Properties

Label 855.2.k.i.406.2
Level $855$
Weight $2$
Character 855.406
Analytic conductor $6.827$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 285)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 406.2
Root \(0.823305 - 1.42601i\) of defining polynomial
Character \(\chi\) \(=\) 855.406
Dual form 855.2.k.i.676.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.823305 - 1.42601i) q^{2} +(-0.355663 + 0.616027i) q^{4} +(0.500000 + 0.866025i) q^{5} +4.47988 q^{7} -2.12194 q^{8} +(0.823305 - 1.42601i) q^{10} +3.44134 q^{11} +(-1.23994 + 2.14764i) q^{13} +(-3.68831 - 6.38834i) q^{14} +(2.45833 + 4.25796i) q^{16} +(3.81400 + 6.60604i) q^{17} +(-3.67522 + 2.34366i) q^{19} -0.711327 q^{20} +(-2.83327 - 4.90737i) q^{22} +(1.93528 - 3.35201i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.08340 q^{26} +(-1.59333 + 2.75973i) q^{28} +(-4.36728 + 7.56435i) q^{29} -0.422654 q^{31} +(1.92598 - 3.33589i) q^{32} +(6.28017 - 10.8776i) q^{34} +(2.23994 + 3.87969i) q^{35} +3.90253 q^{37} +(6.36790 + 3.31135i) q^{38} +(-1.06097 - 1.83766i) q^{40} +(2.64661 + 4.58406i) q^{41} +(-1.23994 - 2.14764i) q^{43} +(-1.22396 + 2.11996i) q^{44} -6.37332 q^{46} +(-0.338665 + 0.586585i) q^{47} +13.0693 q^{49} +1.64661 q^{50} +(-0.882003 - 1.52767i) q^{52} +(5.74928 - 9.95805i) q^{53} +(1.72067 + 2.98028i) q^{55} -9.50605 q^{56} +14.3824 q^{58} +(-4.26526 - 7.38765i) q^{59} +(-4.10117 + 7.10343i) q^{61} +(0.347973 + 0.602707i) q^{62} +3.49067 q^{64} -2.47988 q^{65} +(4.81729 - 8.34379i) q^{67} -5.42600 q^{68} +(3.68831 - 6.38834i) q^{70} +(-1.92594 - 3.33583i) q^{71} +(-8.39260 - 14.5364i) q^{73} +(-3.21298 - 5.56504i) q^{74} +(-0.136613 - 3.09759i) q^{76} +15.4168 q^{77} +(-6.06262 - 10.5008i) q^{79} +(-2.45833 + 4.25796i) q^{80} +(4.35794 - 7.54817i) q^{82} +2.03855 q^{83} +(-3.81400 + 6.60604i) q^{85} +(-2.04170 + 3.53633i) q^{86} -7.30232 q^{88} +(-1.57255 + 2.72374i) q^{89} +(-5.55478 + 9.62117i) q^{91} +(1.37662 + 2.38437i) q^{92} +1.11530 q^{94} +(-3.86728 - 2.01101i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(-10.7600 - 18.6370i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.823305 1.42601i −0.582165 1.00834i −0.995222 0.0976341i \(-0.968873\pi\)
0.413058 0.910705i \(-0.364461\pi\)
\(3\) 0 0
\(4\) −0.355663 + 0.616027i −0.177832 + 0.308014i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 4.47988 1.69324 0.846618 0.532201i \(-0.178635\pi\)
0.846618 + 0.532201i \(0.178635\pi\)
\(8\) −2.12194 −0.750220
\(9\) 0 0
\(10\) 0.823305 1.42601i 0.260352 0.450943i
\(11\) 3.44134 1.03760 0.518801 0.854895i \(-0.326379\pi\)
0.518801 + 0.854895i \(0.326379\pi\)
\(12\) 0 0
\(13\) −1.23994 + 2.14764i −0.343898 + 0.595648i −0.985153 0.171680i \(-0.945081\pi\)
0.641255 + 0.767328i \(0.278414\pi\)
\(14\) −3.68831 6.38834i −0.985742 1.70736i
\(15\) 0 0
\(16\) 2.45833 + 4.25796i 0.614583 + 1.06449i
\(17\) 3.81400 + 6.60604i 0.925030 + 1.60220i 0.791513 + 0.611153i \(0.209294\pi\)
0.133518 + 0.991046i \(0.457373\pi\)
\(18\) 0 0
\(19\) −3.67522 + 2.34366i −0.843154 + 0.537672i
\(20\) −0.711327 −0.159058
\(21\) 0 0
\(22\) −2.83327 4.90737i −0.604055 1.04625i
\(23\) 1.93528 3.35201i 0.403535 0.698942i −0.590615 0.806953i \(-0.701115\pi\)
0.994150 + 0.108011i \(0.0344482\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 4.08340 0.800820
\(27\) 0 0
\(28\) −1.59333 + 2.75973i −0.301111 + 0.521540i
\(29\) −4.36728 + 7.56435i −0.810983 + 1.40466i 0.101193 + 0.994867i \(0.467734\pi\)
−0.912177 + 0.409797i \(0.865599\pi\)
\(30\) 0 0
\(31\) −0.422654 −0.0759108 −0.0379554 0.999279i \(-0.512084\pi\)
−0.0379554 + 0.999279i \(0.512084\pi\)
\(32\) 1.92598 3.33589i 0.340468 0.589707i
\(33\) 0 0
\(34\) 6.28017 10.8776i 1.07704 1.86549i
\(35\) 2.23994 + 3.87969i 0.378619 + 0.655787i
\(36\) 0 0
\(37\) 3.90253 0.641573 0.320786 0.947152i \(-0.396053\pi\)
0.320786 + 0.947152i \(0.396053\pi\)
\(38\) 6.36790 + 3.31135i 1.03301 + 0.537172i
\(39\) 0 0
\(40\) −1.06097 1.83766i −0.167754 0.290559i
\(41\) 2.64661 + 4.58406i 0.413331 + 0.715911i 0.995252 0.0973351i \(-0.0310319\pi\)
−0.581921 + 0.813246i \(0.697699\pi\)
\(42\) 0 0
\(43\) −1.23994 2.14764i −0.189089 0.327512i 0.755858 0.654736i \(-0.227220\pi\)
−0.944947 + 0.327224i \(0.893887\pi\)
\(44\) −1.22396 + 2.11996i −0.184518 + 0.319595i
\(45\) 0 0
\(46\) −6.37332 −0.939695
\(47\) −0.338665 + 0.586585i −0.0493994 + 0.0855622i −0.889668 0.456608i \(-0.849064\pi\)
0.840268 + 0.542171i \(0.182397\pi\)
\(48\) 0 0
\(49\) 13.0693 1.86705
\(50\) 1.64661 0.232866
\(51\) 0 0
\(52\) −0.882003 1.52767i −0.122312 0.211850i
\(53\) 5.74928 9.95805i 0.789725 1.36784i −0.136411 0.990652i \(-0.543557\pi\)
0.926136 0.377191i \(-0.123110\pi\)
\(54\) 0 0
\(55\) 1.72067 + 2.98028i 0.232015 + 0.401861i
\(56\) −9.50605 −1.27030
\(57\) 0 0
\(58\) 14.3824 1.88850
\(59\) −4.26526 7.38765i −0.555290 0.961791i −0.997881 0.0650670i \(-0.979274\pi\)
0.442591 0.896724i \(-0.354059\pi\)
\(60\) 0 0
\(61\) −4.10117 + 7.10343i −0.525101 + 0.909501i 0.474472 + 0.880271i \(0.342639\pi\)
−0.999573 + 0.0292304i \(0.990694\pi\)
\(62\) 0.347973 + 0.602707i 0.0441926 + 0.0765439i
\(63\) 0 0
\(64\) 3.49067 0.436334
\(65\) −2.47988 −0.307591
\(66\) 0 0
\(67\) 4.81729 8.34379i 0.588525 1.01936i −0.405901 0.913917i \(-0.633042\pi\)
0.994426 0.105438i \(-0.0336246\pi\)
\(68\) −5.42600 −0.657999
\(69\) 0 0
\(70\) 3.68831 6.38834i 0.440837 0.763553i
\(71\) −1.92594 3.33583i −0.228567 0.395890i 0.728816 0.684709i \(-0.240071\pi\)
−0.957384 + 0.288819i \(0.906737\pi\)
\(72\) 0 0
\(73\) −8.39260 14.5364i −0.982280 1.70136i −0.653451 0.756969i \(-0.726679\pi\)
−0.328829 0.944389i \(-0.606654\pi\)
\(74\) −3.21298 5.56504i −0.373501 0.646923i
\(75\) 0 0
\(76\) −0.136613 3.09759i −0.0156706 0.355318i
\(77\) 15.4168 1.75690
\(78\) 0 0
\(79\) −6.06262 10.5008i −0.682098 1.18143i −0.974339 0.225084i \(-0.927734\pi\)
0.292241 0.956345i \(-0.405599\pi\)
\(80\) −2.45833 + 4.25796i −0.274850 + 0.476054i
\(81\) 0 0
\(82\) 4.35794 7.54817i 0.481254 0.833556i
\(83\) 2.03855 0.223759 0.111880 0.993722i \(-0.464313\pi\)
0.111880 + 0.993722i \(0.464313\pi\)
\(84\) 0 0
\(85\) −3.81400 + 6.60604i −0.413686 + 0.716525i
\(86\) −2.04170 + 3.53633i −0.220162 + 0.381332i
\(87\) 0 0
\(88\) −7.30232 −0.778430
\(89\) −1.57255 + 2.72374i −0.166690 + 0.288716i −0.937254 0.348647i \(-0.886641\pi\)
0.770564 + 0.637363i \(0.219975\pi\)
\(90\) 0 0
\(91\) −5.55478 + 9.62117i −0.582300 + 1.00857i
\(92\) 1.37662 + 2.38437i 0.143522 + 0.248588i
\(93\) 0 0
\(94\) 1.11530 0.115034
\(95\) −3.86728 2.01101i −0.396774 0.206325i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) −10.7600 18.6370i −1.08693 1.88262i
\(99\) 0 0
\(100\) −0.355663 0.616027i −0.0355663 0.0616027i
\(101\) −1.00934 + 1.74823i −0.100433 + 0.173955i −0.911863 0.410494i \(-0.865356\pi\)
0.811430 + 0.584450i \(0.198690\pi\)
\(102\) 0 0
\(103\) 6.48898 0.639378 0.319689 0.947523i \(-0.396422\pi\)
0.319689 + 0.947523i \(0.396422\pi\)
\(104\) 2.63108 4.55717i 0.257999 0.446867i
\(105\) 0 0
\(106\) −18.9337 −1.83900
\(107\) −3.96145 −0.382968 −0.191484 0.981496i \(-0.561330\pi\)
−0.191484 + 0.981496i \(0.561330\pi\)
\(108\) 0 0
\(109\) 1.48402 + 2.57039i 0.142143 + 0.246199i 0.928303 0.371824i \(-0.121267\pi\)
−0.786160 + 0.618023i \(0.787934\pi\)
\(110\) 2.83327 4.90737i 0.270142 0.467899i
\(111\) 0 0
\(112\) 11.0130 + 19.0751i 1.04063 + 1.80243i
\(113\) 8.71719 0.820044 0.410022 0.912076i \(-0.365521\pi\)
0.410022 + 0.912076i \(0.365521\pi\)
\(114\) 0 0
\(115\) 3.87057 0.360932
\(116\) −3.10656 5.38072i −0.288437 0.499588i
\(117\) 0 0
\(118\) −7.02323 + 12.1646i −0.646541 + 1.11984i
\(119\) 17.0863 + 29.5943i 1.56629 + 2.71290i
\(120\) 0 0
\(121\) 0.842790 0.0766172
\(122\) 13.5061 1.22278
\(123\) 0 0
\(124\) 0.150322 0.260366i 0.0134994 0.0233816i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 2.28867 3.96410i 0.203087 0.351757i −0.746435 0.665459i \(-0.768236\pi\)
0.949522 + 0.313702i \(0.101569\pi\)
\(128\) −6.72584 11.6495i −0.594486 1.02968i
\(129\) 0 0
\(130\) 2.04170 + 3.53633i 0.179069 + 0.310156i
\(131\) −10.3364 17.9031i −0.903094 1.56420i −0.823456 0.567380i \(-0.807957\pi\)
−0.0796380 0.996824i \(-0.525376\pi\)
\(132\) 0 0
\(133\) −16.4646 + 10.4993i −1.42766 + 0.910405i
\(134\) −15.8644 −1.37047
\(135\) 0 0
\(136\) −8.09309 14.0176i −0.693976 1.20200i
\(137\) 8.81400 15.2663i 0.753031 1.30429i −0.193317 0.981136i \(-0.561925\pi\)
0.946347 0.323151i \(-0.104742\pi\)
\(138\) 0 0
\(139\) −5.86728 + 10.1624i −0.497656 + 0.861966i −0.999996 0.00270444i \(-0.999139\pi\)
0.502340 + 0.864670i \(0.332472\pi\)
\(140\) −3.18666 −0.269322
\(141\) 0 0
\(142\) −3.17128 + 5.49282i −0.266128 + 0.460947i
\(143\) −4.26705 + 7.39075i −0.356829 + 0.618045i
\(144\) 0 0
\(145\) −8.73456 −0.725365
\(146\) −13.8193 + 23.9358i −1.14370 + 1.98094i
\(147\) 0 0
\(148\) −1.38799 + 2.40407i −0.114092 + 0.197613i
\(149\) −10.7824 18.6757i −0.883332 1.52998i −0.847613 0.530614i \(-0.821961\pi\)
−0.0357187 0.999362i \(-0.511372\pi\)
\(150\) 0 0
\(151\) 18.3102 1.49006 0.745032 0.667029i \(-0.232434\pi\)
0.745032 + 0.667029i \(0.232434\pi\)
\(152\) 7.79862 4.97311i 0.632551 0.403372i
\(153\) 0 0
\(154\) −12.6927 21.9844i −1.02281 1.77156i
\(155\) −0.211327 0.366029i −0.0169742 0.0294001i
\(156\) 0 0
\(157\) 5.71527 + 9.89914i 0.456128 + 0.790038i 0.998752 0.0499382i \(-0.0159024\pi\)
−0.542624 + 0.839976i \(0.682569\pi\)
\(158\) −9.98278 + 17.2907i −0.794187 + 1.37557i
\(159\) 0 0
\(160\) 3.85195 0.304524
\(161\) 8.66984 15.0166i 0.683279 1.18347i
\(162\) 0 0
\(163\) −8.19876 −0.642177 −0.321088 0.947049i \(-0.604049\pi\)
−0.321088 + 0.947049i \(0.604049\pi\)
\(164\) −3.76521 −0.294014
\(165\) 0 0
\(166\) −1.67835 2.90698i −0.130265 0.225625i
\(167\) −4.42206 + 7.65924i −0.342189 + 0.592690i −0.984839 0.173471i \(-0.944502\pi\)
0.642650 + 0.766160i \(0.277835\pi\)
\(168\) 0 0
\(169\) 3.42510 + 5.93244i 0.263469 + 0.456342i
\(170\) 12.5603 0.963334
\(171\) 0 0
\(172\) 1.76401 0.134504
\(173\) 8.77310 + 15.1955i 0.667007 + 1.15529i 0.978737 + 0.205119i \(0.0657581\pi\)
−0.311731 + 0.950171i \(0.600909\pi\)
\(174\) 0 0
\(175\) −2.23994 + 3.87969i −0.169324 + 0.293277i
\(176\) 8.45995 + 14.6531i 0.637693 + 1.10452i
\(177\) 0 0
\(178\) 5.17877 0.388165
\(179\) −4.30890 −0.322062 −0.161031 0.986949i \(-0.551482\pi\)
−0.161031 + 0.986949i \(0.551482\pi\)
\(180\) 0 0
\(181\) −3.17193 + 5.49395i −0.235768 + 0.408362i −0.959496 0.281724i \(-0.909094\pi\)
0.723728 + 0.690086i \(0.242427\pi\)
\(182\) 18.2931 1.35598
\(183\) 0 0
\(184\) −4.10656 + 7.11277i −0.302740 + 0.524361i
\(185\) 1.95127 + 3.37969i 0.143460 + 0.248480i
\(186\) 0 0
\(187\) 13.1252 + 22.7336i 0.959813 + 1.66244i
\(188\) −0.240901 0.417254i −0.0175695 0.0304313i
\(189\) 0 0
\(190\) 0.316239 + 7.17044i 0.0229424 + 0.520198i
\(191\) −0.845796 −0.0611997 −0.0305998 0.999532i \(-0.509742\pi\)
−0.0305998 + 0.999532i \(0.509742\pi\)
\(192\) 0 0
\(193\) 6.59039 + 11.4149i 0.474387 + 0.821662i 0.999570 0.0293275i \(-0.00933658\pi\)
−0.525183 + 0.850989i \(0.676003\pi\)
\(194\) −1.64661 + 2.85201i −0.118220 + 0.204763i
\(195\) 0 0
\(196\) −4.64828 + 8.05106i −0.332020 + 0.575076i
\(197\) −6.91212 −0.492468 −0.246234 0.969210i \(-0.579193\pi\)
−0.246234 + 0.969210i \(0.579193\pi\)
\(198\) 0 0
\(199\) 6.69062 11.5885i 0.474285 0.821486i −0.525281 0.850929i \(-0.676040\pi\)
0.999566 + 0.0294426i \(0.00937321\pi\)
\(200\) 1.06097 1.83766i 0.0750220 0.129942i
\(201\) 0 0
\(202\) 3.32398 0.233875
\(203\) −19.5649 + 33.8874i −1.37319 + 2.37843i
\(204\) 0 0
\(205\) −2.64661 + 4.58406i −0.184847 + 0.320165i
\(206\) −5.34241 9.25332i −0.372223 0.644710i
\(207\) 0 0
\(208\) −12.1927 −0.845415
\(209\) −12.6477 + 8.06531i −0.874858 + 0.557889i
\(210\) 0 0
\(211\) 7.37512 + 12.7741i 0.507724 + 0.879404i 0.999960 + 0.00894190i \(0.00284633\pi\)
−0.492236 + 0.870462i \(0.663820\pi\)
\(212\) 4.08962 + 7.08343i 0.280876 + 0.486492i
\(213\) 0 0
\(214\) 3.26149 + 5.64906i 0.222951 + 0.386162i
\(215\) 1.23994 2.14764i 0.0845632 0.146468i
\(216\) 0 0
\(217\) −1.89344 −0.128535
\(218\) 2.44360 4.23244i 0.165501 0.286657i
\(219\) 0 0
\(220\) −2.44791 −0.165038
\(221\) −18.9165 −1.27246
\(222\) 0 0
\(223\) 1.14417 + 1.98176i 0.0766192 + 0.132708i 0.901789 0.432176i \(-0.142254\pi\)
−0.825170 + 0.564884i \(0.808921\pi\)
\(224\) 8.62814 14.9444i 0.576492 0.998513i
\(225\) 0 0
\(226\) −7.17691 12.4308i −0.477401 0.826882i
\(227\) 4.19493 0.278427 0.139214 0.990262i \(-0.455543\pi\)
0.139214 + 0.990262i \(0.455543\pi\)
\(228\) 0 0
\(229\) −26.2742 −1.73625 −0.868123 0.496348i \(-0.834674\pi\)
−0.868123 + 0.496348i \(0.834674\pi\)
\(230\) −3.18666 5.51946i −0.210122 0.363942i
\(231\) 0 0
\(232\) 9.26712 16.0511i 0.608416 1.05381i
\(233\) −2.78125 4.81726i −0.182206 0.315589i 0.760426 0.649425i \(-0.224990\pi\)
−0.942631 + 0.333836i \(0.891657\pi\)
\(234\) 0 0
\(235\) −0.677330 −0.0441841
\(236\) 6.06799 0.394993
\(237\) 0 0
\(238\) 28.1344 48.7302i 1.82368 3.15871i
\(239\) 6.84901 0.443026 0.221513 0.975157i \(-0.428901\pi\)
0.221513 + 0.975157i \(0.428901\pi\)
\(240\) 0 0
\(241\) −7.42122 + 12.8539i −0.478043 + 0.827994i −0.999683 0.0251714i \(-0.991987\pi\)
0.521641 + 0.853165i \(0.325320\pi\)
\(242\) −0.693873 1.20182i −0.0446039 0.0772561i
\(243\) 0 0
\(244\) −2.91727 5.05286i −0.186759 0.323476i
\(245\) 6.53467 + 11.3184i 0.417484 + 0.723104i
\(246\) 0 0
\(247\) −0.476272 10.7991i −0.0303044 0.687127i
\(248\) 0.896847 0.0569498
\(249\) 0 0
\(250\) 0.823305 + 1.42601i 0.0520704 + 0.0901886i
\(251\) −2.40128 + 4.15913i −0.151567 + 0.262522i −0.931804 0.362962i \(-0.881765\pi\)
0.780237 + 0.625484i \(0.215099\pi\)
\(252\) 0 0
\(253\) 6.65996 11.5354i 0.418708 0.725224i
\(254\) −7.53711 −0.472920
\(255\) 0 0
\(256\) −7.58417 + 13.1362i −0.474011 + 0.821010i
\(257\) 1.74862 3.02871i 0.109076 0.188926i −0.806320 0.591479i \(-0.798544\pi\)
0.915396 + 0.402554i \(0.131877\pi\)
\(258\) 0 0
\(259\) 17.4829 1.08633
\(260\) 0.882003 1.52767i 0.0546995 0.0947423i
\(261\) 0 0
\(262\) −17.0200 + 29.4795i −1.05150 + 1.82125i
\(263\) −2.61621 4.53141i −0.161322 0.279419i 0.774021 0.633160i \(-0.218243\pi\)
−0.935343 + 0.353741i \(0.884909\pi\)
\(264\) 0 0
\(265\) 11.4986 0.706351
\(266\) 28.5274 + 14.8344i 1.74913 + 0.909558i
\(267\) 0 0
\(268\) 3.42667 + 5.93516i 0.209317 + 0.362547i
\(269\) −7.94917 13.7684i −0.484670 0.839472i 0.515175 0.857085i \(-0.327727\pi\)
−0.999845 + 0.0176124i \(0.994393\pi\)
\(270\) 0 0
\(271\) −4.99789 8.65661i −0.303600 0.525851i 0.673348 0.739325i \(-0.264855\pi\)
−0.976949 + 0.213474i \(0.931522\pi\)
\(272\) −18.7522 + 32.4797i −1.13702 + 1.96937i
\(273\) 0 0
\(274\) −29.0264 −1.75355
\(275\) −1.72067 + 2.98028i −0.103760 + 0.179718i
\(276\) 0 0
\(277\) 4.08619 0.245515 0.122758 0.992437i \(-0.460826\pi\)
0.122758 + 0.992437i \(0.460826\pi\)
\(278\) 19.3222 1.15887
\(279\) 0 0
\(280\) −4.75303 8.23248i −0.284048 0.491985i
\(281\) −5.81920 + 10.0792i −0.347144 + 0.601272i −0.985741 0.168270i \(-0.946182\pi\)
0.638596 + 0.769542i \(0.279515\pi\)
\(282\) 0 0
\(283\) −2.17910 3.77432i −0.129534 0.224360i 0.793962 0.607967i \(-0.208015\pi\)
−0.923496 + 0.383607i \(0.874682\pi\)
\(284\) 2.73995 0.162586
\(285\) 0 0
\(286\) 14.0523 0.830932
\(287\) 11.8565 + 20.5361i 0.699867 + 1.21221i
\(288\) 0 0
\(289\) −20.5932 + 35.6684i −1.21136 + 2.09814i
\(290\) 7.19121 + 12.4555i 0.422282 + 0.731414i
\(291\) 0 0
\(292\) 11.9398 0.698722
\(293\) 7.20233 0.420765 0.210382 0.977619i \(-0.432529\pi\)
0.210382 + 0.977619i \(0.432529\pi\)
\(294\) 0 0
\(295\) 4.26526 7.38765i 0.248333 0.430126i
\(296\) −8.28096 −0.481321
\(297\) 0 0
\(298\) −17.7545 + 30.7517i −1.02849 + 1.78140i
\(299\) 4.79927 + 8.31258i 0.277549 + 0.480729i
\(300\) 0 0
\(301\) −5.55478 9.62117i −0.320172 0.554555i
\(302\) −15.0749 26.1105i −0.867463 1.50249i
\(303\) 0 0
\(304\) −19.0141 9.88746i −1.09053 0.567085i
\(305\) −8.20233 −0.469664
\(306\) 0 0
\(307\) −8.14056 14.0999i −0.464606 0.804722i 0.534577 0.845120i \(-0.320471\pi\)
−0.999184 + 0.0403979i \(0.987137\pi\)
\(308\) −5.48318 + 9.49715i −0.312433 + 0.541150i
\(309\) 0 0
\(310\) −0.347973 + 0.602707i −0.0197635 + 0.0342315i
\(311\) 4.07709 0.231191 0.115595 0.993296i \(-0.463122\pi\)
0.115595 + 0.993296i \(0.463122\pi\)
\(312\) 0 0
\(313\) 10.7777 18.6674i 0.609189 1.05515i −0.382186 0.924086i \(-0.624828\pi\)
0.991374 0.131060i \(-0.0418382\pi\)
\(314\) 9.41083 16.3000i 0.531084 0.919864i
\(315\) 0 0
\(316\) 8.62501 0.485195
\(317\) −7.13339 + 12.3554i −0.400651 + 0.693948i −0.993805 0.111141i \(-0.964549\pi\)
0.593154 + 0.805089i \(0.297883\pi\)
\(318\) 0 0
\(319\) −15.0293 + 26.0315i −0.841478 + 1.45748i
\(320\) 1.74534 + 3.02301i 0.0975672 + 0.168991i
\(321\) 0 0
\(322\) −28.5517 −1.59112
\(323\) −29.4996 15.3400i −1.64140 0.853539i
\(324\) 0 0
\(325\) −1.23994 2.14764i −0.0687795 0.119130i
\(326\) 6.75008 + 11.6915i 0.373853 + 0.647532i
\(327\) 0 0
\(328\) −5.61596 9.72712i −0.310089 0.537091i
\(329\) −1.51718 + 2.62783i −0.0836448 + 0.144877i
\(330\) 0 0
\(331\) 23.9646 1.31722 0.658608 0.752486i \(-0.271146\pi\)
0.658608 + 0.752486i \(0.271146\pi\)
\(332\) −0.725036 + 1.25580i −0.0397915 + 0.0689209i
\(333\) 0 0
\(334\) 14.5628 0.796843
\(335\) 9.63457 0.526393
\(336\) 0 0
\(337\) −16.3204 28.2678i −0.889029 1.53984i −0.841025 0.540996i \(-0.818048\pi\)
−0.0480033 0.998847i \(-0.515286\pi\)
\(338\) 5.63980 9.76842i 0.306765 0.531332i
\(339\) 0 0
\(340\) −2.71300 4.69905i −0.147133 0.254842i
\(341\) −1.45449 −0.0787652
\(342\) 0 0
\(343\) 27.1899 1.46812
\(344\) 2.63108 + 4.55717i 0.141858 + 0.245706i
\(345\) 0 0
\(346\) 14.4459 25.0210i 0.776616 1.34514i
\(347\) 8.41457 + 14.5745i 0.451718 + 0.782398i 0.998493 0.0548811i \(-0.0174780\pi\)
−0.546775 + 0.837280i \(0.684145\pi\)
\(348\) 0 0
\(349\) 2.46947 0.132188 0.0660939 0.997813i \(-0.478946\pi\)
0.0660939 + 0.997813i \(0.478946\pi\)
\(350\) 7.37662 0.394297
\(351\) 0 0
\(352\) 6.62793 11.4799i 0.353270 0.611881i
\(353\) −27.7653 −1.47780 −0.738900 0.673815i \(-0.764654\pi\)
−0.738900 + 0.673815i \(0.764654\pi\)
\(354\) 0 0
\(355\) 1.92594 3.33583i 0.102218 0.177048i
\(356\) −1.11860 1.93747i −0.0592857 0.102686i
\(357\) 0 0
\(358\) 3.54754 + 6.14452i 0.187493 + 0.324748i
\(359\) −10.0245 17.3629i −0.529072 0.916379i −0.999425 0.0339009i \(-0.989207\pi\)
0.470354 0.882478i \(-0.344126\pi\)
\(360\) 0 0
\(361\) 8.01455 17.2269i 0.421818 0.906680i
\(362\) 10.4459 0.549023
\(363\) 0 0
\(364\) −3.95127 6.84380i −0.207103 0.358712i
\(365\) 8.39260 14.5364i 0.439289 0.760871i
\(366\) 0 0
\(367\) 3.33741 5.78056i 0.174211 0.301743i −0.765677 0.643225i \(-0.777596\pi\)
0.939888 + 0.341483i \(0.110929\pi\)
\(368\) 19.0303 0.992023
\(369\) 0 0
\(370\) 3.21298 5.56504i 0.167035 0.289313i
\(371\) 25.7561 44.6109i 1.33719 2.31608i
\(372\) 0 0
\(373\) −12.4380 −0.644014 −0.322007 0.946737i \(-0.604357\pi\)
−0.322007 + 0.946737i \(0.604357\pi\)
\(374\) 21.6122 37.4334i 1.11754 1.93563i
\(375\) 0 0
\(376\) 0.718628 1.24470i 0.0370604 0.0641905i
\(377\) −10.8303 18.7587i −0.557790 0.966121i
\(378\) 0 0
\(379\) 21.3994 1.09921 0.549607 0.835423i \(-0.314777\pi\)
0.549607 + 0.835423i \(0.314777\pi\)
\(380\) 2.61429 1.66711i 0.134110 0.0855207i
\(381\) 0 0
\(382\) 0.696349 + 1.20611i 0.0356283 + 0.0617100i
\(383\) 5.35405 + 9.27348i 0.273579 + 0.473853i 0.969776 0.243998i \(-0.0784592\pi\)
−0.696197 + 0.717851i \(0.745126\pi\)
\(384\) 0 0
\(385\) 7.70839 + 13.3513i 0.392856 + 0.680446i
\(386\) 10.8518 18.7959i 0.552342 0.956685i
\(387\) 0 0
\(388\) 1.42265 0.0722243
\(389\) −1.75466 + 3.03917i −0.0889650 + 0.154092i −0.907074 0.420971i \(-0.861689\pi\)
0.818109 + 0.575063i \(0.195023\pi\)
\(390\) 0 0
\(391\) 29.5247 1.49313
\(392\) −27.7324 −1.40070
\(393\) 0 0
\(394\) 5.69079 + 9.85673i 0.286698 + 0.496575i
\(395\) 6.06262 10.5008i 0.305044 0.528351i
\(396\) 0 0
\(397\) −15.5995 27.0191i −0.782916 1.35605i −0.930236 0.366961i \(-0.880398\pi\)
0.147321 0.989089i \(-0.452935\pi\)
\(398\) −22.0337 −1.10445
\(399\) 0 0
\(400\) −4.91667 −0.245833
\(401\) −9.87661 17.1068i −0.493214 0.854272i 0.506755 0.862090i \(-0.330845\pi\)
−0.999969 + 0.00781786i \(0.997511\pi\)
\(402\) 0 0
\(403\) 0.524065 0.907708i 0.0261055 0.0452161i
\(404\) −0.717971 1.24356i −0.0357204 0.0618696i
\(405\) 0 0
\(406\) 64.4315 3.19768
\(407\) 13.4299 0.665697
\(408\) 0 0
\(409\) 1.06951 1.85244i 0.0528838 0.0915974i −0.838372 0.545099i \(-0.816492\pi\)
0.891255 + 0.453502i \(0.149825\pi\)
\(410\) 8.71588 0.430446
\(411\) 0 0
\(412\) −2.30789 + 3.99739i −0.113702 + 0.196937i
\(413\) −19.1079 33.0958i −0.940237 1.62854i
\(414\) 0 0
\(415\) 1.01927 + 1.76543i 0.0500341 + 0.0866616i
\(416\) 4.77619 + 8.27260i 0.234172 + 0.405598i
\(417\) 0 0
\(418\) 21.9141 + 11.3955i 1.07185 + 0.557370i
\(419\) 5.70341 0.278630 0.139315 0.990248i \(-0.455510\pi\)
0.139315 + 0.990248i \(0.455510\pi\)
\(420\) 0 0
\(421\) −19.5265 33.8209i −0.951664 1.64833i −0.741823 0.670595i \(-0.766039\pi\)
−0.209841 0.977736i \(-0.567295\pi\)
\(422\) 12.1439 21.0339i 0.591158 1.02392i
\(423\) 0 0
\(424\) −12.1996 + 21.1304i −0.592467 + 1.02618i
\(425\) −7.62799 −0.370012
\(426\) 0 0
\(427\) −18.3727 + 31.8225i −0.889119 + 1.54000i
\(428\) 1.40894 2.44036i 0.0681039 0.117959i
\(429\) 0 0
\(430\) −4.08340 −0.196919
\(431\) 0.868782 1.50477i 0.0418477 0.0724824i −0.844343 0.535803i \(-0.820009\pi\)
0.886191 + 0.463321i \(0.153342\pi\)
\(432\) 0 0
\(433\) −11.8156 + 20.4652i −0.567821 + 0.983495i 0.428960 + 0.903324i \(0.358880\pi\)
−0.996781 + 0.0801716i \(0.974453\pi\)
\(434\) 1.55888 + 2.70005i 0.0748285 + 0.129607i
\(435\) 0 0
\(436\) −2.11124 −0.101110
\(437\) 0.743359 + 16.8550i 0.0355597 + 0.806285i
\(438\) 0 0
\(439\) 1.58465 + 2.74469i 0.0756310 + 0.130997i 0.901360 0.433070i \(-0.142570\pi\)
−0.825730 + 0.564066i \(0.809236\pi\)
\(440\) −3.65116 6.32399i −0.174062 0.301485i
\(441\) 0 0
\(442\) 15.5741 + 26.9751i 0.740783 + 1.28307i
\(443\) 11.5916 20.0773i 0.550736 0.953902i −0.447486 0.894291i \(-0.647681\pi\)
0.998222 0.0596114i \(-0.0189861\pi\)
\(444\) 0 0
\(445\) −3.14511 −0.149092
\(446\) 1.88400 3.26318i 0.0892100 0.154516i
\(447\) 0 0
\(448\) 15.6378 0.738816
\(449\) −13.2505 −0.625328 −0.312664 0.949864i \(-0.601221\pi\)
−0.312664 + 0.949864i \(0.601221\pi\)
\(450\) 0 0
\(451\) 9.10788 + 15.7753i 0.428873 + 0.742830i
\(452\) −3.10038 + 5.37002i −0.145830 + 0.252585i
\(453\) 0 0
\(454\) −3.45371 5.98200i −0.162091 0.280749i
\(455\) −11.1096 −0.520825
\(456\) 0 0
\(457\) 4.13077 0.193229 0.0966146 0.995322i \(-0.469199\pi\)
0.0966146 + 0.995322i \(0.469199\pi\)
\(458\) 21.6317 + 37.4672i 1.01078 + 1.75073i
\(459\) 0 0
\(460\) −1.37662 + 2.38437i −0.0641852 + 0.111172i
\(461\) 10.9292 + 18.9300i 0.509026 + 0.881658i 0.999945 + 0.0104535i \(0.00332750\pi\)
−0.490920 + 0.871205i \(0.663339\pi\)
\(462\) 0 0
\(463\) 30.9461 1.43819 0.719094 0.694913i \(-0.244557\pi\)
0.719094 + 0.694913i \(0.244557\pi\)
\(464\) −42.9449 −1.99367
\(465\) 0 0
\(466\) −4.57963 + 7.93216i −0.212147 + 0.367450i
\(467\) −0.394259 −0.0182441 −0.00912207 0.999958i \(-0.502904\pi\)
−0.00912207 + 0.999958i \(0.502904\pi\)
\(468\) 0 0
\(469\) 21.5809 37.3792i 0.996512 1.72601i
\(470\) 0.557649 + 0.965877i 0.0257224 + 0.0445526i
\(471\) 0 0
\(472\) 9.05065 + 15.6762i 0.416590 + 0.721555i
\(473\) −4.26705 7.39075i −0.196199 0.339827i
\(474\) 0 0
\(475\) −0.192054 4.35467i −0.00881205 0.199806i
\(476\) −24.3078 −1.11415
\(477\) 0 0
\(478\) −5.63883 9.76674i −0.257914 0.446720i
\(479\) −3.52119 + 6.09888i −0.160887 + 0.278665i −0.935187 0.354154i \(-0.884769\pi\)
0.774300 + 0.632819i \(0.218102\pi\)
\(480\) 0 0
\(481\) −4.83891 + 8.38124i −0.220635 + 0.382152i
\(482\) 24.4397 1.11320
\(483\) 0 0
\(484\) −0.299749 + 0.519181i −0.0136250 + 0.0235991i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) 0.689174 0.0312295 0.0156147 0.999878i \(-0.495029\pi\)
0.0156147 + 0.999878i \(0.495029\pi\)
\(488\) 8.70244 15.0731i 0.393941 0.682326i
\(489\) 0 0
\(490\) 10.7600 18.6370i 0.486089 0.841932i
\(491\) 4.54736 + 7.87626i 0.205219 + 0.355450i 0.950203 0.311633i \(-0.100876\pi\)
−0.744983 + 0.667083i \(0.767543\pi\)
\(492\) 0 0
\(493\) −66.6272 −3.00074
\(494\) −15.0074 + 9.57008i −0.675215 + 0.430578i
\(495\) 0 0
\(496\) −1.03902 1.79964i −0.0466535 0.0808063i
\(497\) −8.62799 14.9441i −0.387018 0.670336i
\(498\) 0 0
\(499\) 11.5404 + 19.9886i 0.516619 + 0.894811i 0.999814 + 0.0192976i \(0.00614300\pi\)
−0.483195 + 0.875513i \(0.660524\pi\)
\(500\) 0.355663 0.616027i 0.0159058 0.0275496i
\(501\) 0 0
\(502\) 7.90793 0.352948
\(503\) −10.5982 + 18.3567i −0.472552 + 0.818483i −0.999507 0.0314099i \(-0.990000\pi\)
0.526955 + 0.849893i \(0.323334\pi\)
\(504\) 0 0
\(505\) −2.01868 −0.0898302
\(506\) −21.9327 −0.975029
\(507\) 0 0
\(508\) 1.62799 + 2.81977i 0.0722306 + 0.125107i
\(509\) 9.12649 15.8075i 0.404525 0.700657i −0.589741 0.807592i \(-0.700770\pi\)
0.994266 + 0.106935i \(0.0341037\pi\)
\(510\) 0 0
\(511\) −37.5979 65.1214i −1.66323 2.88080i
\(512\) −1.92701 −0.0851627
\(513\) 0 0
\(514\) −5.75861 −0.254001
\(515\) 3.24449 + 5.61962i 0.142969 + 0.247630i
\(516\) 0 0
\(517\) −1.16546 + 2.01864i −0.0512569 + 0.0887795i
\(518\) −14.3938 24.9307i −0.632425 1.09539i
\(519\) 0 0
\(520\) 5.26217 0.230761
\(521\) 34.4874 1.51092 0.755461 0.655194i \(-0.227413\pi\)
0.755461 + 0.655194i \(0.227413\pi\)
\(522\) 0 0
\(523\) −8.06993 + 13.9775i −0.352874 + 0.611195i −0.986752 0.162238i \(-0.948129\pi\)
0.633878 + 0.773433i \(0.281462\pi\)
\(524\) 14.7051 0.642395
\(525\) 0 0
\(526\) −4.30788 + 7.46147i −0.187833 + 0.325336i
\(527\) −1.61200 2.79207i −0.0702198 0.121624i
\(528\) 0 0
\(529\) 4.00935 + 6.94440i 0.174320 + 0.301931i
\(530\) −9.46683 16.3970i −0.411213 0.712241i
\(531\) 0 0
\(532\) −0.612011 13.8768i −0.0265341 0.601637i
\(533\) −13.1266 −0.568574
\(534\) 0 0
\(535\) −1.98073 3.43072i −0.0856343 0.148323i
\(536\) −10.2220 + 17.7050i −0.441523 + 0.764741i
\(537\) 0 0
\(538\) −13.0892 + 22.6711i −0.564315 + 0.977423i
\(539\) 44.9759 1.93725
\(540\) 0 0
\(541\) −8.46634 + 14.6641i −0.363996 + 0.630460i −0.988615 0.150470i \(-0.951921\pi\)
0.624618 + 0.780930i \(0.285255\pi\)
\(542\) −8.22959 + 14.2541i −0.353491 + 0.612264i
\(543\) 0 0
\(544\) 29.3827 1.25977
\(545\) −1.48402 + 2.57039i −0.0635683 + 0.110104i
\(546\) 0 0
\(547\) 14.6871 25.4389i 0.627977 1.08769i −0.359981 0.932960i \(-0.617217\pi\)
0.987957 0.154728i \(-0.0494500\pi\)
\(548\) 6.26963 + 10.8593i 0.267825 + 0.463887i
\(549\) 0 0
\(550\) 5.66654 0.241622
\(551\) −1.67751 38.0361i −0.0714643 1.62039i
\(552\) 0 0
\(553\) −27.1598 47.0422i −1.15495 2.00044i
\(554\) −3.36418 5.82693i −0.142930 0.247563i
\(555\) 0 0
\(556\) −4.17355 7.22880i −0.176998 0.306570i
\(557\) 4.29322 7.43608i 0.181910 0.315077i −0.760621 0.649196i \(-0.775105\pi\)
0.942531 + 0.334119i \(0.108439\pi\)
\(558\) 0 0
\(559\) 6.14981 0.260109
\(560\) −11.0130 + 19.0751i −0.465386 + 0.806072i
\(561\) 0 0
\(562\) 19.1639 0.808381
\(563\) −2.59685 −0.109444 −0.0547221 0.998502i \(-0.517427\pi\)
−0.0547221 + 0.998502i \(0.517427\pi\)
\(564\) 0 0
\(565\) 4.35859 + 7.54931i 0.183367 + 0.317602i
\(566\) −3.58814 + 6.21483i −0.150821 + 0.261229i
\(567\) 0 0
\(568\) 4.08674 + 7.07844i 0.171476 + 0.297005i
\(569\) 33.8768 1.42019 0.710094 0.704107i \(-0.248652\pi\)
0.710094 + 0.704107i \(0.248652\pi\)
\(570\) 0 0
\(571\) −10.6731 −0.446657 −0.223329 0.974743i \(-0.571692\pi\)
−0.223329 + 0.974743i \(0.571692\pi\)
\(572\) −3.03527 5.25724i −0.126911 0.219816i
\(573\) 0 0
\(574\) 19.5230 33.8149i 0.814876 1.41141i
\(575\) 1.93528 + 3.35201i 0.0807069 + 0.139788i
\(576\) 0 0
\(577\) −11.6607 −0.485440 −0.242720 0.970096i \(-0.578040\pi\)
−0.242720 + 0.970096i \(0.578040\pi\)
\(578\) 67.8178 2.82085
\(579\) 0 0
\(580\) 3.10656 5.38072i 0.128993 0.223422i
\(581\) 9.13244 0.378877
\(582\) 0 0
\(583\) 19.7852 34.2690i 0.819419 1.41928i
\(584\) 17.8086 + 30.8454i 0.736926 + 1.27639i
\(585\) 0 0
\(586\) −5.92972 10.2706i −0.244954 0.424274i
\(587\) 20.1362 + 34.8770i 0.831112 + 1.43953i 0.897157 + 0.441711i \(0.145628\pi\)
−0.0660456 + 0.997817i \(0.521038\pi\)
\(588\) 0 0
\(589\) 1.55335 0.990555i 0.0640045 0.0408151i
\(590\) −14.0465 −0.578284
\(591\) 0 0
\(592\) 9.59373 + 16.6168i 0.394300 + 0.682948i
\(593\) −7.05130 + 12.2132i −0.289562 + 0.501537i −0.973705 0.227811i \(-0.926843\pi\)
0.684143 + 0.729348i \(0.260176\pi\)
\(594\) 0 0
\(595\) −17.0863 + 29.5943i −0.700468 + 1.21325i
\(596\) 15.3397 0.628338
\(597\) 0 0
\(598\) 7.90253 13.6876i 0.323159 0.559727i
\(599\) −5.24355 + 9.08209i −0.214246 + 0.371084i −0.953039 0.302848i \(-0.902063\pi\)
0.738793 + 0.673932i \(0.235396\pi\)
\(600\) 0 0
\(601\) 21.0718 0.859539 0.429769 0.902939i \(-0.358595\pi\)
0.429769 + 0.902939i \(0.358595\pi\)
\(602\) −9.14657 + 15.8423i −0.372786 + 0.645685i
\(603\) 0 0
\(604\) −6.51227 + 11.2796i −0.264981 + 0.458960i
\(605\) 0.421395 + 0.729877i 0.0171321 + 0.0296737i
\(606\) 0 0
\(607\) −22.2759 −0.904149 −0.452074 0.891980i \(-0.649316\pi\)
−0.452074 + 0.891980i \(0.649316\pi\)
\(608\) 0.739784 + 16.7740i 0.0300022 + 0.680274i
\(609\) 0 0
\(610\) 6.75303 + 11.6966i 0.273422 + 0.473581i
\(611\) −0.839849 1.45466i −0.0339766 0.0588493i
\(612\) 0 0
\(613\) 8.94766 + 15.4978i 0.361393 + 0.625950i 0.988190 0.153232i \(-0.0489681\pi\)
−0.626798 + 0.779182i \(0.715635\pi\)
\(614\) −13.4043 + 23.2170i −0.540955 + 0.936961i
\(615\) 0 0
\(616\) −32.7135 −1.31806
\(617\) 8.81560 15.2691i 0.354903 0.614710i −0.632198 0.774806i \(-0.717847\pi\)
0.987101 + 0.160097i \(0.0511806\pi\)
\(618\) 0 0
\(619\) −49.2003 −1.97753 −0.988763 0.149490i \(-0.952237\pi\)
−0.988763 + 0.149490i \(0.952237\pi\)
\(620\) 0.300645 0.0120742
\(621\) 0 0
\(622\) −3.35669 5.81396i −0.134591 0.233118i
\(623\) −7.04485 + 12.2020i −0.282246 + 0.488865i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −35.4932 −1.41859
\(627\) 0 0
\(628\) −8.13085 −0.324456
\(629\) 14.8843 + 25.7803i 0.593474 + 1.02793i
\(630\) 0 0
\(631\) 16.6592 28.8547i 0.663194 1.14869i −0.316578 0.948567i \(-0.602534\pi\)
0.979772 0.200119i \(-0.0641329\pi\)
\(632\) 12.8645 + 22.2820i 0.511724 + 0.886332i
\(633\) 0 0
\(634\) 23.4918 0.932980
\(635\) 4.57735 0.181646
\(636\) 0 0
\(637\) −16.2052 + 28.0682i −0.642073 + 1.11210i
\(638\) 49.4947 1.95951
\(639\) 0 0
\(640\) 6.72584 11.6495i 0.265862 0.460487i
\(641\) 6.61110 + 11.4508i 0.261123 + 0.452278i 0.966541 0.256514i \(-0.0825739\pi\)
−0.705418 + 0.708792i \(0.749241\pi\)
\(642\) 0 0
\(643\) 0.951267 + 1.64764i 0.0375143 + 0.0649767i 0.884173 0.467160i \(-0.154723\pi\)
−0.846659 + 0.532136i \(0.821389\pi\)
\(644\) 6.16709 + 10.6817i 0.243017 + 0.420918i
\(645\) 0 0
\(646\) 2.41227 + 54.6961i 0.0949093 + 2.15199i
\(647\) −27.2141 −1.06989 −0.534947 0.844885i \(-0.679669\pi\)
−0.534947 + 0.844885i \(0.679669\pi\)
\(648\) 0 0
\(649\) −14.6782 25.4234i −0.576170 0.997956i
\(650\) −2.04170 + 3.53633i −0.0800820 + 0.138706i
\(651\) 0 0
\(652\) 2.91600 5.05066i 0.114199 0.197799i
\(653\) 43.6980 1.71004 0.855018 0.518599i \(-0.173546\pi\)
0.855018 + 0.518599i \(0.173546\pi\)
\(654\) 0 0
\(655\) 10.3364 17.9031i 0.403876 0.699533i
\(656\) −13.0125 + 22.5383i −0.508053 + 0.879974i
\(657\) 0 0
\(658\) 4.99640 0.194780
\(659\) −3.43672 + 5.95258i −0.133876 + 0.231879i −0.925167 0.379559i \(-0.876076\pi\)
0.791292 + 0.611439i \(0.209409\pi\)
\(660\) 0 0
\(661\) −18.6491 + 32.3012i −0.725367 + 1.25637i 0.233456 + 0.972367i \(0.424996\pi\)
−0.958823 + 0.284005i \(0.908337\pi\)
\(662\) −19.7302 34.1737i −0.766837 1.32820i
\(663\) 0 0
\(664\) −4.32568 −0.167869
\(665\) −17.3249 9.00908i −0.671833 0.349357i
\(666\) 0 0
\(667\) 16.9038 + 29.2783i 0.654520 + 1.13366i
\(668\) −3.14553 5.44822i −0.121704 0.210798i
\(669\) 0 0
\(670\) −7.93220 13.7390i −0.306447 0.530783i
\(671\) −14.1135 + 24.4453i −0.544845 + 0.943700i
\(672\) 0 0
\(673\) 50.6185 1.95120 0.975601 0.219553i \(-0.0704597\pi\)
0.975601 + 0.219553i \(0.0704597\pi\)
\(674\) −26.8733 + 46.5460i −1.03512 + 1.79288i
\(675\) 0 0
\(676\) −4.87273 −0.187413
\(677\) −33.8725 −1.30182 −0.650912 0.759153i \(-0.725613\pi\)
−0.650912 + 0.759153i \(0.725613\pi\)
\(678\) 0 0
\(679\) −4.47988 7.75938i −0.171922 0.297778i
\(680\) 8.09309 14.0176i 0.310356 0.537552i
\(681\) 0 0
\(682\) 1.19749 + 2.07412i 0.0458543 + 0.0794220i
\(683\) −47.0846 −1.80164 −0.900822 0.434190i \(-0.857035\pi\)
−0.900822 + 0.434190i \(0.857035\pi\)
\(684\) 0 0
\(685\) 17.6280 0.673531
\(686\) −22.3856 38.7729i −0.854685 1.48036i
\(687\) 0 0
\(688\) 6.09637 10.5592i 0.232422 0.402567i
\(689\) 14.2575 + 24.6948i 0.543169 + 0.940796i
\(690\) 0 0
\(691\) 3.91269 0.148846 0.0744228 0.997227i \(-0.476289\pi\)
0.0744228 + 0.997227i \(0.476289\pi\)
\(692\) −12.4811 −0.474460
\(693\) 0 0
\(694\) 13.8555 23.9985i 0.525949 0.910970i
\(695\) −11.7346 −0.445117
\(696\) 0 0
\(697\) −20.1883 + 34.9672i −0.764688 + 1.32448i
\(698\) −2.03313 3.52148i −0.0769551 0.133290i
\(699\) 0 0
\(700\) −1.59333 2.75973i −0.0602222 0.104308i
\(701\) 6.60352 + 11.4376i 0.249411 + 0.431993i 0.963363 0.268202i \(-0.0864295\pi\)
−0.713951 + 0.700195i \(0.753096\pi\)
\(702\) 0 0
\(703\) −14.3427 + 9.14620i −0.540945 + 0.344955i
\(704\) 12.0126 0.452741
\(705\) 0 0
\(706\) 22.8594 + 39.5936i 0.860323 + 1.49012i
\(707\) −4.52173 + 7.83186i −0.170057 + 0.294547i
\(708\) 0 0
\(709\) 8.99856 15.5860i 0.337948 0.585343i −0.646099 0.763254i \(-0.723600\pi\)
0.984047 + 0.177911i \(0.0569338\pi\)
\(710\) −6.34256 −0.238032
\(711\) 0 0
\(712\) 3.33687 5.77963i 0.125054 0.216601i
\(713\) −0.817955 + 1.41674i −0.0306326 + 0.0530573i
\(714\) 0 0
\(715\) −8.53410 −0.319157
\(716\) 1.53252 2.65440i 0.0572728 0.0991995i
\(717\) 0 0
\(718\) −16.5064 + 28.5899i −0.616014 + 1.06697i
\(719\) −6.23909 10.8064i −0.232679 0.403012i 0.725917 0.687783i \(-0.241416\pi\)
−0.958596 + 0.284771i \(0.908082\pi\)
\(720\) 0 0
\(721\) 29.0698 1.08262
\(722\) −31.1641 + 2.75423i −1.15981 + 0.102502i
\(723\) 0 0
\(724\) −2.25628 3.90800i −0.0838541 0.145240i
\(725\) −4.36728 7.56435i −0.162197 0.280933i
\(726\) 0 0
\(727\) 21.7065 + 37.5968i 0.805051 + 1.39439i 0.916257 + 0.400592i \(0.131195\pi\)
−0.111206 + 0.993797i \(0.535471\pi\)
\(728\) 11.7869 20.4156i 0.436853 0.756651i
\(729\) 0 0
\(730\) −27.6387 −1.02295
\(731\) 9.45826 16.3822i 0.349826 0.605917i
\(732\) 0 0
\(733\) −28.5740 −1.05540 −0.527702 0.849430i \(-0.676946\pi\)
−0.527702 + 0.849430i \(0.676946\pi\)
\(734\) −10.9908 −0.405678
\(735\) 0 0
\(736\) −7.45462 12.9118i −0.274781 0.475935i
\(737\) 16.5779 28.7138i 0.610655 1.05769i
\(738\) 0 0
\(739\) 4.61769 + 7.99807i 0.169864 + 0.294214i 0.938372 0.345627i \(-0.112334\pi\)
−0.768508 + 0.639841i \(0.779000\pi\)
\(740\) −2.77598 −0.102047
\(741\) 0 0
\(742\) −84.8205 −3.11386
\(743\) −2.51875 4.36259i −0.0924038 0.160048i 0.816118 0.577885i \(-0.196122\pi\)
−0.908522 + 0.417837i \(0.862788\pi\)
\(744\) 0 0
\(745\) 10.7824 18.6757i 0.395038 0.684226i
\(746\) 10.2402 + 17.7366i 0.374922 + 0.649384i
\(747\) 0 0
\(748\) −18.6727 −0.682741
\(749\) −17.7468 −0.648456
\(750\) 0 0
\(751\) −6.41366 + 11.1088i −0.234038 + 0.405365i −0.958993 0.283431i \(-0.908527\pi\)
0.724955 + 0.688796i \(0.241861\pi\)
\(752\) −3.33021 −0.121440
\(753\) 0 0
\(754\) −17.8333 + 30.8882i −0.649452 + 1.12488i
\(755\) 9.15510 + 15.8571i 0.333188 + 0.577099i
\(756\) 0 0
\(757\) −12.9425 22.4171i −0.470404 0.814764i 0.529023 0.848608i \(-0.322559\pi\)
−0.999427 + 0.0338435i \(0.989225\pi\)
\(758\) −17.6183 30.5157i −0.639924 1.10838i
\(759\) 0 0
\(760\) 8.20614 + 4.26725i 0.297668 + 0.154789i
\(761\) 28.9722 1.05024 0.525121 0.851028i \(-0.324020\pi\)
0.525121 + 0.851028i \(0.324020\pi\)
\(762\) 0 0
\(763\) 6.64822 + 11.5151i 0.240682 + 0.416873i
\(764\) 0.300819 0.521033i 0.0108832 0.0188503i
\(765\) 0 0
\(766\) 8.81603 15.2698i 0.318536 0.551721i
\(767\) 21.1547 0.763852
\(768\) 0 0
\(769\) −2.72690 + 4.72313i −0.0983345 + 0.170320i −0.910995 0.412417i \(-0.864685\pi\)
0.812661 + 0.582737i \(0.198018\pi\)
\(770\) 12.6927 21.9844i 0.457414 0.792263i
\(771\) 0 0
\(772\) −9.37584 −0.337444
\(773\) −23.5060 + 40.7135i −0.845451 + 1.46436i 0.0397783 + 0.999209i \(0.487335\pi\)
−0.885229 + 0.465155i \(0.845999\pi\)
\(774\) 0 0
\(775\) 0.211327 0.366029i 0.00759108 0.0131481i
\(776\) 2.12194 + 3.67531i 0.0761733 + 0.131936i
\(777\) 0 0
\(778\) 5.77850 0.207169
\(779\) −20.4704 10.6447i −0.733427 0.381387i
\(780\) 0 0
\(781\) −6.62782 11.4797i −0.237162 0.410776i
\(782\) −24.3078 42.1024i −0.869246 1.50558i
\(783\) 0 0
\(784\) 32.1288 + 55.6487i 1.14746 + 1.98745i
\(785\) −5.71527 + 9.89914i −0.203987 + 0.353316i
\(786\) 0 0
\(787\) 3.86923 0.137923 0.0689616 0.997619i \(-0.478031\pi\)
0.0689616 + 0.997619i \(0.478031\pi\)
\(788\) 2.45839 4.25805i 0.0875764 0.151687i
\(789\) 0 0
\(790\) −19.9656 −0.710343
\(791\) 39.0520 1.38853
\(792\) 0 0
\(793\) −10.1704 17.6157i −0.361162 0.625550i
\(794\) −25.6863 + 44.4899i −0.911572 + 1.57889i
\(795\) 0 0
\(796\) 4.75921 + 8.24320i 0.168686 + 0.292173i
\(797\) 12.6814 0.449198 0.224599 0.974451i \(-0.427893\pi\)
0.224599 + 0.974451i \(0.427893\pi\)
\(798\) 0 0
\(799\) −5.16667 −0.182784
\(800\) 1.92598 + 3.33589i 0.0680935 + 0.117941i
\(801\) 0 0
\(802\) −16.2629 + 28.1682i −0.574264 + 0.994654i
\(803\) −28.8818 50.0247i −1.01922 1.76533i
\(804\) 0 0
\(805\) 17.3397 0.611143
\(806\) −1.72586 −0.0607909
\(807\) 0 0
\(808\) 2.14176 3.70964i 0.0753470 0.130505i
\(809\) −33.2439 −1.16879 −0.584397 0.811468i \(-0.698669\pi\)
−0.584397 + 0.811468i \(0.698669\pi\)
\(810\) 0 0
\(811\) 1.43265 2.48142i 0.0503072 0.0871346i −0.839775 0.542934i \(-0.817313\pi\)
0.890082 + 0.455800i \(0.150647\pi\)
\(812\) −13.9170 24.1050i −0.488392 0.845920i
\(813\) 0 0
\(814\) −11.0569 19.1512i −0.387545 0.671248i
\(815\) −4.09938 7.10034i −0.143595 0.248714i
\(816\) 0 0
\(817\) 9.59039 + 4.98706i 0.335525 + 0.174475i
\(818\) −3.52213 −0.123148
\(819\) 0 0
\(820\) −1.88261 3.26077i −0.0657434 0.113871i
\(821\) −7.18851 + 12.4509i −0.250881 + 0.434538i −0.963769 0.266740i \(-0.914054\pi\)
0.712888 + 0.701278i \(0.247387\pi\)
\(822\) 0 0
\(823\) −28.3639 + 49.1277i −0.988702 + 1.71248i −0.364540 + 0.931188i \(0.618774\pi\)
−0.624163 + 0.781294i \(0.714560\pi\)
\(824\) −13.7692 −0.479674
\(825\) 0 0
\(826\) −31.4632 + 54.4959i −1.09475 + 1.89616i
\(827\) 10.0977 17.4897i 0.351131 0.608177i −0.635317 0.772252i \(-0.719130\pi\)
0.986448 + 0.164074i \(0.0524637\pi\)
\(828\) 0 0
\(829\) 38.0954 1.32311 0.661554 0.749898i \(-0.269897\pi\)
0.661554 + 0.749898i \(0.269897\pi\)
\(830\) 1.67835 2.90698i 0.0582562 0.100903i
\(831\) 0 0
\(832\) −4.32822 + 7.49670i −0.150054 + 0.259901i
\(833\) 49.8464 + 86.3365i 1.72708 + 2.99138i
\(834\) 0 0
\(835\) −8.84413 −0.306064
\(836\) −0.470132 10.6598i −0.0162599 0.368679i
\(837\) 0 0
\(838\) −4.69565 8.13311i −0.162209 0.280954i
\(839\) 19.1320 + 33.1376i 0.660511 + 1.14404i 0.980482 + 0.196611i \(0.0629934\pi\)
−0.319971 + 0.947427i \(0.603673\pi\)
\(840\) 0 0
\(841\) −23.6462 40.9565i −0.815388 1.41229i
\(842\) −32.1526 + 55.6899i −1.10805 + 1.91920i
\(843\) 0 0
\(844\) −10.4922 −0.361158
\(845\) −3.42510 + 5.93244i −0.117827 + 0.204082i
\(846\) 0 0
\(847\) 3.77560 0.129731
\(848\) 56.5346 1.94141
\(849\) 0 0
\(850\) 6.28017 + 10.8776i 0.215408 + 0.373098i
\(851\) 7.55251 13.0813i 0.258897 0.448422i
\(852\) 0 0
\(853\) −1.71697 2.97387i −0.0587878 0.101823i 0.835134 0.550047i \(-0.185390\pi\)
−0.893922 + 0.448224i \(0.852057\pi\)
\(854\) 60.5055 2.07046
\(855\) 0 0
\(856\) 8.40598 0.287311
\(857\) −13.6630 23.6650i −0.466719 0.808382i 0.532558 0.846394i \(-0.321231\pi\)
−0.999277 + 0.0380118i \(0.987898\pi\)
\(858\) 0 0
\(859\) 22.0603 38.2096i 0.752689 1.30370i −0.193826 0.981036i \(-0.562090\pi\)
0.946515 0.322660i \(-0.104577\pi\)
\(860\) 0.882003 + 1.52767i 0.0300760 + 0.0520932i
\(861\) 0 0
\(862\) −2.86109 −0.0974491
\(863\) 41.3721 1.40832 0.704161 0.710040i \(-0.251323\pi\)
0.704161 + 0.710040i \(0.251323\pi\)
\(864\) 0 0
\(865\) −8.77310 + 15.1955i −0.298294 + 0.516661i
\(866\) 38.9114 1.32226
\(867\) 0 0
\(868\) 0.673427 1.16641i 0.0228576 0.0395905i
\(869\) −20.8635 36.1367i −0.707746 1.22585i
\(870\) 0 0
\(871\) 11.9463 + 20.6916i 0.404785 + 0.701108i
\(872\) −3.14900 5.45423i −0.106639 0.184703i
\(873\) 0 0
\(874\) 23.4234 14.9369i 0.792307 0.505247i
\(875\) −4.47988 −0.151448
\(876\) 0 0
\(877\) −28.3151 49.0432i −0.956134 1.65607i −0.731751 0.681572i \(-0.761297\pi\)
−0.224383 0.974501i \(-0.572037\pi\)
\(878\) 2.60929 4.51943i 0.0880594 0.152523i
\(879\) 0 0
\(880\) −8.45995 + 14.6531i −0.285185 + 0.493955i
\(881\) 1.34253 0.0452311 0.0226156 0.999744i \(-0.492801\pi\)
0.0226156 + 0.999744i \(0.492801\pi\)
\(882\) 0 0
\(883\) −13.3420 + 23.1089i −0.448993 + 0.777678i −0.998321 0.0579288i \(-0.981550\pi\)
0.549328 + 0.835607i \(0.314884\pi\)
\(884\) 6.72791 11.6531i 0.226284 0.391936i
\(885\) 0 0
\(886\) −38.1739 −1.28248
\(887\) 13.8879 24.0545i 0.466309 0.807671i −0.532950 0.846147i \(-0.678917\pi\)
0.999260 + 0.0384753i \(0.0122501\pi\)
\(888\) 0 0
\(889\) 10.2530 17.7587i 0.343874 0.595607i
\(890\) 2.58938 + 4.48494i 0.0867963 + 0.150336i
\(891\) 0 0
\(892\) −1.62776 −0.0545013
\(893\) −0.130084 2.94955i −0.00435310 0.0987028i
\(894\) 0 0
\(895\) −2.15445 3.73161i −0.0720153 0.124734i
\(896\) −30.1310 52.1884i −1.00660 1.74349i
\(897\) 0 0
\(898\) 10.9092 + 18.8953i 0.364044 + 0.630543i
\(899\) 1.84585 3.19710i 0.0615624 0.106629i
\(900\) 0 0
\(901\) 87.7110 2.92208
\(902\) 14.9971 25.9758i 0.499350 0.864899i
\(903\) 0 0
\(904\) −18.4974 −0.615214
\(905\) −6.34387 −0.210877
\(906\) 0 0
\(907\) −3.69599 6.40164i −0.122723 0.212563i 0.798117 0.602502i \(-0.205829\pi\)
−0.920841 + 0.389939i \(0.872496\pi\)
\(908\) −1.49198 + 2.58419i −0.0495132 + 0.0857594i
\(909\) 0 0
\(910\) 9.14657 + 15.8423i 0.303206 + 0.525168i
\(911\) −13.3084 −0.440926 −0.220463 0.975395i \(-0.570757\pi\)
−0.220463 + 0.975395i \(0.570757\pi\)
\(912\) 0 0
\(913\) 7.01532 0.232173
\(914\) −3.40088 5.89050i −0.112491 0.194841i
\(915\) 0 0
\(916\) 9.34477 16.1856i 0.308760 0.534788i
\(917\) −46.3058 80.2039i −1.52915 2.64857i
\(918\) 0 0
\(919\) −27.8298 −0.918022 −0.459011 0.888431i \(-0.651796\pi\)
−0.459011 + 0.888431i \(0.651796\pi\)
\(920\) −8.21312 −0.270779
\(921\) 0 0
\(922\) 17.9962 31.1704i 0.592674 1.02654i
\(923\) 9.55222 0.314415
\(924\) 0 0
\(925\) −1.95127 + 3.37969i −0.0641573 + 0.111124i
\(926\) −25.4781 44.1294i −0.837262 1.45018i
\(927\) 0 0
\(928\) 16.8225 + 29.1375i 0.552227 + 0.956485i
\(929\) 3.17108 + 5.49247i 0.104040 + 0.180202i 0.913345 0.407186i \(-0.133490\pi\)
−0.809306 + 0.587388i \(0.800156\pi\)
\(930\) 0 0
\(931\) −48.0327 + 30.6300i −1.57421 + 1.00386i
\(932\) 3.95675 0.129608
\(933\) 0 0
\(934\) 0.324596 + 0.562216i 0.0106211 + 0.0183963i
\(935\) −13.1252 + 22.7336i −0.429241 + 0.743468i
\(936\) 0 0
\(937\) 21.9869 38.0825i 0.718282 1.24410i −0.243398 0.969926i \(-0.578262\pi\)
0.961680 0.274174i \(-0.0884045\pi\)
\(938\) −71.0706 −2.32054
\(939\) 0 0
\(940\) 0.240901 0.417254i 0.00785734 0.0136093i
\(941\) 7.97283 13.8093i 0.259907 0.450172i −0.706310 0.707903i \(-0.749642\pi\)
0.966217 + 0.257731i \(0.0829749\pi\)
\(942\) 0 0
\(943\) 20.4878 0.667174
\(944\) 20.9709 36.3226i 0.682544 1.18220i
\(945\) 0 0
\(946\) −7.02617 + 12.1697i −0.228441 + 0.395671i
\(947\) −1.55287 2.68965i −0.0504615 0.0874018i 0.839691 0.543064i \(-0.182736\pi\)
−0.890153 + 0.455662i \(0.849403\pi\)
\(948\) 0 0
\(949\) 41.6253 1.35121
\(950\) −6.05166 + 3.85909i −0.196342 + 0.125205i
\(951\) 0 0
\(952\) −36.2561 62.7973i −1.17507 2.03527i
\(953\) −10.2628 17.7757i −0.332445 0.575812i 0.650545 0.759467i \(-0.274540\pi\)
−0.982991 + 0.183655i \(0.941207\pi\)
\(954\) 0 0
\(955\) −0.422898 0.732481i −0.0136847 0.0237025i
\(956\) −2.43594 + 4.21918i −0.0787840 + 0.136458i
\(957\) 0 0
\(958\) 11.5961 0.374651
\(959\) 39.4857 68.3912i 1.27506 2.20847i
\(960\) 0 0
\(961\) −30.8214 −0.994238
\(962\) 15.9356 0.513784
\(963\) 0 0
\(964\) −5.27891 9.14334i −0.170022 0.294487i
\(965\) −6.59039 + 11.4149i −0.212152 + 0.367458i
\(966\) 0 0
\(967\) −12.4113 21.4970i −0.399120 0.691296i 0.594498 0.804097i \(-0.297351\pi\)
−0.993618 + 0.112801i \(0.964018\pi\)
\(968\) −1.78835 −0.0574798
\(969\) 0 0
\(970\) −3.29322 −0.105739
\(971\) −18.2999 31.6963i −0.587271 1.01718i −0.994588 0.103896i \(-0.966869\pi\)
0.407318 0.913287i \(-0.366464\pi\)
\(972\) 0 0
\(973\) −26.2847 + 45.5264i −0.842649 + 1.45951i
\(974\) −0.567401 0.982767i −0.0181807 0.0314899i
\(975\) 0 0
\(976\) −40.3282 −1.29087
\(977\) −31.6228 −1.01170 −0.505851 0.862621i \(-0.668822\pi\)
−0.505851 + 0.862621i \(0.668822\pi\)
\(978\) 0 0
\(979\) −5.41168 + 9.37331i −0.172958 + 0.299572i
\(980\) −9.29656 −0.296968
\(981\) 0 0
\(982\) 7.48773 12.9691i 0.238943 0.413862i
\(983\) 22.8804 + 39.6300i 0.729771 + 1.26400i 0.956980 + 0.290154i \(0.0937067\pi\)
−0.227209 + 0.973846i \(0.572960\pi\)
\(984\) 0 0
\(985\) −3.45606 5.98607i −0.110119 0.190732i
\(986\) 54.8545 + 95.0108i 1.74692 + 3.02576i
\(987\) 0 0
\(988\) 6.82190 + 3.54743i 0.217034 + 0.112859i
\(989\) −9.59855 −0.305216
\(990\) 0 0
\(991\) −13.2056 22.8728i −0.419490 0.726579i 0.576398 0.817169i \(-0.304458\pi\)
−0.995888 + 0.0905905i \(0.971125\pi\)
\(992\) −0.814021 + 1.40993i −0.0258452 + 0.0447652i
\(993\) 0 0
\(994\) −14.2069 + 24.6072i −0.450617 + 0.780492i
\(995\) 13.3812 0.424214
\(996\) 0 0
\(997\) 20.5781 35.6423i 0.651714 1.12880i −0.330992 0.943633i \(-0.607383\pi\)
0.982707 0.185169i \(-0.0592832\pi\)
\(998\) 19.0025 32.9134i 0.601515 1.04185i
\(999\) 0 0
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 855.2.k.i.406.2 10
3.2 odd 2 285.2.i.f.121.4 yes 10
19.11 even 3 inner 855.2.k.i.676.2 10
57.11 odd 6 285.2.i.f.106.4 10
57.26 odd 6 5415.2.a.y.1.2 5
57.50 even 6 5415.2.a.z.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.2.i.f.106.4 10 57.11 odd 6
285.2.i.f.121.4 yes 10 3.2 odd 2
855.2.k.i.406.2 10 1.1 even 1 trivial
855.2.k.i.676.2 10 19.11 even 3 inner
5415.2.a.y.1.2 5 57.26 odd 6
5415.2.a.z.1.4 5 57.50 even 6