Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Root | \(0.500000 - 0.564882i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.a.323.3 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 0.366025i | −0.965926 | − | 0.258819i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | −3.12976 | −1.39967 | −0.699837 | − | 0.714303i | \(-0.746744\pi\) | ||||
−0.699837 | + | 0.714303i | \(0.746744\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.27534 | + | 1.14557i | 1.35198 | + | 0.362262i | ||||
\(11\) | 0.397714i | 0.119915i | 0.998201 | + | 0.0599577i | \(0.0190966\pi\) | ||||
−0.998201 | + | 0.0599577i | \(0.980903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.55068i | 1.81683i | 0.418069 | + | 0.908415i | \(0.362707\pi\) | ||||
−0.418069 | + | 0.908415i | \(0.637293\pi\) | |||||||
\(14\) | −0.366025 | + | 1.36603i | −0.0978244 | + | 0.365086i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.527479 | −0.121012 | −0.0605060 | − | 0.998168i | \(-0.519271\pi\) | ||||
−0.0605060 | + | 0.998168i | \(0.519271\pi\) | |||||||
\(20\) | −5.42091 | − | 3.12976i | −1.21215 | − | 0.699837i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.145573 | − | 0.543288i | 0.0310364 | − | 0.115829i | ||||
\(23\) | 8.21634 | 1.71323 | 0.856613 | − | 0.515960i | \(-0.172565\pi\) | ||||
0.856613 | + | 0.515960i | \(0.172565\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.79543 | 0.959086 | ||||||||
\(26\) | 2.39771 | − | 8.94839i | 0.470230 | − | 1.75492i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 1.73205i | 0.188982 | − | 0.327327i | ||||
\(29\) | −4.73205 | −0.878720 | −0.439360 | − | 0.898311i | \(-0.644795\pi\) | ||||
−0.439360 | + | 0.898311i | \(0.644795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.55068i | − | 1.35614i | −0.734997 | − | 0.678071i | \(-0.762816\pi\) | ||
0.734997 | − | 0.678071i | \(-0.237184\pi\) | |||||||
\(32\) | −1.46410 | − | 5.46410i | −0.258819 | − | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.732051 | + | 2.73205i | −0.125546 | + | 0.468543i | ||||
\(35\) | 3.12976i | 0.529027i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.35452i | − | 0.551480i | −0.961232 | − | 0.275740i | \(-0.911077\pi\) | ||
0.961232 | − | 0.275740i | \(-0.0889229\pi\) | |||||||
\(38\) | 0.720550 | + | 0.193071i | 0.116889 | + | 0.0313202i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.25953 | + | 6.25953i | 0.989719 | + | 0.989719i | ||||
\(41\) | 7.48429i | 1.16885i | 0.811448 | + | 0.584425i | \(0.198680\pi\) | ||||
−0.811448 | + | 0.584425i | \(0.801320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.62247 | 0.247425 | 0.123712 | − | 0.992318i | \(-0.460520\pi\) | ||||
0.123712 | + | 0.992318i | \(0.460520\pi\) | |||||||
\(44\) | −0.397714 | + | 0.688861i | −0.0599577 | + | 0.103850i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11.2237 | − | 3.00739i | −1.65485 | − | 0.443415i | ||||
\(47\) | −10.4557 | −1.52512 | −0.762559 | − | 0.646919i | \(-0.776057\pi\) | ||||
−0.762559 | + | 0.646919i | \(0.776057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −6.55068 | − | 1.75525i | −0.926406 | − | 0.248230i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.55068 | + | 11.3461i | −0.908415 | + | 1.57342i | ||||
\(53\) | 0.795428 | 0.109260 | 0.0546302 | − | 0.998507i | \(-0.482602\pi\) | ||||
0.0546302 | + | 0.998507i | \(0.482602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.24475i | − | 0.167842i | ||||||
\(56\) | −2.00000 | + | 2.00000i | −0.267261 | + | 0.267261i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.46410 | + | 1.73205i | 0.848778 | + | 0.227429i | ||||
\(59\) | 2.47252i | 0.321895i | 0.986963 | + | 0.160947i | \(0.0514550\pi\) | ||||
−0.986963 | + | 0.160947i | \(0.948545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.4641i | − | 1.46783i | −0.679243 | − | 0.733914i | \(-0.737692\pi\) | ||
0.679243 | − | 0.733914i | \(-0.262308\pi\) | |||||||
\(62\) | −2.76374 | + | 10.3144i | −0.350995 | + | 1.30993i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | − | 20.5021i | − | 2.54297i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.55068 | −0.800293 | −0.400146 | − | 0.916451i | \(-0.631041\pi\) | ||||
−0.400146 | + | 0.916451i | \(0.631041\pi\) | |||||||
\(68\) | 2.00000 | − | 3.46410i | 0.242536 | − | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.14557 | − | 4.27534i | 0.136922 | − | 0.511001i | ||||
\(71\) | −2.21634 | −0.263031 | −0.131516 | − | 0.991314i | \(-0.541984\pi\) | ||||
−0.131516 | + | 0.991314i | \(0.541984\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.75525 | −0.673601 | −0.336800 | − | 0.941576i | \(-0.609345\pi\) | ||||
−0.336800 | + | 0.941576i | \(0.609345\pi\) | |||||||
\(74\) | −1.22784 | + | 4.58237i | −0.142734 | + | 0.532689i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.913620 | − | 0.527479i | −0.104799 | − | 0.0605060i | ||||
\(77\) | 0.397714 | 0.0453237 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.2911i | − | 1.15784i | −0.815383 | − | 0.578922i | \(-0.803473\pi\) | ||
0.815383 | − | 0.578922i | \(-0.196527\pi\) | |||||||
\(80\) | −6.25953 | − | 10.8418i | −0.699837 | − | 1.21215i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.73944 | − | 10.2237i | 0.302521 | − | 1.12902i | ||||
\(83\) | − | 8.36930i | − | 0.918650i | −0.888268 | − | 0.459325i | \(-0.848091\pi\) | ||
0.888268 | − | 0.459325i | \(-0.151909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.25953i | 0.678941i | ||||||||
\(86\) | −2.21634 | − | 0.593866i | −0.238994 | − | 0.0640383i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.795428 | − | 0.795428i | 0.0847929 | − | 0.0847929i | ||||
\(89\) | − | 5.31114i | − | 0.562980i | −0.959564 | − | 0.281490i | \(-0.909171\pi\) | ||
0.959564 | − | 0.281490i | \(-0.0908286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.55068 | 0.686697 | ||||||||
\(92\) | 14.2311 | + | 8.21634i | 1.48370 | + | 0.856613i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.2827 | + | 3.82705i | 1.47315 | + | 0.394730i | ||||
\(95\) | 1.65089 | 0.169377 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −19.1014 | −1.93945 | −0.969724 | − | 0.244202i | \(-0.921474\pi\) | ||||
−0.969724 | + | 0.244202i | \(0.921474\pi\) | |||||||
\(98\) | 1.36603 | + | 0.366025i | 0.137989 | + | 0.0369741i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.30593 | + | 4.79543i | 0.830593 | + | 0.479543i | ||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.0148i | − | 1.67652i | −0.545274 | − | 0.838258i | \(-0.683574\pi\) | ||
0.545274 | − | 0.838258i | \(-0.316426\pi\) | |||||||
\(104\) | 13.1014 | − | 13.1014i | 1.28469 | − | 1.28469i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.08658 | − | 0.291147i | −0.105537 | − | 0.0282787i | ||||
\(107\) | 1.91362i | 0.184997i | 0.995713 | + | 0.0924983i | \(0.0294853\pi\) | ||||
−0.995713 | + | 0.0924983i | \(0.970515\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.07816i | 0.677964i | 0.940793 | + | 0.338982i | \(0.110083\pi\) | ||||
−0.940793 | + | 0.338982i | \(0.889917\pi\) | |||||||
\(110\) | −0.455611 | + | 1.70036i | −0.0434408 | + | 0.162123i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.46410 | − | 2.00000i | 0.327327 | − | 0.188982i | ||||
\(113\) | − | 9.98316i | − | 0.939137i | −0.882896 | − | 0.469568i | \(-0.844410\pi\) | ||
0.882896 | − | 0.469568i | \(-0.155590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.7152 | −2.39796 | ||||||||
\(116\) | −8.19615 | − | 4.73205i | −0.760994 | − | 0.439360i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.905006 | − | 3.37753i | 0.0833125 | − | 0.310927i | ||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8418 | 0.985620 | ||||||||
\(122\) | −4.19615 | + | 15.6603i | −0.379902 | + | 1.41781i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.55068 | − | 13.0782i | 0.678071 | − | 1.17445i | ||||
\(125\) | 0.640262 | 0.0572668 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.75525i | 0.688167i | 0.938939 | + | 0.344084i | \(0.111810\pi\) | ||||
−0.938939 | + | 0.344084i | \(0.888190\pi\) | |||||||
\(128\) | 2.92820 | − | 10.9282i | 0.258819 | − | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.50428 | + | 28.0064i | −0.658169 | + | 2.45632i | ||||
\(131\) | 14.9052i | 1.30227i | 0.758960 | + | 0.651137i | \(0.225708\pi\) | ||||
−0.758960 | + | 0.651137i | \(0.774292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.527479i | 0.0457382i | ||||||||
\(134\) | 8.94839 | + | 2.39771i | 0.773023 | + | 0.207131i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | + | 4.00000i | −0.342997 | + | 0.342997i | ||||
\(137\) | − | 22.4557i | − | 1.91852i | −0.282527 | − | 0.959259i | \(-0.591173\pi\) | ||
0.282527 | − | 0.959259i | \(-0.408827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.05496 | 0.259118 | 0.129559 | − | 0.991572i | \(-0.458644\pi\) | ||||
0.129559 | + | 0.991572i | \(0.458644\pi\) | |||||||
\(140\) | −3.12976 | + | 5.42091i | −0.264513 | + | 0.458151i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.02758 | + | 0.811237i | 0.254069 | + | 0.0680775i | ||||
\(143\) | −2.60530 | −0.217866 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.8102 | 1.22992 | ||||||||
\(146\) | 7.86182 | + | 2.10657i | 0.650648 | + | 0.174341i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.35452 | − | 5.81021i | 0.275740 | − | 0.477596i | ||||
\(149\) | 7.01458 | 0.574657 | 0.287329 | − | 0.957832i | \(-0.407233\pi\) | ||||
0.287329 | + | 0.957832i | \(0.407233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.81001i | − | 0.798327i | −0.916880 | − | 0.399164i | \(-0.869301\pi\) | ||
0.916880 | − | 0.399164i | \(-0.130699\pi\) | |||||||
\(152\) | 1.05496 | + | 1.05496i | 0.0855684 | + | 0.0855684i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.543288 | − | 0.145573i | −0.0437794 | − | 0.0117306i | ||||
\(155\) | 23.6318i | 1.89816i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.8966i | − | 0.869642i | −0.900517 | − | 0.434821i | \(-0.856812\pi\) | ||
0.900517 | − | 0.434821i | \(-0.143188\pi\) | |||||||
\(158\) | −3.76682 | + | 14.0580i | −0.299672 | + | 1.11839i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.58229 | + | 17.1014i | 0.362262 | + | 1.35198i | ||||
\(161\) | − | 8.21634i | − | 0.647538i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0148 | −0.784418 | −0.392209 | − | 0.919876i | \(-0.628289\pi\) | ||||
−0.392209 | + | 0.919876i | \(0.628289\pi\) | |||||||
\(164\) | −7.48429 | + | 12.9632i | −0.584425 | + | 1.01225i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.06338 | + | 11.4327i | −0.237764 | + | 0.887348i | ||||
\(167\) | −14.5655 | −1.12711 | −0.563554 | − | 0.826079i | \(-0.690566\pi\) | ||||
−0.563554 | + | 0.826079i | \(0.690566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −29.9114 | −2.30087 | ||||||||
\(170\) | 2.29115 | − | 8.55068i | 0.175723 | − | 0.655807i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.81021 | + | 1.62247i | 0.214276 | + | 0.123712i | ||||
\(173\) | −14.3175 | −1.08854 | −0.544270 | − | 0.838910i | \(-0.683193\pi\) | ||||
−0.544270 | + | 0.838910i | \(0.683193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.79543i | − | 0.362500i | ||||||
\(176\) | −1.37772 | + | 0.795428i | −0.103850 | + | 0.0599577i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.94401 | + | 7.25515i | −0.145710 | + | 0.543797i | ||||
\(179\) | − | 19.8104i | − | 1.48070i | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||
0.672222 | − | 0.740349i | \(-0.265340\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.1732i | − | 1.49946i | −0.661745 | − | 0.749729i | \(-0.730184\pi\) | ||
0.661745 | − | 0.749729i | \(-0.269816\pi\) | |||||||
\(182\) | −8.94839 | − | 2.39771i | −0.663299 | − | 0.177730i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.4327 | − | 16.4327i | −1.21143 | − | 1.21143i | ||||
\(185\) | 10.4989i | 0.771892i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.795428 | 0.0581675 | ||||||||
\(188\) | −18.1098 | − | 10.4557i | −1.32079 | − | 0.762559i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.25515 | − | 0.604266i | −0.163606 | − | 0.0438381i | ||||
\(191\) | 6.43549 | 0.465656 | 0.232828 | − | 0.972518i | \(-0.425202\pi\) | ||||
0.232828 | + | 0.972518i | \(0.425202\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.98316 | −0.718604 | −0.359302 | − | 0.933221i | \(-0.616985\pi\) | ||||
−0.359302 | + | 0.933221i | \(0.616985\pi\) | |||||||
\(194\) | 26.0929 | + | 6.99158i | 1.87336 | + | 0.501966i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.73205 | − | 1.00000i | −0.123718 | − | 0.0714286i | ||||
\(197\) | −23.6373 | −1.68408 | −0.842042 | − | 0.539412i | \(-0.818647\pi\) | ||||
−0.842042 | + | 0.539412i | \(0.818647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6202i | 1.53262i | 0.642473 | + | 0.766308i | \(0.277908\pi\) | ||||
−0.642473 | + | 0.766308i | \(0.722092\pi\) | |||||||
\(200\) | −9.59086 | − | 9.59086i | −0.678176 | − | 0.678176i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.73205 | + | 0.732051i | 0.192226 | + | 0.0515069i | ||||
\(203\) | 4.73205i | 0.332125i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 23.4241i | − | 1.63601i | ||||||
\(206\) | −6.22784 | + | 23.2426i | −0.433914 | + | 1.61939i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −22.6922 | + | 13.1014i | −1.57342 | + | 0.908415i | ||||
\(209\) | − | 0.209786i | − | 0.0145112i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.51906 | 0.173419 | 0.0867096 | − | 0.996234i | \(-0.472365\pi\) | ||||
0.0867096 | + | 0.996234i | \(0.472365\pi\) | |||||||
\(212\) | 1.37772 | + | 0.795428i | 0.0946223 | + | 0.0546302i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.700434 | − | 2.61405i | 0.0478807 | − | 0.178693i | ||||
\(215\) | −5.07796 | −0.346314 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.55068 | −0.512573 | ||||||||
\(218\) | 2.59078 | − | 9.66894i | 0.175470 | − | 0.654863i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.24475 | − | 2.15597i | 0.0839211 | − | 0.145356i | ||||
\(221\) | 13.1014 | 0.881292 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.882003i | 0.0590633i | 0.999564 | + | 0.0295316i | \(0.00940158\pi\) | ||||
−0.999564 | + | 0.0295316i | \(0.990598\pi\) | |||||||
\(224\) | −5.46410 | + | 1.46410i | −0.365086 | + | 0.0978244i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.65409 | + | 13.6373i | −0.243066 | + | 0.907136i | ||||
\(227\) | 8.47868i | 0.562750i | 0.959598 | + | 0.281375i | \(0.0907905\pi\) | ||||
−0.959598 | + | 0.281375i | \(0.909210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.4641i | − | 0.889733i | −0.895597 | − | 0.444866i | \(-0.853251\pi\) | ||
0.895597 | − | 0.444866i | \(-0.146749\pi\) | |||||||
\(230\) | 35.1276 | + | 9.41242i | 2.31625 | + | 0.620637i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.46410 | + | 9.46410i | 0.621349 | + | 0.621349i | ||||
\(233\) | − | 17.4641i | − | 1.14411i | −0.820215 | − | 0.572056i | \(-0.806146\pi\) | ||
0.820215 | − | 0.572056i | \(-0.193854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7238 | 2.13467 | ||||||||
\(236\) | −2.47252 | + | 4.28253i | −0.160947 | + | 0.278769i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.73205 | + | 0.732051i | 0.177093 | + | 0.0474518i | ||||
\(239\) | 27.6836 | 1.79071 | 0.895353 | − | 0.445357i | \(-0.146923\pi\) | ||||
0.895353 | + | 0.445357i | \(0.146923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9116 | 1.41145 | 0.705724 | − | 0.708487i | \(-0.250622\pi\) | ||||
0.705724 | + | 0.708487i | \(0.250622\pi\) | |||||||
\(242\) | −14.8102 | − | 3.96838i | −0.952036 | − | 0.255097i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.4641 | − | 19.8564i | 0.733914 | − | 1.27118i | ||||
\(245\) | 3.12976 | 0.199953 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.45534i | − | 0.219858i | ||||||
\(248\) | −15.1014 | + | 15.1014i | −0.958937 | + | 0.958937i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.874614 | − | 0.234352i | −0.0553154 | − | 0.0148217i | ||||
\(251\) | 15.9136i | 1.00446i | 0.864734 | + | 0.502229i | \(0.167487\pi\) | ||||
−0.864734 | + | 0.502229i | \(0.832513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.26775i | 0.205442i | ||||||||
\(254\) | 2.83862 | − | 10.5939i | 0.178111 | − | 0.664718i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 3.70344i | 0.231014i | 0.993307 | + | 0.115507i | \(0.0368493\pi\) | ||||
−0.993307 | + | 0.115507i | \(0.963151\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.35452 | −0.208440 | ||||||||
\(260\) | 20.5021 | − | 35.5106i | 1.27148 | − | 2.20228i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.45568 | − | 20.3609i | 0.337053 | − | 1.25790i | ||||
\(263\) | 22.1995 | 1.36888 | 0.684440 | − | 0.729069i | \(-0.260047\pi\) | ||||
0.684440 | + | 0.729069i | \(0.260047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.48950 | −0.152929 | ||||||||
\(266\) | 0.193071 | − | 0.720550i | 0.0118379 | − | 0.0441797i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.3461 | − | 6.55068i | −0.693074 | − | 0.400146i | ||||
\(269\) | −16.2480 | −0.990655 | −0.495328 | − | 0.868706i | \(-0.664952\pi\) | ||||
−0.495328 | + | 0.868706i | \(0.664952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3755i | 1.11623i | 0.829764 | + | 0.558115i | \(0.188475\pi\) | ||||
−0.829764 | + | 0.558115i | \(0.811525\pi\) | |||||||
\(272\) | 6.92820 | − | 4.00000i | 0.420084 | − | 0.242536i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.21935 | + | 30.6750i | −0.496549 | + | 1.85315i | ||||
\(275\) | 1.90721i | 0.115009i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 31.7764i | − | 1.90926i | −0.297798 | − | 0.954629i | \(-0.596252\pi\) | ||
0.297798 | − | 0.954629i | \(-0.403748\pi\) | |||||||
\(278\) | −4.17315 | − | 1.11819i | −0.250289 | − | 0.0670647i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.25953 | − | 6.25953i | 0.374078 | − | 0.374078i | ||||
\(281\) | − | 4.86483i | − | 0.290211i | −0.989416 | − | 0.145106i | \(-0.953648\pi\) | ||
0.989416 | − | 0.145106i | \(-0.0463522\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.7386 | −1.47056 | −0.735279 | − | 0.677765i | \(-0.762949\pi\) | ||||
−0.735279 | + | 0.677765i | \(0.762949\pi\) | |||||||
\(284\) | −3.83881 | − | 2.21634i | −0.227792 | − | 0.131516i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.55890 | + | 0.953605i | 0.210442 | + | 0.0563878i | ||||
\(287\) | 7.48429 | 0.441784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −20.2311 | − | 5.42091i | −1.18801 | − | 0.318327i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.96838 | − | 5.75525i | −0.583355 | − | 0.336800i | ||||
\(293\) | 15.9428 | 0.931388 | 0.465694 | − | 0.884946i | \(-0.345805\pi\) | ||||
0.465694 | + | 0.884946i | \(0.345805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.73841i | − | 0.450548i | ||||||
\(296\) | −6.70905 | + | 6.70905i | −0.389956 | + | 0.389956i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.58210 | − | 2.56752i | −0.555076 | − | 0.148732i | ||||
\(299\) | 53.8226i | 3.11264i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.62247i | − | 0.0935178i | ||||||
\(302\) | −3.59071 | + | 13.4007i | −0.206622 | + | 0.771125i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.05496 | − | 1.82724i | −0.0605060 | − | 0.104799i | ||||
\(305\) | 35.8799i | 2.05448i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.64567 | −0.322215 | −0.161108 | − | 0.986937i | \(-0.551507\pi\) | ||||
−0.161108 | + | 0.986937i | \(0.551507\pi\) | |||||||
\(308\) | 0.688861 | + | 0.397714i | 0.0392515 | + | 0.0226619i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.64985 | − | 32.2817i | 0.491279 | − | 1.83348i | ||||
\(311\) | 19.0084 | 1.07787 | 0.538934 | − | 0.842348i | \(-0.318827\pi\) | ||||
0.538934 | + | 0.842348i | \(0.318827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.24475 | 0.126881 | 0.0634404 | − | 0.997986i | \(-0.479793\pi\) | ||||
0.0634404 | + | 0.997986i | \(0.479793\pi\) | |||||||
\(314\) | −3.98843 | + | 14.8850i | −0.225080 | + | 0.840010i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2911 | − | 17.8248i | 0.578922 | − | 1.00272i | ||||
\(317\) | 24.4852 | 1.37523 | 0.687614 | − | 0.726076i | \(-0.258658\pi\) | ||||
0.687614 | + | 0.726076i | \(0.258658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.88200i | − | 0.105372i | ||||||
\(320\) | − | 25.0381i | − | 1.39967i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.00739 | + | 11.2237i | −0.167595 | + | 0.625474i | ||||
\(323\) | 1.05496i | 0.0586994i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.4133i | 1.74250i | ||||||||
\(326\) | 13.6804 | + | 3.66566i | 0.757690 | + | 0.203022i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.9686 | − | 14.9686i | 0.826501 | − | 0.826501i | ||||
\(329\) | 10.4557i | 0.576440i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.34591 | 0.238873 | 0.119436 | − | 0.992842i | \(-0.461891\pi\) | ||||
0.119436 | + | 0.992842i | \(0.461891\pi\) | |||||||
\(332\) | 8.36930 | − | 14.4961i | 0.459325 | − | 0.795574i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.8968 | + | 5.33133i | 1.08870 | + | 0.291717i | ||||
\(335\) | 20.5021 | 1.12015 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5655 | −1.50159 | −0.750793 | − | 0.660538i | \(-0.770328\pi\) | ||||
−0.750793 | + | 0.660538i | \(0.770328\pi\) | |||||||
\(338\) | 40.8597 | + | 10.9483i | 2.22247 | + | 0.595510i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.25953 | + | 10.8418i | −0.339471 | + | 0.587980i | ||||
\(341\) | 3.00301 | 0.162622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −3.24495 | − | 3.24495i | −0.174956 | − | 0.174956i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.5581 | + | 5.24057i | 1.05145 | + | 0.281735i | ||||
\(347\) | 20.8364i | 1.11856i | 0.828980 | + | 0.559279i | \(0.188922\pi\) | ||||
−0.828980 | + | 0.559279i | \(0.811078\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.88181i | 0.261317i | 0.991427 | + | 0.130659i | \(0.0417092\pi\) | ||||
−0.991427 | + | 0.130659i | \(0.958291\pi\) | |||||||
\(350\) | −1.75525 | + | 6.55068i | −0.0938220 | + | 0.350148i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.17315 | − | 0.582294i | 0.115829 | − | 0.0310364i | ||||
\(353\) | − | 7.44391i | − | 0.396200i | −0.980182 | − | 0.198100i | \(-0.936523\pi\) | ||
0.980182 | − | 0.198100i | \(-0.0634770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.93662 | 0.368158 | ||||||||
\(356\) | 5.31114 | − | 9.19916i | 0.281490 | − | 0.487555i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.25111 | + | 27.0615i | −0.383233 | + | 1.43025i | ||||
\(359\) | 22.3923 | 1.18182 | 0.590910 | − | 0.806737i | \(-0.298769\pi\) | ||||
0.590910 | + | 0.806737i | \(0.298769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7218 | −0.985356 | ||||||||
\(362\) | −7.38389 | + | 27.5570i | −0.388088 | + | 1.44837i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.3461 | + | 6.55068i | 0.594697 | + | 0.343349i | ||||
\(365\) | 18.0126 | 0.942821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.2575i | 1.84042i | 0.391419 | + | 0.920212i | \(0.371984\pi\) | ||||
−0.391419 | + | 0.920212i | \(0.628016\pi\) | |||||||
\(368\) | 16.4327 | + | 28.4622i | 0.856613 | + | 1.48370i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.84285 | − | 14.3417i | 0.199780 | − | 0.745591i | ||||
\(371\) | − | 0.795428i | − | 0.0412966i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2681i | 0.583442i | 0.956503 | + | 0.291721i | \(0.0942279\pi\) | ||||
−0.956503 | + | 0.291721i | \(0.905772\pi\) | |||||||
\(374\) | −1.08658 | − | 0.291147i | −0.0561855 | − | 0.0150548i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.9114 | + | 20.9114i | 1.07842 | + | 1.07842i | ||||
\(377\) | − | 30.9981i | − | 1.59649i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.47888 | −0.281431 | −0.140716 | − | 0.990050i | \(-0.544940\pi\) | ||||
−0.140716 | + | 0.990050i | \(0.544940\pi\) | |||||||
\(380\) | 2.85942 | + | 1.65089i | 0.146685 | + | 0.0846886i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.79105 | − | 2.35555i | −0.449789 | − | 0.120521i | ||||
\(383\) | −31.6668 | −1.61810 | −0.809049 | − | 0.587741i | \(-0.800017\pi\) | ||||
−0.809049 | + | 0.587741i | \(0.800017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.24475 | −0.0634384 | ||||||||
\(386\) | 13.6373 | + | 3.65409i | 0.694118 | + | 0.185988i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −33.0845 | − | 19.1014i | −1.67961 | − | 0.969724i | ||||
\(389\) | −25.1014 | −1.27269 | −0.636345 | − | 0.771405i | \(-0.719554\pi\) | ||||
−0.636345 | + | 0.771405i | \(0.719554\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.4327i | − | 0.831036i | ||||||
\(392\) | 2.00000 | + | 2.00000i | 0.101015 | + | 0.101015i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.2891 | + | 8.65183i | 1.62670 | + | 0.435873i | ||||
\(395\) | 32.2089i | 1.62060i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.04640i | 0.203083i | 0.994831 | + | 0.101541i | \(0.0323774\pi\) | ||||
−0.994831 | + | 0.101541i | \(0.967623\pi\) | |||||||
\(398\) | 7.91355 | − | 29.5338i | 0.396670 | − | 1.48039i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.59086 | + | 16.6119i | 0.479543 | + | 0.830593i | ||||
\(401\) | − | 5.87339i | − | 0.293303i | −0.989188 | − | 0.146652i | \(-0.953150\pi\) | ||
0.989188 | − | 0.146652i | \(-0.0468496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.4620 | 2.46388 | ||||||||
\(404\) | −3.46410 | − | 2.00000i | −0.172345 | − | 0.0995037i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.73205 | − | 6.46410i | 0.0859602 | − | 0.320808i | ||||
\(407\) | 1.33414 | 0.0661309 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1101 | 1.24162 | 0.620808 | − | 0.783963i | \(-0.286805\pi\) | ||||
0.620808 | + | 0.783963i | \(0.286805\pi\) | |||||||
\(410\) | −8.57380 | + | 31.9979i | −0.423430 | + | 1.58026i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.0148 | − | 29.4705i | 0.838258 | − | 1.45191i | ||||
\(413\) | 2.47252 | 0.121665 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.1939i | 1.28581i | ||||||||
\(416\) | 35.7936 | − | 9.59086i | 1.75492 | − | 0.470230i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0767869 | + | 0.286573i | −0.00375577 | + | 0.0140167i | ||||
\(419\) | − | 12.3059i | − | 0.601184i | −0.953753 | − | 0.300592i | \(-0.902816\pi\) | ||
0.953753 | − | 0.300592i | \(-0.0971842\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4095i | 1.09217i | 0.837729 | + | 0.546086i | \(0.183883\pi\) | ||||
−0.837729 | + | 0.546086i | \(0.816117\pi\) | |||||||
\(422\) | −3.44110 | − | 0.922040i | −0.167510 | − | 0.0448842i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.59086 | − | 1.59086i | −0.0772588 | − | 0.0772588i | ||||
\(425\) | − | 9.59086i | − | 0.465225i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.4641 | −0.554787 | ||||||||
\(428\) | −1.91362 | + | 3.31449i | −0.0924983 | + | 0.160212i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.93662 | + | 1.85866i | 0.334514 | + | 0.0896327i | ||||
\(431\) | −21.4041 | −1.03100 | −0.515499 | − | 0.856890i | \(-0.672393\pi\) | ||||
−0.515499 | + | 0.856890i | \(0.672393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3925 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(434\) | 10.3144 | + | 2.76374i | 0.495108 | + | 0.132664i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.07816 | + | 12.2597i | −0.338982 | + | 0.587134i | ||||
\(437\) | −4.33395 | −0.207321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 18.3755i | − | 0.877013i | −0.898728 | − | 0.438507i | \(-0.855508\pi\) | ||
0.898728 | − | 0.438507i | \(-0.144492\pi\) | |||||||
\(440\) | −2.48950 | + | 2.48950i | −0.118682 | + | 0.118682i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.8968 | − | 4.79543i | −0.851263 | − | 0.228095i | ||||
\(443\) | 8.58770i | 0.408014i | 0.978969 | + | 0.204007i | \(0.0653965\pi\) | ||||
−0.978969 | + | 0.204007i | \(0.934603\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6226i | 0.787988i | ||||||||
\(446\) | 0.322836 | − | 1.20484i | 0.0152867 | − | 0.0570508i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | − | 7.78687i | − | 0.367485i | −0.982974 | − | 0.183742i | \(-0.941179\pi\) | ||
0.982974 | − | 0.183742i | \(-0.0588212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.97661 | −0.140163 | ||||||||
\(452\) | 9.98316 | − | 17.2913i | 0.469568 | − | 0.813316i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.10341 | − | 11.5821i | 0.145650 | − | 0.543575i | ||||
\(455\) | −20.5021 | −0.961152 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3205 | 0.482773 | 0.241387 | − | 0.970429i | \(-0.422398\pi\) | ||||
0.241387 | + | 0.970429i | \(0.422398\pi\) | |||||||
\(458\) | −4.92820 | + | 18.3923i | −0.230280 | + | 0.859416i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −44.5401 | − | 25.7152i | −2.07669 | − | 1.19898i | ||||
\(461\) | 22.2016 | 1.03403 | 0.517015 | − | 0.855976i | \(-0.327043\pi\) | ||||
0.517015 | + | 0.855976i | \(0.327043\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.9028i | 1.29675i | 0.761320 | + | 0.648377i | \(0.224552\pi\) | ||||
−0.761320 | + | 0.648377i | \(0.775448\pi\) | |||||||
\(464\) | −9.46410 | − | 16.3923i | −0.439360 | − | 0.760994i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.39230 | + | 23.8564i | −0.296118 | + | 1.10513i | ||||
\(467\) | − | 21.9602i | − | 1.01619i | −0.861300 | − | 0.508097i | \(-0.830349\pi\) | ||
0.861300 | − | 0.508097i | \(-0.169651\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.55068i | 0.302482i | ||||||||
\(470\) | −44.7016 | − | 11.9778i | −2.06193 | − | 0.552492i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.94504 | − | 4.94504i | 0.227614 | − | 0.227614i | ||||
\(473\) | 0.645280i | 0.0296700i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.52949 | −0.116061 | ||||||||
\(476\) | −3.46410 | − | 2.00000i | −0.158777 | − | 0.0916698i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −37.8166 | − | 10.1329i | −1.72969 | − | 0.463469i | ||||
\(479\) | 6.13278 | 0.280214 | 0.140107 | − | 0.990136i | \(-0.455255\pi\) | ||||
0.140107 | + | 0.990136i | \(0.455255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.9744 | 1.00195 | ||||||||
\(482\) | −29.9317 | − | 8.02019i | −1.36335 | − | 0.365310i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.7786 | + | 10.8418i | 0.853572 | + | 0.492810i | ||||
\(485\) | 59.7827 | 2.71459 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.7848i | − | 0.896535i | −0.893899 | − | 0.448268i | \(-0.852041\pi\) | ||
0.893899 | − | 0.448268i | \(-0.147959\pi\) | |||||||
\(488\) | −22.9282 | + | 22.9282i | −1.03791 | + | 1.03791i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.27534 | − | 1.14557i | −0.193140 | − | 0.0517517i | ||||
\(491\) | − | 28.3809i | − | 1.28081i | −0.768037 | − | 0.640405i | \(-0.778766\pi\) | ||
0.768037 | − | 0.640405i | \(-0.221234\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.46410i | 0.426242i | ||||||||
\(494\) | −1.26474 | + | 4.72009i | −0.0569035 | + | 0.212367i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.1563 | − | 15.1014i | 1.17445 | − | 0.678071i | ||||
\(497\) | 2.21634i | 0.0994164i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.7407 | 0.480818 | 0.240409 | − | 0.970672i | \(-0.422718\pi\) | ||||
0.240409 | + | 0.970672i | \(0.422718\pi\) | |||||||
\(500\) | 1.10897 | + | 0.640262i | 0.0495945 | + | 0.0286334i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.82479 | − | 21.7384i | 0.259973 | − | 0.970233i | ||||
\(503\) | −14.7321 | −0.656870 | −0.328435 | − | 0.944527i | \(-0.606521\pi\) | ||||
−0.328435 | + | 0.944527i | \(0.606521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.25953 | 0.278545 | ||||||||
\(506\) | 1.19608 | − | 4.46383i | 0.0531723 | − | 0.198442i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.75525 | + | 13.4325i | −0.344084 | + | 0.595970i | ||||
\(509\) | −23.2913 | −1.03237 | −0.516185 | − | 0.856477i | \(-0.672648\pi\) | ||||
−0.516185 | + | 0.856477i | \(0.672648\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.75525i | 0.254597i | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.35555 | − | 5.05900i | 0.0597909 | − | 0.223143i | ||||
\(515\) | 53.2523i | 2.34657i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.15837i | − | 0.182885i | ||||||
\(518\) | 4.58237 | + | 1.22784i | 0.201338 | + | 0.0539482i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −41.0042 | + | 41.0042i | −1.79815 | + | 1.79815i | ||||
\(521\) | 1.91027i | 0.0836905i | 0.999124 | + | 0.0418453i | \(0.0133237\pi\) | ||||
−0.999124 | + | 0.0418453i | \(0.986676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.5885 | 1.11891 | 0.559453 | − | 0.828862i | \(-0.311011\pi\) | ||||
0.559453 | + | 0.828862i | \(0.311011\pi\) | |||||||
\(524\) | −14.9052 | + | 25.8166i | −0.651137 | + | 1.12780i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.3251 | − | 8.12558i | −1.32224 | − | 0.354292i | ||||
\(527\) | −15.1014 | −0.657825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.5082 | 1.93514 | ||||||||
\(530\) | 3.40072 | + | 0.911221i | 0.147718 | + | 0.0395809i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.527479 | + | 0.913620i | −0.0228691 | + | 0.0396105i | ||||
\(533\) | −49.0272 | −2.12360 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.98918i | − | 0.258935i | ||||||
\(536\) | 13.1014 | + | 13.1014i | 0.565892 | + | 0.565892i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.1951 | + | 5.94717i | 0.956900 | + | 0.256400i | ||||
\(539\) | − | 0.397714i | − | 0.0171308i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.91959i | 0.340490i | 0.985402 | + | 0.170245i | \(0.0544559\pi\) | ||||
−0.985402 | + | 0.170245i | \(0.945544\pi\) | |||||||
\(542\) | 6.72589 | − | 25.1014i | 0.288902 | − | 1.07820i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.9282 | + | 2.92820i | −0.468543 | + | 0.125546i | ||||
\(545\) | − | 22.1530i | − | 0.948929i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.65409 | −0.327265 | −0.163633 | − | 0.986521i | \(-0.552321\pi\) | ||||
−0.163633 | + | 0.986521i | \(0.552321\pi\) | |||||||
\(548\) | 22.4557 | − | 38.8944i | 0.959259 | − | 1.66149i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.698087 | − | 2.60530i | 0.0297665 | − | 0.111090i | ||||
\(551\) | 2.49606 | 0.106336 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2911 | −0.437624 | ||||||||
\(554\) | −11.6310 | + | 43.4073i | −0.494152 | + | 1.84420i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.29134 | + | 3.05496i | 0.224403 | + | 0.129559i | ||||
\(557\) | −27.6373 | −1.17103 | −0.585514 | − | 0.810662i | \(-0.699107\pi\) | ||||
−0.585514 | + | 0.810662i | \(0.699107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6283i | 0.449529i | ||||||||
\(560\) | −10.8418 | + | 6.25953i | −0.458151 | + | 0.264513i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.78065 | + | 6.64548i | −0.0751122 | + | 0.280322i | ||||
\(563\) | − | 33.9198i | − | 1.42955i | −0.699355 | − | 0.714774i | \(-0.746529\pi\) | ||
0.699355 | − | 0.714774i | \(-0.253471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.2449i | 1.31448i | ||||||||
\(566\) | 33.7936 | + | 9.05496i | 1.42045 | + | 0.380608i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.43268 | + | 4.43268i | 0.185991 | + | 0.185991i | ||||
\(569\) | − | 18.7382i | − | 0.785547i | −0.919635 | − | 0.392773i | \(-0.871516\pi\) | ||
0.919635 | − | 0.392773i | \(-0.128484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2449 | 0.637981 | 0.318991 | − | 0.947758i | \(-0.396656\pi\) | ||||
0.318991 | + | 0.947758i | \(0.396656\pi\) | |||||||
\(572\) | −4.51251 | − | 2.60530i | −0.188677 | − | 0.108933i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.2237 | − | 2.73944i | −0.426730 | − | 0.114342i | ||||
\(575\) | 39.4009 | 1.64313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.49366 | 0.0621818 | 0.0310909 | − | 0.999517i | \(-0.490102\pi\) | ||||
0.0310909 | + | 0.999517i | \(0.490102\pi\) | |||||||
\(578\) | −17.7583 | − | 4.75833i | −0.738649 | − | 0.197920i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.6520 | + | 14.8102i | 1.06514 | + | 0.614960i | ||||
\(581\) | −8.36930 | −0.347217 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.316353i | 0.0131020i | ||||||||
\(584\) | 11.5105 | + | 11.5105i | 0.476308 | + | 0.476308i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.7783 | − | 5.83546i | −0.899651 | − | 0.241061i | ||||
\(587\) | 16.2195i | 0.669452i | 0.942315 | + | 0.334726i | \(0.108644\pi\) | ||||
−0.942315 | + | 0.334726i | \(0.891356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.98282i | 0.164109i | ||||||||
\(590\) | −2.83245 | + | 10.5709i | −0.116610 | + | 0.435196i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.6204 | − | 6.70905i | 0.477596 | − | 0.275740i | ||||
\(593\) | 21.3871i | 0.878263i | 0.898423 | + | 0.439131i | \(0.144714\pi\) | ||||
−0.898423 | + | 0.439131i | \(0.855286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.25953 | 0.256616 | ||||||||
\(596\) | 12.1496 | + | 7.01458i | 0.497668 | + | 0.287329i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.7004 | − | 73.5230i | 0.805611 | − | 3.00658i | ||||
\(599\) | 11.7672 | 0.480795 | 0.240398 | − | 0.970674i | \(-0.422722\pi\) | ||||
0.240398 | + | 0.970674i | \(0.422722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.7552 | −0.642670 | −0.321335 | − | 0.946966i | \(-0.604132\pi\) | ||||
−0.321335 | + | 0.946966i | \(0.604132\pi\) | |||||||
\(602\) | −0.593866 | + | 2.21634i | −0.0242042 | + | 0.0903313i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.81001 | − | 16.9914i | 0.399164 | − | 0.691372i | ||||
\(605\) | −33.9324 | −1.37955 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.95400i | 0.0793102i | 0.999213 | + | 0.0396551i | \(0.0126259\pi\) | ||||
−0.999213 | + | 0.0396551i | \(0.987374\pi\) | |||||||
\(608\) | 0.772283 | + | 2.88220i | 0.0313202 | + | 0.116889i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.1330 | − | 49.0129i | 0.531738 | − | 1.98447i | ||||
\(611\) | − | 68.4918i | − | 2.77088i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.47046i | − | 0.140171i | −0.997541 | − | 0.0700853i | \(-0.977673\pi\) | ||
0.997541 | − | 0.0700853i | \(-0.0223271\pi\) | |||||||
\(614\) | 7.71213 | + | 2.06646i | 0.311236 | + | 0.0833955i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.795428 | − | 0.795428i | −0.0320487 | − | 0.0320487i | ||||
\(617\) | 24.9456i | 1.00427i | 0.864789 | + | 0.502136i | \(0.167452\pi\) | ||||
−0.864789 | + | 0.502136i | \(0.832548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.3233 | −1.50015 | −0.750075 | − | 0.661353i | \(-0.769983\pi\) | ||||
−0.750075 | + | 0.661353i | \(0.769983\pi\) | |||||||
\(620\) | −23.6318 | + | 40.9316i | −0.949078 | + | 1.64385i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.9660 | − | 6.95756i | −1.04114 | − | 0.278973i | ||||
\(623\) | −5.31114 | −0.212786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.9810 | −1.03924 | ||||||||
\(626\) | −3.06639 | − | 0.821636i | −0.122557 | − | 0.0328392i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.8966 | − | 18.8734i | 0.434821 | − | 0.753132i | ||||
\(629\) | −6.70905 | −0.267507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.51886i | − | 0.378940i | −0.981887 | − | 0.189470i | \(-0.939323\pi\) | ||
0.981887 | − | 0.189470i | \(-0.0606770\pi\) | |||||||
\(632\) | −20.5823 | + | 20.5823i | −0.818720 | + | 0.818720i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.4475 | − | 8.96222i | −1.32837 | − | 0.355935i | ||||
\(635\) | − | 24.2721i | − | 0.963209i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.55068i | − | 0.259547i | ||||||
\(638\) | −0.688861 | + | 2.57086i | −0.0272723 | + | 0.101781i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.16459 | + | 34.2027i | −0.362262 | + | 1.35198i | ||||
\(641\) | − | 41.9263i | − | 1.65599i | −0.560735 | − | 0.827995i | \(-0.689481\pi\) | ||
0.560735 | − | 0.827995i | \(-0.310519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.79303 | 0.110146 | 0.0550732 | − | 0.998482i | \(-0.482461\pi\) | ||||
0.0550732 | + | 0.998482i | \(0.482461\pi\) | |||||||
\(644\) | 8.21634 | − | 14.2311i | 0.323769 | − | 0.560785i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.386141 | − | 1.44110i | 0.0151925 | − | 0.0566993i | ||||
\(647\) | −30.2089 | −1.18763 | −0.593817 | − | 0.804600i | \(-0.702380\pi\) | ||||
−0.593817 | + | 0.804600i | \(0.702380\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.983356 | −0.0386001 | ||||||||
\(650\) | 11.4981 | − | 42.9114i | 0.450991 | − | 1.68312i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.3461 | − | 10.0148i | −0.679326 | − | 0.392209i | ||||
\(653\) | −36.8020 | −1.44017 | −0.720086 | − | 0.693884i | \(-0.755898\pi\) | ||||
−0.720086 | + | 0.693884i | \(0.755898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 46.6498i | − | 1.82276i | ||||||
\(656\) | −25.9263 | + | 14.9686i | −1.01225 | + | 0.584425i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.82705 | − | 14.2827i | 0.149194 | − | 0.556799i | ||||
\(659\) | − | 27.5858i | − | 1.07459i | −0.843394 | − | 0.537296i | \(-0.819446\pi\) | ||
0.843394 | − | 0.537296i | \(-0.180554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 43.9007i | − | 1.70754i | −0.520650 | − | 0.853770i | \(-0.674310\pi\) | ||
0.520650 | − | 0.853770i | \(-0.325690\pi\) | |||||||
\(662\) | −5.93662 | − | 1.59071i | −0.230733 | − | 0.0618248i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.7386 | + | 16.7386i | −0.649584 | + | 0.649584i | ||||
\(665\) | − | 1.65089i | − | 0.0640186i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.8801 | −1.50544 | ||||||||
\(668\) | −25.2281 | − | 14.5655i | −0.976105 | − | 0.563554i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.0064 | − | 7.50428i | −1.08198 | − | 0.289916i | ||||
\(671\) | 4.55943 | 0.176015 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.78085 | −0.0686465 | −0.0343233 | − | 0.999411i | \(-0.510928\pi\) | ||||
−0.0343233 | + | 0.999411i | \(0.510928\pi\) | |||||||
\(674\) | 37.6551 | + | 10.0897i | 1.45042 | + | 0.388639i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −51.8080 | − | 29.9114i | −1.99262 | − | 1.15044i | ||||
\(677\) | 45.7356 | 1.75776 | 0.878881 | − | 0.477041i | \(-0.158291\pi\) | ||||
0.878881 | + | 0.477041i | \(0.158291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1014i | 0.733043i | ||||||||
\(680\) | 12.5191 | − | 12.5191i | 0.480084 | − | 0.480084i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.10219 | − | 1.09918i | −0.157081 | − | 0.0420897i | ||||
\(683\) | 23.5159i | 0.899811i | 0.893076 | + | 0.449906i | \(0.148542\pi\) | ||||
−0.893076 | + | 0.449906i | \(0.851458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 70.2810i | 2.68530i | ||||||||
\(686\) | 0.366025 | − | 1.36603i | 0.0139749 | − | 0.0521551i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.24495 | + | 5.62041i | 0.123712 | + | 0.214276i | ||||
\(689\) | 5.21059i | 0.198508i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.3501 | −1.19261 | −0.596306 | − | 0.802757i | \(-0.703366\pi\) | ||||
−0.596306 | + | 0.802757i | \(0.703366\pi\) | |||||||
\(692\) | −24.7986 | − | 14.3175i | −0.942703 | − | 0.544270i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.62666 | − | 28.4631i | 0.289504 | − | 1.08044i | ||||
\(695\) | −9.56130 | −0.362681 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.9686 | 0.566975 | ||||||||
\(698\) | 1.78687 | − | 6.66867i | 0.0676339 | − | 0.252413i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.79543 | − | 8.30593i | 0.181250 | − | 0.313934i | ||||
\(701\) | −1.40072 | −0.0529046 | −0.0264523 | − | 0.999650i | \(-0.508421\pi\) | ||||
−0.0264523 | + | 0.999650i | \(0.508421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.76944i | 0.0667357i | ||||||||
\(704\) | −3.18171 | −0.119915 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.72466 | + | 10.1686i | −0.102544 | + | 0.382699i | ||||
\(707\) | 2.00000i | 0.0752177i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.4709i | 1.48236i | 0.671307 | + | 0.741179i | \(0.265733\pi\) | ||||
−0.671307 | + | 0.741179i | \(0.734267\pi\) | |||||||
\(710\) | −9.47560 | − | 2.53898i | −0.355613 | − | 0.0952862i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.6223 | + | 10.6223i | −0.398087 | + | 0.398087i | ||||
\(713\) | − | 62.0389i | − | 2.32338i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.15396 | 0.304941 | ||||||||
\(716\) | 19.8104 | − | 34.3126i | 0.740349 | − | 1.28232i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.5885 | − | 8.19615i | −1.14155 | − | 0.305878i | ||||
\(719\) | −12.0694 | −0.450113 | −0.225056 | − | 0.974346i | \(-0.572257\pi\) | ||||
−0.225056 | + | 0.974346i | \(0.572257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0148 | −0.633663 | ||||||||
\(722\) | 25.5744 | + | 6.85264i | 0.951781 | + | 0.255029i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.1732 | − | 34.9409i | 0.749729 | − | 1.29857i | ||||
\(725\) | −22.6922 | −0.842768 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.39230i | − | 0.0887257i | −0.999015 | − | 0.0443628i | \(-0.985874\pi\) | ||
0.999015 | − | 0.0443628i | \(-0.0141258\pi\) | |||||||
\(728\) | −13.1014 | − | 13.1014i | −0.485568 | − | 0.485568i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.6056 | − | 6.59306i | −0.910695 | − | 0.244020i | ||||
\(731\) | − | 3.24495i | − | 0.120019i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.5802i | − | 0.538533i | −0.963066 | − | 0.269267i | \(-0.913219\pi\) | ||
0.963066 | − | 0.269267i | \(-0.0867813\pi\) | |||||||
\(734\) | 12.9051 | − | 48.1626i | 0.476337 | − | 1.77771i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.0296 | − | 44.8949i | −0.443415 | − | 1.65485i | ||||
\(737\) | − | 2.60530i | − | 0.0959673i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3459 | 1.11629 | 0.558146 | − | 0.829743i | \(-0.311513\pi\) | ||||
0.558146 | + | 0.829743i | \(0.311513\pi\) | |||||||
\(740\) | −10.4989 | + | 18.1846i | −0.385946 | + | 0.668478i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.291147 | + | 1.08658i | −0.0106883 | + | 0.0398894i | ||||
\(743\) | 16.6659 | 0.611411 | 0.305706 | − | 0.952126i | \(-0.401108\pi\) | ||||
0.305706 | + | 0.952126i | \(0.401108\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.9540 | −0.804332 | ||||||||
\(746\) | 4.12443 | − | 15.3926i | 0.151006 | − | 0.563562i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.37772 | + | 0.795428i | 0.0503745 | + | 0.0290837i | ||||
\(749\) | 1.91362 | 0.0699222 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.10155i | − | 0.0766866i | −0.999265 | − | 0.0383433i | \(-0.987792\pi\) | ||
0.999265 | − | 0.0383433i | \(-0.0122080\pi\) | |||||||
\(752\) | −20.9114 | − | 36.2195i | −0.762559 | − | 1.32079i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.3461 | + | 42.3442i | −0.413201 | + | 1.54209i | ||||
\(755\) | 30.7030i | 1.11740i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.2408i | 1.42623i | 0.701046 | + | 0.713116i | \(0.252717\pi\) | ||||
−0.701046 | + | 0.713116i | \(0.747283\pi\) | |||||||
\(758\) | 7.48429 | + | 2.00541i | 0.271842 | + | 0.0728397i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.30177 | − | 3.30177i | −0.119768 | − | 0.119768i | ||||
\(761\) | 22.7618i | 0.825113i | 0.910932 | + | 0.412556i | \(0.135364\pi\) | ||||
−0.910932 | + | 0.412556i | \(0.864636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.07816 | 0.256246 | ||||||||
\(764\) | 11.1466 | + | 6.43549i | 0.403270 | + | 0.232828i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.2577 | + | 11.5909i | 1.56296 | + | 0.418795i | ||||
\(767\) | −16.1967 | −0.584828 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.9030 | −1.90773 | −0.953865 | − | 0.300234i | \(-0.902935\pi\) | ||||
−0.953865 | + | 0.300234i | \(0.902935\pi\) | |||||||
\(770\) | 1.70036 | + | 0.455611i | 0.0612768 | + | 0.0164191i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.2913 | − | 9.98316i | −0.622329 | − | 0.359302i | ||||
\(773\) | −6.27110 | −0.225556 | −0.112778 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112778 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 36.2087i | − | 1.30066i | ||||||
\(776\) | 38.2027 | + | 38.2027i | 1.37140 | + | 1.37140i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.2891 | + | 9.18773i | 1.22932 | + | 0.329396i | ||||
\(779\) | − | 3.94780i | − | 0.141445i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.881470i | − | 0.0315415i | ||||||
\(782\) | −6.01478 | + | 22.4475i | −0.215088 | + | 0.802719i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.00000 | − | 3.46410i | −0.0714286 | − | 0.123718i | ||||
\(785\) | 34.1038i | 1.21722i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5651 | −0.733065 | −0.366533 | − | 0.930405i | \(-0.619455\pi\) | ||||
−0.366533 | + | 0.930405i | \(0.619455\pi\) | |||||||
\(788\) | −40.9409 | − | 23.6373i | −1.45846 | − | 0.842042i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.7893 | − | 43.9981i | 0.419443 | − | 1.56538i | ||||
\(791\) | −9.98316 | −0.354960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 75.0976 | 2.66679 | ||||||||
\(794\) | 1.48108 | − | 5.52748i | 0.0525617 | − | 0.196163i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.6202 | + | 37.4473i | −0.766308 | + | 1.32728i | ||||
\(797\) | 16.6802 | 0.590845 | 0.295422 | − | 0.955367i | \(-0.404540\pi\) | ||||
0.295422 | + | 0.955367i | \(0.404540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9114i | 0.739791i | ||||||||
\(800\) | −7.02099 | − | 26.2027i | −0.248230 | − | 0.926406i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.14981 | + | 8.02320i | −0.0759124 | + | 0.283309i | ||||
\(803\) | − | 2.28894i | − | 0.0807751i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.7152i | 0.906342i | ||||||||
\(806\) | −67.5664 | − | 18.1044i | −2.37993 | − | 0.637699i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.00000 | + | 4.00000i | 0.140720 | + | 0.140720i | ||||
\(809\) | 54.5485i | 1.91782i | 0.283707 | + | 0.958911i | \(0.408436\pi\) | ||||
−0.283707 | + | 0.958911i | \(0.591564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.77845 | −0.343368 | −0.171684 | − | 0.985152i | \(-0.554921\pi\) | ||||
−0.171684 | + | 0.985152i | \(0.554921\pi\) | |||||||
\(812\) | −4.73205 | + | 8.19615i | −0.166062 | + | 0.287629i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.82247 | − | 0.488330i | −0.0638776 | − | 0.0171159i | ||||
\(815\) | 31.3439 | 1.09793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.855821 | −0.0299414 | ||||||||
\(818\) | −34.3010 | − | 9.19094i | −1.19931 | − | 0.321354i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.4241 | − | 40.5717i | 0.818004 | − | 1.41682i | ||||
\(821\) | −28.5488 | −0.996359 | −0.498179 | − | 0.867074i | \(-0.665998\pi\) | ||||
−0.498179 | + | 0.867074i | \(0.665998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.5912i | 1.17092i | 0.810702 | + | 0.585459i | \(0.199086\pi\) | ||||
−0.810702 | + | 0.585459i | \(0.800914\pi\) | |||||||
\(824\) | −34.0296 | + | 34.0296i | −1.18548 | + | 1.18548i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.37753 | − | 0.905006i | −0.117519 | − | 0.0314892i | ||||
\(827\) | − | 25.9650i | − | 0.902893i | −0.892298 | − | 0.451446i | \(-0.850908\pi\) | ||
0.892298 | − | 0.451446i | \(-0.149092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.7613i | 0.825263i | 0.910898 | + | 0.412631i | \(0.135390\pi\) | ||||
−0.910898 | + | 0.412631i | \(0.864610\pi\) | |||||||
\(830\) | 9.58765 | − | 35.7816i | 0.332792 | − | 1.24200i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −52.4054 | −1.81683 | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.5864 | 1.57758 | ||||||||
\(836\) | 0.209786 | − | 0.363360i | 0.00725559 | − | 0.0125671i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.50428 | + | 16.8102i | −0.155598 | + | 0.580699i | ||||
\(839\) | −2.77243 | −0.0957148 | −0.0478574 | − | 0.998854i | \(-0.515239\pi\) | ||||
−0.0478574 | + | 0.998854i | \(0.515239\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.60770 | −0.227852 | ||||||||
\(842\) | 8.20244 | − | 30.6119i | 0.282675 | − | 1.05496i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.36314 | + | 2.51906i | 0.150185 | + | 0.0867096i | ||||
\(845\) | 93.6155 | 3.22047 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.8418i | − | 0.372529i | ||||||
\(848\) | 1.59086 | + | 2.75544i | 0.0546302 | + | 0.0946223i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.51050 | + | 13.1014i | −0.120409 | + | 0.449373i | ||||
\(851\) | − | 27.5619i | − | 0.944810i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.236670i | − | 0.00810344i | −0.999992 | − | 0.00405172i | \(-0.998710\pi\) | ||
0.999992 | − | 0.00405172i | \(-0.00128971\pi\) | |||||||
\(854\) | 15.6603 | + | 4.19615i | 0.535883 | + | 0.143589i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.82724 | − | 3.82724i | 0.130812 | − | 0.130812i | ||||
\(857\) | − | 21.2139i | − | 0.724654i | −0.932051 | − | 0.362327i | \(-0.881982\pi\) | ||
0.932051 | − | 0.362327i | \(-0.118018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6199 | 0.430585 | 0.215292 | − | 0.976550i | \(-0.430930\pi\) | ||||
0.215292 | + | 0.976550i | \(0.430930\pi\) | |||||||
\(860\) | −8.79529 | − | 5.07796i | −0.299917 | − | 0.173157i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.2385 | + | 7.83443i | 0.995868 | + | 0.266842i | ||||
\(863\) | −25.8396 | −0.879589 | −0.439795 | − | 0.898098i | \(-0.644949\pi\) | ||||
−0.439795 | + | 0.898098i | \(0.644949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.8104 | 1.52360 | ||||||||
\(866\) | −26.4906 | − | 7.09815i | −0.900189 | − | 0.241205i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.0782 | − | 7.55068i | −0.443902 | − | 0.256287i | ||||
\(869\) | 4.09293 | 0.138843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 42.9114i | − | 1.45400i | ||||||
\(872\) | 14.1563 | − | 14.1563i | 0.479393 | − | 0.479393i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.92028 | + | 1.58633i | 0.200256 | + | 0.0536586i | ||||
\(875\) | − | 0.640262i | − | 0.0216448i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 55.0972i | − | 1.86050i | −0.366925 | − | 0.930251i | \(-0.619589\pi\) | ||
0.366925 | − | 0.930251i | \(-0.380411\pi\) | |||||||
\(878\) | −6.72589 | + | 25.1014i | −0.226988 | + | 0.847130i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.31195 | − | 2.48950i | 0.145356 | − | 0.0839211i | ||||
\(881\) | 33.7034i | 1.13550i | 0.823202 | + | 0.567749i | \(0.192186\pi\) | ||||
−0.823202 | + | 0.567749i | \(0.807814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8396 | 0.667655 | 0.333827 | − | 0.942634i | \(-0.391660\pi\) | ||||
0.333827 | + | 0.942634i | \(0.391660\pi\) | |||||||
\(884\) | 22.6922 | + | 13.1014i | 0.763222 | + | 0.440646i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.14332 | − | 11.7310i | 0.105602 | − | 0.394111i | ||||
\(887\) | −17.5967 | −0.590840 | −0.295420 | − | 0.955367i | \(-0.595460\pi\) | ||||
−0.295420 | + | 0.955367i | \(0.595460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.75525 | 0.260103 | ||||||||
\(890\) | 6.08430 | − | 22.7069i | 0.203946 | − | 0.761138i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.882003 | + | 1.52767i | −0.0295316 | + | 0.0511503i | ||||
\(893\) | 5.51515 | 0.184558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.0019i | 2.07249i | ||||||||
\(896\) | −10.9282 | − | 2.92820i | −0.365086 | − | 0.0978244i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.85019 | + | 10.6371i | −0.0951121 | + | 0.354963i | ||||
\(899\) | 35.7302i | 1.19167i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.59086i | − | 0.0529991i | ||||||
\(902\) | 4.06612 | + | 1.08951i | 0.135387 | + | 0.0362768i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.9663 | + | 19.9663i | −0.664070 | + | 0.664070i | ||||
\(905\) | 63.1372i | 2.09875i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8190 | −0.359238 | −0.179619 | − | 0.983736i | \(-0.557486\pi\) | ||||
−0.179619 | + | 0.983736i | \(0.557486\pi\) | |||||||
\(908\) | −8.47868 | + | 14.6855i | −0.281375 | + | 0.487356i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28.0064 | + | 7.50428i | 0.928402 | + | 0.248765i | ||||
\(911\) | 33.4364 | 1.10780 | 0.553899 | − | 0.832584i | \(-0.313139\pi\) | ||||
0.553899 | + | 0.832584i | \(0.313139\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.32859 | 0.110160 | ||||||||
\(914\) | −14.0981 | − | 3.77757i | −0.466323 | − | 0.124951i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.4641 | − | 23.3205i | 0.444866 | − | 0.770531i | ||||
\(917\) | 14.9052 | 0.492213 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.70049i | 0.122068i | 0.998136 | + | 0.0610339i | \(0.0194398\pi\) | ||||
−0.998136 | + | 0.0610339i | \(0.980560\pi\) | |||||||
\(920\) | 51.4304 | + | 51.4304i | 1.69561 | + | 1.69561i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.3279 | − | 8.12634i | −0.998796 | − | 0.267627i | ||||
\(923\) | − | 14.5185i | − | 0.477883i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 16.0864i | − | 0.528917i | ||||||
\(926\) | 10.2131 | − | 38.1159i | 0.335624 | − | 1.25257i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.92820 | + | 25.8564i | 0.227429 | + | 0.848778i | ||||
\(929\) | − | 17.0318i | − | 0.558796i | −0.960175 | − | 0.279398i | \(-0.909865\pi\) | ||
0.960175 | − | 0.279398i | \(-0.0901348\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.527479 | 0.0172874 | ||||||||
\(932\) | 17.4641 | − | 30.2487i | 0.572056 | − | 0.990829i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.03798 | + | 29.9981i | −0.263011 | + | 0.981569i | ||||
\(935\) | −2.48950 | −0.0814155 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.6077 | −0.379207 | −0.189603 | − | 0.981861i | \(-0.560720\pi\) | ||||
−0.189603 | + | 0.981861i | \(0.560720\pi\) | |||||||
\(938\) | 2.39771 | − | 8.94839i | 0.0782881 | − | 0.292175i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 56.6793 | + | 32.7238i | 1.84868 | + | 1.06733i | ||||
\(941\) | −50.5834 | −1.64897 | −0.824486 | − | 0.565882i | \(-0.808536\pi\) | ||||
−0.824486 | + | 0.565882i | \(0.808536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.4935i | 2.00250i | ||||||||
\(944\) | −8.56506 | + | 4.94504i | −0.278769 | + | 0.160947i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.236189 | − | 0.881470i | 0.00767917 | − | 0.0286590i | ||||
\(947\) | 42.8764i | 1.39330i | 0.717413 | + | 0.696648i | \(0.245326\pi\) | ||||
−0.717413 | + | 0.696648i | \(0.754674\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 37.7008i | − | 1.22382i | ||||||
\(950\) | 3.45534 | + | 0.925857i | 0.112106 | + | 0.0300388i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.00000 | + | 4.00000i | 0.129641 | + | 0.129641i | ||||
\(953\) | − | 11.4074i | − | 0.369523i | −0.982783 | − | 0.184761i | \(-0.940849\pi\) | ||
0.982783 | − | 0.184761i | \(-0.0591512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.1416 | −0.651766 | ||||||||
\(956\) | 47.9495 | + | 27.6836i | 1.55080 | + | 0.895353i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.37753 | − | 2.24475i | −0.270666 | − | 0.0725246i | ||||
\(959\) | −22.4557 | −0.725132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.0127 | −0.839120 | ||||||||
\(962\) | −30.0176 | − | 8.04319i | −0.967806 | − | 0.259323i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37.9519 | + | 21.9116i | 1.22235 | + | 0.705724i | ||||
\(965\) | 31.2449 | 1.00581 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.7090i | − | 0.794589i | −0.917691 | − | 0.397295i | \(-0.869949\pi\) | ||
0.917691 | − | 0.397295i | \(-0.130051\pi\) | |||||||
\(968\) | −21.6836 | − | 21.6836i | −0.696939 | − | 0.696939i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −81.6647 | − | 21.8820i | −2.62210 | − | 0.702589i | ||||
\(971\) | − | 28.3585i | − | 0.910067i | −0.890474 | − | 0.455034i | \(-0.849627\pi\) | ||
0.890474 | − | 0.455034i | \(-0.150373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3.05496i | − | 0.0979375i | ||||||
\(974\) | −7.24174 | + | 27.0265i | −0.232040 | + | 0.865986i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.7128 | − | 22.9282i | 1.27118 | − | 0.733914i | ||||
\(977\) | − | 23.4704i | − | 0.750885i | −0.926846 | − | 0.375442i | \(-0.877491\pi\) | ||
0.926846 | − | 0.375442i | \(-0.122509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.11231 | 0.0675099 | ||||||||
\(980\) | 5.42091 | + | 3.12976i | 0.173165 | + | 0.0999767i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.3881 | + | 38.7690i | −0.331498 | + | 1.23717i | ||||
\(983\) | −26.2425 | −0.837007 | −0.418504 | − | 0.908215i | \(-0.637445\pi\) | ||||
−0.418504 | + | 0.908215i | \(0.637445\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 73.9790 | 2.35717 | ||||||||
\(986\) | 3.46410 | − | 12.9282i | 0.110319 | − | 0.411718i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.45534 | − | 5.98483i | 0.109929 | − | 0.190403i | ||||
\(989\) | 13.3308 | 0.423895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.2579i | 1.40590i | 0.711241 | + | 0.702949i | \(0.248134\pi\) | ||||
−0.711241 | + | 0.702949i | \(0.751866\pi\) | |||||||
\(992\) | −41.2577 | + | 11.0550i | −1.30993 | + | 0.350995i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.811237 | − | 3.02758i | 0.0257309 | − | 0.0960289i | ||||
\(995\) | − | 67.6662i | − | 2.14516i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 28.1271i | − | 0.890796i | −0.895333 | − | 0.445398i | \(-0.853062\pi\) | ||
0.895333 | − | 0.445398i | \(-0.146938\pi\) | |||||||
\(998\) | −14.6720 | − | 3.93136i | −0.464435 | − | 0.124445i | ||||
\(999\) | 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 | 1512.2.j.a.323.1 | ✓ | 8 | |
3.2 | odd | 2 | 1512.2.j.b.323.8 | yes | 8 | ||
4.3 | odd | 2 | 6048.2.j.a.5615.4 | 8 | |||
8.3 | odd | 2 | 1512.2.j.b.323.6 | yes | 8 | ||
8.5 | even | 2 | 6048.2.j.b.5615.5 | 8 | |||
12.11 | even | 2 | 6048.2.j.b.5615.6 | 8 | |||
24.5 | odd | 2 | 6048.2.j.a.5615.3 | 8 | |||
24.11 | even | 2 | inner | 1512.2.j.a.323.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.a.323.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1512.2.j.a.323.3 | yes | 8 | 24.11 | even | 2 | inner | |
1512.2.j.b.323.6 | yes | 8 | 8.3 | odd | 2 | ||
1512.2.j.b.323.8 | yes | 8 | 3.2 | odd | 2 | ||
6048.2.j.a.5615.3 | 8 | 24.5 | odd | 2 | |||
6048.2.j.a.5615.4 | 8 | 4.3 | odd | 2 | |||
6048.2.j.b.5615.5 | 8 | 8.5 | even | 2 | |||
6048.2.j.b.5615.6 | 8 | 12.11 | even | 2 |