Properties

Label 546.2.z.a.131.7
Level $546$
Weight $2$
Character 546.131
Analytic conductor $4.360$
Analytic rank $0$
Dimension $32$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(131,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.z (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.7
Character \(\chi\) \(=\) 546.131
Dual form 546.2.z.a.521.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.11404 - 1.32624i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.737837 - 1.27797i) q^{5} +(-1.62791 + 0.591542i) q^{6} +(2.24993 - 1.39206i) q^{7} -1.00000i q^{8} +(-0.517844 - 2.95497i) q^{9} +(-1.27797 + 0.737837i) q^{10} +(0.616972 - 0.356209i) q^{11} +(1.70558 + 0.301663i) q^{12} +1.00000i q^{13} +(-2.64452 + 0.0805913i) q^{14} +(-0.872923 - 2.40226i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.629942 + 1.09109i) q^{17} +(-1.02902 + 2.81800i) q^{18} +(-1.83612 - 1.06009i) q^{19} +1.47567 q^{20} +(0.660299 - 4.53476i) q^{21} -0.712418 q^{22} +(1.87219 + 1.08091i) q^{23} +(-1.32624 - 1.11404i) q^{24} +(1.41119 + 2.44426i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-4.49590 - 2.60516i) q^{27} +(2.33052 + 1.25247i) q^{28} -1.97689i q^{29} +(-0.445155 + 2.51688i) q^{30} +(-1.42876 + 0.824895i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.214910 - 1.21509i) q^{33} -1.25988i q^{34} +(-0.118927 - 3.90245i) q^{35} +(2.30016 - 1.92595i) q^{36} +(0.738591 - 1.27928i) q^{37} +(1.06009 + 1.83612i) q^{38} +(1.32624 + 1.11404i) q^{39} +(-1.27797 - 0.737837i) q^{40} +4.74235 q^{41} +(-2.83921 + 3.59706i) q^{42} -8.19918 q^{43} +(0.616972 + 0.356209i) q^{44} +(-4.15845 - 1.51850i) q^{45} +(-1.08091 - 1.87219i) q^{46} +(1.02924 - 1.78269i) q^{47} +(0.591542 + 1.62791i) q^{48} +(3.12436 - 6.26405i) q^{49} -2.82239i q^{50} +(2.14883 + 0.380060i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(-11.4944 + 6.63632i) q^{53} +(2.59099 + 4.50408i) q^{54} -1.05130i q^{55} +(-1.39206 - 2.24993i) q^{56} +(-3.45144 + 1.25417i) q^{57} +(-0.988443 + 1.71203i) q^{58} +(4.88092 + 8.45400i) q^{59} +(1.64395 - 1.95710i) q^{60} +(-3.61623 - 2.08783i) q^{61} +1.64979 q^{62} +(-5.27859 - 5.92760i) q^{63} -1.00000 q^{64} +(1.27797 + 0.737837i) q^{65} +(-0.793660 + 0.944840i) q^{66} +(-3.50829 - 6.07654i) q^{67} +(-0.629942 + 1.09109i) q^{68} +(3.51925 - 1.27881i) q^{69} +(-1.84823 + 3.43909i) q^{70} -4.81777i q^{71} +(-2.95497 + 0.517844i) q^{72} +(-1.31716 + 0.760465i) q^{73} +(-1.27928 + 0.738591i) q^{74} +(4.81381 + 0.851409i) q^{75} -2.12017i q^{76} +(0.892281 - 1.66030i) q^{77} +(-0.591542 - 1.62791i) q^{78} +(1.00421 - 1.73934i) q^{79} +(0.737837 + 1.27797i) q^{80} +(-8.46368 + 3.06042i) q^{81} +(-4.10699 - 2.37117i) q^{82} +16.6965 q^{83} +(4.25736 - 1.69554i) q^{84} +1.85918 q^{85} +(7.10070 + 4.09959i) q^{86} +(-2.62183 - 2.20232i) q^{87} +(-0.356209 - 0.616972i) q^{88} +(1.87730 - 3.25158i) q^{89} +(2.84207 + 3.39428i) q^{90} +(1.39206 + 2.24993i) q^{91} +2.16182i q^{92} +(-0.497680 + 2.81385i) q^{93} +(-1.78269 + 1.02924i) q^{94} +(-2.70952 + 1.56434i) q^{95} +(0.301663 - 1.70558i) q^{96} +5.98973i q^{97} +(-5.83780 + 3.86265i) q^{98} +(-1.37208 - 1.63867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30}+ \cdots + 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 1.11404 1.32624i 0.643189 0.765707i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.737837 1.27797i 0.329971 0.571526i −0.652535 0.757759i \(-0.726294\pi\)
0.982506 + 0.186233i \(0.0596278\pi\)
\(6\) −1.62791 + 0.591542i −0.664590 + 0.241496i
\(7\) 2.24993 1.39206i 0.850393 0.526148i
\(8\) 1.00000i 0.353553i
\(9\) −0.517844 2.95497i −0.172615 0.984989i
\(10\) −1.27797 + 0.737837i −0.404130 + 0.233324i
\(11\) 0.616972 0.356209i 0.186024 0.107401i −0.404096 0.914717i \(-0.632414\pi\)
0.590120 + 0.807316i \(0.299080\pi\)
\(12\) 1.70558 + 0.301663i 0.492358 + 0.0870825i
\(13\) 1.00000i 0.277350i
\(14\) −2.64452 + 0.0805913i −0.706779 + 0.0215389i
\(15\) −0.872923 2.40226i −0.225388 0.620260i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.629942 + 1.09109i 0.152783 + 0.264628i 0.932250 0.361816i \(-0.117843\pi\)
−0.779466 + 0.626444i \(0.784510\pi\)
\(18\) −1.02902 + 2.81800i −0.242542 + 0.664209i
\(19\) −1.83612 1.06009i −0.421236 0.243201i 0.274370 0.961624i \(-0.411531\pi\)
−0.695606 + 0.718424i \(0.744864\pi\)
\(20\) 1.47567 0.329971
\(21\) 0.660299 4.53476i 0.144089 0.989565i
\(22\) −0.712418 −0.151888
\(23\) 1.87219 + 1.08091i 0.390379 + 0.225386i 0.682325 0.731049i \(-0.260969\pi\)
−0.291945 + 0.956435i \(0.594302\pi\)
\(24\) −1.32624 1.11404i −0.270718 0.227402i
\(25\) 1.41119 + 2.44426i 0.282239 + 0.488852i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −4.49590 2.60516i −0.865237 0.501363i
\(28\) 2.33052 + 1.25247i 0.440427 + 0.236694i
\(29\) 1.97689i 0.367098i −0.983011 0.183549i \(-0.941241\pi\)
0.983011 0.183549i \(-0.0587587\pi\)
\(30\) −0.445155 + 2.51688i −0.0812739 + 0.459517i
\(31\) −1.42876 + 0.824895i −0.256613 + 0.148156i −0.622789 0.782390i \(-0.714000\pi\)
0.366176 + 0.930546i \(0.380667\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0.214910 1.21509i 0.0374110 0.211519i
\(34\) 1.25988i 0.216068i
\(35\) −0.118927 3.90245i −0.0201023 0.659635i
\(36\) 2.30016 1.92595i 0.383359 0.320992i
\(37\) 0.738591 1.27928i 0.121424 0.210312i −0.798906 0.601456i \(-0.794587\pi\)
0.920329 + 0.391144i \(0.127921\pi\)
\(38\) 1.06009 + 1.83612i 0.171969 + 0.297859i
\(39\) 1.32624 + 1.11404i 0.212369 + 0.178389i
\(40\) −1.27797 0.737837i −0.202065 0.116662i
\(41\) 4.74235 0.740630 0.370315 0.928906i \(-0.379250\pi\)
0.370315 + 0.928906i \(0.379250\pi\)
\(42\) −2.83921 + 3.59706i −0.438100 + 0.555039i
\(43\) −8.19918 −1.25036 −0.625182 0.780479i \(-0.714975\pi\)
−0.625182 + 0.780479i \(0.714975\pi\)
\(44\) 0.616972 + 0.356209i 0.0930121 + 0.0537005i
\(45\) −4.15845 1.51850i −0.619905 0.226364i
\(46\) −1.08091 1.87219i −0.159372 0.276040i
\(47\) 1.02924 1.78269i 0.150130 0.260032i −0.781145 0.624349i \(-0.785364\pi\)
0.931275 + 0.364317i \(0.118698\pi\)
\(48\) 0.591542 + 1.62791i 0.0853817 + 0.234968i
\(49\) 3.12436 6.26405i 0.446337 0.894865i
\(50\) 2.82239i 0.399146i
\(51\) 2.14883 + 0.380060i 0.300896 + 0.0532190i
\(52\) −0.866025 + 0.500000i −0.120096 + 0.0693375i
\(53\) −11.4944 + 6.63632i −1.57888 + 0.911568i −0.583867 + 0.811849i \(0.698461\pi\)
−0.995016 + 0.0997187i \(0.968206\pi\)
\(54\) 2.59099 + 4.50408i 0.352589 + 0.612928i
\(55\) 1.05130i 0.141757i
\(56\) −1.39206 2.24993i −0.186021 0.300659i
\(57\) −3.45144 + 1.25417i −0.457155 + 0.166119i
\(58\) −0.988443 + 1.71203i −0.129789 + 0.224801i
\(59\) 4.88092 + 8.45400i 0.635442 + 1.10062i 0.986421 + 0.164234i \(0.0525153\pi\)
−0.350979 + 0.936383i \(0.614151\pi\)
\(60\) 1.64395 1.95710i 0.212234 0.252661i
\(61\) −3.61623 2.08783i −0.463011 0.267319i 0.250299 0.968169i \(-0.419471\pi\)
−0.713309 + 0.700849i \(0.752805\pi\)
\(62\) 1.64979 0.209524
\(63\) −5.27859 5.92760i −0.665040 0.746808i
\(64\) −1.00000 −0.125000
\(65\) 1.27797 + 0.737837i 0.158513 + 0.0915174i
\(66\) −0.793660 + 0.944840i −0.0976928 + 0.116302i
\(67\) −3.50829 6.07654i −0.428606 0.742368i 0.568143 0.822930i \(-0.307662\pi\)
−0.996750 + 0.0805619i \(0.974329\pi\)
\(68\) −0.629942 + 1.09109i −0.0763916 + 0.132314i
\(69\) 3.51925 1.27881i 0.423667 0.153951i
\(70\) −1.84823 + 3.43909i −0.220906 + 0.411050i
\(71\) 4.81777i 0.571764i −0.958265 0.285882i \(-0.907714\pi\)
0.958265 0.285882i \(-0.0922865\pi\)
\(72\) −2.95497 + 0.517844i −0.348246 + 0.0610285i
\(73\) −1.31716 + 0.760465i −0.154162 + 0.0890057i −0.575097 0.818085i \(-0.695036\pi\)
0.420934 + 0.907091i \(0.361702\pi\)
\(74\) −1.27928 + 0.738591i −0.148713 + 0.0858594i
\(75\) 4.81381 + 0.851409i 0.555850 + 0.0983122i
\(76\) 2.12017i 0.243201i
\(77\) 0.892281 1.66030i 0.101685 0.189209i
\(78\) −0.591542 1.62791i −0.0669790 0.184324i
\(79\) 1.00421 1.73934i 0.112983 0.195692i −0.803989 0.594644i \(-0.797293\pi\)
0.916971 + 0.398953i \(0.130626\pi\)
\(80\) 0.737837 + 1.27797i 0.0824927 + 0.142881i
\(81\) −8.46368 + 3.06042i −0.940408 + 0.340047i
\(82\) −4.10699 2.37117i −0.453542 0.261852i
\(83\) 16.6965 1.83268 0.916342 0.400397i \(-0.131128\pi\)
0.916342 + 0.400397i \(0.131128\pi\)
\(84\) 4.25736 1.69554i 0.464516 0.184999i
\(85\) 1.85918 0.201656
\(86\) 7.10070 + 4.09959i 0.765688 + 0.442070i
\(87\) −2.62183 2.20232i −0.281090 0.236114i
\(88\) −0.356209 0.616972i −0.0379720 0.0657695i
\(89\) 1.87730 3.25158i 0.198994 0.344667i −0.749209 0.662334i \(-0.769566\pi\)
0.948202 + 0.317667i \(0.102899\pi\)
\(90\) 2.84207 + 3.39428i 0.299581 + 0.357788i
\(91\) 1.39206 + 2.24993i 0.145927 + 0.235857i
\(92\) 2.16182i 0.225386i
\(93\) −0.497680 + 2.81385i −0.0516070 + 0.291782i
\(94\) −1.78269 + 1.02924i −0.183871 + 0.106158i
\(95\) −2.70952 + 1.56434i −0.277991 + 0.160498i
\(96\) 0.301663 1.70558i 0.0307883 0.174075i
\(97\) 5.98973i 0.608164i 0.952646 + 0.304082i \(0.0983498\pi\)
−0.952646 + 0.304082i \(0.901650\pi\)
\(98\) −5.83780 + 3.86265i −0.589707 + 0.390187i
\(99\) −1.37208 1.63867i −0.137899 0.164693i
\(100\) −1.41119 + 2.44426i −0.141119 + 0.244426i
\(101\) 4.48679 + 7.77135i 0.446453 + 0.773279i 0.998152 0.0607643i \(-0.0193538\pi\)
−0.551700 + 0.834043i \(0.686020\pi\)
\(102\) −1.67091 1.40356i −0.165445 0.138973i
\(103\) 4.95116 + 2.85856i 0.487853 + 0.281662i 0.723683 0.690132i \(-0.242448\pi\)
−0.235830 + 0.971794i \(0.575781\pi\)
\(104\) 1.00000 0.0980581
\(105\) −5.30809 4.18975i −0.518017 0.408878i
\(106\) 13.2726 1.28915
\(107\) 2.23780 + 1.29199i 0.216336 + 0.124902i 0.604253 0.796793i \(-0.293472\pi\)
−0.387916 + 0.921695i \(0.626805\pi\)
\(108\) 0.00817995 5.19615i 0.000787116 0.499999i
\(109\) 5.72625 + 9.91816i 0.548476 + 0.949987i 0.998379 + 0.0569104i \(0.0181249\pi\)
−0.449904 + 0.893077i \(0.648542\pi\)
\(110\) −0.525648 + 0.910449i −0.0501186 + 0.0868080i
\(111\) −0.873815 2.40471i −0.0829389 0.228245i
\(112\) 0.0805913 + 2.64452i 0.00761517 + 0.249884i
\(113\) 4.53409i 0.426532i −0.976994 0.213266i \(-0.931590\pi\)
0.976994 0.213266i \(-0.0684100\pi\)
\(114\) 3.61612 + 0.639577i 0.338681 + 0.0599019i
\(115\) 2.76275 1.59507i 0.257627 0.148741i
\(116\) 1.71203 0.988443i 0.158958 0.0917746i
\(117\) 2.95497 0.517844i 0.273187 0.0478747i
\(118\) 9.76184i 0.898650i
\(119\) 2.93618 + 1.57796i 0.269159 + 0.144652i
\(120\) −2.40226 + 0.872923i −0.219295 + 0.0796866i
\(121\) −5.24623 + 9.08674i −0.476930 + 0.826067i
\(122\) 2.08783 + 3.61623i 0.189023 + 0.327398i
\(123\) 5.28315 6.28951i 0.476366 0.567106i
\(124\) −1.42876 0.824895i −0.128306 0.0740778i
\(125\) 11.5433 1.03246
\(126\) 1.60759 + 7.77275i 0.143216 + 0.692452i
\(127\) 15.7161 1.39458 0.697289 0.716790i \(-0.254390\pi\)
0.697289 + 0.716790i \(0.254390\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −9.13419 + 10.8741i −0.804221 + 0.957412i
\(130\) −0.737837 1.27797i −0.0647126 0.112085i
\(131\) −7.04632 + 12.2046i −0.615640 + 1.06632i 0.374632 + 0.927174i \(0.377769\pi\)
−0.990272 + 0.139146i \(0.955564\pi\)
\(132\) 1.15975 0.421425i 0.100943 0.0366804i
\(133\) −5.60685 + 0.170868i −0.486176 + 0.0148161i
\(134\) 7.01658i 0.606141i
\(135\) −6.64656 + 3.82345i −0.572045 + 0.329071i
\(136\) 1.09109 0.629942i 0.0935603 0.0540170i
\(137\) −12.1811 + 7.03277i −1.04070 + 0.600850i −0.920032 0.391843i \(-0.871838\pi\)
−0.120670 + 0.992693i \(0.538504\pi\)
\(138\) −3.68716 0.652141i −0.313872 0.0555139i
\(139\) 1.53247i 0.129983i 0.997886 + 0.0649913i \(0.0207020\pi\)
−0.997886 + 0.0649913i \(0.979298\pi\)
\(140\) 3.32016 2.05422i 0.280605 0.173613i
\(141\) −1.21768 3.35101i −0.102547 0.282206i
\(142\) −2.40888 + 4.17231i −0.202149 + 0.350132i
\(143\) 0.356209 + 0.616972i 0.0297877 + 0.0515938i
\(144\) 2.81800 + 1.02902i 0.234833 + 0.0857515i
\(145\) −2.52640 1.45862i −0.209806 0.121132i
\(146\) 1.52093 0.125873
\(147\) −4.82701 11.1220i −0.398125 0.917331i
\(148\) 1.47718 0.121424
\(149\) 14.5145 + 8.37995i 1.18907 + 0.686512i 0.958096 0.286447i \(-0.0924742\pi\)
0.230978 + 0.972959i \(0.425808\pi\)
\(150\) −3.74317 3.14424i −0.305629 0.256726i
\(151\) 7.58068 + 13.1301i 0.616907 + 1.06851i 0.990047 + 0.140739i \(0.0449479\pi\)
−0.373140 + 0.927775i \(0.621719\pi\)
\(152\) −1.06009 + 1.83612i −0.0859844 + 0.148929i
\(153\) 2.89793 2.42647i 0.234284 0.196169i
\(154\) −1.60289 + 0.991726i −0.129165 + 0.0799155i
\(155\) 2.43455i 0.195548i
\(156\) −0.301663 + 1.70558i −0.0241523 + 0.136556i
\(157\) −13.4848 + 7.78544i −1.07620 + 0.621345i −0.929869 0.367890i \(-0.880080\pi\)
−0.146333 + 0.989235i \(0.546747\pi\)
\(158\) −1.73934 + 1.00421i −0.138375 + 0.0798907i
\(159\) −4.00386 + 22.6375i −0.317526 + 1.79527i
\(160\) 1.47567i 0.116662i
\(161\) 5.71699 0.174224i 0.450562 0.0137308i
\(162\) 8.85997 + 1.58143i 0.696105 + 0.124249i
\(163\) 11.7901 20.4210i 0.923468 1.59949i 0.129462 0.991584i \(-0.458675\pi\)
0.794006 0.607910i \(-0.207992\pi\)
\(164\) 2.37117 + 4.10699i 0.185158 + 0.320702i
\(165\) −1.39428 1.17118i −0.108544 0.0911765i
\(166\) −14.4596 8.34827i −1.12228 0.647951i
\(167\) 13.6759 1.05828 0.529138 0.848536i \(-0.322515\pi\)
0.529138 + 0.848536i \(0.322515\pi\)
\(168\) −4.53476 0.660299i −0.349864 0.0509432i
\(169\) −1.00000 −0.0769231
\(170\) −1.61009 0.929588i −0.123489 0.0712962i
\(171\) −2.18170 + 5.97465i −0.166839 + 0.456893i
\(172\) −4.09959 7.10070i −0.312591 0.541423i
\(173\) −12.7552 + 22.0927i −0.969760 + 1.67967i −0.273517 + 0.961867i \(0.588187\pi\)
−0.696243 + 0.717807i \(0.745146\pi\)
\(174\) 1.16941 + 3.21818i 0.0886528 + 0.243970i
\(175\) 6.57763 + 3.53495i 0.497222 + 0.267217i
\(176\) 0.712418i 0.0537005i
\(177\) 16.6496 + 2.94478i 1.25146 + 0.221343i
\(178\) −3.25158 + 1.87730i −0.243716 + 0.140710i
\(179\) 5.27781 3.04714i 0.394482 0.227754i −0.289618 0.957142i \(-0.593528\pi\)
0.684100 + 0.729388i \(0.260195\pi\)
\(180\) −0.764168 4.36057i −0.0569577 0.325018i
\(181\) 18.2078i 1.35338i 0.736270 + 0.676688i \(0.236585\pi\)
−0.736270 + 0.676688i \(0.763415\pi\)
\(182\) −0.0805913 2.64452i −0.00597383 0.196025i
\(183\) −6.79758 + 2.47008i −0.502492 + 0.182594i
\(184\) 1.08091 1.87219i 0.0796859 0.138020i
\(185\) −1.08992 1.88779i −0.0801324 0.138793i
\(186\) 1.83793 2.18802i 0.134763 0.160434i
\(187\) 0.777313 + 0.448782i 0.0568427 + 0.0328182i
\(188\) 2.05848 0.150130
\(189\) −13.7420 + 0.397132i −0.999583 + 0.0288871i
\(190\) 3.12869 0.226979
\(191\) −7.38111 4.26148i −0.534078 0.308350i 0.208597 0.978002i \(-0.433110\pi\)
−0.742676 + 0.669651i \(0.766444\pi\)
\(192\) −1.11404 + 1.32624i −0.0803987 + 0.0957134i
\(193\) 5.24285 + 9.08089i 0.377389 + 0.653657i 0.990681 0.136199i \(-0.0434887\pi\)
−0.613293 + 0.789856i \(0.710155\pi\)
\(194\) 2.99486 5.18725i 0.215019 0.372423i
\(195\) 2.40226 0.872923i 0.172029 0.0625113i
\(196\) 6.98701 0.426251i 0.499072 0.0304465i
\(197\) 27.5463i 1.96259i −0.192501 0.981297i \(-0.561660\pi\)
0.192501 0.981297i \(-0.438340\pi\)
\(198\) 0.368921 + 2.10517i 0.0262181 + 0.149608i
\(199\) 15.6308 9.02443i 1.10804 0.639725i 0.169716 0.985493i \(-0.445715\pi\)
0.938320 + 0.345768i \(0.112382\pi\)
\(200\) 2.44426 1.41119i 0.172835 0.0997865i
\(201\) −11.9673 2.11664i −0.844111 0.149296i
\(202\) 8.97359i 0.631379i
\(203\) −2.75194 4.44785i −0.193148 0.312178i
\(204\) 0.745274 + 2.05097i 0.0521796 + 0.143597i
\(205\) 3.49908 6.06058i 0.244386 0.423289i
\(206\) −2.85856 4.95116i −0.199165 0.344964i
\(207\) 2.22456 6.09202i 0.154617 0.423424i
\(208\) −0.866025 0.500000i −0.0600481 0.0346688i
\(209\) −1.51045 −0.104480
\(210\) 2.50207 + 6.28248i 0.172659 + 0.433532i
\(211\) −2.97983 −0.205140 −0.102570 0.994726i \(-0.532707\pi\)
−0.102570 + 0.994726i \(0.532707\pi\)
\(212\) −11.4944 6.63632i −0.789441 0.455784i
\(213\) −6.38953 5.36717i −0.437804 0.367752i
\(214\) −1.29199 2.23780i −0.0883189 0.152973i
\(215\) −6.04966 + 10.4783i −0.412583 + 0.714615i
\(216\) −2.60516 + 4.49590i −0.177258 + 0.305908i
\(217\) −2.06631 + 3.84487i −0.140270 + 0.261007i
\(218\) 11.4525i 0.775662i
\(219\) −0.458808 + 2.59407i −0.0310033 + 0.175291i
\(220\) 0.910449 0.525648i 0.0613825 0.0354392i
\(221\) −1.09109 + 0.629942i −0.0733947 + 0.0423745i
\(222\) −0.445610 + 2.51945i −0.0299074 + 0.169094i
\(223\) 2.54971i 0.170741i −0.996349 0.0853705i \(-0.972793\pi\)
0.996349 0.0853705i \(-0.0272074\pi\)
\(224\) 1.25247 2.33052i 0.0836840 0.155714i
\(225\) 6.49193 5.43578i 0.432795 0.362385i
\(226\) −2.26705 + 3.92664i −0.150802 + 0.261196i
\(227\) −4.12234 7.14010i −0.273609 0.473905i 0.696174 0.717873i \(-0.254884\pi\)
−0.969783 + 0.243968i \(0.921551\pi\)
\(228\) −2.81187 2.36195i −0.186220 0.156424i
\(229\) −6.90443 3.98628i −0.456258 0.263421i 0.254212 0.967149i \(-0.418184\pi\)
−0.710469 + 0.703728i \(0.751517\pi\)
\(230\) −3.19015 −0.210352
\(231\) −1.20793 3.03302i −0.0794763 0.199558i
\(232\) −1.97689 −0.129789
\(233\) −22.7059 13.1093i −1.48752 0.858818i −0.487617 0.873058i \(-0.662134\pi\)
−0.999899 + 0.0142398i \(0.995467\pi\)
\(234\) −2.81800 1.02902i −0.184218 0.0672690i
\(235\) −1.51882 2.63067i −0.0990768 0.171606i
\(236\) −4.88092 + 8.45400i −0.317721 + 0.550309i
\(237\) −1.18807 3.26952i −0.0771732 0.212378i
\(238\) −1.75383 2.83465i −0.113684 0.183743i
\(239\) 16.1711i 1.04602i −0.852325 0.523012i \(-0.824808\pi\)
0.852325 0.523012i \(-0.175192\pi\)
\(240\) 2.51688 + 0.445155i 0.162464 + 0.0287347i
\(241\) −11.4305 + 6.59939i −0.736302 + 0.425104i −0.820723 0.571326i \(-0.806429\pi\)
0.0844211 + 0.996430i \(0.473096\pi\)
\(242\) 9.08674 5.24623i 0.584118 0.337240i
\(243\) −5.36998 + 14.6343i −0.344484 + 0.938792i
\(244\) 4.17566i 0.267319i
\(245\) −5.70001 8.61469i −0.364160 0.550372i
\(246\) −7.72010 + 2.80530i −0.492215 + 0.178859i
\(247\) 1.06009 1.83612i 0.0674517 0.116830i
\(248\) 0.824895 + 1.42876i 0.0523809 + 0.0907264i
\(249\) 18.6006 22.1437i 1.17876 1.40330i
\(250\) −9.99678 5.77165i −0.632252 0.365031i
\(251\) −10.1448 −0.640337 −0.320168 0.947361i \(-0.603740\pi\)
−0.320168 + 0.947361i \(0.603740\pi\)
\(252\) 2.49416 7.53520i 0.157117 0.474673i
\(253\) 1.54012 0.0968266
\(254\) −13.6105 7.85804i −0.854001 0.493058i
\(255\) 2.07119 2.46572i 0.129703 0.154409i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.4826 23.3525i 0.841020 1.45669i −0.0480126 0.998847i \(-0.515289\pi\)
0.889033 0.457843i \(-0.151378\pi\)
\(258\) 13.3475 4.85016i 0.830979 0.301958i
\(259\) −0.119048 3.90644i −0.00739729 0.242734i
\(260\) 1.47567i 0.0915174i
\(261\) −5.84163 + 1.02372i −0.361588 + 0.0633665i
\(262\) 12.2046 7.04632i 0.754002 0.435323i
\(263\) −24.6665 + 14.2412i −1.52100 + 0.878152i −0.521311 + 0.853367i \(0.674557\pi\)
−0.999693 + 0.0247857i \(0.992110\pi\)
\(264\) −1.21509 0.214910i −0.0747833 0.0132268i
\(265\) 19.5861i 1.20316i
\(266\) 4.94111 + 2.65545i 0.302959 + 0.162816i
\(267\) −2.22101 6.11214i −0.135923 0.374057i
\(268\) 3.50829 6.07654i 0.214303 0.371184i
\(269\) −1.07074 1.85458i −0.0652844 0.113076i 0.831536 0.555471i \(-0.187462\pi\)
−0.896820 + 0.442395i \(0.854129\pi\)
\(270\) 7.66782 + 0.0120709i 0.466648 + 0.000734614i
\(271\) 18.3465 + 10.5924i 1.11447 + 0.643441i 0.939984 0.341219i \(-0.110840\pi\)
0.174488 + 0.984659i \(0.444173\pi\)
\(272\) −1.25988 −0.0763916
\(273\) 4.53476 + 0.660299i 0.274456 + 0.0399631i
\(274\) 14.0655 0.849730
\(275\) 1.74133 + 1.00536i 0.105006 + 0.0606255i
\(276\) 2.86710 + 2.40835i 0.172579 + 0.144966i
\(277\) 9.41135 + 16.3009i 0.565473 + 0.979429i 0.997005 + 0.0773311i \(0.0246398\pi\)
−0.431532 + 0.902098i \(0.642027\pi\)
\(278\) 0.766236 1.32716i 0.0459558 0.0795977i
\(279\) 3.17741 + 3.79478i 0.190227 + 0.227187i
\(280\) −3.90245 + 0.118927i −0.233216 + 0.00710722i
\(281\) 21.8958i 1.30619i −0.757274 0.653097i \(-0.773469\pi\)
0.757274 0.653097i \(-0.226531\pi\)
\(282\) −0.620965 + 3.51089i −0.0369779 + 0.209071i
\(283\) 1.19367 0.689163i 0.0709561 0.0409665i −0.464102 0.885782i \(-0.653623\pi\)
0.535058 + 0.844815i \(0.320290\pi\)
\(284\) 4.17231 2.40888i 0.247581 0.142941i
\(285\) −0.943807 + 5.33622i −0.0559063 + 0.316090i
\(286\) 0.712418i 0.0421262i
\(287\) 10.6699 6.60161i 0.629827 0.389681i
\(288\) −1.92595 2.30016i −0.113488 0.135538i
\(289\) 7.70635 13.3478i 0.453315 0.785164i
\(290\) 1.45862 + 2.52640i 0.0856531 + 0.148355i
\(291\) 7.94383 + 6.67277i 0.465676 + 0.391165i
\(292\) −1.31716 0.760465i −0.0770812 0.0445029i
\(293\) −23.4405 −1.36941 −0.684703 0.728822i \(-0.740068\pi\)
−0.684703 + 0.728822i \(0.740068\pi\)
\(294\) −1.38071 + 12.0455i −0.0805248 + 0.702507i
\(295\) 14.4053 0.838709
\(296\) −1.27928 0.738591i −0.0743564 0.0429297i
\(297\) −3.70183 0.00582755i −0.214802 0.000338149i
\(298\) −8.37995 14.5145i −0.485437 0.840802i
\(299\) −1.08091 + 1.87219i −0.0625107 + 0.108272i
\(300\) 1.66956 + 4.59458i 0.0963922 + 0.265268i
\(301\) −18.4476 + 11.4137i −1.06330 + 0.657876i
\(302\) 15.1614i 0.872438i
\(303\) 15.3052 + 2.70699i 0.879259 + 0.155513i
\(304\) 1.83612 1.06009i 0.105309 0.0608002i
\(305\) −5.33637 + 3.08096i −0.305560 + 0.176415i
\(306\) −3.72292 + 0.652422i −0.212825 + 0.0372965i
\(307\) 7.51595i 0.428958i −0.976729 0.214479i \(-0.931195\pi\)
0.976729 0.214479i \(-0.0688054\pi\)
\(308\) 1.88401 0.0574147i 0.107351 0.00327151i
\(309\) 9.30692 3.38191i 0.529452 0.192390i
\(310\) 1.21728 2.10838i 0.0691366 0.119748i
\(311\) 3.07687 + 5.32930i 0.174473 + 0.302197i 0.939979 0.341233i \(-0.110844\pi\)
−0.765505 + 0.643429i \(0.777511\pi\)
\(312\) 1.11404 1.32624i 0.0630699 0.0750838i
\(313\) −22.5207 13.0024i −1.27295 0.734936i −0.297405 0.954751i \(-0.596121\pi\)
−0.975542 + 0.219815i \(0.929455\pi\)
\(314\) 15.5709 0.878715
\(315\) −11.4700 + 2.37228i −0.646264 + 0.133663i
\(316\) 2.00842 0.112983
\(317\) −11.8361 6.83359i −0.664783 0.383813i 0.129314 0.991604i \(-0.458723\pi\)
−0.794097 + 0.607791i \(0.792056\pi\)
\(318\) 14.7862 17.6027i 0.829169 0.987113i
\(319\) −0.704185 1.21968i −0.0394268 0.0682892i
\(320\) −0.737837 + 1.27797i −0.0412463 + 0.0714407i
\(321\) 4.20649 1.52854i 0.234783 0.0853147i
\(322\) −5.03817 2.70761i −0.280766 0.150889i
\(323\) 2.67117i 0.148628i
\(324\) −6.88224 5.79955i −0.382347 0.322197i
\(325\) −2.44426 + 1.41119i −0.135583 + 0.0782789i
\(326\) −20.4210 + 11.7901i −1.13101 + 0.652991i
\(327\) 19.5332 + 3.45479i 1.08019 + 0.191050i
\(328\) 4.74235i 0.261852i
\(329\) −0.165895 5.44369i −0.00914611 0.300120i
\(330\) 0.621886 + 1.71141i 0.0342337 + 0.0942101i
\(331\) −3.55757 + 6.16188i −0.195541 + 0.338688i −0.947078 0.321004i \(-0.895980\pi\)
0.751536 + 0.659692i \(0.229313\pi\)
\(332\) 8.34827 + 14.4596i 0.458171 + 0.793575i
\(333\) −4.16270 1.52005i −0.228114 0.0832981i
\(334\) −11.8437 6.83797i −0.648059 0.374157i
\(335\) −10.3542 −0.565710
\(336\) 3.59706 + 2.83921i 0.196236 + 0.154892i
\(337\) 1.82826 0.0995918 0.0497959 0.998759i \(-0.484143\pi\)
0.0497959 + 0.998759i \(0.484143\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) −6.01331 5.05115i −0.326598 0.274341i
\(340\) 0.929588 + 1.61009i 0.0504140 + 0.0873196i
\(341\) −0.587670 + 1.01787i −0.0318241 + 0.0551210i
\(342\) 4.87673 4.08335i 0.263703 0.220802i
\(343\) −1.69032 18.4430i −0.0912689 0.995826i
\(344\) 8.19918i 0.442070i
\(345\) 0.962347 5.44105i 0.0518110 0.292936i
\(346\) 22.0927 12.7552i 1.18771 0.685724i
\(347\) 18.1042 10.4525i 0.971884 0.561117i 0.0720736 0.997399i \(-0.477038\pi\)
0.899810 + 0.436282i \(0.143705\pi\)
\(348\) 0.596352 3.37173i 0.0319678 0.180744i
\(349\) 30.2526i 1.61939i 0.586853 + 0.809694i \(0.300367\pi\)
−0.586853 + 0.809694i \(0.699633\pi\)
\(350\) −3.92892 6.35017i −0.210010 0.339431i
\(351\) 2.60516 4.49590i 0.139053 0.239974i
\(352\) 0.356209 0.616972i 0.0189860 0.0328847i
\(353\) 3.37558 + 5.84667i 0.179664 + 0.311187i 0.941765 0.336271i \(-0.109166\pi\)
−0.762102 + 0.647457i \(0.775832\pi\)
\(354\) −12.9466 10.8751i −0.688103 0.578003i
\(355\) −6.15697 3.55473i −0.326778 0.188665i
\(356\) 3.75460 0.198994
\(357\) 5.36378 2.13619i 0.283881 0.113059i
\(358\) −6.09429 −0.322093
\(359\) −6.61905 3.82151i −0.349340 0.201692i 0.315054 0.949074i \(-0.397977\pi\)
−0.664395 + 0.747382i \(0.731311\pi\)
\(360\) −1.51850 + 4.15845i −0.0800317 + 0.219169i
\(361\) −7.25243 12.5616i −0.381707 0.661136i
\(362\) 9.10391 15.7684i 0.478491 0.828770i
\(363\) 6.20673 + 17.0807i 0.325769 + 0.896506i
\(364\) −1.25247 + 2.33052i −0.0656471 + 0.122152i
\(365\) 2.24440i 0.117477i
\(366\) 7.12192 + 1.25964i 0.372269 + 0.0658425i
\(367\) 16.0066 9.24140i 0.835537 0.482397i −0.0202079 0.999796i \(-0.506433\pi\)
0.855745 + 0.517398i \(0.173099\pi\)
\(368\) −1.87219 + 1.08091i −0.0975949 + 0.0563464i
\(369\) −2.45579 14.0135i −0.127844 0.729513i
\(370\) 2.17984i 0.113324i
\(371\) −16.6235 + 30.9321i −0.863051 + 1.60592i
\(372\) −2.68570 + 0.975921i −0.139247 + 0.0505991i
\(373\) 2.56061 4.43510i 0.132583 0.229641i −0.792088 0.610406i \(-0.791006\pi\)
0.924672 + 0.380765i \(0.124339\pi\)
\(374\) −0.448782 0.777313i −0.0232060 0.0401939i
\(375\) 12.8597 15.3092i 0.664070 0.790564i
\(376\) −1.78269 1.02924i −0.0919353 0.0530789i
\(377\) 1.97689 0.101815
\(378\) 12.0995 + 6.52707i 0.622330 + 0.335716i
\(379\) −17.1215 −0.879471 −0.439736 0.898127i \(-0.644928\pi\)
−0.439736 + 0.898127i \(0.644928\pi\)
\(380\) −2.70952 1.56434i −0.138995 0.0802491i
\(381\) 17.5083 20.8434i 0.896978 1.06784i
\(382\) 4.26148 + 7.38111i 0.218036 + 0.377650i
\(383\) −8.37015 + 14.4975i −0.427695 + 0.740789i −0.996668 0.0815673i \(-0.974007\pi\)
0.568973 + 0.822356i \(0.307341\pi\)
\(384\) 1.62791 0.591542i 0.0830737 0.0301870i
\(385\) −1.46346 2.36534i −0.0745850 0.120549i
\(386\) 10.4857i 0.533709i
\(387\) 4.24589 + 24.2283i 0.215831 + 1.23160i
\(388\) −5.18725 + 2.99486i −0.263343 + 0.152041i
\(389\) −17.2918 + 9.98343i −0.876729 + 0.506180i −0.869579 0.493795i \(-0.835609\pi\)
−0.00715063 + 0.999974i \(0.502276\pi\)
\(390\) −2.51688 0.445155i −0.127447 0.0225413i
\(391\) 2.72364i 0.137741i
\(392\) −6.26405 3.12436i −0.316383 0.157804i
\(393\) 8.33639 + 22.9415i 0.420515 + 1.15725i
\(394\) −13.7732 + 23.8558i −0.693882 + 1.20184i
\(395\) −1.48189 2.56670i −0.0745618 0.129145i
\(396\) 0.733091 2.00759i 0.0368392 0.100885i
\(397\) 7.52672 + 4.34555i 0.377755 + 0.218097i 0.676841 0.736129i \(-0.263348\pi\)
−0.299086 + 0.954226i \(0.596682\pi\)
\(398\) −18.0489 −0.904707
\(399\) −6.01963 + 7.62640i −0.301358 + 0.381798i
\(400\) −2.82239 −0.141119
\(401\) 9.22909 + 5.32841i 0.460879 + 0.266088i 0.712414 0.701760i \(-0.247602\pi\)
−0.251535 + 0.967848i \(0.580935\pi\)
\(402\) 9.30570 + 7.81673i 0.464126 + 0.389863i
\(403\) −0.824895 1.42876i −0.0410910 0.0711716i
\(404\) −4.48679 + 7.77135i −0.223226 + 0.386639i
\(405\) −2.33368 + 13.0744i −0.115962 + 0.649673i
\(406\) 0.159320 + 5.22792i 0.00790691 + 0.259457i
\(407\) 1.05237i 0.0521641i
\(408\) 0.380060 2.14883i 0.0188158 0.106383i
\(409\) −17.2644 + 9.96762i −0.853671 + 0.492867i −0.861888 0.507099i \(-0.830718\pi\)
0.00821693 + 0.999966i \(0.497384\pi\)
\(410\) −6.06058 + 3.49908i −0.299311 + 0.172807i
\(411\) −4.24304 + 23.9899i −0.209294 + 1.18333i
\(412\) 5.71711i 0.281662i
\(413\) 22.7502 + 12.2264i 1.11946 + 0.601621i
\(414\) −4.97253 + 4.16356i −0.244387 + 0.204628i
\(415\) 12.3193 21.3377i 0.604732 1.04743i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 2.03243 + 1.70723i 0.0995285 + 0.0836034i
\(418\) 1.30809 + 0.755225i 0.0639807 + 0.0369393i
\(419\) −20.2944 −0.991446 −0.495723 0.868481i \(-0.665097\pi\)
−0.495723 + 0.868481i \(0.665097\pi\)
\(420\) 0.974385 6.69182i 0.0475451 0.326527i
\(421\) −18.9286 −0.922523 −0.461261 0.887264i \(-0.652603\pi\)
−0.461261 + 0.887264i \(0.652603\pi\)
\(422\) 2.58061 + 1.48992i 0.125622 + 0.0725280i
\(423\) −5.80078 2.11821i −0.282044 0.102991i
\(424\) 6.63632 + 11.4944i 0.322288 + 0.558219i
\(425\) −1.77794 + 3.07948i −0.0862427 + 0.149377i
\(426\) 2.84991 + 7.84287i 0.138079 + 0.379988i
\(427\) −11.0426 + 0.336522i −0.534391 + 0.0162855i
\(428\) 2.58399i 0.124902i
\(429\) 1.21509 + 0.214910i 0.0586649 + 0.0103759i
\(430\) 10.4783 6.04966i 0.505309 0.291740i
\(431\) −2.25497 + 1.30191i −0.108618 + 0.0627107i −0.553325 0.832966i \(-0.686641\pi\)
0.444707 + 0.895676i \(0.353308\pi\)
\(432\) 4.50408 2.59099i 0.216703 0.124659i
\(433\) 28.2873i 1.35940i 0.733489 + 0.679701i \(0.237890\pi\)
−0.733489 + 0.679701i \(0.762110\pi\)
\(434\) 3.71191 2.29660i 0.178177 0.110240i
\(435\) −4.74899 + 1.72567i −0.227697 + 0.0827395i
\(436\) −5.72625 + 9.91816i −0.274238 + 0.474994i
\(437\) −2.29172 3.96938i −0.109628 0.189881i
\(438\) 1.69437 2.01712i 0.0809603 0.0963819i
\(439\) 34.5408 + 19.9421i 1.64854 + 0.951785i 0.977653 + 0.210227i \(0.0674203\pi\)
0.670888 + 0.741559i \(0.265913\pi\)
\(440\) −1.05130 −0.0501186
\(441\) −20.1280 5.98859i −0.958477 0.285171i
\(442\) 1.25988 0.0599265
\(443\) −12.0320 6.94666i −0.571656 0.330046i 0.186154 0.982520i \(-0.440398\pi\)
−0.757810 + 0.652475i \(0.773731\pi\)
\(444\) 1.64563 1.95910i 0.0780984 0.0929749i
\(445\) −2.77029 4.79828i −0.131324 0.227460i
\(446\) −1.27485 + 2.20811i −0.0603661 + 0.104557i
\(447\) 27.2835 9.91419i 1.29047 0.468925i
\(448\) −2.24993 + 1.39206i −0.106299 + 0.0657685i
\(449\) 21.7353i 1.02575i 0.858463 + 0.512875i \(0.171420\pi\)
−0.858463 + 0.512875i \(0.828580\pi\)
\(450\) −8.34007 + 1.46156i −0.393154 + 0.0688984i
\(451\) 2.92590 1.68927i 0.137775 0.0795445i
\(452\) 3.92664 2.26705i 0.184694 0.106633i
\(453\) 25.8589 + 4.57361i 1.21496 + 0.214887i
\(454\) 8.24468i 0.386942i
\(455\) 3.90245 0.118927i 0.182950 0.00557536i
\(456\) 1.25417 + 3.45144i 0.0587320 + 0.161629i
\(457\) 4.34511 7.52596i 0.203256 0.352050i −0.746320 0.665588i \(-0.768181\pi\)
0.949576 + 0.313538i \(0.101514\pi\)
\(458\) 3.98628 + 6.90443i 0.186267 + 0.322623i
\(459\) 0.0103058 6.54654i 0.000481033 0.305566i
\(460\) 2.76275 + 1.59507i 0.128814 + 0.0743706i
\(461\) −35.1161 −1.63552 −0.817760 0.575559i \(-0.804785\pi\)
−0.817760 + 0.575559i \(0.804785\pi\)
\(462\) −0.470409 + 3.23064i −0.0218854 + 0.150303i
\(463\) −20.9880 −0.975395 −0.487698 0.873013i \(-0.662163\pi\)
−0.487698 + 0.873013i \(0.662163\pi\)
\(464\) 1.71203 + 0.988443i 0.0794791 + 0.0458873i
\(465\) 3.22881 + 2.71218i 0.149732 + 0.125774i
\(466\) 13.1093 + 22.7059i 0.607276 + 1.05183i
\(467\) 17.2987 29.9621i 0.800486 1.38648i −0.118810 0.992917i \(-0.537908\pi\)
0.919297 0.393566i \(-0.128759\pi\)
\(468\) 1.92595 + 2.30016i 0.0890271 + 0.106325i
\(469\) −16.3523 8.78805i −0.755079 0.405794i
\(470\) 3.03764i 0.140116i
\(471\) −4.69715 + 26.5574i −0.216433 + 1.22370i
\(472\) 8.45400 4.88092i 0.389127 0.224663i
\(473\) −5.05867 + 2.92062i −0.232598 + 0.134290i
\(474\) −0.605865 + 3.42552i −0.0278283 + 0.157339i
\(475\) 5.98395i 0.274563i
\(476\) 0.101536 + 3.33179i 0.00465388 + 0.152712i
\(477\) 25.5624 + 30.5291i 1.17042 + 1.39783i
\(478\) −8.08557 + 14.0046i −0.369825 + 0.640556i
\(479\) 19.4526 + 33.6929i 0.888813 + 1.53947i 0.841280 + 0.540599i \(0.181802\pi\)
0.0475326 + 0.998870i \(0.484864\pi\)
\(480\) −1.95710 1.64395i −0.0893291 0.0750359i
\(481\) 1.27928 + 0.738591i 0.0583300 + 0.0336768i
\(482\) 13.1988 0.601188
\(483\) 6.13788 7.77622i 0.279283 0.353830i
\(484\) −10.4925 −0.476930
\(485\) 7.65469 + 4.41944i 0.347582 + 0.200676i
\(486\) 11.9677 9.98870i 0.542866 0.453097i
\(487\) −13.4920 23.3688i −0.611381 1.05894i −0.991008 0.133803i \(-0.957281\pi\)
0.379627 0.925140i \(-0.376052\pi\)
\(488\) −2.08783 + 3.61623i −0.0945117 + 0.163699i
\(489\) −13.9486 38.3862i −0.630779 1.73588i
\(490\) 0.629008 + 10.3105i 0.0284157 + 0.465783i
\(491\) 27.1248i 1.22413i −0.790809 0.612063i \(-0.790340\pi\)
0.790809 0.612063i \(-0.209660\pi\)
\(492\) 8.08845 + 1.43059i 0.364655 + 0.0644959i
\(493\) 2.15696 1.24532i 0.0971447 0.0560865i
\(494\) −1.83612 + 1.06009i −0.0826112 + 0.0476956i
\(495\) −3.10655 + 0.544407i −0.139629 + 0.0244693i
\(496\) 1.64979i 0.0740778i
\(497\) −6.70660 10.8396i −0.300832 0.486224i
\(498\) −27.1804 + 9.87671i −1.21798 + 0.442586i
\(499\) 21.1584 36.6475i 0.947182 1.64057i 0.195860 0.980632i \(-0.437250\pi\)
0.751322 0.659936i \(-0.229416\pi\)
\(500\) 5.77165 + 9.99678i 0.258116 + 0.447070i
\(501\) 15.2355 18.1376i 0.680672 0.810329i
\(502\) 8.78569 + 5.07242i 0.392125 + 0.226393i
\(503\) 35.3532 1.57632 0.788160 0.615471i \(-0.211034\pi\)
0.788160 + 0.615471i \(0.211034\pi\)
\(504\) −5.92760 + 5.27859i −0.264036 + 0.235127i
\(505\) 13.2421 0.589265
\(506\) −1.33378 0.770061i −0.0592940 0.0342334i
\(507\) −1.11404 + 1.32624i −0.0494761 + 0.0589005i
\(508\) 7.85804 + 13.6105i 0.348644 + 0.603870i
\(509\) −3.45844 + 5.99019i −0.153293 + 0.265511i −0.932436 0.361335i \(-0.882321\pi\)
0.779143 + 0.626846i \(0.215654\pi\)
\(510\) −3.02656 + 1.09978i −0.134019 + 0.0486991i
\(511\) −1.90492 + 3.54456i −0.0842685 + 0.156802i
\(512\) 1.00000i 0.0441942i
\(513\) 5.49335 + 9.54944i 0.242537 + 0.421618i
\(514\) −23.3525 + 13.4826i −1.03004 + 0.594691i
\(515\) 7.30630 4.21830i 0.321954 0.185880i
\(516\) −13.9844 2.47339i −0.615627 0.108885i
\(517\) 1.46650i 0.0644964i
\(518\) −1.85012 + 3.44260i −0.0812897 + 0.151259i
\(519\) 15.0905 + 41.5285i 0.662398 + 1.82290i
\(520\) 0.737837 1.27797i 0.0323563 0.0560427i
\(521\) 2.68088 + 4.64342i 0.117452 + 0.203432i 0.918757 0.394823i \(-0.129194\pi\)
−0.801306 + 0.598255i \(0.795861\pi\)
\(522\) 5.57086 + 2.03425i 0.243830 + 0.0890368i
\(523\) −10.4865 6.05436i −0.458541 0.264739i 0.252890 0.967495i \(-0.418619\pi\)
−0.711430 + 0.702757i \(0.751952\pi\)
\(524\) −14.0926 −0.615640
\(525\) 12.0159 4.78548i 0.524418 0.208855i
\(526\) 28.4825 1.24189
\(527\) −1.80007 1.03927i −0.0784123 0.0452714i
\(528\) 0.944840 + 0.793660i 0.0411189 + 0.0345396i
\(529\) −9.16326 15.8712i −0.398403 0.690054i
\(530\) 9.79304 16.9620i 0.425382 0.736784i
\(531\) 22.4538 18.8008i 0.974410 0.815886i
\(532\) −2.95140 4.77024i −0.127959 0.206816i
\(533\) 4.74235i 0.205414i
\(534\) −1.13262 + 6.40378i −0.0490134 + 0.277118i
\(535\) 3.30226 1.90656i 0.142769 0.0824278i
\(536\) −6.07654 + 3.50829i −0.262467 + 0.151535i
\(537\) 1.83842 10.3943i 0.0793336 0.448547i
\(538\) 2.14149i 0.0923260i
\(539\) −0.303669 4.97767i −0.0130800 0.214404i
\(540\) −6.63449 3.84436i −0.285503 0.165435i
\(541\) −6.78137 + 11.7457i −0.291554 + 0.504986i −0.974177 0.225784i \(-0.927506\pi\)
0.682624 + 0.730770i \(0.260839\pi\)
\(542\) −10.5924 18.3465i −0.454981 0.788050i
\(543\) 24.1480 + 20.2842i 1.03629 + 0.870477i
\(544\) 1.09109 + 0.629942i 0.0467801 + 0.0270085i
\(545\) 16.9002 0.723923
\(546\) −3.59706 2.83921i −0.153940 0.121507i
\(547\) −33.1898 −1.41909 −0.709547 0.704658i \(-0.751101\pi\)
−0.709547 + 0.704658i \(0.751101\pi\)
\(548\) −12.1811 7.03277i −0.520351 0.300425i
\(549\) −4.29683 + 11.7670i −0.183384 + 0.502204i
\(550\) −1.00536 1.74133i −0.0428687 0.0742508i
\(551\) −2.09567 + 3.62981i −0.0892786 + 0.154635i
\(552\) −1.27881 3.51925i −0.0544297 0.149789i
\(553\) −0.161861 5.31132i −0.00688305 0.225860i
\(554\) 18.8227i 0.799700i
\(555\) −3.71789 0.657575i −0.157815 0.0279125i
\(556\) −1.32716 + 0.766236i −0.0562841 + 0.0324956i
\(557\) 21.4609 12.3905i 0.909329 0.525001i 0.0291135 0.999576i \(-0.490732\pi\)
0.880215 + 0.474575i \(0.157398\pi\)
\(558\) −0.854333 4.87508i −0.0361668 0.206379i
\(559\) 8.19918i 0.346789i
\(560\) 3.43909 + 1.84823i 0.145328 + 0.0781021i
\(561\) 1.46115 0.530947i 0.0616898 0.0224166i
\(562\) −10.9479 + 18.9623i −0.461809 + 0.799878i
\(563\) 6.39650 + 11.0791i 0.269580 + 0.466927i 0.968753 0.248026i \(-0.0797817\pi\)
−0.699173 + 0.714952i \(0.746448\pi\)
\(564\) 2.29322 2.73004i 0.0965619 0.114955i
\(565\) −5.79444 3.34542i −0.243774 0.140743i
\(566\) −1.37833 −0.0579354
\(567\) −14.7824 + 18.6676i −0.620802 + 0.783967i
\(568\) −4.81777 −0.202149
\(569\) 25.9976 + 15.0097i 1.08988 + 0.629240i 0.933544 0.358464i \(-0.116699\pi\)
0.156333 + 0.987704i \(0.450033\pi\)
\(570\) 3.48547 4.14940i 0.145990 0.173799i
\(571\) −11.1007 19.2270i −0.464551 0.804626i 0.534630 0.845086i \(-0.320451\pi\)
−0.999181 + 0.0404599i \(0.987118\pi\)
\(572\) −0.356209 + 0.616972i −0.0148938 + 0.0257969i
\(573\) −13.8746 + 5.04169i −0.579619 + 0.210620i
\(574\) −12.5413 + 0.382192i −0.523462 + 0.0159524i
\(575\) 6.10150i 0.254450i
\(576\) 0.517844 + 2.95497i 0.0215768 + 0.123124i
\(577\) 10.9229 6.30634i 0.454727 0.262536i −0.255098 0.966915i \(-0.582108\pi\)
0.709824 + 0.704379i \(0.248774\pi\)
\(578\) −13.3478 + 7.70635i −0.555195 + 0.320542i
\(579\) 17.8842 + 3.16315i 0.743242 + 0.131456i
\(580\) 2.91724i 0.121132i
\(581\) 37.5660 23.2425i 1.55850 0.964262i
\(582\) −3.54317 9.75071i −0.146869 0.404180i
\(583\) −4.72783 + 8.18885i −0.195807 + 0.339147i
\(584\) 0.760465 + 1.31716i 0.0314683 + 0.0545046i
\(585\) 1.51850 4.15845i 0.0627821 0.171931i
\(586\) 20.3000 + 11.7202i 0.838587 + 0.484158i
\(587\) −23.0865 −0.952884 −0.476442 0.879206i \(-0.658074\pi\)
−0.476442 + 0.879206i \(0.658074\pi\)
\(588\) 7.21847 9.74134i 0.297685 0.401726i
\(589\) 3.49784 0.144126
\(590\) −12.4753 7.20265i −0.513602 0.296528i
\(591\) −36.5331 30.6876i −1.50277 1.26232i
\(592\) 0.738591 + 1.27928i 0.0303559 + 0.0525779i
\(593\) 11.8378 20.5037i 0.486122 0.841987i −0.513751 0.857939i \(-0.671745\pi\)
0.999873 + 0.0159520i \(0.00507790\pi\)
\(594\) 3.20296 + 1.85596i 0.131419 + 0.0761510i
\(595\) 4.18301 2.58808i 0.171487 0.106101i
\(596\) 16.7599i 0.686512i
\(597\) 5.44466 30.7838i 0.222835 1.25990i
\(598\) 1.87219 1.08091i 0.0765597 0.0442018i
\(599\) 1.09795 0.633902i 0.0448611 0.0259005i −0.477402 0.878685i \(-0.658421\pi\)
0.522263 + 0.852785i \(0.325088\pi\)
\(600\) 0.851409 4.81381i 0.0347586 0.196523i
\(601\) 25.2631i 1.03050i −0.857040 0.515251i \(-0.827699\pi\)
0.857040 0.515251i \(-0.172301\pi\)
\(602\) 21.6829 0.660783i 0.883730 0.0269315i
\(603\) −16.1392 + 13.5136i −0.657241 + 0.550316i
\(604\) −7.58068 + 13.1301i −0.308454 + 0.534257i
\(605\) 7.74172 + 13.4091i 0.314746 + 0.545156i
\(606\) −11.9012 9.99691i −0.483452 0.406097i
\(607\) 13.9578 + 8.05855i 0.566530 + 0.327086i 0.755762 0.654846i \(-0.227267\pi\)
−0.189232 + 0.981932i \(0.560600\pi\)
\(608\) −2.12017 −0.0859844
\(609\) −8.96469 1.30534i −0.363268 0.0528948i
\(610\) 6.16191 0.249489
\(611\) 1.78269 + 1.02924i 0.0721200 + 0.0416385i
\(612\) 3.55035 + 1.29644i 0.143514 + 0.0524056i
\(613\) −9.56329 16.5641i −0.386258 0.669018i 0.605685 0.795704i \(-0.292899\pi\)
−0.991943 + 0.126687i \(0.959566\pi\)
\(614\) −3.75798 + 6.50900i −0.151660 + 0.262682i
\(615\) −4.13970 11.3923i −0.166929 0.459384i
\(616\) −1.66030 0.892281i −0.0668956 0.0359510i
\(617\) 4.04245i 0.162743i −0.996684 0.0813715i \(-0.974070\pi\)
0.996684 0.0813715i \(-0.0259300\pi\)
\(618\) −9.75099 1.72464i −0.392242 0.0693751i
\(619\) −38.4517 + 22.2001i −1.54550 + 0.892297i −0.547027 + 0.837115i \(0.684240\pi\)
−0.998476 + 0.0551818i \(0.982426\pi\)
\(620\) −2.10838 + 1.21728i −0.0846747 + 0.0488870i
\(621\) −5.60126 9.73703i −0.224771 0.390734i
\(622\) 6.15375i 0.246743i
\(623\) −0.302589 9.92914i −0.0121230 0.397803i
\(624\) −1.62791 + 0.591542i −0.0651684 + 0.0236806i
\(625\) 1.46109 2.53069i 0.0584438 0.101228i
\(626\) 13.0024 + 22.5207i 0.519678 + 0.900109i
\(627\) −1.68270 + 2.00323i −0.0672005 + 0.0800011i
\(628\) −13.4848 7.78544i −0.538101 0.310673i
\(629\) 1.86108 0.0742060
\(630\) 11.1195 + 3.68056i 0.443011 + 0.146637i
\(631\) 12.5677 0.500314 0.250157 0.968205i \(-0.419518\pi\)
0.250157 + 0.968205i \(0.419518\pi\)
\(632\) −1.73934 1.00421i −0.0691874 0.0399454i
\(633\) −3.31964 + 3.95198i −0.131944 + 0.157077i
\(634\) 6.83359 + 11.8361i 0.271397 + 0.470073i
\(635\) 11.5959 20.0847i 0.460170 0.797037i
\(636\) −21.6066 + 7.85132i −0.856757 + 0.311325i
\(637\) 6.26405 + 3.12436i 0.248191 + 0.123792i
\(638\) 1.40837i 0.0557579i
\(639\) −14.2363 + 2.49485i −0.563181 + 0.0986947i
\(640\) 1.27797 0.737837i 0.0505162 0.0291656i
\(641\) −20.6913 + 11.9462i −0.817259 + 0.471845i −0.849470 0.527636i \(-0.823078\pi\)
0.0322113 + 0.999481i \(0.489745\pi\)
\(642\) −4.40720 0.779492i −0.173938 0.0307641i
\(643\) 23.9933i 0.946205i −0.881007 0.473103i \(-0.843134\pi\)
0.881007 0.473103i \(-0.156866\pi\)
\(644\) 3.00938 + 4.86395i 0.118586 + 0.191666i
\(645\) 7.15726 + 19.6966i 0.281817 + 0.775551i
\(646\) −1.33559 + 2.31330i −0.0525479 + 0.0910157i
\(647\) −3.31341 5.73900i −0.130264 0.225623i 0.793514 0.608551i \(-0.208249\pi\)
−0.923778 + 0.382928i \(0.874916\pi\)
\(648\) 3.06042 + 8.46368i 0.120225 + 0.332485i
\(649\) 6.02279 + 3.47726i 0.236415 + 0.136494i
\(650\) 2.82239 0.110703
\(651\) 2.79729 + 7.02376i 0.109634 + 0.275283i
\(652\) 23.5801 0.923468
\(653\) 13.2630 + 7.65742i 0.519023 + 0.299658i 0.736535 0.676400i \(-0.236461\pi\)
−0.217512 + 0.976058i \(0.569794\pi\)
\(654\) −15.1888 12.7585i −0.593929 0.498897i
\(655\) 10.3981 + 18.0100i 0.406286 + 0.703708i
\(656\) −2.37117 + 4.10699i −0.0925788 + 0.160351i
\(657\) 2.92924 + 3.49838i 0.114280 + 0.136485i
\(658\) −2.57817 + 4.79732i −0.100508 + 0.187019i
\(659\) 25.8336i 1.00633i 0.864189 + 0.503167i \(0.167832\pi\)
−0.864189 + 0.503167i \(0.832168\pi\)
\(660\) 0.317137 1.79307i 0.0123445 0.0697951i
\(661\) −18.6895 + 10.7904i −0.726936 + 0.419697i −0.817300 0.576212i \(-0.804530\pi\)
0.0903641 + 0.995909i \(0.471197\pi\)
\(662\) 6.16188 3.55757i 0.239488 0.138269i
\(663\) −0.380060 + 2.14883i −0.0147603 + 0.0834537i
\(664\) 16.6965i 0.647951i
\(665\) −3.91858 + 7.29146i −0.151956 + 0.282751i
\(666\) 2.84498 + 3.39775i 0.110241 + 0.131660i
\(667\) 2.13684 3.70111i 0.0827387 0.143308i
\(668\) 6.83797 + 11.8437i 0.264569 + 0.458247i
\(669\) −3.38153 2.84047i −0.130738 0.109819i
\(670\) 8.96699 + 5.17709i 0.346425 + 0.200009i
\(671\) −2.97482 −0.114842
\(672\) −1.69554 4.25736i −0.0654070 0.164231i
\(673\) −23.3592 −0.900431 −0.450216 0.892920i \(-0.648653\pi\)
−0.450216 + 0.892920i \(0.648653\pi\)
\(674\) −1.58332 0.914131i −0.0609873 0.0352110i
\(675\) 0.0230870 14.6655i 0.000888619 0.564477i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) 10.1408 17.5644i 0.389743 0.675054i −0.602672 0.797989i \(-0.705897\pi\)
0.992415 + 0.122935i \(0.0392307\pi\)
\(678\) 2.68211 + 7.38108i 0.103006 + 0.283469i
\(679\) 8.33803 + 13.4765i 0.319984 + 0.517179i
\(680\) 1.85918i 0.0712962i
\(681\) −14.0620 2.48711i −0.538855 0.0953063i
\(682\) 1.01787 0.587670i 0.0389764 0.0225031i
\(683\) −16.7121 + 9.64873i −0.639470 + 0.369198i −0.784410 0.620242i \(-0.787034\pi\)
0.144940 + 0.989440i \(0.453701\pi\)
\(684\) −6.26505 + 1.09792i −0.239550 + 0.0419800i
\(685\) 20.7561i 0.793051i
\(686\) −7.75762 + 16.8172i −0.296187 + 0.642085i
\(687\) −12.9786 + 4.71610i −0.495163 + 0.179931i
\(688\) 4.09959 7.10070i 0.156295 0.270712i
\(689\) −6.63632 11.4944i −0.252824 0.437903i
\(690\) −3.55394 + 4.23091i −0.135296 + 0.161068i
\(691\) 5.44524 + 3.14381i 0.207147 + 0.119596i 0.599985 0.800011i \(-0.295173\pi\)
−0.392838 + 0.919608i \(0.628507\pi\)
\(692\) −25.5104 −0.969760
\(693\) −5.36821 1.77688i −0.203921 0.0674982i
\(694\) −20.9049 −0.793540
\(695\) 1.95845 + 1.13071i 0.0742884 + 0.0428904i
\(696\) −2.20232 + 2.62183i −0.0834789 + 0.0993803i
\(697\) 2.98740 + 5.17433i 0.113156 + 0.195992i
\(698\) 15.1263 26.1996i 0.572540 0.991668i
\(699\) −42.6814 + 15.5094i −1.61436 + 0.586619i
\(700\) 0.227460 + 7.46387i 0.00859718 + 0.282108i
\(701\) 34.1003i 1.28795i 0.765046 + 0.643976i \(0.222716\pi\)
−0.765046 + 0.643976i \(0.777284\pi\)
\(702\) −4.50408 + 2.59099i −0.169996 + 0.0977906i
\(703\) −2.71229 + 1.56594i −0.102296 + 0.0590606i
\(704\) −0.616972 + 0.356209i −0.0232530 + 0.0134251i
\(705\) −5.18093 0.916342i −0.195125 0.0345114i
\(706\) 6.75115i 0.254083i
\(707\) 20.9131 + 11.2391i 0.786519 + 0.422691i
\(708\) 5.77454 + 15.8914i 0.217021 + 0.597234i
\(709\) 23.4010 40.5318i 0.878844 1.52220i 0.0262328 0.999656i \(-0.491649\pi\)
0.852611 0.522546i \(-0.175018\pi\)
\(710\) 3.55473 + 6.15697i 0.133406 + 0.231067i
\(711\) −5.65973 2.06670i −0.212256 0.0775074i
\(712\) −3.25158 1.87730i −0.121858 0.0703549i
\(713\) −3.56656 −0.133569
\(714\) −5.71326 0.831899i −0.213813 0.0311330i
\(715\) 1.05130 0.0393163
\(716\) 5.27781 + 3.04714i 0.197241 + 0.113877i
\(717\) −21.4469 18.0152i −0.800948 0.672792i
\(718\) 3.82151 + 6.61905i 0.142618 + 0.247021i
\(719\) −10.4968 + 18.1810i −0.391465 + 0.678037i −0.992643 0.121078i \(-0.961365\pi\)
0.601178 + 0.799115i \(0.294698\pi\)
\(720\) 3.39428 2.84207i 0.126497 0.105918i
\(721\) 15.1190 0.460750i 0.563062 0.0171592i
\(722\) 14.5049i 0.539815i
\(723\) −3.98158 + 22.5116i −0.148076 + 0.837214i
\(724\) −15.7684 + 9.10391i −0.586029 + 0.338344i
\(725\) 4.83202 2.78977i 0.179457 0.103609i
\(726\) 3.16518 17.8957i 0.117471 0.664172i
\(727\) 17.4752i 0.648121i −0.946036 0.324060i \(-0.894952\pi\)
0.946036 0.324060i \(-0.105048\pi\)
\(728\) 2.24993 1.39206i 0.0833879 0.0515930i
\(729\) 13.4263 + 23.4251i 0.497271 + 0.867595i
\(730\) 1.12220 1.94370i 0.0415344 0.0719397i
\(731\) −5.16501 8.94605i −0.191035 0.330882i
\(732\) −5.53794 4.65184i −0.204688 0.171937i
\(733\) 13.0692 + 7.54551i 0.482722 + 0.278700i 0.721550 0.692362i \(-0.243430\pi\)
−0.238828 + 0.971062i \(0.576763\pi\)
\(734\) −18.4828 −0.682213
\(735\) −17.7752 2.03748i −0.655648 0.0751537i
\(736\) 2.16182 0.0796859
\(737\) −4.32904 2.49937i −0.159462 0.0920655i
\(738\) −4.87996 + 13.3639i −0.179634 + 0.491933i
\(739\) −25.1280 43.5229i −0.924348 1.60102i −0.792607 0.609733i \(-0.791277\pi\)
−0.131740 0.991284i \(-0.542057\pi\)
\(740\) 1.08992 1.88779i 0.0400662 0.0693967i
\(741\) −1.25417 3.45144i −0.0460732 0.126792i
\(742\) 29.8625 18.4762i 1.09629 0.678284i
\(743\) 11.2555i 0.412925i 0.978455 + 0.206462i \(0.0661951\pi\)
−0.978455 + 0.206462i \(0.933805\pi\)
\(744\) 2.81385 + 0.497680i 0.103161 + 0.0182458i
\(745\) 21.4187 12.3661i 0.784719 0.453058i
\(746\) −4.43510 + 2.56061i −0.162381 + 0.0937505i
\(747\) −8.64620 49.3377i −0.316348 1.80517i
\(748\) 0.897564i 0.0328182i
\(749\) 6.83342 0.208247i 0.249688 0.00760918i
\(750\) −18.7914 + 6.82834i −0.686165 + 0.249336i
\(751\) −20.0363 + 34.7039i −0.731136 + 1.26636i 0.225262 + 0.974298i \(0.427676\pi\)
−0.956398 + 0.292066i \(0.905657\pi\)
\(752\) 1.02924 + 1.78269i 0.0375324 + 0.0650081i
\(753\) −11.3017 + 13.4545i −0.411858 + 0.490311i
\(754\) −1.71203 0.988443i −0.0623486 0.0359970i
\(755\) 22.3732 0.814245
\(756\) −7.21492 11.7023i −0.262404 0.425610i
\(757\) 7.74903 0.281643 0.140822 0.990035i \(-0.455026\pi\)
0.140822 + 0.990035i \(0.455026\pi\)
\(758\) 14.8276 + 8.56074i 0.538564 + 0.310940i
\(759\) 1.71575 2.04258i 0.0622779 0.0741408i
\(760\) 1.56434 + 2.70952i 0.0567447 + 0.0982847i
\(761\) 13.4912 23.3675i 0.489057 0.847071i −0.510864 0.859661i \(-0.670674\pi\)
0.999921 + 0.0125906i \(0.00400782\pi\)
\(762\) −25.5843 + 9.29673i −0.926822 + 0.336785i
\(763\) 26.6903 + 14.3439i 0.966254 + 0.519284i
\(764\) 8.52297i 0.308350i
\(765\) −0.962763 5.49381i −0.0348088 0.198629i
\(766\) 14.4975 8.37015i 0.523817 0.302426i
\(767\) −8.45400 + 4.88092i −0.305256 + 0.176240i
\(768\) −1.70558 0.301663i −0.0615448 0.0108853i
\(769\) 17.8098i 0.642236i −0.947039 0.321118i \(-0.895941\pi\)
0.947039 0.321118i \(-0.104059\pi\)
\(770\) 0.0847254 + 2.78018i 0.00305329 + 0.100191i
\(771\) −15.9510 43.8968i −0.574462 1.58090i
\(772\) −5.24285 + 9.08089i −0.188694 + 0.326828i
\(773\) −2.47459 4.28611i −0.0890047 0.154161i 0.818086 0.575096i \(-0.195035\pi\)
−0.907091 + 0.420935i \(0.861702\pi\)
\(774\) 8.43711 23.1053i 0.303266 0.830503i
\(775\) −4.03252 2.32817i −0.144852 0.0836305i
\(776\) 5.98973 0.215019
\(777\) −5.31352 4.19403i −0.190621 0.150460i
\(778\) 19.9669 0.715846
\(779\) −8.70754 5.02730i −0.311980 0.180122i
\(780\) 1.95710 + 1.64395i 0.0700755 + 0.0588630i
\(781\) −1.71613 2.97243i −0.0614080 0.106362i
\(782\) 1.36182 2.35875i 0.0486987 0.0843486i
\(783\) −5.15010 + 8.88789i −0.184049 + 0.317627i
\(784\) 3.86265 + 5.83780i 0.137952 + 0.208493i
\(785\) 22.9775i 0.820103i
\(786\) 4.25122 24.0361i 0.151636 0.857340i
\(787\) −22.3467 + 12.9019i −0.796575 + 0.459903i −0.842272 0.539053i \(-0.818782\pi\)
0.0456973 + 0.998955i \(0.485449\pi\)
\(788\) 23.8558 13.7732i 0.849828 0.490648i
\(789\) −8.59209 + 48.5791i −0.305887 + 1.72946i
\(790\) 2.96377i 0.105446i
\(791\) −6.31171 10.2014i −0.224419 0.362720i
\(792\) −1.63867 + 1.37208i −0.0582277 + 0.0487548i
\(793\) 2.08783 3.61623i 0.0741410 0.128416i
\(794\) −4.34555 7.52672i −0.154218 0.267113i
\(795\) 25.9759 + 21.8196i 0.921270 + 0.773862i
\(796\) 15.6308 + 9.02443i 0.554018 + 0.319862i
\(797\) −25.3698 −0.898645 −0.449323 0.893370i \(-0.648335\pi\)
−0.449323 + 0.893370i \(0.648335\pi\)
\(798\) 9.02635 3.59485i 0.319529 0.127256i
\(799\) 2.59344 0.0917493
\(800\) 2.44426 + 1.41119i 0.0864176 + 0.0498932i
\(801\) −10.5805 3.86356i −0.373843 0.136512i
\(802\) −5.32841 9.22909i −0.188153 0.325890i
\(803\) −0.541769 + 0.938372i −0.0191186 + 0.0331144i
\(804\) −4.15061 11.4223i −0.146381 0.402835i
\(805\) 3.99555 7.43470i 0.140825 0.262039i
\(806\) 1.64979i 0.0581114i
\(807\) −3.65247 0.646006i −0.128573 0.0227405i
\(808\) 7.77135 4.48679i 0.273395 0.157845i
\(809\) 22.2087 12.8222i 0.780816 0.450804i −0.0559033 0.998436i \(-0.517804\pi\)
0.836719 + 0.547632i \(0.184471\pi\)
\(810\) 8.55824 10.1559i 0.300706 0.356843i
\(811\) 25.6113i 0.899333i −0.893196 0.449667i \(-0.851543\pi\)
0.893196 0.449667i \(-0.148457\pi\)
\(812\) 2.47599 4.60717i 0.0868901 0.161680i
\(813\) 34.4868 12.5317i 1.20950 0.439505i
\(814\) −0.526185 + 0.911380i −0.0184428 + 0.0319438i
\(815\) −17.3983 30.1347i −0.609435 1.05557i
\(816\) −1.40356 + 1.67091i −0.0491343 + 0.0584936i
\(817\) 15.0547 + 8.69185i 0.526698 + 0.304089i
\(818\) 19.9352 0.697019
\(819\) 5.92760 5.27859i 0.207127 0.184449i
\(820\) 6.99816 0.244386
\(821\) 14.5678 + 8.41070i 0.508418 + 0.293536i 0.732183 0.681108i \(-0.238501\pi\)
−0.223765 + 0.974643i \(0.571835\pi\)
\(822\) 15.6695 18.6543i 0.546537 0.650644i
\(823\) −7.99185 13.8423i −0.278578 0.482512i 0.692453 0.721463i \(-0.256530\pi\)
−0.971032 + 0.238951i \(0.923196\pi\)
\(824\) 2.85856 4.95116i 0.0995825 0.172482i
\(825\) 3.27326 1.18943i 0.113960 0.0414105i
\(826\) −13.5890 21.9635i −0.472823 0.764206i
\(827\) 49.9019i 1.73526i −0.497210 0.867630i \(-0.665642\pi\)
0.497210 0.867630i \(-0.334358\pi\)
\(828\) 6.38812 1.11949i 0.222002 0.0389048i
\(829\) 31.7041 18.3044i 1.10113 0.635737i 0.164611 0.986359i \(-0.447363\pi\)
0.936517 + 0.350622i \(0.114030\pi\)
\(830\) −21.3377 + 12.3193i −0.740642 + 0.427610i
\(831\) 32.1036 + 5.67810i 1.11366 + 0.196971i
\(832\) 1.00000i 0.0346688i
\(833\) 8.80282 0.537027i 0.305000 0.0186069i
\(834\) −0.906521 2.49472i −0.0313903 0.0863851i
\(835\) 10.0906 17.4774i 0.349200 0.604832i
\(836\) −0.755225 1.30809i −0.0261200 0.0452412i
\(837\) 8.57255 + 0.0134952i 0.296311 + 0.000466463i
\(838\) 17.5755 + 10.1472i 0.607134 + 0.350529i
\(839\) −41.4486 −1.43097 −0.715483 0.698630i \(-0.753793\pi\)
−0.715483 + 0.698630i \(0.753793\pi\)
\(840\) −4.18975 + 5.30809i −0.144560 + 0.183147i
\(841\) 25.0919 0.865239
\(842\) 16.3926 + 9.46429i 0.564927 + 0.326161i
\(843\) −29.0392 24.3927i −1.00016 0.840131i
\(844\) −1.48992 2.58061i −0.0512850 0.0888283i
\(845\) −0.737837 + 1.27797i −0.0253824 + 0.0439635i
\(846\) 3.96452 + 4.73482i 0.136303 + 0.162786i
\(847\) 0.845602 + 27.7476i 0.0290552 + 0.953417i
\(848\) 13.2726i 0.455784i
\(849\) 0.415789 2.35085i 0.0142699 0.0806808i
\(850\) 3.07948 1.77794i 0.105625 0.0609828i
\(851\) 2.76557 1.59670i 0.0948025 0.0547343i
\(852\) 1.45334 8.21708i 0.0497906 0.281513i
\(853\) 34.2914i 1.17412i 0.809545 + 0.587058i \(0.199714\pi\)
−0.809545 + 0.587058i \(0.800286\pi\)
\(854\) 9.73146 + 5.22988i 0.333004 + 0.178963i
\(855\) 6.02569 + 7.19646i 0.206074 + 0.246114i
\(856\) 1.29199 2.23780i 0.0441594 0.0764864i
\(857\) −0.370855 0.642339i −0.0126682 0.0219419i 0.859622 0.510931i \(-0.170699\pi\)
−0.872290 + 0.488989i \(0.837366\pi\)
\(858\) −0.944840 0.793660i −0.0322563 0.0270951i
\(859\) 10.0183 + 5.78405i 0.341819 + 0.197349i 0.661076 0.750319i \(-0.270100\pi\)
−0.319257 + 0.947668i \(0.603433\pi\)
\(860\) −12.0993 −0.412583
\(861\) 3.13137 21.5054i 0.106717 0.732902i
\(862\) 2.60381 0.0886863
\(863\) −22.7050 13.1087i −0.772886 0.446226i 0.0610174 0.998137i \(-0.480565\pi\)
−0.833903 + 0.551911i \(0.813899\pi\)
\(864\) −5.19615 0.00817995i −0.176776 0.000278288i
\(865\) 18.8225 + 32.6015i 0.639985 + 1.10849i
\(866\) 14.1437 24.4975i 0.480621 0.832460i
\(867\) −9.11726 25.0904i −0.309638 0.852115i
\(868\) −4.36291 + 0.132959i −0.148087 + 0.00451292i
\(869\) 1.43084i 0.0485378i
\(870\) 4.97558 + 0.880021i 0.168688 + 0.0298355i
\(871\) 6.07654 3.50829i 0.205896 0.118874i
\(872\) 9.91816 5.72625i 0.335871 0.193915i
\(873\) 17.6994 3.10174i 0.599036 0.104978i
\(874\) 4.58344i 0.155037i
\(875\) 25.9716 16.0689i 0.878000 0.543228i
\(876\) −2.47593 + 0.899694i −0.0836540 + 0.0303979i
\(877\) −8.17596 + 14.1612i −0.276083 + 0.478189i −0.970408 0.241472i \(-0.922370\pi\)
0.694325 + 0.719662i \(0.255703\pi\)
\(878\) −19.9421 34.5408i −0.673014 1.16569i
\(879\) −26.1135 + 31.0878i −0.880788 + 1.04856i
\(880\) 0.910449 + 0.525648i 0.0306912 + 0.0177196i
\(881\) −52.8947 −1.78207 −0.891033 0.453938i \(-0.850019\pi\)
−0.891033 + 0.453938i \(0.850019\pi\)
\(882\) 14.4371 + 15.2503i 0.486122 + 0.513503i
\(883\) −54.9388 −1.84884 −0.924419 0.381378i \(-0.875450\pi\)
−0.924419 + 0.381378i \(0.875450\pi\)
\(884\) −1.09109 0.629942i −0.0366974 0.0211872i
\(885\) 16.0480 19.1049i 0.539449 0.642205i
\(886\) 6.94666 + 12.0320i 0.233378 + 0.404222i
\(887\) 16.1173 27.9160i 0.541166 0.937328i −0.457671 0.889122i \(-0.651316\pi\)
0.998837 0.0482060i \(-0.0153504\pi\)
\(888\) −2.40471 + 0.873815i −0.0806969 + 0.0293233i
\(889\) 35.3601 21.8777i 1.18594 0.733754i
\(890\) 5.54057i 0.185720i
\(891\) −4.13170 + 4.90303i −0.138417 + 0.164258i
\(892\) 2.20811 1.27485i 0.0739330 0.0426853i
\(893\) −3.77962 + 2.18216i −0.126480 + 0.0730233i
\(894\) −28.5853 5.05583i −0.956036 0.169092i
\(895\) 8.99318i 0.300609i
\(896\) 2.64452 0.0805913i 0.0883473 0.00269237i
\(897\) 1.27881 + 3.51925i 0.0426982 + 0.117504i
\(898\) 10.8676 18.8233i 0.362657 0.628141i
\(899\) 1.63072 + 2.82450i 0.0543877 + 0.0942022i
\(900\) 7.95349 + 2.90429i 0.265116 + 0.0968096i
\(901\) −14.4816 8.36098i −0.482454 0.278545i
\(902\) −3.37853 −0.112493
\(903\) −5.41391 + 37.1813i −0.180164 + 1.23732i
\(904\) −4.53409 −0.150802
\(905\) 23.2691 + 13.4344i 0.773489 + 0.446574i
\(906\) −20.1077 16.8903i −0.668032 0.561143i
\(907\) 11.4807 + 19.8851i 0.381210 + 0.660274i 0.991235 0.132107i \(-0.0421743\pi\)
−0.610026 + 0.792382i \(0.708841\pi\)
\(908\) 4.12234 7.14010i 0.136805 0.236953i
\(909\) 20.6406 17.2827i 0.684607 0.573230i
\(910\) −3.43909 1.84823i −0.114005 0.0612683i
\(911\) 14.0418i 0.465225i 0.972570 + 0.232612i \(0.0747274\pi\)
−0.972570 + 0.232612i \(0.925273\pi\)
\(912\) 0.639577 3.61612i 0.0211785 0.119742i
\(913\) 10.3013 5.94746i 0.340923 0.196832i
\(914\) −7.52596 + 4.34511i −0.248937 + 0.143724i
\(915\) −1.85882 + 10.5096i −0.0614506 + 0.347438i
\(916\) 7.97255i 0.263421i
\(917\) 1.13574 + 37.2683i 0.0375056 + 1.23071i
\(918\) −3.28219 + 5.66431i −0.108329 + 0.186950i
\(919\) 4.86603 8.42821i 0.160516 0.278021i −0.774538 0.632527i \(-0.782018\pi\)
0.935054 + 0.354506i \(0.115351\pi\)
\(920\) −1.59507 2.76275i −0.0525880 0.0910851i
\(921\) −9.96798 8.37305i −0.328456 0.275901i
\(922\) 30.4115 + 17.5581i 1.00155 + 0.578244i
\(923\) 4.81777 0.158579
\(924\) 2.02271 2.56261i 0.0665422 0.0843038i
\(925\) 4.16918 0.137082
\(926\) 18.1761 + 10.4940i 0.597305 + 0.344854i
\(927\) 5.88301 16.1108i 0.193224 0.529149i
\(928\) −0.988443 1.71203i −0.0324472 0.0562002i
\(929\) −8.24313 + 14.2775i −0.270448 + 0.468430i −0.968977 0.247152i \(-0.920505\pi\)
0.698528 + 0.715582i \(0.253839\pi\)
\(930\) −1.44014 3.96322i −0.0472241 0.129959i
\(931\) −12.3772 + 8.18949i −0.405645 + 0.268400i
\(932\) 26.2186i 0.858818i
\(933\) 10.4957 + 1.85635i 0.343614 + 0.0607743i
\(934\) −29.9621 + 17.2987i −0.980391 + 0.566029i
\(935\) 1.14706 0.662255i 0.0375129 0.0216581i
\(936\) −0.517844 2.95497i −0.0169262 0.0965862i
\(937\) 20.8956i 0.682629i 0.939949 + 0.341315i \(0.110872\pi\)
−0.939949 + 0.341315i \(0.889128\pi\)
\(938\) 9.76748 + 15.7868i 0.318919 + 0.515458i
\(939\) −42.3332 + 15.3829i −1.38149 + 0.502001i
\(940\) 1.51882 2.63067i 0.0495384 0.0858031i
\(941\) 9.05103 + 15.6768i 0.295055 + 0.511051i 0.974998 0.222215i \(-0.0713286\pi\)
−0.679943 + 0.733265i \(0.737995\pi\)
\(942\) 17.3465 20.6508i 0.565180 0.672838i
\(943\) 8.87860 + 5.12606i 0.289127 + 0.166927i
\(944\) −9.76184 −0.317721
\(945\) −9.63182 + 17.8549i −0.313323 + 0.580819i
\(946\) 5.84125 0.189915
\(947\) −33.3244 19.2399i −1.08290 0.625212i −0.151222 0.988500i \(-0.548321\pi\)
−0.931677 + 0.363288i \(0.881654\pi\)
\(948\) 2.23746 2.66366i 0.0726692 0.0865115i
\(949\) −0.760465 1.31716i −0.0246857 0.0427570i
\(950\) −2.99198 + 5.18226i −0.0970726 + 0.168135i
\(951\) −22.2489 + 8.08471i −0.721470 + 0.262165i
\(952\) 1.57796 2.93618i 0.0511421 0.0951623i
\(953\) 37.1230i 1.20253i 0.799049 + 0.601265i \(0.205337\pi\)
−0.799049 + 0.601265i \(0.794663\pi\)
\(954\) −6.87315 39.2202i −0.222526 1.26980i
\(955\) −10.8921 + 6.28856i −0.352460 + 0.203493i
\(956\) 14.0046 8.08557i 0.452942 0.261506i
\(957\) −2.40208 0.424852i −0.0776484 0.0137335i
\(958\) 38.9052i 1.25697i
\(959\) −17.6166 + 32.7800i −0.568870 + 1.05852i
\(960\) 0.872923 + 2.40226i 0.0281735 + 0.0775325i
\(961\) −14.1391 + 24.4896i −0.456100 + 0.789988i
\(962\) −0.738591 1.27928i −0.0238131 0.0412455i
\(963\) 2.65897 7.28168i 0.0856842 0.234649i
\(964\) −11.4305 6.59939i −0.368151 0.212552i
\(965\) 15.4735 0.498109
\(966\) −9.20367 + 3.66546i −0.296123 + 0.117934i
\(967\) −44.8131 −1.44109 −0.720545 0.693408i \(-0.756109\pi\)
−0.720545 + 0.693408i \(0.756109\pi\)
\(968\) 9.08674 + 5.24623i 0.292059 + 0.168620i
\(969\) −3.54262 2.97578i −0.113806 0.0955960i
\(970\) −4.41944 7.65469i −0.141900 0.245777i
\(971\) −7.29756 + 12.6397i −0.234190 + 0.405629i −0.959037 0.283281i \(-0.908577\pi\)
0.724847 + 0.688910i \(0.241910\pi\)
\(972\) −15.3587 + 2.66662i −0.492630 + 0.0855319i
\(973\) 2.13329 + 3.44795i 0.0683900 + 0.110536i
\(974\) 26.9840i 0.864623i
\(975\) −0.851409 + 4.81381i −0.0272669 + 0.154165i
\(976\) 3.61623 2.08783i 0.115753 0.0668298i
\(977\) 2.96708 1.71305i 0.0949254 0.0548052i −0.451786 0.892126i \(-0.649213\pi\)
0.546711 + 0.837321i \(0.315880\pi\)
\(978\) −7.11323 + 40.2177i −0.227456 + 1.28602i
\(979\) 2.67485i 0.0854885i
\(980\) 4.61054 9.24370i 0.147278 0.295279i
\(981\) 26.3425 22.0570i 0.841053 0.704224i
\(982\) −13.5624 + 23.4908i −0.432794 + 0.749621i
\(983\) −3.81097 6.60079i −0.121551 0.210533i 0.798828 0.601559i \(-0.205453\pi\)
−0.920380 + 0.391026i \(0.872120\pi\)
\(984\) −6.28951 5.28315i −0.200502 0.168421i
\(985\) −35.2034 20.3247i −1.12167 0.647598i
\(986\) −2.49065 −0.0793183
\(987\) −7.40447 5.84445i −0.235687 0.186031i
\(988\) 2.12017 0.0674517
\(989\) −15.3505 8.86259i −0.488116 0.281814i
\(990\) 2.96255 + 1.08180i 0.0941561 + 0.0343820i
\(991\) 14.0329 + 24.3057i 0.445770 + 0.772096i 0.998106 0.0615255i \(-0.0195966\pi\)
−0.552335 + 0.833622i \(0.686263\pi\)
\(992\) −0.824895 + 1.42876i −0.0261904 + 0.0453632i
\(993\) 4.20890 + 11.5828i 0.133565 + 0.367568i
\(994\) 0.388270 + 12.7407i 0.0123152 + 0.404110i
\(995\) 26.6342i 0.844362i
\(996\) 28.4773 + 5.03672i 0.902337 + 0.159595i
\(997\) 31.0262 17.9130i 0.982609 0.567309i 0.0795519 0.996831i \(-0.474651\pi\)
0.903057 + 0.429521i \(0.141318\pi\)
\(998\) −36.6475 + 21.1584i −1.16006 + 0.669759i
\(999\) −6.65335 + 3.82736i −0.210503 + 0.121092i
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 546.2.z.a.131.7 32
3.2 odd 2 546.2.z.b.131.16 yes 32
7.3 odd 6 546.2.z.b.521.16 yes 32
21.17 even 6 inner 546.2.z.a.521.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.z.a.131.7 32 1.1 even 1 trivial
546.2.z.a.521.7 yes 32 21.17 even 6 inner
546.2.z.b.131.16 yes 32 3.2 odd 2
546.2.z.b.521.16 yes 32 7.3 odd 6