Properties

Label 200.2.f.d.149.2
Level $200$
Weight $2$
Character 200.149
Analytic conductor $1.597$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,2,Mod(149,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 200.f (of order \(2\), degree \(1\), 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: \(1.59700804043\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 3x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.2
Root \(-1.32288 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 200.149
Dual form 200.2.f.d.149.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32288 + 0.500000i) q^{2} +2.64575 q^{3} +(1.50000 - 1.32288i) q^{4} +(-3.50000 + 1.32288i) q^{6} +4.00000i q^{7} +(-1.32288 + 2.50000i) q^{8} +4.00000 q^{9} +O(q^{10})\) \(q+(-1.32288 + 0.500000i) q^{2} +2.64575 q^{3} +(1.50000 - 1.32288i) q^{4} +(-3.50000 + 1.32288i) q^{6} +4.00000i q^{7} +(-1.32288 + 2.50000i) q^{8} +4.00000 q^{9} -2.64575i q^{11} +(3.96863 - 3.50000i) q^{12} +(-2.00000 - 5.29150i) q^{14} +(0.500000 - 3.96863i) q^{16} -3.00000i q^{17} +(-5.29150 + 2.00000i) q^{18} +2.64575i q^{19} +10.5830i q^{21} +(1.32288 + 3.50000i) q^{22} -4.00000i q^{23} +(-3.50000 + 6.61438i) q^{24} +2.64575 q^{27} +(5.29150 + 6.00000i) q^{28} +4.00000 q^{31} +(1.32288 + 5.50000i) q^{32} -7.00000i q^{33} +(1.50000 + 3.96863i) q^{34} +(6.00000 - 5.29150i) q^{36} -10.5830 q^{37} +(-1.32288 - 3.50000i) q^{38} -5.00000 q^{41} +(-5.29150 - 14.0000i) q^{42} +5.29150 q^{43} +(-3.50000 - 3.96863i) q^{44} +(2.00000 + 5.29150i) q^{46} -8.00000i q^{47} +(1.32288 - 10.5000i) q^{48} -9.00000 q^{49} -7.93725i q^{51} -10.5830 q^{53} +(-3.50000 + 1.32288i) q^{54} +(-10.0000 - 5.29150i) q^{56} +7.00000i q^{57} +5.29150i q^{59} -10.5830i q^{61} +(-5.29150 + 2.00000i) q^{62} +16.0000i q^{63} +(-4.50000 - 6.61438i) q^{64} +(3.50000 + 9.26013i) q^{66} +7.93725 q^{67} +(-3.96863 - 4.50000i) q^{68} -10.5830i q^{69} +8.00000 q^{71} +(-5.29150 + 10.0000i) q^{72} +7.00000i q^{73} +(14.0000 - 5.29150i) q^{74} +(3.50000 + 3.96863i) q^{76} +10.5830 q^{77} -4.00000 q^{79} -5.00000 q^{81} +(6.61438 - 2.50000i) q^{82} -7.93725 q^{83} +(14.0000 + 15.8745i) q^{84} +(-7.00000 + 2.64575i) q^{86} +(6.61438 + 3.50000i) q^{88} +1.00000 q^{89} +(-5.29150 - 6.00000i) q^{92} +10.5830 q^{93} +(4.00000 + 10.5830i) q^{94} +(3.50000 + 14.5516i) q^{96} -2.00000i q^{97} +(11.9059 - 4.50000i) q^{98} -10.5830i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{4} - 14 q^{6} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{4} - 14 q^{6} + 16 q^{9} - 8 q^{14} + 2 q^{16} - 14 q^{24} + 16 q^{31} + 6 q^{34} + 24 q^{36} - 20 q^{41} - 14 q^{44} + 8 q^{46} - 36 q^{49} - 14 q^{54} - 40 q^{56} - 18 q^{64} + 14 q^{66} + 32 q^{71} + 56 q^{74} + 14 q^{76} - 16 q^{79} - 20 q^{81} + 56 q^{84} - 28 q^{86} + 4 q^{89} + 16 q^{94} + 14 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(177\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32288 + 0.500000i −0.935414 + 0.353553i
\(3\) 2.64575 1.52753 0.763763 0.645497i \(-0.223350\pi\)
0.763763 + 0.645497i \(0.223350\pi\)
\(4\) 1.50000 1.32288i 0.750000 0.661438i
\(5\) 0 0
\(6\) −3.50000 + 1.32288i −1.42887 + 0.540062i
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) −1.32288 + 2.50000i −0.467707 + 0.883883i
\(9\) 4.00000 1.33333
\(10\) 0 0
\(11\) 2.64575i 0.797724i −0.917011 0.398862i \(-0.869405\pi\)
0.917011 0.398862i \(-0.130595\pi\)
\(12\) 3.96863 3.50000i 1.14564 1.01036i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.00000 5.29150i −0.534522 1.41421i
\(15\) 0 0
\(16\) 0.500000 3.96863i 0.125000 0.992157i
\(17\) 3.00000i 0.727607i −0.931476 0.363803i \(-0.881478\pi\)
0.931476 0.363803i \(-0.118522\pi\)
\(18\) −5.29150 + 2.00000i −1.24722 + 0.471405i
\(19\) 2.64575i 0.606977i 0.952835 + 0.303488i \(0.0981514\pi\)
−0.952835 + 0.303488i \(0.901849\pi\)
\(20\) 0 0
\(21\) 10.5830i 2.30940i
\(22\) 1.32288 + 3.50000i 0.282038 + 0.746203i
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) −3.50000 + 6.61438i −0.714435 + 1.35015i
\(25\) 0 0
\(26\) 0 0
\(27\) 2.64575 0.509175
\(28\) 5.29150 + 6.00000i 1.00000 + 1.13389i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.32288 + 5.50000i 0.233854 + 0.972272i
\(33\) 7.00000i 1.21854i
\(34\) 1.50000 + 3.96863i 0.257248 + 0.680614i
\(35\) 0 0
\(36\) 6.00000 5.29150i 1.00000 0.881917i
\(37\) −10.5830 −1.73984 −0.869918 0.493197i \(-0.835828\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) −1.32288 3.50000i −0.214599 0.567775i
\(39\) 0 0
\(40\) 0 0
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) −5.29150 14.0000i −0.816497 2.16025i
\(43\) 5.29150 0.806947 0.403473 0.914991i \(-0.367803\pi\)
0.403473 + 0.914991i \(0.367803\pi\)
\(44\) −3.50000 3.96863i −0.527645 0.598293i
\(45\) 0 0
\(46\) 2.00000 + 5.29150i 0.294884 + 0.780189i
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 1.32288 10.5000i 0.190941 1.51554i
\(49\) −9.00000 −1.28571
\(50\) 0 0
\(51\) 7.93725i 1.11144i
\(52\) 0 0
\(53\) −10.5830 −1.45369 −0.726844 0.686803i \(-0.759014\pi\)
−0.726844 + 0.686803i \(0.759014\pi\)
\(54\) −3.50000 + 1.32288i −0.476290 + 0.180021i
\(55\) 0 0
\(56\) −10.0000 5.29150i −1.33631 0.707107i
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) 5.29150i 0.688895i 0.938806 + 0.344447i \(0.111934\pi\)
−0.938806 + 0.344447i \(0.888066\pi\)
\(60\) 0 0
\(61\) 10.5830i 1.35501i −0.735516 0.677507i \(-0.763060\pi\)
0.735516 0.677507i \(-0.236940\pi\)
\(62\) −5.29150 + 2.00000i −0.672022 + 0.254000i
\(63\) 16.0000i 2.01581i
\(64\) −4.50000 6.61438i −0.562500 0.826797i
\(65\) 0 0
\(66\) 3.50000 + 9.26013i 0.430820 + 1.13984i
\(67\) 7.93725 0.969690 0.484845 0.874600i \(-0.338876\pi\)
0.484845 + 0.874600i \(0.338876\pi\)
\(68\) −3.96863 4.50000i −0.481267 0.545705i
\(69\) 10.5830i 1.27404i
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −5.29150 + 10.0000i −0.623610 + 1.17851i
\(73\) 7.00000i 0.819288i 0.912245 + 0.409644i \(0.134347\pi\)
−0.912245 + 0.409644i \(0.865653\pi\)
\(74\) 14.0000 5.29150i 1.62747 0.615125i
\(75\) 0 0
\(76\) 3.50000 + 3.96863i 0.401478 + 0.455233i
\(77\) 10.5830 1.20605
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −5.00000 −0.555556
\(82\) 6.61438 2.50000i 0.730436 0.276079i
\(83\) −7.93725 −0.871227 −0.435613 0.900134i \(-0.643469\pi\)
−0.435613 + 0.900134i \(0.643469\pi\)
\(84\) 14.0000 + 15.8745i 1.52753 + 1.73205i
\(85\) 0 0
\(86\) −7.00000 + 2.64575i −0.754829 + 0.285299i
\(87\) 0 0
\(88\) 6.61438 + 3.50000i 0.705095 + 0.373101i
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.29150 6.00000i −0.551677 0.625543i
\(93\) 10.5830 1.09741
\(94\) 4.00000 + 10.5830i 0.412568 + 1.09155i
\(95\) 0 0
\(96\) 3.50000 + 14.5516i 0.357217 + 1.48517i
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 11.9059 4.50000i 1.20268 0.454569i
\(99\) 10.5830i 1.06363i
\(100\) 0 0
\(101\) 10.5830i 1.05305i 0.850160 + 0.526524i \(0.176505\pi\)
−0.850160 + 0.526524i \(0.823495\pi\)
\(102\) 3.96863 + 10.5000i 0.392953 + 1.03965i
\(103\) 8.00000i 0.788263i −0.919054 0.394132i \(-0.871045\pi\)
0.919054 0.394132i \(-0.128955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 14.0000 5.29150i 1.35980 0.513956i
\(107\) −2.64575 −0.255774 −0.127887 0.991789i \(-0.540820\pi\)
−0.127887 + 0.991789i \(0.540820\pi\)
\(108\) 3.96863 3.50000i 0.381881 0.336788i
\(109\) 10.5830i 1.01367i 0.862044 + 0.506834i \(0.169184\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) −28.0000 −2.65764
\(112\) 15.8745 + 2.00000i 1.50000 + 0.188982i
\(113\) 15.0000i 1.41108i 0.708669 + 0.705541i \(0.249296\pi\)
−0.708669 + 0.705541i \(0.750704\pi\)
\(114\) −3.50000 9.26013i −0.327805 0.867291i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −2.64575 7.00000i −0.243561 0.644402i
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) 4.00000 0.363636
\(122\) 5.29150 + 14.0000i 0.479070 + 1.26750i
\(123\) −13.2288 −1.19280
\(124\) 6.00000 5.29150i 0.538816 0.475191i
\(125\) 0 0
\(126\) −8.00000 21.1660i −0.712697 1.88562i
\(127\) 12.0000i 1.06483i 0.846484 + 0.532414i \(0.178715\pi\)
−0.846484 + 0.532414i \(0.821285\pi\)
\(128\) 9.26013 + 6.50000i 0.818488 + 0.574524i
\(129\) 14.0000 1.23263
\(130\) 0 0
\(131\) 15.8745i 1.38696i 0.720475 + 0.693481i \(0.243924\pi\)
−0.720475 + 0.693481i \(0.756076\pi\)
\(132\) −9.26013 10.5000i −0.805991 0.913908i
\(133\) −10.5830 −0.917663
\(134\) −10.5000 + 3.96863i −0.907062 + 0.342837i
\(135\) 0 0
\(136\) 7.50000 + 3.96863i 0.643120 + 0.340307i
\(137\) 19.0000i 1.62328i −0.584158 0.811640i \(-0.698575\pi\)
0.584158 0.811640i \(-0.301425\pi\)
\(138\) 5.29150 + 14.0000i 0.450443 + 1.19176i
\(139\) 18.5203i 1.57087i −0.618945 0.785434i \(-0.712440\pi\)
0.618945 0.785434i \(-0.287560\pi\)
\(140\) 0 0
\(141\) 21.1660i 1.78250i
\(142\) −10.5830 + 4.00000i −0.888106 + 0.335673i
\(143\) 0 0
\(144\) 2.00000 15.8745i 0.166667 1.32288i
\(145\) 0 0
\(146\) −3.50000 9.26013i −0.289662 0.766374i
\(147\) −23.8118 −1.96396
\(148\) −15.8745 + 14.0000i −1.30488 + 1.15079i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) −6.61438 3.50000i −0.536497 0.283887i
\(153\) 12.0000i 0.970143i
\(154\) −14.0000 + 5.29150i −1.12815 + 0.426401i
\(155\) 0 0
\(156\) 0 0
\(157\) 10.5830 0.844616 0.422308 0.906452i \(-0.361220\pi\)
0.422308 + 0.906452i \(0.361220\pi\)
\(158\) 5.29150 2.00000i 0.420969 0.159111i
\(159\) −28.0000 −2.22054
\(160\) 0 0
\(161\) 16.0000 1.26098
\(162\) 6.61438 2.50000i 0.519675 0.196419i
\(163\) 13.2288 1.03616 0.518078 0.855333i \(-0.326648\pi\)
0.518078 + 0.855333i \(0.326648\pi\)
\(164\) −7.50000 + 6.61438i −0.585652 + 0.516496i
\(165\) 0 0
\(166\) 10.5000 3.96863i 0.814958 0.308025i
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) −26.4575 14.0000i −2.04124 1.08012i
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 10.5830i 0.809303i
\(172\) 7.93725 7.00000i 0.605210 0.533745i
\(173\) 21.1660 1.60922 0.804611 0.593802i \(-0.202374\pi\)
0.804611 + 0.593802i \(0.202374\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −10.5000 1.32288i −0.791467 0.0997155i
\(177\) 14.0000i 1.05230i
\(178\) −1.32288 + 0.500000i −0.0991537 + 0.0374766i
\(179\) 23.8118i 1.77977i 0.456180 + 0.889887i \(0.349217\pi\)
−0.456180 + 0.889887i \(0.650783\pi\)
\(180\) 0 0
\(181\) 10.5830i 0.786629i −0.919404 0.393314i \(-0.871328\pi\)
0.919404 0.393314i \(-0.128672\pi\)
\(182\) 0 0
\(183\) 28.0000i 2.06982i
\(184\) 10.0000 + 5.29150i 0.737210 + 0.390095i
\(185\) 0 0
\(186\) −14.0000 + 5.29150i −1.02653 + 0.387992i
\(187\) −7.93725 −0.580429
\(188\) −10.5830 12.0000i −0.771845 0.875190i
\(189\) 10.5830i 0.769800i
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) −11.9059 17.5000i −0.859233 1.26295i
\(193\) 5.00000i 0.359908i −0.983675 0.179954i \(-0.942405\pi\)
0.983675 0.179954i \(-0.0575949\pi\)
\(194\) 1.00000 + 2.64575i 0.0717958 + 0.189954i
\(195\) 0 0
\(196\) −13.5000 + 11.9059i −0.964286 + 0.850420i
\(197\) 10.5830 0.754008 0.377004 0.926212i \(-0.376954\pi\)
0.377004 + 0.926212i \(0.376954\pi\)
\(198\) 5.29150 + 14.0000i 0.376051 + 0.994937i
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 0 0
\(201\) 21.0000 1.48123
\(202\) −5.29150 14.0000i −0.372309 0.985037i
\(203\) 0 0
\(204\) −10.5000 11.9059i −0.735147 0.833578i
\(205\) 0 0
\(206\) 4.00000 + 10.5830i 0.278693 + 0.737353i
\(207\) 16.0000i 1.11208i
\(208\) 0 0
\(209\) 7.00000 0.484200
\(210\) 0 0
\(211\) 7.93725i 0.546423i 0.961954 + 0.273212i \(0.0880859\pi\)
−0.961954 + 0.273212i \(0.911914\pi\)
\(212\) −15.8745 + 14.0000i −1.09027 + 0.961524i
\(213\) 21.1660 1.45027
\(214\) 3.50000 1.32288i 0.239255 0.0904299i
\(215\) 0 0
\(216\) −3.50000 + 6.61438i −0.238145 + 0.450051i
\(217\) 16.0000i 1.08615i
\(218\) −5.29150 14.0000i −0.358386 0.948200i
\(219\) 18.5203i 1.25148i
\(220\) 0 0
\(221\) 0 0
\(222\) 37.0405 14.0000i 2.48600 0.939618i
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) −22.0000 + 5.29150i −1.46994 + 0.353553i
\(225\) 0 0
\(226\) −7.50000 19.8431i −0.498893 1.31995i
\(227\) 15.8745 1.05363 0.526814 0.849981i \(-0.323386\pi\)
0.526814 + 0.849981i \(0.323386\pi\)
\(228\) 9.26013 + 10.5000i 0.613267 + 0.695379i
\(229\) 21.1660i 1.39869i 0.714785 + 0.699345i \(0.246525\pi\)
−0.714785 + 0.699345i \(0.753475\pi\)
\(230\) 0 0
\(231\) 28.0000 1.84226
\(232\) 0 0
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.00000 + 7.93725i 0.455661 + 0.516671i
\(237\) −10.5830 −0.687440
\(238\) −15.8745 + 6.00000i −1.02899 + 0.388922i
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) −21.0000 −1.35273 −0.676364 0.736567i \(-0.736446\pi\)
−0.676364 + 0.736567i \(0.736446\pi\)
\(242\) −5.29150 + 2.00000i −0.340151 + 0.128565i
\(243\) −21.1660 −1.35780
\(244\) −14.0000 15.8745i −0.896258 1.01626i
\(245\) 0 0
\(246\) 17.5000 6.61438i 1.11576 0.421717i
\(247\) 0 0
\(248\) −5.29150 + 10.0000i −0.336011 + 0.635001i
\(249\) −21.0000 −1.33082
\(250\) 0 0
\(251\) 7.93725i 0.500995i 0.968117 + 0.250498i \(0.0805942\pi\)
−0.968117 + 0.250498i \(0.919406\pi\)
\(252\) 21.1660 + 24.0000i 1.33333 + 1.51186i
\(253\) −10.5830 −0.665348
\(254\) −6.00000 15.8745i −0.376473 0.996055i
\(255\) 0 0
\(256\) −15.5000 3.96863i −0.968750 0.248039i
\(257\) 14.0000i 0.873296i 0.899632 + 0.436648i \(0.143834\pi\)
−0.899632 + 0.436648i \(0.856166\pi\)
\(258\) −18.5203 + 7.00000i −1.15302 + 0.435801i
\(259\) 42.3320i 2.63038i
\(260\) 0 0
\(261\) 0 0
\(262\) −7.93725 21.0000i −0.490365 1.29738i
\(263\) 12.0000i 0.739952i −0.929041 0.369976i \(-0.879366\pi\)
0.929041 0.369976i \(-0.120634\pi\)
\(264\) 17.5000 + 9.26013i 1.07705 + 0.569922i
\(265\) 0 0
\(266\) 14.0000 5.29150i 0.858395 0.324443i
\(267\) 2.64575 0.161917
\(268\) 11.9059 10.5000i 0.727267 0.641390i
\(269\) 21.1660i 1.29051i −0.763965 0.645257i \(-0.776750\pi\)
0.763965 0.645257i \(-0.223250\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) −11.9059 1.50000i −0.721900 0.0909509i
\(273\) 0 0
\(274\) 9.50000 + 25.1346i 0.573916 + 1.51844i
\(275\) 0 0
\(276\) −14.0000 15.8745i −0.842701 0.955533i
\(277\) −21.1660 −1.27174 −0.635871 0.771795i \(-0.719359\pi\)
−0.635871 + 0.771795i \(0.719359\pi\)
\(278\) 9.26013 + 24.5000i 0.555386 + 1.46941i
\(279\) 16.0000 0.957895
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 10.5830 + 28.0000i 0.630209 + 1.66738i
\(283\) 13.2288 0.786368 0.393184 0.919460i \(-0.371374\pi\)
0.393184 + 0.919460i \(0.371374\pi\)
\(284\) 12.0000 10.5830i 0.712069 0.627986i
\(285\) 0 0
\(286\) 0 0
\(287\) 20.0000i 1.18056i
\(288\) 5.29150 + 22.0000i 0.311805 + 1.29636i
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 5.29150i 0.310193i
\(292\) 9.26013 + 10.5000i 0.541908 + 0.614466i
\(293\) 10.5830 0.618266 0.309133 0.951019i \(-0.399961\pi\)
0.309133 + 0.951019i \(0.399961\pi\)
\(294\) 31.5000 11.9059i 1.83712 0.694365i
\(295\) 0 0
\(296\) 14.0000 26.4575i 0.813733 1.53781i
\(297\) 7.00000i 0.406181i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 21.1660i 1.21999i
\(302\) −5.29150 + 2.00000i −0.304492 + 0.115087i
\(303\) 28.0000i 1.60856i
\(304\) 10.5000 + 1.32288i 0.602216 + 0.0758721i
\(305\) 0 0
\(306\) 6.00000 + 15.8745i 0.342997 + 0.907485i
\(307\) −2.64575 −0.151001 −0.0755005 0.997146i \(-0.524055\pi\)
−0.0755005 + 0.997146i \(0.524055\pi\)
\(308\) 15.8745 14.0000i 0.904534 0.797724i
\(309\) 21.1660i 1.20409i
\(310\) 0 0
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 0 0
\(313\) 6.00000i 0.339140i −0.985518 0.169570i \(-0.945762\pi\)
0.985518 0.169570i \(-0.0542379\pi\)
\(314\) −14.0000 + 5.29150i −0.790066 + 0.298617i
\(315\) 0 0
\(316\) −6.00000 + 5.29150i −0.337526 + 0.297670i
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 37.0405 14.0000i 2.07713 0.785081i
\(319\) 0 0
\(320\) 0 0
\(321\) −7.00000 −0.390702
\(322\) −21.1660 + 8.00000i −1.17954 + 0.445823i
\(323\) 7.93725 0.441641
\(324\) −7.50000 + 6.61438i −0.416667 + 0.367465i
\(325\) 0 0
\(326\) −17.5000 + 6.61438i −0.969235 + 0.366337i
\(327\) 28.0000i 1.54840i
\(328\) 6.61438 12.5000i 0.365218 0.690197i
\(329\) 32.0000 1.76422
\(330\) 0 0
\(331\) 2.64575i 0.145424i −0.997353 0.0727118i \(-0.976835\pi\)
0.997353 0.0727118i \(-0.0231653\pi\)
\(332\) −11.9059 + 10.5000i −0.653420 + 0.576262i
\(333\) −42.3320 −2.31978
\(334\) 0 0
\(335\) 0 0
\(336\) 42.0000 + 5.29150i 2.29129 + 0.288675i
\(337\) 15.0000i 0.817102i −0.912735 0.408551i \(-0.866034\pi\)
0.912735 0.408551i \(-0.133966\pi\)
\(338\) 17.1974 6.50000i 0.935414 0.353553i
\(339\) 39.6863i 2.15546i
\(340\) 0 0
\(341\) 10.5830i 0.573102i
\(342\) −5.29150 14.0000i −0.286132 0.757033i
\(343\) 8.00000i 0.431959i
\(344\) −7.00000 + 13.2288i −0.377415 + 0.713247i
\(345\) 0 0
\(346\) −28.0000 + 10.5830i −1.50529 + 0.568946i
\(347\) −2.64575 −0.142031 −0.0710157 0.997475i \(-0.522624\pi\)
−0.0710157 + 0.997475i \(0.522624\pi\)
\(348\) 0 0
\(349\) 10.5830i 0.566495i −0.959047 0.283248i \(-0.908588\pi\)
0.959047 0.283248i \(-0.0914118\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 14.5516 3.50000i 0.775605 0.186551i
\(353\) 18.0000i 0.958043i 0.877803 + 0.479022i \(0.159008\pi\)
−0.877803 + 0.479022i \(0.840992\pi\)
\(354\) −7.00000 18.5203i −0.372046 0.984341i
\(355\) 0 0
\(356\) 1.50000 1.32288i 0.0794998 0.0701123i
\(357\) 31.7490 1.68034
\(358\) −11.9059 31.5000i −0.629245 1.66483i
\(359\) −36.0000 −1.90001 −0.950004 0.312239i \(-0.898921\pi\)
−0.950004 + 0.312239i \(0.898921\pi\)
\(360\) 0 0
\(361\) 12.0000 0.631579
\(362\) 5.29150 + 14.0000i 0.278115 + 0.735824i
\(363\) 10.5830 0.555464
\(364\) 0 0
\(365\) 0 0
\(366\) 14.0000 + 37.0405i 0.731792 + 1.93614i
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −15.8745 2.00000i −0.827516 0.104257i
\(369\) −20.0000 −1.04116
\(370\) 0 0
\(371\) 42.3320i 2.19777i
\(372\) 15.8745 14.0000i 0.823055 0.725866i
\(373\) −10.5830 −0.547967 −0.273984 0.961734i \(-0.588341\pi\)
−0.273984 + 0.961734i \(0.588341\pi\)
\(374\) 10.5000 3.96863i 0.542942 0.205213i
\(375\) 0 0
\(376\) 20.0000 + 10.5830i 1.03142 + 0.545777i
\(377\) 0 0
\(378\) −5.29150 14.0000i −0.272166 0.720082i
\(379\) 7.93725i 0.407709i −0.979001 0.203855i \(-0.934653\pi\)
0.979001 0.203855i \(-0.0653470\pi\)
\(380\) 0 0
\(381\) 31.7490i 1.62655i
\(382\) −5.29150 + 2.00000i −0.270737 + 0.102329i
\(383\) 36.0000i 1.83951i 0.392488 + 0.919757i \(0.371614\pi\)
−0.392488 + 0.919757i \(0.628386\pi\)
\(384\) 24.5000 + 17.1974i 1.25026 + 0.877600i
\(385\) 0 0
\(386\) 2.50000 + 6.61438i 0.127247 + 0.336663i
\(387\) 21.1660 1.07593
\(388\) −2.64575 3.00000i −0.134318 0.152302i
\(389\) 10.5830i 0.536580i 0.963338 + 0.268290i \(0.0864585\pi\)
−0.963338 + 0.268290i \(0.913542\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 11.9059 22.5000i 0.601338 1.13642i
\(393\) 42.0000i 2.11862i
\(394\) −14.0000 + 5.29150i −0.705310 + 0.266582i
\(395\) 0 0
\(396\) −14.0000 15.8745i −0.703526 0.797724i
\(397\) −21.1660 −1.06229 −0.531146 0.847280i \(-0.678238\pi\)
−0.531146 + 0.847280i \(0.678238\pi\)
\(398\) −31.7490 + 12.0000i −1.59143 + 0.601506i
\(399\) −28.0000 −1.40175
\(400\) 0 0
\(401\) 27.0000 1.34832 0.674158 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) −27.7804 + 10.5000i −1.38556 + 0.523692i
\(403\) 0 0
\(404\) 14.0000 + 15.8745i 0.696526 + 0.789786i
\(405\) 0 0
\(406\) 0 0
\(407\) 28.0000i 1.38791i
\(408\) 19.8431 + 10.5000i 0.982382 + 0.519827i
\(409\) −3.00000 −0.148340 −0.0741702 0.997246i \(-0.523631\pi\)
−0.0741702 + 0.997246i \(0.523631\pi\)
\(410\) 0 0
\(411\) 50.2693i 2.47960i
\(412\) −10.5830 12.0000i −0.521387 0.591198i
\(413\) −21.1660 −1.04151
\(414\) 8.00000 + 21.1660i 0.393179 + 1.04025i
\(415\) 0 0
\(416\) 0 0
\(417\) 49.0000i 2.39954i
\(418\) −9.26013 + 3.50000i −0.452928 + 0.171191i
\(419\) 18.5203i 0.904774i −0.891822 0.452387i \(-0.850573\pi\)
0.891822 0.452387i \(-0.149427\pi\)
\(420\) 0 0
\(421\) 21.1660i 1.03157i −0.856719 0.515784i \(-0.827501\pi\)
0.856719 0.515784i \(-0.172499\pi\)
\(422\) −3.96863 10.5000i −0.193190 0.511132i
\(423\) 32.0000i 1.55589i
\(424\) 14.0000 26.4575i 0.679900 1.28489i
\(425\) 0 0
\(426\) −28.0000 + 10.5830i −1.35660 + 0.512748i
\(427\) 42.3320 2.04859
\(428\) −3.96863 + 3.50000i −0.191831 + 0.169179i
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 1.32288 10.5000i 0.0636469 0.505181i
\(433\) 37.0000i 1.77811i −0.457804 0.889053i \(-0.651364\pi\)
0.457804 0.889053i \(-0.348636\pi\)
\(434\) −8.00000 21.1660i −0.384012 1.01600i
\(435\) 0 0
\(436\) 14.0000 + 15.8745i 0.670478 + 0.760251i
\(437\) 10.5830 0.506254
\(438\) −9.26013 24.5000i −0.442466 1.17066i
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) −36.0000 −1.71429
\(442\) 0 0
\(443\) −29.1033 −1.38274 −0.691369 0.722502i \(-0.742992\pi\)
−0.691369 + 0.722502i \(0.742992\pi\)
\(444\) −42.0000 + 37.0405i −1.99323 + 1.75787i
\(445\) 0 0
\(446\) −8.00000 21.1660i −0.378811 1.00224i
\(447\) 0 0
\(448\) 26.4575 18.0000i 1.25000 0.850420i
\(449\) −27.0000 −1.27421 −0.637104 0.770778i \(-0.719868\pi\)
−0.637104 + 0.770778i \(0.719868\pi\)
\(450\) 0 0
\(451\) 13.2288i 0.622918i
\(452\) 19.8431 + 22.5000i 0.933343 + 1.05831i
\(453\) 10.5830 0.497233
\(454\) −21.0000 + 7.93725i −0.985579 + 0.372514i
\(455\) 0 0
\(456\) −17.5000 9.26013i −0.819513 0.433645i
\(457\) 27.0000i 1.26301i −0.775373 0.631503i \(-0.782438\pi\)
0.775373 0.631503i \(-0.217562\pi\)
\(458\) −10.5830 28.0000i −0.494511 1.30835i
\(459\) 7.93725i 0.370479i
\(460\) 0 0
\(461\) 42.3320i 1.97160i 0.167927 + 0.985799i \(0.446293\pi\)
−0.167927 + 0.985799i \(0.553707\pi\)
\(462\) −37.0405 + 14.0000i −1.72328 + 0.651339i
\(463\) 8.00000i 0.371792i 0.982569 + 0.185896i \(0.0595187\pi\)
−0.982569 + 0.185896i \(0.940481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 3.00000 + 7.93725i 0.138972 + 0.367686i
\(467\) −26.4575 −1.22431 −0.612154 0.790739i \(-0.709697\pi\)
−0.612154 + 0.790739i \(0.709697\pi\)
\(468\) 0 0
\(469\) 31.7490i 1.46603i
\(470\) 0 0
\(471\) 28.0000 1.29017
\(472\) −13.2288 7.00000i −0.608903 0.322201i
\(473\) 14.0000i 0.643721i
\(474\) 14.0000 5.29150i 0.643041 0.243047i
\(475\) 0 0
\(476\) 18.0000 15.8745i 0.825029 0.727607i
\(477\) −42.3320 −1.93825
\(478\) −10.5830 + 4.00000i −0.484055 + 0.182956i
\(479\) −4.00000 −0.182765 −0.0913823 0.995816i \(-0.529129\pi\)
−0.0913823 + 0.995816i \(0.529129\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 27.7804 10.5000i 1.26536 0.478262i
\(483\) 42.3320 1.92617
\(484\) 6.00000 5.29150i 0.272727 0.240523i
\(485\) 0 0
\(486\) 28.0000 10.5830i 1.27011 0.480055i
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 26.4575 + 14.0000i 1.19768 + 0.633750i
\(489\) 35.0000 1.58275
\(490\) 0 0
\(491\) 5.29150i 0.238802i −0.992846 0.119401i \(-0.961903\pi\)
0.992846 0.119401i \(-0.0380974\pi\)
\(492\) −19.8431 + 17.5000i −0.894598 + 0.788961i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.00000 15.8745i 0.0898027 0.712786i
\(497\) 32.0000i 1.43540i
\(498\) 27.7804 10.5000i 1.24487 0.470516i
\(499\) 26.4575i 1.18440i 0.805791 + 0.592200i \(0.201741\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −3.96863 10.5000i −0.177128 0.468638i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −40.0000 21.1660i −1.78174 0.942809i
\(505\) 0 0
\(506\) 14.0000 5.29150i 0.622376 0.235236i
\(507\) −34.3948 −1.52753
\(508\) 15.8745 + 18.0000i 0.704317 + 0.798621i
\(509\) 31.7490i 1.40725i −0.710571 0.703625i \(-0.751563\pi\)
0.710571 0.703625i \(-0.248437\pi\)
\(510\) 0 0
\(511\) −28.0000 −1.23865
\(512\) 22.4889 2.50000i 0.993878 0.110485i
\(513\) 7.00000i 0.309058i
\(514\) −7.00000 18.5203i −0.308757 0.816894i
\(515\) 0 0
\(516\) 21.0000 18.5203i 0.924473 0.815309i
\(517\) −21.1660 −0.930880
\(518\) 21.1660 + 56.0000i 0.929981 + 2.46050i
\(519\) 56.0000 2.45813
\(520\) 0 0
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) 0 0
\(523\) 2.64575 0.115691 0.0578453 0.998326i \(-0.481577\pi\)
0.0578453 + 0.998326i \(0.481577\pi\)
\(524\) 21.0000 + 23.8118i 0.917389 + 1.04022i
\(525\) 0 0
\(526\) 6.00000 + 15.8745i 0.261612 + 0.692161i
\(527\) 12.0000i 0.522728i
\(528\) −27.7804 3.50000i −1.20899 0.152318i
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 21.1660i 0.918527i
\(532\) −15.8745 + 14.0000i −0.688247 + 0.606977i
\(533\) 0 0
\(534\) −3.50000 + 1.32288i −0.151460 + 0.0572464i
\(535\) 0 0
\(536\) −10.5000 + 19.8431i −0.453531 + 0.857093i
\(537\) 63.0000i 2.71865i
\(538\) 10.5830 + 28.0000i 0.456266 + 1.20717i
\(539\) 23.8118i 1.02565i
\(540\) 0 0
\(541\) 21.1660i 0.909998i 0.890492 + 0.454999i \(0.150360\pi\)
−0.890492 + 0.454999i \(0.849640\pi\)
\(542\) 26.4575 10.0000i 1.13645 0.429537i
\(543\) 28.0000i 1.20160i
\(544\) 16.5000 3.96863i 0.707432 0.170153i
\(545\) 0 0
\(546\) 0 0
\(547\) 18.5203 0.791869 0.395935 0.918279i \(-0.370421\pi\)
0.395935 + 0.918279i \(0.370421\pi\)
\(548\) −25.1346 28.5000i −1.07370 1.21746i
\(549\) 42.3320i 1.80669i
\(550\) 0 0
\(551\) 0 0
\(552\) 26.4575 + 14.0000i 1.12611 + 0.595880i
\(553\) 16.0000i 0.680389i
\(554\) 28.0000 10.5830i 1.18961 0.449629i
\(555\) 0 0
\(556\) −24.5000 27.7804i −1.03903 1.17815i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) −21.1660 + 8.00000i −0.896029 + 0.338667i
\(559\) 0 0
\(560\) 0 0
\(561\) −21.0000 −0.886621
\(562\) 29.1033 11.0000i 1.22765 0.464007i
\(563\) −15.8745 −0.669031 −0.334515 0.942390i \(-0.608573\pi\)
−0.334515 + 0.942390i \(0.608573\pi\)
\(564\) −28.0000 31.7490i −1.17901 1.33687i
\(565\) 0 0
\(566\) −17.5000 + 6.61438i −0.735580 + 0.278023i
\(567\) 20.0000i 0.839921i
\(568\) −10.5830 + 20.0000i −0.444053 + 0.839181i
\(569\) −11.0000 −0.461144 −0.230572 0.973055i \(-0.574060\pi\)
−0.230572 + 0.973055i \(0.574060\pi\)
\(570\) 0 0
\(571\) 37.0405i 1.55010i 0.631901 + 0.775049i \(0.282275\pi\)
−0.631901 + 0.775049i \(0.717725\pi\)
\(572\) 0 0
\(573\) 10.5830 0.442111
\(574\) 10.0000 + 26.4575i 0.417392 + 1.10432i
\(575\) 0 0
\(576\) −18.0000 26.4575i −0.750000 1.10240i
\(577\) 7.00000i 0.291414i −0.989328 0.145707i \(-0.953454\pi\)
0.989328 0.145707i \(-0.0465456\pi\)
\(578\) −10.5830 + 4.00000i −0.440195 + 0.166378i
\(579\) 13.2288i 0.549768i
\(580\) 0 0
\(581\) 31.7490i 1.31717i
\(582\) 2.64575 + 7.00000i 0.109670 + 0.290159i
\(583\) 28.0000i 1.15964i
\(584\) −17.5000 9.26013i −0.724155 0.383187i
\(585\) 0 0
\(586\) −14.0000 + 5.29150i −0.578335 + 0.218590i
\(587\) 7.93725 0.327606 0.163803 0.986493i \(-0.447624\pi\)
0.163803 + 0.986493i \(0.447624\pi\)
\(588\) −35.7176 + 31.5000i −1.47297 + 1.29904i
\(589\) 10.5830i 0.436065i
\(590\) 0 0
\(591\) 28.0000 1.15177
\(592\) −5.29150 + 42.0000i −0.217479 + 1.72619i
\(593\) 41.0000i 1.68367i −0.539736 0.841834i \(-0.681476\pi\)
0.539736 0.841834i \(-0.318524\pi\)
\(594\) 3.50000 + 9.26013i 0.143607 + 0.379948i
\(595\) 0 0
\(596\) 0 0
\(597\) 63.4980 2.59880
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) −10.5830 28.0000i −0.431331 1.14119i
\(603\) 31.7490 1.29292
\(604\) 6.00000 5.29150i 0.244137 0.215308i
\(605\) 0 0
\(606\) −14.0000 37.0405i −0.568711 1.50467i
\(607\) 8.00000i 0.324710i −0.986732 0.162355i \(-0.948091\pi\)
0.986732 0.162355i \(-0.0519090\pi\)
\(608\) −14.5516 + 3.50000i −0.590147 + 0.141944i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −15.8745 18.0000i −0.641689 0.727607i
\(613\) 10.5830 0.427444 0.213722 0.976895i \(-0.431441\pi\)
0.213722 + 0.976895i \(0.431441\pi\)
\(614\) 3.50000 1.32288i 0.141249 0.0533869i
\(615\) 0 0
\(616\) −14.0000 + 26.4575i −0.564076 + 1.06600i
\(617\) 6.00000i 0.241551i 0.992680 + 0.120775i \(0.0385381\pi\)
−0.992680 + 0.120775i \(0.961462\pi\)
\(618\) 10.5830 + 28.0000i 0.425711 + 1.12633i
\(619\) 5.29150i 0.212683i 0.994330 + 0.106342i \(0.0339137\pi\)
−0.994330 + 0.106342i \(0.966086\pi\)
\(620\) 0 0
\(621\) 10.5830i 0.424681i
\(622\) 5.29150 2.00000i 0.212170 0.0801927i
\(623\) 4.00000i 0.160257i
\(624\) 0 0
\(625\) 0 0
\(626\) 3.00000 + 7.93725i 0.119904 + 0.317236i
\(627\) 18.5203 0.739628
\(628\) 15.8745 14.0000i 0.633462 0.558661i
\(629\) 31.7490i 1.26592i
\(630\) 0 0
\(631\) 36.0000 1.43314 0.716569 0.697517i \(-0.245712\pi\)
0.716569 + 0.697517i \(0.245712\pi\)
\(632\) 5.29150 10.0000i 0.210485 0.397779i
\(633\) 21.0000i 0.834675i
\(634\) 0 0
\(635\) 0 0
\(636\) −42.0000 + 37.0405i −1.66541 + 1.46875i
\(637\) 0 0
\(638\) 0 0
\(639\) 32.0000 1.26590
\(640\) 0 0
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 9.26013 3.50000i 0.365468 0.138134i
\(643\) −15.8745 −0.626029 −0.313015 0.949748i \(-0.601339\pi\)
−0.313015 + 0.949748i \(0.601339\pi\)
\(644\) 24.0000 21.1660i 0.945732 0.834058i
\(645\) 0 0
\(646\) −10.5000 + 3.96863i −0.413117 + 0.156144i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 6.61438 12.5000i 0.259837 0.491046i
\(649\) 14.0000 0.549548
\(650\) 0 0
\(651\) 42.3320i 1.65912i
\(652\) 19.8431 17.5000i 0.777117 0.685353i
\(653\) 31.7490 1.24243 0.621217 0.783638i \(-0.286638\pi\)
0.621217 + 0.783638i \(0.286638\pi\)
\(654\) −14.0000 37.0405i −0.547443 1.44840i
\(655\) 0 0
\(656\) −2.50000 + 19.8431i −0.0976086 + 0.774744i
\(657\) 28.0000i 1.09238i
\(658\) −42.3320 + 16.0000i −1.65027 + 0.623745i
\(659\) 7.93725i 0.309192i −0.987978 0.154596i \(-0.950592\pi\)
0.987978 0.154596i \(-0.0494075\pi\)
\(660\) 0 0
\(661\) 21.1660i 0.823262i −0.911351 0.411631i \(-0.864959\pi\)
0.911351 0.411631i \(-0.135041\pi\)
\(662\) 1.32288 + 3.50000i 0.0514150 + 0.136031i
\(663\) 0 0
\(664\) 10.5000 19.8431i 0.407479 0.770063i
\(665\) 0 0
\(666\) 56.0000 21.1660i 2.16996 0.820166i
\(667\) 0 0
\(668\) 0 0
\(669\) 42.3320i 1.63665i
\(670\) 0 0
\(671\) −28.0000 −1.08093
\(672\) −58.2065 + 14.0000i −2.24537 + 0.540062i
\(673\) 34.0000i 1.31060i 0.755367 + 0.655302i \(0.227459\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(674\) 7.50000 + 19.8431i 0.288889 + 0.764329i
\(675\) 0 0
\(676\) −19.5000 + 17.1974i −0.750000 + 0.661438i
\(677\) −42.3320 −1.62695 −0.813476 0.581599i \(-0.802427\pi\)
−0.813476 + 0.581599i \(0.802427\pi\)
\(678\) −19.8431 52.5000i −0.762071 2.01625i
\(679\) 8.00000 0.307012
\(680\) 0 0
\(681\) 42.0000 1.60944
\(682\) 5.29150 + 14.0000i 0.202622 + 0.536088i
\(683\) 23.8118 0.911132 0.455566 0.890202i \(-0.349437\pi\)
0.455566 + 0.890202i \(0.349437\pi\)
\(684\) 14.0000 + 15.8745i 0.535303 + 0.606977i
\(685\) 0 0
\(686\) 4.00000 + 10.5830i 0.152721 + 0.404061i
\(687\) 56.0000i 2.13653i
\(688\) 2.64575 21.0000i 0.100868 0.800617i
\(689\) 0 0
\(690\) 0 0
\(691\) 23.8118i 0.905842i −0.891551 0.452921i \(-0.850382\pi\)
0.891551 0.452921i \(-0.149618\pi\)
\(692\) 31.7490 28.0000i 1.20692 1.06440i
\(693\) 42.3320 1.60806
\(694\) 3.50000 1.32288i 0.132858 0.0502157i
\(695\) 0 0
\(696\) 0 0
\(697\) 15.0000i 0.568166i
\(698\) 5.29150 + 14.0000i 0.200286 + 0.529908i
\(699\) 15.8745i 0.600429i
\(700\) 0 0
\(701\) 21.1660i 0.799429i −0.916640 0.399715i \(-0.869109\pi\)
0.916640 0.399715i \(-0.130891\pi\)
\(702\) 0 0
\(703\) 28.0000i 1.05604i
\(704\) −17.5000 + 11.9059i −0.659556 + 0.448720i
\(705\) 0 0
\(706\) −9.00000 23.8118i −0.338719 0.896167i
\(707\) −42.3320 −1.59206
\(708\) 18.5203 + 21.0000i 0.696034 + 0.789228i
\(709\) 21.1660i 0.794906i 0.917622 + 0.397453i \(0.130106\pi\)
−0.917622 + 0.397453i \(0.869894\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) −1.32288 + 2.50000i −0.0495769 + 0.0936915i
\(713\) 16.0000i 0.599205i
\(714\) −42.0000 + 15.8745i −1.57181 + 0.594089i
\(715\) 0 0
\(716\) 31.5000 + 35.7176i 1.17721 + 1.33483i
\(717\) 21.1660 0.790459
\(718\) 47.6235 18.0000i 1.77729 0.671754i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) 32.0000 1.19174
\(722\) −15.8745 + 6.00000i −0.590788 + 0.223297i
\(723\) −55.5608 −2.06633
\(724\) −14.0000 15.8745i −0.520306 0.589971i
\(725\) 0 0
\(726\) −14.0000 + 5.29150i −0.519589 + 0.196386i
\(727\) 16.0000i 0.593407i −0.954970 0.296704i \(-0.904113\pi\)
0.954970 0.296704i \(-0.0958873\pi\)
\(728\) 0 0
\(729\) −41.0000 −1.51852
\(730\) 0 0
\(731\) 15.8745i 0.587140i
\(732\) −37.0405 42.0000i −1.36906 1.55236i
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 22.0000 5.29150i 0.810931 0.195047i
\(737\) 21.0000i 0.773545i
\(738\) 26.4575 10.0000i 0.973915 0.368105i
\(739\) 15.8745i 0.583953i −0.956425 0.291977i \(-0.905687\pi\)
0.956425 0.291977i \(-0.0943129\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 21.1660 + 56.0000i 0.777029 + 2.05582i
\(743\) 36.0000i 1.32071i −0.750953 0.660356i \(-0.770405\pi\)
0.750953 0.660356i \(-0.229595\pi\)
\(744\) −14.0000 + 26.4575i −0.513265 + 0.969979i
\(745\) 0 0
\(746\) 14.0000 5.29150i 0.512576 0.193736i
\(747\) −31.7490 −1.16164
\(748\) −11.9059 + 10.5000i −0.435322 + 0.383918i
\(749\) 10.5830i 0.386695i
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −31.7490 4.00000i −1.15777 0.145865i
\(753\) 21.0000i 0.765283i
\(754\) 0 0
\(755\) 0 0
\(756\) 14.0000 + 15.8745i 0.509175 + 0.577350i
\(757\) 21.1660 0.769292 0.384646 0.923064i \(-0.374324\pi\)
0.384646 + 0.923064i \(0.374324\pi\)
\(758\) 3.96863 + 10.5000i 0.144147 + 0.381377i
\(759\) −28.0000 −1.01634
\(760\) 0 0
\(761\) −29.0000 −1.05125 −0.525625 0.850717i \(-0.676168\pi\)
−0.525625 + 0.850717i \(0.676168\pi\)
\(762\) −15.8745 42.0000i −0.575073 1.52150i
\(763\) −42.3320 −1.53252
\(764\) 6.00000 5.29150i 0.217072 0.191440i
\(765\) 0 0
\(766\) −18.0000 47.6235i −0.650366 1.72071i
\(767\) 0 0
\(768\) −41.0091 10.5000i −1.47979 0.378886i
\(769\) 21.0000 0.757279 0.378640 0.925544i \(-0.376392\pi\)
0.378640 + 0.925544i \(0.376392\pi\)
\(770\) 0 0
\(771\) 37.0405i 1.33398i
\(772\) −6.61438 7.50000i −0.238057 0.269931i
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) −28.0000 + 10.5830i −1.00644 + 0.380398i
\(775\) 0 0
\(776\) 5.00000 + 2.64575i 0.179490 + 0.0949769i
\(777\) 112.000i 4.01798i
\(778\) −5.29150 14.0000i −0.189710 0.501924i
\(779\) 13.2288i 0.473969i
\(780\) 0 0
\(781\) 21.1660i 0.757379i
\(782\) 15.8745 6.00000i 0.567671 0.214560i
\(783\) 0 0
\(784\) −4.50000 + 35.7176i −0.160714 + 1.27563i
\(785\) 0 0
\(786\) −21.0000 55.5608i −0.749045 1.98179i
\(787\) −26.4575 −0.943108 −0.471554 0.881837i \(-0.656307\pi\)
−0.471554 + 0.881837i \(0.656307\pi\)
\(788\) 15.8745 14.0000i 0.565506 0.498729i
\(789\) 31.7490i 1.13029i
\(790\) 0 0
\(791\) −60.0000 −2.13335
\(792\) 26.4575 + 14.0000i 0.940127 + 0.497468i
\(793\) 0 0
\(794\) 28.0000 10.5830i 0.993683 0.375577i
\(795\) 0 0
\(796\) 36.0000 31.7490i 1.27599 1.12531i
\(797\) 31.7490 1.12461 0.562304 0.826931i \(-0.309915\pi\)
0.562304 + 0.826931i \(0.309915\pi\)
\(798\) 37.0405 14.0000i 1.31122 0.495595i
\(799\) −24.0000 −0.849059
\(800\) 0 0
\(801\) 4.00000 0.141333
\(802\) −35.7176 + 13.5000i −1.26123 + 0.476702i
\(803\) 18.5203 0.653566
\(804\) 31.5000 27.7804i 1.11092 0.979739i
\(805\) 0 0
\(806\) 0 0
\(807\) 56.0000i 1.97129i
\(808\) −26.4575 14.0000i −0.930772 0.492518i
\(809\) −10.0000 −0.351581 −0.175791 0.984428i \(-0.556248\pi\)
−0.175791 + 0.984428i \(0.556248\pi\)
\(810\) 0 0
\(811\) 5.29150i 0.185810i −0.995675 0.0929049i \(-0.970385\pi\)
0.995675 0.0929049i \(-0.0296153\pi\)
\(812\) 0 0
\(813\) −52.9150 −1.85581
\(814\) −14.0000 37.0405i −0.490700 1.29827i
\(815\) 0 0
\(816\) −31.5000 3.96863i −1.10272 0.138930i
\(817\) 14.0000i 0.489798i
\(818\) 3.96863 1.50000i 0.138760 0.0524463i
\(819\) 0 0
\(820\) 0 0
\(821\) 10.5830i 0.369349i 0.982800 + 0.184675i \(0.0591232\pi\)
−0.982800 + 0.184675i \(0.940877\pi\)
\(822\) 25.1346 + 66.5000i 0.876671 + 2.31945i
\(823\) 24.0000i 0.836587i 0.908312 + 0.418294i \(0.137372\pi\)
−0.908312 + 0.418294i \(0.862628\pi\)
\(824\) 20.0000 + 10.5830i 0.696733 + 0.368676i
\(825\) 0 0
\(826\) 28.0000 10.5830i 0.974245 0.368230i
\(827\) −13.2288 −0.460009 −0.230004 0.973190i \(-0.573874\pi\)
−0.230004 + 0.973190i \(0.573874\pi\)
\(828\) −21.1660 24.0000i −0.735570 0.834058i
\(829\) 21.1660i 0.735126i −0.929999 0.367563i \(-0.880192\pi\)
0.929999 0.367563i \(-0.119808\pi\)
\(830\) 0 0
\(831\) −56.0000 −1.94262
\(832\) 0 0
\(833\) 27.0000i 0.935495i
\(834\) 24.5000 + 64.8209i 0.848366 + 2.24456i
\(835\) 0 0
\(836\) 10.5000 9.26013i 0.363150 0.320268i
\(837\) 10.5830 0.365802
\(838\) 9.26013 + 24.5000i 0.319886 + 0.846338i
\(839\) −40.0000 −1.38095 −0.690477 0.723355i \(-0.742599\pi\)
−0.690477 + 0.723355i \(0.742599\pi\)
\(840\) 0 0
\(841\) 29.0000 1.00000
\(842\) 10.5830 + 28.0000i 0.364714 + 0.964944i
\(843\) −58.2065 −2.00474
\(844\) 10.5000 + 11.9059i 0.361425 + 0.409817i
\(845\) 0 0
\(846\) 16.0000 + 42.3320i 0.550091 + 1.45540i
\(847\) 16.0000i 0.549767i
\(848\) −5.29150 + 42.0000i −0.181711 + 1.44229i
\(849\) 35.0000 1.20120
\(850\) 0 0
\(851\) 42.3320i 1.45112i
\(852\) 31.7490 28.0000i 1.08770 0.959264i
\(853\) −52.9150 −1.81178 −0.905888 0.423517i \(-0.860795\pi\)
−0.905888 + 0.423517i \(0.860795\pi\)
\(854\) −56.0000 + 21.1660i −1.91628 + 0.724286i
\(855\) 0 0
\(856\) 3.50000 6.61438i 0.119628 0.226075i
\(857\) 21.0000i 0.717346i 0.933463 + 0.358673i \(0.116771\pi\)
−0.933463 + 0.358673i \(0.883229\pi\)
\(858\) 0 0
\(859\) 2.64575i 0.0902719i 0.998981 + 0.0451359i \(0.0143721\pi\)
−0.998981 + 0.0451359i \(0.985628\pi\)
\(860\) 0 0
\(861\) 52.9150i 1.80334i
\(862\) −15.8745 + 6.00000i −0.540688 + 0.204361i
\(863\) 24.0000i 0.816970i −0.912765 0.408485i \(-0.866057\pi\)
0.912765 0.408485i \(-0.133943\pi\)
\(864\) 3.50000 + 14.5516i 0.119072 + 0.495057i
\(865\) 0 0
\(866\) 18.5000 + 48.9464i 0.628656 + 1.66327i
\(867\) 21.1660 0.718835
\(868\) 21.1660 + 24.0000i 0.718421 + 0.814613i
\(869\) 10.5830i 0.359004i
\(870\) 0 0
\(871\) 0 0
\(872\) −26.4575 14.0000i −0.895964 0.474100i
\(873\) 8.00000i 0.270759i
\(874\) −14.0000 + 5.29150i −0.473557 + 0.178988i
\(875\) 0 0
\(876\) 24.5000 + 27.7804i 0.827778 + 0.938612i
\(877\) 42.3320 1.42945 0.714725 0.699405i \(-0.246552\pi\)
0.714725 + 0.699405i \(0.246552\pi\)
\(878\) 10.5830 4.00000i 0.357159 0.134993i
\(879\) 28.0000 0.944417
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 47.6235 18.0000i 1.60357 0.606092i
\(883\) 44.9778 1.51362 0.756811 0.653633i \(-0.226756\pi\)
0.756811 + 0.653633i \(0.226756\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 38.5000 14.5516i 1.29343 0.488872i
\(887\) 56.0000i 1.88030i 0.340766 + 0.940148i \(0.389313\pi\)
−0.340766 + 0.940148i \(0.610687\pi\)
\(888\) 37.0405 70.0000i 1.24300 2.34905i
\(889\) −48.0000 −1.60987
\(890\) 0 0
\(891\) 13.2288i 0.443180i
\(892\) 21.1660 + 24.0000i 0.708690 + 0.803579i
\(893\) 21.1660 0.708294
\(894\) 0 0
\(895\) 0 0
\(896\) −26.0000 + 37.0405i −0.868599 + 1.23744i
\(897\) 0 0
\(898\) 35.7176 13.5000i 1.19191 0.450501i
\(899\) 0 0
\(900\) 0 0
\(901\) 31.7490i 1.05771i
\(902\) −6.61438 17.5000i −0.220235 0.582686i
\(903\) 56.0000i 1.86356i
\(904\) −37.5000 19.8431i −1.24723 0.659973i
\(905\) 0 0
\(906\) −14.0000 + 5.29150i −0.465119 + 0.175798i
\(907\) −5.29150 −0.175701 −0.0878507 0.996134i \(-0.528000\pi\)
−0.0878507 + 0.996134i \(0.528000\pi\)
\(908\) 23.8118 21.0000i 0.790221 0.696909i
\(909\) 42.3320i 1.40406i
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 27.7804 + 3.50000i 0.919901 + 0.115897i
\(913\) 21.0000i 0.694999i
\(914\) 13.5000 + 35.7176i 0.446540 + 1.18143i
\(915\) 0 0
\(916\) 28.0000 + 31.7490i 0.925146 + 1.04902i
\(917\) −63.4980 −2.09689
\(918\) 3.96863 + 10.5000i 0.130984 + 0.346552i
\(919\) −4.00000 −0.131948 −0.0659739 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) 0 0
\(921\) −7.00000 −0.230658
\(922\) −21.1660 56.0000i −0.697065 1.84426i
\(923\) 0 0
\(924\) 42.0000 37.0405i 1.38170 1.21854i
\(925\) 0 0
\(926\) −4.00000 10.5830i −0.131448 0.347779i
\(927\) 32.0000i 1.05102i
\(928\) 0 0
\(929\) 14.0000 0.459325 0.229663 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) 0 0
\(931\) 23.8118i 0.780399i
\(932\) −7.93725 9.00000i −0.259993 0.294805i
\(933\) −10.5830 −0.346472
\(934\) 35.0000 13.2288i 1.14523 0.432858i
\(935\) 0 0
\(936\) 0 0
\(937\) 7.00000i 0.228680i −0.993442 0.114340i \(-0.963525\pi\)
0.993442 0.114340i \(-0.0364753\pi\)
\(938\) −15.8745 42.0000i −0.518321 1.37135i
\(939\) 15.8745i 0.518045i
\(940\) 0 0
\(941\) 42.3320i 1.37998i −0.723817 0.689992i \(-0.757614\pi\)
0.723817 0.689992i \(-0.242386\pi\)
\(942\) −37.0405 + 14.0000i −1.20685 + 0.456145i
\(943\) 20.0000i 0.651290i
\(944\) 21.0000 + 2.64575i 0.683492 + 0.0861119i
\(945\) 0 0
\(946\) 7.00000 + 18.5203i 0.227590 + 0.602146i
\(947\) 15.8745 0.515852 0.257926 0.966165i \(-0.416961\pi\)
0.257926 + 0.966165i \(0.416961\pi\)
\(948\) −15.8745 + 14.0000i −0.515580 + 0.454699i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −15.8745 + 30.0000i −0.514496 + 0.972306i
\(953\) 5.00000i 0.161966i −0.996715 0.0809829i \(-0.974194\pi\)
0.996715 0.0809829i \(-0.0258059\pi\)
\(954\) 56.0000 21.1660i 1.81307 0.685275i
\(955\) 0 0
\(956\) 12.0000 10.5830i 0.388108 0.342279i
\(957\) 0 0
\(958\) 5.29150 2.00000i 0.170961 0.0646171i
\(959\) 76.0000 2.45417
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) −10.5830 −0.341033
\(964\) −31.5000 + 27.7804i −1.01455 + 0.894746i
\(965\) 0 0
\(966\) −56.0000 + 21.1660i −1.80177 + 0.681005i
\(967\) 8.00000i 0.257263i 0.991692 + 0.128631i \(0.0410584\pi\)
−0.991692 + 0.128631i \(0.958942\pi\)
\(968\) −5.29150 + 10.0000i −0.170075 + 0.321412i
\(969\) 21.0000 0.674617
\(970\) 0 0
\(971\) 23.8118i 0.764156i −0.924130 0.382078i \(-0.875209\pi\)
0.924130 0.382078i \(-0.124791\pi\)
\(972\) −31.7490 + 28.0000i −1.01835 + 0.898100i
\(973\) 74.0810 2.37493
\(974\) 6.00000 + 15.8745i 0.192252 + 0.508652i
\(975\) 0 0
\(976\) −42.0000 5.29150i −1.34439 0.169377i
\(977\) 37.0000i 1.18373i 0.806035 + 0.591867i \(0.201609\pi\)
−0.806035 + 0.591867i \(0.798391\pi\)
\(978\) −46.3006 + 17.5000i −1.48053 + 0.559588i
\(979\) 2.64575i 0.0845586i
\(980\) 0 0
\(981\) 42.3320i 1.35156i
\(982\) 2.64575 + 7.00000i 0.0844293 + 0.223379i
\(983\) 28.0000i 0.893061i 0.894768 + 0.446531i \(0.147341\pi\)
−0.894768 + 0.446531i \(0.852659\pi\)
\(984\) 17.5000 33.0719i 0.557880 1.05429i
\(985\) 0 0
\(986\) 0 0
\(987\) 84.6640 2.69489
\(988\) 0 0
\(989\) 21.1660i 0.673040i
\(990\) 0 0
\(991\) 44.0000 1.39771 0.698853 0.715265i \(-0.253694\pi\)
0.698853 + 0.715265i \(0.253694\pi\)
\(992\) 5.29150 + 22.0000i 0.168005 + 0.698501i
\(993\) 7.00000i 0.222138i
\(994\) −16.0000 42.3320i −0.507489 1.34269i
\(995\) 0 0
\(996\) −31.5000 + 27.7804i −0.998116 + 0.880255i
\(997\) 42.3320 1.34067 0.670334 0.742059i \(-0.266151\pi\)
0.670334 + 0.742059i \(0.266151\pi\)
\(998\) −13.2288 35.0000i −0.418749 1.10791i
\(999\) −28.0000 −0.885881
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 200.2.f.d.149.2 4
3.2 odd 2 1800.2.d.m.1549.3 4
4.3 odd 2 800.2.f.d.49.1 4
5.2 odd 4 200.2.d.b.101.1 2
5.3 odd 4 200.2.d.c.101.2 yes 2
5.4 even 2 inner 200.2.f.d.149.3 4
8.3 odd 2 800.2.f.d.49.3 4
8.5 even 2 inner 200.2.f.d.149.4 4
12.11 even 2 7200.2.d.m.2449.1 4
15.2 even 4 1800.2.k.f.901.2 2
15.8 even 4 1800.2.k.d.901.1 2
15.14 odd 2 1800.2.d.m.1549.2 4
20.3 even 4 800.2.d.a.401.1 2
20.7 even 4 800.2.d.d.401.2 2
20.19 odd 2 800.2.f.d.49.4 4
24.5 odd 2 1800.2.d.m.1549.1 4
24.11 even 2 7200.2.d.m.2449.2 4
40.3 even 4 800.2.d.a.401.2 2
40.13 odd 4 200.2.d.c.101.1 yes 2
40.19 odd 2 800.2.f.d.49.2 4
40.27 even 4 800.2.d.d.401.1 2
40.29 even 2 inner 200.2.f.d.149.1 4
40.37 odd 4 200.2.d.b.101.2 yes 2
60.23 odd 4 7200.2.k.b.3601.1 2
60.47 odd 4 7200.2.k.i.3601.1 2
60.59 even 2 7200.2.d.m.2449.3 4
80.3 even 4 6400.2.a.cb.1.2 2
80.13 odd 4 6400.2.a.bg.1.1 2
80.27 even 4 6400.2.a.bh.1.2 2
80.37 odd 4 6400.2.a.cc.1.1 2
80.43 even 4 6400.2.a.cb.1.1 2
80.53 odd 4 6400.2.a.bg.1.2 2
80.67 even 4 6400.2.a.bh.1.1 2
80.77 odd 4 6400.2.a.cc.1.2 2
120.29 odd 2 1800.2.d.m.1549.4 4
120.53 even 4 1800.2.k.d.901.2 2
120.59 even 2 7200.2.d.m.2449.4 4
120.77 even 4 1800.2.k.f.901.1 2
120.83 odd 4 7200.2.k.b.3601.2 2
120.107 odd 4 7200.2.k.i.3601.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.2.d.b.101.1 2 5.2 odd 4
200.2.d.b.101.2 yes 2 40.37 odd 4
200.2.d.c.101.1 yes 2 40.13 odd 4
200.2.d.c.101.2 yes 2 5.3 odd 4
200.2.f.d.149.1 4 40.29 even 2 inner
200.2.f.d.149.2 4 1.1 even 1 trivial
200.2.f.d.149.3 4 5.4 even 2 inner
200.2.f.d.149.4 4 8.5 even 2 inner
800.2.d.a.401.1 2 20.3 even 4
800.2.d.a.401.2 2 40.3 even 4
800.2.d.d.401.1 2 40.27 even 4
800.2.d.d.401.2 2 20.7 even 4
800.2.f.d.49.1 4 4.3 odd 2
800.2.f.d.49.2 4 40.19 odd 2
800.2.f.d.49.3 4 8.3 odd 2
800.2.f.d.49.4 4 20.19 odd 2
1800.2.d.m.1549.1 4 24.5 odd 2
1800.2.d.m.1549.2 4 15.14 odd 2
1800.2.d.m.1549.3 4 3.2 odd 2
1800.2.d.m.1549.4 4 120.29 odd 2
1800.2.k.d.901.1 2 15.8 even 4
1800.2.k.d.901.2 2 120.53 even 4
1800.2.k.f.901.1 2 120.77 even 4
1800.2.k.f.901.2 2 15.2 even 4
6400.2.a.bg.1.1 2 80.13 odd 4
6400.2.a.bg.1.2 2 80.53 odd 4
6400.2.a.bh.1.1 2 80.67 even 4
6400.2.a.bh.1.2 2 80.27 even 4
6400.2.a.cb.1.1 2 80.43 even 4
6400.2.a.cb.1.2 2 80.3 even 4
6400.2.a.cc.1.1 2 80.37 odd 4
6400.2.a.cc.1.2 2 80.77 odd 4
7200.2.d.m.2449.1 4 12.11 even 2
7200.2.d.m.2449.2 4 24.11 even 2
7200.2.d.m.2449.3 4 60.59 even 2
7200.2.d.m.2449.4 4 120.59 even 2
7200.2.k.b.3601.1 2 60.23 odd 4
7200.2.k.b.3601.2 2 120.83 odd 4
7200.2.k.i.3601.1 2 60.47 odd 4
7200.2.k.i.3601.2 2 120.107 odd 4