Properties

Label 490.2.i.d.79.3
Level $490$
Weight $2$
Character 490.79
Analytic conductor $3.913$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [490,2,Mod(79,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("490.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.i (of order \(6\), degree \(2\), 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: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.3
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 490.79
Dual form 490.2.i.d.459.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.19067 - 0.448288i) q^{5} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.19067 - 0.448288i) q^{5} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.67303 - 1.48356i) q^{10} +(2.00000 + 3.46410i) q^{11} +4.24264i q^{13} +(-0.500000 + 0.866025i) q^{16} +(3.67423 - 2.12132i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(-2.82843 + 4.89898i) q^{19} +(-0.707107 - 2.12132i) q^{20} +4.00000i q^{22} +(4.59808 + 1.96410i) q^{25} +(-2.12132 + 3.67423i) q^{26} +4.00000 q^{29} +(-2.82843 - 4.89898i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.24264 q^{34} -3.00000 q^{36} +(-5.19615 - 3.00000i) q^{37} +(-4.89898 + 2.82843i) q^{38} +(0.448288 - 2.19067i) q^{40} +1.41421 q^{41} -12.0000i q^{43} +(-2.00000 + 3.46410i) q^{44} +(4.45069 - 5.01910i) q^{45} +(3.00000 + 4.00000i) q^{50} +(-3.67423 + 2.12132i) q^{52} +(-10.3923 + 6.00000i) q^{53} +(-2.82843 - 8.48528i) q^{55} +(3.46410 + 2.00000i) q^{58} +(5.65685 + 9.79796i) q^{59} +(3.53553 - 6.12372i) q^{61} -5.65685i q^{62} -1.00000 q^{64} +(1.90192 - 9.29423i) q^{65} +(10.3923 - 6.00000i) q^{67} +(3.67423 + 2.12132i) q^{68} +8.00000 q^{71} +(-2.59808 - 1.50000i) q^{72} +(-3.67423 + 2.12132i) q^{73} +(-3.00000 - 5.19615i) q^{74} -5.65685 q^{76} +(1.48356 - 1.67303i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.22474 + 0.707107i) q^{82} +16.9706i q^{83} +(-9.00000 + 3.00000i) q^{85} +(6.00000 - 10.3923i) q^{86} +(-3.46410 + 2.00000i) q^{88} +(2.12132 - 3.67423i) q^{89} +(6.36396 - 2.12132i) q^{90} +(8.39230 - 9.46410i) q^{95} -4.24264i q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 12 q^{9} + 16 q^{11} - 4 q^{16} + 16 q^{25} + 32 q^{29} - 24 q^{36} - 16 q^{44} + 24 q^{50} - 8 q^{64} + 36 q^{65} + 64 q^{71} - 24 q^{74} - 36 q^{81} - 72 q^{85} + 48 q^{86} - 16 q^{95} - 96 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.19067 0.448288i −0.979698 0.200480i
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) −1.67303 1.48356i −0.529059 0.469144i
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 0 0
\(13\) 4.24264i 1.17670i 0.808608 + 0.588348i \(0.200222\pi\)
−0.808608 + 0.588348i \(0.799778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.67423 2.12132i 0.891133 0.514496i 0.0168199 0.999859i \(-0.494646\pi\)
0.874313 + 0.485363i \(0.161312\pi\)
\(18\) −2.59808 + 1.50000i −0.612372 + 0.353553i
\(19\) −2.82843 + 4.89898i −0.648886 + 1.12390i 0.334504 + 0.942394i \(0.391431\pi\)
−0.983389 + 0.181509i \(0.941902\pi\)
\(20\) −0.707107 2.12132i −0.158114 0.474342i
\(21\) 0 0
\(22\) 4.00000i 0.852803i
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) 4.59808 + 1.96410i 0.919615 + 0.392820i
\(26\) −2.12132 + 3.67423i −0.416025 + 0.720577i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) −2.82843 4.89898i −0.508001 0.879883i −0.999957 0.00926296i \(-0.997051\pi\)
0.491957 0.870620i \(-0.336282\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.24264 0.727607
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) −5.19615 3.00000i −0.854242 0.493197i 0.00783774 0.999969i \(-0.497505\pi\)
−0.862080 + 0.506772i \(0.830838\pi\)
\(38\) −4.89898 + 2.82843i −0.794719 + 0.458831i
\(39\) 0 0
\(40\) 0.448288 2.19067i 0.0708805 0.346375i
\(41\) 1.41421 0.220863 0.110432 0.993884i \(-0.464777\pi\)
0.110432 + 0.993884i \(0.464777\pi\)
\(42\) 0 0
\(43\) 12.0000i 1.82998i −0.403473 0.914991i \(-0.632197\pi\)
0.403473 0.914991i \(-0.367803\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 4.45069 5.01910i 0.663470 0.748203i
\(46\) 0 0
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 3.00000 + 4.00000i 0.424264 + 0.565685i
\(51\) 0 0
\(52\) −3.67423 + 2.12132i −0.509525 + 0.294174i
\(53\) −10.3923 + 6.00000i −1.42749 + 0.824163i −0.996922 0.0783936i \(-0.975021\pi\)
−0.430570 + 0.902557i \(0.641688\pi\)
\(54\) 0 0
\(55\) −2.82843 8.48528i −0.381385 1.14416i
\(56\) 0 0
\(57\) 0 0
\(58\) 3.46410 + 2.00000i 0.454859 + 0.262613i
\(59\) 5.65685 + 9.79796i 0.736460 + 1.27559i 0.954080 + 0.299552i \(0.0968372\pi\)
−0.217620 + 0.976034i \(0.569829\pi\)
\(60\) 0 0
\(61\) 3.53553 6.12372i 0.452679 0.784063i −0.545873 0.837868i \(-0.683802\pi\)
0.998551 + 0.0538056i \(0.0171351\pi\)
\(62\) 5.65685i 0.718421i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.90192 9.29423i 0.235905 1.15281i
\(66\) 0 0
\(67\) 10.3923 6.00000i 1.26962 0.733017i 0.294706 0.955588i \(-0.404778\pi\)
0.974916 + 0.222571i \(0.0714450\pi\)
\(68\) 3.67423 + 2.12132i 0.445566 + 0.257248i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −2.59808 1.50000i −0.306186 0.176777i
\(73\) −3.67423 + 2.12132i −0.430037 + 0.248282i −0.699362 0.714767i \(-0.746533\pi\)
0.269326 + 0.963049i \(0.413199\pi\)
\(74\) −3.00000 5.19615i −0.348743 0.604040i
\(75\) 0 0
\(76\) −5.65685 −0.648886
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) 1.48356 1.67303i 0.165867 0.187051i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 1.22474 + 0.707107i 0.135250 + 0.0780869i
\(83\) 16.9706i 1.86276i 0.364047 + 0.931381i \(0.381395\pi\)
−0.364047 + 0.931381i \(0.618605\pi\)
\(84\) 0 0
\(85\) −9.00000 + 3.00000i −0.976187 + 0.325396i
\(86\) 6.00000 10.3923i 0.646997 1.12063i
\(87\) 0 0
\(88\) −3.46410 + 2.00000i −0.369274 + 0.213201i
\(89\) 2.12132 3.67423i 0.224860 0.389468i −0.731418 0.681930i \(-0.761141\pi\)
0.956277 + 0.292462i \(0.0944744\pi\)
\(90\) 6.36396 2.12132i 0.670820 0.223607i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.39230 9.46410i 0.861032 0.970996i
\(96\) 0 0
\(97\) 4.24264i 0.430775i −0.976529 0.215387i \(-0.930899\pi\)
0.976529 0.215387i \(-0.0691014\pi\)
\(98\) 0 0
\(99\) −12.0000 −1.20605
\(100\) 0.598076 + 4.96410i 0.0598076 + 0.496410i
\(101\) 4.94975 + 8.57321i 0.492518 + 0.853067i 0.999963 0.00861771i \(-0.00274313\pi\)
−0.507445 + 0.861684i \(0.669410\pi\)
\(102\) 0 0
\(103\) 14.6969 + 8.48528i 1.44813 + 0.836080i 0.998370 0.0570688i \(-0.0181754\pi\)
0.449762 + 0.893148i \(0.351509\pi\)
\(104\) −4.24264 −0.416025
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i \(-0.136370\pi\)
0.0950377 + 0.995474i \(0.469703\pi\)
\(108\) 0 0
\(109\) −6.00000 10.3923i −0.574696 0.995402i −0.996075 0.0885176i \(-0.971787\pi\)
0.421379 0.906885i \(-0.361546\pi\)
\(110\) 1.79315 8.76268i 0.170970 0.835489i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.00000 + 3.46410i 0.185695 + 0.321634i
\(117\) −11.0227 6.36396i −1.01905 0.588348i
\(118\) 11.3137i 1.04151i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 6.12372 3.53553i 0.554416 0.320092i
\(123\) 0 0
\(124\) 2.82843 4.89898i 0.254000 0.439941i
\(125\) −9.19239 6.36396i −0.822192 0.569210i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 6.29423 7.09808i 0.552040 0.622542i
\(131\) 8.48528 14.6969i 0.741362 1.28408i −0.210513 0.977591i \(-0.567513\pi\)
0.951875 0.306486i \(-0.0991534\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 2.12132 + 3.67423i 0.181902 + 0.315063i
\(137\) −5.19615 + 3.00000i −0.443937 + 0.256307i −0.705266 0.708942i \(-0.749173\pi\)
0.261329 + 0.965250i \(0.415839\pi\)
\(138\) 0 0
\(139\) 5.65685 0.479808 0.239904 0.970797i \(-0.422884\pi\)
0.239904 + 0.970797i \(0.422884\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.92820 + 4.00000i 0.581402 + 0.335673i
\(143\) −14.6969 + 8.48528i −1.22902 + 0.709575i
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) −8.76268 1.79315i −0.727701 0.148913i
\(146\) −4.24264 −0.351123
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) 5.00000 8.66025i 0.409616 0.709476i −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −4.89898 2.82843i −0.397360 0.229416i
\(153\) 12.7279i 1.02899i
\(154\) 0 0
\(155\) 4.00000 + 12.0000i 0.321288 + 0.963863i
\(156\) 0 0
\(157\) 3.67423 2.12132i 0.293236 0.169300i −0.346164 0.938174i \(-0.612516\pi\)
0.639400 + 0.768874i \(0.279183\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.12132 0.707107i 0.167705 0.0559017i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 10.3923 + 6.00000i 0.813988 + 0.469956i 0.848339 0.529454i \(-0.177603\pi\)
−0.0343508 + 0.999410i \(0.510936\pi\)
\(164\) 0.707107 + 1.22474i 0.0552158 + 0.0956365i
\(165\) 0 0
\(166\) −8.48528 + 14.6969i −0.658586 + 1.14070i
\(167\) 16.9706i 1.31322i −0.754230 0.656611i \(-0.771989\pi\)
0.754230 0.656611i \(-0.228011\pi\)
\(168\) 0 0
\(169\) −5.00000 −0.384615
\(170\) −9.29423 1.90192i −0.712835 0.145871i
\(171\) −8.48528 14.6969i −0.648886 1.12390i
\(172\) 10.3923 6.00000i 0.792406 0.457496i
\(173\) −3.67423 2.12132i −0.279347 0.161281i 0.353781 0.935328i \(-0.384896\pi\)
−0.633128 + 0.774047i \(0.718229\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 0 0
\(178\) 3.67423 2.12132i 0.275396 0.159000i
\(179\) 10.0000 + 17.3205i 0.747435 + 1.29460i 0.949048 + 0.315130i \(0.102048\pi\)
−0.201613 + 0.979465i \(0.564618\pi\)
\(180\) 6.57201 + 1.34486i 0.489849 + 0.100240i
\(181\) 15.5563 1.15629 0.578147 0.815933i \(-0.303776\pi\)
0.578147 + 0.815933i \(0.303776\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.0382 + 8.90138i 0.738023 + 0.654443i
\(186\) 0 0
\(187\) 14.6969 + 8.48528i 1.07475 + 0.620505i
\(188\) 0 0
\(189\) 0 0
\(190\) 12.0000 4.00000i 0.870572 0.290191i
\(191\) −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) 0 0
\(193\) −20.7846 + 12.0000i −1.49611 + 0.863779i −0.999990 0.00447566i \(-0.998575\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) 2.12132 3.67423i 0.152302 0.263795i
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) −10.3923 6.00000i −0.738549 0.426401i
\(199\) −5.65685 9.79796i −0.401004 0.694559i 0.592844 0.805318i \(-0.298005\pi\)
−0.993847 + 0.110759i \(0.964672\pi\)
\(200\) −1.96410 + 4.59808i −0.138883 + 0.325133i
\(201\) 0 0
\(202\) 9.89949i 0.696526i
\(203\) 0 0
\(204\) 0 0
\(205\) −3.09808 0.633975i −0.216379 0.0442787i
\(206\) 8.48528 + 14.6969i 0.591198 + 1.02398i
\(207\) 0 0
\(208\) −3.67423 2.12132i −0.254762 0.147087i
\(209\) −22.6274 −1.56517
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −10.3923 6.00000i −0.713746 0.412082i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) −5.37945 + 26.2880i −0.366876 + 1.79283i
\(216\) 0 0
\(217\) 0 0
\(218\) 12.0000i 0.812743i
\(219\) 0 0
\(220\) 5.93426 6.69213i 0.400087 0.451183i
\(221\) 9.00000 + 15.5885i 0.605406 + 1.04859i
\(222\) 0 0
\(223\) 16.9706i 1.13643i −0.822879 0.568216i \(-0.807634\pi\)
0.822879 0.568216i \(-0.192366\pi\)
\(224\) 0 0
\(225\) −12.0000 + 9.00000i −0.800000 + 0.600000i
\(226\) 0 0
\(227\) −14.6969 + 8.48528i −0.975470 + 0.563188i −0.900899 0.434028i \(-0.857092\pi\)
−0.0745706 + 0.997216i \(0.523759\pi\)
\(228\) 0 0
\(229\) −7.77817 + 13.4722i −0.513996 + 0.890268i 0.485872 + 0.874030i \(0.338502\pi\)
−0.999868 + 0.0162376i \(0.994831\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.00000i 0.262613i
\(233\) −5.19615 3.00000i −0.340411 0.196537i 0.320043 0.947403i \(-0.396303\pi\)
−0.660454 + 0.750867i \(0.729636\pi\)
\(234\) −6.36396 11.0227i −0.416025 0.720577i
\(235\) 0 0
\(236\) −5.65685 + 9.79796i −0.368230 + 0.637793i
\(237\) 0 0
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) −7.77817 13.4722i −0.501036 0.867820i −0.999999 0.00119700i \(-0.999619\pi\)
0.498963 0.866623i \(-0.333714\pi\)
\(242\) −4.33013 + 2.50000i −0.278351 + 0.160706i
\(243\) 0 0
\(244\) 7.07107 0.452679
\(245\) 0 0
\(246\) 0 0
\(247\) −20.7846 12.0000i −1.32249 0.763542i
\(248\) 4.89898 2.82843i 0.311086 0.179605i
\(249\) 0 0
\(250\) −4.77886 10.1075i −0.302242 0.639257i
\(251\) 5.65685 0.357057 0.178529 0.983935i \(-0.442866\pi\)
0.178529 + 0.983935i \(0.442866\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.0227 6.36396i −0.687577 0.396973i 0.115126 0.993351i \(-0.463273\pi\)
−0.802704 + 0.596378i \(0.796606\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 9.00000 3.00000i 0.558156 0.186052i
\(261\) −6.00000 + 10.3923i −0.371391 + 0.643268i
\(262\) 14.6969 8.48528i 0.907980 0.524222i
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 25.4558 8.48528i 1.56374 0.521247i
\(266\) 0 0
\(267\) 0 0
\(268\) 10.3923 + 6.00000i 0.634811 + 0.366508i
\(269\) −10.6066 18.3712i −0.646696 1.12011i −0.983907 0.178681i \(-0.942817\pi\)
0.337211 0.941429i \(-0.390516\pi\)
\(270\) 0 0
\(271\) −5.65685 + 9.79796i −0.343629 + 0.595184i −0.985104 0.171961i \(-0.944990\pi\)
0.641474 + 0.767144i \(0.278323\pi\)
\(272\) 4.24264i 0.257248i
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 2.39230 + 19.8564i 0.144261 + 1.19739i
\(276\) 0 0
\(277\) −10.3923 + 6.00000i −0.624413 + 0.360505i −0.778585 0.627539i \(-0.784062\pi\)
0.154172 + 0.988044i \(0.450729\pi\)
\(278\) 4.89898 + 2.82843i 0.293821 + 0.169638i
\(279\) 16.9706 1.01600
\(280\) 0 0
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 0 0
\(283\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) 4.00000 + 6.92820i 0.237356 + 0.411113i
\(285\) 0 0
\(286\) −16.9706 −1.00349
\(287\) 0 0
\(288\) 3.00000i 0.176777i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −6.69213 5.93426i −0.392975 0.348471i
\(291\) 0 0
\(292\) −3.67423 2.12132i −0.215018 0.124141i
\(293\) 4.24264i 0.247858i −0.992291 0.123929i \(-0.960451\pi\)
0.992291 0.123929i \(-0.0395495\pi\)
\(294\) 0 0
\(295\) −8.00000 24.0000i −0.465778 1.39733i
\(296\) 3.00000 5.19615i 0.174371 0.302020i
\(297\) 0 0
\(298\) 8.66025 5.00000i 0.501675 0.289642i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −2.82843 4.89898i −0.162221 0.280976i
\(305\) −10.4904 + 11.8301i −0.600677 + 0.677391i
\(306\) −6.36396 + 11.0227i −0.363803 + 0.630126i
\(307\) 16.9706i 0.968561i 0.874913 + 0.484281i \(0.160919\pi\)
−0.874913 + 0.484281i \(0.839081\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.53590 + 12.3923i −0.144029 + 0.703836i
\(311\) 8.48528 + 14.6969i 0.481156 + 0.833387i 0.999766 0.0216240i \(-0.00688367\pi\)
−0.518610 + 0.855011i \(0.673550\pi\)
\(312\) 0 0
\(313\) −11.0227 6.36396i −0.623040 0.359712i 0.155012 0.987913i \(-0.450459\pi\)
−0.778052 + 0.628200i \(0.783792\pi\)
\(314\) 4.24264 0.239426
\(315\) 0 0
\(316\) 0 0
\(317\) 10.3923 + 6.00000i 0.583690 + 0.336994i 0.762598 0.646872i \(-0.223923\pi\)
−0.178908 + 0.983866i \(0.557257\pi\)
\(318\) 0 0
\(319\) 8.00000 + 13.8564i 0.447914 + 0.775810i
\(320\) 2.19067 + 0.448288i 0.122462 + 0.0250600i
\(321\) 0 0
\(322\) 0 0
\(323\) 24.0000i 1.33540i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) −8.33298 + 19.5080i −0.462230 + 1.08211i
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) 0 0
\(328\) 1.41421i 0.0780869i
\(329\) 0 0
\(330\) 0 0
\(331\) −6.00000 + 10.3923i −0.329790 + 0.571213i −0.982470 0.186421i \(-0.940311\pi\)
0.652680 + 0.757634i \(0.273645\pi\)
\(332\) −14.6969 + 8.48528i −0.806599 + 0.465690i
\(333\) 15.5885 9.00000i 0.854242 0.493197i
\(334\) 8.48528 14.6969i 0.464294 0.804181i
\(335\) −25.4558 + 8.48528i −1.39080 + 0.463600i
\(336\) 0 0
\(337\) 18.0000i 0.980522i 0.871576 + 0.490261i \(0.163099\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −4.33013 2.50000i −0.235528 0.135982i
\(339\) 0 0
\(340\) −7.09808 6.29423i −0.384947 0.341352i
\(341\) 11.3137 19.5959i 0.612672 1.06118i
\(342\) 16.9706i 0.917663i
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) −2.12132 3.67423i −0.114043 0.197528i
\(347\) 10.3923 6.00000i 0.557888 0.322097i −0.194409 0.980921i \(-0.562279\pi\)
0.752297 + 0.658824i \(0.228946\pi\)
\(348\) 0 0
\(349\) −24.0416 −1.28692 −0.643459 0.765480i \(-0.722502\pi\)
−0.643459 + 0.765480i \(0.722502\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.46410 2.00000i −0.184637 0.106600i
\(353\) 18.3712 10.6066i 0.977799 0.564532i 0.0761940 0.997093i \(-0.475723\pi\)
0.901605 + 0.432561i \(0.142390\pi\)
\(354\) 0 0
\(355\) −17.5254 3.58630i −0.930150 0.190341i
\(356\) 4.24264 0.224860
\(357\) 0 0
\(358\) 20.0000i 1.05703i
\(359\) 8.00000 13.8564i 0.422224 0.731313i −0.573933 0.818902i \(-0.694583\pi\)
0.996157 + 0.0875892i \(0.0279163\pi\)
\(360\) 5.01910 + 4.45069i 0.264530 + 0.234572i
\(361\) −6.50000 11.2583i −0.342105 0.592544i
\(362\) 13.4722 + 7.77817i 0.708083 + 0.408812i
\(363\) 0 0
\(364\) 0 0
\(365\) 9.00000 3.00000i 0.471082 0.157027i
\(366\) 0 0
\(367\) 14.6969 8.48528i 0.767174 0.442928i −0.0646916 0.997905i \(-0.520606\pi\)
0.831866 + 0.554977i \(0.187273\pi\)
\(368\) 0 0
\(369\) −2.12132 + 3.67423i −0.110432 + 0.191273i
\(370\) 4.24264 + 12.7279i 0.220564 + 0.661693i
\(371\) 0 0
\(372\) 0 0
\(373\) −10.3923 6.00000i −0.538093 0.310668i 0.206213 0.978507i \(-0.433886\pi\)
−0.744306 + 0.667839i \(0.767219\pi\)
\(374\) 8.48528 + 14.6969i 0.438763 + 0.759961i
\(375\) 0 0
\(376\) 0 0
\(377\) 16.9706i 0.874028i
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 12.3923 + 2.53590i 0.635712 + 0.130089i
\(381\) 0 0
\(382\) −6.92820 + 4.00000i −0.354478 + 0.204658i
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −24.0000 −1.22157
\(387\) 31.1769 + 18.0000i 1.58481 + 0.914991i
\(388\) 3.67423 2.12132i 0.186531 0.107694i
\(389\) −10.0000 17.3205i −0.507020 0.878185i −0.999967 0.00812520i \(-0.997414\pi\)
0.492947 0.870059i \(-0.335920\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −6.00000 + 10.3923i −0.302276 + 0.523557i
\(395\) 0 0
\(396\) −6.00000 10.3923i −0.301511 0.522233i
\(397\) 25.7196 + 14.8492i 1.29083 + 0.745262i 0.978802 0.204810i \(-0.0656577\pi\)
0.312030 + 0.950072i \(0.398991\pi\)
\(398\) 11.3137i 0.567105i
\(399\) 0 0
\(400\) −4.00000 + 3.00000i −0.200000 + 0.150000i
\(401\) 4.00000 6.92820i 0.199750 0.345978i −0.748697 0.662912i \(-0.769320\pi\)
0.948447 + 0.316934i \(0.102654\pi\)
\(402\) 0 0
\(403\) 20.7846 12.0000i 1.03536 0.597763i
\(404\) −4.94975 + 8.57321i −0.246259 + 0.426533i
\(405\) 6.36396 + 19.0919i 0.316228 + 0.948683i
\(406\) 0 0
\(407\) 24.0000i 1.18964i
\(408\) 0 0
\(409\) 4.94975 + 8.57321i 0.244749 + 0.423918i 0.962061 0.272834i \(-0.0879610\pi\)
−0.717312 + 0.696752i \(0.754628\pi\)
\(410\) −2.36603 2.09808i −0.116850 0.103617i
\(411\) 0 0
\(412\) 16.9706i 0.836080i
\(413\) 0 0
\(414\) 0 0
\(415\) 7.60770 37.1769i 0.373447 1.82494i
\(416\) −2.12132 3.67423i −0.104006 0.180144i
\(417\) 0 0
\(418\) −19.5959 11.3137i −0.958468 0.553372i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 10.3923 + 6.00000i 0.505889 + 0.292075i
\(423\) 0 0
\(424\) −6.00000 10.3923i −0.291386 0.504695i
\(425\) 21.0609 2.53742i 1.02160 0.123083i
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) −17.8028 + 20.0764i −0.858526 + 0.968170i
\(431\) −8.00000 13.8564i −0.385346 0.667440i 0.606471 0.795106i \(-0.292585\pi\)
−0.991817 + 0.127666i \(0.959251\pi\)
\(432\) 0 0
\(433\) 29.6985i 1.42722i −0.700544 0.713609i \(-0.747059\pi\)
0.700544 0.713609i \(-0.252941\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.00000 10.3923i 0.287348 0.497701i
\(437\) 0 0
\(438\) 0 0
\(439\) 19.7990 34.2929i 0.944954 1.63671i 0.189111 0.981956i \(-0.439439\pi\)
0.755843 0.654753i \(-0.227227\pi\)
\(440\) 8.48528 2.82843i 0.404520 0.134840i
\(441\) 0 0
\(442\) 18.0000i 0.856173i
\(443\) 10.3923 + 6.00000i 0.493753 + 0.285069i 0.726130 0.687557i \(-0.241317\pi\)
−0.232377 + 0.972626i \(0.574650\pi\)
\(444\) 0 0
\(445\) −6.29423 + 7.09808i −0.298375 + 0.336481i
\(446\) 8.48528 14.6969i 0.401790 0.695920i
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) −14.8923 + 1.79423i −0.702030 + 0.0845807i
\(451\) 2.82843 + 4.89898i 0.133185 + 0.230684i
\(452\) 0 0
\(453\) 0 0
\(454\) −16.9706 −0.796468
\(455\) 0 0
\(456\) 0 0
\(457\) −20.7846 12.0000i −0.972263 0.561336i −0.0723376 0.997380i \(-0.523046\pi\)
−0.899925 + 0.436044i \(0.856379\pi\)
\(458\) −13.4722 + 7.77817i −0.629514 + 0.363450i
\(459\) 0 0
\(460\) 0 0
\(461\) 21.2132 0.987997 0.493999 0.869463i \(-0.335535\pi\)
0.493999 + 0.869463i \(0.335535\pi\)
\(462\) 0 0
\(463\) 24.0000i 1.11537i −0.830051 0.557687i \(-0.811689\pi\)
0.830051 0.557687i \(-0.188311\pi\)
\(464\) −2.00000 + 3.46410i −0.0928477 + 0.160817i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −14.6969 8.48528i −0.680093 0.392652i 0.119797 0.992798i \(-0.461776\pi\)
−0.799890 + 0.600146i \(0.795109\pi\)
\(468\) 12.7279i 0.588348i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −9.79796 + 5.65685i −0.450988 + 0.260378i
\(473\) 41.5692 24.0000i 1.91135 1.10352i
\(474\) 0 0
\(475\) −22.6274 + 16.9706i −1.03822 + 0.778663i
\(476\) 0 0
\(477\) 36.0000i 1.64833i
\(478\) 6.92820 + 4.00000i 0.316889 + 0.182956i
\(479\) 8.48528 + 14.6969i 0.387702 + 0.671520i 0.992140 0.125132i \(-0.0399355\pi\)
−0.604438 + 0.796652i \(0.706602\pi\)
\(480\) 0 0
\(481\) 12.7279 22.0454i 0.580343 1.00518i
\(482\) 15.5563i 0.708572i
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) −1.90192 + 9.29423i −0.0863619 + 0.422029i
\(486\) 0 0
\(487\) −20.7846 + 12.0000i −0.941841 + 0.543772i −0.890537 0.454911i \(-0.849671\pi\)
−0.0513038 + 0.998683i \(0.516338\pi\)
\(488\) 6.12372 + 3.53553i 0.277208 + 0.160046i
\(489\) 0 0
\(490\) 0 0
\(491\) −4.00000 −0.180517 −0.0902587 0.995918i \(-0.528769\pi\)
−0.0902587 + 0.995918i \(0.528769\pi\)
\(492\) 0 0
\(493\) 14.6969 8.48528i 0.661917 0.382158i
\(494\) −12.0000 20.7846i −0.539906 0.935144i
\(495\) 26.2880 + 5.37945i 1.18156 + 0.241788i
\(496\) 5.65685 0.254000
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0.915158 11.1428i 0.0409271 0.498322i
\(501\) 0 0
\(502\) 4.89898 + 2.82843i 0.218652 + 0.126239i
\(503\) 33.9411i 1.51336i −0.653785 0.756680i \(-0.726820\pi\)
0.653785 0.756680i \(-0.273180\pi\)
\(504\) 0 0
\(505\) −7.00000 21.0000i −0.311496 0.934488i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.36396 + 11.0227i −0.282078 + 0.488573i −0.971896 0.235409i \(-0.924357\pi\)
0.689819 + 0.723982i \(0.257690\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.36396 11.0227i −0.280702 0.486191i
\(515\) −28.3923 25.1769i −1.25111 1.10943i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 9.29423 + 1.90192i 0.407579 + 0.0834049i
\(521\) 6.36396 + 11.0227i 0.278810 + 0.482913i 0.971089 0.238716i \(-0.0767266\pi\)
−0.692279 + 0.721630i \(0.743393\pi\)
\(522\) −10.3923 + 6.00000i −0.454859 + 0.262613i
\(523\) −29.3939 16.9706i −1.28530 0.742071i −0.307492 0.951551i \(-0.599490\pi\)
−0.977813 + 0.209480i \(0.932823\pi\)
\(524\) 16.9706 0.741362
\(525\) 0 0
\(526\) 0 0
\(527\) −20.7846 12.0000i −0.905392 0.522728i
\(528\) 0 0
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 26.2880 + 5.37945i 1.14188 + 0.233668i
\(531\) −33.9411 −1.47292
\(532\) 0 0
\(533\) 6.00000i 0.259889i
\(534\) 0 0
\(535\) −20.0764 17.8028i −0.867978 0.769681i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 0 0
\(538\) 21.2132i 0.914566i
\(539\) 0 0
\(540\) 0 0
\(541\) 15.0000 25.9808i 0.644900 1.11700i −0.339424 0.940633i \(-0.610232\pi\)
0.984325 0.176367i \(-0.0564345\pi\)
\(542\) −9.79796 + 5.65685i −0.420858 + 0.242983i
\(543\) 0 0
\(544\) −2.12132 + 3.67423i −0.0909509 + 0.157532i
\(545\) 8.48528 + 25.4558i 0.363470 + 1.09041i
\(546\) 0 0
\(547\) 12.0000i 0.513083i 0.966533 + 0.256541i \(0.0825830\pi\)
−0.966533 + 0.256541i \(0.917417\pi\)
\(548\) −5.19615 3.00000i −0.221969 0.128154i
\(549\) 10.6066 + 18.3712i 0.452679 + 0.784063i
\(550\) −7.85641 + 18.3923i −0.334998 + 0.784251i
\(551\) −11.3137 + 19.5959i −0.481980 + 0.834814i
\(552\) 0 0
\(553\) 0 0
\(554\) −12.0000 −0.509831
\(555\) 0 0
\(556\) 2.82843 + 4.89898i 0.119952 + 0.207763i
\(557\) 10.3923 6.00000i 0.440336 0.254228i −0.263404 0.964686i \(-0.584845\pi\)
0.703740 + 0.710457i \(0.251512\pi\)
\(558\) 14.6969 + 8.48528i 0.622171 + 0.359211i
\(559\) 50.9117 2.15333
\(560\) 0 0
\(561\) 0 0
\(562\) 13.8564 + 8.00000i 0.584497 + 0.337460i
\(563\) 29.3939 16.9706i 1.23880 0.715224i 0.269954 0.962873i \(-0.412991\pi\)
0.968850 + 0.247649i \(0.0796580\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 8.00000i 0.335673i
\(569\) −4.00000 + 6.92820i −0.167689 + 0.290445i −0.937607 0.347697i \(-0.886964\pi\)
0.769918 + 0.638143i \(0.220297\pi\)
\(570\) 0 0
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) −14.6969 8.48528i −0.614510 0.354787i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −18.3712 + 10.6066i −0.764802 + 0.441559i −0.831017 0.556247i \(-0.812241\pi\)
0.0662152 + 0.997805i \(0.478908\pi\)
\(578\) 0.866025 0.500000i 0.0360219 0.0207973i
\(579\) 0 0
\(580\) −2.82843 8.48528i −0.117444 0.352332i
\(581\) 0 0
\(582\) 0 0
\(583\) −41.5692 24.0000i −1.72162 0.993978i
\(584\) −2.12132 3.67423i −0.0877809 0.152041i
\(585\) 21.2942 + 18.8827i 0.880408 + 0.780703i
\(586\) 2.12132 3.67423i 0.0876309 0.151781i
\(587\) 16.9706i 0.700450i 0.936666 + 0.350225i \(0.113895\pi\)
−0.936666 + 0.350225i \(0.886105\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) 5.07180 24.7846i 0.208803 1.02037i
\(591\) 0 0
\(592\) 5.19615 3.00000i 0.213561 0.123299i
\(593\) 11.0227 + 6.36396i 0.452648 + 0.261337i 0.708948 0.705261i \(-0.249170\pi\)
−0.256300 + 0.966597i \(0.582503\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 0 0
\(599\) 8.00000 + 13.8564i 0.326871 + 0.566157i 0.981889 0.189456i \(-0.0606724\pi\)
−0.655018 + 0.755613i \(0.727339\pi\)
\(600\) 0 0
\(601\) −26.8701 −1.09605 −0.548026 0.836461i \(-0.684621\pi\)
−0.548026 + 0.836461i \(0.684621\pi\)
\(602\) 0 0
\(603\) 36.0000i 1.46603i
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 7.41782 8.36516i 0.301577 0.340092i
\(606\) 0 0
\(607\) 14.6969 + 8.48528i 0.596530 + 0.344407i 0.767675 0.640839i \(-0.221413\pi\)
−0.171145 + 0.985246i \(0.554747\pi\)
\(608\) 5.65685i 0.229416i
\(609\) 0 0
\(610\) −15.0000 + 5.00000i −0.607332 + 0.202444i
\(611\) 0 0
\(612\) −11.0227 + 6.36396i −0.445566 + 0.257248i
\(613\) 5.19615 3.00000i 0.209871 0.121169i −0.391381 0.920229i \(-0.628002\pi\)
0.601251 + 0.799060i \(0.294669\pi\)
\(614\) −8.48528 + 14.6969i −0.342438 + 0.593120i
\(615\) 0 0
\(616\) 0 0
\(617\) 42.0000i 1.69086i −0.534089 0.845428i \(-0.679345\pi\)
0.534089 0.845428i \(-0.320655\pi\)
\(618\) 0 0
\(619\) 22.6274 + 39.1918i 0.909473 + 1.57525i 0.814798 + 0.579745i \(0.196848\pi\)
0.0946744 + 0.995508i \(0.469819\pi\)
\(620\) −8.39230 + 9.46410i −0.337043 + 0.380087i
\(621\) 0 0
\(622\) 16.9706i 0.680458i
\(623\) 0 0
\(624\) 0 0
\(625\) 17.2846 + 18.0622i 0.691384 + 0.722487i
\(626\) −6.36396 11.0227i −0.254355 0.440556i
\(627\) 0 0
\(628\) 3.67423 + 2.12132i 0.146618 + 0.0846499i
\(629\) −25.4558 −1.01499
\(630\) 0 0
\(631\) 24.0000 0.955425 0.477712 0.878516i \(-0.341466\pi\)
0.477712 + 0.878516i \(0.341466\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 16.0000i 0.633446i
\(639\) −12.0000 + 20.7846i −0.474713 + 0.822226i
\(640\) 1.67303 + 1.48356i 0.0661324 + 0.0586430i
\(641\) 20.0000 + 34.6410i 0.789953 + 1.36824i 0.925995 + 0.377535i \(0.123228\pi\)
−0.136043 + 0.990703i \(0.543438\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) −14.6969 + 8.48528i −0.577796 + 0.333591i −0.760257 0.649622i \(-0.774927\pi\)
0.182461 + 0.983213i \(0.441594\pi\)
\(648\) 7.79423 4.50000i 0.306186 0.176777i
\(649\) −22.6274 + 39.1918i −0.888204 + 1.53841i
\(650\) −16.9706 + 12.7279i −0.665640 + 0.499230i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 15.5885 + 9.00000i 0.610023 + 0.352197i 0.772975 0.634437i \(-0.218768\pi\)
−0.162951 + 0.986634i \(0.552101\pi\)
\(654\) 0 0
\(655\) −25.1769 + 28.3923i −0.983743 + 1.10938i
\(656\) −0.707107 + 1.22474i −0.0276079 + 0.0478183i
\(657\) 12.7279i 0.496564i
\(658\) 0 0
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) −12.0208 20.8207i −0.467556 0.809830i 0.531757 0.846897i \(-0.321532\pi\)
−0.999313 + 0.0370669i \(0.988199\pi\)
\(662\) −10.3923 + 6.00000i −0.403908 + 0.233197i
\(663\) 0 0
\(664\) −16.9706 −0.658586
\(665\) 0 0
\(666\) 18.0000 0.697486
\(667\) 0 0
\(668\) 14.6969 8.48528i 0.568642 0.328305i
\(669\) 0 0
\(670\) −26.2880 5.37945i −1.01560 0.207826i
\(671\) 28.2843 1.09190
\(672\) 0 0
\(673\) 18.0000i 0.693849i 0.937893 + 0.346925i \(0.112774\pi\)
−0.937893 + 0.346925i \(0.887226\pi\)
\(674\) −9.00000 + 15.5885i −0.346667 + 0.600445i
\(675\) 0 0
\(676\) −2.50000 4.33013i −0.0961538 0.166543i
\(677\) −18.3712 10.6066i −0.706062 0.407645i 0.103540 0.994625i \(-0.466983\pi\)
−0.809601 + 0.586981i \(0.800317\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.00000 9.00000i −0.115045 0.345134i
\(681\) 0 0
\(682\) 19.5959 11.3137i 0.750366 0.433224i
\(683\) 10.3923 6.00000i 0.397650 0.229584i −0.287819 0.957685i \(-0.592930\pi\)
0.685470 + 0.728101i \(0.259597\pi\)
\(684\) 8.48528 14.6969i 0.324443 0.561951i
\(685\) 12.7279 4.24264i 0.486309 0.162103i
\(686\) 0 0
\(687\) 0 0
\(688\) 10.3923 + 6.00000i 0.396203 + 0.228748i
\(689\) −25.4558 44.0908i −0.969790 1.67973i
\(690\) 0 0
\(691\) −2.82843 + 4.89898i −0.107598 + 0.186366i −0.914797 0.403914i \(-0.867649\pi\)
0.807198 + 0.590280i \(0.200983\pi\)
\(692\) 4.24264i 0.161281i
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −12.3923 2.53590i −0.470067 0.0961921i
\(696\) 0 0
\(697\) 5.19615 3.00000i 0.196818 0.113633i
\(698\) −20.8207 12.0208i −0.788074 0.454995i
\(699\) 0 0
\(700\) 0 0
\(701\) −44.0000 −1.66186 −0.830929 0.556379i \(-0.812190\pi\)
−0.830929 + 0.556379i \(0.812190\pi\)
\(702\) 0 0
\(703\) 29.3939 16.9706i 1.10861 0.640057i
\(704\) −2.00000 3.46410i −0.0753778 0.130558i
\(705\) 0 0
\(706\) 21.2132 0.798369
\(707\) 0 0
\(708\) 0 0
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) −13.3843 11.8685i −0.502302 0.445417i
\(711\) 0 0
\(712\) 3.67423 + 2.12132i 0.137698 + 0.0794998i
\(713\) 0 0
\(714\) 0 0
\(715\) 36.0000 12.0000i 1.34632 0.448775i
\(716\) −10.0000 + 17.3205i −0.373718 + 0.647298i
\(717\) 0 0
\(718\) 13.8564 8.00000i 0.517116 0.298557i
\(719\) 2.82843 4.89898i 0.105483 0.182701i −0.808453 0.588561i \(-0.799695\pi\)
0.913935 + 0.405860i \(0.133028\pi\)
\(720\) 2.12132 + 6.36396i 0.0790569 + 0.237171i
\(721\) 0 0
\(722\) 13.0000i 0.483810i
\(723\) 0 0
\(724\) 7.77817 + 13.4722i 0.289074 + 0.500690i
\(725\) 18.3923 + 7.85641i 0.683073 + 0.291780i
\(726\) 0 0
\(727\) 16.9706i 0.629403i 0.949191 + 0.314702i \(0.101904\pi\)
−0.949191 + 0.314702i \(0.898096\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 9.29423 + 1.90192i 0.343995 + 0.0703934i
\(731\) −25.4558 44.0908i −0.941518 1.63076i
\(732\) 0 0
\(733\) −11.0227 6.36396i −0.407133 0.235058i 0.282424 0.959290i \(-0.408861\pi\)
−0.689557 + 0.724231i \(0.742195\pi\)
\(734\) 16.9706 0.626395
\(735\) 0 0
\(736\) 0 0
\(737\) 41.5692 + 24.0000i 1.53122 + 0.884051i
\(738\) −3.67423 + 2.12132i −0.135250 + 0.0780869i
\(739\) 10.0000 + 17.3205i 0.367856 + 0.637145i 0.989230 0.146369i \(-0.0467586\pi\)
−0.621374 + 0.783514i \(0.713425\pi\)
\(740\) −2.68973 + 13.1440i −0.0988763 + 0.483184i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −14.8356 + 16.7303i −0.543536 + 0.612952i
\(746\) −6.00000 10.3923i −0.219676 0.380489i
\(747\) −44.0908 25.4558i −1.61320 0.931381i
\(748\) 16.9706i 0.620505i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −8.48528 + 14.6969i −0.309016 + 0.535231i
\(755\) 5.65685 + 16.9706i 0.205874 + 0.617622i
\(756\) 0 0
\(757\) 42.0000i 1.52652i 0.646094 + 0.763258i \(0.276401\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(758\) −17.3205 10.0000i −0.629109 0.363216i
\(759\) 0 0
\(760\) 9.46410 + 8.39230i 0.343299 + 0.304421i
\(761\) −23.3345 + 40.4166i −0.845876 + 1.46510i 0.0389826 + 0.999240i \(0.487588\pi\)
−0.884858 + 0.465860i \(0.845745\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) 5.70577 27.8827i 0.206293 1.00810i
\(766\) 0 0
\(767\) −41.5692 + 24.0000i −1.50098 + 0.866590i
\(768\) 0 0
\(769\) 7.07107 0.254989 0.127495 0.991839i \(-0.459306\pi\)
0.127495 + 0.991839i \(0.459306\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −20.7846 12.0000i −0.748054 0.431889i
\(773\) −33.0681 + 19.0919i −1.18938 + 0.686687i −0.958165 0.286216i \(-0.907602\pi\)
−0.231212 + 0.972903i \(0.574269\pi\)
\(774\) 18.0000 + 31.1769i 0.646997 + 1.12063i
\(775\) −3.38323 28.0812i −0.121529 1.00871i
\(776\) 4.24264 0.152302
\(777\) 0 0
\(778\) 20.0000i 0.717035i
\(779\) −4.00000 + 6.92820i −0.143315 + 0.248229i
\(780\) 0 0
\(781\) 16.0000 + 27.7128i 0.572525 + 0.991642i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9.00000 + 3.00000i −0.321224 + 0.107075i
\(786\) 0 0
\(787\) 44.0908 25.4558i 1.57167 0.907403i 0.575703 0.817659i \(-0.304728\pi\)
0.995965 0.0897439i \(-0.0286049\pi\)
\(788\) −10.3923 + 6.00000i −0.370211 + 0.213741i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 12.0000i 0.426401i
\(793\) 25.9808 + 15.0000i 0.922604 + 0.532666i
\(794\) 14.8492 + 25.7196i 0.526980 + 0.912756i
\(795\) 0 0
\(796\) 5.65685 9.79796i 0.200502 0.347279i
\(797\) 4.24264i 0.150282i 0.997173 + 0.0751410i \(0.0239407\pi\)
−0.997173 + 0.0751410i \(0.976059\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −4.96410 + 0.598076i −0.175507 + 0.0211452i
\(801\) 6.36396 + 11.0227i 0.224860 + 0.389468i
\(802\) 6.92820 4.00000i 0.244643 0.141245i
\(803\) −14.6969 8.48528i −0.518644 0.299439i
\(804\) 0 0
\(805\) 0 0
\(806\) 24.0000 0.845364
\(807\) 0 0
\(808\) −8.57321 + 4.94975i −0.301605 + 0.174132i
\(809\) −13.0000 22.5167i −0.457056 0.791644i 0.541748 0.840541i \(-0.317763\pi\)
−0.998804 + 0.0488972i \(0.984429\pi\)
\(810\) −4.03459 + 19.7160i −0.141761 + 0.692751i
\(811\) −45.2548 −1.58911 −0.794556 0.607191i \(-0.792296\pi\)
−0.794556 + 0.607191i \(0.792296\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 12.0000 20.7846i 0.420600 0.728500i
\(815\) −20.0764 17.8028i −0.703245 0.623604i
\(816\) 0 0
\(817\) 58.7878 + 33.9411i 2.05672 + 1.18745i
\(818\) 9.89949i 0.346128i
\(819\) 0 0
\(820\) −1.00000 3.00000i −0.0349215 0.104765i
\(821\) −5.00000 + 8.66025i −0.174501 + 0.302245i −0.939989 0.341206i \(-0.889165\pi\)
0.765487 + 0.643451i \(0.222498\pi\)
\(822\) 0 0
\(823\) −20.7846 + 12.0000i −0.724506 + 0.418294i −0.816409 0.577474i \(-0.804038\pi\)
0.0919029 + 0.995768i \(0.470705\pi\)
\(824\) −8.48528 + 14.6969i −0.295599 + 0.511992i
\(825\) 0 0
\(826\) 0 0
\(827\) 36.0000i 1.25184i 0.779886 + 0.625921i \(0.215277\pi\)
−0.779886 + 0.625921i \(0.784723\pi\)
\(828\) 0 0
\(829\) −7.77817 13.4722i −0.270147 0.467909i 0.698752 0.715364i \(-0.253739\pi\)
−0.968899 + 0.247455i \(0.920406\pi\)
\(830\) 25.1769 28.3923i 0.873903 0.985511i
\(831\) 0 0
\(832\) 4.24264i 0.147087i
\(833\) 0 0
\(834\) 0 0
\(835\) −7.60770 + 37.1769i −0.263275 + 1.28656i
\(836\) −11.3137 19.5959i −0.391293 0.677739i
\(837\) 0 0
\(838\) 0 0
\(839\) 22.6274 0.781185 0.390593 0.920564i \(-0.372270\pi\)
0.390593 + 0.920564i \(0.372270\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) −5.19615 3.00000i −0.179071 0.103387i
\(843\) 0 0
\(844\) 6.00000 + 10.3923i 0.206529 + 0.357718i
\(845\) 10.9534 + 2.24144i 0.376807 + 0.0771078i
\(846\) 0 0
\(847\) 0 0
\(848\) 12.0000i 0.412082i
\(849\) 0 0
\(850\) 19.5080 + 8.33298i 0.669118 + 0.285819i
\(851\) 0 0
\(852\) 0 0
\(853\) 46.6690i 1.59792i −0.601386 0.798959i \(-0.705384\pi\)
0.601386 0.798959i \(-0.294616\pi\)
\(854\) 0 0
\(855\) 12.0000 + 36.0000i 0.410391 + 1.23117i
\(856\) −6.00000 + 10.3923i −0.205076 + 0.355202i
\(857\) 11.0227 6.36396i 0.376528 0.217389i −0.299778 0.954009i \(-0.596913\pi\)
0.676307 + 0.736620i \(0.263579\pi\)
\(858\) 0 0
\(859\) −2.82843 + 4.89898i −0.0965047 + 0.167151i −0.910236 0.414091i \(-0.864100\pi\)
0.813731 + 0.581242i \(0.197433\pi\)
\(860\) −25.4558 + 8.48528i −0.868037 + 0.289346i
\(861\) 0 0
\(862\) 16.0000i 0.544962i
\(863\) −20.7846 12.0000i −0.707516 0.408485i 0.102624 0.994720i \(-0.467276\pi\)
−0.810141 + 0.586235i \(0.800609\pi\)
\(864\) 0 0
\(865\) 7.09808 + 6.29423i 0.241342 + 0.214010i
\(866\) 14.8492 25.7196i 0.504598 0.873989i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 25.4558 + 44.0908i 0.862538 + 1.49396i
\(872\) 10.3923 6.00000i 0.351928 0.203186i
\(873\) 11.0227 + 6.36396i 0.373062 + 0.215387i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −15.5885 9.00000i −0.526385 0.303908i 0.213158 0.977018i \(-0.431625\pi\)
−0.739543 + 0.673109i \(0.764958\pi\)
\(878\) 34.2929 19.7990i 1.15733 0.668184i
\(879\) 0 0
\(880\) 8.76268 + 1.79315i 0.295390 + 0.0604471i
\(881\) 32.5269 1.09586 0.547930 0.836524i \(-0.315416\pi\)
0.547930 + 0.836524i \(0.315416\pi\)
\(882\) 0 0
\(883\) 12.0000i 0.403832i −0.979403 0.201916i \(-0.935283\pi\)
0.979403 0.201916i \(-0.0647168\pi\)
\(884\) −9.00000 + 15.5885i −0.302703 + 0.524297i
\(885\) 0 0
\(886\) 6.00000 + 10.3923i 0.201574 + 0.349136i
\(887\) 14.6969 + 8.48528i 0.493475 + 0.284908i 0.726015 0.687679i \(-0.241370\pi\)
−0.232540 + 0.972587i \(0.574704\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −9.00000 + 3.00000i −0.301681 + 0.100560i
\(891\) 18.0000 31.1769i 0.603023 1.04447i
\(892\) 14.6969 8.48528i 0.492090 0.284108i
\(893\) 0 0
\(894\) 0 0
\(895\) −14.1421 42.4264i −0.472719 1.41816i
\(896\) 0 0
\(897\) 0 0
\(898\) 1.73205 + 1.00000i 0.0577993 + 0.0333704i
\(899\) −11.3137 19.5959i −0.377333 0.653560i
\(900\) −13.7942 5.89230i −0.459808 0.196410i
\(901\) −25.4558 + 44.0908i −0.848057 + 1.46888i
\(902\) 5.65685i 0.188353i
\(903\) 0 0
\(904\) 0 0
\(905\) −34.0788 6.97372i −1.13282 0.231814i
\(906\) 0 0
\(907\) 10.3923 6.00000i 0.345071 0.199227i −0.317441 0.948278i \(-0.602824\pi\)
0.662512 + 0.749051i \(0.269490\pi\)
\(908\) −14.6969 8.48528i −0.487735 0.281594i
\(909\) −29.6985 −0.985037
\(910\) 0 0
\(911\) −40.0000 −1.32526 −0.662630 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) 0 0
\(913\) −58.7878 + 33.9411i −1.94559 + 1.12329i
\(914\) −12.0000 20.7846i −0.396925 0.687494i
\(915\) 0 0
\(916\) −15.5563 −0.513996
\(917\) 0 0
\(918\) 0 0
\(919\) 24.0000 41.5692i 0.791687 1.37124i −0.133235 0.991084i \(-0.542536\pi\)
0.924922 0.380158i \(-0.124130\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 18.3712 + 10.6066i 0.605022 + 0.349310i
\(923\) 33.9411i 1.11719i
\(924\) 0 0
\(925\) −18.0000 24.0000i −0.591836 0.789115i
\(926\) 12.0000 20.7846i 0.394344 0.683025i
\(927\) −44.0908 + 25.4558i −1.44813 + 0.836080i
\(928\) −3.46410 + 2.00000i −0.113715 + 0.0656532i
\(929\) 14.8492 25.7196i 0.487188 0.843834i −0.512704 0.858566i \(-0.671356\pi\)
0.999891 + 0.0147316i \(0.00468937\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 6.00000i 0.196537i
\(933\) 0 0
\(934\) −8.48528 14.6969i −0.277647 0.480899i
\(935\) −28.3923 25.1769i −0.928528 0.823373i
\(936\) 6.36396 11.0227i 0.208013 0.360288i
\(937\) 4.24264i 0.138601i −0.997596 0.0693005i \(-0.977923\pi\)
0.997596 0.0693005i \(-0.0220767\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 24.7487 + 42.8661i 0.806786 + 1.39739i 0.915079 + 0.403275i \(0.132128\pi\)
−0.108293 + 0.994119i \(0.534538\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −11.3137 −0.368230
\(945\) 0 0
\(946\) 48.0000 1.56061
\(947\) −10.3923 6.00000i −0.337705 0.194974i 0.321552 0.946892i \(-0.395796\pi\)
−0.659256 + 0.751918i \(0.729129\pi\)
\(948\) 0 0
\(949\) −9.00000 15.5885i −0.292152 0.506023i
\(950\) −28.0812 + 3.38323i −0.911074 + 0.109766i
\(951\) 0 0
\(952\) 0 0
\(953\) 24.0000i 0.777436i −0.921357 0.388718i \(-0.872918\pi\)
0.921357 0.388718i \(-0.127082\pi\)
\(954\) 18.0000 31.1769i 0.582772 1.00939i
\(955\) 11.8685 13.3843i 0.384056 0.433105i
\(956\) 4.00000 + 6.92820i 0.129369 + 0.224074i
\(957\) 0 0
\(958\) 16.9706i 0.548294i
\(959\) 0 0
\(960\) 0 0
\(961\) −0.500000 + 0.866025i −0.0161290 + 0.0279363i
\(962\) 22.0454 12.7279i 0.710772 0.410365i
\(963\) −31.1769 + 18.0000i −1.00466 + 0.580042i
\(964\) 7.77817 13.4722i 0.250518 0.433910i
\(965\) 50.9117 16.9706i 1.63891 0.546302i
\(966\) 0 0
\(967\) 24.0000i 0.771788i 0.922543 + 0.385894i \(0.126107\pi\)
−0.922543 + 0.385894i \(0.873893\pi\)
\(968\) −4.33013 2.50000i −0.139176 0.0803530i
\(969\) 0 0
\(970\) −6.29423 + 7.09808i −0.202096 + 0.227905i
\(971\) 22.6274 39.1918i 0.726148 1.25773i −0.232351 0.972632i \(-0.574642\pi\)
0.958500 0.285094i \(-0.0920248\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −24.0000 −0.769010
\(975\) 0 0
\(976\) 3.53553 + 6.12372i 0.113170 + 0.196016i
\(977\) 25.9808 15.0000i 0.831198 0.479893i −0.0230645 0.999734i \(-0.507342\pi\)
0.854263 + 0.519841i \(0.174009\pi\)
\(978\) 0 0
\(979\) 16.9706 0.542382
\(980\) 0 0
\(981\) 36.0000 1.14939
\(982\) −3.46410 2.00000i −0.110544 0.0638226i
\(983\) −14.6969 + 8.48528i −0.468760 + 0.270638i −0.715720 0.698387i \(-0.753901\pi\)
0.246961 + 0.969025i \(0.420568\pi\)
\(984\) 0 0
\(985\) 5.37945 26.2880i 0.171404 0.837607i
\(986\) 16.9706 0.540453
\(987\) 0 0
\(988\) 24.0000i 0.763542i
\(989\) 0 0
\(990\) 20.0764 + 17.8028i 0.638070 + 0.565809i
\(991\) −24.0000 41.5692i −0.762385 1.32049i −0.941618 0.336683i \(-0.890695\pi\)
0.179233 0.983807i \(-0.442638\pi\)
\(992\) 4.89898 + 2.82843i 0.155543 + 0.0898027i
\(993\) 0 0
\(994\) 0 0
\(995\) 8.00000 + 24.0000i 0.253617 + 0.760851i
\(996\) 0 0
\(997\) −33.0681 + 19.0919i −1.04728 + 0.604646i −0.921886 0.387461i \(-0.873352\pi\)
−0.125392 + 0.992107i \(0.540019\pi\)
\(998\) 3.46410 2.00000i 0.109654 0.0633089i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 490.2.i.d.79.3 8
5.4 even 2 inner 490.2.i.d.79.2 8
7.2 even 3 490.2.c.g.99.2 yes 4
7.3 odd 6 inner 490.2.i.d.459.1 8
7.4 even 3 inner 490.2.i.d.459.2 8
7.5 odd 6 490.2.c.g.99.1 4
7.6 odd 2 inner 490.2.i.d.79.4 8
35.2 odd 12 2450.2.a.bo.1.2 2
35.4 even 6 inner 490.2.i.d.459.3 8
35.9 even 6 490.2.c.g.99.4 yes 4
35.12 even 12 2450.2.a.bo.1.1 2
35.19 odd 6 490.2.c.g.99.3 yes 4
35.23 odd 12 2450.2.a.bi.1.1 2
35.24 odd 6 inner 490.2.i.d.459.4 8
35.33 even 12 2450.2.a.bi.1.2 2
35.34 odd 2 inner 490.2.i.d.79.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
490.2.c.g.99.1 4 7.5 odd 6
490.2.c.g.99.2 yes 4 7.2 even 3
490.2.c.g.99.3 yes 4 35.19 odd 6
490.2.c.g.99.4 yes 4 35.9 even 6
490.2.i.d.79.1 8 35.34 odd 2 inner
490.2.i.d.79.2 8 5.4 even 2 inner
490.2.i.d.79.3 8 1.1 even 1 trivial
490.2.i.d.79.4 8 7.6 odd 2 inner
490.2.i.d.459.1 8 7.3 odd 6 inner
490.2.i.d.459.2 8 7.4 even 3 inner
490.2.i.d.459.3 8 35.4 even 6 inner
490.2.i.d.459.4 8 35.24 odd 6 inner
2450.2.a.bi.1.1 2 35.23 odd 12
2450.2.a.bi.1.2 2 35.33 even 12
2450.2.a.bo.1.1 2 35.12 even 12
2450.2.a.bo.1.2 2 35.2 odd 12