Properties

Label 1089.2.e.o.364.11
Level $1089$
Weight $2$
Character 1089.364
Analytic conductor $8.696$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1089,2,Mod(364,1089)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1089.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.69570878012\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 364.11
Character \(\chi\) \(=\) 1089.364
Dual form 1089.2.e.o.727.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.288906 + 0.500400i) q^{2} +(-1.33220 + 1.10691i) q^{3} +(0.833067 - 1.44291i) q^{4} +(-1.50221 + 2.60191i) q^{5} +(-0.938776 - 0.346842i) q^{6} +(-0.582160 - 1.00833i) q^{7} +2.11834 q^{8} +(0.549521 - 2.94924i) q^{9} -1.73599 q^{10} +(0.487356 + 2.84438i) q^{12} +(-1.97309 + 3.41748i) q^{13} +(0.336379 - 0.582626i) q^{14} +(-0.878818 - 5.12908i) q^{15} +(-1.05413 - 1.82581i) q^{16} +0.314191 q^{17} +(1.63456 - 0.577073i) q^{18} -6.36839 q^{19} +(2.50289 + 4.33513i) q^{20} +(1.89168 + 0.698904i) q^{21} +(0.0427501 - 0.0740453i) q^{23} +(-2.82205 + 2.34480i) q^{24} +(-2.01329 - 3.48713i) q^{25} -2.28015 q^{26} +(2.53246 + 4.53725i) q^{27} -1.93991 q^{28} +(-3.84991 - 6.66824i) q^{29} +(2.31269 - 1.92158i) q^{30} +(-3.26442 + 5.65414i) q^{31} +(2.72743 - 4.72404i) q^{32} +(0.0907715 + 0.157221i) q^{34} +3.49812 q^{35} +(-3.79771 - 3.24983i) q^{36} -6.24309 q^{37} +(-1.83987 - 3.18674i) q^{38} +(-1.15428 - 6.73680i) q^{39} +(-3.18219 + 5.51172i) q^{40} +(2.90454 - 5.03080i) q^{41} +(0.196787 + 1.14851i) q^{42} +(-3.39229 - 5.87562i) q^{43} +(6.84817 + 5.86020i) q^{45} +0.0494030 q^{46} +(0.163868 + 0.283827i) q^{47} +(3.42532 + 1.26552i) q^{48} +(2.82218 - 4.88816i) q^{49} +(1.16331 - 2.01490i) q^{50} +(-0.418565 + 0.347779i) q^{51} +(3.28742 + 5.69398i) q^{52} -2.42269 q^{53} +(-1.53880 + 2.57808i) q^{54} +(-1.23321 - 2.13598i) q^{56} +(8.48398 - 7.04920i) q^{57} +(2.22452 - 3.85299i) q^{58} +(1.14802 - 1.98842i) q^{59} +(-8.13293 - 3.00481i) q^{60} +(-6.84360 - 11.8535i) q^{61} -3.77244 q^{62} +(-3.29372 + 1.16283i) q^{63} -1.06465 q^{64} +(-5.92799 - 10.2676i) q^{65} +(-5.83989 + 10.1150i) q^{67} +(0.261742 - 0.453350i) q^{68} +(0.0250094 + 0.145964i) q^{69} +(1.01063 + 1.75046i) q^{70} +8.71765 q^{71} +(1.16407 - 6.24749i) q^{72} -2.94656 q^{73} +(-1.80367 - 3.12404i) q^{74} +(6.54203 + 2.41703i) q^{75} +(-5.30529 + 9.18904i) q^{76} +(3.03761 - 2.52391i) q^{78} +(-4.44360 - 7.69654i) q^{79} +6.33413 q^{80} +(-8.39605 - 3.24134i) q^{81} +3.35655 q^{82} +(2.47889 + 4.29357i) q^{83} +(2.58435 - 2.14730i) q^{84} +(-0.471981 + 0.817496i) q^{85} +(1.96011 - 3.39500i) q^{86} +(12.5100 + 4.62195i) q^{87} +2.12862 q^{89} +(-0.953966 + 5.11987i) q^{90} +4.59461 q^{91} +(-0.0712273 - 0.123369i) q^{92} +(-1.90973 - 11.1459i) q^{93} +(-0.0946848 + 0.163999i) q^{94} +(9.56668 - 16.5700i) q^{95} +(1.59559 + 9.31238i) q^{96} +(0.0444196 + 0.0769370i) q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.288906 + 0.500400i 0.204287 + 0.353836i 0.949905 0.312537i \(-0.101179\pi\)
−0.745618 + 0.666374i \(0.767846\pi\)
\(3\) −1.33220 + 1.10691i −0.769147 + 0.639072i
\(4\) 0.833067 1.44291i 0.416533 0.721457i
\(5\) −1.50221 + 2.60191i −0.671810 + 1.16361i 0.305580 + 0.952166i \(0.401150\pi\)
−0.977390 + 0.211443i \(0.932184\pi\)
\(6\) −0.938776 0.346842i −0.383254 0.141598i
\(7\) −0.582160 1.00833i −0.220036 0.381113i 0.734783 0.678303i \(-0.237284\pi\)
−0.954819 + 0.297189i \(0.903951\pi\)
\(8\) 2.11834 0.748945
\(9\) 0.549521 2.94924i 0.183174 0.983081i
\(10\) −1.73599 −0.548970
\(11\) 0 0
\(12\) 0.487356 + 2.84438i 0.140688 + 0.821101i
\(13\) −1.97309 + 3.41748i −0.547236 + 0.947840i 0.451227 + 0.892409i \(0.350986\pi\)
−0.998463 + 0.0554305i \(0.982347\pi\)
\(14\) 0.336379 0.582626i 0.0899011 0.155713i
\(15\) −0.878818 5.12908i −0.226910 1.32432i
\(16\) −1.05413 1.82581i −0.263533 0.456453i
\(17\) 0.314191 0.0762024 0.0381012 0.999274i \(-0.487869\pi\)
0.0381012 + 0.999274i \(0.487869\pi\)
\(18\) 1.63456 0.577073i 0.385270 0.136018i
\(19\) −6.36839 −1.46101 −0.730504 0.682908i \(-0.760715\pi\)
−0.730504 + 0.682908i \(0.760715\pi\)
\(20\) 2.50289 + 4.33513i 0.559663 + 0.969365i
\(21\) 1.89168 + 0.698904i 0.412799 + 0.152513i
\(22\) 0 0
\(23\) 0.0427501 0.0740453i 0.00891401 0.0154395i −0.861534 0.507700i \(-0.830496\pi\)
0.870448 + 0.492260i \(0.163829\pi\)
\(24\) −2.82205 + 2.34480i −0.576049 + 0.478630i
\(25\) −2.01329 3.48713i −0.402659 0.697425i
\(26\) −2.28015 −0.447173
\(27\) 2.53246 + 4.53725i 0.487372 + 0.873195i
\(28\) −1.93991 −0.366609
\(29\) −3.84991 6.66824i −0.714910 1.23826i −0.962994 0.269522i \(-0.913134\pi\)
0.248084 0.968739i \(-0.420199\pi\)
\(30\) 2.31269 1.92158i 0.422238 0.350831i
\(31\) −3.26442 + 5.65414i −0.586307 + 1.01551i 0.408404 + 0.912801i \(0.366085\pi\)
−0.994711 + 0.102712i \(0.967248\pi\)
\(32\) 2.72743 4.72404i 0.482146 0.835101i
\(33\) 0 0
\(34\) 0.0907715 + 0.157221i 0.0155672 + 0.0269632i
\(35\) 3.49812 0.591290
\(36\) −3.79771 3.24983i −0.632952 0.541638i
\(37\) −6.24309 −1.02636 −0.513179 0.858282i \(-0.671532\pi\)
−0.513179 + 0.858282i \(0.671532\pi\)
\(38\) −1.83987 3.18674i −0.298466 0.516958i
\(39\) −1.15428 6.73680i −0.184833 1.07875i
\(40\) −3.18219 + 5.51172i −0.503149 + 0.871480i
\(41\) 2.90454 5.03080i 0.453612 0.785679i −0.544995 0.838439i \(-0.683468\pi\)
0.998607 + 0.0527599i \(0.0168018\pi\)
\(42\) 0.196787 + 1.14851i 0.0303649 + 0.177220i
\(43\) −3.39229 5.87562i −0.517320 0.896024i −0.999798 0.0201157i \(-0.993597\pi\)
0.482478 0.875908i \(-0.339737\pi\)
\(44\) 0 0
\(45\) 6.84817 + 5.86020i 1.02086 + 0.873587i
\(46\) 0.0494030 0.00728408
\(47\) 0.163868 + 0.283827i 0.0239026 + 0.0414005i 0.877729 0.479157i \(-0.159058\pi\)
−0.853827 + 0.520557i \(0.825724\pi\)
\(48\) 3.42532 + 1.26552i 0.494402 + 0.182663i
\(49\) 2.82218 4.88816i 0.403168 0.698308i
\(50\) 1.16331 2.01490i 0.164516 0.284950i
\(51\) −0.418565 + 0.347779i −0.0586108 + 0.0486988i
\(52\) 3.28742 + 5.69398i 0.455884 + 0.789614i
\(53\) −2.42269 −0.332782 −0.166391 0.986060i \(-0.553211\pi\)
−0.166391 + 0.986060i \(0.553211\pi\)
\(54\) −1.53880 + 2.57808i −0.209404 + 0.350832i
\(55\) 0 0
\(56\) −1.23321 2.13598i −0.164795 0.285433i
\(57\) 8.48398 7.04920i 1.12373 0.933690i
\(58\) 2.22452 3.85299i 0.292094 0.505922i
\(59\) 1.14802 1.98842i 0.149459 0.258870i −0.781569 0.623819i \(-0.785580\pi\)
0.931028 + 0.364949i \(0.118913\pi\)
\(60\) −8.13293 3.00481i −1.04996 0.387919i
\(61\) −6.84360 11.8535i −0.876233 1.51768i −0.855443 0.517897i \(-0.826715\pi\)
−0.0207900 0.999784i \(-0.506618\pi\)
\(62\) −3.77244 −0.479100
\(63\) −3.29372 + 1.16283i −0.414970 + 0.146503i
\(64\) −1.06465 −0.133081
\(65\) −5.92799 10.2676i −0.735277 1.27354i
\(66\) 0 0
\(67\) −5.83989 + 10.1150i −0.713456 + 1.23574i 0.250096 + 0.968221i \(0.419538\pi\)
−0.963552 + 0.267521i \(0.913795\pi\)
\(68\) 0.261742 0.453350i 0.0317408 0.0549767i
\(69\) 0.0250094 + 0.145964i 0.00301078 + 0.0175719i
\(70\) 1.01063 + 1.75046i 0.120793 + 0.209220i
\(71\) 8.71765 1.03459 0.517297 0.855806i \(-0.326938\pi\)
0.517297 + 0.855806i \(0.326938\pi\)
\(72\) 1.16407 6.24749i 0.137187 0.736273i
\(73\) −2.94656 −0.344869 −0.172434 0.985021i \(-0.555163\pi\)
−0.172434 + 0.985021i \(0.555163\pi\)
\(74\) −1.80367 3.12404i −0.209672 0.363162i
\(75\) 6.54203 + 2.41703i 0.755409 + 0.279095i
\(76\) −5.30529 + 9.18904i −0.608559 + 1.05405i
\(77\) 0 0
\(78\) 3.03761 2.52391i 0.343942 0.285776i
\(79\) −4.44360 7.69654i −0.499944 0.865928i 0.500056 0.865993i \(-0.333313\pi\)
−1.00000 6.50093e-5i \(0.999979\pi\)
\(80\) 6.33413 0.708178
\(81\) −8.39605 3.24134i −0.932895 0.360149i
\(82\) 3.35655 0.370669
\(83\) 2.47889 + 4.29357i 0.272094 + 0.471280i 0.969398 0.245495i \(-0.0789506\pi\)
−0.697304 + 0.716775i \(0.745617\pi\)
\(84\) 2.58435 2.14730i 0.281976 0.234290i
\(85\) −0.471981 + 0.817496i −0.0511936 + 0.0886699i
\(86\) 1.96011 3.39500i 0.211364 0.366093i
\(87\) 12.5100 + 4.62195i 1.34121 + 0.495525i
\(88\) 0 0
\(89\) 2.12862 0.225634 0.112817 0.993616i \(-0.464013\pi\)
0.112817 + 0.993616i \(0.464013\pi\)
\(90\) −0.953966 + 5.11987i −0.100557 + 0.539681i
\(91\) 4.59461 0.481646
\(92\) −0.0712273 0.123369i −0.00742596 0.0128621i
\(93\) −1.90973 11.1459i −0.198030 1.15577i
\(94\) −0.0946848 + 0.163999i −0.00976599 + 0.0169152i
\(95\) 9.56668 16.5700i 0.981521 1.70004i
\(96\) 1.59559 + 9.31238i 0.162849 + 0.950441i
\(97\) 0.0444196 + 0.0769370i 0.00451013 + 0.00781177i 0.868272 0.496089i \(-0.165231\pi\)
−0.863762 + 0.503901i \(0.831898\pi\)
\(98\) 3.26138 0.329449
\(99\) 0 0
\(100\) −6.70883 −0.670883
\(101\) −1.02824 1.78097i −0.102314 0.177213i 0.810324 0.585983i \(-0.199291\pi\)
−0.912638 + 0.408770i \(0.865958\pi\)
\(102\) −0.294955 0.108974i −0.0292049 0.0107901i
\(103\) 1.50836 2.61255i 0.148623 0.257422i −0.782096 0.623158i \(-0.785849\pi\)
0.930719 + 0.365736i \(0.119183\pi\)
\(104\) −4.17966 + 7.23938i −0.409849 + 0.709880i
\(105\) −4.66020 + 3.87208i −0.454788 + 0.377877i
\(106\) −0.699931 1.21232i −0.0679833 0.117750i
\(107\) −11.9929 −1.15939 −0.579697 0.814832i \(-0.696829\pi\)
−0.579697 + 0.814832i \(0.696829\pi\)
\(108\) 8.65657 + 0.125714i 0.832979 + 0.0120968i
\(109\) −5.20013 −0.498082 −0.249041 0.968493i \(-0.580115\pi\)
−0.249041 + 0.968493i \(0.580115\pi\)
\(110\) 0 0
\(111\) 8.31705 6.91051i 0.789420 0.655916i
\(112\) −1.22735 + 2.12583i −0.115974 + 0.200872i
\(113\) −9.61378 + 16.6515i −0.904388 + 1.56645i −0.0826514 + 0.996579i \(0.526339\pi\)
−0.821737 + 0.569867i \(0.806995\pi\)
\(114\) 5.97849 + 2.20882i 0.559937 + 0.206875i
\(115\) 0.128440 + 0.222464i 0.0119770 + 0.0207449i
\(116\) −12.8289 −1.19114
\(117\) 8.99474 + 7.69709i 0.831564 + 0.711596i
\(118\) 1.32667 0.122130
\(119\) −0.182909 0.316808i −0.0167673 0.0290417i
\(120\) −1.86163 10.8651i −0.169943 0.991844i
\(121\) 0 0
\(122\) 3.95432 6.84907i 0.358007 0.620086i
\(123\) 1.69920 + 9.91709i 0.153211 + 0.894194i
\(124\) 5.43896 + 9.42055i 0.488433 + 0.845990i
\(125\) −2.92455 −0.261580
\(126\) −1.53346 1.31223i −0.136611 0.116903i
\(127\) 13.1829 1.16980 0.584898 0.811107i \(-0.301135\pi\)
0.584898 + 0.811107i \(0.301135\pi\)
\(128\) −5.76244 9.98084i −0.509332 0.882190i
\(129\) 11.0230 + 4.07256i 0.970518 + 0.358569i
\(130\) 3.42527 5.93274i 0.300416 0.520335i
\(131\) −8.98588 + 15.5640i −0.785100 + 1.35983i 0.143839 + 0.989601i \(0.454055\pi\)
−0.928939 + 0.370233i \(0.879278\pi\)
\(132\) 0 0
\(133\) 3.70742 + 6.42144i 0.321474 + 0.556810i
\(134\) −6.74872 −0.583001
\(135\) −15.6098 0.226691i −1.34348 0.0195105i
\(136\) 0.665561 0.0570714
\(137\) 8.20087 + 14.2043i 0.700648 + 1.21356i 0.968239 + 0.250025i \(0.0804388\pi\)
−0.267592 + 0.963532i \(0.586228\pi\)
\(138\) −0.0658148 + 0.0546845i −0.00560253 + 0.00465505i
\(139\) −5.95080 + 10.3071i −0.504740 + 0.874236i 0.495245 + 0.868754i \(0.335078\pi\)
−0.999985 + 0.00548243i \(0.998255\pi\)
\(140\) 2.91416 5.04748i 0.246292 0.426590i
\(141\) −0.532475 0.196729i −0.0448425 0.0165676i
\(142\) 2.51858 + 4.36231i 0.211355 + 0.366077i
\(143\) 0 0
\(144\) −5.96403 + 2.10557i −0.497002 + 0.175464i
\(145\) 23.1336 1.92114
\(146\) −0.851279 1.47446i −0.0704524 0.122027i
\(147\) 1.65102 + 9.63590i 0.136174 + 0.794755i
\(148\) −5.20091 + 9.00824i −0.427512 + 0.740473i
\(149\) −2.26586 + 3.92458i −0.185626 + 0.321514i −0.943787 0.330553i \(-0.892765\pi\)
0.758161 + 0.652067i \(0.226098\pi\)
\(150\) 0.680551 + 3.97193i 0.0555667 + 0.324306i
\(151\) −1.46543 2.53820i −0.119255 0.206556i 0.800218 0.599710i \(-0.204717\pi\)
−0.919473 + 0.393154i \(0.871384\pi\)
\(152\) −13.4904 −1.09422
\(153\) 0.172654 0.926624i 0.0139583 0.0749131i
\(154\) 0 0
\(155\) −9.80771 16.9874i −0.787774 1.36446i
\(156\) −10.6822 3.94667i −0.855261 0.315986i
\(157\) 9.02682 15.6349i 0.720419 1.24780i −0.240413 0.970671i \(-0.577283\pi\)
0.960832 0.277131i \(-0.0893837\pi\)
\(158\) 2.56756 4.44715i 0.204264 0.353796i
\(159\) 3.22752 2.68169i 0.255959 0.212672i
\(160\) 8.19436 + 14.1930i 0.647821 + 1.12206i
\(161\) −0.0995496 −0.00784561
\(162\) −0.803704 5.13783i −0.0631449 0.403666i
\(163\) −5.82347 −0.456130 −0.228065 0.973646i \(-0.573240\pi\)
−0.228065 + 0.973646i \(0.573240\pi\)
\(164\) −4.83934 8.38199i −0.377889 0.654523i
\(165\) 0 0
\(166\) −1.43233 + 2.48087i −0.111171 + 0.192553i
\(167\) −2.51086 + 4.34894i −0.194296 + 0.336531i −0.946670 0.322206i \(-0.895576\pi\)
0.752373 + 0.658737i \(0.228909\pi\)
\(168\) 4.00722 + 1.48051i 0.309163 + 0.114224i
\(169\) −1.28613 2.22765i −0.0989334 0.171358i
\(170\) −0.545433 −0.0418328
\(171\) −3.49956 + 18.7819i −0.267618 + 1.43629i
\(172\) −11.3040 −0.861923
\(173\) −7.79493 13.5012i −0.592638 1.02648i −0.993876 0.110505i \(-0.964753\pi\)
0.401238 0.915974i \(-0.368580\pi\)
\(174\) 1.30138 + 7.59530i 0.0986574 + 0.575798i
\(175\) −2.34412 + 4.06013i −0.177199 + 0.306917i
\(176\) 0 0
\(177\) 0.671606 + 3.91972i 0.0504810 + 0.294624i
\(178\) 0.614972 + 1.06516i 0.0460941 + 0.0798373i
\(179\) 7.04887 0.526857 0.263428 0.964679i \(-0.415147\pi\)
0.263428 + 0.964679i \(0.415147\pi\)
\(180\) 14.1607 4.99938i 1.05548 0.372632i
\(181\) 2.49770 0.185652 0.0928262 0.995682i \(-0.470410\pi\)
0.0928262 + 0.995682i \(0.470410\pi\)
\(182\) 1.32741 + 2.29914i 0.0983942 + 0.170424i
\(183\) 22.2377 + 8.21598i 1.64386 + 0.607343i
\(184\) 0.0905590 0.156853i 0.00667610 0.0115633i
\(185\) 9.37845 16.2440i 0.689518 1.19428i
\(186\) 5.02565 4.17573i 0.368499 0.306180i
\(187\) 0 0
\(188\) 0.546051 0.0398249
\(189\) 3.10075 5.19496i 0.225547 0.377878i
\(190\) 11.0555 0.802050
\(191\) 5.91149 + 10.2390i 0.427740 + 0.740868i 0.996672 0.0815168i \(-0.0259764\pi\)
−0.568932 + 0.822385i \(0.692643\pi\)
\(192\) 1.41833 1.17847i 0.102359 0.0850486i
\(193\) 3.37333 5.84278i 0.242817 0.420572i −0.718698 0.695322i \(-0.755262\pi\)
0.961516 + 0.274750i \(0.0885951\pi\)
\(194\) −0.0256662 + 0.0444551i −0.00184272 + 0.00319169i
\(195\) 19.2625 + 7.11676i 1.37942 + 0.509642i
\(196\) −4.70213 8.14432i −0.335866 0.581737i
\(197\) 20.6474 1.47107 0.735534 0.677488i \(-0.236931\pi\)
0.735534 + 0.677488i \(0.236931\pi\)
\(198\) 0 0
\(199\) −13.2862 −0.941832 −0.470916 0.882178i \(-0.656077\pi\)
−0.470916 + 0.882178i \(0.656077\pi\)
\(200\) −4.26483 7.38691i −0.301569 0.522333i
\(201\) −3.41642 19.9394i −0.240976 1.40642i
\(202\) 0.594131 1.02906i 0.0418029 0.0724047i
\(203\) −4.48253 + 7.76397i −0.314612 + 0.544924i
\(204\) 0.153123 + 0.893676i 0.0107207 + 0.0625699i
\(205\) 8.72647 + 15.1147i 0.609483 + 1.05566i
\(206\) 1.74309 0.121447
\(207\) −0.194885 0.166770i −0.0135455 0.0115913i
\(208\) 8.31958 0.576859
\(209\) 0 0
\(210\) −3.28395 1.21329i −0.226614 0.0837252i
\(211\) −4.17251 + 7.22700i −0.287247 + 0.497527i −0.973152 0.230165i \(-0.926074\pi\)
0.685904 + 0.727692i \(0.259407\pi\)
\(212\) −2.01826 + 3.49574i −0.138615 + 0.240088i
\(213\) −11.6137 + 9.64961i −0.795755 + 0.661180i
\(214\) −3.46481 6.00123i −0.236850 0.410235i
\(215\) 20.3838 1.39016
\(216\) 5.36460 + 9.61142i 0.365015 + 0.653975i
\(217\) 7.60166 0.516034
\(218\) −1.50235 2.60214i −0.101752 0.176239i
\(219\) 3.92541 3.26156i 0.265255 0.220396i
\(220\) 0 0
\(221\) −0.619925 + 1.07374i −0.0417007 + 0.0722277i
\(222\) 5.86086 + 2.16536i 0.393355 + 0.145330i
\(223\) 0.191828 + 0.332255i 0.0128457 + 0.0222495i 0.872377 0.488834i \(-0.162578\pi\)
−0.859531 + 0.511083i \(0.829244\pi\)
\(224\) −6.35120 −0.424357
\(225\) −11.3907 + 4.02144i −0.759382 + 0.268096i
\(226\) −11.1099 −0.739020
\(227\) 9.00701 + 15.6006i 0.597817 + 1.03545i 0.993143 + 0.116908i \(0.0372982\pi\)
−0.395326 + 0.918541i \(0.629368\pi\)
\(228\) −3.10368 18.1141i −0.205546 1.19964i
\(229\) −6.71393 + 11.6289i −0.443669 + 0.768458i −0.997958 0.0638664i \(-0.979657\pi\)
0.554289 + 0.832324i \(0.312990\pi\)
\(230\) −0.0742139 + 0.128542i −0.00489352 + 0.00847583i
\(231\) 0 0
\(232\) −8.15540 14.1256i −0.535428 0.927389i
\(233\) 3.36965 0.220753 0.110377 0.993890i \(-0.464794\pi\)
0.110377 + 0.993890i \(0.464794\pi\)
\(234\) −1.25299 + 6.72470i −0.0819104 + 0.439607i
\(235\) −0.984658 −0.0642320
\(236\) −1.91275 3.31298i −0.124509 0.215656i
\(237\) 14.4391 + 5.33469i 0.937920 + 0.346526i
\(238\) 0.105687 0.183056i 0.00685068 0.0118657i
\(239\) −11.5984 + 20.0890i −0.750238 + 1.29945i 0.197469 + 0.980309i \(0.436728\pi\)
−0.947707 + 0.319141i \(0.896606\pi\)
\(240\) −8.43834 + 7.01129i −0.544693 + 0.452577i
\(241\) 7.58206 + 13.1325i 0.488404 + 0.845940i 0.999911 0.0133389i \(-0.00424604\pi\)
−0.511507 + 0.859279i \(0.670913\pi\)
\(242\) 0 0
\(243\) 14.7731 4.97552i 0.947694 0.319180i
\(244\) −22.8047 −1.45992
\(245\) 8.47903 + 14.6861i 0.541706 + 0.938262i
\(246\) −4.47160 + 3.71538i −0.285099 + 0.236884i
\(247\) 12.5654 21.7639i 0.799516 1.38480i
\(248\) −6.91513 + 11.9774i −0.439111 + 0.760563i
\(249\) −8.05495 2.97600i −0.510462 0.188596i
\(250\) −0.844920 1.46344i −0.0534375 0.0925564i
\(251\) −0.582306 −0.0367548 −0.0183774 0.999831i \(-0.505850\pi\)
−0.0183774 + 0.999831i \(0.505850\pi\)
\(252\) −1.06602 + 5.72127i −0.0671531 + 0.360406i
\(253\) 0 0
\(254\) 3.80863 + 6.59673i 0.238974 + 0.413916i
\(255\) −0.276116 1.61151i −0.0172911 0.100917i
\(256\) 2.26495 3.92302i 0.141560 0.245189i
\(257\) 5.48571 9.50153i 0.342189 0.592689i −0.642650 0.766160i \(-0.722165\pi\)
0.984839 + 0.173471i \(0.0554983\pi\)
\(258\) 1.14669 + 6.69248i 0.0713899 + 0.416656i
\(259\) 3.63448 + 6.29510i 0.225835 + 0.391158i
\(260\) −19.7537 −1.22507
\(261\) −21.7819 + 7.68998i −1.34826 + 0.475998i
\(262\) −10.3843 −0.641544
\(263\) −7.19768 12.4668i −0.443828 0.768733i 0.554142 0.832422i \(-0.313047\pi\)
−0.997970 + 0.0636896i \(0.979713\pi\)
\(264\) 0 0
\(265\) 3.63940 6.30363i 0.223567 0.387229i
\(266\) −2.14219 + 3.71039i −0.131346 + 0.227498i
\(267\) −2.83575 + 2.35618i −0.173545 + 0.144196i
\(268\) 9.73004 + 16.8529i 0.594357 + 1.02946i
\(269\) 0.488976 0.0298134 0.0149067 0.999889i \(-0.495255\pi\)
0.0149067 + 0.999889i \(0.495255\pi\)
\(270\) −4.39633 7.87665i −0.267552 0.479357i
\(271\) −21.9389 −1.33270 −0.666348 0.745641i \(-0.732143\pi\)
−0.666348 + 0.745641i \(0.732143\pi\)
\(272\) −0.331199 0.573653i −0.0200819 0.0347828i
\(273\) −6.12094 + 5.08580i −0.370456 + 0.307806i
\(274\) −4.73856 + 8.20743i −0.286267 + 0.495829i
\(275\) 0 0
\(276\) 0.231447 + 0.0855109i 0.0139315 + 0.00514715i
\(277\) 1.43476 + 2.48508i 0.0862065 + 0.149314i 0.905905 0.423482i \(-0.139192\pi\)
−0.819698 + 0.572796i \(0.805859\pi\)
\(278\) −6.87689 −0.412448
\(279\) 14.8816 + 12.7346i 0.890935 + 0.762402i
\(280\) 7.41019 0.442843
\(281\) 9.08903 + 15.7427i 0.542206 + 0.939129i 0.998777 + 0.0494416i \(0.0157442\pi\)
−0.456571 + 0.889687i \(0.650922\pi\)
\(282\) −0.0553920 0.323287i −0.00329855 0.0192514i
\(283\) −10.2686 + 17.7857i −0.610402 + 1.05725i 0.380770 + 0.924670i \(0.375659\pi\)
−0.991173 + 0.132578i \(0.957674\pi\)
\(284\) 7.26238 12.5788i 0.430943 0.746415i
\(285\) 5.59665 + 32.6640i 0.331517 + 1.93485i
\(286\) 0 0
\(287\) −6.76362 −0.399244
\(288\) −12.4336 10.6398i −0.732655 0.626956i
\(289\) −16.9013 −0.994193
\(290\) 6.68342 + 11.5760i 0.392464 + 0.679768i
\(291\) −0.144338 0.0533273i −0.00846124 0.00312610i
\(292\) −2.45468 + 4.25163i −0.143649 + 0.248808i
\(293\) 0.430033 0.744840i 0.0251228 0.0435140i −0.853191 0.521599i \(-0.825336\pi\)
0.878313 + 0.478085i \(0.158669\pi\)
\(294\) −4.34481 + 3.61004i −0.253395 + 0.210542i
\(295\) 3.44913 + 5.97407i 0.200816 + 0.347824i
\(296\) −13.2250 −0.768685
\(297\) 0 0
\(298\) −2.61848 −0.151684
\(299\) 0.168699 + 0.292196i 0.00975612 + 0.0168981i
\(300\) 8.93751 7.42604i 0.516007 0.428743i
\(301\) −3.94971 + 6.84110i −0.227658 + 0.394315i
\(302\) 0.846744 1.46660i 0.0487247 0.0843936i
\(303\) 3.34119 + 1.23444i 0.191946 + 0.0709167i
\(304\) 6.71313 + 11.6275i 0.385024 + 0.666882i
\(305\) 41.1222 2.35465
\(306\) 0.513563 0.181311i 0.0293585 0.0103649i
\(307\) −3.48920 −0.199139 −0.0995696 0.995031i \(-0.531747\pi\)
−0.0995696 + 0.995031i \(0.531747\pi\)
\(308\) 0 0
\(309\) 0.882412 + 5.15005i 0.0501986 + 0.292976i
\(310\) 5.66701 9.81555i 0.321865 0.557486i
\(311\) −5.42265 + 9.39231i −0.307490 + 0.532589i −0.977813 0.209481i \(-0.932822\pi\)
0.670322 + 0.742070i \(0.266156\pi\)
\(312\) −2.44516 14.2708i −0.138430 0.807925i
\(313\) 14.1405 + 24.4921i 0.799270 + 1.38438i 0.920092 + 0.391702i \(0.128114\pi\)
−0.120822 + 0.992674i \(0.538553\pi\)
\(314\) 10.4316 0.588690
\(315\) 1.92229 10.3168i 0.108309 0.581285i
\(316\) −14.8072 −0.832973
\(317\) 0.556263 + 0.963477i 0.0312429 + 0.0541142i 0.881224 0.472699i \(-0.156720\pi\)
−0.849981 + 0.526813i \(0.823387\pi\)
\(318\) 2.27437 + 0.840291i 0.127540 + 0.0471212i
\(319\) 0 0
\(320\) 1.59933 2.77013i 0.0894055 0.154855i
\(321\) 15.9769 13.2750i 0.891744 0.740936i
\(322\) −0.0287605 0.0498146i −0.00160276 0.00277606i
\(323\) −2.00089 −0.111332
\(324\) −11.6714 + 9.41453i −0.648414 + 0.523029i
\(325\) 15.8896 0.881396
\(326\) −1.68244 2.91407i −0.0931816 0.161395i
\(327\) 6.92762 5.75605i 0.383098 0.318310i
\(328\) 6.15278 10.6569i 0.339731 0.588431i
\(329\) 0.190795 0.330466i 0.0105188 0.0182192i
\(330\) 0 0
\(331\) 6.18915 + 10.7199i 0.340187 + 0.589221i 0.984467 0.175569i \(-0.0561764\pi\)
−0.644281 + 0.764789i \(0.722843\pi\)
\(332\) 8.26033 0.453344
\(333\) −3.43071 + 18.4124i −0.188002 + 1.00899i
\(334\) −2.90161 −0.158769
\(335\) −17.5455 30.3897i −0.958615 1.66037i
\(336\) −0.718017 4.19059i −0.0391710 0.228616i
\(337\) 6.73681 11.6685i 0.366977 0.635623i −0.622114 0.782927i \(-0.713726\pi\)
0.989091 + 0.147303i \(0.0470593\pi\)
\(338\) 0.743144 1.28716i 0.0404217 0.0700124i
\(339\) −5.62420 32.8248i −0.305465 1.78280i
\(340\) 0.786384 + 1.36206i 0.0426477 + 0.0738679i
\(341\) 0 0
\(342\) −10.4095 + 3.67503i −0.562882 + 0.198723i
\(343\) −14.7221 −0.794918
\(344\) −7.18601 12.4465i −0.387444 0.671072i
\(345\) −0.417354 0.154196i −0.0224696 0.00830164i
\(346\) 4.50400 7.80117i 0.242137 0.419393i
\(347\) 4.86958 8.43437i 0.261413 0.452781i −0.705205 0.709004i \(-0.749145\pi\)
0.966618 + 0.256223i \(0.0824782\pi\)
\(348\) 17.0907 14.2004i 0.916158 0.761222i
\(349\) −2.22010 3.84532i −0.118839 0.205835i 0.800469 0.599374i \(-0.204584\pi\)
−0.919308 + 0.393539i \(0.871251\pi\)
\(350\) −2.70892 −0.144798
\(351\) −20.5027 0.297748i −1.09436 0.0158926i
\(352\) 0 0
\(353\) −16.2618 28.1662i −0.865527 1.49914i −0.866523 0.499137i \(-0.833651\pi\)
0.000996749 1.00000i \(-0.499683\pi\)
\(354\) −1.76740 + 1.46850i −0.0939361 + 0.0780501i
\(355\) −13.0958 + 22.6825i −0.695051 + 1.20386i
\(356\) 1.77328 3.07142i 0.0939839 0.162785i
\(357\) 0.594348 + 0.219589i 0.0314563 + 0.0116219i
\(358\) 2.03646 + 3.52725i 0.107630 + 0.186421i
\(359\) 27.7701 1.46565 0.732825 0.680417i \(-0.238201\pi\)
0.732825 + 0.680417i \(0.238201\pi\)
\(360\) 14.5067 + 12.4139i 0.764571 + 0.654268i
\(361\) 21.5564 1.13455
\(362\) 0.721600 + 1.24985i 0.0379264 + 0.0656905i
\(363\) 0 0
\(364\) 3.82761 6.62962i 0.200621 0.347487i
\(365\) 4.42637 7.66669i 0.231687 0.401293i
\(366\) 2.31333 + 13.5014i 0.120920 + 0.705729i
\(367\) −0.586098 1.01515i −0.0305941 0.0529905i 0.850323 0.526261i \(-0.176407\pi\)
−0.880917 + 0.473271i \(0.843073\pi\)
\(368\) −0.180257 −0.00939655
\(369\) −13.2409 11.3307i −0.689296 0.589853i
\(370\) 10.8380 0.563439
\(371\) 1.41040 + 2.44288i 0.0732241 + 0.126828i
\(372\) −17.6734 6.52966i −0.916325 0.338547i
\(373\) 10.8834 18.8506i 0.563520 0.976046i −0.433665 0.901074i \(-0.642780\pi\)
0.997186 0.0749719i \(-0.0238867\pi\)
\(374\) 0 0
\(375\) 3.89609 3.23720i 0.201193 0.167168i
\(376\) 0.347127 + 0.601242i 0.0179017 + 0.0310067i
\(377\) 30.3848 1.56490
\(378\) 3.49539 + 0.0507612i 0.179783 + 0.00261087i
\(379\) −16.2469 −0.834545 −0.417273 0.908781i \(-0.637014\pi\)
−0.417273 + 0.908781i \(0.637014\pi\)
\(380\) −15.9394 27.6078i −0.817672 1.41625i
\(381\) −17.5623 + 14.5922i −0.899744 + 0.747584i
\(382\) −3.41573 + 5.91622i −0.174764 + 0.302700i
\(383\) −3.09667 + 5.36360i −0.158233 + 0.274067i −0.934231 0.356667i \(-0.883913\pi\)
0.775999 + 0.630734i \(0.217246\pi\)
\(384\) 18.7246 + 6.91801i 0.955534 + 0.353033i
\(385\) 0 0
\(386\) 3.89830 0.198418
\(387\) −19.1928 + 6.77591i −0.975623 + 0.344439i
\(388\) 0.148018 0.00751447
\(389\) 0.361607 + 0.626321i 0.0183342 + 0.0317557i 0.875047 0.484038i \(-0.160830\pi\)
−0.856713 + 0.515794i \(0.827497\pi\)
\(390\) 2.00383 + 11.6950i 0.101468 + 0.592202i
\(391\) 0.0134317 0.0232643i 0.000679269 0.00117653i
\(392\) 5.97832 10.3548i 0.301951 0.522994i
\(393\) −5.25688 30.6809i −0.265174 1.54765i
\(394\) 5.96517 + 10.3320i 0.300521 + 0.520517i
\(395\) 26.7009 1.34347
\(396\) 0 0
\(397\) 4.08994 0.205268 0.102634 0.994719i \(-0.467273\pi\)
0.102634 + 0.994719i \(0.467273\pi\)
\(398\) −3.83846 6.64840i −0.192404 0.333254i
\(399\) −12.0470 4.45089i −0.603103 0.222823i
\(400\) −4.24456 + 7.35179i −0.212228 + 0.367590i
\(401\) 2.82313 4.88981i 0.140981 0.244185i −0.786886 0.617099i \(-0.788308\pi\)
0.927866 + 0.372913i \(0.121641\pi\)
\(402\) 8.99065 7.47019i 0.448413 0.372579i
\(403\) −12.8820 22.3122i −0.641696 1.11145i
\(404\) −3.42638 −0.170469
\(405\) 21.0463 16.9766i 1.04580 0.843574i
\(406\) −5.18012 −0.257085
\(407\) 0 0
\(408\) −0.886662 + 0.736713i −0.0438963 + 0.0364727i
\(409\) 4.72439 8.18288i 0.233606 0.404617i −0.725261 0.688474i \(-0.758281\pi\)
0.958867 + 0.283857i \(0.0916141\pi\)
\(410\) −5.04226 + 8.73345i −0.249019 + 0.431314i
\(411\) −26.6481 9.84543i −1.31445 0.485639i
\(412\) −2.51312 4.35286i −0.123813 0.214450i
\(413\) −2.67332 −0.131545
\(414\) 0.0271480 0.145701i 0.00133425 0.00716084i
\(415\) −14.8953 −0.731182
\(416\) 10.7629 + 18.6419i 0.527694 + 0.913993i
\(417\) −3.48131 20.3181i −0.170480 0.994981i
\(418\) 0 0
\(419\) −0.0757820 + 0.131258i −0.00370219 + 0.00641238i −0.867871 0.496790i \(-0.834512\pi\)
0.864168 + 0.503203i \(0.167845\pi\)
\(420\) 1.70483 + 9.94996i 0.0831871 + 0.485508i
\(421\) −8.48828 14.7021i −0.413693 0.716538i 0.581597 0.813477i \(-0.302428\pi\)
−0.995290 + 0.0969391i \(0.969095\pi\)
\(422\) −4.82185 −0.234724
\(423\) 0.927124 0.327317i 0.0450783 0.0159147i
\(424\) −5.13208 −0.249236
\(425\) −0.632558 1.09562i −0.0306836 0.0531455i
\(426\) −8.18392 3.02364i −0.396512 0.146496i
\(427\) −7.96814 + 13.8012i −0.385605 + 0.667888i
\(428\) −9.99085 + 17.3047i −0.482926 + 0.836453i
\(429\) 0 0
\(430\) 5.88900 + 10.2000i 0.283993 + 0.491890i
\(431\) 25.3694 1.22200 0.610999 0.791631i \(-0.290768\pi\)
0.610999 + 0.791631i \(0.290768\pi\)
\(432\) 5.61462 9.40666i 0.270134 0.452578i
\(433\) 16.5347 0.794607 0.397303 0.917687i \(-0.369946\pi\)
0.397303 + 0.917687i \(0.369946\pi\)
\(434\) 2.19616 + 3.80387i 0.105419 + 0.182592i
\(435\) −30.8185 + 25.6067i −1.47764 + 1.22774i
\(436\) −4.33205 + 7.50333i −0.207468 + 0.359344i
\(437\) −0.272249 + 0.471549i −0.0130234 + 0.0225573i
\(438\) 2.76616 + 1.02199i 0.132172 + 0.0488326i
\(439\) −19.6207 33.9840i −0.936443 1.62197i −0.772040 0.635574i \(-0.780763\pi\)
−0.164403 0.986393i \(-0.552570\pi\)
\(440\) 0 0
\(441\) −12.8655 11.0094i −0.612643 0.524259i
\(442\) −0.716400 −0.0340757
\(443\) −16.0947 27.8768i −0.764681 1.32447i −0.940415 0.340029i \(-0.889563\pi\)
0.175734 0.984438i \(-0.443770\pi\)
\(444\) −3.04261 17.7577i −0.144396 0.842743i
\(445\) −3.19765 + 5.53849i −0.151583 + 0.262549i
\(446\) −0.110840 + 0.191981i −0.00524845 + 0.00909057i
\(447\) −1.32556 7.73642i −0.0626969 0.365920i
\(448\) 0.619798 + 1.07352i 0.0292827 + 0.0507191i
\(449\) −25.8443 −1.21967 −0.609833 0.792530i \(-0.708764\pi\)
−0.609833 + 0.792530i \(0.708764\pi\)
\(450\) −5.30318 4.53810i −0.249994 0.213928i
\(451\) 0 0
\(452\) 16.0178 + 27.7437i 0.753415 + 1.30495i
\(453\) 4.76180 + 1.75930i 0.223729 + 0.0826592i
\(454\) −5.20436 + 9.01422i −0.244253 + 0.423058i
\(455\) −6.90208 + 11.9548i −0.323575 + 0.560448i
\(456\) 17.9719 14.9326i 0.841612 0.699282i
\(457\) −6.35814 11.0126i −0.297421 0.515149i 0.678124 0.734947i \(-0.262793\pi\)
−0.975545 + 0.219799i \(0.929460\pi\)
\(458\) −7.75879 −0.362544
\(459\) 0.795675 + 1.42556i 0.0371389 + 0.0665395i
\(460\) 0.427995 0.0199554
\(461\) −9.51087 16.4733i −0.442965 0.767238i 0.554943 0.831889i \(-0.312740\pi\)
−0.997908 + 0.0646502i \(0.979407\pi\)
\(462\) 0 0
\(463\) 11.4334 19.8032i 0.531353 0.920331i −0.467977 0.883741i \(-0.655017\pi\)
0.999330 0.0365903i \(-0.0116497\pi\)
\(464\) −8.11663 + 14.0584i −0.376805 + 0.652646i
\(465\) 31.8693 + 11.7745i 1.47791 + 0.546029i
\(466\) 0.973513 + 1.68617i 0.0450971 + 0.0781105i
\(467\) 15.9228 0.736821 0.368411 0.929663i \(-0.379902\pi\)
0.368411 + 0.929663i \(0.379902\pi\)
\(468\) 18.5994 6.56644i 0.859760 0.303534i
\(469\) 13.5990 0.627944
\(470\) −0.284474 0.492723i −0.0131218 0.0227276i
\(471\) 5.28082 + 30.8207i 0.243328 + 1.42014i
\(472\) 2.43188 4.21215i 0.111936 0.193880i
\(473\) 0 0
\(474\) 1.50206 + 8.76655i 0.0689920 + 0.402661i
\(475\) 12.8214 + 22.2074i 0.588288 + 1.01894i
\(476\) −0.609502 −0.0279365
\(477\) −1.33132 + 7.14511i −0.0609570 + 0.327152i
\(478\) −13.4034 −0.613057
\(479\) −8.19498 14.1941i −0.374438 0.648546i 0.615805 0.787899i \(-0.288831\pi\)
−0.990243 + 0.139353i \(0.955498\pi\)
\(480\) −26.6269 9.83761i −1.21535 0.449024i
\(481\) 12.3181 21.3357i 0.561659 0.972822i
\(482\) −4.38101 + 7.58813i −0.199549 + 0.345630i
\(483\) 0.132620 0.110192i 0.00603442 0.00501391i
\(484\) 0 0
\(485\) −0.266911 −0.0121198
\(486\) 6.75778 + 5.95500i 0.306539 + 0.270124i
\(487\) 22.7865 1.03256 0.516278 0.856421i \(-0.327317\pi\)
0.516278 + 0.856421i \(0.327317\pi\)
\(488\) −14.4970 25.1096i −0.656250 1.13666i
\(489\) 7.75804 6.44603i 0.350831 0.291500i
\(490\) −4.89929 + 8.48582i −0.221327 + 0.383350i
\(491\) −21.8215 + 37.7960i −0.984791 + 1.70571i −0.341928 + 0.939726i \(0.611080\pi\)
−0.642863 + 0.765981i \(0.722253\pi\)
\(492\) 15.7250 + 5.80980i 0.708940 + 0.261926i
\(493\) −1.20961 2.09510i −0.0544779 0.0943585i
\(494\) 14.5209 0.653324
\(495\) 0 0
\(496\) 13.7645 0.618045
\(497\) −5.07507 8.79027i −0.227648 0.394298i
\(498\) −0.837937 4.89048i −0.0375488 0.219148i
\(499\) 10.0518 17.4102i 0.449978 0.779385i −0.548406 0.836212i \(-0.684765\pi\)
0.998384 + 0.0568270i \(0.0180983\pi\)
\(500\) −2.43635 + 4.21987i −0.108957 + 0.188718i
\(501\) −1.46889 8.57296i −0.0656253 0.383011i
\(502\) −0.168232 0.291386i −0.00750854 0.0130052i
\(503\) 10.6083 0.473001 0.236500 0.971631i \(-0.424000\pi\)
0.236500 + 0.971631i \(0.424000\pi\)
\(504\) −6.97721 + 2.46327i −0.310790 + 0.109723i
\(505\) 6.17856 0.274942
\(506\) 0 0
\(507\) 4.17919 + 1.54405i 0.185604 + 0.0685736i
\(508\) 10.9823 19.0218i 0.487259 0.843957i
\(509\) 22.2342 38.5107i 0.985513 1.70696i 0.345878 0.938280i \(-0.387581\pi\)
0.639635 0.768679i \(-0.279086\pi\)
\(510\) 0.726627 0.603743i 0.0321756 0.0267342i
\(511\) 1.71537 + 2.97111i 0.0758835 + 0.131434i
\(512\) −20.4323 −0.902989
\(513\) −16.1277 28.8950i −0.712055 1.27574i
\(514\) 6.33942 0.279620
\(515\) 4.53175 + 7.84922i 0.199693 + 0.345878i
\(516\) 15.0592 12.5125i 0.662946 0.550831i
\(517\) 0 0
\(518\) −2.10004 + 3.63738i −0.0922707 + 0.159817i
\(519\) 25.3290 + 9.35809i 1.11182 + 0.410774i
\(520\) −12.5575 21.7502i −0.550682 0.953809i
\(521\) 16.9511 0.742643 0.371322 0.928504i \(-0.378905\pi\)
0.371322 + 0.928504i \(0.378905\pi\)
\(522\) −10.1410 8.67796i −0.443858 0.379824i
\(523\) −30.2142 −1.32117 −0.660587 0.750749i \(-0.729693\pi\)
−0.660587 + 0.750749i \(0.729693\pi\)
\(524\) 14.9717 + 25.9317i 0.654041 + 1.13283i
\(525\) −1.37134 8.00363i −0.0598504 0.349307i
\(526\) 4.15891 7.20344i 0.181337 0.314085i
\(527\) −1.02565 + 1.77648i −0.0446780 + 0.0773845i
\(528\) 0 0
\(529\) 11.4963 + 19.9123i 0.499841 + 0.865750i
\(530\) 4.20578 0.182688
\(531\) −5.23348 4.47846i −0.227114 0.194348i
\(532\) 12.3541 0.535619
\(533\) 11.4618 + 19.8524i 0.496465 + 0.859903i
\(534\) −1.99830 0.738296i −0.0864750 0.0319492i
\(535\) 18.0158 31.2044i 0.778893 1.34908i
\(536\) −12.3709 + 21.4269i −0.534339 + 0.925503i
\(537\) −9.39051 + 7.80243i −0.405230 + 0.336700i
\(538\) 0.141268 + 0.244683i 0.00609050 + 0.0105491i
\(539\) 0 0
\(540\) −13.3311 + 22.3348i −0.573680 + 0.961136i
\(541\) −11.8312 −0.508663 −0.254332 0.967117i \(-0.581855\pi\)
−0.254332 + 0.967117i \(0.581855\pi\)
\(542\) −6.33829 10.9782i −0.272253 0.471556i
\(543\) −3.32744 + 2.76471i −0.142794 + 0.118645i
\(544\) 0.856932 1.48425i 0.0367406 0.0636367i
\(545\) 7.81170 13.5303i 0.334617 0.579573i
\(546\) −4.31331 1.59360i −0.184593 0.0681999i
\(547\) 1.27290 + 2.20474i 0.0544255 + 0.0942677i 0.891955 0.452125i \(-0.149334\pi\)
−0.837529 + 0.546393i \(0.816001\pi\)
\(548\) 27.3275 1.16737
\(549\) −38.7194 + 13.6697i −1.65251 + 0.583409i
\(550\) 0 0
\(551\) 24.5177 + 42.4659i 1.04449 + 1.80911i
\(552\) 0.0529784 + 0.309200i 0.00225491 + 0.0131604i
\(553\) −5.17377 + 8.96123i −0.220011 + 0.381070i
\(554\) −0.829023 + 1.43591i −0.0352218 + 0.0610060i
\(555\) 5.48654 + 32.0213i 0.232890 + 1.35923i
\(556\) 9.91483 + 17.1730i 0.420482 + 0.728297i
\(557\) −9.67543 −0.409961 −0.204981 0.978766i \(-0.565713\pi\)
−0.204981 + 0.978766i \(0.565713\pi\)
\(558\) −2.07304 + 11.1258i −0.0877586 + 0.470994i
\(559\) 26.7731 1.13238
\(560\) −3.68748 6.38690i −0.155824 0.269896i
\(561\) 0 0
\(562\) −5.25175 + 9.09630i −0.221532 + 0.383704i
\(563\) −11.9936 + 20.7735i −0.505470 + 0.875501i 0.494510 + 0.869172i \(0.335348\pi\)
−0.999980 + 0.00632830i \(0.997986\pi\)
\(564\) −0.727450 + 0.604427i −0.0306312 + 0.0254510i
\(565\) −28.8839 50.0284i −1.21515 2.10471i
\(566\) −11.8666 −0.498790
\(567\) 1.61950 + 10.3530i 0.0680127 + 0.434784i
\(568\) 18.4669 0.774854
\(569\) −18.8096 32.5791i −0.788538 1.36579i −0.926863 0.375401i \(-0.877505\pi\)
0.138325 0.990387i \(-0.455828\pi\)
\(570\) −14.7281 + 12.2374i −0.616894 + 0.512568i
\(571\) −7.37740 + 12.7780i −0.308735 + 0.534744i −0.978086 0.208202i \(-0.933239\pi\)
0.669351 + 0.742946i \(0.266572\pi\)
\(572\) 0 0
\(573\) −19.2089 7.09695i −0.802463 0.296479i
\(574\) −1.95405 3.38451i −0.0815605 0.141267i
\(575\) −0.344274 −0.0143572
\(576\) −0.585049 + 3.13992i −0.0243770 + 0.130830i
\(577\) −22.3068 −0.928644 −0.464322 0.885667i \(-0.653702\pi\)
−0.464322 + 0.885667i \(0.653702\pi\)
\(578\) −4.88288 8.45740i −0.203101 0.351782i
\(579\) 1.97345 + 11.5177i 0.0820137 + 0.478660i
\(580\) 19.2718 33.3797i 0.800217 1.38602i
\(581\) 2.88622 4.99909i 0.119741 0.207397i
\(582\) −0.0150151 0.0876332i −0.000622396 0.00363251i
\(583\) 0 0
\(584\) −6.24181 −0.258288
\(585\) −33.5391 + 11.8408i −1.38667 + 0.489558i
\(586\) 0.496957 0.0205291
\(587\) 1.25008 + 2.16521i 0.0515965 + 0.0893677i 0.890670 0.454650i \(-0.150236\pi\)
−0.839074 + 0.544018i \(0.816902\pi\)
\(588\) 15.2792 + 5.64507i 0.630102 + 0.232799i
\(589\) 20.7891 36.0078i 0.856599 1.48367i
\(590\) −1.99295 + 3.45189i −0.0820484 + 0.142112i
\(591\) −27.5065 + 22.8547i −1.13147 + 0.940119i
\(592\) 6.58105 + 11.3987i 0.270479 + 0.468484i
\(593\) 10.8953 0.447417 0.223708 0.974656i \(-0.428184\pi\)
0.223708 + 0.974656i \(0.428184\pi\)
\(594\) 0 0
\(595\) 1.09907 0.0450577
\(596\) 3.77522 + 6.53887i 0.154639 + 0.267843i
\(597\) 17.6999 14.7065i 0.724407 0.601899i
\(598\) −0.0974764 + 0.168834i −0.00398611 + 0.00690414i
\(599\) 18.4190 31.9027i 0.752582 1.30351i −0.193986 0.981004i \(-0.562142\pi\)
0.946568 0.322506i \(-0.104525\pi\)
\(600\) 13.8582 + 5.12008i 0.565759 + 0.209026i
\(601\) −7.72714 13.3838i −0.315197 0.545937i 0.664283 0.747482i \(-0.268737\pi\)
−0.979479 + 0.201545i \(0.935404\pi\)
\(602\) −4.56438 −0.186030
\(603\) 26.6224 + 22.7816i 1.08415 + 0.927740i
\(604\) −4.88321 −0.198695
\(605\) 0 0
\(606\) 0.347575 + 2.02857i 0.0141193 + 0.0824049i
\(607\) −12.7385 + 22.0636i −0.517038 + 0.895536i 0.482766 + 0.875749i \(0.339632\pi\)
−0.999804 + 0.0197865i \(0.993701\pi\)
\(608\) −17.3693 + 30.0845i −0.704419 + 1.22009i
\(609\) −2.62235 15.3049i −0.106263 0.620186i
\(610\) 11.8805 + 20.5776i 0.481026 + 0.833161i
\(611\) −1.29330 −0.0523214
\(612\) −1.19321 1.02106i −0.0482325 0.0412741i
\(613\) 37.7740 1.52568 0.762839 0.646588i \(-0.223805\pi\)
0.762839 + 0.646588i \(0.223805\pi\)
\(614\) −1.00805 1.74600i −0.0406816 0.0704626i
\(615\) −28.3559 10.4764i −1.14342 0.422450i
\(616\) 0 0
\(617\) −20.9464 + 36.2802i −0.843271 + 1.46059i 0.0438437 + 0.999038i \(0.486040\pi\)
−0.887115 + 0.461549i \(0.847294\pi\)
\(618\) −2.32215 + 1.92944i −0.0934107 + 0.0776135i
\(619\) 2.99480 + 5.18715i 0.120371 + 0.208489i 0.919914 0.392120i \(-0.128258\pi\)
−0.799543 + 0.600609i \(0.794925\pi\)
\(620\) −32.6819 −1.31254
\(621\) 0.444225 + 0.00645119i 0.0178261 + 0.000258877i
\(622\) −6.26655 −0.251266
\(623\) −1.23920 2.14636i −0.0496475 0.0859920i
\(624\) −11.0834 + 9.20899i −0.443689 + 0.368655i
\(625\) 14.4598 25.0451i 0.578391 1.00180i
\(626\) −8.17057 + 14.1518i −0.326562 + 0.565621i
\(627\) 0 0
\(628\) −15.0399 26.0498i −0.600157 1.03950i
\(629\) −1.96152 −0.0782109
\(630\) 5.71788 2.01867i 0.227806 0.0804257i
\(631\) −21.4994 −0.855878 −0.427939 0.903808i \(-0.640760\pi\)
−0.427939 + 0.903808i \(0.640760\pi\)
\(632\) −9.41303 16.3038i −0.374430 0.648532i
\(633\) −2.44098 14.2464i −0.0970202 0.566243i
\(634\) −0.321416 + 0.556708i −0.0127651 + 0.0221097i
\(635\) −19.8036 + 34.3008i −0.785881 + 1.36119i
\(636\) −1.18071 6.89105i −0.0468184 0.273248i
\(637\) 11.1368 + 19.2895i 0.441256 + 0.764278i
\(638\) 0 0
\(639\) 4.79053 25.7104i 0.189510 1.01709i
\(640\) 34.6257 1.36870
\(641\) −6.41850 11.1172i −0.253516 0.439102i 0.710976 0.703217i \(-0.248254\pi\)
−0.964491 + 0.264115i \(0.914920\pi\)
\(642\) 11.2586 + 4.15963i 0.444342 + 0.164167i
\(643\) −14.1778 + 24.5566i −0.559117 + 0.968419i 0.438453 + 0.898754i \(0.355527\pi\)
−0.997570 + 0.0696654i \(0.977807\pi\)
\(644\) −0.0829314 + 0.143641i −0.00326796 + 0.00566027i
\(645\) −27.1553 + 22.5629i −1.06924 + 0.888414i
\(646\) −0.578069 1.00124i −0.0227438 0.0393934i
\(647\) −17.4948 −0.687792 −0.343896 0.939008i \(-0.611747\pi\)
−0.343896 + 0.939008i \(0.611747\pi\)
\(648\) −17.7857 6.86625i −0.698687 0.269732i
\(649\) 0 0
\(650\) 4.59060 + 7.95116i 0.180058 + 0.311870i
\(651\) −10.1269 + 8.41431i −0.396906 + 0.329783i
\(652\) −4.85134 + 8.40277i −0.189993 + 0.329078i
\(653\) 14.6511 25.3765i 0.573342 0.993058i −0.422877 0.906187i \(-0.638980\pi\)
0.996220 0.0868708i \(-0.0276867\pi\)
\(654\) 4.88176 + 1.80362i 0.190892 + 0.0705272i
\(655\) −26.9974 46.7609i −1.05488 1.82710i
\(656\) −12.2471 −0.478168
\(657\) −1.61920 + 8.69012i −0.0631709 + 0.339034i
\(658\) 0.220487 0.00859547
\(659\) 13.7935 + 23.8911i 0.537319 + 0.930664i 0.999047 + 0.0436422i \(0.0138961\pi\)
−0.461728 + 0.887021i \(0.652771\pi\)
\(660\) 0 0
\(661\) −14.8776 + 25.7688i −0.578672 + 1.00229i 0.416960 + 0.908925i \(0.363096\pi\)
−0.995632 + 0.0933649i \(0.970238\pi\)
\(662\) −3.57617 + 6.19410i −0.138992 + 0.240741i
\(663\) −0.362665 2.11664i −0.0140848 0.0822034i
\(664\) 5.25113 + 9.09522i 0.203783 + 0.352963i
\(665\) −22.2774 −0.863879
\(666\) −10.2047 + 3.60272i −0.395424 + 0.139603i
\(667\) −0.658336 −0.0254909
\(668\) 4.18343 + 7.24592i 0.161862 + 0.280353i
\(669\) −0.623329 0.230296i −0.0240993 0.00890376i
\(670\) 10.1380 17.5596i 0.391666 0.678385i
\(671\) 0 0
\(672\) 8.46107 7.03017i 0.326393 0.271195i
\(673\) 4.82684 + 8.36033i 0.186061 + 0.322267i 0.943934 0.330136i \(-0.107094\pi\)
−0.757873 + 0.652403i \(0.773761\pi\)
\(674\) 7.78522 0.299875
\(675\) 10.7234 17.9658i 0.412743 0.691505i
\(676\) −4.28574 −0.164836
\(677\) −0.0490576 0.0849702i −0.00188544 0.00326567i 0.865081 0.501632i \(-0.167267\pi\)
−0.866967 + 0.498366i \(0.833933\pi\)
\(678\) 14.8006 12.2976i 0.568415 0.472287i
\(679\) 0.0517187 0.0895793i 0.00198478 0.00343774i
\(680\) −0.999815 + 1.73173i −0.0383412 + 0.0664088i
\(681\) −29.2676 10.8132i −1.12153 0.414364i
\(682\) 0 0
\(683\) 30.5246 1.16799 0.583996 0.811756i \(-0.301488\pi\)
0.583996 + 0.811756i \(0.301488\pi\)
\(684\) 24.1853 + 20.6962i 0.924749 + 0.791337i
\(685\) −49.2778 −1.88281
\(686\) −4.25330 7.36693i −0.162392 0.281271i
\(687\) −3.92775 22.9237i −0.149853 0.874593i
\(688\) −7.15185 + 12.3874i −0.272662 + 0.472264i
\(689\) 4.78018 8.27952i 0.182110 0.315424i
\(690\) −0.0434163 0.253392i −0.00165283 0.00964647i
\(691\) −16.4008 28.4071i −0.623918 1.08066i −0.988749 0.149583i \(-0.952207\pi\)
0.364832 0.931074i \(-0.381127\pi\)
\(692\) −25.9748 −0.987413
\(693\) 0 0
\(694\) 5.62741 0.213614
\(695\) −17.8788 30.9669i −0.678180 1.17464i
\(696\) 26.5003 + 9.79085i 1.00449 + 0.371121i
\(697\) 0.912577 1.58063i 0.0345663 0.0598707i
\(698\) 1.28280 2.22187i 0.0485547 0.0840991i
\(699\) −4.48906 + 3.72989i −0.169792 + 0.141077i
\(700\) 3.90561 + 6.76472i 0.147618 + 0.255682i
\(701\) 8.74920 0.330453 0.165226 0.986256i \(-0.447165\pi\)
0.165226 + 0.986256i \(0.447165\pi\)
\(702\) −5.77437 10.3456i −0.217940 0.390469i
\(703\) 39.7584 1.49952
\(704\) 0 0
\(705\) 1.31176 1.08992i 0.0494039 0.0410489i
\(706\) 9.39625 16.2748i 0.353632 0.612509i
\(707\) −1.19720 + 2.07362i −0.0450254 + 0.0779863i
\(708\) 6.21531 + 2.29632i 0.233586 + 0.0863010i
\(709\) −13.3879 23.1886i −0.502795 0.870866i −0.999995 0.00322996i \(-0.998972\pi\)
0.497200 0.867636i \(-0.334361\pi\)
\(710\) −15.1338 −0.567961
\(711\) −25.1408 + 8.87583i −0.942853 + 0.332870i
\(712\) 4.50914 0.168987
\(713\) 0.279108 + 0.483430i 0.0104527 + 0.0181046i
\(714\) 0.0618286 + 0.360852i 0.00231388 + 0.0135046i
\(715\) 0 0
\(716\) 5.87217 10.1709i 0.219453 0.380105i
\(717\) −6.78524 39.6009i −0.253399 1.47892i
\(718\) 8.02295 + 13.8962i 0.299414 + 0.518600i
\(719\) −15.0047 −0.559582 −0.279791 0.960061i \(-0.590265\pi\)
−0.279791 + 0.960061i \(0.590265\pi\)
\(720\) 3.48074 18.6809i 0.129720 0.696196i
\(721\) −3.51242 −0.130809
\(722\) 6.22777 + 10.7868i 0.231774 + 0.401444i
\(723\) −24.6373 9.10253i −0.916271 0.338527i
\(724\) 2.08075 3.60396i 0.0773304 0.133940i
\(725\) −15.5020 + 26.8502i −0.575730 + 0.997193i
\(726\) 0 0
\(727\) −13.7663 23.8438i −0.510562 0.884319i −0.999925 0.0122391i \(-0.996104\pi\)
0.489363 0.872080i \(-0.337229\pi\)
\(728\) 9.73292 0.360726
\(729\) −14.1733 + 22.9808i −0.524937 + 0.851141i
\(730\) 5.11522 0.189323
\(731\) −1.06583 1.84606i −0.0394210 0.0682792i
\(732\) 30.3805 25.2426i 1.12289 0.932995i
\(733\) 23.8698 41.3438i 0.881653 1.52707i 0.0321496 0.999483i \(-0.489765\pi\)
0.849503 0.527584i \(-0.176902\pi\)
\(734\) 0.338655 0.586567i 0.0125000 0.0216506i
\(735\) −27.5519 10.1794i −1.01627 0.375472i
\(736\) −0.233195 0.403906i −0.00859570 0.0148882i
\(737\) 0 0
\(738\) 1.84450 9.89928i 0.0678968 0.364398i
\(739\) −1.48849 −0.0547549 −0.0273774 0.999625i \(-0.508716\pi\)
−0.0273774 + 0.999625i \(0.508716\pi\)
\(740\) −15.6258 27.0646i −0.574414 0.994914i
\(741\) 7.35093 + 42.9025i 0.270043 + 1.57606i
\(742\) −0.814943 + 1.41152i −0.0299175 + 0.0518187i
\(743\) −9.08009 + 15.7272i −0.333116 + 0.576974i −0.983121 0.182956i \(-0.941433\pi\)
0.650005 + 0.759930i \(0.274767\pi\)
\(744\) −4.04546 23.6107i −0.148314 0.865609i
\(745\) −6.80761 11.7911i −0.249411 0.431993i
\(746\) 12.5771 0.460481
\(747\) 14.0250 4.95145i 0.513147 0.181164i
\(748\) 0 0
\(749\) 6.98177 + 12.0928i 0.255108 + 0.441860i
\(750\) 2.74550 + 1.01436i 0.100251 + 0.0370391i
\(751\) 2.19733 3.80588i 0.0801816 0.138879i −0.823146 0.567829i \(-0.807783\pi\)
0.903328 + 0.428951i \(0.141117\pi\)
\(752\) 0.345477 0.598384i 0.0125983 0.0218208i
\(753\) 0.775748 0.644557i 0.0282698 0.0234890i
\(754\) 8.77835 + 15.2046i 0.319689 + 0.553717i
\(755\) 8.80557 0.320467
\(756\) −4.91275 8.80187i −0.178675 0.320121i
\(757\) −13.7659 −0.500331 −0.250165 0.968203i \(-0.580485\pi\)
−0.250165 + 0.968203i \(0.580485\pi\)
\(758\) −4.69382 8.12993i −0.170487 0.295292i
\(759\) 0 0
\(760\) 20.2655 35.1008i 0.735105 1.27324i
\(761\) −15.5531 + 26.9387i −0.563798 + 0.976526i 0.433363 + 0.901220i \(0.357327\pi\)
−0.997160 + 0.0753068i \(0.976006\pi\)
\(762\) −12.3758 4.57239i −0.448329 0.165640i
\(763\) 3.02731 + 5.24345i 0.109596 + 0.189826i
\(764\) 19.6987 0.712672
\(765\) 2.15163 + 1.84122i 0.0777923 + 0.0665694i
\(766\) −3.57859 −0.129300
\(767\) 4.53027 + 7.84665i 0.163578 + 0.283326i
\(768\) 1.32503 + 7.73334i 0.0478130 + 0.279053i
\(769\) 10.9677 18.9966i 0.395504 0.685034i −0.597661 0.801749i \(-0.703903\pi\)
0.993165 + 0.116715i \(0.0372365\pi\)
\(770\) 0 0
\(771\) 3.20922 + 18.7301i 0.115577 + 0.674549i
\(772\) −5.62041 9.73484i −0.202283 0.350365i
\(773\) −12.7166 −0.457385 −0.228693 0.973499i \(-0.573445\pi\)
−0.228693 + 0.973499i \(0.573445\pi\)
\(774\) −8.93557 7.64646i −0.321182 0.274846i
\(775\) 26.2889 0.944326
\(776\) 0.0940957 + 0.162978i 0.00337784 + 0.00585059i
\(777\) −11.8099 4.36332i −0.423679 0.156533i
\(778\) −0.208941 + 0.361896i −0.00749089 + 0.0129746i
\(779\) −18.4972 + 32.0381i −0.662731 + 1.14788i
\(780\) 26.3158 21.8654i 0.942258 0.782908i
\(781\) 0 0
\(782\) 0.0155220 0.000555064
\(783\) 20.5057 34.3550i 0.732815 1.22775i
\(784\) −11.8998 −0.424993
\(785\) 27.1204 + 46.9740i 0.967970 + 1.67657i
\(786\) 13.8340 11.4944i 0.493442 0.409993i
\(787\) −8.63083 + 14.9490i −0.307656 + 0.532875i −0.977849 0.209311i \(-0.932878\pi\)
0.670193 + 0.742187i \(0.266211\pi\)
\(788\) 17.2007 29.7924i 0.612749 1.06131i
\(789\) 23.3883 + 8.64107i 0.832645 + 0.307630i
\(790\) 7.71406 + 13.3611i 0.274454 + 0.475368i
\(791\) 22.3870 0.795991
\(792\) 0 0
\(793\) 54.0120 1.91802
\(794\) 1.18161 + 2.04660i 0.0419337 + 0.0726312i
\(795\) 2.12911 + 12.4262i 0.0755116 + 0.440711i
\(796\) −11.0683 + 19.1708i −0.392304 + 0.679491i
\(797\) −17.6008 + 30.4854i −0.623451 + 1.07985i 0.365388 + 0.930855i \(0.380936\pi\)
−0.988838 + 0.148993i \(0.952397\pi\)
\(798\) −1.25322 7.31419i −0.0443633 0.258920i
\(799\) 0.0514857 + 0.0891759i 0.00182143 + 0.00315482i
\(800\) −21.9644 −0.776560
\(801\) 1.16972 6.27782i 0.0413301 0.221816i
\(802\) 3.26248 0.115202
\(803\) 0 0
\(804\) −31.6170 11.6812i −1.11504 0.411966i
\(805\) 0.149545 0.259019i 0.00527076 0.00912922i
\(806\) 7.44335 12.8923i 0.262181 0.454110i
\(807\) −0.651414 + 0.541250i −0.0229309 + 0.0190529i
\(808\) −2.17816 3.77269i −0.0766275 0.132723i
\(809\) 19.0808 0.670845 0.335423 0.942068i \(-0.391121\pi\)
0.335423 + 0.942068i \(0.391121\pi\)
\(810\) 14.5755 + 5.62695i 0.512131 + 0.197711i
\(811\) 31.0588 1.09062 0.545311 0.838234i \(-0.316412\pi\)
0.545311 + 0.838234i \(0.316412\pi\)
\(812\) 7.46849 + 12.9358i 0.262093 + 0.453958i
\(813\) 29.2271 24.2843i 1.02504 0.851688i
\(814\) 0 0
\(815\) 8.74810 15.1522i 0.306433 0.530757i
\(816\) 1.07620 + 0.397616i 0.0376746 + 0.0139193i
\(817\) 21.6034 + 37.4182i 0.755808 + 1.30910i
\(818\) 5.45961 0.190891
\(819\) 2.52483 13.5506i 0.0882248 0.473497i
\(820\) 29.0789 1.01548
\(821\) 17.0043 + 29.4522i 0.593453 + 1.02789i 0.993763 + 0.111511i \(0.0355689\pi\)
−0.400311 + 0.916380i \(0.631098\pi\)
\(822\) −2.77213 16.1791i −0.0966891 0.564311i
\(823\) −7.77800 + 13.4719i −0.271124 + 0.469601i −0.969150 0.246472i \(-0.920729\pi\)
0.698026 + 0.716073i \(0.254062\pi\)
\(824\) 3.19521 5.53426i 0.111310 0.192795i
\(825\) 0 0
\(826\) −0.772337 1.33773i −0.0268730 0.0465455i
\(827\) −16.0277 −0.557337 −0.278669 0.960387i \(-0.589893\pi\)
−0.278669 + 0.960387i \(0.589893\pi\)
\(828\) −0.402987 + 0.142273i −0.0140048 + 0.00494431i
\(829\) 19.0994 0.663351 0.331675 0.943394i \(-0.392386\pi\)
0.331675 + 0.943394i \(0.392386\pi\)
\(830\) −4.30334 7.45361i −0.149371 0.258719i
\(831\) −4.66214 1.72248i −0.161728 0.0597523i
\(832\) 2.10065 3.63843i 0.0728269 0.126140i
\(833\) 0.886702 1.53581i 0.0307224 0.0532128i
\(834\) 9.16140 7.61207i 0.317233 0.263584i
\(835\) −7.54371 13.0661i −0.261061 0.452171i
\(836\) 0 0
\(837\) −33.9213 0.492616i −1.17249 0.0170273i
\(838\) −0.0875755 −0.00302524
\(839\) −0.743960 1.28858i −0.0256844 0.0444866i 0.852898 0.522078i \(-0.174843\pi\)
−0.878582 + 0.477592i \(0.841510\pi\)
\(840\) −9.87186 + 8.20237i −0.340612 + 0.283009i
\(841\) −15.1436 + 26.2295i −0.522193 + 0.904465i
\(842\) 4.90463 8.49507i 0.169025 0.292759i
\(843\) −29.5341 10.9117i −1.01721 0.375819i
\(844\) 6.95196 + 12.0411i 0.239296 + 0.414473i
\(845\) 7.72819 0.265858
\(846\) 0.431641 + 0.369369i 0.0148401 + 0.0126992i
\(847\) 0 0
\(848\) 2.55384 + 4.42338i 0.0876993 + 0.151900i
\(849\) −6.00726 35.0604i −0.206169 1.20327i
\(850\) 0.365500 0.633064i 0.0125365 0.0217139i
\(851\) −0.266893 + 0.462271i −0.00914896 + 0.0158465i
\(852\) 4.24860 + 24.7963i 0.145555 + 0.849506i
\(853\) 18.9010 + 32.7376i 0.647159 + 1.12091i 0.983798 + 0.179279i \(0.0573765\pi\)
−0.336639 + 0.941634i \(0.609290\pi\)
\(854\) −9.20818 −0.315097
\(855\) −43.6118 37.3200i −1.49149 1.27632i
\(856\) −25.4049 −0.868322
\(857\) 9.91348 + 17.1706i 0.338638 + 0.586538i 0.984177 0.177189i \(-0.0567005\pi\)
−0.645539 + 0.763727i \(0.723367\pi\)
\(858\) 0 0
\(859\) 7.85764 13.6098i 0.268099 0.464362i −0.700272 0.713876i \(-0.746938\pi\)
0.968371 + 0.249515i \(0.0802711\pi\)
\(860\) 16.9811 29.4120i 0.579049 1.00294i
\(861\) 9.01050 7.48668i 0.307077 0.255146i
\(862\) 7.32936 + 12.6948i 0.249639 + 0.432387i
\(863\) 8.12774 0.276671 0.138336 0.990385i \(-0.455825\pi\)
0.138336 + 0.990385i \(0.455825\pi\)
\(864\) 28.3413 + 0.411581i 0.964189 + 0.0140023i
\(865\) 46.8386 1.59256
\(866\) 4.77697 + 8.27396i 0.162328 + 0.281161i
\(867\) 22.5159 18.7081i 0.764681 0.635361i
\(868\) 6.33269 10.9685i 0.214945 0.372296i
\(869\) 0 0
\(870\) −21.7172 8.02368i −0.736283 0.272028i
\(871\) −23.0452 39.9155i −0.780857 1.35248i
\(872\) −11.0156 −0.373036
\(873\) 0.251315 0.0887257i 0.00850574 0.00300291i
\(874\) −0.314618 −0.0106421
\(875\) 1.70256 + 2.94891i 0.0575569 + 0.0996915i
\(876\) −1.43603 8.38113i −0.0485188 0.283172i
\(877\) −1.26676 + 2.19410i −0.0427756 + 0.0740895i −0.886621 0.462498i \(-0.846953\pi\)
0.843845 + 0.536587i \(0.180287\pi\)
\(878\) 11.3371 19.6364i 0.382607 0.662695i
\(879\) 0.251576 + 1.46828i 0.00848544 + 0.0495239i
\(880\) 0 0
\(881\) −47.4109 −1.59731 −0.798657 0.601786i \(-0.794456\pi\)
−0.798657 + 0.601786i \(0.794456\pi\)
\(882\) 1.79220 9.61859i 0.0603464 0.323875i
\(883\) 26.5129 0.892231 0.446116 0.894975i \(-0.352807\pi\)
0.446116 + 0.894975i \(0.352807\pi\)
\(884\) 1.03288 + 1.78900i 0.0347394 + 0.0601705i
\(885\) −11.2077 4.14080i −0.376742 0.139192i
\(886\) 9.29970 16.1076i 0.312430 0.541144i
\(887\) −23.9147 + 41.4214i −0.802976 + 1.39080i 0.114673 + 0.993403i \(0.463418\pi\)
−0.917649 + 0.397392i \(0.869915\pi\)
\(888\) 17.6183 14.6388i 0.591232 0.491245i
\(889\) −7.67457 13.2927i −0.257397 0.445825i
\(890\) −3.69528 −0.123866
\(891\) 0 0
\(892\) 0.639221 0.0214027
\(893\) −1.04357 1.80752i −0.0349219 0.0604865i
\(894\) 3.48834 2.89841i 0.116668 0.0969373i
\(895\) −10.5889 + 18.3405i −0.353948 + 0.613056i
\(896\) −6.70932 + 11.6209i −0.224143 + 0.388227i
\(897\) −0.548174 0.202529i −0.0183030 0.00676226i
\(898\) −7.46657 12.9325i −0.249163 0.431562i
\(899\) 50.2709 1.67663
\(900\) −3.68664 + 19.7860i −0.122888 + 0.659532i
\(901\) −0.761187 −0.0253588
\(902\) 0 0
\(903\) −2.31064 13.4857i −0.0768933 0.448776i
\(904\) −20.3652 + 35.2736i −0.677337 + 1.17318i
\(905\) −3.75208 + 6.49879i −0.124723 + 0.216027i
\(906\) 0.495358 + 2.89108i 0.0164572 + 0.0960496i
\(907\) −23.7292 41.1001i −0.787914 1.36471i −0.927243 0.374461i \(-0.877828\pi\)
0.139328 0.990246i \(-0.455506\pi\)
\(908\) 30.0138 0.996042
\(909\) −5.81754 + 2.05385i −0.192956 + 0.0681221i
\(910\) −7.97621 −0.264409
\(911\) 14.2161 + 24.6230i 0.471001 + 0.815797i 0.999450 0.0331677i \(-0.0105595\pi\)
−0.528449 + 0.848965i \(0.677226\pi\)
\(912\) −21.8138 8.05935i −0.722326 0.266872i
\(913\) 0 0
\(914\) 3.67381 6.36322i 0.121519 0.210477i
\(915\) −54.7831 + 45.5184i −1.81107 + 1.50479i
\(916\) 11.1863 + 19.3753i 0.369606 + 0.640176i
\(917\) 20.9249 0.691001
\(918\) −0.483476 + 0.810009i −0.0159571 + 0.0267343i
\(919\) −38.3728 −1.26580 −0.632901 0.774233i \(-0.718136\pi\)
−0.632901 + 0.774233i \(0.718136\pi\)
\(920\) 0.272078 + 0.471253i 0.00897015 + 0.0155368i
\(921\) 4.64832 3.86221i 0.153167 0.127264i
\(922\) 5.49549 9.51848i 0.180984 0.313474i
\(923\) −17.2007 + 29.7924i −0.566167 + 0.980629i
\(924\) 0 0
\(925\) 12.5692 + 21.7704i 0.413272 + 0.715808i
\(926\) 13.2127 0.434195
\(927\) −6.87617 5.88416i −0.225843 0.193261i
\(928\) −42.0014 −1.37876
\(929\) −6.69383 11.5941i −0.219618 0.380389i 0.735073 0.677987i \(-0.237148\pi\)
−0.954691 + 0.297599i \(0.903814\pi\)
\(930\) 3.31529 + 19.3491i 0.108713 + 0.634483i
\(931\) −17.9727 + 31.1297i −0.589033 + 1.02023i
\(932\) 2.80715 4.86212i 0.0919511 0.159264i
\(933\) −3.17233 18.5148i −0.103857 0.606147i
\(934\) 4.60021 + 7.96779i 0.150523 + 0.260714i
\(935\) 0 0
\(936\) 19.0539 + 16.3050i 0.622795 + 0.532946i
\(937\) 24.6705 0.805950 0.402975 0.915211i \(-0.367976\pi\)
0.402975 + 0.915211i \(0.367976\pi\)
\(938\) 3.92884 + 6.80494i 0.128281 + 0.222189i
\(939\) −45.9485 16.9762i −1.49947 0.553998i
\(940\) −0.820286 + 1.42078i −0.0267548 + 0.0463406i
\(941\) 4.15115 7.19000i 0.135324 0.234387i −0.790397 0.612594i \(-0.790126\pi\)
0.925721 + 0.378207i \(0.123459\pi\)
\(942\) −13.8970 + 11.5468i −0.452789 + 0.376215i
\(943\) −0.248338 0.430134i −0.00808701 0.0140071i
\(944\) −4.84065 −0.157550
\(945\) 8.85883 + 15.8718i 0.288178 + 0.516311i
\(946\) 0 0
\(947\) −18.9748 32.8653i −0.616598 1.06798i −0.990102 0.140351i \(-0.955177\pi\)
0.373503 0.927629i \(-0.378156\pi\)
\(948\) 19.7262 16.3902i 0.640678 0.532330i
\(949\) 5.81382 10.0698i 0.188725 0.326880i
\(950\) −7.40838 + 12.8317i −0.240360 + 0.416315i
\(951\) −1.80753 0.667814i −0.0586133 0.0216553i
\(952\) −0.387463 0.671106i −0.0125578 0.0217507i
\(953\) 48.6705 1.57659 0.788297 0.615295i \(-0.210963\pi\)
0.788297 + 0.615295i \(0.210963\pi\)
\(954\) −3.96004 + 1.39807i −0.128211 + 0.0452642i
\(955\) −35.5213 −1.14944
\(956\) 19.3245 + 33.4710i 0.624998 + 1.08253i
\(957\) 0 0
\(958\) 4.73516 8.20154i 0.152986 0.264980i
\(959\) 9.54844 16.5384i 0.308335 0.534052i
\(960\) 0.935635 + 5.46068i 0.0301975 + 0.176243i
\(961\) −5.81285 10.0682i −0.187511 0.324779i
\(962\) 14.2352 0.458960
\(963\) −6.59033 + 35.3698i −0.212370 + 1.13978i
\(964\) 25.2655 0.813746
\(965\) 10.1349 + 17.5542i 0.326255 + 0.565090i
\(966\) 0.0934548 + 0.0345280i 0.00300686 + 0.00111092i
\(967\) 5.48901 9.50724i 0.176515 0.305732i −0.764170 0.645015i \(-0.776851\pi\)
0.940684 + 0.339283i \(0.110184\pi\)
\(968\) 0 0
\(969\) 2.66559 2.21479i 0.0856309 0.0711494i
\(970\) −0.0771122 0.133562i −0.00247592 0.00428843i
\(971\) 13.0636 0.419231 0.209615 0.977784i \(-0.432779\pi\)
0.209615 + 0.977784i \(0.432779\pi\)
\(972\) 5.12773 25.4612i 0.164472 0.816669i
\(973\) 13.8573 0.444244
\(974\) 6.58316 + 11.4024i 0.210938 + 0.365355i
\(975\) −21.1681 + 17.5883i −0.677923 + 0.563276i
\(976\) −14.4281 + 24.9903i −0.461833 + 0.799919i
\(977\) 5.53815 9.59236i 0.177181 0.306887i −0.763733 0.645533i \(-0.776635\pi\)
0.940914 + 0.338646i \(0.109969\pi\)
\(978\) 5.46694 + 2.01982i 0.174813 + 0.0645869i
\(979\) 0 0
\(980\) 28.2544 0.902554
\(981\) −2.85758 + 15.3364i −0.0912355 + 0.489655i
\(982\) −25.2175 −0.804721
\(983\) 13.2157 + 22.8903i 0.421517 + 0.730088i 0.996088 0.0883661i \(-0.0281645\pi\)
−0.574571 + 0.818455i \(0.694831\pi\)
\(984\) 3.59947 + 21.0077i 0.114747 + 0.669702i
\(985\) −31.0168 + 53.7228i −0.988279 + 1.71175i
\(986\) 0.698925 1.21057i 0.0222583 0.0385525i
\(987\) 0.111618 + 0.651439i 0.00355283 + 0.0207355i
\(988\) −20.9356 36.2615i −0.666050 1.15363i
\(989\) −0.580083 −0.0184456
\(990\) 0 0
\(991\) −18.9911 −0.603272 −0.301636 0.953423i \(-0.597533\pi\)
−0.301636 + 0.953423i \(0.597533\pi\)
\(992\) 17.8069 + 30.8425i 0.565370 + 0.979250i
\(993\) −20.1111 7.43030i −0.638208 0.235793i
\(994\) 2.93243 5.07913i 0.0930112 0.161100i
\(995\) 19.9587 34.5694i 0.632733 1.09593i
\(996\) −11.0044 + 9.14340i −0.348688 + 0.289720i
\(997\) 11.0566 + 19.1506i 0.350165 + 0.606504i 0.986278 0.165092i \(-0.0527921\pi\)
−0.636113 + 0.771596i \(0.719459\pi\)
\(998\) 11.6161 0.367700
\(999\) −15.8104 28.3265i −0.500218 0.896210i
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 1089.2.e.o.364.11 36
9.4 even 3 9801.2.a.co.1.8 18
9.5 odd 6 9801.2.a.cn.1.11 18
9.7 even 3 inner 1089.2.e.o.727.11 36
11.2 odd 10 99.2.m.b.4.4 72
11.6 odd 10 99.2.m.b.58.6 yes 72
11.10 odd 2 1089.2.e.p.364.8 36
33.2 even 10 297.2.n.b.37.6 72
33.17 even 10 297.2.n.b.91.4 72
99.2 even 30 297.2.n.b.235.4 72
99.13 odd 30 891.2.f.f.730.4 36
99.32 even 6 9801.2.a.cp.1.8 18
99.43 odd 6 1089.2.e.p.727.8 36
99.50 even 30 891.2.f.e.487.6 36
99.61 odd 30 99.2.m.b.25.4 yes 72
99.68 even 30 891.2.f.e.730.6 36
99.76 odd 6 9801.2.a.cm.1.11 18
99.79 odd 30 99.2.m.b.70.6 yes 72
99.83 even 30 297.2.n.b.289.6 72
99.94 odd 30 891.2.f.f.487.4 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.4 72 11.2 odd 10
99.2.m.b.25.4 yes 72 99.61 odd 30
99.2.m.b.58.6 yes 72 11.6 odd 10
99.2.m.b.70.6 yes 72 99.79 odd 30
297.2.n.b.37.6 72 33.2 even 10
297.2.n.b.91.4 72 33.17 even 10
297.2.n.b.235.4 72 99.2 even 30
297.2.n.b.289.6 72 99.83 even 30
891.2.f.e.487.6 36 99.50 even 30
891.2.f.e.730.6 36 99.68 even 30
891.2.f.f.487.4 36 99.94 odd 30
891.2.f.f.730.4 36 99.13 odd 30
1089.2.e.o.364.11 36 1.1 even 1 trivial
1089.2.e.o.727.11 36 9.7 even 3 inner
1089.2.e.p.364.8 36 11.10 odd 2
1089.2.e.p.727.8 36 99.43 odd 6
9801.2.a.cm.1.11 18 99.76 odd 6
9801.2.a.cn.1.11 18 9.5 odd 6
9801.2.a.co.1.8 18 9.4 even 3
9801.2.a.cp.1.8 18 99.32 even 6