Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 149.5 | ||
Character | \(\chi\) | \(=\) | 950.149 |
Dual form | 950.2.u.g.899.5 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.642788 | − | 0.766044i | 0.454519 | − | 0.541675i | ||||
\(3\) | 0.197144 | + | 0.541649i | 0.113821 | + | 0.312721i | 0.983503 | − | 0.180892i | \(-0.0578983\pi\) |
−0.869682 | + | 0.493613i | \(0.835676\pi\) | |||||||
\(4\) | −0.173648 | − | 0.984808i | −0.0868241 | − | 0.492404i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.541649 | + | 0.197144i | 0.221127 | + | 0.0804837i | ||||
\(7\) | −4.21251 | + | 2.43209i | −1.59218 | + | 0.919245i | −0.599247 | + | 0.800564i | \(0.704533\pi\) |
−0.992932 | + | 0.118681i | \(0.962134\pi\) | |||||||
\(8\) | −0.866025 | − | 0.500000i | −0.306186 | − | 0.176777i | ||||
\(9\) | 2.04362 | − | 1.71480i | 0.681205 | − | 0.571599i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.68454 | − | 4.64975i | 0.809418 | − | 1.40195i | −0.103850 | − | 0.994593i | \(-0.533116\pi\) |
0.913268 | − | 0.407360i | \(-0.133550\pi\) | |||||||
\(12\) | 0.499186 | − | 0.288205i | 0.144103 | − | 0.0831977i | ||||
\(13\) | 1.31923 | − | 3.62457i | 0.365890 | − | 1.00527i | −0.611019 | − | 0.791616i | \(-0.709240\pi\) |
0.976909 | − | 0.213658i | \(-0.0685377\pi\) | |||||||
\(14\) | −0.844657 | + | 4.79029i | −0.225744 | + | 1.28026i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.939693 | + | 0.342020i | −0.234923 | + | 0.0855050i | ||||
\(17\) | −0.901248 | + | 1.07407i | −0.218585 | + | 0.260499i | −0.864183 | − | 0.503178i | \(-0.832164\pi\) |
0.645598 | + | 0.763678i | \(0.276608\pi\) | |||||||
\(18\) | − | 2.66775i | − | 0.628795i | ||||||
\(19\) | −4.35299 | + | 0.226908i | −0.998644 | + | 0.0520563i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.14781 | − | 1.80223i | −0.468691 | − | 0.393278i | ||||
\(22\) | −1.83633 | − | 5.04528i | −0.391507 | − | 1.07566i | ||||
\(23\) | 5.25780 | − | 0.927092i | 1.09633 | − | 0.193312i | 0.403902 | − | 0.914802i | \(-0.367654\pi\) |
0.692425 | + | 0.721490i | \(0.256543\pi\) | |||||||
\(24\) | 0.100093 | − | 0.567654i | 0.0204313 | − | 0.115872i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.92859 | − | 3.34042i | −0.378228 | − | 0.655110i | ||||
\(27\) | 2.82926 | + | 1.63348i | 0.544492 | + | 0.314363i | ||||
\(28\) | 3.12664 | + | 3.72618i | 0.590879 | + | 0.704183i | ||||
\(29\) | 2.78364 | − | 2.33575i | 0.516908 | − | 0.433738i | −0.346644 | − | 0.937997i | \(-0.612679\pi\) |
0.863552 | + | 0.504259i | \(0.168234\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.10189 | − | 7.10468i | −0.736721 | − | 1.27604i | −0.953964 | − | 0.299920i | \(-0.903040\pi\) |
0.217244 | − | 0.976117i | \(-0.430293\pi\) | |||||||
\(32\) | −0.342020 | + | 0.939693i | −0.0604612 | + | 0.166116i | ||||
\(33\) | 3.04777 | + | 0.537405i | 0.530549 | + | 0.0935501i | ||||
\(34\) | 0.243471 | + | 1.38079i | 0.0417549 | + | 0.236804i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.04362 | − | 1.71480i | −0.340603 | − | 0.285800i | ||||
\(37\) | − | 10.4594i | − | 1.71951i | −0.510706 | − | 0.859755i | \(-0.670616\pi\) | ||
0.510706 | − | 0.859755i | \(-0.329384\pi\) | |||||||
\(38\) | −2.62423 | + | 3.48044i | −0.425706 | + | 0.564601i | ||||
\(39\) | 2.22332 | 0.356016 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.79322 | − | 0.652678i | 0.280054 | − | 0.101931i | −0.198175 | − | 0.980167i | \(-0.563501\pi\) |
0.478228 | + | 0.878236i | \(0.341279\pi\) | |||||||
\(42\) | −2.76117 | + | 0.486869i | −0.426058 | + | 0.0751256i | ||||
\(43\) | −1.45618 | − | 0.256764i | −0.222065 | − | 0.0391561i | 0.0615084 | − | 0.998107i | \(-0.480409\pi\) |
−0.283574 | + | 0.958950i | \(0.591520\pi\) | |||||||
\(44\) | −5.04528 | − | 1.83633i | −0.760604 | − | 0.276837i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.66945 | − | 4.62363i | 0.393590 | − | 0.681717i | ||||
\(47\) | −2.00570 | − | 2.39030i | −0.292561 | − | 0.348661i | 0.599664 | − | 0.800252i | \(-0.295301\pi\) |
−0.892225 | + | 0.451591i | \(0.850857\pi\) | |||||||
\(48\) | −0.370510 | − | 0.441556i | −0.0534785 | − | 0.0637331i | ||||
\(49\) | 8.33016 | − | 14.4283i | 1.19002 | − | 2.06118i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.759442 | − | 0.276414i | −0.106343 | − | 0.0387058i | ||||
\(52\) | −3.79858 | − | 0.669793i | −0.526769 | − | 0.0928835i | ||||
\(53\) | −1.77266 | + | 0.312568i | −0.243494 | + | 0.0429346i | −0.294063 | − | 0.955786i | \(-0.595008\pi\) |
0.0505691 | + | 0.998721i | \(0.483896\pi\) | |||||||
\(54\) | 3.06993 | − | 1.11736i | 0.417765 | − | 0.152054i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.86419 | 0.650004 | ||||||||
\(57\) | −0.981070 | − | 2.31306i | −0.129946 | − | 0.306372i | ||||
\(58\) | − | 3.63378i | − | 0.477139i | ||||||
\(59\) | 5.61133 | + | 4.70846i | 0.730532 | + | 0.612990i | 0.930277 | − | 0.366859i | \(-0.119567\pi\) |
−0.199744 | + | 0.979848i | \(0.564011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.40916 | + | 7.99176i | 0.180425 | + | 1.02324i | 0.931694 | + | 0.363244i | \(0.118331\pi\) |
−0.751269 | + | 0.659996i | \(0.770558\pi\) | |||||||
\(62\) | −8.07914 | − | 1.42457i | −1.02605 | − | 0.180921i | ||||
\(63\) | −4.43820 | + | 12.1939i | −0.559161 | + | 1.53628i | ||||
\(64\) | 0.500000 | + | 0.866025i | 0.0625000 | + | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.37075 | − | 1.98929i | 0.291819 | − | 0.244865i | ||||
\(67\) | 5.42827 | + | 6.46916i | 0.663169 | + | 0.790334i | 0.987837 | − | 0.155494i | \(-0.0496970\pi\) |
−0.324668 | + | 0.945828i | \(0.605253\pi\) | |||||||
\(68\) | 1.21425 | + | 0.701047i | 0.147249 | + | 0.0850144i | ||||
\(69\) | 1.53870 | + | 2.66511i | 0.185238 | + | 0.320842i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.04647 | − | 5.93485i | 0.124194 | − | 0.704337i | −0.857590 | − | 0.514334i | \(-0.828039\pi\) |
0.981783 | − | 0.190003i | \(-0.0608498\pi\) | |||||||
\(72\) | −2.62722 | + | 0.463250i | −0.309621 | + | 0.0545945i | ||||
\(73\) | −0.436515 | − | 1.19931i | −0.0510902 | − | 0.140369i | 0.911523 | − | 0.411249i | \(-0.134907\pi\) |
−0.962613 | + | 0.270880i | \(0.912685\pi\) | |||||||
\(74\) | −8.01234 | − | 6.72316i | −0.931416 | − | 0.781551i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.979350 | + | 4.24746i | 0.112339 | + | 0.487217i | ||||
\(77\) | 26.1162i | 2.97621i | ||||||||
\(78\) | 1.42912 | − | 1.70316i | 0.161816 | − | 0.192845i | ||||
\(79\) | −15.6290 | + | 5.68848i | −1.75840 | + | 0.640004i | −0.999931 | − | 0.0117101i | \(-0.996272\pi\) |
−0.758465 | + | 0.651714i | \(0.774050\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.06275 | − | 6.02717i | 0.118084 | − | 0.669685i | ||||
\(82\) | 0.652678 | − | 1.79322i | 0.0720762 | − | 0.198028i | ||||
\(83\) | −12.5236 | + | 7.23049i | −1.37464 | + | 0.793649i | −0.991508 | − | 0.130044i | \(-0.958488\pi\) |
−0.383133 | + | 0.923693i | \(0.625155\pi\) | |||||||
\(84\) | −1.40188 | + | 2.42814i | −0.152958 | + | 0.264931i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.13271 | + | 0.950453i | −0.122143 | + | 0.102490i | ||||
\(87\) | 1.81393 | + | 1.04727i | 0.194474 | + | 0.112280i | ||||
\(88\) | −4.64975 | + | 2.68454i | −0.495665 | + | 0.286172i | ||||
\(89\) | 9.02905 | + | 3.28630i | 0.957077 | + | 0.348348i | 0.772887 | − | 0.634543i | \(-0.218812\pi\) |
0.184190 | + | 0.982891i | \(0.441034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.25800 | + | 18.4770i | 0.341531 | + | 1.93692i | ||||
\(92\) | −1.82601 | − | 5.01693i | −0.190375 | − | 0.523051i | ||||
\(93\) | 3.03958 | − | 3.62243i | 0.315189 | − | 0.375628i | ||||
\(94\) | −3.12031 | −0.321836 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.576411 | −0.0588297 | ||||||||
\(97\) | 3.90758 | − | 4.65687i | 0.396755 | − | 0.472834i | −0.530273 | − | 0.847827i | \(-0.677911\pi\) |
0.927028 | + | 0.374993i | \(0.122355\pi\) | |||||||
\(98\) | −5.69817 | − | 15.6556i | −0.575602 | − | 1.58145i | ||||
\(99\) | −2.48722 | − | 14.1057i | −0.249975 | − | 1.41768i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.17995 | − | 0.429466i | −0.117409 | − | 0.0427335i | 0.282647 | − | 0.959224i | \(-0.408787\pi\) |
−0.400057 | + | 0.916490i | \(0.631010\pi\) | |||||||
\(102\) | −0.699906 | + | 0.404091i | −0.0693010 | + | 0.0400109i | ||||
\(103\) | 6.38005 | + | 3.68352i | 0.628645 | + | 0.362948i | 0.780227 | − | 0.625496i | \(-0.215103\pi\) |
−0.151582 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(104\) | −2.95477 | + | 2.47935i | −0.289739 | + | 0.243120i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.900005 | + | 1.55885i | −0.0874162 | + | 0.151409i | ||||
\(107\) | −7.56108 | + | 4.36539i | −0.730957 | + | 0.422018i | −0.818772 | − | 0.574119i | \(-0.805345\pi\) |
0.0878153 | + | 0.996137i | \(0.472011\pi\) | |||||||
\(108\) | 1.11736 | − | 3.06993i | 0.107518 | − | 0.295404i | ||||
\(109\) | −1.41173 | + | 8.00630i | −0.135219 | + | 0.766865i | 0.839488 | + | 0.543378i | \(0.182855\pi\) |
−0.974707 | + | 0.223487i | \(0.928256\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.66531 | − | 2.06200i | 0.537727 | − | 0.195717i | ||||
\(112\) | 3.12664 | − | 3.72618i | 0.295440 | − | 0.352091i | ||||
\(113\) | 4.48210i | 0.421640i | 0.977525 | + | 0.210820i | \(0.0676134\pi\) | ||||
−0.977525 | + | 0.210820i | \(0.932387\pi\) | |||||||
\(114\) | −2.40253 | − | 0.735261i | −0.225017 | − | 0.0688635i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.78364 | − | 2.33575i | −0.258454 | − | 0.216869i | ||||
\(117\) | −3.51939 | − | 9.66944i | −0.325368 | − | 0.893940i | ||||
\(118\) | 7.21378 | − | 1.27198i | 0.664082 | − | 0.117096i | ||||
\(119\) | 1.18429 | − | 6.71643i | 0.108564 | − | 0.615694i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.91346 | − | 15.4386i | −0.810314 | − | 1.40351i | ||||
\(122\) | 7.02784 | + | 4.05753i | 0.636271 | + | 0.367351i | ||||
\(123\) | 0.707045 | + | 0.842623i | 0.0637521 | + | 0.0759768i | ||||
\(124\) | −6.28445 | + | 5.27328i | −0.564361 | + | 0.473555i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.48822 | + | 11.2379i | 0.578017 | + | 1.00115i | ||||
\(127\) | −0.0476033 | + | 0.130789i | −0.00422411 | + | 0.0116057i | −0.941787 | − | 0.336211i | \(-0.890855\pi\) |
0.937563 | + | 0.347816i | \(0.113077\pi\) | |||||||
\(128\) | 0.984808 | + | 0.173648i | 0.0870455 | + | 0.0153485i | ||||
\(129\) | −0.148001 | − | 0.839357i | −0.0130308 | − | 0.0739013i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.52200 | + | 7.98991i | 0.831941 | + | 0.698082i | 0.955736 | − | 0.294226i | \(-0.0950620\pi\) |
−0.123795 | + | 0.992308i | \(0.539506\pi\) | |||||||
\(132\) | − | 3.09479i | − | 0.269367i | ||||||
\(133\) | 17.7851 | − | 11.5427i | 1.54217 | − | 1.00088i | ||||
\(134\) | 8.44489 | 0.729528 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.31754 | − | 0.479544i | 0.112978 | − | 0.0411206i | ||||
\(137\) | 14.1631 | − | 2.49734i | 1.21004 | − | 0.213362i | 0.468004 | − | 0.883726i | \(-0.344973\pi\) |
0.742032 | + | 0.670364i | \(0.233862\pi\) | |||||||
\(138\) | 3.03065 | + | 0.534386i | 0.257986 | + | 0.0454899i | ||||
\(139\) | 16.7746 | + | 6.10544i | 1.42280 | + | 0.517857i | 0.934859 | − | 0.355020i | \(-0.115526\pi\) |
0.487941 | + | 0.872877i | \(0.337748\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.899291 | − | 1.55762i | 0.0757340 | − | 0.131175i | ||||
\(142\) | −3.87370 | − | 4.61650i | −0.325074 | − | 0.387408i | ||||
\(143\) | −13.3118 | − | 15.8644i | −1.11319 | − | 1.32665i | ||||
\(144\) | −1.33388 | + | 2.31034i | −0.111156 | + | 0.192528i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.19931 | − | 0.436515i | −0.0992559 | − | 0.0361262i | ||||
\(147\) | 9.45729 | + | 1.66758i | 0.780024 | + | 0.137539i | ||||
\(148\) | −10.3005 | + | 1.81625i | −0.846694 | + | 0.149295i | ||||
\(149\) | −2.71250 | + | 0.987271i | −0.222217 | + | 0.0808804i | −0.450729 | − | 0.892661i | \(-0.648836\pi\) |
0.228512 | + | 0.973541i | \(0.426614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.01805 | 0.164226 | 0.0821132 | − | 0.996623i | \(-0.473833\pi\) | ||||
0.0821132 | + | 0.996623i | \(0.473833\pi\) | |||||||
\(152\) | 3.88325 | + | 1.97999i | 0.314973 | + | 0.160598i | ||||
\(153\) | 3.74044i | 0.302396i | ||||||||
\(154\) | 20.0061 | + | 16.7871i | 1.61214 | + | 1.35275i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.386076 | − | 2.18954i | −0.0309108 | − | 0.175304i | ||||
\(157\) | −10.8717 | − | 1.91697i | −0.867655 | − | 0.152991i | −0.277936 | − | 0.960600i | \(-0.589650\pi\) |
−0.589719 | + | 0.807609i | \(0.700761\pi\) | |||||||
\(158\) | −5.68848 | + | 15.6290i | −0.452551 | + | 1.24337i | ||||
\(159\) | −0.518772 | − | 0.898540i | −0.0411413 | − | 0.0712589i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.8938 | + | 16.6928i | −1.56785 | + | 1.31558i | ||||
\(162\) | −3.93395 | − | 4.68830i | −0.309081 | − | 0.368348i | ||||
\(163\) | −5.13439 | − | 2.96434i | −0.402157 | − | 0.232185i | 0.285257 | − | 0.958451i | \(-0.407921\pi\) |
−0.687414 | + | 0.726266i | \(0.741254\pi\) | |||||||
\(164\) | −0.954151 | − | 1.65264i | −0.0745067 | − | 0.129049i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.51112 | + | 14.2413i | −0.194901 | + | 1.10534i | ||||
\(167\) | −7.11784 | + | 1.25507i | −0.550795 | + | 0.0971200i | −0.442118 | − | 0.896957i | \(-0.645773\pi\) |
−0.108677 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(168\) | 0.958946 | + | 2.63468i | 0.0739843 | + | 0.203270i | ||||
\(169\) | −1.43852 | − | 1.20707i | −0.110656 | − | 0.0928512i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.50673 | + | 7.92821i | −0.650526 | + | 0.606285i | ||||
\(172\) | 1.47864i | 0.112745i | ||||||||
\(173\) | −3.31585 | + | 3.95167i | −0.252099 | + | 0.300440i | −0.877221 | − | 0.480087i | \(-0.840605\pi\) |
0.625121 | + | 0.780528i | \(0.285049\pi\) | |||||||
\(174\) | 1.96823 | − | 0.716378i | 0.149211 | − | 0.0543085i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.932329 | + | 5.28750i | −0.0702770 | + | 0.398560i | ||||
\(177\) | −1.44409 | + | 3.96761i | −0.108545 | + | 0.298224i | ||||
\(178\) | 8.32122 | − | 4.80426i | 0.623701 | − | 0.360094i | ||||
\(179\) | 4.09186 | − | 7.08730i | 0.305840 | − | 0.529730i | −0.671608 | − | 0.740906i | \(-0.734396\pi\) |
0.977448 | + | 0.211177i | \(0.0677295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.62934 | + | 2.20628i | −0.195437 | + | 0.163991i | −0.735255 | − | 0.677791i | \(-0.762938\pi\) |
0.539818 | + | 0.841782i | \(0.318493\pi\) | |||||||
\(182\) | 16.2484 | + | 9.38103i | 1.20441 | + | 0.695368i | ||||
\(183\) | −4.05092 | + | 2.33880i | −0.299453 | + | 0.172889i | ||||
\(184\) | −5.01693 | − | 1.82601i | −0.369853 | − | 0.134616i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.821137 | − | 4.65690i | −0.0602087 | − | 0.341461i | ||||
\(187\) | 2.57471 | + | 7.07395i | 0.188281 | + | 0.517298i | ||||
\(188\) | −2.00570 | + | 2.39030i | −0.146281 | + | 0.174330i | ||||
\(189\) | −15.8911 | −1.15591 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.77584 | 0.273210 | 0.136605 | − | 0.990626i | \(-0.456381\pi\) | ||||
0.136605 | + | 0.990626i | \(0.456381\pi\) | |||||||
\(192\) | −0.370510 | + | 0.441556i | −0.0267392 | + | 0.0318666i | ||||
\(193\) | 4.16508 | + | 11.4435i | 0.299809 | + | 0.823718i | 0.994531 | + | 0.104440i | \(0.0333050\pi\) |
−0.694722 | + | 0.719278i | \(0.744473\pi\) | |||||||
\(194\) | −1.05563 | − | 5.98676i | −0.0757896 | − | 0.429824i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.6556 | − | 5.69817i | −1.11826 | − | 0.407012i | ||||
\(197\) | 6.23743 | − | 3.60118i | 0.444399 | − | 0.256574i | −0.261063 | − | 0.965322i | \(-0.584073\pi\) |
0.705462 | + | 0.708748i | \(0.250740\pi\) | |||||||
\(198\) | −12.4044 | − | 7.16167i | −0.881541 | − | 0.508958i | ||||
\(199\) | −4.47147 | + | 3.75201i | −0.316974 | + | 0.265973i | −0.787367 | − | 0.616484i | \(-0.788557\pi\) |
0.470393 | + | 0.882457i | \(0.344112\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.43386 | + | 4.21557i | −0.171671 | + | 0.297344i | ||||
\(202\) | −1.08745 | + | 0.627838i | −0.0765125 | + | 0.0441745i | ||||
\(203\) | −6.04534 | + | 16.6094i | −0.424299 | + | 1.16575i | ||||
\(204\) | −0.140339 | + | 0.795903i | −0.00982571 | + | 0.0557244i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.92276 | − | 2.51968i | 0.482332 | − | 0.175554i | ||||
\(207\) | 9.15514 | − | 10.9107i | 0.636327 | − | 0.758344i | ||||
\(208\) | 3.85718i | 0.267448i | ||||||||
\(209\) | −10.6307 | + | 20.8495i | −0.735340 | + | 1.44219i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.17443 | + | 6.85916i | 0.562751 | + | 0.472204i | 0.879231 | − | 0.476395i | \(-0.158057\pi\) |
−0.316481 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(212\) | 0.615640 | + | 1.69146i | 0.0422823 | + | 0.116170i | ||||
\(213\) | 3.42091 | − | 0.603199i | 0.234397 | − | 0.0413305i | ||||
\(214\) | −1.51608 | + | 8.59814i | −0.103637 | + | 0.587757i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.63348 | − | 2.82926i | −0.111144 | − | 0.192507i | ||||
\(217\) | 34.5585 | + | 19.9523i | 2.34598 | + | 1.35445i | ||||
\(218\) | 5.22574 | + | 6.22780i | 0.353932 | + | 0.421800i | ||||
\(219\) | 0.563551 | − | 0.472875i | 0.0380812 | − | 0.0319539i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.70407 | + | 4.68358i | 0.181895 | + | 0.315052i | ||||
\(222\) | 2.06200 | − | 5.66531i | 0.138393 | − | 0.380231i | ||||
\(223\) | 0.0979573 | + | 0.0172725i | 0.00655971 | + | 0.00115665i | 0.176927 | − | 0.984224i | \(-0.443384\pi\) |
−0.170367 | + | 0.985381i | \(0.554495\pi\) | |||||||
\(224\) | −0.844657 | − | 4.79029i | −0.0564360 | − | 0.320065i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.43349 | + | 2.88104i | 0.228392 | + | 0.191644i | ||||
\(227\) | − | 13.8262i | − | 0.917680i | −0.888519 | − | 0.458840i | \(-0.848265\pi\) | ||
0.888519 | − | 0.458840i | \(-0.151735\pi\) | |||||||
\(228\) | −2.10756 | + | 1.36782i | −0.139576 | + | 0.0905864i | ||||
\(229\) | −15.5752 | −1.02924 | −0.514619 | − | 0.857419i | \(-0.672066\pi\) | ||||
−0.514619 | + | 0.857419i | \(0.672066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.1458 | + | 5.14865i | −0.930725 | + | 0.338756i | ||||
\(232\) | −3.57857 | + | 0.630999i | −0.234945 | + | 0.0414271i | ||||
\(233\) | 15.0095 | + | 2.64658i | 0.983307 | + | 0.173384i | 0.642113 | − | 0.766610i | \(-0.278058\pi\) |
0.341193 | + | 0.939993i | \(0.389169\pi\) | |||||||
\(234\) | −9.66944 | − | 3.51939i | −0.632111 | − | 0.230070i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.66253 | − | 6.34369i | 0.238411 | − | 0.412939i | ||||
\(237\) | −6.16232 | − | 7.34396i | −0.400285 | − | 0.477042i | ||||
\(238\) | −4.38384 | − | 5.22446i | −0.284162 | − | 0.338651i | ||||
\(239\) | 8.41167 | − | 14.5694i | 0.544106 | − | 0.942419i | −0.454557 | − | 0.890718i | \(-0.650202\pi\) |
0.998663 | − | 0.0517011i | \(-0.0164643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.55776 | + | 3.11477i | 0.551254 | + | 0.200640i | 0.602604 | − | 0.798041i | \(-0.294130\pi\) |
−0.0513496 | + | 0.998681i | \(0.516352\pi\) | |||||||
\(242\) | −17.5561 | − | 3.09561i | −1.12855 | − | 0.198993i | ||||
\(243\) | 13.1261 | − | 2.31448i | 0.842039 | − | 0.148474i | ||||
\(244\) | 7.62565 | − | 2.77551i | 0.488182 | − | 0.177684i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.09997 | 0.0701313 | ||||||||
\(247\) | −4.92017 | + | 16.0770i | −0.313063 | + | 1.02296i | ||||
\(248\) | 8.20377i | 0.520940i | ||||||||
\(249\) | −6.38533 | − | 5.35793i | −0.404654 | − | 0.339545i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.91829 | + | 16.5504i | 0.184201 | + | 1.04465i | 0.926978 | + | 0.375116i | \(0.122397\pi\) |
−0.742777 | + | 0.669539i | \(0.766492\pi\) | |||||||
\(252\) | 12.7793 | + | 2.25334i | 0.805020 | + | 0.141947i | ||||
\(253\) | 9.80400 | − | 26.9363i | 0.616372 | − | 1.69347i | ||||
\(254\) | 0.0695914 | + | 0.120536i | 0.00436655 | + | 0.00756309i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | − | 0.642788i | 0.0478778 | − | 0.0401742i | ||||
\(257\) | −6.36185 | − | 7.58176i | −0.396841 | − | 0.472937i | 0.530213 | − | 0.847865i | \(-0.322112\pi\) |
−0.927054 | + | 0.374927i | \(0.877668\pi\) | |||||||
\(258\) | −0.738118 | − | 0.426153i | −0.0459532 | − | 0.0265311i | ||||
\(259\) | 25.4382 | + | 44.0602i | 1.58065 | + | 2.73777i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.68335 | − | 9.54674i | 0.104197 | − | 0.590929i | ||||
\(262\) | 12.2412 | − | 2.15846i | 0.756267 | − | 0.133350i | ||||
\(263\) | −7.66554 | − | 21.0609i | −0.472677 | − | 1.29867i | −0.915593 | − | 0.402107i | \(-0.868278\pi\) |
0.442915 | − | 0.896564i | \(-0.353944\pi\) | |||||||
\(264\) | −2.37075 | − | 1.98929i | −0.145909 | − | 0.122432i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.58983 | − | 21.0437i | 0.158793 | − | 1.29027i | ||||
\(267\) | 5.53845i | 0.338948i | ||||||||
\(268\) | 5.42827 | − | 6.46916i | 0.331584 | − | 0.395167i | ||||
\(269\) | 7.02217 | − | 2.55586i | 0.428149 | − | 0.155834i | −0.118952 | − | 0.992900i | \(-0.537953\pi\) |
0.547101 | + | 0.837066i | \(0.315731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.84950 | + | 10.4890i | −0.112349 | + | 0.637163i | 0.875680 | + | 0.482893i | \(0.160414\pi\) |
−0.988029 | + | 0.154271i | \(0.950697\pi\) | |||||||
\(272\) | 0.479544 | − | 1.31754i | 0.0290766 | − | 0.0798874i | ||||
\(273\) | −9.36576 | + | 5.40733i | −0.566842 | + | 0.327266i | ||||
\(274\) | 7.19080 | − | 12.4548i | 0.434412 | − | 0.752424i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.35743 | − | 1.97812i | 0.141900 | − | 0.119069i | ||||
\(277\) | 2.01467 | + | 1.16317i | 0.121050 | + | 0.0698880i | 0.559302 | − | 0.828964i | \(-0.311069\pi\) |
−0.438253 | + | 0.898852i | \(0.644402\pi\) | |||||||
\(278\) | 15.4595 | − | 8.92555i | 0.927200 | − | 0.535319i | ||||
\(279\) | −20.5658 | − | 7.48532i | −1.23124 | − | 0.448135i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.96472 | − | 16.8137i | −0.176860 | − | 1.00302i | −0.935975 | − | 0.352067i | \(-0.885479\pi\) |
0.759115 | − | 0.650957i | \(-0.225632\pi\) | |||||||
\(282\) | −0.615151 | − | 1.69011i | −0.0366317 | − | 0.100645i | ||||
\(283\) | 5.44307 | − | 6.48680i | 0.323557 | − | 0.385600i | −0.579607 | − | 0.814896i | \(-0.696794\pi\) |
0.903164 | + | 0.429296i | \(0.141238\pi\) | |||||||
\(284\) | −6.02641 | −0.357601 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.7095 | −1.22458 | ||||||||
\(287\) | −5.96658 | + | 7.11069i | −0.352196 | + | 0.419731i | ||||
\(288\) | 0.912424 | + | 2.50687i | 0.0537651 | + | 0.147718i | ||||
\(289\) | 2.61065 | + | 14.8057i | 0.153568 | + | 0.870925i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.29275 | + | 1.19846i | 0.193024 | + | 0.0702551i | ||||
\(292\) | −1.10529 | + | 0.638142i | −0.0646824 | + | 0.0373444i | ||||
\(293\) | −2.24512 | − | 1.29622i | −0.131161 | − | 0.0757260i | 0.432984 | − | 0.901402i | \(-0.357461\pi\) |
−0.564145 | + | 0.825676i | \(0.690794\pi\) | |||||||
\(294\) | 7.35647 | − | 6.17281i | 0.429038 | − | 0.360006i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.22969 | + | 9.05808i | −0.303969 | + | 0.526490i | ||||
\(297\) | 15.1905 | − | 8.77025i | 0.881443 | − | 0.508901i | ||||
\(298\) | −0.987271 | + | 2.71250i | −0.0571911 | + | 0.157131i | ||||
\(299\) | 3.57596 | − | 20.2803i | 0.206803 | − | 1.17284i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.75864 | − | 2.45994i | 0.389562 | − | 0.141789i | ||||
\(302\) | 1.29718 | − | 1.54591i | 0.0746441 | − | 0.0889573i | ||||
\(303\) | − | 0.723785i | − | 0.0415804i | ||||||
\(304\) | 4.01286 | − | 1.70203i | 0.230154 | − | 0.0976183i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.86534 | + | 2.40431i | 0.163801 | + | 0.137445i | ||||
\(307\) | 1.40970 | + | 3.87311i | 0.0804557 | + | 0.221050i | 0.973398 | − | 0.229121i | \(-0.0735852\pi\) |
−0.892942 | + | 0.450171i | \(0.851363\pi\) | |||||||
\(308\) | 25.7194 | − | 4.53502i | 1.46550 | − | 0.258407i | ||||
\(309\) | −0.737387 | + | 4.18193i | −0.0419485 | + | 0.237902i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.24153 | − | 2.15040i | −0.0704008 | − | 0.121938i | 0.828676 | − | 0.559728i | \(-0.189094\pi\) |
−0.899077 | + | 0.437791i | \(0.855761\pi\) | |||||||
\(312\) | −1.92545 | − | 1.11166i | −0.109007 | − | 0.0629354i | ||||
\(313\) | −3.45913 | − | 4.12243i | −0.195522 | − | 0.233014i | 0.659372 | − | 0.751817i | \(-0.270822\pi\) |
−0.854894 | + | 0.518803i | \(0.826378\pi\) | |||||||
\(314\) | −8.45667 | + | 7.09599i | −0.477238 | + | 0.400450i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.31600 | + | 14.4037i | 0.467812 | + | 0.810273i | ||||
\(317\) | 6.65753 | − | 18.2914i | 0.373924 | − | 1.02735i | −0.599906 | − | 0.800071i | \(-0.704795\pi\) |
0.973830 | − | 0.227278i | \(-0.0729825\pi\) | |||||||
\(318\) | −1.02178 | − | 0.180168i | −0.0572987 | − | 0.0101033i | ||||
\(319\) | −3.38788 | − | 19.2136i | −0.189685 | − | 1.07576i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.85513 | − | 3.23484i | −0.215172 | − | 0.180551i | ||||
\(322\) | 25.9695i | 1.44722i | ||||||||
\(323\) | 3.67941 | − | 4.87990i | 0.204728 | − | 0.271525i | ||||
\(324\) | −6.12015 | −0.340008 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.57114 | + | 2.02773i | −0.308557 | + | 0.112306i | ||||
\(327\) | −4.61492 | + | 0.813735i | −0.255206 | + | 0.0449996i | ||||
\(328\) | −1.87931 | − | 0.331373i | −0.103768 | − | 0.0182970i | ||||
\(329\) | 14.2625 | + | 5.19111i | 0.786315 | + | 0.286195i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.35511 | − | 16.2035i | 0.514203 | − | 0.890626i | −0.485661 | − | 0.874147i | \(-0.661421\pi\) |
0.999864 | − | 0.0164787i | \(-0.00524557\pi\) | |||||||
\(332\) | 9.29534 | + | 11.0778i | 0.510148 | + | 0.607971i | ||||
\(333\) | −17.9357 | − | 21.3749i | −0.982870 | − | 1.17134i | ||||
\(334\) | −3.61382 | + | 6.25932i | −0.197739 | + | 0.342495i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.63468 | + | 0.958946i | 0.143734 | + | 0.0523148i | ||||
\(337\) | −24.7159 | − | 4.35808i | −1.34636 | − | 0.237400i | −0.546436 | − | 0.837501i | \(-0.684016\pi\) |
−0.799924 | + | 0.600101i | \(0.795127\pi\) | |||||||
\(338\) | −1.84933 | + | 0.326087i | −0.100590 | + | 0.0177368i | ||||
\(339\) | −2.42772 | + | 0.883619i | −0.131856 | + | 0.0479916i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.0466 | −2.38526 | ||||||||
\(342\) | 0.605335 | + | 11.6127i | 0.0327328 | + | 0.627942i | ||||
\(343\) | 46.9896i | 2.53720i | ||||||||
\(344\) | 1.13271 | + | 0.950453i | 0.0610714 | + | 0.0512450i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.895772 | + | 5.08018i | 0.0481570 | + | 0.273112i | ||||
\(347\) | 22.4078 | + | 3.95111i | 1.20292 | + | 0.212107i | 0.738958 | − | 0.673751i | \(-0.235318\pi\) |
0.463957 | + | 0.885857i | \(0.346429\pi\) | |||||||
\(348\) | 0.716378 | − | 1.96823i | 0.0384019 | − | 0.105508i | ||||
\(349\) | 6.58190 | + | 11.4002i | 0.352321 | + | 0.610238i | 0.986656 | − | 0.162820i | \(-0.0520591\pi\) |
−0.634335 | + | 0.773059i | \(0.718726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.65310 | − | 8.09992i | 0.515245 | − | 0.432341i | ||||
\(352\) | 3.45117 | + | 4.11295i | 0.183948 | + | 0.219221i | ||||
\(353\) | −10.6570 | − | 6.15281i | −0.567213 | − | 0.327481i | 0.188822 | − | 0.982011i | \(-0.439533\pi\) |
−0.756036 | + | 0.654530i | \(0.772866\pi\) | |||||||
\(354\) | 2.11112 | + | 3.65657i | 0.112205 | + | 0.194345i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.66850 | − | 9.46254i | 0.0884304 | − | 0.501513i | ||||
\(357\) | 3.87142 | − | 0.682636i | 0.204897 | − | 0.0361290i | ||||
\(358\) | −2.79899 | − | 7.69017i | −0.147931 | − | 0.406438i | ||||
\(359\) | −9.62244 | − | 8.07418i | −0.507853 | − | 0.426139i | 0.352520 | − | 0.935804i | \(-0.385325\pi\) |
−0.860373 | + | 0.509665i | \(0.829769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8970 | − | 1.97546i | 0.994580 | − | 0.103972i | ||||
\(362\) | 3.43236i | 0.180401i | ||||||||
\(363\) | 6.60504 | − | 7.87158i | 0.346675 | − | 0.413151i | ||||
\(364\) | 17.6306 | − | 6.41700i | 0.924093 | − | 0.336342i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.812257 | + | 4.60654i | −0.0424574 | + | 0.240788i | ||||
\(367\) | 0.918156 | − | 2.52261i | 0.0479274 | − | 0.131679i | −0.913420 | − | 0.407019i | \(-0.866568\pi\) |
0.961347 | + | 0.275340i | \(0.0887904\pi\) | |||||||
\(368\) | −4.62363 | + | 2.66945i | −0.241023 | + | 0.139155i | ||||
\(369\) | 2.54544 | − | 4.40883i | 0.132510 | − | 0.229514i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.70717 | − | 5.62798i | 0.348219 | − | 0.292190i | ||||
\(372\) | −4.09521 | − | 2.36437i | −0.212327 | − | 0.122587i | ||||
\(373\) | 16.0582 | − | 9.27119i | 0.831461 | − | 0.480044i | −0.0228917 | − | 0.999738i | \(-0.507287\pi\) |
0.854353 | + | 0.519694i | \(0.173954\pi\) | |||||||
\(374\) | 7.07395 | + | 2.57471i | 0.365785 | + | 0.133135i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.541837 | + | 3.07291i | 0.0279431 | + | 0.158473i | ||||
\(377\) | −4.79381 | − | 13.1709i | −0.246894 | − | 0.678334i | ||||
\(378\) | −10.2146 | + | 12.1733i | −0.525381 | + | 0.626125i | ||||
\(379\) | −11.5855 | −0.595108 | −0.297554 | − | 0.954705i | \(-0.596171\pi\) | ||||
−0.297554 | + | 0.954705i | \(0.596171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0802265 | −0.00411013 | ||||||||
\(382\) | 2.42706 | − | 2.89246i | 0.124179 | − | 0.147991i | ||||
\(383\) | 9.94564 | + | 27.3254i | 0.508199 | + | 1.39626i | 0.883094 | + | 0.469197i | \(0.155457\pi\) |
−0.374895 | + | 0.927067i | \(0.622321\pi\) | |||||||
\(384\) | 0.100093 | + | 0.567654i | 0.00510783 | + | 0.0289680i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.4435 | + | 4.16508i | 0.582457 | + | 0.211997i | ||||
\(387\) | −3.41617 | + | 1.97233i | −0.173654 | + | 0.100259i | ||||
\(388\) | −5.26467 | − | 3.03956i | −0.267273 | − | 0.154310i | ||||
\(389\) | −22.8144 | + | 19.1436i | −1.15674 | + | 0.970618i | −0.999856 | − | 0.0169993i | \(-0.994589\pi\) |
−0.156882 | + | 0.987617i | \(0.550144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.74282 | + | 6.48276i | −0.189283 | + | 0.327847i | ||||
\(392\) | −14.4283 | + | 8.33016i | −0.728737 | + | 0.420737i | ||||
\(393\) | −2.45052 | + | 6.73274i | −0.123612 | + | 0.339622i | ||||
\(394\) | 1.25068 | − | 7.09294i | 0.0630082 | − | 0.357337i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −13.4595 | + | 4.89887i | −0.676367 | + | 0.246178i | ||||
\(397\) | −4.03025 | + | 4.80307i | −0.202273 | + | 0.241059i | −0.857639 | − | 0.514252i | \(-0.828070\pi\) |
0.655367 | + | 0.755311i | \(0.272514\pi\) | |||||||
\(398\) | 5.83709i | 0.292587i | ||||||||
\(399\) | 9.75834 | + | 7.35772i | 0.488528 | + | 0.368347i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.58485 | + | 6.36445i | 0.378769 | + | 0.317825i | 0.812219 | − | 0.583353i | \(-0.198259\pi\) |
−0.433450 | + | 0.901178i | \(0.642704\pi\) | |||||||
\(402\) | 1.66486 | + | 4.57417i | 0.0830357 | + | 0.228139i | ||||
\(403\) | −31.1627 | + | 5.49483i | −1.55233 | + | 0.273717i | ||||
\(404\) | −0.218046 | + | 1.23660i | −0.0108482 | + | 0.0615231i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.83769 | + | 15.3073i | 0.438607 | + | 0.759690i | ||||
\(407\) | −48.6335 | − | 28.0786i | −2.41067 | − | 1.39180i | ||||
\(408\) | 0.519489 | + | 0.619103i | 0.0257185 | + | 0.0306502i | ||||
\(409\) | 23.4859 | − | 19.7070i | 1.16130 | − | 0.974449i | 0.161380 | − | 0.986892i | \(-0.448405\pi\) |
0.999923 | + | 0.0124433i | \(0.00396092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.14486 | + | 7.17910i | 0.204451 | + | 0.354119i | ||||
\(412\) | 2.51968 | − | 6.92276i | 0.124136 | − | 0.341060i | ||||
\(413\) | −35.0892 | − | 6.18717i | −1.72663 | − | 0.304451i | ||||
\(414\) | −2.47325 | − | 14.0265i | −0.121554 | − | 0.689365i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.95477 | + | 2.47935i | 0.144870 | + | 0.121560i | ||||
\(417\) | 10.2896i | 0.503882i | ||||||||
\(418\) | 9.13834 | + | 21.5454i | 0.446971 | + | 1.05382i | ||||
\(419\) | −17.9296 | −0.875916 | −0.437958 | − | 0.898995i | \(-0.644298\pi\) | ||||
−0.437958 | + | 0.898995i | \(0.644298\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2850 | − | 11.0228i | 1.47600 | − | 0.537220i | 0.526278 | − | 0.850313i | \(-0.323587\pi\) |
0.949723 | + | 0.313093i | \(0.101365\pi\) | |||||||
\(422\) | 10.5088 | − | 1.85299i | 0.511562 | − | 0.0902022i | ||||
\(423\) | −8.19775 | − | 1.44549i | −0.398588 | − | 0.0702819i | ||||
\(424\) | 1.69146 | + | 0.615640i | 0.0821444 | + | 0.0298981i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.73684 | − | 3.00830i | 0.0841503 | − | 0.145753i | ||||
\(427\) | −25.3728 | − | 30.2382i | −1.22788 | − | 1.46333i | ||||
\(428\) | 5.61204 | + | 6.68816i | 0.271268 | + | 0.323285i | ||||
\(429\) | 5.96858 | − | 10.3379i | 0.288166 | − | 0.499118i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.30703 | + | 0.475720i | 0.0629575 | + | 0.0229146i | 0.373307 | − | 0.927708i | \(-0.378224\pi\) |
−0.310349 | + | 0.950623i | \(0.600446\pi\) | |||||||
\(432\) | −3.21732 | − | 0.567300i | −0.154793 | − | 0.0272942i | ||||
\(433\) | 32.7483 | − | 5.77441i | 1.57378 | − | 0.277500i | 0.682478 | − | 0.730906i | \(-0.260902\pi\) |
0.891304 | + | 0.453406i | \(0.149791\pi\) | |||||||
\(434\) | 37.4981 | − | 13.6482i | 1.79997 | − | 0.655135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.12981 | 0.389347 | ||||||||
\(437\) | −22.6768 | + | 5.22866i | −1.08478 | + | 0.250121i | ||||
\(438\) | − | 0.735663i | − | 0.0351513i | ||||||
\(439\) | 27.6648 | + | 23.2135i | 1.32037 | + | 1.10792i | 0.986227 | + | 0.165397i | \(0.0528906\pi\) |
0.334141 | + | 0.942523i | \(0.391554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.71789 | − | 43.7704i | −0.367519 | − | 2.08430i | ||||
\(442\) | 5.32597 | + | 0.939112i | 0.253330 | + | 0.0446690i | ||||
\(443\) | −10.9404 | + | 30.0586i | −0.519795 | + | 1.42813i | 0.350951 | + | 0.936394i | \(0.385858\pi\) |
−0.870746 | + | 0.491732i | \(0.836364\pi\) | |||||||
\(444\) | −3.01445 | − | 5.22118i | −0.143059 | − | 0.247786i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0761973 | − | 0.0639371i | 0.00360805 | − | 0.00302751i | ||||
\(447\) | −1.06951 | − | 1.27459i | −0.0505860 | − | 0.0602860i | ||||
\(448\) | −4.21251 | − | 2.43209i | −0.199022 | − | 0.114906i | ||||
\(449\) | −1.09116 | − | 1.88995i | −0.0514951 | − | 0.0891922i | 0.839129 | − | 0.543933i | \(-0.183065\pi\) |
−0.890624 | + | 0.454741i | \(0.849732\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.77917 | − | 10.0902i | 0.0837777 | − | 0.475127i | ||||
\(452\) | 4.41400 | − | 0.778308i | 0.207617 | − | 0.0366085i | ||||
\(453\) | 0.397846 | + | 1.09307i | 0.0186924 | + | 0.0513570i | ||||
\(454\) | −10.5915 | − | 8.88734i | −0.497084 | − | 0.417103i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.306897 | + | 2.49370i | −0.0143718 | + | 0.116778i | ||||
\(457\) | − | 37.2037i | − | 1.74031i | −0.492774 | − | 0.870157i | \(-0.664017\pi\) | ||
0.492774 | − | 0.870157i | \(-0.335983\pi\) | |||||||
\(458\) | −10.0115 | + | 11.9313i | −0.467808 | + | 0.557512i | ||||
\(459\) | −4.30433 | + | 1.56665i | −0.200909 | + | 0.0731248i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.847556 | + | 4.80673i | −0.0394746 | + | 0.223872i | −0.998163 | − | 0.0605870i | \(-0.980703\pi\) |
0.958688 | + | 0.284459i | \(0.0918138\pi\) | |||||||
\(462\) | −5.14865 | + | 14.1458i | −0.239537 | + | 0.658122i | ||||
\(463\) | 17.5133 | − | 10.1113i | 0.813914 | − | 0.469913i | −0.0343994 | − | 0.999408i | \(-0.510952\pi\) |
0.848313 | + | 0.529495i | \(0.177619\pi\) | |||||||
\(464\) | −1.81689 | + | 3.14694i | −0.0843470 | + | 0.146093i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.6753 | − | 9.79677i | 0.540850 | − | 0.453827i | ||||
\(467\) | −33.7859 | − | 19.5063i | −1.56342 | − | 0.902644i | −0.996907 | − | 0.0785944i | \(-0.974957\pi\) |
−0.566518 | − | 0.824049i | \(-0.691710\pi\) | |||||||
\(468\) | −8.91140 | + | 5.14500i | −0.411930 | + | 0.237828i | ||||
\(469\) | −38.6003 | − | 14.0493i | −1.78239 | − | 0.648739i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.10496 | − | 6.26656i | −0.0509140 | − | 0.288748i | ||||
\(472\) | −2.50532 | − | 6.88331i | −0.115317 | − | 0.316830i | ||||
\(473\) | −5.10305 | + | 6.08158i | −0.234639 | + | 0.279631i | ||||
\(474\) | −9.58686 | −0.440339 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.82004 | −0.312596 | ||||||||
\(477\) | −3.08665 | + | 3.67853i | −0.141328 | + | 0.168428i | ||||
\(478\) | −5.75392 | − | 15.8088i | −0.263178 | − | 0.723076i | ||||
\(479\) | 5.39865 | + | 30.6172i | 0.246670 | + | 1.39894i | 0.816581 | + | 0.577231i | \(0.195867\pi\) |
−0.569911 | + | 0.821707i | \(0.693022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.9107 | − | 13.7984i | −1.72858 | − | 0.629151i | ||||
\(482\) | 7.88688 | − | 4.55349i | 0.359237 | − | 0.207406i | ||||
\(483\) | −12.9636 | − | 7.48453i | −0.589864 | − | 0.340558i | ||||
\(484\) | −13.6562 | + | 11.4589i | −0.620737 | + | 0.520860i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.66429 | − | 11.5429i | 0.302298 | − | 0.523596i | ||||
\(487\) | −24.2263 | + | 13.9870i | −1.09780 | + | 0.633813i | −0.935641 | − | 0.352952i | \(-0.885178\pi\) |
−0.162155 | + | 0.986765i | \(0.551845\pi\) | |||||||
\(488\) | 2.77551 | − | 7.62565i | 0.125641 | − | 0.345197i | ||||
\(489\) | 0.593418 | − | 3.36544i | 0.0268353 | − | 0.152191i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.79400 | + | 1.01693i | −0.126091 | + | 0.0458935i | −0.404295 | − | 0.914629i | \(-0.632483\pi\) |
0.278204 | + | 0.960522i | \(0.410261\pi\) | |||||||
\(492\) | 0.707045 | − | 0.842623i | 0.0318760 | − | 0.0379884i | ||||
\(493\) | 5.09490i | 0.229463i | ||||||||
\(494\) | 9.15311 | + | 14.1032i | 0.411818 | + | 0.634533i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.28445 | + | 5.27328i | 0.282180 | + | 0.236777i | ||||
\(497\) | 10.0258 | + | 27.5458i | 0.449720 | + | 1.23560i | ||||
\(498\) | −8.20883 | + | 1.44744i | −0.367846 | + | 0.0648612i | ||||
\(499\) | −3.20155 | + | 18.1569i | −0.143321 | + | 0.812815i | 0.825379 | + | 0.564580i | \(0.190962\pi\) |
−0.968700 | + | 0.248235i | \(0.920149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.08304 | − | 3.60794i | −0.0930636 | − | 0.161191i | ||||
\(502\) | 14.5542 | + | 8.40288i | 0.649586 | + | 0.375039i | ||||
\(503\) | −2.10120 | − | 2.50412i | −0.0936881 | − | 0.111653i | 0.717163 | − | 0.696905i | \(-0.245440\pi\) |
−0.810852 | + | 0.585252i | \(0.800996\pi\) | |||||||
\(504\) | 9.94053 | − | 8.34110i | 0.442786 | − | 0.371542i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.3325 | − | 24.8246i | −0.637157 | − | 1.10359i | ||||
\(507\) | 0.370209 | − | 1.01714i | 0.0164416 | − | 0.0451728i | ||||
\(508\) | 0.137068 | + | 0.0241688i | 0.00608142 | + | 0.00107232i | ||||
\(509\) | −6.53272 | − | 37.0489i | −0.289558 | − | 1.64216i | −0.688536 | − | 0.725202i | \(-0.741746\pi\) |
0.398978 | − | 0.916960i | \(-0.369365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.75567 | + | 3.99048i | 0.210378 | + | 0.176528i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −12.6864 | − | 6.46852i | −0.560118 | − | 0.285592i | ||||
\(514\) | −9.89728 | −0.436550 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.800905 | + | 0.291506i | −0.0352579 | + | 0.0128328i | ||||
\(517\) | −16.4987 | + | 2.90916i | −0.725610 | + | 0.127945i | ||||
\(518\) | 50.1034 | + | 8.83459i | 2.20142 | + | 0.388169i | ||||
\(519\) | −2.79412 | − | 1.01698i | −0.122648 | − | 0.0446403i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.7203 | + | 27.2284i | −0.688719 | + | 1.19290i | 0.283533 | + | 0.958962i | \(0.408493\pi\) |
−0.972252 | + | 0.233934i | \(0.924840\pi\) | |||||||
\(522\) | −6.23119 | − | 7.42605i | −0.272732 | − | 0.325029i | ||||
\(523\) | −2.88381 | − | 3.43679i | −0.126100 | − | 0.150280i | 0.699300 | − | 0.714828i | \(-0.253495\pi\) |
−0.825400 | + | 0.564548i | \(0.809051\pi\) | |||||||
\(524\) | 6.21505 | − | 10.7648i | 0.271506 | − | 0.470261i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.0609 | − | 7.66554i | −0.918299 | − | 0.334233i | ||||
\(527\) | 11.3277 | + | 1.99738i | 0.493443 | + | 0.0870073i | ||||
\(528\) | −3.04777 | + | 0.537405i | −0.132637 | + | 0.0233875i | ||||
\(529\) | 5.17201 | − | 1.88246i | 0.224870 | − | 0.0818460i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.5415 | 0.848027 | ||||||||
\(532\) | −14.4557 | − | 15.5106i | −0.626735 | − | 0.672469i | ||||
\(533\) | − | 7.36067i | − | 0.318826i | ||||||
\(534\) | 4.24270 | + | 3.56005i | 0.183599 | + | 0.154058i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.46644 | − | 8.31660i | −0.0633406 | − | 0.359222i | ||||
\(537\) | 4.64551 | + | 0.819129i | 0.200469 | + | 0.0353480i | ||||
\(538\) | 2.55586 | − | 7.02217i | 0.110191 | − | 0.302747i | ||||
\(539\) | −44.7252 | − | 77.4664i | −1.92645 | − | 3.33671i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0269 | − | 14.2873i | 0.732045 | − | 0.614259i | −0.198643 | − | 0.980072i | \(-0.563653\pi\) |
0.930688 | + | 0.365813i | \(0.119209\pi\) | |||||||
\(542\) | 6.84623 | + | 8.15902i | 0.294071 | + | 0.350460i | ||||
\(543\) | −1.71339 | − | 0.989225i | −0.0735285 | − | 0.0424517i | ||||
\(544\) | −0.701047 | − | 1.21425i | −0.0300571 | − | 0.0520605i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.87794 | + | 10.6504i | −0.0803686 | + | 0.455793i | ||||
\(547\) | 28.4071 | − | 5.00894i | 1.21460 | − | 0.214167i | 0.470600 | − | 0.882347i | \(-0.344038\pi\) |
0.744000 | + | 0.668180i | \(0.232926\pi\) | |||||||
\(548\) | −4.91880 | − | 13.5143i | −0.210121 | − | 0.577302i | ||||
\(549\) | 16.5840 | + | 13.9157i | 0.707790 | + | 0.593906i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.5871 | + | 10.7991i | −0.493629 | + | 0.460058i | ||||
\(552\) | − | 3.07740i | − | 0.130983i | ||||||
\(553\) | 52.0023 | − | 61.9739i | 2.21136 | − | 2.63540i | ||||
\(554\) | 2.18604 | − | 0.795654i | 0.0928760 | − | 0.0338041i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.09981 | − | 17.5799i | 0.131461 | − | 0.745554i | ||||
\(557\) | −9.58721 | + | 26.3406i | −0.406223 | + | 1.11609i | 0.552937 | + | 0.833223i | \(0.313507\pi\) |
−0.959160 | + | 0.282865i | \(0.908715\pi\) | |||||||
\(558\) | −18.9535 | + | 10.9428i | −0.802366 | + | 0.463246i | ||||
\(559\) | −2.85170 | + | 4.93929i | −0.120614 | + | 0.208910i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.32401 | + | 2.78917i | −0.140340 | + | 0.117759i | ||||
\(562\) | −14.7858 | − | 8.53656i | −0.623699 | − | 0.360093i | ||||
\(563\) | 5.69177 | − | 3.28614i | 0.239879 | − | 0.138494i | −0.375242 | − | 0.926927i | \(-0.622440\pi\) |
0.615121 | + | 0.788432i | \(0.289107\pi\) | |||||||
\(564\) | −1.69011 | − | 0.615151i | −0.0711666 | − | 0.0259025i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.47044 | − | 8.33927i | −0.0618071 | − | 0.350526i | ||||
\(567\) | 10.1818 | + | 27.9742i | 0.427595 | + | 1.17481i | ||||
\(568\) | −3.87370 | + | 4.61650i | −0.162537 | + | 0.193704i | ||||
\(569\) | −3.90032 | −0.163510 | −0.0817549 | − | 0.996652i | \(-0.526052\pi\) | ||||
−0.0817549 | + | 0.996652i | \(0.526052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1559 | 0.759802 | 0.379901 | − | 0.925027i | \(-0.375958\pi\) | ||||
0.379901 | + | 0.925027i | \(0.375958\pi\) | |||||||
\(572\) | −13.3118 | + | 15.8644i | −0.556594 | + | 0.663323i | ||||
\(573\) | 0.744385 | + | 2.04518i | 0.0310971 | + | 0.0854386i | ||||
\(574\) | 1.61186 | + | 9.14132i | 0.0672778 | + | 0.381551i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.50687 | + | 0.912424i | 0.104453 | + | 0.0380177i | ||||
\(577\) | 12.1402 | − | 7.00915i | 0.505403 | − | 0.291795i | −0.225539 | − | 0.974234i | \(-0.572414\pi\) |
0.730942 | + | 0.682439i | \(0.239081\pi\) | |||||||
\(578\) | 13.0199 | + | 7.51707i | 0.541558 | + | 0.312669i | ||||
\(579\) | −5.37721 | + | 4.51202i | −0.223469 | + | 0.187513i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.1705 | − | 60.9170i | 1.45912 | − | 2.52726i | ||||
\(582\) | 3.03461 | − | 1.75203i | 0.125789 | − | 0.0726241i | ||||
\(583\) | −3.30541 | + | 9.08155i | −0.136896 | + | 0.376119i | ||||
\(584\) | −0.221624 | + | 1.25689i | −0.00917088 | + | 0.0520106i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.43610 | + | 0.886667i | −0.100634 | + | 0.0366279i | ||||
\(587\) | 4.89246 | − | 5.83061i | 0.201933 | − | 0.240655i | −0.655568 | − | 0.755136i | \(-0.727571\pi\) |
0.857502 | + | 0.514481i | \(0.172015\pi\) | |||||||
\(588\) | − | 9.60319i | − | 0.396029i | ||||||
\(589\) | 19.4676 | + | 29.9958i | 0.802148 | + | 1.23596i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.18025 | + | 2.66855i | 0.130818 | + | 0.109769i | ||||
\(592\) | 3.57732 | + | 9.82860i | 0.147027 | + | 0.403953i | ||||
\(593\) | −9.27933 | + | 1.63620i | −0.381056 | + | 0.0671905i | −0.360896 | − | 0.932606i | \(-0.617529\pi\) |
−0.0201608 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(594\) | 3.04587 | − | 17.2740i | 0.124974 | − | 0.708761i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.44329 | + | 2.49986i | 0.0591196 | + | 0.102398i | ||||
\(597\) | −2.91380 | − | 1.68228i | −0.119254 | − | 0.0688512i | ||||
\(598\) | −13.2370 | − | 15.7753i | −0.541302 | − | 0.645099i | ||||
\(599\) | −10.7502 | + | 9.02053i | −0.439243 | + | 0.368569i | −0.835426 | − | 0.549603i | \(-0.814779\pi\) |
0.396183 | + | 0.918172i | \(0.370335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.78599 | + | 11.7537i | 0.276806 | + | 0.479443i | 0.970589 | − | 0.240742i | \(-0.0773906\pi\) |
−0.693783 | + | 0.720184i | \(0.744057\pi\) | |||||||
\(602\) | 2.45994 | − | 6.75864i | 0.100260 | − | 0.275462i | ||||
\(603\) | 22.1866 | + | 3.91210i | 0.903508 | + | 0.159313i | ||||
\(604\) | −0.350430 | − | 1.98739i | −0.0142588 | − | 0.0808657i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.554451 | − | 0.465240i | −0.0225231 | − | 0.0188991i | ||||
\(607\) | 2.07689i | 0.0842984i | 0.999111 | + | 0.0421492i | \(0.0134205\pi\) | ||||
−0.999111 | + | 0.0421492i | \(0.986580\pi\) | |||||||
\(608\) | 1.27559 | − | 4.16808i | 0.0517318 | − | 0.169038i | ||||
\(609\) | −10.1883 | −0.412850 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.3098 | + | 4.11642i | −0.457545 | + | 0.166533i | ||||
\(612\) | 3.68361 | − | 0.649520i | 0.148901 | − | 0.0262553i | ||||
\(613\) | 16.2680 | + | 2.86849i | 0.657059 | + | 0.115857i | 0.492230 | − | 0.870465i | \(-0.336182\pi\) |
0.164828 | + | 0.986322i | \(0.447293\pi\) | |||||||
\(614\) | 3.87311 | + | 1.40970i | 0.156306 | + | 0.0568908i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.0581 | − | 22.6173i | 0.526125 | − | 0.911275i | ||||
\(617\) | 14.7080 | + | 17.5283i | 0.592120 | + | 0.705661i | 0.976012 | − | 0.217717i | \(-0.0698610\pi\) |
−0.383892 | + | 0.923378i | \(0.625417\pi\) | |||||||
\(618\) | 2.72956 | + | 3.25297i | 0.109799 | + | 0.130853i | ||||
\(619\) | −6.66514 | + | 11.5444i | −0.267895 | + | 0.464007i | −0.968318 | − | 0.249721i | \(-0.919661\pi\) |
0.700423 | + | 0.713728i | \(0.252995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.3901 | + | 5.96550i | 0.657711 | + | 0.239387i | ||||
\(622\) | −2.44534 | − | 0.431179i | −0.0980492 | − | 0.0172887i | ||||
\(623\) | −46.0276 | + | 8.11590i | −1.84406 | + | 0.325157i | ||||
\(624\) | −2.08924 | + | 0.760421i | −0.0836365 | + | 0.0304412i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.38145 | −0.215086 | ||||||||
\(627\) | −13.3889 | − | 1.64775i | −0.534700 | − | 0.0658048i | ||||
\(628\) | 11.0394i | 0.440520i | ||||||||
\(629\) | 11.2341 | + | 9.42649i | 0.447931 | + | 0.375859i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51546 | + | 8.59462i | 0.0603297 | + | 0.342147i | 1.00000 | 6.52024e-5i | \(2.07546e-5\pi\) | |
−0.939670 | + | 0.342081i | \(0.888868\pi\) | |||||||
\(632\) | 16.3793 | + | 2.88812i | 0.651534 | + | 0.114883i | ||||
\(633\) | −2.10372 | + | 5.77991i | −0.0836152 | + | 0.229731i | ||||
\(634\) | −9.73266 | − | 16.8575i | −0.386533 | − | 0.669495i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.794805 | + | 0.666921i | −0.0315161 | + | 0.0264451i | ||||
\(637\) | −41.3068 | − | 49.2275i | −1.63663 | − | 1.95046i | ||||
\(638\) | −16.8962 | − | 9.75501i | −0.668926 | − | 0.386204i | ||||
\(639\) | −8.03848 | − | 13.9230i | −0.317997 | − | 0.550787i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.151753 | + | 0.860632i | −0.00599387 | + | 0.0339929i | −0.987658 | − | 0.156626i | \(-0.949938\pi\) |
0.981664 | + | 0.190619i | \(0.0610494\pi\) | |||||||
\(642\) | −4.95606 | + | 0.873887i | −0.195600 | + | 0.0344896i | ||||
\(643\) | −6.50122 | − | 17.8620i | −0.256383 | − | 0.704407i | −0.999383 | − | 0.0351158i | \(-0.988820\pi\) |
0.743000 | − | 0.669291i | \(-0.233402\pi\) | |||||||
\(644\) | 19.8938 | + | 16.6928i | 0.783924 | + | 0.657790i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.37314 | − | 5.95533i | −0.0540255 | − | 0.234309i | ||||
\(647\) | 14.4175i | 0.566810i | 0.959000 | + | 0.283405i | \(0.0914641\pi\) | ||||
−0.959000 | + | 0.283405i | \(0.908536\pi\) | |||||||
\(648\) | −3.93395 | + | 4.68830i | −0.154540 | + | 0.184174i | ||||
\(649\) | 36.9570 | − | 13.4512i | 1.45069 | − | 0.528007i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.99417 | + | 22.6520i | −0.156544 | + | 0.887804i | ||||
\(652\) | −2.02773 | + | 5.57114i | −0.0794121 | + | 0.218183i | ||||
\(653\) | −9.06528 | + | 5.23384i | −0.354752 | + | 0.204816i | −0.666776 | − | 0.745258i | \(-0.732326\pi\) |
0.312024 | + | 0.950074i | \(0.398993\pi\) | |||||||
\(654\) | −2.34306 | + | 4.05829i | −0.0916207 | + | 0.158692i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.46184 | + | 1.22663i | −0.0570755 | + | 0.0478920i | ||||
\(657\) | −2.94865 | − | 1.70240i | −0.115038 | − | 0.0664171i | ||||
\(658\) | 13.1444 | − | 7.58889i | 0.512420 | − | 0.295846i | ||||
\(659\) | 5.20991 | + | 1.89625i | 0.202949 | + | 0.0738675i | 0.441495 | − | 0.897264i | \(-0.354448\pi\) |
−0.238545 | + | 0.971131i | \(0.576671\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00125 | + | 28.3635i | 0.194526 | + | 1.10321i | 0.913092 | + | 0.407753i | \(0.133688\pi\) |
−0.718566 | + | 0.695459i | \(0.755201\pi\) | |||||||
\(662\) | −6.39927 | − | 17.5818i | −0.248715 | − | 0.683338i | ||||
\(663\) | −2.00376 | + | 2.38799i | −0.0778198 | + | 0.0927420i | ||||
\(664\) | 14.4610 | 0.561195 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −27.9030 | −1.08122 | ||||||||
\(667\) | 12.4703 | − | 14.8616i | 0.482854 | − | 0.575443i | ||||
\(668\) | 2.47200 | + | 6.79176i | 0.0956445 | + | 0.262781i | ||||
\(669\) | 0.00995606 | + | 0.0564636i | 0.000384924 | + | 0.00218301i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.9427 | + | 14.9019i | 1.58057 | + | 0.575282i | ||||
\(672\) | 2.42814 | − | 1.40188i | 0.0936674 | − | 0.0540789i | ||||
\(673\) | 34.5899 | + | 19.9705i | 1.33334 | + | 0.769807i | 0.985811 | − | 0.167861i | \(-0.0536860\pi\) |
0.347533 | + | 0.937668i | \(0.387019\pi\) | |||||||
\(674\) | −19.2255 | + | 16.1322i | −0.740540 | + | 0.621387i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.938930 | + | 1.62627i | −0.0361127 | + | 0.0625490i | ||||
\(677\) | 12.6270 | − | 7.29022i | 0.485296 | − | 0.280186i | −0.237325 | − | 0.971430i | \(-0.576271\pi\) |
0.722621 | + | 0.691245i | \(0.242937\pi\) | |||||||
\(678\) | −0.883619 | + | 2.42772i | −0.0339352 | + | 0.0932361i | ||||
\(679\) | −5.13477 | + | 29.1207i | −0.197054 | + | 1.11755i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.48897 | − | 2.72576i | 0.286978 | − | 0.104451i | ||||
\(682\) | −28.3126 | + | 33.7417i | −1.08415 | + | 1.29204i | ||||
\(683\) | 26.6159i | 1.01843i | 0.860640 | + | 0.509214i | \(0.170064\pi\) | ||||
−0.860640 | + | 0.509214i | \(0.829936\pi\) | |||||||
\(684\) | 9.28494 | + | 7.00078i | 0.355018 | + | 0.267681i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 35.9961 | + | 30.2043i | 1.37434 | + | 1.15321i | ||||
\(687\) | −3.07056 | − | 8.43628i | −0.117149 | − | 0.321864i | ||||
\(688\) | 1.45618 | − | 0.256764i | 0.0555163 | − | 0.00978902i | ||||
\(689\) | −1.20563 | + | 6.83749i | −0.0459310 | + | 0.260488i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6248 | − | 32.2591i | −0.708521 | − | 1.22719i | −0.965406 | − | 0.260752i | \(-0.916029\pi\) |
0.256885 | − | 0.966442i | \(-0.417304\pi\) | |||||||
\(692\) | 4.46743 | + | 2.57927i | 0.169826 | + | 0.0980492i | ||||
\(693\) | 44.7839 | + | 53.3714i | 1.70120 | + | 2.02741i | ||||
\(694\) | 17.4302 | − | 14.6257i | 0.661642 | − | 0.555183i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.04727 | − | 1.81393i | −0.0396968 | − | 0.0687569i | ||||
\(697\) | −0.915115 | + | 2.51426i | −0.0346625 | + | 0.0952344i | ||||
\(698\) | 12.9638 | + | 2.28587i | 0.490688 | + | 0.0865215i | ||||
\(699\) | 1.52552 | + | 8.65165i | 0.0577004 | + | 0.327235i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.3425 | − | 25.4604i | −1.14602 | − | 0.961626i | −0.146402 | − | 0.989225i | \(-0.546769\pi\) |
−0.999619 | + | 0.0275989i | \(0.991214\pi\) | |||||||
\(702\) | − | 12.6012i | − | 0.475603i | ||||||
\(703\) | 2.37332 | + | 45.5295i | 0.0895114 | + | 1.71718i | ||||
\(704\) | 5.36907 | 0.202354 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.5635 | + | 4.20877i | −0.435198 | + | 0.158399i | ||||
\(707\) | 6.01505 | − | 1.06062i | 0.226219 | − | 0.0398886i | ||||
\(708\) | 4.15810 | + | 0.733185i | 0.156271 | + | 0.0275548i | ||||
\(709\) | −34.4453 | − | 12.5371i | −1.29362 | − | 0.470839i | −0.398707 | − | 0.917079i | \(-0.630541\pi\) |
−0.894914 | + | 0.446239i | \(0.852763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.1850 | + | 38.4256i | −0.832003 | + | 1.44107i | ||||
\(712\) | −6.17623 | − | 7.36055i | −0.231464 | − | 0.275848i | ||||
\(713\) | −28.1536 | − | 33.5521i | −1.05436 | − | 1.25654i | ||||
\(714\) | 1.96557 | − | 3.40447i | 0.0735597 | − | 0.127409i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.69017 | − | 2.79899i | −0.287395 | − | 0.104603i | ||||
\(717\) | 9.54983 | + | 1.68389i | 0.356645 | + | 0.0628861i | ||||
\(718\) | −12.3704 | + | 2.18123i | −0.461658 | + | 0.0814028i | ||||
\(719\) | 10.3333 | − | 3.76101i | 0.385367 | − | 0.140262i | −0.142069 | − | 0.989857i | \(-0.545376\pi\) |
0.527436 | + | 0.849595i | \(0.323153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.8347 | −1.33455 | ||||||||
\(722\) | 10.6335 | − | 15.7458i | 0.395737 | − | 0.585997i | ||||
\(723\) | 5.24936i | 0.195226i | ||||||||
\(724\) | 2.62934 | + | 2.20628i | 0.0977187 | + | 0.0819957i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.78434 | − | 10.1195i | −0.0662232 | − | 0.375570i | ||||
\(727\) | 44.7236 | + | 7.88597i | 1.65871 | + | 0.292475i | 0.922992 | − | 0.384818i | \(-0.125736\pi\) |
0.735714 | + | 0.677293i | \(0.236847\pi\) | |||||||
\(728\) | 6.41700 | − | 17.6306i | 0.237830 | − | 0.653432i | ||||
\(729\) | −5.33885 | − | 9.24717i | −0.197735 | − | 0.342488i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.58816 | − | 1.33262i | 0.0587402 | − | 0.0492889i | ||||
\(732\) | 3.00670 | + | 3.58325i | 0.111131 | + | 0.132441i | ||||
\(733\) | −23.4118 | − | 13.5168i | −0.864735 | − | 0.499255i | 0.000859816 | − | 1.00000i | \(-0.499726\pi\) |
−0.865595 | + | 0.500744i | \(0.833060\pi\) | |||||||
\(734\) | −1.34225 | − | 2.32485i | −0.0495435 | − | 0.0858119i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.927092 | + | 5.25780i | −0.0341731 | + | 0.193805i | ||||
\(737\) | 44.6524 | − | 7.87342i | 1.64479 | − | 0.290021i | ||||
\(738\) | −1.74118 | − | 4.78386i | −0.0640938 | − | 0.176096i | ||||
\(739\) | 0.964167 | + | 0.809032i | 0.0354675 | + | 0.0297607i | 0.660349 | − | 0.750959i | \(-0.270408\pi\) |
−0.624882 | + | 0.780720i | \(0.714853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.67809 | + | 0.504490i | −0.355534 | + | 0.0185329i | ||||
\(742\) | − | 8.75559i | − | 0.321428i | ||||||
\(743\) | 33.5678 | − | 40.0045i | 1.23148 | − | 1.46762i | 0.395867 | − | 0.918308i | \(-0.370444\pi\) |
0.835615 | − | 0.549315i | \(-0.185111\pi\) | |||||||
\(744\) | −4.44356 | + | 1.61733i | −0.162909 | + | 0.0592940i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.21985 | − | 18.2607i | 0.117887 | − | 0.668571i | ||||
\(747\) | −13.1945 | + | 36.2517i | −0.482763 | + | 1.32638i | ||||
\(748\) | 6.51938 | − | 3.76397i | 0.238372 | − | 0.137624i | ||||
\(749\) | 21.2341 | − | 36.7785i | 0.775876 | − | 1.34386i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.810409 | − | 0.680014i | 0.0295723 | − | 0.0248141i | −0.627882 | − | 0.778309i | \(-0.716078\pi\) |
0.657454 | + | 0.753495i | \(0.271633\pi\) | |||||||
\(752\) | 2.70227 | + | 1.56016i | 0.0985417 | + | 0.0568931i | ||||
\(753\) | −8.38920 | + | 4.84351i | −0.305720 | + | 0.176507i | ||||
\(754\) | −13.1709 | − | 4.79381i | −0.479655 | − | 0.174580i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.75945 | + | 15.6496i | 0.100360 | + | 0.569172i | ||||
\(757\) | −0.632944 | − | 1.73900i | −0.0230047 | − | 0.0632050i | 0.927659 | − | 0.373429i | \(-0.121818\pi\) |
−0.950663 | + | 0.310224i | \(0.899596\pi\) | |||||||
\(758\) | −7.44703 | + | 8.87503i | −0.270488 | + | 0.322355i | ||||
\(759\) | 16.5228 | 0.599739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.8442 | −1.15435 | −0.577176 | − | 0.816620i | \(-0.695845\pi\) | ||||
−0.577176 | + | 0.816620i | \(0.695845\pi\) | |||||||
\(762\) | −0.0515686 | + | 0.0614570i | −0.00186813 | + | 0.00222635i | ||||
\(763\) | −13.5252 | − | 37.1601i | −0.489644 | − | 1.34529i | ||||
\(764\) | −0.655668 | − | 3.71848i | −0.0237212 | − | 0.134530i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.3254 | + | 9.94564i | 0.987308 | + | 0.359351i | ||||
\(767\) | 24.4688 | − | 14.1271i | 0.883517 | − | 0.510099i | ||||
\(768\) | 0.499186 | + | 0.288205i | 0.0180128 | + | 0.0103997i | ||||
\(769\) | −0.0929228 | + | 0.0779715i | −0.00335088 | + | 0.00281172i | −0.644462 | − | 0.764637i | \(-0.722918\pi\) |
0.641111 | + | 0.767448i | \(0.278474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.85245 | − | 4.94059i | 0.102728 | − | 0.177931i | ||||
\(772\) | 10.5463 | − | 6.08894i | 0.379571 | − | 0.219146i | ||||
\(773\) | 11.9131 | − | 32.7308i | 0.428483 | − | 1.17725i | −0.518251 | − | 0.855229i | \(-0.673417\pi\) |
0.946734 | − | 0.322018i | \(-0.104361\pi\) | |||||||
\(774\) | −0.684981 | + | 3.88472i | −0.0246211 | + | 0.139633i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.71250 | + | 2.07918i | −0.205067 | + | 0.0746382i | ||||
\(777\) | −18.8502 | + | 22.4648i | −0.676246 | + | 0.805919i | ||||
\(778\) | 29.7821i | 1.06774i | ||||||||
\(779\) | −7.65776 | + | 3.24800i | −0.274368 | + | 0.116372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.7863 | − | 20.7982i | −0.886923 | − | 0.744217i | ||||
\(782\) | 2.56024 | + | 7.03421i | 0.0915541 | + | 0.251543i | ||||
\(783\) | 11.6910 | − | 2.06144i | 0.417803 | − | 0.0736700i | ||||
\(784\) | −2.89303 | + | 16.4072i | −0.103323 | + | 0.585972i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.58242 | + | 6.20493i | 0.127781 | + | 0.221323i | ||||
\(787\) | −16.6039 | − | 9.58626i | −0.591865 | − | 0.341713i | 0.173970 | − | 0.984751i | \(-0.444340\pi\) |
−0.765834 | + | 0.643038i | \(0.777674\pi\) | |||||||
\(788\) | −4.62959 | − | 5.51733i | −0.164922 | − | 0.196547i | ||||
\(789\) | 9.89640 | − | 8.30406i | 0.352321 | − | 0.295632i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9009 | − | 18.8809i | −0.387591 | − | 0.671327i | ||||
\(792\) | −4.89887 | + | 13.4595i | −0.174074 | + | 0.478264i | ||||
\(793\) | 30.8257 | + | 5.43540i | 1.09465 | + | 0.193017i | ||||
\(794\) | 1.08877 | + | 6.17471i | 0.0386389 | + | 0.219132i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.47147 | + | 3.75201i | 0.158487 | + | 0.132986i | ||||
\(797\) | − | 22.4041i | − | 0.793593i | −0.917907 | − | 0.396796i | \(-0.870122\pi\) | ||
0.917907 | − | 0.396796i | \(-0.129878\pi\) | |||||||
\(798\) | 11.9089 | − | 2.74587i | 0.421570 | − | 0.0972028i | ||||
\(799\) | 4.37497 | 0.154775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0872 | − | 8.76704i | 0.851081 | − | 0.309768i | ||||
\(802\) | 9.75090 | − | 1.71935i | 0.344316 | − | 0.0607122i | ||||
\(803\) | −6.74835 | − | 1.18992i | −0.238144 | − | 0.0419912i | ||||
\(804\) | 4.57417 | + | 1.66486i | 0.161318 | + | 0.0587151i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.8217 | + | 27.4040i | −0.557297 | + | 0.965266i | ||||
\(807\) | 2.76876 | + | 3.29968i | 0.0974649 | + | 0.116154i | ||||
\(808\) | 0.807133 | + | 0.961904i | 0.0283948 | + | 0.0338396i | ||||
\(809\) | 22.7973 | − | 39.4861i | 0.801511 | − | 1.38826i | −0.117110 | − | 0.993119i | \(-0.537363\pi\) |
0.918621 | − | 0.395139i | \(-0.129304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.6230 | − | 12.9657i | −1.25089 | − | 0.455288i | −0.370191 | − | 0.928956i | \(-0.620708\pi\) |
−0.880704 | + | 0.473667i | \(0.842930\pi\) | |||||||
\(812\) | 17.4069 | + | 3.06930i | 0.610861 | + | 0.107711i | ||||
\(813\) | −6.04599 | + | 1.06607i | −0.212042 | + | 0.0373888i | ||||
\(814\) | −52.7704 | + | 19.2069i | −1.84960 | + | 0.673200i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.808181 | 0.0282920 | ||||||||
\(817\) | 6.39699 | + | 0.787270i | 0.223802 | + | 0.0275431i | ||||
\(818\) | − | 30.6587i | − | 1.07196i | ||||||
\(819\) | 38.3424 | + | 32.1731i | 1.33979 | + | 1.12422i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.63416 | + | 54.6380i | 0.336235 | + | 1.90688i | 0.414689 | + | 0.909963i | \(0.363890\pi\) |
−0.0784541 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(822\) | 8.16377 | + | 1.43949i | 0.284744 | + | 0.0502081i | ||||
\(823\) | 2.19203 | − | 6.02255i | 0.0764094 | − | 0.209933i | −0.895607 | − | 0.444846i | \(-0.853258\pi\) |
0.972016 | + | 0.234913i | \(0.0754806\pi\) | |||||||
\(824\) | −3.68352 | − | 6.38005i | −0.128322 | − | 0.222260i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.2945 | + | 22.9028i | −0.949699 | + | 0.796892i | ||||
\(827\) | 2.82341 | + | 3.36481i | 0.0981796 | + | 0.117006i | 0.812897 | − | 0.582407i | \(-0.197889\pi\) |
−0.714717 | + | 0.699413i | \(0.753445\pi\) | |||||||
\(828\) | −12.3347 | − | 7.12144i | −0.428660 | − | 0.247487i | ||||
\(829\) | 25.0469 | + | 43.3826i | 0.869916 | + | 1.50674i | 0.862082 | + | 0.506769i | \(0.169160\pi\) |
0.00783422 | + | 0.999969i | \(0.497506\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.232849 | + | 1.32055i | −0.00807745 | + | 0.0458095i | ||||
\(832\) | 3.79858 | − | 0.669793i | 0.131692 | − | 0.0232209i | ||||
\(833\) | 7.98936 | + | 21.9506i | 0.276815 | + | 0.760543i | ||||
\(834\) | 7.88227 | + | 6.61401i | 0.272941 | + | 0.229024i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 22.3787 | + | 6.84871i | 0.773984 | + | 0.236868i | ||||
\(837\) | − | 26.8013i | − | 0.926390i | ||||||
\(838\) | −11.5249 | + | 13.7348i | −0.398121 | + | 0.474462i | ||||
\(839\) | 28.3895 | − | 10.3329i | 0.980115 | − | 0.356733i | 0.198230 | − | 0.980156i | \(-0.436481\pi\) |
0.781885 | + | 0.623423i | \(0.214258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.74289 | + | 15.5557i | −0.0945823 | + | 0.536403i | ||||
\(842\) | 11.0228 | − | 30.2850i | 0.379872 | − | 1.04369i | ||||
\(843\) | 8.52266 | − | 4.92056i | 0.293536 | − | 0.169473i | ||||
\(844\) | 5.33548 | − | 9.24132i | 0.183655 | − | 0.318099i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.37672 | + | 5.35070i | −0.219236 | + | 0.183961i | ||||
\(847\) | 75.0961 | + | 43.3567i | 2.58033 | + | 1.48975i | ||||
\(848\) | 1.55885 | − | 0.900005i | 0.0535313 | − | 0.0309063i | ||||
\(849\) | 4.58664 | + | 1.66940i | 0.157413 | + | 0.0572937i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.69680 | − | 54.9933i | −0.332402 | − | 1.88515i | ||||
\(852\) | −1.18807 | − | 3.26420i | −0.0407026 | − | 0.111830i | ||||
\(853\) | −7.61549 | + | 9.07579i | −0.260750 | + | 0.310749i | −0.880497 | − | 0.474052i | \(-0.842791\pi\) |
0.619747 | + | 0.784802i | \(0.287235\pi\) | |||||||
\(854\) | −39.4731 | −1.35074 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.73078 | 0.298412 | ||||||||
\(857\) | −30.5978 | + | 36.4650i | −1.04520 | + | 1.24562i | −0.0765828 | + | 0.997063i | \(0.524401\pi\) |
−0.968617 | + | 0.248558i | \(0.920043\pi\) | |||||||
\(858\) | −4.08275 | − | 11.2173i | −0.139383 | − | 0.382951i | ||||
\(859\) | −1.97498 | − | 11.2007i | −0.0673853 | − | 0.382161i | −0.999785 | − | 0.0207325i | \(-0.993400\pi\) |
0.932400 | − | 0.361429i | \(-0.117711\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.02777 | − | 1.82996i | −0.171346 | − | 0.0623648i | ||||
\(862\) | 1.20457 | − | 0.695457i | 0.0410277 | − | 0.0236873i | ||||
\(863\) | −42.3239 | − | 24.4357i | −1.44072 | − | 0.831801i | −0.442825 | − | 0.896608i | \(-0.646024\pi\) |
−0.997898 | + | 0.0648068i | \(0.979357\pi\) | |||||||
\(864\) | −2.50263 | + | 2.09996i | −0.0851412 | + | 0.0714420i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.6267 | − | 28.7984i | 0.565000 | − | 0.978608i | ||||
\(867\) | −7.50483 | + | 4.33292i | −0.254878 | + | 0.147154i | ||||
\(868\) | 13.6482 | − | 37.4981i | 0.463250 | − | 1.27277i | ||||
\(869\) | −15.5065 | + | 87.9417i | −0.526022 | + | 2.98322i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.6091 | − | 11.1408i | 1.03715 | − | 0.377491i | ||||
\(872\) | 5.22574 | − | 6.22780i | 0.176966 | − | 0.210900i | ||||
\(873\) | − | 16.2176i | − | 0.548882i | ||||||
\(874\) | −10.5710 | + | 20.7323i | −0.357568 | + | 0.701282i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.563551 | − | 0.472875i | −0.0190406 | − | 0.0159770i | ||||
\(877\) | 10.0837 | + | 27.7048i | 0.340503 | + | 0.935524i | 0.985249 | + | 0.171127i | \(0.0547410\pi\) |
−0.644746 | + | 0.764397i | \(0.723037\pi\) | |||||||
\(878\) | 35.5652 | − | 6.27110i | 1.20027 | − | 0.211639i | ||||
\(879\) | 0.259484 | − | 1.47161i | 0.00875218 | − | 0.0496361i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.8616 | + | 36.1334i | 0.702846 | + | 1.21736i | 0.967463 | + | 0.253011i | \(0.0814209\pi\) |
−0.264618 | + | 0.964353i | \(0.585246\pi\) | |||||||
\(882\) | −38.4910 | − | 22.2228i | −1.29606 | − | 0.748280i | ||||
\(883\) | −3.80618 | − | 4.53603i | −0.128088 | − | 0.152650i | 0.698189 | − | 0.715914i | \(-0.253990\pi\) |
−0.826277 | + | 0.563264i | \(0.809545\pi\) | |||||||
\(884\) | 4.14287 | − | 3.47628i | 0.139340 | − | 0.116920i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.9938 | + | 27.7021i | 0.537323 | + | 0.930672i | ||||
\(887\) | −4.72909 | + | 12.9931i | −0.158787 | + | 0.436265i | −0.993418 | − | 0.114545i | \(-0.963459\pi\) |
0.834631 | + | 0.550810i | \(0.185681\pi\) | |||||||
\(888\) | −5.93730 | − | 1.04691i | −0.199243 | − | 0.0351319i | ||||
\(889\) | −0.117562 | − | 0.666726i | −0.00394290 | − | 0.0223613i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.1718 | − | 21.1217i | −0.843288 | − | 0.707603i | ||||
\(892\) | − | 0.0994685i | − | 0.00333045i | ||||||
\(893\) | 9.27316 | + | 9.94983i | 0.310315 | + | 0.332958i | ||||
\(894\) | −1.66386 | −0.0556478 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.57084 | + | 1.66365i | −0.152701 | + | 0.0555787i | ||||
\(897\) | 11.6898 | − | 2.06122i | 0.390310 | − | 0.0688222i | ||||
\(898\) | −2.14917 | − | 0.378957i | −0.0717187 | − | 0.0126459i | ||||
\(899\) | −28.0129 | − | 10.1959i | −0.934282 | − | 0.340051i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26189 | − | 2.18566i | 0.0420397 | − | 0.0728149i | ||||
\(902\) | −6.58588 | − | 7.84875i | −0.219286 | − | 0.261335i | ||||
\(903\) | 2.66485 | + | 3.17585i | 0.0886807 | + | 0.105686i | ||||
\(904\) | 2.24105 | − | 3.88161i | 0.0745362 | − | 0.129100i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.09307 | + | 0.397846i | 0.0363149 | + | 0.0132175i | ||||
\(907\) | 8.22903 | + | 1.45100i | 0.273240 | + | 0.0481797i | 0.308589 | − | 0.951195i | \(-0.400143\pi\) |
−0.0353489 | + | 0.999375i | \(0.511254\pi\) | |||||||
\(908\) | −13.6162 | + | 2.40090i | −0.451869 | + | 0.0796767i | ||||
\(909\) | −3.14781 | + | 1.14571i | −0.104406 | + | 0.0380008i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.5762 | 1.31122 | 0.655609 | − | 0.755101i | \(-0.272412\pi\) | ||||
0.655609 | + | 0.755101i | \(0.272412\pi\) | |||||||
\(912\) | 1.71302 | + | 1.83802i | 0.0567237 | + | 0.0608628i | ||||
\(913\) | 77.6420i | 2.56958i | ||||||||
\(914\) | −28.4997 | − | 23.9141i | −0.942685 | − | 0.791007i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.70460 | + | 15.3386i | 0.0893626 | + | 0.506800i | ||||
\(917\) | −59.5437 | − | 10.4992i | −1.96631 | − | 0.346713i | ||||
\(918\) | −1.56665 | + | 4.30433i | −0.0517071 | + | 0.142064i | ||||
\(919\) | −19.0623 | − | 33.0169i | −0.628807 | − | 1.08913i | −0.987791 | − | 0.155782i | \(-0.950210\pi\) |
0.358984 | − | 0.933344i | \(-0.383123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.81995 | + | 1.52712i | −0.0599695 | + | 0.0503204i | ||||
\(922\) | 3.13737 | + | 3.73897i | 0.103324 | + | 0.123136i | ||||
\(923\) | −20.1307 | − | 11.6225i | −0.662611 | − | 0.382559i | ||||
\(924\) | 7.52682 | + | 13.0368i | 0.247614 | + | 0.428880i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.51163 | − | 19.9154i | 0.115399 | − | 0.654462i | ||||
\(927\) | 19.3549 | − | 3.41279i | 0.635697 | − | 0.112091i | ||||
\(928\) | 1.24283 | + | 3.41464i | 0.0407977 | + | 0.112091i | ||||
\(929\) | −29.3240 | − | 24.6058i | −0.962090 | − | 0.807289i | 0.0192022 | − | 0.999816i | \(-0.493887\pi\) |
−0.981292 | + | 0.192527i | \(0.938332\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.9872 | + | 64.6962i | −1.08111 | + | 2.12033i | ||||
\(932\) | − | 15.2411i | − | 0.499238i | ||||||
\(933\) | 0.919999 | − | 1.09641i | 0.0301194 | − | 0.0358949i | ||||
\(934\) | −36.6598 | + | 13.3431i | −1.19955 | + | 0.436599i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.78684 | + | 10.1337i | −0.0584047 | + | 0.331230i | ||||
\(937\) | 0.644843 | − | 1.77169i | 0.0210661 | − | 0.0578787i | −0.928714 | − | 0.370797i | \(-0.879084\pi\) |
0.949780 | + | 0.312919i | \(0.101307\pi\) | |||||||
\(938\) | −35.5742 | + | 20.5388i | −1.16154 | + | 0.670615i | ||||
\(939\) | 1.55096 | − | 2.68635i | 0.0506138 | − | 0.0876656i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.3282 | + | 9.50548i | −0.369288 | + | 0.309870i | −0.808480 | − | 0.588524i | \(-0.799709\pi\) |
0.439192 | + | 0.898393i | \(0.355265\pi\) | |||||||
\(942\) | −5.51072 | − | 3.18161i | −0.179549 | − | 0.103663i | ||||
\(943\) | 8.82329 | − | 5.09413i | 0.287326 | − | 0.165888i | ||||
\(944\) | −6.88331 | − | 2.50532i | −0.224033 | − | 0.0815412i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.37858 | + | 7.81833i | 0.0448216 | + | 0.254196i | ||||
\(947\) | 1.94275 | + | 5.33767i | 0.0631310 | + | 0.173451i | 0.967248 | − | 0.253835i | \(-0.0816920\pi\) |
−0.904117 | + | 0.427286i | \(0.859470\pi\) | |||||||
\(948\) | −6.16232 | + | 7.34396i | −0.200143 | + | 0.238521i | ||||
\(949\) | −4.92286 | −0.159803 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2200 | 0.363834 | ||||||||
\(952\) | −4.38384 | + | 5.22446i | −0.142081 | + | 0.169326i | ||||
\(953\) | −4.40396 | − | 12.0998i | −0.142658 | − | 0.391950i | 0.847701 | − | 0.530475i | \(-0.177986\pi\) |
−0.990359 | + | 0.138524i | \(0.955764\pi\) | |||||||
\(954\) | 0.833855 | + | 4.72902i | 0.0269970 | + | 0.153108i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.8088 | − | 5.75392i | −0.511292 | − | 0.186095i | ||||
\(957\) | 9.73913 | − | 5.62289i | 0.314821 | − | 0.181762i | ||||
\(958\) | 26.9244 | + | 15.5448i | 0.869886 | + | 0.502229i | ||||
\(959\) | −53.5885 | + | 44.9661i | −1.73046 | + | 1.45203i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.1509 | + | 31.4384i | −0.585514 | + | 1.01414i | ||||
\(962\) | −34.9387 | + | 20.1719i | −1.12647 | + | 0.650367i | ||||
\(963\) | −7.96618 | + | 21.8869i | −0.256706 | + | 0.705295i | ||||
\(964\) | 1.58141 | − | 8.96862i | 0.0509338 | − | 0.288860i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.0663 | + | 5.11972i | −0.452577 | + | 0.164724i | ||||
\(967\) | 31.3467 | − | 37.3576i | 1.00804 | − | 1.20134i | 0.0286047 | − | 0.999591i | \(-0.490894\pi\) |
0.979438 | − | 0.201747i | \(-0.0646620\pi\) | |||||||
\(968\) | 17.8269i | 0.572979i | ||||||||
\(969\) | 3.36856 | + | 1.03090i | 0.108214 | + | 0.0331174i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9752 | + | 19.2784i | 0.737308 | + | 0.618675i | 0.932113 | − | 0.362167i | \(-0.117963\pi\) |
−0.194805 | + | 0.980842i | \(0.562407\pi\) | |||||||
\(972\) | −4.55864 | − | 12.5248i | −0.146218 | − | 0.401732i | ||||
\(973\) | −85.5120 | + | 15.0781i | −2.74139 | + | 0.483381i | ||||
\(974\) | −4.85765 | + | 27.5491i | −0.155649 | + | 0.882730i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.05753 | − | 7.02784i | −0.129878 | − | 0.224956i | ||||
\(977\) | 46.5081 | + | 26.8514i | 1.48792 | + | 0.859054i | 0.999905 | − | 0.0137792i | \(-0.00438620\pi\) |
0.488019 | + | 0.872833i | \(0.337720\pi\) | |||||||
\(978\) | −2.19664 | − | 2.61785i | −0.0702407 | − | 0.0837096i | ||||
\(979\) | 39.5193 | − | 33.1606i | 1.26304 | − | 1.05982i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.8442 | + | 18.7826i | 0.346227 | + | 0.599683i | ||||
\(982\) | −1.01693 | + | 2.79400i | −0.0324516 | + | 0.0891600i | ||||
\(983\) | 57.0469 | + | 10.0589i | 1.81951 | + | 0.320829i | 0.976246 | − | 0.216665i | \(-0.0695180\pi\) |
0.843267 | + | 0.537495i | \(0.180629\pi\) | |||||||
\(984\) | −0.191007 | − | 1.08326i | −0.00608908 | − | 0.0345329i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.90292 | + | 3.27494i | 0.124294 | + | 0.104295i | ||||
\(987\) | 8.74864i | 0.278472i | ||||||||
\(988\) | 16.6872 | + | 2.05367i | 0.530890 | + | 0.0653360i | ||||
\(989\) | −7.89434 | −0.251025 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.56906 | − | 2.39094i | 0.208673 | − | 0.0759508i | −0.235569 | − | 0.971858i | \(-0.575695\pi\) |
0.444242 | + | 0.895907i | \(0.353473\pi\) | |||||||
\(992\) | 8.07914 | − | 1.42457i | 0.256513 | − | 0.0452302i | ||||
\(993\) | 10.6209 | + | 1.87275i | 0.337045 | + | 0.0594301i | ||||
\(994\) | 27.5458 | + | 10.0258i | 0.873698 | + | 0.318000i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.16773 | + | 7.21872i | −0.132060 | + | 0.228734i | ||||
\(997\) | 24.4042 | + | 29.0837i | 0.772887 | + | 0.921091i | 0.998589 | − | 0.0531052i | \(-0.0169119\pi\) |
−0.225702 | + | 0.974196i | \(0.572467\pi\) | |||||||
\(998\) | 11.8511 | + | 14.1236i | 0.375140 | + | 0.447074i | ||||
\(999\) | 17.0851 | − | 29.5923i | 0.540550 | − | 0.936260i |
(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 | 950.2.u.g.149.5 | 36 | ||
5.2 | odd | 4 | 950.2.l.i.301.2 | 18 | |||
5.3 | odd | 4 | 190.2.k.d.111.2 | yes | 18 | ||
5.4 | even | 2 | inner | 950.2.u.g.149.2 | 36 | ||
19.6 | even | 9 | inner | 950.2.u.g.899.2 | 36 | ||
95.33 | even | 36 | 3610.2.a.bj.1.4 | 9 | |||
95.43 | odd | 36 | 3610.2.a.bi.1.6 | 9 | |||
95.44 | even | 18 | inner | 950.2.u.g.899.5 | 36 | ||
95.63 | odd | 36 | 190.2.k.d.101.2 | ✓ | 18 | ||
95.82 | odd | 36 | 950.2.l.i.101.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.d.101.2 | ✓ | 18 | 95.63 | odd | 36 | ||
190.2.k.d.111.2 | yes | 18 | 5.3 | odd | 4 | ||
950.2.l.i.101.2 | 18 | 95.82 | odd | 36 | |||
950.2.l.i.301.2 | 18 | 5.2 | odd | 4 | |||
950.2.u.g.149.2 | 36 | 5.4 | even | 2 | inner | ||
950.2.u.g.149.5 | 36 | 1.1 | even | 1 | trivial | ||
950.2.u.g.899.2 | 36 | 19.6 | even | 9 | inner | ||
950.2.u.g.899.5 | 36 | 95.44 | even | 18 | inner | ||
3610.2.a.bi.1.6 | 9 | 95.43 | odd | 36 | |||
3610.2.a.bj.1.4 | 9 | 95.33 | even | 36 |