Properties

Label 804.2.j.b.499.1
Level $804$
Weight $2$
Character 804.499
Analytic conductor $6.420$
Analytic rank $0$
Dimension $68$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(499,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.499");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.j (of order \(6\), degree \(2\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 499.1
Character \(\chi\) \(=\) 804.499
Dual form 804.2.j.b.775.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41416 + 0.0125113i) q^{2} +1.00000 q^{3} +(1.99969 - 0.0353860i) q^{4} +0.567637i q^{5} +(-1.41416 + 0.0125113i) q^{6} +(1.03281 - 1.78888i) q^{7} +(-2.82743 + 0.0750601i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.41416 + 0.0125113i) q^{2} +1.00000 q^{3} +(1.99969 - 0.0353860i) q^{4} +0.567637i q^{5} +(-1.41416 + 0.0125113i) q^{6} +(1.03281 - 1.78888i) q^{7} +(-2.82743 + 0.0750601i) q^{8} +1.00000 q^{9} +(-0.00710190 - 0.802729i) q^{10} +(-0.251452 + 0.435527i) q^{11} +(1.99969 - 0.0353860i) q^{12} +(3.90313 - 2.25347i) q^{13} +(-1.43817 + 2.54268i) q^{14} +0.567637i q^{15} +(3.99750 - 0.141522i) q^{16} +(-2.27908 - 3.94748i) q^{17} +(-1.41416 + 0.0125113i) q^{18} +(-4.21365 + 2.43275i) q^{19} +(0.0200864 + 1.13510i) q^{20} +(1.03281 - 1.78888i) q^{21} +(0.350144 - 0.619050i) q^{22} +(4.01670 - 2.31904i) q^{23} +(-2.82743 + 0.0750601i) q^{24} +4.67779 q^{25} +(-5.49144 + 3.23560i) q^{26} +1.00000 q^{27} +(2.00199 - 3.61374i) q^{28} +(-0.433527 + 0.750890i) q^{29} +(-0.00710190 - 0.802729i) q^{30} +(4.20035 - 7.27522i) q^{31} +(-5.65132 + 0.250148i) q^{32} +(-0.251452 + 0.435527i) q^{33} +(3.27237 + 5.55385i) q^{34} +(1.01543 + 0.586261i) q^{35} +(1.99969 - 0.0353860i) q^{36} +(-0.346835 - 0.600736i) q^{37} +(5.92832 - 3.49301i) q^{38} +(3.90313 - 2.25347i) q^{39} +(-0.0426070 - 1.60496i) q^{40} +(8.12044 + 4.68834i) q^{41} +(-1.43817 + 2.54268i) q^{42} -8.56474 q^{43} +(-0.487413 + 0.879816i) q^{44} +0.567637i q^{45} +(-5.65123 + 3.32975i) q^{46} +(-7.71589 - 4.45477i) q^{47} +(3.99750 - 0.141522i) q^{48} +(1.36661 + 2.36705i) q^{49} +(-6.61513 + 0.0585253i) q^{50} +(-2.27908 - 3.94748i) q^{51} +(7.72529 - 4.64435i) q^{52} +14.4612i q^{53} +(-1.41416 + 0.0125113i) q^{54} +(-0.247222 - 0.142733i) q^{55} +(-2.78592 + 5.13545i) q^{56} +(-4.21365 + 2.43275i) q^{57} +(0.603681 - 1.06730i) q^{58} -7.96043i q^{59} +(0.0200864 + 1.13510i) q^{60} +(7.38094 - 4.26139i) q^{61} +(-5.84894 + 10.3409i) q^{62} +(1.03281 - 1.78888i) q^{63} +(7.98873 - 0.424455i) q^{64} +(1.27915 + 2.21556i) q^{65} +(0.350144 - 0.619050i) q^{66} +(6.54149 - 4.92025i) q^{67} +(-4.69713 - 7.81307i) q^{68} +(4.01670 - 2.31904i) q^{69} +(-1.44332 - 0.816361i) q^{70} +(4.35912 + 2.51674i) q^{71} +(-2.82743 + 0.0750601i) q^{72} +(-3.10591 - 5.37959i) q^{73} +(0.497995 + 0.845196i) q^{74} +4.67779 q^{75} +(-8.33989 + 5.01384i) q^{76} +(0.519403 + 0.899632i) q^{77} +(-5.49144 + 3.23560i) q^{78} +(-4.84032 + 8.38369i) q^{79} +(0.0803331 + 2.26913i) q^{80} +1.00000 q^{81} +(-11.5422 - 6.52846i) q^{82} +(6.79123 - 3.92092i) q^{83} +(2.00199 - 3.61374i) q^{84} +(2.24074 - 1.29369i) q^{85} +(12.1119 - 0.107156i) q^{86} +(-0.433527 + 0.750890i) q^{87} +(0.678272 - 1.25030i) q^{88} +10.6280 q^{89} +(-0.00710190 - 0.802729i) q^{90} -9.30961i q^{91} +(7.95007 - 4.77949i) q^{92} +(4.20035 - 7.27522i) q^{93} +(10.9672 + 6.20321i) q^{94} +(-1.38092 - 2.39182i) q^{95} +(-5.65132 + 0.250148i) q^{96} +(9.20546 - 5.31478i) q^{97} +(-1.96222 - 3.33028i) q^{98} +(-0.251452 + 0.435527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41416 + 0.0125113i −0.999961 + 0.00884685i
\(3\) 1.00000 0.577350
\(4\) 1.99969 0.0353860i 0.999843 0.0176930i
\(5\) 0.567637i 0.253855i 0.991912 + 0.126928i \(0.0405116\pi\)
−0.991912 + 0.126928i \(0.959488\pi\)
\(6\) −1.41416 + 0.0125113i −0.577328 + 0.00510773i
\(7\) 1.03281 1.78888i 0.390365 0.676132i −0.602133 0.798396i \(-0.705682\pi\)
0.992498 + 0.122264i \(0.0390155\pi\)
\(8\) −2.82743 + 0.0750601i −0.999648 + 0.0265378i
\(9\) 1.00000 0.333333
\(10\) −0.00710190 0.802729i −0.00224582 0.253845i
\(11\) −0.251452 + 0.435527i −0.0758156 + 0.131316i −0.901441 0.432903i \(-0.857489\pi\)
0.825625 + 0.564219i \(0.190823\pi\)
\(12\) 1.99969 0.0353860i 0.577260 0.0102151i
\(13\) 3.90313 2.25347i 1.08253 0.625000i 0.150954 0.988541i \(-0.451765\pi\)
0.931578 + 0.363540i \(0.118432\pi\)
\(14\) −1.43817 + 2.54268i −0.384368 + 0.679559i
\(15\) 0.567637i 0.146563i
\(16\) 3.99750 0.141522i 0.999374 0.0353805i
\(17\) −2.27908 3.94748i −0.552758 0.957404i −0.998074 0.0620311i \(-0.980242\pi\)
0.445317 0.895373i \(-0.353091\pi\)
\(18\) −1.41416 + 0.0125113i −0.333320 + 0.00294895i
\(19\) −4.21365 + 2.43275i −0.966676 + 0.558111i −0.898221 0.439543i \(-0.855140\pi\)
−0.0684551 + 0.997654i \(0.521807\pi\)
\(20\) 0.0200864 + 1.13510i 0.00449146 + 0.253815i
\(21\) 1.03281 1.78888i 0.225377 0.390365i
\(22\) 0.350144 0.619050i 0.0746509 0.131982i
\(23\) 4.01670 2.31904i 0.837539 0.483553i −0.0188878 0.999822i \(-0.506013\pi\)
0.856427 + 0.516268i \(0.172679\pi\)
\(24\) −2.82743 + 0.0750601i −0.577147 + 0.0153216i
\(25\) 4.67779 0.935558
\(26\) −5.49144 + 3.23560i −1.07696 + 0.634553i
\(27\) 1.00000 0.192450
\(28\) 2.00199 3.61374i 0.378341 0.682933i
\(29\) −0.433527 + 0.750890i −0.0805039 + 0.139437i −0.903466 0.428659i \(-0.858986\pi\)
0.822963 + 0.568096i \(0.192320\pi\)
\(30\) −0.00710190 0.802729i −0.00129662 0.146558i
\(31\) 4.20035 7.27522i 0.754405 1.30667i −0.191265 0.981539i \(-0.561259\pi\)
0.945670 0.325129i \(-0.105408\pi\)
\(32\) −5.65132 + 0.250148i −0.999022 + 0.0442204i
\(33\) −0.251452 + 0.435527i −0.0437721 + 0.0758156i
\(34\) 3.27237 + 5.55385i 0.561206 + 0.952477i
\(35\) 1.01543 + 0.586261i 0.171640 + 0.0990961i
\(36\) 1.99969 0.0353860i 0.333281 0.00589767i
\(37\) −0.346835 0.600736i −0.0570193 0.0987603i 0.836107 0.548567i \(-0.184826\pi\)
−0.893126 + 0.449806i \(0.851493\pi\)
\(38\) 5.92832 3.49301i 0.961701 0.566641i
\(39\) 3.90313 2.25347i 0.625000 0.360844i
\(40\) −0.0426070 1.60496i −0.00673675 0.253766i
\(41\) 8.12044 + 4.68834i 1.26820 + 0.732196i 0.974647 0.223747i \(-0.0718290\pi\)
0.293553 + 0.955943i \(0.405162\pi\)
\(42\) −1.43817 + 2.54268i −0.221915 + 0.392343i
\(43\) −8.56474 −1.30611 −0.653055 0.757310i \(-0.726513\pi\)
−0.653055 + 0.757310i \(0.726513\pi\)
\(44\) −0.487413 + 0.879816i −0.0734803 + 0.132637i
\(45\) 0.567637i 0.0846184i
\(46\) −5.65123 + 3.32975i −0.833229 + 0.490944i
\(47\) −7.71589 4.45477i −1.12548 0.649795i −0.182684 0.983172i \(-0.558479\pi\)
−0.942794 + 0.333377i \(0.891812\pi\)
\(48\) 3.99750 0.141522i 0.576989 0.0204269i
\(49\) 1.36661 + 2.36705i 0.195231 + 0.338149i
\(50\) −6.61513 + 0.0585253i −0.935521 + 0.00827673i
\(51\) −2.27908 3.94748i −0.319135 0.552758i
\(52\) 7.72529 4.64435i 1.07130 0.644056i
\(53\) 14.4612i 1.98639i 0.116443 + 0.993197i \(0.462851\pi\)
−0.116443 + 0.993197i \(0.537149\pi\)
\(54\) −1.41416 + 0.0125113i −0.192443 + 0.00170258i
\(55\) −0.247222 0.142733i −0.0333353 0.0192462i
\(56\) −2.78592 + 5.13545i −0.372284 + 0.686253i
\(57\) −4.21365 + 2.43275i −0.558111 + 0.322225i
\(58\) 0.603681 1.06730i 0.0792671 0.140144i
\(59\) 7.96043i 1.03636i −0.855272 0.518180i \(-0.826610\pi\)
0.855272 0.518180i \(-0.173390\pi\)
\(60\) 0.0200864 + 1.13510i 0.00259315 + 0.146540i
\(61\) 7.38094 4.26139i 0.945032 0.545615i 0.0534981 0.998568i \(-0.482963\pi\)
0.891534 + 0.452953i \(0.149630\pi\)
\(62\) −5.84894 + 10.3409i −0.742816 + 1.31329i
\(63\) 1.03281 1.78888i 0.130122 0.225377i
\(64\) 7.98873 0.424455i 0.998591 0.0530568i
\(65\) 1.27915 + 2.21556i 0.158660 + 0.274807i
\(66\) 0.350144 0.619050i 0.0430997 0.0761998i
\(67\) 6.54149 4.92025i 0.799170 0.601105i
\(68\) −4.69713 7.81307i −0.569610 0.947474i
\(69\) 4.01670 2.31904i 0.483553 0.279180i
\(70\) −1.44332 0.816361i −0.172510 0.0975738i
\(71\) 4.35912 + 2.51674i 0.517332 + 0.298682i 0.735842 0.677153i \(-0.236786\pi\)
−0.218510 + 0.975835i \(0.570120\pi\)
\(72\) −2.82743 + 0.0750601i −0.333216 + 0.00884592i
\(73\) −3.10591 5.37959i −0.363519 0.629634i 0.625018 0.780610i \(-0.285092\pi\)
−0.988537 + 0.150976i \(0.951758\pi\)
\(74\) 0.497995 + 0.845196i 0.0578908 + 0.0982520i
\(75\) 4.67779 0.540144
\(76\) −8.33989 + 5.01384i −0.956650 + 0.575127i
\(77\) 0.519403 + 0.899632i 0.0591914 + 0.102523i
\(78\) −5.49144 + 3.23560i −0.621784 + 0.366359i
\(79\) −4.84032 + 8.38369i −0.544579 + 0.943238i 0.454054 + 0.890974i \(0.349977\pi\)
−0.998633 + 0.0522644i \(0.983356\pi\)
\(80\) 0.0803331 + 2.26913i 0.00898151 + 0.253696i
\(81\) 1.00000 0.111111
\(82\) −11.5422 6.52846i −1.27463 0.720947i
\(83\) 6.79123 3.92092i 0.745434 0.430377i −0.0786075 0.996906i \(-0.525047\pi\)
0.824042 + 0.566529i \(0.191714\pi\)
\(84\) 2.00199 3.61374i 0.218435 0.394291i
\(85\) 2.24074 1.29369i 0.243042 0.140320i
\(86\) 12.1119 0.107156i 1.30606 0.0115550i
\(87\) −0.433527 + 0.750890i −0.0464789 + 0.0805039i
\(88\) 0.678272 1.25030i 0.0723040 0.133282i
\(89\) 10.6280 1.12656 0.563281 0.826265i \(-0.309539\pi\)
0.563281 + 0.826265i \(0.309539\pi\)
\(90\) −0.00710190 0.802729i −0.000748606 0.0846151i
\(91\) 9.30961i 0.975913i
\(92\) 7.95007 4.77949i 0.828853 0.498296i
\(93\) 4.20035 7.27522i 0.435556 0.754405i
\(94\) 10.9672 + 6.20321i 1.13118 + 0.639813i
\(95\) −1.38092 2.39182i −0.141679 0.245396i
\(96\) −5.65132 + 0.250148i −0.576786 + 0.0255306i
\(97\) 9.20546 5.31478i 0.934673 0.539634i 0.0463866 0.998924i \(-0.485229\pi\)
0.888286 + 0.459290i \(0.151896\pi\)
\(98\) −1.96222 3.33028i −0.198215 0.336409i
\(99\) −0.251452 + 0.435527i −0.0252719 + 0.0437721i
\(100\) 9.35411 0.165528i 0.935411 0.0165528i
\(101\) −9.18807 5.30473i −0.914247 0.527841i −0.0324517 0.999473i \(-0.510332\pi\)
−0.881795 + 0.471633i \(0.843665\pi\)
\(102\) 3.27237 + 5.55385i 0.324012 + 0.549913i
\(103\) 3.59279 + 2.07430i 0.354009 + 0.204387i 0.666449 0.745550i \(-0.267813\pi\)
−0.312441 + 0.949937i \(0.601147\pi\)
\(104\) −10.8667 + 6.66450i −1.06557 + 0.653508i
\(105\) 1.01543 + 0.586261i 0.0990961 + 0.0572132i
\(106\) −0.180928 20.4504i −0.0175733 1.98632i
\(107\) 5.03323i 0.486581i −0.969953 0.243291i \(-0.921773\pi\)
0.969953 0.243291i \(-0.0782269\pi\)
\(108\) 1.99969 0.0353860i 0.192420 0.00340502i
\(109\) 2.83143i 0.271202i 0.990764 + 0.135601i \(0.0432965\pi\)
−0.990764 + 0.135601i \(0.956703\pi\)
\(110\) 0.351396 + 0.198755i 0.0335043 + 0.0189505i
\(111\) −0.346835 0.600736i −0.0329201 0.0570193i
\(112\) 3.87548 7.29719i 0.366199 0.689520i
\(113\) −7.14336 4.12422i −0.671991 0.387974i 0.124839 0.992177i \(-0.460158\pi\)
−0.796831 + 0.604203i \(0.793492\pi\)
\(114\) 5.92832 3.49301i 0.555238 0.327150i
\(115\) 1.31637 + 2.28003i 0.122753 + 0.212614i
\(116\) −0.840346 + 1.51689i −0.0780242 + 0.140839i
\(117\) 3.90313 2.25347i 0.360844 0.208333i
\(118\) 0.0995956 + 11.2573i 0.00916852 + 1.03632i
\(119\) −9.41540 −0.863108
\(120\) −0.0426070 1.60496i −0.00388946 0.146512i
\(121\) 5.37354 + 9.30725i 0.488504 + 0.846114i
\(122\) −10.3845 + 6.11862i −0.940168 + 0.553954i
\(123\) 8.12044 + 4.68834i 0.732196 + 0.422733i
\(124\) 8.14194 14.6968i 0.731168 1.31981i
\(125\) 5.49348i 0.491351i
\(126\) −1.43817 + 2.54268i −0.128123 + 0.226520i
\(127\) 10.1229 + 5.84445i 0.898261 + 0.518611i 0.876636 0.481155i \(-0.159783\pi\)
0.0216255 + 0.999766i \(0.493116\pi\)
\(128\) −11.2920 + 0.700196i −0.998083 + 0.0618892i
\(129\) −8.56474 −0.754083
\(130\) −1.83665 3.11715i −0.161085 0.273392i
\(131\) 6.99256i 0.610943i 0.952201 + 0.305471i \(0.0988141\pi\)
−0.952201 + 0.305471i \(0.901186\pi\)
\(132\) −0.487413 + 0.879816i −0.0424239 + 0.0765781i
\(133\) 10.0503i 0.871467i
\(134\) −9.18914 + 7.03986i −0.793821 + 0.608151i
\(135\) 0.567637i 0.0488545i
\(136\) 6.74023 + 10.9902i 0.577970 + 0.942398i
\(137\) 14.5906i 1.24656i −0.781998 0.623282i \(-0.785799\pi\)
0.781998 0.623282i \(-0.214201\pi\)
\(138\) −5.65123 + 3.32975i −0.481065 + 0.283447i
\(139\) −20.5318 −1.74149 −0.870743 0.491738i \(-0.836362\pi\)
−0.870743 + 0.491738i \(0.836362\pi\)
\(140\) 2.05129 + 1.13641i 0.173366 + 0.0960438i
\(141\) −7.71589 4.45477i −0.649795 0.375159i
\(142\) −6.19597 3.50453i −0.519954 0.294093i
\(143\) 2.26656i 0.189539i
\(144\) 3.99750 0.141522i 0.333125 0.0117935i
\(145\) −0.426233 0.246086i −0.0353968 0.0204363i
\(146\) 4.45955 + 7.56874i 0.369075 + 0.626393i
\(147\) 1.36661 + 2.36705i 0.112716 + 0.195231i
\(148\) −0.714819 1.18901i −0.0587577 0.0977360i
\(149\) −7.52955 −0.616845 −0.308422 0.951249i \(-0.599801\pi\)
−0.308422 + 0.951249i \(0.599801\pi\)
\(150\) −6.61513 + 0.0585253i −0.540123 + 0.00477857i
\(151\) −15.9680 + 9.21910i −1.29945 + 0.750240i −0.980310 0.197466i \(-0.936729\pi\)
−0.319144 + 0.947706i \(0.603395\pi\)
\(152\) 11.7312 7.19471i 0.951525 0.583568i
\(153\) −2.27908 3.94748i −0.184253 0.319135i
\(154\) −0.745773 1.26572i −0.0600961 0.101995i
\(155\) 4.12969 + 2.38428i 0.331704 + 0.191510i
\(156\) 7.72529 4.64435i 0.618518 0.371846i
\(157\) 7.24765 + 12.5533i 0.578425 + 1.00186i 0.995660 + 0.0930634i \(0.0296659\pi\)
−0.417235 + 0.908799i \(0.637001\pi\)
\(158\) 6.74009 11.9164i 0.536213 0.948019i
\(159\) 14.4612i 1.14685i
\(160\) −0.141994 3.20790i −0.0112256 0.253607i
\(161\) 9.58050i 0.755049i
\(162\) −1.41416 + 0.0125113i −0.111107 + 0.000982983i
\(163\) −4.97065 2.86980i −0.389331 0.224780i 0.292539 0.956254i \(-0.405500\pi\)
−0.681870 + 0.731473i \(0.738833\pi\)
\(164\) 16.4042 + 9.08786i 1.28096 + 0.709643i
\(165\) −0.247222 0.142733i −0.0192462 0.0111118i
\(166\) −9.55482 + 5.62977i −0.741598 + 0.436955i
\(167\) 8.12255 + 4.68956i 0.628542 + 0.362889i 0.780187 0.625546i \(-0.215124\pi\)
−0.151645 + 0.988435i \(0.548457\pi\)
\(168\) −2.78592 + 5.13545i −0.214938 + 0.396208i
\(169\) 3.65626 6.33283i 0.281251 0.487141i
\(170\) −3.15257 + 1.85752i −0.241791 + 0.142465i
\(171\) −4.21365 + 2.43275i −0.322225 + 0.186037i
\(172\) −17.1268 + 0.303072i −1.30591 + 0.0231090i
\(173\) 6.21674 + 10.7677i 0.472650 + 0.818654i 0.999510 0.0312980i \(-0.00996410\pi\)
−0.526860 + 0.849952i \(0.676631\pi\)
\(174\) 0.603681 1.06730i 0.0457649 0.0809119i
\(175\) 4.83126 8.36798i 0.365209 0.632560i
\(176\) −0.943541 + 1.77660i −0.0711221 + 0.133917i
\(177\) 7.96043i 0.598343i
\(178\) −15.0296 + 0.132970i −1.12652 + 0.00996653i
\(179\) −20.9617 −1.56675 −0.783377 0.621547i \(-0.786504\pi\)
−0.783377 + 0.621547i \(0.786504\pi\)
\(180\) 0.0200864 + 1.13510i 0.00149715 + 0.0846052i
\(181\) −4.79979 + 8.31348i −0.356765 + 0.617936i −0.987418 0.158129i \(-0.949454\pi\)
0.630653 + 0.776065i \(0.282787\pi\)
\(182\) 0.116476 + 13.1653i 0.00863375 + 0.975875i
\(183\) 7.38094 4.26139i 0.545615 0.315011i
\(184\) −11.1829 + 6.85842i −0.824412 + 0.505610i
\(185\) 0.341000 0.196876i 0.0250708 0.0144746i
\(186\) −5.84894 + 10.3409i −0.428865 + 0.758229i
\(187\) 2.29231 0.167630
\(188\) −15.5870 8.63511i −1.13680 0.629780i
\(189\) 1.03281 1.78888i 0.0751257 0.130122i
\(190\) 1.98276 + 3.36514i 0.143845 + 0.244133i
\(191\) −2.48806 4.30945i −0.180030 0.311821i 0.761861 0.647741i \(-0.224286\pi\)
−0.941890 + 0.335920i \(0.890953\pi\)
\(192\) 7.98873 0.424455i 0.576537 0.0306324i
\(193\) −21.8223 −1.57081 −0.785403 0.618985i \(-0.787544\pi\)
−0.785403 + 0.618985i \(0.787544\pi\)
\(194\) −12.9515 + 7.63111i −0.929862 + 0.547882i
\(195\) 1.27915 + 2.21556i 0.0916022 + 0.158660i
\(196\) 2.81656 + 4.68499i 0.201183 + 0.334642i
\(197\) 19.2043 + 11.0876i 1.36825 + 0.789958i 0.990704 0.136034i \(-0.0434356\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(198\) 0.350144 0.619050i 0.0248836 0.0439940i
\(199\) −15.0830 + 8.70816i −1.06920 + 0.617305i −0.927964 0.372670i \(-0.878442\pi\)
−0.141240 + 0.989975i \(0.545109\pi\)
\(200\) −13.2261 + 0.351115i −0.935228 + 0.0248276i
\(201\) 6.54149 4.92025i 0.461401 0.347048i
\(202\) 13.0597 + 7.38678i 0.918881 + 0.519732i
\(203\) 0.895500 + 1.55105i 0.0628518 + 0.108862i
\(204\) −4.69713 7.81307i −0.328865 0.547025i
\(205\) −2.66128 + 4.60947i −0.185872 + 0.321939i
\(206\) −5.10673 2.88844i −0.355803 0.201247i
\(207\) 4.01670 2.31904i 0.279180 0.161184i
\(208\) 15.2838 9.56062i 1.05974 0.662910i
\(209\) 2.44688i 0.169254i
\(210\) −1.44332 0.816361i −0.0995984 0.0563343i
\(211\) −17.0716 + 9.85630i −1.17526 + 0.678536i −0.954913 0.296886i \(-0.904052\pi\)
−0.220345 + 0.975422i \(0.570718\pi\)
\(212\) 0.511723 + 28.9178i 0.0351453 + 1.98608i
\(213\) 4.35912 + 2.51674i 0.298682 + 0.172444i
\(214\) 0.0629725 + 7.11779i 0.00430471 + 0.486562i
\(215\) 4.86167i 0.331563i
\(216\) −2.82743 + 0.0750601i −0.192382 + 0.00510720i
\(217\) −8.67631 15.0278i −0.588986 1.02015i
\(218\) −0.0354250 4.00410i −0.00239928 0.271192i
\(219\) −3.10591 5.37959i −0.209878 0.363519i
\(220\) −0.499416 0.276674i −0.0336707 0.0186534i
\(221\) −17.7911 10.2717i −1.19676 0.690947i
\(222\) 0.497995 + 0.845196i 0.0334233 + 0.0567258i
\(223\) 4.69841i 0.314629i −0.987549 0.157315i \(-0.949716\pi\)
0.987549 0.157315i \(-0.0502836\pi\)
\(224\) −5.38925 + 10.3679i −0.360084 + 0.692732i
\(225\) 4.67779 0.311853
\(226\) 10.1534 + 5.74293i 0.675397 + 0.382014i
\(227\) 11.2279 + 6.48243i 0.745222 + 0.430254i 0.823965 0.566641i \(-0.191757\pi\)
−0.0787430 + 0.996895i \(0.525091\pi\)
\(228\) −8.33989 + 5.01384i −0.552322 + 0.332050i
\(229\) −19.2661 + 11.1233i −1.27314 + 0.735048i −0.975578 0.219654i \(-0.929507\pi\)
−0.297563 + 0.954702i \(0.596174\pi\)
\(230\) −1.89009 3.20785i −0.124629 0.211519i
\(231\) 0.519403 + 0.899632i 0.0341742 + 0.0591914i
\(232\) 1.16940 2.15563i 0.0767752 0.141524i
\(233\) −11.9482 6.89831i −0.782754 0.451923i 0.0546516 0.998505i \(-0.482595\pi\)
−0.837405 + 0.546582i \(0.815929\pi\)
\(234\) −5.49144 + 3.23560i −0.358987 + 0.211518i
\(235\) 2.52869 4.37983i 0.164954 0.285708i
\(236\) −0.281688 15.9184i −0.0183363 1.03620i
\(237\) −4.84032 + 8.38369i −0.314413 + 0.544579i
\(238\) 13.3149 0.117799i 0.863075 0.00763579i
\(239\) −10.8958 + 18.8721i −0.704790 + 1.22073i 0.261977 + 0.965074i \(0.415625\pi\)
−0.966767 + 0.255658i \(0.917708\pi\)
\(240\) 0.0803331 + 2.26913i 0.00518548 + 0.146472i
\(241\) −3.30840 −0.213113 −0.106557 0.994307i \(-0.533983\pi\)
−0.106557 + 0.994307i \(0.533983\pi\)
\(242\) −7.71549 13.0947i −0.495970 0.841759i
\(243\) 1.00000 0.0641500
\(244\) 14.6088 8.78262i 0.935231 0.562250i
\(245\) −1.34362 + 0.775742i −0.0858410 + 0.0495603i
\(246\) −11.5422 6.52846i −0.735907 0.416239i
\(247\) −10.9643 + 18.9907i −0.697639 + 1.20835i
\(248\) −11.3301 + 20.8855i −0.719463 + 1.32623i
\(249\) 6.79123 3.92092i 0.430377 0.248478i
\(250\) −0.0687307 7.76864i −0.00434691 0.491332i
\(251\) −2.25380 3.90370i −0.142259 0.246400i 0.786088 0.618115i \(-0.212103\pi\)
−0.928347 + 0.371715i \(0.878770\pi\)
\(252\) 2.00199 3.61374i 0.126114 0.227644i
\(253\) 2.33251i 0.146644i
\(254\) −14.3885 8.13833i −0.902814 0.510644i
\(255\) 2.24074 1.29369i 0.140320 0.0810140i
\(256\) 15.9599 1.13147i 0.997496 0.0707166i
\(257\) −5.15090 + 8.92162i −0.321304 + 0.556516i −0.980757 0.195230i \(-0.937455\pi\)
0.659453 + 0.751746i \(0.270788\pi\)
\(258\) 12.1119 0.107156i 0.754054 0.00667126i
\(259\) −1.43286 −0.0890333
\(260\) 2.63631 + 4.38516i 0.163497 + 0.271956i
\(261\) −0.433527 + 0.750890i −0.0268346 + 0.0464789i
\(262\) −0.0874862 9.88859i −0.00540492 0.610919i
\(263\) 7.32912i 0.451933i 0.974135 + 0.225966i \(0.0725539\pi\)
−0.974135 + 0.225966i \(0.927446\pi\)
\(264\) 0.678272 1.25030i 0.0417447 0.0769505i
\(265\) −8.20870 −0.504257
\(266\) −0.125742 14.2126i −0.00770974 0.871433i
\(267\) 10.6280 0.650421
\(268\) 12.9068 10.0704i 0.788410 0.615150i
\(269\) −3.52992 −0.215223 −0.107611 0.994193i \(-0.534320\pi\)
−0.107611 + 0.994193i \(0.534320\pi\)
\(270\) −0.00710190 0.802729i −0.000432208 0.0488525i
\(271\) −3.15572 −0.191697 −0.0958483 0.995396i \(-0.530556\pi\)
−0.0958483 + 0.995396i \(0.530556\pi\)
\(272\) −9.66926 15.4575i −0.586285 0.937248i
\(273\) 9.30961i 0.563443i
\(274\) 0.182548 + 20.6335i 0.0110282 + 1.24651i
\(275\) −1.17624 + 2.03730i −0.0709298 + 0.122854i
\(276\) 7.95007 4.77949i 0.478538 0.287692i
\(277\) −4.91436 −0.295275 −0.147638 0.989042i \(-0.547167\pi\)
−0.147638 + 0.989042i \(0.547167\pi\)
\(278\) 29.0352 0.256880i 1.74142 0.0154067i
\(279\) 4.20035 7.27522i 0.251468 0.435556i
\(280\) −2.91507 1.58139i −0.174209 0.0945063i
\(281\) −0.219861 + 0.126937i −0.0131158 + 0.00757241i −0.506544 0.862214i \(-0.669077\pi\)
0.493428 + 0.869787i \(0.335744\pi\)
\(282\) 10.9672 + 6.20321i 0.653088 + 0.369396i
\(283\) 9.68330i 0.575612i 0.957689 + 0.287806i \(0.0929259\pi\)
−0.957689 + 0.287806i \(0.907074\pi\)
\(284\) 8.80593 + 4.87844i 0.522536 + 0.289482i
\(285\) −1.38092 2.39182i −0.0817986 0.141679i
\(286\) −0.0283576 3.20527i −0.00167682 0.189532i
\(287\) 16.7737 9.68431i 0.990121 0.571647i
\(288\) −5.65132 + 0.250148i −0.333007 + 0.0147401i
\(289\) −1.88839 + 3.27079i −0.111082 + 0.192400i
\(290\) 0.605840 + 0.342672i 0.0355762 + 0.0201224i
\(291\) 9.20546 5.31478i 0.539634 0.311558i
\(292\) −6.40121 10.6476i −0.374602 0.623104i
\(293\) −1.34689 −0.0786864 −0.0393432 0.999226i \(-0.512527\pi\)
−0.0393432 + 0.999226i \(0.512527\pi\)
\(294\) −1.96222 3.33028i −0.114439 0.194226i
\(295\) 4.51864 0.263085
\(296\) 1.02574 + 1.67250i 0.0596201 + 0.0972124i
\(297\) −0.251452 + 0.435527i −0.0145907 + 0.0252719i
\(298\) 10.6480 0.0942047i 0.616821 0.00545713i
\(299\) 10.4518 18.1030i 0.604442 1.04692i
\(300\) 9.35411 0.165528i 0.540060 0.00955677i
\(301\) −8.84573 + 15.3213i −0.509860 + 0.883103i
\(302\) 22.4659 13.2371i 1.29277 0.761707i
\(303\) −9.18807 5.30473i −0.527841 0.304749i
\(304\) −16.4997 + 10.3212i −0.946325 + 0.591963i
\(305\) 2.41892 + 4.18970i 0.138507 + 0.239901i
\(306\) 3.27237 + 5.55385i 0.187069 + 0.317492i
\(307\) −5.07786 + 2.93171i −0.289809 + 0.167321i −0.637856 0.770156i \(-0.720178\pi\)
0.348047 + 0.937477i \(0.386845\pi\)
\(308\) 1.07048 + 1.78060i 0.0609961 + 0.101459i
\(309\) 3.59279 + 2.07430i 0.204387 + 0.118003i
\(310\) −5.86986 3.32008i −0.333386 0.188568i
\(311\) 19.1012 1.08313 0.541563 0.840660i \(-0.317833\pi\)
0.541563 + 0.840660i \(0.317833\pi\)
\(312\) −10.8667 + 6.66450i −0.615204 + 0.377303i
\(313\) 14.8429i 0.838968i 0.907763 + 0.419484i \(0.137789\pi\)
−0.907763 + 0.419484i \(0.862211\pi\)
\(314\) −10.4064 17.6617i −0.587266 0.996706i
\(315\) 1.01543 + 0.586261i 0.0572132 + 0.0330320i
\(316\) −9.38247 + 16.9360i −0.527805 + 0.952726i
\(317\) −16.1773 28.0199i −0.908608 1.57376i −0.815999 0.578053i \(-0.803813\pi\)
−0.0926086 0.995703i \(-0.529521\pi\)
\(318\) −0.180928 20.4504i −0.0101460 1.14680i
\(319\) −0.218022 0.377625i −0.0122069 0.0211430i
\(320\) 0.240936 + 4.53470i 0.0134688 + 0.253498i
\(321\) 5.03323i 0.280928i
\(322\) 0.119865 + 13.5483i 0.00667980 + 0.755020i
\(323\) 19.2065 + 11.0888i 1.06868 + 0.617000i
\(324\) 1.99969 0.0353860i 0.111094 0.00196589i
\(325\) 18.2580 10.5413i 1.01277 0.584724i
\(326\) 7.06519 + 3.99617i 0.391304 + 0.221327i
\(327\) 2.83143i 0.156579i
\(328\) −23.3119 12.6464i −1.28718 0.698282i
\(329\) −15.9381 + 9.20184i −0.878694 + 0.507314i
\(330\) 0.351396 + 0.198755i 0.0193437 + 0.0109411i
\(331\) 7.43209 12.8728i 0.408505 0.707551i −0.586218 0.810154i \(-0.699384\pi\)
0.994722 + 0.102603i \(0.0327170\pi\)
\(332\) 13.4416 8.08092i 0.737703 0.443498i
\(333\) −0.346835 0.600736i −0.0190064 0.0329201i
\(334\) −11.5452 6.53015i −0.631728 0.357314i
\(335\) 2.79292 + 3.71320i 0.152594 + 0.202874i
\(336\) 3.87548 7.29719i 0.211425 0.398094i
\(337\) 12.2525 7.07401i 0.667439 0.385346i −0.127667 0.991817i \(-0.540749\pi\)
0.795105 + 0.606471i \(0.207415\pi\)
\(338\) −5.09130 + 9.00137i −0.276930 + 0.489610i
\(339\) −7.14336 4.12422i −0.387974 0.223997i
\(340\) 4.43499 2.66627i 0.240521 0.144599i
\(341\) 2.11237 + 3.65873i 0.114391 + 0.198131i
\(342\) 5.92832 3.49301i 0.320567 0.188880i
\(343\) 20.1051 1.08557
\(344\) 24.2162 0.642871i 1.30565 0.0346613i
\(345\) 1.31637 + 2.28003i 0.0708712 + 0.122753i
\(346\) −8.92618 15.1495i −0.479874 0.814441i
\(347\) 2.10226 3.64122i 0.112855 0.195471i −0.804065 0.594541i \(-0.797334\pi\)
0.916920 + 0.399070i \(0.130667\pi\)
\(348\) −0.840346 + 1.51689i −0.0450473 + 0.0813136i
\(349\) −0.844089 −0.0451831 −0.0225915 0.999745i \(-0.507192\pi\)
−0.0225915 + 0.999745i \(0.507192\pi\)
\(350\) −6.72747 + 11.8941i −0.359598 + 0.635766i
\(351\) 3.90313 2.25347i 0.208333 0.120281i
\(352\) 1.31209 2.52420i 0.0699345 0.134541i
\(353\) 23.0822 13.3265i 1.22854 0.709300i 0.261818 0.965117i \(-0.415678\pi\)
0.966725 + 0.255817i \(0.0823446\pi\)
\(354\) 0.0995956 + 11.2573i 0.00529345 + 0.598319i
\(355\) −1.42859 + 2.47440i −0.0758219 + 0.131327i
\(356\) 21.2526 0.376081i 1.12639 0.0199323i
\(357\) −9.41540 −0.498316
\(358\) 29.6432 0.262259i 1.56669 0.0138608i
\(359\) 16.8556i 0.889605i 0.895629 + 0.444803i \(0.146726\pi\)
−0.895629 + 0.444803i \(0.853274\pi\)
\(360\) −0.0426070 1.60496i −0.00224558 0.0845886i
\(361\) 2.33654 4.04700i 0.122976 0.213000i
\(362\) 6.68365 11.8166i 0.351285 0.621068i
\(363\) 5.37354 + 9.30725i 0.282038 + 0.488504i
\(364\) −0.329430 18.6163i −0.0172668 0.975760i
\(365\) 3.05366 1.76303i 0.159836 0.0922813i
\(366\) −10.3845 + 6.11862i −0.542807 + 0.319825i
\(367\) 4.32877 7.49765i 0.225960 0.391374i −0.730647 0.682755i \(-0.760781\pi\)
0.956607 + 0.291381i \(0.0941148\pi\)
\(368\) 15.7285 9.83881i 0.819907 0.512883i
\(369\) 8.12044 + 4.68834i 0.422733 + 0.244065i
\(370\) −0.479765 + 0.282681i −0.0249418 + 0.0146959i
\(371\) 25.8692 + 14.9356i 1.34306 + 0.775419i
\(372\) 8.14194 14.6968i 0.422140 0.761993i
\(373\) 8.48203 + 4.89711i 0.439183 + 0.253562i 0.703251 0.710942i \(-0.251731\pi\)
−0.264068 + 0.964504i \(0.585064\pi\)
\(374\) −3.24169 + 0.0286799i −0.167624 + 0.00148300i
\(375\) 5.49348i 0.283682i
\(376\) 22.1505 + 12.0164i 1.14233 + 0.619698i
\(377\) 3.90776i 0.201260i
\(378\) −1.43817 + 2.54268i −0.0739716 + 0.130781i
\(379\) 18.0207 + 31.2128i 0.925661 + 1.60329i 0.790494 + 0.612469i \(0.209824\pi\)
0.135167 + 0.990823i \(0.456843\pi\)
\(380\) −2.84604 4.73403i −0.145999 0.242851i
\(381\) 10.1229 + 5.84445i 0.518611 + 0.299420i
\(382\) 3.57243 + 6.06312i 0.182781 + 0.310216i
\(383\) −7.95385 13.7765i −0.406423 0.703945i 0.588063 0.808815i \(-0.299891\pi\)
−0.994486 + 0.104870i \(0.966557\pi\)
\(384\) −11.2920 + 0.700196i −0.576244 + 0.0357317i
\(385\) −0.510665 + 0.294833i −0.0260259 + 0.0150261i
\(386\) 30.8602 0.273026i 1.57074 0.0138967i
\(387\) −8.56474 −0.435370
\(388\) 18.2200 10.9536i 0.924979 0.556086i
\(389\) 15.4391 + 26.7414i 0.782795 + 1.35584i 0.930307 + 0.366781i \(0.119540\pi\)
−0.147512 + 0.989060i \(0.547127\pi\)
\(390\) −1.83665 3.11715i −0.0930022 0.157843i
\(391\) −18.3087 10.5706i −0.925912 0.534576i
\(392\) −4.04168 6.59008i −0.204136 0.332849i
\(393\) 6.99256i 0.352728i
\(394\) −27.2966 15.4393i −1.37518 0.777822i
\(395\) −4.75889 2.74755i −0.239446 0.138244i
\(396\) −0.487413 + 0.879816i −0.0244934 + 0.0442124i
\(397\) −27.7523 −1.39285 −0.696423 0.717631i \(-0.745226\pi\)
−0.696423 + 0.717631i \(0.745226\pi\)
\(398\) 21.2208 12.5034i 1.06370 0.626740i
\(399\) 10.0503i 0.503142i
\(400\) 18.6994 0.662009i 0.934972 0.0331005i
\(401\) 30.4324i 1.51972i −0.650086 0.759860i \(-0.725267\pi\)
0.650086 0.759860i \(-0.274733\pi\)
\(402\) −9.18914 + 7.03986i −0.458313 + 0.351116i
\(403\) 37.8615i 1.88601i
\(404\) −18.5610 10.2827i −0.923443 0.511582i
\(405\) 0.567637i 0.0282061i
\(406\) −1.28578 2.18223i −0.0638124 0.108302i
\(407\) 0.348849 0.0172918
\(408\) 6.74023 + 10.9902i 0.333691 + 0.544094i
\(409\) −30.8839 17.8308i −1.52711 0.881678i −0.999481 0.0322035i \(-0.989748\pi\)
−0.527630 0.849474i \(-0.676919\pi\)
\(410\) 3.70580 6.55181i 0.183016 0.323571i
\(411\) 14.5906i 0.719704i
\(412\) 7.25787 + 4.02082i 0.357569 + 0.198091i
\(413\) −14.2402 8.22160i −0.700716 0.404559i
\(414\) −5.65123 + 3.32975i −0.277743 + 0.163648i
\(415\) 2.22566 + 3.85496i 0.109253 + 0.189232i
\(416\) −21.4941 + 13.7114i −1.05384 + 0.672259i
\(417\) −20.5318 −1.00545
\(418\) 0.0306137 + 3.46027i 0.00149736 + 0.169247i
\(419\) 10.8492 6.26380i 0.530019 0.306007i −0.211005 0.977485i \(-0.567674\pi\)
0.741024 + 0.671478i \(0.234340\pi\)
\(420\) 2.05129 + 1.13641i 0.100093 + 0.0554509i
\(421\) 5.47166 + 9.47719i 0.266672 + 0.461890i 0.968000 0.250949i \(-0.0807425\pi\)
−0.701328 + 0.712839i \(0.747409\pi\)
\(422\) 24.0186 14.1520i 1.16921 0.688906i
\(423\) −7.71589 4.45477i −0.375159 0.216598i
\(424\) −1.08546 40.8880i −0.0527145 1.98570i
\(425\) −10.6610 18.4655i −0.517137 0.895707i
\(426\) −6.19597 3.50453i −0.300196 0.169795i
\(427\) 17.6048i 0.851955i
\(428\) −0.178106 10.0649i −0.00860908 0.486505i
\(429\) 2.26656i 0.109430i
\(430\) 0.0608259 + 6.87517i 0.00293329 + 0.331550i
\(431\) −23.1169 13.3466i −1.11350 0.642882i −0.173769 0.984786i \(-0.555595\pi\)
−0.939735 + 0.341905i \(0.888928\pi\)
\(432\) 3.99750 0.141522i 0.192330 0.00680897i
\(433\) 24.8881 + 14.3691i 1.19604 + 0.690536i 0.959671 0.281126i \(-0.0907080\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(434\) 12.4577 + 21.1431i 0.597988 + 1.01490i
\(435\) −0.426233 0.246086i −0.0204363 0.0117989i
\(436\) 0.100193 + 5.66198i 0.00479838 + 0.271160i
\(437\) −11.2833 + 19.5432i −0.539753 + 0.934880i
\(438\) 4.45955 + 7.56874i 0.213086 + 0.361648i
\(439\) −5.89975 + 3.40622i −0.281580 + 0.162570i −0.634138 0.773220i \(-0.718645\pi\)
0.352559 + 0.935790i \(0.385312\pi\)
\(440\) 0.709715 + 0.385012i 0.0338344 + 0.0183547i
\(441\) 1.36661 + 2.36705i 0.0650769 + 0.112716i
\(442\) 25.2879 + 14.3032i 1.20282 + 0.680333i
\(443\) 2.14957 3.72316i 0.102129 0.176893i −0.810433 0.585832i \(-0.800768\pi\)
0.912562 + 0.408939i \(0.134101\pi\)
\(444\) −0.714819 1.18901i −0.0339238 0.0564279i
\(445\) 6.03284i 0.285984i
\(446\) 0.0587834 + 6.64430i 0.00278347 + 0.314617i
\(447\) −7.52955 −0.356136
\(448\) 7.49153 14.7292i 0.353942 0.695891i
\(449\) −2.34265 + 4.05758i −0.110556 + 0.191489i −0.915995 0.401190i \(-0.868597\pi\)
0.805438 + 0.592680i \(0.201930\pi\)
\(450\) −6.61513 + 0.0585253i −0.311840 + 0.00275891i
\(451\) −4.08380 + 2.35778i −0.192299 + 0.111024i
\(452\) −14.4304 7.99438i −0.678750 0.376024i
\(453\) −15.9680 + 9.21910i −0.750240 + 0.433151i
\(454\) −15.9591 9.02671i −0.748999 0.423644i
\(455\) 5.28449 0.247741
\(456\) 11.7312 7.19471i 0.549363 0.336923i
\(457\) −19.9700 + 34.5891i −0.934159 + 1.61801i −0.158033 + 0.987434i \(0.550515\pi\)
−0.776127 + 0.630577i \(0.782818\pi\)
\(458\) 27.1062 15.9711i 1.26659 0.746282i
\(459\) −2.27908 3.94748i −0.106378 0.184253i
\(460\) 2.71302 + 4.51276i 0.126495 + 0.210409i
\(461\) 17.3662 0.808822 0.404411 0.914577i \(-0.367476\pi\)
0.404411 + 0.914577i \(0.367476\pi\)
\(462\) −0.745773 1.26572i −0.0346965 0.0588868i
\(463\) −8.53232 14.7784i −0.396531 0.686811i 0.596765 0.802416i \(-0.296453\pi\)
−0.993295 + 0.115605i \(0.963119\pi\)
\(464\) −1.62675 + 3.06303i −0.0755201 + 0.142198i
\(465\) 4.12969 + 2.38428i 0.191510 + 0.110568i
\(466\) 16.9830 + 9.60581i 0.786721 + 0.444981i
\(467\) −20.9631 + 12.1030i −0.970055 + 0.560061i −0.899253 0.437429i \(-0.855889\pi\)
−0.0708017 + 0.997490i \(0.522556\pi\)
\(468\) 7.72529 4.64435i 0.357102 0.214685i
\(469\) −2.04562 16.7836i −0.0944580 0.774994i
\(470\) −3.52118 + 6.22541i −0.162420 + 0.287157i
\(471\) 7.24765 + 12.5533i 0.333954 + 0.578425i
\(472\) 0.597511 + 22.5076i 0.0275027 + 1.03600i
\(473\) 2.15362 3.73018i 0.0990235 0.171514i
\(474\) 6.74009 11.9164i 0.309583 0.547339i
\(475\) −19.7105 + 11.3799i −0.904381 + 0.522145i
\(476\) −18.8279 + 0.333173i −0.862973 + 0.0152710i
\(477\) 14.4612i 0.662132i
\(478\) 15.1723 26.8244i 0.693963 1.22692i
\(479\) 28.8135 16.6355i 1.31652 0.760095i 0.333356 0.942801i \(-0.391819\pi\)
0.983168 + 0.182706i \(0.0584857\pi\)
\(480\) −0.141994 3.20790i −0.00648109 0.146420i
\(481\) −2.70748 1.56316i −0.123450 0.0712742i
\(482\) 4.67861 0.0413925i 0.213105 0.00188538i
\(483\) 9.58050i 0.435928i
\(484\) 11.0748 + 18.4214i 0.503398 + 0.837338i
\(485\) 3.01687 + 5.22537i 0.136989 + 0.237272i
\(486\) −1.41416 + 0.0125113i −0.0641475 + 0.000567525i
\(487\) 7.54173 + 13.0627i 0.341749 + 0.591926i 0.984758 0.173933i \(-0.0556476\pi\)
−0.643009 + 0.765859i \(0.722314\pi\)
\(488\) −20.5492 + 12.6028i −0.930220 + 0.570502i
\(489\) −4.97065 2.86980i −0.224780 0.129777i
\(490\) 1.89039 1.11383i 0.0853992 0.0503178i
\(491\) 17.2830i 0.779969i 0.920821 + 0.389985i \(0.127520\pi\)
−0.920821 + 0.389985i \(0.872480\pi\)
\(492\) 16.4042 + 9.08786i 0.739560 + 0.409712i
\(493\) 3.95216 0.177996
\(494\) 15.2676 26.9930i 0.686922 1.21447i
\(495\) −0.247222 0.142733i −0.0111118 0.00641539i
\(496\) 15.7613 29.6771i 0.707702 1.33254i
\(497\) 9.00427 5.19862i 0.403897 0.233190i
\(498\) −9.55482 + 5.62977i −0.428162 + 0.252276i
\(499\) −2.30235 3.98778i −0.103067 0.178518i 0.809880 0.586596i \(-0.199532\pi\)
−0.912947 + 0.408078i \(0.866199\pi\)
\(500\) 0.194392 + 10.9852i 0.00869348 + 0.491274i
\(501\) 8.12255 + 4.68956i 0.362889 + 0.209514i
\(502\) 3.23608 + 5.49226i 0.144433 + 0.245131i
\(503\) 3.09904 5.36769i 0.138179 0.239334i −0.788628 0.614870i \(-0.789208\pi\)
0.926807 + 0.375537i \(0.122542\pi\)
\(504\) −2.78592 + 5.13545i −0.124095 + 0.228751i
\(505\) 3.01117 5.21549i 0.133995 0.232086i
\(506\) −0.0291828 3.29853i −0.00129733 0.146638i
\(507\) 3.65626 6.33283i 0.162380 0.281251i
\(508\) 20.4494 + 11.3289i 0.907296 + 0.502637i
\(509\) −11.5141 −0.510354 −0.255177 0.966894i \(-0.582134\pi\)
−0.255177 + 0.966894i \(0.582134\pi\)
\(510\) −3.15257 + 1.85752i −0.139598 + 0.0822522i
\(511\) −12.8312 −0.567621
\(512\) −22.5557 + 1.79975i −0.996832 + 0.0795385i
\(513\) −4.21365 + 2.43275i −0.186037 + 0.107408i
\(514\) 7.17257 12.6810i 0.316368 0.559336i
\(515\) −1.17745 + 2.03940i −0.0518847 + 0.0898669i
\(516\) −17.1268 + 0.303072i −0.753965 + 0.0133420i
\(517\) 3.88035 2.24032i 0.170657 0.0985291i
\(518\) 2.02628 0.0179269i 0.0890298 0.000787664i
\(519\) 6.21674 + 10.7677i 0.272885 + 0.472650i
\(520\) −3.78302 6.16833i −0.165896 0.270499i
\(521\) 0.906106i 0.0396972i 0.999803 + 0.0198486i \(0.00631842\pi\)
−0.999803 + 0.0198486i \(0.993682\pi\)
\(522\) 0.603681 1.06730i 0.0264224 0.0467145i
\(523\) 3.05551 1.76410i 0.133608 0.0771386i −0.431706 0.902014i \(-0.642088\pi\)
0.565314 + 0.824876i \(0.308755\pi\)
\(524\) 0.247439 + 13.9829i 0.0108094 + 0.610847i
\(525\) 4.83126 8.36798i 0.210853 0.365209i
\(526\) −0.0916970 10.3645i −0.00399818 0.451915i
\(527\) −38.2917 −1.66801
\(528\) −0.943541 + 1.77660i −0.0410623 + 0.0773168i
\(529\) −0.744097 + 1.28881i −0.0323520 + 0.0560354i
\(530\) 11.6084 0.102702i 0.504237 0.00446108i
\(531\) 7.96043i 0.345453i
\(532\) 0.355638 + 20.0974i 0.0154189 + 0.871331i
\(533\) 42.2601 1.83049
\(534\) −15.0296 + 0.132970i −0.650396 + 0.00575418i
\(535\) 2.85705 0.123521
\(536\) −18.1263 + 14.4027i −0.782937 + 0.622101i
\(537\) −20.9617 −0.904566
\(538\) 4.99186 0.0441640i 0.215215 0.00190404i
\(539\) −1.37455 −0.0592061
\(540\) 0.0200864 + 1.13510i 0.000864382 + 0.0488468i
\(541\) 41.5109i 1.78469i −0.451352 0.892346i \(-0.649058\pi\)
0.451352 0.892346i \(-0.350942\pi\)
\(542\) 4.46269 0.0394823i 0.191689 0.00169591i
\(543\) −4.79979 + 8.31348i −0.205979 + 0.356765i
\(544\) 13.8673 + 21.7384i 0.594554 + 0.932025i
\(545\) −1.60723 −0.0688461
\(546\) 0.116476 + 13.1653i 0.00498470 + 0.563421i
\(547\) 7.82240 13.5488i 0.334462 0.579304i −0.648920 0.760857i \(-0.724779\pi\)
0.983381 + 0.181552i \(0.0581122\pi\)
\(548\) −0.516305 29.1767i −0.0220554 1.24637i
\(549\) 7.38094 4.26139i 0.315011 0.181872i
\(550\) 1.63790 2.89579i 0.0698402 0.123477i
\(551\) 4.21865i 0.179720i
\(552\) −11.1829 + 6.85842i −0.475974 + 0.291914i
\(553\) 9.99825 + 17.3175i 0.425169 + 0.736414i
\(554\) 6.94968 0.0614851i 0.295264 0.00261225i
\(555\) 0.341000 0.196876i 0.0144746 0.00835694i
\(556\) −41.0572 + 0.726539i −1.74121 + 0.0308121i
\(557\) −6.31743 + 10.9421i −0.267678 + 0.463632i −0.968262 0.249938i \(-0.919590\pi\)
0.700584 + 0.713570i \(0.252923\pi\)
\(558\) −5.84894 + 10.3409i −0.247605 + 0.437764i
\(559\) −33.4293 + 19.3004i −1.41391 + 0.816320i
\(560\) 4.14216 + 2.19987i 0.175038 + 0.0929614i
\(561\) 2.29231 0.0967815
\(562\) 0.309330 0.182259i 0.0130483 0.00768815i
\(563\) −16.5374 −0.696969 −0.348484 0.937315i \(-0.613304\pi\)
−0.348484 + 0.937315i \(0.613304\pi\)
\(564\) −15.5870 8.63511i −0.656331 0.363604i
\(565\) 2.34106 4.05484i 0.0984893 0.170588i
\(566\) −0.121151 13.6937i −0.00509235 0.575590i
\(567\) 1.03281 1.78888i 0.0433739 0.0751257i
\(568\) −12.5140 6.78871i −0.525076 0.284848i
\(569\) 15.0544 26.0750i 0.631115 1.09312i −0.356209 0.934406i \(-0.615931\pi\)
0.987324 0.158717i \(-0.0507356\pi\)
\(570\) 1.98276 + 3.36514i 0.0830488 + 0.140950i
\(571\) 17.1865 + 9.92262i 0.719232 + 0.415249i 0.814470 0.580206i \(-0.197028\pi\)
−0.0952382 + 0.995455i \(0.530361\pi\)
\(572\) 0.0802044 + 4.53240i 0.00335351 + 0.189509i
\(573\) −2.48806 4.30945i −0.103940 0.180030i
\(574\) −23.5995 + 13.9050i −0.985025 + 0.580384i
\(575\) 18.7893 10.8480i 0.783566 0.452392i
\(576\) 7.98873 0.424455i 0.332864 0.0176856i
\(577\) −15.7427 9.08907i −0.655379 0.378383i 0.135135 0.990827i \(-0.456853\pi\)
−0.790514 + 0.612444i \(0.790186\pi\)
\(578\) 2.62956 4.64905i 0.109375 0.193375i
\(579\) −21.8223 −0.906905
\(580\) −0.861041 0.477012i −0.0357528 0.0198069i
\(581\) 16.1982i 0.672016i
\(582\) −12.9515 + 7.63111i −0.536856 + 0.316320i
\(583\) −6.29823 3.63629i −0.260846 0.150600i
\(584\) 9.18554 + 14.9773i 0.380100 + 0.619765i
\(585\) 1.27915 + 2.21556i 0.0528865 + 0.0916022i
\(586\) 1.90472 0.0168514i 0.0786833 0.000696127i
\(587\) 19.8016 + 34.2974i 0.817300 + 1.41561i 0.907664 + 0.419697i \(0.137864\pi\)
−0.0903640 + 0.995909i \(0.528803\pi\)
\(588\) 2.81656 + 4.68499i 0.116153 + 0.193206i
\(589\) 40.8736i 1.68417i
\(590\) −6.39007 + 0.0565342i −0.263075 + 0.00232748i
\(591\) 19.2043 + 11.0876i 0.789958 + 0.456082i
\(592\) −1.47149 2.35235i −0.0604778 0.0966811i
\(593\) 19.2570 11.1181i 0.790792 0.456564i −0.0494492 0.998777i \(-0.515747\pi\)
0.840241 + 0.542213i \(0.182413\pi\)
\(594\) 0.350144 0.619050i 0.0143666 0.0253999i
\(595\) 5.34454i 0.219105i
\(596\) −15.0567 + 0.266441i −0.616748 + 0.0109138i
\(597\) −15.0830 + 8.70816i −0.617305 + 0.356401i
\(598\) −14.5540 + 25.7313i −0.595157 + 1.05223i
\(599\) −0.873519 + 1.51298i −0.0356910 + 0.0618187i −0.883319 0.468772i \(-0.844697\pi\)
0.847628 + 0.530591i \(0.178030\pi\)
\(600\) −13.2261 + 0.351115i −0.539954 + 0.0143342i
\(601\) −1.37648 2.38413i −0.0561478 0.0972508i 0.836585 0.547837i \(-0.184548\pi\)
−0.892733 + 0.450586i \(0.851215\pi\)
\(602\) 12.3176 21.7774i 0.502027 0.887579i
\(603\) 6.54149 4.92025i 0.266390 0.200368i
\(604\) −31.6047 + 19.0004i −1.28598 + 0.773114i
\(605\) −5.28314 + 3.05023i −0.214790 + 0.124009i
\(606\) 13.0597 + 7.38678i 0.530516 + 0.300067i
\(607\) −6.24508 3.60560i −0.253480 0.146347i 0.367877 0.929875i \(-0.380085\pi\)
−0.621357 + 0.783528i \(0.713418\pi\)
\(608\) 23.2041 14.8023i 0.941051 0.600312i
\(609\) 0.895500 + 1.55105i 0.0362875 + 0.0628518i
\(610\) −3.47316 5.89463i −0.140624 0.238667i
\(611\) −40.1548 −1.62449
\(612\) −4.69713 7.81307i −0.189870 0.315825i
\(613\) 22.5754 + 39.1017i 0.911810 + 1.57930i 0.811506 + 0.584344i \(0.198648\pi\)
0.100304 + 0.994957i \(0.468019\pi\)
\(614\) 7.14422 4.20943i 0.288317 0.169879i
\(615\) −2.66128 + 4.60947i −0.107313 + 0.185872i
\(616\) −1.53610 2.50466i −0.0618913 0.100916i
\(617\) −30.6940 −1.23569 −0.617847 0.786299i \(-0.711995\pi\)
−0.617847 + 0.786299i \(0.711995\pi\)
\(618\) −5.10673 2.88844i −0.205423 0.116190i
\(619\) 6.23764 3.60131i 0.250712 0.144749i −0.369378 0.929279i \(-0.620429\pi\)
0.620090 + 0.784530i \(0.287096\pi\)
\(620\) 8.34245 + 4.62167i 0.335041 + 0.185611i
\(621\) 4.01670 2.31904i 0.161184 0.0930599i
\(622\) −27.0121 + 0.238981i −1.08308 + 0.00958226i
\(623\) 10.9767 19.0121i 0.439771 0.761705i
\(624\) 15.2838 9.56062i 0.611842 0.382731i
\(625\) 20.2706 0.810825
\(626\) −0.185704 20.9901i −0.00742222 0.838935i
\(627\) 2.44688i 0.0977188i
\(628\) 14.9372 + 24.8462i 0.596061 + 0.991471i
\(629\) −1.58093 + 2.73825i −0.0630357 + 0.109181i
\(630\) −1.44332 0.816361i −0.0575032 0.0325246i
\(631\) 7.04131 + 12.1959i 0.280310 + 0.485511i 0.971461 0.237199i \(-0.0762294\pi\)
−0.691151 + 0.722710i \(0.742896\pi\)
\(632\) 13.0564 24.0676i 0.519356 0.957358i
\(633\) −17.0716 + 9.85630i −0.678536 + 0.391753i
\(634\) 23.2278 + 39.4222i 0.922495 + 1.56566i
\(635\) −3.31753 + 5.74613i −0.131652 + 0.228028i
\(636\) 0.511723 + 28.9178i 0.0202911 + 1.14667i
\(637\) 10.6681 + 6.15925i 0.422687 + 0.244038i
\(638\) 0.313042 + 0.531294i 0.0123935 + 0.0210341i
\(639\) 4.35912 + 2.51674i 0.172444 + 0.0995606i
\(640\) −0.397457 6.40977i −0.0157109 0.253369i
\(641\) −9.05911 5.23028i −0.357813 0.206584i 0.310308 0.950636i \(-0.399568\pi\)
−0.668121 + 0.744053i \(0.732901\pi\)
\(642\) 0.0629725 + 7.11779i 0.00248532 + 0.280917i
\(643\) 12.9178i 0.509427i −0.967017 0.254713i \(-0.918019\pi\)
0.967017 0.254713i \(-0.0819811\pi\)
\(644\) −0.339016 19.1580i −0.0133591 0.754931i
\(645\) 4.86167i 0.191428i
\(646\) −27.2997 15.4411i −1.07409 0.607522i
\(647\) 9.11408 + 15.7861i 0.358312 + 0.620614i 0.987679 0.156494i \(-0.0500192\pi\)
−0.629367 + 0.777108i \(0.716686\pi\)
\(648\) −2.82743 + 0.0750601i −0.111072 + 0.00294864i
\(649\) 3.46699 + 2.00166i 0.136091 + 0.0785722i
\(650\) −25.6878 + 15.1354i −1.00756 + 0.593661i
\(651\) −8.67631 15.0278i −0.340051 0.588986i
\(652\) −10.0413 5.56282i −0.393247 0.217857i
\(653\) 12.1302 7.00335i 0.474690 0.274062i −0.243511 0.969898i \(-0.578299\pi\)
0.718201 + 0.695836i \(0.244966\pi\)
\(654\) −0.0354250 4.00410i −0.00138523 0.156573i
\(655\) −3.96924 −0.155091
\(656\) 33.1249 + 17.5924i 1.29331 + 0.686868i
\(657\) −3.10591 5.37959i −0.121173 0.209878i
\(658\) 22.4238 13.2123i 0.874171 0.515068i
\(659\) 14.6230 + 8.44257i 0.569630 + 0.328876i 0.757001 0.653413i \(-0.226664\pi\)
−0.187372 + 0.982289i \(0.559997\pi\)
\(660\) −0.499416 0.276674i −0.0194398 0.0107695i
\(661\) 10.6171i 0.412957i 0.978451 + 0.206479i \(0.0662004\pi\)
−0.978451 + 0.206479i \(0.933800\pi\)
\(662\) −10.3491 + 18.2971i −0.402229 + 0.711137i
\(663\) −17.7911 10.2717i −0.690947 0.398919i
\(664\) −18.9074 + 11.5959i −0.733751 + 0.450007i
\(665\) −5.70490 −0.221227
\(666\) 0.497995 + 0.845196i 0.0192969 + 0.0327507i
\(667\) 4.02146i 0.155712i
\(668\) 16.4085 + 9.09022i 0.634864 + 0.351711i
\(669\) 4.69841i 0.181651i
\(670\) −3.99609 5.21610i −0.154382 0.201516i
\(671\) 4.28613i 0.165464i
\(672\) −5.38925 + 10.3679i −0.207895 + 0.399949i
\(673\) 41.9851i 1.61841i −0.587529 0.809203i \(-0.699899\pi\)
0.587529 0.809203i \(-0.300101\pi\)
\(674\) −17.2385 + 10.1571i −0.664003 + 0.391235i
\(675\) 4.67779 0.180048
\(676\) 7.08729 12.7931i 0.272588 0.492041i
\(677\) −14.1927 8.19415i −0.545469 0.314927i 0.201823 0.979422i \(-0.435313\pi\)
−0.747293 + 0.664495i \(0.768647\pi\)
\(678\) 10.1534 + 5.74293i 0.389941 + 0.220556i
\(679\) 21.9566i 0.842616i
\(680\) −6.23842 + 3.82601i −0.239233 + 0.146721i
\(681\) 11.2279 + 6.48243i 0.430254 + 0.248407i
\(682\) −3.03300 5.14760i −0.116140 0.197112i
\(683\) 8.84052 + 15.3122i 0.338273 + 0.585906i 0.984108 0.177571i \(-0.0568239\pi\)
−0.645835 + 0.763477i \(0.723491\pi\)
\(684\) −8.33989 + 5.01384i −0.318883 + 0.191709i
\(685\) 8.28220 0.316447
\(686\) −28.4318 + 0.251542i −1.08553 + 0.00960391i
\(687\) −19.2661 + 11.1233i −0.735048 + 0.424380i
\(688\) −34.2375 + 1.21210i −1.30529 + 0.0462108i
\(689\) 32.5878 + 56.4438i 1.24150 + 2.15034i
\(690\) −1.89009 3.20785i −0.0719544 0.122121i
\(691\) 27.6376 + 15.9566i 1.05139 + 0.607018i 0.923037 0.384711i \(-0.125699\pi\)
0.128349 + 0.991729i \(0.459032\pi\)
\(692\) 12.8126 + 21.3121i 0.487061 + 0.810163i
\(693\) 0.519403 + 0.899632i 0.0197305 + 0.0341742i
\(694\) −2.92737 + 5.17557i −0.111122 + 0.196462i
\(695\) 11.6546i 0.442085i
\(696\) 1.16940 2.15563i 0.0443262 0.0817090i
\(697\) 42.7404i 1.61891i
\(698\) 1.19368 0.0105607i 0.0451813 0.000399728i
\(699\) −11.9482 6.89831i −0.451923 0.260918i
\(700\) 9.36489 16.9043i 0.353960 0.638923i
\(701\) 30.6740 + 17.7096i 1.15854 + 0.668883i 0.950954 0.309334i \(-0.100106\pi\)
0.207586 + 0.978217i \(0.433439\pi\)
\(702\) −5.49144 + 3.23560i −0.207261 + 0.122120i
\(703\) 2.92288 + 1.68752i 0.110238 + 0.0636462i
\(704\) −1.82392 + 3.58604i −0.0687415 + 0.135154i
\(705\) 2.52869 4.37983i 0.0952361 0.164954i
\(706\) −32.4752 + 19.1346i −1.22222 + 0.720141i
\(707\) −18.9790 + 10.9575i −0.713780 + 0.412101i
\(708\) −0.281688 15.9184i −0.0105865 0.598249i
\(709\) −8.88087 15.3821i −0.333528 0.577687i 0.649673 0.760214i \(-0.274906\pi\)
−0.983201 + 0.182526i \(0.941573\pi\)
\(710\) 1.98930 3.51707i 0.0746571 0.131993i
\(711\) −4.84032 + 8.38369i −0.181526 + 0.314413i
\(712\) −30.0499 + 0.797737i −1.12617 + 0.0298965i
\(713\) 38.9631i 1.45918i
\(714\) 13.3149 0.117799i 0.498296 0.00440852i
\(715\) −1.28658 −0.0481155
\(716\) −41.9169 + 0.741752i −1.56651 + 0.0277206i
\(717\) −10.8958 + 18.8721i −0.406911 + 0.704790i
\(718\) −0.210886 23.8365i −0.00787020 0.889570i
\(719\) −5.68667 + 3.28320i −0.212077 + 0.122443i −0.602276 0.798288i \(-0.705739\pi\)
0.390199 + 0.920730i \(0.372406\pi\)
\(720\) 0.0803331 + 2.26913i 0.00299384 + 0.0845654i
\(721\) 7.42134 4.28471i 0.276385 0.159571i
\(722\) −3.25360 + 5.75233i −0.121086 + 0.214080i
\(723\) −3.30840 −0.123041
\(724\) −9.30389 + 16.7942i −0.345776 + 0.624151i
\(725\) −2.02795 + 3.51250i −0.0753160 + 0.130451i
\(726\) −7.71549 13.0947i −0.286349 0.485990i
\(727\) 21.8417 + 37.8310i 0.810065 + 1.40307i 0.912818 + 0.408367i \(0.133902\pi\)
−0.102753 + 0.994707i \(0.532765\pi\)
\(728\) 0.698781 + 26.3223i 0.0258985 + 0.975569i
\(729\) 1.00000 0.0370370
\(730\) −4.29630 + 2.53141i −0.159013 + 0.0936917i
\(731\) 19.5197 + 33.8091i 0.721963 + 1.25048i
\(732\) 14.6088 8.78262i 0.539956 0.324615i
\(733\) −1.69271 0.977289i −0.0625218 0.0360970i 0.468413 0.883510i \(-0.344826\pi\)
−0.530935 + 0.847413i \(0.678159\pi\)
\(734\) −6.02776 + 10.6570i −0.222489 + 0.393358i
\(735\) −1.34362 + 0.775742i −0.0495603 + 0.0286137i
\(736\) −22.1195 + 14.1104i −0.815337 + 0.520117i
\(737\) 0.498036 + 4.08620i 0.0183454 + 0.150517i
\(738\) −11.5422 6.52846i −0.424876 0.240316i
\(739\) −10.5730 18.3129i −0.388933 0.673652i 0.603373 0.797459i \(-0.293823\pi\)
−0.992306 + 0.123807i \(0.960490\pi\)
\(740\) 0.674927 0.405758i 0.0248108 0.0149160i
\(741\) −10.9643 + 18.9907i −0.402782 + 0.697639i
\(742\) −36.7701 20.7977i −1.34987 0.763506i
\(743\) 39.0412 22.5404i 1.43228 0.826928i 0.434987 0.900437i \(-0.356753\pi\)
0.997295 + 0.0735085i \(0.0234196\pi\)
\(744\) −11.3301 + 20.8855i −0.415382 + 0.765698i
\(745\) 4.27406i 0.156589i
\(746\) −12.0562 6.81916i −0.441409 0.249667i
\(747\) 6.79123 3.92092i 0.248478 0.143459i
\(748\) 4.58391 0.0811158i 0.167604 0.00296589i
\(749\) −9.00383 5.19837i −0.328993 0.189944i
\(750\) −0.0687307 7.76864i −0.00250969 0.283671i
\(751\) 10.7942i 0.393884i 0.980415 + 0.196942i \(0.0631011\pi\)
−0.980415 + 0.196942i \(0.936899\pi\)
\(752\) −31.4747 16.7160i −1.14776 0.609568i
\(753\) −2.25380 3.90370i −0.0821332 0.142259i
\(754\) −0.0488913 5.52619i −0.00178051 0.201252i
\(755\) −5.23311 9.06401i −0.190452 0.329873i
\(756\) 2.00199 3.61374i 0.0728117 0.131430i
\(757\) 6.66198 + 3.84629i 0.242134 + 0.139796i 0.616157 0.787623i \(-0.288689\pi\)
−0.374023 + 0.927419i \(0.622022\pi\)
\(758\) −25.8746 43.9143i −0.939809 1.59504i
\(759\) 2.33251i 0.0846647i
\(760\) 4.08399 + 6.65906i 0.148142 + 0.241550i
\(761\) −17.2468 −0.625197 −0.312598 0.949885i \(-0.601199\pi\)
−0.312598 + 0.949885i \(0.601199\pi\)
\(762\) −14.3885 8.13833i −0.521240 0.294821i
\(763\) 5.06508 + 2.92433i 0.183368 + 0.105868i
\(764\) −5.12784 8.52951i −0.185519 0.308587i
\(765\) 2.24074 1.29369i 0.0810140 0.0467735i
\(766\) 11.4204 + 19.3826i 0.412635 + 0.700322i
\(767\) −17.9386 31.0706i −0.647726 1.12189i
\(768\) 15.9599 1.13147i 0.575905 0.0408283i
\(769\) −35.3176 20.3906i −1.27358 0.735304i −0.297923 0.954590i \(-0.596294\pi\)
−0.975661 + 0.219286i \(0.929627\pi\)
\(770\) 0.718472 0.423329i 0.0258919 0.0152557i
\(771\) −5.15090 + 8.92162i −0.185505 + 0.321304i
\(772\) −43.6378 + 0.772205i −1.57056 + 0.0277923i
\(773\) 6.37842 11.0477i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929852\pi\)
\(774\) 12.1119 0.107156i 0.435353 0.00385165i
\(775\) 19.6483 34.0319i 0.705789 1.22246i
\(776\) −25.6289 + 15.7181i −0.920023 + 0.564248i
\(777\) −1.43286 −0.0514034
\(778\) −22.1680 37.6234i −0.794760 1.34886i
\(779\) −45.6222 −1.63459
\(780\) 2.63631 + 4.38516i 0.0943950 + 0.157014i
\(781\) −2.19222 + 1.26568i −0.0784436 + 0.0452895i
\(782\) 26.0237 + 14.7194i 0.930605 + 0.526363i
\(783\) −0.433527 + 0.750890i −0.0154930 + 0.0268346i
\(784\) 5.79802 + 9.26885i 0.207072 + 0.331030i
\(785\) −7.12572 + 4.11404i −0.254328 + 0.146836i
\(786\) −0.0874862 9.88859i −0.00312053 0.352714i
\(787\) 13.0709 + 22.6395i 0.465928 + 0.807011i 0.999243 0.0389057i \(-0.0123872\pi\)
−0.533315 + 0.845917i \(0.679054\pi\)
\(788\) 38.7949 + 21.4921i 1.38201 + 0.765626i
\(789\) 7.32912i 0.260923i
\(790\) 6.76421 + 3.82593i 0.240660 + 0.136120i
\(791\) −14.7555 + 8.51906i −0.524643 + 0.302903i
\(792\) 0.678272 1.25030i 0.0241013 0.0444274i
\(793\) 19.2058 33.2655i 0.682019 1.18129i
\(794\) 39.2461 0.347218i 1.39279 0.0123223i
\(795\) −8.20870 −0.291133
\(796\) −29.8531 + 17.9473i −1.05811 + 0.636126i
\(797\) −24.0620 + 41.6765i −0.852318 + 1.47626i 0.0267926 + 0.999641i \(0.491471\pi\)
−0.879111 + 0.476617i \(0.841863\pi\)
\(798\) −0.125742 14.2126i −0.00445122 0.503122i
\(799\) 40.6111i 1.43672i
\(800\) −26.4357 + 1.17014i −0.934642 + 0.0413707i
\(801\) 10.6280 0.375521
\(802\) 0.380750 + 43.0362i 0.0134447 + 1.51966i
\(803\) 3.12395 0.110242
\(804\) 12.9068 10.0704i 0.455189 0.355157i
\(805\) 5.43825 0.191673
\(806\) 0.473697 + 53.5421i 0.0166853 + 1.88594i
\(807\) −3.52992 −0.124259
\(808\) 26.3768 + 14.3091i 0.927933 + 0.503393i
\(809\) 31.5695i 1.10992i −0.831876 0.554962i \(-0.812733\pi\)
0.831876 0.554962i \(-0.187267\pi\)
\(810\) −0.00710190 0.802729i −0.000249535 0.0282050i
\(811\) 11.3567 19.6704i 0.398788 0.690721i −0.594788 0.803882i \(-0.702764\pi\)
0.993577 + 0.113161i \(0.0360975\pi\)
\(812\) 1.84560 + 3.06993i 0.0647680 + 0.107733i
\(813\) −3.15572 −0.110676
\(814\) −0.493328 + 0.00436456i −0.0172911 + 0.000152978i
\(815\) 1.62901 2.82153i 0.0570617 0.0988337i
\(816\) −9.66926 15.4575i −0.338492 0.541120i
\(817\) 36.0888 20.8359i 1.26259 0.728955i
\(818\) 43.8978 + 24.8292i 1.53485 + 0.868133i
\(819\) 9.30961i 0.325304i
\(820\) −5.15861 + 9.31166i −0.180146 + 0.325177i
\(821\) −7.34108 12.7151i −0.256206 0.443761i 0.709017 0.705192i \(-0.249139\pi\)
−0.965222 + 0.261431i \(0.915806\pi\)
\(822\) 0.182548 + 20.6335i 0.00636711 + 0.719675i
\(823\) 5.91436 3.41466i 0.206162 0.119027i −0.393365 0.919383i \(-0.628689\pi\)
0.599526 + 0.800355i \(0.295356\pi\)
\(824\) −10.3141 5.59527i −0.359308 0.194920i
\(825\) −1.17624 + 2.03730i −0.0409513 + 0.0709298i
\(826\) 20.2408 + 11.4485i 0.704268 + 0.398344i
\(827\) −7.63475 + 4.40792i −0.265486 + 0.153278i −0.626835 0.779152i \(-0.715650\pi\)
0.361348 + 0.932431i \(0.382316\pi\)
\(828\) 7.95007 4.77949i 0.276284 0.166099i
\(829\) 3.92127 0.136191 0.0680957 0.997679i \(-0.478308\pi\)
0.0680957 + 0.997679i \(0.478308\pi\)
\(830\) −3.19567 5.42367i −0.110923 0.188258i
\(831\) −4.91436 −0.170477
\(832\) 30.2245 19.6591i 1.04785 0.681556i
\(833\) 6.22924 10.7894i 0.215830 0.373829i
\(834\) 29.0352 0.256880i 1.00541 0.00889504i
\(835\) −2.66197 + 4.61066i −0.0921212 + 0.159559i
\(836\) −0.0865852 4.89299i −0.00299461 0.169227i
\(837\) 4.20035 7.27522i 0.145185 0.251468i
\(838\) −15.2641 + 8.99374i −0.527291 + 0.310684i
\(839\) −27.3826 15.8094i −0.945353 0.545800i −0.0537184 0.998556i \(-0.517107\pi\)
−0.891634 + 0.452757i \(0.850441\pi\)
\(840\) −2.91507 1.58139i −0.100580 0.0545632i
\(841\) 14.1241 + 24.4637i 0.487038 + 0.843575i
\(842\) −7.85637 13.3338i −0.270748 0.459513i
\(843\) −0.219861 + 0.126937i −0.00757241 + 0.00437193i
\(844\) −33.7891 + 20.3136i −1.16307 + 0.699223i
\(845\) 3.59475 + 2.07543i 0.123663 + 0.0713970i
\(846\) 10.9672 + 6.20321i 0.377061 + 0.213271i
\(847\) 22.1994 0.762779
\(848\) 2.04657 + 57.8085i 0.0702796 + 1.98515i
\(849\) 9.68330i 0.332330i
\(850\) 15.3074 + 25.9797i 0.525040 + 0.891097i
\(851\) −2.78626 1.60865i −0.0955118 0.0551438i
\(852\) 8.80593 + 4.87844i 0.301686 + 0.167132i
\(853\) 25.8580 + 44.7873i 0.885360 + 1.53349i 0.845300 + 0.534292i \(0.179422\pi\)
0.0400603 + 0.999197i \(0.487245\pi\)
\(854\) 0.220259 + 24.8959i 0.00753712 + 0.851922i
\(855\) −1.38092 2.39182i −0.0472265 0.0817986i
\(856\) 0.377795 + 14.2311i 0.0129128 + 0.486410i
\(857\) 42.2264i 1.44242i −0.692714 0.721212i \(-0.743585\pi\)
0.692714 0.721212i \(-0.256415\pi\)
\(858\) −0.0283576 3.20527i −0.000968114 0.109426i
\(859\) −7.66460 4.42516i −0.261513 0.150984i 0.363512 0.931590i \(-0.381578\pi\)
−0.625024 + 0.780605i \(0.714911\pi\)
\(860\) −0.172035 9.72181i −0.00586634 0.331511i
\(861\) 16.7737 9.68431i 0.571647 0.330040i
\(862\) 32.8580 + 18.5849i 1.11915 + 0.633005i
\(863\) 38.0295i 1.29454i −0.762261 0.647269i \(-0.775911\pi\)
0.762261 0.647269i \(-0.224089\pi\)
\(864\) −5.65132 + 0.250148i −0.192262 + 0.00851022i
\(865\) −6.11216 + 3.52886i −0.207820 + 0.119985i
\(866\) −35.3754 20.0088i −1.20211 0.679928i
\(867\) −1.88839 + 3.27079i −0.0641332 + 0.111082i
\(868\) −17.8817 29.7439i −0.606944 1.00957i
\(869\) −2.43422 4.21619i −0.0825751 0.143024i
\(870\) 0.605840 + 0.342672i 0.0205399 + 0.0116177i
\(871\) 14.4446 33.9454i 0.489437 1.15020i
\(872\) −0.212528 8.00568i −0.00719710 0.271107i
\(873\) 9.20546 5.31478i 0.311558 0.179878i
\(874\) 15.7118 27.7784i 0.531461 0.939618i
\(875\) 9.82715 + 5.67371i 0.332218 + 0.191806i
\(876\) −6.40121 10.6476i −0.216277 0.359749i
\(877\) 0.732342 + 1.26845i 0.0247294 + 0.0428326i 0.878125 0.478431i \(-0.158794\pi\)
−0.853396 + 0.521263i \(0.825461\pi\)
\(878\) 8.30056 4.89075i 0.280130 0.165055i
\(879\) −1.34689 −0.0454296
\(880\) −1.00847 0.535589i −0.0339954 0.0180547i
\(881\) 17.0588 + 29.5467i 0.574725 + 0.995454i 0.996071 + 0.0885537i \(0.0282245\pi\)
−0.421346 + 0.906900i \(0.638442\pi\)
\(882\) −1.96222 3.33028i −0.0660715 0.112136i
\(883\) 24.4683 42.3803i 0.823422 1.42621i −0.0796966 0.996819i \(-0.525395\pi\)
0.903119 0.429390i \(-0.141272\pi\)
\(884\) −35.9400 19.9106i −1.20879 0.669665i
\(885\) 4.51864 0.151892
\(886\) −2.99325 + 5.29203i −0.100560 + 0.177789i
\(887\) 27.0340 15.6081i 0.907714 0.524069i 0.0280187 0.999607i \(-0.491080\pi\)
0.879695 + 0.475539i \(0.157747\pi\)
\(888\) 1.02574 + 1.67250i 0.0344217 + 0.0561256i
\(889\) 20.9100 12.0724i 0.701299 0.404895i
\(890\) −0.0754788 8.53138i −0.00253006 0.285973i
\(891\) −0.251452 + 0.435527i −0.00842395 + 0.0145907i
\(892\) −0.166258 9.39536i −0.00556673 0.314580i
\(893\) 43.3493 1.45063
\(894\) 10.6480 0.0942047i 0.356122 0.00315068i
\(895\) 11.8987i 0.397729i
\(896\) −10.4099 + 20.9232i −0.347771 + 0.698995i
\(897\) 10.4518 18.1030i 0.348975 0.604442i
\(898\) 3.26211 5.76738i 0.108858 0.192460i
\(899\) 3.64193 + 6.30800i 0.121465 + 0.210384i
\(900\) 9.35411 0.165528i 0.311804 0.00551761i
\(901\) 57.0852 32.9581i 1.90178 1.09799i
\(902\) 5.74564 3.38537i 0.191309 0.112721i
\(903\) −8.84573 + 15.3213i −0.294368 + 0.509860i
\(904\) 20.5069 + 11.1248i 0.682051 + 0.370005i
\(905\) −4.71904 2.72454i −0.156866 0.0905668i
\(906\) 22.4659 13.2371i 0.746379 0.439772i
\(907\) −4.08998 2.36135i −0.135806 0.0784074i 0.430558 0.902563i \(-0.358317\pi\)
−0.566364 + 0.824156i \(0.691650\pi\)
\(908\) 22.6817 + 12.5655i 0.752718 + 0.417001i
\(909\) −9.18807 5.30473i −0.304749 0.175947i
\(910\) −7.47310 + 0.0661159i −0.247731 + 0.00219172i
\(911\) 15.5917i 0.516576i −0.966068 0.258288i \(-0.916842\pi\)
0.966068 0.258288i \(-0.0831584\pi\)
\(912\) −16.4997 + 10.3212i −0.546361 + 0.341770i
\(913\) 3.94369i 0.130517i
\(914\) 27.8080 49.1643i 0.919808 1.62621i
\(915\) 2.41892 + 4.18970i 0.0799671 + 0.138507i
\(916\) −38.1326 + 22.9249i −1.25994 + 0.757458i
\(917\) 12.5088 + 7.22197i 0.413078 + 0.238491i
\(918\) 3.27237 + 5.55385i 0.108004 + 0.183304i
\(919\) 4.70137 + 8.14301i 0.155084 + 0.268613i 0.933090 0.359644i \(-0.117102\pi\)
−0.778006 + 0.628257i \(0.783769\pi\)
\(920\) −3.89310 6.34781i −0.128352 0.209281i
\(921\) −5.07786 + 2.93171i −0.167321 + 0.0966030i
\(922\) −24.5585 + 0.217274i −0.808791 + 0.00715553i
\(923\) 22.6856 0.746705
\(924\) 1.07048 + 1.78060i 0.0352161 + 0.0585775i
\(925\) −1.62242 2.81011i −0.0533448 0.0923960i
\(926\) 12.2510 + 20.7923i 0.402591 + 0.683277i
\(927\) 3.59279 + 2.07430i 0.118003 + 0.0681290i
\(928\) 2.26216 4.35197i 0.0742592 0.142860i
\(929\) 46.0965i 1.51238i 0.654354 + 0.756189i \(0.272941\pi\)
−0.654354 + 0.756189i \(0.727059\pi\)
\(930\) −5.86986 3.32008i −0.192480 0.108870i
\(931\) −11.5169 6.64926i −0.377450 0.217921i
\(932\) −24.1368 13.3717i −0.790627 0.438003i
\(933\) 19.1012 0.625344
\(934\) 29.4937 17.3779i 0.965062 0.568621i
\(935\) 1.30120i 0.0425539i
\(936\) −10.8667 + 6.66450i −0.355188 + 0.217836i
\(937\) 51.8263i 1.69309i −0.532315 0.846546i \(-0.678678\pi\)
0.532315 0.846546i \(-0.321322\pi\)
\(938\) 3.10282 + 23.7091i 0.101311 + 0.774128i
\(939\) 14.8429i 0.484378i
\(940\) 4.90161 8.84776i 0.159873 0.288582i
\(941\) 49.4762i 1.61288i 0.591316 + 0.806440i \(0.298608\pi\)
−0.591316 + 0.806440i \(0.701392\pi\)
\(942\) −10.4064 17.6617i −0.339058 0.575448i
\(943\) 43.4898 1.41622
\(944\) −1.12658 31.8218i −0.0366669 1.03571i
\(945\) 1.01543 + 0.586261i 0.0330320 + 0.0190711i
\(946\) −2.99889 + 5.30201i −0.0975023 + 0.172383i
\(947\) 29.9429i 0.973015i 0.873676 + 0.486507i \(0.161729\pi\)
−0.873676 + 0.486507i \(0.838271\pi\)
\(948\) −9.38247 + 16.9360i −0.304728 + 0.550057i
\(949\) −24.2455 13.9982i −0.787043 0.454399i
\(950\) 27.7314 16.3396i 0.899727 0.530125i
\(951\) −16.1773 28.0199i −0.524585 0.908608i
\(952\) 26.6214 0.706721i 0.862805 0.0229050i
\(953\) −41.5955 −1.34741 −0.673705 0.739001i \(-0.735298\pi\)
−0.673705 + 0.739001i \(0.735298\pi\)
\(954\) −0.180928 20.4504i −0.00585778 0.662106i
\(955\) 2.44621 1.41232i 0.0791574 0.0457015i
\(956\) −21.1204 + 38.1238i −0.683081 + 1.23301i
\(957\) −0.218022 0.377625i −0.00704765 0.0122069i
\(958\) −40.5387 + 23.8857i −1.30975 + 0.771712i
\(959\) −26.1009 15.0693i −0.842841 0.486614i
\(960\) 0.240936 + 4.53470i 0.00777619 + 0.146357i
\(961\) −19.7859 34.2701i −0.638254 1.10549i
\(962\) 3.84836 + 2.17669i 0.124076 + 0.0701792i
\(963\) 5.03323i 0.162194i
\(964\) −6.61577 + 0.117071i −0.213080 + 0.00377061i
\(965\) 12.3872i 0.398757i
\(966\) 0.119865 + 13.5483i 0.00385659 + 0.435911i
\(967\) 3.19424 + 1.84419i 0.102720 + 0.0593052i 0.550480 0.834848i \(-0.314445\pi\)
−0.447760 + 0.894154i \(0.647778\pi\)
\(968\) −15.8919 25.9123i −0.510786 0.832852i
\(969\) 19.2065 + 11.0888i 0.617000 + 0.356225i
\(970\) −4.33170 7.35175i −0.139083 0.236050i
\(971\) 8.92628 + 5.15359i 0.286458 + 0.165387i 0.636343 0.771406i \(-0.280446\pi\)
−0.349885 + 0.936792i \(0.613780\pi\)
\(972\) 1.99969 0.0353860i 0.0641400 0.00113501i
\(973\) −21.2054 + 36.7289i −0.679815 + 1.17747i
\(974\) −10.8286 18.3783i −0.346972 0.588879i
\(975\) 18.2580 10.5413i 0.584724 0.337590i
\(976\) 28.9022 18.0794i 0.925137 0.578709i
\(977\) −10.3662 17.9548i −0.331645 0.574425i 0.651190 0.758915i \(-0.274270\pi\)
−0.982834 + 0.184490i \(0.940937\pi\)
\(978\) 7.06519 + 3.99617i 0.225920 + 0.127783i
\(979\) −2.67242 + 4.62877i −0.0854110 + 0.147936i
\(980\) −2.65938 + 1.59879i −0.0849507 + 0.0510713i
\(981\) 2.83143i 0.0904007i
\(982\) −0.216233 24.4408i −0.00690027 0.779939i
\(983\) 21.4317 0.683567 0.341783 0.939779i \(-0.388969\pi\)
0.341783 + 0.939779i \(0.388969\pi\)
\(984\) −23.3119 12.6464i −0.743156 0.403154i
\(985\) −6.29373 + 10.9011i −0.200535 + 0.347337i
\(986\) −5.58898 + 0.0494468i −0.177990 + 0.00157471i
\(987\) −15.9381 + 9.20184i −0.507314 + 0.292898i
\(988\) −21.2531 + 38.3633i −0.676151 + 1.22050i
\(989\) −34.4020 + 19.8620i −1.09392 + 0.631574i
\(990\) 0.351396 + 0.198755i 0.0111681 + 0.00631684i
\(991\) 27.3814 0.869800 0.434900 0.900479i \(-0.356784\pi\)
0.434900 + 0.900479i \(0.356784\pi\)
\(992\) −21.9176 + 42.1653i −0.695886 + 1.33875i
\(993\) 7.43209 12.8728i 0.235850 0.408505i
\(994\) −12.6684 + 7.46432i −0.401818 + 0.236754i
\(995\) −4.94308 8.56166i −0.156706 0.271423i
\(996\) 13.4416 8.08092i 0.425913 0.256054i
\(997\) −28.0470 −0.888256 −0.444128 0.895963i \(-0.646486\pi\)
−0.444128 + 0.895963i \(0.646486\pi\)
\(998\) 3.30578 + 5.61055i 0.104643 + 0.177599i
\(999\) −0.346835 0.600736i −0.0109734 0.0190064i
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 804.2.j.b.499.1 yes 68
4.3 odd 2 804.2.j.a.499.12 68
67.38 odd 6 804.2.j.a.775.12 yes 68
268.239 even 6 inner 804.2.j.b.775.1 yes 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.j.a.499.12 68 4.3 odd 2
804.2.j.a.775.12 yes 68 67.38 odd 6
804.2.j.b.499.1 yes 68 1.1 even 1 trivial
804.2.j.b.775.1 yes 68 268.239 even 6 inner