Properties

Label 1134.2.m.g.377.4
Level $1134$
Weight $2$
Character 1134.377
Analytic conductor $9.055$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(377,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.377");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 377.4
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1134.377
Dual form 1134.2.m.g.755.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} -2.44949i q^{10} +(2.12132 + 1.22474i) q^{13} +(2.09077 - 1.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.89898 q^{17} +2.44949i q^{19} +(-1.22474 - 2.12132i) q^{20} +(-5.19615 - 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.44949 q^{26} +(1.00000 - 2.44949i) q^{28} +(-5.19615 + 3.00000i) q^{29} +(-0.866025 - 0.500000i) q^{32} +(4.24264 - 2.44949i) q^{34} +(2.44949 - 6.00000i) q^{35} -2.00000 q^{37} +(1.22474 + 2.12132i) q^{38} +(-2.12132 - 1.22474i) q^{40} +(2.44949 - 4.24264i) q^{41} +(-2.00000 - 3.46410i) q^{43} -6.00000 q^{46} +(-2.44949 - 4.24264i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(2.12132 - 1.22474i) q^{52} +6.00000i q^{53} +(-0.358719 - 2.62132i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(6.12372 - 10.6066i) q^{59} +(-10.6066 + 6.12372i) q^{61} -1.00000 q^{64} +(5.19615 - 3.00000i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(2.44949 - 4.24264i) q^{68} +(-0.878680 - 6.42090i) q^{70} +9.79796i q^{73} +(-1.73205 + 1.00000i) q^{74} +(2.12132 + 1.22474i) q^{76} +(5.00000 + 8.66025i) q^{79} -2.44949 q^{80} -4.89898i q^{82} +(-1.22474 - 2.12132i) q^{83} +(6.00000 - 10.3923i) q^{85} +(-3.46410 - 2.00000i) q^{86} +(6.00000 + 2.44949i) q^{91} +(-5.19615 + 3.00000i) q^{92} +(-4.24264 - 2.44949i) q^{94} +(5.19615 + 3.00000i) q^{95} +(4.24264 - 2.44949i) q^{97} +(4.89898 - 5.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 4 q^{7} - 4 q^{16} - 4 q^{25} + 8 q^{28} - 16 q^{37} - 16 q^{43} - 48 q^{46} + 20 q^{49} - 24 q^{58} - 8 q^{64} - 32 q^{67} - 24 q^{70} + 40 q^{79} + 48 q^{85} + 48 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.22474 2.12132i 0.547723 0.948683i −0.450708 0.892672i \(-0.648828\pi\)
0.998430 0.0560116i \(-0.0178384\pi\)
\(6\) 0 0
\(7\) 2.62132 0.358719i 0.990766 0.135583i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.44949i 0.774597i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) 0 0
\(13\) 2.12132 + 1.22474i 0.588348 + 0.339683i 0.764444 0.644690i \(-0.223014\pi\)
−0.176096 + 0.984373i \(0.556347\pi\)
\(14\) 2.09077 1.62132i 0.558782 0.433316i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.89898 1.18818 0.594089 0.804400i \(-0.297513\pi\)
0.594089 + 0.804400i \(0.297513\pi\)
\(18\) 0 0
\(19\) 2.44949i 0.561951i 0.959715 + 0.280976i \(0.0906580\pi\)
−0.959715 + 0.280976i \(0.909342\pi\)
\(20\) −1.22474 2.12132i −0.273861 0.474342i
\(21\) 0 0
\(22\) 0 0
\(23\) −5.19615 3.00000i −1.08347 0.625543i −0.151642 0.988436i \(-0.548456\pi\)
−0.931831 + 0.362892i \(0.881789\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 2.44949 0.480384
\(27\) 0 0
\(28\) 1.00000 2.44949i 0.188982 0.462910i
\(29\) −5.19615 + 3.00000i −0.964901 + 0.557086i −0.897678 0.440652i \(-0.854747\pi\)
−0.0672232 + 0.997738i \(0.521414\pi\)
\(30\) 0 0
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.24264 2.44949i 0.727607 0.420084i
\(35\) 2.44949 6.00000i 0.414039 1.01419i
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 1.22474 + 2.12132i 0.198680 + 0.344124i
\(39\) 0 0
\(40\) −2.12132 1.22474i −0.335410 0.193649i
\(41\) 2.44949 4.24264i 0.382546 0.662589i −0.608879 0.793263i \(-0.708381\pi\)
0.991425 + 0.130674i \(0.0417140\pi\)
\(42\) 0 0
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) −2.44949 4.24264i −0.357295 0.618853i 0.630213 0.776422i \(-0.282968\pi\)
−0.987508 + 0.157569i \(0.949634\pi\)
\(48\) 0 0
\(49\) 6.74264 1.88064i 0.963234 0.268662i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 0 0
\(52\) 2.12132 1.22474i 0.294174 0.169842i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.358719 2.62132i −0.0479359 0.350289i
\(57\) 0 0
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) 6.12372 10.6066i 0.797241 1.38086i −0.124165 0.992262i \(-0.539625\pi\)
0.921406 0.388600i \(-0.127041\pi\)
\(60\) 0 0
\(61\) −10.6066 + 6.12372i −1.35804 + 0.784063i −0.989359 0.145495i \(-0.953523\pi\)
−0.368677 + 0.929557i \(0.620189\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.19615 3.00000i 0.644503 0.372104i
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 2.44949 4.24264i 0.297044 0.514496i
\(69\) 0 0
\(70\) −0.878680 6.42090i −0.105022 0.767444i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 9.79796i 1.14676i 0.819288 + 0.573382i \(0.194369\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) −1.73205 + 1.00000i −0.201347 + 0.116248i
\(75\) 0 0
\(76\) 2.12132 + 1.22474i 0.243332 + 0.140488i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) −2.44949 −0.273861
\(81\) 0 0
\(82\) 4.89898i 0.541002i
\(83\) −1.22474 2.12132i −0.134433 0.232845i 0.790948 0.611884i \(-0.209588\pi\)
−0.925381 + 0.379039i \(0.876255\pi\)
\(84\) 0 0
\(85\) 6.00000 10.3923i 0.650791 1.12720i
\(86\) −3.46410 2.00000i −0.373544 0.215666i
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 6.00000 + 2.44949i 0.628971 + 0.256776i
\(92\) −5.19615 + 3.00000i −0.541736 + 0.312772i
\(93\) 0 0
\(94\) −4.24264 2.44949i −0.437595 0.252646i
\(95\) 5.19615 + 3.00000i 0.533114 + 0.307794i
\(96\) 0 0
\(97\) 4.24264 2.44949i 0.430775 0.248708i −0.268902 0.963168i \(-0.586661\pi\)
0.699677 + 0.714460i \(0.253327\pi\)
\(98\) 4.89898 5.00000i 0.494872 0.505076i
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −3.67423 6.36396i −0.365600 0.633238i 0.623272 0.782005i \(-0.285803\pi\)
−0.988872 + 0.148767i \(0.952470\pi\)
\(102\) 0 0
\(103\) −8.48528 4.89898i −0.836080 0.482711i 0.0198501 0.999803i \(-0.493681\pi\)
−0.855930 + 0.517092i \(0.827014\pi\)
\(104\) 1.22474 2.12132i 0.120096 0.208013i
\(105\) 0 0
\(106\) 3.00000 + 5.19615i 0.291386 + 0.504695i
\(107\) 12.0000i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.62132 2.09077i −0.153200 0.197559i
\(113\) −5.19615 3.00000i −0.488813 0.282216i 0.235269 0.971930i \(-0.424403\pi\)
−0.724082 + 0.689714i \(0.757736\pi\)
\(114\) 0 0
\(115\) −12.7279 + 7.34847i −1.18688 + 0.685248i
\(116\) 6.00000i 0.557086i
\(117\) 0 0
\(118\) 12.2474i 1.12747i
\(119\) 12.8418 1.75736i 1.17721 0.161097i
\(120\) 0 0
\(121\) −5.50000 + 9.52628i −0.500000 + 0.866025i
\(122\) −6.12372 + 10.6066i −0.554416 + 0.960277i
\(123\) 0 0
\(124\) 0 0
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 3.00000 5.19615i 0.263117 0.455733i
\(131\) −3.67423 + 6.36396i −0.321019 + 0.556022i −0.980699 0.195525i \(-0.937359\pi\)
0.659679 + 0.751547i \(0.270692\pi\)
\(132\) 0 0
\(133\) 0.878680 + 6.42090i 0.0761912 + 0.556762i
\(134\) 8.00000i 0.691095i
\(135\) 0 0
\(136\) 4.89898i 0.420084i
\(137\) −10.3923 + 6.00000i −0.887875 + 0.512615i −0.873247 0.487278i \(-0.837990\pi\)
−0.0146279 + 0.999893i \(0.504656\pi\)
\(138\) 0 0
\(139\) −2.12132 1.22474i −0.179928 0.103882i 0.407331 0.913281i \(-0.366460\pi\)
−0.587259 + 0.809399i \(0.699793\pi\)
\(140\) −3.97141 5.12132i −0.335645 0.432831i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 14.6969i 1.22051i
\(146\) 4.89898 + 8.48528i 0.405442 + 0.702247i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) 5.19615 + 3.00000i 0.425685 + 0.245770i 0.697507 0.716578i \(-0.254293\pi\)
−0.271821 + 0.962348i \(0.587626\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 2.44949 0.198680
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.36396 + 3.67423i 0.507899 + 0.293236i 0.731970 0.681337i \(-0.238601\pi\)
−0.224070 + 0.974573i \(0.571935\pi\)
\(158\) 8.66025 + 5.00000i 0.688973 + 0.397779i
\(159\) 0 0
\(160\) −2.12132 + 1.22474i −0.167705 + 0.0968246i
\(161\) −14.6969 6.00000i −1.15828 0.472866i
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −2.44949 4.24264i −0.191273 0.331295i
\(165\) 0 0
\(166\) −2.12132 1.22474i −0.164646 0.0950586i
\(167\) −2.44949 + 4.24264i −0.189547 + 0.328305i −0.945099 0.326783i \(-0.894035\pi\)
0.755552 + 0.655089i \(0.227369\pi\)
\(168\) 0 0
\(169\) −3.50000 6.06218i −0.269231 0.466321i
\(170\) 12.0000i 0.920358i
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 11.0227 + 19.0919i 0.838041 + 1.45153i 0.891531 + 0.452961i \(0.149632\pi\)
−0.0534899 + 0.998568i \(0.517034\pi\)
\(174\) 0 0
\(175\) −1.62132 2.09077i −0.122560 0.158047i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 24.0000i 1.79384i 0.442189 + 0.896922i \(0.354202\pi\)
−0.442189 + 0.896922i \(0.645798\pi\)
\(180\) 0 0
\(181\) 12.2474i 0.910346i 0.890403 + 0.455173i \(0.150423\pi\)
−0.890403 + 0.455173i \(0.849577\pi\)
\(182\) 6.42090 0.878680i 0.475949 0.0651321i
\(183\) 0 0
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) −2.44949 + 4.24264i −0.180090 + 0.311925i
\(186\) 0 0
\(187\) 0 0
\(188\) −4.89898 −0.357295
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 0 0
\(193\) −2.00000 + 3.46410i −0.143963 + 0.249351i −0.928986 0.370116i \(-0.879318\pi\)
0.785022 + 0.619467i \(0.212651\pi\)
\(194\) 2.44949 4.24264i 0.175863 0.304604i
\(195\) 0 0
\(196\) 1.74264 6.77962i 0.124474 0.484258i
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 0 0
\(199\) 9.79796i 0.694559i −0.937762 0.347279i \(-0.887106\pi\)
0.937762 0.347279i \(-0.112894\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) 0 0
\(202\) −6.36396 3.67423i −0.447767 0.258518i
\(203\) −12.5446 + 9.72792i −0.880460 + 0.682766i
\(204\) 0 0
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) −9.79796 −0.682656
\(207\) 0 0
\(208\) 2.44949i 0.169842i
\(209\) 0 0
\(210\) 0 0
\(211\) 4.00000 6.92820i 0.275371 0.476957i −0.694857 0.719148i \(-0.744533\pi\)
0.970229 + 0.242190i \(0.0778659\pi\)
\(212\) 5.19615 + 3.00000i 0.356873 + 0.206041i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −9.79796 −0.668215
\(216\) 0 0
\(217\) 0 0
\(218\) 8.66025 5.00000i 0.586546 0.338643i
\(219\) 0 0
\(220\) 0 0
\(221\) 10.3923 + 6.00000i 0.699062 + 0.403604i
\(222\) 0 0
\(223\) −12.7279 + 7.34847i −0.852325 + 0.492090i −0.861435 0.507869i \(-0.830434\pi\)
0.00910984 + 0.999959i \(0.497100\pi\)
\(224\) −2.44949 1.00000i −0.163663 0.0668153i
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 3.67423 + 6.36396i 0.243868 + 0.422391i 0.961813 0.273709i \(-0.0882505\pi\)
−0.717945 + 0.696100i \(0.754917\pi\)
\(228\) 0 0
\(229\) 19.0919 + 11.0227i 1.26163 + 0.728401i 0.973389 0.229158i \(-0.0735973\pi\)
0.288238 + 0.957559i \(0.406931\pi\)
\(230\) −7.34847 + 12.7279i −0.484544 + 0.839254i
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 24.0000i 1.57229i −0.618041 0.786146i \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) −6.12372 10.6066i −0.398621 0.690431i
\(237\) 0 0
\(238\) 10.2426 7.94282i 0.663932 0.514856i
\(239\) 5.19615 + 3.00000i 0.336111 + 0.194054i 0.658551 0.752536i \(-0.271170\pi\)
−0.322440 + 0.946590i \(0.604503\pi\)
\(240\) 0 0
\(241\) 21.2132 12.2474i 1.36646 0.788928i 0.375988 0.926624i \(-0.377303\pi\)
0.990474 + 0.137697i \(0.0439700\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 0 0
\(244\) 12.2474i 0.784063i
\(245\) 4.26858 16.6066i 0.272710 1.06096i
\(246\) 0 0
\(247\) −3.00000 + 5.19615i −0.190885 + 0.330623i
\(248\) 0 0
\(249\) 0 0
\(250\) 8.48528 4.89898i 0.536656 0.309839i
\(251\) −17.1464 −1.08227 −0.541136 0.840935i \(-0.682006\pi\)
−0.541136 + 0.840935i \(0.682006\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 6.92820 4.00000i 0.434714 0.250982i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −14.6969 + 25.4558i −0.916770 + 1.58789i −0.112481 + 0.993654i \(0.535880\pi\)
−0.804289 + 0.594238i \(0.797454\pi\)
\(258\) 0 0
\(259\) −5.24264 + 0.717439i −0.325762 + 0.0445795i
\(260\) 6.00000i 0.372104i
\(261\) 0 0
\(262\) 7.34847i 0.453990i
\(263\) −20.7846 + 12.0000i −1.28163 + 0.739952i −0.977147 0.212565i \(-0.931818\pi\)
−0.304487 + 0.952517i \(0.598485\pi\)
\(264\) 0 0
\(265\) 12.7279 + 7.34847i 0.781870 + 0.451413i
\(266\) 3.97141 + 5.12132i 0.243503 + 0.314008i
\(267\) 0 0
\(268\) 4.00000 + 6.92820i 0.244339 + 0.423207i
\(269\) −12.2474 −0.746740 −0.373370 0.927682i \(-0.621798\pi\)
−0.373370 + 0.927682i \(0.621798\pi\)
\(270\) 0 0
\(271\) 24.4949i 1.48796i −0.668202 0.743980i \(-0.732936\pi\)
0.668202 0.743980i \(-0.267064\pi\)
\(272\) −2.44949 4.24264i −0.148522 0.257248i
\(273\) 0 0
\(274\) −6.00000 + 10.3923i −0.362473 + 0.627822i
\(275\) 0 0
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) −2.44949 −0.146911
\(279\) 0 0
\(280\) −6.00000 2.44949i −0.358569 0.146385i
\(281\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 0 0
\(283\) −19.0919 11.0227i −1.13489 0.655232i −0.189733 0.981836i \(-0.560762\pi\)
−0.945161 + 0.326604i \(0.894096\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.89898 12.0000i 0.289178 0.708338i
\(288\) 0 0
\(289\) 7.00000 0.411765
\(290\) 7.34847 + 12.7279i 0.431517 + 0.747409i
\(291\) 0 0
\(292\) 8.48528 + 4.89898i 0.496564 + 0.286691i
\(293\) −1.22474 + 2.12132i −0.0715504 + 0.123929i −0.899581 0.436754i \(-0.856128\pi\)
0.828031 + 0.560683i \(0.189461\pi\)
\(294\) 0 0
\(295\) −15.0000 25.9808i −0.873334 1.51266i
\(296\) 2.00000i 0.116248i
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −7.34847 12.7279i −0.424973 0.736075i
\(300\) 0 0
\(301\) −6.48528 8.36308i −0.373805 0.482040i
\(302\) 6.92820 + 4.00000i 0.398673 + 0.230174i
\(303\) 0 0
\(304\) 2.12132 1.22474i 0.121666 0.0702439i
\(305\) 30.0000i 1.71780i
\(306\) 0 0
\(307\) 7.34847i 0.419399i −0.977766 0.209700i \(-0.932751\pi\)
0.977766 0.209700i \(-0.0672486\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.79796 + 16.9706i −0.555591 + 0.962312i 0.442266 + 0.896884i \(0.354175\pi\)
−0.997857 + 0.0654284i \(0.979159\pi\)
\(312\) 0 0
\(313\) 29.6985 17.1464i 1.67866 0.969173i 0.716139 0.697958i \(-0.245908\pi\)
0.962519 0.271216i \(-0.0874257\pi\)
\(314\) 7.34847 0.414698
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i \(-0.497978\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.22474 + 2.12132i −0.0684653 + 0.118585i
\(321\) 0 0
\(322\) −15.7279 + 2.15232i −0.876483 + 0.119944i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 2.44949i 0.135873i
\(326\) −13.8564 + 8.00000i −0.767435 + 0.443079i
\(327\) 0 0
\(328\) −4.24264 2.44949i −0.234261 0.135250i
\(329\) −7.94282 10.2426i −0.437902 0.564695i
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) −2.44949 −0.134433
\(333\) 0 0
\(334\) 4.89898i 0.268060i
\(335\) 9.79796 + 16.9706i 0.535320 + 0.927201i
\(336\) 0 0
\(337\) 16.0000 27.7128i 0.871576 1.50961i 0.0112091 0.999937i \(-0.496432\pi\)
0.860366 0.509676i \(-0.170235\pi\)
\(338\) −6.06218 3.50000i −0.329739 0.190375i
\(339\) 0 0
\(340\) −6.00000 10.3923i −0.325396 0.563602i
\(341\) 0 0
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) −3.46410 + 2.00000i −0.186772 + 0.107833i
\(345\) 0 0
\(346\) 19.0919 + 11.0227i 1.02639 + 0.592584i
\(347\) 10.3923 + 6.00000i 0.557888 + 0.322097i 0.752297 0.658824i \(-0.228946\pi\)
−0.194409 + 0.980921i \(0.562279\pi\)
\(348\) 0 0
\(349\) 2.12132 1.22474i 0.113552 0.0655591i −0.442149 0.896942i \(-0.645784\pi\)
0.555700 + 0.831383i \(0.312450\pi\)
\(350\) −2.44949 1.00000i −0.130931 0.0534522i
\(351\) 0 0
\(352\) 0 0
\(353\) 4.89898 + 8.48528i 0.260746 + 0.451626i 0.966440 0.256891i \(-0.0826980\pi\)
−0.705694 + 0.708517i \(0.749365\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 12.0000 + 20.7846i 0.634220 + 1.09850i
\(359\) 6.00000i 0.316668i −0.987386 0.158334i \(-0.949388\pi\)
0.987386 0.158334i \(-0.0506123\pi\)
\(360\) 0 0
\(361\) 13.0000 0.684211
\(362\) 6.12372 + 10.6066i 0.321856 + 0.557471i
\(363\) 0 0
\(364\) 5.12132 3.97141i 0.268430 0.208158i
\(365\) 20.7846 + 12.0000i 1.08792 + 0.628109i
\(366\) 0 0
\(367\) 4.24264 2.44949i 0.221464 0.127862i −0.385164 0.922848i \(-0.625855\pi\)
0.606628 + 0.794986i \(0.292522\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) 4.89898i 0.254686i
\(371\) 2.15232 + 15.7279i 0.111743 + 0.816553i
\(372\) 0 0
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −4.24264 + 2.44949i −0.218797 + 0.126323i
\(377\) −14.6969 −0.756931
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 5.19615 3.00000i 0.266557 0.153897i
\(381\) 0 0
\(382\) 0 0
\(383\) 17.1464 29.6985i 0.876142 1.51752i 0.0205998 0.999788i \(-0.493442\pi\)
0.855542 0.517734i \(-0.173224\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.00000i 0.203595i
\(387\) 0 0
\(388\) 4.89898i 0.248708i
\(389\) −5.19615 + 3.00000i −0.263455 + 0.152106i −0.625910 0.779895i \(-0.715272\pi\)
0.362454 + 0.932002i \(0.381939\pi\)
\(390\) 0 0
\(391\) −25.4558 14.6969i −1.28736 0.743256i
\(392\) −1.88064 6.74264i −0.0949865 0.340555i
\(393\) 0 0
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 24.4949 1.23247
\(396\) 0 0
\(397\) 7.34847i 0.368809i −0.982850 0.184405i \(-0.940964\pi\)
0.982850 0.184405i \(-0.0590357\pi\)
\(398\) −4.89898 8.48528i −0.245564 0.425329i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −25.9808 15.0000i −1.29742 0.749064i −0.317460 0.948272i \(-0.602830\pi\)
−0.979957 + 0.199207i \(0.936163\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −7.34847 −0.365600
\(405\) 0 0
\(406\) −6.00000 + 14.6969i −0.297775 + 0.729397i
\(407\) 0 0
\(408\) 0 0
\(409\) 29.6985 + 17.1464i 1.46850 + 0.847836i 0.999377 0.0352988i \(-0.0112383\pi\)
0.469119 + 0.883135i \(0.344572\pi\)
\(410\) −10.3923 6.00000i −0.513239 0.296319i
\(411\) 0 0
\(412\) −8.48528 + 4.89898i −0.418040 + 0.241355i
\(413\) 12.2474 30.0000i 0.602658 1.47620i
\(414\) 0 0
\(415\) −6.00000 −0.294528
\(416\) −1.22474 2.12132i −0.0600481 0.104006i
\(417\) 0 0
\(418\) 0 0
\(419\) −6.12372 + 10.6066i −0.299164 + 0.518166i −0.975945 0.218018i \(-0.930041\pi\)
0.676781 + 0.736184i \(0.263374\pi\)
\(420\) 0 0
\(421\) −1.00000 1.73205i −0.0487370 0.0844150i 0.840628 0.541613i \(-0.182186\pi\)
−0.889365 + 0.457198i \(0.848853\pi\)
\(422\) 8.00000i 0.389434i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) −2.44949 4.24264i −0.118818 0.205798i
\(426\) 0 0
\(427\) −25.6066 + 19.8570i −1.23919 + 0.960949i
\(428\) −10.3923 6.00000i −0.502331 0.290021i
\(429\) 0 0
\(430\) −8.48528 + 4.89898i −0.409197 + 0.236250i
\(431\) 30.0000i 1.44505i 0.691345 + 0.722525i \(0.257018\pi\)
−0.691345 + 0.722525i \(0.742982\pi\)
\(432\) 0 0
\(433\) 14.6969i 0.706290i −0.935569 0.353145i \(-0.885112\pi\)
0.935569 0.353145i \(-0.114888\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 7.34847 12.7279i 0.351525 0.608859i
\(438\) 0 0
\(439\) 12.7279 7.34847i 0.607471 0.350723i −0.164504 0.986376i \(-0.552602\pi\)
0.771975 + 0.635653i \(0.219269\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) 31.1769 18.0000i 1.48126 0.855206i 0.481486 0.876454i \(-0.340097\pi\)
0.999774 + 0.0212481i \(0.00676401\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −7.34847 + 12.7279i −0.347960 + 0.602685i
\(447\) 0 0
\(448\) −2.62132 + 0.358719i −0.123846 + 0.0169479i
\(449\) 36.0000i 1.69895i −0.527633 0.849473i \(-0.676920\pi\)
0.527633 0.849473i \(-0.323080\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −5.19615 + 3.00000i −0.244406 + 0.141108i
\(453\) 0 0
\(454\) 6.36396 + 3.67423i 0.298675 + 0.172440i
\(455\) 12.5446 9.72792i 0.588101 0.456052i
\(456\) 0 0
\(457\) −14.0000 24.2487i −0.654892 1.13431i −0.981921 0.189292i \(-0.939381\pi\)
0.327028 0.945015i \(-0.393953\pi\)
\(458\) 22.0454 1.03011
\(459\) 0 0
\(460\) 14.6969i 0.685248i
\(461\) −15.9217 27.5772i −0.741547 1.28440i −0.951791 0.306748i \(-0.900759\pi\)
0.210244 0.977649i \(-0.432574\pi\)
\(462\) 0 0
\(463\) −7.00000 + 12.1244i −0.325318 + 0.563467i −0.981577 0.191069i \(-0.938805\pi\)
0.656259 + 0.754536i \(0.272138\pi\)
\(464\) 5.19615 + 3.00000i 0.241225 + 0.139272i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) −7.34847 −0.340047 −0.170023 0.985440i \(-0.554384\pi\)
−0.170023 + 0.985440i \(0.554384\pi\)
\(468\) 0 0
\(469\) −8.00000 + 19.5959i −0.369406 + 0.904855i
\(470\) −10.3923 + 6.00000i −0.479361 + 0.276759i
\(471\) 0 0
\(472\) −10.6066 6.12372i −0.488208 0.281867i
\(473\) 0 0
\(474\) 0 0
\(475\) 2.12132 1.22474i 0.0973329 0.0561951i
\(476\) 4.89898 12.0000i 0.224544 0.550019i
\(477\) 0 0
\(478\) 6.00000 0.274434
\(479\) −12.2474 21.2132i −0.559600 0.969256i −0.997530 0.0702467i \(-0.977621\pi\)
0.437929 0.899009i \(-0.355712\pi\)
\(480\) 0 0
\(481\) −4.24264 2.44949i −0.193448 0.111687i
\(482\) 12.2474 21.2132i 0.557856 0.966235i
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 12.0000i 0.544892i
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 6.12372 + 10.6066i 0.277208 + 0.480138i
\(489\) 0 0
\(490\) −4.60660 16.5160i −0.208105 0.746118i
\(491\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) −25.4558 + 14.6969i −1.14647 + 0.661917i
\(494\) 6.00000i 0.269953i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i \(-0.685590\pi\)
0.998233 + 0.0594153i \(0.0189236\pi\)
\(500\) 4.89898 8.48528i 0.219089 0.379473i
\(501\) 0 0
\(502\) −14.8492 + 8.57321i −0.662754 + 0.382641i
\(503\) 39.1918 1.74748 0.873739 0.486395i \(-0.161689\pi\)
0.873739 + 0.486395i \(0.161689\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) 0 0
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) 6.12372 10.6066i 0.271429 0.470129i −0.697799 0.716294i \(-0.745837\pi\)
0.969228 + 0.246165i \(0.0791704\pi\)
\(510\) 0 0
\(511\) 3.51472 + 25.6836i 0.155482 + 1.13618i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 29.3939i 1.29651i
\(515\) −20.7846 + 12.0000i −0.915879 + 0.528783i
\(516\) 0 0
\(517\) 0 0
\(518\) −4.18154 + 3.24264i −0.183726 + 0.142473i
\(519\) 0 0
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) −4.89898 −0.214628 −0.107314 0.994225i \(-0.534225\pi\)
−0.107314 + 0.994225i \(0.534225\pi\)
\(522\) 0 0
\(523\) 2.44949i 0.107109i −0.998565 0.0535544i \(-0.982945\pi\)
0.998565 0.0535544i \(-0.0170550\pi\)
\(524\) 3.67423 + 6.36396i 0.160510 + 0.278011i
\(525\) 0 0
\(526\) −12.0000 + 20.7846i −0.523225 + 0.906252i
\(527\) 0 0
\(528\) 0 0
\(529\) 6.50000 + 11.2583i 0.282609 + 0.489493i
\(530\) 14.6969 0.638394
\(531\) 0 0
\(532\) 6.00000 + 2.44949i 0.260133 + 0.106199i
\(533\) 10.3923 6.00000i 0.450141 0.259889i
\(534\) 0 0
\(535\) −25.4558 14.6969i −1.10055 0.635404i
\(536\) 6.92820 + 4.00000i 0.299253 + 0.172774i
\(537\) 0 0
\(538\) −10.6066 + 6.12372i −0.457283 + 0.264013i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −12.2474 21.2132i −0.526073 0.911185i
\(543\) 0 0
\(544\) −4.24264 2.44949i −0.181902 0.105021i
\(545\) 12.2474 21.2132i 0.524623 0.908674i
\(546\) 0 0
\(547\) −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i \(-0.221375\pi\)
−0.938779 + 0.344519i \(0.888042\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 0 0
\(550\) 0 0
\(551\) −7.34847 12.7279i −0.313055 0.542228i
\(552\) 0 0
\(553\) 16.2132 + 20.9077i 0.689456 + 0.889086i
\(554\) 19.0526 + 11.0000i 0.809466 + 0.467345i
\(555\) 0 0
\(556\) −2.12132 + 1.22474i −0.0899640 + 0.0519408i
\(557\) 18.0000i 0.762684i 0.924434 + 0.381342i \(0.124538\pi\)
−0.924434 + 0.381342i \(0.875462\pi\)
\(558\) 0 0
\(559\) 9.79796i 0.414410i
\(560\) −6.42090 + 0.878680i −0.271332 + 0.0371310i
\(561\) 0 0
\(562\) 0 0
\(563\) 11.0227 19.0919i 0.464552 0.804627i −0.534630 0.845087i \(-0.679549\pi\)
0.999181 + 0.0404596i \(0.0128822\pi\)
\(564\) 0 0
\(565\) −12.7279 + 7.34847i −0.535468 + 0.309152i
\(566\) −22.0454 −0.926638
\(567\) 0 0
\(568\) 0 0
\(569\) −5.19615 + 3.00000i −0.217834 + 0.125767i −0.604947 0.796266i \(-0.706806\pi\)
0.387113 + 0.922032i \(0.373472\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.75736 12.8418i −0.0733508 0.536006i
\(575\) 6.00000i 0.250217i
\(576\) 0 0
\(577\) 19.5959i 0.815789i −0.913029 0.407894i \(-0.866263\pi\)
0.913029 0.407894i \(-0.133737\pi\)
\(578\) 6.06218 3.50000i 0.252153 0.145581i
\(579\) 0 0
\(580\) 12.7279 + 7.34847i 0.528498 + 0.305129i
\(581\) −3.97141 5.12132i −0.164762 0.212468i
\(582\) 0 0
\(583\) 0 0
\(584\) 9.79796 0.405442
\(585\) 0 0
\(586\) 2.44949i 0.101187i
\(587\) 3.67423 + 6.36396i 0.151652 + 0.262669i 0.931835 0.362883i \(-0.118207\pi\)
−0.780183 + 0.625551i \(0.784874\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −25.9808 15.0000i −1.06961 0.617540i
\(591\) 0 0
\(592\) 1.00000 + 1.73205i 0.0410997 + 0.0711868i
\(593\) 39.1918 1.60942 0.804708 0.593671i \(-0.202322\pi\)
0.804708 + 0.593671i \(0.202322\pi\)
\(594\) 0 0
\(595\) 12.0000 29.3939i 0.491952 1.20503i
\(596\) 5.19615 3.00000i 0.212843 0.122885i
\(597\) 0 0
\(598\) −12.7279 7.34847i −0.520483 0.300501i
\(599\) −20.7846 12.0000i −0.849236 0.490307i 0.0111569 0.999938i \(-0.496449\pi\)
−0.860393 + 0.509631i \(0.829782\pi\)
\(600\) 0 0
\(601\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) −9.79796 4.00000i −0.399335 0.163028i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 13.4722 + 23.3345i 0.547723 + 0.948683i
\(606\) 0 0
\(607\) −4.24264 2.44949i −0.172203 0.0994217i 0.411421 0.911445i \(-0.365033\pi\)
−0.583624 + 0.812024i \(0.698366\pi\)
\(608\) 1.22474 2.12132i 0.0496700 0.0860309i
\(609\) 0 0
\(610\) 15.0000 + 25.9808i 0.607332 + 1.05193i
\(611\) 12.0000i 0.485468i
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) −3.67423 6.36396i −0.148280 0.256829i
\(615\) 0 0
\(616\) 0 0
\(617\) −15.5885 9.00000i −0.627568 0.362326i 0.152242 0.988343i \(-0.451351\pi\)
−0.779809 + 0.626017i \(0.784684\pi\)
\(618\) 0 0
\(619\) 23.3345 13.4722i 0.937894 0.541493i 0.0485943 0.998819i \(-0.484526\pi\)
0.889299 + 0.457325i \(0.151193\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 19.5959i 0.785725i
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 17.1464 29.6985i 0.685309 1.18699i
\(627\) 0 0
\(628\) 6.36396 3.67423i 0.253950 0.146618i
\(629\) −9.79796 −0.390670
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) 8.66025 5.00000i 0.344486 0.198889i
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 9.79796 16.9706i 0.388820 0.673456i
\(636\) 0 0
\(637\) 16.6066 + 4.26858i 0.657978 + 0.169127i
\(638\) 0 0
\(639\) 0 0
\(640\) 2.44949i 0.0968246i
\(641\) −25.9808 + 15.0000i −1.02618 + 0.592464i −0.915888 0.401435i \(-0.868512\pi\)
−0.110291 + 0.993899i \(0.535178\pi\)
\(642\) 0 0
\(643\) −19.0919 11.0227i −0.752910 0.434693i 0.0738342 0.997271i \(-0.476476\pi\)
−0.826745 + 0.562578i \(0.809810\pi\)
\(644\) −12.5446 + 9.72792i −0.494327 + 0.383334i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −44.0908 −1.73339 −0.866694 0.498839i \(-0.833760\pi\)
−0.866694 + 0.498839i \(0.833760\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −1.22474 2.12132i −0.0480384 0.0832050i
\(651\) 0 0
\(652\) −8.00000 + 13.8564i −0.313304 + 0.542659i
\(653\) −5.19615 3.00000i −0.203341 0.117399i 0.394872 0.918736i \(-0.370789\pi\)
−0.598213 + 0.801337i \(0.704122\pi\)
\(654\) 0 0
\(655\) 9.00000 + 15.5885i 0.351659 + 0.609091i
\(656\) −4.89898 −0.191273
\(657\) 0 0
\(658\) −12.0000 4.89898i −0.467809 0.190982i
\(659\) −31.1769 + 18.0000i −1.21448 + 0.701180i −0.963732 0.266872i \(-0.914010\pi\)
−0.250748 + 0.968052i \(0.580677\pi\)
\(660\) 0 0
\(661\) −10.6066 6.12372i −0.412549 0.238185i 0.279335 0.960194i \(-0.409886\pi\)
−0.691884 + 0.722008i \(0.743219\pi\)
\(662\) 6.92820 + 4.00000i 0.269272 + 0.155464i
\(663\) 0 0
\(664\) −2.12132 + 1.22474i −0.0823232 + 0.0475293i
\(665\) 14.6969 + 6.00000i 0.569923 + 0.232670i
\(666\) 0 0
\(667\) 36.0000 1.39393
\(668\) 2.44949 + 4.24264i 0.0947736 + 0.164153i
\(669\) 0 0
\(670\) 16.9706 + 9.79796i 0.655630 + 0.378528i
\(671\) 0 0
\(672\) 0 0
\(673\) −17.0000 29.4449i −0.655302 1.13502i −0.981818 0.189824i \(-0.939208\pi\)
0.326516 0.945192i \(-0.394125\pi\)
\(674\) 32.0000i 1.23259i
\(675\) 0 0
\(676\) −7.00000 −0.269231
\(677\) 3.67423 + 6.36396i 0.141212 + 0.244587i 0.927953 0.372696i \(-0.121567\pi\)
−0.786741 + 0.617283i \(0.788233\pi\)
\(678\) 0 0
\(679\) 10.2426 7.94282i 0.393076 0.304817i
\(680\) −10.3923 6.00000i −0.398527 0.230089i
\(681\) 0 0
\(682\) 0 0
\(683\) 24.0000i 0.918334i −0.888350 0.459167i \(-0.848148\pi\)
0.888350 0.459167i \(-0.151852\pi\)
\(684\) 0 0
\(685\) 29.3939i 1.12308i
\(686\) 11.0482 14.8640i 0.421822 0.567509i
\(687\) 0 0
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) −7.34847 + 12.7279i −0.279954 + 0.484895i
\(690\) 0 0
\(691\) −31.8198 + 18.3712i −1.21048 + 0.698872i −0.962864 0.269985i \(-0.912981\pi\)
−0.247618 + 0.968858i \(0.579648\pi\)
\(692\) 22.0454 0.838041
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −5.19615 + 3.00000i −0.197101 + 0.113796i
\(696\) 0 0
\(697\) 12.0000 20.7846i 0.454532 0.787273i
\(698\) 1.22474 2.12132i 0.0463573 0.0802932i
\(699\) 0 0
\(700\) −2.62132 + 0.358719i −0.0990766 + 0.0135583i
\(701\) 30.0000i 1.13308i 0.824033 + 0.566542i \(0.191719\pi\)
−0.824033 + 0.566542i \(0.808281\pi\)
\(702\) 0 0
\(703\) 4.89898i 0.184769i
\(704\) 0 0
\(705\) 0 0
\(706\) 8.48528 + 4.89898i 0.319348 + 0.184376i
\(707\) −11.9142 15.3640i −0.448080 0.577821i
\(708\) 0 0
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 20.7846 + 12.0000i 0.776757 + 0.448461i
\(717\) 0 0
\(718\) −3.00000 5.19615i −0.111959 0.193919i
\(719\) 24.4949 0.913506 0.456753 0.889594i \(-0.349012\pi\)
0.456753 + 0.889594i \(0.349012\pi\)
\(720\) 0 0
\(721\) −24.0000 9.79796i −0.893807 0.364895i
\(722\) 11.2583 6.50000i 0.418992 0.241905i
\(723\) 0 0
\(724\) 10.6066 + 6.12372i 0.394191 + 0.227586i
\(725\) 5.19615 + 3.00000i 0.192980 + 0.111417i
\(726\) 0 0
\(727\) 25.4558 14.6969i 0.944105 0.545079i 0.0528602 0.998602i \(-0.483166\pi\)
0.891245 + 0.453523i \(0.149833\pi\)
\(728\) 2.44949 6.00000i 0.0907841 0.222375i
\(729\) 0 0
\(730\) 24.0000 0.888280
\(731\) −9.79796 16.9706i −0.362391 0.627679i
\(732\) 0 0
\(733\) −19.0919 11.0227i −0.705175 0.407133i 0.104097 0.994567i \(-0.466805\pi\)
−0.809272 + 0.587434i \(0.800138\pi\)
\(734\) 2.44949 4.24264i 0.0904123 0.156599i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) 0 0
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 2.44949 + 4.24264i 0.0900450 + 0.155963i
\(741\) 0 0
\(742\) 9.72792 + 12.5446i 0.357123 + 0.460528i
\(743\) −5.19615 3.00000i −0.190628 0.110059i 0.401648 0.915794i \(-0.368437\pi\)
−0.592277 + 0.805735i \(0.701771\pi\)
\(744\) 0 0
\(745\) 12.7279 7.34847i 0.466315 0.269227i
\(746\) 14.0000i 0.512576i
\(747\) 0 0
\(748\) 0 0
\(749\) −4.30463 31.4558i −0.157288 1.14937i
\(750\) 0 0
\(751\) 4.00000 6.92820i 0.145962 0.252814i −0.783769 0.621052i \(-0.786706\pi\)
0.929731 + 0.368238i \(0.120039\pi\)
\(752\) −2.44949 + 4.24264i −0.0893237 + 0.154713i
\(753\) 0 0
\(754\) −12.7279 + 7.34847i −0.463524 + 0.267615i
\(755\) 19.5959 0.713168
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −17.3205 + 10.0000i −0.629109 + 0.363216i
\(759\) 0 0
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) 2.44949 4.24264i 0.0887939 0.153796i −0.818208 0.574923i \(-0.805032\pi\)
0.907002 + 0.421127i \(0.138365\pi\)
\(762\) 0 0
\(763\) 26.2132 3.58719i 0.948982 0.129865i
\(764\) 0 0
\(765\) 0 0
\(766\) 34.2929i 1.23905i
\(767\) 25.9808 15.0000i 0.938111 0.541619i
\(768\) 0 0
\(769\) 29.6985 + 17.1464i 1.07095 + 0.618316i 0.928442 0.371477i \(-0.121149\pi\)
0.142513 + 0.989793i \(0.454482\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.00000 + 3.46410i 0.0719816 + 0.124676i
\(773\) 26.9444 0.969122 0.484561 0.874757i \(-0.338979\pi\)
0.484561 + 0.874757i \(0.338979\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.44949 4.24264i −0.0879316 0.152302i
\(777\) 0 0
\(778\) −3.00000 + 5.19615i −0.107555 + 0.186291i
\(779\) 10.3923 + 6.00000i 0.372343 + 0.214972i
\(780\) 0 0
\(781\) 0 0
\(782\) −29.3939 −1.05112
\(783\) 0 0
\(784\) −5.00000 4.89898i −0.178571 0.174964i
\(785\) 15.5885 9.00000i 0.556376 0.321224i
\(786\) 0 0
\(787\) 27.5772 + 15.9217i 0.983020 + 0.567547i 0.903180 0.429261i \(-0.141226\pi\)
0.0798393 + 0.996808i \(0.474559\pi\)
\(788\) 15.5885 + 9.00000i 0.555316 + 0.320612i
\(789\) 0 0
\(790\) 21.2132 12.2474i 0.754732 0.435745i
\(791\) −14.6969 6.00000i −0.522563 0.213335i
\(792\) 0 0
\(793\) −30.0000 −1.06533
\(794\) −3.67423 6.36396i −0.130394 0.225849i
\(795\) 0 0
\(796\) −8.48528 4.89898i −0.300753 0.173640i
\(797\) 3.67423 6.36396i 0.130148 0.225423i −0.793585 0.608459i \(-0.791788\pi\)
0.923734 + 0.383036i \(0.125121\pi\)
\(798\) 0 0
\(799\) −12.0000 20.7846i −0.424529 0.735307i
\(800\) 1.00000i 0.0353553i
\(801\) 0 0
\(802\) −30.0000 −1.05934
\(803\) 0 0
\(804\) 0 0
\(805\) −30.7279 + 23.8284i −1.08302 + 0.839842i
\(806\) 0 0
\(807\) 0 0
\(808\) −6.36396 + 3.67423i −0.223883 + 0.129259i
\(809\) 6.00000i 0.210949i −0.994422 0.105474i \(-0.966364\pi\)
0.994422 0.105474i \(-0.0336361\pi\)
\(810\) 0 0
\(811\) 36.7423i 1.29020i −0.764099 0.645099i \(-0.776816\pi\)
0.764099 0.645099i \(-0.223184\pi\)
\(812\) 2.15232 + 15.7279i 0.0755315 + 0.551942i
\(813\) 0 0
\(814\) 0 0
\(815\) −19.5959 + 33.9411i −0.686415 + 1.18891i
\(816\) 0 0
\(817\) 8.48528 4.89898i 0.296862 0.171394i
\(818\) 34.2929 1.19902
\(819\) 0 0
\(820\) −12.0000 −0.419058
\(821\) −25.9808 + 15.0000i −0.906735 + 0.523504i −0.879379 0.476122i \(-0.842042\pi\)
−0.0273557 + 0.999626i \(0.508709\pi\)
\(822\) 0 0
\(823\) −7.00000 + 12.1244i −0.244005 + 0.422628i −0.961851 0.273573i \(-0.911795\pi\)
0.717847 + 0.696201i \(0.245128\pi\)
\(824\) −4.89898 + 8.48528i −0.170664 + 0.295599i
\(825\) 0 0
\(826\) −4.39340 32.1045i −0.152866 1.11706i
\(827\) 12.0000i 0.417281i −0.977992 0.208640i \(-0.933096\pi\)
0.977992 0.208640i \(-0.0669038\pi\)
\(828\) 0 0
\(829\) 26.9444i 0.935817i 0.883777 + 0.467909i \(0.154992\pi\)
−0.883777 + 0.467909i \(0.845008\pi\)
\(830\) −5.19615 + 3.00000i −0.180361 + 0.104132i
\(831\) 0 0
\(832\) −2.12132 1.22474i −0.0735436 0.0424604i
\(833\) 33.0321 9.21320i 1.14449 0.319219i
\(834\) 0 0
\(835\) 6.00000 + 10.3923i 0.207639 + 0.359641i
\(836\) 0 0
\(837\) 0 0
\(838\) 12.2474i 0.423081i
\(839\) 12.2474 + 21.2132i 0.422829 + 0.732361i 0.996215 0.0869242i \(-0.0277038\pi\)
−0.573386 + 0.819285i \(0.694370\pi\)
\(840\) 0 0
\(841\) 3.50000 6.06218i 0.120690 0.209041i
\(842\) −1.73205 1.00000i −0.0596904 0.0344623i
\(843\) 0 0
\(844\) −4.00000 6.92820i −0.137686 0.238479i
\(845\) −17.1464 −0.589855
\(846\) 0 0
\(847\) −11.0000 + 26.9444i −0.377964 + 0.925820i
\(848\) 5.19615 3.00000i 0.178437 0.103020i
\(849\) 0 0
\(850\) −4.24264 2.44949i −0.145521 0.0840168i
\(851\) 10.3923 + 6.00000i 0.356244 + 0.205677i
\(852\) 0 0
\(853\) −2.12132 + 1.22474i −0.0726326 + 0.0419345i −0.535876 0.844296i \(-0.680019\pi\)
0.463244 + 0.886231i \(0.346685\pi\)
\(854\) −12.2474 + 30.0000i −0.419099 + 1.02658i
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −2.44949 4.24264i −0.0836730 0.144926i 0.821152 0.570710i \(-0.193332\pi\)
−0.904825 + 0.425784i \(0.859998\pi\)
\(858\) 0 0
\(859\) −23.3345 13.4722i −0.796164 0.459665i 0.0459643 0.998943i \(-0.485364\pi\)
−0.842128 + 0.539278i \(0.818697\pi\)
\(860\) −4.89898 + 8.48528i −0.167054 + 0.289346i
\(861\) 0 0
\(862\) 15.0000 + 25.9808i 0.510902 + 0.884908i
\(863\) 24.0000i 0.816970i −0.912765 0.408485i \(-0.866057\pi\)
0.912765 0.408485i \(-0.133943\pi\)
\(864\) 0 0
\(865\) 54.0000 1.83606
\(866\) −7.34847 12.7279i −0.249711 0.432512i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −16.9706 + 9.79796i −0.575026 + 0.331991i
\(872\) 10.0000i 0.338643i
\(873\) 0 0
\(874\) 14.6969i 0.497131i
\(875\) 25.6836 3.51472i 0.868264 0.118819i
\(876\) 0 0
\(877\) 11.0000 19.0526i 0.371444 0.643359i −0.618344 0.785907i \(-0.712196\pi\)
0.989788 + 0.142548i \(0.0455296\pi\)
\(878\) 7.34847 12.7279i 0.247999 0.429547i
\(879\) 0 0
\(880\) 0 0
\(881\) −29.3939 −0.990305 −0.495152 0.868806i \(-0.664888\pi\)
−0.495152 + 0.868806i \(0.664888\pi\)
\(882\) 0 0
\(883\) −56.0000 −1.88455 −0.942275 0.334840i \(-0.891318\pi\)
−0.942275 + 0.334840i \(0.891318\pi\)
\(884\) 10.3923 6.00000i 0.349531 0.201802i
\(885\) 0 0
\(886\) 18.0000 31.1769i 0.604722 1.04741i
\(887\) −2.44949 + 4.24264i −0.0822458 + 0.142454i −0.904214 0.427079i \(-0.859543\pi\)
0.821968 + 0.569533i \(0.192876\pi\)
\(888\) 0 0
\(889\) 20.9706 2.86976i 0.703330 0.0962485i
\(890\) 0 0
\(891\) 0 0
\(892\) 14.6969i 0.492090i
\(893\) 10.3923 6.00000i 0.347765 0.200782i
\(894\) 0 0
\(895\) 50.9117 + 29.3939i 1.70179 + 0.982529i
\(896\) −2.09077 + 1.62132i −0.0698477 + 0.0541645i
\(897\) 0 0
\(898\) −18.0000 31.1769i −0.600668 1.04039i
\(899\) 0 0
\(900\) 0 0
\(901\) 29.3939i 0.979252i
\(902\) 0 0
\(903\) 0 0
\(904\) −3.00000 + 5.19615i −0.0997785 + 0.172821i
\(905\) 25.9808 + 15.0000i 0.863630 + 0.498617i
\(906\) 0 0
\(907\) −14.0000 24.2487i −0.464862 0.805165i 0.534333 0.845274i \(-0.320563\pi\)
−0.999195 + 0.0401089i \(0.987230\pi\)
\(908\) 7.34847 0.243868
\(909\) 0 0
\(910\) 6.00000 14.6969i 0.198898 0.487199i
\(911\) 25.9808 15.0000i 0.860781 0.496972i −0.00349271 0.999994i \(-0.501112\pi\)
0.864274 + 0.503022i \(0.167778\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −24.2487 14.0000i −0.802076 0.463079i
\(915\) 0 0
\(916\) 19.0919 11.0227i 0.630814 0.364200i
\(917\) −7.34847 + 18.0000i −0.242668 + 0.594412i
\(918\) 0 0
\(919\) 10.0000 0.329870 0.164935 0.986304i \(-0.447259\pi\)
0.164935 + 0.986304i \(0.447259\pi\)
\(920\) 7.34847 + 12.7279i 0.242272 + 0.419627i
\(921\) 0 0
\(922\) −27.5772 15.9217i −0.908206 0.524353i
\(923\) 0 0
\(924\) 0 0
\(925\) 1.00000 + 1.73205i 0.0328798 + 0.0569495i
\(926\) 14.0000i 0.460069i
\(927\) 0 0
\(928\) 6.00000 0.196960
\(929\) 12.2474 + 21.2132i 0.401826 + 0.695983i 0.993946 0.109867i \(-0.0350424\pi\)
−0.592121 + 0.805849i \(0.701709\pi\)
\(930\) 0 0
\(931\) 4.60660 + 16.5160i 0.150975 + 0.541291i
\(932\) −20.7846 12.0000i −0.680823 0.393073i
\(933\) 0 0
\(934\) −6.36396 + 3.67423i −0.208235 + 0.120225i
\(935\) 0 0
\(936\) 0 0
\(937\) 19.5959i 0.640171i −0.947389 0.320085i \(-0.896288\pi\)
0.947389 0.320085i \(-0.103712\pi\)
\(938\) 2.86976 + 20.9706i 0.0937008 + 0.684713i
\(939\) 0 0
\(940\) −6.00000 + 10.3923i −0.195698 + 0.338960i
\(941\) −15.9217 + 27.5772i −0.519032 + 0.898990i 0.480723 + 0.876872i \(0.340374\pi\)
−0.999755 + 0.0221175i \(0.992959\pi\)
\(942\) 0 0
\(943\) −25.4558 + 14.6969i −0.828956 + 0.478598i
\(944\) −12.2474 −0.398621
\(945\) 0 0
\(946\) 0 0
\(947\) −10.3923 + 6.00000i −0.337705 + 0.194974i −0.659256 0.751918i \(-0.729129\pi\)
0.321552 + 0.946892i \(0.395796\pi\)
\(948\) 0 0
\(949\) −12.0000 + 20.7846i −0.389536 + 0.674697i
\(950\) 1.22474 2.12132i 0.0397360 0.0688247i
\(951\) 0 0
\(952\) −1.75736 12.8418i −0.0569563 0.416205i
\(953\) 36.0000i 1.16615i 0.812417 + 0.583077i \(0.198151\pi\)
−0.812417 + 0.583077i \(0.801849\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 5.19615 3.00000i 0.168056 0.0970269i
\(957\) 0 0
\(958\) −21.2132 12.2474i −0.685367 0.395697i
\(959\) −25.0892 + 19.4558i −0.810174 + 0.628262i
\(960\) 0 0
\(961\) −15.5000 26.8468i −0.500000 0.866025i
\(962\) −4.89898 −0.157949
\(963\) 0 0
\(964\) 24.4949i 0.788928i
\(965\) 4.89898 + 8.48528i 0.157704 + 0.273151i
\(966\) 0 0
\(967\) −4.00000 + 6.92820i −0.128631 + 0.222796i −0.923147 0.384448i \(-0.874392\pi\)
0.794515 + 0.607244i \(0.207725\pi\)
\(968\) 9.52628 + 5.50000i 0.306186 + 0.176777i
\(969\) 0 0
\(970\) −6.00000 10.3923i −0.192648 0.333677i
\(971\) −41.6413 −1.33633 −0.668167 0.744011i \(-0.732921\pi\)
−0.668167 + 0.744011i \(0.732921\pi\)
\(972\) 0 0
\(973\) −6.00000 2.44949i −0.192351 0.0785270i
\(974\) −27.7128 + 16.0000i −0.887976 + 0.512673i
\(975\) 0 0
\(976\) 10.6066 + 6.12372i 0.339509 + 0.196016i
\(977\) 10.3923 + 6.00000i 0.332479 + 0.191957i 0.656941 0.753942i \(-0.271850\pi\)
−0.324462 + 0.945899i \(0.605183\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −12.2474 12.0000i −0.391230 0.383326i
\(981\) 0 0
\(982\) 0 0
\(983\) 17.1464 + 29.6985i 0.546886 + 0.947235i 0.998486 + 0.0550138i \(0.0175203\pi\)
−0.451599 + 0.892221i \(0.649146\pi\)
\(984\) 0 0
\(985\) 38.1838 + 22.0454i 1.21664 + 0.702425i
\(986\) −14.6969 + 25.4558i −0.468046 + 0.810679i
\(987\) 0 0
\(988\) 3.00000 + 5.19615i 0.0954427 + 0.165312i
\(989\) 24.0000i 0.763156i
\(990\) 0 0
\(991\) −38.0000 −1.20711 −0.603555 0.797321i \(-0.706250\pi\)
−0.603555 + 0.797321i \(0.706250\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −20.7846 12.0000i −0.658916 0.380426i
\(996\) 0 0
\(997\) −6.36396 + 3.67423i −0.201549 + 0.116364i −0.597378 0.801960i \(-0.703791\pi\)
0.395829 + 0.918324i \(0.370457\pi\)
\(998\) 20.0000i 0.633089i
\(999\) 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 1134.2.m.g.377.4 8
3.2 odd 2 inner 1134.2.m.g.377.1 8
7.6 odd 2 inner 1134.2.m.g.377.3 8
9.2 odd 6 inner 1134.2.m.g.755.3 8
9.4 even 3 42.2.d.a.41.4 yes 4
9.5 odd 6 42.2.d.a.41.1 4
9.7 even 3 inner 1134.2.m.g.755.2 8
21.20 even 2 inner 1134.2.m.g.377.2 8
36.23 even 6 336.2.k.b.209.4 4
36.31 odd 6 336.2.k.b.209.2 4
45.4 even 6 1050.2.b.b.251.1 4
45.13 odd 12 1050.2.d.e.1049.4 4
45.14 odd 6 1050.2.b.b.251.4 4
45.22 odd 12 1050.2.d.b.1049.1 4
45.23 even 12 1050.2.d.b.1049.3 4
45.32 even 12 1050.2.d.e.1049.2 4
63.4 even 3 294.2.f.b.215.1 8
63.5 even 6 294.2.f.b.227.1 8
63.13 odd 6 42.2.d.a.41.3 yes 4
63.20 even 6 inner 1134.2.m.g.755.4 8
63.23 odd 6 294.2.f.b.227.2 8
63.31 odd 6 294.2.f.b.215.2 8
63.32 odd 6 294.2.f.b.215.3 8
63.34 odd 6 inner 1134.2.m.g.755.1 8
63.40 odd 6 294.2.f.b.227.3 8
63.41 even 6 42.2.d.a.41.2 yes 4
63.58 even 3 294.2.f.b.227.4 8
63.59 even 6 294.2.f.b.215.4 8
72.5 odd 6 1344.2.k.c.1217.4 4
72.13 even 6 1344.2.k.c.1217.2 4
72.59 even 6 1344.2.k.d.1217.1 4
72.67 odd 6 1344.2.k.d.1217.3 4
252.139 even 6 336.2.k.b.209.3 4
252.167 odd 6 336.2.k.b.209.1 4
315.13 even 12 1050.2.d.e.1049.1 4
315.104 even 6 1050.2.b.b.251.3 4
315.139 odd 6 1050.2.b.b.251.2 4
315.167 odd 12 1050.2.d.e.1049.3 4
315.202 even 12 1050.2.d.b.1049.4 4
315.293 odd 12 1050.2.d.b.1049.2 4
504.13 odd 6 1344.2.k.c.1217.3 4
504.139 even 6 1344.2.k.d.1217.2 4
504.293 even 6 1344.2.k.c.1217.1 4
504.419 odd 6 1344.2.k.d.1217.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.d.a.41.1 4 9.5 odd 6
42.2.d.a.41.2 yes 4 63.41 even 6
42.2.d.a.41.3 yes 4 63.13 odd 6
42.2.d.a.41.4 yes 4 9.4 even 3
294.2.f.b.215.1 8 63.4 even 3
294.2.f.b.215.2 8 63.31 odd 6
294.2.f.b.215.3 8 63.32 odd 6
294.2.f.b.215.4 8 63.59 even 6
294.2.f.b.227.1 8 63.5 even 6
294.2.f.b.227.2 8 63.23 odd 6
294.2.f.b.227.3 8 63.40 odd 6
294.2.f.b.227.4 8 63.58 even 3
336.2.k.b.209.1 4 252.167 odd 6
336.2.k.b.209.2 4 36.31 odd 6
336.2.k.b.209.3 4 252.139 even 6
336.2.k.b.209.4 4 36.23 even 6
1050.2.b.b.251.1 4 45.4 even 6
1050.2.b.b.251.2 4 315.139 odd 6
1050.2.b.b.251.3 4 315.104 even 6
1050.2.b.b.251.4 4 45.14 odd 6
1050.2.d.b.1049.1 4 45.22 odd 12
1050.2.d.b.1049.2 4 315.293 odd 12
1050.2.d.b.1049.3 4 45.23 even 12
1050.2.d.b.1049.4 4 315.202 even 12
1050.2.d.e.1049.1 4 315.13 even 12
1050.2.d.e.1049.2 4 45.32 even 12
1050.2.d.e.1049.3 4 315.167 odd 12
1050.2.d.e.1049.4 4 45.13 odd 12
1134.2.m.g.377.1 8 3.2 odd 2 inner
1134.2.m.g.377.2 8 21.20 even 2 inner
1134.2.m.g.377.3 8 7.6 odd 2 inner
1134.2.m.g.377.4 8 1.1 even 1 trivial
1134.2.m.g.755.1 8 63.34 odd 6 inner
1134.2.m.g.755.2 8 9.7 even 3 inner
1134.2.m.g.755.3 8 9.2 odd 6 inner
1134.2.m.g.755.4 8 63.20 even 6 inner
1344.2.k.c.1217.1 4 504.293 even 6
1344.2.k.c.1217.2 4 72.13 even 6
1344.2.k.c.1217.3 4 504.13 odd 6
1344.2.k.c.1217.4 4 72.5 odd 6
1344.2.k.d.1217.1 4 72.59 even 6
1344.2.k.d.1217.2 4 504.139 even 6
1344.2.k.d.1217.3 4 72.67 odd 6
1344.2.k.d.1217.4 4 504.419 odd 6