Properties

Label 630.2.m.d.197.2
Level $630$
Weight $2$
Character 630.197
Analytic conductor $5.031$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(197,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.197");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.m (of order \(4\), degree \(2\), 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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1698758656.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 197.2
Root \(-2.16053i\) of defining polynomial
Character \(\chi\) \(=\) 630.197
Dual form 630.2.m.d.323.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23483 - 0.0743018i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23483 - 0.0743018i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.52773 + 1.63280i) q^{10} +5.26561i q^{11} +(-3.16053 + 3.16053i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(3.05545 - 3.05545i) q^{17} +(-0.0743018 - 2.23483i) q^{20} +(-3.72335 - 3.72335i) q^{22} +(4.32106 + 4.32106i) q^{23} +(4.98896 - 0.332104i) q^{25} -4.46967i q^{26} +(-0.707107 + 0.707107i) q^{28} +9.96230 q^{29} +1.26561 q^{31} +(0.707107 - 0.707107i) q^{32} +4.32106i q^{34} +(-1.63280 - 1.52773i) q^{35} +(-2.93351 - 2.93351i) q^{37} +(1.63280 + 1.52773i) q^{40} +10.6798i q^{41} +(0.597714 - 0.597714i) q^{43} +5.26561 q^{44} -6.11091 q^{46} +(-3.42614 + 3.42614i) q^{47} +1.00000i q^{49} +(-3.29289 + 3.76256i) q^{50} +(3.16053 + 3.16053i) q^{52} +(-9.88388 - 9.88388i) q^{53} +(0.391244 + 11.7678i) q^{55} -1.00000i q^{56} +(-7.04441 + 7.04441i) q^{58} +3.12563 q^{59} +3.05545 q^{61} +(-0.894921 + 0.894921i) q^{62} +1.00000i q^{64} +(-6.82843 + 7.29809i) q^{65} +(4.59771 + 4.59771i) q^{67} +(-3.05545 - 3.05545i) q^{68} +(2.23483 - 0.0743018i) q^{70} +9.23654i q^{71} +(10.2160 - 10.2160i) q^{73} +4.14860 q^{74} +(3.72335 - 3.72335i) q^{77} +3.57969i q^{79} +(-2.23483 + 0.0743018i) q^{80} +(-7.55178 - 7.55178i) q^{82} +(-6.21016 - 6.21016i) q^{83} +(6.60140 - 7.05545i) q^{85} +0.845296i q^{86} +(-3.72335 + 3.72335i) q^{88} -3.61916 q^{89} +4.46967 q^{91} +(4.32106 - 4.32106i) q^{92} -4.84530i q^{94} +(-4.63630 - 4.63630i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{13} + 8 q^{14} - 8 q^{16} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 4 q^{25} + 24 q^{29} - 8 q^{31} - 4 q^{35} - 4 q^{37} + 4 q^{40} - 12 q^{43} + 24 q^{44} + 12 q^{47} - 32 q^{50} + 4 q^{52} - 32 q^{53} - 24 q^{55} + 12 q^{58} + 16 q^{59} - 4 q^{62} - 32 q^{65} + 20 q^{67} + 36 q^{73} + 40 q^{74} + 4 q^{77} - 12 q^{82} - 56 q^{83} + 32 q^{85} - 4 q^{88} + 72 q^{89} - 8 q^{92} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 2.23483 0.0743018i 0.999448 0.0332288i
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0 0
\(10\) −1.52773 + 1.63280i −0.483109 + 0.516338i
\(11\) 5.26561i 1.58764i 0.608152 + 0.793821i \(0.291911\pi\)
−0.608152 + 0.793821i \(0.708089\pi\)
\(12\) 0 0
\(13\) −3.16053 + 3.16053i −0.876574 + 0.876574i −0.993178 0.116605i \(-0.962799\pi\)
0.116605 + 0.993178i \(0.462799\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.05545 3.05545i 0.741056 0.741056i −0.231725 0.972781i \(-0.574437\pi\)
0.972781 + 0.231725i \(0.0744370\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −0.0743018 2.23483i −0.0166144 0.499724i
\(21\) 0 0
\(22\) −3.72335 3.72335i −0.793821 0.793821i
\(23\) 4.32106 + 4.32106i 0.901004 + 0.901004i 0.995523 0.0945192i \(-0.0301314\pi\)
−0.0945192 + 0.995523i \(0.530131\pi\)
\(24\) 0 0
\(25\) 4.98896 0.332104i 0.997792 0.0664208i
\(26\) 4.46967i 0.876574i
\(27\) 0 0
\(28\) −0.707107 + 0.707107i −0.133631 + 0.133631i
\(29\) 9.96230 1.84995 0.924977 0.380024i \(-0.124084\pi\)
0.924977 + 0.380024i \(0.124084\pi\)
\(30\) 0 0
\(31\) 1.26561 0.227310 0.113655 0.993520i \(-0.463744\pi\)
0.113655 + 0.993520i \(0.463744\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0 0
\(34\) 4.32106i 0.741056i
\(35\) −1.63280 1.52773i −0.275994 0.258233i
\(36\) 0 0
\(37\) −2.93351 2.93351i −0.482265 0.482265i 0.423589 0.905854i \(-0.360770\pi\)
−0.905854 + 0.423589i \(0.860770\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 1.63280 + 1.52773i 0.258169 + 0.241555i
\(41\) 10.6798i 1.66791i 0.551834 + 0.833954i \(0.313928\pi\)
−0.551834 + 0.833954i \(0.686072\pi\)
\(42\) 0 0
\(43\) 0.597714 0.597714i 0.0911506 0.0911506i −0.660061 0.751212i \(-0.729470\pi\)
0.751212 + 0.660061i \(0.229470\pi\)
\(44\) 5.26561 0.793821
\(45\) 0 0
\(46\) −6.11091 −0.901004
\(47\) −3.42614 + 3.42614i −0.499754 + 0.499754i −0.911361 0.411607i \(-0.864968\pi\)
0.411607 + 0.911361i \(0.364968\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) −3.29289 + 3.76256i −0.465685 + 0.532106i
\(51\) 0 0
\(52\) 3.16053 + 3.16053i 0.438287 + 0.438287i
\(53\) −9.88388 9.88388i −1.35766 1.35766i −0.876800 0.480855i \(-0.840326\pi\)
−0.480855 0.876800i \(-0.659674\pi\)
\(54\) 0 0
\(55\) 0.391244 + 11.7678i 0.0527554 + 1.58676i
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) −7.04441 + 7.04441i −0.924977 + 0.924977i
\(59\) 3.12563 0.406923 0.203461 0.979083i \(-0.434781\pi\)
0.203461 + 0.979083i \(0.434781\pi\)
\(60\) 0 0
\(61\) 3.05545 0.391211 0.195605 0.980683i \(-0.437333\pi\)
0.195605 + 0.980683i \(0.437333\pi\)
\(62\) −0.894921 + 0.894921i −0.113655 + 0.113655i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −6.82843 + 7.29809i −0.846962 + 0.905217i
\(66\) 0 0
\(67\) 4.59771 + 4.59771i 0.561700 + 0.561700i 0.929790 0.368090i \(-0.119988\pi\)
−0.368090 + 0.929790i \(0.619988\pi\)
\(68\) −3.05545 3.05545i −0.370528 0.370528i
\(69\) 0 0
\(70\) 2.23483 0.0743018i 0.267114 0.00888076i
\(71\) 9.23654i 1.09618i 0.836421 + 0.548088i \(0.184644\pi\)
−0.836421 + 0.548088i \(0.815356\pi\)
\(72\) 0 0
\(73\) 10.2160 10.2160i 1.19569 1.19569i 0.220246 0.975444i \(-0.429314\pi\)
0.975444 0.220246i \(-0.0706861\pi\)
\(74\) 4.14860 0.482265
\(75\) 0 0
\(76\) 0 0
\(77\) 3.72335 3.72335i 0.424315 0.424315i
\(78\) 0 0
\(79\) 3.57969i 0.402746i 0.979515 + 0.201373i \(0.0645403\pi\)
−0.979515 + 0.201373i \(0.935460\pi\)
\(80\) −2.23483 + 0.0743018i −0.249862 + 0.00830719i
\(81\) 0 0
\(82\) −7.55178 7.55178i −0.833954 0.833954i
\(83\) −6.21016 6.21016i −0.681653 0.681653i 0.278719 0.960373i \(-0.410090\pi\)
−0.960373 + 0.278719i \(0.910090\pi\)
\(84\) 0 0
\(85\) 6.60140 7.05545i 0.716023 0.765271i
\(86\) 0.845296i 0.0911506i
\(87\) 0 0
\(88\) −3.72335 + 3.72335i −0.396910 + 0.396910i
\(89\) −3.61916 −0.383630 −0.191815 0.981431i \(-0.561437\pi\)
−0.191815 + 0.981431i \(0.561437\pi\)
\(90\) 0 0
\(91\) 4.46967 0.468548
\(92\) 4.32106 4.32106i 0.450502 0.450502i
\(93\) 0 0
\(94\) 4.84530i 0.499754i
\(95\) 0 0
\(96\) 0 0
\(97\) −4.63630 4.63630i −0.470745 0.470745i 0.431411 0.902156i \(-0.358016\pi\)
−0.902156 + 0.431411i \(0.858016\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) 0 0
\(100\) −0.332104 4.98896i −0.0332104 0.498896i
\(101\) 2.12652i 0.211597i −0.994388 0.105798i \(-0.966260\pi\)
0.994388 0.105798i \(-0.0337398\pi\)
\(102\) 0 0
\(103\) −10.9225 + 10.9225i −1.07622 + 1.07622i −0.0793778 + 0.996845i \(0.525293\pi\)
−0.996845 + 0.0793778i \(0.974707\pi\)
\(104\) −4.46967 −0.438287
\(105\) 0 0
\(106\) 13.9779 1.35766
\(107\) −6.40811 + 6.40811i −0.619496 + 0.619496i −0.945402 0.325906i \(-0.894331\pi\)
0.325906 + 0.945402i \(0.394331\pi\)
\(108\) 0 0
\(109\) 9.55760i 0.915452i −0.889093 0.457726i \(-0.848664\pi\)
0.889093 0.457726i \(-0.151336\pi\)
\(110\) −8.59771 8.04441i −0.819760 0.767005i
\(111\) 0 0
\(112\) 0.707107 + 0.707107i 0.0668153 + 0.0668153i
\(113\) 3.29809 + 3.29809i 0.310259 + 0.310259i 0.845010 0.534751i \(-0.179595\pi\)
−0.534751 + 0.845010i \(0.679595\pi\)
\(114\) 0 0
\(115\) 9.97792 + 9.33579i 0.930446 + 0.870567i
\(116\) 9.96230i 0.924977i
\(117\) 0 0
\(118\) −2.21016 + 2.21016i −0.203461 + 0.203461i
\(119\) −4.32106 −0.396111
\(120\) 0 0
\(121\) −16.7266 −1.52060
\(122\) −2.16053 + 2.16053i −0.195605 + 0.195605i
\(123\) 0 0
\(124\) 1.26561i 0.113655i
\(125\) 11.1248 1.11289i 0.995034 0.0995396i
\(126\) 0 0
\(127\) −8.32106 8.32106i −0.738375 0.738375i 0.233889 0.972263i \(-0.424855\pi\)
−0.972263 + 0.233889i \(0.924855\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 0 0
\(130\) −0.332104 9.98896i −0.0291275 0.876090i
\(131\) 17.4246i 1.52240i −0.648520 0.761198i \(-0.724612\pi\)
0.648520 0.761198i \(-0.275388\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.50215 −0.561700
\(135\) 0 0
\(136\) 4.32106 0.370528
\(137\) 2.35876 2.35876i 0.201523 0.201523i −0.599130 0.800652i \(-0.704487\pi\)
0.800652 + 0.599130i \(0.204487\pi\)
\(138\) 0 0
\(139\) 21.8449i 1.85286i −0.376464 0.926431i \(-0.622860\pi\)
0.376464 0.926431i \(-0.377140\pi\)
\(140\) −1.52773 + 1.63280i −0.129116 + 0.137997i
\(141\) 0 0
\(142\) −6.53122 6.53122i −0.548088 0.548088i
\(143\) −16.6421 16.6421i −1.39168 1.39168i
\(144\) 0 0
\(145\) 22.2641 0.740217i 1.84893 0.0614717i
\(146\) 14.4476i 1.19569i
\(147\) 0 0
\(148\) −2.93351 + 2.93351i −0.241133 + 0.241133i
\(149\) 6.08541 0.498536 0.249268 0.968435i \(-0.419810\pi\)
0.249268 + 0.968435i \(0.419810\pi\)
\(150\) 0 0
\(151\) 22.7530 1.85162 0.925808 0.377995i \(-0.123386\pi\)
0.925808 + 0.377995i \(0.123386\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 5.26561i 0.424315i
\(155\) 2.82843 0.0940371i 0.227185 0.00755324i
\(156\) 0 0
\(157\) −10.7181 10.7181i −0.855400 0.855400i 0.135392 0.990792i \(-0.456771\pi\)
−0.990792 + 0.135392i \(0.956771\pi\)
\(158\) −2.53122 2.53122i −0.201373 0.201373i
\(159\) 0 0
\(160\) 1.52773 1.63280i 0.120777 0.129085i
\(161\) 6.11091i 0.481607i
\(162\) 0 0
\(163\) −4.04441 + 4.04441i −0.316783 + 0.316783i −0.847530 0.530747i \(-0.821911\pi\)
0.530747 + 0.847530i \(0.321911\pi\)
\(164\) 10.6798 0.833954
\(165\) 0 0
\(166\) 8.78249 0.681653
\(167\) 5.76929 5.76929i 0.446441 0.446441i −0.447729 0.894169i \(-0.647767\pi\)
0.894169 + 0.447729i \(0.147767\pi\)
\(168\) 0 0
\(169\) 6.97792i 0.536763i
\(170\) 0.321063 + 9.65685i 0.0246244 + 0.740647i
\(171\) 0 0
\(172\) −0.597714 0.597714i −0.0455753 0.0455753i
\(173\) −6.14492 6.14492i −0.467189 0.467189i 0.433813 0.901003i \(-0.357168\pi\)
−0.901003 + 0.433813i \(0.857168\pi\)
\(174\) 0 0
\(175\) −3.76256 3.29289i −0.284423 0.248919i
\(176\) 5.26561i 0.396910i
\(177\) 0 0
\(178\) 2.55913 2.55913i 0.191815 0.191815i
\(179\) 0.391244 0.0292430 0.0146215 0.999893i \(-0.495346\pi\)
0.0146215 + 0.999893i \(0.495346\pi\)
\(180\) 0 0
\(181\) −15.0113 −1.11578 −0.557890 0.829915i \(-0.688389\pi\)
−0.557890 + 0.829915i \(0.688389\pi\)
\(182\) −3.16053 + 3.16053i −0.234274 + 0.234274i
\(183\) 0 0
\(184\) 6.11091i 0.450502i
\(185\) −6.77386 6.33793i −0.498024 0.465974i
\(186\) 0 0
\(187\) 16.0888 + 16.0888i 1.17653 + 1.17653i
\(188\) 3.42614 + 3.42614i 0.249877 + 0.249877i
\(189\) 0 0
\(190\) 0 0
\(191\) 23.3474i 1.68936i 0.535270 + 0.844681i \(0.320210\pi\)
−0.535270 + 0.844681i \(0.679790\pi\)
\(192\) 0 0
\(193\) 6.69059 6.69059i 0.481599 0.481599i −0.424043 0.905642i \(-0.639389\pi\)
0.905642 + 0.424043i \(0.139389\pi\)
\(194\) 6.55672 0.470745
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −0.375629 + 0.375629i −0.0267625 + 0.0267625i −0.720361 0.693599i \(-0.756024\pi\)
0.693599 + 0.720361i \(0.256024\pi\)
\(198\) 0 0
\(199\) 18.0481i 1.27940i −0.768626 0.639698i \(-0.779059\pi\)
0.768626 0.639698i \(-0.220941\pi\)
\(200\) 3.76256 + 3.29289i 0.266053 + 0.232843i
\(201\) 0 0
\(202\) 1.50368 + 1.50368i 0.105798 + 0.105798i
\(203\) −7.04441 7.04441i −0.494421 0.494421i
\(204\) 0 0
\(205\) 0.793530 + 23.8676i 0.0554225 + 1.66699i
\(206\) 15.4467i 1.07622i
\(207\) 0 0
\(208\) 3.16053 3.16053i 0.219143 0.219143i
\(209\) 0 0
\(210\) 0 0
\(211\) −8.22181 −0.566013 −0.283006 0.959118i \(-0.591332\pi\)
−0.283006 + 0.959118i \(0.591332\pi\)
\(212\) −9.88388 + 9.88388i −0.678828 + 0.678828i
\(213\) 0 0
\(214\) 9.06244i 0.619496i
\(215\) 1.29138 1.38020i 0.0880714 0.0941290i
\(216\) 0 0
\(217\) −0.894921 0.894921i −0.0607512 0.0607512i
\(218\) 6.75825 + 6.75825i 0.457726 + 0.457726i
\(219\) 0 0
\(220\) 11.7678 0.391244i 0.793382 0.0263777i
\(221\) 19.3137i 1.29918i
\(222\) 0 0
\(223\) −13.2365 + 13.2365i −0.886384 + 0.886384i −0.994174 0.107789i \(-0.965623\pi\)
0.107789 + 0.994174i \(0.465623\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −4.66421 −0.310259
\(227\) 5.46878 5.46878i 0.362976 0.362976i −0.501932 0.864907i \(-0.667377\pi\)
0.864907 + 0.501932i \(0.167377\pi\)
\(228\) 0 0
\(229\) 13.0966i 0.865445i −0.901527 0.432723i \(-0.857553\pi\)
0.901527 0.432723i \(-0.142447\pi\)
\(230\) −13.6569 + 0.454051i −0.900506 + 0.0299393i
\(231\) 0 0
\(232\) 7.04441 + 7.04441i 0.462488 + 0.462488i
\(233\) 0.642125 + 0.642125i 0.0420670 + 0.0420670i 0.727827 0.685760i \(-0.240530\pi\)
−0.685760 + 0.727827i \(0.740530\pi\)
\(234\) 0 0
\(235\) −7.40229 + 7.91142i −0.482872 + 0.516084i
\(236\) 3.12563i 0.203461i
\(237\) 0 0
\(238\) 3.05545 3.05545i 0.198056 0.198056i
\(239\) −25.4246 −1.64458 −0.822291 0.569068i \(-0.807304\pi\)
−0.822291 + 0.569068i \(0.807304\pi\)
\(240\) 0 0
\(241\) −7.46878 −0.481106 −0.240553 0.970636i \(-0.577329\pi\)
−0.240553 + 0.970636i \(0.577329\pi\)
\(242\) 11.8275 11.8275i 0.760302 0.760302i
\(243\) 0 0
\(244\) 3.05545i 0.195605i
\(245\) 0.0743018 + 2.23483i 0.00474697 + 0.142778i
\(246\) 0 0
\(247\) 0 0
\(248\) 0.894921 + 0.894921i 0.0568276 + 0.0568276i
\(249\) 0 0
\(250\) −7.07950 + 8.65336i −0.447747 + 0.547287i
\(251\) 1.23654i 0.0780497i 0.999238 + 0.0390249i \(0.0124252\pi\)
−0.999238 + 0.0390249i \(0.987575\pi\)
\(252\) 0 0
\(253\) −22.7530 + 22.7530i −1.43047 + 1.43047i
\(254\) 11.7678 0.738375
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.8076 10.8076i 0.674159 0.674159i −0.284513 0.958672i \(-0.591832\pi\)
0.958672 + 0.284513i \(0.0918318\pi\)
\(258\) 0 0
\(259\) 4.14860i 0.257782i
\(260\) 7.29809 + 6.82843i 0.452609 + 0.423481i
\(261\) 0 0
\(262\) 12.3211 + 12.3211i 0.761198 + 0.761198i
\(263\) −6.99265 6.99265i −0.431185 0.431185i 0.457846 0.889031i \(-0.348621\pi\)
−0.889031 + 0.457846i \(0.848621\pi\)
\(264\) 0 0
\(265\) −22.8232 21.3544i −1.40202 1.31179i
\(266\) 0 0
\(267\) 0 0
\(268\) 4.59771 4.59771i 0.280850 0.280850i
\(269\) 21.7374 1.32535 0.662677 0.748905i \(-0.269420\pi\)
0.662677 + 0.748905i \(0.269420\pi\)
\(270\) 0 0
\(271\) −4.98566 −0.302857 −0.151429 0.988468i \(-0.548387\pi\)
−0.151429 + 0.988468i \(0.548387\pi\)
\(272\) −3.05545 + 3.05545i −0.185264 + 0.185264i
\(273\) 0 0
\(274\) 3.33579i 0.201523i
\(275\) 1.74873 + 26.2699i 0.105452 + 1.58414i
\(276\) 0 0
\(277\) 1.80787 + 1.80787i 0.108624 + 0.108624i 0.759330 0.650706i \(-0.225527\pi\)
−0.650706 + 0.759330i \(0.725527\pi\)
\(278\) 15.4467 + 15.4467i 0.926431 + 0.926431i
\(279\) 0 0
\(280\) −0.0743018 2.23483i −0.00444038 0.133557i
\(281\) 8.66296i 0.516789i 0.966040 + 0.258394i \(0.0831934\pi\)
−0.966040 + 0.258394i \(0.916807\pi\)
\(282\) 0 0
\(283\) −1.55760 + 1.55760i −0.0925899 + 0.0925899i −0.751885 0.659295i \(-0.770855\pi\)
0.659295 + 0.751885i \(0.270855\pi\)
\(284\) 9.23654 0.548088
\(285\) 0 0
\(286\) 23.5355 1.39168
\(287\) 7.55178 7.55178i 0.445767 0.445767i
\(288\) 0 0
\(289\) 1.67158i 0.0983284i
\(290\) −15.2197 + 16.2665i −0.893730 + 0.955202i
\(291\) 0 0
\(292\) −10.2160 10.2160i −0.597845 0.597845i
\(293\) 5.39366 + 5.39366i 0.315101 + 0.315101i 0.846882 0.531781i \(-0.178477\pi\)
−0.531781 + 0.846882i \(0.678477\pi\)
\(294\) 0 0
\(295\) 6.98527 0.232240i 0.406698 0.0135215i
\(296\) 4.14860i 0.241133i
\(297\) 0 0
\(298\) −4.30303 + 4.30303i −0.249268 + 0.249268i
\(299\) −27.3137 −1.57959
\(300\) 0 0
\(301\) −0.845296 −0.0487220
\(302\) −16.0888 + 16.0888i −0.925808 + 0.925808i
\(303\) 0 0
\(304\) 0 0
\(305\) 6.82843 0.227026i 0.390995 0.0129994i
\(306\) 0 0
\(307\) −1.46878 1.46878i −0.0838277 0.0838277i 0.663950 0.747777i \(-0.268879\pi\)
−0.747777 + 0.663950i \(0.768879\pi\)
\(308\) −3.72335 3.72335i −0.212157 0.212157i
\(309\) 0 0
\(310\) −1.93351 + 2.06649i −0.109816 + 0.117369i
\(311\) 30.9822i 1.75684i −0.477889 0.878420i \(-0.658598\pi\)
0.477889 0.878420i \(-0.341402\pi\)
\(312\) 0 0
\(313\) 6.74720 6.74720i 0.381375 0.381375i −0.490223 0.871597i \(-0.663085\pi\)
0.871597 + 0.490223i \(0.163085\pi\)
\(314\) 15.1577 0.855400
\(315\) 0 0
\(316\) 3.57969 0.201373
\(317\) 20.4151 20.4151i 1.14663 1.14663i 0.159415 0.987212i \(-0.449039\pi\)
0.987212 0.159415i \(-0.0509606\pi\)
\(318\) 0 0
\(319\) 52.4576i 2.93706i
\(320\) 0.0743018 + 2.23483i 0.00415360 + 0.124931i
\(321\) 0 0
\(322\) 4.32106 + 4.32106i 0.240803 + 0.240803i
\(323\) 0 0
\(324\) 0 0
\(325\) −14.7181 + 16.8174i −0.816415 + 0.932861i
\(326\) 5.71966i 0.316783i
\(327\) 0 0
\(328\) −7.55178 + 7.55178i −0.416977 + 0.416977i
\(329\) 4.84530 0.267130
\(330\) 0 0
\(331\) −18.2513 −1.00318 −0.501590 0.865105i \(-0.667251\pi\)
−0.501590 + 0.865105i \(0.667251\pi\)
\(332\) −6.21016 + 6.21016i −0.340827 + 0.340827i
\(333\) 0 0
\(334\) 8.15900i 0.446441i
\(335\) 10.6167 + 9.93351i 0.580055 + 0.542725i
\(336\) 0 0
\(337\) −7.21016 7.21016i −0.392762 0.392762i 0.482909 0.875671i \(-0.339580\pi\)
−0.875671 + 0.482909i \(0.839580\pi\)
\(338\) 4.93413 + 4.93413i 0.268381 + 0.268381i
\(339\) 0 0
\(340\) −7.05545 6.60140i −0.382636 0.358011i
\(341\) 6.66421i 0.360887i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0.845296 0.0455753
\(345\) 0 0
\(346\) 8.69022 0.467189
\(347\) 10.8284 10.8284i 0.581300 0.581300i −0.353960 0.935261i \(-0.615165\pi\)
0.935261 + 0.353960i \(0.115165\pi\)
\(348\) 0 0
\(349\) 16.0598i 0.859659i 0.902910 + 0.429829i \(0.141426\pi\)
−0.902910 + 0.429829i \(0.858574\pi\)
\(350\) 4.98896 0.332104i 0.266671 0.0177517i
\(351\) 0 0
\(352\) 3.72335 + 3.72335i 0.198455 + 0.198455i
\(353\) 9.26561 + 9.26561i 0.493159 + 0.493159i 0.909300 0.416141i \(-0.136618\pi\)
−0.416141 + 0.909300i \(0.636618\pi\)
\(354\) 0 0
\(355\) 0.686292 + 20.6421i 0.0364246 + 1.09557i
\(356\) 3.61916i 0.191815i
\(357\) 0 0
\(358\) −0.276651 + 0.276651i −0.0146215 + 0.0146215i
\(359\) −7.35787 −0.388334 −0.194167 0.980969i \(-0.562200\pi\)
−0.194167 + 0.980969i \(0.562200\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 10.6146 10.6146i 0.557890 0.557890i
\(363\) 0 0
\(364\) 4.46967i 0.234274i
\(365\) 22.0720 23.5901i 1.15530 1.23476i
\(366\) 0 0
\(367\) 23.1443 + 23.1443i 1.20812 + 1.20812i 0.971635 + 0.236487i \(0.0759959\pi\)
0.236487 + 0.971635i \(0.424004\pi\)
\(368\) −4.32106 4.32106i −0.225251 0.225251i
\(369\) 0 0
\(370\) 9.27144 0.308249i 0.481999 0.0160251i
\(371\) 13.9779i 0.725697i
\(372\) 0 0
\(373\) 0.0812231 0.0812231i 0.00420557 0.00420557i −0.705001 0.709206i \(-0.749053\pi\)
0.709206 + 0.705001i \(0.249053\pi\)
\(374\) −22.7530 −1.17653
\(375\) 0 0
\(376\) −4.84530 −0.249877
\(377\) −31.4862 + 31.4862i −1.62162 + 1.62162i
\(378\) 0 0
\(379\) 12.3548i 0.634623i 0.948321 + 0.317312i \(0.102780\pi\)
−0.948321 + 0.317312i \(0.897220\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −16.5091 16.5091i −0.844681 0.844681i
\(383\) 11.7546 + 11.7546i 0.600631 + 0.600631i 0.940480 0.339849i \(-0.110376\pi\)
−0.339849 + 0.940480i \(0.610376\pi\)
\(384\) 0 0
\(385\) 8.04441 8.59771i 0.409981 0.438180i
\(386\) 9.46192i 0.481599i
\(387\) 0 0
\(388\) −4.63630 + 4.63630i −0.235372 + 0.235372i
\(389\) −11.4960 −0.582873 −0.291436 0.956590i \(-0.594133\pi\)
−0.291436 + 0.956590i \(0.594133\pi\)
\(390\) 0 0
\(391\) 26.4056 1.33539
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 0.531220i 0.0267625i
\(395\) 0.265977 + 8.00000i 0.0133828 + 0.402524i
\(396\) 0 0
\(397\) −11.2424 11.2424i −0.564238 0.564238i 0.366270 0.930509i \(-0.380635\pi\)
−0.930509 + 0.366270i \(0.880635\pi\)
\(398\) 12.7619 + 12.7619i 0.639698 + 0.639698i
\(399\) 0 0
\(400\) −4.98896 + 0.332104i −0.249448 + 0.0166052i
\(401\) 29.5269i 1.47450i 0.675619 + 0.737251i \(0.263877\pi\)
−0.675619 + 0.737251i \(0.736123\pi\)
\(402\) 0 0
\(403\) −4.00000 + 4.00000i −0.199254 + 0.199254i
\(404\) −2.12652 −0.105798
\(405\) 0 0
\(406\) 9.96230 0.494421
\(407\) 15.4467 15.4467i 0.765664 0.765664i
\(408\) 0 0
\(409\) 26.2916i 1.30004i −0.759919 0.650018i \(-0.774761\pi\)
0.759919 0.650018i \(-0.225239\pi\)
\(410\) −17.4381 16.3158i −0.861205 0.805782i
\(411\) 0 0
\(412\) 10.9225 + 10.9225i 0.538111 + 0.538111i
\(413\) −2.21016 2.21016i −0.108755 0.108755i
\(414\) 0 0
\(415\) −14.3401 13.4172i −0.703927 0.658626i
\(416\) 4.46967i 0.219143i
\(417\) 0 0
\(418\) 0 0
\(419\) 20.5980 1.00628 0.503138 0.864206i \(-0.332179\pi\)
0.503138 + 0.864206i \(0.332179\pi\)
\(420\) 0 0
\(421\) −1.73402 −0.0845111 −0.0422556 0.999107i \(-0.513454\pi\)
−0.0422556 + 0.999107i \(0.513454\pi\)
\(422\) 5.81370 5.81370i 0.283006 0.283006i
\(423\) 0 0
\(424\) 13.9779i 0.678828i
\(425\) 14.2288 16.2583i 0.690198 0.788641i
\(426\) 0 0
\(427\) −2.16053 2.16053i −0.104555 0.104555i
\(428\) 6.40811 + 6.40811i 0.309748 + 0.309748i
\(429\) 0 0
\(430\) 0.0628070 + 1.88909i 0.00302882 + 0.0911002i
\(431\) 1.70102i 0.0819353i −0.999160 0.0409676i \(-0.986956\pi\)
0.999160 0.0409676i \(-0.0130441\pi\)
\(432\) 0 0
\(433\) 2.88757 2.88757i 0.138768 0.138768i −0.634311 0.773078i \(-0.718716\pi\)
0.773078 + 0.634311i \(0.218716\pi\)
\(434\) 1.26561 0.0607512
\(435\) 0 0
\(436\) −9.55760 −0.457726
\(437\) 0 0
\(438\) 0 0
\(439\) 32.8011i 1.56551i −0.622328 0.782756i \(-0.713813\pi\)
0.622328 0.782756i \(-0.286187\pi\)
\(440\) −8.04441 + 8.59771i −0.383502 + 0.409880i
\(441\) 0 0
\(442\) −13.6569 13.6569i −0.649590 0.649590i
\(443\) 20.0650 + 20.0650i 0.953315 + 0.953315i 0.998958 0.0456425i \(-0.0145335\pi\)
−0.0456425 + 0.998958i \(0.514534\pi\)
\(444\) 0 0
\(445\) −8.08821 + 0.268910i −0.383418 + 0.0127475i
\(446\) 18.7193i 0.886384i
\(447\) 0 0
\(448\) 0.707107 0.707107i 0.0334077 0.0334077i
\(449\) −11.9767 −0.565214 −0.282607 0.959236i \(-0.591199\pi\)
−0.282607 + 0.959236i \(0.591199\pi\)
\(450\) 0 0
\(451\) −56.2358 −2.64804
\(452\) 3.29809 3.29809i 0.155129 0.155129i
\(453\) 0 0
\(454\) 7.73402i 0.362976i
\(455\) 9.98896 0.332104i 0.468290 0.0155693i
\(456\) 0 0
\(457\) 6.46878 + 6.46878i 0.302597 + 0.302597i 0.842029 0.539432i \(-0.181361\pi\)
−0.539432 + 0.842029i \(0.681361\pi\)
\(458\) 9.26067 + 9.26067i 0.432723 + 0.432723i
\(459\) 0 0
\(460\) 9.33579 9.97792i 0.435284 0.465223i
\(461\) 37.0915i 1.72752i −0.503901 0.863761i \(-0.668102\pi\)
0.503901 0.863761i \(-0.331898\pi\)
\(462\) 0 0
\(463\) −0.232240 + 0.232240i −0.0107931 + 0.0107931i −0.712483 0.701690i \(-0.752429\pi\)
0.701690 + 0.712483i \(0.252429\pi\)
\(464\) −9.96230 −0.462488
\(465\) 0 0
\(466\) −0.908103 −0.0420670
\(467\) −22.1997 + 22.1997i −1.02728 + 1.02728i −0.0276636 + 0.999617i \(0.508807\pi\)
−0.999617 + 0.0276636i \(0.991193\pi\)
\(468\) 0 0
\(469\) 6.50215i 0.300241i
\(470\) −0.360014 10.8284i −0.0166062 0.499478i
\(471\) 0 0
\(472\) 2.21016 + 2.21016i 0.101731 + 0.101731i
\(473\) 3.14733 + 3.14733i 0.144714 + 0.144714i
\(474\) 0 0
\(475\) 0 0
\(476\) 4.32106i 0.198056i
\(477\) 0 0
\(478\) 17.9779 17.9779i 0.822291 0.822291i
\(479\) −20.7751 −0.949239 −0.474620 0.880191i \(-0.657414\pi\)
−0.474620 + 0.880191i \(0.657414\pi\)
\(480\) 0 0
\(481\) 18.5429 0.845482
\(482\) 5.28123 5.28123i 0.240553 0.240553i
\(483\) 0 0
\(484\) 16.7266i 0.760302i
\(485\) −10.7058 10.0169i −0.486127 0.454843i
\(486\) 0 0
\(487\) −1.00735 1.00735i −0.0456476 0.0456476i 0.683915 0.729562i \(-0.260276\pi\)
−0.729562 + 0.683915i \(0.760276\pi\)
\(488\) 2.16053 + 2.16053i 0.0978027 + 0.0978027i
\(489\) 0 0
\(490\) −1.63280 1.52773i −0.0737626 0.0690156i
\(491\) 6.95620i 0.313929i −0.987604 0.156964i \(-0.949829\pi\)
0.987604 0.156964i \(-0.0501708\pi\)
\(492\) 0 0
\(493\) 30.4393 30.4393i 1.37092 1.37092i
\(494\) 0 0
\(495\) 0 0
\(496\) −1.26561 −0.0568276
\(497\) 6.53122 6.53122i 0.292965 0.292965i
\(498\) 0 0
\(499\) 20.9969i 0.939951i −0.882679 0.469976i \(-0.844263\pi\)
0.882679 0.469976i \(-0.155737\pi\)
\(500\) −1.11289 11.1248i −0.0497698 0.497517i
\(501\) 0 0
\(502\) −0.874366 0.874366i −0.0390249 0.0390249i
\(503\) −7.29315 7.29315i −0.325186 0.325186i 0.525567 0.850752i \(-0.323853\pi\)
−0.850752 + 0.525567i \(0.823853\pi\)
\(504\) 0 0
\(505\) −0.158004 4.75242i −0.00703110 0.211480i
\(506\) 32.1776i 1.43047i
\(507\) 0 0
\(508\) −8.32106 + 8.32106i −0.369187 + 0.369187i
\(509\) −0.545062 −0.0241595 −0.0120797 0.999927i \(-0.503845\pi\)
−0.0120797 + 0.999927i \(0.503845\pi\)
\(510\) 0 0
\(511\) −14.4476 −0.639123
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 15.2843i 0.674159i
\(515\) −23.5983 + 25.2214i −1.03987 + 1.11139i
\(516\) 0 0
\(517\) −18.0407 18.0407i −0.793430 0.793430i
\(518\) −2.93351 2.93351i −0.128891 0.128891i
\(519\) 0 0
\(520\) −9.98896 + 0.332104i −0.438045 + 0.0145637i
\(521\) 21.6963i 0.950533i −0.879842 0.475267i \(-0.842352\pi\)
0.879842 0.475267i \(-0.157648\pi\)
\(522\) 0 0
\(523\) 26.9822 26.9822i 1.17985 1.17985i 0.200068 0.979782i \(-0.435884\pi\)
0.979782 0.200068i \(-0.0641163\pi\)
\(524\) −17.4246 −0.761198
\(525\) 0 0
\(526\) 9.88909 0.431185
\(527\) 3.86701 3.86701i 0.168450 0.168450i
\(528\) 0 0
\(529\) 14.3432i 0.623616i
\(530\) 31.2383 1.03858i 1.35691 0.0451132i
\(531\) 0 0
\(532\) 0 0
\(533\) −33.7539 33.7539i −1.46204 1.46204i
\(534\) 0 0
\(535\) −13.8449 + 14.7972i −0.598568 + 0.639739i
\(536\) 6.50215i 0.280850i
\(537\) 0 0
\(538\) −15.3707 + 15.3707i −0.662677 + 0.662677i
\(539\) −5.26561 −0.226806
\(540\) 0 0
\(541\) −15.2249 −0.654569 −0.327284 0.944926i \(-0.606134\pi\)
−0.327284 + 0.944926i \(0.606134\pi\)
\(542\) 3.52539 3.52539i 0.151429 0.151429i
\(543\) 0 0
\(544\) 4.32106i 0.185264i
\(545\) −0.710147 21.3596i −0.0304194 0.914947i
\(546\) 0 0
\(547\) 6.84898 + 6.84898i 0.292841 + 0.292841i 0.838202 0.545360i \(-0.183607\pi\)
−0.545360 + 0.838202i \(0.683607\pi\)
\(548\) −2.35876 2.35876i −0.100761 0.100761i
\(549\) 0 0
\(550\) −19.8122 17.3391i −0.844794 0.739341i
\(551\) 0 0
\(552\) 0 0
\(553\) 2.53122 2.53122i 0.107638 0.107638i
\(554\) −2.55672 −0.108624
\(555\) 0 0
\(556\) −21.8449 −0.926431
\(557\) −25.8839 + 25.8839i −1.09674 + 1.09674i −0.101945 + 0.994790i \(0.532507\pi\)
−0.994790 + 0.101945i \(0.967493\pi\)
\(558\) 0 0
\(559\) 3.77819i 0.159800i
\(560\) 1.63280 + 1.52773i 0.0689986 + 0.0645582i
\(561\) 0 0
\(562\) −6.12563 6.12563i −0.258394 0.258394i
\(563\) 14.9926 + 14.9926i 0.631865 + 0.631865i 0.948535 0.316671i \(-0.102565\pi\)
−0.316671 + 0.948535i \(0.602565\pi\)
\(564\) 0 0
\(565\) 7.61574 + 7.12563i 0.320397 + 0.299778i
\(566\) 2.20278i 0.0925899i
\(567\) 0 0
\(568\) −6.53122 + 6.53122i −0.274044 + 0.274044i
\(569\) 4.97742 0.208664 0.104332 0.994543i \(-0.466730\pi\)
0.104332 + 0.994543i \(0.466730\pi\)
\(570\) 0 0
\(571\) 34.6949 1.45194 0.725968 0.687728i \(-0.241392\pi\)
0.725968 + 0.687728i \(0.241392\pi\)
\(572\) −16.6421 + 16.6421i −0.695842 + 0.695842i
\(573\) 0 0
\(574\) 10.6798i 0.445767i
\(575\) 22.9926 + 20.1226i 0.958860 + 0.839169i
\(576\) 0 0
\(577\) 32.5782 + 32.5782i 1.35625 + 1.35625i 0.878495 + 0.477751i \(0.158548\pi\)
0.477751 + 0.878495i \(0.341452\pi\)
\(578\) 1.18199 + 1.18199i 0.0491642 + 0.0491642i
\(579\) 0 0
\(580\) −0.740217 22.2641i −0.0307358 0.924466i
\(581\) 8.78249i 0.364359i
\(582\) 0 0
\(583\) 52.0447 52.0447i 2.15547 2.15547i
\(584\) 14.4476 0.597845
\(585\) 0 0
\(586\) −7.62778 −0.315101
\(587\) 18.4320 18.4320i 0.760769 0.760769i −0.215693 0.976461i \(-0.569201\pi\)
0.976461 + 0.215693i \(0.0692009\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −4.77511 + 5.10355i −0.196588 + 0.210110i
\(591\) 0 0
\(592\) 2.93351 + 2.93351i 0.120566 + 0.120566i
\(593\) 22.1213 + 22.1213i 0.908413 + 0.908413i 0.996144 0.0877310i \(-0.0279616\pi\)
−0.0877310 + 0.996144i \(0.527962\pi\)
\(594\) 0 0
\(595\) −9.65685 + 0.321063i −0.395892 + 0.0131623i
\(596\) 6.08541i 0.249268i
\(597\) 0 0
\(598\) 19.3137 19.3137i 0.789796 0.789796i
\(599\) −17.6906 −0.722818 −0.361409 0.932407i \(-0.617704\pi\)
−0.361409 + 0.932407i \(0.617704\pi\)
\(600\) 0 0
\(601\) 18.6979 0.762705 0.381353 0.924430i \(-0.375458\pi\)
0.381353 + 0.924430i \(0.375458\pi\)
\(602\) 0.597714 0.597714i 0.0243610 0.0243610i
\(603\) 0 0
\(604\) 22.7530i 0.925808i
\(605\) −37.3813 + 1.24282i −1.51976 + 0.0505278i
\(606\) 0 0
\(607\) 5.23654 + 5.23654i 0.212545 + 0.212545i 0.805348 0.592803i \(-0.201979\pi\)
−0.592803 + 0.805348i \(0.701979\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −4.66790 + 4.98896i −0.188998 + 0.201997i
\(611\) 21.6569i 0.876143i
\(612\) 0 0
\(613\) 21.4426 21.4426i 0.866060 0.866060i −0.125973 0.992034i \(-0.540205\pi\)
0.992034 + 0.125973i \(0.0402054\pi\)
\(614\) 2.07717 0.0838277
\(615\) 0 0
\(616\) 5.26561 0.212157
\(617\) 2.18109 2.18109i 0.0878073 0.0878073i −0.661839 0.749646i \(-0.730224\pi\)
0.749646 + 0.661839i \(0.230224\pi\)
\(618\) 0 0
\(619\) 19.7573i 0.794114i 0.917794 + 0.397057i \(0.129969\pi\)
−0.917794 + 0.397057i \(0.870031\pi\)
\(620\) −0.0940371 2.82843i −0.00377662 0.113592i
\(621\) 0 0
\(622\) 21.9077 + 21.9077i 0.878420 + 0.878420i
\(623\) 2.55913 + 2.55913i 0.102529 + 0.102529i
\(624\) 0 0
\(625\) 24.7794 3.31371i 0.991177 0.132548i
\(626\) 9.54199i 0.381375i
\(627\) 0 0
\(628\) −10.7181 + 10.7181i −0.427700 + 0.427700i
\(629\) −17.9264 −0.714771
\(630\) 0 0
\(631\) 2.15507 0.0857920 0.0428960 0.999080i \(-0.486342\pi\)
0.0428960 + 0.999080i \(0.486342\pi\)
\(632\) −2.53122 + 2.53122i −0.100687 + 0.100687i
\(633\) 0 0
\(634\) 28.8713i 1.14663i
\(635\) −19.2145 17.9779i −0.762502 0.713432i
\(636\) 0 0
\(637\) −3.16053 3.16053i −0.125225 0.125225i
\(638\) −37.0931 37.0931i −1.46853 1.46853i
\(639\) 0 0
\(640\) −1.63280 1.52773i −0.0645423 0.0603887i
\(641\) 39.5147i 1.56074i 0.625320 + 0.780368i \(0.284968\pi\)
−0.625320 + 0.780368i \(0.715032\pi\)
\(642\) 0 0
\(643\) 9.61574 9.61574i 0.379208 0.379208i −0.491608 0.870816i \(-0.663591\pi\)
0.870816 + 0.491608i \(0.163591\pi\)
\(644\) −6.11091 −0.240803
\(645\) 0 0
\(646\) 0 0
\(647\) −14.6510 + 14.6510i −0.575991 + 0.575991i −0.933796 0.357805i \(-0.883525\pi\)
0.357805 + 0.933796i \(0.383525\pi\)
\(648\) 0 0
\(649\) 16.4584i 0.646048i
\(650\) −1.48440 22.2990i −0.0582228 0.874638i
\(651\) 0 0
\(652\) 4.04441 + 4.04441i 0.158391 + 0.158391i
\(653\) −32.0836 32.0836i −1.25553 1.25553i −0.953206 0.302323i \(-0.902238\pi\)
−0.302323 0.953206i \(-0.597762\pi\)
\(654\) 0 0
\(655\) −1.29468 38.9411i −0.0505873 1.52155i
\(656\) 10.6798i 0.416977i
\(657\) 0 0
\(658\) −3.42614 + 3.42614i −0.133565 + 0.133565i
\(659\) −38.5499 −1.50169 −0.750845 0.660479i \(-0.770353\pi\)
−0.750845 + 0.660479i \(0.770353\pi\)
\(660\) 0 0
\(661\) −39.4176 −1.53317 −0.766584 0.642144i \(-0.778045\pi\)
−0.766584 + 0.642144i \(0.778045\pi\)
\(662\) 12.9056 12.9056i 0.501590 0.501590i
\(663\) 0 0
\(664\) 8.78249i 0.340827i
\(665\) 0 0
\(666\) 0 0
\(667\) 43.0477 + 43.0477i 1.66681 + 1.66681i
\(668\) −5.76929 5.76929i −0.223220 0.223220i
\(669\) 0 0
\(670\) −14.5312 + 0.483121i −0.561390 + 0.0186646i
\(671\) 16.0888i 0.621102i
\(672\) 0 0
\(673\) −13.3431 + 13.3431i −0.514340 + 0.514340i −0.915853 0.401513i \(-0.868484\pi\)
0.401513 + 0.915853i \(0.368484\pi\)
\(674\) 10.1967 0.392762
\(675\) 0 0
\(676\) −6.97792 −0.268381
\(677\) −18.1024 + 18.1024i −0.695731 + 0.695731i −0.963487 0.267755i \(-0.913718\pi\)
0.267755 + 0.963487i \(0.413718\pi\)
\(678\) 0 0
\(679\) 6.55672i 0.251624i
\(680\) 9.65685 0.321063i 0.370323 0.0123122i
\(681\) 0 0
\(682\) −4.71231 4.71231i −0.180444 0.180444i
\(683\) −27.4077 27.4077i −1.04873 1.04873i −0.998750 0.0499779i \(-0.984085\pi\)
−0.0499779 0.998750i \(-0.515915\pi\)
\(684\) 0 0
\(685\) 5.09618 5.44670i 0.194715 0.208108i
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −0.597714 + 0.597714i −0.0227876 + 0.0227876i
\(689\) 62.4766 2.38017
\(690\) 0 0
\(691\) −12.9221 −0.491579 −0.245789 0.969323i \(-0.579047\pi\)
−0.245789 + 0.969323i \(0.579047\pi\)
\(692\) −6.14492 + 6.14492i −0.233595 + 0.233595i
\(693\) 0 0
\(694\) 15.3137i 0.581300i
\(695\) −1.62312 48.8198i −0.0615684 1.85184i
\(696\) 0 0
\(697\) 32.6317 + 32.6317i 1.23601 + 1.23601i
\(698\) −11.3560 11.3560i −0.429829 0.429829i
\(699\) 0 0
\(700\) −3.29289 + 3.76256i −0.124460 + 0.142211i
\(701\) 13.5732i 0.512653i 0.966590 + 0.256327i \(0.0825123\pi\)
−0.966590 + 0.256327i \(0.917488\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −5.26561 −0.198455
\(705\) 0 0
\(706\) −13.1036 −0.493159
\(707\) −1.50368 + 1.50368i −0.0565516 + 0.0565516i
\(708\) 0 0
\(709\) 40.4429i 1.51886i 0.650586 + 0.759432i \(0.274523\pi\)
−0.650586 + 0.759432i \(0.725477\pi\)
\(710\) −15.0815 14.1109i −0.565997 0.529573i
\(711\) 0 0
\(712\) −2.55913 2.55913i −0.0959074 0.0959074i
\(713\) 5.46878 + 5.46878i 0.204807 + 0.204807i
\(714\) 0 0
\(715\) −38.4289 35.9558i −1.43716 1.34467i
\(716\) 0.391244i 0.0146215i
\(717\) 0 0
\(718\) 5.20280 5.20280i 0.194167 0.194167i
\(719\) −16.9706 −0.632895 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 0 0
\(721\) 15.4467 0.575265
\(722\) −13.4350 + 13.4350i −0.500000 + 0.500000i
\(723\) 0 0
\(724\) 15.0113i 0.557890i
\(725\) 49.7015 3.30852i 1.84587 0.122875i
\(726\) 0 0
\(727\) −29.8787 29.8787i −1.10814 1.10814i −0.993395 0.114743i \(-0.963395\pi\)
−0.114743 0.993395i \(-0.536605\pi\)
\(728\) 3.16053 + 3.16053i 0.117137 + 0.117137i
\(729\) 0 0
\(730\) 1.07348 + 32.2879i 0.0397313 + 1.19503i
\(731\) 3.65258i 0.135095i
\(732\) 0 0
\(733\) −8.55913 + 8.55913i −0.316139 + 0.316139i −0.847282 0.531143i \(-0.821763\pi\)
0.531143 + 0.847282i \(0.321763\pi\)
\(734\) −32.7309 −1.20812
\(735\) 0 0
\(736\) 6.11091 0.225251
\(737\) −24.2098 + 24.2098i −0.891778 + 0.891778i
\(738\) 0 0
\(739\) 35.3584i 1.30068i −0.759644 0.650339i \(-0.774627\pi\)
0.759644 0.650339i \(-0.225373\pi\)
\(740\) −6.33793 + 6.77386i −0.232987 + 0.249012i
\(741\) 0 0
\(742\) −9.88388 9.88388i −0.362849 0.362849i
\(743\) 35.1733 + 35.1733i 1.29038 + 1.29038i 0.934548 + 0.355837i \(0.115804\pi\)
0.355837 + 0.934548i \(0.384196\pi\)
\(744\) 0 0
\(745\) 13.5999 0.452157i 0.498261 0.0165657i
\(746\) 0.114867i 0.00420557i
\(747\) 0 0
\(748\) 16.0888 16.0888i 0.588266 0.588266i
\(749\) 9.06244 0.331134
\(750\) 0 0
\(751\) 16.2358 0.592452 0.296226 0.955118i \(-0.404272\pi\)
0.296226 + 0.955118i \(0.404272\pi\)
\(752\) 3.42614 3.42614i 0.124939 0.124939i
\(753\) 0 0
\(754\) 44.5282i 1.62162i
\(755\) 50.8492 1.69059i 1.85059 0.0615269i
\(756\) 0 0
\(757\) −1.76016 1.76016i −0.0639741 0.0639741i 0.674396 0.738370i \(-0.264404\pi\)
−0.738370 + 0.674396i \(0.764404\pi\)
\(758\) −8.73616 8.73616i −0.317312 0.317312i
\(759\) 0 0
\(760\) 0 0
\(761\) 29.0125i 1.05170i 0.850576 + 0.525852i \(0.176253\pi\)
−0.850576 + 0.525852i \(0.823747\pi\)
\(762\) 0 0
\(763\) −6.75825 + 6.75825i −0.244665 + 0.244665i
\(764\) 23.3474 0.844681
\(765\) 0 0
\(766\) −16.6235 −0.600631
\(767\) −9.87867 + 9.87867i −0.356698 + 0.356698i
\(768\) 0 0
\(769\) 29.2439i 1.05456i 0.849691 + 0.527281i \(0.176789\pi\)
−0.849691 + 0.527281i \(0.823211\pi\)
\(770\) 0.391244 + 11.7678i 0.0140995 + 0.424081i
\(771\) 0 0
\(772\) −6.69059 6.69059i −0.240800 0.240800i
\(773\) 8.95467 + 8.95467i 0.322077 + 0.322077i 0.849564 0.527486i \(-0.176865\pi\)
−0.527486 + 0.849564i \(0.676865\pi\)
\(774\) 0 0
\(775\) 6.31408 0.420314i 0.226808 0.0150981i
\(776\) 6.55672i 0.235372i
\(777\) 0 0
\(778\) 8.12893 8.12893i 0.291436 0.291436i
\(779\) 0 0
\(780\) 0 0
\(781\) −48.6360 −1.74033
\(782\) −18.6716 + 18.6716i −0.667694 + 0.667694i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) −24.7496 23.1569i −0.883352 0.826504i
\(786\) 0 0
\(787\) −29.9264 29.9264i −1.06676 1.06676i −0.997606 0.0691541i \(-0.977970\pi\)
−0.0691541 0.997606i \(-0.522030\pi\)
\(788\) 0.375629 + 0.375629i 0.0133812 + 0.0133812i
\(789\) 0 0
\(790\) −5.84493 5.46878i −0.207953 0.194570i
\(791\) 4.66421i 0.165840i
\(792\) 0 0
\(793\) −9.65685 + 9.65685i −0.342925 + 0.342925i
\(794\) 15.8991 0.564238
\(795\) 0 0
\(796\) −18.0481 −0.639698
\(797\) −7.21473 + 7.21473i −0.255559 + 0.255559i −0.823245 0.567686i \(-0.807839\pi\)
0.567686 + 0.823245i \(0.307839\pi\)
\(798\) 0 0
\(799\) 20.9368i 0.740692i
\(800\) 3.29289 3.76256i 0.116421 0.133027i
\(801\) 0 0
\(802\) −20.8787 20.8787i −0.737251 0.737251i
\(803\) 53.7934 + 53.7934i 1.89833 + 1.89833i
\(804\) 0 0
\(805\) −0.454051 13.6569i −0.0160032 0.481341i
\(806\) 5.65685i 0.199254i
\(807\) 0 0
\(808\) 1.50368 1.50368i 0.0528992 0.0528992i
\(809\) 33.5606 1.17993 0.589964 0.807429i \(-0.299142\pi\)
0.589964 + 0.807429i \(0.299142\pi\)
\(810\) 0 0
\(811\) 44.7236 1.57046 0.785229 0.619206i \(-0.212545\pi\)
0.785229 + 0.619206i \(0.212545\pi\)
\(812\) −7.04441 + 7.04441i −0.247210 + 0.247210i
\(813\) 0 0
\(814\) 21.8449i 0.765664i
\(815\) −8.73808 + 9.33909i −0.306081 + 0.327134i
\(816\) 0 0
\(817\) 0 0
\(818\) 18.5910 + 18.5910i 0.650018 + 0.650018i
\(819\) 0 0
\(820\) 23.8676 0.793530i 0.833494 0.0277113i
\(821\) 47.8955i 1.67156i −0.549061 0.835782i \(-0.685015\pi\)
0.549061 0.835782i \(-0.314985\pi\)
\(822\) 0 0
\(823\) −37.8926 + 37.8926i −1.32085 + 1.32085i −0.407769 + 0.913085i \(0.633693\pi\)
−0.913085 + 0.407769i \(0.866307\pi\)
\(824\) −15.4467 −0.538111
\(825\) 0 0
\(826\) 3.12563 0.108755
\(827\) 13.7405 13.7405i 0.477803 0.477803i −0.426626 0.904428i \(-0.640298\pi\)
0.904428 + 0.426626i \(0.140298\pi\)
\(828\) 0 0
\(829\) 12.9445i 0.449583i −0.974407 0.224791i \(-0.927830\pi\)
0.974407 0.224791i \(-0.0721701\pi\)
\(830\) 19.6274 0.652555i 0.681277 0.0226505i
\(831\) 0 0
\(832\) −3.16053 3.16053i −0.109572 0.109572i
\(833\) 3.05545 + 3.05545i 0.105865 + 0.105865i
\(834\) 0 0
\(835\) 12.4647 13.3221i 0.431360 0.461029i
\(836\) 0 0
\(837\) 0 0
\(838\) −14.5650 + 14.5650i −0.503138 + 0.503138i
\(839\) 6.27763 0.216728 0.108364 0.994111i \(-0.465439\pi\)
0.108364 + 0.994111i \(0.465439\pi\)
\(840\) 0 0
\(841\) 70.2475 2.42233
\(842\) 1.22614 1.22614i 0.0422556 0.0422556i
\(843\) 0 0
\(844\) 8.22181i 0.283006i
\(845\) −0.518472 15.5945i −0.0178360 0.536466i
\(846\) 0 0
\(847\) 11.8275 + 11.8275i 0.406399 + 0.406399i
\(848\) 9.88388 + 9.88388i 0.339414 + 0.339414i
\(849\) 0 0
\(850\) 1.43504 + 21.5576i 0.0492216 + 0.739420i
\(851\) 25.3517i 0.869046i
\(852\) 0 0
\(853\) 16.2350 16.2350i 0.555876 0.555876i −0.372254 0.928131i \(-0.621415\pi\)
0.928131 + 0.372254i \(0.121415\pi\)
\(854\) 3.05545 0.104555
\(855\) 0 0
\(856\) −9.06244 −0.309748
\(857\) −33.9488 + 33.9488i −1.15967 + 1.15967i −0.175124 + 0.984546i \(0.556033\pi\)
−0.984546 + 0.175124i \(0.943967\pi\)
\(858\) 0 0
\(859\) 50.2444i 1.71432i 0.515053 + 0.857158i \(0.327772\pi\)
−0.515053 + 0.857158i \(0.672228\pi\)
\(860\) −1.38020 1.29138i −0.0470645 0.0440357i
\(861\) 0 0
\(862\) 1.20280 + 1.20280i 0.0409676 + 0.0409676i
\(863\) 7.09190 + 7.09190i 0.241411 + 0.241411i 0.817434 0.576023i \(-0.195396\pi\)
−0.576023 + 0.817434i \(0.695396\pi\)
\(864\) 0 0
\(865\) −14.1894 13.2763i −0.482455 0.451407i
\(866\) 4.08364i 0.138768i
\(867\) 0 0
\(868\) −0.894921 + 0.894921i −0.0303756 + 0.0303756i
\(869\) −18.8492 −0.639416
\(870\) 0 0
\(871\) −29.0624 −0.984743
\(872\) 6.75825 6.75825i 0.228863 0.228863i
\(873\) 0 0
\(874\) 0 0
\(875\) −8.65336 7.07950i −0.292537 0.239331i
\(876\) 0 0
\(877\) 29.0150 + 29.0150i 0.979765 + 0.979765i 0.999799 0.0200339i \(-0.00637743\pi\)
−0.0200339 + 0.999799i \(0.506377\pi\)
\(878\) 23.1939 + 23.1939i 0.782756 + 0.782756i
\(879\) 0 0
\(880\) −0.391244 11.7678i −0.0131888 0.396691i
\(881\) 15.5887i 0.525197i −0.964905 0.262598i \(-0.915421\pi\)
0.964905 0.262598i \(-0.0845794\pi\)
\(882\) 0 0
\(883\) 22.8048 22.8048i 0.767443 0.767443i −0.210213 0.977656i \(-0.567416\pi\)
0.977656 + 0.210213i \(0.0674156\pi\)
\(884\) 19.3137 0.649590
\(885\) 0 0
\(886\) −28.3761 −0.953315
\(887\) 16.2013 16.2013i 0.543985 0.543985i −0.380710 0.924695i \(-0.624320\pi\)
0.924695 + 0.380710i \(0.124320\pi\)
\(888\) 0 0
\(889\) 11.7678i 0.394678i
\(890\) 5.52908 5.90938i 0.185335 0.198083i
\(891\) 0 0
\(892\) 13.2365 + 13.2365i 0.443192 + 0.443192i
\(893\) 0 0
\(894\) 0 0
\(895\) 0.874366 0.0290702i 0.0292268 0.000971708i
\(896\) 1.00000i 0.0334077i
\(897\) 0 0
\(898\) 8.46878 8.46878i 0.282607 0.282607i
\(899\) 12.6084 0.420513
\(900\) 0 0
\(901\) −60.3995 −2.01220
\(902\) 39.7647 39.7647i 1.32402 1.32402i
\(903\) 0 0
\(904\) 4.66421i 0.155129i
\(905\) −33.5477 + 1.11537i −1.11516 + 0.0370760i
\(906\) 0 0
\(907\) −19.9114 19.9114i −0.661148 0.661148i 0.294503 0.955651i \(-0.404846\pi\)
−0.955651 + 0.294503i \(0.904846\pi\)
\(908\) −5.46878 5.46878i −0.181488 0.181488i
\(909\) 0 0
\(910\) −6.82843 + 7.29809i −0.226360 + 0.241929i
\(911\) 28.4723i 0.943331i 0.881778 + 0.471665i \(0.156347\pi\)
−0.881778 + 0.471665i \(0.843653\pi\)
\(912\) 0 0
\(913\) 32.7003 32.7003i 1.08222 1.08222i
\(914\) −9.14824 −0.302597
\(915\) 0 0
\(916\) −13.0966 −0.432723
\(917\) −12.3211 + 12.3211i −0.406877 + 0.406877i
\(918\) 0 0
\(919\) 57.2261i 1.88772i −0.330353 0.943858i \(-0.607168\pi\)
0.330353 0.943858i \(-0.392832\pi\)
\(920\) 0.454051 + 13.6569i 0.0149696 + 0.450253i
\(921\) 0 0
\(922\) 26.2276 + 26.2276i 0.863761 + 0.863761i
\(923\) −29.1924 29.1924i −0.960879 0.960879i
\(924\) 0 0
\(925\) −15.6094 13.6609i −0.513233 0.449168i
\(926\) 0.328437i 0.0107931i
\(927\) 0 0
\(928\) 7.04441 7.04441i 0.231244 0.231244i
\(929\) 28.6166 0.938881 0.469441 0.882964i \(-0.344456\pi\)
0.469441 + 0.882964i \(0.344456\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0.642125 0.642125i 0.0210335 0.0210335i
\(933\) 0 0
\(934\) 31.3952i 1.02728i
\(935\) 37.1513 + 34.7604i 1.21498 + 1.13679i
\(936\) 0 0
\(937\) −4.09342 4.09342i −0.133726 0.133726i 0.637075 0.770802i \(-0.280144\pi\)
−0.770802 + 0.637075i \(0.780144\pi\)
\(938\) 4.59771 + 4.59771i 0.150121 + 0.150121i
\(939\) 0 0
\(940\) 7.91142 + 7.40229i 0.258042 + 0.241436i
\(941\) 18.7890i 0.612502i 0.951951 + 0.306251i \(0.0990748\pi\)
−0.951951 + 0.306251i \(0.900925\pi\)
\(942\) 0 0
\(943\) −46.1482 + 46.1482i −1.50279 + 1.50279i
\(944\) −3.12563 −0.101731
\(945\) 0 0
\(946\) −4.45100 −0.144714
\(947\) 22.6009 22.6009i 0.734429 0.734429i −0.237065 0.971494i \(-0.576185\pi\)
0.971494 + 0.237065i \(0.0761854\pi\)
\(948\) 0 0
\(949\) 64.5759i 2.09622i
\(950\) 0 0
\(951\) 0 0
\(952\) −3.05545 3.05545i −0.0990278 0.0990278i
\(953\) 29.8241 + 29.8241i 0.966097 + 0.966097i 0.999444 0.0333465i \(-0.0106165\pi\)
−0.0333465 + 0.999444i \(0.510616\pi\)
\(954\) 0 0
\(955\) 1.73476 + 52.1776i 0.0561354 + 1.68843i
\(956\) 25.4246i 0.822291i
\(957\) 0 0
\(958\) 14.6902 14.6902i 0.474620 0.474620i
\(959\) −3.33579 −0.107718
\(960\) 0 0
\(961\) −29.3982 −0.948330
\(962\) −13.1118 + 13.1118i −0.422741 + 0.422741i
\(963\) 0 0
\(964\) 7.46878i 0.240553i
\(965\) 14.4552 15.4495i 0.465330 0.497336i
\(966\) 0 0
\(967\) 10.4975 + 10.4975i 0.337576 + 0.337576i 0.855454 0.517878i \(-0.173278\pi\)
−0.517878 + 0.855454i \(0.673278\pi\)
\(968\) −11.8275 11.8275i −0.380151 0.380151i
\(969\) 0 0
\(970\) 14.6532 0.487176i 0.470485 0.0156423i
\(971\) 15.3579i 0.492858i −0.969161 0.246429i \(-0.920743\pi\)
0.969161 0.246429i \(-0.0792572\pi\)
\(972\) 0 0
\(973\) −15.4467 + 15.4467i −0.495198 + 0.495198i
\(974\) 1.42461 0.0456476
\(975\) 0 0
\(976\) −3.05545 −0.0978027
\(977\) −15.5459 + 15.5459i −0.497359 + 0.497359i −0.910615 0.413256i \(-0.864391\pi\)
0.413256 + 0.910615i \(0.364391\pi\)
\(978\) 0 0
\(979\) 19.0571i 0.609066i
\(980\) 2.23483 0.0743018i 0.0713891 0.00237348i
\(981\) 0 0
\(982\) 4.91878 + 4.91878i 0.156964 + 0.156964i
\(983\) 42.6546 + 42.6546i 1.36047 + 1.36047i 0.873317 + 0.487153i \(0.161965\pi\)
0.487153 + 0.873317i \(0.338035\pi\)
\(984\) 0 0
\(985\) −0.811559 + 0.867379i −0.0258584 + 0.0276370i
\(986\) 43.0477i 1.37092i
\(987\) 0 0
\(988\) 0 0
\(989\) 5.16552 0.164254
\(990\) 0 0
\(991\) 8.98099 0.285291 0.142645 0.989774i \(-0.454439\pi\)
0.142645 + 0.989774i \(0.454439\pi\)
\(992\) 0.894921 0.894921i 0.0284138 0.0284138i
\(993\) 0 0
\(994\) 9.23654i 0.292965i
\(995\) −1.34101 40.3345i −0.0425128 1.27869i
\(996\) 0 0
\(997\) −25.7038 25.7038i −0.814047 0.814047i 0.171191 0.985238i \(-0.445239\pi\)
−0.985238 + 0.171191i \(0.945239\pi\)
\(998\) 14.8471 + 14.8471i 0.469976 + 0.469976i
\(999\) 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 630.2.m.d.197.2 yes 8
3.2 odd 2 630.2.m.c.197.3 8
5.2 odd 4 3150.2.m.i.2843.2 8
5.3 odd 4 630.2.m.c.323.3 yes 8
5.4 even 2 3150.2.m.j.1457.4 8
15.2 even 4 3150.2.m.j.2843.3 8
15.8 even 4 inner 630.2.m.d.323.2 yes 8
15.14 odd 2 3150.2.m.i.1457.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.m.c.197.3 8 3.2 odd 2
630.2.m.c.323.3 yes 8 5.3 odd 4
630.2.m.d.197.2 yes 8 1.1 even 1 trivial
630.2.m.d.323.2 yes 8 15.8 even 4 inner
3150.2.m.i.1457.1 8 15.14 odd 2
3150.2.m.i.2843.2 8 5.2 odd 4
3150.2.m.j.1457.4 8 5.4 even 2
3150.2.m.j.2843.3 8 15.2 even 4