Properties

Label 39.2.k.b.11.2
Level $39$
Weight $2$
Character 39.11
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 11.2
Root \(0.500000 + 0.564882i\) of defining polynomial
Character \(\chi\) \(=\) 39.11
Dual form 39.2.k.b.32.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.45466 + 0.389774i) q^{2} +(-1.60523 - 0.650571i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-1.06488 + 1.06488i) q^{5} +(-2.08148 - 1.57203i) q^{6} +(0.366025 + 1.36603i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(2.15351 + 2.08863i) q^{9} +O(q^{10})\) \(q+(1.45466 + 0.389774i) q^{2} +(-1.60523 - 0.650571i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-1.06488 + 1.06488i) q^{5} +(-2.08148 - 1.57203i) q^{6} +(0.366025 + 1.36603i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(2.15351 + 2.08863i) q^{9} +(-1.96410 + 1.13397i) q^{10} +(1.06488 - 3.97420i) q^{11} +(-0.285334 - 0.366025i) q^{12} +(3.59808 + 0.232051i) q^{13} +2.12976i q^{14} +(2.40216 - 1.01660i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-2.51954 + 4.36397i) q^{17} +(2.31853 + 3.87762i) q^{18} +(-3.73205 + 1.00000i) q^{19} +(-0.389774 + 0.104440i) q^{20} +(0.301143 - 2.43091i) q^{21} +(3.09808 - 5.36603i) q^{22} +(1.76080 + 4.16067i) q^{24} +2.73205i q^{25} +(5.14352 + 1.73999i) q^{26} +(-2.09808 - 4.75374i) q^{27} +(-0.0980762 + 0.366025i) q^{28} +(6.20840 - 3.58442i) q^{29} +(3.89056 - 0.542499i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(-0.389774 - 1.45466i) q^{32} +(-4.29488 + 5.68671i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(-1.84443 - 1.06488i) q^{35} +(0.219901 + 0.773185i) q^{36} +(-5.23205 - 1.40192i) q^{37} -5.81863 q^{38} +(-5.62477 - 2.71330i) q^{39} +3.92820 q^{40} +(-5.42885 - 1.45466i) q^{41} +(1.38556 - 3.41876i) q^{42} +(1.90192 + 1.09808i) q^{43} +(0.779548 - 0.779548i) q^{44} +(-4.51739 + 0.0690922i) q^{45} +(4.25953 + 4.25953i) q^{47} +(1.06782 + 7.65796i) q^{48} +(4.33013 - 2.50000i) q^{49} +(-1.06488 + 3.97420i) q^{50} +(6.88351 - 5.36603i) q^{51} +(0.803848 + 0.535898i) q^{52} +0.779548i q^{53} +(-1.19909 - 7.73284i) q^{54} +(3.09808 + 5.36603i) q^{55} +(1.84443 - 3.19465i) q^{56} +(6.64136 + 0.822738i) q^{57} +(10.4282 - 2.79423i) q^{58} +(2.90931 - 0.779548i) q^{59} +(0.693622 + 0.0859264i) q^{60} +(3.50000 - 6.06218i) q^{61} +(-2.62398 - 4.54486i) q^{62} +(-2.06488 + 3.70625i) q^{63} +6.66025i q^{64} +(-4.07863 + 3.58442i) q^{65} +(-8.46410 + 6.59817i) q^{66} +(-1.53590 + 5.73205i) q^{67} +(-1.16932 + 0.675108i) q^{68} +(-2.26795 - 2.26795i) q^{70} +(0.779548 + 2.90931i) q^{71} +(-0.119671 - 7.82434i) q^{72} +(-0.901924 + 0.901924i) q^{73} +(-7.06440 - 4.07863i) q^{74} +(1.77739 - 4.38556i) q^{75} +(-1.00000 - 0.267949i) q^{76} +5.81863 q^{77} +(-7.12453 - 6.13931i) q^{78} +2.00000 q^{79} +(6.49373 + 1.73999i) q^{80} +(0.275241 + 8.99579i) q^{81} +(-7.33013 - 4.23205i) q^{82} +(-2.90931 + 2.90931i) q^{83} +(0.395560 - 0.523749i) q^{84} +(-1.96410 - 7.33013i) q^{85} +(2.33864 + 2.33864i) q^{86} +(-12.2978 + 1.71481i) q^{87} +(-9.29423 + 5.36603i) q^{88} +(2.41510 - 9.01327i) q^{89} +(-6.59817 - 1.66025i) q^{90} +(1.00000 + 5.00000i) q^{91} +(2.35237 + 5.55852i) q^{93} +(4.53590 + 7.85641i) q^{94} +(2.90931 - 5.03908i) q^{95} +(-0.320682 + 2.58863i) q^{96} +(1.63397 - 0.437822i) q^{97} +(7.27328 - 1.94887i) q^{98} +(10.5939 - 6.33434i) 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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.45466 + 0.389774i 1.02860 + 0.275612i 0.733380 0.679818i \(-0.237941\pi\)
0.295217 + 0.955430i \(0.404608\pi\)
\(3\) −1.60523 0.650571i −0.926779 0.375608i
\(4\) 0.232051 + 0.133975i 0.116025 + 0.0669873i
\(5\) −1.06488 + 1.06488i −0.476230 + 0.476230i −0.903924 0.427694i \(-0.859326\pi\)
0.427694 + 0.903924i \(0.359326\pi\)
\(6\) −2.08148 1.57203i −0.849760 0.641780i
\(7\) 0.366025 + 1.36603i 0.138345 + 0.516309i 0.999962 + 0.00875026i \(0.00278533\pi\)
−0.861617 + 0.507559i \(0.830548\pi\)
\(8\) −1.84443 1.84443i −0.652105 0.652105i
\(9\) 2.15351 + 2.08863i 0.717838 + 0.696210i
\(10\) −1.96410 + 1.13397i −0.621103 + 0.358594i
\(11\) 1.06488 3.97420i 0.321074 1.19826i −0.597126 0.802148i \(-0.703691\pi\)
0.918200 0.396117i \(-0.129643\pi\)
\(12\) −0.285334 0.366025i −0.0823689 0.105662i
\(13\) 3.59808 + 0.232051i 0.997927 + 0.0643593i
\(14\) 2.12976i 0.569204i
\(15\) 2.40216 1.01660i 0.620235 0.262484i
\(16\) −2.23205 3.86603i −0.558013 0.966506i
\(17\) −2.51954 + 4.36397i −0.611078 + 1.05842i 0.379981 + 0.924994i \(0.375930\pi\)
−0.991059 + 0.133424i \(0.957403\pi\)
\(18\) 2.31853 + 3.87762i 0.546482 + 0.913965i
\(19\) −3.73205 + 1.00000i −0.856191 + 0.229416i −0.660107 0.751171i \(-0.729489\pi\)
−0.196084 + 0.980587i \(0.562823\pi\)
\(20\) −0.389774 + 0.104440i −0.0871561 + 0.0233534i
\(21\) 0.301143 2.43091i 0.0657148 0.530468i
\(22\) 3.09808 5.36603i 0.660512 1.14404i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 1.76080 + 4.16067i 0.359421 + 0.849292i
\(25\) 2.73205i 0.546410i
\(26\) 5.14352 + 1.73999i 1.00873 + 0.341240i
\(27\) −2.09808 4.75374i −0.403775 0.914858i
\(28\) −0.0980762 + 0.366025i −0.0185347 + 0.0691723i
\(29\) 6.20840 3.58442i 1.15287 0.665610i 0.203286 0.979119i \(-0.434838\pi\)
0.949585 + 0.313509i \(0.101505\pi\)
\(30\) 3.89056 0.542499i 0.710316 0.0990463i
\(31\) −2.46410 2.46410i −0.442566 0.442566i 0.450308 0.892873i \(-0.351314\pi\)
−0.892873 + 0.450308i \(0.851314\pi\)
\(32\) −0.389774 1.45466i −0.0689030 0.257149i
\(33\) −4.29488 + 5.68671i −0.747642 + 0.989929i
\(34\) −5.36603 + 5.36603i −0.920266 + 0.920266i
\(35\) −1.84443 1.06488i −0.311766 0.179998i
\(36\) 0.219901 + 0.773185i 0.0366502 + 0.128864i
\(37\) −5.23205 1.40192i −0.860144 0.230475i −0.198323 0.980137i \(-0.563549\pi\)
−0.661821 + 0.749662i \(0.730216\pi\)
\(38\) −5.81863 −0.943906
\(39\) −5.62477 2.71330i −0.900684 0.434476i
\(40\) 3.92820 0.621103
\(41\) −5.42885 1.45466i −0.847844 0.227179i −0.191361 0.981520i \(-0.561290\pi\)
−0.656483 + 0.754341i \(0.727957\pi\)
\(42\) 1.38556 3.41876i 0.213797 0.527526i
\(43\) 1.90192 + 1.09808i 0.290041 + 0.167455i 0.637960 0.770069i \(-0.279778\pi\)
−0.347920 + 0.937524i \(0.613112\pi\)
\(44\) 0.779548 0.779548i 0.117521 0.117521i
\(45\) −4.51739 + 0.0690922i −0.673412 + 0.0102997i
\(46\) 0 0
\(47\) 4.25953 + 4.25953i 0.621316 + 0.621316i 0.945868 0.324552i \(-0.105213\pi\)
−0.324552 + 0.945868i \(0.605213\pi\)
\(48\) 1.06782 + 7.65796i 0.154127 + 1.10533i
\(49\) 4.33013 2.50000i 0.618590 0.357143i
\(50\) −1.06488 + 3.97420i −0.150597 + 0.562036i
\(51\) 6.88351 5.36603i 0.963884 0.751394i
\(52\) 0.803848 + 0.535898i 0.111474 + 0.0743157i
\(53\) 0.779548i 0.107079i 0.998566 + 0.0535396i \(0.0170503\pi\)
−0.998566 + 0.0535396i \(0.982950\pi\)
\(54\) −1.19909 7.73284i −0.163176 1.05231i
\(55\) 3.09808 + 5.36603i 0.417745 + 0.723555i
\(56\) 1.84443 3.19465i 0.246472 0.426903i
\(57\) 6.64136 + 0.822738i 0.879670 + 0.108974i
\(58\) 10.4282 2.79423i 1.36929 0.366900i
\(59\) 2.90931 0.779548i 0.378760 0.101489i −0.0644157 0.997923i \(-0.520518\pi\)
0.443176 + 0.896435i \(0.353852\pi\)
\(60\) 0.693622 + 0.0859264i 0.0895462 + 0.0110931i
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) −2.62398 4.54486i −0.333246 0.577198i
\(63\) −2.06488 + 3.70625i −0.260151 + 0.466943i
\(64\) 6.66025i 0.832532i
\(65\) −4.07863 + 3.58442i −0.505892 + 0.444593i
\(66\) −8.46410 + 6.59817i −1.04186 + 0.812179i
\(67\) −1.53590 + 5.73205i −0.187640 + 0.700281i 0.806410 + 0.591357i \(0.201407\pi\)
−0.994050 + 0.108925i \(0.965259\pi\)
\(68\) −1.16932 + 0.675108i −0.141801 + 0.0818689i
\(69\) 0 0
\(70\) −2.26795 2.26795i −0.271072 0.271072i
\(71\) 0.779548 + 2.90931i 0.0925153 + 0.345272i 0.996631 0.0820158i \(-0.0261358\pi\)
−0.904116 + 0.427288i \(0.859469\pi\)
\(72\) −0.119671 7.82434i −0.0141034 0.922107i
\(73\) −0.901924 + 0.901924i −0.105562 + 0.105562i −0.757915 0.652353i \(-0.773782\pi\)
0.652353 + 0.757915i \(0.273782\pi\)
\(74\) −7.06440 4.07863i −0.821220 0.474132i
\(75\) 1.77739 4.38556i 0.205236 0.506401i
\(76\) −1.00000 0.267949i −0.114708 0.0307359i
\(77\) 5.81863 0.663094
\(78\) −7.12453 6.13931i −0.806694 0.695140i
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 6.49373 + 1.73999i 0.726022 + 0.194537i
\(81\) 0.275241 + 8.99579i 0.0305823 + 0.999532i
\(82\) −7.33013 4.23205i −0.809477 0.467352i
\(83\) −2.90931 + 2.90931i −0.319339 + 0.319339i −0.848513 0.529174i \(-0.822502\pi\)
0.529174 + 0.848513i \(0.322502\pi\)
\(84\) 0.395560 0.523749i 0.0431592 0.0571457i
\(85\) −1.96410 7.33013i −0.213037 0.795064i
\(86\) 2.33864 + 2.33864i 0.252182 + 0.252182i
\(87\) −12.2978 + 1.71481i −1.31846 + 0.183846i
\(88\) −9.29423 + 5.36603i −0.990768 + 0.572020i
\(89\) 2.41510 9.01327i 0.256000 0.955405i −0.711531 0.702654i \(-0.751998\pi\)
0.967531 0.252751i \(-0.0813353\pi\)
\(90\) −6.59817 1.66025i −0.695509 0.175006i
\(91\) 1.00000 + 5.00000i 0.104828 + 0.524142i
\(92\) 0 0
\(93\) 2.35237 + 5.55852i 0.243929 + 0.576392i
\(94\) 4.53590 + 7.85641i 0.467842 + 0.810326i
\(95\) 2.90931 5.03908i 0.298489 0.516998i
\(96\) −0.320682 + 2.58863i −0.0327295 + 0.264201i
\(97\) 1.63397 0.437822i 0.165905 0.0444541i −0.174910 0.984584i \(-0.555964\pi\)
0.340815 + 0.940130i \(0.389297\pi\)
\(98\) 7.27328 1.94887i 0.734712 0.196866i
\(99\) 10.5939 6.33434i 1.06472 0.636625i
\(100\) −0.366025 + 0.633975i −0.0366025 + 0.0633975i
\(101\) 3.01375 + 5.21997i 0.299880 + 0.519407i 0.976108 0.217285i \(-0.0697202\pi\)
−0.676229 + 0.736692i \(0.736387\pi\)
\(102\) 12.1047 5.12271i 1.19854 0.507224i
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) −6.20840 7.06440i −0.608784 0.692722i
\(105\) 2.26795 + 2.90931i 0.221329 + 0.283920i
\(106\) −0.303848 + 1.13397i −0.0295123 + 0.110141i
\(107\) −16.4675 + 9.50749i −1.59197 + 0.919123i −0.598999 + 0.800749i \(0.704435\pi\)
−0.992969 + 0.118374i \(0.962232\pi\)
\(108\) 0.150021 1.38420i 0.0144357 0.133195i
\(109\) −13.1962 13.1962i −1.26396 1.26396i −0.949156 0.314806i \(-0.898060\pi\)
−0.314806 0.949156i \(-0.601940\pi\)
\(110\) 2.41510 + 9.01327i 0.230271 + 0.859382i
\(111\) 7.48658 + 5.65423i 0.710595 + 0.536676i
\(112\) 4.46410 4.46410i 0.421818 0.421818i
\(113\) 8.90883 + 5.14352i 0.838073 + 0.483861i 0.856609 0.515967i \(-0.172567\pi\)
−0.0185360 + 0.999828i \(0.505901\pi\)
\(114\) 9.34022 + 3.78543i 0.874792 + 0.354538i
\(115\) 0 0
\(116\) 1.92089 0.178350
\(117\) 7.26384 + 8.01478i 0.671542 + 0.740967i
\(118\) 4.53590 0.417563
\(119\) −6.88351 1.84443i −0.631010 0.169079i
\(120\) −6.30566 2.55558i −0.575626 0.233291i
\(121\) −5.13397 2.96410i −0.466725 0.269464i
\(122\) 7.45418 7.45418i 0.674869 0.674869i
\(123\) 7.76819 + 5.86691i 0.700434 + 0.529002i
\(124\) −0.241670 0.901924i −0.0217026 0.0809951i
\(125\) −8.23373 8.23373i −0.736447 0.736447i
\(126\) −4.44829 + 4.58648i −0.396285 + 0.408596i
\(127\) 7.90192 4.56218i 0.701182 0.404828i −0.106605 0.994301i \(-0.533998\pi\)
0.807788 + 0.589474i \(0.200665\pi\)
\(128\) −3.37554 + 12.5977i −0.298359 + 1.11349i
\(129\) −2.33864 3.00000i −0.205906 0.264135i
\(130\) −7.33013 + 3.62436i −0.642895 + 0.317877i
\(131\) 7.94839i 0.694454i −0.937781 0.347227i \(-0.887123\pi\)
0.937781 0.347227i \(-0.112877\pi\)
\(132\) −1.75850 + 0.744201i −0.153058 + 0.0647743i
\(133\) −2.73205 4.73205i −0.236899 0.410321i
\(134\) −4.46841 + 7.73951i −0.386012 + 0.668592i
\(135\) 7.29638 + 2.82797i 0.627973 + 0.243393i
\(136\) 12.6962 3.40192i 1.08869 0.291713i
\(137\) −6.49373 + 1.73999i −0.554797 + 0.148657i −0.525315 0.850908i \(-0.676052\pi\)
−0.0294822 + 0.999565i \(0.509386\pi\)
\(138\) 0 0
\(139\) −9.19615 + 15.9282i −0.780007 + 1.35101i 0.151929 + 0.988391i \(0.451451\pi\)
−0.931937 + 0.362621i \(0.881882\pi\)
\(140\) −0.285334 0.494214i −0.0241152 0.0417687i
\(141\) −4.06639 9.60864i −0.342452 0.809194i
\(142\) 4.53590i 0.380644i
\(143\) 4.75374 14.0524i 0.397528 1.17512i
\(144\) 3.26795 12.9875i 0.272329 1.08229i
\(145\) −2.79423 + 10.4282i −0.232048 + 0.866015i
\(146\) −1.66354 + 0.960443i −0.137675 + 0.0794868i
\(147\) −8.57727 + 1.19601i −0.707441 + 0.0986455i
\(148\) −1.02628 1.02628i −0.0843597 0.0843597i
\(149\) −2.23420 8.33816i −0.183033 0.683089i −0.995043 0.0994454i \(-0.968293\pi\)
0.812010 0.583644i \(-0.198374\pi\)
\(150\) 4.29488 5.68671i 0.350675 0.464318i
\(151\) 0.535898 0.535898i 0.0436108 0.0436108i −0.684965 0.728576i \(-0.740183\pi\)
0.728576 + 0.684965i \(0.240183\pi\)
\(152\) 8.72794 + 5.03908i 0.707929 + 0.408723i
\(153\) −14.5406 + 4.13548i −1.17554 + 0.334334i
\(154\) 8.46410 + 2.26795i 0.682057 + 0.182757i
\(155\) 5.24796 0.421526
\(156\) −0.941718 1.38320i −0.0753978 0.110745i
\(157\) −4.80385 −0.383389 −0.191694 0.981455i \(-0.561398\pi\)
−0.191694 + 0.981455i \(0.561398\pi\)
\(158\) 2.90931 + 0.779548i 0.231453 + 0.0620175i
\(159\) 0.507152 1.25135i 0.0402197 0.0992387i
\(160\) 1.96410 + 1.13397i 0.155276 + 0.0896486i
\(161\) 0 0
\(162\) −3.10594 + 13.1931i −0.244026 + 1.03655i
\(163\) −1.07180 4.00000i −0.0839496 0.313304i 0.911164 0.412045i \(-0.135185\pi\)
−0.995113 + 0.0987406i \(0.968519\pi\)
\(164\) −1.06488 1.06488i −0.0831533 0.0831533i
\(165\) −1.48214 10.6292i −0.115384 0.827483i
\(166\) −5.36603 + 3.09808i −0.416484 + 0.240457i
\(167\) −3.47998 + 12.9875i −0.269289 + 1.00500i 0.690283 + 0.723539i \(0.257486\pi\)
−0.959573 + 0.281461i \(0.909181\pi\)
\(168\) −5.03908 + 3.92820i −0.388773 + 0.303067i
\(169\) 12.8923 + 1.66987i 0.991716 + 0.128452i
\(170\) 11.4284i 0.876516i
\(171\) −10.1257 5.64136i −0.774328 0.431406i
\(172\) 0.294229 + 0.509619i 0.0224347 + 0.0388581i
\(173\) 8.72794 15.1172i 0.663573 1.14934i −0.316097 0.948727i \(-0.602373\pi\)
0.979670 0.200615i \(-0.0642941\pi\)
\(174\) −18.5575 2.29892i −1.40684 0.174281i
\(175\) −3.73205 + 1.00000i −0.282117 + 0.0755929i
\(176\) −17.7412 + 4.75374i −1.33729 + 0.358327i
\(177\) −5.17726 0.641364i −0.389147 0.0482078i
\(178\) 7.02628 12.1699i 0.526642 0.912171i
\(179\) 13.2728 + 22.9892i 0.992056 + 1.71829i 0.604972 + 0.796247i \(0.293184\pi\)
0.387084 + 0.922045i \(0.373482\pi\)
\(180\) −1.05752 0.589182i −0.0788228 0.0439150i
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) −0.494214 + 7.66306i −0.0366336 + 0.568024i
\(183\) −9.56218 + 7.45418i −0.706857 + 0.551029i
\(184\) 0 0
\(185\) 7.06440 4.07863i 0.519385 0.299867i
\(186\) 1.25532 + 9.00263i 0.0920449 + 0.660105i
\(187\) 14.6603 + 14.6603i 1.07206 + 1.07206i
\(188\) 0.417759 + 1.55910i 0.0304682 + 0.113709i
\(189\) 5.72579 4.60602i 0.416490 0.335038i
\(190\) 6.19615 6.19615i 0.449516 0.449516i
\(191\) −4.18307 2.41510i −0.302677 0.174750i 0.340968 0.940075i \(-0.389245\pi\)
−0.643645 + 0.765324i \(0.722579\pi\)
\(192\) 4.33297 10.6912i 0.312705 0.771573i
\(193\) 0.133975 + 0.0358984i 0.00964370 + 0.00258402i 0.263638 0.964622i \(-0.415078\pi\)
−0.253994 + 0.967206i \(0.581744\pi\)
\(194\) 2.54752 0.182902
\(195\) 8.87906 3.10037i 0.635843 0.222022i
\(196\) 1.33975 0.0956961
\(197\) 3.97420 + 1.06488i 0.283150 + 0.0758697i 0.397599 0.917559i \(-0.369844\pi\)
−0.114449 + 0.993429i \(0.536510\pi\)
\(198\) 17.8794 5.08507i 1.27063 0.361380i
\(199\) 11.1962 + 6.46410i 0.793674 + 0.458228i 0.841254 0.540639i \(-0.181818\pi\)
−0.0475802 + 0.998867i \(0.515151\pi\)
\(200\) 5.03908 5.03908i 0.356317 0.356317i
\(201\) 6.19458 8.20204i 0.436932 0.578527i
\(202\) 2.34936 + 8.76795i 0.165301 + 0.616911i
\(203\) 7.16884 + 7.16884i 0.503154 + 0.503154i
\(204\) 2.31623 0.322975i 0.162169 0.0226128i
\(205\) 7.33013 4.23205i 0.511958 0.295579i
\(206\) 2.70043 10.0782i 0.188148 0.702178i
\(207\) 0 0
\(208\) −7.13397 14.4282i −0.494652 1.00042i
\(209\) 15.8968i 1.09960i
\(210\) 2.16511 + 5.11604i 0.149407 + 0.353040i
\(211\) 0.901924 + 1.56218i 0.0620910 + 0.107545i 0.895400 0.445263i \(-0.146890\pi\)
−0.833309 + 0.552808i \(0.813556\pi\)
\(212\) −0.104440 + 0.180895i −0.00717294 + 0.0124239i
\(213\) 0.641364 5.17726i 0.0439455 0.354740i
\(214\) −27.6603 + 7.41154i −1.89082 + 0.506643i
\(215\) −3.19465 + 0.856003i −0.217873 + 0.0583789i
\(216\) −4.89819 + 12.6377i −0.333280 + 0.859887i
\(217\) 2.46410 4.26795i 0.167274 0.289727i
\(218\) −14.0524 24.3394i −0.951745 1.64847i
\(219\) 2.03456 0.861027i 0.137483 0.0581828i
\(220\) 1.66025i 0.111934i
\(221\) −10.0782 + 15.1172i −0.677930 + 1.01690i
\(222\) 8.68653 + 11.1430i 0.583002 + 0.747872i
\(223\) 6.70577 25.0263i 0.449052 1.67588i −0.255960 0.966687i \(-0.582391\pi\)
0.705011 0.709196i \(-0.250942\pi\)
\(224\) 1.84443 1.06488i 0.123236 0.0711505i
\(225\) −5.70625 + 5.88351i −0.380416 + 0.392234i
\(226\) 10.9545 + 10.9545i 0.728681 + 0.728681i
\(227\) −5.24796 19.5856i −0.348319 1.29994i −0.888686 0.458515i \(-0.848381\pi\)
0.540367 0.841429i \(-0.318285\pi\)
\(228\) 1.43091 + 1.08069i 0.0947642 + 0.0715705i
\(229\) −14.1244 + 14.1244i −0.933364 + 0.933364i −0.997914 0.0645507i \(-0.979439\pi\)
0.0645507 + 0.997914i \(0.479439\pi\)
\(230\) 0 0
\(231\) −9.34022 3.78543i −0.614541 0.249063i
\(232\) −18.0622 4.83975i −1.18584 0.317745i
\(233\) −17.4559 −1.14357 −0.571786 0.820403i \(-0.693749\pi\)
−0.571786 + 0.820403i \(0.693749\pi\)
\(234\) 7.44244 + 14.4900i 0.486527 + 0.947241i
\(235\) −9.07180 −0.591779
\(236\) 0.779548 + 0.208879i 0.0507443 + 0.0135969i
\(237\) −3.21046 1.30114i −0.208542 0.0845183i
\(238\) −9.29423 5.36603i −0.602455 0.347828i
\(239\) −6.59817 + 6.59817i −0.426800 + 0.426800i −0.887537 0.460737i \(-0.847585\pi\)
0.460737 + 0.887537i \(0.347585\pi\)
\(240\) −9.29194 7.01772i −0.599792 0.452992i
\(241\) 3.76795 + 14.0622i 0.242715 + 0.905825i 0.974518 + 0.224309i \(0.0720123\pi\)
−0.731803 + 0.681516i \(0.761321\pi\)
\(242\) −6.31284 6.31284i −0.405805 0.405805i
\(243\) 5.41058 14.6194i 0.347089 0.937832i
\(244\) 1.62436 0.937822i 0.103989 0.0600379i
\(245\) −1.94887 + 7.27328i −0.124509 + 0.464673i
\(246\) 9.01327 + 11.5622i 0.574665 + 0.737178i
\(247\) −13.6603 + 2.73205i −0.869181 + 0.173836i
\(248\) 9.08973i 0.577198i
\(249\) 6.56283 2.77739i 0.415902 0.176010i
\(250\) −8.76795 15.1865i −0.554534 0.960481i
\(251\) −0.494214 + 0.856003i −0.0311945 + 0.0540304i −0.881201 0.472741i \(-0.843264\pi\)
0.850007 + 0.526772i \(0.176598\pi\)
\(252\) −0.975700 + 0.583396i −0.0614634 + 0.0367505i
\(253\) 0 0
\(254\) 13.2728 3.55644i 0.832810 0.223151i
\(255\) −1.61594 + 13.0443i −0.101194 + 0.816867i
\(256\) −3.16025 + 5.47372i −0.197516 + 0.342108i
\(257\) −10.7533 18.6252i −0.670770 1.16181i −0.977686 0.210071i \(-0.932630\pi\)
0.306916 0.951737i \(-0.400703\pi\)
\(258\) −2.23260 5.27551i −0.138996 0.328439i
\(259\) 7.66025i 0.475985i
\(260\) −1.42667 + 0.285334i −0.0884784 + 0.0176957i
\(261\) 20.8564 + 5.24796i 1.29098 + 0.324840i
\(262\) 3.09808 11.5622i 0.191400 0.714314i
\(263\) 19.3003 11.1430i 1.19011 0.687109i 0.231777 0.972769i \(-0.425546\pi\)
0.958331 + 0.285660i \(0.0922127\pi\)
\(264\) 18.4103 2.56713i 1.13308 0.157996i
\(265\) −0.830127 0.830127i −0.0509943 0.0509943i
\(266\) −2.12976 7.94839i −0.130584 0.487347i
\(267\) −9.74056 + 12.8972i −0.596113 + 0.789294i
\(268\) −1.12436 + 1.12436i −0.0686810 + 0.0686810i
\(269\) 12.4168 + 7.16884i 0.757066 + 0.437092i 0.828241 0.560372i \(-0.189342\pi\)
−0.0711756 + 0.997464i \(0.522675\pi\)
\(270\) 9.51146 + 6.95767i 0.578849 + 0.423430i
\(271\) 7.46410 + 2.00000i 0.453412 + 0.121491i 0.478295 0.878199i \(-0.341255\pi\)
−0.0248835 + 0.999690i \(0.507921\pi\)
\(272\) 22.4950 1.36396
\(273\) 1.64763 8.67671i 0.0997191 0.525138i
\(274\) −10.1244 −0.611635
\(275\) 10.8577 + 2.90931i 0.654744 + 0.175438i
\(276\) 0 0
\(277\) 23.8923 + 13.7942i 1.43555 + 0.828815i 0.997536 0.0701536i \(-0.0223490\pi\)
0.438013 + 0.898969i \(0.355682\pi\)
\(278\) −19.5856 + 19.5856i −1.17467 + 1.17467i
\(279\) −0.159877 10.4531i −0.00957158 0.625809i
\(280\) 1.43782 + 5.36603i 0.0859263 + 0.320681i
\(281\) 12.1315 + 12.1315i 0.723703 + 0.723703i 0.969357 0.245655i \(-0.0790030\pi\)
−0.245655 + 0.969357i \(0.579003\pi\)
\(282\) −2.17000 15.5622i −0.129221 0.926718i
\(283\) −5.70577 + 3.29423i −0.339173 + 0.195822i −0.659906 0.751348i \(-0.729404\pi\)
0.320733 + 0.947170i \(0.396071\pi\)
\(284\) −0.208879 + 0.779548i −0.0123947 + 0.0462577i
\(285\) −7.94839 + 6.19615i −0.470822 + 0.367028i
\(286\) 12.3923 18.5885i 0.732772 1.09916i
\(287\) 7.94839i 0.469179i
\(288\) 2.19886 3.94672i 0.129569 0.232562i
\(289\) −4.19615 7.26795i −0.246832 0.427526i
\(290\) −8.12929 + 14.0803i −0.477368 + 0.826826i
\(291\) −2.90774 0.360213i −0.170455 0.0211161i
\(292\) −0.330127 + 0.0884573i −0.0193192 + 0.00517657i
\(293\) 1.73999 0.466229i 0.101651 0.0272374i −0.207635 0.978206i \(-0.566577\pi\)
0.309286 + 0.950969i \(0.399910\pi\)
\(294\) −12.9432 1.60341i −0.754860 0.0935127i
\(295\) −2.26795 + 3.92820i −0.132045 + 0.228709i
\(296\) 7.06440 + 12.2359i 0.410610 + 0.711198i
\(297\) −21.1265 + 3.27599i −1.22588 + 0.190092i
\(298\) 13.0000i 0.753070i
\(299\) 0 0
\(300\) 1.00000 0.779548i 0.0577350 0.0450072i
\(301\) −0.803848 + 3.00000i −0.0463330 + 0.172917i
\(302\) 0.988427 0.570669i 0.0568776 0.0328383i
\(303\) −1.44179 10.3399i −0.0828289 0.594012i
\(304\) 12.1962 + 12.1962i 0.699497 + 0.699497i
\(305\) 2.72842 + 10.1826i 0.156229 + 0.583054i
\(306\) −22.7635 + 0.348161i −1.30130 + 0.0199030i
\(307\) 8.39230 8.39230i 0.478974 0.478974i −0.425829 0.904803i \(-0.640018\pi\)
0.904803 + 0.425829i \(0.140018\pi\)
\(308\) 1.35022 + 0.779548i 0.0769357 + 0.0444189i
\(309\) −4.50729 + 11.1213i −0.256411 + 0.632671i
\(310\) 7.63397 + 2.04552i 0.433581 + 0.116178i
\(311\) −10.0782 −0.571480 −0.285740 0.958307i \(-0.592239\pi\)
−0.285740 + 0.958307i \(0.592239\pi\)
\(312\) 5.37000 + 15.3790i 0.304016 + 0.870664i
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) −6.98795 1.87241i −0.394353 0.105666i
\(315\) −1.74786 6.14557i −0.0984807 0.346264i
\(316\) 0.464102 + 0.267949i 0.0261078 + 0.0150733i
\(317\) 11.3519 11.3519i 0.637587 0.637587i −0.312373 0.949960i \(-0.601124\pi\)
0.949960 + 0.312373i \(0.101124\pi\)
\(318\) 1.22548 1.62261i 0.0687213 0.0909916i
\(319\) −7.63397 28.4904i −0.427421 1.59516i
\(320\) −7.09239 7.09239i −0.396477 0.396477i
\(321\) 32.6193 4.54843i 1.82063 0.253869i
\(322\) 0 0
\(323\) 5.03908 18.8061i 0.280382 1.04640i
\(324\) −1.14134 + 2.12436i −0.0634076 + 0.118020i
\(325\) −0.633975 + 9.83013i −0.0351666 + 0.545277i
\(326\) 6.23638i 0.345401i
\(327\) 12.5978 + 29.7679i 0.696659 + 1.64617i
\(328\) 7.33013 + 12.6962i 0.404739 + 0.701028i
\(329\) −4.25953 + 7.37772i −0.234835 + 0.406747i
\(330\) 1.98699 16.0396i 0.109380 0.882948i
\(331\) −33.0526 + 8.85641i −1.81673 + 0.486792i −0.996376 0.0850595i \(-0.972892\pi\)
−0.820357 + 0.571852i \(0.806225\pi\)
\(332\) −1.06488 + 0.285334i −0.0584430 + 0.0156598i
\(333\) −8.33919 13.9469i −0.456985 0.764285i
\(334\) −10.1244 + 17.5359i −0.553980 + 0.959522i
\(335\) −4.46841 7.73951i −0.244135 0.422855i
\(336\) −10.0701 + 4.26168i −0.549370 + 0.232494i
\(337\) 18.4641i 1.00580i 0.864344 + 0.502902i \(0.167734\pi\)
−0.864344 + 0.502902i \(0.832266\pi\)
\(338\) 18.1030 + 7.45418i 0.984673 + 0.405454i
\(339\) −10.9545 14.0524i −0.594966 0.763219i
\(340\) 0.526279 1.96410i 0.0285415 0.106518i
\(341\) −12.4168 + 7.16884i −0.672407 + 0.388215i
\(342\) −12.5305 12.1530i −0.677571 0.657157i
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) −1.48264 5.53329i −0.0799386 0.298335i
\(345\) 0 0
\(346\) 18.5885 18.5885i 0.999322 0.999322i
\(347\) −17.8177 10.2870i −0.956502 0.552237i −0.0614076 0.998113i \(-0.519559\pi\)
−0.895095 + 0.445876i \(0.852892\pi\)
\(348\) −3.08346 1.24967i −0.165291 0.0669895i
\(349\) 27.4904 + 7.36603i 1.47153 + 0.394294i 0.903454 0.428684i \(-0.141023\pi\)
0.568072 + 0.822979i \(0.307689\pi\)
\(350\) −5.81863 −0.311019
\(351\) −6.44593 17.5912i −0.344058 0.938948i
\(352\) −6.19615 −0.330256
\(353\) −13.6626 3.66088i −0.727186 0.194849i −0.123810 0.992306i \(-0.539511\pi\)
−0.603376 + 0.797457i \(0.706178\pi\)
\(354\) −7.28115 2.95093i −0.386989 0.156840i
\(355\) −3.92820 2.26795i −0.208487 0.120370i
\(356\) 1.76798 1.76798i 0.0937025 0.0937025i
\(357\) 9.84967 + 7.43895i 0.521300 + 0.393711i
\(358\) 10.3468 + 38.6147i 0.546845 + 2.04085i
\(359\) −18.2354 18.2354i −0.962429 0.962429i 0.0368904 0.999319i \(-0.488255\pi\)
−0.999319 + 0.0368904i \(0.988255\pi\)
\(360\) 8.45944 + 8.20457i 0.445852 + 0.432419i
\(361\) −3.52628 + 2.03590i −0.185594 + 0.107153i
\(362\) 1.16932 4.36397i 0.0614582 0.229365i
\(363\) 6.31284 + 8.09808i 0.331338 + 0.425039i
\(364\) −0.437822 + 1.29423i −0.0229481 + 0.0678360i
\(365\) 1.92089i 0.100544i
\(366\) −16.8151 + 7.11618i −0.878941 + 0.371969i
\(367\) −15.1962 26.3205i −0.793233 1.37392i −0.923955 0.382500i \(-0.875063\pi\)
0.130723 0.991419i \(-0.458270\pi\)
\(368\) 0 0
\(369\) −8.65286 14.4715i −0.450450 0.753356i
\(370\) 11.8660 3.17949i 0.616885 0.165294i
\(371\) −1.06488 + 0.285334i −0.0552859 + 0.0148138i
\(372\) −0.198831 + 1.60502i −0.0103089 + 0.0832162i
\(373\) −5.79423 + 10.0359i −0.300014 + 0.519639i −0.976139 0.217148i \(-0.930325\pi\)
0.676125 + 0.736787i \(0.263658\pi\)
\(374\) 15.6114 + 27.0398i 0.807249 + 1.39820i
\(375\) 7.86038 + 18.5736i 0.405908 + 0.959138i
\(376\) 15.7128i 0.810326i
\(377\) 23.1701 11.4564i 1.19332 0.590032i
\(378\) 10.1244 4.46841i 0.520741 0.229830i
\(379\) 3.83013 14.2942i 0.196740 0.734245i −0.795069 0.606519i \(-0.792565\pi\)
0.991809 0.127726i \(-0.0407679\pi\)
\(380\) 1.35022 0.779548i 0.0692647 0.0399900i
\(381\) −15.6524 + 2.18257i −0.801897 + 0.111816i
\(382\) −5.14359 5.14359i −0.263169 0.263169i
\(383\) 8.51906 + 31.7936i 0.435304 + 1.62458i 0.740339 + 0.672234i \(0.234665\pi\)
−0.305035 + 0.952341i \(0.598668\pi\)
\(384\) 13.6142 18.0261i 0.694748 0.919893i
\(385\) −6.19615 + 6.19615i −0.315785 + 0.315785i
\(386\) 0.180895 + 0.104440i 0.00920730 + 0.00531584i
\(387\) 1.80234 + 6.33714i 0.0916182 + 0.322135i
\(388\) 0.437822 + 0.117314i 0.0222271 + 0.00595572i
\(389\) −22.4950 −1.14054 −0.570270 0.821457i \(-0.693161\pi\)
−0.570270 + 0.821457i \(0.693161\pi\)
\(390\) 14.1244 1.04915i 0.715218 0.0531255i
\(391\) 0 0
\(392\) −12.5977 3.37554i −0.636280 0.170491i
\(393\) −5.17100 + 12.7590i −0.260842 + 0.643605i
\(394\) 5.36603 + 3.09808i 0.270336 + 0.156079i
\(395\) −2.12976 + 2.12976i −0.107160 + 0.107160i
\(396\) 3.30696 0.0505790i 0.166181 0.00254169i
\(397\) −3.56218 13.2942i −0.178781 0.667218i −0.995877 0.0907168i \(-0.971084\pi\)
0.817096 0.576501i \(-0.195582\pi\)
\(398\) 13.7670 + 13.7670i 0.690078 + 0.690078i
\(399\) 1.30703 + 9.37341i 0.0654332 + 0.469258i
\(400\) 10.5622 6.09808i 0.528109 0.304904i
\(401\) 3.22263 12.0270i 0.160931 0.600601i −0.837594 0.546294i \(-0.816038\pi\)
0.998524 0.0543073i \(-0.0172951\pi\)
\(402\) 12.2079 9.51666i 0.608876 0.474648i
\(403\) −8.29423 9.43782i −0.413165 0.470131i
\(404\) 1.61507i 0.0803525i
\(405\) −9.87256 9.28636i −0.490571 0.461443i
\(406\) 7.63397 + 13.2224i 0.378868 + 0.656218i
\(407\) −11.1430 + 19.3003i −0.552340 + 0.956681i
\(408\) −22.5934 2.79889i −1.11854 0.138566i
\(409\) 28.9904 7.76795i 1.43348 0.384100i 0.543236 0.839580i \(-0.317199\pi\)
0.890246 + 0.455480i \(0.150532\pi\)
\(410\) 12.3124 3.29909i 0.608064 0.162930i
\(411\) 11.5559 + 1.43156i 0.570011 + 0.0706135i
\(412\) 0.928203 1.60770i 0.0457293 0.0792055i
\(413\) 2.12976 + 3.68886i 0.104799 + 0.181517i
\(414\) 0 0
\(415\) 6.19615i 0.304157i
\(416\) −1.06488 5.32441i −0.0522102 0.261051i
\(417\) 25.1244 19.5856i 1.23034 0.959113i
\(418\) −6.19615 + 23.1244i −0.303064 + 1.13105i
\(419\) 8.23373 4.75374i 0.402244 0.232236i −0.285208 0.958466i \(-0.592063\pi\)
0.687452 + 0.726230i \(0.258729\pi\)
\(420\) 0.136505 + 0.978956i 0.00666078 + 0.0477682i
\(421\) −7.83013 7.83013i −0.381617 0.381617i 0.490067 0.871685i \(-0.336972\pi\)
−0.871685 + 0.490067i \(0.836972\pi\)
\(422\) 0.703093 + 2.62398i 0.0342260 + 0.127733i
\(423\) 0.276369 + 18.0695i 0.0134375 + 0.878571i
\(424\) 1.43782 1.43782i 0.0698268 0.0698268i
\(425\) −11.9226 6.88351i −0.578330 0.333899i
\(426\) 2.95093 7.28115i 0.142973 0.352773i
\(427\) 9.56218 + 2.56218i 0.462746 + 0.123992i
\(428\) −5.09505 −0.246278
\(429\) −16.7729 + 19.4646i −0.809803 + 0.939759i
\(430\) −4.98076 −0.240194
\(431\) 36.5473 + 9.79282i 1.76042 + 0.471704i 0.986800 0.161944i \(-0.0517764\pi\)
0.773622 + 0.633648i \(0.218443\pi\)
\(432\) −13.6951 + 18.7218i −0.658905 + 0.900754i
\(433\) −26.8923 15.5263i −1.29236 0.746145i −0.313289 0.949658i \(-0.601431\pi\)
−0.979072 + 0.203512i \(0.934764\pi\)
\(434\) 5.24796 5.24796i 0.251910 0.251910i
\(435\) 11.2697 14.9218i 0.540339 0.715445i
\(436\) −1.29423 4.83013i −0.0619823 0.231321i
\(437\) 0 0
\(438\) 3.29519 0.459481i 0.157450 0.0219548i
\(439\) 1.09808 0.633975i 0.0524083 0.0302580i −0.473567 0.880758i \(-0.657034\pi\)
0.525975 + 0.850500i \(0.323700\pi\)
\(440\) 4.18307 15.6114i 0.199420 0.744247i
\(441\) 14.5466 + 3.66025i 0.692694 + 0.174298i
\(442\) −20.5526 + 18.0622i −0.977586 + 0.859130i
\(443\) 11.2195i 0.533054i 0.963827 + 0.266527i \(0.0858762\pi\)
−0.963827 + 0.266527i \(0.914124\pi\)
\(444\) 0.979744 + 2.31508i 0.0464966 + 0.109869i
\(445\) 7.02628 + 12.1699i 0.333078 + 0.576907i
\(446\) 19.5092 33.7909i 0.923787 1.60005i
\(447\) −1.83816 + 14.8382i −0.0869422 + 0.701821i
\(448\) −9.09808 + 2.43782i −0.429844 + 0.115176i
\(449\) 19.8710 5.32441i 0.937769 0.251275i 0.242605 0.970125i \(-0.421998\pi\)
0.695165 + 0.718851i \(0.255331\pi\)
\(450\) −10.5939 + 6.33434i −0.499400 + 0.298603i
\(451\) −11.5622 + 20.0263i −0.544442 + 0.943001i
\(452\) 1.37820 + 2.38711i 0.0648251 + 0.112280i
\(453\) −1.20888 + 0.511599i −0.0567981 + 0.0240370i
\(454\) 30.5359i 1.43312i
\(455\) −6.38929 4.25953i −0.299535 0.199690i
\(456\) −10.7321 13.7670i −0.502574 0.644700i
\(457\) −1.00962 + 3.76795i −0.0472280 + 0.176257i −0.985511 0.169611i \(-0.945749\pi\)
0.938283 + 0.345868i \(0.112416\pi\)
\(458\) −26.0514 + 15.0408i −1.21730 + 0.702809i
\(459\) 26.0314 + 2.82130i 1.21504 + 0.131687i
\(460\) 0 0
\(461\) 5.50531 + 20.5461i 0.256408 + 0.956927i 0.967302 + 0.253628i \(0.0816238\pi\)
−0.710894 + 0.703299i \(0.751710\pi\)
\(462\) −12.1113 9.14708i −0.563471 0.425561i
\(463\) 23.0526 23.0526i 1.07134 1.07134i 0.0740918 0.997251i \(-0.476394\pi\)
0.997251 0.0740918i \(-0.0236058\pi\)
\(464\) −27.7149 16.0012i −1.28663 0.742838i
\(465\) −8.42417 3.41417i −0.390661 0.158328i
\(466\) −25.3923 6.80385i −1.17628 0.315182i
\(467\) 19.1679 0.886984 0.443492 0.896278i \(-0.353739\pi\)
0.443492 + 0.896278i \(0.353739\pi\)
\(468\) 0.611803 + 2.83301i 0.0282806 + 0.130956i
\(469\) −8.39230 −0.387521
\(470\) −13.1963 3.53595i −0.608702 0.163101i
\(471\) 7.71127 + 3.12525i 0.355317 + 0.144004i
\(472\) −6.80385 3.92820i −0.313172 0.180810i
\(473\) 6.38929 6.38929i 0.293780 0.293780i
\(474\) −4.16296 3.14407i −0.191211 0.144412i
\(475\) −2.73205 10.1962i −0.125355 0.467832i
\(476\) −1.35022 1.35022i −0.0618871 0.0618871i
\(477\) −1.62819 + 1.67877i −0.0745496 + 0.0768655i
\(478\) −12.1699 + 7.02628i −0.556637 + 0.321375i
\(479\) −5.32441 + 19.8710i −0.243279 + 0.907928i 0.730962 + 0.682418i \(0.239072\pi\)
−0.974241 + 0.225510i \(0.927595\pi\)
\(480\) −2.41510 3.09808i −0.110234 0.141407i
\(481\) −18.5000 6.25833i −0.843527 0.285355i
\(482\) 21.9243i 0.998624i
\(483\) 0 0
\(484\) −0.794229 1.37564i −0.0361013 0.0625293i
\(485\) −1.27376 + 2.20622i −0.0578385 + 0.100179i
\(486\) 13.5688 19.1572i 0.615492 0.868990i
\(487\) 5.56218 1.49038i 0.252046 0.0675356i −0.130584 0.991437i \(-0.541685\pi\)
0.382630 + 0.923902i \(0.375018\pi\)
\(488\) −17.6368 + 4.72576i −0.798379 + 0.213925i
\(489\) −0.881808 + 7.11819i −0.0398767 + 0.321896i
\(490\) −5.66987 + 9.82051i −0.256139 + 0.443645i
\(491\) −14.2612 24.7012i −0.643600 1.11475i −0.984623 0.174693i \(-0.944107\pi\)
0.341023 0.940055i \(-0.389227\pi\)
\(492\) 1.01660 + 2.40216i 0.0458317 + 0.108298i
\(493\) 36.1244i 1.62696i
\(494\) −20.9359 1.35022i −0.941949 0.0607491i
\(495\) −4.53590 + 18.0265i −0.203873 + 0.810233i
\(496\) −4.02628 + 15.0263i −0.180785 + 0.674700i
\(497\) −3.68886 + 2.12976i −0.165468 + 0.0955330i
\(498\) 10.6292 1.48214i 0.476306 0.0664161i
\(499\) −2.46410 2.46410i −0.110308 0.110308i 0.649798 0.760107i \(-0.274853\pi\)
−0.760107 + 0.649798i \(0.774853\pi\)
\(500\) −0.807533 3.01375i −0.0361140 0.134779i
\(501\) 14.0354 18.5839i 0.627057 0.830266i
\(502\) −1.05256 + 1.05256i −0.0469780 + 0.0469780i
\(503\) 2.83286 + 1.63555i 0.126311 + 0.0729256i 0.561824 0.827257i \(-0.310100\pi\)
−0.435513 + 0.900182i \(0.643433\pi\)
\(504\) 10.6444 3.02738i 0.474141 0.134850i
\(505\) −8.76795 2.34936i −0.390169 0.104545i
\(506\) 0 0
\(507\) −19.6087 11.0679i −0.870854 0.491542i
\(508\) 2.44486 0.108473
\(509\) −14.1568 3.79330i −0.627489 0.168135i −0.0689588 0.997620i \(-0.521968\pi\)
−0.558530 + 0.829484i \(0.688634\pi\)
\(510\) −7.43497 + 18.3451i −0.329226 + 0.812337i
\(511\) −1.56218 0.901924i −0.0691067 0.0398988i
\(512\) 11.7137 11.7137i 0.517678 0.517678i
\(513\) 12.5839 + 15.6431i 0.555591 + 0.690661i
\(514\) −8.38269 31.2846i −0.369744 1.37990i
\(515\) 7.37772 + 7.37772i 0.325101 + 0.325101i
\(516\) −0.140760 1.00947i −0.00619663 0.0444395i
\(517\) 21.4641 12.3923i 0.943990 0.545013i
\(518\) 2.98577 11.1430i 0.131187 0.489597i
\(519\) −23.8452 + 18.5885i −1.04669 + 0.815943i
\(520\) 14.1340 + 0.911543i 0.619816 + 0.0399738i
\(521\) 2.49155i 0.109157i 0.998509 + 0.0545785i \(0.0173815\pi\)
−0.998509 + 0.0545785i \(0.982618\pi\)
\(522\) 28.2934 + 15.7633i 1.23837 + 0.689939i
\(523\) 19.4904 + 33.7583i 0.852255 + 1.47615i 0.879169 + 0.476511i \(0.158099\pi\)
−0.0269137 + 0.999638i \(0.508568\pi\)
\(524\) 1.06488 1.84443i 0.0465196 0.0805743i
\(525\) 6.64136 + 0.822738i 0.289853 + 0.0359072i
\(526\) 32.4186 8.68653i 1.41352 0.378751i
\(527\) 16.9617 4.54486i 0.738862 0.197977i
\(528\) 31.5713 + 3.91108i 1.37397 + 0.170208i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −0.883988 1.53111i −0.0383980 0.0665072i
\(531\) 7.89343 + 4.39771i 0.342546 + 0.190845i
\(532\) 1.46410i 0.0634769i
\(533\) −19.1959 6.49373i −0.831465 0.281275i
\(534\) −19.1962 + 14.9643i −0.830699 + 0.647570i
\(535\) 7.41154 27.6603i 0.320429 1.19586i
\(536\) 13.4052 7.73951i 0.579018 0.334296i
\(537\) −6.34978 45.5378i −0.274013 1.96510i
\(538\) 15.2679 + 15.2679i 0.658248 + 0.658248i
\(539\) −5.32441 19.8710i −0.229339 0.855904i
\(540\) 1.31425 + 1.63376i 0.0565565 + 0.0703060i
\(541\) −12.6865 + 12.6865i −0.545437 + 0.545437i −0.925118 0.379681i \(-0.876034\pi\)
0.379681 + 0.925118i \(0.376034\pi\)
\(542\) 10.0782 + 5.81863i 0.432894 + 0.249931i
\(543\) −1.95171 + 4.81568i −0.0837561 + 0.206661i
\(544\) 7.33013 + 1.96410i 0.314277 + 0.0842102i
\(545\) 28.1047 1.20387
\(546\) 5.77869 11.9794i 0.247305 0.512672i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −1.73999 0.466229i −0.0743287 0.0199163i
\(549\) 20.1990 5.74477i 0.862070 0.245181i
\(550\) 14.6603 + 8.46410i 0.625115 + 0.360911i
\(551\) −19.5856 + 19.5856i −0.834376 + 0.834376i
\(552\) 0 0
\(553\) 0.732051 + 2.73205i 0.0311300 + 0.116179i
\(554\) 29.3785 + 29.3785i 1.24817 + 1.24817i
\(555\) −13.9934 + 1.95124i −0.593988 + 0.0828255i
\(556\) −4.26795 + 2.46410i −0.181001 + 0.104501i
\(557\) −6.62616 + 24.7292i −0.280759 + 1.04781i 0.671123 + 0.741346i \(0.265812\pi\)
−0.951883 + 0.306462i \(0.900855\pi\)
\(558\) 3.84177 15.2679i 0.162635 0.646344i
\(559\) 6.58846 + 4.39230i 0.278662 + 0.185775i
\(560\) 9.50749i 0.401765i
\(561\) −13.9955 33.0706i −0.590891 1.39624i
\(562\) 12.9186 + 22.3756i 0.544938 + 0.943860i
\(563\) −5.03908 + 8.72794i −0.212372 + 0.367839i −0.952456 0.304675i \(-0.901452\pi\)
0.740085 + 0.672514i \(0.234785\pi\)
\(564\) 0.343706 2.77449i 0.0144726 0.116827i
\(565\) −14.9641 + 4.00962i −0.629544 + 0.168686i
\(566\) −9.58394 + 2.56801i −0.402843 + 0.107941i
\(567\) −12.1877 + 3.66867i −0.511837 + 0.154070i
\(568\) 3.92820 6.80385i 0.164824 0.285483i
\(569\) −1.35022 2.33864i −0.0566040 0.0980411i 0.836335 0.548219i \(-0.184694\pi\)
−0.892939 + 0.450178i \(0.851361\pi\)
\(570\) −13.9773 + 5.91520i −0.585444 + 0.247760i
\(571\) 1.94744i 0.0814979i −0.999169 0.0407489i \(-0.987026\pi\)
0.999169 0.0407489i \(-0.0129744\pi\)
\(572\) 2.98577 2.62398i 0.124841 0.109714i
\(573\) 5.14359 + 6.59817i 0.214877 + 0.275643i
\(574\) 3.09808 11.5622i 0.129311 0.482596i
\(575\) 0 0
\(576\) −13.9108 + 14.3429i −0.579617 + 0.597623i
\(577\) −22.4904 22.4904i −0.936287 0.936287i 0.0618016 0.998088i \(-0.480315\pi\)
−0.998088 + 0.0618016i \(0.980315\pi\)
\(578\) −3.27110 12.2079i −0.136060 0.507783i
\(579\) −0.191705 0.144785i −0.00796700 0.00601707i
\(580\) −2.04552 + 2.04552i −0.0849355 + 0.0849355i
\(581\) −5.03908 2.90931i −0.209056 0.120699i
\(582\) −4.08936 1.65735i −0.169509 0.0686992i
\(583\) 3.09808 + 0.830127i 0.128309 + 0.0343803i
\(584\) 3.32707 0.137675
\(585\) −16.2699 0.799664i −0.672679 0.0330620i
\(586\) 2.71281 0.112065
\(587\) −18.0265 4.83020i −0.744035 0.199364i −0.133164 0.991094i \(-0.542514\pi\)
−0.610871 + 0.791730i \(0.709181\pi\)
\(588\) −2.15060 0.871601i −0.0886892 0.0359442i
\(589\) 11.6603 + 6.73205i 0.480452 + 0.277389i
\(590\) −4.83020 + 4.83020i −0.198856 + 0.198856i
\(591\) −5.68671 4.29488i −0.233920 0.176668i
\(592\) 6.25833 + 23.3564i 0.257216 + 0.959942i
\(593\) −10.3635 10.3635i −0.425578 0.425578i 0.461541 0.887119i \(-0.347297\pi\)
−0.887119 + 0.461541i \(0.847297\pi\)
\(594\) −32.0087 3.46913i −1.31333 0.142340i
\(595\) 9.29423 5.36603i 0.381026 0.219986i
\(596\) 0.598653 2.23420i 0.0245218 0.0915166i
\(597\) −13.7670 17.6603i −0.563446 0.722786i
\(598\) 0 0
\(599\) 20.7270i 0.846881i −0.905924 0.423441i \(-0.860822\pi\)
0.905924 0.423441i \(-0.139178\pi\)
\(600\) −11.3671 + 4.81059i −0.464062 + 0.196391i
\(601\) −11.7942 20.4282i −0.481097 0.833284i 0.518668 0.854976i \(-0.326428\pi\)
−0.999765 + 0.0216919i \(0.993095\pi\)
\(602\) −2.33864 + 4.05065i −0.0953160 + 0.165092i
\(603\) −15.2797 + 9.13612i −0.622238 + 0.372052i
\(604\) 0.196152 0.0525589i 0.00798133 0.00213859i
\(605\) 8.62350 2.31066i 0.350595 0.0939417i
\(606\) 1.93291 15.6030i 0.0785192 0.633828i
\(607\) 0.0980762 0.169873i 0.00398079 0.00689493i −0.864028 0.503444i \(-0.832066\pi\)
0.868009 + 0.496549i \(0.165400\pi\)
\(608\) 2.90931 + 5.03908i 0.117988 + 0.204362i
\(609\) −6.84378 16.1715i −0.277324 0.655301i
\(610\) 15.8756i 0.642786i
\(611\) 14.3377 + 16.3145i 0.580041 + 0.660016i
\(612\) −3.92820 0.988427i −0.158788 0.0399548i
\(613\) −11.3564 + 42.3827i −0.458681 + 1.71182i 0.218354 + 0.975870i \(0.429931\pi\)
−0.677035 + 0.735951i \(0.736735\pi\)
\(614\) 15.4790 8.93682i 0.624683 0.360661i
\(615\) −14.5198 + 2.02463i −0.585494 + 0.0816411i
\(616\) −10.7321 10.7321i −0.432407 0.432407i
\(617\) 4.78173 + 17.8457i 0.192505 + 0.718439i 0.992899 + 0.118964i \(0.0379573\pi\)
−0.800393 + 0.599475i \(0.795376\pi\)
\(618\) −10.8914 + 14.4209i −0.438115 + 0.580094i
\(619\) −31.6603 + 31.6603i −1.27253 + 1.27253i −0.327778 + 0.944755i \(0.606300\pi\)
−0.944755 + 0.327778i \(0.893700\pi\)
\(620\) 1.21779 + 0.703093i 0.0489077 + 0.0282369i
\(621\) 0 0
\(622\) −14.6603 3.92820i −0.587823 0.157507i
\(623\) 13.1963 0.528701
\(624\) 2.06508 + 27.8017i 0.0826693 + 1.11296i
\(625\) 3.87564 0.155026
\(626\) 2.90931 + 0.779548i 0.116280 + 0.0311570i
\(627\) 10.3420 25.5180i 0.413019 1.01909i
\(628\) −1.11474 0.643594i −0.0444828 0.0256822i
\(629\) 19.3003 19.3003i 0.769554 0.769554i
\(630\) −0.147150 9.62097i −0.00586260 0.383309i
\(631\) 5.73205 + 21.3923i 0.228189 + 0.851614i 0.981102 + 0.193493i \(0.0619818\pi\)
−0.752912 + 0.658121i \(0.771352\pi\)
\(632\) −3.68886 3.68886i −0.146735 0.146735i
\(633\) −0.431485 3.09442i −0.0171500 0.122992i
\(634\) 20.9378 12.0885i 0.831547 0.480094i
\(635\) −3.55644 + 13.2728i −0.141133 + 0.526715i
\(636\) 0.285334 0.222432i 0.0113142 0.00882000i
\(637\) 16.1603 7.99038i 0.640293 0.316590i
\(638\) 44.4192i 1.75857i
\(639\) −4.39771 + 7.89343i −0.173971 + 0.312259i
\(640\) −9.82051 17.0096i −0.388190 0.672364i
\(641\) 22.6758 39.2757i 0.895642 1.55130i 0.0626345 0.998037i \(-0.480050\pi\)
0.833008 0.553261i \(-0.186617\pi\)
\(642\) 49.2228 + 6.09776i 1.94267 + 0.240659i
\(643\) 7.00000 1.87564i 0.276053 0.0739682i −0.118136 0.992997i \(-0.537692\pi\)
0.394190 + 0.919029i \(0.371025\pi\)
\(644\) 0 0
\(645\) 5.68503 + 0.704266i 0.223848 + 0.0277305i
\(646\) 14.6603 25.3923i 0.576800 0.999047i
\(647\) −8.23373 14.2612i −0.323701 0.560667i 0.657547 0.753413i \(-0.271594\pi\)
−0.981249 + 0.192746i \(0.938261\pi\)
\(648\) 16.0844 17.0998i 0.631857 0.671742i
\(649\) 12.3923i 0.486441i
\(650\) −4.75374 + 14.0524i −0.186457 + 0.551179i
\(651\) −6.73205 + 5.24796i −0.263850 + 0.205684i
\(652\) 0.287187 1.07180i 0.0112471 0.0419748i
\(653\) −8.36615 + 4.83020i −0.327393 + 0.189020i −0.654683 0.755904i \(-0.727198\pi\)
0.327290 + 0.944924i \(0.393865\pi\)
\(654\) 6.72272 + 48.2123i 0.262879 + 1.88525i
\(655\) 8.46410 + 8.46410i 0.330720 + 0.330720i
\(656\) 6.49373 + 24.2349i 0.253538 + 0.946216i
\(657\) −3.82609 + 0.0585190i −0.149270 + 0.00228304i
\(658\) −9.07180 + 9.07180i −0.353655 + 0.353655i
\(659\) 23.4834 + 13.5581i 0.914783 + 0.528150i 0.881967 0.471311i \(-0.156219\pi\)
0.0328158 + 0.999461i \(0.489553\pi\)
\(660\) 1.08011 2.66509i 0.0420434 0.103738i
\(661\) 9.42820 + 2.52628i 0.366715 + 0.0982609i 0.437470 0.899233i \(-0.355874\pi\)
−0.0707559 + 0.997494i \(0.522541\pi\)
\(662\) −51.5321 −2.00285
\(663\) 26.0126 17.7100i 1.01024 0.687801i
\(664\) 10.7321 0.416484
\(665\) 7.94839 + 2.12976i 0.308225 + 0.0825887i
\(666\) −6.69452 23.5383i −0.259408 0.912092i
\(667\) 0 0
\(668\) −2.54752 + 2.54752i −0.0985666 + 0.0985666i
\(669\) −27.0457 + 35.8103i −1.04565 + 1.38451i
\(670\) −3.48334 13.0000i −0.134573 0.502234i
\(671\) −20.3652 20.3652i −0.786189 0.786189i
\(672\) −3.65351 + 0.509445i −0.140937 + 0.0196523i
\(673\) −36.9904 + 21.3564i −1.42587 + 0.823229i −0.996792 0.0800364i \(-0.974496\pi\)
−0.429082 + 0.903265i \(0.641163\pi\)
\(674\) −7.19683 + 26.8589i −0.277211 + 1.03457i
\(675\) 12.9875 5.73205i 0.499888 0.220627i
\(676\) 2.76795 + 2.11474i 0.106460 + 0.0813360i
\(677\) 9.66040i 0.371279i −0.982618 0.185640i \(-0.940564\pi\)
0.982618 0.185640i \(-0.0594357\pi\)
\(678\) −10.4578 24.7111i −0.401628 0.949025i
\(679\) 1.19615 + 2.07180i 0.0459041 + 0.0795083i
\(680\) −9.89726 + 17.1426i −0.379543 + 0.657387i
\(681\) −4.31769 + 34.8536i −0.165454 + 1.33559i
\(682\) −20.8564 + 5.58846i −0.798633 + 0.213993i
\(683\) −45.2752 + 12.1315i −1.73241 + 0.464198i −0.980736 0.195338i \(-0.937420\pi\)
−0.751673 + 0.659536i \(0.770753\pi\)
\(684\) −1.59387 2.66566i −0.0609430 0.101924i
\(685\) 5.06218 8.76795i 0.193416 0.335006i
\(686\) 12.7786 + 22.1332i 0.487889 + 0.845048i
\(687\) 31.8617 13.4839i 1.21560 0.514443i
\(688\) 9.80385i 0.373768i
\(689\) −0.180895 + 2.80487i −0.00689154 + 0.106857i
\(690\) 0 0
\(691\) 4.88269 18.2224i 0.185746 0.693214i −0.808723 0.588189i \(-0.799841\pi\)
0.994470 0.105025i \(-0.0334922\pi\)
\(692\) 4.05065 2.33864i 0.153983 0.0889019i
\(693\) 12.5305 + 12.1530i 0.475994 + 0.461653i
\(694\) −21.9090 21.9090i −0.831653 0.831653i
\(695\) −7.16884 26.7545i −0.271930 1.01486i
\(696\) 25.8453 + 19.5196i 0.979664 + 0.739890i
\(697\) 20.0263 20.0263i 0.758549 0.758549i
\(698\) 37.1180 + 21.4301i 1.40494 + 0.811140i
\(699\) 28.0207 + 11.3563i 1.05984 + 0.429535i
\(700\) −1.00000 0.267949i −0.0377964 0.0101275i
\(701\) −12.7786 −0.482641 −0.241320 0.970446i \(-0.577580\pi\)
−0.241320 + 0.970446i \(0.577580\pi\)
\(702\) −2.52002 28.1016i −0.0951121 1.06063i
\(703\) 20.9282 0.789322
\(704\) 26.4692 + 7.09239i 0.997594 + 0.267304i
\(705\) 14.5623 + 5.90185i 0.548448 + 0.222277i
\(706\) −18.4474 10.6506i −0.694279 0.400842i
\(707\) −6.02751 + 6.02751i −0.226688 + 0.226688i
\(708\) −1.11546 0.842451i −0.0419216 0.0316612i
\(709\) −3.03590 11.3301i −0.114016 0.425512i 0.885196 0.465219i \(-0.154024\pi\)
−0.999211 + 0.0397068i \(0.987358\pi\)
\(710\) −4.83020 4.83020i −0.181274 0.181274i
\(711\) 4.30703 + 4.17726i 0.161526 + 0.156660i
\(712\) −21.0788 + 12.1699i −0.789963 + 0.456085i
\(713\) 0 0
\(714\) 11.4284 + 14.6603i 0.427696 + 0.548646i
\(715\) 9.90192 + 20.0263i 0.370311 + 0.748940i
\(716\) 7.11287i 0.265821i
\(717\) 14.8842 6.29899i 0.555859 0.235240i
\(718\) −19.4186 33.6340i −0.724695 1.25521i
\(719\) −3.68886 + 6.38929i −0.137571 + 0.238280i −0.926577 0.376106i \(-0.877263\pi\)
0.789005 + 0.614386i \(0.210596\pi\)
\(720\) 10.3501 + 17.3101i 0.385727 + 0.645110i
\(721\) 9.46410 2.53590i 0.352462 0.0944418i
\(722\) −5.92307 + 1.58708i −0.220434 + 0.0590650i
\(723\) 3.10003 25.0243i 0.115292 0.930665i
\(724\) 0.401924 0.696152i 0.0149374 0.0258723i
\(725\) 9.79282 + 16.9617i 0.363696 + 0.629940i
\(726\) 6.02659 + 14.2405i 0.223668 + 0.528515i
\(727\) 19.5167i 0.723833i 0.932211 + 0.361916i \(0.117877\pi\)
−0.932211 + 0.361916i \(0.882123\pi\)
\(728\) 7.37772 11.0666i 0.273437 0.410155i
\(729\) −18.1962 + 19.9474i −0.673932 + 0.738794i
\(730\) 0.748711 2.79423i 0.0277110 0.103419i
\(731\) −9.58394 + 5.53329i −0.354475 + 0.204656i
\(732\) −3.21758 + 0.448659i −0.118925 + 0.0165829i
\(733\) −6.77757 6.77757i −0.250335 0.250335i 0.570773 0.821108i \(-0.306644\pi\)
−0.821108 + 0.570773i \(0.806644\pi\)
\(734\) −11.8461 44.2104i −0.437249 1.63183i
\(735\) 7.86017 10.4074i 0.289927 0.383883i
\(736\) 0 0
\(737\) 21.1447 + 12.2079i 0.778876 + 0.449685i
\(738\) −6.94633 24.4237i −0.255698 0.899049i
\(739\) −11.1244 2.98076i −0.409216 0.109649i 0.0483378 0.998831i \(-0.484608\pi\)
−0.457554 + 0.889182i \(0.651274\pi\)
\(740\) 2.18573 0.0803492
\(741\) 23.7052 + 4.50141i 0.870833 + 0.165363i
\(742\) −1.66025 −0.0609498
\(743\) 8.51906 + 2.28268i 0.312534 + 0.0837432i 0.411677 0.911330i \(-0.364943\pi\)
−0.0991426 + 0.995073i \(0.531610\pi\)
\(744\) 5.91352 14.5911i 0.216800 0.534935i
\(745\) 11.2583 + 6.50000i 0.412473 + 0.238142i
\(746\) −12.3403 + 12.3403i −0.451812 + 0.451812i
\(747\) −12.3417 + 0.188763i −0.451560 + 0.00690649i
\(748\) 1.43782 + 5.36603i 0.0525720 + 0.196201i
\(749\) −19.0150 19.0150i −0.694792 0.694792i
\(750\) 4.19463 + 30.0820i 0.153166 + 1.09844i
\(751\) −29.2750 + 16.9019i −1.06826 + 0.616760i −0.927705 0.373313i \(-0.878222\pi\)
−0.140554 + 0.990073i \(0.544888\pi\)
\(752\) 6.95996 25.9749i 0.253804 0.947208i
\(753\) 1.35022 1.05256i 0.0492046 0.0383574i
\(754\) 38.1699 7.63397i 1.39006 0.278013i
\(755\) 1.14134i 0.0415375i
\(756\) 1.94576 0.301720i 0.0707667 0.0109735i
\(757\) −8.39230 14.5359i −0.305024 0.528316i 0.672243 0.740331i \(-0.265331\pi\)
−0.977267 + 0.212014i \(0.931998\pi\)
\(758\) 11.1430 19.3003i 0.404733 0.701019i
\(759\) 0 0
\(760\) −14.6603 + 3.92820i −0.531783 + 0.142491i
\(761\) −17.7412 + 4.75374i −0.643118 + 0.172323i −0.565616 0.824669i \(-0.691361\pi\)
−0.0775029 + 0.996992i \(0.524695\pi\)
\(762\) −23.6196 2.92602i −0.855647 0.105998i
\(763\) 13.1962 22.8564i 0.477733 0.827457i
\(764\) −0.647124 1.12085i −0.0234121 0.0405510i
\(765\) 11.0802 19.8878i 0.400606 0.719045i
\(766\) 49.5692i 1.79101i
\(767\) 10.6488 2.12976i 0.384507 0.0769014i
\(768\) 8.63397 6.73060i 0.311552 0.242870i
\(769\) −10.8301 + 40.4186i −0.390544 + 1.45753i 0.438694 + 0.898636i \(0.355441\pi\)
−0.829238 + 0.558895i \(0.811225\pi\)
\(770\) −11.4284 + 6.59817i −0.411850 + 0.237782i
\(771\) 5.14442 + 36.8935i 0.185272 + 1.32869i
\(772\) 0.0262794 + 0.0262794i 0.000945818 + 0.000945818i
\(773\) −11.1430 41.5864i −0.400787 1.49576i −0.811695 0.584081i \(-0.801455\pi\)
0.410908 0.911677i \(-0.365212\pi\)
\(774\) 0.151737 + 9.92087i 0.00545407 + 0.356598i
\(775\) 6.73205 6.73205i 0.241822 0.241822i
\(776\) −3.82129 2.20622i −0.137176 0.0791987i
\(777\) −4.98354 + 12.2965i −0.178784 + 0.441133i
\(778\) −32.7224 8.76795i −1.17316 0.314346i
\(779\) 21.7154 0.778035
\(780\) 2.47576 + 0.470125i 0.0886466 + 0.0168332i
\(781\) 12.3923 0.443432
\(782\) 0 0
\(783\) −30.0651 21.9928i −1.07444 0.785957i
\(784\) −19.3301 11.1603i −0.690362 0.398581i
\(785\) 5.11553 5.11553i 0.182581 0.182581i
\(786\) −12.4951 + 16.5444i −0.445687 + 0.590120i
\(787\) 4.29423 + 16.0263i 0.153073 + 0.571275i 0.999263 + 0.0383938i \(0.0122241\pi\)
−0.846190 + 0.532881i \(0.821109\pi\)
\(788\) 0.779548 + 0.779548i 0.0277702 + 0.0277702i
\(789\) −38.2307 + 5.33089i −1.36105 + 0.189785i
\(790\) −3.92820 + 2.26795i −0.139759 + 0.0806900i
\(791\) −3.76532 + 14.0524i −0.133879 + 0.499644i
\(792\) −31.2229 7.85641i −1.10946 0.279165i
\(793\) 14.0000 21.0000i 0.497155 0.745732i
\(794\) 20.7270i 0.735573i
\(795\) 0.792486 + 1.87260i 0.0281066 + 0.0664143i
\(796\) 1.73205 + 3.00000i 0.0613909 + 0.106332i
\(797\) −20.1563 + 34.9118i −0.713973 + 1.23664i 0.249381 + 0.968405i \(0.419773\pi\)
−0.963354 + 0.268232i \(0.913561\pi\)
\(798\) −1.75224 + 14.1445i −0.0620286 + 0.500711i
\(799\) −29.3205 + 7.85641i −1.03729 + 0.277940i
\(800\) 3.97420 1.06488i 0.140509 0.0376493i
\(801\) 24.0264 14.3660i 0.848929 0.507596i
\(802\) 9.37564 16.2391i 0.331066 0.573422i
\(803\) 2.62398 + 4.54486i 0.0925982 + 0.160385i
\(804\) 2.53632 1.07337i 0.0894491 0.0378550i
\(805\) 0 0
\(806\) −8.38664 16.9617i −0.295407 0.597449i
\(807\) −15.2679 19.5856i −0.537457 0.689447i
\(808\) 4.06922 15.1865i 0.143155 0.534260i
\(809\) −24.0261 + 13.8715i −0.844712 + 0.487694i −0.858863 0.512205i \(-0.828829\pi\)
0.0141514 + 0.999900i \(0.495495\pi\)
\(810\) −10.7416 17.3565i −0.377421 0.609846i
\(811\) 19.0000 + 19.0000i 0.667180 + 0.667180i 0.957062 0.289882i \(-0.0936161\pi\)
−0.289882 + 0.957062i \(0.593616\pi\)
\(812\) 0.703093 + 2.62398i 0.0246737 + 0.0920836i
\(813\) −10.6804 8.06639i −0.374579 0.282901i
\(814\) −23.7321 + 23.7321i −0.831808 + 0.831808i
\(815\) 5.40087 + 3.11819i 0.189184 + 0.109226i
\(816\) −36.1095 14.6346i −1.26409 0.512313i
\(817\) −8.19615 2.19615i −0.286747 0.0768336i
\(818\) 45.1988 1.58034
\(819\) −8.28964 + 12.8562i −0.289664 + 0.449232i
\(820\) 2.26795 0.0792002
\(821\) 41.5864 + 11.1430i 1.45137 + 0.388895i 0.896502 0.443040i \(-0.146100\pi\)
0.554873 + 0.831935i \(0.312767\pi\)
\(822\) 16.2519 + 6.58662i 0.566850 + 0.229735i
\(823\) −7.39230 4.26795i −0.257680 0.148771i 0.365596 0.930774i \(-0.380865\pi\)
−0.623276 + 0.782002i \(0.714199\pi\)
\(824\) −12.7786 + 12.7786i −0.445163 + 0.445163i
\(825\) −15.5364 11.7338i −0.540907 0.408519i
\(826\) 1.66025 + 6.19615i 0.0577676 + 0.215592i
\(827\) 31.7936 + 31.7936i 1.10557 + 1.10557i 0.993726 + 0.111845i \(0.0356760\pi\)
0.111845 + 0.993726i \(0.464324\pi\)
\(828\) 0 0
\(829\) 41.6769 24.0622i 1.44750 0.835714i 0.449167 0.893448i \(-0.351721\pi\)
0.998332 + 0.0577338i \(0.0183875\pi\)
\(830\) 2.41510 9.01327i 0.0838293 0.312855i
\(831\) −29.3785 37.6865i −1.01913 1.30733i
\(832\) −1.54552 + 23.9641i −0.0535812 + 0.830806i
\(833\) 25.1954i 0.872968i
\(834\) 44.1813 18.6976i 1.52987 0.647444i
\(835\) −10.1244 17.5359i −0.350368 0.606855i
\(836\) −2.12976 + 3.68886i −0.0736595 + 0.127582i
\(837\) −6.54383 + 16.8836i −0.226188 + 0.583582i
\(838\) 13.8301 3.70577i 0.477754 0.128014i
\(839\) 9.79282 2.62398i 0.338086 0.0905898i −0.0857819 0.996314i \(-0.527339\pi\)
0.423868 + 0.905724i \(0.360672\pi\)
\(840\) 1.18295 9.54910i 0.0408157 0.329475i
\(841\) 11.1962 19.3923i 0.386074 0.668700i
\(842\) −8.33816 14.4421i −0.287352 0.497708i
\(843\) −11.5814 27.3662i −0.398884 0.942540i
\(844\) 0.483340i 0.0166372i
\(845\) −15.5070 + 11.9506i −0.533457 + 0.411112i
\(846\) −6.64102 + 26.3927i −0.228323 + 0.907400i
\(847\) 2.16987 8.09808i 0.0745577 0.278253i
\(848\) 3.01375 1.73999i 0.103493 0.0597515i
\(849\) 11.3022 1.57598i 0.387890 0.0540873i
\(850\) −14.6603 14.6603i −0.502843 0.502843i
\(851\) 0 0
\(852\) 0.842451 1.11546i 0.0288619 0.0382151i
\(853\) −22.3660 + 22.3660i −0.765798 + 0.765798i −0.977364 0.211566i \(-0.932144\pi\)
0.211566 + 0.977364i \(0.432144\pi\)
\(854\) 12.9110 + 7.45418i 0.441806 + 0.255077i
\(855\) 16.7900 4.77524i 0.574207 0.163310i
\(856\) 47.9090 + 12.8372i 1.63749 + 0.438765i
\(857\) −3.32707 −0.113651 −0.0568253 0.998384i \(-0.518098\pi\)
−0.0568253 + 0.998384i \(0.518098\pi\)
\(858\) −31.9856 + 21.7766i −1.09197 + 0.743442i
\(859\) 39.1769 1.33670 0.668350 0.743847i \(-0.267001\pi\)
0.668350 + 0.743847i \(0.267001\pi\)
\(860\) −0.856003 0.229365i −0.0291895 0.00782129i
\(861\) −5.17100 + 12.7590i −0.176227 + 0.434825i
\(862\) 49.3468 + 28.4904i 1.68076 + 0.970386i
\(863\) 18.2354 18.2354i 0.620741 0.620741i −0.324980 0.945721i \(-0.605358\pi\)
0.945721 + 0.324980i \(0.105358\pi\)
\(864\) −6.09729 + 4.90487i −0.207434 + 0.166867i
\(865\) 6.80385 + 25.3923i 0.231338 + 0.863364i
\(866\) −33.0673 33.0673i −1.12367 1.12367i
\(867\) 2.00746 + 14.3966i 0.0681769 + 0.488935i
\(868\) 1.14359 0.660254i 0.0388161 0.0224105i
\(869\) 2.12976 7.94839i 0.0722473 0.269631i
\(870\) 22.2096 17.3135i 0.752977 0.586981i
\(871\) −6.85641 + 20.2679i −0.232320 + 0.686753i
\(872\) 48.6788i 1.64847i
\(873\) 4.43324 + 2.46991i 0.150042 + 0.0835939i
\(874\) 0 0
\(875\) 8.23373 14.2612i 0.278351 0.482118i
\(876\) 0.587477 + 0.0727771i 0.0198490 + 0.00245891i
\(877\) 28.9904 7.76795i 0.978936 0.262305i 0.266339 0.963879i \(-0.414186\pi\)
0.712596 + 0.701574i \(0.247519\pi\)
\(878\) 1.84443 0.494214i 0.0622465 0.0166789i
\(879\) −3.09640 0.383584i −0.104439 0.0129380i
\(880\) 13.8301 23.9545i 0.466213 0.807505i
\(881\) −11.7417 20.3372i −0.395588 0.685178i 0.597588 0.801803i \(-0.296126\pi\)
−0.993176 + 0.116625i \(0.962792\pi\)
\(882\) 19.7336 + 10.9943i 0.664464 + 0.370197i
\(883\) 33.3731i 1.12309i −0.827445 0.561547i \(-0.810207\pi\)
0.827445 0.561547i \(-0.189793\pi\)
\(884\) −4.36397 + 2.15775i −0.146776 + 0.0725730i
\(885\) 6.19615 4.83020i 0.208281 0.162365i
\(886\) −4.37307 + 16.3205i −0.146916 + 0.548298i
\(887\) 21.8683 12.6257i 0.734266 0.423929i −0.0857146 0.996320i \(-0.527317\pi\)
0.819981 + 0.572391i \(0.193984\pi\)
\(888\) −3.37965 24.2373i −0.113414 0.813351i
\(889\) 9.12436 + 9.12436i 0.306021 + 0.306021i
\(890\) 5.47732 + 20.4416i 0.183600 + 0.685206i
\(891\) 36.0441 + 8.48560i 1.20752 + 0.284278i
\(892\) 4.90897 4.90897i 0.164364 0.164364i
\(893\) −20.1563 11.6373i −0.674505 0.389426i
\(894\) −8.45743 + 20.8680i −0.282859 + 0.697929i
\(895\) −38.6147 10.3468i −1.29075 0.345855i
\(896\) −18.4443 −0.616181
\(897\) 0 0
\(898\) 30.9808 1.03384
\(899\) −24.1305 6.46575i −0.804797 0.215645i
\(900\) −2.11238 + 0.600781i −0.0704127 + 0.0200260i
\(901\) −3.40192 1.96410i −0.113335 0.0654337i
\(902\) −24.6247 + 24.6247i −0.819913 + 0.819913i
\(903\) 3.24207 4.29272i 0.107889 0.142853i
\(904\) −6.94486 25.9186i −0.230983 0.862039i
\(905\) 3.19465 + 3.19465i 0.106194 + 0.106194i
\(906\) −1.95791 + 0.273011i −0.0650473 + 0.00907018i
\(907\) −15.0000 + 8.66025i −0.498067 + 0.287559i −0.727915 0.685668i \(-0.759510\pi\)
0.229848 + 0.973227i \(0.426177\pi\)
\(908\) 1.40619 5.24796i 0.0466659 0.174160i
\(909\) −4.41244 + 17.5359i −0.146351 + 0.581629i
\(910\) −7.63397 8.68653i −0.253064 0.287956i
\(911\) 1.55910i 0.0516552i −0.999666 0.0258276i \(-0.991778\pi\)
0.999666 0.0258276i \(-0.00822209\pi\)
\(912\) −11.6431 27.5121i −0.385543 0.911016i
\(913\) 8.46410 + 14.6603i 0.280121 + 0.485184i
\(914\) −2.93730 + 5.08755i −0.0971572 + 0.168281i
\(915\) 2.24477 18.1204i 0.0742099 0.599043i
\(916\) −5.16987 + 1.38526i −0.170817 + 0.0457704i
\(917\) 10.8577 2.90931i 0.358553 0.0960740i
\(918\) 36.7670 + 14.2504i 1.21349 + 0.470333i
\(919\) −6.70577 + 11.6147i −0.221203 + 0.383135i −0.955174 0.296046i \(-0.904332\pi\)
0.733971 + 0.679181i \(0.237665\pi\)
\(920\) 0 0
\(921\) −18.9314 + 8.01177i −0.623809 + 0.263997i
\(922\) 32.0333i 1.05496i
\(923\) 2.12976 + 10.6488i 0.0701021 + 0.350510i
\(924\) −1.66025 2.12976i −0.0546183 0.0700641i
\(925\) 3.83013 14.2942i 0.125934 0.469991i
\(926\) 42.5188 24.5483i 1.39726 0.806706i
\(927\) 14.4705 14.9200i 0.475272 0.490036i
\(928\) −7.63397 7.63397i −0.250597 0.250597i
\(929\) 5.27594 + 19.6901i 0.173098 + 0.646011i 0.996868 + 0.0790861i \(0.0252002\pi\)
−0.823770 + 0.566924i \(0.808133\pi\)
\(930\) −10.9235 8.24997i −0.358196 0.270527i
\(931\) −13.6603 + 13.6603i −0.447697 + 0.447697i
\(932\) −4.05065 2.33864i −0.132683 0.0766048i
\(933\) 16.1777 + 6.55656i 0.529635 + 0.214652i
\(934\) 27.8827 + 7.47114i 0.912349 + 0.244463i
\(935\) −31.2229 −1.02110
\(936\) 1.38506 28.1803i 0.0452721 0.921103i
\(937\) −37.0000 −1.20874 −0.604369 0.796705i \(-0.706575\pi\)
−0.604369 + 0.796705i \(0.706575\pi\)
\(938\) −12.2079 3.27110i −0.398603 0.106805i
\(939\) −3.21046 1.30114i −0.104769 0.0424612i
\(940\) −2.10512 1.21539i −0.0686614 0.0396417i
\(941\) 9.14570 9.14570i 0.298141 0.298141i −0.542144 0.840285i \(-0.682387\pi\)
0.840285 + 0.542144i \(0.182387\pi\)
\(942\) 9.99911 + 7.55181i 0.325789 + 0.246051i
\(943\) 0 0
\(944\) −9.50749 9.50749i −0.309442 0.309442i
\(945\) −1.19242 + 11.0022i −0.0387895 + 0.357900i
\(946\) 11.7846 6.80385i 0.383151 0.221212i
\(947\) 2.77689 10.3635i 0.0902368 0.336768i −0.906018 0.423240i \(-0.860893\pi\)
0.996254 + 0.0864720i \(0.0275593\pi\)
\(948\) −0.570669 0.732051i −0.0185345 0.0237759i
\(949\) −3.45448 + 3.03590i −0.112137 + 0.0985494i
\(950\) 15.8968i 0.515760i
\(951\) −25.6076 + 10.8372i −0.830385 + 0.351420i
\(952\) 9.29423 + 16.0981i 0.301228 + 0.521742i
\(953\) 0.988427 1.71201i 0.0320183 0.0554573i −0.849572 0.527472i \(-0.823140\pi\)
0.881591 + 0.472015i \(0.156473\pi\)
\(954\) −3.02279 + 1.80740i −0.0978666 + 0.0585169i
\(955\) 7.02628 1.88269i 0.227365 0.0609223i
\(956\) −2.41510 + 0.647124i −0.0781099 + 0.0209295i
\(957\) −6.28076 + 50.7000i −0.203028 + 1.63890i
\(958\) −15.4904 + 26.8301i −0.500471 + 0.866842i
\(959\) −4.75374 8.23373i −0.153506 0.265881i
\(960\) 6.77079 + 15.9990i 0.218526 + 0.516366i
\(961\) 18.8564i 0.608271i
\(962\) −24.4718 16.3145i −0.789003 0.526002i
\(963\) −55.3205 13.9199i −1.78268 0.448563i
\(964\) −1.00962 + 3.76795i −0.0325176 + 0.121357i
\(965\) −0.180895 + 0.104440i −0.00582321 + 0.00336203i
\(966\) 0 0
\(967\) −27.8564 27.8564i −0.895802 0.895802i 0.0992599 0.995062i \(-0.468352\pi\)
−0.995062 + 0.0992599i \(0.968352\pi\)
\(968\) 4.00218 + 14.9363i 0.128635 + 0.480072i
\(969\) −20.3236 + 26.9098i −0.652887 + 0.864467i
\(970\) −2.71281 + 2.71281i −0.0871032 + 0.0871032i
\(971\) −41.4335 23.9216i −1.32966 0.767682i −0.344416 0.938817i \(-0.611923\pi\)
−0.985247 + 0.171136i \(0.945256\pi\)
\(972\) 3.21415 2.66755i 0.103094 0.0855618i
\(973\) −25.1244 6.73205i −0.805450 0.215820i
\(974\) 8.67197 0.277868
\(975\) 7.41287 15.3671i 0.237402 0.492143i
\(976\) −31.2487 −1.00025
\(977\) −22.8847 6.13194i −0.732147 0.196178i −0.126562 0.991959i \(-0.540394\pi\)
−0.605585 + 0.795780i \(0.707061\pi\)
\(978\) −4.05721 + 10.0108i −0.129735 + 0.320111i
\(979\) −33.2487 19.1962i −1.06263 0.613512i
\(980\) −1.42667 + 1.42667i −0.0455734 + 0.0455734i
\(981\) −0.856198 55.9800i −0.0273363 1.78730i
\(982\) −11.1173 41.4904i −0.354768 1.32401i
\(983\) 30.4433 + 30.4433i 0.970992 + 0.970992i 0.999591 0.0285990i \(-0.00910459\pi\)
−0.0285990 + 0.999591i \(0.509105\pi\)
\(984\) −3.50677 25.1490i −0.111792 0.801721i
\(985\) −5.36603 + 3.09808i −0.170976 + 0.0987129i
\(986\) −14.0803 + 52.5485i −0.448409 + 1.67349i
\(987\) 11.6373 9.07180i 0.370418 0.288758i
\(988\) −3.53590 1.19615i −0.112492 0.0380547i
\(989\) 0 0
\(990\) −13.6245 + 24.4545i −0.433014 + 0.777214i
\(991\) 28.7846 + 49.8564i 0.914373 + 1.58374i 0.807816 + 0.589434i \(0.200649\pi\)
0.106557 + 0.994307i \(0.466017\pi\)
\(992\) −2.62398 + 4.54486i −0.0833114 + 0.144300i
\(993\) 58.8186 + 7.28650i 1.86655 + 0.231230i
\(994\) −6.19615 + 1.66025i −0.196530 + 0.0526601i
\(995\) −18.8061 + 5.03908i −0.596193 + 0.159750i
\(996\) 1.89501 + 0.234755i 0.0600457 + 0.00743851i
\(997\) 3.50000 6.06218i 0.110846 0.191991i −0.805266 0.592914i \(-0.797977\pi\)
0.916112 + 0.400923i \(0.131311\pi\)
\(998\) −2.62398 4.54486i −0.0830606 0.143865i
\(999\) 4.31286 + 27.8132i 0.136453 + 0.879970i
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.11.2 yes 8
3.2 odd 2 inner 39.2.k.b.11.1 8
4.3 odd 2 624.2.cn.c.401.2 8
5.2 odd 4 975.2.bp.e.674.1 8
5.3 odd 4 975.2.bp.f.674.2 8
5.4 even 2 975.2.bo.d.401.1 8
12.11 even 2 624.2.cn.c.401.1 8
13.2 odd 12 507.2.f.f.239.3 8
13.3 even 3 507.2.f.f.437.2 8
13.4 even 6 507.2.k.f.488.2 8
13.5 odd 4 507.2.k.e.80.2 8
13.6 odd 12 inner 39.2.k.b.32.1 yes 8
13.7 odd 12 507.2.k.d.188.2 8
13.8 odd 4 507.2.k.f.80.1 8
13.9 even 3 507.2.k.e.488.1 8
13.10 even 6 507.2.f.e.437.3 8
13.11 odd 12 507.2.f.e.239.2 8
13.12 even 2 507.2.k.d.89.1 8
15.2 even 4 975.2.bp.e.674.2 8
15.8 even 4 975.2.bp.f.674.1 8
15.14 odd 2 975.2.bo.d.401.2 8
39.2 even 12 507.2.f.f.239.2 8
39.5 even 4 507.2.k.e.80.1 8
39.8 even 4 507.2.k.f.80.2 8
39.11 even 12 507.2.f.e.239.3 8
39.17 odd 6 507.2.k.f.488.1 8
39.20 even 12 507.2.k.d.188.1 8
39.23 odd 6 507.2.f.e.437.2 8
39.29 odd 6 507.2.f.f.437.3 8
39.32 even 12 inner 39.2.k.b.32.2 yes 8
39.35 odd 6 507.2.k.e.488.2 8
39.38 odd 2 507.2.k.d.89.2 8
52.19 even 12 624.2.cn.c.305.1 8
65.19 odd 12 975.2.bo.d.851.2 8
65.32 even 12 975.2.bp.f.149.1 8
65.58 even 12 975.2.bp.e.149.2 8
156.71 odd 12 624.2.cn.c.305.2 8
195.32 odd 12 975.2.bp.f.149.2 8
195.149 even 12 975.2.bo.d.851.1 8
195.188 odd 12 975.2.bp.e.149.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.k.b.11.1 8 3.2 odd 2 inner
39.2.k.b.11.2 yes 8 1.1 even 1 trivial
39.2.k.b.32.1 yes 8 13.6 odd 12 inner
39.2.k.b.32.2 yes 8 39.32 even 12 inner
507.2.f.e.239.2 8 13.11 odd 12
507.2.f.e.239.3 8 39.11 even 12
507.2.f.e.437.2 8 39.23 odd 6
507.2.f.e.437.3 8 13.10 even 6
507.2.f.f.239.2 8 39.2 even 12
507.2.f.f.239.3 8 13.2 odd 12
507.2.f.f.437.2 8 13.3 even 3
507.2.f.f.437.3 8 39.29 odd 6
507.2.k.d.89.1 8 13.12 even 2
507.2.k.d.89.2 8 39.38 odd 2
507.2.k.d.188.1 8 39.20 even 12
507.2.k.d.188.2 8 13.7 odd 12
507.2.k.e.80.1 8 39.5 even 4
507.2.k.e.80.2 8 13.5 odd 4
507.2.k.e.488.1 8 13.9 even 3
507.2.k.e.488.2 8 39.35 odd 6
507.2.k.f.80.1 8 13.8 odd 4
507.2.k.f.80.2 8 39.8 even 4
507.2.k.f.488.1 8 39.17 odd 6
507.2.k.f.488.2 8 13.4 even 6
624.2.cn.c.305.1 8 52.19 even 12
624.2.cn.c.305.2 8 156.71 odd 12
624.2.cn.c.401.1 8 12.11 even 2
624.2.cn.c.401.2 8 4.3 odd 2
975.2.bo.d.401.1 8 5.4 even 2
975.2.bo.d.401.2 8 15.14 odd 2
975.2.bo.d.851.1 8 195.149 even 12
975.2.bo.d.851.2 8 65.19 odd 12
975.2.bp.e.149.1 8 195.188 odd 12
975.2.bp.e.149.2 8 65.58 even 12
975.2.bp.e.674.1 8 5.2 odd 4
975.2.bp.e.674.2 8 15.2 even 4
975.2.bp.f.149.1 8 65.32 even 12
975.2.bp.f.149.2 8 195.32 odd 12
975.2.bp.f.674.1 8 15.8 even 4
975.2.bp.f.674.2 8 5.3 odd 4