Properties

Label 855.2.k.i.676.2
Level $855$
Weight $2$
Character 855.676
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 676.2
Root \(0.823305 + 1.42601i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.i.406.2

$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.413058 + 0.910705i \(0.364461\pi\)
−0.995222 + 0.0976341i \(0.968873\pi\)
\(3\) 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 0.641255 0.767328i \(-0.278414\pi\)
−0.985153 + 0.171680i \(0.945081\pi\)
\(14\) −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 0.133518 0.991046i \(-0.457373\pi\)
0.791513 0.611153i \(-0.209294\pi\)
\(18\) 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 0.994150 0.108011i \(-0.0344482\pi\)
−0.590615 + 0.806953i \(0.701115\pi\)
\(24\) 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 −0.912177 0.409797i \(-0.865599\pi\)
0.101193 0.994867i \(-0.467734\pi\)
\(30\) 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 −0.581921 0.813246i \(-0.697699\pi\)
0.995252 + 0.0973351i \(0.0310319\pi\)
\(42\) 0 0
\(43\) −1.23994 + 2.14764i −0.189089 + 0.327512i −0.944947 0.327224i \(-0.893887\pi\)
0.755858 + 0.654736i \(0.227220\pi\)
\(44\) −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 0.840268 0.542171i \(-0.182397\pi\)
−0.889668 + 0.456608i \(0.849064\pi\)
\(48\) 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 0.926136 + 0.377191i \(0.123110\pi\)
−0.136411 + 0.990652i \(0.543557\pi\)
\(54\) 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 0.442591 + 0.896724i \(0.354059\pi\)
−0.997881 + 0.0650670i \(0.979274\pi\)
\(60\) 0 0
\(61\) −4.10117 7.10343i −0.525101 0.909501i −0.999573 0.0292304i \(-0.990694\pi\)
0.474472 0.880271i \(-0.342639\pi\)
\(62\) 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 0.994426 + 0.105438i \(0.0336246\pi\)
−0.405901 + 0.913917i \(0.633042\pi\)
\(68\) −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 −0.957384 0.288819i \(-0.906737\pi\)
0.728816 + 0.684709i \(0.240071\pi\)
\(72\) 0 0
\(73\) −8.39260 + 14.5364i −0.982280 + 1.70136i −0.328829 + 0.944389i \(0.606654\pi\)
−0.653451 + 0.756969i \(0.726679\pi\)
\(74\) −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 0.292241 + 0.956345i \(0.405599\pi\)
−0.974339 + 0.225084i \(0.927734\pi\)
\(80\) −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 0.770564 0.637363i \(-0.219975\pi\)
−0.937254 + 0.348647i \(0.886641\pi\)
\(90\) 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 −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −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 0.811430 0.584450i \(-0.198690\pi\)
−0.911863 + 0.410494i \(0.865356\pi\)
\(102\) 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 −0.786160 0.618023i \(-0.787934\pi\)
0.928303 + 0.371824i \(0.121267\pi\)
\(110\) 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 0.949522 0.313702i \(-0.101569\pi\)
−0.746435 + 0.665459i \(0.768236\pi\)
\(128\) −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 −0.0796380 + 0.996824i \(0.525376\pi\)
−0.823456 + 0.567380i \(0.807957\pi\)
\(132\) 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 0.946347 + 0.323151i \(0.104742\pi\)
−0.193317 + 0.981136i \(0.561925\pi\)
\(138\) 0 0
\(139\) −5.86728 10.1624i −0.497656 0.861966i 0.502340 0.864670i \(-0.332472\pi\)
−0.999996 + 0.00270444i \(0.999139\pi\)
\(140\) −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 −0.0357187 + 0.999362i \(0.511372\pi\)
−0.847613 + 0.530614i \(0.821961\pi\)
\(150\) 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 −0.542624 0.839976i \(-0.682569\pi\)
0.998752 + 0.0499382i \(0.0159024\pi\)
\(158\) −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 0.642650 0.766160i \(-0.277835\pi\)
−0.984839 + 0.173471i \(0.944502\pi\)
\(168\) 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 −0.311731 0.950171i \(-0.600909\pi\)
0.978737 0.205119i \(-0.0657581\pi\)
\(174\) 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 0.723728 0.690086i \(-0.242427\pi\)
−0.959496 + 0.281724i \(0.909094\pi\)
\(182\) 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 −0.525183 0.850989i \(-0.676003\pi\)
0.999570 + 0.0293275i \(0.00933658\pi\)
\(194\) −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 0.999566 0.0294426i \(-0.00937321\pi\)
−0.525281 + 0.850929i \(0.676040\pi\)
\(200\) 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 −0.492236 0.870462i \(-0.663820\pi\)
0.999960 0.00894190i \(-0.00284633\pi\)
\(212\) 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 −0.825170 0.564884i \(-0.808921\pi\)
0.901789 + 0.432176i \(0.142254\pi\)
\(224\) 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 −0.942631 0.333836i \(-0.891657\pi\)
0.760426 + 0.649425i \(0.224990\pi\)
\(234\) 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 0.521641 0.853165i \(-0.325320\pi\)
−0.999683 + 0.0251714i \(0.991987\pi\)
\(242\) −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 0.780237 0.625484i \(-0.215099\pi\)
−0.931804 + 0.362962i \(0.881765\pi\)
\(252\) 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 0.915396 0.402554i \(-0.131877\pi\)
−0.806320 + 0.591479i \(0.798544\pi\)
\(258\) 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 −0.935343 0.353741i \(-0.884909\pi\)
0.774021 + 0.633160i \(0.218243\pi\)
\(264\) 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 −0.999845 0.0176124i \(-0.994393\pi\)
0.515175 + 0.857085i \(0.327727\pi\)
\(270\) 0 0
\(271\) −4.99789 + 8.65661i −0.303600 + 0.525851i −0.976949 0.213474i \(-0.931522\pi\)
0.673348 + 0.739325i \(0.264855\pi\)
\(272\) −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 0.638596 0.769542i \(-0.279515\pi\)
−0.985741 + 0.168270i \(0.946182\pi\)
\(282\) 0 0
\(283\) −2.17910 + 3.77432i −0.129534 + 0.224360i −0.923496 0.383607i \(-0.874682\pi\)
0.793962 + 0.607967i \(0.208015\pi\)
\(284\) 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 −0.999184 0.0403979i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(308\) −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 0.991374 + 0.131060i \(0.0418382\pi\)
−0.382186 + 0.924086i \(0.624828\pi\)
\(314\) 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 0.593154 0.805089i \(-0.297883\pi\)
−0.993805 + 0.111141i \(0.964549\pi\)
\(318\) 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 −0.0480033 + 0.998847i \(0.515286\pi\)
−0.841025 + 0.540996i \(0.818048\pi\)
\(338\) 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 −0.546775 0.837280i \(-0.684145\pi\)
0.998493 + 0.0548811i \(0.0174780\pi\)
\(348\) 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 0.470354 + 0.882478i \(0.344126\pi\)
−0.999425 + 0.0339009i \(0.989207\pi\)
\(360\) 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 0.939888 0.341483i \(-0.110929\pi\)
−0.765677 + 0.643225i \(0.777596\pi\)
\(368\) 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 −0.696197 0.717851i \(-0.745126\pi\)
0.969776 + 0.243998i \(0.0784592\pi\)
\(384\) 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 0.818109 0.575063i \(-0.195023\pi\)
−0.907074 + 0.420971i \(0.861689\pi\)
\(390\) 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 0.147321 + 0.989089i \(0.452935\pi\)
−0.930236 + 0.366961i \(0.880398\pi\)
\(398\) −22.0337 −1.10445
\(399\) 0 0
\(400\) −4.91667 −0.245833
\(401\) −9.87661 + 17.1068i −0.493214 + 0.854272i −0.999969 0.00781786i \(-0.997511\pi\)
0.506755 + 0.862090i \(0.330845\pi\)
\(402\) 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 0.891255 0.453502i \(-0.149825\pi\)
−0.838372 + 0.545099i \(0.816492\pi\)
\(410\) 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 −0.209841 + 0.977736i \(0.567295\pi\)
−0.741823 + 0.670595i \(0.766039\pi\)
\(422\) 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 0.886191 0.463321i \(-0.153342\pi\)
−0.844343 + 0.535803i \(0.820009\pi\)
\(432\) 0 0
\(433\) −11.8156 20.4652i −0.567821 0.983495i −0.996781 0.0801716i \(-0.974453\pi\)
0.428960 0.903324i \(-0.358880\pi\)
\(434\) 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 −0.825730 0.564066i \(-0.809236\pi\)
0.901360 + 0.433070i \(0.142570\pi\)
\(440\) −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 0.998222 + 0.0596114i \(0.0189861\pi\)
−0.447486 + 0.894291i \(0.647681\pi\)
\(444\) 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 −0.490920 0.871205i \(-0.663339\pi\)
0.999945 0.0104535i \(-0.00332750\pi\)
\(462\) 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 0.774300 0.632819i \(-0.218102\pi\)
−0.935187 + 0.354154i \(0.884769\pi\)
\(480\) 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 −0.744983 0.667083i \(-0.767543\pi\)
0.950203 + 0.311633i \(0.100876\pi\)
\(492\) 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 −0.483195 0.875513i \(-0.660524\pi\)
0.999814 0.0192976i \(-0.00614300\pi\)
\(500\) 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 0.526955 0.849893i \(-0.323334\pi\)
−0.999507 + 0.0314099i \(0.990000\pi\)
\(504\) 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 0.994266 0.106935i \(-0.0341037\pi\)
−0.589741 + 0.807592i \(0.700770\pi\)
\(510\) 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 0.633878 0.773433i \(-0.281462\pi\)
−0.986752 + 0.162238i \(0.948129\pi\)
\(524\) 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 0.624618 0.780930i \(-0.285255\pi\)
−0.988615 + 0.150470i \(0.951921\pi\)
\(542\) −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 0.987957 + 0.154728i \(0.0494500\pi\)
−0.359981 + 0.932960i \(0.617217\pi\)
\(548\) 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 0.942531 0.334119i \(-0.108439\pi\)
−0.760621 + 0.649196i \(0.775105\pi\)
\(558\) 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 −0.0660456 0.997817i \(-0.521038\pi\)
0.897157 0.441711i \(-0.145628\pi\)
\(588\) 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 0.684143 0.729348i \(-0.260176\pi\)
−0.973705 + 0.227811i \(0.926843\pi\)
\(594\) 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 0.738793 0.673932i \(-0.235396\pi\)
−0.953039 + 0.302848i \(0.902063\pi\)
\(600\) 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 −0.626798 0.779182i \(-0.715635\pi\)
0.988190 + 0.153232i \(0.0489681\pi\)
\(614\) −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 0.987101 0.160097i \(-0.0511806\pi\)
−0.632198 + 0.774806i \(0.717847\pi\)
\(618\) 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 0.979772 + 0.200119i \(0.0641329\pi\)
−0.316578 + 0.948567i \(0.602534\pi\)
\(632\) 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 −0.705418 0.708792i \(-0.749241\pi\)
0.966541 + 0.256514i \(0.0825739\pi\)
\(642\) 0 0
\(643\) 0.951267 1.64764i 0.0375143 0.0649767i −0.846659 0.532136i \(-0.821389\pi\)
0.884173 + 0.467160i \(0.154723\pi\)
\(644\) 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 0.791292 0.611439i \(-0.209409\pi\)
−0.925167 + 0.379559i \(0.876076\pi\)
\(660\) 0 0
\(661\) −18.6491 32.3012i −0.725367 1.25637i −0.958823 0.284005i \(-0.908337\pi\)
0.233456 0.972367i \(-0.424996\pi\)
\(662\) −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 −0.713951 0.700195i \(-0.753096\pi\)
0.963363 + 0.268202i \(0.0864295\pi\)
\(702\) 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 0.984047 0.177911i \(-0.0569338\pi\)
−0.646099 + 0.763254i \(0.723600\pi\)
\(710\) −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 −0.958596 0.284771i \(-0.908082\pi\)
0.725917 + 0.687783i \(0.241416\pi\)
\(720\) 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 −0.111206 0.993797i \(-0.535471\pi\)
0.916257 0.400592i \(-0.131195\pi\)
\(728\) 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 −0.768508 0.639841i \(-0.779000\pi\)
0.938372 + 0.345627i \(0.112334\pi\)
\(740\) −2.77598 −0.102047
\(741\) 0 0
\(742\) −84.8205 −3.11386
\(743\) −2.51875 + 4.36259i −0.0924038 + 0.160048i −0.908522 0.417837i \(-0.862788\pi\)
0.816118 + 0.577885i \(0.196122\pi\)
\(744\) 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 0.724955 0.688796i \(-0.241861\pi\)
−0.958993 + 0.283431i \(0.908527\pi\)
\(752\) −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 −0.999427 0.0338435i \(-0.989225\pi\)
0.529023 + 0.848608i \(0.322559\pi\)
\(758\) −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 0.812661 0.582737i \(-0.198018\pi\)
−0.910995 + 0.412417i \(0.864685\pi\)
\(770\) 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 −0.885229 0.465155i \(-0.845999\pi\)
0.0397783 0.999209i \(-0.487335\pi\)
\(774\) 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 0.890082 0.455800i \(-0.150647\pi\)
−0.839775 + 0.542934i \(0.817313\pi\)
\(812\) −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 0.712888 0.701278i \(-0.247387\pi\)
−0.963769 + 0.266740i \(0.914054\pi\)
\(822\) 0 0
\(823\) −28.3639 49.1277i −0.988702 1.71248i −0.624163 0.781294i \(-0.714560\pi\)
−0.364540 0.931188i \(-0.618774\pi\)
\(824\) −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 0.986448 0.164074i \(-0.0524637\pi\)
−0.635317 + 0.772252i \(0.719130\pi\)
\(828\) 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 −0.319971 0.947427i \(-0.603673\pi\)
0.980482 0.196611i \(-0.0629934\pi\)
\(840\) 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 −0.893922 0.448224i \(-0.852057\pi\)
0.835134 + 0.550047i \(0.185390\pi\)
\(854\) 60.5055 2.07046
\(855\) 0 0
\(856\) 8.40598 0.287311
\(857\) −13.6630 + 23.6650i −0.466719 + 0.808382i −0.999277 0.0380118i \(-0.987898\pi\)
0.532558 + 0.846394i \(0.321231\pi\)
\(858\) 0 0
\(859\) 22.0603 + 38.2096i 0.752689 + 1.30370i 0.946515 + 0.322660i \(0.104577\pi\)
−0.193826 + 0.981036i \(0.562090\pi\)
\(860\) 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 −0.224383 + 0.974501i \(0.572037\pi\)
−0.731751 + 0.681572i \(0.761297\pi\)
\(878\) 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 0.549328 0.835607i \(-0.314884\pi\)
−0.998321 + 0.0579288i \(0.981550\pi\)
\(884\) 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 0.999260 0.0384753i \(-0.0122501\pi\)
−0.532950 + 0.846147i \(0.678917\pi\)
\(888\) 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 −0.920841 0.389939i \(-0.872496\pi\)
0.798117 + 0.602502i \(0.205829\pi\)
\(908\) −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 −0.809306 0.587388i \(-0.800156\pi\)
0.913345 + 0.407186i \(0.133490\pi\)
\(930\) 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 0.961680 + 0.274174i \(0.0884045\pi\)
−0.243398 + 0.969926i \(0.578262\pi\)
\(938\) −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 0.966217 0.257731i \(-0.0829749\pi\)
−0.706310 + 0.707903i \(0.749642\pi\)
\(942\) 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 −0.890153 0.455662i \(-0.849403\pi\)
0.839691 + 0.543064i \(0.182736\pi\)
\(948\) 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 −0.982991 0.183655i \(-0.941207\pi\)
0.650545 + 0.759467i \(0.274540\pi\)
\(954\) 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 −0.993618 0.112801i \(-0.964018\pi\)
0.594498 + 0.804097i \(0.297351\pi\)
\(968\) −1.78835 −0.0574798
\(969\) 0 0
\(970\) −3.29322 −0.105739
\(971\) −18.2999 + 31.6963i −0.587271 + 1.01718i 0.407318 + 0.913287i \(0.366464\pi\)
−0.994588 + 0.103896i \(0.966869\pi\)
\(972\) 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 −0.227209 0.973846i \(-0.572960\pi\)
0.956980 0.290154i \(-0.0937067\pi\)
\(984\) 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 −0.995888 0.0905905i \(-0.971125\pi\)
0.576398 + 0.817169i \(0.304458\pi\)
\(992\) −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 0.982707 + 0.185169i \(0.0592832\pi\)
−0.330992 + 0.943633i \(0.607383\pi\)
\(998\) 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.676.2 10
3.2 odd 2 285.2.i.f.106.4 10
19.7 even 3 inner 855.2.k.i.406.2 10
57.8 even 6 5415.2.a.z.1.4 5
57.11 odd 6 5415.2.a.y.1.2 5
57.26 odd 6 285.2.i.f.121.4 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.2.i.f.106.4 10 3.2 odd 2
285.2.i.f.121.4 yes 10 57.26 odd 6
855.2.k.i.406.2 10 19.7 even 3 inner
855.2.k.i.676.2 10 1.1 even 1 trivial
5415.2.a.y.1.2 5 57.11 odd 6
5415.2.a.z.1.4 5 57.8 even 6