Properties

Label 1053.2.e.b.352.1
Level $1053$
Weight $2$
Character 1053.352
Analytic conductor $8.408$
Analytic rank $0$
Dimension $2$
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] = [1053,2,Mod(352,1053)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1053, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1053.352");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.e (of order \(3\), 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: \(8.40824733284\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 352.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1053.352
Dual form 1053.2.e.b.703.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(2.00000 + 3.46410i) q^{7} -3.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(2.00000 + 3.46410i) q^{7} -3.00000 q^{8} +2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(2.00000 - 3.46410i) q^{14} +(0.500000 + 0.866025i) q^{16} +2.00000 q^{17} +(1.00000 + 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{26} +4.00000 q^{28} +(5.00000 + 8.66025i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(-1.00000 - 1.73205i) q^{34} -8.00000 q^{35} -2.00000 q^{37} +(3.00000 - 5.19615i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(6.00000 + 10.3923i) q^{43} -4.00000 q^{44} +(-4.50000 + 7.79423i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} +6.00000 q^{53} +8.00000 q^{55} +(-6.00000 - 10.3923i) q^{56} +(5.00000 - 8.66025i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} +4.00000 q^{62} +7.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(4.00000 - 6.92820i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} +2.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(8.00000 - 13.8564i) q^{77} +(-4.00000 - 6.92820i) q^{79} -2.00000 q^{80} +6.00000 q^{82} +(-2.00000 - 3.46410i) q^{83} +(-2.00000 + 3.46410i) q^{85} +(6.00000 - 10.3923i) q^{86} +(6.00000 + 10.3923i) q^{88} -2.00000 q^{89} -4.00000 q^{91} +(-5.00000 - 8.66025i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} + 4 q^{10} - 4 q^{11} - q^{13} + 4 q^{14} + q^{16} + 4 q^{17} + 2 q^{20} - 4 q^{22} + q^{25} + 2 q^{26} + 8 q^{28} + 10 q^{29} - 4 q^{31} - 5 q^{32} - 2 q^{34} - 16 q^{35} - 4 q^{37} + 6 q^{40} - 6 q^{41} + 12 q^{43} - 8 q^{44} - 9 q^{49} + q^{50} + q^{52} + 12 q^{53} + 16 q^{55} - 12 q^{56} + 10 q^{58} - 12 q^{59} + 2 q^{61} + 8 q^{62} + 14 q^{64} - 2 q^{65} + 8 q^{67} + 2 q^{68} + 8 q^{70} + 4 q^{73} + 2 q^{74} + 16 q^{77} - 8 q^{79} - 4 q^{80} + 12 q^{82} - 4 q^{83} - 4 q^{85} + 12 q^{86} + 12 q^{88} - 4 q^{89} - 8 q^{91} - 10 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(730\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −3.00000 −1.06066
\(9\) 0 0
\(10\) 2.00000 0.632456
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) 2.00000 3.46410i 0.534522 0.925820i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 + 1.73205i 0.223607 + 0.387298i
\(21\) 0 0
\(22\) −2.00000 + 3.46410i −0.426401 + 0.738549i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 4.00000 0.755929
\(29\) 5.00000 + 8.66025i 0.928477 + 1.60817i 0.785872 + 0.618389i \(0.212214\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) −8.00000 −1.35225
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 3.00000 5.19615i 0.474342 0.821584i
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 6.00000 + 10.3923i 0.914991 + 1.58481i 0.806914 + 0.590669i \(0.201136\pi\)
0.108078 + 0.994142i \(0.465531\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) −6.00000 10.3923i −0.801784 1.38873i
\(57\) 0 0
\(58\) 5.00000 8.66025i 0.656532 1.13715i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 0 0
\(67\) 4.00000 6.92820i 0.488678 0.846415i −0.511237 0.859440i \(-0.670813\pi\)
0.999915 + 0.0130248i \(0.00414604\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) 4.00000 + 6.92820i 0.478091 + 0.828079i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 0 0
\(76\) 0 0
\(77\) 8.00000 13.8564i 0.911685 1.57908i
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) −2.00000 −0.223607
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −2.00000 3.46410i −0.219529 0.380235i 0.735135 0.677920i \(-0.237119\pi\)
−0.954664 + 0.297686i \(0.903785\pi\)
\(84\) 0 0
\(85\) −2.00000 + 3.46410i −0.216930 + 0.375735i
\(86\) 6.00000 10.3923i 0.646997 1.12063i
\(87\) 0 0
\(88\) 6.00000 + 10.3923i 0.639602 + 1.10782i
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −5.00000 8.66025i −0.507673 0.879316i −0.999961 0.00888289i \(-0.997172\pi\)
0.492287 0.870433i \(-0.336161\pi\)
\(98\) 9.00000 0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) 1.50000 2.59808i 0.147087 0.254762i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −4.00000 6.92820i −0.381385 0.660578i
\(111\) 0 0
\(112\) −2.00000 + 3.46410i −0.188982 + 0.327327i
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 4.00000 + 6.92820i 0.366679 + 0.635107i
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 1.00000 1.73205i 0.0905357 0.156813i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) 0 0
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) −4.00000 + 6.92820i −0.338062 + 0.585540i
\(141\) 0 0
\(142\) 0 0
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) −20.0000 −1.66091
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −2.00000 3.46410i −0.162758 0.281905i 0.773099 0.634285i \(-0.218706\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −16.0000 −1.28932
\(155\) −4.00000 6.92820i −0.321288 0.556487i
\(156\) 0 0
\(157\) 9.00000 15.5885i 0.718278 1.24409i −0.243403 0.969925i \(-0.578264\pi\)
0.961681 0.274169i \(-0.0884028\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 0 0
\(160\) −5.00000 8.66025i −0.395285 0.684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 0 0
\(166\) −2.00000 + 3.46410i −0.155230 + 0.268866i
\(167\) 4.00000 6.92820i 0.309529 0.536120i −0.668730 0.743505i \(-0.733162\pi\)
0.978259 + 0.207385i \(0.0664952\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) 12.0000 0.914991
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) 2.00000 3.46410i 0.150756 0.261116i
\(177\) 0 0
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 2.00000 + 3.46410i 0.148250 + 0.256776i
\(183\) 0 0
\(184\) 0 0
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) 0 0
\(187\) −4.00000 6.92820i −0.292509 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) 0 0
\(193\) −9.00000 + 15.5885i −0.647834 + 1.12208i 0.335805 + 0.941932i \(0.390992\pi\)
−0.983639 + 0.180150i \(0.942342\pi\)
\(194\) −5.00000 + 8.66025i −0.358979 + 0.621770i
\(195\) 0 0
\(196\) 4.50000 + 7.79423i 0.321429 + 0.556731i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) 0 0
\(202\) 9.00000 15.5885i 0.633238 1.09680i
\(203\) −20.0000 + 34.6410i −1.40372 + 2.43132i
\(204\) 0 0
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) 10.0000 17.3205i 0.688428 1.19239i −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −24.0000 −1.63679
\(216\) 0 0
\(217\) −16.0000 −1.08615
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) 0 0
\(220\) 4.00000 6.92820i 0.269680 0.467099i
\(221\) −1.00000 + 1.73205i −0.0672673 + 0.116510i
\(222\) 0 0
\(223\) −2.00000 3.46410i −0.133930 0.231973i 0.791258 0.611482i \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) −20.0000 −1.33631
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 10.0000 + 17.3205i 0.663723 + 1.14960i 0.979630 + 0.200812i \(0.0643581\pi\)
−0.315906 + 0.948790i \(0.602309\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −15.0000 25.9808i −0.984798 1.70572i
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000 + 10.3923i 0.390567 + 0.676481i
\(237\) 0 0
\(238\) 4.00000 6.92820i 0.259281 0.449089i
\(239\) 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 0 0
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) 5.00000 0.321412
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −9.00000 15.5885i −0.574989 0.995910i
\(246\) 0 0
\(247\) 0 0
\(248\) 6.00000 10.3923i 0.381000 0.659912i
\(249\) 0 0
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8.00000 + 13.8564i 0.501965 + 0.869428i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −13.0000 + 22.5167i −0.810918 + 1.40455i 0.101305 + 0.994855i \(0.467698\pi\)
−0.912222 + 0.409695i \(0.865635\pi\)
\(258\) 0 0
\(259\) −4.00000 6.92820i −0.248548 0.430498i
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) 4.00000 0.247121
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) −6.00000 + 10.3923i −0.368577 + 0.638394i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) 22.0000 1.34136 0.670682 0.741745i \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(270\) 0 0
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) −3.00000 + 5.19615i −0.181237 + 0.313911i
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 12.0000 0.719712
\(279\) 0 0
\(280\) 24.0000 1.43427
\(281\) 5.00000 + 8.66025i 0.298275 + 0.516627i 0.975741 0.218926i \(-0.0702554\pi\)
−0.677466 + 0.735554i \(0.736922\pi\)
\(282\) 0 0
\(283\) −6.00000 + 10.3923i −0.356663 + 0.617758i −0.987401 0.158237i \(-0.949419\pi\)
0.630738 + 0.775996i \(0.282752\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −2.00000 3.46410i −0.118262 0.204837i
\(287\) −24.0000 −1.41668
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 10.0000 + 17.3205i 0.587220 + 1.01710i
\(291\) 0 0
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) 3.00000 5.19615i 0.175262 0.303562i −0.764990 0.644042i \(-0.777256\pi\)
0.940252 + 0.340480i \(0.110589\pi\)
\(294\) 0 0
\(295\) −12.0000 20.7846i −0.698667 1.21013i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −24.0000 + 41.5692i −1.38334 + 2.39601i
\(302\) −2.00000 + 3.46410i −0.115087 + 0.199337i
\(303\) 0 0
\(304\) 0 0
\(305\) −4.00000 −0.229039
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) −8.00000 13.8564i −0.455842 0.789542i
\(309\) 0 0
\(310\) −4.00000 + 6.92820i −0.227185 + 0.393496i
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) −18.0000 −1.01580
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −13.0000 22.5167i −0.730153 1.26466i −0.956818 0.290689i \(-0.906116\pi\)
0.226665 0.973973i \(-0.427218\pi\)
\(318\) 0 0
\(319\) 20.0000 34.6410i 1.11979 1.93952i
\(320\) −7.00000 + 12.1244i −0.391312 + 0.677772i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) 0 0
\(328\) 9.00000 15.5885i 0.496942 0.860729i
\(329\) 0 0
\(330\) 0 0
\(331\) 8.00000 + 13.8564i 0.439720 + 0.761617i 0.997668 0.0682590i \(-0.0217444\pi\)
−0.557948 + 0.829876i \(0.688411\pi\)
\(332\) −4.00000 −0.219529
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) 8.00000 + 13.8564i 0.437087 + 0.757056i
\(336\) 0 0
\(337\) −9.00000 + 15.5885i −0.490261 + 0.849157i −0.999937 0.0112091i \(-0.996432\pi\)
0.509676 + 0.860366i \(0.329765\pi\)
\(338\) −0.500000 + 0.866025i −0.0271964 + 0.0471056i
\(339\) 0 0
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) −18.0000 31.1769i −0.970495 1.68095i
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) 13.0000 + 22.5167i 0.695874 + 1.20529i 0.969885 + 0.243563i \(0.0783162\pi\)
−0.274011 + 0.961727i \(0.588351\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) 1.00000 + 1.73205i 0.0532246 + 0.0921878i 0.891410 0.453197i \(-0.149717\pi\)
−0.838186 + 0.545385i \(0.816383\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.00000 + 1.73205i −0.0529999 + 0.0917985i
\(357\) 0 0
\(358\) −2.00000 3.46410i −0.105703 0.183083i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 0 0
\(364\) −2.00000 + 3.46410i −0.104828 + 0.181568i
\(365\) −2.00000 + 3.46410i −0.104685 + 0.181319i
\(366\) 0 0
\(367\) −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 0 0
\(376\) 0 0
\(377\) −10.0000 −0.515026
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.00000 + 6.92820i −0.204658 + 0.354478i
\(383\) 8.00000 13.8564i 0.408781 0.708029i −0.585973 0.810331i \(-0.699287\pi\)
0.994753 + 0.102302i \(0.0326207\pi\)
\(384\) 0 0
\(385\) 16.0000 + 27.7128i 0.815436 + 1.41238i
\(386\) 18.0000 0.916176
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) −11.0000 19.0526i −0.557722 0.966003i −0.997686 0.0679877i \(-0.978342\pi\)
0.439964 0.898015i \(-0.354991\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 13.5000 23.3827i 0.681853 1.18100i
\(393\) 0 0
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) 16.0000 0.805047
\(396\) 0 0
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) −4.00000 6.92820i −0.200502 0.347279i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −11.0000 + 19.0526i −0.549314 + 0.951439i 0.449008 + 0.893528i \(0.351777\pi\)
−0.998322 + 0.0579116i \(0.981556\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 18.0000 0.895533
\(405\) 0 0
\(406\) 40.0000 1.98517
\(407\) 4.00000 + 6.92820i 0.198273 + 0.343418i
\(408\) 0 0
\(409\) −17.0000 + 29.4449i −0.840596 + 1.45595i 0.0487958 + 0.998809i \(0.484462\pi\)
−0.889392 + 0.457146i \(0.848872\pi\)
\(410\) −6.00000 + 10.3923i −0.296319 + 0.513239i
\(411\) 0 0
\(412\) 0 0
\(413\) −48.0000 −2.36193
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) −2.50000 4.33013i −0.122573 0.212302i
\(417\) 0 0
\(418\) 0 0
\(419\) −2.00000 + 3.46410i −0.0977064 + 0.169232i −0.910735 0.412991i \(-0.864484\pi\)
0.813029 + 0.582224i \(0.197817\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) −18.0000 −0.874157
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) −4.00000 + 6.92820i −0.193574 + 0.335279i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 0 0
\(430\) 12.0000 + 20.7846i 0.578691 + 1.00232i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 8.00000 + 13.8564i 0.384012 + 0.665129i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) 0 0
\(439\) −16.0000 27.7128i −0.763638 1.32266i −0.940963 0.338508i \(-0.890078\pi\)
0.177325 0.984152i \(-0.443256\pi\)
\(440\) −24.0000 −1.14416
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) 2.00000 + 3.46410i 0.0950229 + 0.164584i 0.909618 0.415445i \(-0.136374\pi\)
−0.814595 + 0.580030i \(0.803041\pi\)
\(444\) 0 0
\(445\) 2.00000 3.46410i 0.0948091 0.164214i
\(446\) −2.00000 + 3.46410i −0.0947027 + 0.164030i
\(447\) 0 0
\(448\) 14.0000 + 24.2487i 0.661438 + 1.14564i
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) 0 0
\(454\) 10.0000 17.3205i 0.469323 0.812892i
\(455\) 4.00000 6.92820i 0.187523 0.324799i
\(456\) 0 0
\(457\) −1.00000 1.73205i −0.0467780 0.0810219i 0.841688 0.539964i \(-0.181562\pi\)
−0.888466 + 0.458942i \(0.848229\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) 19.0000 + 32.9090i 0.884918 + 1.53272i 0.845807 + 0.533488i \(0.179119\pi\)
0.0391109 + 0.999235i \(0.487547\pi\)
\(462\) 0 0
\(463\) −2.00000 + 3.46410i −0.0929479 + 0.160990i −0.908750 0.417340i \(-0.862962\pi\)
0.815802 + 0.578331i \(0.196296\pi\)
\(464\) −5.00000 + 8.66025i −0.232119 + 0.402042i
\(465\) 0 0
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 32.0000 1.47762
\(470\) 0 0
\(471\) 0 0
\(472\) 18.0000 31.1769i 0.828517 1.43503i
\(473\) 24.0000 41.5692i 1.10352 1.91135i
\(474\) 0 0
\(475\) 0 0
\(476\) 8.00000 0.366679
\(477\) 0 0
\(478\) −24.0000 −1.09773
\(479\) 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i \(0.0180558\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(480\) 0 0
\(481\) 1.00000 1.73205i 0.0455961 0.0789747i
\(482\) −5.00000 + 8.66025i −0.227744 + 0.394464i
\(483\) 0 0
\(484\) 2.50000 + 4.33013i 0.113636 + 0.196824i
\(485\) 20.0000 0.908153
\(486\) 0 0
\(487\) 12.0000 0.543772 0.271886 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) −3.00000 5.19615i −0.135804 0.235219i
\(489\) 0 0
\(490\) −9.00000 + 15.5885i −0.406579 + 0.704215i
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 0 0
\(493\) 10.0000 + 17.3205i 0.450377 + 0.780076i
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 12.0000 20.7846i 0.537194 0.930447i −0.461860 0.886953i \(-0.652818\pi\)
0.999054 0.0434940i \(-0.0138489\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) −8.00000 −0.356702 −0.178351 0.983967i \(-0.557076\pi\)
−0.178351 + 0.983967i \(0.557076\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) −8.00000 + 13.8564i −0.354943 + 0.614779i
\(509\) −5.00000 + 8.66025i −0.221621 + 0.383859i −0.955300 0.295637i \(-0.904468\pi\)
0.733679 + 0.679496i \(0.237801\pi\)
\(510\) 0 0
\(511\) 4.00000 + 6.92820i 0.176950 + 0.306486i
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) 26.0000 1.14681
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −4.00000 + 6.92820i −0.175750 + 0.304408i
\(519\) 0 0
\(520\) 3.00000 + 5.19615i 0.131559 + 0.227866i
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 44.0000 1.92399 0.961993 0.273075i \(-0.0880406\pi\)
0.961993 + 0.273075i \(0.0880406\pi\)
\(524\) 2.00000 + 3.46410i 0.0873704 + 0.151330i
\(525\) 0 0
\(526\) −12.0000 + 20.7846i −0.523225 + 0.906252i
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 0 0
\(533\) −3.00000 5.19615i −0.129944 0.225070i
\(534\) 0 0
\(535\) −12.0000 + 20.7846i −0.518805 + 0.898597i
\(536\) −12.0000 + 20.7846i −0.518321 + 0.897758i
\(537\) 0 0
\(538\) −11.0000 19.0526i −0.474244 0.821414i
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 6.00000 + 10.3923i 0.257722 + 0.446388i
\(543\) 0 0
\(544\) −5.00000 + 8.66025i −0.214373 + 0.371305i
\(545\) 2.00000 3.46410i 0.0856706 0.148386i
\(546\) 0 0
\(547\) −2.00000 3.46410i −0.0855138 0.148114i 0.820096 0.572226i \(-0.193920\pi\)
−0.905610 + 0.424111i \(0.860587\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) −4.00000 −0.170561
\(551\) 0 0
\(552\) 0 0
\(553\) 16.0000 27.7128i 0.680389 1.17847i
\(554\) 5.00000 8.66025i 0.212430 0.367939i
\(555\) 0 0
\(556\) 6.00000 + 10.3923i 0.254457 + 0.440732i
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) −4.00000 6.92820i −0.169031 0.292770i
\(561\) 0 0
\(562\) 5.00000 8.66025i 0.210912 0.365311i
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 0 0
\(565\) 6.00000 + 10.3923i 0.252422 + 0.437208i
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) 0 0
\(569\) −17.0000 29.4449i −0.712677 1.23439i −0.963849 0.266450i \(-0.914149\pi\)
0.251172 0.967943i \(-0.419184\pi\)
\(570\) 0 0
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 2.00000 3.46410i 0.0836242 0.144841i
\(573\) 0 0
\(574\) 12.0000 + 20.7846i 0.500870 + 0.867533i
\(575\) 0 0
\(576\) 0 0
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 0 0
\(580\) −10.0000 + 17.3205i −0.415227 + 0.719195i
\(581\) 8.00000 13.8564i 0.331896 0.574861i
\(582\) 0 0
\(583\) −12.0000 20.7846i −0.496989 0.860811i
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −14.0000 24.2487i −0.577842 1.00085i −0.995726 0.0923513i \(-0.970562\pi\)
0.417885 0.908500i \(-0.362772\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −12.0000 + 20.7846i −0.494032 + 0.855689i
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) 20.0000 34.6410i 0.817178 1.41539i −0.0905757 0.995890i \(-0.528871\pi\)
0.907754 0.419504i \(-0.137796\pi\)
\(600\) 0 0
\(601\) 19.0000 + 32.9090i 0.775026 + 1.34238i 0.934780 + 0.355228i \(0.115597\pi\)
−0.159754 + 0.987157i \(0.551070\pi\)
\(602\) 48.0000 1.95633
\(603\) 0 0
\(604\) −4.00000 −0.162758
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 2.00000 + 3.46410i 0.0809776 + 0.140257i
\(611\) 0 0
\(612\) 0 0
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 8.00000 + 13.8564i 0.322854 + 0.559199i
\(615\) 0 0
\(616\) −24.0000 + 41.5692i −0.966988 + 1.67487i
\(617\) −11.0000 + 19.0526i −0.442843 + 0.767027i −0.997899 0.0647859i \(-0.979364\pi\)
0.555056 + 0.831813i \(0.312697\pi\)
\(618\) 0 0
\(619\) −12.0000 20.7846i −0.482321 0.835404i 0.517473 0.855699i \(-0.326873\pi\)
−0.999794 + 0.0202954i \(0.993539\pi\)
\(620\) −8.00000 −0.321288
\(621\) 0 0
\(622\) 0 0
\(623\) −4.00000 6.92820i −0.160257 0.277573i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 3.00000 5.19615i 0.119904 0.207680i
\(627\) 0 0
\(628\) −9.00000 15.5885i −0.359139 0.622047i
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 12.0000 + 20.7846i 0.477334 + 0.826767i
\(633\) 0 0
\(634\) −13.0000 + 22.5167i −0.516296 + 0.894251i
\(635\) 16.0000 27.7128i 0.634941 1.09975i
\(636\) 0 0
\(637\) −4.50000 7.79423i −0.178296 0.308819i
\(638\) −40.0000 −1.58362
\(639\) 0 0
\(640\) −6.00000 −0.237171
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 0 0
\(643\) 20.0000 34.6410i 0.788723 1.36611i −0.138027 0.990429i \(-0.544076\pi\)
0.926750 0.375680i \(-0.122591\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) 0 0
\(649\) 48.0000 1.88416
\(650\) 0.500000 + 0.866025i 0.0196116 + 0.0339683i
\(651\) 0 0
\(652\) 4.00000 6.92820i 0.156652 0.271329i
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 0 0
\(655\) −4.00000 6.92820i −0.156293 0.270707i
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) −14.0000 24.2487i −0.545363 0.944596i −0.998584 0.0531977i \(-0.983059\pi\)
0.453221 0.891398i \(-0.350275\pi\)
\(660\) 0 0
\(661\) −15.0000 + 25.9808i −0.583432 + 1.01053i 0.411636 + 0.911348i \(0.364957\pi\)
−0.995069 + 0.0991864i \(0.968376\pi\)
\(662\) 8.00000 13.8564i 0.310929 0.538545i
\(663\) 0 0
\(664\) 6.00000 + 10.3923i 0.232845 + 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −4.00000 6.92820i −0.154765 0.268060i
\(669\) 0 0
\(670\) 8.00000 13.8564i 0.309067 0.535320i
\(671\) 4.00000 6.92820i 0.154418 0.267460i
\(672\) 0 0
\(673\) 7.00000 + 12.1244i 0.269830 + 0.467360i 0.968818 0.247774i \(-0.0796991\pi\)
−0.698988 + 0.715134i \(0.746366\pi\)
\(674\) 18.0000 0.693334
\(675\) 0 0
\(676\) −1.00000 −0.0384615
\(677\) −11.0000 19.0526i −0.422764 0.732249i 0.573444 0.819244i \(-0.305607\pi\)
−0.996209 + 0.0869952i \(0.972274\pi\)
\(678\) 0 0
\(679\) 20.0000 34.6410i 0.767530 1.32940i
\(680\) 6.00000 10.3923i 0.230089 0.398527i
\(681\) 0 0
\(682\) −8.00000 13.8564i −0.306336 0.530589i
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 4.00000 + 6.92820i 0.152721 + 0.264520i
\(687\) 0 0
\(688\) −6.00000 + 10.3923i −0.228748 + 0.396203i
\(689\) −3.00000 + 5.19615i −0.114291 + 0.197958i
\(690\) 0 0
\(691\) 12.0000 + 20.7846i 0.456502 + 0.790684i 0.998773 0.0495194i \(-0.0157690\pi\)
−0.542272 + 0.840203i \(0.682436\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −12.0000 20.7846i −0.455186 0.788405i
\(696\) 0 0
\(697\) −6.00000 + 10.3923i −0.227266 + 0.393637i
\(698\) 13.0000 22.5167i 0.492057 0.852268i
\(699\) 0 0
\(700\) 2.00000 + 3.46410i 0.0755929 + 0.130931i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −14.0000 24.2487i −0.527645 0.913908i
\(705\) 0 0
\(706\) 1.00000 1.73205i 0.0376355 0.0651866i
\(707\) −36.0000 + 62.3538i −1.35392 + 2.34506i
\(708\) 0 0
\(709\) 13.0000 + 22.5167i 0.488225 + 0.845631i 0.999908 0.0135434i \(-0.00431112\pi\)
−0.511683 + 0.859174i \(0.670978\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) −4.00000 + 6.92820i −0.149592 + 0.259100i
\(716\) 2.00000 3.46410i 0.0747435 0.129460i
\(717\) 0 0
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 9.50000 + 16.4545i 0.353553 + 0.612372i
\(723\) 0 0
\(724\) −5.00000 + 8.66025i −0.185824 + 0.321856i
\(725\) −5.00000 + 8.66025i −0.185695 + 0.321634i
\(726\) 0 0
\(727\) −4.00000 6.92820i −0.148352 0.256953i 0.782267 0.622944i \(-0.214063\pi\)
−0.930618 + 0.365991i \(0.880730\pi\)
\(728\) 12.0000 0.444750
\(729\) 0 0
\(730\) 4.00000 0.148047
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 0 0
\(733\) −15.0000 + 25.9808i −0.554038 + 0.959621i 0.443940 + 0.896056i \(0.353580\pi\)
−0.997978 + 0.0635649i \(0.979753\pi\)
\(734\) −8.00000 + 13.8564i −0.295285 + 0.511449i
\(735\) 0 0
\(736\) 0 0
\(737\) −32.0000 −1.17874
\(738\) 0 0
\(739\) 32.0000 1.17714 0.588570 0.808447i \(-0.299691\pi\)
0.588570 + 0.808447i \(0.299691\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) 12.0000 20.7846i 0.440534 0.763027i
\(743\) −24.0000 + 41.5692i −0.880475 + 1.52503i −0.0296605 + 0.999560i \(0.509443\pi\)
−0.850814 + 0.525467i \(0.823891\pi\)
\(744\) 0 0
\(745\) 6.00000 + 10.3923i 0.219823 + 0.380745i
\(746\) −26.0000 −0.951928
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) 24.0000 + 41.5692i 0.876941 + 1.51891i
\(750\) 0 0
\(751\) −4.00000 + 6.92820i −0.145962 + 0.252814i −0.929731 0.368238i \(-0.879961\pi\)
0.783769 + 0.621052i \(0.213294\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 5.00000 + 8.66025i 0.182089 + 0.315388i
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 12.0000 + 20.7846i 0.435860 + 0.754931i
\(759\) 0 0
\(760\) 0 0
\(761\) 5.00000 8.66025i 0.181250 0.313934i −0.761057 0.648686i \(-0.775319\pi\)
0.942306 + 0.334752i \(0.108652\pi\)
\(762\) 0 0
\(763\) −4.00000 6.92820i −0.144810 0.250818i
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) −6.00000 10.3923i −0.216647 0.375244i
\(768\) 0 0
\(769\) 15.0000 25.9808i 0.540914 0.936890i −0.457938 0.888984i \(-0.651412\pi\)
0.998852 0.0479061i \(-0.0152548\pi\)
\(770\) 16.0000 27.7128i 0.576600 0.998700i
\(771\) 0 0
\(772\) 9.00000 + 15.5885i 0.323917 + 0.561041i
\(773\) 10.0000 0.359675 0.179838 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 15.0000 + 25.9808i 0.538469 + 0.932655i
\(777\) 0 0
\(778\) −11.0000 + 19.0526i −0.394369 + 0.683067i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −9.00000 −0.321429
\(785\) 18.0000 + 31.1769i 0.642448 + 1.11275i
\(786\) 0 0
\(787\) 16.0000 27.7128i 0.570338 0.987855i −0.426193 0.904632i \(-0.640145\pi\)
0.996531 0.0832226i \(-0.0265213\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i
\(789\) 0 0
\(790\) −8.00000 13.8564i −0.284627 0.492989i
\(791\) 24.0000 0.853342
\(792\) 0 0
\(793\) −2.00000 −0.0710221
\(794\) −19.0000 32.9090i −0.674285 1.16790i
\(795\) 0 0
\(796\) 4.00000 6.92820i 0.141776 0.245564i
\(797\) −23.0000 + 39.8372i −0.814702 + 1.41110i 0.0948400 + 0.995493i \(0.469766\pi\)
−0.909542 + 0.415612i \(0.863567\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −5.00000 −0.176777
\(801\) 0 0
\(802\) 22.0000 0.776847
\(803\) −4.00000 6.92820i −0.141157 0.244491i
\(804\) 0 0
\(805\) 0 0
\(806\) −2.00000 + 3.46410i −0.0704470 + 0.122018i
\(807\) 0 0
\(808\) −27.0000 46.7654i −0.949857 1.64520i
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0
\(811\) 8.00000 0.280918 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(812\) 20.0000 + 34.6410i 0.701862 + 1.21566i
\(813\) 0 0
\(814\) 4.00000 6.92820i 0.140200 0.242833i
\(815\) −8.00000 + 13.8564i −0.280228 + 0.485369i
\(816\) 0 0
\(817\) 0 0
\(818\) 34.0000 1.18878
\(819\) 0 0
\(820\) −12.0000 −0.419058
\(821\) 11.0000 + 19.0526i 0.383903 + 0.664939i 0.991616 0.129217i \(-0.0412465\pi\)
−0.607714 + 0.794156i \(0.707913\pi\)
\(822\) 0 0
\(823\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 24.0000 + 41.5692i 0.835067 + 1.44638i
\(827\) 4.00000 0.139094 0.0695468 0.997579i \(-0.477845\pi\)
0.0695468 + 0.997579i \(0.477845\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −4.00000 6.92820i −0.138842 0.240481i
\(831\) 0 0
\(832\) −3.50000 + 6.06218i −0.121341 + 0.210168i
\(833\) −9.00000 + 15.5885i −0.311832 + 0.540108i
\(834\) 0 0
\(835\) 8.00000 + 13.8564i 0.276851 + 0.479521i
\(836\) 0 0
\(837\) 0 0
\(838\) 4.00000 0.138178
\(839\) −24.0000 41.5692i −0.828572 1.43513i −0.899158 0.437623i \(-0.855820\pi\)
0.0705865 0.997506i \(-0.477513\pi\)
\(840\) 0 0
\(841\) −35.5000 + 61.4878i −1.22414 + 2.12027i
\(842\) 5.00000 8.66025i 0.172311 0.298452i
\(843\) 0 0
\(844\) −10.0000 17.3205i −0.344214 0.596196i
\(845\) 2.00000 0.0688021
\(846\) 0 0
\(847\) −20.0000 −0.687208
\(848\) 3.00000 + 5.19615i 0.103020 + 0.178437i
\(849\) 0 0
\(850\) 1.00000 1.73205i 0.0342997 0.0594089i
\(851\) 0 0
\(852\) 0 0
\(853\) −15.0000 25.9808i −0.513590 0.889564i −0.999876 0.0157644i \(-0.994982\pi\)
0.486286 0.873800i \(-0.338351\pi\)
\(854\) 8.00000 0.273754
\(855\) 0 0
\(856\) −36.0000 −1.23045
\(857\) 23.0000 + 39.8372i 0.785665 + 1.36081i 0.928601 + 0.371080i \(0.121012\pi\)
−0.142936 + 0.989732i \(0.545654\pi\)
\(858\) 0 0
\(859\) 22.0000 38.1051i 0.750630 1.30013i −0.196887 0.980426i \(-0.563083\pi\)
0.947518 0.319704i \(-0.103583\pi\)
\(860\) −12.0000 + 20.7846i −0.409197 + 0.708749i
\(861\) 0 0
\(862\) 0 0
\(863\) 16.0000 0.544646 0.272323 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) 0 0
\(865\) 12.0000 0.408012
\(866\) −17.0000 29.4449i −0.577684 1.00058i
\(867\) 0 0
\(868\) −8.00000 + 13.8564i −0.271538 + 0.470317i
\(869\) −16.0000 + 27.7128i −0.542763 + 0.940093i
\(870\) 0 0
\(871\) 4.00000 + 6.92820i 0.135535 + 0.234753i
\(872\) 6.00000 0.203186
\(873\) 0 0
\(874\) 0 0
\(875\) −24.0000 41.5692i −0.811348 1.40530i
\(876\) 0 0
\(877\) 5.00000 8.66025i 0.168838 0.292436i −0.769174 0.639040i \(-0.779332\pi\)
0.938012 + 0.346604i \(0.112665\pi\)
\(878\) −16.0000 + 27.7128i −0.539974 + 0.935262i
\(879\) 0 0
\(880\) 4.00000 + 6.92820i 0.134840 + 0.233550i
\(881\) 58.0000 1.95407 0.977035 0.213080i \(-0.0683494\pi\)
0.977035 + 0.213080i \(0.0683494\pi\)
\(882\) 0 0
\(883\) −44.0000 −1.48072 −0.740359 0.672212i \(-0.765344\pi\)
−0.740359 + 0.672212i \(0.765344\pi\)
\(884\) 1.00000 + 1.73205i 0.0336336 + 0.0582552i
\(885\) 0 0
\(886\) 2.00000 3.46410i 0.0671913 0.116379i
\(887\) 24.0000 41.5692i 0.805841 1.39576i −0.109881 0.993945i \(-0.535047\pi\)
0.915722 0.401813i \(-0.131620\pi\)
\(888\) 0 0
\(889\) −32.0000 55.4256i −1.07325 1.85892i
\(890\) −4.00000 −0.134080
\(891\) 0 0
\(892\) −4.00000 −0.133930
\(893\) 0 0
\(894\) 0 0
\(895\) −4.00000 + 6.92820i −0.133705 + 0.231584i
\(896\) −6.00000 + 10.3923i −0.200446 + 0.347183i
\(897\) 0 0
\(898\) −11.0000 19.0526i −0.367075 0.635792i
\(899\) −40.0000 −1.33407
\(900\) 0 0
\(901\) 12.0000 0.399778
\(902\) −12.0000 20.7846i −0.399556 0.692052i
\(903\) 0 0
\(904\) −9.00000 + 15.5885i −0.299336 + 0.518464i
\(905\) 10.0000 17.3205i 0.332411 0.575753i
\(906\) 0 0
\(907\) −6.00000 10.3923i −0.199227 0.345071i 0.749051 0.662512i \(-0.230510\pi\)
−0.948278 + 0.317441i \(0.897176\pi\)
\(908\) 20.0000 0.663723
\(909\) 0 0
\(910\) −8.00000 −0.265197
\(911\) 20.0000 + 34.6410i 0.662630 + 1.14771i 0.979922 + 0.199380i \(0.0638929\pi\)
−0.317293 + 0.948328i \(0.602774\pi\)
\(912\) 0 0
\(913\) −8.00000 + 13.8564i −0.264761 + 0.458580i
\(914\) −1.00000 + 1.73205i −0.0330771 + 0.0572911i
\(915\) 0 0
\(916\) −5.00000 8.66025i −0.165205 0.286143i
\(917\) −16.0000 −0.528367
\(918\) 0 0
\(919\) −48.0000 −1.58337 −0.791687 0.610927i \(-0.790797\pi\)
−0.791687 + 0.610927i \(0.790797\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 19.0000 32.9090i 0.625732 1.08380i
\(923\) 0 0
\(924\) 0 0
\(925\) −1.00000 1.73205i −0.0328798 0.0569495i
\(926\) 4.00000 0.131448
\(927\) 0 0
\(928\) −50.0000 −1.64133
\(929\) −15.0000 25.9808i −0.492134 0.852401i 0.507825 0.861460i \(-0.330450\pi\)
−0.999959 + 0.00905914i \(0.997116\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −7.00000 + 12.1244i −0.229293 + 0.397146i
\(933\) 0 0
\(934\) −6.00000 10.3923i −0.196326 0.340047i
\(935\) 16.0000 0.523256
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) −16.0000 27.7128i −0.522419 0.904855i
\(939\) 0 0
\(940\) 0 0
\(941\) 7.00000 12.1244i 0.228193 0.395243i −0.729079 0.684429i \(-0.760051\pi\)
0.957273 + 0.289187i \(0.0933848\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −12.0000 −0.390567
\(945\) 0 0
\(946\) −48.0000 −1.56061
\(947\) 30.0000 + 51.9615i 0.974869 + 1.68852i 0.680367 + 0.732872i \(0.261821\pi\)
0.294502 + 0.955651i \(0.404846\pi\)
\(948\) 0 0
\(949\) −1.00000 + 1.73205i −0.0324614 + 0.0562247i
\(950\) 0 0
\(951\) 0 0
\(952\) −12.0000 20.7846i −0.388922 0.673633i
\(953\) −30.0000 −0.971795 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(954\) 0 0
\(955\) 16.0000 0.517748
\(956\) −12.0000 20.7846i −0.388108 0.672222i
\(957\) 0 0
\(958\) 12.0000 20.7846i 0.387702 0.671520i
\(959\) 12.0000 20.7846i 0.387500 0.671170i
\(960\) 0 0
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) −2.00000 −0.0644826
\(963\) 0 0
\(964\) −10.0000 −0.322078
\(965\) −18.0000 31.1769i −0.579441 1.00362i
\(966\) 0 0
\(967\) 26.0000 45.0333i 0.836104 1.44817i −0.0570251 0.998373i \(-0.518161\pi\)
0.893129 0.449801i \(-0.148505\pi\)
\(968\) 7.50000 12.9904i 0.241059 0.417527i
\(969\) 0 0
\(970\) −10.0000 17.3205i −0.321081 0.556128i
\(971\) −60.0000 −1.92549 −0.962746 0.270408i \(-0.912841\pi\)
−0.962746 + 0.270408i \(0.912841\pi\)
\(972\) 0 0
\(973\) −48.0000 −1.53881
\(974\) −6.00000 10.3923i −0.192252 0.332991i
\(975\) 0 0
\(976\) −1.00000 + 1.73205i −0.0320092 + 0.0554416i
\(977\) 21.0000 36.3731i 0.671850 1.16368i −0.305530 0.952183i \(-0.598833\pi\)
0.977379 0.211495i \(-0.0678332\pi\)
\(978\) 0 0
\(979\) 4.00000 + 6.92820i 0.127841 + 0.221426i
\(980\) −18.0000 −0.574989
\(981\) 0 0
\(982\) −12.0000 −0.382935
\(983\) −8.00000 13.8564i −0.255160 0.441951i 0.709779 0.704425i \(-0.248795\pi\)
−0.964939 + 0.262474i \(0.915462\pi\)
\(984\) 0 0
\(985\) −18.0000 + 31.1769i −0.573528 + 0.993379i
\(986\) 10.0000 17.3205i 0.318465 0.551597i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) −10.0000 17.3205i −0.317500 0.549927i
\(993\) 0 0
\(994\) 0 0
\(995\) −8.00000 + 13.8564i −0.253617 + 0.439278i
\(996\) 0 0
\(997\) 13.0000 + 22.5167i 0.411714 + 0.713110i 0.995077 0.0991016i \(-0.0315969\pi\)
−0.583363 + 0.812211i \(0.698264\pi\)
\(998\) −24.0000 −0.759707
\(999\) 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 1053.2.e.b.352.1 2
3.2 odd 2 1053.2.e.d.352.1 2
9.2 odd 6 1053.2.e.d.703.1 2
9.4 even 3 39.2.a.a.1.1 1
9.5 odd 6 117.2.a.a.1.1 1
9.7 even 3 inner 1053.2.e.b.703.1 2
36.23 even 6 1872.2.a.h.1.1 1
36.31 odd 6 624.2.a.i.1.1 1
45.4 even 6 975.2.a.f.1.1 1
45.13 odd 12 975.2.c.f.274.1 2
45.14 odd 6 2925.2.a.p.1.1 1
45.22 odd 12 975.2.c.f.274.2 2
45.23 even 12 2925.2.c.e.2224.2 2
45.32 even 12 2925.2.c.e.2224.1 2
63.13 odd 6 1911.2.a.f.1.1 1
63.41 even 6 5733.2.a.e.1.1 1
72.5 odd 6 7488.2.a.bl.1.1 1
72.13 even 6 2496.2.a.q.1.1 1
72.59 even 6 7488.2.a.by.1.1 1
72.67 odd 6 2496.2.a.e.1.1 1
99.76 odd 6 4719.2.a.c.1.1 1
117.4 even 6 507.2.e.b.484.1 2
117.5 even 12 1521.2.b.b.1351.2 2
117.22 even 3 507.2.e.a.484.1 2
117.31 odd 12 507.2.b.a.337.1 2
117.49 even 6 507.2.e.b.22.1 2
117.58 odd 12 507.2.j.e.361.1 4
117.67 odd 12 507.2.j.e.316.2 4
117.76 odd 12 507.2.j.e.316.1 4
117.77 odd 6 1521.2.a.e.1.1 1
117.85 odd 12 507.2.j.e.361.2 4
117.86 even 12 1521.2.b.b.1351.1 2
117.94 even 3 507.2.e.a.22.1 2
117.103 even 6 507.2.a.a.1.1 1
117.112 odd 12 507.2.b.a.337.2 2
468.103 odd 6 8112.2.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.a.a.1.1 1 9.4 even 3
117.2.a.a.1.1 1 9.5 odd 6
507.2.a.a.1.1 1 117.103 even 6
507.2.b.a.337.1 2 117.31 odd 12
507.2.b.a.337.2 2 117.112 odd 12
507.2.e.a.22.1 2 117.94 even 3
507.2.e.a.484.1 2 117.22 even 3
507.2.e.b.22.1 2 117.49 even 6
507.2.e.b.484.1 2 117.4 even 6
507.2.j.e.316.1 4 117.76 odd 12
507.2.j.e.316.2 4 117.67 odd 12
507.2.j.e.361.1 4 117.58 odd 12
507.2.j.e.361.2 4 117.85 odd 12
624.2.a.i.1.1 1 36.31 odd 6
975.2.a.f.1.1 1 45.4 even 6
975.2.c.f.274.1 2 45.13 odd 12
975.2.c.f.274.2 2 45.22 odd 12
1053.2.e.b.352.1 2 1.1 even 1 trivial
1053.2.e.b.703.1 2 9.7 even 3 inner
1053.2.e.d.352.1 2 3.2 odd 2
1053.2.e.d.703.1 2 9.2 odd 6
1521.2.a.e.1.1 1 117.77 odd 6
1521.2.b.b.1351.1 2 117.86 even 12
1521.2.b.b.1351.2 2 117.5 even 12
1872.2.a.h.1.1 1 36.23 even 6
1911.2.a.f.1.1 1 63.13 odd 6
2496.2.a.e.1.1 1 72.67 odd 6
2496.2.a.q.1.1 1 72.13 even 6
2925.2.a.p.1.1 1 45.14 odd 6
2925.2.c.e.2224.1 2 45.32 even 12
2925.2.c.e.2224.2 2 45.23 even 12
4719.2.a.c.1.1 1 99.76 odd 6
5733.2.a.e.1.1 1 63.41 even 6
7488.2.a.bl.1.1 1 72.5 odd 6
7488.2.a.by.1.1 1 72.59 even 6
8112.2.a.s.1.1 1 468.103 odd 6