Properties

Label 507.2.f.g.239.8
Level $507$
Weight $2$
Character 507.239
Analytic conductor $4.048$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(239,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.239");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.f (of order \(4\), 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 239.8
Character \(\chi\) \(=\) 507.239
Dual form 507.2.f.g.437.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.928351 - 0.928351i) q^{2} +(-1.37245 + 1.05658i) q^{3} -0.276330i q^{4} +(-2.12536 - 2.12536i) q^{5} +(2.25500 + 0.293240i) q^{6} +(-2.06528 - 2.06528i) q^{7} +(-2.11323 + 2.11323i) q^{8} +(0.767265 - 2.90022i) q^{9} +O(q^{10})\) \(q+(-0.928351 - 0.928351i) q^{2} +(-1.37245 + 1.05658i) q^{3} -0.276330i q^{4} +(-2.12536 - 2.12536i) q^{5} +(2.25500 + 0.293240i) q^{6} +(-2.06528 - 2.06528i) q^{7} +(-2.11323 + 2.11323i) q^{8} +(0.767265 - 2.90022i) q^{9} +3.94616i q^{10} +(-1.88395 + 1.88395i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(5.16258 + 0.671341i) q^{15} +3.37098 q^{16} +0.198832 q^{17} +(-3.40472 + 1.98013i) q^{18} +(3.75211 - 3.75211i) q^{19} +(-0.587301 + 0.587301i) q^{20} +(5.01665 + 0.652364i) q^{21} +3.49793 q^{22} -3.30077 q^{23} +(0.667511 - 5.13312i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(-0.570700 + 0.570700i) q^{28} +3.73266i q^{29} +(-4.16944 - 5.41592i) q^{30} +(-0.550550 + 0.550550i) q^{31} +(1.09701 + 1.09701i) q^{32} +(0.595087 - 4.57618i) q^{33} +(-0.184586 - 0.184586i) q^{34} +8.77893i q^{35} +(-0.801420 - 0.212019i) q^{36} +(3.60812 + 3.60812i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(2.69398 + 2.69398i) q^{41} +(-4.05158 - 5.26283i) q^{42} +11.6558i q^{43} +(0.520592 + 0.520592i) q^{44} +(-7.79473 + 4.53331i) q^{45} +(3.06427 + 3.06427i) q^{46} +(-4.29586 + 4.29586i) q^{47} +(-4.62652 + 3.56172i) q^{48} +1.53077i q^{49} +(3.74525 - 3.74525i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(2.58064 - 6.31501i) q^{54} +8.00814 q^{55} +8.72884 q^{56} +(-1.18519 + 9.11402i) q^{57} +(3.46521 - 3.46521i) q^{58} +(2.36073 - 2.36073i) q^{59} +(0.185512 - 1.42658i) q^{60} -2.70094 q^{61} +1.02221 q^{62} +(-7.57440 + 4.40516i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(-5.33624 + 5.33624i) q^{67} -0.0549435i q^{68} +(4.53015 - 3.48753i) q^{69} +(8.14992 - 8.14992i) q^{70} +(3.78131 + 3.78131i) q^{71} +(4.50744 + 7.75026i) q^{72} +(-3.46215 - 3.46215i) q^{73} -6.69920i q^{74} +(-4.26258 - 5.53690i) q^{75} +(-1.03682 - 1.03682i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(-7.16454 - 7.16454i) q^{80} +(-7.82261 - 4.45048i) q^{81} -5.00192i q^{82} +(1.84014 + 1.84014i) q^{83} +(0.180268 - 1.38625i) q^{84} +(-0.422590 - 0.422590i) q^{85} +(10.8207 - 10.8207i) q^{86} +(-3.94386 - 5.12290i) q^{87} -7.96245i q^{88} +(0.776855 - 0.776855i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(0.173903 - 1.33731i) q^{93} +7.97613 q^{94} -15.9492 q^{95} +(-2.66469 - 0.346516i) q^{96} +(-8.60129 + 8.60129i) q^{97} +(1.42109 - 1.42109i) q^{98} +(4.01839 + 6.90936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.928351 0.928351i −0.656443 0.656443i 0.298094 0.954537i \(-0.403649\pi\)
−0.954537 + 0.298094i \(0.903649\pi\)
\(3\) −1.37245 + 1.05658i −0.792387 + 0.610018i
\(4\) 0.276330i 0.138165i
\(5\) −2.12536 2.12536i −0.950489 0.950489i 0.0483414 0.998831i \(-0.484606\pi\)
−0.998831 + 0.0483414i \(0.984606\pi\)
\(6\) 2.25500 + 0.293240i 0.920599 + 0.119715i
\(7\) −2.06528 2.06528i −0.780603 0.780603i 0.199330 0.979932i \(-0.436124\pi\)
−0.979932 + 0.199330i \(0.936124\pi\)
\(8\) −2.11323 + 2.11323i −0.747141 + 0.747141i
\(9\) 0.767265 2.90022i 0.255755 0.966742i
\(10\) 3.94616i 1.24788i
\(11\) −1.88395 + 1.88395i −0.568032 + 0.568032i −0.931577 0.363545i \(-0.881566\pi\)
0.363545 + 0.931577i \(0.381566\pi\)
\(12\) 0.291966 + 0.379251i 0.0842833 + 0.109480i
\(13\) 0 0
\(14\) 3.83461i 1.02484i
\(15\) 5.16258 + 0.671341i 1.33297 + 0.173340i
\(16\) 3.37098 0.842745
\(17\) 0.198832 0.0482240 0.0241120 0.999709i \(-0.492324\pi\)
0.0241120 + 0.999709i \(0.492324\pi\)
\(18\) −3.40472 + 1.98013i −0.802499 + 0.466722i
\(19\) 3.75211 3.75211i 0.860793 0.860793i −0.130637 0.991430i \(-0.541702\pi\)
0.991430 + 0.130637i \(0.0417024\pi\)
\(20\) −0.587301 + 0.587301i −0.131325 + 0.131325i
\(21\) 5.01665 + 0.652364i 1.09472 + 0.142358i
\(22\) 3.49793 0.745761
\(23\) −3.30077 −0.688257 −0.344129 0.938923i \(-0.611826\pi\)
−0.344129 + 0.938923i \(0.611826\pi\)
\(24\) 0.667511 5.13312i 0.136255 1.04779i
\(25\) 4.03430i 0.806861i
\(26\) 0 0
\(27\) 2.01129 + 4.79111i 0.387073 + 0.922049i
\(28\) −0.570700 + 0.570700i −0.107852 + 0.107852i
\(29\) 3.73266i 0.693137i 0.938025 + 0.346568i \(0.112653\pi\)
−0.938025 + 0.346568i \(0.887347\pi\)
\(30\) −4.16944 5.41592i −0.761232 0.988808i
\(31\) −0.550550 + 0.550550i −0.0988817 + 0.0988817i −0.754817 0.655935i \(-0.772274\pi\)
0.655935 + 0.754817i \(0.272274\pi\)
\(32\) 1.09701 + 1.09701i 0.193926 + 0.193926i
\(33\) 0.595087 4.57618i 0.103591 0.796611i
\(34\) −0.184586 0.184586i −0.0316563 0.0316563i
\(35\) 8.77893i 1.48391i
\(36\) −0.801420 0.212019i −0.133570 0.0353365i
\(37\) 3.60812 + 3.60812i 0.593171 + 0.593171i 0.938487 0.345315i \(-0.112228\pi\)
−0.345315 + 0.938487i \(0.612228\pi\)
\(38\) −6.96655 −1.13012
\(39\) 0 0
\(40\) 8.98276 1.42030
\(41\) 2.69398 + 2.69398i 0.420729 + 0.420729i 0.885455 0.464726i \(-0.153847\pi\)
−0.464726 + 0.885455i \(0.653847\pi\)
\(42\) −4.05158 5.26283i −0.625173 0.812072i
\(43\) 11.6558i 1.77749i 0.458398 + 0.888747i \(0.348423\pi\)
−0.458398 + 0.888747i \(0.651577\pi\)
\(44\) 0.520592 + 0.520592i 0.0784823 + 0.0784823i
\(45\) −7.79473 + 4.53331i −1.16197 + 0.675785i
\(46\) 3.06427 + 3.06427i 0.451802 + 0.451802i
\(47\) −4.29586 + 4.29586i −0.626616 + 0.626616i −0.947215 0.320599i \(-0.896116\pi\)
0.320599 + 0.947215i \(0.396116\pi\)
\(48\) −4.62652 + 3.56172i −0.667780 + 0.514090i
\(49\) 1.53077i 0.218681i
\(50\) 3.74525 3.74525i 0.529658 0.529658i
\(51\) −0.272889 + 0.210083i −0.0382120 + 0.0294175i
\(52\) 0 0
\(53\) 13.6276i 1.87189i −0.352142 0.935947i \(-0.614546\pi\)
0.352142 0.935947i \(-0.385454\pi\)
\(54\) 2.58064 6.31501i 0.351181 0.859364i
\(55\) 8.00814 1.07982
\(56\) 8.72884 1.16644
\(57\) −1.18519 + 9.11402i −0.156982 + 1.20718i
\(58\) 3.46521 3.46521i 0.455005 0.455005i
\(59\) 2.36073 2.36073i 0.307341 0.307341i −0.536536 0.843877i \(-0.680268\pi\)
0.843877 + 0.536536i \(0.180268\pi\)
\(60\) 0.185512 1.42658i 0.0239495 0.184170i
\(61\) −2.70094 −0.345820 −0.172910 0.984938i \(-0.555317\pi\)
−0.172910 + 0.984938i \(0.555317\pi\)
\(62\) 1.02221 0.129820
\(63\) −7.57440 + 4.40516i −0.954284 + 0.554998i
\(64\) 8.77879i 1.09735i
\(65\) 0 0
\(66\) −4.80075 + 3.69585i −0.590932 + 0.454928i
\(67\) −5.33624 + 5.33624i −0.651925 + 0.651925i −0.953456 0.301531i \(-0.902502\pi\)
0.301531 + 0.953456i \(0.402502\pi\)
\(68\) 0.0549435i 0.00666287i
\(69\) 4.53015 3.48753i 0.545366 0.419850i
\(70\) 8.14992 8.14992i 0.974102 0.974102i
\(71\) 3.78131 + 3.78131i 0.448759 + 0.448759i 0.894942 0.446183i \(-0.147217\pi\)
−0.446183 + 0.894942i \(0.647217\pi\)
\(72\) 4.50744 + 7.75026i 0.531207 + 0.913377i
\(73\) −3.46215 3.46215i −0.405214 0.405214i 0.474852 0.880066i \(-0.342502\pi\)
−0.880066 + 0.474852i \(0.842502\pi\)
\(74\) 6.69920i 0.778766i
\(75\) −4.26258 5.53690i −0.492200 0.639346i
\(76\) −1.03682 1.03682i −0.118932 0.118932i
\(77\) 7.78177 0.886815
\(78\) 0 0
\(79\) −11.1376 −1.25308 −0.626540 0.779389i \(-0.715530\pi\)
−0.626540 + 0.779389i \(0.715530\pi\)
\(80\) −7.16454 7.16454i −0.801020 0.801020i
\(81\) −7.82261 4.45048i −0.869179 0.494498i
\(82\) 5.00192i 0.552370i
\(83\) 1.84014 + 1.84014i 0.201981 + 0.201981i 0.800848 0.598867i \(-0.204382\pi\)
−0.598867 + 0.800848i \(0.704382\pi\)
\(84\) 0.180268 1.38625i 0.0196689 0.151252i
\(85\) −0.422590 0.422590i −0.0458364 0.0458364i
\(86\) 10.8207 10.8207i 1.16682 1.16682i
\(87\) −3.94386 5.12290i −0.422826 0.549233i
\(88\) 7.96245i 0.848800i
\(89\) 0.776855 0.776855i 0.0823464 0.0823464i −0.664734 0.747080i \(-0.731455\pi\)
0.747080 + 0.664734i \(0.231455\pi\)
\(90\) 11.4447 + 3.02775i 1.20638 + 0.319153i
\(91\) 0 0
\(92\) 0.912102i 0.0950932i
\(93\) 0.173903 1.33731i 0.0180329 0.138672i
\(94\) 7.97613 0.822675
\(95\) −15.9492 −1.63635
\(96\) −2.66469 0.346516i −0.271964 0.0353661i
\(97\) −8.60129 + 8.60129i −0.873329 + 0.873329i −0.992834 0.119505i \(-0.961869\pi\)
0.119505 + 0.992834i \(0.461869\pi\)
\(98\) 1.42109 1.42109i 0.143552 0.143552i
\(99\) 4.01839 + 6.90936i 0.403863 + 0.694417i
\(100\) 1.11480 0.111480
\(101\) 12.3938 1.23323 0.616616 0.787264i \(-0.288503\pi\)
0.616616 + 0.787264i \(0.288503\pi\)
\(102\) 0.448367 + 0.0583056i 0.0443949 + 0.00577312i
\(103\) 5.68798i 0.560453i 0.959934 + 0.280226i \(0.0904096\pi\)
−0.959934 + 0.280226i \(0.909590\pi\)
\(104\) 0 0
\(105\) −9.27566 12.0487i −0.905212 1.17583i
\(106\) −12.6512 + 12.6512i −1.22879 + 1.22879i
\(107\) 7.76865i 0.751024i −0.926818 0.375512i \(-0.877467\pi\)
0.926818 0.375512i \(-0.122533\pi\)
\(108\) 1.32393 0.555781i 0.127395 0.0534801i
\(109\) 7.18355 7.18355i 0.688060 0.688060i −0.273743 0.961803i \(-0.588262\pi\)
0.961803 + 0.273743i \(0.0882618\pi\)
\(110\) −7.43436 7.43436i −0.708838 0.708838i
\(111\) −8.76426 1.13970i −0.831867 0.108176i
\(112\) −6.96202 6.96202i −0.657849 0.657849i
\(113\) 17.0878i 1.60749i −0.594977 0.803743i \(-0.702839\pi\)
0.594977 0.803743i \(-0.297161\pi\)
\(114\) 9.56127 7.36073i 0.895495 0.689396i
\(115\) 7.01531 + 7.01531i 0.654181 + 0.654181i
\(116\) 1.03145 0.0957674
\(117\) 0 0
\(118\) −4.38317 −0.403504
\(119\) −0.410645 0.410645i −0.0376438 0.0376438i
\(120\) −12.3284 + 9.49103i −1.12543 + 0.866408i
\(121\) 3.90147i 0.354679i
\(122\) 2.50742 + 2.50742i 0.227011 + 0.227011i
\(123\) −6.54378 0.850953i −0.590033 0.0767279i
\(124\) 0.152134 + 0.152134i 0.0136620 + 0.0136620i
\(125\) −2.05245 + 2.05245i −0.183577 + 0.183577i
\(126\) 11.1212 + 2.94216i 0.990758 + 0.262109i
\(127\) 9.62527i 0.854104i 0.904227 + 0.427052i \(0.140448\pi\)
−0.904227 + 0.427052i \(0.859552\pi\)
\(128\) −5.95577 + 5.95577i −0.526420 + 0.526420i
\(129\) −12.3153 15.9971i −1.08430 1.40846i
\(130\) 0 0
\(131\) 11.9013i 1.03982i 0.854221 + 0.519910i \(0.174035\pi\)
−0.854221 + 0.519910i \(0.825965\pi\)
\(132\) −1.26454 0.164441i −0.110064 0.0143127i
\(133\) −15.4983 −1.34387
\(134\) 9.90780 0.855904
\(135\) 5.90811 14.4575i 0.508489 1.24431i
\(136\) −0.420179 + 0.420179i −0.0360301 + 0.0360301i
\(137\) −12.3006 + 12.3006i −1.05091 + 1.05091i −0.0522743 + 0.998633i \(0.516647\pi\)
−0.998633 + 0.0522743i \(0.983353\pi\)
\(138\) −7.44322 0.967917i −0.633609 0.0823945i
\(139\) 2.32905 0.197547 0.0987737 0.995110i \(-0.468508\pi\)
0.0987737 + 0.995110i \(0.468508\pi\)
\(140\) 2.42588 0.205025
\(141\) 1.35694 10.4348i 0.114275 0.878770i
\(142\) 7.02076i 0.589169i
\(143\) 0 0
\(144\) 2.58644 9.77660i 0.215536 0.814717i
\(145\) 7.93324 7.93324i 0.658819 0.658819i
\(146\) 6.42818i 0.532000i
\(147\) −1.61738 2.10091i −0.133400 0.173280i
\(148\) 0.997033 0.997033i 0.0819556 0.0819556i
\(149\) −11.1552 11.1552i −0.913867 0.913867i 0.0827065 0.996574i \(-0.473644\pi\)
−0.996574 + 0.0827065i \(0.973644\pi\)
\(150\) −1.18302 + 9.09735i −0.0965931 + 0.742795i
\(151\) −8.56897 8.56897i −0.697333 0.697333i 0.266502 0.963834i \(-0.414132\pi\)
−0.963834 + 0.266502i \(0.914132\pi\)
\(152\) 15.8582i 1.28627i
\(153\) 0.152557 0.576659i 0.0123335 0.0466201i
\(154\) −7.22421 7.22421i −0.582143 0.582143i
\(155\) 2.34023 0.187972
\(156\) 0 0
\(157\) −3.26731 −0.260759 −0.130380 0.991464i \(-0.541620\pi\)
−0.130380 + 0.991464i \(0.541620\pi\)
\(158\) 10.3396 + 10.3396i 0.822576 + 0.822576i
\(159\) 14.3987 + 18.7033i 1.14189 + 1.48326i
\(160\) 4.66310i 0.368650i
\(161\) 6.81701 + 6.81701i 0.537256 + 0.537256i
\(162\) 3.13052 + 11.3937i 0.245956 + 0.895176i
\(163\) 4.12124 + 4.12124i 0.322800 + 0.322800i 0.849840 0.527040i \(-0.176698\pi\)
−0.527040 + 0.849840i \(0.676698\pi\)
\(164\) 0.744429 0.744429i 0.0581302 0.0581302i
\(165\) −10.9908 + 8.46126i −0.855633 + 0.658708i
\(166\) 3.41659i 0.265179i
\(167\) −1.11810 + 1.11810i −0.0865215 + 0.0865215i −0.749043 0.662521i \(-0.769486\pi\)
0.662521 + 0.749043i \(0.269486\pi\)
\(168\) −11.9799 + 9.22274i −0.924272 + 0.711550i
\(169\) 0 0
\(170\) 0.784624i 0.0601779i
\(171\) −8.00310 13.7608i −0.612012 1.05232i
\(172\) 3.22085 0.245588
\(173\) −12.4232 −0.944518 −0.472259 0.881460i \(-0.656561\pi\)
−0.472259 + 0.881460i \(0.656561\pi\)
\(174\) −1.09456 + 8.41714i −0.0829787 + 0.638101i
\(175\) 8.33197 8.33197i 0.629838 0.629838i
\(176\) −6.35076 + 6.35076i −0.478706 + 0.478706i
\(177\) −0.745689 + 5.73431i −0.0560494 + 0.431017i
\(178\) −1.44239 −0.108111
\(179\) −16.3028 −1.21853 −0.609265 0.792966i \(-0.708536\pi\)
−0.609265 + 0.792966i \(0.708536\pi\)
\(180\) 1.25269 + 2.15392i 0.0933700 + 0.160544i
\(181\) 9.29621i 0.690982i 0.938422 + 0.345491i \(0.112288\pi\)
−0.938422 + 0.345491i \(0.887712\pi\)
\(182\) 0 0
\(183\) 3.70692 2.85377i 0.274024 0.210957i
\(184\) 6.97529 6.97529i 0.514225 0.514225i
\(185\) 15.3371i 1.12761i
\(186\) −1.40293 + 1.08005i −0.102868 + 0.0791928i
\(187\) −0.374590 + 0.374590i −0.0273928 + 0.0273928i
\(188\) 1.18708 + 1.18708i 0.0865765 + 0.0865765i
\(189\) 5.74110 14.0489i 0.417604 1.02190i
\(190\) 14.8064 + 14.8064i 1.07417 + 1.07417i
\(191\) 2.02830i 0.146763i −0.997304 0.0733813i \(-0.976621\pi\)
0.997304 0.0733813i \(-0.0233790\pi\)
\(192\) 9.27552 + 12.0485i 0.669403 + 0.869525i
\(193\) 2.80915 + 2.80915i 0.202207 + 0.202207i 0.800945 0.598738i \(-0.204331\pi\)
−0.598738 + 0.800945i \(0.704331\pi\)
\(194\) 15.9700 1.14658
\(195\) 0 0
\(196\) 0.422998 0.0302142
\(197\) 4.87188 + 4.87188i 0.347107 + 0.347107i 0.859031 0.511924i \(-0.171067\pi\)
−0.511924 + 0.859031i \(0.671067\pi\)
\(198\) 2.68384 10.1448i 0.190732 0.720958i
\(199\) 6.34056i 0.449470i 0.974420 + 0.224735i \(0.0721517\pi\)
−0.974420 + 0.224735i \(0.927848\pi\)
\(200\) −8.52542 8.52542i −0.602838 0.602838i
\(201\) 1.68557 12.9619i 0.118891 0.914264i
\(202\) −11.5058 11.5058i −0.809547 0.809547i
\(203\) 7.70898 7.70898i 0.541065 0.541065i
\(204\) 0.0580523 + 0.0754074i 0.00406448 + 0.00527958i
\(205\) 11.4514i 0.799797i
\(206\) 5.28044 5.28044i 0.367905 0.367905i
\(207\) −2.53256 + 9.57296i −0.176025 + 0.665367i
\(208\) 0 0
\(209\) 14.1376i 0.977916i
\(210\) −2.57433 + 19.7965i −0.177646 + 1.36609i
\(211\) −0.802275 −0.0552309 −0.0276154 0.999619i \(-0.508791\pi\)
−0.0276154 + 0.999619i \(0.508791\pi\)
\(212\) −3.76572 −0.258631
\(213\) −9.18494 1.19441i −0.629342 0.0818396i
\(214\) −7.21203 + 7.21203i −0.493005 + 0.493005i
\(215\) 24.7728 24.7728i 1.68949 1.68949i
\(216\) −14.3751 5.87440i −0.978098 0.399702i
\(217\) 2.27408 0.154375
\(218\) −13.3377 −0.903344
\(219\) 8.40969 + 1.09360i 0.568274 + 0.0738984i
\(220\) 2.21289i 0.149193i
\(221\) 0 0
\(222\) 7.07826 + 9.19435i 0.475062 + 0.617084i
\(223\) −2.18501 + 2.18501i −0.146319 + 0.146319i −0.776471 0.630152i \(-0.782992\pi\)
0.630152 + 0.776471i \(0.282992\pi\)
\(224\) 4.53128i 0.302759i
\(225\) 11.7004 + 3.09538i 0.780026 + 0.206359i
\(226\) −15.8635 + 15.8635i −1.05522 + 1.05522i
\(227\) 18.3243 + 18.3243i 1.21622 + 1.21622i 0.968944 + 0.247281i \(0.0795371\pi\)
0.247281 + 0.968944i \(0.420463\pi\)
\(228\) 2.51848 + 0.327503i 0.166790 + 0.0216894i
\(229\) 19.6410 + 19.6410i 1.29791 + 1.29791i 0.929768 + 0.368147i \(0.120008\pi\)
0.368147 + 0.929768i \(0.379992\pi\)
\(230\) 13.0253i 0.858865i
\(231\) −10.6801 + 8.22208i −0.702701 + 0.540973i
\(232\) −7.88797 7.88797i −0.517871 0.517871i
\(233\) −14.4551 −0.946988 −0.473494 0.880797i \(-0.657007\pi\)
−0.473494 + 0.880797i \(0.657007\pi\)
\(234\) 0 0
\(235\) 18.2605 1.19118
\(236\) −0.652342 0.652342i −0.0424638 0.0424638i
\(237\) 15.2859 11.7678i 0.992925 0.764402i
\(238\) 0.762445i 0.0494220i
\(239\) 4.24248 + 4.24248i 0.274423 + 0.274423i 0.830878 0.556455i \(-0.187839\pi\)
−0.556455 + 0.830878i \(0.687839\pi\)
\(240\) 17.4029 + 2.26308i 1.12336 + 0.146081i
\(241\) 17.4503 + 17.4503i 1.12407 + 1.12407i 0.991123 + 0.132947i \(0.0424440\pi\)
0.132947 + 0.991123i \(0.457556\pi\)
\(242\) 3.62193 3.62193i 0.232827 0.232827i
\(243\) 15.4385 2.15715i 0.990379 0.138381i
\(244\) 0.746353i 0.0477804i
\(245\) 3.25343 3.25343i 0.207854 0.207854i
\(246\) 5.28494 + 6.86491i 0.336956 + 0.437691i
\(247\) 0 0
\(248\) 2.32688i 0.147757i
\(249\) −4.46977 0.581248i −0.283260 0.0368351i
\(250\) 3.81079 0.241016
\(251\) 21.7299 1.37158 0.685789 0.727801i \(-0.259457\pi\)
0.685789 + 0.727801i \(0.259457\pi\)
\(252\) 1.21728 + 2.09304i 0.0766814 + 0.131849i
\(253\) 6.21847 6.21847i 0.390952 0.390952i
\(254\) 8.93562 8.93562i 0.560671 0.560671i
\(255\) 1.02649 + 0.133484i 0.0642812 + 0.00835912i
\(256\) −6.49950 −0.406219
\(257\) 16.3112 1.01746 0.508732 0.860925i \(-0.330115\pi\)
0.508732 + 0.860925i \(0.330115\pi\)
\(258\) −3.41795 + 26.2838i −0.212792 + 1.63636i
\(259\) 14.9036i 0.926062i
\(260\) 0 0
\(261\) 10.8255 + 2.86394i 0.670084 + 0.177273i
\(262\) 11.0486 11.0486i 0.682583 0.682583i
\(263\) 11.4962i 0.708887i 0.935077 + 0.354444i \(0.115330\pi\)
−0.935077 + 0.354444i \(0.884670\pi\)
\(264\) 8.41298 + 10.9281i 0.517783 + 0.672578i
\(265\) −28.9635 + 28.9635i −1.77922 + 1.77922i
\(266\) 14.3879 + 14.3879i 0.882177 + 0.882177i
\(267\) −0.245387 + 1.88701i −0.0150174 + 0.115483i
\(268\) 1.47457 + 1.47457i 0.0900734 + 0.0900734i
\(269\) 11.1389i 0.679151i 0.940579 + 0.339576i \(0.110283\pi\)
−0.940579 + 0.339576i \(0.889717\pi\)
\(270\) −18.9065 + 7.93687i −1.15061 + 0.483023i
\(271\) 4.29686 + 4.29686i 0.261016 + 0.261016i 0.825467 0.564451i \(-0.190912\pi\)
−0.564451 + 0.825467i \(0.690912\pi\)
\(272\) 0.670260 0.0406405
\(273\) 0 0
\(274\) 22.8384 1.37972
\(275\) −7.60042 7.60042i −0.458323 0.458323i
\(276\) −0.963712 1.25182i −0.0580086 0.0753507i
\(277\) 27.7810i 1.66920i −0.550857 0.834600i \(-0.685699\pi\)
0.550857 0.834600i \(-0.314301\pi\)
\(278\) −2.16218 2.16218i −0.129679 0.129679i
\(279\) 1.17430 + 2.01914i 0.0703035 + 0.120883i
\(280\) −18.5519 18.5519i −1.10869 1.10869i
\(281\) −11.6187 + 11.6187i −0.693113 + 0.693113i −0.962916 0.269803i \(-0.913042\pi\)
0.269803 + 0.962916i \(0.413042\pi\)
\(282\) −10.9469 + 8.42744i −0.651877 + 0.501847i
\(283\) 26.5871i 1.58044i 0.612824 + 0.790219i \(0.290033\pi\)
−0.612824 + 0.790219i \(0.709967\pi\)
\(284\) 1.04489 1.04489i 0.0620028 0.0620028i
\(285\) 21.8895 16.8516i 1.29662 0.998203i
\(286\) 0 0
\(287\) 11.1277i 0.656845i
\(288\) 4.02329 2.33989i 0.237074 0.137879i
\(289\) −16.9605 −0.997674
\(290\) −14.7296 −0.864955
\(291\) 2.71691 20.8929i 0.159268 1.22476i
\(292\) −0.956698 + 0.956698i −0.0559865 + 0.0559865i
\(293\) −2.04702 + 2.04702i −0.119588 + 0.119588i −0.764368 0.644780i \(-0.776949\pi\)
0.644780 + 0.764368i \(0.276949\pi\)
\(294\) −0.448883 + 3.45188i −0.0261794 + 0.201318i
\(295\) −10.0348 −0.584249
\(296\) −15.2496 −0.886365
\(297\) −12.8154 5.23703i −0.743623 0.303883i
\(298\) 20.7118i 1.19980i
\(299\) 0 0
\(300\) −1.53001 + 1.17788i −0.0883354 + 0.0680049i
\(301\) 24.0725 24.0725i 1.38752 1.38752i
\(302\) 15.9100i 0.915519i
\(303\) −17.0100 + 13.0951i −0.977197 + 0.752294i
\(304\) 12.6483 12.6483i 0.725429 0.725429i
\(305\) 5.74048 + 5.74048i 0.328699 + 0.328699i
\(306\) −0.676968 + 0.393715i −0.0386997 + 0.0225072i
\(307\) −13.9565 13.9565i −0.796541 0.796541i 0.186007 0.982548i \(-0.440445\pi\)
−0.982548 + 0.186007i \(0.940445\pi\)
\(308\) 2.15034i 0.122527i
\(309\) −6.00982 7.80649i −0.341887 0.444096i
\(310\) −2.17256 2.17256i −0.123393 0.123393i
\(311\) −26.9755 −1.52964 −0.764821 0.644243i \(-0.777172\pi\)
−0.764821 + 0.644243i \(0.777172\pi\)
\(312\) 0 0
\(313\) −23.9660 −1.35464 −0.677320 0.735689i \(-0.736859\pi\)
−0.677320 + 0.735689i \(0.736859\pi\)
\(314\) 3.03321 + 3.03321i 0.171174 + 0.171174i
\(315\) 25.4609 + 6.73576i 1.43456 + 0.379517i
\(316\) 3.07766i 0.173132i
\(317\) −21.6899 21.6899i −1.21823 1.21823i −0.968253 0.249973i \(-0.919578\pi\)
−0.249973 0.968253i \(-0.580422\pi\)
\(318\) 3.99615 30.7302i 0.224093 1.72326i
\(319\) −7.03214 7.03214i −0.393724 0.393724i
\(320\) −18.6581 + 18.6581i −1.04302 + 1.04302i
\(321\) 8.20823 + 10.6621i 0.458139 + 0.595102i
\(322\) 12.6571i 0.705355i
\(323\) 0.746041 0.746041i 0.0415108 0.0415108i
\(324\) −1.22980 + 2.16162i −0.0683224 + 0.120090i
\(325\) 0 0
\(326\) 7.65191i 0.423800i
\(327\) −2.26908 + 17.4491i −0.125481 + 0.964939i
\(328\) −11.3860 −0.628688
\(329\) 17.7443 0.978276
\(330\) 18.0583 + 2.34831i 0.994079 + 0.129270i
\(331\) −0.469219 + 0.469219i −0.0257906 + 0.0257906i −0.719885 0.694094i \(-0.755805\pi\)
0.694094 + 0.719885i \(0.255805\pi\)
\(332\) 0.508486 0.508486i 0.0279068 0.0279068i
\(333\) 13.2327 7.69597i 0.725150 0.421737i
\(334\) 2.07598 0.113593
\(335\) 22.6828 1.23930
\(336\) 16.9110 + 2.19911i 0.922571 + 0.119971i
\(337\) 25.0872i 1.36659i 0.730143 + 0.683294i \(0.239453\pi\)
−0.730143 + 0.683294i \(0.760547\pi\)
\(338\) 0 0
\(339\) 18.0547 + 23.4522i 0.980596 + 1.27375i
\(340\) −0.116775 + 0.116775i −0.00633299 + 0.00633299i
\(341\) 2.07442i 0.112336i
\(342\) −5.34519 + 20.2045i −0.289035 + 1.09254i
\(343\) −11.2955 + 11.2955i −0.609900 + 0.609900i
\(344\) −24.6314 24.6314i −1.32804 1.32804i
\(345\) −17.0405 2.21594i −0.917428 0.119302i
\(346\) 11.5331 + 11.5331i 0.620023 + 0.620023i
\(347\) 16.4102i 0.880947i 0.897766 + 0.440474i \(0.145189\pi\)
−0.897766 + 0.440474i \(0.854811\pi\)
\(348\) −1.41561 + 1.08981i −0.0758849 + 0.0584199i
\(349\) −21.1952 21.1952i −1.13456 1.13456i −0.989410 0.145145i \(-0.953635\pi\)
−0.145145 0.989410i \(-0.546365\pi\)
\(350\) −15.4700 −0.826905
\(351\) 0 0
\(352\) −4.13344 −0.220313
\(353\) 4.76452 + 4.76452i 0.253590 + 0.253590i 0.822441 0.568851i \(-0.192612\pi\)
−0.568851 + 0.822441i \(0.692612\pi\)
\(354\) 6.01571 4.63118i 0.319731 0.246145i
\(355\) 16.0733i 0.853081i
\(356\) −0.214669 0.214669i −0.0113774 0.0113774i
\(357\) 0.997472 + 0.129711i 0.0527918 + 0.00686505i
\(358\) 15.1347 + 15.1347i 0.799896 + 0.799896i
\(359\) 6.76884 6.76884i 0.357246 0.357246i −0.505551 0.862797i \(-0.668711\pi\)
0.862797 + 0.505551i \(0.168711\pi\)
\(360\) 6.89216 26.0520i 0.363248 1.37306i
\(361\) 9.15665i 0.481929i
\(362\) 8.63014 8.63014i 0.453590 0.453590i
\(363\) −4.12223 5.35459i −0.216361 0.281043i
\(364\) 0 0
\(365\) 14.7166i 0.770303i
\(366\) −6.09063 0.792025i −0.318362 0.0413998i
\(367\) −12.0267 −0.627790 −0.313895 0.949458i \(-0.601634\pi\)
−0.313895 + 0.949458i \(0.601634\pi\)
\(368\) −11.1268 −0.580026
\(369\) 9.88015 5.74615i 0.514340 0.299133i
\(370\) −14.2382 + 14.2382i −0.740209 + 0.740209i
\(371\) −28.1448 + 28.1448i −1.46121 + 1.46121i
\(372\) −0.369539 0.0480548i −0.0191597 0.00249152i
\(373\) 13.3586 0.691684 0.345842 0.938293i \(-0.387593\pi\)
0.345842 + 0.938293i \(0.387593\pi\)
\(374\) 0.695502 0.0359636
\(375\) 0.648313 4.98549i 0.0334787 0.257449i
\(376\) 18.1563i 0.936340i
\(377\) 0 0
\(378\) −18.3720 + 7.71252i −0.944955 + 0.396689i
\(379\) −21.8973 + 21.8973i −1.12479 + 1.12479i −0.133777 + 0.991011i \(0.542711\pi\)
−0.991011 + 0.133777i \(0.957289\pi\)
\(380\) 4.40724i 0.226087i
\(381\) −10.1699 13.2102i −0.521019 0.676781i
\(382\) −1.88297 + 1.88297i −0.0963413 + 0.0963413i
\(383\) −7.25053 7.25053i −0.370485 0.370485i 0.497169 0.867654i \(-0.334373\pi\)
−0.867654 + 0.497169i \(0.834373\pi\)
\(384\) 1.88126 14.4668i 0.0960026 0.738255i
\(385\) −16.5390 16.5390i −0.842908 0.842908i
\(386\) 5.21576i 0.265475i
\(387\) 33.8045 + 8.94310i 1.71838 + 0.454603i
\(388\) 2.37680 + 2.37680i 0.120664 + 0.120664i
\(389\) 30.1074 1.52650 0.763252 0.646101i \(-0.223602\pi\)
0.763252 + 0.646101i \(0.223602\pi\)
\(390\) 0 0
\(391\) −0.656299 −0.0331905
\(392\) −3.23487 3.23487i −0.163386 0.163386i
\(393\) −12.5747 16.3340i −0.634310 0.823941i
\(394\) 9.04562i 0.455712i
\(395\) 23.6714 + 23.6714i 1.19104 + 1.19104i
\(396\) 1.90927 1.11040i 0.0959443 0.0557998i
\(397\) −2.42682 2.42682i −0.121799 0.121799i 0.643580 0.765379i \(-0.277448\pi\)
−0.765379 + 0.643580i \(0.777448\pi\)
\(398\) 5.88626 5.88626i 0.295052 0.295052i
\(399\) 21.2707 16.3753i 1.06487 0.819788i
\(400\) 13.5996i 0.679978i
\(401\) −14.1084 + 14.1084i −0.704541 + 0.704541i −0.965382 0.260841i \(-0.916000\pi\)
0.260841 + 0.965382i \(0.416000\pi\)
\(402\) −13.5980 + 10.4684i −0.678207 + 0.522117i
\(403\) 0 0
\(404\) 3.42479i 0.170390i
\(405\) 7.16698 + 26.0847i 0.356130 + 1.29616i
\(406\) −14.3133 −0.710356
\(407\) −13.5950 −0.673880
\(408\) 0.132723 1.02063i 0.00657076 0.0505288i
\(409\) −3.91823 + 3.91823i −0.193744 + 0.193744i −0.797312 0.603568i \(-0.793745\pi\)
0.603568 + 0.797312i \(0.293745\pi\)
\(410\) −10.6309 + 10.6309i −0.525021 + 0.525021i
\(411\) 3.88540 29.8785i 0.191653 1.47380i
\(412\) 1.57176 0.0774351
\(413\) −9.75114 −0.479822
\(414\) 11.2382 6.53596i 0.552326 0.321225i
\(415\) 7.82191i 0.383962i
\(416\) 0 0
\(417\) −3.19652 + 2.46083i −0.156534 + 0.120508i
\(418\) 13.1246 13.1246i 0.641946 0.641946i
\(419\) 34.4340i 1.68221i 0.540871 + 0.841106i \(0.318095\pi\)
−0.540871 + 0.841106i \(0.681905\pi\)
\(420\) −3.32942 + 2.56315i −0.162459 + 0.125069i
\(421\) 18.6143 18.6143i 0.907208 0.907208i −0.0888383 0.996046i \(-0.528315\pi\)
0.996046 + 0.0888383i \(0.0283154\pi\)
\(422\) 0.744792 + 0.744792i 0.0362559 + 0.0362559i
\(423\) 9.16290 + 15.7550i 0.445515 + 0.766036i
\(424\) 28.7983 + 28.7983i 1.39857 + 1.39857i
\(425\) 0.802150i 0.0389100i
\(426\) 7.41801 + 9.63567i 0.359404 + 0.466850i
\(427\) 5.57821 + 5.57821i 0.269948 + 0.269948i
\(428\) −2.14672 −0.103765
\(429\) 0 0
\(430\) −45.9956 −2.21811
\(431\) −7.99634 7.99634i −0.385170 0.385170i 0.487791 0.872961i \(-0.337803\pi\)
−0.872961 + 0.487791i \(0.837803\pi\)
\(432\) 6.78002 + 16.1507i 0.326204 + 0.777052i
\(433\) 6.20615i 0.298249i −0.988818 0.149124i \(-0.952355\pi\)
0.988818 0.149124i \(-0.0476455\pi\)
\(434\) −2.11114 2.11114i −0.101338 0.101338i
\(435\) −2.50589 + 19.2701i −0.120148 + 0.923932i
\(436\) −1.98503 1.98503i −0.0950659 0.0950659i
\(437\) −12.3848 + 12.3848i −0.592447 + 0.592447i
\(438\) −6.79190 8.82238i −0.324530 0.421550i
\(439\) 38.7828i 1.85100i −0.378745 0.925501i \(-0.623644\pi\)
0.378745 0.925501i \(-0.376356\pi\)
\(440\) −16.9231 + 16.9231i −0.806775 + 0.806775i
\(441\) 4.43957 + 1.17451i 0.211408 + 0.0559288i
\(442\) 0 0
\(443\) 18.3132i 0.870087i −0.900409 0.435043i \(-0.856733\pi\)
0.900409 0.435043i \(-0.143267\pi\)
\(444\) −0.314935 + 2.42183i −0.0149461 + 0.114935i
\(445\) −3.30219 −0.156539
\(446\) 4.05691 0.192100
\(447\) 27.0963 + 3.52361i 1.28161 + 0.166661i
\(448\) −18.1307 + 18.1307i −0.856593 + 0.856593i
\(449\) 1.37117 1.37117i 0.0647096 0.0647096i −0.674011 0.738721i \(-0.735430\pi\)
0.738721 + 0.674011i \(0.235430\pi\)
\(450\) −7.98846 13.7357i −0.376580 0.647505i
\(451\) −10.1506 −0.477975
\(452\) −4.72188 −0.222099
\(453\) 20.8144 + 2.70670i 0.977944 + 0.127172i
\(454\) 34.0227i 1.59676i
\(455\) 0 0
\(456\) −16.7555 21.7646i −0.784646 1.01922i
\(457\) 4.12048 4.12048i 0.192748 0.192748i −0.604134 0.796882i \(-0.706481\pi\)
0.796882 + 0.604134i \(0.206481\pi\)
\(458\) 36.4675i 1.70401i
\(459\) 0.399910 + 0.952628i 0.0186662 + 0.0444649i
\(460\) 1.93854 1.93854i 0.0903851 0.0903851i
\(461\) −10.1185 10.1185i −0.471264 0.471264i 0.431060 0.902323i \(-0.358140\pi\)
−0.902323 + 0.431060i \(0.858140\pi\)
\(462\) 17.5479 + 2.28193i 0.816401 + 0.106165i
\(463\) −2.99038 2.99038i −0.138975 0.138975i 0.634197 0.773172i \(-0.281331\pi\)
−0.773172 + 0.634197i \(0.781331\pi\)
\(464\) 12.5827i 0.584138i
\(465\) −3.21186 + 2.47265i −0.148947 + 0.114666i
\(466\) 13.4194 + 13.4194i 0.621643 + 0.621643i
\(467\) 37.5105 1.73578 0.867888 0.496759i \(-0.165477\pi\)
0.867888 + 0.496759i \(0.165477\pi\)
\(468\) 0 0
\(469\) 22.0417 1.01779
\(470\) −16.9521 16.9521i −0.781944 0.781944i
\(471\) 4.48423 3.45218i 0.206622 0.159068i
\(472\) 9.97755i 0.459254i
\(473\) −21.9589 21.9589i −1.00967 1.00967i
\(474\) −25.1153 3.26600i −1.15358 0.150012i
\(475\) 15.1371 + 15.1371i 0.694540 + 0.694540i
\(476\) −0.113474 + 0.113474i −0.00520106 + 0.00520106i
\(477\) −39.5231 10.4560i −1.80964 0.478746i
\(478\) 7.87701i 0.360286i
\(479\) −1.44413 + 1.44413i −0.0659840 + 0.0659840i −0.739329 0.673345i \(-0.764857\pi\)
0.673345 + 0.739329i \(0.264857\pi\)
\(480\) 4.92695 + 6.39989i 0.224883 + 0.292114i
\(481\) 0 0
\(482\) 32.3999i 1.47578i
\(483\) −16.5588 2.15330i −0.753450 0.0979786i
\(484\) 1.07810 0.0490043
\(485\) 36.5617 1.66018
\(486\) −16.3349 12.3297i −0.740967 0.559288i
\(487\) 17.7349 17.7349i 0.803647 0.803647i −0.180017 0.983664i \(-0.557615\pi\)
0.983664 + 0.180017i \(0.0576151\pi\)
\(488\) 5.70772 5.70772i 0.258377 0.258377i
\(489\) −10.0106 1.30178i −0.452697 0.0588687i
\(490\) −6.04065 −0.272889
\(491\) −7.53217 −0.339922 −0.169961 0.985451i \(-0.554364\pi\)
−0.169961 + 0.985451i \(0.554364\pi\)
\(492\) −0.235144 + 1.80825i −0.0106011 + 0.0815221i
\(493\) 0.742173i 0.0334258i
\(494\) 0 0
\(495\) 6.14436 23.2254i 0.276169 1.04390i
\(496\) −1.85589 + 1.85589i −0.0833321 + 0.0833321i
\(497\) 15.6189i 0.700604i
\(498\) 3.60991 + 4.68911i 0.161764 + 0.210124i
\(499\) 8.71539 8.71539i 0.390154 0.390154i −0.484588 0.874742i \(-0.661030\pi\)
0.874742 + 0.484588i \(0.161030\pi\)
\(500\) 0.567155 + 0.567155i 0.0253640 + 0.0253640i
\(501\) 0.353178 2.71592i 0.0157788 0.121338i
\(502\) −20.1729 20.1729i −0.900362 0.900362i
\(503\) 2.34970i 0.104768i 0.998627 + 0.0523839i \(0.0166819\pi\)
−0.998627 + 0.0523839i \(0.983318\pi\)
\(504\) 6.69733 25.3156i 0.298323 1.12765i
\(505\) −26.3413 26.3413i −1.17217 1.17217i
\(506\) −11.5458 −0.513276
\(507\) 0 0
\(508\) 2.65975 0.118008
\(509\) −21.1961 21.1961i −0.939499 0.939499i 0.0587720 0.998271i \(-0.481282\pi\)
−0.998271 + 0.0587720i \(0.981282\pi\)
\(510\) −0.829020 1.07686i −0.0367096 0.0476842i
\(511\) 14.3006i 0.632622i
\(512\) 17.9453 + 17.9453i 0.793080 + 0.793080i
\(513\) 25.5233 + 10.4302i 1.12688 + 0.460503i
\(514\) −15.1425 15.1425i −0.667907 0.667907i
\(515\) 12.0890 12.0890i 0.532705 0.532705i
\(516\) −4.42048 + 3.40310i −0.194601 + 0.149813i
\(517\) 16.1864i 0.711876i
\(518\) −13.8357 + 13.8357i −0.607907 + 0.607907i
\(519\) 17.0503 13.1261i 0.748424 0.576174i
\(520\) 0 0
\(521\) 5.94611i 0.260504i −0.991481 0.130252i \(-0.958421\pi\)
0.991481 0.130252i \(-0.0415786\pi\)
\(522\) −7.39116 12.7086i −0.323502 0.556242i
\(523\) −0.859946 −0.0376028 −0.0188014 0.999823i \(-0.505985\pi\)
−0.0188014 + 0.999823i \(0.505985\pi\)
\(524\) 3.28869 0.143667
\(525\) −2.63184 + 20.2387i −0.114863 + 0.883288i
\(526\) 10.6725 10.6725i 0.465344 0.465344i
\(527\) −0.109467 + 0.109467i −0.00476847 + 0.00476847i
\(528\) 2.00603 15.4262i 0.0873011 0.671340i
\(529\) −12.1049 −0.526302
\(530\) 53.7766 2.33591
\(531\) −5.03534 8.65796i −0.218515 0.375723i
\(532\) 4.28266i 0.185677i
\(533\) 0 0
\(534\) 1.97961 1.52400i 0.0856662 0.0659500i
\(535\) −16.5112 + 16.5112i −0.713841 + 0.713841i
\(536\) 22.5534i 0.974160i
\(537\) 22.3749 17.2253i 0.965548 0.743326i
\(538\) 10.3408 10.3408i 0.445824 0.445824i
\(539\) −2.88389 2.88389i −0.124218 0.124218i
\(540\) −3.99506 1.63259i −0.171920 0.0702555i
\(541\) −5.67009 5.67009i −0.243776 0.243776i 0.574634 0.818410i \(-0.305144\pi\)
−0.818410 + 0.574634i \(0.805144\pi\)
\(542\) 7.97798i 0.342684i
\(543\) −9.82221 12.7586i −0.421512 0.547525i
\(544\) 0.218122 + 0.218122i 0.00935190 + 0.00935190i
\(545\) −30.5353 −1.30799
\(546\) 0 0
\(547\) −29.3587 −1.25529 −0.627643 0.778501i \(-0.715980\pi\)
−0.627643 + 0.778501i \(0.715980\pi\)
\(548\) 3.39902 + 3.39902i 0.145199 + 0.145199i
\(549\) −2.07234 + 7.83335i −0.0884453 + 0.334319i
\(550\) 14.1117i 0.601725i
\(551\) 14.0053 + 14.0053i 0.596647 + 0.596647i
\(552\) −2.20330 + 16.9432i −0.0937786 + 0.721152i
\(553\) 23.0023 + 23.0023i 0.978158 + 0.978158i
\(554\) −25.7905 + 25.7905i −1.09573 + 1.09573i
\(555\) 16.2049 + 21.0495i 0.687860 + 0.893501i
\(556\) 0.643588i 0.0272942i
\(557\) 26.4446 26.4446i 1.12050 1.12050i 0.128828 0.991667i \(-0.458878\pi\)
0.991667 0.128828i \(-0.0411216\pi\)
\(558\) 0.784303 2.96463i 0.0332022 0.125503i
\(559\) 0 0
\(560\) 29.5936i 1.25056i
\(561\) 0.118323 0.909894i 0.00499558 0.0384157i
\(562\) 21.5724 0.909978
\(563\) 13.4052 0.564963 0.282481 0.959273i \(-0.408842\pi\)
0.282481 + 0.959273i \(0.408842\pi\)
\(564\) −2.88346 0.374965i −0.121415 0.0157889i
\(565\) −36.3177 + 36.3177i −1.52790 + 1.52790i
\(566\) 24.6821 24.6821i 1.03747 1.03747i
\(567\) 6.96439 + 25.3474i 0.292477 + 1.06449i
\(568\) −15.9816 −0.670572
\(569\) −22.6791 −0.950759 −0.475380 0.879781i \(-0.657689\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(570\) −35.9653 4.67693i −1.50642 0.195895i
\(571\) 21.9369i 0.918032i 0.888428 + 0.459016i \(0.151798\pi\)
−0.888428 + 0.459016i \(0.848202\pi\)
\(572\) 0 0
\(573\) 2.14307 + 2.78375i 0.0895279 + 0.116293i
\(574\) −10.3304 + 10.3304i −0.431181 + 0.431181i
\(575\) 13.3163i 0.555328i
\(576\) −25.4605 6.73566i −1.06085 0.280652i
\(577\) −18.7633 + 18.7633i −0.781126 + 0.781126i −0.980021 0.198895i \(-0.936265\pi\)
0.198895 + 0.980021i \(0.436265\pi\)
\(578\) 15.7453 + 15.7453i 0.654916 + 0.654916i
\(579\) −6.82354 0.887333i −0.283577 0.0368763i
\(580\) −2.19219 2.19219i −0.0910259 0.0910259i
\(581\) 7.60081i 0.315335i
\(582\) −21.9181 + 16.8737i −0.908537 + 0.699436i
\(583\) 25.6737 + 25.6737i 1.06330 + 1.06330i
\(584\) 14.6327 0.605504
\(585\) 0 0
\(586\) 3.80070 0.157005
\(587\) 8.65842 + 8.65842i 0.357371 + 0.357371i 0.862843 0.505472i \(-0.168682\pi\)
−0.505472 + 0.862843i \(0.668682\pi\)
\(588\) −0.580546 + 0.446933i −0.0239413 + 0.0184312i
\(589\) 4.13145i 0.170233i
\(590\) 9.31581 + 9.31581i 0.383526 + 0.383526i
\(591\) −11.8340 1.53889i −0.486785 0.0633015i
\(592\) 12.1629 + 12.1629i 0.499892 + 0.499892i
\(593\) 32.4467 32.4467i 1.33243 1.33243i 0.429232 0.903194i \(-0.358784\pi\)
0.903194 0.429232i \(-0.141216\pi\)
\(594\) 7.03536 + 16.7590i 0.288664 + 0.687628i
\(595\) 1.74554i 0.0715600i
\(596\) −3.08251 + 3.08251i −0.126265 + 0.126265i
\(597\) −6.69933 8.70213i −0.274185 0.356155i
\(598\) 0 0
\(599\) 11.5870i 0.473430i −0.971579 0.236715i \(-0.923929\pi\)
0.971579 0.236715i \(-0.0760708\pi\)
\(600\) 20.7086 + 2.69294i 0.845424 + 0.109939i
\(601\) −4.53417 −0.184953 −0.0924764 0.995715i \(-0.529478\pi\)
−0.0924764 + 0.995715i \(0.529478\pi\)
\(602\) −44.6955 −1.82165
\(603\) 11.3820 + 19.5706i 0.463510 + 0.796977i
\(604\) −2.36787 + 2.36787i −0.0963472 + 0.0963472i
\(605\) 8.29203 8.29203i 0.337119 0.337119i
\(606\) 27.9481 + 3.63437i 1.13531 + 0.147636i
\(607\) 13.0328 0.528986 0.264493 0.964388i \(-0.414795\pi\)
0.264493 + 0.964388i \(0.414795\pi\)
\(608\) 8.23223 0.333861
\(609\) −2.43505 + 18.7254i −0.0986733 + 0.758792i
\(610\) 10.6583i 0.431544i
\(611\) 0 0
\(612\) −0.159348 0.0421562i −0.00644128 0.00170406i
\(613\) 2.54348 2.54348i 0.102730 0.102730i −0.653874 0.756604i \(-0.726857\pi\)
0.756604 + 0.653874i \(0.226857\pi\)
\(614\) 25.9131i 1.04577i
\(615\) 12.0993 + 15.7165i 0.487891 + 0.633749i
\(616\) −16.4447 + 16.4447i −0.662575 + 0.662575i
\(617\) −4.69608 4.69608i −0.189057 0.189057i 0.606231 0.795288i \(-0.292681\pi\)
−0.795288 + 0.606231i \(0.792681\pi\)
\(618\) −1.66794 + 12.8264i −0.0670945 + 0.515953i
\(619\) 13.3334 + 13.3334i 0.535916 + 0.535916i 0.922327 0.386411i \(-0.126285\pi\)
−0.386411 + 0.922327i \(0.626285\pi\)
\(620\) 0.646677i 0.0259712i
\(621\) −6.63880 15.8143i −0.266406 0.634607i
\(622\) 25.0427 + 25.0427i 1.00412 + 1.00412i
\(623\) −3.20885 −0.128560
\(624\) 0 0
\(625\) 28.8959 1.15584
\(626\) 22.2489 + 22.2489i 0.889243 + 0.889243i
\(627\) −14.9375 19.4032i −0.596547 0.774888i
\(628\) 0.902856i 0.0360279i
\(629\) 0.717411 + 0.717411i 0.0286051 + 0.0286051i
\(630\) −17.3835 29.8898i −0.692573 1.19084i
\(631\) 1.04182 + 1.04182i 0.0414743 + 0.0414743i 0.727540 0.686065i \(-0.240664\pi\)
−0.686065 + 0.727540i \(0.740664\pi\)
\(632\) 23.5364 23.5364i 0.936227 0.936227i
\(633\) 1.10109 0.847670i 0.0437642 0.0336918i
\(634\) 40.2717i 1.59939i
\(635\) 20.4571 20.4571i 0.811817 0.811817i
\(636\) 5.16828 3.97879i 0.204936 0.157769i
\(637\) 0 0
\(638\) 13.0566i 0.516915i
\(639\) 13.8679 8.06538i 0.548606 0.319061i
\(640\) 25.3163 1.00071
\(641\) −14.8607 −0.586961 −0.293481 0.955965i \(-0.594814\pi\)
−0.293481 + 0.955965i \(0.594814\pi\)
\(642\) 2.27808 17.5183i 0.0899086 0.691392i
\(643\) 34.3565 34.3565i 1.35489 1.35489i 0.474791 0.880099i \(-0.342524\pi\)
0.880099 0.474791i \(-0.157476\pi\)
\(644\) 1.88375 1.88375i 0.0742300 0.0742300i
\(645\) −7.82503 + 60.1740i −0.308110 + 2.36935i
\(646\) −1.38518 −0.0544990
\(647\) −37.6742 −1.48112 −0.740562 0.671988i \(-0.765441\pi\)
−0.740562 + 0.671988i \(0.765441\pi\)
\(648\) 25.9359 7.12609i 1.01886 0.279939i
\(649\) 8.89499i 0.349159i
\(650\) 0 0
\(651\) −3.12107 + 2.40275i −0.122324 + 0.0941714i
\(652\) 1.13882 1.13882i 0.0445998 0.0445998i
\(653\) 22.2714i 0.871548i 0.900056 + 0.435774i \(0.143525\pi\)
−0.900056 + 0.435774i \(0.856475\pi\)
\(654\) 18.3054 14.0924i 0.715798 0.551056i
\(655\) 25.2945 25.2945i 0.988339 0.988339i
\(656\) 9.08136 + 9.08136i 0.354568 + 0.354568i
\(657\) −12.6974 + 7.38463i −0.495373 + 0.288102i
\(658\) −16.4729 16.4729i −0.642182 0.642182i
\(659\) 26.8010i 1.04402i −0.852939 0.522010i \(-0.825182\pi\)
0.852939 0.522010i \(-0.174818\pi\)
\(660\) 2.33810 + 3.03709i 0.0910106 + 0.118219i
\(661\) −12.3552 12.3552i −0.480561 0.480561i 0.424750 0.905311i \(-0.360362\pi\)
−0.905311 + 0.424750i \(0.860362\pi\)
\(662\) 0.871200 0.0338602
\(663\) 0 0
\(664\) −7.77728 −0.301817
\(665\) 32.9395 + 32.9395i 1.27734 + 1.27734i
\(666\) −19.4292 5.14006i −0.752866 0.199173i
\(667\) 12.3206i 0.477057i
\(668\) 0.308966 + 0.308966i 0.0119543 + 0.0119543i
\(669\) 0.690183 5.30747i 0.0266840 0.205199i
\(670\) −21.0576 21.0576i −0.813527 0.813527i
\(671\) 5.08844 5.08844i 0.196437 0.196437i
\(672\) 4.78768 + 6.21898i 0.184689 + 0.239902i
\(673\) 35.6073i 1.37256i 0.727336 + 0.686281i \(0.240758\pi\)
−0.727336 + 0.686281i \(0.759242\pi\)
\(674\) 23.2897 23.2897i 0.897087 0.897087i
\(675\) −19.3288 + 8.11416i −0.743965 + 0.312314i
\(676\) 0 0
\(677\) 16.3795i 0.629517i 0.949172 + 0.314758i \(0.101924\pi\)
−0.949172 + 0.314758i \(0.898076\pi\)
\(678\) 5.01083 38.5330i 0.192440 1.47985i
\(679\) 35.5282 1.36345
\(680\) 1.78606 0.0684924
\(681\) −44.5104 5.78813i −1.70564 0.221801i
\(682\) −1.92579 + 1.92579i −0.0737421 + 0.0737421i
\(683\) −27.1629 + 27.1629i −1.03936 + 1.03936i −0.0401670 + 0.999193i \(0.512789\pi\)
−0.999193 + 0.0401670i \(0.987211\pi\)
\(684\) −3.80253 + 2.21150i −0.145394 + 0.0845588i
\(685\) 52.2862 1.99775
\(686\) 20.9724 0.800729
\(687\) −47.7088 6.20404i −1.82020 0.236699i
\(688\) 39.2915i 1.49797i
\(689\) 0 0
\(690\) 13.7624 + 17.8767i 0.523924 + 0.680554i
\(691\) −13.6599 + 13.6599i −0.519648 + 0.519648i −0.917465 0.397817i \(-0.869768\pi\)
0.397817 + 0.917465i \(0.369768\pi\)
\(692\) 3.43291i 0.130500i
\(693\) 5.97068 22.5689i 0.226807 0.857321i
\(694\) 15.2344 15.2344i 0.578292 0.578292i
\(695\) −4.95007 4.95007i −0.187767 0.187767i
\(696\) 19.1602 + 2.49159i 0.726265 + 0.0944435i
\(697\) 0.535651 + 0.535651i 0.0202892 + 0.0202892i
\(698\) 39.3532i 1.48954i
\(699\) 19.8390 15.2731i 0.750381 0.577680i
\(700\) −2.30238 2.30238i −0.0870216 0.0870216i
\(701\) −12.7471 −0.481453 −0.240726 0.970593i \(-0.577386\pi\)
−0.240726 + 0.970593i \(0.577386\pi\)
\(702\) 0 0
\(703\) 27.0761 1.02120
\(704\) 16.5388 + 16.5388i 0.623329 + 0.623329i
\(705\) −25.0617 + 19.2937i −0.943879 + 0.726644i
\(706\) 8.84629i 0.332935i
\(707\) −25.5967 25.5967i −0.962664 0.962664i
\(708\) 1.58456 + 0.206057i 0.0595515 + 0.00774408i
\(709\) −30.8214 30.8214i −1.15752 1.15752i −0.985007 0.172517i \(-0.944810\pi\)
−0.172517 0.985007i \(-0.555190\pi\)
\(710\) −14.9216 + 14.9216i −0.559999 + 0.559999i
\(711\) −8.54551 + 32.3016i −0.320482 + 1.21140i
\(712\) 3.28335i 0.123049i
\(713\) 1.81724 1.81724i 0.0680560 0.0680560i
\(714\) −0.805586 1.04642i −0.0301483 0.0391613i
\(715\) 0 0
\(716\) 4.50497i 0.168359i
\(717\) −10.3051 1.34008i −0.384852 0.0500462i
\(718\) −12.5677 −0.469023
\(719\) −35.5618 −1.32623 −0.663116 0.748517i \(-0.730766\pi\)
−0.663116 + 0.748517i \(0.730766\pi\)
\(720\) −26.2759 + 15.2817i −0.979245 + 0.569515i
\(721\) 11.7473 11.7473i 0.437491 0.437491i
\(722\) −8.50058 + 8.50058i −0.316359 + 0.316359i
\(723\) −42.3873 5.51205i −1.57640 0.204995i
\(724\) 2.56883 0.0954696
\(725\) −15.0587 −0.559265
\(726\) −1.14407 + 8.79781i −0.0424603 + 0.326518i
\(727\) 26.2936i 0.975176i −0.873074 0.487588i \(-0.837877\pi\)
0.873074 0.487588i \(-0.162123\pi\)
\(728\) 0 0
\(729\) −18.9094 + 19.2726i −0.700349 + 0.713801i
\(730\) 13.6622 13.6622i 0.505660 0.505660i
\(731\) 2.31755i 0.0857178i
\(732\) −0.788584 1.02434i −0.0291469 0.0378606i
\(733\) −5.72217 + 5.72217i −0.211353 + 0.211353i −0.804842 0.593489i \(-0.797750\pi\)
0.593489 + 0.804842i \(0.297750\pi\)
\(734\) 11.1650 + 11.1650i 0.412109 + 0.412109i
\(735\) −1.02767 + 7.90271i −0.0379061 + 0.291496i
\(736\) −3.62099 3.62099i −0.133471 0.133471i
\(737\) 20.1064i 0.740629i
\(738\) −14.5067 3.83780i −0.533999 0.141271i
\(739\) −14.5261 14.5261i −0.534352 0.534352i 0.387512 0.921865i \(-0.373335\pi\)
−0.921865 + 0.387512i \(0.873335\pi\)
\(740\) −4.23811 −0.155796
\(741\) 0 0
\(742\) 52.2565 1.91840
\(743\) −24.3184 24.3184i −0.892156 0.892156i 0.102570 0.994726i \(-0.467294\pi\)
−0.994726 + 0.102570i \(0.967294\pi\)
\(744\) 2.45854 + 3.19354i 0.0901345 + 0.117081i
\(745\) 47.4175i 1.73724i
\(746\) −12.4015 12.4015i −0.454051 0.454051i
\(747\) 6.74869 3.92494i 0.246922 0.143606i
\(748\) 0.103511 + 0.103511i 0.00378473 + 0.00378473i
\(749\) −16.0445 + 16.0445i −0.586252 + 0.586252i
\(750\) −5.23014 + 4.02642i −0.190978 + 0.147024i
\(751\) 29.8891i 1.09067i 0.838219 + 0.545334i \(0.183597\pi\)
−0.838219 + 0.545334i \(0.816403\pi\)
\(752\) −14.4813 + 14.4813i −0.528077 + 0.528077i
\(753\) −29.8233 + 22.9594i −1.08682 + 0.836687i
\(754\) 0 0
\(755\) 36.4243i 1.32562i
\(756\) −3.88213 1.58644i −0.141192 0.0576983i
\(757\) 22.3067 0.810752 0.405376 0.914150i \(-0.367141\pi\)
0.405376 + 0.914150i \(0.367141\pi\)
\(758\) 40.6567 1.47672
\(759\) −1.96424 + 15.1049i −0.0712975 + 0.548274i
\(760\) 33.7043 33.7043i 1.22258 1.22258i
\(761\) 18.7246 18.7246i 0.678767 0.678767i −0.280954 0.959721i \(-0.590651\pi\)
0.959721 + 0.280954i \(0.0906508\pi\)
\(762\) −2.82251 + 21.7050i −0.102249 + 0.786288i
\(763\) −29.6721 −1.07420
\(764\) −0.560481 −0.0202775
\(765\) −1.54985 + 0.901368i −0.0560348 + 0.0325890i
\(766\) 13.4621i 0.486404i
\(767\) 0 0
\(768\) 8.92027 6.86726i 0.321882 0.247801i
\(769\) 8.68256 8.68256i 0.313101 0.313101i −0.533009 0.846110i \(-0.678939\pi\)
0.846110 + 0.533009i \(0.178939\pi\)
\(770\) 30.7081i 1.10664i
\(771\) −22.3864 + 17.2341i −0.806225 + 0.620671i
\(772\) 0.776254 0.776254i 0.0279380 0.0279380i
\(773\) 16.3016 + 16.3016i 0.586326 + 0.586326i 0.936634 0.350308i \(-0.113923\pi\)
−0.350308 + 0.936634i \(0.613923\pi\)
\(774\) −23.0801 39.6847i −0.829596 1.42644i
\(775\) −2.22108 2.22108i −0.0797837 0.0797837i
\(776\) 36.3531i 1.30500i
\(777\) 15.7468 + 20.4545i 0.564915 + 0.733800i
\(778\) −27.9502 27.9502i −1.00206 1.00206i
\(779\) 20.2162 0.724321
\(780\) 0 0
\(781\) −14.2476 −0.509818
\(782\) 0.609276 + 0.609276i 0.0217877 + 0.0217877i
\(783\) −17.8836 + 7.50746i −0.639106 + 0.268295i
\(784\) 5.16019i 0.184293i
\(785\) 6.94420 + 6.94420i 0.247849 + 0.247849i
\(786\) −3.48993 + 26.8374i −0.124482 + 0.957258i
\(787\) −35.0163 35.0163i −1.24819 1.24819i −0.956516 0.291678i \(-0.905786\pi\)
−0.291678 0.956516i \(-0.594214\pi\)
\(788\) 1.34625 1.34625i 0.0479581 0.0479581i
\(789\) −12.1467 15.7780i −0.432434 0.561713i
\(790\) 43.9508i 1.56370i
\(791\) −35.2911 + 35.2911i −1.25481 + 1.25481i
\(792\) −23.0929 6.10931i −0.820570 0.217085i
\(793\) 0 0
\(794\) 4.50589i 0.159908i
\(795\) 9.14877 70.3535i 0.324473 2.49518i
\(796\) 1.75209 0.0621012
\(797\) −5.10731 −0.180910 −0.0904550 0.995901i \(-0.528832\pi\)
−0.0904550 + 0.995901i \(0.528832\pi\)
\(798\) −34.9487 4.54473i −1.23717 0.160882i
\(799\) −0.854157 + 0.854157i −0.0302179 + 0.0302179i
\(800\) −4.42568 + 4.42568i −0.156472 + 0.156472i
\(801\) −1.65700 2.84911i −0.0585472 0.100668i
\(802\) 26.1951 0.924982
\(803\) 13.0450 0.460349
\(804\) −3.58178 0.465774i −0.126319 0.0164266i
\(805\) 28.9772i 1.02131i
\(806\) 0 0
\(807\) −11.7692 15.2877i −0.414295 0.538151i
\(808\) −26.1910 + 26.1910i −0.921398 + 0.921398i
\(809\) 0.250395i 0.00880341i −0.999990 0.00440171i \(-0.998599\pi\)
0.999990 0.00440171i \(-0.00140111\pi\)
\(810\) 17.5623 30.8692i 0.617076 1.08463i
\(811\) −0.345058 + 0.345058i −0.0121166 + 0.0121166i −0.713139 0.701023i \(-0.752727\pi\)
0.701023 + 0.713139i \(0.252727\pi\)
\(812\) −2.13023 2.13023i −0.0747563 0.0747563i
\(813\) −10.4372 1.35726i −0.366050 0.0476011i
\(814\) 12.6210 + 12.6210i 0.442364 + 0.442364i
\(815\) 17.5182i 0.613637i
\(816\) −0.919902 + 0.708186i −0.0322030 + 0.0247915i
\(817\) 43.7339 + 43.7339i 1.53005 + 1.53005i
\(818\) 7.27498 0.254364
\(819\) 0 0
\(820\) −3.16436 −0.110504
\(821\) 20.3341 + 20.3341i 0.709665 + 0.709665i 0.966465 0.256799i \(-0.0826679\pi\)
−0.256799 + 0.966465i \(0.582668\pi\)
\(822\) −31.3447 + 24.1307i −1.09327 + 0.841655i
\(823\) 2.01893i 0.0703754i 0.999381 + 0.0351877i \(0.0112029\pi\)
−0.999381 + 0.0351877i \(0.988797\pi\)
\(824\) −12.0200 12.0200i −0.418737 0.418737i
\(825\) 18.4617 + 2.40076i 0.642754 + 0.0835837i
\(826\) 9.05248 + 9.05248i 0.314976 + 0.314976i
\(827\) −0.657151 + 0.657151i −0.0228514 + 0.0228514i −0.718440 0.695589i \(-0.755144\pi\)
0.695589 + 0.718440i \(0.255144\pi\)
\(828\) 2.64530 + 0.699824i 0.0919306 + 0.0243206i
\(829\) 46.5124i 1.61544i 0.589564 + 0.807722i \(0.299300\pi\)
−0.589564 + 0.807722i \(0.700700\pi\)
\(830\) −7.26148 + 7.26148i −0.252049 + 0.252049i
\(831\) 29.3530 + 38.1282i 1.01824 + 1.32265i
\(832\) 0 0
\(833\) 0.304367i 0.0105457i
\(834\) 5.25201 + 0.682971i 0.181862 + 0.0236493i
\(835\) 4.75274 0.164475
\(836\) 3.90664 0.135114
\(837\) −3.74506 1.53043i −0.129448 0.0528993i
\(838\) 31.9668 31.9668i 1.10428 1.10428i
\(839\) 30.7448 30.7448i 1.06143 1.06143i 0.0634447 0.997985i \(-0.479791\pi\)
0.997985 0.0634447i \(-0.0202086\pi\)
\(840\) 45.0633 + 5.86003i 1.55483 + 0.202190i
\(841\) 15.0673 0.519561
\(842\) −34.5613 −1.19106
\(843\) 3.67002 28.2222i 0.126402 0.972026i
\(844\) 0.221693i 0.00763098i
\(845\) 0 0
\(846\) 6.11981 23.1326i 0.210403 0.795314i
\(847\) 8.05764 8.05764i 0.276864 0.276864i
\(848\) 45.9383i 1.57753i
\(849\) −28.0915 36.4896i −0.964097 1.25232i
\(850\) 0.744677 0.744677i 0.0255422 0.0255422i
\(851\) −11.9096 11.9096i −0.408254 0.408254i
\(852\) −0.330052 + 2.53808i −0.0113074 + 0.0869531i
\(853\) −0.0191114 0.0191114i −0.000654362 0.000654362i 0.706780 0.707434i \(-0.250147\pi\)
−0.707434 + 0.706780i \(0.750147\pi\)
\(854\) 10.3571i 0.354411i
\(855\) −12.2372 + 46.2561i −0.418505 + 1.58193i
\(856\) 16.4170 + 16.4170i 0.561121 + 0.561121i
\(857\) 5.89068 0.201222 0.100611 0.994926i \(-0.467920\pi\)
0.100611 + 0.994926i \(0.467920\pi\)
\(858\) 0 0
\(859\) 11.6341 0.396949 0.198475 0.980106i \(-0.436401\pi\)
0.198475 + 0.980106i \(0.436401\pi\)
\(860\) −6.84547 6.84547i −0.233429 0.233429i
\(861\) 11.7573 + 15.2722i 0.400687 + 0.520475i
\(862\) 14.8468i 0.505685i
\(863\) −19.9075 19.9075i −0.677660 0.677660i 0.281811 0.959470i \(-0.409065\pi\)
−0.959470 + 0.281811i \(0.909065\pi\)
\(864\) −3.04950 + 7.46232i −0.103746 + 0.253873i
\(865\) 26.4038 + 26.4038i 0.897755 + 0.897755i
\(866\) −5.76148 + 5.76148i −0.195783 + 0.195783i
\(867\) 23.2775 17.9201i 0.790544 0.608600i
\(868\) 0.628398i 0.0213292i
\(869\) 20.9827 20.9827i 0.711790 0.711790i
\(870\) 20.2158 15.5631i 0.685379 0.527638i
\(871\) 0 0
\(872\) 30.3610i 1.02815i
\(873\) 18.3462 + 31.5452i 0.620925 + 1.06764i
\(874\) 22.9949 0.777815
\(875\) 8.47779 0.286601
\(876\) 0.302194 2.32385i 0.0102102 0.0785158i
\(877\) −9.85124 + 9.85124i −0.332653 + 0.332653i −0.853593 0.520940i \(-0.825581\pi\)
0.520940 + 0.853593i \(0.325581\pi\)
\(878\) −36.0040 + 36.0040i −1.21508 + 1.21508i
\(879\) 0.646595 4.97228i 0.0218091 0.167711i
\(880\) 26.9953 0.910010
\(881\) 7.66652 0.258292 0.129146 0.991626i \(-0.458776\pi\)
0.129146 + 0.991626i \(0.458776\pi\)
\(882\) −3.03113 5.21183i −0.102063 0.175492i
\(883\) 7.52156i 0.253121i −0.991959 0.126560i \(-0.959606\pi\)
0.991959 0.126560i \(-0.0403937\pi\)
\(884\) 0 0
\(885\) 13.7723 10.6026i 0.462951 0.356403i
\(886\) −17.0011 + 17.0011i −0.571162 + 0.571162i
\(887\) 42.1524i 1.41534i −0.706543 0.707670i \(-0.749746\pi\)
0.706543 0.707670i \(-0.250254\pi\)
\(888\) 20.9294 16.1125i 0.702344 0.540699i
\(889\) 19.8789 19.8789i 0.666716 0.666716i
\(890\) 3.06559 + 3.06559i 0.102759 + 0.102759i
\(891\) 23.1219 6.35291i 0.774612 0.212831i
\(892\) 0.603784 + 0.603784i 0.0202162 + 0.0202162i
\(893\) 32.2371i 1.07877i
\(894\) −21.8838 28.4260i −0.731902 0.950709i
\(895\) 34.6494 + 34.6494i 1.15820 + 1.15820i
\(896\) 24.6007 0.821850
\(897\) 0 0
\(898\) −2.54586 −0.0849564
\(899\) −2.05501 2.05501i −0.0685385 0.0685385i
\(900\) 0.855348 3.23317i 0.0285116 0.107772i
\(901\) 2.70961i 0.0902701i
\(902\) 9.42336 + 9.42336i 0.313764 + 0.313764i
\(903\) −7.60383 + 58.4731i −0.253040 + 1.94586i
\(904\) 36.1105 + 36.1105i 1.20102 + 1.20102i
\(905\) 19.7578 19.7578i 0.656771 0.656771i
\(906\) −16.8103 21.8358i −0.558483 0.725445i
\(907\) 37.3530i 1.24029i −0.784489 0.620143i \(-0.787075\pi\)
0.784489 0.620143i \(-0.212925\pi\)
\(908\) 5.06355 5.06355i 0.168040 0.168040i
\(909\) 9.50935 35.9449i 0.315405 1.19222i
\(910\) 0 0
\(911\) 20.5977i 0.682434i 0.939985 + 0.341217i \(0.110839\pi\)
−0.939985 + 0.341217i \(0.889161\pi\)
\(912\) −3.99524 + 30.7232i −0.132296 + 1.01735i
\(913\) −6.93345 −0.229464
\(914\) −7.65050 −0.253056
\(915\) −13.9438 1.81326i −0.460969 0.0599444i
\(916\) 5.42741 5.42741i 0.179327 0.179327i
\(917\) 24.5795 24.5795i 0.811687 0.811687i
\(918\) 0.513116 1.25563i 0.0169353 0.0414419i
\(919\) −39.3357 −1.29756 −0.648782 0.760974i \(-0.724721\pi\)
−0.648782 + 0.760974i \(0.724721\pi\)
\(920\) −29.6500 −0.977531
\(921\) 33.9009 + 4.40848i 1.11707 + 0.145264i
\(922\) 18.7869i 0.618715i
\(923\) 0 0
\(924\) 2.27201 + 2.95124i 0.0747437 + 0.0970888i
\(925\) −14.5562 + 14.5562i −0.478606 + 0.478606i
\(926\) 5.55224i 0.182458i
\(927\) 16.4964 + 4.36418i 0.541813 + 0.143339i
\(928\) −4.09478 + 4.09478i −0.134418 + 0.134418i
\(929\) 14.8752 + 14.8752i 0.488041 + 0.488041i 0.907688 0.419647i \(-0.137846\pi\)
−0.419647 + 0.907688i \(0.637846\pi\)
\(930\) 5.27722 + 0.686250i 0.173047 + 0.0225030i
\(931\) 5.74361 + 5.74361i 0.188239 + 0.188239i
\(932\) 3.99439i 0.130841i
\(933\) 37.0227 28.5019i 1.21207 0.933110i
\(934\) −34.8228 34.8228i −1.13944 1.13944i
\(935\) 1.59228 0.0520730
\(936\) 0 0
\(937\) 2.05438 0.0671138 0.0335569 0.999437i \(-0.489317\pi\)
0.0335569 + 0.999437i \(0.489317\pi\)
\(938\) −20.4624 20.4624i −0.668121 0.668121i
\(939\) 32.8923 25.3221i 1.07340 0.826355i
\(940\) 5.04593i 0.164580i
\(941\) 41.3493 + 41.3493i 1.34795 + 1.34795i 0.887888 + 0.460059i \(0.152172\pi\)
0.460059 + 0.887888i \(0.347828\pi\)
\(942\) −7.36777 0.958105i −0.240055 0.0312167i
\(943\) −8.89220 8.89220i −0.289570 0.289570i
\(944\) 7.95798 7.95798i 0.259010 0.259010i
\(945\) −42.0608 + 17.6570i −1.36824 + 0.574382i
\(946\) 40.7712i 1.32559i
\(947\) −21.4029 + 21.4029i −0.695502 + 0.695502i −0.963437 0.267935i \(-0.913659\pi\)
0.267935 + 0.963437i \(0.413659\pi\)
\(948\) −3.25181 4.22395i −0.105614 0.137188i
\(949\) 0 0
\(950\) 28.1052i 0.911852i
\(951\) 52.6856 + 6.85123i 1.70845 + 0.222166i
\(952\) 1.73558 0.0562504
\(953\) −9.48367 −0.307206 −0.153603 0.988133i \(-0.549088\pi\)
−0.153603 + 0.988133i \(0.549088\pi\)
\(954\) 26.9845 + 46.3981i 0.873654 + 1.50219i
\(955\) −4.31087 + 4.31087i −0.139496 + 0.139496i
\(956\) 1.17233 1.17233i 0.0379157 0.0379157i
\(957\) 17.0813 + 2.22125i 0.552161 + 0.0718030i
\(958\) 2.68132 0.0866295
\(959\) 50.8082 1.64068
\(960\) 5.89356 45.3212i 0.190214 1.46273i
\(961\) 30.3938i 0.980445i
\(962\) 0 0
\(963\) −22.5308 5.96062i −0.726046 0.192078i
\(964\) 4.82204 4.82204i 0.155307 0.155307i
\(965\) 11.9409i 0.384392i
\(966\) 13.3733 + 17.3714i 0.430280 + 0.558914i
\(967\) −17.7922 + 17.7922i −0.572158 + 0.572158i −0.932731 0.360573i \(-0.882581\pi\)
0.360573 + 0.932731i \(0.382581\pi\)
\(968\) −8.24472 8.24472i −0.264995 0.264995i
\(969\) −0.235654 + 1.81216i −0.00757028 + 0.0582150i
\(970\) −33.9421 33.9421i −1.08981 1.08981i
\(971\) 18.5328i 0.594745i 0.954761 + 0.297373i \(0.0961104\pi\)
−0.954761 + 0.297373i \(0.903890\pi\)
\(972\) −0.596086 4.26612i −0.0191195 0.136836i
\(973\) −4.81014 4.81014i −0.154206 0.154206i
\(974\) −32.9285 −1.05510
\(975\) 0 0
\(976\) −9.10483 −0.291439
\(977\) −21.7724 21.7724i −0.696561 0.696561i 0.267107 0.963667i \(-0.413932\pi\)
−0.963667 + 0.267107i \(0.913932\pi\)
\(978\) 8.08488 + 10.5019i 0.258526 + 0.335814i
\(979\) 2.92711i 0.0935508i
\(980\) −0.899023 0.899023i −0.0287182 0.0287182i
\(981\) −15.3222 26.3456i −0.489201 0.841151i
\(982\) 6.99249 + 6.99249i 0.223139 + 0.223139i
\(983\) −19.1428 + 19.1428i −0.610561 + 0.610561i −0.943092 0.332531i \(-0.892097\pi\)
0.332531 + 0.943092i \(0.392097\pi\)
\(984\) 15.6268 12.0303i 0.498164 0.383511i
\(985\) 20.7090i 0.659843i
\(986\) 0.688997 0.688997i 0.0219421 0.0219421i
\(987\) −24.3533 + 18.7483i −0.775173 + 0.596766i
\(988\) 0 0
\(989\) 38.4731i 1.22337i
\(990\) −27.2654 + 15.8572i −0.866552 + 0.503974i
\(991\) 6.24334 0.198326 0.0991631 0.995071i \(-0.468383\pi\)
0.0991631 + 0.995071i \(0.468383\pi\)
\(992\) −1.20792 −0.0383515
\(993\) 0.148213 1.13975i 0.00470341 0.0361689i
\(994\) −14.4998 + 14.4998i −0.459907 + 0.459907i
\(995\) 13.4760 13.4760i 0.427217 0.427217i
\(996\) −0.160617 + 1.23513i −0.00508933 + 0.0391367i
\(997\) −1.83522 −0.0581220 −0.0290610 0.999578i \(-0.509252\pi\)
−0.0290610 + 0.999578i \(0.509252\pi\)
\(998\) −16.1819 −0.512228
\(999\) −10.0299 + 24.5439i −0.317332 + 0.776534i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 507.2.f.g.239.8 yes 48
3.2 odd 2 inner 507.2.f.g.239.17 yes 48
13.2 odd 12 507.2.k.k.488.7 96
13.3 even 3 507.2.k.k.188.17 96
13.4 even 6 507.2.k.k.80.18 96
13.5 odd 4 inner 507.2.f.g.437.8 yes 48
13.6 odd 12 507.2.k.k.89.18 96
13.7 odd 12 507.2.k.k.89.8 96
13.8 odd 4 inner 507.2.f.g.437.18 yes 48
13.9 even 3 507.2.k.k.80.8 96
13.10 even 6 507.2.k.k.188.7 96
13.11 odd 12 507.2.k.k.488.17 96
13.12 even 2 inner 507.2.f.g.239.18 yes 48
39.2 even 12 507.2.k.k.488.18 96
39.5 even 4 inner 507.2.f.g.437.17 yes 48
39.8 even 4 inner 507.2.f.g.437.7 yes 48
39.11 even 12 507.2.k.k.488.8 96
39.17 odd 6 507.2.k.k.80.7 96
39.20 even 12 507.2.k.k.89.17 96
39.23 odd 6 507.2.k.k.188.18 96
39.29 odd 6 507.2.k.k.188.8 96
39.32 even 12 507.2.k.k.89.7 96
39.35 odd 6 507.2.k.k.80.17 96
39.38 odd 2 inner 507.2.f.g.239.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.f.g.239.7 48 39.38 odd 2 inner
507.2.f.g.239.8 yes 48 1.1 even 1 trivial
507.2.f.g.239.17 yes 48 3.2 odd 2 inner
507.2.f.g.239.18 yes 48 13.12 even 2 inner
507.2.f.g.437.7 yes 48 39.8 even 4 inner
507.2.f.g.437.8 yes 48 13.5 odd 4 inner
507.2.f.g.437.17 yes 48 39.5 even 4 inner
507.2.f.g.437.18 yes 48 13.8 odd 4 inner
507.2.k.k.80.7 96 39.17 odd 6
507.2.k.k.80.8 96 13.9 even 3
507.2.k.k.80.17 96 39.35 odd 6
507.2.k.k.80.18 96 13.4 even 6
507.2.k.k.89.7 96 39.32 even 12
507.2.k.k.89.8 96 13.7 odd 12
507.2.k.k.89.17 96 39.20 even 12
507.2.k.k.89.18 96 13.6 odd 12
507.2.k.k.188.7 96 13.10 even 6
507.2.k.k.188.8 96 39.29 odd 6
507.2.k.k.188.17 96 13.3 even 3
507.2.k.k.188.18 96 39.23 odd 6
507.2.k.k.488.7 96 13.2 odd 12
507.2.k.k.488.8 96 39.11 even 12
507.2.k.k.488.17 96 13.11 odd 12
507.2.k.k.488.18 96 39.2 even 12