Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(647,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + 16903 x^{8} - 23292 x^{7} + 26994 x^{6} - 25716 x^{5} + 19962 x^{4} + \cdots + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 971.7 | ||
Root | \(0.500000 + 0.0390518i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.971 |
Dual form | 1134.2.k.c.647.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.860850 | − | 1.49104i | 0.384984 | − | 0.666812i | −0.606783 | − | 0.794868i | \(-0.707540\pi\) |
0.991767 | + | 0.128056i | \(0.0408736\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25833 | + | 1.37838i | −0.853570 | + | 0.520978i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.49104 | − | 0.860850i | 0.471507 | − | 0.272225i | ||||
\(11\) | 1.47921 | − | 0.854023i | 0.445999 | − | 0.257498i | −0.260140 | − | 0.965571i | \(-0.583769\pi\) |
0.706139 | + | 0.708073i | \(0.250435\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.28315i | 0.355881i | 0.984041 | + | 0.177941i | \(0.0569435\pi\) | ||||
−0.984041 | + | 0.177941i | \(0.943056\pi\) | |||||||
\(14\) | −2.64496 | + | 0.0645439i | −0.706896 | + | 0.0172501i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.60152 | + | 4.50597i | 0.630962 | + | 1.09286i | 0.987355 | + | 0.158522i | \(0.0506729\pi\) |
−0.356394 | + | 0.934336i | \(0.615994\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.39385 | + | 1.38209i | 0.549187 | + | 0.317074i | 0.748794 | − | 0.662803i | \(-0.230633\pi\) |
−0.199607 | + | 0.979876i | \(0.563966\pi\) | |||||||
\(20\) | 1.72170 | 0.384984 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.70805 | 0.364157 | ||||||||
\(23\) | 4.71463 | + | 2.72199i | 0.983069 | + | 0.567575i | 0.903195 | − | 0.429230i | \(-0.141215\pi\) |
0.0798736 | + | 0.996805i | \(0.474548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.01787 | + | 1.76301i | 0.203575 | + | 0.352602i | ||||
\(26\) | −0.641574 | + | 1.11124i | −0.125823 | + | 0.217932i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.32288 | − | 1.26659i | −0.438983 | − | 0.239362i | ||||
\(29\) | 1.44960i | 0.269185i | 0.990901 | + | 0.134592i | \(0.0429725\pi\) | ||||
−0.990901 | + | 0.134592i | \(0.957028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.82274 | − | 3.36176i | 1.04579 | − | 0.603790i | 0.124325 | − | 0.992242i | \(-0.460323\pi\) |
0.921469 | + | 0.388452i | \(0.126990\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.20305i | 0.892315i | ||||||||
\(35\) | 0.111125 | + | 4.55384i | 0.0187836 | + | 0.769739i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.75959 | − | 6.51181i | 0.618073 | − | 1.07053i | −0.371764 | − | 0.928327i | \(-0.621247\pi\) |
0.989837 | − | 0.142207i | \(-0.0454198\pi\) | |||||||
\(38\) | 1.38209 | + | 2.39385i | 0.224205 | + | 0.388334i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.49104 | + | 0.860850i | 0.235754 | + | 0.136112i | ||||
\(41\) | 8.96434 | 1.39999 | 0.699997 | − | 0.714145i | \(-0.253184\pi\) | ||||
0.699997 | + | 0.714145i | \(0.253184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.37200 | −1.27672 | −0.638359 | − | 0.769739i | \(-0.720386\pi\) | ||||
−0.638359 | + | 0.769739i | \(0.720386\pi\) | |||||||
\(44\) | 1.47921 | + | 0.854023i | 0.222999 | + | 0.128749i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.72199 | + | 4.71463i | 0.401336 | + | 0.695135i | ||||
\(47\) | −2.61809 | + | 4.53466i | −0.381887 | + | 0.661448i | −0.991332 | − | 0.131381i | \(-0.958059\pi\) |
0.609445 | + | 0.792828i | \(0.291392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.20014 | − | 6.22568i | 0.457164 | − | 0.889383i | ||||
\(50\) | 2.03575i | 0.287898i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.11124 | + | 0.641574i | −0.154101 | + | 0.0889703i | ||||
\(53\) | −9.46059 | + | 5.46207i | −1.29951 | + | 0.750273i | −0.980320 | − | 0.197417i | \(-0.936745\pi\) |
−0.319192 | + | 0.947690i | \(0.603411\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.94074i | − | 0.396530i | ||||||
\(56\) | −1.37838 | − | 2.25833i | −0.184194 | − | 0.301783i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.724802 | + | 1.25539i | −0.0951711 | + | 0.164841i | ||||
\(59\) | 2.08655 | + | 3.61401i | 0.271646 | + | 0.470504i | 0.969283 | − | 0.245946i | \(-0.0790987\pi\) |
−0.697638 | + | 0.716451i | \(0.745765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.28575 | − | 1.31968i | −0.292660 | − | 0.168967i | 0.346481 | − | 0.938057i | \(-0.387377\pi\) |
−0.639141 | + | 0.769090i | \(0.720710\pi\) | |||||||
\(62\) | 6.72352 | 0.853888 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.91322 | + | 1.10460i | 0.237306 | + | 0.137009i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.31994 | − | 7.48235i | −0.527764 | − | 0.914115i | −0.999476 | − | 0.0323619i | \(-0.989697\pi\) |
0.471712 | − | 0.881753i | \(-0.343636\pi\) | |||||||
\(68\) | −2.60152 | + | 4.50597i | −0.315481 | + | 0.546429i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.18068 | + | 3.99930i | −0.260641 | + | 0.478008i | ||||
\(71\) | − | 5.07491i | − | 0.602282i | −0.953580 | − | 0.301141i | \(-0.902633\pi\) | ||
0.953580 | − | 0.301141i | \(-0.0973674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.18155 | − | 4.72362i | 0.957578 | − | 0.552858i | 0.0621516 | − | 0.998067i | \(-0.480204\pi\) |
0.895427 | + | 0.445209i | \(0.146870\pi\) | |||||||
\(74\) | 6.51181 | − | 3.75959i | 0.756982 | − | 0.437044i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.76418i | 0.317074i | ||||||||
\(77\) | −2.16339 | + | 3.96758i | −0.246541 | + | 0.452148i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.73747 | + | 11.6696i | −0.758024 | + | 1.31294i | 0.185833 | + | 0.982581i | \(0.440502\pi\) |
−0.943857 | + | 0.330355i | \(0.892832\pi\) | |||||||
\(80\) | 0.860850 | + | 1.49104i | 0.0962460 | + | 0.166703i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.76335 | + | 4.48217i | 0.857318 | + | 0.494973i | ||||
\(83\) | −6.07609 | −0.666937 | −0.333469 | − | 0.942761i | \(-0.608219\pi\) | ||||
−0.333469 | + | 0.942761i | \(0.608219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.95809 | 0.971641 | ||||||||
\(86\) | −7.25036 | − | 4.18600i | −0.781826 | − | 0.451388i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.854023 | + | 1.47921i | 0.0910391 | + | 0.157684i | ||||
\(89\) | 4.16679 | − | 7.21709i | 0.441679 | − | 0.765010i | −0.556136 | − | 0.831092i | \(-0.687717\pi\) |
0.997814 | + | 0.0660818i | \(0.0210498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.76866 | − | 2.89778i | −0.185406 | − | 0.303770i | ||||
\(92\) | 5.44399i | 0.567575i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.53466 | + | 2.61809i | −0.467714 | + | 0.270035i | ||||
\(95\) | 4.12150 | − | 2.37955i | 0.422857 | − | 0.244136i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.0571i | − | 1.02115i | −0.859834 | − | 0.510574i | \(-0.829433\pi\) | ||
0.859834 | − | 0.510574i | \(-0.170567\pi\) | |||||||
\(98\) | 5.88425 | − | 3.79152i | 0.594399 | − | 0.383002i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.01787 | + | 1.76301i | −0.101787 | + | 0.176301i | ||||
\(101\) | 7.90634 | + | 13.6942i | 0.786710 | + | 1.36262i | 0.927972 | + | 0.372650i | \(0.121551\pi\) |
−0.141261 | + | 0.989972i | \(0.545116\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.5857 | − | 7.26634i | −1.24010 | − | 0.715973i | −0.270988 | − | 0.962583i | \(-0.587350\pi\) |
−0.969115 | + | 0.246609i | \(0.920684\pi\) | |||||||
\(104\) | −1.28315 | −0.125823 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.9241 | −1.06105 | ||||||||
\(107\) | −3.01627 | − | 1.74144i | −0.291594 | − | 0.168352i | 0.347067 | − | 0.937841i | \(-0.387178\pi\) |
−0.638660 | + | 0.769489i | \(0.720511\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.53452 | − | 7.85401i | −0.434328 | − | 0.752278i | 0.562913 | − | 0.826516i | \(-0.309681\pi\) |
−0.997241 | + | 0.0742384i | \(0.976347\pi\) | |||||||
\(110\) | 1.47037 | − | 2.54676i | 0.140194 | − | 0.242824i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0645439 | − | 2.64496i | −0.00609883 | − | 0.249926i | ||||
\(113\) | − | 6.62531i | − | 0.623257i | −0.950204 | − | 0.311628i | \(-0.899126\pi\) | ||
0.950204 | − | 0.311628i | \(-0.100874\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.11719 | − | 4.68646i | 0.756931 | − | 0.437015i | ||||
\(116\) | −1.25539 | + | 0.724802i | −0.116560 | + | 0.0672961i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.17310i | 0.384165i | ||||||||
\(119\) | −12.0860 | − | 6.59010i | −1.10793 | − | 0.604114i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.04129 | + | 6.99972i | −0.367390 | + | 0.636338i | ||||
\(122\) | −1.31968 | − | 2.28575i | −0.119478 | − | 0.206942i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.82274 | + | 3.36176i | 0.522897 | + | 0.301895i | ||||
\(125\) | 12.1134 | 1.08346 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4923 | −1.72966 | −0.864830 | − | 0.502065i | \(-0.832574\pi\) | ||||
−0.864830 | + | 0.502065i | \(0.832574\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.10460 | + | 1.91322i | 0.0968797 | + | 0.167801i | ||||
\(131\) | −5.31336 | + | 9.20301i | −0.464230 | + | 0.804071i | −0.999166 | − | 0.0408220i | \(-0.987002\pi\) |
0.534936 | + | 0.844893i | \(0.320336\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.31116 | + | 0.178411i | −0.633958 | + | 0.0154702i | ||||
\(134\) | − | 8.63987i | − | 0.746371i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.50597 | + | 2.60152i | −0.386384 | + | 0.223079i | ||||
\(137\) | 1.76722 | − | 1.02030i | 0.150984 | − | 0.0871704i | −0.422605 | − | 0.906314i | \(-0.638884\pi\) |
0.573588 | + | 0.819144i | \(0.305551\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9136i | 1.51941i | 0.650266 | + | 0.759707i | \(0.274658\pi\) | ||||
−0.650266 | + | 0.759707i | \(0.725342\pi\) | |||||||
\(140\) | −3.88817 | + | 2.37316i | −0.328611 | + | 0.200568i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.53746 | − | 4.39500i | 0.212939 | − | 0.368821i | ||||
\(143\) | 1.09584 | + | 1.89805i | 0.0916386 | + | 0.158723i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.16141 | + | 1.24789i | 0.179495 | + | 0.103632i | ||||
\(146\) | 9.44724 | 0.781860 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.51919 | 0.618073 | ||||||||
\(149\) | 9.22227 | + | 5.32448i | 0.755518 | + | 0.436198i | 0.827684 | − | 0.561194i | \(-0.189658\pi\) |
−0.0721664 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.09396 | − | 8.82301i | −0.414541 | − | 0.718006i | 0.580839 | − | 0.814018i | \(-0.302725\pi\) |
−0.995380 | + | 0.0960123i | \(0.969391\pi\) | |||||||
\(152\) | −1.38209 | + | 2.39385i | −0.112102 | + | 0.194167i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.85734 | + | 2.35433i | −0.310833 | + | 0.189718i | ||||
\(155\) | − | 11.5759i | − | 0.929797i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.72429 | − | 2.15022i | 0.297231 | − | 0.171606i | −0.343967 | − | 0.938982i | \(-0.611771\pi\) |
0.641198 | + | 0.767375i | \(0.278438\pi\) | |||||||
\(158\) | −11.6696 | + | 6.73747i | −0.928386 | + | 0.536004i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.72170i | 0.136112i | ||||||||
\(161\) | −14.3992 | + | 0.351376i | −1.13481 | + | 0.0276923i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.30789 | + | 7.46149i | −0.337420 | + | 0.584429i | −0.983947 | − | 0.178463i | \(-0.942888\pi\) |
0.646527 | + | 0.762891i | \(0.276221\pi\) | |||||||
\(164\) | 4.48217 | + | 7.76335i | 0.349999 | + | 0.606216i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.26205 | − | 3.03804i | −0.408414 | − | 0.235798i | ||||
\(167\) | 13.9852 | 1.08220 | 0.541102 | − | 0.840957i | \(-0.318007\pi\) | ||||
0.541102 | + | 0.840957i | \(0.318007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3535 | 0.873348 | ||||||||
\(170\) | 7.75793 | + | 4.47904i | 0.595006 | + | 0.343527i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.18600 | − | 7.25036i | −0.319179 | − | 0.552835i | ||||
\(173\) | −8.01193 | + | 13.8771i | −0.609135 | + | 1.05505i | 0.382248 | + | 0.924060i | \(0.375150\pi\) |
−0.991383 | + | 0.130994i | \(0.958183\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.72879 | − | 2.57845i | −0.357463 | − | 0.194912i | ||||
\(176\) | 1.70805i | 0.128749i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.21709 | − | 4.16679i | 0.540944 | − | 0.312314i | ||||
\(179\) | 3.23826 | − | 1.86961i | 0.242039 | − | 0.139741i | −0.374075 | − | 0.927399i | \(-0.622040\pi\) |
0.616113 | + | 0.787658i | \(0.288706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.07693i | − | 0.0800478i | −0.999199 | − | 0.0400239i | \(-0.987257\pi\) | ||
0.999199 | − | 0.0400239i | \(-0.0127434\pi\) | |||||||
\(182\) | −0.0828194 | − | 3.39388i | −0.00613898 | − | 0.251571i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.72199 | + | 4.71463i | −0.200668 | + | 0.347567i | ||||
\(185\) | −6.47289 | − | 11.2114i | −0.475897 | − | 0.824277i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.69640 | + | 4.44352i | 0.562817 | + | 0.324942i | ||||
\(188\) | −5.23617 | −0.381887 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.75910 | 0.345261 | ||||||||
\(191\) | −14.5988 | − | 8.42859i | −1.05633 | − | 0.609872i | −0.131914 | − | 0.991261i | \(-0.542112\pi\) |
−0.924414 | + | 0.381389i | \(0.875446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.11546 | − | 12.3243i | −0.512182 | − | 0.887125i | −0.999900 | − | 0.0141241i | \(-0.995504\pi\) |
0.487718 | − | 0.873001i | \(-0.337829\pi\) | |||||||
\(194\) | 5.02857 | − | 8.70974i | 0.361030 | − | 0.625323i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.99167 | − | 0.341433i | 0.499405 | − | 0.0243880i | ||||
\(197\) | − | 19.4230i | − | 1.38383i | −0.721979 | − | 0.691915i | \(-0.756767\pi\) | ||
0.721979 | − | 0.691915i | \(-0.243233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.99323 | − | 4.03754i | 0.495737 | − | 0.286214i | −0.231214 | − | 0.972903i | \(-0.574270\pi\) |
0.726951 | + | 0.686689i | \(0.240937\pi\) | |||||||
\(200\) | −1.76301 | + | 1.01787i | −0.124664 | + | 0.0719745i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.8127i | 1.11258i | ||||||||
\(203\) | −1.99810 | − | 3.27369i | −0.140239 | − | 0.229768i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.71696 | − | 13.3662i | 0.538976 | − | 0.933533i | ||||
\(206\) | −7.26634 | − | 12.5857i | −0.506270 | − | 0.876885i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.11124 | − | 0.641574i | −0.0770506 | − | 0.0444852i | ||||
\(209\) | 4.72135 | 0.326583 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9133 | 1.37089 | 0.685444 | − | 0.728125i | \(-0.259608\pi\) | ||||
0.685444 | + | 0.728125i | \(0.259608\pi\) | |||||||
\(212\) | −9.46059 | − | 5.46207i | −0.649756 | − | 0.375137i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.74144 | − | 3.01627i | −0.119043 | − | 0.206188i | ||||
\(215\) | −7.20703 | + | 12.4829i | −0.491516 | + | 0.851330i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.51591 | + | 15.6179i | −0.578097 | + | 1.06021i | ||||
\(218\) | − | 9.06903i | − | 0.614232i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.54676 | − | 1.47037i | 0.171702 | − | 0.0991324i | ||||
\(221\) | −5.78183 | + | 3.33814i | −0.388928 | + | 0.224548i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.2100i | − | 1.42033i | −0.704036 | − | 0.710164i | \(-0.748621\pi\) | ||
0.704036 | − | 0.710164i | \(-0.251379\pi\) | |||||||
\(224\) | 1.26659 | − | 2.32288i | 0.0846273 | − | 0.155204i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.31266 | − | 5.73769i | 0.220355 | − | 0.381665i | ||||
\(227\) | −6.79579 | − | 11.7707i | −0.451053 | − | 0.781246i | 0.547399 | − | 0.836872i | \(-0.315618\pi\) |
−0.998452 | + | 0.0556258i | \(0.982285\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.8769 | − | 12.0533i | −1.37959 | − | 0.796504i | −0.387476 | − | 0.921880i | \(-0.626653\pi\) |
−0.992109 | + | 0.125376i | \(0.959986\pi\) | |||||||
\(230\) | 9.37292 | 0.618032 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.44960 | −0.0951711 | ||||||||
\(233\) | −15.9891 | − | 9.23129i | −1.04748 | − | 0.604762i | −0.125536 | − | 0.992089i | \(-0.540065\pi\) |
−0.921942 | + | 0.387327i | \(0.873398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.50756 | + | 7.80732i | 0.294041 | + | 0.509294i | ||||
\(236\) | −2.08655 | + | 3.61401i | −0.135823 | + | 0.235252i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.17177 | − | 11.7502i | −0.464877 | − | 0.761653i | ||||
\(239\) | − | 23.1917i | − | 1.50015i | −0.661355 | − | 0.750073i | \(-0.730019\pi\) | ||
0.661355 | − | 0.750073i | \(-0.269981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.4458 | − | 12.9591i | 1.44586 | − | 0.834770i | 0.447632 | − | 0.894218i | \(-0.352267\pi\) |
0.998231 | + | 0.0594484i | \(0.0189342\pi\) | |||||||
\(242\) | −6.99972 | + | 4.04129i | −0.449959 | + | 0.259784i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.63936i | − | 0.168967i | ||||||
\(245\) | −6.52787 | − | 10.1309i | −0.417050 | − | 0.647240i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.77343 | + | 3.07167i | −0.112841 | + | 0.195446i | ||||
\(248\) | 3.36176 | + | 5.82274i | 0.213472 | + | 0.369744i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.4906 | + | 6.05672i | 0.663481 | + | 0.383061i | ||||
\(251\) | 17.9492 | 1.13295 | 0.566473 | − | 0.824081i | \(-0.308308\pi\) | ||||
0.566473 | + | 0.824081i | \(0.308308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.29858 | 0.584597 | ||||||||
\(254\) | −16.8808 | − | 9.74614i | −1.05920 | − | 0.611527i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.31001 | − | 7.46516i | 0.268851 | − | 0.465664i | −0.699714 | − | 0.714423i | \(-0.746689\pi\) |
0.968565 | + | 0.248759i | \(0.0800226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.485318 | + | 19.8880i | 0.0301562 | + | 1.23578i | ||||
\(260\) | 2.20920i | 0.137009i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.20301 | + | 5.31336i | −0.568564 | + | 0.328260i | ||||
\(263\) | 16.9777 | − | 9.80208i | 1.04689 | − | 0.604422i | 0.125113 | − | 0.992143i | \(-0.460071\pi\) |
0.921777 | + | 0.387720i | \(0.126737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.8081i | 1.15537i | ||||||||
\(266\) | −6.42086 | − | 3.50107i | −0.393688 | − | 0.214665i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.31994 | − | 7.48235i | 0.263882 | − | 0.457057i | ||||
\(269\) | −6.95328 | − | 12.0434i | −0.423949 | − | 0.734301i | 0.572373 | − | 0.819994i | \(-0.306023\pi\) |
−0.996322 | + | 0.0856923i | \(0.972690\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.90381 | − | 1.09916i | −0.115648 | − | 0.0667694i | 0.441060 | − | 0.897478i | \(-0.354603\pi\) |
−0.556708 | + | 0.830708i | \(0.687936\pi\) | |||||||
\(272\) | −5.20305 | −0.315481 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.04061 | 0.123278 | ||||||||
\(275\) | 3.01130 | + | 1.73857i | 0.181588 | + | 0.104840i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.259978 | + | 0.450295i | 0.0156206 | + | 0.0270556i | 0.873730 | − | 0.486411i | \(-0.161694\pi\) |
−0.858109 | + | 0.513467i | \(0.828361\pi\) | |||||||
\(278\) | −8.95681 | + | 15.5137i | −0.537194 | + | 0.930447i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.55384 | + | 0.111125i | −0.272144 | + | 0.00664101i | ||||
\(281\) | − | 19.7706i | − | 1.17942i | −0.807616 | − | 0.589709i | \(-0.799242\pi\) | ||
0.807616 | − | 0.589709i | \(-0.200758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.1815 | + | 16.2706i | −1.67522 | + | 0.967187i | −0.710575 | + | 0.703621i | \(0.751565\pi\) |
−0.964641 | + | 0.263566i | \(0.915101\pi\) | |||||||
\(284\) | 4.39500 | − | 2.53746i | 0.260796 | − | 0.150570i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.19168i | 0.129597i | ||||||||
\(287\) | −20.2445 | + | 12.3563i | −1.19499 | + | 0.729367i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.03584 | + | 8.72233i | −0.296226 | + | 0.513078i | ||||
\(290\) | 1.24789 | + | 2.16141i | 0.0732787 | + | 0.126922i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.18155 | + | 4.72362i | 0.478789 | + | 0.276429i | ||||
\(293\) | −25.5700 | −1.49382 | −0.746909 | − | 0.664927i | \(-0.768463\pi\) | ||||
−0.746909 | + | 0.664927i | \(0.768463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.18483 | 0.418317 | ||||||||
\(296\) | 6.51181 | + | 3.75959i | 0.378491 | + | 0.218522i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.32448 | + | 9.22227i | 0.308439 | + | 0.534232i | ||||
\(299\) | −3.49272 | + | 6.04957i | −0.201989 | + | 0.349856i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.9068 | − | 11.5398i | 1.08977 | − | 0.665142i | ||||
\(302\) | − | 10.1879i | − | 0.586249i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.39385 | + | 1.38209i | −0.137297 | + | 0.0792684i | ||||
\(305\) | −3.93538 | + | 2.27209i | −0.225339 | + | 0.130100i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.85183i | 0.276909i | 0.990369 | + | 0.138454i | \(0.0442134\pi\) | ||||
−0.990369 | + | 0.138454i | \(0.955787\pi\) | |||||||
\(308\) | −4.51772 | + | 0.110244i | −0.257421 | + | 0.00628173i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.78794 | − | 10.0250i | 0.328733 | − | 0.569382i | ||||
\(311\) | −2.17193 | − | 3.76189i | −0.123159 | − | 0.213317i | 0.797853 | − | 0.602852i | \(-0.205969\pi\) |
−0.921012 | + | 0.389535i | \(0.872636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5391 | + | 11.2809i | 1.10442 | + | 0.637635i | 0.937378 | − | 0.348315i | \(-0.113246\pi\) |
0.167039 | + | 0.985950i | \(0.446579\pi\) | |||||||
\(314\) | 4.30044 | 0.242688 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.4749 | −0.758024 | ||||||||
\(317\) | 29.6293 | + | 17.1065i | 1.66415 | + | 0.960795i | 0.970703 | + | 0.240282i | \(0.0772399\pi\) |
0.693442 | + | 0.720513i | \(0.256093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23799 | + | 2.14427i | 0.0693144 | + | 0.120056i | ||||
\(320\) | −0.860850 | + | 1.49104i | −0.0481230 | + | 0.0833515i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.6457 | − | 6.89528i | −0.704718 | − | 0.384259i | ||||
\(323\) | 14.3822i | 0.800245i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.26220 | + | 1.30608i | −0.125484 | + | 0.0724485i | ||||
\(326\) | −7.46149 | + | 4.30789i | −0.413254 | + | 0.238592i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.96434i | 0.494973i | ||||||||
\(329\) | −0.337963 | − | 13.8495i | −0.0186325 | − | 0.763547i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.28003 | − | 3.94913i | 0.125322 | − | 0.217064i | −0.796537 | − | 0.604590i | \(-0.793337\pi\) |
0.921859 | + | 0.387526i | \(0.126670\pi\) | |||||||
\(332\) | −3.03804 | − | 5.26205i | −0.166734 | − | 0.288792i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1115 | + | 6.99258i | 0.662712 | + | 0.382617i | ||||
\(335\) | −14.8753 | −0.812723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.7531 | 1.67523 | 0.837613 | − | 0.546264i | \(-0.183950\pi\) | ||||
0.837613 | + | 0.546264i | \(0.183950\pi\) | |||||||
\(338\) | 9.83245 | + | 5.67676i | 0.534815 | + | 0.308775i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.47904 | + | 7.75793i | 0.242910 | + | 0.420733i | ||||
\(341\) | 5.74204 | − | 9.94550i | 0.310949 | − | 0.538579i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.35435 | + | 18.4707i | 0.0731278 | + | 0.997323i | ||||
\(344\) | − | 8.37200i | − | 0.451388i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.8771 | + | 8.01193i | −0.746035 | + | 0.430724i | ||||
\(347\) | −20.6474 | + | 11.9208i | −1.10841 | + | 0.639940i | −0.938417 | − | 0.345506i | \(-0.887707\pi\) |
−0.169992 | + | 0.985446i | \(0.554374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.14373i | − | 0.168280i | −0.996454 | − | 0.0841401i | \(-0.973186\pi\) | ||
0.996454 | − | 0.0841401i | \(-0.0268143\pi\) | |||||||
\(350\) | −2.80603 | − | 4.59740i | −0.149989 | − | 0.245741i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.854023 | + | 1.47921i | −0.0455196 | + | 0.0788422i | ||||
\(353\) | 13.8459 | + | 23.9818i | 0.736944 | + | 1.27642i | 0.953865 | + | 0.300236i | \(0.0970653\pi\) |
−0.216921 | + | 0.976189i | \(0.569601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.56688 | − | 4.36874i | −0.401608 | − | 0.231869i | ||||
\(356\) | 8.33357 | 0.441679 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.73922 | 0.197624 | ||||||||
\(359\) | 18.1125 | + | 10.4572i | 0.955940 | + | 0.551912i | 0.894921 | − | 0.446225i | \(-0.147232\pi\) |
0.0610187 | + | 0.998137i | \(0.480565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.67965 | − | 9.83744i | −0.298929 | − | 0.517760i | ||||
\(362\) | 0.538466 | − | 0.932651i | 0.0283012 | − | 0.0490190i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.62522 | − | 2.98060i | 0.0851845 | − | 0.156226i | ||||
\(365\) | − | 16.2653i | − | 0.851366i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.01292 | + | 0.584811i | −0.0528741 | + | 0.0305269i | −0.526204 | − | 0.850358i | \(-0.676385\pi\) |
0.473330 | + | 0.880885i | \(0.343052\pi\) | |||||||
\(368\) | −4.71463 | + | 2.72199i | −0.245767 | + | 0.141894i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 12.9458i | − | 0.673019i | ||||||
\(371\) | 13.8364 | − | 25.3755i | 0.718348 | − | 1.31743i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.85503 | + | 8.40915i | −0.251384 | + | 0.435409i | −0.963907 | − | 0.266239i | \(-0.914219\pi\) |
0.712523 | + | 0.701648i | \(0.247552\pi\) | |||||||
\(374\) | 4.44352 | + | 7.69640i | 0.229769 | + | 0.397971i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.53466 | − | 2.61809i | −0.233857 | − | 0.135017i | ||||
\(377\) | −1.86006 | −0.0957978 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.1452 | −0.777958 | −0.388979 | − | 0.921247i | \(-0.627172\pi\) | ||||
−0.388979 | + | 0.921247i | \(0.627172\pi\) | |||||||
\(380\) | 4.12150 | + | 2.37955i | 0.211428 | + | 0.122068i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.42859 | − | 14.5988i | −0.431244 | − | 0.746937i | ||||
\(383\) | −15.9902 | + | 27.6958i | −0.817059 | + | 1.41519i | 0.0907815 | + | 0.995871i | \(0.471064\pi\) |
−0.907840 | + | 0.419316i | \(0.862270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.05346 | + | 6.64118i | 0.206583 | + | 0.338466i | ||||
\(386\) | − | 14.2309i | − | 0.724335i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.70974 | − | 5.02857i | 0.442170 | − | 0.255287i | ||||
\(389\) | −21.6056 | + | 12.4740i | −1.09545 | + | 0.632457i | −0.935021 | − | 0.354591i | \(-0.884620\pi\) |
−0.160426 | + | 0.987048i | \(0.551287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.3253i | 1.43247i | ||||||||
\(392\) | 6.22568 | + | 3.20014i | 0.314444 | + | 0.161632i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.71149 | − | 16.8208i | 0.489258 | − | 0.847420i | ||||
\(395\) | 11.5999 | + | 20.0916i | 0.583654 | + | 1.01092i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.280202 | + | 0.161774i | 0.0140629 | + | 0.00811923i | 0.507015 | − | 0.861937i | \(-0.330749\pi\) |
−0.492952 | + | 0.870056i | \(0.664082\pi\) | |||||||
\(398\) | 8.07509 | 0.404768 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.03575 | −0.101787 | ||||||||
\(401\) | −16.4678 | − | 9.50768i | −0.822362 | − | 0.474791i | 0.0288684 | − | 0.999583i | \(-0.490810\pi\) |
−0.851230 | + | 0.524792i | \(0.824143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.31364 | + | 7.47144i | 0.214877 | + | 0.372179i | ||||
\(404\) | −7.90634 | + | 13.6942i | −0.393355 | + | 0.681311i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0935631 | − | 3.83415i | −0.00464346 | − | 0.190286i | ||||
\(407\) | − | 12.8431i | − | 0.636609i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.90841 | − | 2.25652i | 0.193258 | − | 0.111578i | −0.400249 | − | 0.916407i | \(-0.631076\pi\) |
0.593507 | + | 0.804829i | \(0.297743\pi\) | |||||||
\(410\) | 13.3662 | − | 7.71696i | 0.660108 | − | 0.381113i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 14.5327i | − | 0.715973i | ||||||
\(413\) | −9.69361 | − | 5.28559i | −0.476991 | − | 0.260087i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.23060 | + | 9.05967i | −0.256760 | + | 0.444722i | ||||
\(416\) | −0.641574 | − | 1.11124i | −0.0314558 | − | 0.0544830i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.08881 | + | 2.36068i | 0.199990 | + | 0.115464i | ||||
\(419\) | 29.2149 | 1.42724 | 0.713621 | − | 0.700532i | \(-0.247054\pi\) | ||||
0.713621 | + | 0.700532i | \(0.247054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.3361 | −1.77092 | −0.885458 | − | 0.464720i | \(-0.846155\pi\) | ||||
−0.885458 | + | 0.464720i | \(0.846155\pi\) | |||||||
\(422\) | 17.2454 | + | 9.95665i | 0.839494 | + | 0.484682i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.46207 | − | 9.46059i | −0.265262 | − | 0.459447i | ||||
\(425\) | −5.29604 | + | 9.17301i | −0.256896 | + | 0.444957i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.98100 | − | 0.170354i | 0.337834 | − | 0.00824403i | ||||
\(428\) | − | 3.48289i | − | 0.168352i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.4829 | + | 7.20703i | −0.601981 | + | 0.347554i | ||||
\(431\) | 10.4967 | − | 6.06028i | 0.505609 | − | 0.291913i | −0.225418 | − | 0.974262i | \(-0.572375\pi\) |
0.731027 | + | 0.682349i | \(0.239041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.4160i | − | 1.50976i | −0.655864 | − | 0.754879i | \(-0.727696\pi\) | ||
0.655864 | − | 0.754879i | \(-0.272304\pi\) | |||||||
\(434\) | −15.1839 | + | 9.26755i | −0.728853 | + | 0.444857i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.53452 | − | 7.85401i | 0.217164 | − | 0.376139i | ||||
\(437\) | 7.52409 | + | 13.0321i | 0.359926 | + | 0.623410i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.80118 | − | 1.61726i | −0.133693 | − | 0.0771877i | 0.431662 | − | 0.902036i | \(-0.357927\pi\) |
−0.565355 | + | 0.824848i | \(0.691261\pi\) | |||||||
\(440\) | 2.94074 | 0.140194 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.67628 | −0.317558 | ||||||||
\(443\) | 7.65097 | + | 4.41729i | 0.363509 | + | 0.209872i | 0.670619 | − | 0.741802i | \(-0.266029\pi\) |
−0.307110 | + | 0.951674i | \(0.599362\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.17396 | − | 12.4257i | −0.340078 | − | 0.589033i | ||||
\(446\) | 10.6050 | − | 18.3684i | 0.502162 | − | 0.869770i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.25833 | − | 1.37838i | 0.106696 | − | 0.0651223i | ||||
\(449\) | − | 6.83193i | − | 0.322419i | −0.986920 | − | 0.161209i | \(-0.948461\pi\) | ||
0.986920 | − | 0.161209i | \(-0.0515395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.2602 | − | 7.65575i | 0.624396 | − | 0.360495i | ||||
\(452\) | 5.73769 | − | 3.31266i | 0.269878 | − | 0.155814i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 13.5916i | − | 0.637885i | ||||||
\(455\) | −5.84325 | + | 0.142590i | −0.273936 | + | 0.00668473i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.21190 | + | 15.9555i | −0.430915 | + | 0.746366i | −0.996952 | − | 0.0780133i | \(-0.975142\pi\) |
0.566038 | + | 0.824379i | \(0.308476\pi\) | |||||||
\(458\) | −12.0533 | − | 20.8769i | −0.563213 | − | 0.975514i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.11719 | + | 4.68646i | 0.378466 | + | 0.218507i | ||||
\(461\) | 29.9065 | 1.39289 | 0.696443 | − | 0.717612i | \(-0.254765\pi\) | ||||
0.696443 | + | 0.717612i | \(0.254765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.32509 | 0.0615821 | 0.0307911 | − | 0.999526i | \(-0.490197\pi\) | ||||
0.0307911 | + | 0.999526i | \(0.490197\pi\) | |||||||
\(464\) | −1.25539 | − | 0.724802i | −0.0582802 | − | 0.0336481i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.23129 | − | 15.9891i | −0.427631 | − | 0.740679i | ||||
\(467\) | 13.6817 | − | 23.6973i | 0.633112 | − | 1.09658i | −0.353800 | − | 0.935321i | \(-0.615111\pi\) |
0.986912 | − | 0.161260i | \(-0.0515559\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0694 | + | 10.9431i | 0.926718 | + | 0.505307i | ||||
\(470\) | 9.01512i | 0.415836i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.61401 | + | 2.08655i | −0.166348 | + | 0.0960413i | ||||
\(473\) | −12.3839 | + | 7.14987i | −0.569414 | + | 0.328752i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.62718i | 0.258193i | ||||||||
\(476\) | −0.335825 | − | 13.7619i | −0.0153925 | − | 0.630774i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.5958 | − | 20.0846i | 0.530381 | − | 0.918648i | ||||
\(479\) | −8.41054 | − | 14.5675i | −0.384287 | − | 0.665605i | 0.607383 | − | 0.794409i | \(-0.292219\pi\) |
−0.991670 | + | 0.128804i | \(0.958886\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.35561 | + | 4.82412i | 0.380983 | + | 0.219961i | ||||
\(482\) | 25.9182 | 1.18054 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.08258 | −0.367390 | ||||||||
\(485\) | −14.9956 | − | 8.65769i | −0.680913 | − | 0.393126i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.357602 | + | 0.619385i | 0.0162045 | + | 0.0280670i | 0.874014 | − | 0.485901i | \(-0.161508\pi\) |
−0.857809 | + | 0.513968i | \(0.828175\pi\) | |||||||
\(488\) | 1.31968 | − | 2.28575i | 0.0597390 | − | 0.103471i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.587845 | − | 12.0376i | −0.0265561 | − | 0.543801i | ||||
\(491\) | 5.36907i | 0.242303i | 0.992634 | + | 0.121151i | \(0.0386586\pi\) | ||||
−0.992634 | + | 0.121151i | \(0.961341\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.53187 | + | 3.77118i | −0.294181 | + | 0.169845i | ||||
\(494\) | −3.07167 | + | 1.77343i | −0.138201 | + | 0.0797903i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.72352i | 0.301895i | ||||||||
\(497\) | 6.99515 | + | 11.4609i | 0.313776 | + | 0.514089i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0464 | + | 20.8649i | −0.539269 | + | 0.934041i | 0.459675 | + | 0.888087i | \(0.347966\pi\) |
−0.998944 | + | 0.0459536i | \(0.985367\pi\) | |||||||
\(500\) | 6.05672 | + | 10.4906i | 0.270865 | + | 0.469152i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.5445 | + | 8.97461i | 0.693784 | + | 0.400557i | ||||
\(503\) | 26.8386 | 1.19667 | 0.598336 | − | 0.801245i | \(-0.295829\pi\) | ||||
0.598336 | + | 0.801245i | \(0.295829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.2247 | 1.21148 | ||||||||
\(506\) | 8.05281 | + | 4.64929i | 0.357991 | + | 0.206686i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.74614 | − | 16.8808i | −0.432415 | − | 0.748965i | ||||
\(509\) | −20.1952 | + | 34.9791i | −0.895137 | + | 1.55042i | −0.0615030 | + | 0.998107i | \(0.519589\pi\) |
−0.833634 | + | 0.552317i | \(0.813744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9657 | + | 21.9448i | −0.529333 | + | 0.970781i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.46516 | − | 4.31001i | 0.329274 | − | 0.190107i | ||||
\(515\) | −21.6687 | + | 12.5105i | −0.954839 | + | 0.551277i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.94362i | 0.393340i | ||||||||
\(518\) | −9.52369 | + | 17.4661i | −0.418447 | + | 0.767419i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.10460 | + | 1.91322i | −0.0484399 | + | 0.0839003i | ||||
\(521\) | 15.1983 | + | 26.3243i | 0.665852 | + | 1.15329i | 0.979054 | + | 0.203602i | \(0.0652649\pi\) |
−0.313202 | + | 0.949686i | \(0.601402\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.53367 | − | 3.19487i | −0.241971 | − | 0.139702i | 0.374112 | − | 0.927384i | \(-0.377948\pi\) |
−0.616082 | + | 0.787682i | \(0.711281\pi\) | |||||||
\(524\) | −10.6267 | −0.464230 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.6042 | 0.854782 | ||||||||
\(527\) | 30.2960 | + | 17.4914i | 1.31971 | + | 0.761937i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.31851 | + | 5.74782i | 0.144283 | + | 0.249905i | ||||
\(530\) | −9.40405 | + | 16.2883i | −0.408486 | + | 0.707518i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.81009 | − | 6.24245i | −0.165188 | − | 0.270644i | ||||
\(533\) | 11.5026i | 0.498232i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.19311 | + | 2.99825i | −0.224518 | + | 0.129625i | ||||
\(536\) | 7.48235 | − | 4.31994i | 0.323188 | − | 0.186593i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 13.9066i | − | 0.599555i | ||||||
\(539\) | −0.583182 | − | 11.9421i | −0.0251194 | − | 0.514382i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.909263 | + | 1.57489i | −0.0390923 | + | 0.0677098i | −0.884910 | − | 0.465763i | \(-0.845780\pi\) |
0.845817 | + | 0.533473i | \(0.179113\pi\) | |||||||
\(542\) | −1.09916 | − | 1.90381i | −0.0472131 | − | 0.0817755i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.50597 | − | 2.60152i | −0.193192 | − | 0.111539i | ||||
\(545\) | −15.6142 | −0.668837 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.7214 | −1.86939 | −0.934695 | − | 0.355450i | \(-0.884327\pi\) | ||||
−0.934695 | + | 0.355450i | \(0.884327\pi\) | |||||||
\(548\) | 1.76722 | + | 1.02030i | 0.0754918 | + | 0.0435852i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.73857 | + | 3.01130i | 0.0741331 | + | 0.128402i | ||||
\(551\) | −2.00348 | + | 3.47014i | −0.0853513 | + | 0.147833i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.869725 | − | 35.6407i | −0.0369845 | − | 1.51560i | ||||
\(554\) | 0.519956i | 0.0220908i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.5137 | + | 8.95681i | −0.657926 | + | 0.379854i | ||||
\(557\) | 22.5591 | − | 13.0245i | 0.955859 | − | 0.551865i | 0.0609627 | − | 0.998140i | \(-0.480583\pi\) |
0.894896 | + | 0.446275i | \(0.147250\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.7425i | − | 0.454360i | ||||||
\(560\) | −3.99930 | − | 2.18068i | −0.169001 | − | 0.0921506i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.88532 | − | 17.1219i | 0.416987 | − | 0.722243i | ||||
\(563\) | −2.00985 | − | 3.48116i | −0.0847051 | − | 0.146713i | 0.820560 | − | 0.571560i | \(-0.193661\pi\) |
−0.905265 | + | 0.424846i | \(0.860328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.87858 | − | 5.70340i | −0.415595 | − | 0.239944i | ||||
\(566\) | −32.5412 | −1.36781 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.07491 | 0.212939 | ||||||||
\(569\) | −2.17982 | − | 1.25852i | −0.0913826 | − | 0.0527598i | 0.453612 | − | 0.891199i | \(-0.350135\pi\) |
−0.544995 | + | 0.838439i | \(0.683468\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.44662 | + | 2.50561i | 0.0605390 | + | 0.104857i | 0.894706 | − | 0.446655i | \(-0.147385\pi\) |
−0.834167 | + | 0.551511i | \(0.814051\pi\) | |||||||
\(572\) | −1.09584 | + | 1.89805i | −0.0458193 | + | 0.0793613i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.7104 | + | 0.578594i | −0.989651 | + | 0.0241500i | ||||
\(575\) | 11.0826i | 0.462176i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.76783 | − | 1.59801i | 0.115226 | − | 0.0665258i | −0.441279 | − | 0.897370i | \(-0.645475\pi\) |
0.556505 | + | 0.830844i | \(0.312142\pi\) | |||||||
\(578\) | −8.72233 | + | 5.03584i | −0.362801 | + | 0.209463i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.49578i | 0.103632i | ||||||||
\(581\) | 13.7218 | − | 8.37515i | 0.569278 | − | 0.347460i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.32947 | + | 16.1591i | −0.386387 | + | 0.669242i | ||||
\(584\) | 4.72362 | + | 8.18155i | 0.195465 | + | 0.338555i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.1443 | − | 12.7850i | −0.914772 | − | 0.528144i | ||||
\(587\) | 27.5816 | 1.13841 | 0.569207 | − | 0.822194i | \(-0.307250\pi\) | ||||
0.569207 | + | 0.822194i | \(0.307250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.5850 | 0.765783 | ||||||||
\(590\) | 6.22225 | + | 3.59242i | 0.256166 | + | 0.147897i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.75959 | + | 6.51181i | 0.154518 | + | 0.267634i | ||||
\(593\) | −15.1199 | + | 26.1884i | −0.620899 | + | 1.07543i | 0.368420 | + | 0.929660i | \(0.379899\pi\) |
−0.989319 | + | 0.145769i | \(0.953434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.2303 | + | 12.3476i | −0.829363 | + | 0.506204i | ||||
\(596\) | 10.6490i | 0.436198i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.04957 | + | 3.49272i | −0.247385 | + | 0.142828i | ||||
\(599\) | −2.87629 | + | 1.66063i | −0.117522 | + | 0.0678515i | −0.557609 | − | 0.830104i | \(-0.688281\pi\) |
0.440087 | + | 0.897955i | \(0.354948\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0946i | 0.411766i | 0.978577 | + | 0.205883i | \(0.0660067\pi\) | ||||
−0.978577 | + | 0.205883i | \(0.933993\pi\) | |||||||
\(602\) | 22.1436 | − | 0.540361i | 0.902507 | − | 0.0220235i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.09396 | − | 8.82301i | 0.207270 | − | 0.359003i | ||||
\(605\) | 6.95789 | + | 12.0514i | 0.282879 | + | 0.489960i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.1038 | − | 10.4523i | −0.734812 | − | 0.424244i | 0.0853682 | − | 0.996349i | \(-0.472793\pi\) |
−0.820180 | + | 0.572106i | \(0.806127\pi\) | |||||||
\(608\) | −2.76418 | −0.112102 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.54418 | −0.183989 | ||||||||
\(611\) | −5.81864 | − | 3.35939i | −0.235397 | − | 0.135907i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.11525 | + | 3.66372i | 0.0854341 | + | 0.147976i | 0.905576 | − | 0.424184i | \(-0.139439\pi\) |
−0.820142 | + | 0.572160i | \(0.806106\pi\) | |||||||
\(614\) | −2.42592 | + | 4.20181i | −0.0979020 | + | 0.169571i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.96758 | − | 2.16339i | −0.159858 | − | 0.0871653i | ||||
\(617\) | 6.22012i | 0.250412i | 0.992131 | + | 0.125206i | \(0.0399593\pi\) | ||||
−0.992131 | + | 0.125206i | \(0.960041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7546 | + | 13.7148i | −0.954780 | + | 0.551242i | −0.894562 | − | 0.446943i | \(-0.852513\pi\) |
−0.0602173 | + | 0.998185i | \(0.519179\pi\) | |||||||
\(620\) | 10.0250 | − | 5.78794i | 0.402614 | − | 0.232449i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 4.34386i | − | 0.174173i | ||||||
\(623\) | 0.537881 | + | 22.0420i | 0.0215498 | + | 0.883094i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.33850 | − | 9.24655i | 0.213540 | − | 0.369862i | ||||
\(626\) | 11.2809 | + | 19.5391i | 0.450876 | + | 0.780941i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.72429 | + | 2.15022i | 0.148616 | + | 0.0858032i | ||||
\(629\) | 39.1227 | 1.55992 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.0610 | −0.599570 | −0.299785 | − | 0.954007i | \(-0.596915\pi\) | ||||
−0.299785 | + | 0.954007i | \(0.596915\pi\) | |||||||
\(632\) | −11.6696 | − | 6.73747i | −0.464193 | − | 0.268002i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.1065 | + | 29.6293i | 0.679384 | + | 1.17673i | ||||
\(635\) | −16.7799 | + | 29.0637i | −0.665891 | + | 1.15336i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.98847 | + | 4.10626i | 0.316515 | + | 0.162696i | ||||
\(638\) | 2.47599i | 0.0980253i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.49104 | + | 0.860850i | −0.0589384 | + | 0.0340281i | ||||
\(641\) | 21.2390 | − | 12.2623i | 0.838890 | − | 0.484333i | −0.0179970 | − | 0.999838i | \(-0.505729\pi\) |
0.856887 | + | 0.515505i | \(0.172396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.1029i | − | 1.73925i | −0.493714 | − | 0.869625i | \(-0.664361\pi\) | ||
0.493714 | − | 0.869625i | \(-0.335639\pi\) | |||||||
\(644\) | −7.50388 | − | 12.2943i | −0.295694 | − | 0.484465i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.19108 | + | 12.4553i | −0.282929 | + | 0.490048i | ||||
\(647\) | 3.67645 | + | 6.36779i | 0.144536 | + | 0.250344i | 0.929200 | − | 0.369578i | \(-0.120498\pi\) |
−0.784664 | + | 0.619922i | \(0.787164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.17290 | + | 3.56393i | 0.242308 | + | 0.139896i | ||||
\(650\) | −2.61217 | −0.102458 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.61578 | −0.337420 | ||||||||
\(653\) | −4.37627 | − | 2.52664i | −0.171257 | − | 0.0988750i | 0.411922 | − | 0.911219i | \(-0.364858\pi\) |
−0.583178 | + | 0.812344i | \(0.698191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.14801 | + | 15.8448i | 0.357442 | + | 0.619109i | ||||
\(656\) | −4.48217 | + | 7.76335i | −0.174999 | + | 0.303108i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.63206 | − | 12.1630i | 0.258545 | − | 0.474163i | ||||
\(659\) | 2.83130i | 0.110292i | 0.998478 | + | 0.0551460i | \(0.0175624\pi\) | ||||
−0.998478 | + | 0.0551460i | \(0.982438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5374 | − | 14.7440i | 0.993290 | − | 0.573476i | 0.0870338 | − | 0.996205i | \(-0.472261\pi\) |
0.906256 | + | 0.422729i | \(0.138928\pi\) | |||||||
\(662\) | 3.94913 | − | 2.28003i | 0.153487 | − | 0.0886159i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.07609i | − | 0.235798i | ||||||
\(665\) | −6.02780 | + | 11.0548i | −0.233748 | + | 0.428687i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.94581 | + | 6.83435i | −0.152782 | + | 0.264627i | ||||
\(668\) | 6.99258 | + | 12.1115i | 0.270551 | + | 0.468608i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.8824 | − | 7.43764i | −0.497689 | − | 0.287341i | ||||
\(671\) | −4.50814 | −0.174035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.2177 | 1.12626 | 0.563130 | − | 0.826368i | \(-0.309597\pi\) | ||||
0.563130 | + | 0.826368i | \(0.309597\pi\) | |||||||
\(674\) | 26.6329 | + | 15.3765i | 1.02586 | + | 0.592282i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.67676 | + | 9.83245i | 0.218337 | + | 0.378171i | ||||
\(677\) | −11.4401 | + | 19.8149i | −0.439680 | + | 0.761548i | −0.997665 | − | 0.0683033i | \(-0.978241\pi\) |
0.557985 | + | 0.829851i | \(0.311575\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8625 | + | 22.7124i | 0.531996 | + | 0.871621i | ||||
\(680\) | 8.95809i | 0.343527i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.94550 | − | 5.74204i | 0.380833 | − | 0.219874i | ||||
\(683\) | −13.0677 | + | 7.54464i | −0.500021 | + | 0.288688i | −0.728722 | − | 0.684809i | \(-0.759886\pi\) |
0.228701 | + | 0.973497i | \(0.426552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.51331i | − | 0.134237i | ||||||
\(686\) | −8.06244 | + | 16.6732i | −0.307825 | + | 0.636587i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.18600 | − | 7.25036i | 0.159590 | − | 0.276417i | ||||
\(689\) | −7.00865 | − | 12.1393i | −0.267008 | − | 0.462472i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.1708 | − | 13.9550i | −0.919499 | − | 0.530873i | −0.0360240 | − | 0.999351i | \(-0.511469\pi\) |
−0.883475 | + | 0.468478i | \(0.844803\pi\) | |||||||
\(692\) | −16.0239 | −0.609135 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.8415 | −0.905012 | ||||||||
\(695\) | 26.7099 | + | 15.4210i | 1.01316 | + | 0.584950i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.3209 | + | 40.3930i | 0.883343 | + | 1.53000i | ||||
\(698\) | 1.57187 | − | 2.72255i | 0.0594960 | − | 0.103050i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.131395 | − | 5.38448i | −0.00496627 | − | 0.203514i | ||||
\(701\) | − | 27.9911i | − | 1.05721i | −0.848868 | − | 0.528605i | \(-0.822715\pi\) | ||
0.848868 | − | 0.528605i | \(-0.177285\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.9998 | − | 10.3922i | 0.678876 | − | 0.391949i | ||||
\(704\) | −1.47921 | + | 0.854023i | −0.0557499 | + | 0.0321872i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.6919i | 1.04220i | ||||||||
\(707\) | −36.7309 | − | 20.0281i | −1.38141 | − | 0.753235i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5397 | + | 19.9873i | −0.433382 | + | 0.750640i | −0.997162 | − | 0.0752852i | \(-0.976013\pi\) |
0.563780 | + | 0.825925i | \(0.309347\pi\) | |||||||
\(710\) | −4.36874 | − | 7.56688i | −0.163956 | − | 0.283980i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.21709 | + | 4.16679i | 0.270472 | + | 0.156157i | ||||
\(713\) | 36.6028 | 1.37078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.77341 | 0.141118 | ||||||||
\(716\) | 3.23826 | + | 1.86961i | 0.121019 | + | 0.0698705i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.4572 | + | 18.1125i | 0.390261 | + | 0.675951i | ||||
\(719\) | 9.45610 | − | 16.3784i | 0.352653 | − | 0.610813i | −0.634061 | − | 0.773283i | \(-0.718613\pi\) |
0.986713 | + | 0.162471i | \(0.0519463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.4384 | − | 0.937996i | 1.43152 | − | 0.0349328i | ||||
\(722\) | − | 11.3593i | − | 0.422749i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.932651 | − | 0.538466i | 0.0346617 | − | 0.0200119i | ||||
\(725\) | −2.55566 | + | 1.47551i | −0.0949150 | + | 0.0547992i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.34127i | − | 0.198097i | −0.995083 | − | 0.0990484i | \(-0.968420\pi\) | ||
0.995083 | − | 0.0990484i | \(-0.0315799\pi\) | |||||||
\(728\) | 2.89778 | − | 1.76866i | 0.107399 | − | 0.0655511i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.13266 | − | 14.0862i | 0.301003 | − | 0.521353i | ||||
\(731\) | −21.7799 | − | 37.7240i | −0.805560 | − | 1.39527i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.6896 | − | 25.8016i | −1.65065 | − | 0.953003i | −0.976805 | − | 0.214129i | \(-0.931309\pi\) |
−0.673844 | − | 0.738874i | \(-0.735358\pi\) | |||||||
\(734\) | −1.16962 | −0.0431715 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.44399 | −0.200668 | ||||||||
\(737\) | −12.7802 | − | 7.37865i | −0.470765 | − | 0.271796i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.0639 | + | 31.2875i | 0.664490 | + | 1.15093i | 0.979423 | + | 0.201817i | \(0.0646847\pi\) |
−0.314933 | + | 0.949114i | \(0.601982\pi\) | |||||||
\(740\) | 6.47289 | − | 11.2114i | 0.237948 | − | 0.412139i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.6704 | − | 15.0576i | 0.905678 | − | 0.552782i | ||||
\(743\) | − | 3.88507i | − | 0.142529i | −0.997457 | − | 0.0712647i | \(-0.977296\pi\) | ||
0.997457 | − | 0.0712647i | \(-0.0227035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.8780 | − | 9.16716i | 0.581724 | − | 0.335859i | ||||
\(746\) | −8.40915 | + | 4.85503i | −0.307881 | + | 0.177755i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.88704i | 0.324942i | ||||||||
\(749\) | 9.21212 | − | 0.224799i | 0.336603 | − | 0.00821399i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.55761 | + | 2.69786i | −0.0568380 | + | 0.0984463i | −0.893044 | − | 0.449969i | \(-0.851435\pi\) |
0.836206 | + | 0.548415i | \(0.184769\pi\) | |||||||
\(752\) | −2.61809 | − | 4.53466i | −0.0954718 | − | 0.165362i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.61086 | − | 0.930028i | −0.0586639 | − | 0.0338696i | ||||
\(755\) | −17.5406 | −0.638366 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.55505 | −0.0565193 | −0.0282597 | − | 0.999601i | \(-0.508997\pi\) | ||||
−0.0282597 | + | 0.999601i | \(0.508997\pi\) | |||||||
\(758\) | −13.1161 | − | 7.57261i | −0.476400 | − | 0.275050i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.37955 | + | 4.12150i | 0.0863153 | + | 0.149502i | ||||
\(761\) | 24.4514 | − | 42.3511i | 0.886364 | − | 1.53523i | 0.0422217 | − | 0.999108i | \(-0.486556\pi\) |
0.844142 | − | 0.536119i | \(-0.180110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.0663 | + | 11.4867i | 0.762650 | + | 0.415847i | ||||
\(764\) | − | 16.8572i | − | 0.609872i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.6958 | + | 15.9902i | −1.00069 | + | 0.577748i | ||||
\(767\) | −4.63732 | + | 2.67736i | −0.167444 | + | 0.0966737i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3089i | 0.696298i | 0.937439 | + | 0.348149i | \(0.113190\pi\) | ||||
−0.937439 | + | 0.348149i | \(0.886810\pi\) | |||||||
\(770\) | 0.189807 | + | 7.77816i | 0.00684017 | + | 0.280305i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.11546 | − | 12.3243i | 0.256091 | − | 0.443563i | ||||
\(773\) | 21.5416 | + | 37.3112i | 0.774798 | + | 1.34199i | 0.934908 | + | 0.354890i | \(0.115482\pi\) |
−0.160110 | + | 0.987099i | \(0.551185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.8536 | + | 6.84369i | 0.425795 | + | 0.245833i | ||||
\(776\) | 10.0571 | 0.361030 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.9480 | −0.894429 | ||||||||
\(779\) | 21.4593 | + | 12.3895i | 0.768860 | + | 0.443901i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.33409 | − | 7.50687i | −0.155086 | − | 0.268617i | ||||
\(782\) | −14.1627 | + | 24.5304i | −0.506456 | + | 0.877207i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.79152 | + | 5.88425i | 0.135412 | + | 0.210152i | ||||
\(785\) | − | 7.40408i | − | 0.264263i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.16193 | + | 2.98024i | −0.184003 | + | 0.106234i | −0.589172 | − | 0.808008i | \(-0.700546\pi\) |
0.405169 | + | 0.914242i | \(0.367213\pi\) | |||||||
\(788\) | 16.8208 | − | 9.71149i | 0.599216 | − | 0.345958i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23.1998i | 0.825412i | ||||||||
\(791\) | 9.13219 | + | 14.9622i | 0.324703 | + | 0.531993i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.69334 | − | 2.93296i | 0.0601324 | − | 0.104152i | ||||
\(794\) | 0.161774 | + | 0.280202i | 0.00574116 | + | 0.00994398i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.99323 | + | 4.03754i | 0.247868 | + | 0.143107i | ||||
\(797\) | 2.12036 | 0.0751068 | 0.0375534 | − | 0.999295i | \(-0.488044\pi\) | ||||
0.0375534 | + | 0.999295i | \(0.488044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2440 | −0.963825 | ||||||||
\(800\) | −1.76301 | − | 1.01787i | −0.0623318 | − | 0.0359873i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.50768 | − | 16.4678i | −0.335728 | − | 0.581498i | ||||
\(803\) | 8.06816 | − | 13.9745i | 0.284719 | − | 0.493148i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8716 | + | 21.7721i | −0.418419 | + | 0.767367i | ||||
\(806\) | 8.62727i | 0.303883i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.6942 | + | 7.90634i | −0.481760 | + | 0.278144i | ||||
\(809\) | −31.7884 | + | 18.3530i | −1.11762 | + | 0.645258i | −0.940792 | − | 0.338983i | \(-0.889917\pi\) |
−0.176828 | + | 0.984242i | \(0.556584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 46.1908i | − | 1.62198i | −0.585060 | − | 0.810990i | \(-0.698929\pi\) | ||
0.585060 | − | 0.810990i | \(-0.301071\pi\) | |||||||
\(812\) | 1.83605 | − | 3.36725i | 0.0644326 | − | 0.118167i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.42156 | − | 11.1225i | 0.225075 | − | 0.389842i | ||||
\(815\) | 7.41690 | + | 12.8464i | 0.259803 | + | 0.449991i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.0413 | − | 11.5709i | −0.701157 | − | 0.404813i | ||||
\(818\) | 4.51304 | 0.157795 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.4339 | 0.538976 | ||||||||
\(821\) | −0.193084 | − | 0.111477i | −0.00673867 | − | 0.00389057i | 0.496627 | − | 0.867964i | \(-0.334572\pi\) |
−0.503366 | + | 0.864074i | \(0.667905\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5354 | − | 21.7119i | −0.436956 | − | 0.756829i | 0.560497 | − | 0.828156i | \(-0.310610\pi\) |
−0.997453 | + | 0.0713268i | \(0.977277\pi\) | |||||||
\(824\) | 7.26634 | − | 12.5857i | 0.253135 | − | 0.438442i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.75212 | − | 9.42426i | −0.200142 | − | 0.327912i | ||||
\(827\) | 25.6351i | 0.891421i | 0.895177 | + | 0.445711i | \(0.147049\pi\) | ||||
−0.895177 | + | 0.445711i | \(0.852951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.72963 | + | 3.30800i | −0.198998 | + | 0.114892i | −0.596188 | − | 0.802845i | \(-0.703319\pi\) |
0.397190 | + | 0.917736i | \(0.369985\pi\) | |||||||
\(830\) | −9.05967 | + | 5.23060i | −0.314466 | + | 0.181557i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.28315i | − | 0.0444852i | ||||||
\(833\) | 36.3780 | − | 1.77649i | 1.26042 | − | 0.0615517i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0391 | − | 20.8524i | 0.416631 | − | 0.721626i | ||||
\(836\) | 2.36068 | + | 4.08881i | 0.0816457 | + | 0.141414i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.3009 | + | 14.6075i | 0.874004 | + | 0.504607i | ||||
\(839\) | −11.4826 | −0.396424 | −0.198212 | − | 0.980159i | \(-0.563513\pi\) | ||||
−0.198212 | + | 0.980159i | \(0.563513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8987 | 0.927540 | ||||||||
\(842\) | −31.4680 | − | 18.1681i | −1.08446 | − | 0.626113i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.95665 | + | 17.2454i | 0.342722 | + | 0.593612i | ||||
\(845\) | 9.77369 | − | 16.9285i | 0.336225 | − | 0.582359i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.521681 | − | 21.3781i | −0.0179252 | − | 0.734561i | ||||
\(848\) | − | 10.9241i | − | 0.375137i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.17301 | + | 5.29604i | −0.314632 | + | 0.181653i | ||||
\(851\) | 35.4502 | − | 20.4672i | 1.21522 | − | 0.701606i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 18.0012i | − | 0.616351i | −0.951330 | − | 0.308175i | \(-0.900282\pi\) | ||
0.951330 | − | 0.308175i | \(-0.0997184\pi\) | |||||||
\(854\) | 6.13090 | + | 3.34297i | 0.209795 | + | 0.114394i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.74144 | − | 3.01627i | 0.0595213 | − | 0.103094i | ||||
\(857\) | −19.4641 | − | 33.7129i | −0.664882 | − | 1.15161i | −0.979317 | − | 0.202331i | \(-0.935148\pi\) |
0.314435 | − | 0.949279i | \(-0.398185\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.5963 | + | 18.2421i | 1.07805 | + | 0.622414i | 0.930370 | − | 0.366621i | \(-0.119485\pi\) |
0.147682 | + | 0.989035i | \(0.452819\pi\) | |||||||
\(860\) | −14.4141 | −0.491516 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.1206 | 0.412828 | ||||||||
\(863\) | −32.9539 | − | 19.0259i | −1.12176 | − | 0.647650i | −0.179912 | − | 0.983683i | \(-0.557581\pi\) |
−0.941850 | + | 0.336033i | \(0.890915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7941 | + | 23.8921i | 0.469015 | + | 0.812357i | ||||
\(866\) | 15.7080 | − | 27.2071i | 0.533780 | − | 0.924534i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −17.7835 | + | 0.433962i | −0.603610 | + | 0.0147296i | ||||
\(869\) | 23.0158i | 0.780757i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.60097 | − | 5.54312i | 0.325316 | − | 0.187822i | ||||
\(872\) | 7.85401 | − | 4.53452i | 0.265970 | − | 0.153558i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 15.0482i | 0.509012i | ||||||||
\(875\) | −27.3562 | + | 16.6969i | −0.924809 | + | 0.564459i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.00470 | + | 12.1325i | −0.236532 | + | 0.409685i | −0.959717 | − | 0.280969i | \(-0.909344\pi\) |
0.723185 | + | 0.690655i | \(0.242677\pi\) | |||||||
\(878\) | −1.61726 | − | 2.80118i | −0.0545799 | − | 0.0945352i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.54676 | + | 1.47037i | 0.0858512 | + | 0.0495662i | ||||
\(881\) | −12.6046 | −0.424659 | −0.212330 | − | 0.977198i | \(-0.568105\pi\) | ||||
−0.212330 | + | 0.977198i | \(0.568105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.76793 | 0.261412 | 0.130706 | − | 0.991421i | \(-0.458276\pi\) | ||||
0.130706 | + | 0.991421i | \(0.458276\pi\) | |||||||
\(884\) | −5.78183 | − | 3.33814i | −0.194464 | − | 0.112274i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.41729 | + | 7.65097i | 0.148402 | + | 0.257039i | ||||
\(887\) | −4.55420 | + | 7.88810i | −0.152915 | + | 0.264857i | −0.932298 | − | 0.361691i | \(-0.882199\pi\) |
0.779383 | + | 0.626548i | \(0.215533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.0201 | − | 26.8677i | 1.47639 | − | 0.901115i | ||||
\(890\) | − | 14.3479i | − | 0.480943i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.3684 | − | 10.6050i | 0.615020 | − | 0.355082i | ||||
\(893\) | −12.5346 | + | 7.23687i | −0.419455 | + | 0.242173i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.43781i | − | 0.215192i | ||||||
\(896\) | 2.64496 | − | 0.0645439i | 0.0883620 | − | 0.00215626i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.41597 | − | 5.91663i | 0.113992 | − | 0.197440i | ||||
\(899\) | 4.87322 | + | 8.44066i | 0.162531 | + | 0.281512i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.2239 | − | 28.4194i | −1.63988 | − | 0.946788i | ||||
\(902\) | 15.3115 | 0.509817 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.62531 | 0.220355 | ||||||||
\(905\) | −1.60575 | − | 0.927078i | −0.0533768 | − | 0.0308171i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.18365 | − | 2.05014i | −0.0393023 | − | 0.0680737i | 0.845705 | − | 0.533651i | \(-0.179180\pi\) |
−0.885007 | + | 0.465577i | \(0.845847\pi\) | |||||||
\(908\) | 6.79579 | − | 11.7707i | 0.225526 | − | 0.390623i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.13170 | − | 2.79814i | −0.170114 | − | 0.0927573i | ||||
\(911\) | − | 6.15544i | − | 0.203939i | −0.994788 | − | 0.101969i | \(-0.967486\pi\) | ||
0.994788 | − | 0.101969i | \(-0.0325144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.98782 | + | 5.18912i | −0.297453 | + | 0.171735i | ||||
\(914\) | −15.9555 | + | 9.21190i | −0.527760 | + | 0.304703i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 24.1066i | − | 0.796504i | ||||||
\(917\) | −0.685890 | − | 28.1073i | −0.0226501 | − | 0.928184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.2826 | + | 24.7382i | −0.471140 | + | 0.816038i | −0.999455 | − | 0.0330102i | \(-0.989491\pi\) |
0.528315 | + | 0.849048i | \(0.322824\pi\) | |||||||
\(920\) | 4.68646 | + | 8.11719i | 0.154508 | + | 0.267616i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.8998 | + | 14.9533i | 0.852965 | + | 0.492460i | ||||
\(923\) | 6.51187 | 0.214341 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.3072 | 0.503296 | ||||||||
\(926\) | 1.14756 | + | 0.662545i | 0.0377112 | + | 0.0217726i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.724802 | − | 1.25539i | −0.0237928 | − | 0.0412103i | ||||
\(929\) | 3.84812 | − | 6.66515i | 0.126253 | − | 0.218676i | −0.795969 | − | 0.605337i | \(-0.793038\pi\) |
0.922222 | + | 0.386661i | \(0.126372\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.2651 | − | 10.4805i | 0.533068 | − | 0.343483i | ||||
\(932\) | − | 18.4626i | − | 0.604762i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.6973 | − | 13.6817i | 0.775400 | − | 0.447677i | ||||
\(935\) | 13.2509 | − | 7.65041i | 0.433351 | − | 0.250195i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.1750i | 0.920436i | 0.887806 | + | 0.460218i | \(0.152229\pi\) | ||||
−0.887806 | + | 0.460218i | \(0.847771\pi\) | |||||||
\(938\) | 11.9090 | + | 19.5117i | 0.388843 | + | 0.637080i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.50756 | + | 7.80732i | −0.147020 | + | 0.254647i | ||||
\(941\) | −19.2950 | − | 33.4199i | −0.628999 | − | 1.08946i | −0.987753 | − | 0.156026i | \(-0.950132\pi\) |
0.358754 | − | 0.933432i | \(-0.383202\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.2636 | + | 24.4009i | 1.37629 | + | 0.794602i | ||||
\(944\) | −4.17310 | −0.135823 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.2997 | −0.464925 | ||||||||
\(947\) | −19.3980 | − | 11.1995i | −0.630351 | − | 0.363933i | 0.150537 | − | 0.988604i | \(-0.451900\pi\) |
−0.780888 | + | 0.624671i | \(0.785233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.06111 | + | 10.4981i | 0.196752 | + | 0.340784i | ||||
\(950\) | −2.81359 | + | 4.87328i | −0.0912849 | + | 0.158110i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.59010 | − | 12.0860i | 0.213586 | − | 0.391711i | ||||
\(953\) | 38.8771i | 1.25935i | 0.776858 | + | 0.629676i | \(0.216812\pi\) | ||||
−0.776858 | + | 0.629676i | \(0.783188\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.1347 | + | 14.5115i | −0.813339 | + | 0.469582i | ||||
\(956\) | 20.0846 | − | 11.5958i | 0.649582 | − | 0.375036i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 16.8211i | − | 0.543464i | ||||||
\(959\) | −2.58460 | + | 4.74008i | −0.0834612 | + | 0.153065i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.10284 | − | 12.3025i | 0.229124 | − | 0.396854i | ||||
\(962\) | 4.82412 | + | 8.35561i | 0.155536 | + | 0.269396i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.4458 | + | 12.9591i | 0.722932 | + | 0.417385i | ||||
\(965\) | −24.5014 | −0.788727 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.5790 | −0.661777 | −0.330889 | − | 0.943670i | \(-0.607348\pi\) | ||||
−0.330889 | + | 0.943670i | \(0.607348\pi\) | |||||||
\(968\) | −6.99972 | − | 4.04129i | −0.224980 | − | 0.129892i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.65769 | − | 14.9956i | −0.277982 | − | 0.481479i | ||||
\(971\) | 1.02171 | − | 1.76966i | 0.0327884 | − | 0.0567912i | −0.849166 | − | 0.528127i | \(-0.822895\pi\) |
0.881954 | + | 0.471336i | \(0.156228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.6918 | − | 40.4550i | −0.791581 | − | 1.29693i | ||||
\(974\) | 0.715204i | 0.0229166i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.28575 | − | 1.31968i | 0.0731651 | − | 0.0422419i | ||||
\(977\) | 40.0652 | − | 23.1317i | 1.28180 | − | 0.740048i | 0.304623 | − | 0.952473i | \(-0.401469\pi\) |
0.977177 | + | 0.212425i | \(0.0681361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14.2341i | − | 0.454925i | ||||||
\(980\) | 5.50969 | − | 10.7188i | 0.176001 | − | 0.342398i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.68453 | + | 4.64975i | −0.0856669 | + | 0.148379i | ||||
\(983\) | −9.65581 | − | 16.7244i | −0.307972 | − | 0.533424i | 0.669946 | − | 0.742410i | \(-0.266317\pi\) |
−0.977919 | + | 0.208986i | \(0.932984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.9604 | − | 16.7203i | −0.922754 | − | 0.532753i | ||||
\(986\) | −7.54235 | −0.240197 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.54686 | −0.112841 | ||||||||
\(989\) | −39.4709 | − | 22.7885i | −1.25510 | − | 0.724633i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.313252 | + | 0.542568i | 0.00995077 | + | 0.0172352i | 0.870958 | − | 0.491358i | \(-0.163499\pi\) |
−0.861007 | + | 0.508593i | \(0.830166\pi\) | |||||||
\(992\) | −3.36176 | + | 5.82274i | −0.106736 | + | 0.184872i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.327555 | + | 13.4230i | 0.0103894 | + | 0.425751i | ||||
\(995\) | − | 13.9029i | − | 0.440751i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.6691 | − | 13.0880i | 0.717939 | − | 0.414502i | −0.0960546 | − | 0.995376i | \(-0.530622\pi\) |
0.813994 | + | 0.580874i | \(0.197289\pi\) | |||||||
\(998\) | −20.8649 | + | 12.0464i | −0.660467 | + | 0.381321i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.k.c.971.7 | yes | 16 | |
3.2 | odd | 2 | 1134.2.k.d.971.2 | yes | 16 | ||
7.3 | odd | 6 | 1134.2.k.d.647.2 | yes | 16 | ||
9.2 | odd | 6 | 1134.2.l.g.215.6 | 16 | |||
9.4 | even | 3 | 1134.2.t.h.593.2 | 16 | |||
9.5 | odd | 6 | 1134.2.t.g.593.7 | 16 | |||
9.7 | even | 3 | 1134.2.l.h.215.3 | 16 | |||
21.17 | even | 6 | inner | 1134.2.k.c.647.7 | ✓ | 16 | |
63.31 | odd | 6 | 1134.2.l.g.269.2 | 16 | |||
63.38 | even | 6 | 1134.2.t.h.1025.2 | 16 | |||
63.52 | odd | 6 | 1134.2.t.g.1025.7 | 16 | |||
63.59 | even | 6 | 1134.2.l.h.269.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.k.c.647.7 | ✓ | 16 | 21.17 | even | 6 | inner | |
1134.2.k.c.971.7 | yes | 16 | 1.1 | even | 1 | trivial | |
1134.2.k.d.647.2 | yes | 16 | 7.3 | odd | 6 | ||
1134.2.k.d.971.2 | yes | 16 | 3.2 | odd | 2 | ||
1134.2.l.g.215.6 | 16 | 9.2 | odd | 6 | |||
1134.2.l.g.269.2 | 16 | 63.31 | odd | 6 | |||
1134.2.l.h.215.3 | 16 | 9.7 | even | 3 | |||
1134.2.l.h.269.7 | 16 | 63.59 | even | 6 | |||
1134.2.t.g.593.7 | 16 | 9.5 | odd | 6 | |||
1134.2.t.g.1025.7 | 16 | 63.52 | odd | 6 | |||
1134.2.t.h.593.2 | 16 | 9.4 | even | 3 | |||
1134.2.t.h.1025.2 | 16 | 63.38 | even | 6 |