Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (of order \(4\), 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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.6 | ||
Root | \(-1.31011 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.323 |
Dual form | 2070.2.j.j.737.6 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.85363 | − | 1.25063i | −0.828967 | − | 0.559297i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.08825 | + | 3.08825i | −1.16725 | + | 1.16725i | −0.184398 | + | 0.982852i | \(0.559034\pi\) |
−0.982852 | + | 0.184398i | \(0.940966\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.426386 | − | 2.19504i | −0.134835 | − | 0.694132i | ||||
\(11\) | 1.10820i | 0.334135i | 0.985945 | + | 0.167068i | \(0.0534298\pi\) | ||||
−0.985945 | + | 0.167068i | \(0.946570\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.55227 | − | 2.55227i | −0.707872 | − | 0.707872i | 0.258215 | − | 0.966087i | \(-0.416866\pi\) |
−0.966087 | + | 0.258215i | \(0.916866\pi\) | |||||||
\(14\) | −4.36745 | −1.16725 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.10820 | + | 1.10820i | 0.268778 | + | 0.268778i | 0.828608 | − | 0.559830i | \(-0.189133\pi\) |
−0.559830 | + | 0.828608i | \(0.689133\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.95731i | − | 1.82553i | −0.408483 | − | 0.912766i | \(-0.633942\pi\) | ||
0.408483 | − | 0.912766i | \(-0.366058\pi\) | |||||||
\(20\) | 1.25063 | − | 1.85363i | 0.279648 | − | 0.414484i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.783617 | + | 0.783617i | −0.167068 | + | 0.167068i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.87187 | + | 4.63639i | 0.374374 | + | 0.927278i | ||||
\(26\) | − | 3.60945i | − | 0.707872i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.08825 | − | 3.08825i | −0.583625 | − | 0.583625i | ||||
\(29\) | 6.30046 | 1.16997 | 0.584983 | − | 0.811045i | \(-0.301101\pi\) | ||||
0.584983 | + | 0.811045i | \(0.301101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.74374 | 0.672395 | 0.336198 | − | 0.941791i | \(-0.390859\pi\) | ||||
0.336198 | + | 0.941791i | \(0.390859\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.56723i | 0.268778i | ||||||||
\(35\) | 9.58672 | − | 1.86222i | 1.62045 | − | 0.314773i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.56245 | − | 4.56245i | 0.750062 | − | 0.750062i | −0.224428 | − | 0.974491i | \(-0.572051\pi\) |
0.974491 | + | 0.224428i | \(0.0720515\pi\) | |||||||
\(38\) | 5.62667 | − | 5.62667i | 0.912766 | − | 0.912766i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.19504 | − | 0.426386i | 0.347066 | − | 0.0674176i | ||||
\(41\) | − | 4.15924i | − | 0.649564i | −0.945789 | − | 0.324782i | \(-0.894709\pi\) | ||
0.945789 | − | 0.324782i | \(-0.105291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.87187 | − | 3.87187i | −0.590455 | − | 0.590455i | 0.347300 | − | 0.937754i | \(-0.387099\pi\) |
−0.937754 | + | 0.347300i | \(0.887099\pi\) | |||||||
\(44\) | −1.10820 | −0.167068 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 6.32747 | + | 6.32747i | 0.922957 | + | 0.922957i | 0.997237 | − | 0.0742808i | \(-0.0236661\pi\) |
−0.0742808 | + | 0.997237i | \(0.523666\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 12.0746i | − | 1.72494i | ||||||
\(50\) | −1.95481 | + | 4.60203i | −0.276452 | + | 0.650826i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.55227 | − | 2.55227i | 0.353936 | − | 0.353936i | ||||
\(53\) | −3.25022 | + | 3.25022i | −0.446453 | + | 0.446453i | −0.894173 | − | 0.447721i | \(-0.852236\pi\) |
0.447721 | + | 0.894173i | \(0.352236\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.38595 | − | 2.05419i | 0.186881 | − | 0.276987i | ||||
\(56\) | − | 4.36745i | − | 0.583625i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.45510 | + | 4.45510i | 0.584983 | + | 0.584983i | ||||
\(59\) | −12.9339 | −1.68386 | −0.841928 | − | 0.539589i | \(-0.818580\pi\) | ||||
−0.841928 | + | 0.539589i | \(0.818580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0995 | 1.67722 | 0.838608 | − | 0.544736i | \(-0.183370\pi\) | ||||
0.838608 | + | 0.544736i | \(0.183370\pi\) | |||||||
\(62\) | 2.64722 | + | 2.64722i | 0.336198 | + | 0.336198i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 1.53902 | + | 7.92289i | 0.190892 | + | 0.982713i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0854412 | − | 0.0854412i | 0.0104383 | − | 0.0104383i | −0.701868 | − | 0.712307i | \(-0.747651\pi\) |
0.712307 | + | 0.701868i | \(0.247651\pi\) | |||||||
\(68\) | −1.10820 | + | 1.10820i | −0.134389 | + | 0.134389i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.09562 | + | 5.46205i | 0.967612 | + | 0.652839i | ||||
\(71\) | 2.39084i | 0.283741i | 0.989885 | + | 0.141870i | \(0.0453116\pi\) | ||||
−0.989885 | + | 0.141870i | \(0.954688\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.36995 | + | 2.36995i | 0.277381 | + | 0.277381i | 0.832063 | − | 0.554682i | \(-0.187160\pi\) |
−0.554682 | + | 0.832063i | \(0.687160\pi\) | |||||||
\(74\) | 6.45228 | 0.750062 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.95731 | 0.912766 | ||||||||
\(77\) | −3.42241 | − | 3.42241i | −0.390019 | − | 0.390019i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.4194i | − | 1.50980i | −0.655843 | − | 0.754898i | \(-0.727686\pi\) | ||
0.655843 | − | 0.754898i | \(-0.272314\pi\) | |||||||
\(80\) | 1.85363 | + | 1.25063i | 0.207242 | + | 0.139824i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.94103 | − | 2.94103i | 0.324782 | − | 0.324782i | ||||
\(83\) | 4.53963 | − | 4.53963i | 0.498289 | − | 0.498289i | −0.412616 | − | 0.910905i | \(-0.635385\pi\) |
0.910905 | + | 0.412616i | \(0.135385\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.668247 | − | 3.44014i | −0.0724815 | − | 0.373135i | ||||
\(86\) | − | 5.47565i | − | 0.590455i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.783617 | − | 0.783617i | −0.0835338 | − | 0.0835338i | ||||
\(89\) | 1.98703 | 0.210625 | 0.105312 | − | 0.994439i | \(-0.466416\pi\) | ||||
0.105312 | + | 0.994439i | \(0.466416\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.7641 | 1.65253 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.94840i | 0.922957i | ||||||||
\(95\) | −9.95162 | + | 14.7499i | −1.02101 | + | 1.51331i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.85409 | − | 1.85409i | 0.188255 | − | 0.188255i | −0.606687 | − | 0.794941i | \(-0.707502\pi\) |
0.794941 | + | 0.606687i | \(0.207502\pi\) | |||||||
\(98\) | 8.53804 | − | 8.53804i | 0.862472 | − | 0.862472i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.63639 | + | 1.87187i | −0.463639 | + | 0.187187i | ||||
\(101\) | − | 4.75010i | − | 0.472653i | −0.971674 | − | 0.236326i | \(-0.924057\pi\) | ||
0.971674 | − | 0.236326i | \(-0.0759434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.86841 | − | 7.86841i | −0.775297 | − | 0.775297i | 0.203730 | − | 0.979027i | \(-0.434694\pi\) |
−0.979027 | + | 0.203730i | \(0.934694\pi\) | |||||||
\(104\) | 3.60945 | 0.353936 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.59651 | −0.446453 | ||||||||
\(107\) | −5.84343 | − | 5.84343i | −0.564906 | − | 0.564906i | 0.365791 | − | 0.930697i | \(-0.380799\pi\) |
−0.930697 | + | 0.365791i | \(0.880799\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.5666i | − | 1.58679i | −0.608707 | − | 0.793395i | \(-0.708311\pi\) | ||
0.608707 | − | 0.793395i | \(-0.291689\pi\) | |||||||
\(110\) | 2.43254 | − | 0.472522i | 0.231934 | − | 0.0450532i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.08825 | − | 3.08825i | 0.291812 | − | 0.291812i | ||||
\(113\) | −1.82387 | + | 1.82387i | −0.171575 | + | 0.171575i | −0.787671 | − | 0.616096i | \(-0.788713\pi\) |
0.616096 | + | 0.787671i | \(0.288713\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.19504 | + | 0.426386i | −0.204688 | + | 0.0397607i | ||||
\(116\) | 6.30046i | 0.584983i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.14568 | − | 9.14568i | −0.841928 | − | 0.841928i | ||||
\(119\) | −6.84481 | −0.627463 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.77189 | 0.888354 | ||||||||
\(122\) | 9.26272 | + | 9.26272i | 0.838608 | + | 0.838608i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.74374i | 0.336198i | ||||||||
\(125\) | 2.32864 | − | 10.9351i | 0.208280 | − | 0.978069i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.15328 | + | 4.15328i | −0.368544 | + | 0.368544i | −0.866946 | − | 0.498402i | \(-0.833920\pi\) |
0.498402 | + | 0.866946i | \(0.333920\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.51408 | + | 6.69058i | −0.395911 | + | 0.586803i | ||||
\(131\) | − | 0.125728i | − | 0.0109849i | −0.999985 | − | 0.00549245i | \(-0.998252\pi\) | ||
0.999985 | − | 0.00549245i | \(-0.00174831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.5742 | + | 24.5742i | 2.13085 | + | 2.13085i | ||||
\(134\) | 0.120832 | 0.0104383 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.56723 | −0.134389 | ||||||||
\(137\) | −10.2258 | − | 10.2258i | −0.873645 | − | 0.873645i | 0.119223 | − | 0.992868i | \(-0.461960\pi\) |
−0.992868 | + | 0.119223i | \(0.961960\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.8803i | − | 1.26213i | −0.775731 | − | 0.631064i | \(-0.782618\pi\) | ||
0.775731 | − | 0.631064i | \(-0.217382\pi\) | |||||||
\(140\) | 1.86222 | + | 9.58672i | 0.157386 | + | 0.810226i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.69058 | + | 1.69058i | −0.141870 | + | 0.141870i | ||||
\(143\) | 2.82843 | − | 2.82843i | 0.236525 | − | 0.236525i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6787 | − | 7.87953i | −0.969864 | − | 0.654359i | ||||
\(146\) | 3.35161i | 0.277381i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.56245 | + | 4.56245i | 0.375031 | + | 0.375031i | ||||
\(149\) | 2.44724 | 0.200486 | 0.100243 | − | 0.994963i | \(-0.468038\pi\) | ||||
0.100243 | + | 0.994963i | \(0.468038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0052 | −1.79076 | −0.895378 | − | 0.445307i | \(-0.853094\pi\) | ||||
−0.895378 | + | 0.445307i | \(0.853094\pi\) | |||||||
\(152\) | 5.62667 | + | 5.62667i | 0.456383 | + | 0.456383i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 4.84001i | − | 0.390019i | ||||||
\(155\) | −6.93950 | − | 4.68202i | −0.557394 | − | 0.376069i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.65225 | + | 1.65225i | −0.131864 | + | 0.131864i | −0.769958 | − | 0.638094i | \(-0.779723\pi\) |
0.638094 | + | 0.769958i | \(0.279723\pi\) | |||||||
\(158\) | 9.48892 | − | 9.48892i | 0.754898 | − | 0.754898i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.426386 | + | 2.19504i | 0.0337088 | + | 0.173533i | ||||
\(161\) | 4.36745i | 0.344203i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.60543 | − | 3.60543i | −0.282399 | − | 0.282399i | 0.551666 | − | 0.834065i | \(-0.313992\pi\) |
−0.834065 | + | 0.551666i | \(0.813992\pi\) | |||||||
\(164\) | 4.15924 | 0.324782 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.42001 | 0.498289 | ||||||||
\(167\) | 17.0620 | + | 17.0620i | 1.32030 | + | 1.32030i | 0.913533 | + | 0.406765i | \(0.133343\pi\) |
0.406765 | + | 0.913533i | \(0.366657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.0281519i | 0.00216553i | ||||||||
\(170\) | 1.96002 | − | 2.90507i | 0.150327 | − | 0.222808i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.87187 | − | 3.87187i | 0.295227 | − | 0.295227i | ||||
\(173\) | 12.9466 | − | 12.9466i | 0.984308 | − | 0.984308i | −0.0155704 | − | 0.999879i | \(-0.504956\pi\) |
0.999879 | + | 0.0155704i | \(0.00495640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.0991 | − | 8.53754i | −1.51935 | − | 0.645377i | ||||
\(176\) | − | 1.10820i | − | 0.0835338i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.40504 | + | 1.40504i | 0.105312 | + | 0.105312i | ||||
\(179\) | −9.01390 | −0.673731 | −0.336865 | − | 0.941553i | \(-0.609367\pi\) | ||||
−0.336865 | + | 0.941553i | \(0.609367\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.72272 | 0.202379 | 0.101189 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101189 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(182\) | 11.1469 | + | 11.1469i | 0.826263 | + | 0.826263i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | −14.1630 | + | 2.75116i | −1.04128 | + | 0.202270i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.22811 | + | 1.22811i | −0.0898083 | + | 0.0898083i | ||||
\(188\) | −6.32747 | + | 6.32747i | −0.461478 | + | 0.461478i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.4666 | + | 3.39289i | −1.26716 | + | 0.246146i | ||||
\(191\) | 21.7099i | 1.57087i | 0.618941 | + | 0.785437i | \(0.287562\pi\) | ||||
−0.618941 | + | 0.785437i | \(0.712438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5672 | + | 10.5672i | 0.760646 | + | 0.760646i | 0.976439 | − | 0.215793i | \(-0.0692337\pi\) |
−0.215793 | + | 0.976439i | \(0.569234\pi\) | |||||||
\(194\) | 2.62208 | 0.188255 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0746 | 0.862472 | ||||||||
\(197\) | −2.44764 | − | 2.44764i | −0.174387 | − | 0.174387i | 0.614517 | − | 0.788904i | \(-0.289351\pi\) |
−0.788904 | + | 0.614517i | \(0.789351\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.89032i | 0.417553i | 0.977963 | + | 0.208777i | \(0.0669482\pi\) | ||||
−0.977963 | + | 0.208777i | \(0.933052\pi\) | |||||||
\(200\) | −4.60203 | − | 1.95481i | −0.325413 | − | 0.138226i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.35883 | − | 3.35883i | 0.236326 | − | 0.236326i | ||||
\(203\) | −19.4574 | + | 19.4574i | −1.36564 | + | 1.36564i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.20165 | + | 7.70968i | −0.363299 | + | 0.538467i | ||||
\(206\) | − | 11.1276i | − | 0.775297i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.55227 | + | 2.55227i | 0.176968 | + | 0.176968i | ||||
\(209\) | 8.81830 | 0.609975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.5443 | −1.41432 | −0.707162 | − | 0.707051i | \(-0.750025\pi\) | ||||
−0.707162 | + | 0.707051i | \(0.750025\pi\) | |||||||
\(212\) | −3.25022 | − | 3.25022i | −0.223226 | − | 0.223226i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 8.26386i | − | 0.564906i | ||||||
\(215\) | 2.33474 | + | 12.0193i | 0.159228 | + | 0.819707i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.5616 | + | 11.5616i | −0.784853 | + | 0.784853i | ||||
\(218\) | 11.7143 | − | 11.7143i | 0.793395 | − | 0.793395i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.05419 | + | 1.38595i | 0.138494 | + | 0.0934404i | ||||
\(221\) | − | 5.65685i | − | 0.380521i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0089 | − | 16.0089i | −1.07204 | − | 1.07204i | −0.997195 | − | 0.0748413i | \(-0.976155\pi\) |
−0.0748413 | − | 0.997195i | \(-0.523845\pi\) | |||||||
\(224\) | 4.36745 | 0.291812 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.57934 | −0.171575 | ||||||||
\(227\) | −5.02446 | − | 5.02446i | −0.333485 | − | 0.333485i | 0.520423 | − | 0.853908i | \(-0.325774\pi\) |
−0.853908 | + | 0.520423i | \(0.825774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.7509i | − | 0.776520i | −0.921550 | − | 0.388260i | \(-0.873076\pi\) | ||
0.921550 | − | 0.388260i | \(-0.126924\pi\) | |||||||
\(230\) | −1.85363 | − | 1.25063i | −0.122225 | − | 0.0824638i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.45510 | + | 4.45510i | −0.292492 | + | 0.292492i | ||||
\(233\) | −16.0418 | + | 16.0418i | −1.05093 | + | 1.05093i | −0.0523010 | + | 0.998631i | \(0.516656\pi\) |
−0.998631 | + | 0.0523010i | \(0.983344\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.81547 | − | 19.6421i | −0.248894 | − | 1.28131i | ||||
\(236\) | − | 12.9339i | − | 0.841928i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.84001 | − | 4.84001i | −0.313731 | − | 0.313731i | ||||
\(239\) | 15.8376 | 1.02445 | 0.512223 | − | 0.858852i | \(-0.328822\pi\) | ||||
0.512223 | + | 0.858852i | \(0.328822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.54557 | −0.0995588 | −0.0497794 | − | 0.998760i | \(-0.515852\pi\) | ||||
−0.0497794 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(242\) | 6.90977 | + | 6.90977i | 0.444177 | + | 0.444177i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.0995i | 0.838608i | ||||||||
\(245\) | −15.1008 | + | 22.3818i | −0.964756 | + | 1.42992i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.3092 | + | 20.3092i | −1.29224 | + | 1.29224i | ||||
\(248\) | −2.64722 | + | 2.64722i | −0.168099 | + | 0.168099i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.37891 | − | 6.08572i | 0.593175 | − | 0.384895i | ||||
\(251\) | − | 2.42064i | − | 0.152789i | −0.997078 | − | 0.0763946i | \(-0.975659\pi\) | ||
0.997078 | − | 0.0763946i | \(-0.0243409\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.783617 | + | 0.783617i | 0.0492655 | + | 0.0492655i | ||||
\(254\) | −5.87362 | −0.368544 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.5298 | + | 18.5298i | 1.15586 | + | 1.15586i | 0.985357 | + | 0.170501i | \(0.0545388\pi\) |
0.170501 | + | 0.985357i | \(0.445461\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.1800i | 1.75102i | ||||||||
\(260\) | −7.92289 | + | 1.53902i | −0.491357 | + | 0.0954461i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0889031 | − | 0.0889031i | 0.00549245 | − | 0.00549245i | ||||
\(263\) | 14.2120 | − | 14.2120i | 0.876350 | − | 0.876350i | −0.116805 | − | 0.993155i | \(-0.537265\pi\) |
0.993155 | + | 0.116805i | \(0.0372652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0895 | − | 1.95989i | 0.619794 | − | 0.120395i | ||||
\(266\) | 34.7531i | 2.13085i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0854412 | + | 0.0854412i | 0.00521915 | + | 0.00521915i | ||||
\(269\) | 25.2330 | 1.53849 | 0.769243 | − | 0.638956i | \(-0.220634\pi\) | ||||
0.769243 | + | 0.638956i | \(0.220634\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2766 | 0.988735 | 0.494367 | − | 0.869253i | \(-0.335400\pi\) | ||||
0.494367 | + | 0.869253i | \(0.335400\pi\) | |||||||
\(272\) | −1.10820 | − | 1.10820i | −0.0671946 | − | 0.0671946i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 14.4614i | − | 0.873645i | ||||||
\(275\) | −5.13805 | + | 2.07441i | −0.309836 | + | 0.125091i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.8997 | + | 12.8997i | −0.775065 | + | 0.775065i | −0.978987 | − | 0.203922i | \(-0.934631\pi\) |
0.203922 | + | 0.978987i | \(0.434631\pi\) | |||||||
\(278\) | 10.5219 | − | 10.5219i | 0.631064 | − | 0.631064i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.46205 | + | 8.09562i | −0.326420 | + | 0.483806i | ||||
\(281\) | − | 0.578255i | − | 0.0344958i | −0.999851 | − | 0.0172479i | \(-0.994510\pi\) | ||
0.999851 | − | 0.0172479i | \(-0.00549045\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6049 | − | 11.6049i | −0.689841 | − | 0.689841i | 0.272356 | − | 0.962197i | \(-0.412197\pi\) |
−0.962197 | + | 0.272356i | \(0.912197\pi\) | |||||||
\(284\) | −2.39084 | −0.141870 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 12.8448 | + | 12.8448i | 0.758203 | + | 0.758203i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.5438i | − | 0.855517i | ||||||
\(290\) | −2.68643 | − | 13.8298i | −0.157753 | − | 0.812112i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.36995 | + | 2.36995i | −0.138691 | + | 0.138691i | ||||
\(293\) | 4.23175 | − | 4.23175i | 0.247221 | − | 0.247221i | −0.572608 | − | 0.819829i | \(-0.694068\pi\) |
0.819829 | + | 0.572608i | \(0.194068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.9747 | + | 16.1755i | 1.39586 | + | 0.941776i | ||||
\(296\) | 6.45228i | 0.375031i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.73046 | + | 1.73046i | 0.100243 | + | 0.100243i | ||||
\(299\) | −3.60945 | −0.208740 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.9146 | 1.37842 | ||||||||
\(302\) | −15.5600 | − | 15.5600i | −0.895378 | − | 0.895378i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.95731i | 0.456383i | ||||||||
\(305\) | −24.2815 | − | 16.3825i | −1.39036 | − | 0.938061i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.67562 | − | 9.67562i | 0.552217 | − | 0.552217i | −0.374863 | − | 0.927080i | \(-0.622310\pi\) |
0.927080 | + | 0.374863i | \(0.122310\pi\) | |||||||
\(308\) | 3.42241 | − | 3.42241i | 0.195010 | − | 0.195010i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.59628 | − | 8.21765i | −0.0906626 | − | 0.466731i | ||||
\(311\) | 15.6457i | 0.887185i | 0.896229 | + | 0.443593i | \(0.146296\pi\) | ||||
−0.896229 | + | 0.443593i | \(0.853704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.21225 | − | 1.21225i | −0.0685205 | − | 0.0685205i | 0.672016 | − | 0.740537i | \(-0.265429\pi\) |
−0.740537 | + | 0.672016i | \(0.765429\pi\) | |||||||
\(314\) | −2.33663 | −0.131864 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4194 | 0.754898 | ||||||||
\(317\) | −14.1728 | − | 14.1728i | −0.796024 | − | 0.796024i | 0.186442 | − | 0.982466i | \(-0.440304\pi\) |
−0.982466 | + | 0.186442i | \(0.940304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.98218i | 0.390927i | ||||||||
\(320\) | −1.25063 | + | 1.85363i | −0.0699121 | + | 0.103621i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.08825 | + | 3.08825i | −0.172102 | + | 0.172102i | ||||
\(323\) | 8.81830 | − | 8.81830i | 0.490663 | − | 0.490663i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.05580 | − | 16.6108i | 0.391385 | − | 0.921403i | ||||
\(326\) | − | 5.09884i | − | 0.282399i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.94103 | + | 2.94103i | 0.162391 | + | 0.162391i | ||||
\(329\) | −39.0817 | −2.15464 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7203 | 1.08392 | 0.541962 | − | 0.840403i | \(-0.317681\pi\) | ||||
0.541962 | + | 0.840403i | \(0.317681\pi\) | |||||||
\(332\) | 4.53963 | + | 4.53963i | 0.249145 | + | 0.249145i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.1293i | 1.32030i | ||||||||
\(335\) | −0.265231 | + | 0.0515211i | −0.0144911 | + | 0.00281490i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.7496 | + | 10.7496i | −0.585566 | + | 0.585566i | −0.936427 | − | 0.350862i | \(-0.885889\pi\) |
0.350862 | + | 0.936427i | \(0.385889\pi\) | |||||||
\(338\) | −0.0199064 | + | 0.0199064i | −0.00108277 | + | 0.00108277i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.44014 | − | 0.668247i | 0.186568 | − | 0.0362408i | ||||
\(341\) | 4.14882i | 0.224671i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.6717 | + | 15.6717i | 0.846191 | + | 0.846191i | ||||
\(344\) | 5.47565 | 0.295227 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.3092 | 0.984308 | ||||||||
\(347\) | 2.65585 | + | 2.65585i | 0.142574 | + | 0.142574i | 0.774791 | − | 0.632217i | \(-0.217855\pi\) |
−0.632217 | + | 0.774791i | \(0.717855\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7.28234i | − | 0.389815i | −0.980822 | − | 0.194907i | \(-0.937559\pi\) | ||
0.980822 | − | 0.194907i | \(-0.0624407\pi\) | |||||||
\(350\) | −8.17529 | − | 20.2492i | −0.436988 | − | 1.08236i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.783617 | − | 0.783617i | 0.0417669 | − | 0.0417669i | ||||
\(353\) | −14.4162 | + | 14.4162i | −0.767299 | + | 0.767299i | −0.977630 | − | 0.210331i | \(-0.932546\pi\) |
0.210331 | + | 0.977630i | \(0.432546\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.99005 | − | 4.43173i | 0.158695 | − | 0.235212i | ||||
\(356\) | 1.98703i | 0.105312i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.37379 | − | 6.37379i | −0.336865 | − | 0.336865i | ||||
\(359\) | 27.4379 | 1.44812 | 0.724059 | − | 0.689739i | \(-0.242275\pi\) | ||||
0.724059 | + | 0.689739i | \(0.242275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −44.3188 | −2.33257 | ||||||||
\(362\) | 1.92526 | + | 1.92526i | 0.101189 | + | 0.101189i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.7641i | 0.826263i | ||||||||
\(365\) | −1.42908 | − | 7.35691i | −0.0748015 | − | 0.385078i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.15460 | + | 4.15460i | −0.216868 | + | 0.216868i | −0.807177 | − | 0.590309i | \(-0.799006\pi\) |
0.590309 | + | 0.807177i | \(0.299006\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.9601 | − | 8.06939i | −0.621777 | − | 0.419508i | ||||
\(371\) | − | 20.0750i | − | 1.04224i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.45229 | − | 7.45229i | −0.385865 | − | 0.385865i | 0.487345 | − | 0.873210i | \(-0.337966\pi\) |
−0.873210 | + | 0.487345i | \(0.837966\pi\) | |||||||
\(374\) | −1.73681 | −0.0898083 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.94840 | −0.461478 | ||||||||
\(377\) | −16.0805 | − | 16.0805i | −0.828187 | − | 0.828187i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.7341i | 1.98964i | 0.101668 | + | 0.994818i | \(0.467582\pi\) | ||||
−0.101668 | + | 0.994818i | \(0.532418\pi\) | |||||||
\(380\) | −14.7499 | − | 9.95162i | −0.756653 | − | 0.510507i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.3512 | + | 15.3512i | −0.785437 | + | 0.785437i | ||||
\(383\) | 20.6426 | − | 20.6426i | 1.05479 | − | 1.05479i | 0.0563772 | − | 0.998410i | \(-0.482045\pi\) |
0.998410 | − | 0.0563772i | \(-0.0179550\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.06372 | + | 10.6240i | 0.105177 | + | 0.541450i | ||||
\(386\) | 14.9443i | 0.760646i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.85409 | + | 1.85409i | 0.0941273 | + | 0.0941273i | ||||
\(389\) | −18.0487 | −0.915107 | −0.457553 | − | 0.889182i | \(-0.651274\pi\) | ||||
−0.457553 | + | 0.889182i | \(0.651274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.56723 | 0.0792584 | ||||||||
\(392\) | 8.53804 | + | 8.53804i | 0.431236 | + | 0.431236i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 3.46149i | − | 0.174387i | ||||||
\(395\) | −16.7826 | + | 24.8745i | −0.844424 | + | 1.25157i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5389 | − | 17.5389i | 0.880250 | − | 0.880250i | −0.113310 | − | 0.993560i | \(-0.536145\pi\) |
0.993560 | + | 0.113310i | \(0.0361452\pi\) | |||||||
\(398\) | −4.16508 | + | 4.16508i | −0.208777 | + | 0.208777i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.87187 | − | 4.63639i | −0.0935935 | − | 0.231819i | ||||
\(401\) | − | 36.2950i | − | 1.81248i | −0.422760 | − | 0.906242i | \(-0.638939\pi\) | ||
0.422760 | − | 0.906242i | \(-0.361061\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.55503 | − | 9.55503i | −0.475970 | − | 0.475970i | ||||
\(404\) | 4.75010 | 0.236326 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.5170 | −1.36564 | ||||||||
\(407\) | 5.05611 | + | 5.05611i | 0.250622 | + | 0.250622i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 35.7342i | − | 1.76694i | −0.468487 | − | 0.883471i | \(-0.655201\pi\) | ||
0.468487 | − | 0.883471i | \(-0.344799\pi\) | |||||||
\(410\) | −9.12969 | + | 1.77344i | −0.450883 | + | 0.0875841i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.86841 | − | 7.86841i | 0.387649 | − | 0.387649i | ||||
\(413\) | 39.9433 | − | 39.9433i | 1.96548 | − | 1.96548i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0922 | + | 2.73740i | −0.691757 | + | 0.134374i | ||||
\(416\) | 3.60945i | 0.176968i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.23548 | + | 6.23548i | 0.304987 | + | 0.304987i | ||||
\(419\) | −22.7578 | −1.11179 | −0.555894 | − | 0.831253i | \(-0.687624\pi\) | ||||
−0.555894 | + | 0.831253i | \(0.687624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.261330 | 0.0127364 | 0.00636822 | − | 0.999980i | \(-0.497973\pi\) | ||||
0.00636822 | + | 0.999980i | \(0.497973\pi\) | |||||||
\(422\) | −14.5270 | − | 14.5270i | −0.707162 | − | 0.707162i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 4.59651i | − | 0.223226i | ||||||
\(425\) | −3.06364 | + | 7.21246i | −0.148609 | + | 0.349856i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.4545 | + | 40.4545i | −1.95773 | + | 1.95773i | ||||
\(428\) | 5.84343 | − | 5.84343i | 0.282453 | − | 0.282453i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.84799 | + | 10.1498i | −0.330239 | + | 0.489468i | ||||
\(431\) | − | 14.2837i | − | 0.688023i | −0.938965 | − | 0.344011i | \(-0.888214\pi\) | ||
0.938965 | − | 0.344011i | \(-0.111786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.70752 | + | 1.70752i | 0.0820580 | + | 0.0820580i | 0.746944 | − | 0.664886i | \(-0.231520\pi\) |
−0.664886 | + | 0.746944i | \(0.731520\pi\) | |||||||
\(434\) | −16.3506 | −0.784853 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.5666 | 0.793395 | ||||||||
\(437\) | −5.62667 | − | 5.62667i | −0.269160 | − | 0.269160i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.5652i | 1.55425i | 0.629345 | + | 0.777126i | \(0.283323\pi\) | ||||
−0.629345 | + | 0.777126i | \(0.716677\pi\) | |||||||
\(440\) | 0.472522 | + | 2.43254i | 0.0225266 | + | 0.115967i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | − | 4.00000i | 0.190261 | − | 0.190261i | ||||
\(443\) | 2.27042 | − | 2.27042i | 0.107871 | − | 0.107871i | −0.651111 | − | 0.758982i | \(-0.725697\pi\) |
0.758982 | + | 0.651111i | \(0.225697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.68321 | − | 2.48503i | −0.174601 | − | 0.117802i | ||||
\(446\) | − | 22.6400i | − | 1.07204i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.08825 | + | 3.08825i | 0.145906 | + | 0.145906i | ||||
\(449\) | −29.5592 | −1.39499 | −0.697493 | − | 0.716591i | \(-0.745701\pi\) | ||||
−0.697493 | + | 0.716591i | \(0.745701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.60927 | 0.217042 | ||||||||
\(452\) | −1.82387 | − | 1.82387i | −0.0857877 | − | 0.0857877i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 7.10566i | − | 0.333485i | ||||||
\(455\) | −29.2208 | − | 19.7150i | −1.36989 | − | 0.924253i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.6819 | + | 24.6819i | −1.15457 | + | 1.15457i | −0.168945 | + | 0.985625i | \(0.554036\pi\) |
−0.985625 | + | 0.168945i | \(0.945964\pi\) | |||||||
\(458\) | 8.30912 | − | 8.30912i | 0.388260 | − | 0.388260i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.426386 | − | 2.19504i | −0.0198804 | − | 0.102344i | ||||
\(461\) | 29.3487i | 1.36691i | 0.729995 | + | 0.683453i | \(0.239522\pi\) | ||||
−0.729995 | + | 0.683453i | \(0.760478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.4243 | + | 10.4243i | 0.484457 | + | 0.484457i | 0.906552 | − | 0.422095i | \(-0.138705\pi\) |
−0.422095 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(464\) | −6.30046 | −0.292492 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.6865 | −1.05093 | ||||||||
\(467\) | 12.1339 | + | 12.1339i | 0.561489 | + | 0.561489i | 0.929730 | − | 0.368241i | \(-0.120040\pi\) |
−0.368241 | + | 0.929730i | \(0.620040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.527728i | 0.0243682i | ||||||||
\(470\) | 11.1911 | − | 16.5870i | 0.516207 | − | 0.765101i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.14568 | − | 9.14568i | 0.420964 | − | 0.420964i | ||||
\(473\) | 4.29081 | − | 4.29081i | 0.197292 | − | 0.197292i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 36.8932 | − | 14.8950i | 1.69278 | − | 0.683431i | ||||
\(476\) | − | 6.84481i | − | 0.313731i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.1988 | + | 11.1988i | 0.512223 | + | 0.512223i | ||||
\(479\) | −32.2536 | −1.47370 | −0.736851 | − | 0.676055i | \(-0.763688\pi\) | ||||
−0.736851 | + | 0.676055i | \(0.763688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.2892 | −1.06190 | ||||||||
\(482\) | −1.09288 | − | 1.09288i | −0.0497794 | − | 0.0497794i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.77189i | 0.444177i | ||||||||
\(485\) | −5.75558 | + | 1.11802i | −0.261347 | + | 0.0507667i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.93521 | − | 9.93521i | 0.450207 | − | 0.450207i | −0.445216 | − | 0.895423i | \(-0.646873\pi\) |
0.895423 | + | 0.445216i | \(0.146873\pi\) | |||||||
\(488\) | −9.26272 | + | 9.26272i | −0.419304 | + | 0.419304i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −26.5042 | + | 5.14845i | −1.19734 | + | 0.232583i | ||||
\(491\) | 12.6998i | 0.573132i | 0.958061 | + | 0.286566i | \(0.0925138\pi\) | ||||
−0.958061 | + | 0.286566i | \(0.907486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.98218 | + | 6.98218i | 0.314462 | + | 0.314462i | ||||
\(494\) | −28.7215 | −1.29224 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.74374 | −0.168099 | ||||||||
\(497\) | −7.38353 | − | 7.38353i | −0.331196 | − | 0.331196i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 37.9477i | − | 1.69877i | −0.527773 | − | 0.849385i | \(-0.676973\pi\) | ||
0.527773 | − | 0.849385i | \(-0.323027\pi\) | |||||||
\(500\) | 10.9351 | + | 2.32864i | 0.489035 | + | 0.104140i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.71165 | − | 1.71165i | 0.0763946 | − | 0.0763946i | ||||
\(503\) | 12.3759 | − | 12.3759i | 0.551816 | − | 0.551816i | −0.375149 | − | 0.926965i | \(-0.622408\pi\) |
0.926965 | + | 0.375149i | \(0.122408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.94060 | + | 8.80492i | −0.264353 | + | 0.391814i | ||||
\(506\) | 1.10820i | 0.0492655i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.15328 | − | 4.15328i | −0.184272 | − | 0.184272i | ||||
\(509\) | 25.9750 | 1.15132 | 0.575660 | − | 0.817689i | \(-0.304745\pi\) | ||||
0.575660 | + | 0.817689i | \(0.304745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6380 | −0.647546 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.2051i | 1.15586i | ||||||||
\(515\) | 4.74466 | + | 24.4255i | 0.209075 | + | 1.07632i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.01211 | + | 7.01211i | −0.308392 | + | 0.308392i | ||||
\(518\) | −19.9263 | + | 19.9263i | −0.875510 | + | 0.875510i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.69058 | − | 4.51408i | −0.293401 | − | 0.197955i | ||||
\(521\) | − | 34.6906i | − | 1.51982i | −0.650027 | − | 0.759911i | \(-0.725243\pi\) | ||
0.650027 | − | 0.759911i | \(-0.274757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5419 | + | 15.5419i | 0.679598 | + | 0.679598i | 0.959909 | − | 0.280311i | \(-0.0904376\pi\) |
−0.280311 | + | 0.959909i | \(0.590438\pi\) | |||||||
\(524\) | 0.125728 | 0.00549245 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.0988 | 0.876350 | ||||||||
\(527\) | 4.14882 | + | 4.14882i | 0.180725 | + | 0.180725i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | 8.52022 | + | 5.74852i | 0.370095 | + | 0.249700i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −24.5742 | + | 24.5742i | −1.06543 | + | 1.06543i | ||||
\(533\) | −10.6155 | + | 10.6155i | −0.459808 | + | 0.459808i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.52360 | + | 18.1395i | 0.152338 | + | 0.784239i | ||||
\(536\) | 0.120832i | 0.00521915i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.8425 | + | 17.8425i | 0.769243 | + | 0.769243i | ||||
\(539\) | 13.3811 | 0.576365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.6475 | 1.79057 | 0.895283 | − | 0.445498i | \(-0.146973\pi\) | ||||
0.895283 | + | 0.445498i | \(0.146973\pi\) | |||||||
\(542\) | 11.5093 | + | 11.5093i | 0.494367 | + | 0.494367i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1.56723i | − | 0.0671946i | ||||||
\(545\) | −20.7186 | + | 30.7083i | −0.887487 | + | 1.31540i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.06634 | − | 1.06634i | 0.0455936 | − | 0.0455936i | −0.683942 | − | 0.729536i | \(-0.739736\pi\) |
0.729536 | + | 0.683942i | \(0.239736\pi\) | |||||||
\(548\) | 10.2258 | − | 10.2258i | 0.436822 | − | 0.436822i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.09998 | − | 2.16632i | −0.217464 | − | 0.0923724i | ||||
\(551\) | − | 50.1348i | − | 2.13581i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 41.4424 | + | 41.4424i | 1.76231 | + | 1.76231i | ||||
\(554\) | −18.2429 | −0.775065 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.8803 | 0.631064 | ||||||||
\(557\) | −3.96379 | − | 3.96379i | −0.167951 | − | 0.167951i | 0.618127 | − | 0.786078i | \(-0.287892\pi\) |
−0.786078 | + | 0.618127i | \(0.787892\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.7641i | 0.835932i | ||||||||
\(560\) | −9.58672 | + | 1.86222i | −0.405113 | + | 0.0786932i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.408888 | − | 0.408888i | 0.0172479 | − | 0.0172479i | ||||
\(563\) | −8.82368 | + | 8.82368i | −0.371874 | + | 0.371874i | −0.868159 | − | 0.496286i | \(-0.834697\pi\) |
0.496286 | + | 0.868159i | \(0.334697\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.66176 | − | 1.09980i | 0.238192 | − | 0.0462688i | ||||
\(566\) | − | 16.4118i | − | 0.689841i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.69058 | − | 1.69058i | −0.0709352 | − | 0.0709352i | ||||
\(569\) | −7.43475 | −0.311681 | −0.155841 | − | 0.987782i | \(-0.549809\pi\) | ||||
−0.155841 | + | 0.987782i | \(0.549809\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0631 | 0.672218 | 0.336109 | − | 0.941823i | \(-0.390889\pi\) | ||||
0.336109 | + | 0.941823i | \(0.390889\pi\) | |||||||
\(572\) | 2.82843 | + | 2.82843i | 0.118262 | + | 0.118262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.1653i | 0.758203i | ||||||||
\(575\) | 4.60203 | + | 1.95481i | 0.191918 | + | 0.0815213i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.9207 | − | 29.9207i | 1.24561 | − | 1.24561i | 0.287977 | − | 0.957637i | \(-0.407017\pi\) |
0.957637 | − | 0.287977i | \(-0.0929828\pi\) | |||||||
\(578\) | 10.2840 | − | 10.2840i | 0.427758 | − | 0.427758i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.87953 | − | 11.6787i | 0.327179 | − | 0.484932i | ||||
\(581\) | 28.0390i | 1.16326i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.60190 | − | 3.60190i | −0.149176 | − | 0.149176i | ||||
\(584\) | −3.35161 | −0.138691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.98460 | 0.247221 | ||||||||
\(587\) | −20.5169 | − | 20.5169i | −0.846821 | − | 0.846821i | 0.142914 | − | 0.989735i | \(-0.454353\pi\) |
−0.989735 | + | 0.142914i | \(0.954353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 29.7901i | − | 1.22748i | ||||||
\(590\) | 5.51486 | + | 28.3905i | 0.227043 | + | 1.16882i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.56245 | + | 4.56245i | −0.187516 | + | 0.187516i | ||||
\(593\) | 2.71761 | − | 2.71761i | 0.111599 | − | 0.111599i | −0.649102 | − | 0.760701i | \(-0.724855\pi\) |
0.760701 | + | 0.649102i | \(0.224855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.6877 | + | 8.56030i | 0.520146 | + | 0.350938i | ||||
\(596\) | 2.44724i | 0.100243i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.55227 | − | 2.55227i | −0.104370 | − | 0.104370i | ||||
\(599\) | 19.0438 | 0.778109 | 0.389054 | − | 0.921215i | \(-0.372802\pi\) | ||||
0.389054 | + | 0.921215i | \(0.372802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0798 | 0.859862 | 0.429931 | − | 0.902862i | \(-0.358538\pi\) | ||||
0.429931 | + | 0.902862i | \(0.358538\pi\) | |||||||
\(602\) | 16.9102 | + | 16.9102i | 0.689208 | + | 0.689208i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 22.0052i | − | 0.895378i | ||||||
\(605\) | −18.1134 | − | 12.2210i | −0.736416 | − | 0.496853i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.74186 | + | 7.74186i | −0.314233 | + | 0.314233i | −0.846547 | − | 0.532314i | \(-0.821322\pi\) |
0.532314 | + | 0.846547i | \(0.321322\pi\) | |||||||
\(608\) | −5.62667 | + | 5.62667i | −0.228192 | + | 0.228192i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.58544 | − | 28.7538i | −0.226148 | − | 1.16421i | ||||
\(611\) | − | 32.2988i | − | 1.30667i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.8900 | − | 12.8900i | −0.520623 | − | 0.520623i | 0.397136 | − | 0.917760i | \(-0.370004\pi\) |
−0.917760 | + | 0.397136i | \(0.870004\pi\) | |||||||
\(614\) | 13.6834 | 0.552217 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.84001 | 0.195010 | ||||||||
\(617\) | 23.2475 | + | 23.2475i | 0.935908 | + | 0.935908i | 0.998066 | − | 0.0621580i | \(-0.0197983\pi\) |
−0.0621580 | + | 0.998066i | \(0.519798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 37.9833i | − | 1.52668i | −0.645998 | − | 0.763339i | \(-0.723559\pi\) | ||
0.645998 | − | 0.763339i | \(-0.276441\pi\) | |||||||
\(620\) | 4.68202 | − | 6.93950i | 0.188034 | − | 0.278697i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.0632 | + | 11.0632i | −0.443593 | + | 0.443593i | ||||
\(623\) | −6.13645 | + | 6.13645i | −0.245852 | + | 0.245852i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.9922 | + | 17.3574i | −0.719688 | + | 0.694297i | ||||
\(626\) | − | 1.71438i | − | 0.0685205i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.65225 | − | 1.65225i | −0.0659319 | − | 0.0659319i | ||||
\(629\) | 10.1122 | 0.403201 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.85775 | −0.392431 | −0.196215 | − | 0.980561i | \(-0.562865\pi\) | ||||
−0.196215 | + | 0.980561i | \(0.562865\pi\) | |||||||
\(632\) | 9.48892 | + | 9.48892i | 0.377449 | + | 0.377449i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 20.0434i | − | 0.796024i | ||||||
\(635\) | 12.8928 | − | 2.50443i | 0.511636 | − | 0.0993853i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.8176 | + | 30.8176i | −1.22104 | + | 1.22104i | ||||
\(638\) | −4.93715 | + | 4.93715i | −0.195464 | + | 0.195464i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.19504 | + | 0.426386i | −0.0867665 | + | 0.0168544i | ||||
\(641\) | − | 44.7416i | − | 1.76719i | −0.468253 | − | 0.883594i | \(-0.655116\pi\) | ||
0.468253 | − | 0.883594i | \(-0.344884\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.28923 | + | 6.28923i | 0.248023 | + | 0.248023i | 0.820159 | − | 0.572136i | \(-0.193885\pi\) |
−0.572136 | + | 0.820159i | \(0.693885\pi\) | |||||||
\(644\) | −4.36745 | −0.172102 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4710 | 0.490663 | ||||||||
\(647\) | 9.27300 | + | 9.27300i | 0.364559 | + | 0.364559i | 0.865488 | − | 0.500929i | \(-0.167008\pi\) |
−0.500929 | + | 0.865488i | \(0.667008\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.3334i | − | 0.562636i | ||||||
\(650\) | 16.7348 | − | 6.75642i | 0.656394 | − | 0.265009i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.60543 | − | 3.60543i | 0.141199 | − | 0.141199i | ||||
\(653\) | −26.6242 | + | 26.6242i | −1.04189 | + | 1.04189i | −0.0428031 | + | 0.999084i | \(0.513629\pi\) |
−0.999084 | + | 0.0428031i | \(0.986371\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.157239 | + | 0.233053i | −0.00614382 | + | 0.00910613i | ||||
\(656\) | 4.15924i | 0.162391i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −27.6349 | − | 27.6349i | −1.07732 | − | 1.07732i | ||||
\(659\) | 13.1521 | 0.512331 | 0.256166 | − | 0.966633i | \(-0.417541\pi\) | ||||
0.256166 | + | 0.966633i | \(0.417541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4920 | −0.797045 | −0.398522 | − | 0.917159i | \(-0.630477\pi\) | ||||
−0.398522 | + | 0.917159i | \(0.630477\pi\) | |||||||
\(662\) | 13.9443 | + | 13.9443i | 0.541962 | + | 0.541962i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.42001i | 0.249145i | ||||||||
\(665\) | −14.8183 | − | 76.2845i | −0.574628 | − | 2.95819i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.45510 | − | 4.45510i | 0.172502 | − | 0.172502i | ||||
\(668\) | −17.0620 | + | 17.0620i | −0.660149 | + | 0.660149i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.223978 | − | 0.151116i | −0.00865301 | − | 0.00583811i | ||||
\(671\) | 14.5168i | 0.560417i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6709 | − | 10.6709i | −0.411332 | − | 0.411332i | 0.470870 | − | 0.882202i | \(-0.343940\pi\) |
−0.882202 | + | 0.470870i | \(0.843940\pi\) | |||||||
\(674\) | −15.2022 | −0.585566 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.0281519 | −0.00108277 | ||||||||
\(677\) | 13.7900 | + | 13.7900i | 0.529993 | + | 0.529993i | 0.920570 | − | 0.390577i | \(-0.127725\pi\) |
−0.390577 | + | 0.920570i | \(0.627725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4518i | 0.439480i | ||||||||
\(680\) | 2.90507 | + | 1.96002i | 0.111404 | + | 0.0751634i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.93366 | + | 2.93366i | −0.112335 | + | 0.112335i | ||||
\(683\) | −31.3149 | + | 31.3149i | −1.19823 | + | 1.19823i | −0.223534 | + | 0.974696i | \(0.571760\pi\) |
−0.974696 | + | 0.223534i | \(0.928240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.16614 | + | 31.7433i | 0.235596 | + | 1.21285i | ||||
\(686\) | 22.1631i | 0.846191i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.87187 | + | 3.87187i | 0.147614 | + | 0.147614i | ||||
\(689\) | 16.5909 | 0.632063 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.8286 | −1.32494 | −0.662471 | − | 0.749088i | \(-0.730492\pi\) | ||||
−0.662471 | + | 0.749088i | \(0.730492\pi\) | |||||||
\(692\) | 12.9466 | + | 12.9466i | 0.492154 | + | 0.492154i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.75594i | 0.142574i | ||||||||
\(695\) | −18.6097 | + | 27.5825i | −0.705905 | + | 1.04626i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.60927 | − | 4.60927i | 0.174589 | − | 0.174589i | ||||
\(698\) | 5.14939 | − | 5.14939i | 0.194907 | − | 0.194907i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.53754 | − | 20.0991i | 0.322689 | − | 0.759676i | ||||
\(701\) | − | 11.9697i | − | 0.452090i | −0.974117 | − | 0.226045i | \(-0.927420\pi\) | ||
0.974117 | − | 0.226045i | \(-0.0725797\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.3048 | − | 36.3048i | −1.36926 | − | 1.36926i | ||||
\(704\) | 1.10820 | 0.0417669 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.3877 | −0.767299 | ||||||||
\(707\) | 14.6695 | + | 14.6695i | 0.551704 | + | 0.551704i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.35453i | 0.0884261i | 0.999022 | + | 0.0442130i | \(0.0140780\pi\) | ||||
−0.999022 | + | 0.0442130i | \(0.985922\pi\) | |||||||
\(710\) | 5.24799 | − | 1.01942i | 0.196954 | − | 0.0382583i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.40504 | + | 1.40504i | −0.0526562 | + | 0.0526562i | ||||
\(713\) | 2.64722 | − | 2.64722i | 0.0991393 | − | 0.0991393i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.78015 | + | 1.70555i | −0.328359 | + | 0.0637838i | ||||
\(716\) | − | 9.01390i | − | 0.336865i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.4015 | + | 19.4015i | 0.724059 | + | 0.724059i | ||||
\(719\) | −9.59308 | −0.357761 | −0.178881 | − | 0.983871i | \(-0.557248\pi\) | ||||
−0.178881 | + | 0.983871i | \(0.557248\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.5993 | 1.80993 | ||||||||
\(722\) | −31.3381 | − | 31.3381i | −1.16628 | − | 1.16628i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.72272i | 0.101189i | ||||||||
\(725\) | 11.7936 | + | 29.2114i | 0.438005 | + | 1.08488i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.1915 | − | 23.1915i | 0.860124 | − | 0.860124i | −0.131228 | − | 0.991352i | \(-0.541892\pi\) |
0.991352 | + | 0.131228i | \(0.0418920\pi\) | |||||||
\(728\) | −11.1469 | + | 11.1469i | −0.413132 | + | 0.413132i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.19161 | − | 6.21264i | 0.155138 | − | 0.229940i | ||||
\(731\) | − | 8.58162i | − | 0.317403i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.04410 | − | 3.04410i | −0.112436 | − | 0.112436i | 0.648650 | − | 0.761087i | \(-0.275334\pi\) |
−0.761087 | + | 0.648650i | \(0.775334\pi\) | |||||||
\(734\) | −5.87549 | −0.216868 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0.0946860 | + | 0.0946860i | 0.00348780 | + | 0.00348780i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.1345i | 0.556730i | 0.960475 | + | 0.278365i | \(0.0897925\pi\) | ||||
−0.960475 | + | 0.278365i | \(0.910207\pi\) | |||||||
\(740\) | −2.75116 | − | 14.1630i | −0.101135 | − | 0.520642i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.1952 | − | 14.1952i | 0.521122 | − | 0.521122i | ||||
\(743\) | −12.7074 | + | 12.7074i | −0.466188 | + | 0.466188i | −0.900677 | − | 0.434489i | \(-0.856929\pi\) |
0.434489 | + | 0.900677i | \(0.356929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.53627 | − | 3.06058i | −0.166196 | − | 0.112131i | ||||
\(746\) | − | 10.5391i | − | 0.385865i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.22811 | − | 1.22811i | −0.0449041 | − | 0.0449041i | ||||
\(749\) | 36.0920 | 1.31877 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.67001 | −0.170411 | −0.0852055 | − | 0.996363i | \(-0.527155\pi\) | ||||
−0.0852055 | + | 0.996363i | \(0.527155\pi\) | |||||||
\(752\) | −6.32747 | − | 6.32747i | −0.230739 | − | 0.230739i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 22.7412i | − | 0.828187i | ||||||
\(755\) | 40.7894 | + | 27.5202i | 1.48448 | + | 1.00156i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.30627 | + | 5.30627i | −0.192860 | + | 0.192860i | −0.796931 | − | 0.604071i | \(-0.793544\pi\) |
0.604071 | + | 0.796931i | \(0.293544\pi\) | |||||||
\(758\) | −27.3891 | + | 27.3891i | −0.994818 | + | 0.994818i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.39289 | − | 17.4666i | −0.123073 | − | 0.633580i | ||||
\(761\) | − | 31.4820i | − | 1.14122i | −0.821220 | − | 0.570611i | \(-0.806706\pi\) | ||
0.821220 | − | 0.570611i | \(-0.193294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.1618 | + | 51.1618i | 1.85218 | + | 1.85218i | ||||
\(764\) | −21.7099 | −0.785437 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.1930 | 1.05479 | ||||||||
\(767\) | 33.0109 | + | 33.0109i | 1.19195 | + | 1.19195i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.30478i | 0.263417i | 0.991288 | + | 0.131708i | \(0.0420463\pi\) | ||||
−0.991288 | + | 0.131708i | \(0.957954\pi\) | |||||||
\(770\) | −6.05304 | + | 8.97158i | −0.218137 | + | 0.323313i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.5672 | + | 10.5672i | −0.380323 | + | 0.380323i | ||||
\(773\) | 11.7702 | − | 11.7702i | 0.423346 | − | 0.423346i | −0.463008 | − | 0.886354i | \(-0.653230\pi\) |
0.886354 | + | 0.463008i | \(0.153230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.00779 | + | 17.3574i | 0.251727 | + | 0.623497i | ||||
\(776\) | 2.62208i | 0.0941273i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.7624 | − | 12.7624i | −0.457553 | − | 0.457553i | ||||
\(779\) | −33.0963 | −1.18580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.64953 | −0.0948078 | ||||||||
\(782\) | 1.10820 | + | 1.10820i | 0.0396292 | + | 0.0396292i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0746i | 0.431236i | ||||||||
\(785\) | 5.12900 | − | 0.996308i | 0.183062 | − | 0.0355597i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.17730 | + | 8.17730i | −0.291489 | + | 0.291489i | −0.837668 | − | 0.546179i | \(-0.816082\pi\) |
0.546179 | + | 0.837668i | \(0.316082\pi\) | |||||||
\(788\) | 2.44764 | − | 2.44764i | 0.0871937 | − | 0.0871937i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −29.4560 | + | 5.72183i | −1.04800 | + | 0.203574i | ||||
\(791\) | − | 11.2652i | − | 0.400543i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.4334 | − | 33.4334i | −1.18725 | − | 1.18725i | ||||
\(794\) | 24.8037 | 0.880250 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.89032 | −0.208777 | ||||||||
\(797\) | 19.1263 | + | 19.1263i | 0.677490 | + | 0.677490i | 0.959432 | − | 0.281942i | \(-0.0909785\pi\) |
−0.281942 | + | 0.959432i | \(0.590979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0242i | 0.496141i | ||||||||
\(800\) | 1.95481 | − | 4.60203i | 0.0691130 | − | 0.162706i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.6644 | − | 25.6644i | 0.906242 | − | 0.906242i | ||||
\(803\) | −2.62638 | + | 2.62638i | −0.0926828 | + | 0.0926828i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.46205 | − | 8.09562i | 0.192512 | − | 0.285333i | ||||
\(806\) | − | 13.5128i | − | 0.475970i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.35883 | + | 3.35883i | 0.118163 | + | 0.118163i | ||||
\(809\) | 32.6423 | 1.14764 | 0.573820 | − | 0.818981i | \(-0.305461\pi\) | ||||
0.573820 | + | 0.818981i | \(0.305461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.3856 | −0.856294 | −0.428147 | − | 0.903709i | \(-0.640833\pi\) | ||||
−0.428147 | + | 0.903709i | \(0.640833\pi\) | |||||||
\(812\) | −19.4574 | − | 19.4574i | −0.682822 | − | 0.682822i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.15042i | 0.250622i | ||||||||
\(815\) | 2.17408 | + | 11.1922i | 0.0761546 | + | 0.392044i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.8097 | + | 30.8097i | −1.07789 | + | 1.07789i | ||||
\(818\) | 25.2679 | − | 25.2679i | 0.883471 | − | 0.883471i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.70968 | − | 5.20165i | −0.269234 | − | 0.181650i | ||||
\(821\) | − | 27.6947i | − | 0.966551i | −0.875468 | − | 0.483275i | \(-0.839447\pi\) | ||
0.875468 | − | 0.483275i | \(-0.160553\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.48297 | + | 8.48297i | 0.295698 | + | 0.295698i | 0.839326 | − | 0.543628i | \(-0.182950\pi\) |
−0.543628 | + | 0.839326i | \(0.682950\pi\) | |||||||
\(824\) | 11.1276 | 0.387649 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 56.4884 | 1.96548 | ||||||||
\(827\) | −23.1817 | − | 23.1817i | −0.806108 | − | 0.806108i | 0.177934 | − | 0.984042i | \(-0.443058\pi\) |
−0.984042 | + | 0.177934i | \(0.943058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.4679i | 1.64863i | 0.566133 | + | 0.824314i | \(0.308439\pi\) | ||||
−0.566133 | + | 0.824314i | \(0.691561\pi\) | |||||||
\(830\) | −11.9003 | − | 8.02903i | −0.413065 | − | 0.278692i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.55227 | + | 2.55227i | −0.0884840 | + | 0.0884840i | ||||
\(833\) | 13.3811 | − | 13.3811i | 0.463627 | − | 0.463627i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.2884 | − | 52.9648i | −0.356045 | − | 1.83292i | ||||
\(836\) | 8.81830i | 0.304987i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.0922 | − | 16.0922i | −0.555894 | − | 0.555894i | ||||
\(839\) | −38.1279 | −1.31632 | −0.658161 | − | 0.752878i | \(-0.728665\pi\) | ||||
−0.658161 | + | 0.752878i | \(0.728665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6959 | 0.368823 | ||||||||
\(842\) | 0.184788 | + | 0.184788i | 0.00636822 | + | 0.00636822i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 20.5443i | − | 0.707162i | ||||||
\(845\) | 0.0352075 | − | 0.0521831i | 0.00121117 | − | 0.00179515i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.1781 | + | 30.1781i | −1.03693 | + | 1.03693i | ||||
\(848\) | 3.25022 | − | 3.25022i | 0.111613 | − | 0.111613i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.26630 | + | 2.93366i | −0.249232 | + | 0.100624i | ||||
\(851\) | − | 6.45228i | − | 0.221181i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.1724 | − | 34.1724i | −1.17004 | − | 1.17004i | −0.982199 | − | 0.187843i | \(-0.939850\pi\) |
−0.187843 | − | 0.982199i | \(-0.560150\pi\) | |||||||
\(854\) | −57.2113 | −1.95773 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.26386 | 0.282453 | ||||||||
\(857\) | 9.46775 | + | 9.46775i | 0.323412 | + | 0.323412i | 0.850075 | − | 0.526662i | \(-0.176557\pi\) |
−0.526662 | + | 0.850075i | \(0.676557\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.52135i | 0.188386i | 0.995554 | + | 0.0941930i | \(0.0300271\pi\) | ||||
−0.995554 | + | 0.0941930i | \(0.969973\pi\) | |||||||
\(860\) | −12.0193 | + | 2.33474i | −0.409853 | + | 0.0796141i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.1001 | − | 10.1001i | 0.344011 | − | 0.344011i | ||||
\(863\) | 14.2872 | − | 14.2872i | 0.486341 | − | 0.486341i | −0.420808 | − | 0.907150i | \(-0.638253\pi\) |
0.907150 | + | 0.420808i | \(0.138253\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.1894 | + | 7.80679i | −1.36648 | + | 0.265439i | ||||
\(866\) | 2.41479i | 0.0820580i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.5616 | − | 11.5616i | −0.392427 | − | 0.392427i | ||||
\(869\) | 14.8713 | 0.504476 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.436138 | −0.0147780 | ||||||||
\(872\) | 11.7143 | + | 11.7143i | 0.396698 | + | 0.396698i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 7.95731i | − | 0.269160i | ||||||
\(875\) | 26.5791 | + | 40.9619i | 0.898536 | + | 1.38477i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.2973 | − | 30.2973i | 1.02307 | − | 1.02307i | 0.0233412 | − | 0.999728i | \(-0.492570\pi\) |
0.999728 | − | 0.0233412i | \(-0.00743040\pi\) | |||||||
\(878\) | −23.0271 | + | 23.0271i | −0.777126 | + | 0.777126i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.38595 | + | 2.05419i | −0.0467202 | + | 0.0692468i | ||||
\(881\) | − | 13.6379i | − | 0.459474i | −0.973253 | − | 0.229737i | \(-0.926213\pi\) | ||
0.973253 | − | 0.229737i | \(-0.0737865\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.8929 | + | 32.8929i | 1.10694 | + | 1.10694i | 0.993551 | + | 0.113385i | \(0.0361692\pi\) |
0.113385 | + | 0.993551i | \(0.463831\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.21085 | 0.107871 | ||||||||
\(887\) | −7.35218 | − | 7.35218i | −0.246862 | − | 0.246862i | 0.572819 | − | 0.819682i | \(-0.305850\pi\) |
−0.819682 | + | 0.572819i | \(0.805850\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 25.6527i | − | 0.860365i | ||||||
\(890\) | −0.847242 | − | 4.36161i | −0.0283996 | − | 0.146201i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.0089 | − | 16.0089i | 0.536018 | − | 0.536018i | ||||
\(893\) | 50.3497 | − | 50.3497i | 1.68489 | − | 1.68489i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.7084 | + | 11.2730i | 0.558501 | + | 0.376816i | ||||
\(896\) | 4.36745i | 0.145906i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.9015 | − | 20.9015i | −0.697493 | − | 0.697493i | ||||
\(899\) | 23.5873 | 0.786680 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.20380 | −0.239994 | ||||||||
\(902\) | 3.25925 | + | 3.25925i | 0.108521 | + | 0.108521i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.57934i | − | 0.0857877i | ||||||
\(905\) | −5.04692 | − | 3.40511i | −0.167765 | − | 0.113190i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.4804 | + | 30.4804i | −1.01209 | + | 1.01209i | −0.0121594 | + | 0.999926i | \(0.503871\pi\) |
−0.999926 | + | 0.0121594i | \(0.996129\pi\) | |||||||
\(908\) | 5.02446 | − | 5.02446i | 0.166743 | − | 0.166743i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.72160 | − | 34.6028i | −0.222819 | − | 1.14707i | ||||
\(911\) | − | 19.2942i | − | 0.639245i | −0.947545 | − | 0.319622i | \(-0.896444\pi\) | ||
0.947545 | − | 0.319622i | \(-0.103556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.03082 | + | 5.03082i | 0.166496 | + | 0.166496i | ||||
\(914\) | −34.9055 | −1.15457 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.7509 | 0.388260 | ||||||||
\(917\) | 0.388280 | + | 0.388280i | 0.0128221 | + | 0.0128221i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 44.0851i | − | 1.45423i | −0.686515 | − | 0.727116i | \(-0.740860\pi\) | ||
0.686515 | − | 0.727116i | \(-0.259140\pi\) | |||||||
\(920\) | 1.25063 | − | 1.85363i | 0.0412319 | − | 0.0611123i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.7527 | + | 20.7527i | −0.683453 | + | 0.683453i | ||||
\(923\) | 6.10207 | − | 6.10207i | 0.200852 | − | 0.200852i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.6936 | + | 12.6130i | 0.976320 | + | 0.414712i | ||||
\(926\) | 14.7422i | 0.484457i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.45510 | − | 4.45510i | −0.146246 | − | 0.146246i | ||||
\(929\) | 20.4079 | 0.669562 | 0.334781 | − | 0.942296i | \(-0.391338\pi\) | ||||
0.334781 | + | 0.942296i | \(0.391338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −96.0814 | −3.14894 | ||||||||
\(932\) | −16.0418 | − | 16.0418i | −0.525466 | − | 0.525466i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.1599i | 0.561489i | ||||||||
\(935\) | 3.81236 | − | 0.740552i | 0.124678 | − | 0.0242186i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.1021 | − | 39.1021i | 1.27741 | − | 1.27741i | 0.335299 | − | 0.942112i | \(-0.391163\pi\) |
0.942112 | − | 0.335299i | \(-0.108837\pi\) | |||||||
\(938\) | −0.373160 | + | 0.373160i | −0.0121841 | + | 0.0121841i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.6421 | − | 3.81547i | 0.640654 | − | 0.124447i | ||||
\(941\) | − | 47.0848i | − | 1.53492i | −0.641097 | − | 0.767460i | \(-0.721520\pi\) | ||
0.641097 | − | 0.767460i | \(-0.278480\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.94103 | − | 2.94103i | −0.0957730 | − | 0.0957730i | ||||
\(944\) | 12.9339 | 0.420964 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.06812 | 0.197292 | ||||||||
\(947\) | 12.9557 | + | 12.9557i | 0.421005 | + | 0.421005i | 0.885550 | − | 0.464545i | \(-0.153782\pi\) |
−0.464545 | + | 0.885550i | \(0.653782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.0975i | − | 0.392701i | ||||||
\(950\) | 36.6198 | + | 15.5550i | 1.18810 | + | 0.504672i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.84001 | − | 4.84001i | 0.156866 | − | 0.156866i | ||||
\(953\) | −27.0525 | + | 27.0525i | −0.876318 | + | 0.876318i | −0.993151 | − | 0.116834i | \(-0.962726\pi\) |
0.116834 | + | 0.993151i | \(0.462726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.1510 | − | 40.2421i | 0.878586 | − | 1.30220i | ||||
\(956\) | 15.8376i | 0.512223i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.8067 | − | 22.8067i | −0.736851 | − | 0.736851i | ||||
\(959\) | 63.1594 | 2.03952 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.9844 | −0.547885 | ||||||||
\(962\) | −16.4680 | − | 16.4680i | −0.530948 | − | 0.530948i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.54557i | − | 0.0497794i | ||||||
\(965\) | −6.37206 | − | 32.8034i | −0.205124 | − | 1.05598i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.85145 | − | 8.85145i | 0.284644 | − | 0.284644i | −0.550314 | − | 0.834958i | \(-0.685492\pi\) |
0.834958 | + | 0.550314i | \(0.185492\pi\) | |||||||
\(968\) | −6.90977 | + | 6.90977i | −0.222088 | + | 0.222088i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.86037 | − | 3.27925i | −0.156057 | − | 0.105290i | ||||
\(971\) | − | 44.1980i | − | 1.41838i | −0.705016 | − | 0.709191i | \(-0.749060\pi\) | ||
0.705016 | − | 0.709191i | \(-0.250940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.9540 | + | 45.9540i | 1.47322 | + | 1.47322i | ||||
\(974\) | 14.0505 | 0.450207 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.0995 | −0.419304 | ||||||||
\(977\) | 32.5914 | + | 32.5914i | 1.04269 | + | 1.04269i | 0.999047 | + | 0.0436453i | \(0.0138971\pi\) |
0.0436453 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.20203i | 0.0703771i | ||||||||
\(980\) | −22.3818 | − | 15.1008i | −0.714961 | − | 0.482378i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.98008 | + | 8.98008i | −0.286566 | + | 0.286566i | ||||
\(983\) | −31.9835 | + | 31.9835i | −1.02012 | + | 1.02012i | −0.0203217 | + | 0.999793i | \(0.506469\pi\) |
−0.999793 | + | 0.0203217i | \(0.993531\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.47593 | + | 7.59811i | 0.0470271 | + | 0.242096i | ||||
\(986\) | 9.87430i | 0.314462i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.3092 | − | 20.3092i | −0.646122 | − | 0.646122i | ||||
\(989\) | −5.47565 | −0.174116 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.6342 | 1.57668 | 0.788341 | − | 0.615239i | \(-0.210940\pi\) | ||||
0.788341 | + | 0.615239i | \(0.210940\pi\) | |||||||
\(992\) | −2.64722 | − | 2.64722i | −0.0840494 | − | 0.0840494i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 10.4419i | − | 0.331196i | ||||||
\(995\) | 7.36658 | − | 10.9184i | 0.233536 | − | 0.346138i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.0016 | − | 10.0016i | 0.316752 | − | 0.316752i | −0.530766 | − | 0.847518i | \(-0.678096\pi\) |
0.847518 | + | 0.530766i | \(0.178096\pi\) | |||||||
\(998\) | 26.8330 | − | 26.8330i | 0.849385 | − | 0.849385i | ||||
\(999\) | 0 | 0 |
(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 | 2070.2.j.j.323.6 | yes | 20 | |
3.2 | odd | 2 | inner | 2070.2.j.j.323.5 | ✓ | 20 | |
5.2 | odd | 4 | inner | 2070.2.j.j.737.5 | yes | 20 | |
15.2 | even | 4 | inner | 2070.2.j.j.737.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.j.323.5 | ✓ | 20 | 3.2 | odd | 2 | inner | |
2070.2.j.j.323.6 | yes | 20 | 1.1 | even | 1 | trivial | |
2070.2.j.j.737.5 | yes | 20 | 5.2 | odd | 4 | inner | |
2070.2.j.j.737.6 | yes | 20 | 15.2 | even | 4 | inner |