Properties

Label 966.2.g.e.643.9
Level $966$
Weight $2$
Character 966.643
Analytic conductor $7.714$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 643.9
Root \(2.55383 + 2.55383i\) of defining polynomial
Character \(\chi\) \(=\) 966.643
Dual form 966.2.g.e.643.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -4.19800 q^{5} +1.00000i q^{6} +(2.55383 - 0.691340i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -4.19800 q^{5} +1.00000i q^{6} +(2.55383 - 0.691340i) q^{7} +1.00000 q^{8} -1.00000 q^{9} -4.19800 q^{10} -5.99105i q^{11} +1.00000i q^{12} -0.756485i q^{13} +(2.55383 - 0.691340i) q^{14} -4.19800i q^{15} +1.00000 q^{16} +5.10766 q^{17} -1.00000 q^{18} -1.02228 q^{19} -4.19800 q^{20} +(0.691340 + 2.55383i) q^{21} -5.99105i q^{22} +(3.53113 - 3.24517i) q^{23} +1.00000i q^{24} +12.6232 q^{25} -0.756485i q^{26} -1.00000i q^{27} +(2.55383 - 0.691340i) q^{28} +0.951991 q^{29} -4.19800i q^{30} +1.00000 q^{32} +5.99105 q^{33} +5.10766 q^{34} +(-10.7210 + 2.90225i) q^{35} -1.00000 q^{36} +9.30566i q^{37} -1.02228 q^{38} +0.756485 q^{39} -4.19800 q^{40} -4.75648i q^{41} +(0.691340 + 2.55383i) q^{42} +7.92299i q^{43} -5.99105i q^{44} +4.19800 q^{45} +(3.53113 - 3.24517i) q^{46} -9.62324i q^{47} +1.00000i q^{48} +(6.04410 - 3.53113i) q^{49} +12.6232 q^{50} +5.10766i q^{51} -0.756485i q^{52} -9.19304i q^{53} -1.00000i q^{54} +25.1505i q^{55} +(2.55383 - 0.691340i) q^{56} -1.02228i q^{57} +0.951991 q^{58} +0.291524i q^{59} -4.19800i q^{60} -4.08538 q^{61} +(-2.55383 + 0.691340i) q^{63} +1.00000 q^{64} +3.17573i q^{65} +5.99105 q^{66} -13.1433i q^{67} +5.10766 q^{68} +(3.24517 + 3.53113i) q^{69} +(-10.7210 + 2.90225i) q^{70} -3.70848 q^{71} -1.00000 q^{72} -12.8668i q^{73} +9.30566i q^{74} +12.6232i q^{75} -1.02228 q^{76} +(-4.14185 - 15.3001i) q^{77} +0.756485 q^{78} +3.20199i q^{79} -4.19800 q^{80} +1.00000 q^{81} -4.75648i q^{82} -12.4814 q^{83} +(0.691340 + 2.55383i) q^{84} -21.4420 q^{85} +7.92299i q^{86} +0.951991i q^{87} -5.99105i q^{88} -1.24379 q^{89} +4.19800 q^{90} +(-0.522988 - 1.93193i) q^{91} +(3.53113 - 3.24517i) q^{92} -9.62324i q^{94} +4.29152 q^{95} +1.00000i q^{96} +14.4370 q^{97} +(6.04410 - 3.53113i) q^{98} +5.99105i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9}+O(q^{10}) \) 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
\(5\) −4.19800 −1.87740 −0.938702 0.344729i \(-0.887971\pi\)
−0.938702 + 0.344729i \(0.887971\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 2.55383 0.691340i 0.965257 0.261302i
\(8\) 1.00000 0.353553
\(9\) −1.00000 −0.333333
\(10\) −4.19800 −1.32753
\(11\) 5.99105i 1.80637i −0.429252 0.903185i \(-0.641223\pi\)
0.429252 0.903185i \(-0.358777\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.756485i 0.209811i −0.994482 0.104906i \(-0.966546\pi\)
0.994482 0.104906i \(-0.0334540\pi\)
\(14\) 2.55383 0.691340i 0.682540 0.184768i
\(15\) 4.19800i 1.08392i
\(16\) 1.00000 0.250000
\(17\) 5.10766 1.23879 0.619395 0.785080i \(-0.287378\pi\)
0.619395 + 0.785080i \(0.287378\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.02228 −0.234527 −0.117263 0.993101i \(-0.537412\pi\)
−0.117263 + 0.993101i \(0.537412\pi\)
\(20\) −4.19800 −0.938702
\(21\) 0.691340 + 2.55383i 0.150863 + 0.557291i
\(22\) 5.99105i 1.27730i
\(23\) 3.53113 3.24517i 0.736291 0.676665i
\(24\) 1.00000i 0.204124i
\(25\) 12.6232 2.52465
\(26\) 0.756485i 0.148359i
\(27\) 1.00000i 0.192450i
\(28\) 2.55383 0.691340i 0.482629 0.130651i
\(29\) 0.951991 0.176780 0.0883901 0.996086i \(-0.471828\pi\)
0.0883901 + 0.996086i \(0.471828\pi\)
\(30\) 4.19800i 0.766447i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.99105 1.04291
\(34\) 5.10766 0.875957
\(35\) −10.7210 + 2.90225i −1.81218 + 0.490569i
\(36\) −1.00000 −0.166667
\(37\) 9.30566i 1.52984i 0.644124 + 0.764921i \(0.277222\pi\)
−0.644124 + 0.764921i \(0.722778\pi\)
\(38\) −1.02228 −0.165835
\(39\) 0.756485 0.121135
\(40\) −4.19800 −0.663763
\(41\) 4.75648i 0.742838i −0.928465 0.371419i \(-0.878871\pi\)
0.928465 0.371419i \(-0.121129\pi\)
\(42\) 0.691340 + 2.55383i 0.106676 + 0.394065i
\(43\) 7.92299i 1.20824i 0.796892 + 0.604122i \(0.206476\pi\)
−0.796892 + 0.604122i \(0.793524\pi\)
\(44\) 5.99105i 0.903185i
\(45\) 4.19800 0.625801
\(46\) 3.53113 3.24517i 0.520637 0.478474i
\(47\) 9.62324i 1.40369i −0.712328 0.701847i \(-0.752359\pi\)
0.712328 0.701847i \(-0.247641\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.04410 3.53113i 0.863443 0.504447i
\(50\) 12.6232 1.78520
\(51\) 5.10766i 0.715216i
\(52\) 0.756485i 0.104906i
\(53\) 9.19304i 1.26276i −0.775473 0.631381i \(-0.782488\pi\)
0.775473 0.631381i \(-0.217512\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 25.1505i 3.39129i
\(56\) 2.55383 0.691340i 0.341270 0.0923842i
\(57\) 1.02228i 0.135404i
\(58\) 0.951991 0.125003
\(59\) 0.291524i 0.0379532i 0.999820 + 0.0189766i \(0.00604080\pi\)
−0.999820 + 0.0189766i \(0.993959\pi\)
\(60\) 4.19800i 0.541960i
\(61\) −4.08538 −0.523080 −0.261540 0.965193i \(-0.584230\pi\)
−0.261540 + 0.965193i \(0.584230\pi\)
\(62\) 0 0
\(63\) −2.55383 + 0.691340i −0.321752 + 0.0871006i
\(64\) 1.00000 0.125000
\(65\) 3.17573i 0.393900i
\(66\) 5.99105 0.737447
\(67\) 13.1433i 1.60571i −0.596177 0.802853i \(-0.703314\pi\)
0.596177 0.802853i \(-0.296686\pi\)
\(68\) 5.10766 0.619395
\(69\) 3.24517 + 3.53113i 0.390673 + 0.425098i
\(70\) −10.7210 + 2.90225i −1.28140 + 0.346885i
\(71\) −3.70848 −0.440115 −0.220058 0.975487i \(-0.570625\pi\)
−0.220058 + 0.975487i \(0.570625\pi\)
\(72\) −1.00000 −0.117851
\(73\) 12.8668i 1.50594i −0.658055 0.752970i \(-0.728621\pi\)
0.658055 0.752970i \(-0.271379\pi\)
\(74\) 9.30566i 1.08176i
\(75\) 12.6232i 1.45761i
\(76\) −1.02228 −0.117263
\(77\) −4.14185 15.3001i −0.472008 1.74361i
\(78\) 0.756485 0.0856550
\(79\) 3.20199i 0.360252i 0.983644 + 0.180126i \(0.0576506\pi\)
−0.983644 + 0.180126i \(0.942349\pi\)
\(80\) −4.19800 −0.469351
\(81\) 1.00000 0.111111
\(82\) 4.75648i 0.525266i
\(83\) −12.4814 −1.37001 −0.685005 0.728538i \(-0.740200\pi\)
−0.685005 + 0.728538i \(0.740200\pi\)
\(84\) 0.691340 + 2.55383i 0.0754314 + 0.278646i
\(85\) −21.4420 −2.32571
\(86\) 7.92299i 0.854357i
\(87\) 0.951991i 0.102064i
\(88\) 5.99105i 0.638648i
\(89\) −1.24379 −0.131842 −0.0659209 0.997825i \(-0.520998\pi\)
−0.0659209 + 0.997825i \(0.520998\pi\)
\(90\) 4.19800 0.442508
\(91\) −0.522988 1.93193i −0.0548240 0.202522i
\(92\) 3.53113 3.24517i 0.368146 0.338332i
\(93\) 0 0
\(94\) 9.62324i 0.992561i
\(95\) 4.29152 0.440301
\(96\) 1.00000i 0.102062i
\(97\) 14.4370 1.46586 0.732929 0.680305i \(-0.238153\pi\)
0.732929 + 0.680305i \(0.238153\pi\)
\(98\) 6.04410 3.53113i 0.610546 0.356698i
\(99\) 5.99105i 0.602123i
\(100\) 12.6232 1.26232
\(101\) 18.9549i 1.88609i 0.332668 + 0.943044i \(0.392051\pi\)
−0.332668 + 0.943044i \(0.607949\pi\)
\(102\) 5.10766i 0.505734i
\(103\) 6.46407 0.636924 0.318462 0.947936i \(-0.396834\pi\)
0.318462 + 0.947936i \(0.396834\pi\)
\(104\) 0.756485i 0.0741794i
\(105\) −2.90225 10.7210i −0.283230 1.04626i
\(106\) 9.19304i 0.892907i
\(107\) 0.360402i 0.0348414i −0.999848 0.0174207i \(-0.994455\pi\)
0.999848 0.0174207i \(-0.00554546\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 0.909657i 0.0871293i −0.999051 0.0435647i \(-0.986129\pi\)
0.999051 0.0435647i \(-0.0138715\pi\)
\(110\) 25.1505i 2.39800i
\(111\) −9.30566 −0.883255
\(112\) 2.55383 0.691340i 0.241314 0.0653255i
\(113\) 8.50863i 0.800424i 0.916422 + 0.400212i \(0.131064\pi\)
−0.916422 + 0.400212i \(0.868936\pi\)
\(114\) 1.02228i 0.0957450i
\(115\) −14.8237 + 13.6232i −1.38232 + 1.27037i
\(116\) 0.951991 0.0883901
\(117\) 0.756485i 0.0699371i
\(118\) 0.291524i 0.0268370i
\(119\) 13.0441 3.53113i 1.19575 0.323698i
\(120\) 4.19800i 0.383224i
\(121\) −24.8927 −2.26297
\(122\) −4.08538 −0.369873
\(123\) 4.75648 0.428878
\(124\) 0 0
\(125\) −32.0024 −2.86238
\(126\) −2.55383 + 0.691340i −0.227513 + 0.0615894i
\(127\) −10.3058 −0.914489 −0.457245 0.889341i \(-0.651164\pi\)
−0.457245 + 0.889341i \(0.651164\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.92299 −0.697580
\(130\) 3.17573i 0.278530i
\(131\) 1.90398i 0.166352i −0.996535 0.0831758i \(-0.973494\pi\)
0.996535 0.0831758i \(-0.0265063\pi\)
\(132\) 5.99105 0.521454
\(133\) −2.61072 + 0.706741i −0.226378 + 0.0612822i
\(134\) 13.1433i 1.13541i
\(135\) 4.19800i 0.361307i
\(136\) 5.10766 0.437978
\(137\) 14.8601i 1.26958i 0.772684 + 0.634791i \(0.218914\pi\)
−0.772684 + 0.634791i \(0.781086\pi\)
\(138\) 3.24517 + 3.53113i 0.276247 + 0.300590i
\(139\) 4.46496i 0.378713i −0.981908 0.189357i \(-0.939360\pi\)
0.981908 0.189357i \(-0.0606402\pi\)
\(140\) −10.7210 + 2.90225i −0.906089 + 0.245285i
\(141\) 9.62324 0.810423
\(142\) −3.70848 −0.311208
\(143\) −4.53214 −0.378997
\(144\) −1.00000 −0.0833333
\(145\) −3.99646 −0.331888
\(146\) 12.8668i 1.06486i
\(147\) 3.53113 + 6.04410i 0.291243 + 0.498509i
\(148\) 9.30566i 0.764921i
\(149\) 15.7697i 1.29191i 0.763377 + 0.645954i \(0.223540\pi\)
−0.763377 + 0.645954i \(0.776460\pi\)
\(150\) 12.6232i 1.03068i
\(151\) −13.9148 −1.13237 −0.566184 0.824279i \(-0.691581\pi\)
−0.566184 + 0.824279i \(0.691581\pi\)
\(152\) −1.02228 −0.0829176
\(153\) −5.10766 −0.412930
\(154\) −4.14185 15.3001i −0.333760 1.23292i
\(155\) 0 0
\(156\) 0.756485 0.0605673
\(157\) 12.7066 1.01410 0.507050 0.861917i \(-0.330736\pi\)
0.507050 + 0.861917i \(0.330736\pi\)
\(158\) 3.20199i 0.254737i
\(159\) 9.19304 0.729056
\(160\) −4.19800 −0.331881
\(161\) 6.77439 10.7288i 0.533897 0.845550i
\(162\) 1.00000 0.0785674
\(163\) 19.6375 1.53813 0.769063 0.639173i \(-0.220723\pi\)
0.769063 + 0.639173i \(0.220723\pi\)
\(164\) 4.75648i 0.371419i
\(165\) −25.1505 −1.95796
\(166\) −12.4814 −0.968744
\(167\) 1.25776i 0.0973287i 0.998815 + 0.0486643i \(0.0154965\pi\)
−0.998815 + 0.0486643i \(0.984504\pi\)
\(168\) 0.691340 + 2.55383i 0.0533380 + 0.197032i
\(169\) 12.4277 0.955979
\(170\) −21.4420 −1.64452
\(171\) 1.02228 0.0781755
\(172\) 7.92299i 0.604122i
\(173\) 6.08820i 0.462877i 0.972850 + 0.231439i \(0.0743432\pi\)
−0.972850 + 0.231439i \(0.925657\pi\)
\(174\) 0.951991i 0.0721702i
\(175\) 32.2376 8.72695i 2.43693 0.659695i
\(176\) 5.99105i 0.451592i
\(177\) −0.291524 −0.0219123
\(178\) −1.24379 −0.0932262
\(179\) 7.81874 0.584400 0.292200 0.956357i \(-0.405613\pi\)
0.292200 + 0.956357i \(0.405613\pi\)
\(180\) 4.19800 0.312901
\(181\) −13.4800 −1.00196 −0.500979 0.865459i \(-0.667027\pi\)
−0.500979 + 0.865459i \(0.667027\pi\)
\(182\) −0.522988 1.93193i −0.0387665 0.143204i
\(183\) 4.08538i 0.302000i
\(184\) 3.53113 3.24517i 0.260318 0.239237i
\(185\) 39.0652i 2.87213i
\(186\) 0 0
\(187\) 30.6003i 2.23771i
\(188\) 9.62324i 0.701847i
\(189\) −0.691340 2.55383i −0.0502876 0.185764i
\(190\) 4.29152 0.311340
\(191\) 8.25712i 0.597464i 0.954337 + 0.298732i \(0.0965637\pi\)
−0.954337 + 0.298732i \(0.903436\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −10.7565 −0.774269 −0.387134 0.922023i \(-0.626535\pi\)
−0.387134 + 0.922023i \(0.626535\pi\)
\(194\) 14.4370 1.03652
\(195\) −3.17573 −0.227419
\(196\) 6.04410 3.53113i 0.431721 0.252223i
\(197\) 6.79280 0.483967 0.241984 0.970280i \(-0.422202\pi\)
0.241984 + 0.970280i \(0.422202\pi\)
\(198\) 5.99105i 0.425765i
\(199\) 7.28481 0.516406 0.258203 0.966091i \(-0.416870\pi\)
0.258203 + 0.966091i \(0.416870\pi\)
\(200\) 12.6232 0.892598
\(201\) 13.1433 0.927055
\(202\) 18.9549i 1.33367i
\(203\) 2.43122 0.658149i 0.170638 0.0461930i
\(204\) 5.10766i 0.357608i
\(205\) 19.9677i 1.39461i
\(206\) 6.46407 0.450373
\(207\) −3.53113 + 3.24517i −0.245430 + 0.225555i
\(208\) 0.756485i 0.0524528i
\(209\) 6.12452i 0.423642i
\(210\) −2.90225 10.7210i −0.200274 0.739819i
\(211\) −5.84081 −0.402098 −0.201049 0.979581i \(-0.564435\pi\)
−0.201049 + 0.979581i \(0.564435\pi\)
\(212\) 9.19304i 0.631381i
\(213\) 3.70848i 0.254101i
\(214\) 0.360402i 0.0246366i
\(215\) 33.2607i 2.26836i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) 0.909657i 0.0616097i
\(219\) 12.8668 0.869455
\(220\) 25.1505i 1.69564i
\(221\) 3.86387i 0.259912i
\(222\) −9.30566 −0.624555
\(223\) 3.60899i 0.241676i −0.992672 0.120838i \(-0.961442\pi\)
0.992672 0.120838i \(-0.0385581\pi\)
\(224\) 2.55383 0.691340i 0.170635 0.0461921i
\(225\) −12.6232 −0.841549
\(226\) 8.50863i 0.565986i
\(227\) 10.1264 0.672113 0.336056 0.941842i \(-0.390907\pi\)
0.336056 + 0.941842i \(0.390907\pi\)
\(228\) 1.02228i 0.0677020i
\(229\) 11.6607 0.770558 0.385279 0.922800i \(-0.374105\pi\)
0.385279 + 0.922800i \(0.374105\pi\)
\(230\) −14.8237 + 13.6232i −0.977445 + 0.898290i
\(231\) 15.3001 4.14185i 1.00667 0.272514i
\(232\) 0.951991 0.0625013
\(233\) −11.1505 −0.730491 −0.365245 0.930911i \(-0.619015\pi\)
−0.365245 + 0.930911i \(0.619015\pi\)
\(234\) 0.756485i 0.0494530i
\(235\) 40.3984i 2.63530i
\(236\) 0.291524i 0.0189766i
\(237\) −3.20199 −0.207992
\(238\) 13.0441 3.53113i 0.845523 0.228889i
\(239\) −10.6712 −0.690266 −0.345133 0.938554i \(-0.612166\pi\)
−0.345133 + 0.938554i \(0.612166\pi\)
\(240\) 4.19800i 0.270980i
\(241\) −14.4370 −0.929970 −0.464985 0.885318i \(-0.653940\pi\)
−0.464985 + 0.885318i \(0.653940\pi\)
\(242\) −24.8927 −1.60016
\(243\) 1.00000i 0.0641500i
\(244\) −4.08538 −0.261540
\(245\) −25.3731 + 14.8237i −1.62103 + 0.947051i
\(246\) 4.75648 0.303262
\(247\) 0.773337i 0.0492063i
\(248\) 0 0
\(249\) 12.4814i 0.790976i
\(250\) −32.0024 −2.02401
\(251\) 9.30566 0.587368 0.293684 0.955903i \(-0.405119\pi\)
0.293684 + 0.955903i \(0.405119\pi\)
\(252\) −2.55383 + 0.691340i −0.160876 + 0.0435503i
\(253\) −19.4420 21.1552i −1.22231 1.33001i
\(254\) −10.3058 −0.646642
\(255\) 21.4420i 1.34275i
\(256\) 1.00000 0.0625000
\(257\) 12.1842i 0.760030i 0.924980 + 0.380015i \(0.124081\pi\)
−0.924980 + 0.380015i \(0.875919\pi\)
\(258\) −7.92299 −0.493264
\(259\) 6.43338 + 23.7651i 0.399751 + 1.47669i
\(260\) 3.17573i 0.196950i
\(261\) −0.951991 −0.0589268
\(262\) 1.90398i 0.117628i
\(263\) 16.3952i 1.01097i 0.862835 + 0.505486i \(0.168687\pi\)
−0.862835 + 0.505486i \(0.831313\pi\)
\(264\) 5.99105 0.368724
\(265\) 38.5924i 2.37071i
\(266\) −2.61072 + 0.706741i −0.160074 + 0.0433331i
\(267\) 1.24379i 0.0761189i
\(268\) 13.1433i 0.802853i
\(269\) 19.3175i 1.17781i 0.808204 + 0.588903i \(0.200440\pi\)
−0.808204 + 0.588903i \(0.799560\pi\)
\(270\) 4.19800i 0.255482i
\(271\) 9.51297i 0.577872i 0.957348 + 0.288936i \(0.0933014\pi\)
−0.957348 + 0.288936i \(0.906699\pi\)
\(272\) 5.10766 0.309697
\(273\) 1.93193 0.522988i 0.116926 0.0316527i
\(274\) 14.8601i 0.897730i
\(275\) 75.6265i 4.56045i
\(276\) 3.24517 + 3.53113i 0.195336 + 0.212549i
\(277\) 5.60899 0.337011 0.168506 0.985701i \(-0.446106\pi\)
0.168506 + 0.985701i \(0.446106\pi\)
\(278\) 4.46496i 0.267791i
\(279\) 0 0
\(280\) −10.7210 + 2.90225i −0.640702 + 0.173442i
\(281\) 19.4973i 1.16311i 0.813507 + 0.581555i \(0.197556\pi\)
−0.813507 + 0.581555i \(0.802444\pi\)
\(282\) 9.62324 0.573055
\(283\) 20.0766 1.19343 0.596716 0.802452i \(-0.296472\pi\)
0.596716 + 0.802452i \(0.296472\pi\)
\(284\) −3.70848 −0.220058
\(285\) 4.29152i 0.254208i
\(286\) −4.53214 −0.267991
\(287\) −3.28835 12.1473i −0.194105 0.717030i
\(288\) −1.00000 −0.0589256
\(289\) 9.08820 0.534600
\(290\) −3.99646 −0.234680
\(291\) 14.4370i 0.846313i
\(292\) 12.8668i 0.752970i
\(293\) −23.1198 −1.35067 −0.675336 0.737510i \(-0.736001\pi\)
−0.675336 + 0.737510i \(0.736001\pi\)
\(294\) 3.53113 + 6.04410i 0.205940 + 0.352499i
\(295\) 1.22382i 0.0712535i
\(296\) 9.30566i 0.540881i
\(297\) −5.99105 −0.347636
\(298\) 15.7697i 0.913516i
\(299\) −2.45492 2.67125i −0.141972 0.154482i
\(300\) 12.6232i 0.728803i
\(301\) 5.47747 + 20.2340i 0.315716 + 1.16627i
\(302\) −13.9148 −0.800705
\(303\) −18.9549 −1.08893
\(304\) −1.02228 −0.0586316
\(305\) 17.1505 0.982032
\(306\) −5.10766 −0.291986
\(307\) 17.6596i 1.00788i 0.863737 + 0.503942i \(0.168117\pi\)
−0.863737 + 0.503942i \(0.831883\pi\)
\(308\) −4.14185 15.3001i −0.236004 0.871806i
\(309\) 6.46407i 0.367728i
\(310\) 0 0
\(311\) 10.6712i 0.605111i −0.953132 0.302555i \(-0.902160\pi\)
0.953132 0.302555i \(-0.0978397\pi\)
\(312\) 0.756485 0.0428275
\(313\) −12.2599 −0.692969 −0.346485 0.938056i \(-0.612625\pi\)
−0.346485 + 0.938056i \(0.612625\pi\)
\(314\) 12.7066 0.717077
\(315\) 10.7210 2.90225i 0.604059 0.163523i
\(316\) 3.20199i 0.180126i
\(317\) 15.5869 0.875449 0.437724 0.899109i \(-0.355785\pi\)
0.437724 + 0.899109i \(0.355785\pi\)
\(318\) 9.19304 0.515520
\(319\) 5.70343i 0.319331i
\(320\) −4.19800 −0.234676
\(321\) 0.360402 0.0201157
\(322\) 6.77439 10.7288i 0.377522 0.597894i
\(323\) −5.22145 −0.290529
\(324\) 1.00000 0.0555556
\(325\) 9.54929i 0.529699i
\(326\) 19.6375 1.08762
\(327\) 0.909657 0.0503041
\(328\) 4.75648i 0.262633i
\(329\) −6.65293 24.5761i −0.366788 1.35492i
\(330\) −25.1505 −1.38449
\(331\) 34.0172 1.86975 0.934877 0.354971i \(-0.115509\pi\)
0.934877 + 0.354971i \(0.115509\pi\)
\(332\) −12.4814 −0.685005
\(333\) 9.30566i 0.509947i
\(334\) 1.25776i 0.0688218i
\(335\) 55.1755i 3.01456i
\(336\) 0.691340 + 2.55383i 0.0377157 + 0.139323i
\(337\) 11.0361i 0.601172i 0.953755 + 0.300586i \(0.0971823\pi\)
−0.953755 + 0.300586i \(0.902818\pi\)
\(338\) 12.4277 0.675979
\(339\) −8.50863 −0.462125
\(340\) −21.4420 −1.16285
\(341\) 0 0
\(342\) 1.02228 0.0552784
\(343\) 12.9944 13.1964i 0.701631 0.712540i
\(344\) 7.92299i 0.427179i
\(345\) −13.6232 14.8237i −0.733450 0.798081i
\(346\) 6.08820i 0.327304i
\(347\) −30.6742 −1.64668 −0.823339 0.567550i \(-0.807891\pi\)
−0.823339 + 0.567550i \(0.807891\pi\)
\(348\) 0.951991i 0.0510321i
\(349\) 34.6997i 1.85743i 0.370789 + 0.928717i \(0.379087\pi\)
−0.370789 + 0.928717i \(0.620913\pi\)
\(350\) 32.2376 8.72695i 1.72317 0.466475i
\(351\) −0.756485 −0.0403782
\(352\) 5.99105i 0.319324i
\(353\) 6.85250i 0.364722i 0.983232 + 0.182361i \(0.0583739\pi\)
−0.983232 + 0.182361i \(0.941626\pi\)
\(354\) −0.291524 −0.0154943
\(355\) 15.5682 0.826274
\(356\) −1.24379 −0.0659209
\(357\) 3.53113 + 13.0441i 0.186887 + 0.690367i
\(358\) 7.81874 0.413233
\(359\) 9.38829i 0.495495i −0.968825 0.247748i \(-0.920310\pi\)
0.968825 0.247748i \(-0.0796904\pi\)
\(360\) 4.19800 0.221254
\(361\) −17.9549 −0.944997
\(362\) −13.4800 −0.708491
\(363\) 24.8927i 1.30653i
\(364\) −0.522988 1.93193i −0.0274120 0.101261i
\(365\) 54.0147i 2.82726i
\(366\) 4.08538i 0.213546i
\(367\) 32.4254 1.69259 0.846297 0.532711i \(-0.178827\pi\)
0.846297 + 0.532711i \(0.178827\pi\)
\(368\) 3.53113 3.24517i 0.184073 0.169166i
\(369\) 4.75648i 0.247613i
\(370\) 39.0652i 2.03090i
\(371\) −6.35552 23.4775i −0.329962 1.21889i
\(372\) 0 0
\(373\) 7.17591i 0.371555i −0.982592 0.185777i \(-0.940520\pi\)
0.982592 0.185777i \(-0.0594803\pi\)
\(374\) 30.6003i 1.58230i
\(375\) 32.0024i 1.65260i
\(376\) 9.62324i 0.496281i
\(377\) 0.720167i 0.0370905i
\(378\) −0.691340 2.55383i −0.0355587 0.131355i
\(379\) 24.3373i 1.25012i −0.780576 0.625061i \(-0.785074\pi\)
0.780576 0.625061i \(-0.214926\pi\)
\(380\) 4.29152 0.220151
\(381\) 10.3058i 0.527981i
\(382\) 8.25712i 0.422471i
\(383\) −23.3687 −1.19409 −0.597043 0.802209i \(-0.703658\pi\)
−0.597043 + 0.802209i \(0.703658\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 17.3875 + 64.2300i 0.886150 + 3.27346i
\(386\) −10.7565 −0.547491
\(387\) 7.92299i 0.402748i
\(388\) 14.4370 0.732929
\(389\) 26.2103i 1.32891i −0.747326 0.664457i \(-0.768663\pi\)
0.747326 0.664457i \(-0.231337\pi\)
\(390\) −3.17573 −0.160809
\(391\) 18.0358 16.5752i 0.912110 0.838245i
\(392\) 6.04410 3.53113i 0.305273 0.178349i
\(393\) 1.90398 0.0960432
\(394\) 6.79280 0.342216
\(395\) 13.4420i 0.676339i
\(396\) 5.99105i 0.301062i
\(397\) 6.77073i 0.339813i −0.985460 0.169907i \(-0.945653\pi\)
0.985460 0.169907i \(-0.0543466\pi\)
\(398\) 7.28481 0.365154
\(399\) −0.706741 2.61072i −0.0353813 0.130700i
\(400\) 12.6232 0.631162
\(401\) 20.0330i 1.00040i −0.865910 0.500199i \(-0.833260\pi\)
0.865910 0.500199i \(-0.166740\pi\)
\(402\) 13.1433 0.655527
\(403\) 0 0
\(404\) 18.9549i 0.943044i
\(405\) −4.19800 −0.208600
\(406\) 2.43122 0.658149i 0.120660 0.0326634i
\(407\) 55.7507 2.76346
\(408\) 5.10766i 0.252867i
\(409\) 35.4592i 1.75334i −0.481089 0.876672i \(-0.659758\pi\)
0.481089 0.876672i \(-0.340242\pi\)
\(410\) 19.9677i 0.986136i
\(411\) −14.8601 −0.732994
\(412\) 6.46407 0.318462
\(413\) 0.201542 + 0.744503i 0.00991725 + 0.0366346i
\(414\) −3.53113 + 3.24517i −0.173546 + 0.159491i
\(415\) 52.3969 2.57206
\(416\) 0.756485i 0.0370897i
\(417\) 4.46496 0.218650
\(418\) 6.12452i 0.299560i
\(419\) 15.1214 0.738731 0.369365 0.929284i \(-0.379575\pi\)
0.369365 + 0.929284i \(0.379575\pi\)
\(420\) −2.90225 10.7210i −0.141615 0.523131i
\(421\) 32.6016i 1.58890i −0.607327 0.794452i \(-0.707758\pi\)
0.607327 0.794452i \(-0.292242\pi\)
\(422\) −5.84081 −0.284326
\(423\) 9.62324i 0.467898i
\(424\) 9.19304i 0.446454i
\(425\) 64.4752 3.12751
\(426\) 3.70848i 0.179676i
\(427\) −10.4334 + 2.82439i −0.504906 + 0.136682i
\(428\) 0.360402i 0.0174207i
\(429\) 4.53214i 0.218814i
\(430\) 33.2607i 1.60397i
\(431\) 26.5106i 1.27697i 0.769634 + 0.638486i \(0.220439\pi\)
−0.769634 + 0.638486i \(0.779561\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −30.1831 −1.45051 −0.725253 0.688483i \(-0.758277\pi\)
−0.725253 + 0.688483i \(0.758277\pi\)
\(434\) 0 0
\(435\) 3.99646i 0.191616i
\(436\) 0.909657i 0.0435647i
\(437\) −3.60979 + 3.31746i −0.172680 + 0.158696i
\(438\) 12.8668 0.614797
\(439\) 27.8295i 1.32823i 0.747630 + 0.664115i \(0.231192\pi\)
−0.747630 + 0.664115i \(0.768808\pi\)
\(440\) 25.1505i 1.19900i
\(441\) −6.04410 + 3.53113i −0.287814 + 0.168149i
\(442\) 3.86387i 0.183785i
\(443\) 15.1362 0.719143 0.359571 0.933118i \(-0.382923\pi\)
0.359571 + 0.933118i \(0.382923\pi\)
\(444\) −9.30566 −0.441627
\(445\) 5.22145 0.247520
\(446\) 3.60899i 0.170891i
\(447\) −15.7697 −0.745883
\(448\) 2.55383 0.691340i 0.120657 0.0326627i
\(449\) 24.6634 1.16394 0.581969 0.813211i \(-0.302282\pi\)
0.581969 + 0.813211i \(0.302282\pi\)
\(450\) −12.6232 −0.595065
\(451\) −28.4963 −1.34184
\(452\) 8.50863i 0.400212i
\(453\) 13.9148i 0.653772i
\(454\) 10.1264 0.475255
\(455\) 2.19551 + 8.11027i 0.102927 + 0.380215i
\(456\) 1.02228i 0.0478725i
\(457\) 19.6573i 0.919530i 0.888041 + 0.459765i \(0.152066\pi\)
−0.888041 + 0.459765i \(0.847934\pi\)
\(458\) 11.6607 0.544867
\(459\) 5.10766i 0.238405i
\(460\) −14.8237 + 13.6232i −0.691158 + 0.635187i
\(461\) 2.38754i 0.111199i −0.998453 0.0555995i \(-0.982293\pi\)
0.998453 0.0555995i \(-0.0177070\pi\)
\(462\) 15.3001 4.14185i 0.711826 0.192696i
\(463\) −6.69678 −0.311226 −0.155613 0.987818i \(-0.549735\pi\)
−0.155613 + 0.987818i \(0.549735\pi\)
\(464\) 0.951991 0.0441951
\(465\) 0 0
\(466\) −11.1505 −0.516535
\(467\) −25.9198 −1.19943 −0.599713 0.800215i \(-0.704719\pi\)
−0.599713 + 0.800215i \(0.704719\pi\)
\(468\) 0.756485i 0.0349685i
\(469\) −9.08646 33.5657i −0.419574 1.54992i
\(470\) 40.3984i 1.86344i
\(471\) 12.7066i 0.585491i
\(472\) 0.291524i 0.0134185i
\(473\) 47.4670 2.18254
\(474\) −3.20199 −0.147072
\(475\) −12.9044 −0.592097
\(476\) 13.0441 3.53113i 0.597875 0.161849i
\(477\) 9.19304i 0.420921i
\(478\) −10.6712 −0.488091
\(479\) 22.6930 1.03687 0.518435 0.855117i \(-0.326515\pi\)
0.518435 + 0.855117i \(0.326515\pi\)
\(480\) 4.19800i 0.191612i
\(481\) 7.03959 0.320978
\(482\) −14.4370 −0.657588
\(483\) 10.7288 + 6.77439i 0.488178 + 0.308245i
\(484\) −24.8927 −1.13149
\(485\) −60.6067 −2.75201
\(486\) 1.00000i 0.0453609i
\(487\) 5.33171 0.241603 0.120801 0.992677i \(-0.461454\pi\)
0.120801 + 0.992677i \(0.461454\pi\)
\(488\) −4.08538 −0.184937
\(489\) 19.6375i 0.888038i
\(490\) −25.3731 + 14.8237i −1.14624 + 0.669666i
\(491\) −3.21798 −0.145225 −0.0726126 0.997360i \(-0.523134\pi\)
−0.0726126 + 0.997360i \(0.523134\pi\)
\(492\) 4.75648 0.214439
\(493\) 4.86245 0.218994
\(494\) 0.773337i 0.0347941i
\(495\) 25.1505i 1.13043i
\(496\) 0 0
\(497\) −9.47082 + 2.56382i −0.424824 + 0.115003i
\(498\) 12.4814i 0.559305i
\(499\) −11.4170 −0.511093 −0.255546 0.966797i \(-0.582255\pi\)
−0.255546 + 0.966797i \(0.582255\pi\)
\(500\) −32.0024 −1.43119
\(501\) −1.25776 −0.0561927
\(502\) 9.30566 0.415332
\(503\) −0.177843 −0.00792964 −0.00396482 0.999992i \(-0.501262\pi\)
−0.00396482 + 0.999992i \(0.501262\pi\)
\(504\) −2.55383 + 0.691340i −0.113757 + 0.0307947i
\(505\) 79.5729i 3.54095i
\(506\) −19.4420 21.1552i −0.864301 0.940462i
\(507\) 12.4277i 0.551935i
\(508\) −10.3058 −0.457245
\(509\) 19.0623i 0.844920i 0.906382 + 0.422460i \(0.138833\pi\)
−0.906382 + 0.422460i \(0.861167\pi\)
\(510\) 21.4420i 0.949467i
\(511\) −8.89530 32.8595i −0.393505 1.45362i
\(512\) 1.00000 0.0441942
\(513\) 1.02228i 0.0451346i
\(514\) 12.1842i 0.537423i
\(515\) −27.1362 −1.19576
\(516\) −7.92299 −0.348790
\(517\) −57.6533 −2.53559
\(518\) 6.43338 + 23.7651i 0.282666 + 1.04418i
\(519\) −6.08820 −0.267242
\(520\) 3.17573i 0.139265i
\(521\) 40.3332 1.76703 0.883514 0.468405i \(-0.155171\pi\)
0.883514 + 0.468405i \(0.155171\pi\)
\(522\) −0.951991 −0.0416675
\(523\) 32.4890 1.42064 0.710322 0.703877i \(-0.248549\pi\)
0.710322 + 0.703877i \(0.248549\pi\)
\(524\) 1.90398i 0.0831758i
\(525\) 8.72695 + 32.2376i 0.380875 + 1.40696i
\(526\) 16.3952i 0.714866i
\(527\) 0 0
\(528\) 5.99105 0.260727
\(529\) 1.93774 22.9182i 0.0842497 0.996445i
\(530\) 38.5924i 1.67635i
\(531\) 0.291524i 0.0126511i
\(532\) −2.61072 + 0.706741i −0.113189 + 0.0306411i
\(533\) −3.59821 −0.155856
\(534\) 1.24379i 0.0538242i
\(535\) 1.51297i 0.0654114i
\(536\) 13.1433i 0.567703i
\(537\) 7.81874i 0.337404i
\(538\) 19.3175i 0.832835i
\(539\) −21.1552 36.2105i −0.911218 1.55970i
\(540\) 4.19800i 0.180653i
\(541\) −25.4939 −1.09607 −0.548033 0.836457i \(-0.684623\pi\)
−0.548033 + 0.836457i \(0.684623\pi\)
\(542\) 9.51297i 0.408617i
\(543\) 13.4800i 0.578481i
\(544\) 5.10766 0.218989
\(545\) 3.81874i 0.163577i
\(546\) 1.93193 0.522988i 0.0826791 0.0223818i
\(547\) 15.3538 0.656480 0.328240 0.944594i \(-0.393544\pi\)
0.328240 + 0.944594i \(0.393544\pi\)
\(548\) 14.8601i 0.634791i
\(549\) 4.08538 0.174360
\(550\) 75.6265i 3.22472i
\(551\) −0.973199 −0.0414597
\(552\) 3.24517 + 3.53113i 0.138124 + 0.150295i
\(553\) 2.21367 + 8.17735i 0.0941346 + 0.347736i
\(554\) 5.60899 0.238303
\(555\) 39.0652 1.65823
\(556\) 4.46496i 0.189357i
\(557\) 35.3796i 1.49908i 0.661957 + 0.749542i \(0.269726\pi\)
−0.661957 + 0.749542i \(0.730274\pi\)
\(558\) 0 0
\(559\) 5.99362 0.253503
\(560\) −10.7210 + 2.90225i −0.453045 + 0.122642i
\(561\) 30.6003 1.29194
\(562\) 19.4973i 0.822443i
\(563\) −21.0100 −0.885466 −0.442733 0.896654i \(-0.645991\pi\)
−0.442733 + 0.896654i \(0.645991\pi\)
\(564\) 9.62324 0.405211
\(565\) 35.7193i 1.50272i
\(566\) 20.0766 0.843884
\(567\) 2.55383 0.691340i 0.107251 0.0290335i
\(568\) −3.70848 −0.155604
\(569\) 6.39130i 0.267937i 0.990986 + 0.133969i \(0.0427721\pi\)
−0.990986 + 0.133969i \(0.957228\pi\)
\(570\) 4.29152i 0.179752i
\(571\) 22.0348i 0.922129i −0.887367 0.461065i \(-0.847468\pi\)
0.887367 0.461065i \(-0.152532\pi\)
\(572\) −4.53214 −0.189498
\(573\) −8.25712 −0.344946
\(574\) −3.28835 12.1473i −0.137253 0.507017i
\(575\) 44.5743 40.9645i 1.85888 1.70834i
\(576\) −1.00000 −0.0416667
\(577\) 15.3175i 0.637674i 0.947810 + 0.318837i \(0.103292\pi\)
−0.947810 + 0.318837i \(0.896708\pi\)
\(578\) 9.08820 0.378019
\(579\) 10.7565i 0.447024i
\(580\) −3.99646 −0.165944
\(581\) −31.8754 + 8.62888i −1.32241 + 0.357986i
\(582\) 14.4370i 0.598434i
\(583\) −55.0760 −2.28101
\(584\) 12.8668i 0.532430i
\(585\) 3.17573i 0.131300i
\(586\) −23.1198 −0.955069
\(587\) 22.6634i 0.935420i −0.883882 0.467710i \(-0.845079\pi\)
0.883882 0.467710i \(-0.154921\pi\)
\(588\) 3.53113 + 6.04410i 0.145621 + 0.249254i
\(589\) 0 0
\(590\) 1.22382i 0.0503839i
\(591\) 6.79280i 0.279419i
\(592\) 9.30566i 0.382460i
\(593\) 40.5704i 1.66603i −0.553254 0.833013i \(-0.686614\pi\)
0.553254 0.833013i \(-0.313386\pi\)
\(594\) −5.99105 −0.245816
\(595\) −54.7592 + 14.8237i −2.24491 + 0.607712i
\(596\) 15.7697i 0.645954i
\(597\) 7.28481i 0.298147i
\(598\) −2.45492 2.67125i −0.100389 0.109235i
\(599\) −1.15828 −0.0473259 −0.0236629 0.999720i \(-0.507533\pi\)
−0.0236629 + 0.999720i \(0.507533\pi\)
\(600\) 12.6232i 0.515341i
\(601\) 2.34340i 0.0955894i −0.998857 0.0477947i \(-0.984781\pi\)
0.998857 0.0477947i \(-0.0152193\pi\)
\(602\) 5.47747 + 20.2340i 0.223245 + 0.824675i
\(603\) 13.1433i 0.535235i
\(604\) −13.9148 −0.566184
\(605\) 104.500 4.24851
\(606\) −18.9549 −0.769992
\(607\) 29.1220i 1.18202i 0.806663 + 0.591012i \(0.201271\pi\)
−0.806663 + 0.591012i \(0.798729\pi\)
\(608\) −1.02228 −0.0414588
\(609\) 0.658149 + 2.43122i 0.0266696 + 0.0985181i
\(610\) 17.1505 0.694402
\(611\) −7.27983 −0.294511
\(612\) −5.10766 −0.206465
\(613\) 18.9255i 0.764393i 0.924081 + 0.382197i \(0.124832\pi\)
−0.924081 + 0.382197i \(0.875168\pi\)
\(614\) 17.6596i 0.712682i
\(615\) −19.9677 −0.805177
\(616\) −4.14185 15.3001i −0.166880 0.616460i
\(617\) 21.7218i 0.874488i −0.899343 0.437244i \(-0.855955\pi\)
0.899343 0.437244i \(-0.144045\pi\)
\(618\) 6.46407i 0.260023i
\(619\) 21.6707 0.871019 0.435510 0.900184i \(-0.356568\pi\)
0.435510 + 0.900184i \(0.356568\pi\)
\(620\) 0 0
\(621\) −3.24517 3.53113i −0.130224 0.141699i
\(622\) 10.6712i 0.427878i
\(623\) −3.17643 + 0.859883i −0.127261 + 0.0344505i
\(624\) 0.756485 0.0302836
\(625\) 71.2299 2.84920
\(626\) −12.2599 −0.490003
\(627\) −6.12452 −0.244590
\(628\) 12.7066 0.507050
\(629\) 47.5302i 1.89515i
\(630\) 10.7210 2.90225i 0.427134 0.115628i
\(631\) 41.5434i 1.65382i 0.562337 + 0.826908i \(0.309903\pi\)
−0.562337 + 0.826908i \(0.690097\pi\)
\(632\) 3.20199i 0.127368i
\(633\) 5.84081i 0.232151i
\(634\) 15.5869 0.619036
\(635\) 43.2637 1.71687
\(636\) 9.19304 0.364528
\(637\) −2.67125 4.57227i −0.105839 0.181160i
\(638\) 5.70343i 0.225801i
\(639\) 3.70848 0.146705
\(640\) −4.19800 −0.165941
\(641\) 24.5273i 0.968770i −0.874855 0.484385i \(-0.839043\pi\)
0.874855 0.484385i \(-0.160957\pi\)
\(642\) 0.360402 0.0142239
\(643\) 0.644573 0.0254195 0.0127097 0.999919i \(-0.495954\pi\)
0.0127097 + 0.999919i \(0.495954\pi\)
\(644\) 6.77439 10.7288i 0.266948 0.422775i
\(645\) 33.2607 1.30964
\(646\) −5.22145 −0.205435
\(647\) 2.67125i 0.105018i 0.998620 + 0.0525088i \(0.0167217\pi\)
−0.998620 + 0.0525088i \(0.983278\pi\)
\(648\) 1.00000 0.0392837
\(649\) 1.74654 0.0685575
\(650\) 9.54929i 0.374554i
\(651\) 0 0
\(652\) 19.6375 0.769063
\(653\) −28.5263 −1.11632 −0.558160 0.829733i \(-0.688493\pi\)
−0.558160 + 0.829733i \(0.688493\pi\)
\(654\) 0.909657 0.0355704
\(655\) 7.99292i 0.312309i
\(656\) 4.75648i 0.185710i
\(657\) 12.8668i 0.501980i
\(658\) −6.65293 24.5761i −0.259358 0.958077i
\(659\) 25.0003i 0.973875i −0.873437 0.486937i \(-0.838114\pi\)
0.873437 0.486937i \(-0.161886\pi\)
\(660\) −25.1505 −0.978980
\(661\) −20.4997 −0.797346 −0.398673 0.917093i \(-0.630529\pi\)
−0.398673 + 0.917093i \(0.630529\pi\)
\(662\) 34.0172 1.32212
\(663\) 3.86387 0.150060
\(664\) −12.4814 −0.484372
\(665\) 10.9598 2.96690i 0.425004 0.115051i
\(666\) 9.30566i 0.360587i
\(667\) 3.36160 3.08937i 0.130162 0.119621i
\(668\) 1.25776i 0.0486643i
\(669\) 3.60899 0.139532
\(670\) 55.1755i 2.13161i
\(671\) 24.4757i 0.944875i
\(672\) 0.691340 + 2.55383i 0.0266690 + 0.0985161i
\(673\) 25.1362 0.968930 0.484465 0.874811i \(-0.339014\pi\)
0.484465 + 0.874811i \(0.339014\pi\)
\(674\) 11.0361i 0.425093i
\(675\) 12.6232i 0.485869i
\(676\) 12.4277 0.477990
\(677\) 20.5271 0.788921 0.394461 0.918913i \(-0.370931\pi\)
0.394461 + 0.918913i \(0.370931\pi\)
\(678\) −8.50863 −0.326772
\(679\) 36.8697 9.98089i 1.41493 0.383031i
\(680\) −21.4420 −0.822262
\(681\) 10.1264i 0.388044i
\(682\) 0 0
\(683\) 30.0535 1.14997 0.574983 0.818165i \(-0.305009\pi\)
0.574983 + 0.818165i \(0.305009\pi\)
\(684\) 1.02228 0.0390878
\(685\) 62.3827i 2.38352i
\(686\) 12.9944 13.1964i 0.496128 0.503842i
\(687\) 11.6607i 0.444882i
\(688\) 7.92299i 0.302061i
\(689\) −6.95440 −0.264942
\(690\) −13.6232 14.8237i −0.518628 0.564328i
\(691\) 17.3317i 0.659329i 0.944098 + 0.329665i \(0.106936\pi\)
−0.944098 + 0.329665i \(0.893064\pi\)
\(692\) 6.08820i 0.231439i
\(693\) 4.14185 + 15.3001i 0.157336 + 0.581204i
\(694\) −30.6742 −1.16438
\(695\) 18.7439i 0.710998i
\(696\) 0.951991i 0.0360851i
\(697\) 24.2945i 0.920220i
\(698\) 34.6997i 1.31340i
\(699\) 11.1505i 0.421749i
\(700\) 32.2376 8.72695i 1.21847 0.329848i
\(701\) 4.28320i 0.161774i 0.996723 + 0.0808871i \(0.0257753\pi\)
−0.996723 + 0.0808871i \(0.974225\pi\)
\(702\) −0.756485 −0.0285517
\(703\) 9.51297i 0.358788i
\(704\) 5.99105i 0.225796i
\(705\) −40.3984 −1.52149
\(706\) 6.85250i 0.257897i
\(707\) 13.1043 + 48.4077i 0.492838 + 1.82056i
\(708\) −0.291524 −0.0109561
\(709\) 27.4541i 1.03106i −0.856871 0.515530i \(-0.827595\pi\)
0.856871 0.515530i \(-0.172405\pi\)
\(710\) 15.5682 0.584264
\(711\) 3.20199i 0.120084i
\(712\) −1.24379 −0.0466131
\(713\) 0 0
\(714\) 3.53113 + 13.0441i 0.132149 + 0.488163i
\(715\) 19.0259 0.711530
\(716\) 7.81874 0.292200
\(717\) 10.6712i 0.398525i
\(718\) 9.38829i 0.350368i
\(719\) 27.8109i 1.03717i 0.855025 + 0.518586i \(0.173541\pi\)
−0.855025 + 0.518586i \(0.826459\pi\)
\(720\) 4.19800 0.156450
\(721\) 16.5081 4.46887i 0.614796 0.166429i
\(722\) −17.9549 −0.668214
\(723\) 14.4370i 0.536919i
\(724\) −13.4800 −0.500979
\(725\) 12.0172 0.446308
\(726\) 24.8927i 0.923854i
\(727\) −14.3244 −0.531263 −0.265631 0.964075i \(-0.585580\pi\)
−0.265631 + 0.964075i \(0.585580\pi\)
\(728\) −0.522988 1.93193i −0.0193832 0.0716022i
\(729\) −1.00000 −0.0370370
\(730\) 54.0147i 1.99917i
\(731\) 40.4679i 1.49676i
\(732\) 4.08538i 0.151000i
\(733\) −7.94925 −0.293612 −0.146806 0.989165i \(-0.546899\pi\)
−0.146806 + 0.989165i \(0.546899\pi\)
\(734\) 32.4254 1.19684
\(735\) −14.8237 25.3731i −0.546780 0.935903i
\(736\) 3.53113 3.24517i 0.130159 0.119619i
\(737\) −78.7420 −2.90050
\(738\) 4.75648i 0.175089i
\(739\) 4.10731 0.151090 0.0755449 0.997142i \(-0.475930\pi\)
0.0755449 + 0.997142i \(0.475930\pi\)
\(740\) 39.0652i 1.43607i
\(741\) −0.773337 −0.0284093
\(742\) −6.35552 23.4775i −0.233318 0.861885i
\(743\) 7.36361i 0.270145i −0.990836 0.135072i \(-0.956873\pi\)
0.990836 0.135072i \(-0.0431267\pi\)
\(744\) 0 0
\(745\) 66.2014i 2.42543i
\(746\) 7.17591i 0.262729i
\(747\) 12.4814 0.456670
\(748\) 30.6003i 1.11886i
\(749\) −0.249160 0.920406i −0.00910412 0.0336309i
\(750\) 32.0024i 1.16856i
\(751\) 44.0633i 1.60789i 0.594702 + 0.803946i \(0.297270\pi\)
−0.594702 + 0.803946i \(0.702730\pi\)
\(752\) 9.62324i 0.350923i
\(753\) 9.30566i 0.339117i
\(754\) 0.720167i 0.0262269i
\(755\) 58.4142 2.12591
\(756\) −0.691340 2.55383i −0.0251438 0.0928819i
\(757\) 30.5446i 1.11016i 0.831796 + 0.555082i \(0.187313\pi\)
−0.831796 + 0.555082i \(0.812687\pi\)
\(758\) 24.3373i 0.883970i
\(759\) 21.1552 19.4420i 0.767884 0.705699i
\(760\) 4.29152 0.155670
\(761\) 15.4091i 0.558581i 0.960207 + 0.279290i \(0.0900992\pi\)
−0.960207 + 0.279290i \(0.909901\pi\)
\(762\) 10.3058i 0.373339i
\(763\) −0.628882 2.32311i −0.0227671 0.0841022i
\(764\) 8.25712i 0.298732i
\(765\) 21.4420 0.775236
\(766\) −23.3687 −0.844346
\(767\) 0.220534 0.00796301
\(768\) 1.00000i 0.0360844i
\(769\) 44.2623 1.59614 0.798069 0.602566i \(-0.205855\pi\)
0.798069 + 0.602566i \(0.205855\pi\)
\(770\) 17.3875 + 64.2300i 0.626602 + 2.31469i
\(771\) −12.1842 −0.438804
\(772\) −10.7565 −0.387134
\(773\) 11.5480 0.415354 0.207677 0.978197i \(-0.433410\pi\)
0.207677 + 0.978197i \(0.433410\pi\)
\(774\) 7.92299i 0.284786i
\(775\) 0 0
\(776\) 14.4370 0.518259
\(777\) −23.7651 + 6.43338i −0.852568 + 0.230796i
\(778\) 26.2103i 0.939685i
\(779\) 4.86245i 0.174215i
\(780\) −3.17573 −0.113709
\(781\) 22.2177i 0.795011i
\(782\) 18.0358 16.5752i 0.644959 0.592729i
\(783\) 0.951991i 0.0340214i
\(784\) 6.04410 3.53113i 0.215861 0.126112i
\(785\) −53.3425 −1.90388
\(786\) 1.90398 0.0679128
\(787\) 6.93070 0.247053 0.123526 0.992341i \(-0.460580\pi\)
0.123526 + 0.992341i \(0.460580\pi\)
\(788\) 6.79280 0.241984
\(789\) −16.3952 −0.583685
\(790\) 13.4420i 0.478244i
\(791\) 5.88235 + 21.7296i 0.209152 + 0.772615i
\(792\) 5.99105i 0.212883i
\(793\) 3.09053i 0.109748i
\(794\) 6.77073i 0.240284i
\(795\) −38.5924 −1.36873
\(796\) 7.28481 0.258203
\(797\) −16.1852 −0.573311 −0.286655 0.958034i \(-0.592543\pi\)
−0.286655 + 0.958034i \(0.592543\pi\)
\(798\) −0.706741 2.61072i −0.0250184 0.0924186i
\(799\) 49.1522i 1.73888i
\(800\) 12.6232 0.446299
\(801\) 1.24379 0.0439472
\(802\) 20.0330i 0.707389i
\(803\) −77.0854 −2.72028
\(804\) 13.1433 0.463527
\(805\) −28.4389 + 45.0396i −1.00234 + 1.58744i
\(806\) 0 0
\(807\) −19.3175 −0.680007
\(808\) 18.9549i 0.666833i
\(809\) 31.7620 1.11669 0.558346 0.829608i \(-0.311436\pi\)
0.558346 + 0.829608i \(0.311436\pi\)
\(810\) −4.19800 −0.147503
\(811\) 34.9173i 1.22611i −0.790039 0.613056i \(-0.789940\pi\)
0.790039 0.613056i \(-0.210060\pi\)
\(812\) 2.43122 0.658149i 0.0853192 0.0230965i
\(813\) −9.51297 −0.333634
\(814\) 55.7507 1.95406
\(815\) −82.4382 −2.88769
\(816\) 5.10766i 0.178804i
\(817\) 8.09949i 0.283365i
\(818\) 35.4592i 1.23980i
\(819\) 0.522988 + 1.93193i 0.0182747 + 0.0675072i
\(820\) 19.9677i 0.697304i
\(821\) −40.3166 −1.40706 −0.703529 0.710667i \(-0.748393\pi\)
−0.703529 + 0.710667i \(0.748393\pi\)
\(822\) −14.8601 −0.518305
\(823\) −19.5982 −0.683151 −0.341575 0.939854i \(-0.610960\pi\)
−0.341575 + 0.939854i \(0.610960\pi\)
\(824\) 6.46407 0.225187
\(825\) 75.6265 2.63298
\(826\) 0.201542 + 0.744503i 0.00701255 + 0.0259046i
\(827\) 16.6620i 0.579394i −0.957118 0.289697i \(-0.906445\pi\)
0.957118 0.289697i \(-0.0935546\pi\)
\(828\) −3.53113 + 3.24517i −0.122715 + 0.112777i
\(829\) 8.96624i 0.311410i −0.987804 0.155705i \(-0.950235\pi\)
0.987804 0.155705i \(-0.0497650\pi\)
\(830\) 52.3969 1.81872
\(831\) 5.60899i 0.194574i
\(832\) 0.756485i 0.0262264i
\(833\) 30.8712 18.0358i 1.06962 0.624904i
\(834\) 4.46496 0.154609
\(835\) 5.28010i 0.182725i
\(836\) 6.12452i 0.211821i
\(837\) 0 0
\(838\) 15.1214 0.522361
\(839\) 20.2054 0.697568 0.348784 0.937203i \(-0.386595\pi\)
0.348784 + 0.937203i \(0.386595\pi\)
\(840\) −2.90225 10.7210i −0.100137 0.369909i
\(841\) −28.0937 −0.968749
\(842\) 32.6016i 1.12353i
\(843\) −19.4973 −0.671522
\(844\) −5.84081 −0.201049
\(845\) −52.1717 −1.79476
\(846\) 9.62324i 0.330854i
\(847\) −63.5717 + 17.2093i −2.18435 + 0.591319i
\(848\) 9.19304i 0.315690i
\(849\) 20.0766i 0.689028i
\(850\) 64.4752 2.21148
\(851\) 30.1985 + 32.8595i 1.03519 + 1.12641i
\(852\) 3.70848i 0.127050i
\(853\) 19.5410i 0.669070i 0.942383 + 0.334535i \(0.108579\pi\)
−0.942383 + 0.334535i \(0.891421\pi\)
\(854\) −10.4334 + 2.82439i −0.357023 + 0.0966486i
\(855\) −4.29152 −0.146767
\(856\) 0.360402i 0.0123183i
\(857\) 37.1249i 1.26816i 0.773266 + 0.634081i \(0.218622\pi\)
−0.773266 + 0.634081i \(0.781378\pi\)
\(858\) 4.53214i 0.154725i
\(859\) 33.1897i 1.13242i 0.824261 + 0.566210i \(0.191591\pi\)
−0.824261 + 0.566210i \(0.808409\pi\)
\(860\) 33.2607i 1.13418i
\(861\) 12.1473 3.28835i 0.413977 0.112067i
\(862\) 26.5106i 0.902955i
\(863\) 8.36251 0.284663 0.142332 0.989819i \(-0.454540\pi\)
0.142332 + 0.989819i \(0.454540\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) 25.5583i 0.869007i
\(866\) −30.1831 −1.02566
\(867\) 9.08820i 0.308651i
\(868\) 0 0
\(869\) 19.1833 0.650749
\(870\) 3.99646i 0.135493i
\(871\) −9.94268 −0.336895
\(872\) 0.909657i 0.0308049i
\(873\) −14.4370 −0.488619
\(874\) −3.60979 + 3.31746i −0.122103 + 0.112215i
\(875\) −81.7286 + 22.1245i −2.76293 + 0.747945i
\(876\) 12.8668 0.434727
\(877\) −28.6349 −0.966933 −0.483466 0.875363i \(-0.660622\pi\)
−0.483466 + 0.875363i \(0.660622\pi\)
\(878\) 27.8295i 0.939201i
\(879\) 23.1198i 0.779810i
\(880\) 25.1505i 0.847822i
\(881\) −38.6663 −1.30270 −0.651351 0.758777i \(-0.725797\pi\)
−0.651351 + 0.758777i \(0.725797\pi\)
\(882\) −6.04410 + 3.53113i −0.203515 + 0.118899i
\(883\) −33.6547 −1.13257 −0.566285 0.824209i \(-0.691620\pi\)
−0.566285 + 0.824209i \(0.691620\pi\)
\(884\) 3.86387i 0.129956i
\(885\) 1.22382 0.0411382
\(886\) 15.1362 0.508511
\(887\) 40.3200i 1.35381i −0.736069 0.676907i \(-0.763320\pi\)
0.736069 0.676907i \(-0.236680\pi\)
\(888\) −9.30566 −0.312278
\(889\) −26.3192 + 7.12479i −0.882717 + 0.238958i
\(890\) 5.22145 0.175023
\(891\) 5.99105i 0.200708i
\(892\) 3.60899i 0.120838i
\(893\) 9.83762i 0.329203i
\(894\) −15.7697 −0.527419
\(895\) −32.8231 −1.09716
\(896\) 2.55383 0.691340i 0.0853175 0.0230960i
\(897\) 2.67125 2.45492i 0.0891903 0.0819675i
\(898\) 24.6634 0.823029
\(899\) 0 0
\(900\) −12.6232 −0.420775
\(901\) 46.9549i 1.56430i
\(902\) −28.4963 −0.948824
\(903\) −20.2340 + 5.47747i −0.673344 + 0.182279i
\(904\) 8.50863i 0.282993i
\(905\) 56.5890 1.88108
\(906\) 13.9148i 0.462287i
\(907\) 35.2555i 1.17064i −0.810803 0.585320i \(-0.800969\pi\)
0.810803 0.585320i \(-0.199031\pi\)
\(908\) 10.1264 0.336056
\(909\) 18.9549i 0.628696i
\(910\) 2.19551 + 8.11027i 0.0727803 + 0.268853i
\(911\) 40.2070i 1.33212i 0.745900 + 0.666058i \(0.232020\pi\)
−0.745900 + 0.666058i \(0.767980\pi\)
\(912\) 1.02228i 0.0338510i
\(913\) 74.7766i 2.47475i
\(914\) 19.6573i 0.650206i
\(915\) 17.1505i 0.566977i
\(916\) 11.6607 0.385279
\(917\) −1.31630 4.86245i −0.0434680 0.160572i
\(918\) 5.10766i 0.168578i
\(919\) 23.1371i 0.763222i −0.924323 0.381611i \(-0.875369\pi\)
0.924323 0.381611i \(-0.124631\pi\)
\(920\) −14.8237 + 13.6232i −0.488723 + 0.449145i
\(921\) −17.6596 −0.581902
\(922\) 2.38754i 0.0786295i
\(923\) 2.80541i 0.0923411i
\(924\) 15.3001 4.14185i 0.503337 0.136257i
\(925\) 117.468i 3.86231i
\(926\) −6.69678 −0.220070
\(927\) −6.46407 −0.212308
\(928\) 0.951991 0.0312506
\(929\) 1.51593i 0.0497360i −0.999691 0.0248680i \(-0.992083\pi\)
0.999691 0.0248680i \(-0.00791654\pi\)
\(930\) 0 0
\(931\) −6.17875 + 3.60979i −0.202500 + 0.118306i
\(932\) −11.1505 −0.365245
\(933\) 10.6712 0.349361
\(934\) −25.9198 −0.848123
\(935\) 128.460i 4.20109i
\(936\) 0.756485i 0.0247265i
\(937\) −19.3648 −0.632620 −0.316310 0.948656i \(-0.602444\pi\)
−0.316310 + 0.948656i \(0.602444\pi\)
\(938\) −9.08646 33.5657i −0.296684 1.09596i
\(939\) 12.2599i 0.400086i
\(940\) 40.3984i 1.31765i
\(941\) −14.9614 −0.487728 −0.243864 0.969809i \(-0.578415\pi\)
−0.243864 + 0.969809i \(0.578415\pi\)
\(942\) 12.7066i 0.414004i
\(943\) −15.4356 16.7958i −0.502652 0.546945i
\(944\) 0.291524i 0.00948830i
\(945\) 2.90225 + 10.7210i 0.0944101 + 0.348754i
\(946\) 47.4670 1.54329
\(947\) −35.4121 −1.15074 −0.575369 0.817894i \(-0.695142\pi\)
−0.575369 + 0.817894i \(0.695142\pi\)
\(948\) −3.20199 −0.103996
\(949\) −9.73350 −0.315963
\(950\) −12.9044 −0.418676
\(951\) 15.5869i 0.505440i
\(952\) 13.0441 3.53113i 0.422762 0.114445i
\(953\) 21.1263i 0.684349i 0.939636 + 0.342175i \(0.111163\pi\)
−0.939636 + 0.342175i \(0.888837\pi\)
\(954\) 9.19304i 0.297636i
\(955\) 34.6634i 1.12168i
\(956\) −10.6712 −0.345133
\(957\) 5.70343 0.184366
\(958\) 22.6930 0.733177
\(959\) 10.2734 + 37.9501i 0.331744 + 1.22547i
\(960\) 4.19800i 0.135490i
\(961\) 31.0000 1.00000
\(962\) 7.03959 0.226966
\(963\) 0.360402i 0.0116138i
\(964\) −14.4370 −0.464985
\(965\) 45.1558 1.45362
\(966\) 10.7288 + 6.77439i 0.345194 + 0.217962i
\(967\) −59.4670 −1.91233 −0.956165 0.292828i \(-0.905404\pi\)
−0.956165 + 0.292828i \(0.905404\pi\)
\(968\) −24.8927 −0.800081
\(969\) 5.22145i 0.167737i
\(970\) −60.6067 −1.94596
\(971\) 21.1500 0.678737 0.339369 0.940654i \(-0.389787\pi\)
0.339369 + 0.940654i \(0.389787\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) −3.08680 11.4028i −0.0989584 0.365555i
\(974\) 5.33171 0.170839
\(975\) 9.54929 0.305822
\(976\) −4.08538 −0.130770
\(977\) 1.75409i 0.0561183i −0.999606 0.0280592i \(-0.991067\pi\)
0.999606 0.0280592i \(-0.00893268\pi\)
\(978\) 19.6375i 0.627938i
\(979\) 7.45162i 0.238155i
\(980\) −25.3731 + 14.8237i −0.810516 + 0.473525i
\(981\) 0.909657i 0.0290431i
\(982\) −3.21798 −0.102690
\(983\) 43.8468 1.39849 0.699247 0.714880i \(-0.253519\pi\)
0.699247 + 0.714880i \(0.253519\pi\)
\(984\) 4.75648 0.151631
\(985\) −28.5162 −0.908602
\(986\) 4.86245 0.154852
\(987\) 24.5761 6.65293i 0.782266 0.211765i
\(988\) 0.773337i 0.0246031i
\(989\) 25.7114 + 27.9771i 0.817576 + 0.889619i
\(990\) 25.1505i 0.799334i
\(991\) 40.4411 1.28465 0.642326 0.766431i \(-0.277969\pi\)
0.642326 + 0.766431i \(0.277969\pi\)
\(992\) 0 0
\(993\) 34.0172i 1.07950i
\(994\) −9.47082 + 2.56382i −0.300396 + 0.0813193i
\(995\) −30.5817 −0.969504
\(996\) 12.4814i 0.395488i
\(997\) 18.7154i 0.592722i −0.955076 0.296361i \(-0.904227\pi\)
0.955076 0.296361i \(-0.0957732\pi\)
\(998\) −11.4170 −0.361397
\(999\) 9.30566 0.294418
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.643.9 yes 16
3.2 odd 2 2898.2.g.j.2575.15 16
7.6 odd 2 inner 966.2.g.e.643.8 yes 16
21.20 even 2 2898.2.g.j.2575.1 16
23.22 odd 2 inner 966.2.g.e.643.16 yes 16
69.68 even 2 2898.2.g.j.2575.2 16
161.160 even 2 inner 966.2.g.e.643.1 16
483.482 odd 2 2898.2.g.j.2575.16 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.g.e.643.1 16 161.160 even 2 inner
966.2.g.e.643.8 yes 16 7.6 odd 2 inner
966.2.g.e.643.9 yes 16 1.1 even 1 trivial
966.2.g.e.643.16 yes 16 23.22 odd 2 inner
2898.2.g.j.2575.1 16 21.20 even 2
2898.2.g.j.2575.2 16 69.68 even 2
2898.2.g.j.2575.15 16 3.2 odd 2
2898.2.g.j.2575.16 16 483.482 odd 2