Properties

Label 950.2.u.e.199.3
Level $950$
Weight $2$
Character 950.199
Analytic conductor $7.586$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(99,950)]
 
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([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.3
Character \(\chi\) \(=\) 950.199
Dual form 950.2.u.e.549.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.984808 - 0.173648i) q^{2} +(-1.07851 - 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.28531 - 1.07851i) q^{6} +(2.14383 + 1.23774i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +O(q^{10})\) \(q+(0.984808 - 0.173648i) q^{2} +(-1.07851 - 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.28531 - 1.07851i) q^{6} +(2.14383 + 1.23774i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +(-1.45059 - 2.51250i) q^{11} +(-1.45307 - 0.838929i) q^{12} +(0.833484 - 0.993308i) q^{13} +(2.32619 + 0.846665i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-1.22411 + 0.215843i) q^{17} -0.184793i q^{18} +(4.22186 - 1.08440i) q^{19} +(-0.721249 - 4.09041i) q^{21} +(-1.86485 - 2.22244i) q^{22} +(0.750979 + 2.06330i) q^{23} +(-1.57667 - 0.573861i) q^{24} +(0.648336 - 1.12295i) q^{26} +(-4.62772 + 2.67181i) q^{27} +(2.43788 + 0.429863i) q^{28} +(1.12586 - 6.38509i) q^{29} +(3.04442 - 5.27310i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-1.66488 + 4.57422i) q^{33} +(-1.16803 + 0.425128i) q^{34} +(-0.0320889 - 0.181985i) q^{36} +1.44520i q^{37} +(3.96942 - 1.80104i) q^{38} -2.17563 q^{39} +(1.82601 - 1.53221i) q^{41} +(-1.42058 - 3.90302i) q^{42} +(3.14685 - 8.64591i) q^{43} +(-2.22244 - 1.86485i) q^{44} +(1.09786 + 1.90155i) q^{46} +(-10.9588 - 1.93233i) q^{47} +(-1.65237 - 0.291357i) q^{48} +(-0.435991 - 0.755158i) q^{49} +(1.59763 + 1.34057i) q^{51} +(0.443488 - 1.21847i) q^{52} +(4.11677 + 11.3107i) q^{53} +(-4.09346 + 3.43482i) q^{54} +2.47548 q^{56} +(-5.94709 - 4.25688i) q^{57} -6.48359i q^{58} +(0.351292 + 1.99228i) q^{59} +(1.25853 - 0.458067i) q^{61} +(2.08251 - 5.72164i) q^{62} +(0.294044 - 0.350428i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.845282 + 4.79383i) q^{66} +(3.31520 + 0.584560i) q^{67} +(-1.07646 + 0.621495i) q^{68} +(1.84205 - 3.19052i) q^{69} +(-14.2805 - 5.19768i) q^{71} +(-0.0632028 - 0.173648i) q^{72} +(-0.360357 - 0.429457i) q^{73} +(0.250956 + 1.42324i) q^{74} +(3.59636 - 2.46296i) q^{76} -7.18185i q^{77} +(-2.14258 + 0.377794i) q^{78} +(-4.96611 + 4.16706i) q^{79} +(7.90420 + 2.87689i) q^{81} +(1.53221 - 1.82601i) q^{82} +(-7.32198 - 4.22735i) q^{83} +(-2.07675 - 3.59705i) q^{84} +(1.59770 - 9.06100i) q^{86} +(-9.42109 + 5.43927i) q^{87} +(-2.51250 - 1.45059i) q^{88} +(9.11595 + 7.64919i) q^{89} +(3.01631 - 1.09785i) q^{91} +(1.41138 + 1.68202i) q^{92} +(-10.0610 + 1.77403i) q^{93} -11.1279 q^{94} -1.67786 q^{96} +(2.66454 - 0.469830i) q^{97} +(-0.560499 - 0.667976i) q^{98} +(-0.503786 + 0.183363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 36 q^{9} + 12 q^{11} + 24 q^{21} + 12 q^{29} + 12 q^{31} + 36 q^{36} + 72 q^{39} - 12 q^{41} - 12 q^{44} - 24 q^{46} + 36 q^{49} + 24 q^{56} + 48 q^{59} - 60 q^{61} + 12 q^{64} + 48 q^{66} - 12 q^{69} - 84 q^{71} - 12 q^{74} + 36 q^{76} - 120 q^{79} + 36 q^{81} + 48 q^{84} - 72 q^{86} + 24 q^{89} + 48 q^{91} - 120 q^{94} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.984808 0.173648i 0.696364 0.122788i
\(3\) −1.07851 1.28531i −0.622676 0.742076i 0.358852 0.933394i \(-0.383168\pi\)
−0.981528 + 0.191318i \(0.938724\pi\)
\(4\) 0.939693 0.342020i 0.469846 0.171010i
\(5\) 0 0
\(6\) −1.28531 1.07851i −0.524727 0.440298i
\(7\) 2.14383 + 1.23774i 0.810292 + 0.467822i 0.847057 0.531502i \(-0.178372\pi\)
−0.0367651 + 0.999324i \(0.511705\pi\)
\(8\) 0.866025 0.500000i 0.306186 0.176777i
\(9\) 0.0320889 0.181985i 0.0106963 0.0606617i
\(10\) 0 0
\(11\) −1.45059 2.51250i −0.437371 0.757548i 0.560115 0.828415i \(-0.310757\pi\)
−0.997486 + 0.0708665i \(0.977424\pi\)
\(12\) −1.45307 0.838929i −0.419465 0.242178i
\(13\) 0.833484 0.993308i 0.231167 0.275494i −0.637975 0.770057i \(-0.720228\pi\)
0.869142 + 0.494563i \(0.164672\pi\)
\(14\) 2.32619 + 0.846665i 0.621701 + 0.226281i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) −1.22411 + 0.215843i −0.296889 + 0.0523496i −0.320109 0.947381i \(-0.603719\pi\)
0.0232194 + 0.999730i \(0.492608\pi\)
\(18\) 0.184793i 0.0435560i
\(19\) 4.22186 1.08440i 0.968561 0.248777i
\(20\) 0 0
\(21\) −0.721249 4.09041i −0.157390 0.892600i
\(22\) −1.86485 2.22244i −0.397587 0.473826i
\(23\) 0.750979 + 2.06330i 0.156590 + 0.430227i 0.993034 0.117824i \(-0.0375920\pi\)
−0.836445 + 0.548052i \(0.815370\pi\)
\(24\) −1.57667 0.573861i −0.321837 0.117139i
\(25\) 0 0
\(26\) 0.648336 1.12295i 0.127149 0.220229i
\(27\) −4.62772 + 2.67181i −0.890605 + 0.514191i
\(28\) 2.43788 + 0.429863i 0.460715 + 0.0812365i
\(29\) 1.12586 6.38509i 0.209068 1.18568i −0.681842 0.731500i \(-0.738821\pi\)
0.890909 0.454181i \(-0.150068\pi\)
\(30\) 0 0
\(31\) 3.04442 5.27310i 0.546795 0.947076i −0.451697 0.892171i \(-0.649181\pi\)
0.998492 0.0549047i \(-0.0174855\pi\)
\(32\) 0.642788 0.766044i 0.113630 0.135419i
\(33\) −1.66488 + 4.57422i −0.289818 + 0.796270i
\(34\) −1.16803 + 0.425128i −0.200315 + 0.0729088i
\(35\) 0 0
\(36\) −0.0320889 0.181985i −0.00534815 0.0303309i
\(37\) 1.44520i 0.237589i 0.992919 + 0.118794i \(0.0379029\pi\)
−0.992919 + 0.118794i \(0.962097\pi\)
\(38\) 3.96942 1.80104i 0.643924 0.292167i
\(39\) −2.17563 −0.348380
\(40\) 0 0
\(41\) 1.82601 1.53221i 0.285175 0.239290i −0.488967 0.872302i \(-0.662626\pi\)
0.774142 + 0.633012i \(0.218182\pi\)
\(42\) −1.42058 3.90302i −0.219201 0.602249i
\(43\) 3.14685 8.64591i 0.479891 1.31849i −0.429696 0.902974i \(-0.641379\pi\)
0.909586 0.415515i \(-0.136399\pi\)
\(44\) −2.22244 1.86485i −0.335045 0.281136i
\(45\) 0 0
\(46\) 1.09786 + 1.90155i 0.161870 + 0.280368i
\(47\) −10.9588 1.93233i −1.59851 0.281860i −0.697802 0.716291i \(-0.745838\pi\)
−0.900705 + 0.434431i \(0.856950\pi\)
\(48\) −1.65237 0.291357i −0.238499 0.0420538i
\(49\) −0.435991 0.755158i −0.0622844 0.107880i
\(50\) 0 0
\(51\) 1.59763 + 1.34057i 0.223713 + 0.187718i
\(52\) 0.443488 1.21847i 0.0615007 0.168972i
\(53\) 4.11677 + 11.3107i 0.565482 + 1.55365i 0.811481 + 0.584379i \(0.198662\pi\)
−0.245999 + 0.969270i \(0.579116\pi\)
\(54\) −4.09346 + 3.43482i −0.557049 + 0.467420i
\(55\) 0 0
\(56\) 2.47548 0.330800
\(57\) −5.94709 4.25688i −0.787711 0.563838i
\(58\) 6.48359i 0.851337i
\(59\) 0.351292 + 1.99228i 0.0457343 + 0.259372i 0.999099 0.0424499i \(-0.0135163\pi\)
−0.953364 + 0.301822i \(0.902405\pi\)
\(60\) 0 0
\(61\) 1.25853 0.458067i 0.161138 0.0586494i −0.260192 0.965557i \(-0.583786\pi\)
0.421330 + 0.906908i \(0.361564\pi\)
\(62\) 2.08251 5.72164i 0.264479 0.726650i
\(63\) 0.294044 0.350428i 0.0370460 0.0441497i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) −0.845282 + 4.79383i −0.104047 + 0.590080i
\(67\) 3.31520 + 0.584560i 0.405016 + 0.0714153i 0.372445 0.928054i \(-0.378519\pi\)
0.0325710 + 0.999469i \(0.489630\pi\)
\(68\) −1.07646 + 0.621495i −0.130540 + 0.0753673i
\(69\) 1.84205 3.19052i 0.221757 0.384094i
\(70\) 0 0
\(71\) −14.2805 5.19768i −1.69478 0.616851i −0.699569 0.714565i \(-0.746625\pi\)
−0.995215 + 0.0977142i \(0.968847\pi\)
\(72\) −0.0632028 0.173648i −0.00744852 0.0204646i
\(73\) −0.360357 0.429457i −0.0421766 0.0502641i 0.744544 0.667574i \(-0.232667\pi\)
−0.786720 + 0.617310i \(0.788223\pi\)
\(74\) 0.250956 + 1.42324i 0.0291730 + 0.165448i
\(75\) 0 0
\(76\) 3.59636 2.46296i 0.412531 0.282521i
\(77\) 7.18185i 0.818447i
\(78\) −2.14258 + 0.377794i −0.242599 + 0.0427768i
\(79\) −4.96611 + 4.16706i −0.558731 + 0.468831i −0.877885 0.478872i \(-0.841046\pi\)
0.319154 + 0.947703i \(0.396601\pi\)
\(80\) 0 0
\(81\) 7.90420 + 2.87689i 0.878244 + 0.319655i
\(82\) 1.53221 1.82601i 0.169204 0.201649i
\(83\) −7.32198 4.22735i −0.803692 0.464012i 0.0410686 0.999156i \(-0.486924\pi\)
−0.844760 + 0.535145i \(0.820257\pi\)
\(84\) −2.07675 3.59705i −0.226593 0.392470i
\(85\) 0 0
\(86\) 1.59770 9.06100i 0.172284 0.977073i
\(87\) −9.42109 + 5.43927i −1.01005 + 0.583151i
\(88\) −2.51250 1.45059i −0.267834 0.154634i
\(89\) 9.11595 + 7.64919i 0.966289 + 0.810812i 0.981965 0.189065i \(-0.0605456\pi\)
−0.0156760 + 0.999877i \(0.504990\pi\)
\(90\) 0 0
\(91\) 3.01631 1.09785i 0.316195 0.115086i
\(92\) 1.41138 + 1.68202i 0.147146 + 0.175362i
\(93\) −10.0610 + 1.77403i −1.04328 + 0.183958i
\(94\) −11.1279 −1.14775
\(95\) 0 0
\(96\) −1.67786 −0.171246
\(97\) 2.66454 0.469830i 0.270543 0.0477040i −0.0367308 0.999325i \(-0.511694\pi\)
0.307274 + 0.951621i \(0.400583\pi\)
\(98\) −0.560499 0.667976i −0.0566189 0.0674758i
\(99\) −0.503786 + 0.183363i −0.0506324 + 0.0184287i
\(100\) 0 0
\(101\) 0.0902852 + 0.0757583i 0.00898372 + 0.00753823i 0.647268 0.762262i \(-0.275911\pi\)
−0.638285 + 0.769800i \(0.720356\pi\)
\(102\) 1.80615 + 1.04278i 0.178835 + 0.103251i
\(103\) −1.50808 + 0.870691i −0.148596 + 0.0857918i −0.572454 0.819937i \(-0.694009\pi\)
0.423859 + 0.905728i \(0.360675\pi\)
\(104\) 0.225165 1.27697i 0.0220792 0.125217i
\(105\) 0 0
\(106\) 6.01832 + 10.4240i 0.584551 + 1.01247i
\(107\) 14.4681 + 8.35318i 1.39869 + 0.807533i 0.994255 0.107035i \(-0.0341358\pi\)
0.404432 + 0.914568i \(0.367469\pi\)
\(108\) −3.43482 + 4.09346i −0.330516 + 0.393893i
\(109\) 19.0267 + 6.92515i 1.82243 + 0.663309i 0.994778 + 0.102063i \(0.0325442\pi\)
0.827649 + 0.561246i \(0.189678\pi\)
\(110\) 0 0
\(111\) 1.85753 1.55865i 0.176309 0.147941i
\(112\) 2.43788 0.429863i 0.230358 0.0406183i
\(113\) 16.5448i 1.55641i 0.628012 + 0.778204i \(0.283869\pi\)
−0.628012 + 0.778204i \(0.716131\pi\)
\(114\) −6.59594 3.15951i −0.617766 0.295915i
\(115\) 0 0
\(116\) −1.12586 6.38509i −0.104534 0.592840i
\(117\) −0.154022 0.183556i −0.0142393 0.0169697i
\(118\) 0.691910 + 1.90101i 0.0636955 + 0.175002i
\(119\) −2.89144 1.05240i −0.265057 0.0964730i
\(120\) 0 0
\(121\) 1.29155 2.23703i 0.117414 0.203366i
\(122\) 1.15987 0.669649i 0.105009 0.0606272i
\(123\) −3.93873 0.694505i −0.355143 0.0626214i
\(124\) 1.05732 5.99634i 0.0949499 0.538488i
\(125\) 0 0
\(126\) 0.228725 0.396164i 0.0203765 0.0352931i
\(127\) −0.0842392 + 0.100392i −0.00747502 + 0.00890838i −0.769769 0.638323i \(-0.779629\pi\)
0.762294 + 0.647231i \(0.224073\pi\)
\(128\) 0.342020 0.939693i 0.0302306 0.0830579i
\(129\) −14.5066 + 5.27997i −1.27724 + 0.464876i
\(130\) 0 0
\(131\) 2.22302 + 12.6074i 0.194226 + 1.10151i 0.913516 + 0.406802i \(0.133356\pi\)
−0.719290 + 0.694710i \(0.755533\pi\)
\(132\) 4.86778i 0.423686i
\(133\) 10.3932 + 2.90081i 0.901201 + 0.251532i
\(134\) 3.36634 0.290808
\(135\) 0 0
\(136\) −0.952186 + 0.798979i −0.0816492 + 0.0685119i
\(137\) 5.34535 + 14.6862i 0.456684 + 1.25473i 0.927939 + 0.372732i \(0.121579\pi\)
−0.471255 + 0.881997i \(0.656199\pi\)
\(138\) 1.26004 3.46192i 0.107261 0.294698i
\(139\) 8.79431 + 7.37930i 0.745924 + 0.625904i 0.934421 0.356169i \(-0.115917\pi\)
−0.188498 + 0.982074i \(0.560362\pi\)
\(140\) 0 0
\(141\) 9.33549 + 16.1695i 0.786190 + 1.36172i
\(142\) −14.9661 2.63893i −1.25593 0.221454i
\(143\) −3.70474 0.653245i −0.309806 0.0546271i
\(144\) −0.0923963 0.160035i −0.00769969 0.0133363i
\(145\) 0 0
\(146\) −0.429457 0.360357i −0.0355421 0.0298233i
\(147\) −0.500396 + 1.37483i −0.0412720 + 0.113394i
\(148\) 0.494286 + 1.35804i 0.0406301 + 0.111630i
\(149\) 11.6068 9.73926i 0.950866 0.797871i −0.0285771 0.999592i \(-0.509098\pi\)
0.979443 + 0.201720i \(0.0646532\pi\)
\(150\) 0 0
\(151\) −5.78759 −0.470988 −0.235494 0.971876i \(-0.575671\pi\)
−0.235494 + 0.971876i \(0.575671\pi\)
\(152\) 3.11404 3.05004i 0.252582 0.247391i
\(153\) 0.229695i 0.0185698i
\(154\) −1.24711 7.07274i −0.100495 0.569937i
\(155\) 0 0
\(156\) −2.04442 + 0.744109i −0.163685 + 0.0595764i
\(157\) −3.76870 + 10.3544i −0.300775 + 0.826372i 0.693591 + 0.720369i \(0.256028\pi\)
−0.994366 + 0.106003i \(0.966195\pi\)
\(158\) −4.16706 + 4.96611i −0.331514 + 0.395082i
\(159\) 10.0979 17.4900i 0.800814 1.38705i
\(160\) 0 0
\(161\) −0.943857 + 5.35288i −0.0743864 + 0.421866i
\(162\) 8.28368 + 1.46064i 0.650828 + 0.114758i
\(163\) 19.2078 11.0896i 1.50447 0.868605i 0.504481 0.863423i \(-0.331684\pi\)
0.999987 0.00518168i \(-0.00164939\pi\)
\(164\) 1.19184 2.06434i 0.0930675 0.161198i
\(165\) 0 0
\(166\) −7.94481 2.89168i −0.616637 0.224438i
\(167\) 5.94713 + 16.3396i 0.460203 + 1.26440i 0.925333 + 0.379155i \(0.123785\pi\)
−0.465130 + 0.885242i \(0.653993\pi\)
\(168\) −2.66982 3.18177i −0.205981 0.245479i
\(169\) 1.96546 + 11.1467i 0.151189 + 0.857438i
\(170\) 0 0
\(171\) −0.0618692 0.803112i −0.00473125 0.0614155i
\(172\) 9.20078i 0.701553i
\(173\) 2.11553 0.373025i 0.160841 0.0283606i −0.0926478 0.995699i \(-0.529533\pi\)
0.253489 + 0.967338i \(0.418422\pi\)
\(174\) −8.33344 + 6.99259i −0.631757 + 0.530107i
\(175\) 0 0
\(176\) −2.72623 0.992265i −0.205497 0.0747948i
\(177\) 2.18183 2.60020i 0.163996 0.195443i
\(178\) 10.3057 + 5.95001i 0.772447 + 0.445972i
\(179\) −5.19089 8.99089i −0.387985 0.672011i 0.604193 0.796838i \(-0.293496\pi\)
−0.992178 + 0.124827i \(0.960162\pi\)
\(180\) 0 0
\(181\) −2.89049 + 16.3928i −0.214848 + 1.21846i 0.666322 + 0.745664i \(0.267868\pi\)
−0.881170 + 0.472800i \(0.843243\pi\)
\(182\) 2.77984 1.60494i 0.206056 0.118966i
\(183\) −1.94609 1.12358i −0.143859 0.0830571i
\(184\) 1.68202 + 1.41138i 0.124000 + 0.104048i
\(185\) 0 0
\(186\) −9.60011 + 3.49415i −0.703914 + 0.256204i
\(187\) 2.31799 + 2.76247i 0.169508 + 0.202012i
\(188\) −10.9588 + 1.93233i −0.799254 + 0.140930i
\(189\) −13.2281 −0.962200
\(190\) 0 0
\(191\) −21.7916 −1.57679 −0.788393 0.615172i \(-0.789086\pi\)
−0.788393 + 0.615172i \(0.789086\pi\)
\(192\) −1.65237 + 0.291357i −0.119249 + 0.0210269i
\(193\) −14.7264 17.5503i −1.06003 1.26330i −0.963426 0.267974i \(-0.913646\pi\)
−0.0966060 0.995323i \(-0.530799\pi\)
\(194\) 2.54247 0.925384i 0.182539 0.0664387i
\(195\) 0 0
\(196\) −0.667976 0.560499i −0.0477126 0.0400356i
\(197\) 4.29163 + 2.47777i 0.305766 + 0.176534i 0.645030 0.764157i \(-0.276845\pi\)
−0.339264 + 0.940691i \(0.610178\pi\)
\(198\) −0.464292 + 0.268059i −0.0329958 + 0.0190501i
\(199\) −4.27197 + 24.2276i −0.302832 + 1.71745i 0.330704 + 0.943734i \(0.392714\pi\)
−0.633537 + 0.773713i \(0.718397\pi\)
\(200\) 0 0
\(201\) −2.82412 4.89153i −0.199198 0.345022i
\(202\) 0.102069 + 0.0589295i 0.00718154 + 0.00414626i
\(203\) 10.3167 12.2950i 0.724094 0.862941i
\(204\) 1.95979 + 0.713304i 0.137212 + 0.0499413i
\(205\) 0 0
\(206\) −1.33398 + 1.11934i −0.0929426 + 0.0779881i
\(207\) 0.399588 0.0704581i 0.0277733 0.00489717i
\(208\) 1.29667i 0.0899080i
\(209\) −8.84875 9.03442i −0.612081 0.624924i
\(210\) 0 0
\(211\) −0.638032 3.61846i −0.0439239 0.249105i 0.954938 0.296806i \(-0.0959215\pi\)
−0.998862 + 0.0477014i \(0.984810\pi\)
\(212\) 7.73700 + 9.22060i 0.531379 + 0.633273i
\(213\) 8.72096 + 23.9607i 0.597551 + 1.64176i
\(214\) 15.6988 + 5.71391i 1.07315 + 0.390595i
\(215\) 0 0
\(216\) −2.67181 + 4.62772i −0.181794 + 0.314876i
\(217\) 13.0535 7.53642i 0.886127 0.511606i
\(218\) 19.9402 + 3.51599i 1.35052 + 0.238133i
\(219\) −0.163339 + 0.926343i −0.0110374 + 0.0625965i
\(220\) 0 0
\(221\) −0.805875 + 1.39582i −0.0542090 + 0.0938927i
\(222\) 1.55865 1.85753i 0.104610 0.124669i
\(223\) −2.54920 + 7.00387i −0.170707 + 0.469014i −0.995314 0.0966918i \(-0.969174\pi\)
0.824607 + 0.565706i \(0.191396\pi\)
\(224\) 2.32619 0.846665i 0.155425 0.0565702i
\(225\) 0 0
\(226\) 2.87298 + 16.2935i 0.191108 + 1.08383i
\(227\) 11.4167i 0.757750i −0.925448 0.378875i \(-0.876311\pi\)
0.925448 0.378875i \(-0.123689\pi\)
\(228\) −7.04438 1.96614i −0.466525 0.130211i
\(229\) 3.19332 0.211021 0.105510 0.994418i \(-0.466352\pi\)
0.105510 + 0.994418i \(0.466352\pi\)
\(230\) 0 0
\(231\) −9.23093 + 7.74567i −0.607350 + 0.509627i
\(232\) −2.21752 6.09258i −0.145587 0.399997i
\(233\) 7.96876 21.8940i 0.522051 1.43432i −0.346183 0.938167i \(-0.612522\pi\)
0.868234 0.496156i \(-0.165255\pi\)
\(234\) −0.183556 0.154022i −0.0119994 0.0100687i
\(235\) 0 0
\(236\) 1.01150 + 1.75198i 0.0658433 + 0.114044i
\(237\) 10.7120 + 1.88881i 0.695817 + 0.122691i
\(238\) −3.03025 0.534316i −0.196422 0.0346345i
\(239\) −4.11104 7.12053i −0.265921 0.460589i 0.701883 0.712292i \(-0.252343\pi\)
−0.967805 + 0.251703i \(0.919009\pi\)
\(240\) 0 0
\(241\) 15.9574 + 13.3899i 1.02791 + 0.862518i 0.990601 0.136786i \(-0.0436773\pi\)
0.0373080 + 0.999304i \(0.488122\pi\)
\(242\) 0.883473 2.42732i 0.0567918 0.156034i
\(243\) 0.655868 + 1.80198i 0.0420740 + 0.115597i
\(244\) 1.02596 0.860884i 0.0656805 0.0551124i
\(245\) 0 0
\(246\) −3.99949 −0.254998
\(247\) 2.44171 5.09743i 0.155363 0.324342i
\(248\) 6.08885i 0.386642i
\(249\) 2.46333 + 13.9703i 0.156107 + 0.885330i
\(250\) 0 0
\(251\) −10.7939 + 3.92864i −0.681302 + 0.247974i −0.659406 0.751787i \(-0.729192\pi\)
−0.0218955 + 0.999760i \(0.506970\pi\)
\(252\) 0.156457 0.429863i 0.00985589 0.0270788i
\(253\) 4.09468 4.87985i 0.257430 0.306793i
\(254\) −0.0655264 + 0.113495i −0.00411149 + 0.00712132i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) 1.82847 + 0.322408i 0.114057 + 0.0201112i 0.230385 0.973100i \(-0.426001\pi\)
−0.116329 + 0.993211i \(0.537113\pi\)
\(258\) −13.3694 + 7.71881i −0.832340 + 0.480552i
\(259\) −1.78878 + 3.09826i −0.111149 + 0.192516i
\(260\) 0 0
\(261\) −1.12586 0.409781i −0.0696892 0.0253648i
\(262\) 4.37850 + 12.0298i 0.270505 + 0.743205i
\(263\) −6.59082 7.85464i −0.406407 0.484338i 0.523555 0.851992i \(-0.324605\pi\)
−0.929963 + 0.367654i \(0.880161\pi\)
\(264\) 0.845282 + 4.79383i 0.0520235 + 0.295040i
\(265\) 0 0
\(266\) 10.7390 + 1.05199i 0.658449 + 0.0645014i
\(267\) 19.9666i 1.22193i
\(268\) 3.31520 0.584560i 0.202508 0.0357077i
\(269\) −20.2958 + 17.0302i −1.23746 + 1.03835i −0.239738 + 0.970838i \(0.577061\pi\)
−0.997719 + 0.0675114i \(0.978494\pi\)
\(270\) 0 0
\(271\) −23.4094 8.52031i −1.42202 0.517572i −0.487385 0.873187i \(-0.662049\pi\)
−0.934633 + 0.355615i \(0.884272\pi\)
\(272\) −0.798979 + 0.952186i −0.0484452 + 0.0577347i
\(273\) −4.66419 2.69287i −0.282289 0.162980i
\(274\) 7.81438 + 13.5349i 0.472084 + 0.817673i
\(275\) 0 0
\(276\) 0.639737 3.62813i 0.0385076 0.218388i
\(277\) −12.4407 + 7.18265i −0.747490 + 0.431564i −0.824786 0.565444i \(-0.808705\pi\)
0.0772960 + 0.997008i \(0.475371\pi\)
\(278\) 9.94211 + 5.74008i 0.596288 + 0.344267i
\(279\) −0.861933 0.723248i −0.0516026 0.0432997i
\(280\) 0 0
\(281\) 25.2726 9.19849i 1.50764 0.548736i 0.549614 0.835419i \(-0.314775\pi\)
0.958025 + 0.286683i \(0.0925527\pi\)
\(282\) 12.0015 + 14.3028i 0.714678 + 0.851720i
\(283\) −19.8587 + 3.50163i −1.18048 + 0.208150i −0.729243 0.684255i \(-0.760127\pi\)
−0.451235 + 0.892405i \(0.649016\pi\)
\(284\) −15.1970 −0.901776
\(285\) 0 0
\(286\) −3.76189 −0.222445
\(287\) 5.81114 1.02466i 0.343021 0.0604838i
\(288\) −0.118782 0.141559i −0.00699932 0.00834146i
\(289\) −14.5229 + 5.28591i −0.854290 + 0.310936i
\(290\) 0 0
\(291\) −3.47760 2.91805i −0.203860 0.171059i
\(292\) −0.485507 0.280308i −0.0284122 0.0164038i
\(293\) −17.3197 + 9.99952i −1.01183 + 0.584178i −0.911726 0.410799i \(-0.865250\pi\)
−0.100100 + 0.994977i \(0.531916\pi\)
\(294\) −0.254058 + 1.44083i −0.0148170 + 0.0840311i
\(295\) 0 0
\(296\) 0.722598 + 1.25158i 0.0420002 + 0.0727464i
\(297\) 13.4259 + 7.75144i 0.779049 + 0.449784i
\(298\) 9.73926 11.6068i 0.564180 0.672364i
\(299\) 2.67542 + 0.973773i 0.154723 + 0.0563147i
\(300\) 0 0
\(301\) 17.4477 14.6404i 1.00567 0.843858i
\(302\) −5.69967 + 1.00500i −0.327979 + 0.0578315i
\(303\) 0.197751i 0.0113605i
\(304\) 2.53709 3.54445i 0.145512 0.203288i
\(305\) 0 0
\(306\) 0.0398862 + 0.226206i 0.00228014 + 0.0129313i
\(307\) −12.4713 14.8627i −0.711772 0.848257i 0.282032 0.959405i \(-0.408992\pi\)
−0.993804 + 0.111148i \(0.964547\pi\)
\(308\) −2.45634 6.74873i −0.139963 0.384544i
\(309\) 2.74559 + 0.999312i 0.156191 + 0.0568489i
\(310\) 0 0
\(311\) −2.69949 + 4.67566i −0.153074 + 0.265132i −0.932356 0.361541i \(-0.882251\pi\)
0.779282 + 0.626673i \(0.215584\pi\)
\(312\) −1.88415 + 1.08782i −0.106669 + 0.0615854i
\(313\) 15.9375 + 2.81021i 0.900841 + 0.158843i 0.604842 0.796345i \(-0.293236\pi\)
0.295999 + 0.955188i \(0.404347\pi\)
\(314\) −1.91342 + 10.8515i −0.107980 + 0.612388i
\(315\) 0 0
\(316\) −3.24140 + 5.61427i −0.182343 + 0.315827i
\(317\) 1.57543 1.87753i 0.0884852 0.105453i −0.719985 0.693989i \(-0.755851\pi\)
0.808470 + 0.588537i \(0.200296\pi\)
\(318\) 6.90736 18.9778i 0.387345 1.06422i
\(319\) −17.6757 + 6.43344i −0.989651 + 0.360203i
\(320\) 0 0
\(321\) −4.86752 27.6051i −0.271678 1.54076i
\(322\) 5.43546i 0.302906i
\(323\) −4.93394 + 2.23867i −0.274532 + 0.124563i
\(324\) 8.41147 0.467304
\(325\) 0 0
\(326\) 16.9903 14.2565i 0.941003 0.789595i
\(327\) −11.6194 31.9241i −0.642555 1.76541i
\(328\) 0.815270 2.23994i 0.0450158 0.123680i
\(329\) −21.1021 17.7068i −1.16340 0.976206i
\(330\) 0 0
\(331\) −1.51812 2.62947i −0.0834436 0.144529i 0.821283 0.570521i \(-0.193259\pi\)
−0.904727 + 0.425992i \(0.859925\pi\)
\(332\) −8.32625 1.46814i −0.456962 0.0805748i
\(333\) 0.263004 + 0.0463747i 0.0144125 + 0.00254132i
\(334\) 8.69412 + 15.0587i 0.475721 + 0.823973i
\(335\) 0 0
\(336\) −3.18177 2.66982i −0.173580 0.145651i
\(337\) −2.07369 + 5.69742i −0.112961 + 0.310358i −0.983272 0.182145i \(-0.941696\pi\)
0.870310 + 0.492504i \(0.163918\pi\)
\(338\) 3.87120 + 10.6360i 0.210566 + 0.578525i
\(339\) 21.2653 17.8437i 1.15497 0.969138i
\(340\) 0 0
\(341\) −17.6649 −0.956608
\(342\) −0.200388 0.780168i −0.0108358 0.0421866i
\(343\) 19.4870i 1.05220i
\(344\) −1.59770 9.06100i −0.0861422 0.488537i
\(345\) 0 0
\(346\) 2.01862 0.734716i 0.108522 0.0394986i
\(347\) 0.983940 2.70335i 0.0528207 0.145124i −0.910477 0.413561i \(-0.864285\pi\)
0.963297 + 0.268437i \(0.0865072\pi\)
\(348\) −6.99259 + 8.33344i −0.374842 + 0.446719i
\(349\) 16.3979 28.4020i 0.877761 1.52033i 0.0239680 0.999713i \(-0.492370\pi\)
0.853793 0.520613i \(-0.174297\pi\)
\(350\) 0 0
\(351\) −1.20320 + 6.82367i −0.0642219 + 0.364220i
\(352\) −2.85711 0.503786i −0.152285 0.0268519i
\(353\) −18.3605 + 10.6004i −0.977231 + 0.564204i −0.901433 0.432919i \(-0.857484\pi\)
−0.0757977 + 0.997123i \(0.524150\pi\)
\(354\) 1.69716 2.93957i 0.0902031 0.156236i
\(355\) 0 0
\(356\) 11.1824 + 4.07005i 0.592664 + 0.215712i
\(357\) 1.76577 + 4.85142i 0.0934546 + 0.256764i
\(358\) −6.67328 7.95291i −0.352694 0.420324i
\(359\) −3.22806 18.3072i −0.170370 0.966218i −0.943353 0.331791i \(-0.892347\pi\)
0.772983 0.634427i \(-0.218764\pi\)
\(360\) 0 0
\(361\) 16.6482 9.15633i 0.876220 0.481912i
\(362\) 16.6456i 0.874876i
\(363\) −4.26823 + 0.752605i −0.224024 + 0.0395015i
\(364\) 2.45892 2.06328i 0.128882 0.108145i
\(365\) 0 0
\(366\) −2.11163 0.768571i −0.110377 0.0401739i
\(367\) 13.9628 16.6403i 0.728855 0.868615i −0.266605 0.963806i \(-0.585902\pi\)
0.995459 + 0.0951910i \(0.0303462\pi\)
\(368\) 1.90155 + 1.09786i 0.0991249 + 0.0572298i
\(369\) −0.220244 0.381474i −0.0114654 0.0198587i
\(370\) 0 0
\(371\) −5.17411 + 29.3438i −0.268626 + 1.52345i
\(372\) −8.84751 + 5.10811i −0.458722 + 0.264843i
\(373\) 19.4123 + 11.2077i 1.00513 + 0.580312i 0.909762 0.415130i \(-0.136264\pi\)
0.0953679 + 0.995442i \(0.469597\pi\)
\(374\) 2.76247 + 2.31799i 0.142844 + 0.119860i
\(375\) 0 0
\(376\) −10.4568 + 3.80596i −0.539267 + 0.196277i
\(377\) −5.40397 6.44020i −0.278318 0.331687i
\(378\) −13.0271 + 2.29703i −0.670042 + 0.118146i
\(379\) 8.45251 0.434176 0.217088 0.976152i \(-0.430344\pi\)
0.217088 + 0.976152i \(0.430344\pi\)
\(380\) 0 0
\(381\) 0.219888 0.0112652
\(382\) −21.4605 + 3.78407i −1.09802 + 0.193610i
\(383\) 6.32838 + 7.54187i 0.323365 + 0.385372i 0.903098 0.429435i \(-0.141287\pi\)
−0.579732 + 0.814807i \(0.696843\pi\)
\(384\) −1.57667 + 0.573861i −0.0804591 + 0.0292847i
\(385\) 0 0
\(386\) −17.5503 14.7264i −0.893286 0.749556i
\(387\) −1.47245 0.850118i −0.0748487 0.0432139i
\(388\) 2.34315 1.35282i 0.118956 0.0686791i
\(389\) 1.47850 8.38497i 0.0749627 0.425135i −0.924112 0.382122i \(-0.875193\pi\)
0.999075 0.0430125i \(-0.0136955\pi\)
\(390\) 0 0
\(391\) −1.36463 2.36360i −0.0690121 0.119532i
\(392\) −0.755158 0.435991i −0.0381412 0.0220208i
\(393\) 13.8069 16.4544i 0.696466 0.830016i
\(394\) 4.65669 + 1.69490i 0.234601 + 0.0853877i
\(395\) 0 0
\(396\) −0.410690 + 0.344610i −0.0206380 + 0.0173173i
\(397\) −24.1425 + 4.25698i −1.21168 + 0.213651i −0.742740 0.669580i \(-0.766474\pi\)
−0.468938 + 0.883231i \(0.655363\pi\)
\(398\) 24.6013i 1.23315i
\(399\) −7.48063 16.4870i −0.374500 0.825383i
\(400\) 0 0
\(401\) −0.863801 4.89886i −0.0431362 0.244637i 0.955614 0.294622i \(-0.0951938\pi\)
−0.998750 + 0.0499849i \(0.984083\pi\)
\(402\) −3.63062 4.32681i −0.181079 0.215802i
\(403\) −2.70033 7.41909i −0.134513 0.369571i
\(404\) 0.110751 + 0.0403101i 0.00551008 + 0.00200550i
\(405\) 0 0
\(406\) 8.02501 13.8997i 0.398274 0.689831i
\(407\) 3.63106 2.09639i 0.179985 0.103914i
\(408\) 2.05388 + 0.362154i 0.101682 + 0.0179293i
\(409\) −3.14232 + 17.8210i −0.155377 + 0.881189i 0.803062 + 0.595895i \(0.203203\pi\)
−0.958440 + 0.285295i \(0.907909\pi\)
\(410\) 0 0
\(411\) 13.1114 22.7096i 0.646739 1.12018i
\(412\) −1.11934 + 1.33398i −0.0551459 + 0.0657203i
\(413\) −1.71281 + 4.70591i −0.0842819 + 0.231563i
\(414\) 0.381282 0.138775i 0.0187390 0.00682043i
\(415\) 0 0
\(416\) −0.225165 1.27697i −0.0110396 0.0626087i
\(417\) 19.2621i 0.943268i
\(418\) −10.2831 7.36059i −0.502964 0.360018i
\(419\) 10.5816 0.516945 0.258472 0.966019i \(-0.416781\pi\)
0.258472 + 0.966019i \(0.416781\pi\)
\(420\) 0 0
\(421\) −18.5815 + 15.5917i −0.905605 + 0.759893i −0.971278 0.237949i \(-0.923525\pi\)
0.0656729 + 0.997841i \(0.479081\pi\)
\(422\) −1.25668 3.45269i −0.0611741 0.168074i
\(423\) −0.703312 + 1.93233i −0.0341962 + 0.0939533i
\(424\) 9.22060 + 7.73700i 0.447792 + 0.375742i
\(425\) 0 0
\(426\) 12.7492 + 22.0823i 0.617701 + 1.06989i
\(427\) 3.26504 + 0.575715i 0.158006 + 0.0278608i
\(428\) 16.4526 + 2.90103i 0.795264 + 0.140227i
\(429\) 3.15596 + 5.46628i 0.152371 + 0.263914i
\(430\) 0 0
\(431\) 27.3497 + 22.9491i 1.31739 + 1.10542i 0.986852 + 0.161626i \(0.0516738\pi\)
0.330536 + 0.943794i \(0.392771\pi\)
\(432\) −1.82763 + 5.02137i −0.0879318 + 0.241591i
\(433\) 11.3099 + 31.0738i 0.543521 + 1.49331i 0.842311 + 0.538992i \(0.181195\pi\)
−0.298790 + 0.954319i \(0.596583\pi\)
\(434\) 11.5465 9.68864i 0.554248 0.465069i
\(435\) 0 0
\(436\) 20.2478 0.969693
\(437\) 5.40796 + 7.89659i 0.258698 + 0.377745i
\(438\) 0.940634i 0.0449452i
\(439\) −1.02662 5.82227i −0.0489981 0.277882i 0.950458 0.310852i \(-0.100614\pi\)
−0.999456 + 0.0329703i \(0.989503\pi\)
\(440\) 0 0
\(441\) −0.151418 + 0.0551116i −0.00721038 + 0.00262436i
\(442\) −0.551251 + 1.51455i −0.0262203 + 0.0720398i
\(443\) 7.60590 9.06436i 0.361367 0.430661i −0.554474 0.832201i \(-0.687081\pi\)
0.915841 + 0.401540i \(0.131525\pi\)
\(444\) 1.21242 2.09997i 0.0575388 0.0996601i
\(445\) 0 0
\(446\) −1.29426 + 7.34013i −0.0612851 + 0.347565i
\(447\) −25.0360 4.41452i −1.18416 0.208800i
\(448\) 2.14383 1.23774i 0.101287 0.0584778i
\(449\) −3.79197 + 6.56789i −0.178954 + 0.309958i −0.941523 0.336950i \(-0.890605\pi\)
0.762568 + 0.646908i \(0.223938\pi\)
\(450\) 0 0
\(451\) −6.49848 2.36525i −0.306001 0.111375i
\(452\) 5.65867 + 15.5471i 0.266161 + 0.731273i
\(453\) 6.24195 + 7.43887i 0.293273 + 0.349509i
\(454\) −1.98248 11.2432i −0.0930424 0.527670i
\(455\) 0 0
\(456\) −7.27877 0.713026i −0.340860 0.0333905i
\(457\) 13.0616i 0.610995i 0.952193 + 0.305497i \(0.0988227\pi\)
−0.952193 + 0.305497i \(0.901177\pi\)
\(458\) 3.14481 0.554515i 0.146947 0.0259108i
\(459\) 5.08813 4.26945i 0.237493 0.199281i
\(460\) 0 0
\(461\) 29.3589 + 10.6858i 1.36738 + 0.497685i 0.918328 0.395821i \(-0.129540\pi\)
0.449051 + 0.893506i \(0.351762\pi\)
\(462\) −7.74567 + 9.23093i −0.360361 + 0.429462i
\(463\) −12.0928 6.98180i −0.562002 0.324472i 0.191947 0.981405i \(-0.438520\pi\)
−0.753949 + 0.656933i \(0.771853\pi\)
\(464\) −3.24179 5.61495i −0.150496 0.260668i
\(465\) 0 0
\(466\) 4.04585 22.9451i 0.187420 1.06291i
\(467\) −10.2252 + 5.90352i −0.473165 + 0.273182i −0.717564 0.696493i \(-0.754743\pi\)
0.244399 + 0.969675i \(0.421409\pi\)
\(468\) −0.207513 0.119808i −0.00959228 0.00553811i
\(469\) 6.38370 + 5.35656i 0.294772 + 0.247343i
\(470\) 0 0
\(471\) 17.3732 6.32334i 0.800517 0.291364i
\(472\) 1.30037 + 1.54971i 0.0598542 + 0.0713314i
\(473\) −26.2877 + 4.63523i −1.20871 + 0.213128i
\(474\) 10.8772 0.499607
\(475\) 0 0
\(476\) −3.07700 −0.141034
\(477\) 2.19049 0.386242i 0.100296 0.0176848i
\(478\) −5.28505 6.29848i −0.241733 0.288086i
\(479\) −30.1189 + 10.9624i −1.37617 + 0.500884i −0.921014 0.389529i \(-0.872638\pi\)
−0.455153 + 0.890413i \(0.650415\pi\)
\(480\) 0 0
\(481\) 1.43552 + 1.20455i 0.0654543 + 0.0549227i
\(482\) 18.0401 + 10.4155i 0.821705 + 0.474412i
\(483\) 7.89809 4.55996i 0.359375 0.207485i
\(484\) 0.448551 2.54386i 0.0203887 0.115630i
\(485\) 0 0
\(486\) 0.958815 + 1.66072i 0.0434927 + 0.0753316i
\(487\) 15.1334 + 8.73726i 0.685759 + 0.395923i 0.802021 0.597296i \(-0.203758\pi\)
−0.116263 + 0.993219i \(0.537091\pi\)
\(488\) 0.860884 1.02596i 0.0389704 0.0464431i
\(489\) −34.9693 12.7278i −1.58137 0.575570i
\(490\) 0 0
\(491\) −1.62811 + 1.36614i −0.0734754 + 0.0616531i −0.678786 0.734336i \(-0.737493\pi\)
0.605310 + 0.795990i \(0.293049\pi\)
\(492\) −3.93873 + 0.694505i −0.177572 + 0.0313107i
\(493\) 8.05903i 0.362961i
\(494\) 1.51946 5.44399i 0.0683637 0.244937i
\(495\) 0 0
\(496\) −1.05732 5.99634i −0.0474749 0.269244i
\(497\) −24.1816 28.8185i −1.08469 1.29269i
\(498\) 4.85182 + 13.3303i 0.217415 + 0.597344i
\(499\) 34.1891 + 12.4438i 1.53051 + 0.557062i 0.963747 0.266817i \(-0.0859719\pi\)
0.566767 + 0.823878i \(0.308194\pi\)
\(500\) 0 0
\(501\) 14.5875 25.2663i 0.651722 1.12882i
\(502\) −9.94767 + 5.74329i −0.443986 + 0.256336i
\(503\) −9.07677 1.60048i −0.404713 0.0713619i −0.0324139 0.999475i \(-0.510319\pi\)
−0.372299 + 0.928113i \(0.621431\pi\)
\(504\) 0.0794355 0.450501i 0.00353834 0.0200669i
\(505\) 0 0
\(506\) 3.18509 5.51674i 0.141595 0.245249i
\(507\) 12.2072 14.5480i 0.542142 0.646100i
\(508\) −0.0448227 + 0.123149i −0.00198869 + 0.00546387i
\(509\) 16.3916 5.96606i 0.726546 0.264441i 0.0478437 0.998855i \(-0.484765\pi\)
0.678702 + 0.734414i \(0.262543\pi\)
\(510\) 0 0
\(511\) −0.240988 1.36671i −0.0106607 0.0604597i
\(512\) 1.00000i 0.0441942i
\(513\) −16.6403 + 16.2983i −0.734686 + 0.719588i
\(514\) 1.85667 0.0818943
\(515\) 0 0
\(516\) −11.8259 + 9.92310i −0.520606 + 0.436840i
\(517\) 11.0418 + 30.3371i 0.485618 + 1.33422i
\(518\) −1.22360 + 3.36181i −0.0537618 + 0.147709i
\(519\) −2.76107 2.31681i −0.121197 0.101697i
\(520\) 0 0
\(521\) −10.5137 18.2102i −0.460611 0.797802i 0.538380 0.842702i \(-0.319037\pi\)
−0.998992 + 0.0448997i \(0.985703\pi\)
\(522\) −1.17992 0.208051i −0.0516435 0.00910615i
\(523\) 8.44161 + 1.48848i 0.369126 + 0.0650868i 0.355134 0.934815i \(-0.384435\pi\)
0.0139914 + 0.999902i \(0.495546\pi\)
\(524\) 6.40094 + 11.0867i 0.279626 + 0.484327i
\(525\) 0 0
\(526\) −7.85464 6.59082i −0.342478 0.287373i
\(527\) −2.58854 + 7.11195i −0.112758 + 0.309801i
\(528\) 1.66488 + 4.57422i 0.0724546 + 0.199067i
\(529\) 13.9258 11.6851i 0.605469 0.508049i
\(530\) 0 0
\(531\) 0.373837 0.0162231
\(532\) 10.7585 0.828800i 0.466440 0.0359330i
\(533\) 3.09086i 0.133880i
\(534\) −3.46716 19.6632i −0.150038 0.850911i
\(535\) 0 0
\(536\) 3.16333 1.15136i 0.136635 0.0497311i
\(537\) −5.95770 + 16.3687i −0.257094 + 0.706360i
\(538\) −17.0302 + 20.2958i −0.734224 + 0.875014i
\(539\) −1.26489 + 2.19086i −0.0544827 + 0.0943668i
\(540\) 0 0
\(541\) 3.75653 21.3044i 0.161506 0.915946i −0.791088 0.611702i \(-0.790485\pi\)
0.952594 0.304244i \(-0.0984038\pi\)
\(542\) −24.5333 4.32588i −1.05379 0.185812i
\(543\) 24.1872 13.9645i 1.03797 0.599275i
\(544\) −0.621495 + 1.07646i −0.0266464 + 0.0461529i
\(545\) 0 0
\(546\) −5.06094 1.84203i −0.216588 0.0788316i
\(547\) −10.7349 29.4938i −0.458989 1.26106i −0.926239 0.376937i \(-0.876977\pi\)
0.467249 0.884126i \(-0.345245\pi\)
\(548\) 10.0460 + 11.9723i 0.429143 + 0.511432i
\(549\) −0.0429766 0.243732i −0.00183420 0.0104022i
\(550\) 0 0
\(551\) −2.17073 28.1778i −0.0924761 1.20042i
\(552\) 3.68410i 0.156806i
\(553\) −15.8042 + 2.78672i −0.672065 + 0.118503i
\(554\) −11.0045 + 9.23384i −0.467535 + 0.392308i
\(555\) 0 0
\(556\) 10.7878 + 3.92644i 0.457505 + 0.166518i
\(557\) −3.66096 + 4.36296i −0.155120 + 0.184864i −0.838007 0.545659i \(-0.816279\pi\)
0.682888 + 0.730523i \(0.260724\pi\)
\(558\) −0.974429 0.562587i −0.0412509 0.0238162i
\(559\) −5.96520 10.3320i −0.252301 0.436998i
\(560\) 0 0
\(561\) 1.05068 5.95868i 0.0443596 0.251576i
\(562\) 23.2914 13.4473i 0.982488 0.567240i
\(563\) 6.97904 + 4.02935i 0.294132 + 0.169817i 0.639804 0.768538i \(-0.279016\pi\)
−0.345672 + 0.938355i \(0.612349\pi\)
\(564\) 14.3028 + 12.0015i 0.602257 + 0.505353i
\(565\) 0 0
\(566\) −18.9490 + 6.89686i −0.796484 + 0.289896i
\(567\) 13.3844 + 15.9509i 0.562093 + 0.669876i
\(568\) −14.9661 + 2.63893i −0.627964 + 0.110727i
\(569\) −22.1220 −0.927404 −0.463702 0.885991i \(-0.653479\pi\)
−0.463702 + 0.885991i \(0.653479\pi\)
\(570\) 0 0
\(571\) 45.8413 1.91840 0.959200 0.282729i \(-0.0912396\pi\)
0.959200 + 0.282729i \(0.0912396\pi\)
\(572\) −3.70474 + 0.653245i −0.154903 + 0.0273136i
\(573\) 23.5024 + 28.0091i 0.981826 + 1.17009i
\(574\) 5.54492 2.01819i 0.231441 0.0842375i
\(575\) 0 0
\(576\) −0.141559 0.118782i −0.00589830 0.00494926i
\(577\) −27.4535 15.8503i −1.14291 0.659857i −0.195757 0.980652i \(-0.562716\pi\)
−0.947148 + 0.320796i \(0.896050\pi\)
\(578\) −13.3844 + 7.72749i −0.556718 + 0.321421i
\(579\) −6.67507 + 37.8562i −0.277406 + 1.57325i
\(580\) 0 0
\(581\) −10.4647 18.1254i −0.434150 0.751970i
\(582\) −3.93148 2.26984i −0.162965 0.0940880i
\(583\) 22.4465 26.7507i 0.929639 1.10790i
\(584\) −0.526806 0.191742i −0.0217994 0.00793434i
\(585\) 0 0
\(586\) −15.3201 + 12.8551i −0.632869 + 0.531041i
\(587\) −12.6088 + 2.22328i −0.520422 + 0.0917644i −0.427688 0.903926i \(-0.640672\pi\)
−0.0927341 + 0.995691i \(0.529561\pi\)
\(588\) 1.46306i 0.0603356i
\(589\) 7.13500 25.5636i 0.293993 1.05333i
\(590\) 0 0
\(591\) −1.44383 8.18839i −0.0593914 0.336825i
\(592\) 0.928954 + 1.10708i 0.0381798 + 0.0455009i
\(593\) −12.6662 34.8002i −0.520140 1.42907i −0.870365 0.492407i \(-0.836117\pi\)
0.350225 0.936665i \(-0.386105\pi\)
\(594\) 14.5679 + 5.30230i 0.597730 + 0.217556i
\(595\) 0 0
\(596\) 7.57580 13.1217i 0.310317 0.537485i
\(597\) 35.7474 20.6388i 1.46304 0.844688i
\(598\) 2.80387 + 0.494397i 0.114659 + 0.0202174i
\(599\) −1.00225 + 5.68403i −0.0409507 + 0.232243i −0.998413 0.0563153i \(-0.982065\pi\)
0.957462 + 0.288558i \(0.0931759\pi\)
\(600\) 0 0
\(601\) −8.26350 + 14.3128i −0.337075 + 0.583831i −0.983881 0.178823i \(-0.942771\pi\)
0.646806 + 0.762655i \(0.276104\pi\)
\(602\) 14.6404 17.4477i 0.596697 0.711116i
\(603\) 0.212762 0.584560i 0.00866435 0.0238051i
\(604\) −5.43856 + 1.97947i −0.221292 + 0.0805436i
\(605\) 0 0
\(606\) −0.0343390 0.194746i −0.00139493 0.00791103i
\(607\) 2.34282i 0.0950920i −0.998869 0.0475460i \(-0.984860\pi\)
0.998869 0.0475460i \(-0.0151401\pi\)
\(608\) 1.88306 3.93117i 0.0763683 0.159430i
\(609\) −26.9296 −1.09124
\(610\) 0 0
\(611\) −11.0534 + 9.27490i −0.447173 + 0.375222i
\(612\) 0.0785604 + 0.215843i 0.00317562 + 0.00872493i
\(613\) 10.2703 28.2173i 0.414812 1.13969i −0.539789 0.841800i \(-0.681496\pi\)
0.954601 0.297886i \(-0.0962816\pi\)
\(614\) −14.8627 12.4713i −0.599808 0.503299i
\(615\) 0 0
\(616\) −3.59092 6.21966i −0.144682 0.250597i
\(617\) −15.9792 2.81756i −0.643298 0.113431i −0.157524 0.987515i \(-0.550351\pi\)
−0.485774 + 0.874084i \(0.661462\pi\)
\(618\) 2.87740 + 0.507364i 0.115746 + 0.0204092i
\(619\) 23.8503 + 41.3099i 0.958624 + 1.66039i 0.725848 + 0.687855i \(0.241448\pi\)
0.232776 + 0.972530i \(0.425219\pi\)
\(620\) 0 0
\(621\) −8.98807 7.54188i −0.360679 0.302645i
\(622\) −1.84656 + 5.07338i −0.0740403 + 0.203424i
\(623\) 10.0753 + 27.6818i 0.403660 + 1.10905i
\(624\) −1.66663 + 1.39847i −0.0667186 + 0.0559835i
\(625\) 0 0
\(626\) 16.1834 0.646818
\(627\) −2.06862 + 21.1171i −0.0826128 + 0.843336i
\(628\) 11.0189i 0.439704i
\(629\) −0.311935 1.76907i −0.0124377 0.0705376i
\(630\) 0 0
\(631\) 11.5071 4.18824i 0.458090 0.166731i −0.102660 0.994717i \(-0.532735\pi\)
0.560750 + 0.827985i \(0.310513\pi\)
\(632\) −2.21725 + 6.09184i −0.0881973 + 0.242320i
\(633\) −3.96273 + 4.72260i −0.157504 + 0.187706i
\(634\) 1.22547 2.12258i 0.0486696 0.0842983i
\(635\) 0 0
\(636\) 3.50696 19.8889i 0.139060 0.788648i
\(637\) −1.11350 0.196339i −0.0441183 0.00777925i
\(638\) −16.2900 + 9.40506i −0.644929 + 0.372350i
\(639\) −1.40415 + 2.43205i −0.0555471 + 0.0962104i
\(640\) 0 0
\(641\) 27.9385 + 10.1688i 1.10350 + 0.401643i 0.828607 0.559831i \(-0.189134\pi\)
0.274897 + 0.961474i \(0.411356\pi\)
\(642\) −9.58714 26.3404i −0.378374 1.03957i
\(643\) −13.5109 16.1016i −0.532817 0.634987i 0.430744 0.902474i \(-0.358251\pi\)
−0.963561 + 0.267487i \(0.913807\pi\)
\(644\) 0.943857 + 5.35288i 0.0371932 + 0.210933i
\(645\) 0 0
\(646\) −4.47024 + 3.06143i −0.175879 + 0.120451i
\(647\) 10.8225i 0.425476i −0.977109 0.212738i \(-0.931762\pi\)
0.977109 0.212738i \(-0.0682381\pi\)
\(648\) 8.28368 1.46064i 0.325414 0.0573792i
\(649\) 4.49602 3.77261i 0.176484 0.148088i
\(650\) 0 0
\(651\) −23.7649 8.64972i −0.931420 0.339009i
\(652\) 14.2565 16.9903i 0.558328 0.665390i
\(653\) −37.1937 21.4738i −1.45550 0.840334i −0.456716 0.889613i \(-0.650974\pi\)
−0.998785 + 0.0492789i \(0.984308\pi\)
\(654\) −16.9865 29.4214i −0.664223 1.15047i
\(655\) 0 0
\(656\) 0.413923 2.34748i 0.0161610 0.0916536i
\(657\) −0.0897182 + 0.0517988i −0.00350024 + 0.00202086i
\(658\) −23.8563 13.7734i −0.930015 0.536944i
\(659\) 4.59278 + 3.85380i 0.178909 + 0.150123i 0.727845 0.685742i \(-0.240522\pi\)
−0.548935 + 0.835865i \(0.684967\pi\)
\(660\) 0 0
\(661\) −16.9338 + 6.16342i −0.658650 + 0.239729i −0.649654 0.760230i \(-0.725086\pi\)
−0.00899680 + 0.999960i \(0.502864\pi\)
\(662\) −1.95166 2.32590i −0.0758535 0.0903986i
\(663\) 2.66320 0.469594i 0.103430 0.0182375i
\(664\) −8.45470 −0.328106
\(665\) 0 0
\(666\) 0.267061 0.0103484
\(667\) 14.0198 2.47207i 0.542850 0.0957191i
\(668\) 11.1770 + 13.3202i 0.432449 + 0.515373i
\(669\) 11.7515 4.27719i 0.454339 0.165366i
\(670\) 0 0
\(671\) −2.97651 2.49759i −0.114907 0.0964183i
\(672\) −3.59705 2.07675i −0.138759 0.0801126i
\(673\) 23.6912 13.6781i 0.913231 0.527254i 0.0317614 0.999495i \(-0.489888\pi\)
0.881469 + 0.472242i \(0.156555\pi\)
\(674\) −1.05284 + 5.97096i −0.0405539 + 0.229993i
\(675\) 0 0
\(676\) 5.65932 + 9.80223i 0.217666 + 0.377009i
\(677\) −26.1566 15.1015i −1.00528 0.580398i −0.0954734 0.995432i \(-0.530436\pi\)
−0.909806 + 0.415034i \(0.863770\pi\)
\(678\) 17.8437 21.2653i 0.685284 0.816689i
\(679\) 6.29385 + 2.29077i 0.241536 + 0.0879118i
\(680\) 0 0
\(681\) −14.6740 + 12.3129i −0.562308 + 0.471833i
\(682\) −17.3965 + 3.06748i −0.666148 + 0.117460i
\(683\) 42.2829i 1.61791i −0.587871 0.808955i \(-0.700034\pi\)
0.587871 0.808955i \(-0.299966\pi\)
\(684\) −0.332819 0.733518i −0.0127256 0.0280468i
\(685\) 0 0
\(686\) −3.38388 19.1909i −0.129197 0.732712i
\(687\) −3.44402 4.10442i −0.131398 0.156594i
\(688\) −3.14685 8.64591i −0.119973 0.329622i
\(689\) 14.6663 + 5.33810i 0.558742 + 0.203365i
\(690\) 0 0
\(691\) −7.96853 + 13.8019i −0.303137 + 0.525049i −0.976845 0.213949i \(-0.931367\pi\)
0.673708 + 0.738998i \(0.264701\pi\)
\(692\) 1.86037 1.07408i 0.0707205 0.0408305i
\(693\) −1.30699 0.230457i −0.0496484 0.00875435i
\(694\) 0.499559 2.83314i 0.0189630 0.107545i
\(695\) 0 0
\(696\) −5.43927 + 9.42109i −0.206175 + 0.357106i
\(697\) −1.90452 + 2.26972i −0.0721387 + 0.0859716i
\(698\) 11.2168 30.8180i 0.424564 1.16648i
\(699\) −36.7350 + 13.3704i −1.38945 + 0.505717i
\(700\) 0 0
\(701\) −1.03691 5.88059i −0.0391634 0.222107i 0.958944 0.283594i \(-0.0915268\pi\)
−0.998108 + 0.0614872i \(0.980416\pi\)
\(702\) 6.92893i 0.261516i
\(703\) 1.56716 + 6.10141i 0.0591067 + 0.230119i
\(704\) −2.90119 −0.109343
\(705\) 0 0
\(706\) −16.2408 + 13.6277i −0.611231 + 0.512884i
\(707\) 0.0997871 + 0.274163i 0.00375288 + 0.0103110i
\(708\) 1.16093 3.18962i 0.0436303 0.119873i
\(709\) −35.7131 29.9669i −1.34123 1.12543i −0.981307 0.192450i \(-0.938357\pi\)
−0.359928 0.932980i \(-0.617199\pi\)
\(710\) 0 0
\(711\) 0.598986 + 1.03747i 0.0224637 + 0.0389083i
\(712\) 11.7192 + 2.06642i 0.439197 + 0.0774423i
\(713\) 13.1663 + 2.32157i 0.493080 + 0.0869434i
\(714\) 2.58139 + 4.47109i 0.0966059 + 0.167326i
\(715\) 0 0
\(716\) −7.95291 6.67328i −0.297214 0.249392i
\(717\) −4.71833 + 12.9635i −0.176209 + 0.484131i
\(718\) −6.35803 17.4685i −0.237280 0.651920i
\(719\) 31.8698 26.7420i 1.18854 0.997307i 0.188661 0.982042i \(-0.439585\pi\)
0.999883 0.0152650i \(-0.00485920\pi\)
\(720\) 0 0
\(721\) −4.31076 −0.160541
\(722\) 14.8053 11.9081i 0.550995 0.443175i
\(723\) 34.9514i 1.29986i
\(724\) 2.89049 + 16.3928i 0.107424 + 0.609232i
\(725\) 0 0
\(726\) −4.07270 + 1.48234i −0.151152 + 0.0550149i
\(727\) 7.10304 19.5154i 0.263437 0.723787i −0.735493 0.677533i \(-0.763049\pi\)
0.998930 0.0462546i \(-0.0147286\pi\)
\(728\) 2.06328 2.45892i 0.0764701 0.0911335i
\(729\) 14.2260 24.6401i 0.526888 0.912596i
\(730\) 0 0
\(731\) −1.98592 + 11.2627i −0.0734521 + 0.416567i
\(732\) −2.21301 0.390214i −0.0817953 0.0144227i
\(733\) 25.5184 14.7331i 0.942545 0.544179i 0.0517877 0.998658i \(-0.483508\pi\)
0.890757 + 0.454480i \(0.150175\pi\)
\(734\) 10.8612 18.8121i 0.400893 0.694367i
\(735\) 0 0
\(736\) 2.06330 + 0.750979i 0.0760542 + 0.0276814i
\(737\) −3.34031 9.17742i −0.123042 0.338054i
\(738\) −0.283140 0.337433i −0.0104225 0.0124211i
\(739\) −4.63253 26.2724i −0.170410 0.966446i −0.943309 0.331916i \(-0.892305\pi\)
0.772898 0.634530i \(-0.218806\pi\)
\(740\) 0 0
\(741\) −9.18520 + 2.35924i −0.337427 + 0.0866690i
\(742\) 29.7965i 1.09386i
\(743\) −44.5252 + 7.85099i −1.63347 + 0.288025i −0.913761 0.406252i \(-0.866836\pi\)
−0.719708 + 0.694276i \(0.755725\pi\)
\(744\) −7.82608 + 6.56686i −0.286918 + 0.240753i
\(745\) 0 0
\(746\) 21.0636 + 7.66651i 0.771192 + 0.280691i
\(747\) −1.00427 + 1.19684i −0.0367443 + 0.0437901i
\(748\) 3.12302 + 1.80307i 0.114189 + 0.0659269i
\(749\) 20.6782 + 35.8156i 0.755564 + 1.30867i
\(750\) 0 0
\(751\) −0.599478 + 3.39981i −0.0218753 + 0.124061i −0.993790 0.111273i \(-0.964507\pi\)
0.971915 + 0.235334i \(0.0756183\pi\)
\(752\) −9.63702 + 5.56394i −0.351426 + 0.202896i
\(753\) 16.6908 + 9.63642i 0.608246 + 0.351171i
\(754\) −6.44020 5.40397i −0.234538 0.196801i
\(755\) 0 0
\(756\) −12.4303 + 4.52427i −0.452086 + 0.164546i
\(757\) 25.9373 + 30.9109i 0.942708 + 1.12348i 0.992194 + 0.124701i \(0.0397972\pi\)
−0.0494862 + 0.998775i \(0.515758\pi\)
\(758\) 8.32410 1.46776i 0.302345 0.0533116i
\(759\) −10.6883 −0.387960
\(760\) 0 0
\(761\) −12.4450 −0.451132 −0.225566 0.974228i \(-0.572423\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(762\) 0.216547 0.0381832i 0.00784469 0.00138323i
\(763\) 32.2185 + 38.3965i 1.16639 + 1.39005i
\(764\) −20.4774 + 7.45317i −0.740847 + 0.269646i
\(765\) 0 0
\(766\) 7.54187 + 6.32838i 0.272499 + 0.228654i
\(767\) 2.27174 + 1.31159i 0.0820277 + 0.0473587i
\(768\) −1.45307 + 0.838929i −0.0524331 + 0.0302722i
\(769\) −5.55178 + 31.4857i −0.200202 + 1.13540i 0.704610 + 0.709594i \(0.251122\pi\)
−0.904813 + 0.425810i \(0.859989\pi\)
\(770\) 0 0
\(771\) −1.55762 2.69787i −0.0560962 0.0971615i
\(772\) −19.8409 11.4551i −0.714089 0.412279i
\(773\) −22.6745 + 27.0224i −0.815545 + 0.971929i −0.999940 0.0109230i \(-0.996523\pi\)
0.184395 + 0.982852i \(0.440967\pi\)
\(774\) −1.59770 0.581515i −0.0574281 0.0209021i
\(775\) 0 0
\(776\) 2.07264 1.73915i 0.0744035 0.0624320i
\(777\) 5.91144 1.04235i 0.212072 0.0373940i
\(778\) 8.51432i 0.305253i
\(779\) 6.04765 8.44888i 0.216679 0.302712i
\(780\) 0 0
\(781\) 7.65603 + 43.4195i 0.273954 + 1.55367i
\(782\) −1.75433 2.09073i −0.0627347 0.0747643i
\(783\) 11.8496 + 32.5565i 0.423470 + 1.16347i
\(784\) −0.819394 0.298235i −0.0292641 0.0106513i
\(785\) 0 0
\(786\) 10.7399 18.6020i 0.383078 0.663511i
\(787\) −34.2030 + 19.7471i −1.21921 + 0.703909i −0.964748 0.263175i \(-0.915230\pi\)
−0.254458 + 0.967084i \(0.581897\pi\)
\(788\) 4.88026 + 0.860522i 0.173852 + 0.0306548i
\(789\) −2.98743 + 16.9425i −0.106355 + 0.603171i
\(790\) 0 0
\(791\) −20.4782 + 35.4694i −0.728123 + 1.26115i
\(792\) −0.344610 + 0.410690i −0.0122452 + 0.0145932i
\(793\) 0.593962 1.63190i 0.0210922 0.0579504i
\(794\) −23.0365 + 8.38460i −0.817535 + 0.297558i
\(795\) 0 0
\(796\) 4.27197 + 24.2276i 0.151416 + 0.858724i
\(797\) 18.0151i 0.638128i −0.947733 0.319064i \(-0.896631\pi\)
0.947733 0.319064i \(-0.103369\pi\)
\(798\) −10.2299 14.9375i −0.362135 0.528783i
\(799\) 13.8318 0.489335
\(800\) 0 0
\(801\) 1.68456 1.41351i 0.0595210 0.0499440i
\(802\) −1.70136 4.67444i −0.0600770 0.165060i
\(803\) −0.556279 + 1.52837i −0.0196307 + 0.0539348i
\(804\) −4.32681 3.63062i −0.152595 0.128042i
\(805\) 0 0
\(806\) −3.94762 6.83747i −0.139049 0.240840i
\(807\) 43.7783 + 7.71929i 1.54107 + 0.271732i
\(808\) 0.116068 + 0.0204660i 0.00408327 + 0.000719991i
\(809\) 14.5518 + 25.2045i 0.511615 + 0.886144i 0.999909 + 0.0134647i \(0.00428607\pi\)
−0.488294 + 0.872679i \(0.662381\pi\)
\(810\) 0 0
\(811\) 12.3496 + 10.3626i 0.433654 + 0.363879i 0.833328 0.552779i \(-0.186432\pi\)
−0.399675 + 0.916657i \(0.630877\pi\)
\(812\) 5.48943 15.0821i 0.192641 0.529277i
\(813\) 14.2959 + 39.2776i 0.501378 + 1.37753i
\(814\) 3.21186 2.69507i 0.112576 0.0944622i
\(815\) 0 0
\(816\) 2.08556 0.0730092
\(817\) 3.90998 39.9142i 0.136793 1.39642i
\(818\) 18.0959i 0.632707i
\(819\) −0.103002 0.584152i −0.00359917 0.0204119i
\(820\) 0 0
\(821\) −27.8660 + 10.1424i −0.972530 + 0.353972i −0.778932 0.627109i \(-0.784238\pi\)
−0.193598 + 0.981081i \(0.562016\pi\)
\(822\) 8.96874 24.6414i 0.312821 0.859468i
\(823\) −15.2315 + 18.1522i −0.530937 + 0.632746i −0.963130 0.269035i \(-0.913295\pi\)
0.432194 + 0.901781i \(0.357740\pi\)
\(824\) −0.870691 + 1.50808i −0.0303320 + 0.0525365i
\(825\) 0 0
\(826\) −0.869617 + 4.93184i −0.0302579 + 0.171601i
\(827\) 37.4692 + 6.60682i 1.30293 + 0.229742i 0.781689 0.623668i \(-0.214358\pi\)
0.521241 + 0.853410i \(0.325469\pi\)
\(828\) 0.351391 0.202876i 0.0122117 0.00705042i
\(829\) 11.9638 20.7219i 0.415520 0.719701i −0.579963 0.814643i \(-0.696933\pi\)
0.995483 + 0.0949413i \(0.0302664\pi\)
\(830\) 0 0
\(831\) 22.6494 + 8.24369i 0.785698 + 0.285971i
\(832\) −0.443488 1.21847i −0.0153752 0.0422429i
\(833\) 0.696694 + 0.830288i 0.0241390 + 0.0287678i
\(834\) −3.34482 18.9694i −0.115822 0.656858i
\(835\) 0 0
\(836\) −11.4051 5.46312i −0.394452 0.188946i
\(837\) 32.5365i 1.12463i
\(838\) 10.4208 1.83747i 0.359982 0.0634745i
\(839\) −13.6980 + 11.4940i −0.472908 + 0.396817i −0.847854 0.530230i \(-0.822106\pi\)
0.374946 + 0.927047i \(0.377661\pi\)
\(840\) 0 0
\(841\) −12.2507 4.45888i −0.422437 0.153755i
\(842\) −15.5917 + 18.5815i −0.537325 + 0.640359i
\(843\) −39.0796 22.5626i −1.34597 0.777099i
\(844\) −1.83714 3.18202i −0.0632369 0.109530i
\(845\) 0 0
\(846\) −0.357081 + 2.02511i −0.0122767 + 0.0696246i
\(847\) 5.53773 3.19721i 0.190279 0.109858i
\(848\) 10.4240 + 6.01832i 0.357963 + 0.206670i
\(849\) 25.9184 + 21.7481i 0.889518 + 0.746394i
\(850\) 0 0
\(851\) −2.98187 + 1.08531i −0.102217 + 0.0372040i
\(852\) 16.3901 + 19.5329i 0.561514 + 0.669186i
\(853\) 35.3934 6.24081i 1.21185 0.213681i 0.469033 0.883181i \(-0.344602\pi\)
0.742813 + 0.669499i \(0.233491\pi\)
\(854\) 3.31541 0.113451
\(855\) 0 0
\(856\) 16.7064 0.571012
\(857\) −5.25121 + 0.925930i −0.179378 + 0.0316292i −0.262615 0.964901i \(-0.584585\pi\)
0.0832376 + 0.996530i \(0.473474\pi\)
\(858\) 4.05722 + 4.83521i 0.138511 + 0.165071i
\(859\) −8.81020 + 3.20665i −0.300600 + 0.109410i −0.487917 0.872890i \(-0.662243\pi\)
0.187317 + 0.982300i \(0.440021\pi\)
\(860\) 0 0
\(861\) −7.58436 6.36403i −0.258474 0.216886i
\(862\) 30.9192 + 17.8512i 1.05311 + 0.608015i
\(863\) 4.57608 2.64200i 0.155772 0.0899348i −0.420088 0.907483i \(-0.638001\pi\)
0.575860 + 0.817549i \(0.304667\pi\)
\(864\) −0.927912 + 5.26245i −0.0315682 + 0.179032i
\(865\) 0 0
\(866\) 16.5340 + 28.6378i 0.561849 + 0.973151i
\(867\) 22.4571 + 12.9656i 0.762684 + 0.440336i
\(868\) 9.68864 11.5465i 0.328854 0.391913i
\(869\) 17.6736 + 6.43265i 0.599535 + 0.218213i
\(870\) 0 0
\(871\) 3.34382 2.80580i 0.113301 0.0950707i
\(872\) 19.9402 3.51599i 0.675260 0.119066i
\(873\) 0.499982i 0.0169218i
\(874\) 6.69703 + 6.83754i 0.226530 + 0.231283i
\(875\) 0 0
\(876\) 0.163339 + 0.926343i 0.00551872 + 0.0312982i
\(877\) 32.4457 + 38.6673i 1.09561 + 1.30570i 0.948569 + 0.316572i \(0.102532\pi\)
0.147045 + 0.989130i \(0.453024\pi\)
\(878\) −2.02205 5.55555i −0.0682410 0.187491i
\(879\) 31.5319 + 11.4767i 1.06354 + 0.387098i
\(880\) 0 0
\(881\) −10.2170 + 17.6964i −0.344221 + 0.596208i −0.985212 0.171340i \(-0.945190\pi\)
0.640991 + 0.767549i \(0.278524\pi\)
\(882\) −0.139548 + 0.0805678i −0.00469881 + 0.00271286i
\(883\) −0.124596 0.0219697i −0.00419300 0.000739339i 0.171551 0.985175i \(-0.445122\pi\)
−0.175744 + 0.984436i \(0.556233\pi\)
\(884\) −0.279877 + 1.58726i −0.00941329 + 0.0533854i
\(885\) 0 0
\(886\) 5.91634 10.2474i 0.198763 0.344268i
\(887\) 16.6336 19.8231i 0.558500 0.665594i −0.410728 0.911758i \(-0.634726\pi\)
0.969228 + 0.246163i \(0.0791700\pi\)
\(888\) 0.829342 2.27860i 0.0278309 0.0764648i
\(889\) −0.304854 + 0.110958i −0.0102245 + 0.00372141i
\(890\) 0 0
\(891\) −4.23758 24.0325i −0.141964 0.805120i
\(892\) 7.45336i 0.249557i
\(893\) −48.3620 + 3.72565i −1.61837 + 0.124674i
\(894\) −25.4222 −0.850247
\(895\) 0 0
\(896\) 1.89633 1.59121i 0.0633520 0.0531586i
\(897\) −1.63385 4.48897i −0.0545527 0.149882i
\(898\) −2.59386 + 7.12658i −0.0865583 + 0.237817i
\(899\) −30.2416 25.3757i −1.00861 0.846327i
\(900\) 0 0
\(901\) −7.48071 12.9570i −0.249218 0.431659i
\(902\) −6.81047 1.20087i −0.226764 0.0399846i
\(903\) −37.6350 6.63606i −1.25241 0.220834i
\(904\) 8.27242 + 14.3283i 0.275137 + 0.476551i
\(905\) 0 0
\(906\) 7.43887 + 6.24195i 0.247140 + 0.207375i
\(907\) −18.4176 + 50.6020i −0.611547 + 1.68021i 0.115229 + 0.993339i \(0.463240\pi\)
−0.726777 + 0.686874i \(0.758982\pi\)
\(908\) −3.90473 10.7281i −0.129583 0.356026i
\(909\) 0.0166840 0.0139996i 0.000553374 0.000464336i
\(910\) 0 0
\(911\) 2.63989 0.0874634 0.0437317 0.999043i \(-0.486075\pi\)
0.0437317 + 0.999043i \(0.486075\pi\)
\(912\) −7.29201 + 0.561752i −0.241463 + 0.0186015i
\(913\) 24.5287i 0.811781i
\(914\) 2.26812 + 12.8631i 0.0750227 + 0.425475i
\(915\) 0 0
\(916\) 3.00074 1.09218i 0.0991474 0.0360867i
\(917\) −10.8389 + 29.7796i −0.357932 + 0.983410i
\(918\) 4.26945 5.08813i 0.140913 0.167933i
\(919\) −15.6083 + 27.0343i −0.514869 + 0.891779i 0.484982 + 0.874524i \(0.338826\pi\)
−0.999851 + 0.0172553i \(0.994507\pi\)
\(920\) 0 0
\(921\) −5.65286 + 32.0589i −0.186268 + 1.05638i
\(922\) 30.7684 + 5.42530i 1.01330 + 0.178673i
\(923\) −17.0655 + 9.85275i −0.561717 + 0.324307i
\(924\) −6.02506 + 10.4357i −0.198210 + 0.343310i
\(925\) 0 0
\(926\) −13.1215 4.77583i −0.431199 0.156944i
\(927\) 0.110060 + 0.302388i 0.00361485 + 0.00993172i
\(928\) −4.16757 4.96672i −0.136807 0.163040i
\(929\) −0.849031 4.81509i −0.0278558 0.157978i 0.967707 0.252078i \(-0.0811139\pi\)
−0.995563 + 0.0940997i \(0.970003\pi\)
\(930\) 0 0
\(931\) −2.65958 2.71538i −0.0871642 0.0889931i
\(932\) 23.2991i 0.763187i
\(933\) 8.92110 1.57303i 0.292064 0.0514987i
\(934\) −9.04471 + 7.58941i −0.295952 + 0.248333i
\(935\) 0 0
\(936\) −0.225165 0.0819532i −0.00735974 0.00267872i
\(937\) −5.11059 + 6.09056i −0.166956 + 0.198970i −0.843035 0.537859i \(-0.819233\pi\)
0.676079 + 0.736829i \(0.263678\pi\)
\(938\) 7.21688 + 4.16667i 0.235639 + 0.136046i
\(939\) −13.5767 23.5155i −0.443059 0.767401i
\(940\) 0 0
\(941\) −4.40739 + 24.9956i −0.143677 + 0.814832i 0.824743 + 0.565508i \(0.191320\pi\)
−0.968420 + 0.249325i \(0.919791\pi\)
\(942\) 16.0113 9.24411i 0.521675 0.301189i
\(943\) 4.53269 + 2.61695i 0.147605 + 0.0852197i
\(944\) 1.54971 + 1.30037i 0.0504389 + 0.0423233i
\(945\) 0 0
\(946\) −25.0834 + 9.12962i −0.815532 + 0.296829i
\(947\) −19.0425 22.6940i −0.618799 0.737456i 0.362064 0.932153i \(-0.382072\pi\)
−0.980863 + 0.194697i \(0.937628\pi\)
\(948\) 10.7120 1.88881i 0.347908 0.0613456i
\(949\) −0.726934 −0.0235973
\(950\) 0 0
\(951\) −4.11233 −0.133351
\(952\) −3.03025 + 0.534316i −0.0982111 + 0.0173173i
\(953\) −9.63837 11.4866i −0.312217 0.372086i 0.587001 0.809586i \(-0.300308\pi\)
−0.899218 + 0.437500i \(0.855864\pi\)
\(954\) 2.09014 0.760748i 0.0676708 0.0246301i
\(955\) 0 0
\(956\) −6.29848 5.28505i −0.203707 0.170931i
\(957\) 27.3324 + 15.7803i 0.883530 + 0.510106i
\(958\) −27.7577 + 16.0259i −0.896811 + 0.517774i
\(959\) −6.71823 + 38.1010i −0.216943 + 1.23034i
\(960\) 0 0
\(961\) −3.03703 5.26029i −0.0979688 0.169687i
\(962\) 1.62288 + 0.936972i 0.0523239 + 0.0302092i
\(963\) 1.98442 2.36494i 0.0639471 0.0762092i
\(964\) 19.5747 + 7.12460i 0.630458 + 0.229468i
\(965\) 0 0
\(966\) 6.98627 5.86218i 0.224779 0.188612i
\(967\) −13.6825 + 2.41259i −0.439998 + 0.0775835i −0.389259 0.921128i \(-0.627269\pi\)
−0.0507392 + 0.998712i \(0.516158\pi\)
\(968\) 2.58310i 0.0830240i
\(969\) 8.19869 + 3.92724i 0.263380 + 0.126161i
\(970\) 0 0
\(971\) −2.47187 14.0186i −0.0793260 0.449880i −0.998437 0.0558821i \(-0.982203\pi\)
0.919111 0.393998i \(-0.128908\pi\)
\(972\) 1.23263 + 1.46899i 0.0395366 + 0.0471179i
\(973\) 9.71985 + 26.7051i 0.311604 + 0.856125i
\(974\) 16.4207 + 5.97664i 0.526152 + 0.191504i
\(975\) 0 0
\(976\) 0.669649 1.15987i 0.0214349 0.0371264i
\(977\) 7.14552 4.12547i 0.228606 0.131985i −0.381323 0.924442i \(-0.624531\pi\)
0.609929 + 0.792456i \(0.291198\pi\)
\(978\) −36.6482 6.46207i −1.17188 0.206634i
\(979\) 5.99507 33.9997i 0.191603 1.08664i
\(980\) 0 0
\(981\) 1.87082 3.24035i 0.0597307 0.103457i
\(982\) −1.36614 + 1.62811i −0.0435954 + 0.0519549i
\(983\) −4.49274 + 12.3437i −0.143296 + 0.393703i −0.990491 0.137580i \(-0.956068\pi\)
0.847194 + 0.531283i \(0.178290\pi\)
\(984\) −3.75829 + 1.36791i −0.119810 + 0.0436073i
\(985\) 0 0
\(986\) 1.39944 + 7.93660i 0.0445671 + 0.252753i
\(987\) 46.2197i 1.47119i
\(988\) 0.551036 5.62513i 0.0175308 0.178959i
\(989\) 20.2023 0.642396
\(990\) 0 0
\(991\) −19.4973 + 16.3602i −0.619352 + 0.519698i −0.897600 0.440811i \(-0.854691\pi\)
0.278248 + 0.960509i \(0.410246\pi\)
\(992\) −2.08251 5.72164i −0.0661197 0.181662i
\(993\) −1.74238 + 4.78716i −0.0552929 + 0.151916i
\(994\) −28.8185 24.1816i −0.914068 0.766994i
\(995\) 0 0
\(996\) 7.09289 + 12.2852i 0.224747 + 0.389273i
\(997\) 22.1625 + 3.90784i 0.701892 + 0.123763i 0.513194 0.858273i \(-0.328462\pi\)
0.188698 + 0.982035i \(0.439573\pi\)
\(998\) 35.8305 + 6.31789i 1.13420 + 0.199989i
\(999\) −3.86130 6.68796i −0.122166 0.211598i
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.u.e.199.3 24
5.2 odd 4 950.2.l.h.351.1 12
5.3 odd 4 190.2.k.b.161.2 yes 12
5.4 even 2 inner 950.2.u.e.199.2 24
19.17 even 9 inner 950.2.u.e.549.2 24
95.13 even 36 3610.2.a.be.1.2 6
95.17 odd 36 950.2.l.h.701.1 12
95.63 odd 36 3610.2.a.bc.1.5 6
95.74 even 18 inner 950.2.u.e.549.3 24
95.93 odd 36 190.2.k.b.131.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.b.131.2 12 95.93 odd 36
190.2.k.b.161.2 yes 12 5.3 odd 4
950.2.l.h.351.1 12 5.2 odd 4
950.2.l.h.701.1 12 95.17 odd 36
950.2.u.e.199.2 24 5.4 even 2 inner
950.2.u.e.199.3 24 1.1 even 1 trivial
950.2.u.e.549.2 24 19.17 even 9 inner
950.2.u.e.549.3 24 95.74 even 18 inner
3610.2.a.bc.1.5 6 95.63 odd 36
3610.2.a.be.1.2 6 95.13 even 36