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 | 199.14 | ||
Root | \(0.120653 - 1.40906i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.199 |
Dual form | 300.3.f.b.199.13 |
$q$-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 | \(-0.513567\pi\) | ||||
−0.0426100 | + | 0.999092i | \(0.513567\pi\) | |||||||
\(8\) | −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 | \(0.138602\pi\) | ||||
−0.906688 | + | 0.421801i | \(0.861398\pi\) | |||||||
\(12\) | −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 | \(0.0593782\pi\) | ||||
−0.982651 | + | 0.185462i | \(0.940622\pi\) | |||||||
\(20\) | 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 | \(-0.254351\pi\) | ||||
0.697376 | + | 0.716705i | \(0.254351\pi\) | |||||||
\(24\) | −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 | \(-0.595012\pi\) | ||
0.294076 | − | 0.955782i | \(-0.404988\pi\) | |||||||
\(32\) | 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 | \(-0.362047\pi\) | ||||
0.419950 | + | 0.907547i | \(0.362047\pi\) | |||||||
\(44\) | −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 | \(-0.211441\pi\) | ||||
0.787373 | + | 0.616477i | \(0.211441\pi\) | |||||||
\(48\) | −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 | \(-0.900174\pi\) | ||
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 | \(0.522803\pi\) | |||||||
\(62\) | 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 | \(-0.674229\pi\) | ||||
−0.520432 | + | 0.853903i | \(0.674229\pi\) | |||||||
\(68\) | −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 | \(-0.863074\pi\) | ||
0.908897 | − | 0.417021i | \(-0.136926\pi\) | |||||||
\(72\) | −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 | \(-0.863116\pi\) | ||
0.908951 | − | 0.416902i | \(-0.136884\pi\) | |||||||
\(80\) | 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 | \(-0.213900\pi\) | ||||
0.782586 | + | 0.622542i | \(0.213900\pi\) | |||||||
\(84\) | 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 | \(-0.762833\pi\) | ||||
−0.735033 | + | 0.678032i | \(0.762833\pi\) | |||||||
\(104\) | −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 | \(-0.373526\pi\) | ||||
0.386959 | + | 0.922097i | \(0.373526\pi\) | |||||||
\(108\) | −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 | \(-0.314974\pi\) | ||||
0.549091 | + | 0.835763i | \(0.314974\pi\) | |||||||
\(128\) | 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 | \(0.0779056\pi\) | ||||
−0.970198 | + | 0.242312i | \(0.922094\pi\) | |||||||
\(132\) | −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 | \(0.0343684\pi\) | ||||
−0.994177 | + | 0.107762i | \(0.965632\pi\) | |||||||
\(140\) | 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 | \(0.118222\pi\) | ||||
−0.931818 | + | 0.362926i | \(0.881778\pi\) | |||||||
\(152\) | −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 | \(-0.596043\pi\) | ||||
−0.297171 | + | 0.954824i | \(0.596043\pi\) | |||||||
\(164\) | −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 | \(-0.651040\pi\) | ||||
−0.456901 | + | 0.889518i | \(0.651040\pi\) | |||||||
\(168\) | 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 | \(0.114484\pi\) | ||||
−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 | \(0.907201\pi\) | |||||||
\(182\) | 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 | \(0.113337\pi\) | ||||
−0.937278 | + | 0.348584i | \(0.886663\pi\) | |||||||
\(192\) | 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 | \(-0.782164\pi\) | ||
0.774828 | − | 0.632172i | \(-0.217836\pi\) | |||||||
\(200\) | 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 | \(0.181865\pi\) | ||||
−0.841173 | + | 0.540766i | \(0.818135\pi\) | |||||||
\(212\) | −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 | \(-0.561732\pi\) | ||||
−0.192724 | + | 0.981253i | \(0.561732\pi\) | |||||||
\(224\) | −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 | \(-0.713652\pi\) | ||||
−0.621932 | + | 0.783071i | \(0.713652\pi\) | |||||||
\(228\) | −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 | \(-0.950730\pi\) | ||
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 | \(0.479268\pi\) | |||||||
\(242\) | 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 | \(0.0501398\pi\) | ||||
−0.987620 | + | 0.156868i | \(0.949860\pi\) | |||||||
\(252\) | 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 | \(-0.437426\pi\) | ||||
0.195317 | + | 0.980740i | \(0.437426\pi\) | |||||||
\(264\) | −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 | \(-0.789870\pi\) | ||
0.789904 | − | 0.613230i | \(-0.210130\pi\) | |||||||
\(272\) | 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 | \(-0.614532\pi\) | ||||
−0.352100 | + | 0.935963i | \(0.614532\pi\) | |||||||
\(284\) | 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 | \(-0.320372\pi\) | ||||
0.534839 | + | 0.844954i | \(0.320372\pi\) | |||||||
\(308\) | 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 | \(-0.950966\pi\) | ||
0.988158 | − | 0.153437i | \(-0.0490342\pi\) | |||||||
\(312\) | −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 | \(-0.741859\pi\) | ||
0.688794 | − | 0.724958i | \(-0.258141\pi\) | |||||||
\(332\) | −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 | \(-0.505572\pi\) | ||||
−0.0175049 | + | 0.999847i | \(0.505572\pi\) | |||||||
\(348\) | 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 | \(-0.624343\pi\) | ||
0.380776 | − | 0.924667i | \(-0.375657\pi\) | |||||||
\(360\) | 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 | \(-0.502639\pi\) | ||||
−0.00829059 | + | 0.999966i | \(0.502639\pi\) | |||||||
\(368\) | −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 | \(0.178101\pi\) | ||||
−0.847510 | + | 0.530780i | \(0.821899\pi\) | |||||||
\(380\) | 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 | \(-0.642579\pi\) | ||||
−0.433096 | + | 0.901348i | \(0.642579\pi\) | |||||||
\(384\) | 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 | \(0.0658691\pi\) | ||||
−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 | \(0.307595\pi\) | |||||||
\(422\) | −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 | \(-0.890498\pi\) | ||
0.941410 | − | 0.337265i | \(-0.109502\pi\) | |||||||
\(432\) | −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 | \(-0.877874\pi\) | ||
0.927298 | − | 0.374325i | \(-0.122126\pi\) | |||||||
\(440\) | 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 | \(-0.339148\pi\) | ||||
0.484097 | + | 0.875014i | \(0.339148\pi\) | |||||||
\(444\) | 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 | \(-0.677982\pi\) | ||||
−0.530463 | + | 0.847708i | \(0.677982\pi\) | |||||||
\(464\) | 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 | \(-0.355194\pi\) | ||||
0.439393 | + | 0.898295i | \(0.355194\pi\) | |||||||
\(468\) | −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 | \(0.0665778\pi\) | ||||
−0.978206 | + | 0.207638i | \(0.933422\pi\) | |||||||
\(480\) | 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 | \(-0.567421\pi\) | ||||
−0.210228 | + | 0.977652i | \(0.567421\pi\) | |||||||
\(488\) | 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 | \(-0.703208\pi\) | ||
0.595908 | − | 0.803053i | \(-0.296792\pi\) | |||||||
\(492\) | −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 | \(0.266060\pi\) | ||||
−0.670545 | + | 0.741869i | \(0.733940\pi\) | |||||||
\(500\) | 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 | \(-0.522446\pi\) | ||||
−0.0704572 | + | 0.997515i | \(0.522446\pi\) | |||||||
\(504\) | 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 | \(-0.446674\pi\) | ||||
0.166746 | + | 0.986000i | \(0.446674\pi\) | |||||||
\(524\) | −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 | \(-0.457340\pi\) | ||||
0.133619 | + | 0.991033i | \(0.457340\pi\) | |||||||
\(548\) | 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 | \(-0.369797\pi\) | ||||
0.397734 | + | 0.917501i | \(0.369797\pi\) | |||||||
\(564\) | −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 | \(0.305970\pi\) | ||||
−0.572509 | + | 0.819899i | \(0.694030\pi\) | |||||||
\(572\) | 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 | \(-0.592927\pi\) | ||||
−0.287810 | + | 0.957688i | \(0.592927\pi\) | |||||||
\(588\) | 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 | \(-0.780230\pi\) | ||
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 | \(0.728311\pi\) | |||||||
\(602\) | −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 | \(-0.358231\pi\) | ||||
0.430802 | + | 0.902446i | \(0.358231\pi\) | |||||||
\(608\) | 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 | \(0.134492\pi\) | ||||
−0.912059 | + | 0.410059i | \(0.865508\pi\) | |||||||
\(620\) | 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 | \(-0.881189\pi\) | ||
0.931145 | − | 0.364648i | \(-0.118811\pi\) | |||||||
\(632\) | 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 | \(-0.651815\pi\) | ||||
−0.459063 | + | 0.888404i | \(0.651815\pi\) | |||||||
\(644\) | 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 | \(-0.420626\pi\) | ||||
0.246786 | + | 0.969070i | \(0.420626\pi\) | |||||||
\(648\) | −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 | \(-0.804833\pi\) | ||
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 | \(0.369397\pi\) | |||||||
\(662\) | 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 | \(-0.548069\pi\) | ||||
−0.150441 | + | 0.988619i | \(0.548069\pi\) | |||||||
\(684\) | −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 | \(-0.974744\pi\) | ||
0.996854 | − | 0.0792593i | \(-0.0252555\pi\) | |||||||
\(692\) | 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 | \(-0.915451\pi\) | ||
0.964930 | − | 0.262507i | \(-0.0845494\pi\) | |||||||
\(720\) | 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 | \(-0.538003\pi\) | ||||
−0.119108 | + | 0.992881i | \(0.538003\pi\) | |||||||
\(728\) | 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 | \(-0.885247\pi\) | ||
0.935718 | − | 0.352749i | \(-0.114753\pi\) | |||||||
\(740\) | 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 | \(-0.829525\pi\) | ||||
−0.859981 | + | 0.510326i | \(0.829525\pi\) | |||||||
\(744\) | 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 | \(0.282673\pi\) | ||||
−0.630930 | + | 0.775840i | \(0.717327\pi\) | |||||||
\(752\) | −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 | \(-0.675658\pi\) | ||||
−0.524260 | + | 0.851558i | \(0.675658\pi\) | |||||||
\(788\) | −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 | \(-0.915716\pi\) | ||
0.965148 | − | 0.261703i | \(-0.0842841\pi\) | |||||||
\(812\) | −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 | \(-0.646087\pi\) | ||||
−0.443002 | + | 0.896521i | \(0.646087\pi\) | |||||||
\(824\) | 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 | \(-0.513974\pi\) | ||||
−0.0438865 | + | 0.999037i | \(0.513974\pi\) | |||||||
\(828\) | −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 | \(0.0135621\pi\) | ||||
−0.999092 | + | 0.0425936i | \(0.986438\pi\) | |||||||
\(840\) | 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 | \(-0.793264\pi\) | ||
0.796397 | − | 0.604774i | \(-0.206736\pi\) | |||||||
\(860\) | 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 | \(-0.513294\pi\) | ||||
−0.0417535 | + | 0.999128i | \(0.513294\pi\) | |||||||
\(864\) | 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 | \(-0.409540\pi\) | ||||
0.280379 | + | 0.959889i | \(0.409540\pi\) | |||||||
\(884\) | 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 | \(-0.784919\pi\) | ||||
−0.780272 | + | 0.625440i | \(0.784919\pi\) | |||||||
\(888\) | 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 | \(-0.322951\pi\) | ||||
0.527977 | + | 0.849259i | \(0.322951\pi\) | |||||||
\(908\) | 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 | \(0.126463\pi\) | ||||
−0.922111 | + | 0.386926i | \(0.873537\pi\) | |||||||
\(912\) | 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 | \(-0.892858\pi\) | ||
0.943884 | − | 0.330277i | \(-0.107142\pi\) | |||||||
\(920\) | 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 | \(-0.405589\pi\) | ||||
0.292271 | + | 0.956336i | \(0.405589\pi\) | |||||||
\(948\) | 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 | \(-0.633350\pi\) | ||||
−0.406784 | + | 0.913524i | \(0.633350\pi\) | |||||||
\(968\) | −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 | \(-0.768800\pi\) | ||
0.747612 | − | 0.664135i | \(-0.231200\pi\) | |||||||
\(972\) | −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 | \(-0.336310\pi\) | ||||
0.491880 | + | 0.870663i | \(0.336310\pi\) | |||||||
\(984\) | −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 | \(0.207749\pi\) | ||||
−0.794469 | + | 0.607305i | \(0.792251\pi\) | |||||||
\(992\) | −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.199.14 | 16 | ||
3.2 | odd | 2 | 900.3.f.f.199.3 | 16 | |||
4.3 | odd | 2 | inner | 300.3.f.b.199.4 | 16 | ||
5.2 | odd | 4 | 300.3.c.d.151.4 | 8 | |||
5.3 | odd | 4 | 60.3.c.a.31.5 | ✓ | 8 | ||
5.4 | even | 2 | inner | 300.3.f.b.199.3 | 16 | ||
12.11 | even | 2 | 900.3.f.f.199.13 | 16 | |||
15.2 | even | 4 | 900.3.c.u.451.5 | 8 | |||
15.8 | even | 4 | 180.3.c.b.91.4 | 8 | |||
15.14 | odd | 2 | 900.3.f.f.199.14 | 16 | |||
20.3 | even | 4 | 60.3.c.a.31.6 | yes | 8 | ||
20.7 | even | 4 | 300.3.c.d.151.3 | 8 | |||
20.19 | odd | 2 | inner | 300.3.f.b.199.13 | 16 | ||
40.3 | even | 4 | 960.3.e.c.511.6 | 8 | |||
40.13 | odd | 4 | 960.3.e.c.511.1 | 8 | |||
60.23 | odd | 4 | 180.3.c.b.91.3 | 8 | |||
60.47 | odd | 4 | 900.3.c.u.451.6 | 8 | |||
60.59 | even | 2 | 900.3.f.f.199.4 | 16 | |||
120.53 | even | 4 | 2880.3.e.j.2431.7 | 8 | |||
120.83 | odd | 4 | 2880.3.e.j.2431.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.5 | ✓ | 8 | 5.3 | odd | 4 | ||
60.3.c.a.31.6 | yes | 8 | 20.3 | even | 4 | ||
180.3.c.b.91.3 | 8 | 60.23 | odd | 4 | |||
180.3.c.b.91.4 | 8 | 15.8 | even | 4 | |||
300.3.c.d.151.3 | 8 | 20.7 | even | 4 | |||
300.3.c.d.151.4 | 8 | 5.2 | odd | 4 | |||
300.3.f.b.199.3 | 16 | 5.4 | even | 2 | inner | ||
300.3.f.b.199.4 | 16 | 4.3 | odd | 2 | inner | ||
300.3.f.b.199.13 | 16 | 20.19 | odd | 2 | inner | ||
300.3.f.b.199.14 | 16 | 1.1 | even | 1 | trivial | ||
900.3.c.u.451.5 | 8 | 15.2 | even | 4 | |||
900.3.c.u.451.6 | 8 | 60.47 | odd | 4 | |||
900.3.f.f.199.3 | 16 | 3.2 | odd | 2 | |||
900.3.f.f.199.4 | 16 | 60.59 | even | 2 | |||
900.3.f.f.199.13 | 16 | 12.11 | even | 2 | |||
900.3.f.f.199.14 | 16 | 15.14 | odd | 2 | |||
960.3.e.c.511.1 | 8 | 40.13 | odd | 4 | |||
960.3.e.c.511.6 | 8 | 40.3 | even | 4 | |||
2880.3.e.j.2431.6 | 8 | 120.83 | odd | 4 | |||
2880.3.e.j.2431.7 | 8 | 120.53 | even | 4 |