Properties

Label 39.2.k.b.32.1
Level $39$
Weight $2$
Character 39.32
Analytic conductor $0.311$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 32.1
Root \(0.500000 + 1.56488i\) of defining polynomial
Character \(\chi\) \(=\) 39.32
Dual form 39.2.k.b.11.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.45466 + 0.389774i) q^{2} +(0.239203 + 1.71545i) q^{3} +(0.232051 - 0.133975i) q^{4} +(1.06488 + 1.06488i) q^{5} +(-1.01660 - 2.40216i) q^{6} +(0.366025 - 1.36603i) q^{7} +(1.84443 - 1.84443i) q^{8} +(-2.88556 + 0.820682i) q^{9} +O(q^{10})\) \(q+(-1.45466 + 0.389774i) q^{2} +(0.239203 + 1.71545i) q^{3} +(0.232051 - 0.133975i) q^{4} +(1.06488 + 1.06488i) q^{5} +(-1.01660 - 2.40216i) q^{6} +(0.366025 - 1.36603i) q^{7} +(1.84443 - 1.84443i) q^{8} +(-2.88556 + 0.820682i) 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} +(-1.57203 + 2.08148i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(2.51954 + 4.36397i) q^{17} +(3.87762 - 2.31853i) q^{18} +(-3.73205 - 1.00000i) q^{19} +(0.389774 + 0.104440i) q^{20} +(2.43091 + 0.301143i) q^{21} +(3.09808 + 5.36603i) q^{22} +(3.60523 + 2.72284i) 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} +(1.47546 - 3.64058i) q^{30} +(-2.46410 + 2.46410i) q^{31} +(0.389774 - 1.45466i) q^{32} +(6.56283 - 2.77739i) q^{33} +(-5.36603 - 5.36603i) q^{34} +(1.84443 - 1.06488i) q^{35} +(-0.559647 + 0.577032i) q^{36} +(-5.23205 + 1.40192i) q^{37} +5.81863 q^{38} +(1.25874 + 6.11683i) q^{39} +3.92820 q^{40} +(5.42885 - 1.45466i) q^{41} +(-3.65351 + 0.509445i) q^{42} +(1.90192 - 1.09808i) q^{43} +(-0.779548 - 0.779548i) q^{44} +(-3.94672 - 2.19886i) q^{45} +(-4.25953 + 4.25953i) q^{47} +(-7.16590 - 2.90422i) 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} +(4.90487 + 6.09729i) q^{54} +(3.09808 - 5.36603i) q^{55} +(-1.84443 - 3.19465i) q^{56} +(0.822738 - 6.64136i) q^{57} +(10.4282 + 2.79423i) q^{58} +(-2.90931 - 0.779548i) q^{59} +(-0.0859264 + 0.693622i) q^{60} +(3.50000 + 6.06218i) q^{61} +(2.62398 - 4.54486i) q^{62} +(0.0648824 + 4.24214i) 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} +(-3.80853 + 6.83591i) q^{72} +(-0.901924 - 0.901924i) q^{73} +(7.06440 - 4.07863i) q^{74} +(4.68671 - 0.653513i) q^{75} +(-1.00000 + 0.267949i) q^{76} -5.81863 q^{77} +(-4.21522 - 8.40726i) q^{78} +2.00000 q^{79} +(-6.49373 + 1.73999i) q^{80} +(7.65296 - 4.73626i) q^{81} +(-7.33013 + 4.23205i) q^{82} +(2.90931 + 2.90931i) q^{83} +(0.604440 - 0.255799i) q^{84} +(-1.96410 + 7.33013i) q^{85} +(-2.33864 + 2.33864i) q^{86} +(4.66384 - 11.5076i) 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} +(-4.81647 - 3.63763i) q^{93} +(4.53590 - 7.85641i) q^{94} +(-2.90931 - 5.03908i) q^{95} +(2.58863 + 0.320682i) q^{96} +(1.63397 + 0.437822i) q^{97} +(-7.27328 - 1.94887i) q^{98} +(6.33434 + 10.5939i) 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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{12}\right)\)

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 \(-0.762059\pi\)
−0.295217 + 0.955430i \(0.595392\pi\)
\(3\) 0.239203 + 1.71545i 0.138104 + 0.990418i
\(4\) 0.232051 0.133975i 0.116025 0.0669873i
\(5\) 1.06488 + 1.06488i 0.476230 + 0.476230i 0.903924 0.427694i \(-0.140674\pi\)
−0.427694 + 0.903924i \(0.640674\pi\)
\(6\) −1.01660 2.40216i −0.415024 0.980678i
\(7\) 0.366025 1.36603i 0.138345 0.516309i −0.861617 0.507559i \(-0.830548\pi\)
0.999962 0.00875026i \(-0.00278533\pi\)
\(8\) 1.84443 1.84443i 0.652105 0.652105i
\(9\) −2.88556 + 0.820682i −0.961855 + 0.273561i
\(10\) −1.96410 1.13397i −0.621103 0.358594i
\(11\) −1.06488 3.97420i −0.321074 1.19826i −0.918200 0.396117i \(-0.870357\pi\)
0.597126 0.802148i \(-0.296309\pi\)
\(12\) 0.285334 + 0.366025i 0.0823689 + 0.105662i
\(13\) 3.59808 0.232051i 0.997927 0.0643593i
\(14\) 2.12976i 0.569204i
\(15\) −1.57203 + 2.08148i −0.405897 + 0.537436i
\(16\) −2.23205 + 3.86603i −0.558013 + 0.966506i
\(17\) 2.51954 + 4.36397i 0.611078 + 1.05842i 0.991059 + 0.133424i \(0.0425971\pi\)
−0.379981 + 0.924994i \(0.624070\pi\)
\(18\) 3.87762 2.31853i 0.913965 0.546482i
\(19\) −3.73205 1.00000i −0.856191 0.229416i −0.196084 0.980587i \(-0.562823\pi\)
−0.660107 + 0.751171i \(0.729489\pi\)
\(20\) 0.389774 + 0.104440i 0.0871561 + 0.0233534i
\(21\) 2.43091 + 0.301143i 0.530468 + 0.0657148i
\(22\) 3.09808 + 5.36603i 0.660512 + 1.14404i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 3.60523 + 2.72284i 0.735914 + 0.555798i
\(25\) 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 \(-0.565162\pi\)
−0.949585 + 0.313509i \(0.898495\pi\)
\(30\) 1.47546 3.64058i 0.269381 0.664675i
\(31\) −2.46410 + 2.46410i −0.442566 + 0.442566i −0.892873 0.450308i \(-0.851314\pi\)
0.450308 + 0.892873i \(0.351314\pi\)
\(32\) 0.389774 1.45466i 0.0689030 0.257149i
\(33\) 6.56283 2.77739i 1.14244 0.483482i
\(34\) −5.36603 5.36603i −0.920266 0.920266i
\(35\) 1.84443 1.06488i 0.311766 0.179998i
\(36\) −0.559647 + 0.577032i −0.0932745 + 0.0961720i
\(37\) −5.23205 + 1.40192i −0.860144 + 0.230475i −0.661821 0.749662i \(-0.730216\pi\)
−0.198323 + 0.980137i \(0.563549\pi\)
\(38\) 5.81863 0.943906
\(39\) 1.25874 + 6.11683i 0.201560 + 0.979476i
\(40\) 3.92820 0.621103
\(41\) 5.42885 1.45466i 0.847844 0.227179i 0.191361 0.981520i \(-0.438710\pi\)
0.656483 + 0.754341i \(0.272043\pi\)
\(42\) −3.65351 + 0.509445i −0.563749 + 0.0786091i
\(43\) 1.90192 1.09808i 0.290041 0.167455i −0.347920 0.937524i \(-0.613112\pi\)
0.637960 + 0.770069i \(0.279778\pi\)
\(44\) −0.779548 0.779548i −0.117521 0.117521i
\(45\) −3.94672 2.19886i −0.588342 0.327786i
\(46\) 0 0
\(47\) −4.25953 + 4.25953i −0.621316 + 0.621316i −0.945868 0.324552i \(-0.894787\pi\)
0.324552 + 0.945868i \(0.394787\pi\)
\(48\) −7.16590 2.90422i −1.03431 0.419188i
\(49\) 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 \(0.982950\pi\)
\(54\) 4.90487 + 6.09729i 0.667468 + 0.829736i
\(55\) 3.09808 5.36603i 0.417745 0.723555i
\(56\) −1.84443 3.19465i −0.246472 0.426903i
\(57\) 0.822738 6.64136i 0.108974 0.879670i
\(58\) 10.4282 + 2.79423i 1.36929 + 0.366900i
\(59\) −2.90931 0.779548i −0.378760 0.101489i 0.0644157 0.997923i \(-0.479482\pi\)
−0.443176 + 0.896435i \(0.646148\pi\)
\(60\) −0.0859264 + 0.693622i −0.0110931 + 0.0895462i
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 2.62398 4.54486i 0.333246 0.577198i
\(63\) 0.0648824 + 4.24214i 0.00817442 + 0.534460i
\(64\) 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 −0.994050 0.108925i \(-0.965259\pi\)
0.806410 0.591357i \(-0.201407\pi\)
\(68\) 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 \(-0.973864\pi\)
0.904116 + 0.427288i \(0.140531\pi\)
\(72\) −3.80853 + 6.83591i −0.448840 + 0.805620i
\(73\) −0.901924 0.901924i −0.105562 0.105562i 0.652353 0.757915i \(-0.273782\pi\)
−0.757915 + 0.652353i \(0.773782\pi\)
\(74\) 7.06440 4.07863i 0.821220 0.474132i
\(75\) 4.68671 0.653513i 0.541174 0.0754612i
\(76\) −1.00000 + 0.267949i −0.114708 + 0.0307359i
\(77\) −5.81863 −0.663094
\(78\) −4.21522 8.40726i −0.477279 0.951934i
\(79\) 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
\(81\) 7.65296 4.73626i 0.850329 0.526251i
\(82\) −7.33013 + 4.23205i −0.809477 + 0.467352i
\(83\) 2.90931 + 2.90931i 0.319339 + 0.319339i 0.848513 0.529174i \(-0.177498\pi\)
−0.529174 + 0.848513i \(0.677498\pi\)
\(84\) 0.604440 0.255799i 0.0659498 0.0279100i
\(85\) −1.96410 + 7.33013i −0.213037 + 0.795064i
\(86\) −2.33864 + 2.33864i −0.252182 + 0.252182i
\(87\) 4.66384 11.5076i 0.500017 1.23375i
\(88\) −9.29423 5.36603i −0.990768 0.572020i
\(89\) −2.41510 9.01327i −0.256000 0.955405i −0.967531 0.252751i \(-0.918665\pi\)
0.711531 0.702654i \(-0.248002\pi\)
\(90\) 6.59817 + 1.66025i 0.695509 + 0.175006i
\(91\) 1.00000 5.00000i 0.104828 0.524142i
\(92\) 0 0
\(93\) −4.81647 3.63763i −0.499445 0.377205i
\(94\) 4.53590 7.85641i 0.467842 0.810326i
\(95\) −2.90931 5.03908i −0.298489 0.516998i
\(96\) 2.58863 + 0.320682i 0.264201 + 0.0327295i
\(97\) 1.63397 + 0.437822i 0.165905 + 0.0444541i 0.340815 0.940130i \(-0.389297\pi\)
−0.174910 + 0.984584i \(0.555964\pi\)
\(98\) −7.27328 1.94887i −0.734712 0.196866i
\(99\) 6.33434 + 10.5939i 0.636625 + 1.06472i
\(100\) −0.366025 0.633975i −0.0366025 0.0633975i
\(101\) −3.01375 + 5.21997i −0.299880 + 0.519407i −0.976108 0.217285i \(-0.930280\pi\)
0.676229 + 0.736692i \(0.263613\pi\)
\(102\) 7.92160 10.4887i 0.784356 1.03854i
\(103\) 6.92820i 0.682656i 0.939944 + 0.341328i \(0.110877\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(104\) 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 0.992969 + 0.118374i \(0.0377682\pi\)
0.598999 + 0.800749i \(0.295565\pi\)
\(108\) −1.12374 0.822021i −0.108132 0.0790990i
\(109\) −13.1962 + 13.1962i −1.26396 + 1.26396i −0.314806 + 0.949156i \(0.601940\pi\)
−0.949156 + 0.314806i \(0.898060\pi\)
\(110\) −2.41510 + 9.01327i −0.230271 + 0.859382i
\(111\) −3.65646 8.64000i −0.347055 0.820072i
\(112\) 4.46410 + 4.46410i 0.421818 + 0.421818i
\(113\) −8.90883 + 5.14352i −0.838073 + 0.483861i −0.856609 0.515967i \(-0.827433\pi\)
0.0185360 + 0.999828i \(0.494099\pi\)
\(114\) 1.39183 + 9.98158i 0.130357 + 0.934861i
\(115\) 0 0
\(116\) −1.92089 −0.178350
\(117\) −10.1920 + 3.62247i −0.942254 + 0.334898i
\(118\) 4.53590 0.417563
\(119\) 6.88351 1.84443i 0.631010 0.169079i
\(120\) 0.939636 + 6.73865i 0.0857767 + 0.615152i
\(121\) −5.13397 + 2.96410i −0.466725 + 0.269464i
\(122\) −7.45418 7.45418i −0.674869 0.674869i
\(123\) 3.79399 + 8.96499i 0.342093 + 0.808346i
\(124\) −0.241670 + 0.901924i −0.0217026 + 0.0809951i
\(125\) 8.23373 8.23373i 0.736447 0.736447i
\(126\) −1.74786 6.14557i −0.155712 0.547491i
\(127\) 7.90192 + 4.56218i 0.701182 + 0.404828i 0.807788 0.589474i \(-0.200665\pi\)
−0.106605 + 0.994301i \(0.533998\pi\)
\(128\) 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 \(-0.112877\pi\)
\(132\) 1.15081 1.52375i 0.100165 0.132625i
\(133\) −2.73205 + 4.73205i −0.236899 + 0.410321i
\(134\) 4.46841 + 7.73951i 0.386012 + 0.668592i
\(135\) 2.82797 7.29638i 0.243393 0.627973i
\(136\) 12.6962 + 3.40192i 1.08869 + 0.291713i
\(137\) 6.49373 + 1.73999i 0.554797 + 0.148657i 0.525315 0.850908i \(-0.323948\pi\)
0.0294822 + 0.999565i \(0.490614\pi\)
\(138\) 0 0
\(139\) −9.19615 15.9282i −0.780007 1.35101i −0.931937 0.362621i \(-0.881882\pi\)
0.151929 0.988391i \(-0.451451\pi\)
\(140\) 0.285334 0.494214i 0.0241152 0.0417687i
\(141\) −8.32592 6.28814i −0.701169 0.529557i
\(142\) 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
\(147\) −3.25286 + 8.02614i −0.268291 + 0.661985i
\(148\) −1.02628 + 1.02628i −0.0843597 + 0.0843597i
\(149\) 2.23420 8.33816i 0.183033 0.683089i −0.812010 0.583644i \(-0.801626\pi\)
0.995043 0.0994454i \(-0.0317068\pi\)
\(150\) −6.56283 + 2.77739i −0.535853 + 0.226773i
\(151\) 0.535898 + 0.535898i 0.0436108 + 0.0436108i 0.728576 0.684965i \(-0.240183\pi\)
−0.684965 + 0.728576i \(0.740183\pi\)
\(152\) −8.72794 + 5.03908i −0.707929 + 0.408723i
\(153\) −10.8517 10.5248i −0.877310 0.850878i
\(154\) 8.46410 2.26795i 0.682057 0.182757i
\(155\) −5.24796 −0.421526
\(156\) 1.11159 + 1.25078i 0.0889985 + 0.100142i
\(157\) −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
\(159\) −1.33728 + 0.186470i −0.106053 + 0.0147880i
\(160\) 1.96410 1.13397i 0.155276 0.0896486i
\(161\) 0 0
\(162\) −9.28636 + 9.87256i −0.729605 + 0.775661i
\(163\) −1.07180 + 4.00000i −0.0839496 + 0.313304i −0.995113 0.0987406i \(-0.968519\pi\)
0.911164 + 0.412045i \(0.135185\pi\)
\(164\) 1.06488 1.06488i 0.0831533 0.0831533i
\(165\) 9.94624 + 4.03104i 0.774313 + 0.313816i
\(166\) −5.36603 3.09808i −0.416484 0.240457i
\(167\) 3.47998 + 12.9875i 0.269289 + 1.00500i 0.959573 + 0.281461i \(0.0908192\pi\)
−0.690283 + 0.723539i \(0.742514\pi\)
\(168\) 5.03908 3.92820i 0.388773 0.303067i
\(169\) 12.8923 1.66987i 0.991716 0.128452i
\(170\) 11.4284i 0.876516i
\(171\) 11.5898 0.177262i 0.886291 0.0135556i
\(172\) 0.294229 0.509619i 0.0224347 0.0388581i
\(173\) −8.72794 15.1172i −0.663573 1.14934i −0.979670 0.200615i \(-0.935706\pi\)
0.316097 0.948727i \(-0.397627\pi\)
\(174\) −2.29892 + 18.5575i −0.174281 + 1.40684i
\(175\) −3.73205 1.00000i −0.282117 0.0755929i
\(176\) 17.7412 + 4.75374i 1.33729 + 0.358327i
\(177\) 0.641364 5.17726i 0.0482078 0.389147i
\(178\) 7.02628 + 12.1699i 0.526642 + 0.912171i
\(179\) −13.2728 + 22.9892i −0.992056 + 1.71829i −0.387084 + 0.922045i \(0.626518\pi\)
−0.604972 + 0.796247i \(0.706816\pi\)
\(180\) −1.21043 + 0.0185132i −0.0902201 + 0.00137989i
\(181\) 3.00000i 0.222988i 0.993765 + 0.111494i \(0.0355636\pi\)
−0.993765 + 0.111494i \(0.964436\pi\)
\(182\) 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
\(186\) 8.42417 + 3.41417i 0.617690 + 0.250339i
\(187\) 14.6603 14.6603i 1.07206 1.07206i
\(188\) −0.417759 + 1.55910i −0.0304682 + 0.113709i
\(189\) −7.26168 + 1.12603i −0.528210 + 0.0819070i
\(190\) 6.19615 + 6.19615i 0.449516 + 0.449516i
\(191\) 4.18307 2.41510i 0.302677 0.174750i −0.340968 0.940075i \(-0.610755\pi\)
0.643645 + 0.765324i \(0.277421\pi\)
\(192\) 11.4254 1.59315i 0.824554 0.114976i
\(193\) 0.133975 0.0358984i 0.00964370 0.00258402i −0.253994 0.967206i \(-0.581744\pi\)
0.263638 + 0.964622i \(0.415078\pi\)
\(194\) −2.54752 −0.182902
\(195\) −5.17329 + 7.85411i −0.370467 + 0.562445i
\(196\) 1.33975 0.0956961
\(197\) −3.97420 + 1.06488i −0.283150 + 0.0758697i −0.397599 0.917559i \(-0.630156\pi\)
0.114449 + 0.993429i \(0.463490\pi\)
\(198\) −13.3435 12.9415i −0.948281 0.919711i
\(199\) 11.1962 6.46410i 0.793674 0.458228i −0.0475802 0.998867i \(-0.515151\pi\)
0.841254 + 0.540639i \(0.181818\pi\)
\(200\) −5.03908 5.03908i −0.356317 0.356317i
\(201\) 9.46568 4.00588i 0.667657 0.282553i
\(202\) 2.34936 8.76795i 0.165301 0.616911i
\(203\) −7.16884 + 7.16884i −0.503154 + 0.503154i
\(204\) −0.878413 + 2.16741i −0.0615012 + 0.151749i
\(205\) 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
\(210\) −4.43306 3.34806i −0.305910 0.231038i
\(211\) 0.901924 1.56218i 0.0620910 0.107545i −0.833309 0.552808i \(-0.813556\pi\)
0.895400 + 0.445263i \(0.146890\pi\)
\(212\) 0.104440 + 0.180895i 0.00717294 + 0.0124239i
\(213\) −5.17726 0.641364i −0.354740 0.0439455i
\(214\) −27.6603 7.41154i −1.89082 0.506643i
\(215\) 3.19465 + 0.856003i 0.217873 + 0.0583789i
\(216\) −12.6377 4.89819i −0.859887 0.333280i
\(217\) 2.46410 + 4.26795i 0.167274 + 0.289727i
\(218\) 14.0524 24.3394i 0.951745 1.64847i
\(219\) 1.33147 1.76295i 0.0899722 0.119129i
\(220\) 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 0.705011 + 0.709196i \(0.250942\pi\)
−0.255960 + 0.966687i \(0.582391\pi\)
\(224\) −1.84443 1.06488i −0.123236 0.0711505i
\(225\) 2.24214 + 7.88351i 0.149476 + 0.525567i
\(226\) 10.9545 10.9545i 0.728681 0.728681i
\(227\) 5.24796 19.5856i 0.348319 1.29994i −0.540367 0.841429i \(-0.681715\pi\)
0.888686 0.458515i \(-0.151619\pi\)
\(228\) −0.698857 1.65136i −0.0462829 0.109364i
\(229\) −14.1244 14.1244i −0.933364 0.933364i 0.0645507 0.997914i \(-0.479439\pi\)
−0.997914 + 0.0645507i \(0.979439\pi\)
\(230\) 0 0
\(231\) −1.39183 9.98158i −0.0915757 0.656740i
\(232\) −18.0622 + 4.83975i −1.18584 + 0.317745i
\(233\) 17.4559 1.14357 0.571786 0.820403i \(-0.306251\pi\)
0.571786 + 0.820403i \(0.306251\pi\)
\(234\) 13.4140 9.24205i 0.876899 0.604172i
\(235\) −9.07180 −0.591779
\(236\) −0.779548 + 0.208879i −0.0507443 + 0.0135969i
\(237\) 0.478405 + 3.43091i 0.0310757 + 0.222861i
\(238\) −9.29423 + 5.36603i −0.602455 + 0.347828i
\(239\) 6.59817 + 6.59817i 0.426800 + 0.426800i 0.887537 0.460737i \(-0.152415\pi\)
−0.460737 + 0.887537i \(0.652415\pi\)
\(240\) −4.53819 10.7235i −0.292939 0.692198i
\(241\) 3.76795 14.0622i 0.242715 0.905825i −0.731803 0.681516i \(-0.761321\pi\)
0.974518 0.224309i \(-0.0720123\pi\)
\(242\) 6.31284 6.31284i 0.405805 0.405805i
\(243\) 9.95544 + 11.9954i 0.638642 + 0.769504i
\(244\) 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
\(249\) −4.29488 + 5.68671i −0.272177 + 0.360380i
\(250\) −8.76795 + 15.1865i −0.554534 + 0.960481i
\(251\) 0.494214 + 0.856003i 0.0311945 + 0.0540304i 0.881201 0.472741i \(-0.156736\pi\)
−0.850007 + 0.526772i \(0.823402\pi\)
\(252\) 0.583396 + 0.975700i 0.0367505 + 0.0614634i
\(253\) 0 0
\(254\) −13.2728 3.55644i −0.832810 0.223151i
\(255\) −13.0443 1.61594i −0.816867 0.101194i
\(256\) −3.16025 5.47372i −0.197516 0.342108i
\(257\) 10.7533 18.6252i 0.670770 1.16181i −0.306916 0.951737i \(-0.599297\pi\)
0.977686 0.210071i \(-0.0673696\pi\)
\(258\) −4.57125 3.45243i −0.284593 0.214939i
\(259\) 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 \(-0.574454\pi\)
−0.958331 + 0.285660i \(0.907787\pi\)
\(264\) 6.98197 17.2274i 0.429710 1.06027i
\(265\) −0.830127 + 0.830127i −0.0509943 + 0.0509943i
\(266\) 2.12976 7.94839i 0.130584 0.487347i
\(267\) 14.8842 6.29899i 0.910896 0.385492i
\(268\) −1.12436 1.12436i −0.0686810 0.0686810i
\(269\) −12.4168 + 7.16884i −0.757066 + 0.437092i −0.828241 0.560372i \(-0.810658\pi\)
0.0711756 + 0.997464i \(0.477325\pi\)
\(270\) −1.26979 + 11.7160i −0.0772769 + 0.713013i
\(271\) 7.46410 2.00000i 0.453412 0.121491i −0.0248835 0.999690i \(-0.507921\pi\)
0.478295 + 0.878199i \(0.341255\pi\)
\(272\) −22.4950 −1.36396
\(273\) 8.81647 + 0.519441i 0.533597 + 0.0314380i
\(274\) −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 0.438013 0.898969i \(-0.355682\pi\)
0.997536 + 0.0701536i \(0.0223490\pi\)
\(278\) 19.5856 + 19.5856i 1.17467 + 1.17467i
\(279\) 5.08808 9.13257i 0.304615 0.546752i
\(280\) 1.43782 5.36603i 0.0859263 0.320681i
\(281\) −12.1315 + 12.1315i −0.723703 + 0.723703i −0.969357 0.245655i \(-0.920997\pi\)
0.245655 + 0.969357i \(0.420997\pi\)
\(282\) 14.5623 + 5.90185i 0.867172 + 0.351450i
\(283\) −5.70577 3.29423i −0.339173 0.195822i 0.320733 0.947170i \(-0.396071\pi\)
−0.659906 + 0.751348i \(0.729404\pi\)
\(284\) 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
\(288\) 0.0690922 + 4.51739i 0.00407129 + 0.266189i
\(289\) −4.19615 + 7.26795i −0.246832 + 0.427526i
\(290\) 8.12929 + 14.0803i 0.477368 + 0.826826i
\(291\) −0.360213 + 2.90774i −0.0211161 + 0.170455i
\(292\) −0.330127 0.0884573i −0.0193192 0.00517657i
\(293\) −1.73999 0.466229i −0.101651 0.0272374i 0.207635 0.978206i \(-0.433423\pi\)
−0.309286 + 0.950969i \(0.600090\pi\)
\(294\) 1.60341 12.9432i 0.0935127 0.754860i
\(295\) −2.26795 3.92820i −0.132045 0.228709i
\(296\) −7.06440 + 12.2359i −0.410610 + 0.711198i
\(297\) −16.6581 + 13.4003i −0.966601 + 0.777567i
\(298\) 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
\(303\) −9.67552 3.92132i −0.555844 0.225274i
\(304\) 12.1962 12.1962i 0.699497 0.699497i
\(305\) −2.72842 + 10.1826i −0.156229 + 0.583054i
\(306\) 19.8878 + 11.0802i 1.13691 + 0.633414i
\(307\) 8.39230 + 8.39230i 0.478974 + 0.478974i 0.904803 0.425829i \(-0.140018\pi\)
−0.425829 + 0.904803i \(0.640018\pi\)
\(308\) −1.35022 + 0.779548i −0.0769357 + 0.0444189i
\(309\) −11.8850 + 1.65724i −0.676115 + 0.0942773i
\(310\) 7.63397 2.04552i 0.433581 0.116178i
\(311\) 10.0782 0.571480 0.285740 0.958307i \(-0.407761\pi\)
0.285740 + 0.958307i \(0.407761\pi\)
\(312\) 13.6037 + 8.96040i 0.770159 + 0.507283i
\(313\) 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
\(315\) −4.44829 + 4.58648i −0.250633 + 0.258419i
\(316\) 0.464102 0.267949i 0.0261078 0.0150733i
\(317\) −11.3519 11.3519i −0.637587 0.637587i 0.312373 0.949960i \(-0.398876\pi\)
−0.949960 + 0.312373i \(0.898876\pi\)
\(318\) 1.87260 0.792486i 0.105010 0.0444404i
\(319\) −7.63397 + 28.4904i −0.427421 + 1.59516i
\(320\) 7.09239 7.09239i 0.396477 0.396477i
\(321\) −12.3706 + 30.5234i −0.690460 + 1.70365i
\(322\) 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
\(327\) −25.7939 19.4808i −1.42641 1.07729i
\(328\) 7.33013 12.6962i 0.404739 0.701028i
\(329\) 4.25953 + 7.37772i 0.234835 + 0.406747i
\(330\) −16.0396 1.98699i −0.882948 0.109380i
\(331\) −33.0526 8.85641i −1.81673 0.486792i −0.820357 0.571852i \(-0.806225\pi\)
−0.996376 + 0.0850595i \(0.972892\pi\)
\(332\) 1.06488 + 0.285334i 0.0584430 + 0.0156598i
\(333\) 13.9469 8.33919i 0.764285 0.456985i
\(334\) −10.1244 17.5359i −0.553980 0.959522i
\(335\) 4.46841 7.73951i 0.244135 0.422855i
\(336\) −6.59014 + 8.72579i −0.359521 + 0.476031i
\(337\) 18.4641i 1.00580i −0.864344 0.502902i \(-0.832266\pi\)
0.864344 0.502902i \(-0.167734\pi\)
\(338\) −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
\(342\) −16.7900 + 4.77524i −0.907900 + 0.258215i
\(343\) 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 \(-0.480441\pi\)
0.895095 + 0.445876i \(0.147108\pi\)
\(348\) −0.459481 3.29519i −0.0246308 0.176641i
\(349\) 27.4904 7.36603i 1.47153 0.394294i 0.568072 0.822979i \(-0.307689\pi\)
0.903454 + 0.428684i \(0.141023\pi\)
\(350\) 5.81863 0.311019
\(351\) −8.65215 16.6175i −0.461818 0.886975i
\(352\) −6.19615 −0.330256
\(353\) 13.6626 3.66088i 0.727186 0.194849i 0.123810 0.992306i \(-0.460489\pi\)
0.603376 + 0.797457i \(0.293822\pi\)
\(354\) 1.08500 + 7.78112i 0.0576670 + 0.413562i
\(355\) −3.92820 + 2.26795i −0.208487 + 0.120370i
\(356\) −1.76798 1.76798i −0.0937025 0.0937025i
\(357\) 4.81059 + 11.3671i 0.254603 + 0.601613i
\(358\) 10.3468 38.6147i 0.546845 2.04085i
\(359\) 18.2354 18.2354i 0.962429 0.962429i −0.0368904 0.999319i \(-0.511745\pi\)
0.999319 + 0.0368904i \(0.0117452\pi\)
\(360\) −11.3351 + 3.22381i −0.597411 + 0.169909i
\(361\) −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
\(366\) 11.0042 14.5704i 0.575201 0.761605i
\(367\) −15.1962 + 26.3205i −0.793233 + 1.37392i 0.130723 + 0.991419i \(0.458270\pi\)
−0.923955 + 0.382500i \(0.875063\pi\)
\(368\) 0 0
\(369\) −14.4715 + 8.65286i −0.753356 + 0.450450i
\(370\) 11.8660 + 3.17949i 0.616885 + 0.165294i
\(371\) 1.06488 + 0.285334i 0.0552859 + 0.0148138i
\(372\) −1.60502 0.198831i −0.0832162 0.0103089i
\(373\) −5.79423 10.0359i −0.300014 0.519639i 0.676125 0.736787i \(-0.263658\pi\)
−0.976139 + 0.217148i \(0.930325\pi\)
\(374\) −15.6114 + 27.0398i −0.807249 + 1.39820i
\(375\) 16.0941 + 12.1550i 0.831096 + 0.627684i
\(376\) 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 0.991809 + 0.127726i \(0.0407679\pi\)
−0.795069 + 0.606519i \(0.792565\pi\)
\(380\) −1.35022 0.779548i −0.0692647 0.0399900i
\(381\) −5.93605 + 14.6467i −0.304113 + 0.750372i
\(382\) −5.14359 + 5.14359i −0.263169 + 0.263169i
\(383\) −8.51906 + 31.7936i −0.435304 + 1.62458i 0.305035 + 0.952341i \(0.401332\pi\)
−0.740339 + 0.672234i \(0.765335\pi\)
\(384\) −20.8033 + 8.80399i −1.06162 + 0.449277i
\(385\) −6.19615 6.19615i −0.315785 0.315785i
\(386\) −0.180895 + 0.104440i −0.00920730 + 0.00531584i
\(387\) −4.58695 + 4.72944i −0.233168 + 0.240411i
\(388\) 0.437822 0.117314i 0.0222271 0.00595572i
\(389\) 22.4950 1.14054 0.570270 0.821457i \(-0.306839\pi\)
0.570270 + 0.821457i \(0.306839\pi\)
\(390\) 4.46403 13.4415i 0.226045 0.680634i
\(391\) 0 0
\(392\) 12.5977 3.37554i 0.636280 0.170491i
\(393\) 13.6351 1.90128i 0.687800 0.0959066i
\(394\) 5.36603 3.09808i 0.270336 0.156079i
\(395\) 2.12976 + 2.12976i 0.107160 + 0.107160i
\(396\) 2.88920 + 1.60968i 0.145188 + 0.0808892i
\(397\) −3.56218 + 13.2942i −0.178781 + 0.667218i 0.817096 + 0.576501i \(0.195582\pi\)
−0.995877 + 0.0907168i \(0.971084\pi\)
\(398\) −13.7670 + 13.7670i −0.690078 + 0.690078i
\(399\) −8.77113 3.55479i −0.439106 0.177962i
\(400\) 10.5622 + 6.09808i 0.528109 + 0.304904i
\(401\) −3.22263 12.0270i −0.160931 0.600601i −0.998524 0.0543073i \(-0.982705\pi\)
0.837594 0.546294i \(-0.183962\pi\)
\(402\) −12.2079 + 9.51666i −0.608876 + 0.474648i
\(403\) −8.29423 + 9.43782i −0.413165 + 0.470131i
\(404\) 1.61507i 0.0803525i
\(405\) 13.1931 + 3.10594i 0.655569 + 0.154336i
\(406\) 7.63397 13.2224i 0.378868 0.656218i
\(407\) 11.1430 + 19.3003i 0.552340 + 0.956681i
\(408\) −2.79889 + 22.5934i −0.138566 + 1.11854i
\(409\) 28.9904 + 7.76795i 1.43348 + 0.384100i 0.890246 0.455480i \(-0.150532\pi\)
0.543236 + 0.839580i \(0.317199\pi\)
\(410\) −12.3124 3.29909i −0.608064 0.162930i
\(411\) −1.43156 + 11.5559i −0.0706135 + 0.570011i
\(412\) 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 \(-0.407937\pi\)
−0.687452 + 0.726230i \(0.741271\pi\)
\(420\) 0.916053 + 0.371261i 0.0446988 + 0.0181157i
\(421\) −7.83013 + 7.83013i −0.381617 + 0.381617i −0.871685 0.490067i \(-0.836972\pi\)
0.490067 + 0.871685i \(0.336972\pi\)
\(422\) −0.703093 + 2.62398i −0.0342260 + 0.127733i
\(423\) 8.79543 15.7869i 0.427648 0.767584i
\(424\) 1.43782 + 1.43782i 0.0698268 + 0.0698268i
\(425\) 11.9226 6.88351i 0.578330 0.333899i
\(426\) 7.78112 1.08500i 0.376997 0.0525683i
\(427\) 9.56218 2.56218i 0.462746 0.123992i
\(428\) 5.09505 0.246278
\(429\) 22.9691 11.5162i 1.10896 0.556007i
\(430\) −4.98076 −0.240194
\(431\) −36.5473 + 9.79282i −1.76042 + 0.471704i −0.986800 0.161944i \(-0.948224\pi\)
−0.773622 + 0.633648i \(0.781557\pi\)
\(432\) 23.0611 + 2.49938i 1.10953 + 0.120252i
\(433\) −26.8923 + 15.5263i −1.29236 + 0.746145i −0.979072 0.203512i \(-0.934764\pi\)
−0.313289 + 0.949658i \(0.601431\pi\)
\(434\) −5.24796 5.24796i −0.251910 0.251910i
\(435\) 17.2207 7.28782i 0.825670 0.349424i
\(436\) −1.29423 + 4.83013i −0.0619823 + 0.231321i
\(437\) 0 0
\(438\) −1.24967 + 3.08346i −0.0597117 + 0.147333i
\(439\) 1.09808 + 0.633975i 0.0524083 + 0.0302580i 0.525975 0.850500i \(-0.323700\pi\)
−0.473567 + 0.880758i \(0.657034\pi\)
\(440\) −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 \(0.914124\pi\)
\(444\) −2.00602 1.51505i −0.0952017 0.0719009i
\(445\) 7.02628 12.1699i 0.333078 0.576907i
\(446\) −19.5092 33.7909i −0.923787 1.60005i
\(447\) 14.8382 + 1.83816i 0.701821 + 0.0869422i
\(448\) −9.09808 2.43782i −0.429844 0.115176i
\(449\) −19.8710 5.32441i −0.937769 0.251275i −0.242605 0.970125i \(-0.578002\pi\)
−0.695165 + 0.718851i \(0.744669\pi\)
\(450\) −6.33434 10.5939i −0.298603 0.499400i
\(451\) −11.5622 20.0263i −0.544442 0.943001i
\(452\) −1.37820 + 2.38711i −0.0648251 + 0.112280i
\(453\) −0.791121 + 1.04750i −0.0371701 + 0.0492157i
\(454\) 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 0.938283 0.345868i \(-0.112416\pi\)
−0.985511 + 0.169611i \(0.945749\pi\)
\(458\) 26.0514 + 15.0408i 1.21730 + 0.702809i
\(459\) 15.4590 21.1332i 0.721565 0.986412i
\(460\) 0 0
\(461\) −5.50531 + 20.5461i −0.256408 + 0.956927i 0.710894 + 0.703299i \(0.248290\pi\)
−0.967302 + 0.253628i \(0.918376\pi\)
\(462\) 5.91520 + 13.9773i 0.275200 + 0.650282i
\(463\) 23.0526 + 23.0526i 1.07134 + 1.07134i 0.997251 + 0.0740918i \(0.0236058\pi\)
0.0740918 + 0.997251i \(0.476394\pi\)
\(464\) 27.7149 16.0012i 1.28663 0.742838i
\(465\) −1.25532 9.00263i −0.0582143 0.417487i
\(466\) −25.3923 + 6.80385i −1.17628 + 0.315182i
\(467\) −19.1679 −0.886984 −0.443492 0.896278i \(-0.646261\pi\)
−0.443492 + 0.896278i \(0.646261\pi\)
\(468\) −1.87975 + 2.20607i −0.0868916 + 0.101976i
\(469\) −8.39230 −0.387521
\(470\) 13.1963 3.53595i 0.608702 0.163101i
\(471\) −1.14909 8.24078i −0.0529474 0.379715i
\(472\) −6.80385 + 3.92820i −0.313172 + 0.180810i
\(473\) −6.38929 6.38929i −0.293780 0.293780i
\(474\) −2.03319 4.80432i −0.0933877 0.220670i
\(475\) −2.73205 + 10.1962i −0.125355 + 0.467832i
\(476\) 1.35022 1.35022i 0.0618871 0.0618871i
\(477\) −0.639761 2.24944i −0.0292926 0.102995i
\(478\) −12.1699 7.02628i −0.556637 0.321375i
\(479\) 5.32441 + 19.8710i 0.243279 + 0.907928i 0.974241 + 0.225510i \(0.0724049\pi\)
−0.730962 + 0.682418i \(0.760928\pi\)
\(480\) 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
\(486\) −19.1572 13.5688i −0.868990 0.615492i
\(487\) 5.56218 + 1.49038i 0.252046 + 0.0675356i 0.382630 0.923902i \(-0.375018\pi\)
−0.130584 + 0.991437i \(0.541685\pi\)
\(488\) 17.6368 + 4.72576i 0.798379 + 0.213925i
\(489\) −7.11819 0.881808i −0.321896 0.0398767i
\(490\) −5.66987 9.82051i −0.256139 0.443645i
\(491\) 14.2612 24.7012i 0.643600 1.11475i −0.341023 0.940055i \(-0.610773\pi\)
0.984623 0.174693i \(-0.0558934\pi\)
\(492\) 2.08148 + 1.57203i 0.0938403 + 0.0708728i
\(493\) 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
\(498\) 4.03104 9.94624i 0.180635 0.445702i
\(499\) −2.46410 + 2.46410i −0.110308 + 0.110308i −0.760107 0.649798i \(-0.774853\pi\)
0.649798 + 0.760107i \(0.274853\pi\)
\(500\) 0.807533 3.01375i 0.0361140 0.134779i
\(501\) −21.4470 + 9.07638i −0.958181 + 0.405503i
\(502\) −1.05256 1.05256i −0.0469780 0.0469780i
\(503\) −2.83286 + 1.63555i −0.126311 + 0.0729256i −0.561824 0.827257i \(-0.689900\pi\)
0.435513 + 0.900182i \(0.356567\pi\)
\(504\) 7.94401 + 7.70467i 0.353854 + 0.343193i
\(505\) −8.76795 + 2.34936i −0.390169 + 0.104545i
\(506\) 0 0
\(507\) 5.94846 + 21.7167i 0.264180 + 0.964473i
\(508\) 2.44486 0.108473
\(509\) 14.1568 3.79330i 0.627489 0.168135i 0.0689588 0.997620i \(-0.478032\pi\)
0.558530 + 0.829484i \(0.311366\pi\)
\(510\) 19.6048 2.73370i 0.868117 0.121050i
\(511\) −1.56218 + 0.901924i −0.0691067 + 0.0398988i
\(512\) −11.7137 11.7137i −0.517678 0.517678i
\(513\) 3.07638 + 19.8393i 0.135826 + 0.875926i
\(514\) −8.38269 + 31.2846i −0.369744 + 1.37990i
\(515\) −7.37772 + 7.37772i −0.325101 + 0.325101i
\(516\) 0.944608 + 0.382834i 0.0415841 + 0.0168533i
\(517\) 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 \(0.982618\pi\)
\(522\) −32.3844 + 0.495311i −1.41743 + 0.0216792i
\(523\) 19.4904 33.7583i 0.852255 1.47615i −0.0269137 0.999638i \(-0.508568\pi\)
0.879169 0.476511i \(-0.158099\pi\)
\(524\) −1.06488 1.84443i −0.0465196 0.0805743i
\(525\) 0.822738 6.64136i 0.0359072 0.289853i
\(526\) 32.4186 + 8.68653i 1.41352 + 0.378751i
\(527\) −16.9617 4.54486i −0.738862 0.197977i
\(528\) −3.91108 + 31.5713i −0.170208 + 1.37397i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0.883988 1.53111i 0.0383980 0.0665072i
\(531\) 9.03477 0.138184i 0.392076 0.00599669i
\(532\) 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
\(537\) −42.6117 17.2698i −1.83883 0.745247i
\(538\) 15.2679 15.2679i 0.658248 0.658248i
\(539\) 5.32441 19.8710i 0.229339 0.855904i
\(540\) −0.321296 2.07201i −0.0138264 0.0891650i
\(541\) −12.6865 12.6865i −0.545437 0.545437i 0.379681 0.925118i \(-0.376034\pi\)
−0.925118 + 0.379681i \(0.876034\pi\)
\(542\) −10.0782 + 5.81863i −0.432894 + 0.249931i
\(543\) −5.14636 + 0.717608i −0.220852 + 0.0307955i
\(544\) 7.33013 1.96410i 0.314277 0.0842102i
\(545\) −28.1047 −1.20387
\(546\) −13.0274 + 2.68082i −0.557521 + 0.114729i
\(547\) 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
\(549\) −15.0746 14.6204i −0.643368 0.623984i
\(550\) 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
\(555\) 5.30689 13.0943i 0.225265 0.555821i
\(556\) −4.26795 2.46410i −0.181001 0.104501i
\(557\) 6.62616 + 24.7292i 0.280759 + 1.04781i 0.951883 + 0.306462i \(0.0991454\pi\)
−0.671123 + 0.741346i \(0.734188\pi\)
\(558\) −3.84177 + 15.2679i −0.162635 + 0.646344i
\(559\) 6.58846 4.39230i 0.278662 0.185775i
\(560\) 9.50749i 0.401765i
\(561\) 28.6558 + 21.6422i 1.20985 + 0.913735i
\(562\) 12.9186 22.3756i 0.544938 0.943860i
\(563\) 5.03908 + 8.72794i 0.212372 + 0.367839i 0.952456 0.304675i \(-0.0985479\pi\)
−0.740085 + 0.672514i \(0.765215\pi\)
\(564\) −2.77449 0.343706i −0.116827 0.0144726i
\(565\) −14.9641 4.00962i −0.629544 0.168686i
\(566\) 9.58394 + 2.56801i 0.402843 + 0.107941i
\(567\) −3.66867 12.1877i −0.154070 0.511837i
\(568\) 3.92820 + 6.80385i 0.164824 + 0.285483i
\(569\) 1.35022 2.33864i 0.0566040 0.0980411i −0.836335 0.548219i \(-0.815306\pi\)
0.892939 + 0.450178i \(0.148639\pi\)
\(570\) −9.14708 + 12.1113i −0.383129 + 0.507289i
\(571\) 1.94744i 0.0814979i 0.999169 + 0.0407489i \(0.0129744\pi\)
−0.999169 + 0.0407489i \(0.987026\pi\)
\(572\) −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
\(576\) 5.46595 + 19.2186i 0.227748 + 0.800775i
\(577\) −22.4904 + 22.4904i −0.936287 + 0.936287i −0.998088 0.0618016i \(-0.980315\pi\)
0.0618016 + 0.998088i \(0.480315\pi\)
\(578\) 3.27110 12.2079i 0.136060 0.507783i
\(579\) 0.0936291 + 0.221240i 0.00389109 + 0.00919443i
\(580\) −2.04552 2.04552i −0.0849355 0.0849355i
\(581\) 5.03908 2.90931i 0.209056 0.120699i
\(582\) −0.609374 4.37016i −0.0252594 0.181149i
\(583\) 3.09808 0.830127i 0.128309 0.0343803i
\(584\) −3.32707 −0.137675
\(585\) −14.7108 6.99582i −0.608218 0.289241i
\(586\) 2.71281 0.112065
\(587\) 18.0265 4.83020i 0.744035 0.199364i 0.133164 0.991094i \(-0.457486\pi\)
0.610871 + 0.791730i \(0.290819\pi\)
\(588\) 0.320471 + 2.29827i 0.0132160 + 0.0947792i
\(589\) 11.6603 6.73205i 0.480452 0.277389i
\(590\) 4.83020 + 4.83020i 0.198856 + 0.198856i
\(591\) −2.77739 6.56283i −0.114247 0.269959i
\(592\) 6.25833 23.3564i 0.257216 0.959942i
\(593\) 10.3635 10.3635i 0.425578 0.425578i −0.461541 0.887119i \(-0.652703\pi\)
0.887119 + 0.461541i \(0.152703\pi\)
\(594\) 19.0087 25.9858i 0.779937 1.06621i
\(595\) 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 \(-0.139178\pi\)
\(600\) 7.43895 9.84967i 0.303694 0.402111i
\(601\) −11.7942 + 20.4282i −0.481097 + 0.833284i −0.999765 0.0216919i \(-0.993095\pi\)
0.518668 + 0.854976i \(0.326428\pi\)
\(602\) 2.33864 + 4.05065i 0.0953160 + 0.165092i
\(603\) 9.13612 + 15.2797i 0.372052 + 0.622238i
\(604\) 0.196152 + 0.0525589i 0.00798133 + 0.00213859i
\(605\) −8.62350 2.31066i −0.350595 0.0939417i
\(606\) 15.6030 + 1.93291i 0.633828 + 0.0785192i
\(607\) 0.0980762 + 0.169873i 0.00398079 + 0.00689493i 0.868009 0.496549i \(-0.165400\pi\)
−0.864028 + 0.503444i \(0.832066\pi\)
\(608\) −2.90931 + 5.03908i −0.117988 + 0.204362i
\(609\) −14.0126 10.5830i −0.567820 0.428845i
\(610\) 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 −0.677035 0.735951i \(-0.736735\pi\)
0.218354 0.975870i \(-0.429931\pi\)
\(614\) −15.4790 8.93682i −0.624683 0.360661i
\(615\) −5.50650 + 13.5868i −0.222044 + 0.547873i
\(616\) −10.7321 + 10.7321i −0.432407 + 0.432407i
\(617\) −4.78173 + 17.8457i −0.192505 + 0.718439i 0.800393 + 0.599475i \(0.204624\pi\)
−0.992899 + 0.118964i \(0.962043\pi\)
\(618\) 16.6427 7.04319i 0.669466 0.283319i
\(619\) −31.6603 31.6603i −1.27253 1.27253i −0.944755 0.327778i \(-0.893700\pi\)
−0.327778 0.944755i \(-0.606300\pi\)
\(620\) −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
\(624\) −26.4574 8.78674i −1.05914 0.351751i
\(625\) 3.87564 0.155026
\(626\) −2.90931 + 0.779548i −0.116280 + 0.0311570i
\(627\) −27.2702 + 3.80255i −1.08907 + 0.151859i
\(628\) −1.11474 + 0.643594i −0.0444828 + 0.0256822i
\(629\) −19.3003 19.3003i −0.769554 0.769554i
\(630\) 4.68305 8.40558i 0.186577 0.334886i
\(631\) 5.73205 21.3923i 0.228189 0.851614i −0.752912 0.658121i \(-0.771352\pi\)
0.981102 0.193493i \(-0.0619818\pi\)
\(632\) 3.68886 3.68886i 0.146735 0.146735i
\(633\) 2.89559 + 1.17353i 0.115089 + 0.0466437i
\(634\) 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
\(639\) −0.138184 9.03477i −0.00546649 0.357410i
\(640\) −9.82051 + 17.0096i −0.388190 + 0.672364i
\(641\) −22.6758 39.2757i −0.895642 1.55130i −0.833008 0.553261i \(-0.813383\pi\)
−0.0626345 0.998037i \(-0.519950\pi\)
\(642\) 6.09776 49.2228i 0.240659 1.94267i
\(643\) 7.00000 + 1.87564i 0.276053 + 0.0739682i 0.394190 0.919029i \(-0.371025\pi\)
−0.118136 + 0.992997i \(0.537692\pi\)
\(644\) 0 0
\(645\) −0.704266 + 5.68503i −0.0277305 + 0.223848i
\(646\) 14.6603 + 25.3923i 0.576800 + 0.999047i
\(647\) 8.23373 14.2612i 0.323701 0.560667i −0.657547 0.753413i \(-0.728406\pi\)
0.981249 + 0.192746i \(0.0617394\pi\)
\(648\) 5.37965 22.8511i 0.211333 0.897674i
\(649\) 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 \(-0.272802\pi\)
−0.327290 + 0.944924i \(0.606135\pi\)
\(654\) 45.1145 + 18.2841i 1.76411 + 0.714966i
\(655\) 8.46410 8.46410i 0.330720 0.330720i
\(656\) −6.49373 + 24.2349i −0.253538 + 0.946216i
\(657\) 3.34275 + 1.86237i 0.130413 + 0.0726578i
\(658\) −9.07180 9.07180i −0.353655 0.353655i
\(659\) −23.4834 + 13.5581i −0.914783 + 0.528150i −0.881967 0.471311i \(-0.843781\pi\)
−0.0328158 + 0.999461i \(0.510447\pi\)
\(660\) 2.84809 0.397137i 0.110862 0.0154585i
\(661\) 9.42820 2.52628i 0.366715 0.0982609i −0.0707559 0.997494i \(-0.522541\pi\)
0.437470 + 0.899233i \(0.355874\pi\)
\(662\) 51.5321 2.00285
\(663\) −23.5222 + 20.9047i −0.913526 + 0.811871i
\(664\) 10.7321 0.416484
\(665\) −7.94839 + 2.12976i −0.308225 + 0.0825887i
\(666\) −17.0375 + 17.5668i −0.660191 + 0.680699i
\(667\) 0 0
\(668\) 2.54752 + 2.54752i 0.0985666 + 0.0985666i
\(669\) −41.3274 + 17.4898i −1.59781 + 0.676194i
\(670\) −3.48334 + 13.0000i −0.134573 + 0.502234i
\(671\) 20.3652 20.3652i 0.786189 0.786189i
\(672\) 1.38556 3.41876i 0.0534493 0.131881i
\(673\) −36.9904 21.3564i −1.42587 0.823229i −0.429082 0.903265i \(-0.641163\pi\)
−0.996792 + 0.0800364i \(0.974496\pi\)
\(674\) 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 \(-0.0594357\pi\)
\(678\) 21.4123 + 16.1716i 0.822333 + 0.621065i
\(679\) 1.19615 2.07180i 0.0459041 0.0795083i
\(680\) 9.89726 + 17.1426i 0.379543 + 0.657387i
\(681\) 34.8536 + 4.31769i 1.33559 + 0.165454i
\(682\) −20.8564 5.58846i −0.798633 0.213993i
\(683\) 45.2752 + 12.1315i 1.73241 + 0.464198i 0.980736 0.195338i \(-0.0625804\pi\)
0.751673 + 0.659536i \(0.229247\pi\)
\(684\) 2.66566 1.59387i 0.101924 0.0609430i
\(685\) 5.06218 + 8.76795i 0.193416 + 0.335006i
\(686\) −12.7786 + 22.1332i −0.487889 + 0.845048i
\(687\) 20.8511 27.6083i 0.795519 1.05332i
\(688\) 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 0.994470 + 0.105025i \(0.0334922\pi\)
−0.808723 + 0.588189i \(0.799841\pi\)
\(692\) −4.05065 2.33864i −0.153983 0.0889019i
\(693\) 16.7900 4.77524i 0.637800 0.181396i
\(694\) −21.9090 + 21.9090i −0.831653 + 0.831653i
\(695\) 7.16884 26.7545i 0.271930 1.01486i
\(696\) −12.6229 29.8272i −0.478469 1.13060i
\(697\) 20.0263 + 20.0263i 0.758549 + 0.758549i
\(698\) −37.1180 + 21.4301i −1.40494 + 0.811140i
\(699\) 4.17549 + 29.9448i 0.157932 + 1.13261i
\(700\) −1.00000 + 0.267949i −0.0377964 + 0.0101275i
\(701\) 12.7786 0.482641 0.241320 0.970446i \(-0.422420\pi\)
0.241320 + 0.970446i \(0.422420\pi\)
\(702\) 19.0630 + 20.8003i 0.719485 + 0.785058i
\(703\) 20.9282 0.789322
\(704\) −26.4692 + 7.09239i −0.997594 + 0.267304i
\(705\) −2.17000 15.5622i −0.0817268 0.586108i
\(706\) −18.4474 + 10.6506i −0.694279 + 0.400842i
\(707\) 6.02751 + 6.02751i 0.226688 + 0.226688i
\(708\) −0.544793 1.28731i −0.0204746 0.0483802i
\(709\) −3.03590 + 11.3301i −0.114016 + 0.425512i −0.999211 0.0397068i \(-0.987358\pi\)
0.885196 + 0.465219i \(0.154024\pi\)
\(710\) 4.83020 4.83020i 0.181274 0.181274i
\(711\) −5.77113 + 1.64136i −0.216434 + 0.0615559i
\(712\) −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
\(717\) −9.74056 + 12.8972i −0.363768 + 0.481653i
\(718\) −19.4186 + 33.6340i −0.724695 + 1.25521i
\(719\) 3.68886 + 6.38929i 0.137571 + 0.238280i 0.926577 0.376106i \(-0.122737\pi\)
−0.789005 + 0.614386i \(0.789404\pi\)
\(720\) 17.3101 10.3501i 0.645110 0.385727i
\(721\) 9.46410 + 2.53590i 0.352462 + 0.0944418i
\(722\) 5.92307 + 1.58708i 0.220434 + 0.0590650i
\(723\) 25.0243 + 3.10003i 0.930665 + 0.115292i
\(724\) 0.401924 + 0.696152i 0.0149374 + 0.0258723i
\(725\) −9.79282 + 16.9617i −0.363696 + 0.629940i
\(726\) 12.3394 + 9.31934i 0.457959 + 0.345873i
\(727\) 19.5167i 0.723833i −0.932211 0.361916i \(-0.882123\pi\)
0.932211 0.361916i \(-0.117877\pi\)
\(728\) −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
\(732\) −1.22024 + 3.01084i −0.0451014 + 0.111284i
\(733\) −6.77757 + 6.77757i −0.250335 + 0.250335i −0.821108 0.570773i \(-0.806644\pi\)
0.570773 + 0.821108i \(0.306644\pi\)
\(734\) 11.8461 44.2104i 0.437249 1.63183i
\(735\) −12.0108 + 5.08298i −0.443025 + 0.187489i
\(736\) 0 0
\(737\) −21.1447 + 12.2079i −0.778876 + 0.449685i
\(738\) 17.6784 18.2276i 0.650750 0.670966i
\(739\) −11.1244 + 2.98076i −0.409216 + 0.109649i −0.457554 0.889182i \(-0.651274\pi\)
0.0483378 + 0.998831i \(0.484608\pi\)
\(740\) −2.18573 −0.0803492
\(741\) 1.41914 24.0870i 0.0521334 0.884860i
\(742\) −1.66025 −0.0609498
\(743\) −8.51906 + 2.28268i −0.312534 + 0.0837432i −0.411677 0.911330i \(-0.635057\pi\)
0.0991426 + 0.995073i \(0.468390\pi\)
\(744\) −15.5930 + 2.17429i −0.571667 + 0.0797132i
\(745\) 11.2583 6.50000i 0.412473 0.238142i
\(746\) 12.3403 + 12.3403i 0.451812 + 0.451812i
\(747\) −10.7826 6.00739i −0.394516 0.219799i
\(748\) 1.43782 5.36603i 0.0525720 0.196201i
\(749\) 19.0150 19.0150i 0.694792 0.694792i
\(750\) −28.1491 11.4084i −1.02786 0.416574i
\(751\) −29.2750 16.9019i −1.06826 0.616760i −0.140554 0.990073i \(-0.544888\pi\)
−0.927705 + 0.373313i \(0.878222\pi\)
\(752\) −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
\(756\) −1.53422 + 1.23418i −0.0557990 + 0.0448866i
\(757\) −8.39230 + 14.5359i −0.305024 + 0.528316i −0.977267 0.212014i \(-0.931998\pi\)
0.672243 + 0.740331i \(0.265331\pi\)
\(758\) −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 \(-0.308639\pi\)
0.0775029 + 0.996992i \(0.475305\pi\)
\(762\) 2.92602 23.6196i 0.105998 0.855647i
\(763\) 13.1962 + 22.8564i 0.477733 + 0.827457i
\(764\) 0.647124 1.12085i 0.0234121 0.0405510i
\(765\) −0.348161 22.7635i −0.0125878 0.823014i
\(766\) 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 −0.829238 0.558895i \(-0.811225\pi\)
0.438694 0.898636i \(-0.355441\pi\)
\(770\) 11.4284 + 6.59817i 0.411850 + 0.237782i
\(771\) 34.5229 + 13.9915i 1.24331 + 0.503893i
\(772\) 0.0262794 0.0262794i 0.000945818 0.000945818i
\(773\) 11.1430 41.5864i 0.400787 1.49576i −0.410908 0.911677i \(-0.634788\pi\)
0.811695 0.584081i \(-0.198545\pi\)
\(774\) 4.82903 8.66759i 0.173576 0.311550i
\(775\) 6.73205 + 6.73205i 0.241822 + 0.241822i
\(776\) 3.82129 2.20622i 0.137176 0.0791987i
\(777\) −13.1408 + 1.83235i −0.471424 + 0.0657353i
\(778\) −32.7224 + 8.76795i −1.17316 + 0.314346i
\(779\) −21.7154 −0.778035
\(780\) −0.148214 + 2.51564i −0.00530693 + 0.0900745i
\(781\) 12.3923 0.443432
\(782\) 0 0
\(783\) −4.01372 + 37.0335i −0.143439 + 1.32347i
\(784\) −19.3301 + 11.1603i −0.690362 + 0.398581i
\(785\) −5.11553 5.11553i −0.182581 0.182581i
\(786\) −19.0933 + 8.08031i −0.681036 + 0.288215i
\(787\) 4.29423 16.0263i 0.153073 0.571275i −0.846190 0.532881i \(-0.821109\pi\)
0.999263 0.0383938i \(-0.0122241\pi\)
\(788\) −0.779548 + 0.779548i −0.0277702 + 0.0277702i
\(789\) 14.4987 35.7742i 0.516167 1.27360i
\(790\) −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
\(795\) −1.62261 1.22548i −0.0575482 0.0434632i
\(796\) 1.73205 3.00000i 0.0613909 0.106332i
\(797\) 20.1563 + 34.9118i 0.713973 + 1.23664i 0.963354 + 0.268232i \(0.0864395\pi\)
−0.249381 + 0.968405i \(0.580227\pi\)
\(798\) 14.1445 + 1.75224i 0.500711 + 0.0620286i
\(799\) −29.3205 7.85641i −1.03729 0.277940i
\(800\) −3.97420 1.06488i −0.140509 0.0376493i
\(801\) 14.3660 + 24.0264i 0.507596 + 0.848929i
\(802\) 9.37564 + 16.2391i 0.331066 + 0.573422i
\(803\) −2.62398 + 4.54486i −0.0925982 + 0.160385i
\(804\) 1.65983 2.19773i 0.0585377 0.0775079i
\(805\) 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 \(-0.171171\pi\)
−0.0141514 + 0.999900i \(0.504505\pi\)
\(810\) −20.4020 + 0.624232i −0.716853 + 0.0219333i
\(811\) 19.0000 19.0000i 0.667180 0.667180i −0.289882 0.957062i \(-0.593616\pi\)
0.957062 + 0.289882i \(0.0936161\pi\)
\(812\) −0.703093 + 2.62398i −0.0246737 + 0.0920836i
\(813\) 5.21634 + 12.3259i 0.182945 + 0.432289i
\(814\) −23.7321 23.7321i −0.831808 0.831808i
\(815\) −5.40087 + 3.11819i −0.189184 + 0.109226i
\(816\) −5.38085 38.5891i −0.188367 1.35089i
\(817\) −8.19615 + 2.19615i −0.286747 + 0.0768336i
\(818\) −45.1988 −1.58034
\(819\) 1.21785 + 15.2485i 0.0425549 + 0.532826i
\(820\) 2.26795 0.0792002
\(821\) −41.5864 + 11.1430i −1.45137 + 0.388895i −0.896502 0.443040i \(-0.853900\pi\)
−0.554873 + 0.831935i \(0.687233\pi\)
\(822\) −2.42177 17.3679i −0.0844690 0.605774i
\(823\) −7.39230 + 4.26795i −0.257680 + 0.148771i −0.623276 0.782002i \(-0.714199\pi\)
0.365596 + 0.930774i \(0.380865\pi\)
\(824\) 12.7786 + 12.7786i 0.445163 + 0.445163i
\(825\) −7.58798 17.9300i −0.264180 0.624242i
\(826\) 1.66025 6.19615i 0.0577676 0.215592i
\(827\) −31.7936 + 31.7936i −1.10557 + 1.10557i −0.111845 + 0.993726i \(0.535676\pi\)
−0.993726 + 0.111845i \(0.964324\pi\)
\(828\) 0 0
\(829\) 41.6769 + 24.0622i 1.44750 + 0.835714i 0.998332 0.0577338i \(-0.0183875\pi\)
0.449167 + 0.893448i \(0.351721\pi\)
\(830\) −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
\(834\) −28.9133 + 38.2832i −1.00119 + 1.32564i
\(835\) −10.1244 + 17.5359i −0.350368 + 0.606855i
\(836\) 2.12976 + 3.68886i 0.0736595 + 0.127582i
\(837\) 16.8836 + 6.54383i 0.583582 + 0.226188i
\(838\) 13.8301 + 3.70577i 0.477754 + 0.128014i
\(839\) −9.79282 2.62398i −0.338086 0.0905898i 0.0857819 0.996314i \(-0.472661\pi\)
−0.423868 + 0.905724i \(0.639328\pi\)
\(840\) 9.54910 + 1.18295i 0.329475 + 0.0408157i
\(841\) 11.1962 + 19.3923i 0.386074 + 0.668700i
\(842\) 8.33816 14.4421i 0.287352 0.497708i
\(843\) −23.7128 17.9091i −0.816714 0.616822i
\(844\) 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
\(849\) 4.28626 10.5760i 0.147104 0.362967i
\(850\) −14.6603 + 14.6603i −0.502843 + 0.502843i
\(851\) 0 0
\(852\) −1.28731 + 0.544793i −0.0441027 + 0.0186643i
\(853\) −22.3660 22.3660i −0.765798 0.765798i 0.211566 0.977364i \(-0.432144\pi\)
−0.977364 + 0.211566i \(0.932144\pi\)
\(854\) −12.9110 + 7.45418i −0.441806 + 0.255077i
\(855\) 12.5305 + 12.1530i 0.428534 + 0.415623i
\(856\) 47.9090 12.8372i 1.63749 0.438765i
\(857\) 3.32707 0.113651 0.0568253 0.998384i \(-0.481902\pi\)
0.0568253 + 0.998384i \(0.481902\pi\)
\(858\) −28.9234 + 25.7048i −0.987428 + 0.877549i
\(859\) 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
\(861\) 13.6351 1.90128i 0.464683 0.0647953i
\(862\) 49.3468 28.4904i 1.68076 0.970386i
\(863\) −18.2354 18.2354i −0.620741 0.620741i 0.324980 0.945721i \(-0.394642\pi\)
−0.945721 + 0.324980i \(0.894642\pi\)
\(864\) −7.73284 + 1.19909i −0.263077 + 0.0407940i
\(865\) 6.80385 25.3923i 0.231338 0.863364i
\(866\) 33.0673 33.0673i 1.12367 1.12367i
\(867\) −13.4716 5.45979i −0.457518 0.185424i
\(868\) 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
\(873\) −5.07425 + 0.0776093i −0.171737 + 0.00262668i
\(874\) 0 0
\(875\) −8.23373 14.2612i −0.278351 0.482118i
\(876\) 0.0727771 0.587477i 0.00245891 0.0198490i
\(877\) 28.9904 + 7.76795i 0.978936 + 0.262305i 0.712596 0.701574i \(-0.247519\pi\)
0.266339 + 0.963879i \(0.414186\pi\)
\(878\) −1.84443 0.494214i −0.0622465 0.0166789i
\(879\) 0.383584 3.09640i 0.0129380 0.104439i
\(880\) 13.8301 + 23.9545i 0.466213 + 0.807505i
\(881\) 11.7417 20.3372i 0.395588 0.685178i −0.597588 0.801803i \(-0.703874\pi\)
0.993176 + 0.116625i \(0.0372076\pi\)
\(882\) 22.5869 0.345461i 0.760541 0.0116323i
\(883\) 33.3731i 1.12309i 0.827445 + 0.561547i \(0.189793\pi\)
−0.827445 + 0.561547i \(0.810207\pi\)
\(884\) 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 \(-0.472683\pi\)
−0.819981 + 0.572391i \(0.806016\pi\)
\(888\) −22.6800 9.19180i −0.761089 0.308457i
\(889\) 9.12436 9.12436i 0.306021 0.306021i
\(890\) −5.47732 + 20.4416i −0.183600 + 0.685206i
\(891\) −26.9723 25.3708i −0.903607 0.849954i
\(892\) 4.90897 + 4.90897i 0.164364 + 0.164364i
\(893\) 20.1563 11.6373i 0.674505 0.389426i
\(894\) −22.3009 + 3.10963i −0.745854 + 0.104002i
\(895\) −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
\(900\) 1.57648 + 1.52898i 0.0525494 + 0.0509661i
\(901\) −3.40192 + 1.96410i −0.113335 + 0.0654337i
\(902\) 24.6247 + 24.6247i 0.819913 + 0.819913i
\(903\) 4.95408 2.09657i 0.164861 0.0697695i
\(904\) −6.94486 + 25.9186i −0.230983 + 0.862039i
\(905\) −3.19465 + 3.19465i −0.106194 + 0.106194i
\(906\) 0.742522 1.83211i 0.0246686 0.0608677i
\(907\) −15.0000 8.66025i −0.498067 0.287559i 0.229848 0.973227i \(-0.426177\pi\)
−0.727915 + 0.685668i \(0.759510\pi\)
\(908\) −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 \(-0.00822209\pi\)
\(912\) 23.8393 + 18.0046i 0.789398 + 0.596191i
\(913\) 8.46410 14.6603i 0.280121 0.485184i
\(914\) 2.93730 + 5.08755i 0.0971572 + 0.168281i
\(915\) −18.1204 2.24477i −0.599043 0.0742099i
\(916\) −5.16987 1.38526i −0.170817 0.0457704i
\(917\) −10.8577 2.90931i −0.358553 0.0960740i
\(918\) −14.2504 + 36.7670i −0.470333 + 1.21349i
\(919\) −6.70577 11.6147i −0.221203 0.383135i 0.733971 0.679181i \(-0.237665\pi\)
−0.955174 + 0.296046i \(0.904332\pi\)
\(920\) 0 0
\(921\) −12.3892 + 16.4041i −0.408236 + 0.540533i
\(922\) 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
\(927\) −5.68585 19.9918i −0.186748 0.656616i
\(928\) −7.63397 + 7.63397i −0.250597 + 0.250597i
\(929\) −5.27594 + 19.6901i −0.173098 + 0.646011i 0.823770 + 0.566924i \(0.191867\pi\)
−0.996868 + 0.0790861i \(0.974800\pi\)
\(930\) 5.33506 + 12.6064i 0.174943 + 0.413381i
\(931\) −13.6603 13.6603i −0.447697 0.447697i
\(932\) 4.05065 2.33864i 0.132683 0.0766048i
\(933\) 2.41072 + 17.2886i 0.0789234 + 0.566004i
\(934\) 27.8827 7.47114i 0.912349 0.244463i
\(935\) 31.2229 1.02110
\(936\) −12.1171 + 25.4799i −0.396060 + 0.832837i
\(937\) −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
\(939\) 0.478405 + 3.43091i 0.0156122 + 0.111963i
\(940\) −2.10512 + 1.21539i −0.0686614 + 0.0396417i
\(941\) −9.14570 9.14570i −0.298141 0.298141i 0.542144 0.840285i \(-0.317613\pi\)
−0.840285 + 0.542144i \(0.817613\pi\)
\(942\) 4.88358 + 11.5396i 0.159116 + 0.375981i
\(943\) 0 0
\(944\) 9.50749 9.50749i 0.309442 0.309442i
\(945\) −8.93193 6.53374i −0.290556 0.212543i
\(946\) 11.7846 + 6.80385i 0.383151 + 0.221212i
\(947\) −2.77689 10.3635i −0.0902368 0.336768i 0.906018 0.423240i \(-0.139107\pi\)
−0.996254 + 0.0864720i \(0.972441\pi\)
\(948\) 0.570669 + 0.732051i 0.0185345 + 0.0237759i
\(949\) −3.45448 3.03590i −0.112137 0.0985494i
\(950\) 15.8968i 0.515760i
\(951\) 16.7583 22.1891i 0.543425 0.719531i
\(952\) 9.29423 16.0981i 0.301228 0.521742i
\(953\) −0.988427 1.71201i −0.0320183 0.0554573i 0.849572 0.527472i \(-0.176860\pi\)
−0.881591 + 0.472015i \(0.843527\pi\)
\(954\) 1.80740 + 3.02279i 0.0585169 + 0.0978666i
\(955\) 7.02628 + 1.88269i 0.227365 + 0.0609223i
\(956\) 2.41510 + 0.647124i 0.0781099 + 0.0209295i
\(957\) −50.7000 6.28076i −1.63890 0.203028i
\(958\) −15.4904 26.8301i −0.500471 0.866842i
\(959\) 4.75374 8.23373i 0.153506 0.265881i
\(960\) 13.8632 + 10.4701i 0.447432 + 0.337923i
\(961\) 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 −0.995062 0.0992599i \(-0.968352\pi\)
0.0992599 + 0.995062i \(0.468352\pi\)
\(968\) −4.00218 + 14.9363i −0.128635 + 0.480072i
\(969\) 31.0556 13.1428i 0.997651 0.422207i
\(970\) −2.71281 2.71281i −0.0871032 0.0871032i
\(971\) 41.4335 23.9216i 1.32966 0.767682i 0.344416 0.938817i \(-0.388077\pi\)
0.985247 + 0.171136i \(0.0547436\pi\)
\(972\) 3.91725 + 1.44976i 0.125646 + 0.0465011i
\(973\) −25.1244 + 6.73205i −0.805450 + 0.215820i
\(974\) −8.67197 −0.277868
\(975\) 16.7115 3.43895i 0.535196 0.110134i
\(976\) −31.2487 −1.00025
\(977\) 22.8847 6.13194i 0.732147 0.196178i 0.126562 0.991959i \(-0.459606\pi\)
0.605585 + 0.795780i \(0.292939\pi\)
\(978\) 10.6982 1.49176i 0.342092 0.0477012i
\(979\) −33.2487 + 19.1962i −1.06263 + 0.613512i
\(980\) 1.42667 + 1.42667i 0.0455734 + 0.0455734i
\(981\) 27.2485 48.9082i 0.869978 1.56152i
\(982\) −11.1173 + 41.4904i −0.354768 + 1.32401i
\(983\) −30.4433 + 30.4433i −0.970992 + 0.970992i −0.999591 0.0285990i \(-0.990895\pi\)
0.0285990 + 0.999591i \(0.490895\pi\)
\(984\) 23.5330 + 9.53754i 0.750206 + 0.304046i
\(985\) −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
\(990\) −0.428106 27.9904i −0.0136061 0.889594i
\(991\) 28.7846 49.8564i 0.914373 1.58374i 0.106557 0.994307i \(-0.466017\pi\)
0.807816 0.589434i \(-0.200649\pi\)
\(992\) 2.62398 + 4.54486i 0.0833114 + 0.144300i
\(993\) 7.28650 58.8186i 0.231230 1.86655i
\(994\) −6.19615 1.66025i −0.196530 0.0526601i
\(995\) 18.8061 + 5.03908i 0.596193 + 0.159750i
\(996\) −0.234755 + 1.89501i −0.00743851 + 0.0600457i
\(997\) 3.50000 + 6.06218i 0.110846 + 0.191991i 0.916112 0.400923i \(-0.131311\pi\)
−0.805266 + 0.592914i \(0.797977\pi\)
\(998\) 2.62398 4.54486i 0.0830606 0.143865i
\(999\) 17.6416 + 21.9305i 0.558156 + 0.693850i
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.32.1 yes 8
3.2 odd 2 inner 39.2.k.b.32.2 yes 8
4.3 odd 2 624.2.cn.c.305.1 8
5.2 odd 4 975.2.bp.f.149.1 8
5.3 odd 4 975.2.bp.e.149.2 8
5.4 even 2 975.2.bo.d.851.2 8
12.11 even 2 624.2.cn.c.305.2 8
13.2 odd 12 507.2.k.d.89.1 8
13.3 even 3 507.2.k.e.80.2 8
13.4 even 6 507.2.f.e.239.2 8
13.5 odd 4 507.2.k.f.488.2 8
13.6 odd 12 507.2.f.e.437.3 8
13.7 odd 12 507.2.f.f.437.2 8
13.8 odd 4 507.2.k.e.488.1 8
13.9 even 3 507.2.f.f.239.3 8
13.10 even 6 507.2.k.f.80.1 8
13.11 odd 12 inner 39.2.k.b.11.2 yes 8
13.12 even 2 507.2.k.d.188.2 8
15.2 even 4 975.2.bp.f.149.2 8
15.8 even 4 975.2.bp.e.149.1 8
15.14 odd 2 975.2.bo.d.851.1 8
39.2 even 12 507.2.k.d.89.2 8
39.5 even 4 507.2.k.f.488.1 8
39.8 even 4 507.2.k.e.488.2 8
39.11 even 12 inner 39.2.k.b.11.1 8
39.17 odd 6 507.2.f.e.239.3 8
39.20 even 12 507.2.f.f.437.3 8
39.23 odd 6 507.2.k.f.80.2 8
39.29 odd 6 507.2.k.e.80.1 8
39.32 even 12 507.2.f.e.437.2 8
39.35 odd 6 507.2.f.f.239.2 8
39.38 odd 2 507.2.k.d.188.1 8
52.11 even 12 624.2.cn.c.401.2 8
65.24 odd 12 975.2.bo.d.401.1 8
65.37 even 12 975.2.bp.e.674.1 8
65.63 even 12 975.2.bp.f.674.2 8
156.11 odd 12 624.2.cn.c.401.1 8
195.89 even 12 975.2.bo.d.401.2 8
195.128 odd 12 975.2.bp.f.674.1 8
195.167 odd 12 975.2.bp.e.674.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.k.b.11.1 8 39.11 even 12 inner
39.2.k.b.11.2 yes 8 13.11 odd 12 inner
39.2.k.b.32.1 yes 8 1.1 even 1 trivial
39.2.k.b.32.2 yes 8 3.2 odd 2 inner
507.2.f.e.239.2 8 13.4 even 6
507.2.f.e.239.3 8 39.17 odd 6
507.2.f.e.437.2 8 39.32 even 12
507.2.f.e.437.3 8 13.6 odd 12
507.2.f.f.239.2 8 39.35 odd 6
507.2.f.f.239.3 8 13.9 even 3
507.2.f.f.437.2 8 13.7 odd 12
507.2.f.f.437.3 8 39.20 even 12
507.2.k.d.89.1 8 13.2 odd 12
507.2.k.d.89.2 8 39.2 even 12
507.2.k.d.188.1 8 39.38 odd 2
507.2.k.d.188.2 8 13.12 even 2
507.2.k.e.80.1 8 39.29 odd 6
507.2.k.e.80.2 8 13.3 even 3
507.2.k.e.488.1 8 13.8 odd 4
507.2.k.e.488.2 8 39.8 even 4
507.2.k.f.80.1 8 13.10 even 6
507.2.k.f.80.2 8 39.23 odd 6
507.2.k.f.488.1 8 39.5 even 4
507.2.k.f.488.2 8 13.5 odd 4
624.2.cn.c.305.1 8 4.3 odd 2
624.2.cn.c.305.2 8 12.11 even 2
624.2.cn.c.401.1 8 156.11 odd 12
624.2.cn.c.401.2 8 52.11 even 12
975.2.bo.d.401.1 8 65.24 odd 12
975.2.bo.d.401.2 8 195.89 even 12
975.2.bo.d.851.1 8 15.14 odd 2
975.2.bo.d.851.2 8 5.4 even 2
975.2.bp.e.149.1 8 15.8 even 4
975.2.bp.e.149.2 8 5.3 odd 4
975.2.bp.e.674.1 8 65.37 even 12
975.2.bp.e.674.2 8 195.167 odd 12
975.2.bp.f.149.1 8 5.2 odd 4
975.2.bp.f.149.2 8 15.2 even 4
975.2.bp.f.674.1 8 195.128 odd 12
975.2.bp.f.674.2 8 65.63 even 12