Properties

Label 560.2.ci.b.257.1
Level $560$
Weight $2$
Character 560.257
Analytic conductor $4.472$
Analytic rank $0$
Dimension $4$
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] = [560,2,Mod(17,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 257.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 560.257
Dual form 560.2.ci.b.353.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.133975 - 0.500000i) q^{3} +(0.133975 - 2.23205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})\) \(q+(0.133975 - 0.500000i) q^{3} +(0.133975 - 2.23205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(2.36603 + 1.36603i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(-1.09808 - 0.366025i) q^{15} +(3.73205 + 1.00000i) q^{17} +(-0.366025 + 0.633975i) q^{19} +(0.767949 - 1.13397i) q^{21} +(-0.0358984 - 0.133975i) q^{23} +(-4.96410 - 0.598076i) q^{25} +(2.09808 - 2.09808i) q^{27} -3.00000i q^{29} +(6.46410 - 3.73205i) q^{31} +(-1.36603 + 0.366025i) q^{33} +(2.26795 - 5.46410i) q^{35} +(-4.73205 + 1.26795i) q^{37} +(-1.26795 + 0.732051i) q^{39} -6.46410i q^{41} +(-2.83013 + 2.83013i) q^{43} +(3.36603 - 5.09808i) q^{45} +(-2.36603 - 8.83013i) q^{47} +(5.50000 + 4.33013i) q^{49} +(1.00000 - 1.73205i) q^{51} +(6.83013 + 1.83013i) q^{53} +(-5.46410 + 2.73205i) q^{55} +(0.267949 + 0.267949i) q^{57} +(4.09808 + 7.09808i) q^{59} +(1.33013 + 0.767949i) q^{61} +(4.73205 + 5.46410i) q^{63} +(-4.73205 + 4.19615i) q^{65} +(-2.86603 + 10.6962i) q^{67} -0.0717968 q^{69} -1.26795 q^{71} +(-3.46410 + 12.9282i) q^{73} +(-0.964102 + 2.40192i) q^{75} +(-1.36603 - 7.09808i) q^{77} +(-2.83013 - 1.63397i) q^{79} +(3.33013 + 5.76795i) q^{81} +(2.09808 + 2.09808i) q^{83} +(2.73205 - 8.19615i) q^{85} +(-1.50000 - 0.401924i) q^{87} +(-0.330127 + 0.571797i) q^{89} +(-3.26795 - 6.73205i) q^{91} +(-1.00000 - 3.73205i) q^{93} +(1.36603 + 0.901924i) q^{95} +(-5.92820 + 5.92820i) q^{97} -7.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9} - 2 q^{11} - 8 q^{13} + 6 q^{15} + 8 q^{17} + 2 q^{19} + 10 q^{21} - 14 q^{23} - 6 q^{25} - 2 q^{27} + 12 q^{31} - 2 q^{33} + 16 q^{35} - 12 q^{37} - 12 q^{39} + 6 q^{43} + 10 q^{45} - 6 q^{47} + 22 q^{49} + 4 q^{51} + 10 q^{53} - 8 q^{55} + 8 q^{57} + 6 q^{59} - 12 q^{61} + 12 q^{63} - 12 q^{65} - 8 q^{67} - 28 q^{69} - 12 q^{71} + 10 q^{75} - 2 q^{77} + 6 q^{79} - 4 q^{81} - 2 q^{83} + 4 q^{85} - 6 q^{87} + 16 q^{89} - 20 q^{91} - 4 q^{93} + 2 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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 0
\(3\) 0.133975 0.500000i 0.0773503 0.288675i −0.916406 0.400251i \(-0.868923\pi\)
0.993756 + 0.111576i \(0.0355897\pi\)
\(4\) 0 0
\(5\) 0.133975 2.23205i 0.0599153 0.998203i
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 0 0
\(9\) 2.36603 + 1.36603i 0.788675 + 0.455342i
\(10\) 0 0
\(11\) −1.36603 2.36603i −0.411872 0.713384i 0.583222 0.812313i \(-0.301792\pi\)
−0.995094 + 0.0989291i \(0.968458\pi\)
\(12\) 0 0
\(13\) −2.00000 2.00000i −0.554700 0.554700i 0.373094 0.927794i \(-0.378297\pi\)
−0.927794 + 0.373094i \(0.878297\pi\)
\(14\) 0 0
\(15\) −1.09808 0.366025i −0.283522 0.0945074i
\(16\) 0 0
\(17\) 3.73205 + 1.00000i 0.905155 + 0.242536i 0.681229 0.732070i \(-0.261446\pi\)
0.223926 + 0.974606i \(0.428112\pi\)
\(18\) 0 0
\(19\) −0.366025 + 0.633975i −0.0839720 + 0.145444i −0.904953 0.425512i \(-0.860094\pi\)
0.820981 + 0.570956i \(0.193427\pi\)
\(20\) 0 0
\(21\) 0.767949 1.13397i 0.167580 0.247454i
\(22\) 0 0
\(23\) −0.0358984 0.133975i −0.00748533 0.0279356i 0.962082 0.272760i \(-0.0879364\pi\)
−0.969567 + 0.244824i \(0.921270\pi\)
\(24\) 0 0
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) 0 0
\(27\) 2.09808 2.09808i 0.403775 0.403775i
\(28\) 0 0
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) 0 0
\(31\) 6.46410 3.73205i 1.16099 0.670296i 0.209447 0.977820i \(-0.432834\pi\)
0.951540 + 0.307524i \(0.0995004\pi\)
\(32\) 0 0
\(33\) −1.36603 + 0.366025i −0.237795 + 0.0637168i
\(34\) 0 0
\(35\) 2.26795 5.46410i 0.383353 0.923602i
\(36\) 0 0
\(37\) −4.73205 + 1.26795i −0.777944 + 0.208450i −0.625878 0.779921i \(-0.715259\pi\)
−0.152066 + 0.988370i \(0.548593\pi\)
\(38\) 0 0
\(39\) −1.26795 + 0.732051i −0.203034 + 0.117222i
\(40\) 0 0
\(41\) 6.46410i 1.00952i −0.863259 0.504762i \(-0.831580\pi\)
0.863259 0.504762i \(-0.168420\pi\)
\(42\) 0 0
\(43\) −2.83013 + 2.83013i −0.431590 + 0.431590i −0.889169 0.457579i \(-0.848717\pi\)
0.457579 + 0.889169i \(0.348717\pi\)
\(44\) 0 0
\(45\) 3.36603 5.09808i 0.501777 0.759976i
\(46\) 0 0
\(47\) −2.36603 8.83013i −0.345120 1.28801i −0.892472 0.451103i \(-0.851031\pi\)
0.547351 0.836903i \(-0.315636\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 1.00000 1.73205i 0.140028 0.242536i
\(52\) 0 0
\(53\) 6.83013 + 1.83013i 0.938190 + 0.251387i 0.695344 0.718677i \(-0.255252\pi\)
0.242846 + 0.970065i \(0.421919\pi\)
\(54\) 0 0
\(55\) −5.46410 + 2.73205i −0.736779 + 0.368390i
\(56\) 0 0
\(57\) 0.267949 + 0.267949i 0.0354907 + 0.0354907i
\(58\) 0 0
\(59\) 4.09808 + 7.09808i 0.533524 + 0.924091i 0.999233 + 0.0391530i \(0.0124660\pi\)
−0.465709 + 0.884938i \(0.654201\pi\)
\(60\) 0 0
\(61\) 1.33013 + 0.767949i 0.170305 + 0.0983258i 0.582730 0.812666i \(-0.301985\pi\)
−0.412424 + 0.910992i \(0.635318\pi\)
\(62\) 0 0
\(63\) 4.73205 + 5.46410i 0.596182 + 0.688412i
\(64\) 0 0
\(65\) −4.73205 + 4.19615i −0.586939 + 0.520469i
\(66\) 0 0
\(67\) −2.86603 + 10.6962i −0.350141 + 1.30674i 0.536350 + 0.843996i \(0.319803\pi\)
−0.886490 + 0.462747i \(0.846864\pi\)
\(68\) 0 0
\(69\) −0.0717968 −0.00864332
\(70\) 0 0
\(71\) −1.26795 −0.150478 −0.0752389 0.997166i \(-0.523972\pi\)
−0.0752389 + 0.997166i \(0.523972\pi\)
\(72\) 0 0
\(73\) −3.46410 + 12.9282i −0.405442 + 1.51313i 0.397796 + 0.917474i \(0.369775\pi\)
−0.803238 + 0.595658i \(0.796891\pi\)
\(74\) 0 0
\(75\) −0.964102 + 2.40192i −0.111325 + 0.277350i
\(76\) 0 0
\(77\) −1.36603 7.09808i −0.155673 0.808901i
\(78\) 0 0
\(79\) −2.83013 1.63397i −0.318414 0.183837i 0.332271 0.943184i \(-0.392185\pi\)
−0.650686 + 0.759347i \(0.725518\pi\)
\(80\) 0 0
\(81\) 3.33013 + 5.76795i 0.370014 + 0.640883i
\(82\) 0 0
\(83\) 2.09808 + 2.09808i 0.230294 + 0.230294i 0.812815 0.582522i \(-0.197934\pi\)
−0.582522 + 0.812815i \(0.697934\pi\)
\(84\) 0 0
\(85\) 2.73205 8.19615i 0.296333 0.888998i
\(86\) 0 0
\(87\) −1.50000 0.401924i −0.160817 0.0430908i
\(88\) 0 0
\(89\) −0.330127 + 0.571797i −0.0349934 + 0.0606103i −0.882992 0.469389i \(-0.844474\pi\)
0.847998 + 0.529999i \(0.177808\pi\)
\(90\) 0 0
\(91\) −3.26795 6.73205i −0.342574 0.705711i
\(92\) 0 0
\(93\) −1.00000 3.73205i −0.103695 0.386996i
\(94\) 0 0
\(95\) 1.36603 + 0.901924i 0.140151 + 0.0925354i
\(96\) 0 0
\(97\) −5.92820 + 5.92820i −0.601918 + 0.601918i −0.940821 0.338903i \(-0.889944\pi\)
0.338903 + 0.940821i \(0.389944\pi\)
\(98\) 0 0
\(99\) 7.46410i 0.750170i
\(100\) 0 0
\(101\) 7.16025 4.13397i 0.712472 0.411346i −0.0995037 0.995037i \(-0.531726\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 0 0
\(103\) −4.59808 + 1.23205i −0.453062 + 0.121398i −0.478132 0.878288i \(-0.658686\pi\)
0.0250698 + 0.999686i \(0.492019\pi\)
\(104\) 0 0
\(105\) −2.42820 1.86603i −0.236968 0.182105i
\(106\) 0 0
\(107\) −12.6962 + 3.40192i −1.22738 + 0.328876i −0.813560 0.581481i \(-0.802474\pi\)
−0.413823 + 0.910357i \(0.635807\pi\)
\(108\) 0 0
\(109\) −8.76795 + 5.06218i −0.839817 + 0.484869i −0.857202 0.514980i \(-0.827799\pi\)
0.0173849 + 0.999849i \(0.494466\pi\)
\(110\) 0 0
\(111\) 2.53590i 0.240697i
\(112\) 0 0
\(113\) −7.73205 + 7.73205i −0.727370 + 0.727370i −0.970095 0.242725i \(-0.921959\pi\)
0.242725 + 0.970095i \(0.421959\pi\)
\(114\) 0 0
\(115\) −0.303848 + 0.0621778i −0.0283339 + 0.00579811i
\(116\) 0 0
\(117\) −2.00000 7.46410i −0.184900 0.690056i
\(118\) 0 0
\(119\) 8.46410 + 5.73205i 0.775903 + 0.525456i
\(120\) 0 0
\(121\) 1.76795 3.06218i 0.160723 0.278380i
\(122\) 0 0
\(123\) −3.23205 0.866025i −0.291424 0.0780869i
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) −0.464102 0.464102i −0.0411824 0.0411824i 0.686216 0.727398i \(-0.259271\pi\)
−0.727398 + 0.686216i \(0.759271\pi\)
\(128\) 0 0
\(129\) 1.03590 + 1.79423i 0.0912058 + 0.157973i
\(130\) 0 0
\(131\) 13.3923 + 7.73205i 1.17009 + 0.675552i 0.953702 0.300755i \(-0.0972385\pi\)
0.216390 + 0.976307i \(0.430572\pi\)
\(132\) 0 0
\(133\) −1.46410 + 1.26795i −0.126954 + 0.109945i
\(134\) 0 0
\(135\) −4.40192 4.96410i −0.378857 0.427242i
\(136\) 0 0
\(137\) −3.53590 + 13.1962i −0.302092 + 1.12742i 0.633327 + 0.773884i \(0.281689\pi\)
−0.935420 + 0.353539i \(0.884978\pi\)
\(138\) 0 0
\(139\) 5.66025 0.480096 0.240048 0.970761i \(-0.422837\pi\)
0.240048 + 0.970761i \(0.422837\pi\)
\(140\) 0 0
\(141\) −4.73205 −0.398511
\(142\) 0 0
\(143\) −2.00000 + 7.46410i −0.167248 + 0.624180i
\(144\) 0 0
\(145\) −6.69615 0.401924i −0.556085 0.0333780i
\(146\) 0 0
\(147\) 2.90192 2.16987i 0.239347 0.178968i
\(148\) 0 0
\(149\) 0.696152 + 0.401924i 0.0570310 + 0.0329269i 0.528244 0.849092i \(-0.322850\pi\)
−0.471213 + 0.882019i \(0.656184\pi\)
\(150\) 0 0
\(151\) 6.92820 + 12.0000i 0.563809 + 0.976546i 0.997159 + 0.0753205i \(0.0239980\pi\)
−0.433350 + 0.901226i \(0.642669\pi\)
\(152\) 0 0
\(153\) 7.46410 + 7.46410i 0.603437 + 0.603437i
\(154\) 0 0
\(155\) −7.46410 14.9282i −0.599531 1.19906i
\(156\) 0 0
\(157\) −4.63397 1.24167i −0.369831 0.0990960i 0.0691164 0.997609i \(-0.477982\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 0 0
\(159\) 1.83013 3.16987i 0.145139 0.251387i
\(160\) 0 0
\(161\) 0.0262794 0.366025i 0.00207111 0.0288468i
\(162\) 0 0
\(163\) 3.63397 + 13.5622i 0.284635 + 1.06227i 0.949106 + 0.314958i \(0.101990\pi\)
−0.664471 + 0.747314i \(0.731343\pi\)
\(164\) 0 0
\(165\) 0.633975 + 3.09808i 0.0493549 + 0.241185i
\(166\) 0 0
\(167\) −11.7583 + 11.7583i −0.909887 + 0.909887i −0.996263 0.0863757i \(-0.972471\pi\)
0.0863757 + 0.996263i \(0.472471\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) −1.73205 + 1.00000i −0.132453 + 0.0764719i
\(172\) 0 0
\(173\) 19.9282 5.33975i 1.51511 0.405973i 0.596984 0.802253i \(-0.296366\pi\)
0.918130 + 0.396280i \(0.129699\pi\)
\(174\) 0 0
\(175\) −11.8923 5.79423i −0.898974 0.438003i
\(176\) 0 0
\(177\) 4.09808 1.09808i 0.308030 0.0825365i
\(178\) 0 0
\(179\) −6.80385 + 3.92820i −0.508543 + 0.293608i −0.732235 0.681052i \(-0.761523\pi\)
0.223691 + 0.974660i \(0.428189\pi\)
\(180\) 0 0
\(181\) 1.19615i 0.0889093i −0.999011 0.0444547i \(-0.985845\pi\)
0.999011 0.0444547i \(-0.0141550\pi\)
\(182\) 0 0
\(183\) 0.562178 0.562178i 0.0415574 0.0415574i
\(184\) 0 0
\(185\) 2.19615 + 10.7321i 0.161464 + 0.789036i
\(186\) 0 0
\(187\) −2.73205 10.1962i −0.199787 0.745617i
\(188\) 0 0
\(189\) 7.06218 3.42820i 0.513698 0.249365i
\(190\) 0 0
\(191\) 6.63397 11.4904i 0.480018 0.831415i −0.519720 0.854337i \(-0.673964\pi\)
0.999737 + 0.0229220i \(0.00729695\pi\)
\(192\) 0 0
\(193\) −7.83013 2.09808i −0.563625 0.151023i −0.0342537 0.999413i \(-0.510905\pi\)
−0.529371 + 0.848390i \(0.677572\pi\)
\(194\) 0 0
\(195\) 1.46410 + 2.92820i 0.104846 + 0.209693i
\(196\) 0 0
\(197\) −10.1244 10.1244i −0.721330 0.721330i 0.247546 0.968876i \(-0.420376\pi\)
−0.968876 + 0.247546i \(0.920376\pi\)
\(198\) 0 0
\(199\) 5.53590 + 9.58846i 0.392429 + 0.679708i 0.992769 0.120037i \(-0.0383014\pi\)
−0.600340 + 0.799745i \(0.704968\pi\)
\(200\) 0 0
\(201\) 4.96410 + 2.86603i 0.350141 + 0.202154i
\(202\) 0 0
\(203\) 2.59808 7.50000i 0.182349 0.526397i
\(204\) 0 0
\(205\) −14.4282 0.866025i −1.00771 0.0604858i
\(206\) 0 0
\(207\) 0.0980762 0.366025i 0.00681677 0.0254405i
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 0.196152 0.0135037 0.00675184 0.999977i \(-0.497851\pi\)
0.00675184 + 0.999977i \(0.497851\pi\)
\(212\) 0 0
\(213\) −0.169873 + 0.633975i −0.0116395 + 0.0434392i
\(214\) 0 0
\(215\) 5.93782 + 6.69615i 0.404956 + 0.456674i
\(216\) 0 0
\(217\) 19.3923 3.73205i 1.31644 0.253348i
\(218\) 0 0
\(219\) 6.00000 + 3.46410i 0.405442 + 0.234082i
\(220\) 0 0
\(221\) −5.46410 9.46410i −0.367555 0.636624i
\(222\) 0 0
\(223\) −18.1244 18.1244i −1.21370 1.21370i −0.969802 0.243895i \(-0.921575\pi\)
−0.243895 0.969802i \(-0.578425\pi\)
\(224\) 0 0
\(225\) −10.9282 8.19615i −0.728547 0.546410i
\(226\) 0 0
\(227\) 19.0263 + 5.09808i 1.26282 + 0.338371i 0.827275 0.561797i \(-0.189890\pi\)
0.435543 + 0.900168i \(0.356556\pi\)
\(228\) 0 0
\(229\) −9.19615 + 15.9282i −0.607699 + 1.05257i 0.383920 + 0.923366i \(0.374574\pi\)
−0.991619 + 0.129199i \(0.958759\pi\)
\(230\) 0 0
\(231\) −3.73205 0.267949i −0.245551 0.0176298i
\(232\) 0 0
\(233\) −1.73205 6.46410i −0.113470 0.423477i 0.885698 0.464263i \(-0.153681\pi\)
−0.999168 + 0.0407854i \(0.987014\pi\)
\(234\) 0 0
\(235\) −20.0263 + 4.09808i −1.30637 + 0.267329i
\(236\) 0 0
\(237\) −1.19615 + 1.19615i −0.0776984 + 0.0776984i
\(238\) 0 0
\(239\) 2.39230i 0.154745i −0.997002 0.0773727i \(-0.975347\pi\)
0.997002 0.0773727i \(-0.0246531\pi\)
\(240\) 0 0
\(241\) 21.4641 12.3923i 1.38262 0.798259i 0.390155 0.920749i \(-0.372422\pi\)
0.992470 + 0.122491i \(0.0390882\pi\)
\(242\) 0 0
\(243\) 11.9282 3.19615i 0.765195 0.205033i
\(244\) 0 0
\(245\) 10.4019 11.6962i 0.664555 0.747240i
\(246\) 0 0
\(247\) 2.00000 0.535898i 0.127257 0.0340984i
\(248\) 0 0
\(249\) 1.33013 0.767949i 0.0842934 0.0486668i
\(250\) 0 0
\(251\) 21.8564i 1.37956i −0.724017 0.689782i \(-0.757706\pi\)
0.724017 0.689782i \(-0.242294\pi\)
\(252\) 0 0
\(253\) −0.267949 + 0.267949i −0.0168458 + 0.0168458i
\(254\) 0 0
\(255\) −3.73205 2.46410i −0.233710 0.154308i
\(256\) 0 0
\(257\) −0.732051 2.73205i −0.0456641 0.170421i 0.939328 0.343020i \(-0.111450\pi\)
−0.984992 + 0.172600i \(0.944783\pi\)
\(258\) 0 0
\(259\) −12.9282 0.928203i −0.803319 0.0576757i
\(260\) 0 0
\(261\) 4.09808 7.09808i 0.253665 0.439360i
\(262\) 0 0
\(263\) 15.1603 + 4.06218i 0.934821 + 0.250485i 0.693909 0.720062i \(-0.255887\pi\)
0.240912 + 0.970547i \(0.422553\pi\)
\(264\) 0 0
\(265\) 5.00000 15.0000i 0.307148 0.921443i
\(266\) 0 0
\(267\) 0.241670 + 0.241670i 0.0147899 + 0.0147899i
\(268\) 0 0
\(269\) 11.4282 + 19.7942i 0.696790 + 1.20688i 0.969574 + 0.244800i \(0.0787223\pi\)
−0.272784 + 0.962075i \(0.587944\pi\)
\(270\) 0 0
\(271\) −18.4186 10.6340i −1.11885 0.645968i −0.177742 0.984077i \(-0.556879\pi\)
−0.941107 + 0.338109i \(0.890213\pi\)
\(272\) 0 0
\(273\) −3.80385 + 0.732051i −0.230219 + 0.0443057i
\(274\) 0 0
\(275\) 5.36603 + 12.5622i 0.323584 + 0.757528i
\(276\) 0 0
\(277\) −1.39230 + 5.19615i −0.0836555 + 0.312207i −0.995056 0.0993135i \(-0.968335\pi\)
0.911401 + 0.411520i \(0.135002\pi\)
\(278\) 0 0
\(279\) 20.3923 1.22086
\(280\) 0 0
\(281\) −0.928203 −0.0553720 −0.0276860 0.999617i \(-0.508814\pi\)
−0.0276860 + 0.999617i \(0.508814\pi\)
\(282\) 0 0
\(283\) 0.509619 1.90192i 0.0302937 0.113058i −0.949123 0.314904i \(-0.898028\pi\)
0.979417 + 0.201847i \(0.0646943\pi\)
\(284\) 0 0
\(285\) 0.633975 0.562178i 0.0375534 0.0333005i
\(286\) 0 0
\(287\) 5.59808 16.1603i 0.330444 0.953910i
\(288\) 0 0
\(289\) −1.79423 1.03590i −0.105543 0.0609352i
\(290\) 0 0
\(291\) 2.16987 + 3.75833i 0.127200 + 0.220317i
\(292\) 0 0
\(293\) −2.39230 2.39230i −0.139760 0.139760i 0.633765 0.773525i \(-0.281508\pi\)
−0.773525 + 0.633765i \(0.781508\pi\)
\(294\) 0 0
\(295\) 16.3923 8.19615i 0.954397 0.477198i
\(296\) 0 0
\(297\) −7.83013 2.09808i −0.454350 0.121743i
\(298\) 0 0
\(299\) −0.196152 + 0.339746i −0.0113438 + 0.0196480i
\(300\) 0 0
\(301\) −9.52628 + 4.62436i −0.549086 + 0.266543i
\(302\) 0 0
\(303\) −1.10770 4.13397i −0.0636354 0.237491i
\(304\) 0 0
\(305\) 1.89230 2.86603i 0.108353 0.164108i
\(306\) 0 0
\(307\) −6.29423 + 6.29423i −0.359231 + 0.359231i −0.863529 0.504299i \(-0.831751\pi\)
0.504299 + 0.863529i \(0.331751\pi\)
\(308\) 0 0
\(309\) 2.46410i 0.140178i
\(310\) 0 0
\(311\) 13.2224 7.63397i 0.749775 0.432883i −0.0758374 0.997120i \(-0.524163\pi\)
0.825613 + 0.564237i \(0.190830\pi\)
\(312\) 0 0
\(313\) −5.19615 + 1.39230i −0.293704 + 0.0786977i −0.402662 0.915349i \(-0.631915\pi\)
0.108958 + 0.994046i \(0.465248\pi\)
\(314\) 0 0
\(315\) 12.8301 9.83013i 0.722896 0.553865i
\(316\) 0 0
\(317\) 9.19615 2.46410i 0.516507 0.138398i 0.00885679 0.999961i \(-0.497181\pi\)
0.507651 + 0.861563i \(0.330514\pi\)
\(318\) 0 0
\(319\) −7.09808 + 4.09808i −0.397416 + 0.229448i
\(320\) 0 0
\(321\) 6.80385i 0.379754i
\(322\) 0 0
\(323\) −2.00000 + 2.00000i −0.111283 + 0.111283i
\(324\) 0 0
\(325\) 8.73205 + 11.1244i 0.484367 + 0.617068i
\(326\) 0 0
\(327\) 1.35641 + 5.06218i 0.0750094 + 0.279939i
\(328\) 0 0
\(329\) 1.73205 24.1244i 0.0954911 1.33002i
\(330\) 0 0
\(331\) −0.928203 + 1.60770i −0.0510187 + 0.0883669i −0.890407 0.455165i \(-0.849580\pi\)
0.839388 + 0.543532i \(0.182913\pi\)
\(332\) 0 0
\(333\) −12.9282 3.46410i −0.708461 0.189832i
\(334\) 0 0
\(335\) 23.4904 + 7.83013i 1.28342 + 0.427806i
\(336\) 0 0
\(337\) 9.53590 + 9.53590i 0.519453 + 0.519453i 0.917406 0.397953i \(-0.130279\pi\)
−0.397953 + 0.917406i \(0.630279\pi\)
\(338\) 0 0
\(339\) 2.83013 + 4.90192i 0.153711 + 0.266236i
\(340\) 0 0
\(341\) −17.6603 10.1962i −0.956356 0.552153i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) −0.00961894 + 0.160254i −0.000517866 + 0.00862779i
\(346\) 0 0
\(347\) 7.79423 29.0885i 0.418416 1.56155i −0.359477 0.933154i \(-0.617045\pi\)
0.777893 0.628396i \(-0.216288\pi\)
\(348\) 0 0
\(349\) 6.26795 0.335516 0.167758 0.985828i \(-0.446347\pi\)
0.167758 + 0.985828i \(0.446347\pi\)
\(350\) 0 0
\(351\) −8.39230 −0.447948
\(352\) 0 0
\(353\) 3.63397 13.5622i 0.193417 0.721842i −0.799254 0.600993i \(-0.794772\pi\)
0.992671 0.120849i \(-0.0385615\pi\)
\(354\) 0 0
\(355\) −0.169873 + 2.83013i −0.00901592 + 0.150208i
\(356\) 0 0
\(357\) 4.00000 3.46410i 0.211702 0.183340i
\(358\) 0 0
\(359\) −29.6603 17.1244i −1.56541 0.903789i −0.996693 0.0812542i \(-0.974107\pi\)
−0.568715 0.822535i \(-0.692559\pi\)
\(360\) 0 0
\(361\) 9.23205 + 15.9904i 0.485897 + 0.841599i
\(362\) 0 0
\(363\) −1.29423 1.29423i −0.0679294 0.0679294i
\(364\) 0 0
\(365\) 28.3923 + 9.46410i 1.48612 + 0.495374i
\(366\) 0 0
\(367\) −0.500000 0.133975i −0.0260998 0.00699342i 0.245746 0.969334i \(-0.420967\pi\)
−0.271845 + 0.962341i \(0.587634\pi\)
\(368\) 0 0
\(369\) 8.83013 15.2942i 0.459678 0.796186i
\(370\) 0 0
\(371\) 15.4904 + 10.4904i 0.804221 + 0.544633i
\(372\) 0 0
\(373\) 2.07180 + 7.73205i 0.107274 + 0.400350i 0.998593 0.0530251i \(-0.0168863\pi\)
−0.891320 + 0.453376i \(0.850220\pi\)
\(374\) 0 0
\(375\) 5.23205 + 2.47372i 0.270182 + 0.127742i
\(376\) 0 0
\(377\) −6.00000 + 6.00000i −0.309016 + 0.309016i
\(378\) 0 0
\(379\) 2.33975i 0.120185i −0.998193 0.0600923i \(-0.980860\pi\)
0.998193 0.0600923i \(-0.0191395\pi\)
\(380\) 0 0
\(381\) −0.294229 + 0.169873i −0.0150738 + 0.00870286i
\(382\) 0 0
\(383\) −30.5526 + 8.18653i −1.56116 + 0.418312i −0.933031 0.359795i \(-0.882847\pi\)
−0.628131 + 0.778107i \(0.716180\pi\)
\(384\) 0 0
\(385\) −16.0263 + 2.09808i −0.816775 + 0.106928i
\(386\) 0 0
\(387\) −10.5622 + 2.83013i −0.536906 + 0.143863i
\(388\) 0 0
\(389\) −4.26795 + 2.46410i −0.216394 + 0.124935i −0.604279 0.796773i \(-0.706539\pi\)
0.387886 + 0.921707i \(0.373206\pi\)
\(390\) 0 0
\(391\) 0.535898i 0.0271015i
\(392\) 0 0
\(393\) 5.66025 5.66025i 0.285522 0.285522i
\(394\) 0 0
\(395\) −4.02628 + 6.09808i −0.202584 + 0.306828i
\(396\) 0 0
\(397\) −0.973721 3.63397i −0.0488696 0.182384i 0.937177 0.348855i \(-0.113429\pi\)
−0.986046 + 0.166471i \(0.946763\pi\)
\(398\) 0 0
\(399\) 0.437822 + 0.901924i 0.0219185 + 0.0451527i
\(400\) 0 0
\(401\) −5.50000 + 9.52628i −0.274657 + 0.475720i −0.970049 0.242911i \(-0.921898\pi\)
0.695392 + 0.718631i \(0.255231\pi\)
\(402\) 0 0
\(403\) −20.3923 5.46410i −1.01581 0.272186i
\(404\) 0 0
\(405\) 13.3205 6.66025i 0.661901 0.330951i
\(406\) 0 0
\(407\) 9.46410 + 9.46410i 0.469118 + 0.469118i
\(408\) 0 0
\(409\) −10.4282 18.0622i −0.515641 0.893117i −0.999835 0.0181564i \(-0.994220\pi\)
0.484194 0.874961i \(-0.339113\pi\)
\(410\) 0 0
\(411\) 6.12436 + 3.53590i 0.302092 + 0.174413i
\(412\) 0 0
\(413\) 4.09808 + 21.2942i 0.201653 + 1.04782i
\(414\) 0 0
\(415\) 4.96410 4.40192i 0.243678 0.216082i
\(416\) 0 0
\(417\) 0.758330 2.83013i 0.0371356 0.138592i
\(418\) 0 0
\(419\) −23.8564 −1.16546 −0.582731 0.812665i \(-0.698016\pi\)
−0.582731 + 0.812665i \(0.698016\pi\)
\(420\) 0 0
\(421\) −17.3397 −0.845088 −0.422544 0.906343i \(-0.638863\pi\)
−0.422544 + 0.906343i \(0.638863\pi\)
\(422\) 0 0
\(423\) 6.46410 24.1244i 0.314295 1.17297i
\(424\) 0 0
\(425\) −17.9282 7.19615i −0.869646 0.349065i
\(426\) 0 0
\(427\) 2.66025 + 3.07180i 0.128739 + 0.148655i
\(428\) 0 0
\(429\) 3.46410 + 2.00000i 0.167248 + 0.0965609i
\(430\) 0 0
\(431\) 3.09808 + 5.36603i 0.149229 + 0.258472i 0.930943 0.365165i \(-0.118987\pi\)
−0.781714 + 0.623637i \(0.785654\pi\)
\(432\) 0 0
\(433\) −17.5359 17.5359i −0.842721 0.842721i 0.146491 0.989212i \(-0.453202\pi\)
−0.989212 + 0.146491i \(0.953202\pi\)
\(434\) 0 0
\(435\) −1.09808 + 3.29423i −0.0526487 + 0.157946i
\(436\) 0 0
\(437\) 0.0980762 + 0.0262794i 0.00469162 + 0.00125712i
\(438\) 0 0
\(439\) −1.66025 + 2.87564i −0.0792396 + 0.137247i −0.902922 0.429804i \(-0.858583\pi\)
0.823682 + 0.567051i \(0.191916\pi\)
\(440\) 0 0
\(441\) 7.09808 + 17.7583i 0.338004 + 0.845635i
\(442\) 0 0
\(443\) 3.50000 + 13.0622i 0.166290 + 0.620603i 0.997872 + 0.0652010i \(0.0207689\pi\)
−0.831582 + 0.555402i \(0.812564\pi\)
\(444\) 0 0
\(445\) 1.23205 + 0.813467i 0.0584048 + 0.0385620i
\(446\) 0 0
\(447\) 0.294229 0.294229i 0.0139165 0.0139165i
\(448\) 0 0
\(449\) 33.0526i 1.55985i −0.625875 0.779923i \(-0.715258\pi\)
0.625875 0.779923i \(-0.284742\pi\)
\(450\) 0 0
\(451\) −15.2942 + 8.83013i −0.720177 + 0.415794i
\(452\) 0 0
\(453\) 6.92820 1.85641i 0.325515 0.0872216i
\(454\) 0 0
\(455\) −15.4641 + 6.39230i −0.724968 + 0.299676i
\(456\) 0 0
\(457\) −11.7321 + 3.14359i −0.548802 + 0.147051i −0.522557 0.852604i \(-0.675022\pi\)
−0.0262453 + 0.999656i \(0.508355\pi\)
\(458\) 0 0
\(459\) 9.92820 5.73205i 0.463409 0.267549i
\(460\) 0 0
\(461\) 5.60770i 0.261176i −0.991437 0.130588i \(-0.958313\pi\)
0.991437 0.130588i \(-0.0416866\pi\)
\(462\) 0 0
\(463\) 4.75833 4.75833i 0.221138 0.221138i −0.587839 0.808978i \(-0.700021\pi\)
0.808978 + 0.587839i \(0.200021\pi\)
\(464\) 0 0
\(465\) −8.46410 + 1.73205i −0.392513 + 0.0803219i
\(466\) 0 0
\(467\) −3.64359 13.5981i −0.168605 0.629244i −0.997553 0.0699173i \(-0.977726\pi\)
0.828947 0.559327i \(-0.188940\pi\)
\(468\) 0 0
\(469\) −16.4282 + 24.2583i −0.758584 + 1.12015i
\(470\) 0 0
\(471\) −1.24167 + 2.15064i −0.0572131 + 0.0990960i
\(472\) 0 0
\(473\) 10.5622 + 2.83013i 0.485649 + 0.130129i
\(474\) 0 0
\(475\) 2.19615 2.92820i 0.100766 0.134355i
\(476\) 0 0
\(477\) 13.6603 + 13.6603i 0.625460 + 0.625460i
\(478\) 0 0
\(479\) −6.53590 11.3205i −0.298633 0.517247i 0.677191 0.735808i \(-0.263197\pi\)
−0.975823 + 0.218560i \(0.929864\pi\)
\(480\) 0 0
\(481\) 12.0000 + 6.92820i 0.547153 + 0.315899i
\(482\) 0 0
\(483\) −0.179492 0.0621778i −0.00816717 0.00282919i
\(484\) 0 0
\(485\) 12.4378 + 14.0263i 0.564772 + 0.636901i
\(486\) 0 0
\(487\) −7.29423 + 27.2224i −0.330533 + 1.23357i 0.578098 + 0.815967i \(0.303795\pi\)
−0.908631 + 0.417599i \(0.862872\pi\)
\(488\) 0 0
\(489\) 7.26795 0.328668
\(490\) 0 0
\(491\) −37.7128 −1.70196 −0.850978 0.525202i \(-0.823990\pi\)
−0.850978 + 0.525202i \(0.823990\pi\)
\(492\) 0 0
\(493\) 3.00000 11.1962i 0.135113 0.504249i
\(494\) 0 0
\(495\) −16.6603 1.00000i −0.748823 0.0449467i
\(496\) 0 0
\(497\) −3.16987 1.09808i −0.142188 0.0492554i
\(498\) 0 0
\(499\) 9.97372 + 5.75833i 0.446485 + 0.257778i 0.706345 0.707868i \(-0.250343\pi\)
−0.259860 + 0.965646i \(0.583676\pi\)
\(500\) 0 0
\(501\) 4.30385 + 7.45448i 0.192282 + 0.333042i
\(502\) 0 0
\(503\) 17.6340 + 17.6340i 0.786260 + 0.786260i 0.980879 0.194619i \(-0.0623470\pi\)
−0.194619 + 0.980879i \(0.562347\pi\)
\(504\) 0 0
\(505\) −8.26795 16.5359i −0.367919 0.735838i
\(506\) 0 0
\(507\) −2.50000 0.669873i −0.111029 0.0297501i
\(508\) 0 0
\(509\) −19.4545 + 33.6962i −0.862305 + 1.49356i 0.00739389 + 0.999973i \(0.497646\pi\)
−0.869699 + 0.493583i \(0.835687\pi\)
\(510\) 0 0
\(511\) −19.8564 + 29.3205i −0.878396 + 1.29706i
\(512\) 0 0
\(513\) 0.562178 + 2.09808i 0.0248208 + 0.0926323i
\(514\) 0 0
\(515\) 2.13397 + 10.4282i 0.0940342 + 0.459522i
\(516\) 0 0
\(517\) −17.6603 + 17.6603i −0.776697 + 0.776697i
\(518\) 0 0
\(519\) 10.6795i 0.468778i
\(520\) 0 0
\(521\) −20.6603 + 11.9282i −0.905142 + 0.522584i −0.878865 0.477071i \(-0.841699\pi\)
−0.0262772 + 0.999655i \(0.508365\pi\)
\(522\) 0 0
\(523\) 42.8827 11.4904i 1.87513 0.502439i 0.875307 0.483568i \(-0.160659\pi\)
0.999822 0.0188717i \(-0.00600740\pi\)
\(524\) 0 0
\(525\) −4.49038 + 5.16987i −0.195976 + 0.225632i
\(526\) 0 0
\(527\) 27.8564 7.46410i 1.21344 0.325141i
\(528\) 0 0
\(529\) 19.9019 11.4904i 0.865301 0.499582i
\(530\) 0 0
\(531\) 22.3923i 0.971743i
\(532\) 0 0
\(533\) −12.9282 + 12.9282i −0.559983 + 0.559983i
\(534\) 0 0
\(535\) 5.89230 + 28.7942i 0.254747 + 1.24488i
\(536\) 0 0
\(537\) 1.05256 + 3.92820i 0.0454213 + 0.169514i
\(538\) 0 0
\(539\) 2.73205 18.9282i 0.117678 0.815295i
\(540\) 0 0
\(541\) −18.3564 + 31.7942i −0.789204 + 1.36694i 0.137252 + 0.990536i \(0.456173\pi\)
−0.926455 + 0.376404i \(0.877160\pi\)
\(542\) 0 0
\(543\) −0.598076 0.160254i −0.0256659 0.00687716i
\(544\) 0 0
\(545\) 10.1244 + 20.2487i 0.433680 + 0.867359i
\(546\) 0 0
\(547\) 16.7583 + 16.7583i 0.716534 + 0.716534i 0.967894 0.251359i \(-0.0808776\pi\)
−0.251359 + 0.967894i \(0.580878\pi\)
\(548\) 0 0
\(549\) 2.09808 + 3.63397i 0.0895437 + 0.155094i
\(550\) 0 0
\(551\) 1.90192 + 1.09808i 0.0810247 + 0.0467796i
\(552\) 0 0
\(553\) −5.66025 6.53590i −0.240698 0.277935i
\(554\) 0 0
\(555\) 5.66025 + 0.339746i 0.240264 + 0.0144214i
\(556\) 0 0
\(557\) 8.36603 31.2224i 0.354480 1.32294i −0.526658 0.850077i \(-0.676555\pi\)
0.881138 0.472860i \(-0.156778\pi\)
\(558\) 0 0
\(559\) 11.3205 0.478806
\(560\) 0 0
\(561\) −5.46410 −0.230695
\(562\) 0 0
\(563\) 6.35641 23.7224i 0.267891 0.999781i −0.692567 0.721354i \(-0.743520\pi\)
0.960457 0.278427i \(-0.0898132\pi\)
\(564\) 0 0
\(565\) 16.2224 + 18.2942i 0.682483 + 0.769644i
\(566\) 0 0
\(567\) 3.33013 + 17.3038i 0.139852 + 0.726693i
\(568\) 0 0
\(569\) −25.0526 14.4641i −1.05026 0.606367i −0.127536 0.991834i \(-0.540707\pi\)
−0.922722 + 0.385467i \(0.874040\pi\)
\(570\) 0 0
\(571\) −9.02628 15.6340i −0.377738 0.654261i 0.612995 0.790087i \(-0.289965\pi\)
−0.990733 + 0.135826i \(0.956631\pi\)
\(572\) 0 0
\(573\) −4.85641 4.85641i −0.202879 0.202879i
\(574\) 0 0
\(575\) 0.0980762 + 0.686533i 0.00409006 + 0.0286304i
\(576\) 0 0
\(577\) 5.63397 + 1.50962i 0.234545 + 0.0628463i 0.374177 0.927357i \(-0.377925\pi\)
−0.139632 + 0.990204i \(0.544592\pi\)
\(578\) 0 0
\(579\) −2.09808 + 3.63397i −0.0871931 + 0.151023i
\(580\) 0 0
\(581\) 3.42820 + 7.06218i 0.142226 + 0.292989i
\(582\) 0 0
\(583\) −5.00000 18.6603i −0.207079 0.772829i
\(584\) 0 0
\(585\) −16.9282 + 3.46410i −0.699895 + 0.143223i
\(586\) 0 0
\(587\) −15.7846 + 15.7846i −0.651501 + 0.651501i −0.953354 0.301854i \(-0.902395\pi\)
0.301854 + 0.953354i \(0.402395\pi\)
\(588\) 0 0
\(589\) 5.46410i 0.225144i
\(590\) 0 0
\(591\) −6.41858 + 3.70577i −0.264025 + 0.152435i
\(592\) 0 0
\(593\) 20.7583 5.56218i 0.852442 0.228411i 0.193962 0.981009i \(-0.437866\pi\)
0.658481 + 0.752598i \(0.271199\pi\)
\(594\) 0 0
\(595\) 13.9282 18.1244i 0.571001 0.743026i
\(596\) 0 0
\(597\) 5.53590 1.48334i 0.226569 0.0607090i
\(598\) 0 0
\(599\) 15.3397 8.85641i 0.626765 0.361863i −0.152733 0.988267i \(-0.548807\pi\)
0.779498 + 0.626405i \(0.215474\pi\)
\(600\) 0 0
\(601\) 41.1769i 1.67964i −0.542864 0.839821i \(-0.682660\pi\)
0.542864 0.839821i \(-0.317340\pi\)
\(602\) 0 0
\(603\) −21.3923 + 21.3923i −0.871162 + 0.871162i
\(604\) 0 0
\(605\) −6.59808 4.35641i −0.268250 0.177113i
\(606\) 0 0
\(607\) −3.40192 12.6962i −0.138080 0.515321i −0.999966 0.00821951i \(-0.997384\pi\)
0.861886 0.507101i \(-0.169283\pi\)
\(608\) 0 0
\(609\) −3.40192 2.30385i −0.137853 0.0933566i
\(610\) 0 0
\(611\) −12.9282 + 22.3923i −0.523019 + 0.905896i
\(612\) 0 0
\(613\) 24.3923 + 6.53590i 0.985196 + 0.263982i 0.715231 0.698888i \(-0.246321\pi\)
0.269965 + 0.962870i \(0.412988\pi\)
\(614\) 0 0
\(615\) −2.36603 + 7.09808i −0.0954074 + 0.286222i
\(616\) 0 0
\(617\) 33.9090 + 33.9090i 1.36512 + 1.36512i 0.867249 + 0.497874i \(0.165886\pi\)
0.497874 + 0.867249i \(0.334114\pi\)
\(618\) 0 0
\(619\) −5.09808 8.83013i −0.204909 0.354913i 0.745195 0.666847i \(-0.232357\pi\)
−0.950104 + 0.311934i \(0.899023\pi\)
\(620\) 0 0
\(621\) −0.356406 0.205771i −0.0143021 0.00825732i
\(622\) 0 0
\(623\) −1.32051 + 1.14359i −0.0529050 + 0.0458171i
\(624\) 0 0
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 0 0
\(627\) 0.267949 1.00000i 0.0107009 0.0399362i
\(628\) 0 0
\(629\) −18.9282 −0.754717
\(630\) 0 0
\(631\) 4.58846 0.182664 0.0913318 0.995821i \(-0.470888\pi\)
0.0913318 + 0.995821i \(0.470888\pi\)
\(632\) 0 0
\(633\) 0.0262794 0.0980762i 0.00104451 0.00389818i
\(634\) 0 0
\(635\) −1.09808 + 0.973721i −0.0435758 + 0.0386409i
\(636\) 0 0
\(637\) −2.33975 19.6603i −0.0927041 0.778968i
\(638\) 0 0
\(639\) −3.00000 1.73205i −0.118678 0.0685189i
\(640\) 0 0
\(641\) −5.33013 9.23205i −0.210527 0.364644i 0.741352 0.671116i \(-0.234185\pi\)
−0.951880 + 0.306472i \(0.900851\pi\)
\(642\) 0 0
\(643\) −17.5359 17.5359i −0.691548 0.691548i 0.271024 0.962573i \(-0.412638\pi\)
−0.962573 + 0.271024i \(0.912638\pi\)
\(644\) 0 0
\(645\) 4.14359 2.07180i 0.163154 0.0815769i
\(646\) 0 0
\(647\) −39.5526 10.5981i −1.55497 0.416653i −0.623904 0.781501i \(-0.714454\pi\)
−0.931067 + 0.364847i \(0.881121\pi\)
\(648\) 0 0
\(649\) 11.1962 19.3923i 0.439487 0.761215i
\(650\) 0 0
\(651\) 0.732051 10.1962i 0.0286913 0.399619i
\(652\) 0 0
\(653\) −5.26795 19.6603i −0.206151 0.769365i −0.989096 0.147274i \(-0.952950\pi\)
0.782945 0.622091i \(-0.213717\pi\)
\(654\) 0 0
\(655\) 19.0526 28.8564i 0.744445 1.12751i
\(656\) 0 0
\(657\) −25.8564 + 25.8564i −1.00875 + 1.00875i
\(658\) 0 0
\(659\) 27.6603i 1.07749i 0.842469 + 0.538745i \(0.181101\pi\)
−0.842469 + 0.538745i \(0.818899\pi\)
\(660\) 0 0
\(661\) −41.7224 + 24.0885i −1.62281 + 0.936932i −0.636652 + 0.771151i \(0.719681\pi\)
−0.986163 + 0.165781i \(0.946985\pi\)
\(662\) 0 0
\(663\) −5.46410 + 1.46410i −0.212208 + 0.0568610i
\(664\) 0 0
\(665\) 2.63397 + 3.43782i 0.102141 + 0.133313i
\(666\) 0 0
\(667\) −0.401924 + 0.107695i −0.0155626 + 0.00416997i
\(668\) 0 0
\(669\) −11.4904 + 6.63397i −0.444244 + 0.256484i
\(670\) 0 0
\(671\) 4.19615i 0.161991i
\(672\) 0 0
\(673\) 4.39230 4.39230i 0.169311 0.169311i −0.617366 0.786676i \(-0.711800\pi\)
0.786676 + 0.617366i \(0.211800\pi\)
\(674\) 0 0
\(675\) −11.6699 + 9.16025i −0.449174 + 0.352578i
\(676\) 0 0
\(677\) −6.92820 25.8564i −0.266272 0.993742i −0.961467 0.274921i \(-0.911348\pi\)
0.695194 0.718822i \(-0.255318\pi\)
\(678\) 0 0
\(679\) −19.9545 + 9.68653i −0.765783 + 0.371735i
\(680\) 0 0
\(681\) 5.09808 8.83013i 0.195359 0.338371i
\(682\) 0 0
\(683\) −17.0622 4.57180i −0.652866 0.174935i −0.0828417 0.996563i \(-0.526400\pi\)
−0.570024 + 0.821628i \(0.693066\pi\)
\(684\) 0 0
\(685\) 28.9808 + 9.66025i 1.10730 + 0.369099i
\(686\) 0 0
\(687\) 6.73205 + 6.73205i 0.256844 + 0.256844i
\(688\) 0 0
\(689\) −10.0000 17.3205i −0.380970 0.659859i
\(690\) 0 0
\(691\) 44.0263 + 25.4186i 1.67484 + 0.966969i 0.964867 + 0.262738i \(0.0846255\pi\)
0.709971 + 0.704231i \(0.248708\pi\)
\(692\) 0 0
\(693\) 6.46410 18.6603i 0.245551 0.708844i
\(694\) 0 0
\(695\) 0.758330 12.6340i 0.0287651 0.479234i
\(696\) 0 0
\(697\) 6.46410 24.1244i 0.244845 0.913775i
\(698\) 0 0
\(699\) −3.46410 −0.131024
\(700\) 0 0
\(701\) −20.2679 −0.765510 −0.382755 0.923850i \(-0.625025\pi\)
−0.382755 + 0.923850i \(0.625025\pi\)
\(702\) 0 0
\(703\) 0.928203 3.46410i 0.0350078 0.130651i
\(704\) 0 0
\(705\) −0.633975 + 10.5622i −0.0238769 + 0.397795i
\(706\) 0 0
\(707\) 21.4808 4.13397i 0.807867 0.155474i
\(708\) 0 0
\(709\) 18.9904 + 10.9641i 0.713199 + 0.411765i 0.812244 0.583317i \(-0.198246\pi\)
−0.0990456 + 0.995083i \(0.531579\pi\)
\(710\) 0 0
\(711\) −4.46410 7.73205i −0.167417 0.289975i
\(712\) 0 0
\(713\) −0.732051 0.732051i −0.0274155 0.0274155i
\(714\) 0 0
\(715\) 16.3923 + 5.46410i 0.613037 + 0.204346i
\(716\) 0 0
\(717\) −1.19615 0.320508i −0.0446711 0.0119696i
\(718\) 0 0
\(719\) −19.2942 + 33.4186i −0.719553 + 1.24630i 0.241624 + 0.970370i \(0.422320\pi\)
−0.961177 + 0.275933i \(0.911013\pi\)
\(720\) 0 0
\(721\) −12.5622 0.901924i −0.467840 0.0335894i
\(722\) 0 0
\(723\) −3.32051 12.3923i −0.123491 0.460875i
\(724\) 0 0
\(725\) −1.79423 + 14.8923i −0.0666360 + 0.553086i
\(726\) 0 0
\(727\) 10.0981 10.0981i 0.374517 0.374517i −0.494602 0.869119i \(-0.664686\pi\)
0.869119 + 0.494602i \(0.164686\pi\)
\(728\) 0 0
\(729\) 13.5885i 0.503276i
\(730\) 0 0
\(731\) −13.3923 + 7.73205i −0.495332 + 0.285980i
\(732\) 0 0
\(733\) −4.36603 + 1.16987i −0.161263 + 0.0432102i −0.338547 0.940949i \(-0.609935\pi\)
0.177284 + 0.984160i \(0.443269\pi\)
\(734\) 0 0
\(735\) −4.45448 6.76795i −0.164306 0.249640i
\(736\) 0 0
\(737\) 29.2224 7.83013i 1.07642 0.288426i
\(738\) 0 0
\(739\) 19.5622 11.2942i 0.719606 0.415465i −0.0950014 0.995477i \(-0.530286\pi\)
0.814608 + 0.580012i \(0.196952\pi\)
\(740\) 0 0
\(741\) 1.07180i 0.0393734i
\(742\) 0 0
\(743\) 6.16987 6.16987i 0.226351 0.226351i −0.584816 0.811166i \(-0.698833\pi\)
0.811166 + 0.584816i \(0.198833\pi\)
\(744\) 0 0
\(745\) 0.990381 1.50000i 0.0362848 0.0549557i
\(746\) 0 0
\(747\) 2.09808 + 7.83013i 0.0767646 + 0.286489i
\(748\) 0 0
\(749\) −34.6865 2.49038i −1.26742 0.0909965i
\(750\) 0 0
\(751\) −3.19615 + 5.53590i −0.116629 + 0.202008i −0.918430 0.395584i \(-0.870542\pi\)
0.801801 + 0.597592i \(0.203876\pi\)
\(752\) 0 0
\(753\) −10.9282 2.92820i −0.398246 0.106710i
\(754\) 0 0
\(755\) 27.7128 13.8564i 1.00857 0.504286i
\(756\) 0 0
\(757\) 12.7321 + 12.7321i 0.462754 + 0.462754i 0.899557 0.436803i \(-0.143889\pi\)
−0.436803 + 0.899557i \(0.643889\pi\)
\(758\) 0 0
\(759\) 0.0980762 + 0.169873i 0.00355994 + 0.00616600i
\(760\) 0 0
\(761\) 24.9282 + 14.3923i 0.903647 + 0.521721i 0.878382 0.477960i \(-0.158624\pi\)
0.0252651 + 0.999681i \(0.491957\pi\)
\(762\) 0 0
\(763\) −26.3038 + 5.06218i −0.952263 + 0.183263i
\(764\) 0 0
\(765\) 17.6603 15.6603i 0.638508 0.566198i
\(766\) 0 0
\(767\) 6.00000 22.3923i 0.216647 0.808539i
\(768\) 0 0
\(769\) 15.1769 0.547294 0.273647 0.961830i \(-0.411770\pi\)
0.273647 + 0.961830i \(0.411770\pi\)
\(770\) 0 0
\(771\) −1.46410 −0.0527283
\(772\) 0 0
\(773\) 4.07180 15.1962i 0.146452 0.546568i −0.853234 0.521528i \(-0.825362\pi\)
0.999686 0.0250395i \(-0.00797116\pi\)
\(774\) 0 0
\(775\) −34.3205 + 14.6603i −1.23283 + 0.526612i
\(776\) 0 0
\(777\) −2.19615 + 6.33975i −0.0787865 + 0.227437i
\(778\) 0 0
\(779\) 4.09808 + 2.36603i 0.146829 + 0.0847717i
\(780\) 0 0
\(781\) 1.73205 + 3.00000i 0.0619777 + 0.107348i
\(782\) 0 0
\(783\) −6.29423 6.29423i −0.224937 0.224937i
\(784\) 0 0
\(785\) −3.39230 + 10.1769i −0.121077 + 0.363230i
\(786\) 0 0
\(787\) −31.1865 8.35641i −1.11168 0.297874i −0.344168 0.938908i \(-0.611839\pi\)
−0.767512 + 0.641034i \(0.778506\pi\)
\(788\) 0 0
\(789\) 4.06218 7.03590i 0.144617 0.250485i
\(790\) 0 0
\(791\) −26.0263 + 12.6340i −0.925388 + 0.449212i
\(792\) 0 0
\(793\) −1.12436 4.19615i −0.0399270 0.149010i
\(794\) 0 0
\(795\) −6.83013 4.50962i −0.242240 0.159940i
\(796\) 0 0
\(797\) 22.5359 22.5359i 0.798262 0.798262i −0.184559 0.982821i \(-0.559086\pi\)
0.982821 + 0.184559i \(0.0590857\pi\)
\(798\) 0 0
\(799\) 35.3205i 1.24955i
\(800\) 0 0
\(801\) −1.56218 + 0.901924i −0.0551968 + 0.0318679i
\(802\) 0 0
\(803\) 35.3205 9.46410i 1.24643 0.333981i
\(804\) 0 0
\(805\) −0.813467 0.107695i −0.0286709 0.00379576i
\(806\) 0 0
\(807\) 11.4282 3.06218i 0.402292 0.107794i
\(808\) 0 0
\(809\) −3.99038 + 2.30385i −0.140294 + 0.0809990i −0.568504 0.822680i \(-0.692478\pi\)
0.428210 + 0.903679i \(0.359144\pi\)
\(810\) 0 0
\(811\) 42.9282i 1.50741i −0.657211 0.753707i \(-0.728264\pi\)
0.657211 0.753707i \(-0.271736\pi\)
\(812\) 0 0
\(813\) −7.78461 + 7.78461i −0.273018 + 0.273018i
\(814\) 0 0
\(815\) 30.7583 6.29423i 1.07742 0.220477i
\(816\) 0 0
\(817\) −0.758330 2.83013i −0.0265306 0.0990136i
\(818\) 0 0
\(819\) 1.46410 20.3923i 0.0511599 0.712565i
\(820\) 0 0
\(821\) 24.6603 42.7128i 0.860649 1.49069i −0.0106549 0.999943i \(-0.503392\pi\)
0.871304 0.490744i \(-0.163275\pi\)
\(822\) 0 0
\(823\) 53.3827 + 14.3038i 1.86080 + 0.498601i 0.999947 0.0102479i \(-0.00326207\pi\)
0.860856 + 0.508849i \(0.169929\pi\)
\(824\) 0 0
\(825\) 7.00000 1.00000i 0.243709 0.0348155i
\(826\) 0 0
\(827\) 33.2224 + 33.2224i 1.15526 + 1.15526i 0.985483 + 0.169774i \(0.0543038\pi\)
0.169774 + 0.985483i \(0.445696\pi\)
\(828\) 0 0
\(829\) −7.26795 12.5885i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(830\) 0 0
\(831\) 2.41154 + 1.39230i 0.0836555 + 0.0482985i
\(832\) 0 0
\(833\) 16.1962 + 21.6603i 0.561163 + 0.750483i
\(834\) 0 0
\(835\) 24.6699 + 27.8205i 0.853736 + 0.962768i
\(836\) 0 0
\(837\) 5.73205 21.3923i 0.198129 0.739426i
\(838\) 0 0
\(839\) −6.87564 −0.237374 −0.118687 0.992932i \(-0.537868\pi\)
−0.118687 + 0.992932i \(0.537868\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) 0 0
\(843\) −0.124356 + 0.464102i −0.00428304 + 0.0159845i
\(844\) 0 0
\(845\) −11.1603 0.669873i −0.383924 0.0230443i
\(846\) 0 0
\(847\) 7.07180 6.12436i 0.242990 0.210435i
\(848\) 0 0
\(849\) −0.882686 0.509619i −0.0302937 0.0174901i
\(850\) 0 0
\(851\) 0.339746 + 0.588457i 0.0116463 + 0.0201721i
\(852\) 0 0
\(853\) −18.1244 18.1244i −0.620566 0.620566i 0.325110 0.945676i \(-0.394599\pi\)
−0.945676 + 0.325110i \(0.894599\pi\)
\(854\) 0 0
\(855\) 2.00000 + 4.00000i 0.0683986 + 0.136797i
\(856\) 0 0
\(857\) −11.0981 2.97372i −0.379103 0.101580i 0.0642351 0.997935i \(-0.479539\pi\)
−0.443338 + 0.896354i \(0.646206\pi\)
\(858\) 0 0
\(859\) 17.4641 30.2487i 0.595867 1.03207i −0.397556 0.917578i \(-0.630142\pi\)
0.993424 0.114495i \(-0.0365250\pi\)
\(860\) 0 0
\(861\) −7.33013 4.96410i −0.249810 0.169176i
\(862\) 0 0
\(863\) −13.3827 49.9449i −0.455552 1.70014i −0.686460 0.727167i \(-0.740836\pi\)
0.230908 0.972976i \(-0.425830\pi\)
\(864\) 0 0
\(865\) −9.24871 45.1962i −0.314466 1.53672i
\(866\) 0 0
\(867\) −0.758330 + 0.758330i −0.0257542 + 0.0257542i
\(868\) 0 0
\(869\) 8.92820i 0.302869i
\(870\) 0 0
\(871\) 27.1244 15.6603i 0.919074 0.530627i
\(872\) 0 0
\(873\) −22.1244 + 5.92820i −0.748796 + 0.200639i
\(874\) 0 0
\(875\) −14.5263 + 25.7679i −0.491078 + 0.871116i
\(876\) 0 0
\(877\) −39.1506 + 10.4904i −1.32202 + 0.354235i −0.849735 0.527209i \(-0.823238\pi\)
−0.472288 + 0.881444i \(0.656572\pi\)
\(878\) 0 0
\(879\) −1.51666 + 0.875644i −0.0511557 + 0.0295348i
\(880\) 0 0
\(881\) 25.1436i 0.847109i 0.905871 + 0.423555i \(0.139218\pi\)
−0.905871 + 0.423555i \(0.860782\pi\)
\(882\) 0 0
\(883\) −8.07180 + 8.07180i −0.271638 + 0.271638i −0.829759 0.558122i \(-0.811522\pi\)
0.558122 + 0.829759i \(0.311522\pi\)
\(884\) 0 0
\(885\) −1.90192 9.29423i −0.0639325 0.312422i
\(886\) 0 0
\(887\) −2.91858 10.8923i −0.0979965 0.365728i 0.899460 0.437003i \(-0.143960\pi\)
−0.997457 + 0.0712748i \(0.977293\pi\)
\(888\) 0 0
\(889\) −0.758330 1.56218i −0.0254336 0.0523938i
\(890\) 0 0
\(891\) 9.09808 15.7583i 0.304797 0.527924i
\(892\) 0 0
\(893\) 6.46410 + 1.73205i 0.216313 + 0.0579609i
\(894\) 0 0
\(895\) 7.85641 + 15.7128i 0.262611 + 0.525221i
\(896\) 0 0
\(897\) 0.143594 + 0.143594i 0.00479445 + 0.00479445i
\(898\) 0 0
\(899\) −11.1962 19.3923i −0.373413 0.646770i
\(900\) 0 0
\(901\) 23.6603 + 13.6603i 0.788237 + 0.455089i
\(902\) 0 0
\(903\) 1.03590 + 5.38269i 0.0344725 + 0.179125i
\(904\) 0 0
\(905\) −2.66987 0.160254i −0.0887496 0.00532702i
\(906\) 0 0
\(907\) 8.69615 32.4545i 0.288751 1.07763i −0.657304 0.753626i \(-0.728303\pi\)
0.946055 0.324007i \(-0.105030\pi\)
\(908\) 0 0
\(909\) 22.5885 0.749212
\(910\) 0 0
\(911\) 7.51666 0.249038 0.124519 0.992217i \(-0.460261\pi\)
0.124519 + 0.992217i \(0.460261\pi\)
\(912\) 0 0
\(913\) 2.09808 7.83013i 0.0694362 0.259139i
\(914\) 0 0
\(915\) −1.17949 1.33013i −0.0389928 0.0439726i
\(916\) 0 0
\(917\) 26.7846 + 30.9282i 0.884506 + 1.02134i
\(918\) 0 0
\(919\) 48.6673 + 28.0981i 1.60539 + 0.926870i 0.990384 + 0.138344i \(0.0441780\pi\)
0.615002 + 0.788526i \(0.289155\pi\)
\(920\) 0 0
\(921\) 2.30385 + 3.99038i 0.0759144 + 0.131488i
\(922\) 0 0
\(923\) 2.53590 + 2.53590i 0.0834701 + 0.0834701i
\(924\) 0 0
\(925\) 24.2487 3.46410i 0.797293 0.113899i
\(926\) 0 0
\(927\) −12.5622 3.36603i −0.412596 0.110555i
\(928\) 0 0
\(929\) −18.1603 + 31.4545i −0.595819 + 1.03199i 0.397612 + 0.917554i \(0.369839\pi\)
−0.993431 + 0.114435i \(0.963494\pi\)
\(930\) 0 0
\(931\) −4.75833 + 1.90192i −0.155948 + 0.0623330i
\(932\) 0 0
\(933\) −2.04552 7.63397i −0.0669672 0.249925i
\(934\) 0 0
\(935\) −23.1244 + 4.73205i −0.756247 + 0.154755i
\(936\) 0 0
\(937\) 17.0718 17.0718i 0.557711 0.557711i −0.370944 0.928655i \(-0.620966\pi\)
0.928655 + 0.370944i \(0.120966\pi\)
\(938\) 0 0
\(939\) 2.78461i 0.0908723i
\(940\) 0 0
\(941\) 35.1962 20.3205i 1.14736 0.662430i 0.199119 0.979975i \(-0.436192\pi\)
0.948243 + 0.317546i \(0.102859\pi\)
\(942\) 0 0
\(943\) −0.866025 + 0.232051i −0.0282017 + 0.00755661i
\(944\) 0 0
\(945\) −6.70577 16.2224i −0.218139 0.527716i
\(946\) 0 0
\(947\) 1.30385 0.349365i 0.0423694 0.0113528i −0.237572 0.971370i \(-0.576352\pi\)
0.279941 + 0.960017i \(0.409685\pi\)
\(948\) 0 0
\(949\) 32.7846 18.9282i 1.06423 0.614435i
\(950\) 0 0
\(951\) 4.92820i 0.159808i
\(952\) 0 0
\(953\) −37.8564 + 37.8564i −1.22629 + 1.22629i −0.260932 + 0.965357i \(0.584030\pi\)
−0.965357 + 0.260932i \(0.915970\pi\)
\(954\) 0 0
\(955\) −24.7583 16.3468i −0.801161 0.528970i
\(956\) 0 0
\(957\) 1.09808 + 4.09808i 0.0354958 + 0.132472i
\(958\) 0 0
\(959\) −20.2679 + 29.9282i −0.654486 + 0.966432i
\(960\) 0 0
\(961\) 12.3564 21.4019i 0.398594 0.690385i
\(962\) 0 0
\(963\) −34.6865 9.29423i −1.11776 0.299502i
\(964\) 0 0
\(965\) −5.73205 + 17.1962i −0.184521 + 0.553564i
\(966\) 0 0
\(967\) 13.5622 + 13.5622i 0.436130 + 0.436130i 0.890707 0.454577i \(-0.150210\pi\)
−0.454577 + 0.890707i \(0.650210\pi\)
\(968\) 0 0
\(969\) 0.732051 + 1.26795i 0.0235169 + 0.0407324i
\(970\) 0 0
\(971\) −29.0718 16.7846i −0.932958 0.538644i −0.0452124 0.998977i \(-0.514396\pi\)
−0.887746 + 0.460334i \(0.847730\pi\)
\(972\) 0 0
\(973\) 14.1506 + 4.90192i 0.453649 + 0.157148i
\(974\) 0 0
\(975\) 6.73205 2.87564i 0.215598 0.0920943i
\(976\) 0 0
\(977\) −0.150635 + 0.562178i −0.00481924 + 0.0179857i −0.968294 0.249815i \(-0.919630\pi\)
0.963474 + 0.267801i \(0.0862969\pi\)
\(978\) 0 0
\(979\) 1.80385 0.0576512
\(980\) 0 0
\(981\) −27.6603 −0.883124
\(982\) 0 0
\(983\) −14.5000 + 54.1147i −0.462478 + 1.72599i 0.202639 + 0.979253i \(0.435048\pi\)
−0.665118 + 0.746739i \(0.731619\pi\)
\(984\) 0 0
\(985\) −23.9545 + 21.2417i −0.763253 + 0.676816i
\(986\) 0 0
\(987\) −11.8301 4.09808i −0.376557 0.130443i
\(988\) 0 0
\(989\) 0.480762 + 0.277568i 0.0152873 + 0.00882615i
\(990\) 0 0
\(991\) 15.8564 + 27.4641i 0.503695 + 0.872426i 0.999991 + 0.00427229i \(0.00135992\pi\)
−0.496296 + 0.868154i \(0.665307\pi\)
\(992\) 0 0
\(993\) 0.679492 + 0.679492i 0.0215630 + 0.0215630i
\(994\) 0 0
\(995\) 22.1436 11.0718i 0.701999 0.351000i
\(996\) 0 0
\(997\) −39.8827 10.6865i −1.26310 0.338446i −0.435715 0.900085i \(-0.643504\pi\)
−0.827382 + 0.561639i \(0.810171\pi\)
\(998\) 0 0
\(999\) −7.26795 + 12.5885i −0.229948 + 0.398281i
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 560.2.ci.b.257.1 4
4.3 odd 2 35.2.k.b.12.1 yes 4
5.3 odd 4 560.2.ci.a.33.1 4
7.3 odd 6 560.2.ci.a.17.1 4
12.11 even 2 315.2.bz.a.82.1 4
20.3 even 4 35.2.k.a.33.1 yes 4
20.7 even 4 175.2.o.b.68.1 4
20.19 odd 2 175.2.o.a.82.1 4
28.3 even 6 35.2.k.a.17.1 4
28.11 odd 6 245.2.l.a.227.1 4
28.19 even 6 245.2.f.a.97.1 4
28.23 odd 6 245.2.f.b.97.1 4
28.27 even 2 245.2.l.b.117.1 4
35.3 even 12 inner 560.2.ci.b.353.1 4
60.23 odd 4 315.2.bz.b.208.1 4
84.59 odd 6 315.2.bz.b.262.1 4
140.3 odd 12 35.2.k.b.3.1 yes 4
140.23 even 12 245.2.f.a.48.1 4
140.59 even 6 175.2.o.b.157.1 4
140.83 odd 4 245.2.l.a.68.1 4
140.87 odd 12 175.2.o.a.143.1 4
140.103 odd 12 245.2.f.b.48.1 4
140.123 even 12 245.2.l.b.178.1 4
420.143 even 12 315.2.bz.a.73.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.k.a.17.1 4 28.3 even 6
35.2.k.a.33.1 yes 4 20.3 even 4
35.2.k.b.3.1 yes 4 140.3 odd 12
35.2.k.b.12.1 yes 4 4.3 odd 2
175.2.o.a.82.1 4 20.19 odd 2
175.2.o.a.143.1 4 140.87 odd 12
175.2.o.b.68.1 4 20.7 even 4
175.2.o.b.157.1 4 140.59 even 6
245.2.f.a.48.1 4 140.23 even 12
245.2.f.a.97.1 4 28.19 even 6
245.2.f.b.48.1 4 140.103 odd 12
245.2.f.b.97.1 4 28.23 odd 6
245.2.l.a.68.1 4 140.83 odd 4
245.2.l.a.227.1 4 28.11 odd 6
245.2.l.b.117.1 4 28.27 even 2
245.2.l.b.178.1 4 140.123 even 12
315.2.bz.a.73.1 4 420.143 even 12
315.2.bz.a.82.1 4 12.11 even 2
315.2.bz.b.208.1 4 60.23 odd 4
315.2.bz.b.262.1 4 84.59 odd 6
560.2.ci.a.17.1 4 7.3 odd 6
560.2.ci.a.33.1 4 5.3 odd 4
560.2.ci.b.257.1 4 1.1 even 1 trivial
560.2.ci.b.353.1 4 35.3 even 12 inner