Properties

Label 39.2.k.b.20.2
Level $39$
Weight $2$
Character 39.20
Analytic conductor $0.311$
Analytic rank $0$
Dimension $8$
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] = [39,2,Mod(2,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39.k (of order \(12\), degree \(4\), 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: \(0.311416567883\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: 8.0.56070144.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 20.2
Root \(0.500000 - 2.19293i\) of defining polynomial
Character \(\chi\) \(=\) 39.20
Dual form 39.2.k.b.2.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.619657 + 2.31259i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(1.69293 - 1.69293i) q^{5} +(1.89551 - 3.68825i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +O(q^{10})\) \(q+(0.619657 + 2.31259i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(1.69293 - 1.69293i) q^{5} +(1.89551 - 3.68825i) q^{6} +(-1.36603 - 0.366025i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +(4.96410 + 2.86603i) q^{10} +(-1.69293 + 0.453620i) q^{11} +(6.31812 + 1.36603i) q^{12} +(-1.59808 - 3.23205i) q^{13} -3.38587i q^{14} +(-4.14187 + 0.202571i) q^{15} +(1.23205 - 2.13397i) q^{16} +(1.07328 + 1.85897i) q^{17} +(-6.72326 + 2.52711i) q^{18} +(-0.267949 + 1.00000i) q^{19} +(-2.31259 + 8.63071i) q^{20} +(1.32691 + 2.05896i) q^{21} +(-2.09808 - 3.63397i) q^{22} +(0.350863 + 7.17394i) q^{24} -0.732051i q^{25} +(6.48415 - 5.69846i) q^{26} +(3.09808 - 4.17156i) q^{27} +(5.09808 - 1.36603i) q^{28} +(4.79122 + 2.76621i) q^{29} +(-3.03500 - 9.45293i) q^{30} +(4.46410 + 4.46410i) q^{31} +(-2.31259 - 0.619657i) q^{32} +(2.69999 + 1.38761i) q^{33} +(-3.63397 + 3.63397i) q^{34} +(-2.93225 + 1.69293i) q^{35} +(-6.51754 - 9.10360i) q^{36} +(-1.76795 - 6.59808i) q^{37} -2.47863 q^{38} +(-1.70983 + 6.00637i) q^{39} -9.92820 q^{40} +(-0.166037 - 0.619657i) q^{41} +(-3.93930 + 4.34444i) q^{42} +(7.09808 - 4.09808i) q^{43} +(4.62518 - 4.62518i) q^{44} +(5.55017 + 4.55896i) q^{45} +(-6.77174 - 6.77174i) q^{47} +(-4.06364 + 1.30469i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(1.69293 - 0.453620i) q^{50} +(0.785693 - 3.63397i) q^{51} +(11.1962 + 7.46410i) q^{52} +4.62518i q^{53} +(11.5669 + 4.57965i) q^{54} +(-2.09808 + 3.63397i) q^{55} +(2.93225 + 5.07880i) q^{56} +(1.50726 - 0.971364i) q^{57} +(-3.42820 + 12.7942i) q^{58} +(1.23931 - 4.62518i) q^{59} +(13.0087 - 8.38356i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-7.55743 + 13.0899i) q^{62} +(0.692934 - 4.18567i) q^{63} -10.6603i q^{64} +(-8.17709 - 2.76621i) q^{65} +(-1.53590 + 7.10381i) q^{66} +(-8.46410 + 2.26795i) q^{67} +(-6.93777 - 4.00552i) q^{68} +(-5.73205 - 5.73205i) q^{70} +(4.62518 + 1.23931i) q^{71} +(7.89635 - 9.61317i) q^{72} +(-6.09808 + 6.09808i) q^{73} +(14.1631 - 8.17709i) q^{74} +(-0.851708 + 0.939303i) q^{75} +(-1.00000 - 3.73205i) q^{76} +2.47863 q^{77} +(-14.9498 - 0.232259i) q^{78} +2.00000 q^{79} +(-1.52690 - 5.69846i) q^{80} +(-8.82860 + 1.74811i) q^{81} +(1.33013 - 0.767949i) q^{82} +(-1.23931 + 1.23931i) q^{83} +(-8.13071 - 4.17862i) q^{84} +(4.96410 + 1.33013i) q^{85} +(13.8755 + 13.8755i) q^{86} +(-2.92931 - 9.12372i) q^{87} +(6.29423 + 3.63397i) q^{88} +(-9.70398 + 2.60017i) q^{89} +(-7.10381 + 15.6603i) q^{90} +(1.00000 + 5.00000i) q^{91} +(-0.534160 - 10.9217i) q^{93} +(11.4641 - 19.8564i) q^{94} +(1.23931 + 2.14655i) q^{95} +(2.24637 + 3.48568i) q^{96} +(3.36603 - 12.5622i) q^{97} +(3.09828 - 11.5630i) q^{98} +(-1.84997 - 4.92177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9} + 12 q^{10} + 8 q^{13} - 14 q^{15} - 4 q^{16} + 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{22} + 18 q^{24} + 4 q^{27} + 20 q^{28} + 18 q^{30} + 8 q^{31} + 16 q^{33} - 36 q^{34} - 36 q^{36} - 28 q^{37} - 14 q^{39} - 24 q^{40} - 16 q^{42} + 36 q^{43} - 20 q^{45} - 14 q^{48} + 48 q^{52} + 46 q^{54} + 4 q^{55} + 16 q^{57} + 28 q^{58} + 44 q^{60} + 28 q^{61} - 8 q^{63} - 40 q^{66} - 40 q^{67} - 32 q^{70} + 12 q^{72} - 28 q^{73} + 12 q^{75} - 8 q^{76} - 80 q^{78} + 16 q^{79} + 4 q^{81} - 24 q^{82} + 4 q^{84} + 12 q^{85} - 34 q^{87} - 12 q^{88} + 8 q^{91} + 4 q^{93} + 64 q^{94} + 16 q^{96} + 20 q^{97} + 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.619657 + 2.31259i 0.438164 + 1.63525i 0.733380 + 0.679818i \(0.237941\pi\)
−0.295217 + 0.955430i \(0.595392\pi\)
\(3\) −1.28311 1.16345i −0.740805 0.671721i
\(4\) −3.23205 + 1.86603i −1.61603 + 0.933013i
\(5\) 1.69293 1.69293i 0.757103 0.757103i −0.218691 0.975794i \(-0.570179\pi\)
0.975794 + 0.218691i \(0.0701787\pi\)
\(6\) 1.89551 3.68825i 0.773837 1.50572i
\(7\) −1.36603 0.366025i −0.516309 0.138345i −0.00875026 0.999962i \(-0.502785\pi\)
−0.507559 + 0.861617i \(0.669452\pi\)
\(8\) −2.93225 2.93225i −1.03671 1.03671i
\(9\) 0.292748 + 2.98568i 0.0975828 + 0.995227i
\(10\) 4.96410 + 2.86603i 1.56979 + 0.906317i
\(11\) −1.69293 + 0.453620i −0.510439 + 0.136772i −0.504840 0.863213i \(-0.668449\pi\)
−0.00559833 + 0.999984i \(0.501782\pi\)
\(12\) 6.31812 + 1.36603i 1.82388 + 0.394338i
\(13\) −1.59808 3.23205i −0.443227 0.896410i
\(14\) 3.38587i 0.904911i
\(15\) −4.14187 + 0.202571i −1.06943 + 0.0523036i
\(16\) 1.23205 2.13397i 0.308013 0.533494i
\(17\) 1.07328 + 1.85897i 0.260308 + 0.450867i 0.966324 0.257330i \(-0.0828426\pi\)
−0.706016 + 0.708196i \(0.749509\pi\)
\(18\) −6.72326 + 2.52711i −1.58469 + 0.595644i
\(19\) −0.267949 + 1.00000i −0.0614718 + 0.229416i −0.989826 0.142280i \(-0.954557\pi\)
0.928355 + 0.371695i \(0.121223\pi\)
\(20\) −2.31259 + 8.63071i −0.517111 + 1.92988i
\(21\) 1.32691 + 2.05896i 0.289555 + 0.449302i
\(22\) −2.09808 3.63397i −0.447311 0.774766i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0.350863 + 7.17394i 0.0716197 + 1.46437i
\(25\) 0.732051i 0.146410i
\(26\) 6.48415 5.69846i 1.27165 1.11756i
\(27\) 3.09808 4.17156i 0.596225 0.802817i
\(28\) 5.09808 1.36603i 0.963446 0.258155i
\(29\) 4.79122 + 2.76621i 0.889707 + 0.513673i 0.873847 0.486202i \(-0.161618\pi\)
0.0158603 + 0.999874i \(0.494951\pi\)
\(30\) −3.03500 9.45293i −0.554113 1.72586i
\(31\) 4.46410 + 4.46410i 0.801776 + 0.801776i 0.983373 0.181597i \(-0.0581266\pi\)
−0.181597 + 0.983373i \(0.558127\pi\)
\(32\) −2.31259 0.619657i −0.408812 0.109541i
\(33\) 2.69999 + 1.38761i 0.470008 + 0.241551i
\(34\) −3.63397 + 3.63397i −0.623222 + 0.623222i
\(35\) −2.93225 + 1.69293i −0.495640 + 0.286158i
\(36\) −6.51754 9.10360i −1.08626 1.51727i
\(37\) −1.76795 6.59808i −0.290649 1.08472i −0.944612 0.328190i \(-0.893561\pi\)
0.653963 0.756527i \(-0.273105\pi\)
\(38\) −2.47863 −0.402086
\(39\) −1.70983 + 6.00637i −0.273793 + 0.961789i
\(40\) −9.92820 −1.56979
\(41\) −0.166037 0.619657i −0.0259306 0.0967741i 0.951748 0.306881i \(-0.0992854\pi\)
−0.977678 + 0.210107i \(0.932619\pi\)
\(42\) −3.93930 + 4.34444i −0.607848 + 0.670362i
\(43\) 7.09808 4.09808i 1.08245 0.624951i 0.150891 0.988550i \(-0.451786\pi\)
0.931555 + 0.363600i \(0.118452\pi\)
\(44\) 4.62518 4.62518i 0.697272 0.697272i
\(45\) 5.55017 + 4.55896i 0.827370 + 0.679610i
\(46\) 0 0
\(47\) −6.77174 6.77174i −0.987759 0.987759i 0.0121668 0.999926i \(-0.496127\pi\)
−0.999926 + 0.0121668i \(0.996127\pi\)
\(48\) −4.06364 + 1.30469i −0.586536 + 0.188316i
\(49\) −4.33013 2.50000i −0.618590 0.357143i
\(50\) 1.69293 0.453620i 0.239417 0.0641516i
\(51\) 0.785693 3.63397i 0.110019 0.508858i
\(52\) 11.1962 + 7.46410i 1.55263 + 1.03508i
\(53\) 4.62518i 0.635318i 0.948205 + 0.317659i \(0.102897\pi\)
−0.948205 + 0.317659i \(0.897103\pi\)
\(54\) 11.5669 + 4.57965i 1.57405 + 0.623211i
\(55\) −2.09808 + 3.63397i −0.282905 + 0.490005i
\(56\) 2.93225 + 5.07880i 0.391838 + 0.678683i
\(57\) 1.50726 0.971364i 0.199642 0.128660i
\(58\) −3.42820 + 12.7942i −0.450145 + 1.67996i
\(59\) 1.23931 4.62518i 0.161345 0.602147i −0.837133 0.546999i \(-0.815770\pi\)
0.998478 0.0551484i \(-0.0175632\pi\)
\(60\) 13.0087 8.38356i 1.67942 1.08231i
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) −7.55743 + 13.0899i −0.959794 + 1.66241i
\(63\) 0.692934 4.18567i 0.0873015 0.527345i
\(64\) 10.6603i 1.33253i
\(65\) −8.17709 2.76621i −1.01424 0.343106i
\(66\) −1.53590 + 7.10381i −0.189056 + 0.874418i
\(67\) −8.46410 + 2.26795i −1.03405 + 0.277074i −0.735647 0.677365i \(-0.763122\pi\)
−0.298407 + 0.954439i \(0.596455\pi\)
\(68\) −6.93777 4.00552i −0.841328 0.485741i
\(69\) 0 0
\(70\) −5.73205 5.73205i −0.685111 0.685111i
\(71\) 4.62518 + 1.23931i 0.548908 + 0.147079i 0.522606 0.852575i \(-0.324960\pi\)
0.0263025 + 0.999654i \(0.491627\pi\)
\(72\) 7.89635 9.61317i 0.930594 1.13292i
\(73\) −6.09808 + 6.09808i −0.713726 + 0.713726i −0.967313 0.253587i \(-0.918390\pi\)
0.253587 + 0.967313i \(0.418390\pi\)
\(74\) 14.1631 8.17709i 1.64643 0.950567i
\(75\) −0.851708 + 0.939303i −0.0983467 + 0.108461i
\(76\) −1.00000 3.73205i −0.114708 0.428096i
\(77\) 2.47863 0.282466
\(78\) −14.9498 0.232259i −1.69273 0.0262981i
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) −1.52690 5.69846i −0.170712 0.637107i
\(81\) −8.82860 + 1.74811i −0.980955 + 0.194234i
\(82\) 1.33013 0.767949i 0.146888 0.0848058i
\(83\) −1.23931 + 1.23931i −0.136032 + 0.136032i −0.771844 0.635812i \(-0.780665\pi\)
0.635812 + 0.771844i \(0.280665\pi\)
\(84\) −8.13071 4.17862i −0.887133 0.455924i
\(85\) 4.96410 + 1.33013i 0.538432 + 0.144273i
\(86\) 13.8755 + 13.8755i 1.49624 + 1.49624i
\(87\) −2.92931 9.12372i −0.314054 0.978165i
\(88\) 6.29423 + 3.63397i 0.670967 + 0.387383i
\(89\) −9.70398 + 2.60017i −1.02862 + 0.275618i −0.733390 0.679808i \(-0.762063\pi\)
−0.295230 + 0.955426i \(0.595396\pi\)
\(90\) −7.10381 + 15.6603i −0.748807 + 1.65074i
\(91\) 1.00000 + 5.00000i 0.104828 + 0.524142i
\(92\) 0 0
\(93\) −0.534160 10.9217i −0.0553898 1.13253i
\(94\) 11.4641 19.8564i 1.18243 2.04803i
\(95\) 1.23931 + 2.14655i 0.127151 + 0.220232i
\(96\) 2.24637 + 3.48568i 0.229269 + 0.355756i
\(97\) 3.36603 12.5622i 0.341768 1.27550i −0.554575 0.832134i \(-0.687119\pi\)
0.896343 0.443362i \(-0.146214\pi\)
\(98\) 3.09828 11.5630i 0.312974 1.16803i
\(99\) −1.84997 4.92177i −0.185929 0.494656i
\(100\) 1.36603 + 2.36603i 0.136603 + 0.236603i
\(101\) 9.87002 17.0954i 0.982104 1.70105i 0.327944 0.944697i \(-0.393644\pi\)
0.654160 0.756356i \(-0.273022\pi\)
\(102\) 8.89076 0.434830i 0.880316 0.0430546i
\(103\) 6.92820i 0.682656i 0.939944 + 0.341328i \(0.110877\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(104\) −4.79122 + 14.1631i −0.469818 + 1.38881i
\(105\) 5.73205 + 1.23931i 0.559391 + 0.120945i
\(106\) −10.6962 + 2.86603i −1.03890 + 0.278373i
\(107\) 14.4507 + 8.34312i 1.39700 + 0.806560i 0.994078 0.108673i \(-0.0346600\pi\)
0.402925 + 0.915233i \(0.367993\pi\)
\(108\) −2.22890 + 19.2638i −0.214476 + 1.85366i
\(109\) −2.80385 2.80385i −0.268560 0.268560i 0.559960 0.828520i \(-0.310817\pi\)
−0.828520 + 0.559960i \(0.810817\pi\)
\(110\) −9.70398 2.60017i −0.925239 0.247917i
\(111\) −5.40808 + 10.5230i −0.513313 + 0.998798i
\(112\) −2.46410 + 2.46410i −0.232836 + 0.232836i
\(113\) −11.2309 + 6.48415i −1.05651 + 0.609978i −0.924465 0.381266i \(-0.875488\pi\)
−0.132047 + 0.991243i \(0.542155\pi\)
\(114\) 3.18035 + 2.88377i 0.297867 + 0.270090i
\(115\) 0 0
\(116\) −20.6473 −1.91705
\(117\) 9.18204 5.71753i 0.848880 0.528585i
\(118\) 11.4641 1.05536
\(119\) −0.785693 2.93225i −0.0720244 0.268799i
\(120\) 12.7390 + 11.5510i 1.16291 + 1.05446i
\(121\) −6.86603 + 3.96410i −0.624184 + 0.360373i
\(122\) −11.8505 + 11.8505i −1.07290 + 1.07290i
\(123\) −0.507899 + 0.988265i −0.0457957 + 0.0891088i
\(124\) −22.7583 6.09808i −2.04376 0.547623i
\(125\) 7.22536 + 7.22536i 0.646255 + 0.646255i
\(126\) 10.1091 0.991207i 0.900592 0.0883037i
\(127\) 13.0981 + 7.56218i 1.16227 + 0.671035i 0.951846 0.306576i \(-0.0991834\pi\)
0.210420 + 0.977611i \(0.432517\pi\)
\(128\) 20.0276 5.36639i 1.77021 0.474326i
\(129\) −13.8755 3.00000i −1.22167 0.264135i
\(130\) 1.33013 20.6244i 0.116660 1.80888i
\(131\) 0.907241i 0.0792660i 0.999214 + 0.0396330i \(0.0126189\pi\)
−0.999214 + 0.0396330i \(0.987381\pi\)
\(132\) −11.3158 + 0.553435i −0.984915 + 0.0481703i
\(133\) 0.732051 1.26795i 0.0634769 0.109945i
\(134\) −10.4897 18.1687i −0.906170 1.56953i
\(135\) −1.81734 12.3070i −0.156412 1.05922i
\(136\) 2.30385 8.59808i 0.197553 0.737279i
\(137\) 1.52690 5.69846i 0.130452 0.486852i −0.869524 0.493891i \(-0.835574\pi\)
0.999975 + 0.00703925i \(0.00224068\pi\)
\(138\) 0 0
\(139\) 1.19615 + 2.07180i 0.101456 + 0.175728i 0.912285 0.409556i \(-0.134316\pi\)
−0.810829 + 0.585284i \(0.800983\pi\)
\(140\) 6.31812 10.9433i 0.533978 0.924877i
\(141\) 0.810284 + 16.5675i 0.0682383 + 1.39523i
\(142\) 11.4641i 0.962046i
\(143\) 4.17156 + 4.74673i 0.348843 + 0.396941i
\(144\) 6.73205 + 3.05379i 0.561004 + 0.254483i
\(145\) 12.7942 3.42820i 1.06250 0.284697i
\(146\) −17.8811 10.3236i −1.47985 0.854391i
\(147\) 2.64740 + 8.24568i 0.218354 + 0.680092i
\(148\) 18.0263 + 18.0263i 1.48175 + 1.48175i
\(149\) −5.24484 1.40535i −0.429674 0.115131i 0.0374992 0.999297i \(-0.488061\pi\)
−0.467173 + 0.884166i \(0.654728\pi\)
\(150\) −2.69999 1.38761i −0.220453 0.113298i
\(151\) 7.46410 7.46410i 0.607420 0.607420i −0.334851 0.942271i \(-0.608686\pi\)
0.942271 + 0.334851i \(0.108686\pi\)
\(152\) 3.71794 2.14655i 0.301565 0.174109i
\(153\) −5.23610 + 3.74867i −0.423313 + 0.303062i
\(154\) 1.53590 + 5.73205i 0.123766 + 0.461902i
\(155\) 15.1149 1.21405
\(156\) −5.68177 22.6035i −0.454905 1.80973i
\(157\) −15.1962 −1.21278 −0.606392 0.795165i \(-0.707384\pi\)
−0.606392 + 0.795165i \(0.707384\pi\)
\(158\) 1.23931 + 4.62518i 0.0985945 + 0.367960i
\(159\) 5.38119 5.93462i 0.426756 0.470646i
\(160\) −4.96410 + 2.86603i −0.392447 + 0.226579i
\(161\) 0 0
\(162\) −9.51336 19.3337i −0.747440 1.51900i
\(163\) −14.9282 4.00000i −1.16927 0.313304i −0.378606 0.925558i \(-0.623596\pi\)
−0.790661 + 0.612254i \(0.790263\pi\)
\(164\) 1.69293 + 1.69293i 0.132196 + 0.132196i
\(165\) 6.92003 2.22178i 0.538723 0.172965i
\(166\) −3.63397 2.09808i −0.282051 0.162842i
\(167\) 11.3969 3.05379i 0.881920 0.236310i 0.210685 0.977554i \(-0.432431\pi\)
0.671235 + 0.741244i \(0.265764\pi\)
\(168\) 2.14655 9.92820i 0.165610 0.765978i
\(169\) −7.89230 + 10.3301i −0.607100 + 0.794625i
\(170\) 12.3042i 0.943686i
\(171\) −3.06412 0.507263i −0.234319 0.0387914i
\(172\) −15.2942 + 26.4904i −1.16617 + 2.01987i
\(173\) 3.71794 + 6.43966i 0.282670 + 0.489598i 0.972041 0.234809i \(-0.0754466\pi\)
−0.689372 + 0.724408i \(0.742113\pi\)
\(174\) 19.2843 12.4279i 1.46194 0.942154i
\(175\) −0.267949 + 1.00000i −0.0202551 + 0.0755929i
\(176\) −1.11777 + 4.17156i −0.0842548 + 0.314443i
\(177\) −6.97136 + 4.49274i −0.524000 + 0.337695i
\(178\) −12.0263 20.8301i −0.901408 1.56128i
\(179\) −9.37191 + 16.2326i −0.700489 + 1.21328i 0.267805 + 0.963473i \(0.413702\pi\)
−0.968295 + 0.249810i \(0.919632\pi\)
\(180\) −26.4456 4.37804i −1.97114 0.326320i
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) −10.9433 + 5.41087i −0.811171 + 0.401081i
\(183\) 2.56218 11.8505i 0.189402 0.876017i
\(184\) 0 0
\(185\) −14.1631 8.17709i −1.04129 0.601191i
\(186\) 24.9265 8.00301i 1.82770 0.586809i
\(187\) −2.66025 2.66025i −0.194537 0.194537i
\(188\) 34.5228 + 9.25036i 2.51784 + 0.674652i
\(189\) −5.75895 + 4.56448i −0.418902 + 0.332017i
\(190\) −4.19615 + 4.19615i −0.304421 + 0.304421i
\(191\) −16.8078 + 9.70398i −1.21617 + 0.702156i −0.964096 0.265553i \(-0.914446\pi\)
−0.252073 + 0.967708i \(0.581112\pi\)
\(192\) −12.4027 + 13.6783i −0.895089 + 0.987146i
\(193\) 1.86603 + 6.96410i 0.134319 + 0.501287i 1.00000 0.000689767i \(0.000219560\pi\)
−0.865680 + 0.500597i \(0.833114\pi\)
\(194\) 31.1370 2.23550
\(195\) 7.27375 + 13.0630i 0.520884 + 0.935462i
\(196\) 18.6603 1.33288
\(197\) −0.453620 1.69293i −0.0323191 0.120617i 0.947882 0.318622i \(-0.103220\pi\)
−0.980201 + 0.198006i \(0.936554\pi\)
\(198\) 10.2357 7.32803i 0.727418 0.520780i
\(199\) 0.803848 0.464102i 0.0569832 0.0328993i −0.471238 0.882006i \(-0.656193\pi\)
0.528221 + 0.849107i \(0.322859\pi\)
\(200\) −2.14655 + 2.14655i −0.151784 + 0.151784i
\(201\) 13.4990 + 6.93756i 0.952149 + 0.489338i
\(202\) 45.6506 + 12.2321i 3.21197 + 0.860644i
\(203\) −5.53242 5.53242i −0.388300 0.388300i
\(204\) 4.24169 + 13.2113i 0.296978 + 0.924977i
\(205\) −1.33013 0.767949i −0.0929001 0.0536359i
\(206\) −16.0221 + 4.29311i −1.11631 + 0.299115i
\(207\) 0 0
\(208\) −8.86603 0.571797i −0.614748 0.0396470i
\(209\) 1.81448i 0.125510i
\(210\) 0.685879 + 14.0238i 0.0473302 + 0.967737i
\(211\) 6.09808 10.5622i 0.419809 0.727130i −0.576111 0.817371i \(-0.695430\pi\)
0.995920 + 0.0902411i \(0.0287638\pi\)
\(212\) −8.63071 14.9488i −0.592759 1.02669i
\(213\) −4.49274 6.97136i −0.307837 0.477670i
\(214\) −10.3397 + 38.5885i −0.706810 + 2.63785i
\(215\) 5.07880 18.9543i 0.346371 1.29268i
\(216\) −21.3164 + 3.14772i −1.45040 + 0.214176i
\(217\) −4.46410 7.73205i −0.303043 0.524886i
\(218\) 4.74673 8.22158i 0.321489 0.556835i
\(219\) 14.9193 0.729677i 1.00816 0.0493070i
\(220\) 15.6603i 1.05581i
\(221\) 4.29311 6.43966i 0.288786 0.433179i
\(222\) −27.6865 5.98604i −1.85820 0.401757i
\(223\) 22.2942 5.97372i 1.49293 0.400030i 0.582206 0.813041i \(-0.302190\pi\)
0.910726 + 0.413011i \(0.135523\pi\)
\(224\) 2.93225 + 1.69293i 0.195919 + 0.113114i
\(225\) 2.18567 0.214307i 0.145711 0.0142871i
\(226\) −21.9545 21.9545i −1.46039 1.46039i
\(227\) −15.1149 4.05001i −1.00321 0.268809i −0.280419 0.959878i \(-0.590474\pi\)
−0.722789 + 0.691069i \(0.757140\pi\)
\(228\) −3.05896 + 5.95209i −0.202585 + 0.394187i
\(229\) 10.1244 10.1244i 0.669036 0.669036i −0.288457 0.957493i \(-0.593142\pi\)
0.957493 + 0.288457i \(0.0931421\pi\)
\(230\) 0 0
\(231\) −3.18035 2.88377i −0.209252 0.189738i
\(232\) −5.93782 22.1603i −0.389837 1.45489i
\(233\) −7.43588 −0.487141 −0.243570 0.969883i \(-0.578319\pi\)
−0.243570 + 0.969883i \(0.578319\pi\)
\(234\) 18.9120 + 17.6914i 1.23632 + 1.15652i
\(235\) −22.9282 −1.49567
\(236\) 4.62518 + 17.2614i 0.301074 + 1.12362i
\(237\) −2.56622 2.32691i −0.166694 0.151149i
\(238\) 6.29423 3.63397i 0.407994 0.235556i
\(239\) −7.10381 + 7.10381i −0.459507 + 0.459507i −0.898494 0.438986i \(-0.855338\pi\)
0.438986 + 0.898494i \(0.355338\pi\)
\(240\) −4.67072 + 9.08823i −0.301493 + 0.586643i
\(241\) 7.23205 + 1.93782i 0.465857 + 0.124826i 0.484110 0.875007i \(-0.339144\pi\)
−0.0182524 + 0.999833i \(0.505810\pi\)
\(242\) −13.4219 13.4219i −0.862794 0.862794i
\(243\) 13.3619 + 8.02865i 0.857167 + 0.515038i
\(244\) −22.6244 13.0622i −1.44838 0.836220i
\(245\) −11.5630 + 3.09828i −0.738730 + 0.197942i
\(246\) −2.60017 0.562178i −0.165781 0.0358431i
\(247\) 3.66025 0.732051i 0.232896 0.0465793i
\(248\) 26.1797i 1.66241i
\(249\) 3.03206 0.148292i 0.192149 0.00939765i
\(250\) −12.2321 + 21.1865i −0.773623 + 1.33995i
\(251\) −10.9433 18.9543i −0.690735 1.19639i −0.971597 0.236640i \(-0.923954\pi\)
0.280863 0.959748i \(-0.409379\pi\)
\(252\) 5.57097 + 14.8213i 0.350938 + 0.933656i
\(253\) 0 0
\(254\) −9.37191 + 34.9764i −0.588046 + 2.19462i
\(255\) −4.82195 7.48221i −0.301962 0.468554i
\(256\) 14.1603 + 24.5263i 0.885016 + 1.53289i
\(257\) 8.29863 14.3737i 0.517655 0.896604i −0.482135 0.876097i \(-0.660139\pi\)
0.999790 0.0205071i \(-0.00652807\pi\)
\(258\) −1.66030 33.9474i −0.103366 2.11347i
\(259\) 9.66025i 0.600259i
\(260\) 31.5906 6.31812i 1.95916 0.391833i
\(261\) −6.85641 + 15.1149i −0.424401 + 0.935586i
\(262\) −2.09808 + 0.562178i −0.129620 + 0.0347315i
\(263\) 10.3681 + 5.98604i 0.639326 + 0.369115i 0.784355 0.620312i \(-0.212994\pi\)
−0.145029 + 0.989427i \(0.546327\pi\)
\(264\) −3.84823 11.9858i −0.236842 0.737677i
\(265\) 7.83013 + 7.83013i 0.481001 + 0.481001i
\(266\) 3.38587 + 0.907241i 0.207601 + 0.0556265i
\(267\) 15.4765 + 7.95383i 0.947145 + 0.486766i
\(268\) 23.1244 23.1244i 1.41254 1.41254i
\(269\) 9.58244 5.53242i 0.584251 0.337318i −0.178570 0.983927i \(-0.557147\pi\)
0.762821 + 0.646610i \(0.223814\pi\)
\(270\) 27.3350 11.8289i 1.66355 0.719883i
\(271\) 0.535898 + 2.00000i 0.0325535 + 0.121491i 0.980291 0.197561i \(-0.0633021\pi\)
−0.947737 + 0.319052i \(0.896635\pi\)
\(272\) 5.28933 0.320713
\(273\) 4.53416 7.57901i 0.274420 0.458703i
\(274\) 14.1244 0.853284
\(275\) 0.332073 + 1.23931i 0.0200248 + 0.0747334i
\(276\) 0 0
\(277\) 3.10770 1.79423i 0.186723 0.107805i −0.403724 0.914881i \(-0.632285\pi\)
0.590448 + 0.807076i \(0.298951\pi\)
\(278\) −4.05001 + 4.05001i −0.242904 + 0.242904i
\(279\) −12.0215 + 14.6352i −0.719710 + 0.876189i
\(280\) 13.5622 + 3.63397i 0.810495 + 0.217172i
\(281\) 15.9006 + 15.9006i 0.948547 + 0.948547i 0.998740 0.0501922i \(-0.0159834\pi\)
−0.0501922 + 0.998740i \(0.515983\pi\)
\(282\) −37.8117 + 12.1400i −2.25166 + 0.722928i
\(283\) −21.2942 12.2942i −1.26581 0.730816i −0.291618 0.956535i \(-0.594194\pi\)
−0.974192 + 0.225719i \(0.927527\pi\)
\(284\) −17.2614 + 4.62518i −1.02428 + 0.274454i
\(285\) 0.907241 4.19615i 0.0537403 0.248559i
\(286\) −8.39230 + 12.5885i −0.496247 + 0.744371i
\(287\) 0.907241i 0.0535527i
\(288\) 1.17309 7.08606i 0.0691251 0.417550i
\(289\) 6.19615 10.7321i 0.364480 0.631297i
\(290\) 15.8561 + 27.4635i 0.931100 + 1.61271i
\(291\) −18.9345 + 12.2025i −1.10996 + 0.715320i
\(292\) 8.33013 31.0885i 0.487484 1.81931i
\(293\) −5.69846 + 21.2669i −0.332908 + 1.24243i 0.573212 + 0.819407i \(0.305697\pi\)
−0.906120 + 0.423021i \(0.860970\pi\)
\(294\) −17.4284 + 11.2318i −1.01645 + 0.655054i
\(295\) −5.73205 9.92820i −0.333733 0.578042i
\(296\) −14.1631 + 24.5313i −0.823215 + 1.42585i
\(297\) −3.35253 + 8.46753i −0.194534 + 0.491336i
\(298\) 13.0000i 0.753070i
\(299\) 0 0
\(300\) 1.00000 4.62518i 0.0577350 0.267035i
\(301\) −11.1962 + 3.00000i −0.645335 + 0.172917i
\(302\) 21.8866 + 12.6362i 1.25943 + 0.727133i
\(303\) −32.5540 + 10.4520i −1.87018 + 0.600449i
\(304\) 1.80385 + 1.80385i 0.103458 + 0.103458i
\(305\) 16.1881 + 4.33760i 0.926930 + 0.248370i
\(306\) −11.9137 9.78605i −0.681063 0.559431i
\(307\) −12.3923 + 12.3923i −0.707266 + 0.707266i −0.965960 0.258693i \(-0.916708\pi\)
0.258693 + 0.965960i \(0.416708\pi\)
\(308\) −8.01105 + 4.62518i −0.456472 + 0.263544i
\(309\) 8.06065 8.88965i 0.458554 0.505715i
\(310\) 9.36603 + 34.9545i 0.531954 + 1.98528i
\(311\) 4.29311 0.243440 0.121720 0.992564i \(-0.461159\pi\)
0.121720 + 0.992564i \(0.461159\pi\)
\(312\) 22.6258 12.5985i 1.28093 0.713250i
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) −9.41640 35.1425i −0.531398 1.98321i
\(315\) −5.91297 8.25916i −0.333158 0.465351i
\(316\) −6.46410 + 3.73205i −0.363634 + 0.209944i
\(317\) 11.2754 11.2754i 0.633288 0.633288i −0.315603 0.948891i \(-0.602207\pi\)
0.948891 + 0.315603i \(0.102207\pi\)
\(318\) 17.0588 + 8.76706i 0.956612 + 0.491632i
\(319\) −9.36603 2.50962i −0.524397 0.140512i
\(320\) −18.0471 18.0471i −1.00886 1.00886i
\(321\) −8.83503 27.5179i −0.493123 1.53590i
\(322\) 0 0
\(323\) −2.14655 + 0.575167i −0.119437 + 0.0320032i
\(324\) 25.2725 22.1244i 1.40403 1.22913i
\(325\) −2.36603 + 1.16987i −0.131243 + 0.0648929i
\(326\) 37.0015i 2.04932i
\(327\) 0.335500 + 6.85980i 0.0185532 + 0.379348i
\(328\) −1.33013 + 2.30385i −0.0734440 + 0.127209i
\(329\) 6.77174 + 11.7290i 0.373338 + 0.646640i
\(330\) 9.42610 + 14.6265i 0.518890 + 0.805160i
\(331\) 5.05256 18.8564i 0.277714 1.03644i −0.676287 0.736638i \(-0.736412\pi\)
0.954001 0.299804i \(-0.0969212\pi\)
\(332\) 1.69293 6.31812i 0.0929118 0.346752i
\(333\) 19.1822 7.21011i 1.05118 0.395112i
\(334\) 14.1244 + 24.4641i 0.772850 + 1.33862i
\(335\) −10.4897 + 18.1687i −0.573112 + 0.992660i
\(336\) 6.02859 0.294847i 0.328886 0.0160852i
\(337\) 11.5359i 0.628400i 0.949357 + 0.314200i \(0.101736\pi\)
−0.949357 + 0.314200i \(0.898264\pi\)
\(338\) −28.7799 11.8505i −1.56542 0.644584i
\(339\) 21.9545 + 4.74673i 1.19240 + 0.257807i
\(340\) −18.5263 + 4.96410i −1.00473 + 0.269216i
\(341\) −9.58244 5.53242i −0.518918 0.299597i
\(342\) −0.725614 7.40039i −0.0392367 0.400167i
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) −32.8299 8.79674i −1.77007 0.474289i
\(345\) 0 0
\(346\) −12.5885 + 12.5885i −0.676760 + 0.676760i
\(347\) 22.4618 12.9683i 1.20581 0.696175i 0.243969 0.969783i \(-0.421550\pi\)
0.961841 + 0.273608i \(0.0882171\pi\)
\(348\) 26.4928 + 24.0222i 1.42016 + 1.28772i
\(349\) 1.50962 + 5.63397i 0.0808080 + 0.301580i 0.994487 0.104856i \(-0.0334382\pi\)
−0.913679 + 0.406436i \(0.866772\pi\)
\(350\) −2.47863 −0.132488
\(351\) −18.4337 3.34667i −0.983916 0.178632i
\(352\) 4.19615 0.223656
\(353\) 7.05932 + 26.3457i 0.375730 + 1.40224i 0.852276 + 0.523093i \(0.175222\pi\)
−0.476546 + 0.879149i \(0.658111\pi\)
\(354\) −14.7097 13.3380i −0.781813 0.708904i
\(355\) 9.92820 5.73205i 0.526934 0.304226i
\(356\) 26.5118 26.5118i 1.40512 1.40512i
\(357\) −2.40340 + 4.67652i −0.127202 + 0.247508i
\(358\) −43.3468 11.6147i −2.29095 0.613858i
\(359\) −12.0611 12.0611i −0.636559 0.636559i 0.313146 0.949705i \(-0.398617\pi\)
−0.949705 + 0.313146i \(0.898617\pi\)
\(360\) −2.90646 29.6425i −0.153184 1.56229i
\(361\) 15.5263 + 8.96410i 0.817173 + 0.471795i
\(362\) 6.93777 1.85897i 0.364641 0.0977053i
\(363\) 13.4219 + 2.90192i 0.704468 + 0.152311i
\(364\) −12.5622 14.2942i −0.658437 0.749221i
\(365\) 20.6473i 1.08073i
\(366\) 28.9931 1.41800i 1.51549 0.0741199i
\(367\) −4.80385 + 8.32051i −0.250759 + 0.434327i −0.963735 0.266861i \(-0.914013\pi\)
0.712976 + 0.701188i \(0.247347\pi\)
\(368\) 0 0
\(369\) 1.80149 0.677136i 0.0937819 0.0352503i
\(370\) 10.1340 37.8205i 0.526840 1.96619i
\(371\) 1.69293 6.31812i 0.0878928 0.328020i
\(372\) 22.1066 + 34.3028i 1.14618 + 1.77852i
\(373\) 9.79423 + 16.9641i 0.507126 + 0.878368i 0.999966 + 0.00824796i \(0.00262544\pi\)
−0.492840 + 0.870120i \(0.664041\pi\)
\(374\) 4.50363 7.80052i 0.232877 0.403355i
\(375\) −0.864563 17.6773i −0.0446459 0.912852i
\(376\) 39.7128i 2.04803i
\(377\) 1.28380 19.9061i 0.0661192 1.02522i
\(378\) −14.1244 10.4897i −0.726478 0.539531i
\(379\) −4.83013 + 1.29423i −0.248107 + 0.0664801i −0.380729 0.924687i \(-0.624327\pi\)
0.132622 + 0.991167i \(0.457660\pi\)
\(380\) −8.01105 4.62518i −0.410958 0.237267i
\(381\) −8.00804 24.9421i −0.410264 1.27782i
\(382\) −32.8564 32.8564i −1.68108 1.68108i
\(383\) −13.5435 3.62896i −0.692039 0.185431i −0.104377 0.994538i \(-0.533285\pi\)
−0.587662 + 0.809106i \(0.699952\pi\)
\(384\) −31.9412 16.4156i −1.62999 0.837703i
\(385\) 4.19615 4.19615i 0.213856 0.213856i
\(386\) −14.9488 + 8.63071i −0.760875 + 0.439291i
\(387\) 14.3135 + 19.9929i 0.727596 + 1.01630i
\(388\) 12.5622 + 46.8827i 0.637748 + 2.38011i
\(389\) −5.28933 −0.268180 −0.134090 0.990969i \(-0.542811\pi\)
−0.134090 + 0.990969i \(0.542811\pi\)
\(390\) −25.7022 + 24.9158i −1.30148 + 1.26166i
\(391\) 0 0
\(392\) 5.36639 + 20.0276i 0.271043 + 1.01155i
\(393\) 1.05553 1.16409i 0.0532446 0.0587206i
\(394\) 3.63397 2.09808i 0.183077 0.105700i
\(395\) 3.38587 3.38587i 0.170362 0.170362i
\(396\) 15.1633 + 12.4553i 0.761986 + 0.625903i
\(397\) 8.56218 + 2.29423i 0.429723 + 0.115144i 0.467196 0.884154i \(-0.345264\pi\)
−0.0374729 + 0.999298i \(0.511931\pi\)
\(398\) 1.57139 + 1.57139i 0.0787665 + 0.0787665i
\(399\) −2.41450 + 0.775212i −0.120876 + 0.0388091i
\(400\) −1.56218 0.901924i −0.0781089 0.0450962i
\(401\) 27.1314 7.26985i 1.35488 0.363039i 0.492946 0.870060i \(-0.335920\pi\)
0.861933 + 0.507021i \(0.169253\pi\)
\(402\) −7.67898 + 35.5167i −0.382993 + 1.77141i
\(403\) 7.29423 21.5622i 0.363351 1.07409i
\(404\) 73.6708i 3.66526i
\(405\) −11.9868 + 17.9057i −0.595629 + 0.889739i
\(406\) 9.36603 16.2224i 0.464828 0.805106i
\(407\) 5.98604 + 10.3681i 0.296717 + 0.513929i
\(408\) −12.9596 + 8.35187i −0.641594 + 0.413479i
\(409\) 3.00962 11.2321i 0.148816 0.555389i −0.850740 0.525587i \(-0.823846\pi\)
0.999556 0.0298020i \(-0.00948767\pi\)
\(410\) 0.951730 3.55190i 0.0470026 0.175416i
\(411\) −8.58908 + 5.53528i −0.423668 + 0.273035i
\(412\) −12.9282 22.3923i −0.636927 1.10319i
\(413\) −3.38587 + 5.86450i −0.166608 + 0.288573i
\(414\) 0 0
\(415\) 4.19615i 0.205981i
\(416\) 1.69293 + 8.46467i 0.0830029 + 0.415015i
\(417\) 0.875644 4.05001i 0.0428805 0.198330i
\(418\) 4.19615 1.12436i 0.205241 0.0549940i
\(419\) −7.22536 4.17156i −0.352982 0.203794i 0.313016 0.949748i \(-0.398661\pi\)
−0.665998 + 0.745954i \(0.731994\pi\)
\(420\) −20.8389 + 6.69063i −1.01683 + 0.326469i
\(421\) 0.830127 + 0.830127i 0.0404579 + 0.0404579i 0.727046 0.686588i \(-0.240893\pi\)
−0.686588 + 0.727046i \(0.740893\pi\)
\(422\) 28.2047 + 7.55743i 1.37298 + 0.367890i
\(423\) 18.2358 22.2007i 0.886657 1.07943i
\(424\) 13.5622 13.5622i 0.658638 0.658638i
\(425\) 1.36086 0.785693i 0.0660114 0.0381117i
\(426\) 13.3380 14.7097i 0.646226 0.712688i
\(427\) −2.56218 9.56218i −0.123992 0.462746i
\(428\) −62.2739 −3.01012
\(429\) 0.170025 10.9440i 0.00820890 0.528381i
\(430\) 46.9808 2.26561
\(431\) 0.542599 + 2.02501i 0.0261361 + 0.0975412i 0.977762 0.209718i \(-0.0672547\pi\)
−0.951626 + 0.307260i \(0.900588\pi\)
\(432\) −5.08502 11.7508i −0.244653 0.565360i
\(433\) −6.10770 + 3.52628i −0.293517 + 0.169462i −0.639527 0.768769i \(-0.720870\pi\)
0.346010 + 0.938231i \(0.387536\pi\)
\(434\) 15.1149 15.1149i 0.725536 0.725536i
\(435\) −20.4050 10.4867i −0.978344 0.502800i
\(436\) 14.2942 + 3.83013i 0.684569 + 0.183430i
\(437\) 0 0
\(438\) 10.9323 + 34.0502i 0.522366 + 1.62698i
\(439\) −4.09808 2.36603i −0.195591 0.112924i 0.399007 0.916948i \(-0.369355\pi\)
−0.594597 + 0.804024i \(0.702688\pi\)
\(440\) 16.8078 4.50363i 0.801280 0.214702i
\(441\) 6.19657 13.6603i 0.295075 0.650488i
\(442\) 17.5526 + 5.93782i 0.834890 + 0.282433i
\(443\) 29.5656i 1.40470i −0.711830 0.702351i \(-0.752134\pi\)
0.711830 0.702351i \(-0.247866\pi\)
\(444\) −2.15697 44.1025i −0.102365 2.09301i
\(445\) −12.0263 + 20.8301i −0.570100 + 0.987443i
\(446\) 27.6295 + 47.8558i 1.30830 + 2.26604i
\(447\) 5.09465 + 7.90535i 0.240969 + 0.373910i
\(448\) −3.90192 + 14.5622i −0.184349 + 0.687998i
\(449\) −2.26810 + 8.46467i −0.107038 + 0.399472i −0.998568 0.0534890i \(-0.982966\pi\)
0.891530 + 0.452961i \(0.149632\pi\)
\(450\) 1.84997 + 4.92177i 0.0872084 + 0.232014i
\(451\) 0.562178 + 0.973721i 0.0264719 + 0.0458507i
\(452\) 24.1992 41.9142i 1.13823 1.97148i
\(453\) −18.2614 + 0.893131i −0.857996 + 0.0419629i
\(454\) 37.4641i 1.75828i
\(455\) 10.1576 + 6.77174i 0.476196 + 0.317464i
\(456\) −7.26795 1.57139i −0.340353 0.0735869i
\(457\) −26.9904 + 7.23205i −1.26256 + 0.338301i −0.827175 0.561945i \(-0.810053\pi\)
−0.435382 + 0.900246i \(0.643387\pi\)
\(458\) 29.6871 + 17.1399i 1.38719 + 0.800893i
\(459\) 11.0799 + 1.28199i 0.517166 + 0.0598382i
\(460\) 0 0
\(461\) −23.4135 6.27363i −1.09048 0.292192i −0.331595 0.943422i \(-0.607587\pi\)
−0.758880 + 0.651230i \(0.774253\pi\)
\(462\) 4.69825 9.14181i 0.218582 0.425315i
\(463\) −15.0526 + 15.0526i −0.699552 + 0.699552i −0.964314 0.264762i \(-0.914707\pi\)
0.264762 + 0.964314i \(0.414707\pi\)
\(464\) 11.8060 6.81623i 0.548082 0.316435i
\(465\) −19.3940 17.5854i −0.899377 0.815506i
\(466\) −4.60770 17.1962i −0.213447 0.796596i
\(467\) −30.4728 −1.41011 −0.705057 0.709151i \(-0.749079\pi\)
−0.705057 + 0.709151i \(0.749079\pi\)
\(468\) −19.0078 + 35.6133i −0.878635 + 1.64622i
\(469\) 12.3923 0.572223
\(470\) −14.2076 53.0236i −0.655349 2.44579i
\(471\) 19.4984 + 17.6800i 0.898437 + 0.814653i
\(472\) −17.1962 + 9.92820i −0.791517 + 0.456983i
\(473\) −10.1576 + 10.1576i −0.467047 + 0.467047i
\(474\) 3.79101 7.37651i 0.174127 0.338814i
\(475\) 0.732051 + 0.196152i 0.0335888 + 0.00900009i
\(476\) 8.01105 + 8.01105i 0.367186 + 0.367186i
\(477\) −13.8093 + 1.35401i −0.632285 + 0.0619960i
\(478\) −20.8301 12.0263i −0.952748 0.550069i
\(479\) 8.46467 2.26810i 0.386761 0.103632i −0.0601988 0.998186i \(-0.519173\pi\)
0.446959 + 0.894554i \(0.352507\pi\)
\(480\) 9.70398 + 2.09808i 0.442924 + 0.0957636i
\(481\) −18.5000 + 16.2583i −0.843527 + 0.741316i
\(482\) 17.9256i 0.816487i
\(483\) 0 0
\(484\) 14.7942 25.6244i 0.672465 1.16474i
\(485\) −15.5685 26.9654i −0.706928 1.22444i
\(486\) −10.2872 + 35.8756i −0.466636 + 1.62735i
\(487\) −6.56218 + 24.4904i −0.297361 + 1.10977i 0.641964 + 0.766735i \(0.278120\pi\)
−0.939324 + 0.343030i \(0.888547\pi\)
\(488\) 7.51294 28.0387i 0.340095 1.26925i
\(489\) 14.5007 + 22.5007i 0.655746 + 1.01752i
\(490\) −14.3301 24.8205i −0.647369 1.12128i
\(491\) −12.5147 + 21.6761i −0.564780 + 0.978227i 0.432290 + 0.901734i \(0.357706\pi\)
−0.997070 + 0.0764928i \(0.975628\pi\)
\(492\) −0.202571 4.14187i −0.00913261 0.186730i
\(493\) 11.8756i 0.534852i
\(494\) 3.96104 + 8.01105i 0.178215 + 0.360434i
\(495\) −11.4641 5.20035i −0.515273 0.233738i
\(496\) 15.0263 4.02628i 0.674700 0.180785i
\(497\) −5.86450 3.38587i −0.263059 0.151877i
\(498\) 2.22178 + 6.92003i 0.0995602 + 0.310094i
\(499\) 4.46410 + 4.46410i 0.199841 + 0.199841i 0.799932 0.600091i \(-0.204869\pi\)
−0.600091 + 0.799932i \(0.704869\pi\)
\(500\) −36.8354 9.87002i −1.64733 0.441401i
\(501\) −18.1765 9.34143i −0.812064 0.417345i
\(502\) 37.0526 37.0526i 1.65374 1.65374i
\(503\) 24.8188 14.3292i 1.10662 0.638906i 0.168666 0.985673i \(-0.446054\pi\)
0.937951 + 0.346767i \(0.112721\pi\)
\(504\) −14.3053 + 10.2416i −0.637208 + 0.456196i
\(505\) −12.2321 45.6506i −0.544319 2.03143i
\(506\) 0 0
\(507\) 22.1453 4.07236i 0.983509 0.180860i
\(508\) −56.4449 −2.50434
\(509\) −3.88398 14.4952i −0.172154 0.642489i −0.997019 0.0771582i \(-0.975415\pi\)
0.824865 0.565330i \(-0.191251\pi\)
\(510\) 14.3153 15.7876i 0.633893 0.699087i
\(511\) 10.5622 6.09808i 0.467243 0.269763i
\(512\) −18.6223 + 18.6223i −0.822996 + 0.822996i
\(513\) 3.34143 + 4.21584i 0.147528 + 0.186134i
\(514\) 38.3827 + 10.2846i 1.69299 + 0.453635i
\(515\) 11.7290 + 11.7290i 0.516841 + 0.516841i
\(516\) 50.4445 16.1960i 2.22070 0.712988i
\(517\) 14.5359 + 8.39230i 0.639288 + 0.369093i
\(518\) −22.3402 + 5.98604i −0.981573 + 0.263012i
\(519\) 2.72172 12.5885i 0.119470 0.552572i
\(520\) 15.8660 + 32.0885i 0.695771 + 1.40717i
\(521\) 33.2835i 1.45818i −0.684419 0.729089i \(-0.739944\pi\)
0.684419 0.729089i \(-0.260056\pi\)
\(522\) −39.2031 6.49004i −1.71587 0.284061i
\(523\) −6.49038 + 11.2417i −0.283805 + 0.491564i −0.972319 0.233659i \(-0.924930\pi\)
0.688514 + 0.725223i \(0.258263\pi\)
\(524\) −1.69293 2.93225i −0.0739562 0.128096i
\(525\) 1.50726 0.971364i 0.0657823 0.0423938i
\(526\) −7.41858 + 27.6865i −0.323466 + 1.20719i
\(527\) −3.50742 + 13.0899i −0.152785 + 0.570203i
\(528\) 6.28764 4.05211i 0.273634 0.176345i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) −13.2559 + 22.9599i −0.575799 + 0.997313i
\(531\) 14.1721 + 2.34618i 0.615018 + 0.101816i
\(532\) 5.46410i 0.236899i
\(533\) −1.73742 + 1.52690i −0.0752562 + 0.0661373i
\(534\) −8.80385 + 40.7194i −0.380980 + 1.76210i
\(535\) 38.5885 10.3397i 1.66832 0.447026i
\(536\) 31.4690 + 18.1687i 1.35926 + 0.784766i
\(537\) 30.9111 9.92447i 1.33391 0.428273i
\(538\) 18.7321 + 18.7321i 0.807596 + 0.807596i
\(539\) 8.46467 + 2.26810i 0.364599 + 0.0976940i
\(540\) 28.8389 + 36.3857i 1.24103 + 1.56579i
\(541\) 23.6865 23.6865i 1.01836 1.01836i 0.0185354 0.999828i \(-0.494100\pi\)
0.999828 0.0185354i \(-0.00590034\pi\)
\(542\) −4.29311 + 2.47863i −0.184405 + 0.106466i
\(543\) −3.49036 + 3.84933i −0.149786 + 0.165191i
\(544\) −1.33013 4.96410i −0.0570287 0.212834i
\(545\) −9.49346 −0.406655
\(546\) 20.3368 + 5.78927i 0.870333 + 0.247758i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 5.69846 + 21.2669i 0.243426 + 0.908479i
\(549\) −17.0751 + 12.2246i −0.728748 + 0.521732i
\(550\) −2.66025 + 1.53590i −0.113434 + 0.0654909i
\(551\) −4.05001 + 4.05001i −0.172536 + 0.172536i
\(552\) 0 0
\(553\) −2.73205 0.732051i −0.116179 0.0311300i
\(554\) 6.07502 + 6.07502i 0.258103 + 0.258103i
\(555\) 8.65920 + 26.9703i 0.367563 + 1.14482i
\(556\) −7.73205 4.46410i −0.327912 0.189320i
\(557\) −39.3140 + 10.5342i −1.66579 + 0.446347i −0.963971 0.266009i \(-0.914295\pi\)
−0.701819 + 0.712355i \(0.747628\pi\)
\(558\) −41.2946 18.7321i −1.74814 0.792991i
\(559\) −24.5885 16.3923i −1.03998 0.693321i
\(560\) 8.34312i 0.352561i
\(561\) 0.318318 + 6.50849i 0.0134394 + 0.274788i
\(562\) −26.9186 + 46.6244i −1.13549 + 1.96673i
\(563\) 2.14655 + 3.71794i 0.0904665 + 0.156693i 0.907708 0.419603i \(-0.137831\pi\)
−0.817241 + 0.576296i \(0.804498\pi\)
\(564\) −33.5342 52.0350i −1.41205 2.19107i
\(565\) −8.03590 + 29.9904i −0.338073 + 1.26170i
\(566\) 15.2364 56.8630i 0.640434 2.39013i
\(567\) 12.6999 + 0.843533i 0.533347 + 0.0354250i
\(568\) −9.92820 17.1962i −0.416578 0.721535i
\(569\) 8.01105 13.8755i 0.335841 0.581693i −0.647805 0.761806i \(-0.724313\pi\)
0.983646 + 0.180113i \(0.0576463\pi\)
\(570\) 10.2662 0.502098i 0.430002 0.0210306i
\(571\) 40.0526i 1.67615i −0.545557 0.838074i \(-0.683682\pi\)
0.545557 0.838074i \(-0.316318\pi\)
\(572\) −22.3402 7.55743i −0.934091 0.315992i
\(573\) 32.8564 + 7.10381i 1.37260 + 0.296766i
\(574\) −2.09808 + 0.562178i −0.0875720 + 0.0234648i
\(575\) 0 0
\(576\) 31.8281 3.12077i 1.32617 0.130032i
\(577\) 3.49038 + 3.49038i 0.145306 + 0.145306i 0.776018 0.630711i \(-0.217237\pi\)
−0.630711 + 0.776018i \(0.717237\pi\)
\(578\) 28.6583 + 7.67898i 1.19203 + 0.319403i
\(579\) 5.70810 11.1068i 0.237220 0.461581i
\(580\) −34.9545 + 34.9545i −1.45141 + 1.45141i
\(581\) 2.14655 1.23931i 0.0890541 0.0514154i
\(582\) −39.9522 36.2264i −1.65607 1.50163i
\(583\) −2.09808 7.83013i −0.0868934 0.324291i
\(584\) 35.7621 1.47985
\(585\) 5.86520 25.2240i 0.242496 1.04288i
\(586\) −52.7128 −2.17755
\(587\) 5.20035 + 19.4080i 0.214641 + 0.801053i 0.986292 + 0.165006i \(0.0527645\pi\)
−0.771651 + 0.636046i \(0.780569\pi\)
\(588\) −23.9432 21.7104i −0.987400 0.895320i
\(589\) −5.66025 + 3.26795i −0.233227 + 0.134654i
\(590\) 19.4080 19.4080i 0.799013 0.799013i
\(591\) −1.38761 + 2.69999i −0.0570785 + 0.111063i
\(592\) −16.2583 4.35641i −0.668213 0.179047i
\(593\) 10.6112 + 10.6112i 0.435751 + 0.435751i 0.890579 0.454828i \(-0.150299\pi\)
−0.454828 + 0.890579i \(0.650299\pi\)
\(594\) −21.6593 2.50608i −0.888694 0.102826i
\(595\) −6.29423 3.63397i −0.258038 0.148978i
\(596\) 19.5740 5.24484i 0.801782 0.214837i
\(597\) −1.57139 0.339746i −0.0643126 0.0139049i
\(598\) 0 0
\(599\) 21.2224i 0.867126i 0.901123 + 0.433563i \(0.142744\pi\)
−0.901123 + 0.433563i \(0.857256\pi\)
\(600\) 5.25169 0.256850i 0.214399 0.0104859i
\(601\) 3.79423 6.57180i 0.154770 0.268069i −0.778205 0.628010i \(-0.783870\pi\)
0.932975 + 0.359941i \(0.117203\pi\)
\(602\) −13.8755 24.0331i −0.565525 0.979518i
\(603\) −9.24923 24.6072i −0.376658 1.00208i
\(604\) −10.1962 + 38.0526i −0.414876 + 1.54834i
\(605\) −4.91277 + 18.3347i −0.199732 + 0.745411i
\(606\) −44.3434 68.8075i −1.80133 2.79511i
\(607\) −5.09808 8.83013i −0.206925 0.358404i 0.743820 0.668380i \(-0.233012\pi\)
−0.950744 + 0.309977i \(0.899679\pi\)
\(608\) 1.23931 2.14655i 0.0502608 0.0870543i
\(609\) 0.661992 + 13.5354i 0.0268253 + 0.548483i
\(610\) 40.1244i 1.62459i
\(611\) −11.0648 + 32.7083i −0.447636 + 1.32324i
\(612\) 9.92820 21.8866i 0.401324 0.884713i
\(613\) 16.3564 4.38269i 0.660629 0.177015i 0.0870991 0.996200i \(-0.472240\pi\)
0.573530 + 0.819185i \(0.305574\pi\)
\(614\) −36.3373 20.9794i −1.46645 0.846658i
\(615\) 0.813227 + 2.53291i 0.0327925 + 0.102137i
\(616\) −7.26795 7.26795i −0.292834 0.292834i
\(617\) 36.3818 + 9.74847i 1.46468 + 0.392459i 0.901102 0.433607i \(-0.142759\pi\)
0.563574 + 0.826066i \(0.309426\pi\)
\(618\) 25.5530 + 13.1324i 1.02789 + 0.528264i
\(619\) −14.3397 + 14.3397i −0.576363 + 0.576363i −0.933899 0.357536i \(-0.883617\pi\)
0.357536 + 0.933899i \(0.383617\pi\)
\(620\) −48.8520 + 28.2047i −1.96194 + 1.13273i
\(621\) 0 0
\(622\) 2.66025 + 9.92820i 0.106666 + 0.398085i
\(623\) 14.2076 0.569216
\(624\) 10.7108 + 11.0489i 0.428777 + 0.442310i
\(625\) 28.1244 1.12497
\(626\) 1.23931 + 4.62518i 0.0495329 + 0.184859i
\(627\) −2.11107 + 2.32818i −0.0843078 + 0.0929786i
\(628\) 49.1147 28.3564i 1.95989 1.13154i
\(629\) 10.3681 10.3681i 0.413404 0.413404i
\(630\) 15.4360 18.7921i 0.614986 0.748696i
\(631\) 2.26795 + 0.607695i 0.0902856 + 0.0241920i 0.303679 0.952774i \(-0.401785\pi\)
−0.213393 + 0.976966i \(0.568452\pi\)
\(632\) −5.86450 5.86450i −0.233277 0.233277i
\(633\) −20.1131 + 6.45761i −0.799425 + 0.256667i
\(634\) 33.0622 + 19.0885i 1.31307 + 0.758099i
\(635\) 34.9764 9.37191i 1.38800 0.371913i
\(636\) −6.31812 + 29.2224i −0.250530 + 1.15874i
\(637\) −1.16025 + 17.9904i −0.0459709 + 0.712805i
\(638\) 23.2149i 0.919086i
\(639\) −2.34618 + 14.1721i −0.0928136 + 0.560641i
\(640\) 24.8205 42.9904i 0.981117 1.69934i
\(641\) −9.65949 16.7307i −0.381527 0.660824i 0.609754 0.792591i \(-0.291268\pi\)
−0.991281 + 0.131767i \(0.957935\pi\)
\(642\) 58.1629 37.4835i 2.29551 1.47935i
\(643\) 7.00000 26.1244i 0.276053 1.03024i −0.679079 0.734065i \(-0.737621\pi\)
0.955132 0.296179i \(-0.0957125\pi\)
\(644\) 0 0
\(645\) −28.5692 + 18.4116i −1.12491 + 0.724955i
\(646\) −2.66025 4.60770i −0.104666 0.181287i
\(647\) 7.22536 12.5147i 0.284058 0.492003i −0.688322 0.725405i \(-0.741652\pi\)
0.972380 + 0.233402i \(0.0749858\pi\)
\(648\) 31.0135 + 20.7618i 1.21833 + 0.815599i
\(649\) 8.39230i 0.329427i
\(650\) −4.17156 4.74673i −0.163622 0.186182i
\(651\) −3.26795 + 15.1149i −0.128081 + 0.592398i
\(652\) 55.7128 14.9282i 2.18188 0.584634i
\(653\) −33.6156 19.4080i −1.31548 0.759492i −0.332482 0.943110i \(-0.607886\pi\)
−0.982998 + 0.183617i \(0.941219\pi\)
\(654\) −15.6560 + 5.02659i −0.612198 + 0.196555i
\(655\) 1.53590 + 1.53590i 0.0600125 + 0.0600125i
\(656\) −1.52690 0.409131i −0.0596153 0.0159739i
\(657\) −19.9921 16.4217i −0.779967 0.640672i
\(658\) −22.9282 + 22.9282i −0.893834 + 0.893834i
\(659\) 27.1759 15.6900i 1.05862 0.611197i 0.133572 0.991039i \(-0.457355\pi\)
0.925051 + 0.379842i \(0.124022\pi\)
\(660\) −18.2200 + 20.0938i −0.709212 + 0.782152i
\(661\) −4.42820 16.5263i −0.172237 0.642798i −0.997006 0.0773274i \(-0.975361\pi\)
0.824769 0.565470i \(-0.191305\pi\)
\(662\) 46.7380 1.81652
\(663\) −13.0008 + 3.26797i −0.504909 + 0.126917i
\(664\) 7.26795 0.282051
\(665\) −0.907241 3.38587i −0.0351813 0.131298i
\(666\) 28.5604 + 39.8928i 1.10669 + 1.54581i
\(667\) 0 0
\(668\) −31.1370 + 31.1370i −1.20473 + 1.20473i
\(669\) −35.5561 18.2734i −1.37468 0.706489i
\(670\) −48.5167 13.0000i −1.87436 0.502234i
\(671\) −8.67520 8.67520i −0.334902 0.334902i
\(672\) −1.79275 5.58376i −0.0691568 0.215398i
\(673\) −11.0096 6.35641i −0.424390 0.245021i 0.272564 0.962138i \(-0.412128\pi\)
−0.696954 + 0.717116i \(0.745462\pi\)
\(674\) −26.6778 + 7.14830i −1.02759 + 0.275342i
\(675\) −3.05379 2.26795i −0.117541 0.0872934i
\(676\) 6.23205 48.1147i 0.239694 1.85057i
\(677\) 38.8159i 1.49182i 0.666048 + 0.745909i \(0.267985\pi\)
−0.666048 + 0.745909i \(0.732015\pi\)
\(678\) 2.62700 + 53.7131i 0.100889 + 2.06284i
\(679\) −9.19615 + 15.9282i −0.352916 + 0.611268i
\(680\) −10.6557 18.4562i −0.408628 0.707764i
\(681\) 14.6820 + 22.7821i 0.562617 + 0.873011i
\(682\) 6.85641 25.5885i 0.262545 0.979833i
\(683\) −4.26054 + 15.9006i −0.163025 + 0.608418i 0.835259 + 0.549857i \(0.185318\pi\)
−0.998284 + 0.0585607i \(0.981349\pi\)
\(684\) 10.8500 4.07823i 0.414859 0.155935i
\(685\) −7.06218 12.2321i −0.269832 0.467363i
\(686\) −20.3152 + 35.1870i −0.775638 + 1.34344i
\(687\) −24.7699 + 1.21145i −0.945031 + 0.0462196i
\(688\) 20.1962i 0.769971i
\(689\) 14.9488 7.39139i 0.569505 0.281590i
\(690\) 0 0
\(691\) −41.8827 + 11.2224i −1.59329 + 0.426921i −0.943008 0.332770i \(-0.892017\pi\)
−0.650284 + 0.759691i \(0.725350\pi\)
\(692\) −24.0331 13.8755i −0.913603 0.527469i
\(693\) 0.725614 + 7.40039i 0.0275638 + 0.281118i
\(694\) 43.9090 + 43.9090i 1.66676 + 1.66676i
\(695\) 5.53242 + 1.48241i 0.209857 + 0.0562309i
\(696\) −18.1636 + 35.3425i −0.688488 + 1.33965i
\(697\) 0.973721 0.973721i 0.0368823 0.0368823i
\(698\) −12.0936 + 6.98226i −0.457751 + 0.264283i
\(699\) 9.54106 + 8.65131i 0.360876 + 0.327223i
\(700\) −1.00000 3.73205i −0.0377964 0.141058i
\(701\) 20.3152 0.767295 0.383647 0.923480i \(-0.374668\pi\)
0.383647 + 0.923480i \(0.374668\pi\)
\(702\) −3.68307 44.7033i −0.139009 1.68722i
\(703\) 7.07180 0.266718
\(704\) 4.83571 + 18.0471i 0.182253 + 0.680176i
\(705\) 29.4194 + 26.6759i 1.10800 + 1.00467i
\(706\) −56.5526 + 32.6506i −2.12838 + 1.22882i
\(707\) −19.7400 + 19.7400i −0.742401 + 0.742401i
\(708\) 14.1482 27.5295i 0.531724 1.03462i
\(709\) −9.96410 2.66987i −0.374210 0.100269i 0.0668121 0.997766i \(-0.478717\pi\)
−0.441022 + 0.897496i \(0.645384\pi\)
\(710\) 19.4080 + 19.4080i 0.728368 + 0.728368i
\(711\) 0.585497 + 5.97136i 0.0219578 + 0.223944i
\(712\) 36.0788 + 20.8301i 1.35211 + 0.780642i
\(713\) 0 0
\(714\) −12.3042 2.66025i −0.460472 0.0995575i
\(715\) 15.0981 + 0.973721i 0.564636 + 0.0364151i
\(716\) 69.9529i 2.61426i
\(717\) 17.3799 0.850019i 0.649065 0.0317446i
\(718\) 20.4186 35.3660i 0.762015 1.31985i
\(719\) −5.86450 10.1576i −0.218709 0.378815i 0.735705 0.677302i \(-0.236851\pi\)
−0.954413 + 0.298488i \(0.903518\pi\)
\(720\) 16.5668 6.22704i 0.617408 0.232068i
\(721\) 2.53590 9.46410i 0.0944418 0.352462i
\(722\) −11.1093 + 41.4606i −0.413447 + 1.54300i
\(723\) −7.02496 10.9006i −0.261261 0.405398i
\(724\) 5.59808 + 9.69615i 0.208051 + 0.360355i
\(725\) 2.02501 3.50742i 0.0752069 0.130262i
\(726\) 1.60603 + 32.8376i 0.0596052 + 1.21872i
\(727\) 25.5167i 0.946361i −0.880966 0.473180i \(-0.843106\pi\)
0.880966 0.473180i \(-0.156894\pi\)
\(728\) 11.7290 17.5935i 0.434705 0.652058i
\(729\) −7.80385 25.8476i −0.289031 0.957320i
\(730\) −47.7487 + 12.7942i −1.76726 + 0.473536i
\(731\) 15.2364 + 8.79674i 0.563539 + 0.325359i
\(732\) 13.8323 + 43.0826i 0.511257 + 1.59238i
\(733\) −36.2224 36.2224i −1.33791 1.33791i −0.898086 0.439820i \(-0.855042\pi\)
−0.439820 0.898086i \(-0.644958\pi\)
\(734\) −22.2187 5.95347i −0.820106 0.219747i
\(735\) 18.4413 + 9.47753i 0.680216 + 0.349584i
\(736\) 0 0
\(737\) 13.3004 7.67898i 0.489926 0.282859i
\(738\) 2.68224 + 3.74652i 0.0987348 + 0.137911i
\(739\) 13.1244 + 48.9808i 0.482787 + 1.80179i 0.589825 + 0.807531i \(0.299197\pi\)
−0.107037 + 0.994255i \(0.534136\pi\)
\(740\) 61.0346 2.24368
\(741\) −5.54822 3.31924i −0.203819 0.121935i
\(742\) 15.6603 0.574906
\(743\) −13.5435 50.5449i −0.496862 1.85431i −0.519343 0.854566i \(-0.673823\pi\)
0.0224808 0.999747i \(-0.492844\pi\)
\(744\) −30.4589 + 33.5915i −1.11668 + 1.23152i
\(745\) −11.2583 + 6.50000i −0.412473 + 0.238142i
\(746\) −33.1620 + 33.1620i −1.21415 + 1.21415i
\(747\) −4.06300 3.33739i −0.148658 0.122109i
\(748\) 13.5622 + 3.63397i 0.495882 + 0.132871i
\(749\) −16.6862 16.6862i −0.609702 0.609702i
\(750\) 40.3446 12.9532i 1.47318 0.472986i
\(751\) 38.2750 + 22.0981i 1.39667 + 0.806370i 0.994043 0.108992i \(-0.0347622\pi\)
0.402632 + 0.915362i \(0.368096\pi\)
\(752\) −22.7938 + 6.10759i −0.831206 + 0.222721i
\(753\) −8.01105 + 37.0526i −0.291939 + 1.35027i
\(754\) 46.8301 9.36603i 1.70545 0.341091i
\(755\) 25.2725i 0.919759i
\(756\) 10.0958 25.4990i 0.367180 0.927389i
\(757\) 12.3923 21.4641i 0.450406 0.780126i −0.548005 0.836475i \(-0.684613\pi\)
0.998411 + 0.0563489i \(0.0179459\pi\)
\(758\) −5.98604 10.3681i −0.217423 0.376587i
\(759\) 0 0
\(760\) 2.66025 9.92820i 0.0964976 0.360134i
\(761\) −1.11777 + 4.17156i −0.0405190 + 0.151219i −0.983222 0.182415i \(-0.941608\pi\)
0.942703 + 0.333634i \(0.108275\pi\)
\(762\) 52.7187 33.9749i 1.90980 1.23078i
\(763\) 2.80385 + 4.85641i 0.101506 + 0.175814i
\(764\) 36.2158 62.7275i 1.31024 2.26940i
\(765\) −2.51810 + 15.2106i −0.0910423 + 0.549941i
\(766\) 33.5692i 1.21291i
\(767\) −16.9293 + 3.38587i −0.611283 + 0.122257i
\(768\) 10.3660 47.9447i 0.374052 1.73006i
\(769\) −2.16987 + 0.581416i −0.0782476 + 0.0209664i −0.297730 0.954650i \(-0.596230\pi\)
0.219483 + 0.975616i \(0.429563\pi\)
\(770\) 12.3042 + 7.10381i 0.443411 + 0.256004i
\(771\) −27.3712 + 8.78792i −0.985748 + 0.316489i
\(772\) −19.0263 19.0263i −0.684771 0.684771i
\(773\) 5.98604 + 1.60396i 0.215303 + 0.0576903i 0.364858 0.931063i \(-0.381117\pi\)
−0.149555 + 0.988753i \(0.547784\pi\)
\(774\) −37.3659 + 45.4900i −1.34309 + 1.63510i
\(775\) 3.26795 3.26795i 0.117388 0.117388i
\(776\) −46.7054 + 26.9654i −1.67663 + 0.968001i
\(777\) 11.2393 12.3952i 0.403206 0.444675i
\(778\) −3.27757 12.2321i −0.117507 0.438540i
\(779\) 0.664146 0.0237955
\(780\) −47.8851 28.6473i −1.71456 1.02574i
\(781\) −8.39230 −0.300300
\(782\) 0 0
\(783\) 26.3830 11.4169i 0.942851 0.408008i
\(784\) −10.6699 + 6.16025i −0.381067 + 0.220009i
\(785\) −25.7261 + 25.7261i −0.918203 + 0.918203i
\(786\) 3.34613 + 1.71968i 0.119353 + 0.0613389i
\(787\) −11.2942 3.02628i −0.402596 0.107875i 0.0518385 0.998655i \(-0.483492\pi\)
−0.454434 + 0.890780i \(0.650159\pi\)
\(788\) 4.62518 + 4.62518i 0.164765 + 0.164765i
\(789\) −6.33898 19.7436i −0.225674 0.702891i
\(790\) 9.92820 + 5.73205i 0.353230 + 0.203937i
\(791\) 17.7150 4.74673i 0.629874 0.168774i
\(792\) −9.00727 + 19.8564i −0.320059 + 0.705567i
\(793\) 14.0000 21.0000i 0.497155 0.745732i
\(794\) 21.2224i 0.753157i
\(795\) −0.936928 19.1569i −0.0332294 0.679426i
\(796\) −1.73205 + 3.00000i −0.0613909 + 0.106332i
\(797\) 8.58622 + 14.8718i 0.304139 + 0.526785i 0.977069 0.212921i \(-0.0682978\pi\)
−0.672930 + 0.739706i \(0.734964\pi\)
\(798\) −3.28891 5.10339i −0.116426 0.180658i
\(799\) 5.32051 19.8564i 0.188226 0.702469i
\(800\) −0.453620 + 1.69293i −0.0160379 + 0.0598543i
\(801\) −10.6041 28.2118i −0.374678 0.996815i
\(802\) 33.6244 + 58.2391i 1.18732 + 2.05649i
\(803\) 7.55743 13.0899i 0.266696 0.461931i
\(804\) −56.5752 + 2.76699i −1.99526 + 0.0975841i
\(805\) 0 0
\(806\) 54.3844 + 3.50742i 1.91561 + 0.123543i
\(807\) −18.7321 4.05001i −0.659399 0.142567i
\(808\) −79.0692 + 21.1865i −2.78165 + 0.745340i
\(809\) 17.6705 + 10.2021i 0.621263 + 0.358686i 0.777361 0.629055i \(-0.216558\pi\)
−0.156097 + 0.987742i \(0.549891\pi\)
\(810\) −48.8362 16.6252i −1.71593 0.584150i
\(811\) 19.0000 + 19.0000i 0.667180 + 0.667180i 0.957062 0.289882i \(-0.0936161\pi\)
−0.289882 + 0.957062i \(0.593616\pi\)
\(812\) 28.2047 + 7.55743i 0.989791 + 0.265214i
\(813\) 1.63929 3.18972i 0.0574925 0.111868i
\(814\) −20.2679 + 20.2679i −0.710391 + 0.710391i
\(815\) −32.0442 + 18.5007i −1.12246 + 0.648052i
\(816\) −6.78680 6.15389i −0.237585 0.215429i
\(817\) 2.19615 + 8.19615i 0.0768336 + 0.286747i
\(818\) 27.8401 0.973405
\(819\) −14.6357 + 4.44942i −0.511411 + 0.155475i
\(820\) 5.73205 0.200172
\(821\) −1.60396 5.98604i −0.0559784 0.208914i 0.932272 0.361758i \(-0.117823\pi\)
−0.988250 + 0.152844i \(0.951157\pi\)
\(822\) −18.1231 16.4330i −0.632116 0.573168i
\(823\) 13.3923 7.73205i 0.466826 0.269522i −0.248084 0.968739i \(-0.579801\pi\)
0.714910 + 0.699216i \(0.246468\pi\)
\(824\) 20.3152 20.3152i 0.707714 0.707714i
\(825\) 1.01580 1.97653i 0.0353656 0.0688139i
\(826\) −15.6603 4.19615i −0.544890 0.146003i
\(827\) −3.62896 3.62896i −0.126191 0.126191i 0.641190 0.767382i \(-0.278441\pi\)
−0.767382 + 0.641190i \(0.778441\pi\)
\(828\) 0 0
\(829\) −20.6769 11.9378i −0.718139 0.414618i 0.0959284 0.995388i \(-0.469418\pi\)
−0.814067 + 0.580771i \(0.802751\pi\)
\(830\) −9.70398 + 2.60017i −0.336830 + 0.0902534i
\(831\) −6.07502 1.31347i −0.210740 0.0455636i
\(832\) −34.4545 + 17.0359i −1.19449 + 0.590614i
\(833\) 10.7328i 0.371868i
\(834\) 9.90862 0.484612i 0.343108 0.0167807i
\(835\) 14.1244 24.4641i 0.488793 0.846615i
\(836\) 3.38587 + 5.86450i 0.117103 + 0.202828i
\(837\) 32.4524 4.79215i 1.12172 0.165641i
\(838\) 5.16987 19.2942i 0.178590 0.666508i
\(839\) 2.02501 7.55743i 0.0699110 0.260911i −0.922120 0.386903i \(-0.873545\pi\)
0.992031 + 0.125992i \(0.0402114\pi\)
\(840\) −13.1738 20.4418i −0.454540 0.705308i
\(841\) 0.803848 + 1.39230i 0.0277189 + 0.0480105i
\(842\) −1.40535 + 2.43414i −0.0484316 + 0.0838859i
\(843\) −1.90261 38.9017i −0.0655294 1.33985i
\(844\) 45.5167i 1.56675i
\(845\) 4.12707 + 30.8494i 0.141976 + 1.06125i
\(846\) 62.6410 + 28.4152i 2.15364 + 0.976936i
\(847\) 10.8301 2.90192i 0.372128 0.0997113i
\(848\) 9.87002 + 5.69846i 0.338938 + 0.195686i
\(849\) 13.0191 + 40.5497i 0.446814 + 1.39166i
\(850\) 2.66025 + 2.66025i 0.0912460 + 0.0912460i
\(851\) 0 0
\(852\) 27.5295 + 14.1482i 0.943145 + 0.484711i
\(853\) −20.6340 + 20.6340i −0.706494 + 0.706494i −0.965796 0.259302i \(-0.916507\pi\)
0.259302 + 0.965796i \(0.416507\pi\)
\(854\) 20.5257 11.8505i 0.702376 0.405517i
\(855\) −6.04612 + 4.32860i −0.206773 + 0.148035i
\(856\) −17.9090 66.8372i −0.612116 2.28445i
\(857\) −35.7621 −1.22161 −0.610806 0.791781i \(-0.709154\pi\)
−0.610806 + 0.791781i \(0.709154\pi\)
\(858\) 25.4144 6.38833i 0.867632 0.218094i
\(859\) −23.1769 −0.790786 −0.395393 0.918512i \(-0.629392\pi\)
−0.395393 + 0.918512i \(0.629392\pi\)
\(860\) 18.9543 + 70.7386i 0.646338 + 2.41217i
\(861\) 1.05553 1.16409i 0.0359725 0.0396721i
\(862\) −4.34679 + 2.50962i −0.148052 + 0.0854780i
\(863\) 12.0611 12.0611i 0.410563 0.410563i −0.471371 0.881935i \(-0.656241\pi\)
0.881935 + 0.471371i \(0.156241\pi\)
\(864\) −9.74952 + 7.72737i −0.331685 + 0.262890i
\(865\) 17.1962 + 4.60770i 0.584687 + 0.156666i
\(866\) −11.9395 11.9395i −0.405721 0.405721i
\(867\) −20.4366 + 6.56147i −0.694063 + 0.222839i
\(868\) 28.8564 + 16.6603i 0.979450 + 0.565486i
\(869\) −3.38587 + 0.907241i −0.114858 + 0.0307760i
\(870\) 11.6074 53.6865i 0.393529 1.82014i
\(871\) 20.8564 + 23.7321i 0.706692 + 0.804130i
\(872\) 16.4432i 0.556835i
\(873\) 38.4921 + 6.37233i 1.30276 + 0.215671i
\(874\) 0 0
\(875\) −7.22536 12.5147i −0.244262 0.423074i
\(876\) −46.8585 + 30.1982i −1.58320 + 1.02030i
\(877\) 3.00962 11.2321i 0.101628 0.379279i −0.896313 0.443422i \(-0.853764\pi\)
0.997941 + 0.0641422i \(0.0204311\pi\)
\(878\) 2.93225 10.9433i 0.0989586 0.369318i
\(879\) 32.0549 20.6579i 1.08118 0.696775i
\(880\) 5.16987 + 8.95448i 0.174276 + 0.301856i
\(881\) −13.5880 + 23.5350i −0.457790 + 0.792916i −0.998844 0.0480724i \(-0.984692\pi\)
0.541054 + 0.840988i \(0.318026\pi\)
\(882\) 35.4303 + 5.86546i 1.19300 + 0.197500i
\(883\) 39.3731i 1.32501i 0.749058 + 0.662505i \(0.230506\pi\)
−0.749058 + 0.662505i \(0.769494\pi\)
\(884\) −1.85897 + 28.8244i −0.0625239 + 0.969468i
\(885\) −4.19615 + 19.4080i −0.141052 + 0.652392i
\(886\) 68.3731 18.3205i 2.29704 0.615490i
\(887\) −46.4949 26.8438i −1.56115 0.901328i −0.997142 0.0755567i \(-0.975927\pi\)
−0.564005 0.825772i \(-0.690740\pi\)
\(888\) 46.7139 14.9982i 1.56761 0.503306i
\(889\) −15.1244 15.1244i −0.507255 0.507255i
\(890\) −55.6237 14.9043i −1.86451 0.499594i
\(891\) 14.1533 6.96426i 0.474152 0.233311i
\(892\) −60.9090 + 60.9090i −2.03938 + 2.03938i
\(893\) 8.58622 4.95725i 0.287327 0.165888i
\(894\) −15.1249 + 16.6804i −0.505853 + 0.557878i
\(895\) 11.6147 + 43.3468i 0.388238 + 1.44892i
\(896\) −29.3225 −0.979595
\(897\) 0 0
\(898\) −20.9808 −0.700137
\(899\) 9.03984 + 33.7371i 0.301495 + 1.12520i
\(900\) −6.66430 + 4.77117i −0.222143 + 0.159039i
\(901\) −8.59808 + 4.96410i −0.286443 + 0.165378i
\(902\) −1.90346 + 1.90346i −0.0633783 + 0.0633783i
\(903\) 17.8563 + 9.17688i 0.594219 + 0.305387i
\(904\) 51.9449 + 13.9186i 1.72766 + 0.462925i
\(905\) −5.07880 5.07880i −0.168825 0.168825i
\(906\) −13.3813 41.6777i −0.444562 1.38465i
\(907\) −15.0000 8.66025i −0.498067 0.287559i 0.229848 0.973227i \(-0.426177\pi\)
−0.727915 + 0.685668i \(0.759510\pi\)
\(908\) 56.4094 15.1149i 1.87201 0.501604i
\(909\) 53.9308 + 24.4641i 1.78877 + 0.811423i
\(910\) −9.36603 + 27.6865i −0.310481 + 0.917800i
\(911\) 9.25036i 0.306478i −0.988189 0.153239i \(-0.951030\pi\)
0.988189 0.153239i \(-0.0489705\pi\)
\(912\) −0.215843 4.41323i −0.00714727 0.146137i
\(913\) 1.53590 2.66025i 0.0508308 0.0880416i
\(914\) −33.4495 57.9363i −1.10641 1.91636i
\(915\) −15.7246 24.3998i −0.519839 0.806632i
\(916\) −13.8301 + 51.6147i −0.456960 + 1.70540i
\(917\) 0.332073 1.23931i 0.0109660 0.0409257i
\(918\) 3.90102 + 26.4177i 0.128753 + 0.871913i
\(919\) −22.2942 38.6147i −0.735419 1.27378i −0.954539 0.298085i \(-0.903652\pi\)
0.219121 0.975698i \(-0.429681\pi\)
\(920\) 0 0
\(921\) 30.3186 1.48282i 0.999031 0.0488607i
\(922\) 58.0333i 1.91123i
\(923\) −3.38587 16.9293i −0.111447 0.557236i
\(924\) 15.6603 + 3.38587i 0.515185 + 0.111387i
\(925\) −4.83013 + 1.29423i −0.158814 + 0.0425540i
\(926\) −44.1378 25.4830i −1.45046 0.837423i
\(927\) −20.6854 + 2.02822i −0.679398 + 0.0666155i
\(928\) −9.36603 9.36603i −0.307455 0.307455i
\(929\) 47.3251 + 12.6807i 1.55269 + 0.416041i 0.930339 0.366701i \(-0.119513\pi\)
0.622347 + 0.782742i \(0.286179\pi\)
\(930\) 28.6503 55.7474i 0.939480 1.82803i
\(931\) 3.66025 3.66025i 0.119960 0.119960i
\(932\) 24.0331 13.8755i 0.787232 0.454509i
\(933\) −5.50854 4.99484i −0.180341 0.163524i
\(934\) −18.8827 70.4711i −0.617860 2.30589i
\(935\) −9.00727 −0.294569
\(936\) −43.6892 10.1588i −1.42803 0.332052i
\(937\) −37.0000 −1.20874 −0.604369 0.796705i \(-0.706575\pi\)
−0.604369 + 0.796705i \(0.706575\pi\)
\(938\) 7.67898 + 28.6583i 0.250727 + 0.935728i
\(939\) −2.56622 2.32691i −0.0837455 0.0759358i
\(940\) 74.1051 42.7846i 2.41704 1.39548i
\(941\) 38.2408 38.2408i 1.24661 1.24661i 0.289407 0.957206i \(-0.406542\pi\)
0.957206 0.289407i \(-0.0934582\pi\)
\(942\) −28.8044 + 56.0473i −0.938498 + 1.82612i
\(943\) 0 0
\(944\) −8.34312 8.34312i −0.271546 0.271546i
\(945\) −2.02215 + 17.4769i −0.0657805 + 0.568523i
\(946\) −29.7846 17.1962i −0.968381 0.559095i
\(947\) −39.6016 + 10.6112i −1.28688 + 0.344818i −0.836475 0.548006i \(-0.815387\pi\)
−0.450405 + 0.892824i \(0.648721\pi\)
\(948\) 12.6362 + 2.73205i 0.410406 + 0.0887329i
\(949\) 29.4545 + 9.96410i 0.956133 + 0.323448i
\(950\) 1.81448i 0.0588695i
\(951\) −27.5859 + 1.34918i −0.894535 + 0.0437500i
\(952\) −6.29423 + 10.9019i −0.203997 + 0.353333i
\(953\) 21.8866 + 37.9087i 0.708976 + 1.22798i 0.965237 + 0.261375i \(0.0841760\pi\)
−0.256261 + 0.966608i \(0.582491\pi\)
\(954\) −11.6883 31.0963i −0.378423 1.00678i
\(955\) −12.0263 + 44.8827i −0.389161 + 1.45237i
\(956\) 9.70398 36.2158i 0.313849 1.17130i
\(957\) 9.09782 + 14.1171i 0.294091 + 0.456340i
\(958\) 10.4904 + 18.1699i 0.338929 + 0.587042i
\(959\) −4.17156 + 7.22536i −0.134707 + 0.233319i
\(960\) 2.15946 + 44.1534i 0.0696963 + 1.42505i
\(961\) 8.85641i 0.285691i
\(962\) −49.0625 32.7083i −1.58184 1.05456i
\(963\) −20.6795 + 45.5877i −0.666387 + 1.46904i
\(964\) −26.9904 + 7.23205i −0.869302 + 0.232929i
\(965\) 14.9488 + 8.63071i 0.481220 + 0.277832i
\(966\) 0 0
\(967\) −0.143594 0.143594i −0.00461766 0.00461766i 0.704794 0.709412i \(-0.251039\pi\)
−0.709412 + 0.704794i \(0.751039\pi\)
\(968\) 31.7566 + 8.50916i 1.02070 + 0.273495i
\(969\) 3.42345 + 1.75941i 0.109977 + 0.0565205i
\(970\) 52.7128 52.7128i 1.69251 1.69251i
\(971\) −45.5551 + 26.3013i −1.46193 + 0.844047i −0.999101 0.0423987i \(-0.986500\pi\)
−0.462832 + 0.886446i \(0.653167\pi\)
\(972\) −58.1681 1.01535i −1.86574 0.0325673i
\(973\) −0.875644 3.26795i −0.0280719 0.104766i
\(974\) −60.7025 −1.94503
\(975\) 4.39697 + 1.25169i 0.140816 + 0.0400860i
\(976\) 17.2487 0.552118
\(977\) −7.60192 28.3707i −0.243207 0.907661i −0.974276 0.225357i \(-0.927645\pi\)
0.731069 0.682303i \(-0.239022\pi\)
\(978\) −43.0495 + 47.4770i −1.37657 + 1.51815i
\(979\) 15.2487 8.80385i 0.487351 0.281372i
\(980\) 31.5906 31.5906i 1.00912 1.00912i
\(981\) 7.55058 9.19222i 0.241071 0.293485i
\(982\) −57.8827 15.5096i −1.84711 0.494932i
\(983\) 4.38209 + 4.38209i 0.139767 + 0.139767i 0.773528 0.633762i \(-0.218490\pi\)
−0.633762 + 0.773528i \(0.718490\pi\)
\(984\) 4.38712 1.40855i 0.139856 0.0449029i
\(985\) −3.63397 2.09808i −0.115788 0.0668503i
\(986\) −27.4635 + 7.35882i −0.874616 + 0.234353i
\(987\) 4.95725 22.9282i 0.157791 0.729813i
\(988\) −10.4641 + 9.19615i −0.332907 + 0.292569i
\(989\) 0 0
\(990\) 4.92247 29.7342i 0.156446 0.945015i
\(991\) −12.7846 + 22.1436i −0.406117 + 0.703414i −0.994451 0.105203i \(-0.966451\pi\)
0.588334 + 0.808618i \(0.299784\pi\)
\(992\) −7.55743 13.0899i −0.239949 0.415603i
\(993\) −28.4216 + 18.3164i −0.901931 + 0.581255i
\(994\) 4.19615 15.6603i 0.133094 0.496713i
\(995\) 0.575167 2.14655i 0.0182340 0.0680503i
\(996\) −9.52306 + 6.13719i −0.301750 + 0.194464i
\(997\) 3.50000 + 6.06218i 0.110846 + 0.191991i 0.916112 0.400923i \(-0.131311\pi\)
−0.805266 + 0.592914i \(0.797977\pi\)
\(998\) −7.55743 + 13.0899i −0.239226 + 0.414352i
\(999\) −33.0015 13.0662i −1.04412 0.413397i
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 39.2.k.b.20.2 yes 8
3.2 odd 2 inner 39.2.k.b.20.1 yes 8
4.3 odd 2 624.2.cn.c.449.2 8
5.2 odd 4 975.2.bp.e.449.1 8
5.3 odd 4 975.2.bp.f.449.2 8
5.4 even 2 975.2.bo.d.176.1 8
12.11 even 2 624.2.cn.c.449.1 8
13.2 odd 12 inner 39.2.k.b.2.1 8
13.3 even 3 507.2.k.e.89.1 8
13.4 even 6 507.2.f.e.437.1 8
13.5 odd 4 507.2.k.e.188.2 8
13.6 odd 12 507.2.f.f.239.1 8
13.7 odd 12 507.2.f.e.239.4 8
13.8 odd 4 507.2.k.f.188.1 8
13.9 even 3 507.2.f.f.437.4 8
13.10 even 6 507.2.k.f.89.2 8
13.11 odd 12 507.2.k.d.80.2 8
13.12 even 2 507.2.k.d.488.1 8
15.2 even 4 975.2.bp.e.449.2 8
15.8 even 4 975.2.bp.f.449.1 8
15.14 odd 2 975.2.bo.d.176.2 8
39.2 even 12 inner 39.2.k.b.2.2 yes 8
39.5 even 4 507.2.k.e.188.1 8
39.8 even 4 507.2.k.f.188.2 8
39.11 even 12 507.2.k.d.80.1 8
39.17 odd 6 507.2.f.e.437.4 8
39.20 even 12 507.2.f.e.239.1 8
39.23 odd 6 507.2.k.f.89.1 8
39.29 odd 6 507.2.k.e.89.2 8
39.32 even 12 507.2.f.f.239.4 8
39.35 odd 6 507.2.f.f.437.1 8
39.38 odd 2 507.2.k.d.488.2 8
52.15 even 12 624.2.cn.c.353.1 8
65.2 even 12 975.2.bp.f.899.1 8
65.28 even 12 975.2.bp.e.899.2 8
65.54 odd 12 975.2.bo.d.626.2 8
156.119 odd 12 624.2.cn.c.353.2 8
195.2 odd 12 975.2.bp.f.899.2 8
195.119 even 12 975.2.bo.d.626.1 8
195.158 odd 12 975.2.bp.e.899.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.k.b.2.1 8 13.2 odd 12 inner
39.2.k.b.2.2 yes 8 39.2 even 12 inner
39.2.k.b.20.1 yes 8 3.2 odd 2 inner
39.2.k.b.20.2 yes 8 1.1 even 1 trivial
507.2.f.e.239.1 8 39.20 even 12
507.2.f.e.239.4 8 13.7 odd 12
507.2.f.e.437.1 8 13.4 even 6
507.2.f.e.437.4 8 39.17 odd 6
507.2.f.f.239.1 8 13.6 odd 12
507.2.f.f.239.4 8 39.32 even 12
507.2.f.f.437.1 8 39.35 odd 6
507.2.f.f.437.4 8 13.9 even 3
507.2.k.d.80.1 8 39.11 even 12
507.2.k.d.80.2 8 13.11 odd 12
507.2.k.d.488.1 8 13.12 even 2
507.2.k.d.488.2 8 39.38 odd 2
507.2.k.e.89.1 8 13.3 even 3
507.2.k.e.89.2 8 39.29 odd 6
507.2.k.e.188.1 8 39.5 even 4
507.2.k.e.188.2 8 13.5 odd 4
507.2.k.f.89.1 8 39.23 odd 6
507.2.k.f.89.2 8 13.10 even 6
507.2.k.f.188.1 8 13.8 odd 4
507.2.k.f.188.2 8 39.8 even 4
624.2.cn.c.353.1 8 52.15 even 12
624.2.cn.c.353.2 8 156.119 odd 12
624.2.cn.c.449.1 8 12.11 even 2
624.2.cn.c.449.2 8 4.3 odd 2
975.2.bo.d.176.1 8 5.4 even 2
975.2.bo.d.176.2 8 15.14 odd 2
975.2.bo.d.626.1 8 195.119 even 12
975.2.bo.d.626.2 8 65.54 odd 12
975.2.bp.e.449.1 8 5.2 odd 4
975.2.bp.e.449.2 8 15.2 even 4
975.2.bp.e.899.1 8 195.158 odd 12
975.2.bp.e.899.2 8 65.28 even 12
975.2.bp.f.449.1 8 15.8 even 4
975.2.bp.f.449.2 8 5.3 odd 4
975.2.bp.f.899.1 8 65.2 even 12
975.2.bp.f.899.2 8 195.2 odd 12