Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [130,2,Mod(101,130)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(130, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("130.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.l (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.03805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.121 |
Dual form | 130.2.l.a.101.2 |
$q$-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 \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 1.36603 | − | 2.36603i | 0.788675 | − | 1.36603i | −0.138104 | − | 0.990418i | \(-0.544101\pi\) |
0.926779 | − | 0.375608i | \(-0.122566\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 2.36603 | − | 1.36603i | 0.965926 | − | 0.557678i | ||||
\(7\) | −2.59808 | + | 1.50000i | −0.981981 | + | 0.566947i | −0.902867 | − | 0.429919i | \(-0.858542\pi\) |
−0.0791130 | + | 0.996866i | \(0.525209\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.23205 | − | 3.86603i | −0.744017 | − | 1.28868i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −2.59808 | − | 1.50000i | −0.783349 | − | 0.452267i | 0.0542666 | − | 0.998526i | \(-0.482718\pi\) |
−0.837616 | + | 0.546259i | \(0.816051\pi\) | |||||||
\(12\) | 2.73205 | 0.788675 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 2.36603 | + | 1.36603i | 0.610905 | + | 0.352706i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.09808 | + | 1.90192i | 0.266323 | + | 0.461284i | 0.967909 | − | 0.251300i | \(-0.0808580\pi\) |
−0.701587 | + | 0.712584i | \(0.747525\pi\) | |||||||
\(18\) | − | 4.46410i | − | 1.05220i | ||||||
\(19\) | −5.59808 | + | 3.23205i | −1.28429 | + | 0.741483i | −0.977629 | − | 0.210337i | \(-0.932544\pi\) |
−0.306658 | + | 0.951820i | \(0.599211\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | 8.19615i | 1.78855i | ||||||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | −1.26795 | + | 2.19615i | −0.264386 | + | 0.457929i | −0.967402 | − | 0.253244i | \(-0.918503\pi\) |
0.703017 | + | 0.711173i | \(0.251836\pi\) | |||||||
\(24\) | 2.36603 | + | 1.36603i | 0.482963 | + | 0.278839i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.46410 | + | 1.00000i | 0.679366 | + | 0.196116i | ||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | −2.59808 | − | 1.50000i | −0.490990 | − | 0.283473i | ||||
\(29\) | 4.73205 | − | 8.19615i | 0.878720 | − | 1.52199i | 0.0259731 | − | 0.999663i | \(-0.491732\pi\) |
0.852747 | − | 0.522325i | \(-0.174935\pi\) | |||||||
\(30\) | 1.36603 | + | 2.36603i | 0.249401 | + | 0.431975i | ||||
\(31\) | − | 1.26795i | − | 0.227730i | −0.993496 | − | 0.113865i | \(-0.963677\pi\) | ||
0.993496 | − | 0.113865i | \(-0.0363232\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −7.09808 | + | 4.09808i | −1.23562 | + | 0.713384i | ||||
\(34\) | 2.19615i | 0.376637i | ||||||||
\(35\) | −1.50000 | − | 2.59808i | −0.253546 | − | 0.439155i | ||||
\(36\) | 2.23205 | − | 3.86603i | 0.372008 | − | 0.644338i | ||||
\(37\) | 9.69615 | + | 5.59808i | 1.59404 | + | 0.920318i | 0.992604 | + | 0.121395i | \(0.0387368\pi\) |
0.601433 | + | 0.798923i | \(0.294597\pi\) | |||||||
\(38\) | −6.46410 | −1.04862 | ||||||||
\(39\) | 2.73205 | − | 9.46410i | 0.437478 | − | 1.51547i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.00000 | − | 5.19615i | −1.40556 | − | 0.811503i | −0.410608 | − | 0.911812i | \(-0.634683\pi\) |
−0.994956 | + | 0.100309i | \(0.968017\pi\) | |||||||
\(42\) | −4.09808 | + | 7.09808i | −0.632347 | + | 1.09526i | ||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | − | 3.00000i | − | 0.452267i | ||||||
\(45\) | 3.86603 | − | 2.23205i | 0.576313 | − | 0.332734i | ||||
\(46\) | −2.19615 | + | 1.26795i | −0.323805 | + | 0.186949i | ||||
\(47\) | − | 3.00000i | − | 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 1.36603 | + | 2.36603i | 0.197169 | + | 0.341506i | ||||
\(49\) | 1.00000 | − | 1.73205i | 0.142857 | − | 0.247436i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 2.50000 | + | 2.59808i | 0.346688 | + | 0.360288i | ||||
\(53\) | −6.46410 | −0.887913 | −0.443956 | − | 0.896048i | \(-0.646425\pi\) | ||||
−0.443956 | + | 0.896048i | \(0.646425\pi\) | |||||||
\(54\) | −3.46410 | − | 2.00000i | −0.471405 | − | 0.272166i | ||||
\(55\) | 1.50000 | − | 2.59808i | 0.202260 | − | 0.350325i | ||||
\(56\) | −1.50000 | − | 2.59808i | −0.200446 | − | 0.347183i | ||||
\(57\) | 17.6603i | 2.33916i | ||||||||
\(58\) | 8.19615 | − | 4.73205i | 1.07621 | − | 0.621349i | ||||
\(59\) | 9.00000 | − | 5.19615i | 1.17170 | − | 0.676481i | 0.217620 | − | 0.976034i | \(-0.430171\pi\) |
0.954080 | + | 0.299552i | \(0.0968372\pi\) | |||||||
\(60\) | 2.73205i | 0.352706i | ||||||||
\(61\) | 2.09808 | + | 3.63397i | 0.268631 | + | 0.465283i | 0.968509 | − | 0.248980i | \(-0.0800954\pi\) |
−0.699877 | + | 0.714263i | \(0.746762\pi\) | |||||||
\(62\) | 0.633975 | − | 1.09808i | 0.0805149 | − | 0.139456i | ||||
\(63\) | 11.5981 | + | 6.69615i | 1.46122 | + | 0.843636i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.866025 | + | 3.50000i | 0.107417 | + | 0.434122i | ||||
\(66\) | −8.19615 | −1.00888 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | −1.09808 | + | 1.90192i | −0.133161 | + | 0.230642i | ||||
\(69\) | 3.46410 | + | 6.00000i | 0.417029 | + | 0.722315i | ||||
\(70\) | − | 3.00000i | − | 0.358569i | ||||||
\(71\) | 5.19615 | − | 3.00000i | 0.616670 | − | 0.356034i | −0.158901 | − | 0.987294i | \(-0.550795\pi\) |
0.775571 | + | 0.631260i | \(0.217462\pi\) | |||||||
\(72\) | 3.86603 | − | 2.23205i | 0.455615 | − | 0.263050i | ||||
\(73\) | 5.66025i | 0.662483i | 0.943546 | + | 0.331241i | \(0.107467\pi\) | ||||
−0.943546 | + | 0.331241i | \(0.892533\pi\) | |||||||
\(74\) | 5.59808 | + | 9.69615i | 0.650763 | + | 1.12715i | ||||
\(75\) | −1.36603 | + | 2.36603i | −0.157735 | + | 0.273205i | ||||
\(76\) | −5.59808 | − | 3.23205i | −0.642143 | − | 0.370742i | ||||
\(77\) | 9.00000 | 1.02565 | ||||||||
\(78\) | 7.09808 | − | 6.83013i | 0.803699 | − | 0.773360i | ||||
\(79\) | 6.19615 | 0.697122 | 0.348561 | − | 0.937286i | \(-0.386670\pi\) | ||||
0.348561 | + | 0.937286i | \(0.386670\pi\) | |||||||
\(80\) | −0.866025 | − | 0.500000i | −0.0968246 | − | 0.0559017i | ||||
\(81\) | 1.23205 | − | 2.13397i | 0.136895 | − | 0.237108i | ||||
\(82\) | −5.19615 | − | 9.00000i | −0.573819 | − | 0.993884i | ||||
\(83\) | − | 2.19615i | − | 0.241059i | −0.992710 | − | 0.120530i | \(-0.961541\pi\) | ||
0.992710 | − | 0.120530i | \(-0.0384592\pi\) | |||||||
\(84\) | −7.09808 | + | 4.09808i | −0.774464 | + | 0.447137i | ||||
\(85\) | −1.90192 | + | 1.09808i | −0.206293 | + | 0.119103i | ||||
\(86\) | − | 2.00000i | − | 0.215666i | ||||||
\(87\) | −12.9282 | − | 22.3923i | −1.38605 | − | 2.40071i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −14.8923 | − | 8.59808i | −1.57858 | − | 0.911394i | −0.995058 | − | 0.0992979i | \(-0.968340\pi\) |
−0.583523 | − | 0.812096i | \(-0.698326\pi\) | |||||||
\(90\) | 4.46410 | 0.470558 | ||||||||
\(91\) | −7.79423 | + | 7.50000i | −0.817057 | + | 0.786214i | ||||
\(92\) | −2.53590 | −0.264386 | ||||||||
\(93\) | −3.00000 | − | 1.73205i | −0.311086 | − | 0.179605i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | −3.23205 | − | 5.59808i | −0.331601 | − | 0.574351i | ||||
\(96\) | 2.73205i | 0.278839i | ||||||||
\(97\) | 13.0981 | − | 7.56218i | 1.32991 | − | 0.767823i | 0.344623 | − | 0.938741i | \(-0.388007\pi\) |
0.985285 | + | 0.170918i | \(0.0546734\pi\) | |||||||
\(98\) | 1.73205 | − | 1.00000i | 0.174964 | − | 0.101015i | ||||
\(99\) | 13.3923i | 1.34598i | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.63397 | + | 6.29423i | −0.361594 | + | 0.626299i | −0.988223 | − | 0.153018i | \(-0.951101\pi\) |
0.626629 | + | 0.779317i | \(0.284434\pi\) | |||||||
\(102\) | 5.19615 | + | 3.00000i | 0.514496 | + | 0.297044i | ||||
\(103\) | 1.19615 | 0.117860 | 0.0589302 | − | 0.998262i | \(-0.481231\pi\) | ||||
0.0589302 | + | 0.998262i | \(0.481231\pi\) | |||||||
\(104\) | 0.866025 | + | 3.50000i | 0.0849208 | + | 0.343203i | ||||
\(105\) | −8.19615 | −0.799863 | ||||||||
\(106\) | −5.59808 | − | 3.23205i | −0.543733 | − | 0.313925i | ||||
\(107\) | −0.169873 | + | 0.294229i | −0.0164222 | + | 0.0284442i | −0.874120 | − | 0.485710i | \(-0.838561\pi\) |
0.857697 | + | 0.514155i | \(0.171894\pi\) | |||||||
\(108\) | −2.00000 | − | 3.46410i | −0.192450 | − | 0.333333i | ||||
\(109\) | 15.4641i | 1.48119i | 0.671950 | + | 0.740596i | \(0.265457\pi\) | ||||
−0.671950 | + | 0.740596i | \(0.734543\pi\) | |||||||
\(110\) | 2.59808 | − | 1.50000i | 0.247717 | − | 0.143019i | ||||
\(111\) | 26.4904 | − | 15.2942i | 2.51436 | − | 1.45166i | ||||
\(112\) | − | 3.00000i | − | 0.283473i | ||||||
\(113\) | 3.46410 | + | 6.00000i | 0.325875 | + | 0.564433i | 0.981689 | − | 0.190490i | \(-0.0610077\pi\) |
−0.655814 | + | 0.754923i | \(0.727674\pi\) | |||||||
\(114\) | −8.83013 | + | 15.2942i | −0.827017 | + | 1.43244i | ||||
\(115\) | −2.19615 | − | 1.26795i | −0.204792 | − | 0.118237i | ||||
\(116\) | 9.46410 | 0.878720 | ||||||||
\(117\) | −11.1603 | − | 11.5981i | −1.03177 | − | 1.07224i | ||||
\(118\) | 10.3923 | 0.956689 | ||||||||
\(119\) | −5.70577 | − | 3.29423i | −0.523047 | − | 0.301981i | ||||
\(120\) | −1.36603 | + | 2.36603i | −0.124700 | + | 0.215988i | ||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 4.19615i | 0.379902i | ||||||||
\(123\) | −24.5885 | + | 14.1962i | −2.21707 | + | 1.28002i | ||||
\(124\) | 1.09808 | − | 0.633975i | 0.0986102 | − | 0.0569326i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 6.69615 | + | 11.5981i | 0.596541 | + | 1.03324i | ||||
\(127\) | −10.5981 | + | 18.3564i | −0.940427 | + | 1.62887i | −0.175769 | + | 0.984431i | \(0.556241\pi\) |
−0.764658 | + | 0.644436i | \(0.777092\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −5.46410 | −0.481087 | ||||||||
\(130\) | −1.00000 | + | 3.46410i | −0.0877058 | + | 0.303822i | ||||
\(131\) | −18.1244 | −1.58353 | −0.791766 | − | 0.610824i | \(-0.790838\pi\) | ||||
−0.791766 | + | 0.610824i | \(0.790838\pi\) | |||||||
\(132\) | −7.09808 | − | 4.09808i | −0.617808 | − | 0.356692i | ||||
\(133\) | 9.69615 | − | 16.7942i | 0.840763 | − | 1.45624i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 4.00000i | − | 0.344265i | ||||||
\(136\) | −1.90192 | + | 1.09808i | −0.163089 | + | 0.0941593i | ||||
\(137\) | 7.09808 | − | 4.09808i | 0.606430 | − | 0.350122i | −0.165137 | − | 0.986271i | \(-0.552807\pi\) |
0.771567 | + | 0.636148i | \(0.219473\pi\) | |||||||
\(138\) | 6.92820i | 0.589768i | ||||||||
\(139\) | 4.59808 | + | 7.96410i | 0.390004 | + | 0.675506i | 0.992450 | − | 0.122653i | \(-0.0391404\pi\) |
−0.602446 | + | 0.798160i | \(0.705807\pi\) | |||||||
\(140\) | 1.50000 | − | 2.59808i | 0.126773 | − | 0.219578i | ||||
\(141\) | −7.09808 | − | 4.09808i | −0.597766 | − | 0.345120i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −10.3923 | − | 3.00000i | −0.869048 | − | 0.250873i | ||||
\(144\) | 4.46410 | 0.372008 | ||||||||
\(145\) | 8.19615 | + | 4.73205i | 0.680653 | + | 0.392975i | ||||
\(146\) | −2.83013 | + | 4.90192i | −0.234223 | + | 0.405686i | ||||
\(147\) | −2.73205 | − | 4.73205i | −0.225336 | − | 0.390293i | ||||
\(148\) | 11.1962i | 0.920318i | ||||||||
\(149\) | −5.19615 | + | 3.00000i | −0.425685 | + | 0.245770i | −0.697507 | − | 0.716578i | \(-0.745707\pi\) |
0.271821 | + | 0.962348i | \(0.412374\pi\) | |||||||
\(150\) | −2.36603 | + | 1.36603i | −0.193185 | + | 0.111536i | ||||
\(151\) | 6.33975i | 0.515921i | 0.966155 | + | 0.257961i | \(0.0830505\pi\) | ||||
−0.966155 | + | 0.257961i | \(0.916950\pi\) | |||||||
\(152\) | −3.23205 | − | 5.59808i | −0.262154 | − | 0.454064i | ||||
\(153\) | 4.90192 | − | 8.49038i | 0.396297 | − | 0.686407i | ||||
\(154\) | 7.79423 | + | 4.50000i | 0.628077 | + | 0.362620i | ||||
\(155\) | 1.26795 | 0.101844 | ||||||||
\(156\) | 9.56218 | − | 2.36603i | 0.765587 | − | 0.189434i | ||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | 5.36603 | + | 3.09808i | 0.426898 | + | 0.246470i | ||||
\(159\) | −8.83013 | + | 15.2942i | −0.700275 | + | 1.21291i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | − | 7.60770i | − | 0.599570i | ||||||
\(162\) | 2.13397 | − | 1.23205i | 0.167661 | − | 0.0967991i | ||||
\(163\) | 6.29423 | − | 3.63397i | 0.493002 | − | 0.284635i | −0.232817 | − | 0.972521i | \(-0.574794\pi\) |
0.725819 | + | 0.687886i | \(0.241461\pi\) | |||||||
\(164\) | − | 10.3923i | − | 0.811503i | ||||||
\(165\) | −4.09808 | − | 7.09808i | −0.319035 | − | 0.552584i | ||||
\(166\) | 1.09808 | − | 1.90192i | 0.0852272 | − | 0.147618i | ||||
\(167\) | −2.59808 | − | 1.50000i | −0.201045 | − | 0.116073i | 0.396098 | − | 0.918208i | \(-0.370364\pi\) |
−0.597143 | + | 0.802135i | \(0.703697\pi\) | |||||||
\(168\) | −8.19615 | −0.632347 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | −2.19615 | −0.168437 | ||||||||
\(171\) | 24.9904 | + | 14.4282i | 1.91106 | + | 1.10335i | ||||
\(172\) | 1.00000 | − | 1.73205i | 0.0762493 | − | 0.132068i | ||||
\(173\) | 7.50000 | + | 12.9904i | 0.570214 | + | 0.987640i | 0.996544 | + | 0.0830722i | \(0.0264732\pi\) |
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(174\) | − | 25.8564i | − | 1.96017i | ||||||
\(175\) | 2.59808 | − | 1.50000i | 0.196396 | − | 0.113389i | ||||
\(176\) | 2.59808 | − | 1.50000i | 0.195837 | − | 0.113067i | ||||
\(177\) | − | 28.3923i | − | 2.13410i | ||||||
\(178\) | −8.59808 | − | 14.8923i | −0.644453 | − | 1.11623i | ||||
\(179\) | 1.26795 | − | 2.19615i | 0.0947710 | − | 0.164148i | −0.814742 | − | 0.579824i | \(-0.803121\pi\) |
0.909513 | + | 0.415675i | \(0.136455\pi\) | |||||||
\(180\) | 3.86603 | + | 2.23205i | 0.288157 | + | 0.166367i | ||||
\(181\) | −16.5885 | −1.23301 | −0.616505 | − | 0.787351i | \(-0.711452\pi\) | ||||
−0.616505 | + | 0.787351i | \(0.711452\pi\) | |||||||
\(182\) | −10.5000 | + | 2.59808i | −0.778312 | + | 0.192582i | ||||
\(183\) | 11.4641 | 0.847451 | ||||||||
\(184\) | −2.19615 | − | 1.26795i | −0.161903 | − | 0.0934745i | ||||
\(185\) | −5.59808 | + | 9.69615i | −0.411579 | + | 0.712875i | ||||
\(186\) | −1.73205 | − | 3.00000i | −0.127000 | − | 0.219971i | ||||
\(187\) | − | 6.58846i | − | 0.481796i | ||||||
\(188\) | 2.59808 | − | 1.50000i | 0.189484 | − | 0.109399i | ||||
\(189\) | 10.3923 | − | 6.00000i | 0.755929 | − | 0.436436i | ||||
\(190\) | − | 6.46410i | − | 0.468955i | ||||||
\(191\) | 9.63397 | + | 16.6865i | 0.697090 | + | 1.20740i | 0.969471 | + | 0.245206i | \(0.0788555\pi\) |
−0.272381 | + | 0.962189i | \(0.587811\pi\) | |||||||
\(192\) | −1.36603 | + | 2.36603i | −0.0985844 | + | 0.170753i | ||||
\(193\) | −3.80385 | − | 2.19615i | −0.273807 | − | 0.158083i | 0.356809 | − | 0.934177i | \(-0.383865\pi\) |
−0.630616 | + | 0.776095i | \(0.717198\pi\) | |||||||
\(194\) | 15.1244 | 1.08587 | ||||||||
\(195\) | 9.46410 | + | 2.73205i | 0.677738 | + | 0.195646i | ||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 8.30385 | + | 4.79423i | 0.591625 | + | 0.341575i | 0.765740 | − | 0.643151i | \(-0.222373\pi\) |
−0.174115 | + | 0.984725i | \(0.555706\pi\) | |||||||
\(198\) | −6.69615 | + | 11.5981i | −0.475875 | + | 0.824239i | ||||
\(199\) | −7.19615 | − | 12.4641i | −0.510122 | − | 0.883557i | −0.999931 | − | 0.0117273i | \(-0.996267\pi\) |
0.489810 | − | 0.871829i | \(-0.337066\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.29423 | + | 3.63397i | −0.442860 | + | 0.255686i | ||||
\(203\) | 28.3923i | 1.99275i | ||||||||
\(204\) | 3.00000 | + | 5.19615i | 0.210042 | + | 0.363803i | ||||
\(205\) | 5.19615 | − | 9.00000i | 0.362915 | − | 0.628587i | ||||
\(206\) | 1.03590 | + | 0.598076i | 0.0721745 | + | 0.0416699i | ||||
\(207\) | 11.3205 | 0.786830 | ||||||||
\(208\) | −1.00000 | + | 3.46410i | −0.0693375 | + | 0.240192i | ||||
\(209\) | 19.3923 | 1.34139 | ||||||||
\(210\) | −7.09808 | − | 4.09808i | −0.489814 | − | 0.282794i | ||||
\(211\) | −6.79423 | + | 11.7679i | −0.467734 | + | 0.810139i | −0.999320 | − | 0.0368651i | \(-0.988263\pi\) |
0.531586 | + | 0.847004i | \(0.321596\pi\) | |||||||
\(212\) | −3.23205 | − | 5.59808i | −0.221978 | − | 0.384477i | ||||
\(213\) | − | 16.3923i | − | 1.12318i | ||||||
\(214\) | −0.294229 | + | 0.169873i | −0.0201131 | + | 0.0116123i | ||||
\(215\) | 1.73205 | − | 1.00000i | 0.118125 | − | 0.0681994i | ||||
\(216\) | − | 4.00000i | − | 0.272166i | ||||||
\(217\) | 1.90192 | + | 3.29423i | 0.129111 | + | 0.223627i | ||||
\(218\) | −7.73205 | + | 13.3923i | −0.523681 | + | 0.907041i | ||||
\(219\) | 13.3923 | + | 7.73205i | 0.904968 | + | 0.522484i | ||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | 5.49038 | + | 5.70577i | 0.369323 | + | 0.383812i | ||||
\(222\) | 30.5885 | 2.05296 | ||||||||
\(223\) | −0.401924 | − | 0.232051i | −0.0269148 | − | 0.0155393i | 0.486482 | − | 0.873690i | \(-0.338280\pi\) |
−0.513397 | + | 0.858151i | \(0.671613\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | 2.23205 | + | 3.86603i | 0.148803 | + | 0.257735i | ||||
\(226\) | 6.92820i | 0.460857i | ||||||||
\(227\) | 3.80385 | − | 2.19615i | 0.252470 | − | 0.145764i | −0.368425 | − | 0.929658i | \(-0.620103\pi\) |
0.620895 | + | 0.783894i | \(0.286769\pi\) | |||||||
\(228\) | −15.2942 | + | 8.83013i | −1.01289 | + | 0.584789i | ||||
\(229\) | 4.73205i | 0.312703i | 0.987701 | + | 0.156351i | \(0.0499732\pi\) | ||||
−0.987701 | + | 0.156351i | \(0.950027\pi\) | |||||||
\(230\) | −1.26795 | − | 2.19615i | −0.0836061 | − | 0.144810i | ||||
\(231\) | 12.2942 | − | 21.2942i | 0.808901 | − | 1.40106i | ||||
\(232\) | 8.19615 | + | 4.73205i | 0.538104 | + | 0.310674i | ||||
\(233\) | 1.26795 | 0.0830661 | 0.0415331 | − | 0.999137i | \(-0.486776\pi\) | ||||
0.0415331 | + | 0.999137i | \(0.486776\pi\) | |||||||
\(234\) | −3.86603 | − | 15.6244i | −0.252730 | − | 1.02140i | ||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 9.00000 | + | 5.19615i | 0.585850 | + | 0.338241i | ||||
\(237\) | 8.46410 | − | 14.6603i | 0.549802 | − | 0.952286i | ||||
\(238\) | −3.29423 | − | 5.70577i | −0.213533 | − | 0.369850i | ||||
\(239\) | 8.19615i | 0.530165i | 0.964226 | + | 0.265083i | \(0.0853992\pi\) | ||||
−0.964226 | + | 0.265083i | \(0.914601\pi\) | |||||||
\(240\) | −2.36603 | + | 1.36603i | −0.152726 | + | 0.0881766i | ||||
\(241\) | −7.50000 | + | 4.33013i | −0.483117 | + | 0.278928i | −0.721715 | − | 0.692191i | \(-0.756646\pi\) |
0.238597 | + | 0.971119i | \(0.423312\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | −9.36603 | − | 16.2224i | −0.600831 | − | 1.04067i | ||||
\(244\) | −2.09808 | + | 3.63397i | −0.134316 | + | 0.232641i | ||||
\(245\) | 1.73205 | + | 1.00000i | 0.110657 | + | 0.0638877i | ||||
\(246\) | −28.3923 | −1.81023 | ||||||||
\(247\) | −16.7942 | + | 16.1603i | −1.06859 | + | 1.02825i | ||||
\(248\) | 1.26795 | 0.0805149 | ||||||||
\(249\) | −5.19615 | − | 3.00000i | −0.329293 | − | 0.190117i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −3.40192 | − | 5.89230i | −0.214728 | − | 0.371919i | 0.738461 | − | 0.674296i | \(-0.235553\pi\) |
−0.953188 | + | 0.302378i | \(0.902220\pi\) | |||||||
\(252\) | 13.3923i | 0.843636i | ||||||||
\(253\) | 6.58846 | − | 3.80385i | 0.414213 | − | 0.239146i | ||||
\(254\) | −18.3564 | + | 10.5981i | −1.15178 | + | 0.664982i | ||||
\(255\) | 6.00000i | 0.375735i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.92820 | + | 12.0000i | −0.432169 | + | 0.748539i | −0.997060 | − | 0.0766265i | \(-0.975585\pi\) |
0.564890 | + | 0.825166i | \(0.308918\pi\) | |||||||
\(258\) | −4.73205 | − | 2.73205i | −0.294605 | − | 0.170090i | ||||
\(259\) | −33.5885 | −2.08709 | ||||||||
\(260\) | −2.59808 | + | 2.50000i | −0.161126 | + | 0.155043i | ||||
\(261\) | −42.2487 | −2.61513 | ||||||||
\(262\) | −15.6962 | − | 9.06218i | −0.969712 | − | 0.559863i | ||||
\(263\) | 13.7942 | − | 23.8923i | 0.850589 | − | 1.47326i | −0.0300894 | − | 0.999547i | \(-0.509579\pi\) |
0.880678 | − | 0.473715i | \(-0.157087\pi\) | |||||||
\(264\) | −4.09808 | − | 7.09808i | −0.252219 | − | 0.436856i | ||||
\(265\) | − | 6.46410i | − | 0.397087i | ||||||
\(266\) | 16.7942 | − | 9.69615i | 1.02972 | − | 0.594509i | ||||
\(267\) | −40.6865 | + | 23.4904i | −2.48998 | + | 1.43759i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.43782 | + | 2.49038i | 0.0876656 | + | 0.151841i | 0.906524 | − | 0.422154i | \(-0.138726\pi\) |
−0.818858 | + | 0.573996i | \(0.805393\pi\) | |||||||
\(270\) | 2.00000 | − | 3.46410i | 0.121716 | − | 0.210819i | ||||
\(271\) | −2.19615 | − | 1.26795i | −0.133407 | − | 0.0770224i | 0.431811 | − | 0.901964i | \(-0.357875\pi\) |
−0.565218 | + | 0.824942i | \(0.691208\pi\) | |||||||
\(272\) | −2.19615 | −0.133161 | ||||||||
\(273\) | 7.09808 | + | 28.6865i | 0.429595 | + | 1.73619i | ||||
\(274\) | 8.19615 | 0.495148 | ||||||||
\(275\) | 2.59808 | + | 1.50000i | 0.156670 | + | 0.0904534i | ||||
\(276\) | −3.46410 | + | 6.00000i | −0.208514 | + | 0.361158i | ||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | 9.19615i | 0.551549i | ||||||||
\(279\) | −4.90192 | + | 2.83013i | −0.293471 | + | 0.169435i | ||||
\(280\) | 2.59808 | − | 1.50000i | 0.155265 | − | 0.0896421i | ||||
\(281\) | − | 10.3923i | − | 0.619953i | −0.950744 | − | 0.309976i | \(-0.899679\pi\) | ||
0.950744 | − | 0.309976i | \(-0.100321\pi\) | |||||||
\(282\) | −4.09808 | − | 7.09808i | −0.244037 | − | 0.422684i | ||||
\(283\) | 15.1962 | − | 26.3205i | 0.903317 | − | 1.56459i | 0.0801576 | − | 0.996782i | \(-0.474458\pi\) |
0.823160 | − | 0.567810i | \(-0.192209\pi\) | |||||||
\(284\) | 5.19615 | + | 3.00000i | 0.308335 | + | 0.178017i | ||||
\(285\) | −17.6603 | −1.04610 | ||||||||
\(286\) | −7.50000 | − | 7.79423i | −0.443484 | − | 0.460882i | ||||
\(287\) | 31.1769 | 1.84032 | ||||||||
\(288\) | 3.86603 | + | 2.23205i | 0.227808 | + | 0.131525i | ||||
\(289\) | 6.08846 | − | 10.5455i | 0.358145 | − | 0.620325i | ||||
\(290\) | 4.73205 | + | 8.19615i | 0.277876 | + | 0.481295i | ||||
\(291\) | − | 41.3205i | − | 2.42225i | ||||||
\(292\) | −4.90192 | + | 2.83013i | −0.286863 | + | 0.165621i | ||||
\(293\) | −0.696152 | + | 0.401924i | −0.0406697 | + | 0.0234806i | −0.520197 | − | 0.854046i | \(-0.674141\pi\) |
0.479527 | + | 0.877527i | \(0.340808\pi\) | |||||||
\(294\) | − | 5.46410i | − | 0.318673i | ||||||
\(295\) | 5.19615 | + | 9.00000i | 0.302532 | + | 0.524000i | ||||
\(296\) | −5.59808 | + | 9.69615i | −0.325382 | + | 0.563577i | ||||
\(297\) | 10.3923 | + | 6.00000i | 0.603023 | + | 0.348155i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −2.53590 | + | 8.78461i | −0.146655 | + | 0.508027i | ||||
\(300\) | −2.73205 | −0.157735 | ||||||||
\(301\) | 5.19615 | + | 3.00000i | 0.299501 | + | 0.172917i | ||||
\(302\) | −3.16987 | + | 5.49038i | −0.182406 | + | 0.315936i | ||||
\(303\) | 9.92820 | + | 17.1962i | 0.570360 | + | 0.987893i | ||||
\(304\) | − | 6.46410i | − | 0.370742i | ||||||
\(305\) | −3.63397 | + | 2.09808i | −0.208081 | + | 0.120135i | ||||
\(306\) | 8.49038 | − | 4.90192i | 0.485363 | − | 0.280224i | ||||
\(307\) | 20.5359i | 1.17205i | 0.810295 | + | 0.586023i | \(0.199307\pi\) | ||||
−0.810295 | + | 0.586023i | \(0.800693\pi\) | |||||||
\(308\) | 4.50000 | + | 7.79423i | 0.256411 | + | 0.444117i | ||||
\(309\) | 1.63397 | − | 2.83013i | 0.0929536 | − | 0.161000i | ||||
\(310\) | 1.09808 | + | 0.633975i | 0.0623665 | + | 0.0360073i | ||||
\(311\) | 15.1244 | 0.857624 | 0.428812 | − | 0.903394i | \(-0.358932\pi\) | ||||
0.428812 | + | 0.903394i | \(0.358932\pi\) | |||||||
\(312\) | 9.46410 | + | 2.73205i | 0.535799 | + | 0.154672i | ||||
\(313\) | 5.60770 | 0.316966 | 0.158483 | − | 0.987362i | \(-0.449340\pi\) | ||||
0.158483 | + | 0.987362i | \(0.449340\pi\) | |||||||
\(314\) | −11.2583 | − | 6.50000i | −0.635344 | − | 0.366816i | ||||
\(315\) | −6.69615 | + | 11.5981i | −0.377285 | + | 0.653478i | ||||
\(316\) | 3.09808 | + | 5.36603i | 0.174280 | + | 0.301863i | ||||
\(317\) | 12.8038i | 0.719136i | 0.933119 | + | 0.359568i | \(0.117076\pi\) | ||||
−0.933119 | + | 0.359568i | \(0.882924\pi\) | |||||||
\(318\) | −15.2942 | + | 8.83013i | −0.857658 | + | 0.495169i | ||||
\(319\) | −24.5885 | + | 14.1962i | −1.37669 | + | 0.794832i | ||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 0.464102 | + | 0.803848i | 0.0259036 | + | 0.0448664i | ||||
\(322\) | 3.80385 | − | 6.58846i | 0.211980 | − | 0.367160i | ||||
\(323\) | −12.2942 | − | 7.09808i | −0.684069 | − | 0.394948i | ||||
\(324\) | 2.46410 | 0.136895 | ||||||||
\(325\) | −3.50000 | + | 0.866025i | −0.194145 | + | 0.0480384i | ||||
\(326\) | 7.26795 | 0.402534 | ||||||||
\(327\) | 36.5885 | + | 21.1244i | 2.02335 | + | 1.16818i | ||||
\(328\) | 5.19615 | − | 9.00000i | 0.286910 | − | 0.496942i | ||||
\(329\) | 4.50000 | + | 7.79423i | 0.248093 | + | 0.429710i | ||||
\(330\) | − | 8.19615i | − | 0.451183i | ||||||
\(331\) | 0.803848 | − | 0.464102i | 0.0441835 | − | 0.0255093i | −0.477746 | − | 0.878498i | \(-0.658546\pi\) |
0.521929 | + | 0.852989i | \(0.325213\pi\) | |||||||
\(332\) | 1.90192 | − | 1.09808i | 0.104382 | − | 0.0602648i | ||||
\(333\) | − | 49.9808i | − | 2.73893i | ||||||
\(334\) | −1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.09808 | − | 4.09808i | −0.387232 | − | 0.223568i | ||||
\(337\) | −4.19615 | −0.228579 | −0.114289 | − | 0.993447i | \(-0.536459\pi\) | ||||
−0.114289 | + | 0.993447i | \(0.536459\pi\) | |||||||
\(338\) | 12.9904 | + | 0.500000i | 0.706584 | + | 0.0271964i | ||||
\(339\) | 18.9282 | 1.02804 | ||||||||
\(340\) | −1.90192 | − | 1.09808i | −0.103146 | − | 0.0595515i | ||||
\(341\) | −1.90192 | + | 3.29423i | −0.102995 | + | 0.178392i | ||||
\(342\) | 14.4282 | + | 24.9904i | 0.780188 | + | 1.35133i | ||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | 1.73205 | − | 1.00000i | 0.0933859 | − | 0.0539164i | ||||
\(345\) | −6.00000 | + | 3.46410i | −0.323029 | + | 0.186501i | ||||
\(346\) | 15.0000i | 0.806405i | ||||||||
\(347\) | 12.6340 | + | 21.8827i | 0.678227 | + | 1.17472i | 0.975514 | + | 0.219936i | \(0.0705848\pi\) |
−0.297287 | + | 0.954788i | \(0.596082\pi\) | |||||||
\(348\) | 12.9282 | − | 22.3923i | 0.693024 | − | 1.20035i | ||||
\(349\) | −29.4904 | − | 17.0263i | −1.57858 | − | 0.911396i | −0.995057 | − | 0.0993018i | \(-0.968339\pi\) |
−0.583527 | − | 0.812094i | \(-0.698328\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | −14.0000 | + | 3.46410i | −0.747265 | + | 0.184900i | ||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | −17.4904 | − | 10.0981i | −0.930919 | − | 0.537466i | −0.0438169 | − | 0.999040i | \(-0.513952\pi\) |
−0.887102 | + | 0.461573i | \(0.847285\pi\) | |||||||
\(354\) | 14.1962 | − | 24.5885i | 0.754517 | − | 1.30686i | ||||
\(355\) | 3.00000 | + | 5.19615i | 0.159223 | + | 0.275783i | ||||
\(356\) | − | 17.1962i | − | 0.911394i | ||||||
\(357\) | −15.5885 | + | 9.00000i | −0.825029 | + | 0.476331i | ||||
\(358\) | 2.19615 | − | 1.26795i | 0.116070 | − | 0.0670132i | ||||
\(359\) | − | 22.3923i | − | 1.18182i | −0.806737 | − | 0.590910i | \(-0.798769\pi\) | ||
0.806737 | − | 0.590910i | \(-0.201231\pi\) | |||||||
\(360\) | 2.23205 | + | 3.86603i | 0.117639 | + | 0.203757i | ||||
\(361\) | 11.3923 | − | 19.7321i | 0.599595 | − | 1.03853i | ||||
\(362\) | −14.3660 | − | 8.29423i | −0.755062 | − | 0.435935i | ||||
\(363\) | −5.46410 | −0.286791 | ||||||||
\(364\) | −10.3923 | − | 3.00000i | −0.544705 | − | 0.157243i | ||||
\(365\) | −5.66025 | −0.296271 | ||||||||
\(366\) | 9.92820 | + | 5.73205i | 0.518955 | + | 0.299619i | ||||
\(367\) | 13.1962 | − | 22.8564i | 0.688834 | − | 1.19309i | −0.283382 | − | 0.959007i | \(-0.591456\pi\) |
0.972216 | − | 0.234088i | \(-0.0752102\pi\) | |||||||
\(368\) | −1.26795 | − | 2.19615i | −0.0660964 | − | 0.114482i | ||||
\(369\) | 46.3923i | 2.41509i | ||||||||
\(370\) | −9.69615 | + | 5.59808i | −0.504079 | + | 0.291030i | ||||
\(371\) | 16.7942 | − | 9.69615i | 0.871913 | − | 0.503399i | ||||
\(372\) | − | 3.46410i | − | 0.179605i | ||||||
\(373\) | −10.1962 | − | 17.6603i | −0.527937 | − | 0.914413i | −0.999470 | − | 0.0325648i | \(-0.989632\pi\) |
0.471533 | − | 0.881848i | \(-0.343701\pi\) | |||||||
\(374\) | 3.29423 | − | 5.70577i | 0.170341 | − | 0.295038i | ||||
\(375\) | −2.36603 | − | 1.36603i | −0.122181 | − | 0.0705412i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 9.46410 | − | 32.7846i | 0.487426 | − | 1.68849i | ||||
\(378\) | 12.0000 | 0.617213 | ||||||||
\(379\) | 10.2058 | + | 5.89230i | 0.524235 | + | 0.302667i | 0.738666 | − | 0.674072i | \(-0.235456\pi\) |
−0.214430 | + | 0.976739i | \(0.568790\pi\) | |||||||
\(380\) | 3.23205 | − | 5.59808i | 0.165801 | − | 0.287175i | ||||
\(381\) | 28.9545 | + | 50.1506i | 1.48338 | + | 2.56929i | ||||
\(382\) | 19.2679i | 0.985834i | ||||||||
\(383\) | −1.39230 | + | 0.803848i | −0.0711435 | + | 0.0410747i | −0.535150 | − | 0.844757i | \(-0.679745\pi\) |
0.464006 | + | 0.885832i | \(0.346411\pi\) | |||||||
\(384\) | −2.36603 | + | 1.36603i | −0.120741 | + | 0.0697097i | ||||
\(385\) | 9.00000i | 0.458682i | ||||||||
\(386\) | −2.19615 | − | 3.80385i | −0.111781 | − | 0.193611i | ||||
\(387\) | −4.46410 | + | 7.73205i | −0.226923 | + | 0.393042i | ||||
\(388\) | 13.0981 | + | 7.56218i | 0.664954 | + | 0.383911i | ||||
\(389\) | 19.2679 | 0.976924 | 0.488462 | − | 0.872585i | \(-0.337558\pi\) | ||||
0.488462 | + | 0.872585i | \(0.337558\pi\) | |||||||
\(390\) | 6.83013 | + | 7.09808i | 0.345857 | + | 0.359425i | ||||
\(391\) | −5.56922 | −0.281648 | ||||||||
\(392\) | 1.73205 | + | 1.00000i | 0.0874818 | + | 0.0505076i | ||||
\(393\) | −24.7583 | + | 42.8827i | −1.24889 | + | 2.16315i | ||||
\(394\) | 4.79423 | + | 8.30385i | 0.241530 | + | 0.418342i | ||||
\(395\) | 6.19615i | 0.311762i | ||||||||
\(396\) | −11.5981 | + | 6.69615i | −0.582825 | + | 0.336494i | ||||
\(397\) | 0.696152 | − | 0.401924i | 0.0349389 | − | 0.0201720i | −0.482429 | − | 0.875935i | \(-0.660245\pi\) |
0.517368 | + | 0.855763i | \(0.326912\pi\) | |||||||
\(398\) | − | 14.3923i | − | 0.721421i | ||||||
\(399\) | −26.4904 | − | 45.8827i | −1.32618 | − | 2.29701i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −4.50000 | − | 2.59808i | −0.224719 | − | 0.129742i | 0.383414 | − | 0.923576i | \(-0.374748\pi\) |
−0.608134 | + | 0.793835i | \(0.708081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.09808 | − | 4.43782i | −0.0546991 | − | 0.221064i | ||||
\(404\) | −7.26795 | −0.361594 | ||||||||
\(405\) | 2.13397 | + | 1.23205i | 0.106038 | + | 0.0612211i | ||||
\(406\) | −14.1962 | + | 24.5885i | −0.704543 | + | 1.22030i | ||||
\(407\) | −16.7942 | − | 29.0885i | −0.832459 | − | 1.44186i | ||||
\(408\) | 6.00000i | 0.297044i | ||||||||
\(409\) | 17.0885 | − | 9.86603i | 0.844970 | − | 0.487844i | −0.0139806 | − | 0.999902i | \(-0.504450\pi\) |
0.858950 | + | 0.512059i | \(0.171117\pi\) | |||||||
\(410\) | 9.00000 | − | 5.19615i | 0.444478 | − | 0.256620i | ||||
\(411\) | − | 22.3923i | − | 1.10453i | ||||||
\(412\) | 0.598076 | + | 1.03590i | 0.0294651 | + | 0.0510351i | ||||
\(413\) | −15.5885 | + | 27.0000i | −0.767058 | + | 1.32858i | ||||
\(414\) | 9.80385 | + | 5.66025i | 0.481833 | + | 0.278186i | ||||
\(415\) | 2.19615 | 0.107805 | ||||||||
\(416\) | −2.59808 | + | 2.50000i | −0.127381 | + | 0.122573i | ||||
\(417\) | 25.1244 | 1.23034 | ||||||||
\(418\) | 16.7942 | + | 9.69615i | 0.821433 | + | 0.474254i | ||||
\(419\) | −8.66025 | + | 15.0000i | −0.423081 | + | 0.732798i | −0.996239 | − | 0.0866469i | \(-0.972385\pi\) |
0.573158 | + | 0.819445i | \(0.305718\pi\) | |||||||
\(420\) | −4.09808 | − | 7.09808i | −0.199966 | − | 0.346351i | ||||
\(421\) | − | 27.1244i | − | 1.32196i | −0.750403 | − | 0.660980i | \(-0.770141\pi\) | ||
0.750403 | − | 0.660980i | \(-0.229859\pi\) | |||||||
\(422\) | −11.7679 | + | 6.79423i | −0.572855 | + | 0.330738i | ||||
\(423\) | −11.5981 | + | 6.69615i | −0.563918 | + | 0.325578i | ||||
\(424\) | − | 6.46410i | − | 0.313925i | ||||||
\(425\) | −1.09808 | − | 1.90192i | −0.0532645 | − | 0.0922569i | ||||
\(426\) | 8.19615 | − | 14.1962i | 0.397105 | − | 0.687806i | ||||
\(427\) | −10.9019 | − | 6.29423i | −0.527581 | − | 0.304599i | ||||
\(428\) | −0.339746 | −0.0164222 | ||||||||
\(429\) | −21.2942 | + | 20.4904i | −1.02810 | + | 0.989285i | ||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | −1.90192 | − | 1.09808i | −0.0916124 | − | 0.0528925i | 0.453494 | − | 0.891259i | \(-0.350177\pi\) |
−0.545106 | + | 0.838367i | \(0.683511\pi\) | |||||||
\(432\) | 2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | ||||
\(433\) | 6.19615 | + | 10.7321i | 0.297768 | + | 0.515749i | 0.975625 | − | 0.219444i | \(-0.0704245\pi\) |
−0.677857 | + | 0.735194i | \(0.737091\pi\) | |||||||
\(434\) | 3.80385i | 0.182591i | ||||||||
\(435\) | 22.3923 | − | 12.9282i | 1.07363 | − | 0.619860i | ||||
\(436\) | −13.3923 | + | 7.73205i | −0.641375 | + | 0.370298i | ||||
\(437\) | − | 16.3923i | − | 0.784150i | ||||||
\(438\) | 7.73205 | + | 13.3923i | 0.369452 | + | 0.639909i | ||||
\(439\) | 17.2942 | − | 29.9545i | 0.825408 | − | 1.42965i | −0.0761982 | − | 0.997093i | \(-0.524278\pi\) |
0.901607 | − | 0.432557i | \(-0.142388\pi\) | |||||||
\(440\) | 2.59808 | + | 1.50000i | 0.123858 | + | 0.0715097i | ||||
\(441\) | −8.92820 | −0.425153 | ||||||||
\(442\) | 1.90192 | + | 7.68653i | 0.0904653 | + | 0.365611i | ||||
\(443\) | −1.60770 | −0.0763839 | −0.0381920 | − | 0.999270i | \(-0.512160\pi\) | ||||
−0.0381920 | + | 0.999270i | \(0.512160\pi\) | |||||||
\(444\) | 26.4904 | + | 15.2942i | 1.25718 | + | 0.725832i | ||||
\(445\) | 8.59808 | − | 14.8923i | 0.407588 | − | 0.705963i | ||||
\(446\) | −0.232051 | − | 0.401924i | −0.0109879 | − | 0.0190316i | ||||
\(447\) | 16.3923i | 0.775329i | ||||||||
\(448\) | 2.59808 | − | 1.50000i | 0.122748 | − | 0.0708683i | ||||
\(449\) | 13.5000 | − | 7.79423i | 0.637104 | − | 0.367832i | −0.146394 | − | 0.989226i | \(-0.546767\pi\) |
0.783498 | + | 0.621394i | \(0.213433\pi\) | |||||||
\(450\) | 4.46410i | 0.210440i | ||||||||
\(451\) | 15.5885 | + | 27.0000i | 0.734032 | + | 1.27138i | ||||
\(452\) | −3.46410 | + | 6.00000i | −0.162938 | + | 0.282216i | ||||
\(453\) | 15.0000 | + | 8.66025i | 0.704761 | + | 0.406894i | ||||
\(454\) | 4.39230 | 0.206141 | ||||||||
\(455\) | −7.50000 | − | 7.79423i | −0.351605 | − | 0.365399i | ||||
\(456\) | −17.6603 | −0.827017 | ||||||||
\(457\) | −30.8827 | − | 17.8301i | −1.44463 | − | 0.834058i | −0.446477 | − | 0.894795i | \(-0.647322\pi\) |
−0.998154 | + | 0.0607368i | \(0.980655\pi\) | |||||||
\(458\) | −2.36603 | + | 4.09808i | −0.110557 | + | 0.191491i | ||||
\(459\) | −4.39230 | − | 7.60770i | −0.205015 | − | 0.355097i | ||||
\(460\) | − | 2.53590i | − | 0.118237i | ||||||
\(461\) | −0.509619 | + | 0.294229i | −0.0237353 | + | 0.0137036i | −0.511821 | − | 0.859092i | \(-0.671029\pi\) |
0.488085 | + | 0.872796i | \(0.337695\pi\) | |||||||
\(462\) | 21.2942 | − | 12.2942i | 0.990697 | − | 0.571979i | ||||
\(463\) | 0.928203i | 0.0431373i | 0.999767 | + | 0.0215686i | \(0.00686604\pi\) | ||||
−0.999767 | + | 0.0215686i | \(0.993134\pi\) | |||||||
\(464\) | 4.73205 | + | 8.19615i | 0.219680 | + | 0.380497i | ||||
\(465\) | 1.73205 | − | 3.00000i | 0.0803219 | − | 0.139122i | ||||
\(466\) | 1.09808 | + | 0.633975i | 0.0508674 | + | 0.0293683i | ||||
\(467\) | −10.1436 | −0.469390 | −0.234695 | − | 0.972069i | \(-0.575409\pi\) | ||||
−0.234695 | + | 0.972069i | \(0.575409\pi\) | |||||||
\(468\) | 4.46410 | − | 15.4641i | 0.206353 | − | 0.714828i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.59808 | + | 1.50000i | 0.119840 | + | 0.0691898i | ||||
\(471\) | −17.7583 | + | 30.7583i | −0.818261 | + | 1.41727i | ||||
\(472\) | 5.19615 | + | 9.00000i | 0.239172 | + | 0.414259i | ||||
\(473\) | 6.00000i | 0.275880i | ||||||||
\(474\) | 14.6603 | − | 8.46410i | 0.673368 | − | 0.388769i | ||||
\(475\) | 5.59808 | − | 3.23205i | 0.256857 | − | 0.148297i | ||||
\(476\) | − | 6.58846i | − | 0.301981i | ||||||
\(477\) | 14.4282 | + | 24.9904i | 0.660622 | + | 1.14423i | ||||
\(478\) | −4.09808 | + | 7.09808i | −0.187442 | + | 0.324658i | ||||
\(479\) | −9.50962 | − | 5.49038i | −0.434506 | − | 0.250862i | 0.266759 | − | 0.963763i | \(-0.414047\pi\) |
−0.701264 | + | 0.712901i | \(0.747381\pi\) | |||||||
\(480\) | −2.73205 | −0.124700 | ||||||||
\(481\) | 38.7846 | + | 11.1962i | 1.76843 | + | 0.510501i | ||||
\(482\) | −8.66025 | −0.394464 | ||||||||
\(483\) | −18.0000 | − | 10.3923i | −0.819028 | − | 0.472866i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 7.56218 | + | 13.0981i | 0.343381 | + | 0.594753i | ||||
\(486\) | − | 18.7321i | − | 0.849703i | ||||||
\(487\) | −28.7942 | + | 16.6244i | −1.30479 | + | 0.753321i | −0.981222 | − | 0.192883i | \(-0.938216\pi\) |
−0.323569 | + | 0.946204i | \(0.604883\pi\) | |||||||
\(488\) | −3.63397 | + | 2.09808i | −0.164502 | + | 0.0949754i | ||||
\(489\) | − | 19.8564i | − | 0.897938i | ||||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | −1.66987 | + | 2.89230i | −0.0753603 | + | 0.130528i | −0.901243 | − | 0.433314i | \(-0.857344\pi\) |
0.825883 | + | 0.563842i | \(0.190677\pi\) | |||||||
\(492\) | −24.5885 | − | 14.1962i | −1.10853 | − | 0.640012i | ||||
\(493\) | 20.7846 | 0.936092 | ||||||||
\(494\) | −22.6244 | + | 5.59808i | −1.01792 | + | 0.251869i | ||||
\(495\) | −13.3923 | −0.601939 | ||||||||
\(496\) | 1.09808 | + | 0.633975i | 0.0493051 | + | 0.0284663i | ||||
\(497\) | −9.00000 | + | 15.5885i | −0.403705 | + | 0.699238i | ||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | 1.85641i | 0.0831042i | 0.999136 | + | 0.0415521i | \(0.0132302\pi\) | ||||
−0.999136 | + | 0.0415521i | \(0.986770\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | −7.09808 | + | 4.09808i | −0.317119 | + | 0.183089i | ||||
\(502\) | − | 6.80385i | − | 0.303671i | ||||||
\(503\) | 4.66987 | + | 8.08846i | 0.208219 | + | 0.360646i | 0.951154 | − | 0.308718i | \(-0.0998999\pi\) |
−0.742934 | + | 0.669364i | \(0.766567\pi\) | |||||||
\(504\) | −6.69615 | + | 11.5981i | −0.298270 | + | 0.516619i | ||||
\(505\) | −6.29423 | − | 3.63397i | −0.280089 | − | 0.161710i | ||||
\(506\) | 7.60770 | 0.338203 | ||||||||
\(507\) | 1.36603 | − | 35.4904i | 0.0606673 | − | 1.57618i | ||||
\(508\) | −21.1962 | −0.940427 | ||||||||
\(509\) | 1.39230 | + | 0.803848i | 0.0617128 | + | 0.0356299i | 0.530539 | − | 0.847661i | \(-0.321990\pi\) |
−0.468826 | + | 0.883290i | \(0.655323\pi\) | |||||||
\(510\) | −3.00000 | + | 5.19615i | −0.132842 | + | 0.230089i | ||||
\(511\) | −8.49038 | − | 14.7058i | −0.375592 | − | 0.650545i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 22.3923 | − | 12.9282i | 0.988644 | − | 0.570794i | ||||
\(514\) | −12.0000 | + | 6.92820i | −0.529297 | + | 0.305590i | ||||
\(515\) | 1.19615i | 0.0527088i | ||||||||
\(516\) | −2.73205 | − | 4.73205i | −0.120272 | − | 0.208317i | ||||
\(517\) | −4.50000 | + | 7.79423i | −0.197910 | + | 0.342790i | ||||
\(518\) | −29.0885 | − | 16.7942i | −1.27807 | − | 0.737896i | ||||
\(519\) | 40.9808 | 1.79886 | ||||||||
\(520\) | −3.50000 | + | 0.866025i | −0.153485 | + | 0.0379777i | ||||
\(521\) | −0.464102 | −0.0203327 | −0.0101663 | − | 0.999948i | \(-0.503236\pi\) | ||||
−0.0101663 | + | 0.999948i | \(0.503236\pi\) | |||||||
\(522\) | −36.5885 | − | 21.1244i | −1.60143 | − | 0.924588i | ||||
\(523\) | −9.19615 | + | 15.9282i | −0.402120 | + | 0.696492i | −0.993982 | − | 0.109548i | \(-0.965060\pi\) |
0.591862 | + | 0.806039i | \(0.298393\pi\) | |||||||
\(524\) | −9.06218 | − | 15.6962i | −0.395883 | − | 0.685690i | ||||
\(525\) | − | 8.19615i | − | 0.357709i | ||||||
\(526\) | 23.8923 | − | 13.7942i | 1.04175 | − | 0.601457i | ||||
\(527\) | 2.41154 | − | 1.39230i | 0.105048 | − | 0.0606498i | ||||
\(528\) | − | 8.19615i | − | 0.356692i | ||||||
\(529\) | 8.28461 | + | 14.3494i | 0.360200 | + | 0.623885i | ||||
\(530\) | 3.23205 | − | 5.59808i | 0.140391 | − | 0.243165i | ||||
\(531\) | −40.1769 | − | 23.1962i | −1.74353 | − | 1.00663i | ||||
\(532\) | 19.3923 | 0.840763 | ||||||||
\(533\) | −36.0000 | − | 10.3923i | −1.55933 | − | 0.450141i | ||||
\(534\) | −46.9808 | −2.03306 | ||||||||
\(535\) | −0.294229 | − | 0.169873i | −0.0127206 | − | 0.00734425i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.46410 | − | 6.00000i | −0.149487 | − | 0.258919i | ||||
\(538\) | 2.87564i | 0.123978i | ||||||||
\(539\) | −5.19615 | + | 3.00000i | −0.223814 | + | 0.129219i | ||||
\(540\) | 3.46410 | − | 2.00000i | 0.149071 | − | 0.0860663i | ||||
\(541\) | 16.0526i | 0.690153i | 0.938574 | + | 0.345077i | \(0.112147\pi\) | ||||
−0.938574 | + | 0.345077i | \(0.887853\pi\) | |||||||
\(542\) | −1.26795 | − | 2.19615i | −0.0544631 | − | 0.0943328i | ||||
\(543\) | −22.6603 | + | 39.2487i | −0.972445 | + | 1.68432i | ||||
\(544\) | −1.90192 | − | 1.09808i | −0.0815443 | − | 0.0470796i | ||||
\(545\) | −15.4641 | −0.662409 | ||||||||
\(546\) | −8.19615 | + | 28.3923i | −0.350763 | + | 1.21508i | ||||
\(547\) | 34.7846 | 1.48728 | 0.743641 | − | 0.668579i | \(-0.233097\pi\) | ||||
0.743641 | + | 0.668579i | \(0.233097\pi\) | |||||||
\(548\) | 7.09808 | + | 4.09808i | 0.303215 | + | 0.175061i | ||||
\(549\) | 9.36603 | − | 16.2224i | 0.399732 | − | 0.692357i | ||||
\(550\) | 1.50000 | + | 2.59808i | 0.0639602 | + | 0.110782i | ||||
\(551\) | 61.1769i | 2.60622i | ||||||||
\(552\) | −6.00000 | + | 3.46410i | −0.255377 | + | 0.147442i | ||||
\(553\) | −16.0981 | + | 9.29423i | −0.684560 | + | 0.395231i | ||||
\(554\) | 1.00000i | 0.0424859i | ||||||||
\(555\) | 15.2942 | + | 26.4904i | 0.649204 | + | 1.12445i | ||||
\(556\) | −4.59808 | + | 7.96410i | −0.195002 | + | 0.337753i | ||||
\(557\) | 14.8923 | + | 8.59808i | 0.631007 | + | 0.364312i | 0.781142 | − | 0.624353i | \(-0.214637\pi\) |
−0.150135 | + | 0.988666i | \(0.547971\pi\) | |||||||
\(558\) | −5.66025 | −0.239618 | ||||||||
\(559\) | −5.00000 | − | 5.19615i | −0.211477 | − | 0.219774i | ||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | −15.5885 | − | 9.00000i | −0.658145 | − | 0.379980i | ||||
\(562\) | 5.19615 | − | 9.00000i | 0.219186 | − | 0.379642i | ||||
\(563\) | −10.7321 | − | 18.5885i | −0.452302 | − | 0.783410i | 0.546227 | − | 0.837637i | \(-0.316064\pi\) |
−0.998529 | + | 0.0542274i | \(0.982730\pi\) | |||||||
\(564\) | − | 8.19615i | − | 0.345120i | ||||||
\(565\) | −6.00000 | + | 3.46410i | −0.252422 | + | 0.145736i | ||||
\(566\) | 26.3205 | − | 15.1962i | 1.10633 | − | 0.638742i | ||||
\(567\) | 7.39230i | 0.310448i | ||||||||
\(568\) | 3.00000 | + | 5.19615i | 0.125877 | + | 0.218026i | ||||
\(569\) | −10.6244 | + | 18.4019i | −0.445396 | + | 0.771449i | −0.998080 | − | 0.0619424i | \(-0.980270\pi\) |
0.552684 | + | 0.833391i | \(0.313604\pi\) | |||||||
\(570\) | −15.2942 | − | 8.83013i | −0.640605 | − | 0.369853i | ||||
\(571\) | 34.3731 | 1.43847 | 0.719234 | − | 0.694768i | \(-0.244493\pi\) | ||||
0.719234 | + | 0.694768i | \(0.244493\pi\) | |||||||
\(572\) | −2.59808 | − | 10.5000i | −0.108631 | − | 0.439027i | ||||
\(573\) | 52.6410 | 2.19911 | ||||||||
\(574\) | 27.0000 | + | 15.5885i | 1.12696 | + | 0.650650i | ||||
\(575\) | 1.26795 | − | 2.19615i | 0.0528771 | − | 0.0915859i | ||||
\(576\) | 2.23205 | + | 3.86603i | 0.0930021 | + | 0.161084i | ||||
\(577\) | − | 32.4449i | − | 1.35070i | −0.737499 | − | 0.675349i | \(-0.763993\pi\) | ||
0.737499 | − | 0.675349i | \(-0.236007\pi\) | |||||||
\(578\) | 10.5455 | − | 6.08846i | 0.438636 | − | 0.253246i | ||||
\(579\) | −10.3923 | + | 6.00000i | −0.431889 | + | 0.249351i | ||||
\(580\) | 9.46410i | 0.392975i | ||||||||
\(581\) | 3.29423 | + | 5.70577i | 0.136668 | + | 0.236715i | ||||
\(582\) | 20.6603 | − | 35.7846i | 0.856395 | − | 1.48332i | ||||
\(583\) | 16.7942 | + | 9.69615i | 0.695546 | + | 0.401574i | ||||
\(584\) | −5.66025 | −0.234223 | ||||||||
\(585\) | 11.5981 | − | 11.1603i | 0.479521 | − | 0.461420i | ||||
\(586\) | −0.803848 | −0.0332066 | ||||||||
\(587\) | −25.9808 | − | 15.0000i | −1.07234 | − | 0.619116i | −0.143521 | − | 0.989647i | \(-0.545842\pi\) |
−0.928820 | + | 0.370531i | \(0.879176\pi\) | |||||||
\(588\) | 2.73205 | − | 4.73205i | 0.112668 | − | 0.195146i | ||||
\(589\) | 4.09808 | + | 7.09808i | 0.168858 | + | 0.292471i | ||||
\(590\) | 10.3923i | 0.427844i | ||||||||
\(591\) | 22.6865 | − | 13.0981i | 0.933199 | − | 0.538783i | ||||
\(592\) | −9.69615 | + | 5.59808i | −0.398509 | + | 0.230080i | ||||
\(593\) | − | 20.7846i | − | 0.853522i | −0.904365 | − | 0.426761i | \(-0.859655\pi\) | ||
0.904365 | − | 0.426761i | \(-0.140345\pi\) | |||||||
\(594\) | 6.00000 | + | 10.3923i | 0.246183 | + | 0.426401i | ||||
\(595\) | 3.29423 | − | 5.70577i | 0.135050 | − | 0.233914i | ||||
\(596\) | −5.19615 | − | 3.00000i | −0.212843 | − | 0.122885i | ||||
\(597\) | −39.3205 | −1.60928 | ||||||||
\(598\) | −6.58846 | + | 6.33975i | −0.269422 | + | 0.259251i | ||||
\(599\) | 7.85641 | 0.321004 | 0.160502 | − | 0.987036i | \(-0.448689\pi\) | ||||
0.160502 | + | 0.987036i | \(0.448689\pi\) | |||||||
\(600\) | −2.36603 | − | 1.36603i | −0.0965926 | − | 0.0557678i | ||||
\(601\) | −1.89230 | + | 3.27757i | −0.0771887 | + | 0.133695i | −0.902036 | − | 0.431661i | \(-0.857928\pi\) |
0.824847 | + | 0.565356i | \(0.191261\pi\) | |||||||
\(602\) | 3.00000 | + | 5.19615i | 0.122271 | + | 0.211779i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.49038 | + | 3.16987i | −0.223400 | + | 0.128980i | ||||
\(605\) | 1.73205 | − | 1.00000i | 0.0704179 | − | 0.0406558i | ||||
\(606\) | 19.8564i | 0.806611i | ||||||||
\(607\) | 3.20577 | + | 5.55256i | 0.130118 | + | 0.225371i | 0.923722 | − | 0.383064i | \(-0.125131\pi\) |
−0.793604 | + | 0.608435i | \(0.791798\pi\) | |||||||
\(608\) | 3.23205 | − | 5.59808i | 0.131077 | − | 0.227032i | ||||
\(609\) | 67.1769 | + | 38.7846i | 2.72215 | + | 1.57163i | ||||
\(610\) | −4.19615 | −0.169897 | ||||||||
\(611\) | −2.59808 | − | 10.5000i | −0.105107 | − | 0.424785i | ||||
\(612\) | 9.80385 | 0.396297 | ||||||||
\(613\) | 23.3038 | + | 13.4545i | 0.941234 | + | 0.543421i | 0.890347 | − | 0.455283i | \(-0.150462\pi\) |
0.0508868 | + | 0.998704i | \(0.483795\pi\) | |||||||
\(614\) | −10.2679 | + | 17.7846i | −0.414381 | + | 0.717728i | ||||
\(615\) | −14.1962 | − | 24.5885i | −0.572444 | − | 0.991502i | ||||
\(616\) | 9.00000i | 0.362620i | ||||||||
\(617\) | −15.5885 | + | 9.00000i | −0.627568 | + | 0.362326i | −0.779809 | − | 0.626017i | \(-0.784684\pi\) |
0.152242 | + | 0.988343i | \(0.451351\pi\) | |||||||
\(618\) | 2.83013 | − | 1.63397i | 0.113844 | − | 0.0657281i | ||||
\(619\) | 10.6077i | 0.426359i | 0.977013 | + | 0.213180i | \(0.0683820\pi\) | ||||
−0.977013 | + | 0.213180i | \(0.931618\pi\) | |||||||
\(620\) | 0.633975 | + | 1.09808i | 0.0254610 | + | 0.0440998i | ||||
\(621\) | 5.07180 | − | 8.78461i | 0.203524 | − | 0.352514i | ||||
\(622\) | 13.0981 | + | 7.56218i | 0.525185 | + | 0.303216i | ||||
\(623\) | 51.5885 | 2.06685 | ||||||||
\(624\) | 6.83013 | + | 7.09808i | 0.273424 | + | 0.284150i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.85641 | + | 2.80385i | 0.194101 | + | 0.112064i | ||||
\(627\) | 26.4904 | − | 45.8827i | 1.05792 | − | 1.83238i | ||||
\(628\) | −6.50000 | − | 11.2583i | −0.259378 | − | 0.449256i | ||||
\(629\) | 24.5885i | 0.980406i | ||||||||
\(630\) | −11.5981 | + | 6.69615i | −0.462078 | + | 0.266781i | ||||
\(631\) | −18.0000 | + | 10.3923i | −0.716569 | + | 0.413711i | −0.813488 | − | 0.581581i | \(-0.802434\pi\) |
0.0969198 | + | 0.995292i | \(0.469101\pi\) | |||||||
\(632\) | 6.19615i | 0.246470i | ||||||||
\(633\) | 18.5622 | + | 32.1506i | 0.737780 | + | 1.27787i | ||||
\(634\) | −6.40192 | + | 11.0885i | −0.254253 | + | 0.440379i | ||||
\(635\) | −18.3564 | − | 10.5981i | −0.728452 | − | 0.420572i | ||||
\(636\) | −17.6603 | −0.700275 | ||||||||
\(637\) | 2.00000 | − | 6.92820i | 0.0792429 | − | 0.274505i | ||||
\(638\) | −28.3923 | −1.12406 | ||||||||
\(639\) | −23.1962 | − | 13.3923i | −0.917626 | − | 0.529791i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −22.9641 | − | 39.7750i | −0.907027 | − | 1.57102i | −0.818172 | − | 0.574973i | \(-0.805012\pi\) |
−0.0888552 | − | 0.996045i | \(-0.528321\pi\) | |||||||
\(642\) | 0.928203i | 0.0366333i | ||||||||
\(643\) | 6.29423 | − | 3.63397i | 0.248220 | − | 0.143310i | −0.370729 | − | 0.928741i | \(-0.620892\pi\) |
0.618949 | + | 0.785431i | \(0.287559\pi\) | |||||||
\(644\) | 6.58846 | − | 3.80385i | 0.259622 | − | 0.149893i | ||||
\(645\) | − | 5.46410i | − | 0.215149i | ||||||
\(646\) | −7.09808 | − | 12.2942i | −0.279270 | − | 0.483710i | ||||
\(647\) | 5.59808 | − | 9.69615i | 0.220083 | − | 0.381195i | −0.734750 | − | 0.678338i | \(-0.762700\pi\) |
0.954833 | + | 0.297143i | \(0.0960338\pi\) | |||||||
\(648\) | 2.13397 | + | 1.23205i | 0.0838304 | + | 0.0483995i | ||||
\(649\) | −31.1769 | −1.22380 | ||||||||
\(650\) | −3.46410 | − | 1.00000i | −0.135873 | − | 0.0392232i | ||||
\(651\) | 10.3923 | 0.407307 | ||||||||
\(652\) | 6.29423 | + | 3.63397i | 0.246501 | + | 0.142317i | ||||
\(653\) | 9.69615 | − | 16.7942i | 0.379440 | − | 0.657209i | −0.611541 | − | 0.791213i | \(-0.709450\pi\) |
0.990981 | + | 0.134004i | \(0.0427834\pi\) | |||||||
\(654\) | 21.1244 | + | 36.5885i | 0.826028 | + | 1.43072i | ||||
\(655\) | − | 18.1244i | − | 0.708177i | ||||||
\(656\) | 9.00000 | − | 5.19615i | 0.351391 | − | 0.202876i | ||||
\(657\) | 21.8827 | − | 12.6340i | 0.853725 | − | 0.492898i | ||||
\(658\) | 9.00000i | 0.350857i | ||||||||
\(659\) | −14.6603 | − | 25.3923i | −0.571082 | − | 0.989144i | −0.996455 | − | 0.0841255i | \(-0.973190\pi\) |
0.425373 | − | 0.905018i | \(-0.360143\pi\) | |||||||
\(660\) | 4.09808 | − | 7.09808i | 0.159517 | − | 0.276292i | ||||
\(661\) | 25.9019 | + | 14.9545i | 1.00747 | + | 0.581662i | 0.910449 | − | 0.413621i | \(-0.135736\pi\) |
0.0970187 | + | 0.995283i | \(0.469069\pi\) | |||||||
\(662\) | 0.928203 | 0.0360756 | ||||||||
\(663\) | 21.0000 | − | 5.19615i | 0.815572 | − | 0.201802i | ||||
\(664\) | 2.19615 | 0.0852272 | ||||||||
\(665\) | 16.7942 | + | 9.69615i | 0.651252 | + | 0.376001i | ||||
\(666\) | 24.9904 | − | 43.2846i | 0.968358 | − | 1.67724i | ||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | − | 3.00000i | − | 0.116073i | ||||||
\(669\) | −1.09808 | + | 0.633975i | −0.0424541 | + | 0.0245109i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 12.5885i | − | 0.485972i | ||||||
\(672\) | −4.09808 | − | 7.09808i | −0.158087 | − | 0.273814i | ||||
\(673\) | −1.80385 | + | 3.12436i | −0.0695332 | + | 0.120435i | −0.898696 | − | 0.438572i | \(-0.855484\pi\) |
0.829163 | + | 0.559007i | \(0.188818\pi\) | |||||||
\(674\) | −3.63397 | − | 2.09808i | −0.139975 | − | 0.0808149i | ||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 11.0000 | + | 6.92820i | 0.423077 | + | 0.266469i | ||||
\(677\) | 1.85641 | 0.0713475 | 0.0356737 | − | 0.999363i | \(-0.488642\pi\) | ||||
0.0356737 | + | 0.999363i | \(0.488642\pi\) | |||||||
\(678\) | 16.3923 | + | 9.46410i | 0.629543 | + | 0.363467i | ||||
\(679\) | −22.6865 | + | 39.2942i | −0.870629 | + | 1.50797i | ||||
\(680\) | −1.09808 | − | 1.90192i | −0.0421093 | − | 0.0729354i | ||||
\(681\) | − | 12.0000i | − | 0.459841i | ||||||
\(682\) | −3.29423 | + | 1.90192i | −0.126143 | + | 0.0728284i | ||||
\(683\) | 27.0000 | − | 15.5885i | 1.03313 | − | 0.596476i | 0.115248 | − | 0.993337i | \(-0.463234\pi\) |
0.917879 | + | 0.396861i | \(0.129901\pi\) | |||||||
\(684\) | 28.8564i | 1.10335i | ||||||||
\(685\) | 4.09808 | + | 7.09808i | 0.156579 | + | 0.271204i | ||||
\(686\) | 7.50000 | − | 12.9904i | 0.286351 | − | 0.495975i | ||||
\(687\) | 11.1962 | + | 6.46410i | 0.427160 | + | 0.246621i | ||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | −22.6244 | + | 5.59808i | −0.861919 | + | 0.213270i | ||||
\(690\) | −6.92820 | −0.263752 | ||||||||
\(691\) | −16.2058 | − | 9.35641i | −0.616497 | − | 0.355934i | 0.159007 | − | 0.987277i | \(-0.449171\pi\) |
−0.775504 | + | 0.631343i | \(0.782504\pi\) | |||||||
\(692\) | −7.50000 | + | 12.9904i | −0.285107 | + | 0.493820i | ||||
\(693\) | −20.0885 | − | 34.7942i | −0.763097 | − | 1.32172i | ||||
\(694\) | 25.2679i | 0.959158i | ||||||||
\(695\) | −7.96410 | + | 4.59808i | −0.302096 | + | 0.174415i | ||||
\(696\) | 22.3923 | − | 12.9282i | 0.848778 | − | 0.490042i | ||||
\(697\) | − | 22.8231i | − | 0.864486i | ||||||
\(698\) | −17.0263 | − | 29.4904i | −0.644454 | − | 1.11623i | ||||
\(699\) | 1.73205 | − | 3.00000i | 0.0655122 | − | 0.113470i | ||||
\(700\) | 2.59808 | + | 1.50000i | 0.0981981 | + | 0.0566947i | ||||
\(701\) | −29.9090 | −1.12965 | −0.564823 | − | 0.825212i | \(-0.691056\pi\) | ||||
−0.564823 | + | 0.825212i | \(0.691056\pi\) | |||||||
\(702\) | −13.8564 | − | 4.00000i | −0.522976 | − | 0.150970i | ||||
\(703\) | −72.3731 | −2.72960 | ||||||||
\(704\) | 2.59808 | + | 1.50000i | 0.0979187 | + | 0.0565334i | ||||
\(705\) | 4.09808 | − | 7.09808i | 0.154342 | − | 0.267329i | ||||
\(706\) | −10.0981 | − | 17.4904i | −0.380046 | − | 0.658259i | ||||
\(707\) | − | 21.8038i | − | 0.820018i | ||||||
\(708\) | 24.5885 | − | 14.1962i | 0.924091 | − | 0.533524i | ||||
\(709\) | 35.4904 | − | 20.4904i | 1.33287 | − | 0.769532i | 0.347131 | − | 0.937817i | \(-0.387156\pi\) |
0.985738 | + | 0.168284i | \(0.0538227\pi\) | |||||||
\(710\) | 6.00000i | 0.225176i | ||||||||
\(711\) | −13.8301 | − | 23.9545i | −0.518670 | − | 0.898363i | ||||
\(712\) | 8.59808 | − | 14.8923i | 0.322227 | − | 0.558113i | ||||
\(713\) | 2.78461 | + | 1.60770i | 0.104284 | + | 0.0602087i | ||||
\(714\) | −18.0000 | −0.673633 | ||||||||
\(715\) | 3.00000 | − | 10.3923i | 0.112194 | − | 0.388650i | ||||
\(716\) | 2.53590 | 0.0947710 | ||||||||
\(717\) | 19.3923 | + | 11.1962i | 0.724219 | + | 0.418128i | ||||
\(718\) | 11.1962 | − | 19.3923i | 0.417837 | − | 0.723714i | ||||
\(719\) | 0.928203 | + | 1.60770i | 0.0346161 | + | 0.0599569i | 0.882814 | − | 0.469722i | \(-0.155646\pi\) |
−0.848198 | + | 0.529679i | \(0.822312\pi\) | |||||||
\(720\) | 4.46410i | 0.166367i | ||||||||
\(721\) | −3.10770 | + | 1.79423i | −0.115737 | + | 0.0668206i | ||||
\(722\) | 19.7321 | − | 11.3923i | 0.734351 | − | 0.423978i | ||||
\(723\) | 23.6603i | 0.879934i | ||||||||
\(724\) | −8.29423 | − | 14.3660i | −0.308253 | − | 0.533909i | ||||
\(725\) | −4.73205 | + | 8.19615i | −0.175744 | + | 0.304397i | ||||
\(726\) | −4.73205 | − | 2.73205i | −0.175623 | − | 0.101396i | ||||
\(727\) | −38.3731 | −1.42318 | −0.711589 | − | 0.702596i | \(-0.752024\pi\) | ||||
−0.711589 | + | 0.702596i | \(0.752024\pi\) | |||||||
\(728\) | −7.50000 | − | 7.79423i | −0.277968 | − | 0.288873i | ||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | −4.90192 | − | 2.83013i | −0.181428 | − | 0.104748i | ||||
\(731\) | 2.19615 | − | 3.80385i | 0.0812276 | − | 0.140690i | ||||
\(732\) | 5.73205 | + | 9.92820i | 0.211863 | + | 0.366957i | ||||
\(733\) | 50.9090i | 1.88037i | 0.340670 | + | 0.940183i | \(0.389346\pi\) | ||||
−0.340670 | + | 0.940183i | \(0.610654\pi\) | |||||||
\(734\) | 22.8564 | − | 13.1962i | 0.843645 | − | 0.487079i | ||||
\(735\) | 4.73205 | − | 2.73205i | 0.174544 | − | 0.100773i | ||||
\(736\) | − | 2.53590i | − | 0.0934745i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −23.1962 | + | 40.1769i | −0.853862 | + | 1.47893i | ||||
\(739\) | 43.7942 | + | 25.2846i | 1.61100 | + | 0.930109i | 0.989140 | + | 0.146979i | \(0.0469549\pi\) |
0.621857 | + | 0.783131i | \(0.286378\pi\) | |||||||
\(740\) | −11.1962 | −0.411579 | ||||||||
\(741\) | 15.2942 | + | 61.8109i | 0.561848 | + | 2.27068i | ||||
\(742\) | 19.3923 | 0.711914 | ||||||||
\(743\) | 29.7846 | + | 17.1962i | 1.09269 | + | 0.630866i | 0.934292 | − | 0.356509i | \(-0.116033\pi\) |
0.158400 | + | 0.987375i | \(0.449367\pi\) | |||||||
\(744\) | 1.73205 | − | 3.00000i | 0.0635001 | − | 0.109985i | ||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | − | 20.3923i | − | 0.746615i | ||||||
\(747\) | −8.49038 | + | 4.90192i | −0.310647 | + | 0.179352i | ||||
\(748\) | 5.70577 | − | 3.29423i | 0.208624 | − | 0.120449i | ||||
\(749\) | − | 1.01924i | − | 0.0372421i | ||||||
\(750\) | −1.36603 | − | 2.36603i | −0.0498802 | − | 0.0863950i | ||||
\(751\) | −0.196152 | + | 0.339746i | −0.00715770 | + | 0.0123975i | −0.869582 | − | 0.493788i | \(-0.835612\pi\) |
0.862424 | + | 0.506186i | \(0.168945\pi\) | |||||||
\(752\) | 2.59808 | + | 1.50000i | 0.0947421 | + | 0.0546994i | ||||
\(753\) | −18.5885 | −0.677401 | ||||||||
\(754\) | 24.5885 | − | 23.6603i | 0.895459 | − | 0.861656i | ||||
\(755\) | −6.33975 | −0.230727 | ||||||||
\(756\) | 10.3923 | + | 6.00000i | 0.377964 | + | 0.218218i | ||||
\(757\) | −1.89230 | + | 3.27757i | −0.0687770 | + | 0.119125i | −0.898363 | − | 0.439253i | \(-0.855243\pi\) |
0.829586 | + | 0.558379i | \(0.188576\pi\) | |||||||
\(758\) | 5.89230 | + | 10.2058i | 0.214018 | + | 0.370690i | ||||
\(759\) | − | 20.7846i | − | 0.754434i | ||||||
\(760\) | 5.59808 | − | 3.23205i | 0.203064 | − | 0.117239i | ||||
\(761\) | −25.2846 | + | 14.5981i | −0.916566 | + | 0.529180i | −0.882538 | − | 0.470241i | \(-0.844167\pi\) |
−0.0340283 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(762\) | 57.9090i | 2.09782i | ||||||||
\(763\) | −23.1962 | − | 40.1769i | −0.839757 | − | 1.45450i | ||||
\(764\) | −9.63397 | + | 16.6865i | −0.348545 | + | 0.603698i | ||||
\(765\) | 8.49038 | + | 4.90192i | 0.306970 | + | 0.177229i | ||||
\(766\) | −1.60770 | −0.0580884 | ||||||||
\(767\) | 27.0000 | − | 25.9808i | 0.974913 | − | 0.938111i | ||||
\(768\) | −2.73205 | −0.0985844 | ||||||||
\(769\) | −33.0000 | − | 19.0526i | −1.19001 | − | 0.687053i | −0.231701 | − | 0.972787i | \(-0.574429\pi\) |
−0.958309 | + | 0.285734i | \(0.907763\pi\) | |||||||
\(770\) | −4.50000 | + | 7.79423i | −0.162169 | + | 0.280885i | ||||
\(771\) | 18.9282 | + | 32.7846i | 0.681683 | + | 1.18071i | ||||
\(772\) | − | 4.39230i | − | 0.158083i | ||||||
\(773\) | −29.0885 | + | 16.7942i | −1.04624 | + | 0.604046i | −0.921594 | − | 0.388155i | \(-0.873113\pi\) |
−0.124645 | + | 0.992201i | \(0.539779\pi\) | |||||||
\(774\) | −7.73205 | + | 4.46410i | −0.277923 | + | 0.160459i | ||||
\(775\) | 1.26795i | 0.0455461i | ||||||||
\(776\) | 7.56218 | + | 13.0981i | 0.271466 | + | 0.470194i | ||||
\(777\) | −45.8827 | + | 79.4711i | −1.64603 | + | 2.85101i | ||||
\(778\) | 16.6865 | + | 9.63397i | 0.598241 | + | 0.345395i | ||||
\(779\) | 67.1769 | 2.40686 | ||||||||
\(780\) | 2.36603 | + | 9.56218i | 0.0847173 | + | 0.342381i | ||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | −4.82309 | − | 2.78461i | −0.172473 | − | 0.0995774i | ||||
\(783\) | −18.9282 | + | 32.7846i | −0.676439 | + | 1.17163i | ||||
\(784\) | 1.00000 | + | 1.73205i | 0.0357143 | + | 0.0618590i | ||||
\(785\) | − | 13.0000i | − | 0.463990i | ||||||
\(786\) | −42.8827 | + | 24.7583i | −1.52957 | + | 0.883100i | ||||
\(787\) | −31.9019 | + | 18.4186i | −1.13718 | + | 0.656552i | −0.945731 | − | 0.324951i | \(-0.894652\pi\) |
−0.191450 | + | 0.981502i | \(0.561319\pi\) | |||||||
\(788\) | 9.58846i | 0.341575i | ||||||||
\(789\) | −37.6865 | − | 65.2750i | −1.34168 | − | 2.32385i | ||||
\(790\) | −3.09808 | + | 5.36603i | −0.110225 | + | 0.190915i | ||||
\(791\) | −18.0000 | − | 10.3923i | −0.640006 | − | 0.369508i | ||||
\(792\) | −13.3923 | −0.475875 | ||||||||
\(793\) | 10.4904 | + | 10.9019i | 0.372524 | + | 0.387139i | ||||
\(794\) | 0.803848 | 0.0285275 | ||||||||
\(795\) | −15.2942 | − | 8.83013i | −0.542430 | − | 0.313172i | ||||
\(796\) | 7.19615 | − | 12.4641i | 0.255061 | − | 0.441778i | ||||
\(797\) | −0.464102 | − | 0.803848i | −0.0164393 | − | 0.0284737i | 0.857689 | − | 0.514169i | \(-0.171900\pi\) |
−0.874128 | + | 0.485696i | \(0.838566\pi\) | |||||||
\(798\) | − | 52.9808i | − | 1.87550i | ||||||
\(799\) | 5.70577 | − | 3.29423i | 0.201856 | − | 0.116541i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | 76.7654i | 2.71237i | ||||||||
\(802\) | −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 | ||||||||
\(806\) | 1.26795 | − | 4.39230i | 0.0446616 | − | 0.154712i | ||||
\(807\) | 7.85641 | 0.276559 | ||||||||
\(808\) | −6.29423 | − | 3.63397i | −0.221430 | − | 0.127843i | ||||
\(809\) | −12.0000 | + | 20.7846i | −0.421898 | + | 0.730748i | −0.996125 | − | 0.0879478i | \(-0.971969\pi\) |
0.574228 | + | 0.818696i | \(0.305302\pi\) | |||||||
\(810\) | 1.23205 | + | 2.13397i | 0.0432899 | + | 0.0749802i | ||||
\(811\) | − | 22.6077i | − | 0.793864i | −0.917848 | − | 0.396932i | \(-0.870075\pi\) | ||
0.917848 | − | 0.396932i | \(-0.129925\pi\) | |||||||
\(812\) | −24.5885 | + | 14.1962i | −0.862886 | + | 0.498187i | ||||
\(813\) | −6.00000 | + | 3.46410i | −0.210429 | + | 0.121491i | ||||
\(814\) | − | 33.5885i | − | 1.17727i | ||||||
\(815\) | 3.63397 | + | 6.29423i | 0.127293 | + | 0.220477i | ||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | 11.1962 | + | 6.46410i | 0.391704 | + | 0.226150i | ||||
\(818\) | 19.7321 | 0.689915 | ||||||||
\(819\) | 46.3923 | + | 13.3923i | 1.62108 | + | 0.467965i | ||||
\(820\) | 10.3923 | 0.362915 | ||||||||
\(821\) | −8.49038 | − | 4.90192i | −0.296316 | − | 0.171078i | 0.344471 | − | 0.938797i | \(-0.388058\pi\) |
−0.640787 | + | 0.767719i | \(0.721392\pi\) | |||||||
\(822\) | 11.1962 | − | 19.3923i | 0.390511 | − | 0.676384i | ||||
\(823\) | 8.40192 | + | 14.5526i | 0.292873 | + | 0.507270i | 0.974488 | − | 0.224441i | \(-0.0720555\pi\) |
−0.681615 | + | 0.731711i | \(0.738722\pi\) | |||||||
\(824\) | 1.19615i | 0.0416699i | ||||||||
\(825\) | 7.09808 | − | 4.09808i | 0.247123 | − | 0.142677i | ||||
\(826\) | −27.0000 | + | 15.5885i | −0.939450 | + | 0.542392i | ||||
\(827\) | 11.4115i | 0.396818i | 0.980119 | + | 0.198409i | \(0.0635775\pi\) | ||||
−0.980119 | + | 0.198409i | \(0.936423\pi\) | |||||||
\(828\) | 5.66025 | + | 9.80385i | 0.196707 | + | 0.340707i | ||||
\(829\) | 10.0000 | − | 17.3205i | 0.347314 | − | 0.601566i | −0.638457 | − | 0.769657i | \(-0.720427\pi\) |
0.985771 | + | 0.168091i | \(0.0537604\pi\) | |||||||
\(830\) | 1.90192 | + | 1.09808i | 0.0660167 | + | 0.0381148i | ||||
\(831\) | 2.73205 | 0.0947738 | ||||||||
\(832\) | −3.50000 | + | 0.866025i | −0.121341 | + | 0.0300240i | ||||
\(833\) | 4.39230 | 0.152184 | ||||||||
\(834\) | 21.7583 | + | 12.5622i | 0.753429 | + | 0.434993i | ||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | 9.69615 | + | 16.7942i | 0.335348 | + | 0.580841i | ||||
\(837\) | 5.07180i | 0.175307i | ||||||||
\(838\) | −15.0000 | + | 8.66025i | −0.518166 | + | 0.299164i | ||||
\(839\) | −27.8827 | + | 16.0981i | −0.962617 | + | 0.555767i | −0.896978 | − | 0.442076i | \(-0.854242\pi\) |
−0.0656397 | + | 0.997843i | \(0.520909\pi\) | |||||||
\(840\) | − | 8.19615i | − | 0.282794i | ||||||
\(841\) | −30.2846 | − | 52.4545i | −1.04430 | − | 1.80878i | ||||
\(842\) | 13.5622 | − | 23.4904i | 0.467384 | − | 0.809532i | ||||
\(843\) | −24.5885 | − | 14.1962i | −0.846871 | − | 0.488941i | ||||
\(844\) | −13.5885 | −0.467734 | ||||||||
\(845\) | 6.06218 | + | 11.5000i | 0.208545 | + | 0.395612i | ||||
\(846\) | −13.3923 | −0.460437 | ||||||||
\(847\) | 5.19615 | + | 3.00000i | 0.178542 | + | 0.103081i | ||||
\(848\) | 3.23205 | − | 5.59808i | 0.110989 | − | 0.192239i | ||||
\(849\) | −41.5167 | − | 71.9090i | −1.42485 | − | 2.46791i | ||||
\(850\) | − | 2.19615i | − | 0.0753274i | ||||||
\(851\) | −24.5885 | + | 14.1962i | −0.842881 | + | 0.486638i | ||||
\(852\) | 14.1962 | − | 8.19615i | 0.486352 | − | 0.280796i | ||||
\(853\) | 13.8564i | 0.474434i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) | ||||
−0.971457 | + | 0.237217i | \(0.923765\pi\) | |||||||
\(854\) | −6.29423 | − | 10.9019i | −0.215384 | − | 0.373056i | ||||
\(855\) | −14.4282 | + | 24.9904i | −0.493434 | + | 0.854653i | ||||
\(856\) | −0.294229 | − | 0.169873i | −0.0100565 | − | 0.00580614i | ||||
\(857\) | −13.2679 | −0.453225 | −0.226612 | − | 0.973985i | \(-0.572765\pi\) | ||||
−0.226612 | + | 0.973985i | \(0.572765\pi\) | |||||||
\(858\) | −28.6865 | + | 7.09808i | −0.979342 | + | 0.242324i | ||||
\(859\) | 52.3731 | 1.78695 | 0.893473 | − | 0.449117i | \(-0.148261\pi\) | ||||
0.893473 | + | 0.449117i | \(0.148261\pi\) | |||||||
\(860\) | 1.73205 | + | 1.00000i | 0.0590624 | + | 0.0340997i | ||||
\(861\) | 42.5885 | − | 73.7654i | 1.45141 | − | 2.51392i | ||||
\(862\) | −1.09808 | − | 1.90192i | −0.0374006 | − | 0.0647798i | ||||
\(863\) | 19.1769i | 0.652790i | 0.945234 | + | 0.326395i | \(0.105834\pi\) | ||||
−0.945234 | + | 0.326395i | \(0.894166\pi\) | |||||||
\(864\) | 3.46410 | − | 2.00000i | 0.117851 | − | 0.0680414i | ||||
\(865\) | −12.9904 | + | 7.50000i | −0.441686 | + | 0.255008i | ||||
\(866\) | 12.3923i | 0.421108i | ||||||||
\(867\) | −16.6340 | − | 28.8109i | −0.564919 | − | 0.978469i | ||||
\(868\) | −1.90192 | + | 3.29423i | −0.0645555 | + | 0.111813i | ||||
\(869\) | −16.0981 | − | 9.29423i | −0.546090 | − | 0.315285i | ||||
\(870\) | 25.8564 | 0.876614 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.4641 | −0.523681 | ||||||||
\(873\) | −58.4711 | − | 33.7583i | −1.97895 | − | 1.14255i | ||||
\(874\) | 8.19615 | − | 14.1962i | 0.277239 | − | 0.480192i | ||||
\(875\) | 1.50000 | + | 2.59808i | 0.0507093 | + | 0.0878310i | ||||
\(876\) | 15.4641i | 0.522484i | ||||||||
\(877\) | 17.7846 | − | 10.2679i | 0.600544 | − | 0.346724i | −0.168712 | − | 0.985665i | \(-0.553961\pi\) |
0.769255 | + | 0.638941i | \(0.220627\pi\) | |||||||
\(878\) | 29.9545 | − | 17.2942i | 1.01091 | − | 0.583652i | ||||
\(879\) | 2.19615i | 0.0740744i | ||||||||
\(880\) | 1.50000 | + | 2.59808i | 0.0505650 | + | 0.0875811i | ||||
\(881\) | 4.16025 | − | 7.20577i | 0.140163 | − | 0.242769i | −0.787395 | − | 0.616449i | \(-0.788571\pi\) |
0.927558 | + | 0.373680i | \(0.121904\pi\) | |||||||
\(882\) | −7.73205 | − | 4.46410i | −0.260352 | − | 0.150314i | ||||
\(883\) | −26.5885 | −0.894773 | −0.447386 | − | 0.894341i | \(-0.647645\pi\) | ||||
−0.447386 | + | 0.894341i | \(0.647645\pi\) | |||||||
\(884\) | −2.19615 | + | 7.60770i | −0.0738646 | + | 0.255874i | ||||
\(885\) | 28.3923 | 0.954397 | ||||||||
\(886\) | −1.39230 | − | 0.803848i | −0.0467754 | − | 0.0270058i | ||||
\(887\) | −26.3827 | + | 45.6962i | −0.885844 | + | 1.53433i | −0.0411005 | + | 0.999155i | \(0.513086\pi\) |
−0.844743 | + | 0.535172i | \(0.820247\pi\) | |||||||
\(888\) | 15.2942 | + | 26.4904i | 0.513241 | + | 0.888959i | ||||
\(889\) | − | 63.5885i | − | 2.13269i | ||||||
\(890\) | 14.8923 | − | 8.59808i | 0.499191 | − | 0.288208i | ||||
\(891\) | −6.40192 | + | 3.69615i | −0.214473 | + | 0.123826i | ||||
\(892\) | − | 0.464102i | − | 0.0155393i | ||||||
\(893\) | 9.69615 | + | 16.7942i | 0.324469 | + | 0.561997i | ||||
\(894\) | −8.19615 | + | 14.1962i | −0.274120 | + | 0.474790i | ||||
\(895\) | 2.19615 | + | 1.26795i | 0.0734093 | + | 0.0423829i | ||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | 17.3205 | + | 18.0000i | 0.578315 | + | 0.601003i | ||||
\(898\) | 15.5885 | 0.520194 | ||||||||
\(899\) | −10.3923 | − | 6.00000i | −0.346603 | − | 0.200111i | ||||
\(900\) | −2.23205 | + | 3.86603i | −0.0744017 | + | 0.128868i | ||||
\(901\) | −7.09808 | − | 12.2942i | −0.236471 | − | 0.409580i | ||||
\(902\) | 31.1769i | 1.03808i | ||||||||
\(903\) | 14.1962 | − | 8.19615i | 0.472418 | − | 0.272751i | ||||
\(904\) | −6.00000 | + | 3.46410i | −0.199557 | + | 0.115214i | ||||
\(905\) | − | 16.5885i | − | 0.551419i | ||||||
\(906\) | 8.66025 | + | 15.0000i | 0.287718 | + | 0.498342i | ||||
\(907\) | 13.2942 | − | 23.0263i | 0.441428 | − | 0.764575i | −0.556368 | − | 0.830936i | \(-0.687806\pi\) |
0.997796 | + | 0.0663609i | \(0.0211389\pi\) | |||||||
\(908\) | 3.80385 | + | 2.19615i | 0.126235 | + | 0.0728819i | ||||
\(909\) | 32.4449 | 1.07613 | ||||||||
\(910\) | −2.59808 | − | 10.5000i | −0.0861254 | − | 0.348072i | ||||
\(911\) | −14.5359 | −0.481596 | −0.240798 | − | 0.970575i | \(-0.577409\pi\) | ||||
−0.240798 | + | 0.970575i | \(0.577409\pi\) | |||||||
\(912\) | −15.2942 | − | 8.83013i | −0.506443 | − | 0.292395i | ||||
\(913\) | −3.29423 | + | 5.70577i | −0.109023 | + | 0.188833i | ||||
\(914\) | −17.8301 | − | 30.8827i | −0.589768 | − | 1.02151i | ||||
\(915\) | 11.4641i | 0.378992i | ||||||||
\(916\) | −4.09808 | + | 2.36603i | −0.135404 | + | 0.0781757i | ||||
\(917\) | 47.0885 | − | 27.1865i | 1.55500 | − | 0.897778i | ||||
\(918\) | − | 8.78461i | − | 0.289935i | ||||||
\(919\) | 5.39230 | + | 9.33975i | 0.177876 | + | 0.308090i | 0.941153 | − | 0.337982i | \(-0.109744\pi\) |
−0.763277 | + | 0.646071i | \(0.776411\pi\) | |||||||
\(920\) | 1.26795 | − | 2.19615i | 0.0418030 | − | 0.0724050i | ||||
\(921\) | 48.5885 | + | 28.0526i | 1.60104 | + | 0.924363i | ||||
\(922\) | −0.588457 | −0.0193798 | ||||||||
\(923\) | 15.5885 | − | 15.0000i | 0.513100 | − | 0.493731i | ||||
\(924\) | 24.5885 | 0.808901 | ||||||||
\(925\) | −9.69615 | − | 5.59808i | −0.318808 | − | 0.184064i | ||||
\(926\) | −0.464102 | + | 0.803848i | −0.0152513 | + | 0.0264161i | ||||
\(927\) | −2.66987 | − | 4.62436i | −0.0876901 | − | 0.151884i | ||||
\(928\) | 9.46410i | 0.310674i | ||||||||
\(929\) | 38.7846 | − | 22.3923i | 1.27248 | − | 0.734668i | 0.297027 | − | 0.954869i | \(-0.404005\pi\) |
0.975454 | + | 0.220201i | \(0.0706714\pi\) | |||||||
\(930\) | 3.00000 | − | 1.73205i | 0.0983739 | − | 0.0567962i | ||||
\(931\) | 12.9282i | 0.423705i | ||||||||
\(932\) | 0.633975 | + | 1.09808i | 0.0207665 | + | 0.0359687i | ||||
\(933\) | 20.6603 | − | 35.7846i | 0.676386 | − | 1.17154i | ||||
\(934\) | −8.78461 | − | 5.07180i | −0.287441 | − | 0.165954i | ||||
\(935\) | 6.58846 | 0.215466 | ||||||||
\(936\) | 11.5981 | − | 11.1603i | 0.379095 | − | 0.364784i | ||||
\(937\) | −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 | ||||
\(941\) | − | 44.7846i | − | 1.45994i | −0.683481 | − | 0.729968i | \(-0.739535\pi\) | ||
0.683481 | − | 0.729968i | \(-0.260465\pi\) | |||||||
\(942\) | −30.7583 | + | 17.7583i | −1.00216 | + | 0.578598i | ||||
\(943\) | 22.8231 | − | 13.1769i | 0.743222 | − | 0.429099i | ||||
\(944\) | 10.3923i | 0.338241i | ||||||||
\(945\) | 6.00000 | + | 10.3923i | 0.195180 | + | 0.338062i | ||||
\(946\) | −3.00000 | + | 5.19615i | −0.0975384 | + | 0.168941i | ||||
\(947\) | 49.6865 | + | 28.6865i | 1.61460 | + | 0.932187i | 0.988286 | + | 0.152612i | \(0.0487686\pi\) |
0.626309 | + | 0.779575i | \(0.284565\pi\) | |||||||
\(948\) | 16.9282 | 0.549802 | ||||||||
\(949\) | 4.90192 | + | 19.8109i | 0.159123 | + | 0.643089i | ||||
\(950\) | 6.46410 | 0.209723 | ||||||||
\(951\) | 30.2942 | + | 17.4904i | 0.982358 | + | 0.567164i | ||||
\(952\) | 3.29423 | − | 5.70577i | 0.106767 | − | 0.184925i | ||||
\(953\) | −12.2942 | − | 21.2942i | −0.398249 | − | 0.689788i | 0.595261 | − | 0.803533i | \(-0.297049\pi\) |
−0.993510 | + | 0.113745i | \(0.963715\pi\) | |||||||
\(954\) | 28.8564i | 0.934261i | ||||||||
\(955\) | −16.6865 | + | 9.63397i | −0.539964 | + | 0.311748i | ||||
\(956\) | −7.09808 | + | 4.09808i | −0.229568 | + | 0.132541i | ||||
\(957\) | 77.5692i | 2.50746i | ||||||||
\(958\) | −5.49038 | − | 9.50962i | −0.177386 | − | 0.307242i | ||||
\(959\) | −12.2942 | + | 21.2942i | −0.397001 | + | 0.687627i | ||||
\(960\) | −2.36603 | − | 1.36603i | −0.0763631 | − | 0.0440883i | ||||
\(961\) | 29.3923 | 0.948139 | ||||||||
\(962\) | 27.9904 | + | 29.0885i | 0.902446 | + | 0.937850i | ||||
\(963\) | 1.51666 | 0.0488737 | ||||||||
\(964\) | −7.50000 | − | 4.33013i | −0.241559 | − | 0.139464i | ||||
\(965\) | 2.19615 | − | 3.80385i | 0.0706966 | − | 0.122450i | ||||
\(966\) | −10.3923 | − | 18.0000i | −0.334367 | − | 0.579141i | ||||
\(967\) | − | 38.5692i | − | 1.24030i | −0.784482 | − | 0.620151i | \(-0.787071\pi\) | ||
0.784482 | − | 0.620151i | \(-0.212929\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | −33.5885 | + | 19.3923i | −1.07902 | + | 0.622971i | ||||
\(970\) | 15.1244i | 0.485614i | ||||||||
\(971\) | 23.3827 | + | 40.5000i | 0.750386 | + | 1.29971i | 0.947636 | + | 0.319354i | \(0.103466\pi\) |
−0.197250 | + | 0.980353i | \(0.563201\pi\) | |||||||
\(972\) | 9.36603 | − | 16.2224i | 0.300415 | − | 0.520335i | ||||
\(973\) | −23.8923 | − | 13.7942i | −0.765952 | − | 0.442223i | ||||
\(974\) | −33.2487 | −1.06536 | ||||||||
\(975\) | −2.73205 | + | 9.46410i | −0.0874957 | + | 0.303094i | ||||
\(976\) | −4.19615 | −0.134316 | ||||||||
\(977\) | 3.80385 | + | 2.19615i | 0.121696 | + | 0.0702611i | 0.559612 | − | 0.828755i | \(-0.310950\pi\) |
−0.437916 | + | 0.899016i | \(0.644283\pi\) | |||||||
\(978\) | 9.92820 | − | 17.1962i | 0.317469 | − | 0.549872i | ||||
\(979\) | 25.7942 | + | 44.6769i | 0.824387 | + | 1.42788i | ||||
\(980\) | 2.00000i | 0.0638877i | ||||||||
\(981\) | 59.7846 | − | 34.5167i | 1.90878 | − | 1.10203i | ||||
\(982\) | −2.89230 | + | 1.66987i | −0.0922972 | + | 0.0532878i | ||||
\(983\) | 38.5692i | 1.23017i | 0.788462 | + | 0.615084i | \(0.210878\pi\) | ||||
−0.788462 | + | 0.615084i | \(0.789122\pi\) | |||||||
\(984\) | −14.1962 | − | 24.5885i | −0.452557 | − | 0.783851i | ||||
\(985\) | −4.79423 | + | 8.30385i | −0.152757 | + | 0.264583i | ||||
\(986\) | 18.0000 | + | 10.3923i | 0.573237 | + | 0.330958i | ||||
\(987\) | 24.5885 | 0.782659 | ||||||||
\(988\) | −22.3923 | − | 6.46410i | −0.712394 | − | 0.205650i | ||||
\(989\) | 5.07180 | 0.161274 | ||||||||
\(990\) | −11.5981 | − | 6.69615i | −0.368611 | − | 0.212818i | ||||
\(991\) | −25.5885 | + | 44.3205i | −0.812844 | + | 1.40789i | 0.0980215 | + | 0.995184i | \(0.468749\pi\) |
−0.910866 | + | 0.412703i | \(0.864585\pi\) | |||||||
\(992\) | 0.633975 | + | 1.09808i | 0.0201287 | + | 0.0348640i | ||||
\(993\) | − | 2.53590i | − | 0.0804743i | ||||||
\(994\) | −15.5885 | + | 9.00000i | −0.494436 | + | 0.285463i | ||||
\(995\) | 12.4641 | − | 7.19615i | 0.395139 | − | 0.228133i | ||||
\(996\) | − | 6.00000i | − | 0.190117i | ||||||
\(997\) | 21.2846 | + | 36.8660i | 0.674090 | + | 1.16756i | 0.976734 | + | 0.214455i | \(0.0687975\pi\) |
−0.302644 | + | 0.953104i | \(0.597869\pi\) | |||||||
\(998\) | −0.928203 | + | 1.60770i | −0.0293818 | + | 0.0508907i | ||||
\(999\) | −38.7846 | − | 22.3923i | −1.22709 | − | 0.708461i |
(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 | 130.2.l.a.121.2 | yes | 4 | |
3.2 | odd | 2 | 1170.2.bs.c.901.1 | 4 | |||
4.3 | odd | 2 | 1040.2.da.a.641.1 | 4 | |||
5.2 | odd | 4 | 650.2.n.a.199.1 | 4 | |||
5.3 | odd | 4 | 650.2.n.b.199.2 | 4 | |||
5.4 | even | 2 | 650.2.m.a.251.1 | 4 | |||
13.2 | odd | 12 | 1690.2.e.n.991.2 | 4 | |||
13.3 | even | 3 | 1690.2.l.g.361.1 | 4 | |||
13.4 | even | 6 | 1690.2.d.f.1351.3 | 4 | |||
13.5 | odd | 4 | 1690.2.e.n.191.2 | 4 | |||
13.6 | odd | 12 | 1690.2.a.j.1.1 | 2 | |||
13.7 | odd | 12 | 1690.2.a.m.1.1 | 2 | |||
13.8 | odd | 4 | 1690.2.e.l.191.2 | 4 | |||
13.9 | even | 3 | 1690.2.d.f.1351.1 | 4 | |||
13.10 | even | 6 | inner | 130.2.l.a.101.2 | ✓ | 4 | |
13.11 | odd | 12 | 1690.2.e.l.991.2 | 4 | |||
13.12 | even | 2 | 1690.2.l.g.1161.1 | 4 | |||
39.23 | odd | 6 | 1170.2.bs.c.361.1 | 4 | |||
52.23 | odd | 6 | 1040.2.da.a.881.1 | 4 | |||
65.19 | odd | 12 | 8450.2.a.bm.1.2 | 2 | |||
65.23 | odd | 12 | 650.2.n.a.49.1 | 4 | |||
65.49 | even | 6 | 650.2.m.a.101.1 | 4 | |||
65.59 | odd | 12 | 8450.2.a.bf.1.2 | 2 | |||
65.62 | odd | 12 | 650.2.n.b.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.l.a.101.2 | ✓ | 4 | 13.10 | even | 6 | inner | |
130.2.l.a.121.2 | yes | 4 | 1.1 | even | 1 | trivial | |
650.2.m.a.101.1 | 4 | 65.49 | even | 6 | |||
650.2.m.a.251.1 | 4 | 5.4 | even | 2 | |||
650.2.n.a.49.1 | 4 | 65.23 | odd | 12 | |||
650.2.n.a.199.1 | 4 | 5.2 | odd | 4 | |||
650.2.n.b.49.2 | 4 | 65.62 | odd | 12 | |||
650.2.n.b.199.2 | 4 | 5.3 | odd | 4 | |||
1040.2.da.a.641.1 | 4 | 4.3 | odd | 2 | |||
1040.2.da.a.881.1 | 4 | 52.23 | odd | 6 | |||
1170.2.bs.c.361.1 | 4 | 39.23 | odd | 6 | |||
1170.2.bs.c.901.1 | 4 | 3.2 | odd | 2 | |||
1690.2.a.j.1.1 | 2 | 13.6 | odd | 12 | |||
1690.2.a.m.1.1 | 2 | 13.7 | odd | 12 | |||
1690.2.d.f.1351.1 | 4 | 13.9 | even | 3 | |||
1690.2.d.f.1351.3 | 4 | 13.4 | even | 6 | |||
1690.2.e.l.191.2 | 4 | 13.8 | odd | 4 | |||
1690.2.e.l.991.2 | 4 | 13.11 | odd | 12 | |||
1690.2.e.n.191.2 | 4 | 13.5 | odd | 4 | |||
1690.2.e.n.991.2 | 4 | 13.2 | odd | 12 | |||
1690.2.l.g.361.1 | 4 | 13.3 | even | 3 | |||
1690.2.l.g.1161.1 | 4 | 13.12 | even | 2 | |||
8450.2.a.bf.1.2 | 2 | 65.59 | odd | 12 | |||
8450.2.a.bm.1.2 | 2 | 65.19 | odd | 12 |