Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1428,2,Mod(169,1428)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1428, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1428.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1428.d (of order \(2\), degree \(1\), 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: | \(11.4026374086\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 43x^{10} + 647x^{8} + 4049x^{6} + 10288x^{4} + 9088x^{2} + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(-4.02527i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1428.169 |
Dual form | 1428.2.d.c.169.12 |
$q$-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 \(\left(\mathbb{Z}/1428\mathbb{Z}\right)^\times\).
\(n\) | \(409\) | \(715\) | \(953\) | \(1261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 4.02527i | − | 1.80016i | −0.435728 | − | 0.900078i | \(-0.643509\pi\) | ||
0.435728 | − | 0.900078i | \(-0.356491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.54643i | 1.06929i | 0.845077 | + | 0.534644i | \(0.179554\pi\) | ||||
−0.845077 | + | 0.534644i | \(0.820446\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.79991 | −1.05391 | −0.526953 | − | 0.849895i | \(-0.676666\pi\) | ||||
−0.526953 | + | 0.849895i | \(0.676666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.02527 | −1.03932 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.32819 | − | 2.43375i | −0.807205 | − | 0.590271i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49247 | −0.342397 | −0.171198 | − | 0.985237i | \(-0.554764\pi\) | ||||
−0.171198 | + | 0.985237i | \(0.554764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.97132i | − | 0.828077i | −0.910259 | − | 0.414038i | \(-0.864118\pi\) | ||
0.910259 | − | 0.414038i | \(-0.135882\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.2028 | −2.24056 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.29238i | 1.35416i | 0.735909 | + | 0.677081i | \(0.236755\pi\) | ||||
−0.735909 | + | 0.677081i | \(0.763245\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20770i | 0.755725i | 0.925862 | + | 0.377862i | \(0.123341\pi\) | ||||
−0.925862 | + | 0.377862i | \(0.876659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.54643 | 0.617354 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.02527 | 0.680395 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.3606i | − | 1.86767i | −0.357704 | − | 0.933835i | \(-0.616440\pi\) | ||
0.357704 | − | 0.933835i | \(-0.383560\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.79991i | 0.608473i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.45016i | − | 0.694998i | −0.937680 | − | 0.347499i | \(-0.887031\pi\) | ||
0.937680 | − | 0.347499i | \(-0.112969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.7356 | −1.94216 | −0.971082 | − | 0.238748i | \(-0.923263\pi\) | ||||
−0.971082 | + | 0.238748i | \(0.923263\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.02527i | 0.600052i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.20770 | 0.613756 | 0.306878 | − | 0.951749i | \(-0.400716\pi\) | ||||
0.306878 | + | 0.951749i | \(0.400716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.43375 | + | 3.32819i | −0.340793 | + | 0.466040i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.40291 | −0.604786 | −0.302393 | − | 0.953183i | \(-0.597785\pi\) | ||||
−0.302393 | + | 0.953183i | \(0.597785\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.2753 | 1.92489 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.49247i | 0.197683i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.93570 | 0.902952 | 0.451476 | − | 0.892283i | \(-0.350898\pi\) | ||||
0.451476 | + | 0.892283i | \(0.350898\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8032i | 1.76732i | 0.468130 | + | 0.883659i | \(0.344928\pi\) | ||||
−0.468130 | + | 0.883659i | \(0.655072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.2957i | 1.89719i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.17493 | −0.387880 | −0.193940 | − | 0.981013i | \(-0.562127\pi\) | ||||
−0.193940 | + | 0.981013i | \(0.562127\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.97132 | −0.478090 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.18919i | 0.615843i | 0.951412 | + | 0.307922i | \(0.0996334\pi\) | ||||
−0.951412 | + | 0.307922i | \(0.900367\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.225362i | − | 0.0263766i | −0.999913 | − | 0.0131883i | \(-0.995802\pi\) | ||
0.999913 | − | 0.0131883i | \(-0.00419809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.2028i | 1.29359i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.54643 | −0.404153 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.64764i | 0.635409i | 0.948190 | + | 0.317705i | \(0.102912\pi\) | ||||
−0.948190 | + | 0.317705i | \(0.897088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6927 | 1.17367 | 0.586837 | − | 0.809705i | \(-0.300373\pi\) | ||||
0.586837 | + | 0.809705i | \(0.300373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.79650 | + | 13.3969i | −1.06258 | + | 1.45310i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.29238 | 0.781826 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.07861 | 0.326332 | 0.163166 | − | 0.986599i | \(-0.447829\pi\) | ||||
0.163166 | + | 0.986599i | \(0.447829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.79991i | − | 0.398339i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.20770 | 0.436318 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00761i | 0.616368i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.8757i | − | 1.61194i | −0.591959 | − | 0.805968i | \(-0.701645\pi\) | ||
0.591959 | − | 0.805968i | \(-0.298355\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.54643i | − | 0.356430i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8218 | −1.17631 | −0.588155 | − | 0.808748i | \(-0.700146\pi\) | ||||
−0.588155 | + | 0.808748i | \(0.700146\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.02527 | −0.593688 | −0.296844 | − | 0.954926i | \(-0.595934\pi\) | ||||
−0.296844 | + | 0.954926i | \(0.595934\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 4.02527i | − | 0.392826i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.6790i | − | 1.12906i | −0.825414 | − | 0.564528i | \(-0.809058\pi\) | ||
0.825414 | − | 0.564528i | \(-0.190942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.31828i | − | 0.796747i | −0.917223 | − | 0.398373i | \(-0.869575\pi\) | ||
0.917223 | − | 0.398373i | \(-0.130425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.3606 | −1.07830 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9351i | 1.21684i | 0.793617 | + | 0.608418i | \(0.208195\pi\) | ||||
−0.793617 | + | 0.608418i | \(0.791805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.9856 | −1.49067 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.79991 | 0.351302 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.43375 | − | 3.32819i | 0.223101 | − | 0.305095i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.57716 | −0.143378 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.45016 | −0.401257 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.9680i | 2.23321i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4748 | −1.19570 | −0.597848 | − | 0.801610i | \(-0.703977\pi\) | ||||
−0.597848 | + | 0.801610i | \(0.703977\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.7356i | 1.12131i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 14.3012i | − | 1.24950i | −0.780825 | − | 0.624750i | \(-0.785201\pi\) | ||
0.780825 | − | 0.624750i | \(-0.214799\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.49247i | − | 0.129414i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.02527 | 0.346440 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9099 | −1.10296 | −0.551482 | − | 0.834187i | \(-0.685938\pi\) | ||||
−0.551482 | + | 0.834187i | \(0.685938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.7855i | − | 1.84783i | −0.382604 | − | 0.923913i | \(-0.624973\pi\) | ||
0.382604 | − | 0.923913i | \(-0.375027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.20770i | − | 0.354352i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 13.4761i | − | 1.12693i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 29.3538 | 2.43770 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.59982 | −0.131062 | −0.0655312 | − | 0.997851i | \(-0.520874\pi\) | ||||
−0.0655312 | + | 0.997851i | \(0.520874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.10933 | −0.171655 | −0.0858276 | − | 0.996310i | \(-0.527353\pi\) | ||||
−0.0858276 | + | 0.996310i | \(0.527353\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.32819 | + | 2.43375i | 0.269068 | + | 0.196757i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.9371 | 1.36042 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.58266 | 0.445545 | 0.222772 | − | 0.974870i | \(-0.428489\pi\) | ||||
0.222772 | + | 0.974870i | \(0.428489\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.40291i | 0.349173i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.97132 | 0.312984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.9549i | − | 1.24968i | −0.780751 | − | 0.624842i | \(-0.785163\pi\) | ||
0.780751 | − | 0.624842i | \(-0.214837\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 14.2753i | − | 1.11133i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.4964i | 1.27653i | 0.769817 | + | 0.638264i | \(0.220347\pi\) | ||||
−0.769817 | + | 0.638264i | \(0.779653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.43932 | 0.110717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.49247 | 0.114132 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.329815i | 0.0250753i | 0.999921 | + | 0.0125377i | \(0.00399097\pi\) | ||||
−0.999921 | + | 0.0125377i | \(0.996009\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 11.2028i | − | 0.846853i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.93570i | − | 0.521319i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.32254 | −0.547312 | −0.273656 | − | 0.961828i | \(-0.588233\pi\) | ||||
−0.273656 | + | 0.961828i | \(0.588233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.37446i | − | 0.250822i | −0.992105 | − | 0.125411i | \(-0.959975\pi\) | ||
0.992105 | − | 0.125411i | \(-0.0400249\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.8032 | 1.02036 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −45.7295 | −3.36210 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.63111 | − | 11.8032i | 0.631170 | − | 0.863136i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1283 | −0.877576 | −0.438788 | − | 0.898591i | \(-0.644592\pi\) | ||||
−0.438788 | + | 0.898591i | \(0.644592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.72544i | 0.556089i | 0.960568 | + | 0.278045i | \(0.0896864\pi\) | ||||
−0.960568 | + | 0.278045i | \(0.910314\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.2957 | 1.09535 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.10858i | 0.221477i | 0.993850 | + | 0.110739i | \(0.0353216\pi\) | ||||
−0.993850 | + | 0.110739i | \(0.964678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.4126i | − | 1.51790i | −0.651151 | − | 0.758948i | \(-0.725714\pi\) | ||
0.651151 | − | 0.758948i | \(-0.274286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.17493i | 0.223943i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.29238 | −0.511825 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.9131 | −1.25111 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.97132i | 0.276026i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.29295i | − | 0.366121i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.531496i | 0.0365897i | 0.999833 | + | 0.0182948i | \(0.00582375\pi\) | ||||
−0.999833 | + | 0.0182948i | \(0.994176\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.18919 | 0.355557 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 51.2643i | 3.49620i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.20770 | −0.285637 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.225362 | −0.0152285 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.6468 | + | 9.24802i | 0.850718 | + | 0.622089i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.7382 | 1.05391 | 0.526955 | − | 0.849893i | \(-0.323334\pi\) | ||||
0.526955 | + | 0.849893i | \(0.323334\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.2028 | 0.746854 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 26.4883i | − | 1.75809i | −0.476738 | − | 0.879046i | \(-0.658181\pi\) | ||
0.476738 | − | 0.879046i | \(-0.341819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9835 | −0.725812 | −0.362906 | − | 0.931826i | \(-0.618215\pi\) | ||||
−0.362906 | + | 0.931826i | \(0.618215\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.54643i | 0.233338i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.4597i | 0.816263i | 0.912923 | + | 0.408131i | \(0.133819\pi\) | ||||
−0.912923 | + | 0.408131i | \(0.866181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 16.9371i | − | 1.10486i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.64764 | 0.366854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5452 | 1.26427 | 0.632136 | − | 0.774857i | \(-0.282178\pi\) | ||||
0.632136 | + | 0.774857i | \(0.282178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8607i | 1.21492i | 0.794349 | + | 0.607461i | \(0.207812\pi\) | ||||
−0.794349 | + | 0.607461i | \(0.792188\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.02527i | 0.257165i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.67126 | 0.360854 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 10.6927i | − | 0.677621i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.2705 | 1.53194 | 0.765971 | − | 0.642875i | \(-0.222259\pi\) | ||||
0.765971 | + | 0.642875i | \(0.222259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0840 | 0.885453 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.3969 | + | 9.79650i | 0.838945 | + | 0.613481i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.49394 | −0.0931895 | −0.0465948 | − | 0.998914i | \(-0.514837\pi\) | ||||
−0.0465948 | + | 0.998914i | \(0.514837\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3606 | 0.705913 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 7.29238i | − | 0.451387i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.7786 | −1.03461 | −0.517305 | − | 0.855801i | \(-0.673065\pi\) | ||||
−0.517305 | + | 0.855801i | \(0.673065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.7229i | 1.08871i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.07861i | − | 0.188408i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 28.6209i | − | 1.74505i | −0.488573 | − | 0.872523i | \(-0.662482\pi\) | ||
0.488573 | − | 0.872523i | \(-0.337518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.53479 | 0.275469 | 0.137734 | − | 0.990469i | \(-0.456018\pi\) | ||||
0.137734 | + | 0.990469i | \(0.456018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.79991 | −0.229981 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 39.7300i | − | 2.39581i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.3988i | − | 1.70632i | −0.521650 | − | 0.853159i | \(-0.674683\pi\) | ||
0.521650 | − | 0.853159i | \(-0.325317\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4.20770i | − | 0.251908i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.69268 | 0.279942 | 0.139971 | − | 0.990156i | \(-0.455299\pi\) | ||||
0.139971 | + | 0.990156i | \(0.455299\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.67348i | 0.337253i | 0.985680 | + | 0.168627i | \(0.0539332\pi\) | ||||
−0.985680 | + | 0.168627i | \(0.946067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00761 | 0.355860 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.45016 | 0.262685 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.15374 | + | 16.2000i | 0.303161 | + | 0.952939i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.8757 | −0.930652 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.94865 | 0.405945 | 0.202972 | − | 0.979184i | \(-0.434940\pi\) | ||||
0.202972 | + | 0.979184i | \(0.434940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 27.9181i | − | 1.62545i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.54643 | −0.205785 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.0906i | 0.872714i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 12.7356i | − | 0.734069i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.8218i | 0.679143i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 55.5616 | 3.18145 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.40450 | −0.365524 | −0.182762 | − | 0.983157i | \(-0.558504\pi\) | ||||
−0.182762 | + | 0.983157i | \(0.558504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.02527i | 0.342766i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.57256i | − | 0.315991i | −0.987440 | − | 0.157996i | \(-0.949497\pi\) | ||
0.987440 | − | 0.157996i | \(-0.0505032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.23758i | 0.352569i | 0.984339 | + | 0.176284i | \(0.0564078\pi\) | ||||
−0.984339 | + | 0.176284i | \(0.943592\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.02527 | −0.226798 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.11223i | 0.118635i | 0.998239 | + | 0.0593173i | \(0.0188924\pi\) | ||||
−0.998239 | + | 0.0593173i | \(0.981108\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.8619 | −1.44799 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.6790 | −0.651861 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.96724 | + | 3.63230i | 0.276384 | + | 0.202107i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42.5697 | 2.36134 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.31828 | −0.460002 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.20770i | 0.231978i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6906 | −0.752505 | −0.376253 | − | 0.926517i | \(-0.622788\pi\) | ||||
−0.376253 | + | 0.926517i | \(0.622788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.3606i | 0.622557i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7800i | 0.698245i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.03276i | − | 0.274152i | −0.990561 | − | 0.137076i | \(-0.956230\pi\) | ||
0.990561 | − | 0.137076i | \(-0.0437705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9351 | 0.702540 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.9223 | −0.808088 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.9856i | 0.860637i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 0.545806i | − | 0.0293004i | −0.999893 | − | 0.0146502i | \(-0.995337\pi\) | ||
0.999893 | − | 0.0146502i | \(-0.00466347\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.3682 | −1.46499 | −0.732493 | − | 0.680775i | \(-0.761643\pi\) | ||||
−0.732493 | + | 0.680775i | \(0.761643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.79991i | − | 0.202824i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.2575 | 1.82334 | 0.911672 | − | 0.410919i | \(-0.134792\pi\) | ||||
0.911672 | + | 0.410919i | \(0.134792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.8879 | 1.10861 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.32819 | − | 2.43375i | −0.176147 | − | 0.128808i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.9314 | 1.21027 | 0.605137 | − | 0.796121i | \(-0.293118\pi\) | ||||
0.605137 | + | 0.796121i | \(0.293118\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7725 | −0.882765 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.57716i | 0.0827793i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.907142 | −0.0474820 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000i | 0.417597i | 0.977959 | + | 0.208798i | \(0.0669552\pi\) | ||||
−0.977959 | + | 0.208798i | \(0.933045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.45016i | 0.231666i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.40291i | − | 0.228587i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0342 | −1.14089 | −0.570445 | − | 0.821336i | \(-0.693229\pi\) | ||||
−0.570445 | + | 0.821336i | \(0.693229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.9680 | 1.28934 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 27.7104i | − | 1.42716i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.73095i | − | 0.345746i | −0.984944 | − | 0.172873i | \(-0.944695\pi\) | ||
0.984944 | − | 0.172873i | \(-0.0553049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4748i | 0.690335i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5135 | −0.741604 | −0.370802 | − | 0.928712i | \(-0.620917\pi\) | ||||
−0.370802 | + | 0.928712i | \(0.620917\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.2753i | 0.727539i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.7356 | 0.647388 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.22145 | −0.163334 | −0.0816670 | − | 0.996660i | \(-0.526024\pi\) | ||||
−0.0816670 | + | 0.996660i | \(0.526024\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.66518 | + | 13.2173i | −0.488789 | + | 0.668428i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.3012 | −0.721399 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.7333 | 1.14384 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.1530i | − | 1.46315i | −0.681763 | − | 0.731573i | \(-0.738786\pi\) | ||
0.681763 | − | 0.731573i | \(-0.261214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.49247 | −0.0747171 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.9706i | − | 1.59654i | −0.602302 | − | 0.798269i | \(-0.705750\pi\) | ||
0.602302 | − | 0.798269i | \(-0.294250\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 15.9889i | − | 0.796462i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 4.02527i | − | 0.200017i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.2895 | 1.99708 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.7658 | −1.27404 | −0.637019 | − | 0.770848i | \(-0.719833\pi\) | ||||
−0.637019 | + | 0.770848i | \(0.719833\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.9099i | 0.636797i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.93570i | 0.341284i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 43.0409i | − | 2.11280i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7855 | −1.06684 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.32633i | 0.260208i | 0.991500 | + | 0.130104i | \(0.0415312\pi\) | ||||
−0.991500 | + | 0.130104i | \(0.958469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.24637 | −0.353167 | −0.176583 | − | 0.984286i | \(-0.556505\pi\) | ||||
−0.176583 | + | 0.984286i | \(0.556505\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.20770 | −0.204585 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37.2851 | + | 27.2648i | 1.80859 | + | 1.32254i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8032 | −0.667984 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.4761 | −0.650633 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.1577i | − | 1.01913i | −0.860433 | − | 0.509564i | \(-0.829807\pi\) | ||
0.860433 | − | 0.509564i | \(-0.170193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.59901 | −0.461299 | −0.230649 | − | 0.973037i | \(-0.574085\pi\) | ||||
−0.230649 | + | 0.973037i | \(0.574085\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 29.3538i | − | 1.40741i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.92708i | 0.283531i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.3634i | 1.44917i | 0.689187 | + | 0.724583i | \(0.257968\pi\) | ||||
−0.689187 | + | 0.724583i | \(0.742032\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.7910 | −1.65297 | −0.826486 | − | 0.562957i | \(-0.809664\pi\) | ||||
−0.826486 | + | 0.562957i | \(0.809664\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.3922i | − | 0.587448i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.59982i | 0.0756689i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 23.7010i | − | 1.11852i | −0.828993 | − | 0.559259i | \(-0.811086\pi\) | ||
0.828993 | − | 0.559259i | \(-0.188914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7822 | 0.743153 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.10933i | 0.0991052i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.2957 | −0.717072 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.4240 | 1.46995 | 0.734977 | − | 0.678092i | \(-0.237193\pi\) | ||||
0.734977 | + | 0.678092i | \(0.237193\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.43375 | − | 3.32819i | 0.113598 | − | 0.155347i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.9554 | −1.62804 | −0.814018 | − | 0.580840i | \(-0.802724\pi\) | ||||
−0.814018 | + | 0.580840i | \(0.802724\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.3061 | 0.850755 | 0.425377 | − | 0.905016i | \(-0.360141\pi\) | ||||
0.425377 | + | 0.905016i | \(0.360141\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 16.9371i | − | 0.785440i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.0478 | 0.511230 | 0.255615 | − | 0.966779i | \(-0.417722\pi\) | ||||
0.255615 | + | 0.966779i | \(0.417722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.17493i | − | 0.146605i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.58266i | − | 0.257236i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 45.1660i | − | 2.07673i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.7199 | 0.767161 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.40291 | 0.201595 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 11.4968i | − | 0.525302i | −0.964891 | − | 0.262651i | \(-0.915403\pi\) | ||
0.964891 | − | 0.262651i | \(-0.0845967\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.1692i | 1.96835i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 3.97132i | − | 0.180701i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −63.9041 | −2.90174 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.5791i | 1.38567i | 0.721096 | + | 0.692835i | \(0.243639\pi\) | ||||
−0.721096 | + | 0.692835i | \(0.756361\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.9549 | −0.721506 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.4795 | 1.64630 | 0.823148 | − | 0.567828i | \(-0.192216\pi\) | ||||
0.823148 | + | 0.567828i | \(0.192216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.7478 | − | 24.2705i | 0.799322 | − | 1.09309i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.2753 | −0.641629 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.18919 | −0.232767 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.7116i | 0.748115i | 0.927405 | + | 0.374058i | \(0.122034\pi\) | ||||
−0.927405 | + | 0.374058i | \(0.877966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.4964 | 0.737004 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.2686i | 0.636206i | 0.948056 | + | 0.318103i | \(0.103046\pi\) | ||||
−0.948056 | + | 0.318103i | \(0.896954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47.5858i | 2.11754i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.43932i | − | 0.0639224i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.6361 | 1.22495 | 0.612475 | − | 0.790490i | \(-0.290174\pi\) | ||||
0.612475 | + | 0.790490i | \(0.290174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.225362 | 0.00996941 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.49247i | − | 0.0658943i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.2534i | 1.06873i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9223i | 0.656282i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.329815 | 0.0144773 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 39.5867i | − | 1.73433i | −0.498024 | − | 0.867163i | \(-0.665941\pi\) | ||
0.498024 | − | 0.867163i | \(-0.334059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.41386 | −0.324185 | −0.162093 | − | 0.986776i | \(-0.551824\pi\) | ||||
−0.162093 | + | 0.986776i | \(0.551824\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.2028 | −0.488931 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2405 | − | 14.0040i | 0.446082 | − | 0.610025i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.22865 | 0.314289 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.93570 | −0.300984 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.9102i | 0.732462i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47.0114 | −2.03248 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.32254i | 0.315991i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.54643i | − | 0.152756i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5.00936i | − | 0.215369i | −0.994185 | − | 0.107685i | \(-0.965656\pi\) | ||
0.994185 | − | 0.107685i | \(-0.0343437\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.37446 | −0.144812 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.4833 | −1.43427 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.5766i | 1.47839i | 0.673493 | + | 0.739194i | \(0.264793\pi\) | ||||
−0.673493 | + | 0.739194i | \(0.735207\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 13.8032i | − | 0.589106i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.8837i | − | 0.463660i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.64764 | −0.240162 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 45.7295i | 1.94111i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.1327 | −0.683564 | −0.341782 | − | 0.939779i | \(-0.611030\pi\) | ||||
−0.341782 | + | 0.939779i | \(0.611030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.3942 | 2.04686 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.8032 | − | 8.63111i | −0.498332 | − | 0.364406i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4329 | −0.776854 | −0.388427 | − | 0.921480i | \(-0.626981\pi\) | ||||
−0.388427 | + | 0.921480i | \(0.626981\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 52.0675 | 2.19049 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.0096 | 1.55152 | 0.775761 | − | 0.631026i | \(-0.217366\pi\) | ||||
0.775761 | + | 0.631026i | \(0.217366\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.4862i | − | 0.648078i | −0.946044 | − | 0.324039i | \(-0.894959\pi\) | ||
0.946044 | − | 0.324039i | \(-0.105041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.1283i | 0.506669i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.4899i | 1.85536i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.2314 | −1.63322 | −0.816611 | − | 0.577188i | \(-0.804150\pi\) | ||||
−0.816611 | + | 0.577188i | \(0.804150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.72544 | 0.321058 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.6927i | 0.443607i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 15.6146i | − | 0.646690i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 15.2957i | − | 0.632398i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.8605 | 1.52140 | 0.760698 | − | 0.649106i | \(-0.224857\pi\) | ||||
0.760698 | + | 0.649106i | \(0.224857\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.27987i | − | 0.258758i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.10858 | 0.127870 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.7165 | −1.63096 | −0.815480 | − | 0.578785i | \(-0.803527\pi\) | ||||
−0.815480 | + | 0.578785i | \(0.803527\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.3969 | − | 9.79650i | −0.549219 | − | 0.401617i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.4126 | −0.876358 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.9426 | 1.55029 | 0.775147 | − | 0.631781i | \(-0.217676\pi\) | ||||
0.775147 | + | 0.631781i | \(0.217676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.81826i | 0.114959i | 0.998347 | + | 0.0574795i | \(0.0183064\pi\) | ||||
−0.998347 | + | 0.0574795i | \(0.981694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.17493 | 0.129293 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.34849i | 0.258103i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.32123i | − | 0.215982i | −0.994152 | − | 0.107991i | \(-0.965558\pi\) | ||
0.994152 | − | 0.107991i | \(-0.0344418\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.29238i | 0.295502i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.9889 | −0.646841 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.7793 | 0.920049 | 0.460024 | − | 0.887906i | \(-0.347841\pi\) | ||||
0.460024 | + | 0.887906i | \(0.347841\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.9131i | 0.722326i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.2908i | − | 0.977913i | −0.872308 | − | 0.488956i | \(-0.837378\pi\) | ||
0.872308 | − | 0.488956i | \(-0.162622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.7786i | 0.995936i | 0.867195 | + | 0.497968i | \(0.165920\pi\) | ||||
−0.867195 | + | 0.497968i | \(0.834080\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.97132 | 0.159363 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.07861i | 0.123342i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 44.4890 | 1.77956 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.29295 | −0.211380 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.6488 | + | 37.8102i | −1.10243 | + | 1.50759i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.76043 | 0.388557 | 0.194278 | − | 0.980946i | \(-0.437763\pi\) | ||||
0.194278 | + | 0.980946i | \(0.437763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.531496 | 0.0211251 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 54.2398i | 2.15244i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.79991 | 0.150558 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5.18919i | − | 0.205281i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.7916i | 1.37419i | 0.726570 | + | 0.687093i | \(0.241113\pi\) | ||||
−0.726570 | + | 0.687093i | \(0.758887\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 45.8855i | − | 1.80955i | −0.425893 | − | 0.904774i | \(-0.640040\pi\) | ||
0.425893 | − | 0.904774i | \(-0.359960\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 51.2643 | 2.01853 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.4357 | −0.606839 | −0.303419 | − | 0.952857i | \(-0.598128\pi\) | ||||
−0.303419 | + | 0.952857i | \(0.598128\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.5970i | 0.965516i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.20770i | 0.164913i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.66864i | 0.378363i | 0.981942 | + | 0.189182i | \(0.0605835\pi\) | ||||
−0.981942 | + | 0.189182i | \(0.939417\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.5661 | −2.24929 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.225362i | 0.00879220i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3756 | −0.404178 | −0.202089 | − | 0.979367i | \(-0.564773\pi\) | ||||
−0.202089 | + | 0.979367i | \(0.564773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.5894 | −1.88991 | −0.944954 | − | 0.327202i | \(-0.893894\pi\) | ||||
−0.944954 | + | 0.327202i | \(0.893894\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.24802 | − | 12.6468i | 0.359164 | − | 0.491162i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.00761 | −0.232965 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.9604 | 1.12135 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 15.7382i | − | 0.608475i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.9521 | −1.88977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.3194i | 0.975989i | 0.872847 | + | 0.487995i | \(0.162271\pi\) | ||||
−0.872847 | + | 0.487995i | \(0.837729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 11.2028i | − | 0.431197i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.64564i | − | 0.101680i | −0.998707 | − | 0.0508401i | \(-0.983810\pi\) | ||
0.998707 | − | 0.0508401i | \(-0.0161899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.8757 | 0.609254 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.4883 | −1.01503 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.9903i | 0.611853i | 0.952055 | + | 0.305926i | \(0.0989662\pi\) | ||||
−0.952055 | + | 0.305926i | \(0.901034\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.9657i | 1.98551i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9835i | 0.419048i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.7306 | 0.637387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4728i | 0.512529i | 0.966607 | + | 0.256264i | \(0.0824917\pi\) | ||||
−0.966607 | + | 0.256264i | \(0.917508\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.54643 | 0.134718 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −87.6927 | −3.32637 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.8306 | + | 14.8110i | −0.410237 | + | 0.561006i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.4597 | 0.471269 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.8140 | −0.597288 | −0.298644 | − | 0.954365i | \(-0.596534\pi\) | ||||
−0.298644 | + | 0.954365i | \(0.596534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9554i | 0.639484i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.9371 | −0.637889 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 11.8218i | − | 0.444603i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 8.00000i | − | 0.300446i | −0.988652 | − | 0.150223i | \(-0.952001\pi\) | ||
0.988652 | − | 0.150223i | \(-0.0479992\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5.64764i | − | 0.211803i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.7101 | 0.625798 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −54.2450 | −2.02865 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 19.5452i | − | 0.729928i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.78606i | 0.141196i | 0.997505 | + | 0.0705981i | \(0.0224908\pi\) | ||||
−0.997505 | + | 0.0705981i | \(0.977509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.02527i | − | 0.224393i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.8607 | 0.701436 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 81.6952i | − | 3.03408i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.7337 | −1.25111 | −0.625557 | − | 0.780178i | \(-0.715128\pi\) | ||||
−0.625557 | + | 0.780178i | \(0.715128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.3866 | + | 30.9953i | 1.56772 | + | 1.14640i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.3129 | 1.41512 | 0.707560 | − | 0.706653i | \(-0.249796\pi\) | ||||
0.707560 | + | 0.706653i | \(0.249796\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.02527 | 0.148474 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 11.2597i | − | 0.414756i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3912 | 1.11796 | 0.558979 | − | 0.829182i | \(-0.311193\pi\) | ||||
0.558979 | + | 0.829182i | \(0.311193\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 5.67126i | − | 0.208339i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.2427i | 1.36630i | 0.730278 | + | 0.683151i | \(0.239391\pi\) | ||||
−0.730278 | + | 0.683151i | \(0.760609\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.43971i | 0.235933i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.6927 | −0.391225 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6790 | 0.426743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.0450i | 1.05987i | 0.848039 | + | 0.529934i | \(0.177783\pi\) | ||||
−0.848039 | + | 0.529934i | \(0.822217\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 24.2705i | − | 0.884467i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.49065i | 0.309006i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.4692 | −1.21646 | −0.608230 | − | 0.793761i | \(-0.708120\pi\) | ||||
−0.608230 | + | 0.793761i | \(0.708120\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 14.0840i | − | 0.511216i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.9761 | −1.12288 | −0.561442 | − | 0.827516i | \(-0.689753\pi\) | ||||
−0.561442 | + | 0.827516i | \(0.689753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.31828 | 0.301142 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.79650 | − | 13.3969i | 0.354193 | − | 0.484365i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.3551 | −0.951626 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0089 | 0.865783 | 0.432892 | − | 0.901446i | \(-0.357493\pi\) | ||||
0.432892 | + | 0.901446i | \(0.357493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.49394i | 0.0538030i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.37904 | 0.0855683 | 0.0427841 | − | 0.999084i | \(-0.486377\pi\) | ||||
0.0427841 | + | 0.999084i | \(0.486377\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 47.1381i | − | 1.69325i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 11.3606i | − | 0.407559i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.64174i | 0.237965i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4031 | −0.658514 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.29238 | −0.260609 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 22.4717i | − | 0.802051i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.8238i | − | 0.670997i | −0.942041 | − | 0.335498i | \(-0.891095\pi\) | ||
0.942041 | − | 0.335498i | \(-0.108905\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.7786i | 0.597332i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9351 | −0.459921 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 52.4509i | − | 1.86259i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.7229 | 0.628566 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.1455 | 0.359370 | 0.179685 | − | 0.983724i | \(-0.442492\pi\) | ||||
0.179685 | + | 0.983724i | \(0.442492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0040 | − | 10.2405i | −0.495427 | − | 0.362282i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.07861 | −0.108777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.799229 | 0.0282042 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 15.9856i | − | 0.563419i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.6209 | −1.00750 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.0198i | − | 0.949964i | −0.879995 | − | 0.474982i | \(-0.842454\pi\) | ||
0.879995 | − | 0.474982i | \(-0.157546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.32100i | 0.221960i | 0.993823 | + | 0.110980i | \(0.0353990\pi\) | ||||
−0.993823 | + | 0.110980i | \(0.964601\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.53479i | − | 0.159042i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64.2228 | −2.24963 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.0076 | 0.664990 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.79991i | 0.132780i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4679i | 0.609635i | 0.952411 | + | 0.304818i | \(0.0985955\pi\) | ||||
−0.952411 | + | 0.304818i | \(0.901404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.9467i | 1.53189i | 0.642908 | + | 0.765943i | \(0.277728\pi\) | ||||
−0.642908 | + | 0.765943i | \(0.722272\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39.7300 | −1.38322 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 56.6175i | − | 1.96878i | −0.175993 | − | 0.984391i | \(-0.556314\pi\) | ||
0.175993 | − | 0.984391i | \(-0.443686\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.9631 | −0.936468 | −0.468234 | − | 0.883604i | \(-0.655110\pi\) | ||||
−0.468234 | + | 0.883604i | \(0.655110\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.3988 | −0.985144 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.32819 | + | 2.43375i | 0.115315 | + | 0.0843244i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 66.4024 | 2.29795 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.20770 | −0.145439 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.88596i | 0.0651106i | 0.999470 | + | 0.0325553i | \(0.0103645\pi\) | ||||
−0.999470 | + | 0.0325553i | \(0.989636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1788 | −0.833753 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 4.69268i | − | 0.161624i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 5.79365i | − | 0.199308i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.57716i | − | 0.0541918i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.67348 | 0.194713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.1165 | −1.54657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 51.6040i | − | 1.76689i | −0.468539 | − | 0.883443i | \(-0.655219\pi\) | ||
0.468539 | − | 0.883443i | \(-0.344781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.00761i | − | 0.205456i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.5395i | 1.65808i | 0.559190 | + | 0.829040i | \(0.311112\pi\) | ||||
−0.559190 | + | 0.829040i | \(0.688888\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.36582 | 0.251319 | 0.125659 | − | 0.992073i | \(-0.459895\pi\) | ||||
0.125659 | + | 0.992073i | \(0.459895\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 4.45016i | − | 0.151661i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.7936 | 1.49075 | 0.745375 | − | 0.666645i | \(-0.232270\pi\) | ||||
0.745375 | + | 0.666645i | \(0.232270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.32759 | 0.0451395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.2000 | − | 5.15374i | 0.550180 | − | 0.175030i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.0290 | −0.679436 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0645 | 0.408789 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.8757i | 0.537312i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.9680 | −0.844073 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.5900i | 1.67454i | 0.546793 | + | 0.837268i | \(0.315849\pi\) | ||||
−0.546793 | + | 0.837268i | \(0.684151\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 6.94865i | − | 0.234372i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.7745i | − | 0.800984i | −0.916300 | − | 0.400492i | \(-0.868839\pi\) | ||
0.916300 | − | 0.400492i | \(-0.131161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.98568 | 0.100476 | 0.0502381 | − | 0.998737i | \(-0.484002\pi\) | ||||
0.0502381 | + | 0.998737i | \(0.484002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.9181 | −0.938457 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 15.0154i | − | 0.504168i | −0.967705 | − | 0.252084i | \(-0.918884\pi\) | ||
0.967705 | − | 0.252084i | \(-0.0811158\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.4748i | − | 0.451931i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.54643i | 0.118810i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.27987 | −0.210148 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.4752i | 0.985247i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.0906 | 0.503862 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.6841 | −1.02337 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.6537 | + | 10.7156i | 0.488186 | + | 0.356987i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.7356 | −0.423815 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.5831 | −0.451518 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39.1586i | − | 1.30024i | −0.759831 | − | 0.650120i | \(-0.774718\pi\) | ||
0.759831 | − | 0.650120i | \(-0.225282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.8218 | 0.392103 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 17.4113i | − | 0.576861i | −0.957501 | − | 0.288430i | \(-0.906867\pi\) | ||
0.957501 | − | 0.288430i | \(-0.0931334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.9208i | 1.25500i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 55.5616i | − | 1.83681i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.3012 | 0.472267 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −57.1727 | −1.88595 | −0.942977 | − | 0.332859i | \(-0.891987\pi\) | ||||
−0.942977 | + | 0.332859i | \(0.891987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.40450i | 0.211035i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 19.7184i | − | 0.649040i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 127.271i | 4.18463i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.02527 | 0.197896 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 6.09643i | − | 0.200018i | −0.994987 | − | 0.100009i | \(-0.968113\pi\) | ||
0.994987 | − | 0.100009i | \(-0.0318871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.49247 | 0.0489138 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.57256 | −0.182437 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −47.5111 | − | 34.7426i | −1.55378 | − | 1.13620i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.3510 | 1.64490 | 0.822448 | − | 0.568840i | \(-0.192607\pi\) | ||||
0.822448 | + | 0.568840i | \(0.192607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.23758 | 0.203556 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.9192i | 0.421153i | 0.977577 | + | 0.210576i | \(0.0675341\pi\) | ||||
−0.977577 | + | 0.210576i | \(0.932466\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.6730 | −0.575512 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.02527i | 0.130942i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.01283i | 0.130399i | 0.997872 | + | 0.0651997i | \(0.0207685\pi\) | ||||
−0.997872 | + | 0.0651997i | \(0.979232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.856354i | 0.0277984i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.11223 | 0.0684938 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.65422 | 0.118372 | 0.0591859 | − | 0.998247i | \(-0.481150\pi\) | ||||
0.0591859 | + | 0.998247i | \(0.481150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.8199i | 1.57977i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.8619i | 0.835997i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 12.9099i | − | 0.416881i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2953 | 0.428880 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.6790i | 0.376352i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.0970 | 1.00105 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.57044 | 0.307765 | 0.153882 | − | 0.988089i | \(-0.450822\pi\) | ||||
0.153882 | + | 0.988089i | \(0.450822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.63230 | − | 4.96724i | 0.116686 | − | 0.159571i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.4539 | 1.61914 | 0.809571 | − | 0.587022i | \(-0.199700\pi\) | ||||
0.809571 | + | 0.587022i | \(0.199700\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.7855 | 0.698412 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 42.5697i | − | 1.36332i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.7281 | 0.471194 | 0.235597 | − | 0.971851i | \(-0.424295\pi\) | ||||
0.235597 | + | 0.971851i | \(0.424295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.9181i | 0.348943i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.31828i | 0.265582i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.7957i | 1.10981i | 0.831913 | + | 0.554905i | \(0.187246\pi\) | ||||
−0.831913 | + | 0.554905i | \(0.812754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.5129 | 0.398693 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.20770 | 0.133932 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.5771i | 1.60826i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7910i | 1.45460i | 0.686320 | + | 0.727299i | \(0.259225\pi\) | ||||
−0.686320 | + | 0.727299i | \(0.740775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6906i | 0.434459i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −86.1914 | −2.73245 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 27.7393i | − | 0.878513i | −0.898362 | − | 0.439256i | \(-0.855242\pi\) | ||
0.898362 | − | 0.439256i | \(-0.144758\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.3606 | 0.359433 |
(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 | 1428.2.d.c.169.1 | ✓ | 12 | |
3.2 | odd | 2 | 4284.2.d.f.3025.12 | 12 | |||
17.16 | even | 2 | inner | 1428.2.d.c.169.12 | yes | 12 | |
51.50 | odd | 2 | 4284.2.d.f.3025.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1428.2.d.c.169.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1428.2.d.c.169.12 | yes | 12 | 17.16 | even | 2 | inner | |
4284.2.d.f.3025.1 | 12 | 51.50 | odd | 2 | |||
4284.2.d.f.3025.12 | 12 | 3.2 | odd | 2 |