Properties

Label 2646.2.t.a.1979.5
Level $2646$
Weight $2$
Character 2646.1979
Analytic conductor $21.128$
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] = [2646,2,Mod(1979,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.1979");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1979.5
Root \(-1.69547 - 0.354107i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1979
Dual form 2646.2.t.a.2285.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.79035 q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.79035 q^{5} -1.00000i q^{8} +(-1.55049 + 0.895175i) q^{10} -2.40150i q^{11} +(-4.23601 + 2.44566i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(1.83233 + 3.17369i) q^{17} +(-2.61281 - 1.50851i) q^{19} +(-0.895175 + 1.55049i) q^{20} +(-1.20075 - 2.07976i) q^{22} -3.76638i q^{23} -1.79465 q^{25} +(-2.44566 + 4.23601i) q^{26} +(5.68202 + 3.28052i) q^{29} +(4.02408 + 2.32330i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.17369 + 1.83233i) q^{34} +(-4.68202 + 8.10950i) q^{37} -3.01701 q^{38} +1.79035i q^{40} +(4.04094 + 6.99911i) q^{41} +(-3.48127 + 6.02973i) q^{43} +(-2.07976 - 1.20075i) q^{44} +(-1.88319 - 3.26178i) q^{46} +(-2.56802 - 4.44794i) q^{47} +(-1.55421 + 0.897324i) q^{50} +4.89133i q^{52} +4.29953i q^{55} +6.56103 q^{58} +(-7.29501 + 12.6353i) q^{59} +(-9.81058 + 5.66414i) q^{61} +4.64661 q^{62} -1.00000 q^{64} +(7.58394 - 4.37859i) q^{65} +(-0.285115 + 0.493834i) q^{67} +3.66466 q^{68} -5.96254i q^{71} +(-10.7226 + 6.19070i) q^{73} +9.36404i q^{74} +(-2.61281 + 1.50851i) q^{76} +(-1.51831 - 2.62979i) q^{79} +(0.895175 + 1.55049i) q^{80} +(6.99911 + 4.04094i) q^{82} +(7.00270 - 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} +6.96254i q^{86} -2.40150 q^{88} +(-1.87432 + 3.24641i) q^{89} +(-3.26178 - 1.88319i) q^{92} +(-4.44794 - 2.56802i) q^{94} +(4.67784 + 2.70075i) q^{95} +(4.77256 + 2.75544i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.79035 −0.800669 −0.400334 0.916369i \(-0.631106\pi\)
−0.400334 + 0.916369i \(0.631106\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.55049 + 0.895175i −0.490307 + 0.283079i
\(11\) 2.40150i 0.724081i −0.932162 0.362040i \(-0.882080\pi\)
0.932162 0.362040i \(-0.117920\pi\)
\(12\) 0 0
\(13\) −4.23601 + 2.44566i −1.17486 + 0.678305i −0.954820 0.297186i \(-0.903952\pi\)
−0.220039 + 0.975491i \(0.570618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.83233 + 3.17369i 0.444406 + 0.769734i 0.998011 0.0630460i \(-0.0200815\pi\)
−0.553605 + 0.832780i \(0.686748\pi\)
\(18\) 0 0
\(19\) −2.61281 1.50851i −0.599419 0.346075i 0.169394 0.985548i \(-0.445819\pi\)
−0.768813 + 0.639474i \(0.779152\pi\)
\(20\) −0.895175 + 1.55049i −0.200167 + 0.346700i
\(21\) 0 0
\(22\) −1.20075 2.07976i −0.256001 0.443407i
\(23\) 3.76638i 0.785345i −0.919678 0.392673i \(-0.871551\pi\)
0.919678 0.392673i \(-0.128449\pi\)
\(24\) 0 0
\(25\) −1.79465 −0.358930
\(26\) −2.44566 + 4.23601i −0.479634 + 0.830750i
\(27\) 0 0
\(28\) 0 0
\(29\) 5.68202 + 3.28052i 1.05512 + 0.609176i 0.924080 0.382200i \(-0.124833\pi\)
0.131045 + 0.991376i \(0.458167\pi\)
\(30\) 0 0
\(31\) 4.02408 + 2.32330i 0.722746 + 0.417278i 0.815763 0.578387i \(-0.196318\pi\)
−0.0930163 + 0.995665i \(0.529651\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 3.17369 + 1.83233i 0.544284 + 0.314242i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.68202 + 8.10950i −0.769719 + 1.33319i 0.167996 + 0.985788i \(0.446271\pi\)
−0.937715 + 0.347405i \(0.887063\pi\)
\(38\) −3.01701 −0.489424
\(39\) 0 0
\(40\) 1.79035i 0.283079i
\(41\) 4.04094 + 6.99911i 0.631088 + 1.09308i 0.987330 + 0.158683i \(0.0507248\pi\)
−0.356241 + 0.934394i \(0.615942\pi\)
\(42\) 0 0
\(43\) −3.48127 + 6.02973i −0.530888 + 0.919526i 0.468462 + 0.883484i \(0.344808\pi\)
−0.999350 + 0.0360419i \(0.988525\pi\)
\(44\) −2.07976 1.20075i −0.313536 0.181020i
\(45\) 0 0
\(46\) −1.88319 3.26178i −0.277661 0.480924i
\(47\) −2.56802 4.44794i −0.374584 0.648799i 0.615680 0.787996i \(-0.288881\pi\)
−0.990265 + 0.139197i \(0.955548\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.55421 + 0.897324i −0.219799 + 0.126901i
\(51\) 0 0
\(52\) 4.89133i 0.678305i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 4.29953i 0.579749i
\(56\) 0 0
\(57\) 0 0
\(58\) 6.56103 0.861506
\(59\) −7.29501 + 12.6353i −0.949729 + 1.64498i −0.203735 + 0.979026i \(0.565308\pi\)
−0.745994 + 0.665953i \(0.768025\pi\)
\(60\) 0 0
\(61\) −9.81058 + 5.66414i −1.25612 + 0.725219i −0.972317 0.233665i \(-0.924928\pi\)
−0.283799 + 0.958884i \(0.591595\pi\)
\(62\) 4.64661 0.590120
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 7.58394 4.37859i 0.940672 0.543097i
\(66\) 0 0
\(67\) −0.285115 + 0.493834i −0.0348324 + 0.0603315i −0.882916 0.469531i \(-0.844423\pi\)
0.848084 + 0.529862i \(0.177756\pi\)
\(68\) 3.66466 0.444406
\(69\) 0 0
\(70\) 0 0
\(71\) 5.96254i 0.707623i −0.935317 0.353811i \(-0.884885\pi\)
0.935317 0.353811i \(-0.115115\pi\)
\(72\) 0 0
\(73\) −10.7226 + 6.19070i −1.25499 + 0.724567i −0.972096 0.234585i \(-0.924627\pi\)
−0.282891 + 0.959152i \(0.591294\pi\)
\(74\) 9.36404i 1.08855i
\(75\) 0 0
\(76\) −2.61281 + 1.50851i −0.299710 + 0.173037i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.51831 2.62979i −0.170824 0.295875i 0.767884 0.640588i \(-0.221309\pi\)
−0.938708 + 0.344713i \(0.887976\pi\)
\(80\) 0.895175 + 1.55049i 0.100084 + 0.173350i
\(81\) 0 0
\(82\) 6.99911 + 4.04094i 0.772922 + 0.446247i
\(83\) 7.00270 12.1290i 0.768646 1.33133i −0.169651 0.985504i \(-0.554264\pi\)
0.938297 0.345830i \(-0.112403\pi\)
\(84\) 0 0
\(85\) −3.28052 5.68202i −0.355822 0.616302i
\(86\) 6.96254i 0.750790i
\(87\) 0 0
\(88\) −2.40150 −0.256001
\(89\) −1.87432 + 3.24641i −0.198677 + 0.344119i −0.948100 0.317973i \(-0.896998\pi\)
0.749423 + 0.662092i \(0.230331\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.26178 1.88319i −0.340064 0.196336i
\(93\) 0 0
\(94\) −4.44794 2.56802i −0.458770 0.264871i
\(95\) 4.67784 + 2.70075i 0.479936 + 0.277091i
\(96\) 0 0
\(97\) 4.77256 + 2.75544i 0.484580 + 0.279772i 0.722323 0.691556i \(-0.243074\pi\)
−0.237743 + 0.971328i \(0.576408\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.897324 + 1.55421i −0.0897324 + 0.155421i
\(101\) −0.250324 −0.0249082 −0.0124541 0.999922i \(-0.503964\pi\)
−0.0124541 + 0.999922i \(0.503964\pi\)
\(102\) 0 0
\(103\) 0.167931i 0.0165468i 0.999966 + 0.00827339i \(0.00263353\pi\)
−0.999966 + 0.00827339i \(0.997366\pi\)
\(104\) 2.44566 + 4.23601i 0.239817 + 0.415375i
\(105\) 0 0
\(106\) 0 0
\(107\) −6.92024 3.99540i −0.669004 0.386250i 0.126695 0.991942i \(-0.459563\pi\)
−0.795699 + 0.605692i \(0.792896\pi\)
\(108\) 0 0
\(109\) 9.47667 + 16.4141i 0.907700 + 1.57218i 0.817251 + 0.576282i \(0.195497\pi\)
0.0904491 + 0.995901i \(0.471170\pi\)
\(110\) 2.14977 + 3.72350i 0.204972 + 0.355022i
\(111\) 0 0
\(112\) 0 0
\(113\) 1.00418 0.579764i 0.0944653 0.0545396i −0.452023 0.892006i \(-0.649298\pi\)
0.546488 + 0.837467i \(0.315964\pi\)
\(114\) 0 0
\(115\) 6.74314i 0.628801i
\(116\) 5.68202 3.28052i 0.527562 0.304588i
\(117\) 0 0
\(118\) 14.5900i 1.34312i
\(119\) 0 0
\(120\) 0 0
\(121\) 5.23278 0.475707
\(122\) −5.66414 + 9.81058i −0.512807 + 0.888208i
\(123\) 0 0
\(124\) 4.02408 2.32330i 0.361373 0.208639i
\(125\) 12.1648 1.08805
\(126\) 0 0
\(127\) 1.40150 0.124363 0.0621817 0.998065i \(-0.480194\pi\)
0.0621817 + 0.998065i \(0.480194\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 4.37859 7.58394i 0.384028 0.665156i
\(131\) −10.4918 −0.916671 −0.458335 0.888779i \(-0.651554\pi\)
−0.458335 + 0.888779i \(0.651554\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.570231i 0.0492604i
\(135\) 0 0
\(136\) 3.17369 1.83233i 0.272142 0.157121i
\(137\) 4.72056i 0.403305i −0.979457 0.201652i \(-0.935369\pi\)
0.979457 0.201652i \(-0.0646311\pi\)
\(138\) 0 0
\(139\) −2.04707 + 1.18187i −0.173630 + 0.100245i −0.584296 0.811540i \(-0.698629\pi\)
0.410666 + 0.911786i \(0.365296\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.98127 5.16371i −0.250182 0.433329i
\(143\) 5.87327 + 10.1728i 0.491148 + 0.850692i
\(144\) 0 0
\(145\) −10.1728 5.87327i −0.844805 0.487749i
\(146\) −6.19070 + 10.7226i −0.512346 + 0.887410i
\(147\) 0 0
\(148\) 4.68202 + 8.10950i 0.384860 + 0.666597i
\(149\) 17.3640i 1.42252i 0.702930 + 0.711259i \(0.251875\pi\)
−0.702930 + 0.711259i \(0.748125\pi\)
\(150\) 0 0
\(151\) −11.2328 −0.914110 −0.457055 0.889438i \(-0.651096\pi\)
−0.457055 + 0.889438i \(0.651096\pi\)
\(152\) −1.50851 + 2.61281i −0.122356 + 0.211927i
\(153\) 0 0
\(154\) 0 0
\(155\) −7.20451 4.15953i −0.578680 0.334101i
\(156\) 0 0
\(157\) −11.9885 6.92154i −0.956783 0.552399i −0.0616014 0.998101i \(-0.519621\pi\)
−0.895181 + 0.445702i \(0.852954\pi\)
\(158\) −2.62979 1.51831i −0.209215 0.120790i
\(159\) 0 0
\(160\) 1.55049 + 0.895175i 0.122577 + 0.0707698i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.16789 3.75489i 0.169802 0.294106i −0.768548 0.639792i \(-0.779020\pi\)
0.938350 + 0.345686i \(0.112354\pi\)
\(164\) 8.08188 0.631088
\(165\) 0 0
\(166\) 14.0054i 1.08703i
\(167\) 6.20756 + 10.7518i 0.480355 + 0.832000i 0.999746 0.0225370i \(-0.00717435\pi\)
−0.519391 + 0.854537i \(0.673841\pi\)
\(168\) 0 0
\(169\) 5.46254 9.46139i 0.420195 0.727799i
\(170\) −5.68202 3.28052i −0.435791 0.251604i
\(171\) 0 0
\(172\) 3.48127 + 6.02973i 0.265444 + 0.459763i
\(173\) −8.70908 15.0846i −0.662139 1.14686i −0.980052 0.198739i \(-0.936315\pi\)
0.317913 0.948120i \(-0.397018\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.07976 + 1.20075i −0.156768 + 0.0905101i
\(177\) 0 0
\(178\) 3.74863i 0.280972i
\(179\) −11.3640 + 6.56103i −0.849388 + 0.490395i −0.860444 0.509544i \(-0.829814\pi\)
0.0110562 + 0.999939i \(0.496481\pi\)
\(180\) 0 0
\(181\) 13.3577i 0.992873i 0.868073 + 0.496437i \(0.165359\pi\)
−0.868073 + 0.496437i \(0.834641\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.76638 −0.277661
\(185\) 8.38245 14.5188i 0.616290 1.06745i
\(186\) 0 0
\(187\) 7.62164 4.40035i 0.557349 0.321786i
\(188\) −5.13604 −0.374584
\(189\) 0 0
\(190\) 5.40150 0.391866
\(191\) −8.01361 + 4.62666i −0.579845 + 0.334774i −0.761072 0.648668i \(-0.775326\pi\)
0.181227 + 0.983441i \(0.441993\pi\)
\(192\) 0 0
\(193\) 12.2801 21.2698i 0.883941 1.53103i 0.0370176 0.999315i \(-0.488214\pi\)
0.846923 0.531716i \(-0.178452\pi\)
\(194\) 5.51087 0.395658
\(195\) 0 0
\(196\) 0 0
\(197\) 12.4861i 0.889598i 0.895630 + 0.444799i \(0.146725\pi\)
−0.895630 + 0.444799i \(0.853275\pi\)
\(198\) 0 0
\(199\) 0.155144 0.0895727i 0.0109979 0.00634964i −0.494491 0.869183i \(-0.664645\pi\)
0.505489 + 0.862833i \(0.331312\pi\)
\(200\) 1.79465i 0.126901i
\(201\) 0 0
\(202\) −0.216787 + 0.125162i −0.0152531 + 0.00880637i
\(203\) 0 0
\(204\) 0 0
\(205\) −7.23469 12.5309i −0.505293 0.875193i
\(206\) 0.0839657 + 0.145433i 0.00585017 + 0.0101328i
\(207\) 0 0
\(208\) 4.23601 + 2.44566i 0.293715 + 0.169576i
\(209\) −3.62268 + 6.27467i −0.250586 + 0.434028i
\(210\) 0 0
\(211\) 7.56103 + 13.0961i 0.520523 + 0.901572i 0.999715 + 0.0238622i \(0.00759629\pi\)
−0.479192 + 0.877710i \(0.659070\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −7.99080 −0.546240
\(215\) 6.23269 10.7953i 0.425066 0.736235i
\(216\) 0 0
\(217\) 0 0
\(218\) 16.4141 + 9.47667i 1.11170 + 0.641841i
\(219\) 0 0
\(220\) 3.72350 + 2.14977i 0.251039 + 0.144937i
\(221\) −15.5236 8.96254i −1.04423 0.602885i
\(222\) 0 0
\(223\) −7.27049 4.19762i −0.486868 0.281093i 0.236406 0.971654i \(-0.424030\pi\)
−0.723274 + 0.690561i \(0.757364\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.579764 1.00418i 0.0385653 0.0667971i
\(227\) 2.42522 0.160967 0.0804836 0.996756i \(-0.474354\pi\)
0.0804836 + 0.996756i \(0.474354\pi\)
\(228\) 0 0
\(229\) 2.01975i 0.133469i 0.997771 + 0.0667344i \(0.0212580\pi\)
−0.997771 + 0.0667344i \(0.978742\pi\)
\(230\) 3.37157 + 5.83973i 0.222315 + 0.385061i
\(231\) 0 0
\(232\) 3.28052 5.68202i 0.215376 0.373043i
\(233\) 11.0236 + 6.36446i 0.722178 + 0.416950i 0.815554 0.578681i \(-0.196432\pi\)
−0.0933759 + 0.995631i \(0.529766\pi\)
\(234\) 0 0
\(235\) 4.59766 + 7.96337i 0.299918 + 0.519473i
\(236\) 7.29501 + 12.6353i 0.474864 + 0.822489i
\(237\) 0 0
\(238\) 0 0
\(239\) −15.1117 + 8.72474i −0.977494 + 0.564356i −0.901513 0.432753i \(-0.857542\pi\)
−0.0759814 + 0.997109i \(0.524209\pi\)
\(240\) 0 0
\(241\) 11.4332i 0.736476i −0.929732 0.368238i \(-0.879961\pi\)
0.929732 0.368238i \(-0.120039\pi\)
\(242\) 4.53172 2.61639i 0.291310 0.168188i
\(243\) 0 0
\(244\) 11.3283i 0.725219i
\(245\) 0 0
\(246\) 0 0
\(247\) 14.7572 0.938977
\(248\) 2.32330 4.02408i 0.147530 0.255529i
\(249\) 0 0
\(250\) 10.5350 6.08240i 0.666293 0.384685i
\(251\) 27.3560 1.72669 0.863347 0.504611i \(-0.168364\pi\)
0.863347 + 0.504611i \(0.168364\pi\)
\(252\) 0 0
\(253\) −9.04499 −0.568653
\(254\) 1.21374 0.700752i 0.0761567 0.0439691i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.49673 0.218120 0.109060 0.994035i \(-0.465216\pi\)
0.109060 + 0.994035i \(0.465216\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 8.75718i 0.543097i
\(261\) 0 0
\(262\) −9.08614 + 5.24589i −0.561344 + 0.324092i
\(263\) 9.64348i 0.594643i −0.954777 0.297321i \(-0.903907\pi\)
0.954777 0.297321i \(-0.0960932\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.285115 + 0.493834i 0.0174162 + 0.0301657i
\(269\) −3.45554 5.98517i −0.210688 0.364922i 0.741242 0.671238i \(-0.234237\pi\)
−0.951930 + 0.306316i \(0.900904\pi\)
\(270\) 0 0
\(271\) −17.8672 10.3156i −1.08535 0.626629i −0.153017 0.988224i \(-0.548899\pi\)
−0.932335 + 0.361595i \(0.882232\pi\)
\(272\) 1.83233 3.17369i 0.111101 0.192433i
\(273\) 0 0
\(274\) −2.36028 4.08812i −0.142590 0.246973i
\(275\) 4.30986i 0.259894i
\(276\) 0 0
\(277\) −15.5144 −0.932168 −0.466084 0.884740i \(-0.654336\pi\)
−0.466084 + 0.884740i \(0.654336\pi\)
\(278\) −1.18187 + 2.04707i −0.0708841 + 0.122775i
\(279\) 0 0
\(280\) 0 0
\(281\) −11.7759 6.79883i −0.702492 0.405584i 0.105783 0.994389i \(-0.466265\pi\)
−0.808275 + 0.588805i \(0.799599\pi\)
\(282\) 0 0
\(283\) 4.71796 + 2.72392i 0.280454 + 0.161920i 0.633629 0.773637i \(-0.281565\pi\)
−0.353175 + 0.935557i \(0.614898\pi\)
\(284\) −5.16371 2.98127i −0.306410 0.176906i
\(285\) 0 0
\(286\) 10.1728 + 5.87327i 0.601530 + 0.347294i
\(287\) 0 0
\(288\) 0 0
\(289\) 1.78512 3.09191i 0.105007 0.181877i
\(290\) −11.7465 −0.689781
\(291\) 0 0
\(292\) 12.3814i 0.724567i
\(293\) −12.2311 21.1849i −0.714550 1.23764i −0.963133 0.269026i \(-0.913298\pi\)
0.248583 0.968610i \(-0.420035\pi\)
\(294\) 0 0
\(295\) 13.0606 22.6216i 0.760418 1.31708i
\(296\) 8.10950 + 4.68202i 0.471355 + 0.272137i
\(297\) 0 0
\(298\) 8.68202 + 15.0377i 0.502936 + 0.871111i
\(299\) 9.21130 + 15.9544i 0.532703 + 0.922670i
\(300\) 0 0
\(301\) 0 0
\(302\) −9.72787 + 5.61639i −0.559776 + 0.323187i
\(303\) 0 0
\(304\) 3.01701i 0.173037i
\(305\) 17.5644 10.1408i 1.00573 0.580660i
\(306\) 0 0
\(307\) 31.2223i 1.78195i −0.454053 0.890975i \(-0.650022\pi\)
0.454053 0.890975i \(-0.349978\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −8.31905 −0.472491
\(311\) 5.45501 9.44836i 0.309325 0.535767i −0.668889 0.743362i \(-0.733230\pi\)
0.978215 + 0.207594i \(0.0665634\pi\)
\(312\) 0 0
\(313\) −2.96532 + 1.71203i −0.167610 + 0.0967694i −0.581458 0.813576i \(-0.697518\pi\)
0.413849 + 0.910346i \(0.364184\pi\)
\(314\) −13.8431 −0.781210
\(315\) 0 0
\(316\) −3.03663 −0.170824
\(317\) 16.4953 9.52357i 0.926468 0.534897i 0.0407755 0.999168i \(-0.487017\pi\)
0.885693 + 0.464272i \(0.153684\pi\)
\(318\) 0 0
\(319\) 7.87817 13.6454i 0.441093 0.763995i
\(320\) 1.79035 0.100084
\(321\) 0 0
\(322\) 0 0
\(323\) 11.0563i 0.615191i
\(324\) 0 0
\(325\) 7.60215 4.38910i 0.421692 0.243464i
\(326\) 4.33577i 0.240136i
\(327\) 0 0
\(328\) 6.99911 4.04094i 0.386461 0.223123i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0366251 0.0634366i −0.00201310 0.00348679i 0.865017 0.501742i \(-0.167307\pi\)
−0.867030 + 0.498256i \(0.833974\pi\)
\(332\) −7.00270 12.1290i −0.384323 0.665667i
\(333\) 0 0
\(334\) 10.7518 + 6.20756i 0.588313 + 0.339663i
\(335\) 0.510456 0.884136i 0.0278892 0.0483055i
\(336\) 0 0
\(337\) 1.11639 + 1.93364i 0.0608136 + 0.105332i 0.894829 0.446408i \(-0.147297\pi\)
−0.834016 + 0.551741i \(0.813964\pi\)
\(338\) 10.9251i 0.594246i
\(339\) 0 0
\(340\) −6.56103 −0.355822
\(341\) 5.57943 9.66385i 0.302143 0.523327i
\(342\) 0 0
\(343\) 0 0
\(344\) 6.02973 + 3.48127i 0.325101 + 0.187697i
\(345\) 0 0
\(346\) −15.0846 8.70908i −0.810952 0.468203i
\(347\) 27.5751 + 15.9205i 1.48031 + 0.854656i 0.999751 0.0223084i \(-0.00710156\pi\)
0.480556 + 0.876964i \(0.340435\pi\)
\(348\) 0 0
\(349\) −12.7613 7.36772i −0.683095 0.394385i 0.117925 0.993022i \(-0.462376\pi\)
−0.801020 + 0.598637i \(0.795709\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.20075 + 2.07976i −0.0640003 + 0.110852i
\(353\) −2.15957 −0.114943 −0.0574713 0.998347i \(-0.518304\pi\)
−0.0574713 + 0.998347i \(0.518304\pi\)
\(354\) 0 0
\(355\) 10.6750i 0.566571i
\(356\) 1.87432 + 3.24641i 0.0993385 + 0.172059i
\(357\) 0 0
\(358\) −6.56103 + 11.3640i −0.346761 + 0.600608i
\(359\) −28.2712 16.3224i −1.49210 0.861463i −0.492139 0.870517i \(-0.663785\pi\)
−0.999959 + 0.00905364i \(0.997118\pi\)
\(360\) 0 0
\(361\) −4.94882 8.57161i −0.260464 0.451138i
\(362\) 6.67887 + 11.5681i 0.351034 + 0.608008i
\(363\) 0 0
\(364\) 0 0
\(365\) 19.1972 11.0835i 1.00483 0.580138i
\(366\) 0 0
\(367\) 29.7003i 1.55034i −0.631751 0.775171i \(-0.717664\pi\)
0.631751 0.775171i \(-0.282336\pi\)
\(368\) −3.26178 + 1.88319i −0.170032 + 0.0981682i
\(369\) 0 0
\(370\) 16.7649i 0.871566i
\(371\) 0 0
\(372\) 0 0
\(373\) −2.01672 −0.104422 −0.0522109 0.998636i \(-0.516627\pi\)
−0.0522109 + 0.998636i \(0.516627\pi\)
\(374\) 4.40035 7.62164i 0.227537 0.394105i
\(375\) 0 0
\(376\) −4.44794 + 2.56802i −0.229385 + 0.132436i
\(377\) −32.0921 −1.65283
\(378\) 0 0
\(379\) −18.8709 −0.969332 −0.484666 0.874699i \(-0.661059\pi\)
−0.484666 + 0.874699i \(0.661059\pi\)
\(380\) 4.67784 2.70075i 0.239968 0.138546i
\(381\) 0 0
\(382\) −4.62666 + 8.01361i −0.236721 + 0.410012i
\(383\) −0.836511 −0.0427437 −0.0213719 0.999772i \(-0.506803\pi\)
−0.0213719 + 0.999772i \(0.506803\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 24.5602i 1.25008i
\(387\) 0 0
\(388\) 4.77256 2.75544i 0.242290 0.139886i
\(389\) 24.8219i 1.25852i 0.777195 + 0.629260i \(0.216642\pi\)
−0.777195 + 0.629260i \(0.783358\pi\)
\(390\) 0 0
\(391\) 11.9533 6.90127i 0.604507 0.349012i
\(392\) 0 0
\(393\) 0 0
\(394\) 6.24305 + 10.8133i 0.314520 + 0.544765i
\(395\) 2.71831 + 4.70825i 0.136773 + 0.236898i
\(396\) 0 0
\(397\) 2.62744 + 1.51695i 0.131867 + 0.0761336i 0.564482 0.825445i \(-0.309076\pi\)
−0.432615 + 0.901579i \(0.642409\pi\)
\(398\) 0.0895727 0.155144i 0.00448987 0.00777669i
\(399\) 0 0
\(400\) 0.897324 + 1.55421i 0.0448662 + 0.0777105i
\(401\) 13.0771i 0.653038i −0.945191 0.326519i \(-0.894124\pi\)
0.945191 0.326519i \(-0.105876\pi\)
\(402\) 0 0
\(403\) −22.7281 −1.13217
\(404\) −0.125162 + 0.216787i −0.00622705 + 0.0107856i
\(405\) 0 0
\(406\) 0 0
\(407\) 19.4750 + 11.2439i 0.965339 + 0.557339i
\(408\) 0 0
\(409\) −4.82124 2.78354i −0.238395 0.137637i 0.376044 0.926602i \(-0.377284\pi\)
−0.614439 + 0.788965i \(0.710618\pi\)
\(410\) −12.5309 7.23469i −0.618855 0.357296i
\(411\) 0 0
\(412\) 0.145433 + 0.0839657i 0.00716496 + 0.00413669i
\(413\) 0 0
\(414\) 0 0
\(415\) −12.5373 + 21.7152i −0.615431 + 1.06596i
\(416\) 4.89133 0.239817
\(417\) 0 0
\(418\) 7.24536i 0.354382i
\(419\) −8.19938 14.2017i −0.400566 0.693800i 0.593228 0.805034i \(-0.297853\pi\)
−0.993794 + 0.111234i \(0.964520\pi\)
\(420\) 0 0
\(421\) −7.72892 + 13.3869i −0.376684 + 0.652437i −0.990578 0.136952i \(-0.956269\pi\)
0.613893 + 0.789389i \(0.289603\pi\)
\(422\) 13.0961 + 7.56103i 0.637508 + 0.368065i
\(423\) 0 0
\(424\) 0 0
\(425\) −3.28839 5.69566i −0.159510 0.276280i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.92024 + 3.99540i −0.334502 + 0.193125i
\(429\) 0 0
\(430\) 12.4654i 0.601134i
\(431\) −21.6737 + 12.5133i −1.04398 + 0.602744i −0.920959 0.389660i \(-0.872593\pi\)
−0.123024 + 0.992404i \(0.539259\pi\)
\(432\) 0 0
\(433\) 2.25168i 0.108209i −0.998535 0.0541044i \(-0.982770\pi\)
0.998535 0.0541044i \(-0.0172304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 18.9533 0.907700
\(437\) −5.68161 + 9.84084i −0.271788 + 0.470751i
\(438\) 0 0
\(439\) −16.2293 + 9.37000i −0.774583 + 0.447206i −0.834507 0.550997i \(-0.814248\pi\)
0.0599239 + 0.998203i \(0.480914\pi\)
\(440\) 4.29953 0.204972
\(441\) 0 0
\(442\) −17.9251 −0.852609
\(443\) −1.04314 + 0.602256i −0.0495610 + 0.0286141i −0.524576 0.851364i \(-0.675776\pi\)
0.475015 + 0.879978i \(0.342443\pi\)
\(444\) 0 0
\(445\) 3.35568 5.81221i 0.159074 0.275525i
\(446\) −8.39524 −0.397526
\(447\) 0 0
\(448\) 0 0
\(449\) 26.8022i 1.26487i 0.774612 + 0.632436i \(0.217945\pi\)
−0.774612 + 0.632436i \(0.782055\pi\)
\(450\) 0 0
\(451\) 16.8084 9.70433i 0.791476 0.456959i
\(452\) 1.15953i 0.0545396i
\(453\) 0 0
\(454\) 2.10030 1.21261i 0.0985719 0.0569105i
\(455\) 0 0
\(456\) 0 0
\(457\) −6.92442 11.9934i −0.323911 0.561030i 0.657381 0.753559i \(-0.271664\pi\)
−0.981291 + 0.192529i \(0.938331\pi\)
\(458\) 1.00987 + 1.74915i 0.0471883 + 0.0817326i
\(459\) 0 0
\(460\) 5.83973 + 3.37157i 0.272279 + 0.157200i
\(461\) −2.40241 + 4.16110i −0.111892 + 0.193802i −0.916533 0.399959i \(-0.869024\pi\)
0.804641 + 0.593761i \(0.202358\pi\)
\(462\) 0 0
\(463\) 10.5194 + 18.2201i 0.488877 + 0.846760i 0.999918 0.0127960i \(-0.00407321\pi\)
−0.511041 + 0.859556i \(0.670740\pi\)
\(464\) 6.56103i 0.304588i
\(465\) 0 0
\(466\) 12.7289 0.589656
\(467\) 2.91151 5.04288i 0.134729 0.233357i −0.790765 0.612120i \(-0.790317\pi\)
0.925494 + 0.378763i \(0.123650\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.96337 + 4.59766i 0.367323 + 0.212074i
\(471\) 0 0
\(472\) 12.6353 + 7.29501i 0.581588 + 0.335780i
\(473\) 14.4804 + 8.36028i 0.665811 + 0.384406i
\(474\) 0 0
\(475\) 4.68907 + 2.70724i 0.215149 + 0.124217i
\(476\) 0 0
\(477\) 0 0
\(478\) −8.72474 + 15.1117i −0.399060 + 0.691193i
\(479\) 26.9561 1.23166 0.615828 0.787881i \(-0.288822\pi\)
0.615828 + 0.787881i \(0.288822\pi\)
\(480\) 0 0
\(481\) 45.8026i 2.08842i
\(482\) −5.71659 9.90142i −0.260383 0.450997i
\(483\) 0 0
\(484\) 2.61639 4.53172i 0.118927 0.205987i
\(485\) −8.54455 4.93320i −0.387988 0.224005i
\(486\) 0 0
\(487\) 6.81338 + 11.8011i 0.308744 + 0.534760i 0.978088 0.208193i \(-0.0667581\pi\)
−0.669344 + 0.742953i \(0.733425\pi\)
\(488\) 5.66414 + 9.81058i 0.256404 + 0.444104i
\(489\) 0 0
\(490\) 0 0
\(491\) 33.7430 19.4815i 1.52280 0.879188i 0.523162 0.852234i \(-0.324752\pi\)
0.999637 0.0269544i \(-0.00858088\pi\)
\(492\) 0 0
\(493\) 24.0440i 1.08289i
\(494\) 12.7801 7.37859i 0.575004 0.331979i
\(495\) 0 0
\(496\) 4.64661i 0.208639i
\(497\) 0 0
\(498\) 0 0
\(499\) 26.0097 1.16435 0.582176 0.813063i \(-0.302201\pi\)
0.582176 + 0.813063i \(0.302201\pi\)
\(500\) 6.08240 10.5350i 0.272013 0.471141i
\(501\) 0 0
\(502\) 23.6910 13.6780i 1.05738 0.610478i
\(503\) −10.5271 −0.469378 −0.234689 0.972070i \(-0.575407\pi\)
−0.234689 + 0.972070i \(0.575407\pi\)
\(504\) 0 0
\(505\) 0.448168 0.0199432
\(506\) −7.83319 + 4.52249i −0.348228 + 0.201049i
\(507\) 0 0
\(508\) 0.700752 1.21374i 0.0310908 0.0538509i
\(509\) 0.938871 0.0416147 0.0208074 0.999784i \(-0.493376\pi\)
0.0208074 + 0.999784i \(0.493376\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.02826 1.74837i 0.133571 0.0771172i
\(515\) 0.300656i 0.0132485i
\(516\) 0 0
\(517\) −10.6818 + 6.16711i −0.469783 + 0.271229i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.37859 7.58394i −0.192014 0.332578i
\(521\) −19.7527 34.2127i −0.865382 1.49889i −0.866667 0.498887i \(-0.833742\pi\)
0.00128461 0.999999i \(-0.499591\pi\)
\(522\) 0 0
\(523\) 21.0697 + 12.1646i 0.921315 + 0.531922i 0.884054 0.467384i \(-0.154803\pi\)
0.0372609 + 0.999306i \(0.488137\pi\)
\(524\) −5.24589 + 9.08614i −0.229168 + 0.396930i
\(525\) 0 0
\(526\) −4.82174 8.35150i −0.210238 0.364143i
\(527\) 17.0283i 0.741763i
\(528\) 0 0
\(529\) 8.81436 0.383233
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −34.2349 19.7655i −1.48288 0.856141i
\(534\) 0 0
\(535\) 12.3896 + 7.15316i 0.535651 + 0.309258i
\(536\) 0.493834 + 0.285115i 0.0213304 + 0.0123151i
\(537\) 0 0
\(538\) −5.98517 3.45554i −0.258039 0.148979i
\(539\) 0 0
\(540\) 0 0
\(541\) −21.3640 + 37.0036i −0.918512 + 1.59091i −0.116835 + 0.993151i \(0.537275\pi\)
−0.801677 + 0.597758i \(0.796058\pi\)
\(542\) −20.6312 −0.886187
\(543\) 0 0
\(544\) 3.66466i 0.157121i
\(545\) −16.9665 29.3869i −0.726767 1.25880i
\(546\) 0 0
\(547\) −12.2477 + 21.2136i −0.523672 + 0.907026i 0.475949 + 0.879473i \(0.342105\pi\)
−0.999620 + 0.0275530i \(0.991229\pi\)
\(548\) −4.08812 2.36028i −0.174636 0.100826i
\(549\) 0 0
\(550\) 2.15493 + 3.73244i 0.0918864 + 0.159152i
\(551\) −9.89735 17.1427i −0.421641 0.730304i
\(552\) 0 0
\(553\) 0 0
\(554\) −13.4358 + 7.75718i −0.570834 + 0.329571i
\(555\) 0 0
\(556\) 2.36375i 0.100245i
\(557\) −2.20344 + 1.27216i −0.0933627 + 0.0539030i −0.545954 0.837815i \(-0.683833\pi\)
0.452592 + 0.891718i \(0.350499\pi\)
\(558\) 0 0
\(559\) 34.0560i 1.44042i
\(560\) 0 0
\(561\) 0 0
\(562\) −13.5977 −0.573583
\(563\) 7.90707 13.6954i 0.333243 0.577194i −0.649902 0.760018i \(-0.725190\pi\)
0.983146 + 0.182823i \(0.0585236\pi\)
\(564\) 0 0
\(565\) −1.79783 + 1.03798i −0.0756354 + 0.0436681i
\(566\) 5.44783 0.228990
\(567\) 0 0
\(568\) −5.96254 −0.250182
\(569\) −5.52793 + 3.19155i −0.231743 + 0.133797i −0.611376 0.791340i \(-0.709384\pi\)
0.379633 + 0.925137i \(0.376050\pi\)
\(570\) 0 0
\(571\) 3.91188 6.77557i 0.163707 0.283549i −0.772488 0.635029i \(-0.780988\pi\)
0.936195 + 0.351480i \(0.114322\pi\)
\(572\) 11.7465 0.491148
\(573\) 0 0
\(574\) 0 0
\(575\) 6.75933i 0.281884i
\(576\) 0 0
\(577\) 12.4012 7.15986i 0.516270 0.298069i −0.219137 0.975694i \(-0.570324\pi\)
0.735407 + 0.677625i \(0.236991\pi\)
\(578\) 3.57023i 0.148502i
\(579\) 0 0
\(580\) −10.1728 + 5.87327i −0.422403 + 0.243874i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 6.19070 + 10.7226i 0.256173 + 0.443705i
\(585\) 0 0
\(586\) −21.1849 12.2311i −0.875141 0.505263i
\(587\) 2.37575 4.11492i 0.0980577 0.169841i −0.812823 0.582511i \(-0.802070\pi\)
0.910881 + 0.412670i \(0.135404\pi\)
\(588\) 0 0
\(589\) −7.00943 12.1407i −0.288819 0.500249i
\(590\) 26.1212i 1.07539i
\(591\) 0 0
\(592\) 9.36404 0.384860
\(593\) 1.79035 3.10098i 0.0735208 0.127342i −0.826921 0.562318i \(-0.809910\pi\)
0.900442 + 0.434976i \(0.143243\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.0377 + 8.68202i 0.615968 + 0.355629i
\(597\) 0 0
\(598\) 15.9544 + 9.21130i 0.652426 + 0.376678i
\(599\) −13.0471 7.53277i −0.533091 0.307780i 0.209183 0.977877i \(-0.432920\pi\)
−0.742274 + 0.670096i \(0.766253\pi\)
\(600\) 0 0
\(601\) −19.8704 11.4722i −0.810530 0.467960i 0.0366096 0.999330i \(-0.488344\pi\)
−0.847140 + 0.531370i \(0.821678\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.61639 + 9.72787i −0.228528 + 0.395821i
\(605\) −9.36850 −0.380884
\(606\) 0 0
\(607\) 24.4832i 0.993741i 0.867825 + 0.496870i \(0.165518\pi\)
−0.867825 + 0.496870i \(0.834482\pi\)
\(608\) 1.50851 + 2.61281i 0.0611780 + 0.105963i
\(609\) 0 0
\(610\) 10.1408 17.5644i 0.410589 0.711161i
\(611\) 21.7563 + 12.5610i 0.880167 + 0.508165i
\(612\) 0 0
\(613\) 0.440043 + 0.762177i 0.0177732 + 0.0307840i 0.874775 0.484529i \(-0.161009\pi\)
−0.857002 + 0.515313i \(0.827676\pi\)
\(614\) −15.6111 27.0393i −0.630014 1.09122i
\(615\) 0 0
\(616\) 0 0
\(617\) 11.7607 6.79005i 0.473468 0.273357i −0.244222 0.969719i \(-0.578533\pi\)
0.717690 + 0.696362i \(0.245199\pi\)
\(618\) 0 0
\(619\) 35.4869i 1.42634i 0.700992 + 0.713169i \(0.252741\pi\)
−0.700992 + 0.713169i \(0.747259\pi\)
\(620\) −7.20451 + 4.15953i −0.289340 + 0.167051i
\(621\) 0 0
\(622\) 10.9100i 0.437452i
\(623\) 0 0
\(624\) 0 0
\(625\) −12.8060 −0.512240
\(626\) −1.71203 + 2.96532i −0.0684263 + 0.118518i
\(627\) 0 0
\(628\) −11.9885 + 6.92154i −0.478391 + 0.276199i
\(629\) −34.3161 −1.36827
\(630\) 0 0
\(631\) 26.9822 1.07415 0.537073 0.843536i \(-0.319530\pi\)
0.537073 + 0.843536i \(0.319530\pi\)
\(632\) −2.62979 + 1.51831i −0.104608 + 0.0603952i
\(633\) 0 0
\(634\) 9.52357 16.4953i 0.378229 0.655112i
\(635\) −2.50918 −0.0995739
\(636\) 0 0
\(637\) 0 0
\(638\) 15.7563i 0.623800i
\(639\) 0 0
\(640\) 1.55049 0.895175i 0.0612884 0.0353849i
\(641\) 1.07708i 0.0425420i 0.999774 + 0.0212710i \(0.00677128\pi\)
−0.999774 + 0.0212710i \(0.993229\pi\)
\(642\) 0 0
\(643\) 33.3126 19.2330i 1.31372 0.758477i 0.331010 0.943627i \(-0.392611\pi\)
0.982710 + 0.185150i \(0.0592773\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.52817 9.57507i −0.217503 0.376726i
\(647\) −4.47605 7.75275i −0.175972 0.304792i 0.764525 0.644594i \(-0.222973\pi\)
−0.940497 + 0.339802i \(0.889640\pi\)
\(648\) 0 0
\(649\) 30.3438 + 17.5190i 1.19110 + 0.687680i
\(650\) 4.38910 7.60215i 0.172155 0.298181i
\(651\) 0 0
\(652\) −2.16789 3.75489i −0.0849010 0.147053i
\(653\) 11.3846i 0.445513i 0.974874 + 0.222757i \(0.0715055\pi\)
−0.974874 + 0.222757i \(0.928494\pi\)
\(654\) 0 0
\(655\) 18.7839 0.733949
\(656\) 4.04094 6.99911i 0.157772 0.273269i
\(657\) 0 0
\(658\) 0 0
\(659\) −31.4373 18.1503i −1.22462 0.707036i −0.258723 0.965952i \(-0.583302\pi\)
−0.965900 + 0.258915i \(0.916635\pi\)
\(660\) 0 0
\(661\) 31.2425 + 18.0379i 1.21519 + 0.701593i 0.963886 0.266315i \(-0.0858060\pi\)
0.251308 + 0.967907i \(0.419139\pi\)
\(662\) −0.0634366 0.0366251i −0.00246553 0.00142348i
\(663\) 0 0
\(664\) −12.1290 7.00270i −0.470698 0.271757i
\(665\) 0 0
\(666\) 0 0
\(667\) 12.3557 21.4007i 0.478414 0.828637i
\(668\) 12.4151 0.480355
\(669\) 0 0
\(670\) 1.02091i 0.0394413i
\(671\) 13.6025 + 23.5602i 0.525117 + 0.909530i
\(672\) 0 0
\(673\) 4.78512 8.28806i 0.184453 0.319481i −0.758939 0.651161i \(-0.774282\pi\)
0.943392 + 0.331680i \(0.107615\pi\)
\(674\) 1.93364 + 1.11639i 0.0744811 + 0.0430017i
\(675\) 0 0
\(676\) −5.46254 9.46139i −0.210098 0.363900i
\(677\) −7.81408 13.5344i −0.300320 0.520169i 0.675889 0.737004i \(-0.263760\pi\)
−0.976208 + 0.216835i \(0.930427\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −5.68202 + 3.28052i −0.217896 + 0.125802i
\(681\) 0 0
\(682\) 11.1589i 0.427294i
\(683\) 9.63996 5.56563i 0.368863 0.212963i −0.304099 0.952640i \(-0.598355\pi\)
0.672961 + 0.739678i \(0.265022\pi\)
\(684\) 0 0
\(685\) 8.45145i 0.322913i
\(686\) 0 0
\(687\) 0 0
\(688\) 6.96254 0.265444
\(689\) 0 0
\(690\) 0 0
\(691\) −2.61903 + 1.51210i −0.0996324 + 0.0575228i −0.548988 0.835830i \(-0.684987\pi\)
0.449356 + 0.893353i \(0.351654\pi\)
\(692\) −17.4182 −0.662139
\(693\) 0 0
\(694\) 31.8409 1.20867
\(695\) 3.66497 2.11597i 0.139020 0.0802633i
\(696\) 0 0
\(697\) −14.8087 + 25.6494i −0.560919 + 0.971540i
\(698\) −14.7354 −0.557745
\(699\) 0 0
\(700\) 0 0
\(701\) 50.1486i 1.89409i 0.321103 + 0.947044i \(0.395946\pi\)
−0.321103 + 0.947044i \(0.604054\pi\)
\(702\) 0 0
\(703\) 24.4664 14.1257i 0.922769 0.532761i
\(704\) 2.40150i 0.0905101i
\(705\) 0 0
\(706\) −1.87025 + 1.07979i −0.0703876 + 0.0406383i
\(707\) 0 0
\(708\) 0 0
\(709\) 1.80385 + 3.12436i 0.0677449 + 0.117338i 0.897908 0.440183i \(-0.145086\pi\)
−0.830163 + 0.557520i \(0.811753\pi\)
\(710\) 5.33751 + 9.24484i 0.200313 + 0.346953i
\(711\) 0 0
\(712\) 3.24641 + 1.87432i 0.121664 + 0.0702429i
\(713\) 8.75046 15.1562i 0.327707 0.567605i
\(714\) 0 0
\(715\) −10.5152 18.2129i −0.393246 0.681123i
\(716\) 13.1221i 0.490395i
\(717\) 0 0
\(718\) −32.6448 −1.21829
\(719\) −17.1580 + 29.7186i −0.639887 + 1.10832i 0.345571 + 0.938393i \(0.387685\pi\)
−0.985457 + 0.169924i \(0.945648\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −8.57161 4.94882i −0.319002 0.184176i
\(723\) 0 0
\(724\) 11.5681 + 6.67887i 0.429927 + 0.248218i
\(725\) −10.1972 5.88737i −0.378716 0.218651i
\(726\) 0 0
\(727\) 19.4757 + 11.2443i 0.722315 + 0.417029i 0.815604 0.578610i \(-0.196405\pi\)
−0.0932892 + 0.995639i \(0.529738\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 11.0835 19.1972i 0.410220 0.710521i
\(731\) −25.5154 −0.943720
\(732\) 0 0
\(733\) 31.1845i 1.15182i 0.817512 + 0.575912i \(0.195353\pi\)
−0.817512 + 0.575912i \(0.804647\pi\)
\(734\) −14.8501 25.7212i −0.548129 0.949387i
\(735\) 0 0
\(736\) −1.88319 + 3.26178i −0.0694154 + 0.120231i
\(737\) 1.18595 + 0.684706i 0.0436849 + 0.0252215i
\(738\) 0 0
\(739\) −2.04314 3.53882i −0.0751581 0.130178i 0.825997 0.563675i \(-0.190613\pi\)
−0.901155 + 0.433497i \(0.857279\pi\)
\(740\) −8.38245 14.5188i −0.308145 0.533723i
\(741\) 0 0
\(742\) 0 0
\(743\) 1.78246 1.02910i 0.0653921 0.0377542i −0.466947 0.884285i \(-0.654646\pi\)
0.532340 + 0.846531i \(0.321313\pi\)
\(744\) 0 0
\(745\) 31.0877i 1.13897i
\(746\) −1.74653 + 1.00836i −0.0639450 + 0.0369187i
\(747\) 0 0
\(748\) 8.80071i 0.321786i
\(749\) 0 0
\(750\) 0 0
\(751\) 23.8105 0.868859 0.434429 0.900706i \(-0.356950\pi\)
0.434429 + 0.900706i \(0.356950\pi\)
\(752\) −2.56802 + 4.44794i −0.0936461 + 0.162200i
\(753\) 0 0
\(754\) −27.7926 + 16.0461i −1.01215 + 0.584363i
\(755\) 20.1106 0.731900
\(756\) 0 0
\(757\) 10.0754 0.366197 0.183098 0.983095i \(-0.441387\pi\)
0.183098 + 0.983095i \(0.441387\pi\)
\(758\) −16.3427 + 9.43544i −0.593592 + 0.342711i
\(759\) 0 0
\(760\) 2.70075 4.67784i 0.0979666 0.169683i
\(761\) 27.8735 1.01041 0.505207 0.862998i \(-0.331416\pi\)
0.505207 + 0.862998i \(0.331416\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 9.25333i 0.334774i
\(765\) 0 0
\(766\) −0.724440 + 0.418256i −0.0261751 + 0.0151122i
\(767\) 71.3645i 2.57682i
\(768\) 0 0
\(769\) −6.21166 + 3.58631i −0.223998 + 0.129326i −0.607800 0.794090i \(-0.707948\pi\)
0.383802 + 0.923415i \(0.374615\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.2801 21.2698i −0.441970 0.765515i
\(773\) −1.07077 1.85462i −0.0385128 0.0667061i 0.846127 0.532982i \(-0.178929\pi\)
−0.884639 + 0.466276i \(0.845595\pi\)
\(774\) 0 0
\(775\) −7.22181 4.16951i −0.259415 0.149773i
\(776\) 2.75544 4.77256i 0.0989144 0.171325i
\(777\) 0 0
\(778\) 12.4109 + 21.4964i 0.444954 + 0.770682i
\(779\) 24.3831i 0.873615i
\(780\) 0 0
\(781\) −14.3191 −0.512376
\(782\) 6.90127 11.9533i 0.246789 0.427451i
\(783\) 0 0
\(784\) 0 0
\(785\) 21.4635 + 12.3920i 0.766066 + 0.442288i
\(786\) 0 0
\(787\) −15.8961 9.17759i −0.566633 0.327146i 0.189170 0.981944i \(-0.439420\pi\)
−0.755804 + 0.654798i \(0.772753\pi\)
\(788\) 10.8133 + 6.24305i 0.385207 + 0.222400i
\(789\) 0 0
\(790\) 4.70825 + 2.71831i 0.167512 + 0.0967131i
\(791\) 0 0
\(792\) 0 0
\(793\) 27.7052 47.9868i 0.983839 1.70406i
\(794\) 3.03390 0.107669
\(795\) 0 0
\(796\) 0.179145i 0.00634964i
\(797\) −12.4226 21.5166i −0.440031 0.762156i 0.557660 0.830069i \(-0.311699\pi\)
−0.997691 + 0.0679130i \(0.978366\pi\)
\(798\) 0 0
\(799\) 9.41094 16.3002i 0.332935 0.576660i
\(800\) 1.55421 + 0.897324i 0.0549497 + 0.0317252i
\(801\) 0 0
\(802\) −6.53854 11.3251i −0.230884 0.399903i
\(803\) 14.8670 + 25.7504i 0.524645 + 0.908712i
\(804\) 0 0
\(805\) 0 0
\(806\) −19.6831 + 11.3640i −0.693307 + 0.400281i
\(807\) 0 0
\(808\) 0.250324i 0.00880637i
\(809\) −32.7237 + 18.8930i −1.15050 + 0.664244i −0.949010 0.315246i \(-0.897913\pi\)
−0.201494 + 0.979490i \(0.564580\pi\)
\(810\) 0 0
\(811\) 36.5165i 1.28227i −0.767429 0.641134i \(-0.778464\pi\)
0.767429 0.641134i \(-0.221536\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 22.4878 0.788196
\(815\) −3.88128 + 6.72257i −0.135955 + 0.235481i
\(816\) 0 0
\(817\) 18.1918 10.5030i 0.636449 0.367454i
\(818\) −5.56709 −0.194649
\(819\) 0 0
\(820\) −14.4694 −0.505293
\(821\) −5.52142 + 3.18779i −0.192699 + 0.111255i −0.593245 0.805022i \(-0.702154\pi\)
0.400547 + 0.916276i \(0.368820\pi\)
\(822\) 0 0
\(823\) −14.0293 + 24.2995i −0.489032 + 0.847028i −0.999920 0.0126187i \(-0.995983\pi\)
0.510888 + 0.859647i \(0.329317\pi\)
\(824\) 0.167931 0.00585017
\(825\) 0 0
\(826\) 0 0
\(827\) 0.581579i 0.0202235i −0.999949 0.0101117i \(-0.996781\pi\)
0.999949 0.0101117i \(-0.00321872\pi\)
\(828\) 0 0
\(829\) −44.9680 + 25.9623i −1.56180 + 0.901708i −0.564729 + 0.825276i \(0.691019\pi\)
−0.997075 + 0.0764314i \(0.975647\pi\)
\(830\) 25.0746i 0.870351i
\(831\) 0 0
\(832\) 4.23601 2.44566i 0.146857 0.0847881i
\(833\) 0 0
\(834\) 0 0
\(835\) −11.1137 19.2495i −0.384606 0.666156i
\(836\) 3.62268 + 6.27467i 0.125293 + 0.217014i
\(837\) 0 0
\(838\) −14.2017 8.19938i −0.490591 0.283243i
\(839\) 3.33038 5.76838i 0.114977 0.199147i −0.802793 0.596257i \(-0.796654\pi\)
0.917771 + 0.397111i \(0.129987\pi\)
\(840\) 0 0
\(841\) 7.02357 + 12.1652i 0.242192 + 0.419489i
\(842\) 15.4578i 0.532712i
\(843\) 0 0
\(844\) 15.1221 0.520523
\(845\) −9.77985 + 16.9392i −0.336437 + 0.582726i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) −5.69566 3.28839i −0.195360 0.112791i
\(851\) 30.5435 + 17.6343i 1.04702 + 0.604495i
\(852\) 0 0
\(853\) −19.2287 11.1017i −0.658378 0.380115i 0.133281 0.991078i \(-0.457449\pi\)
−0.791659 + 0.610964i \(0.790782\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −3.99540 + 6.92024i −0.136560 + 0.236529i
\(857\) −15.2966 −0.522522 −0.261261 0.965268i \(-0.584138\pi\)
−0.261261 + 0.965268i \(0.584138\pi\)
\(858\) 0 0
\(859\) 4.25646i 0.145229i 0.997360 + 0.0726143i \(0.0231342\pi\)
−0.997360 + 0.0726143i \(0.976866\pi\)
\(860\) −6.23269 10.7953i −0.212533 0.368118i
\(861\) 0 0
\(862\) −12.5133 + 21.6737i −0.426204 + 0.738208i
\(863\) 20.4922 + 11.8312i 0.697562 + 0.402738i 0.806439 0.591317i \(-0.201392\pi\)
−0.108876 + 0.994055i \(0.534725\pi\)
\(864\) 0 0
\(865\) 15.5923 + 27.0067i 0.530154 + 0.918254i
\(866\) −1.12584 1.95001i −0.0382576 0.0662641i
\(867\) 0 0
\(868\) 0 0
\(869\) −6.31546 + 3.64623i −0.214237 + 0.123690i
\(870\) 0 0
\(871\) 2.78919i 0.0945079i
\(872\) 16.4141 9.47667i 0.555851 0.320920i
\(873\) 0 0
\(874\) 11.3632i 0.384367i
\(875\) 0 0
\(876\) 0 0
\(877\) −20.3923 −0.688599 −0.344300 0.938860i \(-0.611884\pi\)
−0.344300 + 0.938860i \(0.611884\pi\)
\(878\) −9.37000 + 16.2293i −0.316222 + 0.547713i
\(879\) 0 0
\(880\) 3.72350 2.14977i 0.125519 0.0724686i
\(881\) −32.4586 −1.09356 −0.546780 0.837276i \(-0.684147\pi\)
−0.546780 + 0.837276i \(0.684147\pi\)
\(882\) 0 0
\(883\) −24.8311 −0.835632 −0.417816 0.908532i \(-0.637204\pi\)
−0.417816 + 0.908532i \(0.637204\pi\)
\(884\) −15.5236 + 8.96254i −0.522114 + 0.301443i
\(885\) 0 0
\(886\) −0.602256 + 1.04314i −0.0202332 + 0.0350449i
\(887\) −9.72119 −0.326405 −0.163203 0.986593i \(-0.552182\pi\)
−0.163203 + 0.986593i \(0.552182\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 6.71136i 0.224965i
\(891\) 0 0
\(892\) −7.27049 + 4.19762i −0.243434 + 0.140547i
\(893\) 15.4955i 0.518537i
\(894\) 0 0
\(895\) 20.3456 11.7465i 0.680079 0.392644i
\(896\) 0 0
\(897\) 0 0
\(898\) 13.4011 + 23.2114i 0.447200 + 0.774573i
\(899\) 15.2433 + 26.4021i 0.508392 + 0.880560i
\(900\) 0 0
\(901\) 0 0
\(902\) 9.70433 16.8084i 0.323119 0.559658i
\(903\) 0 0
\(904\) −0.579764 1.00418i −0.0192827 0.0333985i
\(905\) 23.9150i 0.794963i
\(906\) 0 0
\(907\) −16.0863 −0.534136 −0.267068 0.963678i \(-0.586055\pi\)
−0.267068 + 0.963678i \(0.586055\pi\)
\(908\) 1.21261 2.10030i 0.0402418 0.0697009i
\(909\) 0 0
\(910\) 0 0
\(911\) −27.0087 15.5935i −0.894838 0.516635i −0.0193161 0.999813i \(-0.506149\pi\)
−0.875522 + 0.483179i \(0.839482\pi\)
\(912\) 0 0
\(913\) −29.1279 16.8170i −0.963993 0.556562i
\(914\) −11.9934 6.92442i −0.396708 0.229039i
\(915\) 0 0
\(916\) 1.74915 + 1.00987i 0.0577936 + 0.0333672i
\(917\) 0 0
\(918\) 0 0
\(919\) −12.8832 + 22.3143i −0.424977 + 0.736082i −0.996418 0.0845609i \(-0.973051\pi\)
0.571441 + 0.820643i \(0.306385\pi\)
\(920\) 6.74314 0.222315
\(921\) 0 0
\(922\) 4.80483i 0.158239i
\(923\) 14.5824 + 25.2574i 0.479984 + 0.831357i
\(924\) 0 0
\(925\) 8.40258 14.5537i 0.276275 0.478522i
\(926\) 18.2201 + 10.5194i 0.598750 + 0.345689i
\(927\) 0 0
\(928\) −3.28052 5.68202i −0.107688 0.186521i
\(929\) 27.3744 + 47.4138i 0.898124 + 1.55560i 0.829891 + 0.557926i \(0.188403\pi\)
0.0682329 + 0.997669i \(0.478264\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 11.0236 6.36446i 0.361089 0.208475i
\(933\) 0 0
\(934\) 5.82302i 0.190535i
\(935\) −13.6454 + 7.87817i −0.446252 + 0.257644i
\(936\) 0 0
\(937\) 58.2065i 1.90152i 0.309924 + 0.950761i \(0.399696\pi\)
−0.309924 + 0.950761i \(0.600304\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 9.19531 0.299918
\(941\) −16.6658 + 28.8660i −0.543289 + 0.941005i 0.455423 + 0.890275i \(0.349488\pi\)
−0.998712 + 0.0507297i \(0.983845\pi\)
\(942\) 0 0
\(943\) 26.3613 15.2197i 0.858443 0.495622i
\(944\) 14.5900 0.474864
\(945\) 0 0
\(946\) 16.7206 0.543632
\(947\) −6.59497 + 3.80761i −0.214308 + 0.123731i −0.603312 0.797505i \(-0.706153\pi\)
0.389004 + 0.921236i \(0.372819\pi\)
\(948\) 0 0
\(949\) 30.2808 52.4478i 0.982955 1.70253i
\(950\) 5.41447 0.175669
\(951\) 0 0
\(952\) 0 0
\(953\) 55.7861i 1.80709i −0.428495 0.903544i \(-0.640956\pi\)
0.428495 0.903544i \(-0.359044\pi\)
\(954\) 0 0
\(955\) 14.3472 8.28334i 0.464264 0.268043i
\(956\) 17.4495i 0.564356i
\(957\) 0 0
\(958\) 23.3447 13.4781i 0.754232 0.435456i
\(959\) 0 0
\(960\) 0 0
\(961\) −4.70451 8.14845i −0.151758 0.262853i
\(962\) −22.9013 39.6662i −0.738367 1.27889i
\(963\) 0 0
\(964\) −9.90142 5.71659i −0.318903 0.184119i
\(965\) −21.9857 + 38.0803i −0.707744 + 1.22585i
\(966\) 0 0
\(967\) −13.3369 23.1003i −0.428887 0.742855i 0.567887 0.823106i \(-0.307761\pi\)
−0.996775 + 0.0802517i \(0.974428\pi\)
\(968\) 5.23278i 0.168188i
\(969\) 0 0
\(970\) −9.86639 −0.316791
\(971\) −4.29971 + 7.44731i −0.137984 + 0.238996i −0.926733 0.375719i \(-0.877396\pi\)
0.788749 + 0.614715i \(0.210729\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 11.8011 + 6.81338i 0.378132 + 0.218315i
\(975\) 0 0
\(976\) 9.81058 + 5.66414i 0.314029 + 0.181305i
\(977\) −12.7973 7.38854i −0.409423 0.236380i 0.281119 0.959673i \(-0.409295\pi\)
−0.690542 + 0.723293i \(0.742628\pi\)
\(978\) 0 0
\(979\) 7.79627 + 4.50118i 0.249170 + 0.143858i
\(980\) 0 0
\(981\) 0 0
\(982\) 19.4815 33.7430i 0.621680 1.07678i
\(983\) 20.5135 0.654280 0.327140 0.944976i \(-0.393915\pi\)
0.327140 + 0.944976i \(0.393915\pi\)
\(984\) 0 0
\(985\) 22.3545i 0.712273i
\(986\) 12.0220 + 20.8227i 0.382858 + 0.663130i
\(987\) 0 0
\(988\) 7.37859 12.7801i 0.234744 0.406589i
\(989\) 22.7103 + 13.1118i 0.722145 + 0.416931i
\(990\) 0 0
\(991\) 4.64647 + 8.04792i 0.147600 + 0.255651i 0.930340 0.366698i \(-0.119512\pi\)
−0.782740 + 0.622349i \(0.786179\pi\)
\(992\) −2.32330 4.02408i −0.0737650 0.127765i
\(993\) 0 0
\(994\) 0 0
\(995\) −0.277763 + 0.160366i −0.00880567 + 0.00508396i
\(996\) 0 0
\(997\) 0.0199668i 0.000632354i 1.00000 0.000316177i \(0.000100642\pi\)
−1.00000 0.000316177i \(0.999899\pi\)
\(998\) 22.5250 13.0048i 0.713018 0.411661i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2646.2.t.a.1979.5 16
3.2 odd 2 882.2.t.b.803.2 16
7.2 even 3 378.2.m.a.251.4 16
7.3 odd 6 2646.2.l.b.521.5 16
7.4 even 3 2646.2.l.b.521.8 16
7.5 odd 6 378.2.m.a.251.1 16
7.6 odd 2 inner 2646.2.t.a.1979.8 16
9.4 even 3 882.2.l.a.509.7 16
9.5 odd 6 2646.2.l.b.1097.1 16
21.2 odd 6 126.2.m.a.83.8 yes 16
21.5 even 6 126.2.m.a.83.5 yes 16
21.11 odd 6 882.2.l.a.227.2 16
21.17 even 6 882.2.l.a.227.3 16
21.20 even 2 882.2.t.b.803.3 16
28.19 even 6 3024.2.cc.b.2897.3 16
28.23 odd 6 3024.2.cc.b.2897.6 16
63.2 odd 6 1134.2.d.a.1133.6 16
63.4 even 3 882.2.t.b.815.3 16
63.5 even 6 378.2.m.a.125.4 16
63.13 odd 6 882.2.l.a.509.6 16
63.16 even 3 1134.2.d.a.1133.11 16
63.23 odd 6 378.2.m.a.125.1 16
63.31 odd 6 882.2.t.b.815.2 16
63.32 odd 6 inner 2646.2.t.a.2285.8 16
63.40 odd 6 126.2.m.a.41.8 yes 16
63.41 even 6 2646.2.l.b.1097.4 16
63.47 even 6 1134.2.d.a.1133.3 16
63.58 even 3 126.2.m.a.41.5 16
63.59 even 6 inner 2646.2.t.a.2285.5 16
63.61 odd 6 1134.2.d.a.1133.14 16
84.23 even 6 1008.2.cc.b.209.1 16
84.47 odd 6 1008.2.cc.b.209.8 16
252.23 even 6 3024.2.cc.b.881.3 16
252.103 even 6 1008.2.cc.b.545.1 16
252.131 odd 6 3024.2.cc.b.881.6 16
252.247 odd 6 1008.2.cc.b.545.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.5 16 63.58 even 3
126.2.m.a.41.8 yes 16 63.40 odd 6
126.2.m.a.83.5 yes 16 21.5 even 6
126.2.m.a.83.8 yes 16 21.2 odd 6
378.2.m.a.125.1 16 63.23 odd 6
378.2.m.a.125.4 16 63.5 even 6
378.2.m.a.251.1 16 7.5 odd 6
378.2.m.a.251.4 16 7.2 even 3
882.2.l.a.227.2 16 21.11 odd 6
882.2.l.a.227.3 16 21.17 even 6
882.2.l.a.509.6 16 63.13 odd 6
882.2.l.a.509.7 16 9.4 even 3
882.2.t.b.803.2 16 3.2 odd 2
882.2.t.b.803.3 16 21.20 even 2
882.2.t.b.815.2 16 63.31 odd 6
882.2.t.b.815.3 16 63.4 even 3
1008.2.cc.b.209.1 16 84.23 even 6
1008.2.cc.b.209.8 16 84.47 odd 6
1008.2.cc.b.545.1 16 252.103 even 6
1008.2.cc.b.545.8 16 252.247 odd 6
1134.2.d.a.1133.3 16 63.47 even 6
1134.2.d.a.1133.6 16 63.2 odd 6
1134.2.d.a.1133.11 16 63.16 even 3
1134.2.d.a.1133.14 16 63.61 odd 6
2646.2.l.b.521.5 16 7.3 odd 6
2646.2.l.b.521.8 16 7.4 even 3
2646.2.l.b.1097.1 16 9.5 odd 6
2646.2.l.b.1097.4 16 63.41 even 6
2646.2.t.a.1979.5 16 1.1 even 1 trivial
2646.2.t.a.1979.8 16 7.6 odd 2 inner
2646.2.t.a.2285.5 16 63.59 even 6 inner
2646.2.t.a.2285.8 16 63.32 odd 6 inner
3024.2.cc.b.881.3 16 252.23 even 6
3024.2.cc.b.881.6 16 252.131 odd 6
3024.2.cc.b.2897.3 16 28.19 even 6
3024.2.cc.b.2897.6 16 28.23 odd 6