Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(199,300)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(-0.120653 - 1.40906i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.199 |
Dual form | 300.3.f.b.199.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.08539 | + | 1.67986i | −0.542693 | + | 0.839931i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −1.64388 | − | 3.64660i | −0.410969 | − | 0.911649i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.87994 | − | 2.90961i | 0.313324 | − | 0.484935i | ||||
\(7\) | 0.596540 | 0.0852199 | 0.0426100 | − | 0.999092i | \(-0.486433\pi\) | ||||
0.0426100 | + | 0.999092i | \(0.486433\pi\) | |||||||
\(8\) | 7.91002 | + | 1.19648i | 0.988753 | + | 0.149560i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 9.27963i | − | 0.843602i | −0.906688 | − | 0.421801i | \(-0.861398\pi\) | ||
0.906688 | − | 0.421801i | \(-0.138602\pi\) | |||||||
\(12\) | 2.84728 | + | 6.31609i | 0.237273 | + | 0.526341i | ||||
\(13\) | 23.5117i | 1.80859i | 0.426907 | + | 0.904295i | \(0.359603\pi\) | ||||
−0.426907 | + | 0.904295i | \(0.640397\pi\) | |||||||
\(14\) | −0.647476 | + | 1.00210i | −0.0462483 | + | 0.0715789i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −10.5953 | + | 11.9891i | −0.662209 | + | 0.749319i | ||||
\(17\) | 3.97751i | 0.233971i | 0.993134 | + | 0.116986i | \(0.0373231\pi\) | ||||
−0.993134 | + | 0.116986i | \(0.962677\pi\) | |||||||
\(18\) | −3.25616 | + | 5.03959i | −0.180898 | + | 0.279977i | ||||
\(19\) | − | 7.04756i | − | 0.370924i | −0.982651 | − | 0.185462i | \(-0.940622\pi\) | ||
0.982651 | − | 0.185462i | \(-0.0593782\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.03324 | −0.0492018 | ||||||||
\(22\) | 15.5885 | + | 10.0720i | 0.708568 | + | 0.457817i | ||||
\(23\) | −32.0793 | −1.39475 | −0.697376 | − | 0.716705i | \(-0.745649\pi\) | ||||
−0.697376 | + | 0.716705i | \(0.745649\pi\) | |||||||
\(24\) | −13.7006 | − | 2.07237i | −0.570857 | − | 0.0863486i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −39.4964 | − | 25.5192i | −1.51909 | − | 0.981509i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −0.980637 | − | 2.17534i | −0.0350227 | − | 0.0776907i | ||||
\(29\) | −35.6734 | −1.23012 | −0.615059 | − | 0.788481i | \(-0.710868\pi\) | ||||
−0.615059 | + | 0.788481i | \(0.710868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 59.2585i | 1.91156i | 0.294076 | + | 0.955782i | \(0.404988\pi\) | ||||
−0.294076 | + | 0.955782i | \(0.595012\pi\) | |||||||
\(32\) | −8.64000 | − | 30.8115i | −0.270000 | − | 0.962860i | ||||
\(33\) | 16.0728i | 0.487054i | ||||||||
\(34\) | −6.68167 | − | 4.31713i | −0.196520 | − | 0.126974i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.93163 | − | 10.9398i | −0.136990 | − | 0.303883i | ||||
\(37\) | − | 5.38761i | − | 0.145611i | −0.997346 | − | 0.0728055i | \(-0.976805\pi\) | ||
0.997346 | − | 0.0728055i | \(-0.0231952\pi\) | |||||||
\(38\) | 11.8389 | + | 7.64932i | 0.311551 | + | 0.201298i | ||||
\(39\) | − | 40.7234i | − | 1.04419i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.0791 | 0.977539 | 0.488769 | − | 0.872413i | \(-0.337446\pi\) | ||||
0.488769 | + | 0.872413i | \(0.337446\pi\) | |||||||
\(42\) | 1.12146 | − | 1.73570i | 0.0267014 | − | 0.0413261i | ||||
\(43\) | −36.1157 | −0.839901 | −0.419950 | − | 0.907547i | \(-0.637953\pi\) | ||||
−0.419950 | + | 0.907547i | \(0.637953\pi\) | |||||||
\(44\) | −33.8391 | + | 15.2545i | −0.769070 | + | 0.346694i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 34.8184 | − | 53.8888i | 0.756922 | − | 1.17150i | ||||
\(47\) | −74.0131 | −1.57475 | −0.787373 | − | 0.616477i | \(-0.788559\pi\) | ||||
−0.787373 | + | 0.616477i | \(0.788559\pi\) | |||||||
\(48\) | 18.3517 | − | 20.7657i | 0.382327 | − | 0.432620i | ||||
\(49\) | −48.6441 | −0.992738 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.88925i | − | 0.135083i | ||||||
\(52\) | 85.7376 | − | 38.6503i | 1.64880 | − | 0.743275i | ||||
\(53\) | 2.55123i | 0.0481364i | 0.999710 | + | 0.0240682i | \(0.00766189\pi\) | ||||
−0.999710 | + | 0.0240682i | \(0.992338\pi\) | |||||||
\(54\) | 5.63983 | − | 8.72882i | 0.104441 | − | 0.161645i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.71864 | + | 0.713748i | 0.0842614 | + | 0.0127455i | ||||
\(57\) | 12.2067i | 0.214153i | ||||||||
\(58\) | 38.7194 | − | 59.9265i | 0.667576 | − | 1.03321i | ||||
\(59\) | 36.4026i | 0.616993i | 0.951225 | + | 0.308497i | \(0.0998259\pi\) | ||||
−0.951225 | + | 0.308497i | \(0.900174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.73223 | −0.143151 | −0.0715757 | − | 0.997435i | \(-0.522803\pi\) | ||||
−0.0715757 | + | 0.997435i | \(0.522803\pi\) | |||||||
\(62\) | −99.5461 | − | 64.3183i | −1.60558 | − | 1.03739i | ||||
\(63\) | 1.78962 | 0.0284066 | ||||||||
\(64\) | 61.1369 | + | 18.9284i | 0.955264 | + | 0.295756i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −27.0001 | − | 17.4452i | −0.409092 | − | 0.264321i | ||||
\(67\) | 69.7379 | 1.04086 | 0.520432 | − | 0.853903i | \(-0.325771\pi\) | ||||
0.520432 | + | 0.853903i | \(0.325771\pi\) | |||||||
\(68\) | 14.5044 | − | 6.53853i | 0.213300 | − | 0.0961548i | ||||
\(69\) | 55.5630 | 0.805261 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59.2170i | 0.834043i | 0.908897 | + | 0.417021i | \(0.136926\pi\) | ||||
−0.908897 | + | 0.417021i | \(0.863074\pi\) | |||||||
\(72\) | 23.7301 | + | 3.58944i | 0.329584 | + | 0.0498534i | ||||
\(73\) | 83.0019i | 1.13701i | 0.822679 | + | 0.568506i | \(0.192478\pi\) | ||||
−0.822679 | + | 0.568506i | \(0.807522\pi\) | |||||||
\(74\) | 9.05044 | + | 5.84763i | 0.122303 | + | 0.0790220i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −25.6996 | + | 11.5853i | −0.338153 | + | 0.152438i | ||||
\(77\) | − | 5.53566i | − | 0.0718917i | ||||||
\(78\) | 68.4098 | + | 44.2006i | 0.877048 | + | 0.566675i | ||||
\(79\) | 65.8705i | 0.833804i | 0.908951 | + | 0.416902i | \(0.136884\pi\) | ||||
−0.908951 | + | 0.416902i | \(0.863116\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −43.5013 | + | 67.3274i | −0.530503 | + | 0.821065i | ||||
\(83\) | −129.909 | −1.56517 | −0.782586 | − | 0.622542i | \(-0.786100\pi\) | ||||
−0.782586 | + | 0.622542i | \(0.786100\pi\) | |||||||
\(84\) | 1.69851 | + | 3.76780i | 0.0202204 | + | 0.0448547i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 39.1995 | − | 60.6695i | 0.455808 | − | 0.705459i | ||||
\(87\) | 61.7882 | 0.710209 | ||||||||
\(88\) | 11.1029 | − | 73.4020i | 0.126169 | − | 0.834114i | ||||
\(89\) | 130.466 | 1.46591 | 0.732956 | − | 0.680277i | \(-0.238140\pi\) | ||||
0.732956 | + | 0.680277i | \(0.238140\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.0256i | 0.154128i | ||||||||
\(92\) | 52.7344 | + | 116.980i | 0.573200 | + | 1.27152i | ||||
\(93\) | − | 102.639i | − | 1.10364i | ||||||
\(94\) | 80.3327 | − | 124.332i | 0.854603 | − | 1.32268i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.9649 | + | 53.3671i | 0.155885 | + | 0.555908i | ||||
\(97\) | 93.1113i | 0.959911i | 0.877293 | + | 0.479955i | \(0.159347\pi\) | ||||
−0.877293 | + | 0.479955i | \(0.840653\pi\) | |||||||
\(98\) | 52.7977 | − | 81.7155i | 0.538752 | − | 0.833831i | ||||
\(99\) | − | 27.8389i | − | 0.281201i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.66081 | −0.0362457 | −0.0181228 | − | 0.999836i | \(-0.505769\pi\) | ||||
−0.0181228 | + | 0.999836i | \(0.505769\pi\) | |||||||
\(102\) | 11.5730 | + | 7.47749i | 0.113461 | + | 0.0733087i | ||||
\(103\) | 151.417 | 1.47007 | 0.735033 | − | 0.678032i | \(-0.237167\pi\) | ||||
0.735033 | + | 0.678032i | \(0.237167\pi\) | |||||||
\(104\) | −28.1313 | + | 185.978i | −0.270493 | + | 1.78825i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.28571 | − | 2.76907i | −0.0404313 | − | 0.0261233i | ||||
\(107\) | −82.8092 | −0.773918 | −0.386959 | − | 0.922097i | \(-0.626474\pi\) | ||||
−0.386959 | + | 0.922097i | \(0.626474\pi\) | |||||||
\(108\) | 8.54183 | + | 18.9483i | 0.0790910 | + | 0.175447i | ||||
\(109\) | 7.36835 | 0.0675996 | 0.0337998 | − | 0.999429i | \(-0.489239\pi\) | ||||
0.0337998 | + | 0.999429i | \(0.489239\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.33161i | 0.0840685i | ||||||||
\(112\) | −6.32054 | + | 7.15197i | −0.0564334 | + | 0.0638569i | ||||
\(113\) | − | 65.0370i | − | 0.575549i | −0.957698 | − | 0.287774i | \(-0.907085\pi\) | ||
0.957698 | − | 0.287774i | \(-0.0929153\pi\) | |||||||
\(114\) | −20.5056 | − | 13.2490i | −0.179874 | − | 0.116219i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 58.6427 | + | 130.087i | 0.505540 | + | 1.12144i | ||||
\(117\) | 70.5350i | 0.602864i | ||||||||
\(118\) | −61.1514 | − | 39.5109i | −0.518232 | − | 0.334838i | ||||
\(119\) | 2.37274i | 0.0199390i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34.8885 | 0.288335 | ||||||||
\(122\) | 9.47784 | − | 14.6689i | 0.0776872 | − | 0.120237i | ||||
\(123\) | −69.4190 | −0.564382 | ||||||||
\(124\) | 216.092 | − | 97.4136i | 1.74268 | − | 0.785593i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.94243 | + | 3.00631i | −0.0154161 | + | 0.0238596i | ||||
\(127\) | −139.469 | −1.09818 | −0.549091 | − | 0.835763i | \(-0.685026\pi\) | ||||
−0.549091 | + | 0.835763i | \(0.685026\pi\) | |||||||
\(128\) | −98.1542 | + | 82.1569i | −0.766829 | + | 0.641851i | ||||
\(129\) | 62.5543 | 0.484917 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 63.4856i | − | 0.484623i | −0.970198 | − | 0.242312i | \(-0.922094\pi\) | ||
0.970198 | − | 0.242312i | \(-0.0779056\pi\) | |||||||
\(132\) | 58.6110 | − | 26.4217i | 0.444023 | − | 0.200164i | ||||
\(133\) | − | 4.20415i | − | 0.0316101i | ||||||
\(134\) | −75.6925 | + | 117.150i | −0.564870 | + | 0.874254i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.75901 | + | 31.4622i | −0.0349927 | + | 0.231340i | ||||
\(137\) | − | 138.157i | − | 1.00845i | −0.863573 | − | 0.504223i | \(-0.831779\pi\) | ||
0.863573 | − | 0.504223i | \(-0.168221\pi\) | |||||||
\(138\) | −60.3073 | + | 93.3382i | −0.437009 | + | 0.676363i | ||||
\(139\) | − | 29.9578i | − | 0.215523i | −0.994177 | − | 0.107762i | \(-0.965632\pi\) | ||
0.994177 | − | 0.107762i | \(-0.0343684\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 128.194 | 0.909180 | ||||||||
\(142\) | −99.4765 | − | 64.2733i | −0.700539 | − | 0.452629i | ||||
\(143\) | 218.180 | 1.52573 | ||||||||
\(144\) | −31.7860 | + | 35.9673i | −0.220736 | + | 0.249773i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −139.432 | − | 90.0891i | −0.955012 | − | 0.617048i | ||||
\(147\) | 84.2541 | 0.573157 | ||||||||
\(148\) | −19.6464 | + | 8.85655i | −0.132746 | + | 0.0598416i | ||||
\(149\) | 47.3823 | 0.318002 | 0.159001 | − | 0.987278i | \(-0.449173\pi\) | ||||
0.159001 | + | 0.987278i | \(0.449173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 109.604i | − | 0.725852i | −0.931818 | − | 0.362926i | \(-0.881778\pi\) | ||
0.931818 | − | 0.362926i | \(-0.118222\pi\) | |||||||
\(152\) | 8.43227 | − | 55.7463i | 0.0554755 | − | 0.366752i | ||||
\(153\) | 11.9325i | 0.0779904i | ||||||||
\(154\) | 9.29915 | + | 6.00833i | 0.0603841 | + | 0.0390151i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −148.502 | + | 66.9442i | −0.951936 | + | 0.429130i | ||||
\(157\) | − | 177.588i | − | 1.13113i | −0.824703 | − | 0.565566i | \(-0.808658\pi\) | ||
0.824703 | − | 0.565566i | \(-0.191342\pi\) | |||||||
\(158\) | −110.653 | − | 71.4950i | −0.700338 | − | 0.452500i | ||||
\(159\) | − | 4.41886i | − | 0.0277916i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.1366 | −0.118861 | ||||||||
\(162\) | −9.76847 | + | 15.1188i | −0.0602992 | + | 0.0933257i | ||||
\(163\) | 96.8778 | 0.594342 | 0.297171 | − | 0.954824i | \(-0.403957\pi\) | ||||
0.297171 | + | 0.954824i | \(0.403957\pi\) | |||||||
\(164\) | −65.8850 | − | 146.152i | −0.401738 | − | 0.891173i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 141.002 | − | 218.230i | 0.849408 | − | 1.31464i | ||||
\(167\) | 152.605 | 0.913801 | 0.456901 | − | 0.889518i | \(-0.348960\pi\) | ||||
0.456901 | + | 0.889518i | \(0.348960\pi\) | |||||||
\(168\) | −8.17292 | − | 1.23625i | −0.0486484 | − | 0.00735862i | ||||
\(169\) | −383.799 | −2.27100 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 21.1427i | − | 0.123641i | ||||||
\(172\) | 59.3698 | + | 131.700i | 0.345173 | + | 0.765695i | ||||
\(173\) | − | 155.773i | − | 0.900422i | −0.892922 | − | 0.450211i | \(-0.851349\pi\) | ||
0.892922 | − | 0.450211i | \(-0.148651\pi\) | |||||||
\(174\) | −67.0640 | + | 103.796i | −0.385425 | + | 0.596527i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 111.254 | + | 98.3209i | 0.632127 | + | 0.558641i | ||||
\(177\) | − | 63.0512i | − | 0.356221i | ||||||
\(178\) | −141.606 | + | 219.165i | −0.795540 | + | 1.23126i | ||||
\(179\) | − | 126.001i | − | 0.703915i | −0.936016 | − | 0.351957i | \(-0.885516\pi\) | ||
0.936016 | − | 0.351957i | \(-0.114484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −346.725 | −1.91561 | −0.957803 | − | 0.287424i | \(-0.907201\pi\) | ||||
−0.957803 | + | 0.287424i | \(0.907201\pi\) | |||||||
\(182\) | −23.5612 | − | 15.2232i | −0.129457 | − | 0.0836442i | ||||
\(183\) | 15.1247 | 0.0826485 | ||||||||
\(184\) | −253.748 | − | 38.3823i | −1.37906 | − | 0.208599i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 172.419 | + | 111.403i | 0.926983 | + | 0.598939i | ||||
\(187\) | 36.9098 | 0.197379 | ||||||||
\(188\) | 121.668 | + | 269.896i | 0.647171 | + | 1.43562i | ||||
\(189\) | −3.09971 | −0.0164006 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 133.159i | − | 0.697167i | −0.937278 | − | 0.348584i | \(-0.886663\pi\) | ||
0.937278 | − | 0.348584i | \(-0.113337\pi\) | |||||||
\(192\) | −105.892 | − | 32.7849i | −0.551522 | − | 0.170755i | ||||
\(193\) | 136.246i | 0.705940i | 0.935635 | + | 0.352970i | \(0.114828\pi\) | ||||
−0.935635 | + | 0.352970i | \(0.885172\pi\) | |||||||
\(194\) | −156.414 | − | 101.062i | −0.806259 | − | 0.520937i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 79.9649 | + | 177.386i | 0.407984 | + | 0.905029i | ||||
\(197\) | 74.8945i | 0.380175i | 0.981767 | + | 0.190087i | \(0.0608772\pi\) | ||||
−0.981767 | + | 0.190087i | \(0.939123\pi\) | |||||||
\(198\) | 46.7655 | + | 30.2159i | 0.236189 | + | 0.152606i | ||||
\(199\) | 251.605i | 1.26434i | 0.774828 | + | 0.632172i | \(0.217836\pi\) | ||||
−0.774828 | + | 0.632172i | \(0.782164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −120.790 | −0.600943 | ||||||||
\(202\) | 3.97339 | − | 6.14966i | 0.0196703 | − | 0.0304439i | ||||
\(203\) | −21.2806 | −0.104831 | ||||||||
\(204\) | −25.1223 | + | 11.3251i | −0.123149 | + | 0.0555150i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −164.346 | + | 254.359i | −0.797794 | + | 1.23475i | ||||
\(207\) | −96.2379 | −0.464917 | ||||||||
\(208\) | −281.884 | − | 249.114i | −1.35521 | − | 1.19767i | ||||
\(209\) | −65.3987 | −0.312913 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 228.203i | − | 1.08153i | −0.841173 | − | 0.540766i | \(-0.818135\pi\) | ||
0.841173 | − | 0.540766i | \(-0.181865\pi\) | |||||||
\(212\) | 9.30331 | − | 4.19390i | 0.0438835 | − | 0.0197826i | ||||
\(213\) | − | 102.567i | − | 0.481535i | ||||||
\(214\) | 89.8799 | − | 139.108i | 0.420000 | − | 0.650038i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −41.1017 | − | 6.21710i | −0.190286 | − | 0.0287829i | ||||
\(217\) | 35.3500i | 0.162903i | ||||||||
\(218\) | −7.99751 | + | 12.3778i | −0.0366858 | + | 0.0567790i | ||||
\(219\) | − | 143.763i | − | 0.656454i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −93.5179 | −0.423158 | ||||||||
\(222\) | −15.6758 | − | 10.1284i | −0.0706118 | − | 0.0456234i | ||||
\(223\) | 85.9549 | 0.385448 | 0.192724 | − | 0.981253i | \(-0.438268\pi\) | ||||
0.192724 | + | 0.981253i | \(0.438268\pi\) | |||||||
\(224\) | −5.15410 | − | 18.3803i | −0.0230094 | − | 0.0820549i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 109.253 | + | 70.5902i | 0.483421 | + | 0.312346i | ||||
\(227\) | 282.357 | 1.24386 | 0.621932 | − | 0.783071i | \(-0.286348\pi\) | ||||
0.621932 | + | 0.783071i | \(0.286348\pi\) | |||||||
\(228\) | 44.5130 | − | 20.0663i | 0.195233 | − | 0.0880103i | ||||
\(229\) | −138.263 | −0.603768 | −0.301884 | − | 0.953345i | \(-0.597615\pi\) | ||||
−0.301884 | + | 0.953345i | \(0.597615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.58805i | 0.0415067i | ||||||||
\(232\) | −282.178 | − | 42.6826i | −1.21628 | − | 0.183977i | ||||
\(233\) | 0.522939i | 0.00224438i | 0.999999 | + | 0.00112219i | \(0.000357204\pi\) | ||||
−0.999999 | + | 0.00112219i | \(0.999643\pi\) | |||||||
\(234\) | −118.489 | − | 76.5577i | −0.506364 | − | 0.327170i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 132.746 | − | 59.8413i | 0.562482 | − | 0.253565i | ||||
\(237\) | − | 114.091i | − | 0.481397i | ||||||
\(238\) | −3.98588 | − | 2.57534i | −0.0167474 | − | 0.0108208i | ||||
\(239\) | 73.6928i | 0.308338i | 0.988044 | + | 0.154169i | \(0.0492700\pi\) | ||||
−0.988044 | + | 0.154169i | \(0.950730\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 31.3705 | 0.130168 | 0.0650840 | − | 0.997880i | \(-0.479268\pi\) | ||||
0.0650840 | + | 0.997880i | \(0.479268\pi\) | |||||||
\(242\) | −37.8675 | + | 58.6080i | −0.156477 | + | 0.242182i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 14.3547 | + | 31.8429i | 0.0588307 | + | 0.130504i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 75.3464 | − | 116.614i | 0.306286 | − | 0.474042i | ||||
\(247\) | 165.700 | 0.670850 | ||||||||
\(248\) | −70.9016 | + | 468.736i | −0.285894 | + | 1.89006i | ||||
\(249\) | 225.010 | 0.903653 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 78.7478i | − | 0.313736i | −0.987620 | − | 0.156868i | \(-0.949860\pi\) | ||
0.987620 | − | 0.156868i | \(-0.0501398\pi\) | |||||||
\(252\) | −2.94191 | − | 6.52602i | −0.0116742 | − | 0.0258969i | ||||
\(253\) | 297.684i | 1.17662i | ||||||||
\(254\) | 151.378 | − | 234.289i | 0.595975 | − | 0.922397i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.4772 | − | 254.057i | −0.122958 | − | 0.992412i | ||||
\(257\) | 243.954i | 0.949236i | 0.880192 | + | 0.474618i | \(0.157414\pi\) | ||||
−0.880192 | + | 0.474618i | \(0.842586\pi\) | |||||||
\(258\) | −67.8956 | + | 105.083i | −0.263161 | + | 0.407297i | ||||
\(259\) | − | 3.21392i | − | 0.0124090i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −107.020 | −0.410039 | ||||||||
\(262\) | 106.647 | + | 68.9064i | 0.407050 | + | 0.263002i | ||||
\(263\) | −102.737 | −0.390635 | −0.195317 | − | 0.980740i | \(-0.562574\pi\) | ||||
−0.195317 | + | 0.980740i | \(0.562574\pi\) | |||||||
\(264\) | −19.2308 | + | 127.136i | −0.0728439 | + | 0.481576i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.06239 | + | 4.56312i | 0.0265503 | + | 0.0171546i | ||||
\(267\) | −225.974 | −0.846344 | ||||||||
\(268\) | −114.640 | − | 254.306i | −0.427763 | − | 0.948903i | ||||
\(269\) | 123.646 | 0.459651 | 0.229825 | − | 0.973232i | \(-0.426184\pi\) | ||||
0.229825 | + | 0.973232i | \(0.426184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 332.371i | 1.22646i | 0.789904 | + | 0.613230i | \(0.210130\pi\) | ||||
−0.789904 | + | 0.613230i | \(0.789870\pi\) | |||||||
\(272\) | −47.6868 | − | 42.1431i | −0.175319 | − | 0.154938i | ||||
\(273\) | − | 24.2931i | − | 0.0889858i | ||||||
\(274\) | 232.085 | + | 149.954i | 0.847026 | + | 0.547277i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −91.3386 | − | 202.616i | −0.330937 | − | 0.734115i | ||||
\(277\) | − | 125.916i | − | 0.454571i | −0.973828 | − | 0.227286i | \(-0.927015\pi\) | ||
0.973828 | − | 0.227286i | \(-0.0729851\pi\) | |||||||
\(278\) | 50.3249 | + | 32.5157i | 0.181025 | + | 0.116963i | ||||
\(279\) | 177.775i | 0.637188i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 52.5628 | 0.187056 | 0.0935281 | − | 0.995617i | \(-0.470186\pi\) | ||||
0.0935281 | + | 0.995617i | \(0.470186\pi\) | |||||||
\(282\) | −139.140 | + | 215.349i | −0.493405 | + | 0.763649i | ||||
\(283\) | 199.288 | 0.704199 | 0.352100 | − | 0.935963i | \(-0.385468\pi\) | ||||
0.352100 | + | 0.935963i | \(0.385468\pi\) | |||||||
\(284\) | 215.941 | − | 97.3454i | 0.760355 | − | 0.342766i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −236.809 | + | 366.512i | −0.828004 | + | 1.28151i | ||||
\(287\) | 23.9088 | 0.0833058 | ||||||||
\(288\) | −25.9200 | − | 92.4346i | −0.0900001 | − | 0.320953i | ||||
\(289\) | 273.179 | 0.945258 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 161.274i | − | 0.554205i | ||||||
\(292\) | 302.674 | − | 136.445i | 1.03656 | − | 0.467276i | ||||
\(293\) | − | 102.161i | − | 0.348672i | −0.984686 | − | 0.174336i | \(-0.944222\pi\) | ||
0.984686 | − | 0.174336i | \(-0.0557779\pi\) | |||||||
\(294\) | −91.4482 | + | 141.535i | −0.311048 | + | 0.481413i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.44617 | − | 42.6161i | 0.0217776 | − | 0.143973i | ||||
\(297\) | 48.2184i | 0.162351i | ||||||||
\(298\) | −51.4281 | + | 79.5957i | −0.172577 | + | 0.267100i | ||||
\(299\) | − | 754.238i | − | 2.52254i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.5445 | −0.0715763 | ||||||||
\(302\) | 184.119 | + | 118.962i | 0.609666 | + | 0.393915i | ||||
\(303\) | 6.34071 | 0.0209264 | ||||||||
\(304\) | 84.4939 | + | 74.6713i | 0.277941 | + | 0.245629i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −20.0450 | − | 12.9514i | −0.0655065 | − | 0.0423248i | ||||
\(307\) | −328.391 | −1.06968 | −0.534839 | − | 0.844954i | \(-0.679628\pi\) | ||||
−0.534839 | + | 0.844954i | \(0.679628\pi\) | |||||||
\(308\) | −20.1863 | + | 9.09994i | −0.0655401 | + | 0.0295453i | ||||
\(309\) | −262.262 | −0.848743 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 95.4377i | 0.306874i | 0.988158 | + | 0.153437i | \(0.0490342\pi\) | ||||
−0.988158 | + | 0.153437i | \(0.950966\pi\) | |||||||
\(312\) | 48.7248 | − | 322.123i | 0.156169 | − | 1.03245i | ||||
\(313\) | − | 550.408i | − | 1.75849i | −0.476368 | − | 0.879246i | \(-0.658047\pi\) | ||
0.476368 | − | 0.879246i | \(-0.341953\pi\) | |||||||
\(314\) | 298.323 | + | 192.751i | 0.950073 | + | 0.613858i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 240.203 | − | 108.283i | 0.760137 | − | 0.342668i | ||||
\(317\) | 439.394i | 1.38610i | 0.720889 | + | 0.693051i | \(0.243734\pi\) | ||||
−0.720889 | + | 0.693051i | \(0.756266\pi\) | |||||||
\(318\) | 7.42307 | + | 4.79617i | 0.0233430 | + | 0.0150823i | ||||
\(319\) | 331.036i | 1.03773i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 143.430 | 0.446822 | ||||||||
\(322\) | 20.7706 | − | 32.1468i | 0.0645048 | − | 0.0998348i | ||||
\(323\) | 28.0317 | 0.0867855 | ||||||||
\(324\) | −14.7949 | − | 32.8194i | −0.0456632 | − | 0.101294i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −105.150 | + | 162.741i | −0.322545 | + | 0.499206i | ||||
\(327\) | −12.7624 | −0.0390286 | ||||||||
\(328\) | 317.026 | + | 47.9539i | 0.966544 | + | 0.146201i | ||||
\(329\) | −44.1517 | −0.134200 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 479.922i | 1.44992i | 0.688794 | + | 0.724958i | \(0.258141\pi\) | ||||
−0.688794 | + | 0.724958i | \(0.741859\pi\) | |||||||
\(332\) | 213.555 | + | 473.727i | 0.643237 | + | 1.42689i | ||||
\(333\) | − | 16.1628i | − | 0.0485370i | ||||||
\(334\) | −165.635 | + | 256.355i | −0.495913 | + | 0.767530i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.9475 | − | 12.3876i | 0.0325819 | − | 0.0368678i | ||||
\(337\) | 58.8437i | 0.174610i | 0.996182 | + | 0.0873052i | \(0.0278255\pi\) | ||||
−0.996182 | + | 0.0873052i | \(0.972174\pi\) | |||||||
\(338\) | 416.570 | − | 644.730i | 1.23246 | − | 1.90748i | ||||
\(339\) | 112.647i | 0.332293i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 549.897 | 1.61260 | ||||||||
\(342\) | 35.5168 | + | 22.9480i | 0.103850 | + | 0.0670993i | ||||
\(343\) | −58.2486 | −0.169821 | ||||||||
\(344\) | −285.676 | − | 43.2118i | −0.830454 | − | 0.125616i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 261.677 | + | 169.074i | 0.756293 | + | 0.488653i | ||||
\(347\) | 12.1484 | 0.0350099 | 0.0175049 | − | 0.999847i | \(-0.494428\pi\) | ||||
0.0175049 | + | 0.999847i | \(0.494428\pi\) | |||||||
\(348\) | −101.572 | − | 225.317i | −0.291874 | − | 0.647462i | ||||
\(349\) | 30.9277 | 0.0886180 | 0.0443090 | − | 0.999018i | \(-0.485891\pi\) | ||||
0.0443090 | + | 0.999018i | \(0.485891\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 122.170i | − | 0.348063i | ||||||
\(352\) | −285.919 | + | 80.1760i | −0.812271 | + | 0.227773i | ||||
\(353\) | 288.065i | 0.816048i | 0.912971 | + | 0.408024i | \(0.133782\pi\) | ||||
−0.912971 | + | 0.408024i | \(0.866218\pi\) | |||||||
\(354\) | 105.917 | + | 68.4348i | 0.299201 | + | 0.193319i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −214.470 | − | 475.757i | −0.602444 | − | 1.33640i | ||||
\(357\) | − | 4.10971i | − | 0.0115118i | ||||||
\(358\) | 211.664 | + | 136.759i | 0.591240 | + | 0.382010i | ||||
\(359\) | 663.911i | 1.84933i | 0.380776 | + | 0.924667i | \(0.375657\pi\) | ||||
−0.380776 | + | 0.924667i | \(0.624343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 311.332 | 0.862415 | ||||||||
\(362\) | 376.330 | − | 582.450i | 1.03959 | − | 1.60898i | ||||
\(363\) | −60.4287 | −0.166470 | ||||||||
\(364\) | 51.1459 | − | 23.0564i | 0.140511 | − | 0.0633418i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16.4161 | + | 25.4074i | −0.0448527 | + | 0.0694190i | ||||
\(367\) | 6.08529 | 0.0165812 | 0.00829059 | − | 0.999966i | \(-0.497361\pi\) | ||||
0.00829059 | + | 0.999966i | \(0.497361\pi\) | |||||||
\(368\) | 339.891 | − | 384.602i | 0.923618 | − | 1.04511i | ||||
\(369\) | 120.237 | 0.325846 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52191i | 0.00410218i | ||||||||
\(372\) | −374.282 | + | 168.725i | −1.00613 | + | 0.453562i | ||||
\(373\) | 204.741i | 0.548903i | 0.961601 | + | 0.274451i | \(0.0884963\pi\) | ||||
−0.961601 | + | 0.274451i | \(0.911504\pi\) | |||||||
\(374\) | −40.0614 | + | 62.0034i | −0.107116 | + | 0.165784i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −585.445 | − | 88.5552i | −1.55703 | − | 0.235519i | ||||
\(377\) | − | 838.742i | − | 2.22478i | ||||||
\(378\) | 3.36438 | − | 5.20709i | 0.00890048 | − | 0.0137754i | ||||
\(379\) | − | 402.331i | − | 1.06156i | −0.847510 | − | 0.530780i | \(-0.821899\pi\) | ||
0.847510 | − | 0.530780i | \(-0.178101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 241.568 | 0.634036 | ||||||||
\(382\) | 223.689 | + | 144.529i | 0.585573 | + | 0.378348i | ||||
\(383\) | 331.751 | 0.866191 | 0.433096 | − | 0.901348i | \(-0.357421\pi\) | ||||
0.433096 | + | 0.901348i | \(0.357421\pi\) | |||||||
\(384\) | 170.008 | − | 142.300i | 0.442729 | − | 0.370573i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −228.875 | − | 147.880i | −0.592941 | − | 0.383109i | ||||
\(387\) | −108.347 | −0.279967 | ||||||||
\(388\) | 339.540 | − | 153.063i | 0.875102 | − | 0.394493i | ||||
\(389\) | 623.310 | 1.60234 | 0.801169 | − | 0.598438i | \(-0.204212\pi\) | ||||
0.801169 | + | 0.598438i | \(0.204212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 127.596i | − | 0.326332i | ||||||
\(392\) | −384.776 | − | 58.2018i | −0.981572 | − | 0.148474i | ||||
\(393\) | 109.960i | 0.279797i | ||||||||
\(394\) | −125.812 | − | 81.2894i | −0.319321 | − | 0.206318i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −101.517 | + | 45.7636i | −0.256357 | + | 0.115565i | ||||
\(397\) | − | 355.449i | − | 0.895338i | −0.894199 | − | 0.447669i | \(-0.852254\pi\) | ||
0.894199 | − | 0.447669i | \(-0.147746\pi\) | |||||||
\(398\) | −422.661 | − | 273.088i | −1.06196 | − | 0.686151i | ||||
\(399\) | 7.28180i | 0.0182501i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −542.927 | −1.35393 | −0.676966 | − | 0.736014i | \(-0.736706\pi\) | ||||
−0.676966 | + | 0.736014i | \(0.736706\pi\) | |||||||
\(402\) | 131.103 | − | 202.910i | 0.326128 | − | 0.504751i | ||||
\(403\) | −1393.27 | −3.45724 | ||||||||
\(404\) | 6.01792 | + | 13.3495i | 0.0148958 | + | 0.0330433i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.0977 | − | 35.7485i | 0.0568908 | − | 0.0880505i | ||||
\(407\) | −49.9950 | −0.122838 | ||||||||
\(408\) | 8.24285 | − | 54.4941i | 0.0202031 | − | 0.133564i | ||||
\(409\) | 108.497 | 0.265273 | 0.132636 | − | 0.991165i | \(-0.457656\pi\) | ||||
0.132636 | + | 0.991165i | \(0.457656\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 239.295i | 0.582227i | ||||||||
\(412\) | −248.910 | − | 552.156i | −0.604151 | − | 1.34018i | ||||
\(413\) | 21.7156i | 0.0525801i | ||||||||
\(414\) | 104.455 | − | 161.666i | 0.252307 | − | 0.390499i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 724.431 | − | 203.141i | 1.74142 | − | 0.488320i | ||||
\(417\) | 51.8884i | 0.124433i | ||||||||
\(418\) | 70.9828 | − | 109.861i | 0.169815 | − | 0.262825i | ||||
\(419\) | − | 172.176i | − | 0.410921i | −0.978665 | − | 0.205460i | \(-0.934131\pi\) | ||
0.978665 | − | 0.205460i | \(-0.0658691\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 478.522 | 1.13663 | 0.568316 | − | 0.822810i | \(-0.307595\pi\) | ||||
0.568316 | + | 0.822810i | \(0.307595\pi\) | |||||||
\(422\) | 383.350 | + | 247.688i | 0.908412 | + | 0.586940i | ||||
\(423\) | −222.039 | −0.524915 | ||||||||
\(424\) | −3.05250 | + | 20.1803i | −0.00719929 | + | 0.0475950i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 172.298 | + | 111.325i | 0.404456 | + | 0.261326i | ||||
\(427\) | −5.20912 | −0.0121993 | ||||||||
\(428\) | 136.128 | + | 301.972i | 0.318056 | + | 0.705541i | ||||
\(429\) | −377.898 | −0.880882 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 290.722i | 0.674530i | 0.941410 | + | 0.337265i | \(0.109502\pi\) | ||||
−0.941410 | + | 0.337265i | \(0.890498\pi\) | |||||||
\(432\) | 55.0550 | − | 62.2972i | 0.127442 | − | 0.144207i | ||||
\(433\) | − | 53.7726i | − | 0.124186i | −0.998070 | − | 0.0620931i | \(-0.980222\pi\) | ||
0.998070 | − | 0.0620931i | \(-0.0197776\pi\) | |||||||
\(434\) | −59.3832 | − | 38.3684i | −0.136828 | − | 0.0884065i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1127 | − | 26.8694i | −0.0277813 | − | 0.0616271i | ||||
\(437\) | 226.081i | 0.517347i | ||||||||
\(438\) | 241.503 | + | 156.039i | 0.551376 | + | 0.356253i | ||||
\(439\) | 328.657i | 0.748650i | 0.927298 | + | 0.374325i | \(0.122126\pi\) | ||||
−0.927298 | + | 0.374325i | \(0.877874\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145.932 | −0.330913 | ||||||||
\(442\) | 101.503 | − | 157.097i | 0.229645 | − | 0.355424i | ||||
\(443\) | −428.910 | −0.968194 | −0.484097 | − | 0.875014i | \(-0.660852\pi\) | ||||
−0.484097 | + | 0.875014i | \(0.660852\pi\) | |||||||
\(444\) | 34.0286 | − | 15.3400i | 0.0766410 | − | 0.0345496i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −93.2942 | + | 144.392i | −0.209180 | + | 0.323750i | ||||
\(447\) | −82.0685 | −0.183599 | ||||||||
\(448\) | 36.4706 | + | 11.2915i | 0.0814075 | + | 0.0252043i | ||||
\(449\) | −409.229 | −0.911423 | −0.455711 | − | 0.890128i | \(-0.650615\pi\) | ||||
−0.455711 | + | 0.890128i | \(0.650615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 371.919i | − | 0.824654i | ||||||
\(452\) | −237.164 | + | 106.913i | −0.524698 | + | 0.236533i | ||||
\(453\) | 189.839i | 0.419071i | ||||||||
\(454\) | −306.466 | + | 474.321i | −0.675036 | + | 1.04476i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.6051 | + | 96.5555i | −0.0320288 | + | 0.211745i | ||||
\(457\) | 768.561i | 1.68175i | 0.541228 | + | 0.840876i | \(0.317960\pi\) | ||||
−0.541228 | + | 0.840876i | \(0.682040\pi\) | |||||||
\(458\) | 150.068 | − | 232.262i | 0.327660 | − | 0.507123i | ||||
\(459\) | − | 20.6677i | − | 0.0450278i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −316.563 | −0.686687 | −0.343343 | − | 0.939210i | \(-0.611559\pi\) | ||||
−0.343343 | + | 0.939210i | \(0.611559\pi\) | |||||||
\(462\) | −16.1066 | − | 10.4067i | −0.0348628 | − | 0.0225254i | ||||
\(463\) | 491.208 | 1.06093 | 0.530463 | − | 0.847708i | \(-0.322018\pi\) | ||||
0.530463 | + | 0.847708i | \(0.322018\pi\) | |||||||
\(464\) | 377.972 | − | 427.692i | 0.814596 | − | 0.921751i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.878466 | − | 0.567591i | −0.00188512 | − | 0.00121801i | ||||
\(467\) | −410.393 | −0.878785 | −0.439393 | − | 0.898295i | \(-0.644806\pi\) | ||||
−0.439393 | + | 0.898295i | \(0.644806\pi\) | |||||||
\(468\) | 257.213 | − | 115.951i | 0.549600 | − | 0.247758i | ||||
\(469\) | 41.6014 | 0.0887024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 307.591i | 0.653060i | ||||||||
\(472\) | −43.5550 | + | 287.945i | −0.0922776 | + | 0.610054i | ||||
\(473\) | 335.141i | 0.708542i | ||||||||
\(474\) | 191.657 | + | 123.833i | 0.404341 | + | 0.261251i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.65243 | − | 3.90049i | 0.0181774 | − | 0.00819431i | ||||
\(477\) | 7.65369i | 0.0160455i | ||||||||
\(478\) | −123.794 | − | 79.9851i | −0.258983 | − | 0.167333i | ||||
\(479\) | − | 198.918i | − | 0.415277i | −0.978206 | − | 0.207638i | \(-0.933422\pi\) | ||
0.978206 | − | 0.207638i | \(-0.0665778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 126.672 | 0.263351 | ||||||||
\(482\) | −34.0491 | + | 52.6981i | −0.0706413 | + | 0.109332i | ||||
\(483\) | 33.1455 | 0.0686242 | ||||||||
\(484\) | −57.3524 | − | 127.224i | −0.118497 | − | 0.262860i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.9195 | − | 26.1865i | 0.0348138 | − | 0.0538816i | ||||
\(487\) | 204.762 | 0.420456 | 0.210228 | − | 0.977652i | \(-0.432579\pi\) | ||||
0.210228 | + | 0.977652i | \(0.432579\pi\) | |||||||
\(488\) | −69.0721 | − | 10.4479i | −0.141541 | − | 0.0214097i | ||||
\(489\) | −167.797 | −0.343144 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 788.598i | 1.60611i | 0.595908 | + | 0.803053i | \(0.296792\pi\) | ||||
−0.595908 | + | 0.803053i | \(0.703208\pi\) | |||||||
\(492\) | 114.116 | + | 253.143i | 0.231944 | + | 0.514519i | ||||
\(493\) | − | 141.891i | − | 0.287812i | ||||||
\(494\) | −179.848 | + | 278.353i | −0.364066 | + | 0.563468i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −710.456 | − | 627.864i | −1.43237 | − | 1.26586i | ||||
\(497\) | 35.3253i | 0.0710771i | ||||||||
\(498\) | −244.222 | + | 377.985i | −0.490406 | + | 0.759006i | ||||
\(499\) | − | 740.385i | − | 1.48374i | −0.670545 | − | 0.741869i | \(-0.733940\pi\) | ||
0.670545 | − | 0.741869i | \(-0.266060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −264.319 | −0.527583 | ||||||||
\(502\) | 132.285 | + | 85.4717i | 0.263517 | + | 0.170262i | ||||
\(503\) | 70.8800 | 0.140914 | 0.0704572 | − | 0.997515i | \(-0.477554\pi\) | ||||
0.0704572 | + | 0.997515i | \(0.477554\pi\) | |||||||
\(504\) | 14.1559 | + | 2.14124i | 0.0280871 | + | 0.00424850i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −500.068 | − | 323.102i | −0.988277 | − | 0.638541i | ||||
\(507\) | 664.760 | 1.31116 | ||||||||
\(508\) | 229.270 | + | 508.588i | 0.451318 | + | 1.00116i | ||||
\(509\) | −522.642 | −1.02680 | −0.513400 | − | 0.858149i | \(-0.671614\pi\) | ||||
−0.513400 | + | 0.858149i | \(0.671614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49.5139i | 0.0968961i | ||||||||
\(512\) | 460.946 | + | 222.873i | 0.900286 | + | 0.435299i | ||||
\(513\) | 36.6202i | 0.0713844i | ||||||||
\(514\) | −409.809 | − | 264.784i | −0.797293 | − | 0.515144i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −102.831 | − | 228.110i | −0.199286 | − | 0.442074i | ||||
\(517\) | 686.813i | 1.32846i | ||||||||
\(518\) | 5.39894 | + | 3.48834i | 0.0104227 | + | 0.00673425i | ||||
\(519\) | 269.807i | 0.519859i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 304.082 | 0.583650 | 0.291825 | − | 0.956472i | \(-0.405738\pi\) | ||||
0.291825 | + | 0.956472i | \(0.405738\pi\) | |||||||
\(522\) | 116.158 | − | 179.779i | 0.222525 | − | 0.344405i | ||||
\(523\) | −174.416 | −0.333491 | −0.166746 | − | 0.986000i | \(-0.553326\pi\) | ||||
−0.166746 | + | 0.986000i | \(0.553326\pi\) | |||||||
\(524\) | −231.507 | + | 104.362i | −0.441806 | + | 0.199165i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 111.509 | − | 172.584i | 0.211995 | − | 0.328106i | ||||
\(527\) | −235.701 | −0.447251 | ||||||||
\(528\) | −192.698 | − | 170.297i | −0.364959 | − | 0.322532i | ||||
\(529\) | 500.081 | 0.945333 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 109.208i | 0.205664i | ||||||||
\(532\) | −15.3308 | + | 6.91109i | −0.0288174 | + | 0.0129908i | ||||
\(533\) | 942.327i | 1.76797i | ||||||||
\(534\) | 245.269 | − | 379.605i | 0.459305 | − | 0.710871i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 551.628 | + | 83.4401i | 1.02916 | + | 0.155672i | ||||
\(537\) | 218.240i | 0.406405i | ||||||||
\(538\) | −134.204 | + | 207.708i | −0.249449 | + | 0.386075i | ||||
\(539\) | 451.399i | 0.837476i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −262.199 | −0.484655 | −0.242328 | − | 0.970194i | \(-0.577911\pi\) | ||||
−0.242328 | + | 0.970194i | \(0.577911\pi\) | |||||||
\(542\) | −558.337 | − | 360.750i | −1.03014 | − | 0.665591i | ||||
\(543\) | 600.545 | 1.10598 | ||||||||
\(544\) | 122.553 | − | 34.3657i | 0.225281 | − | 0.0631722i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 40.8091 | + | 26.3674i | 0.0747420 | + | 0.0482920i | ||||
\(547\) | −146.179 | −0.267237 | −0.133619 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133619 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(548\) | −503.804 | + | 227.113i | −0.919350 | + | 0.414440i | ||||
\(549\) | −26.1967 | −0.0477171 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 251.411i | 0.456281i | ||||||||
\(552\) | 439.504 | + | 66.4800i | 0.796203 | + | 0.120435i | ||||
\(553\) | 39.2944i | 0.0710568i | ||||||||
\(554\) | 211.522 | + | 136.668i | 0.381809 | + | 0.246693i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −109.244 | + | 49.2468i | −0.196482 | + | 0.0885734i | ||||
\(557\) | 187.700i | 0.336984i | 0.985703 | + | 0.168492i | \(0.0538898\pi\) | ||||
−0.985703 | + | 0.168492i | \(0.946110\pi\) | |||||||
\(558\) | −298.638 | − | 192.955i | −0.535194 | − | 0.345797i | ||||
\(559\) | − | 849.142i | − | 1.51904i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −63.9296 | −0.113957 | ||||||||
\(562\) | −57.0509 | + | 88.2982i | −0.101514 | + | 0.157114i | ||||
\(563\) | −447.848 | −0.795467 | −0.397734 | − | 0.917501i | \(-0.630203\pi\) | ||||
−0.397734 | + | 0.917501i | \(0.630203\pi\) | |||||||
\(564\) | −210.736 | − | 467.473i | −0.373645 | − | 0.828853i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −216.305 | + | 334.777i | −0.382164 | + | 0.591479i | ||||
\(567\) | 5.36886 | 0.00946888 | ||||||||
\(568\) | −70.8520 | + | 468.408i | −0.124740 | + | 0.824662i | ||||
\(569\) | −1078.91 | −1.89615 | −0.948077 | − | 0.318042i | \(-0.896975\pi\) | ||||
−0.948077 | + | 0.318042i | \(0.896975\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 936.324i | − | 1.63980i | −0.572509 | − | 0.819899i | \(-0.694030\pi\) | ||
0.572509 | − | 0.819899i | \(-0.305970\pi\) | |||||||
\(572\) | −358.660 | − | 795.613i | −0.627028 | − | 1.39093i | ||||
\(573\) | 230.638i | 0.402510i | ||||||||
\(574\) | −25.9502 | + | 40.1634i | −0.0452095 | + | 0.0699711i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 183.411 | + | 56.7851i | 0.318421 | + | 0.0985853i | ||||
\(577\) | − | 544.832i | − | 0.944250i | −0.881532 | − | 0.472125i | \(-0.843487\pi\) | ||
0.881532 | − | 0.472125i | \(-0.156513\pi\) | |||||||
\(578\) | −296.505 | + | 458.904i | −0.512985 | + | 0.793951i | ||||
\(579\) | − | 235.986i | − | 0.407575i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −77.4960 | −0.133384 | ||||||||
\(582\) | 270.917 | + | 175.044i | 0.465494 | + | 0.300763i | ||||
\(583\) | 23.6745 | 0.0406080 | ||||||||
\(584\) | −99.3101 | + | 656.547i | −0.170052 | + | 1.12422i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 171.616 | + | 110.884i | 0.292861 | + | 0.189222i | ||||
\(587\) | 337.889 | 0.575619 | 0.287810 | − | 0.957688i | \(-0.407073\pi\) | ||||
0.287810 | + | 0.957688i | \(0.407073\pi\) | |||||||
\(588\) | −138.503 | − | 307.241i | −0.235550 | − | 0.522519i | ||||
\(589\) | 417.628 | 0.709045 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 129.721i | − | 0.219494i | ||||||
\(592\) | 64.5926 | + | 57.0836i | 0.109109 | + | 0.0964249i | ||||
\(593\) | − | 567.269i | − | 0.956608i | −0.878194 | − | 0.478304i | \(-0.841252\pi\) | ||
0.878194 | − | 0.478304i | \(-0.158748\pi\) | |||||||
\(594\) | −81.0002 | − | 52.3355i | −0.136364 | − | 0.0881069i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −77.8906 | − | 172.784i | −0.130689 | − | 0.289906i | ||||
\(597\) | − | 435.792i | − | 0.729969i | ||||||
\(598\) | 1267.02 | + | 818.640i | 2.11876 | + | 1.36896i | ||||
\(599\) | 762.966i | 1.27373i | 0.770974 | + | 0.636867i | \(0.219770\pi\) | ||||
−0.770974 | + | 0.636867i | \(0.780230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −790.102 | −1.31464 | −0.657322 | − | 0.753609i | \(-0.728311\pi\) | ||||
−0.657322 | + | 0.753609i | \(0.728311\pi\) | |||||||
\(602\) | 23.3841 | − | 36.1917i | 0.0388440 | − | 0.0601192i | ||||
\(603\) | 209.214 | 0.346955 | ||||||||
\(604\) | −399.680 | + | 180.175i | −0.661722 | + | 0.298302i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.88212 | + | 10.6515i | −0.0113566 | + | 0.0175768i | ||||
\(607\) | −522.994 | −0.861605 | −0.430802 | − | 0.902446i | \(-0.641769\pi\) | ||||
−0.430802 | + | 0.902446i | \(0.641769\pi\) | |||||||
\(608\) | −217.146 | + | 60.8909i | −0.357148 | + | 0.100150i | ||||
\(609\) | 36.8591 | 0.0605240 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1740.17i | − | 2.84807i | ||||||
\(612\) | 43.5131 | − | 19.6156i | 0.0710999 | − | 0.0320516i | ||||
\(613\) | − | 1026.91i | − | 1.67522i | −0.546270 | − | 0.837609i | \(-0.683953\pi\) | ||
0.546270 | − | 0.837609i | \(-0.316047\pi\) | |||||||
\(614\) | 356.431 | − | 551.652i | 0.580506 | − | 0.898455i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.62332 | − | 43.7872i | 0.0107521 | − | 0.0710831i | ||||
\(617\) | − | 479.223i | − | 0.776698i | −0.921512 | − | 0.388349i | \(-0.873046\pi\) | ||
0.921512 | − | 0.388349i | \(-0.126954\pi\) | |||||||
\(618\) | 284.655 | − | 440.563i | 0.460607 | − | 0.712886i | ||||
\(619\) | − | 507.654i | − | 0.820119i | −0.912059 | − | 0.410059i | \(-0.865508\pi\) | ||
0.912059 | − | 0.410059i | \(-0.134492\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 166.689 | 0.268420 | ||||||||
\(622\) | −160.322 | − | 103.587i | −0.257753 | − | 0.166538i | ||||
\(623\) | 77.8282 | 0.124925 | ||||||||
\(624\) | 488.237 | + | 431.479i | 0.782432 | + | 0.691473i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 924.609 | + | 597.405i | 1.47701 | + | 0.954321i | ||||
\(627\) | 113.274 | 0.180660 | ||||||||
\(628\) | −647.591 | + | 291.932i | −1.03120 | + | 0.464860i | ||||
\(629\) | 21.4293 | 0.0340688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 460.186i | 0.729297i | 0.931145 | + | 0.364648i | \(0.118811\pi\) | ||||
−0.931145 | + | 0.364648i | \(0.881189\pi\) | |||||||
\(632\) | −78.8128 | + | 521.037i | −0.124704 | + | 0.824426i | ||||
\(633\) | 395.259i | 0.624423i | ||||||||
\(634\) | −738.122 | − | 476.912i | −1.16423 | − | 0.752228i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −16.1138 | + | 7.26405i | −0.0253362 | + | 0.0114215i | ||||
\(637\) | − | 1143.71i | − | 1.79546i | ||||||
\(638\) | −556.095 | − | 359.302i | −0.871622 | − | 0.563169i | ||||
\(639\) | 177.651i | 0.278014i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 250.774 | 0.391223 | 0.195612 | − | 0.980681i | \(-0.437331\pi\) | ||||
0.195612 | + | 0.980681i | \(0.437331\pi\) | |||||||
\(642\) | −155.677 | + | 240.942i | −0.242487 | + | 0.375299i | ||||
\(643\) | 590.355 | 0.918126 | 0.459063 | − | 0.888404i | \(-0.348185\pi\) | ||||
0.459063 | + | 0.888404i | \(0.348185\pi\) | |||||||
\(644\) | 31.4581 | + | 69.7834i | 0.0488480 | + | 0.108359i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.4252 | + | 47.0894i | −0.0470979 | + | 0.0728939i | ||||
\(647\) | −319.341 | −0.493572 | −0.246786 | − | 0.969070i | \(-0.579374\pi\) | ||||
−0.246786 | + | 0.969070i | \(0.579374\pi\) | |||||||
\(648\) | 71.1902 | + | 10.7683i | 0.109861 | + | 0.0166178i | ||||
\(649\) | 337.803 | 0.520497 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 61.2280i | − | 0.0940523i | ||||||
\(652\) | −159.255 | − | 353.274i | −0.244256 | − | 0.541832i | ||||
\(653\) | − | 88.5949i | − | 0.135674i | −0.997696 | − | 0.0678369i | \(-0.978390\pi\) | ||
0.997696 | − | 0.0678369i | \(-0.0216097\pi\) | |||||||
\(654\) | 13.8521 | − | 21.4390i | 0.0211806 | − | 0.0327814i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −424.652 | + | 480.512i | −0.647335 | + | 0.732488i | ||||
\(657\) | 249.006i | 0.379004i | ||||||||
\(658\) | 47.9216 | − | 74.1688i | 0.0728292 | − | 0.112719i | ||||
\(659\) | 758.423i | 1.15087i | 0.817847 | + | 0.575435i | \(0.195167\pi\) | ||||
−0.817847 | + | 0.575435i | \(0.804833\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 527.327 | 0.797771 | 0.398885 | − | 0.917001i | \(-0.369397\pi\) | ||||
0.398885 | + | 0.917001i | \(0.369397\pi\) | |||||||
\(662\) | −806.203 | − | 520.900i | −1.21783 | − | 0.786859i | ||||
\(663\) | 161.978 | 0.244310 | ||||||||
\(664\) | −1027.59 | − | 155.434i | −1.54757 | − | 0.234087i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.1513 | + | 17.5429i | 0.0407677 | + | 0.0263407i | ||||
\(667\) | 1144.38 | 1.71571 | ||||||||
\(668\) | −250.863 | − | 556.488i | −0.375544 | − | 0.833066i | ||||
\(669\) | −148.878 | −0.222538 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 81.0318i | 0.120763i | ||||||||
\(672\) | 8.92717 | + | 31.8356i | 0.0132845 | + | 0.0473744i | ||||
\(673\) | − | 120.657i | − | 0.179283i | −0.995974 | − | 0.0896415i | \(-0.971428\pi\) | ||
0.995974 | − | 0.0896415i | \(-0.0285721\pi\) | |||||||
\(674\) | −98.8493 | − | 63.8681i | −0.146661 | − | 0.0947598i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 630.918 | + | 1399.56i | 0.933311 | + | 2.07036i | ||||
\(677\) | − | 219.196i | − | 0.323776i | −0.986809 | − | 0.161888i | \(-0.948242\pi\) | ||
0.986809 | − | 0.161888i | \(-0.0517583\pi\) | |||||||
\(678\) | −189.232 | − | 122.266i | −0.279103 | − | 0.180333i | ||||
\(679\) | 55.5446i | 0.0818035i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −489.057 | −0.718145 | ||||||||
\(682\) | −596.850 | + | 923.751i | −0.875146 | + | 1.35447i | ||||
\(683\) | 205.502 | 0.300881 | 0.150441 | − | 0.988619i | \(-0.451931\pi\) | ||||
0.150441 | + | 0.988619i | \(0.451931\pi\) | |||||||
\(684\) | −77.0988 | + | 34.7559i | −0.112718 | + | 0.0508128i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 63.2222 | − | 97.8496i | 0.0921606 | − | 0.142638i | ||||
\(687\) | 239.478 | 0.348585 | ||||||||
\(688\) | 382.659 | − | 432.995i | 0.556190 | − | 0.629354i | ||||
\(689\) | −59.9837 | −0.0870591 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 109.536i | 0.158519i | 0.996854 | + | 0.0792593i | \(0.0252555\pi\) | ||||
−0.996854 | + | 0.0792593i | \(0.974744\pi\) | |||||||
\(692\) | −568.042 | + | 256.071i | −0.820869 | + | 0.370045i | ||||
\(693\) | − | 16.6070i | − | 0.0239639i | ||||||
\(694\) | −13.1857 | + | 20.4077i | −0.0189996 | + | 0.0294059i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 488.746 | + | 73.9284i | 0.702221 | + | 0.106219i | ||||
\(697\) | 159.415i | 0.228716i | ||||||||
\(698\) | −33.5685 | + | 51.9543i | −0.0480924 | + | 0.0744331i | ||||
\(699\) | − | 0.905758i | − | 0.00129579i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 168.847 | 0.240865 | 0.120433 | − | 0.992721i | \(-0.461572\pi\) | ||||
0.120433 | + | 0.992721i | \(0.461572\pi\) | |||||||
\(702\) | 205.229 | + | 132.602i | 0.292349 | + | 0.188892i | ||||
\(703\) | −37.9695 | −0.0540106 | ||||||||
\(704\) | 175.648 | − | 567.327i | 0.249500 | − | 0.805863i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −483.909 | − | 312.661i | −0.685424 | − | 0.442863i | ||||
\(707\) | −2.18382 | −0.00308885 | ||||||||
\(708\) | −229.922 | + | 103.648i | −0.324749 | + | 0.146396i | ||||
\(709\) | 554.846 | 0.782576 | 0.391288 | − | 0.920268i | \(-0.372030\pi\) | ||||
0.391288 | + | 0.920268i | \(0.372030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 197.612i | 0.277935i | ||||||||
\(712\) | 1031.99 | + | 156.100i | 1.44942 | + | 0.219242i | ||||
\(713\) | − | 1900.97i | − | 2.66616i | ||||||
\(714\) | 6.90374 | + | 4.46062i | 0.00966911 | + | 0.00624737i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −459.474 | + | 207.130i | −0.641723 | + | 0.289287i | ||||
\(717\) | − | 127.640i | − | 0.178019i | ||||||
\(718\) | −1115.28 | − | 720.600i | −1.55331 | − | 1.00362i | ||||
\(719\) | 377.485i | 0.525014i | 0.964930 | + | 0.262507i | \(0.0845494\pi\) | ||||
−0.964930 | + | 0.262507i | \(0.915451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 90.3261 | 0.125279 | ||||||||
\(722\) | −337.915 | + | 522.995i | −0.468027 | + | 0.724369i | ||||
\(723\) | −54.3353 | −0.0751525 | ||||||||
\(724\) | 569.972 | + | 1264.37i | 0.787255 | + | 1.74636i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 65.5885 | − | 101.512i | 0.0903423 | − | 0.139824i | ||||
\(727\) | 173.183 | 0.238216 | 0.119108 | − | 0.992881i | \(-0.461997\pi\) | ||||
0.119108 | + | 0.992881i | \(0.461997\pi\) | |||||||
\(728\) | −16.7814 | + | 110.943i | −0.0230514 | + | 0.152394i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 143.651i | − | 0.196513i | ||||||
\(732\) | −24.8631 | − | 55.1536i | −0.0339659 | − | 0.0753464i | ||||
\(733\) | − | 278.722i | − | 0.380249i | −0.981760 | − | 0.190124i | \(-0.939111\pi\) | ||
0.981760 | − | 0.190124i | \(-0.0608891\pi\) | |||||||
\(734\) | −6.60489 | + | 10.2225i | −0.00899849 | + | 0.0139270i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 277.165 | + | 988.412i | 0.376583 | + | 1.34295i | ||||
\(737\) | − | 647.142i | − | 0.878075i | ||||||
\(738\) | −130.504 | + | 201.982i | −0.176834 | + | 0.273688i | ||||
\(739\) | 521.363i | 0.705498i | 0.935718 | + | 0.352749i | \(0.114753\pi\) | ||||
−0.935718 | + | 0.352749i | \(0.885247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −287.001 | −0.387315 | ||||||||
\(742\) | −2.55660 | − | 1.65186i | −0.00344555 | − | 0.00222622i | ||||
\(743\) | 1277.93 | 1.71996 | 0.859981 | − | 0.510326i | \(-0.170475\pi\) | ||||
0.859981 | + | 0.510326i | \(0.170475\pi\) | |||||||
\(744\) | 122.805 | − | 811.874i | 0.165061 | − | 1.09123i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −343.936 | − | 222.223i | −0.461041 | − | 0.297886i | ||||
\(747\) | −389.728 | −0.521724 | ||||||||
\(748\) | −60.6751 | − | 134.595i | −0.0811164 | − | 0.179940i | ||||
\(749\) | −49.3989 | −0.0659532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1165.31i | − | 1.55168i | −0.630930 | − | 0.775840i | \(-0.717327\pi\) | ||
0.630930 | − | 0.775840i | \(-0.282673\pi\) | |||||||
\(752\) | 784.194 | − | 887.350i | 1.04281 | − | 1.17999i | ||||
\(753\) | 136.395i | 0.181136i | ||||||||
\(754\) | 1408.97 | + | 910.359i | 1.86866 | + | 1.20737i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.09554 | + | 11.3034i | 0.00674013 | + | 0.0149516i | ||||
\(757\) | 1063.75i | 1.40522i | 0.711574 | + | 0.702611i | \(0.247983\pi\) | ||||
−0.711574 | + | 0.702611i | \(0.752017\pi\) | |||||||
\(758\) | 675.861 | + | 436.685i | 0.891638 | + | 0.576101i | ||||
\(759\) | − | 515.604i | − | 0.679320i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −677.847 | −0.890732 | −0.445366 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445366 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(762\) | −262.194 | + | 405.800i | −0.344087 | + | 0.532546i | ||||
\(763\) | 4.39551 | 0.00576083 | ||||||||
\(764\) | −485.577 | + | 218.897i | −0.635572 | + | 0.286514i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −360.078 | + | 557.296i | −0.470076 | + | 0.727541i | ||||
\(767\) | −855.887 | −1.11589 | ||||||||
\(768\) | 54.5201 | + | 440.040i | 0.0709898 | + | 0.572969i | ||||
\(769\) | 1289.59 | 1.67697 | 0.838486 | − | 0.544922i | \(-0.183441\pi\) | ||||
0.838486 | + | 0.544922i | \(0.183441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 422.540i | − | 0.548042i | ||||||
\(772\) | 496.836 | − | 223.972i | 0.643570 | − | 0.290119i | ||||
\(773\) | 750.339i | 0.970684i | 0.874324 | + | 0.485342i | \(0.161305\pi\) | ||||
−0.874324 | + | 0.485342i | \(0.838695\pi\) | |||||||
\(774\) | 117.599 | − | 182.008i | 0.151936 | − | 0.235153i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −111.406 | + | 736.513i | −0.143564 | + | 0.949114i | ||||
\(777\) | 5.56667i | 0.00716432i | ||||||||
\(778\) | −676.532 | + | 1047.07i | −0.869578 | + | 1.34585i | ||||
\(779\) | − | 282.460i | − | 0.362593i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 549.512 | 0.703600 | ||||||||
\(782\) | 214.343 | + | 138.491i | 0.274096 | + | 0.177098i | ||||
\(783\) | 185.365 | 0.236736 | ||||||||
\(784\) | 515.402 | − | 583.200i | 0.657400 | − | 0.743877i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −184.718 | − | 119.349i | −0.235011 | − | 0.151844i | ||||
\(787\) | 825.185 | 1.04852 | 0.524260 | − | 0.851558i | \(-0.324342\pi\) | ||||
0.524260 | + | 0.851558i | \(0.324342\pi\) | |||||||
\(788\) | 273.110 | − | 123.117i | 0.346586 | − | 0.156240i | ||||
\(789\) | 177.946 | 0.225533 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 38.7971i | − | 0.0490482i | ||||||
\(792\) | 33.3087 | − | 220.206i | 0.0420564 | − | 0.278038i | ||||
\(793\) | − | 205.309i | − | 0.258902i | ||||||
\(794\) | 597.106 | + | 385.799i | 0.752022 | + | 0.485893i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 917.500 | − | 413.606i | 1.15264 | − | 0.519606i | ||||
\(797\) | 1113.70i | 1.39737i | 0.715430 | + | 0.698684i | \(0.246231\pi\) | ||||
−0.715430 | + | 0.698684i | \(0.753769\pi\) | |||||||
\(798\) | −12.2324 | − | 7.90356i | −0.0153288 | − | 0.00990421i | ||||
\(799\) | − | 294.388i | − | 0.368445i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 391.398 | 0.488637 | ||||||||
\(802\) | 589.285 | − | 912.043i | 0.734770 | − | 1.13721i | ||||
\(803\) | 770.226 | 0.959186 | ||||||||
\(804\) | 198.563 | + | 440.471i | 0.246969 | + | 0.547849i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1512.23 | − | 2340.50i | 1.87622 | − | 2.90384i | ||||
\(807\) | −214.161 | −0.265379 | ||||||||
\(808\) | −28.9571 | − | 4.38009i | −0.0358380 | − | 0.00542090i | ||||
\(809\) | 1049.54 | 1.29733 | 0.648664 | − | 0.761075i | \(-0.275328\pi\) | ||||
0.648664 | + | 0.761075i | \(0.275328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 424.482i | 0.523406i | 0.965148 | + | 0.261703i | \(0.0842841\pi\) | ||||
−0.965148 | + | 0.261703i | \(0.915716\pi\) | |||||||
\(812\) | 34.9827 | + | 77.6018i | 0.0430821 | + | 0.0955688i | ||||
\(813\) | − | 575.683i | − | 0.708097i | ||||||
\(814\) | 54.2638 | − | 83.9847i | 0.0666632 | − | 0.103175i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 82.5959 | + | 72.9940i | 0.101220 | + | 0.0894534i | ||||
\(817\) | 254.528i | 0.311540i | ||||||||
\(818\) | −117.761 | + | 182.259i | −0.143962 | + | 0.222811i | ||||
\(819\) | 42.0769i | 0.0513760i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1257.98 | −1.53225 | −0.766126 | − | 0.642690i | \(-0.777818\pi\) | ||||
−0.766126 | + | 0.642690i | \(0.777818\pi\) | |||||||
\(822\) | −401.983 | − | 259.728i | −0.489031 | − | 0.315970i | ||||
\(823\) | 729.181 | 0.886004 | 0.443002 | − | 0.896521i | \(-0.353913\pi\) | ||||
0.443002 | + | 0.896521i | \(0.353913\pi\) | |||||||
\(824\) | 1197.71 | + | 181.167i | 1.45353 | + | 0.219863i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.4792 | − | 23.5698i | −0.0441637 | − | 0.0285349i | ||||
\(827\) | 72.5882 | 0.0877729 | 0.0438865 | − | 0.999037i | \(-0.486026\pi\) | ||||
0.0438865 | + | 0.999037i | \(0.486026\pi\) | |||||||
\(828\) | 158.203 | + | 350.941i | 0.191067 | + | 0.423842i | ||||
\(829\) | −900.257 | −1.08596 | −0.542978 | − | 0.839747i | \(-0.682703\pi\) | ||||
−0.542978 | + | 0.839747i | \(0.682703\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 218.093i | 0.262447i | ||||||||
\(832\) | −445.038 | + | 1437.43i | −0.534901 | + | 1.72768i | ||||
\(833\) | − | 193.482i | − | 0.232272i | ||||||
\(834\) | −87.1653 | − | 56.3189i | −0.104515 | − | 0.0675286i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 107.507 | + | 238.483i | 0.128597 | + | 0.285266i | ||||
\(837\) | − | 307.916i | − | 0.367881i | ||||||
\(838\) | 289.232 | + | 186.877i | 0.345145 | + | 0.223004i | ||||
\(839\) | − | 71.4721i | − | 0.0851872i | −0.999092 | − | 0.0425936i | \(-0.986438\pi\) | ||
0.999092 | − | 0.0425936i | \(-0.0135621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 431.594 | 0.513191 | ||||||||
\(842\) | −519.381 | + | 803.851i | −0.616842 | + | 0.954693i | ||||
\(843\) | −91.0414 | −0.107997 | ||||||||
\(844\) | −832.165 | + | 375.138i | −0.985978 | + | 0.444476i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 240.998 | − | 372.995i | 0.284868 | − | 0.440893i | ||||
\(847\) | 20.8124 | 0.0245719 | ||||||||
\(848\) | −30.5870 | − | 27.0312i | −0.0360695 | − | 0.0318764i | ||||
\(849\) | −345.178 | −0.406570 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 172.831i | 0.203091i | ||||||||
\(852\) | −374.020 | + | 168.607i | −0.438991 | + | 0.197896i | ||||
\(853\) | − | 882.349i | − | 1.03441i | −0.855862 | − | 0.517203i | \(-0.826973\pi\) | ||
0.855862 | − | 0.517203i | \(-0.173027\pi\) | |||||||
\(854\) | 5.65391 | − | 8.75061i | 0.00662050 | − | 0.0102466i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −655.022 | − | 99.0796i | −0.765213 | − | 0.115747i | ||||
\(857\) | − | 370.111i | − | 0.431868i | −0.976408 | − | 0.215934i | \(-0.930720\pi\) | ||
0.976408 | − | 0.215934i | \(-0.0692796\pi\) | |||||||
\(858\) | 410.165 | − | 634.817i | 0.478048 | − | 0.739880i | ||||
\(859\) | 1039.00i | 1.20955i | 0.796397 | + | 0.604774i | \(0.206736\pi\) | ||||
−0.796397 | + | 0.604774i | \(0.793264\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −41.4112 | −0.0480966 | ||||||||
\(862\) | −488.373 | − | 315.546i | −0.566558 | − | 0.366062i | ||||
\(863\) | 72.0666 | 0.0835071 | 0.0417535 | − | 0.999128i | \(-0.486706\pi\) | ||||
0.0417535 | + | 0.999128i | \(0.486706\pi\) | |||||||
\(864\) | 44.8948 | + | 160.101i | 0.0519616 | + | 0.185303i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 90.3306 | + | 58.3640i | 0.104308 | + | 0.0673950i | ||||
\(867\) | −473.161 | −0.545745 | ||||||||
\(868\) | 128.907 | − | 58.1110i | 0.148511 | − | 0.0669482i | ||||
\(869\) | 611.254 | 0.703399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1639.66i | 1.88250i | ||||||||
\(872\) | 58.2838 | + | 8.81609i | 0.0668393 | + | 0.0101102i | ||||
\(873\) | 279.334i | 0.319970i | ||||||||
\(874\) | −379.785 | − | 245.385i | −0.434536 | − | 0.280761i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −524.247 | + | 236.329i | −0.598456 | + | 0.269782i | ||||
\(877\) | 14.4444i | 0.0164703i | 0.999966 | + | 0.00823514i | \(0.00262136\pi\) | ||||
−0.999966 | + | 0.00823514i | \(0.997379\pi\) | |||||||
\(878\) | −552.099 | − | 356.720i | −0.628815 | − | 0.406287i | ||||
\(879\) | 176.948i | 0.201306i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1589.22 | 1.80388 | 0.901942 | − | 0.431858i | \(-0.142142\pi\) | ||||
0.901942 | + | 0.431858i | \(0.142142\pi\) | |||||||
\(882\) | 158.393 | − | 245.146i | 0.179584 | − | 0.277944i | ||||
\(883\) | −495.149 | −0.560758 | −0.280379 | − | 0.959889i | \(-0.590460\pi\) | ||||
−0.280379 | + | 0.959889i | \(0.590460\pi\) | |||||||
\(884\) | 153.732 | + | 341.022i | 0.173905 | + | 0.385772i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 465.533 | − | 720.510i | 0.525432 | − | 0.813216i | ||||
\(887\) | 1384.20 | 1.56054 | 0.780272 | − | 0.625440i | \(-0.215081\pi\) | ||||
0.780272 | + | 0.625440i | \(0.215081\pi\) | |||||||
\(888\) | −11.1651 | + | 73.8132i | −0.0125733 | + | 0.0831230i | ||||
\(889\) | −83.1988 | −0.0935870 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 83.5166i | − | 0.0937336i | ||||||
\(892\) | −141.299 | − | 313.443i | −0.158407 | − | 0.351393i | ||||
\(893\) | 521.611i | 0.584111i | ||||||||
\(894\) | 89.0760 | − | 137.864i | 0.0996376 | − | 0.154210i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −58.5528 | + | 49.0099i | −0.0653491 | + | 0.0546985i | ||||
\(897\) | 1306.38i | 1.45639i | ||||||||
\(898\) | 444.171 | − | 687.448i | 0.494623 | − | 0.765533i | ||||
\(899\) | − | 2113.95i | − | 2.35145i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.1475 | −0.0112625 | ||||||||
\(902\) | 624.773 | + | 403.676i | 0.692653 | + | 0.447534i | ||||
\(903\) | 37.3161 | 0.0413246 | ||||||||
\(904\) | 77.8155 | − | 514.444i | 0.0860791 | − | 0.569075i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −318.903 | − | 206.049i | −0.351991 | − | 0.227427i | ||||
\(907\) | −957.750 | −1.05595 | −0.527977 | − | 0.849259i | \(-0.677049\pi\) | ||||
−0.527977 | + | 0.849259i | \(0.677049\pi\) | |||||||
\(908\) | −464.160 | − | 1029.64i | −0.511189 | − | 1.13397i | ||||
\(909\) | −10.9824 | −0.0120819 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 704.979i | − | 0.773852i | −0.922111 | − | 0.386926i | \(-0.873537\pi\) | ||
0.922111 | − | 0.386926i | \(-0.126463\pi\) | |||||||
\(912\) | −146.348 | − | 129.335i | −0.160469 | − | 0.141814i | ||||
\(913\) | 1205.51i | 1.32038i | ||||||||
\(914\) | −1291.08 | − | 834.185i | −1.41256 | − | 0.912675i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 227.287 | + | 504.189i | 0.248130 | + | 0.550424i | ||||
\(917\) | − | 37.8717i | − | 0.0412996i | ||||||
\(918\) | 34.7190 | + | 22.4325i | 0.0378202 | + | 0.0244362i | ||||
\(919\) | 607.048i | 0.660553i | 0.943884 | + | 0.330277i | \(0.107142\pi\) | ||||
−0.943884 | + | 0.330277i | \(0.892858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 568.790 | 0.617578 | ||||||||
\(922\) | 343.593 | − | 531.782i | 0.372660 | − | 0.576770i | ||||
\(923\) | −1392.29 | −1.50844 | ||||||||
\(924\) | 34.9638 | − | 15.7616i | 0.0378396 | − | 0.0170580i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −533.151 | + | 825.163i | −0.575757 | + | 0.891104i | ||||
\(927\) | 454.250 | 0.490022 | ||||||||
\(928\) | 308.219 | + | 1099.15i | 0.332132 | + | 1.18443i | ||||
\(929\) | −1011.21 | −1.08849 | −0.544247 | − | 0.838925i | \(-0.683185\pi\) | ||||
−0.544247 | + | 0.838925i | \(0.683185\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 342.822i | 0.368230i | ||||||||
\(932\) | 1.90695 | − | 0.859647i | 0.00204608 | − | 0.000922368i | ||||
\(933\) | − | 165.303i | − | 0.177174i | ||||||
\(934\) | 445.434 | − | 689.403i | 0.476910 | − | 0.738119i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −84.3938 | + | 557.934i | −0.0901643 | + | 0.596083i | ||||
\(937\) | − | 363.105i | − | 0.387519i | −0.981049 | − | 0.193760i | \(-0.937932\pi\) | ||
0.981049 | − | 0.193760i | \(-0.0620682\pi\) | |||||||
\(938\) | −45.1536 | + | 69.8846i | −0.0481381 | + | 0.0745039i | ||||
\(939\) | 953.334i | 1.01527i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1106.51 | −1.17588 | −0.587942 | − | 0.808903i | \(-0.700061\pi\) | ||||
−0.587942 | + | 0.808903i | \(0.700061\pi\) | |||||||
\(942\) | −516.711 | − | 333.855i | −0.548525 | − | 0.354411i | ||||
\(943\) | −1285.71 | −1.36342 | ||||||||
\(944\) | −436.435 | − | 385.698i | −0.462325 | − | 0.408579i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −562.990 | − | 363.757i | −0.595127 | − | 0.384521i | ||||
\(947\) | −553.561 | −0.584541 | −0.292271 | − | 0.956336i | \(-0.594411\pi\) | ||||
−0.292271 | + | 0.956336i | \(0.594411\pi\) | |||||||
\(948\) | −416.044 | + | 187.552i | −0.438865 | + | 0.197839i | ||||
\(949\) | −1951.51 | −2.05639 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 761.053i | − | 0.800266i | ||||||
\(952\) | −2.83894 | + | 18.7684i | −0.00298208 | + | 0.0197147i | ||||
\(953\) | 1674.84i | 1.75744i | 0.477342 | + | 0.878718i | \(0.341600\pi\) | ||||
−0.477342 | + | 0.878718i | \(0.658400\pi\) | |||||||
\(954\) | −12.8571 | − | 8.30720i | −0.0134771 | − | 0.00870776i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 268.728 | − | 121.142i | 0.281096 | − | 0.126717i | ||||
\(957\) | − | 573.371i | − | 0.599134i | ||||||
\(958\) | 334.154 | + | 215.902i | 0.348804 | + | 0.225368i | ||||
\(959\) | − | 82.4162i | − | 0.0859398i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2550.57 | −2.65408 | ||||||||
\(962\) | −137.488 | + | 212.791i | −0.142919 | + | 0.221196i | ||||
\(963\) | −248.428 | −0.257973 | ||||||||
\(964\) | −51.5692 | − | 114.396i | −0.0534950 | − | 0.118668i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −35.9757 | + | 55.6799i | −0.0372419 | + | 0.0576396i | ||||
\(967\) | 786.720 | 0.813568 | 0.406784 | − | 0.913524i | \(-0.366650\pi\) | ||||
0.406784 | + | 0.913524i | \(0.366650\pi\) | |||||||
\(968\) | 275.969 | + | 41.7435i | 0.285092 | + | 0.0431234i | ||||
\(969\) | −48.5524 | −0.0501057 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1289.75i | 1.32827i | 0.747612 | + | 0.664135i | \(0.231200\pi\) | ||||
−0.747612 | + | 0.664135i | \(0.768800\pi\) | |||||||
\(972\) | 25.6255 | + | 56.8448i | 0.0263637 | + | 0.0584823i | ||||
\(973\) | − | 17.8710i | − | 0.0183669i | ||||||
\(974\) | −222.246 | + | 343.972i | −0.228178 | + | 0.353154i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 92.5210 | − | 104.692i | 0.0947961 | − | 0.107266i | ||||
\(977\) | 495.847i | 0.507520i | 0.967267 | + | 0.253760i | \(0.0816674\pi\) | ||||
−0.967267 | + | 0.253760i | \(0.918333\pi\) | |||||||
\(978\) | 182.125 | − | 281.876i | 0.186222 | − | 0.288217i | ||||
\(979\) | − | 1210.68i | − | 1.23665i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.1051 | 0.0225332 | ||||||||
\(982\) | −1324.74 | − | 855.933i | −1.34902 | − | 0.871622i | ||||
\(983\) | −967.035 | −0.983759 | −0.491880 | − | 0.870663i | \(-0.663690\pi\) | ||||
−0.491880 | + | 0.870663i | \(0.663690\pi\) | |||||||
\(984\) | −549.106 | − | 83.0585i | −0.558035 | − | 0.0844091i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 238.358 | + | 154.007i | 0.241742 | + | 0.156194i | ||||
\(987\) | 76.4730 | 0.0774803 | ||||||||
\(988\) | −272.390 | − | 604.241i | −0.275698 | − | 0.611580i | ||||
\(989\) | 1158.57 | 1.17145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1203.68i | − | 1.21461i | −0.794469 | − | 0.607305i | \(-0.792251\pi\) | ||
0.794469 | − | 0.607305i | \(-0.207749\pi\) | |||||||
\(992\) | 1825.84 | − | 511.994i | 1.84057 | − | 0.516123i | ||||
\(993\) | − | 831.249i | − | 0.837109i | ||||||
\(994\) | −59.3417 | − | 38.3416i | −0.0596999 | − | 0.0385730i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −369.888 | − | 820.519i | −0.371373 | − | 0.823814i | ||||
\(997\) | − | 1274.55i | − | 1.27838i | −0.769047 | − | 0.639192i | \(-0.779269\pi\) | ||
0.769047 | − | 0.639192i | \(-0.220731\pi\) | |||||||
\(998\) | 1243.74 | + | 803.603i | 1.24624 | + | 0.805214i | ||||
\(999\) | 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.f.b.199.4 | 16 | ||
3.2 | odd | 2 | 900.3.f.f.199.13 | 16 | |||
4.3 | odd | 2 | inner | 300.3.f.b.199.14 | 16 | ||
5.2 | odd | 4 | 300.3.c.d.151.3 | 8 | |||
5.3 | odd | 4 | 60.3.c.a.31.6 | yes | 8 | ||
5.4 | even | 2 | inner | 300.3.f.b.199.13 | 16 | ||
12.11 | even | 2 | 900.3.f.f.199.3 | 16 | |||
15.2 | even | 4 | 900.3.c.u.451.6 | 8 | |||
15.8 | even | 4 | 180.3.c.b.91.3 | 8 | |||
15.14 | odd | 2 | 900.3.f.f.199.4 | 16 | |||
20.3 | even | 4 | 60.3.c.a.31.5 | ✓ | 8 | ||
20.7 | even | 4 | 300.3.c.d.151.4 | 8 | |||
20.19 | odd | 2 | inner | 300.3.f.b.199.3 | 16 | ||
40.3 | even | 4 | 960.3.e.c.511.1 | 8 | |||
40.13 | odd | 4 | 960.3.e.c.511.6 | 8 | |||
60.23 | odd | 4 | 180.3.c.b.91.4 | 8 | |||
60.47 | odd | 4 | 900.3.c.u.451.5 | 8 | |||
60.59 | even | 2 | 900.3.f.f.199.14 | 16 | |||
120.53 | even | 4 | 2880.3.e.j.2431.6 | 8 | |||
120.83 | odd | 4 | 2880.3.e.j.2431.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.5 | ✓ | 8 | 20.3 | even | 4 | ||
60.3.c.a.31.6 | yes | 8 | 5.3 | odd | 4 | ||
180.3.c.b.91.3 | 8 | 15.8 | even | 4 | |||
180.3.c.b.91.4 | 8 | 60.23 | odd | 4 | |||
300.3.c.d.151.3 | 8 | 5.2 | odd | 4 | |||
300.3.c.d.151.4 | 8 | 20.7 | even | 4 | |||
300.3.f.b.199.3 | 16 | 20.19 | odd | 2 | inner | ||
300.3.f.b.199.4 | 16 | 1.1 | even | 1 | trivial | ||
300.3.f.b.199.13 | 16 | 5.4 | even | 2 | inner | ||
300.3.f.b.199.14 | 16 | 4.3 | odd | 2 | inner | ||
900.3.c.u.451.5 | 8 | 60.47 | odd | 4 | |||
900.3.c.u.451.6 | 8 | 15.2 | even | 4 | |||
900.3.f.f.199.3 | 16 | 12.11 | even | 2 | |||
900.3.f.f.199.4 | 16 | 15.14 | odd | 2 | |||
900.3.f.f.199.13 | 16 | 3.2 | odd | 2 | |||
900.3.f.f.199.14 | 16 | 60.59 | even | 2 | |||
960.3.e.c.511.1 | 8 | 40.3 | even | 4 | |||
960.3.e.c.511.6 | 8 | 40.13 | odd | 4 | |||
2880.3.e.j.2431.6 | 8 | 120.53 | even | 4 | |||
2880.3.e.j.2431.7 | 8 | 120.83 | odd | 4 |