Properties

Label 722.2.c.j.429.2
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [722,2,Mod(429,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.429");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.2
Root \(-1.32288 + 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.j.653.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.822876 - 1.42526i) q^{5} +(-1.32288 - 2.29129i) q^{6} +3.64575 q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.822876 - 1.42526i) q^{5} +(-1.32288 - 2.29129i) q^{6} +3.64575 q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(-0.822876 - 1.42526i) q^{10} -4.64575 q^{11} -2.64575 q^{12} +(1.00000 + 1.73205i) q^{13} +(1.82288 - 3.15731i) q^{14} +(-2.17712 - 3.77089i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.00000 q^{18} -1.64575 q^{20} +(4.82288 - 8.35347i) q^{21} +(-2.32288 + 4.02334i) q^{22} +(0.822876 + 1.42526i) q^{23} +(-1.32288 + 2.29129i) q^{24} +(1.14575 + 1.98450i) q^{25} +2.00000 q^{26} -2.64575 q^{27} +(-1.82288 - 3.15731i) q^{28} +(0.822876 + 1.42526i) q^{29} -4.35425 q^{30} +5.64575 q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.14575 + 10.6448i) q^{33} +(3.00000 - 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{36} -0.354249 q^{37} +5.29150 q^{39} +(-0.822876 + 1.42526i) q^{40} +(-0.145751 + 0.252449i) q^{41} +(-4.82288 - 8.35347i) q^{42} +(-5.64575 + 9.77873i) q^{43} +(2.32288 + 4.02334i) q^{44} -6.58301 q^{45} +1.64575 q^{46} +(-2.17712 - 3.77089i) q^{47} +(1.32288 + 2.29129i) q^{48} +6.29150 q^{49} +2.29150 q^{50} +(1.00000 - 1.73205i) q^{52} +(-6.29150 - 10.8972i) q^{53} +(-1.32288 + 2.29129i) q^{54} +(-3.82288 + 6.62141i) q^{55} -3.64575 q^{56} +1.64575 q^{58} +(-3.96863 + 6.87386i) q^{59} +(-2.17712 + 3.77089i) q^{60} +(-0.468627 - 0.811686i) q^{61} +(2.82288 - 4.88936i) q^{62} +(-7.29150 - 12.6293i) q^{63} +1.00000 q^{64} +3.29150 q^{65} +(6.14575 + 10.6448i) q^{66} +(0.322876 + 0.559237i) q^{67} +4.35425 q^{69} +(-3.00000 - 5.19615i) q^{70} +(-1.35425 + 2.34563i) q^{71} +(2.00000 + 3.46410i) q^{72} +(-0.854249 + 1.47960i) q^{73} +(-0.177124 + 0.306788i) q^{74} +6.06275 q^{75} -16.9373 q^{77} +(2.64575 - 4.58258i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(0.822876 + 1.42526i) q^{80} +(2.50000 - 4.33013i) q^{81} +(0.145751 + 0.252449i) q^{82} +7.93725 q^{83} -9.64575 q^{84} +(5.64575 + 9.77873i) q^{86} +4.35425 q^{87} +4.64575 q^{88} +(-3.29150 + 5.70105i) q^{90} +(3.64575 + 6.31463i) q^{91} +(0.822876 - 1.42526i) q^{92} +(7.46863 - 12.9360i) q^{93} -4.35425 q^{94} +2.64575 q^{96} +(-1.85425 + 3.21165i) q^{97} +(3.14575 - 5.44860i) q^{98} +(9.29150 + 16.0934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} + 2 q^{10} - 8 q^{11} + 4 q^{13} + 2 q^{14} - 14 q^{15} - 2 q^{16} - 16 q^{18} + 4 q^{20} + 14 q^{21} - 4 q^{22} - 2 q^{23} - 6 q^{25} + 8 q^{26} - 2 q^{28} - 2 q^{29} - 28 q^{30} + 12 q^{31} + 2 q^{32} - 14 q^{33} + 12 q^{35} - 8 q^{36} - 12 q^{37} + 2 q^{40} + 10 q^{41} - 14 q^{42} - 12 q^{43} + 4 q^{44} + 16 q^{45} - 4 q^{46} - 14 q^{47} + 4 q^{49} - 12 q^{50} + 4 q^{52} - 4 q^{53} - 10 q^{55} - 4 q^{56} - 4 q^{58} - 14 q^{60} + 14 q^{61} + 6 q^{62} - 8 q^{63} + 4 q^{64} - 8 q^{65} + 14 q^{66} - 4 q^{67} + 28 q^{69} - 12 q^{70} - 16 q^{71} + 8 q^{72} - 14 q^{73} - 6 q^{74} + 56 q^{75} - 36 q^{77} - 8 q^{79} - 2 q^{80} + 10 q^{81} - 10 q^{82} - 28 q^{84} + 12 q^{86} + 28 q^{87} + 8 q^{88} + 8 q^{90} + 4 q^{91} - 2 q^{92} + 14 q^{93} - 28 q^{94} - 18 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.32288 2.29129i 0.763763 1.32288i −0.177136 0.984186i \(-0.556683\pi\)
0.940898 0.338689i \(-0.109984\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.822876 1.42526i 0.368001 0.637397i −0.621252 0.783611i \(-0.713376\pi\)
0.989253 + 0.146214i \(0.0467089\pi\)
\(6\) −1.32288 2.29129i −0.540062 0.935414i
\(7\) 3.64575 1.37796 0.688982 0.724778i \(-0.258058\pi\)
0.688982 + 0.724778i \(0.258058\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 3.46410i −0.666667 1.15470i
\(10\) −0.822876 1.42526i −0.260216 0.450708i
\(11\) −4.64575 −1.40075 −0.700373 0.713777i \(-0.746983\pi\)
−0.700373 + 0.713777i \(0.746983\pi\)
\(12\) −2.64575 −0.763763
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 1.82288 3.15731i 0.487184 0.843827i
\(15\) −2.17712 3.77089i −0.562131 0.973640i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −4.00000 −0.942809
\(19\) 0 0
\(20\) −1.64575 −0.368001
\(21\) 4.82288 8.35347i 1.05244 1.82288i
\(22\) −2.32288 + 4.02334i −0.495239 + 0.857779i
\(23\) 0.822876 + 1.42526i 0.171581 + 0.297188i 0.938973 0.343991i \(-0.111779\pi\)
−0.767391 + 0.641179i \(0.778446\pi\)
\(24\) −1.32288 + 2.29129i −0.270031 + 0.467707i
\(25\) 1.14575 + 1.98450i 0.229150 + 0.396900i
\(26\) 2.00000 0.392232
\(27\) −2.64575 −0.509175
\(28\) −1.82288 3.15731i −0.344491 0.596676i
\(29\) 0.822876 + 1.42526i 0.152804 + 0.264665i 0.932257 0.361796i \(-0.117836\pi\)
−0.779453 + 0.626461i \(0.784503\pi\)
\(30\) −4.35425 −0.794973
\(31\) 5.64575 1.01401 0.507003 0.861944i \(-0.330753\pi\)
0.507003 + 0.861944i \(0.330753\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −6.14575 + 10.6448i −1.06984 + 1.85301i
\(34\) 0 0
\(35\) 3.00000 5.19615i 0.507093 0.878310i
\(36\) −2.00000 + 3.46410i −0.333333 + 0.577350i
\(37\) −0.354249 −0.0582381 −0.0291191 0.999576i \(-0.509270\pi\)
−0.0291191 + 0.999576i \(0.509270\pi\)
\(38\) 0 0
\(39\) 5.29150 0.847319
\(40\) −0.822876 + 1.42526i −0.130108 + 0.225354i
\(41\) −0.145751 + 0.252449i −0.0227625 + 0.0394259i −0.877182 0.480158i \(-0.840579\pi\)
0.854420 + 0.519583i \(0.173913\pi\)
\(42\) −4.82288 8.35347i −0.744186 1.28897i
\(43\) −5.64575 + 9.77873i −0.860969 + 1.49124i 0.0100257 + 0.999950i \(0.496809\pi\)
−0.870995 + 0.491292i \(0.836525\pi\)
\(44\) 2.32288 + 4.02334i 0.350187 + 0.606541i
\(45\) −6.58301 −0.981336
\(46\) 1.64575 0.242653
\(47\) −2.17712 3.77089i −0.317566 0.550041i 0.662413 0.749138i \(-0.269532\pi\)
−0.979980 + 0.199098i \(0.936199\pi\)
\(48\) 1.32288 + 2.29129i 0.190941 + 0.330719i
\(49\) 6.29150 0.898786
\(50\) 2.29150 0.324067
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) −6.29150 10.8972i −0.864204 1.49685i −0.867835 0.496852i \(-0.834489\pi\)
0.00363070 0.999993i \(-0.498844\pi\)
\(54\) −1.32288 + 2.29129i −0.180021 + 0.311805i
\(55\) −3.82288 + 6.62141i −0.515476 + 0.892831i
\(56\) −3.64575 −0.487184
\(57\) 0 0
\(58\) 1.64575 0.216098
\(59\) −3.96863 + 6.87386i −0.516671 + 0.894901i 0.483141 + 0.875542i \(0.339496\pi\)
−0.999813 + 0.0193585i \(0.993838\pi\)
\(60\) −2.17712 + 3.77089i −0.281066 + 0.486820i
\(61\) −0.468627 0.811686i −0.0600015 0.103926i 0.834464 0.551062i \(-0.185777\pi\)
−0.894466 + 0.447136i \(0.852444\pi\)
\(62\) 2.82288 4.88936i 0.358506 0.620950i
\(63\) −7.29150 12.6293i −0.918643 1.59114i
\(64\) 1.00000 0.125000
\(65\) 3.29150 0.408261
\(66\) 6.14575 + 10.6448i 0.756490 + 1.31028i
\(67\) 0.322876 + 0.559237i 0.0394455 + 0.0683217i 0.885074 0.465450i \(-0.154108\pi\)
−0.845629 + 0.533772i \(0.820774\pi\)
\(68\) 0 0
\(69\) 4.35425 0.524190
\(70\) −3.00000 5.19615i −0.358569 0.621059i
\(71\) −1.35425 + 2.34563i −0.160720 + 0.278375i −0.935127 0.354313i \(-0.884715\pi\)
0.774407 + 0.632687i \(0.218048\pi\)
\(72\) 2.00000 + 3.46410i 0.235702 + 0.408248i
\(73\) −0.854249 + 1.47960i −0.0999822 + 0.173174i −0.911677 0.410907i \(-0.865212\pi\)
0.811695 + 0.584082i \(0.198545\pi\)
\(74\) −0.177124 + 0.306788i −0.0205903 + 0.0356634i
\(75\) 6.06275 0.700066
\(76\) 0 0
\(77\) −16.9373 −1.93018
\(78\) 2.64575 4.58258i 0.299572 0.518875i
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0.822876 + 1.42526i 0.0920003 + 0.159349i
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) 0.145751 + 0.252449i 0.0160955 + 0.0278783i
\(83\) 7.93725 0.871227 0.435613 0.900134i \(-0.356531\pi\)
0.435613 + 0.900134i \(0.356531\pi\)
\(84\) −9.64575 −1.05244
\(85\) 0 0
\(86\) 5.64575 + 9.77873i 0.608797 + 1.05447i
\(87\) 4.35425 0.466824
\(88\) 4.64575 0.495239
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) −3.29150 + 5.70105i −0.346955 + 0.600943i
\(91\) 3.64575 + 6.31463i 0.382179 + 0.661953i
\(92\) 0.822876 1.42526i 0.0857907 0.148594i
\(93\) 7.46863 12.9360i 0.774461 1.34141i
\(94\) −4.35425 −0.449106
\(95\) 0 0
\(96\) 2.64575 0.270031
\(97\) −1.85425 + 3.21165i −0.188270 + 0.326094i −0.944674 0.328012i \(-0.893621\pi\)
0.756403 + 0.654106i \(0.226955\pi\)
\(98\) 3.14575 5.44860i 0.317769 0.550392i
\(99\) 9.29150 + 16.0934i 0.933831 + 1.61744i
\(100\) 1.14575 1.98450i 0.114575 0.198450i
\(101\) 6.82288 + 11.8176i 0.678902 + 1.17589i 0.975312 + 0.220831i \(0.0708770\pi\)
−0.296411 + 0.955061i \(0.595790\pi\)
\(102\) 0 0
\(103\) 13.2915 1.30965 0.654825 0.755780i \(-0.272742\pi\)
0.654825 + 0.755780i \(0.272742\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) −7.93725 13.7477i −0.774597 1.34164i
\(106\) −12.5830 −1.22217
\(107\) −15.2915 −1.47829 −0.739143 0.673549i \(-0.764769\pi\)
−0.739143 + 0.673549i \(0.764769\pi\)
\(108\) 1.32288 + 2.29129i 0.127294 + 0.220479i
\(109\) 7.29150 12.6293i 0.698399 1.20966i −0.270622 0.962686i \(-0.587229\pi\)
0.969021 0.246977i \(-0.0794373\pi\)
\(110\) 3.82288 + 6.62141i 0.364497 + 0.631327i
\(111\) −0.468627 + 0.811686i −0.0444801 + 0.0770418i
\(112\) −1.82288 + 3.15731i −0.172246 + 0.298338i
\(113\) 15.5830 1.46593 0.732963 0.680269i \(-0.238137\pi\)
0.732963 + 0.680269i \(0.238137\pi\)
\(114\) 0 0
\(115\) 2.70850 0.252569
\(116\) 0.822876 1.42526i 0.0764021 0.132332i
\(117\) 4.00000 6.92820i 0.369800 0.640513i
\(118\) 3.96863 + 6.87386i 0.365342 + 0.632790i
\(119\) 0 0
\(120\) 2.17712 + 3.77089i 0.198743 + 0.344234i
\(121\) 10.5830 0.962091
\(122\) −0.937254 −0.0848550
\(123\) 0.385622 + 0.667916i 0.0347703 + 0.0602240i
\(124\) −2.82288 4.88936i −0.253502 0.439078i
\(125\) 12.0000 1.07331
\(126\) −14.5830 −1.29916
\(127\) −6.64575 11.5108i −0.589715 1.02142i −0.994270 0.106903i \(-0.965907\pi\)
0.404554 0.914514i \(-0.367427\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 14.9373 + 25.8721i 1.31515 + 2.27791i
\(130\) 1.64575 2.85052i 0.144342 0.250008i
\(131\) −0.968627 + 1.67771i −0.0846293 + 0.146582i −0.905233 0.424915i \(-0.860304\pi\)
0.820604 + 0.571497i \(0.193637\pi\)
\(132\) 12.2915 1.06984
\(133\) 0 0
\(134\) 0.645751 0.0557844
\(135\) −2.17712 + 3.77089i −0.187377 + 0.324547i
\(136\) 0 0
\(137\) −7.79150 13.4953i −0.665673 1.15298i −0.979102 0.203368i \(-0.934811\pi\)
0.313429 0.949612i \(-0.398522\pi\)
\(138\) 2.17712 3.77089i 0.185329 0.320999i
\(139\) −9.32288 16.1477i −0.790756 1.36963i −0.925499 0.378749i \(-0.876354\pi\)
0.134743 0.990881i \(-0.456979\pi\)
\(140\) −6.00000 −0.507093
\(141\) −11.5203 −0.970181
\(142\) 1.35425 + 2.34563i 0.113646 + 0.196841i
\(143\) −4.64575 8.04668i −0.388497 0.672897i
\(144\) 4.00000 0.333333
\(145\) 2.70850 0.224928
\(146\) 0.854249 + 1.47960i 0.0706981 + 0.122453i
\(147\) 8.32288 14.4156i 0.686459 1.18898i
\(148\) 0.177124 + 0.306788i 0.0145595 + 0.0252178i
\(149\) −5.46863 + 9.47194i −0.448007 + 0.775972i −0.998256 0.0590292i \(-0.981200\pi\)
0.550249 + 0.835001i \(0.314533\pi\)
\(150\) 3.03137 5.25049i 0.247511 0.428701i
\(151\) −12.9373 −1.05282 −0.526409 0.850231i \(-0.676462\pi\)
−0.526409 + 0.850231i \(0.676462\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −8.46863 + 14.6681i −0.682421 + 1.18199i
\(155\) 4.64575 8.04668i 0.373156 0.646325i
\(156\) −2.64575 4.58258i −0.211830 0.366900i
\(157\) 5.29150 9.16515i 0.422308 0.731459i −0.573857 0.818956i \(-0.694553\pi\)
0.996165 + 0.0874969i \(0.0278868\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) −33.2915 −2.64019
\(160\) 1.64575 0.130108
\(161\) 3.00000 + 5.19615i 0.236433 + 0.409514i
\(162\) −2.50000 4.33013i −0.196419 0.340207i
\(163\) 3.93725 0.308390 0.154195 0.988040i \(-0.450722\pi\)
0.154195 + 0.988040i \(0.450722\pi\)
\(164\) 0.291503 0.0227625
\(165\) 10.1144 + 17.5186i 0.787403 + 1.36382i
\(166\) 3.96863 6.87386i 0.308025 0.533515i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) −4.82288 + 8.35347i −0.372093 + 0.644484i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 11.2915 0.860969
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 2.17712 3.77089i 0.165047 0.285870i
\(175\) 4.17712 + 7.23499i 0.315761 + 0.546914i
\(176\) 2.32288 4.02334i 0.175093 0.303271i
\(177\) 10.5000 + 18.1865i 0.789228 + 1.36698i
\(178\) 0 0
\(179\) −4.06275 −0.303664 −0.151832 0.988406i \(-0.548517\pi\)
−0.151832 + 0.988406i \(0.548517\pi\)
\(180\) 3.29150 + 5.70105i 0.245334 + 0.424931i
\(181\) 11.1144 + 19.2507i 0.826125 + 1.43089i 0.901056 + 0.433702i \(0.142793\pi\)
−0.0749311 + 0.997189i \(0.523874\pi\)
\(182\) 7.29150 0.540482
\(183\) −2.47974 −0.183308
\(184\) −0.822876 1.42526i −0.0606632 0.105072i
\(185\) −0.291503 + 0.504897i −0.0214317 + 0.0371208i
\(186\) −7.46863 12.9360i −0.547626 0.948517i
\(187\) 0 0
\(188\) −2.17712 + 3.77089i −0.158783 + 0.275020i
\(189\) −9.64575 −0.701625
\(190\) 0 0
\(191\) 6.58301 0.476330 0.238165 0.971225i \(-0.423454\pi\)
0.238165 + 0.971225i \(0.423454\pi\)
\(192\) 1.32288 2.29129i 0.0954703 0.165359i
\(193\) 7.29150 12.6293i 0.524854 0.909074i −0.474727 0.880133i \(-0.657453\pi\)
0.999581 0.0289406i \(-0.00921336\pi\)
\(194\) 1.85425 + 3.21165i 0.133127 + 0.230583i
\(195\) 4.35425 7.54178i 0.311814 0.540078i
\(196\) −3.14575 5.44860i −0.224697 0.389186i
\(197\) −7.64575 −0.544737 −0.272369 0.962193i \(-0.587807\pi\)
−0.272369 + 0.962193i \(0.587807\pi\)
\(198\) 18.5830 1.32064
\(199\) 9.93725 + 17.2118i 0.704433 + 1.22011i 0.966896 + 0.255172i \(0.0821321\pi\)
−0.262462 + 0.964942i \(0.584535\pi\)
\(200\) −1.14575 1.98450i −0.0810169 0.140325i
\(201\) 1.70850 0.120508
\(202\) 13.6458 0.960112
\(203\) 3.00000 + 5.19615i 0.210559 + 0.364698i
\(204\) 0 0
\(205\) 0.239870 + 0.415468i 0.0167533 + 0.0290175i
\(206\) 6.64575 11.5108i 0.463031 0.801994i
\(207\) 3.29150 5.70105i 0.228775 0.396250i
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) −15.8745 −1.09545
\(211\) −6.64575 + 11.5108i −0.457512 + 0.792435i −0.998829 0.0483843i \(-0.984593\pi\)
0.541316 + 0.840819i \(0.317926\pi\)
\(212\) −6.29150 + 10.8972i −0.432102 + 0.748423i
\(213\) 3.58301 + 6.20595i 0.245503 + 0.425224i
\(214\) −7.64575 + 13.2428i −0.522653 + 0.905261i
\(215\) 9.29150 + 16.0934i 0.633675 + 1.09756i
\(216\) 2.64575 0.180021
\(217\) 20.5830 1.39727
\(218\) −7.29150 12.6293i −0.493843 0.855361i
\(219\) 2.26013 + 3.91466i 0.152725 + 0.264528i
\(220\) 7.64575 0.515476
\(221\) 0 0
\(222\) 0.468627 + 0.811686i 0.0314522 + 0.0544768i
\(223\) −9.40588 + 16.2915i −0.629864 + 1.09096i 0.357714 + 0.933831i \(0.383556\pi\)
−0.987579 + 0.157126i \(0.949777\pi\)
\(224\) 1.82288 + 3.15731i 0.121796 + 0.210957i
\(225\) 4.58301 7.93800i 0.305534 0.529200i
\(226\) 7.79150 13.4953i 0.518283 0.897693i
\(227\) 7.35425 0.488119 0.244059 0.969760i \(-0.421521\pi\)
0.244059 + 0.969760i \(0.421521\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 1.35425 2.34563i 0.0892965 0.154666i
\(231\) −22.4059 + 38.8081i −1.47420 + 2.55339i
\(232\) −0.822876 1.42526i −0.0540244 0.0935731i
\(233\) −9.43725 + 16.3458i −0.618255 + 1.07085i 0.371549 + 0.928413i \(0.378827\pi\)
−0.989804 + 0.142436i \(0.954507\pi\)
\(234\) −4.00000 6.92820i −0.261488 0.452911i
\(235\) −7.16601 −0.467459
\(236\) 7.93725 0.516671
\(237\) 5.29150 + 9.16515i 0.343720 + 0.595341i
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 4.35425 0.281066
\(241\) −3.79150 6.56708i −0.244232 0.423022i 0.717683 0.696370i \(-0.245203\pi\)
−0.961915 + 0.273347i \(0.911869\pi\)
\(242\) 5.29150 9.16515i 0.340151 0.589158i
\(243\) −10.5830 18.3303i −0.678900 1.17589i
\(244\) −0.468627 + 0.811686i −0.0300008 + 0.0519629i
\(245\) 5.17712 8.96704i 0.330754 0.572883i
\(246\) 0.771243 0.0491727
\(247\) 0 0
\(248\) −5.64575 −0.358506
\(249\) 10.5000 18.1865i 0.665410 1.15252i
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −14.6144 25.3128i −0.922451 1.59773i −0.795610 0.605810i \(-0.792849\pi\)
−0.126842 0.991923i \(-0.540484\pi\)
\(252\) −7.29150 + 12.6293i −0.459321 + 0.795568i
\(253\) −3.82288 6.62141i −0.240342 0.416285i
\(254\) −13.2915 −0.833983
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.14575 + 10.6448i 0.383361 + 0.664001i 0.991540 0.129798i \(-0.0414330\pi\)
−0.608179 + 0.793800i \(0.708100\pi\)
\(258\) 29.8745 1.85991
\(259\) −1.29150 −0.0802501
\(260\) −1.64575 2.85052i −0.102065 0.176782i
\(261\) 3.29150 5.70105i 0.203739 0.352886i
\(262\) 0.968627 + 1.67771i 0.0598420 + 0.103649i
\(263\) 5.46863 9.47194i 0.337210 0.584065i −0.646697 0.762747i \(-0.723850\pi\)
0.983907 + 0.178682i \(0.0571834\pi\)
\(264\) 6.14575 10.6448i 0.378245 0.655139i
\(265\) −20.7085 −1.27211
\(266\) 0 0
\(267\) 0 0
\(268\) 0.322876 0.559237i 0.0197228 0.0341608i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 2.17712 + 3.77089i 0.132496 + 0.229489i
\(271\) −6.17712 + 10.6991i −0.375234 + 0.649924i −0.990362 0.138503i \(-0.955771\pi\)
0.615128 + 0.788427i \(0.289104\pi\)
\(272\) 0 0
\(273\) 19.2915 1.16757
\(274\) −15.5830 −0.941404
\(275\) −5.32288 9.21949i −0.320981 0.555956i
\(276\) −2.17712 3.77089i −0.131047 0.226981i
\(277\) −27.5203 −1.65353 −0.826766 0.562546i \(-0.809822\pi\)
−0.826766 + 0.562546i \(0.809822\pi\)
\(278\) −18.6458 −1.11830
\(279\) −11.2915 19.5575i −0.676005 1.17087i
\(280\) −3.00000 + 5.19615i −0.179284 + 0.310530i
\(281\) 12.7288 + 22.0469i 0.759334 + 1.31520i 0.943191 + 0.332252i \(0.107808\pi\)
−0.183857 + 0.982953i \(0.558858\pi\)
\(282\) −5.76013 + 9.97684i −0.343011 + 0.594112i
\(283\) −15.3229 + 26.5400i −0.910850 + 1.57764i −0.0979848 + 0.995188i \(0.531240\pi\)
−0.812866 + 0.582451i \(0.802094\pi\)
\(284\) 2.70850 0.160720
\(285\) 0 0
\(286\) −9.29150 −0.549418
\(287\) −0.531373 + 0.920365i −0.0313660 + 0.0543274i
\(288\) 2.00000 3.46410i 0.117851 0.204124i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 1.35425 2.34563i 0.0795242 0.137740i
\(291\) 4.90588 + 8.49723i 0.287588 + 0.498117i
\(292\) 1.70850 0.0999822
\(293\) −28.9373 −1.69053 −0.845266 0.534345i \(-0.820558\pi\)
−0.845266 + 0.534345i \(0.820558\pi\)
\(294\) −8.32288 14.4156i −0.485400 0.840737i
\(295\) 6.53137 + 11.3127i 0.380271 + 0.658649i
\(296\) 0.354249 0.0205903
\(297\) 12.2915 0.713225
\(298\) 5.46863 + 9.47194i 0.316789 + 0.548695i
\(299\) −1.64575 + 2.85052i −0.0951763 + 0.164850i
\(300\) −3.03137 5.25049i −0.175016 0.303137i
\(301\) −20.5830 + 35.6508i −1.18638 + 2.05488i
\(302\) −6.46863 + 11.2040i −0.372228 + 0.644717i
\(303\) 36.1033 2.07408
\(304\) 0 0
\(305\) −1.54249 −0.0883225
\(306\) 0 0
\(307\) 0.322876 0.559237i 0.0184275 0.0319173i −0.856665 0.515874i \(-0.827467\pi\)
0.875092 + 0.483956i \(0.160801\pi\)
\(308\) 8.46863 + 14.6681i 0.482545 + 0.835792i
\(309\) 17.5830 30.4547i 1.00026 1.73250i
\(310\) −4.64575 8.04668i −0.263861 0.457021i
\(311\) 13.6458 0.773780 0.386890 0.922126i \(-0.373549\pi\)
0.386890 + 0.922126i \(0.373549\pi\)
\(312\) −5.29150 −0.299572
\(313\) −4.43725 7.68555i −0.250808 0.434413i 0.712940 0.701225i \(-0.247363\pi\)
−0.963749 + 0.266812i \(0.914030\pi\)
\(314\) −5.29150 9.16515i −0.298617 0.517219i
\(315\) −24.0000 −1.35225
\(316\) 4.00000 0.225018
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) −16.6458 + 28.8313i −0.933447 + 1.61678i
\(319\) −3.82288 6.62141i −0.214040 0.370728i
\(320\) 0.822876 1.42526i 0.0460001 0.0796746i
\(321\) −20.2288 + 35.0372i −1.12906 + 1.95559i
\(322\) 6.00000 0.334367
\(323\) 0 0
\(324\) −5.00000 −0.277778
\(325\) −2.29150 + 3.96900i −0.127110 + 0.220160i
\(326\) 1.96863 3.40976i 0.109032 0.188849i
\(327\) −19.2915 33.4139i −1.06682 1.84779i
\(328\) 0.145751 0.252449i 0.00804777 0.0139391i
\(329\) −7.93725 13.7477i −0.437595 0.757937i
\(330\) 20.2288 1.11356
\(331\) −19.8118 −1.08895 −0.544476 0.838776i \(-0.683272\pi\)
−0.544476 + 0.838776i \(0.683272\pi\)
\(332\) −3.96863 6.87386i −0.217807 0.377252i
\(333\) 0.708497 + 1.22715i 0.0388254 + 0.0672476i
\(334\) −12.0000 −0.656611
\(335\) 1.06275 0.0580640
\(336\) 4.82288 + 8.35347i 0.263109 + 0.455719i
\(337\) −4.85425 + 8.40781i −0.264428 + 0.458002i −0.967414 0.253202i \(-0.918516\pi\)
0.702986 + 0.711204i \(0.251850\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 20.6144 35.7052i 1.11962 1.93924i
\(340\) 0 0
\(341\) −26.2288 −1.42037
\(342\) 0 0
\(343\) −2.58301 −0.139469
\(344\) 5.64575 9.77873i 0.304399 0.527234i
\(345\) 3.58301 6.20595i 0.192903 0.334117i
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) 11.6144 20.1167i 0.623492 1.07992i −0.365338 0.930875i \(-0.619047\pi\)
0.988830 0.149046i \(-0.0476201\pi\)
\(348\) −2.17712 3.77089i −0.116706 0.202141i
\(349\) 21.1660 1.13299 0.566495 0.824065i \(-0.308299\pi\)
0.566495 + 0.824065i \(0.308299\pi\)
\(350\) 8.35425 0.446553
\(351\) −2.64575 4.58258i −0.141220 0.244600i
\(352\) −2.32288 4.02334i −0.123810 0.214445i
\(353\) 12.8745 0.685241 0.342620 0.939474i \(-0.388686\pi\)
0.342620 + 0.939474i \(0.388686\pi\)
\(354\) 21.0000 1.11614
\(355\) 2.22876 + 3.86032i 0.118290 + 0.204884i
\(356\) 0 0
\(357\) 0 0
\(358\) −2.03137 + 3.51844i −0.107361 + 0.185955i
\(359\) 2.46863 4.27579i 0.130289 0.225667i −0.793499 0.608572i \(-0.791743\pi\)
0.923788 + 0.382904i \(0.125076\pi\)
\(360\) 6.58301 0.346955
\(361\) 0 0
\(362\) 22.2288 1.16832
\(363\) 14.0000 24.2487i 0.734809 1.27273i
\(364\) 3.64575 6.31463i 0.191089 0.330976i
\(365\) 1.40588 + 2.43506i 0.0735872 + 0.127457i
\(366\) −1.23987 + 2.14752i −0.0648091 + 0.112253i
\(367\) −8.11438 14.0545i −0.423567 0.733640i 0.572718 0.819752i \(-0.305889\pi\)
−0.996285 + 0.0861125i \(0.972556\pi\)
\(368\) −1.64575 −0.0857907
\(369\) 1.16601 0.0607001
\(370\) 0.291503 + 0.504897i 0.0151545 + 0.0262484i
\(371\) −22.9373 39.7285i −1.19084 2.06260i
\(372\) −14.9373 −0.774461
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 15.8745 27.4955i 0.819756 1.41986i
\(376\) 2.17712 + 3.77089i 0.112277 + 0.194469i
\(377\) −1.64575 + 2.85052i −0.0847605 + 0.146810i
\(378\) −4.82288 + 8.35347i −0.248062 + 0.429656i
\(379\) −10.7085 −0.550059 −0.275029 0.961436i \(-0.588688\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(380\) 0 0
\(381\) −35.1660 −1.80161
\(382\) 3.29150 5.70105i 0.168408 0.291691i
\(383\) 2.76013 4.78068i 0.141036 0.244282i −0.786851 0.617143i \(-0.788290\pi\)
0.927887 + 0.372861i \(0.121623\pi\)
\(384\) −1.32288 2.29129i −0.0675077 0.116927i
\(385\) −13.9373 + 24.1400i −0.710308 + 1.23029i
\(386\) −7.29150 12.6293i −0.371128 0.642812i
\(387\) 45.1660 2.29592
\(388\) 3.70850 0.188270
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) −4.35425 7.54178i −0.220486 0.381893i
\(391\) 0 0
\(392\) −6.29150 −0.317769
\(393\) 2.56275 + 4.43881i 0.129273 + 0.223908i
\(394\) −3.82288 + 6.62141i −0.192594 + 0.333582i
\(395\) 3.29150 + 5.70105i 0.165613 + 0.286851i
\(396\) 9.29150 16.0934i 0.466916 0.808721i
\(397\) −10.5314 + 18.2409i −0.528554 + 0.915483i 0.470891 + 0.882191i \(0.343932\pi\)
−0.999446 + 0.0332919i \(0.989401\pi\)
\(398\) 19.8745 0.996219
\(399\) 0 0
\(400\) −2.29150 −0.114575
\(401\) 13.7915 23.8876i 0.688715 1.19289i −0.283539 0.958961i \(-0.591509\pi\)
0.972254 0.233928i \(-0.0751581\pi\)
\(402\) 0.854249 1.47960i 0.0426061 0.0737958i
\(403\) 5.64575 + 9.77873i 0.281235 + 0.487113i
\(404\) 6.82288 11.8176i 0.339451 0.587946i
\(405\) −4.11438 7.12631i −0.204445 0.354109i
\(406\) 6.00000 0.297775
\(407\) 1.64575 0.0815769
\(408\) 0 0
\(409\) −3.79150 6.56708i −0.187478 0.324721i 0.756931 0.653495i \(-0.226698\pi\)
−0.944409 + 0.328774i \(0.893365\pi\)
\(410\) 0.479741 0.0236927
\(411\) −41.2288 −2.03366
\(412\) −6.64575 11.5108i −0.327413 0.567095i
\(413\) −14.4686 + 25.0604i −0.711955 + 1.23314i
\(414\) −3.29150 5.70105i −0.161769 0.280191i
\(415\) 6.53137 11.3127i 0.320612 0.555317i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) −49.3320 −2.41580
\(418\) 0 0
\(419\) −31.7490 −1.55104 −0.775520 0.631322i \(-0.782512\pi\)
−0.775520 + 0.631322i \(0.782512\pi\)
\(420\) −7.93725 + 13.7477i −0.387298 + 0.670820i
\(421\) −12.4059 + 21.4876i −0.604626 + 1.04724i 0.387485 + 0.921876i \(0.373344\pi\)
−0.992111 + 0.125366i \(0.959989\pi\)
\(422\) 6.64575 + 11.5108i 0.323510 + 0.560336i
\(423\) −8.70850 + 15.0836i −0.423422 + 0.733388i
\(424\) 6.29150 + 10.8972i 0.305542 + 0.529215i
\(425\) 0 0
\(426\) 7.16601 0.347194
\(427\) −1.70850 2.95920i −0.0826800 0.143206i
\(428\) 7.64575 + 13.2428i 0.369571 + 0.640116i
\(429\) −24.5830 −1.18688
\(430\) 18.5830 0.896152
\(431\) 13.9373 + 24.1400i 0.671334 + 1.16278i 0.977526 + 0.210815i \(0.0676117\pi\)
−0.306192 + 0.951970i \(0.599055\pi\)
\(432\) 1.32288 2.29129i 0.0636469 0.110240i
\(433\) 8.93725 + 15.4798i 0.429497 + 0.743911i 0.996829 0.0795788i \(-0.0253575\pi\)
−0.567332 + 0.823489i \(0.692024\pi\)
\(434\) 10.2915 17.8254i 0.494008 0.855647i
\(435\) 3.58301 6.20595i 0.171792 0.297552i
\(436\) −14.5830 −0.698399
\(437\) 0 0
\(438\) 4.52026 0.215986
\(439\) 5.40588 9.36326i 0.258009 0.446884i −0.707700 0.706513i \(-0.750267\pi\)
0.965708 + 0.259629i \(0.0836004\pi\)
\(440\) 3.82288 6.62141i 0.182248 0.315664i
\(441\) −12.5830 21.7944i −0.599191 1.03783i
\(442\) 0 0
\(443\) −5.32288 9.21949i −0.252897 0.438031i 0.711425 0.702762i \(-0.248050\pi\)
−0.964322 + 0.264731i \(0.914717\pi\)
\(444\) 0.937254 0.0444801
\(445\) 0 0
\(446\) 9.40588 + 16.2915i 0.445381 + 0.771423i
\(447\) 14.4686 + 25.0604i 0.684343 + 1.18532i
\(448\) 3.64575 0.172246
\(449\) 24.2915 1.14639 0.573193 0.819420i \(-0.305704\pi\)
0.573193 + 0.819420i \(0.305704\pi\)
\(450\) −4.58301 7.93800i −0.216045 0.374201i
\(451\) 0.677124 1.17281i 0.0318845 0.0552256i
\(452\) −7.79150 13.4953i −0.366481 0.634765i
\(453\) −17.1144 + 29.6430i −0.804104 + 1.39275i
\(454\) 3.67712 6.36897i 0.172576 0.298910i
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) 32.8745 1.53780 0.768902 0.639366i \(-0.220803\pi\)
0.768902 + 0.639366i \(0.220803\pi\)
\(458\) 10.0000 17.3205i 0.467269 0.809334i
\(459\) 0 0
\(460\) −1.35425 2.34563i −0.0631422 0.109365i
\(461\) −9.58301 + 16.5983i −0.446325 + 0.773058i −0.998143 0.0609066i \(-0.980601\pi\)
0.551818 + 0.833964i \(0.313934\pi\)
\(462\) 22.4059 + 38.8081i 1.04242 + 1.80552i
\(463\) −38.4575 −1.78727 −0.893636 0.448792i \(-0.851854\pi\)
−0.893636 + 0.448792i \(0.851854\pi\)
\(464\) −1.64575 −0.0764021
\(465\) −12.2915 21.2895i −0.570005 0.987277i
\(466\) 9.43725 + 16.3458i 0.437172 + 0.757205i
\(467\) −19.3542 −0.895608 −0.447804 0.894132i \(-0.647794\pi\)
−0.447804 + 0.894132i \(0.647794\pi\)
\(468\) −8.00000 −0.369800
\(469\) 1.17712 + 2.03884i 0.0543546 + 0.0941448i
\(470\) −3.58301 + 6.20595i −0.165272 + 0.286259i
\(471\) −14.0000 24.2487i −0.645086 1.11732i
\(472\) 3.96863 6.87386i 0.182671 0.316395i
\(473\) 26.2288 45.4295i 1.20600 2.08885i
\(474\) 10.5830 0.486094
\(475\) 0 0
\(476\) 0 0
\(477\) −25.1660 + 43.5888i −1.15227 + 1.99579i
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) −3.29150 5.70105i −0.150393 0.260488i 0.780979 0.624557i \(-0.214720\pi\)
−0.931372 + 0.364069i \(0.881387\pi\)
\(480\) 2.17712 3.77089i 0.0993717 0.172117i
\(481\) −0.354249 0.613577i −0.0161523 0.0279767i
\(482\) −7.58301 −0.345396
\(483\) 15.8745 0.722315
\(484\) −5.29150 9.16515i −0.240523 0.416598i
\(485\) 3.05163 + 5.28558i 0.138567 + 0.240006i
\(486\) −21.1660 −0.960110
\(487\) −4.22876 −0.191623 −0.0958116 0.995399i \(-0.530545\pi\)
−0.0958116 + 0.995399i \(0.530545\pi\)
\(488\) 0.468627 + 0.811686i 0.0212137 + 0.0367433i
\(489\) 5.20850 9.02138i 0.235536 0.407961i
\(490\) −5.17712 8.96704i −0.233879 0.405090i
\(491\) −19.6458 + 34.0274i −0.886600 + 1.53564i −0.0427320 + 0.999087i \(0.513606\pi\)
−0.843868 + 0.536550i \(0.819727\pi\)
\(492\) 0.385622 0.667916i 0.0173852 0.0301120i
\(493\) 0 0
\(494\) 0 0
\(495\) 30.5830 1.37460
\(496\) −2.82288 + 4.88936i −0.126751 + 0.219539i
\(497\) −4.93725 + 8.55157i −0.221466 + 0.383591i
\(498\) −10.5000 18.1865i −0.470516 0.814958i
\(499\) 2.38562 4.13202i 0.106795 0.184975i −0.807675 0.589628i \(-0.799274\pi\)
0.914470 + 0.404653i \(0.132608\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) −31.7490 −1.41844
\(502\) −29.2288 −1.30454
\(503\) 20.4686 + 35.4527i 0.912651 + 1.58076i 0.810305 + 0.586009i \(0.199302\pi\)
0.102346 + 0.994749i \(0.467365\pi\)
\(504\) 7.29150 + 12.6293i 0.324789 + 0.562552i
\(505\) 22.4575 0.999346
\(506\) −7.64575 −0.339895
\(507\) −11.9059 20.6216i −0.528759 0.915837i
\(508\) −6.64575 + 11.5108i −0.294858 + 0.510708i
\(509\) −15.8745 27.4955i −0.703625 1.21871i −0.967185 0.254072i \(-0.918230\pi\)
0.263560 0.964643i \(-0.415103\pi\)
\(510\) 0 0
\(511\) −3.11438 + 5.39426i −0.137772 + 0.238628i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 12.2915 0.542155
\(515\) 10.9373 18.9439i 0.481953 0.834767i
\(516\) 14.9373 25.8721i 0.657576 1.13895i
\(517\) 10.1144 + 17.5186i 0.444830 + 0.770468i
\(518\) −0.645751 + 1.11847i −0.0283727 + 0.0491429i
\(519\) 7.93725 + 13.7477i 0.348407 + 0.603458i
\(520\) −3.29150 −0.144342
\(521\) 11.7085 0.512959 0.256479 0.966550i \(-0.417437\pi\)
0.256479 + 0.966550i \(0.417437\pi\)
\(522\) −3.29150 5.70105i −0.144065 0.249528i
\(523\) −0.937254 1.62337i −0.0409833 0.0709851i 0.844806 0.535072i \(-0.179716\pi\)
−0.885789 + 0.464087i \(0.846382\pi\)
\(524\) 1.93725 0.0846293
\(525\) 22.1033 0.964666
\(526\) −5.46863 9.47194i −0.238443 0.412996i
\(527\) 0 0
\(528\) −6.14575 10.6448i −0.267459 0.463253i
\(529\) 10.1458 17.5730i 0.441120 0.764042i
\(530\) −10.3542 + 17.9341i −0.449760 + 0.779007i
\(531\) 31.7490 1.37779
\(532\) 0 0
\(533\) −0.583005 −0.0252528
\(534\) 0 0
\(535\) −12.5830 + 21.7944i −0.544011 + 0.942254i
\(536\) −0.322876 0.559237i −0.0139461 0.0241554i
\(537\) −5.37451 + 9.30892i −0.231927 + 0.401710i
\(538\) 0 0
\(539\) −29.2288 −1.25897
\(540\) 4.35425 0.187377
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) 6.17712 + 10.6991i 0.265330 + 0.459565i
\(543\) 58.8118 2.52385
\(544\) 0 0
\(545\) −12.0000 20.7846i −0.514024 0.890315i
\(546\) 9.64575 16.7069i 0.412800 0.714991i
\(547\) 5.64575 + 9.77873i 0.241395 + 0.418108i 0.961112 0.276159i \(-0.0890618\pi\)
−0.719717 + 0.694268i \(0.755728\pi\)
\(548\) −7.79150 + 13.4953i −0.332836 + 0.576490i
\(549\) −1.87451 + 3.24674i −0.0800020 + 0.138568i
\(550\) −10.6458 −0.453936
\(551\) 0 0
\(552\) −4.35425 −0.185329
\(553\) −7.29150 + 12.6293i −0.310066 + 0.537050i
\(554\) −13.7601 + 23.8332i −0.584612 + 1.01258i
\(555\) 0.771243 + 1.33583i 0.0327375 + 0.0567029i
\(556\) −9.32288 + 16.1477i −0.395378 + 0.684815i
\(557\) 2.70850 + 4.69126i 0.114763 + 0.198775i 0.917685 0.397309i \(-0.130056\pi\)
−0.802922 + 0.596084i \(0.796723\pi\)
\(558\) −22.5830 −0.956015
\(559\) −22.5830 −0.955159
\(560\) 3.00000 + 5.19615i 0.126773 + 0.219578i
\(561\) 0 0
\(562\) 25.4575 1.07386
\(563\) −10.0627 −0.424094 −0.212047 0.977259i \(-0.568013\pi\)
−0.212047 + 0.977259i \(0.568013\pi\)
\(564\) 5.76013 + 9.97684i 0.242545 + 0.420101i
\(565\) 12.8229 22.2099i 0.539462 0.934376i
\(566\) 15.3229 + 26.5400i 0.644069 + 1.11556i
\(567\) 9.11438 15.7866i 0.382768 0.662973i
\(568\) 1.35425 2.34563i 0.0568230 0.0984203i
\(569\) −6.58301 −0.275974 −0.137987 0.990434i \(-0.544063\pi\)
−0.137987 + 0.990434i \(0.544063\pi\)
\(570\) 0 0
\(571\) 7.81176 0.326912 0.163456 0.986551i \(-0.447736\pi\)
0.163456 + 0.986551i \(0.447736\pi\)
\(572\) −4.64575 + 8.04668i −0.194249 + 0.336448i
\(573\) 8.70850 15.0836i 0.363803 0.630125i
\(574\) 0.531373 + 0.920365i 0.0221791 + 0.0384153i
\(575\) −1.88562 + 3.26599i −0.0786359 + 0.136201i
\(576\) −2.00000 3.46410i −0.0833333 0.144338i
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 17.0000 0.707107
\(579\) −19.2915 33.4139i −0.801727 1.38863i
\(580\) −1.35425 2.34563i −0.0562321 0.0973969i
\(581\) 28.9373 1.20052
\(582\) 9.81176 0.406711
\(583\) 29.2288 + 50.6257i 1.21053 + 2.09670i
\(584\) 0.854249 1.47960i 0.0353491 0.0612264i
\(585\) −6.58301 11.4021i −0.272174 0.471419i
\(586\) −14.4686 + 25.0604i −0.597693 + 1.03524i
\(587\) 7.06275 12.2330i 0.291511 0.504911i −0.682656 0.730739i \(-0.739175\pi\)
0.974167 + 0.225828i \(0.0725088\pi\)
\(588\) −16.6458 −0.686459
\(589\) 0 0
\(590\) 13.0627 0.537785
\(591\) −10.1144 + 17.5186i −0.416050 + 0.720620i
\(592\) 0.177124 0.306788i 0.00727977 0.0126089i
\(593\) −14.8542 25.7283i −0.609991 1.05654i −0.991241 0.132063i \(-0.957840\pi\)
0.381250 0.924472i \(-0.375494\pi\)
\(594\) 6.14575 10.6448i 0.252163 0.436760i
\(595\) 0 0
\(596\) 10.9373 0.448007
\(597\) 52.5830 2.15208
\(598\) 1.64575 + 2.85052i 0.0672998 + 0.116567i
\(599\) −8.46863 14.6681i −0.346019 0.599322i 0.639520 0.768775i \(-0.279133\pi\)
−0.985538 + 0.169453i \(0.945800\pi\)
\(600\) −6.06275 −0.247511
\(601\) −10.4170 −0.424918 −0.212459 0.977170i \(-0.568147\pi\)
−0.212459 + 0.977170i \(0.568147\pi\)
\(602\) 20.5830 + 35.6508i 0.838901 + 1.45302i
\(603\) 1.29150 2.23695i 0.0525941 0.0910956i
\(604\) 6.46863 + 11.2040i 0.263205 + 0.455884i
\(605\) 8.70850 15.0836i 0.354051 0.613234i
\(606\) 18.0516 31.2663i 0.733297 1.27011i
\(607\) −6.93725 −0.281574 −0.140787 0.990040i \(-0.544963\pi\)
−0.140787 + 0.990040i \(0.544963\pi\)
\(608\) 0 0
\(609\) 15.8745 0.643268
\(610\) −0.771243 + 1.33583i −0.0312267 + 0.0540863i
\(611\) 4.35425 7.54178i 0.176154 0.305108i
\(612\) 0 0
\(613\) −3.70850 + 6.42331i −0.149785 + 0.259435i −0.931148 0.364642i \(-0.881191\pi\)
0.781363 + 0.624077i \(0.214525\pi\)
\(614\) −0.322876 0.559237i −0.0130302 0.0225690i
\(615\) 1.26927 0.0511821
\(616\) 16.9373 0.682421
\(617\) 15.4373 + 26.7381i 0.621480 + 1.07644i 0.989210 + 0.146503i \(0.0468018\pi\)
−0.367730 + 0.929933i \(0.619865\pi\)
\(618\) −17.5830 30.4547i −0.707292 1.22507i
\(619\) −8.45751 −0.339936 −0.169968 0.985450i \(-0.554366\pi\)
−0.169968 + 0.985450i \(0.554366\pi\)
\(620\) −9.29150 −0.373156
\(621\) −2.17712 3.77089i −0.0873650 0.151321i
\(622\) 6.82288 11.8176i 0.273572 0.473841i
\(623\) 0 0
\(624\) −2.64575 + 4.58258i −0.105915 + 0.183450i
\(625\) 4.14575 7.18065i 0.165830 0.287226i
\(626\) −8.87451 −0.354697
\(627\) 0 0
\(628\) −10.5830 −0.422308
\(629\) 0 0
\(630\) −12.0000 + 20.7846i −0.478091 + 0.828079i
\(631\) 12.4059 + 21.4876i 0.493870 + 0.855408i 0.999975 0.00706354i \(-0.00224841\pi\)
−0.506105 + 0.862472i \(0.668915\pi\)
\(632\) 2.00000 3.46410i 0.0795557 0.137795i
\(633\) 17.5830 + 30.4547i 0.698862 + 1.21046i
\(634\) −6.00000 −0.238290
\(635\) −21.8745 −0.868063
\(636\) 16.6458 + 28.8313i 0.660047 + 1.14323i
\(637\) 6.29150 + 10.8972i 0.249278 + 0.431763i
\(638\) −7.64575 −0.302698
\(639\) 10.8340 0.428586
\(640\) −0.822876 1.42526i −0.0325270 0.0563384i
\(641\) 6.43725 11.1497i 0.254256 0.440385i −0.710437 0.703761i \(-0.751503\pi\)
0.964693 + 0.263376i \(0.0848360\pi\)
\(642\) 20.2288 + 35.0372i 0.798365 + 1.38281i
\(643\) 3.26013 5.64671i 0.128567 0.222685i −0.794555 0.607193i \(-0.792296\pi\)
0.923122 + 0.384508i \(0.125629\pi\)
\(644\) 3.00000 5.19615i 0.118217 0.204757i
\(645\) 49.1660 1.93591
\(646\) 0 0
\(647\) −22.4575 −0.882896 −0.441448 0.897287i \(-0.645535\pi\)
−0.441448 + 0.897287i \(0.645535\pi\)
\(648\) −2.50000 + 4.33013i −0.0982093 + 0.170103i
\(649\) 18.4373 31.9343i 0.723726 1.25353i
\(650\) 2.29150 + 3.96900i 0.0898801 + 0.155677i
\(651\) 27.2288 47.1616i 1.06718 1.84841i
\(652\) −1.96863 3.40976i −0.0770974 0.133537i
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) −38.5830 −1.50871
\(655\) 1.59412 + 2.76110i 0.0622874 + 0.107885i
\(656\) −0.145751 0.252449i −0.00569063 0.00985646i
\(657\) 6.83399 0.266619
\(658\) −15.8745 −0.618853
\(659\) −9.29150 16.0934i −0.361946 0.626908i 0.626335 0.779554i \(-0.284554\pi\)
−0.988281 + 0.152646i \(0.951221\pi\)
\(660\) 10.1144 17.5186i 0.393702 0.681911i
\(661\) 8.11438 + 14.0545i 0.315613 + 0.546657i 0.979568 0.201115i \(-0.0644566\pi\)
−0.663955 + 0.747773i \(0.731123\pi\)
\(662\) −9.90588 + 17.1575i −0.385003 + 0.666845i
\(663\) 0 0
\(664\) −7.93725 −0.308025
\(665\) 0 0
\(666\) 1.41699 0.0549074
\(667\) −1.35425 + 2.34563i −0.0524367 + 0.0908231i
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 24.8856 + 43.1032i 0.962134 + 1.66646i
\(670\) 0.531373 0.920365i 0.0205287 0.0355568i
\(671\) 2.17712 + 3.77089i 0.0840470 + 0.145574i
\(672\) 9.64575 0.372093
\(673\) 13.8745 0.534823 0.267411 0.963582i \(-0.413832\pi\)
0.267411 + 0.963582i \(0.413832\pi\)
\(674\) 4.85425 + 8.40781i 0.186979 + 0.323857i
\(675\) −3.03137 5.25049i −0.116678 0.202092i
\(676\) −9.00000 −0.346154
\(677\) 11.4170 0.438791 0.219395 0.975636i \(-0.429592\pi\)
0.219395 + 0.975636i \(0.429592\pi\)
\(678\) −20.6144 35.7052i −0.791690 1.37125i
\(679\) −6.76013 + 11.7089i −0.259430 + 0.449346i
\(680\) 0 0
\(681\) 9.72876 16.8507i 0.372807 0.645720i
\(682\) −13.1144 + 22.7148i −0.502175 + 0.869793i
\(683\) 5.41699 0.207276 0.103638 0.994615i \(-0.466952\pi\)
0.103638 + 0.994615i \(0.466952\pi\)
\(684\) 0 0
\(685\) −25.6458 −0.979874
\(686\) −1.29150 + 2.23695i −0.0493098 + 0.0854071i
\(687\) 26.4575 45.8258i 1.00942 1.74836i
\(688\) −5.64575 9.77873i −0.215242 0.372811i
\(689\) 12.5830 21.7944i 0.479374 0.830301i
\(690\) −3.58301 6.20595i −0.136403 0.236256i
\(691\) 2.58301 0.0982622 0.0491311 0.998792i \(-0.484355\pi\)
0.0491311 + 0.998792i \(0.484355\pi\)
\(692\) 6.00000 0.228086
\(693\) 33.8745 + 58.6724i 1.28679 + 2.22878i
\(694\) −11.6144 20.1167i −0.440876 0.763619i
\(695\) −30.6863 −1.16400
\(696\) −4.35425 −0.165047
\(697\) 0 0
\(698\) 10.5830 18.3303i 0.400573 0.693812i
\(699\) 24.9686 + 43.2469i 0.944400 + 1.63575i
\(700\) 4.17712 7.23499i 0.157880 0.273457i
\(701\) −5.17712 + 8.96704i −0.195537 + 0.338681i −0.947077 0.321008i \(-0.895978\pi\)
0.751539 + 0.659688i \(0.229312\pi\)
\(702\) −5.29150 −0.199715
\(703\) 0 0
\(704\) −4.64575 −0.175093
\(705\) −9.47974 + 16.4194i −0.357028 + 0.618390i
\(706\) 6.43725 11.1497i 0.242269 0.419623i
\(707\) 24.8745 + 43.0839i 0.935502 + 1.62034i
\(708\) 10.5000 18.1865i 0.394614 0.683492i
\(709\) −1.82288 3.15731i −0.0684595 0.118575i 0.829764 0.558115i \(-0.188475\pi\)
−0.898223 + 0.439539i \(0.855142\pi\)
\(710\) 4.45751 0.167287
\(711\) 16.0000 0.600047
\(712\) 0 0
\(713\) 4.64575 + 8.04668i 0.173985 + 0.301350i
\(714\) 0 0
\(715\) −15.2915 −0.571870
\(716\) 2.03137 + 3.51844i 0.0759160 + 0.131490i
\(717\) −15.8745 + 27.4955i −0.592844 + 1.02684i
\(718\) −2.46863 4.27579i −0.0921283 0.159571i
\(719\) −1.35425 + 2.34563i −0.0505050 + 0.0874771i −0.890173 0.455623i \(-0.849416\pi\)
0.839668 + 0.543100i \(0.182750\pi\)
\(720\) 3.29150 5.70105i 0.122667 0.212466i
\(721\) 48.4575 1.80465
\(722\) 0 0
\(723\) −20.0627 −0.746142
\(724\) 11.1144 19.2507i 0.413063 0.715445i
\(725\) −1.88562 + 3.26599i −0.0700302 + 0.121296i
\(726\) −14.0000 24.2487i −0.519589 0.899954i
\(727\) −0.708497 + 1.22715i −0.0262767 + 0.0455126i −0.878865 0.477071i \(-0.841698\pi\)
0.852588 + 0.522584i \(0.175032\pi\)
\(728\) −3.64575 6.31463i −0.135121 0.234036i
\(729\) −41.0000 −1.51852
\(730\) 2.81176 0.104068
\(731\) 0 0
\(732\) 1.23987 + 2.14752i 0.0458269 + 0.0793746i
\(733\) −16.1033 −0.594788 −0.297394 0.954755i \(-0.596117\pi\)
−0.297394 + 0.954755i \(0.596117\pi\)
\(734\) −16.2288 −0.599014
\(735\) −13.6974 23.7246i −0.505236 0.875094i
\(736\) −0.822876 + 1.42526i −0.0303316 + 0.0525359i
\(737\) −1.50000 2.59808i −0.0552532 0.0957014i
\(738\) 0.583005 1.00979i 0.0214607 0.0371711i
\(739\) 16.9059 29.2818i 0.621893 1.07715i −0.367240 0.930126i \(-0.619697\pi\)
0.989133 0.147024i \(-0.0469694\pi\)
\(740\) 0.583005 0.0214317
\(741\) 0 0
\(742\) −45.8745 −1.68411
\(743\) −23.7601 + 41.1538i −0.871675 + 1.50978i −0.0114112 + 0.999935i \(0.503632\pi\)
−0.860263 + 0.509850i \(0.829701\pi\)
\(744\) −7.46863 + 12.9360i −0.273813 + 0.474258i
\(745\) 9.00000 + 15.5885i 0.329734 + 0.571117i
\(746\) 2.00000 3.46410i 0.0732252 0.126830i
\(747\) −15.8745 27.4955i −0.580818 1.00601i
\(748\) 0 0
\(749\) −55.7490 −2.03702
\(750\) −15.8745 27.4955i −0.579655 1.00399i
\(751\) −3.93725 6.81952i −0.143672 0.248848i 0.785204 0.619237i \(-0.212558\pi\)
−0.928877 + 0.370389i \(0.879225\pi\)
\(752\) 4.35425 0.158783
\(753\) −77.3320 −2.81814
\(754\) 1.64575 + 2.85052i 0.0599347 + 0.103810i
\(755\) −10.6458 + 18.4390i −0.387439 + 0.671063i
\(756\) 4.82288 + 8.35347i 0.175406 + 0.303813i
\(757\) 2.29150 3.96900i 0.0832861 0.144256i −0.821374 0.570391i \(-0.806792\pi\)
0.904660 + 0.426135i \(0.140125\pi\)
\(758\) −5.35425 + 9.27383i −0.194475 + 0.336841i
\(759\) −20.2288 −0.734257
\(760\) 0 0
\(761\) 42.8745 1.55420 0.777100 0.629377i \(-0.216690\pi\)
0.777100 + 0.629377i \(0.216690\pi\)
\(762\) −17.5830 + 30.4547i −0.636965 + 1.10326i
\(763\) 26.5830 46.0431i 0.962369 1.66687i
\(764\) −3.29150 5.70105i −0.119082 0.206257i
\(765\) 0 0
\(766\) −2.76013 4.78068i −0.0997275 0.172733i
\(767\) −15.8745 −0.573195
\(768\) −2.64575 −0.0954703
\(769\) −17.6458 30.5633i −0.636322 1.10214i −0.986233 0.165359i \(-0.947122\pi\)
0.349911 0.936783i \(-0.386212\pi\)
\(770\) 13.9373 + 24.1400i 0.502264 + 0.869946i
\(771\) 32.5203 1.17119
\(772\) −14.5830 −0.524854
\(773\) −2.46863 4.27579i −0.0887903 0.153789i 0.818210 0.574920i \(-0.194967\pi\)
−0.907000 + 0.421130i \(0.861633\pi\)
\(774\) 22.5830 39.1149i 0.811729 1.40596i
\(775\) 6.46863 + 11.2040i 0.232360 + 0.402459i
\(776\) 1.85425 3.21165i 0.0665636 0.115292i
\(777\) −1.70850 + 2.95920i −0.0612920 + 0.106161i
\(778\) −12.0000 −0.430221
\(779\) 0 0
\(780\) −8.70850 −0.311814
\(781\) 6.29150 10.8972i 0.225128 0.389933i
\(782\) 0 0
\(783\) −2.17712 3.77089i −0.0778041 0.134761i
\(784\) −3.14575 + 5.44860i −0.112348 + 0.194593i
\(785\) −8.70850 15.0836i −0.310820 0.538355i
\(786\) 5.12549 0.182820
\(787\) 42.5203 1.51568 0.757842 0.652438i \(-0.226254\pi\)
0.757842 + 0.652438i \(0.226254\pi\)
\(788\) 3.82288 + 6.62141i 0.136184 + 0.235878i
\(789\) −14.4686 25.0604i −0.515097 0.892174i
\(790\) 6.58301 0.234213
\(791\) 56.8118 2.01999
\(792\) −9.29150 16.0934i −0.330159 0.571852i
\(793\) 0.937254 1.62337i 0.0332829 0.0576476i
\(794\) 10.5314 + 18.2409i 0.373744 + 0.647344i
\(795\) −27.3948 + 47.4491i −0.971592 + 1.68285i
\(796\) 9.93725 17.2118i 0.352217 0.610057i
\(797\) 44.8118 1.58731 0.793657 0.608365i \(-0.208174\pi\)
0.793657 + 0.608365i \(0.208174\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.14575 + 1.98450i −0.0405084 + 0.0701627i
\(801\) 0 0
\(802\) −13.7915 23.8876i −0.486995 0.843500i
\(803\) 3.96863 6.87386i 0.140050 0.242573i
\(804\) −0.854249 1.47960i −0.0301270 0.0521815i
\(805\) 9.87451 0.348031
\(806\) 11.2915 0.397726
\(807\) 0 0
\(808\) −6.82288 11.8176i −0.240028 0.415741i
\(809\) −9.00000 −0.316423 −0.158212 0.987405i \(-0.550573\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(810\) −8.22876 −0.289129
\(811\) −15.6458 27.0992i −0.549397 0.951583i −0.998316 0.0580106i \(-0.981524\pi\)
0.448919 0.893572i \(-0.351809\pi\)
\(812\) 3.00000 5.19615i 0.105279 0.182349i
\(813\) 16.3431 + 28.3071i 0.573179 + 0.992775i
\(814\) 0.822876 1.42526i 0.0288418 0.0499554i
\(815\) 3.23987 5.61162i 0.113488 0.196566i
\(816\) 0 0
\(817\) 0 0
\(818\) −7.58301 −0.265134
\(819\) 14.5830 25.2585i 0.509571 0.882604i
\(820\) 0.239870 0.415468i 0.00837664 0.0145088i
\(821\) 3.00000 + 5.19615i 0.104701 + 0.181347i 0.913616 0.406578i \(-0.133278\pi\)
−0.808915 + 0.587925i \(0.799945\pi\)
\(822\) −20.6144 + 35.7052i −0.719009 + 1.24536i
\(823\) 15.9373 + 27.6041i 0.555538 + 0.962220i 0.997861 + 0.0653641i \(0.0208209\pi\)
−0.442324 + 0.896855i \(0.645846\pi\)
\(824\) −13.2915 −0.463031
\(825\) −28.1660 −0.980615
\(826\) 14.4686 + 25.0604i 0.503428 + 0.871963i
\(827\) −26.3229 45.5926i −0.915336 1.58541i −0.806408 0.591359i \(-0.798592\pi\)
−0.108928 0.994050i \(-0.534742\pi\)
\(828\) −6.58301 −0.228775
\(829\) 17.1660 0.596200 0.298100 0.954535i \(-0.403647\pi\)
0.298100 + 0.954535i \(0.403647\pi\)
\(830\) −6.53137 11.3127i −0.226707 0.392669i
\(831\) −36.4059 + 63.0568i −1.26291 + 2.18742i
\(832\) 1.00000 + 1.73205i 0.0346688 + 0.0600481i
\(833\) 0 0
\(834\) −24.6660 + 42.7228i −0.854114 + 1.47937i
\(835\) −19.7490 −0.683443
\(836\) 0 0
\(837\) −14.9373 −0.516307
\(838\) −15.8745 + 27.4955i −0.548376 + 0.949815i
\(839\) −20.7601 + 35.9576i −0.716719 + 1.24139i 0.245573 + 0.969378i \(0.421024\pi\)
−0.962293 + 0.272016i \(0.912310\pi\)
\(840\) 7.93725 + 13.7477i 0.273861 + 0.474342i
\(841\) 13.1458 22.7691i 0.453302 0.785142i
\(842\) 12.4059 + 21.4876i 0.427535 + 0.740512i
\(843\) 67.3542 2.31980
\(844\) 13.2915 0.457512
\(845\) −7.40588 12.8274i −0.254770 0.441275i
\(846\) 8.70850 + 15.0836i 0.299404 + 0.518583i
\(847\) 38.5830 1.32573
\(848\) 12.5830 0.432102
\(849\) 40.5405 + 70.2182i 1.39135 + 2.40988i
\(850\) 0 0
\(851\) −0.291503 0.504897i −0.00999258 0.0173077i
\(852\) 3.58301 6.20595i 0.122752 0.212612i
\(853\) −4.29150 + 7.43310i −0.146938 + 0.254505i −0.930094 0.367321i \(-0.880275\pi\)
0.783156 + 0.621825i \(0.213609\pi\)
\(854\) −3.41699 −0.116927
\(855\) 0 0
\(856\) 15.2915 0.522653
\(857\) 10.5000 18.1865i 0.358673 0.621240i −0.629066 0.777352i \(-0.716563\pi\)
0.987739 + 0.156112i \(0.0498959\pi\)
\(858\) −12.2915 + 21.2895i −0.419625 + 0.726812i
\(859\) −6.61438 11.4564i −0.225680 0.390889i 0.730843 0.682545i \(-0.239127\pi\)
−0.956523 + 0.291656i \(0.905794\pi\)
\(860\) 9.29150 16.0934i 0.316838 0.548779i
\(861\) 1.40588 + 2.43506i 0.0479123 + 0.0829865i
\(862\) 27.8745 0.949410
\(863\) 31.0627 1.05739 0.528694 0.848812i \(-0.322682\pi\)
0.528694 + 0.848812i \(0.322682\pi\)
\(864\) −1.32288 2.29129i −0.0450051 0.0779512i
\(865\) 4.93725 + 8.55157i 0.167872 + 0.290762i
\(866\) 17.8745 0.607401
\(867\) 44.9778 1.52753
\(868\) −10.2915 17.8254i −0.349316 0.605034i
\(869\) 9.29150 16.0934i 0.315193 0.545930i
\(870\) −3.58301 6.20595i −0.121475 0.210401i
\(871\) −0.645751 + 1.11847i −0.0218804 + 0.0378980i
\(872\) −7.29150 + 12.6293i −0.246921 + 0.427680i
\(873\) 14.8340 0.502054
\(874\) 0 0
\(875\) 43.7490 1.47899
\(876\) 2.26013 3.91466i 0.0763627 0.132264i
\(877\) −20.8229 + 36.0663i −0.703139 + 1.21787i 0.264221 + 0.964462i \(0.414885\pi\)
−0.967359 + 0.253409i \(0.918448\pi\)
\(878\) −5.40588 9.36326i −0.182440 0.315995i
\(879\) −38.2804 + 66.3036i −1.29117 + 2.23636i
\(880\) −3.82288 6.62141i −0.128869 0.223208i
\(881\) −36.8745 −1.24233 −0.621167 0.783678i \(-0.713341\pi\)
−0.621167 + 0.783678i \(0.713341\pi\)
\(882\) −25.1660 −0.847384
\(883\) 14.1974 + 24.5906i 0.477780 + 0.827539i 0.999676 0.0254701i \(-0.00810828\pi\)
−0.521896 + 0.853009i \(0.674775\pi\)
\(884\) 0 0
\(885\) 34.5608 1.16175
\(886\) −10.6458 −0.357651
\(887\) −8.70850 15.0836i −0.292403 0.506456i 0.681975 0.731376i \(-0.261121\pi\)
−0.974377 + 0.224919i \(0.927788\pi\)
\(888\) 0.468627 0.811686i 0.0157261 0.0272384i
\(889\) −24.2288 41.9654i −0.812606 1.40748i
\(890\) 0 0
\(891\) −11.6144 + 20.1167i −0.389096 + 0.673935i
\(892\) 18.8118 0.629864
\(893\) 0 0
\(894\) 28.9373 0.967807
\(895\) −3.34313 + 5.79048i −0.111749 + 0.193554i
\(896\) 1.82288 3.15731i 0.0608980 0.105478i
\(897\) 4.35425 + 7.54178i 0.145384 + 0.251813i
\(898\) 12.1458 21.0371i 0.405309 0.702016i
\(899\) 4.64575 + 8.04668i 0.154944 + 0.268372i
\(900\) −9.16601 −0.305534
\(901\) 0 0
\(902\) −0.677124 1.17281i −0.0225458 0.0390504i
\(903\) 54.4575 + 94.3232i 1.81223 + 3.13888i
\(904\) −15.5830 −0.518283
\(905\) 36.5830 1.21606
\(906\) 17.1144 + 29.6430i 0.568587 + 0.984822i
\(907\) 19.9686 34.5867i 0.663047 1.14843i −0.316763 0.948505i \(-0.602596\pi\)
0.979811 0.199927i \(-0.0640706\pi\)
\(908\) −3.67712 6.36897i −0.122030 0.211362i
\(909\) 27.2915 47.2703i 0.905202 1.56786i
\(910\) 6.00000 10.3923i 0.198898 0.344502i
\(911\) −16.9373 −0.561156 −0.280578 0.959831i \(-0.590526\pi\)
−0.280578 + 0.959831i \(0.590526\pi\)
\(912\) 0 0
\(913\) −36.8745 −1.22037
\(914\) 16.4373 28.4702i 0.543696 0.941709i
\(915\) −2.04052 + 3.53428i −0.0674575 + 0.116840i
\(916\) −10.0000 17.3205i −0.330409 0.572286i
\(917\) −3.53137 + 6.11652i −0.116616 + 0.201985i
\(918\) 0 0
\(919\) −19.8745 −0.655600 −0.327800 0.944747i \(-0.606307\pi\)
−0.327800 + 0.944747i \(0.606307\pi\)
\(920\) −2.70850 −0.0892965
\(921\) −0.854249 1.47960i −0.0281485 0.0487545i
\(922\) 9.58301 + 16.5983i 0.315599 + 0.546634i
\(923\) −5.41699 −0.178303
\(924\) 44.8118 1.47420
\(925\) −0.405881 0.703006i −0.0133453 0.0231147i
\(926\) −19.2288 + 33.3052i −0.631896 + 1.09448i
\(927\) −26.5830 46.0431i −0.873100 1.51225i
\(928\) −0.822876 + 1.42526i −0.0270122 + 0.0467865i
\(929\) 4.79150 8.29913i 0.157204 0.272285i −0.776655 0.629926i \(-0.783085\pi\)
0.933859 + 0.357640i \(0.116419\pi\)
\(930\) −24.5830 −0.806108
\(931\) 0 0
\(932\) 18.8745 0.618255
\(933\) 18.0516 31.2663i 0.590984 1.02361i
\(934\) −9.67712 + 16.7613i −0.316645 + 0.548446i
\(935\) 0 0
\(936\) −4.00000 + 6.92820i −0.130744 + 0.226455i
\(937\) −3.56275 6.17086i −0.116390 0.201593i 0.801945 0.597398i \(-0.203799\pi\)
−0.918334 + 0.395805i \(0.870466\pi\)
\(938\) 2.35425 0.0768689
\(939\) −23.4797 −0.766232
\(940\) 3.58301 + 6.20595i 0.116865 + 0.202416i
\(941\) 8.41699 + 14.5787i 0.274386 + 0.475251i 0.969980 0.243184i \(-0.0781920\pi\)
−0.695594 + 0.718435i \(0.744859\pi\)
\(942\) −28.0000 −0.912289
\(943\) −0.479741 −0.0156225
\(944\) −3.96863 6.87386i −0.129168 0.223725i
\(945\) −7.93725 + 13.7477i −0.258199 + 0.447214i
\(946\) −26.2288 45.4295i −0.852770 1.47704i
\(947\) 3.87451 6.71084i 0.125905 0.218073i −0.796182 0.605058i \(-0.793150\pi\)
0.922086 + 0.386985i \(0.126483\pi\)
\(948\) 5.29150 9.16515i 0.171860 0.297670i
\(949\) −3.41699 −0.110920
\(950\) 0 0
\(951\) −15.8745 −0.514766
\(952\) 0 0
\(953\) −6.72876 + 11.6545i −0.217966 + 0.377528i −0.954186 0.299214i \(-0.903275\pi\)
0.736220 + 0.676742i \(0.236609\pi\)
\(954\) 25.1660 + 43.5888i 0.814780 + 1.41124i
\(955\) 5.41699 9.38251i 0.175290 0.303611i
\(956\) 6.00000 + 10.3923i 0.194054 + 0.336111i
\(957\) −20.2288 −0.653903
\(958\) −6.58301 −0.212687
\(959\) −28.4059 49.2004i −0.917274 1.58876i
\(960\) −2.17712 3.77089i −0.0702664 0.121705i
\(961\) 0.874508 0.0282099
\(962\) −0.708497 −0.0228429
\(963\) 30.5830 + 52.9713i 0.985524 + 1.70698i
\(964\) −3.79150 + 6.56708i −0.122116 + 0.211511i
\(965\) −12.0000 20.7846i −0.386294 0.669080i
\(966\) 7.93725 13.7477i 0.255377 0.442326i
\(967\) 6.64575 11.5108i 0.213713 0.370162i −0.739161 0.673529i \(-0.764778\pi\)
0.952874 + 0.303367i \(0.0981109\pi\)
\(968\) −10.5830 −0.340151
\(969\) 0 0
\(970\) 6.10326 0.195964
\(971\) −27.1974 + 47.1073i −0.872806 + 1.51174i −0.0137234 + 0.999906i \(0.504368\pi\)
−0.859082 + 0.511838i \(0.828965\pi\)
\(972\) −10.5830 + 18.3303i −0.339450 + 0.587945i
\(973\) −33.9889 58.8705i −1.08963 1.88730i
\(974\) −2.11438 + 3.66221i −0.0677491 + 0.117345i
\(975\) 6.06275 + 10.5010i 0.194163 + 0.336301i
\(976\) 0.937254 0.0300008
\(977\) 7.45751 0.238587 0.119293 0.992859i \(-0.461937\pi\)
0.119293 + 0.992859i \(0.461937\pi\)
\(978\) −5.20850 9.02138i −0.166549 0.288472i
\(979\) 0 0
\(980\) −10.3542 −0.330754
\(981\) −58.3320 −1.86240
\(982\) 19.6458 + 34.0274i 0.626921 + 1.08586i
\(983\) 15.8745 27.4955i 0.506318 0.876969i −0.493655 0.869658i \(-0.664339\pi\)
0.999973 0.00731102i \(-0.00232719\pi\)
\(984\) −0.385622 0.667916i −0.0122932 0.0212924i
\(985\) −6.29150 + 10.8972i −0.200464 + 0.347214i
\(986\) 0 0
\(987\) −42.0000 −1.33687
\(988\) 0 0
\(989\) −18.5830 −0.590905
\(990\) 15.2915 26.4857i 0.485996 0.841770i
\(991\) −1.41699 + 2.45431i −0.0450123 + 0.0779636i −0.887654 0.460511i \(-0.847666\pi\)
0.842641 + 0.538475i \(0.180999\pi\)
\(992\) 2.82288 + 4.88936i 0.0896264 + 0.155237i
\(993\) −26.2085 + 45.3944i −0.831702 + 1.44055i
\(994\) 4.93725 + 8.55157i 0.156600 + 0.271239i
\(995\) 32.7085 1.03693
\(996\) −21.0000 −0.665410
\(997\) −8.11438 14.0545i −0.256985 0.445111i 0.708448 0.705763i \(-0.249396\pi\)
−0.965433 + 0.260652i \(0.916062\pi\)
\(998\) −2.38562 4.13202i −0.0755155 0.130797i
\(999\) 0.937254 0.0296534
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 722.2.c.j.429.2 4
19.2 odd 18 722.2.e.n.595.1 12
19.3 odd 18 722.2.e.n.99.2 12
19.4 even 9 722.2.e.o.423.1 12
19.5 even 9 722.2.e.o.389.1 12
19.6 even 9 722.2.e.o.415.2 12
19.7 even 3 inner 722.2.c.j.653.2 4
19.8 odd 6 722.2.a.j.1.2 2
19.9 even 9 722.2.e.o.245.1 12
19.10 odd 18 722.2.e.n.245.2 12
19.11 even 3 722.2.a.g.1.1 2
19.12 odd 6 38.2.c.b.7.1 4
19.13 odd 18 722.2.e.n.415.1 12
19.14 odd 18 722.2.e.n.389.2 12
19.15 odd 18 722.2.e.n.423.2 12
19.16 even 9 722.2.e.o.99.1 12
19.17 even 9 722.2.e.o.595.2 12
19.18 odd 2 38.2.c.b.11.1 yes 4
57.8 even 6 6498.2.a.ba.1.2 2
57.11 odd 6 6498.2.a.bg.1.2 2
57.50 even 6 342.2.g.f.235.1 4
57.56 even 2 342.2.g.f.163.1 4
76.11 odd 6 5776.2.a.z.1.2 2
76.27 even 6 5776.2.a.ba.1.1 2
76.31 even 6 304.2.i.e.273.2 4
76.75 even 2 304.2.i.e.49.2 4
95.12 even 12 950.2.j.g.349.3 8
95.18 even 4 950.2.j.g.49.3 8
95.37 even 4 950.2.j.g.49.2 8
95.69 odd 6 950.2.e.k.501.2 4
95.88 even 12 950.2.j.g.349.2 8
95.94 odd 2 950.2.e.k.201.2 4
152.37 odd 2 1216.2.i.l.961.2 4
152.69 odd 6 1216.2.i.l.577.2 4
152.75 even 2 1216.2.i.k.961.1 4
152.107 even 6 1216.2.i.k.577.1 4
228.107 odd 6 2736.2.s.v.577.1 4
228.227 odd 2 2736.2.s.v.1873.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.c.b.7.1 4 19.12 odd 6
38.2.c.b.11.1 yes 4 19.18 odd 2
304.2.i.e.49.2 4 76.75 even 2
304.2.i.e.273.2 4 76.31 even 6
342.2.g.f.163.1 4 57.56 even 2
342.2.g.f.235.1 4 57.50 even 6
722.2.a.g.1.1 2 19.11 even 3
722.2.a.j.1.2 2 19.8 odd 6
722.2.c.j.429.2 4 1.1 even 1 trivial
722.2.c.j.653.2 4 19.7 even 3 inner
722.2.e.n.99.2 12 19.3 odd 18
722.2.e.n.245.2 12 19.10 odd 18
722.2.e.n.389.2 12 19.14 odd 18
722.2.e.n.415.1 12 19.13 odd 18
722.2.e.n.423.2 12 19.15 odd 18
722.2.e.n.595.1 12 19.2 odd 18
722.2.e.o.99.1 12 19.16 even 9
722.2.e.o.245.1 12 19.9 even 9
722.2.e.o.389.1 12 19.5 even 9
722.2.e.o.415.2 12 19.6 even 9
722.2.e.o.423.1 12 19.4 even 9
722.2.e.o.595.2 12 19.17 even 9
950.2.e.k.201.2 4 95.94 odd 2
950.2.e.k.501.2 4 95.69 odd 6
950.2.j.g.49.2 8 95.37 even 4
950.2.j.g.49.3 8 95.18 even 4
950.2.j.g.349.2 8 95.88 even 12
950.2.j.g.349.3 8 95.12 even 12
1216.2.i.k.577.1 4 152.107 even 6
1216.2.i.k.961.1 4 152.75 even 2
1216.2.i.l.577.2 4 152.69 odd 6
1216.2.i.l.961.2 4 152.37 odd 2
2736.2.s.v.577.1 4 228.107 odd 6
2736.2.s.v.1873.1 4 228.227 odd 2
5776.2.a.z.1.2 2 76.11 odd 6
5776.2.a.ba.1.1 2 76.27 even 6
6498.2.a.ba.1.2 2 57.8 even 6
6498.2.a.bg.1.2 2 57.11 odd 6