Properties

Label 432.2.y.e.37.18
Level $432$
Weight $2$
Character 432.37
Analytic conductor $3.450$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(37,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.y (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.18
Character \(\chi\) \(=\) 432.37
Dual form 432.2.y.e.397.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40500 + 0.161164i) q^{2} +(1.94805 + 0.452871i) q^{4} +(0.846545 - 0.226831i) q^{5} +(-0.567074 + 0.327400i) q^{7} +(2.66403 + 0.950239i) q^{8} +O(q^{10})\) \(q+(1.40500 + 0.161164i) q^{2} +(1.94805 + 0.452871i) q^{4} +(0.846545 - 0.226831i) q^{5} +(-0.567074 + 0.327400i) q^{7} +(2.66403 + 0.950239i) q^{8} +(1.22595 - 0.182265i) q^{10} +(1.54155 - 5.75313i) q^{11} +(1.19068 + 4.44367i) q^{13} +(-0.849504 + 0.368606i) q^{14} +(3.58982 + 1.76443i) q^{16} -2.75816 q^{17} +(-1.73499 + 1.73499i) q^{19} +(1.75184 - 0.0585035i) q^{20} +(3.09307 - 7.83471i) q^{22} +(3.50762 + 2.02512i) q^{23} +(-3.66494 + 2.11595i) q^{25} +(0.956743 + 6.43525i) q^{26} +(-1.25296 + 0.380982i) q^{28} +(-2.47312 - 0.662669i) q^{29} +(2.08801 - 3.61654i) q^{31} +(4.75933 + 3.05758i) q^{32} +(-3.87522 - 0.444516i) q^{34} +(-0.405789 + 0.405789i) q^{35} +(-4.30563 - 4.30563i) q^{37} +(-2.71728 + 2.15804i) q^{38} +(2.47076 + 0.200136i) q^{40} +(-6.15806 - 3.55536i) q^{41} +(0.225483 - 0.841515i) q^{43} +(5.60844 - 10.5093i) q^{44} +(4.60183 + 3.41060i) q^{46} +(-4.65521 - 8.06305i) q^{47} +(-3.28562 + 5.69086i) q^{49} +(-5.49026 + 2.38226i) q^{50} +(0.307095 + 9.19572i) q^{52} +(7.64584 + 7.64584i) q^{53} -5.21996i q^{55} +(-1.82181 + 0.333348i) q^{56} +(-3.36793 - 1.32963i) q^{58} +(-6.83351 + 1.83103i) q^{59} +(-3.77755 - 1.01219i) q^{61} +(3.51651 - 4.74473i) q^{62} +(6.19409 + 5.06293i) q^{64} +(2.01592 + 3.49168i) q^{65} +(3.11705 + 11.6330i) q^{67} +(-5.37305 - 1.24909i) q^{68} +(-0.635532 + 0.504735i) q^{70} -4.34835i q^{71} -0.656583i q^{73} +(-5.35550 - 6.74332i) q^{74} +(-4.16557 + 2.59412i) q^{76} +(1.00941 + 3.76715i) q^{77} +(-8.16172 - 14.1365i) q^{79} +(3.43917 + 0.679389i) q^{80} +(-8.07908 - 5.98774i) q^{82} +(-5.36845 - 1.43847i) q^{83} +(-2.33491 + 0.625638i) q^{85} +(0.452426 - 1.14599i) q^{86} +(9.57357 - 13.8617i) q^{88} -5.11081i q^{89} +(-2.13006 - 2.13006i) q^{91} +(5.91591 + 5.53355i) q^{92} +(-5.24109 - 12.0788i) q^{94} +(-1.07520 + 1.86230i) q^{95} +(3.05669 + 5.29434i) q^{97} +(-5.53346 + 7.46613i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40500 + 0.161164i 0.993485 + 0.113960i
\(3\) 0 0
\(4\) 1.94805 + 0.452871i 0.974026 + 0.226435i
\(5\) 0.846545 0.226831i 0.378587 0.101442i −0.0645072 0.997917i \(-0.520548\pi\)
0.443094 + 0.896475i \(0.353881\pi\)
\(6\) 0 0
\(7\) −0.567074 + 0.327400i −0.214334 + 0.123746i −0.603324 0.797496i \(-0.706157\pi\)
0.388990 + 0.921242i \(0.372824\pi\)
\(8\) 2.66403 + 0.950239i 0.941876 + 0.335960i
\(9\) 0 0
\(10\) 1.22595 0.182265i 0.387681 0.0576374i
\(11\) 1.54155 5.75313i 0.464794 1.73463i −0.192778 0.981242i \(-0.561750\pi\)
0.657572 0.753392i \(-0.271584\pi\)
\(12\) 0 0
\(13\) 1.19068 + 4.44367i 0.330234 + 1.23245i 0.908944 + 0.416918i \(0.136890\pi\)
−0.578710 + 0.815534i \(0.696444\pi\)
\(14\) −0.849504 + 0.368606i −0.227039 + 0.0985140i
\(15\) 0 0
\(16\) 3.58982 + 1.76443i 0.897454 + 0.441108i
\(17\) −2.75816 −0.668953 −0.334477 0.942404i \(-0.608559\pi\)
−0.334477 + 0.942404i \(0.608559\pi\)
\(18\) 0 0
\(19\) −1.73499 + 1.73499i −0.398034 + 0.398034i −0.877539 0.479505i \(-0.840816\pi\)
0.479505 + 0.877539i \(0.340816\pi\)
\(20\) 1.75184 0.0585035i 0.391723 0.0130818i
\(21\) 0 0
\(22\) 3.09307 7.83471i 0.659445 1.67037i
\(23\) 3.50762 + 2.02512i 0.731389 + 0.422268i 0.818930 0.573893i \(-0.194568\pi\)
−0.0875410 + 0.996161i \(0.527901\pi\)
\(24\) 0 0
\(25\) −3.66494 + 2.11595i −0.732988 + 0.423191i
\(26\) 0.956743 + 6.43525i 0.187633 + 1.26206i
\(27\) 0 0
\(28\) −1.25296 + 0.380982i −0.236787 + 0.0719988i
\(29\) −2.47312 0.662669i −0.459246 0.123055i 0.0217764 0.999763i \(-0.493068\pi\)
−0.481022 + 0.876708i \(0.659734\pi\)
\(30\) 0 0
\(31\) 2.08801 3.61654i 0.375018 0.649550i −0.615312 0.788284i \(-0.710970\pi\)
0.990330 + 0.138734i \(0.0443033\pi\)
\(32\) 4.75933 + 3.05758i 0.841339 + 0.540508i
\(33\) 0 0
\(34\) −3.87522 0.444516i −0.664595 0.0762339i
\(35\) −0.405789 + 0.405789i −0.0685909 + 0.0685909i
\(36\) 0 0
\(37\) −4.30563 4.30563i −0.707841 0.707841i 0.258240 0.966081i \(-0.416858\pi\)
−0.966081 + 0.258240i \(0.916858\pi\)
\(38\) −2.71728 + 2.15804i −0.440801 + 0.350081i
\(39\) 0 0
\(40\) 2.47076 + 0.200136i 0.390662 + 0.0316443i
\(41\) −6.15806 3.55536i −0.961728 0.555254i −0.0650233 0.997884i \(-0.520712\pi\)
−0.896704 + 0.442630i \(0.854046\pi\)
\(42\) 0 0
\(43\) 0.225483 0.841515i 0.0343859 0.128330i −0.946599 0.322412i \(-0.895506\pi\)
0.980985 + 0.194082i \(0.0621729\pi\)
\(44\) 5.60844 10.5093i 0.845504 1.58433i
\(45\) 0 0
\(46\) 4.60183 + 3.41060i 0.678503 + 0.502866i
\(47\) −4.65521 8.06305i −0.679032 1.17612i −0.975273 0.221004i \(-0.929067\pi\)
0.296241 0.955113i \(-0.404267\pi\)
\(48\) 0 0
\(49\) −3.28562 + 5.69086i −0.469374 + 0.812980i
\(50\) −5.49026 + 2.38226i −0.776440 + 0.336903i
\(51\) 0 0
\(52\) 0.307095 + 9.19572i 0.0425865 + 1.27522i
\(53\) 7.64584 + 7.64584i 1.05024 + 1.05024i 0.998669 + 0.0515677i \(0.0164218\pi\)
0.0515677 + 0.998669i \(0.483578\pi\)
\(54\) 0 0
\(55\) 5.21996i 0.703859i
\(56\) −1.82181 + 0.333348i −0.243449 + 0.0445455i
\(57\) 0 0
\(58\) −3.36793 1.32963i −0.442231 0.174589i
\(59\) −6.83351 + 1.83103i −0.889647 + 0.238380i −0.674565 0.738216i \(-0.735669\pi\)
−0.215082 + 0.976596i \(0.569002\pi\)
\(60\) 0 0
\(61\) −3.77755 1.01219i −0.483666 0.129598i 0.00874306 0.999962i \(-0.497217\pi\)
−0.492409 + 0.870364i \(0.663884\pi\)
\(62\) 3.51651 4.74473i 0.446597 0.602581i
\(63\) 0 0
\(64\) 6.19409 + 5.06293i 0.774261 + 0.632866i
\(65\) 2.01592 + 3.49168i 0.250045 + 0.433090i
\(66\) 0 0
\(67\) 3.11705 + 11.6330i 0.380809 + 1.42120i 0.844669 + 0.535289i \(0.179797\pi\)
−0.463860 + 0.885908i \(0.653536\pi\)
\(68\) −5.37305 1.24909i −0.651578 0.151475i
\(69\) 0 0
\(70\) −0.635532 + 0.504735i −0.0759606 + 0.0603274i
\(71\) 4.34835i 0.516054i −0.966138 0.258027i \(-0.916928\pi\)
0.966138 0.258027i \(-0.0830723\pi\)
\(72\) 0 0
\(73\) 0.656583i 0.0768472i −0.999262 0.0384236i \(-0.987766\pi\)
0.999262 0.0384236i \(-0.0122336\pi\)
\(74\) −5.35550 6.74332i −0.622564 0.783896i
\(75\) 0 0
\(76\) −4.16557 + 2.59412i −0.477824 + 0.297566i
\(77\) 1.00941 + 3.76715i 0.115032 + 0.429307i
\(78\) 0 0
\(79\) −8.16172 14.1365i −0.918266 1.59048i −0.802048 0.597259i \(-0.796256\pi\)
−0.116217 0.993224i \(-0.537077\pi\)
\(80\) 3.43917 + 0.679389i 0.384511 + 0.0759580i
\(81\) 0 0
\(82\) −8.07908 5.98774i −0.892186 0.661235i
\(83\) −5.36845 1.43847i −0.589264 0.157893i −0.0481470 0.998840i \(-0.515332\pi\)
−0.541117 + 0.840948i \(0.681998\pi\)
\(84\) 0 0
\(85\) −2.33491 + 0.625638i −0.253257 + 0.0678599i
\(86\) 0.452426 1.14599i 0.0487863 0.123575i
\(87\) 0 0
\(88\) 9.57357 13.8617i 1.02055 1.47766i
\(89\) 5.11081i 0.541744i −0.962615 0.270872i \(-0.912688\pi\)
0.962615 0.270872i \(-0.0873121\pi\)
\(90\) 0 0
\(91\) −2.13006 2.13006i −0.223291 0.223291i
\(92\) 5.91591 + 5.53355i 0.616776 + 0.576912i
\(93\) 0 0
\(94\) −5.24109 12.0788i −0.540578 1.24584i
\(95\) −1.07520 + 1.86230i −0.110313 + 0.191068i
\(96\) 0 0
\(97\) 3.05669 + 5.29434i 0.310360 + 0.537559i 0.978440 0.206530i \(-0.0662171\pi\)
−0.668080 + 0.744089i \(0.732884\pi\)
\(98\) −5.53346 + 7.46613i −0.558963 + 0.754193i
\(99\) 0 0
\(100\) −8.09775 + 2.46225i −0.809775 + 0.246225i
\(101\) −3.30688 + 12.3415i −0.329047 + 1.22802i 0.581133 + 0.813809i \(0.302610\pi\)
−0.910180 + 0.414213i \(0.864057\pi\)
\(102\) 0 0
\(103\) 1.82866 + 1.05577i 0.180183 + 0.104029i 0.587379 0.809312i \(-0.300160\pi\)
−0.407196 + 0.913341i \(0.633493\pi\)
\(104\) −1.05055 + 12.9695i −0.103015 + 1.27176i
\(105\) 0 0
\(106\) 9.51018 + 11.9746i 0.923710 + 1.16308i
\(107\) −7.26738 7.26738i −0.702564 0.702564i 0.262396 0.964960i \(-0.415487\pi\)
−0.964960 + 0.262396i \(0.915487\pi\)
\(108\) 0 0
\(109\) 5.73169 5.73169i 0.548996 0.548996i −0.377154 0.926150i \(-0.623097\pi\)
0.926150 + 0.377154i \(0.123097\pi\)
\(110\) 0.841268 7.33404i 0.0802118 0.699273i
\(111\) 0 0
\(112\) −2.61337 + 0.174744i −0.246940 + 0.0165118i
\(113\) −0.907975 + 1.57266i −0.0854151 + 0.147943i −0.905568 0.424201i \(-0.860555\pi\)
0.820153 + 0.572144i \(0.193888\pi\)
\(114\) 0 0
\(115\) 3.42872 + 0.918723i 0.319730 + 0.0856713i
\(116\) −4.51766 2.41092i −0.419454 0.223848i
\(117\) 0 0
\(118\) −9.89618 + 1.47129i −0.911017 + 0.135443i
\(119\) 1.56408 0.903023i 0.143379 0.0827800i
\(120\) 0 0
\(121\) −21.1959 12.2374i −1.92690 1.11249i
\(122\) −5.14433 2.03094i −0.465746 0.183872i
\(123\) 0 0
\(124\) 5.70538 6.09961i 0.512358 0.547761i
\(125\) −5.72115 + 5.72115i −0.511715 + 0.511715i
\(126\) 0 0
\(127\) 19.2026 1.70395 0.851976 0.523581i \(-0.175404\pi\)
0.851976 + 0.523581i \(0.175404\pi\)
\(128\) 7.88674 + 8.11168i 0.697096 + 0.716978i
\(129\) 0 0
\(130\) 2.26964 + 5.23071i 0.199061 + 0.458764i
\(131\) 3.12885 + 11.6770i 0.273369 + 1.02023i 0.956927 + 0.290330i \(0.0937650\pi\)
−0.683558 + 0.729896i \(0.739568\pi\)
\(132\) 0 0
\(133\) 0.415831 1.55190i 0.0360571 0.134567i
\(134\) 2.50464 + 16.8467i 0.216368 + 1.45534i
\(135\) 0 0
\(136\) −7.34783 2.62092i −0.630071 0.224742i
\(137\) 2.88080 1.66323i 0.246123 0.142099i −0.371865 0.928287i \(-0.621281\pi\)
0.617988 + 0.786188i \(0.287948\pi\)
\(138\) 0 0
\(139\) 10.4536 2.80104i 0.886666 0.237582i 0.213385 0.976968i \(-0.431551\pi\)
0.673281 + 0.739387i \(0.264884\pi\)
\(140\) −0.974268 + 0.606728i −0.0823407 + 0.0512779i
\(141\) 0 0
\(142\) 0.700796 6.10943i 0.0588095 0.512692i
\(143\) 27.4005 2.29134
\(144\) 0 0
\(145\) −2.24392 −0.186347
\(146\) 0.105817 0.922499i 0.00875751 0.0763466i
\(147\) 0 0
\(148\) −6.43770 10.3375i −0.529176 0.849736i
\(149\) 19.1223 5.12380i 1.56656 0.419758i 0.631827 0.775110i \(-0.282305\pi\)
0.934733 + 0.355351i \(0.115639\pi\)
\(150\) 0 0
\(151\) 5.09441 2.94126i 0.414577 0.239356i −0.278177 0.960530i \(-0.589730\pi\)
0.692754 + 0.721174i \(0.256397\pi\)
\(152\) −6.27071 + 2.97340i −0.508622 + 0.241175i
\(153\) 0 0
\(154\) 0.811086 + 5.45553i 0.0653592 + 0.439619i
\(155\) 0.947251 3.53519i 0.0760851 0.283953i
\(156\) 0 0
\(157\) 5.09096 + 18.9997i 0.406303 + 1.51634i 0.801640 + 0.597808i \(0.203961\pi\)
−0.395336 + 0.918536i \(0.629372\pi\)
\(158\) −9.18893 21.1772i −0.731032 1.68477i
\(159\) 0 0
\(160\) 4.72254 + 1.50881i 0.373350 + 0.119282i
\(161\) −2.65210 −0.209015
\(162\) 0 0
\(163\) 5.00716 5.00716i 0.392191 0.392191i −0.483277 0.875468i \(-0.660554\pi\)
0.875468 + 0.483277i \(0.160554\pi\)
\(164\) −10.3861 9.71483i −0.811019 0.758601i
\(165\) 0 0
\(166\) −7.31084 2.88625i −0.567431 0.224017i
\(167\) −14.5023 8.37292i −1.12222 0.647916i −0.180255 0.983620i \(-0.557692\pi\)
−0.941967 + 0.335704i \(0.891026\pi\)
\(168\) 0 0
\(169\) −7.07014 + 4.08195i −0.543857 + 0.313996i
\(170\) −3.38138 + 0.502718i −0.259340 + 0.0385567i
\(171\) 0 0
\(172\) 0.820350 1.53720i 0.0625511 0.117210i
\(173\) 16.2848 + 4.36351i 1.23811 + 0.331751i 0.817733 0.575597i \(-0.195230\pi\)
0.420379 + 0.907349i \(0.361897\pi\)
\(174\) 0 0
\(175\) 1.38553 2.39980i 0.104736 0.181408i
\(176\) 15.6849 17.9327i 1.18229 1.35173i
\(177\) 0 0
\(178\) 0.823677 7.18068i 0.0617372 0.538215i
\(179\) −6.56566 + 6.56566i −0.490740 + 0.490740i −0.908539 0.417799i \(-0.862802\pi\)
0.417799 + 0.908539i \(0.362802\pi\)
\(180\) 0 0
\(181\) 15.4877 + 15.4877i 1.15119 + 1.15119i 0.986315 + 0.164875i \(0.0527219\pi\)
0.164875 + 0.986315i \(0.447278\pi\)
\(182\) −2.64945 3.33602i −0.196390 0.247282i
\(183\) 0 0
\(184\) 7.42004 + 8.72807i 0.547013 + 0.643442i
\(185\) −4.62156 2.66826i −0.339784 0.196174i
\(186\) 0 0
\(187\) −4.25184 + 15.8681i −0.310925 + 1.16039i
\(188\) −5.41707 17.8155i −0.395080 1.29933i
\(189\) 0 0
\(190\) −1.81079 + 2.44324i −0.131368 + 0.177252i
\(191\) 1.73038 + 2.99710i 0.125206 + 0.216863i 0.921813 0.387634i \(-0.126708\pi\)
−0.796608 + 0.604497i \(0.793374\pi\)
\(192\) 0 0
\(193\) 4.93395 8.54585i 0.355153 0.615144i −0.631991 0.774976i \(-0.717762\pi\)
0.987144 + 0.159832i \(0.0510953\pi\)
\(194\) 3.44139 + 7.93118i 0.247078 + 0.569426i
\(195\) 0 0
\(196\) −8.97778 + 9.59813i −0.641270 + 0.685581i
\(197\) −4.95292 4.95292i −0.352881 0.352881i 0.508299 0.861180i \(-0.330274\pi\)
−0.861180 + 0.508299i \(0.830274\pi\)
\(198\) 0 0
\(199\) 19.3983i 1.37511i 0.726132 + 0.687556i \(0.241316\pi\)
−0.726132 + 0.687556i \(0.758684\pi\)
\(200\) −11.7742 + 2.15439i −0.832559 + 0.152339i
\(201\) 0 0
\(202\) −6.63517 + 16.8068i −0.466849 + 1.18252i
\(203\) 1.61940 0.433916i 0.113659 0.0304549i
\(204\) 0 0
\(205\) −6.01954 1.61293i −0.420423 0.112652i
\(206\) 2.39911 + 1.77808i 0.167154 + 0.123884i
\(207\) 0 0
\(208\) −3.56623 + 18.0528i −0.247274 + 1.25174i
\(209\) 7.30705 + 12.6562i 0.505439 + 0.875446i
\(210\) 0 0
\(211\) −0.499784 1.86522i −0.0344066 0.128407i 0.946586 0.322450i \(-0.104506\pi\)
−0.980993 + 0.194043i \(0.937840\pi\)
\(212\) 11.4319 + 18.3571i 0.785148 + 1.26077i
\(213\) 0 0
\(214\) −9.03943 11.3819i −0.617923 0.778051i
\(215\) 0.763527i 0.0520721i
\(216\) 0 0
\(217\) 2.73446i 0.185627i
\(218\) 8.97677 7.12928i 0.607983 0.482856i
\(219\) 0 0
\(220\) 2.36396 10.1687i 0.159378 0.685577i
\(221\) −3.28408 12.2564i −0.220911 0.824452i
\(222\) 0 0
\(223\) −6.56173 11.3653i −0.439406 0.761074i 0.558237 0.829681i \(-0.311478\pi\)
−0.997644 + 0.0686072i \(0.978144\pi\)
\(224\) −3.69994 0.175665i −0.247213 0.0117371i
\(225\) 0 0
\(226\) −1.52916 + 2.06325i −0.101718 + 0.137246i
\(227\) −4.02317 1.07800i −0.267027 0.0715497i 0.122821 0.992429i \(-0.460806\pi\)
−0.389848 + 0.920879i \(0.627473\pi\)
\(228\) 0 0
\(229\) 26.9787 7.22892i 1.78280 0.477701i 0.791713 0.610894i \(-0.209190\pi\)
0.991090 + 0.133193i \(0.0425231\pi\)
\(230\) 4.66929 + 1.84339i 0.307884 + 0.121550i
\(231\) 0 0
\(232\) −5.95876 4.11542i −0.391211 0.270191i
\(233\) 6.78106i 0.444242i −0.975019 0.222121i \(-0.928702\pi\)
0.975019 0.222121i \(-0.0712980\pi\)
\(234\) 0 0
\(235\) −5.76980 5.76980i −0.376380 0.376380i
\(236\) −14.1412 + 0.472253i −0.920517 + 0.0307411i
\(237\) 0 0
\(238\) 2.34307 1.01667i 0.151879 0.0659012i
\(239\) 4.09048 7.08492i 0.264591 0.458286i −0.702865 0.711323i \(-0.748096\pi\)
0.967456 + 0.253038i \(0.0814296\pi\)
\(240\) 0 0
\(241\) −0.259428 0.449343i −0.0167112 0.0289447i 0.857549 0.514403i \(-0.171986\pi\)
−0.874260 + 0.485458i \(0.838653\pi\)
\(242\) −27.8080 20.6096i −1.78756 1.32484i
\(243\) 0 0
\(244\) −6.90048 3.68255i −0.441758 0.235751i
\(245\) −1.49056 + 5.56285i −0.0952285 + 0.355397i
\(246\) 0 0
\(247\) −9.77552 5.64390i −0.622002 0.359113i
\(248\) 8.99909 7.65045i 0.571443 0.485804i
\(249\) 0 0
\(250\) −8.96025 + 7.11617i −0.566696 + 0.450066i
\(251\) 13.9609 + 13.9609i 0.881207 + 0.881207i 0.993657 0.112450i \(-0.0358699\pi\)
−0.112450 + 0.993657i \(0.535870\pi\)
\(252\) 0 0
\(253\) 17.0580 17.0580i 1.07243 1.07243i
\(254\) 26.9796 + 3.09476i 1.69285 + 0.194183i
\(255\) 0 0
\(256\) 9.77357 + 12.6680i 0.610848 + 0.791748i
\(257\) 8.72443 15.1112i 0.544215 0.942609i −0.454441 0.890777i \(-0.650161\pi\)
0.998656 0.0518315i \(-0.0165059\pi\)
\(258\) 0 0
\(259\) 3.85127 + 1.03195i 0.239307 + 0.0641220i
\(260\) 2.34585 + 7.71494i 0.145483 + 0.478460i
\(261\) 0 0
\(262\) 2.51412 + 16.9105i 0.155323 + 1.04473i
\(263\) 9.06417 5.23320i 0.558921 0.322693i −0.193791 0.981043i \(-0.562079\pi\)
0.752712 + 0.658350i \(0.228745\pi\)
\(264\) 0 0
\(265\) 8.20687 + 4.73824i 0.504144 + 0.291068i
\(266\) 0.834353 2.11341i 0.0511575 0.129581i
\(267\) 0 0
\(268\) 0.803940 + 24.0733i 0.0491084 + 1.47051i
\(269\) −14.8881 + 14.8881i −0.907746 + 0.907746i −0.996090 0.0883440i \(-0.971843\pi\)
0.0883440 + 0.996090i \(0.471843\pi\)
\(270\) 0 0
\(271\) −1.64797 −0.100107 −0.0500534 0.998747i \(-0.515939\pi\)
−0.0500534 + 0.998747i \(0.515939\pi\)
\(272\) −9.90130 4.86659i −0.600355 0.295080i
\(273\) 0 0
\(274\) 4.31558 1.87256i 0.260714 0.113125i
\(275\) 6.52368 + 24.3467i 0.393393 + 1.46816i
\(276\) 0 0
\(277\) 3.13780 11.7104i 0.188532 0.703612i −0.805315 0.592848i \(-0.798004\pi\)
0.993847 0.110764i \(-0.0353298\pi\)
\(278\) 15.1388 2.25072i 0.907965 0.134989i
\(279\) 0 0
\(280\) −1.46663 + 0.695437i −0.0876479 + 0.0415603i
\(281\) −2.28116 + 1.31703i −0.136083 + 0.0785674i −0.566496 0.824065i \(-0.691701\pi\)
0.430413 + 0.902632i \(0.358368\pi\)
\(282\) 0 0
\(283\) −10.3823 + 2.78192i −0.617162 + 0.165368i −0.553837 0.832625i \(-0.686837\pi\)
−0.0633245 + 0.997993i \(0.520170\pi\)
\(284\) 1.96924 8.47081i 0.116853 0.502650i
\(285\) 0 0
\(286\) 38.4977 + 4.41597i 2.27642 + 0.261122i
\(287\) 4.65610 0.274841
\(288\) 0 0
\(289\) −9.39253 −0.552502
\(290\) −3.15271 0.361639i −0.185133 0.0212361i
\(291\) 0 0
\(292\) 0.297347 1.27906i 0.0174009 0.0748512i
\(293\) −3.95963 + 1.06098i −0.231324 + 0.0619831i −0.372619 0.927984i \(-0.621540\pi\)
0.141295 + 0.989968i \(0.454873\pi\)
\(294\) 0 0
\(295\) −5.36954 + 3.10010i −0.312627 + 0.180495i
\(296\) −7.37894 15.5617i −0.428892 0.904505i
\(297\) 0 0
\(298\) 27.6926 4.11712i 1.60419 0.238499i
\(299\) −4.82254 + 17.9980i −0.278895 + 1.04085i
\(300\) 0 0
\(301\) 0.147646 + 0.551024i 0.00851020 + 0.0317605i
\(302\) 7.63167 3.31143i 0.439153 0.190552i
\(303\) 0 0
\(304\) −9.28956 + 3.16702i −0.532793 + 0.181641i
\(305\) −3.42747 −0.196256
\(306\) 0 0
\(307\) 5.40346 5.40346i 0.308392 0.308392i −0.535894 0.844286i \(-0.680025\pi\)
0.844286 + 0.535894i \(0.180025\pi\)
\(308\) 0.260342 + 7.79574i 0.0148344 + 0.444203i
\(309\) 0 0
\(310\) 1.90063 4.81428i 0.107949 0.273433i
\(311\) 13.4939 + 7.79068i 0.765167 + 0.441769i 0.831148 0.556052i \(-0.187684\pi\)
−0.0659811 + 0.997821i \(0.521018\pi\)
\(312\) 0 0
\(313\) 25.4594 14.6990i 1.43905 0.830835i 0.441265 0.897377i \(-0.354530\pi\)
0.997784 + 0.0665417i \(0.0211965\pi\)
\(314\) 4.09074 + 27.5151i 0.230854 + 1.55277i
\(315\) 0 0
\(316\) −9.49745 31.2349i −0.534273 1.75710i
\(317\) −5.27629 1.41378i −0.296346 0.0794057i 0.107583 0.994196i \(-0.465689\pi\)
−0.403929 + 0.914790i \(0.632356\pi\)
\(318\) 0 0
\(319\) −7.62485 + 13.2066i −0.426909 + 0.739429i
\(320\) 6.39201 + 2.88098i 0.357324 + 0.161052i
\(321\) 0 0
\(322\) −3.72621 0.427423i −0.207653 0.0238194i
\(323\) 4.78538 4.78538i 0.266266 0.266266i
\(324\) 0 0
\(325\) −13.7664 13.7664i −0.763620 0.763620i
\(326\) 7.84203 6.22808i 0.434330 0.344942i
\(327\) 0 0
\(328\) −13.0268 15.3232i −0.719285 0.846083i
\(329\) 5.27969 + 3.04823i 0.291079 + 0.168054i
\(330\) 0 0
\(331\) −6.68483 + 24.9481i −0.367432 + 1.37127i 0.496663 + 0.867944i \(0.334559\pi\)
−0.864094 + 0.503330i \(0.832108\pi\)
\(332\) −9.80658 5.23343i −0.538206 0.287222i
\(333\) 0 0
\(334\) −19.0263 14.1012i −1.04108 0.771583i
\(335\) 5.27746 + 9.14082i 0.288338 + 0.499416i
\(336\) 0 0
\(337\) −1.97680 + 3.42392i −0.107683 + 0.186513i −0.914831 0.403836i \(-0.867677\pi\)
0.807148 + 0.590349i \(0.201010\pi\)
\(338\) −10.5914 + 4.59569i −0.576097 + 0.249972i
\(339\) 0 0
\(340\) −4.83186 + 0.161362i −0.262045 + 0.00875110i
\(341\) −17.5877 17.5877i −0.952425 0.952425i
\(342\) 0 0
\(343\) 8.88645i 0.479823i
\(344\) 1.40033 2.02756i 0.0755009 0.109318i
\(345\) 0 0
\(346\) 22.1769 + 8.75525i 1.19224 + 0.470685i
\(347\) −4.56059 + 1.22201i −0.244825 + 0.0656008i −0.379145 0.925337i \(-0.623782\pi\)
0.134320 + 0.990938i \(0.457115\pi\)
\(348\) 0 0
\(349\) −7.74559 2.07543i −0.414612 0.111095i 0.0454819 0.998965i \(-0.485518\pi\)
−0.460094 + 0.887870i \(0.652184\pi\)
\(350\) 2.33343 3.14843i 0.124727 0.168291i
\(351\) 0 0
\(352\) 24.9274 22.6677i 1.32863 1.20819i
\(353\) −6.95793 12.0515i −0.370333 0.641436i 0.619283 0.785168i \(-0.287423\pi\)
−0.989617 + 0.143731i \(0.954090\pi\)
\(354\) 0 0
\(355\) −0.986340 3.68107i −0.0523495 0.195371i
\(356\) 2.31453 9.95612i 0.122670 0.527673i
\(357\) 0 0
\(358\) −10.2829 + 8.16660i −0.543468 + 0.431618i
\(359\) 0.491573i 0.0259443i −0.999916 0.0129721i \(-0.995871\pi\)
0.999916 0.0129721i \(-0.00412927\pi\)
\(360\) 0 0
\(361\) 12.9796i 0.683138i
\(362\) 19.2641 + 24.2562i 1.01250 + 1.27488i
\(363\) 0 0
\(364\) −3.18483 5.11411i −0.166930 0.268052i
\(365\) −0.148933 0.555827i −0.00779553 0.0290933i
\(366\) 0 0
\(367\) 3.97080 + 6.87763i 0.207274 + 0.359010i 0.950855 0.309637i \(-0.100207\pi\)
−0.743581 + 0.668646i \(0.766874\pi\)
\(368\) 9.01852 + 13.4588i 0.470123 + 0.701587i
\(369\) 0 0
\(370\) −6.06327 4.49374i −0.315214 0.233618i
\(371\) −6.83901 1.83251i −0.355064 0.0951390i
\(372\) 0 0
\(373\) 21.8895 5.86527i 1.13340 0.303692i 0.357103 0.934065i \(-0.383765\pi\)
0.776293 + 0.630373i \(0.217098\pi\)
\(374\) −8.53120 + 21.6094i −0.441138 + 1.11740i
\(375\) 0 0
\(376\) −4.73977 25.9038i −0.244435 1.33588i
\(377\) 11.7787i 0.606635i
\(378\) 0 0
\(379\) −24.5680 24.5680i −1.26197 1.26197i −0.950135 0.311839i \(-0.899055\pi\)
−0.311839 0.950135i \(-0.600945\pi\)
\(380\) −2.93792 + 3.14093i −0.150712 + 0.161126i
\(381\) 0 0
\(382\) 1.94816 + 4.48980i 0.0996764 + 0.229718i
\(383\) −3.67713 + 6.36897i −0.187892 + 0.325439i −0.944547 0.328375i \(-0.893499\pi\)
0.756655 + 0.653814i \(0.226832\pi\)
\(384\) 0 0
\(385\) 1.70901 + 2.96010i 0.0870995 + 0.150861i
\(386\) 8.30948 11.2117i 0.422941 0.570663i
\(387\) 0 0
\(388\) 3.55694 + 11.6979i 0.180576 + 0.593873i
\(389\) 4.98406 18.6007i 0.252702 0.943095i −0.716653 0.697430i \(-0.754327\pi\)
0.969355 0.245665i \(-0.0790065\pi\)
\(390\) 0 0
\(391\) −9.67459 5.58563i −0.489265 0.282477i
\(392\) −14.1607 + 12.0385i −0.715221 + 0.608035i
\(393\) 0 0
\(394\) −6.16062 7.75709i −0.310368 0.390796i
\(395\) −10.1159 10.1159i −0.508985 0.508985i
\(396\) 0 0
\(397\) −23.3235 + 23.3235i −1.17057 + 1.17057i −0.188500 + 0.982073i \(0.560362\pi\)
−0.982073 + 0.188500i \(0.939638\pi\)
\(398\) −3.12631 + 27.2547i −0.156708 + 1.36615i
\(399\) 0 0
\(400\) −16.8899 + 1.12935i −0.844496 + 0.0564676i
\(401\) 4.61036 7.98538i 0.230231 0.398771i −0.727645 0.685954i \(-0.759385\pi\)
0.957876 + 0.287183i \(0.0927186\pi\)
\(402\) 0 0
\(403\) 18.5568 + 4.97229i 0.924382 + 0.247687i
\(404\) −12.0311 + 22.5442i −0.598568 + 1.12162i
\(405\) 0 0
\(406\) 2.34519 0.348664i 0.116390 0.0173039i
\(407\) −31.4082 + 18.1335i −1.55685 + 0.898845i
\(408\) 0 0
\(409\) −17.2773 9.97503i −0.854306 0.493234i 0.00779552 0.999970i \(-0.497519\pi\)
−0.862101 + 0.506736i \(0.830852\pi\)
\(410\) −8.19752 3.23630i −0.404846 0.159830i
\(411\) 0 0
\(412\) 3.08419 + 2.88485i 0.151947 + 0.142126i
\(413\) 3.27562 3.27562i 0.161183 0.161183i
\(414\) 0 0
\(415\) −4.87092 −0.239104
\(416\) −7.92002 + 24.7895i −0.388311 + 1.21540i
\(417\) 0 0
\(418\) 8.22669 + 18.9596i 0.402380 + 0.927343i
\(419\) −7.85913 29.3307i −0.383943 1.43290i −0.839826 0.542856i \(-0.817343\pi\)
0.455882 0.890040i \(-0.349324\pi\)
\(420\) 0 0
\(421\) −2.70420 + 10.0922i −0.131795 + 0.491864i −0.999991 0.00435733i \(-0.998613\pi\)
0.868196 + 0.496222i \(0.165280\pi\)
\(422\) −0.401591 2.70118i −0.0195491 0.131491i
\(423\) 0 0
\(424\) 13.1034 + 27.6341i 0.636356 + 1.34203i
\(425\) 10.1085 5.83615i 0.490335 0.283095i
\(426\) 0 0
\(427\) 2.47354 0.662784i 0.119703 0.0320744i
\(428\) −10.8660 17.4484i −0.525230 0.843401i
\(429\) 0 0
\(430\) 0.123053 1.07276i 0.00593414 0.0517329i
\(431\) −11.3639 −0.547382 −0.273691 0.961818i \(-0.588244\pi\)
−0.273691 + 0.961818i \(0.588244\pi\)
\(432\) 0 0
\(433\) −9.65126 −0.463810 −0.231905 0.972738i \(-0.574496\pi\)
−0.231905 + 0.972738i \(0.574496\pi\)
\(434\) −0.440696 + 3.84192i −0.0211541 + 0.184418i
\(435\) 0 0
\(436\) 13.7613 8.56992i 0.659049 0.410425i
\(437\) −9.59925 + 2.57211i −0.459194 + 0.123041i
\(438\) 0 0
\(439\) −13.6132 + 7.85957i −0.649722 + 0.375117i −0.788350 0.615228i \(-0.789064\pi\)
0.138628 + 0.990345i \(0.455731\pi\)
\(440\) 4.96021 13.9061i 0.236469 0.662948i
\(441\) 0 0
\(442\) −2.63886 17.7495i −0.125518 0.844256i
\(443\) 4.97116 18.5526i 0.236187 0.881461i −0.741424 0.671037i \(-0.765849\pi\)
0.977610 0.210424i \(-0.0674843\pi\)
\(444\) 0 0
\(445\) −1.15929 4.32653i −0.0549556 0.205097i
\(446\) −7.38757 17.0257i −0.349812 0.806191i
\(447\) 0 0
\(448\) −5.17011 0.843106i −0.244265 0.0398330i
\(449\) −35.3101 −1.66639 −0.833194 0.552982i \(-0.813490\pi\)
−0.833194 + 0.552982i \(0.813490\pi\)
\(450\) 0 0
\(451\) −29.9474 + 29.9474i −1.41017 + 1.41017i
\(452\) −2.48099 + 2.65243i −0.116696 + 0.124760i
\(453\) 0 0
\(454\) −5.47882 2.16299i −0.257134 0.101514i
\(455\) −2.28636 1.32003i −0.107186 0.0618839i
\(456\) 0 0
\(457\) 0.565406 0.326437i 0.0264486 0.0152701i −0.486717 0.873559i \(-0.661806\pi\)
0.513166 + 0.858289i \(0.328473\pi\)
\(458\) 39.0701 5.80865i 1.82563 0.271420i
\(459\) 0 0
\(460\) 6.26326 + 3.34249i 0.292026 + 0.155844i
\(461\) 3.91317 + 1.04853i 0.182255 + 0.0488350i 0.348792 0.937200i \(-0.386592\pi\)
−0.166537 + 0.986035i \(0.553259\pi\)
\(462\) 0 0
\(463\) −21.0971 + 36.5413i −0.980466 + 1.69822i −0.319894 + 0.947453i \(0.603647\pi\)
−0.660571 + 0.750763i \(0.729686\pi\)
\(464\) −7.70880 6.74250i −0.357872 0.313013i
\(465\) 0 0
\(466\) 1.09286 9.52739i 0.0506258 0.441348i
\(467\) 0.180878 0.180878i 0.00837005 0.00837005i −0.702909 0.711279i \(-0.748116\pi\)
0.711279 + 0.702909i \(0.248116\pi\)
\(468\) 0 0
\(469\) −5.57625 5.57625i −0.257487 0.257487i
\(470\) −7.17668 9.03645i −0.331036 0.416820i
\(471\) 0 0
\(472\) −19.9446 1.61554i −0.918023 0.0743613i
\(473\) −4.49375 2.59447i −0.206623 0.119294i
\(474\) 0 0
\(475\) 2.68747 10.0298i 0.123310 0.460198i
\(476\) 3.45587 1.05081i 0.158399 0.0481638i
\(477\) 0 0
\(478\) 6.88896 9.29508i 0.315094 0.425147i
\(479\) −6.98122 12.0918i −0.318980 0.552490i 0.661295 0.750126i \(-0.270007\pi\)
−0.980276 + 0.197636i \(0.936674\pi\)
\(480\) 0 0
\(481\) 14.0062 24.2594i 0.638627 1.10613i
\(482\) −0.292079 0.673138i −0.0133038 0.0306606i
\(483\) 0 0
\(484\) −35.7487 33.4381i −1.62494 1.51992i
\(485\) 3.78855 + 3.78855i 0.172029 + 0.172029i
\(486\) 0 0
\(487\) 2.93338i 0.132924i 0.997789 + 0.0664621i \(0.0211712\pi\)
−0.997789 + 0.0664621i \(0.978829\pi\)
\(488\) −9.10168 6.28609i −0.412014 0.284558i
\(489\) 0 0
\(490\) −2.99077 + 7.57558i −0.135109 + 0.342230i
\(491\) −17.7814 + 4.76452i −0.802465 + 0.215020i −0.636666 0.771140i \(-0.719687\pi\)
−0.165799 + 0.986160i \(0.553020\pi\)
\(492\) 0 0
\(493\) 6.82126 + 1.82775i 0.307214 + 0.0823178i
\(494\) −12.8250 9.50515i −0.577025 0.427657i
\(495\) 0 0
\(496\) 13.8767 9.29856i 0.623082 0.417518i
\(497\) 1.42365 + 2.46583i 0.0638594 + 0.110608i
\(498\) 0 0
\(499\) −4.74054 17.6919i −0.212216 0.791999i −0.987128 0.159931i \(-0.948873\pi\)
0.774913 0.632068i \(-0.217794\pi\)
\(500\) −13.7360 + 8.55415i −0.614294 + 0.382553i
\(501\) 0 0
\(502\) 17.3651 + 21.8651i 0.775044 + 0.975889i
\(503\) 7.01136i 0.312621i 0.987708 + 0.156311i \(0.0499601\pi\)
−0.987708 + 0.156311i \(0.950040\pi\)
\(504\) 0 0
\(505\) 11.1977i 0.498292i
\(506\) 26.7156 21.2173i 1.18765 0.943225i
\(507\) 0 0
\(508\) 37.4076 + 8.69628i 1.65969 + 0.385835i
\(509\) −1.25064 4.66745i −0.0554336 0.206881i 0.932654 0.360771i \(-0.117486\pi\)
−0.988088 + 0.153890i \(0.950820\pi\)
\(510\) 0 0
\(511\) 0.214965 + 0.372331i 0.00950950 + 0.0164709i
\(512\) 11.6902 + 19.3736i 0.516641 + 0.856202i
\(513\) 0 0
\(514\) 14.6932 19.8251i 0.648090 0.874449i
\(515\) 1.78752 + 0.478965i 0.0787676 + 0.0211057i
\(516\) 0 0
\(517\) −53.5640 + 14.3524i −2.35574 + 0.631219i
\(518\) 5.24473 + 2.07057i 0.230440 + 0.0909756i
\(519\) 0 0
\(520\) 2.05255 + 11.2176i 0.0900101 + 0.491922i
\(521\) 28.0687i 1.22971i 0.788640 + 0.614855i \(0.210785\pi\)
−0.788640 + 0.614855i \(0.789215\pi\)
\(522\) 0 0
\(523\) 14.5264 + 14.5264i 0.635193 + 0.635193i 0.949366 0.314173i \(-0.101727\pi\)
−0.314173 + 0.949366i \(0.601727\pi\)
\(524\) 0.806982 + 24.1644i 0.0352532 + 1.05563i
\(525\) 0 0
\(526\) 13.5786 5.89183i 0.592054 0.256896i
\(527\) −5.75907 + 9.97501i −0.250869 + 0.434518i
\(528\) 0 0
\(529\) −3.29774 5.71185i −0.143380 0.248341i
\(530\) 10.7670 + 7.97988i 0.467689 + 0.346624i
\(531\) 0 0
\(532\) 1.51287 2.83487i 0.0655913 0.122907i
\(533\) 8.46657 31.5977i 0.366728 1.36865i
\(534\) 0 0
\(535\) −7.80063 4.50370i −0.337251 0.194712i
\(536\) −2.75021 + 33.9526i −0.118791 + 1.46653i
\(537\) 0 0
\(538\) −23.3173 + 18.5184i −1.00528 + 0.798386i
\(539\) 27.6753 + 27.6753i 1.19206 + 1.19206i
\(540\) 0 0
\(541\) 18.4081 18.4081i 0.791427 0.791427i −0.190299 0.981726i \(-0.560946\pi\)
0.981726 + 0.190299i \(0.0609458\pi\)
\(542\) −2.31539 0.265593i −0.0994547 0.0114082i
\(543\) 0 0
\(544\) −13.1270 8.43329i −0.562816 0.361575i
\(545\) 3.55201 6.15226i 0.152151 0.263534i
\(546\) 0 0
\(547\) −15.9583 4.27602i −0.682328 0.182829i −0.0990263 0.995085i \(-0.531573\pi\)
−0.583302 + 0.812256i \(0.698239\pi\)
\(548\) 6.36518 1.93543i 0.271907 0.0826775i
\(549\) 0 0
\(550\) 5.24197 + 35.2585i 0.223518 + 1.50343i
\(551\) 5.44055 3.14110i 0.231775 0.133816i
\(552\) 0 0
\(553\) 9.25660 + 5.34430i 0.393631 + 0.227263i
\(554\) 6.29591 15.9475i 0.267488 0.677543i
\(555\) 0 0
\(556\) 21.6328 0.722436i 0.917433 0.0306381i
\(557\) 15.4219 15.4219i 0.653447 0.653447i −0.300375 0.953821i \(-0.597112\pi\)
0.953821 + 0.300375i \(0.0971117\pi\)
\(558\) 0 0
\(559\) 4.00789 0.169516
\(560\) −2.17270 + 0.740721i −0.0918131 + 0.0313012i
\(561\) 0 0
\(562\) −3.41729 + 1.48279i −0.144150 + 0.0625476i
\(563\) −1.67165 6.23868i −0.0704516 0.262929i 0.921712 0.387875i \(-0.126791\pi\)
−0.992164 + 0.124946i \(0.960124\pi\)
\(564\) 0 0
\(565\) −0.411914 + 1.53728i −0.0173293 + 0.0646740i
\(566\) −15.0354 + 2.23535i −0.631986 + 0.0939589i
\(567\) 0 0
\(568\) 4.13197 11.5841i 0.173374 0.486059i
\(569\) −7.90864 + 4.56605i −0.331547 + 0.191419i −0.656528 0.754302i \(-0.727976\pi\)
0.324981 + 0.945721i \(0.394642\pi\)
\(570\) 0 0
\(571\) 27.5804 7.39016i 1.15421 0.309268i 0.369556 0.929208i \(-0.379510\pi\)
0.784649 + 0.619940i \(0.212843\pi\)
\(572\) 53.3776 + 12.4089i 2.23183 + 0.518841i
\(573\) 0 0
\(574\) 6.54182 + 0.750395i 0.273050 + 0.0313209i
\(575\) −17.1403 −0.714799
\(576\) 0 0
\(577\) 0.350515 0.0145921 0.00729607 0.999973i \(-0.497678\pi\)
0.00729607 + 0.999973i \(0.497678\pi\)
\(578\) −13.1965 1.51374i −0.548902 0.0629631i
\(579\) 0 0
\(580\) −4.37127 1.01620i −0.181507 0.0421956i
\(581\) 3.51526 0.941911i 0.145838 0.0390771i
\(582\) 0 0
\(583\) 55.7739 32.2011i 2.30992 1.33363i
\(584\) 0.623910 1.74915i 0.0258176 0.0723805i
\(585\) 0 0
\(586\) −5.73427 + 0.852527i −0.236881 + 0.0352176i
\(587\) −0.259943 + 0.970122i −0.0107290 + 0.0400412i −0.971083 0.238743i \(-0.923265\pi\)
0.960354 + 0.278784i \(0.0899314\pi\)
\(588\) 0 0
\(589\) 2.65198 + 9.89733i 0.109273 + 0.407812i
\(590\) −8.04383 + 3.49027i −0.331159 + 0.143692i
\(591\) 0 0
\(592\) −7.85943 23.0534i −0.323021 0.947489i
\(593\) −7.12791 −0.292708 −0.146354 0.989232i \(-0.546754\pi\)
−0.146354 + 0.989232i \(0.546754\pi\)
\(594\) 0 0
\(595\) 1.11923 1.11923i 0.0458841 0.0458841i
\(596\) 39.5717 1.32151i 1.62092 0.0541313i
\(597\) 0 0
\(598\) −9.67629 + 24.5099i −0.395693 + 1.00229i
\(599\) 1.83973 + 1.06217i 0.0751695 + 0.0433991i 0.537114 0.843510i \(-0.319515\pi\)
−0.461944 + 0.886909i \(0.652848\pi\)
\(600\) 0 0
\(601\) 32.6223 18.8345i 1.33069 0.768275i 0.345286 0.938497i \(-0.387782\pi\)
0.985406 + 0.170222i \(0.0544485\pi\)
\(602\) 0.118638 + 0.797984i 0.00483533 + 0.0325234i
\(603\) 0 0
\(604\) 11.2562 3.42262i 0.458007 0.139264i
\(605\) −20.7191 5.55166i −0.842351 0.225707i
\(606\) 0 0
\(607\) 10.2096 17.6835i 0.414393 0.717750i −0.580971 0.813924i \(-0.697327\pi\)
0.995365 + 0.0961740i \(0.0306605\pi\)
\(608\) −13.5622 + 2.95253i −0.550022 + 0.119741i
\(609\) 0 0
\(610\) −4.81559 0.552384i −0.194978 0.0223654i
\(611\) 30.2867 30.2867i 1.22527 1.22527i
\(612\) 0 0
\(613\) −10.2801 10.2801i −0.415208 0.415208i 0.468340 0.883548i \(-0.344852\pi\)
−0.883548 + 0.468340i \(0.844852\pi\)
\(614\) 8.46271 6.72103i 0.341527 0.271239i
\(615\) 0 0
\(616\) −0.890610 + 10.9950i −0.0358837 + 0.443000i
\(617\) 41.2817 + 23.8340i 1.66194 + 0.959521i 0.971788 + 0.235856i \(0.0757895\pi\)
0.690152 + 0.723665i \(0.257544\pi\)
\(618\) 0 0
\(619\) −1.41291 + 5.27305i −0.0567896 + 0.211942i −0.988490 0.151286i \(-0.951659\pi\)
0.931700 + 0.363228i \(0.118325\pi\)
\(620\) 3.44628 6.45775i 0.138406 0.259350i
\(621\) 0 0
\(622\) 17.7033 + 13.1206i 0.709838 + 0.526090i
\(623\) 1.67328 + 2.89820i 0.0670385 + 0.116114i
\(624\) 0 0
\(625\) 7.03430 12.1838i 0.281372 0.487350i
\(626\) 38.1394 16.5489i 1.52436 0.661428i
\(627\) 0 0
\(628\) 1.31304 + 39.3180i 0.0523961 + 1.56896i
\(629\) 11.8756 + 11.8756i 0.473513 + 0.473513i
\(630\) 0 0
\(631\) 20.7362i 0.825496i 0.910845 + 0.412748i \(0.135431\pi\)
−0.910845 + 0.412748i \(0.864569\pi\)
\(632\) −8.30999 45.4157i −0.330554 1.80654i
\(633\) 0 0
\(634\) −7.18534 2.83671i −0.285366 0.112660i
\(635\) 16.2558 4.35574i 0.645094 0.172852i
\(636\) 0 0
\(637\) −29.2004 7.82422i −1.15696 0.310007i
\(638\) −12.8413 + 17.3265i −0.508394 + 0.685961i
\(639\) 0 0
\(640\) 8.51647 + 5.07794i 0.336643 + 0.200723i
\(641\) −3.67059 6.35766i −0.144980 0.251112i 0.784386 0.620273i \(-0.212978\pi\)
−0.929365 + 0.369161i \(0.879645\pi\)
\(642\) 0 0
\(643\) −2.23207 8.33019i −0.0880241 0.328511i 0.907846 0.419305i \(-0.137726\pi\)
−0.995870 + 0.0907942i \(0.971059\pi\)
\(644\) −5.16644 1.20106i −0.203586 0.0473284i
\(645\) 0 0
\(646\) 7.49470 5.95223i 0.294875 0.234188i
\(647\) 11.6387i 0.457566i 0.973477 + 0.228783i \(0.0734746\pi\)
−0.973477 + 0.228783i \(0.926525\pi\)
\(648\) 0 0
\(649\) 42.1367i 1.65401i
\(650\) −17.1231 21.5604i −0.671623 0.845668i
\(651\) 0 0
\(652\) 12.0218 7.48661i 0.470810 0.293198i
\(653\) 5.20569 + 19.4279i 0.203715 + 0.760273i 0.989838 + 0.142203i \(0.0454186\pi\)
−0.786123 + 0.618070i \(0.787915\pi\)
\(654\) 0 0
\(655\) 5.29742 + 9.17541i 0.206988 + 0.358513i
\(656\) −15.8331 23.6286i −0.618180 0.922540i
\(657\) 0 0
\(658\) 6.92670 + 5.13366i 0.270031 + 0.200131i
\(659\) 14.5489 + 3.89836i 0.566744 + 0.151859i 0.530803 0.847495i \(-0.321890\pi\)
0.0359413 + 0.999354i \(0.488557\pi\)
\(660\) 0 0
\(661\) −9.83468 + 2.63519i −0.382525 + 0.102497i −0.444957 0.895552i \(-0.646781\pi\)
0.0624321 + 0.998049i \(0.480114\pi\)
\(662\) −13.4129 + 33.9748i −0.521308 + 1.32047i
\(663\) 0 0
\(664\) −12.9348 8.93344i −0.501968 0.346685i
\(665\) 1.40808i 0.0546030i
\(666\) 0 0
\(667\) −7.33276 7.33276i −0.283926 0.283926i
\(668\) −24.4594 22.8786i −0.946364 0.885198i
\(669\) 0 0
\(670\) 5.94166 + 13.6934i 0.229546 + 0.529022i
\(671\) −11.6465 + 20.1724i −0.449610 + 0.778747i
\(672\) 0 0
\(673\) 16.1240 + 27.9276i 0.621534 + 1.07653i 0.989200 + 0.146571i \(0.0468236\pi\)
−0.367666 + 0.929958i \(0.619843\pi\)
\(674\) −3.32922 + 4.49202i −0.128237 + 0.173026i
\(675\) 0 0
\(676\) −15.6216 + 4.74999i −0.600831 + 0.182692i
\(677\) −9.43821 + 35.2239i −0.362740 + 1.35376i 0.507719 + 0.861523i \(0.330489\pi\)
−0.870459 + 0.492241i \(0.836178\pi\)
\(678\) 0 0
\(679\) −3.46674 2.00152i −0.133041 0.0768113i
\(680\) −6.81477 0.552008i −0.261335 0.0211685i
\(681\) 0 0
\(682\) −21.8762 27.5452i −0.837682 1.05476i
\(683\) 1.95185 + 1.95185i 0.0746855 + 0.0746855i 0.743463 0.668777i \(-0.233182\pi\)
−0.668777 + 0.743463i \(0.733182\pi\)
\(684\) 0 0
\(685\) 2.06146 2.06146i 0.0787642 0.0787642i
\(686\) 1.43217 12.4855i 0.0546807 0.476697i
\(687\) 0 0
\(688\) 2.29424 2.62303i 0.0874670 0.100002i
\(689\) −24.8719 + 43.0793i −0.947542 + 1.64119i
\(690\) 0 0
\(691\) 1.50428 + 0.403069i 0.0572253 + 0.0153335i 0.287318 0.957835i \(-0.407236\pi\)
−0.230093 + 0.973169i \(0.573903\pi\)
\(692\) 29.7476 + 15.8753i 1.13083 + 0.603487i
\(693\) 0 0
\(694\) −6.60458 + 0.981917i −0.250706 + 0.0372731i
\(695\) 8.21412 4.74242i 0.311579 0.179890i
\(696\) 0 0
\(697\) 16.9849 + 9.80626i 0.643351 + 0.371439i
\(698\) −10.5481 4.16428i −0.399251 0.157620i
\(699\) 0 0
\(700\) 3.78588 4.04748i 0.143093 0.152980i
\(701\) 21.5819 21.5819i 0.815136 0.815136i −0.170263 0.985399i \(-0.554462\pi\)
0.985399 + 0.170263i \(0.0544617\pi\)
\(702\) 0 0
\(703\) 14.9404 0.563489
\(704\) 38.6762 27.8307i 1.45766 1.04891i
\(705\) 0 0
\(706\) −7.83363 18.0537i −0.294823 0.679461i
\(707\) −2.16535 8.08119i −0.0814363 0.303925i
\(708\) 0 0
\(709\) −5.51773 + 20.5925i −0.207223 + 0.773366i 0.781538 + 0.623858i \(0.214436\pi\)
−0.988760 + 0.149508i \(0.952231\pi\)
\(710\) −0.792553 5.33087i −0.0297440 0.200064i
\(711\) 0 0
\(712\) 4.85649 13.6153i 0.182005 0.510256i
\(713\) 14.6479 8.45696i 0.548568 0.316716i
\(714\) 0 0
\(715\) 23.1958 6.21528i 0.867472 0.232438i
\(716\) −15.7636 + 9.81685i −0.589115 + 0.366873i
\(717\) 0 0
\(718\) 0.0792239 0.690661i 0.00295661 0.0257752i
\(719\) −28.4354 −1.06046 −0.530230 0.847854i \(-0.677894\pi\)
−0.530230 + 0.847854i \(0.677894\pi\)
\(720\) 0 0
\(721\) −1.38264 −0.0514923
\(722\) −2.09185 + 18.2364i −0.0778505 + 0.678688i
\(723\) 0 0
\(724\) 23.1569 + 37.1847i 0.860619 + 1.38196i
\(725\) 10.4660 2.80436i 0.388697 0.104151i
\(726\) 0 0
\(727\) 23.2100 13.4003i 0.860812 0.496990i −0.00347239 0.999994i \(-0.501105\pi\)
0.864284 + 0.503004i \(0.167772\pi\)
\(728\) −3.65047 7.69860i −0.135296 0.285329i
\(729\) 0 0
\(730\) −0.119672 0.804940i −0.00442927 0.0297922i
\(731\) −0.621920 + 2.32104i −0.0230025 + 0.0858466i
\(732\) 0 0
\(733\) −6.44950 24.0699i −0.238218 0.889041i −0.976672 0.214737i \(-0.931110\pi\)
0.738454 0.674304i \(-0.235556\pi\)
\(734\) 4.47055 + 10.3030i 0.165011 + 0.380292i
\(735\) 0 0
\(736\) 10.5019 + 20.3630i 0.387107 + 0.750592i
\(737\) 71.7313 2.64226
\(738\) 0 0
\(739\) −9.91976 + 9.91976i −0.364904 + 0.364904i −0.865615 0.500711i \(-0.833072\pi\)
0.500711 + 0.865615i \(0.333072\pi\)
\(740\) −7.79467 7.29088i −0.286538 0.268018i
\(741\) 0 0
\(742\) −9.31347 3.67687i −0.341908 0.134982i
\(743\) 15.1283 + 8.73432i 0.555003 + 0.320431i 0.751137 0.660146i \(-0.229506\pi\)
−0.196134 + 0.980577i \(0.562839\pi\)
\(744\) 0 0
\(745\) 15.0257 8.67507i 0.550497 0.317830i
\(746\) 31.7000 4.71292i 1.16062 0.172552i
\(747\) 0 0
\(748\) −15.4690 + 28.9863i −0.565602 + 1.05984i
\(749\) 6.50048 + 1.74180i 0.237522 + 0.0636439i
\(750\) 0 0
\(751\) −1.95134 + 3.37983i −0.0712056 + 0.123332i −0.899430 0.437065i \(-0.856018\pi\)
0.828224 + 0.560397i \(0.189351\pi\)
\(752\) −2.48463 37.1587i −0.0906052 1.35504i
\(753\) 0 0
\(754\) 1.89831 16.5491i 0.0691322 0.602683i
\(755\) 3.64548 3.64548i 0.132673 0.132673i
\(756\) 0 0
\(757\) 16.8568 + 16.8568i 0.612670 + 0.612670i 0.943641 0.330971i \(-0.107376\pi\)
−0.330971 + 0.943641i \(0.607376\pi\)
\(758\) −30.5586 38.4775i −1.10994 1.39757i
\(759\) 0 0
\(760\) −4.63398 + 3.93951i −0.168092 + 0.142901i
\(761\) −34.1207 19.6996i −1.23688 0.714111i −0.268422 0.963302i \(-0.586502\pi\)
−0.968454 + 0.249191i \(0.919835\pi\)
\(762\) 0 0
\(763\) −1.37373 + 5.12685i −0.0497325 + 0.185604i
\(764\) 2.01357 + 6.62215i 0.0728483 + 0.239581i
\(765\) 0 0
\(766\) −6.19281 + 8.35579i −0.223755 + 0.301907i
\(767\) −16.2730 28.1857i −0.587584 1.01773i
\(768\) 0 0
\(769\) 10.1180 17.5249i 0.364866 0.631966i −0.623889 0.781513i \(-0.714448\pi\)
0.988755 + 0.149547i \(0.0477816\pi\)
\(770\) 1.92411 + 4.43437i 0.0693399 + 0.159804i
\(771\) 0 0
\(772\) 13.4818 14.4133i 0.485219 0.518747i
\(773\) 2.34590 + 2.34590i 0.0843761 + 0.0843761i 0.748035 0.663659i \(-0.230997\pi\)
−0.663659 + 0.748035i \(0.730997\pi\)
\(774\) 0 0
\(775\) 17.6725i 0.634816i
\(776\) 3.11222 + 17.0089i 0.111722 + 0.610582i
\(777\) 0 0
\(778\) 10.0004 25.3308i 0.358531 0.908153i
\(779\) 16.8527 4.51566i 0.603810 0.161790i
\(780\) 0 0
\(781\) −25.0166 6.70318i −0.895164 0.239859i
\(782\) −12.6926 9.40700i −0.453886 0.336394i
\(783\) 0 0
\(784\) −21.8359 + 14.6319i −0.779853 + 0.522567i
\(785\) 8.61946 + 14.9293i 0.307642 + 0.532851i
\(786\) 0 0
\(787\) −8.00353 29.8696i −0.285295 1.06474i −0.948623 0.316407i \(-0.897523\pi\)
0.663328 0.748328i \(-0.269143\pi\)
\(788\) −7.40552 11.8916i −0.263811 0.423620i
\(789\) 0 0
\(790\) −12.5825 15.8431i −0.447665 0.563673i
\(791\) 1.18908i 0.0422790i
\(792\) 0 0
\(793\) 17.9914i 0.638893i
\(794\) −36.5284 + 29.0106i −1.29635 + 1.02955i
\(795\) 0 0
\(796\) −8.78493 + 37.7890i −0.311374 + 1.33939i
\(797\) −5.59514 20.8814i −0.198190 0.739655i −0.991418 0.130730i \(-0.958268\pi\)
0.793228 0.608925i \(-0.208399\pi\)
\(798\) 0 0
\(799\) 12.8398 + 22.2392i 0.454240 + 0.786767i
\(800\) −23.9124 1.13530i −0.845429 0.0401390i
\(801\) 0 0
\(802\) 7.76452 10.4764i 0.274175 0.369936i
\(803\) −3.77741 1.01215i −0.133302 0.0357181i
\(804\) 0 0
\(805\) −2.24513 + 0.601580i −0.0791303 + 0.0212029i
\(806\) 25.2710 + 9.97676i 0.890134 + 0.351417i
\(807\) 0 0
\(808\) −20.5370 + 29.7357i −0.722488 + 1.04610i
\(809\) 16.4138i 0.577078i 0.957468 + 0.288539i \(0.0931695\pi\)
−0.957468 + 0.288539i \(0.906831\pi\)
\(810\) 0 0
\(811\) 2.03580 + 2.03580i 0.0714865 + 0.0714865i 0.741946 0.670460i \(-0.233903\pi\)
−0.670460 + 0.741946i \(0.733903\pi\)
\(812\) 3.35118 0.111914i 0.117603 0.00392742i
\(813\) 0 0
\(814\) −47.0510 + 20.4157i −1.64914 + 0.715571i
\(815\) 3.10301 5.37456i 0.108694 0.188263i
\(816\) 0 0
\(817\) 1.06881 + 1.85123i 0.0373928 + 0.0647663i
\(818\) −22.6670 16.7994i −0.792531 0.587377i
\(819\) 0 0
\(820\) −10.9959 5.86815i −0.383995 0.204925i
\(821\) −2.92634 + 10.9213i −0.102130 + 0.381155i −0.998004 0.0631541i \(-0.979884\pi\)
0.895874 + 0.444309i \(0.146551\pi\)
\(822\) 0 0
\(823\) −9.22371 5.32531i −0.321518 0.185629i 0.330551 0.943788i \(-0.392766\pi\)
−0.652069 + 0.758159i \(0.726099\pi\)
\(824\) 3.86835 + 4.55027i 0.134760 + 0.158516i
\(825\) 0 0
\(826\) 5.13016 4.07434i 0.178501 0.141764i
\(827\) −25.0775 25.0775i −0.872029 0.872029i 0.120665 0.992693i \(-0.461497\pi\)
−0.992693 + 0.120665i \(0.961497\pi\)
\(828\) 0 0
\(829\) 21.3779 21.3779i 0.742484 0.742484i −0.230571 0.973055i \(-0.574059\pi\)
0.973055 + 0.230571i \(0.0740594\pi\)
\(830\) −6.84365 0.785017i −0.237547 0.0272483i
\(831\) 0 0
\(832\) −15.1228 + 33.5528i −0.524289 + 1.16323i
\(833\) 9.06227 15.6963i 0.313989 0.543845i
\(834\) 0 0
\(835\) −14.1761 3.79848i −0.490584 0.131452i
\(836\) 8.50290 + 27.9641i 0.294079 + 0.967157i
\(837\) 0 0
\(838\) −6.31503 42.4762i −0.218149 1.46732i
\(839\) 26.6311 15.3755i 0.919407 0.530820i 0.0359612 0.999353i \(-0.488551\pi\)
0.883446 + 0.468533i \(0.155217\pi\)
\(840\) 0 0
\(841\) −19.4376 11.2223i −0.670261 0.386975i
\(842\) −5.42590 + 13.7437i −0.186989 + 0.473641i
\(843\) 0 0
\(844\) −0.128903 3.85988i −0.00443701 0.132863i
\(845\) −5.05928 + 5.05928i −0.174045 + 0.174045i
\(846\) 0 0
\(847\) 16.0262 0.550665
\(848\) 13.9566 + 40.9377i 0.479272 + 1.40581i
\(849\) 0 0
\(850\) 15.1430 6.57067i 0.519402 0.225372i
\(851\) −6.38307 23.8220i −0.218809 0.816606i
\(852\) 0 0
\(853\) −10.3808 + 38.7416i −0.355431 + 1.32649i 0.524511 + 0.851404i \(0.324248\pi\)
−0.879942 + 0.475082i \(0.842418\pi\)
\(854\) 3.58215 0.532566i 0.122579 0.0182240i
\(855\) 0 0
\(856\) −12.4548 26.2662i −0.425695 0.897762i
\(857\) −47.6428 + 27.5066i −1.62745 + 0.939606i −0.642594 + 0.766206i \(0.722142\pi\)
−0.984851 + 0.173400i \(0.944525\pi\)
\(858\) 0 0
\(859\) 30.6273 8.20655i 1.04499 0.280004i 0.304809 0.952413i \(-0.401407\pi\)
0.740179 + 0.672409i \(0.234741\pi\)
\(860\) 0.345779 1.48739i 0.0117910 0.0507196i
\(861\) 0 0
\(862\) −15.9663 1.83146i −0.543815 0.0623796i
\(863\) −3.26635 −0.111188 −0.0555940 0.998453i \(-0.517705\pi\)
−0.0555940 + 0.998453i \(0.517705\pi\)
\(864\) 0 0
\(865\) 14.7756 0.502386
\(866\) −13.5600 1.55543i −0.460788 0.0528558i
\(867\) 0 0
\(868\) −1.23836 + 5.32687i −0.0420325 + 0.180806i
\(869\) −93.9109 + 25.1634i −3.18571 + 0.853608i
\(870\) 0 0
\(871\) −47.9818 + 27.7023i −1.62580 + 0.938657i
\(872\) 20.7159 9.82291i 0.701527 0.332646i
\(873\) 0 0
\(874\) −13.9015 + 2.06676i −0.470225 + 0.0699094i
\(875\) 1.37121 5.11741i 0.0463553 0.173000i
\(876\) 0 0
\(877\) 9.53436 + 35.5827i 0.321952 + 1.20154i 0.917340 + 0.398104i \(0.130332\pi\)
−0.595388 + 0.803439i \(0.703002\pi\)
\(878\) −20.3932 + 8.84875i −0.688237 + 0.298631i
\(879\) 0 0
\(880\) 9.21025 18.7387i 0.310478 0.631681i
\(881\) 24.2794 0.817994 0.408997 0.912536i \(-0.365879\pi\)
0.408997 + 0.912536i \(0.365879\pi\)
\(882\) 0 0
\(883\) 17.8136 17.8136i 0.599475 0.599475i −0.340698 0.940173i \(-0.610663\pi\)
0.940173 + 0.340698i \(0.110663\pi\)
\(884\) −0.847019 25.3633i −0.0284883 0.853060i
\(885\) 0 0
\(886\) 9.97448 25.2652i 0.335099 0.848803i
\(887\) −3.04467 1.75784i −0.102230 0.0590225i 0.448013 0.894027i \(-0.352132\pi\)
−0.550243 + 0.835004i \(0.685465\pi\)
\(888\) 0 0
\(889\) −10.8893 + 6.28692i −0.365214 + 0.210857i
\(890\) −0.931523 6.26561i −0.0312247 0.210024i
\(891\) 0 0
\(892\) −7.63561 25.1117i −0.255659 0.840803i
\(893\) 22.0660 + 5.91258i 0.738412 + 0.197857i
\(894\) 0 0
\(895\) −4.06883 + 7.04742i −0.136006 + 0.235569i
\(896\) −7.12813 2.01780i −0.238134 0.0674099i
\(897\) 0 0
\(898\) −49.6107 5.69071i −1.65553 0.189902i
\(899\) −7.56046 + 7.56046i −0.252155 + 0.252155i
\(900\) 0 0
\(901\) −21.0885 21.0885i −0.702559 0.702559i
\(902\) −46.9025 + 37.2496i −1.56168 + 1.24028i
\(903\) 0 0
\(904\) −3.91327 + 3.32681i −0.130153 + 0.110648i
\(905\) 16.6241 + 9.59793i 0.552604 + 0.319046i
\(906\) 0 0
\(907\) 7.82207 29.1924i 0.259727 0.969316i −0.705672 0.708539i \(-0.749355\pi\)
0.965399 0.260777i \(-0.0839788\pi\)
\(908\) −7.34915 3.92198i −0.243890 0.130156i
\(909\) 0 0
\(910\) −2.99959 2.22312i −0.0994354 0.0736956i
\(911\) 25.9833 + 45.0044i 0.860866 + 1.49106i 0.871094 + 0.491116i \(0.163411\pi\)
−0.0102283 + 0.999948i \(0.503256\pi\)
\(912\) 0 0
\(913\) −16.5514 + 28.6679i −0.547772 + 0.948769i
\(914\) 0.847006 0.367522i 0.0280165 0.0121565i
\(915\) 0 0
\(916\) 55.8297 1.86446i 1.84466 0.0616034i
\(917\) −5.59735 5.59735i −0.184841 0.184841i
\(918\) 0 0
\(919\) 24.7771i 0.817322i −0.912686 0.408661i \(-0.865996\pi\)
0.912686 0.408661i \(-0.134004\pi\)
\(920\) 8.26120 + 5.70561i 0.272364 + 0.188108i
\(921\) 0 0
\(922\) 5.32902 + 2.10385i 0.175502 + 0.0692866i
\(923\) 19.3226 5.17748i 0.636011 0.170419i
\(924\) 0 0
\(925\) 24.8904 + 6.66936i 0.818391 + 0.219287i
\(926\) −35.5306 + 47.9404i −1.16761 + 1.57542i
\(927\) 0 0
\(928\) −9.74422 10.7156i −0.319870 0.351757i
\(929\) −18.9049 32.7442i −0.620249 1.07430i −0.989439 0.144949i \(-0.953698\pi\)
0.369190 0.929354i \(-0.379635\pi\)
\(930\) 0 0
\(931\) −4.17306 15.5741i −0.136767 0.510420i
\(932\) 3.07094 13.2099i 0.100592 0.432703i
\(933\) 0 0
\(934\) 0.283285 0.224983i 0.00926937 0.00736167i
\(935\) 14.3975i 0.470849i
\(936\) 0 0
\(937\) 18.8873i 0.617022i 0.951221 + 0.308511i \(0.0998307\pi\)
−0.951221 + 0.308511i \(0.900169\pi\)
\(938\) −6.93594 8.73332i −0.226466 0.285153i
\(939\) 0 0
\(940\) −8.62689 13.8528i −0.281378 0.451830i
\(941\) −2.22556 8.30590i −0.0725511 0.270765i 0.920116 0.391647i \(-0.128094\pi\)
−0.992667 + 0.120882i \(0.961428\pi\)
\(942\) 0 0
\(943\) −14.4001 24.9417i −0.468931 0.812213i
\(944\) −27.7618 5.48418i −0.903568 0.178495i
\(945\) 0 0
\(946\) −5.89559 4.36946i −0.191682 0.142063i
\(947\) 29.3101 + 7.85363i 0.952452 + 0.255209i 0.701402 0.712766i \(-0.252558\pi\)
0.251049 + 0.967974i \(0.419224\pi\)
\(948\) 0 0
\(949\) 2.91764 0.781778i 0.0947105 0.0253776i
\(950\) 5.39234 13.6587i 0.174951 0.443148i
\(951\) 0 0
\(952\) 5.02485 0.919428i 0.162856 0.0297988i
\(953\) 53.9237i 1.74676i 0.487038 + 0.873381i \(0.338077\pi\)
−0.487038 + 0.873381i \(0.661923\pi\)
\(954\) 0 0
\(955\) 2.14468 + 2.14468i 0.0694002 + 0.0694002i
\(956\) 11.1770 11.9493i 0.361491 0.386469i
\(957\) 0 0
\(958\) −7.85985 18.1141i −0.253940 0.585241i
\(959\) −1.08908 + 1.88635i −0.0351684 + 0.0609134i
\(960\) 0 0
\(961\) 6.78043 + 11.7441i 0.218724 + 0.378840i
\(962\) 23.5884 31.8272i 0.760521 1.02615i
\(963\) 0 0
\(964\) −0.301886 0.992831i −0.00972309 0.0319769i
\(965\) 2.23835 8.35362i 0.0720549 0.268913i
\(966\) 0 0
\(967\) 17.5688 + 10.1433i 0.564973 + 0.326187i 0.755139 0.655565i \(-0.227569\pi\)
−0.190166 + 0.981752i \(0.560903\pi\)
\(968\) −44.8379 52.7420i −1.44114 1.69519i
\(969\) 0 0
\(970\) 4.71233 + 5.93349i 0.151304 + 0.190513i
\(971\) −8.82647 8.82647i −0.283255 0.283255i 0.551151 0.834406i \(-0.314189\pi\)
−0.834406 + 0.551151i \(0.814189\pi\)
\(972\) 0 0
\(973\) −5.01092 + 5.01092i −0.160643 + 0.160643i
\(974\) −0.472755 + 4.12140i −0.0151481 + 0.132058i
\(975\) 0 0
\(976\) −11.7748 10.2988i −0.376901 0.329657i
\(977\) −21.4183 + 37.0976i −0.685233 + 1.18686i 0.288131 + 0.957591i \(0.406966\pi\)
−0.973364 + 0.229267i \(0.926367\pi\)
\(978\) 0 0
\(979\) −29.4031 7.87854i −0.939728 0.251799i
\(980\) −5.42294 + 10.1617i −0.173230 + 0.324603i
\(981\) 0 0
\(982\) −25.7508 + 3.82843i −0.821741 + 0.122170i
\(983\) 16.9469 9.78431i 0.540523 0.312071i −0.204768 0.978811i \(-0.565644\pi\)
0.745291 + 0.666740i \(0.232311\pi\)
\(984\) 0 0
\(985\) −5.31635 3.06940i −0.169393 0.0977991i
\(986\) 9.28931 + 3.66733i 0.295832 + 0.116792i
\(987\) 0 0
\(988\) −16.4873 15.4217i −0.524530 0.490628i
\(989\) 2.49508 2.49508i 0.0793390 0.0793390i
\(990\) 0 0
\(991\) −26.7726 −0.850459 −0.425230 0.905086i \(-0.639807\pi\)
−0.425230 + 0.905086i \(0.639807\pi\)
\(992\) 20.9954 10.8281i 0.666604 0.343791i
\(993\) 0 0
\(994\) 1.60282 + 3.69394i 0.0508385 + 0.117165i
\(995\) 4.40015 + 16.4216i 0.139494 + 0.520599i
\(996\) 0 0
\(997\) 2.37990 8.88189i 0.0753720 0.281292i −0.917945 0.396707i \(-0.870153\pi\)
0.993317 + 0.115415i \(0.0368196\pi\)
\(998\) −3.80916 25.6212i −0.120577 0.811024i
\(999\) 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 432.2.y.e.37.18 72
3.2 odd 2 144.2.x.e.85.1 yes 72
4.3 odd 2 1728.2.bc.e.1009.12 72
9.2 odd 6 144.2.x.e.133.11 yes 72
9.7 even 3 inner 432.2.y.e.181.8 72
12.11 even 2 576.2.bb.e.49.17 72
16.3 odd 4 1728.2.bc.e.145.7 72
16.13 even 4 inner 432.2.y.e.253.8 72
36.7 odd 6 1728.2.bc.e.1585.7 72
36.11 even 6 576.2.bb.e.241.9 72
48.29 odd 4 144.2.x.e.13.11 72
48.35 even 4 576.2.bb.e.337.9 72
144.29 odd 12 144.2.x.e.61.1 yes 72
144.61 even 12 inner 432.2.y.e.397.18 72
144.83 even 12 576.2.bb.e.529.17 72
144.115 odd 12 1728.2.bc.e.721.12 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.11 72 48.29 odd 4
144.2.x.e.61.1 yes 72 144.29 odd 12
144.2.x.e.85.1 yes 72 3.2 odd 2
144.2.x.e.133.11 yes 72 9.2 odd 6
432.2.y.e.37.18 72 1.1 even 1 trivial
432.2.y.e.181.8 72 9.7 even 3 inner
432.2.y.e.253.8 72 16.13 even 4 inner
432.2.y.e.397.18 72 144.61 even 12 inner
576.2.bb.e.49.17 72 12.11 even 2
576.2.bb.e.241.9 72 36.11 even 6
576.2.bb.e.337.9 72 48.35 even 4
576.2.bb.e.529.17 72 144.83 even 12
1728.2.bc.e.145.7 72 16.3 odd 4
1728.2.bc.e.721.12 72 144.115 odd 12
1728.2.bc.e.1009.12 72 4.3 odd 2
1728.2.bc.e.1585.7 72 36.7 odd 6