Properties

Label 637.2.g.i.263.4
Level $637$
Weight $2$
Character 637.263
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(263,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.100088711424.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 263.4
Root \(1.87694 + 1.08365i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.i.373.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.651388 - 1.12824i) q^{2} +2.88145 q^{3} +(0.151388 + 0.262211i) q^{4} +(-1.44073 - 2.49541i) q^{5} +(1.87694 - 3.25096i) q^{6} +3.00000 q^{8} +5.30278 q^{9} +O(q^{10})\) \(q+(0.651388 - 1.12824i) q^{2} +2.88145 q^{3} +(0.151388 + 0.262211i) q^{4} +(-1.44073 - 2.49541i) q^{5} +(1.87694 - 3.25096i) q^{6} +3.00000 q^{8} +5.30278 q^{9} -3.75389 q^{10} -5.90833 q^{11} +(0.436217 + 0.755550i) q^{12} +(3.31767 - 1.41176i) q^{13} +(-4.15139 - 7.19041i) q^{15} +(1.65139 - 2.86029i) q^{16} +(0.436217 + 0.755550i) q^{17} +(3.45416 - 5.98279i) q^{18} +2.88145 q^{19} +(0.436217 - 0.755550i) q^{20} +(-3.84861 + 6.66599i) q^{22} +(-3.30278 + 5.72058i) q^{23} +8.64436 q^{24} +(-1.65139 + 2.86029i) q^{25} +(0.568293 - 4.66272i) q^{26} +6.63534 q^{27} +(-0.651388 - 1.12824i) q^{29} -10.8167 q^{30} +(-0.436217 + 0.755550i) q^{31} +(0.848612 + 1.46984i) q^{32} -17.0246 q^{33} +1.13659 q^{34} +(0.802776 + 1.39045i) q^{36} +(-0.697224 + 1.20763i) q^{37} +(1.87694 - 3.25096i) q^{38} +(9.55971 - 4.06792i) q^{39} +(-4.32218 - 7.48624i) q^{40} +(-3.75389 - 6.50192i) q^{41} +(-2.75694 + 4.77516i) q^{43} +(-0.894449 - 1.54923i) q^{44} +(-7.63985 - 13.2326i) q^{45} +(4.30278 + 7.45263i) q^{46} +(6.19912 + 10.7372i) q^{47} +(4.75840 - 8.24179i) q^{48} +(2.15139 + 3.72631i) q^{50} +(1.25694 + 2.17708i) q^{51} +(0.872434 + 0.656208i) q^{52} +(-4.80278 + 8.31865i) q^{53} +(4.32218 - 7.48624i) q^{54} +(8.51229 + 14.7437i) q^{55} +8.30278 q^{57} -1.69722 q^{58} +(-3.31767 - 5.74637i) q^{59} +(1.25694 - 2.17708i) q^{60} +5.76291 q^{61} +(0.568293 + 0.984312i) q^{62} +8.81665 q^{64} +(-8.30278 - 6.24500i) q^{65} +(-11.0896 + 19.2077i) q^{66} +1.00000 q^{67} +(-0.132076 + 0.228762i) q^{68} +(-9.51680 + 16.4836i) q^{69} +(-2.00000 + 3.46410i) q^{71} +15.9083 q^{72} +(2.88145 - 4.99082i) q^{73} +(0.908327 + 1.57327i) q^{74} +(-4.75840 + 8.24179i) q^{75} +(0.436217 + 0.755550i) q^{76} +(1.63751 - 13.4354i) q^{78} +(-0.302776 - 0.524423i) q^{79} -9.51680 q^{80} +3.21110 q^{81} -9.78095 q^{82} -6.63534 q^{83} +(1.25694 - 2.17708i) q^{85} +(3.59167 + 6.22096i) q^{86} +(-1.87694 - 3.25096i) q^{87} -17.7250 q^{88} +(-4.32218 + 7.48624i) q^{89} -19.9060 q^{90} -2.00000 q^{92} +(-1.25694 + 2.17708i) q^{93} +16.1521 q^{94} +(-4.15139 - 7.19041i) q^{95} +(2.44524 + 4.23527i) q^{96} +(3.88596 - 6.73069i) q^{97} -31.3305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9} - 4 q^{11} - 26 q^{15} + 6 q^{16} + 6 q^{18} - 38 q^{22} - 12 q^{23} - 6 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44} + 20 q^{46} + 10 q^{50} - 26 q^{51} - 24 q^{53} + 52 q^{57} - 28 q^{58} - 26 q^{60} - 16 q^{64} - 52 q^{65} + 8 q^{67} - 16 q^{71} + 84 q^{72} - 36 q^{74} + 78 q^{78} + 12 q^{79} - 32 q^{81} - 26 q^{85} + 72 q^{86} - 12 q^{88} - 16 q^{92} + 26 q^{93} - 26 q^{95} - 92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.651388 1.12824i 0.460601 0.797784i −0.538390 0.842696i \(-0.680967\pi\)
0.998991 + 0.0449118i \(0.0143007\pi\)
\(3\) 2.88145 1.66361 0.831804 0.555069i \(-0.187308\pi\)
0.831804 + 0.555069i \(0.187308\pi\)
\(4\) 0.151388 + 0.262211i 0.0756939 + 0.131106i
\(5\) −1.44073 2.49541i −0.644313 1.11598i −0.984460 0.175610i \(-0.943810\pi\)
0.340147 0.940372i \(-0.389523\pi\)
\(6\) 1.87694 3.25096i 0.766259 1.32720i
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) 5.30278 1.76759
\(10\) −3.75389 −1.18708
\(11\) −5.90833 −1.78143 −0.890714 0.454565i \(-0.849795\pi\)
−0.890714 + 0.454565i \(0.849795\pi\)
\(12\) 0.436217 + 0.755550i 0.125925 + 0.218108i
\(13\) 3.31767 1.41176i 0.920156 0.391551i
\(14\) 0 0
\(15\) −4.15139 7.19041i −1.07188 1.85656i
\(16\) 1.65139 2.86029i 0.412847 0.715072i
\(17\) 0.436217 + 0.755550i 0.105798 + 0.183248i 0.914064 0.405570i \(-0.132927\pi\)
−0.808266 + 0.588818i \(0.799594\pi\)
\(18\) 3.45416 5.98279i 0.814154 1.41016i
\(19\) 2.88145 0.661051 0.330525 0.943797i \(-0.392774\pi\)
0.330525 + 0.943797i \(0.392774\pi\)
\(20\) 0.436217 0.755550i 0.0975411 0.168946i
\(21\) 0 0
\(22\) −3.84861 + 6.66599i −0.820527 + 1.42119i
\(23\) −3.30278 + 5.72058i −0.688676 + 1.19282i 0.283590 + 0.958946i \(0.408475\pi\)
−0.972266 + 0.233877i \(0.924859\pi\)
\(24\) 8.64436 1.76452
\(25\) −1.65139 + 2.86029i −0.330278 + 0.572058i
\(26\) 0.568293 4.66272i 0.111451 0.914435i
\(27\) 6.63534 1.27697
\(28\) 0 0
\(29\) −0.651388 1.12824i −0.120960 0.209508i 0.799187 0.601083i \(-0.205264\pi\)
−0.920146 + 0.391575i \(0.871931\pi\)
\(30\) −10.8167 −1.97484
\(31\) −0.436217 + 0.755550i −0.0783469 + 0.135701i −0.902537 0.430613i \(-0.858298\pi\)
0.824190 + 0.566313i \(0.191631\pi\)
\(32\) 0.848612 + 1.46984i 0.150015 + 0.259833i
\(33\) −17.0246 −2.96360
\(34\) 1.13659 0.194923
\(35\) 0 0
\(36\) 0.802776 + 1.39045i 0.133796 + 0.231741i
\(37\) −0.697224 + 1.20763i −0.114623 + 0.198533i −0.917629 0.397438i \(-0.869899\pi\)
0.803006 + 0.595971i \(0.203233\pi\)
\(38\) 1.87694 3.25096i 0.304481 0.527376i
\(39\) 9.55971 4.06792i 1.53078 0.651388i
\(40\) −4.32218 7.48624i −0.683397 1.18368i
\(41\) −3.75389 6.50192i −0.586259 1.01543i −0.994717 0.102653i \(-0.967267\pi\)
0.408458 0.912777i \(-0.366066\pi\)
\(42\) 0 0
\(43\) −2.75694 + 4.77516i −0.420429 + 0.728205i −0.995981 0.0895602i \(-0.971454\pi\)
0.575552 + 0.817765i \(0.304787\pi\)
\(44\) −0.894449 1.54923i −0.134843 0.233555i
\(45\) −7.63985 13.2326i −1.13888 1.97260i
\(46\) 4.30278 + 7.45263i 0.634410 + 1.09883i
\(47\) 6.19912 + 10.7372i 0.904235 + 1.56618i 0.821941 + 0.569573i \(0.192892\pi\)
0.0822947 + 0.996608i \(0.473775\pi\)
\(48\) 4.75840 8.24179i 0.686816 1.18960i
\(49\) 0 0
\(50\) 2.15139 + 3.72631i 0.304252 + 0.526980i
\(51\) 1.25694 + 2.17708i 0.176007 + 0.304853i
\(52\) 0.872434 + 0.656208i 0.120985 + 0.0909997i
\(53\) −4.80278 + 8.31865i −0.659712 + 1.14265i 0.320978 + 0.947087i \(0.395988\pi\)
−0.980690 + 0.195568i \(0.937345\pi\)
\(54\) 4.32218 7.48624i 0.588174 1.01875i
\(55\) 8.51229 + 14.7437i 1.14780 + 1.98804i
\(56\) 0 0
\(57\) 8.30278 1.09973
\(58\) −1.69722 −0.222856
\(59\) −3.31767 5.74637i −0.431924 0.748114i 0.565115 0.825012i \(-0.308832\pi\)
−0.997039 + 0.0768979i \(0.975498\pi\)
\(60\) 1.25694 2.17708i 0.162270 0.281060i
\(61\) 5.76291 0.737865 0.368932 0.929456i \(-0.379723\pi\)
0.368932 + 0.929456i \(0.379723\pi\)
\(62\) 0.568293 + 0.984312i 0.0721733 + 0.125008i
\(63\) 0 0
\(64\) 8.81665 1.10208
\(65\) −8.30278 6.24500i −1.02983 0.774597i
\(66\) −11.0896 + 19.2077i −1.36504 + 2.36431i
\(67\) 1.00000 0.122169 0.0610847 0.998133i \(-0.480544\pi\)
0.0610847 + 0.998133i \(0.480544\pi\)
\(68\) −0.132076 + 0.228762i −0.0160166 + 0.0277415i
\(69\) −9.51680 + 16.4836i −1.14569 + 1.98439i
\(70\) 0 0
\(71\) −2.00000 + 3.46410i −0.237356 + 0.411113i −0.959955 0.280155i \(-0.909614\pi\)
0.722599 + 0.691268i \(0.242948\pi\)
\(72\) 15.9083 1.87481
\(73\) 2.88145 4.99082i 0.337249 0.584132i −0.646666 0.762774i \(-0.723837\pi\)
0.983914 + 0.178642i \(0.0571704\pi\)
\(74\) 0.908327 + 1.57327i 0.105591 + 0.182889i
\(75\) −4.75840 + 8.24179i −0.549452 + 0.951680i
\(76\) 0.436217 + 0.755550i 0.0500375 + 0.0866675i
\(77\) 0 0
\(78\) 1.63751 13.4354i 0.185411 1.52126i
\(79\) −0.302776 0.524423i −0.0340649 0.0590022i 0.848490 0.529211i \(-0.177512\pi\)
−0.882555 + 0.470209i \(0.844179\pi\)
\(80\) −9.51680 −1.06401
\(81\) 3.21110 0.356789
\(82\) −9.78095 −1.08012
\(83\) −6.63534 −0.728323 −0.364162 0.931336i \(-0.618644\pi\)
−0.364162 + 0.931336i \(0.618644\pi\)
\(84\) 0 0
\(85\) 1.25694 2.17708i 0.136334 0.236138i
\(86\) 3.59167 + 6.22096i 0.387300 + 0.670823i
\(87\) −1.87694 3.25096i −0.201230 0.348540i
\(88\) −17.7250 −1.88949
\(89\) −4.32218 + 7.48624i −0.458150 + 0.793539i −0.998863 0.0476677i \(-0.984821\pi\)
0.540713 + 0.841207i \(0.318154\pi\)
\(90\) −19.9060 −2.09828
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) −1.25694 + 2.17708i −0.130339 + 0.225753i
\(94\) 16.1521 1.66597
\(95\) −4.15139 7.19041i −0.425923 0.737721i
\(96\) 2.44524 + 4.23527i 0.249566 + 0.432261i
\(97\) 3.88596 6.73069i 0.394560 0.683398i −0.598485 0.801134i \(-0.704230\pi\)
0.993045 + 0.117736i \(0.0375638\pi\)
\(98\) 0 0
\(99\) −31.3305 −3.14884
\(100\) −1.00000 −0.100000
\(101\) −8.64436 −0.860146 −0.430073 0.902794i \(-0.641512\pi\)
−0.430073 + 0.902794i \(0.641512\pi\)
\(102\) 3.27502 0.324275
\(103\) −2.44524 4.23527i −0.240936 0.417314i 0.720045 0.693927i \(-0.244121\pi\)
−0.960981 + 0.276613i \(0.910788\pi\)
\(104\) 9.95301 4.23527i 0.975973 0.415303i
\(105\) 0 0
\(106\) 6.25694 + 10.8373i 0.607728 + 1.05262i
\(107\) −4.65139 + 8.05644i −0.449667 + 0.778845i −0.998364 0.0571755i \(-0.981791\pi\)
0.548698 + 0.836021i \(0.315124\pi\)
\(108\) 1.00451 + 1.73986i 0.0966590 + 0.167418i
\(109\) 3.10555 5.37897i 0.297458 0.515212i −0.678096 0.734974i \(-0.737195\pi\)
0.975554 + 0.219761i \(0.0705279\pi\)
\(110\) 22.1792 2.11470
\(111\) −2.00902 + 3.47972i −0.190688 + 0.330281i
\(112\) 0 0
\(113\) 7.40833 12.8316i 0.696917 1.20710i −0.272613 0.962124i \(-0.587888\pi\)
0.969530 0.244972i \(-0.0787786\pi\)
\(114\) 5.40833 9.36750i 0.506536 0.877346i
\(115\) 19.0336 1.77489
\(116\) 0.197224 0.341603i 0.0183118 0.0317170i
\(117\) 17.5929 7.48624i 1.62646 0.692103i
\(118\) −8.64436 −0.795778
\(119\) 0 0
\(120\) −12.4542 21.5712i −1.13690 1.96918i
\(121\) 23.9083 2.17348
\(122\) 3.75389 6.50192i 0.339861 0.588657i
\(123\) −10.8167 18.7350i −0.975305 1.68928i
\(124\) −0.264152 −0.0237215
\(125\) −4.89047 −0.437417
\(126\) 0 0
\(127\) 1.45416 + 2.51868i 0.129036 + 0.223497i 0.923303 0.384071i \(-0.125478\pi\)
−0.794267 + 0.607569i \(0.792145\pi\)
\(128\) 4.04584 7.00759i 0.357605 0.619390i
\(129\) −7.94399 + 13.7594i −0.699430 + 1.21145i
\(130\) −12.4542 + 5.29958i −1.09230 + 0.464804i
\(131\) −8.51229 14.7437i −0.743722 1.28816i −0.950790 0.309837i \(-0.899725\pi\)
0.207068 0.978327i \(-0.433608\pi\)
\(132\) −2.57731 4.46404i −0.224326 0.388544i
\(133\) 0 0
\(134\) 0.651388 1.12824i 0.0562713 0.0974648i
\(135\) −9.55971 16.5579i −0.822769 1.42508i
\(136\) 1.30865 + 2.26665i 0.112216 + 0.194364i
\(137\) −1.34861 2.33586i −0.115220 0.199566i 0.802648 0.596453i \(-0.203424\pi\)
−0.917868 + 0.396887i \(0.870091\pi\)
\(138\) 12.3982 + 21.4744i 1.05541 + 1.82802i
\(139\) −8.51229 + 14.7437i −0.722003 + 1.25055i 0.238193 + 0.971218i \(0.423445\pi\)
−0.960196 + 0.279327i \(0.909889\pi\)
\(140\) 0 0
\(141\) 17.8625 + 30.9387i 1.50429 + 2.60551i
\(142\) 2.60555 + 4.51295i 0.218653 + 0.378718i
\(143\) −19.6019 + 8.34113i −1.63919 + 0.697520i
\(144\) 8.75694 15.1675i 0.729745 1.26396i
\(145\) −1.87694 + 3.25096i −0.155872 + 0.269978i
\(146\) −3.75389 6.50192i −0.310674 0.538103i
\(147\) 0 0
\(148\) −0.422205 −0.0347050
\(149\) 0.513878 0.0420985 0.0210493 0.999778i \(-0.493299\pi\)
0.0210493 + 0.999778i \(0.493299\pi\)
\(150\) 6.19912 + 10.7372i 0.506156 + 0.876689i
\(151\) 3.10555 5.37897i 0.252726 0.437735i −0.711549 0.702636i \(-0.752006\pi\)
0.964275 + 0.264902i \(0.0853395\pi\)
\(152\) 8.64436 0.701150
\(153\) 2.31316 + 4.00651i 0.187008 + 0.323907i
\(154\) 0 0
\(155\) 2.51388 0.201920
\(156\) 2.51388 + 1.89083i 0.201271 + 0.151388i
\(157\) −4.75840 + 8.24179i −0.379761 + 0.657766i −0.991027 0.133659i \(-0.957327\pi\)
0.611266 + 0.791425i \(0.290661\pi\)
\(158\) −0.788897 −0.0627613
\(159\) −13.8390 + 23.9698i −1.09750 + 1.90093i
\(160\) 2.44524 4.23527i 0.193313 0.334828i
\(161\) 0 0
\(162\) 2.09167 3.62288i 0.164337 0.284641i
\(163\) −17.2111 −1.34808 −0.674039 0.738696i \(-0.735442\pi\)
−0.674039 + 0.738696i \(0.735442\pi\)
\(164\) 1.13659 1.96862i 0.0887524 0.153724i
\(165\) 24.5278 + 42.4833i 1.90948 + 3.30732i
\(166\) −4.32218 + 7.48624i −0.335466 + 0.581045i
\(167\) −2.44524 4.23527i −0.189218 0.327735i 0.755772 0.654835i \(-0.227262\pi\)
−0.944990 + 0.327100i \(0.893929\pi\)
\(168\) 0 0
\(169\) 9.01388 9.36750i 0.693375 0.720577i
\(170\) −1.63751 2.83625i −0.125591 0.217530i
\(171\) 15.2797 1.16847
\(172\) −1.66947 −0.127296
\(173\) 23.9241 1.81891 0.909456 0.415799i \(-0.136498\pi\)
0.909456 + 0.415799i \(0.136498\pi\)
\(174\) −4.89047 −0.370746
\(175\) 0 0
\(176\) −9.75694 + 16.8995i −0.735457 + 1.27385i
\(177\) −9.55971 16.5579i −0.718552 1.24457i
\(178\) 5.63083 + 9.75289i 0.422049 + 0.731010i
\(179\) 14.3944 1.07589 0.537946 0.842979i \(-0.319200\pi\)
0.537946 + 0.842979i \(0.319200\pi\)
\(180\) 2.31316 4.00651i 0.172413 0.298628i
\(181\) 9.25264 0.687744 0.343872 0.939017i \(-0.388261\pi\)
0.343872 + 0.939017i \(0.388261\pi\)
\(182\) 0 0
\(183\) 16.6056 1.22752
\(184\) −9.90833 + 17.1617i −0.730452 + 1.26518i
\(185\) 4.01804 0.295412
\(186\) 1.63751 + 2.83625i 0.120068 + 0.207964i
\(187\) −2.57731 4.46404i −0.188472 0.326443i
\(188\) −1.87694 + 3.25096i −0.136890 + 0.237101i
\(189\) 0 0
\(190\) −10.8167 −0.784723
\(191\) 19.3028 1.39670 0.698350 0.715757i \(-0.253918\pi\)
0.698350 + 0.715757i \(0.253918\pi\)
\(192\) 25.4048 1.83343
\(193\) −1.81665 −0.130766 −0.0653828 0.997860i \(-0.520827\pi\)
−0.0653828 + 0.997860i \(0.520827\pi\)
\(194\) −5.06254 8.76857i −0.363469 0.629547i
\(195\) −23.9241 17.9947i −1.71324 1.28863i
\(196\) 0 0
\(197\) 5.95416 + 10.3129i 0.424217 + 0.734765i 0.996347 0.0853980i \(-0.0272162\pi\)
−0.572130 + 0.820163i \(0.693883\pi\)
\(198\) −20.4083 + 35.3483i −1.45036 + 2.51209i
\(199\) −0.436217 0.755550i −0.0309226 0.0535595i 0.850150 0.526541i \(-0.176511\pi\)
−0.881073 + 0.472981i \(0.843178\pi\)
\(200\) −4.95416 + 8.58086i −0.350312 + 0.606759i
\(201\) 2.88145 0.203242
\(202\) −5.63083 + 9.75289i −0.396184 + 0.686211i
\(203\) 0 0
\(204\) −0.380571 + 0.659168i −0.0266453 + 0.0461510i
\(205\) −10.8167 + 18.7350i −0.755468 + 1.30851i
\(206\) −6.37119 −0.443902
\(207\) −17.5139 + 30.3349i −1.21730 + 2.10842i
\(208\) 1.44073 11.8209i 0.0998964 0.819629i
\(209\) −17.0246 −1.17761
\(210\) 0 0
\(211\) −7.50000 12.9904i −0.516321 0.894295i −0.999820 0.0189499i \(-0.993968\pi\)
0.483499 0.875345i \(-0.339366\pi\)
\(212\) −2.90833 −0.199745
\(213\) −5.76291 + 9.98165i −0.394868 + 0.683931i
\(214\) 6.05971 + 10.4957i 0.414234 + 0.717474i
\(215\) 15.8880 1.08355
\(216\) 19.9060 1.35443
\(217\) 0 0
\(218\) −4.04584 7.00759i −0.274019 0.474614i
\(219\) 8.30278 14.3808i 0.561050 0.971766i
\(220\) −2.57731 + 4.46404i −0.173762 + 0.300965i
\(221\) 2.51388 + 1.89083i 0.169102 + 0.127191i
\(222\) 2.61730 + 4.53330i 0.175662 + 0.304255i
\(223\) 6.76742 + 11.7215i 0.453180 + 0.784930i 0.998582 0.0532444i \(-0.0169562\pi\)
−0.545402 + 0.838175i \(0.683623\pi\)
\(224\) 0 0
\(225\) −8.75694 + 15.1675i −0.583796 + 1.01116i
\(226\) −9.65139 16.7167i −0.642001 1.11198i
\(227\) −13.7069 23.7410i −0.909759 1.57575i −0.814399 0.580306i \(-0.802933\pi\)
−0.0953602 0.995443i \(-0.530400\pi\)
\(228\) 1.25694 + 2.17708i 0.0832428 + 0.144181i
\(229\) −10.3892 17.9947i −0.686540 1.18912i −0.972950 0.231015i \(-0.925796\pi\)
0.286411 0.958107i \(-0.407538\pi\)
\(230\) 12.3982 21.4744i 0.817516 1.41598i
\(231\) 0 0
\(232\) −1.95416 3.38471i −0.128297 0.222217i
\(233\) 11.9542 + 20.7052i 0.783143 + 1.35644i 0.930102 + 0.367301i \(0.119718\pi\)
−0.146959 + 0.989143i \(0.546948\pi\)
\(234\) 3.01353 24.7254i 0.197001 1.61635i
\(235\) 17.8625 30.9387i 1.16522 2.01822i
\(236\) 1.00451 1.73986i 0.0653880 0.113255i
\(237\) −0.872434 1.51110i −0.0566707 0.0981565i
\(238\) 0 0
\(239\) 11.6056 0.750701 0.375350 0.926883i \(-0.377522\pi\)
0.375350 + 0.926883i \(0.377522\pi\)
\(240\) −27.4222 −1.77010
\(241\) 1.00451 + 1.73986i 0.0647062 + 0.112074i 0.896564 0.442915i \(-0.146056\pi\)
−0.831857 + 0.554989i \(0.812722\pi\)
\(242\) 15.5736 26.9743i 1.00111 1.73397i
\(243\) −10.6534 −0.683415
\(244\) 0.872434 + 1.51110i 0.0558519 + 0.0967383i
\(245\) 0 0
\(246\) −28.1833 −1.79690
\(247\) 9.55971 4.06792i 0.608270 0.258835i
\(248\) −1.30865 + 2.26665i −0.0830994 + 0.143932i
\(249\) −19.1194 −1.21164
\(250\) −3.18559 + 5.51761i −0.201475 + 0.348964i
\(251\) 11.2617 19.5058i 0.710830 1.23119i −0.253716 0.967279i \(-0.581653\pi\)
0.964546 0.263915i \(-0.0850138\pi\)
\(252\) 0 0
\(253\) 19.5139 33.7990i 1.22683 2.12493i
\(254\) 3.78890 0.237737
\(255\) 3.62181 6.27316i 0.226807 0.392841i
\(256\) 3.54584 + 6.14157i 0.221615 + 0.383848i
\(257\) 11.3937 19.7345i 0.710722 1.23101i −0.253865 0.967240i \(-0.581702\pi\)
0.964587 0.263767i \(-0.0849649\pi\)
\(258\) 10.3492 + 17.9254i 0.644316 + 1.11599i
\(259\) 0 0
\(260\) 0.380571 3.12250i 0.0236020 0.193649i
\(261\) −3.45416 5.98279i −0.213807 0.370325i
\(262\) −22.1792 −1.37024
\(263\) −13.4222 −0.827649 −0.413824 0.910357i \(-0.635807\pi\)
−0.413824 + 0.910357i \(0.635807\pi\)
\(264\) −51.0737 −3.14337
\(265\) 27.6780 1.70024
\(266\) 0 0
\(267\) −12.4542 + 21.5712i −0.762182 + 1.32014i
\(268\) 0.151388 + 0.262211i 0.00924748 + 0.0160171i
\(269\) −4.75840 8.24179i −0.290125 0.502511i 0.683714 0.729750i \(-0.260363\pi\)
−0.973839 + 0.227239i \(0.927030\pi\)
\(270\) −24.9083 −1.51587
\(271\) −14.8435 + 25.7097i −0.901678 + 1.56175i −0.0763615 + 0.997080i \(0.524330\pi\)
−0.825316 + 0.564671i \(0.809003\pi\)
\(272\) 2.88145 0.174714
\(273\) 0 0
\(274\) −3.51388 −0.212281
\(275\) 9.75694 16.8995i 0.588366 1.01908i
\(276\) −5.76291 −0.346886
\(277\) −7.10555 12.3072i −0.426931 0.739467i 0.569667 0.821875i \(-0.307072\pi\)
−0.996599 + 0.0824088i \(0.973739\pi\)
\(278\) 11.0896 + 19.2077i 0.665110 + 1.15200i
\(279\) −2.31316 + 4.00651i −0.138485 + 0.239864i
\(280\) 0 0
\(281\) 2.18335 0.130248 0.0651238 0.997877i \(-0.479256\pi\)
0.0651238 + 0.997877i \(0.479256\pi\)
\(282\) 46.5416 2.77151
\(283\) 4.01804 0.238848 0.119424 0.992843i \(-0.461895\pi\)
0.119424 + 0.992843i \(0.461895\pi\)
\(284\) −1.21110 −0.0718657
\(285\) −11.9620 20.7188i −0.708570 1.22728i
\(286\) −3.35766 + 27.5489i −0.198543 + 1.62900i
\(287\) 0 0
\(288\) 4.50000 + 7.79423i 0.265165 + 0.459279i
\(289\) 8.11943 14.0633i 0.477613 0.827251i
\(290\) 2.44524 + 4.23527i 0.143589 + 0.248704i
\(291\) 11.1972 19.3942i 0.656393 1.13691i
\(292\) 1.74487 0.102111
\(293\) −1.74487 + 3.02220i −0.101936 + 0.176559i −0.912482 0.409116i \(-0.865837\pi\)
0.810546 + 0.585675i \(0.199170\pi\)
\(294\) 0 0
\(295\) −9.55971 + 16.5579i −0.556588 + 0.964039i
\(296\) −2.09167 + 3.62288i −0.121576 + 0.210576i
\(297\) −39.2038 −2.27483
\(298\) 0.334734 0.579776i 0.0193906 0.0335855i
\(299\) −2.88145 + 23.6417i −0.166639 + 1.36724i
\(300\) −2.88145 −0.166361
\(301\) 0 0
\(302\) −4.04584 7.00759i −0.232812 0.403242i
\(303\) −24.9083 −1.43095
\(304\) 4.75840 8.24179i 0.272913 0.472699i
\(305\) −8.30278 14.3808i −0.475416 0.823444i
\(306\) 6.02706 0.344544
\(307\) 15.2797 0.872059 0.436029 0.899932i \(-0.356384\pi\)
0.436029 + 0.899932i \(0.356384\pi\)
\(308\) 0 0
\(309\) −7.04584 12.2037i −0.400824 0.694247i
\(310\) 1.63751 2.83625i 0.0930043 0.161088i
\(311\) 8.51229 14.7437i 0.482687 0.836039i −0.517115 0.855916i \(-0.672994\pi\)
0.999802 + 0.0198768i \(0.00632739\pi\)
\(312\) 28.6791 12.2037i 1.62364 0.690901i
\(313\) −6.63534 11.4927i −0.375052 0.649609i 0.615283 0.788306i \(-0.289042\pi\)
−0.990335 + 0.138698i \(0.955708\pi\)
\(314\) 6.19912 + 10.7372i 0.349837 + 0.605935i
\(315\) 0 0
\(316\) 0.0916731 0.158782i 0.00515701 0.00893221i
\(317\) −4.10555 7.11102i −0.230591 0.399395i 0.727391 0.686223i \(-0.240733\pi\)
−0.957982 + 0.286828i \(0.907399\pi\)
\(318\) 18.0291 + 31.2273i 1.01102 + 1.75114i
\(319\) 3.84861 + 6.66599i 0.215481 + 0.373224i
\(320\) −12.7024 22.0012i −0.710085 1.22990i
\(321\) −13.4028 + 23.2143i −0.748069 + 1.29569i
\(322\) 0 0
\(323\) 1.25694 + 2.17708i 0.0699380 + 0.121136i
\(324\) 0.486122 + 0.841988i 0.0270068 + 0.0467771i
\(325\) −1.44073 + 11.8209i −0.0799171 + 0.655703i
\(326\) −11.2111 + 19.4182i −0.620926 + 1.07547i
\(327\) 8.94850 15.4993i 0.494853 0.857111i
\(328\) −11.2617 19.5058i −0.621821 1.07703i
\(329\) 0 0
\(330\) 63.9083 3.51804
\(331\) 0.697224 0.0383229 0.0191615 0.999816i \(-0.493900\pi\)
0.0191615 + 0.999816i \(0.493900\pi\)
\(332\) −1.00451 1.73986i −0.0551296 0.0954873i
\(333\) −3.69722 + 6.40378i −0.202607 + 0.350925i
\(334\) −6.37119 −0.348616
\(335\) −1.44073 2.49541i −0.0787153 0.136339i
\(336\) 0 0
\(337\) −7.11943 −0.387820 −0.193910 0.981019i \(-0.562117\pi\)
−0.193910 + 0.981019i \(0.562117\pi\)
\(338\) −4.69722 16.2717i −0.255495 0.885062i
\(339\) 21.3468 36.9737i 1.15940 2.00813i
\(340\) 0.761141 0.0412787
\(341\) 2.57731 4.46404i 0.139569 0.241741i
\(342\) 9.95301 17.2391i 0.538197 0.932185i
\(343\) 0 0
\(344\) −8.27082 + 14.3255i −0.445933 + 0.772378i
\(345\) 54.8444 2.95272
\(346\) 15.5838 26.9920i 0.837793 1.45110i
\(347\) −0.394449 0.683205i −0.0211751 0.0366764i 0.855244 0.518226i \(-0.173407\pi\)
−0.876419 + 0.481550i \(0.840074\pi\)
\(348\) 0.568293 0.984312i 0.0304637 0.0527647i
\(349\) −11.9620 20.7188i −0.640313 1.10905i −0.985363 0.170470i \(-0.945471\pi\)
0.345050 0.938584i \(-0.387862\pi\)
\(350\) 0 0
\(351\) 22.0139 9.36750i 1.17501 0.500000i
\(352\) −5.01388 8.68429i −0.267241 0.462874i
\(353\) 6.37119 0.339104 0.169552 0.985521i \(-0.445768\pi\)
0.169552 + 0.985521i \(0.445768\pi\)
\(354\) −24.9083 −1.32386
\(355\) 11.5258 0.611727
\(356\) −2.61730 −0.138717
\(357\) 0 0
\(358\) 9.37637 16.2403i 0.495556 0.858329i
\(359\) 11.4542 + 19.8392i 0.604528 + 1.04707i 0.992126 + 0.125244i \(0.0399714\pi\)
−0.387598 + 0.921828i \(0.626695\pi\)
\(360\) −22.9196 39.6978i −1.20797 2.09226i
\(361\) −10.6972 −0.563012
\(362\) 6.02706 10.4392i 0.316775 0.548671i
\(363\) 68.8907 3.61583
\(364\) 0 0
\(365\) −16.6056 −0.869174
\(366\) 10.8167 18.7350i 0.565396 0.979294i
\(367\) −28.2862 −1.47653 −0.738265 0.674511i \(-0.764354\pi\)
−0.738265 + 0.674511i \(0.764354\pi\)
\(368\) 10.9083 + 18.8938i 0.568636 + 0.984906i
\(369\) −19.9060 34.4782i −1.03627 1.79487i
\(370\) 2.61730 4.53330i 0.136067 0.235675i
\(371\) 0 0
\(372\) −0.761141 −0.0394633
\(373\) −16.3028 −0.844126 −0.422063 0.906567i \(-0.638694\pi\)
−0.422063 + 0.906567i \(0.638694\pi\)
\(374\) −6.71532 −0.347241
\(375\) −14.0917 −0.727691
\(376\) 18.5974 + 32.2116i 0.959086 + 1.66119i
\(377\) −3.75389 2.82352i −0.193335 0.145418i
\(378\) 0 0
\(379\) −6.55971 11.3618i −0.336950 0.583614i 0.646908 0.762568i \(-0.276062\pi\)
−0.983857 + 0.178954i \(0.942729\pi\)
\(380\) 1.25694 2.17708i 0.0644796 0.111682i
\(381\) 4.19010 + 7.25747i 0.214666 + 0.371812i
\(382\) 12.5736 21.7781i 0.643321 1.11426i
\(383\) −19.2977 −0.986069 −0.493034 0.870010i \(-0.664112\pi\)
−0.493034 + 0.870010i \(0.664112\pi\)
\(384\) 11.6579 20.1921i 0.594914 1.03042i
\(385\) 0 0
\(386\) −1.18335 + 2.04962i −0.0602307 + 0.104323i
\(387\) −14.6194 + 25.3216i −0.743147 + 1.28717i
\(388\) 2.35315 0.119463
\(389\) 3.51388 6.08622i 0.178161 0.308583i −0.763090 0.646292i \(-0.776319\pi\)
0.941251 + 0.337709i \(0.109652\pi\)
\(390\) −35.8861 + 15.2705i −1.81716 + 0.773252i
\(391\) −5.76291 −0.291443
\(392\) 0 0
\(393\) −24.5278 42.4833i −1.23726 2.14300i
\(394\) 15.5139 0.781578
\(395\) −0.872434 + 1.51110i −0.0438969 + 0.0760317i
\(396\) −4.74306 8.21522i −0.238348 0.412830i
\(397\) 5.76291 0.289232 0.144616 0.989488i \(-0.453805\pi\)
0.144616 + 0.989488i \(0.453805\pi\)
\(398\) −1.13659 −0.0569719
\(399\) 0 0
\(400\) 5.45416 + 9.44689i 0.272708 + 0.472344i
\(401\) −7.55971 + 13.0938i −0.377514 + 0.653874i −0.990700 0.136065i \(-0.956554\pi\)
0.613186 + 0.789939i \(0.289888\pi\)
\(402\) 1.87694 3.25096i 0.0936135 0.162143i
\(403\) −0.380571 + 3.12250i −0.0189576 + 0.155543i
\(404\) −1.30865 2.26665i −0.0651078 0.112770i
\(405\) −4.62632 8.01302i −0.229884 0.398170i
\(406\) 0 0
\(407\) 4.11943 7.13506i 0.204193 0.353672i
\(408\) 3.77082 + 6.53125i 0.186683 + 0.323345i
\(409\) 8.07607 + 13.9882i 0.399336 + 0.691670i 0.993644 0.112567i \(-0.0359074\pi\)
−0.594308 + 0.804237i \(0.702574\pi\)
\(410\) 14.0917 + 24.4075i 0.695938 + 1.20540i
\(411\) −3.88596 6.73069i −0.191680 0.332000i
\(412\) 0.740358 1.28234i 0.0364748 0.0631763i
\(413\) 0 0
\(414\) 22.8167 + 39.5196i 1.12138 + 1.94228i
\(415\) 9.55971 + 16.5579i 0.469268 + 0.812796i
\(416\) 4.89047 + 3.67841i 0.239775 + 0.180349i
\(417\) −24.5278 + 42.4833i −1.20113 + 2.08042i
\(418\) −11.0896 + 19.2077i −0.542410 + 0.939482i
\(419\) −4.19010 7.25747i −0.204700 0.354551i 0.745337 0.666688i \(-0.232289\pi\)
−0.950037 + 0.312137i \(0.898955\pi\)
\(420\) 0 0
\(421\) −31.0278 −1.51220 −0.756100 0.654456i \(-0.772898\pi\)
−0.756100 + 0.654456i \(0.772898\pi\)
\(422\) −19.5416 −0.951272
\(423\) 32.8726 + 56.9370i 1.59832 + 2.76837i
\(424\) −14.4083 + 24.9560i −0.699730 + 1.21197i
\(425\) −2.88145 −0.139771
\(426\) 7.50778 + 13.0038i 0.363753 + 0.630039i
\(427\) 0 0
\(428\) −2.81665 −0.136148
\(429\) −56.4819 + 24.0346i −2.72697 + 1.16040i
\(430\) 10.3492 17.9254i 0.499085 0.864440i
\(431\) 25.9361 1.24930 0.624649 0.780906i \(-0.285242\pi\)
0.624649 + 0.780906i \(0.285242\pi\)
\(432\) 10.9575 18.9790i 0.527194 0.913127i
\(433\) 4.19010 7.25747i 0.201364 0.348772i −0.747604 0.664144i \(-0.768796\pi\)
0.948968 + 0.315372i \(0.102129\pi\)
\(434\) 0 0
\(435\) −5.40833 + 9.36750i −0.259309 + 0.449137i
\(436\) 1.88057 0.0900630
\(437\) −9.51680 + 16.4836i −0.455250 + 0.788516i
\(438\) −10.8167 18.7350i −0.516840 0.895193i
\(439\) 7.63985 13.2326i 0.364630 0.631558i −0.624087 0.781355i \(-0.714529\pi\)
0.988717 + 0.149797i \(0.0478621\pi\)
\(440\) 25.5369 + 44.2311i 1.21742 + 2.10864i
\(441\) 0 0
\(442\) 3.77082 1.60458i 0.179359 0.0763223i
\(443\) −15.1194 26.1876i −0.718346 1.24421i −0.961655 0.274263i \(-0.911566\pi\)
0.243309 0.969949i \(-0.421767\pi\)
\(444\) −1.21656 −0.0577356
\(445\) 24.9083 1.18077
\(446\) 17.6329 0.834940
\(447\) 1.48072 0.0700355
\(448\) 0 0
\(449\) −4.21110 + 7.29384i −0.198734 + 0.344218i −0.948118 0.317918i \(-0.897016\pi\)
0.749384 + 0.662136i \(0.230350\pi\)
\(450\) 11.4083 + 19.7598i 0.537794 + 0.931486i
\(451\) 22.1792 + 38.4155i 1.04438 + 1.80891i
\(452\) 4.48612 0.211009
\(453\) 8.94850 15.4993i 0.420437 0.728219i
\(454\) −35.7140 −1.67614
\(455\) 0 0
\(456\) 24.9083 1.16644
\(457\) −6.69722 + 11.5999i −0.313283 + 0.542622i −0.979071 0.203519i \(-0.934762\pi\)
0.665788 + 0.746141i \(0.268095\pi\)
\(458\) −27.0697 −1.26488
\(459\) 2.89445 + 5.01333i 0.135101 + 0.234002i
\(460\) 2.88145 + 4.99082i 0.134348 + 0.232698i
\(461\) 6.33120 10.9660i 0.294873 0.510736i −0.680082 0.733136i \(-0.738056\pi\)
0.974955 + 0.222400i \(0.0713892\pi\)
\(462\) 0 0
\(463\) −28.2111 −1.31108 −0.655541 0.755160i \(-0.727559\pi\)
−0.655541 + 0.755160i \(0.727559\pi\)
\(464\) −4.30278 −0.199751
\(465\) 7.24362 0.335915
\(466\) 31.1472 1.44287
\(467\) 7.07156 + 12.2483i 0.327233 + 0.566784i 0.981962 0.189080i \(-0.0605506\pi\)
−0.654729 + 0.755864i \(0.727217\pi\)
\(468\) 4.62632 + 3.47972i 0.213852 + 0.160850i
\(469\) 0 0
\(470\) −23.2708 40.3062i −1.07340 1.85919i
\(471\) −13.7111 + 23.7483i −0.631774 + 1.09427i
\(472\) −9.95301 17.2391i −0.458125 0.793495i
\(473\) 16.2889 28.2132i 0.748964 1.29724i
\(474\) −2.27317 −0.104410
\(475\) −4.75840 + 8.24179i −0.218330 + 0.378159i
\(476\) 0 0
\(477\) −25.4680 + 44.1119i −1.16610 + 2.01975i
\(478\) 7.55971 13.0938i 0.345773 0.598897i
\(479\) −1.13659 −0.0519319 −0.0259660 0.999663i \(-0.508266\pi\)
−0.0259660 + 0.999663i \(0.508266\pi\)
\(480\) 7.04584 12.2037i 0.321597 0.557022i
\(481\) −0.608282 + 4.99082i −0.0277353 + 0.227562i
\(482\) 2.61730 0.119215
\(483\) 0 0
\(484\) 3.61943 + 6.26904i 0.164520 + 0.284956i
\(485\) −22.3944 −1.01688
\(486\) −6.93948 + 12.0195i −0.314781 + 0.545217i
\(487\) 13.8486 + 23.9865i 0.627541 + 1.08693i 0.988044 + 0.154174i \(0.0492717\pi\)
−0.360503 + 0.932758i \(0.617395\pi\)
\(488\) 17.2887 0.782624
\(489\) −49.5930 −2.24267
\(490\) 0 0
\(491\) 6.36249 + 11.0202i 0.287135 + 0.497333i 0.973125 0.230279i \(-0.0739638\pi\)
−0.685990 + 0.727611i \(0.740630\pi\)
\(492\) 3.27502 5.67250i 0.147649 0.255736i
\(493\) 0.568293 0.984312i 0.0255946 0.0443312i
\(494\) 1.63751 13.4354i 0.0736750 0.604488i
\(495\) 45.1387 + 78.1826i 2.02884 + 3.51405i
\(496\) 1.44073 + 2.49541i 0.0646905 + 0.112047i
\(497\) 0 0
\(498\) −12.4542 + 21.5712i −0.558084 + 0.966631i
\(499\) −15.6653 27.1330i −0.701274 1.21464i −0.968020 0.250875i \(-0.919282\pi\)
0.266746 0.963767i \(-0.414052\pi\)
\(500\) −0.740358 1.28234i −0.0331098 0.0573479i
\(501\) −7.04584 12.2037i −0.314785 0.545223i
\(502\) −14.6714 25.4116i −0.654818 1.13418i
\(503\) 12.9665 22.4587i 0.578150 1.00138i −0.417542 0.908658i \(-0.637108\pi\)
0.995692 0.0927268i \(-0.0295583\pi\)
\(504\) 0 0
\(505\) 12.4542 + 21.5712i 0.554203 + 0.959908i
\(506\) −25.4222 44.0326i −1.13015 1.95749i
\(507\) 25.9731 26.9920i 1.15350 1.19876i
\(508\) −0.440285 + 0.762596i −0.0195345 + 0.0338347i
\(509\) 1.30865 2.26665i 0.0580049 0.100467i −0.835565 0.549392i \(-0.814859\pi\)
0.893570 + 0.448924i \(0.148193\pi\)
\(510\) −4.71841 8.17252i −0.208935 0.361885i
\(511\) 0 0
\(512\) 25.4222 1.12351
\(513\) 19.1194 0.844143
\(514\) −14.8435 25.7097i −0.654718 1.13400i
\(515\) −7.04584 + 12.2037i −0.310477 + 0.537761i
\(516\) −4.81049 −0.211770
\(517\) −36.6265 63.4389i −1.61083 2.79004i
\(518\) 0 0
\(519\) 68.9361 3.02596
\(520\) −24.9083 18.7350i −1.09230 0.821584i
\(521\) 14.4073 24.9541i 0.631194 1.09326i −0.356114 0.934442i \(-0.615899\pi\)
0.987308 0.158817i \(-0.0507681\pi\)
\(522\) −9.00000 −0.393919
\(523\) 4.62632 8.01302i 0.202295 0.350385i −0.746973 0.664855i \(-0.768493\pi\)
0.949267 + 0.314470i \(0.101827\pi\)
\(524\) 2.57731 4.46404i 0.112590 0.195012i
\(525\) 0 0
\(526\) −8.74306 + 15.1434i −0.381216 + 0.660285i
\(527\) −0.761141 −0.0331558
\(528\) −28.1142 + 48.6952i −1.22351 + 2.11919i
\(529\) −10.3167 17.8690i −0.448550 0.776912i
\(530\) 18.0291 31.2273i 0.783133 1.35643i
\(531\) −17.5929 30.4717i −0.763465 1.32236i
\(532\) 0 0
\(533\) −21.6333 16.2717i −0.937043 0.704804i
\(534\) 16.2250 + 28.1025i 0.702124 + 1.21611i
\(535\) 26.8055 1.15890
\(536\) 3.00000 0.129580
\(537\) 41.4769 1.78986
\(538\) −12.3982 −0.534526
\(539\) 0 0
\(540\) 2.89445 5.01333i 0.124557 0.215739i
\(541\) 9.46804 + 16.3991i 0.407063 + 0.705054i 0.994559 0.104173i \(-0.0332196\pi\)
−0.587496 + 0.809227i \(0.699886\pi\)
\(542\) 19.3377 + 33.4939i 0.830627 + 1.43869i
\(543\) 26.6611 1.14414
\(544\) −0.740358 + 1.28234i −0.0317426 + 0.0549798i
\(545\) −17.8970 −0.766623
\(546\) 0 0
\(547\) 29.0000 1.23995 0.619975 0.784621i \(-0.287143\pi\)
0.619975 + 0.784621i \(0.287143\pi\)
\(548\) 0.408327 0.707243i 0.0174429 0.0302119i
\(549\) 30.5594 1.30424
\(550\) −12.7111 22.0163i −0.542003 0.938777i
\(551\) −1.87694 3.25096i −0.0799605 0.138496i
\(552\) −28.5504 + 49.4507i −1.21519 + 2.10476i
\(553\) 0 0
\(554\) −18.5139 −0.786579
\(555\) 11.5778 0.491450
\(556\) −5.15463 −0.218605
\(557\) 16.9083 0.716429 0.358214 0.933639i \(-0.383386\pi\)
0.358214 + 0.933639i \(0.383386\pi\)
\(558\) 3.01353 + 5.21959i 0.127573 + 0.220963i
\(559\) −2.40525 + 19.7345i −0.101731 + 0.834682i
\(560\) 0 0
\(561\) −7.42641 12.8629i −0.313543 0.543073i
\(562\) 1.42221 2.46333i 0.0599921 0.103909i
\(563\) 9.51680 + 16.4836i 0.401085 + 0.694700i 0.993857 0.110671i \(-0.0352998\pi\)
−0.592772 + 0.805370i \(0.701966\pi\)
\(564\) −5.40833 + 9.36750i −0.227732 + 0.394443i
\(565\) −42.6935 −1.79613
\(566\) 2.61730 4.53330i 0.110013 0.190549i
\(567\) 0 0
\(568\) −6.00000 + 10.3923i −0.251754 + 0.436051i
\(569\) 13.6972 23.7243i 0.574218 0.994574i −0.421909 0.906638i \(-0.638640\pi\)
0.996126 0.0879356i \(-0.0280270\pi\)
\(570\) −31.1677 −1.30547
\(571\) −10.8625 + 18.8144i −0.454581 + 0.787358i −0.998664 0.0516739i \(-0.983544\pi\)
0.544083 + 0.839031i \(0.316878\pi\)
\(572\) −5.15463 3.87709i −0.215526 0.162109i
\(573\) 55.6201 2.32356
\(574\) 0 0
\(575\) −10.9083 18.8938i −0.454909 0.787925i
\(576\) 46.7527 1.94803
\(577\) −16.8525 + 29.1894i −0.701579 + 1.21517i 0.266333 + 0.963881i \(0.414188\pi\)
−0.967912 + 0.251289i \(0.919145\pi\)
\(578\) −10.5778 18.3213i −0.439978 0.762065i
\(579\) −5.23460 −0.217543
\(580\) −1.13659 −0.0471942
\(581\) 0 0
\(582\) −14.5875 25.2662i −0.604670 1.04732i
\(583\) 28.3764 49.1493i 1.17523 2.03556i
\(584\) 8.64436 14.9725i 0.357706 0.619565i
\(585\) −44.0278 33.1158i −1.82032 1.36917i
\(586\) 2.27317 + 3.93725i 0.0939038 + 0.162646i
\(587\) 14.2752 + 24.7254i 0.589200 + 1.02052i 0.994337 + 0.106269i \(0.0338904\pi\)
−0.405137 + 0.914256i \(0.632776\pi\)
\(588\) 0 0
\(589\) −1.25694 + 2.17708i −0.0517913 + 0.0897051i
\(590\) 12.4542 + 21.5712i 0.512730 + 0.888074i
\(591\) 17.1566 + 29.7162i 0.705730 + 1.22236i
\(592\) 2.30278 + 3.98852i 0.0946435 + 0.163927i
\(593\) 11.3937 + 19.7345i 0.467885 + 0.810400i 0.999327 0.0366946i \(-0.0116829\pi\)
−0.531442 + 0.847095i \(0.678350\pi\)
\(594\) −25.5369 + 44.2311i −1.04779 + 1.81483i
\(595\) 0 0
\(596\) 0.0777949 + 0.134745i 0.00318660 + 0.00551936i
\(597\) −1.25694 2.17708i −0.0514431 0.0891020i
\(598\) 24.7965 + 18.6509i 1.01400 + 0.762691i
\(599\) −3.75694 + 6.50721i −0.153504 + 0.265877i −0.932513 0.361135i \(-0.882389\pi\)
0.779009 + 0.627013i \(0.215723\pi\)
\(600\) −14.2752 + 24.7254i −0.582782 + 1.00941i
\(601\) 14.7114 + 25.4809i 0.600091 + 1.03939i 0.992807 + 0.119728i \(0.0382023\pi\)
−0.392716 + 0.919660i \(0.628464\pi\)
\(602\) 0 0
\(603\) 5.30278 0.215946
\(604\) 1.88057 0.0765193
\(605\) −34.4454 59.6611i −1.40040 2.42557i
\(606\) −16.2250 + 28.1025i −0.659095 + 1.14159i
\(607\) 20.4343 0.829404 0.414702 0.909957i \(-0.363886\pi\)
0.414702 + 0.909957i \(0.363886\pi\)
\(608\) 2.44524 + 4.23527i 0.0991674 + 0.171763i
\(609\) 0 0
\(610\) −21.6333 −0.875907
\(611\) 35.7250 + 26.8708i 1.44528 + 1.08708i
\(612\) −0.700369 + 1.21307i −0.0283107 + 0.0490356i
\(613\) 21.0917 0.851885 0.425942 0.904750i \(-0.359943\pi\)
0.425942 + 0.904750i \(0.359943\pi\)
\(614\) 9.95301 17.2391i 0.401671 0.695714i
\(615\) −31.1677 + 53.9840i −1.25680 + 2.17685i
\(616\) 0 0
\(617\) 20.9222 36.2383i 0.842296 1.45890i −0.0456524 0.998957i \(-0.514537\pi\)
0.887949 0.459943i \(-0.152130\pi\)
\(618\) −18.3583 −0.738479
\(619\) −11.2617 + 19.5058i −0.452644 + 0.784003i −0.998549 0.0538439i \(-0.982853\pi\)
0.545905 + 0.837847i \(0.316186\pi\)
\(620\) 0.380571 + 0.659168i 0.0152841 + 0.0264728i
\(621\) −21.9150 + 37.9580i −0.879420 + 1.52320i
\(622\) −11.0896 19.2077i −0.444652 0.770160i
\(623\) 0 0
\(624\) 4.15139 34.0612i 0.166189 1.36354i
\(625\) 15.3028 + 26.5052i 0.612111 + 1.06021i
\(626\) −17.2887 −0.690996
\(627\) −49.0555 −1.95909
\(628\) −2.88145 −0.114983
\(629\) −1.21656 −0.0485076
\(630\) 0 0
\(631\) −6.04584 + 10.4717i −0.240681 + 0.416872i −0.960908 0.276866i \(-0.910704\pi\)
0.720227 + 0.693738i \(0.244037\pi\)
\(632\) −0.908327 1.57327i −0.0361313 0.0625813i
\(633\) −21.6109 37.4312i −0.858956 1.48776i
\(634\) −10.6972 −0.424841
\(635\) 4.19010 7.25747i 0.166279 0.288004i
\(636\) −8.38021 −0.332297
\(637\) 0 0
\(638\) 10.0278 0.397003
\(639\) −10.6056 + 18.3694i −0.419549 + 0.726680i
\(640\) −23.3158 −0.921637
\(641\) −1.75694 3.04311i −0.0693949 0.120196i 0.829240 0.558892i \(-0.188774\pi\)
−0.898635 + 0.438697i \(0.855440\pi\)
\(642\) 17.4608 + 30.2430i 0.689122 + 1.19359i
\(643\) 4.19010 7.25747i 0.165242 0.286207i −0.771499 0.636230i \(-0.780493\pi\)
0.936741 + 0.350023i \(0.113826\pi\)
\(644\) 0 0
\(645\) 45.7805 1.80261
\(646\) 3.27502 0.128854
\(647\) −2.27317 −0.0893676 −0.0446838 0.999001i \(-0.514228\pi\)
−0.0446838 + 0.999001i \(0.514228\pi\)
\(648\) 9.63331 0.378432
\(649\) 19.6019 + 33.9515i 0.769441 + 1.33271i
\(650\) 12.3982 + 9.32544i 0.486299 + 0.365774i
\(651\) 0 0
\(652\) −2.60555 4.51295i −0.102041 0.176741i
\(653\) −10.8764 + 18.8384i −0.425625 + 0.737204i −0.996479 0.0838475i \(-0.973279\pi\)
0.570853 + 0.821052i \(0.306612\pi\)
\(654\) −11.6579 20.1921i −0.455860 0.789572i
\(655\) −24.5278 + 42.4833i −0.958379 + 1.65996i
\(656\) −24.7965 −0.968141
\(657\) 15.2797 26.4652i 0.596118 1.03251i
\(658\) 0 0
\(659\) −11.8167 + 20.4670i −0.460311 + 0.797283i −0.998976 0.0452373i \(-0.985596\pi\)
0.538665 + 0.842520i \(0.318929\pi\)
\(660\) −7.42641 + 12.8629i −0.289073 + 0.500688i
\(661\) −9.78095 −0.380435 −0.190217 0.981742i \(-0.560919\pi\)
−0.190217 + 0.981742i \(0.560919\pi\)
\(662\) 0.454163 0.786634i 0.0176516 0.0305734i
\(663\) 7.24362 + 5.44835i 0.281319 + 0.211596i
\(664\) −19.9060 −0.772504
\(665\) 0 0
\(666\) 4.81665 + 8.34269i 0.186642 + 0.323273i
\(667\) 8.60555 0.333208
\(668\) 0.740358 1.28234i 0.0286453 0.0496151i
\(669\) 19.5000 + 33.7750i 0.753914 + 1.30582i
\(670\) −3.75389 −0.145025
\(671\) −34.0491 −1.31445
\(672\) 0 0
\(673\) −6.10555 10.5751i −0.235352 0.407641i 0.724023 0.689776i \(-0.242291\pi\)
−0.959375 + 0.282135i \(0.908958\pi\)
\(674\) −4.63751 + 8.03240i −0.178630 + 0.309397i
\(675\) −10.9575 + 18.9790i −0.421755 + 0.730501i
\(676\) 3.82086 + 0.945417i 0.146956 + 0.0363622i
\(677\) −3.18559 5.51761i −0.122432 0.212059i 0.798294 0.602268i \(-0.205736\pi\)
−0.920726 + 0.390209i \(0.872403\pi\)
\(678\) −27.8100 48.1684i −1.06804 1.84990i
\(679\) 0 0
\(680\) 3.77082 6.53125i 0.144604 0.250462i
\(681\) −39.4958 68.4087i −1.51348 2.62143i
\(682\) −3.35766 5.81564i −0.128571 0.222692i
\(683\) −1.80278 3.12250i −0.0689813 0.119479i 0.829472 0.558549i \(-0.188642\pi\)
−0.898453 + 0.439069i \(0.855308\pi\)
\(684\) 2.31316 + 4.00651i 0.0884459 + 0.153193i
\(685\) −3.88596 + 6.73069i −0.148475 + 0.257166i
\(686\) 0 0
\(687\) −29.9361 51.8508i −1.14213 1.97823i
\(688\) 9.10555 + 15.7713i 0.347146 + 0.601274i
\(689\) −4.19010 + 34.3789i −0.159630 + 1.30973i
\(690\) 35.7250 61.8775i 1.36003 2.35564i
\(691\) −16.4563 + 28.5031i −0.626026 + 1.08431i 0.362315 + 0.932056i \(0.381986\pi\)
−0.988341 + 0.152254i \(0.951347\pi\)
\(692\) 3.62181 + 6.27316i 0.137681 + 0.238470i
\(693\) 0 0
\(694\) −1.02776 −0.0390131
\(695\) 49.0555 1.86078
\(696\) −5.63083 9.75289i −0.213436 0.369682i
\(697\) 3.27502 5.67250i 0.124050 0.214861i
\(698\) −31.1677 −1.17971
\(699\) 34.4454 + 59.6611i 1.30284 + 2.25659i
\(700\) 0 0
\(701\) −27.0278 −1.02082 −0.510412 0.859930i \(-0.670507\pi\)
−0.510412 + 0.859930i \(0.670507\pi\)
\(702\) 3.77082 30.9387i 0.142320 1.16771i
\(703\) −2.00902 + 3.47972i −0.0757716 + 0.131240i
\(704\) −52.0917 −1.96328
\(705\) 51.4699 89.1486i 1.93847 3.35753i
\(706\) 4.15012 7.18821i 0.156192 0.270532i
\(707\) 0 0
\(708\) 2.89445 5.01333i 0.108780 0.188413i
\(709\) 0.275019 0.0103286 0.00516428 0.999987i \(-0.498356\pi\)
0.00516428 + 0.999987i \(0.498356\pi\)
\(710\) 7.50778 13.0038i 0.281762 0.488026i
\(711\) −1.60555 2.78090i −0.0602129 0.104292i
\(712\) −12.9665 + 22.4587i −0.485942 + 0.841676i
\(713\) −2.88145 4.99082i −0.107911 0.186908i
\(714\) 0 0
\(715\) 49.0555 + 36.8975i 1.83457 + 1.37989i
\(716\) 2.17914 + 3.77439i 0.0814384 + 0.141056i
\(717\) 33.4409 1.24887
\(718\) 29.8444 1.11378
\(719\) 21.6509 0.807442 0.403721 0.914882i \(-0.367717\pi\)
0.403721 + 0.914882i \(0.367717\pi\)
\(720\) −50.4654 −1.88074
\(721\) 0 0
\(722\) −6.96804 + 12.0690i −0.259324 + 0.449162i
\(723\) 2.89445 + 5.01333i 0.107646 + 0.186448i
\(724\) 1.40074 + 2.42615i 0.0520580 + 0.0901671i
\(725\) 4.30278 0.159801
\(726\) 44.8746 77.7251i 1.66545 2.88465i
\(727\) −23.3958 −0.867701 −0.433850 0.900985i \(-0.642845\pi\)
−0.433850 + 0.900985i \(0.642845\pi\)
\(728\) 0 0
\(729\) −40.3305 −1.49372
\(730\) −10.8167 + 18.7350i −0.400342 + 0.693413i
\(731\) −4.81049 −0.177923
\(732\) 2.51388 + 4.35416i 0.0929156 + 0.160935i
\(733\) 20.0381 + 34.7070i 0.740124 + 1.28193i 0.952438 + 0.304731i \(0.0985666\pi\)
−0.212314 + 0.977201i \(0.568100\pi\)
\(734\) −18.4253 + 31.9136i −0.680091 + 1.17795i
\(735\) 0 0
\(736\) −11.2111 −0.413247
\(737\) −5.90833 −0.217636
\(738\) −51.8662 −1.90922
\(739\) −18.7889 −0.691161 −0.345580 0.938389i \(-0.612318\pi\)
−0.345580 + 0.938389i \(0.612318\pi\)
\(740\) 0.608282 + 1.05358i 0.0223609 + 0.0387302i
\(741\) 27.5459 11.7215i 1.01192 0.430600i
\(742\) 0 0
\(743\) 18.8486 + 32.6468i 0.691489 + 1.19769i 0.971350 + 0.237653i \(0.0763781\pi\)
−0.279862 + 0.960040i \(0.590289\pi\)
\(744\) −3.77082 + 6.53125i −0.138245 + 0.239447i
\(745\) −0.740358 1.28234i −0.0271246 0.0469812i
\(746\) −10.6194 + 18.3934i −0.388805 + 0.673430i
\(747\) −35.1857 −1.28738
\(748\) 0.780347 1.35160i 0.0285323 0.0494194i
\(749\) 0 0
\(750\) −9.17914 + 15.8987i −0.335175 + 0.580540i
\(751\) 2.19722 3.80570i 0.0801779 0.138872i −0.823148 0.567826i \(-0.807785\pi\)
0.903326 + 0.428954i \(0.141118\pi\)
\(752\) 40.9486 1.49324
\(753\) 32.4500 56.2050i 1.18254 2.04822i
\(754\) −5.63083 + 2.39607i −0.205063 + 0.0872597i
\(755\) −17.8970 −0.651339
\(756\) 0 0
\(757\) 22.1194 + 38.3120i 0.803944 + 1.39247i 0.917001 + 0.398884i \(0.130602\pi\)
−0.113057 + 0.993588i \(0.536064\pi\)
\(758\) −17.0917 −0.620798
\(759\) 56.2283 97.3903i 2.04096 3.53505i
\(760\) −12.4542 21.5712i −0.451760 0.782471i
\(761\) −4.28219 −0.155229 −0.0776147 0.996983i \(-0.524730\pi\)
−0.0776147 + 0.996983i \(0.524730\pi\)
\(762\) 10.9175 0.395500
\(763\) 0 0
\(764\) 2.92221 + 5.06141i 0.105722 + 0.183115i
\(765\) 6.66527 11.5446i 0.240983 0.417395i
\(766\) −12.5703 + 21.7724i −0.454184 + 0.786670i
\(767\) −19.1194 14.3808i −0.690363 0.519262i
\(768\) 10.2172 + 17.6966i 0.368680 + 0.638573i
\(769\) 15.4518 + 26.7632i 0.557205 + 0.965107i 0.997728 + 0.0673662i \(0.0214596\pi\)
−0.440523 + 0.897741i \(0.645207\pi\)
\(770\) 0 0
\(771\) 32.8305 56.8641i 1.18236 2.04791i
\(772\) −0.275019 0.476347i −0.00989816 0.0171441i
\(773\) 17.4608 + 30.2430i 0.628021 + 1.08776i 0.987948 + 0.154784i \(0.0494681\pi\)
−0.359927 + 0.932980i \(0.617199\pi\)
\(774\) 19.0458 + 32.9884i 0.684588 + 1.18574i
\(775\) −1.44073 2.49541i −0.0517524 0.0896379i
\(776\) 11.6579 20.1921i 0.418494 0.724853i
\(777\) 0 0
\(778\) −4.57779 7.92897i −0.164122 0.284267i
\(779\) −10.8167 18.7350i −0.387547 0.671251i
\(780\) 1.09660 8.99734i 0.0392644 0.322156i
\(781\) 11.8167 20.4670i 0.422833 0.732368i
\(782\) −3.75389 + 6.50192i −0.134239 + 0.232508i
\(783\) −4.32218 7.48624i −0.154462 0.267536i
\(784\) 0 0
\(785\) 27.4222 0.978740
\(786\) −63.9083 −2.27953
\(787\) −20.7785 35.9893i −0.740672 1.28288i −0.952190 0.305507i \(-0.901174\pi\)
0.211518 0.977374i \(-0.432159\pi\)
\(788\) −1.80278 + 3.12250i −0.0642212 + 0.111234i
\(789\) −38.6755 −1.37688
\(790\) 1.13659 + 1.96862i 0.0404379 + 0.0700405i
\(791\) 0 0
\(792\) −93.9916 −3.33985
\(793\) 19.1194 8.13583i 0.678951 0.288912i
\(794\) 3.75389 6.50192i 0.133220 0.230745i
\(795\) 79.7527 2.82854
\(796\) 0.132076 0.228762i 0.00468131 0.00810826i
\(797\) −17.2887 + 29.9449i −0.612398 + 1.06070i 0.378437 + 0.925627i \(0.376462\pi\)
−0.990835 + 0.135077i \(0.956872\pi\)
\(798\) 0 0
\(799\) −5.40833 + 9.36750i −0.191333 + 0.331398i
\(800\) −5.60555 −0.198186
\(801\) −22.9196 + 39.6978i −0.809823 + 1.40265i
\(802\) 9.84861 + 17.0583i 0.347767 + 0.602349i
\(803\) −17.0246 + 29.4874i −0.600784 + 1.04059i
\(804\) 0.436217 + 0.755550i 0.0153842 + 0.0266462i
\(805\) 0 0
\(806\) 3.27502 + 2.46333i 0.115358 + 0.0867672i
\(807\) −13.7111 23.7483i −0.482654 0.835981i
\(808\) −25.9331 −0.912323
\(809\) −16.0278 −0.563506 −0.281753 0.959487i \(-0.590916\pi\)
−0.281753 + 0.959487i \(0.590916\pi\)
\(810\) −12.0541 −0.423539
\(811\) 21.9150 0.769541 0.384771 0.923012i \(-0.374281\pi\)
0.384771 + 0.923012i \(0.374281\pi\)
\(812\) 0 0
\(813\) −42.7708 + 74.0812i −1.50004 + 2.59814i
\(814\) −5.36669 9.29538i −0.188102 0.325803i
\(815\) 24.7965 + 42.9488i 0.868583 + 1.50443i
\(816\) 8.30278 0.290655
\(817\) −7.94399 + 13.7594i −0.277925 + 0.481380i
\(818\) 21.0426 0.735738
\(819\) 0 0
\(820\) −6.55004 −0.228737
\(821\) −0.922205 + 1.59731i −0.0321852 + 0.0557464i −0.881669 0.471868i \(-0.843580\pi\)
0.849484 + 0.527614i \(0.176913\pi\)
\(822\) −10.1251 −0.353153
\(823\) 22.1333 + 38.3360i 0.771519 + 1.33631i 0.936731 + 0.350051i \(0.113836\pi\)
−0.165212 + 0.986258i \(0.552831\pi\)
\(824\) −7.33571 12.7058i −0.255552 0.442628i
\(825\) 28.1142 48.6952i 0.978810 1.69535i
\(826\) 0 0
\(827\) 51.7527 1.79962 0.899809 0.436283i \(-0.143705\pi\)
0.899809 + 0.436283i \(0.143705\pi\)
\(828\) −10.6056 −0.368568
\(829\) −15.6238 −0.542638 −0.271319 0.962489i \(-0.587460\pi\)
−0.271319 + 0.962489i \(0.587460\pi\)
\(830\) 24.9083 0.864581
\(831\) −20.4743 35.4626i −0.710246 1.23018i
\(832\) 29.2508 12.4470i 1.01409 0.431521i
\(833\) 0 0
\(834\) 31.9542 + 55.3462i 1.10648 + 1.91648i
\(835\) −7.04584 + 12.2037i −0.243831 + 0.422328i
\(836\) −2.57731 4.46404i −0.0891382 0.154392i
\(837\) −2.89445 + 5.01333i −0.100047 + 0.173286i
\(838\) −10.9175 −0.377140
\(839\) 11.8300 20.4901i 0.408415 0.707396i −0.586297 0.810096i \(-0.699415\pi\)
0.994712 + 0.102700i \(0.0327481\pi\)
\(840\) 0 0
\(841\) 13.6514 23.6449i 0.470738 0.815341i
\(842\) −20.2111 + 35.0067i −0.696521 + 1.20641i
\(843\) 6.29121 0.216681
\(844\) 2.27082 3.93317i 0.0781648 0.135385i
\(845\) −36.3623 8.99734i −1.25090 0.309518i
\(846\) 85.6512 2.94475
\(847\) 0 0
\(848\) 15.8625 + 27.4746i 0.544720 + 0.943483i
\(849\) 11.5778 0.397349
\(850\) −1.87694 + 3.25096i −0.0643786 + 0.111507i
\(851\) −4.60555 7.97705i −0.157876 0.273450i
\(852\) −3.48974 −0.119556
\(853\) −14.1431 −0.484251 −0.242126 0.970245i \(-0.577845\pi\)
−0.242126 + 0.970245i \(0.577845\pi\)
\(854\) 0 0
\(855\) −22.0139 38.1292i −0.752859 1.30399i
\(856\) −13.9542 + 24.1693i −0.476943 + 0.826090i
\(857\) 23.7920 41.2089i 0.812719 1.40767i −0.0982356 0.995163i \(-0.531320\pi\)
0.910954 0.412507i \(-0.135347\pi\)
\(858\) −9.67494 + 79.3808i −0.330297 + 2.71002i
\(859\) −12.3982 21.4744i −0.423023 0.732697i 0.573211 0.819408i \(-0.305698\pi\)
−0.996234 + 0.0867110i \(0.972364\pi\)
\(860\) 2.40525 + 4.16601i 0.0820183 + 0.142060i
\(861\) 0 0
\(862\) 16.8944 29.2620i 0.575427 0.996669i
\(863\) 5.90833 + 10.2335i 0.201122 + 0.348353i 0.948890 0.315607i \(-0.102208\pi\)
−0.747768 + 0.663960i \(0.768875\pi\)
\(864\) 5.63083 + 9.75289i 0.191565 + 0.331800i
\(865\) −34.4680 59.7004i −1.17195 2.02987i
\(866\) −5.45877 9.45486i −0.185496 0.321289i
\(867\) 23.3958 40.5226i 0.794562 1.37622i
\(868\) 0 0
\(869\) 1.78890 + 3.09846i 0.0606842 + 0.105108i
\(870\) 7.04584 + 12.2037i 0.238876 + 0.413746i
\(871\) 3.31767 1.41176i 0.112415 0.0478356i
\(872\) 9.31665 16.1369i 0.315502 0.546465i
\(873\) 20.6064 35.6913i 0.697421 1.20797i
\(874\) 12.3982 + 21.4744i 0.419377 + 0.726382i
\(875\) 0 0
\(876\) 5.02776 0.169872
\(877\) −38.3944 −1.29649 −0.648244 0.761432i \(-0.724496\pi\)
−0.648244 + 0.761432i \(0.724496\pi\)
\(878\) −9.95301 17.2391i −0.335898 0.581792i
\(879\) −5.02776 + 8.70833i −0.169582 + 0.293725i
\(880\) 56.2283 1.89546
\(881\) −17.7249 30.7005i −0.597168 1.03433i −0.993237 0.116105i \(-0.962959\pi\)
0.396069 0.918221i \(-0.370374\pi\)
\(882\) 0 0
\(883\) −31.6056 −1.06361 −0.531806 0.846866i \(-0.678486\pi\)
−0.531806 + 0.846866i \(0.678486\pi\)
\(884\) −0.115227 + 0.945417i −0.00387552 + 0.0317978i
\(885\) −27.5459 + 47.7109i −0.925944 + 1.60378i
\(886\) −39.3944 −1.32348
\(887\) −23.0516 + 39.9266i −0.773998 + 1.34060i 0.161358 + 0.986896i \(0.448413\pi\)
−0.935356 + 0.353708i \(0.884921\pi\)
\(888\) −6.02706 + 10.4392i −0.202255 + 0.350316i
\(889\) 0 0
\(890\) 16.2250 28.1025i 0.543863 0.941998i
\(891\) −18.9722 −0.635594
\(892\) −2.04901 + 3.54899i −0.0686059 + 0.118829i
\(893\) 17.8625 + 30.9387i 0.597745 + 1.03533i
\(894\) 0.964521 1.67060i 0.0322584 0.0558732i
\(895\) −20.7385 35.9201i −0.693211 1.20068i
\(896\) 0 0
\(897\) −8.30278 + 68.1225i −0.277222 + 2.27454i
\(898\) 5.48612 + 9.50224i 0.183074 + 0.317094i
\(899\) 1.13659 0.0379073
\(900\) −5.30278 −0.176759
\(901\) −8.38021 −0.279185
\(902\) 57.7890 1.92416
\(903\) 0 0
\(904\) 22.2250 38.4948i 0.739192 1.28032i
\(905\) −13.3305 23.0892i −0.443122 0.767510i
\(906\) −11.6579 20.1921i −0.387307 0.670836i
\(907\) 18.8444 0.625718 0.312859 0.949800i \(-0.398713\pi\)
0.312859 + 0.949800i \(0.398713\pi\)
\(908\) 4.15012 7.18821i 0.137726 0.238549i
\(909\) −45.8391 −1.52039
\(910\) 0 0
\(911\) −10.9361 −0.362329 −0.181164 0.983453i \(-0.557987\pi\)
−0.181164 + 0.983453i \(0.557987\pi\)
\(912\) 13.7111 23.7483i 0.454020 0.786386i
\(913\) 39.2038 1.29746
\(914\) 8.72498 + 15.1121i 0.288597 + 0.499864i
\(915\) −23.9241 41.4377i −0.790905 1.36989i
\(916\) 3.14561 5.44835i 0.103934 0.180019i
\(917\) 0 0
\(918\) 7.54163 0.248911
\(919\) −11.4500 −0.377699 −0.188850 0.982006i \(-0.560476\pi\)
−0.188850 + 0.982006i \(0.560476\pi\)
\(920\) 57.1008 1.88256
\(921\) 44.0278 1.45076
\(922\) −8.24813 14.2862i −0.271638 0.470490i
\(923\) −1.74487 + 14.3163i −0.0574330 + 0.471226i
\(924\) 0 0
\(925\) −2.30278 3.98852i −0.0757148 0.131142i
\(926\) −18.3764 + 31.8288i −0.603885 + 1.04596i
\(927\) −12.9665 22.4587i −0.425877 0.737641i
\(928\) 1.10555 1.91487i 0.0362915 0.0628587i
\(929\) 8.38021 0.274946 0.137473 0.990506i \(-0.456102\pi\)
0.137473 + 0.990506i \(0.456102\pi\)
\(930\) 4.71841 8.17252i 0.154723 0.267988i
\(931\) 0 0
\(932\) −3.61943 + 6.26904i −0.118558 + 0.205349i
\(933\) 24.5278 42.4833i 0.803003 1.39084i
\(934\) 18.4253 0.602895
\(935\) −7.42641 + 12.8629i −0.242869 + 0.420662i
\(936\) 52.7786 22.4587i 1.72512 0.734086i
\(937\) 46.4474 1.51737 0.758685 0.651458i \(-0.225842\pi\)
0.758685 + 0.651458i \(0.225842\pi\)
\(938\) 0 0
\(939\) −19.1194 33.1158i −0.623939 1.08069i
\(940\) 10.8167 0.352800
\(941\) −22.3513 + 38.7135i −0.728630 + 1.26202i 0.228832 + 0.973466i \(0.426509\pi\)
−0.957462 + 0.288559i \(0.906824\pi\)
\(942\) 17.8625 + 30.9387i 0.581991 + 1.00804i
\(943\) 49.5930 1.61497
\(944\) −21.9150 −0.713274
\(945\) 0 0
\(946\) −21.2208 36.7555i −0.689947 1.19502i
\(947\) −26.5597 + 46.0028i −0.863075 + 1.49489i 0.00587143 + 0.999983i \(0.498131\pi\)
−0.868946 + 0.494907i \(0.835202\pi\)
\(948\) 0.264152 0.457524i 0.00857925 0.0148597i
\(949\) 2.51388 20.6258i 0.0816039 0.669543i
\(950\) 6.19912 + 10.7372i 0.201126 + 0.348361i
\(951\) −11.8300 20.4901i −0.383613 0.664437i
\(952\) 0 0
\(953\) −20.8028 + 36.0315i −0.673868 + 1.16717i 0.302930 + 0.953013i \(0.402035\pi\)
−0.976798 + 0.214161i \(0.931298\pi\)
\(954\) 33.1791 + 57.4680i 1.07421 + 1.86059i
\(955\) −27.8100 48.1684i −0.899911 1.55869i
\(956\) 1.75694 + 3.04311i 0.0568235 + 0.0984211i
\(957\) 11.0896 + 19.2077i 0.358476 + 0.620898i
\(958\) −0.740358 + 1.28234i −0.0239199 + 0.0414305i
\(959\) 0 0
\(960\) −36.6013 63.3954i −1.18130 2.04608i
\(961\) 15.1194 + 26.1876i 0.487724 + 0.844762i
\(962\) 5.23460 + 3.93725i 0.168770 + 0.126942i
\(963\) −24.6653 + 42.7215i −0.794827 + 1.37668i
\(964\) −0.304141 + 0.526788i −0.00979573 + 0.0169667i
\(965\) 2.61730 + 4.53330i 0.0842539 + 0.145932i
\(966\) 0 0
\(967\) 22.4500 0.721942 0.360971 0.932577i \(-0.382445\pi\)
0.360971 + 0.932577i \(0.382445\pi\)
\(968\) 71.7250 2.30533
\(969\) 3.62181 + 6.27316i 0.116349 + 0.201523i
\(970\) −14.5875 + 25.2662i −0.468375 + 0.811250i
\(971\) 10.1251 0.324929 0.162465 0.986714i \(-0.448056\pi\)
0.162465 + 0.986714i \(0.448056\pi\)
\(972\) −1.61279 2.79344i −0.0517303 0.0895996i
\(973\) 0 0
\(974\) 36.0833 1.15618
\(975\) −4.15139 + 34.0612i −0.132951 + 1.09083i
\(976\) 9.51680 16.4836i 0.304625 0.527626i
\(977\) −40.0278 −1.28060 −0.640301 0.768124i \(-0.721190\pi\)
−0.640301 + 0.768124i \(0.721190\pi\)
\(978\) −32.3043 + 55.9526i −1.03298 + 1.78917i
\(979\) 25.5369 44.2311i 0.816161 1.41363i
\(980\) 0 0
\(981\) 16.4680 28.5235i 0.525784 0.910685i
\(982\) 16.5778 0.529019
\(983\) 6.50327 11.2640i 0.207422 0.359265i −0.743480 0.668758i \(-0.766826\pi\)
0.950902 + 0.309493i \(0.100159\pi\)
\(984\) −32.4500 56.2050i −1.03447 1.79175i
\(985\) 17.1566 29.7162i 0.546656 0.946836i
\(986\) −0.740358 1.28234i −0.0235778 0.0408380i
\(987\) 0 0
\(988\) 2.51388 + 1.89083i 0.0799771 + 0.0601554i
\(989\) −18.2111 31.5426i −0.579079 1.00299i
\(990\) 117.611 3.73793
\(991\) −46.3305 −1.47174 −0.735869 0.677124i \(-0.763226\pi\)
−0.735869 + 0.677124i \(0.763226\pi\)
\(992\) −1.48072 −0.0470128
\(993\) 2.00902 0.0637543
\(994\) 0 0
\(995\) −1.25694 + 2.17708i −0.0398476 + 0.0690182i
\(996\) −2.89445 5.01333i −0.0917141 0.158854i
\(997\) 22.0871 + 38.2560i 0.699506 + 1.21158i 0.968638 + 0.248476i \(0.0799298\pi\)
−0.269132 + 0.963103i \(0.586737\pi\)
\(998\) −40.8167 −1.29203
\(999\) −4.62632 + 8.01302i −0.146370 + 0.253521i
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 637.2.g.i.263.4 8
7.2 even 3 637.2.h.j.471.1 8
7.3 odd 6 637.2.f.h.393.4 yes 8
7.4 even 3 637.2.f.h.393.3 yes 8
7.5 odd 6 637.2.h.j.471.2 8
7.6 odd 2 inner 637.2.g.i.263.3 8
13.9 even 3 637.2.h.j.165.1 8
91.3 odd 6 8281.2.a.bu.1.1 4
91.9 even 3 inner 637.2.g.i.373.4 8
91.10 odd 6 8281.2.a.bo.1.3 4
91.48 odd 6 637.2.h.j.165.2 8
91.61 odd 6 inner 637.2.g.i.373.3 8
91.74 even 3 637.2.f.h.295.3 8
91.81 even 3 8281.2.a.bu.1.2 4
91.87 odd 6 637.2.f.h.295.4 yes 8
91.88 even 6 8281.2.a.bo.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.h.295.3 8 91.74 even 3
637.2.f.h.295.4 yes 8 91.87 odd 6
637.2.f.h.393.3 yes 8 7.4 even 3
637.2.f.h.393.4 yes 8 7.3 odd 6
637.2.g.i.263.3 8 7.6 odd 2 inner
637.2.g.i.263.4 8 1.1 even 1 trivial
637.2.g.i.373.3 8 91.61 odd 6 inner
637.2.g.i.373.4 8 91.9 even 3 inner
637.2.h.j.165.1 8 13.9 even 3
637.2.h.j.165.2 8 91.48 odd 6
637.2.h.j.471.1 8 7.2 even 3
637.2.h.j.471.2 8 7.5 odd 6
8281.2.a.bo.1.3 4 91.10 odd 6
8281.2.a.bo.1.4 4 91.88 even 6
8281.2.a.bu.1.1 4 91.3 odd 6
8281.2.a.bu.1.2 4 91.81 even 3