Properties

Label 630.2.m.c.323.2
Level $630$
Weight $2$
Character 630.323
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 323.2
Root \(-0.692297i\) of defining polynomial
Character \(\chi\) \(=\) 630.323
Dual form 630.2.m.c.197.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.19663 + 1.88893i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.19663 + 1.88893i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.489528 - 2.18183i) q^{10} +6.36365i q^{11} +(-1.69230 - 1.69230i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(0.979056 + 0.979056i) q^{17} +(-1.88893 + 1.19663i) q^{20} +(4.49978 - 4.49978i) q^{22} +(-1.38459 + 1.38459i) q^{23} +(-2.13613 + 4.52072i) q^{25} +2.39327i q^{26} +(0.707107 + 0.707107i) q^{28} -5.81975 q^{29} +2.36365 q^{31} +(0.707107 + 0.707107i) q^{32} -1.38459i q^{34} +(2.18183 + 0.489528i) q^{35} +(0.157074 - 0.157074i) q^{37} +(2.18183 + 0.489528i) q^{40} +8.94944i q^{41} +(5.88438 + 5.88438i) q^{43} -6.36365 q^{44} +1.95811 q^{46} +(3.05595 + 3.05595i) q^{47} -1.00000i q^{49} +(4.70711 - 1.68616i) q^{50} +(1.69230 - 1.69230i) q^{52} +(0.192517 - 0.192517i) q^{53} +(-12.0205 + 7.61497i) q^{55} -1.00000i q^{56} +(4.11519 + 4.11519i) q^{58} +10.3842 q^{59} -0.979056 q^{61} +(-1.67135 - 1.67135i) q^{62} -1.00000i q^{64} +(1.17157 - 5.22170i) q^{65} +(9.88438 - 9.88438i) q^{67} +(-0.979056 + 0.979056i) q^{68} +(-1.19663 - 1.88893i) q^{70} -12.3423i q^{71} +(4.71324 + 4.71324i) q^{73} -0.222136 q^{74} +(4.49978 + 4.49978i) q^{77} +6.68541i q^{79} +(-1.19663 - 1.88893i) q^{80} +(6.32821 - 6.32821i) q^{82} +(11.3427 - 11.3427i) q^{83} +(-0.677798 + 3.02094i) q^{85} -8.32176i q^{86} +(4.49978 + 4.49978i) q^{88} -11.8371 q^{89} -2.39327 q^{91} +(-1.38459 - 1.38459i) q^{92} -4.32176i q^{94} +(-9.39866 + 9.39866i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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
\(5\) 1.19663 + 1.88893i 0.535151 + 0.844756i
\(6\) 0 0
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) 0.489528 2.18183i 0.154802 0.689954i
\(11\) 6.36365i 1.91871i 0.282197 + 0.959356i \(0.408937\pi\)
−0.282197 + 0.959356i \(0.591063\pi\)
\(12\) 0 0
\(13\) −1.69230 1.69230i −0.469359 0.469359i 0.432348 0.901707i \(-0.357685\pi\)
−0.901707 + 0.432348i \(0.857685\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0.979056 + 0.979056i 0.237456 + 0.237456i 0.815796 0.578340i \(-0.196299\pi\)
−0.578340 + 0.815796i \(0.696299\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −1.88893 + 1.19663i −0.422378 + 0.267576i
\(21\) 0 0
\(22\) 4.49978 4.49978i 0.959356 0.959356i
\(23\) −1.38459 + 1.38459i −0.288708 + 0.288708i −0.836569 0.547861i \(-0.815442\pi\)
0.547861 + 0.836569i \(0.315442\pi\)
\(24\) 0 0
\(25\) −2.13613 + 4.52072i −0.427226 + 0.904145i
\(26\) 2.39327i 0.469359i
\(27\) 0 0
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) −5.81975 −1.08070 −0.540350 0.841440i \(-0.681708\pi\)
−0.540350 + 0.841440i \(0.681708\pi\)
\(30\) 0 0
\(31\) 2.36365 0.424524 0.212262 0.977213i \(-0.431917\pi\)
0.212262 + 0.977213i \(0.431917\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0 0
\(34\) 1.38459i 0.237456i
\(35\) 2.18183 + 0.489528i 0.368796 + 0.0827454i
\(36\) 0 0
\(37\) 0.157074 0.157074i 0.0258227 0.0258227i −0.694078 0.719900i \(-0.744188\pi\)
0.719900 + 0.694078i \(0.244188\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 2.18183 + 0.489528i 0.344977 + 0.0774012i
\(41\) 8.94944i 1.39767i 0.715284 + 0.698834i \(0.246297\pi\)
−0.715284 + 0.698834i \(0.753703\pi\)
\(42\) 0 0
\(43\) 5.88438 + 5.88438i 0.897359 + 0.897359i 0.995202 0.0978430i \(-0.0311943\pi\)
−0.0978430 + 0.995202i \(0.531194\pi\)
\(44\) −6.36365 −0.959356
\(45\) 0 0
\(46\) 1.95811 0.288708
\(47\) 3.05595 + 3.05595i 0.445756 + 0.445756i 0.893941 0.448185i \(-0.147929\pi\)
−0.448185 + 0.893941i \(0.647929\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 4.70711 1.68616i 0.665685 0.238459i
\(51\) 0 0
\(52\) 1.69230 1.69230i 0.234679 0.234679i
\(53\) 0.192517 0.192517i 0.0264442 0.0264442i −0.693761 0.720205i \(-0.744048\pi\)
0.720205 + 0.693761i \(0.244048\pi\)
\(54\) 0 0
\(55\) −12.0205 + 7.61497i −1.62084 + 1.02680i
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 4.11519 + 4.11519i 0.540350 + 0.540350i
\(59\) 10.3842 1.35190 0.675951 0.736947i \(-0.263733\pi\)
0.675951 + 0.736947i \(0.263733\pi\)
\(60\) 0 0
\(61\) −0.979056 −0.125355 −0.0626777 0.998034i \(-0.519964\pi\)
−0.0626777 + 0.998034i \(0.519964\pi\)
\(62\) −1.67135 1.67135i −0.212262 0.212262i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 1.17157 5.22170i 0.145316 0.647672i
\(66\) 0 0
\(67\) 9.88438 9.88438i 1.20757 1.20757i 0.235756 0.971812i \(-0.424243\pi\)
0.971812 0.235756i \(-0.0757568\pi\)
\(68\) −0.979056 + 0.979056i −0.118728 + 0.118728i
\(69\) 0 0
\(70\) −1.19663 1.88893i −0.143025 0.225771i
\(71\) 12.3423i 1.46476i −0.680897 0.732379i \(-0.738410\pi\)
0.680897 0.732379i \(-0.261590\pi\)
\(72\) 0 0
\(73\) 4.71324 + 4.71324i 0.551643 + 0.551643i 0.926915 0.375272i \(-0.122451\pi\)
−0.375272 + 0.926915i \(0.622451\pi\)
\(74\) −0.222136 −0.0258227
\(75\) 0 0
\(76\) 0 0
\(77\) 4.49978 + 4.49978i 0.512798 + 0.512798i
\(78\) 0 0
\(79\) 6.68541i 0.752168i 0.926586 + 0.376084i \(0.122730\pi\)
−0.926586 + 0.376084i \(0.877270\pi\)
\(80\) −1.19663 1.88893i −0.133788 0.211189i
\(81\) 0 0
\(82\) 6.32821 6.32821i 0.698834 0.698834i
\(83\) 11.3427 11.3427i 1.24502 1.24502i 0.287133 0.957891i \(-0.407298\pi\)
0.957891 0.287133i \(-0.0927022\pi\)
\(84\) 0 0
\(85\) −0.677798 + 3.02094i −0.0735175 + 0.327667i
\(86\) 8.32176i 0.897359i
\(87\) 0 0
\(88\) 4.49978 + 4.49978i 0.479678 + 0.479678i
\(89\) −11.8371 −1.25473 −0.627365 0.778725i \(-0.715867\pi\)
−0.627365 + 0.778725i \(0.715867\pi\)
\(90\) 0 0
\(91\) −2.39327 −0.250883
\(92\) −1.38459 1.38459i −0.144354 0.144354i
\(93\) 0 0
\(94\) 4.32176i 0.445756i
\(95\) 0 0
\(96\) 0 0
\(97\) −9.39866 + 9.39866i −0.954289 + 0.954289i −0.999000 0.0447111i \(-0.985763\pi\)
0.0447111 + 0.999000i \(0.485763\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) −4.52072 2.13613i −0.452072 0.213613i
\(101\) 16.0501i 1.59705i 0.601964 + 0.798524i \(0.294385\pi\)
−0.601964 + 0.798524i \(0.705615\pi\)
\(102\) 0 0
\(103\) −0.706797 0.706797i −0.0696427 0.0696427i 0.671428 0.741070i \(-0.265681\pi\)
−0.741070 + 0.671428i \(0.765681\pi\)
\(104\) −2.39327 −0.234679
\(105\) 0 0
\(106\) −0.272260 −0.0264442
\(107\) −9.51384 9.51384i −0.919738 0.919738i 0.0772723 0.997010i \(-0.475379\pi\)
−0.997010 + 0.0772723i \(0.975379\pi\)
\(108\) 0 0
\(109\) 14.9577i 1.43269i −0.697749 0.716343i \(-0.745815\pi\)
0.697749 0.716343i \(-0.254185\pi\)
\(110\) 13.8844 + 3.11519i 1.32382 + 0.297021i
\(111\) 0 0
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) 9.22170 9.22170i 0.867504 0.867504i −0.124691 0.992196i \(-0.539794\pi\)
0.992196 + 0.124691i \(0.0397941\pi\)
\(114\) 0 0
\(115\) −4.27226 0.958551i −0.398390 0.0893854i
\(116\) 5.81975i 0.540350i
\(117\) 0 0
\(118\) −7.34271 7.34271i −0.675951 0.675951i
\(119\) 1.38459 0.126926
\(120\) 0 0
\(121\) −29.4961 −2.68146
\(122\) 0.692297 + 0.692297i 0.0626777 + 0.0626777i
\(123\) 0 0
\(124\) 2.36365i 0.212262i
\(125\) −11.0955 + 1.37465i −0.992413 + 0.122953i
\(126\) 0 0
\(127\) −5.38459 + 5.38459i −0.477806 + 0.477806i −0.904429 0.426624i \(-0.859703\pi\)
0.426624 + 0.904429i \(0.359703\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) −4.52072 + 2.86387i −0.396494 + 0.251178i
\(131\) 13.2718i 1.15956i 0.814772 + 0.579782i \(0.196862\pi\)
−0.814772 + 0.579782i \(0.803138\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −13.9786 −1.20757
\(135\) 0 0
\(136\) 1.38459 0.118728
\(137\) −3.56484 3.56484i −0.304565 0.304565i 0.538232 0.842797i \(-0.319092\pi\)
−0.842797 + 0.538232i \(0.819092\pi\)
\(138\) 0 0
\(139\) 1.41359i 0.119899i 0.998201 + 0.0599497i \(0.0190940\pi\)
−0.998201 + 0.0599497i \(0.980906\pi\)
\(140\) −0.489528 + 2.18183i −0.0413727 + 0.184398i
\(141\) 0 0
\(142\) −8.72730 + 8.72730i −0.732379 + 0.732379i
\(143\) 10.7692 10.7692i 0.900565 0.900565i
\(144\) 0 0
\(145\) −6.96412 10.9931i −0.578339 0.912929i
\(146\) 6.66553i 0.551643i
\(147\) 0 0
\(148\) 0.157074 + 0.157074i 0.0129114 + 0.0129114i
\(149\) −20.0609 −1.64345 −0.821726 0.569882i \(-0.806989\pi\)
−0.821726 + 0.569882i \(0.806989\pi\)
\(150\) 0 0
\(151\) 8.81108 0.717035 0.358518 0.933523i \(-0.383282\pi\)
0.358518 + 0.933523i \(0.383282\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 6.36365i 0.512798i
\(155\) 2.82843 + 4.46478i 0.227185 + 0.358619i
\(156\) 0 0
\(157\) 15.2654 15.2654i 1.21831 1.21831i 0.250086 0.968224i \(-0.419541\pi\)
0.968224 0.250086i \(-0.0804589\pi\)
\(158\) 4.72730 4.72730i 0.376084 0.376084i
\(159\) 0 0
\(160\) −0.489528 + 2.18183i −0.0387006 + 0.172488i
\(161\) 1.95811i 0.154321i
\(162\) 0 0
\(163\) 7.11519 + 7.11519i 0.557304 + 0.557304i 0.928539 0.371235i \(-0.121065\pi\)
−0.371235 + 0.928539i \(0.621065\pi\)
\(164\) −8.94944 −0.698834
\(165\) 0 0
\(166\) −16.0410 −1.24502
\(167\) −16.7128 16.7128i −1.29328 1.29328i −0.932749 0.360527i \(-0.882597\pi\)
−0.360527 0.932749i \(-0.617403\pi\)
\(168\) 0 0
\(169\) 7.27226i 0.559405i
\(170\) 2.61541 1.65685i 0.200592 0.127075i
\(171\) 0 0
\(172\) −5.88438 + 5.88438i −0.448679 + 0.448679i
\(173\) 14.7843 14.7843i 1.12403 1.12403i 0.132901 0.991129i \(-0.457571\pi\)
0.991129 0.132901i \(-0.0424292\pi\)
\(174\) 0 0
\(175\) 1.68616 + 4.70711i 0.127462 + 0.355824i
\(176\) 6.36365i 0.479678i
\(177\) 0 0
\(178\) 8.37010 + 8.37010i 0.627365 + 0.627365i
\(179\) 12.0205 0.898455 0.449227 0.893417i \(-0.351699\pi\)
0.449227 + 0.893417i \(0.351699\pi\)
\(180\) 0 0
\(181\) 17.5236 1.30252 0.651259 0.758856i \(-0.274241\pi\)
0.651259 + 0.758856i \(0.274241\pi\)
\(182\) 1.69230 + 1.69230i 0.125441 + 0.125441i
\(183\) 0 0
\(184\) 1.95811i 0.144354i
\(185\) 0.484661 + 0.108742i 0.0356330 + 0.00799484i
\(186\) 0 0
\(187\) −6.23037 + 6.23037i −0.455610 + 0.455610i
\(188\) −3.05595 + 3.05595i −0.222878 + 0.222878i
\(189\) 0 0
\(190\) 0 0
\(191\) 6.30038i 0.455880i −0.973675 0.227940i \(-0.926801\pi\)
0.973675 0.227940i \(-0.0731989\pi\)
\(192\) 0 0
\(193\) −11.6435 11.6435i −0.838119 0.838119i 0.150492 0.988611i \(-0.451914\pi\)
−0.988611 + 0.150492i \(0.951914\pi\)
\(194\) 13.2917 0.954289
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −1.92849 1.92849i −0.137399 0.137399i 0.635062 0.772461i \(-0.280975\pi\)
−0.772461 + 0.635062i \(0.780975\pi\)
\(198\) 0 0
\(199\) 5.67736i 0.402457i −0.979544 0.201229i \(-0.935507\pi\)
0.979544 0.201229i \(-0.0644934\pi\)
\(200\) 1.68616 + 4.70711i 0.119230 + 0.332843i
\(201\) 0 0
\(202\) 11.3492 11.3492i 0.798524 0.798524i
\(203\) −4.11519 + 4.11519i −0.288829 + 0.288829i
\(204\) 0 0
\(205\) −16.9049 + 10.7092i −1.18069 + 0.747964i
\(206\) 0.999561i 0.0696427i
\(207\) 0 0
\(208\) 1.69230 + 1.69230i 0.117340 + 0.117340i
\(209\) 0 0
\(210\) 0 0
\(211\) 7.91622 0.544975 0.272488 0.962159i \(-0.412154\pi\)
0.272488 + 0.962159i \(0.412154\pi\)
\(212\) 0.192517 + 0.192517i 0.0132221 + 0.0132221i
\(213\) 0 0
\(214\) 13.4546i 0.919738i
\(215\) −4.07374 + 18.1566i −0.277827 + 1.23827i
\(216\) 0 0
\(217\) 1.67135 1.67135i 0.113459 0.113459i
\(218\) −10.5767 + 10.5767i −0.716343 + 0.716343i
\(219\) 0 0
\(220\) −7.61497 12.0205i −0.513401 0.810422i
\(221\) 3.31371i 0.222904i
\(222\) 0 0
\(223\) 8.34227 + 8.34227i 0.558640 + 0.558640i 0.928920 0.370280i \(-0.120738\pi\)
−0.370280 + 0.928920i \(0.620738\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −13.0414 −0.867504
\(227\) −3.27270 3.27270i −0.217217 0.217217i 0.590108 0.807324i \(-0.299085\pi\)
−0.807324 + 0.590108i \(0.799085\pi\)
\(228\) 0 0
\(229\) 23.0901i 1.52584i −0.646496 0.762918i \(-0.723766\pi\)
0.646496 0.762918i \(-0.276234\pi\)
\(230\) 2.34315 + 3.69874i 0.154502 + 0.243888i
\(231\) 0 0
\(232\) −4.11519 + 4.11519i −0.270175 + 0.270175i
\(233\) 5.23081 5.23081i 0.342682 0.342682i −0.514693 0.857375i \(-0.672094\pi\)
0.857375 + 0.514693i \(0.172094\pi\)
\(234\) 0 0
\(235\) −2.11562 + 9.42933i −0.138008 + 0.615102i
\(236\) 10.3842i 0.675951i
\(237\) 0 0
\(238\) −0.979056 0.979056i −0.0634628 0.0634628i
\(239\) −5.27182 −0.341006 −0.170503 0.985357i \(-0.554539\pi\)
−0.170503 + 0.985357i \(0.554539\pi\)
\(240\) 0 0
\(241\) −5.27270 −0.339644 −0.169822 0.985475i \(-0.554319\pi\)
−0.169822 + 0.985475i \(0.554319\pi\)
\(242\) 20.8569 + 20.8569i 1.34073 + 1.34073i
\(243\) 0 0
\(244\) 0.979056i 0.0626777i
\(245\) 1.88893 1.19663i 0.120679 0.0764502i
\(246\) 0 0
\(247\) 0 0
\(248\) 1.67135 1.67135i 0.106131 0.106131i
\(249\) 0 0
\(250\) 8.81774 + 6.87368i 0.557683 + 0.434730i
\(251\) 20.3423i 1.28399i −0.766708 0.641996i \(-0.778106\pi\)
0.766708 0.641996i \(-0.221894\pi\)
\(252\) 0 0
\(253\) −8.81108 8.81108i −0.553948 0.553948i
\(254\) 7.61497 0.477806
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.50201 + 2.50201i 0.156071 + 0.156071i 0.780823 0.624752i \(-0.214800\pi\)
−0.624752 + 0.780823i \(0.714800\pi\)
\(258\) 0 0
\(259\) 0.222136i 0.0138028i
\(260\) 5.22170 + 1.17157i 0.323836 + 0.0726579i
\(261\) 0 0
\(262\) 9.38459 9.38459i 0.579782 0.579782i
\(263\) −12.6983 + 12.6983i −0.783011 + 0.783011i −0.980338 0.197327i \(-0.936774\pi\)
0.197327 + 0.980338i \(0.436774\pi\)
\(264\) 0 0
\(265\) 0.594023 + 0.133279i 0.0364905 + 0.00818725i
\(266\) 0 0
\(267\) 0 0
\(268\) 9.88438 + 9.88438i 0.603784 + 0.603784i
\(269\) 26.9196 1.64131 0.820657 0.571421i \(-0.193608\pi\)
0.820657 + 0.571421i \(0.193608\pi\)
\(270\) 0 0
\(271\) 23.1320 1.40517 0.702583 0.711601i \(-0.252030\pi\)
0.702583 + 0.711601i \(0.252030\pi\)
\(272\) −0.979056 0.979056i −0.0593640 0.0593640i
\(273\) 0 0
\(274\) 5.04145i 0.304565i
\(275\) −28.7683 13.5936i −1.73479 0.819724i
\(276\) 0 0
\(277\) 12.2271 12.2271i 0.734654 0.734654i −0.236884 0.971538i \(-0.576126\pi\)
0.971538 + 0.236884i \(0.0761261\pi\)
\(278\) 0.999561 0.999561i 0.0599497 0.0599497i
\(279\) 0 0
\(280\) 1.88893 1.19663i 0.112885 0.0715126i
\(281\) 10.4428i 0.622964i 0.950252 + 0.311482i \(0.100825\pi\)
−0.950252 + 0.311482i \(0.899175\pi\)
\(282\) 0 0
\(283\) 22.9577 + 22.9577i 1.36469 + 1.36469i 0.867829 + 0.496863i \(0.165515\pi\)
0.496863 + 0.867829i \(0.334485\pi\)
\(284\) 12.3423 0.732379
\(285\) 0 0
\(286\) −15.2299 −0.900565
\(287\) 6.32821 + 6.32821i 0.373542 + 0.373542i
\(288\) 0 0
\(289\) 15.0829i 0.887229i
\(290\) −2.84893 + 12.6977i −0.167295 + 0.745634i
\(291\) 0 0
\(292\) −4.71324 + 4.71324i −0.275822 + 0.275822i
\(293\) −18.6413 + 18.6413i −1.08904 + 1.08904i −0.0934082 + 0.995628i \(0.529776\pi\)
−0.995628 + 0.0934082i \(0.970224\pi\)
\(294\) 0 0
\(295\) 12.4260 + 19.6150i 0.723472 + 1.14203i
\(296\) 0.222136i 0.0129114i
\(297\) 0 0
\(298\) 14.1852 + 14.1852i 0.821726 + 0.821726i
\(299\) 4.68629 0.271015
\(300\) 0 0
\(301\) 8.32176 0.479658
\(302\) −6.23037 6.23037i −0.358518 0.358518i
\(303\) 0 0
\(304\) 0 0
\(305\) −1.17157 1.84937i −0.0670841 0.105895i
\(306\) 0 0
\(307\) 0.727302 0.727302i 0.0415093 0.0415093i −0.686047 0.727557i \(-0.740656\pi\)
0.727557 + 0.686047i \(0.240656\pi\)
\(308\) −4.49978 + 4.49978i −0.256399 + 0.256399i
\(309\) 0 0
\(310\) 1.15707 5.15707i 0.0657174 0.292902i
\(311\) 24.2295i 1.37393i 0.726691 + 0.686964i \(0.241057\pi\)
−0.726691 + 0.686964i \(0.758943\pi\)
\(312\) 0 0
\(313\) 3.44054 + 3.44054i 0.194471 + 0.194471i 0.797625 0.603154i \(-0.206090\pi\)
−0.603154 + 0.797625i \(0.706090\pi\)
\(314\) −21.5885 −1.21831
\(315\) 0 0
\(316\) −6.68541 −0.376084
\(317\) −12.9198 12.9198i −0.725649 0.725649i 0.244101 0.969750i \(-0.421507\pi\)
−0.969750 + 0.244101i \(0.921507\pi\)
\(318\) 0 0
\(319\) 37.0349i 2.07355i
\(320\) 1.88893 1.19663i 0.105595 0.0668939i
\(321\) 0 0
\(322\) 1.38459 1.38459i 0.0771604 0.0771604i
\(323\) 0 0
\(324\) 0 0
\(325\) 11.2654 4.03544i 0.624891 0.223846i
\(326\) 10.0624i 0.557304i
\(327\) 0 0
\(328\) 6.32821 + 6.32821i 0.349417 + 0.349417i
\(329\) 4.32176 0.238267
\(330\) 0 0
\(331\) 8.76831 0.481950 0.240975 0.970531i \(-0.422533\pi\)
0.240975 + 0.970531i \(0.422533\pi\)
\(332\) 11.3427 + 11.3427i 0.622512 + 0.622512i
\(333\) 0 0
\(334\) 23.6355i 1.29328i
\(335\) 30.4989 + 6.84293i 1.66633 + 0.373869i
\(336\) 0 0
\(337\) −12.3427 + 12.3427i −0.672350 + 0.672350i −0.958257 0.285907i \(-0.907705\pi\)
0.285907 + 0.958257i \(0.407705\pi\)
\(338\) −5.14226 + 5.14226i −0.279702 + 0.279702i
\(339\) 0 0
\(340\) −3.02094 0.677798i −0.163834 0.0367588i
\(341\) 15.0414i 0.814540i
\(342\) 0 0
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 8.32176 0.448679
\(345\) 0 0
\(346\) −20.9082 −1.12403
\(347\) −5.17157 5.17157i −0.277625 0.277625i 0.554535 0.832160i \(-0.312896\pi\)
−0.832160 + 0.554535i \(0.812896\pi\)
\(348\) 0 0
\(349\) 28.9363i 1.54892i 0.632620 + 0.774462i \(0.281979\pi\)
−0.632620 + 0.774462i \(0.718021\pi\)
\(350\) 2.13613 4.52072i 0.114181 0.241643i
\(351\) 0 0
\(352\) −4.49978 + 4.49978i −0.239839 + 0.239839i
\(353\) −10.3637 + 10.3637i −0.551601 + 0.551601i −0.926903 0.375301i \(-0.877539\pi\)
0.375301 + 0.926903i \(0.377539\pi\)
\(354\) 0 0
\(355\) 23.3137 14.7692i 1.23736 0.783867i
\(356\) 11.8371i 0.627365i
\(357\) 0 0
\(358\) −8.49978 8.49978i −0.449227 0.449227i
\(359\) 13.2308 0.698295 0.349148 0.937068i \(-0.386471\pi\)
0.349148 + 0.937068i \(0.386471\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) −12.3910 12.3910i −0.651259 0.651259i
\(363\) 0 0
\(364\) 2.39327i 0.125441i
\(365\) −3.26296 + 14.5430i −0.170791 + 0.761217i
\(366\) 0 0
\(367\) −3.20943 + 3.20943i −0.167531 + 0.167531i −0.785893 0.618362i \(-0.787796\pi\)
0.618362 + 0.785893i \(0.287796\pi\)
\(368\) 1.38459 1.38459i 0.0721770 0.0721770i
\(369\) 0 0
\(370\) −0.265815 0.419599i −0.0138191 0.0218139i
\(371\) 0.272260i 0.0141350i
\(372\) 0 0
\(373\) −2.26897 2.26897i −0.117483 0.117483i 0.645921 0.763404i \(-0.276473\pi\)
−0.763404 + 0.645921i \(0.776473\pi\)
\(374\) 8.81108 0.455610
\(375\) 0 0
\(376\) 4.32176 0.222878
\(377\) 9.84875 + 9.84875i 0.507236 + 0.507236i
\(378\) 0 0
\(379\) 2.39792i 0.123173i −0.998102 0.0615865i \(-0.980384\pi\)
0.998102 0.0615865i \(-0.0196160\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.45504 + 4.45504i −0.227940 + 0.227940i
\(383\) 16.6838 16.6838i 0.852503 0.852503i −0.137938 0.990441i \(-0.544048\pi\)
0.990441 + 0.137938i \(0.0440476\pi\)
\(384\) 0 0
\(385\) −3.11519 + 13.8844i −0.158765 + 0.707613i
\(386\) 16.4664i 0.838119i
\(387\) 0 0
\(388\) −9.39866 9.39866i −0.477144 0.477144i
\(389\) −22.0782 −1.11941 −0.559706 0.828691i \(-0.689086\pi\)
−0.559706 + 0.828691i \(0.689086\pi\)
\(390\) 0 0
\(391\) −2.71119 −0.137111
\(392\) −0.707107 0.707107i −0.0357143 0.0357143i
\(393\) 0 0
\(394\) 2.72730i 0.137399i
\(395\) −12.6283 + 8.00000i −0.635398 + 0.402524i
\(396\) 0 0
\(397\) 20.9717 20.9717i 1.05254 1.05254i 0.0540003 0.998541i \(-0.482803\pi\)
0.998541 0.0540003i \(-0.0171972\pi\)
\(398\) −4.01450 + 4.01450i −0.201229 + 0.201229i
\(399\) 0 0
\(400\) 2.13613 4.52072i 0.106806 0.226036i
\(401\) 9.29574i 0.464207i 0.972691 + 0.232103i \(0.0745608\pi\)
−0.972691 + 0.232103i \(0.925439\pi\)
\(402\) 0 0
\(403\) −4.00000 4.00000i −0.199254 0.199254i
\(404\) −16.0501 −0.798524
\(405\) 0 0
\(406\) 5.81975 0.288829
\(407\) 0.999561 + 0.999561i 0.0495464 + 0.0495464i
\(408\) 0 0
\(409\) 34.2367i 1.69289i 0.532472 + 0.846447i \(0.321263\pi\)
−0.532472 + 0.846447i \(0.678737\pi\)
\(410\) 19.5261 + 4.38100i 0.964326 + 0.216362i
\(411\) 0 0
\(412\) 0.706797 0.706797i 0.0348214 0.0348214i
\(413\) 7.34271 7.34271i 0.361311 0.361311i
\(414\) 0 0
\(415\) 34.9987 + 7.85253i 1.71802 + 0.385465i
\(416\) 2.39327i 0.117340i
\(417\) 0 0
\(418\) 0 0
\(419\) 13.7753 0.672969 0.336484 0.941689i \(-0.390762\pi\)
0.336484 + 0.941689i \(0.390762\pi\)
\(420\) 0 0
\(421\) 10.6283 0.517991 0.258996 0.965878i \(-0.416608\pi\)
0.258996 + 0.965878i \(0.416608\pi\)
\(422\) −5.59762 5.59762i −0.272488 0.272488i
\(423\) 0 0
\(424\) 0.272260i 0.0132221i
\(425\) −6.51743 + 2.33465i −0.316142 + 0.113247i
\(426\) 0 0
\(427\) −0.692297 + 0.692297i −0.0335026 + 0.0335026i
\(428\) 9.51384 9.51384i 0.459869 0.459869i
\(429\) 0 0
\(430\) 15.7192 9.95811i 0.758049 0.480223i
\(431\) 18.8877i 0.909787i −0.890546 0.454893i \(-0.849677\pi\)
0.890546 0.454893i \(-0.150323\pi\)
\(432\) 0 0
\(433\) −19.3697 19.3697i −0.930846 0.930846i 0.0669125 0.997759i \(-0.478685\pi\)
−0.997759 + 0.0669125i \(0.978685\pi\)
\(434\) −2.36365 −0.113459
\(435\) 0 0
\(436\) 14.9577 0.716343
\(437\) 0 0
\(438\) 0 0
\(439\) 4.86628i 0.232255i −0.993234 0.116127i \(-0.962952\pi\)
0.993234 0.116127i \(-0.0370481\pi\)
\(440\) −3.11519 + 13.8844i −0.148511 + 0.661912i
\(441\) 0 0
\(442\) −2.34315 + 2.34315i −0.111452 + 0.111452i
\(443\) 7.17070 7.17070i 0.340690 0.340690i −0.515937 0.856627i \(-0.672556\pi\)
0.856627 + 0.515937i \(0.172556\pi\)
\(444\) 0 0
\(445\) −14.1647 22.3595i −0.671471 1.05994i
\(446\) 11.7977i 0.558640i
\(447\) 0 0
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) −8.87093 −0.418645 −0.209323 0.977847i \(-0.567126\pi\)
−0.209323 + 0.977847i \(0.567126\pi\)
\(450\) 0 0
\(451\) −56.9511 −2.68172
\(452\) 9.22170 + 9.22170i 0.433752 + 0.433752i
\(453\) 0 0
\(454\) 4.62829i 0.217217i
\(455\) −2.86387 4.52072i −0.134260 0.211935i
\(456\) 0 0
\(457\) 4.27270 4.27270i 0.199868 0.199868i −0.600075 0.799944i \(-0.704863\pi\)
0.799944 + 0.600075i \(0.204863\pi\)
\(458\) −16.3271 + 16.3271i −0.762918 + 0.762918i
\(459\) 0 0
\(460\) 0.958551 4.27226i 0.0446927 0.199195i
\(461\) 0.771724i 0.0359428i −0.999839 0.0179714i \(-0.994279\pi\)
0.999839 0.0179714i \(-0.00572077\pi\)
\(462\) 0 0
\(463\) −19.6150 19.6150i −0.911585 0.911585i 0.0848121 0.996397i \(-0.472971\pi\)
−0.996397 + 0.0848121i \(0.972971\pi\)
\(464\) 5.81975 0.270175
\(465\) 0 0
\(466\) −7.39748 −0.342682
\(467\) −8.18848 8.18848i −0.378918 0.378918i 0.491794 0.870712i \(-0.336341\pi\)
−0.870712 + 0.491794i \(0.836341\pi\)
\(468\) 0 0
\(469\) 13.9786i 0.645473i
\(470\) 8.16352 5.17157i 0.376555 0.238547i
\(471\) 0 0
\(472\) 7.34271 7.34271i 0.337975 0.337975i
\(473\) −37.4461 + 37.4461i −1.72177 + 1.72177i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.38459i 0.0634628i
\(477\) 0 0
\(478\) 3.72774 + 3.72774i 0.170503 + 0.170503i
\(479\) 21.0833 0.963322 0.481661 0.876358i \(-0.340034\pi\)
0.481661 + 0.876358i \(0.340034\pi\)
\(480\) 0 0
\(481\) −0.531630 −0.0242403
\(482\) 3.72836 + 3.72836i 0.169822 + 0.169822i
\(483\) 0 0
\(484\) 29.4961i 1.34073i
\(485\) −29.0002 6.50666i −1.31683 0.295452i
\(486\) 0 0
\(487\) −20.6983 + 20.6983i −0.937930 + 0.937930i −0.998183 0.0602535i \(-0.980809\pi\)
0.0602535 + 0.998183i \(0.480809\pi\)
\(488\) −0.692297 + 0.692297i −0.0313388 + 0.0313388i
\(489\) 0 0
\(490\) −2.18183 0.489528i −0.0985648 0.0221146i
\(491\) 10.2799i 0.463924i 0.972725 + 0.231962i \(0.0745146\pi\)
−0.972725 + 0.231962i \(0.925485\pi\)
\(492\) 0 0
\(493\) −5.69786 5.69786i −0.256619 0.256619i
\(494\) 0 0
\(495\) 0 0
\(496\) −2.36365 −0.106131
\(497\) −8.72730 8.72730i −0.391473 0.391473i
\(498\) 0 0
\(499\) 5.16711i 0.231312i 0.993289 + 0.115656i \(0.0368970\pi\)
−0.993289 + 0.115656i \(0.963103\pi\)
\(500\) −1.37465 11.0955i −0.0614763 0.496206i
\(501\) 0 0
\(502\) −14.3842 + 14.3842i −0.641996 + 0.641996i
\(503\) 0.741801 0.741801i 0.0330753 0.0330753i −0.690376 0.723451i \(-0.742555\pi\)
0.723451 + 0.690376i \(0.242555\pi\)
\(504\) 0 0
\(505\) −30.3176 + 19.2061i −1.34912 + 0.854662i
\(506\) 12.4607i 0.553948i
\(507\) 0 0
\(508\) −5.38459 5.38459i −0.238903 0.238903i
\(509\) 1.96723 0.0871958 0.0435979 0.999049i \(-0.486118\pi\)
0.0435979 + 0.999049i \(0.486118\pi\)
\(510\) 0 0
\(511\) 6.66553 0.294866
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 3.53838i 0.156071i
\(515\) 0.489313 2.18087i 0.0215617 0.0961005i
\(516\) 0 0
\(517\) −19.4470 + 19.4470i −0.855278 + 0.855278i
\(518\) −0.157074 + 0.157074i −0.00690142 + 0.00690142i
\(519\) 0 0
\(520\) −2.86387 4.52072i −0.125589 0.198247i
\(521\) 5.19146i 0.227442i −0.993513 0.113721i \(-0.963723\pi\)
0.993513 0.113721i \(-0.0362770\pi\)
\(522\) 0 0
\(523\) −28.2295 28.2295i −1.23439 1.23439i −0.962261 0.272129i \(-0.912272\pi\)
−0.272129 0.962261i \(-0.587728\pi\)
\(524\) −13.2718 −0.579782
\(525\) 0 0
\(526\) 17.9581 0.783011
\(527\) 2.31415 + 2.31415i 0.100806 + 0.100806i
\(528\) 0 0
\(529\) 19.1658i 0.833295i
\(530\) −0.325795 0.514280i −0.0141516 0.0223389i
\(531\) 0 0
\(532\) 0 0
\(533\) 15.1451 15.1451i 0.656007 0.656007i
\(534\) 0 0
\(535\) 6.58641 29.3556i 0.284755 1.26915i
\(536\) 13.9786i 0.603784i
\(537\) 0 0
\(538\) −19.0350 19.0350i −0.820657 0.820657i
\(539\) 6.36365 0.274102
\(540\) 0 0
\(541\) −14.9167 −0.641317 −0.320659 0.947195i \(-0.603904\pi\)
−0.320659 + 0.947195i \(0.603904\pi\)
\(542\) −16.3568 16.3568i −0.702583 0.702583i
\(543\) 0 0
\(544\) 1.38459i 0.0593640i
\(545\) 28.2540 17.8989i 1.21027 0.766704i
\(546\) 0 0
\(547\) −14.8839 + 14.8839i −0.636391 + 0.636391i −0.949663 0.313272i \(-0.898575\pi\)
0.313272 + 0.949663i \(0.398575\pi\)
\(548\) 3.56484 3.56484i 0.152283 0.152283i
\(549\) 0 0
\(550\) 10.7302 + 29.9544i 0.457535 + 1.27726i
\(551\) 0 0
\(552\) 0 0
\(553\) 4.72730 + 4.72730i 0.201025 + 0.201025i
\(554\) −17.2917 −0.734654
\(555\) 0 0
\(556\) −1.41359 −0.0599497
\(557\) 16.1925 + 16.1925i 0.686099 + 0.686099i 0.961367 0.275268i \(-0.0887667\pi\)
−0.275268 + 0.961367i \(0.588767\pi\)
\(558\) 0 0
\(559\) 19.9162i 0.842367i
\(560\) −2.18183 0.489528i −0.0921990 0.0206863i
\(561\) 0 0
\(562\) 7.38416 7.38416i 0.311482 0.311482i
\(563\) 4.69830 4.69830i 0.198010 0.198010i −0.601136 0.799146i \(-0.705285\pi\)
0.799146 + 0.601136i \(0.205285\pi\)
\(564\) 0 0
\(565\) 28.4542 + 6.38416i 1.19708 + 0.268583i
\(566\) 32.4671i 1.36469i
\(567\) 0 0
\(568\) −8.72730 8.72730i −0.366189 0.366189i
\(569\) 38.1643 1.59993 0.799965 0.600046i \(-0.204851\pi\)
0.799965 + 0.600046i \(0.204851\pi\)
\(570\) 0 0
\(571\) −24.6008 −1.02951 −0.514755 0.857337i \(-0.672117\pi\)
−0.514755 + 0.857337i \(0.672117\pi\)
\(572\) 10.7692 + 10.7692i 0.450282 + 0.450282i
\(573\) 0 0
\(574\) 8.94944i 0.373542i
\(575\) −3.30170 9.21704i −0.137690 0.384377i
\(576\) 0 0
\(577\) −8.01318 + 8.01318i −0.333593 + 0.333593i −0.853949 0.520356i \(-0.825799\pi\)
0.520356 + 0.853949i \(0.325799\pi\)
\(578\) −10.6652 + 10.6652i −0.443615 + 0.443615i
\(579\) 0 0
\(580\) 10.9931 6.96412i 0.456464 0.289169i
\(581\) 16.0410i 0.665493i
\(582\) 0 0
\(583\) 1.22511 + 1.22511i 0.0507388 + 0.0507388i
\(584\) 6.66553 0.275822
\(585\) 0 0
\(586\) 26.3628 1.08904
\(587\) −7.42648 7.42648i −0.306524 0.306524i 0.537036 0.843559i \(-0.319544\pi\)
−0.843559 + 0.537036i \(0.819544\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 5.08334 22.6564i 0.209278 0.932750i
\(591\) 0 0
\(592\) −0.157074 + 0.157074i −0.00645568 + 0.00645568i
\(593\) 13.8157 13.8157i 0.567344 0.567344i −0.364040 0.931383i \(-0.618603\pi\)
0.931383 + 0.364040i \(0.118603\pi\)
\(594\) 0 0
\(595\) 1.65685 + 2.61541i 0.0679244 + 0.107221i
\(596\) 20.0609i 0.821726i
\(597\) 0 0
\(598\) −3.31371 3.31371i −0.135508 0.135508i
\(599\) −0.643527 −0.0262938 −0.0131469 0.999914i \(-0.504185\pi\)
−0.0131469 + 0.999914i \(0.504185\pi\)
\(600\) 0 0
\(601\) 20.0548 0.818051 0.409026 0.912523i \(-0.365869\pi\)
0.409026 + 0.912523i \(0.365869\pi\)
\(602\) −5.88438 5.88438i −0.239829 0.239829i
\(603\) 0 0
\(604\) 8.81108i 0.358518i
\(605\) −35.2960 55.7160i −1.43499 2.26518i
\(606\) 0 0
\(607\) −16.3423 + 16.3423i −0.663312 + 0.663312i −0.956159 0.292847i \(-0.905397\pi\)
0.292847 + 0.956159i \(0.405397\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −0.479276 + 2.13613i −0.0194053 + 0.0864894i
\(611\) 10.3431i 0.418439i
\(612\) 0 0
\(613\) 6.29797 + 6.29797i 0.254373 + 0.254373i 0.822761 0.568388i \(-0.192433\pi\)
−0.568388 + 0.822761i \(0.692433\pi\)
\(614\) −1.02856 −0.0415093
\(615\) 0 0
\(616\) 6.36365 0.256399
\(617\) 15.3632 + 15.3632i 0.618500 + 0.618500i 0.945146 0.326647i \(-0.105919\pi\)
−0.326647 + 0.945146i \(0.605919\pi\)
\(618\) 0 0
\(619\) 35.1462i 1.41264i 0.707891 + 0.706322i \(0.249647\pi\)
−0.707891 + 0.706322i \(0.750353\pi\)
\(620\) −4.46478 + 2.82843i −0.179310 + 0.113592i
\(621\) 0 0
\(622\) 17.1328 17.1328i 0.686964 0.686964i
\(623\) −8.37010 + 8.37010i −0.335341 + 0.335341i
\(624\) 0 0
\(625\) −15.8739 19.3137i −0.634956 0.772548i
\(626\) 4.86566i 0.194471i
\(627\) 0 0
\(628\) 15.2654 + 15.2654i 0.609155 + 0.609155i
\(629\) 0.307568 0.0122635
\(630\) 0 0
\(631\) 22.5864 0.899151 0.449575 0.893242i \(-0.351575\pi\)
0.449575 + 0.893242i \(0.351575\pi\)
\(632\) 4.72730 + 4.72730i 0.188042 + 0.188042i
\(633\) 0 0
\(634\) 18.2714i 0.725649i
\(635\) −16.6145 3.72774i −0.659327 0.147931i
\(636\) 0 0
\(637\) −1.69230 + 1.69230i −0.0670513 + 0.0670513i
\(638\) −26.1876 + 26.1876i −1.03678 + 1.03678i
\(639\) 0 0
\(640\) −2.18183 0.489528i −0.0862442 0.0193503i
\(641\) 6.90352i 0.272673i −0.990663 0.136336i \(-0.956467\pi\)
0.990663 0.136336i \(-0.0435328\pi\)
\(642\) 0 0
\(643\) 30.4542 + 30.4542i 1.20100 + 1.20100i 0.973864 + 0.227131i \(0.0729345\pi\)
0.227131 + 0.973864i \(0.427066\pi\)
\(644\) −1.95811 −0.0771604
\(645\) 0 0
\(646\) 0 0
\(647\) 13.9726 + 13.9726i 0.549320 + 0.549320i 0.926244 0.376924i \(-0.123018\pi\)
−0.376924 + 0.926244i \(0.623018\pi\)
\(648\) 0 0
\(649\) 66.0811i 2.59391i
\(650\) −10.8193 5.11233i −0.424368 0.200522i
\(651\) 0 0
\(652\) −7.11519 + 7.11519i −0.278652 + 0.278652i
\(653\) −7.99597 + 7.99597i −0.312906 + 0.312906i −0.846035 0.533128i \(-0.821016\pi\)
0.533128 + 0.846035i \(0.321016\pi\)
\(654\) 0 0
\(655\) −25.0696 + 15.8815i −0.979549 + 0.620543i
\(656\) 8.94944i 0.349417i
\(657\) 0 0
\(658\) −3.05595 3.05595i −0.119133 0.119133i
\(659\) 27.9020 1.08691 0.543454 0.839439i \(-0.317116\pi\)
0.543454 + 0.839439i \(0.317116\pi\)
\(660\) 0 0
\(661\) −0.294519 −0.0114555 −0.00572774 0.999984i \(-0.501823\pi\)
−0.00572774 + 0.999984i \(0.501823\pi\)
\(662\) −6.20013 6.20013i −0.240975 0.240975i
\(663\) 0 0
\(664\) 16.0410i 0.622512i
\(665\) 0 0
\(666\) 0 0
\(667\) 8.05800 8.05800i 0.312007 0.312007i
\(668\) 16.7128 16.7128i 0.646638 0.646638i
\(669\) 0 0
\(670\) −16.7273 26.4047i −0.646232 1.02010i
\(671\) 6.23037i 0.240521i
\(672\) 0 0
\(673\) −24.6569 24.6569i −0.950452 0.950452i 0.0483773 0.998829i \(-0.484595\pi\)
−0.998829 + 0.0483773i \(0.984595\pi\)
\(674\) 17.4552 0.672350
\(675\) 0 0
\(676\) 7.27226 0.279702
\(677\) −28.7195 28.7195i −1.10378 1.10378i −0.993950 0.109831i \(-0.964969\pi\)
−0.109831 0.993950i \(-0.535031\pi\)
\(678\) 0 0
\(679\) 13.2917i 0.510089i
\(680\) 1.65685 + 2.61541i 0.0635375 + 0.100296i
\(681\) 0 0
\(682\) 10.6359 10.6359i 0.407270 0.407270i
\(683\) 0.221515 0.221515i 0.00847605 0.00847605i −0.702856 0.711332i \(-0.748092\pi\)
0.711332 + 0.702856i \(0.248092\pi\)
\(684\) 0 0
\(685\) 2.46793 10.9996i 0.0942948 0.420272i
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −5.88438 5.88438i −0.224340 0.224340i
\(689\) −0.651591 −0.0248236
\(690\) 0 0
\(691\) −36.2648 −1.37958 −0.689789 0.724010i \(-0.742297\pi\)
−0.689789 + 0.724010i \(0.742297\pi\)
\(692\) 14.7843 + 14.7843i 0.562015 + 0.562015i
\(693\) 0 0
\(694\) 7.31371i 0.277625i
\(695\) −2.67018 + 1.69155i −0.101286 + 0.0641643i
\(696\) 0 0
\(697\) −8.76200 + 8.76200i −0.331885 + 0.331885i
\(698\) 20.4610 20.4610i 0.774462 0.774462i
\(699\) 0 0
\(700\) −4.70711 + 1.68616i −0.177912 + 0.0637310i
\(701\) 21.0497i 0.795036i −0.917594 0.397518i \(-0.869872\pi\)
0.917594 0.397518i \(-0.130128\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 6.36365 0.239839
\(705\) 0 0
\(706\) 14.6564 0.551601
\(707\) 11.3492 + 11.3492i 0.426829 + 0.426829i
\(708\) 0 0
\(709\) 14.3617i 0.539366i 0.962949 + 0.269683i \(0.0869190\pi\)
−0.962949 + 0.269683i \(0.913081\pi\)
\(710\) −26.9287 6.04189i −1.01062 0.226748i
\(711\) 0 0
\(712\) −8.37010 + 8.37010i −0.313683 + 0.313683i
\(713\) −3.27270 + 3.27270i −0.122564 + 0.122564i
\(714\) 0 0
\(715\) 33.2291 + 7.45548i 1.24270 + 0.278819i
\(716\) 12.0205i 0.449227i
\(717\) 0 0
\(718\) −9.35560 9.35560i −0.349148 0.349148i
\(719\) −16.9706 −0.632895 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 0 0
\(721\) −0.999561 −0.0372256
\(722\) −13.4350 13.4350i −0.500000 0.500000i
\(723\) 0 0
\(724\) 17.5236i 0.651259i
\(725\) 12.4317 26.3095i 0.461703 0.977110i
\(726\) 0 0
\(727\) −2.42692 + 2.42692i −0.0900095 + 0.0900095i −0.750678 0.660668i \(-0.770273\pi\)
0.660668 + 0.750678i \(0.270273\pi\)
\(728\) −1.69230 + 1.69230i −0.0627207 + 0.0627207i
\(729\) 0 0
\(730\) 12.5907 7.97621i 0.466004 0.295213i
\(731\) 11.5223i 0.426167i
\(732\) 0 0
\(733\) −14.3701 14.3701i −0.530772 0.530772i 0.390030 0.920802i \(-0.372464\pi\)
−0.920802 + 0.390030i \(0.872464\pi\)
\(734\) 4.53882 0.167531
\(735\) 0 0
\(736\) −1.95811 −0.0721770
\(737\) 62.9007 + 62.9007i 2.31698 + 2.31698i
\(738\) 0 0
\(739\) 38.0886i 1.40111i −0.713598 0.700556i \(-0.752935\pi\)
0.713598 0.700556i \(-0.247065\pi\)
\(740\) −0.108742 + 0.484661i −0.00399742 + 0.0178165i
\(741\) 0 0
\(742\) −0.192517 + 0.192517i −0.00706751 + 0.00706751i
\(743\) −31.4965 + 31.4965i −1.15549 + 1.15549i −0.170061 + 0.985434i \(0.554396\pi\)
−0.985434 + 0.170061i \(0.945604\pi\)
\(744\) 0 0
\(745\) −24.0056 37.8937i −0.879496 1.38832i
\(746\) 3.20881i 0.117483i
\(747\) 0 0
\(748\) −6.23037 6.23037i −0.227805 0.227805i
\(749\) −13.4546 −0.491621
\(750\) 0 0
\(751\) 16.9511 0.618554 0.309277 0.950972i \(-0.399913\pi\)
0.309277 + 0.950972i \(0.399913\pi\)
\(752\) −3.05595 3.05595i −0.111439 0.111439i
\(753\) 0 0
\(754\) 13.9282i 0.507236i
\(755\) 10.5436 + 16.6435i 0.383722 + 0.605720i
\(756\) 0 0
\(757\) −2.34644 + 2.34644i −0.0852826 + 0.0852826i −0.748461 0.663179i \(-0.769207\pi\)
0.663179 + 0.748461i \(0.269207\pi\)
\(758\) −1.69559 + 1.69559i −0.0615865 + 0.0615865i
\(759\) 0 0
\(760\) 0 0
\(761\) 3.07510i 0.111472i 0.998446 + 0.0557361i \(0.0177506\pi\)
−0.998446 + 0.0557361i \(0.982249\pi\)
\(762\) 0 0
\(763\) −10.5767 10.5767i −0.382901 0.382901i
\(764\) 6.30038 0.227940
\(765\) 0 0
\(766\) −23.5945 −0.852503
\(767\) −17.5731 17.5731i −0.634527 0.634527i
\(768\) 0 0
\(769\) 17.4666i 0.629862i 0.949115 + 0.314931i \(0.101981\pi\)
−0.949115 + 0.314931i \(0.898019\pi\)
\(770\) 12.0205 7.61497i 0.433189 0.274424i
\(771\) 0 0
\(772\) 11.6435 11.6435i 0.419060 0.419060i
\(773\) 38.6076 38.6076i 1.38862 1.38862i 0.560395 0.828225i \(-0.310649\pi\)
0.828225 0.560395i \(-0.189351\pi\)
\(774\) 0 0
\(775\) −5.04907 + 10.6854i −0.181368 + 0.383831i
\(776\) 13.2917i 0.477144i
\(777\) 0 0
\(778\) 15.6117 + 15.6117i 0.559706 + 0.559706i
\(779\) 0 0
\(780\) 0 0
\(781\) 78.5419 2.81045
\(782\) 1.91710 + 1.91710i 0.0685554 + 0.0685554i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 47.1023 + 10.5682i 1.68115 + 0.377194i
\(786\) 0 0
\(787\) −12.3076 + 12.3076i −0.438717 + 0.438717i −0.891580 0.452863i \(-0.850403\pi\)
0.452863 + 0.891580i \(0.350403\pi\)
\(788\) 1.92849 1.92849i 0.0686997 0.0686997i
\(789\) 0 0
\(790\) 14.5864 + 3.27270i 0.518961 + 0.116437i
\(791\) 13.0414i 0.463701i
\(792\) 0 0
\(793\) 1.65685 + 1.65685i 0.0588366 + 0.0588366i
\(794\) −29.6585 −1.05254
\(795\) 0 0
\(796\) 5.67736 0.201229
\(797\) −4.88543 4.88543i −0.173051 0.173051i 0.615267 0.788318i \(-0.289048\pi\)
−0.788318 + 0.615267i \(0.789048\pi\)
\(798\) 0 0
\(799\) 5.98389i 0.211695i
\(800\) −4.70711 + 1.68616i −0.166421 + 0.0596149i
\(801\) 0 0
\(802\) 6.57308 6.57308i 0.232103 0.232103i
\(803\) −29.9934 + 29.9934i −1.05844 + 1.05844i
\(804\) 0 0
\(805\) −3.69874 + 2.34315i −0.130364 + 0.0825850i
\(806\) 5.65685i 0.199254i
\(807\) 0 0
\(808\) 11.3492 + 11.3492i 0.399262 + 0.399262i
\(809\) −6.30907 −0.221815 −0.110907 0.993831i \(-0.535376\pi\)
−0.110907 + 0.993831i \(0.535376\pi\)
\(810\) 0 0
\(811\) 41.6632 1.46299 0.731496 0.681846i \(-0.238823\pi\)
0.731496 + 0.681846i \(0.238823\pi\)
\(812\) −4.11519 4.11519i −0.144415 0.144415i
\(813\) 0 0
\(814\) 1.41359i 0.0495464i
\(815\) −4.92582 + 21.9544i −0.172544 + 0.769029i
\(816\) 0 0
\(817\) 0 0
\(818\) 24.2090 24.2090i 0.846447 0.846447i
\(819\) 0 0
\(820\) −10.7092 16.9049i −0.373982 0.590344i
\(821\) 46.4552i 1.62130i 0.585532 + 0.810649i \(0.300886\pi\)
−0.585532 + 0.810649i \(0.699114\pi\)
\(822\) 0 0
\(823\) −27.2942 27.2942i −0.951417 0.951417i 0.0474559 0.998873i \(-0.484889\pi\)
−0.998873 + 0.0474559i \(0.984889\pi\)
\(824\) −0.999561 −0.0348214
\(825\) 0 0
\(826\) −10.3842 −0.361311
\(827\) 37.6528 + 37.6528i 1.30932 + 1.30932i 0.921908 + 0.387409i \(0.126630\pi\)
0.387409 + 0.921908i \(0.373370\pi\)
\(828\) 0 0
\(829\) 16.9791i 0.589707i 0.955542 + 0.294853i \(0.0952708\pi\)
−0.955542 + 0.294853i \(0.904729\pi\)
\(830\) −19.1952 30.3004i −0.666276 1.05174i
\(831\) 0 0
\(832\) −1.69230 + 1.69230i −0.0586699 + 0.0586699i
\(833\) 0.979056 0.979056i 0.0339223 0.0339223i
\(834\) 0 0
\(835\) 11.5702 51.5685i 0.400404 1.78460i
\(836\) 0 0
\(837\) 0 0
\(838\) −9.74063 9.74063i −0.336484 0.336484i
\(839\) 2.63064 0.0908197 0.0454099 0.998968i \(-0.485541\pi\)
0.0454099 + 0.998968i \(0.485541\pi\)
\(840\) 0 0
\(841\) 4.86951 0.167914
\(842\) −7.51534 7.51534i −0.258996 0.258996i
\(843\) 0 0
\(844\) 7.91622i 0.272488i
\(845\) 13.7368 8.70224i 0.472560 0.299366i
\(846\) 0 0
\(847\) −20.8569 + 20.8569i −0.716650 + 0.716650i
\(848\) −0.192517 + 0.192517i −0.00661105 + 0.00661105i
\(849\) 0 0
\(850\) 6.25937 + 2.95767i 0.214695 + 0.101447i
\(851\) 0.434966i 0.0149105i
\(852\) 0 0
\(853\) −35.6700 35.6700i −1.22132 1.22132i −0.967163 0.254155i \(-0.918203\pi\)
−0.254155 0.967163i \(-0.581797\pi\)
\(854\) 0.979056 0.0335026
\(855\) 0 0
\(856\) −13.4546 −0.459869
\(857\) −2.97818 2.97818i −0.101733 0.101733i 0.654409 0.756141i \(-0.272918\pi\)
−0.756141 + 0.654409i \(0.772918\pi\)
\(858\) 0 0
\(859\) 30.9634i 1.05646i 0.849102 + 0.528228i \(0.177144\pi\)
−0.849102 + 0.528228i \(0.822856\pi\)
\(860\) −18.1566 4.07374i −0.619136 0.138913i
\(861\) 0 0
\(862\) −13.3556 + 13.3556i −0.454893 + 0.454893i
\(863\) −0.602516 + 0.602516i −0.0205099 + 0.0205099i −0.717287 0.696777i \(-0.754617\pi\)
0.696777 + 0.717287i \(0.254617\pi\)
\(864\) 0 0
\(865\) 45.6180 + 10.2351i 1.55106 + 0.348005i
\(866\) 27.3928i 0.930846i
\(867\) 0 0
\(868\) 1.67135 + 1.67135i 0.0567294 + 0.0567294i
\(869\) −42.5436 −1.44319
\(870\) 0 0
\(871\) −33.4546 −1.13357
\(872\) −10.5767 10.5767i −0.358171 0.358171i
\(873\) 0 0
\(874\) 0 0
\(875\) −6.87368 + 8.81774i −0.232373 + 0.298094i
\(876\) 0 0
\(877\) 28.7369 28.7369i 0.970376 0.970376i −0.0291975 0.999574i \(-0.509295\pi\)
0.999574 + 0.0291975i \(0.00929516\pi\)
\(878\) −3.44098 + 3.44098i −0.116127 + 0.116127i
\(879\) 0 0
\(880\) 12.0205 7.61497i 0.405211 0.256700i
\(881\) 46.7691i 1.57569i 0.615873 + 0.787845i \(0.288803\pi\)
−0.615873 + 0.787845i \(0.711197\pi\)
\(882\) 0 0
\(883\) −27.4285 27.4285i −0.923041 0.923041i 0.0742022 0.997243i \(-0.476359\pi\)
−0.997243 + 0.0742022i \(0.976359\pi\)
\(884\) 3.31371 0.111452
\(885\) 0 0
\(886\) −10.1409 −0.340690
\(887\) −16.1393 16.1393i −0.541904 0.541904i 0.382183 0.924087i \(-0.375173\pi\)
−0.924087 + 0.382183i \(0.875173\pi\)
\(888\) 0 0
\(889\) 7.61497i 0.255398i
\(890\) −5.79459 + 25.8265i −0.194235 + 0.865706i
\(891\) 0 0
\(892\) −8.34227 + 8.34227i −0.279320 + 0.279320i
\(893\) 0 0
\(894\) 0 0
\(895\) 14.3842 + 22.7059i 0.480809 + 0.758975i
\(896\) 1.00000i 0.0334077i
\(897\) 0 0
\(898\) 6.27270 + 6.27270i 0.209323 + 0.209323i
\(899\) −13.7559 −0.458784
\(900\) 0 0
\(901\) 0.376969 0.0125587
\(902\) 40.2705 + 40.2705i 1.34086 + 1.34086i
\(903\) 0 0
\(904\) 13.0414i 0.433752i
\(905\) 20.9693 + 33.1008i 0.697044 + 1.10031i
\(906\) 0 0
\(907\) −2.57067 + 2.57067i −0.0853576 + 0.0853576i −0.748496 0.663139i \(-0.769224\pi\)
0.663139 + 0.748496i \(0.269224\pi\)
\(908\) 3.27270 3.27270i 0.108608 0.108608i
\(909\) 0 0
\(910\) −1.17157 + 5.22170i −0.0388373 + 0.173098i
\(911\) 37.2138i 1.23295i −0.787375 0.616474i \(-0.788560\pi\)
0.787375 0.616474i \(-0.211440\pi\)
\(912\) 0 0
\(913\) 72.1810 + 72.1810i 2.38884 + 2.38884i
\(914\) −6.04251 −0.199868
\(915\) 0 0
\(916\) 23.0901 0.762918
\(917\) 9.38459 + 9.38459i 0.309907 + 0.309907i
\(918\) 0 0
\(919\) 0.126540i 0.00417416i 0.999998 + 0.00208708i \(0.000664339\pi\)
−0.999998 + 0.00208708i \(0.999336\pi\)
\(920\) −3.69874 + 2.34315i −0.121944 + 0.0772512i
\(921\) 0 0
\(922\) −0.545691 + 0.545691i −0.0179714 + 0.0179714i
\(923\) −20.8868 + 20.8868i −0.687497 + 0.687497i
\(924\) 0 0
\(925\) 0.374557 + 1.04562i 0.0123154 + 0.0343796i
\(926\) 27.7398i 0.911585i
\(927\) 0 0
\(928\) −4.11519 4.11519i −0.135088 0.135088i
\(929\) −44.7882 −1.46945 −0.734727 0.678363i \(-0.762690\pi\)
−0.734727 + 0.678363i \(0.762690\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 5.23081 + 5.23081i 0.171341 + 0.171341i
\(933\) 0 0
\(934\) 11.5803i 0.378918i
\(935\) −19.2242 4.31327i −0.628700 0.141059i
\(936\) 0 0
\(937\) −27.9303 + 27.9303i −0.912443 + 0.912443i −0.996464 0.0840213i \(-0.973224\pi\)
0.0840213 + 0.996464i \(0.473224\pi\)
\(938\) −9.88438 + 9.88438i −0.322736 + 0.322736i
\(939\) 0 0
\(940\) −9.42933 2.11562i −0.307551 0.0690041i
\(941\) 18.3233i 0.597321i 0.954359 + 0.298661i \(0.0965399\pi\)
−0.954359 + 0.298661i \(0.903460\pi\)
\(942\) 0 0
\(943\) −12.3913 12.3913i −0.403518 0.403518i
\(944\) −10.3842 −0.337975
\(945\) 0 0
\(946\) 52.9568 1.72177
\(947\) 32.1360 + 32.1360i 1.04428 + 1.04428i 0.998973 + 0.0453061i \(0.0144263\pi\)
0.0453061 + 0.998973i \(0.485574\pi\)
\(948\) 0 0
\(949\) 15.9524i 0.517837i
\(950\) 0 0
\(951\) 0 0
\(952\) 0.979056 0.979056i 0.0317314 0.0317314i
\(953\) −1.74001 + 1.74001i −0.0563644 + 0.0563644i −0.734727 0.678363i \(-0.762690\pi\)
0.678363 + 0.734727i \(0.262690\pi\)
\(954\) 0 0
\(955\) 11.9010 7.53926i 0.385107 0.243965i
\(956\) 5.27182i 0.170503i
\(957\) 0 0
\(958\) −14.9082 14.9082i −0.481661 0.481661i
\(959\) −5.04145 −0.162797
\(960\) 0 0
\(961\) −25.4132 −0.819779
\(962\) 0.375919 + 0.375919i 0.0121201 + 0.0121201i
\(963\) 0 0
\(964\) 5.27270i 0.169822i
\(965\) 8.06078 35.9269i 0.259486 1.15653i
\(966\) 0 0
\(967\) 19.7140 19.7140i 0.633959 0.633959i −0.315100 0.949059i \(-0.602038\pi\)
0.949059 + 0.315100i \(0.102038\pi\)
\(968\) −20.8569 + 20.8569i −0.670365 + 0.670365i
\(969\) 0 0
\(970\) 15.9053 + 25.1071i 0.510689 + 0.806141i
\(971\) 21.2308i 0.681329i −0.940185 0.340665i \(-0.889348\pi\)
0.940185 0.340665i \(-0.110652\pi\)
\(972\) 0 0
\(973\) 0.999561 + 0.999561i 0.0320445 + 0.0320445i
\(974\) 29.2718 0.937930
\(975\) 0 0
\(976\) 0.979056 0.0313388
\(977\) 12.3013 + 12.3013i 0.393552 + 0.393552i 0.875951 0.482399i \(-0.160235\pi\)
−0.482399 + 0.875951i \(0.660235\pi\)
\(978\) 0 0
\(979\) 75.3272i 2.40747i
\(980\) 1.19663 + 1.88893i 0.0382251 + 0.0603397i
\(981\) 0 0
\(982\) 7.26897 7.26897i 0.231962 0.231962i
\(983\) −23.3087 + 23.3087i −0.743433 + 0.743433i −0.973237 0.229804i \(-0.926192\pi\)
0.229804 + 0.973237i \(0.426192\pi\)
\(984\) 0 0
\(985\) 1.33509 5.95050i 0.0425395 0.189599i
\(986\) 8.05800i 0.256619i
\(987\) 0 0
\(988\) 0 0
\(989\) −16.2949 −0.518149
\(990\) 0 0
\(991\) 10.5606 0.335469 0.167735 0.985832i \(-0.446355\pi\)
0.167735 + 0.985832i \(0.446355\pi\)
\(992\) 1.67135 + 1.67135i 0.0530655 + 0.0530655i
\(993\) 0 0
\(994\) 12.3423i 0.391473i
\(995\) 10.7241 6.79373i 0.339978 0.215376i
\(996\) 0 0
\(997\) 28.3973 28.3973i 0.899353 0.899353i −0.0960261 0.995379i \(-0.530613\pi\)
0.995379 + 0.0960261i \(0.0306132\pi\)
\(998\) 3.65370 3.65370i 0.115656 0.115656i
\(999\) 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.c.323.2 yes 8
3.2 odd 2 630.2.m.d.323.3 yes 8
5.2 odd 4 630.2.m.d.197.3 yes 8
5.3 odd 4 3150.2.m.j.1457.2 8
5.4 even 2 3150.2.m.i.2843.4 8
15.2 even 4 inner 630.2.m.c.197.2 8
15.8 even 4 3150.2.m.i.1457.3 8
15.14 odd 2 3150.2.m.j.2843.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.m.c.197.2 8 15.2 even 4 inner
630.2.m.c.323.2 yes 8 1.1 even 1 trivial
630.2.m.d.197.3 yes 8 5.2 odd 4
630.2.m.d.323.3 yes 8 3.2 odd 2
3150.2.m.i.1457.3 8 15.8 even 4
3150.2.m.i.2843.4 8 5.4 even 2
3150.2.m.j.1457.2 8 5.3 odd 4
3150.2.m.j.2843.1 8 15.14 odd 2