Properties

Label 507.2.k.d.89.2
Level $507$
Weight $2$
Character 507.89
Analytic conductor $4.048$
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] = [507,2,Mod(80,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, 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("507.80");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.k (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.04841538248\)
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: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 89.2
Root \(0.500000 + 0.564882i\) of defining polynomial
Character \(\chi\) \(=\) 507.89
Dual form 507.2.k.d.188.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.45466 + 0.389774i) q^{2} +(0.239203 - 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(-1.06488 + 1.06488i) q^{5} +(1.01660 - 2.40216i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})\) \(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} -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} +(-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} +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} -0.779548i 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} +(-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} +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} +(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 \( 8 q - 2 q^{3} - 12 q^{4} + 2 q^{6} + 4 q^{7} + 4 q^{9} + 12 q^{10} + 14 q^{15} - 4 q^{16} - 4 q^{18} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 18 q^{24} + 4 q^{27} - 20 q^{28} + 18 q^{30} - 8 q^{31} - 16 q^{33} + 36 q^{34} - 36 q^{36} + 28 q^{37} - 24 q^{40} - 16 q^{42} + 36 q^{43} + 20 q^{45} - 14 q^{48} - 46 q^{54} + 4 q^{55} - 16 q^{57} - 28 q^{58} - 44 q^{60} + 28 q^{61} + 8 q^{63} - 40 q^{66} + 40 q^{67} + 32 q^{70} - 12 q^{72} + 28 q^{73} + 12 q^{75} + 8 q^{76} + 16 q^{79} + 4 q^{81} - 24 q^{82} - 4 q^{84} - 12 q^{85} - 34 q^{87} - 12 q^{88} - 4 q^{93} + 64 q^{94} - 16 q^{96} - 20 q^{97} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{12}\right)\)

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 \(0.404608\pi\)
\(3\) 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 \(-0.859326\pi\)
0.427694 + 0.903924i \(0.359326\pi\)
\(6\) 1.01660 2.40216i 0.415024 0.980678i
\(7\) −0.366025 1.36603i −0.138345 0.516309i −0.999962 0.00875026i \(-0.997215\pi\)
0.861617 0.507559i \(-0.169452\pi\)
\(8\) −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 −0.597126 0.802148i \(-0.703691\pi\)
0.918200 0.396117i \(-0.129643\pi\)
\(12\) 0.285334 0.366025i 0.0823689 0.105662i
\(13\) 0 0
\(14\) 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 −0.379981 0.924994i \(-0.624070\pi\)
0.991059 0.133424i \(-0.0425971\pi\)
\(18\) −3.87762 2.31853i −0.913965 0.546482i
\(19\) 3.73205 1.00000i 0.856191 0.229416i 0.196084 0.980587i \(-0.437177\pi\)
0.660107 + 0.751171i \(0.270511\pi\)
\(20\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −3.60523 + 2.72284i −0.735914 + 0.555798i
\(25\) 2.73205i 0.546410i
\(26\) 0 0
\(27\) −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 −0.949585 0.313509i \(-0.898495\pi\)
−0.203286 + 0.979119i \(0.565162\pi\)
\(30\) 1.47546 + 3.64058i 0.269381 + 0.664675i
\(31\) 2.46410 + 2.46410i 0.442566 + 0.442566i 0.892873 0.450308i \(-0.148686\pi\)
−0.450308 + 0.892873i \(0.648686\pi\)
\(32\) −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 \(-0.269784\pi\)
0.198323 + 0.980137i \(0.436451\pi\)
\(38\) 5.81863 0.943906
\(39\) 0 0
\(40\) 3.92820 0.621103
\(41\) −5.42885 1.45466i −0.847844 0.227179i −0.191361 0.981520i \(-0.561290\pi\)
−0.656483 + 0.754341i \(0.727957\pi\)
\(42\) −3.65351 0.509445i −0.563749 0.0786091i
\(43\) 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
\(45\) 3.94672 2.19886i 0.588342 0.327786i
\(46\) 0 0
\(47\) 4.25953 + 4.25953i 0.621316 + 0.621316i 0.945868 0.324552i \(-0.105213\pi\)
−0.324552 + 0.945868i \(0.605213\pi\)
\(48\) −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 0
\(53\) 0.779548i 0.107079i −0.998566 0.0535396i \(-0.982950\pi\)
0.998566 0.0535396i \(-0.0170503\pi\)
\(54\) −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 \(-0.520518\pi\)
0.443176 + 0.896435i \(0.353852\pi\)
\(60\) 0.0859264 + 0.693622i 0.0110931 + 0.0895462i
\(61\) 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
\(63\) −0.0648824 + 4.24214i −0.00817442 + 0.534460i
\(64\) 6.66025i 0.832532i
\(65\) 0 0
\(66\) −8.46410 6.59817i −1.04186 0.812179i
\(67\) 1.53590 5.73205i 0.187640 0.700281i −0.806410 0.591357i \(-0.798593\pi\)
0.994050 0.108925i \(-0.0347408\pi\)
\(68\) 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 \(0.859469\pi\)
\(72\) 3.80853 + 6.83591i 0.448840 + 0.805620i
\(73\) 0.901924 0.901924i 0.105562 0.105562i −0.652353 0.757915i \(-0.726218\pi\)
0.757915 + 0.652353i \(0.226218\pi\)
\(74\) 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
\(78\) 0 0
\(79\) 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 \(-0.822502\pi\)
0.529174 + 0.848513i \(0.322502\pi\)
\(84\) −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 −0.711531 0.702654i \(-0.751998\pi\)
0.967531 0.252751i \(-0.0813353\pi\)
\(90\) 6.59817 1.66025i 0.695509 0.175006i
\(91\) 0 0
\(92\) 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 \(-0.610703\pi\)
0.174910 + 0.984584i \(0.444036\pi\)
\(98\) 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 0.676229 0.736692i \(-0.263613\pi\)
−0.976108 + 0.217285i \(0.930280\pi\)
\(102\) −7.92160 10.4887i −0.784356 1.03854i
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) 0 0
\(105\) 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 \(-0.295565\pi\)
0.992969 0.118374i \(-0.0377682\pi\)
\(108\) −1.12374 + 0.822021i −0.108132 + 0.0790990i
\(109\) 13.1962 + 13.1962i 1.26396 + 1.26396i 0.949156 + 0.314806i \(0.101940\pi\)
0.314806 + 0.949156i \(0.398060\pi\)
\(110\) 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 0.0185360 0.999828i \(-0.494099\pi\)
−0.856609 + 0.515967i \(0.827433\pi\)
\(114\) 1.39183 9.98158i 0.130357 0.934861i
\(115\) 0 0
\(116\) −1.92089 −0.178350
\(117\) 0 0
\(118\) 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 −0.106605 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
\(130\) 0 0
\(131\) 7.94839i 0.694454i 0.937781 + 0.347227i \(0.112877\pi\)
−0.937781 + 0.347227i \(0.887123\pi\)
\(132\) −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 \(-0.676052\pi\)
−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
\(141\) 8.32592 6.28814i 0.701169 0.529557i
\(142\) 4.53590i 0.380644i
\(143\) 0 0
\(144\) 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 −0.995043 0.0994454i \(-0.968293\pi\)
0.812010 0.583644i \(-0.198374\pi\)
\(150\) 6.56283 + 2.77739i 0.535853 + 0.226773i
\(151\) −0.535898 + 0.535898i −0.0436108 + 0.0436108i −0.728576 0.684965i \(-0.759817\pi\)
0.684965 + 0.728576i \(0.259817\pi\)
\(152\) −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
\(156\) 0 0
\(157\) −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 \(-0.0314814\pi\)
−0.911164 + 0.412045i \(0.864815\pi\)
\(164\) −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 0.690283 + 0.723539i \(0.257486\pi\)
−0.959573 + 0.281461i \(0.909181\pi\)
\(168\) 5.03908 + 3.92820i 0.388773 + 0.303067i
\(169\) 0 0
\(170\) 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 0.316097 + 0.948727i \(0.397627\pi\)
−0.979670 + 0.200615i \(0.935706\pi\)
\(174\) 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 −0.604972 0.796247i \(-0.706816\pi\)
−0.387084 0.922045i \(-0.626518\pi\)
\(180\) 1.21043 + 0.0185132i 0.0902201 + 0.00137989i
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) 0 0
\(183\) −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 0.643645 0.765324i \(-0.277421\pi\)
−0.340968 + 0.940075i \(0.610755\pi\)
\(192\) 11.4254 + 1.59315i 0.824554 + 0.114976i
\(193\) −0.133975 0.0358984i −0.00964370 0.00258402i 0.253994 0.967206i \(-0.418256\pi\)
−0.263638 + 0.964622i \(0.584922\pi\)
\(194\) −2.54752 −0.182902
\(195\) 0 0
\(196\) 1.33975 0.0956961
\(197\) 3.97420 + 1.06488i 0.283150 + 0.0758697i 0.397599 0.917559i \(-0.369844\pi\)
−0.114449 + 0.993429i \(0.536510\pi\)
\(198\) −13.3435 + 12.9415i −0.948281 + 0.919711i
\(199\) 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
\(201\) −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
\(208\) 0 0
\(209\) 15.8968i 1.09960i
\(210\) 4.43306 3.34806i 0.305910 0.231038i
\(211\) 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
\(213\) 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
\(221\) 0 0
\(222\) 8.68653 11.1430i 0.583002 0.747872i
\(223\) −6.70577 + 25.0263i −0.449052 + 1.67588i 0.255960 + 0.966687i \(0.417609\pi\)
−0.705011 + 0.709196i \(0.749058\pi\)
\(224\) −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 −0.888686 0.458515i \(-0.848381\pi\)
0.540367 0.841429i \(-0.318285\pi\)
\(228\) 0.698857 1.65136i 0.0462829 0.109364i
\(229\) 14.1244 14.1244i 0.933364 0.933364i −0.0645507 0.997914i \(-0.520561\pi\)
0.997914 + 0.0645507i \(0.0205614\pi\)
\(230\) 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 \(0.306251\pi\)
\(234\) 0 0
\(235\) −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 \(-0.847585\pi\)
0.460737 + 0.887537i \(0.347585\pi\)
\(240\) 4.53819 10.7235i 0.292939 0.692198i
\(241\) −3.76795 14.0622i −0.242715 0.905825i −0.974518 0.224309i \(-0.927988\pi\)
0.731803 0.681516i \(-0.238679\pi\)
\(242\) −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
\(247\) 0 0
\(248\) 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 −0.850007 0.526772i \(-0.823402\pi\)
0.881201 + 0.472741i \(0.156736\pi\)
\(252\) −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 0.977686 + 0.210071i \(0.0673696\pi\)
−0.306916 + 0.951737i \(0.599297\pi\)
\(258\) 4.57125 3.45243i 0.284593 0.214939i
\(259\) 7.66025i 0.475985i
\(260\) 0 0
\(261\) 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 −0.958331 0.285660i \(-0.907787\pi\)
−0.231777 + 0.972769i \(0.574454\pi\)
\(264\) 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 0.0711756 0.997464i \(-0.477325\pi\)
−0.828241 + 0.560372i \(0.810658\pi\)
\(270\) −1.26979 11.7160i −0.0772769 0.713013i
\(271\) −7.46410 2.00000i −0.453412 0.121491i 0.0248835 0.999690i \(-0.492079\pi\)
−0.478295 + 0.878199i \(0.658745\pi\)
\(272\) −22.4950 −1.36396
\(273\) 0 0
\(274\) −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
\(279\) −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 \(-0.0790030\pi\)
−0.245655 + 0.969357i \(0.579003\pi\)
\(282\) 14.5623 5.90185i 0.867172 0.351450i
\(283\) −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
\(286\) 0 0
\(287\) 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 \(-0.566577\pi\)
0.309286 + 0.950969i \(0.399910\pi\)
\(294\) −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 \(-0.859982\pi\)
0.425829 + 0.904803i \(0.359982\pi\)
\(308\) −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 \(0.407761\pi\)
\(312\) 0 0
\(313\) 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 \(-0.601124\pi\)
0.949960 + 0.312373i \(0.101124\pi\)
\(318\) −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 0
\(326\) 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 \(-0.193775\pi\)
0.996376 + 0.0850595i \(0.0271080\pi\)
\(332\) −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 \(0.167734\pi\)
−0.864344 + 0.502902i \(0.832266\pi\)
\(338\) 0 0
\(339\) −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 0.895095 0.445876i \(-0.147108\pi\)
0.0614076 + 0.998113i \(0.480441\pi\)
\(348\) −0.459481 + 3.29519i −0.0246308 + 0.176641i
\(349\) −27.4904 7.36603i −1.47153 0.394294i −0.568072 0.822979i \(-0.692311\pi\)
−0.903454 + 0.428684i \(0.858977\pi\)
\(350\) 5.81863 0.311019
\(351\) 0 0
\(352\) −6.19615 −0.330256
\(353\) −13.6626 3.66088i −0.727186 0.194849i −0.123810 0.992306i \(-0.539511\pi\)
−0.603376 + 0.797457i \(0.706178\pi\)
\(354\) 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 \(-0.488255\pi\)
−0.999319 + 0.0368904i \(0.988255\pi\)
\(360\) −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 0
\(365\) 1.92089i 0.100544i
\(366\) −11.0042 14.5704i −0.575201 0.761605i
\(367\) −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
\(369\) 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 −0.976139 0.217148i \(-0.930325\pi\)
0.676125 + 0.736787i \(0.263658\pi\)
\(374\) −15.6114 27.0398i −0.807249 1.39820i
\(375\) −16.0941 + 12.1550i −0.831096 + 0.627684i
\(376\) 15.7128i 0.810326i
\(377\) 0 0
\(378\) 10.1244 + 4.46841i 0.520741 + 0.229830i
\(379\) −3.83013 + 14.2942i −0.196740 + 0.734245i 0.795069 + 0.606519i \(0.207435\pi\)
−0.991809 + 0.127726i \(0.959232\pi\)
\(380\) −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 0.740339 + 0.672234i \(0.234665\pi\)
−0.305035 + 0.952341i \(0.598668\pi\)
\(384\) 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 \(0.306839\pi\)
\(390\) 0 0
\(391\) 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 0.995877 + 0.0907168i \(0.0289158\pi\)
−0.817096 + 0.576501i \(0.804418\pi\)
\(398\) 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 −0.837594 0.546294i \(-0.816038\pi\)
0.998524 0.0543073i \(-0.0172951\pi\)
\(402\) −12.2079 9.51666i −0.608876 0.474648i
\(403\) 0 0
\(404\) 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 \(-0.849468\pi\)
−0.543236 + 0.839580i \(0.682801\pi\)
\(410\) 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
\(416\) 0 0
\(417\) 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 −0.687452 0.726230i \(-0.741271\pi\)
0.285208 + 0.958466i \(0.407937\pi\)
\(420\) 0.916053 0.371261i 0.0446988 0.0181157i
\(421\) 7.83013 + 7.83013i 0.381617 + 0.381617i 0.871685 0.490067i \(-0.163028\pi\)
−0.490067 + 0.871685i \(0.663028\pi\)
\(422\) 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
\(429\) 0 0
\(430\) −4.98076 −0.240194
\(431\) 36.5473 + 9.79282i 1.76042 + 0.471704i 0.986800 0.161944i \(-0.0517764\pi\)
0.773622 + 0.633648i \(0.218443\pi\)
\(432\) 23.0611 2.49938i 1.10953 0.120252i
\(433\) −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
\(435\) −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 −0.473567 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
\(442\) 0 0
\(443\) 11.2195i 0.533054i −0.963827 0.266527i \(-0.914124\pi\)
0.963827 0.266527i \(-0.0858762\pi\)
\(444\) 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 \(-0.421998\pi\)
0.695165 + 0.718851i \(0.255331\pi\)
\(450\) 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
\(455\) 0 0
\(456\) −10.7321 + 13.7670i −0.502574 + 0.644700i
\(457\) 1.00962 3.76795i 0.0472280 0.176257i −0.938283 0.345868i \(-0.887584\pi\)
0.985511 + 0.169611i \(0.0542511\pi\)
\(458\) 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 0.967302 + 0.253628i \(0.0816238\pi\)
−0.710894 + 0.703299i \(0.751710\pi\)
\(462\) −5.91520 + 13.9773i −0.275200 + 0.650282i
\(463\) −23.0526 + 23.0526i −1.07134 + 1.07134i −0.0740918 + 0.997251i \(0.523606\pi\)
−0.997251 + 0.0740918i \(0.976394\pi\)
\(464\) 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 \(0.646261\pi\)
\(468\) 0 0
\(469\) −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 0.730962 + 0.682418i \(0.239072\pi\)
−0.974241 + 0.225510i \(0.927595\pi\)
\(480\) 2.41510 3.09808i 0.110234 0.141407i
\(481\) 0 0
\(482\) 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 \(-0.624982\pi\)
0.130584 + 0.991437i \(0.458315\pi\)
\(488\) −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 0.984623 + 0.174693i \(0.0558934\pi\)
−0.341023 + 0.940055i \(0.610773\pi\)
\(492\) −2.08148 + 1.57203i −0.0938403 + 0.0708728i
\(493\) 36.1244i 1.62696i
\(494\) 0 0
\(495\) −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 \(-0.225147\pi\)
−0.649798 + 0.760107i \(0.725147\pi\)
\(500\) −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 0.435513 0.900182i \(-0.356567\pi\)
−0.561824 + 0.827257i \(0.689900\pi\)
\(504\) 7.94401 7.70467i 0.353854 0.343193i
\(505\) 8.76795 + 2.34936i 0.390169 + 0.104545i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.44486 0.108473
\(509\) −14.1568 3.79330i −0.627489 0.168135i −0.0689588 0.997620i \(-0.521968\pi\)
−0.558530 + 0.829484i \(0.688634\pi\)
\(510\) 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
\(520\) 0 0
\(521\) 2.49155i 0.109157i −0.998509 0.0545785i \(-0.982618\pi\)
0.998509 0.0545785i \(-0.0173815\pi\)
\(522\) 32.3844 + 0.495311i 1.41743 + 0.0216792i
\(523\) 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
\(525\) −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
\(533\) 0 0
\(534\) −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 \(-0.623966\pi\)
0.925118 + 0.379681i \(0.123966\pi\)
\(542\) −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
\(546\) 0 0
\(547\) 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 0.671123 + 0.741346i \(0.265812\pi\)
−0.951883 + 0.306462i \(0.900855\pi\)
\(558\) −3.84177 15.2679i −0.162635 0.646344i
\(559\) 0 0
\(560\) 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 −0.740085 0.672514i \(-0.765215\pi\)
0.952456 + 0.304675i \(0.0985479\pi\)
\(564\) 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 0.892939 0.450178i \(-0.148639\pi\)
−0.836335 + 0.548219i \(0.815306\pi\)
\(570\) 9.14708 + 12.1113i 0.383129 + 0.507289i
\(571\) 1.94744i 0.0814979i −0.999169 0.0407489i \(-0.987026\pi\)
0.999169 0.0407489i \(-0.0129744\pi\)
\(572\) 0 0
\(573\) 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 \(-0.0196846\pi\)
−0.0618016 + 0.998088i \(0.519685\pi\)
\(578\) −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
\(585\) 0 0
\(586\) 2.71281 0.112065
\(587\) −18.0265 4.83020i −0.744035 0.199364i −0.133164 0.991094i \(-0.542514\pi\)
−0.610871 + 0.791730i \(0.709181\pi\)
\(588\) 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 \(-0.347297\pi\)
−0.887119 + 0.461541i \(0.847297\pi\)
\(594\) 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 \(0.139178\pi\)
−0.905924 + 0.423441i \(0.860822\pi\)
\(600\) −7.43895 9.84967i −0.303694 0.402111i
\(601\) −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
\(603\) −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 −0.864028 0.503444i \(-0.832066\pi\)
0.868009 + 0.496549i \(0.165400\pi\)
\(608\) −2.90931 5.03908i −0.117988 0.204362i
\(609\) 14.0126 10.5830i 0.567820 0.428845i
\(610\) 15.8756i 0.642786i
\(611\) 0 0
\(612\) −3.92820 + 0.988427i −0.158788 + 0.0399548i
\(613\) 11.3564 42.3827i 0.458681 1.71182i −0.218354 0.975870i \(-0.570069\pi\)
0.677035 0.735951i \(-0.263265\pi\)
\(614\) −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 0.992899 + 0.118964i \(0.0379573\pi\)
−0.800393 + 0.599475i \(0.795376\pi\)
\(618\) −16.6427 7.04319i −0.669466 0.283319i
\(619\) 31.6603 31.6603i 1.27253 1.27253i 0.327778 0.944755i \(-0.393700\pi\)
0.944755 0.327778i \(-0.106300\pi\)
\(620\) −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
\(624\) 0 0
\(625\) 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 −0.981102 0.193493i \(-0.938018\pi\)
0.752912 0.658121i \(-0.228648\pi\)
\(632\) −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
\(637\) 0 0
\(638\) 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 −0.0626345 + 0.998037i \(0.519950\pi\)
−0.833008 + 0.553261i \(0.813383\pi\)
\(642\) −6.09776 49.2228i −0.240659 1.94267i
\(643\) −7.00000 + 1.87564i −0.276053 + 0.0739682i −0.394190 0.919029i \(-0.628975\pi\)
0.118136 + 0.992997i \(0.462308\pi\)
\(644\) 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 0.981249 0.192746i \(-0.0617394\pi\)
−0.657547 + 0.753413i \(0.728406\pi\)
\(648\) −5.37965 22.8511i −0.211333 0.897674i
\(649\) 12.3923i 0.486441i
\(650\) 0 0
\(651\) −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 −0.327290 0.944924i \(-0.606135\pi\)
0.654683 + 0.755904i \(0.272802\pi\)
\(654\) 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 −0.0328158 0.999461i \(-0.510447\pi\)
−0.881967 + 0.471311i \(0.843781\pi\)
\(660\) 2.84809 + 0.397137i 0.110862 + 0.0154585i
\(661\) −9.42820 2.52628i −0.366715 0.0982609i 0.0707559 0.997494i \(-0.477459\pi\)
−0.437470 + 0.899233i \(0.644126\pi\)
\(662\) 51.5321 2.00285
\(663\) 0 0
\(664\) 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 −0.996792 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
\(676\) 0 0
\(677\) 9.66040i 0.371279i 0.982618 + 0.185640i \(0.0594357\pi\)
−0.982618 + 0.185640i \(0.940564\pi\)
\(678\) −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 \(-0.937420\pi\)
−0.751673 + 0.659536i \(0.770753\pi\)
\(684\) −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 0
\(690\) 0 0
\(691\) −4.88269 + 18.2224i −0.185746 + 0.693214i 0.808723 + 0.588189i \(0.200159\pi\)
−0.994470 + 0.105025i \(0.966508\pi\)
\(692\) −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 \(0.422420\pi\)
\(702\) 0 0
\(703\) 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 \(-0.0126424\pi\)
−0.885196 + 0.465219i \(0.845976\pi\)
\(710\) −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
\(715\) 0 0
\(716\) 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 −0.789005 0.614386i \(-0.789404\pi\)
0.926577 + 0.376106i \(0.122737\pi\)
\(720\) −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 \(0.117877\pi\)
−0.932211 + 0.361916i \(0.882123\pi\)
\(728\) 0 0
\(729\) −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 \(-0.193356\pi\)
−0.570773 + 0.821108i \(0.693356\pi\)
\(734\) −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 \(-0.348726\pi\)
−0.0483378 + 0.998831i \(0.515392\pi\)
\(740\) −2.18573 −0.0803492
\(741\) 0 0
\(742\) −1.66025 −0.0609498
\(743\) 8.51906 + 2.28268i 0.312534 + 0.0837432i 0.411677 0.911330i \(-0.364943\pi\)
−0.0991426 + 0.995073i \(0.531610\pi\)
\(744\) −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 −0.927705 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
\(754\) 0 0
\(755\) 1.14134i 0.0415375i
\(756\) 1.53422 + 1.23418i 0.0557990 + 0.0448866i
\(757\) −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 \(0.524695\pi\)
\(762\) −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
\(767\) 0 0
\(768\) 8.63397 + 6.73060i 0.311552 + 0.242870i
\(769\) 10.8301 40.4186i 0.390544 1.45753i −0.438694 0.898636i \(-0.644559\pi\)
0.829238 0.558895i \(-0.188775\pi\)
\(770\) 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 −0.811695 0.584081i \(-0.801455\pi\)
0.410908 0.911677i \(-0.365212\pi\)
\(774\) −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 0
\(781\) 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 −0.999263 0.0383938i \(-0.987776\pi\)
0.846190 0.532881i \(-0.178891\pi\)
\(788\) 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
\(793\) 0 0
\(794\) 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 −0.249381 0.968405i \(-0.580227\pi\)
0.963354 0.268232i \(-0.0864395\pi\)
\(798\) −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
\(806\) 0 0
\(807\) −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 −0.0141514 0.999900i \(-0.504505\pi\)
0.858863 + 0.512205i \(0.171171\pi\)
\(810\) −20.4020 0.624232i −0.716853 0.0219333i
\(811\) −19.0000 19.0000i −0.667180 0.667180i 0.289882 0.957062i \(-0.406384\pi\)
−0.957062 + 0.289882i \(0.906384\pi\)
\(812\) 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
\(819\) 0 0
\(820\) 2.26795 0.0792002
\(821\) 41.5864 + 11.1430i 1.45137 + 0.388895i 0.896502 0.443040i \(-0.146100\pi\)
0.554873 + 0.831935i \(0.312767\pi\)
\(822\) −2.42177 + 17.3679i −0.0844690 + 0.605774i
\(823\) −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
\(825\) 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 0.993726 + 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
\(832\) 0 0
\(833\) 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 \(-0.527339\pi\)
0.423868 + 0.905724i \(0.360672\pi\)
\(840\) −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
\(845\) 0 0
\(846\) −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 \(-0.567856\pi\)
0.977364 + 0.211566i \(0.0678562\pi\)
\(854\) −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 \(0.481902\pi\)
\(858\) 0 0
\(859\) 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 \(-0.605358\pi\)
0.945721 + 0.324980i \(0.105358\pi\)
\(864\) 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
\(871\) 0 0
\(872\) 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 \(-0.752481\pi\)
−0.266339 + 0.963879i \(0.585814\pi\)
\(878\) 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 0.993176 0.116625i \(-0.0372076\pi\)
−0.597588 + 0.801803i \(0.703874\pi\)
\(882\) −22.5869 0.345461i −0.760541 0.0116323i
\(883\) 33.3731i 1.12309i −0.827445 0.561547i \(-0.810207\pi\)
0.827445 0.561547i \(-0.189793\pi\)
\(884\) 0 0
\(885\) 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 −0.819981 0.572391i \(-0.806016\pi\)
0.0857146 + 0.996320i \(0.472683\pi\)
\(888\) −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 −0.727915 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
\(910\) 0 0
\(911\) 1.55910i 0.0516552i 0.999666 + 0.0258276i \(0.00822209\pi\)
−0.999666 + 0.0258276i \(0.991778\pi\)
\(912\) −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 −0.955174 0.296046i \(-0.904332\pi\)
0.733971 + 0.679181i \(0.237665\pi\)
\(920\) 0 0
\(921\) 12.3892 + 16.4041i 0.408236 + 0.540533i
\(922\) 32.0333i 1.05496i
\(923\) 0 0
\(924\) −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 0.996868 + 0.0790861i \(0.0252002\pi\)
−0.823770 + 0.566924i \(0.808133\pi\)
\(930\) −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
\(936\) 0 0
\(937\) −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 \(-0.682387\pi\)
0.840285 + 0.542144i \(0.182387\pi\)
\(942\) −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 \(-0.860893\pi\)
0.996254 + 0.0864720i \(0.0275593\pi\)
\(948\) 0.570669 0.732051i 0.0185345 0.0237759i
\(949\) 0 0
\(950\) 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 −0.881591 0.472015i \(-0.843527\pi\)
0.849572 + 0.527472i \(0.176860\pi\)
\(954\) −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
\(962\) 0 0
\(963\) −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 \(-0.0316475\pi\)
−0.0992599 + 0.995062i \(0.531648\pi\)
\(968\) 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 0.985247 0.171136i \(-0.0547436\pi\)
0.344416 + 0.938817i \(0.388077\pi\)
\(972\) 3.91725 1.44976i 0.125646 0.0465011i
\(973\) 25.1244 + 6.73205i 0.805450 + 0.215820i
\(974\) −8.67197 −0.277868
\(975\) 0 0
\(976\) −31.2487 −1.00025
\(977\) −22.8847 6.13194i −0.732147 0.196178i −0.126562 0.991959i \(-0.540394\pi\)
−0.605585 + 0.795780i \(0.707061\pi\)
\(978\) 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 \(-0.00910459\pi\)
−0.0285990 + 0.999591i \(0.509105\pi\)
\(984\) 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
\(988\) 0 0
\(989\) 0 0
\(990\) 0.428106 27.9904i 0.0136061 0.889594i
\(991\) 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
\(993\) −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 −0.805266 0.592914i \(-0.797977\pi\)
0.916112 + 0.400923i \(0.131311\pi\)
\(998\) 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 507.2.k.d.89.2 8
3.2 odd 2 inner 507.2.k.d.89.1 8
13.2 odd 12 507.2.f.e.239.3 8
13.3 even 3 507.2.f.e.437.2 8
13.4 even 6 507.2.k.e.488.2 8
13.5 odd 4 507.2.k.f.80.2 8
13.6 odd 12 inner 507.2.k.d.188.1 8
13.7 odd 12 39.2.k.b.32.2 yes 8
13.8 odd 4 507.2.k.e.80.1 8
13.9 even 3 507.2.k.f.488.1 8
13.10 even 6 507.2.f.f.437.3 8
13.11 odd 12 507.2.f.f.239.2 8
13.12 even 2 39.2.k.b.11.1 8
39.2 even 12 507.2.f.e.239.2 8
39.5 even 4 507.2.k.f.80.1 8
39.8 even 4 507.2.k.e.80.2 8
39.11 even 12 507.2.f.f.239.3 8
39.17 odd 6 507.2.k.e.488.1 8
39.20 even 12 39.2.k.b.32.1 yes 8
39.23 odd 6 507.2.f.f.437.2 8
39.29 odd 6 507.2.f.e.437.3 8
39.32 even 12 inner 507.2.k.d.188.2 8
39.35 odd 6 507.2.k.f.488.2 8
39.38 odd 2 39.2.k.b.11.2 yes 8
52.7 even 12 624.2.cn.c.305.2 8
52.51 odd 2 624.2.cn.c.401.1 8
65.7 even 12 975.2.bp.f.149.2 8
65.12 odd 4 975.2.bp.e.674.2 8
65.33 even 12 975.2.bp.e.149.1 8
65.38 odd 4 975.2.bp.f.674.1 8
65.59 odd 12 975.2.bo.d.851.1 8
65.64 even 2 975.2.bo.d.401.2 8
156.59 odd 12 624.2.cn.c.305.1 8
156.155 even 2 624.2.cn.c.401.2 8
195.38 even 4 975.2.bp.f.674.2 8
195.59 even 12 975.2.bo.d.851.2 8
195.77 even 4 975.2.bp.e.674.1 8
195.98 odd 12 975.2.bp.e.149.2 8
195.137 odd 12 975.2.bp.f.149.1 8
195.194 odd 2 975.2.bo.d.401.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.k.b.11.1 8 13.12 even 2
39.2.k.b.11.2 yes 8 39.38 odd 2
39.2.k.b.32.1 yes 8 39.20 even 12
39.2.k.b.32.2 yes 8 13.7 odd 12
507.2.f.e.239.2 8 39.2 even 12
507.2.f.e.239.3 8 13.2 odd 12
507.2.f.e.437.2 8 13.3 even 3
507.2.f.e.437.3 8 39.29 odd 6
507.2.f.f.239.2 8 13.11 odd 12
507.2.f.f.239.3 8 39.11 even 12
507.2.f.f.437.2 8 39.23 odd 6
507.2.f.f.437.3 8 13.10 even 6
507.2.k.d.89.1 8 3.2 odd 2 inner
507.2.k.d.89.2 8 1.1 even 1 trivial
507.2.k.d.188.1 8 13.6 odd 12 inner
507.2.k.d.188.2 8 39.32 even 12 inner
507.2.k.e.80.1 8 13.8 odd 4
507.2.k.e.80.2 8 39.8 even 4
507.2.k.e.488.1 8 39.17 odd 6
507.2.k.e.488.2 8 13.4 even 6
507.2.k.f.80.1 8 39.5 even 4
507.2.k.f.80.2 8 13.5 odd 4
507.2.k.f.488.1 8 13.9 even 3
507.2.k.f.488.2 8 39.35 odd 6
624.2.cn.c.305.1 8 156.59 odd 12
624.2.cn.c.305.2 8 52.7 even 12
624.2.cn.c.401.1 8 52.51 odd 2
624.2.cn.c.401.2 8 156.155 even 2
975.2.bo.d.401.1 8 195.194 odd 2
975.2.bo.d.401.2 8 65.64 even 2
975.2.bo.d.851.1 8 65.59 odd 12
975.2.bo.d.851.2 8 195.59 even 12
975.2.bp.e.149.1 8 65.33 even 12
975.2.bp.e.149.2 8 195.98 odd 12
975.2.bp.e.674.1 8 195.77 even 4
975.2.bp.e.674.2 8 65.12 odd 4
975.2.bp.f.149.1 8 195.137 odd 12
975.2.bp.f.149.2 8 65.7 even 12
975.2.bp.f.674.1 8 65.38 odd 4
975.2.bp.f.674.2 8 195.38 even 4