Properties

Label 360.2.k.e.181.4
Level $360$
Weight $2$
Character 360.181
Analytic conductor $2.875$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(181,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.181");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.k (of order \(2\), degree \(1\), 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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 181.4
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 360.181
Dual form 360.2.k.e.181.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +1.00000i q^{5} +0.732051 q^{7} +(2.00000 + 2.00000i) q^{8} +(-0.366025 + 1.36603i) q^{10} +2.00000i q^{11} -3.46410i q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.46410 q^{17} +0.535898i q^{19} +(-1.00000 + 1.73205i) q^{20} +(-0.732051 + 2.73205i) q^{22} +6.19615 q^{23} -1.00000 q^{25} +(1.26795 - 4.73205i) q^{26} +(1.26795 + 0.732051i) q^{28} -6.92820i q^{29} -5.46410 q^{31} +(1.46410 + 5.46410i) q^{32} +(-4.73205 - 1.26795i) q^{34} +0.732051i q^{35} -2.00000i q^{37} +(-0.196152 + 0.732051i) q^{38} +(-2.00000 + 2.00000i) q^{40} -1.46410 q^{41} -5.26795i q^{43} +(-2.00000 + 3.46410i) q^{44} +(8.46410 + 2.26795i) q^{46} -3.26795 q^{47} -6.46410 q^{49} +(-1.36603 - 0.366025i) q^{50} +(3.46410 - 6.00000i) q^{52} -11.4641i q^{53} -2.00000 q^{55} +(1.46410 + 1.46410i) q^{56} +(2.53590 - 9.46410i) q^{58} +7.46410i q^{59} -8.92820i q^{61} +(-7.46410 - 2.00000i) q^{62} +8.00000i q^{64} +3.46410 q^{65} +10.7321i q^{67} +(-6.00000 - 3.46410i) q^{68} +(-0.267949 + 1.00000i) q^{70} -5.46410 q^{71} +7.46410 q^{73} +(0.732051 - 2.73205i) q^{74} +(-0.535898 + 0.928203i) q^{76} +1.46410i q^{77} -1.07180 q^{79} +(-3.46410 + 2.00000i) q^{80} +(-2.00000 - 0.535898i) q^{82} -1.26795i q^{83} -3.46410i q^{85} +(1.92820 - 7.19615i) q^{86} +(-4.00000 + 4.00000i) q^{88} -8.92820 q^{89} -2.53590i q^{91} +(10.7321 + 6.19615i) q^{92} +(-4.46410 - 1.19615i) q^{94} -0.535898 q^{95} -14.3923 q^{97} +(-8.83013 - 2.36603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 4 q^{7} + 8 q^{8} + 2 q^{10} + 4 q^{14} + 8 q^{16} - 4 q^{20} + 4 q^{22} + 4 q^{23} - 4 q^{25} + 12 q^{26} + 12 q^{28} - 8 q^{31} - 8 q^{32} - 12 q^{34} + 20 q^{38} - 8 q^{40} + 8 q^{41}+ \cdots - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i
\(3\) 0 0
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.732051 0.276689 0.138345 0.990384i \(-0.455822\pi\)
0.138345 + 0.990384i \(0.455822\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 0 0
\(10\) −0.366025 + 1.36603i −0.115747 + 0.431975i
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) 1.00000 + 0.267949i 0.267261 + 0.0716124i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −3.46410 −0.840168 −0.420084 0.907485i \(-0.637999\pi\)
−0.420084 + 0.907485i \(0.637999\pi\)
\(18\) 0 0
\(19\) 0.535898i 0.122944i 0.998109 + 0.0614718i \(0.0195794\pi\)
−0.998109 + 0.0614718i \(0.980421\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 0 0
\(22\) −0.732051 + 2.73205i −0.156074 + 0.582475i
\(23\) 6.19615 1.29199 0.645994 0.763343i \(-0.276443\pi\)
0.645994 + 0.763343i \(0.276443\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 1.26795 4.73205i 0.248665 0.928032i
\(27\) 0 0
\(28\) 1.26795 + 0.732051i 0.239620 + 0.138345i
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) 0 0
\(31\) −5.46410 −0.981382 −0.490691 0.871334i \(-0.663256\pi\)
−0.490691 + 0.871334i \(0.663256\pi\)
\(32\) 1.46410 + 5.46410i 0.258819 + 0.965926i
\(33\) 0 0
\(34\) −4.73205 1.26795i −0.811540 0.217451i
\(35\) 0.732051i 0.123739i
\(36\) 0 0
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) −0.196152 + 0.732051i −0.0318201 + 0.118754i
\(39\) 0 0
\(40\) −2.00000 + 2.00000i −0.316228 + 0.316228i
\(41\) −1.46410 −0.228654 −0.114327 0.993443i \(-0.536471\pi\)
−0.114327 + 0.993443i \(0.536471\pi\)
\(42\) 0 0
\(43\) 5.26795i 0.803355i −0.915781 0.401677i \(-0.868427\pi\)
0.915781 0.401677i \(-0.131573\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 0 0
\(46\) 8.46410 + 2.26795i 1.24796 + 0.334391i
\(47\) −3.26795 −0.476679 −0.238340 0.971182i \(-0.576603\pi\)
−0.238340 + 0.971182i \(0.576603\pi\)
\(48\) 0 0
\(49\) −6.46410 −0.923443
\(50\) −1.36603 0.366025i −0.193185 0.0517638i
\(51\) 0 0
\(52\) 3.46410 6.00000i 0.480384 0.832050i
\(53\) 11.4641i 1.57472i −0.616496 0.787358i \(-0.711449\pi\)
0.616496 0.787358i \(-0.288551\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 1.46410 + 1.46410i 0.195649 + 0.195649i
\(57\) 0 0
\(58\) 2.53590 9.46410i 0.332980 1.24270i
\(59\) 7.46410i 0.971743i 0.874030 + 0.485872i \(0.161498\pi\)
−0.874030 + 0.485872i \(0.838502\pi\)
\(60\) 0 0
\(61\) 8.92820i 1.14314i −0.820554 0.571570i \(-0.806335\pi\)
0.820554 0.571570i \(-0.193665\pi\)
\(62\) −7.46410 2.00000i −0.947942 0.254000i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 3.46410 0.429669
\(66\) 0 0
\(67\) 10.7321i 1.31113i 0.755139 + 0.655564i \(0.227569\pi\)
−0.755139 + 0.655564i \(0.772431\pi\)
\(68\) −6.00000 3.46410i −0.727607 0.420084i
\(69\) 0 0
\(70\) −0.267949 + 1.00000i −0.0320261 + 0.119523i
\(71\) −5.46410 −0.648470 −0.324235 0.945977i \(-0.605107\pi\)
−0.324235 + 0.945977i \(0.605107\pi\)
\(72\) 0 0
\(73\) 7.46410 0.873607 0.436804 0.899557i \(-0.356111\pi\)
0.436804 + 0.899557i \(0.356111\pi\)
\(74\) 0.732051 2.73205i 0.0850992 0.317594i
\(75\) 0 0
\(76\) −0.535898 + 0.928203i −0.0614718 + 0.106472i
\(77\) 1.46410i 0.166850i
\(78\) 0 0
\(79\) −1.07180 −0.120587 −0.0602933 0.998181i \(-0.519204\pi\)
−0.0602933 + 0.998181i \(0.519204\pi\)
\(80\) −3.46410 + 2.00000i −0.387298 + 0.223607i
\(81\) 0 0
\(82\) −2.00000 0.535898i −0.220863 0.0591801i
\(83\) 1.26795i 0.139176i −0.997576 0.0695878i \(-0.977832\pi\)
0.997576 0.0695878i \(-0.0221684\pi\)
\(84\) 0 0
\(85\) 3.46410i 0.375735i
\(86\) 1.92820 7.19615i 0.207924 0.775981i
\(87\) 0 0
\(88\) −4.00000 + 4.00000i −0.426401 + 0.426401i
\(89\) −8.92820 −0.946388 −0.473194 0.880958i \(-0.656899\pi\)
−0.473194 + 0.880958i \(0.656899\pi\)
\(90\) 0 0
\(91\) 2.53590i 0.265834i
\(92\) 10.7321 + 6.19615i 1.11889 + 0.645994i
\(93\) 0 0
\(94\) −4.46410 1.19615i −0.460437 0.123374i
\(95\) −0.535898 −0.0549820
\(96\) 0 0
\(97\) −14.3923 −1.46132 −0.730659 0.682743i \(-0.760787\pi\)
−0.730659 + 0.682743i \(0.760787\pi\)
\(98\) −8.83013 2.36603i −0.891978 0.239005i
\(99\) 0 0
\(100\) −1.73205 1.00000i −0.173205 0.100000i
\(101\) 2.92820i 0.291367i −0.989331 0.145684i \(-0.953462\pi\)
0.989331 0.145684i \(-0.0465381\pi\)
\(102\) 0 0
\(103\) 15.6603 1.54305 0.771525 0.636199i \(-0.219494\pi\)
0.771525 + 0.636199i \(0.219494\pi\)
\(104\) 6.92820 6.92820i 0.679366 0.679366i
\(105\) 0 0
\(106\) 4.19615 15.6603i 0.407566 1.52106i
\(107\) 2.73205i 0.264117i −0.991242 0.132059i \(-0.957841\pi\)
0.991242 0.132059i \(-0.0421587\pi\)
\(108\) 0 0
\(109\) 16.9282i 1.62143i 0.585443 + 0.810714i \(0.300921\pi\)
−0.585443 + 0.810714i \(0.699079\pi\)
\(110\) −2.73205 0.732051i −0.260491 0.0697983i
\(111\) 0 0
\(112\) 1.46410 + 2.53590i 0.138345 + 0.239620i
\(113\) 12.9282 1.21618 0.608092 0.793867i \(-0.291935\pi\)
0.608092 + 0.793867i \(0.291935\pi\)
\(114\) 0 0
\(115\) 6.19615i 0.577794i
\(116\) 6.92820 12.0000i 0.643268 1.11417i
\(117\) 0 0
\(118\) −2.73205 + 10.1962i −0.251506 + 0.938632i
\(119\) −2.53590 −0.232465
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 3.26795 12.1962i 0.295866 1.10419i
\(123\) 0 0
\(124\) −9.46410 5.46410i −0.849901 0.490691i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 16.7321 1.48473 0.742365 0.669996i \(-0.233704\pi\)
0.742365 + 0.669996i \(0.233704\pi\)
\(128\) −2.92820 + 10.9282i −0.258819 + 0.965926i
\(129\) 0 0
\(130\) 4.73205 + 1.26795i 0.415028 + 0.111207i
\(131\) 19.8564i 1.73486i 0.497557 + 0.867431i \(0.334230\pi\)
−0.497557 + 0.867431i \(0.665770\pi\)
\(132\) 0 0
\(133\) 0.392305i 0.0340171i
\(134\) −3.92820 + 14.6603i −0.339345 + 1.26645i
\(135\) 0 0
\(136\) −6.92820 6.92820i −0.594089 0.594089i
\(137\) −4.92820 −0.421045 −0.210522 0.977589i \(-0.567516\pi\)
−0.210522 + 0.977589i \(0.567516\pi\)
\(138\) 0 0
\(139\) 0.535898i 0.0454543i −0.999742 0.0227272i \(-0.992765\pi\)
0.999742 0.0227272i \(-0.00723490\pi\)
\(140\) −0.732051 + 1.26795i −0.0618696 + 0.107161i
\(141\) 0 0
\(142\) −7.46410 2.00000i −0.626373 0.167836i
\(143\) 6.92820 0.579365
\(144\) 0 0
\(145\) 6.92820 0.575356
\(146\) 10.1962 + 2.73205i 0.843840 + 0.226106i
\(147\) 0 0
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) 7.85641i 0.643622i 0.946804 + 0.321811i \(0.104292\pi\)
−0.946804 + 0.321811i \(0.895708\pi\)
\(150\) 0 0
\(151\) −12.3923 −1.00847 −0.504236 0.863566i \(-0.668226\pi\)
−0.504236 + 0.863566i \(0.668226\pi\)
\(152\) −1.07180 + 1.07180i −0.0869342 + 0.0869342i
\(153\) 0 0
\(154\) −0.535898 + 2.00000i −0.0431839 + 0.161165i
\(155\) 5.46410i 0.438887i
\(156\) 0 0
\(157\) 3.07180i 0.245156i −0.992459 0.122578i \(-0.960884\pi\)
0.992459 0.122578i \(-0.0391162\pi\)
\(158\) −1.46410 0.392305i −0.116478 0.0312101i
\(159\) 0 0
\(160\) −5.46410 + 1.46410i −0.431975 + 0.115747i
\(161\) 4.53590 0.357479
\(162\) 0 0
\(163\) 0.196152i 0.0153638i −0.999970 0.00768192i \(-0.997555\pi\)
0.999970 0.00768192i \(-0.00244526\pi\)
\(164\) −2.53590 1.46410i −0.198020 0.114327i
\(165\) 0 0
\(166\) 0.464102 1.73205i 0.0360213 0.134433i
\(167\) 9.80385 0.758645 0.379322 0.925265i \(-0.376157\pi\)
0.379322 + 0.925265i \(0.376157\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 1.26795 4.73205i 0.0972473 0.362932i
\(171\) 0 0
\(172\) 5.26795 9.12436i 0.401677 0.695726i
\(173\) 2.00000i 0.152057i −0.997106 0.0760286i \(-0.975776\pi\)
0.997106 0.0760286i \(-0.0242240\pi\)
\(174\) 0 0
\(175\) −0.732051 −0.0553378
\(176\) −6.92820 + 4.00000i −0.522233 + 0.301511i
\(177\) 0 0
\(178\) −12.1962 3.26795i −0.914140 0.244943i
\(179\) 8.53590i 0.638003i 0.947754 + 0.319002i \(0.103348\pi\)
−0.947754 + 0.319002i \(0.896652\pi\)
\(180\) 0 0
\(181\) 16.0000i 1.18927i 0.803996 + 0.594635i \(0.202704\pi\)
−0.803996 + 0.594635i \(0.797296\pi\)
\(182\) 0.928203 3.46410i 0.0688030 0.256776i
\(183\) 0 0
\(184\) 12.3923 + 12.3923i 0.913573 + 0.913573i
\(185\) 2.00000 0.147043
\(186\) 0 0
\(187\) 6.92820i 0.506640i
\(188\) −5.66025 3.26795i −0.412816 0.238340i
\(189\) 0 0
\(190\) −0.732051 0.196152i −0.0531085 0.0142304i
\(191\) −15.3205 −1.10855 −0.554277 0.832333i \(-0.687005\pi\)
−0.554277 + 0.832333i \(0.687005\pi\)
\(192\) 0 0
\(193\) 0.535898 0.0385748 0.0192874 0.999814i \(-0.493860\pi\)
0.0192874 + 0.999814i \(0.493860\pi\)
\(194\) −19.6603 5.26795i −1.41152 0.378217i
\(195\) 0 0
\(196\) −11.1962 6.46410i −0.799725 0.461722i
\(197\) 19.4641i 1.38676i 0.720572 + 0.693380i \(0.243879\pi\)
−0.720572 + 0.693380i \(0.756121\pi\)
\(198\) 0 0
\(199\) −1.85641 −0.131597 −0.0657986 0.997833i \(-0.520959\pi\)
−0.0657986 + 0.997833i \(0.520959\pi\)
\(200\) −2.00000 2.00000i −0.141421 0.141421i
\(201\) 0 0
\(202\) 1.07180 4.00000i 0.0754114 0.281439i
\(203\) 5.07180i 0.355970i
\(204\) 0 0
\(205\) 1.46410i 0.102257i
\(206\) 21.3923 + 5.73205i 1.49047 + 0.399371i
\(207\) 0 0
\(208\) 12.0000 6.92820i 0.832050 0.480384i
\(209\) −1.07180 −0.0741377
\(210\) 0 0
\(211\) 26.7846i 1.84393i 0.387275 + 0.921964i \(0.373416\pi\)
−0.387275 + 0.921964i \(0.626584\pi\)
\(212\) 11.4641 19.8564i 0.787358 1.36374i
\(213\) 0 0
\(214\) 1.00000 3.73205i 0.0683586 0.255118i
\(215\) 5.26795 0.359271
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) −6.19615 + 23.1244i −0.419656 + 1.56618i
\(219\) 0 0
\(220\) −3.46410 2.00000i −0.233550 0.134840i
\(221\) 12.0000i 0.807207i
\(222\) 0 0
\(223\) −5.80385 −0.388654 −0.194327 0.980937i \(-0.562252\pi\)
−0.194327 + 0.980937i \(0.562252\pi\)
\(224\) 1.07180 + 4.00000i 0.0716124 + 0.267261i
\(225\) 0 0
\(226\) 17.6603 + 4.73205i 1.17474 + 0.314771i
\(227\) 10.0526i 0.667212i −0.942713 0.333606i \(-0.891735\pi\)
0.942713 0.333606i \(-0.108265\pi\)
\(228\) 0 0
\(229\) 4.00000i 0.264327i −0.991228 0.132164i \(-0.957808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) −2.26795 + 8.46410i −0.149544 + 0.558106i
\(231\) 0 0
\(232\) 13.8564 13.8564i 0.909718 0.909718i
\(233\) 5.32051 0.348558 0.174279 0.984696i \(-0.444241\pi\)
0.174279 + 0.984696i \(0.444241\pi\)
\(234\) 0 0
\(235\) 3.26795i 0.213177i
\(236\) −7.46410 + 12.9282i −0.485872 + 0.841554i
\(237\) 0 0
\(238\) −3.46410 0.928203i −0.224544 0.0601665i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 16.3923 1.05592 0.527961 0.849269i \(-0.322957\pi\)
0.527961 + 0.849269i \(0.322957\pi\)
\(242\) 9.56218 + 2.56218i 0.614680 + 0.164703i
\(243\) 0 0
\(244\) 8.92820 15.4641i 0.571570 0.989988i
\(245\) 6.46410i 0.412976i
\(246\) 0 0
\(247\) 1.85641 0.118120
\(248\) −10.9282 10.9282i −0.693942 0.693942i
\(249\) 0 0
\(250\) 0.366025 1.36603i 0.0231495 0.0863950i
\(251\) 24.9282i 1.57345i −0.617301 0.786727i \(-0.711774\pi\)
0.617301 0.786727i \(-0.288226\pi\)
\(252\) 0 0
\(253\) 12.3923i 0.779098i
\(254\) 22.8564 + 6.12436i 1.43414 + 0.384276i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 2.00000 0.124757 0.0623783 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 0 0
\(259\) 1.46410i 0.0909748i
\(260\) 6.00000 + 3.46410i 0.372104 + 0.214834i
\(261\) 0 0
\(262\) −7.26795 + 27.1244i −0.449015 + 1.67575i
\(263\) 11.6603 0.719002 0.359501 0.933145i \(-0.382947\pi\)
0.359501 + 0.933145i \(0.382947\pi\)
\(264\) 0 0
\(265\) 11.4641 0.704234
\(266\) −0.143594 + 0.535898i −0.00880428 + 0.0328580i
\(267\) 0 0
\(268\) −10.7321 + 18.5885i −0.655564 + 1.13547i
\(269\) 8.92820i 0.544362i 0.962246 + 0.272181i \(0.0877450\pi\)
−0.962246 + 0.272181i \(0.912255\pi\)
\(270\) 0 0
\(271\) −19.3205 −1.17364 −0.586819 0.809718i \(-0.699620\pi\)
−0.586819 + 0.809718i \(0.699620\pi\)
\(272\) −6.92820 12.0000i −0.420084 0.727607i
\(273\) 0 0
\(274\) −6.73205 1.80385i −0.406698 0.108974i
\(275\) 2.00000i 0.120605i
\(276\) 0 0
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 0.196152 0.732051i 0.0117644 0.0439055i
\(279\) 0 0
\(280\) −1.46410 + 1.46410i −0.0874968 + 0.0874968i
\(281\) −10.5359 −0.628519 −0.314260 0.949337i \(-0.601756\pi\)
−0.314260 + 0.949337i \(0.601756\pi\)
\(282\) 0 0
\(283\) 9.66025i 0.574242i −0.957894 0.287121i \(-0.907302\pi\)
0.957894 0.287121i \(-0.0926983\pi\)
\(284\) −9.46410 5.46410i −0.561591 0.324235i
\(285\) 0 0
\(286\) 9.46410 + 2.53590i 0.559624 + 0.149951i
\(287\) −1.07180 −0.0632662
\(288\) 0 0
\(289\) −5.00000 −0.294118
\(290\) 9.46410 + 2.53590i 0.555751 + 0.148913i
\(291\) 0 0
\(292\) 12.9282 + 7.46410i 0.756566 + 0.436804i
\(293\) 15.8564i 0.926341i 0.886269 + 0.463171i \(0.153288\pi\)
−0.886269 + 0.463171i \(0.846712\pi\)
\(294\) 0 0
\(295\) −7.46410 −0.434577
\(296\) 4.00000 4.00000i 0.232495 0.232495i
\(297\) 0 0
\(298\) −2.87564 + 10.7321i −0.166582 + 0.621691i
\(299\) 21.4641i 1.24130i
\(300\) 0 0
\(301\) 3.85641i 0.222280i
\(302\) −16.9282 4.53590i −0.974109 0.261012i
\(303\) 0 0
\(304\) −1.85641 + 1.07180i −0.106472 + 0.0614718i
\(305\) 8.92820 0.511227
\(306\) 0 0
\(307\) 24.9808i 1.42573i −0.701303 0.712864i \(-0.747398\pi\)
0.701303 0.712864i \(-0.252602\pi\)
\(308\) −1.46410 + 2.53590i −0.0834249 + 0.144496i
\(309\) 0 0
\(310\) 2.00000 7.46410i 0.113592 0.423932i
\(311\) −31.3205 −1.77602 −0.888012 0.459821i \(-0.847914\pi\)
−0.888012 + 0.459821i \(0.847914\pi\)
\(312\) 0 0
\(313\) −4.14359 −0.234210 −0.117105 0.993120i \(-0.537361\pi\)
−0.117105 + 0.993120i \(0.537361\pi\)
\(314\) 1.12436 4.19615i 0.0634511 0.236803i
\(315\) 0 0
\(316\) −1.85641 1.07180i −0.104431 0.0602933i
\(317\) 8.53590i 0.479424i −0.970844 0.239712i \(-0.922947\pi\)
0.970844 0.239712i \(-0.0770530\pi\)
\(318\) 0 0
\(319\) 13.8564 0.775810
\(320\) −8.00000 −0.447214
\(321\) 0 0
\(322\) 6.19615 + 1.66025i 0.345298 + 0.0925223i
\(323\) 1.85641i 0.103293i
\(324\) 0 0
\(325\) 3.46410i 0.192154i
\(326\) 0.0717968 0.267949i 0.00397646 0.0148403i
\(327\) 0 0
\(328\) −2.92820 2.92820i −0.161683 0.161683i
\(329\) −2.39230 −0.131892
\(330\) 0 0
\(331\) 14.0000i 0.769510i −0.923019 0.384755i \(-0.874286\pi\)
0.923019 0.384755i \(-0.125714\pi\)
\(332\) 1.26795 2.19615i 0.0695878 0.120530i
\(333\) 0 0
\(334\) 13.3923 + 3.58846i 0.732794 + 0.196352i
\(335\) −10.7321 −0.586355
\(336\) 0 0
\(337\) −19.8564 −1.08165 −0.540824 0.841136i \(-0.681887\pi\)
−0.540824 + 0.841136i \(0.681887\pi\)
\(338\) 1.36603 + 0.366025i 0.0743020 + 0.0199092i
\(339\) 0 0
\(340\) 3.46410 6.00000i 0.187867 0.325396i
\(341\) 10.9282i 0.591795i
\(342\) 0 0
\(343\) −9.85641 −0.532196
\(344\) 10.5359 10.5359i 0.568058 0.568058i
\(345\) 0 0
\(346\) 0.732051 2.73205i 0.0393553 0.146876i
\(347\) 1.66025i 0.0891271i 0.999007 + 0.0445636i \(0.0141897\pi\)
−0.999007 + 0.0445636i \(0.985810\pi\)
\(348\) 0 0
\(349\) 28.0000i 1.49881i −0.662114 0.749403i \(-0.730341\pi\)
0.662114 0.749403i \(-0.269659\pi\)
\(350\) −1.00000 0.267949i −0.0534522 0.0143225i
\(351\) 0 0
\(352\) −10.9282 + 2.92820i −0.582475 + 0.156074i
\(353\) −12.9282 −0.688099 −0.344049 0.938952i \(-0.611799\pi\)
−0.344049 + 0.938952i \(0.611799\pi\)
\(354\) 0 0
\(355\) 5.46410i 0.290004i
\(356\) −15.4641 8.92820i −0.819596 0.473194i
\(357\) 0 0
\(358\) −3.12436 + 11.6603i −0.165127 + 0.616264i
\(359\) −18.9282 −0.998992 −0.499496 0.866316i \(-0.666482\pi\)
−0.499496 + 0.866316i \(0.666482\pi\)
\(360\) 0 0
\(361\) 18.7128 0.984885
\(362\) −5.85641 + 21.8564i −0.307806 + 1.14875i
\(363\) 0 0
\(364\) 2.53590 4.39230i 0.132917 0.230219i
\(365\) 7.46410i 0.390689i
\(366\) 0 0
\(367\) 2.87564 0.150107 0.0750537 0.997179i \(-0.476087\pi\)
0.0750537 + 0.997179i \(0.476087\pi\)
\(368\) 12.3923 + 21.4641i 0.645994 + 1.11889i
\(369\) 0 0
\(370\) 2.73205 + 0.732051i 0.142033 + 0.0380575i
\(371\) 8.39230i 0.435707i
\(372\) 0 0
\(373\) 25.7128i 1.33136i −0.746238 0.665679i \(-0.768142\pi\)
0.746238 0.665679i \(-0.231858\pi\)
\(374\) 2.53590 9.46410i 0.131128 0.489377i
\(375\) 0 0
\(376\) −6.53590 6.53590i −0.337063 0.337063i
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) 36.2487i 1.86197i −0.365056 0.930986i \(-0.618950\pi\)
0.365056 0.930986i \(-0.381050\pi\)
\(380\) −0.928203 0.535898i −0.0476158 0.0274910i
\(381\) 0 0
\(382\) −20.9282 5.60770i −1.07078 0.286915i
\(383\) −21.1244 −1.07940 −0.539702 0.841856i \(-0.681463\pi\)
−0.539702 + 0.841856i \(0.681463\pi\)
\(384\) 0 0
\(385\) −1.46410 −0.0746175
\(386\) 0.732051 + 0.196152i 0.0372604 + 0.00998390i
\(387\) 0 0
\(388\) −24.9282 14.3923i −1.26554 0.730659i
\(389\) 6.78461i 0.343993i −0.985098 0.171997i \(-0.944978\pi\)
0.985098 0.171997i \(-0.0550218\pi\)
\(390\) 0 0
\(391\) −21.4641 −1.08549
\(392\) −12.9282 12.9282i −0.652973 0.652973i
\(393\) 0 0
\(394\) −7.12436 + 26.5885i −0.358920 + 1.33951i
\(395\) 1.07180i 0.0539279i
\(396\) 0 0
\(397\) 32.2487i 1.61852i 0.587453 + 0.809258i \(0.300131\pi\)
−0.587453 + 0.809258i \(0.699869\pi\)
\(398\) −2.53590 0.679492i −0.127113 0.0340599i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 7.85641 0.392330 0.196165 0.980571i \(-0.437151\pi\)
0.196165 + 0.980571i \(0.437151\pi\)
\(402\) 0 0
\(403\) 18.9282i 0.942881i
\(404\) 2.92820 5.07180i 0.145684 0.252331i
\(405\) 0 0
\(406\) 1.85641 6.92820i 0.0921319 0.343841i
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) −11.3205 −0.559763 −0.279882 0.960035i \(-0.590295\pi\)
−0.279882 + 0.960035i \(0.590295\pi\)
\(410\) 0.535898 2.00000i 0.0264661 0.0987730i
\(411\) 0 0
\(412\) 27.1244 + 15.6603i 1.33632 + 0.771525i
\(413\) 5.46410i 0.268871i
\(414\) 0 0
\(415\) 1.26795 0.0622412
\(416\) 18.9282 5.07180i 0.928032 0.248665i
\(417\) 0 0
\(418\) −1.46410 0.392305i −0.0716116 0.0191883i
\(419\) 18.3923i 0.898523i −0.893400 0.449261i \(-0.851687\pi\)
0.893400 0.449261i \(-0.148313\pi\)
\(420\) 0 0
\(421\) 0.143594i 0.00699832i 0.999994 + 0.00349916i \(0.00111382\pi\)
−0.999994 + 0.00349916i \(0.998886\pi\)
\(422\) −9.80385 + 36.5885i −0.477244 + 1.78110i
\(423\) 0 0
\(424\) 22.9282 22.9282i 1.11349 1.11349i
\(425\) 3.46410 0.168034
\(426\) 0 0
\(427\) 6.53590i 0.316294i
\(428\) 2.73205 4.73205i 0.132059 0.228732i
\(429\) 0 0
\(430\) 7.19615 + 1.92820i 0.347029 + 0.0929862i
\(431\) 21.4641 1.03389 0.516945 0.856019i \(-0.327069\pi\)
0.516945 + 0.856019i \(0.327069\pi\)
\(432\) 0 0
\(433\) −19.4641 −0.935385 −0.467693 0.883891i \(-0.654915\pi\)
−0.467693 + 0.883891i \(0.654915\pi\)
\(434\) −5.46410 1.46410i −0.262285 0.0702791i
\(435\) 0 0
\(436\) −16.9282 + 29.3205i −0.810714 + 1.40420i
\(437\) 3.32051i 0.158841i
\(438\) 0 0
\(439\) 40.7846 1.94654 0.973272 0.229657i \(-0.0737605\pi\)
0.973272 + 0.229657i \(0.0737605\pi\)
\(440\) −4.00000 4.00000i −0.190693 0.190693i
\(441\) 0 0
\(442\) −4.39230 + 16.3923i −0.208921 + 0.779702i
\(443\) 20.9808i 0.996826i −0.866940 0.498413i \(-0.833916\pi\)
0.866940 0.498413i \(-0.166084\pi\)
\(444\) 0 0
\(445\) 8.92820i 0.423237i
\(446\) −7.92820 2.12436i −0.375411 0.100591i
\(447\) 0 0
\(448\) 5.85641i 0.276689i
\(449\) 23.3205 1.10056 0.550281 0.834979i \(-0.314520\pi\)
0.550281 + 0.834979i \(0.314520\pi\)
\(450\) 0 0
\(451\) 2.92820i 0.137884i
\(452\) 22.3923 + 12.9282i 1.05325 + 0.608092i
\(453\) 0 0
\(454\) 3.67949 13.7321i 0.172687 0.644477i
\(455\) 2.53590 0.118885
\(456\) 0 0
\(457\) −26.7846 −1.25293 −0.626466 0.779449i \(-0.715499\pi\)
−0.626466 + 0.779449i \(0.715499\pi\)
\(458\) 1.46410 5.46410i 0.0684130 0.255321i
\(459\) 0 0
\(460\) −6.19615 + 10.7321i −0.288897 + 0.500384i
\(461\) 10.9282i 0.508977i 0.967076 + 0.254489i \(0.0819071\pi\)
−0.967076 + 0.254489i \(0.918093\pi\)
\(462\) 0 0
\(463\) −11.2679 −0.523666 −0.261833 0.965113i \(-0.584327\pi\)
−0.261833 + 0.965113i \(0.584327\pi\)
\(464\) 24.0000 13.8564i 1.11417 0.643268i
\(465\) 0 0
\(466\) 7.26795 + 1.94744i 0.336681 + 0.0902135i
\(467\) 25.6603i 1.18741i 0.804681 + 0.593707i \(0.202336\pi\)
−0.804681 + 0.593707i \(0.797664\pi\)
\(468\) 0 0
\(469\) 7.85641i 0.362775i
\(470\) 1.19615 4.46410i 0.0551744 0.205914i
\(471\) 0 0
\(472\) −14.9282 + 14.9282i −0.687126 + 0.687126i
\(473\) 10.5359 0.484441
\(474\) 0 0
\(475\) 0.535898i 0.0245887i
\(476\) −4.39230 2.53590i −0.201321 0.116233i
\(477\) 0 0
\(478\) 27.3205 + 7.32051i 1.24961 + 0.334832i
\(479\) −5.85641 −0.267586 −0.133793 0.991009i \(-0.542716\pi\)
−0.133793 + 0.991009i \(0.542716\pi\)
\(480\) 0 0
\(481\) −6.92820 −0.315899
\(482\) 22.3923 + 6.00000i 1.01994 + 0.273293i
\(483\) 0 0
\(484\) 12.1244 + 7.00000i 0.551107 + 0.318182i
\(485\) 14.3923i 0.653521i
\(486\) 0 0
\(487\) 6.58846 0.298551 0.149276 0.988796i \(-0.452306\pi\)
0.149276 + 0.988796i \(0.452306\pi\)
\(488\) 17.8564 17.8564i 0.808322 0.808322i
\(489\) 0 0
\(490\) 2.36603 8.83013i 0.106886 0.398904i
\(491\) 16.9282i 0.763959i 0.924171 + 0.381980i \(0.124758\pi\)
−0.924171 + 0.381980i \(0.875242\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) 2.53590 + 0.679492i 0.114095 + 0.0305718i
\(495\) 0 0
\(496\) −10.9282 18.9282i −0.490691 0.849901i
\(497\) −4.00000 −0.179425
\(498\) 0 0
\(499\) 31.4641i 1.40853i 0.709939 + 0.704263i \(0.248723\pi\)
−0.709939 + 0.704263i \(0.751277\pi\)
\(500\) 1.00000 1.73205i 0.0447214 0.0774597i
\(501\) 0 0
\(502\) 9.12436 34.0526i 0.407240 1.51984i
\(503\) 0.339746 0.0151485 0.00757426 0.999971i \(-0.497589\pi\)
0.00757426 + 0.999971i \(0.497589\pi\)
\(504\) 0 0
\(505\) 2.92820 0.130303
\(506\) −4.53590 + 16.9282i −0.201645 + 0.752550i
\(507\) 0 0
\(508\) 28.9808 + 16.7321i 1.28581 + 0.742365i
\(509\) 1.85641i 0.0822838i 0.999153 + 0.0411419i \(0.0130996\pi\)
−0.999153 + 0.0411419i \(0.986900\pi\)
\(510\) 0 0
\(511\) 5.46410 0.241718
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 0 0
\(514\) 2.73205 + 0.732051i 0.120506 + 0.0322894i
\(515\) 15.6603i 0.690073i
\(516\) 0 0
\(517\) 6.53590i 0.287448i
\(518\) 0.535898 2.00000i 0.0235460 0.0878750i
\(519\) 0 0
\(520\) 6.92820 + 6.92820i 0.303822 + 0.303822i
\(521\) 43.8564 1.92138 0.960692 0.277616i \(-0.0895444\pi\)
0.960692 + 0.277616i \(0.0895444\pi\)
\(522\) 0 0
\(523\) 11.8038i 0.516146i −0.966125 0.258073i \(-0.916912\pi\)
0.966125 0.258073i \(-0.0830875\pi\)
\(524\) −19.8564 + 34.3923i −0.867431 + 1.50243i
\(525\) 0 0
\(526\) 15.9282 + 4.26795i 0.694503 + 0.186091i
\(527\) 18.9282 0.824525
\(528\) 0 0
\(529\) 15.3923 0.669231
\(530\) 15.6603 + 4.19615i 0.680238 + 0.182269i
\(531\) 0 0
\(532\) −0.392305 + 0.679492i −0.0170086 + 0.0294597i
\(533\) 5.07180i 0.219684i
\(534\) 0 0
\(535\) 2.73205 0.118117
\(536\) −21.4641 + 21.4641i −0.927108 + 0.927108i
\(537\) 0 0
\(538\) −3.26795 + 12.1962i −0.140891 + 0.525813i
\(539\) 12.9282i 0.556857i
\(540\) 0 0
\(541\) 26.9282i 1.15773i −0.815422 0.578867i \(-0.803495\pi\)
0.815422 0.578867i \(-0.196505\pi\)
\(542\) −26.3923 7.07180i −1.13365 0.303760i
\(543\) 0 0
\(544\) −5.07180 18.9282i −0.217451 0.811540i
\(545\) −16.9282 −0.725125
\(546\) 0 0
\(547\) 33.2679i 1.42243i 0.702972 + 0.711217i \(0.251856\pi\)
−0.702972 + 0.711217i \(0.748144\pi\)
\(548\) −8.53590 4.92820i −0.364636 0.210522i
\(549\) 0 0
\(550\) 0.732051 2.73205i 0.0312148 0.116495i
\(551\) 3.71281 0.158171
\(552\) 0 0
\(553\) −0.784610 −0.0333650
\(554\) −0.732051 + 2.73205i −0.0311019 + 0.116074i
\(555\) 0 0
\(556\) 0.535898 0.928203i 0.0227272 0.0393646i
\(557\) 14.7846i 0.626444i −0.949680 0.313222i \(-0.898592\pi\)
0.949680 0.313222i \(-0.101408\pi\)
\(558\) 0 0
\(559\) −18.2487 −0.771838
\(560\) −2.53590 + 1.46410i −0.107161 + 0.0618696i
\(561\) 0 0
\(562\) −14.3923 3.85641i −0.607103 0.162673i
\(563\) 22.0526i 0.929405i 0.885467 + 0.464702i \(0.153839\pi\)
−0.885467 + 0.464702i \(0.846161\pi\)
\(564\) 0 0
\(565\) 12.9282i 0.543894i
\(566\) 3.53590 13.1962i 0.148625 0.554676i
\(567\) 0 0
\(568\) −10.9282 10.9282i −0.458537 0.458537i
\(569\) 13.4641 0.564445 0.282222 0.959349i \(-0.408928\pi\)
0.282222 + 0.959349i \(0.408928\pi\)
\(570\) 0 0
\(571\) 6.78461i 0.283927i 0.989872 + 0.141964i \(0.0453416\pi\)
−0.989872 + 0.141964i \(0.954658\pi\)
\(572\) 12.0000 + 6.92820i 0.501745 + 0.289683i
\(573\) 0 0
\(574\) −1.46410 0.392305i −0.0611104 0.0163745i
\(575\) −6.19615 −0.258397
\(576\) 0 0
\(577\) 39.5692 1.64729 0.823644 0.567107i \(-0.191937\pi\)
0.823644 + 0.567107i \(0.191937\pi\)
\(578\) −6.83013 1.83013i −0.284096 0.0761232i
\(579\) 0 0
\(580\) 12.0000 + 6.92820i 0.498273 + 0.287678i
\(581\) 0.928203i 0.0385084i
\(582\) 0 0
\(583\) 22.9282 0.949589
\(584\) 14.9282 + 14.9282i 0.617733 + 0.617733i
\(585\) 0 0
\(586\) −5.80385 + 21.6603i −0.239755 + 0.894777i
\(587\) 3.80385i 0.157002i 0.996914 + 0.0785008i \(0.0250133\pi\)
−0.996914 + 0.0785008i \(0.974987\pi\)
\(588\) 0 0
\(589\) 2.92820i 0.120655i
\(590\) −10.1962 2.73205i −0.419769 0.112477i
\(591\) 0 0
\(592\) 6.92820 4.00000i 0.284747 0.164399i
\(593\) −32.6410 −1.34041 −0.670203 0.742178i \(-0.733793\pi\)
−0.670203 + 0.742178i \(0.733793\pi\)
\(594\) 0 0
\(595\) 2.53590i 0.103962i
\(596\) −7.85641 + 13.6077i −0.321811 + 0.557393i
\(597\) 0 0
\(598\) 7.85641 29.3205i 0.321272 1.19900i
\(599\) 34.6410 1.41539 0.707697 0.706516i \(-0.249734\pi\)
0.707697 + 0.706516i \(0.249734\pi\)
\(600\) 0 0
\(601\) 18.5359 0.756095 0.378048 0.925786i \(-0.376596\pi\)
0.378048 + 0.925786i \(0.376596\pi\)
\(602\) 1.41154 5.26795i 0.0575302 0.214706i
\(603\) 0 0
\(604\) −21.4641 12.3923i −0.873362 0.504236i
\(605\) 7.00000i 0.284590i
\(606\) 0 0
\(607\) 30.9808 1.25747 0.628735 0.777619i \(-0.283573\pi\)
0.628735 + 0.777619i \(0.283573\pi\)
\(608\) −2.92820 + 0.784610i −0.118754 + 0.0318201i
\(609\) 0 0
\(610\) 12.1962 + 3.26795i 0.493808 + 0.132315i
\(611\) 11.3205i 0.457979i
\(612\) 0 0
\(613\) 26.3923i 1.06598i 0.846123 + 0.532988i \(0.178931\pi\)
−0.846123 + 0.532988i \(0.821069\pi\)
\(614\) 9.14359 34.1244i 0.369005 1.37715i
\(615\) 0 0
\(616\) −2.92820 + 2.92820i −0.117981 + 0.117981i
\(617\) 20.5359 0.826744 0.413372 0.910562i \(-0.364351\pi\)
0.413372 + 0.910562i \(0.364351\pi\)
\(618\) 0 0
\(619\) 1.32051i 0.0530757i 0.999648 + 0.0265379i \(0.00844825\pi\)
−0.999648 + 0.0265379i \(0.991552\pi\)
\(620\) 5.46410 9.46410i 0.219444 0.380087i
\(621\) 0 0
\(622\) −42.7846 11.4641i −1.71551 0.459669i
\(623\) −6.53590 −0.261855
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −5.66025 1.51666i −0.226229 0.0606179i
\(627\) 0 0
\(628\) 3.07180 5.32051i 0.122578 0.212311i
\(629\) 6.92820i 0.276246i
\(630\) 0 0
\(631\) −23.3205 −0.928375 −0.464187 0.885737i \(-0.653654\pi\)
−0.464187 + 0.885737i \(0.653654\pi\)
\(632\) −2.14359 2.14359i −0.0852676 0.0852676i
\(633\) 0 0
\(634\) 3.12436 11.6603i 0.124084 0.463088i
\(635\) 16.7321i 0.663991i
\(636\) 0 0
\(637\) 22.3923i 0.887215i
\(638\) 18.9282 + 5.07180i 0.749375 + 0.200794i
\(639\) 0 0
\(640\) −10.9282 2.92820i −0.431975 0.115747i
\(641\) −0.392305 −0.0154951 −0.00774755 0.999970i \(-0.502466\pi\)
−0.00774755 + 0.999970i \(0.502466\pi\)
\(642\) 0 0
\(643\) 39.1244i 1.54291i 0.636281 + 0.771457i \(0.280472\pi\)
−0.636281 + 0.771457i \(0.719528\pi\)
\(644\) 7.85641 + 4.53590i 0.309586 + 0.178739i
\(645\) 0 0
\(646\) 0.679492 2.53590i 0.0267343 0.0997736i
\(647\) −16.7321 −0.657805 −0.328902 0.944364i \(-0.606679\pi\)
−0.328902 + 0.944364i \(0.606679\pi\)
\(648\) 0 0
\(649\) −14.9282 −0.585983
\(650\) −1.26795 + 4.73205i −0.0497331 + 0.185606i
\(651\) 0 0
\(652\) 0.196152 0.339746i 0.00768192 0.0133055i
\(653\) 12.2487i 0.479329i −0.970856 0.239665i \(-0.922963\pi\)
0.970856 0.239665i \(-0.0770375\pi\)
\(654\) 0 0
\(655\) −19.8564 −0.775854
\(656\) −2.92820 5.07180i −0.114327 0.198020i
\(657\) 0 0
\(658\) −3.26795 0.875644i −0.127398 0.0341362i
\(659\) 17.3205i 0.674711i 0.941377 + 0.337356i \(0.109532\pi\)
−0.941377 + 0.337356i \(0.890468\pi\)
\(660\) 0 0
\(661\) 8.14359i 0.316749i −0.987379 0.158375i \(-0.949375\pi\)
0.987379 0.158375i \(-0.0506253\pi\)
\(662\) 5.12436 19.1244i 0.199164 0.743289i
\(663\) 0 0
\(664\) 2.53590 2.53590i 0.0984119 0.0984119i
\(665\) −0.392305 −0.0152129
\(666\) 0 0
\(667\) 42.9282i 1.66219i
\(668\) 16.9808 + 9.80385i 0.657005 + 0.379322i
\(669\) 0 0
\(670\) −14.6603 3.92820i −0.566375 0.151760i
\(671\) 17.8564 0.689339
\(672\) 0 0
\(673\) 12.5359 0.483223 0.241612 0.970373i \(-0.422324\pi\)
0.241612 + 0.970373i \(0.422324\pi\)
\(674\) −27.1244 7.26795i −1.04479 0.279951i
\(675\) 0 0
\(676\) 1.73205 + 1.00000i 0.0666173 + 0.0384615i
\(677\) 17.6077i 0.676719i −0.941017 0.338359i \(-0.890128\pi\)
0.941017 0.338359i \(-0.109872\pi\)
\(678\) 0 0
\(679\) −10.5359 −0.404331
\(680\) 6.92820 6.92820i 0.265684 0.265684i
\(681\) 0 0
\(682\) 4.00000 14.9282i 0.153168 0.571630i
\(683\) 16.9808i 0.649751i 0.945757 + 0.324875i \(0.105322\pi\)
−0.945757 + 0.324875i \(0.894678\pi\)
\(684\) 0 0
\(685\) 4.92820i 0.188297i
\(686\) −13.4641 3.60770i −0.514062 0.137742i
\(687\) 0 0
\(688\) 18.2487 10.5359i 0.695726 0.401677i
\(689\) −39.7128 −1.51294
\(690\) 0 0
\(691\) 18.0000i 0.684752i 0.939563 + 0.342376i \(0.111232\pi\)
−0.939563 + 0.342376i \(0.888768\pi\)
\(692\) 2.00000 3.46410i 0.0760286 0.131685i
\(693\) 0 0
\(694\) −0.607695 + 2.26795i −0.0230678 + 0.0860902i
\(695\) 0.535898 0.0203278
\(696\) 0 0
\(697\) 5.07180 0.192108
\(698\) 10.2487 38.2487i 0.387919 1.44774i
\(699\) 0 0
\(700\) −1.26795 0.732051i −0.0479240 0.0276689i
\(701\) 19.0718i 0.720332i −0.932888 0.360166i \(-0.882720\pi\)
0.932888 0.360166i \(-0.117280\pi\)
\(702\) 0 0
\(703\) 1.07180 0.0404236
\(704\) −16.0000 −0.603023
\(705\) 0 0
\(706\) −17.6603 4.73205i −0.664652 0.178093i
\(707\) 2.14359i 0.0806181i
\(708\) 0 0
\(709\) 12.7846i 0.480136i −0.970756 0.240068i \(-0.922830\pi\)
0.970756 0.240068i \(-0.0771698\pi\)
\(710\) 2.00000 7.46410i 0.0750587 0.280123i
\(711\) 0 0
\(712\) −17.8564 17.8564i −0.669197 0.669197i
\(713\) −33.8564 −1.26793
\(714\) 0 0
\(715\) 6.92820i 0.259100i
\(716\) −8.53590 + 14.7846i −0.319002 + 0.552527i
\(717\) 0 0
\(718\) −25.8564 6.92820i −0.964953 0.258558i
\(719\) 1.85641 0.0692323 0.0346161 0.999401i \(-0.488979\pi\)
0.0346161 + 0.999401i \(0.488979\pi\)
\(720\) 0 0
\(721\) 11.4641 0.426945
\(722\) 25.5622 + 6.84936i 0.951326 + 0.254907i
\(723\) 0 0
\(724\) −16.0000 + 27.7128i −0.594635 + 1.02994i
\(725\) 6.92820i 0.257307i
\(726\) 0 0
\(727\) −24.0526 −0.892060 −0.446030 0.895018i \(-0.647163\pi\)
−0.446030 + 0.895018i \(0.647163\pi\)
\(728\) 5.07180 5.07180i 0.187973 0.187973i
\(729\) 0 0
\(730\) −2.73205 + 10.1962i −0.101118 + 0.377377i
\(731\) 18.2487i 0.674953i
\(732\) 0 0
\(733\) 35.0718i 1.29541i −0.761893 0.647703i \(-0.775730\pi\)
0.761893 0.647703i \(-0.224270\pi\)
\(734\) 3.92820 + 1.05256i 0.144993 + 0.0388507i
\(735\) 0 0
\(736\) 9.07180 + 33.8564i 0.334391 + 1.24796i
\(737\) −21.4641 −0.790640
\(738\) 0 0
\(739\) 29.3205i 1.07857i 0.842123 + 0.539286i \(0.181306\pi\)
−0.842123 + 0.539286i \(0.818694\pi\)
\(740\) 3.46410 + 2.00000i 0.127343 + 0.0735215i
\(741\) 0 0
\(742\) 3.07180 11.4641i 0.112769 0.420860i
\(743\) −10.9808 −0.402845 −0.201423 0.979504i \(-0.564556\pi\)
−0.201423 + 0.979504i \(0.564556\pi\)
\(744\) 0 0
\(745\) −7.85641 −0.287836
\(746\) 9.41154 35.1244i 0.344581 1.28599i
\(747\) 0 0
\(748\) 6.92820 12.0000i 0.253320 0.438763i
\(749\) 2.00000i 0.0730784i
\(750\) 0 0
\(751\) 26.2487 0.957829 0.478915 0.877862i \(-0.341030\pi\)
0.478915 + 0.877862i \(0.341030\pi\)
\(752\) −6.53590 11.3205i −0.238340 0.412816i
\(753\) 0 0
\(754\) −32.7846 8.78461i −1.19395 0.319917i
\(755\) 12.3923i 0.451002i
\(756\) 0 0
\(757\) 19.0718i 0.693176i −0.938017 0.346588i \(-0.887340\pi\)
0.938017 0.346588i \(-0.112660\pi\)
\(758\) 13.2679 49.5167i 0.481914 1.79853i
\(759\) 0 0
\(760\) −1.07180 1.07180i −0.0388782 0.0388782i
\(761\) 5.71281 0.207089 0.103545 0.994625i \(-0.466982\pi\)
0.103545 + 0.994625i \(0.466982\pi\)
\(762\) 0 0
\(763\) 12.3923i 0.448632i
\(764\) −26.5359 15.3205i −0.960035 0.554277i
\(765\) 0 0
\(766\) −28.8564 7.73205i −1.04262 0.279370i
\(767\) 25.8564 0.933621
\(768\) 0 0
\(769\) 12.9282 0.466203 0.233101 0.972452i \(-0.425113\pi\)
0.233101 + 0.972452i \(0.425113\pi\)
\(770\) −2.00000 0.535898i −0.0720750 0.0193124i
\(771\) 0 0
\(772\) 0.928203 + 0.535898i 0.0334068 + 0.0192874i
\(773\) 22.3923i 0.805395i 0.915333 + 0.402698i \(0.131927\pi\)
−0.915333 + 0.402698i \(0.868073\pi\)
\(774\) 0 0
\(775\) 5.46410 0.196276
\(776\) −28.7846 28.7846i −1.03331 1.03331i
\(777\) 0 0
\(778\) 2.48334 9.26795i 0.0890320 0.332272i
\(779\) 0.784610i 0.0281116i
\(780\) 0 0
\(781\) 10.9282i 0.391042i
\(782\) −29.3205 7.85641i −1.04850 0.280945i
\(783\) 0 0
\(784\) −12.9282 22.3923i −0.461722 0.799725i
\(785\) 3.07180 0.109637
\(786\) 0 0
\(787\) 16.5885i 0.591315i 0.955294 + 0.295657i \(0.0955387\pi\)
−0.955294 + 0.295657i \(0.904461\pi\)
\(788\) −19.4641 + 33.7128i −0.693380 + 1.20097i
\(789\) 0 0
\(790\) 0.392305 1.46410i 0.0139576 0.0520904i
\(791\) 9.46410 0.336505
\(792\) 0 0
\(793\) −30.9282 −1.09829
\(794\) −11.8038 + 44.0526i −0.418903 + 1.56337i
\(795\) 0 0
\(796\) −3.21539 1.85641i −0.113966 0.0657986i
\(797\) 50.1051i 1.77481i −0.460986 0.887407i \(-0.652504\pi\)
0.460986 0.887407i \(-0.347496\pi\)
\(798\) 0 0
\(799\) 11.3205 0.400491
\(800\) −1.46410 5.46410i −0.0517638 0.193185i
\(801\) 0 0
\(802\) 10.7321 + 2.87564i 0.378962 + 0.101543i
\(803\) 14.9282i 0.526805i
\(804\) 0 0
\(805\) 4.53590i 0.159869i
\(806\) −6.92820 + 25.8564i −0.244036 + 0.910753i
\(807\) 0 0
\(808\) 5.85641 5.85641i 0.206028 0.206028i
\(809\) −23.8564 −0.838747 −0.419373 0.907814i \(-0.637750\pi\)
−0.419373 + 0.907814i \(0.637750\pi\)
\(810\) 0 0
\(811\) 28.9282i 1.01581i −0.861414 0.507903i \(-0.830421\pi\)
0.861414 0.507903i \(-0.169579\pi\)
\(812\) 5.07180 8.78461i 0.177985 0.308279i
\(813\) 0 0
\(814\) 5.46410 + 1.46410i 0.191517 + 0.0513167i
\(815\) 0.196152 0.00687092
\(816\) 0 0
\(817\) 2.82309 0.0987673
\(818\) −15.4641 4.14359i −0.540690 0.144877i
\(819\) 0 0
\(820\) 1.46410 2.53590i 0.0511286 0.0885574i
\(821\) 34.7846i 1.21399i −0.794705 0.606996i \(-0.792375\pi\)
0.794705 0.606996i \(-0.207625\pi\)
\(822\) 0 0
\(823\) −9.12436 −0.318055 −0.159028 0.987274i \(-0.550836\pi\)
−0.159028 + 0.987274i \(0.550836\pi\)
\(824\) 31.3205 + 31.3205i 1.09110 + 1.09110i
\(825\) 0 0
\(826\) −2.00000 + 7.46410i −0.0695889 + 0.259709i
\(827\) 23.1244i 0.804113i −0.915615 0.402056i \(-0.868296\pi\)
0.915615 0.402056i \(-0.131704\pi\)
\(828\) 0 0
\(829\) 28.9282i 1.00472i 0.864659 + 0.502359i \(0.167534\pi\)
−0.864659 + 0.502359i \(0.832466\pi\)
\(830\) 1.73205 + 0.464102i 0.0601204 + 0.0161092i
\(831\) 0 0
\(832\) 27.7128 0.960769
\(833\) 22.3923 0.775847
\(834\) 0 0
\(835\) 9.80385i 0.339276i
\(836\) −1.85641 1.07180i −0.0642052 0.0370689i
\(837\) 0 0
\(838\) 6.73205 25.1244i 0.232555 0.867906i
\(839\) −24.7846 −0.855660 −0.427830 0.903859i \(-0.640722\pi\)
−0.427830 + 0.903859i \(0.640722\pi\)
\(840\) 0 0
\(841\) −19.0000 −0.655172
\(842\) −0.0525589 + 0.196152i −0.00181130 + 0.00675986i
\(843\) 0 0
\(844\) −26.7846 + 46.3923i −0.921964 + 1.59689i
\(845\) 1.00000i 0.0344010i
\(846\) 0 0
\(847\) 5.12436 0.176075
\(848\) 39.7128 22.9282i 1.36374 0.787358i
\(849\) 0 0
\(850\) 4.73205 + 1.26795i 0.162308 + 0.0434903i
\(851\) 12.3923i 0.424803i
\(852\) 0 0
\(853\) 21.6077i 0.739833i −0.929065 0.369917i \(-0.879386\pi\)
0.929065 0.369917i \(-0.120614\pi\)
\(854\) 2.39230 8.92820i 0.0818630 0.305517i
\(855\) 0 0
\(856\) 5.46410 5.46410i 0.186759 0.186759i
\(857\) 19.8564 0.678282 0.339141 0.940736i \(-0.389864\pi\)
0.339141 + 0.940736i \(0.389864\pi\)
\(858\) 0 0
\(859\) 28.2487i 0.963834i 0.876217 + 0.481917i \(0.160059\pi\)
−0.876217 + 0.481917i \(0.839941\pi\)
\(860\) 9.12436 + 5.26795i 0.311138 + 0.179636i
\(861\) 0 0
\(862\) 29.3205 + 7.85641i 0.998660 + 0.267590i
\(863\) −47.6603 −1.62237 −0.811187 0.584787i \(-0.801178\pi\)
−0.811187 + 0.584787i \(0.801178\pi\)
\(864\) 0 0
\(865\) 2.00000 0.0680020
\(866\) −26.5885 7.12436i −0.903513 0.242095i
\(867\) 0 0
\(868\) −6.92820 4.00000i −0.235159 0.135769i
\(869\) 2.14359i 0.0727164i
\(870\) 0 0
\(871\) 37.1769 1.25969
\(872\) −33.8564 + 33.8564i −1.14652 + 1.14652i
\(873\) 0 0
\(874\) −1.21539 + 4.53590i −0.0411112 + 0.153429i
\(875\) 0.732051i 0.0247478i
\(876\) 0 0
\(877\) 1.71281i 0.0578376i −0.999582 0.0289188i \(-0.990794\pi\)
0.999582 0.0289188i \(-0.00920642\pi\)
\(878\) 55.7128 + 14.9282i 1.88022 + 0.503802i
\(879\) 0 0
\(880\) −4.00000 6.92820i −0.134840 0.233550i
\(881\) −9.46410 −0.318854 −0.159427 0.987210i \(-0.550965\pi\)
−0.159427 + 0.987210i \(0.550965\pi\)
\(882\) 0 0
\(883\) 27.9090i 0.939211i −0.882876 0.469606i \(-0.844396\pi\)
0.882876 0.469606i \(-0.155604\pi\)
\(884\) −12.0000 + 20.7846i −0.403604 + 0.699062i
\(885\) 0 0
\(886\) 7.67949 28.6603i 0.257998 0.962860i
\(887\) 13.9090 0.467017 0.233509 0.972355i \(-0.424979\pi\)
0.233509 + 0.972355i \(0.424979\pi\)
\(888\) 0 0
\(889\) 12.2487 0.410809
\(890\) 3.26795 12.1962i 0.109542 0.408816i
\(891\) 0 0
\(892\) −10.0526 5.80385i −0.336585 0.194327i
\(893\) 1.75129i 0.0586046i
\(894\) 0 0
\(895\) −8.53590 −0.285324
\(896\) −2.14359 + 8.00000i −0.0716124 + 0.267261i
\(897\) 0 0
\(898\) 31.8564 + 8.53590i 1.06306 + 0.284847i
\(899\) 37.8564i 1.26258i
\(900\) 0 0
\(901\) 39.7128i 1.32303i
\(902\) 1.07180 4.00000i 0.0356869 0.133185i
\(903\) 0 0
\(904\) 25.8564 + 25.8564i 0.859971 + 0.859971i
\(905\) −16.0000 −0.531858
\(906\) 0 0
\(907\) 4.87564i 0.161893i 0.996718 + 0.0809466i \(0.0257943\pi\)
−0.996718 + 0.0809466i \(0.974206\pi\)
\(908\) 10.0526 17.4115i 0.333606 0.577822i
\(909\) 0 0
\(910\) 3.46410 + 0.928203i 0.114834 + 0.0307696i
\(911\) 49.1769 1.62930 0.814652 0.579950i \(-0.196928\pi\)
0.814652 + 0.579950i \(0.196928\pi\)
\(912\) 0 0
\(913\) 2.53590 0.0839260
\(914\) −36.5885 9.80385i −1.21024 0.324282i
\(915\) 0 0
\(916\) 4.00000 6.92820i 0.132164 0.228914i
\(917\) 14.5359i 0.480018i
\(918\) 0 0
\(919\) −38.9282 −1.28412 −0.642061 0.766653i \(-0.721921\pi\)
−0.642061 + 0.766653i \(0.721921\pi\)
\(920\) −12.3923 + 12.3923i −0.408562 + 0.408562i
\(921\) 0 0
\(922\) −4.00000 + 14.9282i −0.131733 + 0.491634i
\(923\) 18.9282i 0.623029i
\(924\) 0 0
\(925\) 2.00000i 0.0657596i
\(926\) −15.3923 4.12436i −0.505823 0.135535i
\(927\) 0 0
\(928\) 37.8564 10.1436i 1.24270 0.332980i
\(929\) 17.4641 0.572979 0.286489 0.958083i \(-0.407512\pi\)
0.286489 + 0.958083i \(0.407512\pi\)
\(930\) 0 0
\(931\) 3.46410i 0.113531i
\(932\) 9.21539 + 5.32051i 0.301860 + 0.174279i
\(933\) 0 0
\(934\) −9.39230 + 35.0526i −0.307326 + 1.14695i
\(935\) 6.92820 0.226576
\(936\) 0 0
\(937\) 4.24871 0.138799 0.0693997 0.997589i \(-0.477892\pi\)
0.0693997 + 0.997589i \(0.477892\pi\)
\(938\) −2.87564 + 10.7321i −0.0938931 + 0.350414i
\(939\) 0 0
\(940\) 3.26795 5.66025i 0.106589 0.184617i
\(941\) 32.0000i 1.04317i 0.853199 + 0.521585i \(0.174659\pi\)
−0.853199 + 0.521585i \(0.825341\pi\)
\(942\) 0 0
\(943\) −9.07180 −0.295418
\(944\) −25.8564 + 14.9282i −0.841554 + 0.485872i
\(945\) 0 0
\(946\) 14.3923 + 3.85641i 0.467934 + 0.125383i
\(947\) 3.12436i 0.101528i 0.998711 + 0.0507640i \(0.0161656\pi\)
−0.998711 + 0.0507640i \(0.983834\pi\)
\(948\) 0 0
\(949\) 25.8564i 0.839334i
\(950\) 0.196152 0.732051i 0.00636402 0.0237509i
\(951\) 0 0
\(952\) −5.07180 5.07180i −0.164378 0.164378i
\(953\) 17.2154 0.557661 0.278831 0.960340i \(-0.410053\pi\)
0.278831 + 0.960340i \(0.410053\pi\)
\(954\) 0 0
\(955\) 15.3205i 0.495760i
\(956\) 34.6410 + 20.0000i 1.12037 + 0.646846i
\(957\) 0 0
\(958\) −8.00000 2.14359i −0.258468 0.0692564i
\(959\) −3.60770 −0.116499
\(960\) 0 0
\(961\) −1.14359 −0.0368901
\(962\) −9.46410 2.53590i −0.305135 0.0817606i
\(963\) 0 0
\(964\) 28.3923 + 16.3923i 0.914455 + 0.527961i
\(965\) 0.535898i 0.0172512i
\(966\) 0 0
\(967\) 16.3397 0.525451 0.262725 0.964871i \(-0.415379\pi\)
0.262725 + 0.964871i \(0.415379\pi\)
\(968\) 14.0000 + 14.0000i 0.449977 + 0.449977i
\(969\) 0 0
\(970\) 5.26795 19.6603i 0.169144 0.631253i
\(971\) 36.9282i 1.18508i −0.805540 0.592541i \(-0.798125\pi\)
0.805540 0.592541i \(-0.201875\pi\)
\(972\) 0 0
\(973\) 0.392305i 0.0125767i
\(974\) 9.00000 + 2.41154i 0.288379 + 0.0772708i
\(975\) 0 0
\(976\) 30.9282 17.8564i 0.989988 0.571570i
\(977\) 24.5359 0.784973 0.392486 0.919758i \(-0.371615\pi\)
0.392486 + 0.919758i \(0.371615\pi\)
\(978\) 0 0
\(979\) 17.8564i 0.570693i
\(980\) 6.46410 11.1962i 0.206488 0.357648i
\(981\) 0 0
\(982\) −6.19615 + 23.1244i −0.197727 + 0.737928i
\(983\) 48.7321 1.55431 0.777156 0.629309i \(-0.216662\pi\)
0.777156 + 0.629309i \(0.216662\pi\)
\(984\) 0 0
\(985\) −19.4641 −0.620178
\(986\) −8.78461 + 32.7846i −0.279759 + 1.04407i
\(987\) 0 0
\(988\) 3.21539 + 1.85641i 0.102295 + 0.0590602i
\(989\) 32.6410i 1.03792i
\(990\) 0 0
\(991\) 41.4641 1.31715 0.658575 0.752515i \(-0.271159\pi\)
0.658575 + 0.752515i \(0.271159\pi\)
\(992\) −8.00000 29.8564i −0.254000 0.947942i
\(993\) 0 0
\(994\) −5.46410 1.46410i −0.173311 0.0464385i
\(995\) 1.85641i 0.0588520i
\(996\) 0 0
\(997\) 11.1769i 0.353976i −0.984213 0.176988i \(-0.943365\pi\)
0.984213 0.176988i \(-0.0566354\pi\)
\(998\) −11.5167 + 42.9808i −0.364554 + 1.36053i
\(999\) 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 360.2.k.e.181.4 4
3.2 odd 2 40.2.d.a.21.1 4
4.3 odd 2 1440.2.k.e.721.3 4
5.2 odd 4 1800.2.d.p.1549.2 4
5.3 odd 4 1800.2.d.l.1549.3 4
5.4 even 2 1800.2.k.j.901.1 4
8.3 odd 2 1440.2.k.e.721.1 4
8.5 even 2 inner 360.2.k.e.181.3 4
12.11 even 2 160.2.d.a.81.1 4
15.2 even 4 200.2.f.c.149.3 4
15.8 even 4 200.2.f.e.149.2 4
15.14 odd 2 200.2.d.f.101.4 4
20.3 even 4 7200.2.d.n.2449.3 4
20.7 even 4 7200.2.d.o.2449.2 4
20.19 odd 2 7200.2.k.j.3601.3 4
24.5 odd 2 40.2.d.a.21.2 yes 4
24.11 even 2 160.2.d.a.81.4 4
40.3 even 4 7200.2.d.o.2449.3 4
40.13 odd 4 1800.2.d.p.1549.1 4
40.19 odd 2 7200.2.k.j.3601.4 4
40.27 even 4 7200.2.d.n.2449.2 4
40.29 even 2 1800.2.k.j.901.2 4
40.37 odd 4 1800.2.d.l.1549.4 4
48.5 odd 4 1280.2.a.o.1.2 2
48.11 even 4 1280.2.a.d.1.1 2
48.29 odd 4 1280.2.a.a.1.1 2
48.35 even 4 1280.2.a.n.1.2 2
60.23 odd 4 800.2.f.e.49.4 4
60.47 odd 4 800.2.f.c.49.1 4
60.59 even 2 800.2.d.e.401.4 4
120.29 odd 2 200.2.d.f.101.3 4
120.53 even 4 200.2.f.c.149.4 4
120.59 even 2 800.2.d.e.401.1 4
120.77 even 4 200.2.f.e.149.1 4
120.83 odd 4 800.2.f.c.49.2 4
120.107 odd 4 800.2.f.e.49.3 4
240.29 odd 4 6400.2.a.ce.1.2 2
240.59 even 4 6400.2.a.cj.1.2 2
240.149 odd 4 6400.2.a.z.1.1 2
240.179 even 4 6400.2.a.be.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.2.d.a.21.1 4 3.2 odd 2
40.2.d.a.21.2 yes 4 24.5 odd 2
160.2.d.a.81.1 4 12.11 even 2
160.2.d.a.81.4 4 24.11 even 2
200.2.d.f.101.3 4 120.29 odd 2
200.2.d.f.101.4 4 15.14 odd 2
200.2.f.c.149.3 4 15.2 even 4
200.2.f.c.149.4 4 120.53 even 4
200.2.f.e.149.1 4 120.77 even 4
200.2.f.e.149.2 4 15.8 even 4
360.2.k.e.181.3 4 8.5 even 2 inner
360.2.k.e.181.4 4 1.1 even 1 trivial
800.2.d.e.401.1 4 120.59 even 2
800.2.d.e.401.4 4 60.59 even 2
800.2.f.c.49.1 4 60.47 odd 4
800.2.f.c.49.2 4 120.83 odd 4
800.2.f.e.49.3 4 120.107 odd 4
800.2.f.e.49.4 4 60.23 odd 4
1280.2.a.a.1.1 2 48.29 odd 4
1280.2.a.d.1.1 2 48.11 even 4
1280.2.a.n.1.2 2 48.35 even 4
1280.2.a.o.1.2 2 48.5 odd 4
1440.2.k.e.721.1 4 8.3 odd 2
1440.2.k.e.721.3 4 4.3 odd 2
1800.2.d.l.1549.3 4 5.3 odd 4
1800.2.d.l.1549.4 4 40.37 odd 4
1800.2.d.p.1549.1 4 40.13 odd 4
1800.2.d.p.1549.2 4 5.2 odd 4
1800.2.k.j.901.1 4 5.4 even 2
1800.2.k.j.901.2 4 40.29 even 2
6400.2.a.z.1.1 2 240.149 odd 4
6400.2.a.be.1.1 2 240.179 even 4
6400.2.a.ce.1.2 2 240.29 odd 4
6400.2.a.cj.1.2 2 240.59 even 4
7200.2.d.n.2449.2 4 40.27 even 4
7200.2.d.n.2449.3 4 20.3 even 4
7200.2.d.o.2449.2 4 20.7 even 4
7200.2.d.o.2449.3 4 40.3 even 4
7200.2.k.j.3601.3 4 20.19 odd 2
7200.2.k.j.3601.4 4 40.19 odd 2