Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1690,2,Mod(191,1690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1690, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1690.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1690 = 2 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1690.e (of order \(3\), degree \(2\), 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: | \(13.4947179416\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1690.991 |
Dual form | 1690.2.e.l.191.2 |
$q$-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 \(\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.36603 | + | 2.36603i | 0.788675 | + | 1.36603i | 0.926779 | + | 0.375608i | \(0.122566\pi\) |
−0.138104 | + | 0.990418i | \(0.544101\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.36603 | − | 2.36603i | 0.557678 | − | 0.965926i | ||||
\(7\) | 1.50000 | − | 2.59808i | 0.566947 | − | 0.981981i | −0.429919 | − | 0.902867i | \(-0.641458\pi\) |
0.996866 | − | 0.0791130i | \(-0.0252088\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.23205 | + | 3.86603i | −0.744017 | + | 1.28868i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | −2.73205 | −0.788675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | −1.36603 | − | 2.36603i | −0.352706 | − | 0.610905i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.09808 | + | 1.90192i | −0.266323 | + | 0.461284i | −0.967909 | − | 0.251300i | \(-0.919142\pi\) |
0.701587 | + | 0.712584i | \(0.252475\pi\) | |||||||
\(18\) | 4.46410 | 1.05220 | ||||||||
\(19\) | −3.23205 | + | 5.59808i | −0.741483 | + | 1.28429i | 0.210337 | + | 0.977629i | \(0.432544\pi\) |
−0.951820 | + | 0.306658i | \(0.900789\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 8.19615 | 1.78855 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 1.26795 | + | 2.19615i | 0.264386 | + | 0.457929i | 0.967402 | − | 0.253244i | \(-0.0814975\pi\) |
−0.703017 | + | 0.711173i | \(0.748164\pi\) | |||||||
\(24\) | 1.36603 | + | 2.36603i | 0.278839 | + | 0.482963i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 1.50000 | + | 2.59808i | 0.283473 | + | 0.490990i | ||||
\(29\) | 4.73205 | + | 8.19615i | 0.878720 | + | 1.52199i | 0.852747 | + | 0.522325i | \(0.174935\pi\) |
0.0259731 | + | 0.999663i | \(0.491732\pi\) | |||||||
\(30\) | −1.36603 | + | 2.36603i | −0.249401 | + | 0.431975i | ||||
\(31\) | 1.26795 | 0.227730 | 0.113865 | − | 0.993496i | \(-0.463677\pi\) | ||||
0.113865 | + | 0.993496i | \(0.463677\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 4.09808 | − | 7.09808i | 0.713384 | − | 1.23562i | ||||
\(34\) | 2.19615 | 0.376637 | ||||||||
\(35\) | −1.50000 | + | 2.59808i | −0.253546 | + | 0.439155i | ||||
\(36\) | −2.23205 | − | 3.86603i | −0.372008 | − | 0.644338i | ||||
\(37\) | 5.59808 | + | 9.69615i | 0.920318 | + | 1.59404i | 0.798923 | + | 0.601433i | \(0.205403\pi\) |
0.121395 | + | 0.992604i | \(0.461263\pi\) | |||||||
\(38\) | 6.46410 | 1.04862 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 5.19615 | + | 9.00000i | 0.811503 | + | 1.40556i | 0.911812 | + | 0.410608i | \(0.134683\pi\) |
−0.100309 | + | 0.994956i | \(0.531983\pi\) | |||||||
\(42\) | −4.09808 | − | 7.09808i | −0.632347 | − | 1.09526i | ||||
\(43\) | 1.00000 | − | 1.73205i | 0.152499 | − | 0.264135i | −0.779647 | − | 0.626219i | \(-0.784601\pi\) |
0.932145 | + | 0.362084i | \(0.117935\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 2.23205 | − | 3.86603i | 0.332734 | − | 0.576313i | ||||
\(46\) | 1.26795 | − | 2.19615i | 0.186949 | − | 0.323805i | ||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 1.36603 | − | 2.36603i | 0.197169 | − | 0.341506i | ||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.46410 | −0.887913 | −0.443956 | − | 0.896048i | \(-0.646425\pi\) | ||||
−0.443956 | + | 0.896048i | \(0.646425\pi\) | |||||||
\(54\) | 2.00000 | + | 3.46410i | 0.272166 | + | 0.471405i | ||||
\(55\) | 1.50000 | + | 2.59808i | 0.202260 | + | 0.350325i | ||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | −17.6603 | −2.33916 | ||||||||
\(58\) | 4.73205 | − | 8.19615i | 0.621349 | − | 1.07621i | ||||
\(59\) | −5.19615 | + | 9.00000i | −0.676481 | + | 1.17170i | 0.299552 | + | 0.954080i | \(0.403163\pi\) |
−0.976034 | + | 0.217620i | \(0.930171\pi\) | |||||||
\(60\) | 2.73205 | 0.352706 | ||||||||
\(61\) | 2.09808 | − | 3.63397i | 0.268631 | − | 0.465283i | −0.699877 | − | 0.714263i | \(-0.746762\pi\) |
0.968509 | + | 0.248980i | \(0.0800954\pi\) | |||||||
\(62\) | −0.633975 | − | 1.09808i | −0.0805149 | − | 0.139456i | ||||
\(63\) | 6.69615 | + | 11.5981i | 0.843636 | + | 1.46122i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.19615 | −1.00888 | ||||||||
\(67\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(68\) | −1.09808 | − | 1.90192i | −0.133161 | − | 0.230642i | ||||
\(69\) | −3.46410 | + | 6.00000i | −0.417029 | + | 0.722315i | ||||
\(70\) | 3.00000 | 0.358569 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | −2.23205 | + | 3.86603i | −0.263050 | + | 0.455615i | ||||
\(73\) | 5.66025 | 0.662483 | 0.331241 | − | 0.943546i | \(-0.392533\pi\) | ||||
0.331241 | + | 0.943546i | \(0.392533\pi\) | |||||||
\(74\) | 5.59808 | − | 9.69615i | 0.650763 | − | 1.12715i | ||||
\(75\) | 1.36603 | + | 2.36603i | 0.157735 | + | 0.273205i | ||||
\(76\) | −3.23205 | − | 5.59808i | −0.370742 | − | 0.642143i | ||||
\(77\) | −9.00000 | −1.02565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.19615 | 0.697122 | 0.348561 | − | 0.937286i | \(-0.386670\pi\) | ||||
0.348561 | + | 0.937286i | \(0.386670\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | 1.23205 | + | 2.13397i | 0.136895 | + | 0.237108i | ||||
\(82\) | 5.19615 | − | 9.00000i | 0.573819 | − | 0.993884i | ||||
\(83\) | 2.19615 | 0.241059 | 0.120530 | − | 0.992710i | \(-0.461541\pi\) | ||||
0.120530 | + | 0.992710i | \(0.461541\pi\) | |||||||
\(84\) | −4.09808 | + | 7.09808i | −0.447137 | + | 0.774464i | ||||
\(85\) | 1.09808 | − | 1.90192i | 0.119103 | − | 0.206293i | ||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −12.9282 | + | 22.3923i | −1.38605 | + | 2.40071i | ||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −8.59808 | − | 14.8923i | −0.911394 | − | 1.57858i | −0.812096 | − | 0.583523i | \(-0.801674\pi\) |
−0.0992979 | − | 0.995058i | \(-0.531660\pi\) | |||||||
\(90\) | −4.46410 | −0.470558 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.53590 | −0.264386 | ||||||||
\(93\) | 1.73205 | + | 3.00000i | 0.179605 | + | 0.311086i | ||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | 3.23205 | − | 5.59808i | 0.331601 | − | 0.574351i | ||||
\(96\) | −2.73205 | −0.278839 | ||||||||
\(97\) | 7.56218 | − | 13.0981i | 0.767823 | − | 1.32991i | −0.170918 | − | 0.985285i | \(-0.554673\pi\) |
0.938741 | − | 0.344623i | \(-0.111993\pi\) | |||||||
\(98\) | −1.00000 | + | 1.73205i | −0.101015 | + | 0.174964i | ||||
\(99\) | 13.3923 | 1.34598 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 3.63397 | + | 6.29423i | 0.361594 | + | 0.626299i | 0.988223 | − | 0.153018i | \(-0.0488993\pi\) |
−0.626629 | + | 0.779317i | \(0.715566\pi\) | |||||||
\(102\) | 3.00000 | + | 5.19615i | 0.297044 | + | 0.514496i | ||||
\(103\) | −1.19615 | −0.117860 | −0.0589302 | − | 0.998262i | \(-0.518769\pi\) | ||||
−0.0589302 | + | 0.998262i | \(0.518769\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.19615 | −0.799863 | ||||||||
\(106\) | 3.23205 | + | 5.59808i | 0.313925 | + | 0.543733i | ||||
\(107\) | −0.169873 | − | 0.294229i | −0.0164222 | − | 0.0284442i | 0.857697 | − | 0.514155i | \(-0.171894\pi\) |
−0.874120 | + | 0.485710i | \(0.838561\pi\) | |||||||
\(108\) | 2.00000 | − | 3.46410i | 0.192450 | − | 0.333333i | ||||
\(109\) | −15.4641 | −1.48119 | −0.740596 | − | 0.671950i | \(-0.765457\pi\) | ||||
−0.740596 | + | 0.671950i | \(0.765457\pi\) | |||||||
\(110\) | 1.50000 | − | 2.59808i | 0.143019 | − | 0.247717i | ||||
\(111\) | −15.2942 | + | 26.4904i | −1.45166 | + | 2.51436i | ||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | 3.46410 | − | 6.00000i | 0.325875 | − | 0.564433i | −0.655814 | − | 0.754923i | \(-0.727674\pi\) |
0.981689 | + | 0.190490i | \(0.0610077\pi\) | |||||||
\(114\) | 8.83013 | + | 15.2942i | 0.827017 | + | 1.43244i | ||||
\(115\) | −1.26795 | − | 2.19615i | −0.118237 | − | 0.204792i | ||||
\(116\) | −9.46410 | −0.878720 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.3923 | 0.956689 | ||||||||
\(119\) | 3.29423 | + | 5.70577i | 0.301981 | + | 0.523047i | ||||
\(120\) | −1.36603 | − | 2.36603i | −0.124700 | − | 0.215988i | ||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −4.19615 | −0.379902 | ||||||||
\(123\) | −14.1962 | + | 24.5885i | −1.28002 | + | 2.21707i | ||||
\(124\) | −0.633975 | + | 1.09808i | −0.0569326 | + | 0.0986102i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.69615 | − | 11.5981i | 0.596541 | − | 1.03324i | ||||
\(127\) | 10.5981 | + | 18.3564i | 0.940427 | + | 1.62887i | 0.764658 | + | 0.644436i | \(0.222908\pi\) |
0.175769 | + | 0.984431i | \(0.443759\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 5.46410 | 0.481087 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.1244 | −1.58353 | −0.791766 | − | 0.610824i | \(-0.790838\pi\) | ||||
−0.791766 | + | 0.610824i | \(0.790838\pi\) | |||||||
\(132\) | 4.09808 | + | 7.09808i | 0.356692 | + | 0.617808i | ||||
\(133\) | 9.69615 | + | 16.7942i | 0.840763 | + | 1.45624i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | −1.09808 | + | 1.90192i | −0.0941593 | + | 0.163089i | ||||
\(137\) | −4.09808 | + | 7.09808i | −0.350122 | + | 0.606430i | −0.986271 | − | 0.165137i | \(-0.947193\pi\) |
0.636148 | + | 0.771567i | \(0.280527\pi\) | |||||||
\(138\) | 6.92820 | 0.589768 | ||||||||
\(139\) | 4.59808 | − | 7.96410i | 0.390004 | − | 0.675506i | −0.602446 | − | 0.798160i | \(-0.705807\pi\) |
0.992450 | + | 0.122653i | \(0.0391404\pi\) | |||||||
\(140\) | −1.50000 | − | 2.59808i | −0.126773 | − | 0.219578i | ||||
\(141\) | −4.09808 | − | 7.09808i | −0.345120 | − | 0.597766i | ||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.46410 | 0.372008 | ||||||||
\(145\) | −4.73205 | − | 8.19615i | −0.392975 | − | 0.680653i | ||||
\(146\) | −2.83013 | − | 4.90192i | −0.234223 | − | 0.405686i | ||||
\(147\) | 2.73205 | − | 4.73205i | 0.225336 | − | 0.390293i | ||||
\(148\) | −11.1962 | −0.920318 | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 1.36603 | − | 2.36603i | 0.111536 | − | 0.193185i | ||||
\(151\) | 6.33975 | 0.515921 | 0.257961 | − | 0.966155i | \(-0.416950\pi\) | ||||
0.257961 | + | 0.966155i | \(0.416950\pi\) | |||||||
\(152\) | −3.23205 | + | 5.59808i | −0.262154 | + | 0.454064i | ||||
\(153\) | −4.90192 | − | 8.49038i | −0.396297 | − | 0.686407i | ||||
\(154\) | 4.50000 | + | 7.79423i | 0.362620 | + | 0.628077i | ||||
\(155\) | −1.26795 | −0.101844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | −3.09808 | − | 5.36603i | −0.246470 | − | 0.426898i | ||||
\(159\) | −8.83013 | − | 15.2942i | −0.700275 | − | 1.21291i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 7.60770 | 0.599570 | ||||||||
\(162\) | 1.23205 | − | 2.13397i | 0.0967991 | − | 0.167661i | ||||
\(163\) | −3.63397 | + | 6.29423i | −0.284635 | + | 0.493002i | −0.972521 | − | 0.232817i | \(-0.925206\pi\) |
0.687886 | + | 0.725819i | \(0.258539\pi\) | |||||||
\(164\) | −10.3923 | −0.811503 | ||||||||
\(165\) | −4.09808 | + | 7.09808i | −0.319035 | + | 0.552584i | ||||
\(166\) | −1.09808 | − | 1.90192i | −0.0852272 | − | 0.147618i | ||||
\(167\) | −1.50000 | − | 2.59808i | −0.116073 | − | 0.201045i | 0.802135 | − | 0.597143i | \(-0.203697\pi\) |
−0.918208 | + | 0.396098i | \(0.870364\pi\) | |||||||
\(168\) | 8.19615 | 0.632347 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.19615 | −0.168437 | ||||||||
\(171\) | −14.4282 | − | 24.9904i | −1.10335 | − | 1.91106i | ||||
\(172\) | 1.00000 | + | 1.73205i | 0.0762493 | + | 0.132068i | ||||
\(173\) | −7.50000 | + | 12.9904i | −0.570214 | + | 0.987640i | 0.426329 | + | 0.904568i | \(0.359807\pi\) |
−0.996544 | + | 0.0830722i | \(0.973527\pi\) | |||||||
\(174\) | 25.8564 | 1.96017 | ||||||||
\(175\) | 1.50000 | − | 2.59808i | 0.113389 | − | 0.196396i | ||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | −28.3923 | −2.13410 | ||||||||
\(178\) | −8.59808 | + | 14.8923i | −0.644453 | + | 1.11623i | ||||
\(179\) | −1.26795 | − | 2.19615i | −0.0947710 | − | 0.164148i | 0.814742 | − | 0.579824i | \(-0.196879\pi\) |
−0.909513 | + | 0.415675i | \(0.863545\pi\) | |||||||
\(180\) | 2.23205 | + | 3.86603i | 0.166367 | + | 0.288157i | ||||
\(181\) | 16.5885 | 1.23301 | 0.616505 | − | 0.787351i | \(-0.288548\pi\) | ||||
0.616505 | + | 0.787351i | \(0.288548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.4641 | 0.847451 | ||||||||
\(184\) | 1.26795 | + | 2.19615i | 0.0934745 | + | 0.161903i | ||||
\(185\) | −5.59808 | − | 9.69615i | −0.411579 | − | 0.712875i | ||||
\(186\) | 1.73205 | − | 3.00000i | 0.127000 | − | 0.219971i | ||||
\(187\) | 6.58846 | 0.481796 | ||||||||
\(188\) | 1.50000 | − | 2.59808i | 0.109399 | − | 0.189484i | ||||
\(189\) | −6.00000 | + | 10.3923i | −0.436436 | + | 0.755929i | ||||
\(190\) | −6.46410 | −0.468955 | ||||||||
\(191\) | 9.63397 | − | 16.6865i | 0.697090 | − | 1.20740i | −0.272381 | − | 0.962189i | \(-0.587811\pi\) |
0.969471 | − | 0.245206i | \(-0.0788555\pi\) | |||||||
\(192\) | 1.36603 | + | 2.36603i | 0.0985844 | + | 0.170753i | ||||
\(193\) | −2.19615 | − | 3.80385i | −0.158083 | − | 0.273807i | 0.776095 | − | 0.630616i | \(-0.217198\pi\) |
−0.934177 | + | 0.356809i | \(0.883865\pi\) | |||||||
\(194\) | −15.1244 | −1.08587 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | −4.79423 | − | 8.30385i | −0.341575 | − | 0.591625i | 0.643151 | − | 0.765740i | \(-0.277627\pi\) |
−0.984725 | + | 0.174115i | \(0.944294\pi\) | |||||||
\(198\) | −6.69615 | − | 11.5981i | −0.475875 | − | 0.824239i | ||||
\(199\) | 7.19615 | − | 12.4641i | 0.510122 | − | 0.883557i | −0.489810 | − | 0.871829i | \(-0.662934\pi\) |
0.999931 | − | 0.0117273i | \(-0.00373299\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.63397 | − | 6.29423i | 0.255686 | − | 0.442860i | ||||
\(203\) | 28.3923 | 1.99275 | ||||||||
\(204\) | 3.00000 | − | 5.19615i | 0.210042 | − | 0.363803i | ||||
\(205\) | −5.19615 | − | 9.00000i | −0.362915 | − | 0.628587i | ||||
\(206\) | 0.598076 | + | 1.03590i | 0.0416699 | + | 0.0721745i | ||||
\(207\) | −11.3205 | −0.786830 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.3923 | 1.34139 | ||||||||
\(210\) | 4.09808 | + | 7.09808i | 0.282794 | + | 0.489814i | ||||
\(211\) | −6.79423 | − | 11.7679i | −0.467734 | − | 0.810139i | 0.531586 | − | 0.847004i | \(-0.321596\pi\) |
−0.999320 | + | 0.0368651i | \(0.988263\pi\) | |||||||
\(212\) | 3.23205 | − | 5.59808i | 0.221978 | − | 0.384477i | ||||
\(213\) | 16.3923 | 1.12318 | ||||||||
\(214\) | −0.169873 | + | 0.294229i | −0.0116123 | + | 0.0201131i | ||||
\(215\) | −1.00000 | + | 1.73205i | −0.0681994 | + | 0.118125i | ||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 1.90192 | − | 3.29423i | 0.129111 | − | 0.223627i | ||||
\(218\) | 7.73205 | + | 13.3923i | 0.523681 | + | 0.907041i | ||||
\(219\) | 7.73205 | + | 13.3923i | 0.522484 | + | 0.904968i | ||||
\(220\) | −3.00000 | −0.202260 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 30.5885 | 2.05296 | ||||||||
\(223\) | 0.232051 | + | 0.401924i | 0.0155393 | + | 0.0269148i | 0.873690 | − | 0.486482i | \(-0.161720\pi\) |
−0.858151 | + | 0.513397i | \(0.828387\pi\) | |||||||
\(224\) | 1.50000 | + | 2.59808i | 0.100223 | + | 0.173591i | ||||
\(225\) | −2.23205 | + | 3.86603i | −0.148803 | + | 0.257735i | ||||
\(226\) | −6.92820 | −0.460857 | ||||||||
\(227\) | 2.19615 | − | 3.80385i | 0.145764 | − | 0.252470i | −0.783894 | − | 0.620895i | \(-0.786769\pi\) |
0.929658 | + | 0.368425i | \(0.120103\pi\) | |||||||
\(228\) | 8.83013 | − | 15.2942i | 0.584789 | − | 1.01289i | ||||
\(229\) | 4.73205 | 0.312703 | 0.156351 | − | 0.987701i | \(-0.450027\pi\) | ||||
0.156351 | + | 0.987701i | \(0.450027\pi\) | |||||||
\(230\) | −1.26795 | + | 2.19615i | −0.0836061 | + | 0.144810i | ||||
\(231\) | −12.2942 | − | 21.2942i | −0.808901 | − | 1.40106i | ||||
\(232\) | 4.73205 | + | 8.19615i | 0.310674 | + | 0.538104i | ||||
\(233\) | −1.26795 | −0.0830661 | −0.0415331 | − | 0.999137i | \(-0.513224\pi\) | ||||
−0.0415331 | + | 0.999137i | \(0.513224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | −5.19615 | − | 9.00000i | −0.338241 | − | 0.585850i | ||||
\(237\) | 8.46410 | + | 14.6603i | 0.549802 | + | 0.952286i | ||||
\(238\) | 3.29423 | − | 5.70577i | 0.213533 | − | 0.369850i | ||||
\(239\) | −8.19615 | −0.530165 | −0.265083 | − | 0.964226i | \(-0.585399\pi\) | ||||
−0.265083 | + | 0.964226i | \(0.585399\pi\) | |||||||
\(240\) | −1.36603 | + | 2.36603i | −0.0881766 | + | 0.152726i | ||||
\(241\) | 4.33013 | − | 7.50000i | 0.278928 | − | 0.483117i | −0.692191 | − | 0.721715i | \(-0.743354\pi\) |
0.971119 | + | 0.238597i | \(0.0766876\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | −9.36603 | + | 16.2224i | −0.600831 | + | 1.04067i | ||||
\(244\) | 2.09808 | + | 3.63397i | 0.134316 | + | 0.232641i | ||||
\(245\) | 1.00000 | + | 1.73205i | 0.0638877 | + | 0.110657i | ||||
\(246\) | 28.3923 | 1.81023 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.26795 | 0.0805149 | ||||||||
\(249\) | 3.00000 | + | 5.19615i | 0.190117 | + | 0.329293i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 3.40192 | − | 5.89230i | 0.214728 | − | 0.371919i | −0.738461 | − | 0.674296i | \(-0.764447\pi\) |
0.953188 | + | 0.302378i | \(0.0977803\pi\) | |||||||
\(252\) | −13.3923 | −0.843636 | ||||||||
\(253\) | 3.80385 | − | 6.58846i | 0.239146 | − | 0.414213i | ||||
\(254\) | 10.5981 | − | 18.3564i | 0.664982 | − | 1.15178i | ||||
\(255\) | 6.00000 | 0.375735 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.92820 | + | 12.0000i | 0.432169 | + | 0.748539i | 0.997060 | − | 0.0766265i | \(-0.0244149\pi\) |
−0.564890 | + | 0.825166i | \(0.691082\pi\) | |||||||
\(258\) | −2.73205 | − | 4.73205i | −0.170090 | − | 0.294605i | ||||
\(259\) | 33.5885 | 2.08709 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.2487 | −2.61513 | ||||||||
\(262\) | 9.06218 | + | 15.6962i | 0.559863 | + | 0.969712i | ||||
\(263\) | 13.7942 | + | 23.8923i | 0.850589 | + | 1.47326i | 0.880678 | + | 0.473715i | \(0.157087\pi\) |
−0.0300894 | + | 0.999547i | \(0.509579\pi\) | |||||||
\(264\) | 4.09808 | − | 7.09808i | 0.252219 | − | 0.436856i | ||||
\(265\) | 6.46410 | 0.397087 | ||||||||
\(266\) | 9.69615 | − | 16.7942i | 0.594509 | − | 1.02972i | ||||
\(267\) | 23.4904 | − | 40.6865i | 1.43759 | − | 2.48998i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.43782 | − | 2.49038i | 0.0876656 | − | 0.151841i | −0.818858 | − | 0.573996i | \(-0.805393\pi\) |
0.906524 | + | 0.422154i | \(0.138726\pi\) | |||||||
\(270\) | −2.00000 | − | 3.46410i | −0.121716 | − | 0.210819i | ||||
\(271\) | −1.26795 | − | 2.19615i | −0.0770224 | − | 0.133407i | 0.824942 | − | 0.565218i | \(-0.191208\pi\) |
−0.901964 | + | 0.431811i | \(0.857875\pi\) | |||||||
\(272\) | 2.19615 | 0.133161 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.19615 | 0.495148 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | −3.46410 | − | 6.00000i | −0.208514 | − | 0.361158i | ||||
\(277\) | −0.500000 | + | 0.866025i | −0.0300421 | + | 0.0520344i | −0.880656 | − | 0.473757i | \(-0.842897\pi\) |
0.850613 | + | 0.525792i | \(0.176231\pi\) | |||||||
\(278\) | −9.19615 | −0.551549 | ||||||||
\(279\) | −2.83013 | + | 4.90192i | −0.169435 | + | 0.293471i | ||||
\(280\) | −1.50000 | + | 2.59808i | −0.0896421 | + | 0.155265i | ||||
\(281\) | −10.3923 | −0.619953 | −0.309976 | − | 0.950744i | \(-0.600321\pi\) | ||||
−0.309976 | + | 0.950744i | \(0.600321\pi\) | |||||||
\(282\) | −4.09808 | + | 7.09808i | −0.244037 | + | 0.422684i | ||||
\(283\) | −15.1962 | − | 26.3205i | −0.903317 | − | 1.56459i | −0.823160 | − | 0.567810i | \(-0.807791\pi\) |
−0.0801576 | − | 0.996782i | \(-0.525542\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | 17.6603 | 1.04610 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.1769 | 1.84032 | ||||||||
\(288\) | −2.23205 | − | 3.86603i | −0.131525 | − | 0.227808i | ||||
\(289\) | 6.08846 | + | 10.5455i | 0.358145 | + | 0.620325i | ||||
\(290\) | −4.73205 | + | 8.19615i | −0.277876 | + | 0.481295i | ||||
\(291\) | 41.3205 | 2.42225 | ||||||||
\(292\) | −2.83013 | + | 4.90192i | −0.165621 | + | 0.286863i | ||||
\(293\) | 0.401924 | − | 0.696152i | 0.0234806 | − | 0.0406697i | −0.854046 | − | 0.520197i | \(-0.825859\pi\) |
0.877527 | + | 0.479527i | \(0.159192\pi\) | |||||||
\(294\) | −5.46410 | −0.318673 | ||||||||
\(295\) | 5.19615 | − | 9.00000i | 0.302532 | − | 0.524000i | ||||
\(296\) | 5.59808 | + | 9.69615i | 0.325382 | + | 0.563577i | ||||
\(297\) | 6.00000 | + | 10.3923i | 0.348155 | + | 0.603023i | ||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.73205 | −0.157735 | ||||||||
\(301\) | −3.00000 | − | 5.19615i | −0.172917 | − | 0.299501i | ||||
\(302\) | −3.16987 | − | 5.49038i | −0.182406 | − | 0.315936i | ||||
\(303\) | −9.92820 | + | 17.1962i | −0.570360 | + | 0.987893i | ||||
\(304\) | 6.46410 | 0.370742 | ||||||||
\(305\) | −2.09808 | + | 3.63397i | −0.120135 | + | 0.208081i | ||||
\(306\) | −4.90192 | + | 8.49038i | −0.280224 | + | 0.485363i | ||||
\(307\) | 20.5359 | 1.17205 | 0.586023 | − | 0.810295i | \(-0.300693\pi\) | ||||
0.586023 | + | 0.810295i | \(0.300693\pi\) | |||||||
\(308\) | 4.50000 | − | 7.79423i | 0.256411 | − | 0.444117i | ||||
\(309\) | −1.63397 | − | 2.83013i | −0.0929536 | − | 0.161000i | ||||
\(310\) | 0.633975 | + | 1.09808i | 0.0360073 | + | 0.0623665i | ||||
\(311\) | −15.1244 | −0.857624 | −0.428812 | − | 0.903394i | \(-0.641068\pi\) | ||||
−0.428812 | + | 0.903394i | \(0.641068\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.60770 | 0.316966 | 0.158483 | − | 0.987362i | \(-0.449340\pi\) | ||||
0.158483 | + | 0.987362i | \(0.449340\pi\) | |||||||
\(314\) | 6.50000 | + | 11.2583i | 0.366816 | + | 0.635344i | ||||
\(315\) | −6.69615 | − | 11.5981i | −0.377285 | − | 0.653478i | ||||
\(316\) | −3.09808 | + | 5.36603i | −0.174280 | + | 0.301863i | ||||
\(317\) | −12.8038 | −0.719136 | −0.359568 | − | 0.933119i | \(-0.617076\pi\) | ||||
−0.359568 | + | 0.933119i | \(0.617076\pi\) | |||||||
\(318\) | −8.83013 | + | 15.2942i | −0.495169 | + | 0.857658i | ||||
\(319\) | 14.1962 | − | 24.5885i | 0.794832 | − | 1.37669i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0.464102 | − | 0.803848i | 0.0259036 | − | 0.0448664i | ||||
\(322\) | −3.80385 | − | 6.58846i | −0.211980 | − | 0.367160i | ||||
\(323\) | −7.09808 | − | 12.2942i | −0.394948 | − | 0.684069i | ||||
\(324\) | −2.46410 | −0.136895 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.26795 | 0.402534 | ||||||||
\(327\) | −21.1244 | − | 36.5885i | −1.16818 | − | 2.02335i | ||||
\(328\) | 5.19615 | + | 9.00000i | 0.286910 | + | 0.496942i | ||||
\(329\) | −4.50000 | + | 7.79423i | −0.248093 | + | 0.429710i | ||||
\(330\) | 8.19615 | 0.451183 | ||||||||
\(331\) | 0.464102 | − | 0.803848i | 0.0255093 | − | 0.0441835i | −0.852989 | − | 0.521929i | \(-0.825213\pi\) |
0.878498 | + | 0.477746i | \(0.158546\pi\) | |||||||
\(332\) | −1.09808 | + | 1.90192i | −0.0602648 | + | 0.104382i | ||||
\(333\) | −49.9808 | −2.73893 | ||||||||
\(334\) | −1.50000 | + | 2.59808i | −0.0820763 | + | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.09808 | − | 7.09808i | −0.223568 | − | 0.387232i | ||||
\(337\) | 4.19615 | 0.228579 | 0.114289 | − | 0.993447i | \(-0.463541\pi\) | ||||
0.114289 | + | 0.993447i | \(0.463541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.9282 | 1.02804 | ||||||||
\(340\) | 1.09808 | + | 1.90192i | 0.0595515 | + | 0.103146i | ||||
\(341\) | −1.90192 | − | 3.29423i | −0.102995 | − | 0.178392i | ||||
\(342\) | −14.4282 | + | 24.9904i | −0.780188 | + | 1.35133i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 1.00000 | − | 1.73205i | 0.0539164 | − | 0.0933859i | ||||
\(345\) | 3.46410 | − | 6.00000i | 0.186501 | − | 0.323029i | ||||
\(346\) | 15.0000 | 0.806405 | ||||||||
\(347\) | 12.6340 | − | 21.8827i | 0.678227 | − | 1.17472i | −0.297287 | − | 0.954788i | \(-0.596082\pi\) |
0.975514 | − | 0.219936i | \(-0.0705848\pi\) | |||||||
\(348\) | −12.9282 | − | 22.3923i | −0.693024 | − | 1.20035i | ||||
\(349\) | −17.0263 | − | 29.4904i | −0.911396 | − | 1.57858i | −0.812094 | − | 0.583527i | \(-0.801672\pi\) |
−0.0993018 | − | 0.995057i | \(-0.531661\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 10.0981 | + | 17.4904i | 0.537466 | + | 0.930919i | 0.999040 | + | 0.0438169i | \(0.0139518\pi\) |
−0.461573 | + | 0.887102i | \(0.652715\pi\) | |||||||
\(354\) | 14.1962 | + | 24.5885i | 0.754517 | + | 1.30686i | ||||
\(355\) | −3.00000 | + | 5.19615i | −0.159223 | + | 0.275783i | ||||
\(356\) | 17.1962 | 0.911394 | ||||||||
\(357\) | −9.00000 | + | 15.5885i | −0.476331 | + | 0.825029i | ||||
\(358\) | −1.26795 | + | 2.19615i | −0.0670132 | + | 0.116070i | ||||
\(359\) | −22.3923 | −1.18182 | −0.590910 | − | 0.806737i | \(-0.701231\pi\) | ||||
−0.590910 | + | 0.806737i | \(0.701231\pi\) | |||||||
\(360\) | 2.23205 | − | 3.86603i | 0.117639 | − | 0.203757i | ||||
\(361\) | −11.3923 | − | 19.7321i | −0.599595 | − | 1.03853i | ||||
\(362\) | −8.29423 | − | 14.3660i | −0.435935 | − | 0.755062i | ||||
\(363\) | 5.46410 | 0.286791 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.66025 | −0.296271 | ||||||||
\(366\) | −5.73205 | − | 9.92820i | −0.299619 | − | 0.518955i | ||||
\(367\) | 13.1962 | + | 22.8564i | 0.688834 | + | 1.19309i | 0.972216 | + | 0.234088i | \(0.0752102\pi\) |
−0.283382 | + | 0.959007i | \(0.591456\pi\) | |||||||
\(368\) | 1.26795 | − | 2.19615i | 0.0660964 | − | 0.114482i | ||||
\(369\) | −46.3923 | −2.41509 | ||||||||
\(370\) | −5.59808 | + | 9.69615i | −0.291030 | + | 0.504079i | ||||
\(371\) | −9.69615 | + | 16.7942i | −0.503399 | + | 0.871913i | ||||
\(372\) | −3.46410 | −0.179605 | ||||||||
\(373\) | −10.1962 | + | 17.6603i | −0.527937 | + | 0.914413i | 0.471533 | + | 0.881848i | \(0.343701\pi\) |
−0.999470 | + | 0.0325648i | \(0.989632\pi\) | |||||||
\(374\) | −3.29423 | − | 5.70577i | −0.170341 | − | 0.295038i | ||||
\(375\) | −1.36603 | − | 2.36603i | −0.0705412 | − | 0.122181i | ||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 12.0000 | 0.617213 | ||||||||
\(379\) | −5.89230 | − | 10.2058i | −0.302667 | − | 0.524235i | 0.674072 | − | 0.738666i | \(-0.264544\pi\) |
−0.976739 | + | 0.214430i | \(0.931210\pi\) | |||||||
\(380\) | 3.23205 | + | 5.59808i | 0.165801 | + | 0.287175i | ||||
\(381\) | −28.9545 | + | 50.1506i | −1.48338 | + | 2.56929i | ||||
\(382\) | −19.2679 | −0.985834 | ||||||||
\(383\) | −0.803848 | + | 1.39230i | −0.0410747 | + | 0.0711435i | −0.885832 | − | 0.464006i | \(-0.846411\pi\) |
0.844757 | + | 0.535150i | \(0.179745\pi\) | |||||||
\(384\) | 1.36603 | − | 2.36603i | 0.0697097 | − | 0.120741i | ||||
\(385\) | 9.00000 | 0.458682 | ||||||||
\(386\) | −2.19615 | + | 3.80385i | −0.111781 | + | 0.193611i | ||||
\(387\) | 4.46410 | + | 7.73205i | 0.226923 | + | 0.393042i | ||||
\(388\) | 7.56218 | + | 13.0981i | 0.383911 | + | 0.664954i | ||||
\(389\) | −19.2679 | −0.976924 | −0.488462 | − | 0.872585i | \(-0.662442\pi\) | ||||
−0.488462 | + | 0.872585i | \(0.662442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.56922 | −0.281648 | ||||||||
\(392\) | −1.00000 | − | 1.73205i | −0.0505076 | − | 0.0874818i | ||||
\(393\) | −24.7583 | − | 42.8827i | −1.24889 | − | 2.16315i | ||||
\(394\) | −4.79423 | + | 8.30385i | −0.241530 | + | 0.418342i | ||||
\(395\) | −6.19615 | −0.311762 | ||||||||
\(396\) | −6.69615 | + | 11.5981i | −0.336494 | + | 0.582825i | ||||
\(397\) | −0.401924 | + | 0.696152i | −0.0201720 | + | 0.0349389i | −0.875935 | − | 0.482429i | \(-0.839755\pi\) |
0.855763 | + | 0.517368i | \(0.173088\pi\) | |||||||
\(398\) | −14.3923 | −0.721421 | ||||||||
\(399\) | −26.4904 | + | 45.8827i | −1.32618 | + | 2.29701i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −2.59808 | − | 4.50000i | −0.129742 | − | 0.224719i | 0.793835 | − | 0.608134i | \(-0.208081\pi\) |
−0.923576 | + | 0.383414i | \(0.874748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.26795 | −0.361594 | ||||||||
\(405\) | −1.23205 | − | 2.13397i | −0.0612211 | − | 0.106038i | ||||
\(406\) | −14.1962 | − | 24.5885i | −0.704543 | − | 1.22030i | ||||
\(407\) | 16.7942 | − | 29.0885i | 0.832459 | − | 1.44186i | ||||
\(408\) | −6.00000 | −0.297044 | ||||||||
\(409\) | 9.86603 | − | 17.0885i | 0.487844 | − | 0.844970i | −0.512059 | − | 0.858950i | \(-0.671117\pi\) |
0.999902 | + | 0.0139806i | \(0.00445032\pi\) | |||||||
\(410\) | −5.19615 | + | 9.00000i | −0.256620 | + | 0.444478i | ||||
\(411\) | −22.3923 | −1.10453 | ||||||||
\(412\) | 0.598076 | − | 1.03590i | 0.0294651 | − | 0.0510351i | ||||
\(413\) | 15.5885 | + | 27.0000i | 0.767058 | + | 1.32858i | ||||
\(414\) | 5.66025 | + | 9.80385i | 0.278186 | + | 0.481833i | ||||
\(415\) | −2.19615 | −0.107805 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.1244 | 1.23034 | ||||||||
\(418\) | −9.69615 | − | 16.7942i | −0.474254 | − | 0.821433i | ||||
\(419\) | −8.66025 | − | 15.0000i | −0.423081 | − | 0.732798i | 0.573158 | − | 0.819445i | \(-0.305718\pi\) |
−0.996239 | + | 0.0866469i | \(0.972385\pi\) | |||||||
\(420\) | 4.09808 | − | 7.09808i | 0.199966 | − | 0.346351i | ||||
\(421\) | 27.1244 | 1.32196 | 0.660980 | − | 0.750403i | \(-0.270141\pi\) | ||||
0.660980 | + | 0.750403i | \(0.270141\pi\) | |||||||
\(422\) | −6.79423 | + | 11.7679i | −0.330738 | + | 0.572855i | ||||
\(423\) | 6.69615 | − | 11.5981i | 0.325578 | − | 0.563918i | ||||
\(424\) | −6.46410 | −0.313925 | ||||||||
\(425\) | −1.09808 | + | 1.90192i | −0.0532645 | + | 0.0922569i | ||||
\(426\) | −8.19615 | − | 14.1962i | −0.397105 | − | 0.687806i | ||||
\(427\) | −6.29423 | − | 10.9019i | −0.304599 | − | 0.527581i | ||||
\(428\) | 0.339746 | 0.0164222 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | 1.09808 | + | 1.90192i | 0.0528925 | + | 0.0916124i | 0.891259 | − | 0.453494i | \(-0.149823\pi\) |
−0.838367 | + | 0.545106i | \(0.816489\pi\) | |||||||
\(432\) | 2.00000 | + | 3.46410i | 0.0962250 | + | 0.166667i | ||||
\(433\) | −6.19615 | + | 10.7321i | −0.297768 | + | 0.515749i | −0.975625 | − | 0.219444i | \(-0.929576\pi\) |
0.677857 | + | 0.735194i | \(0.262909\pi\) | |||||||
\(434\) | −3.80385 | −0.182591 | ||||||||
\(435\) | 12.9282 | − | 22.3923i | 0.619860 | − | 1.07363i | ||||
\(436\) | 7.73205 | − | 13.3923i | 0.370298 | − | 0.641375i | ||||
\(437\) | −16.3923 | −0.784150 | ||||||||
\(438\) | 7.73205 | − | 13.3923i | 0.369452 | − | 0.639909i | ||||
\(439\) | −17.2942 | − | 29.9545i | −0.825408 | − | 1.42965i | −0.901607 | − | 0.432557i | \(-0.857612\pi\) |
0.0761982 | − | 0.997093i | \(-0.475722\pi\) | |||||||
\(440\) | 1.50000 | + | 2.59808i | 0.0715097 | + | 0.123858i | ||||
\(441\) | 8.92820 | 0.425153 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.60770 | −0.0763839 | −0.0381920 | − | 0.999270i | \(-0.512160\pi\) | ||||
−0.0381920 | + | 0.999270i | \(0.512160\pi\) | |||||||
\(444\) | −15.2942 | − | 26.4904i | −0.725832 | − | 1.25718i | ||||
\(445\) | 8.59808 | + | 14.8923i | 0.407588 | + | 0.705963i | ||||
\(446\) | 0.232051 | − | 0.401924i | 0.0109879 | − | 0.0190316i | ||||
\(447\) | −16.3923 | −0.775329 | ||||||||
\(448\) | 1.50000 | − | 2.59808i | 0.0708683 | − | 0.122748i | ||||
\(449\) | −7.79423 | + | 13.5000i | −0.367832 | + | 0.637104i | −0.989226 | − | 0.146394i | \(-0.953233\pi\) |
0.621394 | + | 0.783498i | \(0.286567\pi\) | |||||||
\(450\) | 4.46410 | 0.210440 | ||||||||
\(451\) | 15.5885 | − | 27.0000i | 0.734032 | − | 1.27138i | ||||
\(452\) | 3.46410 | + | 6.00000i | 0.162938 | + | 0.282216i | ||||
\(453\) | 8.66025 | + | 15.0000i | 0.406894 | + | 0.704761i | ||||
\(454\) | −4.39230 | −0.206141 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.6603 | −0.827017 | ||||||||
\(457\) | 17.8301 | + | 30.8827i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446477i | \(0.147322\pi\) |
−0.0607368 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(458\) | −2.36603 | − | 4.09808i | −0.110557 | − | 0.191491i | ||||
\(459\) | 4.39230 | − | 7.60770i | 0.205015 | − | 0.355097i | ||||
\(460\) | 2.53590 | 0.118237 | ||||||||
\(461\) | −0.294229 | + | 0.509619i | −0.0137036 | + | 0.0237353i | −0.872796 | − | 0.488085i | \(-0.837695\pi\) |
0.859092 | + | 0.511821i | \(0.171029\pi\) | |||||||
\(462\) | −12.2942 | + | 21.2942i | −0.571979 | + | 0.990697i | ||||
\(463\) | 0.928203 | 0.0431373 | 0.0215686 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215686 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(464\) | 4.73205 | − | 8.19615i | 0.219680 | − | 0.380497i | ||||
\(465\) | −1.73205 | − | 3.00000i | −0.0803219 | − | 0.139122i | ||||
\(466\) | 0.633975 | + | 1.09808i | 0.0293683 | + | 0.0508674i | ||||
\(467\) | 10.1436 | 0.469390 | 0.234695 | − | 0.972069i | \(-0.424591\pi\) | ||||
0.234695 | + | 0.972069i | \(0.424591\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.50000 | − | 2.59808i | −0.0691898 | − | 0.119840i | ||||
\(471\) | −17.7583 | − | 30.7583i | −0.818261 | − | 1.41727i | ||||
\(472\) | −5.19615 | + | 9.00000i | −0.239172 | + | 0.414259i | ||||
\(473\) | −6.00000 | −0.275880 | ||||||||
\(474\) | 8.46410 | − | 14.6603i | 0.388769 | − | 0.673368i | ||||
\(475\) | −3.23205 | + | 5.59808i | −0.148297 | + | 0.256857i | ||||
\(476\) | −6.58846 | −0.301981 | ||||||||
\(477\) | 14.4282 | − | 24.9904i | 0.660622 | − | 1.14423i | ||||
\(478\) | 4.09808 | + | 7.09808i | 0.187442 | + | 0.324658i | ||||
\(479\) | −5.49038 | − | 9.50962i | −0.250862 | − | 0.434506i | 0.712901 | − | 0.701264i | \(-0.247381\pi\) |
−0.963763 | + | 0.266759i | \(0.914047\pi\) | |||||||
\(480\) | 2.73205 | 0.124700 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8.66025 | −0.394464 | ||||||||
\(483\) | 10.3923 | + | 18.0000i | 0.472866 | + | 0.819028i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −7.56218 | + | 13.0981i | −0.343381 | + | 0.594753i | ||||
\(486\) | 18.7321 | 0.849703 | ||||||||
\(487\) | −16.6244 | + | 28.7942i | −0.753321 | + | 1.30479i | 0.192883 | + | 0.981222i | \(0.438216\pi\) |
−0.946204 | + | 0.323569i | \(0.895117\pi\) | |||||||
\(488\) | 2.09808 | − | 3.63397i | 0.0949754 | − | 0.164502i | ||||
\(489\) | −19.8564 | −0.897938 | ||||||||
\(490\) | 1.00000 | − | 1.73205i | 0.0451754 | − | 0.0782461i | ||||
\(491\) | 1.66987 | + | 2.89230i | 0.0753603 | + | 0.130528i | 0.901243 | − | 0.433314i | \(-0.142656\pi\) |
−0.825883 | + | 0.563842i | \(0.809323\pi\) | |||||||
\(492\) | −14.1962 | − | 24.5885i | −0.640012 | − | 1.10853i | ||||
\(493\) | −20.7846 | −0.936092 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.3923 | −0.601939 | ||||||||
\(496\) | −0.633975 | − | 1.09808i | −0.0284663 | − | 0.0493051i | ||||
\(497\) | −9.00000 | − | 15.5885i | −0.403705 | − | 0.699238i | ||||
\(498\) | 3.00000 | − | 5.19615i | 0.134433 | − | 0.232845i | ||||
\(499\) | −1.85641 | −0.0831042 | −0.0415521 | − | 0.999136i | \(-0.513230\pi\) | ||||
−0.0415521 | + | 0.999136i | \(0.513230\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 4.09808 | − | 7.09808i | 0.183089 | − | 0.317119i | ||||
\(502\) | −6.80385 | −0.303671 | ||||||||
\(503\) | 4.66987 | − | 8.08846i | 0.208219 | − | 0.360646i | −0.742934 | − | 0.669364i | \(-0.766567\pi\) |
0.951154 | + | 0.308718i | \(0.0998999\pi\) | |||||||
\(504\) | 6.69615 | + | 11.5981i | 0.298270 | + | 0.516619i | ||||
\(505\) | −3.63397 | − | 6.29423i | −0.161710 | − | 0.280089i | ||||
\(506\) | −7.60770 | −0.338203 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.1962 | −0.940427 | ||||||||
\(509\) | −0.803848 | − | 1.39230i | −0.0356299 | − | 0.0617128i | 0.847661 | − | 0.530539i | \(-0.178010\pi\) |
−0.883290 | + | 0.468826i | \(0.844677\pi\) | |||||||
\(510\) | −3.00000 | − | 5.19615i | −0.132842 | − | 0.230089i | ||||
\(511\) | 8.49038 | − | 14.7058i | 0.375592 | − | 0.650545i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 12.9282 | − | 22.3923i | 0.570794 | − | 0.988644i | ||||
\(514\) | 6.92820 | − | 12.0000i | 0.305590 | − | 0.529297i | ||||
\(515\) | 1.19615 | 0.0527088 | ||||||||
\(516\) | −2.73205 | + | 4.73205i | −0.120272 | + | 0.208317i | ||||
\(517\) | 4.50000 | + | 7.79423i | 0.197910 | + | 0.342790i | ||||
\(518\) | −16.7942 | − | 29.0885i | −0.737896 | − | 1.27807i | ||||
\(519\) | −40.9808 | −1.79886 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.464102 | −0.0203327 | −0.0101663 | − | 0.999948i | \(-0.503236\pi\) | ||||
−0.0101663 | + | 0.999948i | \(0.503236\pi\) | |||||||
\(522\) | 21.1244 | + | 36.5885i | 0.924588 | + | 1.60143i | ||||
\(523\) | −9.19615 | − | 15.9282i | −0.402120 | − | 0.696492i | 0.591862 | − | 0.806039i | \(-0.298393\pi\) |
−0.993982 | + | 0.109548i | \(0.965060\pi\) | |||||||
\(524\) | 9.06218 | − | 15.6962i | 0.395883 | − | 0.685690i | ||||
\(525\) | 8.19615 | 0.357709 | ||||||||
\(526\) | 13.7942 | − | 23.8923i | 0.601457 | − | 1.04175i | ||||
\(527\) | −1.39230 | + | 2.41154i | −0.0606498 | + | 0.105048i | ||||
\(528\) | −8.19615 | −0.356692 | ||||||||
\(529\) | 8.28461 | − | 14.3494i | 0.360200 | − | 0.623885i | ||||
\(530\) | −3.23205 | − | 5.59808i | −0.140391 | − | 0.243165i | ||||
\(531\) | −23.1962 | − | 40.1769i | −1.00663 | − | 1.74353i | ||||
\(532\) | −19.3923 | −0.840763 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −46.9808 | −2.03306 | ||||||||
\(535\) | 0.169873 | + | 0.294229i | 0.00734425 | + | 0.0127206i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.46410 | − | 6.00000i | 0.149487 | − | 0.258919i | ||||
\(538\) | −2.87564 | −0.123978 | ||||||||
\(539\) | −3.00000 | + | 5.19615i | −0.129219 | + | 0.223814i | ||||
\(540\) | −2.00000 | + | 3.46410i | −0.0860663 | + | 0.149071i | ||||
\(541\) | 16.0526 | 0.690153 | 0.345077 | − | 0.938574i | \(-0.387853\pi\) | ||||
0.345077 | + | 0.938574i | \(0.387853\pi\) | |||||||
\(542\) | −1.26795 | + | 2.19615i | −0.0544631 | + | 0.0943328i | ||||
\(543\) | 22.6603 | + | 39.2487i | 0.972445 | + | 1.68432i | ||||
\(544\) | −1.09808 | − | 1.90192i | −0.0470796 | − | 0.0815443i | ||||
\(545\) | 15.4641 | 0.662409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.7846 | 1.48728 | 0.743641 | − | 0.668579i | \(-0.233097\pi\) | ||||
0.743641 | + | 0.668579i | \(0.233097\pi\) | |||||||
\(548\) | −4.09808 | − | 7.09808i | −0.175061 | − | 0.303215i | ||||
\(549\) | 9.36603 | + | 16.2224i | 0.399732 | + | 0.692357i | ||||
\(550\) | −1.50000 | + | 2.59808i | −0.0639602 | + | 0.110782i | ||||
\(551\) | −61.1769 | −2.60622 | ||||||||
\(552\) | −3.46410 | + | 6.00000i | −0.147442 | + | 0.255377i | ||||
\(553\) | 9.29423 | − | 16.0981i | 0.395231 | − | 0.684560i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | 15.2942 | − | 26.4904i | 0.649204 | − | 1.12445i | ||||
\(556\) | 4.59808 | + | 7.96410i | 0.195002 | + | 0.337753i | ||||
\(557\) | 8.59808 | + | 14.8923i | 0.364312 | + | 0.631007i | 0.988666 | − | 0.150135i | \(-0.0479708\pi\) |
−0.624353 | + | 0.781142i | \(0.714637\pi\) | |||||||
\(558\) | 5.66025 | 0.239618 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 9.00000 | + | 15.5885i | 0.379980 | + | 0.658145i | ||||
\(562\) | 5.19615 | + | 9.00000i | 0.219186 | + | 0.379642i | ||||
\(563\) | 10.7321 | − | 18.5885i | 0.452302 | − | 0.783410i | −0.546227 | − | 0.837637i | \(-0.683936\pi\) |
0.998529 | + | 0.0542274i | \(0.0172696\pi\) | |||||||
\(564\) | 8.19615 | 0.345120 | ||||||||
\(565\) | −3.46410 | + | 6.00000i | −0.145736 | + | 0.252422i | ||||
\(566\) | −15.1962 | + | 26.3205i | −0.638742 | + | 1.10633i | ||||
\(567\) | 7.39230 | 0.310448 | ||||||||
\(568\) | 3.00000 | − | 5.19615i | 0.125877 | − | 0.218026i | ||||
\(569\) | 10.6244 | + | 18.4019i | 0.445396 | + | 0.771449i | 0.998080 | − | 0.0619424i | \(-0.0197295\pi\) |
−0.552684 | + | 0.833391i | \(0.686396\pi\) | |||||||
\(570\) | −8.83013 | − | 15.2942i | −0.369853 | − | 0.640605i | ||||
\(571\) | −34.3731 | −1.43847 | −0.719234 | − | 0.694768i | \(-0.755507\pi\) | ||||
−0.719234 | + | 0.694768i | \(0.755507\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 52.6410 | 2.19911 | ||||||||
\(574\) | −15.5885 | − | 27.0000i | −0.650650 | − | 1.12696i | ||||
\(575\) | 1.26795 | + | 2.19615i | 0.0528771 | + | 0.0915859i | ||||
\(576\) | −2.23205 | + | 3.86603i | −0.0930021 | + | 0.161084i | ||||
\(577\) | 32.4449 | 1.35070 | 0.675349 | − | 0.737499i | \(-0.263993\pi\) | ||||
0.675349 | + | 0.737499i | \(0.263993\pi\) | |||||||
\(578\) | 6.08846 | − | 10.5455i | 0.253246 | − | 0.438636i | ||||
\(579\) | 6.00000 | − | 10.3923i | 0.249351 | − | 0.431889i | ||||
\(580\) | 9.46410 | 0.392975 | ||||||||
\(581\) | 3.29423 | − | 5.70577i | 0.136668 | − | 0.236715i | ||||
\(582\) | −20.6603 | − | 35.7846i | −0.856395 | − | 1.48332i | ||||
\(583\) | 9.69615 | + | 16.7942i | 0.401574 | + | 0.695546i | ||||
\(584\) | 5.66025 | 0.234223 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.803848 | −0.0332066 | ||||||||
\(587\) | 15.0000 | + | 25.9808i | 0.619116 | + | 1.07234i | 0.989647 | + | 0.143521i | \(0.0458424\pi\) |
−0.370531 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(588\) | 2.73205 | + | 4.73205i | 0.112668 | + | 0.195146i | ||||
\(589\) | −4.09808 | + | 7.09808i | −0.168858 | + | 0.292471i | ||||
\(590\) | −10.3923 | −0.427844 | ||||||||
\(591\) | 13.0981 | − | 22.6865i | 0.538783 | − | 0.933199i | ||||
\(592\) | 5.59808 | − | 9.69615i | 0.230080 | − | 0.398509i | ||||
\(593\) | −20.7846 | −0.853522 | −0.426761 | − | 0.904365i | \(-0.640345\pi\) | ||||
−0.426761 | + | 0.904365i | \(0.640345\pi\) | |||||||
\(594\) | 6.00000 | − | 10.3923i | 0.246183 | − | 0.426401i | ||||
\(595\) | −3.29423 | − | 5.70577i | −0.135050 | − | 0.233914i | ||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 39.3205 | 1.60928 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.85641 | 0.321004 | 0.160502 | − | 0.987036i | \(-0.448689\pi\) | ||||
0.160502 | + | 0.987036i | \(0.448689\pi\) | |||||||
\(600\) | 1.36603 | + | 2.36603i | 0.0557678 | + | 0.0965926i | ||||
\(601\) | −1.89230 | − | 3.27757i | −0.0771887 | − | 0.133695i | 0.824847 | − | 0.565356i | \(-0.191261\pi\) |
−0.902036 | + | 0.431661i | \(0.857928\pi\) | |||||||
\(602\) | −3.00000 | + | 5.19615i | −0.122271 | + | 0.211779i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.16987 | + | 5.49038i | −0.128980 | + | 0.223400i | ||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 19.8564 | 0.806611 | ||||||||
\(607\) | 3.20577 | − | 5.55256i | 0.130118 | − | 0.225371i | −0.793604 | − | 0.608435i | \(-0.791798\pi\) |
0.923722 | + | 0.383064i | \(0.125131\pi\) | |||||||
\(608\) | −3.23205 | − | 5.59808i | −0.131077 | − | 0.227032i | ||||
\(609\) | 38.7846 | + | 67.1769i | 1.57163 | + | 2.72215i | ||||
\(610\) | 4.19615 | 0.169897 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 9.80385 | 0.396297 | ||||||||
\(613\) | −13.4545 | − | 23.3038i | −0.543421 | − | 0.941234i | −0.998704 | − | 0.0508868i | \(-0.983795\pi\) |
0.455283 | − | 0.890347i | \(-0.349538\pi\) | |||||||
\(614\) | −10.2679 | − | 17.7846i | −0.414381 | − | 0.717728i | ||||
\(615\) | 14.1962 | − | 24.5885i | 0.572444 | − | 0.991502i | ||||
\(616\) | −9.00000 | −0.362620 | ||||||||
\(617\) | −9.00000 | + | 15.5885i | −0.362326 | + | 0.627568i | −0.988343 | − | 0.152242i | \(-0.951351\pi\) |
0.626017 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(618\) | −1.63397 | + | 2.83013i | −0.0657281 | + | 0.113844i | ||||
\(619\) | 10.6077 | 0.426359 | 0.213180 | − | 0.977013i | \(-0.431618\pi\) | ||||
0.213180 | + | 0.977013i | \(0.431618\pi\) | |||||||
\(620\) | 0.633975 | − | 1.09808i | 0.0254610 | − | 0.0440998i | ||||
\(621\) | −5.07180 | − | 8.78461i | −0.203524 | − | 0.352514i | ||||
\(622\) | 7.56218 | + | 13.0981i | 0.303216 | + | 0.525185i | ||||
\(623\) | −51.5885 | −2.06685 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.80385 | − | 4.85641i | −0.112064 | − | 0.194101i | ||||
\(627\) | 26.4904 | + | 45.8827i | 1.05792 | + | 1.83238i | ||||
\(628\) | 6.50000 | − | 11.2583i | 0.259378 | − | 0.449256i | ||||
\(629\) | −24.5885 | −0.980406 | ||||||||
\(630\) | −6.69615 | + | 11.5981i | −0.266781 | + | 0.462078i | ||||
\(631\) | 10.3923 | − | 18.0000i | 0.413711 | − | 0.716569i | −0.581581 | − | 0.813488i | \(-0.697566\pi\) |
0.995292 | + | 0.0969198i | \(0.0308990\pi\) | |||||||
\(632\) | 6.19615 | 0.246470 | ||||||||
\(633\) | 18.5622 | − | 32.1506i | 0.737780 | − | 1.27787i | ||||
\(634\) | 6.40192 | + | 11.0885i | 0.254253 | + | 0.440379i | ||||
\(635\) | −10.5981 | − | 18.3564i | −0.420572 | − | 0.728452i | ||||
\(636\) | 17.6603 | 0.700275 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −28.3923 | −1.12406 | ||||||||
\(639\) | 13.3923 | + | 23.1962i | 0.529791 | + | 0.917626i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 22.9641 | − | 39.7750i | 0.907027 | − | 1.57102i | 0.0888552 | − | 0.996045i | \(-0.471679\pi\) |
0.818172 | − | 0.574973i | \(-0.194988\pi\) | |||||||
\(642\) | −0.928203 | −0.0366333 | ||||||||
\(643\) | 3.63397 | − | 6.29423i | 0.143310 | − | 0.248220i | −0.785431 | − | 0.618949i | \(-0.787559\pi\) |
0.928741 | + | 0.370729i | \(0.120892\pi\) | |||||||
\(644\) | −3.80385 | + | 6.58846i | −0.149893 | + | 0.259622i | ||||
\(645\) | −5.46410 | −0.215149 | ||||||||
\(646\) | −7.09808 | + | 12.2942i | −0.279270 | + | 0.483710i | ||||
\(647\) | −5.59808 | − | 9.69615i | −0.220083 | − | 0.381195i | 0.734750 | − | 0.678338i | \(-0.237300\pi\) |
−0.954833 | + | 0.297143i | \(0.903966\pi\) | |||||||
\(648\) | 1.23205 | + | 2.13397i | 0.0483995 | + | 0.0838304i | ||||
\(649\) | 31.1769 | 1.22380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.3923 | 0.407307 | ||||||||
\(652\) | −3.63397 | − | 6.29423i | −0.142317 | − | 0.246501i | ||||
\(653\) | 9.69615 | + | 16.7942i | 0.379440 | + | 0.657209i | 0.990981 | − | 0.134004i | \(-0.0427834\pi\) |
−0.611541 | + | 0.791213i | \(0.709450\pi\) | |||||||
\(654\) | −21.1244 | + | 36.5885i | −0.826028 | + | 1.43072i | ||||
\(655\) | 18.1244 | 0.708177 | ||||||||
\(656\) | 5.19615 | − | 9.00000i | 0.202876 | − | 0.351391i | ||||
\(657\) | −12.6340 | + | 21.8827i | −0.492898 | + | 0.853725i | ||||
\(658\) | 9.00000 | 0.350857 | ||||||||
\(659\) | −14.6603 | + | 25.3923i | −0.571082 | + | 0.989144i | 0.425373 | + | 0.905018i | \(0.360143\pi\) |
−0.996455 | + | 0.0841255i | \(0.973190\pi\) | |||||||
\(660\) | −4.09808 | − | 7.09808i | −0.159517 | − | 0.276292i | ||||
\(661\) | 14.9545 | + | 25.9019i | 0.581662 | + | 1.00747i | 0.995283 | + | 0.0970187i | \(0.0309307\pi\) |
−0.413621 | + | 0.910449i | \(0.635736\pi\) | |||||||
\(662\) | −0.928203 | −0.0360756 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.19615 | 0.0852272 | ||||||||
\(665\) | −9.69615 | − | 16.7942i | −0.376001 | − | 0.651252i | ||||
\(666\) | 24.9904 | + | 43.2846i | 0.968358 | + | 1.67724i | ||||
\(667\) | −12.0000 | + | 20.7846i | −0.464642 | + | 0.804783i | ||||
\(668\) | 3.00000 | 0.116073 | ||||||||
\(669\) | −0.633975 | + | 1.09808i | −0.0245109 | + | 0.0424541i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.5885 | −0.485972 | ||||||||
\(672\) | −4.09808 | + | 7.09808i | −0.158087 | + | 0.273814i | ||||
\(673\) | 1.80385 | + | 3.12436i | 0.0695332 | + | 0.120435i | 0.898696 | − | 0.438572i | \(-0.144516\pi\) |
−0.829163 | + | 0.559007i | \(0.811182\pi\) | |||||||
\(674\) | −2.09808 | − | 3.63397i | −0.0808149 | − | 0.139975i | ||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.85641 | 0.0713475 | 0.0356737 | − | 0.999363i | \(-0.488642\pi\) | ||||
0.0356737 | + | 0.999363i | \(0.488642\pi\) | |||||||
\(678\) | −9.46410 | − | 16.3923i | −0.363467 | − | 0.629543i | ||||
\(679\) | −22.6865 | − | 39.2942i | −0.870629 | − | 1.50797i | ||||
\(680\) | 1.09808 | − | 1.90192i | 0.0421093 | − | 0.0729354i | ||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | −1.90192 | + | 3.29423i | −0.0728284 | + | 0.126143i | ||||
\(683\) | −15.5885 | + | 27.0000i | −0.596476 | + | 1.03313i | 0.396861 | + | 0.917879i | \(0.370099\pi\) |
−0.993337 | + | 0.115248i | \(0.963234\pi\) | |||||||
\(684\) | 28.8564 | 1.10335 | ||||||||
\(685\) | 4.09808 | − | 7.09808i | 0.156579 | − | 0.271204i | ||||
\(686\) | −7.50000 | − | 12.9904i | −0.286351 | − | 0.495975i | ||||
\(687\) | 6.46410 | + | 11.1962i | 0.246621 | + | 0.427160i | ||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.92820 | −0.263752 | ||||||||
\(691\) | 9.35641 | + | 16.2058i | 0.355934 | + | 0.616497i | 0.987277 | − | 0.159007i | \(-0.0508293\pi\) |
−0.631343 | + | 0.775504i | \(0.717496\pi\) | |||||||
\(692\) | −7.50000 | − | 12.9904i | −0.285107 | − | 0.493820i | ||||
\(693\) | 20.0885 | − | 34.7942i | 0.763097 | − | 1.32172i | ||||
\(694\) | −25.2679 | −0.959158 | ||||||||
\(695\) | −4.59808 | + | 7.96410i | −0.174415 | + | 0.302096i | ||||
\(696\) | −12.9282 | + | 22.3923i | −0.490042 | + | 0.848778i | ||||
\(697\) | −22.8231 | −0.864486 | ||||||||
\(698\) | −17.0263 | + | 29.4904i | −0.644454 | + | 1.11623i | ||||
\(699\) | −1.73205 | − | 3.00000i | −0.0655122 | − | 0.113470i | ||||
\(700\) | 1.50000 | + | 2.59808i | 0.0566947 | + | 0.0981981i | ||||
\(701\) | 29.9090 | 1.12965 | 0.564823 | − | 0.825212i | \(-0.308944\pi\) | ||||
0.564823 | + | 0.825212i | \(0.308944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −72.3731 | −2.72960 | ||||||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | 4.09808 | + | 7.09808i | 0.154342 | + | 0.267329i | ||||
\(706\) | 10.0981 | − | 17.4904i | 0.380046 | − | 0.658259i | ||||
\(707\) | 21.8038 | 0.820018 | ||||||||
\(708\) | 14.1962 | − | 24.5885i | 0.533524 | − | 0.924091i | ||||
\(709\) | −20.4904 | + | 35.4904i | −0.769532 | + | 1.33287i | 0.168284 | + | 0.985738i | \(0.446177\pi\) |
−0.937817 | + | 0.347131i | \(0.887156\pi\) | |||||||
\(710\) | 6.00000 | 0.225176 | ||||||||
\(711\) | −13.8301 | + | 23.9545i | −0.518670 | + | 0.898363i | ||||
\(712\) | −8.59808 | − | 14.8923i | −0.322227 | − | 0.558113i | ||||
\(713\) | 1.60770 | + | 2.78461i | 0.0602087 | + | 0.104284i | ||||
\(714\) | 18.0000 | 0.673633 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.53590 | 0.0947710 | ||||||||
\(717\) | −11.1962 | − | 19.3923i | −0.418128 | − | 0.724219i | ||||
\(718\) | 11.1962 | + | 19.3923i | 0.417837 | + | 0.723714i | ||||
\(719\) | −0.928203 | + | 1.60770i | −0.0346161 | + | 0.0599569i | −0.882814 | − | 0.469722i | \(-0.844354\pi\) |
0.848198 | + | 0.529679i | \(0.177688\pi\) | |||||||
\(720\) | −4.46410 | −0.166367 | ||||||||
\(721\) | −1.79423 | + | 3.10770i | −0.0668206 | + | 0.115737i | ||||
\(722\) | −11.3923 | + | 19.7321i | −0.423978 | + | 0.734351i | ||||
\(723\) | 23.6603 | 0.879934 | ||||||||
\(724\) | −8.29423 | + | 14.3660i | −0.308253 | + | 0.533909i | ||||
\(725\) | 4.73205 | + | 8.19615i | 0.175744 | + | 0.304397i | ||||
\(726\) | −2.73205 | − | 4.73205i | −0.101396 | − | 0.175623i | ||||
\(727\) | 38.3731 | 1.42318 | 0.711589 | − | 0.702596i | \(-0.247976\pi\) | ||||
0.711589 | + | 0.702596i | \(0.247976\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 2.83013 | + | 4.90192i | 0.104748 | + | 0.181428i | ||||
\(731\) | 2.19615 | + | 3.80385i | 0.0812276 | + | 0.140690i | ||||
\(732\) | −5.73205 | + | 9.92820i | −0.211863 | + | 0.366957i | ||||
\(733\) | −50.9090 | −1.88037 | −0.940183 | − | 0.340670i | \(-0.889346\pi\) | ||||
−0.940183 | + | 0.340670i | \(0.889346\pi\) | |||||||
\(734\) | 13.1962 | − | 22.8564i | 0.487079 | − | 0.843645i | ||||
\(735\) | −2.73205 | + | 4.73205i | −0.100773 | + | 0.174544i | ||||
\(736\) | −2.53590 | −0.0934745 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 23.1962 | + | 40.1769i | 0.853862 | + | 1.47893i | ||||
\(739\) | 25.2846 | + | 43.7942i | 0.930109 | + | 1.61100i | 0.783131 | + | 0.621857i | \(0.213622\pi\) |
0.146979 | + | 0.989140i | \(0.453045\pi\) | |||||||
\(740\) | 11.1962 | 0.411579 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.3923 | 0.711914 | ||||||||
\(743\) | −17.1962 | − | 29.7846i | −0.630866 | − | 1.09269i | −0.987375 | − | 0.158400i | \(-0.949367\pi\) |
0.356509 | − | 0.934292i | \(-0.383967\pi\) | |||||||
\(744\) | 1.73205 | + | 3.00000i | 0.0635001 | + | 0.109985i | ||||
\(745\) | 3.00000 | − | 5.19615i | 0.109911 | − | 0.190372i | ||||
\(746\) | 20.3923 | 0.746615 | ||||||||
\(747\) | −4.90192 | + | 8.49038i | −0.179352 | + | 0.310647i | ||||
\(748\) | −3.29423 | + | 5.70577i | −0.120449 | + | 0.208624i | ||||
\(749\) | −1.01924 | −0.0372421 | ||||||||
\(750\) | −1.36603 | + | 2.36603i | −0.0498802 | + | 0.0863950i | ||||
\(751\) | 0.196152 | + | 0.339746i | 0.00715770 | + | 0.0123975i | 0.869582 | − | 0.493788i | \(-0.164388\pi\) |
−0.862424 | + | 0.506186i | \(0.831055\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | 18.5885 | 0.677401 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.33975 | −0.230727 | ||||||||
\(756\) | −6.00000 | − | 10.3923i | −0.218218 | − | 0.377964i | ||||
\(757\) | −1.89230 | − | 3.27757i | −0.0687770 | − | 0.119125i | 0.829586 | − | 0.558379i | \(-0.188576\pi\) |
−0.898363 | + | 0.439253i | \(0.855243\pi\) | |||||||
\(758\) | −5.89230 | + | 10.2058i | −0.214018 | + | 0.370690i | ||||
\(759\) | 20.7846 | 0.754434 | ||||||||
\(760\) | 3.23205 | − | 5.59808i | 0.117239 | − | 0.203064i | ||||
\(761\) | 14.5981 | − | 25.2846i | 0.529180 | − | 0.916566i | −0.470241 | − | 0.882538i | \(-0.655833\pi\) |
0.999421 | − | 0.0340283i | \(-0.0108337\pi\) | |||||||
\(762\) | 57.9090 | 2.09782 | ||||||||
\(763\) | −23.1962 | + | 40.1769i | −0.839757 | + | 1.45450i | ||||
\(764\) | 9.63397 | + | 16.6865i | 0.348545 | + | 0.603698i | ||||
\(765\) | 4.90192 | + | 8.49038i | 0.177229 | + | 0.306970i | ||||
\(766\) | 1.60770 | 0.0580884 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.73205 | −0.0985844 | ||||||||
\(769\) | 19.0526 | + | 33.0000i | 0.687053 | + | 1.19001i | 0.972787 | + | 0.231701i | \(0.0744293\pi\) |
−0.285734 | + | 0.958309i | \(0.592237\pi\) | |||||||
\(770\) | −4.50000 | − | 7.79423i | −0.162169 | − | 0.280885i | ||||
\(771\) | −18.9282 | + | 32.7846i | −0.681683 | + | 1.18071i | ||||
\(772\) | 4.39230 | 0.158083 | ||||||||
\(773\) | −16.7942 | + | 29.0885i | −0.604046 | + | 1.04624i | 0.388155 | + | 0.921594i | \(0.373113\pi\) |
−0.992201 | + | 0.124645i | \(0.960221\pi\) | |||||||
\(774\) | 4.46410 | − | 7.73205i | 0.160459 | − | 0.277923i | ||||
\(775\) | 1.26795 | 0.0455461 | ||||||||
\(776\) | 7.56218 | − | 13.0981i | 0.271466 | − | 0.470194i | ||||
\(777\) | 45.8827 | + | 79.4711i | 1.64603 | + | 2.85101i | ||||
\(778\) | 9.63397 | + | 16.6865i | 0.345395 | + | 0.598241i | ||||
\(779\) | −67.1769 | −2.40686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | 2.78461 | + | 4.82309i | 0.0995774 | + | 0.172473i | ||||
\(783\) | −18.9282 | − | 32.7846i | −0.676439 | − | 1.17163i | ||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | 13.0000 | 0.463990 | ||||||||
\(786\) | −24.7583 | + | 42.8827i | −0.883100 | + | 1.52957i | ||||
\(787\) | 18.4186 | − | 31.9019i | 0.656552 | − | 1.13718i | −0.324951 | − | 0.945731i | \(-0.605348\pi\) |
0.981502 | − | 0.191450i | \(-0.0613189\pi\) | |||||||
\(788\) | 9.58846 | 0.341575 | ||||||||
\(789\) | −37.6865 | + | 65.2750i | −1.34168 | + | 2.32385i | ||||
\(790\) | 3.09808 | + | 5.36603i | 0.110225 | + | 0.190915i | ||||
\(791\) | −10.3923 | − | 18.0000i | −0.369508 | − | 0.640006i | ||||
\(792\) | 13.3923 | 0.475875 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.803848 | 0.0285275 | ||||||||
\(795\) | 8.83013 | + | 15.2942i | 0.313172 | + | 0.542430i | ||||
\(796\) | 7.19615 | + | 12.4641i | 0.255061 | + | 0.441778i | ||||
\(797\) | 0.464102 | − | 0.803848i | 0.0164393 | − | 0.0284737i | −0.857689 | − | 0.514169i | \(-0.828100\pi\) |
0.874128 | + | 0.485696i | \(0.161434\pi\) | |||||||
\(798\) | 52.9808 | 1.87550 | ||||||||
\(799\) | 3.29423 | − | 5.70577i | 0.116541 | − | 0.201856i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 76.7654 | 2.71237 | ||||||||
\(802\) | −2.59808 | + | 4.50000i | −0.0917413 | + | 0.158901i | ||||
\(803\) | −8.49038 | − | 14.7058i | −0.299619 | − | 0.518955i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.60770 | −0.268136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.85641 | 0.276559 | ||||||||
\(808\) | 3.63397 | + | 6.29423i | 0.127843 | + | 0.221430i | ||||
\(809\) | −12.0000 | − | 20.7846i | −0.421898 | − | 0.730748i | 0.574228 | − | 0.818696i | \(-0.305302\pi\) |
−0.996125 | + | 0.0879478i | \(0.971969\pi\) | |||||||
\(810\) | −1.23205 | + | 2.13397i | −0.0432899 | + | 0.0749802i | ||||
\(811\) | 22.6077 | 0.793864 | 0.396932 | − | 0.917848i | \(-0.370075\pi\) | ||||
0.396932 | + | 0.917848i | \(0.370075\pi\) | |||||||
\(812\) | −14.1962 | + | 24.5885i | −0.498187 | + | 0.862886i | ||||
\(813\) | 3.46410 | − | 6.00000i | 0.121491 | − | 0.210429i | ||||
\(814\) | −33.5885 | −1.17727 | ||||||||
\(815\) | 3.63397 | − | 6.29423i | 0.127293 | − | 0.220477i | ||||
\(816\) | 3.00000 | + | 5.19615i | 0.105021 | + | 0.181902i | ||||
\(817\) | 6.46410 | + | 11.1962i | 0.226150 | + | 0.391704i | ||||
\(818\) | −19.7321 | −0.689915 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.3923 | 0.362915 | ||||||||
\(821\) | 4.90192 | + | 8.49038i | 0.171078 | + | 0.296316i | 0.938797 | − | 0.344471i | \(-0.111942\pi\) |
−0.767719 | + | 0.640787i | \(0.778608\pi\) | |||||||
\(822\) | 11.1962 | + | 19.3923i | 0.390511 | + | 0.676384i | ||||
\(823\) | −8.40192 | + | 14.5526i | −0.292873 | + | 0.507270i | −0.974488 | − | 0.224441i | \(-0.927945\pi\) |
0.681615 | + | 0.731711i | \(0.261278\pi\) | |||||||
\(824\) | −1.19615 | −0.0416699 | ||||||||
\(825\) | 4.09808 | − | 7.09808i | 0.142677 | − | 0.247123i | ||||
\(826\) | 15.5885 | − | 27.0000i | 0.542392 | − | 0.939450i | ||||
\(827\) | 11.4115 | 0.396818 | 0.198409 | − | 0.980119i | \(-0.436423\pi\) | ||||
0.198409 | + | 0.980119i | \(0.436423\pi\) | |||||||
\(828\) | 5.66025 | − | 9.80385i | 0.196707 | − | 0.340707i | ||||
\(829\) | −10.0000 | − | 17.3205i | −0.347314 | − | 0.601566i | 0.638457 | − | 0.769657i | \(-0.279573\pi\) |
−0.985771 | + | 0.168091i | \(0.946240\pi\) | |||||||
\(830\) | 1.09808 | + | 1.90192i | 0.0381148 | + | 0.0660167i | ||||
\(831\) | −2.73205 | −0.0947738 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.39230 | 0.152184 | ||||||||
\(834\) | −12.5622 | − | 21.7583i | −0.434993 | − | 0.753429i | ||||
\(835\) | 1.50000 | + | 2.59808i | 0.0519096 | + | 0.0899101i | ||||
\(836\) | −9.69615 | + | 16.7942i | −0.335348 | + | 0.580841i | ||||
\(837\) | −5.07180 | −0.175307 | ||||||||
\(838\) | −8.66025 | + | 15.0000i | −0.299164 | + | 0.518166i | ||||
\(839\) | 16.0981 | − | 27.8827i | 0.555767 | − | 0.962617i | −0.442076 | − | 0.896978i | \(-0.645758\pi\) |
0.997843 | − | 0.0656397i | \(-0.0209088\pi\) | |||||||
\(840\) | −8.19615 | −0.282794 | ||||||||
\(841\) | −30.2846 | + | 52.4545i | −1.04430 | + | 1.80878i | ||||
\(842\) | −13.5622 | − | 23.4904i | −0.467384 | − | 0.809532i | ||||
\(843\) | −14.1962 | − | 24.5885i | −0.488941 | − | 0.846871i | ||||
\(844\) | 13.5885 | 0.467734 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.3923 | −0.460437 | ||||||||
\(847\) | −3.00000 | − | 5.19615i | −0.103081 | − | 0.178542i | ||||
\(848\) | 3.23205 | + | 5.59808i | 0.110989 | + | 0.192239i | ||||
\(849\) | 41.5167 | − | 71.9090i | 1.42485 | − | 2.46791i | ||||
\(850\) | 2.19615 | 0.0753274 | ||||||||
\(851\) | −14.1962 | + | 24.5885i | −0.486638 | + | 0.842881i | ||||
\(852\) | −8.19615 | + | 14.1962i | −0.280796 | + | 0.486352i | ||||
\(853\) | 13.8564 | 0.474434 | 0.237217 | − | 0.971457i | \(-0.423765\pi\) | ||||
0.237217 | + | 0.971457i | \(0.423765\pi\) | |||||||
\(854\) | −6.29423 | + | 10.9019i | −0.215384 | + | 0.373056i | ||||
\(855\) | 14.4282 | + | 24.9904i | 0.493434 | + | 0.854653i | ||||
\(856\) | −0.169873 | − | 0.294229i | −0.00580614 | − | 0.0100565i | ||||
\(857\) | 13.2679 | 0.453225 | 0.226612 | − | 0.973985i | \(-0.427235\pi\) | ||||
0.226612 | + | 0.973985i | \(0.427235\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.3731 | 1.78695 | 0.893473 | − | 0.449117i | \(-0.148261\pi\) | ||||
0.893473 | + | 0.449117i | \(0.148261\pi\) | |||||||
\(860\) | −1.00000 | − | 1.73205i | −0.0340997 | − | 0.0590624i | ||||
\(861\) | 42.5885 | + | 73.7654i | 1.45141 | + | 2.51392i | ||||
\(862\) | 1.09808 | − | 1.90192i | 0.0374006 | − | 0.0647798i | ||||
\(863\) | −19.1769 | −0.652790 | −0.326395 | − | 0.945234i | \(-0.605834\pi\) | ||||
−0.326395 | + | 0.945234i | \(0.605834\pi\) | |||||||
\(864\) | 2.00000 | − | 3.46410i | 0.0680414 | − | 0.117851i | ||||
\(865\) | 7.50000 | − | 12.9904i | 0.255008 | − | 0.441686i | ||||
\(866\) | 12.3923 | 0.421108 | ||||||||
\(867\) | −16.6340 | + | 28.8109i | −0.564919 | + | 0.978469i | ||||
\(868\) | 1.90192 | + | 3.29423i | 0.0645555 | + | 0.111813i | ||||
\(869\) | −9.29423 | − | 16.0981i | −0.315285 | − | 0.546090i | ||||
\(870\) | −25.8564 | −0.876614 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.4641 | −0.523681 | ||||||||
\(873\) | 33.7583 | + | 58.4711i | 1.14255 | + | 1.97895i | ||||
\(874\) | 8.19615 | + | 14.1962i | 0.277239 | + | 0.480192i | ||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | −15.4641 | −0.522484 | ||||||||
\(877\) | 10.2679 | − | 17.7846i | 0.346724 | − | 0.600544i | −0.638941 | − | 0.769255i | \(-0.720627\pi\) |
0.985665 | + | 0.168712i | \(0.0539607\pi\) | |||||||
\(878\) | −17.2942 | + | 29.9545i | −0.583652 | + | 1.01091i | ||||
\(879\) | 2.19615 | 0.0740744 | ||||||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | −4.16025 | − | 7.20577i | −0.140163 | − | 0.242769i | 0.787395 | − | 0.616449i | \(-0.211429\pi\) |
−0.927558 | + | 0.373680i | \(0.878096\pi\) | |||||||
\(882\) | −4.46410 | − | 7.73205i | −0.150314 | − | 0.260352i | ||||
\(883\) | 26.5885 | 0.894773 | 0.447386 | − | 0.894341i | \(-0.352355\pi\) | ||||
0.447386 | + | 0.894341i | \(0.352355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.3923 | 0.954397 | ||||||||
\(886\) | 0.803848 | + | 1.39230i | 0.0270058 | + | 0.0467754i | ||||
\(887\) | −26.3827 | − | 45.6962i | −0.885844 | − | 1.53433i | −0.844743 | − | 0.535172i | \(-0.820247\pi\) |
−0.0411005 | − | 0.999155i | \(-0.513086\pi\) | |||||||
\(888\) | −15.2942 | + | 26.4904i | −0.513241 | + | 0.888959i | ||||
\(889\) | 63.5885 | 2.13269 | ||||||||
\(890\) | 8.59808 | − | 14.8923i | 0.288208 | − | 0.499191i | ||||
\(891\) | 3.69615 | − | 6.40192i | 0.123826 | − | 0.214473i | ||||
\(892\) | −0.464102 | −0.0155393 | ||||||||
\(893\) | 9.69615 | − | 16.7942i | 0.324469 | − | 0.561997i | ||||
\(894\) | 8.19615 | + | 14.1962i | 0.274120 | + | 0.474790i | ||||
\(895\) | 1.26795 | + | 2.19615i | 0.0423829 | + | 0.0734093i | ||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.5885 | 0.520194 | ||||||||
\(899\) | 6.00000 | + | 10.3923i | 0.200111 | + | 0.346603i | ||||
\(900\) | −2.23205 | − | 3.86603i | −0.0744017 | − | 0.128868i | ||||
\(901\) | 7.09808 | − | 12.2942i | 0.236471 | − | 0.409580i | ||||
\(902\) | −31.1769 | −1.03808 | ||||||||
\(903\) | 8.19615 | − | 14.1962i | 0.272751 | − | 0.472418i | ||||
\(904\) | 3.46410 | − | 6.00000i | 0.115214 | − | 0.199557i | ||||
\(905\) | −16.5885 | −0.551419 | ||||||||
\(906\) | 8.66025 | − | 15.0000i | 0.287718 | − | 0.498342i | ||||
\(907\) | −13.2942 | − | 23.0263i | −0.441428 | − | 0.764575i | 0.556368 | − | 0.830936i | \(-0.312194\pi\) |
−0.997796 | + | 0.0663609i | \(0.978861\pi\) | |||||||
\(908\) | 2.19615 | + | 3.80385i | 0.0728819 | + | 0.126235i | ||||
\(909\) | −32.4449 | −1.07613 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.5359 | −0.481596 | −0.240798 | − | 0.970575i | \(-0.577409\pi\) | ||||
−0.240798 | + | 0.970575i | \(0.577409\pi\) | |||||||
\(912\) | 8.83013 | + | 15.2942i | 0.292395 | + | 0.506443i | ||||
\(913\) | −3.29423 | − | 5.70577i | −0.109023 | − | 0.188833i | ||||
\(914\) | 17.8301 | − | 30.8827i | 0.589768 | − | 1.02151i | ||||
\(915\) | −11.4641 | −0.378992 | ||||||||
\(916\) | −2.36603 | + | 4.09808i | −0.0781757 | + | 0.135404i | ||||
\(917\) | −27.1865 | + | 47.0885i | −0.897778 | + | 1.55500i | ||||
\(918\) | −8.78461 | −0.289935 | ||||||||
\(919\) | 5.39230 | − | 9.33975i | 0.177876 | − | 0.308090i | −0.763277 | − | 0.646071i | \(-0.776411\pi\) |
0.941153 | + | 0.337982i | \(0.109744\pi\) | |||||||
\(920\) | −1.26795 | − | 2.19615i | −0.0418030 | − | 0.0724050i | ||||
\(921\) | 28.0526 | + | 48.5885i | 0.924363 | + | 1.60104i | ||||
\(922\) | 0.588457 | 0.0193798 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 24.5885 | 0.808901 | ||||||||
\(925\) | 5.59808 | + | 9.69615i | 0.184064 | + | 0.318808i | ||||
\(926\) | −0.464102 | − | 0.803848i | −0.0152513 | − | 0.0264161i | ||||
\(927\) | 2.66987 | − | 4.62436i | 0.0876901 | − | 0.151884i | ||||
\(928\) | −9.46410 | −0.310674 | ||||||||
\(929\) | 22.3923 | − | 38.7846i | 0.734668 | − | 1.27248i | −0.220201 | − | 0.975454i | \(-0.570671\pi\) |
0.954869 | − | 0.297027i | \(-0.0959952\pi\) | |||||||
\(930\) | −1.73205 | + | 3.00000i | −0.0567962 | + | 0.0983739i | ||||
\(931\) | 12.9282 | 0.423705 | ||||||||
\(932\) | 0.633975 | − | 1.09808i | 0.0207665 | − | 0.0359687i | ||||
\(933\) | −20.6603 | − | 35.7846i | −0.676386 | − | 1.17154i | ||||
\(934\) | −5.07180 | − | 8.78461i | −0.165954 | − | 0.287441i | ||||
\(935\) | −6.58846 | −0.215466 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.3923 | −0.992873 | −0.496437 | − | 0.868073i | \(-0.665359\pi\) | ||||
−0.496437 | + | 0.868073i | \(0.665359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.66025 | + | 13.2679i | 0.249983 | + | 0.432983i | ||||
\(940\) | −1.50000 | + | 2.59808i | −0.0489246 | + | 0.0847399i | ||||
\(941\) | 44.7846 | 1.45994 | 0.729968 | − | 0.683481i | \(-0.239535\pi\) | ||||
0.729968 | + | 0.683481i | \(0.239535\pi\) | |||||||
\(942\) | −17.7583 | + | 30.7583i | −0.578598 | + | 1.00216i | ||||
\(943\) | −13.1769 | + | 22.8231i | −0.429099 | + | 0.743222i | ||||
\(944\) | 10.3923 | 0.338241 | ||||||||
\(945\) | 6.00000 | − | 10.3923i | 0.195180 | − | 0.338062i | ||||
\(946\) | 3.00000 | + | 5.19615i | 0.0975384 | + | 0.168941i | ||||
\(947\) | 28.6865 | + | 49.6865i | 0.932187 | + | 1.61460i | 0.779575 | + | 0.626309i | \(0.215435\pi\) |
0.152612 | + | 0.988286i | \(0.451231\pi\) | |||||||
\(948\) | −16.9282 | −0.549802 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.46410 | 0.209723 | ||||||||
\(951\) | −17.4904 | − | 30.2942i | −0.567164 | − | 0.982358i | ||||
\(952\) | 3.29423 | + | 5.70577i | 0.106767 | + | 0.184925i | ||||
\(953\) | 12.2942 | − | 21.2942i | 0.398249 | − | 0.689788i | −0.595261 | − | 0.803533i | \(-0.702951\pi\) |
0.993510 | + | 0.113745i | \(0.0362846\pi\) | |||||||
\(954\) | −28.8564 | −0.934261 | ||||||||
\(955\) | −9.63397 | + | 16.6865i | −0.311748 | + | 0.539964i | ||||
\(956\) | 4.09808 | − | 7.09808i | 0.132541 | − | 0.229568i | ||||
\(957\) | 77.5692 | 2.50746 | ||||||||
\(958\) | −5.49038 | + | 9.50962i | −0.177386 | + | 0.307242i | ||||
\(959\) | 12.2942 | + | 21.2942i | 0.397001 | + | 0.687627i | ||||
\(960\) | −1.36603 | − | 2.36603i | −0.0440883 | − | 0.0763631i | ||||
\(961\) | −29.3923 | −0.948139 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.51666 | 0.0488737 | ||||||||
\(964\) | 4.33013 | + | 7.50000i | 0.139464 | + | 0.241559i | ||||
\(965\) | 2.19615 | + | 3.80385i | 0.0706966 | + | 0.122450i | ||||
\(966\) | 10.3923 | − | 18.0000i | 0.334367 | − | 0.579141i | ||||
\(967\) | 38.5692 | 1.24030 | 0.620151 | − | 0.784482i | \(-0.287071\pi\) | ||||
0.620151 | + | 0.784482i | \(0.287071\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | 19.3923 | − | 33.5885i | 0.622971 | − | 1.07902i | ||||
\(970\) | 15.1244 | 0.485614 | ||||||||
\(971\) | 23.3827 | − | 40.5000i | 0.750386 | − | 1.29971i | −0.197250 | − | 0.980353i | \(-0.563201\pi\) |
0.947636 | − | 0.319354i | \(-0.103466\pi\) | |||||||
\(972\) | −9.36603 | − | 16.2224i | −0.300415 | − | 0.520335i | ||||
\(973\) | −13.7942 | − | 23.8923i | −0.442223 | − | 0.765952i | ||||
\(974\) | 33.2487 | 1.06536 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.19615 | −0.134316 | ||||||||
\(977\) | −2.19615 | − | 3.80385i | −0.0702611 | − | 0.121696i | 0.828755 | − | 0.559612i | \(-0.189050\pi\) |
−0.899016 | + | 0.437916i | \(0.855717\pi\) | |||||||
\(978\) | 9.92820 | + | 17.1962i | 0.317469 | + | 0.549872i | ||||
\(979\) | −25.7942 | + | 44.6769i | −0.824387 | + | 1.42788i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | 34.5167 | − | 59.7846i | 1.10203 | − | 1.90878i | ||||
\(982\) | 1.66987 | − | 2.89230i | 0.0532878 | − | 0.0922972i | ||||
\(983\) | 38.5692 | 1.23017 | 0.615084 | − | 0.788462i | \(-0.289122\pi\) | ||||
0.615084 | + | 0.788462i | \(0.289122\pi\) | |||||||
\(984\) | −14.1962 | + | 24.5885i | −0.452557 | + | 0.783851i | ||||
\(985\) | 4.79423 | + | 8.30385i | 0.152757 | + | 0.264583i | ||||
\(986\) | 10.3923 | + | 18.0000i | 0.330958 | + | 0.573237i | ||||
\(987\) | −24.5885 | −0.782659 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.07180 | 0.161274 | ||||||||
\(990\) | 6.69615 | + | 11.5981i | 0.212818 | + | 0.368611i | ||||
\(991\) | −25.5885 | − | 44.3205i | −0.812844 | − | 1.40789i | −0.910866 | − | 0.412703i | \(-0.864585\pi\) |
0.0980215 | − | 0.995184i | \(-0.468749\pi\) | |||||||
\(992\) | −0.633975 | + | 1.09808i | −0.0201287 | + | 0.0348640i | ||||
\(993\) | 2.53590 | 0.0804743 | ||||||||
\(994\) | −9.00000 | + | 15.5885i | −0.285463 | + | 0.494436i | ||||
\(995\) | −7.19615 | + | 12.4641i | −0.228133 | + | 0.395139i | ||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | 21.2846 | − | 36.8660i | 0.674090 | − | 1.16756i | −0.302644 | − | 0.953104i | \(-0.597869\pi\) |
0.976734 | − | 0.214455i | \(-0.0687975\pi\) | |||||||
\(998\) | 0.928203 | + | 1.60770i | 0.0293818 | + | 0.0508907i | ||||
\(999\) | −22.3923 | − | 38.7846i | −0.708461 | − | 1.22709i |
(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 | 1690.2.e.l.991.2 | 4 | ||
13.2 | odd | 12 | 1690.2.d.f.1351.1 | 4 | |||
13.3 | even | 3 | 1690.2.a.m.1.1 | 2 | |||
13.4 | even | 6 | 1690.2.e.n.191.2 | 4 | |||
13.5 | odd | 4 | 1690.2.l.g.361.1 | 4 | |||
13.6 | odd | 12 | 130.2.l.a.121.2 | yes | 4 | ||
13.7 | odd | 12 | 1690.2.l.g.1161.1 | 4 | |||
13.8 | odd | 4 | 130.2.l.a.101.2 | ✓ | 4 | ||
13.9 | even | 3 | inner | 1690.2.e.l.191.2 | 4 | ||
13.10 | even | 6 | 1690.2.a.j.1.1 | 2 | |||
13.11 | odd | 12 | 1690.2.d.f.1351.3 | 4 | |||
13.12 | even | 2 | 1690.2.e.n.991.2 | 4 | |||
39.8 | even | 4 | 1170.2.bs.c.361.1 | 4 | |||
39.32 | even | 12 | 1170.2.bs.c.901.1 | 4 | |||
52.19 | even | 12 | 1040.2.da.a.641.1 | 4 | |||
52.47 | even | 4 | 1040.2.da.a.881.1 | 4 | |||
65.8 | even | 4 | 650.2.n.a.49.1 | 4 | |||
65.19 | odd | 12 | 650.2.m.a.251.1 | 4 | |||
65.29 | even | 6 | 8450.2.a.bf.1.2 | 2 | |||
65.32 | even | 12 | 650.2.n.a.199.1 | 4 | |||
65.34 | odd | 4 | 650.2.m.a.101.1 | 4 | |||
65.47 | even | 4 | 650.2.n.b.49.2 | 4 | |||
65.49 | even | 6 | 8450.2.a.bm.1.2 | 2 | |||
65.58 | even | 12 | 650.2.n.b.199.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.l.a.101.2 | ✓ | 4 | 13.8 | odd | 4 | ||
130.2.l.a.121.2 | yes | 4 | 13.6 | odd | 12 | ||
650.2.m.a.101.1 | 4 | 65.34 | odd | 4 | |||
650.2.m.a.251.1 | 4 | 65.19 | odd | 12 | |||
650.2.n.a.49.1 | 4 | 65.8 | even | 4 | |||
650.2.n.a.199.1 | 4 | 65.32 | even | 12 | |||
650.2.n.b.49.2 | 4 | 65.47 | even | 4 | |||
650.2.n.b.199.2 | 4 | 65.58 | even | 12 | |||
1040.2.da.a.641.1 | 4 | 52.19 | even | 12 | |||
1040.2.da.a.881.1 | 4 | 52.47 | even | 4 | |||
1170.2.bs.c.361.1 | 4 | 39.8 | even | 4 | |||
1170.2.bs.c.901.1 | 4 | 39.32 | even | 12 | |||
1690.2.a.j.1.1 | 2 | 13.10 | even | 6 | |||
1690.2.a.m.1.1 | 2 | 13.3 | even | 3 | |||
1690.2.d.f.1351.1 | 4 | 13.2 | odd | 12 | |||
1690.2.d.f.1351.3 | 4 | 13.11 | odd | 12 | |||
1690.2.e.l.191.2 | 4 | 13.9 | even | 3 | inner | ||
1690.2.e.l.991.2 | 4 | 1.1 | even | 1 | trivial | ||
1690.2.e.n.191.2 | 4 | 13.4 | even | 6 | |||
1690.2.e.n.991.2 | 4 | 13.12 | even | 2 | |||
1690.2.l.g.361.1 | 4 | 13.5 | odd | 4 | |||
1690.2.l.g.1161.1 | 4 | 13.7 | odd | 12 | |||
8450.2.a.bf.1.2 | 2 | 65.29 | even | 6 | |||
8450.2.a.bm.1.2 | 2 | 65.49 | even | 6 |