Properties

Label 605.2.j.g.444.4
Level $605$
Weight $2$
Character 605.444
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
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] = [605,2,Mod(9,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 444.4
Root \(0.972539 + 1.33858i\) of defining polynomial
Character \(\chi\) \(=\) 605.444
Dual form 605.2.j.g.124.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.972539 - 1.33858i) q^{2} +(-1.87813 - 0.610243i) q^{3} +(-0.227943 - 0.701538i) q^{4} +(-1.51945 + 1.64051i) q^{5} +(-2.64342 + 1.92056i) q^{6} +(2.13329 - 0.693148i) q^{7} +(1.98645 + 0.645437i) q^{8} +(0.727943 + 0.528882i) q^{9} +O(q^{10})\) \(q+(0.972539 - 1.33858i) q^{2} +(-1.87813 - 0.610243i) q^{3} +(-0.227943 - 0.701538i) q^{4} +(-1.51945 + 1.64051i) q^{5} +(-2.64342 + 1.92056i) q^{6} +(2.13329 - 0.693148i) q^{7} +(1.98645 + 0.645437i) q^{8} +(0.727943 + 0.528882i) q^{9} +(0.718246 + 3.62937i) q^{10} +1.45668i q^{12} +(2.17466 - 2.99317i) q^{13} +(1.14687 - 3.52970i) q^{14} +(3.85484 - 2.15387i) q^{15} +(3.98940 - 2.89847i) q^{16} +(1.30759 + 1.79974i) q^{17} +(1.41591 - 0.460056i) q^{18} +(1.63372 - 5.02809i) q^{19} +(1.49723 + 0.692004i) q^{20} -4.42960 q^{21} -3.85415i q^{23} +(-3.33695 - 2.42443i) q^{24} +(-0.382569 - 4.98534i) q^{25} +(-1.89166 - 5.82194i) q^{26} +(2.43782 + 3.35538i) q^{27} +(-0.972539 - 1.33858i) q^{28} +(0.0582308 + 0.179216i) q^{29} +(0.865834 - 7.25475i) q^{30} +(-0.555687 - 0.403730i) q^{31} -3.98166i q^{32} +3.68079 q^{34} +(-2.10430 + 4.55289i) q^{35} +(0.205101 - 0.631235i) q^{36} +(2.46624 - 0.801331i) q^{37} +(-5.14166 - 7.07689i) q^{38} +(-5.91087 + 4.29450i) q^{39} +(-4.07715 + 2.27809i) q^{40} +(-2.44619 + 7.52860i) q^{41} +(-4.30795 + 5.92939i) q^{42} -8.41368i q^{43} +(-1.97371 + 0.390594i) q^{45} +(-5.15911 - 3.74831i) q^{46} +(11.4252 + 3.71227i) q^{47} +(-9.26140 + 3.00921i) q^{48} +(-1.59265 + 1.15713i) q^{49} +(-7.04537 - 4.33634i) q^{50} +(-1.35755 - 4.17811i) q^{51} +(-2.59552 - 0.843335i) q^{52} +(7.43935 - 10.2394i) q^{53} +6.86233 q^{54} +4.68506 q^{56} +(-6.13671 + 8.44645i) q^{57} +(0.296528 + 0.0963477i) q^{58} +(0.106206 + 0.326867i) q^{59} +(-2.38971 - 2.21335i) q^{60} +(1.40233 - 1.01885i) q^{61} +(-1.08085 + 0.351191i) q^{62} +(1.91951 + 0.623686i) q^{63} +(2.64900 + 1.92461i) q^{64} +(1.60605 + 8.11552i) q^{65} -0.650461i q^{67} +(0.964532 - 1.32756i) q^{68} +(-2.35197 + 7.23862i) q^{69} +(4.04792 + 7.24465i) q^{70} +(-3.75999 + 2.73179i) q^{71} +(1.10466 + 1.52044i) q^{72} +(-8.42484 + 2.73740i) q^{73} +(1.32587 - 4.08060i) q^{74} +(-2.32375 + 9.59661i) q^{75} -3.89979 q^{76} +12.0888i q^{78} +(5.85264 + 4.25219i) q^{79} +(-1.30670 + 10.9487i) q^{80} +(-3.36512 - 10.3568i) q^{81} +(7.69865 + 10.5963i) q^{82} +(1.87013 + 2.57401i) q^{83} +(1.00970 + 3.10753i) q^{84} +(-4.93932 - 0.589494i) q^{85} +(-11.2624 - 8.18263i) q^{86} -0.372127i q^{87} -9.92195 q^{89} +(-1.39666 + 3.02184i) q^{90} +(2.56448 - 7.89265i) q^{91} +(-2.70383 + 0.878529i) q^{92} +(0.797281 + 1.09736i) q^{93} +(16.0806 - 11.6833i) q^{94} +(5.76629 + 10.3200i) q^{95} +(-2.42978 + 7.47810i) q^{96} +(-1.33316 + 1.83494i) q^{97} +3.25724i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35} - 30 q^{36} - 12 q^{40} - 18 q^{41} + 12 q^{45} - 38 q^{46} - 20 q^{49} + 12 q^{50} + 12 q^{51} + 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} - 20 q^{61} + 22 q^{64} + 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} + 52 q^{74} + 40 q^{75} - 56 q^{76} + 22 q^{79} - 6 q^{80} - 32 q^{81} + 18 q^{84} + 62 q^{85} - 68 q^{86} + 24 q^{89} + 32 q^{90} + 56 q^{94} + 22 q^{95} - 94 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.972539 1.33858i 0.687689 0.946522i −0.312305 0.949982i \(-0.601101\pi\)
0.999994 + 0.00345950i \(0.00110120\pi\)
\(3\) −1.87813 0.610243i −1.08434 0.352324i −0.288284 0.957545i \(-0.593085\pi\)
−0.796058 + 0.605221i \(0.793085\pi\)
\(4\) −0.227943 0.701538i −0.113972 0.350769i
\(5\) −1.51945 + 1.64051i −0.679517 + 0.733660i
\(6\) −2.64342 + 1.92056i −1.07917 + 0.784064i
\(7\) 2.13329 0.693148i 0.806308 0.261985i 0.123275 0.992373i \(-0.460660\pi\)
0.683033 + 0.730387i \(0.260660\pi\)
\(8\) 1.98645 + 0.645437i 0.702316 + 0.228196i
\(9\) 0.727943 + 0.528882i 0.242648 + 0.176294i
\(10\) 0.718246 + 3.62937i 0.227129 + 1.14771i
\(11\) 0 0
\(12\) 1.45668i 0.420508i
\(13\) 2.17466 2.99317i 0.603143 0.830155i −0.392849 0.919603i \(-0.628510\pi\)
0.995991 + 0.0894482i \(0.0285104\pi\)
\(14\) 1.14687 3.52970i 0.306514 0.943353i
\(15\) 3.85484 2.15387i 0.995314 0.556128i
\(16\) 3.98940 2.89847i 0.997350 0.724617i
\(17\) 1.30759 + 1.79974i 0.317137 + 0.436502i 0.937591 0.347741i \(-0.113051\pi\)
−0.620453 + 0.784244i \(0.713051\pi\)
\(18\) 1.41591 0.460056i 0.333732 0.108436i
\(19\) 1.63372 5.02809i 0.374802 1.15352i −0.568810 0.822469i \(-0.692596\pi\)
0.943612 0.331053i \(-0.107404\pi\)
\(20\) 1.49723 + 0.692004i 0.334791 + 0.154737i
\(21\) −4.42960 −0.966617
\(22\) 0 0
\(23\) 3.85415i 0.803647i −0.915717 0.401823i \(-0.868377\pi\)
0.915717 0.401823i \(-0.131623\pi\)
\(24\) −3.33695 2.42443i −0.681152 0.494886i
\(25\) −0.382569 4.98534i −0.0765139 0.997069i
\(26\) −1.89166 5.82194i −0.370986 1.14178i
\(27\) 2.43782 + 3.35538i 0.469159 + 0.645743i
\(28\) −0.972539 1.33858i −0.183793 0.252969i
\(29\) 0.0582308 + 0.179216i 0.0108132 + 0.0332796i 0.956318 0.292330i \(-0.0944305\pi\)
−0.945504 + 0.325609i \(0.894431\pi\)
\(30\) 0.865834 7.25475i 0.158079 1.32453i
\(31\) −0.555687 0.403730i −0.0998043 0.0725121i 0.536764 0.843733i \(-0.319647\pi\)
−0.636568 + 0.771220i \(0.719647\pi\)
\(32\) 3.98166i 0.703866i
\(33\) 0 0
\(34\) 3.68079 0.631251
\(35\) −2.10430 + 4.55289i −0.355692 + 0.769579i
\(36\) 0.205101 0.631235i 0.0341834 0.105206i
\(37\) 2.46624 0.801331i 0.405448 0.131738i −0.0991914 0.995068i \(-0.531626\pi\)
0.504639 + 0.863330i \(0.331626\pi\)
\(38\) −5.14166 7.07689i −0.834087 1.14802i
\(39\) −5.91087 + 4.29450i −0.946496 + 0.687670i
\(40\) −4.07715 + 2.27809i −0.644654 + 0.360198i
\(41\) −2.44619 + 7.52860i −0.382031 + 1.17577i 0.556581 + 0.830793i \(0.312113\pi\)
−0.938611 + 0.344976i \(0.887887\pi\)
\(42\) −4.30795 + 5.92939i −0.664732 + 0.914924i
\(43\) 8.41368i 1.28307i −0.767092 0.641537i \(-0.778297\pi\)
0.767092 0.641537i \(-0.221703\pi\)
\(44\) 0 0
\(45\) −1.97371 + 0.390594i −0.294223 + 0.0582263i
\(46\) −5.15911 3.74831i −0.760669 0.552659i
\(47\) 11.4252 + 3.71227i 1.66654 + 0.541491i 0.982227 0.187699i \(-0.0601031\pi\)
0.684311 + 0.729190i \(0.260103\pi\)
\(48\) −9.26140 + 3.00921i −1.33677 + 0.434342i
\(49\) −1.59265 + 1.15713i −0.227521 + 0.165304i
\(50\) −7.04537 4.33634i −0.996365 0.613251i
\(51\) −1.35755 4.17811i −0.190095 0.585053i
\(52\) −2.59552 0.843335i −0.359934 0.116950i
\(53\) 7.43935 10.2394i 1.02187 1.40649i 0.110991 0.993821i \(-0.464597\pi\)
0.910882 0.412667i \(-0.135403\pi\)
\(54\) 6.86233 0.933845
\(55\) 0 0
\(56\) 4.68506 0.626067
\(57\) −6.13671 + 8.44645i −0.812827 + 1.11876i
\(58\) 0.296528 + 0.0963477i 0.0389360 + 0.0126511i
\(59\) 0.106206 + 0.326867i 0.0138268 + 0.0425545i 0.957732 0.287662i \(-0.0928781\pi\)
−0.943905 + 0.330217i \(0.892878\pi\)
\(60\) −2.38971 2.21335i −0.308510 0.285742i
\(61\) 1.40233 1.01885i 0.179550 0.130451i −0.494380 0.869246i \(-0.664605\pi\)
0.673930 + 0.738795i \(0.264605\pi\)
\(62\) −1.08085 + 0.351191i −0.137269 + 0.0446013i
\(63\) 1.91951 + 0.623686i 0.241835 + 0.0785770i
\(64\) 2.64900 + 1.92461i 0.331125 + 0.240577i
\(65\) 1.60605 + 8.11552i 0.199206 + 1.00661i
\(66\) 0 0
\(67\) 0.650461i 0.0794664i −0.999210 0.0397332i \(-0.987349\pi\)
0.999210 0.0397332i \(-0.0126508\pi\)
\(68\) 0.964532 1.32756i 0.116967 0.160991i
\(69\) −2.35197 + 7.23862i −0.283144 + 0.871428i
\(70\) 4.04792 + 7.24465i 0.483819 + 0.865901i
\(71\) −3.75999 + 2.73179i −0.446229 + 0.324204i −0.788105 0.615541i \(-0.788938\pi\)
0.341876 + 0.939745i \(0.388938\pi\)
\(72\) 1.10466 + 1.52044i 0.130186 + 0.179185i
\(73\) −8.42484 + 2.73740i −0.986053 + 0.320388i −0.757279 0.653091i \(-0.773472\pi\)
−0.228774 + 0.973479i \(0.573472\pi\)
\(74\) 1.32587 4.08060i 0.154129 0.474360i
\(75\) −2.32375 + 9.59661i −0.268324 + 1.10812i
\(76\) −3.89979 −0.447336
\(77\) 0 0
\(78\) 12.0888i 1.36878i
\(79\) 5.85264 + 4.25219i 0.658473 + 0.478409i 0.866147 0.499789i \(-0.166589\pi\)
−0.207674 + 0.978198i \(0.566589\pi\)
\(80\) −1.30670 + 10.9487i −0.146093 + 1.22410i
\(81\) −3.36512 10.3568i −0.373902 1.15075i
\(82\) 7.69865 + 10.5963i 0.850174 + 1.17016i
\(83\) 1.87013 + 2.57401i 0.205273 + 0.282534i 0.899224 0.437488i \(-0.144132\pi\)
−0.693951 + 0.720022i \(0.744132\pi\)
\(84\) 1.00970 + 3.10753i 0.110167 + 0.339059i
\(85\) −4.93932 0.589494i −0.535744 0.0639396i
\(86\) −11.2624 8.18263i −1.21446 0.882356i
\(87\) 0.372127i 0.0398962i
\(88\) 0 0
\(89\) −9.92195 −1.05172 −0.525862 0.850570i \(-0.676257\pi\)
−0.525862 + 0.850570i \(0.676257\pi\)
\(90\) −1.39666 + 3.02184i −0.147221 + 0.318530i
\(91\) 2.56448 7.89265i 0.268830 0.827375i
\(92\) −2.70383 + 0.878529i −0.281894 + 0.0915930i
\(93\) 0.797281 + 1.09736i 0.0826742 + 0.113791i
\(94\) 16.0806 11.6833i 1.65859 1.20504i
\(95\) 5.76629 + 10.3200i 0.591609 + 1.05881i
\(96\) −2.42978 + 7.47810i −0.247989 + 0.763231i
\(97\) −1.33316 + 1.83494i −0.135362 + 0.186310i −0.871317 0.490721i \(-0.836734\pi\)
0.735955 + 0.677031i \(0.236734\pi\)
\(98\) 3.25724i 0.329031i
\(99\) 0 0
\(100\) −3.41020 + 1.40476i −0.341020 + 0.140476i
\(101\) 8.00673 + 5.81723i 0.796699 + 0.578836i 0.909944 0.414731i \(-0.136124\pi\)
−0.113245 + 0.993567i \(0.536124\pi\)
\(102\) −6.91303 2.24618i −0.684492 0.222405i
\(103\) −9.73989 + 3.16468i −0.959700 + 0.311825i −0.746651 0.665216i \(-0.768339\pi\)
−0.213049 + 0.977041i \(0.568339\pi\)
\(104\) 6.25176 4.54217i 0.613035 0.445396i
\(105\) 6.73053 7.26681i 0.656832 0.709168i
\(106\) −6.47123 19.9164i −0.628542 1.93445i
\(107\) 9.55508 + 3.10463i 0.923724 + 0.300136i 0.731994 0.681311i \(-0.238590\pi\)
0.191731 + 0.981448i \(0.438590\pi\)
\(108\) 1.79824 2.47506i 0.173035 0.238163i
\(109\) −8.80173 −0.843053 −0.421527 0.906816i \(-0.638506\pi\)
−0.421527 + 0.906816i \(0.638506\pi\)
\(110\) 0 0
\(111\) −5.12094 −0.486058
\(112\) 6.50148 8.94851i 0.614332 0.845555i
\(113\) 0.220029 + 0.0714918i 0.0206986 + 0.00672538i 0.319348 0.947638i \(-0.396536\pi\)
−0.298649 + 0.954363i \(0.596536\pi\)
\(114\) 5.33811 + 16.4290i 0.499960 + 1.53872i
\(115\) 6.32279 + 5.85618i 0.589603 + 0.546091i
\(116\) 0.112453 0.0817022i 0.0104410 0.00758586i
\(117\) 3.16606 1.02872i 0.292703 0.0951048i
\(118\) 0.540828 + 0.175726i 0.0497873 + 0.0161769i
\(119\) 4.03696 + 2.93302i 0.370068 + 0.268870i
\(120\) 9.04763 1.79051i 0.825932 0.163451i
\(121\) 0 0
\(122\) 2.86801i 0.259658i
\(123\) 9.18855 12.6470i 0.828504 1.14034i
\(124\) −0.156567 + 0.481863i −0.0140601 + 0.0432726i
\(125\) 8.75982 + 6.94735i 0.783502 + 0.621390i
\(126\) 2.70165 1.96286i 0.240682 0.174866i
\(127\) 1.42852 + 1.96619i 0.126761 + 0.174471i 0.867680 0.497123i \(-0.165610\pi\)
−0.740920 + 0.671594i \(0.765610\pi\)
\(128\) 12.7261 4.13496i 1.12484 0.365482i
\(129\) −5.13439 + 15.8020i −0.452058 + 1.39129i
\(130\) 12.4253 + 5.74282i 1.08977 + 0.503679i
\(131\) −1.58846 −0.138785 −0.0693924 0.997589i \(-0.522106\pi\)
−0.0693924 + 0.997589i \(0.522106\pi\)
\(132\) 0 0
\(133\) 11.8588i 1.02829i
\(134\) −0.870697 0.632598i −0.0752167 0.0546482i
\(135\) −9.20868 1.09903i −0.792557 0.0945894i
\(136\) 1.43584 + 4.41907i 0.123123 + 0.378932i
\(137\) −10.9927 15.1301i −0.939169 1.29266i −0.956174 0.292800i \(-0.905413\pi\)
0.0170046 0.999855i \(-0.494587\pi\)
\(138\) 7.40212 + 10.1881i 0.630111 + 0.867273i
\(139\) 3.59306 + 11.0583i 0.304759 + 0.937953i 0.979767 + 0.200142i \(0.0641403\pi\)
−0.675008 + 0.737811i \(0.735860\pi\)
\(140\) 3.67369 + 0.438444i 0.310483 + 0.0370553i
\(141\) −19.1927 13.9443i −1.61632 1.17432i
\(142\) 7.68984i 0.645317i
\(143\) 0 0
\(144\) 4.43700 0.369750
\(145\) −0.382485 0.176781i −0.0317636 0.0146808i
\(146\) −4.52925 + 13.9396i −0.374843 + 1.15365i
\(147\) 3.69733 1.20134i 0.304951 0.0990846i
\(148\) −1.12433 1.54750i −0.0924191 0.127204i
\(149\) −4.78576 + 3.47706i −0.392065 + 0.284852i −0.766301 0.642482i \(-0.777905\pi\)
0.374236 + 0.927333i \(0.377905\pi\)
\(150\) 10.5859 + 12.4436i 0.864338 + 1.01602i
\(151\) −3.94858 + 12.1525i −0.321331 + 0.988954i 0.651739 + 0.758443i \(0.274040\pi\)
−0.973070 + 0.230511i \(0.925960\pi\)
\(152\) 6.49062 8.93357i 0.526459 0.724609i
\(153\) 2.00167i 0.161826i
\(154\) 0 0
\(155\) 1.50666 0.298166i 0.121018 0.0239492i
\(156\) 4.36009 + 3.16779i 0.349087 + 0.253627i
\(157\) −13.6464 4.43398i −1.08910 0.353870i −0.291202 0.956662i \(-0.594055\pi\)
−0.797899 + 0.602791i \(0.794055\pi\)
\(158\) 11.3838 3.69883i 0.905649 0.294263i
\(159\) −20.2206 + 14.6911i −1.60360 + 1.16508i
\(160\) 6.53197 + 6.04992i 0.516398 + 0.478288i
\(161\) −2.67150 8.22203i −0.210544 0.647986i
\(162\) −17.1361 5.56786i −1.34634 0.437452i
\(163\) −2.13199 + 2.93443i −0.166990 + 0.229843i −0.884308 0.466903i \(-0.845370\pi\)
0.717318 + 0.696746i \(0.245370\pi\)
\(164\) 5.83919 0.455964
\(165\) 0 0
\(166\) 5.26430 0.408589
\(167\) −2.24575 + 3.09101i −0.173781 + 0.239190i −0.887019 0.461733i \(-0.847228\pi\)
0.713238 + 0.700922i \(0.247228\pi\)
\(168\) −8.79917 2.85902i −0.678871 0.220578i
\(169\) −0.212666 0.654519i −0.0163589 0.0503476i
\(170\) −5.59277 + 6.03839i −0.428946 + 0.463124i
\(171\) 3.84852 2.79611i 0.294304 0.213824i
\(172\) −5.90252 + 1.91784i −0.450063 + 0.146234i
\(173\) −2.00401 0.651143i −0.152362 0.0495055i 0.231843 0.972753i \(-0.425524\pi\)
−0.384205 + 0.923248i \(0.625524\pi\)
\(174\) −0.498123 0.361908i −0.0377626 0.0274362i
\(175\) −4.27171 10.3700i −0.322911 0.783899i
\(176\) 0 0
\(177\) 0.678711i 0.0510151i
\(178\) −9.64948 + 13.2814i −0.723259 + 0.995481i
\(179\) −1.55249 + 4.77808i −0.116039 + 0.357131i −0.992162 0.124956i \(-0.960121\pi\)
0.876124 + 0.482087i \(0.160121\pi\)
\(180\) 0.723910 + 1.29560i 0.0539571 + 0.0965681i
\(181\) 12.6592 9.19743i 0.940949 0.683640i −0.00769972 0.999970i \(-0.502451\pi\)
0.948649 + 0.316331i \(0.102451\pi\)
\(182\) −8.07093 11.1087i −0.598257 0.823430i
\(183\) −3.25552 + 1.05778i −0.240655 + 0.0781934i
\(184\) 2.48761 7.65608i 0.183389 0.564414i
\(185\) −2.43273 + 5.26348i −0.178858 + 0.386979i
\(186\) 2.24430 0.164560
\(187\) 0 0
\(188\) 8.86140i 0.646284i
\(189\) 7.52636 + 5.46822i 0.547462 + 0.397754i
\(190\) 19.4222 + 2.31798i 1.40903 + 0.168164i
\(191\) 0.962852 + 2.96335i 0.0696695 + 0.214421i 0.979829 0.199837i \(-0.0640413\pi\)
−0.910160 + 0.414258i \(0.864041\pi\)
\(192\) −3.80070 5.23122i −0.274292 0.377530i
\(193\) −5.66412 7.79599i −0.407712 0.561168i 0.554946 0.831886i \(-0.312739\pi\)
−0.962659 + 0.270718i \(0.912739\pi\)
\(194\) 1.15967 + 3.56910i 0.0832595 + 0.256246i
\(195\) 1.93606 16.2221i 0.138644 1.16169i
\(196\) 1.17480 + 0.853543i 0.0839143 + 0.0609673i
\(197\) 14.3974i 1.02577i 0.858457 + 0.512885i \(0.171423\pi\)
−0.858457 + 0.512885i \(0.828577\pi\)
\(198\) 0 0
\(199\) −14.7978 −1.04899 −0.524493 0.851415i \(-0.675745\pi\)
−0.524493 + 0.851415i \(0.675745\pi\)
\(200\) 2.45777 10.1501i 0.173790 0.717717i
\(201\) −0.396939 + 1.22165i −0.0279979 + 0.0861688i
\(202\) 15.5737 5.06020i 1.09576 0.356035i
\(203\) 0.248446 + 0.341957i 0.0174375 + 0.0240007i
\(204\) −2.62166 + 1.90475i −0.183553 + 0.133359i
\(205\) −8.63391 15.4523i −0.603019 1.07924i
\(206\) −5.23623 + 16.1154i −0.364825 + 1.12282i
\(207\) 2.03839 2.80561i 0.141678 0.195003i
\(208\) 18.2441i 1.26500i
\(209\) 0 0
\(210\) −3.18154 16.0766i −0.219547 1.10939i
\(211\) −5.47824 3.98017i −0.377137 0.274006i 0.383027 0.923737i \(-0.374882\pi\)
−0.760164 + 0.649731i \(0.774882\pi\)
\(212\) −8.87907 2.88498i −0.609817 0.198141i
\(213\) 8.72883 2.83617i 0.598089 0.194331i
\(214\) 13.4485 9.77090i 0.919320 0.667925i
\(215\) 13.8028 + 12.7841i 0.941340 + 0.871871i
\(216\) 2.67693 + 8.23875i 0.182142 + 0.560576i
\(217\) −1.46529 0.476100i −0.0994701 0.0323198i
\(218\) −8.56003 + 11.7819i −0.579758 + 0.797969i
\(219\) 17.4935 1.18210
\(220\) 0 0
\(221\) 8.23051 0.553644
\(222\) −4.98031 + 6.85481i −0.334257 + 0.460065i
\(223\) 8.29062 + 2.69379i 0.555181 + 0.180389i 0.573152 0.819449i \(-0.305721\pi\)
−0.0179708 + 0.999839i \(0.505721\pi\)
\(224\) −2.75988 8.49404i −0.184402 0.567532i
\(225\) 2.35817 3.83138i 0.157211 0.255425i
\(226\) 0.309684 0.224999i 0.0205999 0.0149667i
\(227\) 3.62109 1.17656i 0.240340 0.0780912i −0.186370 0.982480i \(-0.559672\pi\)
0.426710 + 0.904388i \(0.359672\pi\)
\(228\) 7.32433 + 2.37982i 0.485065 + 0.157607i
\(229\) −2.19540 1.59505i −0.145076 0.105404i 0.512880 0.858461i \(-0.328579\pi\)
−0.657956 + 0.753056i \(0.728579\pi\)
\(230\) 13.9881 2.76823i 0.922351 0.182532i
\(231\) 0 0
\(232\) 0.393588i 0.0258403i
\(233\) −6.17808 + 8.50340i −0.404740 + 0.557076i −0.961926 0.273312i \(-0.911881\pi\)
0.557186 + 0.830388i \(0.311881\pi\)
\(234\) 1.70209 5.23851i 0.111269 0.342452i
\(235\) −23.4500 + 13.1026i −1.52971 + 0.854720i
\(236\) 0.205101 0.149014i 0.0133509 0.00970001i
\(237\) −8.39717 11.5577i −0.545455 0.750755i
\(238\) 7.85220 2.55133i 0.508983 0.165378i
\(239\) 6.19258 19.0588i 0.400565 1.23281i −0.523978 0.851732i \(-0.675552\pi\)
0.924542 0.381079i \(-0.124448\pi\)
\(240\) 9.13554 19.7658i 0.589697 1.27588i
\(241\) −28.4450 −1.83230 −0.916152 0.400832i \(-0.868721\pi\)
−0.916152 + 0.400832i \(0.868721\pi\)
\(242\) 0 0
\(243\) 9.06251i 0.581361i
\(244\) −1.03442 0.751547i −0.0662217 0.0481129i
\(245\) 0.521660 4.37095i 0.0333277 0.279250i
\(246\) −7.99280 24.5993i −0.509602 1.56839i
\(247\) −11.4971 15.8244i −0.731543 1.00688i
\(248\) −0.843262 1.16065i −0.0535472 0.0737014i
\(249\) −1.94158 5.97557i −0.123043 0.378687i
\(250\) 17.8189 4.96919i 1.12696 0.314279i
\(251\) 19.2845 + 14.0110i 1.21723 + 0.884369i 0.995867 0.0908228i \(-0.0289497\pi\)
0.221362 + 0.975192i \(0.428950\pi\)
\(252\) 1.48877i 0.0937838i
\(253\) 0 0
\(254\) 4.02120 0.252313
\(255\) 8.91697 + 4.12133i 0.558403 + 0.258088i
\(256\) 4.81797 14.8282i 0.301123 0.926761i
\(257\) −23.4686 + 7.62540i −1.46393 + 0.475660i −0.929268 0.369407i \(-0.879561\pi\)
−0.534662 + 0.845066i \(0.679561\pi\)
\(258\) 16.1590 + 22.2409i 1.00601 + 1.38466i
\(259\) 4.70577 3.41894i 0.292402 0.212443i
\(260\) 5.32725 2.97658i 0.330382 0.184600i
\(261\) −0.0523954 + 0.161256i −0.00324319 + 0.00998152i
\(262\) −1.54484 + 2.12629i −0.0954407 + 0.131363i
\(263\) 5.44098i 0.335505i 0.985829 + 0.167753i \(0.0536510\pi\)
−0.985829 + 0.167753i \(0.946349\pi\)
\(264\) 0 0
\(265\) 5.49416 + 27.7625i 0.337504 + 1.70544i
\(266\) −15.8740 11.5331i −0.973296 0.707141i
\(267\) 18.6348 + 6.05480i 1.14043 + 0.370548i
\(268\) −0.456323 + 0.148268i −0.0278743 + 0.00905692i
\(269\) −5.42492 + 3.94143i −0.330763 + 0.240314i −0.740754 0.671776i \(-0.765532\pi\)
0.409991 + 0.912089i \(0.365532\pi\)
\(270\) −10.4269 + 11.2578i −0.634564 + 0.685125i
\(271\) 1.56357 + 4.81219i 0.0949804 + 0.292319i 0.987249 0.159186i \(-0.0508870\pi\)
−0.892268 + 0.451506i \(0.850887\pi\)
\(272\) 10.4330 + 3.38989i 0.632594 + 0.205542i
\(273\) −9.63287 + 13.2585i −0.583008 + 0.802442i
\(274\) −30.9438 −1.86938
\(275\) 0 0
\(276\) 5.61428 0.337940
\(277\) 6.28559 8.65138i 0.377665 0.519811i −0.577299 0.816533i \(-0.695893\pi\)
0.954964 + 0.296722i \(0.0958934\pi\)
\(278\) 18.2969 + 5.94501i 1.09737 + 0.356558i
\(279\) −0.190983 0.587785i −0.0114339 0.0351898i
\(280\) −7.11869 + 7.68590i −0.425423 + 0.459320i
\(281\) −11.0995 + 8.06425i −0.662140 + 0.481073i −0.867385 0.497638i \(-0.834201\pi\)
0.205245 + 0.978711i \(0.434201\pi\)
\(282\) −37.3313 + 12.1297i −2.22304 + 0.722311i
\(283\) −20.8940 6.78888i −1.24202 0.403557i −0.386965 0.922094i \(-0.626477\pi\)
−0.855055 + 0.518537i \(0.826477\pi\)
\(284\) 2.77352 + 2.01508i 0.164578 + 0.119573i
\(285\) −4.53213 22.9013i −0.268460 1.35655i
\(286\) 0 0
\(287\) 17.7563i 1.04812i
\(288\) 2.10583 2.89843i 0.124087 0.170791i
\(289\) 3.72400 11.4613i 0.219059 0.674194i
\(290\) −0.608617 + 0.340063i −0.0357392 + 0.0199692i
\(291\) 3.62361 2.63271i 0.212420 0.154332i
\(292\) 3.84078 + 5.28637i 0.224764 + 0.309362i
\(293\) −13.3510 + 4.33799i −0.779971 + 0.253428i −0.671828 0.740707i \(-0.734491\pi\)
−0.108143 + 0.994135i \(0.534491\pi\)
\(294\) 1.98771 6.11754i 0.115926 0.356782i
\(295\) −0.697603 0.322425i −0.0406160 0.0187723i
\(296\) 5.41627 0.314815
\(297\) 0 0
\(298\) 9.78772i 0.566988i
\(299\) −11.5361 8.38148i −0.667151 0.484714i
\(300\) 7.26206 0.557282i 0.419276 0.0321747i
\(301\) −5.83193 17.9488i −0.336147 1.03455i
\(302\) 12.4270 + 17.1042i 0.715091 + 0.984239i
\(303\) −11.4878 15.8116i −0.659956 0.908352i
\(304\) −8.05617 24.7943i −0.462053 1.42205i
\(305\) −0.459324 + 3.84864i −0.0263008 + 0.220372i
\(306\) 2.67941 + 1.94670i 0.153172 + 0.111286i
\(307\) 6.86951i 0.392064i 0.980598 + 0.196032i \(0.0628056\pi\)
−0.980598 + 0.196032i \(0.937194\pi\)
\(308\) 0 0
\(309\) 20.2241 1.15051
\(310\) 1.06617 2.30677i 0.0605541 0.131016i
\(311\) −1.70008 + 5.23231i −0.0964027 + 0.296697i −0.987617 0.156886i \(-0.949854\pi\)
0.891214 + 0.453583i \(0.149854\pi\)
\(312\) −14.5135 + 4.71571i −0.821664 + 0.266975i
\(313\) 8.36536 + 11.5139i 0.472838 + 0.650806i 0.977109 0.212740i \(-0.0682387\pi\)
−0.504271 + 0.863546i \(0.668239\pi\)
\(314\) −19.2069 + 13.9546i −1.08391 + 0.787506i
\(315\) −3.93975 + 2.20132i −0.221980 + 0.124030i
\(316\) 1.64900 5.07510i 0.0927636 0.285497i
\(317\) 10.9836 15.1176i 0.616900 0.849090i −0.380222 0.924895i \(-0.624153\pi\)
0.997123 + 0.0758046i \(0.0241525\pi\)
\(318\) 41.3547i 2.31906i
\(319\) 0 0
\(320\) −7.18237 + 1.42138i −0.401506 + 0.0794575i
\(321\) −16.0511 11.6618i −0.895888 0.650900i
\(322\) −13.6040 4.42021i −0.758122 0.246329i
\(323\) 11.1855 3.63439i 0.622379 0.202223i
\(324\) −6.49860 + 4.72151i −0.361033 + 0.262306i
\(325\) −15.7539 9.69634i −0.873870 0.537856i
\(326\) 1.85454 + 5.70770i 0.102714 + 0.316120i
\(327\) 16.5308 + 5.37120i 0.914158 + 0.297028i
\(328\) −9.71847 + 13.3763i −0.536613 + 0.738584i
\(329\) 26.9464 1.48560
\(330\) 0 0
\(331\) 0.468249 0.0257373 0.0128686 0.999917i \(-0.495904\pi\)
0.0128686 + 0.999917i \(0.495904\pi\)
\(332\) 1.37948 1.89869i 0.0757089 0.104204i
\(333\) 2.21909 + 0.721027i 0.121606 + 0.0395120i
\(334\) 1.95350 + 6.01226i 0.106891 + 0.328976i
\(335\) 1.06709 + 0.988340i 0.0583013 + 0.0539988i
\(336\) −17.6714 + 12.8390i −0.964055 + 0.700427i
\(337\) 32.4189 10.5335i 1.76597 0.573798i 0.768177 0.640238i \(-0.221164\pi\)
0.997790 + 0.0664400i \(0.0211641\pi\)
\(338\) −1.08295 0.351873i −0.0589050 0.0191394i
\(339\) −0.369617 0.268542i −0.0200748 0.0145852i
\(340\) 0.712333 + 3.59949i 0.0386317 + 0.195210i
\(341\) 0 0
\(342\) 7.87090i 0.425610i
\(343\) −11.8246 + 16.2752i −0.638470 + 0.878779i
\(344\) 5.43050 16.7134i 0.292793 0.901124i
\(345\) −8.30136 14.8571i −0.446930 0.799881i
\(346\) −2.82059 + 2.04928i −0.151636 + 0.110170i
\(347\) 2.11187 + 2.90673i 0.113371 + 0.156042i 0.861932 0.507025i \(-0.169255\pi\)
−0.748561 + 0.663066i \(0.769255\pi\)
\(348\) −0.261061 + 0.0848239i −0.0139943 + 0.00454704i
\(349\) −1.96878 + 6.05927i −0.105386 + 0.324346i −0.989821 0.142319i \(-0.954544\pi\)
0.884435 + 0.466664i \(0.154544\pi\)
\(350\) −18.0355 4.36718i −0.964040 0.233436i
\(351\) 15.3446 0.819037
\(352\) 0 0
\(353\) 12.1971i 0.649186i 0.945854 + 0.324593i \(0.105227\pi\)
−0.945854 + 0.324593i \(0.894773\pi\)
\(354\) −0.908513 0.660073i −0.0482869 0.0350825i
\(355\) 1.23156 10.3191i 0.0653643 0.547682i
\(356\) 2.26164 + 6.96062i 0.119867 + 0.368912i
\(357\) −5.79210 7.97214i −0.306550 0.421930i
\(358\) 4.88601 + 6.72501i 0.258234 + 0.355428i
\(359\) 7.45190 + 22.9346i 0.393296 + 1.21044i 0.930280 + 0.366850i \(0.119564\pi\)
−0.536984 + 0.843593i \(0.680436\pi\)
\(360\) −4.17278 0.498009i −0.219925 0.0262474i
\(361\) −7.24126 5.26109i −0.381119 0.276899i
\(362\) 25.8902i 1.36076i
\(363\) 0 0
\(364\) −6.12155 −0.320856
\(365\) 8.31036 17.9804i 0.434984 0.941137i
\(366\) −1.75019 + 5.38652i −0.0914837 + 0.281558i
\(367\) 19.3920 6.30083i 1.01225 0.328901i 0.244501 0.969649i \(-0.421376\pi\)
0.767751 + 0.640748i \(0.221376\pi\)
\(368\) −11.1711 15.3758i −0.582336 0.801517i
\(369\) −5.76243 + 4.18665i −0.299980 + 0.217948i
\(370\) 4.67969 + 8.37535i 0.243286 + 0.435414i
\(371\) 8.77288 27.0002i 0.455465 1.40178i
\(372\) 0.588107 0.809460i 0.0304919 0.0419685i
\(373\) 7.51997i 0.389369i 0.980866 + 0.194685i \(0.0623684\pi\)
−0.980866 + 0.194685i \(0.937632\pi\)
\(374\) 0 0
\(375\) −12.2125 18.3937i −0.630653 0.949845i
\(376\) 20.2996 + 14.7485i 1.04687 + 0.760596i
\(377\) 0.663056 + 0.215440i 0.0341491 + 0.0110957i
\(378\) 14.6393 4.75661i 0.752967 0.244654i
\(379\) 18.7621 13.6315i 0.963745 0.700202i 0.00972738 0.999953i \(-0.496904\pi\)
0.954017 + 0.299751i \(0.0969036\pi\)
\(380\) 5.92552 6.39765i 0.303973 0.328193i
\(381\) −1.48310 4.56452i −0.0759816 0.233847i
\(382\) 4.90311 + 1.59312i 0.250865 + 0.0815109i
\(383\) −1.43443 + 1.97432i −0.0732958 + 0.100883i −0.844091 0.536200i \(-0.819859\pi\)
0.770795 + 0.637083i \(0.219859\pi\)
\(384\) −26.4246 −1.34848
\(385\) 0 0
\(386\) −15.9442 −0.811537
\(387\) 4.44984 6.12468i 0.226198 0.311335i
\(388\) 1.59116 + 0.517000i 0.0807791 + 0.0262467i
\(389\) −10.4983 32.3104i −0.532284 1.63820i −0.749446 0.662066i \(-0.769680\pi\)
0.217162 0.976136i \(-0.430320\pi\)
\(390\) −19.8318 18.3682i −1.00422 0.930111i
\(391\) 6.93649 5.03966i 0.350794 0.254866i
\(392\) −3.91057 + 1.27062i −0.197513 + 0.0641760i
\(393\) 2.98335 + 0.969349i 0.150490 + 0.0488972i
\(394\) 19.2721 + 14.0020i 0.970915 + 0.705411i
\(395\) −15.8685 + 3.14036i −0.798433 + 0.158009i
\(396\) 0 0
\(397\) 27.4961i 1.37999i −0.723814 0.689995i \(-0.757613\pi\)
0.723814 0.689995i \(-0.242387\pi\)
\(398\) −14.3914 + 19.8081i −0.721376 + 0.992888i
\(399\) −7.23674 + 22.2724i −0.362290 + 1.11501i
\(400\) −15.9761 18.7797i −0.798804 0.938983i
\(401\) 1.52696 1.10940i 0.0762527 0.0554008i −0.549006 0.835819i \(-0.684994\pi\)
0.625259 + 0.780418i \(0.284994\pi\)
\(402\) 1.24925 + 1.71944i 0.0623068 + 0.0857579i
\(403\) −2.41686 + 0.785286i −0.120392 + 0.0391179i
\(404\) 2.25592 6.94302i 0.112236 0.345428i
\(405\) 22.1035 + 10.2160i 1.09833 + 0.507638i
\(406\) 0.699363 0.0347088
\(407\) 0 0
\(408\) 9.17582i 0.454271i
\(409\) −10.9682 7.96888i −0.542344 0.394036i 0.282611 0.959235i \(-0.408799\pi\)
−0.824955 + 0.565199i \(0.808799\pi\)
\(410\) −29.0810 3.47074i −1.43621 0.171408i
\(411\) 11.4127 + 35.1247i 0.562947 + 1.73257i
\(412\) 4.44029 + 6.11153i 0.218757 + 0.301094i
\(413\) 0.453134 + 0.623686i 0.0222973 + 0.0306896i
\(414\) −1.77313 5.45712i −0.0871444 0.268203i
\(415\) −7.06426 0.843099i −0.346771 0.0413861i
\(416\) −11.9178 8.65878i −0.584317 0.424531i
\(417\) 22.9616i 1.12444i
\(418\) 0 0
\(419\) 22.1368 1.08145 0.540727 0.841198i \(-0.318149\pi\)
0.540727 + 0.841198i \(0.318149\pi\)
\(420\) −6.63212 3.06530i −0.323614 0.149571i
\(421\) 5.53219 17.0263i 0.269623 0.829813i −0.720970 0.692967i \(-0.756303\pi\)
0.990592 0.136846i \(-0.0436967\pi\)
\(422\) −10.6556 + 3.46221i −0.518706 + 0.168538i
\(423\) 6.35355 + 8.74491i 0.308920 + 0.425192i
\(424\) 21.3868 15.5384i 1.03863 0.754612i
\(425\) 8.47210 7.20732i 0.410957 0.349606i
\(426\) 4.69267 14.4426i 0.227361 0.699744i
\(427\) 2.28536 3.14553i 0.110596 0.152223i
\(428\) 7.41093i 0.358221i
\(429\) 0 0
\(430\) 30.5364 6.04310i 1.47259 0.291424i
\(431\) 27.0581 + 19.6589i 1.30334 + 0.946934i 0.999982 0.00594140i \(-0.00189122\pi\)
0.303361 + 0.952876i \(0.401891\pi\)
\(432\) 19.4509 + 6.31998i 0.935832 + 0.304070i
\(433\) 29.9501 9.73138i 1.43931 0.467660i 0.517628 0.855606i \(-0.326815\pi\)
0.921682 + 0.387946i \(0.126815\pi\)
\(434\) −2.06235 + 1.49838i −0.0989958 + 0.0719247i
\(435\) 0.610479 + 0.565427i 0.0292702 + 0.0271101i
\(436\) 2.00630 + 6.17475i 0.0960842 + 0.295717i
\(437\) −19.3790 6.29662i −0.927024 0.301208i
\(438\) 17.0131 23.4165i 0.812916 1.11888i
\(439\) 35.6208 1.70009 0.850045 0.526710i \(-0.176575\pi\)
0.850045 + 0.526710i \(0.176575\pi\)
\(440\) 0 0
\(441\) −1.77134 −0.0843495
\(442\) 8.00448 11.0172i 0.380734 0.524036i
\(443\) −22.3380 7.25806i −1.06131 0.344841i −0.274213 0.961669i \(-0.588417\pi\)
−0.787098 + 0.616828i \(0.788417\pi\)
\(444\) 1.16728 + 3.59253i 0.0553969 + 0.170494i
\(445\) 15.0759 16.2771i 0.714665 0.771608i
\(446\) 11.6688 8.47789i 0.552534 0.401439i
\(447\) 11.1102 3.60991i 0.525492 0.170743i
\(448\) 6.98513 + 2.26961i 0.330016 + 0.107229i
\(449\) −25.3966 18.4517i −1.19854 0.870792i −0.204401 0.978887i \(-0.565525\pi\)
−0.994141 + 0.108096i \(0.965525\pi\)
\(450\) −2.83522 6.88277i −0.133653 0.324457i
\(451\) 0 0
\(452\) 0.170655i 0.00802692i
\(453\) 14.8319 20.4144i 0.696864 0.959151i
\(454\) 1.94672 5.99138i 0.0913640 0.281190i
\(455\) 9.05142 + 16.1995i 0.424337 + 0.759445i
\(456\) −17.6419 + 12.8176i −0.826158 + 0.600239i
\(457\) 22.9887 + 31.6412i 1.07536 + 1.48011i 0.864525 + 0.502591i \(0.167620\pi\)
0.210839 + 0.977521i \(0.432380\pi\)
\(458\) −4.27023 + 1.38748i −0.199535 + 0.0648328i
\(459\) −2.85115 + 8.77492i −0.133080 + 0.409578i
\(460\) 2.66709 5.77055i 0.124354 0.269053i
\(461\) 8.88399 0.413769 0.206884 0.978365i \(-0.433668\pi\)
0.206884 + 0.978365i \(0.433668\pi\)
\(462\) 0 0
\(463\) 4.21081i 0.195693i −0.995202 0.0978464i \(-0.968805\pi\)
0.995202 0.0978464i \(-0.0311954\pi\)
\(464\) 0.751758 + 0.546184i 0.0348995 + 0.0253560i
\(465\) −3.01167 0.359434i −0.139663 0.0166683i
\(466\) 5.37410 + 16.5398i 0.248950 + 0.766190i
\(467\) 3.95488 + 5.44342i 0.183010 + 0.251891i 0.890658 0.454673i \(-0.150244\pi\)
−0.707649 + 0.706565i \(0.750244\pi\)
\(468\) −1.44337 1.98662i −0.0667196 0.0918317i
\(469\) −0.450866 1.38762i −0.0208190 0.0640744i
\(470\) −5.26710 + 44.1326i −0.242953 + 2.03569i
\(471\) 22.9240 + 16.6552i 1.05628 + 0.767433i
\(472\) 0.717854i 0.0330419i
\(473\) 0 0
\(474\) −23.6376 −1.08571
\(475\) −25.6917 6.22108i −1.17882 0.285443i
\(476\) 1.13743 3.50064i 0.0521339 0.160452i
\(477\) 10.8309 3.51916i 0.495911 0.161131i
\(478\) −19.4893 26.8247i −0.891420 1.22693i
\(479\) −16.8352 + 12.2315i −0.769218 + 0.558870i −0.901724 0.432313i \(-0.857698\pi\)
0.132506 + 0.991182i \(0.457698\pi\)
\(480\) −8.57601 15.3487i −0.391439 0.700567i
\(481\) 2.96473 9.12450i 0.135180 0.416041i
\(482\) −27.6639 + 38.0760i −1.26005 + 1.73432i
\(483\) 17.0723i 0.776818i
\(484\) 0 0
\(485\) −0.984576 4.97516i −0.0447073 0.225910i
\(486\) 12.1309 + 8.81365i 0.550271 + 0.399795i
\(487\) −15.0071 4.87610i −0.680036 0.220957i −0.0514249 0.998677i \(-0.516376\pi\)
−0.628611 + 0.777720i \(0.716376\pi\)
\(488\) 3.44327 1.11879i 0.155869 0.0506450i
\(489\) 5.79489 4.21023i 0.262054 0.190393i
\(490\) −5.34355 4.94920i −0.241397 0.223582i
\(491\) −5.97340 18.3842i −0.269576 0.829669i −0.990604 0.136763i \(-0.956330\pi\)
0.721028 0.692906i \(-0.243670\pi\)
\(492\) −10.9668 3.56332i −0.494421 0.160647i
\(493\) −0.246401 + 0.339142i −0.0110973 + 0.0152742i
\(494\) −32.3637 −1.45611
\(495\) 0 0
\(496\) −3.38705 −0.152083
\(497\) −6.12761 + 8.43394i −0.274861 + 0.378314i
\(498\) −9.88707 3.21250i −0.443050 0.143956i
\(499\) 12.8117 + 39.4305i 0.573532 + 1.76515i 0.641124 + 0.767437i \(0.278468\pi\)
−0.0675920 + 0.997713i \(0.521532\pi\)
\(500\) 2.87708 7.72894i 0.128667 0.345649i
\(501\) 6.10409 4.43488i 0.272711 0.198136i
\(502\) 37.5099 12.1877i 1.67415 0.543964i
\(503\) −31.0628 10.0929i −1.38502 0.450020i −0.480704 0.876883i \(-0.659619\pi\)
−0.904317 + 0.426862i \(0.859619\pi\)
\(504\) 3.41046 + 2.47784i 0.151914 + 0.110372i
\(505\) −21.7090 + 4.29618i −0.966039 + 0.191178i
\(506\) 0 0
\(507\) 1.35905i 0.0603576i
\(508\) 1.05373 1.45034i 0.0467519 0.0643485i
\(509\) −5.14365 + 15.8305i −0.227988 + 0.701675i 0.769986 + 0.638060i \(0.220263\pi\)
−0.997975 + 0.0636149i \(0.979737\pi\)
\(510\) 14.1889 7.92797i 0.628293 0.351056i
\(511\) −16.0752 + 11.6793i −0.711126 + 0.516663i
\(512\) 0.567200 + 0.780684i 0.0250669 + 0.0345017i
\(513\) 20.8539 6.77583i 0.920720 0.299160i
\(514\) −12.6169 + 38.8307i −0.556505 + 1.71275i
\(515\) 9.60753 20.7870i 0.423358 0.915984i
\(516\) 12.2561 0.539543
\(517\) 0 0
\(518\) 9.62412i 0.422860i
\(519\) 3.36645 + 2.44587i 0.147771 + 0.107362i
\(520\) −2.04772 + 17.1577i −0.0897984 + 0.752414i
\(521\) 4.34362 + 13.3683i 0.190298 + 0.585676i 0.999999 0.00116602i \(-0.000371156\pi\)
−0.809702 + 0.586842i \(0.800371\pi\)
\(522\) 0.164899 + 0.226964i 0.00721742 + 0.00993393i
\(523\) 9.20925 + 12.6754i 0.402692 + 0.554258i 0.961417 0.275095i \(-0.0887092\pi\)
−0.558725 + 0.829353i \(0.688709\pi\)
\(524\) 0.362080 + 1.11437i 0.0158175 + 0.0486814i
\(525\) 1.69463 + 22.0830i 0.0739596 + 0.963783i
\(526\) 7.28322 + 5.29157i 0.317563 + 0.230723i
\(527\) 1.52801i 0.0665611i
\(528\) 0 0
\(529\) 8.14550 0.354152
\(530\) 42.5058 + 19.6457i 1.84633 + 0.853357i
\(531\) −0.0955624 + 0.294111i −0.00414705 + 0.0127633i
\(532\) −8.31938 + 2.70313i −0.360691 + 0.117196i
\(533\) 17.2147 + 23.6940i 0.745652 + 1.02630i
\(534\) 26.2279 19.0557i 1.13499 0.824620i
\(535\) −19.6116 + 10.9579i −0.847884 + 0.473752i
\(536\) 0.419831 1.29211i 0.0181339 0.0558106i
\(537\) 5.83158 8.02648i 0.251651 0.346368i
\(538\) 11.0949i 0.478336i
\(539\) 0 0
\(540\) 1.32805 + 6.71075i 0.0571501 + 0.288785i
\(541\) −32.0681 23.2989i −1.37872 1.00170i −0.996999 0.0774172i \(-0.975333\pi\)
−0.381718 0.924279i \(-0.624667\pi\)
\(542\) 7.96215 + 2.58706i 0.342004 + 0.111124i
\(543\) −29.3883 + 9.54884i −1.26117 + 0.409780i
\(544\) 7.16598 5.20639i 0.307239 0.223222i
\(545\) 13.3738 14.4394i 0.572869 0.618514i
\(546\) 8.37930 + 25.7888i 0.358601 + 1.10366i
\(547\) 39.1516 + 12.7211i 1.67400 + 0.543916i 0.983733 0.179637i \(-0.0574923\pi\)
0.690269 + 0.723553i \(0.257492\pi\)
\(548\) −8.10865 + 11.1606i −0.346385 + 0.476757i
\(549\) 1.55967 0.0665651
\(550\) 0 0
\(551\) 0.996247 0.0424415
\(552\) −9.34414 + 12.8611i −0.397713 + 0.547405i
\(553\) 15.4328 + 5.01441i 0.656268 + 0.213234i
\(554\) −5.46762 16.8276i −0.232297 0.714936i
\(555\) 7.78099 8.40097i 0.330285 0.356601i
\(556\) 6.93880 5.04133i 0.294271 0.213800i
\(557\) −28.4137 + 9.23218i −1.20393 + 0.391180i −0.841205 0.540717i \(-0.818153\pi\)
−0.362724 + 0.931897i \(0.618153\pi\)
\(558\) −0.972539 0.315997i −0.0411708 0.0133772i
\(559\) −25.1836 18.2969i −1.06515 0.773877i
\(560\) 4.80152 + 24.2625i 0.202901 + 1.02528i
\(561\) 0 0
\(562\) 22.7004i 0.957558i
\(563\) −1.26832 + 1.74569i −0.0534533 + 0.0735721i −0.834907 0.550391i \(-0.814479\pi\)
0.781454 + 0.623963i \(0.214479\pi\)
\(564\) −5.40761 + 16.6429i −0.227701 + 0.700793i
\(565\) −0.451605 + 0.252333i −0.0189992 + 0.0106157i
\(566\) −29.4077 + 21.3660i −1.23610 + 0.898079i
\(567\) −14.3575 19.7615i −0.602960 0.829903i
\(568\) −9.23223 + 2.99973i −0.387376 + 0.125866i
\(569\) 0.221654 0.682181i 0.00929222 0.0285985i −0.946303 0.323281i \(-0.895214\pi\)
0.955595 + 0.294683i \(0.0952140\pi\)
\(570\) −35.0630 16.2057i −1.46863 0.678784i
\(571\) 21.6311 0.905235 0.452617 0.891705i \(-0.350490\pi\)
0.452617 + 0.891705i \(0.350490\pi\)
\(572\) 0 0
\(573\) 6.15315i 0.257051i
\(574\) 23.7682 + 17.2686i 0.992068 + 0.720779i
\(575\) −19.2143 + 1.47448i −0.801291 + 0.0614901i
\(576\) 0.910431 + 2.80202i 0.0379346 + 0.116751i
\(577\) 13.7704 + 18.9533i 0.573269 + 0.789037i 0.992937 0.118641i \(-0.0378537\pi\)
−0.419668 + 0.907677i \(0.637854\pi\)
\(578\) −11.7202 16.1314i −0.487495 0.670980i
\(579\) 5.88053 + 18.0984i 0.244387 + 0.752145i
\(580\) −0.0368333 + 0.308624i −0.00152942 + 0.0128149i
\(581\) 5.77370 + 4.19484i 0.239533 + 0.174031i
\(582\) 7.41093i 0.307193i
\(583\) 0 0
\(584\) −18.5023 −0.765633
\(585\) −3.12304 + 6.75705i −0.129122 + 0.279369i
\(586\) −7.17756 + 22.0903i −0.296502 + 0.912540i
\(587\) −2.13735 + 0.694466i −0.0882177 + 0.0286637i −0.352793 0.935701i \(-0.614768\pi\)
0.264576 + 0.964365i \(0.414768\pi\)
\(588\) −1.68557 2.31998i −0.0695116 0.0956745i
\(589\) −2.93783 + 2.13446i −0.121051 + 0.0879488i
\(590\) −1.11004 + 0.620230i −0.0456996 + 0.0255345i
\(591\) 8.78590 27.0402i 0.361404 1.11229i
\(592\) 7.51619 10.3451i 0.308914 0.425183i
\(593\) 25.4034i 1.04319i −0.853193 0.521596i \(-0.825337\pi\)
0.853193 0.521596i \(-0.174663\pi\)
\(594\) 0 0
\(595\) −10.9456 + 2.16612i −0.448726 + 0.0888022i
\(596\) 3.53017 + 2.56482i 0.144601 + 0.105059i
\(597\) 27.7922 + 9.03023i 1.13746 + 0.369583i
\(598\) −22.4387 + 7.29076i −0.917585 + 0.298141i
\(599\) −14.7446 + 10.7126i −0.602448 + 0.437704i −0.846747 0.531996i \(-0.821442\pi\)
0.244299 + 0.969700i \(0.421442\pi\)
\(600\) −10.8100 + 17.5633i −0.441317 + 0.717020i
\(601\) 10.7043 + 32.9444i 0.436637 + 1.34383i 0.891400 + 0.453218i \(0.149724\pi\)
−0.454762 + 0.890613i \(0.650276\pi\)
\(602\) −29.6978 9.64940i −1.21039 0.393280i
\(603\) 0.344017 0.473499i 0.0140095 0.0192824i
\(604\) 9.42547 0.383517
\(605\) 0 0
\(606\) −32.3375 −1.31362
\(607\) 14.9581 20.5881i 0.607131 0.835644i −0.389207 0.921150i \(-0.627251\pi\)
0.996338 + 0.0855067i \(0.0272509\pi\)
\(608\) −20.0201 6.50494i −0.811924 0.263810i
\(609\) −0.257939 0.793855i −0.0104522 0.0321686i
\(610\) 4.70502 + 4.35779i 0.190501 + 0.176442i
\(611\) 35.9574 26.1246i 1.45468 1.05689i
\(612\) 1.40425 0.456268i 0.0567634 0.0184436i
\(613\) 35.2477 + 11.4527i 1.42364 + 0.462569i 0.916757 0.399445i \(-0.130797\pi\)
0.506884 + 0.862014i \(0.330797\pi\)
\(614\) 9.19542 + 6.68086i 0.371097 + 0.269618i
\(615\) 6.78600 + 34.2903i 0.273638 + 1.38272i
\(616\) 0 0
\(617\) 27.5937i 1.11088i 0.831557 + 0.555439i \(0.187450\pi\)
−0.831557 + 0.555439i \(0.812550\pi\)
\(618\) 19.6687 27.0716i 0.791190 1.08898i
\(619\) −6.31739 + 19.4429i −0.253917 + 0.781477i 0.740124 + 0.672471i \(0.234767\pi\)
−0.994041 + 0.109006i \(0.965233\pi\)
\(620\) −0.552608 0.989014i −0.0221933 0.0397198i
\(621\) 12.9321 9.39575i 0.518949 0.377038i
\(622\) 5.35049 + 7.36432i 0.214535 + 0.295282i
\(623\) −21.1664 + 6.87738i −0.848014 + 0.275536i
\(624\) −11.1333 + 34.2649i −0.445691 + 1.37169i
\(625\) −24.7073 + 3.81448i −0.988291 + 0.152579i
\(626\) 23.5480 0.941167
\(627\) 0 0
\(628\) 10.5842i 0.422354i
\(629\) 4.66703 + 3.39079i 0.186087 + 0.135200i
\(630\) −0.884907 + 7.41456i −0.0352555 + 0.295403i
\(631\) 0.234586 + 0.721982i 0.00933873 + 0.0287417i 0.955617 0.294611i \(-0.0951900\pi\)
−0.946279 + 0.323353i \(0.895190\pi\)
\(632\) 8.88145 + 12.2243i 0.353285 + 0.486255i
\(633\) 7.86000 + 10.8184i 0.312407 + 0.429991i
\(634\) −9.55425 29.4050i −0.379448 1.16782i
\(635\) −5.39612 0.644012i −0.214139 0.0255568i
\(636\) 14.9155 + 10.8368i 0.591440 + 0.429706i
\(637\) 7.28342i 0.288579i
\(638\) 0 0
\(639\) −4.18186 −0.165432
\(640\) −12.5531 + 27.1602i −0.496207 + 1.07360i
\(641\) −4.60590 + 14.1755i −0.181922 + 0.559899i −0.999882 0.0153768i \(-0.995105\pi\)
0.817960 + 0.575276i \(0.195105\pi\)
\(642\) −31.2207 + 10.1442i −1.23218 + 0.400361i
\(643\) −16.2432 22.3568i −0.640569 0.881667i 0.358077 0.933692i \(-0.383432\pi\)
−0.998646 + 0.0520249i \(0.983432\pi\)
\(644\) −5.15911 + 3.74831i −0.203297 + 0.147704i
\(645\) −18.1220 32.4334i −0.713554 1.27706i
\(646\) 6.01340 18.5073i 0.236594 0.728162i
\(647\) −14.6820 + 20.2081i −0.577210 + 0.794461i −0.993386 0.114823i \(-0.963370\pi\)
0.416176 + 0.909284i \(0.363370\pi\)
\(648\) 22.7452i 0.893514i
\(649\) 0 0
\(650\) −28.3007 + 11.6579i −1.11004 + 0.457260i
\(651\) 2.46147 + 1.78836i 0.0964725 + 0.0700914i
\(652\) 2.54459 + 0.826787i 0.0996538 + 0.0323795i
\(653\) −26.4042 + 8.57923i −1.03327 + 0.335731i −0.776084 0.630629i \(-0.782797\pi\)
−0.257191 + 0.966361i \(0.582797\pi\)
\(654\) 23.2667 16.9042i 0.909800 0.661008i
\(655\) 2.41358 2.60590i 0.0943066 0.101821i
\(656\) 12.0626 + 37.1248i 0.470964 + 1.44948i
\(657\) −7.58057 2.46308i −0.295746 0.0960938i
\(658\) 26.2064 36.0701i 1.02163 1.40616i
\(659\) −21.5863 −0.840883 −0.420442 0.907320i \(-0.638125\pi\)
−0.420442 + 0.907320i \(0.638125\pi\)
\(660\) 0 0
\(661\) −16.0174 −0.623003 −0.311502 0.950246i \(-0.600832\pi\)
−0.311502 + 0.950246i \(0.600832\pi\)
\(662\) 0.455390 0.626791i 0.0176992 0.0243609i
\(663\) −15.4580 5.02261i −0.600339 0.195062i
\(664\) 2.05356 + 6.32019i 0.0796934 + 0.245271i
\(665\) 19.4545 + 18.0188i 0.754412 + 0.698738i
\(666\) 3.12331 2.26922i 0.121026 0.0879304i
\(667\) 0.690726 0.224431i 0.0267450 0.00868999i
\(668\) 2.68036 + 0.870903i 0.103706 + 0.0336963i
\(669\) −13.9270 10.1186i −0.538450 0.391207i
\(670\) 2.36076 0.467191i 0.0912042 0.0180492i
\(671\) 0 0
\(672\) 17.6372i 0.680368i
\(673\) −18.4253 + 25.3602i −0.710242 + 0.977564i 0.289550 + 0.957163i \(0.406494\pi\)
−0.999792 + 0.0204009i \(0.993506\pi\)
\(674\) 17.4286 53.6396i 0.671324 2.06612i
\(675\) 15.7951 13.4371i 0.607952 0.517192i
\(676\) −0.410694 + 0.298386i −0.0157959 + 0.0114764i
\(677\) 18.0252 + 24.8096i 0.692766 + 0.953510i 0.999998 + 0.00187591i \(0.000597121\pi\)
−0.307232 + 0.951635i \(0.599403\pi\)
\(678\) −0.718933 + 0.233596i −0.0276105 + 0.00897118i
\(679\) −1.57213 + 4.83853i −0.0603330 + 0.185686i
\(680\) −9.43123 4.35902i −0.361671 0.167161i
\(681\) −7.51888 −0.288124
\(682\) 0 0
\(683\) 3.27236i 0.125213i −0.998038 0.0626066i \(-0.980059\pi\)
0.998038 0.0626066i \(-0.0199414\pi\)
\(684\) −2.83882 2.06253i −0.108545 0.0788627i
\(685\) 41.5240 + 4.95577i 1.58655 + 0.189350i
\(686\) 10.2858 + 31.6566i 0.392715 + 1.20865i
\(687\) 3.14989 + 4.33546i 0.120176 + 0.165408i
\(688\) −24.3868 33.5655i −0.929737 1.27967i
\(689\) −14.4701 44.5344i −0.551267 1.69663i
\(690\) −27.9609 3.33706i −1.06445 0.127040i
\(691\) 29.5247 + 21.4510i 1.12317 + 0.816034i 0.984687 0.174330i \(-0.0557761\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(692\) 1.55431i 0.0590862i
\(693\) 0 0
\(694\) 5.94478 0.225661
\(695\) −23.6008 10.9080i −0.895228 0.413765i
\(696\) 0.240184 0.739212i 0.00910417 0.0280197i
\(697\) −16.7482 + 5.44181i −0.634382 + 0.206123i
\(698\) 6.19614 + 8.52825i 0.234527 + 0.322799i
\(699\) 16.7924 12.2004i 0.635147 0.461461i
\(700\) −6.30124 + 5.36054i −0.238164 + 0.202609i
\(701\) −14.3880 + 44.2818i −0.543429 + 1.67250i 0.181267 + 0.983434i \(0.441980\pi\)
−0.724696 + 0.689068i \(0.758020\pi\)
\(702\) 14.9233 20.5401i 0.563242 0.775236i
\(703\) 13.7096i 0.517068i
\(704\) 0 0
\(705\) 52.0381 10.2983i 1.95987 0.387855i
\(706\) 16.3268 + 11.8621i 0.614469 + 0.446438i
\(707\) 21.1129 + 6.85999i 0.794031 + 0.257996i
\(708\) −0.476142 + 0.154708i −0.0178945 + 0.00581427i
\(709\) −28.7982 + 20.9231i −1.08154 + 0.785785i −0.977951 0.208835i \(-0.933033\pi\)
−0.103590 + 0.994620i \(0.533033\pi\)
\(710\) −12.6153 11.6843i −0.473443 0.438504i
\(711\) 2.01148 + 6.19071i 0.0754365 + 0.232170i
\(712\) −19.7095 6.40399i −0.738643 0.240000i
\(713\) −1.55604 + 2.14170i −0.0582741 + 0.0802074i
\(714\) −16.3044 −0.610178
\(715\) 0 0
\(716\) 3.70588 0.138495
\(717\) −23.2610 + 32.0160i −0.868698 + 1.19566i
\(718\) 37.9472 + 12.3298i 1.41618 + 0.460143i
\(719\) −6.82658 21.0101i −0.254589 0.783543i −0.993910 0.110191i \(-0.964854\pi\)
0.739322 0.673352i \(-0.235146\pi\)
\(720\) −6.74179 + 7.27896i −0.251251 + 0.271271i
\(721\) −18.5844 + 13.5024i −0.692120 + 0.502855i
\(722\) −14.0848 + 4.57644i −0.524183 + 0.170317i
\(723\) 53.4235 + 17.3584i 1.98684 + 0.645564i
\(724\) −9.33792 6.78440i −0.347041 0.252140i
\(725\) 0.871176 0.358863i 0.0323547 0.0133278i
\(726\) 0 0
\(727\) 45.5415i 1.68904i −0.535522 0.844521i \(-0.679885\pi\)
0.535522 0.844521i \(-0.320115\pi\)
\(728\) 10.1884 14.0232i 0.377608 0.519733i
\(729\) −4.56501 + 14.0497i −0.169075 + 0.520358i
\(730\) −15.9861 28.6107i −0.591674 1.05893i
\(731\) 15.1425 11.0017i 0.560065 0.406911i
\(732\) 1.48415 + 2.04275i 0.0548556 + 0.0755023i
\(733\) 10.8220 3.51627i 0.399719 0.129877i −0.102257 0.994758i \(-0.532607\pi\)
0.501976 + 0.864881i \(0.332607\pi\)
\(734\) 10.4252 32.0856i 0.384803 1.18430i
\(735\) −3.64709 + 7.89089i −0.134525 + 0.291060i
\(736\) −15.3459 −0.565659
\(737\) 0 0
\(738\) 11.7852i 0.433818i
\(739\) 3.50933 + 2.54968i 0.129093 + 0.0937915i 0.650458 0.759542i \(-0.274577\pi\)
−0.521365 + 0.853334i \(0.674577\pi\)
\(740\) 4.24705 + 0.506874i 0.156125 + 0.0186330i
\(741\) 11.9364 + 36.7364i 0.438494 + 1.34954i
\(742\) −27.6100 38.0019i −1.01360 1.39510i
\(743\) 10.1654 + 13.9915i 0.372934 + 0.513300i 0.953695 0.300774i \(-0.0972451\pi\)
−0.580761 + 0.814074i \(0.697245\pi\)
\(744\) 0.875481 + 2.69445i 0.0320967 + 0.0987834i
\(745\) 1.56754 13.1343i 0.0574303 0.481204i
\(746\) 10.0661 + 7.31346i 0.368547 + 0.267765i
\(747\) 2.86281i 0.104745i
\(748\) 0 0
\(749\) 22.5357 0.823437
\(750\) −36.4987 1.54103i −1.33274 0.0562706i
\(751\) −9.73806 + 29.9707i −0.355347 + 1.09365i 0.600461 + 0.799654i \(0.294984\pi\)
−0.955808 + 0.293991i \(0.905016\pi\)
\(752\) 56.3396 18.3058i 2.05449 0.667546i
\(753\) −27.6688 38.0829i −1.00831 1.38782i
\(754\) 0.933232 0.678033i 0.0339863 0.0246925i
\(755\) −13.9366 24.9427i −0.507206 0.907758i
\(756\) 2.12058 6.52647i 0.0771247 0.237365i
\(757\) −5.45311 + 7.50556i −0.198197 + 0.272794i −0.896534 0.442974i \(-0.853923\pi\)
0.698338 + 0.715768i \(0.253923\pi\)
\(758\) 38.3718i 1.39373i
\(759\) 0 0
\(760\) 4.79350 + 24.2220i 0.173879 + 0.878626i
\(761\) −3.36397 2.44407i −0.121944 0.0885975i 0.525142 0.851015i \(-0.324012\pi\)
−0.647086 + 0.762417i \(0.724012\pi\)
\(762\) −7.55236 2.45391i −0.273593 0.0888958i
\(763\) −18.7767 + 6.10090i −0.679760 + 0.220868i
\(764\) 1.85943 1.35095i 0.0672717 0.0488758i
\(765\) −3.28377 3.04143i −0.118725 0.109963i
\(766\) 1.24776 + 3.84020i 0.0450833 + 0.138752i
\(767\) 1.20933 + 0.392935i 0.0436663 + 0.0141880i
\(768\) −18.0976 + 24.9092i −0.653040 + 0.898833i
\(769\) 16.8800 0.608709 0.304355 0.952559i \(-0.401559\pi\)
0.304355 + 0.952559i \(0.401559\pi\)
\(770\) 0 0
\(771\) 48.7305 1.75499
\(772\) −4.17808 + 5.75064i −0.150373 + 0.206970i
\(773\) −8.06267 2.61972i −0.289994 0.0942248i 0.160407 0.987051i \(-0.448719\pi\)
−0.450402 + 0.892826i \(0.648719\pi\)
\(774\) −3.87076 11.9130i −0.139132 0.428203i
\(775\) −1.80014 + 2.92474i −0.0646631 + 0.105060i
\(776\) −3.83259 + 2.78454i −0.137582 + 0.0999593i
\(777\) −10.9245 + 3.54957i −0.391913 + 0.127340i
\(778\) −53.4602 17.3703i −1.91664 0.622754i
\(779\) 33.8580 + 24.5993i 1.21309 + 0.881361i
\(780\) −11.8217 + 2.33950i −0.423286 + 0.0837676i
\(781\) 0 0
\(782\) 14.1863i 0.507303i
\(783\) −0.459381 + 0.632284i −0.0164169 + 0.0225960i
\(784\) −2.99981 + 9.23247i −0.107136 + 0.329731i
\(785\) 28.0090 15.6499i 0.999683 0.558569i
\(786\) 4.19898 3.05074i 0.149773 0.108816i
\(787\) −31.5150 43.3767i −1.12339 1.54621i −0.800054 0.599928i \(-0.795196\pi\)
−0.323336 0.946284i \(-0.604804\pi\)
\(788\) 10.1003 3.28179i 0.359808 0.116909i
\(789\) 3.32032 10.2189i 0.118207 0.363803i
\(790\) −11.2291 + 24.2955i −0.399515 + 0.864395i
\(791\) 0.518940 0.0184514
\(792\) 0 0
\(793\) 6.41307i 0.227735i
\(794\) −36.8059 26.7410i −1.30619 0.949004i
\(795\) 6.62312 55.4946i 0.234898 1.96819i
\(796\) 3.37305 + 10.3812i 0.119555 + 0.367951i
\(797\) 16.7782 + 23.0932i 0.594315 + 0.818004i 0.995173 0.0981362i \(-0.0312881\pi\)
−0.400858 + 0.916140i \(0.631288\pi\)
\(798\) 22.7755 + 31.3477i 0.806243 + 1.10970i
\(799\) 8.25835 + 25.4166i 0.292159 + 0.899174i
\(800\) −19.8500 + 1.52326i −0.701802 + 0.0538555i
\(801\) −7.22262 5.24754i −0.255199 0.185413i
\(802\) 3.12290i 0.110273i
\(803\) 0 0
\(804\) 0.947515 0.0334163
\(805\) 17.5475 + 8.11029i 0.618470 + 0.285850i
\(806\) −1.29932 + 3.99890i −0.0457666 + 0.140855i
\(807\) 12.5940 4.09203i 0.443329 0.144046i
\(808\) 12.1503 + 16.7235i 0.427446 + 0.588330i
\(809\) −29.8900 + 21.7163i −1.05088 + 0.763506i −0.972379 0.233409i \(-0.925012\pi\)
−0.0784966 + 0.996914i \(0.525012\pi\)
\(810\) 35.1715 19.6520i 1.23580 0.690499i
\(811\) 11.8591 36.4985i 0.416428 1.28163i −0.494539 0.869156i \(-0.664663\pi\)
0.910967 0.412479i \(-0.135337\pi\)
\(812\) 0.183264 0.252241i 0.00643131 0.00885194i
\(813\) 9.99209i 0.350438i
\(814\) 0 0
\(815\) −1.57453 7.95628i −0.0551535 0.278696i
\(816\) −17.5259 12.7333i −0.613530 0.445756i
\(817\) −42.3047 13.7456i −1.48005 0.480899i
\(818\) −21.3340 + 6.93185i −0.745927 + 0.242366i
\(819\) 6.04108 4.38910i 0.211092 0.153368i
\(820\) −8.87233 + 9.57927i −0.309835 + 0.334522i
\(821\) 3.16732 + 9.74799i 0.110540 + 0.340207i 0.990991 0.133930i \(-0.0427599\pi\)
−0.880451 + 0.474138i \(0.842760\pi\)
\(822\) 58.1166 + 18.8832i 2.02705 + 0.658629i
\(823\) 14.8296 20.4112i 0.516926 0.711488i −0.468142 0.883653i \(-0.655076\pi\)
0.985068 + 0.172165i \(0.0550763\pi\)
\(824\) −21.3904 −0.745170
\(825\) 0 0
\(826\) 1.27555 0.0443820
\(827\) −10.7850 + 14.8443i −0.375031 + 0.516186i −0.954260 0.298979i \(-0.903354\pi\)
0.579229 + 0.815165i \(0.303354\pi\)
\(828\) −2.43288 0.790489i −0.0845483 0.0274714i
\(829\) −7.53463 23.1892i −0.261689 0.805395i −0.992438 0.122749i \(-0.960829\pi\)
0.730749 0.682646i \(-0.239171\pi\)
\(830\) −7.99882 + 8.63616i −0.277643 + 0.299766i
\(831\) −17.0846 + 12.4127i −0.592659 + 0.430592i
\(832\) 11.5214 3.74352i 0.399432 0.129783i
\(833\) −4.16506 1.35331i −0.144311 0.0468894i
\(834\) −30.7361 22.3311i −1.06430 0.773262i
\(835\) −1.65855 8.38081i −0.0573964 0.290030i
\(836\) 0 0
\(837\) 2.84876i 0.0984676i
\(838\) 21.5289 29.6320i 0.743704 1.02362i
\(839\) 13.0655 40.2114i 0.451071 1.38825i −0.424616 0.905374i \(-0.639591\pi\)
0.875687 0.482880i \(-0.160409\pi\)
\(840\) 18.0601 10.0910i 0.623134 0.348173i
\(841\) 23.4328 17.0249i 0.808026 0.587066i
\(842\) −17.4109 23.9641i −0.600020 0.825857i
\(843\) 25.7675 8.37236i 0.887479 0.288359i
\(844\) −1.54351 + 4.75044i −0.0531299 + 0.163517i
\(845\) 1.39688 + 0.645624i 0.0480542 + 0.0222101i
\(846\) 17.8849 0.614895
\(847\) 0 0
\(848\) 62.4117i 2.14323i
\(849\) 35.0989 + 25.5009i 1.20459 + 0.875187i
\(850\) −1.40816 18.3500i −0.0482994 0.629400i
\(851\) −3.08845 9.50527i −0.105871 0.325837i
\(852\) −3.97936 5.47712i −0.136331 0.187643i
\(853\) 9.04511 + 12.4495i 0.309699 + 0.426264i 0.935287 0.353890i \(-0.115141\pi\)
−0.625589 + 0.780153i \(0.715141\pi\)
\(854\) −1.98796 6.11831i −0.0680265 0.209364i
\(855\) −1.26056 + 10.5621i −0.0431101 + 0.361216i
\(856\) 16.9768 + 12.3344i 0.580256 + 0.421581i
\(857\) 36.1038i 1.23328i 0.787245 + 0.616641i \(0.211507\pi\)
−0.787245 + 0.616641i \(0.788493\pi\)
\(858\) 0 0
\(859\) −48.3509 −1.64971 −0.824855 0.565344i \(-0.808743\pi\)
−0.824855 + 0.565344i \(0.808743\pi\)
\(860\) 5.82230 12.5972i 0.198539 0.429561i
\(861\) 10.8356 33.3486i 0.369277 1.13652i
\(862\) 52.6301 17.1006i 1.79259 0.582447i
\(863\) −21.8590 30.0863i −0.744088 1.02415i −0.998373 0.0570194i \(-0.981840\pi\)
0.254286 0.967129i \(-0.418160\pi\)
\(864\) 13.3600 9.70660i 0.454516 0.330225i
\(865\) 4.11320 2.29823i 0.139853 0.0781423i
\(866\) 16.1014 49.5549i 0.547146 1.68394i
\(867\) −13.9884 + 19.2533i −0.475070 + 0.653877i
\(868\) 1.13648i 0.0385745i
\(869\) 0 0
\(870\) 1.35059 0.267279i 0.0457892 0.00906160i
\(871\) −1.94694 1.41453i −0.0659694 0.0479296i
\(872\) −17.4842 5.68096i −0.592090 0.192382i
\(873\) −1.94093 + 0.630647i −0.0656906 + 0.0213442i
\(874\) −27.2754 + 19.8167i −0.922604 + 0.670311i
\(875\) 23.5028 + 8.74886i 0.794538 + 0.295765i
\(876\) −3.98752 12.2723i −0.134726 0.414644i
\(877\) −24.5308 7.97055i −0.828347 0.269146i −0.135998 0.990709i \(-0.543424\pi\)
−0.692349 + 0.721563i \(0.743424\pi\)
\(878\) 34.6426 47.6815i 1.16913 1.60917i
\(879\) 27.7221 0.935044
\(880\) 0 0
\(881\) −45.6820 −1.53906 −0.769532 0.638608i \(-0.779511\pi\)
−0.769532 + 0.638608i \(0.779511\pi\)
\(882\) −1.72270 + 2.37109i −0.0580062 + 0.0798387i
\(883\) −4.72324 1.53467i −0.158950 0.0516459i 0.228461 0.973553i \(-0.426631\pi\)
−0.387411 + 0.921907i \(0.626631\pi\)
\(884\) −1.87609 5.77401i −0.0630997 0.194201i
\(885\) 1.11344 + 1.03127i 0.0374277 + 0.0346656i
\(886\) −31.4401 + 22.8426i −1.05625 + 0.767411i
\(887\) −27.5076 + 8.93777i −0.923615 + 0.300101i −0.731949 0.681359i \(-0.761389\pi\)
−0.191666 + 0.981460i \(0.561389\pi\)
\(888\) −10.1725 3.30524i −0.341367 0.110917i
\(889\) 4.41031 + 3.20428i 0.147917 + 0.107468i
\(890\) −7.12641 36.0104i −0.238878 1.20707i
\(891\) 0 0
\(892\) 6.43021i 0.215299i
\(893\) 37.3313 51.3821i 1.24924 1.71944i
\(894\) 5.97289 18.3827i 0.199763 0.614808i
\(895\) −5.47958 9.80692i −0.183162 0.327809i
\(896\) 24.2823 17.6421i 0.811215 0.589382i
\(897\) 16.5517 + 22.7814i 0.552644 + 0.760649i
\(898\) −49.3984 + 16.0505i −1.64845 + 0.535613i
\(899\) 0.0399968 0.123098i 0.00133397 0.00410553i
\(900\) −3.22539 0.781006i −0.107513 0.0260335i
\(901\) 28.1559 0.938010
\(902\) 0 0
\(903\) 37.2692i 1.24024i
\(904\) 0.390933 + 0.284030i 0.0130022 + 0.00944668i
\(905\) −4.14642 + 34.7425i −0.137832 + 1.15488i
\(906\) −12.9018 39.7076i −0.428633 1.31920i
\(907\) −7.78974 10.7217i −0.258654 0.356007i 0.659864 0.751385i \(-0.270614\pi\)
−0.918519 + 0.395378i \(0.870614\pi\)
\(908\) −1.65081 2.27214i −0.0547839 0.0754036i
\(909\) 2.75182 + 8.46923i 0.0912720 + 0.280906i
\(910\) 30.4873 + 3.63857i 1.01064 + 0.120617i
\(911\) −11.1099 8.07183i −0.368088 0.267431i 0.388330 0.921520i \(-0.373052\pi\)
−0.756418 + 0.654089i \(0.773052\pi\)
\(912\) 51.4833i 1.70478i
\(913\) 0 0
\(914\) 64.7117 2.14047
\(915\) 3.21128 6.94796i 0.106162 0.229692i
\(916\) −0.618563 + 1.90374i −0.0204379 + 0.0629014i
\(917\) −3.38865 + 1.10104i −0.111903 + 0.0363596i
\(918\) 8.97313 + 12.3505i 0.296157 + 0.407626i
\(919\) −48.0394 + 34.9027i −1.58467 + 1.15133i −0.673595 + 0.739101i \(0.735251\pi\)
−0.911079 + 0.412232i \(0.864749\pi\)
\(920\) 8.78012 + 15.7140i 0.289472 + 0.518074i
\(921\) 4.19207 12.9019i 0.138133 0.425131i
\(922\) 8.64002 11.8920i 0.284544 0.391641i
\(923\) 17.1950i 0.565981i
\(924\) 0 0
\(925\) −4.93842 11.9885i −0.162374 0.394179i
\(926\) −5.63652 4.09517i −0.185228 0.134576i
\(927\) −8.76383 2.84754i −0.287842 0.0935255i
\(928\) 0.713578 0.231856i 0.0234244 0.00761103i
\(929\) 15.8471 11.5136i 0.519926 0.377749i −0.296650 0.954986i \(-0.595869\pi\)
0.816576 + 0.577238i \(0.195869\pi\)
\(930\) −3.41009 + 3.68181i −0.111821 + 0.120731i
\(931\) 3.21618 + 9.89839i 0.105406 + 0.324407i
\(932\) 7.37371 + 2.39586i 0.241534 + 0.0784791i
\(933\) 6.38596 8.78952i 0.209067 0.287756i
\(934\) 11.1327 0.364275
\(935\) 0 0
\(936\) 6.95320 0.227272
\(937\) 23.8319 32.8018i 0.778554 1.07159i −0.216886 0.976197i \(-0.569590\pi\)
0.995440 0.0953903i \(-0.0304099\pi\)
\(938\) −2.29593 0.745994i −0.0749649 0.0243576i
\(939\) −8.68498 26.7296i −0.283424 0.872288i
\(940\) 14.5372 + 13.4644i 0.474153 + 0.439161i
\(941\) −0.331447 + 0.240811i −0.0108049 + 0.00785020i −0.593175 0.805074i \(-0.702126\pi\)
0.582370 + 0.812924i \(0.302126\pi\)
\(942\) 44.5889 14.4878i 1.45278 0.472038i
\(943\) 29.0164 + 9.42799i 0.944903 + 0.307018i
\(944\) 1.37111 + 0.996169i 0.0446258 + 0.0324225i
\(945\) −20.4066 + 4.03843i −0.663826 + 0.131370i
\(946\) 0 0
\(947\) 2.45729i 0.0798511i −0.999203 0.0399256i \(-0.987288\pi\)
0.999203 0.0399256i \(-0.0127121\pi\)
\(948\) −6.19409 + 8.52544i −0.201175 + 0.276893i
\(949\) −10.1277 + 31.1699i −0.328759 + 1.01182i
\(950\) −33.3137 + 28.3403i −1.08084 + 0.919482i
\(951\) −29.8541 + 21.6903i −0.968086 + 0.703355i
\(952\) 6.12614 + 8.43191i 0.198549 + 0.273280i
\(953\) 58.0396 18.8582i 1.88009 0.610877i 0.893152 0.449755i \(-0.148489\pi\)
0.986935 0.161122i \(-0.0515112\pi\)
\(954\) 5.82273 17.9205i 0.188518 0.580199i
\(955\) −6.32442 2.92308i −0.204653 0.0945887i
\(956\) −14.7820 −0.478085
\(957\) 0 0
\(958\) 34.4309i 1.11241i
\(959\) −33.9380 24.6574i −1.09592 0.796230i
\(960\) 14.3568 + 1.71345i 0.463365 + 0.0553013i
\(961\) −9.43374 29.0341i −0.304314 0.936582i
\(962\) −9.33060 12.8425i −0.300830 0.414058i
\(963\) 5.31357 + 7.31350i 0.171227 + 0.235674i
\(964\) 6.48385 + 19.9552i 0.208831 + 0.642715i
\(965\) 21.3958 + 2.55352i 0.688754 + 0.0822008i
\(966\) 22.8528 + 16.6035i 0.735276 + 0.534209i
\(967\) 17.1997i 0.553106i 0.960999 + 0.276553i \(0.0891921\pi\)
−0.960999 + 0.276553i \(0.910808\pi\)
\(968\) 0 0
\(969\) −23.2258 −0.746119
\(970\) −7.61721 3.52060i −0.244574 0.113040i
\(971\) 8.40803 25.8773i 0.269827 0.830441i −0.720715 0.693231i \(-0.756187\pi\)
0.990542 0.137210i \(-0.0438134\pi\)
\(972\) 6.35769 2.06574i 0.203923 0.0662586i
\(973\) 15.3301 + 21.1000i 0.491460 + 0.676436i
\(974\) −21.1220 + 15.3461i −0.676794 + 0.491720i
\(975\) 23.6709 + 27.8248i 0.758074 + 0.891106i
\(976\) 2.64135 8.12923i 0.0845474 0.260210i
\(977\) 11.2692 15.5107i 0.360532 0.496230i −0.589765 0.807575i \(-0.700780\pi\)
0.950297 + 0.311345i \(0.100780\pi\)
\(978\) 11.8516i 0.378971i
\(979\) 0 0
\(980\) −3.18529 + 0.630365i −0.101750 + 0.0201363i
\(981\) −6.40716 4.65508i −0.204565 0.148625i
\(982\) −30.4182 9.88348i −0.970685 0.315395i
\(983\) 22.9494 7.45672i 0.731973 0.237832i 0.0807665 0.996733i \(-0.474263\pi\)
0.651206 + 0.758901i \(0.274263\pi\)
\(984\) 26.4154 19.1919i 0.842092 0.611816i
\(985\) −23.6191 21.8760i −0.752567 0.697028i
\(986\) 0.214336 + 0.659657i 0.00682584 + 0.0210078i
\(987\) −50.6090 16.4439i −1.61090 0.523414i
\(988\) −8.48072 + 11.6727i −0.269808 + 0.371358i
\(989\) −32.4276 −1.03114
\(990\) 0 0
\(991\) 27.7081 0.880177 0.440089 0.897954i \(-0.354947\pi\)
0.440089 + 0.897954i \(0.354947\pi\)
\(992\) −1.60752 + 2.21256i −0.0510387 + 0.0702488i
\(993\) −0.879435 0.285746i −0.0279080 0.00906786i
\(994\) 5.33020 + 16.4047i 0.169064 + 0.520324i
\(995\) 22.4844 24.2759i 0.712803 0.769599i
\(996\) −3.74952 + 2.72418i −0.118808 + 0.0863191i
\(997\) −31.8520 + 10.3494i −1.00876 + 0.327767i −0.766362 0.642408i \(-0.777935\pi\)
−0.242402 + 0.970176i \(0.577935\pi\)
\(998\) 65.2409 + 21.1981i 2.06517 + 0.671013i
\(999\) 8.70103 + 6.32167i 0.275288 + 0.200009i
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 605.2.j.g.444.4 16
5.4 even 2 inner 605.2.j.g.444.1 16
11.2 odd 10 55.2.j.a.49.4 yes 16
11.3 even 5 inner 605.2.j.g.124.1 16
11.4 even 5 605.2.j.d.9.4 16
11.5 even 5 605.2.b.f.364.7 8
11.6 odd 10 605.2.b.g.364.2 8
11.7 odd 10 55.2.j.a.9.1 16
11.8 odd 10 605.2.j.h.124.4 16
11.9 even 5 605.2.j.d.269.1 16
11.10 odd 2 605.2.j.h.444.1 16
33.2 even 10 495.2.ba.a.379.1 16
33.29 even 10 495.2.ba.a.64.4 16
44.7 even 10 880.2.cd.c.449.1 16
44.35 even 10 880.2.cd.c.49.4 16
55.2 even 20 275.2.h.d.126.4 16
55.4 even 10 605.2.j.d.9.1 16
55.7 even 20 275.2.h.d.251.4 16
55.9 even 10 605.2.j.d.269.4 16
55.13 even 20 275.2.h.d.126.1 16
55.14 even 10 inner 605.2.j.g.124.4 16
55.17 even 20 3025.2.a.bl.1.7 8
55.18 even 20 275.2.h.d.251.1 16
55.19 odd 10 605.2.j.h.124.1 16
55.24 odd 10 55.2.j.a.49.1 yes 16
55.27 odd 20 3025.2.a.bk.1.2 8
55.28 even 20 3025.2.a.bl.1.2 8
55.29 odd 10 55.2.j.a.9.4 yes 16
55.38 odd 20 3025.2.a.bk.1.7 8
55.39 odd 10 605.2.b.g.364.7 8
55.49 even 10 605.2.b.f.364.2 8
55.54 odd 2 605.2.j.h.444.4 16
165.29 even 10 495.2.ba.a.64.1 16
165.134 even 10 495.2.ba.a.379.4 16
220.79 even 10 880.2.cd.c.49.1 16
220.139 even 10 880.2.cd.c.449.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.9.1 16 11.7 odd 10
55.2.j.a.9.4 yes 16 55.29 odd 10
55.2.j.a.49.1 yes 16 55.24 odd 10
55.2.j.a.49.4 yes 16 11.2 odd 10
275.2.h.d.126.1 16 55.13 even 20
275.2.h.d.126.4 16 55.2 even 20
275.2.h.d.251.1 16 55.18 even 20
275.2.h.d.251.4 16 55.7 even 20
495.2.ba.a.64.1 16 165.29 even 10
495.2.ba.a.64.4 16 33.29 even 10
495.2.ba.a.379.1 16 33.2 even 10
495.2.ba.a.379.4 16 165.134 even 10
605.2.b.f.364.2 8 55.49 even 10
605.2.b.f.364.7 8 11.5 even 5
605.2.b.g.364.2 8 11.6 odd 10
605.2.b.g.364.7 8 55.39 odd 10
605.2.j.d.9.1 16 55.4 even 10
605.2.j.d.9.4 16 11.4 even 5
605.2.j.d.269.1 16 11.9 even 5
605.2.j.d.269.4 16 55.9 even 10
605.2.j.g.124.1 16 11.3 even 5 inner
605.2.j.g.124.4 16 55.14 even 10 inner
605.2.j.g.444.1 16 5.4 even 2 inner
605.2.j.g.444.4 16 1.1 even 1 trivial
605.2.j.h.124.1 16 55.19 odd 10
605.2.j.h.124.4 16 11.8 odd 10
605.2.j.h.444.1 16 11.10 odd 2
605.2.j.h.444.4 16 55.54 odd 2
880.2.cd.c.49.1 16 220.79 even 10
880.2.cd.c.49.4 16 44.35 even 10
880.2.cd.c.449.1 16 44.7 even 10
880.2.cd.c.449.4 16 220.139 even 10
3025.2.a.bk.1.2 8 55.27 odd 20
3025.2.a.bk.1.7 8 55.38 odd 20
3025.2.a.bl.1.2 8 55.28 even 20
3025.2.a.bl.1.7 8 55.17 even 20