Properties

Label 930.2.y.b.29.7
Level $930$
Weight $2$
Character 930.29
Analytic conductor $7.426$
Analytic rank $0$
Dimension $128$
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] = [930,2,Mod(29,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.y (of order \(10\), degree \(4\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 29.7
Character \(\chi\) \(=\) 930.29
Dual form 930.2.y.b.449.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(-1.46850 + 0.918426i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.11788 + 0.717333i) q^{5} +(-1.72788 - 0.120141i) q^{6} +(0.344014 - 0.111777i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.31299 - 2.69742i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(-1.46850 + 0.918426i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.11788 + 0.717333i) q^{5} +(-1.72788 - 0.120141i) q^{6} +(0.344014 - 0.111777i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.31299 - 2.69742i) q^{9} +(1.29177 + 1.82520i) q^{10} +(0.958310 + 2.94937i) q^{11} +(-1.32727 - 1.11282i) q^{12} +(-0.514703 + 0.373954i) q^{13} +(0.344014 + 0.111777i) q^{14} +(-3.76893 + 0.891716i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.42872 - 1.11406i) q^{17} +(2.64773 - 1.41050i) q^{18} +(6.21594 + 4.51615i) q^{19} +(-0.0277621 + 2.23590i) q^{20} +(-0.402526 + 0.480096i) q^{21} +(-0.958310 + 2.94937i) q^{22} +(3.39722 + 1.10382i) q^{23} +(-0.419684 - 1.68044i) q^{24} +(3.97087 + 3.03846i) q^{25} -0.636208 q^{26} +(0.549258 + 5.16704i) q^{27} +(0.212612 + 0.292636i) q^{28} +(2.09538 + 1.52238i) q^{29} +(-3.57327 - 1.49391i) q^{30} +(-5.14638 - 2.12480i) q^{31} -1.00000 q^{32} +(-4.11606 - 3.45102i) q^{33} +(-2.11907 - 2.91664i) q^{34} +(0.808763 + 0.0100420i) q^{35} +(2.97113 + 0.415177i) q^{36} -7.20923 q^{37} +(2.37428 + 7.30728i) q^{38} +(0.412393 - 1.02187i) q^{39} +(-1.33669 + 1.79256i) q^{40} +(6.67913 - 9.19304i) q^{41} +(-0.607843 + 0.151807i) q^{42} +(-5.56022 - 4.03974i) q^{43} +(-2.50889 + 1.82281i) q^{44} +(4.71570 - 4.77097i) q^{45} +(2.09960 + 2.88985i) q^{46} +(-7.06025 + 5.12957i) q^{47} +(0.648204 - 1.60619i) q^{48} +(-5.55727 + 4.03759i) q^{49} +(1.42654 + 4.79218i) q^{50} +(6.05826 - 1.51303i) q^{51} +(-0.514703 - 0.373954i) q^{52} +(1.15194 + 0.374287i) q^{53} +(-2.59275 + 4.50307i) q^{54} +(-0.0860946 + 6.93386i) q^{55} +0.361718i q^{56} +(-13.2759 - 0.923079i) q^{57} +(0.800365 + 2.46327i) q^{58} +(2.31107 + 3.18092i) q^{59} +(-2.01274 - 3.30891i) q^{60} +10.8583i q^{61} +(-2.91458 - 4.74397i) q^{62} +(0.150177 - 1.07471i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.35833 + 0.422777i) q^{65} +(-1.30150 - 5.21129i) q^{66} +15.1272i q^{67} -3.60517i q^{68} +(-6.00260 + 1.49913i) q^{69} +(0.648400 + 0.483503i) q^{70} +(7.08557 + 2.30224i) q^{71} +(2.15966 + 2.08227i) q^{72} +(-1.81726 - 5.59295i) q^{73} +(-5.83239 - 4.23748i) q^{74} +(-8.62182 - 0.815027i) q^{75} +(-2.37428 + 7.30728i) q^{76} +(0.659344 + 0.907509i) q^{77} +(0.934272 - 0.584310i) q^{78} +(5.41909 + 1.76077i) q^{79} +(-2.13504 + 0.664526i) q^{80} +(-5.55213 - 7.08335i) q^{81} +(10.8071 - 3.51143i) q^{82} +(7.61938 - 10.4872i) q^{83} +(-0.580985 - 0.234467i) q^{84} +(-6.46248 - 4.81898i) q^{85} +(-2.12382 - 6.53644i) q^{86} +(-4.47527 - 0.311168i) q^{87} -3.10116 q^{88} +(-4.86494 - 14.9727i) q^{89} +(6.61939 - 1.08798i) q^{90} +(-0.135266 + 0.186177i) q^{91} +3.57205i q^{92} +(9.50893 - 1.60630i) q^{93} -8.72695 q^{94} +(9.92507 + 14.0236i) q^{95} +(1.46850 - 0.918426i) q^{96} +(0.210577 - 0.0684205i) q^{97} -6.86916 q^{98} +(9.21395 + 1.28753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) −1.46850 + 0.918426i −0.847839 + 0.530254i
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 2.11788 + 0.717333i 0.947147 + 0.320801i
\(6\) −1.72788 0.120141i −0.705404 0.0490472i
\(7\) 0.344014 0.111777i 0.130025 0.0422477i −0.243282 0.969956i \(-0.578224\pi\)
0.373307 + 0.927708i \(0.378224\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) 1.31299 2.69742i 0.437662 0.899139i
\(10\) 1.29177 + 1.82520i 0.408492 + 0.577178i
\(11\) 0.958310 + 2.94937i 0.288941 + 0.889270i 0.985190 + 0.171469i \(0.0548513\pi\)
−0.696248 + 0.717801i \(0.745149\pi\)
\(12\) −1.32727 1.11282i −0.383149 0.321243i
\(13\) −0.514703 + 0.373954i −0.142753 + 0.103716i −0.656870 0.754004i \(-0.728120\pi\)
0.514117 + 0.857720i \(0.328120\pi\)
\(14\) 0.344014 + 0.111777i 0.0919416 + 0.0298736i
\(15\) −3.76893 + 0.891716i −0.973134 + 0.230240i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −3.42872 1.11406i −0.831587 0.270199i −0.137873 0.990450i \(-0.544027\pi\)
−0.693714 + 0.720251i \(0.744027\pi\)
\(18\) 2.64773 1.41050i 0.624076 0.332459i
\(19\) 6.21594 + 4.51615i 1.42604 + 1.03608i 0.990738 + 0.135788i \(0.0433567\pi\)
0.435297 + 0.900287i \(0.356643\pi\)
\(20\) −0.0277621 + 2.23590i −0.00620779 + 0.499961i
\(21\) −0.402526 + 0.480096i −0.0878383 + 0.104765i
\(22\) −0.958310 + 2.94937i −0.204312 + 0.628809i
\(23\) 3.39722 + 1.10382i 0.708370 + 0.230163i 0.640974 0.767563i \(-0.278531\pi\)
0.0673964 + 0.997726i \(0.478531\pi\)
\(24\) −0.419684 1.68044i −0.0856675 0.343018i
\(25\) 3.97087 + 3.03846i 0.794173 + 0.607691i
\(26\) −0.636208 −0.124771
\(27\) 0.549258 + 5.16704i 0.105705 + 0.994398i
\(28\) 0.212612 + 0.292636i 0.0401799 + 0.0553029i
\(29\) 2.09538 + 1.52238i 0.389103 + 0.282700i 0.765088 0.643926i \(-0.222696\pi\)
−0.375985 + 0.926626i \(0.622696\pi\)
\(30\) −3.57327 1.49391i −0.652386 0.272749i
\(31\) −5.14638 2.12480i −0.924317 0.381625i
\(32\) −1.00000 −0.176777
\(33\) −4.11606 3.45102i −0.716514 0.600746i
\(34\) −2.11907 2.91664i −0.363417 0.500200i
\(35\) 0.808763 + 0.0100420i 0.136706 + 0.00169741i
\(36\) 2.97113 + 0.415177i 0.495189 + 0.0691961i
\(37\) −7.20923 −1.18519 −0.592595 0.805501i \(-0.701896\pi\)
−0.592595 + 0.805501i \(0.701896\pi\)
\(38\) 2.37428 + 7.30728i 0.385159 + 1.18540i
\(39\) 0.412393 1.02187i 0.0660357 0.163630i
\(40\) −1.33669 + 1.79256i −0.211349 + 0.283429i
\(41\) 6.67913 9.19304i 1.04311 1.43571i 0.148469 0.988917i \(-0.452565\pi\)
0.894637 0.446795i \(-0.147435\pi\)
\(42\) −0.607843 + 0.151807i −0.0937922 + 0.0234243i
\(43\) −5.56022 4.03974i −0.847926 0.616055i 0.0766472 0.997058i \(-0.475578\pi\)
−0.924573 + 0.381004i \(0.875578\pi\)
\(44\) −2.50889 + 1.82281i −0.378229 + 0.274800i
\(45\) 4.71570 4.77097i 0.702975 0.711214i
\(46\) 2.09960 + 2.88985i 0.309569 + 0.426085i
\(47\) −7.06025 + 5.12957i −1.02984 + 0.748225i −0.968277 0.249878i \(-0.919610\pi\)
−0.0615664 + 0.998103i \(0.519610\pi\)
\(48\) 0.648204 1.60619i 0.0935603 0.231833i
\(49\) −5.55727 + 4.03759i −0.793895 + 0.576799i
\(50\) 1.42654 + 4.79218i 0.201743 + 0.677717i
\(51\) 6.05826 1.51303i 0.848326 0.211867i
\(52\) −0.514703 0.373954i −0.0713765 0.0518580i
\(53\) 1.15194 + 0.374287i 0.158231 + 0.0514122i 0.387061 0.922054i \(-0.373490\pi\)
−0.228831 + 0.973466i \(0.573490\pi\)
\(54\) −2.59275 + 4.50307i −0.352829 + 0.612790i
\(55\) −0.0860946 + 6.93386i −0.0116090 + 0.934962i
\(56\) 0.361718i 0.0483365i
\(57\) −13.2759 0.923079i −1.75843 0.122265i
\(58\) 0.800365 + 2.46327i 0.105093 + 0.323443i
\(59\) 2.31107 + 3.18092i 0.300876 + 0.414120i 0.932509 0.361147i \(-0.117615\pi\)
−0.631633 + 0.775268i \(0.717615\pi\)
\(60\) −2.01274 3.30891i −0.259843 0.427179i
\(61\) 10.8583i 1.39026i 0.718885 + 0.695129i \(0.244653\pi\)
−0.718885 + 0.695129i \(0.755347\pi\)
\(62\) −2.91458 4.74397i −0.370152 0.602484i
\(63\) 0.150177 1.07471i 0.0189205 0.135401i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −1.35833 + 0.422777i −0.168480 + 0.0524390i
\(66\) −1.30150 5.21129i −0.160204 0.641466i
\(67\) 15.1272i 1.84809i 0.382287 + 0.924043i \(0.375136\pi\)
−0.382287 + 0.924043i \(0.624864\pi\)
\(68\) 3.60517i 0.437191i
\(69\) −6.00260 + 1.49913i −0.722629 + 0.180474i
\(70\) 0.648400 + 0.483503i 0.0774986 + 0.0577896i
\(71\) 7.08557 + 2.30224i 0.840903 + 0.273226i 0.697631 0.716458i \(-0.254238\pi\)
0.143272 + 0.989683i \(0.454238\pi\)
\(72\) 2.15966 + 2.08227i 0.254519 + 0.245398i
\(73\) −1.81726 5.59295i −0.212694 0.654605i −0.999309 0.0371613i \(-0.988168\pi\)
0.786615 0.617443i \(-0.211832\pi\)
\(74\) −5.83239 4.23748i −0.678001 0.492597i
\(75\) −8.62182 0.815027i −0.995562 0.0941112i
\(76\) −2.37428 + 7.30728i −0.272348 + 0.838202i
\(77\) 0.659344 + 0.907509i 0.0751392 + 0.103420i
\(78\) 0.934272 0.584310i 0.105785 0.0661601i
\(79\) 5.41909 + 1.76077i 0.609695 + 0.198102i 0.597560 0.801824i \(-0.296137\pi\)
0.0121356 + 0.999926i \(0.496137\pi\)
\(80\) −2.13504 + 0.664526i −0.238705 + 0.0742963i
\(81\) −5.55213 7.08335i −0.616903 0.787039i
\(82\) 10.8071 3.51143i 1.19344 0.387772i
\(83\) 7.61938 10.4872i 0.836336 1.15112i −0.150375 0.988629i \(-0.548048\pi\)
0.986710 0.162488i \(-0.0519520\pi\)
\(84\) −0.580985 0.234467i −0.0633907 0.0255824i
\(85\) −6.46248 4.81898i −0.700955 0.522692i
\(86\) −2.12382 6.53644i −0.229017 0.704842i
\(87\) −4.47527 0.311168i −0.479799 0.0333607i
\(88\) −3.10116 −0.330584
\(89\) −4.86494 14.9727i −0.515682 1.58711i −0.782037 0.623232i \(-0.785819\pi\)
0.266355 0.963875i \(-0.414181\pi\)
\(90\) 6.61939 1.08798i 0.697745 0.114683i
\(91\) −0.135266 + 0.186177i −0.0141797 + 0.0195167i
\(92\) 3.57205i 0.372412i
\(93\) 9.50893 1.60630i 0.986030 0.166565i
\(94\) −8.72695 −0.900117
\(95\) 9.92507 + 14.0236i 1.01829 + 1.43879i
\(96\) 1.46850 0.918426i 0.149878 0.0937365i
\(97\) 0.210577 0.0684205i 0.0213808 0.00694705i −0.298307 0.954470i \(-0.596422\pi\)
0.319688 + 0.947523i \(0.396422\pi\)
\(98\) −6.86916 −0.693890
\(99\) 9.21395 + 1.28753i 0.926036 + 0.129401i
\(100\) −1.66268 + 4.71545i −0.166268 + 0.471545i
\(101\) −3.28726 1.06810i −0.327095 0.106280i 0.140866 0.990029i \(-0.455011\pi\)
−0.467961 + 0.883749i \(0.655011\pi\)
\(102\) 5.79057 + 2.33689i 0.573352 + 0.231386i
\(103\) 5.77241 7.94505i 0.568773 0.782849i −0.423636 0.905833i \(-0.639246\pi\)
0.992409 + 0.122984i \(0.0392464\pi\)
\(104\) −0.196599 0.605070i −0.0192781 0.0593320i
\(105\) −1.19689 + 0.728042i −0.116805 + 0.0710496i
\(106\) 0.711936 + 0.979895i 0.0691493 + 0.0951759i
\(107\) 1.77438 5.46097i 0.171536 0.527932i −0.827923 0.560842i \(-0.810477\pi\)
0.999458 + 0.0329099i \(0.0104774\pi\)
\(108\) −4.74442 + 2.11908i −0.456532 + 0.203908i
\(109\) −0.546140 + 0.396794i −0.0523108 + 0.0380060i −0.613633 0.789591i \(-0.710293\pi\)
0.561323 + 0.827597i \(0.310293\pi\)
\(110\) −4.14527 + 5.55901i −0.395236 + 0.530030i
\(111\) 10.5868 6.62114i 1.00485 0.628451i
\(112\) −0.212612 + 0.292636i −0.0200900 + 0.0276515i
\(113\) −2.84263 8.74872i −0.267412 0.823011i −0.991128 0.132912i \(-0.957567\pi\)
0.723716 0.690098i \(-0.242433\pi\)
\(114\) −10.1978 8.55014i −0.955114 0.800794i
\(115\) 6.40312 + 4.77471i 0.597094 + 0.445244i
\(116\) −0.800365 + 2.46327i −0.0743120 + 0.228709i
\(117\) 0.332911 + 1.87937i 0.0307776 + 0.173747i
\(118\) 3.93183i 0.361954i
\(119\) −1.30405 −0.119542
\(120\) 0.316591 3.86002i 0.0289007 0.352370i
\(121\) 1.11873 0.812808i 0.101703 0.0738916i
\(122\) −6.38232 + 8.78452i −0.577828 + 0.795313i
\(123\) −1.36518 + 19.6343i −0.123094 + 1.77036i
\(124\) 0.430487 5.55110i 0.0386588 0.498503i
\(125\) 6.23025 + 9.28353i 0.557250 + 0.830344i
\(126\) 0.753195 0.781188i 0.0670999 0.0695937i
\(127\) 7.38582 5.36611i 0.655385 0.476165i −0.209716 0.977762i \(-0.567254\pi\)
0.865101 + 0.501597i \(0.167254\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) 11.8754 + 0.825704i 1.04557 + 0.0726992i
\(130\) −1.34741 0.456373i −0.118176 0.0400266i
\(131\) 20.5246 6.66883i 1.79324 0.582659i 0.793572 0.608476i \(-0.208219\pi\)
0.999667 + 0.0258174i \(0.00821884\pi\)
\(132\) 2.01018 4.98103i 0.174964 0.433543i
\(133\) 2.64317 + 0.858818i 0.229192 + 0.0744690i
\(134\) −8.89157 + 12.2382i −0.768115 + 1.05722i
\(135\) −2.54323 + 11.3372i −0.218886 + 0.975750i
\(136\) 2.11907 2.91664i 0.181708 0.250100i
\(137\) −0.531951 0.732168i −0.0454476 0.0625533i 0.785688 0.618622i \(-0.212309\pi\)
−0.831136 + 0.556069i \(0.812309\pi\)
\(138\) −5.73738 2.31542i −0.488398 0.197102i
\(139\) −2.43192 3.34725i −0.206273 0.283910i 0.693329 0.720621i \(-0.256143\pi\)
−0.899602 + 0.436711i \(0.856143\pi\)
\(140\) 0.240371 + 0.772282i 0.0203150 + 0.0652697i
\(141\) 5.65685 14.0171i 0.476393 1.18045i
\(142\) 4.37912 + 6.02735i 0.367488 + 0.505804i
\(143\) −1.59617 1.15969i −0.133479 0.0969780i
\(144\) 0.523274 + 2.95401i 0.0436062 + 0.246168i
\(145\) 3.34572 + 4.72732i 0.277847 + 0.392583i
\(146\) 1.81726 5.59295i 0.150397 0.462875i
\(147\) 4.45262 11.0331i 0.367246 0.909998i
\(148\) −2.22777 6.85638i −0.183122 0.563591i
\(149\) 21.0917i 1.72790i −0.503581 0.863948i \(-0.667985\pi\)
0.503581 0.863948i \(-0.332015\pi\)
\(150\) −6.49614 5.72715i −0.530407 0.467620i
\(151\) −2.90825 + 0.944947i −0.236670 + 0.0768987i −0.424951 0.905217i \(-0.639709\pi\)
0.188281 + 0.982115i \(0.439709\pi\)
\(152\) −6.21594 + 4.51615i −0.504180 + 0.366308i
\(153\) −7.50695 + 7.78595i −0.606901 + 0.629457i
\(154\) 1.12174i 0.0903926i
\(155\) −9.37525 8.19175i −0.753038 0.657977i
\(156\) 1.09929 + 0.0764344i 0.0880137 + 0.00611965i
\(157\) −2.43102 + 3.34602i −0.194017 + 0.267041i −0.894931 0.446204i \(-0.852776\pi\)
0.700914 + 0.713245i \(0.252776\pi\)
\(158\) 3.34918 + 4.60975i 0.266447 + 0.366732i
\(159\) −2.03537 + 0.508328i −0.161416 + 0.0403130i
\(160\) −2.11788 0.717333i −0.167433 0.0567102i
\(161\) 1.29207 0.101830
\(162\) −0.328279 8.99401i −0.0257921 0.706636i
\(163\) 7.42944 + 2.41397i 0.581919 + 0.189077i 0.585160 0.810918i \(-0.301032\pi\)
−0.00324116 + 0.999995i \(0.501032\pi\)
\(164\) 10.8071 + 3.51143i 0.843890 + 0.274197i
\(165\) −6.24181 10.2614i −0.485924 0.798853i
\(166\) 12.3284 4.00575i 0.956871 0.310906i
\(167\) −2.58853 + 3.56280i −0.200306 + 0.275698i −0.897340 0.441341i \(-0.854503\pi\)
0.697033 + 0.717039i \(0.254503\pi\)
\(168\) −0.332211 0.531182i −0.0256306 0.0409816i
\(169\) −3.89214 + 11.9788i −0.299396 + 0.921445i
\(170\) −2.39573 7.69719i −0.183744 0.590347i
\(171\) 20.3434 10.8374i 1.55570 0.828753i
\(172\) 2.12382 6.53644i 0.161940 0.498399i
\(173\) 12.3328 8.96029i 0.937644 0.681239i −0.0102081 0.999948i \(-0.503249\pi\)
0.947852 + 0.318709i \(0.103249\pi\)
\(174\) −3.43767 2.88224i −0.260609 0.218502i
\(175\) 1.70566 + 0.601420i 0.128936 + 0.0454631i
\(176\) −2.50889 1.82281i −0.189115 0.137400i
\(177\) −6.31525 2.54863i −0.474683 0.191567i
\(178\) 4.86494 14.9727i 0.364642 1.12225i
\(179\) 6.36246 + 19.5817i 0.475553 + 1.46360i 0.845211 + 0.534433i \(0.179475\pi\)
−0.369658 + 0.929168i \(0.620525\pi\)
\(180\) 5.99469 + 3.01059i 0.446818 + 0.224396i
\(181\) 11.0418i 0.820730i 0.911921 + 0.410365i \(0.134599\pi\)
−0.911921 + 0.410365i \(0.865401\pi\)
\(182\) −0.218864 + 0.0711133i −0.0162233 + 0.00527127i
\(183\) −9.97251 15.9454i −0.737189 1.17871i
\(184\) −2.09960 + 2.88985i −0.154785 + 0.213043i
\(185\) −15.2683 5.17142i −1.12255 0.380210i
\(186\) 8.63705 + 4.28969i 0.633299 + 0.314535i
\(187\) 11.1802i 0.817577i
\(188\) −7.06025 5.12957i −0.514922 0.374113i
\(189\) 0.766508 + 1.71614i 0.0557552 + 0.124831i
\(190\) −0.213305 + 17.1791i −0.0154748 + 1.24630i
\(191\) 17.4375i 1.26174i −0.775890 0.630868i \(-0.782699\pi\)
0.775890 0.630868i \(-0.217301\pi\)
\(192\) 1.72788 + 0.120141i 0.124699 + 0.00867040i
\(193\) 18.0688 5.87089i 1.30062 0.422596i 0.424821 0.905277i \(-0.360337\pi\)
0.875796 + 0.482681i \(0.160337\pi\)
\(194\) 0.210577 + 0.0684205i 0.0151185 + 0.00491231i
\(195\) 1.60642 1.86837i 0.115038 0.133797i
\(196\) −5.55727 4.03759i −0.396948 0.288399i
\(197\) 14.8730 4.83252i 1.05966 0.344303i 0.273205 0.961956i \(-0.411916\pi\)
0.786451 + 0.617653i \(0.211916\pi\)
\(198\) 6.69745 + 6.45745i 0.475967 + 0.458911i
\(199\) −7.50039 10.3234i −0.531688 0.731806i 0.455698 0.890134i \(-0.349390\pi\)
−0.987387 + 0.158328i \(0.949390\pi\)
\(200\) −4.11681 + 2.83758i −0.291102 + 0.200647i
\(201\) −13.8933 22.2144i −0.979955 1.56688i
\(202\) −2.03164 2.79631i −0.142946 0.196748i
\(203\) 0.891008 + 0.289506i 0.0625365 + 0.0203193i
\(204\) 3.31108 + 5.29419i 0.231822 + 0.370668i
\(205\) 20.7401 14.6786i 1.44855 1.02520i
\(206\) 9.33996 3.03474i 0.650746 0.211440i
\(207\) 7.43799 7.71442i 0.516976 0.536190i
\(208\) 0.196599 0.605070i 0.0136317 0.0419540i
\(209\) −7.36301 + 22.6610i −0.509310 + 1.56749i
\(210\) −1.39624 0.114517i −0.0963495 0.00790240i
\(211\) −18.1664 −1.25063 −0.625313 0.780374i \(-0.715029\pi\)
−0.625313 + 0.780374i \(0.715029\pi\)
\(212\) 1.21122i 0.0831867i
\(213\) −12.5196 + 3.12673i −0.857829 + 0.214240i
\(214\) 4.64538 3.37507i 0.317552 0.230715i
\(215\) −8.87807 12.5442i −0.605480 0.855510i
\(216\) −5.08388 1.07433i −0.345914 0.0730988i
\(217\) −2.00793 0.155715i −0.136307 0.0105706i
\(218\) −0.675067 −0.0457213
\(219\) 7.80535 + 6.54422i 0.527437 + 0.442218i
\(220\) −6.62110 + 2.06080i −0.446394 + 0.138939i
\(221\) 2.18138 0.708773i 0.146735 0.0476772i
\(222\) 12.4567 + 0.866120i 0.836037 + 0.0581302i
\(223\) 21.1753 1.41801 0.709003 0.705205i \(-0.249145\pi\)
0.709003 + 0.705205i \(0.249145\pi\)
\(224\) −0.344014 + 0.111777i −0.0229854 + 0.00746841i
\(225\) 13.4097 6.72163i 0.893979 0.448109i
\(226\) 2.84263 8.74872i 0.189089 0.581956i
\(227\) 2.16784 + 1.57502i 0.143884 + 0.104538i 0.657399 0.753543i \(-0.271657\pi\)
−0.513514 + 0.858081i \(0.671657\pi\)
\(228\) −3.22457 12.9113i −0.213552 0.855074i
\(229\) 12.9786 17.8634i 0.857647 1.18045i −0.124479 0.992222i \(-0.539726\pi\)
0.982125 0.188227i \(-0.0602742\pi\)
\(230\) 2.37372 + 7.62648i 0.156519 + 0.502875i
\(231\) −1.80173 0.727118i −0.118545 0.0478409i
\(232\) −2.09538 + 1.52238i −0.137569 + 0.0999494i
\(233\) −3.32074 + 2.41266i −0.217549 + 0.158058i −0.691223 0.722642i \(-0.742928\pi\)
0.473674 + 0.880700i \(0.342928\pi\)
\(234\) −0.835333 + 1.71612i −0.0546074 + 0.112186i
\(235\) −18.6324 + 5.79929i −1.21544 + 0.378304i
\(236\) −2.31107 + 3.18092i −0.150438 + 0.207060i
\(237\) −9.57508 + 2.39134i −0.621968 + 0.155335i
\(238\) −1.05500 0.766503i −0.0683856 0.0496850i
\(239\) −7.79845 + 24.0012i −0.504440 + 1.55251i 0.297271 + 0.954793i \(0.403924\pi\)
−0.801710 + 0.597713i \(0.796076\pi\)
\(240\) 2.52499 2.93674i 0.162988 0.189565i
\(241\) 5.02958 1.63421i 0.323984 0.105269i −0.142510 0.989793i \(-0.545517\pi\)
0.466493 + 0.884525i \(0.345517\pi\)
\(242\) 1.38283 0.0888918
\(243\) 14.6588 + 5.30268i 0.940365 + 0.340167i
\(244\) −10.3268 + 3.35539i −0.661107 + 0.214807i
\(245\) −14.6659 + 4.56474i −0.936973 + 0.291630i
\(246\) −12.6452 + 15.0820i −0.806228 + 0.961595i
\(247\) −4.88819 −0.311028
\(248\) 3.61112 4.23790i 0.229307 0.269107i
\(249\) −1.55737 + 22.3983i −0.0986941 + 1.41943i
\(250\) −0.416346 + 11.1726i −0.0263320 + 0.706616i
\(251\) −7.29576 + 5.30068i −0.460504 + 0.334576i −0.793729 0.608271i \(-0.791863\pi\)
0.333225 + 0.942847i \(0.391863\pi\)
\(252\) 1.06852 0.189277i 0.0673103 0.0119234i
\(253\) 11.0775i 0.696436i
\(254\) 9.12937 0.572828
\(255\) 13.9160 + 1.14137i 0.871456 + 0.0714751i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 2.57090 7.91241i 0.160368 0.493562i −0.838297 0.545214i \(-0.816448\pi\)
0.998665 + 0.0516514i \(0.0164485\pi\)
\(258\) 9.12206 + 7.64819i 0.567915 + 0.476156i
\(259\) −2.48007 + 0.805825i −0.154104 + 0.0500715i
\(260\) −0.821832 1.16120i −0.0509679 0.0720148i
\(261\) 6.85772 3.65325i 0.424482 0.226131i
\(262\) 20.5246 + 6.66883i 1.26801 + 0.412002i
\(263\) 2.49512 + 3.43424i 0.153856 + 0.211764i 0.878986 0.476847i \(-0.158221\pi\)
−0.725130 + 0.688612i \(0.758221\pi\)
\(264\) 4.55405 2.84818i 0.280282 0.175294i
\(265\) 2.17118 + 1.61902i 0.133374 + 0.0994555i
\(266\) 1.63357 + 2.24842i 0.100161 + 0.137859i
\(267\) 20.8955 + 17.5194i 1.27878 + 1.07217i
\(268\) −14.3869 + 4.67458i −0.878818 + 0.285545i
\(269\) −11.3258 8.22869i −0.690548 0.501712i 0.186292 0.982494i \(-0.440353\pi\)
−0.876840 + 0.480782i \(0.840353\pi\)
\(270\) −8.72135 + 7.67711i −0.530764 + 0.467214i
\(271\) −8.40376 2.73055i −0.510492 0.165869i 0.0424338 0.999099i \(-0.486489\pi\)
−0.552926 + 0.833230i \(0.686489\pi\)
\(272\) 3.42872 1.11406i 0.207897 0.0675497i
\(273\) 0.0276477 0.397633i 0.00167331 0.0240658i
\(274\) 0.905009i 0.0546736i
\(275\) −5.15623 + 14.6234i −0.310932 + 0.881822i
\(276\) −3.28067 5.24556i −0.197473 0.315746i
\(277\) −6.37976 4.63517i −0.383323 0.278500i 0.379391 0.925236i \(-0.376133\pi\)
−0.762714 + 0.646736i \(0.776133\pi\)
\(278\) 4.13743i 0.248146i
\(279\) −12.4886 + 11.0921i −0.747673 + 0.664067i
\(280\) −0.259472 + 0.766076i −0.0155064 + 0.0457818i
\(281\) 9.45812 13.0180i 0.564224 0.776588i −0.427632 0.903953i \(-0.640652\pi\)
0.991856 + 0.127365i \(0.0406520\pi\)
\(282\) 12.8155 8.01506i 0.763154 0.477290i
\(283\) −24.8950 + 8.08886i −1.47985 + 0.480833i −0.934069 0.357093i \(-0.883768\pi\)
−0.545783 + 0.837926i \(0.683768\pi\)
\(284\) 7.45021i 0.442089i
\(285\) −27.4546 11.4782i −1.62627 0.679909i
\(286\) −0.609684 1.87642i −0.0360514 0.110955i
\(287\) 1.27015 3.90911i 0.0749743 0.230747i
\(288\) −1.31299 + 2.69742i −0.0773685 + 0.158947i
\(289\) −3.23829 2.35276i −0.190488 0.138397i
\(290\) −0.0719048 + 5.79105i −0.00422239 + 0.340062i
\(291\) −0.246393 + 0.293875i −0.0144438 + 0.0172272i
\(292\) 4.75764 3.45663i 0.278420 0.202284i
\(293\) 4.55629 14.0228i 0.266181 0.819222i −0.725238 0.688499i \(-0.758270\pi\)
0.991419 0.130723i \(-0.0417299\pi\)
\(294\) 10.0874 6.30882i 0.588307 0.367938i
\(295\) 2.61281 + 8.39463i 0.152123 + 0.488754i
\(296\) 2.22777 6.85638i 0.129487 0.398519i
\(297\) −14.7132 + 6.57159i −0.853745 + 0.381322i
\(298\) 12.3974 17.0635i 0.718160 0.988462i
\(299\) −2.16134 + 0.702262i −0.124994 + 0.0406129i
\(300\) −1.88915 8.45169i −0.109070 0.487959i
\(301\) −2.36434 0.768222i −0.136278 0.0442796i
\(302\) −2.90825 0.944947i −0.167351 0.0543756i
\(303\) 5.80831 1.45061i 0.333679 0.0833352i
\(304\) −7.68333 −0.440669
\(305\) −7.78899 + 22.9965i −0.445996 + 1.31678i
\(306\) −10.6497 + 1.88649i −0.608804 + 0.107844i
\(307\) −12.6533 17.4157i −0.722161 0.993969i −0.999449 0.0331821i \(-0.989436\pi\)
0.277289 0.960787i \(-0.410564\pi\)
\(308\) −0.659344 + 0.907509i −0.0375696 + 0.0517101i
\(309\) −1.17985 + 16.9688i −0.0671196 + 0.965324i
\(310\) −2.76974 12.1379i −0.157311 0.689386i
\(311\) 14.5275i 0.823781i 0.911233 + 0.411891i \(0.135131\pi\)
−0.911233 + 0.411891i \(0.864869\pi\)
\(312\) 0.844418 + 0.707983i 0.0478057 + 0.0400817i
\(313\) 5.94163 4.31685i 0.335841 0.244003i −0.407064 0.913400i \(-0.633447\pi\)
0.742905 + 0.669397i \(0.233447\pi\)
\(314\) −3.93348 + 1.27806i −0.221979 + 0.0721254i
\(315\) 1.08898 2.16839i 0.0613572 0.122175i
\(316\) 5.69797i 0.320536i
\(317\) 4.60497 + 14.1726i 0.258641 + 0.796015i 0.993090 + 0.117352i \(0.0374405\pi\)
−0.734449 + 0.678663i \(0.762560\pi\)
\(318\) −1.94544 0.785116i −0.109095 0.0440271i
\(319\) −2.48206 + 7.63898i −0.138968 + 0.427701i
\(320\) −1.29177 1.82520i −0.0722119 0.102032i
\(321\) 2.40983 + 9.64908i 0.134503 + 0.538559i
\(322\) 1.04531 + 0.759462i 0.0582528 + 0.0423232i
\(323\) −16.2815 22.4095i −0.905926 1.24690i
\(324\) 5.02096 7.46927i 0.278942 0.414959i
\(325\) −3.18006 0.0789828i −0.176398 0.00438118i
\(326\) 4.59165 + 6.31986i 0.254308 + 0.350025i
\(327\) 0.437581 1.08428i 0.0241983 0.0599609i
\(328\) 6.67913 + 9.19304i 0.368794 + 0.507601i
\(329\) −1.85546 + 2.55382i −0.102295 + 0.140797i
\(330\) 0.981799 11.9705i 0.0540463 0.658956i
\(331\) 2.22699 3.06518i 0.122406 0.168478i −0.743416 0.668829i \(-0.766796\pi\)
0.865822 + 0.500351i \(0.166796\pi\)
\(332\) 12.3284 + 4.00575i 0.676610 + 0.219844i
\(333\) −9.46562 + 19.4463i −0.518713 + 1.06565i
\(334\) −4.18833 + 1.36087i −0.229175 + 0.0744635i
\(335\) −10.8513 + 32.0377i −0.592868 + 1.75041i
\(336\) 0.0434569 0.625004i 0.00237077 0.0340968i
\(337\) 2.83289 + 8.71874i 0.154317 + 0.474940i 0.998091 0.0617591i \(-0.0196710\pi\)
−0.843774 + 0.536699i \(0.819671\pi\)
\(338\) −10.1898 + 7.40330i −0.554250 + 0.402686i
\(339\) 12.2095 + 10.2368i 0.663127 + 0.555984i
\(340\) 2.58611 7.63533i 0.140251 0.414084i
\(341\) 1.33501 17.2148i 0.0722946 0.932235i
\(342\) 22.8282 + 3.18994i 1.23441 + 0.172492i
\(343\) −2.94875 + 4.05861i −0.159218 + 0.219144i
\(344\) 5.56022 4.03974i 0.299787 0.217808i
\(345\) −13.7882 1.13088i −0.742332 0.0608846i
\(346\) 15.2442 0.819531
\(347\) 13.8084i 0.741276i −0.928777 0.370638i \(-0.879139\pi\)
0.928777 0.370638i \(-0.120861\pi\)
\(348\) −1.08699 4.35239i −0.0582690 0.233312i
\(349\) 6.54481 20.1429i 0.350336 1.07822i −0.608329 0.793685i \(-0.708160\pi\)
0.958665 0.284538i \(-0.0918401\pi\)
\(350\) 1.02640 + 1.48912i 0.0548636 + 0.0795969i
\(351\) −2.21494 2.45410i −0.118225 0.130990i
\(352\) −0.958310 2.94937i −0.0510781 0.157202i
\(353\) −6.12174 + 8.42585i −0.325827 + 0.448463i −0.940235 0.340526i \(-0.889395\pi\)
0.614408 + 0.788989i \(0.289395\pi\)
\(354\) −3.61110 5.77390i −0.191928 0.306879i
\(355\) 13.3549 + 9.95860i 0.708807 + 0.528547i
\(356\) 12.7366 9.25366i 0.675037 0.490443i
\(357\) 1.91500 1.19768i 0.101353 0.0633878i
\(358\) −6.36246 + 19.5817i −0.336267 + 1.03492i
\(359\) 9.60275 + 13.2171i 0.506814 + 0.697570i 0.983378 0.181570i \(-0.0581179\pi\)
−0.476564 + 0.879140i \(0.658118\pi\)
\(360\) 3.08023 + 5.95921i 0.162342 + 0.314078i
\(361\) 12.3710 + 38.0741i 0.651107 + 2.00390i
\(362\) −6.49020 + 8.93300i −0.341118 + 0.469508i
\(363\) −0.896358 + 2.22108i −0.0470466 + 0.116577i
\(364\) −0.218864 0.0711133i −0.0114716 0.00372735i
\(365\) 0.163262 13.1488i 0.00854555 0.688239i
\(366\) 1.30452 18.7618i 0.0681882 0.980693i
\(367\) −21.8615 −1.14116 −0.570580 0.821242i \(-0.693282\pi\)
−0.570580 + 0.821242i \(0.693282\pi\)
\(368\) −3.39722 + 1.10382i −0.177092 + 0.0575408i
\(369\) −16.0279 30.0868i −0.834377 1.56625i
\(370\) −9.31264 13.1582i −0.484141 0.684065i
\(371\) 0.438118 0.0227460
\(372\) 4.46610 + 8.54716i 0.231557 + 0.443150i
\(373\) 32.0823i 1.66116i 0.556901 + 0.830579i \(0.311990\pi\)
−0.556901 + 0.830579i \(0.688010\pi\)
\(374\) 6.57155 9.04497i 0.339807 0.467704i
\(375\) −17.6754 7.91085i −0.912752 0.408514i
\(376\) −2.69678 8.29983i −0.139076 0.428031i
\(377\) −1.64780 −0.0848660
\(378\) −0.388603 + 1.83893i −0.0199876 + 0.0945842i
\(379\) 2.37894 + 7.32161i 0.122198 + 0.376086i 0.993380 0.114874i \(-0.0366463\pi\)
−0.871182 + 0.490959i \(0.836646\pi\)
\(380\) −10.2702 + 13.7728i −0.526850 + 0.706531i
\(381\) −5.91770 + 14.6635i −0.303173 + 0.751232i
\(382\) 10.2495 14.1073i 0.524412 0.721791i
\(383\) 6.55617 2.13023i 0.335005 0.108850i −0.136684 0.990615i \(-0.543645\pi\)
0.471689 + 0.881765i \(0.343645\pi\)
\(384\) 1.32727 + 1.11282i 0.0677318 + 0.0567882i
\(385\) 0.745427 + 2.39497i 0.0379905 + 0.122059i
\(386\) 18.0688 + 5.87089i 0.919675 + 0.298821i
\(387\) −18.1974 + 9.69413i −0.925024 + 0.492780i
\(388\) 0.130144 + 0.179127i 0.00660704 + 0.00909381i
\(389\) 7.79733 23.9977i 0.395341 1.21673i −0.533355 0.845891i \(-0.679069\pi\)
0.928696 0.370842i \(-0.120931\pi\)
\(390\) 2.39782 0.567317i 0.121419 0.0287272i
\(391\) −10.4184 7.56941i −0.526881 0.382802i
\(392\) −2.12269 6.53296i −0.107212 0.329964i
\(393\) −24.0155 + 28.6435i −1.21142 + 1.44487i
\(394\) 14.8730 + 4.83252i 0.749290 + 0.243459i
\(395\) 10.2140 + 7.61640i 0.513920 + 0.383223i
\(396\) 1.62275 + 9.16085i 0.0815465 + 0.460350i
\(397\) 5.57161i 0.279631i −0.990178 0.139815i \(-0.955349\pi\)
0.990178 0.139815i \(-0.0446509\pi\)
\(398\) 12.7604i 0.639622i
\(399\) −4.67026 + 1.16638i −0.233805 + 0.0583921i
\(400\) −4.99846 0.124146i −0.249923 0.00620731i
\(401\) −19.3888 14.0868i −0.968228 0.703459i −0.0131809 0.999913i \(-0.504196\pi\)
−0.955047 + 0.296454i \(0.904196\pi\)
\(402\) 1.81740 26.1380i 0.0906434 1.30365i
\(403\) 3.44343 0.830866i 0.171530 0.0413884i
\(404\) 3.45643i 0.171964i
\(405\) −6.67765 18.9844i −0.331815 0.943344i
\(406\) 0.550673 + 0.757936i 0.0273294 + 0.0376157i
\(407\) −6.90867 21.2627i −0.342450 1.05395i
\(408\) −0.433127 + 6.22930i −0.0214430 + 0.308396i
\(409\) 21.9207i 1.08391i −0.840408 0.541955i \(-0.817684\pi\)
0.840408 0.541955i \(-0.182316\pi\)
\(410\) 25.4070 + 0.315467i 1.25476 + 0.0155798i
\(411\) 1.45361 + 0.586631i 0.0717014 + 0.0289364i
\(412\) 9.33996 + 3.03474i 0.460147 + 0.149511i
\(413\) 1.15059 + 0.835955i 0.0566170 + 0.0411347i
\(414\) 10.5519 1.86916i 0.518597 0.0918643i
\(415\) 23.6598 16.7450i 1.16141 0.821980i
\(416\) 0.514703 0.373954i 0.0252354 0.0183346i
\(417\) 6.64547 + 2.68190i 0.325430 + 0.131333i
\(418\) −19.2766 + 14.0053i −0.942850 + 0.685020i
\(419\) −12.3572 17.0082i −0.603687 0.830904i 0.392353 0.919815i \(-0.371661\pi\)
−0.996040 + 0.0889110i \(0.971661\pi\)
\(420\) −1.06227 0.913334i −0.0518334 0.0445661i
\(421\) −0.0928946 + 0.0674919i −0.00452741 + 0.00328935i −0.590047 0.807369i \(-0.700891\pi\)
0.585519 + 0.810659i \(0.300891\pi\)
\(422\) −14.6969 10.6779i −0.715434 0.519793i
\(423\) 4.56659 + 25.7795i 0.222035 + 1.25344i
\(424\) −0.711936 + 0.979895i −0.0345747 + 0.0475879i
\(425\) −10.2300 14.8418i −0.496227 0.719933i
\(426\) −11.9664 4.82926i −0.579775 0.233978i
\(427\) 1.21370 + 3.73539i 0.0587352 + 0.180768i
\(428\) 5.74201 0.277550
\(429\) 3.40907 + 0.237035i 0.164592 + 0.0114442i
\(430\) 0.190804 15.3669i 0.00920137 0.741058i
\(431\) 0.731701 + 1.00710i 0.0352448 + 0.0485103i 0.826276 0.563266i \(-0.190455\pi\)
−0.791031 + 0.611776i \(0.790455\pi\)
\(432\) −3.48147 3.85738i −0.167502 0.185588i
\(433\) 5.00247 0.240403 0.120202 0.992749i \(-0.461646\pi\)
0.120202 + 0.992749i \(0.461646\pi\)
\(434\) −1.53292 1.30621i −0.0735826 0.0626999i
\(435\) −9.25488 3.86927i −0.443738 0.185518i
\(436\) −0.546140 0.396794i −0.0261554 0.0190030i
\(437\) 16.1319 + 22.2037i 0.771694 + 1.06215i
\(438\) 2.46806 + 9.88226i 0.117929 + 0.472193i
\(439\) 6.48390 0.309460 0.154730 0.987957i \(-0.450549\pi\)
0.154730 + 0.987957i \(0.450549\pi\)
\(440\) −6.56789 2.22456i −0.313112 0.106052i
\(441\) 3.59445 + 20.2916i 0.171164 + 0.966266i
\(442\) 2.18138 + 0.708773i 0.103758 + 0.0337129i
\(443\) 8.09711 24.9203i 0.384705 1.18400i −0.551988 0.833852i \(-0.686131\pi\)
0.936694 0.350150i \(-0.113869\pi\)
\(444\) 9.56857 + 8.02255i 0.454104 + 0.380734i
\(445\) 0.437066 35.2003i 0.0207189 1.66865i
\(446\) 17.1312 + 12.4466i 0.811187 + 0.589362i
\(447\) 19.3711 + 30.9731i 0.916223 + 1.46498i
\(448\) −0.344014 0.111777i −0.0162531 0.00528096i
\(449\) 4.95015 3.59650i 0.233612 0.169729i −0.464821 0.885405i \(-0.653881\pi\)
0.698433 + 0.715676i \(0.253881\pi\)
\(450\) 14.7995 + 2.44410i 0.697657 + 0.115216i
\(451\) 33.5144 + 10.8895i 1.57813 + 0.512766i
\(452\) 7.44211 5.40701i 0.350047 0.254324i
\(453\) 3.40290 4.05866i 0.159882 0.190693i
\(454\) 0.828040 + 2.54844i 0.0388618 + 0.119604i
\(455\) −0.420028 + 0.297271i −0.0196912 + 0.0139363i
\(456\) 4.98037 12.3408i 0.233227 0.577913i
\(457\) −8.07408 + 24.8495i −0.377690 + 1.16241i 0.563956 + 0.825805i \(0.309279\pi\)
−0.941646 + 0.336605i \(0.890721\pi\)
\(458\) 20.9997 6.82323i 0.981253 0.318829i
\(459\) 3.87314 18.3282i 0.180783 0.855489i
\(460\) −2.56235 + 7.56519i −0.119470 + 0.352729i
\(461\) −4.08805 12.5817i −0.190399 0.585989i 0.809600 0.586982i \(-0.199684\pi\)
−1.00000 0.000992651i \(0.999684\pi\)
\(462\) −1.03024 1.64728i −0.0479310 0.0766384i
\(463\) −23.8294 17.3131i −1.10745 0.804608i −0.125188 0.992133i \(-0.539953\pi\)
−0.982260 + 0.187525i \(0.939953\pi\)
\(464\) −2.59003 −0.120239
\(465\) 21.2911 + 3.41912i 0.987350 + 0.158558i
\(466\) −4.10466 −0.190144
\(467\) −6.34691 4.61130i −0.293700 0.213386i 0.431171 0.902270i \(-0.358101\pi\)
−0.724871 + 0.688885i \(0.758101\pi\)
\(468\) −1.68451 + 0.897373i −0.0778664 + 0.0414811i
\(469\) 1.69088 + 5.20398i 0.0780774 + 0.240297i
\(470\) −18.4827 6.26013i −0.852542 0.288758i
\(471\) 0.496890 7.14634i 0.0228955 0.329286i
\(472\) −3.73939 + 1.21500i −0.172120 + 0.0559250i
\(473\) 6.58629 20.2705i 0.302838 0.932039i
\(474\) −9.15200 3.69345i −0.420365 0.169646i
\(475\) 10.9606 + 36.8199i 0.502905 + 1.68941i
\(476\) −0.402975 1.24023i −0.0184703 0.0568458i
\(477\) 2.52208 2.61582i 0.115478 0.119770i
\(478\) −20.4166 + 14.8335i −0.933834 + 0.678470i
\(479\) −30.8161 10.0127i −1.40802 0.457494i −0.496246 0.868182i \(-0.665288\pi\)
−0.911776 + 0.410688i \(0.865288\pi\)
\(480\) 3.76893 0.891716i 0.172027 0.0407011i
\(481\) 3.71061 2.69592i 0.169189 0.122923i
\(482\) 5.02958 + 1.63421i 0.229091 + 0.0744362i
\(483\) −1.89741 + 1.18667i −0.0863352 + 0.0539955i
\(484\) 1.11873 + 0.812808i 0.0508516 + 0.0369458i
\(485\) 0.495058 + 0.00614690i 0.0224794 + 0.000279116i
\(486\) 8.74241 + 12.9062i 0.396564 + 0.585438i
\(487\) −7.57747 + 23.3210i −0.343368 + 1.05678i 0.619084 + 0.785325i \(0.287504\pi\)
−0.962452 + 0.271453i \(0.912496\pi\)
\(488\) −10.3268 3.35539i −0.467473 0.151891i
\(489\) −13.1272 + 3.27847i −0.593632 + 0.148258i
\(490\) −14.5481 4.92748i −0.657216 0.222601i
\(491\) −14.4912 −0.653981 −0.326990 0.945028i \(-0.606034\pi\)
−0.326990 + 0.945028i \(0.606034\pi\)
\(492\) −19.0952 + 4.76896i −0.860877 + 0.215001i
\(493\) −5.48845 7.55421i −0.247188 0.340224i
\(494\) −3.95463 2.87321i −0.177927 0.129272i
\(495\) 18.5905 + 9.33630i 0.835580 + 0.419636i
\(496\) 5.41243 1.30597i 0.243026 0.0586396i
\(497\) 2.69487 0.120882
\(498\) −14.4253 + 17.2052i −0.646413 + 0.770983i
\(499\) 1.35325 + 1.86259i 0.0605797 + 0.0833808i 0.838232 0.545314i \(-0.183590\pi\)
−0.777652 + 0.628695i \(0.783590\pi\)
\(500\) −6.90391 + 8.79409i −0.308752 + 0.393284i
\(501\) 0.529083 7.60935i 0.0236377 0.339961i
\(502\) −9.01806 −0.402496
\(503\) −4.94721 15.2259i −0.220585 0.678891i −0.998710 0.0507812i \(-0.983829\pi\)
0.778125 0.628110i \(-0.216171\pi\)
\(504\) 0.975703 + 0.474930i 0.0434613 + 0.0211551i
\(505\) −6.19586 4.62017i −0.275712 0.205595i
\(506\) −6.51119 + 8.96188i −0.289457 + 0.398404i
\(507\) −5.28601 21.1655i −0.234760 0.939993i
\(508\) 7.38582 + 5.36611i 0.327693 + 0.238083i
\(509\) −8.77049 + 6.37214i −0.388745 + 0.282440i −0.764941 0.644100i \(-0.777232\pi\)
0.376196 + 0.926540i \(0.377232\pi\)
\(510\) 10.5874 + 9.10302i 0.468819 + 0.403089i
\(511\) −1.25032 1.72092i −0.0553111 0.0761291i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) −19.9210 + 34.5986i −0.879532 + 1.52756i
\(514\) 6.73070 4.89014i 0.296878 0.215695i
\(515\) 17.9245 12.6859i 0.789850 0.559010i
\(516\) 2.88441 + 11.5493i 0.126979 + 0.508431i
\(517\) −21.8949 15.9076i −0.962939 0.699616i
\(518\) −2.48007 0.805825i −0.108968 0.0354059i
\(519\) −9.88133 + 24.4849i −0.433742 + 1.07477i
\(520\) 0.0176625 1.42249i 0.000774550 0.0623805i
\(521\) 16.9359i 0.741974i 0.928638 + 0.370987i \(0.120981\pi\)
−0.928638 + 0.370987i \(0.879019\pi\)
\(522\) 7.69534 + 1.07532i 0.336816 + 0.0470656i
\(523\) −0.667440 2.05417i −0.0291851 0.0898225i 0.935403 0.353584i \(-0.115037\pi\)
−0.964588 + 0.263761i \(0.915037\pi\)
\(524\) 12.6849 + 17.4592i 0.554141 + 0.762710i
\(525\) −3.05713 + 0.683339i −0.133424 + 0.0298234i
\(526\) 4.24495i 0.185089i
\(527\) 15.2783 + 13.0187i 0.665535 + 0.567104i
\(528\) 5.35842 + 0.372575i 0.233195 + 0.0162142i
\(529\) −8.28469 6.01918i −0.360204 0.261704i
\(530\) 0.804886 + 2.58600i 0.0349620 + 0.112329i
\(531\) 11.6147 2.05742i 0.504034 0.0892846i
\(532\) 2.77919i 0.120493i
\(533\) 7.22937i 0.313139i
\(534\) 6.60719 + 26.4556i 0.285921 + 1.14484i
\(535\) 7.67526 10.2929i 0.331831 0.445000i
\(536\) −14.3869 4.67458i −0.621418 0.201911i
\(537\) −27.3276 22.9122i −1.17927 0.988735i
\(538\) −4.32608 13.3143i −0.186511 0.574020i
\(539\) −17.2340 12.5212i −0.742319 0.539326i
\(540\) −11.5682 + 1.08463i −0.497817 + 0.0466752i
\(541\) 4.16415 12.8159i 0.179031 0.551000i −0.820764 0.571268i \(-0.806452\pi\)
0.999795 + 0.0202678i \(0.00645187\pi\)
\(542\) −5.19381 7.14867i −0.223093 0.307062i
\(543\) −10.1411 16.2149i −0.435195 0.695847i
\(544\) 3.42872 + 1.11406i 0.147005 + 0.0477649i
\(545\) −1.44130 + 0.448600i −0.0617383 + 0.0192159i
\(546\) 0.256090 0.305441i 0.0109596 0.0130717i
\(547\) −26.9319 + 8.75072i −1.15153 + 0.374154i −0.821718 0.569894i \(-0.806984\pi\)
−0.329809 + 0.944048i \(0.606984\pi\)
\(548\) 0.531951 0.732168i 0.0227238 0.0312767i
\(549\) 29.2893 + 14.2568i 1.25004 + 0.608463i
\(550\) −12.7669 + 8.79979i −0.544381 + 0.375224i
\(551\) 6.14946 + 18.9261i 0.261976 + 0.806279i
\(552\) 0.429148 6.17207i 0.0182658 0.262701i
\(553\) 2.06106 0.0876450
\(554\) −2.43685 7.49986i −0.103532 0.318638i
\(555\) 27.1711 6.42858i 1.15335 0.272878i
\(556\) 2.43192 3.34725i 0.103136 0.141955i
\(557\) 37.4093i 1.58509i 0.609817 + 0.792543i \(0.291243\pi\)
−0.609817 + 0.792543i \(0.708757\pi\)
\(558\) −16.6233 + 1.63308i −0.703719 + 0.0691339i
\(559\) 4.37254 0.184939
\(560\) −0.660205 + 0.467255i −0.0278988 + 0.0197451i
\(561\) 10.2682 + 16.4181i 0.433523 + 0.693174i
\(562\) 15.3036 4.97243i 0.645542 0.209749i
\(563\) −4.10697 −0.173088 −0.0865442 0.996248i \(-0.527582\pi\)
−0.0865442 + 0.996248i \(0.527582\pi\)
\(564\) 15.0791 + 1.04846i 0.634946 + 0.0441482i
\(565\) 0.255382 20.5679i 0.0107440 0.865298i
\(566\) −24.8950 8.08886i −1.04641 0.340000i
\(567\) −2.70176 1.81617i −0.113463 0.0762720i
\(568\) −4.37912 + 6.02735i −0.183744 + 0.252902i
\(569\) 4.17820 + 12.8592i 0.175159 + 0.539085i 0.999641 0.0268042i \(-0.00853305\pi\)
−0.824481 + 0.565889i \(0.808533\pi\)
\(570\) −15.4645 25.4234i −0.647737 1.06487i
\(571\) −28.0452 38.6009i −1.17366 1.61540i −0.632980 0.774168i \(-0.718169\pi\)
−0.540676 0.841231i \(-0.681831\pi\)
\(572\) 0.609684 1.87642i 0.0254922 0.0784569i
\(573\) 16.0151 + 25.6070i 0.669040 + 1.06975i
\(574\) 3.32528 2.41596i 0.138795 0.100840i
\(575\) 10.1360 + 14.7055i 0.422700 + 0.613260i
\(576\) −2.64773 + 1.41050i −0.110322 + 0.0587710i
\(577\) 14.4128 19.8375i 0.600012 0.825845i −0.395698 0.918381i \(-0.629497\pi\)
0.995709 + 0.0925357i \(0.0294972\pi\)
\(578\) −1.23692 3.80684i −0.0514490 0.158344i
\(579\) −21.1420 + 25.2162i −0.878631 + 1.04795i
\(580\) −3.46206 + 4.64279i −0.143754 + 0.192781i
\(581\) 1.44895 4.45941i 0.0601125 0.185007i
\(582\) −0.372071 + 0.0929236i −0.0154229 + 0.00385181i
\(583\) 3.75617i 0.155565i
\(584\) 5.88077 0.243348
\(585\) −0.643064 + 4.21909i −0.0265874 + 0.174438i
\(586\) 11.9285 8.66658i 0.492763 0.358013i
\(587\) −14.3424 + 19.7406i −0.591972 + 0.814780i −0.994944 0.100433i \(-0.967977\pi\)
0.402972 + 0.915212i \(0.367977\pi\)
\(588\) 11.8691 + 0.825265i 0.489473 + 0.0340333i
\(589\) −22.3937 36.4494i −0.922716 1.50187i
\(590\) −2.82043 + 8.32716i −0.116115 + 0.342824i
\(591\) −17.4027 + 20.7563i −0.715850 + 0.853800i
\(592\) 5.83239 4.23748i 0.239710 0.174159i
\(593\) 9.47367 + 29.1569i 0.389037 + 1.19733i 0.933509 + 0.358553i \(0.116730\pi\)
−0.544472 + 0.838779i \(0.683270\pi\)
\(594\) −15.7659 3.33166i −0.646883 0.136700i
\(595\) −2.76183 0.935440i −0.113224 0.0383493i
\(596\) 20.0594 6.51768i 0.821663 0.266975i
\(597\) 20.4956 + 8.27136i 0.838829 + 0.338524i
\(598\) −2.16134 0.702262i −0.0883838 0.0287176i
\(599\) −11.2161 + 15.4376i −0.458277 + 0.630764i −0.974150 0.225901i \(-0.927467\pi\)
0.515874 + 0.856665i \(0.327467\pi\)
\(600\) 3.43943 7.94798i 0.140414 0.324475i
\(601\) −19.9772 + 27.4962i −0.814885 + 1.12159i 0.175666 + 0.984450i \(0.443792\pi\)
−0.990551 + 0.137144i \(0.956208\pi\)
\(602\) −1.46124 2.01123i −0.0595559 0.0819716i
\(603\) 40.8045 + 19.8619i 1.66169 + 0.808838i
\(604\) −1.79740 2.47390i −0.0731350 0.100662i
\(605\) 2.95240 0.918928i 0.120032 0.0373597i
\(606\) 5.55167 + 2.24047i 0.225521 + 0.0910131i
\(607\) −3.50284 4.82124i −0.142176 0.195688i 0.731991 0.681315i \(-0.238592\pi\)
−0.874166 + 0.485627i \(0.838592\pi\)
\(608\) −6.21594 4.51615i −0.252090 0.183154i
\(609\) −1.57433 + 0.393185i −0.0637953 + 0.0159327i
\(610\) −19.8184 + 14.0263i −0.802425 + 0.567910i
\(611\) 1.71571 5.28042i 0.0694102 0.213623i
\(612\) −9.72465 4.73354i −0.393096 0.191342i
\(613\) 9.61990 + 29.6070i 0.388544 + 1.19582i 0.933876 + 0.357596i \(0.116404\pi\)
−0.545332 + 0.838220i \(0.683596\pi\)
\(614\) 21.5270i 0.868760i
\(615\) −16.9756 + 40.6038i −0.684523 + 1.63730i
\(616\) −1.06684 + 0.346637i −0.0429842 + 0.0139664i
\(617\) 10.2165 7.42269i 0.411299 0.298826i −0.362829 0.931856i \(-0.618189\pi\)
0.774127 + 0.633030i \(0.218189\pi\)
\(618\) −10.9286 + 13.0346i −0.439611 + 0.524328i
\(619\) 26.7399i 1.07477i −0.843338 0.537383i \(-0.819413\pi\)
0.843338 0.537383i \(-0.180587\pi\)
\(620\) 4.89371 11.4478i 0.196536 0.459754i
\(621\) −3.83756 + 18.1599i −0.153996 + 0.728731i
\(622\) −8.53908 + 11.7530i −0.342386 + 0.471254i
\(623\) −3.34721 4.60704i −0.134103 0.184577i
\(624\) 0.267006 + 1.06911i 0.0106888 + 0.0427985i
\(625\) 6.53556 + 24.1306i 0.261422 + 0.965224i
\(626\) 7.34426 0.293536
\(627\) −9.99988 40.0401i −0.399357 1.59905i
\(628\) −3.93348 1.27806i −0.156963 0.0510003i
\(629\) 24.7184 + 8.03150i 0.985588 + 0.320237i
\(630\) 2.15555 1.11417i 0.0858792 0.0443897i
\(631\) 25.4685 8.27521i 1.01388 0.329431i 0.245484 0.969401i \(-0.421053\pi\)
0.768400 + 0.639970i \(0.221053\pi\)
\(632\) −3.34918 + 4.60975i −0.133223 + 0.183366i
\(633\) 26.6773 16.6845i 1.06033 0.663148i
\(634\) −4.60497 + 14.1726i −0.182887 + 0.562868i
\(635\) 19.4916 6.06671i 0.773500 0.240750i
\(636\) −1.11241 1.77867i −0.0441101 0.0705290i
\(637\) 1.35047 4.15632i 0.0535076 0.164679i
\(638\) −6.49811 + 4.72115i −0.257262 + 0.186912i
\(639\) 15.5134 16.0899i 0.613700 0.636508i
\(640\) 0.0277621 2.23590i 0.00109739 0.0883815i
\(641\) 8.13032 + 5.90702i 0.321128 + 0.233313i 0.736657 0.676267i \(-0.236403\pi\)
−0.415528 + 0.909580i \(0.636403\pi\)
\(642\) −3.72200 + 9.22273i −0.146895 + 0.363992i
\(643\) 3.37817 10.3969i 0.133222 0.410015i −0.862087 0.506760i \(-0.830843\pi\)
0.995309 + 0.0967449i \(0.0308431\pi\)
\(644\) 0.399273 + 1.22884i 0.0157335 + 0.0484229i
\(645\) 24.5584 + 10.2674i 0.966986 + 0.404277i
\(646\) 27.6997i 1.08983i
\(647\) 27.6916 8.99754i 1.08867 0.353730i 0.290937 0.956742i \(-0.406033\pi\)
0.797732 + 0.603012i \(0.206033\pi\)
\(648\) 8.45237 3.09151i 0.332040 0.121446i
\(649\) −7.16700 + 9.86452i −0.281329 + 0.387216i
\(650\) −2.52630 1.93309i −0.0990895 0.0758220i
\(651\) 3.09166 1.61547i 0.121172 0.0633152i
\(652\) 7.81178i 0.305933i
\(653\) 24.6766 + 17.9286i 0.965668 + 0.701599i 0.954460 0.298338i \(-0.0964323\pi\)
0.0112081 + 0.999937i \(0.496432\pi\)
\(654\) 0.991336 0.619999i 0.0387643 0.0242439i
\(655\) 48.2524 + 0.599128i 1.88538 + 0.0234099i
\(656\) 11.3632i 0.443659i
\(657\) −17.4725 2.44156i −0.681669 0.0952543i
\(658\) −3.00219 + 0.975471i −0.117038 + 0.0380278i
\(659\) 7.04300 + 2.28841i 0.274356 + 0.0891437i 0.442964 0.896540i \(-0.353927\pi\)
−0.168608 + 0.985683i \(0.553927\pi\)
\(660\) 7.83039 9.10728i 0.304798 0.354500i
\(661\) −28.4474 20.6682i −1.10647 0.803900i −0.124369 0.992236i \(-0.539691\pi\)
−0.982105 + 0.188336i \(0.939691\pi\)
\(662\) 3.60334 1.17080i 0.140048 0.0455043i
\(663\) −2.55240 + 3.04427i −0.0991270 + 0.118230i
\(664\) 7.61938 + 10.4872i 0.295689 + 0.406982i
\(665\) 4.98187 + 3.71491i 0.193189 + 0.144058i
\(666\) −19.0881 + 10.1686i −0.739649 + 0.394027i
\(667\) 5.43803 + 7.48481i 0.210562 + 0.289813i
\(668\) −4.18833 1.36087i −0.162051 0.0526537i
\(669\) −31.0960 + 19.4480i −1.20224 + 0.751903i
\(670\) −27.6102 + 19.5409i −1.06667 + 0.754930i
\(671\) −32.0251 + 10.4056i −1.23631 + 0.401703i
\(672\) 0.402526 0.480096i 0.0155278 0.0185201i
\(673\) −10.5561 + 32.4882i −0.406906 + 1.25233i 0.512387 + 0.858755i \(0.328761\pi\)
−0.919293 + 0.393574i \(0.871239\pi\)
\(674\) −2.83289 + 8.71874i −0.109119 + 0.335833i
\(675\) −13.5188 + 22.1865i −0.520339 + 0.853960i
\(676\) −12.5952 −0.484432
\(677\) 25.3996i 0.976187i 0.872791 + 0.488093i \(0.162307\pi\)
−0.872791 + 0.488093i \(0.837693\pi\)
\(678\) 3.86065 + 15.4582i 0.148267 + 0.593670i
\(679\) 0.0647935 0.0470752i 0.00248655 0.00180658i
\(680\) 6.58014 4.65704i 0.252337 0.178589i
\(681\) −4.63001 0.321928i −0.177422 0.0123363i
\(682\) 11.1987 13.1424i 0.428819 0.503248i
\(683\) −6.14397 −0.235092 −0.117546 0.993067i \(-0.537503\pi\)
−0.117546 + 0.993067i \(0.537503\pi\)
\(684\) 16.5934 + 15.9988i 0.634464 + 0.611729i
\(685\) −0.601403 1.93223i −0.0229784 0.0738268i
\(686\) −4.77118 + 1.55025i −0.182165 + 0.0591889i
\(687\) −2.65276 + 38.1523i −0.101209 + 1.45560i
\(688\) 6.87282 0.262024
\(689\) −0.732871 + 0.238124i −0.0279202 + 0.00907181i
\(690\) −10.4902 9.01940i −0.399354 0.343363i
\(691\) 1.72623 5.31278i 0.0656688 0.202108i −0.912838 0.408322i \(-0.866114\pi\)
0.978507 + 0.206214i \(0.0661142\pi\)
\(692\) 12.3328 + 8.96029i 0.468822 + 0.340619i
\(693\) 3.31364 0.586979i 0.125875 0.0222975i
\(694\) 8.11640 11.1713i 0.308094 0.424055i
\(695\) −2.74943 8.83358i −0.104292 0.335077i
\(696\) 1.67887 4.16008i 0.0636375 0.157687i
\(697\) −33.1425 + 24.0794i −1.25536 + 0.912073i
\(698\) 17.1345 12.4490i 0.648552 0.471201i
\(699\) 2.66066 6.59284i 0.100635 0.249364i
\(700\) −0.0449059 + 1.80803i −0.00169728 + 0.0683371i
\(701\) −4.52818 + 6.23250i −0.171027 + 0.235398i −0.885923 0.463832i \(-0.846474\pi\)
0.714896 + 0.699231i \(0.246474\pi\)
\(702\) −0.349442 3.28731i −0.0131888 0.124072i
\(703\) −44.8121 32.5579i −1.69012 1.22795i
\(704\) 0.958310 2.94937i 0.0361177 0.111159i
\(705\) 22.0355 25.6288i 0.829904 0.965235i
\(706\) −9.90518 + 3.21839i −0.372786 + 0.121126i
\(707\) −1.25025 −0.0470206
\(708\) 0.472372 6.79373i 0.0177528 0.255324i
\(709\) 19.1764 6.23077i 0.720183 0.234002i 0.0740804 0.997252i \(-0.476398\pi\)
0.646103 + 0.763251i \(0.276398\pi\)
\(710\) 4.95086 + 15.9065i 0.185803 + 0.596961i
\(711\) 11.8647 12.3057i 0.444962 0.461499i
\(712\) 15.7433 0.590004
\(713\) −15.1380 12.8991i −0.566922 0.483076i
\(714\) 2.25325 + 0.156670i 0.0843256 + 0.00586321i
\(715\) −2.54863 3.60107i −0.0953133 0.134673i
\(716\) −16.6571 + 12.1021i −0.622507 + 0.452278i
\(717\) −10.5913 42.4080i −0.395538 1.58376i
\(718\) 16.3372i 0.609698i
\(719\) 5.87557 0.219122 0.109561 0.993980i \(-0.465056\pi\)
0.109561 + 0.993980i \(0.465056\pi\)
\(720\) −1.01078 + 6.63162i −0.0376694 + 0.247146i
\(721\) 1.09772 3.37843i 0.0408811 0.125819i
\(722\) −12.3710 + 38.0741i −0.460402 + 1.41697i
\(723\) −5.88504 + 7.01913i −0.218867 + 0.261044i
\(724\) −10.5014 + 3.41210i −0.390280 + 0.126810i
\(725\) 3.69478 + 12.4119i 0.137221 + 0.460967i
\(726\) −2.03069 + 1.27003i −0.0753659 + 0.0471352i
\(727\) 34.3125 + 11.1488i 1.27258 + 0.413486i 0.865961 0.500112i \(-0.166708\pi\)
0.406618 + 0.913598i \(0.366708\pi\)
\(728\) −0.135266 0.186177i −0.00501328 0.00690018i
\(729\) −26.3966 + 5.67607i −0.977653 + 0.210225i
\(730\) 7.86075 10.5416i 0.290939 0.390163i
\(731\) 14.5639 + 20.0456i 0.538667 + 0.741412i
\(732\) 12.0833 14.4118i 0.446610 0.532676i
\(733\) −7.63726 + 2.48150i −0.282089 + 0.0916562i −0.446644 0.894712i \(-0.647381\pi\)
0.164556 + 0.986368i \(0.447381\pi\)
\(734\) −17.6863 12.8499i −0.652814 0.474297i
\(735\) 17.3446 20.1729i 0.639764 0.744089i
\(736\) −3.39722 1.10382i −0.125223 0.0406875i
\(737\) −44.6159 + 14.4966i −1.64345 + 0.533989i
\(738\) 4.71775 33.7616i 0.173663 1.24278i
\(739\) 1.84481i 0.0678626i −0.999424 0.0339313i \(-0.989197\pi\)
0.999424 0.0339313i \(-0.0108027\pi\)
\(740\) 0.200143 16.1191i 0.00735741 0.592549i
\(741\) 7.17832 4.48945i 0.263702 0.164924i
\(742\) 0.354445 + 0.257520i 0.0130121 + 0.00945384i
\(743\) 32.1066i 1.17788i −0.808178 0.588938i \(-0.799546\pi\)
0.808178 0.588938i \(-0.200454\pi\)
\(744\) −1.41074 + 9.53991i −0.0517203 + 0.349750i
\(745\) 15.1297 44.6697i 0.554311 1.63657i
\(746\) −18.8575 + 25.9551i −0.690422 + 0.950284i
\(747\) −18.2842 34.3222i −0.668982 1.25578i
\(748\) 10.6330 3.45487i 0.388781 0.126323i
\(749\) 2.07698i 0.0758914i
\(750\) −9.64979 16.7893i −0.352361 0.613060i
\(751\) 6.65313 + 20.4762i 0.242776 + 0.747189i 0.995994 + 0.0894176i \(0.0285006\pi\)
−0.753218 + 0.657771i \(0.771499\pi\)
\(752\) 2.69678 8.29983i 0.0983413 0.302664i
\(753\) 5.84554 14.4847i 0.213023 0.527851i
\(754\) −1.33310 0.968553i −0.0485486 0.0352726i
\(755\) −6.83717 0.0848940i −0.248830 0.00308961i
\(756\) −1.39528 + 1.25931i −0.0507459 + 0.0458006i
\(757\) 31.7365 23.0579i 1.15348 0.838054i 0.164542 0.986370i \(-0.447385\pi\)
0.988940 + 0.148316i \(0.0473854\pi\)
\(758\) −2.37894 + 7.32161i −0.0864068 + 0.265933i
\(759\) −10.1739 16.2673i −0.369288 0.590466i
\(760\) −16.4042 + 5.10577i −0.595044 + 0.185206i
\(761\) 5.87060 18.0678i 0.212809 0.654959i −0.786493 0.617599i \(-0.788105\pi\)
0.999302 0.0373594i \(-0.0118946\pi\)
\(762\) −13.4065 + 8.38465i −0.485666 + 0.303744i
\(763\) −0.143527 + 0.197549i −0.00519604 + 0.00715174i
\(764\) 16.5841 5.38850i 0.599991 0.194949i
\(765\) −21.4840 + 11.1048i −0.776754 + 0.401493i
\(766\) 6.55617 + 2.13023i 0.236884 + 0.0769683i
\(767\) −2.37903 0.772994i −0.0859019 0.0279112i
\(768\) 0.419684 + 1.68044i 0.0151440 + 0.0606375i
\(769\) −51.6413 −1.86223 −0.931116 0.364723i \(-0.881164\pi\)
−0.931116 + 0.364723i \(0.881164\pi\)
\(770\) −0.804663 + 2.37572i −0.0289980 + 0.0856150i
\(771\) 3.49160 + 13.9806i 0.125747 + 0.503497i
\(772\) 11.1671 + 15.3702i 0.401913 + 0.553186i
\(773\) 26.0466 35.8501i 0.936833 1.28944i −0.0203010 0.999794i \(-0.506462\pi\)
0.957134 0.289646i \(-0.0935375\pi\)
\(774\) −20.4200 2.85343i −0.733983 0.102565i
\(775\) −13.9795 24.0744i −0.502157 0.864776i
\(776\) 0.221414i 0.00794828i
\(777\) 2.90190 3.46112i 0.104105 0.124167i
\(778\) 20.4137 14.8314i 0.731866 0.531732i
\(779\) 83.0342 26.9795i 2.97501 0.966639i
\(780\) 2.27334 + 0.950437i 0.0813987 + 0.0340311i
\(781\) 23.1043i 0.826736i
\(782\) −3.97948 12.2476i −0.142306 0.437972i
\(783\) −6.71532 + 11.6631i −0.239986 + 0.416805i
\(784\) 2.12269 6.53296i 0.0758103 0.233320i
\(785\) −7.54884 + 5.34262i −0.269429 + 0.190686i
\(786\) −36.2652 + 9.05711i −1.29354 + 0.323056i
\(787\) −6.84969 4.97659i −0.244165 0.177396i 0.458972 0.888451i \(-0.348218\pi\)
−0.703137 + 0.711055i \(0.748218\pi\)
\(788\) 9.19201 + 12.6517i 0.327452 + 0.450699i
\(789\) −6.81818 2.75160i −0.242734 0.0979595i
\(790\) 3.78645 + 12.1654i 0.134716 + 0.432826i
\(791\) −1.95581 2.69194i −0.0695406 0.0957144i
\(792\) −4.07178 + 8.36511i −0.144684 + 0.297241i
\(793\) −4.06049 5.58878i −0.144192 0.198463i
\(794\) 3.27491 4.50752i 0.116222 0.159966i
\(795\) −4.67533 0.383461i −0.165817 0.0136000i
\(796\) 7.50039 10.3234i 0.265844 0.365903i
\(797\) 4.29387 + 1.39516i 0.152097 + 0.0494192i 0.384076 0.923302i \(-0.374520\pi\)
−0.231979 + 0.972721i \(0.574520\pi\)
\(798\) −4.46390 1.80149i −0.158020 0.0637719i
\(799\) 29.9223 9.72234i 1.05857 0.343952i
\(800\) −3.97087 3.03846i −0.140391 0.107426i
\(801\) −46.7753 6.53624i −1.65273 0.230947i
\(802\) −7.40584 22.7928i −0.261509 0.804843i
\(803\) 14.7542 10.7195i 0.520664 0.378285i
\(804\) 16.8339 20.0779i 0.593685 0.708092i
\(805\) 2.73646 + 0.926847i 0.0964476 + 0.0326671i
\(806\) 3.27417 + 1.35181i 0.115328 + 0.0476157i
\(807\) 24.1894 + 1.68191i 0.851508 + 0.0592059i
\(808\) 2.03164 2.79631i 0.0714728 0.0983739i
\(809\) 39.0917 28.4018i 1.37439 0.998553i 0.377011 0.926209i \(-0.376952\pi\)
0.997380 0.0723446i \(-0.0230481\pi\)
\(810\) 5.75644 19.2838i 0.202261 0.677562i
\(811\) 51.6702 1.81439 0.907194 0.420713i \(-0.138220\pi\)
0.907194 + 0.420713i \(0.138220\pi\)
\(812\) 0.936861i 0.0328774i
\(813\) 14.8487 3.70842i 0.520768 0.130060i
\(814\) 6.90867 21.2627i 0.242149 0.745258i
\(815\) 14.0031 + 10.4419i 0.490506 + 0.365764i
\(816\) −4.01190 + 4.78502i −0.140444 + 0.167509i
\(817\) −16.3180 50.2216i −0.570894 1.75703i
\(818\) 12.8847 17.7342i 0.450502 0.620063i
\(819\) 0.324596 + 0.609316i 0.0113423 + 0.0212912i
\(820\) 20.3693 + 15.1891i 0.711325 + 0.530425i
\(821\) −33.2598 + 24.1646i −1.16077 + 0.843352i −0.989876 0.141937i \(-0.954667\pi\)
−0.170899 + 0.985289i \(0.554667\pi\)
\(822\) 0.831184 + 1.32901i 0.0289909 + 0.0463544i
\(823\) 0.0882904 0.271730i 0.00307761 0.00947191i −0.949506 0.313749i \(-0.898415\pi\)
0.952584 + 0.304277i \(0.0984149\pi\)
\(824\) 5.77241 + 7.94505i 0.201092 + 0.276779i
\(825\) −5.85855 26.2100i −0.203969 0.912516i
\(826\) 0.439488 + 1.35260i 0.0152917 + 0.0470631i
\(827\) −26.0232 + 35.8178i −0.904915 + 1.24551i 0.0639590 + 0.997953i \(0.479627\pi\)
−0.968874 + 0.247556i \(0.920373\pi\)
\(828\) 9.63532 + 4.69006i 0.334850 + 0.162991i
\(829\) −0.402874 0.130902i −0.0139924 0.00454640i 0.302012 0.953304i \(-0.402342\pi\)
−0.316005 + 0.948758i \(0.602342\pi\)
\(830\) 28.9836 + 0.359876i 1.00604 + 0.0124915i
\(831\) 13.6257 + 0.947406i 0.472672 + 0.0328652i
\(832\) 0.636208 0.0220565
\(833\) 23.5524 7.65265i 0.816043 0.265149i
\(834\) 3.79992 + 6.07581i 0.131581 + 0.210388i
\(835\) −8.03792 + 5.68877i −0.278164 + 0.196868i
\(836\) −23.8272 −0.824081
\(837\) 8.15224 27.7586i 0.281783 0.959478i
\(838\) 21.0233i 0.726237i
\(839\) −15.1401 + 20.8385i −0.522693 + 0.719425i −0.985995 0.166775i \(-0.946665\pi\)
0.463302 + 0.886201i \(0.346665\pi\)
\(840\) −0.322549 1.36329i −0.0111290 0.0470379i
\(841\) −6.88852 21.2007i −0.237535 0.731058i
\(842\) −0.114824 −0.00395710
\(843\) −1.93320 + 27.8035i −0.0665828 + 0.957604i
\(844\) −5.61372 17.2773i −0.193232 0.594708i
\(845\) −16.8359 + 22.5777i −0.579172 + 0.776697i
\(846\) −11.4584 + 23.5402i −0.393947 + 0.809330i
\(847\) 0.294007 0.404666i 0.0101022 0.0139045i
\(848\) −1.15194 + 0.374287i −0.0395576 + 0.0128531i
\(849\) 29.1292 34.7427i 0.999713 1.19237i
\(850\) 0.447568 18.0203i 0.0153515 0.618091i
\(851\) −24.4914 7.95772i −0.839553 0.272787i
\(852\) −6.84247 10.9406i −0.234419 0.374820i
\(853\) −1.96919 2.71035i −0.0674237 0.0928007i 0.773973 0.633218i \(-0.218266\pi\)
−0.841397 + 0.540417i \(0.818266\pi\)
\(854\) −1.21370 + 3.73539i −0.0415320 + 0.127822i
\(855\) 50.8589 8.35928i 1.73934 0.285881i
\(856\) 4.64538 + 3.37507i 0.158776 + 0.115357i
\(857\) 0.520665 + 1.60244i 0.0177856 + 0.0547384i 0.959555 0.281520i \(-0.0908385\pi\)
−0.941770 + 0.336258i \(0.890839\pi\)
\(858\) 2.61867 + 2.19557i 0.0893999 + 0.0749554i
\(859\) −40.1067 13.0314i −1.36842 0.444627i −0.469576 0.882892i \(-0.655593\pi\)
−0.898846 + 0.438265i \(0.855593\pi\)
\(860\) 9.18680 12.3199i 0.313267 0.420106i
\(861\) 1.72502 + 6.90706i 0.0587884 + 0.235392i
\(862\) 1.24484i 0.0423995i
\(863\) 21.3726i 0.727531i 0.931490 + 0.363766i \(0.118509\pi\)
−0.931490 + 0.363766i \(0.881491\pi\)
\(864\) −0.549258 5.16704i −0.0186861 0.175786i
\(865\) 32.5469 10.1301i 1.10663 0.344435i
\(866\) 4.04708 + 2.94038i 0.137526 + 0.0999181i
\(867\) 6.91627 + 0.480893i 0.234889 + 0.0163320i
\(868\) −0.472391 1.95777i −0.0160340 0.0664511i
\(869\) 17.6703i 0.599424i
\(870\) −5.21306 8.57019i −0.176739 0.290557i
\(871\) −5.65689 7.78604i −0.191676 0.263820i
\(872\) −0.208607 0.642027i −0.00706433 0.0217418i
\(873\) 0.0919257 0.657849i 0.00311121 0.0222648i
\(874\) 27.4452i 0.928349i
\(875\) 3.18098 + 2.49727i 0.107537 + 0.0844230i
\(876\) −3.81194 + 9.44561i −0.128794 + 0.319137i
\(877\) −33.9303 11.0246i −1.14574 0.372275i −0.326206 0.945299i \(-0.605770\pi\)
−0.819539 + 0.573024i \(0.805770\pi\)
\(878\) 5.24559 + 3.81114i 0.177030 + 0.128620i
\(879\) 6.18801 + 24.7771i 0.208716 + 0.835712i
\(880\) −4.00597 5.66022i −0.135041 0.190806i
\(881\) −1.11668 + 0.811318i −0.0376220 + 0.0273340i −0.606437 0.795131i \(-0.707402\pi\)
0.568815 + 0.822465i \(0.307402\pi\)
\(882\) −9.01912 + 18.5290i −0.303689 + 0.623904i
\(883\) 22.1457 16.0898i 0.745263 0.541465i −0.149092 0.988823i \(-0.547635\pi\)
0.894355 + 0.447358i \(0.147635\pi\)
\(884\) 1.34817 + 1.85559i 0.0453437 + 0.0624103i
\(885\) −11.5468 9.92784i −0.388140 0.333721i
\(886\) 21.1985 15.4016i 0.712178 0.517428i
\(887\) −22.6633 16.4659i −0.760960 0.552870i 0.138244 0.990398i \(-0.455854\pi\)
−0.899205 + 0.437528i \(0.855854\pi\)
\(888\) 3.02559 + 12.1146i 0.101532 + 0.406541i
\(889\) 1.94102 2.67158i 0.0650996 0.0896019i
\(890\) 21.0438 28.2207i 0.705390 0.945962i
\(891\) 15.5708 23.1634i 0.521641 0.776002i
\(892\) 6.54354 + 20.1390i 0.219094 + 0.674302i
\(893\) −67.0520 −2.24381
\(894\) −2.53396 + 36.4438i −0.0847484 + 1.21886i
\(895\) −0.571604 + 46.0357i −0.0191066 + 1.53880i
\(896\) −0.212612 0.292636i −0.00710288 0.00977627i
\(897\) 2.52895 3.01630i 0.0844393 0.100711i
\(898\) 6.11873 0.204185
\(899\) −7.54887 12.2870i −0.251769 0.409796i
\(900\) 10.5365 + 10.6763i 0.351216 + 0.355876i
\(901\) −3.53269 2.56665i −0.117691 0.0855075i
\(902\) 20.7130 + 28.5091i 0.689669 + 0.949248i
\(903\) 4.17759 1.04334i 0.139022 0.0347202i
\(904\) 9.19895 0.305953
\(905\) −7.92064 + 23.3852i −0.263291 + 0.777352i
\(906\) 5.13862 1.28336i 0.170719 0.0426366i
\(907\) 41.4771 + 13.4767i 1.37722 + 0.447487i 0.901756 0.432246i \(-0.142279\pi\)
0.475468 + 0.879733i \(0.342279\pi\)
\(908\) −0.828040 + 2.54844i −0.0274795 + 0.0845731i
\(909\) −7.19723 + 7.46472i −0.238717 + 0.247589i
\(910\) −0.514541 0.00638882i −0.0170569 0.000211787i
\(911\) 42.1916 + 30.6540i 1.39787 + 1.01561i 0.994949 + 0.100378i \(0.0320053\pi\)
0.402922 + 0.915234i \(0.367995\pi\)
\(912\) 11.2830 7.05657i 0.373616 0.233666i
\(913\) 38.2324 + 12.4224i 1.26531 + 0.411123i
\(914\) −21.1382 + 15.3578i −0.699190 + 0.507992i
\(915\) −9.68249 40.9240i −0.320093 1.35291i
\(916\) 20.9997 + 6.82323i 0.693851 + 0.225446i
\(917\) 6.31531 4.58834i 0.208550 0.151520i
\(918\) 13.9065 12.5513i 0.458983 0.414254i
\(919\) 13.5111 + 41.5829i 0.445690 + 1.37169i 0.881726 + 0.471763i \(0.156382\pi\)
−0.436036 + 0.899929i \(0.643618\pi\)
\(920\) −6.51969 + 4.61426i −0.214948 + 0.152128i
\(921\) 34.5764 + 13.9539i 1.13933 + 0.459797i
\(922\) 4.08805 12.5817i 0.134633 0.414357i
\(923\) −4.50790 + 1.46470i −0.148379 + 0.0482113i
\(924\) 0.134767 1.93824i 0.00443350 0.0637633i
\(925\) −28.6269 21.9049i −0.941246 0.720229i
\(926\) −9.10203 28.0132i −0.299111 0.920570i
\(927\) −13.8520 26.0024i −0.454960 0.854029i
\(928\) −2.09538 1.52238i −0.0687843 0.0499747i
\(929\) −14.3951 −0.472288 −0.236144 0.971718i \(-0.575884\pi\)
−0.236144 + 0.971718i \(0.575884\pi\)
\(930\) 15.2151 + 15.2807i 0.498924 + 0.501074i
\(931\) −52.7780 −1.72973
\(932\) −3.32074 2.41266i −0.108774 0.0790292i
\(933\) −13.3425 21.3337i −0.436813 0.698434i
\(934\) −2.42430 7.46124i −0.0793256 0.244139i
\(935\) 8.01992 23.6784i 0.262280 0.774365i
\(936\) −1.89026 0.264139i −0.0617850 0.00863364i
\(937\) 16.7414 5.43962i 0.546918 0.177705i −0.0225083 0.999747i \(-0.507165\pi\)
0.569427 + 0.822042i \(0.307165\pi\)
\(938\) −1.69088 + 5.20398i −0.0552090 + 0.169916i
\(939\) −4.76058 + 11.7962i −0.155356 + 0.384956i
\(940\) −11.2732 15.9284i −0.367691 0.519527i
\(941\) 11.1242 + 34.2369i 0.362640 + 1.11609i 0.951446 + 0.307817i \(0.0995983\pi\)
−0.588806 + 0.808275i \(0.700402\pi\)
\(942\) 4.60251 5.48945i 0.149958 0.178856i
\(943\) 32.8380 23.8582i 1.06935 0.776930i
\(944\) −3.73939 1.21500i −0.121707 0.0395450i
\(945\) 0.392331 + 4.18443i 0.0127625 + 0.136119i
\(946\) 17.2431 12.5279i 0.560622 0.407316i
\(947\) −30.0936 9.77800i −0.977910 0.317742i −0.223905 0.974611i \(-0.571881\pi\)
−0.754005 + 0.656869i \(0.771881\pi\)
\(948\) −5.23316 8.36747i −0.169965 0.271763i
\(949\) 3.02685 + 2.19914i 0.0982557 + 0.0713870i
\(950\) −12.7749 + 36.2304i −0.414473 + 1.17547i
\(951\) −19.7789 16.5832i −0.641376 0.537747i
\(952\) 0.402975 1.24023i 0.0130605 0.0401960i
\(953\) 57.9263 + 18.8214i 1.87642 + 0.609685i 0.988830 + 0.149045i \(0.0476199\pi\)
0.887587 + 0.460640i \(0.152380\pi\)
\(954\) 3.57795 0.633798i 0.115840 0.0205200i
\(955\) 12.5085 36.9307i 0.404766 1.19505i
\(956\) −25.2363 −0.816201
\(957\) −3.37094 13.4974i −0.108967 0.436310i
\(958\) −19.0454 26.2137i −0.615328 0.846926i
\(959\) −0.264838 0.192416i −0.00855206 0.00621344i
\(960\) 3.57327 + 1.49391i 0.115327 + 0.0482157i
\(961\) 21.9704 + 21.8701i 0.708724 + 0.705486i
\(962\) 4.58657 0.147877
\(963\) −12.4008 11.9564i −0.399610 0.385291i
\(964\) 3.10845 + 4.27842i 0.100116 + 0.137798i
\(965\) 42.4789 + 0.527441i 1.36744 + 0.0169789i
\(966\) −2.23255 0.155230i −0.0718310 0.00499446i
\(967\) 4.45597 0.143294 0.0716472 0.997430i \(-0.477174\pi\)
0.0716472 + 0.997430i \(0.477174\pi\)
\(968\) 0.427319 + 1.31515i 0.0137345 + 0.0422706i
\(969\) 44.4909 + 17.9551i 1.42925 + 0.576800i
\(970\) 0.396897 + 0.295960i 0.0127436 + 0.00950272i
\(971\) 14.9237 20.5407i 0.478925 0.659184i −0.499373 0.866387i \(-0.666436\pi\)
0.978298 + 0.207204i \(0.0664362\pi\)
\(972\) −0.513318 + 15.5800i −0.0164647 + 0.499729i
\(973\) −1.21076 0.879668i −0.0388151 0.0282008i
\(974\) −19.8381 + 14.4132i −0.635653 + 0.461829i
\(975\) 4.74246 2.80466i 0.151880 0.0898211i
\(976\) −6.38232 8.78452i −0.204293 0.281185i
\(977\) −37.4572 + 27.2143i −1.19836 + 0.870662i −0.994123 0.108259i \(-0.965472\pi\)
−0.204240 + 0.978921i \(0.565472\pi\)
\(978\) −12.5472 5.06363i −0.401214 0.161917i
\(979\) 39.4981 28.6970i 1.26236 0.917162i
\(980\) −8.87335 12.5376i −0.283449 0.400498i
\(981\) 0.353245 + 1.99415i 0.0112782 + 0.0636685i
\(982\) −11.7237 8.51774i −0.374117 0.271812i
\(983\) −53.8902 17.5100i −1.71883 0.558482i −0.727067 0.686567i \(-0.759117\pi\)
−0.991763 + 0.128085i \(0.959117\pi\)
\(984\) −18.2514 7.36569i −0.581835 0.234810i
\(985\) 34.9658 + 0.434154i 1.11410 + 0.0138333i
\(986\) 9.33751i 0.297367i
\(987\) 0.379247 5.45438i 0.0120716 0.173615i
\(988\) −1.51054 4.64895i −0.0480565 0.147903i
\(989\) −14.4302 19.8614i −0.458852 0.631556i
\(990\) 9.55228 + 18.4804i 0.303591 + 0.587347i
\(991\) 8.10705i 0.257529i −0.991675 0.128764i \(-0.958899\pi\)
0.991675 0.128764i \(-0.0411011\pi\)
\(992\) 5.14638 + 2.12480i 0.163398 + 0.0674625i
\(993\) −0.455186 + 6.54655i −0.0144449 + 0.207748i
\(994\) 2.18020 + 1.58401i 0.0691516 + 0.0502416i
\(995\) −8.47963 27.2440i −0.268822 0.863694i
\(996\) −21.7833 + 5.44030i −0.690229 + 0.172383i
\(997\) 1.41851i 0.0449246i −0.999748 0.0224623i \(-0.992849\pi\)
0.999748 0.0224623i \(-0.00715058\pi\)
\(998\) 2.30228i 0.0728775i
\(999\) −3.95972 37.2504i −0.125280 1.17855i
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 930.2.y.b.29.7 yes 128
3.2 odd 2 930.2.y.a.29.7 128
5.4 even 2 930.2.y.a.29.26 yes 128
15.14 odd 2 inner 930.2.y.b.29.26 yes 128
31.15 odd 10 inner 930.2.y.b.449.26 yes 128
93.77 even 10 930.2.y.a.449.26 yes 128
155.139 odd 10 930.2.y.a.449.7 yes 128
465.449 even 10 inner 930.2.y.b.449.7 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.y.a.29.7 128 3.2 odd 2
930.2.y.a.29.26 yes 128 5.4 even 2
930.2.y.a.449.7 yes 128 155.139 odd 10
930.2.y.a.449.26 yes 128 93.77 even 10
930.2.y.b.29.7 yes 128 1.1 even 1 trivial
930.2.y.b.29.26 yes 128 15.14 odd 2 inner
930.2.y.b.449.7 yes 128 465.449 even 10 inner
930.2.y.b.449.26 yes 128 31.15 odd 10 inner