Properties

Label 605.2.j.h.444.4
Level $605$
Weight $2$
Character 605.444
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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.h.124.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.972539 - 1.33858i) q^{2} +(1.87813 + 0.610243i) q^{3} +(-0.227943 - 0.701538i) q^{4} +(-2.02976 + 0.938132i) q^{5} +(2.64342 - 1.92056i) q^{6} +(2.13329 - 0.693148i) q^{7} +(1.98645 + 0.645437i) q^{8} +(0.727943 + 0.528882i) q^{9} +O(q^{10})\) \(q+(0.972539 - 1.33858i) q^{2} +(1.87813 + 0.610243i) q^{3} +(-0.227943 - 0.701538i) q^{4} +(-2.02976 + 0.938132i) 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} +(-4.38464 + 0.523295i) 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} +(1.12080 + 1.21011i) q^{20} +4.42960 q^{21} +3.85415i q^{23} +(3.33695 + 2.42443i) q^{24} +(3.23982 - 3.80836i) 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} +(-3.56376 + 6.37814i) q^{30} +(-0.555687 - 0.403730i) q^{31} -3.98166i q^{32} +3.68079 q^{34} +(-3.67979 + 3.40823i) 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} +(-4.63751 + 0.553474i) 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} +(-1.94696 - 8.04054i) 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} +(1.36656 + 2.95671i) 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} +(0.983462 + 8.24035i) 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} +(8.40884 - 5.17554i) q^{75} +3.89979 q^{76} -12.0888i q^{78} +(-5.85264 - 4.25219i) q^{79} +(-5.37836 + 9.62576i) 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} +(-4.34249 - 2.42635i) q^{85} +(-11.2624 - 8.18263i) q^{86} -0.372127i q^{87} -9.92195 q^{89} +(-2.44235 + 2.26211i) 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} +(-1.40095 - 11.7384i) 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 0.796058 0.605221i \(-0.206915\pi\)
0.288284 + 0.957545i \(0.406915\pi\)
\(4\) −0.227943 0.701538i −0.113972 0.350769i
\(5\) −2.02976 + 0.938132i −0.907734 + 0.419545i
\(6\) 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
\(15\) −4.38464 + 0.523295i −1.13211 + 0.135114i
\(16\) 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 \(0.307404\pi\)
−0.943612 + 0.331053i \(0.892596\pi\)
\(20\) 1.12080 + 1.21011i 0.250619 + 0.270589i
\(21\) 4.42960 0.966617
\(22\) 0 0
\(23\) 3.85415i 0.803647i 0.915717 + 0.401823i \(0.131623\pi\)
−0.915717 + 0.401823i \(0.868377\pi\)
\(24\) 3.33695 + 2.42443i 0.681152 + 0.494886i
\(25\) 3.23982 3.80836i 0.647963 0.761672i
\(26\) −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 0.945504 0.325609i \(-0.105569\pi\)
−0.956318 + 0.292330i \(0.905569\pi\)
\(30\) −3.56376 + 6.37814i −0.650651 + 1.16448i
\(31\) −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
\(35\) −3.67979 + 3.40823i −0.621999 + 0.576096i
\(36\) 0.205101 0.631235i 0.0341834 0.105206i
\(37\) −2.46624 + 0.801331i −0.405448 + 0.131738i −0.504639 0.863330i \(-0.668374\pi\)
0.0991914 + 0.995068i \(0.468374\pi\)
\(38\) 5.14166 + 7.07689i 0.834087 + 1.14802i
\(39\) 5.91087 4.29450i 0.946496 0.687670i
\(40\) −4.63751 + 0.553474i −0.733255 + 0.0875119i
\(41\) 2.44619 7.52860i 0.382031 1.17577i −0.556581 0.830793i \(-0.687887\pi\)
0.938611 0.344976i \(-0.112113\pi\)
\(42\) 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 −0.684311 0.729190i \(-0.739897\pi\)
−0.982227 + 0.187699i \(0.939897\pi\)
\(48\) 9.26140 3.00921i 1.33677 0.434342i
\(49\) −1.59265 + 1.15713i −0.227521 + 0.165304i
\(50\) −1.94696 8.04054i −0.275342 1.13710i
\(51\) 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 \(0.535403\pi\)
−0.910882 + 0.412667i \(0.864597\pi\)
\(54\) −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 \(0.892878\pi\)
\(60\) 1.36656 + 2.95671i 0.176422 + 0.381710i
\(61\) −1.40233 + 1.01885i −0.179550 + 0.130451i −0.673930 0.738795i \(-0.735395\pi\)
0.494380 + 0.869246i \(0.335395\pi\)
\(62\) −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 \(0.0126508\pi\)
−0.999210 + 0.0397332i \(0.987349\pi\)
\(68\) 0.964532 1.32756i 0.116967 0.160991i
\(69\) −2.35197 + 7.23862i −0.283144 + 0.871428i
\(70\) 0.983462 + 8.24035i 0.117546 + 0.984910i
\(71\) −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
\(75\) 8.40884 5.17554i 0.970969 0.597619i
\(76\) 3.89979 0.447336
\(77\) 0 0
\(78\) 12.0888i 1.36878i
\(79\) −5.85264 4.25219i −0.658473 0.478409i 0.207674 0.978198i \(-0.433411\pi\)
−0.866147 + 0.499789i \(0.833411\pi\)
\(80\) −5.37836 + 9.62576i −0.601319 + 1.07619i
\(81\) −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
\(85\) −4.34249 2.42635i −0.471009 0.263174i
\(86\) −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 \(0.676257\pi\)
\(90\) −2.44235 + 2.26211i −0.257446 + 0.238447i
\(91\) 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
\(95\) −1.40095 11.7384i −0.143734 1.20434i
\(96\) 2.42978 7.47810i 0.247989 0.763231i
\(97\) 1.33316 1.83494i 0.135362 0.186310i −0.735955 0.677031i \(-0.763266\pi\)
0.871317 + 0.490721i \(0.163266\pi\)
\(98\) 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 0.113245 0.993567i \(-0.463876\pi\)
−0.909944 + 0.414731i \(0.863876\pi\)
\(102\) 6.91303 + 2.24618i 0.684492 + 0.222405i
\(103\) 9.73989 3.16468i 0.959700 0.311825i 0.213049 0.977041i \(-0.431661\pi\)
0.746651 + 0.665216i \(0.231661\pi\)
\(104\) 6.25176 4.54217i 0.613035 0.445396i
\(105\) −8.99100 + 4.15555i −0.877431 + 0.405540i
\(106\) 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 \(-0.361494\pi\)
0.421527 + 0.906816i \(0.361494\pi\)
\(110\) 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 0.298649 0.954363i \(-0.403464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(114\) 5.33811 + 16.4290i 0.499960 + 1.53872i
\(115\) −3.61571 7.82299i −0.337166 0.729498i
\(116\) −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
\(125\) −3.00329 + 10.7694i −0.268623 + 0.963246i
\(126\) 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
\(130\) 9.30136 + 10.0425i 0.815783 + 0.880784i
\(131\) 1.58846 0.138785 0.0693924 0.997589i \(-0.477894\pi\)
0.0693924 + 0.997589i \(0.477894\pi\)
\(132\) 0 0
\(133\) 11.8588i 1.02829i
\(134\) 0.870697 + 0.632598i 0.0752167 + 0.0546482i
\(135\) 8.09597 + 4.52359i 0.696791 + 0.389329i
\(136\) 1.43584 + 4.41907i 0.123123 + 0.378932i
\(137\) 10.9927 + 15.1301i 0.939169 + 1.29266i 0.956174 + 0.292800i \(0.0945870\pi\)
−0.0170046 + 0.999855i \(0.505413\pi\)
\(138\) 7.40212 + 10.1881i 0.630111 + 0.867273i
\(139\) −3.59306 11.0583i −0.304759 0.937953i −0.979767 0.200142i \(-0.935860\pi\)
0.675008 0.737811i \(-0.264140\pi\)
\(140\) 3.22979 + 1.80463i 0.272967 + 0.152519i
\(141\) −19.1927 13.9443i −1.61632 1.17432i
\(142\) 7.68984i 0.645317i
\(143\) 0 0
\(144\) 4.43700 0.369750
\(145\) 0.286323 + 0.309137i 0.0237778 + 0.0256724i
\(146\) −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 −0.374236 0.927333i \(-0.622095\pi\)
0.766301 + 0.642482i \(0.222095\pi\)
\(150\) 1.25003 16.2893i 0.102064 1.33002i
\(151\) 3.94858 12.1525i 0.321331 0.988954i −0.651739 0.758443i \(-0.725960\pi\)
0.973070 0.230511i \(-0.0740397\pi\)
\(152\) −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 0.797899 0.602791i \(-0.205945\pi\)
0.291202 + 0.956662i \(0.405945\pi\)
\(158\) −11.3838 + 3.69883i −0.905649 + 0.294263i
\(159\) −20.2206 + 14.6911i −1.60360 + 1.16508i
\(160\) 3.73533 + 8.08181i 0.295304 + 0.638923i
\(161\) 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 −0.717318 0.696746i \(-0.754630\pi\)
0.884308 + 0.466903i \(0.154630\pi\)
\(164\) −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
\(170\) −7.47111 + 3.45307i −0.573008 + 0.264838i
\(171\) −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 \(0.160121\pi\)
\(180\) 0.175878 + 1.47366i 0.0131091 + 0.109840i
\(181\) 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
\(185\) 4.25411 3.94017i 0.312769 0.289687i
\(186\) −2.24430 −0.164560
\(187\) 0 0
\(188\) 8.86140i 0.646284i
\(189\) −7.52636 5.46822i −0.547462 0.397754i
\(190\) −17.0754 9.54079i −1.23878 0.692162i
\(191\) 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
\(195\) −7.96881 + 14.2620i −0.570659 + 1.02132i
\(196\) 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 \(0.675745\pi\)
\(200\) 8.89379 5.47402i 0.628886 0.387071i
\(201\) −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
\(205\) 2.09765 + 17.5761i 0.146506 + 1.22757i
\(206\) 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 0.760164 0.649731i \(-0.225118\pi\)
−0.383027 + 0.923737i \(0.625118\pi\)
\(212\) 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
\(215\) 7.89315 + 17.0777i 0.538308 + 1.16469i
\(216\) −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 0.0179708 0.999839i \(-0.494279\pi\)
−0.573152 + 0.819449i \(0.694279\pi\)
\(224\) −2.75988 8.49404i −0.184402 0.567532i
\(225\) 4.37257 1.05879i 0.291505 0.0705860i
\(226\) −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
\(235\) 26.6730 3.18334i 1.73995 0.207658i
\(236\) 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 \(0.324448\pi\)
−0.924542 + 0.381079i \(0.875552\pi\)
\(240\) −15.9753 + 14.7964i −1.03120 + 0.955102i
\(241\) 28.4450 1.83230 0.916152 0.400832i \(-0.131279\pi\)
0.916152 + 0.400832i \(0.131279\pi\)
\(242\) 0 0
\(243\) 9.06251i 0.581361i
\(244\) 1.03442 + 0.751547i 0.0662217 + 0.0481129i
\(245\) 2.14715 3.84280i 0.137176 0.245507i
\(246\) −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
\(250\) 11.4950 + 14.4938i 0.727005 + 0.916670i
\(251\) 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
\(255\) −6.67512 7.20698i −0.418012 0.451319i
\(256\) 4.81797 14.8282i 0.301123 0.926761i
\(257\) 23.4686 7.62540i 1.46393 0.475660i 0.534662 0.845066i \(-0.320439\pi\)
0.929268 + 0.369407i \(0.120439\pi\)
\(258\) −16.1590 22.2409i −1.00601 1.38466i
\(259\) −4.70577 + 3.41894i −0.292402 + 0.212443i
\(260\) 6.05943 0.723175i 0.375790 0.0448494i
\(261\) 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 \(0.365532\pi\)
\(270\) 13.9289 6.43778i 0.847684 0.391791i
\(271\) −1.56357 4.81219i −0.0949804 0.292319i 0.892268 0.451506i \(-0.149113\pi\)
−0.987249 + 0.159186i \(0.949113\pi\)
\(272\) 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
\(280\) −9.50952 + 4.39520i −0.568303 + 0.262664i
\(281\) 11.0995 8.06425i 0.662140 0.481073i −0.205245 0.978711i \(-0.565799\pi\)
0.867385 + 0.497638i \(0.165799\pi\)
\(282\) −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
\(290\) 0.692265 0.0826199i 0.0406512 0.00485161i
\(291\) 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
\(295\) −0.522216 0.563825i −0.0304046 0.0328272i
\(296\) −5.41627 −0.314815
\(297\) 0 0
\(298\) 9.78772i 0.566988i
\(299\) 11.5361 + 8.38148i 0.667151 + 0.484714i
\(300\) −5.54757 4.71939i −0.320289 0.272474i
\(301\) −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
\(305\) 1.89057 3.38360i 0.108254 0.193744i
\(306\) 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
\(310\) 1.86441 1.72681i 0.105891 0.0980765i
\(311\) −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 0.504271 0.863546i \(-0.331761\pi\)
−0.977109 + 0.212740i \(0.931761\pi\)
\(314\) 19.2069 13.9546i 1.08391 0.787506i
\(315\) −4.48123 + 0.534822i −0.252489 + 0.0301338i
\(316\) −1.64900 + 5.07510i −0.0927636 + 0.285497i
\(317\) −10.9836 + 15.1176i −0.616900 + 0.849090i −0.997123 0.0758046i \(-0.975847\pi\)
0.380222 + 0.924895i \(0.375847\pi\)
\(318\) 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
\(325\) −4.35354 17.9792i −0.241491 0.997307i
\(326\) −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
\(335\) −0.610218 1.32028i −0.0333398 0.0721344i
\(336\) 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
\(345\) −2.01686 16.8991i −0.108584 0.909816i
\(346\) −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 −0.884435 0.466664i \(-0.845456\pi\)
0.989821 + 0.142319i \(0.0454557\pi\)
\(350\) −9.72672 15.8033i −0.519915 0.844721i
\(351\) −15.3446 −0.819037
\(352\) 0 0
\(353\) 12.1971i 0.649186i −0.945854 0.324593i \(-0.894773\pi\)
0.945854 0.324593i \(-0.105227\pi\)
\(354\) 0.908513 + 0.660073i 0.0482869 + 0.0350825i
\(355\) 5.06908 9.07224i 0.269039 0.481505i
\(356\) 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 \(-0.880436\pi\)
0.536984 0.843593i \(-0.319564\pi\)
\(360\) −3.66857 2.04980i −0.193351 0.108034i
\(361\) −7.24126 5.26109i −0.381119 0.276899i
\(362\) 25.8902i 1.36076i
\(363\) 0 0
\(364\) −6.12155 −0.320856
\(365\) 14.5323 13.4599i 0.760657 0.704522i
\(366\) −1.75019 + 5.38652i −0.0914837 + 0.281558i
\(367\) −19.3920 + 6.30083i −1.01225 + 0.328901i −0.767751 0.640748i \(-0.778624\pi\)
−0.244501 + 0.969649i \(0.578624\pi\)
\(368\) 11.1711 + 15.3758i 0.582336 + 0.801517i
\(369\) 5.76243 4.18665i 0.299980 0.217948i
\(370\) −1.13696 9.52646i −0.0591075 0.495257i
\(371\) −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 \(0.0969036\pi\)
\(380\) −7.91562 + 3.65852i −0.406063 + 0.187678i
\(381\) 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 −0.770795 0.637083i \(-0.780141\pi\)
0.844091 + 0.536200i \(0.180141\pi\)
\(384\) 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 \(-0.430320\pi\)
\(390\) 11.3409 + 24.5372i 0.574267 + 1.24249i
\(391\) −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 \(0.242387\pi\)
−0.723814 + 0.689995i \(0.757613\pi\)
\(398\) −14.3914 + 19.8081i −0.721376 + 0.992888i
\(399\) −7.23674 + 22.2724i −0.362290 + 1.11501i
\(400\) 1.88651 24.5836i 0.0943257 1.22918i
\(401\) 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
\(405\) 16.5464 + 17.8648i 0.822196 + 0.887708i
\(406\) −0.699363 −0.0347088
\(407\) 0 0
\(408\) 9.17582i 0.454271i
\(409\) 10.9682 + 7.96888i 0.542344 + 0.394036i 0.824955 0.565199i \(-0.191201\pi\)
−0.282611 + 0.959235i \(0.591201\pi\)
\(410\) 25.5671 + 14.2855i 1.26267 + 0.705511i
\(411\) 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
\(415\) −6.21067 3.47019i −0.304870 0.170345i
\(416\) −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 \(0.318149\pi\)
\(420\) 4.96471 + 5.36029i 0.242253 + 0.261555i
\(421\) 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
\(425\) 11.0904 + 0.851066i 0.537965 + 0.0412828i
\(426\) −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 −0.303361 0.952876i \(-0.598109\pi\)
−0.999982 + 0.00594140i \(0.998109\pi\)
\(432\) −19.4509 6.31998i −0.935832 0.304070i
\(433\) −29.9501 + 9.73138i −1.43931 + 0.467660i −0.921682 0.387946i \(-0.873185\pi\)
−0.517628 + 0.855606i \(0.673185\pi\)
\(434\) −2.06235 + 1.49838i −0.0989958 + 0.0719247i
\(435\) 0.349104 + 0.755327i 0.0167383 + 0.0362151i
\(436\) −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 \(-0.823425\pi\)
−0.850045 + 0.526710i \(0.823425\pi\)
\(440\) 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 0.787098 0.616828i \(-0.211583\pi\)
0.274213 + 0.961669i \(0.411583\pi\)
\(444\) 1.16728 + 3.59253i 0.0553969 + 0.170494i
\(445\) 20.1391 9.30810i 0.954686 0.441246i
\(446\) −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
\(455\) 2.19909 + 18.4260i 0.103095 + 0.863823i
\(456\) −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
\(460\) −4.66395 + 4.31975i −0.217458 + 0.201409i
\(461\) −8.88399 −0.413769 −0.206884 0.978365i \(-0.566332\pi\)
−0.206884 + 0.978365i \(0.566332\pi\)
\(462\) 0 0
\(463\) 4.21081i 0.195693i 0.995202 + 0.0978464i \(0.0311954\pi\)
−0.995202 + 0.0978464i \(0.968805\pi\)
\(464\) −0.751758 0.546184i −0.0348995 0.0253560i
\(465\) 2.64776 + 1.47942i 0.122787 + 0.0686067i
\(466\) 5.37410 + 16.5398i 0.248950 + 0.766190i
\(467\) −3.95488 5.44342i −0.183010 0.251891i 0.707649 0.706565i \(-0.249756\pi\)
−0.890658 + 0.454673i \(0.849756\pi\)
\(468\) −1.44337 1.98662i −0.0667196 0.0918317i
\(469\) 0.450866 + 1.38762i 0.0208190 + 0.0640744i
\(470\) 21.6793 38.8000i 0.999993 1.78971i
\(471\) 22.9240 + 16.6552i 1.05628 + 0.767433i
\(472\) 0.717854i 0.0330419i
\(473\) 0 0
\(474\) −23.6376 −1.08571
\(475\) 13.8558 + 22.5119i 0.635747 + 1.03292i
\(476\) 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 −0.132506 0.991182i \(-0.542302\pi\)
0.901724 + 0.432313i \(0.142302\pi\)
\(480\) 2.08358 + 17.4582i 0.0951022 + 0.796853i
\(481\) −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 0.628611 0.777720i \(-0.283624\pi\)
0.0514249 + 0.998677i \(0.483624\pi\)
\(488\) −3.44327 + 1.11879i −0.155869 + 0.0506450i
\(489\) 5.79489 4.21023i 0.262054 0.190393i
\(490\) −3.05572 6.61141i −0.138044 0.298673i
\(491\) 5.97340 + 18.3842i 0.269576 + 0.829669i 0.990604 + 0.136763i \(0.0436700\pi\)
−0.721028 + 0.692906i \(0.756330\pi\)
\(492\) −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 \(0.521532\pi\)
\(500\) 8.23973 0.347895i 0.368492 0.0155583i
\(501\) −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 \(0.979737\pi\)
\(510\) −16.1390 + 1.92614i −0.714646 + 0.0852909i
\(511\) −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
\(515\) −16.8007 + 15.5608i −0.740328 + 0.685692i
\(516\) −12.2561 −0.539543
\(517\) 0 0
\(518\) 9.62412i 0.422860i
\(519\) −3.36645 2.44587i −0.147771 0.107362i
\(520\) −8.42839 + 15.0845i −0.369609 + 0.661498i
\(521\) 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
\(525\) 14.3511 16.8695i 0.626332 0.736245i
\(526\) 7.28322 + 5.29157i 0.317563 + 0.230723i
\(527\) 1.52801i 0.0665611i
\(528\) 0 0
\(529\) 8.14550 0.354152
\(530\) −31.8192 34.3546i −1.38214 1.49227i
\(531\) −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
\(535\) −22.3070 + 2.66228i −0.964417 + 0.115100i
\(536\) −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 \(0.0246674\pi\)
0.381718 + 0.924279i \(0.375333\pi\)
\(542\) −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
\(545\) −17.8654 + 8.25719i −0.765268 + 0.353699i
\(546\) −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
\(555\) 10.3943 4.80412i 0.441212 0.203924i
\(556\) −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
\(565\) 0.513674 0.0613055i 0.0216104 0.00257914i
\(566\) −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 −0.955595 0.294683i \(-0.904786\pi\)
0.946303 + 0.323281i \(0.104786\pi\)
\(570\) −26.2476 28.3390i −1.09939 1.18699i
\(571\) −21.6311 −0.905235 −0.452617 0.891705i \(-0.649510\pi\)
−0.452617 + 0.891705i \(0.649510\pi\)
\(572\) 0 0
\(573\) 6.15315i 0.257051i
\(574\) −23.7682 17.2686i −0.992068 0.720779i
\(575\) 14.6780 + 12.4867i 0.612115 + 0.520733i
\(576\) 0.910431 + 2.80202i 0.0379346 + 0.116751i
\(577\) −13.7704 18.9533i −0.573269 0.789037i 0.419668 0.907677i \(-0.362146\pi\)
−0.992937 + 0.118641i \(0.962146\pi\)
\(578\) −11.7202 16.1314i −0.487495 0.670980i
\(579\) −5.88053 18.0984i −0.244387 0.752145i
\(580\) 0.151606 0.271332i 0.00629508 0.0112664i
\(581\) 5.77370 + 4.19484i 0.239533 + 0.174031i
\(582\) 7.41093i 0.307193i
\(583\) 0 0
\(584\) −18.5023 −0.765633
\(585\) −5.46126 + 5.05823i −0.225795 + 0.209132i
\(586\) −7.17756 + 22.0903i −0.296502 + 0.912540i
\(587\) 2.13735 0.694466i 0.0882177 0.0286637i −0.264576 0.964365i \(-0.585232\pi\)
0.352793 + 0.935701i \(0.385232\pi\)
\(588\) 1.68557 + 2.31998i 0.0695116 + 0.0956745i
\(589\) 2.93783 2.13446i 0.121051 0.0879488i
\(590\) −1.26260 + 0.150688i −0.0519805 + 0.00620373i
\(591\) −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 \(0.421442\pi\)
\(600\) 20.0442 4.85357i 0.818302 0.198146i
\(601\) −10.7043 32.9444i −0.436637 1.34383i −0.891400 0.453218i \(-0.850276\pi\)
0.454762 0.890613i \(-0.349724\pi\)
\(602\) −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
\(610\) −2.69058 5.82137i −0.108938 0.235700i
\(611\) −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 \(-0.812550\pi\)
0.831557 0.555439i \(-0.187450\pi\)
\(618\) 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 \(0.965233\pi\)
\(620\) −0.134259 1.12494i −0.00539196 0.0451788i
\(621\) 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
\(625\) −4.00719 24.6768i −0.160287 0.987070i
\(626\) −23.5480 −0.941167
\(627\) 0 0
\(628\) 10.5842i 0.422354i
\(629\) −4.66703 3.39079i −0.186087 0.135200i
\(630\) −3.64227 + 6.51864i −0.145111 + 0.259709i
\(631\) 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
\(635\) −4.74409 2.65074i −0.188264 0.105192i
\(636\) 14.9155 + 10.8368i 0.591440 + 0.429706i
\(637\) 7.28342i 0.288579i
\(638\) 0 0
\(639\) −4.18186 −0.165432
\(640\) −21.9517 + 20.3317i −0.867718 + 0.803681i
\(641\) −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 0.998646 0.0520249i \(-0.0165675\pi\)
−0.358077 + 0.933692i \(0.616568\pi\)
\(644\) 5.15911 3.74831i 0.203297 0.147704i
\(645\) 4.40284 + 36.8910i 0.173361 + 1.45258i
\(646\) −6.01340 + 18.5073i −0.236594 + 0.728162i
\(647\) 14.6820 20.2081i 0.577210 0.794461i −0.416176 0.909284i \(-0.636630\pi\)
0.993386 + 0.114823i \(0.0366300\pi\)
\(648\) 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 0.257191 0.966361i \(-0.417203\pi\)
0.776084 + 0.630629i \(0.217203\pi\)
\(654\) 23.2667 16.9042i 0.909800 0.661008i
\(655\) −3.22419 + 1.49019i −0.125980 + 0.0582265i
\(656\) −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 \(-0.361875\pi\)
0.420442 + 0.907320i \(0.361875\pi\)
\(660\) 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
\(665\) −11.1251 24.0704i −0.431413 0.933411i
\(666\) −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
\(675\) −20.6766 1.58670i −0.795842 0.0610720i
\(676\) −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
\(680\) −7.06008 7.62262i −0.270742 0.292314i
\(681\) 7.51888 0.288124
\(682\) 0 0
\(683\) 3.27236i 0.125213i 0.998038 + 0.0626066i \(0.0199414\pi\)
−0.998038 + 0.0626066i \(0.980059\pi\)
\(684\) 2.83882 + 2.06253i 0.108545 + 0.0788627i
\(685\) −36.5066 20.3979i −1.39484 0.779364i
\(686\) 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
\(690\) −24.5823 13.7353i −0.935833 0.522893i
\(691\) 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
\(695\) 17.6672 + 19.0749i 0.670154 + 0.723552i
\(696\) 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
\(700\) −8.24866 0.632992i −0.311770 0.0239249i
\(701\) 14.3880 44.2818i 0.543429 1.67250i −0.181267 0.983434i \(-0.558020\pi\)
0.724696 0.689068i \(-0.241980\pi\)
\(702\) −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 \(0.533033\pi\)
\(710\) −7.21409 15.6085i −0.270740 0.585776i
\(711\) −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 \(-0.235146\pi\)
\(720\) −9.00603 + 4.16250i −0.335635 + 0.155127i
\(721\) 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 \(0.320115\pi\)
−0.535522 + 0.844521i \(0.679885\pi\)
\(728\) 10.1884 14.0232i 0.377608 0.519733i
\(729\) −4.56501 + 14.0497i −0.169075 + 0.520358i
\(730\) −3.88391 32.5430i −0.143750 1.20447i
\(731\) 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
\(735\) 6.37767 5.90701i 0.235244 0.217883i
\(736\) 15.3459 0.565659
\(737\) 0 0
\(738\) 11.7852i 0.433818i
\(739\) −3.50933 2.54968i −0.129093 0.0937915i 0.521365 0.853334i \(-0.325423\pi\)
−0.650458 + 0.759542i \(0.725423\pi\)
\(740\) −3.73387 2.08629i −0.137260 0.0766934i
\(741\) 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
\(745\) −6.45199 + 11.5473i −0.236382 + 0.423059i
\(746\) 10.0661 + 7.31346i 0.368547 + 0.267765i
\(747\) 2.86281i 0.104745i
\(748\) 0 0
\(749\) 22.5357 0.823437
\(750\) 12.7443 + 34.2361i 0.465357 + 1.25012i
\(751\) −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
\(755\) 3.38598 + 28.3708i 0.123228 + 1.03252i
\(756\) −2.12058 + 6.52647i −0.0771247 + 0.237365i
\(757\) 5.45311 7.50556i 0.198197 0.272794i −0.698338 0.715768i \(-0.746077\pi\)
0.896534 + 0.442974i \(0.146077\pi\)
\(758\) 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 0.647086 0.762417i \(-0.275988\pi\)
−0.525142 + 0.851015i \(0.675988\pi\)
\(762\) 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
\(765\) −1.87783 4.06291i −0.0678932 0.146895i
\(766\) −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 \(-0.598441\pi\)
−0.304355 + 0.952559i \(0.598441\pi\)
\(770\) 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 0.450402 0.892826i \(-0.351281\pi\)
−0.160407 + 0.987051i \(0.551281\pi\)
\(774\) −3.87076 11.9130i −0.139132 0.428203i
\(775\) −3.33787 + 0.808243i −0.119900 + 0.0290330i
\(776\) 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
\(785\) −31.8585 + 3.80222i −1.13708 + 0.135707i
\(786\) 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
\(790\) 19.6364 18.1873i 0.698632 0.647074i
\(791\) −0.518940 −0.0184514
\(792\) 0 0
\(793\) 6.41307i 0.227735i
\(794\) 36.8059 + 26.7410i 1.30619 + 0.949004i
\(795\) 27.2607 48.7890i 0.966837 1.73037i
\(796\) 3.37305 + 10.3812i 0.119555 + 0.367951i
\(797\) −16.7782 23.0932i −0.594315 0.818004i 0.400858 0.916140i \(-0.368712\pi\)
−0.995173 + 0.0981362i \(0.968712\pi\)
\(798\) 22.7755 + 31.3477i 0.806243 + 1.10970i
\(799\) −8.25835 25.4166i −0.292159 0.899174i
\(800\) −15.1636 12.8999i −0.536114 0.456079i
\(801\) −7.22262 5.24754i −0.255199 0.185413i
\(802\) 3.12290i 0.110273i
\(803\) 0 0
\(804\) 0.947515 0.0334163
\(805\) −13.1358 14.1825i −0.462977 0.499867i
\(806\) −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 0.0784966 0.996914i \(-0.474988\pi\)
0.972379 + 0.233409i \(0.0749880\pi\)
\(810\) 40.0055 4.77454i 1.40565 0.167760i
\(811\) −11.8591 + 36.4985i −0.416428 + 1.28163i 0.494539 + 0.869156i \(0.335337\pi\)
−0.910967 + 0.412479i \(0.864663\pi\)
\(812\) −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
\(820\) 11.8521 5.47793i 0.413894 0.191298i
\(821\) −3.16732 9.74799i −0.110540 0.340207i 0.880451 0.474138i \(-0.157240\pi\)
−0.990991 + 0.133930i \(0.957240\pi\)
\(822\) 58.1166 + 18.8832i 2.02705 + 0.658629i
\(823\) −14.8296 + 20.4112i −0.516926 + 0.711488i −0.985068 0.172165i \(-0.944924\pi\)
0.468142 + 0.883653i \(0.344924\pi\)
\(824\) 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 \(-0.239171\pi\)
\(830\) −10.6852 + 4.93861i −0.370890 + 0.171422i
\(831\) 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 \(-0.160409\pi\)
\(840\) −20.5423 + 2.45167i −0.708777 + 0.0845905i
\(841\) 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
\(845\) 1.04568 + 1.12900i 0.0359727 + 0.0388389i
\(846\) −17.8849 −0.614895
\(847\) 0 0
\(848\) 62.4117i 2.14323i
\(849\) −35.0989 25.5009i −1.20459 0.875187i
\(850\) 11.9251 14.0178i 0.409027 0.480806i
\(851\) −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
\(855\) 5.18843 9.28585i 0.177441 0.317569i
\(856\) 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 \(0.808743\pi\)
\(860\) 10.1815 9.43009i 0.347185 0.321563i
\(861\) 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 \(0.0181597\pi\)
−0.254286 + 0.967129i \(0.581840\pi\)
\(864\) −13.3600 + 9.70660i −0.454516 + 0.330225i
\(865\) 4.67852 0.558367i 0.159074 0.0189851i
\(866\) −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
\(875\) 1.05791 + 25.0560i 0.0357637 + 0.847048i
\(876\) 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 0.387411 0.921907i \(-0.373369\pi\)
−0.228461 + 0.973553i \(0.573369\pi\)
\(884\) −1.87609 5.77401i −0.0630997 0.194201i
\(885\) −0.636721 1.37762i −0.0214031 0.0463081i
\(886\) 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
\(895\) −1.33129 11.1548i −0.0445002 0.372863i
\(896\) 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
\(900\) −1.73948 2.82618i −0.0579827 0.0942060i
\(901\) −28.1559 −0.938010
\(902\) 0 0
\(903\) 37.2692i 1.24024i
\(904\) −0.390933 0.284030i −0.0130022 0.00944668i
\(905\) −17.0666 + 30.5445i −0.567314 + 1.01533i
\(906\) −12.9018 39.7076i −0.428633 1.31920i
\(907\) 7.78974 + 10.7217i 0.258654 + 0.356007i 0.918519 0.395378i \(-0.129386\pi\)
−0.659864 + 0.751385i \(0.729386\pi\)
\(908\) −1.65081 2.27214i −0.0547839 0.0754036i
\(909\) −2.75182 8.46923i −0.0912720 0.280906i
\(910\) 26.8034 + 14.9763i 0.888525 + 0.496460i
\(911\) −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
\(915\) 5.61556 5.20114i 0.185645 0.171944i
\(916\) −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 \(-0.264749\pi\)
0.911079 0.412232i \(-0.135251\pi\)
\(920\) −2.13317 17.8737i −0.0703286 0.589278i
\(921\) −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 \(0.195869\pi\)
\(930\) 4.55538 2.10545i 0.149377 0.0690405i
\(931\) −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
\(940\) −8.31316 17.9865i −0.271146 0.586654i
\(941\) 0.331447 0.240811i 0.0108049 0.00785020i −0.582370 0.812924i \(-0.697874\pi\)
0.593175 + 0.805074i \(0.297874\pi\)
\(942\) 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 \(0.0127121\pi\)
−0.999203 + 0.0399256i \(0.987288\pi\)
\(948\) −6.19409 + 8.52544i −0.201175 + 0.276893i
\(949\) −10.1277 + 31.1699i −0.328759 + 1.01182i
\(950\) 43.6093 + 3.34653i 1.41487 + 0.108576i
\(951\) −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
\(955\) −4.73437 5.11160i −0.153201 0.165407i
\(956\) 14.7820 0.478085
\(957\) 0 0
\(958\) 34.4309i 1.11241i
\(959\) 33.9380 + 24.6574i 1.09592 + 0.796230i
\(960\) −12.6221 7.05253i −0.407375 0.227619i
\(961\) −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
\(965\) 18.8105 + 10.5103i 0.605530 + 0.338337i
\(966\) 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
\(970\) 5.70213 + 6.15647i 0.183084 + 0.197672i
\(971\) 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
\(975\) 2.79514 36.4241i 0.0895162 1.16650i
\(976\) −2.64135 + 8.12923i −0.0845474 + 0.260210i
\(977\) −11.2692 + 15.5107i −0.360532 + 0.496230i −0.950297 0.311345i \(-0.899220\pi\)
0.589765 + 0.807575i \(0.299220\pi\)
\(978\) 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 −0.651206 0.758901i \(-0.725737\pi\)
−0.0807665 + 0.996733i \(0.525737\pi\)
\(984\) 26.4154 19.1919i 0.842092 0.611816i
\(985\) −13.5066 29.2232i −0.430357 0.931127i
\(986\) −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
\(995\) 30.0358 13.8823i 0.952200 0.440097i
\(996\) 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.h.444.4 16
5.4 even 2 inner 605.2.j.h.444.1 16
11.2 odd 10 605.2.j.d.269.4 16
11.3 even 5 inner 605.2.j.h.124.1 16
11.4 even 5 55.2.j.a.9.4 yes 16
11.5 even 5 605.2.b.g.364.7 8
11.6 odd 10 605.2.b.f.364.2 8
11.7 odd 10 605.2.j.d.9.1 16
11.8 odd 10 605.2.j.g.124.4 16
11.9 even 5 55.2.j.a.49.1 yes 16
11.10 odd 2 605.2.j.g.444.1 16
33.20 odd 10 495.2.ba.a.379.4 16
33.26 odd 10 495.2.ba.a.64.1 16
44.15 odd 10 880.2.cd.c.449.4 16
44.31 odd 10 880.2.cd.c.49.1 16
55.4 even 10 55.2.j.a.9.1 16
55.9 even 10 55.2.j.a.49.4 yes 16
55.14 even 10 inner 605.2.j.h.124.4 16
55.17 even 20 3025.2.a.bk.1.7 8
55.19 odd 10 605.2.j.g.124.1 16
55.24 odd 10 605.2.j.d.269.1 16
55.27 odd 20 3025.2.a.bl.1.2 8
55.28 even 20 3025.2.a.bk.1.2 8
55.29 odd 10 605.2.j.d.9.4 16
55.37 odd 20 275.2.h.d.251.1 16
55.38 odd 20 3025.2.a.bl.1.7 8
55.39 odd 10 605.2.b.f.364.7 8
55.42 odd 20 275.2.h.d.126.1 16
55.48 odd 20 275.2.h.d.251.4 16
55.49 even 10 605.2.b.g.364.2 8
55.53 odd 20 275.2.h.d.126.4 16
55.54 odd 2 605.2.j.g.444.4 16
165.59 odd 10 495.2.ba.a.64.4 16
165.119 odd 10 495.2.ba.a.379.1 16
220.59 odd 10 880.2.cd.c.449.1 16
220.119 odd 10 880.2.cd.c.49.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.9.1 16 55.4 even 10
55.2.j.a.9.4 yes 16 11.4 even 5
55.2.j.a.49.1 yes 16 11.9 even 5
55.2.j.a.49.4 yes 16 55.9 even 10
275.2.h.d.126.1 16 55.42 odd 20
275.2.h.d.126.4 16 55.53 odd 20
275.2.h.d.251.1 16 55.37 odd 20
275.2.h.d.251.4 16 55.48 odd 20
495.2.ba.a.64.1 16 33.26 odd 10
495.2.ba.a.64.4 16 165.59 odd 10
495.2.ba.a.379.1 16 165.119 odd 10
495.2.ba.a.379.4 16 33.20 odd 10
605.2.b.f.364.2 8 11.6 odd 10
605.2.b.f.364.7 8 55.39 odd 10
605.2.b.g.364.2 8 55.49 even 10
605.2.b.g.364.7 8 11.5 even 5
605.2.j.d.9.1 16 11.7 odd 10
605.2.j.d.9.4 16 55.29 odd 10
605.2.j.d.269.1 16 55.24 odd 10
605.2.j.d.269.4 16 11.2 odd 10
605.2.j.g.124.1 16 55.19 odd 10
605.2.j.g.124.4 16 11.8 odd 10
605.2.j.g.444.1 16 11.10 odd 2
605.2.j.g.444.4 16 55.54 odd 2
605.2.j.h.124.1 16 11.3 even 5 inner
605.2.j.h.124.4 16 55.14 even 10 inner
605.2.j.h.444.1 16 5.4 even 2 inner
605.2.j.h.444.4 16 1.1 even 1 trivial
880.2.cd.c.49.1 16 44.31 odd 10
880.2.cd.c.49.4 16 220.119 odd 10
880.2.cd.c.449.1 16 220.59 odd 10
880.2.cd.c.449.4 16 44.15 odd 10
3025.2.a.bk.1.2 8 55.28 even 20
3025.2.a.bk.1.7 8 55.17 even 20
3025.2.a.bl.1.2 8 55.27 odd 20
3025.2.a.bl.1.7 8 55.38 odd 20