Properties

Label 462.2.k.d.89.3
Level $462$
Weight $2$
Character 462.89
Analytic conductor $3.689$
Analytic rank $0$
Dimension $8$
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] = [462,2,Mod(89,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.k (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.3
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 462.89
Dual form 462.2.k.d.353.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.09077 + 3.62132i) q^{5} -1.73205 q^{6} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.09077 + 3.62132i) q^{5} -1.73205 q^{6} +(-1.62132 - 2.09077i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(-3.62132 + 2.09077i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-1.50000 - 0.866025i) q^{12} +3.46410i q^{13} +(-0.358719 - 2.62132i) q^{14} -7.24264i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.58346 - 2.74264i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-7.24264 - 4.18154i) q^{19} -4.18154 q^{20} +(4.24264 + 1.73205i) q^{21} +1.00000 q^{22} +(1.07616 + 0.621320i) q^{23} +(-0.866025 - 1.50000i) q^{24} +(-6.24264 - 10.8126i) q^{25} +(-1.73205 + 3.00000i) q^{26} +5.19615i q^{27} +(1.00000 - 2.44949i) q^{28} +8.48528i q^{29} +(3.62132 - 6.27231i) q^{30} +(1.24264 - 0.717439i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.866025 + 1.50000i) q^{33} -3.16693i q^{34} +(10.9612 - 1.50000i) q^{35} +3.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(-4.18154 - 7.24264i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(-3.62132 - 2.09077i) q^{40} +5.19615 q^{41} +(2.80821 + 3.62132i) q^{42} -4.48528 q^{43} +(0.866025 + 0.500000i) q^{44} +(6.27231 + 10.8640i) q^{45} +(0.621320 + 1.07616i) q^{46} +(-2.09077 + 3.62132i) q^{47} -1.73205i q^{48} +(-1.74264 + 6.77962i) q^{49} -12.4853i q^{50} +(4.75039 + 2.74264i) q^{51} +(-3.00000 + 1.73205i) q^{52} +(-7.34847 + 4.24264i) q^{53} +(-2.59808 + 4.50000i) q^{54} +4.18154i q^{55} +(2.09077 - 1.62132i) q^{56} +14.4853 q^{57} +(-4.24264 + 7.34847i) q^{58} +(3.16693 + 5.48528i) q^{59} +(6.27231 - 3.62132i) q^{60} +(0.621320 + 0.358719i) q^{61} +1.43488 q^{62} +(-7.86396 + 1.07616i) q^{63} -1.00000 q^{64} +(-12.5446 - 7.24264i) q^{65} +(-1.50000 + 0.866025i) q^{66} +(1.74264 + 3.01834i) q^{67} +(1.58346 - 2.74264i) q^{68} -2.15232 q^{69} +(10.2426 + 4.18154i) q^{70} +6.00000i q^{71} +(2.59808 + 1.50000i) q^{72} +(-7.24264 + 4.18154i) q^{73} +(-3.46410 + 2.00000i) q^{74} +(18.7279 + 10.8126i) q^{75} -8.36308i q^{76} +(-2.44949 - 1.00000i) q^{77} -6.00000i q^{78} +(2.62132 - 4.54026i) q^{79} +(-2.09077 - 3.62132i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 + 2.59808i) q^{82} +3.16693 q^{83} +(0.621320 + 4.54026i) q^{84} +13.2426 q^{85} +(-3.88437 - 2.24264i) q^{86} +(-7.34847 - 12.7279i) q^{87} +(0.500000 + 0.866025i) q^{88} +(1.01461 - 1.75736i) q^{89} +12.5446i q^{90} +(7.24264 - 5.61642i) q^{91} +1.24264i q^{92} +(-1.24264 + 2.15232i) q^{93} +(-3.62132 + 2.09077i) q^{94} +(30.2854 - 17.4853i) q^{95} +(0.866025 - 1.50000i) q^{96} -0.297173i q^{97} +(-4.89898 + 5.00000i) q^{98} -3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{3} + 4 q^{4} + 4 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{3} + 4 q^{4} + 4 q^{7} + 12 q^{9} - 12 q^{10} - 12 q^{12} - 4 q^{16} - 24 q^{19} + 8 q^{22} - 16 q^{25} + 8 q^{28} + 12 q^{30} - 24 q^{31} + 24 q^{36} - 16 q^{37} - 24 q^{39} - 12 q^{40} + 32 q^{43} - 12 q^{46} + 20 q^{49} - 24 q^{52} + 48 q^{57} - 12 q^{61} - 12 q^{63} - 8 q^{64} - 12 q^{66} - 20 q^{67} + 48 q^{70} - 24 q^{73} + 48 q^{75} + 4 q^{79} - 36 q^{81} + 36 q^{82} - 12 q^{84} + 72 q^{85} + 4 q^{88} + 24 q^{91} + 24 q^{93} - 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.09077 + 3.62132i −0.935021 + 1.61950i −0.160424 + 0.987048i \(0.551286\pi\)
−0.774597 + 0.632456i \(0.782047\pi\)
\(6\) −1.73205 −0.707107
\(7\) −1.62132 2.09077i −0.612801 0.790237i
\(8\) 1.00000i 0.353553i
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −3.62132 + 2.09077i −1.14516 + 0.661160i
\(11\) 0.866025 0.500000i 0.261116 0.150756i
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) −0.358719 2.62132i −0.0958718 0.700577i
\(15\) 7.24264i 1.87004i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.58346 2.74264i −0.384047 0.665188i 0.607590 0.794251i \(-0.292136\pi\)
−0.991636 + 0.129063i \(0.958803\pi\)
\(18\) 2.59808 1.50000i 0.612372 0.353553i
\(19\) −7.24264 4.18154i −1.66158 0.959311i −0.971963 0.235133i \(-0.924448\pi\)
−0.689612 0.724179i \(-0.742219\pi\)
\(20\) −4.18154 −0.935021
\(21\) 4.24264 + 1.73205i 0.925820 + 0.377964i
\(22\) 1.00000 0.213201
\(23\) 1.07616 + 0.621320i 0.224395 + 0.129554i 0.607983 0.793950i \(-0.291979\pi\)
−0.383589 + 0.923504i \(0.625312\pi\)
\(24\) −0.866025 1.50000i −0.176777 0.306186i
\(25\) −6.24264 10.8126i −1.24853 2.16251i
\(26\) −1.73205 + 3.00000i −0.339683 + 0.588348i
\(27\) 5.19615i 1.00000i
\(28\) 1.00000 2.44949i 0.188982 0.462910i
\(29\) 8.48528i 1.57568i 0.615882 + 0.787839i \(0.288800\pi\)
−0.615882 + 0.787839i \(0.711200\pi\)
\(30\) 3.62132 6.27231i 0.661160 1.14516i
\(31\) 1.24264 0.717439i 0.223185 0.128856i −0.384239 0.923234i \(-0.625536\pi\)
0.607424 + 0.794378i \(0.292203\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −0.866025 + 1.50000i −0.150756 + 0.261116i
\(34\) 3.16693i 0.543124i
\(35\) 10.9612 1.50000i 1.85277 0.253546i
\(36\) 3.00000 0.500000
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −4.18154 7.24264i −0.678335 1.17491i
\(39\) −3.00000 5.19615i −0.480384 0.832050i
\(40\) −3.62132 2.09077i −0.572581 0.330580i
\(41\) 5.19615 0.811503 0.405751 0.913984i \(-0.367010\pi\)
0.405751 + 0.913984i \(0.367010\pi\)
\(42\) 2.80821 + 3.62132i 0.433316 + 0.558782i
\(43\) −4.48528 −0.683999 −0.341999 0.939700i \(-0.611104\pi\)
−0.341999 + 0.939700i \(0.611104\pi\)
\(44\) 0.866025 + 0.500000i 0.130558 + 0.0753778i
\(45\) 6.27231 + 10.8640i 0.935021 + 1.61950i
\(46\) 0.621320 + 1.07616i 0.0916087 + 0.158671i
\(47\) −2.09077 + 3.62132i −0.304970 + 0.528224i −0.977255 0.212069i \(-0.931980\pi\)
0.672285 + 0.740293i \(0.265313\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 12.4853i 1.76569i
\(51\) 4.75039 + 2.74264i 0.665188 + 0.384047i
\(52\) −3.00000 + 1.73205i −0.416025 + 0.240192i
\(53\) −7.34847 + 4.24264i −1.00939 + 0.582772i −0.911013 0.412378i \(-0.864698\pi\)
−0.0983769 + 0.995149i \(0.531365\pi\)
\(54\) −2.59808 + 4.50000i −0.353553 + 0.612372i
\(55\) 4.18154i 0.563839i
\(56\) 2.09077 1.62132i 0.279391 0.216658i
\(57\) 14.4853 1.91862
\(58\) −4.24264 + 7.34847i −0.557086 + 0.964901i
\(59\) 3.16693 + 5.48528i 0.412299 + 0.714123i 0.995141 0.0984629i \(-0.0313926\pi\)
−0.582842 + 0.812586i \(0.698059\pi\)
\(60\) 6.27231 3.62132i 0.809752 0.467510i
\(61\) 0.621320 + 0.358719i 0.0795519 + 0.0459293i 0.539248 0.842147i \(-0.318708\pi\)
−0.459696 + 0.888076i \(0.652042\pi\)
\(62\) 1.43488 0.182230
\(63\) −7.86396 + 1.07616i −0.990766 + 0.135583i
\(64\) −1.00000 −0.125000
\(65\) −12.5446 7.24264i −1.55597 0.898339i
\(66\) −1.50000 + 0.866025i −0.184637 + 0.106600i
\(67\) 1.74264 + 3.01834i 0.212897 + 0.368749i 0.952620 0.304163i \(-0.0983766\pi\)
−0.739723 + 0.672912i \(0.765043\pi\)
\(68\) 1.58346 2.74264i 0.192023 0.332594i
\(69\) −2.15232 −0.259108
\(70\) 10.2426 + 4.18154i 1.22423 + 0.499790i
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 2.59808 + 1.50000i 0.306186 + 0.176777i
\(73\) −7.24264 + 4.18154i −0.847687 + 0.489412i −0.859870 0.510513i \(-0.829455\pi\)
0.0121828 + 0.999926i \(0.496122\pi\)
\(74\) −3.46410 + 2.00000i −0.402694 + 0.232495i
\(75\) 18.7279 + 10.8126i 2.16251 + 1.24853i
\(76\) 8.36308i 0.959311i
\(77\) −2.44949 1.00000i −0.279145 0.113961i
\(78\) 6.00000i 0.679366i
\(79\) 2.62132 4.54026i 0.294922 0.510819i −0.680045 0.733170i \(-0.738040\pi\)
0.974967 + 0.222351i \(0.0713731\pi\)
\(80\) −2.09077 3.62132i −0.233755 0.404876i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 4.50000 + 2.59808i 0.496942 + 0.286910i
\(83\) 3.16693 0.347616 0.173808 0.984780i \(-0.444393\pi\)
0.173808 + 0.984780i \(0.444393\pi\)
\(84\) 0.621320 + 4.54026i 0.0677916 + 0.495383i
\(85\) 13.2426 1.43637
\(86\) −3.88437 2.24264i −0.418862 0.241830i
\(87\) −7.34847 12.7279i −0.787839 1.36458i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 1.01461 1.75736i 0.107549 0.186280i −0.807228 0.590240i \(-0.799033\pi\)
0.914777 + 0.403960i \(0.132367\pi\)
\(90\) 12.5446i 1.32232i
\(91\) 7.24264 5.61642i 0.759235 0.588761i
\(92\) 1.24264i 0.129554i
\(93\) −1.24264 + 2.15232i −0.128856 + 0.223185i
\(94\) −3.62132 + 2.09077i −0.373511 + 0.215646i
\(95\) 30.2854 17.4853i 3.10722 1.79395i
\(96\) 0.866025 1.50000i 0.0883883 0.153093i
\(97\) 0.297173i 0.0301733i −0.999886 0.0150867i \(-0.995198\pi\)
0.999886 0.0150867i \(-0.00480242\pi\)
\(98\) −4.89898 + 5.00000i −0.494872 + 0.505076i
\(99\) 3.00000i 0.301511i
\(100\) 6.24264 10.8126i 0.624264 1.08126i
\(101\) −1.01461 1.75736i −0.100958 0.174864i 0.811122 0.584877i \(-0.198857\pi\)
−0.912079 + 0.410013i \(0.865524\pi\)
\(102\) 2.74264 + 4.75039i 0.271562 + 0.470359i
\(103\) 10.2426 + 5.91359i 1.00924 + 0.582683i 0.910968 0.412476i \(-0.135336\pi\)
0.0982691 + 0.995160i \(0.468669\pi\)
\(104\) −3.46410 −0.339683
\(105\) −15.1427 + 11.7426i −1.47778 + 1.14596i
\(106\) −8.48528 −0.824163
\(107\) −12.9904 7.50000i −1.25583 0.725052i −0.283567 0.958952i \(-0.591518\pi\)
−0.972261 + 0.233900i \(0.924851\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) −1.37868 2.38794i −0.132054 0.228723i 0.792414 0.609983i \(-0.208824\pi\)
−0.924468 + 0.381260i \(0.875490\pi\)
\(110\) −2.09077 + 3.62132i −0.199347 + 0.345279i
\(111\) 6.92820i 0.657596i
\(112\) 2.62132 0.358719i 0.247691 0.0338958i
\(113\) 18.0000i 1.69330i 0.532152 + 0.846649i \(0.321383\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) 12.5446 + 7.24264i 1.17491 + 0.678335i
\(115\) −4.50000 + 2.59808i −0.419627 + 0.242272i
\(116\) −7.34847 + 4.24264i −0.682288 + 0.393919i
\(117\) 9.00000 + 5.19615i 0.832050 + 0.480384i
\(118\) 6.33386i 0.583079i
\(119\) −3.16693 + 7.75736i −0.290312 + 0.711116i
\(120\) 7.24264 0.661160
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 0.358719 + 0.621320i 0.0324769 + 0.0562517i
\(123\) −7.79423 + 4.50000i −0.702782 + 0.405751i
\(124\) 1.24264 + 0.717439i 0.111592 + 0.0644279i
\(125\) 31.3000 2.79956
\(126\) −7.34847 3.00000i −0.654654 0.267261i
\(127\) 15.2426 1.35257 0.676283 0.736642i \(-0.263590\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 6.72792 3.88437i 0.592361 0.341999i
\(130\) −7.24264 12.5446i −0.635222 1.10024i
\(131\) 3.16693 5.48528i 0.276696 0.479251i −0.693866 0.720104i \(-0.744094\pi\)
0.970562 + 0.240853i \(0.0774272\pi\)
\(132\) −1.73205 −0.150756
\(133\) 3.00000 + 21.9223i 0.260133 + 1.90091i
\(134\) 3.48528i 0.301082i
\(135\) −18.8169 10.8640i −1.61950 0.935021i
\(136\) 2.74264 1.58346i 0.235179 0.135781i
\(137\) −12.5446 + 7.24264i −1.07176 + 0.618781i −0.928662 0.370928i \(-0.879040\pi\)
−0.143098 + 0.989709i \(0.545706\pi\)
\(138\) −1.86396 1.07616i −0.158671 0.0916087i
\(139\) 3.46410i 0.293821i −0.989150 0.146911i \(-0.953067\pi\)
0.989150 0.146911i \(-0.0469330\pi\)
\(140\) 6.77962 + 8.74264i 0.572982 + 0.738888i
\(141\) 7.24264i 0.609940i
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 1.73205 + 3.00000i 0.144841 + 0.250873i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −30.7279 17.7408i −2.55182 1.47329i
\(146\) −8.36308 −0.692134
\(147\) −3.25736 11.6786i −0.268662 0.963234i
\(148\) −4.00000 −0.328798
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 10.8126 + 18.7279i 0.882843 + 1.52913i
\(151\) 0.378680 + 0.655892i 0.0308165 + 0.0533758i 0.881022 0.473075i \(-0.156856\pi\)
−0.850206 + 0.526450i \(0.823523\pi\)
\(152\) 4.18154 7.24264i 0.339168 0.587456i
\(153\) −9.50079 −0.768093
\(154\) −1.62132 2.09077i −0.130650 0.168479i
\(155\) 6.00000i 0.481932i
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) −16.2426 + 9.37769i −1.29630 + 0.748421i −0.979764 0.200158i \(-0.935855\pi\)
−0.316540 + 0.948579i \(0.602521\pi\)
\(158\) 4.54026 2.62132i 0.361204 0.208541i
\(159\) 7.34847 12.7279i 0.582772 1.00939i
\(160\) 4.18154i 0.330580i
\(161\) −0.445759 3.25736i −0.0351308 0.256716i
\(162\) 9.00000i 0.707107i
\(163\) 6.50000 11.2583i 0.509119 0.881820i −0.490825 0.871258i \(-0.663305\pi\)
0.999944 0.0105623i \(-0.00336213\pi\)
\(164\) 2.59808 + 4.50000i 0.202876 + 0.351391i
\(165\) −3.62132 6.27231i −0.281919 0.488299i
\(166\) 2.74264 + 1.58346i 0.212870 + 0.122901i
\(167\) −2.02922 −0.157026 −0.0785130 0.996913i \(-0.525017\pi\)
−0.0785130 + 0.996913i \(0.525017\pi\)
\(168\) −1.73205 + 4.24264i −0.133631 + 0.327327i
\(169\) 1.00000 0.0769231
\(170\) 11.4685 + 6.62132i 0.879591 + 0.507832i
\(171\) −21.7279 + 12.5446i −1.66158 + 0.959311i
\(172\) −2.24264 3.88437i −0.171000 0.296180i
\(173\) 4.18154 7.24264i 0.317917 0.550648i −0.662137 0.749383i \(-0.730350\pi\)
0.980053 + 0.198735i \(0.0636835\pi\)
\(174\) 14.6969i 1.11417i
\(175\) −12.4853 + 30.5826i −0.943799 + 2.31182i
\(176\) 1.00000i 0.0753778i
\(177\) −9.50079 5.48528i −0.714123 0.412299i
\(178\) 1.75736 1.01461i 0.131720 0.0760484i
\(179\) −12.5446 + 7.24264i −0.937629 + 0.541340i −0.889216 0.457487i \(-0.848750\pi\)
−0.0484128 + 0.998827i \(0.515416\pi\)
\(180\) −6.27231 + 10.8640i −0.467510 + 0.809752i
\(181\) 16.7262i 1.24325i −0.783317 0.621623i \(-0.786474\pi\)
0.783317 0.621623i \(-0.213526\pi\)
\(182\) 9.08052 1.24264i 0.673093 0.0921107i
\(183\) −1.24264 −0.0918586
\(184\) −0.621320 + 1.07616i −0.0458043 + 0.0793355i
\(185\) −8.36308 14.4853i −0.614866 1.06498i
\(186\) −2.15232 + 1.24264i −0.157816 + 0.0911148i
\(187\) −2.74264 1.58346i −0.200562 0.115794i
\(188\) −4.18154 −0.304970
\(189\) 10.8640 8.42463i 0.790237 0.612801i
\(190\) 34.9706 2.53703
\(191\) −15.5885 9.00000i −1.12794 0.651217i −0.184525 0.982828i \(-0.559075\pi\)
−0.943416 + 0.331611i \(0.892408\pi\)
\(192\) 1.50000 0.866025i 0.108253 0.0625000i
\(193\) 8.24264 + 14.2767i 0.593318 + 1.02766i 0.993782 + 0.111345i \(0.0355158\pi\)
−0.400464 + 0.916313i \(0.631151\pi\)
\(194\) 0.148586 0.257359i 0.0106679 0.0184773i
\(195\) 25.0892 1.79668
\(196\) −6.74264 + 1.88064i −0.481617 + 0.134331i
\(197\) 8.48528i 0.604551i −0.953221 0.302276i \(-0.902254\pi\)
0.953221 0.302276i \(-0.0977463\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) 11.4853 6.63103i 0.814170 0.470061i −0.0342319 0.999414i \(-0.510898\pi\)
0.848402 + 0.529353i \(0.177565\pi\)
\(200\) 10.8126 6.24264i 0.764564 0.441421i
\(201\) −5.22792 3.01834i −0.368749 0.212897i
\(202\) 2.02922i 0.142776i
\(203\) 17.7408 13.7574i 1.24516 0.965577i
\(204\) 5.48528i 0.384047i
\(205\) −10.8640 + 18.8169i −0.758772 + 1.31423i
\(206\) 5.91359 + 10.2426i 0.412019 + 0.713639i
\(207\) 3.22848 1.86396i 0.224395 0.129554i
\(208\) −3.00000 1.73205i −0.208013 0.120096i
\(209\) −8.36308 −0.578486
\(210\) −18.9853 + 2.59808i −1.31011 + 0.179284i
\(211\) 12.4853 0.859522 0.429761 0.902943i \(-0.358598\pi\)
0.429761 + 0.902943i \(0.358598\pi\)
\(212\) −7.34847 4.24264i −0.504695 0.291386i
\(213\) −5.19615 9.00000i −0.356034 0.616670i
\(214\) −7.50000 12.9904i −0.512689 0.888004i
\(215\) 9.37769 16.2426i 0.639553 1.10774i
\(216\) −5.19615 −0.353553
\(217\) −3.51472 1.43488i −0.238595 0.0974059i
\(218\) 2.75736i 0.186752i
\(219\) 7.24264 12.5446i 0.489412 0.847687i
\(220\) −3.62132 + 2.09077i −0.244149 + 0.140960i
\(221\) 9.50079 5.48528i 0.639092 0.368980i
\(222\) 3.46410 6.00000i 0.232495 0.402694i
\(223\) 6.33386i 0.424146i 0.977254 + 0.212073i \(0.0680215\pi\)
−0.977254 + 0.212073i \(0.931978\pi\)
\(224\) 2.44949 + 1.00000i 0.163663 + 0.0668153i
\(225\) −37.4558 −2.49706
\(226\) −9.00000 + 15.5885i −0.598671 + 1.03693i
\(227\) 10.9612 + 18.9853i 0.727518 + 1.26010i 0.957929 + 0.287004i \(0.0926594\pi\)
−0.230412 + 0.973093i \(0.574007\pi\)
\(228\) 7.24264 + 12.5446i 0.479656 + 0.830788i
\(229\) 6.00000 + 3.46410i 0.396491 + 0.228914i 0.684969 0.728572i \(-0.259816\pi\)
−0.288478 + 0.957487i \(0.593149\pi\)
\(230\) −5.19615 −0.342624
\(231\) 4.54026 0.621320i 0.298727 0.0408799i
\(232\) −8.48528 −0.557086
\(233\) 22.4912 + 12.9853i 1.47345 + 0.850694i 0.999553 0.0298888i \(-0.00951533\pi\)
0.473892 + 0.880583i \(0.342849\pi\)
\(234\) 5.19615 + 9.00000i 0.339683 + 0.588348i
\(235\) −8.74264 15.1427i −0.570307 0.987801i
\(236\) −3.16693 + 5.48528i −0.206149 + 0.357061i
\(237\) 9.08052i 0.589843i
\(238\) −6.62132 + 5.13461i −0.429196 + 0.332827i
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 6.27231 + 3.62132i 0.404876 + 0.233755i
\(241\) 12.0000 6.92820i 0.772988 0.446285i −0.0609515 0.998141i \(-0.519414\pi\)
0.833939 + 0.551856i \(0.186080\pi\)
\(242\) 0.866025 0.500000i 0.0556702 0.0321412i
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 0.717439i 0.0459293i
\(245\) −20.9077 20.4853i −1.33574 1.30876i
\(246\) −9.00000 −0.573819
\(247\) 14.4853 25.0892i 0.921676 1.59639i
\(248\) 0.717439 + 1.24264i 0.0455574 + 0.0789078i
\(249\) −4.75039 + 2.74264i −0.301044 + 0.173808i
\(250\) 27.1066 + 15.6500i 1.71437 + 0.989793i
\(251\) −14.6969 −0.927663 −0.463831 0.885924i \(-0.653526\pi\)
−0.463831 + 0.885924i \(0.653526\pi\)
\(252\) −4.86396 6.27231i −0.306401 0.395118i
\(253\) 1.24264 0.0781242
\(254\) 13.2005 + 7.62132i 0.828274 + 0.478204i
\(255\) −19.8640 + 11.4685i −1.24393 + 0.718183i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.01461 + 1.75736i −0.0632897 + 0.109621i −0.895934 0.444187i \(-0.853493\pi\)
0.832644 + 0.553808i \(0.186826\pi\)
\(258\) 7.76874 0.483660
\(259\) 10.4853 1.43488i 0.651524 0.0891590i
\(260\) 14.4853i 0.898339i
\(261\) 22.0454 + 12.7279i 1.36458 + 0.787839i
\(262\) 5.48528 3.16693i 0.338882 0.195654i
\(263\) −9.50079 + 5.48528i −0.585844 + 0.338237i −0.763452 0.645864i \(-0.776497\pi\)
0.177609 + 0.984101i \(0.443164\pi\)
\(264\) −1.50000 0.866025i −0.0923186 0.0533002i
\(265\) 35.4815i 2.17961i
\(266\) −8.36308 + 20.4853i −0.512773 + 1.25603i
\(267\) 3.51472i 0.215097i
\(268\) −1.74264 + 3.01834i −0.106449 + 0.184375i
\(269\) 11.4685 + 19.8640i 0.699245 + 1.21113i 0.968729 + 0.248122i \(0.0798135\pi\)
−0.269484 + 0.963005i \(0.586853\pi\)
\(270\) −10.8640 18.8169i −0.661160 1.14516i
\(271\) 6.72792 + 3.88437i 0.408692 + 0.235959i 0.690228 0.723592i \(-0.257510\pi\)
−0.281535 + 0.959551i \(0.590844\pi\)
\(272\) 3.16693 0.192023
\(273\) −6.00000 + 14.6969i −0.363137 + 0.889499i
\(274\) −14.4853 −0.875088
\(275\) −10.8126 6.24264i −0.652023 0.376445i
\(276\) −1.07616 1.86396i −0.0647771 0.112197i
\(277\) −14.2426 24.6690i −0.855757 1.48222i −0.875941 0.482419i \(-0.839758\pi\)
0.0201833 0.999796i \(-0.493575\pi\)
\(278\) 1.73205 3.00000i 0.103882 0.179928i
\(279\) 4.30463i 0.257712i
\(280\) 1.50000 + 10.9612i 0.0896421 + 0.655054i
\(281\) 17.4853i 1.04308i 0.853225 + 0.521542i \(0.174643\pi\)
−0.853225 + 0.521542i \(0.825357\pi\)
\(282\) 3.62132 6.27231i 0.215646 0.373511i
\(283\) −21.2132 + 12.2474i −1.26099 + 0.728035i −0.973267 0.229677i \(-0.926233\pi\)
−0.287727 + 0.957712i \(0.592900\pi\)
\(284\) −5.19615 + 3.00000i −0.308335 + 0.178017i
\(285\) −30.2854 + 52.4558i −1.79395 + 3.10722i
\(286\) 3.46410i 0.204837i
\(287\) −8.42463 10.8640i −0.497290 0.641279i
\(288\) 3.00000i 0.176777i
\(289\) 3.48528 6.03668i 0.205017 0.355099i
\(290\) −17.7408 30.7279i −1.04177 1.80441i
\(291\) 0.257359 + 0.445759i 0.0150867 + 0.0261309i
\(292\) −7.24264 4.18154i −0.423843 0.244706i
\(293\) −12.4215 −0.725673 −0.362837 0.931853i \(-0.618192\pi\)
−0.362837 + 0.931853i \(0.618192\pi\)
\(294\) 3.01834 11.7426i 0.176033 0.684845i
\(295\) −26.4853 −1.54203
\(296\) −3.46410 2.00000i −0.201347 0.116248i
\(297\) 2.59808 + 4.50000i 0.150756 + 0.261116i
\(298\) 0 0
\(299\) −2.15232 + 3.72792i −0.124472 + 0.215591i
\(300\) 21.6251i 1.24853i
\(301\) 7.27208 + 9.37769i 0.419156 + 0.540521i
\(302\) 0.757359i 0.0435811i
\(303\) 3.04384 + 1.75736i 0.174864 + 0.100958i
\(304\) 7.24264 4.18154i 0.415394 0.239828i
\(305\) −2.59808 + 1.50000i −0.148765 + 0.0858898i
\(306\) −8.22792 4.75039i −0.470359 0.271562i
\(307\) 23.6544i 1.35003i −0.737806 0.675013i \(-0.764138\pi\)
0.737806 0.675013i \(-0.235862\pi\)
\(308\) −0.358719 2.62132i −0.0204399 0.149364i
\(309\) −20.4853 −1.16537
\(310\) −3.00000 + 5.19615i −0.170389 + 0.295122i
\(311\) −12.6062 21.8345i −0.714830 1.23812i −0.963025 0.269412i \(-0.913171\pi\)
0.248195 0.968710i \(-0.420163\pi\)
\(312\) 5.19615 3.00000i 0.294174 0.169842i
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) −18.7554 −1.05843
\(315\) 12.5446 30.7279i 0.706809 1.73132i
\(316\) 5.24264 0.294922
\(317\) 21.8608 + 12.6213i 1.22782 + 0.708884i 0.966574 0.256387i \(-0.0825323\pi\)
0.261249 + 0.965271i \(0.415866\pi\)
\(318\) 12.7279 7.34847i 0.713746 0.412082i
\(319\) 4.24264 + 7.34847i 0.237542 + 0.411435i
\(320\) 2.09077 3.62132i 0.116878 0.202438i
\(321\) 25.9808 1.45010
\(322\) 1.24264 3.04384i 0.0692497 0.169626i
\(323\) 26.4853i 1.47368i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 37.4558 21.6251i 2.07768 1.19955i
\(326\) 11.2583 6.50000i 0.623541 0.360002i
\(327\) 4.13604 + 2.38794i 0.228723 + 0.132054i
\(328\) 5.19615i 0.286910i
\(329\) 10.9612 1.50000i 0.604308 0.0826977i
\(330\) 7.24264i 0.398694i
\(331\) −9.50000 + 16.4545i −0.522167 + 0.904420i 0.477500 + 0.878632i \(0.341543\pi\)
−0.999667 + 0.0257885i \(0.991790\pi\)
\(332\) 1.58346 + 2.74264i 0.0869039 + 0.150522i
\(333\) 6.00000 + 10.3923i 0.328798 + 0.569495i
\(334\) −1.75736 1.01461i −0.0961584 0.0555171i
\(335\) −14.5738 −0.796254
\(336\) −3.62132 + 2.80821i −0.197559 + 0.153200i
\(337\) 30.4853 1.66064 0.830320 0.557288i \(-0.188158\pi\)
0.830320 + 0.557288i \(0.188158\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) −15.5885 27.0000i −0.846649 1.46644i
\(340\) 6.62132 + 11.4685i 0.359092 + 0.621965i
\(341\) 0.717439 1.24264i 0.0388515 0.0672928i
\(342\) −25.0892 −1.35667
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 4.48528i 0.241830i
\(345\) 4.50000 7.79423i 0.242272 0.419627i
\(346\) 7.24264 4.18154i 0.389367 0.224801i
\(347\) −0.445759 + 0.257359i −0.0239296 + 0.0138158i −0.511917 0.859035i \(-0.671065\pi\)
0.487987 + 0.872851i \(0.337731\pi\)
\(348\) 7.34847 12.7279i 0.393919 0.682288i
\(349\) 15.4144i 0.825113i −0.910932 0.412556i \(-0.864636\pi\)
0.910932 0.412556i \(-0.135364\pi\)
\(350\) −26.1039 + 20.2426i −1.39531 + 1.08201i
\(351\) −18.0000 −0.960769
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −12.5446 21.7279i −0.667683 1.15646i −0.978550 0.206007i \(-0.933953\pi\)
0.310868 0.950453i \(-0.399380\pi\)
\(354\) −5.48528 9.50079i −0.291539 0.504961i
\(355\) −21.7279 12.5446i −1.15320 0.665799i
\(356\) 2.02922 0.107549
\(357\) −1.96768 14.3787i −0.104141 0.761000i
\(358\) −14.4853 −0.765571
\(359\) 7.34847 + 4.24264i 0.387837 + 0.223918i 0.681223 0.732076i \(-0.261449\pi\)
−0.293385 + 0.955994i \(0.594782\pi\)
\(360\) −10.8640 + 6.27231i −0.572581 + 0.330580i
\(361\) 25.4706 + 44.1163i 1.34056 + 2.32191i
\(362\) 8.36308 14.4853i 0.439554 0.761329i
\(363\) 1.73205i 0.0909091i
\(364\) 8.48528 + 3.46410i 0.444750 + 0.181568i
\(365\) 34.9706i 1.83044i
\(366\) −1.07616 0.621320i −0.0562517 0.0324769i
\(367\) −21.7279 + 12.5446i −1.13419 + 0.654824i −0.944985 0.327114i \(-0.893924\pi\)
−0.189203 + 0.981938i \(0.560591\pi\)
\(368\) −1.07616 + 0.621320i −0.0560986 + 0.0323886i
\(369\) 7.79423 13.5000i 0.405751 0.702782i
\(370\) 16.7262i 0.869552i
\(371\) 20.7846 + 8.48528i 1.07908 + 0.440534i
\(372\) −2.48528 −0.128856
\(373\) −8.86396 + 15.3528i −0.458959 + 0.794939i −0.998906 0.0467591i \(-0.985111\pi\)
0.539948 + 0.841699i \(0.318444\pi\)
\(374\) −1.58346 2.74264i −0.0818790 0.141819i
\(375\) −46.9500 + 27.1066i −2.42449 + 1.39978i
\(376\) −3.62132 2.09077i −0.186755 0.107823i
\(377\) −29.3939 −1.51386
\(378\) 13.6208 1.86396i 0.700577 0.0958718i
\(379\) −0.0294373 −0.00151209 −0.000756045 1.00000i \(-0.500241\pi\)
−0.000756045 1.00000i \(0.500241\pi\)
\(380\) 30.2854 + 17.4853i 1.55361 + 0.896976i
\(381\) −22.8640 + 13.2005i −1.17136 + 0.676283i
\(382\) −9.00000 15.5885i −0.460480 0.797575i
\(383\) −15.7116 + 27.2132i −0.802823 + 1.39053i 0.114928 + 0.993374i \(0.463336\pi\)
−0.917751 + 0.397156i \(0.869997\pi\)
\(384\) 1.73205 0.0883883
\(385\) 8.74264 6.77962i 0.445566 0.345521i
\(386\) 16.4853i 0.839079i
\(387\) −6.72792 + 11.6531i −0.341999 + 0.592361i
\(388\) 0.257359 0.148586i 0.0130654 0.00754334i
\(389\) 24.0131 13.8640i 1.21751 0.702931i 0.253127 0.967433i \(-0.418541\pi\)
0.964385 + 0.264502i \(0.0852077\pi\)
\(390\) 21.7279 + 12.5446i 1.10024 + 0.635222i
\(391\) 3.93535i 0.199019i
\(392\) −6.77962 1.74264i −0.342422 0.0880166i
\(393\) 10.9706i 0.553392i
\(394\) 4.24264 7.34847i 0.213741 0.370211i
\(395\) 10.9612 + 18.9853i 0.551516 + 0.955253i
\(396\) 2.59808 1.50000i 0.130558 0.0753778i
\(397\) 21.2132 + 12.2474i 1.06466 + 0.614682i 0.926718 0.375758i \(-0.122618\pi\)
0.137943 + 0.990440i \(0.455951\pi\)
\(398\) 13.2621 0.664767
\(399\) −23.4853 30.2854i −1.17573 1.51617i
\(400\) 12.4853 0.624264
\(401\) −7.34847 4.24264i −0.366965 0.211867i 0.305167 0.952299i \(-0.401288\pi\)
−0.672132 + 0.740432i \(0.734621\pi\)
\(402\) −3.01834 5.22792i −0.150541 0.260745i
\(403\) 2.48528 + 4.30463i 0.123801 + 0.214429i
\(404\) 1.01461 1.75736i 0.0504788 0.0874319i
\(405\) 37.6339 1.87004
\(406\) 22.2426 3.04384i 1.10388 0.151063i
\(407\) 4.00000i 0.198273i
\(408\) −2.74264 + 4.75039i −0.135781 + 0.235179i
\(409\) 13.2426 7.64564i 0.654806 0.378053i −0.135489 0.990779i \(-0.543260\pi\)
0.790295 + 0.612726i \(0.209927\pi\)
\(410\) −18.8169 + 10.8640i −0.929302 + 0.536533i
\(411\) 12.5446 21.7279i 0.618781 1.07176i
\(412\) 11.8272i 0.582683i
\(413\) 6.33386 15.5147i 0.311669 0.763429i
\(414\) 3.72792 0.183217
\(415\) −6.62132 + 11.4685i −0.325028 + 0.562965i
\(416\) −1.73205 3.00000i −0.0849208 0.147087i
\(417\) 3.00000 + 5.19615i 0.146911 + 0.254457i
\(418\) −7.24264 4.18154i −0.354249 0.204526i
\(419\) −8.36308 −0.408563 −0.204282 0.978912i \(-0.565486\pi\)
−0.204282 + 0.978912i \(0.565486\pi\)
\(420\) −17.7408 7.24264i −0.865661 0.353405i
\(421\) 16.4853 0.803443 0.401722 0.915762i \(-0.368412\pi\)
0.401722 + 0.915762i \(0.368412\pi\)
\(422\) 10.8126 + 6.24264i 0.526348 + 0.303887i
\(423\) 6.27231 + 10.8640i 0.304970 + 0.528224i
\(424\) −4.24264 7.34847i −0.206041 0.356873i
\(425\) −19.7700 + 34.2426i −0.958986 + 1.66101i
\(426\) 10.3923i 0.503509i
\(427\) −0.257359 1.88064i −0.0124545 0.0910104i
\(428\) 15.0000i 0.725052i
\(429\) −5.19615 3.00000i −0.250873 0.144841i
\(430\) 16.2426 9.37769i 0.783290 0.452233i
\(431\) −8.23999 + 4.75736i −0.396906 + 0.229154i −0.685148 0.728404i \(-0.740263\pi\)
0.288242 + 0.957558i \(0.406929\pi\)
\(432\) −4.50000 2.59808i −0.216506 0.125000i
\(433\) 28.8505i 1.38647i 0.720713 + 0.693234i \(0.243815\pi\)
−0.720713 + 0.693234i \(0.756185\pi\)
\(434\) −2.32640 3.00000i −0.111671 0.144005i
\(435\) 61.4558 2.94658
\(436\) 1.37868 2.38794i 0.0660268 0.114362i
\(437\) −5.19615 9.00000i −0.248566 0.430528i
\(438\) 12.5446 7.24264i 0.599405 0.346067i
\(439\) 16.3492 + 9.43924i 0.780307 + 0.450510i 0.836539 0.547907i \(-0.184575\pi\)
−0.0562322 + 0.998418i \(0.517909\pi\)
\(440\) −4.18154 −0.199347
\(441\) 15.0000 + 14.6969i 0.714286 + 0.699854i
\(442\) 10.9706 0.521816
\(443\) 31.1769 + 18.0000i 1.48126 + 0.855206i 0.999774 0.0212481i \(-0.00676401\pi\)
0.481486 + 0.876454i \(0.340097\pi\)
\(444\) 6.00000 3.46410i 0.284747 0.164399i
\(445\) 4.24264 + 7.34847i 0.201120 + 0.348351i
\(446\) −3.16693 + 5.48528i −0.149958 + 0.259736i
\(447\) 0 0
\(448\) 1.62132 + 2.09077i 0.0766002 + 0.0987796i
\(449\) 3.51472i 0.165870i 0.996555 + 0.0829349i \(0.0264294\pi\)
−0.996555 + 0.0829349i \(0.973571\pi\)
\(450\) −32.4377 18.7279i −1.52913 0.882843i
\(451\) 4.50000 2.59808i 0.211897 0.122339i
\(452\) −15.5885 + 9.00000i −0.733219 + 0.423324i
\(453\) −1.13604 0.655892i −0.0533758 0.0308165i
\(454\) 21.9223i 1.02887i
\(455\) 5.19615 + 37.9706i 0.243599 + 1.78009i
\(456\) 14.4853i 0.678335i
\(457\) −10.4853 + 18.1610i −0.490481 + 0.849538i −0.999940 0.0109572i \(-0.996512\pi\)
0.509459 + 0.860495i \(0.329845\pi\)
\(458\) 3.46410 + 6.00000i 0.161867 + 0.280362i
\(459\) 14.2512 8.22792i 0.665188 0.384047i
\(460\) −4.50000 2.59808i −0.209814 0.121136i
\(461\) 6.33386 0.294997 0.147499 0.989062i \(-0.452878\pi\)
0.147499 + 0.989062i \(0.452878\pi\)
\(462\) 4.24264 + 1.73205i 0.197386 + 0.0805823i
\(463\) −29.4558 −1.36893 −0.684465 0.729046i \(-0.739964\pi\)
−0.684465 + 0.729046i \(0.739964\pi\)
\(464\) −7.34847 4.24264i −0.341144 0.196960i
\(465\) −5.19615 9.00000i −0.240966 0.417365i
\(466\) 12.9853 + 22.4912i 0.601532 + 1.04188i
\(467\) 15.5885 27.0000i 0.721348 1.24941i −0.239112 0.970992i \(-0.576856\pi\)
0.960460 0.278419i \(-0.0898104\pi\)
\(468\) 10.3923i 0.480384i
\(469\) 3.48528 8.53716i 0.160935 0.394209i
\(470\) 17.4853i 0.806536i
\(471\) 16.2426 28.1331i 0.748421 1.29630i
\(472\) −5.48528 + 3.16693i −0.252481 + 0.145770i
\(473\) −3.88437 + 2.24264i −0.178603 + 0.103117i
\(474\) −4.54026 + 7.86396i −0.208541 + 0.361204i
\(475\) 104.415i 4.79091i
\(476\) −8.30153 + 1.13604i −0.380500 + 0.0520703i
\(477\) 25.4558i 1.16554i
\(478\) 0 0
\(479\) 15.7116 + 27.2132i 0.717879 + 1.24340i 0.961839 + 0.273618i \(0.0882203\pi\)
−0.243960 + 0.969785i \(0.578446\pi\)
\(480\) 3.62132 + 6.27231i 0.165290 + 0.286291i
\(481\) −12.0000 6.92820i −0.547153 0.315899i
\(482\) 13.8564 0.631142
\(483\) 3.48960 + 4.50000i 0.158782 + 0.204757i
\(484\) 1.00000 0.0454545
\(485\) 1.07616 + 0.621320i 0.0488658 + 0.0282127i
\(486\) 7.79423 + 13.5000i 0.353553 + 0.612372i
\(487\) −7.48528 12.9649i −0.339190 0.587495i 0.645090 0.764106i \(-0.276820\pi\)
−0.984281 + 0.176611i \(0.943486\pi\)
\(488\) −0.358719 + 0.621320i −0.0162385 + 0.0281259i
\(489\) 22.5167i 1.01824i
\(490\) −7.86396 28.1946i −0.355258 1.27370i
\(491\) 19.9706i 0.901259i −0.892711 0.450629i \(-0.851200\pi\)
0.892711 0.450629i \(-0.148800\pi\)
\(492\) −7.79423 4.50000i −0.351391 0.202876i
\(493\) 23.2721 13.4361i 1.04812 0.605133i
\(494\) 25.0892 14.4853i 1.12882 0.651724i
\(495\) 10.8640 + 6.27231i 0.488299 + 0.281919i
\(496\) 1.43488i 0.0644279i
\(497\) 12.5446 9.72792i 0.562703 0.436357i
\(498\) −5.48528 −0.245801
\(499\) 6.48528 11.2328i 0.290321 0.502851i −0.683565 0.729890i \(-0.739571\pi\)
0.973886 + 0.227039i \(0.0729046\pi\)
\(500\) 15.6500 + 27.1066i 0.699889 + 1.21224i
\(501\) 3.04384 1.75736i 0.135989 0.0785130i
\(502\) −12.7279 7.34847i −0.568075 0.327978i
\(503\) −16.7262 −0.745783 −0.372891 0.927875i \(-0.621634\pi\)
−0.372891 + 0.927875i \(0.621634\pi\)
\(504\) −1.07616 7.86396i −0.0479359 0.350289i
\(505\) 8.48528 0.377590
\(506\) 1.07616 + 0.621320i 0.0478411 + 0.0276211i
\(507\) −1.50000 + 0.866025i −0.0666173 + 0.0384615i
\(508\) 7.62132 + 13.2005i 0.338141 + 0.585678i
\(509\) 3.16693 5.48528i 0.140372 0.243131i −0.787265 0.616615i \(-0.788504\pi\)
0.927637 + 0.373484i \(0.121837\pi\)
\(510\) −22.9369 −1.01566
\(511\) 20.4853 + 8.36308i 0.906215 + 0.369961i
\(512\) 1.00000i 0.0441942i
\(513\) 21.7279 37.6339i 0.959311 1.66158i
\(514\) −1.75736 + 1.01461i −0.0775138 + 0.0447526i
\(515\) −42.8300 + 24.7279i −1.88732 + 1.08964i
\(516\) 6.72792 + 3.88437i 0.296180 + 0.171000i
\(517\) 4.18154i 0.183904i
\(518\) 9.79796 + 4.00000i 0.430498 + 0.175750i
\(519\) 14.4853i 0.635833i
\(520\) 7.24264 12.5446i 0.317611 0.550118i
\(521\) 1.13770 + 1.97056i 0.0498438 + 0.0863319i 0.889871 0.456213i \(-0.150794\pi\)
−0.840027 + 0.542544i \(0.817461\pi\)
\(522\) 12.7279 + 22.0454i 0.557086 + 0.964901i
\(523\) −22.7574 13.1390i −0.995110 0.574527i −0.0883121 0.996093i \(-0.528147\pi\)
−0.906798 + 0.421566i \(0.861481\pi\)
\(524\) 6.33386 0.276696
\(525\) −7.75736 56.6864i −0.338559 2.47400i
\(526\) −10.9706 −0.478339
\(527\) −3.93535 2.27208i −0.171427 0.0989733i
\(528\) −0.866025 1.50000i −0.0376889 0.0652791i
\(529\) −10.7279 18.5813i −0.466431 0.807883i
\(530\) 17.7408 30.7279i 0.770610 1.33474i
\(531\) 19.0016 0.824598
\(532\) −17.4853 + 13.5592i −0.758083 + 0.587867i
\(533\) 18.0000i 0.779667i
\(534\) −1.75736 + 3.04384i −0.0760484 + 0.131720i
\(535\) 54.3198 31.3616i 2.34845 1.35588i
\(536\) −3.01834 + 1.74264i −0.130373 + 0.0752706i
\(537\) 12.5446 21.7279i 0.541340 0.937629i
\(538\) 22.9369i 0.988881i
\(539\) 1.88064 + 6.74264i 0.0810048 + 0.290426i
\(540\) 21.7279i 0.935021i
\(541\) −3.37868 + 5.85204i −0.145261 + 0.251599i −0.929470 0.368897i \(-0.879735\pi\)
0.784209 + 0.620496i \(0.213069\pi\)
\(542\) 3.88437 + 6.72792i 0.166848 + 0.288989i
\(543\) 14.4853 + 25.0892i 0.621623 + 1.07668i
\(544\) 2.74264 + 1.58346i 0.117590 + 0.0678905i
\(545\) 11.5300 0.493891
\(546\) −12.5446 + 9.72792i −0.536860 + 0.416317i
\(547\) −11.4558 −0.489817 −0.244908 0.969546i \(-0.578758\pi\)
−0.244908 + 0.969546i \(0.578758\pi\)
\(548\) −12.5446 7.24264i −0.535880 0.309390i
\(549\) 1.86396 1.07616i 0.0795519 0.0459293i
\(550\) −6.24264 10.8126i −0.266187 0.461050i
\(551\) 35.4815 61.4558i 1.51156 2.61811i
\(552\) 2.15232i 0.0916087i
\(553\) −13.7426 + 1.88064i −0.584397 + 0.0799728i
\(554\) 28.4853i 1.21022i
\(555\) 25.0892 + 14.4853i 1.06498 + 0.614866i
\(556\) 3.00000 1.73205i 0.127228 0.0734553i
\(557\) 23.8284 13.7574i 1.00964 0.582918i 0.0985563 0.995131i \(-0.468578\pi\)
0.911087 + 0.412213i \(0.135244\pi\)
\(558\) 2.15232 3.72792i 0.0911148 0.157816i
\(559\) 15.5375i 0.657165i
\(560\) −4.18154 + 10.2426i −0.176702 + 0.432831i
\(561\) 5.48528 0.231589
\(562\) −8.74264 + 15.1427i −0.368786 + 0.638756i
\(563\) −13.5592 23.4853i −0.571454 0.989787i −0.996417 0.0845761i \(-0.973046\pi\)
0.424963 0.905211i \(-0.360287\pi\)
\(564\) 6.27231 3.62132i 0.264112 0.152485i
\(565\) −65.1838 37.6339i −2.74230 1.58327i
\(566\) −24.4949 −1.02960
\(567\) −9.00000 + 22.0454i −0.377964 + 0.925820i
\(568\) −6.00000 −0.251754
\(569\) −24.1977 13.9706i −1.01442 0.585676i −0.101938 0.994791i \(-0.532504\pi\)
−0.912483 + 0.409114i \(0.865838\pi\)
\(570\) −52.4558 + 30.2854i −2.19713 + 1.26852i
\(571\) −6.48528 11.2328i −0.271401 0.470080i 0.697820 0.716273i \(-0.254153\pi\)
−0.969221 + 0.246193i \(0.920820\pi\)
\(572\) −1.73205 + 3.00000i −0.0724207 + 0.125436i
\(573\) 31.1769 1.30243
\(574\) −1.86396 13.6208i −0.0778002 0.568520i
\(575\) 15.5147i 0.647008i
\(576\) −1.50000 + 2.59808i −0.0625000 + 0.108253i
\(577\) 17.7426 10.2437i 0.738636 0.426452i −0.0829373 0.996555i \(-0.526430\pi\)
0.821573 + 0.570103i \(0.193097\pi\)
\(578\) 6.03668 3.48528i 0.251093 0.144969i
\(579\) −24.7279 14.2767i −1.02766 0.593318i
\(580\) 35.4815i 1.47329i
\(581\) −5.13461 6.62132i −0.213019 0.274699i
\(582\) 0.514719i 0.0213358i
\(583\) −4.24264 + 7.34847i −0.175712 + 0.304342i
\(584\) −4.18154 7.24264i −0.173033 0.299703i
\(585\) −37.6339 + 21.7279i −1.55597 + 0.898339i
\(586\) −10.7574 6.21076i −0.444382 0.256564i
\(587\) 12.4215 0.512691 0.256346 0.966585i \(-0.417481\pi\)
0.256346 + 0.966585i \(0.417481\pi\)
\(588\) 8.48528 8.66025i 0.349927 0.357143i
\(589\) −12.0000 −0.494451
\(590\) −22.9369 13.2426i −0.944298 0.545191i
\(591\) 7.34847 + 12.7279i 0.302276 + 0.523557i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) −12.4215 + 21.5147i −0.510091 + 0.883504i 0.489841 + 0.871812i \(0.337055\pi\)
−0.999932 + 0.0116916i \(0.996278\pi\)
\(594\) 5.19615i 0.213201i
\(595\) −21.4706 27.6873i −0.880207 1.13507i
\(596\) 0 0
\(597\) −11.4853 + 19.8931i −0.470061 + 0.814170i
\(598\) −3.72792 + 2.15232i −0.152446 + 0.0880148i
\(599\) 24.0131 13.8640i 0.981148 0.566466i 0.0785315 0.996912i \(-0.474977\pi\)
0.902617 + 0.430446i \(0.141644\pi\)
\(600\) −10.8126 + 18.7279i −0.441421 + 0.764564i
\(601\) 9.79796i 0.399667i 0.979830 + 0.199834i \(0.0640401\pi\)
−0.979830 + 0.199834i \(0.935960\pi\)
\(602\) 1.60896 + 11.7574i 0.0655762 + 0.479194i
\(603\) 10.4558 0.425795
\(604\) −0.378680 + 0.655892i −0.0154083 + 0.0266879i
\(605\) 2.09077 + 3.62132i 0.0850019 + 0.147228i
\(606\) 1.75736 + 3.04384i 0.0713878 + 0.123647i
\(607\) 7.13604 + 4.11999i 0.289643 + 0.167225i 0.637781 0.770218i \(-0.279853\pi\)
−0.348138 + 0.937443i \(0.613186\pi\)
\(608\) 8.36308 0.339168
\(609\) −14.6969 + 36.0000i −0.595550 + 1.45879i
\(610\) −3.00000 −0.121466
\(611\) −12.5446 7.24264i −0.507501 0.293006i
\(612\) −4.75039 8.22792i −0.192023 0.332594i
\(613\) −4.10660 7.11284i −0.165864 0.287285i 0.771098 0.636717i \(-0.219708\pi\)
−0.936962 + 0.349432i \(0.886375\pi\)
\(614\) 11.8272 20.4853i 0.477306 0.826719i
\(615\) 37.6339i 1.51754i
\(616\) 1.00000 2.44949i 0.0402911 0.0986928i
\(617\) 8.48528i 0.341605i −0.985305 0.170802i \(-0.945364\pi\)
0.985305 0.170802i \(-0.0546359\pi\)
\(618\) −17.7408 10.2426i −0.713639 0.412019i
\(619\) 3.77208 2.17781i 0.151613 0.0875336i −0.422274 0.906468i \(-0.638768\pi\)
0.573887 + 0.818934i \(0.305435\pi\)
\(620\) −5.19615 + 3.00000i −0.208683 + 0.120483i
\(621\) −3.22848 + 5.59188i −0.129554 + 0.224395i
\(622\) 25.2123i 1.01092i
\(623\) −5.31925 + 0.727922i −0.213111 + 0.0291636i
\(624\) 6.00000 0.240192
\(625\) −34.2279 + 59.2845i −1.36912 + 2.37138i
\(626\) 0 0
\(627\) 12.5446 7.24264i 0.500984 0.289243i
\(628\) −16.2426 9.37769i −0.648152 0.374211i
\(629\) 12.6677 0.505095
\(630\) 26.2279 20.3389i 1.04495 0.810319i
\(631\) −26.9706 −1.07368 −0.536841 0.843684i \(-0.680382\pi\)
−0.536841 + 0.843684i \(0.680382\pi\)
\(632\) 4.54026 + 2.62132i 0.180602 + 0.104271i
\(633\) −18.7279 + 10.8126i −0.744368 + 0.429761i
\(634\) 12.6213 + 21.8608i 0.501257 + 0.868202i
\(635\) −31.8689 + 55.1985i −1.26468 + 2.19049i
\(636\) 14.6969 0.582772
\(637\) −23.4853 6.03668i −0.930521 0.239182i
\(638\) 8.48528i 0.335936i
\(639\) 15.5885 + 9.00000i 0.616670 + 0.356034i
\(640\) 3.62132 2.09077i 0.143145 0.0826450i
\(641\) 4.30463 2.48528i 0.170023 0.0981627i −0.412574 0.910924i \(-0.635370\pi\)
0.582597 + 0.812761i \(0.302037\pi\)
\(642\) 22.5000 + 12.9904i 0.888004 + 0.512689i
\(643\) 4.65279i 0.183488i 0.995783 + 0.0917441i \(0.0292442\pi\)
−0.995783 + 0.0917441i \(0.970756\pi\)
\(644\) 2.59808 2.01472i 0.102379 0.0793910i
\(645\) 32.4853i 1.27911i
\(646\) −13.2426 + 22.9369i −0.521025 + 0.902441i
\(647\) 7.28692 + 12.6213i 0.286478 + 0.496195i 0.972967 0.230946i \(-0.0741820\pi\)
−0.686488 + 0.727141i \(0.740849\pi\)
\(648\) 7.79423 4.50000i 0.306186 0.176777i
\(649\) 5.48528 + 3.16693i 0.215316 + 0.124313i
\(650\) 43.2503 1.69642
\(651\) 6.51472 0.891519i 0.255332 0.0349414i
\(652\) 13.0000 0.509119
\(653\) −36.5577 21.1066i −1.43061 0.825965i −0.433446 0.901179i \(-0.642703\pi\)
−0.997167 + 0.0752143i \(0.976036\pi\)
\(654\) 2.38794 + 4.13604i 0.0933760 + 0.161732i
\(655\) 13.2426 + 22.9369i 0.517433 + 0.896220i
\(656\) −2.59808 + 4.50000i −0.101438 + 0.175695i
\(657\) 25.0892i 0.978825i
\(658\) 10.2426 + 4.18154i 0.399300 + 0.163013i
\(659\) 7.97056i 0.310489i 0.987876 + 0.155245i \(0.0496165\pi\)
−0.987876 + 0.155245i \(0.950383\pi\)
\(660\) 3.62132 6.27231i 0.140960 0.244149i
\(661\) −23.4853 + 13.5592i −0.913472 + 0.527393i −0.881546 0.472097i \(-0.843497\pi\)
−0.0319251 + 0.999490i \(0.510164\pi\)
\(662\) −16.4545 + 9.50000i −0.639522 + 0.369228i
\(663\) −9.50079 + 16.4558i −0.368980 + 0.639092i
\(664\) 3.16693i 0.122901i
\(665\) −85.6600 34.9706i −3.32175 1.35610i
\(666\) 12.0000i 0.464991i
\(667\) −5.27208 + 9.13151i −0.204136 + 0.353573i
\(668\) −1.01461 1.75736i −0.0392565 0.0679943i
\(669\) −5.48528 9.50079i −0.212073 0.367322i
\(670\) −12.6213 7.28692i −0.487604 0.281518i
\(671\) 0.717439 0.0276964
\(672\) −4.54026 + 0.621320i −0.175144 + 0.0239680i
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) 26.4010 + 15.2426i 1.01693 + 0.587125i
\(675\) 56.1838 32.4377i 2.16251 1.24853i
\(676\) 0.500000 + 0.866025i 0.0192308 + 0.0333087i
\(677\) 8.48617 14.6985i 0.326150 0.564909i −0.655594 0.755113i \(-0.727582\pi\)
0.981744 + 0.190205i \(0.0609152\pi\)
\(678\) 31.1769i 1.19734i
\(679\) −0.621320 + 0.481813i −0.0238441 + 0.0184903i
\(680\) 13.2426i 0.507832i
\(681\) −32.8835 18.9853i −1.26010 0.727518i
\(682\) 1.24264 0.717439i 0.0475832 0.0274722i
\(683\) −20.7846 + 12.0000i −0.795301 + 0.459167i −0.841825 0.539750i \(-0.818519\pi\)
0.0465244 + 0.998917i \(0.485185\pi\)
\(684\) −21.7279 12.5446i −0.830788 0.479656i
\(685\) 60.5708i 2.31429i
\(686\) 18.3967 + 2.13604i 0.702388 + 0.0815543i
\(687\) −12.0000 −0.457829
\(688\) 2.24264 3.88437i 0.0854999 0.148090i
\(689\) −14.6969 25.4558i −0.559909 0.969790i
\(690\) 7.79423 4.50000i 0.296721 0.171312i
\(691\) 0.257359 + 0.148586i 0.00979041 + 0.00565250i 0.504887 0.863185i \(-0.331534\pi\)
−0.495097 + 0.868838i \(0.664867\pi\)
\(692\) 8.36308 0.317917
\(693\) −6.27231 + 4.86396i −0.238265 + 0.184767i
\(694\) −0.514719 −0.0195385
\(695\) 12.5446 + 7.24264i 0.475845 + 0.274729i
\(696\) 12.7279 7.34847i 0.482451 0.278543i
\(697\) −8.22792 14.2512i −0.311655 0.539802i
\(698\) 7.70719 13.3492i 0.291721 0.505276i
\(699\) −44.9823 −1.70139
\(700\) −32.7279 + 4.47871i −1.23700 + 0.169279i
\(701\) 14.4853i 0.547102i 0.961858 + 0.273551i \(0.0881982\pi\)
−0.961858 + 0.273551i \(0.911802\pi\)
\(702\) −15.5885 9.00000i −0.588348 0.339683i
\(703\) 28.9706 16.7262i 1.09265 0.630839i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 26.2279 + 15.1427i 0.987801 + 0.570307i
\(706\) 25.0892i 0.944246i
\(707\) −2.02922 + 4.97056i −0.0763168 + 0.186937i
\(708\) 10.9706i 0.412299i
\(709\) 11.2426 19.4728i 0.422226 0.731317i −0.573931 0.818904i \(-0.694582\pi\)
0.996157 + 0.0875866i \(0.0279155\pi\)
\(710\) −12.5446 21.7279i −0.470791 0.815434i
\(711\) −7.86396 13.6208i −0.294922 0.510819i
\(712\) 1.75736 + 1.01461i 0.0658598 + 0.0380242i
\(713\) 1.78304 0.0667753
\(714\) 5.48528 13.4361i 0.205281 0.502835i
\(715\) −14.4853 −0.541719
\(716\) −12.5446 7.24264i −0.468815 0.270670i
\(717\) 0 0
\(718\) 4.24264 + 7.34847i 0.158334 + 0.274242i
\(719\) −9.31615 + 16.1360i −0.347434 + 0.601773i −0.985793 0.167966i \(-0.946280\pi\)
0.638359 + 0.769739i \(0.279613\pi\)
\(720\) −12.5446 −0.467510
\(721\) −4.24264 31.0028i −0.158004 1.15461i
\(722\) 50.9411i 1.89583i
\(723\) −12.0000 + 20.7846i −0.446285 + 0.772988i
\(724\) 14.4853 8.36308i 0.538341 0.310811i
\(725\) 91.7477 52.9706i 3.40742 1.96728i
\(726\) −0.866025 + 1.50000i −0.0321412 + 0.0556702i
\(727\) 7.76874i 0.288126i −0.989568 0.144063i \(-0.953983\pi\)
0.989568 0.144063i \(-0.0460169\pi\)
\(728\) 5.61642 + 7.24264i 0.208158 + 0.268430i
\(729\) −27.0000 −1.00000
\(730\) 17.4853 30.2854i 0.647159 1.12091i
\(731\) 7.10228 + 12.3015i 0.262687 + 0.454988i
\(732\) −0.621320 1.07616i −0.0229647 0.0397760i
\(733\) 4.86396 + 2.80821i 0.179654 + 0.103724i 0.587130 0.809492i \(-0.300258\pi\)
−0.407476 + 0.913216i \(0.633591\pi\)
\(734\) −25.0892 −0.926061
\(735\) 49.1023 + 12.6213i 1.81117 + 0.465544i
\(736\) −1.24264 −0.0458043
\(737\) 3.01834 + 1.74264i 0.111182 + 0.0641910i
\(738\) 13.5000 7.79423i 0.496942 0.286910i
\(739\) −7.00000 12.1244i −0.257499 0.446002i 0.708072 0.706140i \(-0.249565\pi\)
−0.965571 + 0.260138i \(0.916232\pi\)
\(740\) 8.36308 14.4853i 0.307433 0.532490i
\(741\) 50.1785i 1.84335i
\(742\) 13.7574 + 17.7408i 0.505049 + 0.651284i
\(743\) 12.0000i 0.440237i 0.975473 + 0.220119i \(0.0706445\pi\)
−0.975473 + 0.220119i \(0.929356\pi\)
\(744\) −2.15232 1.24264i −0.0789078 0.0455574i
\(745\) 0 0
\(746\) −15.3528 + 8.86396i −0.562107 + 0.324533i
\(747\) 4.75039 8.22792i 0.173808 0.301044i
\(748\) 3.16693i 0.115794i
\(749\) 5.38079 + 39.3198i 0.196610 + 1.43671i
\(750\) −54.2132 −1.97959
\(751\) −23.7279 + 41.0980i −0.865844 + 1.49969i 0.000362347 1.00000i \(0.499885\pi\)
−0.866207 + 0.499686i \(0.833449\pi\)
\(752\) −2.09077 3.62132i −0.0762425 0.132056i
\(753\) 22.0454 12.7279i 0.803379 0.463831i
\(754\) −25.4558 14.6969i −0.927047 0.535231i
\(755\) −3.16693 −0.115256
\(756\) 12.7279 + 5.19615i 0.462910 + 0.188982i
\(757\) −47.9411 −1.74245 −0.871225 0.490884i \(-0.836674\pi\)
−0.871225 + 0.490884i \(0.836674\pi\)
\(758\) −0.0254934 0.0147186i −0.000925962 0.000534605i
\(759\) −1.86396 + 1.07616i −0.0676575 + 0.0390621i
\(760\) 17.4853 + 30.2854i 0.634258 + 1.09857i
\(761\) −11.9758 + 20.7426i −0.434121 + 0.751920i −0.997223 0.0744671i \(-0.976274\pi\)
0.563102 + 0.826387i \(0.309608\pi\)
\(762\) −26.4010 −0.956408
\(763\) −2.75736 + 6.75412i −0.0998231 + 0.244516i
\(764\) 18.0000i 0.651217i
\(765\) 19.8640 34.4054i 0.718183 1.24393i
\(766\) −27.2132 + 15.7116i −0.983253 + 0.567681i
\(767\) −19.0016 + 10.9706i −0.686107 + 0.396124i
\(768\) 1.50000 + 0.866025i 0.0541266 + 0.0312500i
\(769\) 21.0308i 0.758390i 0.925317 + 0.379195i \(0.123799\pi\)
−0.925317 + 0.379195i \(0.876201\pi\)
\(770\) 10.9612 1.50000i 0.395013 0.0540562i
\(771\) 3.51472i 0.126579i
\(772\) −8.24264 + 14.2767i −0.296659 + 0.513829i
\(773\) 11.5916 + 20.0772i 0.416919 + 0.722125i 0.995628 0.0934090i \(-0.0297764\pi\)
−0.578709 + 0.815534i \(0.696443\pi\)
\(774\) −11.6531 + 6.72792i −0.418862 + 0.241830i
\(775\) −15.5147 8.95743i −0.557305 0.321760i
\(776\) 0.297173 0.0106679
\(777\) −14.4853 + 11.2328i −0.519657 + 0.402976i
\(778\) 27.7279 0.994094
\(779\) −37.6339 21.7279i −1.34837 0.778484i
\(780\) 12.5446 + 21.7279i 0.449170 + 0.777984i
\(781\) 3.00000 + 5.19615i 0.107348 + 0.185933i
\(782\) 1.96768 3.40812i 0.0703640 0.121874i
\(783\) −44.0908 −1.57568
\(784\) −5.00000 4.89898i −0.178571 0.174964i
\(785\) 78.4264i 2.79916i
\(786\) −5.48528 + 9.50079i −0.195654 + 0.338882i
\(787\) −15.7279 + 9.08052i −0.560640 + 0.323686i −0.753402 0.657560i \(-0.771589\pi\)
0.192762 + 0.981245i \(0.438255\pi\)
\(788\) 7.34847 4.24264i 0.261778 0.151138i
\(789\) 9.50079 16.4558i 0.338237 0.585844i
\(790\) 21.9223i 0.779961i
\(791\) 37.6339 29.1838i 1.33811 1.03766i
\(792\) 3.00000 0.106600
\(793\) −1.24264 + 2.15232i −0.0441275 + 0.0764310i
\(794\) 12.2474 + 21.2132i 0.434646 + 0.752828i
\(795\) 30.7279 + 53.2223i 1.08981 + 1.88760i
\(796\) 11.4853 + 6.63103i 0.407085 + 0.235031i
\(797\) −1.90613 −0.0675186 −0.0337593 0.999430i \(-0.510748\pi\)
−0.0337593 + 0.999430i \(0.510748\pi\)
\(798\) −5.19615 37.9706i −0.183942 1.34414i
\(799\) 13.2426 0.468491
\(800\) 10.8126 + 6.24264i 0.382282 + 0.220711i
\(801\) −3.04384 5.27208i −0.107549 0.186280i
\(802\) −4.24264 7.34847i −0.149813 0.259483i
\(803\) −4.18154 + 7.24264i −0.147563 + 0.255587i
\(804\) 6.03668i 0.212897i
\(805\) 12.7279 + 5.19615i 0.448600 + 0.183140i
\(806\) 4.97056i 0.175081i
\(807\) −34.4054 19.8640i −1.21113 0.699245i
\(808\) 1.75736 1.01461i 0.0618237 0.0356939i
\(809\) −2.59808 + 1.50000i −0.0913435 + 0.0527372i −0.544976 0.838452i \(-0.683461\pi\)
0.453632 + 0.891189i \(0.350128\pi\)
\(810\) 32.5919 + 18.8169i 1.14516 + 0.661160i
\(811\) 2.27541i 0.0799004i 0.999202 + 0.0399502i \(0.0127199\pi\)
−0.999202 + 0.0399502i \(0.987280\pi\)
\(812\) 20.7846 + 8.48528i 0.729397 + 0.297775i
\(813\) −13.4558 −0.471917
\(814\) −2.00000 + 3.46410i −0.0701000 + 0.121417i
\(815\) 27.1800 + 47.0772i 0.952074 + 1.64904i
\(816\) −4.75039 + 2.74264i −0.166297 + 0.0960116i
\(817\) 32.4853 + 18.7554i 1.13652 + 0.656168i
\(818\) 15.2913 0.534647
\(819\) −3.72792 27.2416i −0.130264 0.951897i
\(820\) −21.7279 −0.758772
\(821\) 2.15232 + 1.24264i 0.0751164 + 0.0433685i 0.537088 0.843526i \(-0.319524\pi\)
−0.461971 + 0.886895i \(0.652858\pi\)
\(822\) 21.7279 12.5446i 0.757848 0.437544i
\(823\) 6.75736 + 11.7041i 0.235547 + 0.407979i 0.959431 0.281942i \(-0.0909786\pi\)
−0.723885 + 0.689921i \(0.757645\pi\)
\(824\) −5.91359 + 10.2426i −0.206010 + 0.356819i
\(825\) 21.6251 0.752891
\(826\) 13.2426 10.2692i 0.460770 0.357312i
\(827\) 17.4853i 0.608023i 0.952668 + 0.304011i \(0.0983261\pi\)
−0.952668 + 0.304011i \(0.901674\pi\)
\(828\) 3.22848 + 1.86396i 0.112197 + 0.0647771i
\(829\) −28.9706 + 16.7262i −1.00619 + 0.580924i −0.910074 0.414447i \(-0.863975\pi\)
−0.0961156 + 0.995370i \(0.530642\pi\)
\(830\) −11.4685 + 6.62132i −0.398076 + 0.229829i
\(831\) 42.7279 + 24.6690i 1.48222 + 0.855757i
\(832\) 3.46410i 0.120096i
\(833\) 21.3535 5.95584i 0.739854 0.206358i
\(834\) 6.00000i 0.207763i
\(835\) 4.24264 7.34847i 0.146823 0.254304i
\(836\) −4.18154 7.24264i −0.144622 0.250492i
\(837\) 3.72792 + 6.45695i 0.128856 + 0.223185i
\(838\) −7.24264 4.18154i −0.250193 0.144449i
\(839\) 14.8200 0.511644 0.255822 0.966724i \(-0.417654\pi\)
0.255822 + 0.966724i \(0.417654\pi\)
\(840\) −11.7426 15.1427i −0.405160 0.522473i
\(841\) −43.0000 −1.48276
\(842\) 14.2767 + 8.24264i 0.492007 + 0.284060i
\(843\) −15.1427 26.2279i −0.521542 0.903338i
\(844\) 6.24264 + 10.8126i 0.214881 + 0.372184i
\(845\) −2.09077 + 3.62132i −0.0719247 + 0.124577i
\(846\) 12.5446i 0.431293i
\(847\) −2.62132 + 0.358719i −0.0900696 + 0.0123257i
\(848\) 8.48528i 0.291386i
\(849\) 21.2132 36.7423i 0.728035 1.26099i
\(850\) −34.2426 + 19.7700i −1.17451 + 0.678105i
\(851\) −4.30463 + 2.48528i −0.147561 + 0.0851943i
\(852\) 5.19615 9.00000i 0.178017 0.308335i
\(853\) 10.5154i 0.360040i 0.983663 + 0.180020i \(0.0576163\pi\)
−0.983663 + 0.180020i \(0.942384\pi\)
\(854\) 0.717439 1.75736i 0.0245503 0.0601356i
\(855\) 104.912i 3.58790i
\(856\) 7.50000 12.9904i 0.256345 0.444002i
\(857\) −21.3535 36.9853i −0.729420 1.26339i −0.957128 0.289664i \(-0.906457\pi\)
0.227708 0.973729i \(-0.426877\pi\)
\(858\) −3.00000 5.19615i −0.102418 0.177394i
\(859\) −41.4411 23.9260i −1.41395 0.816346i −0.418195 0.908357i \(-0.637337\pi\)
−0.995758 + 0.0920112i \(0.970670\pi\)
\(860\) 18.7554 0.639553
\(861\) 22.0454 + 9.00000i 0.751305 + 0.306719i
\(862\) −9.51472 −0.324073
\(863\) −23.1216 13.3492i −0.787067 0.454413i 0.0518618 0.998654i \(-0.483484\pi\)
−0.838929 + 0.544241i \(0.816818\pi\)
\(864\) −2.59808 4.50000i −0.0883883 0.153093i
\(865\) 17.4853 + 30.2854i 0.594517 + 1.02973i
\(866\) −14.4253 + 24.9853i −0.490190 + 0.849034i
\(867\) 12.0734i 0.410033i
\(868\) −0.514719 3.76127i −0.0174707 0.127666i
\(869\) 5.24264i 0.177844i
\(870\) 53.2223 + 30.7279i 1.80441 + 1.04177i
\(871\) −10.4558 + 6.03668i −0.354283 + 0.204545i
\(872\) 2.38794 1.37868i 0.0808660 0.0466880i
\(873\) −0.772078 0.445759i −0.0261309 0.0150867i
\(874\) 10.3923i 0.351525i
\(875\) −50.7473 65.4411i −1.71557 2.21231i
\(876\) 14.4853 0.489412
\(877\) 3.34924 5.80106i 0.113096 0.195888i −0.803921 0.594736i \(-0.797257\pi\)
0.917017 + 0.398848i \(0.130590\pi\)
\(878\) 9.43924 + 16.3492i 0.318559 + 0.551760i
\(879\) 18.6323 10.7574i 0.628452 0.362837i
\(880\) −3.62132 2.09077i −0.122075 0.0704799i
\(881\) 19.0016 0.640179 0.320090 0.947387i \(-0.396287\pi\)
0.320090 + 0.947387i \(0.396287\pi\)
\(882\) 5.64191 + 20.2279i 0.189973 + 0.681110i
\(883\) 32.4558 1.09223 0.546113 0.837711i \(-0.316107\pi\)
0.546113 + 0.837711i \(0.316107\pi\)
\(884\) 9.50079 + 5.48528i 0.319546 + 0.184490i
\(885\) 39.7279 22.9369i 1.33544 0.771016i
\(886\) 18.0000 + 31.1769i 0.604722 + 1.04741i
\(887\) −21.9223 + 37.9706i −0.736079 + 1.27493i 0.218169 + 0.975911i \(0.429992\pi\)
−0.954248 + 0.299016i \(0.903342\pi\)
\(888\) 6.92820 0.232495
\(889\) −24.7132 31.8689i −0.828854 1.06885i
\(890\) 8.48528i 0.284427i
\(891\) −7.79423 4.50000i −0.261116 0.150756i
\(892\) −5.48528 + 3.16693i −0.183661 + 0.106037i
\(893\) 30.2854 17.4853i 1.01346 0.585123i
\(894\) 0 0
\(895\) 60.5708i 2.02466i
\(896\) 0.358719 + 2.62132i 0.0119840 + 0.0875722i
\(897\) 7.45584i 0.248943i
\(898\) −1.75736 + 3.04384i −0.0586438 + 0.101574i
\(899\) 6.08767 + 10.5442i 0.203035 + 0.351667i
\(900\) −18.7279 32.4377i −0.624264 1.08126i
\(901\) 23.2721 + 13.4361i 0.775305 + 0.447623i
\(902\) 5.19615 0.173013
\(903\) −19.0294 7.76874i −0.633260 0.258527i
\(904\) −18.0000 −0.598671
\(905\) 60.5708 + 34.9706i 2.01344 + 1.16246i
\(906\) −0.655892 1.13604i −0.0217906 0.0377424i
\(907\) −25.2279 43.6960i −0.837679 1.45090i −0.891830 0.452371i \(-0.850578\pi\)
0.0541507 0.998533i \(-0.482755\pi\)
\(908\) −10.9612 + 18.9853i −0.363759 + 0.630049i
\(909\) −6.08767 −0.201915
\(910\) −14.4853 + 35.4815i −0.480182 + 1.17620i
\(911\) 2.27208i 0.0752773i −0.999291 0.0376387i \(-0.988016\pi\)
0.999291 0.0376387i \(-0.0119836\pi\)
\(912\) −7.24264 + 12.5446i −0.239828 + 0.415394i
\(913\) 2.74264 1.58346i 0.0907682 0.0524050i
\(914\) −18.1610 + 10.4853i −0.600714 + 0.346822i
\(915\) 2.59808 4.50000i 0.0858898 0.148765i
\(916\) 6.92820i 0.228914i
\(917\) −16.6031 + 2.27208i −0.548282 + 0.0750306i
\(918\) 16.4558 0.543124
\(919\) −12.8640 + 22.2810i −0.424343 + 0.734983i −0.996359 0.0852590i \(-0.972828\pi\)
0.572016 + 0.820243i \(0.306162\pi\)
\(920\) −2.59808 4.50000i −0.0856560 0.148361i
\(921\) 20.4853 + 35.4815i 0.675013 + 1.16916i
\(922\) 5.48528 + 3.16693i 0.180648 + 0.104297i
\(923\) −20.7846 −0.684134
\(924\) 2.80821 + 3.62132i 0.0923833 + 0.119133i
\(925\) 49.9411 1.64205
\(926\) −25.5095 14.7279i −0.838294 0.483990i
\(927\) 30.7279 17.7408i 1.00924 0.582683i
\(928\) −4.24264 7.34847i −0.139272 0.241225i
\(929\) −4.18154 + 7.24264i −0.137192 + 0.237623i −0.926433 0.376461i \(-0.877141\pi\)
0.789241 + 0.614084i \(0.210474\pi\)
\(930\) 10.3923i 0.340777i
\(931\) 40.9706 41.8154i 1.34276 1.37044i
\(932\) 25.9706i 0.850694i
\(933\) 37.8185 + 21.8345i 1.23812 + 0.714830i
\(934\) 27.0000 15.5885i 0.883467 0.510070i
\(935\) 11.4685 6.62132i 0.375059 0.216540i
\(936\) −5.19615 + 9.00000i −0.169842 + 0.294174i
\(937\) 45.5257i 1.48726i −0.668592 0.743630i \(-0.733103\pi\)
0.668592 0.743630i \(-0.266897\pi\)
\(938\) 7.28692 5.65076i 0.237926 0.184504i
\(939\) 0 0
\(940\) 8.74264 15.1427i 0.285153 0.493900i
\(941\) 5.19615 + 9.00000i 0.169390 + 0.293392i 0.938205 0.346079i \(-0.112487\pi\)
−0.768816 + 0.639470i \(0.779154\pi\)
\(942\) 28.1331 16.2426i 0.916625 0.529214i
\(943\) 5.59188 + 3.22848i 0.182097 + 0.105134i
\(944\) −6.33386 −0.206149
\(945\) 7.79423 + 56.9558i 0.253546 + 1.85277i
\(946\) −4.48528 −0.145829
\(947\) 30.2854 + 17.4853i 0.984143 + 0.568195i 0.903518 0.428549i \(-0.140975\pi\)
0.0806247 + 0.996745i \(0.474308\pi\)
\(948\) −7.86396 + 4.54026i −0.255410 + 0.147461i
\(949\) −14.4853 25.0892i −0.470212 0.814431i
\(950\) −52.2077 + 90.4264i −1.69384 + 2.93382i
\(951\) −43.7215 −1.41777
\(952\) −7.75736 3.16693i −0.251417 0.102641i
\(953\) 25.9706i 0.841269i −0.907230 0.420635i \(-0.861807\pi\)
0.907230 0.420635i \(-0.138193\pi\)
\(954\) −12.7279 + 22.0454i −0.412082 + 0.713746i
\(955\) 65.1838 37.6339i 2.10930 1.21780i
\(956\) 0 0
\(957\) −12.7279 7.34847i −0.411435 0.237542i
\(958\) 31.4231i 1.01523i
\(959\) 35.4815 + 14.4853i 1.14576 + 0.467754i
\(960\) 7.24264i 0.233755i
\(961\) −14.4706 + 25.0637i −0.466792 + 0.808508i
\(962\) −6.92820 12.0000i −0.223374 0.386896i
\(963\) −38.9711 + 22.5000i −1.25583 + 0.725052i
\(964\) 12.0000 + 6.92820i 0.386494 + 0.223142i
\(965\) −68.9339 −2.21906
\(966\) 0.772078 + 5.64191i 0.0248412 + 0.181526i
\(967\) 2.21320 0.0711718 0.0355859 0.999367i \(-0.488670\pi\)
0.0355859 + 0.999367i \(0.488670\pi\)
\(968\) 0.866025 + 0.500000i 0.0278351 + 0.0160706i
\(969\) −22.9369 39.7279i −0.736840 1.27624i
\(970\) 0.621320 + 1.07616i 0.0199494 + 0.0345534i
\(971\) 21.9223 37.9706i 0.703521 1.21853i −0.263702 0.964604i \(-0.584944\pi\)
0.967223 0.253929i \(-0.0817230\pi\)
\(972\) 15.5885i 0.500000i
\(973\) −7.24264 + 5.61642i −0.232188 + 0.180054i
\(974\) 14.9706i 0.479688i
\(975\) −37.4558 + 64.8754i −1.19955 + 2.07768i
\(976\) −0.621320 + 0.358719i −0.0198880 + 0.0114823i
\(977\) −0.891519 + 0.514719i −0.0285222 + 0.0164673i −0.514193 0.857674i \(-0.671909\pi\)
0.485671 + 0.874142i \(0.338575\pi\)
\(978\) −11.2583 + 19.5000i −0.360002 + 0.623541i
\(979\) 2.02922i 0.0648543i
\(980\) 7.28692 28.3492i 0.232772 0.905583i
\(981\) −8.27208 −0.264107
\(982\) 9.98528 17.2950i 0.318643 0.551906i
\(983\) −15.7731 27.3198i −0.503084 0.871366i −0.999994 0.00356437i \(-0.998865\pi\)
0.496910 0.867802i \(-0.334468\pi\)
\(984\) −4.50000 7.79423i −0.143455 0.248471i
\(985\) 30.7279 + 17.7408i 0.979073 + 0.565268i
\(986\) 26.8723 0.855788
\(987\) −15.1427 + 11.7426i −0.481997 + 0.373772i
\(988\) 28.9706 0.921676
\(989\) −4.82687 2.78680i −0.153486 0.0886150i
\(990\) 6.27231 + 10.8640i 0.199347 + 0.345279i
\(991\) 4.00000 + 6.92820i 0.127064 + 0.220082i 0.922538 0.385906i \(-0.126111\pi\)
−0.795474 + 0.605988i \(0.792778\pi\)
\(992\) −0.717439 + 1.24264i −0.0227787 + 0.0394539i
\(993\) 32.9090i 1.04433i
\(994\) 15.7279 2.15232i 0.498859 0.0682673i
\(995\) 55.4558i 1.75807i
\(996\) −4.75039 2.74264i −0.150522 0.0869039i
\(997\) 0.514719 0.297173i 0.0163013 0.00941156i −0.491827 0.870693i \(-0.663671\pi\)
0.508129 + 0.861281i \(0.330337\pi\)
\(998\) 11.2328 6.48528i 0.355569 0.205288i
\(999\) −18.0000 10.3923i −0.569495 0.328798i
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 462.2.k.d.89.3 yes 8
3.2 odd 2 inner 462.2.k.d.89.2 8
7.3 odd 6 inner 462.2.k.d.353.2 yes 8
21.17 even 6 inner 462.2.k.d.353.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.k.d.89.2 8 3.2 odd 2 inner
462.2.k.d.89.3 yes 8 1.1 even 1 trivial
462.2.k.d.353.2 yes 8 7.3 odd 6 inner
462.2.k.d.353.3 yes 8 21.17 even 6 inner