Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 6 x^{10} - 12 x^{9} + 43 x^{8} + 72 x^{7} + 155 x^{6} + 162 x^{5} + 541 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.1 | ||
Root | \(-0.170505 + 0.123879i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.o.251.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.848198 | − | 2.61048i | −0.599766 | − | 1.84589i | −0.529404 | − | 0.848370i | \(-0.677584\pi\) |
−0.0703627 | − | 0.997521i | \(-0.522416\pi\) | |||||||
\(3\) | 0.170505 | + | 0.123879i | 0.0984412 | + | 0.0715217i | 0.635917 | − | 0.771757i | \(-0.280622\pi\) |
−0.537476 | + | 0.843279i | \(0.680622\pi\) | |||||||
\(4\) | −4.47716 | + | 3.25284i | −2.23858 | + | 1.62642i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | 0.178763 | − | 0.550175i | 0.0729796 | − | 0.224608i | ||||
\(7\) | 1.87960 | − | 1.36561i | 0.710422 | − | 0.516152i | −0.172888 | − | 0.984942i | \(-0.555310\pi\) |
0.883310 | + | 0.468790i | \(0.155310\pi\) | |||||||
\(8\) | 7.84779 | + | 5.70176i | 2.77461 | + | 2.01588i | ||||
\(9\) | −0.913325 | − | 2.81093i | −0.304442 | − | 0.936975i | ||||
\(10\) | 2.74483 | 0.867990 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.16634 | −0.336693 | ||||||||
\(13\) | −0.165037 | − | 0.507931i | −0.0457730 | − | 0.140875i | 0.925558 | − | 0.378606i | \(-0.123596\pi\) |
−0.971331 | + | 0.237731i | \(0.923596\pi\) | |||||||
\(14\) | −5.15918 | − | 3.74836i | −1.37885 | − | 1.00179i | ||||
\(15\) | −0.170505 | + | 0.123879i | −0.0440242 | + | 0.0319855i | ||||
\(16\) | 4.80762 | − | 14.7963i | 1.20191 | − | 3.69908i | ||||
\(17\) | 0.748288 | − | 2.30299i | 0.181487 | − | 0.558558i | −0.818384 | − | 0.574672i | \(-0.805130\pi\) |
0.999870 | + | 0.0161141i | \(0.00512951\pi\) | |||||||
\(18\) | −6.56320 | + | 4.76844i | −1.54696 | + | 1.12393i | ||||
\(19\) | −4.00915 | − | 2.91282i | −0.919762 | − | 0.668246i | 0.0237027 | − | 0.999719i | \(-0.492454\pi\) |
−0.943465 | + | 0.331473i | \(0.892454\pi\) | |||||||
\(20\) | −1.71012 | − | 5.26321i | −0.382395 | − | 1.17689i | ||||
\(21\) | 0.489652 | 0.106851 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.53407 | −0.945419 | −0.472709 | − | 0.881218i | \(-0.656724\pi\) | ||||
−0.472709 | + | 0.881218i | \(0.656724\pi\) | |||||||
\(24\) | 0.631760 | + | 1.94436i | 0.128957 | + | 0.396890i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | −1.18596 | + | 0.861652i | −0.232586 | + | 0.168984i | ||||
\(27\) | 0.387870 | − | 1.19374i | 0.0746456 | − | 0.229736i | ||||
\(28\) | −3.97315 | + | 12.2281i | −0.750855 | + | 2.31089i | ||||
\(29\) | 4.44122 | − | 3.22674i | 0.824714 | − | 0.599190i | −0.0933447 | − | 0.995634i | \(-0.529756\pi\) |
0.918059 | + | 0.396444i | \(0.129756\pi\) | |||||||
\(30\) | 0.468007 | + | 0.340027i | 0.0854460 | + | 0.0620801i | ||||
\(31\) | 0.322743 | + | 0.993301i | 0.0579663 | + | 0.178402i | 0.975847 | − | 0.218454i | \(-0.0701013\pi\) |
−0.917881 | + | 0.396856i | \(0.870101\pi\) | |||||||
\(32\) | −23.3026 | −4.11936 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.64663 | −1.13989 | ||||||||
\(35\) | 0.717944 | + | 2.20960i | 0.121355 | + | 0.373491i | ||||
\(36\) | 13.2326 | + | 9.61405i | 2.20543 | + | 1.60234i | ||||
\(37\) | −6.05926 | + | 4.40231i | −0.996136 | + | 0.723735i | −0.961256 | − | 0.275657i | \(-0.911105\pi\) |
−0.0348794 | + | 0.999392i | \(0.511105\pi\) | |||||||
\(38\) | −4.20331 | + | 12.9365i | −0.681868 | + | 2.09857i | ||||
\(39\) | 0.0347825 | − | 0.107049i | 0.00556965 | − | 0.0171416i | ||||
\(40\) | −7.84779 | + | 5.70176i | −1.24085 | + | 0.901527i | ||||
\(41\) | −8.57737 | − | 6.23182i | −1.33956 | − | 0.973247i | −0.999460 | − | 0.0328579i | \(-0.989539\pi\) |
−0.340100 | − | 0.940389i | \(-0.610461\pi\) | |||||||
\(42\) | −0.415322 | − | 1.27823i | −0.0640856 | − | 0.197235i | ||||
\(43\) | 4.32331 | 0.659299 | 0.329650 | − | 0.944103i | \(-0.393069\pi\) | ||||
0.329650 | + | 0.944103i | \(0.393069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.95558 | 0.440592 | ||||||||
\(46\) | 3.84579 | + | 11.8361i | 0.567031 | + | 1.74514i | ||||
\(47\) | −5.47587 | − | 3.97845i | −0.798738 | − | 0.580317i | 0.111806 | − | 0.993730i | \(-0.464337\pi\) |
−0.910544 | + | 0.413413i | \(0.864337\pi\) | |||||||
\(48\) | 2.65268 | − | 1.92729i | 0.382882 | − | 0.278180i | ||||
\(49\) | −0.495110 | + | 1.52379i | −0.0707300 | + | 0.217685i | ||||
\(50\) | −0.848198 | + | 2.61048i | −0.119953 | + | 0.369178i | ||||
\(51\) | 0.412880 | − | 0.299975i | 0.0578148 | − | 0.0420049i | ||||
\(52\) | 2.39112 | + | 1.73725i | 0.331588 | + | 0.240913i | ||||
\(53\) | −1.40110 | − | 4.31216i | −0.192457 | − | 0.592320i | −0.999997 | − | 0.00250794i | \(-0.999202\pi\) |
0.807540 | − | 0.589812i | \(-0.200798\pi\) | |||||||
\(54\) | −3.44523 | −0.468837 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22.5371 | 3.01165 | ||||||||
\(57\) | −0.322743 | − | 0.993301i | −0.0427483 | − | 0.131566i | ||||
\(58\) | −12.1904 | − | 8.85683i | −1.60068 | − | 1.16296i | ||||
\(59\) | 5.21430 | − | 3.78841i | 0.678845 | − | 0.493209i | −0.194130 | − | 0.980976i | \(-0.562188\pi\) |
0.872974 | + | 0.487766i | \(0.162188\pi\) | |||||||
\(60\) | 0.360418 | − | 1.10925i | 0.0465298 | − | 0.143204i | ||||
\(61\) | 2.10088 | − | 6.46586i | 0.268991 | − | 0.827868i | −0.721756 | − | 0.692147i | \(-0.756665\pi\) |
0.990747 | − | 0.135721i | \(-0.0433351\pi\) | |||||||
\(62\) | 2.31925 | − | 1.68503i | 0.294545 | − | 0.213999i | ||||
\(63\) | −5.55531 | − | 4.03617i | −0.699904 | − | 0.508510i | ||||
\(64\) | 10.1500 | + | 31.2385i | 1.26875 | + | 3.90481i | ||||
\(65\) | 0.534070 | 0.0662433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.721104 | 0.0880968 | 0.0440484 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440484 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(68\) | 4.14108 | + | 12.7449i | 0.502180 | + | 1.54555i | ||||
\(69\) | −0.773082 | − | 0.561677i | −0.0930681 | − | 0.0676180i | ||||
\(70\) | 5.15918 | − | 3.74836i | 0.616640 | − | 0.448015i | ||||
\(71\) | 1.40110 | − | 4.31216i | 0.166281 | − | 0.511759i | −0.832848 | − | 0.553502i | \(-0.813291\pi\) |
0.999128 | + | 0.0417431i | \(0.0132911\pi\) | |||||||
\(72\) | 8.85963 | − | 27.2671i | 1.04412 | − | 3.21346i | ||||
\(73\) | −0.864144 | + | 0.627837i | −0.101140 | + | 0.0734828i | −0.637206 | − | 0.770694i | \(-0.719910\pi\) |
0.536066 | + | 0.844176i | \(0.319910\pi\) | |||||||
\(74\) | 16.6316 | + | 12.0836i | 1.93338 | + | 1.40469i | ||||
\(75\) | −0.0651271 | − | 0.200441i | −0.00752024 | − | 0.0231449i | ||||
\(76\) | 27.4245 | 3.14581 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.308953 | −0.0349821 | ||||||||
\(79\) | 1.43589 | + | 4.41921i | 0.161550 | + | 0.497200i | 0.998766 | − | 0.0496734i | \(-0.0158181\pi\) |
−0.837216 | + | 0.546873i | \(0.815818\pi\) | |||||||
\(80\) | 12.5865 | + | 9.14464i | 1.40722 | + | 1.02240i | ||||
\(81\) | −6.95933 | + | 5.05625i | −0.773259 | + | 0.561806i | ||||
\(82\) | −8.99277 | + | 27.6769i | −0.993086 | + | 3.05640i | ||||
\(83\) | 4.20331 | − | 12.9365i | 0.461374 | − | 1.41996i | −0.402113 | − | 0.915590i | \(-0.631724\pi\) |
0.863486 | − | 0.504372i | \(-0.168276\pi\) | |||||||
\(84\) | −2.19225 | + | 1.59276i | −0.239194 | + | 0.173785i | ||||
\(85\) | 1.95904 | + | 1.42333i | 0.212488 | + | 0.154382i | ||||
\(86\) | −3.66703 | − | 11.2859i | −0.395426 | − | 1.21699i | ||||
\(87\) | 1.15698 | 0.124041 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7148 | 1.34776 | 0.673881 | − | 0.738840i | \(-0.264626\pi\) | ||||
0.673881 | + | 0.738840i | \(0.264626\pi\) | |||||||
\(90\) | −2.50692 | − | 7.71550i | −0.264252 | − | 0.813285i | ||||
\(91\) | −1.00384 | − | 0.729332i | −0.105231 | − | 0.0764547i | ||||
\(92\) | 20.2997 | − | 14.7486i | 2.11639 | − | 1.53765i | ||||
\(93\) | −0.0680200 | + | 0.209344i | −0.00705334 | + | 0.0217080i | ||||
\(94\) | −5.74107 | + | 17.6692i | −0.592146 | + | 1.82244i | ||||
\(95\) | 4.00915 | − | 2.91282i | 0.411330 | − | 0.298849i | ||||
\(96\) | −3.97322 | − | 2.88671i | −0.405515 | − | 0.294624i | ||||
\(97\) | 1.47067 | + | 4.52626i | 0.149324 | + | 0.459572i | 0.997542 | − | 0.0700760i | \(-0.0223242\pi\) |
−0.848218 | + | 0.529648i | \(0.822324\pi\) | |||||||
\(98\) | 4.39779 | 0.444244 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.53407 | 0.553407 | ||||||||
\(101\) | −2.03286 | − | 6.25651i | −0.202278 | − | 0.622546i | −0.999814 | − | 0.0192759i | \(-0.993864\pi\) |
0.797537 | − | 0.603271i | \(-0.206136\pi\) | |||||||
\(102\) | −1.13328 | − | 0.823379i | −0.112212 | − | 0.0815267i | ||||
\(103\) | −13.2326 | + | 9.61405i | −1.30385 | + | 0.947300i | −0.999985 | − | 0.00541565i | \(-0.998276\pi\) |
−0.303862 | + | 0.952716i | \(0.598276\pi\) | |||||||
\(104\) | 1.60092 | − | 4.92714i | 0.156984 | − | 0.483146i | ||||
\(105\) | −0.151311 | + | 0.465687i | −0.0147664 | + | 0.0454464i | ||||
\(106\) | −10.0684 | + | 7.31513i | −0.977930 | + | 0.710508i | ||||
\(107\) | −8.26068 | − | 6.00173i | −0.798590 | − | 0.580209i | 0.111910 | − | 0.993718i | \(-0.464303\pi\) |
−0.910500 | + | 0.413509i | \(0.864303\pi\) | |||||||
\(108\) | 2.14650 | + | 6.60625i | 0.206547 | + | 0.635687i | ||||
\(109\) | −12.0919 | −1.15819 | −0.579095 | − | 0.815260i | \(-0.696594\pi\) | ||||
−0.579095 | + | 0.815260i | \(0.696594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.57849 | −0.149823 | ||||||||
\(112\) | −11.1696 | − | 34.3765i | −1.05543 | − | 3.24828i | ||||
\(113\) | 8.77219 | + | 6.37337i | 0.825218 | + | 0.599556i | 0.918202 | − | 0.396111i | \(-0.129641\pi\) |
−0.0929842 | + | 0.995668i | \(0.529641\pi\) | |||||||
\(114\) | −2.31925 | + | 1.68503i | −0.217217 | + | 0.157818i | ||||
\(115\) | 1.40110 | − | 4.31216i | 0.130654 | − | 0.402111i | ||||
\(116\) | −9.38797 | + | 28.8932i | −0.871651 | + | 2.68267i | ||||
\(117\) | −1.27702 | + | 0.927812i | −0.118061 | + | 0.0857763i | ||||
\(118\) | −14.3124 | − | 10.3985i | −1.31756 | − | 0.957263i | ||||
\(119\) | −1.73851 | − | 5.35058i | −0.159369 | − | 0.490487i | ||||
\(120\) | −2.04442 | −0.186629 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −18.6610 | −1.68949 | ||||||||
\(123\) | −0.690492 | − | 2.12512i | −0.0622595 | − | 0.191615i | ||||
\(124\) | −4.67602 | − | 3.39733i | −0.419919 | − | 0.305089i | ||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | −5.82436 | + | 17.9255i | −0.518875 | + | 1.59693i | ||||
\(127\) | −2.50981 | + | 7.72440i | −0.222710 | + | 0.685430i | 0.775806 | + | 0.630971i | \(0.217343\pi\) |
−0.998516 | + | 0.0544589i | \(0.982657\pi\) | |||||||
\(128\) | 35.2339 | − | 25.5989i | 3.11426 | − | 2.26264i | ||||
\(129\) | 0.737147 | + | 0.535569i | 0.0649022 | + | 0.0471542i | ||||
\(130\) | −0.452997 | − | 1.39418i | −0.0397305 | − | 0.122278i | ||||
\(131\) | 5.79861 | 0.506627 | 0.253313 | − | 0.967384i | \(-0.418480\pi\) | ||||
0.253313 | + | 0.967384i | \(0.418480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5134 | −0.998336 | ||||||||
\(134\) | −0.611639 | − | 1.88243i | −0.0528375 | − | 0.162617i | ||||
\(135\) | 1.01546 | + | 0.737773i | 0.0873966 | + | 0.0634974i | ||||
\(136\) | 19.0035 | − | 13.8069i | 1.62954 | − | 1.18393i | ||||
\(137\) | 2.73998 | − | 8.43278i | 0.234092 | − | 0.720461i | −0.763149 | − | 0.646223i | \(-0.776348\pi\) |
0.997241 | − | 0.0742378i | \(-0.0236524\pi\) | |||||||
\(138\) | −0.810523 | + | 2.49453i | −0.0689963 | + | 0.212349i | ||||
\(139\) | 13.6455 | − | 9.91402i | 1.15739 | − | 0.840897i | 0.167948 | − | 0.985796i | \(-0.446286\pi\) |
0.989446 | + | 0.144899i | \(0.0462858\pi\) | |||||||
\(140\) | −10.4018 | − | 7.55738i | −0.879116 | − | 0.638715i | ||||
\(141\) | −0.440816 | − | 1.35669i | −0.0371234 | − | 0.114254i | ||||
\(142\) | −12.4452 | −1.04438 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −45.9823 | −3.83186 | ||||||||
\(145\) | 1.69640 | + | 5.22097i | 0.140878 | + | 0.433578i | ||||
\(146\) | 2.37192 | + | 1.72330i | 0.196302 | + | 0.142622i | ||||
\(147\) | −0.273185 | + | 0.198481i | −0.0225319 | + | 0.0163704i | ||||
\(148\) | 12.8082 | − | 39.4196i | 1.05283 | − | 3.24027i | ||||
\(149\) | 1.38005 | − | 4.24735i | 0.113058 | − | 0.347957i | −0.878479 | − | 0.477781i | \(-0.841441\pi\) |
0.991537 | + | 0.129824i | \(0.0414413\pi\) | |||||||
\(150\) | −0.468007 | + | 0.340027i | −0.0382126 | + | 0.0277631i | ||||
\(151\) | 9.31452 | + | 6.76739i | 0.758005 | + | 0.550723i | 0.898298 | − | 0.439387i | \(-0.144804\pi\) |
−0.140293 | + | 0.990110i | \(0.544804\pi\) | |||||||
\(152\) | −14.8548 | − | 45.7184i | −1.20488 | − | 3.70825i | ||||
\(153\) | −7.15698 | −0.578607 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.04442 | −0.0838897 | ||||||||
\(156\) | 0.192489 | + | 0.592419i | 0.0154114 | + | 0.0474315i | ||||
\(157\) | 4.78223 | + | 3.47449i | 0.381664 | + | 0.277295i | 0.762031 | − | 0.647541i | \(-0.224202\pi\) |
−0.380367 | + | 0.924836i | \(0.624202\pi\) | |||||||
\(158\) | 10.3184 | − | 7.49672i | 0.820884 | − | 0.596407i | ||||
\(159\) | 0.295291 | − | 0.908812i | 0.0234181 | − | 0.0720735i | ||||
\(160\) | 7.20091 | − | 22.1621i | 0.569282 | − | 1.75207i | ||||
\(161\) | −8.52224 | + | 6.19177i | −0.671647 | + | 0.487980i | ||||
\(162\) | 19.1022 | + | 13.8785i | 1.50081 | + | 1.09040i | ||||
\(163\) | 7.26159 | + | 22.3489i | 0.568772 | + | 1.75050i | 0.656469 | + | 0.754353i | \(0.272049\pi\) |
−0.0876971 | + | 0.996147i | \(0.527951\pi\) | |||||||
\(164\) | 58.6734 | 4.58162 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −37.3357 | −2.89781 | ||||||||
\(167\) | 4.39870 | + | 13.5378i | 0.340381 | + | 1.04759i | 0.964010 | + | 0.265865i | \(0.0856577\pi\) |
−0.623629 | + | 0.781721i | \(0.714342\pi\) | |||||||
\(168\) | 3.84269 | + | 2.79188i | 0.296470 | + | 0.215398i | ||||
\(169\) | 10.2865 | − | 7.47355i | 0.791266 | − | 0.574889i | ||||
\(170\) | 2.05392 | − | 6.32132i | 0.157529 | − | 0.484823i | ||||
\(171\) | −4.52606 | + | 13.9298i | −0.346116 | + | 1.06524i | ||||
\(172\) | −19.3562 | + | 14.0631i | −1.47589 | + | 1.07230i | ||||
\(173\) | 5.21430 | + | 3.78841i | 0.396436 | + | 0.288028i | 0.768088 | − | 0.640345i | \(-0.221208\pi\) |
−0.371652 | + | 0.928372i | \(0.621208\pi\) | |||||||
\(174\) | −0.981345 | − | 3.02027i | −0.0743956 | − | 0.228966i | ||||
\(175\) | −2.32331 | −0.175626 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.35837 | 0.102101 | ||||||||
\(178\) | −10.7846 | − | 33.1917i | −0.808343 | − | 2.48782i | ||||
\(179\) | −13.7365 | − | 9.98018i | −1.02672 | − | 0.745954i | −0.0590685 | − | 0.998254i | \(-0.518813\pi\) |
−0.967649 | + | 0.252300i | \(0.918813\pi\) | |||||||
\(180\) | −13.2326 | + | 9.61405i | −0.986300 | + | 0.716589i | ||||
\(181\) | 1.38738 | − | 4.26991i | 0.103123 | − | 0.317380i | −0.886162 | − | 0.463375i | \(-0.846638\pi\) |
0.989285 | + | 0.145995i | \(0.0466383\pi\) | |||||||
\(182\) | −1.05245 | + | 3.23912i | −0.0780131 | + | 0.240100i | ||||
\(183\) | 1.15920 | − | 0.842206i | 0.0856903 | − | 0.0622576i | ||||
\(184\) | −35.5825 | − | 25.8522i | −2.62317 | − | 1.90585i | ||||
\(185\) | −2.31443 | − | 7.12308i | −0.170160 | − | 0.523699i | ||||
\(186\) | 0.604184 | 0.0443009 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 37.4576 | 2.73188 | ||||||||
\(189\) | −0.901144 | − | 2.77344i | −0.0655486 | − | 0.201738i | ||||
\(190\) | −11.0044 | − | 7.99518i | −0.798345 | − | 0.580031i | ||||
\(191\) | 2.23223 | − | 1.62181i | 0.161518 | − | 0.117350i | −0.504090 | − | 0.863651i | \(-0.668172\pi\) |
0.665609 | + | 0.746301i | \(0.268172\pi\) | |||||||
\(192\) | −2.13917 | + | 6.58369i | −0.154381 | + | 0.475137i | ||||
\(193\) | 3.64751 | − | 11.2259i | 0.262554 | − | 0.808058i | −0.729693 | − | 0.683775i | \(-0.760337\pi\) |
0.992247 | − | 0.124283i | \(-0.0396630\pi\) | |||||||
\(194\) | 10.5683 | − | 7.67832i | 0.758760 | − | 0.551271i | ||||
\(195\) | 0.0910617 | + | 0.0661602i | 0.00652106 | + | 0.00473783i | ||||
\(196\) | −2.73998 | − | 8.43278i | −0.195713 | − | 0.602341i | ||||
\(197\) | −6.51035 | −0.463843 | −0.231922 | − | 0.972734i | \(-0.574501\pi\) | ||||
−0.231922 | + | 0.972734i | \(0.574501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9586 | 1.69838 | 0.849190 | − | 0.528087i | \(-0.177090\pi\) | ||||
0.849190 | + | 0.528087i | \(0.177090\pi\) | |||||||
\(200\) | −2.99759 | − | 9.22564i | −0.211962 | − | 0.652351i | ||||
\(201\) | 0.122952 | + | 0.0893298i | 0.00867236 | + | 0.00630083i | ||||
\(202\) | −14.6083 | + | 10.6135i | −1.02783 | + | 0.746765i | ||||
\(203\) | 3.94126 | − | 12.1300i | 0.276622 | − | 0.851356i | ||||
\(204\) | −0.872757 | + | 2.68607i | −0.0611052 | + | 0.188062i | ||||
\(205\) | 8.57737 | − | 6.23182i | 0.599069 | − | 0.435249i | ||||
\(206\) | 36.3212 | + | 26.3889i | 2.53062 | + | 1.83860i | ||||
\(207\) | 4.14108 | + | 12.7449i | 0.287825 | + | 0.885834i | ||||
\(208\) | −8.30895 | −0.576122 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.34401 | 0.0927455 | ||||||||
\(211\) | −5.21211 | − | 16.0412i | −0.358817 | − | 1.10432i | −0.953763 | − | 0.300559i | \(-0.902827\pi\) |
0.594947 | − | 0.803765i | \(-0.297173\pi\) | |||||||
\(212\) | 20.2997 | + | 14.7486i | 1.39419 | + | 1.01294i | ||||
\(213\) | 0.773082 | − | 0.561677i | 0.0529707 | − | 0.0384855i | ||||
\(214\) | −8.66074 | + | 26.6550i | −0.592036 | + | 1.82210i | ||||
\(215\) | −1.33598 | + | 4.11172i | −0.0911129 | + | 0.280417i | ||||
\(216\) | 9.85035 | − | 7.15670i | 0.670231 | − | 0.486952i | ||||
\(217\) | 1.96309 | + | 1.42627i | 0.133263 | + | 0.0968214i | ||||
\(218\) | 10.2563 | + | 31.5656i | 0.694644 | + | 2.13789i | ||||
\(219\) | −0.225117 | −0.0152120 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.29326 | −0.0869939 | ||||||||
\(222\) | 1.33887 | + | 4.12062i | 0.0898591 | + | 0.276558i | ||||
\(223\) | 20.2395 | + | 14.7049i | 1.35534 | + | 0.984710i | 0.998726 | + | 0.0504565i | \(0.0160676\pi\) |
0.356610 | + | 0.934253i | \(0.383932\pi\) | |||||||
\(224\) | −43.7996 | + | 31.8223i | −2.92649 | + | 2.12622i | ||||
\(225\) | −0.913325 | + | 2.81093i | −0.0608883 | + | 0.187395i | ||||
\(226\) | 9.19703 | − | 28.3055i | 0.611777 | − | 1.88286i | ||||
\(227\) | −3.24364 | + | 2.35664i | −0.215288 | + | 0.156416i | −0.690203 | − | 0.723616i | \(-0.742479\pi\) |
0.474915 | + | 0.880032i | \(0.342479\pi\) | |||||||
\(228\) | 4.67602 | + | 3.39733i | 0.309677 | + | 0.224994i | ||||
\(229\) | −5.35609 | − | 16.4844i | −0.353940 | − | 1.08932i | −0.956621 | − | 0.291334i | \(-0.905901\pi\) |
0.602681 | − | 0.797982i | \(-0.294099\pi\) | |||||||
\(230\) | −12.4452 | −0.820614 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 53.2519 | 3.49616 | ||||||||
\(233\) | 0.652816 | + | 2.00916i | 0.0427674 | + | 0.131625i | 0.970160 | − | 0.242464i | \(-0.0779556\pi\) |
−0.927393 | + | 0.374089i | \(0.877956\pi\) | |||||||
\(234\) | 3.50521 | + | 2.54668i | 0.229143 | + | 0.166482i | ||||
\(235\) | 5.47587 | − | 3.97845i | 0.357206 | − | 0.259526i | ||||
\(236\) | −11.0221 | + | 33.9226i | −0.717480 | + | 2.20818i | ||||
\(237\) | −0.302622 | + | 0.931374i | −0.0196574 | + | 0.0604992i | ||||
\(238\) | −12.4930 | + | 9.07670i | −0.809801 | + | 0.588355i | ||||
\(239\) | 19.3637 | + | 14.0686i | 1.25254 | + | 0.910020i | 0.998366 | − | 0.0571394i | \(-0.0181979\pi\) |
0.254169 | + | 0.967160i | \(0.418198\pi\) | |||||||
\(240\) | 1.01323 | + | 3.11842i | 0.0654040 | + | 0.201293i | ||||
\(241\) | −14.5134 | −0.934889 | −0.467444 | − | 0.884023i | \(-0.654825\pi\) | ||||
−0.467444 | + | 0.884023i | \(0.654825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.57849 | −0.357860 | ||||||||
\(244\) | 11.6264 | + | 35.7825i | 0.744307 | + | 2.29074i | ||||
\(245\) | −1.29622 | − | 0.941756i | −0.0828122 | − | 0.0601666i | ||||
\(246\) | −4.96191 | + | 3.60504i | −0.316360 | + | 0.229849i | ||||
\(247\) | −0.817853 | + | 2.51709i | −0.0520388 | + | 0.160159i | ||||
\(248\) | −3.13074 | + | 9.63542i | −0.198802 | + | 0.611850i | ||||
\(249\) | 2.31925 | − | 1.68503i | 0.146976 | − | 0.106784i | ||||
\(250\) | −2.22061 | − | 1.61337i | −0.140444 | − | 0.102038i | ||||
\(251\) | 8.90174 | + | 27.3967i | 0.561873 | + | 1.72927i | 0.677065 | + | 0.735923i | \(0.263252\pi\) |
−0.115192 | + | 0.993343i | \(0.536748\pi\) | |||||||
\(252\) | 38.0011 | 2.39384 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 22.2933 | 1.39880 | ||||||||
\(255\) | 0.157706 | + | 0.485370i | 0.00987594 | + | 0.0303950i | ||||
\(256\) | −43.5648 | − | 31.6517i | −2.72280 | − | 1.97823i | ||||
\(257\) | 22.3690 | − | 16.2521i | 1.39534 | − | 1.01378i | 0.400087 | − | 0.916477i | \(-0.368980\pi\) |
0.995255 | − | 0.0972985i | \(-0.0310202\pi\) | |||||||
\(258\) | 0.772847 | − | 2.37858i | 0.0481154 | − | 0.148084i | ||||
\(259\) | −5.37715 | + | 16.5492i | −0.334120 | + | 1.02831i | ||||
\(260\) | −2.39112 | + | 1.73725i | −0.148291 | + | 0.107740i | ||||
\(261\) | −13.1264 | − | 9.53688i | −0.812503 | − | 0.590318i | ||||
\(262\) | −4.91837 | − | 15.1372i | −0.303858 | − | 0.935178i | ||||
\(263\) | 3.13325 | 0.193205 | 0.0966024 | − | 0.995323i | \(-0.469202\pi\) | ||||
0.0966024 | + | 0.995323i | \(0.469202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.53407 | 0.278526 | ||||||||
\(266\) | 9.76562 | + | 30.0555i | 0.598769 | + | 1.84282i | ||||
\(267\) | 2.16793 | + | 1.57510i | 0.132675 | + | 0.0963943i | ||||
\(268\) | −3.22849 | + | 2.34564i | −0.197212 | + | 0.143283i | ||||
\(269\) | 5.56324 | − | 17.1219i | 0.339197 | − | 1.04394i | −0.625421 | − | 0.780288i | \(-0.715073\pi\) |
0.964618 | − | 0.263653i | \(-0.0849273\pi\) | |||||||
\(270\) | 1.06464 | − | 3.27661i | 0.0647917 | − | 0.199408i | ||||
\(271\) | −16.4495 | + | 11.9512i | −0.999235 | + | 0.725987i | −0.961924 | − | 0.273317i | \(-0.911879\pi\) |
−0.0373108 | + | 0.999304i | \(0.511879\pi\) | |||||||
\(272\) | −30.4784 | − | 22.1439i | −1.84802 | − | 1.34267i | ||||
\(273\) | −0.0808106 | − | 0.248709i | −0.00489088 | − | 0.0150526i | ||||
\(274\) | −24.3377 | −1.47029 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.28826 | 0.318316 | ||||||||
\(277\) | −7.87674 | − | 24.2421i | −0.473267 | − | 1.45657i | −0.848280 | − | 0.529547i | \(-0.822362\pi\) |
0.375013 | − | 0.927019i | \(-0.377638\pi\) | |||||||
\(278\) | −37.4545 | − | 27.2123i | −2.24637 | − | 1.63208i | ||||
\(279\) | 2.49732 | − | 1.81441i | 0.149511 | − | 0.108626i | ||||
\(280\) | −6.96435 | + | 21.4341i | −0.416199 | + | 1.28093i | ||||
\(281\) | 5.64653 | − | 17.3782i | 0.336844 | − | 1.03670i | −0.628963 | − | 0.777435i | \(-0.716520\pi\) |
0.965807 | − | 0.259263i | \(-0.0834798\pi\) | |||||||
\(282\) | −3.16773 | + | 2.30149i | −0.188635 | + | 0.137052i | ||||
\(283\) | 8.94270 | + | 6.49725i | 0.531588 | + | 0.386221i | 0.820951 | − | 0.570998i | \(-0.193444\pi\) |
−0.289363 | + | 0.957219i | \(0.593444\pi\) | |||||||
\(284\) | 7.75381 | + | 23.8638i | 0.460104 | + | 1.41605i | ||||
\(285\) | 1.04442 | 0.0618660 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.6323 | −1.45400 | ||||||||
\(288\) | 21.2829 | + | 65.5019i | 1.25410 | + | 3.85974i | ||||
\(289\) | 9.00944 | + | 6.54574i | 0.529967 | + | 0.385044i | ||||
\(290\) | 12.1904 | − | 8.85683i | 0.715844 | − | 0.520091i | ||||
\(291\) | −0.309952 | + | 0.953935i | −0.0181697 | + | 0.0559207i | ||||
\(292\) | 1.82665 | − | 5.62185i | 0.106897 | − | 0.328994i | ||||
\(293\) | −21.9562 | + | 15.9521i | −1.28269 | + | 0.931931i | −0.999631 | − | 0.0271709i | \(-0.991350\pi\) |
−0.283062 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(294\) | 0.749845 | + | 0.544795i | 0.0437319 | + | 0.0317731i | ||||
\(295\) | 1.99169 | + | 6.12978i | 0.115960 | + | 0.356890i | ||||
\(296\) | −72.6527 | −4.22285 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2582 | −0.710098 | ||||||||
\(299\) | 0.748288 | + | 2.30299i | 0.0432746 | + | 0.133186i | ||||
\(300\) | 0.943587 | + | 0.685556i | 0.0544780 | + | 0.0395806i | ||||
\(301\) | 8.12610 | − | 5.90396i | 0.468381 | − | 0.340299i | ||||
\(302\) | 9.76562 | − | 30.0555i | 0.561948 | − | 1.72950i | ||||
\(303\) | 0.428438 | − | 1.31860i | 0.0246131 | − | 0.0757514i | ||||
\(304\) | −62.3735 | + | 45.3170i | −3.57737 | + | 2.59911i | ||||
\(305\) | 5.50019 | + | 3.99612i | 0.314940 | + | 0.228817i | ||||
\(306\) | 6.07053 | + | 18.6832i | 0.347029 | + | 1.06805i | ||||
\(307\) | 11.7385 | 0.669951 | 0.334976 | − | 0.942227i | \(-0.391272\pi\) | ||||
0.334976 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.44721 | −0.196105 | ||||||||
\(310\) | 0.885873 | + | 2.72644i | 0.0503142 | + | 0.154851i | ||||
\(311\) | −8.60926 | − | 6.25499i | −0.488186 | − | 0.354688i | 0.316300 | − | 0.948659i | \(-0.397559\pi\) |
−0.804486 | + | 0.593971i | \(0.797559\pi\) | |||||||
\(312\) | 0.883336 | − | 0.641781i | 0.0500090 | − | 0.0363337i | ||||
\(313\) | −8.39930 | + | 25.8504i | −0.474756 | + | 1.46115i | 0.371530 | + | 0.928421i | \(0.378833\pi\) |
−0.846286 | + | 0.532729i | \(0.821167\pi\) | |||||||
\(314\) | 5.01384 | − | 15.4310i | 0.282947 | − | 0.870822i | ||||
\(315\) | 5.55531 | − | 4.03617i | 0.313006 | − | 0.227413i | ||||
\(316\) | −20.8037 | − | 15.1148i | −1.17030 | − | 0.850272i | ||||
\(317\) | 1.53869 | + | 4.73560i | 0.0864214 | + | 0.265978i | 0.984923 | − | 0.172992i | \(-0.0553435\pi\) |
−0.898502 | + | 0.438970i | \(0.855343\pi\) | |||||||
\(318\) | −2.62291 | −0.147085 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −32.8461 | −1.83615 | ||||||||
\(321\) | −0.664997 | − | 2.04665i | −0.0371165 | − | 0.114233i | ||||
\(322\) | 23.3921 | + | 16.9953i | 1.30359 | + | 0.947113i | ||||
\(323\) | −9.70820 | + | 7.05342i | −0.540179 | + | 0.392463i | ||||
\(324\) | 14.7108 | − | 45.2753i | 0.817268 | − | 2.51529i | ||||
\(325\) | −0.165037 | + | 0.507931i | −0.00915459 | + | 0.0281749i | ||||
\(326\) | 52.1822 | − | 37.9126i | 2.89010 | − | 2.09978i | ||||
\(327\) | −2.06172 | − | 1.49793i | −0.114014 | − | 0.0828357i | ||||
\(328\) | −31.7811 | − | 97.8121i | −1.75482 | − | 5.40077i | ||||
\(329\) | −15.7255 | −0.866973 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.55477 | 0.415247 | 0.207624 | − | 0.978209i | \(-0.433427\pi\) | ||||
0.207624 | + | 0.978209i | \(0.433427\pi\) | |||||||
\(332\) | 23.2614 | + | 71.5913i | 1.27664 | + | 3.92909i | ||||
\(333\) | 17.9086 | + | 13.0114i | 0.981387 | + | 0.713019i | ||||
\(334\) | 31.6092 | − | 22.9655i | 1.72958 | − | 1.25661i | ||||
\(335\) | −0.222833 | + | 0.685810i | −0.0121747 | + | 0.0374698i | ||||
\(336\) | 2.35406 | − | 7.24506i | 0.128425 | − | 0.395250i | ||||
\(337\) | −2.98612 | + | 2.16954i | −0.162664 | + | 0.118183i | −0.666140 | − | 0.745827i | \(-0.732054\pi\) |
0.503475 | + | 0.864010i | \(0.332054\pi\) | |||||||
\(338\) | −28.2346 | − | 20.5136i | −1.53576 | − | 1.11579i | ||||
\(339\) | 0.706175 | + | 2.17338i | 0.0383542 | + | 0.118042i | ||||
\(340\) | −13.4008 | −0.726761 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 40.2024 | 2.17390 | ||||||||
\(343\) | 6.17590 | + | 19.0075i | 0.333467 | + | 1.02631i | ||||
\(344\) | 33.9285 | + | 24.6505i | 1.82930 | + | 1.32907i | ||||
\(345\) | 0.773082 | − | 0.561677i | 0.0416213 | − | 0.0302397i | ||||
\(346\) | 5.46683 | − | 16.8252i | 0.293899 | − | 0.904528i | ||||
\(347\) | −4.87181 | + | 14.9939i | −0.261533 | + | 0.804915i | 0.730939 | + | 0.682443i | \(0.239082\pi\) |
−0.992472 | + | 0.122472i | \(0.960918\pi\) | |||||||
\(348\) | −5.17997 | + | 3.76346i | −0.277675 | + | 0.201743i | ||||
\(349\) | 8.54143 | + | 6.20571i | 0.457212 | + | 0.332184i | 0.792437 | − | 0.609954i | \(-0.208812\pi\) |
−0.335224 | + | 0.942138i | \(0.608812\pi\) | |||||||
\(350\) | 1.97063 | + | 6.06498i | 0.105335 | + | 0.324187i | ||||
\(351\) | −0.670351 | −0.0357807 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.5528 | −1.30681 | −0.653407 | − | 0.757007i | \(-0.726661\pi\) | ||||
−0.653407 | + | 0.757007i | \(0.726661\pi\) | |||||||
\(354\) | −1.15217 | − | 3.54601i | −0.0612370 | − | 0.188468i | ||||
\(355\) | 3.66814 | + | 2.66506i | 0.194685 | + | 0.141447i | ||||
\(356\) | −56.9260 | + | 41.3592i | −3.01707 | + | 2.19203i | ||||
\(357\) | 0.366401 | − | 1.12767i | 0.0193920 | − | 0.0596824i | ||||
\(358\) | −14.4018 | + | 44.3242i | −0.761159 | + | 2.34261i | ||||
\(359\) | 13.4866 | − | 9.79859i | 0.711795 | − | 0.517150i | −0.171957 | − | 0.985104i | \(-0.555009\pi\) |
0.883752 | + | 0.467955i | \(0.155009\pi\) | |||||||
\(360\) | 23.1948 | + | 16.8520i | 1.22247 | + | 0.888179i | ||||
\(361\) | 1.71745 | + | 5.28577i | 0.0903922 | + | 0.278199i | ||||
\(362\) | −12.3233 | −0.647699 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.86675 | 0.359915 | ||||||||
\(365\) | −0.330074 | − | 1.01586i | −0.0172768 | − | 0.0531726i | ||||
\(366\) | −3.18179 | − | 2.31171i | −0.166315 | − | 0.120835i | ||||
\(367\) | −12.3609 | + | 8.98071i | −0.645233 | + | 0.468789i | −0.861644 | − | 0.507513i | \(-0.830565\pi\) |
0.216411 | + | 0.976302i | \(0.430565\pi\) | |||||||
\(368\) | −21.7981 | + | 67.0876i | −1.13630 | + | 3.49719i | ||||
\(369\) | −9.68326 | + | 29.8020i | −0.504091 | + | 1.55143i | ||||
\(370\) | −16.6316 | + | 12.0836i | −0.864636 | + | 0.628195i | ||||
\(371\) | −8.52224 | − | 6.19177i | −0.442453 | − | 0.321461i | ||||
\(372\) | −0.376427 | − | 1.15852i | −0.0195168 | − | 0.0600667i | ||||
\(373\) | 17.8461 | 0.924033 | 0.462017 | − | 0.886871i | \(-0.347126\pi\) | ||||
0.462017 | + | 0.886871i | \(0.347126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.210756 | 0.0108834 | ||||||||
\(376\) | −20.2893 | − | 62.4442i | −1.04634 | − | 3.22031i | ||||
\(377\) | −2.37192 | − | 1.72330i | −0.122160 | − | 0.0887547i | ||||
\(378\) | −6.47566 | + | 4.70485i | −0.333072 | + | 0.241991i | ||||
\(379\) | 0.584796 | − | 1.79982i | 0.0300390 | − | 0.0924505i | −0.934913 | − | 0.354877i | \(-0.884523\pi\) |
0.964952 | + | 0.262427i | \(0.0845227\pi\) | |||||||
\(380\) | −8.47465 | + | 26.0823i | −0.434740 | + | 1.33799i | ||||
\(381\) | −1.38483 | + | 1.00614i | −0.0709469 | + | 0.0515460i | ||||
\(382\) | −6.12708 | − | 4.45158i | −0.313489 | − | 0.227763i | ||||
\(383\) | 1.64304 | + | 5.05675i | 0.0839553 | + | 0.258388i | 0.984218 | − | 0.176959i | \(-0.0566259\pi\) |
−0.900263 | + | 0.435346i | \(0.856626\pi\) | |||||||
\(384\) | 9.17873 | 0.468400 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.3988 | −1.64906 | ||||||||
\(387\) | −3.94859 | − | 12.1525i | −0.200718 | − | 0.617747i | ||||
\(388\) | −21.3076 | − | 15.4809i | −1.08173 | − | 0.785923i | ||||
\(389\) | 21.7038 | − | 15.7687i | 1.10042 | − | 0.799505i | 0.119295 | − | 0.992859i | \(-0.461936\pi\) |
0.981129 | + | 0.193354i | \(0.0619365\pi\) | |||||||
\(390\) | 0.0954718 | − | 0.293832i | 0.00483440 | − | 0.0148788i | ||||
\(391\) | −3.39279 | + | 10.4419i | −0.171581 | + | 0.528072i | ||||
\(392\) | −12.5738 | + | 9.13542i | −0.635074 | + | 0.461408i | ||||
\(393\) | 0.988692 | + | 0.718327i | 0.0498729 | + | 0.0362348i | ||||
\(394\) | 5.52206 | + | 16.9952i | 0.278198 | + | 0.856204i | ||||
\(395\) | −4.64663 | −0.233797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.5972 | 1.58582 | 0.792909 | − | 0.609340i | \(-0.208565\pi\) | ||||
0.792909 | + | 0.609340i | \(0.208565\pi\) | |||||||
\(398\) | −20.3216 | − | 62.5436i | −1.01863 | − | 3.13503i | ||||
\(399\) | −1.96309 | − | 1.42627i | −0.0982774 | − | 0.0714027i | ||||
\(400\) | −12.5865 | + | 9.14464i | −0.629326 | + | 0.457232i | ||||
\(401\) | −0.969164 | + | 2.98278i | −0.0483977 | + | 0.148953i | −0.972335 | − | 0.233592i | \(-0.924952\pi\) |
0.923937 | + | 0.382545i | \(0.124952\pi\) | |||||||
\(402\) | 0.128906 | − | 0.396733i | 0.00642927 | − | 0.0197873i | ||||
\(403\) | 0.451264 | − | 0.327862i | 0.0224790 | − | 0.0163320i | ||||
\(404\) | 29.4529 | + | 21.3988i | 1.46534 | + | 1.06463i | ||||
\(405\) | −2.65823 | − | 8.18119i | −0.132088 | − | 0.406527i | ||||
\(406\) | −35.0080 | −1.73742 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.95058 | 0.245090 | ||||||||
\(409\) | 0.131190 | + | 0.403760i | 0.00648691 | + | 0.0199646i | 0.954248 | − | 0.299018i | \(-0.0966589\pi\) |
−0.947761 | + | 0.318982i | \(0.896659\pi\) | |||||||
\(410\) | −23.5434 | − | 17.1053i | −1.16272 | − | 0.844769i | ||||
\(411\) | 1.51183 | − | 1.09841i | 0.0745728 | − | 0.0541803i | ||||
\(412\) | 27.9714 | − | 86.0872i | 1.37805 | − | 4.24121i | ||||
\(413\) | 4.62731 | − | 14.2414i | 0.227695 | − | 0.700774i | ||||
\(414\) | 29.7580 | − | 21.6205i | 1.46253 | − | 1.06259i | ||||
\(415\) | 11.0044 | + | 7.99518i | 0.540186 | + | 0.392468i | ||||
\(416\) | 3.84579 | + | 11.8361i | 0.188555 | + | 0.580314i | ||||
\(417\) | 3.55477 | 0.174078 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.71174 | 0.327890 | 0.163945 | − | 0.986469i | \(-0.447578\pi\) | ||||
0.163945 | + | 0.986469i | \(0.447578\pi\) | |||||||
\(420\) | −0.837365 | − | 2.57714i | −0.0408592 | − | 0.125752i | ||||
\(421\) | −2.24897 | − | 1.63397i | −0.109608 | − | 0.0796350i | 0.531631 | − | 0.846976i | \(-0.321579\pi\) |
−0.641239 | + | 0.767341i | \(0.721579\pi\) | |||||||
\(422\) | −37.4545 | + | 27.2123i | −1.82326 | + | 1.32467i | ||||
\(423\) | −6.18188 | + | 19.0259i | −0.300574 | + | 0.925070i | ||||
\(424\) | 13.5913 | − | 41.8297i | 0.660051 | − | 2.03143i | ||||
\(425\) | −1.95904 | + | 1.42333i | −0.0950276 | + | 0.0690416i | ||||
\(426\) | −2.12198 | − | 1.54171i | −0.102810 | − | 0.0746959i | ||||
\(427\) | −4.88102 | − | 15.0222i | −0.236209 | − | 0.726976i | ||||
\(428\) | 56.5070 | 2.73137 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.8667 | 0.572265 | ||||||||
\(431\) | 5.00496 | + | 15.4037i | 0.241081 | + | 0.741969i | 0.996256 | + | 0.0864473i | \(0.0275514\pi\) |
−0.755176 | + | 0.655522i | \(0.772449\pi\) | |||||||
\(432\) | −15.7983 | − | 11.4781i | −0.760095 | − | 0.552241i | ||||
\(433\) | −6.33244 | + | 4.60079i | −0.304318 | + | 0.221100i | −0.729454 | − | 0.684029i | \(-0.760226\pi\) |
0.425137 | + | 0.905129i | \(0.360226\pi\) | |||||||
\(434\) | 2.05816 | − | 6.33437i | 0.0987949 | − | 0.304060i | ||||
\(435\) | −0.357525 | + | 1.10035i | −0.0171420 | + | 0.0527577i | ||||
\(436\) | 54.1372 | − | 39.3330i | 2.59270 | − | 1.88371i | ||||
\(437\) | 18.1778 | + | 13.2069i | 0.869561 | + | 0.631773i | ||||
\(438\) | 0.190944 | + | 0.587664i | 0.00912364 | + | 0.0280797i | ||||
\(439\) | 20.7355 | 0.989650 | 0.494825 | − | 0.868993i | \(-0.335232\pi\) | ||||
0.494825 | + | 0.868993i | \(0.335232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.73546 | 0.225498 | ||||||||
\(442\) | 1.09694 | + | 3.37603i | 0.0521760 | + | 0.160581i | ||||
\(443\) | −4.28991 | − | 3.11680i | −0.203820 | − | 0.148084i | 0.481193 | − | 0.876615i | \(-0.340204\pi\) |
−0.685013 | + | 0.728531i | \(0.740204\pi\) | |||||||
\(444\) | 7.06714 | − | 5.13458i | 0.335392 | − | 0.243676i | ||||
\(445\) | −3.92908 | + | 12.0925i | −0.186256 | + | 0.573238i | ||||
\(446\) | 21.2197 | − | 65.3075i | 1.00478 | − | 3.09240i | ||||
\(447\) | 0.761464 | − | 0.553236i | 0.0360160 | − | 0.0261672i | ||||
\(448\) | 61.7375 | + | 44.8549i | 2.91682 | + | 2.11919i | ||||
\(449\) | −9.27145 | − | 28.5346i | −0.437547 | − | 1.34663i | −0.890454 | − | 0.455072i | \(-0.849613\pi\) |
0.452908 | − | 0.891557i | \(-0.350387\pi\) | |||||||
\(450\) | 8.11256 | 0.382430 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −60.0061 | −2.82245 | ||||||||
\(453\) | 0.749833 | + | 2.30775i | 0.0352302 | + | 0.108428i | ||||
\(454\) | 8.90323 | + | 6.46858i | 0.417849 | + | 0.303585i | ||||
\(455\) | 1.00384 | − | 0.729332i | 0.0470607 | − | 0.0341916i | ||||
\(456\) | 3.13074 | − | 9.63542i | 0.146610 | − | 0.451220i | ||||
\(457\) | 11.5923 | − | 35.6773i | 0.542264 | − | 1.66892i | −0.185145 | − | 0.982711i | \(-0.559276\pi\) |
0.727409 | − | 0.686204i | \(-0.240724\pi\) | |||||||
\(458\) | −38.4891 | + | 27.9640i | −1.79848 | + | 1.30667i | ||||
\(459\) | −2.45894 | − | 1.78653i | −0.114774 | − | 0.0833879i | ||||
\(460\) | 7.75381 | + | 23.8638i | 0.361523 | + | 1.11265i | ||||
\(461\) | 15.7829 | 0.735083 | 0.367542 | − | 0.930007i | \(-0.380200\pi\) | ||||
0.367542 | + | 0.930007i | \(0.380200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5672 | −0.769941 | −0.384970 | − | 0.922929i | \(-0.625788\pi\) | ||||
−0.384970 | + | 0.922929i | \(0.625788\pi\) | |||||||
\(464\) | −26.3922 | − | 81.2268i | −1.22523 | − | 3.77086i | ||||
\(465\) | −0.178079 | − | 0.129382i | −0.00825820 | − | 0.00599993i | ||||
\(466\) | 4.69117 | − | 3.40833i | 0.217314 | − | 0.157888i | ||||
\(467\) | 1.14349 | − | 3.51930i | 0.0529144 | − | 0.162854i | −0.921107 | − | 0.389309i | \(-0.872714\pi\) |
0.974022 | + | 0.226455i | \(0.0727138\pi\) | |||||||
\(468\) | 2.69941 | − | 8.30792i | 0.124780 | − | 0.384034i | ||||
\(469\) | 1.35539 | − | 0.984746i | 0.0625860 | − | 0.0454714i | ||||
\(470\) | −15.0303 | − | 10.9202i | −0.693297 | − | 0.503709i | ||||
\(471\) | 0.384977 | + | 1.18484i | 0.0177388 | + | 0.0545945i | ||||
\(472\) | 62.5214 | 2.87778 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.68802 | 0.123465 | ||||||||
\(475\) | 1.53136 | + | 4.71304i | 0.0702636 | + | 0.216249i | ||||
\(476\) | 25.1882 | + | 18.3003i | 1.15450 | + | 0.838792i | ||||
\(477\) | −10.8415 | + | 7.87680i | −0.496398 | + | 0.360654i | ||||
\(478\) | 20.3015 | − | 62.4817i | 0.928570 | − | 2.85784i | ||||
\(479\) | 0.390763 | − | 1.20264i | 0.0178544 | − | 0.0549502i | −0.941732 | − | 0.336363i | \(-0.890803\pi\) |
0.959587 | + | 0.281413i | \(0.0908031\pi\) | |||||||
\(480\) | 3.97322 | − | 2.88671i | 0.181352 | − | 0.131760i | ||||
\(481\) | 3.23607 | + | 2.35114i | 0.147552 | + | 0.107203i | ||||
\(482\) | 12.3102 | + | 37.8869i | 0.560715 | + | 1.72570i | ||||
\(483\) | −2.22012 | −0.101019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.75919 | −0.216104 | ||||||||
\(486\) | 4.73166 | + | 14.5626i | 0.214633 | + | 0.660571i | ||||
\(487\) | −17.4766 | − | 12.6975i | −0.791938 | − | 0.575377i | 0.116600 | − | 0.993179i | \(-0.462801\pi\) |
−0.908538 | + | 0.417802i | \(0.862801\pi\) | |||||||
\(488\) | 53.3541 | − | 38.7640i | 2.41522 | − | 1.75476i | ||||
\(489\) | −1.53042 | + | 4.71016i | −0.0692082 | + | 0.213001i | ||||
\(490\) | −1.35899 | + | 4.18255i | −0.0613930 | + | 0.188948i | ||||
\(491\) | −20.6599 | + | 15.0103i | −0.932370 | + | 0.677407i | −0.946572 | − | 0.322492i | \(-0.895479\pi\) |
0.0142017 | + | 0.999899i | \(0.495479\pi\) | |||||||
\(492\) | 10.0041 | + | 7.26841i | 0.451020 | + | 0.327685i | ||||
\(493\) | −4.10784 | − | 12.6426i | −0.185008 | − | 0.569396i | ||||
\(494\) | 7.26454 | 0.326847 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.2488 | 0.729594 | ||||||||
\(497\) | −3.25521 | − | 10.0185i | −0.146016 | − | 0.449391i | ||||
\(498\) | −6.36593 | − | 4.62512i | −0.285264 | − | 0.207256i | ||||
\(499\) | −19.7088 | + | 14.3193i | −0.882286 | + | 0.641019i | −0.933855 | − | 0.357651i | \(-0.883578\pi\) |
0.0515690 | + | 0.998669i | \(0.483578\pi\) | |||||||
\(500\) | −1.71012 | + | 5.26321i | −0.0764790 | + | 0.235378i | ||||
\(501\) | −0.927051 | + | 2.85317i | −0.0414176 | + | 0.127470i | ||||
\(502\) | 63.9683 | − | 46.4757i | 2.85505 | − | 2.07431i | ||||
\(503\) | 10.1095 | + | 7.34496i | 0.450759 | + | 0.327495i | 0.789895 | − | 0.613242i | \(-0.210135\pi\) |
−0.339136 | + | 0.940737i | \(0.610135\pi\) | |||||||
\(504\) | −20.5837 | − | 63.3501i | −0.916871 | − | 2.82184i | ||||
\(505\) | 6.57849 | 0.292739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.67971 | 0.119010 | ||||||||
\(508\) | −13.8895 | − | 42.7474i | −0.616246 | − | 1.89661i | ||||
\(509\) | −19.7791 | − | 14.3703i | −0.876691 | − | 0.636954i | 0.0556827 | − | 0.998449i | \(-0.482266\pi\) |
−0.932374 | + | 0.361495i | \(0.882266\pi\) | |||||||
\(510\) | 1.13328 | − | 0.823379i | 0.0501827 | − | 0.0364598i | ||||
\(511\) | −0.766865 | + | 2.36017i | −0.0339241 | + | 0.104408i | ||||
\(512\) | −18.7584 | + | 57.7324i | −0.829012 | + | 2.55144i | ||||
\(513\) | −5.03218 | + | 3.65609i | −0.222176 | + | 0.161420i | ||||
\(514\) | −61.3991 | − | 44.6091i | −2.70820 | − | 1.96762i | ||||
\(515\) | −5.05440 | − | 15.5559i | −0.222724 | − | 0.685473i | ||||
\(516\) | −5.04245 | −0.221981 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 47.7622 | 2.09855 | ||||||||
\(519\) | 0.419760 | + | 1.29189i | 0.0184254 | + | 0.0567076i | ||||
\(520\) | 4.19127 | + | 3.04514i | 0.183799 | + | 0.133538i | ||||
\(521\) | 0.0318902 | − | 0.0231696i | 0.00139713 | − | 0.00101508i | −0.587086 | − | 0.809524i | \(-0.699725\pi\) |
0.588484 | + | 0.808509i | \(0.299725\pi\) | |||||||
\(522\) | −13.7621 | + | 42.3554i | −0.602351 | + | 1.85385i | ||||
\(523\) | −6.51774 | + | 20.0596i | −0.285001 | + | 0.877143i | 0.701397 | + | 0.712771i | \(0.252560\pi\) |
−0.986398 | + | 0.164372i | \(0.947440\pi\) | |||||||
\(524\) | −25.9613 | + | 18.8620i | −1.13412 | + | 0.823989i | ||||
\(525\) | −0.396137 | − | 0.287810i | −0.0172888 | − | 0.0125611i | ||||
\(526\) | −2.65762 | − | 8.17931i | −0.115878 | − | 0.356635i | ||||
\(527\) | 2.52907 | 0.110168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.44221 | −0.106183 | ||||||||
\(530\) | −3.84579 | − | 11.8361i | −0.167050 | − | 0.514128i | ||||
\(531\) | −15.4113 | − | 11.1970i | −0.668794 | − | 0.485907i | ||||
\(532\) | 51.5472 | − | 37.4512i | 2.23485 | − | 1.62372i | ||||
\(533\) | −1.74975 | + | 5.38519i | −0.0757903 | + | 0.233259i | ||||
\(534\) | 2.27293 | − | 6.99535i | 0.0983591 | − | 0.302718i | ||||
\(535\) | 8.26068 | − | 6.00173i | 0.357140 | − | 0.259477i | ||||
\(536\) | 5.65907 | + | 4.11156i | 0.244435 | + | 0.177592i | ||||
\(537\) | −1.10581 | − | 3.40334i | −0.0477194 | − | 0.146865i | ||||
\(538\) | −49.4152 | −2.13044 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.94622 | −0.298918 | ||||||||
\(541\) | −10.3336 | − | 31.8036i | −0.444276 | − | 1.36734i | −0.883276 | − | 0.468854i | \(-0.844667\pi\) |
0.438999 | − | 0.898487i | \(-0.355333\pi\) | |||||||
\(542\) | 45.1510 | + | 32.8041i | 1.93940 | + | 1.40906i | ||||
\(543\) | 0.765509 | − | 0.556175i | 0.0328511 | − | 0.0238677i | ||||
\(544\) | −17.4371 | + | 53.6658i | −0.747608 | + | 2.30090i | ||||
\(545\) | 3.73659 | − | 11.5000i | 0.160058 | − | 0.492608i | ||||
\(546\) | −0.580709 | + | 0.421910i | −0.0248520 | + | 0.0180561i | ||||
\(547\) | −26.5411 | − | 19.2833i | −1.13482 | − | 0.824492i | −0.148428 | − | 0.988923i | \(-0.547421\pi\) |
−0.986389 | + | 0.164431i | \(0.947421\pi\) | |||||||
\(548\) | 15.1632 | + | 46.6676i | 0.647740 | + | 1.99354i | ||||
\(549\) | −20.0938 | −0.857584 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.2044 | −1.15895 | ||||||||
\(552\) | −2.86444 | − | 8.81585i | −0.121919 | − | 0.375228i | ||||
\(553\) | 8.73381 | + | 6.34548i | 0.371399 | + | 0.269837i | ||||
\(554\) | −56.6026 | + | 41.1242i | −2.40481 | + | 1.74720i | ||||
\(555\) | 0.487780 | − | 1.50123i | 0.0207051 | − | 0.0637237i | ||||
\(556\) | −28.8442 | + | 88.7733i | −1.22327 | + | 3.76483i | ||||
\(557\) | −22.9216 | + | 16.6535i | −0.971220 | + | 0.705633i | −0.955729 | − | 0.294247i | \(-0.904931\pi\) |
−0.0154907 | + | 0.999880i | \(0.504931\pi\) | |||||||
\(558\) | −6.85472 | − | 4.98025i | −0.290184 | − | 0.210831i | ||||
\(559\) | −0.713506 | − | 2.19595i | −0.0301781 | − | 0.0928786i | ||||
\(560\) | 36.1456 | 1.52743 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.1550 | −2.11566 | ||||||||
\(563\) | 8.97265 | + | 27.6150i | 0.378152 | + | 1.16383i | 0.941327 | + | 0.337495i | \(0.109580\pi\) |
−0.563175 | + | 0.826338i | \(0.690420\pi\) | |||||||
\(564\) | 6.38672 | + | 4.64022i | 0.268929 | + | 0.195389i | ||||
\(565\) | −8.77219 | + | 6.37337i | −0.369049 | + | 0.268130i | ||||
\(566\) | 9.37579 | − | 28.8557i | 0.394094 | − | 1.21290i | ||||
\(567\) | −6.17590 | + | 19.0075i | −0.259364 | + | 0.798239i | ||||
\(568\) | 35.5825 | − | 25.8522i | 1.49301 | − | 1.08473i | ||||
\(569\) | −23.2267 | − | 16.8752i | −0.973714 | − | 0.707444i | −0.0174187 | − | 0.999848i | \(-0.505545\pi\) |
−0.956295 | + | 0.292404i | \(0.905545\pi\) | |||||||
\(570\) | −0.885873 | − | 2.72644i | −0.0371051 | − | 0.114198i | ||||
\(571\) | 0.824301 | 0.0344959 | 0.0172480 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172480 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.581515 | 0.0242931 | ||||||||
\(574\) | 20.8930 | + | 64.3022i | 0.872059 | + | 2.68392i | ||||
\(575\) | 3.66814 | + | 2.66506i | 0.152972 | + | 0.111141i | ||||
\(576\) | 78.5387 | − | 57.0617i | 3.27245 | − | 2.37757i | ||||
\(577\) | −9.74704 | + | 29.9983i | −0.405775 | + | 1.24885i | 0.514472 | + | 0.857507i | \(0.327988\pi\) |
−0.920247 | + | 0.391339i | \(0.872012\pi\) | |||||||
\(578\) | 9.44577 | − | 29.0711i | 0.392892 | − | 1.20920i | ||||
\(579\) | 2.01257 | − | 1.46222i | 0.0836398 | − | 0.0607678i | ||||
\(580\) | −24.5780 | − | 17.8570i | −1.02055 | − | 0.741471i | ||||
\(581\) | −9.76562 | − | 30.0555i | −0.405146 | − | 1.24691i | ||||
\(582\) | 2.75313 | 0.114121 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.3614 | −0.428758 | ||||||||
\(585\) | −0.487780 | − | 1.50123i | −0.0201672 | − | 0.0620683i | ||||
\(586\) | 60.2658 | + | 43.7857i | 2.48956 | + | 1.80877i | ||||
\(587\) | 21.6603 | − | 15.7371i | 0.894014 | − | 0.649539i | −0.0429072 | − | 0.999079i | \(-0.513662\pi\) |
0.936922 | + | 0.349540i | \(0.113662\pi\) | |||||||
\(588\) | 0.577466 | − | 1.77726i | 0.0238143 | − | 0.0732929i | ||||
\(589\) | 1.59938 | − | 4.92238i | 0.0659013 | − | 0.202823i | ||||
\(590\) | 14.3124 | − | 10.3985i | 0.589230 | − | 0.428101i | ||||
\(591\) | −1.11005 | − | 0.806497i | −0.0456613 | − | 0.0331748i | ||||
\(592\) | 36.0074 | + | 110.819i | 1.47990 | + | 4.55465i | ||||
\(593\) | −11.0731 | −0.454719 | −0.227360 | − | 0.973811i | \(-0.573009\pi\) | ||||
−0.227360 | + | 0.973811i | \(0.573009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.62593 | 0.230641 | ||||||||
\(596\) | 7.63728 | + | 23.5051i | 0.312835 | + | 0.962808i | ||||
\(597\) | 4.08506 | + | 2.96797i | 0.167191 | + | 0.121471i | ||||
\(598\) | 5.37724 | − | 3.90679i | 0.219892 | − | 0.159761i | ||||
\(599\) | −3.68808 | + | 11.3508i | −0.150691 | + | 0.463779i | −0.997699 | − | 0.0678012i | \(-0.978402\pi\) |
0.847008 | + | 0.531580i | \(0.178402\pi\) | |||||||
\(600\) | 0.631760 | − | 1.94436i | 0.0257915 | − | 0.0793780i | ||||
\(601\) | −4.25910 | + | 3.09442i | −0.173732 | + | 0.126224i | −0.671253 | − | 0.741228i | \(-0.734244\pi\) |
0.497521 | + | 0.867452i | \(0.334244\pi\) | |||||||
\(602\) | −22.3047 | − | 16.2053i | −0.909074 | − | 0.660481i | ||||
\(603\) | −0.658602 | − | 2.02697i | −0.0268204 | − | 0.0825446i | ||||
\(604\) | −63.7158 | −2.59256 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.80558 | −0.154591 | ||||||||
\(607\) | 11.0770 | + | 34.0916i | 0.449603 | + | 1.38374i | 0.877356 | + | 0.479840i | \(0.159305\pi\) |
−0.427753 | + | 0.903896i | \(0.640695\pi\) | |||||||
\(608\) | 93.4237 | + | 67.8763i | 3.78883 | + | 2.75275i | ||||
\(609\) | 2.17465 | − | 1.57998i | 0.0881214 | − | 0.0640240i | ||||
\(610\) | 5.76656 | − | 17.7477i | 0.233481 | − | 0.718582i | ||||
\(611\) | −1.11706 | + | 3.43796i | −0.0451914 | + | 0.139085i | ||||
\(612\) | 32.0429 | − | 23.2805i | 1.29526 | − | 0.941060i | ||||
\(613\) | −5.30537 | − | 3.85457i | −0.214282 | − | 0.155685i | 0.475467 | − | 0.879733i | \(-0.342279\pi\) |
−0.689749 | + | 0.724049i | \(0.742279\pi\) | |||||||
\(614\) | −9.95656 | − | 30.6432i | −0.401814 | − | 1.23666i | ||||
\(615\) | 2.23448 | 0.0901029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.7986 | 0.716545 | 0.358272 | − | 0.933617i | \(-0.383366\pi\) | ||||
0.358272 | + | 0.933617i | \(0.383366\pi\) | |||||||
\(618\) | 2.92391 | + | 8.99888i | 0.117617 | + | 0.361988i | ||||
\(619\) | −36.3172 | − | 26.3860i | −1.45971 | − | 1.06054i | −0.983438 | − | 0.181243i | \(-0.941988\pi\) |
−0.476271 | − | 0.879298i | \(-0.658012\pi\) | |||||||
\(620\) | 4.67602 | − | 3.39733i | 0.187794 | − | 0.136440i | ||||
\(621\) | −1.75863 | + | 5.41251i | −0.0705714 | + | 0.217196i | ||||
\(622\) | −9.02621 | + | 27.7798i | −0.361918 | + | 1.11387i | ||||
\(623\) | 23.8987 | − | 17.3634i | 0.957481 | − | 0.695651i | ||||
\(624\) | −1.41672 | − | 1.02931i | −0.0567141 | − | 0.0412052i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 74.6063 | 2.98187 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.7128 | −1.30538 | ||||||||
\(629\) | 5.60442 | + | 17.2486i | 0.223463 | + | 0.687748i | ||||
\(630\) | −15.2484 | − | 11.0786i | −0.607510 | − | 0.441382i | ||||
\(631\) | −17.7265 | + | 12.8791i | −0.705681 | + | 0.512707i | −0.881777 | − | 0.471666i | \(-0.843653\pi\) |
0.176096 | + | 0.984373i | \(0.443653\pi\) | |||||||
\(632\) | −13.9287 | + | 42.8681i | −0.554054 | + | 1.70520i | ||||
\(633\) | 1.09848 | − | 3.38078i | 0.0436608 | − | 0.134374i | ||||
\(634\) | 11.0571 | − | 8.03345i | 0.439133 | − | 0.319049i | ||||
\(635\) | −6.57077 | − | 4.77394i | −0.260753 | − | 0.189448i | ||||
\(636\) | 1.63416 | + | 5.02943i | 0.0647987 | + | 0.199430i | ||||
\(637\) | 0.855693 | 0.0339038 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.4008 | −0.530128 | ||||||||
\(640\) | 13.4581 | + | 41.4199i | 0.531980 | + | 1.63727i | ||||
\(641\) | −28.9090 | − | 21.0036i | −1.14184 | − | 0.829593i | −0.154463 | − | 0.987999i | \(-0.549365\pi\) |
−0.987374 | + | 0.158406i | \(0.949365\pi\) | |||||||
\(642\) | −4.77870 | + | 3.47193i | −0.188600 | + | 0.137026i | ||||
\(643\) | 0.127361 | − | 0.391978i | 0.00502265 | − | 0.0154581i | −0.948514 | − | 0.316736i | \(-0.897413\pi\) |
0.953536 | + | 0.301278i | \(0.0974131\pi\) | |||||||
\(644\) | 18.0145 | − | 55.4431i | 0.709872 | − | 2.18476i | ||||
\(645\) | −0.737147 | + | 0.535569i | −0.0290251 | + | 0.0210880i | ||||
\(646\) | 26.6473 | + | 19.3604i | 1.04843 | + | 0.761726i | ||||
\(647\) | −5.11375 | − | 15.7385i | −0.201042 | − | 0.618744i | −0.999853 | − | 0.0171614i | \(-0.994537\pi\) |
0.798811 | − | 0.601583i | \(-0.205463\pi\) | |||||||
\(648\) | −83.4450 | −3.27803 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.46593 | 0.0574985 | ||||||||
\(651\) | 0.158032 | + | 0.486372i | 0.00619375 | + | 0.0190624i | ||||
\(652\) | −105.209 | − | 76.4386i | −4.12029 | − | 2.99357i | ||||
\(653\) | −8.90568 | + | 6.47036i | −0.348506 | + | 0.253205i | −0.748242 | − | 0.663426i | \(-0.769102\pi\) |
0.399736 | + | 0.916630i | \(0.369102\pi\) | |||||||
\(654\) | −2.16157 | + | 6.65264i | −0.0845242 | + | 0.260139i | ||||
\(655\) | −1.79187 | + | 5.51480i | −0.0700141 | + | 0.215481i | ||||
\(656\) | −133.445 | + | 96.9534i | −5.21015 | + | 3.78539i | ||||
\(657\) | 2.55405 | + | 1.85562i | 0.0996429 | + | 0.0723948i | ||||
\(658\) | 13.3383 | + | 41.0511i | 0.519981 | + | 1.60034i | ||||
\(659\) | 42.9980 | 1.67497 | 0.837483 | − | 0.546464i | \(-0.184026\pi\) | ||||
0.837483 | + | 0.546464i | \(0.184026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.4927 | 0.758177 | 0.379089 | − | 0.925360i | \(-0.376238\pi\) | ||||
0.379089 | + | 0.925360i | \(0.376238\pi\) | |||||||
\(662\) | −6.40794 | − | 19.7216i | −0.249052 | − | 0.766502i | ||||
\(663\) | −0.220507 | − | 0.160208i | −0.00856378 | − | 0.00622195i | ||||
\(664\) | 106.747 | − | 77.5565i | 4.14260 | − | 3.00978i | ||||
\(665\) | 3.55783 | − | 10.9499i | 0.137967 | − | 0.424618i | ||||
\(666\) | 18.7759 | − | 57.7864i | 0.727553 | − | 2.23918i | ||||
\(667\) | −20.1368 | + | 14.6303i | −0.779700 | + | 0.566486i | ||||
\(668\) | −63.7300 | − | 46.3025i | −2.46579 | − | 1.79150i | ||||
\(669\) | 1.62931 | + | 5.01450i | 0.0629928 | + | 0.193872i | ||||
\(670\) | 1.97930 | 0.0764672 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4102 | −0.440157 | ||||||||
\(673\) | −2.10336 | − | 6.47349i | −0.0810788 | − | 0.249535i | 0.902298 | − | 0.431114i | \(-0.141879\pi\) |
−0.983376 | + | 0.181579i | \(0.941879\pi\) | |||||||
\(674\) | 8.19638 | + | 5.95502i | 0.315713 | + | 0.229379i | ||||
\(675\) | −1.01546 | + | 0.737773i | −0.0390850 | + | 0.0283969i | ||||
\(676\) | −21.7438 | + | 66.9205i | −0.836300 | + | 2.57387i | ||||
\(677\) | −0.315412 | + | 0.970739i | −0.0121223 | + | 0.0373085i | −0.956935 | − | 0.290303i | \(-0.906244\pi\) |
0.944812 | + | 0.327612i | \(0.106244\pi\) | |||||||
\(678\) | 5.07461 | − | 3.68692i | 0.194889 | − | 0.141595i | ||||
\(679\) | 8.94537 | + | 6.49919i | 0.343292 | + | 0.249416i | ||||
\(680\) | 7.25870 | + | 22.3400i | 0.278359 | + | 0.856699i | ||||
\(681\) | −0.844996 | −0.0323803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.09820 | 0.0802853 | 0.0401426 | − | 0.999194i | \(-0.487219\pi\) | ||||
0.0401426 | + | 0.999194i | \(0.487219\pi\) | |||||||
\(684\) | −25.0475 | − | 77.0883i | −0.957716 | − | 2.94755i | ||||
\(685\) | 7.17335 | + | 5.21174i | 0.274080 | + | 0.199130i | ||||
\(686\) | 44.3803 | − | 32.2442i | 1.69445 | − | 1.23109i | ||||
\(687\) | 1.12883 | − | 3.47417i | 0.0430675 | − | 0.132548i | ||||
\(688\) | 20.7849 | − | 63.9692i | 0.792415 | − | 2.43880i | ||||
\(689\) | −1.95904 | + | 1.42333i | −0.0746336 | + | 0.0542245i | ||||
\(690\) | −2.12198 | − | 1.54171i | −0.0807822 | − | 0.0586917i | ||||
\(691\) | 3.70666 | + | 11.4079i | 0.141008 | + | 0.433978i | 0.996476 | − | 0.0838776i | \(-0.0267305\pi\) |
−0.855468 | + | 0.517855i | \(0.826730\pi\) | |||||||
\(692\) | −35.6684 | −1.35591 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43.2736 | 1.64264 | ||||||||
\(695\) | 5.21211 | + | 16.0412i | 0.197707 | + | 0.608478i | ||||
\(696\) | 9.07971 | + | 6.59680i | 0.344166 | + | 0.250051i | ||||
\(697\) | −20.7702 | + | 15.0904i | −0.786727 | + | 0.571591i | ||||
\(698\) | 8.95510 | − | 27.5610i | 0.338955 | − | 1.04320i | ||||
\(699\) | −0.137585 | + | 0.423443i | −0.00520394 | + | 0.0160161i | ||||
\(700\) | 10.4018 | − | 7.55738i | 0.393153 | − | 0.285642i | ||||
\(701\) | −23.7523 | − | 17.2570i | −0.897111 | − | 0.651789i | 0.0406113 | − | 0.999175i | \(-0.487069\pi\) |
−0.937722 | + | 0.347386i | \(0.887069\pi\) | |||||||
\(702\) | 0.568590 | + | 1.74994i | 0.0214601 | + | 0.0660473i | ||||
\(703\) | 37.1156 | 1.39984 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.42651 | 0.0537255 | ||||||||
\(706\) | 20.8256 | + | 64.0947i | 0.783783 | + | 2.41224i | ||||
\(707\) | −12.3649 | − | 8.98365i | −0.465031 | − | 0.337865i | ||||
\(708\) | −6.08164 | + | 4.41857i | −0.228562 | + | 0.166060i | ||||
\(709\) | −11.6021 | + | 35.7075i | −0.435725 | + | 1.34102i | 0.456616 | + | 0.889664i | \(0.349061\pi\) |
−0.892342 | + | 0.451361i | \(0.850939\pi\) | |||||||
\(710\) | 3.84579 | − | 11.8361i | 0.144330 | − | 0.444202i | ||||
\(711\) | 11.1106 | − | 8.07234i | 0.416681 | − | 0.302737i | ||||
\(712\) | 99.7829 | + | 72.4965i | 3.73952 | + | 2.71692i | ||||
\(713\) | −1.46334 | − | 4.50369i | −0.0548025 | − | 0.168665i | ||||
\(714\) | −3.25454 | −0.121798 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 93.9647 | 3.51162 | ||||||||
\(717\) | 1.55881 | + | 4.79753i | 0.0582149 | + | 0.179167i | ||||
\(718\) | −37.0184 | − | 26.8954i | −1.38151 | − | 1.00373i | ||||
\(719\) | 3.23202 | − | 2.34820i | 0.120534 | − | 0.0875732i | −0.525885 | − | 0.850556i | \(-0.676266\pi\) |
0.646419 | + | 0.762983i | \(0.276266\pi\) | |||||||
\(720\) | 14.2093 | − | 43.7318i | 0.529550 | − | 1.62979i | ||||
\(721\) | −11.7430 | + | 36.1411i | −0.437331 | + | 1.34597i | ||||
\(722\) | 12.3417 | − | 8.96677i | 0.459310 | − | 0.333708i | ||||
\(723\) | −2.47460 | − | 1.79791i | −0.0920315 | − | 0.0668648i | ||||
\(724\) | 7.67785 | + | 23.6300i | 0.285345 | + | 0.878202i | ||||
\(725\) | −5.48965 | −0.203881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4990 | −0.945706 | −0.472853 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(728\) | −3.71945 | − | 11.4473i | −0.137852 | − | 0.424265i | ||||
\(729\) | 19.9268 | + | 14.4777i | 0.738031 | + | 0.536211i | ||||
\(730\) | −2.37192 | + | 1.72330i | −0.0877889 | + | 0.0637823i | ||||
\(731\) | 3.23509 | − | 9.95657i | 0.119654 | − | 0.368257i | ||||
\(732\) | −2.45034 | + | 7.54137i | −0.0905672 | + | 0.278737i | ||||
\(733\) | 29.2884 | − | 21.2793i | 1.08179 | − | 0.785968i | 0.103797 | − | 0.994598i | \(-0.466901\pi\) |
0.977994 | + | 0.208631i | \(0.0669007\pi\) | |||||||
\(734\) | 33.9285 | + | 24.6505i | 1.25232 | + | 0.909866i | ||||
\(735\) | −0.104347 | − | 0.321148i | −0.00384891 | − | 0.0118457i | ||||
\(736\) | 105.656 | 3.89452 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 86.0111 | 3.16611 | ||||||||
\(739\) | −1.87268 | − | 5.76351i | −0.0688876 | − | 0.212014i | 0.910686 | − | 0.413098i | \(-0.135553\pi\) |
−0.979574 | + | 0.201084i | \(0.935553\pi\) | |||||||
\(740\) | 33.5323 | + | 24.3627i | 1.23267 | + | 0.895590i | ||||
\(741\) | −0.451264 | + | 0.327862i | −0.0165776 | + | 0.0120443i | ||||
\(742\) | −8.93498 | + | 27.4990i | −0.328013 | + | 1.00952i | ||||
\(743\) | 11.2133 | − | 34.5109i | 0.411375 | − | 1.26608i | −0.504078 | − | 0.863658i | \(-0.668168\pi\) |
0.915453 | − | 0.402425i | \(-0.131832\pi\) | |||||||
\(744\) | −1.72743 | + | 1.25505i | −0.0633308 | + | 0.0460125i | ||||
\(745\) | 3.61301 | + | 2.62501i | 0.132371 | + | 0.0961728i | ||||
\(746\) | −15.1370 | − | 46.5868i | −0.554204 | − | 1.70567i | ||||
\(747\) | −40.2024 | −1.47093 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.7228 | −0.866812 | ||||||||
\(750\) | −0.178763 | − | 0.550175i | −0.00652749 | − | 0.0200896i | ||||
\(751\) | 12.7287 | + | 9.24791i | 0.464475 | + | 0.337461i | 0.795284 | − | 0.606237i | \(-0.207322\pi\) |
−0.330809 | + | 0.943698i | \(0.607322\pi\) | |||||||
\(752\) | −85.1925 | + | 61.8959i | −3.10665 | + | 2.25711i | ||||
\(753\) | −1.87609 | + | 5.77402i | −0.0683687 | + | 0.210417i | ||||
\(754\) | −2.48680 | + | 7.65357i | −0.0905638 | + | 0.278727i | ||||
\(755\) | −9.31452 | + | 6.76739i | −0.338990 | + | 0.246291i | ||||
\(756\) | 13.0561 | + | 9.48583i | 0.474847 | + | 0.344996i | ||||
\(757\) | −7.76847 | − | 23.9089i | −0.282350 | − | 0.868984i | −0.987180 | − | 0.159608i | \(-0.948977\pi\) |
0.704830 | − | 0.709376i | \(-0.251023\pi\) | |||||||
\(758\) | −5.19442 | −0.188670 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.0712 | 1.74372 | ||||||||
\(761\) | −4.78078 | − | 14.7137i | −0.173303 | − | 0.533372i | 0.826249 | − | 0.563305i | \(-0.190471\pi\) |
−0.999552 | + | 0.0299332i | \(0.990471\pi\) | |||||||
\(762\) | 3.80111 | + | 2.76167i | 0.137700 | + | 0.100045i | ||||
\(763\) | −22.7279 | + | 16.5128i | −0.822804 | + | 0.597802i | ||||
\(764\) | −4.71855 | + | 14.5222i | −0.170711 | + | 0.525394i | ||||
\(765\) | 2.21163 | − | 6.80669i | 0.0799616 | − | 0.246096i | ||||
\(766\) | 11.8069 | − | 8.57825i | 0.426602 | − | 0.309945i | ||||
\(767\) | −2.78480 | − | 2.02328i | −0.100553 | − | 0.0730564i | ||||
\(768\) | −3.50704 | − | 10.7935i | −0.126549 | − | 0.389479i | ||||
\(769\) | 17.3220 | 0.624647 | 0.312323 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312323 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.82733 | 0.209866 | ||||||||
\(772\) | 20.1856 | + | 62.1249i | 0.726496 | + | 2.23592i | ||||
\(773\) | 18.3639 | + | 13.3422i | 0.660505 | + | 0.479885i | 0.866833 | − | 0.498598i | \(-0.166152\pi\) |
−0.206329 | + | 0.978483i | \(0.566152\pi\) | |||||||
\(774\) | −28.3748 | + | 20.6155i | −1.01991 | + | 0.741008i | ||||
\(775\) | 0.322743 | − | 0.993301i | 0.0115933 | − | 0.0356804i | ||||
\(776\) | −14.2661 | + | 43.9065i | −0.512123 | + | 1.57615i | ||||
\(777\) | −2.96693 | + | 2.15560i | −0.106438 | + | 0.0773317i | ||||
\(778\) | −59.5731 | − | 43.2824i | −2.13580 | − | 1.55175i | ||||
\(779\) | 16.2358 | + | 49.9686i | 0.581708 | + | 1.79031i | ||||
\(780\) | −0.622906 | −0.0223036 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 30.1363 | 1.07767 | ||||||||
\(783\) | −2.12927 | − | 6.55322i | −0.0760940 | − | 0.234193i | ||||
\(784\) | 20.1663 | + | 14.6516i | 0.720223 | + | 0.523273i | ||||
\(785\) | −4.78223 | + | 3.47449i | −0.170685 | + | 0.124010i | ||||
\(786\) | 1.03657 | − | 3.19025i | 0.0369734 | − | 0.113792i | ||||
\(787\) | 0.958331 | − | 2.94944i | 0.0341608 | − | 0.105136i | −0.932522 | − | 0.361113i | \(-0.882397\pi\) |
0.966683 | + | 0.255977i | \(0.0823970\pi\) | |||||||
\(788\) | 29.1478 | − | 21.1772i | 1.03835 | − | 0.754405i | ||||
\(789\) | 0.534236 | + | 0.388145i | 0.0190193 | + | 0.0138183i | ||||
\(790\) | 3.94126 | + | 12.1300i | 0.140224 | + | 0.431564i | ||||
\(791\) | 25.1918 | 0.895716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.63093 | −0.128938 | ||||||||
\(794\) | −26.8007 | − | 82.4840i | −0.951121 | − | 2.92725i | ||||
\(795\) | 0.773082 | + | 0.561677i | 0.0274184 | + | 0.0199206i | ||||
\(796\) | −107.266 | + | 77.9336i | −3.80196 | + | 2.76228i | ||||
\(797\) | −5.89971 | + | 18.1574i | −0.208978 | + | 0.643170i | 0.790548 | + | 0.612400i | \(0.209796\pi\) |
−0.999527 | + | 0.0307695i | \(0.990204\pi\) | |||||||
\(798\) | −2.05816 | + | 6.33437i | −0.0728581 | + | 0.224234i | ||||
\(799\) | −13.2599 | + | 9.63387i | −0.469101 | + | 0.340822i | ||||
\(800\) | 18.8522 | + | 13.6969i | 0.666526 | + | 0.484260i | ||||
\(801\) | −11.6127 | − | 35.7403i | −0.410315 | − | 1.26282i | ||||
\(802\) | 8.60855 | 0.303978 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.841051 | −0.0296616 | ||||||||
\(805\) | −3.25521 | − | 10.0185i | −0.114731 | − | 0.353106i | ||||
\(806\) | −1.23864 | − | 0.899925i | −0.0436292 | − | 0.0316985i | ||||
\(807\) | 3.06961 | − | 2.23020i | 0.108055 | − | 0.0785068i | ||||
\(808\) | 19.7196 | − | 60.6907i | 0.693734 | − | 2.13509i | ||||
\(809\) | 1.38098 | − | 4.25023i | 0.0485528 | − | 0.149430i | −0.923841 | − | 0.382777i | \(-0.874968\pi\) |
0.972394 | + | 0.233347i | \(0.0749678\pi\) | |||||||
\(810\) | −19.1022 | + | 13.8785i | −0.671182 | + | 0.487642i | ||||
\(811\) | 3.93728 | + | 2.86060i | 0.138257 | + | 0.100449i | 0.654764 | − | 0.755834i | \(-0.272768\pi\) |
−0.516507 | + | 0.856283i | \(0.672768\pi\) | |||||||
\(812\) | 21.8112 | + | 67.1280i | 0.765424 | + | 2.35573i | ||||
\(813\) | −4.28523 | −0.150290 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.4990 | −0.823135 | ||||||||
\(816\) | −2.45356 | − | 7.55128i | −0.0858918 | − | 0.264348i | ||||
\(817\) | −17.3328 | − | 12.5930i | −0.606398 | − | 0.440574i | ||||
\(818\) | 0.942735 | − | 0.684937i | 0.0329619 | − | 0.0239483i | ||||
\(819\) | −1.13327 | + | 3.48783i | −0.0395995 | + | 0.121875i | ||||
\(820\) | −18.1311 | + | 55.8017i | −0.633164 | + | 1.94868i | ||||
\(821\) | −13.7573 | + | 9.99529i | −0.480134 | + | 0.348838i | −0.801378 | − | 0.598159i | \(-0.795899\pi\) |
0.321243 | + | 0.946997i | \(0.395899\pi\) | |||||||
\(822\) | −4.14970 | − | 3.01493i | −0.144737 | − | 0.105158i | ||||
\(823\) | −6.72046 | − | 20.6834i | −0.234260 | − | 0.720979i | −0.997219 | − | 0.0745316i | \(-0.976254\pi\) |
0.762958 | − | 0.646448i | \(-0.223746\pi\) | |||||||
\(824\) | −158.664 | −5.52731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.1019 | −1.43012 | ||||||||
\(827\) | −6.39926 | − | 19.6949i | −0.222524 | − | 0.684858i | −0.998534 | − | 0.0541373i | \(-0.982759\pi\) |
0.776009 | − | 0.630721i | \(-0.217241\pi\) | |||||||
\(828\) | −59.9976 | − | 43.5908i | −2.08506 | − | 1.51488i | ||||
\(829\) | −9.14914 | + | 6.64724i | −0.317763 | + | 0.230868i | −0.735220 | − | 0.677828i | \(-0.762921\pi\) |
0.417458 | + | 0.908696i | \(0.362921\pi\) | |||||||
\(830\) | 11.5374 | − | 35.5084i | 0.400468 | − | 1.23251i | ||||
\(831\) | 1.66007 | − | 5.10917i | 0.0575871 | − | 0.177235i | ||||
\(832\) | 14.1919 | − | 10.3110i | 0.492014 | − | 0.357469i | ||||
\(833\) | 3.13880 | + | 2.28047i | 0.108753 | + | 0.0790137i | ||||
\(834\) | −3.01514 | − | 9.27966i | −0.104406 | − | 0.321328i | ||||
\(835\) | −14.2345 | −0.492604 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.31093 | 0.0453122 | ||||||||
\(838\) | −5.69289 | − | 17.5209i | −0.196657 | − | 0.605249i | ||||
\(839\) | 35.1990 | + | 25.5736i | 1.21520 | + | 0.882898i | 0.995693 | − | 0.0927117i | \(-0.0295535\pi\) |
0.219512 | + | 0.975610i | \(0.429554\pi\) | |||||||
\(840\) | −3.84269 | + | 2.79188i | −0.132585 | + | 0.0963289i | ||||
\(841\) | 0.351130 | − | 1.08067i | 0.0121079 | − | 0.0372644i | ||||
\(842\) | −2.35789 | + | 7.25684i | −0.0812583 | + | 0.250087i | ||||
\(843\) | 3.11556 | − | 2.26359i | 0.107306 | − | 0.0779622i | ||||
\(844\) | 75.5151 | + | 54.8649i | 2.59934 | + | 1.88853i | ||||
\(845\) | 3.92908 | + | 12.0925i | 0.135164 | + | 0.415993i | ||||
\(846\) | 54.9102 | 1.88785 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −70.5401 | −2.42236 | ||||||||
\(849\) | 0.719901 | + | 2.21563i | 0.0247069 | + | 0.0760402i | ||||
\(850\) | 5.37724 | + | 3.90679i | 0.184438 | + | 0.134002i | ||||
\(851\) | 27.4731 | − | 19.9604i | 0.941765 | − | 0.684233i | ||||
\(852\) | −1.63416 | + | 5.02943i | −0.0559854 | + | 0.172305i | ||||
\(853\) | −0.344735 | + | 1.06098i | −0.0118035 | + | 0.0363274i | −0.956785 | − | 0.290797i | \(-0.906080\pi\) |
0.944981 | + | 0.327124i | \(0.106080\pi\) | |||||||
\(854\) | −35.0752 | + | 25.4836i | −1.20025 | + | 0.872032i | ||||
\(855\) | −11.8494 | − | 8.60907i | −0.405240 | − | 0.294424i | ||||
\(856\) | −30.6077 | − | 94.2007i | −1.04615 | − | 3.21971i | ||||
\(857\) | 7.80361 | 0.266566 | 0.133283 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133283 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5341 | 1.04181 | 0.520905 | − | 0.853615i | \(-0.325595\pi\) | ||||
0.520905 | + | 0.853615i | \(0.325595\pi\) | |||||||
\(860\) | −7.39339 | − | 22.7545i | −0.252113 | − | 0.775923i | ||||
\(861\) | −4.19993 | − | 3.05143i | −0.143133 | − | 0.103992i | ||||
\(862\) | 35.9659 | − | 26.1307i | 1.22500 | − | 0.890017i | ||||
\(863\) | −1.32556 | + | 4.07965i | −0.0451225 | + | 0.138873i | −0.971080 | − | 0.238756i | \(-0.923260\pi\) |
0.925957 | + | 0.377629i | \(0.123260\pi\) | |||||||
\(864\) | −9.03839 | + | 27.8173i | −0.307492 | + | 0.946364i | ||||
\(865\) | −5.21430 | + | 3.78841i | −0.177292 | + | 0.128810i | ||||
\(866\) | 17.3814 | + | 12.6284i | 0.590646 | + | 0.429129i | ||||
\(867\) | 0.725274 | + | 2.23216i | 0.0246316 | + | 0.0758083i | ||||
\(868\) | −13.4285 | −0.455792 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.17570 | 0.107666 | ||||||||
\(871\) | −0.119009 | − | 0.366271i | −0.00403245 | − | 0.0124106i | ||||
\(872\) | −94.8945 | − | 68.9449i | −3.21353 | − | 2.33477i | ||||
\(873\) | 11.3798 | − | 8.26789i | 0.385147 | − | 0.279826i | ||||
\(874\) | 19.0581 | − | 58.6549i | 0.644651 | − | 1.98403i | ||||
\(875\) | 0.717944 | − | 2.20960i | 0.0242709 | − | 0.0746982i | ||||
\(876\) | 1.00788 | − | 0.732270i | 0.0340532 | − | 0.0247411i | ||||
\(877\) | −9.19401 | − | 6.67984i | −0.310460 | − | 0.225562i | 0.421634 | − | 0.906766i | \(-0.361457\pi\) |
−0.732094 | + | 0.681204i | \(0.761457\pi\) | |||||||
\(878\) | −17.5878 | − | 54.1296i | −0.593559 | − | 1.82679i | ||||
\(879\) | −5.71977 | −0.192923 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3277 | −0.381639 | −0.190820 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190820 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(882\) | −4.01661 | − | 12.3619i | −0.135246 | − | 0.416245i | ||||
\(883\) | −25.3127 | − | 18.3908i | −0.851841 | − | 0.618899i | 0.0738118 | − | 0.997272i | \(-0.476484\pi\) |
−0.925653 | + | 0.378373i | \(0.876484\pi\) | |||||||
\(884\) | 5.79012 | − | 4.20677i | 0.194743 | − | 0.141489i | ||||
\(885\) | −0.419760 | + | 1.29189i | −0.0141101 | + | 0.0434263i | ||||
\(886\) | −4.49767 | + | 13.8424i | −0.151102 | + | 0.465045i | ||||
\(887\) | 22.8806 | − | 16.6237i | 0.768254 | − | 0.558169i | −0.133177 | − | 0.991092i | \(-0.542518\pi\) |
0.901431 | + | 0.432923i | \(0.142518\pi\) | |||||||
\(888\) | −12.3877 | − | 9.00016i | −0.415702 | − | 0.302025i | ||||
\(889\) | 5.83108 | + | 17.9462i | 0.195568 | + | 0.601897i | ||||
\(890\) | 34.8998 | 1.16984 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −138.448 | −4.63558 | ||||||||
\(893\) | 10.3651 | + | 31.9004i | 0.346854 | + | 1.06751i | ||||
\(894\) | −2.09009 | − | 1.51854i | −0.0699029 | − | 0.0507874i | ||||
\(895\) | 13.7365 | − | 9.98018i | 0.459162 | − | 0.333601i | ||||
\(896\) | 31.2675 | − | 96.2314i | 1.04457 | − | 3.21487i | ||||
\(897\) | −0.157706 | + | 0.485370i | −0.00526566 | + | 0.0162060i | ||||
\(898\) | −66.6250 | + | 48.4059i | −2.22331 | + | 1.61533i | ||||
\(899\) | 4.63849 | + | 3.37006i | 0.154702 | + | 0.112398i | ||||
\(900\) | −5.05440 | − | 15.5559i | −0.168480 | − | 0.518529i | ||||
\(901\) | −10.9793 | −0.365774 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.11692 | 0.0704467 | ||||||||
\(904\) | 32.5029 | + | 100.034i | 1.08103 | + | 3.32707i | ||||
\(905\) | 3.63220 | + | 2.63895i | 0.120739 | + | 0.0877217i | ||||
\(906\) | 5.38834 | − | 3.91486i | 0.179016 | − | 0.130062i | ||||
\(907\) | 10.3881 | − | 31.9713i | 0.344931 | − | 1.06159i | −0.616690 | − | 0.787206i | \(-0.711527\pi\) |
0.961621 | − | 0.274382i | \(-0.0884733\pi\) | |||||||
\(908\) | 6.85650 | − | 21.1021i | 0.227541 | − | 0.700299i | ||||
\(909\) | −15.7299 | + | 11.4285i | −0.521729 | + | 0.379058i | ||||
\(910\) | −2.75536 | − | 2.00189i | −0.0913394 | − | 0.0663619i | ||||
\(911\) | 2.32722 | + | 7.16245i | 0.0771043 | + | 0.237302i | 0.982178 | − | 0.187951i | \(-0.0601848\pi\) |
−0.905074 | + | 0.425254i | \(0.860185\pi\) | |||||||
\(912\) | −16.2488 | −0.538053 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −102.968 | −3.40587 | ||||||||
\(915\) | 0.442774 | + | 1.36272i | 0.0146377 | + | 0.0450501i | ||||
\(916\) | 77.6011 | + | 56.3805i | 2.56401 | + | 1.86286i | ||||
\(917\) | 10.8991 | − | 7.91863i | 0.359919 | − | 0.261496i | ||||
\(918\) | −2.57803 | + | 7.93436i | −0.0850876 | + | 0.261873i | ||||
\(919\) | 12.3738 | − | 38.0826i | 0.408174 | − | 1.25623i | −0.510042 | − | 0.860150i | \(-0.670370\pi\) |
0.918216 | − | 0.396080i | \(-0.129630\pi\) | |||||||
\(920\) | 35.5825 | − | 25.8522i | 1.17312 | − | 0.852321i | ||||
\(921\) | 2.00147 | + | 1.45415i | 0.0659508 | + | 0.0479160i | ||||
\(922\) | −13.3870 | − | 41.2010i | −0.440878 | − | 1.35688i | ||||
\(923\) | −2.42151 | −0.0797050 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48965 | 0.246258 | ||||||||
\(926\) | 14.0522 | + | 43.2483i | 0.461785 | + | 1.42123i | ||||
\(927\) | 39.1100 | + | 28.4151i | 1.28454 | + | 0.933275i | ||||
\(928\) | −103.492 | + | 75.1914i | −3.39729 | + | 2.46828i | ||||
\(929\) | 15.8651 | − | 48.8279i | 0.520519 | − | 1.60199i | −0.252492 | − | 0.967599i | \(-0.581250\pi\) |
0.773011 | − | 0.634393i | \(-0.218750\pi\) | |||||||
\(930\) | −0.186703 | + | 0.574613i | −0.00612223 | + | 0.0188423i | ||||
\(931\) | 6.42350 | − | 4.66695i | 0.210522 | − | 0.152953i | ||||
\(932\) | −9.45826 | − | 6.87182i | −0.309815 | − | 0.225094i | ||||
\(933\) | −0.693059 | − | 2.13302i | −0.0226897 | − | 0.0698318i | ||||
\(934\) | −10.1570 | −0.332346 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.3120 | −0.500488 | ||||||||
\(937\) | −11.0786 | − | 34.0964i | −0.361922 | − | 1.11388i | −0.951886 | − | 0.306451i | \(-0.900858\pi\) |
0.589965 | − | 0.807429i | \(-0.299142\pi\) | |||||||
\(938\) | −3.72030 | − | 2.70296i | −0.121472 | − | 0.0882547i | ||||
\(939\) | −4.63445 | + | 3.36712i | −0.151239 | + | 0.109882i | ||||
\(940\) | −11.5750 | + | 35.6243i | −0.377536 | + | 1.16194i | ||||
\(941\) | −0.187638 | + | 0.577491i | −0.00611683 | + | 0.0188257i | −0.954068 | − | 0.299589i | \(-0.903150\pi\) |
0.947952 | + | 0.318415i | \(0.103150\pi\) | |||||||
\(942\) | 2.76647 | − | 2.00995i | 0.0901363 | − | 0.0654879i | ||||
\(943\) | 38.8904 | + | 28.2555i | 1.26645 | + | 0.920126i | ||||
\(944\) | −30.9863 | − | 95.3659i | −1.00852 | − | 3.10389i | ||||
\(945\) | 2.91616 | 0.0948628 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.3851 | −0.857401 | −0.428701 | − | 0.903447i | \(-0.641028\pi\) | ||||
−0.428701 | + | 0.903447i | \(0.641028\pi\) | |||||||
\(948\) | −1.67473 | − | 5.15429i | −0.0543927 | − | 0.167403i | ||||
\(949\) | 0.461513 | + | 0.335309i | 0.0149814 | + | 0.0108846i | ||||
\(950\) | 11.0044 | − | 7.99518i | 0.357031 | − | 0.259398i | ||||
\(951\) | −0.324288 | + | 0.998056i | −0.0105158 | + | 0.0323642i | ||||
\(952\) | 16.8642 | − | 51.9028i | 0.546573 | − | 1.68218i | ||||
\(953\) | 28.6064 | − | 20.7837i | 0.926651 | − | 0.673252i | −0.0185193 | − | 0.999829i | \(-0.505895\pi\) |
0.945171 | + | 0.326577i | \(0.105895\pi\) | |||||||
\(954\) | 29.7580 | + | 21.6205i | 0.963451 | + | 0.699988i | ||||
\(955\) | 0.852636 | + | 2.62414i | 0.0275906 | + | 0.0849153i | ||||
\(956\) | −132.457 | −4.28398 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.47093 | −0.112141 | ||||||||
\(959\) | −6.36582 | − | 19.5920i | −0.205563 | − | 0.632658i | ||||
\(960\) | −5.60042 | − | 4.06894i | −0.180753 | − | 0.131325i | ||||
\(961\) | 24.1970 | − | 17.5802i | 0.780550 | − | 0.567103i | ||||
\(962\) | 3.39279 | − | 10.4419i | 0.109388 | − | 0.336662i | ||||
\(963\) | −9.32574 | + | 28.7017i | −0.300518 | + | 0.924899i | ||||
\(964\) | 64.9787 | − | 47.2098i | 2.09282 | − | 1.52052i | ||||
\(965\) | 9.54932 | + | 6.93799i | 0.307403 | + | 0.223342i | ||||
\(966\) | 1.88310 | + | 5.79558i | 0.0605877 | + | 0.186470i | ||||
\(967\) | −3.86872 | −0.124410 | −0.0622048 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622048 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.52907 | −0.0812455 | ||||||||
\(970\) | 4.03673 | + | 12.4238i | 0.129612 | + | 0.398904i | ||||
\(971\) | −19.5034 | − | 14.1701i | −0.625895 | − | 0.454739i | 0.229081 | − | 0.973407i | \(-0.426428\pi\) |
−0.854976 | + | 0.518668i | \(0.826428\pi\) | |||||||
\(972\) | 24.9758 | − | 18.1460i | 0.801098 | − | 0.582032i | ||||
\(973\) | 12.1094 | − | 37.2688i | 0.388209 | − | 1.19478i | ||||
\(974\) | −18.3229 | + | 56.3922i | −0.587105 | + | 1.80692i | ||||
\(975\) | −0.0910617 | + | 0.0661602i | −0.00291631 | + | 0.00211882i | ||||
\(976\) | −85.5708 | − | 62.1708i | −2.73905 | − | 1.99004i | ||||
\(977\) | 3.34180 | + | 10.2850i | 0.106914 | + | 0.329047i | 0.990175 | − | 0.139835i | \(-0.0446571\pi\) |
−0.883261 | + | 0.468881i | \(0.844657\pi\) | |||||||
\(978\) | 13.5939 | 0.434685 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.86675 | 0.283238 | ||||||||
\(981\) | 11.0438 | + | 33.9893i | 0.352601 | + | 1.08520i | ||||
\(982\) | 56.7080 | + | 41.2007i | 1.80962 | + | 1.31477i | ||||
\(983\) | 31.3158 | − | 22.7522i | 0.998818 | − | 0.725684i | 0.0369838 | − | 0.999316i | \(-0.488225\pi\) |
0.961834 | + | 0.273632i | \(0.0882250\pi\) | |||||||
\(984\) | 6.69805 | − | 20.6145i | 0.213526 | − | 0.657166i | ||||
\(985\) | 2.01181 | − | 6.19171i | 0.0641015 | − | 0.197284i | ||||
\(986\) | −29.5192 | + | 21.4469i | −0.940081 | + | 0.683009i | ||||
\(987\) | −2.68127 | − | 1.94806i | −0.0853458 | − | 0.0620074i | ||||
\(988\) | −4.52606 | − | 13.9298i | −0.143993 | − | 0.443165i | ||||
\(989\) | −19.6022 | −0.623314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.4533 | 1.95213 | 0.976064 | − | 0.217485i | \(-0.0697854\pi\) | ||||
0.976064 | + | 0.217485i | \(0.0697854\pi\) | |||||||
\(992\) | −7.52076 | − | 23.1465i | −0.238784 | − | 0.734902i | ||||
\(993\) | 1.28813 | + | 0.935878i | 0.0408774 | + | 0.0296992i | ||||
\(994\) | −23.3921 | + | 16.9953i | −0.741951 | + | 0.539059i | ||||
\(995\) | −7.40362 | + | 22.7860i | −0.234710 | + | 0.722364i | ||||
\(996\) | −4.90248 | + | 15.0883i | −0.155341 | + | 0.478091i | ||||
\(997\) | 31.0158 | − | 22.5343i | 0.982281 | − | 0.713669i | 0.0240639 | − | 0.999710i | \(-0.492339\pi\) |
0.958217 | + | 0.286041i | \(0.0923395\pi\) | |||||||
\(998\) | 54.0972 | + | 39.3039i | 1.71242 | + | 1.24414i | ||||
\(999\) | 2.90501 | + | 8.94071i | 0.0919105 | + | 0.282871i |
(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 | 605.2.g.o.511.1 | 12 | ||
11.2 | odd | 10 | 605.2.g.p.251.3 | 12 | |||
11.3 | even | 5 | 605.2.a.h.1.1 | yes | 3 | ||
11.4 | even | 5 | inner | 605.2.g.o.366.3 | 12 | ||
11.5 | even | 5 | inner | 605.2.g.o.81.3 | 12 | ||
11.6 | odd | 10 | 605.2.g.p.81.1 | 12 | |||
11.7 | odd | 10 | 605.2.g.p.366.1 | 12 | |||
11.8 | odd | 10 | 605.2.a.g.1.3 | ✓ | 3 | ||
11.9 | even | 5 | inner | 605.2.g.o.251.1 | 12 | ||
11.10 | odd | 2 | 605.2.g.p.511.3 | 12 | |||
33.8 | even | 10 | 5445.2.a.bd.1.1 | 3 | |||
33.14 | odd | 10 | 5445.2.a.bb.1.3 | 3 | |||
44.3 | odd | 10 | 9680.2.a.cb.1.2 | 3 | |||
44.19 | even | 10 | 9680.2.a.bz.1.2 | 3 | |||
55.14 | even | 10 | 3025.2.a.p.1.3 | 3 | |||
55.19 | odd | 10 | 3025.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.g.1.3 | ✓ | 3 | 11.8 | odd | 10 | ||
605.2.a.h.1.1 | yes | 3 | 11.3 | even | 5 | ||
605.2.g.o.81.3 | 12 | 11.5 | even | 5 | inner | ||
605.2.g.o.251.1 | 12 | 11.9 | even | 5 | inner | ||
605.2.g.o.366.3 | 12 | 11.4 | even | 5 | inner | ||
605.2.g.o.511.1 | 12 | 1.1 | even | 1 | trivial | ||
605.2.g.p.81.1 | 12 | 11.6 | odd | 10 | |||
605.2.g.p.251.3 | 12 | 11.2 | odd | 10 | |||
605.2.g.p.366.1 | 12 | 11.7 | odd | 10 | |||
605.2.g.p.511.3 | 12 | 11.10 | odd | 2 | |||
3025.2.a.p.1.3 | 3 | 55.14 | even | 10 | |||
3025.2.a.u.1.1 | 3 | 55.19 | odd | 10 | |||
5445.2.a.bb.1.3 | 3 | 33.14 | odd | 10 | |||
5445.2.a.bd.1.1 | 3 | 33.8 | even | 10 | |||
9680.2.a.bz.1.2 | 3 | 44.19 | even | 10 | |||
9680.2.a.cb.1.2 | 3 | 44.3 | odd | 10 |