Properties

Label 200.2.d.c.101.2
Level $200$
Weight $2$
Character 200.101
Analytic conductor $1.597$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,2,Mod(101,200)]
 
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, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 200.d (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: \(1.59700804043\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-7}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 101.2
Root \(0.500000 + 1.32288i\) of defining polynomial
Character \(\chi\) \(=\) 200.101
Dual form 200.2.d.c.101.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 1.32288i) q^{2} +2.64575i q^{3} +(-1.50000 + 1.32288i) q^{4} +(-3.50000 + 1.32288i) q^{6} +4.00000 q^{7} +(-2.50000 - 1.32288i) q^{8} -4.00000 q^{9} +O(q^{10})\) \(q+(0.500000 + 1.32288i) q^{2} +2.64575i q^{3} +(-1.50000 + 1.32288i) q^{4} +(-3.50000 + 1.32288i) q^{6} +4.00000 q^{7} +(-2.50000 - 1.32288i) q^{8} -4.00000 q^{9} -2.64575i q^{11} +(-3.50000 - 3.96863i) q^{12} +(2.00000 + 5.29150i) q^{14} +(0.500000 - 3.96863i) q^{16} -3.00000 q^{17} +(-2.00000 - 5.29150i) q^{18} -2.64575i q^{19} +10.5830i q^{21} +(3.50000 - 1.32288i) q^{22} +4.00000 q^{23} +(3.50000 - 6.61438i) q^{24} -2.64575i q^{27} +(-6.00000 + 5.29150i) q^{28} +4.00000 q^{31} +(5.50000 - 1.32288i) q^{32} +7.00000 q^{33} +(-1.50000 - 3.96863i) q^{34} +(6.00000 - 5.29150i) q^{36} +10.5830i q^{37} +(3.50000 - 1.32288i) q^{38} -5.00000 q^{41} +(-14.0000 + 5.29150i) q^{42} +5.29150i q^{43} +(3.50000 + 3.96863i) q^{44} +(2.00000 + 5.29150i) q^{46} -8.00000 q^{47} +(10.5000 + 1.32288i) q^{48} +9.00000 q^{49} -7.93725i q^{51} -10.5830i q^{53} +(3.50000 - 1.32288i) q^{54} +(-10.0000 - 5.29150i) q^{56} +7.00000 q^{57} -5.29150i q^{59} -10.5830i q^{61} +(2.00000 + 5.29150i) q^{62} -16.0000 q^{63} +(4.50000 + 6.61438i) q^{64} +(3.50000 + 9.26013i) q^{66} -7.93725i q^{67} +(4.50000 - 3.96863i) q^{68} +10.5830i q^{69} +8.00000 q^{71} +(10.0000 + 5.29150i) q^{72} -7.00000 q^{73} +(-14.0000 + 5.29150i) q^{74} +(3.50000 + 3.96863i) q^{76} -10.5830i q^{77} +4.00000 q^{79} -5.00000 q^{81} +(-2.50000 - 6.61438i) q^{82} -7.93725i q^{83} +(-14.0000 - 15.8745i) q^{84} +(-7.00000 + 2.64575i) q^{86} +(-3.50000 + 6.61438i) q^{88} -1.00000 q^{89} +(-6.00000 + 5.29150i) q^{92} +10.5830i q^{93} +(-4.00000 - 10.5830i) q^{94} +(3.50000 + 14.5516i) q^{96} -2.00000 q^{97} +(4.50000 + 11.9059i) q^{98} +10.5830i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - 3 q^{4} - 7 q^{6} + 8 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - 3 q^{4} - 7 q^{6} + 8 q^{7} - 5 q^{8} - 8 q^{9} - 7 q^{12} + 4 q^{14} + q^{16} - 6 q^{17} - 4 q^{18} + 7 q^{22} + 8 q^{23} + 7 q^{24} - 12 q^{28} + 8 q^{31} + 11 q^{32} + 14 q^{33} - 3 q^{34} + 12 q^{36} + 7 q^{38} - 10 q^{41} - 28 q^{42} + 7 q^{44} + 4 q^{46} - 16 q^{47} + 21 q^{48} + 18 q^{49} + 7 q^{54} - 20 q^{56} + 14 q^{57} + 4 q^{62} - 32 q^{63} + 9 q^{64} + 7 q^{66} + 9 q^{68} + 16 q^{71} + 20 q^{72} - 14 q^{73} - 28 q^{74} + 7 q^{76} + 8 q^{79} - 10 q^{81} - 5 q^{82} - 28 q^{84} - 14 q^{86} - 7 q^{88} - 2 q^{89} - 12 q^{92} - 8 q^{94} + 7 q^{96} - 4 q^{97} + 9 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 1.32288i 0.353553 + 0.935414i
\(3\) 2.64575i 1.52753i 0.645497 + 0.763763i \(0.276650\pi\)
−0.645497 + 0.763763i \(0.723350\pi\)
\(4\) −1.50000 + 1.32288i −0.750000 + 0.661438i
\(5\) 0 0
\(6\) −3.50000 + 1.32288i −1.42887 + 0.540062i
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) −2.50000 1.32288i −0.883883 0.467707i
\(9\) −4.00000 −1.33333
\(10\) 0 0
\(11\) 2.64575i 0.797724i −0.917011 0.398862i \(-0.869405\pi\)
0.917011 0.398862i \(-0.130595\pi\)
\(12\) −3.50000 3.96863i −1.01036 1.14564i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 2.00000 + 5.29150i 0.534522 + 1.41421i
\(15\) 0 0
\(16\) 0.500000 3.96863i 0.125000 0.992157i
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −2.00000 5.29150i −0.471405 1.24722i
\(19\) 2.64575i 0.606977i −0.952835 0.303488i \(-0.901849\pi\)
0.952835 0.303488i \(-0.0981514\pi\)
\(20\) 0 0
\(21\) 10.5830i 2.30940i
\(22\) 3.50000 1.32288i 0.746203 0.282038i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 3.50000 6.61438i 0.714435 1.35015i
\(25\) 0 0
\(26\) 0 0
\(27\) 2.64575i 0.509175i
\(28\) −6.00000 + 5.29150i −1.13389 + 1.00000i
\(29\) 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 \(0.383046\pi\)
\(32\) 5.50000 1.32288i 0.972272 0.233854i
\(33\) 7.00000 1.21854
\(34\) −1.50000 3.96863i −0.257248 0.680614i
\(35\) 0 0
\(36\) 6.00000 5.29150i 1.00000 0.881917i
\(37\) 10.5830i 1.73984i 0.493197 + 0.869918i \(0.335828\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 3.50000 1.32288i 0.567775 0.214599i
\(39\) 0 0
\(40\) 0 0
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) −14.0000 + 5.29150i −2.16025 + 0.816497i
\(43\) 5.29150i 0.806947i 0.914991 + 0.403473i \(0.132197\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 3.50000 + 3.96863i 0.527645 + 0.598293i
\(45\) 0 0
\(46\) 2.00000 + 5.29150i 0.294884 + 0.780189i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 10.5000 + 1.32288i 1.51554 + 0.190941i
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 7.93725i 1.11144i
\(52\) 0 0
\(53\) 10.5830i 1.45369i −0.686803 0.726844i \(-0.740986\pi\)
0.686803 0.726844i \(-0.259014\pi\)
\(54\) 3.50000 1.32288i 0.476290 0.180021i
\(55\) 0 0
\(56\) −10.0000 5.29150i −1.33631 0.707107i
\(57\) 7.00000 0.927173
\(58\) 0 0
\(59\) 5.29150i 0.688895i −0.938806 0.344447i \(-0.888066\pi\)
0.938806 0.344447i \(-0.111934\pi\)
\(60\) 0 0
\(61\) 10.5830i 1.35501i −0.735516 0.677507i \(-0.763060\pi\)
0.735516 0.677507i \(-0.236940\pi\)
\(62\) 2.00000 + 5.29150i 0.254000 + 0.672022i
\(63\) −16.0000 −2.01581
\(64\) 4.50000 + 6.61438i 0.562500 + 0.826797i
\(65\) 0 0
\(66\) 3.50000 + 9.26013i 0.430820 + 1.13984i
\(67\) 7.93725i 0.969690i −0.874600 0.484845i \(-0.838876\pi\)
0.874600 0.484845i \(-0.161124\pi\)
\(68\) 4.50000 3.96863i 0.545705 0.481267i
\(69\) 10.5830i 1.27404i
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 10.0000 + 5.29150i 1.17851 + 0.623610i
\(73\) −7.00000 −0.819288 −0.409644 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −14.0000 + 5.29150i −1.62747 + 0.615125i
\(75\) 0 0
\(76\) 3.50000 + 3.96863i 0.401478 + 0.455233i
\(77\) 10.5830i 1.20605i
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) −5.00000 −0.555556
\(82\) −2.50000 6.61438i −0.276079 0.730436i
\(83\) 7.93725i 0.871227i −0.900134 0.435613i \(-0.856531\pi\)
0.900134 0.435613i \(-0.143469\pi\)
\(84\) −14.0000 15.8745i −1.52753 1.73205i
\(85\) 0 0
\(86\) −7.00000 + 2.64575i −0.754829 + 0.285299i
\(87\) 0 0
\(88\) −3.50000 + 6.61438i −0.373101 + 0.705095i
\(89\) −1.00000 −0.106000 −0.0529999 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.00000 + 5.29150i −0.625543 + 0.551677i
\(93\) 10.5830i 1.09741i
\(94\) −4.00000 10.5830i −0.412568 1.09155i
\(95\) 0 0
\(96\) 3.50000 + 14.5516i 0.357217 + 1.48517i
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 4.50000 + 11.9059i 0.454569 + 1.20268i
\(99\) 10.5830i 1.06363i
\(100\) 0 0
\(101\) 10.5830i 1.05305i 0.850160 + 0.526524i \(0.176505\pi\)
−0.850160 + 0.526524i \(0.823495\pi\)
\(102\) 10.5000 3.96863i 1.03965 0.392953i
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 14.0000 5.29150i 1.35980 0.513956i
\(107\) 2.64575i 0.255774i 0.991789 + 0.127887i \(0.0408196\pi\)
−0.991789 + 0.127887i \(0.959180\pi\)
\(108\) 3.50000 + 3.96863i 0.336788 + 0.381881i
\(109\) 10.5830i 1.01367i −0.862044 0.506834i \(-0.830816\pi\)
0.862044 0.506834i \(-0.169184\pi\)
\(110\) 0 0
\(111\) −28.0000 −2.65764
\(112\) 2.00000 15.8745i 0.188982 1.50000i
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 3.50000 + 9.26013i 0.327805 + 0.867291i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 7.00000 2.64575i 0.644402 0.243561i
\(119\) −12.0000 −1.10004
\(120\) 0 0
\(121\) 4.00000 0.363636
\(122\) 14.0000 5.29150i 1.26750 0.479070i
\(123\) 13.2288i 1.19280i
\(124\) −6.00000 + 5.29150i −0.538816 + 0.475191i
\(125\) 0 0
\(126\) −8.00000 21.1660i −0.712697 1.88562i
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) −6.50000 + 9.26013i −0.574524 + 0.818488i
\(129\) −14.0000 −1.23263
\(130\) 0 0
\(131\) 15.8745i 1.38696i 0.720475 + 0.693481i \(0.243924\pi\)
−0.720475 + 0.693481i \(0.756076\pi\)
\(132\) −10.5000 + 9.26013i −0.913908 + 0.805991i
\(133\) 10.5830i 0.917663i
\(134\) 10.5000 3.96863i 0.907062 0.342837i
\(135\) 0 0
\(136\) 7.50000 + 3.96863i 0.643120 + 0.340307i
\(137\) −19.0000 −1.62328 −0.811640 0.584158i \(-0.801425\pi\)
−0.811640 + 0.584158i \(0.801425\pi\)
\(138\) −14.0000 + 5.29150i −1.19176 + 0.450443i
\(139\) 18.5203i 1.57087i 0.618945 + 0.785434i \(0.287560\pi\)
−0.618945 + 0.785434i \(0.712440\pi\)
\(140\) 0 0
\(141\) 21.1660i 1.78250i
\(142\) 4.00000 + 10.5830i 0.335673 + 0.888106i
\(143\) 0 0
\(144\) −2.00000 + 15.8745i −0.166667 + 1.32288i
\(145\) 0 0
\(146\) −3.50000 9.26013i −0.289662 0.766374i
\(147\) 23.8118i 1.96396i
\(148\) −14.0000 15.8745i −1.15079 1.30488i
\(149\) 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 \(0.447961\pi\)
\(152\) −3.50000 + 6.61438i −0.283887 + 0.536497i
\(153\) 12.0000 0.970143
\(154\) 14.0000 5.29150i 1.12815 0.426401i
\(155\) 0 0
\(156\) 0 0
\(157\) 10.5830i 0.844616i −0.906452 0.422308i \(-0.861220\pi\)
0.906452 0.422308i \(-0.138780\pi\)
\(158\) 2.00000 + 5.29150i 0.159111 + 0.420969i
\(159\) 28.0000 2.22054
\(160\) 0 0
\(161\) 16.0000 1.26098
\(162\) −2.50000 6.61438i −0.196419 0.519675i
\(163\) 13.2288i 1.03616i 0.855333 + 0.518078i \(0.173352\pi\)
−0.855333 + 0.518078i \(0.826648\pi\)
\(164\) 7.50000 6.61438i 0.585652 0.516496i
\(165\) 0 0
\(166\) 10.5000 3.96863i 0.814958 0.308025i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 14.0000 26.4575i 1.08012 2.04124i
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 10.5830i 0.809303i
\(172\) −7.00000 7.93725i −0.533745 0.605210i
\(173\) 21.1660i 1.60922i 0.593802 + 0.804611i \(0.297626\pi\)
−0.593802 + 0.804611i \(0.702374\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −10.5000 1.32288i −0.791467 0.0997155i
\(177\) 14.0000 1.05230
\(178\) −0.500000 1.32288i −0.0374766 0.0991537i
\(179\) 23.8118i 1.77977i −0.456180 0.889887i \(-0.650783\pi\)
0.456180 0.889887i \(-0.349217\pi\)
\(180\) 0 0
\(181\) 10.5830i 0.786629i −0.919404 0.393314i \(-0.871328\pi\)
0.919404 0.393314i \(-0.128672\pi\)
\(182\) 0 0
\(183\) 28.0000 2.06982
\(184\) −10.0000 5.29150i −0.737210 0.390095i
\(185\) 0 0
\(186\) −14.0000 + 5.29150i −1.02653 + 0.387992i
\(187\) 7.93725i 0.580429i
\(188\) 12.0000 10.5830i 0.875190 0.771845i
\(189\) 10.5830i 0.769800i
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) −17.5000 + 11.9059i −1.26295 + 0.859233i
\(193\) 5.00000 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) −1.00000 2.64575i −0.0717958 0.189954i
\(195\) 0 0
\(196\) −13.5000 + 11.9059i −0.964286 + 0.850420i
\(197\) 10.5830i 0.754008i −0.926212 0.377004i \(-0.876954\pi\)
0.926212 0.377004i \(-0.123046\pi\)
\(198\) −14.0000 + 5.29150i −0.994937 + 0.376051i
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 0 0
\(201\) 21.0000 1.48123
\(202\) −14.0000 + 5.29150i −0.985037 + 0.372309i
\(203\) 0 0
\(204\) 10.5000 + 11.9059i 0.735147 + 0.833578i
\(205\) 0 0
\(206\) 4.00000 + 10.5830i 0.278693 + 0.737353i
\(207\) −16.0000 −1.11208
\(208\) 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 \(0.911914\pi\)
\(212\) 14.0000 + 15.8745i 0.961524 + 1.09027i
\(213\) 21.1660i 1.45027i
\(214\) −3.50000 + 1.32288i −0.239255 + 0.0904299i
\(215\) 0 0
\(216\) −3.50000 + 6.61438i −0.238145 + 0.450051i
\(217\) 16.0000 1.08615
\(218\) 14.0000 5.29150i 0.948200 0.358386i
\(219\) 18.5203i 1.25148i
\(220\) 0 0
\(221\) 0 0
\(222\) −14.0000 37.0405i −0.939618 2.48600i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 22.0000 5.29150i 1.46994 0.353553i
\(225\) 0 0
\(226\) −7.50000 19.8431i −0.498893 1.31995i
\(227\) 15.8745i 1.05363i −0.849981 0.526814i \(-0.823386\pi\)
0.849981 0.526814i \(-0.176614\pi\)
\(228\) −10.5000 + 9.26013i −0.695379 + 0.613267i
\(229\) 21.1660i 1.39869i −0.714785 0.699345i \(-0.753475\pi\)
0.714785 0.699345i \(-0.246525\pi\)
\(230\) 0 0
\(231\) 28.0000 1.84226
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.00000 + 7.93725i 0.455661 + 0.516671i
\(237\) 10.5830i 0.687440i
\(238\) −6.00000 15.8745i −0.388922 1.02899i
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) −21.0000 −1.35273 −0.676364 0.736567i \(-0.736446\pi\)
−0.676364 + 0.736567i \(0.736446\pi\)
\(242\) 2.00000 + 5.29150i 0.128565 + 0.340151i
\(243\) 21.1660i 1.35780i
\(244\) 14.0000 + 15.8745i 0.896258 + 1.01626i
\(245\) 0 0
\(246\) 17.5000 6.61438i 1.11576 0.421717i
\(247\) 0 0
\(248\) −10.0000 5.29150i −0.635001 0.336011i
\(249\) 21.0000 1.33082
\(250\) 0 0
\(251\) 7.93725i 0.500995i 0.968117 + 0.250498i \(0.0805942\pi\)
−0.968117 + 0.250498i \(0.919406\pi\)
\(252\) 24.0000 21.1660i 1.51186 1.33333i
\(253\) 10.5830i 0.665348i
\(254\) 6.00000 + 15.8745i 0.376473 + 0.996055i
\(255\) 0 0
\(256\) −15.5000 3.96863i −0.968750 0.248039i
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) −7.00000 18.5203i −0.435801 1.15302i
\(259\) 42.3320i 2.63038i
\(260\) 0 0
\(261\) 0 0
\(262\) −21.0000 + 7.93725i −1.29738 + 0.490365i
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) −17.5000 9.26013i −1.07705 0.569922i
\(265\) 0 0
\(266\) 14.0000 5.29150i 0.858395 0.324443i
\(267\) 2.64575i 0.161917i
\(268\) 10.5000 + 11.9059i 0.641390 + 0.727267i
\(269\) 21.1660i 1.29051i 0.763965 + 0.645257i \(0.223250\pi\)
−0.763965 + 0.645257i \(0.776750\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) −1.50000 + 11.9059i −0.0909509 + 0.721900i
\(273\) 0 0
\(274\) −9.50000 25.1346i −0.573916 1.51844i
\(275\) 0 0
\(276\) −14.0000 15.8745i −0.842701 0.955533i
\(277\) 21.1660i 1.27174i 0.771795 + 0.635871i \(0.219359\pi\)
−0.771795 + 0.635871i \(0.780641\pi\)
\(278\) −24.5000 + 9.26013i −1.46941 + 0.555386i
\(279\) −16.0000 −0.957895
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 28.0000 10.5830i 1.66738 0.630209i
\(283\) 13.2288i 0.786368i 0.919460 + 0.393184i \(0.128626\pi\)
−0.919460 + 0.393184i \(0.871374\pi\)
\(284\) −12.0000 + 10.5830i −0.712069 + 0.627986i
\(285\) 0 0
\(286\) 0 0
\(287\) −20.0000 −1.18056
\(288\) −22.0000 + 5.29150i −1.29636 + 0.311805i
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 5.29150i 0.310193i
\(292\) 10.5000 9.26013i 0.614466 0.541908i
\(293\) 10.5830i 0.618266i 0.951019 + 0.309133i \(0.100039\pi\)
−0.951019 + 0.309133i \(0.899961\pi\)
\(294\) −31.5000 + 11.9059i −1.83712 + 0.694365i
\(295\) 0 0
\(296\) 14.0000 26.4575i 0.813733 1.53781i
\(297\) −7.00000 −0.406181
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 21.1660i 1.21999i
\(302\) 2.00000 + 5.29150i 0.115087 + 0.304492i
\(303\) −28.0000 −1.60856
\(304\) −10.5000 1.32288i −0.602216 0.0758721i
\(305\) 0 0
\(306\) 6.00000 + 15.8745i 0.342997 + 0.907485i
\(307\) 2.64575i 0.151001i 0.997146 + 0.0755005i \(0.0240554\pi\)
−0.997146 + 0.0755005i \(0.975945\pi\)
\(308\) 14.0000 + 15.8745i 0.797724 + 0.904534i
\(309\) 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
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 14.0000 5.29150i 0.790066 0.298617i
\(315\) 0 0
\(316\) −6.00000 + 5.29150i −0.337526 + 0.297670i
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 14.0000 + 37.0405i 0.785081 + 2.07713i
\(319\) 0 0
\(320\) 0 0
\(321\) −7.00000 −0.390702
\(322\) 8.00000 + 21.1660i 0.445823 + 1.17954i
\(323\) 7.93725i 0.441641i
\(324\) 7.50000 6.61438i 0.416667 0.367465i
\(325\) 0 0
\(326\) −17.5000 + 6.61438i −0.969235 + 0.366337i
\(327\) 28.0000 1.54840
\(328\) 12.5000 + 6.61438i 0.690197 + 0.365218i
\(329\) −32.0000 −1.76422
\(330\) 0 0
\(331\) 2.64575i 0.145424i −0.997353 0.0727118i \(-0.976835\pi\)
0.997353 0.0727118i \(-0.0231653\pi\)
\(332\) 10.5000 + 11.9059i 0.576262 + 0.653420i
\(333\) 42.3320i 2.31978i
\(334\) 0 0
\(335\) 0 0
\(336\) 42.0000 + 5.29150i 2.29129 + 0.288675i
\(337\) −15.0000 −0.817102 −0.408551 0.912735i \(-0.633966\pi\)
−0.408551 + 0.912735i \(0.633966\pi\)
\(338\) 6.50000 + 17.1974i 0.353553 + 0.935414i
\(339\) 39.6863i 2.15546i
\(340\) 0 0
\(341\) 10.5830i 0.573102i
\(342\) −14.0000 + 5.29150i −0.757033 + 0.286132i
\(343\) 8.00000 0.431959
\(344\) 7.00000 13.2288i 0.377415 0.713247i
\(345\) 0 0
\(346\) −28.0000 + 10.5830i −1.50529 + 0.568946i
\(347\) 2.64575i 0.142031i 0.997475 + 0.0710157i \(0.0226240\pi\)
−0.997475 + 0.0710157i \(0.977376\pi\)
\(348\) 0 0
\(349\) 10.5830i 0.566495i 0.959047 + 0.283248i \(0.0914118\pi\)
−0.959047 + 0.283248i \(0.908588\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.50000 14.5516i −0.186551 0.775605i
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 7.00000 + 18.5203i 0.372046 + 0.984341i
\(355\) 0 0
\(356\) 1.50000 1.32288i 0.0794998 0.0701123i
\(357\) 31.7490i 1.68034i
\(358\) 31.5000 11.9059i 1.66483 0.629245i
\(359\) 36.0000 1.90001 0.950004 0.312239i \(-0.101079\pi\)
0.950004 + 0.312239i \(0.101079\pi\)
\(360\) 0 0
\(361\) 12.0000 0.631579
\(362\) 14.0000 5.29150i 0.735824 0.278115i
\(363\) 10.5830i 0.555464i
\(364\) 0 0
\(365\) 0 0
\(366\) 14.0000 + 37.0405i 0.731792 + 1.93614i
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 2.00000 15.8745i 0.104257 0.827516i
\(369\) 20.0000 1.04116
\(370\) 0 0
\(371\) 42.3320i 2.19777i
\(372\) −14.0000 15.8745i −0.725866 0.823055i
\(373\) 10.5830i 0.547967i −0.961734 0.273984i \(-0.911659\pi\)
0.961734 0.273984i \(-0.0883414\pi\)
\(374\) −10.5000 + 3.96863i −0.542942 + 0.205213i
\(375\) 0 0
\(376\) 20.0000 + 10.5830i 1.03142 + 0.545777i
\(377\) 0 0
\(378\) 14.0000 5.29150i 0.720082 0.272166i
\(379\) 7.93725i 0.407709i 0.979001 + 0.203855i \(0.0653470\pi\)
−0.979001 + 0.203855i \(0.934653\pi\)
\(380\) 0 0
\(381\) 31.7490i 1.62655i
\(382\) 2.00000 + 5.29150i 0.102329 + 0.270737i
\(383\) −36.0000 −1.83951 −0.919757 0.392488i \(-0.871614\pi\)
−0.919757 + 0.392488i \(0.871614\pi\)
\(384\) −24.5000 17.1974i −1.25026 0.877600i
\(385\) 0 0
\(386\) 2.50000 + 6.61438i 0.127247 + 0.336663i
\(387\) 21.1660i 1.07593i
\(388\) 3.00000 2.64575i 0.152302 0.134318i
\(389\) 10.5830i 0.536580i −0.963338 0.268290i \(-0.913542\pi\)
0.963338 0.268290i \(-0.0864585\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) −22.5000 11.9059i −1.13642 0.601338i
\(393\) −42.0000 −2.11862
\(394\) 14.0000 5.29150i 0.705310 0.266582i
\(395\) 0 0
\(396\) −14.0000 15.8745i −0.703526 0.797724i
\(397\) 21.1660i 1.06229i 0.847280 + 0.531146i \(0.178238\pi\)
−0.847280 + 0.531146i \(0.821762\pi\)
\(398\) −12.0000 31.7490i −0.601506 1.59143i
\(399\) 28.0000 1.40175
\(400\) 0 0
\(401\) 27.0000 1.34832 0.674158 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) 10.5000 + 27.7804i 0.523692 + 1.38556i
\(403\) 0 0
\(404\) −14.0000 15.8745i −0.696526 0.789786i
\(405\) 0 0
\(406\) 0 0
\(407\) 28.0000 1.38791
\(408\) −10.5000 + 19.8431i −0.519827 + 0.982382i
\(409\) 3.00000 0.148340 0.0741702 0.997246i \(-0.476369\pi\)
0.0741702 + 0.997246i \(0.476369\pi\)
\(410\) 0 0
\(411\) 50.2693i 2.47960i
\(412\) −12.0000 + 10.5830i −0.591198 + 0.521387i
\(413\) 21.1660i 1.04151i
\(414\) −8.00000 21.1660i −0.393179 1.04025i
\(415\) 0 0
\(416\) 0 0
\(417\) −49.0000 −2.39954
\(418\) −3.50000 9.26013i −0.171191 0.452928i
\(419\) 18.5203i 0.904774i 0.891822 + 0.452387i \(0.149427\pi\)
−0.891822 + 0.452387i \(0.850573\pi\)
\(420\) 0 0
\(421\) 21.1660i 1.03157i −0.856719 0.515784i \(-0.827501\pi\)
0.856719 0.515784i \(-0.172499\pi\)
\(422\) −10.5000 + 3.96863i −0.511132 + 0.193190i
\(423\) 32.0000 1.55589
\(424\) −14.0000 + 26.4575i −0.679900 + 1.28489i
\(425\) 0 0
\(426\) −28.0000 + 10.5830i −1.35660 + 0.512748i
\(427\) 42.3320i 2.04859i
\(428\) −3.50000 3.96863i −0.169179 0.191831i
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −10.5000 1.32288i −0.505181 0.0636469i
\(433\) 37.0000 1.77811 0.889053 0.457804i \(-0.151364\pi\)
0.889053 + 0.457804i \(0.151364\pi\)
\(434\) 8.00000 + 21.1660i 0.384012 + 1.01600i
\(435\) 0 0
\(436\) 14.0000 + 15.8745i 0.670478 + 0.760251i
\(437\) 10.5830i 0.506254i
\(438\) 24.5000 9.26013i 1.17066 0.442466i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) −36.0000 −1.71429
\(442\) 0 0
\(443\) 29.1033i 1.38274i −0.722502 0.691369i \(-0.757008\pi\)
0.722502 0.691369i \(-0.242992\pi\)
\(444\) 42.0000 37.0405i 1.99323 1.75787i
\(445\) 0 0
\(446\) −8.00000 21.1660i −0.378811 1.00224i
\(447\) 0 0
\(448\) 18.0000 + 26.4575i 0.850420 + 1.25000i
\(449\) 27.0000 1.27421 0.637104 0.770778i \(-0.280132\pi\)
0.637104 + 0.770778i \(0.280132\pi\)
\(450\) 0 0
\(451\) 13.2288i 0.622918i
\(452\) 22.5000 19.8431i 1.05831 0.933343i
\(453\) 10.5830i 0.497233i
\(454\) 21.0000 7.93725i 0.985579 0.372514i
\(455\) 0 0
\(456\) −17.5000 9.26013i −0.819513 0.433645i
\(457\) −27.0000 −1.26301 −0.631503 0.775373i \(-0.717562\pi\)
−0.631503 + 0.775373i \(0.717562\pi\)
\(458\) 28.0000 10.5830i 1.30835 0.494511i
\(459\) 7.93725i 0.370479i
\(460\) 0 0
\(461\) 42.3320i 1.97160i 0.167927 + 0.985799i \(0.446293\pi\)
−0.167927 + 0.985799i \(0.553707\pi\)
\(462\) 14.0000 + 37.0405i 0.651339 + 1.72328i
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 3.00000 + 7.93725i 0.138972 + 0.367686i
\(467\) 26.4575i 1.22431i 0.790739 + 0.612154i \(0.209697\pi\)
−0.790739 + 0.612154i \(0.790303\pi\)
\(468\) 0 0
\(469\) 31.7490i 1.46603i
\(470\) 0 0
\(471\) 28.0000 1.29017
\(472\) −7.00000 + 13.2288i −0.322201 + 0.608903i
\(473\) 14.0000 0.643721
\(474\) −14.0000 + 5.29150i −0.643041 + 0.243047i
\(475\) 0 0
\(476\) 18.0000 15.8745i 0.825029 0.727607i
\(477\) 42.3320i 1.93825i
\(478\) −4.00000 10.5830i −0.182956 0.484055i
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −10.5000 27.7804i −0.478262 1.26536i
\(483\) 42.3320i 1.92617i
\(484\) −6.00000 + 5.29150i −0.272727 + 0.240523i
\(485\) 0 0
\(486\) 28.0000 10.5830i 1.27011 0.480055i
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) −14.0000 + 26.4575i −0.633750 + 1.19768i
\(489\) −35.0000 −1.58275
\(490\) 0 0
\(491\) 5.29150i 0.238802i −0.992846 0.119401i \(-0.961903\pi\)
0.992846 0.119401i \(-0.0380974\pi\)
\(492\) 17.5000 + 19.8431i 0.788961 + 0.894598i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.00000 15.8745i 0.0898027 0.712786i
\(497\) 32.0000 1.43540
\(498\) 10.5000 + 27.7804i 0.470516 + 1.24487i
\(499\) 26.4575i 1.18440i −0.805791 0.592200i \(-0.798259\pi\)
0.805791 0.592200i \(-0.201741\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −10.5000 + 3.96863i −0.468638 + 0.177128i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 40.0000 + 21.1660i 1.78174 + 0.942809i
\(505\) 0 0
\(506\) 14.0000 5.29150i 0.622376 0.235236i
\(507\) 34.3948i 1.52753i
\(508\) −18.0000 + 15.8745i −0.798621 + 0.704317i
\(509\) 31.7490i 1.40725i 0.710571 + 0.703625i \(0.248437\pi\)
−0.710571 + 0.703625i \(0.751563\pi\)
\(510\) 0 0
\(511\) −28.0000 −1.23865
\(512\) −2.50000 22.4889i −0.110485 0.993878i
\(513\) −7.00000 −0.309058
\(514\) 7.00000 + 18.5203i 0.308757 + 0.816894i
\(515\) 0 0
\(516\) 21.0000 18.5203i 0.924473 0.815309i
\(517\) 21.1660i 0.930880i
\(518\) −56.0000 + 21.1660i −2.46050 + 0.929981i
\(519\) −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
\(523\) 2.64575i 0.115691i 0.998326 + 0.0578453i \(0.0184230\pi\)
−0.998326 + 0.0578453i \(0.981577\pi\)
\(524\) −21.0000 23.8118i −0.917389 1.04022i
\(525\) 0 0
\(526\) 6.00000 + 15.8745i 0.261612 + 0.692161i
\(527\) −12.0000 −0.522728
\(528\) 3.50000 27.7804i 0.152318 1.20899i
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 21.1660i 0.918527i
\(532\) 14.0000 + 15.8745i 0.606977 + 0.688247i
\(533\) 0 0
\(534\) 3.50000 1.32288i 0.151460 0.0572464i
\(535\) 0 0
\(536\) −10.5000 + 19.8431i −0.453531 + 0.857093i
\(537\) 63.0000 2.71865
\(538\) −28.0000 + 10.5830i −1.20717 + 0.456266i
\(539\) 23.8118i 1.02565i
\(540\) 0 0
\(541\) 21.1660i 0.909998i 0.890492 + 0.454999i \(0.150360\pi\)
−0.890492 + 0.454999i \(0.849640\pi\)
\(542\) −10.0000 26.4575i −0.429537 1.13645i
\(543\) 28.0000 1.20160
\(544\) −16.5000 + 3.96863i −0.707432 + 0.170153i
\(545\) 0 0
\(546\) 0 0
\(547\) 18.5203i 0.791869i −0.918279 0.395935i \(-0.870421\pi\)
0.918279 0.395935i \(-0.129579\pi\)
\(548\) 28.5000 25.1346i 1.21746 1.07370i
\(549\) 42.3320i 1.80669i
\(550\) 0 0
\(551\) 0 0
\(552\) 14.0000 26.4575i 0.595880 1.12611i
\(553\) 16.0000 0.680389
\(554\) −28.0000 + 10.5830i −1.18961 + 0.449629i
\(555\) 0 0
\(556\) −24.5000 27.7804i −1.03903 1.17815i
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −8.00000 21.1660i −0.338667 0.896029i
\(559\) 0 0
\(560\) 0 0
\(561\) −21.0000 −0.886621
\(562\) −11.0000 29.1033i −0.464007 1.22765i
\(563\) 15.8745i 0.669031i −0.942390 0.334515i \(-0.891427\pi\)
0.942390 0.334515i \(-0.108573\pi\)
\(564\) 28.0000 + 31.7490i 1.17901 + 1.33687i
\(565\) 0 0
\(566\) −17.5000 + 6.61438i −0.735580 + 0.278023i
\(567\) −20.0000 −0.839921
\(568\) −20.0000 10.5830i −0.839181 0.444053i
\(569\) 11.0000 0.461144 0.230572 0.973055i \(-0.425940\pi\)
0.230572 + 0.973055i \(0.425940\pi\)
\(570\) 0 0
\(571\) 37.0405i 1.55010i 0.631901 + 0.775049i \(0.282275\pi\)
−0.631901 + 0.775049i \(0.717725\pi\)
\(572\) 0 0
\(573\) 10.5830i 0.442111i
\(574\) −10.0000 26.4575i −0.417392 1.10432i
\(575\) 0 0
\(576\) −18.0000 26.4575i −0.750000 1.10240i
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) −4.00000 10.5830i −0.166378 0.440195i
\(579\) 13.2288i 0.549768i
\(580\) 0 0
\(581\) 31.7490i 1.31717i
\(582\) 7.00000 2.64575i 0.290159 0.109670i
\(583\) −28.0000 −1.15964
\(584\) 17.5000 + 9.26013i 0.724155 + 0.383187i
\(585\) 0 0
\(586\) −14.0000 + 5.29150i −0.578335 + 0.218590i
\(587\) 7.93725i 0.327606i −0.986493 0.163803i \(-0.947624\pi\)
0.986493 0.163803i \(-0.0523761\pi\)
\(588\) −31.5000 35.7176i −1.29904 1.47297i
\(589\) 10.5830i 0.436065i
\(590\) 0 0
\(591\) 28.0000 1.15177
\(592\) 42.0000 + 5.29150i 1.72619 + 0.217479i
\(593\) 41.0000 1.68367 0.841834 0.539736i \(-0.181476\pi\)
0.841834 + 0.539736i \(0.181476\pi\)
\(594\) −3.50000 9.26013i −0.143607 0.379948i
\(595\) 0 0
\(596\) 0 0
\(597\) 63.4980i 2.59880i
\(598\) 0 0
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) −28.0000 + 10.5830i −1.14119 + 0.431331i
\(603\) 31.7490i 1.29292i
\(604\) −6.00000 + 5.29150i −0.244137 + 0.215308i
\(605\) 0 0
\(606\) −14.0000 37.0405i −0.568711 1.50467i
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −3.50000 14.5516i −0.141944 0.590147i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −18.0000 + 15.8745i −0.727607 + 0.641689i
\(613\) 10.5830i 0.427444i 0.976895 + 0.213722i \(0.0685586\pi\)
−0.976895 + 0.213722i \(0.931441\pi\)
\(614\) −3.50000 + 1.32288i −0.141249 + 0.0533869i
\(615\) 0 0
\(616\) −14.0000 + 26.4575i −0.564076 + 1.06600i
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) −28.0000 + 10.5830i −1.12633 + 0.425711i
\(619\) 5.29150i 0.212683i −0.994330 0.106342i \(-0.966086\pi\)
0.994330 0.106342i \(-0.0339137\pi\)
\(620\) 0 0
\(621\) 10.5830i 0.424681i
\(622\) −2.00000 5.29150i −0.0801927 0.212170i
\(623\) −4.00000 −0.160257
\(624\) 0 0
\(625\) 0 0
\(626\) 3.00000 + 7.93725i 0.119904 + 0.317236i
\(627\) 18.5203i 0.739628i
\(628\) 14.0000 + 15.8745i 0.558661 + 0.633462i
\(629\) 31.7490i 1.26592i
\(630\) 0 0
\(631\) 36.0000 1.43314 0.716569 0.697517i \(-0.245712\pi\)
0.716569 + 0.697517i \(0.245712\pi\)
\(632\) −10.0000 5.29150i −0.397779 0.210485i
\(633\) −21.0000 −0.834675
\(634\) 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 \(0.487424\pi\)
\(642\) −3.50000 9.26013i −0.138134 0.365468i
\(643\) 15.8745i 0.626029i −0.949748 0.313015i \(-0.898661\pi\)
0.949748 0.313015i \(-0.101339\pi\)
\(644\) −24.0000 + 21.1660i −0.945732 + 0.834058i
\(645\) 0 0
\(646\) −10.5000 + 3.96863i −0.413117 + 0.156144i
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 12.5000 + 6.61438i 0.491046 + 0.259837i
\(649\) −14.0000 −0.549548
\(650\) 0 0
\(651\) 42.3320i 1.65912i
\(652\) −17.5000 19.8431i −0.685353 0.777117i
\(653\) 31.7490i 1.24243i 0.783638 + 0.621217i \(0.213362\pi\)
−0.783638 + 0.621217i \(0.786638\pi\)
\(654\) 14.0000 + 37.0405i 0.547443 + 1.44840i
\(655\) 0 0
\(656\) −2.50000 + 19.8431i −0.0976086 + 0.774744i
\(657\) 28.0000 1.09238
\(658\) −16.0000 42.3320i −0.623745 1.65027i
\(659\) 7.93725i 0.309192i 0.987978 + 0.154596i \(0.0494075\pi\)
−0.987978 + 0.154596i \(0.950592\pi\)
\(660\) 0 0
\(661\) 21.1660i 0.823262i −0.911351 0.411631i \(-0.864959\pi\)
0.911351 0.411631i \(-0.135041\pi\)
\(662\) 3.50000 1.32288i 0.136031 0.0514150i
\(663\) 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
\(672\) 14.0000 + 58.2065i 0.540062 + 2.24537i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −7.50000 19.8431i −0.288889 0.764329i
\(675\) 0 0
\(676\) −19.5000 + 17.1974i −0.750000 + 0.661438i
\(677\) 42.3320i 1.62695i 0.581599 + 0.813476i \(0.302427\pi\)
−0.581599 + 0.813476i \(0.697573\pi\)
\(678\) 52.5000 19.8431i 2.01625 0.762071i
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) 42.0000 1.60944
\(682\) 14.0000 5.29150i 0.536088 0.202622i
\(683\) 23.8118i 0.911132i 0.890202 + 0.455566i \(0.150563\pi\)
−0.890202 + 0.455566i \(0.849437\pi\)
\(684\) −14.0000 15.8745i −0.535303 0.606977i
\(685\) 0 0
\(686\) 4.00000 + 10.5830i 0.152721 + 0.404061i
\(687\) 56.0000 2.13653
\(688\) 21.0000 + 2.64575i 0.800617 + 0.100868i
\(689\) 0 0
\(690\) 0 0
\(691\) 23.8118i 0.905842i −0.891551 0.452921i \(-0.850382\pi\)
0.891551 0.452921i \(-0.149618\pi\)
\(692\) −28.0000 31.7490i −1.06440 1.20692i
\(693\) 42.3320i 1.60806i
\(694\) −3.50000 + 1.32288i −0.132858 + 0.0502157i
\(695\) 0 0
\(696\) 0 0
\(697\) 15.0000 0.568166
\(698\) −14.0000 + 5.29150i −0.529908 + 0.200286i
\(699\) 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
\(703\) 28.0000 1.05604
\(704\) 17.5000 11.9059i 0.659556 0.448720i
\(705\) 0 0
\(706\) −9.00000 23.8118i −0.338719 0.896167i
\(707\) 42.3320i 1.59206i
\(708\) −21.0000 + 18.5203i −0.789228 + 0.696034i
\(709\) 21.1660i 0.794906i −0.917622 0.397453i \(-0.869894\pi\)
0.917622 0.397453i \(-0.130106\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) 2.50000 + 1.32288i 0.0936915 + 0.0495769i
\(713\) 16.0000 0.599205
\(714\) 42.0000 15.8745i 1.57181 0.594089i
\(715\) 0 0
\(716\) 31.5000 + 35.7176i 1.17721 + 1.33483i
\(717\) 21.1660i 0.790459i
\(718\) 18.0000 + 47.6235i 0.671754 + 1.77729i
\(719\) 36.0000 1.34257 0.671287 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 0 0
\(721\) 32.0000 1.19174
\(722\) 6.00000 + 15.8745i 0.223297 + 0.590788i
\(723\) 55.5608i 2.06633i
\(724\) 14.0000 + 15.8745i 0.520306 + 0.589971i
\(725\) 0 0
\(726\) −14.0000 + 5.29150i −0.519589 + 0.196386i
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 41.0000 1.51852
\(730\) 0 0
\(731\) 15.8745i 0.587140i
\(732\) −42.0000 + 37.0405i −1.55236 + 1.36906i
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 22.0000 5.29150i 0.810931 0.195047i
\(737\) −21.0000 −0.773545
\(738\) 10.0000 + 26.4575i 0.368105 + 0.973915i
\(739\) 15.8745i 0.583953i 0.956425 + 0.291977i \(0.0943129\pi\)
−0.956425 + 0.291977i \(0.905687\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 56.0000 21.1660i 2.05582 0.777029i
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 14.0000 26.4575i 0.513265 0.969979i
\(745\) 0 0
\(746\) 14.0000 5.29150i 0.512576 0.193736i
\(747\) 31.7490i 1.16164i
\(748\) −10.5000 11.9059i −0.383918 0.435322i
\(749\) 10.5830i 0.386695i
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −4.00000 + 31.7490i −0.145865 + 1.15777i
\(753\) −21.0000 −0.765283
\(754\) 0 0
\(755\) 0 0
\(756\) 14.0000 + 15.8745i 0.509175 + 0.577350i
\(757\) 21.1660i 0.769292i −0.923064 0.384646i \(-0.874324\pi\)
0.923064 0.384646i \(-0.125676\pi\)
\(758\) −10.5000 + 3.96863i −0.381377 + 0.144147i
\(759\) 28.0000 1.01634
\(760\) 0 0
\(761\) −29.0000 −1.05125 −0.525625 0.850717i \(-0.676168\pi\)
−0.525625 + 0.850717i \(0.676168\pi\)
\(762\) −42.0000 + 15.8745i −1.52150 + 0.575073i
\(763\) 42.3320i 1.53252i
\(764\) −6.00000 + 5.29150i −0.217072 + 0.191440i
\(765\) 0 0
\(766\) −18.0000 47.6235i −0.650366 1.72071i
\(767\) 0 0
\(768\) 10.5000 41.0091i 0.378886 1.47979i
\(769\) −21.0000 −0.757279 −0.378640 0.925544i \(-0.623608\pi\)
−0.378640 + 0.925544i \(0.623608\pi\)
\(770\) 0 0
\(771\) 37.0405i 1.33398i
\(772\) −7.50000 + 6.61438i −0.269931 + 0.238057i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 28.0000 10.5830i 1.00644 0.380398i
\(775\) 0 0
\(776\) 5.00000 + 2.64575i 0.179490 + 0.0949769i
\(777\) −112.000 −4.01798
\(778\) 14.0000 5.29150i 0.501924 0.189710i
\(779\) 13.2288i 0.473969i
\(780\) 0 0
\(781\) 21.1660i 0.757379i
\(782\) −6.00000 15.8745i −0.214560 0.567671i
\(783\) 0 0
\(784\) 4.50000 35.7176i 0.160714 1.27563i
\(785\) 0 0
\(786\) −21.0000 55.5608i −0.749045 1.98179i
\(787\) 26.4575i 0.943108i 0.881837 + 0.471554i \(0.156307\pi\)
−0.881837 + 0.471554i \(0.843693\pi\)
\(788\) 14.0000 + 15.8745i 0.498729 + 0.565506i
\(789\) 31.7490i 1.13029i
\(790\) 0 0
\(791\) −60.0000 −2.13335
\(792\) 14.0000 26.4575i 0.497468 0.940127i
\(793\) 0 0
\(794\) −28.0000 + 10.5830i −0.993683 + 0.375577i
\(795\) 0 0
\(796\) 36.0000 31.7490i 1.27599 1.12531i
\(797\) 31.7490i 1.12461i −0.826931 0.562304i \(-0.809915\pi\)
0.826931 0.562304i \(-0.190085\pi\)
\(798\) 14.0000 + 37.0405i 0.495595 + 1.31122i
\(799\) 24.0000 0.849059
\(800\) 0 0
\(801\) 4.00000 0.141333
\(802\) 13.5000 + 35.7176i 0.476702 + 1.26123i
\(803\) 18.5203i 0.653566i
\(804\) −31.5000 + 27.7804i −1.11092 + 0.979739i
\(805\) 0 0
\(806\) 0 0
\(807\) −56.0000 −1.97129
\(808\) 14.0000 26.4575i 0.492518 0.930772i
\(809\) 10.0000 0.351581 0.175791 0.984428i \(-0.443752\pi\)
0.175791 + 0.984428i \(0.443752\pi\)
\(810\) 0 0
\(811\) 5.29150i 0.185810i −0.995675 0.0929049i \(-0.970385\pi\)
0.995675 0.0929049i \(-0.0296153\pi\)
\(812\) 0 0
\(813\) 52.9150i 1.85581i
\(814\) 14.0000 + 37.0405i 0.490700 + 1.29827i
\(815\) 0 0
\(816\) −31.5000 3.96863i −1.10272 0.138930i
\(817\) 14.0000 0.489798
\(818\) 1.50000 + 3.96863i 0.0524463 + 0.138760i
\(819\) 0 0
\(820\) 0 0
\(821\) 10.5830i 0.369349i 0.982800 + 0.184675i \(0.0591232\pi\)
−0.982800 + 0.184675i \(0.940877\pi\)
\(822\) 66.5000 25.1346i 2.31945 0.876671i
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) −20.0000 10.5830i −0.696733 0.368676i
\(825\) 0 0
\(826\) 28.0000 10.5830i 0.974245 0.368230i
\(827\) 13.2288i 0.460009i 0.973190 + 0.230004i \(0.0738741\pi\)
−0.973190 + 0.230004i \(0.926126\pi\)
\(828\) 24.0000 21.1660i 0.834058 0.735570i
\(829\) 21.1660i 0.735126i 0.929999 + 0.367563i \(0.119808\pi\)
−0.929999 + 0.367563i \(0.880192\pi\)
\(830\) 0 0
\(831\) −56.0000 −1.94262
\(832\) 0 0
\(833\) −27.0000 −0.935495
\(834\) −24.5000 64.8209i −0.848366 2.24456i
\(835\) 0 0
\(836\) 10.5000 9.26013i 0.363150 0.320268i
\(837\) 10.5830i 0.365802i
\(838\) −24.5000 + 9.26013i −0.846338 + 0.319886i
\(839\) 40.0000 1.38095 0.690477 0.723355i \(-0.257401\pi\)
0.690477 + 0.723355i \(0.257401\pi\)
\(840\) 0 0
\(841\) 29.0000 1.00000
\(842\) 28.0000 10.5830i 0.964944 0.364714i
\(843\) 58.2065i 2.00474i
\(844\) −10.5000 11.9059i −0.361425 0.409817i
\(845\) 0 0
\(846\) 16.0000 + 42.3320i 0.550091 + 1.45540i
\(847\) 16.0000 0.549767
\(848\) −42.0000 5.29150i −1.44229 0.181711i
\(849\) −35.0000 −1.20120
\(850\) 0 0
\(851\) 42.3320i 1.45112i
\(852\) −28.0000 31.7490i −0.959264 1.08770i
\(853\) 52.9150i 1.81178i −0.423517 0.905888i \(-0.639205\pi\)
0.423517 0.905888i \(-0.360795\pi\)
\(854\) 56.0000 21.1660i 1.91628 0.724286i
\(855\) 0 0
\(856\) 3.50000 6.61438i 0.119628 0.226075i
\(857\) 21.0000 0.717346 0.358673 0.933463i \(-0.383229\pi\)
0.358673 + 0.933463i \(0.383229\pi\)
\(858\) 0 0
\(859\) 2.64575i 0.0902719i −0.998981 0.0451359i \(-0.985628\pi\)
0.998981 0.0451359i \(-0.0143721\pi\)
\(860\) 0 0
\(861\) 52.9150i 1.80334i
\(862\) 6.00000 + 15.8745i 0.204361 + 0.540688i
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) −3.50000 14.5516i −0.119072 0.495057i
\(865\) 0 0
\(866\) 18.5000 + 48.9464i 0.628656 + 1.66327i
\(867\) 21.1660i 0.718835i
\(868\) −24.0000 + 21.1660i −0.814613 + 0.718421i
\(869\) 10.5830i 0.359004i
\(870\) 0 0
\(871\) 0 0
\(872\) −14.0000 + 26.4575i −0.474100 + 0.895964i
\(873\) 8.00000 0.270759
\(874\) 14.0000 5.29150i 0.473557 0.178988i
\(875\) 0 0
\(876\) 24.5000 + 27.7804i 0.827778 + 0.938612i
\(877\) 42.3320i 1.42945i −0.699405 0.714725i \(-0.746552\pi\)
0.699405 0.714725i \(-0.253448\pi\)
\(878\) 4.00000 + 10.5830i 0.134993 + 0.357159i
\(879\) −28.0000 −0.944417
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) −18.0000 47.6235i −0.606092 1.60357i
\(883\) 44.9778i 1.51362i 0.653633 + 0.756811i \(0.273244\pi\)
−0.653633 + 0.756811i \(0.726756\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 38.5000 14.5516i 1.29343 0.488872i
\(887\) 56.0000 1.88030 0.940148 0.340766i \(-0.110687\pi\)
0.940148 + 0.340766i \(0.110687\pi\)
\(888\) 70.0000 + 37.0405i 2.34905 + 1.24300i
\(889\) 48.0000 1.60987
\(890\) 0 0
\(891\) 13.2288i 0.443180i
\(892\) 24.0000 21.1660i 0.803579 0.708690i
\(893\) 21.1660i 0.708294i
\(894\) 0 0
\(895\) 0 0
\(896\) −26.0000 + 37.0405i −0.868599 + 1.23744i
\(897\) 0 0
\(898\) 13.5000 + 35.7176i 0.450501 + 1.19191i
\(899\) 0 0
\(900\) 0 0
\(901\) 31.7490i 1.05771i
\(902\) −17.5000 + 6.61438i −0.582686 + 0.220235i
\(903\) −56.0000 −1.86356
\(904\) 37.5000 + 19.8431i 1.24723 + 0.659973i
\(905\) 0 0
\(906\) −14.0000 + 5.29150i −0.465119 + 0.175798i
\(907\) 5.29150i 0.175701i 0.996134 + 0.0878507i \(0.0279999\pi\)
−0.996134 + 0.0878507i \(0.972000\pi\)
\(908\) 21.0000 + 23.8118i 0.696909 + 0.790221i
\(909\) 42.3320i 1.40406i
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 3.50000 27.7804i 0.115897 0.919901i
\(913\) −21.0000 −0.694999
\(914\) −13.5000 35.7176i −0.446540 1.18143i
\(915\) 0 0
\(916\) 28.0000 + 31.7490i 0.925146 + 1.04902i
\(917\) 63.4980i 2.09689i
\(918\) −10.5000 + 3.96863i −0.346552 + 0.130984i
\(919\) 4.00000 0.131948 0.0659739 0.997821i \(-0.478985\pi\)
0.0659739 + 0.997821i \(0.478985\pi\)
\(920\) 0 0
\(921\) −7.00000 −0.230658
\(922\) −56.0000 + 21.1660i −1.84426 + 0.697065i
\(923\) 0 0
\(924\) −42.0000 + 37.0405i −1.38170 + 1.21854i
\(925\) 0 0
\(926\) −4.00000 10.5830i −0.131448 0.347779i
\(927\) −32.0000 −1.05102
\(928\) 0 0
\(929\) −14.0000 −0.459325 −0.229663 0.973270i \(-0.573762\pi\)
−0.229663 + 0.973270i \(0.573762\pi\)
\(930\) 0 0
\(931\) 23.8118i 0.780399i
\(932\) −9.00000 + 7.93725i −0.294805 + 0.259993i
\(933\) 10.5830i 0.346472i
\(934\) −35.0000 + 13.2288i −1.14523 + 0.432858i
\(935\) 0 0
\(936\) 0 0
\(937\) −7.00000 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 42.0000 15.8745i 1.37135 0.518321i
\(939\) 15.8745i 0.518045i
\(940\) 0 0
\(941\) 42.3320i 1.37998i −0.723817 0.689992i \(-0.757614\pi\)
0.723817 0.689992i \(-0.242386\pi\)
\(942\) 14.0000 + 37.0405i 0.456145 + 1.20685i
\(943\) −20.0000 −0.651290
\(944\) −21.0000 2.64575i −0.683492 0.0861119i
\(945\) 0 0
\(946\) 7.00000 + 18.5203i 0.227590 + 0.602146i
\(947\) 15.8745i 0.515852i −0.966165 0.257926i \(-0.916961\pi\)
0.966165 0.257926i \(-0.0830391\pi\)
\(948\) −14.0000 15.8745i −0.454699 0.515580i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 30.0000 + 15.8745i 0.972306 + 0.514496i
\(953\) 5.00000 0.161966 0.0809829 0.996715i \(-0.474194\pi\)
0.0809829 + 0.996715i \(0.474194\pi\)
\(954\) −56.0000 + 21.1660i −1.81307 + 0.685275i
\(955\) 0 0
\(956\) 12.0000 10.5830i 0.388108 0.342279i
\(957\) 0 0
\(958\) 2.00000 + 5.29150i 0.0646171 + 0.170961i
\(959\) −76.0000 −2.45417
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 10.5830i 0.341033i
\(964\) 31.5000 27.7804i 1.01455 0.894746i
\(965\) 0 0
\(966\) −56.0000 + 21.1660i −1.80177 + 0.681005i
\(967\) 8.00000 0.257263 0.128631 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) −10.0000 5.29150i −0.321412 0.170075i
\(969\) −21.0000 −0.674617
\(970\) 0 0
\(971\) 23.8118i 0.764156i −0.924130 0.382078i \(-0.875209\pi\)
0.924130 0.382078i \(-0.124791\pi\)
\(972\) 28.0000 + 31.7490i 0.898100 + 1.01835i
\(973\) 74.0810i 2.37493i
\(974\) −6.00000 15.8745i −0.192252 0.508652i
\(975\) 0 0
\(976\) −42.0000 5.29150i −1.34439 0.169377i
\(977\) 37.0000 1.18373 0.591867 0.806035i \(-0.298391\pi\)
0.591867 + 0.806035i \(0.298391\pi\)
\(978\) −17.5000 46.3006i −0.559588 1.48053i
\(979\) 2.64575i 0.0845586i
\(980\) 0 0
\(981\) 42.3320i 1.35156i
\(982\) 7.00000 2.64575i 0.223379 0.0844293i
\(983\) −28.0000 −0.893061 −0.446531 0.894768i \(-0.647341\pi\)
−0.446531 + 0.894768i \(0.647341\pi\)
\(984\) −17.5000 + 33.0719i −0.557880 + 1.05429i
\(985\) 0 0
\(986\) 0 0
\(987\) 84.6640i 2.69489i
\(988\) 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 \(0.253694\pi\)
\(992\) 22.0000 5.29150i 0.698501 0.168005i
\(993\) 7.00000 0.222138
\(994\) 16.0000 + 42.3320i 0.507489 + 1.34269i
\(995\) 0 0
\(996\) −31.5000 + 27.7804i −0.998116 + 0.880255i
\(997\) 42.3320i 1.34067i −0.742059 0.670334i \(-0.766151\pi\)
0.742059 0.670334i \(-0.233849\pi\)
\(998\) 35.0000 13.2288i 1.10791 0.418749i
\(999\) 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.d.c.101.2 yes 2
3.2 odd 2 1800.2.k.d.901.1 2
4.3 odd 2 800.2.d.a.401.1 2
5.2 odd 4 200.2.f.d.149.2 4
5.3 odd 4 200.2.f.d.149.3 4
5.4 even 2 200.2.d.b.101.1 2
8.3 odd 2 800.2.d.a.401.2 2
8.5 even 2 inner 200.2.d.c.101.1 yes 2
12.11 even 2 7200.2.k.b.3601.1 2
15.2 even 4 1800.2.d.m.1549.3 4
15.8 even 4 1800.2.d.m.1549.2 4
15.14 odd 2 1800.2.k.f.901.2 2
16.3 odd 4 6400.2.a.cb.1.2 2
16.5 even 4 6400.2.a.bg.1.2 2
16.11 odd 4 6400.2.a.cb.1.1 2
16.13 even 4 6400.2.a.bg.1.1 2
20.3 even 4 800.2.f.d.49.4 4
20.7 even 4 800.2.f.d.49.1 4
20.19 odd 2 800.2.d.d.401.2 2
24.5 odd 2 1800.2.k.d.901.2 2
24.11 even 2 7200.2.k.b.3601.2 2
40.3 even 4 800.2.f.d.49.2 4
40.13 odd 4 200.2.f.d.149.1 4
40.19 odd 2 800.2.d.d.401.1 2
40.27 even 4 800.2.f.d.49.3 4
40.29 even 2 200.2.d.b.101.2 yes 2
40.37 odd 4 200.2.f.d.149.4 4
60.23 odd 4 7200.2.d.m.2449.3 4
60.47 odd 4 7200.2.d.m.2449.1 4
60.59 even 2 7200.2.k.i.3601.1 2
80.19 odd 4 6400.2.a.bh.1.1 2
80.29 even 4 6400.2.a.cc.1.2 2
80.59 odd 4 6400.2.a.bh.1.2 2
80.69 even 4 6400.2.a.cc.1.1 2
120.29 odd 2 1800.2.k.f.901.1 2
120.53 even 4 1800.2.d.m.1549.4 4
120.59 even 2 7200.2.k.i.3601.2 2
120.77 even 4 1800.2.d.m.1549.1 4
120.83 odd 4 7200.2.d.m.2449.4 4
120.107 odd 4 7200.2.d.m.2449.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.2.d.b.101.1 2 5.4 even 2
200.2.d.b.101.2 yes 2 40.29 even 2
200.2.d.c.101.1 yes 2 8.5 even 2 inner
200.2.d.c.101.2 yes 2 1.1 even 1 trivial
200.2.f.d.149.1 4 40.13 odd 4
200.2.f.d.149.2 4 5.2 odd 4
200.2.f.d.149.3 4 5.3 odd 4
200.2.f.d.149.4 4 40.37 odd 4
800.2.d.a.401.1 2 4.3 odd 2
800.2.d.a.401.2 2 8.3 odd 2
800.2.d.d.401.1 2 40.19 odd 2
800.2.d.d.401.2 2 20.19 odd 2
800.2.f.d.49.1 4 20.7 even 4
800.2.f.d.49.2 4 40.3 even 4
800.2.f.d.49.3 4 40.27 even 4
800.2.f.d.49.4 4 20.3 even 4
1800.2.d.m.1549.1 4 120.77 even 4
1800.2.d.m.1549.2 4 15.8 even 4
1800.2.d.m.1549.3 4 15.2 even 4
1800.2.d.m.1549.4 4 120.53 even 4
1800.2.k.d.901.1 2 3.2 odd 2
1800.2.k.d.901.2 2 24.5 odd 2
1800.2.k.f.901.1 2 120.29 odd 2
1800.2.k.f.901.2 2 15.14 odd 2
6400.2.a.bg.1.1 2 16.13 even 4
6400.2.a.bg.1.2 2 16.5 even 4
6400.2.a.bh.1.1 2 80.19 odd 4
6400.2.a.bh.1.2 2 80.59 odd 4
6400.2.a.cb.1.1 2 16.11 odd 4
6400.2.a.cb.1.2 2 16.3 odd 4
6400.2.a.cc.1.1 2 80.69 even 4
6400.2.a.cc.1.2 2 80.29 even 4
7200.2.d.m.2449.1 4 60.47 odd 4
7200.2.d.m.2449.2 4 120.107 odd 4
7200.2.d.m.2449.3 4 60.23 odd 4
7200.2.d.m.2449.4 4 120.83 odd 4
7200.2.k.b.3601.1 2 12.11 even 2
7200.2.k.b.3601.2 2 24.11 even 2
7200.2.k.i.3601.1 2 60.59 even 2
7200.2.k.i.3601.2 2 120.59 even 2