Properties

Label 950.2.l.m.301.5
Level $950$
Weight $2$
Character 950.301
Analytic conductor $7.586$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 301.5
Character \(\chi\) \(=\) 950.301
Dual form 950.2.l.m.101.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.766044 + 0.642788i) q^{2} +(3.03100 - 1.10319i) q^{3} +(0.173648 + 0.984808i) q^{4} +(3.03100 + 1.10319i) q^{6} +(1.36166 + 2.35847i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(5.67178 - 4.75918i) q^{9} +O(q^{10})\) \(q+(0.766044 + 0.642788i) q^{2} +(3.03100 - 1.10319i) q^{3} +(0.173648 + 0.984808i) q^{4} +(3.03100 + 1.10319i) q^{6} +(1.36166 + 2.35847i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(5.67178 - 4.75918i) q^{9} +(-1.18927 + 2.05988i) q^{11} +(1.61276 + 2.79338i) q^{12} +(0.0945198 + 0.0344024i) q^{13} +(-0.472900 + 2.68195i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.17630 - 3.50433i) q^{17} +7.40398 q^{18} +(1.18130 + 4.19577i) q^{19} +(6.72904 + 5.64633i) q^{21} +(-2.23510 + 0.813512i) q^{22} +(-0.235016 - 1.33284i) q^{23} +(-0.560106 + 3.17652i) q^{24} +(0.0502929 + 0.0871099i) q^{26} +(7.10256 - 12.3020i) q^{27} +(-2.08619 + 1.75052i) q^{28} +(-1.61211 + 1.35272i) q^{29} +(-5.26498 - 9.11921i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-1.33224 + 7.55550i) q^{33} +(-0.946690 - 5.36895i) q^{34} +(5.67178 + 4.75918i) q^{36} +1.18731 q^{37} +(-1.79206 + 3.97348i) q^{38} +0.324442 q^{39} +(3.30679 - 1.20357i) q^{41} +(1.52535 + 8.65069i) q^{42} +(1.22895 - 6.96972i) q^{43} +(-2.23510 - 0.813512i) q^{44} +(0.676702 - 1.17208i) q^{46} +(-6.13425 + 5.14725i) q^{47} +(-2.47089 + 2.07332i) q^{48} +(-0.208248 + 0.360697i) q^{49} +(-16.5243 - 6.01435i) q^{51} +(-0.0174665 + 0.0990577i) q^{52} +(1.94049 + 11.0051i) q^{53} +(13.3484 - 4.85844i) q^{54} -2.72332 q^{56} +(8.20927 + 11.4142i) q^{57} -2.10445 q^{58} +(-9.13030 - 7.66123i) q^{59} +(-0.0303598 - 0.172179i) q^{61} +(1.82851 - 10.3700i) q^{62} +(18.9474 + 6.89630i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-5.87714 + 4.93150i) q^{66} +(4.17582 - 3.50393i) q^{67} +(2.72588 - 4.72137i) q^{68} +(-2.18272 - 3.78057i) q^{69} +(0.240963 - 1.36657i) q^{71} +(1.28569 + 7.29149i) q^{72} +(11.3670 - 4.13725i) q^{73} +(0.909534 + 0.763190i) q^{74} +(-3.92690 + 1.89194i) q^{76} -6.47756 q^{77} +(0.248537 + 0.208547i) q^{78} +(-3.51498 + 1.27935i) q^{79} +(4.09930 - 23.2483i) q^{81} +(3.30679 + 1.20357i) q^{82} +(4.50106 + 7.79606i) q^{83} +(-4.39207 + 7.60729i) q^{84} +(5.42148 - 4.54916i) q^{86} +(-3.39398 + 5.87854i) q^{87} +(-1.18927 - 2.05988i) q^{88} +(-7.26423 - 2.64396i) q^{89} +(0.0475671 + 0.269766i) q^{91} +(1.27178 - 0.462891i) q^{92} +(-26.0184 - 21.8320i) q^{93} -8.00769 q^{94} -3.22552 q^{96} +(2.26235 + 1.89834i) q^{97} +(-0.391379 + 0.142450i) q^{98} +(3.05807 + 17.3432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 12 q^{7} - 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 12 q^{7} - 15 q^{8} + 6 q^{11} + 6 q^{14} + 30 q^{18} + 24 q^{19} + 24 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 18 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{33} - 24 q^{37} + 12 q^{38} - 24 q^{39} - 3 q^{41} - 12 q^{42} - 6 q^{43} - 3 q^{44} - 48 q^{47} + 15 q^{49} - 90 q^{51} + 18 q^{53} + 18 q^{54} - 24 q^{56} + 42 q^{57} - 36 q^{58} - 18 q^{59} - 60 q^{61} + 24 q^{62} + 21 q^{63} - 15 q^{64} - 78 q^{66} + 30 q^{67} + 12 q^{68} + 24 q^{69} - 30 q^{73} - 9 q^{74} - 3 q^{76} - 78 q^{77} - 6 q^{79} + 60 q^{81} - 3 q^{82} + 42 q^{83} - 6 q^{84} + 12 q^{86} + 54 q^{87} + 6 q^{88} - 30 q^{89} - 6 q^{91} + 6 q^{92} - 72 q^{93} - 78 q^{94} + 42 q^{97} - 6 q^{98} - 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.766044 + 0.642788i 0.541675 + 0.454519i
\(3\) 3.03100 1.10319i 1.74995 0.636929i 0.750241 0.661165i \(-0.229938\pi\)
0.999706 + 0.0242362i \(0.00771538\pi\)
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) 0 0
\(6\) 3.03100 + 1.10319i 1.23740 + 0.450377i
\(7\) 1.36166 + 2.35847i 0.514660 + 0.891417i 0.999855 + 0.0170114i \(0.00541517\pi\)
−0.485195 + 0.874406i \(0.661251\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 5.67178 4.75918i 1.89059 1.58639i
\(10\) 0 0
\(11\) −1.18927 + 2.05988i −0.358580 + 0.621078i −0.987724 0.156210i \(-0.950072\pi\)
0.629144 + 0.777289i \(0.283406\pi\)
\(12\) 1.61276 + 2.79338i 0.465564 + 0.806380i
\(13\) 0.0945198 + 0.0344024i 0.0262151 + 0.00954150i 0.355094 0.934830i \(-0.384449\pi\)
−0.328879 + 0.944372i \(0.606671\pi\)
\(14\) −0.472900 + 2.68195i −0.126388 + 0.716782i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) −4.17630 3.50433i −1.01290 0.849925i −0.0241821 0.999708i \(-0.507698\pi\)
−0.988719 + 0.149783i \(0.952143\pi\)
\(18\) 7.40398 1.74513
\(19\) 1.18130 + 4.19577i 0.271009 + 0.962577i
\(20\) 0 0
\(21\) 6.72904 + 5.64633i 1.46840 + 1.23213i
\(22\) −2.23510 + 0.813512i −0.476526 + 0.173441i
\(23\) −0.235016 1.33284i −0.0490042 0.277917i 0.950453 0.310869i \(-0.100620\pi\)
−0.999457 + 0.0329524i \(0.989509\pi\)
\(24\) −0.560106 + 3.17652i −0.114331 + 0.648404i
\(25\) 0 0
\(26\) 0.0502929 + 0.0871099i 0.00986325 + 0.0170837i
\(27\) 7.10256 12.3020i 1.36689 2.36752i
\(28\) −2.08619 + 1.75052i −0.394252 + 0.330817i
\(29\) −1.61211 + 1.35272i −0.299360 + 0.251193i −0.780078 0.625682i \(-0.784821\pi\)
0.480718 + 0.876875i \(0.340376\pi\)
\(30\) 0 0
\(31\) −5.26498 9.11921i −0.945618 1.63786i −0.754509 0.656290i \(-0.772125\pi\)
−0.191109 0.981569i \(-0.561208\pi\)
\(32\) −0.939693 0.342020i −0.166116 0.0604612i
\(33\) −1.33224 + 7.55550i −0.231913 + 1.31524i
\(34\) −0.946690 5.36895i −0.162356 0.920766i
\(35\) 0 0
\(36\) 5.67178 + 4.75918i 0.945296 + 0.793197i
\(37\) 1.18731 0.195193 0.0975965 0.995226i \(-0.468885\pi\)
0.0975965 + 0.995226i \(0.468885\pi\)
\(38\) −1.79206 + 3.97348i −0.290711 + 0.644583i
\(39\) 0.324442 0.0519522
\(40\) 0 0
\(41\) 3.30679 1.20357i 0.516433 0.187966i −0.0706374 0.997502i \(-0.522503\pi\)
0.587071 + 0.809536i \(0.300281\pi\)
\(42\) 1.52535 + 8.65069i 0.235367 + 1.33483i
\(43\) 1.22895 6.96972i 0.187413 1.06287i −0.735403 0.677630i \(-0.763007\pi\)
0.922816 0.385242i \(-0.125882\pi\)
\(44\) −2.23510 0.813512i −0.336955 0.122641i
\(45\) 0 0
\(46\) 0.676702 1.17208i 0.0997742 0.172814i
\(47\) −6.13425 + 5.14725i −0.894772 + 0.750803i −0.969162 0.246426i \(-0.920744\pi\)
0.0743895 + 0.997229i \(0.476299\pi\)
\(48\) −2.47089 + 2.07332i −0.356642 + 0.299259i
\(49\) −0.208248 + 0.360697i −0.0297498 + 0.0515281i
\(50\) 0 0
\(51\) −16.5243 6.01435i −2.31386 0.842178i
\(52\) −0.0174665 + 0.0990577i −0.00242217 + 0.0137368i
\(53\) 1.94049 + 11.0051i 0.266547 + 1.51166i 0.764593 + 0.644514i \(0.222940\pi\)
−0.498046 + 0.867151i \(0.665949\pi\)
\(54\) 13.3484 4.85844i 1.81649 0.661149i
\(55\) 0 0
\(56\) −2.72332 −0.363920
\(57\) 8.20927 + 11.4142i 1.08734 + 1.51184i
\(58\) −2.10445 −0.276328
\(59\) −9.13030 7.66123i −1.18866 0.997407i −0.999882 0.0153883i \(-0.995102\pi\)
−0.188782 0.982019i \(-0.560454\pi\)
\(60\) 0 0
\(61\) −0.0303598 0.172179i −0.00388717 0.0220452i 0.982802 0.184660i \(-0.0591184\pi\)
−0.986690 + 0.162615i \(0.948007\pi\)
\(62\) 1.82851 10.3700i 0.232221 1.31699i
\(63\) 18.9474 + 6.89630i 2.38715 + 0.868852i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 0 0
\(66\) −5.87714 + 4.93150i −0.723425 + 0.607026i
\(67\) 4.17582 3.50393i 0.510157 0.428073i −0.351027 0.936365i \(-0.614168\pi\)
0.861184 + 0.508293i \(0.169723\pi\)
\(68\) 2.72588 4.72137i 0.330562 0.572550i
\(69\) −2.18272 3.78057i −0.262768 0.455128i
\(70\) 0 0
\(71\) 0.240963 1.36657i 0.0285970 0.162182i −0.967165 0.254149i \(-0.918205\pi\)
0.995762 + 0.0919676i \(0.0293156\pi\)
\(72\) 1.28569 + 7.29149i 0.151520 + 0.859311i
\(73\) 11.3670 4.13725i 1.33041 0.484229i 0.423629 0.905836i \(-0.360756\pi\)
0.906779 + 0.421607i \(0.138534\pi\)
\(74\) 0.909534 + 0.763190i 0.105731 + 0.0887190i
\(75\) 0 0
\(76\) −3.92690 + 1.89194i −0.450446 + 0.217021i
\(77\) −6.47756 −0.738187
\(78\) 0.248537 + 0.208547i 0.0281412 + 0.0236133i
\(79\) −3.51498 + 1.27935i −0.395466 + 0.143938i −0.532095 0.846684i \(-0.678595\pi\)
0.136629 + 0.990622i \(0.456373\pi\)
\(80\) 0 0
\(81\) 4.09930 23.2483i 0.455478 2.58314i
\(82\) 3.30679 + 1.20357i 0.365173 + 0.132912i
\(83\) 4.50106 + 7.79606i 0.494055 + 0.855729i 0.999977 0.00685072i \(-0.00218067\pi\)
−0.505921 + 0.862580i \(0.668847\pi\)
\(84\) −4.39207 + 7.60729i −0.479214 + 0.830023i
\(85\) 0 0
\(86\) 5.42148 4.54916i 0.584613 0.490549i
\(87\) −3.39398 + 5.87854i −0.363873 + 0.630246i
\(88\) −1.18927 2.05988i −0.126777 0.219584i
\(89\) −7.26423 2.64396i −0.770007 0.280259i −0.0730074 0.997331i \(-0.523260\pi\)
−0.696999 + 0.717072i \(0.745482\pi\)
\(90\) 0 0
\(91\) 0.0475671 + 0.269766i 0.00498638 + 0.0282792i
\(92\) 1.27178 0.462891i 0.132593 0.0482598i
\(93\) −26.0184 21.8320i −2.69798 2.26387i
\(94\) −8.00769 −0.825930
\(95\) 0 0
\(96\) −3.22552 −0.329203
\(97\) 2.26235 + 1.89834i 0.229707 + 0.192747i 0.750375 0.661012i \(-0.229873\pi\)
−0.520668 + 0.853759i \(0.674317\pi\)
\(98\) −0.391379 + 0.142450i −0.0395353 + 0.0143897i
\(99\) 3.05807 + 17.3432i 0.307348 + 1.74305i
\(100\) 0 0
\(101\) −8.05071 2.93022i −0.801075 0.291568i −0.0911434 0.995838i \(-0.529052\pi\)
−0.709932 + 0.704270i \(0.751274\pi\)
\(102\) −8.79240 15.2289i −0.870577 1.50788i
\(103\) 0.890417 1.54225i 0.0877354 0.151962i −0.818818 0.574053i \(-0.805370\pi\)
0.906554 + 0.422091i \(0.138704\pi\)
\(104\) −0.0770532 + 0.0646553i −0.00755569 + 0.00633998i
\(105\) 0 0
\(106\) −5.58743 + 9.67771i −0.542699 + 0.939982i
\(107\) −4.24824 7.35816i −0.410693 0.711340i 0.584273 0.811557i \(-0.301380\pi\)
−0.994966 + 0.100217i \(0.968046\pi\)
\(108\) 13.3484 + 4.85844i 1.28445 + 0.467503i
\(109\) −1.33246 + 7.55678i −0.127627 + 0.723808i 0.852086 + 0.523402i \(0.175337\pi\)
−0.979713 + 0.200406i \(0.935774\pi\)
\(110\) 0 0
\(111\) 3.59874 1.30983i 0.341577 0.124324i
\(112\) −2.08619 1.75052i −0.197126 0.165409i
\(113\) −3.14545 −0.295899 −0.147949 0.988995i \(-0.547267\pi\)
−0.147949 + 0.988995i \(0.547267\pi\)
\(114\) −1.04823 + 14.0206i −0.0981755 + 1.31315i
\(115\) 0 0
\(116\) −1.61211 1.35272i −0.149680 0.125597i
\(117\) 0.699822 0.254714i 0.0646986 0.0235484i
\(118\) −2.06967 11.7377i −0.190529 1.08054i
\(119\) 2.57814 14.6214i 0.236338 1.34034i
\(120\) 0 0
\(121\) 2.67125 + 4.62675i 0.242841 + 0.420613i
\(122\) 0.0874174 0.151411i 0.00791440 0.0137081i
\(123\) 8.69509 7.29604i 0.784010 0.657862i
\(124\) 8.06641 6.76853i 0.724385 0.607832i
\(125\) 0 0
\(126\) 10.0817 + 17.4620i 0.898151 + 1.55564i
\(127\) 10.1214 + 3.68389i 0.898130 + 0.326893i 0.749503 0.662001i \(-0.230292\pi\)
0.148627 + 0.988893i \(0.452515\pi\)
\(128\) 0.173648 0.984808i 0.0153485 0.0870455i
\(129\) −3.96400 22.4810i −0.349011 1.97934i
\(130\) 0 0
\(131\) −3.31899 2.78497i −0.289982 0.243324i 0.486178 0.873860i \(-0.338391\pi\)
−0.776160 + 0.630536i \(0.782835\pi\)
\(132\) −7.67206 −0.667767
\(133\) −8.28707 + 8.49929i −0.718580 + 0.736982i
\(134\) 5.45114 0.470907
\(135\) 0 0
\(136\) 5.12299 1.86462i 0.439293 0.159889i
\(137\) 1.25804 + 7.13470i 0.107482 + 0.609559i 0.990200 + 0.139656i \(0.0445998\pi\)
−0.882718 + 0.469902i \(0.844289\pi\)
\(138\) 0.758049 4.29911i 0.0645294 0.365964i
\(139\) −13.8285 5.03317i −1.17292 0.426908i −0.319224 0.947679i \(-0.603422\pi\)
−0.853696 + 0.520771i \(0.825644\pi\)
\(140\) 0 0
\(141\) −12.9145 + 22.3685i −1.08760 + 1.88377i
\(142\) 1.06300 0.891964i 0.0892051 0.0748520i
\(143\) −0.183275 + 0.153786i −0.0153262 + 0.0128602i
\(144\) −3.70199 + 6.41203i −0.308499 + 0.534336i
\(145\) 0 0
\(146\) 11.3670 + 4.13725i 0.940740 + 0.342401i
\(147\) −0.233282 + 1.32301i −0.0192408 + 0.109120i
\(148\) 0.206175 + 1.16927i 0.0169474 + 0.0961137i
\(149\) 8.16373 2.97136i 0.668799 0.243423i 0.0147684 0.999891i \(-0.495299\pi\)
0.654031 + 0.756468i \(0.273077\pi\)
\(150\) 0 0
\(151\) 8.23583 0.670222 0.335111 0.942179i \(-0.391226\pi\)
0.335111 + 0.942179i \(0.391226\pi\)
\(152\) −4.22430 1.07485i −0.342636 0.0871819i
\(153\) −40.3648 −3.26330
\(154\) −4.96210 4.16370i −0.399857 0.335520i
\(155\) 0 0
\(156\) 0.0563387 + 0.319513i 0.00451070 + 0.0255815i
\(157\) −2.03713 + 11.5531i −0.162581 + 0.922041i 0.788943 + 0.614466i \(0.210629\pi\)
−0.951524 + 0.307575i \(0.900483\pi\)
\(158\) −3.51498 1.27935i −0.279637 0.101779i
\(159\) 18.0224 + 31.2156i 1.42927 + 2.47556i
\(160\) 0 0
\(161\) 2.82345 2.36916i 0.222519 0.186716i
\(162\) 18.0840 15.1743i 1.42081 1.19220i
\(163\) −9.83039 + 17.0267i −0.769975 + 1.33364i 0.167600 + 0.985855i \(0.446398\pi\)
−0.937576 + 0.347781i \(0.886935\pi\)
\(164\) 1.75950 + 3.04755i 0.137394 + 0.237974i
\(165\) 0 0
\(166\) −1.56320 + 8.86535i −0.121328 + 0.688085i
\(167\) 2.91465 + 16.5298i 0.225543 + 1.27912i 0.861645 + 0.507511i \(0.169434\pi\)
−0.636103 + 0.771604i \(0.719455\pi\)
\(168\) −8.25439 + 3.00435i −0.636840 + 0.231791i
\(169\) −9.95083 8.34974i −0.765448 0.642287i
\(170\) 0 0
\(171\) 26.6685 + 18.1755i 2.03939 + 1.38991i
\(172\) 7.07724 0.539634
\(173\) 10.2431 + 8.59496i 0.778766 + 0.653463i 0.942938 0.332969i \(-0.108051\pi\)
−0.164171 + 0.986432i \(0.552495\pi\)
\(174\) −6.37859 + 2.32162i −0.483560 + 0.176001i
\(175\) 0 0
\(176\) 0.413031 2.34241i 0.0311334 0.176566i
\(177\) −36.1257 13.1487i −2.71538 0.988316i
\(178\) −3.86521 6.69475i −0.289710 0.501793i
\(179\) −10.8243 + 18.7483i −0.809047 + 1.40131i 0.104477 + 0.994527i \(0.466683\pi\)
−0.913525 + 0.406784i \(0.866650\pi\)
\(180\) 0 0
\(181\) −6.96216 + 5.84194i −0.517493 + 0.434228i −0.863757 0.503909i \(-0.831895\pi\)
0.346264 + 0.938137i \(0.387450\pi\)
\(182\) −0.136964 + 0.237228i −0.0101524 + 0.0175845i
\(183\) −0.281967 0.488380i −0.0208436 0.0361021i
\(184\) 1.27178 + 0.462891i 0.0937571 + 0.0341248i
\(185\) 0 0
\(186\) −5.89789 33.4486i −0.432454 2.45257i
\(187\) 12.1853 4.43508i 0.891076 0.324325i
\(188\) −6.13425 5.14725i −0.447386 0.375401i
\(189\) 38.6851 2.81393
\(190\) 0 0
\(191\) 6.95613 0.503328 0.251664 0.967815i \(-0.419022\pi\)
0.251664 + 0.967815i \(0.419022\pi\)
\(192\) −2.47089 2.07332i −0.178321 0.149629i
\(193\) 15.3524 5.58781i 1.10509 0.402220i 0.275899 0.961187i \(-0.411024\pi\)
0.829190 + 0.558967i \(0.188802\pi\)
\(194\) 0.512833 + 2.90842i 0.0368193 + 0.208812i
\(195\) 0 0
\(196\) −0.391379 0.142450i −0.0279557 0.0101750i
\(197\) −1.43752 2.48986i −0.102419 0.177395i 0.810262 0.586068i \(-0.199325\pi\)
−0.912681 + 0.408673i \(0.865992\pi\)
\(198\) −8.80536 + 15.2513i −0.625770 + 1.08386i
\(199\) −14.2742 + 11.9774i −1.01187 + 0.849058i −0.988584 0.150671i \(-0.951857\pi\)
−0.0232838 + 0.999729i \(0.507412\pi\)
\(200\) 0 0
\(201\) 8.79138 15.2271i 0.620096 1.07404i
\(202\) −4.28369 7.41957i −0.301400 0.522039i
\(203\) −5.38548 1.96016i −0.377987 0.137576i
\(204\) 3.05357 17.3176i 0.213792 1.21248i
\(205\) 0 0
\(206\) 1.67344 0.609081i 0.116594 0.0424367i
\(207\) −7.67620 6.44110i −0.533533 0.447687i
\(208\) −0.100586 −0.00697437
\(209\) −10.0477 2.55658i −0.695014 0.176843i
\(210\) 0 0
\(211\) −3.41054 2.86178i −0.234791 0.197013i 0.517799 0.855502i \(-0.326751\pi\)
−0.752590 + 0.658489i \(0.771196\pi\)
\(212\) −10.5009 + 3.82202i −0.721207 + 0.262498i
\(213\) −0.777231 4.40789i −0.0532550 0.302024i
\(214\) 1.47540 8.36739i 0.100856 0.571983i
\(215\) 0 0
\(216\) 7.10256 + 12.3020i 0.483268 + 0.837044i
\(217\) 14.3382 24.8346i 0.973343 1.68588i
\(218\) −5.87813 + 4.93233i −0.398117 + 0.334060i
\(219\) 29.8892 25.0800i 2.01972 1.69475i
\(220\) 0 0
\(221\) −0.274185 0.474903i −0.0184437 0.0319454i
\(222\) 3.59874 + 1.30983i 0.241532 + 0.0879103i
\(223\) 3.21314 18.2226i 0.215168 1.22028i −0.665448 0.746445i \(-0.731759\pi\)
0.880615 0.473832i \(-0.157130\pi\)
\(224\) −0.472900 2.68195i −0.0315970 0.179195i
\(225\) 0 0
\(226\) −2.40955 2.02186i −0.160281 0.134492i
\(227\) −1.50594 −0.0999530 −0.0499765 0.998750i \(-0.515915\pi\)
−0.0499765 + 0.998750i \(0.515915\pi\)
\(228\) −9.81525 + 10.0666i −0.650031 + 0.666677i
\(229\) 9.61539 0.635403 0.317702 0.948191i \(-0.397089\pi\)
0.317702 + 0.948191i \(0.397089\pi\)
\(230\) 0 0
\(231\) −19.6335 + 7.14600i −1.29179 + 0.470172i
\(232\) −0.365435 2.07248i −0.0239920 0.136065i
\(233\) −0.998532 + 5.66295i −0.0654160 + 0.370993i 0.934472 + 0.356036i \(0.115872\pi\)
−0.999888 + 0.0149563i \(0.995239\pi\)
\(234\) 0.699822 + 0.254714i 0.0457488 + 0.0166512i
\(235\) 0 0
\(236\) 5.95938 10.3219i 0.387923 0.671902i
\(237\) −9.24252 + 7.75540i −0.600366 + 0.503767i
\(238\) 11.3734 9.54343i 0.737229 0.618609i
\(239\) 8.72159 15.1062i 0.564153 0.977142i −0.432975 0.901406i \(-0.642536\pi\)
0.997128 0.0757357i \(-0.0241305\pi\)
\(240\) 0 0
\(241\) −14.2857 5.19958i −0.920225 0.334935i −0.161897 0.986808i \(-0.551761\pi\)
−0.758328 + 0.651873i \(0.773984\pi\)
\(242\) −0.927716 + 5.26134i −0.0596359 + 0.338212i
\(243\) −5.82231 33.0199i −0.373501 2.11823i
\(244\) 0.164291 0.0597970i 0.0105177 0.00382811i
\(245\) 0 0
\(246\) 11.3506 0.723690
\(247\) −0.0326883 + 0.437223i −0.00207991 + 0.0278198i
\(248\) 10.5300 0.668653
\(249\) 22.2433 + 18.6643i 1.40961 + 1.18280i
\(250\) 0 0
\(251\) 0.382644 + 2.17008i 0.0241523 + 0.136974i 0.994500 0.104741i \(-0.0334012\pi\)
−0.970347 + 0.241715i \(0.922290\pi\)
\(252\) −3.50134 + 19.8571i −0.220564 + 1.25088i
\(253\) 3.02500 + 1.10101i 0.190180 + 0.0692199i
\(254\) 5.38549 + 9.32795i 0.337916 + 0.585287i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) 8.80414 7.38755i 0.549187 0.460823i −0.325479 0.945549i \(-0.605525\pi\)
0.874666 + 0.484727i \(0.161081\pi\)
\(258\) 11.4139 19.7694i 0.710597 1.23079i
\(259\) 1.61672 + 2.80024i 0.100458 + 0.173998i
\(260\) 0 0
\(261\) −2.70567 + 15.3446i −0.167477 + 0.949808i
\(262\) −0.752355 4.26682i −0.0464806 0.263605i
\(263\) −16.7936 + 6.11237i −1.03554 + 0.376905i −0.803187 0.595727i \(-0.796864\pi\)
−0.232351 + 0.972632i \(0.574642\pi\)
\(264\) −5.87714 4.93150i −0.361713 0.303513i
\(265\) 0 0
\(266\) −11.8115 + 1.18401i −0.724210 + 0.0725962i
\(267\) −24.9347 −1.52598
\(268\) 4.17582 + 3.50393i 0.255079 + 0.214036i
\(269\) 0.485375 0.176662i 0.0295938 0.0107713i −0.327181 0.944962i \(-0.606099\pi\)
0.356775 + 0.934190i \(0.383876\pi\)
\(270\) 0 0
\(271\) −3.98871 + 22.6211i −0.242297 + 1.37413i 0.584390 + 0.811473i \(0.301334\pi\)
−0.826687 + 0.562662i \(0.809777\pi\)
\(272\) 5.12299 + 1.86462i 0.310627 + 0.113059i
\(273\) 0.441780 + 0.765185i 0.0267377 + 0.0463111i
\(274\) −3.62238 + 6.27415i −0.218836 + 0.379035i
\(275\) 0 0
\(276\) 3.34411 2.80604i 0.201292 0.168904i
\(277\) 5.05445 8.75457i 0.303693 0.526011i −0.673277 0.739391i \(-0.735114\pi\)
0.976969 + 0.213379i \(0.0684471\pi\)
\(278\) −7.35801 12.7444i −0.441304 0.764361i
\(279\) −73.2618 26.6651i −4.38607 1.59640i
\(280\) 0 0
\(281\) −5.01606 28.4475i −0.299233 1.69703i −0.649481 0.760378i \(-0.725014\pi\)
0.350248 0.936657i \(-0.386097\pi\)
\(282\) −24.2713 + 8.83403i −1.44533 + 0.526059i
\(283\) 9.39720 + 7.88519i 0.558605 + 0.468726i 0.877843 0.478949i \(-0.158982\pi\)
−0.319237 + 0.947675i \(0.603427\pi\)
\(284\) 1.38765 0.0823419
\(285\) 0 0
\(286\) −0.239248 −0.0141470
\(287\) 7.34131 + 6.16009i 0.433344 + 0.363619i
\(288\) −6.95746 + 2.53231i −0.409972 + 0.149218i
\(289\) 2.20912 + 12.5285i 0.129948 + 0.736972i
\(290\) 0 0
\(291\) 8.95141 + 3.25805i 0.524741 + 0.190990i
\(292\) 6.04826 + 10.4759i 0.353947 + 0.613055i
\(293\) 0.915093 1.58499i 0.0534603 0.0925960i −0.838057 0.545583i \(-0.816308\pi\)
0.891517 + 0.452987i \(0.149642\pi\)
\(294\) −1.02912 + 0.863533i −0.0600194 + 0.0503623i
\(295\) 0 0
\(296\) −0.593656 + 1.02824i −0.0345056 + 0.0597654i
\(297\) 16.8938 + 29.2609i 0.980277 + 1.69789i
\(298\) 8.16373 + 2.97136i 0.472912 + 0.172126i
\(299\) 0.0236393 0.134065i 0.00136710 0.00775318i
\(300\) 0 0
\(301\) 18.1113 6.59197i 1.04392 0.379955i
\(302\) 6.30901 + 5.29389i 0.363043 + 0.304629i
\(303\) −27.6343 −1.58755
\(304\) −2.54510 3.53871i −0.145971 0.202959i
\(305\) 0 0
\(306\) −30.9212 25.9460i −1.76765 1.48323i
\(307\) 1.36877 0.498191i 0.0781197 0.0284333i −0.302665 0.953097i \(-0.597876\pi\)
0.380784 + 0.924664i \(0.375654\pi\)
\(308\) −1.12482 6.37915i −0.0640924 0.363486i
\(309\) 0.997455 5.65685i 0.0567432 0.321807i
\(310\) 0 0
\(311\) −9.85085 17.0622i −0.558591 0.967507i −0.997614 0.0690320i \(-0.978009\pi\)
0.439024 0.898475i \(-0.355324\pi\)
\(312\) −0.162221 + 0.280975i −0.00918394 + 0.0159071i
\(313\) −6.70515 + 5.62629i −0.378997 + 0.318017i −0.812309 0.583228i \(-0.801790\pi\)
0.433311 + 0.901244i \(0.357345\pi\)
\(314\) −8.98675 + 7.54078i −0.507152 + 0.425551i
\(315\) 0 0
\(316\) −1.87028 3.23942i −0.105212 0.182232i
\(317\) −7.40399 2.69483i −0.415850 0.151357i 0.125618 0.992079i \(-0.459909\pi\)
−0.541467 + 0.840722i \(0.682131\pi\)
\(318\) −6.25910 + 35.4971i −0.350993 + 1.99058i
\(319\) −0.869204 4.92950i −0.0486661 0.275999i
\(320\) 0 0
\(321\) −20.9939 17.6159i −1.17176 0.983226i
\(322\) 3.68576 0.205399
\(323\) 9.76991 21.6625i 0.543613 1.20533i
\(324\) 23.6069 1.31150
\(325\) 0 0
\(326\) −18.4751 + 6.72438i −1.02324 + 0.372429i
\(327\) 4.29789 + 24.3745i 0.237674 + 1.34791i
\(328\) −0.611069 + 3.46555i −0.0337407 + 0.191353i
\(329\) −20.4924 7.45862i −1.12978 0.411207i
\(330\) 0 0
\(331\) 11.9264 20.6572i 0.655535 1.13542i −0.326224 0.945292i \(-0.605776\pi\)
0.981759 0.190128i \(-0.0608902\pi\)
\(332\) −6.89602 + 5.78645i −0.378468 + 0.317573i
\(333\) 6.73417 5.65064i 0.369030 0.309653i
\(334\) −8.39241 + 14.5361i −0.459212 + 0.795379i
\(335\) 0 0
\(336\) −8.25439 3.00435i −0.450314 0.163901i
\(337\) 3.80768 21.5944i 0.207418 1.17632i −0.686172 0.727439i \(-0.740710\pi\)
0.893590 0.448885i \(-0.148179\pi\)
\(338\) −2.25567 12.7925i −0.122692 0.695822i
\(339\) −9.53385 + 3.47004i −0.517808 + 0.188467i
\(340\) 0 0
\(341\) 25.0460 1.35632
\(342\) 8.74633 + 31.0654i 0.472947 + 1.67983i
\(343\) 17.9290 0.968076
\(344\) 5.42148 + 4.54916i 0.292307 + 0.245274i
\(345\) 0 0
\(346\) 2.32192 + 13.1682i 0.124827 + 0.707929i
\(347\) 1.77470 10.0648i 0.0952710 0.540308i −0.899393 0.437141i \(-0.855991\pi\)
0.994664 0.103168i \(-0.0328978\pi\)
\(348\) −6.37859 2.32162i −0.341928 0.124452i
\(349\) 14.5918 + 25.2738i 0.781083 + 1.35288i 0.931311 + 0.364224i \(0.118666\pi\)
−0.150229 + 0.988651i \(0.548001\pi\)
\(350\) 0 0
\(351\) 1.09455 0.918436i 0.0584227 0.0490225i
\(352\) 1.82207 1.52890i 0.0971169 0.0814907i
\(353\) 10.6172 18.3895i 0.565095 0.978773i −0.431946 0.901900i \(-0.642173\pi\)
0.997041 0.0768738i \(-0.0244938\pi\)
\(354\) −19.2221 33.2936i −1.02164 1.76954i
\(355\) 0 0
\(356\) 1.34237 7.61299i 0.0711457 0.403487i
\(357\) −8.31585 47.1615i −0.440122 2.49605i
\(358\) −20.3431 + 7.40427i −1.07516 + 0.391328i
\(359\) 18.4389 + 15.4721i 0.973170 + 0.816586i 0.983045 0.183365i \(-0.0586990\pi\)
−0.00987517 + 0.999951i \(0.503143\pi\)
\(360\) 0 0
\(361\) −16.2091 + 9.91295i −0.853108 + 0.521734i
\(362\) −9.08845 −0.477678
\(363\) 13.2008 + 11.0767i 0.692860 + 0.581378i
\(364\) −0.257408 + 0.0936888i −0.0134918 + 0.00491063i
\(365\) 0 0
\(366\) 0.0979260 0.555366i 0.00511867 0.0290294i
\(367\) 18.1506 + 6.60629i 0.947456 + 0.344846i 0.769106 0.639121i \(-0.220702\pi\)
0.178350 + 0.983967i \(0.442924\pi\)
\(368\) 0.676702 + 1.17208i 0.0352755 + 0.0610990i
\(369\) 13.0273 22.5640i 0.678176 1.17463i
\(370\) 0 0
\(371\) −23.3128 + 19.5618i −1.21034 + 1.01560i
\(372\) 16.9823 29.4142i 0.880491 1.52505i
\(373\) 16.6405 + 28.8223i 0.861615 + 1.49236i 0.870370 + 0.492399i \(0.163880\pi\)
−0.00875464 + 0.999962i \(0.502787\pi\)
\(374\) 12.1853 + 4.43508i 0.630086 + 0.229332i
\(375\) 0 0
\(376\) −1.39052 7.88604i −0.0717106 0.406691i
\(377\) −0.198912 + 0.0723982i −0.0102445 + 0.00372870i
\(378\) 29.6345 + 24.8663i 1.52424 + 1.27899i
\(379\) 17.9416 0.921600 0.460800 0.887504i \(-0.347563\pi\)
0.460800 + 0.887504i \(0.347563\pi\)
\(380\) 0 0
\(381\) 34.7420 1.77989
\(382\) 5.32870 + 4.47131i 0.272640 + 0.228772i
\(383\) −24.5918 + 8.95070i −1.25658 + 0.457359i −0.882621 0.470084i \(-0.844223\pi\)
−0.373963 + 0.927444i \(0.622001\pi\)
\(384\) −0.560106 3.17652i −0.0285828 0.162101i
\(385\) 0 0
\(386\) 15.3524 + 5.58781i 0.781416 + 0.284412i
\(387\) −26.1999 45.3795i −1.33181 2.30677i
\(388\) −1.47664 + 2.55762i −0.0749653 + 0.129844i
\(389\) 12.5930 10.5668i 0.638492 0.535758i −0.265063 0.964231i \(-0.585393\pi\)
0.903555 + 0.428473i \(0.140948\pi\)
\(390\) 0 0
\(391\) −3.68922 + 6.38992i −0.186572 + 0.323152i
\(392\) −0.208248 0.360697i −0.0105181 0.0182179i
\(393\) −13.1322 4.77974i −0.662433 0.241106i
\(394\) 0.499246 2.83137i 0.0251517 0.142642i
\(395\) 0 0
\(396\) −16.5487 + 6.02322i −0.831602 + 0.302678i
\(397\) 7.56400 + 6.34695i 0.379626 + 0.318544i 0.812556 0.582884i \(-0.198076\pi\)
−0.432929 + 0.901428i \(0.642520\pi\)
\(398\) −18.6336 −0.934017
\(399\) −15.7417 + 34.9036i −0.788072 + 1.74736i
\(400\) 0 0
\(401\) 22.0410 + 18.4946i 1.10067 + 0.923574i 0.997470 0.0710864i \(-0.0226466\pi\)
0.103202 + 0.994660i \(0.467091\pi\)
\(402\) 16.5224 6.01366i 0.824062 0.299934i
\(403\) −0.183922 1.04307i −0.00916181 0.0519592i
\(404\) 1.48771 8.43723i 0.0740164 0.419768i
\(405\) 0 0
\(406\) −2.86556 4.96329i −0.142215 0.246324i
\(407\) −1.41204 + 2.44573i −0.0699922 + 0.121230i
\(408\) 13.4707 11.3033i 0.666901 0.559596i
\(409\) 19.6383 16.4785i 0.971052 0.814810i −0.0116633 0.999932i \(-0.503713\pi\)
0.982715 + 0.185122i \(0.0592682\pi\)
\(410\) 0 0
\(411\) 11.6841 + 20.2374i 0.576333 + 0.998238i
\(412\) 1.67344 + 0.609081i 0.0824443 + 0.0300073i
\(413\) 5.63639 31.9655i 0.277348 1.57292i
\(414\) −1.74005 9.86833i −0.0855190 0.485002i
\(415\) 0 0
\(416\) −0.0770532 0.0646553i −0.00377784 0.00316999i
\(417\) −47.4668 −2.32446
\(418\) −6.05364 8.41699i −0.296093 0.411689i
\(419\) −33.3178 −1.62768 −0.813840 0.581090i \(-0.802627\pi\)
−0.813840 + 0.581090i \(0.802627\pi\)
\(420\) 0 0
\(421\) 0.609988 0.222018i 0.0297290 0.0108205i −0.327113 0.944985i \(-0.606076\pi\)
0.356842 + 0.934165i \(0.383854\pi\)
\(422\) −0.773107 4.38451i −0.0376343 0.213435i
\(423\) −10.2954 + 58.3880i −0.500579 + 2.83892i
\(424\) −10.5009 3.82202i −0.509970 0.185614i
\(425\) 0 0
\(426\) 2.23795 3.87624i 0.108429 0.187804i
\(427\) 0.364738 0.306052i 0.0176509 0.0148109i
\(428\) 6.50868 5.46143i 0.314609 0.263988i
\(429\) −0.385850 + 0.668312i −0.0186290 + 0.0322664i
\(430\) 0 0
\(431\) 0.898248 + 0.326936i 0.0432671 + 0.0157479i 0.363563 0.931570i \(-0.381560\pi\)
−0.320296 + 0.947318i \(0.603782\pi\)
\(432\) −2.46669 + 13.9893i −0.118679 + 0.673061i
\(433\) −0.438254 2.48546i −0.0210611 0.119444i 0.972465 0.233050i \(-0.0748707\pi\)
−0.993526 + 0.113607i \(0.963760\pi\)
\(434\) 26.9471 9.80794i 1.29350 0.470796i
\(435\) 0 0
\(436\) −7.67335 −0.367487
\(437\) 5.31468 2.56056i 0.254236 0.122488i
\(438\) 39.0175 1.86433
\(439\) −8.97963 7.53481i −0.428575 0.359617i 0.402839 0.915271i \(-0.368023\pi\)
−0.831414 + 0.555654i \(0.812468\pi\)
\(440\) 0 0
\(441\) 0.535485 + 3.03689i 0.0254993 + 0.144614i
\(442\) 0.0952236 0.540040i 0.00452932 0.0256871i
\(443\) −17.9136 6.52000i −0.851099 0.309775i −0.120610 0.992700i \(-0.538485\pi\)
−0.730488 + 0.682925i \(0.760707\pi\)
\(444\) 1.91485 + 3.31662i 0.0908747 + 0.157400i
\(445\) 0 0
\(446\) 14.1747 11.8940i 0.671190 0.563196i
\(447\) 21.4663 18.0123i 1.01532 0.851955i
\(448\) 1.36166 2.35847i 0.0643325 0.111427i
\(449\) 13.4465 + 23.2900i 0.634579 + 1.09912i 0.986604 + 0.163133i \(0.0521600\pi\)
−0.352025 + 0.935991i \(0.614507\pi\)
\(450\) 0 0
\(451\) −1.45346 + 8.24297i −0.0684407 + 0.388146i
\(452\) −0.546202 3.09766i −0.0256912 0.145702i
\(453\) 24.9628 9.08571i 1.17285 0.426884i
\(454\) −1.15362 0.968002i −0.0541421 0.0454306i
\(455\) 0 0
\(456\) −13.9896 + 1.40235i −0.655123 + 0.0656709i
\(457\) 30.4123 1.42263 0.711313 0.702876i \(-0.248101\pi\)
0.711313 + 0.702876i \(0.248101\pi\)
\(458\) 7.36582 + 6.18066i 0.344182 + 0.288803i
\(459\) −72.7726 + 26.4871i −3.39674 + 1.23631i
\(460\) 0 0
\(461\) −1.02335 + 5.80373i −0.0476623 + 0.270306i −0.999321 0.0368519i \(-0.988267\pi\)
0.951658 + 0.307158i \(0.0993781\pi\)
\(462\) −19.6335 7.14600i −0.913432 0.332462i
\(463\) 16.2882 + 28.2119i 0.756975 + 1.31112i 0.944387 + 0.328837i \(0.106657\pi\)
−0.187412 + 0.982281i \(0.560010\pi\)
\(464\) 1.05223 1.82251i 0.0488484 0.0846079i
\(465\) 0 0
\(466\) −4.40500 + 3.69623i −0.204058 + 0.171225i
\(467\) −3.11229 + 5.39065i −0.144020 + 0.249449i −0.929007 0.370063i \(-0.879336\pi\)
0.784987 + 0.619512i \(0.212670\pi\)
\(468\) 0.372368 + 0.644960i 0.0172127 + 0.0298133i
\(469\) 13.9499 + 5.07737i 0.644149 + 0.234451i
\(470\) 0 0
\(471\) 6.57081 + 37.2649i 0.302767 + 1.71708i
\(472\) 11.2000 4.07646i 0.515520 0.187634i
\(473\) 12.8953 + 10.8204i 0.592924 + 0.497523i
\(474\) −12.0653 −0.554176
\(475\) 0 0
\(476\) 14.8469 0.680508
\(477\) 63.3813 + 53.1832i 2.90203 + 2.43509i
\(478\) 16.3912 5.96592i 0.749718 0.272875i
\(479\) −0.252128 1.42989i −0.0115200 0.0653334i 0.978506 0.206219i \(-0.0661160\pi\)
−0.990026 + 0.140886i \(0.955005\pi\)
\(480\) 0 0
\(481\) 0.112224 + 0.0408464i 0.00511699 + 0.00186243i
\(482\) −7.60128 13.1658i −0.346229 0.599686i
\(483\) 5.94424 10.2957i 0.270472 0.468472i
\(484\) −4.09260 + 3.43410i −0.186027 + 0.156095i
\(485\) 0 0
\(486\) 16.7647 29.0372i 0.760461 1.31716i
\(487\) 11.3216 + 19.6095i 0.513029 + 0.888593i 0.999886 + 0.0151111i \(0.00481019\pi\)
−0.486856 + 0.873482i \(0.661856\pi\)
\(488\) 0.164291 + 0.0597970i 0.00743710 + 0.00270688i
\(489\) −11.0121 + 62.4528i −0.497985 + 2.82421i
\(490\) 0 0
\(491\) 5.70304 2.07574i 0.257375 0.0936767i −0.210110 0.977678i \(-0.567382\pi\)
0.467485 + 0.884001i \(0.345160\pi\)
\(492\) 8.69509 + 7.29604i 0.392005 + 0.328931i
\(493\) 11.4730 0.516718
\(494\) −0.306082 + 0.313921i −0.0137713 + 0.0141240i
\(495\) 0 0
\(496\) 8.06641 + 6.76853i 0.362193 + 0.303916i
\(497\) 3.55112 1.29250i 0.159289 0.0579766i
\(498\) 5.04214 + 28.5954i 0.225944 + 1.28139i
\(499\) 0.998143 5.66075i 0.0446830 0.253410i −0.954281 0.298910i \(-0.903377\pi\)
0.998964 + 0.0454999i \(0.0144881\pi\)
\(500\) 0 0
\(501\) 27.0699 + 46.8864i 1.20939 + 2.09473i
\(502\) −1.10178 + 1.90834i −0.0491748 + 0.0851733i
\(503\) 8.87376 7.44597i 0.395661 0.331999i −0.423152 0.906059i \(-0.639077\pi\)
0.818814 + 0.574059i \(0.194632\pi\)
\(504\) −15.4461 + 12.9608i −0.688023 + 0.577320i
\(505\) 0 0
\(506\) 1.60957 + 2.78785i 0.0715540 + 0.123935i
\(507\) −39.3723 14.3303i −1.74859 0.636433i
\(508\) −1.87036 + 10.6073i −0.0829839 + 0.470625i
\(509\) −5.74516 32.5824i −0.254650 1.44419i −0.796971 0.604018i \(-0.793565\pi\)
0.542321 0.840171i \(-0.317546\pi\)
\(510\) 0 0
\(511\) 25.2356 + 21.1752i 1.11636 + 0.936735i
\(512\) 1.00000 0.0441942
\(513\) 60.0066 + 15.2684i 2.64936 + 0.674115i
\(514\) 11.4930 0.506934
\(515\) 0 0
\(516\) 21.4511 7.80756i 0.944331 0.343709i
\(517\) −3.30742 18.7573i −0.145460 0.824946i
\(518\) −0.561480 + 3.18431i −0.0246700 + 0.139911i
\(519\) 40.5286 + 14.7512i 1.77901 + 0.647506i
\(520\) 0 0
\(521\) 4.23276 7.33136i 0.185441 0.321193i −0.758284 0.651924i \(-0.773962\pi\)
0.943725 + 0.330731i \(0.107295\pi\)
\(522\) −11.9360 + 10.0155i −0.522424 + 0.438366i
\(523\) −3.35434 + 2.81463i −0.146675 + 0.123075i −0.713173 0.700988i \(-0.752742\pi\)
0.566498 + 0.824063i \(0.308298\pi\)
\(524\) 2.16632 3.75218i 0.0946361 0.163915i
\(525\) 0 0
\(526\) −16.7936 6.11237i −0.732236 0.266512i
\(527\) −9.96860 + 56.5348i −0.434239 + 2.46269i
\(528\) −1.33224 7.55550i −0.0579782 0.328811i
\(529\) 19.8917 7.23998i 0.864856 0.314782i
\(530\) 0 0
\(531\) −88.2462 −3.82956
\(532\) −9.80920 6.68528i −0.425283 0.289844i
\(533\) 0.353962 0.0153318
\(534\) −19.1011 16.0277i −0.826583 0.693586i
\(535\) 0 0
\(536\) 0.946580 + 5.36832i 0.0408861 + 0.231876i
\(537\) −12.1255 + 68.7672i −0.523255 + 2.96753i
\(538\) 0.485375 + 0.176662i 0.0209260 + 0.00761644i
\(539\) −0.495329 0.857935i −0.0213353 0.0369539i
\(540\) 0 0
\(541\) −11.8358 + 9.93142i −0.508861 + 0.426985i −0.860728 0.509065i \(-0.829991\pi\)
0.351867 + 0.936050i \(0.385547\pi\)
\(542\) −17.5961 + 14.7649i −0.755817 + 0.634206i
\(543\) −14.6575 + 25.3875i −0.629013 + 1.08948i
\(544\) 2.72588 + 4.72137i 0.116871 + 0.202427i
\(545\) 0 0
\(546\) −0.153429 + 0.870136i −0.00656614 + 0.0372384i
\(547\) 0.467667 + 2.65227i 0.0199960 + 0.113403i 0.993172 0.116659i \(-0.0372183\pi\)
−0.973176 + 0.230062i \(0.926107\pi\)
\(548\) −6.80786 + 2.47786i −0.290817 + 0.105849i
\(549\) −0.991624 0.832071i −0.0423215 0.0355119i
\(550\) 0 0
\(551\) −7.58008 5.16606i −0.322922 0.220082i
\(552\) 4.36543 0.185805
\(553\) −7.80352 6.54793i −0.331839 0.278446i
\(554\) 9.49926 3.45745i 0.403585 0.146893i
\(555\) 0 0
\(556\) 2.55541 14.4924i 0.108373 0.614616i
\(557\) 18.0263 + 6.56103i 0.763798 + 0.278000i 0.694400 0.719589i \(-0.255670\pi\)
0.0693982 + 0.997589i \(0.477892\pi\)
\(558\) −38.9818 67.5184i −1.65023 2.85828i
\(559\) 0.355935 0.616497i 0.0150544 0.0260751i
\(560\) 0 0
\(561\) 32.0408 26.8854i 1.35276 1.13510i
\(562\) 14.4432 25.0163i 0.609248 1.05525i
\(563\) 11.2236 + 19.4398i 0.473016 + 0.819289i 0.999523 0.0308825i \(-0.00983177\pi\)
−0.526507 + 0.850171i \(0.676498\pi\)
\(564\) −24.2713 8.83403i −1.02201 0.371980i
\(565\) 0 0
\(566\) 2.13017 + 12.0808i 0.0895378 + 0.507794i
\(567\) 60.4123 21.9883i 2.53708 0.923420i
\(568\) 1.06300 + 0.891964i 0.0446026 + 0.0374260i
\(569\) −25.7630 −1.08004 −0.540020 0.841652i \(-0.681583\pi\)
−0.540020 + 0.841652i \(0.681583\pi\)
\(570\) 0 0
\(571\) 22.1970 0.928914 0.464457 0.885596i \(-0.346250\pi\)
0.464457 + 0.885596i \(0.346250\pi\)
\(572\) −0.183275 0.153786i −0.00766311 0.00643011i
\(573\) 21.0840 7.67395i 0.880797 0.320584i
\(574\) 1.66414 + 9.43781i 0.0694599 + 0.393926i
\(575\) 0 0
\(576\) −6.95746 2.53231i −0.289894 0.105513i
\(577\) 11.5629 + 20.0275i 0.481370 + 0.833758i 0.999771 0.0213798i \(-0.00680591\pi\)
−0.518401 + 0.855138i \(0.673473\pi\)
\(578\) −6.36090 + 11.0174i −0.264578 + 0.458263i
\(579\) 40.3686 33.8733i 1.67766 1.40773i
\(580\) 0 0
\(581\) −12.2578 + 21.2312i −0.508541 + 0.880819i
\(582\) 4.76295 + 8.24966i 0.197430 + 0.341960i
\(583\) −24.9770 9.09087i −1.03444 0.376505i
\(584\) −2.10054 + 11.9127i −0.0869209 + 0.492953i
\(585\) 0 0
\(586\) 1.71981 0.625960i 0.0710448 0.0258582i
\(587\) −26.9830 22.6414i −1.11371 0.934512i −0.115438 0.993315i \(-0.536827\pi\)
−0.998270 + 0.0588030i \(0.981272\pi\)
\(588\) −1.34342 −0.0554017
\(589\) 32.0426 32.8632i 1.32029 1.35410i
\(590\) 0 0
\(591\) −7.10392 5.96090i −0.292216 0.245199i
\(592\) −1.11571 + 0.406085i −0.0458553 + 0.0166900i
\(593\) 3.60643 + 20.4531i 0.148098 + 0.839908i 0.964827 + 0.262886i \(0.0846743\pi\)
−0.816728 + 0.577022i \(0.804215\pi\)
\(594\) −5.86715 + 33.2743i −0.240732 + 1.36526i
\(595\) 0 0
\(596\) 4.34383 + 7.52374i 0.177930 + 0.308184i
\(597\) −30.0515 + 52.0507i −1.22993 + 2.13029i
\(598\) 0.104284 0.0875048i 0.00426449 0.00357834i
\(599\) −2.03068 + 1.70394i −0.0829713 + 0.0696212i −0.683330 0.730110i \(-0.739469\pi\)
0.600359 + 0.799731i \(0.295024\pi\)
\(600\) 0 0
\(601\) −7.70749 13.3498i −0.314395 0.544548i 0.664914 0.746920i \(-0.268468\pi\)
−0.979309 + 0.202372i \(0.935135\pi\)
\(602\) 18.1113 + 6.59197i 0.738160 + 0.268668i
\(603\) 7.00846 39.7470i 0.285407 1.61862i
\(604\) 1.43014 + 8.11071i 0.0581914 + 0.330020i
\(605\) 0 0
\(606\) −21.1691 17.7630i −0.859935 0.721571i
\(607\) −30.5539 −1.24015 −0.620073 0.784544i \(-0.712897\pi\)
−0.620073 + 0.784544i \(0.712897\pi\)
\(608\) 0.324980 4.34677i 0.0131797 0.176285i
\(609\) −18.4858 −0.749083
\(610\) 0 0
\(611\) −0.756885 + 0.275484i −0.0306203 + 0.0111449i
\(612\) −7.00927 39.7515i −0.283333 1.60686i
\(613\) −0.724114 + 4.10666i −0.0292467 + 0.165866i −0.995933 0.0900982i \(-0.971282\pi\)
0.966686 + 0.255964i \(0.0823930\pi\)
\(614\) 1.36877 + 0.498191i 0.0552390 + 0.0201053i
\(615\) 0 0
\(616\) 3.23878 5.60973i 0.130494 0.226023i
\(617\) −12.5821 + 10.5577i −0.506538 + 0.425036i −0.859909 0.510447i \(-0.829480\pi\)
0.353371 + 0.935483i \(0.385035\pi\)
\(618\) 4.40025 3.69225i 0.177004 0.148524i
\(619\) −3.76167 + 6.51540i −0.151194 + 0.261876i −0.931667 0.363314i \(-0.881645\pi\)
0.780473 + 0.625190i \(0.214979\pi\)
\(620\) 0 0
\(621\) −18.0658 6.57542i −0.724957 0.263863i
\(622\) 3.42117 19.4024i 0.137176 0.777965i
\(623\) −3.65572 20.7326i −0.146463 0.830635i
\(624\) −0.304875 + 0.110966i −0.0122048 + 0.00444218i
\(625\) 0 0
\(626\) −8.75295 −0.349838
\(627\) −33.2750 + 3.33555i −1.32887 + 0.133209i
\(628\) −11.7314 −0.468133
\(629\) −4.95857 4.16073i −0.197711 0.165899i
\(630\) 0 0
\(631\) −5.83962 33.1181i −0.232472 1.31841i −0.847873 0.530199i \(-0.822117\pi\)
0.615402 0.788214i \(-0.288994\pi\)
\(632\) 0.649542 3.68373i 0.0258374 0.146531i
\(633\) −13.4944 4.91158i −0.536356 0.195218i
\(634\) −3.93958 6.82356i −0.156461 0.270998i
\(635\) 0 0
\(636\) −27.6118 + 23.1691i −1.09488 + 0.918714i
\(637\) −0.0320924 + 0.0269287i −0.00127155 + 0.00106696i
\(638\) 2.50277 4.33493i 0.0990857 0.171622i
\(639\) −5.13706 8.89766i −0.203219 0.351986i
\(640\) 0 0
\(641\) −0.0427768 + 0.242599i −0.00168958 + 0.00958210i −0.985641 0.168855i \(-0.945993\pi\)
0.983951 + 0.178437i \(0.0571041\pi\)
\(642\) −4.75892 26.9892i −0.187820 1.06518i
\(643\) 14.0111 5.09961i 0.552542 0.201109i −0.0506335 0.998717i \(-0.516124\pi\)
0.603176 + 0.797608i \(0.293902\pi\)
\(644\) 2.82345 + 2.36916i 0.111260 + 0.0933580i
\(645\) 0 0
\(646\) 21.4086 10.3144i 0.842308 0.405816i
\(647\) −28.3920 −1.11620 −0.558101 0.829773i \(-0.688470\pi\)
−0.558101 + 0.829773i \(0.688470\pi\)
\(648\) 18.0840 + 15.1743i 0.710405 + 0.596101i
\(649\) 26.6397 9.69605i 1.04570 0.380603i
\(650\) 0 0
\(651\) 16.0619 91.0913i 0.629514 3.57015i
\(652\) −18.4751 6.72438i −0.723540 0.263347i
\(653\) 14.1587 + 24.5237i 0.554074 + 0.959685i 0.997975 + 0.0636088i \(0.0202610\pi\)
−0.443901 + 0.896076i \(0.646406\pi\)
\(654\) −12.3753 + 21.4346i −0.483911 + 0.838159i
\(655\) 0 0
\(656\) −2.69572 + 2.26197i −0.105250 + 0.0883153i
\(657\) 44.7812 77.5632i 1.74708 3.02603i
\(658\) −10.9038 18.8859i −0.425073 0.736249i
\(659\) 36.0245 + 13.1118i 1.40331 + 0.510765i 0.929160 0.369677i \(-0.120532\pi\)
0.474154 + 0.880442i \(0.342754\pi\)
\(660\) 0 0
\(661\) −4.12371 23.3867i −0.160394 0.909637i −0.953688 0.300799i \(-0.902747\pi\)
0.793294 0.608839i \(-0.208364\pi\)
\(662\) 22.4143 8.15815i 0.871158 0.317075i
\(663\) −1.35496 1.13695i −0.0526225 0.0441555i
\(664\) −9.00212 −0.349350
\(665\) 0 0
\(666\) 8.79083 0.340638
\(667\) 2.18183 + 1.83077i 0.0844807 + 0.0708878i
\(668\) −15.7726 + 5.74075i −0.610259 + 0.222116i
\(669\) −10.3640 58.7774i −0.400697 2.27247i
\(670\) 0 0
\(671\) 0.390774 + 0.142230i 0.0150857 + 0.00549074i
\(672\) −4.39207 7.60729i −0.169428 0.293457i
\(673\) 15.5006 26.8478i 0.597504 1.03491i −0.395684 0.918387i \(-0.629492\pi\)
0.993188 0.116521i \(-0.0371742\pi\)
\(674\) 16.7975 14.0948i 0.647015 0.542910i
\(675\) 0 0
\(676\) 6.49494 11.2496i 0.249805 0.432676i
\(677\) −0.919318 1.59230i −0.0353322 0.0611972i 0.847819 0.530286i \(-0.177916\pi\)
−0.883151 + 0.469089i \(0.844582\pi\)
\(678\) −9.53385 3.47004i −0.366145 0.133266i
\(679\) −1.39661 + 7.92058i −0.0535970 + 0.303964i
\(680\) 0 0
\(681\) −4.56451 + 1.66135i −0.174912 + 0.0636629i
\(682\) 19.1864 + 16.0993i 0.734684 + 0.616473i
\(683\) −19.0534 −0.729059 −0.364530 0.931192i \(-0.618770\pi\)
−0.364530 + 0.931192i \(0.618770\pi\)
\(684\) −13.2684 + 29.4195i −0.507330 + 1.12488i
\(685\) 0 0
\(686\) 13.7344 + 11.5245i 0.524383 + 0.440009i
\(687\) 29.1442 10.6076i 1.11192 0.404706i
\(688\) 1.22895 + 6.96972i 0.0468533 + 0.265718i
\(689\) −0.195186 + 1.10696i −0.00743600 + 0.0421716i
\(690\) 0 0
\(691\) 12.6346 + 21.8838i 0.480643 + 0.832499i 0.999753 0.0222086i \(-0.00706979\pi\)
−0.519110 + 0.854708i \(0.673736\pi\)
\(692\) −6.68569 + 11.5800i −0.254152 + 0.440204i
\(693\) −36.7393 + 30.8279i −1.39561 + 1.17106i
\(694\) 7.82905 6.56935i 0.297187 0.249369i
\(695\) 0 0
\(696\) −3.39398 5.87854i −0.128648 0.222826i
\(697\) −18.0278 6.56160i −0.682853 0.248538i
\(698\) −5.06769 + 28.7403i −0.191815 + 1.08784i
\(699\) 3.22078 + 18.2660i 0.121821 + 0.690883i
\(700\) 0 0
\(701\) −12.7045 10.6603i −0.479841 0.402635i 0.370528 0.928821i \(-0.379177\pi\)
−0.850369 + 0.526187i \(0.823621\pi\)
\(702\) 1.42883 0.0539278
\(703\) 1.40257 + 4.98169i 0.0528991 + 0.187888i
\(704\) 2.37855 0.0896449
\(705\) 0 0
\(706\) 19.9538 7.26257i 0.750970 0.273331i
\(707\) −4.05152 22.9773i −0.152373 0.864151i
\(708\) 6.67576 37.8601i 0.250891 1.42287i
\(709\) −27.5288 10.0197i −1.03386 0.376296i −0.231314 0.972879i \(-0.574302\pi\)
−0.802551 + 0.596583i \(0.796525\pi\)
\(710\) 0 0
\(711\) −13.8475 + 23.9846i −0.519323 + 0.899493i
\(712\) 5.92185 4.96902i 0.221931 0.186222i
\(713\) −10.9171 + 9.16055i −0.408849 + 0.343065i
\(714\) 23.9445 41.4732i 0.896102 1.55209i
\(715\) 0 0
\(716\) −20.3431 7.40427i −0.760256 0.276710i
\(717\) 9.77003 55.4086i 0.364868 2.06927i
\(718\) 4.17977 + 23.7046i 0.155988 + 0.884649i
\(719\) 5.87107 2.13690i 0.218954 0.0796928i −0.230214 0.973140i \(-0.573943\pi\)
0.449168 + 0.893447i \(0.351720\pi\)
\(720\) 0 0
\(721\) 4.84979 0.180616
\(722\) −18.7888 2.82522i −0.699246 0.105144i
\(723\) −49.0362 −1.82368
\(724\) −6.96216 5.84194i −0.258747 0.217114i
\(725\) 0 0
\(726\) 2.99237 + 16.9706i 0.111057 + 0.629836i
\(727\) −5.05158 + 28.6489i −0.187353 + 1.06253i 0.735543 + 0.677479i \(0.236927\pi\)
−0.922895 + 0.385051i \(0.874184\pi\)
\(728\) −0.257408 0.0936888i −0.00954017 0.00347234i
\(729\) −18.6643 32.3276i −0.691271 1.19732i
\(730\) 0 0
\(731\) −29.5567 + 24.8010i −1.09319 + 0.917297i
\(732\) 0.431998 0.362489i 0.0159671 0.0133980i
\(733\) 23.6849 41.0234i 0.874821 1.51523i 0.0178674 0.999840i \(-0.494312\pi\)
0.856953 0.515394i \(-0.172354\pi\)
\(734\) 9.65775 + 16.7277i 0.356474 + 0.617431i
\(735\) 0 0
\(736\) −0.235016 + 1.33284i −0.00866281 + 0.0491292i
\(737\) 2.25149 + 12.7688i 0.0829346 + 0.470346i
\(738\) 24.4834 8.91122i 0.901245 0.328026i
\(739\) −6.34777 5.32642i −0.233507 0.195935i 0.518525 0.855063i \(-0.326481\pi\)
−0.752031 + 0.659127i \(0.770926\pi\)
\(740\) 0 0
\(741\) 0.383263 + 1.36128i 0.0140795 + 0.0500080i
\(742\) −30.4328 −1.11722
\(743\) 4.45699 + 3.73986i 0.163511 + 0.137202i 0.720872 0.693068i \(-0.243742\pi\)
−0.557361 + 0.830270i \(0.688186\pi\)
\(744\) 31.9163 11.6166i 1.17011 0.425884i
\(745\) 0 0
\(746\) −5.77920 + 32.7755i −0.211592 + 1.20000i
\(747\) 62.6319 + 22.7961i 2.29158 + 0.834067i
\(748\) 6.48365 + 11.2300i 0.237066 + 0.410610i
\(749\) 11.5693 20.0387i 0.422734 0.732197i
\(750\) 0 0
\(751\) 14.5050 12.1712i 0.529296 0.444132i −0.338562 0.940944i \(-0.609941\pi\)
0.867858 + 0.496812i \(0.165496\pi\)
\(752\) 4.00385 6.93486i 0.146005 0.252888i
\(753\) 3.55381 + 6.15538i 0.129508 + 0.224315i
\(754\) −0.198912 0.0723982i −0.00724396 0.00263659i
\(755\) 0 0
\(756\) 6.71760 + 38.0974i 0.244317 + 1.38559i
\(757\) −14.1638 + 5.15520i −0.514792 + 0.187369i −0.586335 0.810069i \(-0.699430\pi\)
0.0715433 + 0.997437i \(0.477208\pi\)
\(758\) 13.7441 + 11.5327i 0.499208 + 0.418885i
\(759\) 10.3834 0.376893
\(760\) 0 0
\(761\) −6.63681 −0.240584 −0.120292 0.992739i \(-0.538383\pi\)
−0.120292 + 0.992739i \(0.538383\pi\)
\(762\) 26.6139 + 22.3317i 0.964121 + 0.808994i
\(763\) −19.6368 + 7.14720i −0.710899 + 0.258746i
\(764\) 1.20792 + 6.85045i 0.0437010 + 0.247841i
\(765\) 0 0
\(766\) −24.5918 8.95070i −0.888539 0.323402i
\(767\) −0.599429 1.03824i −0.0216441 0.0374887i
\(768\) 1.61276 2.79338i 0.0581955 0.100797i
\(769\) −24.9327 + 20.9210i −0.899095 + 0.754430i −0.970013 0.243052i \(-0.921851\pi\)
0.0709184 + 0.997482i \(0.477407\pi\)
\(770\) 0 0
\(771\) 18.5354 32.1043i 0.667537 1.15621i
\(772\) 8.16884 + 14.1488i 0.294003 + 0.509228i
\(773\) −0.612613 0.222973i −0.0220342 0.00801978i 0.330980 0.943638i \(-0.392621\pi\)
−0.353014 + 0.935618i \(0.614843\pi\)
\(774\) 9.09911 51.6036i 0.327061 1.85485i
\(775\) 0 0
\(776\) −2.77518 + 1.01008i −0.0996233 + 0.0362599i
\(777\) 7.98947 + 6.70396i 0.286621 + 0.240503i
\(778\) 16.4390 0.589368
\(779\) 8.95623 + 12.4527i 0.320890 + 0.446166i
\(780\) 0 0
\(781\) 2.52840 + 2.12158i 0.0904733 + 0.0759161i
\(782\) −6.93347 + 2.52358i −0.247940 + 0.0902429i
\(783\) 5.19104 + 29.4398i 0.185513 + 1.05209i
\(784\) 0.0723239 0.410169i 0.00258300 0.0146489i
\(785\) 0 0
\(786\) −6.98751 12.1027i −0.249236 0.431690i
\(787\) −6.32936 + 10.9628i −0.225617 + 0.390781i −0.956504 0.291718i \(-0.905773\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(788\) 2.20241 1.84804i 0.0784577 0.0658338i
\(789\) −44.1583 + 37.0532i −1.57208 + 1.31913i
\(790\) 0 0
\(791\) −4.28304 7.41844i −0.152287 0.263769i
\(792\) −16.5487 6.02322i −0.588031 0.214026i
\(793\) 0.00305376 0.0173187i 0.000108442 0.000615006i
\(794\) 1.71462 + 9.72409i 0.0608496 + 0.345095i
\(795\) 0 0
\(796\) −14.2742 11.9774i −0.505934 0.424529i
\(797\) 47.2820 1.67482 0.837408 0.546578i \(-0.184070\pi\)
0.837408 + 0.546578i \(0.184070\pi\)
\(798\) −34.4944 + 16.6191i −1.22109 + 0.588309i
\(799\) 43.6561 1.54444
\(800\) 0 0
\(801\) −53.7842 + 19.5758i −1.90037 + 0.691678i
\(802\) 4.99628 + 28.3353i 0.176425 + 1.00055i
\(803\) −4.99623 + 28.3350i −0.176313 + 0.999922i
\(804\) 16.5224 + 6.01366i 0.582700 + 0.212085i
\(805\) 0 0
\(806\) 0.529582 0.917263i 0.0186537 0.0323092i
\(807\) 1.27628 1.07092i 0.0449271 0.0376983i
\(808\) 6.56300 5.50701i 0.230885 0.193736i
\(809\) −24.1710 + 41.8655i −0.849809 + 1.47191i 0.0315702 + 0.999502i \(0.489949\pi\)
−0.881379 + 0.472410i \(0.843384\pi\)
\(810\) 0 0
\(811\) 34.8288 + 12.6766i 1.22300 + 0.445137i 0.871196 0.490935i \(-0.163345\pi\)
0.351808 + 0.936072i \(0.385567\pi\)
\(812\) 0.995197 5.64404i 0.0349246 0.198067i
\(813\) 12.8657 + 72.9649i 0.451219 + 2.55899i
\(814\) −2.65377 + 0.965892i −0.0930145 + 0.0338545i
\(815\) 0 0
\(816\) 17.5848 0.615591
\(817\) 30.6951 3.07694i 1.07389 0.107649i
\(818\) 25.6360 0.896342
\(819\) 1.55366 + 1.30367i 0.0542892 + 0.0455540i
\(820\) 0 0
\(821\) −4.86215 27.5746i −0.169690 0.962362i −0.944096 0.329672i \(-0.893062\pi\)
0.774405 0.632690i \(-0.218049\pi\)
\(822\) −4.05784 + 23.0131i −0.141533 + 0.802675i
\(823\) −7.12142 2.59198i −0.248237 0.0903509i 0.214905 0.976635i \(-0.431056\pi\)
−0.463142 + 0.886284i \(0.653278\pi\)
\(824\) 0.890417 + 1.54225i 0.0310191 + 0.0537267i
\(825\) 0 0
\(826\) 24.8648 20.8640i 0.865156 0.725952i
\(827\) 26.6363 22.3505i 0.926236 0.777204i −0.0489016 0.998804i \(-0.515572\pi\)
0.975138 + 0.221599i \(0.0711276\pi\)
\(828\) 5.01028 8.67807i 0.174119 0.301584i
\(829\) 9.63690 + 16.6916i 0.334703 + 0.579723i 0.983428 0.181300i \(-0.0580306\pi\)
−0.648724 + 0.761023i \(0.724697\pi\)
\(830\) 0 0
\(831\) 5.66206 32.1111i 0.196415 1.11392i
\(832\) −0.0174665 0.0990577i −0.000605544 0.00343421i
\(833\) 2.13371 0.776606i 0.0739286 0.0269078i
\(834\) −36.3617 30.5111i −1.25910 1.05651i
\(835\) 0 0
\(836\) 0.772980 10.3390i 0.0267341 0.357582i
\(837\) −149.579 −5.17021
\(838\) −25.5229 21.4162i −0.881674 0.739812i
\(839\) −28.6196 + 10.4167i −0.988059 + 0.359624i −0.784969 0.619536i \(-0.787321\pi\)
−0.203091 + 0.979160i \(0.565099\pi\)
\(840\) 0 0
\(841\) −4.26676 + 24.1980i −0.147130 + 0.834413i
\(842\) 0.609988 + 0.222018i 0.0210216 + 0.00765123i
\(843\) −46.5867 80.6906i −1.60453 2.77913i
\(844\) 2.22607 3.85567i 0.0766246 0.132718i
\(845\) 0 0
\(846\) −45.4178 + 38.1101i −1.56150 + 1.31025i
\(847\) −7.27469 + 12.6001i −0.249961 + 0.432946i
\(848\) −5.58743 9.67771i −0.191873 0.332334i
\(849\) 37.1818 + 13.5331i 1.27607 + 0.464453i
\(850\) 0 0
\(851\) −0.279037 1.58250i −0.00956528 0.0542474i
\(852\) 4.20596 1.53085i 0.144094 0.0524459i
\(853\) −42.4989 35.6608i −1.45513 1.22100i −0.928723 0.370773i \(-0.879093\pi\)
−0.526411 0.850230i \(-0.676463\pi\)
\(854\) 0.476132 0.0162929
\(855\) 0 0
\(856\) 8.49647 0.290403
\(857\) −40.4823 33.9686i −1.38285 1.16035i −0.968145 0.250390i \(-0.919441\pi\)
−0.414702 0.909957i \(-0.636114\pi\)
\(858\) −0.725161 + 0.263937i −0.0247566 + 0.00901066i
\(859\) −0.271832 1.54164i −0.00927480 0.0526000i 0.979819 0.199886i \(-0.0640573\pi\)
−0.989094 + 0.147286i \(0.952946\pi\)
\(860\) 0 0
\(861\) 29.0473 + 10.5723i 0.989928 + 0.360304i
\(862\) 0.477948 + 0.827830i 0.0162790 + 0.0281960i
\(863\) 27.3298 47.3366i 0.930318 1.61136i 0.147540 0.989056i \(-0.452865\pi\)
0.782778 0.622301i \(-0.213802\pi\)
\(864\) −10.8817 + 9.13087i −0.370205 + 0.310639i
\(865\) 0 0
\(866\) 1.26190 2.18568i 0.0428812 0.0742724i
\(867\) 20.5172 + 35.5368i 0.696800 + 1.20689i
\(868\) 26.9471 + 9.80794i 0.914644 + 0.332903i
\(869\) 1.54497 8.76194i 0.0524094 0.297229i
\(870\) 0 0
\(871\) 0.515240 0.187532i 0.0174583 0.00635429i
\(872\) −5.87813 4.93233i −0.199059 0.167030i
\(873\) 21.8661 0.740055
\(874\) 5.71718 + 1.45471i 0.193387 + 0.0492062i
\(875\) 0 0
\(876\) 29.8892 + 25.0800i 1.00986 + 0.847375i
\(877\) 30.1850 10.9865i 1.01928 0.370986i 0.222288 0.974981i \(-0.428647\pi\)
0.796988 + 0.603995i \(0.206425\pi\)
\(878\) −2.03552 11.5440i −0.0686954 0.389591i
\(879\) 1.02510 5.81362i 0.0345757 0.196088i
\(880\) 0 0
\(881\) −12.5921 21.8102i −0.424239 0.734804i 0.572110 0.820177i \(-0.306125\pi\)
−0.996349 + 0.0853728i \(0.972792\pi\)
\(882\) −1.54187 + 2.67059i −0.0519174 + 0.0899235i
\(883\) −19.4168 + 16.2926i −0.653426 + 0.548290i −0.908108 0.418735i \(-0.862474\pi\)
0.254682 + 0.967025i \(0.418029\pi\)
\(884\) 0.420076 0.352486i 0.0141287 0.0118554i
\(885\) 0 0
\(886\) −9.53160 16.5092i −0.320220 0.554638i
\(887\) −37.9087 13.7977i −1.27285 0.463280i −0.384790 0.923004i \(-0.625726\pi\)
−0.888062 + 0.459724i \(0.847948\pi\)
\(888\) −0.665020 + 3.77152i −0.0223166 + 0.126564i
\(889\) 5.09360 + 28.8873i 0.170834 + 0.968847i
\(890\) 0 0
\(891\) 43.0136 + 36.0927i 1.44101 + 1.20915i
\(892\) 18.5037 0.619551
\(893\) −28.8431 19.6575i −0.965197 0.657812i
\(894\) 28.0222 0.937204
\(895\) 0 0
\(896\) 2.55909 0.931432i 0.0854931 0.0311170i
\(897\) −0.0762490 0.432429i −0.00254588 0.0144384i
\(898\) −4.66992 + 26.4844i −0.155837 + 0.883797i
\(899\) 20.8234 + 7.57910i 0.694499 + 0.252777i
\(900\) 0 0
\(901\) 30.4614 52.7606i 1.01482 1.75771i
\(902\) −6.41189 + 5.38022i −0.213493 + 0.179142i
\(903\) 47.6230 39.9605i 1.58479 1.32980i
\(904\) 1.57272 2.72404i 0.0523080 0.0906002i
\(905\) 0 0
\(906\) 24.9628 + 9.08571i 0.829332 + 0.301852i
\(907\) 3.16525 17.9510i 0.105100 0.596053i −0.886080 0.463532i \(-0.846582\pi\)
0.991180 0.132521i \(-0.0423071\pi\)
\(908\) −0.261504 1.48307i −0.00867833 0.0492172i
\(909\) −59.6073 + 21.6953i −1.97705 + 0.719587i
\(910\) 0 0
\(911\) 31.5891 1.04659 0.523297 0.852150i \(-0.324702\pi\)
0.523297 + 0.852150i \(0.324702\pi\)
\(912\) −11.6181 7.91808i −0.384713 0.262194i
\(913\) −21.4120 −0.708633
\(914\) 23.2971 + 19.5486i 0.770601 + 0.646611i
\(915\) 0 0
\(916\) 1.66970 + 9.46931i 0.0551683 + 0.312875i
\(917\) 2.04891 11.6199i 0.0676609 0.383724i
\(918\) −72.7726 26.4871i −2.40185 0.874204i
\(919\) −15.8297 27.4179i −0.522174 0.904432i −0.999667 0.0257967i \(-0.991788\pi\)
0.477493 0.878636i \(-0.341546\pi\)
\(920\) 0 0
\(921\) 3.59913 3.02003i 0.118595 0.0995134i
\(922\) −4.51450 + 3.78811i −0.148677 + 0.124755i
\(923\) 0.0697890 0.120878i 0.00229713 0.00397875i
\(924\) −10.4467 18.0943i −0.343673 0.595259i
\(925\) 0 0
\(926\) −5.65682 + 32.0814i −0.185895 + 1.05426i
\(927\) −2.28960 12.9849i −0.0752002 0.426481i
\(928\) 1.97754 0.719766i 0.0649159 0.0236275i
\(929\) −17.2986 14.5152i −0.567548 0.476229i 0.313283 0.949660i \(-0.398571\pi\)
−0.880831 + 0.473430i \(0.843016\pi\)
\(930\) 0 0
\(931\) −1.75941 0.447672i −0.0576622 0.0146719i
\(932\) −5.75032 −0.188358
\(933\) −48.6808 40.8480i −1.59374 1.33730i
\(934\) −5.84919 + 2.12893i −0.191391 + 0.0696608i
\(935\) 0 0
\(936\) −0.129322 + 0.733421i −0.00422702 + 0.0239726i
\(937\) −29.1391 10.6058i −0.951932 0.346475i −0.181065 0.983471i \(-0.557955\pi\)
−0.770867 + 0.636996i \(0.780177\pi\)
\(938\) 7.42261 + 12.8563i 0.242357 + 0.419774i
\(939\) −14.1164 + 24.4503i −0.460671 + 0.797906i
\(940\) 0 0
\(941\) −1.60557 + 1.34723i −0.0523401 + 0.0439186i −0.668582 0.743638i \(-0.733099\pi\)
0.616242 + 0.787557i \(0.288654\pi\)
\(942\) −18.9199 + 32.7702i −0.616443 + 1.06771i
\(943\) −2.38132 4.12457i −0.0775464 0.134314i
\(944\) 11.2000 + 4.07646i 0.364528 + 0.132677i
\(945\) 0 0
\(946\) 2.92312 + 16.5778i 0.0950387 + 0.538991i
\(947\) 16.5253 6.01473i 0.537001 0.195453i −0.0592604 0.998243i \(-0.518874\pi\)
0.596262 + 0.802790i \(0.296652\pi\)
\(948\) −9.24252 7.75540i −0.300183 0.251884i
\(949\) 1.21674 0.0394970
\(950\) 0 0
\(951\) −25.4144 −0.824118
\(952\) 11.3734 + 9.54343i 0.368614 + 0.309304i
\(953\) −10.4716 + 3.81135i −0.339208 + 0.123462i −0.506007 0.862529i \(-0.668879\pi\)
0.166799 + 0.985991i \(0.446657\pi\)
\(954\) 14.3674 + 81.4814i 0.465161 + 2.63806i
\(955\) 0 0
\(956\) 16.3912 + 5.96592i 0.530130 + 0.192952i
\(957\) −8.07274 13.9824i −0.260955 0.451987i
\(958\) 0.725975 1.25743i 0.0234552 0.0406256i
\(959\) −15.1139 + 12.6821i −0.488055 + 0.409527i
\(960\) 0 0
\(961\) −39.9400 + 69.1781i −1.28839 + 2.23155i
\(962\) 0.0597134 + 0.103427i 0.00192524 + 0.00333461i
\(963\) −59.1139 21.5157i −1.90492 0.693334i
\(964\) 2.63990 14.9716i 0.0850254 0.482203i
\(965\) 0 0
\(966\) 11.1715 4.06610i 0.359438 0.130825i
\(967\) −28.4207 23.8478i −0.913950 0.766895i 0.0589166 0.998263i \(-0.481235\pi\)
−0.972866 + 0.231368i \(0.925680\pi\)
\(968\) −5.34251 −0.171715
\(969\) 5.71470 76.4370i 0.183583 2.45551i
\(970\) 0 0
\(971\) 7.90649 + 6.63434i 0.253731 + 0.212906i 0.760777 0.649013i \(-0.224818\pi\)
−0.507046 + 0.861919i \(0.669262\pi\)
\(972\) 31.5073 11.4677i 1.01060 0.367827i
\(973\) −6.95921 39.4676i −0.223102 1.26527i
\(974\) −3.93194 + 22.2991i −0.125988 + 0.714511i
\(975\) 0 0
\(976\) 0.0874174 + 0.151411i 0.00279816 + 0.00484656i
\(977\) 17.3817 30.1060i 0.556089 0.963175i −0.441728 0.897149i \(-0.645635\pi\)
0.997818 0.0660264i \(-0.0210322\pi\)
\(978\) −48.5796 + 40.7632i −1.55341 + 1.30346i
\(979\) 14.0854 11.8191i 0.450172 0.377739i
\(980\) 0 0
\(981\) 28.4067 + 49.2018i 0.906955 + 1.57089i
\(982\) 5.70304 + 2.07574i 0.181991 + 0.0662395i
\(983\) −6.82528 + 38.7081i −0.217693 + 1.23460i 0.658480 + 0.752598i \(0.271200\pi\)
−0.876173 + 0.481998i \(0.839911\pi\)
\(984\) 1.97102 + 11.1782i 0.0628337 + 0.356348i
\(985\) 0 0
\(986\) 8.78883 + 7.37470i 0.279893 + 0.234858i
\(987\) −70.3407 −2.23897
\(988\) −0.436257 + 0.0437313i −0.0138792 + 0.00139128i
\(989\) −9.57836 −0.304574
\(990\) 0 0
\(991\) −15.3142 + 5.57390i −0.486470 + 0.177061i −0.573599 0.819136i \(-0.694453\pi\)
0.0871286 + 0.996197i \(0.472231\pi\)
\(992\) 1.82851 + 10.3700i 0.0580552 + 0.329247i
\(993\) 13.3601 75.7689i 0.423970 2.40445i
\(994\) 3.55112 + 1.29250i 0.112635 + 0.0409957i
\(995\) 0 0
\(996\) −14.5183 + 25.1464i −0.460028 + 0.796793i
\(997\) 7.22006 6.05835i 0.228662 0.191870i −0.521257 0.853399i \(-0.674537\pi\)
0.749919 + 0.661530i \(0.230092\pi\)
\(998\) 4.40328 3.69479i 0.139383 0.116957i
\(999\) 8.43295 14.6063i 0.266807 0.462123i
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 950.2.l.m.301.5 30
5.2 odd 4 190.2.p.a.149.1 yes 60
5.3 odd 4 190.2.p.a.149.10 yes 60
5.4 even 2 950.2.l.l.301.1 30
19.6 even 9 inner 950.2.l.m.101.5 30
95.44 even 18 950.2.l.l.101.1 30
95.63 odd 36 190.2.p.a.139.1 60
95.82 odd 36 190.2.p.a.139.10 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.p.a.139.1 60 95.63 odd 36
190.2.p.a.139.10 yes 60 95.82 odd 36
190.2.p.a.149.1 yes 60 5.2 odd 4
190.2.p.a.149.10 yes 60 5.3 odd 4
950.2.l.l.101.1 30 95.44 even 18
950.2.l.l.301.1 30 5.4 even 2
950.2.l.m.101.5 30 19.6 even 9 inner
950.2.l.m.301.5 30 1.1 even 1 trivial