | 0.108601i | ||||
\(926\) | 12093.5 | 0.429176 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6516.90 | − | 20057.0i | −0.230526 | − | 0.709485i | ||||
\(929\) | −6378.19 | − | 19630.0i | −0.225255 | − | 0.693263i | −0.998266 | − | 0.0588699i | \(-0.981250\pi\) |
0.773011 | − | 0.634393i | \(-0.218750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1446.38 | − | 4451.49i | 0.0509163 | − | 0.156704i | ||||
\(932\) | 22452.4 | 0.789112 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1426.10 | + | 1036.12i | −0.0499607 | + | 0.0362986i | ||||
\(935\) | 42.3279 | + | 148.055i | 0.00148050 | + | 0.00517851i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21497.0 | + | 15618.5i | −0.749494 | + | 0.544539i | −0.895670 | − | 0.444719i | \(-0.853303\pi\) |
0.146176 | + | 0.989259i | \(0.453303\pi\) | |||||||
\(938\) | 7032.45 | − | 5109.37i | 0.244795 | − | 0.177854i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6455.74 | + | 22580.9i | 0.224003 | + | 0.783519i | ||||
\(941\) | 10502.5 | − | 7630.51i | 0.363838 | − | 0.264344i | −0.390813 | − | 0.920470i | \(-0.627806\pi\) |
0.754651 | + | 0.656126i | \(0.227806\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3583.81 | −0.123759 | ||||||||
\(944\) | −4945.28 | + | 15220.0i | −0.170503 | + | 0.524755i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 159.025 | + | 489.428i | 0.00546547 | + | 0.0168210i | ||||
\(947\) | −14382.2 | − | 44263.9i | −0.493516 | − | 1.51888i | −0.819257 | − | 0.573426i | \(-0.805614\pi\) |
0.325742 | − | 0.945459i | \(-0.394386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 82443.5 | 2.82005 | ||||||||
\(950\) | 4032.00 | + | 288.324i | 0.137700 | + | 0.00984682i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1043.09 | + | 757.849i | 0.0355113 | + | 0.0258005i | ||||
\(953\) | 11512.2 | + | 35430.8i | 0.391307 | + | 1.20432i | 0.931800 | + | 0.362972i | \(0.118238\pi\) |
−0.540493 | + | 0.841349i | \(0.681762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1603.00 | − | 5607.00i | −0.0543163 | − | 0.189988i | ||||
\(956\) | −2820.12 | + | 8679.45i | −0.0954072 | + | 0.293633i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3863.18 | − | 11889.6i | 0.130286 | − | 0.400978i | ||||
\(959\) | 8004.23 | − | 5815.41i | 0.269520 | − | 0.195818i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4946.94 | + | 3594.16i | 0.166055 | + | 0.120646i | ||||
\(962\) | −31801.1 | + | 23104.9i | −1.06581 | + | 0.774356i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19811.2 | − | 14393.7i | −0.661905 | − | 0.480902i | ||||
\(965\) | −17354.5 | + | 47564.7i | −0.578925 | + | 1.58670i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9790.75 | + | 30132.8i | −0.325594 | + | 1.00207i | 0.645578 | + | 0.763694i | \(0.276616\pi\) |
−0.971172 | + | 0.238380i | \(0.923384\pi\) | |||||||
\(968\) | −25213.5 | −0.837181 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4710.24 | + | 3686.02i | 0.155914 | + | 0.122011i | ||||
\(971\) | −8373.85 | − | 25772.1i | −0.276756 | − | 0.851766i | −0.988750 | − | 0.149581i | \(-0.952208\pi\) |
0.711994 | − | 0.702186i | \(-0.247792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31021.9 | − | 22538.7i | −1.02211 | − | 0.742608i | ||||
\(974\) | 2753.84 | 0.0905943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8635.46 | −0.283211 | ||||||||
\(977\) | 40154.6 | + | 29174.1i | 1.31490 | + | 0.955333i | 0.999981 | + | 0.00621630i | \(0.00197872\pi\) |
0.314923 | + | 0.949117i | \(0.398021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1023.82 | + | 3150.99i | 0.0334233 | + | 0.102866i | ||||
\(980\) | 13444.1 | + | 480.074i | 0.438220 | + | 0.0156484i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4783.11 | 0.155433 | ||||||||
\(983\) | −10741.8 | + | 33059.7i | −0.348534 | + | 1.07268i | 0.611131 | + | 0.791530i | \(0.290715\pi\) |
−0.959665 | + | 0.281147i | \(0.909285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31069.2 | + | 1109.45i | 1.00502 | + | 0.0358884i | ||||
\(986\) | 687.061 | + | 499.179i | 0.0221912 | + | 0.0161228i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10374.6 | + | 7537.56i | −0.334068 | + | 0.242714i | ||||
\(989\) | 12938.5 | + | 9400.36i | 0.415996 | + | 0.302239i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15805.8 | + | 11483.6i | −0.506646 | + | 0.368100i | −0.811550 | − | 0.584283i | \(-0.801376\pi\) |
0.304904 | + | 0.952383i | \(0.401376\pi\) | |||||||
\(992\) | −8777.33 | + | 27013.8i | −0.280928 | + | 0.864607i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3208.97 | − | 9876.21i | 0.102397 | − | 0.315145i | ||||
\(995\) | 19115.0 | − | 52389.7i | 0.609031 | − | 1.66921i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10317.8 | + | 31755.1i | 0.327753 | + | 1.00872i | 0.970183 | + | 0.242375i | \(0.0779264\pi\) |
−0.642430 | + | 0.766344i | \(0.722074\pi\) | |||||||
\(998\) | −343.546 | − | 249.601i | −0.0108965 | − | 0.00791680i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.4.h.a.91.5 | 28 | ||
3.2 | odd | 2 | 75.4.g.b.16.3 | ✓ | 28 | ||
25.11 | even | 5 | inner | 225.4.h.a.136.5 | 28 | ||
75.11 | odd | 10 | 75.4.g.b.61.3 | yes | 28 | ||
75.44 | odd | 10 | 1875.4.a.f.1.6 | 14 | |||
75.56 | odd | 10 | 1875.4.a.g.1.9 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.16.3 | ✓ | 28 | 3.2 | odd | 2 | ||
75.4.g.b.61.3 | yes | 28 | 75.11 | odd | 10 | ||
225.4.h.a.91.5 | 28 | 1.1 | even | 1 | trivial | ||
225.4.h.a.136.5 | 28 | 25.11 | even | 5 | inner | ||
1875.4.a.f.1.6 | 14 | 75.44 | odd | 10 | |||
1875.4.a.g.1.9 | 14 | 75.56 | odd | 10 |