Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(95,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.o (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 287.5 | ||
Character | \(\chi\) | \(=\) | 768.287 |
Dual form | 768.2.o.b.479.5 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.684042 | − | 1.59125i | −0.394932 | − | 0.918710i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.296199 | − | 0.715088i | 0.132464 | − | 0.319797i | −0.843705 | − | 0.536807i | \(-0.819630\pi\) |
0.976169 | + | 0.217010i | \(0.0696303\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.77714 | − | 2.77714i | 1.04966 | − | 1.04966i | 0.0509588 | − | 0.998701i | \(-0.483772\pi\) |
0.998701 | − | 0.0509588i | \(-0.0162277\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.06417 | + | 2.17697i | −0.688057 | + | 0.725656i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.829014 | − | 2.00142i | 0.249957 | − | 0.603450i | −0.748243 | − | 0.663425i | \(-0.769102\pi\) |
0.998200 | + | 0.0599753i | \(0.0191022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.73669 | − | 1.54779i | 1.03637 | − | 0.429279i | 0.201363 | − | 0.979517i | \(-0.435463\pi\) |
0.835008 | + | 0.550237i | \(0.185463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.34050 | + | 0.0178227i | −0.346115 | + | 0.00460179i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.19928 | −1.26101 | −0.630506 | − | 0.776185i | \(-0.717152\pi\) | ||||
−0.630506 | + | 0.776185i | \(0.717152\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.814726 | + | 1.96692i | 0.186911 | + | 0.451243i | 0.989362 | − | 0.145475i | \(-0.0464711\pi\) |
−0.802451 | + | 0.596718i | \(0.796471\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.31881 | − | 2.51945i | −1.37888 | − | 0.549789i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.13184 | − | 4.13184i | 0.861549 | − | 0.861549i | −0.129969 | − | 0.991518i | \(-0.541488\pi\) |
0.991518 | + | 0.129969i | \(0.0414878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.11192 | + | 3.11192i | 0.622383 | + | 0.622383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.87609 | + | 1.79548i | 0.938404 | + | 0.345541i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.45738 | + | 1.43209i | −0.642019 | + | 0.265933i | −0.679850 | − | 0.733351i | \(-0.737955\pi\) |
0.0378308 | + | 0.999284i | \(0.487955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.343074i | − | 0.0616180i | −0.999525 | − | 0.0308090i | \(-0.990192\pi\) | ||
0.999525 | − | 0.0308090i | \(-0.00980836\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.75184 | + | 0.0498828i | −0.653112 | + | 0.00868348i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.16331 | − | 2.80849i | −0.196636 | − | 0.474721i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.31781 | − | 1.78850i | −0.709844 | − | 0.294027i | −0.00160386 | − | 0.999999i | \(-0.500511\pi\) |
−0.708240 | + | 0.705972i | \(0.750511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.01898 | − | 4.88727i | −0.803680 | − | 0.782589i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.37894 | − | 3.37894i | −0.527702 | − | 0.527702i | 0.392184 | − | 0.919887i | \(-0.371720\pi\) |
−0.919887 | + | 0.392184i | \(0.871720\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.15044 | − | 3.79024i | −1.39543 | − | 0.578005i | −0.446868 | − | 0.894600i | \(-0.647461\pi\) |
−0.948561 | + | 0.316595i | \(0.897461\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.945319 | + | 2.12088i | 0.140920 | + | 0.316162i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.84842i | − | 0.707215i | −0.935394 | − | 0.353608i | \(-0.884955\pi\) | ||
0.935394 | − | 0.353608i | \(-0.115045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 8.42499i | − | 1.20357i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.55653 | + | 8.27337i | 0.498014 | + | 1.15850i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.15435 | + | 1.72079i | 0.570644 | + | 0.236369i | 0.649299 | − | 0.760533i | \(-0.275062\pi\) |
−0.0786546 | + | 0.996902i | \(0.525062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18564 | − | 1.18564i | −0.159871 | − | 0.159871i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.57256 | − | 2.64189i | 0.340744 | − | 0.349927i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.08629 | − | 3.34945i | −1.05275 | − | 0.436062i | −0.211875 | − | 0.977297i | \(-0.567957\pi\) |
−0.840871 | + | 0.541235i | \(0.817957\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.47236 | + | 5.96880i | 0.316553 | + | 0.764227i | 0.999432 | + | 0.0336954i | \(0.0107276\pi\) |
−0.682879 | + | 0.730531i | \(0.739272\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.313252 | + | 11.7782i | 0.0394660 | + | 1.48392i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.13052i | − | 0.388293i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.45025 | − | 2.25757i | 0.665854 | − | 0.275806i | −0.0240453 | − | 0.999711i | \(-0.507655\pi\) |
0.689900 | + | 0.723905i | \(0.257655\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.40117 | − | 3.74845i | −1.13177 | − | 0.451261i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.23395 | + | 6.23395i | 0.739834 | + | 0.739834i | 0.972546 | − | 0.232712i | \(-0.0747598\pi\) |
−0.232712 | + | 0.972546i | \(0.574760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.44956 | + | 1.44956i | −0.169658 | + | 0.169658i | −0.786829 | − | 0.617171i | \(-0.788279\pi\) |
0.617171 | + | 0.786829i | \(0.288279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.82316 | − | 7.08053i | 0.325991 | − | 0.817589i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.25592 | − | 7.86050i | −0.371047 | − | 0.895787i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.2460 | −1.49029 | −0.745144 | − | 0.666904i | \(-0.767619\pi\) | ||||
−0.745144 | + | 0.666904i | \(0.767619\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.478386 | − | 8.98728i | −0.0531540 | − | 0.998586i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.19358 | − | 2.56547i | 0.679834 | − | 0.281596i | −0.0159235 | − | 0.999873i | \(-0.505069\pi\) |
0.695758 | + | 0.718277i | \(0.255069\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.54002 | + | 3.71795i | −0.167039 | + | 0.403268i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.64382 | + | 4.52195i | 0.497870 | + | 0.484804i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.26892 | + | 9.26892i | −0.982503 | + | 0.982503i | −0.999850 | − | 0.0173462i | \(-0.994478\pi\) |
0.0173462 | + | 0.999850i | \(0.494478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.07889 | − | 14.6757i | 0.637240 | − | 1.53843i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.545918 | + | 0.234677i | −0.0566091 | + | 0.0243349i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.64784 | 0.169065 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.56950 | 0.971635 | 0.485818 | − | 0.874060i | \(-0.338522\pi\) | ||||
0.485818 | + | 0.874060i | \(0.338522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.64579 | + | 5.93600i | 0.265912 | + | 0.596591i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.02241 | + | 2.46831i | −0.101733 | + | 0.245606i | −0.966548 | − | 0.256485i | \(-0.917436\pi\) |
0.864815 | + | 0.502091i | \(0.167436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.61434 | − | 7.61434i | 0.750263 | − | 0.750263i | −0.224265 | − | 0.974528i | \(-0.571998\pi\) |
0.974528 | + | 0.224265i | \(0.0719982\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.67326 | + | 3.77225i | −0.358473 | + | 0.368134i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.84555 | + | 11.6982i | −0.468437 | + | 1.13091i | 0.496409 | + | 0.868089i | \(0.334652\pi\) |
−0.964846 | + | 0.262817i | \(0.915348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7600 | − | 5.69956i | 1.31796 | − | 0.545919i | 0.390766 | − | 0.920490i | \(-0.372210\pi\) |
0.927198 | + | 0.374571i | \(0.122210\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.107616 | + | 8.09414i | 0.0102145 | + | 0.768262i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.8596 | 1.49195 | 0.745974 | − | 0.665975i | \(-0.231984\pi\) | ||||
0.745974 | + | 0.665975i | \(0.231984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.73078 | − | 4.17848i | −0.161396 | − | 0.389645i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.34369 | + | 11.3296i | −0.401574 | + | 1.04742i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.4391 | + | 14.4391i | −1.32363 | + | 1.32363i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.45977 | + | 4.45977i | 0.405434 | + | 0.405434i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.06541 | + | 7.68809i | −0.276399 | + | 0.693212i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.72248 | − | 2.78454i | 0.601277 | − | 0.249057i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.27121i | 0.201537i | 0.994910 | + | 0.100769i | \(0.0321301\pi\) | ||||
−0.994910 | + | 0.100769i | \(0.967870\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.228063 | + | 17.1533i | 0.0200798 | + | 1.51027i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.57445 | + | 6.21528i | 0.224931 | + | 0.543032i | 0.995547 | − | 0.0942683i | \(-0.0300512\pi\) |
−0.770616 | + | 0.637300i | \(0.780051\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.72502 | + | 3.19981i | 0.669844 | + | 0.277459i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.72822 | − | 2.95501i | 0.234808 | − | 0.254327i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.23933 | + | 8.23933i | 0.703934 | + | 0.703934i | 0.965252 | − | 0.261319i | \(-0.0841574\pi\) |
−0.261319 | + | 0.965252i | \(0.584157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.47443 | + | 1.85337i | 0.379516 | + | 0.157201i | 0.564283 | − | 0.825582i | \(-0.309153\pi\) |
−0.184766 | + | 0.982782i | \(0.559153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.71507 | + | 3.31653i | −0.649726 | + | 0.279302i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.76181i | − | 0.732700i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.89652i | 0.240543i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.4063 | + | 5.76305i | −1.10573 | + | 0.475328i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.7806 | + | 6.12233i | 1.21087 | + | 0.501561i | 0.894497 | − | 0.447073i | \(-0.147534\pi\) |
0.316377 | + | 0.948634i | \(0.397534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.48300 | − | 6.48300i | −0.527579 | − | 0.527579i | 0.392271 | − | 0.919850i | \(-0.371690\pi\) |
−0.919850 | + | 0.392271i | \(0.871690\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.7322 | − | 11.3187i | 0.867648 | − | 0.915061i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.245328 | − | 0.101618i | −0.0197053 | − | 0.00816218i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.376399 | − | 0.908707i | −0.0300399 | − | 0.0725227i | 0.908148 | − | 0.418650i | \(-0.137497\pi\) |
−0.938188 | + | 0.346127i | \(0.887497\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.103542 | − | 7.78772i | −0.00821142 | − | 0.617606i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 22.9494i | − | 1.80867i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.44038 | − | 0.596624i | 0.112819 | − | 0.0467312i | −0.325560 | − | 0.945521i | \(-0.605553\pi\) |
0.438379 | + | 0.898790i | \(0.355553\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.07562 | + | 2.69767i | −0.0837370 | + | 0.210013i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.06006 | + | 3.06006i | 0.236795 | + | 0.236795i | 0.815522 | − | 0.578727i | \(-0.196450\pi\) |
−0.578727 | + | 0.815522i | \(0.696450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.37482 | − | 2.37482i | 0.182679 | − | 0.182679i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.96366 | − | 2.28643i | −0.456053 | − | 0.174848i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.07676 | + | 9.84216i | 0.309950 | + | 0.748286i | 0.999706 | + | 0.0242438i | \(0.00771779\pi\) |
−0.689756 | + | 0.724042i | \(0.742282\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.2844 | 1.30658 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.201541 | + | 15.1585i | 0.0151487 | + | 1.13938i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.90033 | − | 2.02978i | 0.366268 | − | 0.151713i | −0.191956 | − | 0.981404i | \(-0.561483\pi\) |
0.558224 | + | 0.829690i | \(0.311483\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.21135 | − | 17.4097i | 0.536016 | − | 1.29406i | −0.391468 | − | 0.920192i | \(-0.628033\pi\) |
0.927483 | − | 0.373864i | \(-0.121967\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.80668 | − | 8.01706i | 0.577086 | − | 0.592638i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.55787 | + | 2.55787i | −0.188058 | + | 0.188058i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.31028 | + | 10.4059i | −0.315199 | + | 0.760957i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.5279 | − | 8.55527i | 1.34770 | − | 0.622305i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.45750 | −0.394891 | −0.197446 | − | 0.980314i | \(-0.563265\pi\) | ||||
−0.197446 | + | 0.980314i | \(0.563265\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5440 | −0.758971 | −0.379486 | − | 0.925198i | \(-0.623899\pi\) | ||||
−0.379486 | + | 0.925198i | \(0.623899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.98145 | + | 2.14141i | −0.356729 | + | 0.153349i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0524216 | − | 0.126557i | 0.00373489 | − | 0.00901681i | −0.922001 | − | 0.387187i | \(-0.873447\pi\) |
0.925736 | + | 0.378170i | \(0.123447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.64709 | + | 6.64709i | −0.471200 | + | 0.471200i | −0.902303 | − | 0.431103i | \(-0.858125\pi\) |
0.431103 | + | 0.902303i | \(0.358125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.32057 | − | 7.12846i | −0.516353 | − | 0.502803i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.62450 | + | 13.5787i | −0.394763 | + | 0.953041i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.41708 | + | 1.41540i | −0.238659 | + | 0.0988560i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.466058 | + | 17.5237i | 0.0323932 | + | 1.21798i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.61205 | 0.319022 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.88401 | + | 6.96261i | 0.198543 | + | 0.479326i | 0.991524 | − | 0.129920i | \(-0.0414722\pi\) |
−0.792981 | + | 0.609246i | \(0.791472\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.65551 | − | 14.1841i | 0.387509 | − | 0.971878i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.42071 | + | 5.42071i | −0.369689 | + | 0.369689i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.952765 | − | 0.952765i | −0.0646779 | − | 0.0646779i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.29817 | + | 1.31505i | 0.222870 | + | 0.0888632i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.4281 | + | 8.04739i | −1.30688 | + | 0.541326i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.6352i | − | 1.11398i | −0.830520 | − | 0.556988i | \(-0.811957\pi\) | ||
0.830520 | − | 0.556988i | \(-0.188043\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.1981 | + | 0.351013i | −0.879872 | + | 0.0234009i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.09433 | + | 2.64195i | 0.0726335 | + | 0.175353i | 0.956027 | − | 0.293280i | \(-0.0947468\pi\) |
−0.883393 | + | 0.468633i | \(0.844747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.48780 | + | 0.616268i | 0.0983167 | + | 0.0407241i | 0.431300 | − | 0.902209i | \(-0.358055\pi\) |
−0.332983 | + | 0.942933i | \(0.608055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.2808 | + | 10.5579i | −0.676430 | + | 0.694659i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.1523 | + | 14.1523i | 0.927150 | + | 0.927150i | 0.997521 | − | 0.0703713i | \(-0.0224184\pi\) |
−0.0703713 | + | 0.997521i | \(0.522418\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.46705 | − | 1.43610i | −0.226165 | − | 0.0936808i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.06080 | + | 21.0777i | 0.588562 | + | 1.36914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.75051i | 0.371969i | 0.982553 | + | 0.185985i | \(0.0595475\pi\) | ||||
−0.982553 | + | 0.185985i | \(0.940453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.404801i | 0.0260755i | 0.999915 | + | 0.0130378i | \(0.00415016\pi\) | ||||
−0.999915 | + | 0.0130378i | \(0.995850\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.9738 | + | 6.90891i | −0.896419 | + | 0.443207i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.02461 | − | 2.49548i | −0.384898 | − | 0.159430i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.08876 | + | 6.08876i | 0.387418 | + | 0.387418i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.31898 | − | 8.10067i | −0.527194 | − | 0.513359i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.1825 | + | 4.21772i | 0.642712 | + | 0.266220i | 0.680143 | − | 0.733079i | \(-0.261917\pi\) |
−0.0374311 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.84418 | − | 11.6949i | −0.304551 | − | 0.735252i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.96963 | − | 0.0926651i | 0.436455 | − | 0.00580291i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.0174i | 1.68530i | 0.538460 | + | 0.842651i | \(0.319006\pi\) | ||||
−0.538460 | + | 0.842651i | \(0.680994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.9581 | + | 7.02426i | −1.05372 | + | 0.436466i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.01901 | − | 10.4827i | 0.248770 | − | 0.648863i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0909901 | − | 0.0909901i | −0.00561069 | − | 0.00561069i | 0.704296 | − | 0.709907i | \(-0.251263\pi\) |
−0.709907 | + | 0.704296i | \(0.751263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.46103 | − | 2.46103i | 0.151180 | − | 0.151180i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.0895 | + | 8.40886i | 1.29066 | + | 0.514614i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.83071 | − | 21.3192i | −0.538418 | − | 1.29986i | −0.925827 | − | 0.377948i | \(-0.876630\pi\) |
0.387409 | − | 0.921908i | \(-0.373370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.82777 | −0.171775 | −0.0858874 | − | 0.996305i | \(-0.527373\pi\) | ||||
−0.0858874 | + | 0.996305i | \(0.527373\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.5110 | + | 0.365774i | −1.66504 | + | 0.0221377i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.80806 | − | 3.64842i | 0.531146 | − | 0.220008i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.81789 | + | 14.0456i | −0.349563 | + | 0.843920i | 0.647108 | + | 0.762398i | \(0.275978\pi\) |
−0.996672 | + | 0.0815223i | \(0.974022\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.746862 | + | 0.708164i | 0.0447135 | + | 0.0423967i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3239 | − | 11.3239i | 0.675530 | − | 0.675530i | −0.283455 | − | 0.958985i | \(-0.591481\pi\) |
0.958985 | + | 0.283455i | \(0.0914808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.05059 | + | 7.36479i | −0.181339 | + | 0.437791i | −0.988243 | − | 0.152892i | \(-0.951141\pi\) |
0.806904 | + | 0.590683i | \(0.201141\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.12719 | − | 2.62214i | −0.0667693 | − | 0.155322i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.7676 | −1.10782 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0325 | 0.590149 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.54594 | − | 15.2275i | −0.383730 | − | 0.892652i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.77629 | − | 11.5310i | 0.279034 | − | 0.673648i | −0.720775 | − | 0.693169i | \(-0.756214\pi\) |
0.999809 | + | 0.0195210i | \(0.00621412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.79031 | + | 4.79031i | −0.278903 | + | 0.278903i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.63585 | − | 8.27061i | 0.443077 | − | 0.479909i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.04421 | − | 21.8346i | 0.523040 | − | 1.26273i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.9380 | + | 14.8860i | −2.07143 | + | 0.858016i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.62708 | − | 0.0615196i | 0.265819 | − | 0.00353421i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.00053 | 0.286330 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3306 | − | 29.7687i | −0.703744 | − | 1.69899i | −0.715071 | − | 0.699052i | \(-0.753606\pi\) |
0.0113269 | − | 0.999936i | \(-0.496394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.3249 | − | 6.90781i | −0.985577 | − | 0.392971i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.2380 | − | 22.2380i | 1.26100 | − | 1.26100i | 0.310392 | − | 0.950609i | \(-0.399540\pi\) |
0.950609 | − | 0.310392i | \(-0.100460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4230 | − | 13.4230i | −0.758713 | − | 0.758713i | 0.217375 | − | 0.976088i | \(-0.430250\pi\) |
−0.976088 | + | 0.217375i | \(0.930250\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.51526 | + | 3.26470i | 0.479781 | + | 0.183945i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.947076 | − | 0.392292i | 0.0531931 | − | 0.0220333i | −0.355928 | − | 0.934513i | \(-0.615835\pi\) |
0.409121 | + | 0.912480i | \(0.365835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.10688i | 0.453898i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.9293 | − | 0.291562i | 1.22398 | − | 0.0162734i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.23599 | − | 10.2266i | −0.235697 | − | 0.569022i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.4449 | + | 6.81168i | 0.912197 | + | 0.377844i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.4818 | − | 17.9968i | −1.02205 | − | 0.995227i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.4647 | − | 13.4647i | −0.742335 | − | 0.742335i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7914 | + | 8.61208i | 1.14280 | + | 0.473363i | 0.872113 | − | 0.489305i | \(-0.162749\pi\) |
0.270686 | + | 0.962668i | \(0.412749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.8062 | − | 5.70798i | 0.701776 | − | 0.312795i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.56610i | − | 0.249473i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.6373i | 1.61444i | 0.590248 | + | 0.807222i | \(0.299030\pi\) | ||||
−0.590248 | + | 0.807222i | \(0.700970\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.8487 | − | 25.2367i | −0.589218 | − | 1.37067i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.686634 | − | 0.284413i | −0.0371833 | − | 0.0154018i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.95740 | − | 3.95740i | −0.213680 | − | 0.213680i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.46509 | + | 5.61237i | −0.294231 | + | 0.302160i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.8544 | − | 9.05241i | −1.17321 | − | 0.485959i | −0.290956 | − | 0.956736i | \(-0.593973\pi\) |
−0.882252 | + | 0.470778i | \(0.843973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.170032 | − | 0.410493i | −0.00910160 | − | 0.0219732i | 0.919263 | − | 0.393643i | \(-0.128785\pi\) |
−0.928365 | + | 0.371670i | \(0.878785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.9995 | − | 0.837993i | 1.12087 | − | 0.0447288i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.1851i | − | 1.23402i | −0.786956 | − | 0.617010i | \(-0.788344\pi\) | ||
0.786956 | − | 0.617010i | \(-0.211656\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.30432 | − | 2.61133i | 0.334599 | − | 0.138595i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.8533 | + | 13.0993i | 1.73878 | + | 0.693290i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.59655 | + | 7.59655i | 0.400930 | + | 0.400930i | 0.878561 | − | 0.477630i | \(-0.158504\pi\) |
−0.477630 | + | 0.878561i | \(0.658504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2300 | − | 10.2300i | 0.538422 | − | 0.538422i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.04595 | − | 10.1473i | 0.212357 | − | 0.532595i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.607204 | + | 1.46592i | 0.0317825 | + | 0.0767298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4269 | 0.753079 | 0.376540 | − | 0.926401i | \(-0.377114\pi\) | ||||
0.376540 | + | 0.926401i | \(0.377114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.3306 | − | 0.381133i | 0.746020 | − | 0.0198410i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.3161 | − | 6.75834i | 0.847089 | − | 0.350876i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.38447 | + | 10.5851i | −0.227019 | + | 0.548073i | −0.995812 | − | 0.0914248i | \(-0.970858\pi\) |
0.768793 | + | 0.639498i | \(0.220858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.02938 | − | 8.79243i | −0.466275 | − | 0.454039i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.7026 | + | 10.7026i | −0.551211 | + | 0.551211i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.10789 | + | 2.67468i | −0.0569084 | + | 0.137389i | −0.949776 | − | 0.312930i | \(-0.898690\pi\) |
0.892868 | + | 0.450319i | \(0.148690\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.61406 | − | 1.55360i | 0.185154 | − | 0.0795934i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.50037 | −0.178861 | −0.0894304 | − | 0.995993i | \(-0.528505\pi\) | ||||
−0.0894304 | + | 0.995993i | \(0.528505\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.58535 | −0.335621 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.1393 | − | 12.0965i | 1.37957 | − | 0.614901i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.6893 | + | 25.8063i | −0.541969 | + | 1.30843i | 0.381362 | + | 0.924426i | \(0.375455\pi\) |
−0.923332 | + | 0.384004i | \(0.874545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.4826 | + | 21.4826i | −1.08642 | + | 1.08642i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.12905 | − | 8.34813i | 0.410056 | − | 0.421107i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.92344 | + | 9.47203i | −0.197410 | + | 0.476590i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8148 | + | 4.89383i | −0.592966 | + | 0.245614i | −0.658926 | − | 0.752208i | \(-0.728989\pi\) |
0.0659602 | + | 0.997822i | \(0.478989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.192536 | − | 14.4813i | −0.00963887 | − | 0.724970i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.4682 | −1.87107 | −0.935537 | − | 0.353229i | \(-0.885084\pi\) | ||||
−0.935537 | + | 0.353229i | \(0.885084\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.531006 | − | 1.28196i | −0.0264513 | − | 0.0638591i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.56839 | − | 2.31994i | −0.326386 | − | 0.115279i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.15905 | + | 7.15905i | −0.354861 | + | 0.354861i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.85216 | − | 9.85216i | −0.487158 | − | 0.487158i | 0.420250 | − | 0.907408i | \(-0.361942\pi\) |
−0.907408 | + | 0.420250i | \(0.861942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.47481 | − | 18.7469i | 0.368705 | − | 0.924717i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.7586 | + | 13.1549i | −1.56274 | + | 0.647308i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.18885i | − | 0.254710i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.111520 | − | 8.38774i | −0.00546114 | − | 0.410749i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.45030 | + | 13.1582i | 0.266264 | + | 0.642819i | 0.999302 | − | 0.0373695i | \(-0.0118979\pi\) |
−0.733037 | + | 0.680189i | \(0.761898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.4081 | − | 5.55381i | −0.653470 | − | 0.270676i | 0.0312176 | − | 0.999513i | \(-0.490062\pi\) |
−0.684688 | + | 0.728836i | \(0.740062\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.5549 | + | 10.0080i | 0.513195 | + | 0.486605i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.1797 | − | 16.1797i | −0.784832 | − | 0.784832i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.4423 | + | 9.71011i | 1.13445 | + | 0.469905i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.9423 | + | 5.99345i | −0.673139 | + | 0.289367i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 37.0767i | − | 1.78592i | −0.450133 | − | 0.892962i | \(-0.648623\pi\) | ||
0.450133 | − | 0.892962i | \(-0.351377\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.656469i | − | 0.0315479i | −0.999876 | − | 0.0157739i | \(-0.994979\pi\) | ||
0.999876 | − | 0.0157739i | \(-0.00502121\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.60909 | − | 1.98134i | 0.220989 | − | 0.0949980i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.4933 | + | 4.76069i | 0.549801 | + | 0.227735i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.8613 | + | 14.8613i | 0.709293 | + | 0.709293i | 0.966387 | − | 0.257093i | \(-0.0827648\pi\) |
−0.257093 | + | 0.966387i | \(0.582765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.3409 | + | 17.3906i | 0.873378 | + | 0.828125i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.86331 | + | 2.42866i | 0.278574 | + | 0.115389i | 0.517596 | − | 0.855625i | \(-0.326827\pi\) |
−0.239022 | + | 0.971014i | \(0.576827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.88265 | + | 9.37354i | 0.184055 | + | 0.444348i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.368388 | − | 27.7076i | −0.0174241 | − | 1.31053i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.964596i | − | 0.0455221i | −0.999741 | − | 0.0227611i | \(-0.992754\pi\) | ||
0.999741 | − | 0.0227611i | \(-0.00724569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.56386 | + | 3.96148i | −0.450345 | + | 0.186539i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.88145 | + | 14.7507i | −0.276334 | + | 0.693050i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.69388 | − | 8.69388i | −0.407575 | − | 0.407575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.65709 | − | 8.65709i | 0.404962 | − | 0.404962i | −0.475016 | − | 0.879977i | \(-0.657558\pi\) |
0.879977 | + | 0.475016i | \(0.157558\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.3522 | − | 9.33521i | −1.18334 | − | 0.435730i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4022 | − | 29.9416i | −0.577628 | − | 1.39452i | −0.894936 | − | 0.446195i | \(-0.852779\pi\) |
0.317308 | − | 0.948323i | \(-0.397221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0597 | 0.839306 | 0.419653 | − | 0.907685i | \(-0.362152\pi\) | ||||
0.419653 | + | 0.907685i | \(0.362152\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.00611450 | + | 0.459891i | 0.000283553 | + | 0.0213269i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.41999 | + | 1.41660i | −0.158258 | + | 0.0655526i | −0.460406 | − | 0.887708i | \(-0.652296\pi\) |
0.302148 | + | 0.953261i | \(0.402296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.86653 | − | 21.4057i | 0.409418 | − | 0.988423i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.18851 | + | 1.22054i | −0.0547636 | + | 0.0562395i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.1717 | + | 15.1717i | −0.697594 | + | 0.697594i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.58554 | + | 8.65625i | −0.164516 | + | 0.397176i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.3214 | + | 5.49189i | −0.564158 | + | 0.251456i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.0035 | 1.00537 | 0.502684 | − | 0.864470i | \(-0.332346\pi\) | ||||
0.502684 | + | 0.864470i | \(0.332346\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.9025 | −0.861882 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −36.5183 | + | 15.6984i | −1.66164 | + | 0.714300i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.83448 | − | 6.84304i | 0.128707 | − | 0.310726i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.12841 | + | 4.12841i | −0.187076 | + | 0.187076i | −0.794431 | − | 0.607355i | \(-0.792231\pi\) |
0.607355 | + | 0.794431i | \(0.292231\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.93466 | − | 1.88389i | −0.0874882 | − | 0.0851924i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.44901 | − | 13.1551i | 0.245911 | − | 0.593681i | −0.751939 | − | 0.659233i | \(-0.770881\pi\) |
0.997849 | + | 0.0655526i | \(0.0208810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.9759 | − | 7.44586i | 0.809594 | − | 0.335345i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.02845 | − | 0.133736i | 0.226012 | − | 0.00601097i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.6251 | 1.55315 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.4361 | + | 34.8519i | 0.646250 | + | 1.56018i | 0.818109 | + | 0.575063i | \(0.195022\pi\) |
−0.171860 | + | 0.985121i | \(0.554978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.77612 | − | 6.96255i | 0.124028 | − | 0.311064i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.95140 | + | 2.95140i | −0.131596 | + | 0.131596i | −0.769837 | − | 0.638241i | \(-0.779662\pi\) |
0.638241 | + | 0.769837i | \(0.279662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.46222 | + | 1.46222i | 0.0650681 | + | 0.0650681i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.40343 | − | 2.15447i | −0.239975 | − | 0.0956832i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.0107 | − | 16.5730i | 1.77344 | − | 0.734584i | 0.779281 | − | 0.626675i | \(-0.215585\pi\) |
0.994161 | − | 0.107909i | \(-0.0344154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.05125i | 0.356166i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.441103 | + | 11.0537i | 0.0194752 | + | 0.488033i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.18956 | − | 7.70028i | −0.140549 | − | 0.339315i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.70371 | − | 4.01941i | −0.426769 | − | 0.176773i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.8727 | − | 13.2196i | 0.565049 | − | 0.580276i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.10873 | + | 9.10873i | 0.399061 | + | 0.399061i | 0.877902 | − | 0.478841i | \(-0.158943\pi\) |
−0.478841 | + | 0.877902i | \(0.658943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7797 | − | 7.77882i | −0.821181 | − | 0.340144i | −0.0677753 | − | 0.997701i | \(-0.521590\pi\) |
−0.753405 | + | 0.657556i | \(0.771590\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.8233 | − | 27.5039i | −0.516011 | − | 1.20037i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.78374i | 0.0777009i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 11.1443i | − | 0.484534i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.9832 | − | 10.6898i | 1.04078 | − | 0.463896i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.8560 | − | 7.39618i | −0.773427 | − | 0.320364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.92999 | + | 6.92999i | 0.299609 | + | 0.299609i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.58194 | − | 6.40921i | −0.284032 | − | 0.276578i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.8619 | − | 6.98443i | −0.726294 | − | 0.300841i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.91944 | − | 11.8766i | −0.211503 | − | 0.510614i | 0.782151 | − | 0.623088i | \(-0.214122\pi\) |
−0.993655 | + | 0.112475i | \(0.964122\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.6362 | + | 0.433916i | −1.40055 | + | 0.0186211i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.5278i | − | 0.493796i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4330 | − | 8.04942i | 0.830896 | − | 0.344168i | 0.0736387 | − | 0.997285i | \(-0.476539\pi\) |
0.757257 | + | 0.653117i | \(0.226539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0973 | − | 6.93839i | −0.772373 | − | 0.296123i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.63363 | − | 5.63363i | −0.240001 | − | 0.240001i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.7859 | + | 36.7859i | −1.56429 | + | 1.56429i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.81990 | + | 2.32052i | 0.247041 | + | 0.0985007i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3258 | + | 34.5854i | 0.607002 | + | 1.46543i | 0.866245 | + | 0.499620i | \(0.166527\pi\) |
−0.259243 | + | 0.965812i | \(0.583473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.0588 | −1.69431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.5069 | − | 0.259355i | 0.823581 | − | 0.0109500i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.4215 | + | 5.97357i | −0.607793 | + | 0.251756i | −0.665284 | − | 0.746590i | \(-0.731690\pi\) |
0.0574918 | + | 0.998346i | \(0.481690\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.69761 | − | 11.3410i | 0.197630 | − | 0.477121i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.2875 | − | 23.6304i | −1.10397 | − | 0.992382i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.11604 | − | 3.11604i | 0.130631 | − | 0.130631i | −0.638768 | − | 0.769399i | \(-0.720556\pi\) |
0.769399 | + | 0.638768i | \(0.220556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.75950 | + | 11.4904i | −0.199179 | + | 0.480860i | −0.991636 | − | 0.129068i | \(-0.958802\pi\) |
0.792457 | + | 0.609928i | \(0.208802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.73316 | + | 8.68427i | 0.155955 | + | 0.362791i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.7159 | 1.07243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.4677 | −0.768820 | −0.384410 | − | 0.923163i | \(-0.625595\pi\) | ||||
−0.384410 | + | 0.923163i | \(0.625595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.21252 | + | 16.7781i | 0.299742 | + | 0.697275i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0758 | − | 24.3251i | 0.418014 | − | 1.00917i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.88803 | − | 6.88803i | 0.285273 | − | 0.285273i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.81504 | + | 6.46193i | 0.281767 | + | 0.267168i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.04862 | − | 4.94582i | 0.0845558 | − | 0.204136i | −0.875946 | − | 0.482409i | \(-0.839762\pi\) |
0.960502 | + | 0.278273i | \(0.0897620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.674800 | − | 0.279511i | 0.0278047 | − | 0.0115171i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.237243 | + | 0.00315427i | −0.00975886 | + | 0.000129749i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.6090 | −1.09270 | −0.546351 | − | 0.837556i | \(-0.683984\pi\) | ||||
−0.546351 | + | 0.837556i | \(0.683984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.04839 | + | 14.6021i | 0.247960 | + | 0.598628i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.1241 | + | 6.03031i | 0.618988 | + | 0.246804i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7251 | + | 12.7251i | −0.519933 | + | 0.519933i | −0.917551 | − | 0.397618i | \(-0.869837\pi\) |
0.397618 | + | 0.917551i | \(0.369837\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.45474 | − | 6.45474i | −0.263294 | − | 0.263294i | 0.563097 | − | 0.826391i | \(-0.309610\pi\) |
−0.826391 | + | 0.563097i | \(0.809610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.33560 | + | 16.5250i | −0.258006 | + | 0.672952i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.51011 | − | 1.86815i | 0.183362 | − | 0.0759511i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.2504i | 1.22783i | 0.789373 | + | 0.613914i | \(0.210406\pi\) | ||||
−0.789373 | + | 0.613914i | \(0.789594\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.4546 | − | 0.338433i | 1.03147 | − | 0.0137140i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.50433 | − | 18.1171i | −0.303593 | − | 0.732938i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.29750 | + | 0.951656i | 0.0927952 | + | 0.0384370i | 0.428598 | − | 0.903495i | \(-0.359008\pi\) |
−0.335803 | + | 0.941932i | \(0.609008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.58969 | + | 4.46925i | 0.185074 | + | 0.180217i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.87504 | + | 3.87504i | 0.156003 | + | 0.156003i | 0.780793 | − | 0.624790i | \(-0.214815\pi\) |
−0.624790 | + | 0.780793i | \(0.714815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.55208 | − | 3.12818i | −0.303544 | − | 0.125732i | 0.225712 | − | 0.974194i | \(-0.427529\pi\) |
−0.529256 | + | 0.848462i | \(0.677529\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.5659 | − | 12.7286i | 1.10618 | − | 0.510781i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.4821i | 2.06259i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.3726i | 0.654905i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.15484 | − | 7.33894i | −0.125992 | − | 0.293089i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.4495 | + | 9.29889i | 0.895121 | + | 0.370771i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.02275 | − | 3.02275i | −0.120334 | − | 0.120334i | 0.644375 | − | 0.764709i | \(-0.277117\pi\) |
−0.764709 | + | 0.644375i | \(0.777117\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.10648 | − | 9.35190i | 0.361950 | − | 0.371705i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.62411 | + | 0.672730i | 0.0644510 | + | 0.0266965i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0401 | − | 31.4816i | −0.516668 | − | 1.24735i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.4391 | + | 0.703168i | −1.04591 | + | 0.0278169i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.4562i | 1.20295i | 0.798893 | + | 0.601473i | \(0.205419\pi\) | ||||
−0.798893 | + | 0.601473i | \(0.794581\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0821 | + | 7.48986i | −0.713089 | + | 0.295371i | −0.709582 | − | 0.704623i | \(-0.751116\pi\) |
−0.00350703 | + | 0.999994i | \(0.501116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.3337 | + | 4.91772i | 0.485639 | + | 0.193635i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.1003 | + | 28.1003i | 1.10474 | + | 1.10474i | 0.993831 | + | 0.110905i | \(0.0353748\pi\) |
0.110905 | + | 0.993831i | \(0.464625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4073 | + | 13.4073i | −0.526282 | + | 0.526282i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.864358 | + | 2.16782i | −0.0338769 | + | 0.0849636i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.44946 | + | 15.5704i | 0.252387 | + | 0.609316i | 0.998396 | − | 0.0566202i | \(-0.0180324\pi\) |
−0.746009 | + | 0.665936i | \(0.768032\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.20703 | 0.203455 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.163505 | − | 6.14778i | −0.00637894 | − | 0.239848i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0479 | + | 12.4463i | −1.17050 | + | 0.484838i | −0.881358 | − | 0.472448i | \(-0.843370\pi\) |
−0.289143 | + | 0.957286i | \(0.593370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0509 | + | 38.7503i | −0.624308 | + | 1.50721i | 0.222290 | + | 0.974981i | \(0.428647\pi\) |
−0.846598 | + | 0.532233i | \(0.821353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.0951 | + | 25.4103i | 1.01345 | + | 0.986854i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.57629 | − | 4.57629i | 0.177461 | − | 0.177461i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.36817 | + | 20.2025i | −0.324017 | + | 0.782246i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.4708 | + | 11.3792i | −1.02342 | + | 0.439945i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.9957 | 0.540297 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.07753 | 0.0415357 | 0.0207678 | − | 0.999784i | \(-0.493389\pi\) | ||||
0.0207678 | + | 0.999784i | \(0.493389\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.58659 | + | 20.7614i | 0.368988 | + | 0.799106i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6041 | + | 30.4289i | −0.484414 | + | 1.16948i | 0.473078 | + | 0.881021i | \(0.343143\pi\) |
−0.957492 | + | 0.288459i | \(0.906857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.5758 | − | 26.5758i | 1.01989 | − | 1.01989i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.45545 | − | 3.54857i | 0.132413 | − | 0.135981i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.7550 | + | 47.6928i | −0.755904 | + | 1.82491i | −0.233120 | + | 0.972448i | \(0.574893\pi\) |
−0.522784 | + | 0.852465i | \(0.675107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.33233 | − | 3.45136i | 0.318362 | − | 0.131870i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0370816 | − | 2.78902i | −0.00141475 | − | 0.106408i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.1870 | 0.692868 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.23089 | − | 10.2143i | −0.160951 | − | 0.388569i | 0.822745 | − | 0.568411i | \(-0.192441\pi\) |
−0.983696 | + | 0.179842i | \(0.942441\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.8328 | + | 9.13737i | 0.905335 | + | 0.347100i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.65065 | − | 2.65065i | 0.100545 | − | 0.100545i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.5681 | + | 17.5681i | 0.665438 | + | 0.665438i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.8391 | − | 32.2007i | 0.485621 | − | 1.21794i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.1122 | − | 9.15919i | 0.835168 | − | 0.345938i | 0.0762214 | − | 0.997091i | \(-0.475714\pi\) |
0.758946 | + | 0.651153i | \(0.225714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.94993i | − | 0.375269i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0864119 | + | 6.49931i | 0.00325446 | + | 0.244778i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.01547 | + | 9.69421i | 0.151017 | + | 0.364588i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2667 | − | 11.7085i | −1.06158 | − | 0.439721i | −0.217568 | − | 0.976045i | \(-0.569812\pi\) |
−0.844012 | + | 0.536325i | \(0.819812\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.3419 | − | 28.8360i | 1.02540 | − | 1.08144i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.41753 | − | 1.41753i | −0.0530869 | − | 0.0530869i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.26547 | − | 2.59524i | −0.234315 | − | 0.0970566i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.15051 | − | 3.93359i | 0.341732 | − | 0.146903i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.8341i | 0.739687i | 0.929094 | + | 0.369843i | \(0.120589\pi\) | ||||
−0.929094 | + | 0.369843i | \(0.879411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 42.2921i | − | 1.57504i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.644140 | − | 0.276901i | 0.0239558 | − | 0.0102981i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.2156 | − | 6.30252i | −0.565095 | − | 0.234070i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1914 | − | 21.1914i | −0.785946 | − | 0.785946i | 0.194881 | − | 0.980827i | \(-0.437568\pi\) |
−0.980827 | + | 0.194881i | \(0.937568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.5525 | + | 17.5099i | 0.761203 | + | 0.648513i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.5757 | + | 19.7065i | 1.75965 | + | 0.728871i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.2396 | + | 44.0342i | 0.673694 | + | 1.62644i | 0.775283 | + | 0.631614i | \(0.217607\pi\) |
−0.101589 | + | 0.994826i | \(0.532393\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.150156 | + | 11.2937i | 0.00553858 | + | 0.416574i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.7798i | − | 0.470749i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.9807 | − | 6.20519i | 0.551073 | − | 0.228262i | −0.0897317 | − | 0.995966i | \(-0.528601\pi\) |
0.640804 | + | 0.767704i | \(0.278601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.52378 | − | 13.8537i | 0.202921 | − | 0.508929i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.8633 | − | 22.8633i | −0.838773 | − | 0.838773i | 0.149925 | − | 0.988697i | \(-0.452097\pi\) |
−0.988697 | + | 0.149925i | \(0.952097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.75601 | − | 8.75601i | 0.320795 | − | 0.320795i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.19968 | + | 18.7788i | −0.263423 | + | 0.687080i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.0307 | + | 45.9442i | 0.695367 | + | 1.67877i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4070 | −0.927116 | −0.463558 | − | 0.886067i | \(-0.653427\pi\) | ||||
−0.463558 | + | 0.886067i | \(0.653427\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.253785 | − | 19.0880i | −0.00924845 | − | 0.695605i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.55618 | + | 2.71566i | −0.238604 | + | 0.0988329i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.3294 | + | 29.7658i | −0.448120 | + | 1.08186i | 0.524906 | + | 0.851160i | \(0.324101\pi\) |
−0.973026 | + | 0.230697i | \(0.925899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.2959 | + | 15.7081i | −0.555206 | + | 0.570169i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.7667 | − | 23.7667i | 0.861542 | − | 0.861542i | −0.129975 | − | 0.991517i | \(-0.541490\pi\) |
0.991517 | + | 0.129975i | \(0.0414898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.3848 | − | 54.0418i | 0.810385 | − | 1.95644i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.91498 | − | 11.0271i | −0.177701 | − | 0.398684i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.4002 | −1.27823 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.4960 | 0.739104 | 0.369552 | − | 0.929210i | \(-0.379511\pi\) | ||||
0.369552 | + | 0.929210i | \(0.379511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.9916 | − | 18.4811i | 1.54830 | − | 0.665580i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.8280 | − | 43.0405i | 0.641228 | − | 1.54806i | −0.183797 | − | 0.982964i | \(-0.558839\pi\) |
0.825025 | − | 0.565097i | \(-0.191161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.06762 | − | 1.06762i | 0.0383500 | − | 0.0383500i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.7774 | + | 22.1797i | 0.817135 | + | 0.795691i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.89320 | − | 9.39903i | 0.139489 | − | 0.336755i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.6448 | − | 7.30870i | 0.631380 | − | 0.261526i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.4298 | + | 0.775355i | −0.694364 | + | 0.0277089i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.761295 | −0.0271718 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.25890 | + | 22.3530i | 0.330044 | + | 0.796797i | 0.998588 | + | 0.0531241i | \(0.0169179\pi\) |
−0.668544 | + | 0.743673i | \(0.733082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0825472 | + | 0.207029i | −0.00293876 | + | 0.00737044i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.0444 | − | 44.0444i | 1.56604 | − | 1.56604i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.4769 | + | 18.4769i | 0.656133 | + | 0.656133i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.59958 | − | 2.23268i | −0.198596 | − | 0.0791848i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.1390 | − | 8.75605i | 0.748781 | − | 0.310155i | 0.0245368 | − | 0.999699i | \(-0.492189\pi\) |
0.724244 | + | 0.689544i | \(0.242189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.2083i | 0.891806i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.04550 | − | 39.3108i | −0.0369410 | − | 1.38898i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.69947 | + | 4.10287i | 0.0599728 | + | 0.144787i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.4108 | − | 6.79760i | −0.578406 | − | 0.239584i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.8837 | + | 28.6352i | −0.981553 | + | 1.00801i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.3483 | + | 13.3483i | 0.469301 | + | 0.469301i | 0.901688 | − | 0.432387i | \(-0.142329\pi\) |
−0.432387 | + | 0.901688i | \(0.642329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.1422 | − | 7.51474i | −0.637058 | − | 0.263878i | 0.0406904 | − | 0.999172i | \(-0.487044\pi\) |
−0.677749 | + | 0.735294i | \(0.737044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.93431 | + | 4.49970i | 0.0678394 | + | 0.157811i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.20672i | − | 0.0422694i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 21.0862i | − | 0.737713i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.4007 | + | 43.5268i | 0.677917 | + | 1.52095i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.9756 | − | 11.5879i | −0.976355 | − | 0.404420i | −0.163281 | − | 0.986580i | \(-0.552208\pi\) |
−0.813074 | + | 0.582160i | \(0.802208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.0608 | + | 29.0608i | 1.01300 | + | 1.01300i | 0.999914 | + | 0.0130818i | \(0.00416419\pi\) |
0.0130818 | + | 0.999914i | \(0.495836\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.8306 | − | 11.5202i | −0.411890 | − | 0.401081i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.28063 | − | 0.944670i | −0.0793054 | − | 0.0328494i | 0.342678 | − | 0.939453i | \(-0.388666\pi\) |
−0.421984 | + | 0.906604i | \(0.638666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.1205 | + | 46.1610i | 0.664082 | + | 1.60324i | 0.791346 | + | 0.611368i | \(0.209380\pi\) |
−0.127264 | + | 0.991869i | \(0.540620\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.3298 | − | 0.350070i | 0.913372 | − | 0.0121438i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.8039i | 1.51772i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.09460 | − | 1.28183i | 0.107093 | − | 0.0443595i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.615984 | − | 1.67286i | 0.0212915 | − | 0.0578225i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.7898 | − | 26.7898i | −0.924887 | − | 0.924887i | 0.0724830 | − | 0.997370i | \(-0.476908\pi\) |
−0.997370 | + | 0.0724830i | \(0.976908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6035 | + | 10.6035i | −0.365638 | + | 0.365638i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.7653 | − | 10.2732i | −0.887405 | − | 0.353828i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.994788 | − | 2.40163i | −0.0342217 | − | 0.0826186i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.7708 | 0.851135 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.8060 | − | 0.183558i | 0.473820 | − | 0.00629969i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.2303 | + | 10.4507i | −0.864884 | + | 0.358247i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.6540 | − | 40.2063i | 0.570222 | − | 1.37664i | −0.331145 | − | 0.943580i | \(-0.607435\pi\) |
0.901366 | − | 0.433057i | \(-0.142565\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.40143 | + | 3.58730i | −0.116327 | + | 0.122683i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.3920 | − | 26.3920i | 0.901532 | − | 0.901532i | −0.0940369 | − | 0.995569i | \(-0.529977\pi\) |
0.995569 | + | 0.0940369i | \(0.0299772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.8177 | − | 26.1163i | 0.369096 | − | 0.891077i | −0.624803 | − | 0.780782i | \(-0.714821\pi\) |
0.993899 | − | 0.110294i | \(-0.0351793\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.8378 | + | 29.8640i | 0.437512 | + | 1.01776i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.4203 | −1.03552 | −0.517760 | − | 0.855526i | \(-0.673234\pi\) | ||||
−0.517760 | + | 0.855526i | \(0.673234\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.24555 | 0.280357 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.86267 | − | 15.9643i | −0.233069 | − | 0.542176i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.9811 | + | 26.5107i | −0.372508 | + | 0.899313i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.8717 | − | 16.8717i | 0.571675 | − | 0.571675i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.7531 | + | 20.8325i | −0.668541 | + | 0.705073i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9362 | − | 26.4023i | 0.369711 | − | 0.892562i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.8161 | + | 7.37968i | −0.601608 | + | 0.249194i | −0.662636 | − | 0.748942i | \(-0.730562\pi\) |
0.0610277 | + | 0.998136i | \(0.480562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.6159 | + | 0.287395i | −0.729087 | + | 0.00969361i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0163 | −0.606984 | −0.303492 | − | 0.952834i | \(-0.598153\pi\) | ||||
−0.303492 | + | 0.952834i | \(0.598153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.13662 | − | 2.74405i | −0.0382504 | − | 0.0923447i | 0.903600 | − | 0.428378i | \(-0.140915\pi\) |
−0.941850 | + | 0.336033i | \(0.890915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.8994 | + | 4.34582i | 0.366378 | + | 0.146083i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.9649 | + | 33.9649i | −1.14043 | + | 1.14043i | −0.152060 | + | 0.988371i | \(0.548591\pi\) |
−0.988371 | + | 0.152060i | \(0.951409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.30746 | + | 6.30746i | 0.211545 | + | 0.211545i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.3839 | − | 6.49313i | −0.615883 | − | 0.217528i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.53647 | − | 3.95013i | 0.319126 | − | 0.132186i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.10539i | − | 0.137228i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40.9311 | + | 0.544201i | −1.36665 | + | 0.0181703i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.491315 | + | 1.18614i | 0.0163863 | + | 0.0395599i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.5997 | − | 8.94687i | −0.719589 | − | 0.298063i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48.2706 | + | 47.0038i | 1.60634 | + | 1.56419i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.3135 | − | 10.3135i | −0.342833 | − | 0.342833i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.9663 | − | 18.2114i | −1.45988 | − | 0.604701i | −0.495352 | − | 0.868692i | \(-0.664961\pi\) |
−0.964525 | + | 0.263991i | \(0.914961\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.26301 | − | 7.32077i | −0.108227 | − | 0.242815i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0744i | 0.996410i | 0.867059 | + | 0.498205i | \(0.166007\pi\) | ||||
−0.867059 | + | 0.498205i | \(0.833993\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 14.5227i | − | 0.480633i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.42058 | − | 7.95711i | −0.113081 | − | 0.263054i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.4103 | + | 10.1111i | 0.806100 | + | 0.333897i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.8072 | − | 21.8072i | −0.719352 | − | 0.719352i | 0.249121 | − | 0.968472i | \(-0.419858\pi\) |
−0.968472 | + | 0.249121i | \(0.919858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.9348 | + | 39.9841i | −1.28295 | + | 1.31752i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.9432 | + | 13.6455i | 1.08434 | + | 0.449148i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.87102 | − | 19.0023i | −0.258798 | − | 0.624792i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.858871 | + | 32.2935i | 0.0282090 | + | 1.06066i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.8839i | 1.04608i | 0.852309 | + | 0.523038i | \(0.175202\pi\) | ||||
−0.852309 | + | 0.523038i | \(0.824798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.5713 | − | 6.86406i | 0.543102 | − | 0.224960i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.5980 | − | 20.1745i | −1.65650 | − | 0.660485i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.16446 | + | 6.16446i | 0.201599 | + | 0.201599i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.2485 | − | 36.2485i | 1.18419 | − | 1.18419i | 0.205536 | − | 0.978650i | \(-0.434106\pi\) |
0.978650 | − | 0.205536i | \(-0.0658936\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.1775 | + | 30.5413i | −0.397397 | + | 0.996677i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.43068 | − | 15.5250i | −0.209634 | − | 0.506102i | 0.783731 | − | 0.621100i | \(-0.213314\pi\) |
−0.993366 | + | 0.114998i | \(0.963314\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.9225 | −0.909283 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.629833 | − | 15.7831i | −0.0204885 | − | 0.513425i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.2355 | + | 6.72498i | −0.527584 | + | 0.218532i | −0.630545 | − | 0.776153i | \(-0.717168\pi\) |
0.102961 | + | 0.994685i | \(0.467168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.17294 | + | 7.66016i | −0.102998 | + | 0.248659i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.27208 | − | 1.23869i | −0.0412499 | − | 0.0401674i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.946267 | + | 0.946267i | −0.0306526 | + | 0.0306526i | −0.722267 | − | 0.691614i | \(-0.756900\pi\) |
0.691614 | + | 0.722267i | \(0.256900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.61651 | + | 3.90260i | −0.0523090 | + | 0.126285i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.9001 | − | 5.54545i | 0.417001 | − | 0.179259i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.7635 | 1.47778 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8823 | 0.996203 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.4645 | − | 34.6957i | −0.498338 | − | 1.11805i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.12311 | + | 7.53987i | −0.100537 | + | 0.242717i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.1657 | + | 19.1657i | −0.616326 | + | 0.616326i | −0.944587 | − | 0.328261i | \(-0.893537\pi\) |
0.328261 | + | 0.944587i | \(0.393537\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.3755 | + | 13.7359i | −0.429682 | + | 0.441262i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.7803 | − | 33.2686i | 0.442231 | − | 1.06764i | −0.532933 | − | 0.846158i | \(-0.678910\pi\) |
0.975164 | − | 0.221483i | \(-0.0710899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.5732 | − | 7.27905i | 0.563370 | − | 0.233356i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.409867 | − | 30.8274i | −0.0131263 | − | 0.987267i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.7166 | −0.726769 | −0.363384 | − | 0.931639i | \(-0.618379\pi\) | ||||
−0.363384 | + | 0.931639i | \(0.618379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.8669 | + | 26.2350i | 0.347308 | + | 0.838475i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.9951 | + | 41.7199i | −0.510686 | + | 1.33201i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.832934 | + | 0.832934i | −0.0265665 | + | 0.0265665i | −0.720265 | − | 0.693699i | \(-0.755980\pi\) |
0.693699 | + | 0.720265i | \(0.255980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0749722 | − | 0.0749722i | −0.00238881 | − | 0.00238881i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.2154 | + | 30.6363i | −0.388819 | + | 0.975163i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.4688 | + | 22.1475i | −1.70021 | + | 0.704250i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.31878i | 0.105425i | 0.998610 | + | 0.0527123i | \(0.0167866\pi\) | ||||
−0.998610 | + | 0.0527123i | \(0.983213\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.518200 | − | 38.9754i | −0.0164446 | − | 1.23685i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.78439 | + | 6.72212i | 0.0882712 | + | 0.213105i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.7016 | + | 20.1729i | 1.54240 | + | 0.638881i | 0.981921 | − | 0.189290i | \(-0.0606187\pi\) |
0.560475 | + | 0.828172i | \(0.310619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.8428 | − | 16.4734i | −0.564522 | − | 0.521196i |
(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 | 768.2.o.b.287.5 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.287.9 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.287.10 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.143.5 | 56 | |||
8.5 | even | 2 | 96.2.o.a.59.10 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.287.6 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.59.5 | ✓ | 56 | ||
24.11 | even | 2 | 384.2.o.a.143.9 | 56 | |||
32.3 | odd | 8 | 96.2.o.a.83.5 | yes | 56 | ||
32.13 | even | 8 | 768.2.o.a.479.6 | 56 | |||
32.19 | odd | 8 | inner | 768.2.o.b.479.9 | 56 | ||
32.29 | even | 8 | 384.2.o.a.239.9 | 56 | |||
96.29 | odd | 8 | 384.2.o.a.239.5 | 56 | |||
96.35 | even | 8 | 96.2.o.a.83.10 | yes | 56 | ||
96.77 | odd | 8 | 768.2.o.a.479.10 | 56 | |||
96.83 | even | 8 | inner | 768.2.o.b.479.5 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.59.5 | ✓ | 56 | 24.5 | odd | 2 | ||
96.2.o.a.59.10 | yes | 56 | 8.5 | even | 2 | ||
96.2.o.a.83.5 | yes | 56 | 32.3 | odd | 8 | ||
96.2.o.a.83.10 | yes | 56 | 96.35 | even | 8 | ||
384.2.o.a.143.5 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.143.9 | 56 | 24.11 | even | 2 | |||
384.2.o.a.239.5 | 56 | 96.29 | odd | 8 | |||
384.2.o.a.239.9 | 56 | 32.29 | even | 8 | |||
768.2.o.a.287.6 | 56 | 12.11 | even | 2 | |||
768.2.o.a.287.10 | 56 | 4.3 | odd | 2 | |||
768.2.o.a.479.6 | 56 | 32.13 | even | 8 | |||
768.2.o.a.479.10 | 56 | 96.77 | odd | 8 | |||
768.2.o.b.287.5 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.287.9 | 56 | 3.2 | odd | 2 | inner | ||
768.2.o.b.479.5 | 56 | 96.83 | even | 8 | inner | ||
768.2.o.b.479.9 | 56 | 32.19 | odd | 8 | inner |