Properties

Label 966.2.g.e.643.13
Level $966$
Weight $2$
Character 966.643
Analytic conductor $7.714$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(643,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.643");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.g (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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 326x^{12} + 27081x^{8} + 96196x^{4} + 65536 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 643.13
Root \(0.691340 + 0.691340i\) of defining polynomial
Character \(\chi\) \(=\) 966.643
Dual form 966.2.g.e.643.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +0.952834 q^{5} +1.00000i q^{6} +(0.691340 - 2.55383i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +0.952834 q^{5} +1.00000i q^{6} +(0.691340 - 2.55383i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +0.952834 q^{10} +1.02228i q^{11} +1.00000i q^{12} +5.28761i q^{13} +(0.691340 - 2.55383i) q^{14} +0.952834i q^{15} +1.00000 q^{16} +1.38268 q^{17} -1.00000 q^{18} +5.99105 q^{19} +0.952834 q^{20} +(2.55383 + 0.691340i) q^{21} +1.02228i q^{22} +(3.53113 - 3.24517i) q^{23} +1.00000i q^{24} -4.09211 q^{25} +5.28761i q^{26} -1.00000i q^{27} +(0.691340 - 2.55383i) q^{28} +5.57914 q^{29} +0.952834i q^{30} +1.00000 q^{32} -1.02228 q^{33} +1.38268 q^{34} +(0.658732 - 2.43338i) q^{35} -1.00000 q^{36} +0.429846i q^{37} +5.99105 q^{38} -5.28761 q^{39} +0.952834 q^{40} +1.28761i q^{41} +(2.55383 + 0.691340i) q^{42} -4.67781i q^{43} +1.02228i q^{44} -0.952834 q^{45} +(3.53113 - 3.24517i) q^{46} +7.09211i q^{47} +1.00000i q^{48} +(-6.04410 - 3.53113i) q^{49} -4.09211 q^{50} +1.38268i q^{51} +5.28761i q^{52} -8.75641i q^{53} -1.00000i q^{54} +0.974060i q^{55} +(0.691340 - 2.55383i) q^{56} +5.99105i q^{57} +5.57914 q^{58} +1.70848i q^{59} +0.952834i q^{60} -7.37373 q^{61} +(-0.691340 + 2.55383i) q^{63} +1.00000 q^{64} +5.03822i q^{65} -1.02228 q^{66} +11.6217i q^{67} +1.38268 q^{68} +(3.24517 + 3.53113i) q^{69} +(0.658732 - 2.43338i) q^{70} -2.29152 q^{71} -1.00000 q^{72} -2.19551i q^{73} +0.429846i q^{74} -4.09211i q^{75} +5.99105 q^{76} +(2.61072 + 0.706741i) q^{77} -5.28761 q^{78} +9.77869i q^{79} +0.952834 q^{80} +1.00000 q^{81} +1.28761i q^{82} -5.46806 q^{83} +(2.55383 + 0.691340i) q^{84} +1.31746 q^{85} -4.67781i q^{86} +5.57914i q^{87} +1.02228i q^{88} -8.69375 q^{89} -0.952834 q^{90} +(13.5037 + 3.65554i) q^{91} +(3.53113 - 3.24517i) q^{92} +7.09211i q^{94} +5.70848 q^{95} +1.00000i q^{96} -19.2038 q^{97} +(-6.04410 - 3.53113i) q^{98} -1.02228i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9} + 16 q^{16} - 16 q^{18} - 8 q^{23} + 36 q^{25} + 20 q^{29} + 16 q^{32} - 16 q^{35} - 16 q^{36} - 4 q^{39} - 8 q^{46} + 36 q^{50} + 20 q^{58} + 16 q^{64} - 16 q^{70} - 48 q^{71} - 16 q^{72} + 20 q^{77} - 4 q^{78} + 16 q^{81} - 32 q^{85} - 8 q^{92} + 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 0.952834 0.426120 0.213060 0.977039i \(-0.431657\pi\)
0.213060 + 0.977039i \(0.431657\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 0.691340 2.55383i 0.261302 0.965257i
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) 0.952834 0.301313
\(11\) 1.02228i 0.308228i 0.988053 + 0.154114i \(0.0492523\pi\)
−0.988053 + 0.154114i \(0.950748\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 5.28761i 1.46652i 0.679948 + 0.733260i \(0.262002\pi\)
−0.679948 + 0.733260i \(0.737998\pi\)
\(14\) 0.691340 2.55383i 0.184768 0.682540i
\(15\) 0.952834i 0.246021i
\(16\) 1.00000 0.250000
\(17\) 1.38268 0.335349 0.167675 0.985842i \(-0.446374\pi\)
0.167675 + 0.985842i \(0.446374\pi\)
\(18\) −1.00000 −0.235702
\(19\) 5.99105 1.37444 0.687221 0.726449i \(-0.258831\pi\)
0.687221 + 0.726449i \(0.258831\pi\)
\(20\) 0.952834 0.213060
\(21\) 2.55383 + 0.691340i 0.557291 + 0.150863i
\(22\) 1.02228i 0.217950i
\(23\) 3.53113 3.24517i 0.736291 0.676665i
\(24\) 1.00000i 0.204124i
\(25\) −4.09211 −0.818422
\(26\) 5.28761i 1.03699i
\(27\) 1.00000i 0.192450i
\(28\) 0.691340 2.55383i 0.130651 0.482629i
\(29\) 5.57914 1.03602 0.518010 0.855375i \(-0.326673\pi\)
0.518010 + 0.855375i \(0.326673\pi\)
\(30\) 0.952834i 0.173963i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.02228 −0.177956
\(34\) 1.38268 0.237128
\(35\) 0.658732 2.43338i 0.111346 0.411316i
\(36\) −1.00000 −0.166667
\(37\) 0.429846i 0.0706662i 0.999376 + 0.0353331i \(0.0112492\pi\)
−0.999376 + 0.0353331i \(0.988751\pi\)
\(38\) 5.99105 0.971877
\(39\) −5.28761 −0.846696
\(40\) 0.952834 0.150656
\(41\) 1.28761i 0.201091i 0.994932 + 0.100546i \(0.0320589\pi\)
−0.994932 + 0.100546i \(0.967941\pi\)
\(42\) 2.55383 + 0.691340i 0.394065 + 0.106676i
\(43\) 4.67781i 0.713360i −0.934227 0.356680i \(-0.883909\pi\)
0.934227 0.356680i \(-0.116091\pi\)
\(44\) 1.02228i 0.154114i
\(45\) −0.952834 −0.142040
\(46\) 3.53113 3.24517i 0.520637 0.478474i
\(47\) 7.09211i 1.03449i 0.855837 + 0.517245i \(0.173042\pi\)
−0.855837 + 0.517245i \(0.826958\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −6.04410 3.53113i −0.863443 0.504447i
\(50\) −4.09211 −0.578711
\(51\) 1.38268i 0.193614i
\(52\) 5.28761i 0.733260i
\(53\) 8.75641i 1.20279i −0.798954 0.601393i \(-0.794613\pi\)
0.798954 0.601393i \(-0.205387\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0.974060i 0.131342i
\(56\) 0.691340 2.55383i 0.0923842 0.341270i
\(57\) 5.99105i 0.793534i
\(58\) 5.57914 0.732577
\(59\) 1.70848i 0.222425i 0.993797 + 0.111212i \(0.0354734\pi\)
−0.993797 + 0.111212i \(0.964527\pi\)
\(60\) 0.952834i 0.123010i
\(61\) −7.37373 −0.944109 −0.472055 0.881569i \(-0.656488\pi\)
−0.472055 + 0.881569i \(0.656488\pi\)
\(62\) 0 0
\(63\) −0.691340 + 2.55383i −0.0871006 + 0.321752i
\(64\) 1.00000 0.125000
\(65\) 5.03822i 0.624914i
\(66\) −1.02228 −0.125834
\(67\) 11.6217i 1.41982i 0.704294 + 0.709908i \(0.251264\pi\)
−0.704294 + 0.709908i \(0.748736\pi\)
\(68\) 1.38268 0.167675
\(69\) 3.24517 + 3.53113i 0.390673 + 0.425098i
\(70\) 0.658732 2.43338i 0.0787335 0.290844i
\(71\) −2.29152 −0.271954 −0.135977 0.990712i \(-0.543417\pi\)
−0.135977 + 0.990712i \(0.543417\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.19551i 0.256965i −0.991712 0.128482i \(-0.958989\pi\)
0.991712 0.128482i \(-0.0410105\pi\)
\(74\) 0.429846i 0.0499685i
\(75\) 4.09211i 0.472516i
\(76\) 5.99105 0.687221
\(77\) 2.61072 + 0.706741i 0.297519 + 0.0805406i
\(78\) −5.28761 −0.598704
\(79\) 9.77869i 1.10019i 0.835103 + 0.550094i \(0.185408\pi\)
−0.835103 + 0.550094i \(0.814592\pi\)
\(80\) 0.952834 0.106530
\(81\) 1.00000 0.111111
\(82\) 1.28761i 0.142193i
\(83\) −5.46806 −0.600198 −0.300099 0.953908i \(-0.597020\pi\)
−0.300099 + 0.953908i \(0.597020\pi\)
\(84\) 2.55383 + 0.691340i 0.278646 + 0.0754314i
\(85\) 1.31746 0.142899
\(86\) 4.67781i 0.504422i
\(87\) 5.57914i 0.598146i
\(88\) 1.02228i 0.108975i
\(89\) −8.69375 −0.921536 −0.460768 0.887521i \(-0.652426\pi\)
−0.460768 + 0.887521i \(0.652426\pi\)
\(90\) −0.952834 −0.100438
\(91\) 13.5037 + 3.65554i 1.41557 + 0.383204i
\(92\) 3.53113 3.24517i 0.368146 0.338332i
\(93\) 0 0
\(94\) 7.09211i 0.731495i
\(95\) 5.70848 0.585677
\(96\) 1.00000i 0.102062i
\(97\) −19.2038 −1.94985 −0.974923 0.222541i \(-0.928565\pi\)
−0.974923 + 0.222541i \(0.928565\pi\)
\(98\) −6.04410 3.53113i −0.610546 0.356698i
\(99\) 1.02228i 0.102743i
\(100\) −4.09211 −0.409211
\(101\) 15.8927i 1.58138i −0.612216 0.790691i \(-0.709722\pi\)
0.612216 0.790691i \(-0.290278\pi\)
\(102\) 1.38268i 0.136906i
\(103\) 1.74987 0.172420 0.0862099 0.996277i \(-0.472524\pi\)
0.0862099 + 0.996277i \(0.472524\pi\)
\(104\) 5.28761i 0.518493i
\(105\) 2.43338 + 0.658732i 0.237473 + 0.0642856i
\(106\) 8.75641i 0.850498i
\(107\) 11.0987i 1.07295i −0.843915 0.536476i \(-0.819755\pi\)
0.843915 0.536476i \(-0.180245\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 2.33551i 0.223702i −0.993725 0.111851i \(-0.964322\pi\)
0.993725 0.111851i \(-0.0356779\pi\)
\(110\) 0.974060i 0.0928730i
\(111\) −0.429846 −0.0407991
\(112\) 0.691340 2.55383i 0.0653255 0.241314i
\(113\) 10.2322i 0.962567i −0.876565 0.481284i \(-0.840171\pi\)
0.876565 0.481284i \(-0.159829\pi\)
\(114\) 5.99105i 0.561113i
\(115\) 3.36458 3.09211i 0.313749 0.288341i
\(116\) 5.57914 0.518010
\(117\) 5.28761i 0.488840i
\(118\) 1.70848i 0.157278i
\(119\) 0.955901 3.53113i 0.0876273 0.323698i
\(120\) 0.952834i 0.0869814i
\(121\) 9.95495 0.904995
\(122\) −7.37373 −0.667586
\(123\) −1.28761 −0.116100
\(124\) 0 0
\(125\) −8.66327 −0.774866
\(126\) −0.691340 + 2.55383i −0.0615894 + 0.227513i
\(127\) −16.3499 −1.45082 −0.725408 0.688319i \(-0.758349\pi\)
−0.725408 + 0.688319i \(0.758349\pi\)
\(128\) 1.00000 0.0883883
\(129\) 4.67781 0.411859
\(130\) 5.03822i 0.441881i
\(131\) 11.1583i 0.974903i −0.873150 0.487452i \(-0.837927\pi\)
0.873150 0.487452i \(-0.162073\pi\)
\(132\) −1.02228 −0.0889778
\(133\) 4.14185 15.3001i 0.359144 1.32669i
\(134\) 11.6217i 1.00396i
\(135\) 0.952834i 0.0820069i
\(136\) 1.38268 0.118564
\(137\) 0.155798i 0.0133107i −0.999978 0.00665534i \(-0.997882\pi\)
0.999978 0.00665534i \(-0.00211848\pi\)
\(138\) 3.24517 + 3.53113i 0.276247 + 0.300590i
\(139\) 2.99609i 0.254125i 0.991895 + 0.127063i \(0.0405549\pi\)
−0.991895 + 0.127063i \(0.959445\pi\)
\(140\) 0.658732 2.43338i 0.0556730 0.205658i
\(141\) −7.09211 −0.597263
\(142\) −2.29152 −0.192300
\(143\) −5.40541 −0.452023
\(144\) −1.00000 −0.0833333
\(145\) 5.31599 0.441469
\(146\) 2.19551i 0.181701i
\(147\) 3.53113 6.04410i 0.291243 0.498509i
\(148\) 0.429846i 0.0353331i
\(149\) 2.17972i 0.178569i 0.996006 + 0.0892846i \(0.0284581\pi\)
−0.996006 + 0.0892846i \(0.971542\pi\)
\(150\) 4.09211i 0.334119i
\(151\) 1.38363 0.112598 0.0562992 0.998414i \(-0.482070\pi\)
0.0562992 + 0.998414i \(0.482070\pi\)
\(152\) 5.99105 0.485938
\(153\) −1.38268 −0.111783
\(154\) 2.61072 + 0.706741i 0.210378 + 0.0569508i
\(155\) 0 0
\(156\) −5.28761 −0.423348
\(157\) −11.1851 −0.892665 −0.446333 0.894867i \(-0.647270\pi\)
−0.446333 + 0.894867i \(0.647270\pi\)
\(158\) 9.77869i 0.777951i
\(159\) 8.75641 0.694428
\(160\) 0.952834 0.0753281
\(161\) −5.84640 11.2614i −0.460761 0.887524i
\(162\) 1.00000 0.0785674
\(163\) 7.54929 0.591306 0.295653 0.955295i \(-0.404463\pi\)
0.295653 + 0.955295i \(0.404463\pi\)
\(164\) 1.28761i 0.100546i
\(165\) −0.974060 −0.0758305
\(166\) −5.46806 −0.424404
\(167\) 11.9290i 0.923094i 0.887116 + 0.461547i \(0.152706\pi\)
−0.887116 + 0.461547i \(0.847294\pi\)
\(168\) 2.55383 + 0.691340i 0.197032 + 0.0533380i
\(169\) −14.9589 −1.15068
\(170\) 1.31746 0.101045
\(171\) −5.99105 −0.458147
\(172\) 4.67781i 0.356680i
\(173\) 18.0882i 1.37522i −0.726080 0.687610i \(-0.758660\pi\)
0.726080 0.687610i \(-0.241340\pi\)
\(174\) 5.57914i 0.422953i
\(175\) −2.82904 + 10.4505i −0.213855 + 0.789987i
\(176\) 1.02228i 0.0770571i
\(177\) −1.70848 −0.128417
\(178\) −8.69375 −0.651624
\(179\) 1.77464 0.132643 0.0663216 0.997798i \(-0.478874\pi\)
0.0663216 + 0.997798i \(0.478874\pi\)
\(180\) −0.952834 −0.0710200
\(181\) −20.4933 −1.52325 −0.761627 0.648015i \(-0.775599\pi\)
−0.761627 + 0.648015i \(0.775599\pi\)
\(182\) 13.5037 + 3.65554i 1.00096 + 0.270966i
\(183\) 7.37373i 0.545082i
\(184\) 3.53113 3.24517i 0.260318 0.239237i
\(185\) 0.409572i 0.0301123i
\(186\) 0 0
\(187\) 1.41348i 0.103364i
\(188\) 7.09211i 0.517245i
\(189\) −2.55383 0.691340i −0.185764 0.0502876i
\(190\) 5.70848 0.414136
\(191\) 1.68043i 0.121591i 0.998150 + 0.0607957i \(0.0193638\pi\)
−0.998150 + 0.0607957i \(0.980636\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −4.71239 −0.339205 −0.169602 0.985513i \(-0.554248\pi\)
−0.169602 + 0.985513i \(0.554248\pi\)
\(194\) −19.2038 −1.37875
\(195\) −5.03822 −0.360794
\(196\) −6.04410 3.53113i −0.431721 0.252223i
\(197\) 24.9251 1.77584 0.887920 0.459998i \(-0.152150\pi\)
0.887920 + 0.459998i \(0.152150\pi\)
\(198\) 1.02228i 0.0726501i
\(199\) −8.60434 −0.609945 −0.304973 0.952361i \(-0.598647\pi\)
−0.304973 + 0.952361i \(0.598647\pi\)
\(200\) −4.09211 −0.289356
\(201\) −11.6217 −0.819731
\(202\) 15.8927i 1.11821i
\(203\) 3.85708 14.2482i 0.270714 1.00003i
\(204\) 1.38268i 0.0968069i
\(205\) 1.22688i 0.0856892i
\(206\) 1.74987 0.121919
\(207\) −3.53113 + 3.24517i −0.245430 + 0.225555i
\(208\) 5.28761i 0.366630i
\(209\) 6.12452i 0.423642i
\(210\) 2.43338 + 0.658732i 0.167919 + 0.0454568i
\(211\) −19.3460 −1.33183 −0.665915 0.746027i \(-0.731959\pi\)
−0.665915 + 0.746027i \(0.731959\pi\)
\(212\) 8.75641i 0.601393i
\(213\) 2.29152i 0.157013i
\(214\) 11.0987i 0.758692i
\(215\) 4.45718i 0.303977i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) 2.33551i 0.158181i
\(219\) 2.19551 0.148359
\(220\) 0.974060i 0.0656711i
\(221\) 7.31108i 0.491796i
\(222\) −0.429846 −0.0288494
\(223\) 17.7335i 1.18752i 0.804641 + 0.593762i \(0.202358\pi\)
−0.804641 + 0.593762i \(0.797642\pi\)
\(224\) 0.691340 2.55383i 0.0461921 0.170635i
\(225\) 4.09211 0.272807
\(226\) 10.2322i 0.680638i
\(227\) −9.92436 −0.658703 −0.329352 0.944207i \(-0.606830\pi\)
−0.329352 + 0.944207i \(0.606830\pi\)
\(228\) 5.99105i 0.396767i
\(229\) 15.8223 1.04557 0.522783 0.852466i \(-0.324894\pi\)
0.522783 + 0.852466i \(0.324894\pi\)
\(230\) 3.36458 3.09211i 0.221854 0.203888i
\(231\) −0.706741 + 2.61072i −0.0465001 + 0.171773i
\(232\) 5.57914 0.366288
\(233\) 13.0259 0.853358 0.426679 0.904403i \(-0.359683\pi\)
0.426679 + 0.904403i \(0.359683\pi\)
\(234\) 5.28761i 0.345662i
\(235\) 6.75760i 0.440817i
\(236\) 1.70848i 0.111212i
\(237\) −9.77869 −0.635194
\(238\) 0.955901 3.53113i 0.0619619 0.228889i
\(239\) 10.6712 0.690266 0.345133 0.938554i \(-0.387834\pi\)
0.345133 + 0.938554i \(0.387834\pi\)
\(240\) 0.952834i 0.0615052i
\(241\) 19.2038 1.23702 0.618511 0.785776i \(-0.287736\pi\)
0.618511 + 0.785776i \(0.287736\pi\)
\(242\) 9.95495 0.639928
\(243\) 1.00000i 0.0641500i
\(244\) −7.37373 −0.472055
\(245\) −5.75902 3.36458i −0.367930 0.214955i
\(246\) −1.28761 −0.0820953
\(247\) 31.6784i 2.01565i
\(248\) 0 0
\(249\) 5.46806i 0.346524i
\(250\) −8.66327 −0.547913
\(251\) 0.429846 0.0271316 0.0135658 0.999908i \(-0.495682\pi\)
0.0135658 + 0.999908i \(0.495682\pi\)
\(252\) −0.691340 + 2.55383i −0.0435503 + 0.160876i
\(253\) 3.31746 + 3.60979i 0.208567 + 0.226946i
\(254\) −16.3499 −1.02588
\(255\) 1.31746i 0.0825028i
\(256\) 1.00000 0.0625000
\(257\) 21.2465i 1.32532i −0.748921 0.662659i \(-0.769428\pi\)
0.748921 0.662659i \(-0.230572\pi\)
\(258\) 4.67781 0.291228
\(259\) 1.09775 + 0.297169i 0.0682111 + 0.0184652i
\(260\) 5.03822i 0.312457i
\(261\) −5.57914 −0.345340
\(262\) 11.1583i 0.689361i
\(263\) 18.1188i 1.11725i −0.829419 0.558627i \(-0.811328\pi\)
0.829419 0.558627i \(-0.188672\pi\)
\(264\) −1.02228 −0.0629168
\(265\) 8.34340i 0.512531i
\(266\) 4.14185 15.3001i 0.253953 0.938111i
\(267\) 8.69375i 0.532049i
\(268\) 11.6217i 0.709908i
\(269\) 3.44198i 0.209861i −0.994480 0.104931i \(-0.966538\pi\)
0.994480 0.104931i \(-0.0334620\pi\)
\(270\) 0.952834i 0.0579876i
\(271\) 2.57523i 0.156434i −0.996936 0.0782170i \(-0.975077\pi\)
0.996936 0.0782170i \(-0.0249227\pi\)
\(272\) 1.38268 0.0838373
\(273\) −3.65554 + 13.5037i −0.221243 + 0.817279i
\(274\) 0.155798i 0.00941208i
\(275\) 4.18327i 0.252261i
\(276\) 3.24517 + 3.53113i 0.195336 + 0.212549i
\(277\) −15.7335 −0.945335 −0.472667 0.881241i \(-0.656709\pi\)
−0.472667 + 0.881241i \(0.656709\pi\)
\(278\) 2.99609i 0.179694i
\(279\) 0 0
\(280\) 0.658732 2.43338i 0.0393668 0.145422i
\(281\) 24.2115i 1.44434i 0.691717 + 0.722168i \(0.256854\pi\)
−0.691717 + 0.722168i \(0.743146\pi\)
\(282\) −7.09211 −0.422329
\(283\) 24.2383 1.44081 0.720407 0.693551i \(-0.243955\pi\)
0.720407 + 0.693551i \(0.243955\pi\)
\(284\) −2.29152 −0.135977
\(285\) 5.70848i 0.338141i
\(286\) −5.40541 −0.319628
\(287\) 3.28835 + 0.890179i 0.194105 + 0.0525456i
\(288\) −1.00000 −0.0589256
\(289\) −15.0882 −0.887541
\(290\) 5.31599 0.312166
\(291\) 19.2038i 1.12574i
\(292\) 2.19551i 0.128482i
\(293\) −27.2814 −1.59380 −0.796898 0.604114i \(-0.793527\pi\)
−0.796898 + 0.604114i \(0.793527\pi\)
\(294\) 3.53113 6.04410i 0.205940 0.352499i
\(295\) 1.62789i 0.0947796i
\(296\) 0.429846i 0.0249843i
\(297\) 1.02228 0.0593185
\(298\) 2.17972i 0.126268i
\(299\) 17.1592 + 18.6712i 0.992343 + 1.07979i
\(300\) 4.09211i 0.236258i
\(301\) −11.9463 3.23396i −0.688576 0.186402i
\(302\) 1.38363 0.0796191
\(303\) 15.8927 0.913011
\(304\) 5.99105 0.343610
\(305\) −7.02594 −0.402304
\(306\) −1.38268 −0.0790425
\(307\) 25.1206i 1.43371i 0.697223 + 0.716854i \(0.254419\pi\)
−0.697223 + 0.716854i \(0.745581\pi\)
\(308\) 2.61072 + 0.706741i 0.148760 + 0.0402703i
\(309\) 1.74987i 0.0995466i
\(310\) 0 0
\(311\) 10.6712i 0.605111i 0.953132 + 0.302555i \(0.0978397\pi\)
−0.953132 + 0.302555i \(0.902160\pi\)
\(312\) −5.28761 −0.299352
\(313\) 9.21674 0.520961 0.260481 0.965479i \(-0.416119\pi\)
0.260481 + 0.965479i \(0.416119\pi\)
\(314\) −11.1851 −0.631210
\(315\) −0.658732 + 2.43338i −0.0371153 + 0.137105i
\(316\) 9.77869i 0.550094i
\(317\) −25.3048 −1.42126 −0.710630 0.703566i \(-0.751590\pi\)
−0.710630 + 0.703566i \(0.751590\pi\)
\(318\) 8.75641 0.491035
\(319\) 5.70343i 0.319331i
\(320\) 0.952834 0.0532650
\(321\) 11.0987 0.619470
\(322\) −5.84640 11.2614i −0.325807 0.627574i
\(323\) 8.28370 0.460918
\(324\) 1.00000 0.0555556
\(325\) 21.6375i 1.20023i
\(326\) 7.54929 0.418116
\(327\) 2.33551 0.129154
\(328\) 1.28761i 0.0710966i
\(329\) 18.1120 + 4.90306i 0.998549 + 0.270314i
\(330\) −0.974060 −0.0536203
\(331\) −0.830434 −0.0456448 −0.0228224 0.999740i \(-0.507265\pi\)
−0.0228224 + 0.999740i \(0.507265\pi\)
\(332\) −5.46806 −0.300099
\(333\) 0.429846i 0.0235554i
\(334\) 11.9290i 0.652726i
\(335\) 11.0735i 0.605013i
\(336\) 2.55383 + 0.691340i 0.139323 + 0.0377157i
\(337\) 7.58885i 0.413391i −0.978405 0.206695i \(-0.933729\pi\)
0.978405 0.206695i \(-0.0662709\pi\)
\(338\) −14.9589 −0.813655
\(339\) 10.2322 0.555739
\(340\) 1.31746 0.0714495
\(341\) 0 0
\(342\) −5.99105 −0.323959
\(343\) −13.1964 + 12.9944i −0.712540 + 0.701631i
\(344\) 4.67781i 0.252211i
\(345\) 3.09211 + 3.36458i 0.166473 + 0.181143i
\(346\) 18.0882i 0.972428i
\(347\) 30.1431 1.61817 0.809083 0.587695i \(-0.199965\pi\)
0.809083 + 0.587695i \(0.199965\pi\)
\(348\) 5.57914i 0.299073i
\(349\) 22.6115i 1.21037i 0.796086 + 0.605184i \(0.206901\pi\)
−0.796086 + 0.605184i \(0.793099\pi\)
\(350\) −2.82904 + 10.4505i −0.151218 + 0.558605i
\(351\) 5.28761 0.282232
\(352\) 1.02228i 0.0544876i
\(353\) 8.44589i 0.449529i −0.974413 0.224765i \(-0.927839\pi\)
0.974413 0.224765i \(-0.0721613\pi\)
\(354\) −1.70848 −0.0908045
\(355\) −2.18344 −0.115885
\(356\) −8.69375 −0.460768
\(357\) 3.53113 + 0.955901i 0.186887 + 0.0505917i
\(358\) 1.77464 0.0937928
\(359\) 18.7007i 0.986988i −0.869749 0.493494i \(-0.835720\pi\)
0.869749 0.493494i \(-0.164280\pi\)
\(360\) −0.952834 −0.0502188
\(361\) 16.8927 0.889089
\(362\) −20.4933 −1.07710
\(363\) 9.95495i 0.522499i
\(364\) 13.5037 + 3.65554i 0.707785 + 0.191602i
\(365\) 2.09195i 0.109498i
\(366\) 7.37373i 0.385431i
\(367\) 27.7112 1.44651 0.723257 0.690579i \(-0.242644\pi\)
0.723257 + 0.690579i \(0.242644\pi\)
\(368\) 3.53113 3.24517i 0.184073 0.169166i
\(369\) 1.28761i 0.0670305i
\(370\) 0.409572i 0.0212926i
\(371\) −22.3624 6.05365i −1.16100 0.314290i
\(372\) 0 0
\(373\) 31.6157i 1.63700i 0.574507 + 0.818500i \(0.305194\pi\)
−0.574507 + 0.818500i \(0.694806\pi\)
\(374\) 1.41348i 0.0730894i
\(375\) 8.66327i 0.447369i
\(376\) 7.09211i 0.365748i
\(377\) 29.5003i 1.51934i
\(378\) −2.55383 0.691340i −0.131355 0.0355587i
\(379\) 31.2347i 1.60442i −0.597044 0.802209i \(-0.703658\pi\)
0.597044 0.802209i \(-0.296342\pi\)
\(380\) 5.70848 0.292839
\(381\) 16.3499i 0.837629i
\(382\) 1.68043i 0.0859781i
\(383\) 10.3880 0.530804 0.265402 0.964138i \(-0.414495\pi\)
0.265402 + 0.964138i \(0.414495\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 2.48758 + 0.673407i 0.126779 + 0.0343200i
\(386\) −4.71239 −0.239854
\(387\) 4.67781i 0.237787i
\(388\) −19.2038 −0.974923
\(389\) 11.7081i 0.593622i 0.954936 + 0.296811i \(0.0959231\pi\)
−0.954936 + 0.296811i \(0.904077\pi\)
\(390\) −5.03822 −0.255120
\(391\) 4.88242 4.48703i 0.246915 0.226919i
\(392\) −6.04410 3.53113i −0.305273 0.178349i
\(393\) 11.1583 0.562861
\(394\) 24.9251 1.25571
\(395\) 9.31746i 0.468812i
\(396\) 1.02228i 0.0513714i
\(397\) 5.35378i 0.268699i −0.990934 0.134349i \(-0.957106\pi\)
0.990934 0.134349i \(-0.0428944\pi\)
\(398\) −8.60434 −0.431297
\(399\) 15.3001 + 4.14185i 0.765964 + 0.207352i
\(400\) −4.09211 −0.204605
\(401\) 34.9329i 1.74447i −0.489091 0.872233i \(-0.662671\pi\)
0.489091 0.872233i \(-0.337329\pi\)
\(402\) −11.6217 −0.579638
\(403\) 0 0
\(404\) 15.8927i 0.790691i
\(405\) 0.952834 0.0473467
\(406\) 3.85708 14.2482i 0.191424 0.707125i
\(407\) −0.439422 −0.0217813
\(408\) 1.38268i 0.0684528i
\(409\) 22.1479i 1.09514i 0.836759 + 0.547572i \(0.184448\pi\)
−0.836759 + 0.547572i \(0.815552\pi\)
\(410\) 1.22688i 0.0605914i
\(411\) 0.155798 0.00768493
\(412\) 1.74987 0.0862099
\(413\) 4.36316 + 1.18114i 0.214697 + 0.0581200i
\(414\) −3.53113 + 3.24517i −0.173546 + 0.159491i
\(415\) −5.21016 −0.255756
\(416\) 5.28761i 0.259247i
\(417\) −2.99609 −0.146719
\(418\) 6.12452i 0.299560i
\(419\) −0.215119 −0.0105092 −0.00525462 0.999986i \(-0.501673\pi\)
−0.00525462 + 0.999986i \(0.501673\pi\)
\(420\) 2.43338 + 0.658732i 0.118737 + 0.0321428i
\(421\) 16.3757i 0.798105i 0.916928 + 0.399053i \(0.130661\pi\)
−0.916928 + 0.399053i \(0.869339\pi\)
\(422\) −19.3460 −0.941747
\(423\) 7.09211i 0.344830i
\(424\) 8.75641i 0.425249i
\(425\) −5.65807 −0.274457
\(426\) 2.29152i 0.111025i
\(427\) −5.09775 + 18.8313i −0.246698 + 0.911308i
\(428\) 11.0987i 0.536476i
\(429\) 5.40541i 0.260976i
\(430\) 4.45718i 0.214944i
\(431\) 17.1982i 0.828406i 0.910184 + 0.414203i \(0.135940\pi\)
−0.910184 + 0.414203i \(0.864060\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −3.99224 −0.191855 −0.0959274 0.995388i \(-0.530582\pi\)
−0.0959274 + 0.995388i \(0.530582\pi\)
\(434\) 0 0
\(435\) 5.31599i 0.254882i
\(436\) 2.33551i 0.111851i
\(437\) 21.1552 19.4420i 1.01199 0.930036i
\(438\) 2.19551 0.104905
\(439\) 2.76726i 0.132074i −0.997817 0.0660371i \(-0.978964\pi\)
0.997817 0.0660371i \(-0.0210356\pi\)
\(440\) 0.974060i 0.0464365i
\(441\) 6.04410 + 3.53113i 0.287814 + 0.168149i
\(442\) 7.31108i 0.347752i
\(443\) −13.6673 −0.649355 −0.324677 0.945825i \(-0.605256\pi\)
−0.324677 + 0.945825i \(0.605256\pi\)
\(444\) −0.429846 −0.0203996
\(445\) −8.28370 −0.392685
\(446\) 17.7335i 0.839706i
\(447\) −2.17972 −0.103097
\(448\) 0.691340 2.55383i 0.0326627 0.120657i
\(449\) −11.6012 −0.547493 −0.273746 0.961802i \(-0.588263\pi\)
−0.273746 + 0.961802i \(0.588263\pi\)
\(450\) 4.09211 0.192904
\(451\) −1.31630 −0.0619821
\(452\) 10.2322i 0.481284i
\(453\) 1.38363i 0.0650087i
\(454\) −9.92436 −0.465773
\(455\) 12.8668 + 3.48312i 0.603203 + 0.163291i
\(456\) 5.99105i 0.280557i
\(457\) 26.1476i 1.22314i −0.791192 0.611568i \(-0.790539\pi\)
0.791192 0.611568i \(-0.209461\pi\)
\(458\) 15.8223 0.739326
\(459\) 1.38268i 0.0645380i
\(460\) 3.36458 3.09211i 0.156874 0.144170i
\(461\) 5.44980i 0.253822i 0.991914 + 0.126911i \(0.0405063\pi\)
−0.991914 + 0.126911i \(0.959494\pi\)
\(462\) −0.706741 + 2.61072i −0.0328806 + 0.121462i
\(463\) −34.0834 −1.58399 −0.791994 0.610528i \(-0.790957\pi\)
−0.791994 + 0.610528i \(0.790957\pi\)
\(464\) 5.57914 0.259005
\(465\) 0 0
\(466\) 13.0259 0.603415
\(467\) 28.7609 1.33090 0.665449 0.746444i \(-0.268240\pi\)
0.665449 + 0.746444i \(0.268240\pi\)
\(468\) 5.28761i 0.244420i
\(469\) 29.6798 + 8.03454i 1.37049 + 0.371001i
\(470\) 6.75760i 0.311705i
\(471\) 11.1851i 0.515381i
\(472\) 1.70848i 0.0786390i
\(473\) 4.78202 0.219878
\(474\) −9.77869 −0.449150
\(475\) −24.5160 −1.12487
\(476\) 0.955901 3.53113i 0.0438137 0.161849i
\(477\) 8.75641i 0.400928i
\(478\) 10.6712 0.488091
\(479\) 39.5714 1.80806 0.904031 0.427468i \(-0.140594\pi\)
0.904031 + 0.427468i \(0.140594\pi\)
\(480\) 0.952834i 0.0434907i
\(481\) −2.27286 −0.103633
\(482\) 19.2038 0.874707
\(483\) 11.2614 5.84640i 0.512412 0.266021i
\(484\) 9.95495 0.452498
\(485\) −18.2980 −0.830869
\(486\) 1.00000i 0.0453609i
\(487\) −12.8006 −0.580050 −0.290025 0.957019i \(-0.593664\pi\)
−0.290025 + 0.957019i \(0.593664\pi\)
\(488\) −7.37373 −0.333793
\(489\) 7.54929i 0.341391i
\(490\) −5.75902 3.36458i −0.260166 0.151996i
\(491\) 39.4670 1.78112 0.890561 0.454865i \(-0.150312\pi\)
0.890561 + 0.454865i \(0.150312\pi\)
\(492\) −1.28761 −0.0580501
\(493\) 7.71416 0.347428
\(494\) 31.6784i 1.42528i
\(495\) 0.974060i 0.0437808i
\(496\) 0 0
\(497\) −1.58422 + 5.85216i −0.0710621 + 0.262505i
\(498\) 5.46806i 0.245030i
\(499\) −8.58305 −0.384230 −0.192115 0.981372i \(-0.561535\pi\)
−0.192115 + 0.981372i \(0.561535\pi\)
\(500\) −8.66327 −0.387433
\(501\) −11.9290 −0.532949
\(502\) 0.429846 0.0191850
\(503\) −25.3794 −1.13161 −0.565807 0.824538i \(-0.691435\pi\)
−0.565807 + 0.824538i \(0.691435\pi\)
\(504\) −0.691340 + 2.55383i −0.0307947 + 0.113757i
\(505\) 15.1431i 0.673859i
\(506\) 3.31746 + 3.60979i 0.147479 + 0.160475i
\(507\) 14.9589i 0.664346i
\(508\) −16.3499 −0.725408
\(509\) 19.0623i 0.844920i 0.906382 + 0.422460i \(0.138833\pi\)
−0.906382 + 0.422460i \(0.861167\pi\)
\(510\) 1.31746i 0.0583383i
\(511\) −5.60695 1.51784i −0.248037 0.0671453i
\(512\) 1.00000 0.0441942
\(513\) 5.99105i 0.264511i
\(514\) 21.2465i 0.937142i
\(515\) 1.66734 0.0734716
\(516\) 4.67781 0.205929
\(517\) −7.25010 −0.318859
\(518\) 1.09775 + 0.297169i 0.0482325 + 0.0130569i
\(519\) 18.0882 0.793984
\(520\) 5.03822i 0.220940i
\(521\) −26.9484 −1.18063 −0.590316 0.807173i \(-0.700997\pi\)
−0.590316 + 0.807173i \(0.700997\pi\)
\(522\) −5.57914 −0.244192
\(523\) −8.04918 −0.351966 −0.175983 0.984393i \(-0.556310\pi\)
−0.175983 + 0.984393i \(0.556310\pi\)
\(524\) 11.1583i 0.487452i
\(525\) −10.4505 2.82904i −0.456099 0.123469i
\(526\) 18.1188i 0.790018i
\(527\) 0 0
\(528\) −1.02228 −0.0444889
\(529\) 1.93774 22.9182i 0.0842497 0.996445i
\(530\) 8.34340i 0.362414i
\(531\) 1.70848i 0.0741415i
\(532\) 4.14185 15.3001i 0.179572 0.663345i
\(533\) −6.80840 −0.294905
\(534\) 8.69375i 0.376216i
\(535\) 10.5752i 0.457207i
\(536\) 11.6217i 0.501981i
\(537\) 1.77464i 0.0765815i
\(538\) 3.44198i 0.148394i
\(539\) 3.60979 6.17875i 0.155485 0.266137i
\(540\) 0.952834i 0.0410034i
\(541\) 45.6184 1.96129 0.980644 0.195802i \(-0.0627308\pi\)
0.980644 + 0.195802i \(0.0627308\pi\)
\(542\) 2.57523i 0.110615i
\(543\) 20.4933i 0.879452i
\(544\) 1.38268 0.0592819
\(545\) 2.22536i 0.0953238i
\(546\) −3.65554 + 13.5037i −0.156443 + 0.577904i
\(547\) 16.7707 0.717065 0.358532 0.933517i \(-0.383277\pi\)
0.358532 + 0.933517i \(0.383277\pi\)
\(548\) 0.155798i 0.00665534i
\(549\) 7.37373 0.314703
\(550\) 4.18327i 0.178375i
\(551\) 33.4249 1.42395
\(552\) 3.24517 + 3.53113i 0.138124 + 0.150295i
\(553\) 24.9731 + 6.76040i 1.06196 + 0.287481i
\(554\) −15.7335 −0.668453
\(555\) −0.409572 −0.0173853
\(556\) 2.99609i 0.127063i
\(557\) 18.0646i 0.765423i 0.923868 + 0.382712i \(0.125010\pi\)
−0.923868 + 0.382712i \(0.874990\pi\)
\(558\) 0 0
\(559\) 24.7345 1.04616
\(560\) 0.658732 2.43338i 0.0278365 0.102829i
\(561\) −1.41348 −0.0596773
\(562\) 24.2115i 1.02130i
\(563\) −5.55748 −0.234220 −0.117110 0.993119i \(-0.537363\pi\)
−0.117110 + 0.993119i \(0.537363\pi\)
\(564\) −7.09211 −0.298632
\(565\) 9.74962i 0.410169i
\(566\) 24.2383 1.01881
\(567\) 0.691340 2.55383i 0.0290335 0.107251i
\(568\) −2.29152 −0.0961502
\(569\) 4.66769i 0.195680i −0.995202 0.0978399i \(-0.968807\pi\)
0.995202 0.0978399i \(-0.0311933\pi\)
\(570\) 5.70848i 0.239102i
\(571\) 25.3232i 1.05974i −0.848078 0.529871i \(-0.822240\pi\)
0.848078 0.529871i \(-0.177760\pi\)
\(572\) −5.40541 −0.226011
\(573\) −1.68043 −0.0702008
\(574\) 3.28835 + 0.890179i 0.137253 + 0.0371553i
\(575\) −14.4498 + 13.2796i −0.602597 + 0.553797i
\(576\) −1.00000 −0.0416667
\(577\) 7.44198i 0.309814i −0.987929 0.154907i \(-0.950492\pi\)
0.987929 0.154907i \(-0.0495077\pi\)
\(578\) −15.0882 −0.627586
\(579\) 4.71239i 0.195840i
\(580\) 5.31599 0.220735
\(581\) −3.78029 + 13.9645i −0.156833 + 0.579345i
\(582\) 19.2038i 0.796021i
\(583\) 8.95148 0.370732
\(584\) 2.19551i 0.0908507i
\(585\) 5.03822i 0.208305i
\(586\) −27.2814 −1.12698
\(587\) 13.6012i 0.561380i 0.959798 + 0.280690i \(0.0905633\pi\)
−0.959798 + 0.280690i \(0.909437\pi\)
\(588\) 3.53113 6.04410i 0.145621 0.249254i
\(589\) 0 0
\(590\) 1.62789i 0.0670193i
\(591\) 24.9251i 1.02528i
\(592\) 0.429846i 0.0176665i
\(593\) 25.9147i 1.06419i 0.846685 + 0.532095i \(0.178595\pi\)
−0.846685 + 0.532095i \(0.821405\pi\)
\(594\) 1.02228 0.0419445
\(595\) 0.910815 3.36458i 0.0373398 0.137934i
\(596\) 2.17972i 0.0892846i
\(597\) 8.60434i 0.352152i
\(598\) 17.1592 + 18.6712i 0.701692 + 0.763524i
\(599\) 8.09602 0.330794 0.165397 0.986227i \(-0.447109\pi\)
0.165397 + 0.986227i \(0.447109\pi\)
\(600\) 4.09211i 0.167060i
\(601\) 44.5924i 1.81896i 0.415744 + 0.909482i \(0.363521\pi\)
−0.415744 + 0.909482i \(0.636479\pi\)
\(602\) −11.9463 3.23396i −0.486897 0.131806i
\(603\) 11.6217i 0.473272i
\(604\) 1.38363 0.0562992
\(605\) 9.48541 0.385637
\(606\) 15.8927 0.645596
\(607\) 4.30873i 0.174886i −0.996170 0.0874430i \(-0.972130\pi\)
0.996170 0.0874430i \(-0.0278696\pi\)
\(608\) 5.99105 0.242969
\(609\) 14.2482 + 3.85708i 0.577365 + 0.156297i
\(610\) −7.02594 −0.284472
\(611\) −37.5003 −1.51710
\(612\) −1.38268 −0.0558915
\(613\) 3.10372i 0.125358i −0.998034 0.0626789i \(-0.980036\pi\)
0.998034 0.0626789i \(-0.0199644\pi\)
\(614\) 25.1206i 1.01379i
\(615\) −1.22688 −0.0494727
\(616\) 2.61072 + 0.706741i 0.105189 + 0.0284754i
\(617\) 27.8081i 1.11951i 0.828658 + 0.559756i \(0.189105\pi\)
−0.828658 + 0.559756i \(0.810895\pi\)
\(618\) 1.74987i 0.0703901i
\(619\) 45.5624 1.83131 0.915654 0.401968i \(-0.131674\pi\)
0.915654 + 0.401968i \(0.131674\pi\)
\(620\) 0 0
\(621\) −3.24517 3.53113i −0.130224 0.141699i
\(622\) 10.6712i 0.427878i
\(623\) −6.01034 + 22.2024i −0.240799 + 0.889519i
\(624\) −5.28761 −0.211674
\(625\) 12.2059 0.488235
\(626\) 9.21674 0.368375
\(627\) −6.12452 −0.244590
\(628\) −11.1851 −0.446333
\(629\) 0.594339i 0.0236978i
\(630\) −0.658732 + 2.43338i −0.0262445 + 0.0969480i
\(631\) 9.09170i 0.361935i −0.983489 0.180968i \(-0.942077\pi\)
0.983489 0.180968i \(-0.0579229\pi\)
\(632\) 9.77869i 0.388975i
\(633\) 19.3460i 0.768933i
\(634\) −25.3048 −1.00498
\(635\) −15.5787 −0.618222
\(636\) 8.75641 0.347214
\(637\) 18.6712 31.9589i 0.739782 1.26626i
\(638\) 5.70343i 0.225801i
\(639\) 2.29152 0.0906513
\(640\) 0.952834 0.0376641
\(641\) 45.7219i 1.80591i 0.429738 + 0.902954i \(0.358606\pi\)
−0.429738 + 0.902954i \(0.641394\pi\)
\(642\) 11.0987 0.438031
\(643\) 33.7328 1.33029 0.665145 0.746714i \(-0.268370\pi\)
0.665145 + 0.746714i \(0.268370\pi\)
\(644\) −5.84640 11.2614i −0.230381 0.443762i
\(645\) 4.45718 0.175501
\(646\) 8.28370 0.325918
\(647\) 18.6712i 0.734042i −0.930213 0.367021i \(-0.880378\pi\)
0.930213 0.367021i \(-0.119622\pi\)
\(648\) 1.00000 0.0392837
\(649\) −1.74654 −0.0685575
\(650\) 21.6375i 0.848692i
\(651\) 0 0
\(652\) 7.54929 0.295653
\(653\) −25.3161 −0.990696 −0.495348 0.868695i \(-0.664959\pi\)
−0.495348 + 0.868695i \(0.664959\pi\)
\(654\) 2.33551 0.0913258
\(655\) 10.6320i 0.415426i
\(656\) 1.28761i 0.0502729i
\(657\) 2.19551i 0.0856548i
\(658\) 18.1120 + 4.90306i 0.706081 + 0.191141i
\(659\) 42.9498i 1.67309i 0.547901 + 0.836543i \(0.315427\pi\)
−0.547901 + 0.836543i \(0.684573\pi\)
\(660\) −0.974060 −0.0379152
\(661\) −43.2862 −1.68364 −0.841819 0.539759i \(-0.818515\pi\)
−0.841819 + 0.539759i \(0.818515\pi\)
\(662\) −0.830434 −0.0322757
\(663\) −7.31108 −0.283939
\(664\) −5.46806 −0.212202
\(665\) 3.94650 14.5785i 0.153039 0.565329i
\(666\) 0.429846i 0.0166562i
\(667\) 19.7007 18.1053i 0.762812 0.701038i
\(668\) 11.9290i 0.461547i
\(669\) −17.7335 −0.685617
\(670\) 11.0735i 0.427808i
\(671\) 7.53800i 0.291001i
\(672\) 2.55383 + 0.691340i 0.0985161 + 0.0266690i
\(673\) −3.66734 −0.141365 −0.0706827 0.997499i \(-0.522518\pi\)
−0.0706827 + 0.997499i \(0.522518\pi\)
\(674\) 7.58885i 0.292312i
\(675\) 4.09211i 0.157505i
\(676\) −14.9589 −0.575341
\(677\) −9.06801 −0.348512 −0.174256 0.984700i \(-0.555752\pi\)
−0.174256 + 0.984700i \(0.555752\pi\)
\(678\) 10.2322 0.392966
\(679\) −13.2763 + 49.0431i −0.509499 + 1.88210i
\(680\) 1.31746 0.0505224
\(681\) 9.92436i 0.380302i
\(682\) 0 0
\(683\) 19.3823 0.741642 0.370821 0.928704i \(-0.379076\pi\)
0.370821 + 0.928704i \(0.379076\pi\)
\(684\) −5.99105 −0.229074
\(685\) 0.148449i 0.00567195i
\(686\) −13.1964 + 12.9944i −0.503842 + 0.496128i
\(687\) 15.8223i 0.603657i
\(688\) 4.67781i 0.178340i
\(689\) 46.3005 1.76391
\(690\) 3.09211 + 3.36458i 0.117715 + 0.128087i
\(691\) 0.800584i 0.0304556i −0.999884 0.0152278i \(-0.995153\pi\)
0.999884 0.0152278i \(-0.00484735\pi\)
\(692\) 18.0882i 0.687610i
\(693\) −2.61072 0.706741i −0.0991732 0.0268469i
\(694\) 30.1431 1.14422
\(695\) 2.85478i 0.108288i
\(696\) 5.57914i 0.211477i
\(697\) 1.78036i 0.0674358i
\(698\) 22.6115i 0.855860i
\(699\) 13.0259i 0.492686i
\(700\) −2.82904 + 10.4505i −0.106928 + 0.394994i
\(701\) 43.0748i 1.62691i 0.581625 + 0.813457i \(0.302417\pi\)
−0.581625 + 0.813457i \(0.697583\pi\)
\(702\) 5.28761 0.199568
\(703\) 2.57523i 0.0971265i
\(704\) 1.02228i 0.0385285i
\(705\) −6.75760 −0.254506
\(706\) 8.44589i 0.317865i
\(707\) −40.5872 10.9872i −1.52644 0.413218i
\(708\) −1.70848 −0.0642085
\(709\) 3.01430i 0.113204i 0.998397 + 0.0566022i \(0.0180267\pi\)
−0.998397 + 0.0566022i \(0.981973\pi\)
\(710\) −2.18344 −0.0819431
\(711\) 9.77869i 0.366729i
\(712\) −8.69375 −0.325812
\(713\) 0 0
\(714\) 3.53113 + 0.955901i 0.132149 + 0.0357737i
\(715\) −5.15046 −0.192616
\(716\) 1.77464 0.0663216
\(717\) 10.6712i 0.398525i
\(718\) 18.7007i 0.697906i
\(719\) 6.84472i 0.255265i 0.991822 + 0.127633i \(0.0407378\pi\)
−0.991822 + 0.127633i \(0.959262\pi\)
\(720\) −0.952834 −0.0355100
\(721\) 1.20975 4.46887i 0.0450536 0.166429i
\(722\) 16.8927 0.628681
\(723\) 19.2038i 0.714196i
\(724\) −20.4933 −0.761627
\(725\) −22.8304 −0.847901
\(726\) 9.95495i 0.369463i
\(727\) 10.8772 0.403413 0.201706 0.979446i \(-0.435351\pi\)
0.201706 + 0.979446i \(0.435351\pi\)
\(728\) 13.5037 + 3.65554i 0.500479 + 0.135483i
\(729\) −1.00000 −0.0370370
\(730\) 2.09195i 0.0774266i
\(731\) 6.46792i 0.239225i
\(732\) 7.37373i 0.272541i
\(733\) −0.0626552 −0.00231422 −0.00115711 0.999999i \(-0.500368\pi\)
−0.00115711 + 0.999999i \(0.500368\pi\)
\(734\) 27.7112 1.02284
\(735\) 3.36458 5.75902i 0.124104 0.212425i
\(736\) 3.53113 3.24517i 0.130159 0.119619i
\(737\) −11.8806 −0.437628
\(738\) 1.28761i 0.0473977i
\(739\) 38.9549 1.43298 0.716490 0.697597i \(-0.245747\pi\)
0.716490 + 0.697597i \(0.245747\pi\)
\(740\) 0.409572i 0.0150561i
\(741\) −31.6784 −1.16373
\(742\) −22.3624 6.05365i −0.820949 0.222237i
\(743\) 5.61707i 0.206070i −0.994678 0.103035i \(-0.967145\pi\)
0.994678 0.103035i \(-0.0328554\pi\)
\(744\) 0 0
\(745\) 2.07691i 0.0760920i
\(746\) 31.6157i 1.15753i
\(747\) 5.46806 0.200066
\(748\) 1.41348i 0.0516820i
\(749\) −28.3442 7.67298i −1.03568 0.280365i
\(750\) 8.66327i 0.316338i
\(751\) 20.8401i 0.760467i 0.924891 + 0.380233i \(0.124156\pi\)
−0.924891 + 0.380233i \(0.875844\pi\)
\(752\) 7.09211i 0.258623i
\(753\) 0.429846i 0.0156644i
\(754\) 29.5003i 1.07434i
\(755\) 1.31837 0.0479804
\(756\) −2.55383 0.691340i −0.0928819 0.0251438i
\(757\) 42.0037i 1.52665i −0.646014 0.763326i \(-0.723565\pi\)
0.646014 0.763326i \(-0.276435\pi\)
\(758\) 31.2347i 1.13449i
\(759\) −3.60979 + 3.31746i −0.131027 + 0.120416i
\(760\) 5.70848 0.207068
\(761\) 2.34687i 0.0850741i −0.999095 0.0425370i \(-0.986456\pi\)
0.999095 0.0425370i \(-0.0135440\pi\)
\(762\) 16.3499i 0.592293i
\(763\) −5.96450 1.61463i −0.215930 0.0584536i
\(764\) 1.68043i 0.0607957i
\(765\) −1.31746 −0.0476330
\(766\) 10.3880 0.375335
\(767\) −9.03376 −0.326190
\(768\) 1.00000i 0.0360844i
\(769\) −0.553475 −0.0199588 −0.00997941 0.999950i \(-0.503177\pi\)
−0.00997941 + 0.999950i \(0.503177\pi\)
\(770\) 2.48758 + 0.673407i 0.0896463 + 0.0242679i
\(771\) 21.2465 0.765173
\(772\) −4.71239 −0.169602
\(773\) 24.1488 0.868573 0.434287 0.900775i \(-0.357001\pi\)
0.434287 + 0.900775i \(0.357001\pi\)
\(774\) 4.67781i 0.168141i
\(775\) 0 0
\(776\) −19.2038 −0.689375
\(777\) −0.297169 + 1.09775i −0.0106609 + 0.0393817i
\(778\) 11.7081i 0.419754i
\(779\) 7.71416i 0.276388i
\(780\) −5.03822 −0.180397
\(781\) 2.34257i 0.0838239i
\(782\) 4.88242 4.48703i 0.174595 0.160456i
\(783\) 5.57914i 0.199382i
\(784\) −6.04410 3.53113i −0.215861 0.126112i
\(785\) −10.6575 −0.380383
\(786\) 11.1583 0.398003
\(787\) −25.2842 −0.901285 −0.450643 0.892704i \(-0.648805\pi\)
−0.450643 + 0.892704i \(0.648805\pi\)
\(788\) 24.9251 0.887920
\(789\) 18.1188 0.645047
\(790\) 9.31746i 0.331500i
\(791\) −26.1314 7.07395i −0.929125 0.251521i
\(792\) 1.02228i 0.0363250i
\(793\) 38.9894i 1.38456i
\(794\) 5.35378i 0.189999i
\(795\) 8.34340 0.295910
\(796\) −8.60434 −0.304973
\(797\) −48.5161 −1.71853 −0.859265 0.511531i \(-0.829078\pi\)
−0.859265 + 0.511531i \(0.829078\pi\)
\(798\) 15.3001 + 4.14185i 0.541619 + 0.146620i
\(799\) 9.80611i 0.346915i
\(800\) −4.09211 −0.144678
\(801\) 8.69375 0.307179
\(802\) 34.9329i 1.23352i
\(803\) 2.24442 0.0792037
\(804\) −11.6217 −0.409866
\(805\) −5.57065 10.7303i −0.196340 0.378192i
\(806\) 0 0
\(807\) 3.44198 0.121163
\(808\) 15.8927i 0.559103i
\(809\) 19.6738 0.691694 0.345847 0.938291i \(-0.387592\pi\)
0.345847 + 0.938291i \(0.387592\pi\)
\(810\) 0.952834 0.0334792
\(811\) 53.0496i 1.86282i −0.363967 0.931412i \(-0.618578\pi\)
0.363967 0.931412i \(-0.381422\pi\)
\(812\) 3.85708 14.2482i 0.135357 0.500013i
\(813\) 2.57523 0.0903172
\(814\) −0.439422 −0.0154017
\(815\) 7.19322 0.251967
\(816\) 1.38268i 0.0484035i
\(817\) 28.0250i 0.980472i
\(818\) 22.1479i 0.774383i
\(819\) −13.5037 3.65554i −0.471856 0.127735i
\(820\) 1.22688i 0.0428446i
\(821\) −21.8080 −0.761103 −0.380552 0.924760i \(-0.624266\pi\)
−0.380552 + 0.924760i \(0.624266\pi\)
\(822\) 0.155798 0.00543406
\(823\) −22.8084 −0.795051 −0.397525 0.917591i \(-0.630131\pi\)
−0.397525 + 0.917591i \(0.630131\pi\)
\(824\) 1.74987 0.0609596
\(825\) 4.18327 0.145643
\(826\) 4.36316 + 1.18114i 0.151814 + 0.0410970i
\(827\) 19.9503i 0.693741i −0.937913 0.346871i \(-0.887244\pi\)
0.937913 0.346871i \(-0.112756\pi\)
\(828\) −3.53113 + 3.24517i −0.122715 + 0.112777i
\(829\) 18.2205i 0.632825i −0.948622 0.316413i \(-0.897522\pi\)
0.948622 0.316413i \(-0.102478\pi\)
\(830\) −5.21016 −0.180847
\(831\) 15.7335i 0.545789i
\(832\) 5.28761i 0.183315i
\(833\) −8.35705 4.88242i −0.289555 0.169166i
\(834\) −2.99609 −0.103746
\(835\) 11.3664i 0.393349i
\(836\) 6.12452i 0.211821i
\(837\) 0 0
\(838\) −0.215119 −0.00743116
\(839\) 22.1838 0.765871 0.382936 0.923775i \(-0.374913\pi\)
0.382936 + 0.923775i \(0.374913\pi\)
\(840\) 2.43338 + 0.658732i 0.0839594 + 0.0227284i
\(841\) 2.12678 0.0733372
\(842\) 16.3757i 0.564345i
\(843\) −24.2115 −0.833888
\(844\) −19.3460 −0.665915
\(845\) −14.2533 −0.490329
\(846\) 7.09211i 0.243832i
\(847\) 6.88225 25.4233i 0.236477 0.873553i
\(848\) 8.75641i 0.300696i
\(849\) 24.2383i 0.831855i
\(850\) −5.65807 −0.194070
\(851\) 1.39492 + 1.51784i 0.0478173 + 0.0520309i
\(852\) 2.29152i 0.0785063i
\(853\) 51.9476i 1.77865i −0.457275 0.889325i \(-0.651174\pi\)
0.457275 0.889325i \(-0.348826\pi\)
\(854\) −5.09775 + 18.8313i −0.174442 + 0.644392i
\(855\) −5.70848 −0.195226
\(856\) 11.0987i 0.379346i
\(857\) 35.7806i 1.22224i −0.791538 0.611120i \(-0.790719\pi\)
0.791538 0.611120i \(-0.209281\pi\)
\(858\) 5.40541i 0.184538i
\(859\) 6.28506i 0.214443i −0.994235 0.107222i \(-0.965805\pi\)
0.994235 0.107222i \(-0.0341955\pi\)
\(860\) 4.45718i 0.151989i
\(861\) −0.890179 + 3.28835i −0.0303372 + 0.112067i
\(862\) 17.1982i 0.585772i
\(863\) 20.4507 0.696150 0.348075 0.937467i \(-0.386835\pi\)
0.348075 + 0.937467i \(0.386835\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) 17.2350i 0.586009i
\(866\) −3.99224 −0.135662
\(867\) 15.0882i 0.512422i
\(868\) 0 0
\(869\) −9.99653 −0.339109
\(870\) 5.31599i 0.180229i
\(871\) −61.4511 −2.08219
\(872\) 2.33551i 0.0790905i
\(873\) 19.2038 0.649949
\(874\) 21.1552 19.4420i 0.715584 0.657635i
\(875\) −5.98926 + 22.1245i −0.202474 + 0.747945i
\(876\) 2.19551 0.0741793
\(877\) 16.8840 0.570131 0.285065 0.958508i \(-0.407985\pi\)
0.285065 + 0.958508i \(0.407985\pi\)
\(878\) 2.76726i 0.0933906i
\(879\) 27.2814i 0.920178i
\(880\) 0.974060i 0.0328356i
\(881\) 54.6901 1.84256 0.921279 0.388903i \(-0.127146\pi\)
0.921279 + 0.388903i \(0.127146\pi\)
\(882\) 6.04410 + 3.53113i 0.203515 + 0.118899i
\(883\) 13.2811 0.446946 0.223473 0.974710i \(-0.428261\pi\)
0.223473 + 0.974710i \(0.428261\pi\)
\(884\) 7.31108i 0.245898i
\(885\) −1.62789 −0.0547210
\(886\) −13.6673 −0.459163
\(887\) 50.9913i 1.71212i −0.516877 0.856060i \(-0.672906\pi\)
0.516877 0.856060i \(-0.327094\pi\)
\(888\) −0.429846 −0.0144247
\(889\) −11.3033 + 41.7548i −0.379101 + 1.40041i
\(890\) −8.28370 −0.277670
\(891\) 1.02228i 0.0342476i
\(892\) 17.7335i 0.593762i
\(893\) 42.4892i 1.42185i
\(894\) −2.17972 −0.0729006
\(895\) 1.69094 0.0565219
\(896\) 0.691340 2.55383i 0.0230960 0.0853175i
\(897\) −18.6712 + 17.1592i −0.623415 + 0.572929i
\(898\) −11.6012 −0.387136
\(899\) 0 0
\(900\) 4.09211 0.136404
\(901\) 12.1073i 0.403353i
\(902\) −1.31630 −0.0438279
\(903\) 3.23396 11.9463i 0.107619 0.397549i
\(904\) 10.2322i 0.340319i
\(905\) −19.5267 −0.649090
\(906\) 1.38363i 0.0459681i
\(907\) 54.9286i 1.82387i 0.410332 + 0.911936i \(0.365413\pi\)
−0.410332 + 0.911936i \(0.634587\pi\)
\(908\) −9.92436 −0.329352
\(909\) 15.8927i 0.527127i
\(910\) 12.8668 + 3.48312i 0.426529 + 0.115464i
\(911\) 0.862754i 0.0285843i 0.999898 + 0.0142922i \(0.00454949\pi\)
−0.999898 + 0.0142922i \(0.995451\pi\)
\(912\) 5.99105i 0.198384i
\(913\) 5.58988i 0.184998i
\(914\) 26.1476i 0.864887i
\(915\) 7.02594i 0.232270i
\(916\) 15.8223 0.522783
\(917\) −28.4963 7.71416i −0.941032 0.254744i
\(918\) 1.38268i 0.0456352i
\(919\) 23.5411i 0.776551i 0.921543 + 0.388275i \(0.126929\pi\)
−0.921543 + 0.388275i \(0.873071\pi\)
\(920\) 3.36458 3.09211i 0.110927 0.101944i
\(921\) −25.1206 −0.827752
\(922\) 5.44980i 0.179480i
\(923\) 12.1167i 0.398826i
\(924\) −0.706741 + 2.61072i −0.0232501 + 0.0858865i
\(925\) 1.75897i 0.0578347i
\(926\) −34.0834 −1.12005
\(927\) −1.74987 −0.0574733
\(928\) 5.57914 0.183144
\(929\) 50.0471i 1.64199i 0.570935 + 0.820995i \(0.306581\pi\)
−0.570935 + 0.820995i \(0.693419\pi\)
\(930\) 0 0
\(931\) −36.2105 21.1552i −1.18675 0.693333i
\(932\) 13.0259 0.426679
\(933\) −10.6712 −0.349361
\(934\) 28.7609 0.941086
\(935\) 1.34681i 0.0440455i
\(936\) 5.28761i 0.172831i
\(937\) −57.6038 −1.88184 −0.940918 0.338636i \(-0.890035\pi\)
−0.940918 + 0.338636i \(0.890035\pi\)
\(938\) 29.6798 + 8.03454i 0.969081 + 0.262337i
\(939\) 9.21674i 0.300777i
\(940\) 6.75760i 0.220409i
\(941\) −50.1440 −1.63465 −0.817324 0.576178i \(-0.804543\pi\)
−0.817324 + 0.576178i \(0.804543\pi\)
\(942\) 11.1851i 0.364429i
\(943\) 4.17853 + 4.54673i 0.136072 + 0.148062i
\(944\) 1.70848i 0.0556062i
\(945\) −2.43338 0.658732i −0.0791577 0.0214285i
\(946\) 4.78202 0.155477
\(947\) 21.8187 0.709013 0.354506 0.935054i \(-0.384649\pi\)
0.354506 + 0.935054i \(0.384649\pi\)
\(948\) −9.77869 −0.317597
\(949\) 11.6090 0.376844
\(950\) −24.5160 −0.795405
\(951\) 25.3048i 0.820565i
\(952\) 0.955901 3.53113i 0.0309809 0.114445i
\(953\) 34.1070i 1.10483i −0.833568 0.552417i \(-0.813705\pi\)
0.833568 0.552417i \(-0.186295\pi\)
\(954\) 8.75641i 0.283499i
\(955\) 1.60117i 0.0518126i
\(956\) 10.6712 0.345133
\(957\) −5.70343 −0.184366
\(958\) 39.5714 1.27849
\(959\) −0.397881 0.107709i −0.0128482 0.00347811i
\(960\) 0.952834i 0.0307526i
\(961\) 31.0000 1.00000
\(962\) −2.27286 −0.0732799
\(963\) 11.0987i 0.357651i
\(964\) 19.2038 0.618511
\(965\) −4.49012 −0.144542
\(966\) 11.2614 5.84640i 0.362330 0.188105i
\(967\) −16.7820 −0.539674 −0.269837 0.962906i \(-0.586970\pi\)
−0.269837 + 0.962906i \(0.586970\pi\)
\(968\) 9.95495 0.319964
\(969\) 8.28370i 0.266111i
\(970\) −18.2980 −0.587513
\(971\) −55.1233 −1.76899 −0.884496 0.466549i \(-0.845497\pi\)
−0.884496 + 0.466549i \(0.845497\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 7.65150 + 2.07132i 0.245296 + 0.0664033i
\(974\) −12.8006 −0.410157
\(975\) 21.6375 0.692954
\(976\) −7.37373 −0.236027
\(977\) 29.0350i 0.928911i 0.885596 + 0.464456i \(0.153750\pi\)
−0.885596 + 0.464456i \(0.846250\pi\)
\(978\) 7.54929i 0.241400i
\(979\) 8.88743i 0.284043i
\(980\) −5.75902 3.36458i −0.183965 0.107478i
\(981\) 2.33551i 0.0745672i
\(982\) 39.4670 1.25944
\(983\) −46.8899 −1.49556 −0.747778 0.663949i \(-0.768879\pi\)
−0.747778 + 0.663949i \(0.768879\pi\)
\(984\) −1.28761 −0.0410476
\(985\) 23.7495 0.756721
\(986\) 7.71416 0.245669
\(987\) −4.90306 + 18.1120i −0.156066 + 0.576513i
\(988\) 31.6784i 1.00782i
\(989\) −15.1803 16.5180i −0.482706 0.525241i
\(990\) 0.974060i 0.0309577i
\(991\) 21.9325 0.696708 0.348354 0.937363i \(-0.386741\pi\)
0.348354 + 0.937363i \(0.386741\pi\)
\(992\) 0 0
\(993\) 0.830434i 0.0263530i
\(994\) −1.58422 + 5.85216i −0.0502485 + 0.185619i
\(995\) −8.19850 −0.259910
\(996\) 5.46806i 0.173262i
\(997\) 36.4714i 1.15506i −0.816369 0.577530i \(-0.804017\pi\)
0.816369 0.577530i \(-0.195983\pi\)
\(998\) −8.58305 −0.271692
\(999\) 0.429846 0.0135997
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 966.2.g.e.643.13 yes 16
3.2 odd 2 2898.2.g.j.2575.7 16
7.6 odd 2 inner 966.2.g.e.643.4 16
21.20 even 2 2898.2.g.j.2575.9 16
23.22 odd 2 inner 966.2.g.e.643.12 yes 16
69.68 even 2 2898.2.g.j.2575.10 16
161.160 even 2 inner 966.2.g.e.643.5 yes 16
483.482 odd 2 2898.2.g.j.2575.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.g.e.643.4 16 7.6 odd 2 inner
966.2.g.e.643.5 yes 16 161.160 even 2 inner
966.2.g.e.643.12 yes 16 23.22 odd 2 inner
966.2.g.e.643.13 yes 16 1.1 even 1 trivial
2898.2.g.j.2575.7 16 3.2 odd 2
2898.2.g.j.2575.8 16 483.482 odd 2
2898.2.g.j.2575.9 16 21.20 even 2
2898.2.g.j.2575.10 16 69.68 even 2