Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.c (of order \(2\), degree \(1\), 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: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.85100625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.3 | ||
Root | \(-0.600040 + 1.28061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.3.c.d.151.4 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67986 | − | 1.08539i | −0.839931 | − | 0.542693i | ||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 1.64388 | + | 3.64660i | 0.410969 | + | 0.911649i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.87994 | − | 2.90961i | 0.313324 | − | 0.484935i | ||||
\(7\) | 0.596540i | 0.0852199i | 0.999092 | + | 0.0426100i | \(0.0135673\pi\) | ||||
−0.999092 | + | 0.0426100i | \(0.986433\pi\) | |||||||
\(8\) | 1.19648 | − | 7.91002i | 0.149560 | − | 0.988753i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 9.27963i | − | 0.843602i | −0.906688 | − | 0.421801i | \(-0.861398\pi\) | ||
0.906688 | − | 0.421801i | \(-0.138602\pi\) | |||||||
\(12\) | −6.31609 | + | 2.84728i | −0.526341 | + | 0.237273i | ||||
\(13\) | 23.5117 | 1.80859 | 0.904295 | − | 0.426907i | \(-0.140397\pi\) | ||||
0.904295 | + | 0.426907i | \(0.140397\pi\) | |||||||
\(14\) | 0.647476 | − | 1.00210i | 0.0462483 | − | 0.0715789i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −10.5953 | + | 11.9891i | −0.662209 | + | 0.749319i | ||||
\(17\) | −3.97751 | −0.233971 | −0.116986 | − | 0.993134i | \(-0.537323\pi\) | ||||
−0.116986 | + | 0.993134i | \(0.537323\pi\) | |||||||
\(18\) | 5.03959 | + | 3.25616i | 0.279977 | + | 0.180898i | ||||
\(19\) | 7.04756i | 0.370924i | 0.982651 | + | 0.185462i | \(0.0593782\pi\) | ||||
−0.982651 | + | 0.185462i | \(0.940622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.03324 | −0.0492018 | ||||||||
\(22\) | −10.0720 | + | 15.5885i | −0.457817 | + | 0.708568i | ||||
\(23\) | 32.0793i | 1.39475i | 0.716705 | + | 0.697376i | \(0.245649\pi\) | ||||
−0.716705 | + | 0.697376i | \(0.754351\pi\) | |||||||
\(24\) | 13.7006 | + | 2.07237i | 0.570857 | + | 0.0863486i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −39.4964 | − | 25.5192i | −1.51909 | − | 0.981509i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −2.17534 | + | 0.980637i | −0.0776907 | + | 0.0350227i | ||||
\(29\) | 35.6734 | 1.23012 | 0.615059 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 59.2585i | 1.91156i | 0.294076 | + | 0.955782i | \(0.404988\pi\) | ||||
−0.294076 | + | 0.955782i | \(0.595012\pi\) | |||||||
\(32\) | 30.8115 | − | 8.64000i | 0.962860 | − | 0.270000i | ||||
\(33\) | 16.0728 | 0.487054 | ||||||||
\(34\) | 6.68167 | + | 4.31713i | 0.196520 | + | 0.126974i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.93163 | − | 10.9398i | −0.136990 | − | 0.303883i | ||||
\(37\) | 5.38761 | 0.145611 | 0.0728055 | − | 0.997346i | \(-0.476805\pi\) | ||||
0.0728055 | + | 0.997346i | \(0.476805\pi\) | |||||||
\(38\) | 7.64932 | − | 11.8389i | 0.201298 | − | 0.311551i | ||||
\(39\) | 40.7234i | 1.04419i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.0791 | 0.977539 | 0.488769 | − | 0.872413i | \(-0.337446\pi\) | ||||
0.488769 | + | 0.872413i | \(0.337446\pi\) | |||||||
\(42\) | 1.73570 | + | 1.12146i | 0.0413261 | + | 0.0267014i | ||||
\(43\) | 36.1157i | 0.839901i | 0.907547 | + | 0.419950i | \(0.137953\pi\) | ||||
−0.907547 | + | 0.419950i | \(0.862047\pi\) | |||||||
\(44\) | 33.8391 | − | 15.2545i | 0.769070 | − | 0.346694i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 34.8184 | − | 53.8888i | 0.756922 | − | 1.17150i | ||||
\(47\) | − | 74.0131i | − | 1.57475i | −0.616477 | − | 0.787373i | \(-0.711441\pi\) | ||
0.616477 | − | 0.787373i | \(-0.288559\pi\) | |||||||
\(48\) | −20.7657 | − | 18.3517i | −0.432620 | − | 0.382327i | ||||
\(49\) | 48.6441 | 0.992738 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.88925i | − | 0.135083i | ||||||
\(52\) | 38.6503 | + | 85.7376i | 0.743275 | + | 1.64880i | ||||
\(53\) | 2.55123 | 0.0481364 | 0.0240682 | − | 0.999710i | \(-0.492338\pi\) | ||||
0.0240682 | + | 0.999710i | \(0.492338\pi\) | |||||||
\(54\) | −5.63983 | + | 8.72882i | −0.104441 | + | 0.161645i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.71864 | + | 0.713748i | 0.0842614 | + | 0.0127455i | ||||
\(57\) | −12.2067 | −0.214153 | ||||||||
\(58\) | −59.9265 | − | 38.7194i | −1.03321 | − | 0.667576i | ||||
\(59\) | − | 36.4026i | − | 0.616993i | −0.951225 | − | 0.308497i | \(-0.900174\pi\) | ||
0.951225 | − | 0.308497i | \(-0.0998259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.73223 | −0.143151 | −0.0715757 | − | 0.997435i | \(-0.522803\pi\) | ||||
−0.0715757 | + | 0.997435i | \(0.522803\pi\) | |||||||
\(62\) | 64.3183 | − | 99.5461i | 1.03739 | − | 1.60558i | ||||
\(63\) | − | 1.78962i | − | 0.0284066i | ||||||
\(64\) | −61.1369 | − | 18.9284i | −0.955264 | − | 0.295756i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −27.0001 | − | 17.4452i | −0.409092 | − | 0.264321i | ||||
\(67\) | 69.7379i | 1.04086i | 0.853903 | + | 0.520432i | \(0.174229\pi\) | ||||
−0.853903 | + | 0.520432i | \(0.825771\pi\) | |||||||
\(68\) | −6.53853 | − | 14.5044i | −0.0961548 | − | 0.213300i | ||||
\(69\) | −55.5630 | −0.805261 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59.2170i | 0.834043i | 0.908897 | + | 0.417021i | \(0.136926\pi\) | ||||
−0.908897 | + | 0.417021i | \(0.863074\pi\) | |||||||
\(72\) | −3.58944 | + | 23.7301i | −0.0498534 | + | 0.329584i | ||||
\(73\) | 83.0019 | 1.13701 | 0.568506 | − | 0.822679i | \(-0.307522\pi\) | ||||
0.568506 | + | 0.822679i | \(0.307522\pi\) | |||||||
\(74\) | −9.05044 | − | 5.84763i | −0.122303 | − | 0.0790220i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −25.6996 | + | 11.5853i | −0.338153 | + | 0.152438i | ||||
\(77\) | 5.53566 | 0.0718917 | ||||||||
\(78\) | 44.2006 | − | 68.4098i | 0.566675 | − | 0.877048i | ||||
\(79\) | − | 65.8705i | − | 0.833804i | −0.908951 | − | 0.416902i | \(-0.863116\pi\) | ||
0.908951 | − | 0.416902i | \(-0.136884\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −67.3274 | − | 43.5013i | −0.821065 | − | 0.530503i | ||||
\(83\) | 129.909i | 1.56517i | 0.622542 | + | 0.782586i | \(0.286100\pi\) | ||||
−0.622542 | + | 0.782586i | \(0.713900\pi\) | |||||||
\(84\) | −1.69851 | − | 3.76780i | −0.0202204 | − | 0.0448547i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 39.1995 | − | 60.6695i | 0.455808 | − | 0.705459i | ||||
\(87\) | 61.7882i | 0.710209i | ||||||||
\(88\) | −73.4020 | − | 11.1029i | −0.834114 | − | 0.126169i | ||||
\(89\) | −130.466 | −1.46591 | −0.732956 | − | 0.680277i | \(-0.761860\pi\) | ||||
−0.732956 | + | 0.680277i | \(0.761860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.0256i | 0.154128i | ||||||||
\(92\) | −116.980 | + | 52.7344i | −1.27152 | + | 0.573200i | ||||
\(93\) | −102.639 | −1.10364 | ||||||||
\(94\) | −80.3327 | + | 124.332i | −0.854603 | + | 1.32268i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.9649 | + | 53.3671i | 0.155885 | + | 0.555908i | ||||
\(97\) | −93.1113 | −0.959911 | −0.479955 | − | 0.877293i | \(-0.659347\pi\) | ||||
−0.479955 | + | 0.877293i | \(0.659347\pi\) | |||||||
\(98\) | −81.7155 | − | 52.7977i | −0.833831 | − | 0.538752i | ||||
\(99\) | 27.8389i | 0.281201i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.66081 | −0.0362457 | −0.0181228 | − | 0.999836i | \(-0.505769\pi\) | ||||
−0.0181228 | + | 0.999836i | \(0.505769\pi\) | |||||||
\(102\) | −7.47749 | + | 11.5730i | −0.0733087 | + | 0.113461i | ||||
\(103\) | − | 151.417i | − | 1.47007i | −0.678032 | − | 0.735033i | \(-0.737167\pi\) | ||
0.678032 | − | 0.735033i | \(-0.262833\pi\) | |||||||
\(104\) | 28.1313 | − | 185.978i | 0.270493 | − | 1.78825i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.28571 | − | 2.76907i | −0.0404313 | − | 0.0261233i | ||||
\(107\) | − | 82.8092i | − | 0.773918i | −0.922097 | − | 0.386959i | \(-0.873526\pi\) | ||
0.922097 | − | 0.386959i | \(-0.126474\pi\) | |||||||
\(108\) | 18.9483 | − | 8.54183i | 0.175447 | − | 0.0790910i | ||||
\(109\) | −7.36835 | −0.0675996 | −0.0337998 | − | 0.999429i | \(-0.510761\pi\) | ||||
−0.0337998 | + | 0.999429i | \(0.510761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.33161i | 0.0840685i | ||||||||
\(112\) | −7.15197 | − | 6.32054i | −0.0638569 | − | 0.0564334i | ||||
\(113\) | −65.0370 | −0.575549 | −0.287774 | − | 0.957698i | \(-0.592915\pi\) | ||||
−0.287774 | + | 0.957698i | \(0.592915\pi\) | |||||||
\(114\) | 20.5056 | + | 13.2490i | 0.179874 | + | 0.116219i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 58.6427 | + | 130.087i | 0.505540 | + | 1.12144i | ||||
\(117\) | −70.5350 | −0.602864 | ||||||||
\(118\) | −39.5109 | + | 61.1514i | −0.334838 | + | 0.518232i | ||||
\(119\) | − | 2.37274i | − | 0.0199390i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34.8885 | 0.288335 | ||||||||
\(122\) | 14.6689 | + | 9.47784i | 0.120237 | + | 0.0776872i | ||||
\(123\) | 69.4190i | 0.564382i | ||||||||
\(124\) | −216.092 | + | 97.4136i | −1.74268 | + | 0.785593i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.94243 | + | 3.00631i | −0.0154161 | + | 0.0238596i | ||||
\(127\) | − | 139.469i | − | 1.09818i | −0.835763 | − | 0.549091i | \(-0.814974\pi\) | ||
0.835763 | − | 0.549091i | \(-0.185026\pi\) | |||||||
\(128\) | 82.1569 | + | 98.1542i | 0.641851 | + | 0.766829i | ||||
\(129\) | −62.5543 | −0.484917 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 63.4856i | − | 0.484623i | −0.970198 | − | 0.242312i | \(-0.922094\pi\) | ||
0.970198 | − | 0.242312i | \(-0.0779056\pi\) | |||||||
\(132\) | 26.4217 | + | 58.6110i | 0.200164 | + | 0.444023i | ||||
\(133\) | −4.20415 | −0.0316101 | ||||||||
\(134\) | 75.6925 | − | 117.150i | 0.564870 | − | 0.874254i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.75901 | + | 31.4622i | −0.0349927 | + | 0.231340i | ||||
\(137\) | 138.157 | 1.00845 | 0.504223 | − | 0.863573i | \(-0.331779\pi\) | ||||
0.504223 | + | 0.863573i | \(0.331779\pi\) | |||||||
\(138\) | 93.3382 | + | 60.3073i | 0.676363 | + | 0.437009i | ||||
\(139\) | 29.9578i | 0.215523i | 0.994177 | + | 0.107762i | \(0.0343684\pi\) | ||||
−0.994177 | + | 0.107762i | \(0.965632\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 128.194 | 0.909180 | ||||||||
\(142\) | 64.2733 | − | 99.4765i | 0.452629 | − | 0.700539i | ||||
\(143\) | − | 218.180i | − | 1.52573i | ||||||
\(144\) | 31.7860 | − | 35.9673i | 0.220736 | − | 0.249773i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −139.432 | − | 90.0891i | −0.955012 | − | 0.617048i | ||||
\(147\) | 84.2541i | 0.573157i | ||||||||
\(148\) | 8.85655 | + | 19.6464i | 0.0598416 | + | 0.132746i | ||||
\(149\) | −47.3823 | −0.318002 | −0.159001 | − | 0.987278i | \(-0.550827\pi\) | ||||
−0.159001 | + | 0.987278i | \(0.550827\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 109.604i | − | 0.725852i | −0.931818 | − | 0.362926i | \(-0.881778\pi\) | ||
0.931818 | − | 0.362926i | \(-0.118222\pi\) | |||||||
\(152\) | 55.7463 | + | 8.43227i | 0.366752 | + | 0.0554755i | ||||
\(153\) | 11.9325 | 0.0779904 | ||||||||
\(154\) | −9.29915 | − | 6.00833i | −0.0603841 | − | 0.0390151i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −148.502 | + | 66.9442i | −0.951936 | + | 0.429130i | ||||
\(157\) | 177.588 | 1.13113 | 0.565566 | − | 0.824703i | \(-0.308658\pi\) | ||||
0.565566 | + | 0.824703i | \(0.308658\pi\) | |||||||
\(158\) | −71.4950 | + | 110.653i | −0.452500 | + | 0.700338i | ||||
\(159\) | 4.41886i | 0.0277916i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.1366 | −0.118861 | ||||||||
\(162\) | −15.1188 | − | 9.76847i | −0.0933257 | − | 0.0602992i | ||||
\(163\) | − | 96.8778i | − | 0.594342i | −0.954824 | − | 0.297171i | \(-0.903957\pi\) | ||
0.954824 | − | 0.297171i | \(-0.0960432\pi\) | |||||||
\(164\) | 65.8850 | + | 146.152i | 0.401738 | + | 0.891173i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 141.002 | − | 218.230i | 0.849408 | − | 1.31464i | ||||
\(167\) | 152.605i | 0.913801i | 0.889518 | + | 0.456901i | \(0.151040\pi\) | ||||
−0.889518 | + | 0.456901i | \(0.848960\pi\) | |||||||
\(168\) | −1.23625 | + | 8.17292i | −0.00735862 | + | 0.0486484i | ||||
\(169\) | 383.799 | 2.27100 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 21.1427i | − | 0.123641i | ||||||
\(172\) | −131.700 | + | 59.3698i | −0.765695 | + | 0.345173i | ||||
\(173\) | −155.773 | −0.900422 | −0.450211 | − | 0.892922i | \(-0.648651\pi\) | ||||
−0.450211 | + | 0.892922i | \(0.648651\pi\) | |||||||
\(174\) | 67.0640 | − | 103.796i | 0.385425 | − | 0.596527i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 111.254 | + | 98.3209i | 0.632127 | + | 0.558641i | ||||
\(177\) | 63.0512 | 0.356221 | ||||||||
\(178\) | 219.165 | + | 141.606i | 1.23126 | + | 0.795540i | ||||
\(179\) | 126.001i | 0.703915i | 0.936016 | + | 0.351957i | \(0.114484\pi\) | ||||
−0.936016 | + | 0.351957i | \(0.885516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −346.725 | −1.91561 | −0.957803 | − | 0.287424i | \(-0.907201\pi\) | ||||
−0.957803 | + | 0.287424i | \(0.907201\pi\) | |||||||
\(182\) | 15.2232 | − | 23.5612i | 0.0836442 | − | 0.129457i | ||||
\(183\) | − | 15.1247i | − | 0.0826485i | ||||||
\(184\) | 253.748 | + | 38.3823i | 1.37906 | + | 0.208599i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 172.419 | + | 111.403i | 0.926983 | + | 0.598939i | ||||
\(187\) | 36.9098i | 0.197379i | ||||||||
\(188\) | 269.896 | − | 121.668i | 1.43562 | − | 0.647171i | ||||
\(189\) | 3.09971 | 0.0164006 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 133.159i | − | 0.697167i | −0.937278 | − | 0.348584i | \(-0.886663\pi\) | ||
0.937278 | − | 0.348584i | \(-0.113337\pi\) | |||||||
\(192\) | 32.7849 | − | 105.892i | 0.170755 | − | 0.551522i | ||||
\(193\) | 136.246 | 0.705940 | 0.352970 | − | 0.935635i | \(-0.385172\pi\) | ||||
0.352970 | + | 0.935635i | \(0.385172\pi\) | |||||||
\(194\) | 156.414 | + | 101.062i | 0.806259 | + | 0.520937i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 79.9649 | + | 177.386i | 0.407984 | + | 0.905029i | ||||
\(197\) | −74.8945 | −0.380175 | −0.190087 | − | 0.981767i | \(-0.560877\pi\) | ||||
−0.190087 | + | 0.981767i | \(0.560877\pi\) | |||||||
\(198\) | 30.2159 | − | 46.7655i | 0.152606 | − | 0.236189i | ||||
\(199\) | − | 251.605i | − | 1.26434i | −0.774828 | − | 0.632172i | \(-0.782164\pi\) | ||
0.774828 | − | 0.632172i | \(-0.217836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −120.790 | −0.600943 | ||||||||
\(202\) | 6.14966 | + | 3.97339i | 0.0304439 | + | 0.0196703i | ||||
\(203\) | 21.2806i | 0.104831i | ||||||||
\(204\) | 25.1223 | − | 11.3251i | 0.123149 | − | 0.0555150i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −164.346 | + | 254.359i | −0.797794 | + | 1.23475i | ||||
\(207\) | − | 96.2379i | − | 0.464917i | ||||||
\(208\) | −249.114 | + | 281.884i | −1.19767 | + | 1.35521i | ||||
\(209\) | 65.3987 | 0.312913 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 228.203i | − | 1.08153i | −0.841173 | − | 0.540766i | \(-0.818135\pi\) | ||
0.841173 | − | 0.540766i | \(-0.181865\pi\) | |||||||
\(212\) | 4.19390 | + | 9.30331i | 0.0197826 | + | 0.0438835i | ||||
\(213\) | −102.567 | −0.481535 | ||||||||
\(214\) | −89.8799 | + | 139.108i | −0.420000 | + | 0.650038i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −41.1017 | − | 6.21710i | −0.190286 | − | 0.0287829i | ||||
\(217\) | −35.3500 | −0.162903 | ||||||||
\(218\) | 12.3778 | + | 7.99751i | 0.0567790 | + | 0.0366858i | ||||
\(219\) | 143.763i | 0.656454i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −93.5179 | −0.423158 | ||||||||
\(222\) | 10.1284 | − | 15.6758i | 0.0456234 | − | 0.0706118i | ||||
\(223\) | − | 85.9549i | − | 0.385448i | −0.981253 | − | 0.192724i | \(-0.938268\pi\) | ||
0.981253 | − | 0.192724i | \(-0.0617322\pi\) | |||||||
\(224\) | 5.15410 | + | 18.3803i | 0.0230094 | + | 0.0820549i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 109.253 | + | 70.5902i | 0.483421 | + | 0.312346i | ||||
\(227\) | 282.357i | 1.24386i | 0.783071 | + | 0.621932i | \(0.213652\pi\) | ||||
−0.783071 | + | 0.621932i | \(0.786348\pi\) | |||||||
\(228\) | −20.0663 | − | 44.5130i | −0.0880103 | − | 0.195233i | ||||
\(229\) | 138.263 | 0.603768 | 0.301884 | − | 0.953345i | \(-0.402385\pi\) | ||||
0.301884 | + | 0.953345i | \(0.402385\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.58805i | 0.0415067i | ||||||||
\(232\) | 42.6826 | − | 282.178i | 0.183977 | − | 1.21628i | ||||
\(233\) | 0.522939 | 0.00224438 | 0.00112219 | − | 0.999999i | \(-0.499643\pi\) | ||||
0.00112219 | + | 0.999999i | \(0.499643\pi\) | |||||||
\(234\) | 118.489 | + | 76.5577i | 0.506364 | + | 0.327170i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 132.746 | − | 59.8413i | 0.562482 | − | 0.253565i | ||||
\(237\) | 114.091 | 0.481397 | ||||||||
\(238\) | −2.57534 | + | 3.98588i | −0.0108208 | + | 0.0167474i | ||||
\(239\) | − | 73.6928i | − | 0.308338i | −0.988044 | − | 0.154169i | \(-0.950730\pi\) | ||
0.988044 | − | 0.154169i | \(-0.0492700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 31.3705 | 0.130168 | 0.0650840 | − | 0.997880i | \(-0.479268\pi\) | ||||
0.0650840 | + | 0.997880i | \(0.479268\pi\) | |||||||
\(242\) | −58.6080 | − | 37.8675i | −0.242182 | − | 0.156477i | ||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | −14.3547 | − | 31.8429i | −0.0588307 | − | 0.130504i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 75.3464 | − | 116.614i | 0.306286 | − | 0.474042i | ||||
\(247\) | 165.700i | 0.670850i | ||||||||
\(248\) | 468.736 | + | 70.9016i | 1.89006 | + | 0.285894i | ||||
\(249\) | −225.010 | −0.903653 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 78.7478i | − | 0.313736i | −0.987620 | − | 0.156868i | \(-0.949860\pi\) | ||
0.987620 | − | 0.156868i | \(-0.0501398\pi\) | |||||||
\(252\) | 6.52602 | − | 2.94191i | 0.0258969 | − | 0.0116742i | ||||
\(253\) | 297.684 | 1.17662 | ||||||||
\(254\) | −151.378 | + | 234.289i | −0.595975 | + | 0.922397i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.4772 | − | 254.057i | −0.122958 | − | 0.992412i | ||||
\(257\) | −243.954 | −0.949236 | −0.474618 | − | 0.880192i | \(-0.657414\pi\) | ||||
−0.474618 | + | 0.880192i | \(0.657414\pi\) | |||||||
\(258\) | 105.083 | + | 67.8956i | 0.407297 | + | 0.263161i | ||||
\(259\) | 3.21392i | 0.0124090i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −107.020 | −0.410039 | ||||||||
\(262\) | −68.9064 | + | 106.647i | −0.263002 | + | 0.407050i | ||||
\(263\) | 102.737i | 0.390635i | 0.980740 | + | 0.195317i | \(0.0625737\pi\) | ||||
−0.980740 | + | 0.195317i | \(0.937426\pi\) | |||||||
\(264\) | 19.2308 | − | 127.136i | 0.0728439 | − | 0.481576i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.06239 | + | 4.56312i | 0.0265503 | + | 0.0171546i | ||||
\(267\) | − | 225.974i | − | 0.846344i | ||||||
\(268\) | −254.306 | + | 114.640i | −0.948903 | + | 0.427763i | ||||
\(269\) | −123.646 | −0.459651 | −0.229825 | − | 0.973232i | \(-0.573816\pi\) | ||||
−0.229825 | + | 0.973232i | \(0.573816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 332.371i | 1.22646i | 0.789904 | + | 0.613230i | \(0.210130\pi\) | ||||
−0.789904 | + | 0.613230i | \(0.789870\pi\) | |||||||
\(272\) | 42.1431 | − | 47.6868i | 0.154938 | − | 0.175319i | ||||
\(273\) | −24.2931 | −0.0889858 | ||||||||
\(274\) | −232.085 | − | 149.954i | −0.847026 | − | 0.547277i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −91.3386 | − | 202.616i | −0.330937 | − | 0.734115i | ||||
\(277\) | 125.916 | 0.454571 | 0.227286 | − | 0.973828i | \(-0.427015\pi\) | ||||
0.227286 | + | 0.973828i | \(0.427015\pi\) | |||||||
\(278\) | 32.5157 | − | 50.3249i | 0.116963 | − | 0.181025i | ||||
\(279\) | − | 177.775i | − | 0.637188i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 52.5628 | 0.187056 | 0.0935281 | − | 0.995617i | \(-0.470186\pi\) | ||||
0.0935281 | + | 0.995617i | \(0.470186\pi\) | |||||||
\(282\) | −215.349 | − | 139.140i | −0.763649 | − | 0.493405i | ||||
\(283\) | − | 199.288i | − | 0.704199i | −0.935963 | − | 0.352100i | \(-0.885468\pi\) | ||
0.935963 | − | 0.352100i | \(-0.114532\pi\) | |||||||
\(284\) | −215.941 | + | 97.3454i | −0.760355 | + | 0.342766i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −236.809 | + | 366.512i | −0.828004 | + | 1.28151i | ||||
\(287\) | 23.9088i | 0.0833058i | ||||||||
\(288\) | −92.4346 | + | 25.9200i | −0.320953 | + | 0.0900001i | ||||
\(289\) | −273.179 | −0.945258 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 161.274i | − | 0.554205i | ||||||
\(292\) | 136.445 | + | 302.674i | 0.467276 | + | 1.03656i | ||||
\(293\) | −102.161 | −0.348672 | −0.174336 | − | 0.984686i | \(-0.555778\pi\) | ||||
−0.174336 | + | 0.984686i | \(0.555778\pi\) | |||||||
\(294\) | 91.4482 | − | 141.535i | 0.311048 | − | 0.481413i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.44617 | − | 42.6161i | 0.0217776 | − | 0.143973i | ||||
\(297\) | −48.2184 | −0.162351 | ||||||||
\(298\) | 79.5957 | + | 51.4281i | 0.267100 | + | 0.172577i | ||||
\(299\) | 754.238i | 2.52254i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.5445 | −0.0715763 | ||||||||
\(302\) | −118.962 | + | 184.119i | −0.393915 | + | 0.609666i | ||||
\(303\) | − | 6.34071i | − | 0.0209264i | ||||||
\(304\) | −84.4939 | − | 74.6713i | −0.277941 | − | 0.245629i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −20.0450 | − | 12.9514i | −0.0655065 | − | 0.0423248i | ||||
\(307\) | − | 328.391i | − | 1.06968i | −0.844954 | − | 0.534839i | \(-0.820372\pi\) | ||
0.844954 | − | 0.534839i | \(-0.179628\pi\) | |||||||
\(308\) | 9.09994 | + | 20.1863i | 0.0295453 | + | 0.0655401i | ||||
\(309\) | 262.262 | 0.848743 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 95.4377i | 0.306874i | 0.988158 | + | 0.153437i | \(0.0490342\pi\) | ||||
−0.988158 | + | 0.153437i | \(0.950966\pi\) | |||||||
\(312\) | 322.123 | + | 48.7248i | 1.03245 | + | 0.156169i | ||||
\(313\) | −550.408 | −1.75849 | −0.879246 | − | 0.476368i | \(-0.841953\pi\) | ||||
−0.879246 | + | 0.476368i | \(0.841953\pi\) | |||||||
\(314\) | −298.323 | − | 192.751i | −0.950073 | − | 0.613858i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 240.203 | − | 108.283i | 0.760137 | − | 0.342668i | ||||
\(317\) | −439.394 | −1.38610 | −0.693051 | − | 0.720889i | \(-0.743734\pi\) | ||||
−0.693051 | + | 0.720889i | \(0.743734\pi\) | |||||||
\(318\) | 4.79617 | − | 7.42307i | 0.0150823 | − | 0.0233430i | ||||
\(319\) | − | 331.036i | − | 1.03773i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 143.430 | 0.446822 | ||||||||
\(322\) | 32.1468 | + | 20.7706i | 0.0998348 | + | 0.0645048i | ||||
\(323\) | − | 28.0317i | − | 0.0867855i | ||||||
\(324\) | 14.7949 | + | 32.8194i | 0.0456632 | + | 0.101294i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −105.150 | + | 162.741i | −0.322545 | + | 0.499206i | ||||
\(327\) | − | 12.7624i | − | 0.0390286i | ||||||
\(328\) | 47.9539 | − | 317.026i | 0.146201 | − | 0.966544i | ||||
\(329\) | 44.1517 | 0.134200 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 479.922i | 1.44992i | 0.688794 | + | 0.724958i | \(0.258141\pi\) | ||||
−0.688794 | + | 0.724958i | \(0.741859\pi\) | |||||||
\(332\) | −473.727 | + | 213.555i | −1.42689 | + | 0.643237i | ||||
\(333\) | −16.1628 | −0.0485370 | ||||||||
\(334\) | 165.635 | − | 256.355i | 0.495913 | − | 0.767530i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.9475 | − | 12.3876i | 0.0325819 | − | 0.0368678i | ||||
\(337\) | −58.8437 | −0.174610 | −0.0873052 | − | 0.996182i | \(-0.527826\pi\) | ||||
−0.0873052 | + | 0.996182i | \(0.527826\pi\) | |||||||
\(338\) | −644.730 | − | 416.570i | −1.90748 | − | 1.23246i | ||||
\(339\) | − | 112.647i | − | 0.332293i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 549.897 | 1.61260 | ||||||||
\(342\) | −22.9480 | + | 35.5168i | −0.0670993 | + | 0.103850i | ||||
\(343\) | 58.2486i | 0.169821i | ||||||||
\(344\) | 285.676 | + | 43.2118i | 0.830454 | + | 0.125616i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 261.677 | + | 169.074i | 0.756293 | + | 0.488653i | ||||
\(347\) | 12.1484i | 0.0350099i | 0.999847 | + | 0.0175049i | \(0.00557228\pi\) | ||||
−0.999847 | + | 0.0175049i | \(0.994428\pi\) | |||||||
\(348\) | −225.317 | + | 101.572i | −0.647462 | + | 0.291874i | ||||
\(349\) | −30.9277 | −0.0886180 | −0.0443090 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443090 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 122.170i | − | 0.348063i | ||||||
\(352\) | −80.1760 | − | 285.919i | −0.227773 | − | 0.812271i | ||||
\(353\) | 288.065 | 0.816048 | 0.408024 | − | 0.912971i | \(-0.366218\pi\) | ||||
0.408024 | + | 0.912971i | \(0.366218\pi\) | |||||||
\(354\) | −105.917 | − | 68.4348i | −0.299201 | − | 0.193319i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −214.470 | − | 475.757i | −0.602444 | − | 1.33640i | ||||
\(357\) | 4.10971 | 0.0115118 | ||||||||
\(358\) | 136.759 | − | 211.664i | 0.382010 | − | 0.591240i | ||||
\(359\) | − | 663.911i | − | 1.84933i | −0.380776 | − | 0.924667i | \(-0.624343\pi\) | ||
0.380776 | − | 0.924667i | \(-0.375657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 311.332 | 0.862415 | ||||||||
\(362\) | 582.450 | + | 376.330i | 1.60898 | + | 1.03959i | ||||
\(363\) | 60.4287i | 0.166470i | ||||||||
\(364\) | −51.1459 | + | 23.0564i | −0.140511 | + | 0.0633418i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16.4161 | + | 25.4074i | −0.0448527 | + | 0.0694190i | ||||
\(367\) | 6.08529i | 0.0165812i | 0.999966 | + | 0.00829059i | \(0.00263901\pi\) | ||||
−0.999966 | + | 0.00829059i | \(0.997361\pi\) | |||||||
\(368\) | −384.602 | − | 339.891i | −1.04511 | − | 0.923618i | ||||
\(369\) | −120.237 | −0.325846 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52191i | 0.00410218i | ||||||||
\(372\) | −168.725 | − | 374.282i | −0.453562 | − | 1.00613i | ||||
\(373\) | 204.741 | 0.548903 | 0.274451 | − | 0.961601i | \(-0.411504\pi\) | ||||
0.274451 | + | 0.961601i | \(0.411504\pi\) | |||||||
\(374\) | 40.0614 | − | 62.0034i | 0.107116 | − | 0.165784i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −585.445 | − | 88.5552i | −1.55703 | − | 0.235519i | ||||
\(377\) | 838.742 | 2.22478 | ||||||||
\(378\) | −5.20709 | − | 3.36438i | −0.0137754 | − | 0.00890048i | ||||
\(379\) | 402.331i | 1.06156i | 0.847510 | + | 0.530780i | \(0.178101\pi\) | ||||
−0.847510 | + | 0.530780i | \(0.821899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 241.568 | 0.634036 | ||||||||
\(382\) | −144.529 | + | 223.689i | −0.378348 | + | 0.585573i | ||||
\(383\) | − | 331.751i | − | 0.866191i | −0.901348 | − | 0.433096i | \(-0.857421\pi\) | ||
0.901348 | − | 0.433096i | \(-0.142579\pi\) | |||||||
\(384\) | −170.008 | + | 142.300i | −0.442729 | + | 0.370573i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −228.875 | − | 147.880i | −0.592941 | − | 0.383109i | ||||
\(387\) | − | 108.347i | − | 0.279967i | ||||||
\(388\) | −153.063 | − | 339.540i | −0.394493 | − | 0.875102i | ||||
\(389\) | −623.310 | −1.60234 | −0.801169 | − | 0.598438i | \(-0.795788\pi\) | ||||
−0.801169 | + | 0.598438i | \(0.795788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 127.596i | − | 0.326332i | ||||||
\(392\) | 58.2018 | − | 384.776i | 0.148474 | − | 0.981572i | ||||
\(393\) | 109.960 | 0.279797 | ||||||||
\(394\) | 125.812 | + | 81.2894i | 0.319321 | + | 0.206318i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −101.517 | + | 45.7636i | −0.256357 | + | 0.115565i | ||||
\(397\) | 355.449 | 0.895338 | 0.447669 | − | 0.894199i | \(-0.352254\pi\) | ||||
0.447669 | + | 0.894199i | \(0.352254\pi\) | |||||||
\(398\) | −273.088 | + | 422.661i | −0.686151 | + | 1.06196i | ||||
\(399\) | − | 7.28180i | − | 0.0182501i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −542.927 | −1.35393 | −0.676966 | − | 0.736014i | \(-0.736706\pi\) | ||||
−0.676966 | + | 0.736014i | \(0.736706\pi\) | |||||||
\(402\) | 202.910 | + | 131.103i | 0.504751 | + | 0.326128i | ||||
\(403\) | 1393.27i | 3.45724i | ||||||||
\(404\) | −6.01792 | − | 13.3495i | −0.0148958 | − | 0.0330433i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.0977 | − | 35.7485i | 0.0568908 | − | 0.0880505i | ||||
\(407\) | − | 49.9950i | − | 0.122838i | ||||||
\(408\) | −54.4941 | − | 8.24285i | −0.133564 | − | 0.0202031i | ||||
\(409\) | −108.497 | −0.265273 | −0.132636 | − | 0.991165i | \(-0.542344\pi\) | ||||
−0.132636 | + | 0.991165i | \(0.542344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 239.295i | 0.582227i | ||||||||
\(412\) | 552.156 | − | 248.910i | 1.34018 | − | 0.604151i | ||||
\(413\) | 21.7156 | 0.0525801 | ||||||||
\(414\) | −104.455 | + | 161.666i | −0.252307 | + | 0.390499i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 724.431 | − | 203.141i | 1.74142 | − | 0.488320i | ||||
\(417\) | −51.8884 | −0.124433 | ||||||||
\(418\) | −109.861 | − | 70.9828i | −0.262825 | − | 0.169815i | ||||
\(419\) | 172.176i | 0.410921i | 0.978665 | + | 0.205460i | \(0.0658691\pi\) | ||||
−0.978665 | + | 0.205460i | \(0.934131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 478.522 | 1.13663 | 0.568316 | − | 0.822810i | \(-0.307595\pi\) | ||||
0.568316 | + | 0.822810i | \(0.307595\pi\) | |||||||
\(422\) | −247.688 | + | 383.350i | −0.586940 | + | 0.908412i | ||||
\(423\) | 222.039i | 0.524915i | ||||||||
\(424\) | 3.05250 | − | 20.1803i | 0.00719929 | − | 0.0475950i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 172.298 | + | 111.325i | 0.404456 | + | 0.261326i | ||||
\(427\) | − | 5.20912i | − | 0.0121993i | ||||||
\(428\) | 301.972 | − | 136.128i | 0.705541 | − | 0.318056i | ||||
\(429\) | 377.898 | 0.880882 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 290.722i | 0.674530i | 0.941410 | + | 0.337265i | \(0.109502\pi\) | ||||
−0.941410 | + | 0.337265i | \(0.890498\pi\) | |||||||
\(432\) | 62.2972 | + | 55.0550i | 0.144207 | + | 0.127442i | ||||
\(433\) | −53.7726 | −0.124186 | −0.0620931 | − | 0.998070i | \(-0.519778\pi\) | ||||
−0.0620931 | + | 0.998070i | \(0.519778\pi\) | |||||||
\(434\) | 59.3832 | + | 38.3684i | 0.136828 | + | 0.0884065i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1127 | − | 26.8694i | −0.0277813 | − | 0.0616271i | ||||
\(437\) | −226.081 | −0.517347 | ||||||||
\(438\) | 156.039 | − | 241.503i | 0.356253 | − | 0.551376i | ||||
\(439\) | − | 328.657i | − | 0.748650i | −0.927298 | − | 0.374325i | \(-0.877874\pi\) | ||
0.927298 | − | 0.374325i | \(-0.122126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145.932 | −0.330913 | ||||||||
\(442\) | 157.097 | + | 101.503i | 0.355424 | + | 0.229645i | ||||
\(443\) | 428.910i | 0.968194i | 0.875014 | + | 0.484097i | \(0.160852\pi\) | ||||
−0.875014 | + | 0.484097i | \(0.839148\pi\) | |||||||
\(444\) | −34.0286 | + | 15.3400i | −0.0766410 | + | 0.0345496i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −93.2942 | + | 144.392i | −0.209180 | + | 0.323750i | ||||
\(447\) | − | 82.0685i | − | 0.183599i | ||||||
\(448\) | 11.2915 | − | 36.4706i | 0.0252043 | − | 0.0814075i | ||||
\(449\) | 409.229 | 0.911423 | 0.455711 | − | 0.890128i | \(-0.349385\pi\) | ||||
0.455711 | + | 0.890128i | \(0.349385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 371.919i | − | 0.824654i | ||||||
\(452\) | −106.913 | − | 237.164i | −0.236533 | − | 0.524698i | ||||
\(453\) | 189.839 | 0.419071 | ||||||||
\(454\) | 306.466 | − | 474.321i | 0.675036 | − | 1.04476i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.6051 | + | 96.5555i | −0.0320288 | + | 0.211745i | ||||
\(457\) | −768.561 | −1.68175 | −0.840876 | − | 0.541228i | \(-0.817960\pi\) | ||||
−0.840876 | + | 0.541228i | \(0.817960\pi\) | |||||||
\(458\) | −232.262 | − | 150.068i | −0.507123 | − | 0.327660i | ||||
\(459\) | 20.6677i | 0.0450278i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −316.563 | −0.686687 | −0.343343 | − | 0.939210i | \(-0.611559\pi\) | ||||
−0.343343 | + | 0.939210i | \(0.611559\pi\) | |||||||
\(462\) | 10.4067 | − | 16.1066i | 0.0225254 | − | 0.0348628i | ||||
\(463\) | − | 491.208i | − | 1.06093i | −0.847708 | − | 0.530463i | \(-0.822018\pi\) | ||
0.847708 | − | 0.530463i | \(-0.177982\pi\) | |||||||
\(464\) | −377.972 | + | 427.692i | −0.814596 | + | 0.921751i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.878466 | − | 0.567591i | −0.00188512 | − | 0.00121801i | ||||
\(467\) | − | 410.393i | − | 0.878785i | −0.898295 | − | 0.439393i | \(-0.855194\pi\) | ||
0.898295 | − | 0.439393i | \(-0.144806\pi\) | |||||||
\(468\) | −115.951 | − | 257.213i | −0.247758 | − | 0.549600i | ||||
\(469\) | −41.6014 | −0.0887024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 307.591i | 0.653060i | ||||||||
\(472\) | −287.945 | − | 43.5550i | −0.610054 | − | 0.0922776i | ||||
\(473\) | 335.141 | 0.708542 | ||||||||
\(474\) | −191.657 | − | 123.833i | −0.404341 | − | 0.261251i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.65243 | − | 3.90049i | 0.0181774 | − | 0.00819431i | ||||
\(477\) | −7.65369 | −0.0160455 | ||||||||
\(478\) | −79.9851 | + | 123.794i | −0.167333 | + | 0.258983i | ||||
\(479\) | 198.918i | 0.415277i | 0.978206 | + | 0.207638i | \(0.0665778\pi\) | ||||
−0.978206 | + | 0.207638i | \(0.933422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 126.672 | 0.263351 | ||||||||
\(482\) | −52.6981 | − | 34.0491i | −0.109332 | − | 0.0706413i | ||||
\(483\) | − | 33.1455i | − | 0.0686242i | ||||||
\(484\) | 57.3524 | + | 127.224i | 0.118497 | + | 0.262860i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.9195 | − | 26.1865i | 0.0348138 | − | 0.0538816i | ||||
\(487\) | 204.762i | 0.420456i | 0.977652 | + | 0.210228i | \(0.0674206\pi\) | ||||
−0.977652 | + | 0.210228i | \(0.932579\pi\) | |||||||
\(488\) | −10.4479 | + | 69.0721i | −0.0214097 | + | 0.141541i | ||||
\(489\) | 167.797 | 0.343144 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 788.598i | 1.60611i | 0.595908 | + | 0.803053i | \(0.296792\pi\) | ||||
−0.595908 | + | 0.803053i | \(0.703208\pi\) | |||||||
\(492\) | −253.143 | + | 114.116i | −0.514519 | + | 0.231944i | ||||
\(493\) | −141.891 | −0.287812 | ||||||||
\(494\) | 179.848 | − | 278.353i | 0.364066 | − | 0.563468i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −710.456 | − | 627.864i | −1.43237 | − | 1.26586i | ||||
\(497\) | −35.3253 | −0.0710771 | ||||||||
\(498\) | 377.985 | + | 244.222i | 0.759006 | + | 0.490406i | ||||
\(499\) | 740.385i | 1.48374i | 0.670545 | + | 0.741869i | \(0.266060\pi\) | ||||
−0.670545 | + | 0.741869i | \(0.733940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −264.319 | −0.527583 | ||||||||
\(502\) | −85.4717 | + | 132.285i | −0.170262 | + | 0.263517i | ||||
\(503\) | − | 70.8800i | − | 0.140914i | −0.997515 | − | 0.0704572i | \(-0.977554\pi\) | ||
0.997515 | − | 0.0704572i | \(-0.0224458\pi\) | |||||||
\(504\) | −14.1559 | − | 2.14124i | −0.0280871 | − | 0.00424850i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −500.068 | − | 323.102i | −0.988277 | − | 0.638541i | ||||
\(507\) | 664.760i | 1.31116i | ||||||||
\(508\) | 508.588 | − | 229.270i | 1.00116 | − | 0.451318i | ||||
\(509\) | 522.642 | 1.02680 | 0.513400 | − | 0.858149i | \(-0.328386\pi\) | ||||
0.513400 | + | 0.858149i | \(0.328386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49.5139i | 0.0968961i | ||||||||
\(512\) | −222.873 | + | 460.946i | −0.435299 | + | 0.900286i | ||||
\(513\) | 36.6202 | 0.0713844 | ||||||||
\(514\) | 409.809 | + | 264.784i | 0.797293 | + | 0.515144i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −102.831 | − | 228.110i | −0.199286 | − | 0.442074i | ||||
\(517\) | −686.813 | −1.32846 | ||||||||
\(518\) | 3.48834 | − | 5.39894i | 0.00673425 | − | 0.0104227i | ||||
\(519\) | − | 269.807i | − | 0.519859i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 304.082 | 0.583650 | 0.291825 | − | 0.956472i | \(-0.405738\pi\) | ||||
0.291825 | + | 0.956472i | \(0.405738\pi\) | |||||||
\(522\) | 179.779 | + | 116.158i | 0.344405 | + | 0.222525i | ||||
\(523\) | 174.416i | 0.333491i | 0.986000 | + | 0.166746i | \(0.0533259\pi\) | ||||
−0.986000 | + | 0.166746i | \(0.946674\pi\) | |||||||
\(524\) | 231.507 | − | 104.362i | 0.441806 | − | 0.199165i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 111.509 | − | 172.584i | 0.211995 | − | 0.328106i | ||||
\(527\) | − | 235.701i | − | 0.447251i | ||||||
\(528\) | −170.297 | + | 192.698i | −0.322532 | + | 0.364959i | ||||
\(529\) | −500.081 | −0.945333 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 109.208i | 0.205664i | ||||||||
\(532\) | −6.91109 | − | 15.3308i | −0.0129908 | − | 0.0288174i | ||||
\(533\) | 942.327 | 1.76797 | ||||||||
\(534\) | −245.269 | + | 379.605i | −0.459305 | + | 0.710871i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 551.628 | + | 83.4401i | 1.02916 | + | 0.155672i | ||||
\(537\) | −218.240 | −0.406405 | ||||||||
\(538\) | 207.708 | + | 134.204i | 0.386075 | + | 0.249449i | ||||
\(539\) | − | 451.399i | − | 0.837476i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −262.199 | −0.484655 | −0.242328 | − | 0.970194i | \(-0.577911\pi\) | ||||
−0.242328 | + | 0.970194i | \(0.577911\pi\) | |||||||
\(542\) | 360.750 | − | 558.337i | 0.665591 | − | 1.03014i | ||||
\(543\) | − | 600.545i | − | 1.10598i | ||||||
\(544\) | −122.553 | + | 34.3657i | −0.225281 | + | 0.0631722i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 40.8091 | + | 26.3674i | 0.0747420 | + | 0.0482920i | ||||
\(547\) | − | 146.179i | − | 0.267237i | −0.991033 | − | 0.133619i | \(-0.957340\pi\) | ||
0.991033 | − | 0.133619i | \(-0.0426598\pi\) | |||||||
\(548\) | 227.113 | + | 503.804i | 0.414440 | + | 0.919350i | ||||
\(549\) | 26.1967 | 0.0477171 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 251.411i | 0.456281i | ||||||||
\(552\) | −66.4800 | + | 439.504i | −0.120435 | + | 0.796203i | ||||
\(553\) | 39.2944 | 0.0710568 | ||||||||
\(554\) | −211.522 | − | 136.668i | −0.381809 | − | 0.246693i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −109.244 | + | 49.2468i | −0.196482 | + | 0.0885734i | ||||
\(557\) | −187.700 | −0.336984 | −0.168492 | − | 0.985703i | \(-0.553890\pi\) | ||||
−0.168492 | + | 0.985703i | \(0.553890\pi\) | |||||||
\(558\) | −192.955 | + | 298.638i | −0.345797 | + | 0.535194i | ||||
\(559\) | 849.142i | 1.51904i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −63.9296 | −0.113957 | ||||||||
\(562\) | −88.2982 | − | 57.0509i | −0.157114 | − | 0.101514i | ||||
\(563\) | 447.848i | 0.795467i | 0.917501 | + | 0.397734i | \(0.130203\pi\) | ||||
−0.917501 | + | 0.397734i | \(0.869797\pi\) | |||||||
\(564\) | 210.736 | + | 467.473i | 0.373645 | + | 0.828853i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −216.305 | + | 334.777i | −0.382164 | + | 0.591479i | ||||
\(567\) | 5.36886i | 0.00946888i | ||||||||
\(568\) | 468.408 | + | 70.8520i | 0.824662 | + | 0.124740i | ||||
\(569\) | 1078.91 | 1.89615 | 0.948077 | − | 0.318042i | \(-0.103025\pi\) | ||||
0.948077 | + | 0.318042i | \(0.103025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 936.324i | − | 1.63980i | −0.572509 | − | 0.819899i | \(-0.694030\pi\) | ||
0.572509 | − | 0.819899i | \(-0.305970\pi\) | |||||||
\(572\) | 795.613 | − | 358.660i | 1.39093 | − | 0.627028i | ||||
\(573\) | 230.638 | 0.402510 | ||||||||
\(574\) | 25.9502 | − | 40.1634i | 0.0452095 | − | 0.0699711i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 183.411 | + | 56.7851i | 0.318421 | + | 0.0985853i | ||||
\(577\) | 544.832 | 0.944250 | 0.472125 | − | 0.881532i | \(-0.343487\pi\) | ||||
0.472125 | + | 0.881532i | \(0.343487\pi\) | |||||||
\(578\) | 458.904 | + | 296.505i | 0.793951 | + | 0.512985i | ||||
\(579\) | 235.986i | 0.407575i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −77.4960 | −0.133384 | ||||||||
\(582\) | −175.044 | + | 270.917i | −0.300763 | + | 0.465494i | ||||
\(583\) | − | 23.6745i | − | 0.0406080i | ||||||
\(584\) | 99.3101 | − | 656.547i | 0.170052 | − | 1.12422i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 171.616 | + | 110.884i | 0.292861 | + | 0.189222i | ||||
\(587\) | 337.889i | 0.575619i | 0.957688 | + | 0.287810i | \(0.0929271\pi\) | ||||
−0.957688 | + | 0.287810i | \(0.907073\pi\) | |||||||
\(588\) | −307.241 | + | 138.503i | −0.522519 | + | 0.235550i | ||||
\(589\) | −417.628 | −0.709045 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 129.721i | − | 0.219494i | ||||||
\(592\) | −57.0836 | + | 64.5926i | −0.0964249 | + | 0.109109i | ||||
\(593\) | −567.269 | −0.956608 | −0.478304 | − | 0.878194i | \(-0.658748\pi\) | ||||
−0.478304 | + | 0.878194i | \(0.658748\pi\) | |||||||
\(594\) | 81.0002 | + | 52.3355i | 0.136364 | + | 0.0881069i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −77.8906 | − | 172.784i | −0.130689 | − | 0.289906i | ||||
\(597\) | 435.792 | 0.729969 | ||||||||
\(598\) | 818.640 | − | 1267.02i | 1.36896 | − | 2.11876i | ||||
\(599\) | − | 762.966i | − | 1.27373i | −0.770974 | − | 0.636867i | \(-0.780230\pi\) | ||
0.770974 | − | 0.636867i | \(-0.219770\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −790.102 | −1.31464 | −0.657322 | − | 0.753609i | \(-0.728311\pi\) | ||||
−0.657322 | + | 0.753609i | \(0.728311\pi\) | |||||||
\(602\) | 36.1917 | + | 23.3841i | 0.0601192 | + | 0.0388440i | ||||
\(603\) | − | 209.214i | − | 0.346955i | ||||||
\(604\) | 399.680 | − | 180.175i | 0.661722 | − | 0.298302i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.88212 | + | 10.6515i | −0.0113566 | + | 0.0175768i | ||||
\(607\) | − | 522.994i | − | 0.861605i | −0.902446 | − | 0.430802i | \(-0.858231\pi\) | ||
0.902446 | − | 0.430802i | \(-0.141769\pi\) | |||||||
\(608\) | 60.8909 | + | 217.146i | 0.100150 | + | 0.357148i | ||||
\(609\) | −36.8591 | −0.0605240 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1740.17i | − | 2.84807i | ||||||
\(612\) | 19.6156 | + | 43.5131i | 0.0320516 | + | 0.0710999i | ||||
\(613\) | −1026.91 | −1.67522 | −0.837609 | − | 0.546270i | \(-0.816047\pi\) | ||||
−0.837609 | + | 0.546270i | \(0.816047\pi\) | |||||||
\(614\) | −356.431 | + | 551.652i | −0.580506 | + | 0.898455i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.62332 | − | 43.7872i | 0.0107521 | − | 0.0710831i | ||||
\(617\) | 479.223 | 0.776698 | 0.388349 | − | 0.921512i | \(-0.373046\pi\) | ||||
0.388349 | + | 0.921512i | \(0.373046\pi\) | |||||||
\(618\) | −440.563 | − | 284.655i | −0.712886 | − | 0.460607i | ||||
\(619\) | 507.654i | 0.820119i | 0.912059 | + | 0.410059i | \(0.134492\pi\) | ||||
−0.912059 | + | 0.410059i | \(0.865508\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 166.689 | 0.268420 | ||||||||
\(622\) | 103.587 | − | 160.322i | 0.166538 | − | 0.257753i | ||||
\(623\) | − | 77.8282i | − | 0.124925i | ||||||
\(624\) | −488.237 | − | 431.479i | −0.782432 | − | 0.691473i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 924.609 | + | 597.405i | 1.47701 | + | 0.954321i | ||||
\(627\) | 113.274i | 0.180660i | ||||||||
\(628\) | 291.932 | + | 647.591i | 0.464860 | + | 1.03120i | ||||
\(629\) | −21.4293 | −0.0340688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 460.186i | 0.729297i | 0.931145 | + | 0.364648i | \(0.118811\pi\) | ||||
−0.931145 | + | 0.364648i | \(0.881189\pi\) | |||||||
\(632\) | −521.037 | − | 78.8128i | −0.824426 | − | 0.124704i | ||||
\(633\) | 395.259 | 0.624423 | ||||||||
\(634\) | 738.122 | + | 476.912i | 1.16423 | + | 0.752228i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −16.1138 | + | 7.26405i | −0.0253362 | + | 0.0114215i | ||||
\(637\) | 1143.71 | 1.79546 | ||||||||
\(638\) | −359.302 | + | 556.095i | −0.563169 | + | 0.871622i | ||||
\(639\) | − | 177.651i | − | 0.278014i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 250.774 | 0.391223 | 0.195612 | − | 0.980681i | \(-0.437331\pi\) | ||||
0.195612 | + | 0.980681i | \(0.437331\pi\) | |||||||
\(642\) | −240.942 | − | 155.677i | −0.375299 | − | 0.242487i | ||||
\(643\) | − | 590.355i | − | 0.918126i | −0.888404 | − | 0.459063i | \(-0.848185\pi\) | ||
0.888404 | − | 0.459063i | \(-0.151815\pi\) | |||||||
\(644\) | −31.4581 | − | 69.7834i | −0.0488480 | − | 0.108359i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.4252 | + | 47.0894i | −0.0470979 | + | 0.0728939i | ||||
\(647\) | − | 319.341i | − | 0.493572i | −0.969070 | − | 0.246786i | \(-0.920626\pi\) | ||
0.969070 | − | 0.246786i | \(-0.0793744\pi\) | |||||||
\(648\) | 10.7683 | − | 71.1902i | 0.0166178 | − | 0.109861i | ||||
\(649\) | −337.803 | −0.520497 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 61.2280i | − | 0.0940523i | ||||||
\(652\) | 353.274 | − | 159.255i | 0.541832 | − | 0.244256i | ||||
\(653\) | −88.5949 | −0.135674 | −0.0678369 | − | 0.997696i | \(-0.521610\pi\) | ||||
−0.0678369 | + | 0.997696i | \(0.521610\pi\) | |||||||
\(654\) | −13.8521 | + | 21.4390i | −0.0211806 | + | 0.0327814i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −424.652 | + | 480.512i | −0.647335 | + | 0.732488i | ||||
\(657\) | −249.006 | −0.379004 | ||||||||
\(658\) | −74.1688 | − | 47.9216i | −0.112719 | − | 0.0728292i | ||||
\(659\) | − | 758.423i | − | 1.15087i | −0.817847 | − | 0.575435i | \(-0.804833\pi\) | ||
0.817847 | − | 0.575435i | \(-0.195167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 527.327 | 0.797771 | 0.398885 | − | 0.917001i | \(-0.369397\pi\) | ||||
0.398885 | + | 0.917001i | \(0.369397\pi\) | |||||||
\(662\) | 520.900 | − | 806.203i | 0.786859 | − | 1.21783i | ||||
\(663\) | − | 161.978i | − | 0.244310i | ||||||
\(664\) | 1027.59 | + | 155.434i | 1.54757 | + | 0.234087i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.1513 | + | 17.5429i | 0.0407677 | + | 0.0263407i | ||||
\(667\) | 1144.38i | 1.71571i | ||||||||
\(668\) | −556.488 | + | 250.863i | −0.833066 | + | 0.375544i | ||||
\(669\) | 148.878 | 0.222538 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 81.0318i | 0.120763i | ||||||||
\(672\) | −31.8356 | + | 8.92717i | −0.0473744 | + | 0.0132845i | ||||
\(673\) | −120.657 | −0.179283 | −0.0896415 | − | 0.995974i | \(-0.528572\pi\) | ||||
−0.0896415 | + | 0.995974i | \(0.528572\pi\) | |||||||
\(674\) | 98.8493 | + | 63.8681i | 0.146661 | + | 0.0947598i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 630.918 | + | 1399.56i | 0.933311 | + | 2.07036i | ||||
\(677\) | 219.196 | 0.323776 | 0.161888 | − | 0.986809i | \(-0.448242\pi\) | ||||
0.161888 | + | 0.986809i | \(0.448242\pi\) | |||||||
\(678\) | −122.266 | + | 189.232i | −0.180333 | + | 0.279103i | ||||
\(679\) | − | 55.5446i | − | 0.0818035i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −489.057 | −0.718145 | ||||||||
\(682\) | −923.751 | − | 596.850i | −1.35447 | − | 0.875146i | ||||
\(683\) | − | 205.502i | − | 0.300881i | −0.988619 | − | 0.150441i | \(-0.951931\pi\) | ||
0.988619 | − | 0.150441i | \(-0.0480693\pi\) | |||||||
\(684\) | 77.0988 | − | 34.7559i | 0.112718 | − | 0.0508128i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 63.2222 | − | 97.8496i | 0.0921606 | − | 0.142638i | ||||
\(687\) | 239.478i | 0.348585i | ||||||||
\(688\) | −432.995 | − | 382.659i | −0.629354 | − | 0.556190i | ||||
\(689\) | 59.9837 | 0.0870591 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 109.536i | 0.158519i | 0.996854 | + | 0.0792593i | \(0.0252555\pi\) | ||||
−0.996854 | + | 0.0792593i | \(0.974744\pi\) | |||||||
\(692\) | −256.071 | − | 568.042i | −0.370045 | − | 0.820869i | ||||
\(693\) | −16.6070 | −0.0239639 | ||||||||
\(694\) | 13.1857 | − | 20.4077i | 0.0189996 | − | 0.0294059i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 488.746 | + | 73.9284i | 0.702221 | + | 0.106219i | ||||
\(697\) | −159.415 | −0.228716 | ||||||||
\(698\) | 51.9543 | + | 33.5685i | 0.0744331 | + | 0.0480924i | ||||
\(699\) | 0.905758i | 0.00129579i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 168.847 | 0.240865 | 0.120433 | − | 0.992721i | \(-0.461572\pi\) | ||||
0.120433 | + | 0.992721i | \(0.461572\pi\) | |||||||
\(702\) | −132.602 | + | 205.229i | −0.188892 | + | 0.292349i | ||||
\(703\) | 37.9695i | 0.0540106i | ||||||||
\(704\) | −175.648 | + | 567.327i | −0.249500 | + | 0.805863i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −483.909 | − | 312.661i | −0.685424 | − | 0.442863i | ||||
\(707\) | − | 2.18382i | − | 0.00308885i | ||||||
\(708\) | 103.648 | + | 229.922i | 0.146396 | + | 0.324749i | ||||
\(709\) | −554.846 | −0.782576 | −0.391288 | − | 0.920268i | \(-0.627970\pi\) | ||||
−0.391288 | + | 0.920268i | \(0.627970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 197.612i | 0.277935i | ||||||||
\(712\) | −156.100 | + | 1031.99i | −0.219242 | + | 1.44942i | ||||
\(713\) | −1900.97 | −2.66616 | ||||||||
\(714\) | −6.90374 | − | 4.46062i | −0.00966911 | − | 0.00624737i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −459.474 | + | 207.130i | −0.641723 | + | 0.289287i | ||||
\(717\) | 127.640 | 0.178019 | ||||||||
\(718\) | −720.600 | + | 1115.28i | −1.00362 | + | 1.55331i | ||||
\(719\) | − | 377.485i | − | 0.525014i | −0.964930 | − | 0.262507i | \(-0.915451\pi\) | ||
0.964930 | − | 0.262507i | \(-0.0845494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 90.3261 | 0.125279 | ||||||||
\(722\) | −522.995 | − | 337.915i | −0.724369 | − | 0.468027i | ||||
\(723\) | 54.3353i | 0.0751525i | ||||||||
\(724\) | −569.972 | − | 1264.37i | −0.787255 | − | 1.74636i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 65.5885 | − | 101.512i | 0.0903423 | − | 0.139824i | ||||
\(727\) | 173.183i | 0.238216i | 0.992881 | + | 0.119108i | \(0.0380035\pi\) | ||||
−0.992881 | + | 0.119108i | \(0.961997\pi\) | |||||||
\(728\) | 110.943 | + | 16.7814i | 0.152394 | + | 0.0230514i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 143.651i | − | 0.196513i | ||||||
\(732\) | 55.1536 | − | 24.8631i | 0.0753464 | − | 0.0339659i | ||||
\(733\) | −278.722 | −0.380249 | −0.190124 | − | 0.981760i | \(-0.560889\pi\) | ||||
−0.190124 | + | 0.981760i | \(0.560889\pi\) | |||||||
\(734\) | 6.60489 | − | 10.2225i | 0.00899849 | − | 0.0139270i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 277.165 | + | 988.412i | 0.376583 | + | 1.34295i | ||||
\(737\) | 647.142 | 0.878075 | ||||||||
\(738\) | 201.982 | + | 130.504i | 0.273688 | + | 0.176834i | ||||
\(739\) | − | 521.363i | − | 0.705498i | −0.935718 | − | 0.352749i | \(-0.885247\pi\) | ||
0.935718 | − | 0.352749i | \(-0.114753\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −287.001 | −0.387315 | ||||||||
\(742\) | 1.65186 | − | 2.55660i | 0.00222622 | − | 0.00344555i | ||||
\(743\) | − | 1277.93i | − | 1.71996i | −0.510326 | − | 0.859981i | \(-0.670475\pi\) | ||
0.510326 | − | 0.859981i | \(-0.329525\pi\) | |||||||
\(744\) | −122.805 | + | 811.874i | −0.165061 | + | 1.09123i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −343.936 | − | 222.223i | −0.461041 | − | 0.297886i | ||||
\(747\) | − | 389.728i | − | 0.521724i | ||||||
\(748\) | −134.595 | + | 60.6751i | −0.179940 | + | 0.0811164i | ||||
\(749\) | 49.3989 | 0.0659532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1165.31i | − | 1.55168i | −0.630930 | − | 0.775840i | \(-0.717327\pi\) | ||
0.630930 | − | 0.775840i | \(-0.282673\pi\) | |||||||
\(752\) | 887.350 | + | 784.194i | 1.17999 | + | 1.04281i | ||||
\(753\) | 136.395 | 0.181136 | ||||||||
\(754\) | −1408.97 | − | 910.359i | −1.86866 | − | 1.20737i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.09554 | + | 11.3034i | 0.00674013 | + | 0.0149516i | ||||
\(757\) | −1063.75 | −1.40522 | −0.702611 | − | 0.711574i | \(-0.747983\pi\) | ||||
−0.702611 | + | 0.711574i | \(0.747983\pi\) | |||||||
\(758\) | 436.685 | − | 675.861i | 0.576101 | − | 0.891638i | ||||
\(759\) | 515.604i | 0.679320i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −677.847 | −0.890732 | −0.445366 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445366 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(762\) | −405.800 | − | 262.194i | −0.532546 | − | 0.344087i | ||||
\(763\) | − | 4.39551i | − | 0.00576083i | ||||||
\(764\) | 485.577 | − | 218.897i | 0.635572 | − | 0.286514i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −360.078 | + | 557.296i | −0.470076 | + | 0.727541i | ||||
\(767\) | − | 855.887i | − | 1.11589i | ||||||
\(768\) | 440.040 | − | 54.5201i | 0.572969 | − | 0.0709898i | ||||
\(769\) | −1289.59 | −1.67697 | −0.838486 | − | 0.544922i | \(-0.816559\pi\) | ||||
−0.838486 | + | 0.544922i | \(0.816559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 422.540i | − | 0.548042i | ||||||
\(772\) | 223.972 | + | 496.836i | 0.290119 | + | 0.643570i | ||||
\(773\) | 750.339 | 0.970684 | 0.485342 | − | 0.874324i | \(-0.338695\pi\) | ||||
0.485342 | + | 0.874324i | \(0.338695\pi\) | |||||||
\(774\) | −117.599 | + | 182.008i | −0.151936 | + | 0.235153i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −111.406 | + | 736.513i | −0.143564 | + | 0.949114i | ||||
\(777\) | −5.56667 | −0.00716432 | ||||||||
\(778\) | 1047.07 | + | 676.532i | 1.34585 | + | 0.869578i | ||||
\(779\) | 282.460i | 0.362593i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 549.512 | 0.703600 | ||||||||
\(782\) | −138.491 | + | 214.343i | −0.177098 | + | 0.274096i | ||||
\(783\) | − | 185.365i | − | 0.236736i | ||||||
\(784\) | −515.402 | + | 583.200i | −0.657400 | + | 0.743877i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −184.718 | − | 119.349i | −0.235011 | − | 0.151844i | ||||
\(787\) | 825.185i | 1.04852i | 0.851558 | + | 0.524260i | \(0.175658\pi\) | ||||
−0.851558 | + | 0.524260i | \(0.824342\pi\) | |||||||
\(788\) | −123.117 | − | 273.110i | −0.156240 | − | 0.346586i | ||||
\(789\) | −177.946 | −0.225533 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 38.7971i | − | 0.0490482i | ||||||
\(792\) | 220.206 | + | 33.3087i | 0.278038 | + | 0.0420564i | ||||
\(793\) | −205.309 | −0.258902 | ||||||||
\(794\) | −597.106 | − | 385.799i | −0.752022 | − | 0.485893i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 917.500 | − | 413.606i | 1.15264 | − | 0.519606i | ||||
\(797\) | −1113.70 | −1.39737 | −0.698684 | − | 0.715430i | \(-0.746231\pi\) | ||||
−0.698684 | + | 0.715430i | \(0.746231\pi\) | |||||||
\(798\) | −7.90356 | + | 12.2324i | −0.00990421 | + | 0.0153288i | ||||
\(799\) | 294.388i | 0.368445i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 391.398 | 0.488637 | ||||||||
\(802\) | 912.043 | + | 589.285i | 1.13721 | + | 0.734770i | ||||
\(803\) | − | 770.226i | − | 0.959186i | ||||||
\(804\) | −198.563 | − | 440.471i | −0.246969 | − | 0.547849i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1512.23 | − | 2340.50i | 1.87622 | − | 2.90384i | ||||
\(807\) | − | 214.161i | − | 0.265379i | ||||||
\(808\) | −4.38009 | + | 28.9571i | −0.00542090 | + | 0.0358380i | ||||
\(809\) | −1049.54 | −1.29733 | −0.648664 | − | 0.761075i | \(-0.724672\pi\) | ||||
−0.648664 | + | 0.761075i | \(0.724672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 424.482i | 0.523406i | 0.965148 | + | 0.261703i | \(0.0842841\pi\) | ||||
−0.965148 | + | 0.261703i | \(0.915716\pi\) | |||||||
\(812\) | −77.6018 | + | 34.9827i | −0.0955688 | + | 0.0430821i | ||||
\(813\) | −575.683 | −0.708097 | ||||||||
\(814\) | −54.2638 | + | 83.9847i | −0.0666632 | + | 0.103175i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 82.5959 | + | 72.9940i | 0.101220 | + | 0.0894534i | ||||
\(817\) | −254.528 | −0.311540 | ||||||||
\(818\) | 182.259 | + | 117.761i | 0.222811 | + | 0.143962i | ||||
\(819\) | − | 42.0769i | − | 0.0513760i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1257.98 | −1.53225 | −0.766126 | − | 0.642690i | \(-0.777818\pi\) | ||||
−0.766126 | + | 0.642690i | \(0.777818\pi\) | |||||||
\(822\) | 259.728 | − | 401.983i | 0.315970 | − | 0.489031i | ||||
\(823\) | − | 729.181i | − | 0.886004i | −0.896521 | − | 0.443002i | \(-0.853913\pi\) | ||
0.896521 | − | 0.443002i | \(-0.146087\pi\) | |||||||
\(824\) | −1197.71 | − | 181.167i | −1.45353 | − | 0.219863i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.4792 | − | 23.5698i | −0.0441637 | − | 0.0285349i | ||||
\(827\) | 72.5882i | 0.0877729i | 0.999037 | + | 0.0438865i | \(0.0139740\pi\) | ||||
−0.999037 | + | 0.0438865i | \(0.986026\pi\) | |||||||
\(828\) | 350.941 | − | 158.203i | 0.423842 | − | 0.191067i | ||||
\(829\) | 900.257 | 1.08596 | 0.542978 | − | 0.839747i | \(-0.317297\pi\) | ||||
0.542978 | + | 0.839747i | \(0.317297\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 218.093i | 0.262447i | ||||||||
\(832\) | −1437.43 | − | 445.038i | −1.72768 | − | 0.534901i | ||||
\(833\) | −193.482 | −0.232272 | ||||||||
\(834\) | 87.1653 | + | 56.3189i | 0.104515 | + | 0.0675286i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 107.507 | + | 238.483i | 0.128597 | + | 0.285266i | ||||
\(837\) | 307.916 | 0.367881 | ||||||||
\(838\) | 186.877 | − | 289.232i | 0.223004 | − | 0.345145i | ||||
\(839\) | 71.4721i | 0.0851872i | 0.999092 | + | 0.0425936i | \(0.0135621\pi\) | ||||
−0.999092 | + | 0.0425936i | \(0.986438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 431.594 | 0.513191 | ||||||||
\(842\) | −803.851 | − | 519.381i | −0.954693 | − | 0.616842i | ||||
\(843\) | 91.0414i | 0.107997i | ||||||||
\(844\) | 832.165 | − | 375.138i | 0.985978 | − | 0.444476i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 240.998 | − | 372.995i | 0.284868 | − | 0.440893i | ||||
\(847\) | 20.8124i | 0.0245719i | ||||||||
\(848\) | −27.0312 | + | 30.5870i | −0.0318764 | + | 0.0360695i | ||||
\(849\) | 345.178 | 0.406570 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 172.831i | 0.203091i | ||||||||
\(852\) | −168.607 | − | 374.020i | −0.197896 | − | 0.438991i | ||||
\(853\) | −882.349 | −1.03441 | −0.517203 | − | 0.855862i | \(-0.673027\pi\) | ||||
−0.517203 | + | 0.855862i | \(0.673027\pi\) | |||||||
\(854\) | −5.65391 | + | 8.75061i | −0.00662050 | + | 0.0102466i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −655.022 | − | 99.0796i | −0.765213 | − | 0.115747i | ||||
\(857\) | 370.111 | 0.431868 | 0.215934 | − | 0.976408i | \(-0.430720\pi\) | ||||
0.215934 | + | 0.976408i | \(0.430720\pi\) | |||||||
\(858\) | −634.817 | − | 410.165i | −0.739880 | − | 0.478048i | ||||
\(859\) | − | 1039.00i | − | 1.20955i | −0.796397 | − | 0.604774i | \(-0.793264\pi\) | ||
0.796397 | − | 0.604774i | \(-0.206736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −41.4112 | −0.0480966 | ||||||||
\(862\) | 315.546 | − | 488.373i | 0.366062 | − | 0.566558i | ||||
\(863\) | − | 72.0666i | − | 0.0835071i | −0.999128 | − | 0.0417535i | \(-0.986706\pi\) | ||
0.999128 | − | 0.0417535i | \(-0.0132944\pi\) | |||||||
\(864\) | −44.8948 | − | 160.101i | −0.0519616 | − | 0.185303i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 90.3306 | + | 58.3640i | 0.104308 | + | 0.0673950i | ||||
\(867\) | − | 473.161i | − | 0.545745i | ||||||
\(868\) | −58.1110 | − | 128.907i | −0.0669482 | − | 0.148511i | ||||
\(869\) | −611.254 | −0.703399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1639.66i | 1.88250i | ||||||||
\(872\) | −8.81609 | + | 58.2838i | −0.0101102 | + | 0.0668393i | ||||
\(873\) | 279.334 | 0.319970 | ||||||||
\(874\) | 379.785 | + | 245.385i | 0.434536 | + | 0.280761i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −524.247 | + | 236.329i | −0.598456 | + | 0.269782i | ||||
\(877\) | −14.4444 | −0.0164703 | −0.00823514 | − | 0.999966i | \(-0.502621\pi\) | ||||
−0.00823514 | + | 0.999966i | \(0.502621\pi\) | |||||||
\(878\) | −356.720 | + | 552.099i | −0.406287 | + | 0.628815i | ||||
\(879\) | − | 176.948i | − | 0.201306i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1589.22 | 1.80388 | 0.901942 | − | 0.431858i | \(-0.142142\pi\) | ||||
0.901942 | + | 0.431858i | \(0.142142\pi\) | |||||||
\(882\) | 245.146 | + | 158.393i | 0.277944 | + | 0.179584i | ||||
\(883\) | 495.149i | 0.560758i | 0.959889 | + | 0.280379i | \(0.0904601\pi\) | ||||
−0.959889 | + | 0.280379i | \(0.909540\pi\) | |||||||
\(884\) | −153.732 | − | 341.022i | −0.173905 | − | 0.385772i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 465.533 | − | 720.510i | 0.525432 | − | 0.813216i | ||||
\(887\) | 1384.20i | 1.56054i | 0.625440 | + | 0.780272i | \(0.284919\pi\) | ||||
−0.625440 | + | 0.780272i | \(0.715081\pi\) | |||||||
\(888\) | 73.8132 | + | 11.1651i | 0.0831230 | + | 0.0125733i | ||||
\(889\) | 83.1988 | 0.0935870 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 83.5166i | − | 0.0937336i | ||||||
\(892\) | 313.443 | − | 141.299i | 0.351393 | − | 0.158407i | ||||
\(893\) | 521.611 | 0.584111 | ||||||||
\(894\) | −89.0760 | + | 137.864i | −0.0996376 | + | 0.154210i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −58.5528 | + | 49.0099i | −0.0653491 | + | 0.0546985i | ||||
\(897\) | −1306.38 | −1.45639 | ||||||||
\(898\) | −687.448 | − | 444.171i | −0.765533 | − | 0.494623i | ||||
\(899\) | 2113.95i | 2.35145i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.1475 | −0.0112625 | ||||||||
\(902\) | −403.676 | + | 624.773i | −0.447534 | + | 0.692653i | ||||
\(903\) | − | 37.3161i | − | 0.0413246i | ||||||
\(904\) | −77.8155 | + | 514.444i | −0.0860791 | + | 0.569075i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −318.903 | − | 206.049i | −0.351991 | − | 0.227427i | ||||
\(907\) | − | 957.750i | − | 1.05595i | −0.849259 | − | 0.527977i | \(-0.822951\pi\) | ||
0.849259 | − | 0.527977i | \(-0.177049\pi\) | |||||||
\(908\) | −1029.64 | + | 464.160i | −1.13397 | + | 0.511189i | ||||
\(909\) | 10.9824 | 0.0120819 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 704.979i | − | 0.773852i | −0.922111 | − | 0.386926i | \(-0.873537\pi\) | ||
0.922111 | − | 0.386926i | \(-0.126463\pi\) | |||||||
\(912\) | 129.335 | − | 146.348i | 0.141814 | − | 0.160469i | ||||
\(913\) | 1205.51 | 1.32038 | ||||||||
\(914\) | 1291.08 | + | 834.185i | 1.41256 | + | 0.912675i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 227.287 | + | 504.189i | 0.248130 | + | 0.550424i | ||||
\(917\) | 37.8717 | 0.0412996 | ||||||||
\(918\) | 22.4325 | − | 34.7190i | 0.0244362 | − | 0.0378202i | ||||
\(919\) | − | 607.048i | − | 0.660553i | −0.943884 | − | 0.330277i | \(-0.892858\pi\) | ||
0.943884 | − | 0.330277i | \(-0.107142\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 568.790 | 0.617578 | ||||||||
\(922\) | 531.782 | + | 343.593i | 0.576770 | + | 0.372660i | ||||
\(923\) | 1392.29i | 1.50844i | ||||||||
\(924\) | −34.9638 | + | 15.7616i | −0.0378396 | + | 0.0170580i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −533.151 | + | 825.163i | −0.575757 | + | 0.891104i | ||||
\(927\) | 454.250i | 0.490022i | ||||||||
\(928\) | 1099.15 | − | 308.219i | 1.18443 | − | 0.332132i | ||||
\(929\) | 1011.21 | 1.08849 | 0.544247 | − | 0.838925i | \(-0.316815\pi\) | ||||
0.544247 | + | 0.838925i | \(0.316815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 342.822i | 0.368230i | ||||||||
\(932\) | 0.859647 | + | 1.90695i | 0.000922368 | + | 0.00204608i | ||||
\(933\) | −165.303 | −0.177174 | ||||||||
\(934\) | −445.434 | + | 689.403i | −0.476910 | + | 0.738119i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −84.3938 | + | 557.934i | −0.0901643 | + | 0.596083i | ||||
\(937\) | 363.105 | 0.387519 | 0.193760 | − | 0.981049i | \(-0.437932\pi\) | ||||
0.193760 | + | 0.981049i | \(0.437932\pi\) | |||||||
\(938\) | 69.8846 | + | 45.1536i | 0.0745039 | + | 0.0481381i | ||||
\(939\) | − | 953.334i | − | 1.01527i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1106.51 | −1.17588 | −0.587942 | − | 0.808903i | \(-0.700061\pi\) | ||||
−0.587942 | + | 0.808903i | \(0.700061\pi\) | |||||||
\(942\) | 333.855 | − | 516.711i | 0.354411 | − | 0.548525i | ||||
\(943\) | 1285.71i | 1.36342i | ||||||||
\(944\) | 436.435 | + | 385.698i | 0.462325 | + | 0.408579i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −562.990 | − | 363.757i | −0.595127 | − | 0.384521i | ||||
\(947\) | − | 553.561i | − | 0.584541i | −0.956336 | − | 0.292271i | \(-0.905589\pi\) | ||
0.956336 | − | 0.292271i | \(-0.0944108\pi\) | |||||||
\(948\) | 187.552 | + | 416.044i | 0.197839 | + | 0.438865i | ||||
\(949\) | 1951.51 | 2.05639 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 761.053i | − | 0.800266i | ||||||
\(952\) | −18.7684 | − | 2.83894i | −0.0197147 | − | 0.00298208i | ||||
\(953\) | 1674.84 | 1.75744 | 0.878718 | − | 0.477342i | \(-0.158400\pi\) | ||||
0.878718 | + | 0.477342i | \(0.158400\pi\) | |||||||
\(954\) | 12.8571 | + | 8.30720i | 0.0134771 | + | 0.00870776i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 268.728 | − | 121.142i | 0.281096 | − | 0.126717i | ||||
\(957\) | 573.371 | 0.599134 | ||||||||
\(958\) | 215.902 | − | 334.154i | 0.225368 | − | 0.348804i | ||||
\(959\) | 82.4162i | 0.0859398i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2550.57 | −2.65408 | ||||||||
\(962\) | −212.791 | − | 137.488i | −0.221196 | − | 0.142919i | ||||
\(963\) | 248.428i | 0.257973i | ||||||||
\(964\) | 51.5692 | + | 114.396i | 0.0534950 | + | 0.118668i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −35.9757 | + | 55.6799i | −0.0372419 | + | 0.0576396i | ||||
\(967\) | 786.720i | 0.813568i | 0.913524 | + | 0.406784i | \(0.133350\pi\) | ||||
−0.913524 | + | 0.406784i | \(0.866650\pi\) | |||||||
\(968\) | 41.7435 | − | 275.969i | 0.0431234 | − | 0.285092i | ||||
\(969\) | 48.5524 | 0.0501057 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1289.75i | 1.32827i | 0.747612 | + | 0.664135i | \(0.231200\pi\) | ||||
−0.747612 | + | 0.664135i | \(0.768800\pi\) | |||||||
\(972\) | −56.8448 | + | 25.6255i | −0.0584823 | + | 0.0263637i | ||||
\(973\) | −17.8710 | −0.0183669 | ||||||||
\(974\) | 222.246 | − | 343.972i | 0.228178 | − | 0.353154i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 92.5210 | − | 104.692i | 0.0947961 | − | 0.107266i | ||||
\(977\) | −495.847 | −0.507520 | −0.253760 | − | 0.967267i | \(-0.581667\pi\) | ||||
−0.253760 | + | 0.967267i | \(0.581667\pi\) | |||||||
\(978\) | −281.876 | − | 182.125i | −0.288217 | − | 0.186222i | ||||
\(979\) | 1210.68i | 1.23665i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.1051 | 0.0225332 | ||||||||
\(982\) | 855.933 | − | 1324.74i | 0.871622 | − | 1.34902i | ||||
\(983\) | 967.035i | 0.983759i | 0.870663 | + | 0.491880i | \(0.163690\pi\) | ||||
−0.870663 | + | 0.491880i | \(0.836310\pi\) | |||||||
\(984\) | 549.106 | + | 83.0585i | 0.558035 | + | 0.0844091i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 238.358 | + | 154.007i | 0.241742 | + | 0.156194i | ||||
\(987\) | 76.4730i | 0.0774803i | ||||||||
\(988\) | −604.241 | + | 272.390i | −0.611580 | + | 0.275698i | ||||
\(989\) | −1158.57 | −1.17145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1203.68i | − | 1.21461i | −0.794469 | − | 0.607305i | \(-0.792251\pi\) | ||
0.794469 | − | 0.607305i | \(-0.207749\pi\) | |||||||
\(992\) | 511.994 | + | 1825.84i | 0.516123 | + | 1.84057i | ||||
\(993\) | −831.249 | −0.837109 | ||||||||
\(994\) | 59.3417 | + | 38.3416i | 0.0596999 | + | 0.0385730i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −369.888 | − | 820.519i | −0.371373 | − | 0.823814i | ||||
\(997\) | 1274.55 | 1.27838 | 0.639192 | − | 0.769047i | \(-0.279269\pi\) | ||||
0.639192 | + | 0.769047i | \(0.279269\pi\) | |||||||
\(998\) | 803.603 | − | 1243.74i | 0.805214 | − | 1.24624i | ||||
\(999\) | − | 27.9948i | − | 0.0280228i |
(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 | 300.3.c.d.151.3 | 8 | ||
3.2 | odd | 2 | 900.3.c.u.451.6 | 8 | |||
4.3 | odd | 2 | inner | 300.3.c.d.151.4 | 8 | ||
5.2 | odd | 4 | 300.3.f.b.199.13 | 16 | |||
5.3 | odd | 4 | 300.3.f.b.199.4 | 16 | |||
5.4 | even | 2 | 60.3.c.a.31.6 | yes | 8 | ||
12.11 | even | 2 | 900.3.c.u.451.5 | 8 | |||
15.2 | even | 4 | 900.3.f.f.199.4 | 16 | |||
15.8 | even | 4 | 900.3.f.f.199.13 | 16 | |||
15.14 | odd | 2 | 180.3.c.b.91.3 | 8 | |||
20.3 | even | 4 | 300.3.f.b.199.14 | 16 | |||
20.7 | even | 4 | 300.3.f.b.199.3 | 16 | |||
20.19 | odd | 2 | 60.3.c.a.31.5 | ✓ | 8 | ||
40.19 | odd | 2 | 960.3.e.c.511.1 | 8 | |||
40.29 | even | 2 | 960.3.e.c.511.6 | 8 | |||
60.23 | odd | 4 | 900.3.f.f.199.3 | 16 | |||
60.47 | odd | 4 | 900.3.f.f.199.14 | 16 | |||
60.59 | even | 2 | 180.3.c.b.91.4 | 8 | |||
120.29 | odd | 2 | 2880.3.e.j.2431.6 | 8 | |||
120.59 | even | 2 | 2880.3.e.j.2431.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.5 | ✓ | 8 | 20.19 | odd | 2 | ||
60.3.c.a.31.6 | yes | 8 | 5.4 | even | 2 | ||
180.3.c.b.91.3 | 8 | 15.14 | odd | 2 | |||
180.3.c.b.91.4 | 8 | 60.59 | even | 2 | |||
300.3.c.d.151.3 | 8 | 1.1 | even | 1 | trivial | ||
300.3.c.d.151.4 | 8 | 4.3 | odd | 2 | inner | ||
300.3.f.b.199.3 | 16 | 20.7 | even | 4 | |||
300.3.f.b.199.4 | 16 | 5.3 | odd | 4 | |||
300.3.f.b.199.13 | 16 | 5.2 | odd | 4 | |||
300.3.f.b.199.14 | 16 | 20.3 | even | 4 | |||
900.3.c.u.451.5 | 8 | 12.11 | even | 2 | |||
900.3.c.u.451.6 | 8 | 3.2 | odd | 2 | |||
900.3.f.f.199.3 | 16 | 60.23 | odd | 4 | |||
900.3.f.f.199.4 | 16 | 15.2 | even | 4 | |||
900.3.f.f.199.13 | 16 | 15.8 | even | 4 | |||
900.3.f.f.199.14 | 16 | 60.47 | odd | 4 | |||
960.3.e.c.511.1 | 8 | 40.19 | odd | 2 | |||
960.3.e.c.511.6 | 8 | 40.29 | even | 2 | |||
2880.3.e.j.2431.6 | 8 | 120.29 | odd | 2 | |||
2880.3.e.j.2431.7 | 8 | 120.59 | even | 2 |