Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
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([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (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: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.1 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.g.757.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40920 | − | 0.118957i | −0.996456 | − | 0.0841153i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.97170 | + | 0.335269i | 0.985849 | + | 0.167634i | ||||
\(5\) | − | 3.46300i | − | 1.54870i | −0.632757 | − | 0.774351i | \(-0.718077\pi\) | ||
0.632757 | − | 0.774351i | \(-0.281923\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.73864 | − | 0.707009i | −0.968255 | − | 0.249965i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.411948 | + | 4.88007i | −0.130269 | + | 1.54321i | ||||
\(11\) | 3.31902i | 1.00072i | 0.865817 | + | 0.500361i | \(0.166799\pi\) | ||||
−0.865817 | + | 0.500361i | \(0.833201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.10840i | 0.862116i | 0.902324 | + | 0.431058i | \(0.141860\pi\) | ||||
−0.902324 | + | 0.431058i | \(0.858140\pi\) | |||||||
\(14\) | −1.40920 | − | 0.118957i | −0.376625 | − | 0.0317926i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.77519 | + | 1.32210i | 0.943797 | + | 0.330524i | ||||
\(17\) | 1.40277 | 0.340221 | 0.170110 | − | 0.985425i | \(-0.445588\pi\) | ||||
0.170110 | + | 0.985425i | \(0.445588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.80674i | 1.10274i | 0.834260 | + | 0.551371i | \(0.185895\pi\) | ||||
−0.834260 | + | 0.551371i | \(0.814105\pi\) | |||||||
\(20\) | 1.16104 | − | 6.82800i | 0.259616 | − | 1.52679i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.394821 | − | 4.67717i | 0.0841761 | − | 0.997176i | ||||
\(23\) | −8.79960 | −1.83484 | −0.917421 | − | 0.397917i | \(-0.869733\pi\) | ||||
−0.917421 | + | 0.397917i | \(0.869733\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.99238 | −1.39848 | ||||||||
\(26\) | 0.369766 | − | 4.38037i | 0.0725172 | − | 0.859061i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.97170 | + | 0.335269i | 0.372616 | + | 0.0633598i | ||||
\(29\) | 9.87397i | 1.83355i | 0.399404 | + | 0.916775i | \(0.369217\pi\) | ||||
−0.399404 | + | 0.916775i | \(0.630783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.83557 | −1.40731 | −0.703655 | − | 0.710541i | \(-0.748450\pi\) | ||||
−0.703655 | + | 0.710541i | \(0.748450\pi\) | |||||||
\(32\) | −5.16273 | − | 2.31219i | −0.912650 | − | 0.408741i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.97678 | − | 0.166869i | −0.339015 | − | 0.0286178i | ||||
\(35\) | − | 3.46300i | − | 0.585354i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.42317i | 0.891564i | 0.895142 | + | 0.445782i | \(0.147074\pi\) | ||||
−0.895142 | + | 0.445782i | \(0.852926\pi\) | |||||||
\(38\) | 0.571795 | − | 6.77366i | 0.0927574 | − | 1.09883i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.44837 | + | 9.48391i | −0.387122 | + | 1.49954i | ||||
\(41\) | 11.5710 | 1.80708 | 0.903542 | − | 0.428499i | \(-0.140957\pi\) | ||||
0.903542 | + | 0.428499i | \(0.140957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.03957i | 1.07352i | 0.843733 | + | 0.536762i | \(0.180353\pi\) | ||||
−0.843733 | + | 0.536762i | \(0.819647\pi\) | |||||||
\(44\) | −1.11276 | + | 6.54411i | −0.167756 | + | 0.986562i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.4004 | + | 1.04677i | 1.82834 | + | 0.154338i | ||||
\(47\) | −11.2916 | −1.64704 | −0.823522 | − | 0.567284i | \(-0.807994\pi\) | ||||
−0.823522 | + | 0.567284i | \(0.807994\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 9.85368 | + | 0.831793i | 1.39352 | + | 0.117633i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.04215 | + | 6.12884i | −0.144520 | + | 0.849917i | ||||
\(53\) | − | 6.51655i | − | 0.895117i | −0.894255 | − | 0.447559i | \(-0.852294\pi\) | ||
0.894255 | − | 0.447559i | \(-0.147706\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4938 | 1.54982 | ||||||||
\(56\) | −2.73864 | − | 0.707009i | −0.365966 | − | 0.0944780i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.17458 | − | 13.9144i | 0.154230 | − | 1.82705i | ||||
\(59\) | 3.89654i | 0.507287i | 0.967298 | + | 0.253643i | \(0.0816290\pi\) | ||||
−0.967298 | + | 0.253643i | \(0.918371\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.42334i | − | 1.20653i | −0.797539 | − | 0.603267i | \(-0.793865\pi\) | ||
0.797539 | − | 0.603267i | \(-0.206135\pi\) | |||||||
\(62\) | 11.0419 | + | 0.932096i | 1.40232 | + | 0.118376i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00028 | + | 3.87248i | 0.875035 | + | 0.484060i | ||||
\(65\) | 10.7644 | 1.33516 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.909712i | − | 0.111139i | −0.998455 | − | 0.0555695i | \(-0.982303\pi\) | ||
0.998455 | − | 0.0555695i | \(-0.0176974\pi\) | |||||||
\(68\) | 2.76583 | + | 0.470304i | 0.335406 | + | 0.0570327i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.411948 | + | 4.88007i | −0.0492372 | + | 0.583280i | ||||
\(71\) | 6.42314 | 0.762286 | 0.381143 | − | 0.924516i | \(-0.375531\pi\) | ||||
0.381143 | + | 0.924516i | \(0.375531\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.56257 | 0.182884 | 0.0914422 | − | 0.995810i | \(-0.470852\pi\) | ||||
0.0914422 | + | 0.995810i | \(0.470852\pi\) | |||||||
\(74\) | 0.645124 | − | 7.64234i | 0.0749942 | − | 0.888404i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.61155 | + | 9.47744i | −0.184857 | + | 1.08714i | ||||
\(77\) | 3.31902i | 0.378238i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.1619 | −1.25582 | −0.627908 | − | 0.778288i | \(-0.716088\pi\) | ||||
−0.627908 | + | 0.778288i | \(0.716088\pi\) | |||||||
\(80\) | 4.57843 | − | 13.0735i | 0.511884 | − | 1.46166i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.3059 | − | 1.37645i | −1.80068 | − | 0.152003i | ||||
\(83\) | 0.370241i | 0.0406392i | 0.999794 | + | 0.0203196i | \(0.00646837\pi\) | ||||
−0.999794 | + | 0.0203196i | \(0.993532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.85778i | − | 0.526900i | ||||||
\(86\) | 0.837406 | − | 9.92018i | 0.0902999 | − | 1.06972i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.34658 | − | 9.08960i | 0.250146 | − | 0.968954i | ||||
\(89\) | −4.85047 | −0.514149 | −0.257075 | − | 0.966392i | \(-0.582759\pi\) | ||||
−0.257075 | + | 0.966392i | \(0.582759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.10840i | 0.325849i | ||||||||
\(92\) | −17.3502 | − | 2.95023i | −1.80888 | − | 0.307583i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.9121 | + | 1.34321i | 1.64121 | + | 0.138542i | ||||
\(95\) | 16.6457 | 1.70782 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.63283 | 0.165789 | 0.0828946 | − | 0.996558i | \(-0.473584\pi\) | ||||
0.0828946 | + | 0.996558i | \(0.473584\pi\) | |||||||
\(98\) | −1.40920 | − | 0.118957i | −0.142351 | − | 0.0120165i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.7869 | − | 2.34433i | −1.37869 | − | 0.234433i | ||||
\(101\) | 13.1650i | 1.30997i | 0.755643 | + | 0.654983i | \(0.227324\pi\) | ||||
−0.755643 | + | 0.654983i | \(0.772676\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.6983 | 1.54680 | 0.773399 | − | 0.633920i | \(-0.218555\pi\) | ||||
0.773399 | + | 0.633920i | \(0.218555\pi\) | |||||||
\(104\) | 2.19767 | − | 8.51280i | 0.215499 | − | 0.834748i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.775190 | + | 9.18314i | −0.0752931 | + | 0.891945i | ||||
\(107\) | 9.37257i | 0.906081i | 0.891490 | + | 0.453040i | \(0.149661\pi\) | ||||
−0.891490 | + | 0.453040i | \(0.850339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.31490i | − | 0.700640i | −0.936630 | − | 0.350320i | \(-0.886073\pi\) | ||
0.936630 | − | 0.350320i | \(-0.113927\pi\) | |||||||
\(110\) | −16.1970 | − | 1.36727i | −1.54433 | − | 0.130364i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.77519 | + | 1.32210i | 0.356722 | + | 0.124927i | ||||
\(113\) | −10.9153 | −1.02683 | −0.513414 | − | 0.858141i | \(-0.671620\pi\) | ||||
−0.513414 | + | 0.858141i | \(0.671620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.4730i | 2.84162i | ||||||||
\(116\) | −3.31043 | + | 19.4685i | −0.307366 | + | 1.80760i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.463521 | − | 5.49102i | 0.0426706 | − | 0.505489i | ||||
\(119\) | 1.40277 | 0.128591 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0159016 | −0.00144560 | ||||||||
\(122\) | −1.12097 | + | 13.2794i | −0.101488 | + | 1.20226i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.4494 | − | 2.62702i | −1.38740 | − | 0.235914i | ||||
\(125\) | 6.89962i | 0.617121i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.37545 | 0.299523 | 0.149761 | − | 0.988722i | \(-0.452149\pi\) | ||||
0.149761 | + | 0.988722i | \(0.452149\pi\) | |||||||
\(128\) | −9.40414 | − | 6.28984i | −0.831217 | − | 0.555949i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −15.1692 | − | 1.28050i | −1.33043 | − | 0.112307i | ||||
\(131\) | 7.15460i | 0.625100i | 0.949901 | + | 0.312550i | \(0.101183\pi\) | ||||
−0.949901 | + | 0.312550i | \(0.898817\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.80674i | 0.416797i | ||||||||
\(134\) | −0.108217 | + | 1.28197i | −0.00934850 | + | 0.110745i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.84167 | − | 0.991767i | −0.329420 | − | 0.0850434i | ||||
\(137\) | −4.22854 | −0.361269 | −0.180634 | − | 0.983550i | \(-0.557815\pi\) | ||||
−0.180634 | + | 0.983550i | \(0.557815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31473i | 0.281152i | 0.990070 | + | 0.140576i | \(0.0448954\pi\) | ||||
−0.990070 | + | 0.140576i | \(0.955105\pi\) | |||||||
\(140\) | 1.16104 | − | 6.82800i | 0.0981255 | − | 0.577071i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.05150 | − | 0.764077i | −0.759585 | − | 0.0641199i | ||||
\(143\) | −10.3169 | −0.862739 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.1936 | 2.83962 | ||||||||
\(146\) | −2.20197 | − | 0.185878i | −0.182236 | − | 0.0153834i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.81822 | + | 10.6929i | −0.149457 | + | 0.878948i | ||||
\(149\) | 7.08433i | 0.580371i | 0.956970 | + | 0.290185i | \(0.0937169\pi\) | ||||
−0.956970 | + | 0.290185i | \(0.906283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.252443 | 0.0205436 | 0.0102718 | − | 0.999947i | \(-0.496730\pi\) | ||||
0.0102718 | + | 0.999947i | \(0.496730\pi\) | |||||||
\(152\) | 3.39841 | − | 13.1639i | 0.275647 | − | 1.06773i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.394821 | − | 4.67717i | 0.0318156 | − | 0.376897i | ||||
\(155\) | 27.1346i | 2.17950i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.11021i | 0.248222i | 0.992268 | + | 0.124111i | \(0.0396078\pi\) | ||||
−0.992268 | + | 0.124111i | \(0.960392\pi\) | |||||||
\(158\) | 15.7294 | + | 1.32779i | 1.25136 | + | 0.105633i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.00711 | + | 17.8785i | −0.633018 | + | 1.41342i | ||||
\(161\) | −8.79960 | −0.693505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 18.5595i | − | 1.45369i | −0.686800 | − | 0.726847i | \(-0.740985\pi\) | ||
0.686800 | − | 0.726847i | \(-0.259015\pi\) | |||||||
\(164\) | 22.8145 | + | 3.87939i | 1.78151 | + | 0.302930i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0440427 | − | 0.521744i | 0.00341838 | − | 0.0404952i | ||||
\(167\) | 14.3221 | 1.10828 | 0.554140 | − | 0.832424i | \(-0.313047\pi\) | ||||
0.554140 | + | 0.832424i | \(0.313047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.33782 | 0.256755 | ||||||||
\(170\) | −0.577867 | + | 6.84559i | −0.0443204 | + | 0.525033i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.36015 | + | 13.8799i | −0.179960 | + | 1.05833i | ||||
\(173\) | − | 1.40183i | − | 0.106579i | −0.998579 | − | 0.0532896i | \(-0.983029\pi\) | ||
0.998579 | − | 0.0532896i | \(-0.0169707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.99238 | −0.528574 | ||||||||
\(176\) | −4.38807 | + | 12.5299i | −0.330763 | + | 0.944479i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.83530 | + | 0.576998i | 0.512327 | + | 0.0432478i | ||||
\(179\) | − | 3.46849i | − | 0.259247i | −0.991563 | − | 0.129624i | \(-0.958623\pi\) | ||
0.991563 | − | 0.129624i | \(-0.0413769\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.3992i | − | 1.44193i | −0.692972 | − | 0.720965i | \(-0.743699\pi\) | ||
0.692972 | − | 0.720965i | \(-0.256301\pi\) | |||||||
\(182\) | 0.369766 | − | 4.38037i | 0.0274089 | − | 0.324695i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.0989 | + | 6.22139i | 1.77660 | + | 0.458647i | ||||
\(185\) | 18.7805 | 1.38077 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.65581i | 0.340466i | ||||||||
\(188\) | −22.2636 | − | 3.78571i | −1.62374 | − | 0.276101i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.4572 | − | 1.98013i | −1.70176 | − | 0.143654i | ||||
\(191\) | −23.4610 | −1.69758 | −0.848790 | − | 0.528729i | \(-0.822669\pi\) | ||||
−0.848790 | + | 0.528729i | \(0.822669\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.5374 | −1.11840 | −0.559202 | − | 0.829031i | \(-0.688893\pi\) | ||||
−0.559202 | + | 0.829031i | \(0.688893\pi\) | |||||||
\(194\) | −2.30099 | − | 0.194237i | −0.165202 | − | 0.0139454i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.97170 | + | 0.335269i | 0.140836 | + | 0.0239478i | ||||
\(197\) | 14.8278i | 1.05643i | 0.849109 | + | 0.528217i | \(0.177139\pi\) | ||||
−0.849109 | + | 0.528217i | \(0.822861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2095 | 0.936397 | 0.468199 | − | 0.883623i | \(-0.344903\pi\) | ||||
0.468199 | + | 0.883623i | \(0.344903\pi\) | |||||||
\(200\) | 19.1496 | + | 4.94367i | 1.35408 | + | 0.349571i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.56607 | − | 18.5521i | 0.110188 | − | 1.30532i | ||||
\(203\) | 9.87397i | 0.693017i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 40.0703i | − | 2.79863i | ||||||
\(206\) | −22.1220 | − | 1.86742i | −1.54132 | − | 0.130109i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.10962 | + | 11.7348i | −0.284951 | + | 0.813663i | ||||
\(209\) | −15.9537 | −1.10354 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3790i | 0.852206i | 0.904675 | + | 0.426103i | \(0.140114\pi\) | ||||
−0.904675 | + | 0.426103i | \(0.859886\pi\) | |||||||
\(212\) | 2.18480 | − | 12.8487i | 0.150052 | − | 0.882451i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.11493 | − | 13.2078i | 0.0762153 | − | 0.902870i | ||||
\(215\) | 24.3781 | 1.66257 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.83557 | −0.531913 | ||||||||
\(218\) | −0.870158 | + | 10.3082i | −0.0589345 | + | 0.698157i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.6623 | + | 3.85350i | 1.52789 | + | 0.259803i | ||||
\(221\) | 4.36036i | 0.293310i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.91170 | 0.194982 | 0.0974910 | − | 0.995236i | \(-0.468918\pi\) | ||||
0.0974910 | + | 0.995236i | \(0.468918\pi\) | |||||||
\(224\) | −5.16273 | − | 2.31219i | −0.344949 | − | 0.154490i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.3819 | + | 1.29846i | 1.02319 | + | 0.0863720i | ||||
\(227\) | 11.3550i | 0.753658i | 0.926283 | + | 0.376829i | \(0.122986\pi\) | ||||
−0.926283 | + | 0.376829i | \(0.877014\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4776i | 1.15495i | 0.816407 | + | 0.577477i | \(0.195963\pi\) | ||||
−0.816407 | + | 0.577477i | \(0.804037\pi\) | |||||||
\(230\) | 3.62498 | − | 42.9426i | 0.239024 | − | 2.83155i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.98098 | − | 27.0412i | 0.458324 | − | 1.77534i | ||||
\(233\) | −1.98827 | −0.130256 | −0.0651279 | − | 0.997877i | \(-0.520746\pi\) | ||||
−0.0651279 | + | 0.997877i | \(0.520746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.1027i | 2.55078i | ||||||||
\(236\) | −1.30639 | + | 7.68281i | −0.0850387 | + | 0.500108i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.97678 | − | 0.166869i | −0.128136 | − | 0.0108165i | ||||
\(239\) | 21.3430 | 1.38056 | 0.690282 | − | 0.723540i | \(-0.257486\pi\) | ||||
0.690282 | + | 0.723540i | \(0.257486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3714 | −0.861330 | −0.430665 | − | 0.902512i | \(-0.641721\pi\) | ||||
−0.430665 | + | 0.902512i | \(0.641721\pi\) | |||||||
\(242\) | 0.0224085 | + | 0.00189160i | 0.00144047 | + | 0.000121597i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.15935 | − | 18.5800i | 0.202257 | − | 1.18946i | ||||
\(245\) | − | 3.46300i | − | 0.221243i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9413 | −0.950691 | ||||||||
\(248\) | 21.4588 | + | 5.53982i | 1.36264 | + | 0.351779i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.820758 | − | 9.72296i | 0.0519093 | − | 0.614934i | ||||
\(251\) | − | 1.92814i | − | 0.121703i | −0.998147 | − | 0.0608514i | \(-0.980618\pi\) | ||
0.998147 | − | 0.0608514i | \(-0.0193816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 29.2060i | − | 1.83617i | ||||||
\(254\) | −4.75669 | − | 0.401533i | −0.298461 | − | 0.0251944i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.5041 | + | 9.98234i | 0.781507 | + | 0.623896i | ||||
\(257\) | 5.22415 | 0.325873 | 0.162937 | − | 0.986637i | \(-0.447903\pi\) | ||||
0.162937 | + | 0.986637i | \(0.447903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.42317i | 0.336980i | ||||||||
\(260\) | 21.2242 | + | 3.60897i | 1.31627 | + | 0.223819i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.851089 | − | 10.0823i | 0.0525805 | − | 0.622885i | ||||
\(263\) | 4.69624 | 0.289583 | 0.144791 | − | 0.989462i | \(-0.453749\pi\) | ||||
0.144791 | + | 0.989462i | \(0.453749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5668 | −1.38627 | ||||||||
\(266\) | 0.571795 | − | 6.77366i | 0.0350590 | − | 0.415320i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.304998 | − | 1.79368i | 0.0186307 | − | 0.109566i | ||||
\(269\) | 26.9906i | 1.64565i | 0.568297 | + | 0.822824i | \(0.307603\pi\) | ||||
−0.568297 | + | 0.822824i | \(0.692397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.75175 | 0.167157 | 0.0835784 | − | 0.996501i | \(-0.473365\pi\) | ||||
0.0835784 | + | 0.996501i | \(0.473365\pi\) | |||||||
\(272\) | 5.29571 | + | 1.85459i | 0.321099 | + | 0.112451i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.95887 | + | 0.503015i | 0.359988 | + | 0.0303882i | ||||
\(275\) | − | 23.2079i | − | 1.39949i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.0526i | − | 0.724173i | −0.932145 | − | 0.362086i | \(-0.882065\pi\) | ||
0.932145 | − | 0.362086i | \(-0.117935\pi\) | |||||||
\(278\) | 0.394311 | − | 4.67113i | 0.0236492 | − | 0.280156i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.44837 | + | 9.48391i | −0.146318 | + | 0.566772i | ||||
\(281\) | 6.74449 | 0.402342 | 0.201171 | − | 0.979556i | \(-0.435525\pi\) | ||||
0.201171 | + | 0.979556i | \(0.435525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.53083i | − | 0.507105i | −0.967322 | − | 0.253552i | \(-0.918401\pi\) | ||
0.967322 | − | 0.253552i | \(-0.0815991\pi\) | |||||||
\(284\) | 12.6645 | + | 2.15348i | 0.751499 | + | 0.127785i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.5385 | + | 1.22726i | 0.859682 | + | 0.0725696i | ||||
\(287\) | 11.5710 | 0.683014 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0322 | −0.884250 | ||||||||
\(290\) | −48.1856 | − | 4.06756i | −2.82956 | − | 0.238856i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.08091 | + | 0.523879i | 0.180296 | + | 0.0306577i | ||||
\(293\) | 11.2926i | 0.659718i | 0.944030 | + | 0.329859i | \(0.107001\pi\) | ||||
−0.944030 | + | 0.329859i | \(0.892999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.4937 | 0.785636 | ||||||||
\(296\) | 3.83423 | − | 14.8521i | 0.222860 | − | 0.863261i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.842730 | − | 9.98324i | 0.0488180 | − | 0.578314i | ||||
\(299\) | − | 27.3527i | − | 1.58185i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.03957i | 0.405754i | ||||||||
\(302\) | −0.355744 | − | 0.0300299i | −0.0204708 | − | 0.00172803i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.35498 | + | 18.1463i | −0.364483 | + | 1.04076i | ||||
\(305\) | −32.6330 | −1.86856 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.15810i | − | 0.522680i | −0.965247 | − | 0.261340i | \(-0.915836\pi\) | ||
0.965247 | − | 0.261340i | \(-0.0841644\pi\) | |||||||
\(308\) | −1.11276 | + | 6.54411i | −0.0634056 | + | 0.372885i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.22785 | − | 38.2381i | 0.183330 | − | 2.17178i | ||||
\(311\) | −10.0122 | −0.567741 | −0.283870 | − | 0.958863i | \(-0.591619\pi\) | ||||
−0.283870 | + | 0.958863i | \(0.591619\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.3334 | −0.584076 | −0.292038 | − | 0.956407i | \(-0.594333\pi\) | ||||
−0.292038 | + | 0.956407i | \(0.594333\pi\) | |||||||
\(314\) | 0.369981 | − | 4.38291i | 0.0208792 | − | 0.247342i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.0080 | − | 3.74225i | −1.23804 | − | 0.210518i | ||||
\(317\) | − | 34.9339i | − | 1.96208i | −0.193794 | − | 0.981042i | \(-0.562079\pi\) | ||
0.193794 | − | 0.981042i | \(-0.437921\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.7719 | −1.83487 | ||||||||
\(320\) | 13.4104 | − | 24.2420i | 0.749665 | − | 1.35517i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.4004 | + | 1.04677i | 0.691048 | + | 0.0583344i | ||||
\(323\) | 6.74273i | 0.375175i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 21.7352i | − | 1.20565i | ||||||
\(326\) | −2.20778 | + | 26.1541i | −0.122278 | + | 1.44854i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −31.6887 | − | 8.18079i | −1.74972 | − | 0.451708i | ||||
\(329\) | −11.2916 | −0.622524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.71488i | 0.479013i | 0.970895 | + | 0.239507i | \(0.0769857\pi\) | ||||
−0.970895 | + | 0.239507i | \(0.923014\pi\) | |||||||
\(332\) | −0.124130 | + | 0.730003i | −0.00681252 | + | 0.0400641i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.1828 | − | 1.70372i | −1.10435 | − | 0.0932233i | ||||
\(335\) | −3.15034 | −0.172121 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.63703 | −0.470489 | −0.235244 | − | 0.971936i | \(-0.575589\pi\) | ||||
−0.235244 | + | 0.971936i | \(0.575589\pi\) | |||||||
\(338\) | −4.70366 | − | 0.397057i | −0.255846 | − | 0.0215971i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.62866 | − | 9.57808i | 0.0883266 | − | 0.519444i | ||||
\(341\) | − | 26.0064i | − | 1.40833i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.97704 | − | 19.2788i | 0.268344 | − | 1.03945i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.166758 | + | 1.97546i | −0.00896495 | + | 0.106202i | ||||
\(347\) | − | 28.2190i | − | 1.51488i | −0.652907 | − | 0.757438i | \(-0.726451\pi\) | ||
0.652907 | − | 0.757438i | \(-0.273549\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6266i | 0.729416i | 0.931122 | + | 0.364708i | \(0.118831\pi\) | ||||
−0.931122 | + | 0.364708i | \(0.881169\pi\) | |||||||
\(350\) | 9.85368 | + | 0.831793i | 0.526701 | + | 0.0444612i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.67420 | − | 17.1352i | 0.409036 | − | 0.913310i | ||||
\(353\) | 32.4282 | 1.72598 | 0.862990 | − | 0.505220i | \(-0.168589\pi\) | ||||
0.862990 | + | 0.505220i | \(0.168589\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 22.2433i | − | 1.18055i | ||||||
\(356\) | −9.56367 | − | 1.62621i | −0.506874 | − | 0.0861891i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.412602 | + | 4.88781i | −0.0218067 | + | 0.258329i | ||||
\(359\) | 12.9995 | 0.686087 | 0.343044 | − | 0.939319i | \(-0.388542\pi\) | ||||
0.343044 | + | 0.939319i | \(0.388542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.10474 | −0.216039 | ||||||||
\(362\) | −2.30767 | + | 27.3374i | −0.121288 | + | 1.43682i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.04215 | + | 6.12884i | −0.0546236 | + | 0.321238i | ||||
\(365\) | − | 5.41117i | − | 0.283233i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.55576 | −0.394408 | −0.197204 | − | 0.980363i | \(-0.563186\pi\) | ||||
−0.197204 | + | 0.980363i | \(0.563186\pi\) | |||||||
\(368\) | −33.2201 | − | 11.6339i | −1.73172 | − | 0.606460i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −26.4654 | − | 2.23407i | −1.37587 | − | 0.116144i | ||||
\(371\) | − | 6.51655i | − | 0.338323i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 34.6651i | − | 1.79489i | −0.441124 | − | 0.897446i | \(-0.645420\pi\) | ||
0.441124 | − | 0.897446i | \(-0.354580\pi\) | |||||||
\(374\) | 0.553841 | − | 6.56097i | 0.0286384 | − | 0.339260i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.9235 | + | 7.98324i | 1.59476 | + | 0.411704i | ||||
\(377\) | −30.6923 | −1.58073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.308373i | 0.0158401i | 0.999969 | + | 0.00792004i | \(0.00252105\pi\) | ||||
−0.999969 | + | 0.00792004i | \(0.997479\pi\) | |||||||
\(380\) | 32.8204 | + | 5.58080i | 1.68365 | + | 0.286289i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 33.0613 | + | 2.79085i | 1.69156 | + | 0.142793i | ||||
\(383\) | −4.36024 | −0.222798 | −0.111399 | − | 0.993776i | \(-0.535533\pi\) | ||||
−0.111399 | + | 0.993776i | \(0.535533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.4938 | 0.585777 | ||||||||
\(386\) | 21.8953 | + | 1.84828i | 1.11444 | + | 0.0940750i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.21946 | + | 0.547439i | 0.163443 | + | 0.0277920i | ||||
\(389\) | − | 1.33391i | − | 0.0676317i | −0.999428 | − | 0.0338159i | \(-0.989234\pi\) | ||
0.999428 | − | 0.0338159i | \(-0.0107660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3438 | −0.624251 | ||||||||
\(392\) | −2.73864 | − | 0.707009i | −0.138322 | − | 0.0357093i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.76387 | − | 20.8953i | 0.0888623 | − | 1.05269i | ||||
\(395\) | 38.6538i | 1.94488i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.92952i | 0.347783i | 0.984765 | + | 0.173891i | \(0.0556342\pi\) | ||||
−0.984765 | + | 0.173891i | \(0.944366\pi\) | |||||||
\(398\) | −18.6149 | − | 1.57136i | −0.933079 | − | 0.0787653i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.3976 | − | 9.24461i | −1.31988 | − | 0.462231i | ||||
\(401\) | 23.9669 | 1.19685 | 0.598426 | − | 0.801178i | \(-0.295793\pi\) | ||||
0.598426 | + | 0.801178i | \(0.295793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 24.3561i | − | 1.21327i | ||||||
\(404\) | −4.41382 | + | 25.9574i | −0.219596 | + | 1.29143i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.17458 | − | 13.9144i | 0.0582933 | − | 0.690561i | ||||
\(407\) | −17.9996 | −0.892208 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6936 | 1.07268 | 0.536340 | − | 0.844002i | \(-0.319807\pi\) | ||||
0.536340 | + | 0.844002i | \(0.319807\pi\) | |||||||
\(410\) | −4.76665 | + | 56.4672i | −0.235408 | + | 2.78872i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.9523 | + | 5.26314i | 1.52491 | + | 0.259296i | ||||
\(413\) | 3.89654i | 0.191736i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.28214 | 0.0629380 | ||||||||
\(416\) | 7.18722 | − | 16.0479i | 0.352382 | − | 0.786811i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.4819 | + | 1.89780i | 1.09963 | + | 0.0928245i | ||||
\(419\) | 27.5910i | 1.34791i | 0.738772 | + | 0.673955i | \(0.235406\pi\) | ||||
−0.738772 | + | 0.673955i | \(0.764594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 38.3335i | − | 1.86826i | −0.356929 | − | 0.934131i | \(-0.616176\pi\) | ||
0.356929 | − | 0.934131i | \(-0.383824\pi\) | |||||||
\(422\) | 1.47257 | − | 17.4445i | 0.0716836 | − | 0.849186i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.60726 | + | 17.8465i | −0.223748 | + | 0.866702i | ||||
\(425\) | −9.80867 | −0.475790 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.42334i | − | 0.456027i | ||||||
\(428\) | −3.14233 | + | 18.4799i | −0.151890 | + | 0.893259i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −34.3536 | − | 2.89994i | −1.65668 | − | 0.139848i | ||||
\(431\) | −2.22510 | −0.107179 | −0.0535896 | − | 0.998563i | \(-0.517066\pi\) | ||||
−0.0535896 | + | 0.998563i | \(0.517066\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2235 | 1.35633 | 0.678167 | − | 0.734908i | \(-0.262775\pi\) | ||||
0.678167 | + | 0.734908i | \(0.262775\pi\) | |||||||
\(434\) | 11.0419 | + | 0.932096i | 0.530028 | + | 0.0447421i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.45246 | − | 14.4228i | 0.117451 | − | 0.690725i | ||||
\(437\) | − | 42.2974i | − | 2.02336i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.63936 | −0.269152 | −0.134576 | − | 0.990903i | \(-0.542967\pi\) | ||||
−0.134576 | + | 0.990903i | \(0.542967\pi\) | |||||||
\(440\) | −31.4773 | − | 8.12620i | −1.50062 | − | 0.387401i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.518696 | − | 6.14463i | 0.0246718 | − | 0.292270i | ||||
\(443\) | − | 5.81672i | − | 0.276361i | −0.990407 | − | 0.138180i | \(-0.955875\pi\) | ||
0.990407 | − | 0.138180i | \(-0.0441254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.7972i | 0.796264i | ||||||||
\(446\) | −4.10318 | − | 0.346367i | −0.194291 | − | 0.0164010i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.00028 | + | 3.87248i | 0.330732 | + | 0.182958i | ||||
\(449\) | 1.66921 | 0.0787748 | 0.0393874 | − | 0.999224i | \(-0.487459\pi\) | ||||
0.0393874 | + | 0.999224i | \(0.487459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.4043i | 1.80839i | ||||||||
\(452\) | −21.5218 | − | 3.65957i | −1.01230 | − | 0.172132i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.35076 | − | 16.0015i | 0.0633942 | − | 0.750987i | ||||
\(455\) | 10.7644 | 0.504643 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4606 | −0.769994 | −0.384997 | − | 0.922918i | \(-0.625797\pi\) | ||||
−0.384997 | + | 0.922918i | \(0.625797\pi\) | |||||||
\(458\) | 2.07908 | − | 24.6295i | 0.0971493 | − | 1.15086i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.2167 | + | 60.0836i | −0.476354 | + | 2.80141i | ||||
\(461\) | − | 22.7915i | − | 1.06151i | −0.847527 | − | 0.530753i | \(-0.821909\pi\) | ||
0.847527 | − | 0.530753i | \(-0.178091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.3165 | −0.758293 | −0.379146 | − | 0.925337i | \(-0.623782\pi\) | ||||
−0.379146 | + | 0.925337i | \(0.623782\pi\) | |||||||
\(464\) | −13.0544 | + | 37.2761i | −0.606033 | + | 1.73050i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.80187 | + | 0.236518i | 0.129794 | + | 0.0109565i | ||||
\(467\) | − | 33.3073i | − | 1.54128i | −0.637271 | − | 0.770639i | \(-0.719937\pi\) | ||
0.637271 | − | 0.770639i | \(-0.280063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.909712i | − | 0.0420066i | ||||||
\(470\) | 4.65154 | − | 55.1036i | 0.214560 | − | 2.54174i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.75489 | − | 10.6712i | 0.126804 | − | 0.491183i | ||||
\(473\) | −23.3645 | −1.07430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 33.6105i | − | 1.54216i | ||||||
\(476\) | 2.76583 | + | 0.470304i | 0.126772 | + | 0.0215563i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.0766 | − | 2.53890i | −1.37567 | − | 0.116127i | ||||
\(479\) | −28.5717 | −1.30547 | −0.652737 | − | 0.757584i | \(-0.726379\pi\) | ||||
−0.652737 | + | 0.757584i | \(0.726379\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.8574 | −0.768632 | ||||||||
\(482\) | 18.8430 | + | 1.59063i | 0.858277 | + | 0.0724510i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.0313531 | − | 0.00533130i | −0.00142514 | − | 0.000242332i | ||||
\(485\) | − | 5.65451i | − | 0.256758i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0149 | 1.76793 | 0.883967 | − | 0.467550i | \(-0.154863\pi\) | ||||
0.883967 | + | 0.467550i | \(0.154863\pi\) | |||||||
\(488\) | −6.66238 | + | 25.8071i | −0.301592 | + | 1.16823i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.411948 | + | 4.88007i | −0.0186099 | + | 0.220459i | ||||
\(491\) | − | 12.5799i | − | 0.567722i | −0.958866 | − | 0.283861i | \(-0.908385\pi\) | ||
0.958866 | − | 0.283861i | \(-0.0916153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8509i | 0.623811i | ||||||||
\(494\) | 21.0553 | + | 1.77737i | 0.947322 | + | 0.0799677i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.5808 | − | 10.3594i | −1.32822 | − | 0.465151i | ||||
\(497\) | 6.42314 | 0.288117 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3054i | 0.774697i | 0.921933 | + | 0.387349i | \(0.126609\pi\) | ||||
−0.921933 | + | 0.387349i | \(0.873391\pi\) | |||||||
\(500\) | −2.31323 | + | 13.6040i | −0.103451 | + | 0.608388i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.229365 | + | 2.71713i | −0.0102371 | + | 0.121272i | ||||
\(503\) | −18.1289 | −0.808326 | −0.404163 | − | 0.914687i | \(-0.632437\pi\) | ||||
−0.404163 | + | 0.914687i | \(0.632437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.5904 | 2.02875 | ||||||||
\(506\) | −3.47426 | + | 41.1572i | −0.154450 | + | 1.82966i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.65537 | + | 1.13168i | 0.295284 | + | 0.0502103i | ||||
\(509\) | 17.3445i | 0.768780i | 0.923171 | + | 0.384390i | \(0.125588\pi\) | ||||
−0.923171 | + | 0.384390i | \(0.874412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.56257 | 0.0691238 | ||||||||
\(512\) | −16.4333 | − | 15.5546i | −0.726258 | − | 0.687422i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.36188 | − | 0.621449i | −0.324719 | − | 0.0274109i | ||||
\(515\) | − | 54.3632i | − | 2.39553i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 37.4770i | − | 1.64823i | ||||||
\(518\) | 0.645124 | − | 7.64234i | 0.0283451 | − | 0.335785i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −29.4798 | − | 7.61053i | −1.29278 | − | 0.333744i | ||||
\(521\) | 16.7507 | 0.733861 | 0.366930 | − | 0.930248i | \(-0.380409\pi\) | ||||
0.366930 | + | 0.930248i | \(0.380409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8692i | 0.912545i | 0.889840 | + | 0.456273i | \(0.150816\pi\) | ||||
−0.889840 | + | 0.456273i | \(0.849184\pi\) | |||||||
\(524\) | −2.39871 | + | 14.1067i | −0.104788 | + | 0.616254i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.61795 | − | 0.558651i | −0.288556 | − | 0.0243583i | ||||
\(527\) | −10.9915 | −0.478796 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.4329 | 2.36665 | ||||||||
\(530\) | 31.8012 | + | 2.68448i | 1.38136 | + | 0.116606i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.61155 | + | 9.47744i | −0.0698695 | + | 0.410899i | ||||
\(533\) | 35.9673i | 1.55792i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.4572 | 1.40325 | ||||||||
\(536\) | −0.643175 | + | 2.49137i | −0.0277809 | + | 0.107611i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.21072 | − | 38.0352i | 0.138424 | − | 1.63982i | ||||
\(539\) | 3.31902i | 0.142960i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.7498i | 1.62299i | 0.584359 | + | 0.811495i | \(0.301346\pi\) | ||||
−0.584359 | + | 0.811495i | \(0.698654\pi\) | |||||||
\(542\) | −3.87777 | − | 0.327340i | −0.166564 | − | 0.0140604i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.24210 | − | 3.24346i | −0.310503 | − | 0.139062i | ||||
\(545\) | −25.3315 | −1.08508 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.4520i | 1.47306i | 0.676404 | + | 0.736531i | \(0.263537\pi\) | ||||
−0.676404 | + | 0.736531i | \(0.736463\pi\) | |||||||
\(548\) | −8.33741 | − | 1.41770i | −0.356156 | − | 0.0605611i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.76074 | + | 32.7046i | −0.117718 | + | 1.39453i | ||||
\(551\) | −47.4616 | −2.02193 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1619 | −0.474653 | ||||||||
\(554\) | −1.43375 | + | 16.9846i | −0.0609140 | + | 0.721606i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.11133 | + | 6.53566i | −0.0471308 | + | 0.277174i | ||||
\(557\) | − | 27.7136i | − | 1.17426i | −0.809491 | − | 0.587132i | \(-0.800257\pi\) | ||
0.809491 | − | 0.587132i | \(-0.199743\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.8818 | −0.925503 | ||||||||
\(560\) | 4.57843 | − | 13.0735i | 0.193474 | − | 0.552456i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.50434 | − | 0.802304i | −0.400917 | − | 0.0338432i | ||||
\(563\) | − | 0.570384i | − | 0.0240388i | −0.999928 | − | 0.0120194i | \(-0.996174\pi\) | ||
0.999928 | − | 0.0120194i | \(-0.00382599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.7998i | 1.59025i | ||||||||
\(566\) | −1.01480 | + | 12.0217i | −0.0426553 | + | 0.505308i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.5907 | − | 4.54121i | −0.738087 | − | 0.190545i | ||||
\(569\) | 18.4090 | 0.771745 | 0.385872 | − | 0.922552i | \(-0.373901\pi\) | ||||
0.385872 | + | 0.922552i | \(0.373901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.3534i | 1.81428i | 0.420824 | + | 0.907142i | \(0.361741\pi\) | ||||
−0.420824 | + | 0.907142i | \(0.638259\pi\) | |||||||
\(572\) | −20.3417 | − | 3.45892i | −0.850531 | − | 0.144625i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.3059 | − | 1.37645i | −0.680593 | − | 0.0574519i | ||||
\(575\) | 61.5301 | 2.56598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.6209 | −1.64944 | −0.824720 | − | 0.565541i | \(-0.808667\pi\) | ||||
−0.824720 | + | 0.565541i | \(0.808667\pi\) | |||||||
\(578\) | 21.1835 | + | 1.78819i | 0.881116 | + | 0.0743790i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 67.4194 | + | 11.4640i | 2.79944 | + | 0.476018i | ||||
\(581\) | 0.370241i | 0.0153602i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.6286 | 0.895764 | ||||||||
\(584\) | −4.27930 | − | 1.10475i | −0.177079 | − | 0.0457148i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.34333 | − | 15.9135i | 0.0554924 | − | 0.657380i | ||||
\(587\) | 13.4388i | 0.554677i | 0.960772 | + | 0.277338i | \(0.0894523\pi\) | ||||
−0.960772 | + | 0.277338i | \(0.910548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 37.6636i | − | 1.55190i | ||||||
\(590\) | −19.0154 | − | 1.60518i | −0.782852 | − | 0.0660840i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.16997 | + | 20.4735i | −0.294684 | + | 0.841456i | ||||
\(593\) | 22.3157 | 0.916395 | 0.458198 | − | 0.888850i | \(-0.348495\pi\) | ||||
0.458198 | + | 0.888850i | \(0.348495\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 4.85778i | − | 0.199150i | ||||||
\(596\) | −2.37515 | + | 13.9682i | −0.0972901 | + | 0.572158i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.25380 | + | 38.5455i | −0.133058 | + | 1.57624i | ||||
\(599\) | −14.2622 | −0.582740 | −0.291370 | − | 0.956610i | \(-0.594111\pi\) | ||||
−0.291370 | + | 0.956610i | \(0.594111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.40215 | −0.0979858 | −0.0489929 | − | 0.998799i | \(-0.515601\pi\) | ||||
−0.0489929 | + | 0.998799i | \(0.515601\pi\) | |||||||
\(602\) | 0.837406 | − | 9.92018i | 0.0341301 | − | 0.404316i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.497742 | + | 0.0846364i | 0.0202529 | + | 0.00344381i | ||||
\(605\) | 0.0550671i | 0.00223880i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0506 | −0.407940 | −0.203970 | − | 0.978977i | \(-0.565385\pi\) | ||||
−0.203970 | + | 0.978977i | \(0.565385\pi\) | |||||||
\(608\) | 11.1141 | − | 24.8159i | 0.450736 | − | 1.00642i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 45.9865 | + | 3.88193i | 1.86194 | + | 0.157175i | ||||
\(611\) | − | 35.0988i | − | 1.41994i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.57394i | − | 0.103961i | −0.998648 | − | 0.0519803i | \(-0.983447\pi\) | ||
0.998648 | − | 0.0519803i | \(-0.0165533\pi\) | |||||||
\(614\) | −1.08942 | + | 12.9056i | −0.0439654 | + | 0.520828i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.34658 | − | 9.08960i | 0.0945463 | − | 0.366230i | ||||
\(617\) | −36.3495 | −1.46337 | −0.731687 | − | 0.681640i | \(-0.761267\pi\) | ||||
−0.731687 | + | 0.681640i | \(0.761267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16.6498i | − | 0.669211i | −0.942358 | − | 0.334606i | \(-0.891397\pi\) | ||
0.942358 | − | 0.334606i | \(-0.108603\pi\) | |||||||
\(620\) | −9.09739 | + | 53.5013i | −0.365360 | + | 2.14866i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.1092 | + | 1.19102i | 0.565729 | + | 0.0477557i | ||||
\(623\) | −4.85047 | −0.194330 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0685 | −0.442740 | ||||||||
\(626\) | 14.5618 | + | 1.22923i | 0.582006 | + | 0.0491297i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.04276 | + | 6.13240i | −0.0416105 | + | 0.244709i | ||||
\(629\) | 7.60744i | 0.303328i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.7898 | 0.588773 | 0.294387 | − | 0.955686i | \(-0.404885\pi\) | ||||
0.294387 | + | 0.955686i | \(0.404885\pi\) | |||||||
\(632\) | 30.5685 | + | 7.89158i | 1.21595 | + | 0.313910i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.15563 | + | 49.2289i | −0.165041 | + | 1.95513i | ||||
\(635\) | − | 11.6892i | − | 0.463871i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.10840i | 0.123159i | ||||||||
\(638\) | 46.1822 | + | 3.89845i | 1.82837 | + | 0.154341i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.7817 | + | 32.5666i | −0.860998 | + | 1.28731i | ||||
\(641\) | 32.8085 | 1.29586 | 0.647928 | − | 0.761701i | \(-0.275636\pi\) | ||||
0.647928 | + | 0.761701i | \(0.275636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.3479i | 0.605263i | 0.953108 | + | 0.302631i | \(0.0978651\pi\) | ||||
−0.953108 | + | 0.302631i | \(0.902135\pi\) | |||||||
\(644\) | −17.3502 | − | 2.95023i | −0.683692 | − | 0.116255i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.802095 | − | 9.50186i | 0.0315580 | − | 0.373846i | ||||
\(647\) | −6.19107 | −0.243396 | −0.121698 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121698 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9327 | −0.507653 | ||||||||
\(650\) | −2.58555 | + | 30.6292i | −0.101414 | + | 1.20138i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.22243 | − | 36.5938i | 0.243689 | − | 1.43312i | ||||
\(653\) | 17.4848i | 0.684234i | 0.939657 | + | 0.342117i | \(0.111144\pi\) | ||||
−0.939657 | + | 0.342117i | \(0.888856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.7764 | 0.968093 | ||||||||
\(656\) | 43.6827 | + | 15.2980i | 1.70552 | + | 0.597286i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.9121 | + | 1.34321i | 0.620318 | + | 0.0523638i | ||||
\(659\) | 13.8987i | 0.541416i | 0.962661 | + | 0.270708i | \(0.0872578\pi\) | ||||
−0.962661 | + | 0.270708i | \(0.912742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.69978i | − | 0.0661137i | −0.999453 | − | 0.0330568i | \(-0.989476\pi\) | ||
0.999453 | − | 0.0330568i | \(-0.0105242\pi\) | |||||||
\(662\) | 1.03670 | − | 12.2810i | 0.0402923 | − | 0.477316i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.261763 | − | 1.01395i | 0.0101584 | − | 0.0393491i | ||||
\(665\) | 16.6457 | 0.645494 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 86.8869i | − | 3.36428i | ||||||
\(668\) | 28.2389 | + | 4.80176i | 1.09260 | + | 0.185786i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.43946 | + | 0.374755i | 0.171511 | + | 0.0144780i | ||||
\(671\) | 31.2762 | 1.20741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7847 | −0.878284 | −0.439142 | − | 0.898418i | \(-0.644718\pi\) | ||||
−0.439142 | + | 0.898418i | \(0.644718\pi\) | |||||||
\(674\) | 12.1713 | + | 1.02743i | 0.468821 | + | 0.0395753i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.58118 | + | 1.11907i | 0.253122 | + | 0.0430410i | ||||
\(677\) | − | 34.2963i | − | 1.31811i | −0.752093 | − | 0.659057i | \(-0.770956\pi\) | ||
0.752093 | − | 0.659057i | \(-0.229044\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.63283 | 0.0626624 | ||||||||
\(680\) | −3.43449 | + | 13.3037i | −0.131707 | + | 0.510174i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.09365 | + | 36.6483i | −0.118462 | + | 1.40334i | ||||
\(683\) | 10.5590i | 0.404029i | 0.979383 | + | 0.202014i | \(0.0647487\pi\) | ||||
−0.979383 | + | 0.202014i | \(0.935251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6434i | 0.559497i | ||||||||
\(686\) | −1.40920 | − | 0.118957i | −0.0538036 | − | 0.00454180i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.30700 | + | 26.5757i | −0.354826 | + | 1.01319i | ||||
\(689\) | 20.2561 | 0.771695 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.3879i | 0.547342i | 0.961823 | + | 0.273671i | \(0.0882380\pi\) | ||||
−0.961823 | + | 0.273671i | \(0.911762\pi\) | |||||||
\(692\) | 0.469990 | − | 2.76399i | 0.0178664 | − | 0.105071i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.35685 | + | 39.7663i | −0.127424 | + | 1.50951i | ||||
\(695\) | 11.4789 | 0.435421 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.2314 | 0.614807 | ||||||||
\(698\) | 1.62098 | − | 19.2027i | 0.0613551 | − | 0.726831i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.7869 | − | 2.34433i | −0.521095 | − | 0.0886072i | ||||
\(701\) | − | 17.8913i | − | 0.675746i | −0.941192 | − | 0.337873i | \(-0.890292\pi\) | ||
0.941192 | − | 0.337873i | \(-0.109708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.0678 | −0.983165 | ||||||||
\(704\) | −12.8528 | + | 23.2341i | −0.484410 | + | 0.875667i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.6979 | − | 3.85757i | −1.71986 | − | 0.145181i | ||||
\(707\) | 13.1650i | 0.495121i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0614i | 0.828535i | 0.910155 | + | 0.414267i | \(0.135962\pi\) | ||||
−0.910155 | + | 0.414267i | \(0.864038\pi\) | |||||||
\(710\) | −2.64600 | + | 31.3453i | −0.0993026 | + | 1.17637i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.2837 | + | 3.42933i | 0.497828 | + | 0.128519i | ||||
\(713\) | 68.9499 | 2.58219 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.7273i | 1.33613i | ||||||||
\(716\) | 1.16288 | − | 6.83883i | 0.0434588 | − | 0.255579i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.3189 | − | 1.54638i | −0.683656 | − | 0.0577104i | ||||
\(719\) | −15.8888 | −0.592552 | −0.296276 | − | 0.955102i | \(-0.595745\pi\) | ||||
−0.296276 | + | 0.955102i | \(0.595745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.6983 | 0.584634 | ||||||||
\(722\) | 5.78440 | + | 0.488287i | 0.215273 | + | 0.0181722i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.50394 | − | 38.2493i | 0.241717 | − | 1.42153i | ||||
\(725\) | − | 69.0425i | − | 2.56418i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.2510 | −0.973595 | −0.486798 | − | 0.873515i | \(-0.661835\pi\) | ||||
−0.486798 | + | 0.873515i | \(0.661835\pi\) | |||||||
\(728\) | 2.19767 | − | 8.51280i | 0.0814510 | − | 0.315505i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.643696 | + | 7.62542i | −0.0238243 | + | 0.282230i | ||||
\(731\) | 9.87487i | 0.365235i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.1441i | 0.854848i | 0.904051 | + | 0.427424i | \(0.140579\pi\) | ||||
−0.904051 | + | 0.427424i | \(0.859421\pi\) | |||||||
\(734\) | 10.6476 | + | 0.898811i | 0.393010 | + | 0.0331757i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 45.4299 | + | 20.3463i | 1.67457 | + | 0.749975i | ||||
\(737\) | 3.01935 | 0.111219 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2767i | 0.414819i | 0.978254 | + | 0.207409i | \(0.0665032\pi\) | ||||
−0.978254 | + | 0.207409i | \(0.933497\pi\) | |||||||
\(740\) | 37.0294 | + | 6.29650i | 1.36123 | + | 0.231464i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.775190 | + | 9.18314i | −0.0284581 | + | 0.337124i | ||||
\(743\) | −5.16580 | −0.189515 | −0.0947575 | − | 0.995500i | \(-0.530208\pi\) | ||||
−0.0947575 | + | 0.995500i | \(0.530208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.5330 | 0.898821 | ||||||||
\(746\) | −4.12366 | + | 48.8502i | −0.150978 | + | 1.78853i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.56095 | + | 9.17985i | −0.0570739 | + | 0.335649i | ||||
\(749\) | 9.37257i | 0.342466i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.7670 | 1.30516 | 0.652578 | − | 0.757722i | \(-0.273687\pi\) | ||||
0.652578 | + | 0.757722i | \(0.273687\pi\) | |||||||
\(752\) | −42.6278 | − | 14.9286i | −1.55448 | − | 0.544389i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 43.2516 | + | 3.65106i | 1.57513 | + | 0.132964i | ||||
\(755\) | − | 0.874212i | − | 0.0318158i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.6174i | 1.14916i | 0.818450 | + | 0.574578i | \(0.194834\pi\) | ||||
−0.818450 | + | 0.574578i | \(0.805166\pi\) | |||||||
\(758\) | 0.0366832 | − | 0.434560i | 0.00133239 | − | 0.0157839i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −45.5867 | − | 11.7687i | −1.65360 | − | 0.426895i | ||||
\(761\) | 12.7856 | 0.463477 | 0.231738 | − | 0.972778i | \(-0.425559\pi\) | ||||
0.231738 | + | 0.972778i | \(0.425559\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 7.31490i | − | 0.264817i | ||||||
\(764\) | −46.2581 | − | 7.86575i | −1.67356 | − | 0.284573i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.14446 | + | 0.518681i | 0.222008 | + | 0.0187407i | ||||
\(767\) | −12.1120 | −0.437340 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.55622 | 0.236423 | 0.118212 | − | 0.992988i | \(-0.462284\pi\) | ||||
0.118212 | + | 0.992988i | \(0.462284\pi\) | |||||||
\(770\) | −16.1970 | − | 1.36727i | −0.583701 | − | 0.0492728i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30.6350 | − | 5.20920i | −1.10258 | − | 0.187483i | ||||
\(773\) | 27.7250i | 0.997197i | 0.866833 | + | 0.498599i | \(0.166152\pi\) | ||||
−0.866833 | + | 0.498599i | \(0.833848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 54.7893 | 1.96809 | ||||||||
\(776\) | −4.47174 | − | 1.15443i | −0.160526 | − | 0.0414416i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.158677 | + | 1.87974i | −0.00568886 | + | 0.0673920i | ||||
\(779\) | 55.6187i | 1.99275i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3185i | 0.762837i | ||||||||
\(782\) | 17.3949 | + | 1.46838i | 0.622039 | + | 0.0525091i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.77519 | + | 1.32210i | 0.134828 | + | 0.0472178i | ||||
\(785\) | 10.7707 | 0.384421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.9751i | 0.925911i | 0.886382 | + | 0.462955i | \(0.153211\pi\) | ||||
−0.886382 | + | 0.462955i | \(0.846789\pi\) | |||||||
\(788\) | −4.97128 | + | 29.2359i | −0.177095 | + | 1.04148i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.59814 | − | 54.4710i | 0.163594 | − | 1.93799i | ||||
\(791\) | −10.9153 | −0.388105 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.2915 | 1.04017 | ||||||||
\(794\) | 0.824315 | − | 9.76509i | 0.0292538 | − | 0.346550i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.0452 | + | 4.42874i | 0.923146 | + | 0.156972i | ||||
\(797\) | 45.5049i | 1.61187i | 0.592006 | + | 0.805934i | \(0.298336\pi\) | ||||
−0.592006 | + | 0.805934i | \(0.701664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8394 | −0.560358 | ||||||||
\(800\) | 36.0998 | + | 16.1677i | 1.27632 | + | 0.571614i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −33.7742 | − | 2.85103i | −1.19261 | − | 0.100674i | ||||
\(803\) | 5.18619i | 0.183017i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.4730i | 1.07403i | ||||||||
\(806\) | −2.89733 | + | 34.3227i | −0.102054 | + | 1.20897i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.30777 | − | 36.0542i | 0.327446 | − | 1.26838i | ||||
\(809\) | −20.8396 | −0.732682 | −0.366341 | − | 0.930481i | \(-0.619390\pi\) | ||||
−0.366341 | + | 0.930481i | \(0.619390\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 52.1223i | − | 1.83026i | −0.403158 | − | 0.915130i | \(-0.632088\pi\) | ||
0.403158 | − | 0.915130i | \(-0.367912\pi\) | |||||||
\(812\) | −3.31043 | + | 19.4685i | −0.116173 | + | 0.683210i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.3651 | + | 2.14118i | 0.889046 | + | 0.0750484i | ||||
\(815\) | −64.2716 | −2.25134 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.8374 | −1.18382 | ||||||||
\(818\) | −30.5707 | − | 2.58061i | −1.06888 | − | 0.0902288i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.4343 | − | 79.0066i | 0.469147 | − | 2.75903i | ||||
\(821\) | 13.9160i | 0.485673i | 0.970067 | + | 0.242837i | \(0.0780779\pi\) | ||||
−0.970067 | + | 0.242837i | \(0.921922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.31771 | 0.0459323 | 0.0229662 | − | 0.999736i | \(-0.492689\pi\) | ||||
0.0229662 | + | 0.999736i | \(0.492689\pi\) | |||||||
\(824\) | −42.9919 | − | 11.0988i | −1.49769 | − | 0.386646i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.463521 | − | 5.49102i | 0.0161280 | − | 0.191057i | ||||
\(827\) | − | 21.9111i | − | 0.761925i | −0.924591 | − | 0.380962i | \(-0.875593\pi\) | ||
0.924591 | − | 0.380962i | \(-0.124407\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 33.0419i | − | 1.14759i | −0.818999 | − | 0.573795i | \(-0.805470\pi\) | ||
0.818999 | − | 0.573795i | \(-0.194530\pi\) | |||||||
\(830\) | −1.80680 | − | 0.152520i | −0.0627149 | − | 0.00529405i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.0372 | + | 21.7597i | −0.417316 | + | 0.754382i | ||||
\(833\) | 1.40277 | 0.0486029 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 49.5976i | − | 1.71639i | ||||||
\(836\) | −31.4558 | − | 5.34877i | −1.08792 | − | 0.184991i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.28215 | − | 38.8814i | 0.113380 | − | 1.34313i | ||||
\(839\) | −16.2548 | −0.561177 | −0.280589 | − | 0.959828i | \(-0.590530\pi\) | ||||
−0.280589 | + | 0.959828i | \(0.590530\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −68.4952 | −2.36190 | ||||||||
\(842\) | −4.56004 | + | 54.0197i | −0.157149 | + | 1.86164i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.15029 | + | 24.4077i | −0.142859 | + | 0.840147i | ||||
\(845\) | − | 11.5589i | − | 0.397638i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0159016 | −0.000546384 | ||||||||
\(848\) | 8.61552 | − | 24.6012i | 0.295858 | − | 0.844810i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.8224 | + | 1.16681i | 0.474104 | + | 0.0400213i | ||||
\(851\) | − | 47.7217i | − | 1.63588i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.5342i | 1.49058i | 0.666738 | + | 0.745292i | \(0.267690\pi\) | ||||
−0.666738 | + | 0.745292i | \(0.732310\pi\) | |||||||
\(854\) | −1.12097 | + | 13.2794i | −0.0383589 | + | 0.454411i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.62649 | − | 25.6681i | 0.226489 | − | 0.877317i | ||||
\(857\) | 0.968943 | 0.0330985 | 0.0165492 | − | 0.999863i | \(-0.494732\pi\) | ||||
0.0165492 | + | 0.999863i | \(0.494732\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9386i | 0.407341i | 0.979040 | + | 0.203670i | \(0.0652871\pi\) | ||||
−0.979040 | + | 0.203670i | \(0.934713\pi\) | |||||||
\(860\) | 48.0662 | + | 8.17320i | 1.63904 | + | 0.278704i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.13561 | + | 0.264691i | 0.106799 | + | 0.00901542i | ||||
\(863\) | 7.95989 | 0.270958 | 0.135479 | − | 0.990780i | \(-0.456743\pi\) | ||||
0.135479 | + | 0.990780i | \(0.456743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.85455 | −0.165059 | ||||||||
\(866\) | −39.7726 | − | 3.35738i | −1.35153 | − | 0.114088i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.4494 | − | 2.62702i | −0.524386 | − | 0.0891670i | ||||
\(869\) | − | 37.0467i | − | 1.25672i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.82775 | 0.0958148 | ||||||||
\(872\) | −5.17170 | + | 20.0329i | −0.175136 | + | 0.678398i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.03157 | + | 59.6055i | −0.170195 | + | 2.01619i | ||||
\(875\) | 6.89962i | 0.233250i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 26.3998i | − | 0.891459i | −0.895168 | − | 0.445730i | \(-0.852944\pi\) | ||
0.895168 | − | 0.445730i | \(-0.147056\pi\) | |||||||
\(878\) | 7.94699 | + | 0.670841i | 0.268198 | + | 0.0226398i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 43.3912 | + | 15.1959i | 1.46272 | + | 0.512254i | ||||
\(881\) | −32.4550 | −1.09344 | −0.546718 | − | 0.837317i | \(-0.684123\pi\) | ||||
−0.546718 | + | 0.837317i | \(0.684123\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.46140i | − | 0.116486i | −0.998302 | − | 0.0582428i | \(-0.981450\pi\) | ||
0.998302 | − | 0.0582428i | \(-0.0185497\pi\) | |||||||
\(884\) | −1.46189 | + | 8.59732i | −0.0491688 | + | 0.289159i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.691940 | + | 8.19694i | −0.0232462 | + | 0.275381i | ||||
\(887\) | −16.9279 | −0.568385 | −0.284192 | − | 0.958767i | \(-0.591725\pi\) | ||||
−0.284192 | + | 0.958767i | \(0.591725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.37545 | 0.113209 | ||||||||
\(890\) | 1.99814 | − | 23.6706i | 0.0669780 | − | 0.793442i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.74100 | + | 0.976203i | 0.192223 | + | 0.0326857i | ||||
\(893\) | − | 54.2756i | − | 1.81626i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0114 | −0.401497 | ||||||||
\(896\) | −9.40414 | − | 6.28984i | −0.314170 | − | 0.210129i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.35225 | − | 0.198564i | −0.0784956 | − | 0.00662616i | ||||
\(899\) | − | 77.3682i | − | 2.58037i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.14120i | − | 0.304537i | ||||||
\(902\) | 4.56847 | − | 54.1195i | 0.152113 | − | 1.80198i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.8932 | + | 7.71724i | 0.994232 | + | 0.256672i | ||||
\(905\) | −67.1794 | −2.23312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.1236i | 0.967034i | 0.875335 | + | 0.483517i | \(0.160641\pi\) | ||||
−0.875335 | + | 0.483517i | \(0.839359\pi\) | |||||||
\(908\) | −3.80698 | + | 22.3886i | −0.126339 | + | 0.742993i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.1692 | − | 1.28050i | −0.502855 | − | 0.0424482i | ||||
\(911\) | −6.85198 | −0.227016 | −0.113508 | − | 0.993537i | \(-0.536209\pi\) | ||||
−0.113508 | + | 0.993537i | \(0.536209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.22884 | −0.0406685 | ||||||||
\(914\) | 23.1963 | + | 1.95810i | 0.767265 | + | 0.0647682i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.85970 | + | 34.4606i | −0.193610 | + | 1.13861i | ||||
\(917\) | 7.15460i | 0.236266i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.3468 | −1.23196 | −0.615979 | − | 0.787763i | \(-0.711239\pi\) | ||||
−0.615979 | + | 0.787763i | \(0.711239\pi\) | |||||||
\(920\) | 21.5447 | − | 83.4546i | 0.710307 | − | 2.75142i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.71121 | + | 32.1178i | −0.0892889 | + | 1.05774i | ||||
\(923\) | 19.9657i | 0.657179i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 37.9209i | − | 1.24683i | ||||||
\(926\) | 22.9933 | + | 1.94096i | 0.755606 | + | 0.0637840i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.8305 | − | 50.9766i | 0.749447 | − | 1.67339i | ||||
\(929\) | 38.8771 | 1.27552 | 0.637758 | − | 0.770236i | \(-0.279862\pi\) | ||||
0.637758 | + | 0.770236i | \(0.279862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.80674i | 0.157534i | ||||||||
\(932\) | −3.92027 | − | 0.666604i | −0.128413 | − | 0.0218354i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.96214 | + | 46.9367i | −0.129645 | + | 1.53582i | ||||
\(935\) | 16.1231 | 0.527281 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.3583 | −0.403727 | −0.201863 | − | 0.979414i | \(-0.564700\pi\) | ||||
−0.201863 | + | 0.979414i | \(0.564700\pi\) | |||||||
\(938\) | −0.108217 | + | 1.28197i | −0.00353340 | + | 0.0418577i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.1099 | + | 77.0988i | −0.427598 | + | 2.51468i | ||||
\(941\) | 40.1798i | 1.30982i | 0.755705 | + | 0.654912i | \(0.227294\pi\) | ||||
−0.755705 | + | 0.654912i | \(0.772706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −101.820 | −3.31572 | ||||||||
\(944\) | −5.15161 | + | 14.7102i | −0.167671 | + | 0.478776i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.9253 | + | 2.77937i | 1.07049 | + | 0.0903651i | ||||
\(947\) | − | 14.7512i | − | 0.479351i | −0.970853 | − | 0.239676i | \(-0.922959\pi\) | ||
0.970853 | − | 0.239676i | \(-0.0770411\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.85708i | 0.157668i | ||||||||
\(950\) | −3.99821 | + | 47.3640i | −0.129719 | + | 1.53669i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.84167 | − | 0.991767i | −0.124509 | − | 0.0321434i | ||||
\(953\) | −36.2336 | −1.17372 | −0.586861 | − | 0.809687i | \(-0.699637\pi\) | ||||
−0.586861 | + | 0.809687i | \(0.699637\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81.2456i | 2.62905i | ||||||||
\(956\) | 42.0820 | + | 7.15564i | 1.36103 | + | 0.231430i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.2633 | + | 3.39880i | 1.30085 | + | 0.109810i | ||||
\(959\) | −4.22854 | −0.136547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3962 | 0.980523 | ||||||||
\(962\) | 23.7555 | + | 2.00531i | 0.765908 | + | 0.0646537i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.3644 | − | 4.48303i | −0.849141 | − | 0.144389i | ||||
\(965\) | 53.8060i | 1.73208i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.6101 | −1.04867 | −0.524335 | − | 0.851512i | \(-0.675686\pi\) | ||||
−0.524335 | + | 0.851512i | \(0.675686\pi\) | |||||||
\(968\) | 0.0435486 | + | 0.0112425i | 0.00139971 | + | 0.000361349i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.672644 | + | 7.96834i | −0.0215973 | + | 0.255848i | ||||
\(971\) | 37.3897i | 1.19989i | 0.800040 | + | 0.599947i | \(0.204812\pi\) | ||||
−0.800040 | + | 0.599947i | \(0.795188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.31473i | 0.106265i | ||||||||
\(974\) | −54.9798 | − | 4.64109i | −1.76167 | − | 0.148710i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.4586 | − | 35.5749i | 0.398789 | − | 1.13872i | ||||
\(977\) | −3.76353 | −0.120406 | −0.0602029 | − | 0.998186i | \(-0.519175\pi\) | ||||
−0.0602029 | + | 0.998186i | \(0.519175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.0988i | − | 0.514521i | ||||||
\(980\) | 1.16104 | − | 6.82800i | 0.0370879 | − | 0.218112i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.49646 | + | 17.7276i | −0.0477541 | + | 0.565710i | ||||
\(983\) | 36.8112 | 1.17410 | 0.587048 | − | 0.809552i | \(-0.300290\pi\) | ||||
0.587048 | + | 0.809552i | \(0.300290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.3485 | 1.63610 | ||||||||
\(986\) | 1.64766 | − | 19.5187i | 0.0524721 | − | 0.621601i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.4597 | − | 5.00935i | −0.937238 | − | 0.159369i | ||||
\(989\) | − | 61.9454i | − | 1.96975i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.0994 | −1.68676 | −0.843379 | − | 0.537319i | \(-0.819437\pi\) | ||||
−0.843379 | + | 0.537319i | \(0.819437\pi\) | |||||||
\(992\) | 40.4530 | + | 18.1173i | 1.28438 | + | 0.575225i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.05150 | − | 0.764077i | −0.287096 | − | 0.0242351i | ||||
\(995\) | − | 45.7445i | − | 1.45020i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5497i | 0.935847i | 0.883769 | + | 0.467923i | \(0.154998\pi\) | ||||
−0.883769 | + | 0.467923i | \(0.845002\pi\) | |||||||
\(998\) | 2.05860 | − | 24.3868i | 0.0651639 | − | 0.771952i | ||||
\(999\) | 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.c.g.757.1 | ✓ | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.g.757.24 | yes | 24 | |
4.3 | odd | 2 | 6048.2.c.f.3025.2 | 24 | |||
8.3 | odd | 2 | 6048.2.c.f.3025.23 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.g.757.2 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.f.3025.24 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.g.757.23 | yes | 24 | |
24.11 | even | 2 | 6048.2.c.f.3025.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1512.2.c.g.757.2 | yes | 24 | 8.5 | even | 2 | inner | |
1512.2.c.g.757.23 | yes | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.g.757.24 | yes | 24 | 3.2 | odd | 2 | inner | |
6048.2.c.f.3025.1 | 24 | 24.11 | even | 2 | |||
6048.2.c.f.3025.2 | 24 | 4.3 | odd | 2 | |||
6048.2.c.f.3025.23 | 24 | 8.3 | odd | 2 | |||
6048.2.c.f.3025.24 | 24 | 12.11 | even | 2 |