Properties

Label 380.2.f.a.151.7
Level $380$
Weight $2$
Character 380.151
Analytic conductor $3.034$
Analytic rank $0$
Dimension $20$
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] = [380,2,Mod(151,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.f (of order \(2\), degree \(1\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{18} + x^{16} - 9x^{14} + 20x^{12} - 24x^{10} + 80x^{8} - 144x^{6} + 64x^{4} - 256x^{2} + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.7
Root \(0.611950 - 1.27496i\) of defining polynomial
Character \(\chi\) \(=\) 380.151
Dual form 380.2.f.a.151.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.611950 - 1.27496i) q^{2} +3.21061 q^{3} +(-1.25103 + 1.56042i) q^{4} -1.00000 q^{5} +(-1.96474 - 4.09340i) q^{6} -3.02772i q^{7} +(2.75504 + 0.640115i) q^{8} +7.30804 q^{9} +O(q^{10})\) \(q+(-0.611950 - 1.27496i) q^{2} +3.21061 q^{3} +(-1.25103 + 1.56042i) q^{4} -1.00000 q^{5} +(-1.96474 - 4.09340i) q^{6} -3.02772i q^{7} +(2.75504 + 0.640115i) q^{8} +7.30804 q^{9} +(0.611950 + 1.27496i) q^{10} +0.488592i q^{11} +(-4.01659 + 5.00991i) q^{12} -0.943033i q^{13} +(-3.86021 + 1.85281i) q^{14} -3.21061 q^{15} +(-0.869829 - 3.90428i) q^{16} +3.16706 q^{17} +(-4.47216 - 9.31745i) q^{18} +(-2.58768 + 3.50769i) q^{19} +(1.25103 - 1.56042i) q^{20} -9.72083i q^{21} +(0.622934 - 0.298994i) q^{22} -7.08696i q^{23} +(8.84538 + 2.05516i) q^{24} +1.00000 q^{25} +(-1.20233 + 0.577089i) q^{26} +13.8315 q^{27} +(4.72451 + 3.78777i) q^{28} +8.80545i q^{29} +(1.96474 + 4.09340i) q^{30} -3.66325 q^{31} +(-4.44550 + 3.49822i) q^{32} +1.56868i q^{33} +(-1.93809 - 4.03787i) q^{34} +3.02772i q^{35} +(-9.14261 + 11.4036i) q^{36} +1.11751i q^{37} +(6.05569 + 1.15265i) q^{38} -3.02772i q^{39} +(-2.75504 - 0.640115i) q^{40} +1.56868i q^{41} +(-12.3936 + 5.94866i) q^{42} -3.58788i q^{43} +(-0.762409 - 0.611245i) q^{44} -7.30804 q^{45} +(-9.03557 + 4.33687i) q^{46} -0.471362i q^{47} +(-2.79269 - 12.5351i) q^{48} -2.16706 q^{49} +(-0.611950 - 1.27496i) q^{50} +10.1682 q^{51} +(1.47153 + 1.17977i) q^{52} +12.4070i q^{53} +(-8.46417 - 17.6345i) q^{54} -0.488592i q^{55} +(1.93809 - 8.34148i) q^{56} +(-8.30804 + 11.2618i) q^{57} +(11.2266 - 5.38850i) q^{58} -8.65611 q^{59} +(4.01659 - 5.00991i) q^{60} -8.62030 q^{61} +(2.24173 + 4.67049i) q^{62} -22.1267i q^{63} +(7.18051 + 3.52709i) q^{64} +0.943033i q^{65} +(2.00000 - 0.959954i) q^{66} -6.59410 q^{67} +(-3.96210 + 4.94195i) q^{68} -22.7535i q^{69} +(3.86021 - 1.85281i) q^{70} +13.9287 q^{71} +(20.1340 + 4.67799i) q^{72} -11.6960 q^{73} +(1.42477 - 0.683858i) q^{74} +3.21061 q^{75} +(-2.23620 - 8.42611i) q^{76} +1.47932 q^{77} +(-3.86021 + 1.85281i) q^{78} -10.5317 q^{79} +(0.869829 + 3.90428i) q^{80} +22.4834 q^{81} +(2.00000 - 0.959954i) q^{82} +18.0674i q^{83} +(15.1686 + 12.1611i) q^{84} -3.16706 q^{85} +(-4.57439 + 2.19560i) q^{86} +28.2709i q^{87} +(-0.312755 + 1.34609i) q^{88} +9.83998i q^{89} +(4.47216 + 9.31745i) q^{90} -2.85524 q^{91} +(11.0586 + 8.86602i) q^{92} -11.7613 q^{93} +(-0.600967 + 0.288450i) q^{94} +(2.58768 - 3.50769i) q^{95} +(-14.2728 + 11.2314i) q^{96} -1.71549i q^{97} +(1.32614 + 2.76291i) q^{98} +3.57065i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9} - 2 q^{16} + 20 q^{17} - 2 q^{20} + 26 q^{24} + 20 q^{25} - 14 q^{26} - 14 q^{28} + 6 q^{30} - 4 q^{36} + 10 q^{38} - 42 q^{42} + 8 q^{44} - 16 q^{45} - 30 q^{54} - 36 q^{57} + 62 q^{58} - 24 q^{61} - 40 q^{62} + 50 q^{64} + 40 q^{66} + 6 q^{68} - 36 q^{73} - 36 q^{74} - 28 q^{76} - 32 q^{77} + 2 q^{80} + 60 q^{81} + 40 q^{82} - 20 q^{85} + 26 q^{92} - 122 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.611950 1.27496i −0.432714 0.901531i
\(3\) 3.21061 1.85365 0.926825 0.375495i \(-0.122527\pi\)
0.926825 + 0.375495i \(0.122527\pi\)
\(4\) −1.25103 + 1.56042i −0.625517 + 0.780211i
\(5\) −1.00000 −0.447214
\(6\) −1.96474 4.09340i −0.802100 1.67112i
\(7\) 3.02772i 1.14437i −0.820125 0.572185i \(-0.806096\pi\)
0.820125 0.572185i \(-0.193904\pi\)
\(8\) 2.75504 + 0.640115i 0.974054 + 0.226315i
\(9\) 7.30804 2.43601
\(10\) 0.611950 + 1.27496i 0.193516 + 0.403177i
\(11\) 0.488592i 0.147316i 0.997284 + 0.0736580i \(0.0234673\pi\)
−0.997284 + 0.0736580i \(0.976533\pi\)
\(12\) −4.01659 + 5.00991i −1.15949 + 1.44624i
\(13\) 0.943033i 0.261550i −0.991412 0.130775i \(-0.958253\pi\)
0.991412 0.130775i \(-0.0417466\pi\)
\(14\) −3.86021 + 1.85281i −1.03168 + 0.495185i
\(15\) −3.21061 −0.828977
\(16\) −0.869829 3.90428i −0.217457 0.976070i
\(17\) 3.16706 0.768126 0.384063 0.923307i \(-0.374525\pi\)
0.384063 + 0.923307i \(0.374525\pi\)
\(18\) −4.47216 9.31745i −1.05410 2.19614i
\(19\) −2.58768 + 3.50769i −0.593655 + 0.804720i
\(20\) 1.25103 1.56042i 0.279740 0.348921i
\(21\) 9.72083i 2.12126i
\(22\) 0.622934 0.298994i 0.132810 0.0637457i
\(23\) 7.08696i 1.47773i −0.673852 0.738866i \(-0.735361\pi\)
0.673852 0.738866i \(-0.264639\pi\)
\(24\) 8.84538 + 2.05516i 1.80555 + 0.419508i
\(25\) 1.00000 0.200000
\(26\) −1.20233 + 0.577089i −0.235796 + 0.113177i
\(27\) 13.8315 2.66187
\(28\) 4.72451 + 3.78777i 0.892849 + 0.715822i
\(29\) 8.80545i 1.63513i 0.575835 + 0.817566i \(0.304677\pi\)
−0.575835 + 0.817566i \(0.695323\pi\)
\(30\) 1.96474 + 4.09340i 0.358710 + 0.747349i
\(31\) −3.66325 −0.657939 −0.328969 0.944341i \(-0.606701\pi\)
−0.328969 + 0.944341i \(0.606701\pi\)
\(32\) −4.44550 + 3.49822i −0.785861 + 0.618404i
\(33\) 1.56868i 0.273072i
\(34\) −1.93809 4.03787i −0.332379 0.692489i
\(35\) 3.02772i 0.511777i
\(36\) −9.14261 + 11.4036i −1.52377 + 1.90060i
\(37\) 1.11751i 0.183717i 0.995772 + 0.0918584i \(0.0292807\pi\)
−0.995772 + 0.0918584i \(0.970719\pi\)
\(38\) 6.05569 + 1.15265i 0.982363 + 0.186984i
\(39\) 3.02772i 0.484823i
\(40\) −2.75504 0.640115i −0.435610 0.101211i
\(41\) 1.56868i 0.244987i 0.992469 + 0.122493i \(0.0390890\pi\)
−0.992469 + 0.122493i \(0.960911\pi\)
\(42\) −12.3936 + 5.94866i −1.91238 + 0.917899i
\(43\) 3.58788i 0.547147i −0.961851 0.273573i \(-0.911794\pi\)
0.961851 0.273573i \(-0.0882056\pi\)
\(44\) −0.762409 0.611245i −0.114937 0.0921486i
\(45\) −7.30804 −1.08942
\(46\) −9.03557 + 4.33687i −1.33222 + 0.639436i
\(47\) 0.471362i 0.0687552i −0.999409 0.0343776i \(-0.989055\pi\)
0.999409 0.0343776i \(-0.0109449\pi\)
\(48\) −2.79269 12.5351i −0.403090 1.80929i
\(49\) −2.16706 −0.309581
\(50\) −0.611950 1.27496i −0.0865428 0.180306i
\(51\) 10.1682 1.42384
\(52\) 1.47153 + 1.17977i 0.204064 + 0.163604i
\(53\) 12.4070i 1.70423i 0.523351 + 0.852117i \(0.324682\pi\)
−0.523351 + 0.852117i \(0.675318\pi\)
\(54\) −8.46417 17.6345i −1.15183 2.39976i
\(55\) 0.488592i 0.0658817i
\(56\) 1.93809 8.34148i 0.258988 1.11468i
\(57\) −8.30804 + 11.2618i −1.10043 + 1.49167i
\(58\) 11.2266 5.38850i 1.47412 0.707545i
\(59\) −8.65611 −1.12693 −0.563465 0.826140i \(-0.690532\pi\)
−0.563465 + 0.826140i \(0.690532\pi\)
\(60\) 4.01659 5.00991i 0.518539 0.646777i
\(61\) −8.62030 −1.10372 −0.551858 0.833938i \(-0.686081\pi\)
−0.551858 + 0.833938i \(0.686081\pi\)
\(62\) 2.24173 + 4.67049i 0.284699 + 0.593152i
\(63\) 22.1267i 2.78770i
\(64\) 7.18051 + 3.52709i 0.897563 + 0.440886i
\(65\) 0.943033i 0.116969i
\(66\) 2.00000 0.959954i 0.246183 0.118162i
\(67\) −6.59410 −0.805598 −0.402799 0.915288i \(-0.631963\pi\)
−0.402799 + 0.915288i \(0.631963\pi\)
\(68\) −3.96210 + 4.94195i −0.480476 + 0.599300i
\(69\) 22.7535i 2.73920i
\(70\) 3.86021 1.85281i 0.461383 0.221453i
\(71\) 13.9287 1.65304 0.826518 0.562911i \(-0.190318\pi\)
0.826518 + 0.562911i \(0.190318\pi\)
\(72\) 20.1340 + 4.67799i 2.37281 + 0.551306i
\(73\) −11.6960 −1.36892 −0.684458 0.729053i \(-0.739961\pi\)
−0.684458 + 0.729053i \(0.739961\pi\)
\(74\) 1.42477 0.683858i 0.165626 0.0794969i
\(75\) 3.21061 0.370730
\(76\) −2.23620 8.42611i −0.256510 0.966542i
\(77\) 1.47932 0.168584
\(78\) −3.86021 + 1.85281i −0.437083 + 0.209790i
\(79\) −10.5317 −1.18491 −0.592456 0.805603i \(-0.701841\pi\)
−0.592456 + 0.805603i \(0.701841\pi\)
\(80\) 0.869829 + 3.90428i 0.0972499 + 0.436512i
\(81\) 22.4834 2.49815
\(82\) 2.00000 0.959954i 0.220863 0.106009i
\(83\) 18.0674i 1.98316i 0.129499 + 0.991580i \(0.458663\pi\)
−0.129499 + 0.991580i \(0.541337\pi\)
\(84\) 15.1686 + 12.1611i 1.65503 + 1.32688i
\(85\) −3.16706 −0.343516
\(86\) −4.57439 + 2.19560i −0.493270 + 0.236758i
\(87\) 28.2709i 3.03096i
\(88\) −0.312755 + 1.34609i −0.0333398 + 0.143494i
\(89\) 9.83998i 1.04304i 0.853240 + 0.521518i \(0.174634\pi\)
−0.853240 + 0.521518i \(0.825366\pi\)
\(90\) 4.47216 + 9.31745i 0.471407 + 0.982145i
\(91\) −2.85524 −0.299310
\(92\) 11.0586 + 8.86602i 1.15294 + 0.924347i
\(93\) −11.7613 −1.21959
\(94\) −0.600967 + 0.288450i −0.0619850 + 0.0297514i
\(95\) 2.58768 3.50769i 0.265490 0.359882i
\(96\) −14.2728 + 11.2314i −1.45671 + 1.14630i
\(97\) 1.71549i 0.174182i −0.996200 0.0870910i \(-0.972243\pi\)
0.996200 0.0870910i \(-0.0277571\pi\)
\(98\) 1.32614 + 2.76291i 0.133960 + 0.279096i
\(99\) 3.57065i 0.358864i
\(100\) −1.25103 + 1.56042i −0.125103 + 0.156042i
\(101\) 9.47511 0.942808 0.471404 0.881917i \(-0.343747\pi\)
0.471404 + 0.881917i \(0.343747\pi\)
\(102\) −6.22244 12.9640i −0.616114 1.28363i
\(103\) 5.44549 0.536560 0.268280 0.963341i \(-0.413545\pi\)
0.268280 + 0.963341i \(0.413545\pi\)
\(104\) 0.603649 2.59810i 0.0591927 0.254764i
\(105\) 9.72083i 0.948656i
\(106\) 15.8184 7.59248i 1.53642 0.737446i
\(107\) 3.47686 0.336121 0.168060 0.985777i \(-0.446250\pi\)
0.168060 + 0.985777i \(0.446250\pi\)
\(108\) −17.3036 + 21.5829i −1.66504 + 2.07682i
\(109\) 12.5538i 1.20244i −0.799084 0.601219i \(-0.794682\pi\)
0.799084 0.601219i \(-0.205318\pi\)
\(110\) −0.622934 + 0.298994i −0.0593944 + 0.0285079i
\(111\) 3.58788i 0.340546i
\(112\) −11.8210 + 2.63360i −1.11698 + 0.248851i
\(113\) 10.0974i 0.949886i 0.880016 + 0.474943i \(0.157531\pi\)
−0.880016 + 0.474943i \(0.842469\pi\)
\(114\) 19.4425 + 3.70071i 1.82096 + 0.346603i
\(115\) 7.08696i 0.660862i
\(116\) −13.7402 11.0159i −1.27575 1.02280i
\(117\) 6.89173i 0.637141i
\(118\) 5.29711 + 11.0362i 0.487638 + 1.01596i
\(119\) 9.58897i 0.879019i
\(120\) −8.84538 2.05516i −0.807469 0.187610i
\(121\) 10.7613 0.978298
\(122\) 5.27519 + 10.9905i 0.477594 + 0.995034i
\(123\) 5.03643i 0.454119i
\(124\) 4.58285 5.71621i 0.411552 0.513331i
\(125\) −1.00000 −0.0894427
\(126\) −28.2106 + 13.5404i −2.51320 + 1.20628i
\(127\) −4.63898 −0.411643 −0.205822 0.978590i \(-0.565987\pi\)
−0.205822 + 0.978590i \(0.565987\pi\)
\(128\) 0.102771 11.3132i 0.00908376 0.999959i
\(129\) 11.5193i 1.01422i
\(130\) 1.20233 0.577089i 0.105451 0.0506141i
\(131\) 21.6381i 1.89053i −0.326306 0.945264i \(-0.605804\pi\)
0.326306 0.945264i \(-0.394196\pi\)
\(132\) −2.44780 1.96247i −0.213054 0.170811i
\(133\) 10.6203 + 7.83476i 0.920897 + 0.679360i
\(134\) 4.03526 + 8.40720i 0.348594 + 0.726272i
\(135\) −13.8315 −1.19042
\(136\) 8.72539 + 2.02728i 0.748196 + 0.173838i
\(137\) 12.5508 1.07229 0.536145 0.844126i \(-0.319880\pi\)
0.536145 + 0.844126i \(0.319880\pi\)
\(138\) −29.0097 + 13.9240i −2.46947 + 1.18529i
\(139\) 5.97381i 0.506692i −0.967376 0.253346i \(-0.918469\pi\)
0.967376 0.253346i \(-0.0815310\pi\)
\(140\) −4.72451 3.78777i −0.399294 0.320125i
\(141\) 1.51336i 0.127448i
\(142\) −8.52369 17.7585i −0.715292 1.49026i
\(143\) 0.460758 0.0385305
\(144\) −6.35675 28.5326i −0.529729 2.37772i
\(145\) 8.80545i 0.731253i
\(146\) 7.15738 + 14.9119i 0.592349 + 1.23412i
\(147\) −6.95761 −0.573854
\(148\) −1.74378 1.39804i −0.143338 0.114918i
\(149\) −20.3382 −1.66617 −0.833085 0.553146i \(-0.813427\pi\)
−0.833085 + 0.553146i \(0.813427\pi\)
\(150\) −1.96474 4.09340i −0.160420 0.334224i
\(151\) −1.35251 −0.110066 −0.0550330 0.998485i \(-0.517526\pi\)
−0.0550330 + 0.998485i \(0.517526\pi\)
\(152\) −9.37449 + 8.00743i −0.760372 + 0.649488i
\(153\) 23.1450 1.87117
\(154\) −0.905268 1.88607i −0.0729486 0.151984i
\(155\) 3.66325 0.294239
\(156\) 4.72451 + 3.78777i 0.378264 + 0.303265i
\(157\) 6.52895 0.521067 0.260534 0.965465i \(-0.416102\pi\)
0.260534 + 0.965465i \(0.416102\pi\)
\(158\) 6.44489 + 13.4275i 0.512728 + 1.06823i
\(159\) 39.8341i 3.15905i
\(160\) 4.44550 3.49822i 0.351448 0.276559i
\(161\) −21.4573 −1.69107
\(162\) −13.7587 28.6654i −1.08099 2.25216i
\(163\) 9.64331i 0.755322i −0.925944 0.377661i \(-0.876728\pi\)
0.925944 0.377661i \(-0.123272\pi\)
\(164\) −2.44780 1.96247i −0.191141 0.153243i
\(165\) 1.56868i 0.122122i
\(166\) 23.0352 11.0564i 1.78788 0.858141i
\(167\) 0.429732 0.0332536 0.0166268 0.999862i \(-0.494707\pi\)
0.0166268 + 0.999862i \(0.494707\pi\)
\(168\) 6.22244 26.7813i 0.480072 2.06622i
\(169\) 12.1107 0.931591
\(170\) 1.93809 + 4.03787i 0.148644 + 0.309691i
\(171\) −18.9109 + 25.6344i −1.44615 + 1.96031i
\(172\) 5.59860 + 4.48856i 0.426890 + 0.342249i
\(173\) 17.1044i 1.30042i −0.759753 0.650212i \(-0.774680\pi\)
0.759753 0.650212i \(-0.225320\pi\)
\(174\) 36.0442 17.3004i 2.73251 1.31154i
\(175\) 3.02772i 0.228874i
\(176\) 1.90760 0.424991i 0.143791 0.0320349i
\(177\) −27.7914 −2.08893
\(178\) 12.5456 6.02158i 0.940330 0.451337i
\(179\) 11.9559 0.893622 0.446811 0.894628i \(-0.352560\pi\)
0.446811 + 0.894628i \(0.352560\pi\)
\(180\) 9.14261 11.4036i 0.681450 0.849976i
\(181\) 17.8046i 1.32341i 0.749765 + 0.661704i \(0.230166\pi\)
−0.749765 + 0.661704i \(0.769834\pi\)
\(182\) 1.74726 + 3.64031i 0.129516 + 0.269837i
\(183\) −27.6765 −2.04590
\(184\) 4.53647 19.5249i 0.334433 1.43939i
\(185\) 1.11751i 0.0821606i
\(186\) 7.19732 + 14.9951i 0.527733 + 1.09950i
\(187\) 1.54740i 0.113157i
\(188\) 0.735524 + 0.589690i 0.0536436 + 0.0430076i
\(189\) 41.8778i 3.04616i
\(190\) −6.05569 1.15265i −0.439326 0.0836220i
\(191\) 0.848579i 0.0614010i 0.999529 + 0.0307005i \(0.00977381\pi\)
−0.999529 + 0.0307005i \(0.990226\pi\)
\(192\) 23.0538 + 11.3241i 1.66377 + 0.817247i
\(193\) 23.0432i 1.65869i −0.558739 0.829343i \(-0.688715\pi\)
0.558739 0.829343i \(-0.311285\pi\)
\(194\) −2.18718 + 1.04980i −0.157030 + 0.0753710i
\(195\) 3.02772i 0.216819i
\(196\) 2.71107 3.38153i 0.193648 0.241538i
\(197\) 1.14519 0.0815914 0.0407957 0.999168i \(-0.487011\pi\)
0.0407957 + 0.999168i \(0.487011\pi\)
\(198\) 4.55243 2.18506i 0.323527 0.155285i
\(199\) 1.56194i 0.110723i 0.998466 + 0.0553615i \(0.0176311\pi\)
−0.998466 + 0.0553615i \(0.982369\pi\)
\(200\) 2.75504 + 0.640115i 0.194811 + 0.0452629i
\(201\) −21.1711 −1.49330
\(202\) −5.79829 12.0804i −0.407967 0.849971i
\(203\) 26.6604 1.87119
\(204\) −12.7208 + 15.8667i −0.890633 + 1.11089i
\(205\) 1.56868i 0.109561i
\(206\) −3.33237 6.94277i −0.232177 0.483726i
\(207\) 51.7918i 3.59978i
\(208\) −3.68187 + 0.820278i −0.255291 + 0.0568760i
\(209\) −1.71383 1.26432i −0.118548 0.0874548i
\(210\) 12.3936 5.94866i 0.855243 0.410497i
\(211\) −9.54786 −0.657302 −0.328651 0.944451i \(-0.606594\pi\)
−0.328651 + 0.944451i \(0.606594\pi\)
\(212\) −19.3602 15.5216i −1.32966 1.06603i
\(213\) 44.7198 3.06415
\(214\) −2.12767 4.43285i −0.145444 0.303023i
\(215\) 3.58788i 0.244691i
\(216\) 38.1063 + 8.85373i 2.59280 + 0.602420i
\(217\) 11.0913i 0.752925i
\(218\) −16.0056 + 7.68232i −1.08404 + 0.520312i
\(219\) −37.5514 −2.53749
\(220\) 0.762409 + 0.611245i 0.0514016 + 0.0412101i
\(221\) 2.98665i 0.200904i
\(222\) 4.57439 2.19560i 0.307013 0.147359i
\(223\) −8.65072 −0.579295 −0.289647 0.957133i \(-0.593538\pi\)
−0.289647 + 0.957133i \(0.593538\pi\)
\(224\) 10.5916 + 13.4597i 0.707682 + 0.899314i
\(225\) 7.30804 0.487203
\(226\) 12.8738 6.17913i 0.856352 0.411029i
\(227\) −2.31886 −0.153908 −0.0769541 0.997035i \(-0.524519\pi\)
−0.0769541 + 0.997035i \(0.524519\pi\)
\(228\) −7.17959 27.0530i −0.475480 1.79163i
\(229\) −16.7074 −1.10406 −0.552029 0.833825i \(-0.686146\pi\)
−0.552029 + 0.833825i \(0.686146\pi\)
\(230\) 9.03557 4.33687i 0.595788 0.285964i
\(231\) 4.74952 0.312495
\(232\) −5.63650 + 24.2594i −0.370054 + 1.59271i
\(233\) −20.0432 −1.31308 −0.656538 0.754293i \(-0.727980\pi\)
−0.656538 + 0.754293i \(0.727980\pi\)
\(234\) −8.78666 + 4.21740i −0.574402 + 0.275700i
\(235\) 0.471362i 0.0307483i
\(236\) 10.8291 13.5072i 0.704913 0.879242i
\(237\) −33.8133 −2.19641
\(238\) −12.2255 + 5.86797i −0.792463 + 0.380364i
\(239\) 19.1162i 1.23652i −0.785972 0.618262i \(-0.787837\pi\)
0.785972 0.618262i \(-0.212163\pi\)
\(240\) 2.79269 + 12.5351i 0.180267 + 0.809139i
\(241\) 10.4803i 0.675093i −0.941309 0.337546i \(-0.890403\pi\)
0.941309 0.337546i \(-0.109597\pi\)
\(242\) −6.58537 13.7202i −0.423323 0.881966i
\(243\) 30.6910 1.96883
\(244\) 10.7843 13.4513i 0.690393 0.861131i
\(245\) 2.16706 0.138449
\(246\) 6.42123 3.08204i 0.409403 0.196504i
\(247\) 3.30787 + 2.44027i 0.210475 + 0.155271i
\(248\) −10.0924 2.34490i −0.640868 0.148901i
\(249\) 58.0076i 3.67608i
\(250\) 0.611950 + 1.27496i 0.0387031 + 0.0806354i
\(251\) 25.7318i 1.62418i −0.583535 0.812088i \(-0.698331\pi\)
0.583535 0.812088i \(-0.301669\pi\)
\(252\) 34.5269 + 27.6812i 2.17499 + 1.74375i
\(253\) 3.46263 0.217694
\(254\) 2.83883 + 5.91451i 0.178124 + 0.371109i
\(255\) −10.1682 −0.636759
\(256\) −14.4868 + 6.79211i −0.905425 + 0.424507i
\(257\) 10.3042i 0.642757i −0.946951 0.321379i \(-0.895854\pi\)
0.946951 0.321379i \(-0.104146\pi\)
\(258\) −14.6866 + 7.04924i −0.914349 + 0.438866i
\(259\) 3.38349 0.210240
\(260\) −1.47153 1.17977i −0.0912604 0.0731660i
\(261\) 64.3506i 3.98320i
\(262\) −27.5876 + 13.2414i −1.70437 + 0.818059i
\(263\) 3.62234i 0.223363i 0.993744 + 0.111681i \(0.0356236\pi\)
−0.993744 + 0.111681i \(0.964376\pi\)
\(264\) −1.00413 + 4.32178i −0.0618002 + 0.265987i
\(265\) 12.4070i 0.762157i
\(266\) 3.48989 18.3349i 0.213979 1.12419i
\(267\) 31.5924i 1.93342i
\(268\) 8.24945 10.2896i 0.503915 0.628536i
\(269\) 14.9871i 0.913778i 0.889524 + 0.456889i \(0.151036\pi\)
−0.889524 + 0.456889i \(0.848964\pi\)
\(270\) 8.46417 + 17.6345i 0.515113 + 1.07320i
\(271\) 2.44027i 0.148236i 0.997249 + 0.0741179i \(0.0236141\pi\)
−0.997249 + 0.0741179i \(0.976386\pi\)
\(272\) −2.75480 12.3651i −0.167035 0.749744i
\(273\) −9.16706 −0.554816
\(274\) −7.68048 16.0018i −0.463995 0.966702i
\(275\) 0.488592i 0.0294632i
\(276\) 35.5050 + 28.4654i 2.13715 + 1.71341i
\(277\) 22.7032 1.36410 0.682052 0.731303i \(-0.261088\pi\)
0.682052 + 0.731303i \(0.261088\pi\)
\(278\) −7.61635 + 3.65567i −0.456798 + 0.219253i
\(279\) −26.7712 −1.60275
\(280\) −1.93809 + 8.34148i −0.115823 + 0.498499i
\(281\) 7.97768i 0.475908i −0.971276 0.237954i \(-0.923523\pi\)
0.971276 0.237954i \(-0.0764768\pi\)
\(282\) −1.92947 + 0.926102i −0.114898 + 0.0551486i
\(283\) 6.56125i 0.390026i 0.980801 + 0.195013i \(0.0624749\pi\)
−0.980801 + 0.195013i \(0.937525\pi\)
\(284\) −17.4253 + 21.7347i −1.03400 + 1.28972i
\(285\) 8.30804 11.2618i 0.492126 0.667094i
\(286\) −0.281961 0.587447i −0.0166727 0.0347365i
\(287\) 4.74952 0.280355
\(288\) −32.4879 + 25.5651i −1.91437 + 1.50644i
\(289\) −6.96971 −0.409983
\(290\) −11.2266 + 5.38850i −0.659247 + 0.316424i
\(291\) 5.50779i 0.322872i
\(292\) 14.6321 18.2507i 0.856280 1.06804i
\(293\) 7.47982i 0.436976i 0.975840 + 0.218488i \(0.0701124\pi\)
−0.975840 + 0.218488i \(0.929888\pi\)
\(294\) 4.25771 + 8.87065i 0.248315 + 0.517347i
\(295\) 8.65611 0.503978
\(296\) −0.715332 + 3.07877i −0.0415778 + 0.178950i
\(297\) 6.75794i 0.392136i
\(298\) 12.4460 + 25.9303i 0.720975 + 1.50210i
\(299\) −6.68324 −0.386502
\(300\) −4.01659 + 5.00991i −0.231898 + 0.289247i
\(301\) −10.8631 −0.626138
\(302\) 0.827671 + 1.72440i 0.0476271 + 0.0992279i
\(303\) 30.4209 1.74764
\(304\) 15.9459 + 7.05193i 0.914557 + 0.404456i
\(305\) 8.62030 0.493597
\(306\) −14.1636 29.5089i −0.809680 1.68691i
\(307\) 12.2926 0.701574 0.350787 0.936455i \(-0.385914\pi\)
0.350787 + 0.936455i \(0.385914\pi\)
\(308\) −1.85068 + 2.30836i −0.105452 + 0.131531i
\(309\) 17.4834 0.994595
\(310\) −2.24173 4.67049i −0.127321 0.265266i
\(311\) 2.03330i 0.115298i −0.998337 0.0576490i \(-0.981640\pi\)
0.998337 0.0576490i \(-0.0183604\pi\)
\(312\) 1.93809 8.34148i 0.109722 0.472243i
\(313\) 23.5095 1.32883 0.664417 0.747362i \(-0.268680\pi\)
0.664417 + 0.747362i \(0.268680\pi\)
\(314\) −3.99539 8.32414i −0.225473 0.469758i
\(315\) 22.1267i 1.24670i
\(316\) 13.1755 16.4339i 0.741182 0.924480i
\(317\) 10.5447i 0.592250i −0.955149 0.296125i \(-0.904306\pi\)
0.955149 0.296125i \(-0.0956944\pi\)
\(318\) 50.7868 24.3765i 2.84798 1.36697i
\(319\) −4.30227 −0.240881
\(320\) −7.18051 3.52709i −0.401403 0.197170i
\(321\) 11.1629 0.623050
\(322\) 13.1308 + 27.3571i 0.731751 + 1.52455i
\(323\) −8.19535 + 11.1091i −0.456001 + 0.618126i
\(324\) −28.1275 + 35.0835i −1.56264 + 1.94909i
\(325\) 0.943033i 0.0523101i
\(326\) −12.2948 + 5.90123i −0.680947 + 0.326839i
\(327\) 40.3055i 2.22890i
\(328\) −1.00413 + 4.32178i −0.0554441 + 0.238630i
\(329\) −1.42715 −0.0786814
\(330\) −2.00000 + 0.959954i −0.110096 + 0.0528437i
\(331\) 1.08262 0.0595061 0.0297531 0.999557i \(-0.490528\pi\)
0.0297531 + 0.999557i \(0.490528\pi\)
\(332\) −28.1928 22.6030i −1.54728 1.24050i
\(333\) 8.16678i 0.447537i
\(334\) −0.262974 0.547890i −0.0143893 0.0299792i
\(335\) 6.59410 0.360274
\(336\) −37.9528 + 8.45546i −2.07050 + 0.461283i
\(337\) 0.257449i 0.0140241i 0.999975 + 0.00701206i \(0.00223203\pi\)
−0.999975 + 0.00701206i \(0.997768\pi\)
\(338\) −7.41114 15.4406i −0.403113 0.839859i
\(339\) 32.4190i 1.76076i
\(340\) 3.96210 4.94195i 0.214875 0.268015i
\(341\) 1.78983i 0.0969249i
\(342\) 44.2553 + 8.42361i 2.39305 + 0.455497i
\(343\) 14.6328i 0.790095i
\(344\) 2.29665 9.88476i 0.123827 0.532950i
\(345\) 22.7535i 1.22501i
\(346\) −21.8074 + 10.4671i −1.17237 + 0.562712i
\(347\) 16.9053i 0.907523i 0.891123 + 0.453762i \(0.149918\pi\)
−0.891123 + 0.453762i \(0.850082\pi\)
\(348\) −44.1145 35.3679i −2.36479 1.89592i
\(349\) −15.4709 −0.828138 −0.414069 0.910245i \(-0.635893\pi\)
−0.414069 + 0.910245i \(0.635893\pi\)
\(350\) −3.86021 + 1.85281i −0.206337 + 0.0990369i
\(351\) 13.0435i 0.696212i
\(352\) −1.70920 2.17203i −0.0911007 0.115770i
\(353\) −16.0568 −0.854620 −0.427310 0.904105i \(-0.640539\pi\)
−0.427310 + 0.904105i \(0.640539\pi\)
\(354\) 17.0070 + 35.4329i 0.903910 + 1.88324i
\(355\) −13.9287 −0.739260
\(356\) −15.3545 12.3102i −0.813788 0.652437i
\(357\) 30.7865i 1.62939i
\(358\) −7.31639 15.2432i −0.386683 0.805629i
\(359\) 8.15765i 0.430544i 0.976554 + 0.215272i \(0.0690639\pi\)
−0.976554 + 0.215272i \(0.930936\pi\)
\(360\) −20.1340 4.67799i −1.06115 0.246552i
\(361\) −5.60782 18.1536i −0.295148 0.955451i
\(362\) 22.7002 10.8955i 1.19309 0.572657i
\(363\) 34.5503 1.81342
\(364\) 3.57200 4.45537i 0.187224 0.233525i
\(365\) 11.6960 0.612197
\(366\) 16.9366 + 35.2863i 0.885291 + 1.84444i
\(367\) 3.05212i 0.159319i 0.996822 + 0.0796597i \(0.0253834\pi\)
−0.996822 + 0.0796597i \(0.974617\pi\)
\(368\) −27.6695 + 6.16444i −1.44237 + 0.321344i
\(369\) 11.4640i 0.596791i
\(370\) −1.42477 + 0.683858i −0.0740704 + 0.0355521i
\(371\) 37.5649 1.95027
\(372\) 14.7138 18.3525i 0.762873 0.951535i
\(373\) 22.1917i 1.14904i 0.818490 + 0.574521i \(0.194812\pi\)
−0.818490 + 0.574521i \(0.805188\pi\)
\(374\) 1.97287 0.946933i 0.102015 0.0489647i
\(375\) −3.21061 −0.165795
\(376\) 0.301726 1.29862i 0.0155603 0.0669713i
\(377\) 8.30384 0.427669
\(378\) −53.3924 + 25.6271i −2.74621 + 1.31812i
\(379\) 23.4631 1.20522 0.602609 0.798037i \(-0.294128\pi\)
0.602609 + 0.798037i \(0.294128\pi\)
\(380\) 2.23620 + 8.42611i 0.114715 + 0.432251i
\(381\) −14.8940 −0.763042
\(382\) 1.08190 0.519288i 0.0553549 0.0265691i
\(383\) 8.91696 0.455636 0.227818 0.973704i \(-0.426841\pi\)
0.227818 + 0.973704i \(0.426841\pi\)
\(384\) 0.329958 36.3225i 0.0168381 1.85357i
\(385\) −1.47932 −0.0753930
\(386\) −29.3791 + 14.1013i −1.49536 + 0.717737i
\(387\) 26.2204i 1.33286i
\(388\) 2.67689 + 2.14614i 0.135899 + 0.108954i
\(389\) 17.8050 0.902751 0.451375 0.892334i \(-0.350934\pi\)
0.451375 + 0.892334i \(0.350934\pi\)
\(390\) 3.86021 1.85281i 0.195469 0.0938208i
\(391\) 22.4448i 1.13508i
\(392\) −5.97035 1.38717i −0.301548 0.0700626i
\(393\) 69.4716i 3.50438i
\(394\) −0.700799 1.46007i −0.0353058 0.0735572i
\(395\) 10.5317 0.529908
\(396\) −5.57172 4.46700i −0.279989 0.224475i
\(397\) 14.6683 0.736179 0.368089 0.929790i \(-0.380012\pi\)
0.368089 + 0.929790i \(0.380012\pi\)
\(398\) 1.99141 0.955830i 0.0998203 0.0479114i
\(399\) 34.0977 + 25.1544i 1.70702 + 1.25929i
\(400\) −0.869829 3.90428i −0.0434915 0.195214i
\(401\) 18.1350i 0.905621i −0.891607 0.452810i \(-0.850421\pi\)
0.891607 0.452810i \(-0.149579\pi\)
\(402\) 12.9557 + 26.9923i 0.646170 + 1.34625i
\(403\) 3.45457i 0.172084i
\(404\) −11.8537 + 14.7852i −0.589743 + 0.735589i
\(405\) −22.4834 −1.11721
\(406\) −16.3148 33.9909i −0.809692 1.68694i
\(407\) −0.546004 −0.0270644
\(408\) 28.0139 + 6.50883i 1.38689 + 0.322235i
\(409\) 6.24316i 0.308704i 0.988016 + 0.154352i \(0.0493290\pi\)
−0.988016 + 0.154352i \(0.950671\pi\)
\(410\) −2.00000 + 0.959954i −0.0987730 + 0.0474087i
\(411\) 40.2959 1.98765
\(412\) −6.81250 + 8.49726i −0.335628 + 0.418630i
\(413\) 26.2082i 1.28962i
\(414\) −66.0323 + 31.6940i −3.24531 + 1.55768i
\(415\) 18.0674i 0.886896i
\(416\) 3.29894 + 4.19225i 0.161744 + 0.205542i
\(417\) 19.1796i 0.939228i
\(418\) −0.563175 + 2.95876i −0.0275458 + 0.144718i
\(419\) 4.64669i 0.227006i −0.993538 0.113503i \(-0.963793\pi\)
0.993538 0.113503i \(-0.0362071\pi\)
\(420\) −15.1686 12.1611i −0.740151 0.593400i
\(421\) 15.7441i 0.767320i 0.923474 + 0.383660i \(0.125337\pi\)
−0.923474 + 0.383660i \(0.874663\pi\)
\(422\) 5.84282 + 12.1731i 0.284424 + 0.592578i
\(423\) 3.44474i 0.167489i
\(424\) −7.94191 + 34.1818i −0.385693 + 1.66002i
\(425\) 3.16706 0.153625
\(426\) −27.3663 57.0158i −1.32590 2.76242i
\(427\) 26.0998i 1.26306i
\(428\) −4.34967 + 5.42537i −0.210249 + 0.262245i
\(429\) 1.47932 0.0714221
\(430\) 4.57439 2.19560i 0.220597 0.105881i
\(431\) −14.2220 −0.685050 −0.342525 0.939509i \(-0.611282\pi\)
−0.342525 + 0.939509i \(0.611282\pi\)
\(432\) −12.0310 54.0019i −0.578843 2.59817i
\(433\) 30.9395i 1.48686i −0.668815 0.743429i \(-0.733198\pi\)
0.668815 0.743429i \(-0.266802\pi\)
\(434\) 14.1409 6.78731i 0.678785 0.325801i
\(435\) 28.2709i 1.35549i
\(436\) 19.5893 + 15.7053i 0.938155 + 0.752146i
\(437\) 24.8589 + 18.3388i 1.18916 + 0.877263i
\(438\) 22.9796 + 47.8764i 1.09801 + 2.28762i
\(439\) −24.9444 −1.19053 −0.595266 0.803529i \(-0.702953\pi\)
−0.595266 + 0.803529i \(0.702953\pi\)
\(440\) 0.312755 1.34609i 0.0149100 0.0641723i
\(441\) −15.8370 −0.754143
\(442\) −3.80785 + 1.82768i −0.181121 + 0.0869338i
\(443\) 23.4764i 1.11540i −0.830044 0.557698i \(-0.811685\pi\)
0.830044 0.557698i \(-0.188315\pi\)
\(444\) −5.59860 4.48856i −0.265698 0.213018i
\(445\) 9.83998i 0.466460i
\(446\) 5.29381 + 11.0293i 0.250669 + 0.522252i
\(447\) −65.2981 −3.08849
\(448\) 10.6790 21.7405i 0.504536 1.02714i
\(449\) 1.97053i 0.0929951i −0.998918 0.0464976i \(-0.985194\pi\)
0.998918 0.0464976i \(-0.0148060\pi\)
\(450\) −4.47216 9.31745i −0.210820 0.439229i
\(451\) −0.766444 −0.0360904
\(452\) −15.7562 12.6322i −0.741112 0.594170i
\(453\) −4.34240 −0.204024
\(454\) 1.41903 + 2.95645i 0.0665982 + 0.138753i
\(455\) 2.85524 0.133856
\(456\) −30.0979 + 25.7088i −1.40946 + 1.20392i
\(457\) −9.40564 −0.439977 −0.219989 0.975502i \(-0.570602\pi\)
−0.219989 + 0.975502i \(0.570602\pi\)
\(458\) 10.2241 + 21.3013i 0.477742 + 0.995343i
\(459\) 43.8051 2.04465
\(460\) −11.0586 8.86602i −0.515612 0.413380i
\(461\) 18.2902 0.851861 0.425930 0.904756i \(-0.359947\pi\)
0.425930 + 0.904756i \(0.359947\pi\)
\(462\) −2.90647 6.05543i −0.135221 0.281724i
\(463\) 8.89549i 0.413409i 0.978403 + 0.206704i \(0.0662738\pi\)
−0.978403 + 0.206704i \(0.933726\pi\)
\(464\) 34.3790 7.65924i 1.59600 0.355571i
\(465\) 11.7613 0.545416
\(466\) 12.2655 + 25.5543i 0.568187 + 1.18378i
\(467\) 0.513185i 0.0237474i −0.999930 0.0118737i \(-0.996220\pi\)
0.999930 0.0118737i \(-0.00377960\pi\)
\(468\) 10.7540 + 8.62178i 0.497104 + 0.398542i
\(469\) 19.9651i 0.921901i
\(470\) 0.600967 0.288450i 0.0277205 0.0133052i
\(471\) 20.9619 0.965876
\(472\) −23.8479 5.54090i −1.09769 0.255041i
\(473\) 1.75301 0.0806034
\(474\) 20.6921 + 43.1105i 0.950418 + 1.98013i
\(475\) −2.58768 + 3.50769i −0.118731 + 0.160944i
\(476\) 14.9628 + 11.9961i 0.685820 + 0.549841i
\(477\) 90.6710i 4.15154i
\(478\) −24.3723 + 11.6982i −1.11476 + 0.535061i
\(479\) 20.5748i 0.940086i 0.882643 + 0.470043i \(0.155762\pi\)
−0.882643 + 0.470043i \(0.844238\pi\)
\(480\) 14.2728 11.2314i 0.651460 0.512643i
\(481\) 1.05384 0.0480512
\(482\) −13.3619 + 6.41340i −0.608617 + 0.292122i
\(483\) −68.8911 −3.13465
\(484\) −13.4627 + 16.7921i −0.611942 + 0.763279i
\(485\) 1.71549i 0.0778965i
\(486\) −18.7814 39.1298i −0.851941 1.77496i
\(487\) 1.51600 0.0686965 0.0343482 0.999410i \(-0.489064\pi\)
0.0343482 + 0.999410i \(0.489064\pi\)
\(488\) −23.7493 5.51798i −1.07508 0.249787i
\(489\) 30.9610i 1.40010i
\(490\) −1.32614 2.76291i −0.0599087 0.124816i
\(491\) 18.4129i 0.830962i 0.909602 + 0.415481i \(0.136387\pi\)
−0.909602 + 0.415481i \(0.863613\pi\)
\(492\) −7.85895 6.30074i −0.354309 0.284059i
\(493\) 27.8874i 1.25599i
\(494\) 1.08699 5.71072i 0.0489058 0.256937i
\(495\) 3.57065i 0.160489i
\(496\) 3.18640 + 14.3023i 0.143074 + 0.642194i
\(497\) 42.1722i 1.89168i
\(498\) 73.9572 35.4978i 3.31410 1.59069i
\(499\) 8.98900i 0.402403i 0.979550 + 0.201202i \(0.0644846\pi\)
−0.979550 + 0.201202i \(0.935515\pi\)
\(500\) 1.25103 1.56042i 0.0559479 0.0697842i
\(501\) 1.37970 0.0616406
\(502\) −32.8069 + 15.7466i −1.46425 + 0.702804i
\(503\) 10.0185i 0.446703i −0.974738 0.223352i \(-0.928300\pi\)
0.974738 0.223352i \(-0.0716998\pi\)
\(504\) 14.1636 60.9599i 0.630898 2.71537i
\(505\) −9.47511 −0.421637
\(506\) −2.11896 4.41471i −0.0941991 0.196258i
\(507\) 38.8827 1.72684
\(508\) 5.80353 7.23877i 0.257490 0.321168i
\(509\) 17.0538i 0.755898i −0.925826 0.377949i \(-0.876629\pi\)
0.925826 0.377949i \(-0.123371\pi\)
\(510\) 6.22244 + 12.9640i 0.275534 + 0.574058i
\(511\) 35.4122i 1.56654i
\(512\) 17.5249 + 14.3136i 0.774496 + 0.632578i
\(513\) −35.7914 + 48.5165i −1.58023 + 2.14206i
\(514\) −13.1374 + 6.30565i −0.579466 + 0.278130i
\(515\) −5.44549 −0.239957
\(516\) 17.9750 + 14.4110i 0.791303 + 0.634410i
\(517\) 0.230304 0.0101287
\(518\) −2.07053 4.31381i −0.0909738 0.189538i
\(519\) 54.9157i 2.41053i
\(520\) −0.603649 + 2.59810i −0.0264718 + 0.113934i
\(521\) 15.1017i 0.661618i −0.943698 0.330809i \(-0.892678\pi\)
0.943698 0.330809i \(-0.107322\pi\)
\(522\) 82.0443 39.3794i 3.59098 1.72359i
\(523\) 3.49037 0.152623 0.0763117 0.997084i \(-0.475686\pi\)
0.0763117 + 0.997084i \(0.475686\pi\)
\(524\) 33.7645 + 27.0700i 1.47501 + 1.18256i
\(525\) 9.72083i 0.424252i
\(526\) 4.61833 2.21669i 0.201369 0.0966523i
\(527\) −11.6017 −0.505380
\(528\) 6.12456 1.36448i 0.266537 0.0593815i
\(529\) −27.2250 −1.18369
\(530\) −15.8184 + 7.59248i −0.687108 + 0.329796i
\(531\) −63.2592 −2.74522
\(532\) −25.5119 + 6.77059i −1.10608 + 0.293542i
\(533\) 1.47932 0.0640763
\(534\) 40.2790 19.3330i 1.74304 0.836620i
\(535\) −3.47686 −0.150318
\(536\) −18.1670 4.22098i −0.784696 0.182319i
\(537\) 38.3856 1.65646
\(538\) 19.1079 9.17134i 0.823799 0.395405i
\(539\) 1.05881i 0.0456061i
\(540\) 17.3036 21.5829i 0.744630 0.928781i
\(541\) −0.859019 −0.0369321 −0.0184661 0.999829i \(-0.505878\pi\)
−0.0184661 + 0.999829i \(0.505878\pi\)
\(542\) 3.11124 1.49332i 0.133639 0.0641437i
\(543\) 57.1638i 2.45313i
\(544\) −14.0792 + 11.0791i −0.603640 + 0.475012i
\(545\) 12.5538i 0.537747i
\(546\) 5.60979 + 11.6876i 0.240077 + 0.500184i
\(547\) −16.9704 −0.725600 −0.362800 0.931867i \(-0.618179\pi\)
−0.362800 + 0.931867i \(0.618179\pi\)
\(548\) −15.7015 + 19.5846i −0.670735 + 0.836612i
\(549\) −62.9975 −2.68867
\(550\) 0.622934 0.298994i 0.0265620 0.0127491i
\(551\) −30.8868 22.7857i −1.31582 0.970703i
\(552\) 14.5648 62.6868i 0.619921 2.66813i
\(553\) 31.8871i 1.35598i
\(554\) −13.8932 28.9456i −0.590267 1.22978i
\(555\) 3.58788i 0.152297i
\(556\) 9.32165 + 7.47343i 0.395326 + 0.316944i
\(557\) 32.6593 1.38382 0.691910 0.721984i \(-0.256769\pi\)
0.691910 + 0.721984i \(0.256769\pi\)
\(558\) 16.3826 + 34.1321i 0.693532 + 1.44493i
\(559\) −3.38349 −0.143106
\(560\) 11.8210 2.63360i 0.499530 0.111290i
\(561\) 4.96811i 0.209754i
\(562\) −10.1712 + 4.88194i −0.429046 + 0.205932i
\(563\) −9.10359 −0.383671 −0.191835 0.981427i \(-0.561444\pi\)
−0.191835 + 0.981427i \(0.561444\pi\)
\(564\) 2.36148 + 1.89327i 0.0994364 + 0.0797209i
\(565\) 10.0974i 0.424802i
\(566\) 8.36532 4.01516i 0.351621 0.168770i
\(567\) 68.0733i 2.85881i
\(568\) 38.3742 + 8.91598i 1.61015 + 0.374106i
\(569\) 29.8666i 1.25207i 0.779794 + 0.626037i \(0.215324\pi\)
−0.779794 + 0.626037i \(0.784676\pi\)
\(570\) −19.4425 3.70071i −0.814356 0.155006i
\(571\) 28.8364i 1.20677i 0.797451 + 0.603383i \(0.206181\pi\)
−0.797451 + 0.603383i \(0.793819\pi\)
\(572\) −0.576424 + 0.718977i −0.0241015 + 0.0300619i
\(573\) 2.72446i 0.113816i
\(574\) −2.90647 6.05543i −0.121314 0.252749i
\(575\) 7.08696i 0.295547i
\(576\) 52.4755 + 25.7761i 2.18648 + 1.07400i
\(577\) 24.1255 1.00436 0.502180 0.864763i \(-0.332532\pi\)
0.502180 + 0.864763i \(0.332532\pi\)
\(578\) 4.26511 + 8.88608i 0.177405 + 0.369612i
\(579\) 73.9829i 3.07462i
\(580\) 13.7402 + 11.0159i 0.570531 + 0.457411i
\(581\) 54.7031 2.26947
\(582\) −7.02220 + 3.37049i −0.291079 + 0.139711i
\(583\) −6.06196 −0.251061
\(584\) −32.2230 7.48679i −1.33340 0.309806i
\(585\) 6.89173i 0.284938i
\(586\) 9.53645 4.57728i 0.393947 0.189086i
\(587\) 1.98430i 0.0819010i 0.999161 + 0.0409505i \(0.0130386\pi\)
−0.999161 + 0.0409505i \(0.986961\pi\)
\(588\) 8.70420 10.8568i 0.358955 0.447727i
\(589\) 9.47932 12.8496i 0.390588 0.529457i
\(590\) −5.29711 11.0362i −0.218078 0.454352i
\(591\) 3.67676 0.151242
\(592\) 4.36305 0.972039i 0.179320 0.0399506i
\(593\) −37.8922 −1.55604 −0.778022 0.628237i \(-0.783777\pi\)
−0.778022 + 0.628237i \(0.783777\pi\)
\(594\) 8.61609 4.13552i 0.353522 0.169683i
\(595\) 9.58897i 0.393109i
\(596\) 25.4438 31.7361i 1.04222 1.29996i
\(597\) 5.01479i 0.205242i
\(598\) 4.08981 + 8.52084i 0.167245 + 0.348443i
\(599\) 35.0029 1.43018 0.715091 0.699032i \(-0.246385\pi\)
0.715091 + 0.699032i \(0.246385\pi\)
\(600\) 8.84538 + 2.05516i 0.361111 + 0.0839016i
\(601\) 13.3793i 0.545753i −0.962049 0.272877i \(-0.912025\pi\)
0.962049 0.272877i \(-0.0879751\pi\)
\(602\) 6.64766 + 13.8500i 0.270939 + 0.564482i
\(603\) −48.1900 −1.96245
\(604\) 1.69204 2.11049i 0.0688481 0.0858746i
\(605\) −10.7613 −0.437508
\(606\) −18.6161 38.7854i −0.756227 1.57555i
\(607\) 28.7047 1.16509 0.582543 0.812800i \(-0.302058\pi\)
0.582543 + 0.812800i \(0.302058\pi\)
\(608\) −0.767153 24.6457i −0.0311121 0.999516i
\(609\) 85.5963 3.46854
\(610\) −5.27519 10.9905i −0.213586 0.444993i
\(611\) −0.444510 −0.0179830
\(612\) −28.9552 + 36.1160i −1.17045 + 1.45990i
\(613\) −9.72631 −0.392842 −0.196421 0.980520i \(-0.562932\pi\)
−0.196421 + 0.980520i \(0.562932\pi\)
\(614\) −7.52244 15.6725i −0.303581 0.632491i
\(615\) 5.03643i 0.203088i
\(616\) 4.07558 + 0.946933i 0.164210 + 0.0381530i
\(617\) 9.50602 0.382698 0.191349 0.981522i \(-0.438714\pi\)
0.191349 + 0.981522i \(0.438714\pi\)
\(618\) −10.6990 22.2906i −0.430375 0.896658i
\(619\) 37.7438i 1.51705i −0.651643 0.758526i \(-0.725920\pi\)
0.651643 0.758526i \(-0.274080\pi\)
\(620\) −4.58285 + 5.71621i −0.184052 + 0.229569i
\(621\) 98.0230i 3.93353i
\(622\) −2.59237 + 1.24428i −0.103945 + 0.0498911i
\(623\) 29.7927 1.19362
\(624\) −11.8210 + 2.63360i −0.473221 + 0.105428i
\(625\) 1.00000 0.0400000
\(626\) −14.3866 29.9736i −0.575005 1.19798i
\(627\) −5.50245 4.05924i −0.219747 0.162111i
\(628\) −8.16794 + 10.1879i −0.325936 + 0.406542i
\(629\) 3.53921i 0.141118i
\(630\) 28.2106 13.5404i 1.12394 0.539464i
\(631\) 24.8879i 0.990773i 0.868673 + 0.495386i \(0.164973\pi\)
−0.868673 + 0.495386i \(0.835027\pi\)
\(632\) −29.0153 6.74151i −1.15417 0.268163i
\(633\) −30.6545 −1.21841
\(634\) −13.4441 + 6.45284i −0.533932 + 0.256275i
\(635\) 4.63898 0.184092
\(636\) −62.1580 49.8338i −2.46473 1.97604i
\(637\) 2.04361i 0.0809709i
\(638\) 2.63278 + 5.48521i 0.104233 + 0.217162i
\(639\) 101.792 4.02682
\(640\) −0.102771 + 11.3132i −0.00406238 + 0.447195i
\(641\) 17.6954i 0.698925i 0.936950 + 0.349463i \(0.113636\pi\)
−0.936950 + 0.349463i \(0.886364\pi\)
\(642\) −6.83111 14.2322i −0.269602 0.561699i
\(643\) 10.2796i 0.405389i −0.979242 0.202695i \(-0.935030\pi\)
0.979242 0.202695i \(-0.0649699\pi\)
\(644\) 26.8438 33.4824i 1.05779 1.31939i
\(645\) 11.5193i 0.453572i
\(646\) 19.1788 + 3.65051i 0.754578 + 0.143628i
\(647\) 31.9257i 1.25513i 0.778565 + 0.627564i \(0.215948\pi\)
−0.778565 + 0.627564i \(0.784052\pi\)
\(648\) 61.9426 + 14.3919i 2.43334 + 0.565369i
\(649\) 4.22930i 0.166015i
\(650\) −1.20233 + 0.577089i −0.0471592 + 0.0226353i
\(651\) 35.6098i 1.39566i
\(652\) 15.0476 + 12.0641i 0.589311 + 0.472467i
\(653\) 5.72631 0.224088 0.112044 0.993703i \(-0.464260\pi\)
0.112044 + 0.993703i \(0.464260\pi\)
\(654\) −51.3878 + 24.6650i −2.00942 + 0.964476i
\(655\) 21.6381i 0.845470i
\(656\) 6.12456 1.36448i 0.239124 0.0532741i
\(657\) −85.4750 −3.33470
\(658\) 0.873345 + 1.81956i 0.0340465 + 0.0709337i
\(659\) −0.928171 −0.0361564 −0.0180782 0.999837i \(-0.505755\pi\)
−0.0180782 + 0.999837i \(0.505755\pi\)
\(660\) 2.44780 + 1.96247i 0.0952805 + 0.0763891i
\(661\) 15.5689i 0.605560i −0.953060 0.302780i \(-0.902085\pi\)
0.953060 0.302780i \(-0.0979147\pi\)
\(662\) −0.662509 1.38029i −0.0257491 0.0536466i
\(663\) 9.58897i 0.372405i
\(664\) −11.5652 + 49.7765i −0.448818 + 1.93170i
\(665\) −10.6203 7.83476i −0.411837 0.303819i
\(666\) 10.4123 4.99766i 0.403468 0.193656i
\(667\) 62.4039 2.41629
\(668\) −0.537609 + 0.670562i −0.0208007 + 0.0259448i
\(669\) −27.7741 −1.07381
\(670\) −4.03526 8.40720i −0.155896 0.324799i
\(671\) 4.21181i 0.162595i
\(672\) 34.0056 + 43.2139i 1.31179 + 1.66701i
\(673\) 14.6637i 0.565244i −0.959231 0.282622i \(-0.908796\pi\)
0.959231 0.282622i \(-0.0912041\pi\)
\(674\) 0.328236 0.157546i 0.0126432 0.00606843i
\(675\) 13.8315 0.532373
\(676\) −15.1509 + 18.8978i −0.582726 + 0.726838i
\(677\) 20.0120i 0.769123i −0.923099 0.384562i \(-0.874353\pi\)
0.923099 0.384562i \(-0.125647\pi\)
\(678\) 41.3328 19.8388i 1.58738 0.761904i
\(679\) −5.19403 −0.199328
\(680\) −8.72539 2.02728i −0.334603 0.0777428i
\(681\) −7.44496 −0.285292
\(682\) −2.28196 + 1.09529i −0.0873808 + 0.0419408i
\(683\) −39.0637 −1.49473 −0.747366 0.664412i \(-0.768682\pi\)
−0.747366 + 0.664412i \(0.768682\pi\)
\(684\) −16.3423 61.5784i −0.624862 2.35451i
\(685\) −12.5508 −0.479542
\(686\) −18.6561 + 8.95452i −0.712295 + 0.341885i
\(687\) −53.6411 −2.04654
\(688\) −14.0081 + 3.12084i −0.534053 + 0.118981i
\(689\) 11.7002 0.445743
\(690\) 29.0097 13.9240i 1.10438 0.530078i
\(691\) 36.4683i 1.38732i 0.720302 + 0.693660i \(0.244003\pi\)
−0.720302 + 0.693660i \(0.755997\pi\)
\(692\) 26.6901 + 21.3982i 1.01461 + 0.813438i
\(693\) 10.8109 0.410673
\(694\) 21.5535 10.3452i 0.818161 0.392698i
\(695\) 5.97381i 0.226599i
\(696\) −18.0966 + 77.8875i −0.685951 + 2.95232i
\(697\) 4.96811i 0.188181i
\(698\) 9.46742 + 19.7247i 0.358347 + 0.746592i
\(699\) −64.3511 −2.43398
\(700\) 4.72451 + 3.78777i 0.178570 + 0.143164i
\(701\) −32.9543 −1.24467 −0.622333 0.782753i \(-0.713815\pi\)
−0.622333 + 0.782753i \(0.713815\pi\)
\(702\) −16.6300 + 7.98199i −0.627657 + 0.301261i
\(703\) −3.91987 2.89175i −0.147841 0.109064i
\(704\) −1.72330 + 3.50834i −0.0649495 + 0.132225i
\(705\) 1.51336i 0.0569965i
\(706\) 9.82599 + 20.4718i 0.369806 + 0.770466i
\(707\) 28.6879i 1.07892i
\(708\) 34.7680 43.3663i 1.30666 1.62981i
\(709\) 0.863080 0.0324137 0.0162068 0.999869i \(-0.494841\pi\)
0.0162068 + 0.999869i \(0.494841\pi\)
\(710\) 8.52369 + 17.7585i 0.319888 + 0.666466i
\(711\) −76.9663 −2.88646
\(712\) −6.29872 + 27.1096i −0.236054 + 1.01597i
\(713\) 25.9613i 0.972258i
\(714\) −39.2515 + 18.8398i −1.46895 + 0.705062i
\(715\) −0.460758 −0.0172314
\(716\) −14.9572 + 18.6562i −0.558976 + 0.697214i
\(717\) 61.3747i 2.29208i
\(718\) 10.4007 4.99208i 0.388149 0.186303i
\(719\) 30.5363i 1.13881i 0.822057 + 0.569405i \(0.192827\pi\)
−0.822057 + 0.569405i \(0.807173\pi\)
\(720\) 6.35675 + 28.5326i 0.236902 + 1.06335i
\(721\) 16.4874i 0.614023i
\(722\) −19.7133 + 18.2588i −0.733654 + 0.679523i
\(723\) 33.6481i 1.25139i
\(724\) −27.7827 22.2742i −1.03254 0.827814i
\(725\) 8.80545i 0.327026i
\(726\) −21.1431 44.0502i −0.784693 1.63486i
\(727\) 5.68270i 0.210760i 0.994432 + 0.105380i \(0.0336058\pi\)
−0.994432 + 0.105380i \(0.966394\pi\)
\(728\) −7.86630 1.82768i −0.291544 0.0677383i
\(729\) 31.0870 1.15137
\(730\) −7.15738 14.9119i −0.264907 0.551915i
\(731\) 11.3630i 0.420277i
\(732\) 34.6242 43.1869i 1.27975 1.59623i
\(733\) 25.1533 0.929059 0.464529 0.885558i \(-0.346224\pi\)
0.464529 + 0.885558i \(0.346224\pi\)
\(734\) 3.89132 1.86775i 0.143631 0.0689398i
\(735\) 6.95761 0.256635
\(736\) 24.7917 + 31.5051i 0.913836 + 1.16129i
\(737\) 3.22182i 0.118677i
\(738\) 14.6161 7.01539i 0.538026 0.258240i
\(739\) 29.1790i 1.07337i 0.843784 + 0.536683i \(0.180323\pi\)
−0.843784 + 0.536683i \(0.819677\pi\)
\(740\) 1.74378 + 1.39804i 0.0641026 + 0.0513929i
\(741\) 10.6203 + 7.83476i 0.390146 + 0.287817i
\(742\) −22.9879 47.8937i −0.843911 1.75823i
\(743\) −42.1946 −1.54797 −0.773985 0.633204i \(-0.781740\pi\)
−0.773985 + 0.633204i \(0.781740\pi\)
\(744\) −32.4028 7.52857i −1.18794 0.276011i
\(745\) 20.3382 0.745134
\(746\) 28.2934 13.5802i 1.03590 0.497207i
\(747\) 132.038i 4.83101i
\(748\) −2.41460 1.93585i −0.0882864 0.0707817i
\(749\) 10.5269i 0.384646i
\(750\) 1.96474 + 4.09340i 0.0717420 + 0.149470i
\(751\) −37.9019 −1.38306 −0.691529 0.722348i \(-0.743063\pi\)
−0.691529 + 0.722348i \(0.743063\pi\)
\(752\) −1.84033 + 0.410005i −0.0671099 + 0.0149513i
\(753\) 82.6149i 3.01065i
\(754\) −5.08153 10.5870i −0.185059 0.385557i
\(755\) 1.35251 0.0492230
\(756\) 65.3469 + 52.3905i 2.37665 + 1.90542i
\(757\) 9.06683 0.329540 0.164770 0.986332i \(-0.447312\pi\)
0.164770 + 0.986332i \(0.447312\pi\)
\(758\) −14.3582 29.9144i −0.521515 1.08654i
\(759\) 11.1172 0.403528
\(760\) 9.37449 8.00743i 0.340049 0.290460i
\(761\) 35.1190 1.27306 0.636531 0.771251i \(-0.280369\pi\)
0.636531 + 0.771251i \(0.280369\pi\)
\(762\) 9.11438 + 18.9892i 0.330179 + 0.687906i
\(763\) −38.0094 −1.37603
\(764\) −1.32414 1.06160i −0.0479057 0.0384074i
\(765\) −23.1450 −0.836811
\(766\) −5.45674 11.3687i −0.197160 0.410770i
\(767\) 8.16300i 0.294749i
\(768\) −46.5115 + 21.8069i −1.67834 + 0.786887i
\(769\) −34.2519 −1.23515 −0.617577 0.786511i \(-0.711886\pi\)
−0.617577 + 0.786511i \(0.711886\pi\)
\(770\) 0.905268 + 1.88607i 0.0326236 + 0.0679691i
\(771\) 33.0828i 1.19145i
\(772\) 35.9571 + 28.8278i 1.29413 + 1.03754i
\(773\) 9.33048i 0.335594i −0.985822 0.167797i \(-0.946335\pi\)
0.985822 0.167797i \(-0.0536653\pi\)
\(774\) −33.4299 + 16.0456i −1.20161 + 0.576746i
\(775\) −3.66325 −0.131588
\(776\) 1.09811 4.72626i 0.0394199 0.169663i
\(777\) 10.8631 0.389711
\(778\) −10.8958 22.7007i −0.390633 0.813858i
\(779\) −5.50245 4.05924i −0.197146 0.145437i
\(780\) −4.72451 3.78777i −0.169165 0.135624i
\(781\) 6.80546i 0.243519i
\(782\) −28.6162 + 13.7351i −1.02331 + 0.491167i
\(783\) 121.792i 4.35250i
\(784\) 1.88498 + 8.46082i 0.0673205 + 0.302172i
\(785\) −6.52895 −0.233028
\(786\) −88.5733 + 42.5131i −3.15930 + 1.51639i
\(787\) 4.73061 0.168628 0.0843141 0.996439i \(-0.473130\pi\)
0.0843141 + 0.996439i \(0.473130\pi\)
\(788\) −1.43267 + 1.78698i −0.0510368 + 0.0636585i
\(789\) 11.6299i 0.414037i
\(790\) −6.44489 13.4275i −0.229299 0.477729i
\(791\) 30.5722 1.08702
\(792\) −2.28563 + 9.83729i −0.0812162 + 0.349553i
\(793\) 8.12923i 0.288677i
\(794\) −8.97624 18.7014i −0.318555 0.663688i
\(795\) 39.8341i 1.41277i
\(796\) −2.43729 1.95404i −0.0863873 0.0692591i
\(797\) 21.3976i 0.757940i 0.925409 + 0.378970i \(0.123722\pi\)
−0.925409 + 0.378970i \(0.876278\pi\)
\(798\) 11.2047 58.8663i 0.396642 2.08385i
\(799\) 1.49283i 0.0528127i
\(800\) −4.44550 + 3.49822i −0.157172 + 0.123681i
\(801\) 71.9110i 2.54085i
\(802\) −23.1214 + 11.0977i −0.816446 + 0.391875i
\(803\) 5.71458i 0.201663i
\(804\) 26.4858 33.0359i 0.934082 1.16509i
\(805\) 21.4573 0.756270
\(806\) 4.40442 2.11402i 0.155139 0.0744632i
\(807\) 48.1177i 1.69382i
\(808\) 26.1043 + 6.06516i 0.918347 + 0.213371i
\(809\) 37.8352 1.33021 0.665107 0.746748i \(-0.268386\pi\)
0.665107 + 0.746748i \(0.268386\pi\)
\(810\) 13.7587 + 28.6654i 0.483432 + 1.00720i
\(811\) 42.0985 1.47828 0.739139 0.673552i \(-0.235232\pi\)
0.739139 + 0.673552i \(0.235232\pi\)
\(812\) −33.3531 + 41.6015i −1.17046 + 1.45993i
\(813\) 7.83476i 0.274777i
\(814\) 0.334127 + 0.696132i 0.0117112 + 0.0243994i
\(815\) 9.64331i 0.337790i
\(816\) −8.84462 39.6996i −0.309623 1.38976i
\(817\) 12.5852 + 9.28429i 0.440300 + 0.324816i
\(818\) 7.95976 3.82050i 0.278307 0.133581i
\(819\) −20.8662 −0.729124
\(820\) 2.44780 + 1.96247i 0.0854809 + 0.0685325i
\(821\) 29.9355 1.04476 0.522379 0.852713i \(-0.325045\pi\)
0.522379 + 0.852713i \(0.325045\pi\)
\(822\) −24.6591 51.3755i −0.860084 1.79193i
\(823\) 0.318164i 0.0110905i −0.999985 0.00554526i \(-0.998235\pi\)
0.999985 0.00554526i \(-0.00176512\pi\)
\(824\) 15.0026 + 3.48574i 0.522639 + 0.121432i
\(825\) 1.56868i 0.0546144i
\(826\) 33.4144 16.0381i 1.16264 0.558038i
\(827\) 20.0096 0.695802 0.347901 0.937531i \(-0.386895\pi\)
0.347901 + 0.937531i \(0.386895\pi\)
\(828\) 80.8170 + 64.7933i 2.80859 + 2.25172i
\(829\) 3.63983i 0.126417i −0.998000 0.0632083i \(-0.979867\pi\)
0.998000 0.0632083i \(-0.0201333\pi\)
\(830\) −23.0352 + 11.0564i −0.799564 + 0.383772i
\(831\) 72.8913 2.52857
\(832\) 3.32616 6.77146i 0.115314 0.234758i
\(833\) −6.86323 −0.237797
\(834\) −24.4532 + 11.7370i −0.846744 + 0.406417i
\(835\) −0.429732 −0.0148715
\(836\) 4.11693 1.09259i 0.142387 0.0377880i
\(837\) −50.6681 −1.75135
\(838\) −5.92433 + 2.84354i −0.204653 + 0.0982285i
\(839\) −35.9639 −1.24161 −0.620806 0.783964i \(-0.713195\pi\)
−0.620806 + 0.783964i \(0.713195\pi\)
\(840\) −6.22244 + 26.7813i −0.214695 + 0.924042i
\(841\) −48.5360 −1.67366
\(842\) 20.0731 9.63460i 0.691763 0.332030i
\(843\) 25.6132i 0.882167i
\(844\) 11.9447 14.8987i 0.411153 0.512834i
\(845\) −12.1107 −0.416620
\(846\) −4.39189 + 2.10801i −0.150996 + 0.0724748i
\(847\) 32.5821i 1.11953i
\(848\) 48.4404 10.7920i 1.66345 0.370598i
\(849\) 21.0657i 0.722971i
\(850\) −1.93809 4.03787i −0.0664758 0.138498i
\(851\) 7.91972 0.271484
\(852\) −55.9459 + 69.7817i −1.91668 + 2.39068i
\(853\) −26.7120 −0.914602 −0.457301 0.889312i \(-0.651184\pi\)
−0.457301 + 0.889312i \(0.651184\pi\)
\(854\) 33.2762 15.9718i 1.13869 0.546543i
\(855\) 18.9109 25.6344i 0.646739 0.876677i
\(856\) 9.57889 + 2.22559i 0.327400 + 0.0760691i
\(857\) 19.2855i 0.658780i −0.944194 0.329390i \(-0.893157\pi\)
0.944194 0.329390i \(-0.106843\pi\)
\(858\) −0.905268 1.88607i −0.0309054 0.0643892i
\(859\) 27.1922i 0.927787i 0.885891 + 0.463893i \(0.153548\pi\)
−0.885891 + 0.463893i \(0.846452\pi\)
\(860\) −5.59860 4.48856i −0.190911 0.153059i
\(861\) 15.2489 0.519680
\(862\) 8.70316 + 18.1324i 0.296431 + 0.617593i
\(863\) 40.1609 1.36709 0.683547 0.729907i \(-0.260437\pi\)
0.683547 + 0.729907i \(0.260437\pi\)
\(864\) −61.4878 + 48.3855i −2.09186 + 1.64611i
\(865\) 17.1044i 0.581568i
\(866\) −39.4466 + 18.9334i −1.34045 + 0.643385i
\(867\) −22.3770 −0.759964
\(868\) −17.3071 13.8756i −0.587440 0.470967i
\(869\) 5.14571i 0.174556i
\(870\) −36.0442 + 17.3004i −1.22201 + 0.586538i
\(871\) 6.21846i 0.210704i
\(872\) 8.03589 34.5863i 0.272130 1.17124i
\(873\) 12.5369i 0.424310i
\(874\) 8.16878 42.9164i 0.276313 1.45167i
\(875\) 3.02772i 0.102355i
\(876\) 46.9781 58.5960i 1.58724 1.97978i
\(877\) 30.1261i 1.01729i −0.860977 0.508644i \(-0.830147\pi\)
0.860977 0.508644i \(-0.169853\pi\)
\(878\) 15.2647 + 31.8030i 0.515160 + 1.07330i
\(879\) 24.0148i 0.810000i
\(880\) −1.90760 + 0.424991i −0.0643051 + 0.0143265i
\(881\) −34.6286 −1.16667 −0.583333 0.812233i \(-0.698252\pi\)
−0.583333 + 0.812233i \(0.698252\pi\)
\(882\) 9.69145 + 20.1915i 0.326328 + 0.679883i
\(883\) 21.0760i 0.709265i −0.935006 0.354632i \(-0.884606\pi\)
0.935006 0.354632i \(-0.115394\pi\)
\(884\) 4.66043 + 3.73640i 0.156747 + 0.125669i
\(885\) 27.7914 0.934198
\(886\) −29.9314 + 14.3664i −1.00556 + 0.482648i
\(887\) −26.9404 −0.904570 −0.452285 0.891873i \(-0.649391\pi\)
−0.452285 + 0.891873i \(0.649391\pi\)
\(888\) −2.29665 + 9.88476i −0.0770707 + 0.331711i
\(889\) 14.0455i 0.471072i
\(890\) −12.5456 + 6.02158i −0.420528 + 0.201844i
\(891\) 10.9852i 0.368018i
\(892\) 10.8223 13.4988i 0.362359 0.451972i
\(893\) 1.65339 + 1.21973i 0.0553287 + 0.0408169i
\(894\) 39.9592 + 83.2523i 1.33643 + 2.78437i
\(895\) −11.9559 −0.399640
\(896\) −34.2533 0.311161i −1.14432 0.0103952i
\(897\) −21.4573 −0.716438
\(898\) −2.51234 + 1.20587i −0.0838380 + 0.0402403i
\(899\) 32.2566i 1.07582i
\(900\) −9.14261 + 11.4036i −0.304754 + 0.380121i
\(901\) 39.2938i 1.30907i
\(902\) 0.469026 + 0.977183i 0.0156168 + 0.0325367i
\(903\) −34.8772 −1.16064
\(904\) −6.46351 + 27.8188i −0.214973 + 0.925241i
\(905\) 17.8046i 0.591846i
\(906\) 2.65733 + 5.53637i 0.0882839 + 0.183934i
\(907\) 13.8276 0.459137 0.229569 0.973292i \(-0.426268\pi\)
0.229569 + 0.973292i \(0.426268\pi\)
\(908\) 2.90097 3.61840i 0.0962721 0.120081i
\(909\) 69.2445 2.29670
\(910\) −1.74726 3.64031i −0.0579212 0.120675i
\(911\) 4.76877 0.157996 0.0789982 0.996875i \(-0.474828\pi\)
0.0789982 + 0.996875i \(0.474828\pi\)
\(912\) 51.1960 + 22.6410i 1.69527 + 0.749720i
\(913\) −8.82760 −0.292151
\(914\) 5.75578 + 11.9918i 0.190384 + 0.396653i
\(915\) 27.6765 0.914955
\(916\) 20.9016 26.0706i 0.690607 0.861398i
\(917\) −65.5140 −2.16346
\(918\) −26.8066 55.8497i −0.884749 1.84331i
\(919\) 46.6300i 1.53818i −0.639140 0.769091i \(-0.720709\pi\)
0.639140 0.769091i \(-0.279291\pi\)
\(920\) −4.53647 + 19.5249i −0.149563 + 0.643716i
\(921\) 39.4667 1.30047
\(922\) −11.1927 23.3193i −0.368612 0.767979i
\(923\) 13.1353i 0.432352i
\(924\) −5.94181 + 7.41125i −0.195471 + 0.243812i
\(925\) 1.11751i 0.0367434i
\(926\) 11.3414 5.44360i 0.372701 0.178888i
\(927\) 39.7959 1.30707
\(928\) −30.8034 39.1446i −1.01117 1.28499i
\(929\) 23.0589 0.756537 0.378268 0.925696i \(-0.376520\pi\)
0.378268 + 0.925696i \(0.376520\pi\)
\(930\) −7.19732 14.9951i −0.236009 0.491710i
\(931\) 5.60767 7.60139i 0.183784 0.249126i
\(932\) 25.0748 31.2759i 0.821351 1.02448i
\(933\) 6.52815i 0.213722i
\(934\) −0.654289 + 0.314044i −0.0214090 + 0.0102758i
\(935\) 1.54740i 0.0506054i
\(936\) 4.41150 18.9870i 0.144194 0.620609i
\(937\) 8.32894 0.272095 0.136047 0.990702i \(-0.456560\pi\)
0.136047 + 0.990702i \(0.456560\pi\)
\(938\) 25.4546 12.2176i 0.831123 0.398920i
\(939\) 75.4798 2.46319
\(940\) −0.735524 0.589690i −0.0239901 0.0192336i
\(941\) 45.6945i 1.48960i 0.667289 + 0.744799i \(0.267454\pi\)
−0.667289 + 0.744799i \(0.732546\pi\)
\(942\) −12.8277 26.7256i −0.417948 0.870767i
\(943\) 11.1172 0.362025
\(944\) 7.52934 + 33.7959i 0.245059 + 1.09996i
\(945\) 41.8778i 1.36228i
\(946\) −1.07275 2.23501i −0.0348782 0.0726665i
\(947\) 48.3372i 1.57075i −0.619021 0.785375i \(-0.712470\pi\)
0.619021 0.785375i \(-0.287530\pi\)
\(948\) 42.3016 52.7630i 1.37389 1.71366i
\(949\) 11.0297i 0.358040i
\(950\) 6.05569 + 1.15265i 0.196473 + 0.0373969i
\(951\) 33.8550i 1.09782i
\(952\) 6.13804 26.4180i 0.198935 0.856213i
\(953\) 4.66986i 0.151272i −0.997136 0.0756358i \(-0.975901\pi\)
0.997136 0.0756358i \(-0.0240986\pi\)
\(954\) 115.602 55.4861i 3.74274 1.79643i
\(955\) 0.848579i 0.0274594i
\(956\) 29.8293 + 23.9150i 0.964749 + 0.773467i
\(957\) −13.8129 −0.446509
\(958\) 26.2320 12.5908i 0.847517 0.406789i
\(959\) 38.0003i 1.22709i
\(960\) −23.0538 11.3241i −0.744059 0.365484i
\(961\) −17.5806 −0.567116
\(962\) −0.644901 1.34361i −0.0207924 0.0433196i
\(963\) 25.4090 0.818795
\(964\) 16.3536 + 13.1112i 0.526715 + 0.422282i
\(965\) 23.0432i 0.741787i
\(966\) 42.1579 + 87.8332i 1.35641 + 2.82599i
\(967\) 4.19050i 0.134757i −0.997727 0.0673787i \(-0.978536\pi\)
0.997727 0.0673787i \(-0.0214636\pi\)
\(968\) 29.6478 + 6.88845i 0.952915 + 0.221403i
\(969\) −26.3121 + 35.6670i −0.845267 + 1.14579i
\(970\) 2.18718 1.04980i 0.0702262 0.0337069i
\(971\) 9.15781 0.293888 0.146944 0.989145i \(-0.453056\pi\)
0.146944 + 0.989145i \(0.453056\pi\)
\(972\) −38.3955 + 47.8910i −1.23154 + 1.53610i
\(973\) −18.0870 −0.579842
\(974\) −0.927716 1.93283i −0.0297259 0.0619320i
\(975\) 3.02772i 0.0969645i
\(976\) 7.49819 + 33.6560i 0.240011 + 1.07730i
\(977\) 20.6015i 0.659099i −0.944138 0.329549i \(-0.893103\pi\)
0.944138 0.329549i \(-0.106897\pi\)
\(978\) −39.4739 + 18.9466i −1.26224 + 0.605844i
\(979\) −4.80773 −0.153656
\(980\) −2.71107 + 3.38153i −0.0866019 + 0.108019i
\(981\) 91.7439i 2.92916i
\(982\) 23.4757 11.2678i 0.749138 0.359569i
\(983\) 28.8332 0.919636 0.459818 0.888013i \(-0.347915\pi\)
0.459818 + 0.888013i \(0.347915\pi\)
\(984\) −3.22389 + 13.8756i −0.102774 + 0.442337i
\(985\) −1.14519 −0.0364888
\(986\) 35.5553 17.0657i 1.13231 0.543483i
\(987\) −4.58203 −0.145848
\(988\) −7.94611 + 2.10881i −0.252799 + 0.0670903i
\(989\) −25.4272 −0.808536
\(990\) −4.55243 + 2.18506i −0.144686 + 0.0694458i
\(991\) −33.2449 −1.05606 −0.528029 0.849226i \(-0.677069\pi\)
−0.528029 + 0.849226i \(0.677069\pi\)
\(992\) 16.2850 12.8149i 0.517048 0.406872i
\(993\) 3.47587 0.110303
\(994\) −53.7678 + 25.8073i −1.70541 + 0.818558i
\(995\) 1.56194i 0.0495168i
\(996\) −90.5163 72.5694i −2.86812 2.29945i
\(997\) −55.1366 −1.74619 −0.873097 0.487546i \(-0.837892\pi\)
−0.873097 + 0.487546i \(0.837892\pi\)
\(998\) 11.4606 5.50082i 0.362779 0.174125i
\(999\) 15.4567i 0.489030i
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 380.2.f.a.151.7 20
4.3 odd 2 inner 380.2.f.a.151.13 yes 20
19.18 odd 2 inner 380.2.f.a.151.14 yes 20
76.75 even 2 inner 380.2.f.a.151.8 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.f.a.151.7 20 1.1 even 1 trivial
380.2.f.a.151.8 yes 20 76.75 even 2 inner
380.2.f.a.151.13 yes 20 4.3 odd 2 inner
380.2.f.a.151.14 yes 20 19.18 odd 2 inner