Properties

Label 650.2.n.a.199.2
Level $650$
Weight $2$
Character 650.199
Analytic conductor $5.190$
Analytic rank $1$
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] = [650,2,Mod(49,650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(650, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("650.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.n (of order \(6\), 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: \(5.19027613138\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) 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 130)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 650.199
Dual form 650.2.n.a.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.633975 - 0.366025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.633975 - 0.366025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-1.23205 - 2.13397i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.633975 - 0.366025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.633975 - 0.366025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-1.23205 - 2.13397i) q^{9} +(2.59808 + 1.50000i) q^{11} +0.732051i q^{12} +(0.866025 + 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-7.09808 + 4.09808i) q^{17} +2.46410 q^{18} +(0.401924 - 0.232051i) q^{19} +2.19615i q^{21} +(-2.59808 + 1.50000i) q^{22} +(-8.19615 - 4.73205i) q^{23} +(-0.633975 - 0.366025i) q^{24} +(-3.46410 - 1.00000i) q^{26} +4.00000i q^{27} +(-1.50000 + 2.59808i) q^{28} +(-1.26795 + 2.19615i) q^{29} +4.73205i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.09808 - 1.90192i) q^{33} -8.19615i q^{34} +(-1.23205 + 2.13397i) q^{36} +(-0.401924 + 0.696152i) q^{37} +0.464102i q^{38} +(0.732051 - 2.53590i) q^{39} +(-9.00000 - 5.19615i) q^{41} +(-1.90192 - 1.09808i) q^{42} +(1.73205 - 1.00000i) q^{43} -3.00000i q^{44} +(8.19615 - 4.73205i) q^{46} +3.00000 q^{47} +(0.633975 - 0.366025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +6.00000 q^{51} +(2.59808 - 2.50000i) q^{52} +0.464102i q^{53} +(-3.46410 - 2.00000i) q^{54} +(-1.50000 - 2.59808i) q^{56} -0.339746 q^{57} +(-1.26795 - 2.19615i) q^{58} +(-9.00000 + 5.19615i) q^{59} +(-3.09808 - 5.36603i) q^{61} +(-4.09808 - 2.36603i) q^{62} +(-3.69615 + 6.40192i) q^{63} +1.00000 q^{64} +2.19615 q^{66} +(7.09808 + 4.09808i) q^{68} +(3.46410 + 6.00000i) q^{69} +(-5.19615 + 3.00000i) q^{71} +(-1.23205 - 2.13397i) q^{72} -11.6603 q^{73} +(-0.401924 - 0.696152i) q^{74} +(-0.401924 - 0.232051i) q^{76} -9.00000i q^{77} +(1.83013 + 1.90192i) q^{78} +4.19615 q^{79} +(-2.23205 + 3.86603i) q^{81} +(9.00000 - 5.19615i) q^{82} +8.19615 q^{83} +(1.90192 - 1.09808i) q^{84} +2.00000i q^{86} +(1.60770 - 0.928203i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-5.89230 - 3.40192i) q^{89} +(7.79423 - 7.50000i) q^{91} +9.46410i q^{92} +(1.73205 - 3.00000i) q^{93} +(-1.50000 + 2.59808i) q^{94} +0.732051i q^{96} +(-4.56218 - 7.90192i) q^{97} +(-1.00000 - 1.73205i) q^{98} -7.39230i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9} + 12 q^{14} - 2 q^{16} - 18 q^{17} - 4 q^{18} + 12 q^{19} - 12 q^{23} - 6 q^{24} - 6 q^{28} - 12 q^{29} - 2 q^{32} + 6 q^{33} + 2 q^{36} - 12 q^{37} - 4 q^{39} - 36 q^{41} - 18 q^{42} + 12 q^{46} + 12 q^{47} + 6 q^{48} - 4 q^{49} + 24 q^{51} - 6 q^{56} - 36 q^{57} - 12 q^{58} - 36 q^{59} - 2 q^{61} - 6 q^{62} + 6 q^{63} + 4 q^{64} - 12 q^{66} + 18 q^{68} + 2 q^{72} - 12 q^{73} - 12 q^{74} - 12 q^{76} - 10 q^{78} - 4 q^{79} - 2 q^{81} + 36 q^{82} + 12 q^{83} + 18 q^{84} + 48 q^{87} + 18 q^{89} - 6 q^{94} + 6 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −0.633975 0.366025i −0.366025 0.211325i 0.305695 0.952129i \(-0.401111\pi\)
−0.671721 + 0.740805i \(0.734444\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.633975 0.366025i 0.258819 0.149429i
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.23205 2.13397i −0.410684 0.711325i
\(10\) 0 0
\(11\) 2.59808 + 1.50000i 0.783349 + 0.452267i 0.837616 0.546259i \(-0.183949\pi\)
−0.0542666 + 0.998526i \(0.517282\pi\)
\(12\) 0.732051i 0.211325i
\(13\) 0.866025 + 3.50000i 0.240192 + 0.970725i
\(14\) 3.00000 0.801784
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −7.09808 + 4.09808i −1.72154 + 0.993929i −0.805759 + 0.592244i \(0.798242\pi\)
−0.915778 + 0.401685i \(0.868425\pi\)
\(18\) 2.46410 0.580794
\(19\) 0.401924 0.232051i 0.0922076 0.0532361i −0.453187 0.891415i \(-0.649713\pi\)
0.545395 + 0.838179i \(0.316380\pi\)
\(20\) 0 0
\(21\) 2.19615i 0.479240i
\(22\) −2.59808 + 1.50000i −0.553912 + 0.319801i
\(23\) −8.19615 4.73205i −1.70902 0.986701i −0.935781 0.352581i \(-0.885304\pi\)
−0.773234 0.634120i \(-0.781362\pi\)
\(24\) −0.633975 0.366025i −0.129410 0.0747146i
\(25\) 0 0
\(26\) −3.46410 1.00000i −0.679366 0.196116i
\(27\) 4.00000i 0.769800i
\(28\) −1.50000 + 2.59808i −0.283473 + 0.490990i
\(29\) −1.26795 + 2.19615i −0.235452 + 0.407815i −0.959404 0.282035i \(-0.908990\pi\)
0.723952 + 0.689851i \(0.242324\pi\)
\(30\) 0 0
\(31\) 4.73205i 0.849901i 0.905216 + 0.424951i \(0.139709\pi\)
−0.905216 + 0.424951i \(0.860291\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.09808 1.90192i −0.191151 0.331082i
\(34\) 8.19615i 1.40563i
\(35\) 0 0
\(36\) −1.23205 + 2.13397i −0.205342 + 0.355662i
\(37\) −0.401924 + 0.696152i −0.0660759 + 0.114447i −0.897171 0.441684i \(-0.854381\pi\)
0.831095 + 0.556131i \(0.187715\pi\)
\(38\) 0.464102i 0.0752872i
\(39\) 0.732051 2.53590i 0.117222 0.406069i
\(40\) 0 0
\(41\) −9.00000 5.19615i −1.40556 0.811503i −0.410608 0.911812i \(-0.634683\pi\)
−0.994956 + 0.100309i \(0.968017\pi\)
\(42\) −1.90192 1.09808i −0.293473 0.169437i
\(43\) 1.73205 1.00000i 0.264135 0.152499i −0.362084 0.932145i \(-0.617935\pi\)
0.626219 + 0.779647i \(0.284601\pi\)
\(44\) 3.00000i 0.452267i
\(45\) 0 0
\(46\) 8.19615 4.73205i 1.20846 0.697703i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0.633975 0.366025i 0.0915064 0.0528312i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) 2.59808 2.50000i 0.360288 0.346688i
\(53\) 0.464102i 0.0637493i 0.999492 + 0.0318746i \(0.0101477\pi\)
−0.999492 + 0.0318746i \(0.989852\pi\)
\(54\) −3.46410 2.00000i −0.471405 0.272166i
\(55\) 0 0
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) −0.339746 −0.0450005
\(58\) −1.26795 2.19615i −0.166490 0.288369i
\(59\) −9.00000 + 5.19615i −1.17170 + 0.676481i −0.954080 0.299552i \(-0.903163\pi\)
−0.217620 + 0.976034i \(0.569829\pi\)
\(60\) 0 0
\(61\) −3.09808 5.36603i −0.396668 0.687049i 0.596645 0.802506i \(-0.296500\pi\)
−0.993313 + 0.115456i \(0.963167\pi\)
\(62\) −4.09808 2.36603i −0.520456 0.300486i
\(63\) −3.69615 + 6.40192i −0.465671 + 0.806567i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.19615 0.270328
\(67\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(68\) 7.09808 + 4.09808i 0.860768 + 0.496965i
\(69\) 3.46410 + 6.00000i 0.417029 + 0.722315i
\(70\) 0 0
\(71\) −5.19615 + 3.00000i −0.616670 + 0.356034i −0.775571 0.631260i \(-0.782538\pi\)
0.158901 + 0.987294i \(0.449205\pi\)
\(72\) −1.23205 2.13397i −0.145199 0.251491i
\(73\) −11.6603 −1.36473 −0.682365 0.731012i \(-0.739048\pi\)
−0.682365 + 0.731012i \(0.739048\pi\)
\(74\) −0.401924 0.696152i −0.0467227 0.0809261i
\(75\) 0 0
\(76\) −0.401924 0.232051i −0.0461038 0.0266181i
\(77\) 9.00000i 1.02565i
\(78\) 1.83013 + 1.90192i 0.207221 + 0.215350i
\(79\) 4.19615 0.472104 0.236052 0.971740i \(-0.424146\pi\)
0.236052 + 0.971740i \(0.424146\pi\)
\(80\) 0 0
\(81\) −2.23205 + 3.86603i −0.248006 + 0.429558i
\(82\) 9.00000 5.19615i 0.993884 0.573819i
\(83\) 8.19615 0.899645 0.449822 0.893118i \(-0.351487\pi\)
0.449822 + 0.893118i \(0.351487\pi\)
\(84\) 1.90192 1.09808i 0.207517 0.119810i
\(85\) 0 0
\(86\) 2.00000i 0.215666i
\(87\) 1.60770 0.928203i 0.172363 0.0995138i
\(88\) 2.59808 + 1.50000i 0.276956 + 0.159901i
\(89\) −5.89230 3.40192i −0.624583 0.360603i 0.154068 0.988060i \(-0.450762\pi\)
−0.778651 + 0.627457i \(0.784096\pi\)
\(90\) 0 0
\(91\) 7.79423 7.50000i 0.817057 0.786214i
\(92\) 9.46410i 0.986701i
\(93\) 1.73205 3.00000i 0.179605 0.311086i
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 0 0
\(96\) 0.732051i 0.0747146i
\(97\) −4.56218 7.90192i −0.463219 0.802319i 0.535900 0.844281i \(-0.319972\pi\)
−0.999119 + 0.0419625i \(0.986639\pi\)
\(98\) −1.00000 1.73205i −0.101015 0.174964i
\(99\) 7.39230i 0.742955i
\(100\) 0 0
\(101\) −5.36603 + 9.29423i −0.533939 + 0.924810i 0.465274 + 0.885167i \(0.345956\pi\)
−0.999214 + 0.0396438i \(0.987378\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) 9.19615i 0.906124i −0.891479 0.453062i \(-0.850332\pi\)
0.891479 0.453062i \(-0.149668\pi\)
\(104\) 0.866025 + 3.50000i 0.0849208 + 0.343203i
\(105\) 0 0
\(106\) −0.401924 0.232051i −0.0390383 0.0225388i
\(107\) 15.2942 + 8.83013i 1.47855 + 0.853641i 0.999706 0.0242598i \(-0.00772291\pi\)
0.478843 + 0.877900i \(0.341056\pi\)
\(108\) 3.46410 2.00000i 0.333333 0.192450i
\(109\) 8.53590i 0.817591i 0.912626 + 0.408795i \(0.134051\pi\)
−0.912626 + 0.408795i \(0.865949\pi\)
\(110\) 0 0
\(111\) 0.509619 0.294229i 0.0483709 0.0279269i
\(112\) 3.00000 0.283473
\(113\) 6.00000 3.46410i 0.564433 0.325875i −0.190490 0.981689i \(-0.561008\pi\)
0.754923 + 0.655814i \(0.227674\pi\)
\(114\) 0.169873 0.294229i 0.0159101 0.0275570i
\(115\) 0 0
\(116\) 2.53590 0.235452
\(117\) 6.40192 6.16025i 0.591858 0.569516i
\(118\) 10.3923i 0.956689i
\(119\) 21.2942 + 12.2942i 1.95204 + 1.12701i
\(120\) 0 0
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) 6.19615 0.560973
\(123\) 3.80385 + 6.58846i 0.342981 + 0.594061i
\(124\) 4.09808 2.36603i 0.368018 0.212475i
\(125\) 0 0
\(126\) −3.69615 6.40192i −0.329279 0.570329i
\(127\) 9.35641 + 5.40192i 0.830247 + 0.479343i 0.853937 0.520376i \(-0.174208\pi\)
−0.0236904 + 0.999719i \(0.507542\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.46410 −0.128907
\(130\) 0 0
\(131\) 6.12436 0.535087 0.267544 0.963546i \(-0.413788\pi\)
0.267544 + 0.963546i \(0.413788\pi\)
\(132\) −1.09808 + 1.90192i −0.0955753 + 0.165541i
\(133\) −1.20577 0.696152i −0.104554 0.0603641i
\(134\) 0 0
\(135\) 0 0
\(136\) −7.09808 + 4.09808i −0.608655 + 0.351407i
\(137\) −1.09808 1.90192i −0.0938150 0.162492i 0.815298 0.579041i \(-0.196573\pi\)
−0.909113 + 0.416549i \(0.863240\pi\)
\(138\) −6.92820 −0.589768
\(139\) 0.598076 + 1.03590i 0.0507282 + 0.0878638i 0.890274 0.455424i \(-0.150512\pi\)
−0.839546 + 0.543288i \(0.817179\pi\)
\(140\) 0 0
\(141\) −1.90192 1.09808i −0.160171 0.0924747i
\(142\) 6.00000i 0.503509i
\(143\) −3.00000 + 10.3923i −0.250873 + 0.869048i
\(144\) 2.46410 0.205342
\(145\) 0 0
\(146\) 5.83013 10.0981i 0.482505 0.835723i
\(147\) 1.26795 0.732051i 0.104579 0.0603785i
\(148\) 0.803848 0.0660759
\(149\) −5.19615 + 3.00000i −0.425685 + 0.245770i −0.697507 0.716578i \(-0.745707\pi\)
0.271821 + 0.962348i \(0.412374\pi\)
\(150\) 0 0
\(151\) 23.6603i 1.92544i −0.270492 0.962722i \(-0.587187\pi\)
0.270492 0.962722i \(-0.412813\pi\)
\(152\) 0.401924 0.232051i 0.0326003 0.0188218i
\(153\) 17.4904 + 10.0981i 1.41401 + 0.816381i
\(154\) 7.79423 + 4.50000i 0.628077 + 0.362620i
\(155\) 0 0
\(156\) −2.56218 + 0.633975i −0.205138 + 0.0507586i
\(157\) 13.0000i 1.03751i 0.854922 + 0.518756i \(0.173605\pi\)
−0.854922 + 0.518756i \(0.826395\pi\)
\(158\) −2.09808 + 3.63397i −0.166914 + 0.289103i
\(159\) 0.169873 0.294229i 0.0134718 0.0233338i
\(160\) 0 0
\(161\) 28.3923i 2.23763i
\(162\) −2.23205 3.86603i −0.175366 0.303744i
\(163\) −5.36603 9.29423i −0.420300 0.727980i 0.575669 0.817683i \(-0.304742\pi\)
−0.995969 + 0.0897026i \(0.971408\pi\)
\(164\) 10.3923i 0.811503i
\(165\) 0 0
\(166\) −4.09808 + 7.09808i −0.318072 + 0.550918i
\(167\) 1.50000 2.59808i 0.116073 0.201045i −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(168\) 2.19615i 0.169437i
\(169\) −11.5000 + 6.06218i −0.884615 + 0.466321i
\(170\) 0 0
\(171\) −0.990381 0.571797i −0.0757363 0.0437264i
\(172\) −1.73205 1.00000i −0.132068 0.0762493i
\(173\) −12.9904 + 7.50000i −0.987640 + 0.570214i −0.904568 0.426329i \(-0.859807\pi\)
−0.0830722 + 0.996544i \(0.526473\pi\)
\(174\) 1.85641i 0.140734i
\(175\) 0 0
\(176\) −2.59808 + 1.50000i −0.195837 + 0.113067i
\(177\) 7.60770 0.571829
\(178\) 5.89230 3.40192i 0.441647 0.254985i
\(179\) −4.73205 + 8.19615i −0.353690 + 0.612609i −0.986893 0.161377i \(-0.948407\pi\)
0.633203 + 0.773986i \(0.281740\pi\)
\(180\) 0 0
\(181\) 14.5885 1.08435 0.542176 0.840265i \(-0.317601\pi\)
0.542176 + 0.840265i \(0.317601\pi\)
\(182\) 2.59808 + 10.5000i 0.192582 + 0.778312i
\(183\) 4.53590i 0.335303i
\(184\) −8.19615 4.73205i −0.604228 0.348851i
\(185\) 0 0
\(186\) 1.73205 + 3.00000i 0.127000 + 0.219971i
\(187\) −24.5885 −1.79809
\(188\) −1.50000 2.59808i −0.109399 0.189484i
\(189\) 10.3923 6.00000i 0.755929 0.436436i
\(190\) 0 0
\(191\) 11.3660 + 19.6865i 0.822417 + 1.42447i 0.903878 + 0.427791i \(0.140708\pi\)
−0.0814609 + 0.996677i \(0.525959\pi\)
\(192\) −0.633975 0.366025i −0.0457532 0.0264156i
\(193\) 8.19615 14.1962i 0.589972 1.02186i −0.404263 0.914643i \(-0.632472\pi\)
0.994235 0.107219i \(-0.0341945\pi\)
\(194\) 9.12436 0.655091
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 10.7942 18.6962i 0.769057 1.33205i −0.169018 0.985613i \(-0.554060\pi\)
0.938075 0.346433i \(-0.112607\pi\)
\(198\) 6.40192 + 3.69615i 0.454965 + 0.262674i
\(199\) −3.19615 5.53590i −0.226569 0.392429i 0.730220 0.683212i \(-0.239418\pi\)
−0.956789 + 0.290783i \(0.906084\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −5.36603 9.29423i −0.377552 0.653940i
\(203\) 7.60770 0.533956
\(204\) −3.00000 5.19615i −0.210042 0.363803i
\(205\) 0 0
\(206\) 7.96410 + 4.59808i 0.554885 + 0.320363i
\(207\) 23.3205i 1.62089i
\(208\) −3.46410 1.00000i −0.240192 0.0693375i
\(209\) 1.39230 0.0963077
\(210\) 0 0
\(211\) 8.79423 15.2321i 0.605420 1.04862i −0.386565 0.922262i \(-0.626339\pi\)
0.991985 0.126356i \(-0.0403280\pi\)
\(212\) 0.401924 0.232051i 0.0276042 0.0159373i
\(213\) 4.39230 0.300956
\(214\) −15.2942 + 8.83013i −1.04549 + 0.603615i
\(215\) 0 0
\(216\) 4.00000i 0.272166i
\(217\) 12.2942 7.09808i 0.834587 0.481849i
\(218\) −7.39230 4.26795i −0.500670 0.289062i
\(219\) 7.39230 + 4.26795i 0.499526 + 0.288401i
\(220\) 0 0
\(221\) −20.4904 21.2942i −1.37833 1.43240i
\(222\) 0.588457i 0.0394947i
\(223\) 3.23205 5.59808i 0.216434 0.374875i −0.737281 0.675586i \(-0.763891\pi\)
0.953715 + 0.300711i \(0.0972240\pi\)
\(224\) −1.50000 + 2.59808i −0.100223 + 0.173591i
\(225\) 0 0
\(226\) 6.92820i 0.460857i
\(227\) −8.19615 14.1962i −0.543998 0.942232i −0.998669 0.0515725i \(-0.983577\pi\)
0.454672 0.890659i \(-0.349757\pi\)
\(228\) 0.169873 + 0.294229i 0.0112501 + 0.0194858i
\(229\) 1.26795i 0.0837884i 0.999122 + 0.0418942i \(0.0133392\pi\)
−0.999122 + 0.0418942i \(0.986661\pi\)
\(230\) 0 0
\(231\) −3.29423 + 5.70577i −0.216744 + 0.375412i
\(232\) −1.26795 + 2.19615i −0.0832449 + 0.144184i
\(233\) 4.73205i 0.310007i 0.987914 + 0.155003i \(0.0495389\pi\)
−0.987914 + 0.155003i \(0.950461\pi\)
\(234\) 2.13397 + 8.62436i 0.139502 + 0.563792i
\(235\) 0 0
\(236\) 9.00000 + 5.19615i 0.585850 + 0.338241i
\(237\) −2.66025 1.53590i −0.172802 0.0997673i
\(238\) −21.2942 + 12.2942i −1.38030 + 0.796916i
\(239\) 2.19615i 0.142057i −0.997474 0.0710286i \(-0.977372\pi\)
0.997474 0.0710286i \(-0.0226282\pi\)
\(240\) 0 0
\(241\) −7.50000 + 4.33013i −0.483117 + 0.278928i −0.721715 0.692191i \(-0.756646\pi\)
0.238597 + 0.971119i \(0.423312\pi\)
\(242\) 2.00000 0.128565
\(243\) 13.2224 7.63397i 0.848219 0.489720i
\(244\) −3.09808 + 5.36603i −0.198334 + 0.343525i
\(245\) 0 0
\(246\) −7.60770 −0.485049
\(247\) 1.16025 + 1.20577i 0.0738252 + 0.0767214i
\(248\) 4.73205i 0.300486i
\(249\) −5.19615 3.00000i −0.329293 0.190117i
\(250\) 0 0
\(251\) −8.59808 14.8923i −0.542706 0.939994i −0.998747 0.0500355i \(-0.984067\pi\)
0.456042 0.889958i \(-0.349267\pi\)
\(252\) 7.39230 0.465671
\(253\) −14.1962 24.5885i −0.892504 1.54586i
\(254\) −9.35641 + 5.40192i −0.587073 + 0.338947i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.0000 6.92820i −0.748539 0.432169i 0.0766265 0.997060i \(-0.475585\pi\)
−0.825166 + 0.564890i \(0.808918\pi\)
\(258\) 0.732051 1.26795i 0.0455755 0.0789391i
\(259\) 2.41154 0.149846
\(260\) 0 0
\(261\) 6.24871 0.386786
\(262\) −3.06218 + 5.30385i −0.189182 + 0.327673i
\(263\) −3.10770 1.79423i −0.191629 0.110637i 0.401116 0.916027i \(-0.368622\pi\)
−0.592745 + 0.805390i \(0.701956\pi\)
\(264\) −1.09808 1.90192i −0.0675819 0.117055i
\(265\) 0 0
\(266\) 1.20577 0.696152i 0.0739306 0.0426838i
\(267\) 2.49038 + 4.31347i 0.152409 + 0.263980i
\(268\) 0 0
\(269\) −13.5622 23.4904i −0.826901 1.43223i −0.900458 0.434943i \(-0.856769\pi\)
0.0735575 0.997291i \(-0.476565\pi\)
\(270\) 0 0
\(271\) 8.19615 + 4.73205i 0.497881 + 0.287452i 0.727838 0.685749i \(-0.240525\pi\)
−0.229957 + 0.973201i \(0.573859\pi\)
\(272\) 8.19615i 0.496965i
\(273\) −7.68653 + 1.90192i −0.465210 + 0.115110i
\(274\) 2.19615 0.132674
\(275\) 0 0
\(276\) 3.46410 6.00000i 0.208514 0.361158i
\(277\) 0.866025 0.500000i 0.0520344 0.0300421i −0.473757 0.880656i \(-0.657103\pi\)
0.525792 + 0.850613i \(0.323769\pi\)
\(278\) −1.19615 −0.0717405
\(279\) 10.0981 5.83013i 0.604556 0.349041i
\(280\) 0 0
\(281\) 10.3923i 0.619953i −0.950744 0.309976i \(-0.899679\pi\)
0.950744 0.309976i \(-0.100321\pi\)
\(282\) 1.90192 1.09808i 0.113258 0.0653895i
\(283\) 8.32051 + 4.80385i 0.494603 + 0.285559i 0.726482 0.687186i \(-0.241154\pi\)
−0.231879 + 0.972745i \(0.574487\pi\)
\(284\) 5.19615 + 3.00000i 0.308335 + 0.178017i
\(285\) 0 0
\(286\) −7.50000 7.79423i −0.443484 0.460882i
\(287\) 31.1769i 1.84032i
\(288\) −1.23205 + 2.13397i −0.0725993 + 0.125746i
\(289\) 25.0885 43.4545i 1.47579 2.55615i
\(290\) 0 0
\(291\) 6.67949i 0.391559i
\(292\) 5.83013 + 10.0981i 0.341182 + 0.590945i
\(293\) 5.59808 + 9.69615i 0.327043 + 0.566455i 0.981924 0.189277i \(-0.0606144\pi\)
−0.654881 + 0.755732i \(0.727281\pi\)
\(294\) 1.46410i 0.0853881i
\(295\) 0 0
\(296\) −0.401924 + 0.696152i −0.0233613 + 0.0404630i
\(297\) −6.00000 + 10.3923i −0.348155 + 0.603023i
\(298\) 6.00000i 0.347571i
\(299\) 9.46410 32.7846i 0.547323 1.89598i
\(300\) 0 0
\(301\) −5.19615 3.00000i −0.299501 0.172917i
\(302\) 20.4904 + 11.8301i 1.17909 + 0.680747i
\(303\) 6.80385 3.92820i 0.390871 0.225669i
\(304\) 0.464102i 0.0266181i
\(305\) 0 0
\(306\) −17.4904 + 10.0981i −0.999859 + 0.577269i
\(307\) −27.4641 −1.56746 −0.783730 0.621102i \(-0.786685\pi\)
−0.783730 + 0.621102i \(0.786685\pi\)
\(308\) −7.79423 + 4.50000i −0.444117 + 0.256411i
\(309\) −3.36603 + 5.83013i −0.191486 + 0.331664i
\(310\) 0 0
\(311\) −9.12436 −0.517395 −0.258697 0.965958i \(-0.583293\pi\)
−0.258697 + 0.965958i \(0.583293\pi\)
\(312\) 0.732051 2.53590i 0.0414442 0.143567i
\(313\) 26.3923i 1.49178i 0.666068 + 0.745891i \(0.267976\pi\)
−0.666068 + 0.745891i \(0.732024\pi\)
\(314\) −11.2583 6.50000i −0.635344 0.366816i
\(315\) 0 0
\(316\) −2.09808 3.63397i −0.118026 0.204427i
\(317\) −23.1962 −1.30283 −0.651413 0.758723i \(-0.725823\pi\)
−0.651413 + 0.758723i \(0.725823\pi\)
\(318\) 0.169873 + 0.294229i 0.00952600 + 0.0164995i
\(319\) −6.58846 + 3.80385i −0.368883 + 0.212975i
\(320\) 0 0
\(321\) −6.46410 11.1962i −0.360791 0.624908i
\(322\) −24.5885 14.1962i −1.37026 0.791121i
\(323\) −1.90192 + 3.29423i −0.105826 + 0.183296i
\(324\) 4.46410 0.248006
\(325\) 0 0
\(326\) 10.7321 0.594393
\(327\) 3.12436 5.41154i 0.172777 0.299259i
\(328\) −9.00000 5.19615i −0.496942 0.286910i
\(329\) −4.50000 7.79423i −0.248093 0.429710i
\(330\) 0 0
\(331\) 11.1962 6.46410i 0.615396 0.355299i −0.159678 0.987169i \(-0.551046\pi\)
0.775074 + 0.631870i \(0.217712\pi\)
\(332\) −4.09808 7.09808i −0.224911 0.389558i
\(333\) 1.98076 0.108545
\(334\) 1.50000 + 2.59808i 0.0820763 + 0.142160i
\(335\) 0 0
\(336\) −1.90192 1.09808i −0.103758 0.0599050i
\(337\) 6.19615i 0.337526i −0.985657 0.168763i \(-0.946023\pi\)
0.985657 0.168763i \(-0.0539772\pi\)
\(338\) 0.500000 12.9904i 0.0271964 0.706584i
\(339\) −5.07180 −0.275462
\(340\) 0 0
\(341\) −7.09808 + 12.2942i −0.384382 + 0.665770i
\(342\) 0.990381 0.571797i 0.0535537 0.0309192i
\(343\) −15.0000 −0.809924
\(344\) 1.73205 1.00000i 0.0933859 0.0539164i
\(345\) 0 0
\(346\) 15.0000i 0.806405i
\(347\) 24.8827 14.3660i 1.33577 0.771209i 0.349595 0.936901i \(-0.386319\pi\)
0.986178 + 0.165692i \(0.0529858\pi\)
\(348\) −1.60770 0.928203i −0.0861815 0.0497569i
\(349\) 3.50962 + 2.02628i 0.187866 + 0.108464i 0.590983 0.806684i \(-0.298740\pi\)
−0.403117 + 0.915148i \(0.632073\pi\)
\(350\) 0 0
\(351\) −14.0000 + 3.46410i −0.747265 + 0.184900i
\(352\) 3.00000i 0.159901i
\(353\) −4.90192 + 8.49038i −0.260903 + 0.451897i −0.966482 0.256734i \(-0.917354\pi\)
0.705579 + 0.708631i \(0.250687\pi\)
\(354\) −3.80385 + 6.58846i −0.202172 + 0.350173i
\(355\) 0 0
\(356\) 6.80385i 0.360603i
\(357\) −9.00000 15.5885i −0.476331 0.825029i
\(358\) −4.73205 8.19615i −0.250097 0.433180i
\(359\) 1.60770i 0.0848509i −0.999100 0.0424255i \(-0.986492\pi\)
0.999100 0.0424255i \(-0.0135085\pi\)
\(360\) 0 0
\(361\) −9.39230 + 16.2679i −0.494332 + 0.856208i
\(362\) −7.29423 + 12.6340i −0.383376 + 0.664027i
\(363\) 1.46410i 0.0768454i
\(364\) −10.3923 3.00000i −0.544705 0.157243i
\(365\) 0 0
\(366\) −3.92820 2.26795i −0.205330 0.118548i
\(367\) −4.85641 2.80385i −0.253502 0.146360i 0.367865 0.929879i \(-0.380089\pi\)
−0.621367 + 0.783520i \(0.713422\pi\)
\(368\) 8.19615 4.73205i 0.427254 0.246675i
\(369\) 25.6077i 1.33308i
\(370\) 0 0
\(371\) 1.20577 0.696152i 0.0626005 0.0361424i
\(372\) −3.46410 −0.179605
\(373\) −0.339746 + 0.196152i −0.0175914 + 0.0101564i −0.508770 0.860903i \(-0.669900\pi\)
0.491179 + 0.871059i \(0.336566\pi\)
\(374\) 12.2942 21.2942i 0.635719 1.10110i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) −8.78461 2.53590i −0.452430 0.130605i
\(378\) 12.0000i 0.617213i
\(379\) −25.7942 14.8923i −1.32496 0.764966i −0.340445 0.940264i \(-0.610578\pi\)
−0.984515 + 0.175298i \(0.943911\pi\)
\(380\) 0 0
\(381\) −3.95448 6.84936i −0.202594 0.350904i
\(382\) −22.7321 −1.16307
\(383\) 11.1962 + 19.3923i 0.572097 + 0.990900i 0.996350 + 0.0853571i \(0.0272031\pi\)
−0.424254 + 0.905543i \(0.639464\pi\)
\(384\) 0.633975 0.366025i 0.0323524 0.0186787i
\(385\) 0 0
\(386\) 8.19615 + 14.1962i 0.417173 + 0.722565i
\(387\) −4.26795 2.46410i −0.216952 0.125257i
\(388\) −4.56218 + 7.90192i −0.231609 + 0.401159i
\(389\) −22.7321 −1.15256 −0.576280 0.817252i \(-0.695496\pi\)
−0.576280 + 0.817252i \(0.695496\pi\)
\(390\) 0 0
\(391\) 77.5692 3.92284
\(392\) −1.00000 + 1.73205i −0.0505076 + 0.0874818i
\(393\) −3.88269 2.24167i −0.195856 0.113077i
\(394\) 10.7942 + 18.6962i 0.543805 + 0.941899i
\(395\) 0 0
\(396\) −6.40192 + 3.69615i −0.321709 + 0.185739i
\(397\) 5.59808 + 9.69615i 0.280959 + 0.486636i 0.971621 0.236542i \(-0.0760140\pi\)
−0.690662 + 0.723178i \(0.742681\pi\)
\(398\) 6.39230 0.320417
\(399\) 0.509619 + 0.882686i 0.0255129 + 0.0441896i
\(400\) 0 0
\(401\) −4.50000 2.59808i −0.224719 0.129742i 0.383414 0.923576i \(-0.374748\pi\)
−0.608134 + 0.793835i \(0.708081\pi\)
\(402\) 0 0
\(403\) −16.5622 + 4.09808i −0.825021 + 0.204140i
\(404\) 10.7321 0.533939
\(405\) 0 0
\(406\) −3.80385 + 6.58846i −0.188782 + 0.326980i
\(407\) −2.08846 + 1.20577i −0.103521 + 0.0597679i
\(408\) 6.00000 0.297044
\(409\) 14.0885 8.13397i 0.696629 0.402199i −0.109461 0.993991i \(-0.534913\pi\)
0.806091 + 0.591792i \(0.201579\pi\)
\(410\) 0 0
\(411\) 1.60770i 0.0793018i
\(412\) −7.96410 + 4.59808i −0.392363 + 0.226531i
\(413\) 27.0000 + 15.5885i 1.32858 + 0.767058i
\(414\) −20.1962 11.6603i −0.992587 0.573070i
\(415\) 0 0
\(416\) 2.59808 2.50000i 0.127381 0.122573i
\(417\) 0.875644i 0.0428805i
\(418\) −0.696152 + 1.20577i −0.0340499 + 0.0589762i
\(419\) −8.66025 + 15.0000i −0.423081 + 0.732798i −0.996239 0.0866469i \(-0.972385\pi\)
0.573158 + 0.819445i \(0.305718\pi\)
\(420\) 0 0
\(421\) 2.87564i 0.140150i 0.997542 + 0.0700752i \(0.0223239\pi\)
−0.997542 + 0.0700752i \(0.977676\pi\)
\(422\) 8.79423 + 15.2321i 0.428096 + 0.741485i
\(423\) −3.69615 6.40192i −0.179713 0.311272i
\(424\) 0.464102i 0.0225388i
\(425\) 0 0
\(426\) −2.19615 + 3.80385i −0.106404 + 0.184297i
\(427\) −9.29423 + 16.0981i −0.449779 + 0.779041i
\(428\) 17.6603i 0.853641i
\(429\) 5.70577 5.49038i 0.275477 0.265078i
\(430\) 0 0
\(431\) −7.09808 4.09808i −0.341902 0.197397i 0.319211 0.947684i \(-0.396582\pi\)
−0.661113 + 0.750286i \(0.729916\pi\)
\(432\) −3.46410 2.00000i −0.166667 0.0962250i
\(433\) 7.26795 4.19615i 0.349275 0.201654i −0.315091 0.949062i \(-0.602035\pi\)
0.664366 + 0.747407i \(0.268702\pi\)
\(434\) 14.1962i 0.681437i
\(435\) 0 0
\(436\) 7.39230 4.26795i 0.354027 0.204398i
\(437\) −4.39230 −0.210112
\(438\) −7.39230 + 4.26795i −0.353218 + 0.203931i
\(439\) −1.70577 + 2.95448i −0.0814120 + 0.141010i −0.903857 0.427835i \(-0.859276\pi\)
0.822445 + 0.568845i \(0.192610\pi\)
\(440\) 0 0
\(441\) 4.92820 0.234676
\(442\) 28.6865 7.09808i 1.36448 0.337621i
\(443\) 22.3923i 1.06389i −0.846779 0.531945i \(-0.821461\pi\)
0.846779 0.531945i \(-0.178539\pi\)
\(444\) −0.509619 0.294229i −0.0241854 0.0139635i
\(445\) 0 0
\(446\) 3.23205 + 5.59808i 0.153042 + 0.265077i
\(447\) 4.39230 0.207749
\(448\) −1.50000 2.59808i −0.0708683 0.122748i
\(449\) −13.5000 + 7.79423i −0.637104 + 0.367832i −0.783498 0.621394i \(-0.786567\pi\)
0.146394 + 0.989226i \(0.453233\pi\)
\(450\) 0 0
\(451\) −15.5885 27.0000i −0.734032 1.27138i
\(452\) −6.00000 3.46410i −0.282216 0.162938i
\(453\) −8.66025 + 15.0000i −0.406894 + 0.704761i
\(454\) 16.3923 0.769329
\(455\) 0 0
\(456\) −0.339746 −0.0159101
\(457\) 9.16987 15.8827i 0.428949 0.742961i −0.567832 0.823145i \(-0.692217\pi\)
0.996780 + 0.0801841i \(0.0255508\pi\)
\(458\) −1.09808 0.633975i −0.0513097 0.0296237i
\(459\) −16.3923 28.3923i −0.765127 1.32524i
\(460\) 0 0
\(461\) −26.4904 + 15.2942i −1.23378 + 0.712323i −0.967816 0.251660i \(-0.919024\pi\)
−0.265964 + 0.963983i \(0.585690\pi\)
\(462\) −3.29423 5.70577i −0.153261 0.265457i
\(463\) −12.9282 −0.600825 −0.300412 0.953809i \(-0.597124\pi\)
−0.300412 + 0.953809i \(0.597124\pi\)
\(464\) −1.26795 2.19615i −0.0588631 0.101954i
\(465\) 0 0
\(466\) −4.09808 2.36603i −0.189840 0.109604i
\(467\) 37.8564i 1.75179i 0.482506 + 0.875893i \(0.339727\pi\)
−0.482506 + 0.875893i \(0.660273\pi\)
\(468\) −8.53590 2.46410i −0.394572 0.113903i
\(469\) 0 0
\(470\) 0 0
\(471\) 4.75833 8.24167i 0.219252 0.379756i
\(472\) −9.00000 + 5.19615i −0.414259 + 0.239172i
\(473\) 6.00000 0.275880
\(474\) 2.66025 1.53590i 0.122190 0.0705461i
\(475\) 0 0
\(476\) 24.5885i 1.12701i
\(477\) 0.990381 0.571797i 0.0453464 0.0261808i
\(478\) 1.90192 + 1.09808i 0.0869920 + 0.0502248i
\(479\) 35.4904 + 20.4904i 1.62160 + 0.936229i 0.986493 + 0.163803i \(0.0523760\pi\)
0.635104 + 0.772427i \(0.280957\pi\)
\(480\) 0 0
\(481\) −2.78461 0.803848i −0.126967 0.0366523i
\(482\) 8.66025i 0.394464i
\(483\) 10.3923 18.0000i 0.472866 0.819028i
\(484\) −1.00000 + 1.73205i −0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) 15.2679i 0.692568i
\(487\) 7.62436 + 13.2058i 0.345493 + 0.598411i 0.985443 0.170005i \(-0.0543785\pi\)
−0.639951 + 0.768416i \(0.721045\pi\)
\(488\) −3.09808 5.36603i −0.140243 0.242909i
\(489\) 7.85641i 0.355279i
\(490\) 0 0
\(491\) −10.3301 + 17.8923i −0.466192 + 0.807468i −0.999254 0.0386076i \(-0.987708\pi\)
0.533062 + 0.846076i \(0.321041\pi\)
\(492\) 3.80385 6.58846i 0.171491 0.297031i
\(493\) 20.7846i 0.936092i
\(494\) −1.62436 + 0.401924i −0.0730832 + 0.0180834i
\(495\) 0 0
\(496\) −4.09808 2.36603i −0.184009 0.106238i
\(497\) 15.5885 + 9.00000i 0.699238 + 0.403705i
\(498\) 5.19615 3.00000i 0.232845 0.134433i
\(499\) 25.8564i 1.15749i −0.815508 0.578746i \(-0.803542\pi\)
0.815508 0.578746i \(-0.196458\pi\)
\(500\) 0 0
\(501\) −1.90192 + 1.09808i −0.0849717 + 0.0490584i
\(502\) 17.1962 0.767502
\(503\) −23.0885 + 13.3301i −1.02946 + 0.594361i −0.916831 0.399276i \(-0.869262\pi\)
−0.112633 + 0.993637i \(0.535928\pi\)
\(504\) −3.69615 + 6.40192i −0.164640 + 0.285164i
\(505\) 0 0
\(506\) 28.3923 1.26219
\(507\) 9.50962 + 0.366025i 0.422337 + 0.0162558i
\(508\) 10.8038i 0.479343i
\(509\) 19.3923 + 11.1962i 0.859549 + 0.496261i 0.863861 0.503730i \(-0.168039\pi\)
−0.00431237 + 0.999991i \(0.501373\pi\)
\(510\) 0 0
\(511\) 17.4904 + 30.2942i 0.773729 + 1.34014i
\(512\) 1.00000 0.0441942
\(513\) 0.928203 + 1.60770i 0.0409812 + 0.0709815i
\(514\) 12.0000 6.92820i 0.529297 0.305590i
\(515\) 0 0
\(516\) 0.732051 + 1.26795i 0.0322267 + 0.0558184i
\(517\) 7.79423 + 4.50000i 0.342790 + 0.197910i
\(518\) −1.20577 + 2.08846i −0.0529786 + 0.0917615i
\(519\) 10.9808 0.482002
\(520\) 0 0
\(521\) 6.46410 0.283197 0.141599 0.989924i \(-0.454776\pi\)
0.141599 + 0.989924i \(0.454776\pi\)
\(522\) −3.12436 + 5.41154i −0.136749 + 0.236857i
\(523\) 2.07180 + 1.19615i 0.0905933 + 0.0523041i 0.544612 0.838688i \(-0.316677\pi\)
−0.454019 + 0.890992i \(0.650010\pi\)
\(524\) −3.06218 5.30385i −0.133772 0.231700i
\(525\) 0 0
\(526\) 3.10770 1.79423i 0.135502 0.0782321i
\(527\) −19.3923 33.5885i −0.844742 1.46314i
\(528\) 2.19615 0.0955753
\(529\) 33.2846 + 57.6506i 1.44716 + 2.50655i
\(530\) 0 0
\(531\) 22.1769 + 12.8038i 0.962396 + 0.555640i
\(532\) 1.39230i 0.0603641i
\(533\) 10.3923 36.0000i 0.450141 1.55933i
\(534\) −4.98076 −0.215539
\(535\) 0 0
\(536\) 0 0
\(537\) 6.00000 3.46410i 0.258919 0.149487i
\(538\) 27.1244 1.16941
\(539\) −5.19615 + 3.00000i −0.223814 + 0.129219i
\(540\) 0 0
\(541\) 22.0526i 0.948114i 0.880494 + 0.474057i \(0.157211\pi\)
−0.880494 + 0.474057i \(0.842789\pi\)
\(542\) −8.19615 + 4.73205i −0.352055 + 0.203259i
\(543\) −9.24871 5.33975i −0.396900 0.229150i
\(544\) 7.09808 + 4.09808i 0.304328 + 0.175704i
\(545\) 0 0
\(546\) 2.19615 7.60770i 0.0939866 0.325579i
\(547\) 6.78461i 0.290089i 0.989425 + 0.145044i \(0.0463325\pi\)
−0.989425 + 0.145044i \(0.953667\pi\)
\(548\) −1.09808 + 1.90192i −0.0469075 + 0.0812462i
\(549\) −7.63397 + 13.2224i −0.325810 + 0.564320i
\(550\) 0 0
\(551\) 1.17691i 0.0501382i
\(552\) 3.46410 + 6.00000i 0.147442 + 0.255377i
\(553\) −6.29423 10.9019i −0.267658 0.463597i
\(554\) 1.00000i 0.0424859i
\(555\) 0 0
\(556\) 0.598076 1.03590i 0.0253641 0.0439319i
\(557\) −3.40192 + 5.89230i −0.144144 + 0.249665i −0.929053 0.369946i \(-0.879376\pi\)
0.784909 + 0.619611i \(0.212710\pi\)
\(558\) 11.6603i 0.493618i
\(559\) 5.00000 + 5.19615i 0.211477 + 0.219774i
\(560\) 0 0
\(561\) 15.5885 + 9.00000i 0.658145 + 0.379980i
\(562\) 9.00000 + 5.19615i 0.379642 + 0.219186i
\(563\) 12.5885 7.26795i 0.530540 0.306308i −0.210696 0.977552i \(-0.567573\pi\)
0.741236 + 0.671244i \(0.234240\pi\)
\(564\) 2.19615i 0.0924747i
\(565\) 0 0
\(566\) −8.32051 + 4.80385i −0.349737 + 0.201921i
\(567\) 13.3923 0.562424
\(568\) −5.19615 + 3.00000i −0.218026 + 0.125877i
\(569\) −13.6244 + 23.5981i −0.571163 + 0.989283i 0.425284 + 0.905060i \(0.360174\pi\)
−0.996447 + 0.0842230i \(0.973159\pi\)
\(570\) 0 0
\(571\) −38.3731 −1.60586 −0.802931 0.596071i \(-0.796728\pi\)
−0.802931 + 0.596071i \(0.796728\pi\)
\(572\) 10.5000 2.59808i 0.439027 0.108631i
\(573\) 16.6410i 0.695188i
\(574\) −27.0000 15.5885i −1.12696 0.650650i
\(575\) 0 0
\(576\) −1.23205 2.13397i −0.0513355 0.0889156i
\(577\) −26.4449 −1.10091 −0.550457 0.834863i \(-0.685547\pi\)
−0.550457 + 0.834863i \(0.685547\pi\)
\(578\) 25.0885 + 43.4545i 1.04354 + 1.80747i
\(579\) −10.3923 + 6.00000i −0.431889 + 0.249351i
\(580\) 0 0
\(581\) −12.2942 21.2942i −0.510051 0.883433i
\(582\) −5.78461 3.33975i −0.239780 0.138437i
\(583\) −0.696152 + 1.20577i −0.0288317 + 0.0499379i
\(584\) −11.6603 −0.482505
\(585\) 0 0
\(586\) −11.1962 −0.462509
\(587\) 15.0000 25.9808i 0.619116 1.07234i −0.370531 0.928820i \(-0.620824\pi\)
0.989647 0.143521i \(-0.0458424\pi\)
\(588\) −1.26795 0.732051i −0.0522893 0.0301893i
\(589\) 1.09808 + 1.90192i 0.0452454 + 0.0783674i
\(590\) 0 0
\(591\) −13.6865 + 7.90192i −0.562989 + 0.325042i
\(592\) −0.401924 0.696152i −0.0165190 0.0286117i
\(593\) 20.7846 0.853522 0.426761 0.904365i \(-0.359655\pi\)
0.426761 + 0.904365i \(0.359655\pi\)
\(594\) −6.00000 10.3923i −0.246183 0.426401i
\(595\) 0 0
\(596\) 5.19615 + 3.00000i 0.212843 + 0.122885i
\(597\) 4.67949i 0.191519i
\(598\) 23.6603 + 24.5885i 0.967540 + 1.00550i
\(599\) 19.8564 0.811311 0.405655 0.914026i \(-0.367043\pi\)
0.405655 + 0.914026i \(0.367043\pi\)
\(600\) 0 0
\(601\) 18.8923 32.7224i 0.770633 1.33478i −0.166583 0.986027i \(-0.553273\pi\)
0.937216 0.348748i \(-0.113393\pi\)
\(602\) 5.19615 3.00000i 0.211779 0.122271i
\(603\) 0 0
\(604\) −20.4904 + 11.8301i −0.833742 + 0.481361i
\(605\) 0 0
\(606\) 7.85641i 0.319145i
\(607\) 32.5526 18.7942i 1.32127 0.762834i 0.337337 0.941384i \(-0.390474\pi\)
0.983931 + 0.178550i \(0.0571406\pi\)
\(608\) −0.401924 0.232051i −0.0163002 0.00941090i
\(609\) −4.82309 2.78461i −0.195441 0.112838i
\(610\) 0 0
\(611\) 2.59808 + 10.5000i 0.105107 + 0.424785i
\(612\) 20.1962i 0.816381i
\(613\) −19.4545 + 33.6962i −0.785759 + 1.36097i 0.142785 + 0.989754i \(0.454394\pi\)
−0.928545 + 0.371221i \(0.878939\pi\)
\(614\) 13.7321 23.7846i 0.554180 0.959869i
\(615\) 0 0
\(616\) 9.00000i 0.362620i
\(617\) −9.00000 15.5885i −0.362326 0.627568i 0.626017 0.779809i \(-0.284684\pi\)
−0.988343 + 0.152242i \(0.951351\pi\)
\(618\) −3.36603 5.83013i −0.135401 0.234522i
\(619\) 31.3923i 1.26176i 0.775879 + 0.630882i \(0.217307\pi\)
−0.775879 + 0.630882i \(0.782693\pi\)
\(620\) 0 0
\(621\) 18.9282 32.7846i 0.759563 1.31560i
\(622\) 4.56218 7.90192i 0.182927 0.316838i
\(623\) 20.4115i 0.817771i
\(624\) 1.83013 + 1.90192i 0.0732637 + 0.0761379i
\(625\) 0 0
\(626\) −22.8564 13.1962i −0.913526 0.527424i
\(627\) −0.882686 0.509619i −0.0352511 0.0203522i
\(628\) 11.2583 6.50000i 0.449256 0.259378i
\(629\) 6.58846i 0.262699i
\(630\) 0 0
\(631\) −18.0000 + 10.3923i −0.716569 + 0.413711i −0.813488 0.581581i \(-0.802434\pi\)
0.0969198 + 0.995292i \(0.469101\pi\)
\(632\) 4.19615 0.166914
\(633\) −11.1506 + 6.43782i −0.443198 + 0.255880i
\(634\) 11.5981 20.0885i 0.460618 0.797815i
\(635\) 0 0
\(636\) −0.339746 −0.0134718
\(637\) −6.92820 2.00000i −0.274505 0.0792429i
\(638\) 7.60770i 0.301192i
\(639\) 12.8038 + 7.39230i 0.506512 + 0.292435i
\(640\) 0 0
\(641\) −16.0359 27.7750i −0.633380 1.09705i −0.986856 0.161603i \(-0.948334\pi\)
0.353476 0.935444i \(-0.385000\pi\)
\(642\) 12.9282 0.510235
\(643\) −5.36603 9.29423i −0.211615 0.366529i 0.740605 0.671941i \(-0.234539\pi\)
−0.952220 + 0.305412i \(0.901206\pi\)
\(644\) 24.5885 14.1962i 0.968921 0.559407i
\(645\) 0 0
\(646\) −1.90192 3.29423i −0.0748302 0.129610i
\(647\) −0.696152 0.401924i −0.0273686 0.0158013i 0.486253 0.873818i \(-0.338363\pi\)
−0.513622 + 0.858017i \(0.671697\pi\)
\(648\) −2.23205 + 3.86603i −0.0876832 + 0.151872i
\(649\) −31.1769 −1.22380
\(650\) 0 0
\(651\) −10.3923 −0.407307
\(652\) −5.36603 + 9.29423i −0.210150 + 0.363990i
\(653\) −1.20577 0.696152i −0.0471855 0.0272425i 0.476222 0.879325i \(-0.342006\pi\)
−0.523407 + 0.852083i \(0.675339\pi\)
\(654\) 3.12436 + 5.41154i 0.122172 + 0.211608i
\(655\) 0 0
\(656\) 9.00000 5.19615i 0.351391 0.202876i
\(657\) 14.3660 + 24.8827i 0.560472 + 0.970766i
\(658\) 9.00000 0.350857
\(659\) −2.66025 4.60770i −0.103629 0.179490i 0.809548 0.587053i \(-0.199712\pi\)
−0.913177 + 0.407563i \(0.866379\pi\)
\(660\) 0 0
\(661\) 31.0981 + 17.9545i 1.20957 + 0.698348i 0.962666 0.270690i \(-0.0872520\pi\)
0.246909 + 0.969039i \(0.420585\pi\)
\(662\) 12.9282i 0.502469i
\(663\) 5.19615 + 21.0000i 0.201802 + 0.815572i
\(664\) 8.19615 0.318072
\(665\) 0 0
\(666\) −0.990381 + 1.71539i −0.0383765 + 0.0664700i
\(667\) 20.7846 12.0000i 0.804783 0.464642i
\(668\) −3.00000 −0.116073
\(669\) −4.09808 + 2.36603i −0.158441 + 0.0914758i
\(670\) 0 0
\(671\) 18.5885i 0.717599i
\(672\) 1.90192 1.09808i 0.0733683 0.0423592i
\(673\) −21.1244 12.1962i −0.814284 0.470127i 0.0341573 0.999416i \(-0.489125\pi\)
−0.848441 + 0.529289i \(0.822459\pi\)
\(674\) 5.36603 + 3.09808i 0.206692 + 0.119333i
\(675\) 0 0
\(676\) 11.0000 + 6.92820i 0.423077 + 0.266469i
\(677\) 25.8564i 0.993742i 0.867824 + 0.496871i \(0.165518\pi\)
−0.867824 + 0.496871i \(0.834482\pi\)
\(678\) 2.53590 4.39230i 0.0973906 0.168685i
\(679\) −13.6865 + 23.7058i −0.525241 + 0.909744i
\(680\) 0 0
\(681\) 12.0000i 0.459841i
\(682\) −7.09808 12.2942i −0.271799 0.470770i
\(683\) 15.5885 + 27.0000i 0.596476 + 1.03313i 0.993337 + 0.115248i \(0.0367661\pi\)
−0.396861 + 0.917879i \(0.629901\pi\)
\(684\) 1.14359i 0.0437264i
\(685\) 0 0
\(686\) 7.50000 12.9904i 0.286351 0.495975i
\(687\) 0.464102 0.803848i 0.0177066 0.0306687i
\(688\) 2.00000i 0.0762493i
\(689\) −1.62436 + 0.401924i −0.0618830 + 0.0153121i
\(690\) 0 0
\(691\) −31.7942 18.3564i −1.20951 0.698311i −0.246857 0.969052i \(-0.579398\pi\)
−0.962652 + 0.270741i \(0.912731\pi\)
\(692\) 12.9904 + 7.50000i 0.493820 + 0.285107i
\(693\) −19.2058 + 11.0885i −0.729567 + 0.421216i
\(694\) 28.7321i 1.09065i
\(695\) 0 0
\(696\) 1.60770 0.928203i 0.0609395 0.0351835i
\(697\) 85.1769 3.22631
\(698\) −3.50962 + 2.02628i −0.132841 + 0.0766958i
\(699\) 1.73205 3.00000i 0.0655122 0.113470i
\(700\) 0 0
\(701\) 35.9090 1.35626 0.678131 0.734941i \(-0.262790\pi\)
0.678131 + 0.734941i \(0.262790\pi\)
\(702\) 4.00000 13.8564i 0.150970 0.522976i
\(703\) 0.373067i 0.0140705i
\(704\) 2.59808 + 1.50000i 0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) −4.90192 8.49038i −0.184486 0.319540i
\(707\) 32.1962 1.21086
\(708\) −3.80385 6.58846i −0.142957 0.247609i
\(709\) −9.50962 + 5.49038i −0.357141 + 0.206196i −0.667826 0.744317i \(-0.732775\pi\)
0.310685 + 0.950513i \(0.399442\pi\)
\(710\) 0 0
\(711\) −5.16987 8.95448i −0.193885 0.335819i
\(712\) −5.89230 3.40192i −0.220823 0.127492i
\(713\) 22.3923 38.7846i 0.838598 1.45250i
\(714\) 18.0000 0.673633
\(715\) 0 0
\(716\) 9.46410 0.353690
\(717\) −0.803848 + 1.39230i −0.0300202 + 0.0519966i
\(718\) 1.39230 + 0.803848i 0.0519604 + 0.0299993i
\(719\) 12.9282 + 22.3923i 0.482141 + 0.835092i 0.999790 0.0205009i \(-0.00652609\pi\)
−0.517649 + 0.855593i \(0.673193\pi\)
\(720\) 0 0
\(721\) −23.8923 + 13.7942i −0.889796 + 0.513724i
\(722\) −9.39230 16.2679i −0.349545 0.605430i
\(723\) 6.33975 0.235778
\(724\) −7.29423 12.6340i −0.271088 0.469538i
\(725\) 0 0
\(726\) −1.26795 0.732051i −0.0470580 0.0271690i
\(727\) 34.3731i 1.27483i −0.770522 0.637413i \(-0.780004\pi\)
0.770522 0.637413i \(-0.219996\pi\)
\(728\) 7.79423 7.50000i 0.288873 0.277968i
\(729\) 2.21539 0.0820515
\(730\) 0 0
\(731\) −8.19615 + 14.1962i −0.303146 + 0.525064i
\(732\) 3.92820 2.26795i 0.145191 0.0838258i
\(733\) −14.9090 −0.550675 −0.275338 0.961348i \(-0.588790\pi\)
−0.275338 + 0.961348i \(0.588790\pi\)
\(734\) 4.85641 2.80385i 0.179253 0.103492i
\(735\) 0 0
\(736\) 9.46410i 0.348851i
\(737\) 0 0
\(738\) −22.1769 12.8038i −0.816344 0.471316i
\(739\) −28.2058 16.2846i −1.03757 0.599039i −0.118423 0.992963i \(-0.537784\pi\)
−0.919143 + 0.393924i \(0.871117\pi\)
\(740\) 0 0
\(741\) −0.294229 1.18911i −0.0108088 0.0436831i
\(742\) 1.39230i 0.0511131i
\(743\) 6.80385 11.7846i 0.249609 0.432335i −0.713808 0.700341i \(-0.753031\pi\)
0.963417 + 0.268006i \(0.0863646\pi\)
\(744\) 1.73205 3.00000i 0.0635001 0.109985i
\(745\) 0 0
\(746\) 0.392305i 0.0143633i
\(747\) −10.0981 17.4904i −0.369469 0.639940i
\(748\) 12.2942 + 21.2942i 0.449522 + 0.778594i
\(749\) 52.9808i 1.93587i
\(750\) 0 0
\(751\) 10.1962 17.6603i 0.372063 0.644432i −0.617820 0.786320i \(-0.711984\pi\)
0.989883 + 0.141888i \(0.0453172\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 12.5885i 0.458749i
\(754\) 6.58846 6.33975i 0.239937 0.230880i
\(755\) 0 0
\(756\) −10.3923 6.00000i −0.377964 0.218218i
\(757\) −32.7224 18.8923i −1.18932 0.686652i −0.231166 0.972914i \(-0.574254\pi\)
−0.958151 + 0.286262i \(0.907587\pi\)
\(758\) 25.7942 14.8923i 0.936889 0.540913i
\(759\) 20.7846i 0.754434i
\(760\) 0 0
\(761\) 16.2846 9.40192i 0.590317 0.340819i −0.174906 0.984585i \(-0.555962\pi\)
0.765223 + 0.643766i \(0.222629\pi\)
\(762\) 7.90897 0.286512
\(763\) 22.1769 12.8038i 0.802858 0.463530i
\(764\) 11.3660 19.6865i 0.411208 0.712234i
\(765\) 0 0
\(766\) −22.3923 −0.809067
\(767\) −25.9808 27.0000i −0.938111 0.974913i
\(768\) 0.732051i 0.0264156i
\(769\) 33.0000 + 19.0526i 1.19001 + 0.687053i 0.958309 0.285734i \(-0.0922374\pi\)
0.231701 + 0.972787i \(0.425571\pi\)
\(770\) 0 0
\(771\) 5.07180 + 8.78461i 0.182656 + 0.316370i
\(772\) −16.3923 −0.589972
\(773\) 1.20577 + 2.08846i 0.0433686 + 0.0751166i 0.886895 0.461971i \(-0.152858\pi\)
−0.843526 + 0.537088i \(0.819524\pi\)
\(774\) 4.26795 2.46410i 0.153408 0.0885703i
\(775\) 0 0
\(776\) −4.56218 7.90192i −0.163773 0.283663i
\(777\) −1.52886 0.882686i −0.0548474 0.0316662i
\(778\) 11.3660 19.6865i 0.407492 0.705796i
\(779\) −4.82309 −0.172805
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) −38.7846 + 67.1769i −1.38693 + 2.40224i
\(783\) −8.78461 5.07180i −0.313936 0.181251i
\(784\) −1.00000 1.73205i −0.0357143 0.0618590i
\(785\) 0 0
\(786\) 3.88269 2.24167i 0.138491 0.0799577i
\(787\) 21.4186 + 37.0981i 0.763490 + 1.32240i 0.941041 + 0.338292i \(0.109849\pi\)
−0.177551 + 0.984112i \(0.556818\pi\)
\(788\) −21.5885 −0.769057
\(789\) 1.31347 + 2.27499i 0.0467606 + 0.0809918i
\(790\) 0 0
\(791\) −18.0000 10.3923i −0.640006 0.369508i
\(792\) 7.39230i 0.262674i
\(793\) 16.0981 15.4904i 0.571659 0.550080i
\(794\) −11.1962 −0.397337
\(795\) 0 0
\(796\) −3.19615 + 5.53590i −0.113285 + 0.196215i
\(797\) 11.1962 6.46410i 0.396588 0.228970i −0.288423 0.957503i \(-0.593131\pi\)
0.685011 + 0.728533i \(0.259797\pi\)
\(798\) −1.01924 −0.0360806
\(799\) −21.2942 + 12.2942i −0.753336 + 0.434939i
\(800\) 0 0
\(801\) 16.7654i 0.592375i
\(802\) 4.50000 2.59808i 0.158901 0.0917413i
\(803\) −30.2942 17.4904i −1.06906 0.617222i
\(804\) 0 0
\(805\) 0 0
\(806\) 4.73205 16.3923i 0.166679 0.577394i
\(807\) 19.8564i 0.698979i
\(808\) −5.36603 + 9.29423i −0.188776 + 0.326970i
\(809\) 12.0000 20.7846i 0.421898 0.730748i −0.574228 0.818696i \(-0.694698\pi\)
0.996125 + 0.0879478i \(0.0280309\pi\)
\(810\) 0 0
\(811\) 43.3923i 1.52371i 0.647748 + 0.761855i \(0.275711\pi\)
−0.647748 + 0.761855i \(0.724289\pi\)
\(812\) −3.80385 6.58846i −0.133489 0.231210i
\(813\) −3.46410 6.00000i −0.121491 0.210429i
\(814\) 2.41154i 0.0845245i
\(815\) 0 0
\(816\) −3.00000 + 5.19615i −0.105021 + 0.181902i
\(817\) 0.464102 0.803848i 0.0162369 0.0281231i
\(818\) 16.2679i 0.568796i
\(819\) −25.6077 7.39230i −0.894805 0.258308i
\(820\) 0 0
\(821\) 17.4904 + 10.0981i 0.610419 + 0.352425i 0.773129 0.634249i \(-0.218690\pi\)
−0.162711 + 0.986674i \(0.552024\pi\)
\(822\) −1.39230 0.803848i −0.0485622 0.0280374i
\(823\) −23.5526 + 13.5981i −0.820991 + 0.473999i −0.850758 0.525558i \(-0.823857\pi\)
0.0297674 + 0.999557i \(0.490523\pi\)
\(824\) 9.19615i 0.320363i
\(825\) 0 0
\(826\) −27.0000 + 15.5885i −0.939450 + 0.542392i
\(827\) −42.5885 −1.48095 −0.740473 0.672086i \(-0.765398\pi\)
−0.740473 + 0.672086i \(0.765398\pi\)
\(828\) 20.1962 11.6603i 0.701865 0.405222i
\(829\) −10.0000 + 17.3205i −0.347314 + 0.601566i −0.985771 0.168091i \(-0.946240\pi\)
0.638457 + 0.769657i \(0.279573\pi\)
\(830\) 0 0
\(831\) −0.732051 −0.0253946
\(832\) 0.866025 + 3.50000i 0.0300240 + 0.121341i
\(833\) 16.3923i 0.567960i
\(834\) 0.758330 + 0.437822i 0.0262588 + 0.0151605i
\(835\) 0 0
\(836\) −0.696152 1.20577i −0.0240769 0.0417025i
\(837\) −18.9282 −0.654254
\(838\) −8.66025 15.0000i −0.299164 0.518166i
\(839\) −18.8827 + 10.9019i −0.651903 + 0.376376i −0.789185 0.614156i \(-0.789497\pi\)
0.137282 + 0.990532i \(0.456163\pi\)
\(840\) 0 0
\(841\) 11.2846 + 19.5455i 0.389124 + 0.673983i
\(842\) −2.49038 1.43782i −0.0858242 0.0495506i
\(843\) −3.80385 + 6.58846i −0.131011 + 0.226919i
\(844\) −17.5885 −0.605420
\(845\) 0 0
\(846\) 7.39230 0.254153
\(847\) −3.00000 + 5.19615i −0.103081 + 0.178542i
\(848\) −0.401924 0.232051i −0.0138021 0.00796866i
\(849\) −3.51666 6.09103i −0.120691 0.209044i
\(850\) 0 0
\(851\) 6.58846 3.80385i 0.225849 0.130394i
\(852\) −2.19615 3.80385i −0.0752389 0.130318i
\(853\) −13.8564 −0.474434 −0.237217 0.971457i \(-0.576235\pi\)
−0.237217 + 0.971457i \(0.576235\pi\)
\(854\) −9.29423 16.0981i −0.318042 0.550865i
\(855\) 0 0
\(856\) 15.2942 + 8.83013i 0.522746 + 0.301808i
\(857\) 16.7321i 0.571556i 0.958296 + 0.285778i \(0.0922520\pi\)
−0.958296 + 0.285778i \(0.907748\pi\)
\(858\) 1.90192 + 7.68653i 0.0649306 + 0.262414i
\(859\) 20.3731 0.695120 0.347560 0.937658i \(-0.387010\pi\)
0.347560 + 0.937658i \(0.387010\pi\)
\(860\) 0 0
\(861\) 11.4115 19.7654i 0.388904 0.673602i
\(862\) 7.09808 4.09808i 0.241761 0.139581i
\(863\) −43.1769 −1.46976 −0.734880 0.678198i \(-0.762761\pi\)
−0.734880 + 0.678198i \(0.762761\pi\)
\(864\) 3.46410 2.00000i 0.117851 0.0680414i
\(865\) 0 0
\(866\) 8.39230i 0.285182i
\(867\) −31.8109 + 18.3660i −1.08035 + 0.623743i
\(868\) −12.2942 7.09808i −0.417293 0.240924i
\(869\) 10.9019 + 6.29423i 0.369822 + 0.213517i
\(870\) 0 0
\(871\) 0 0
\(872\) 8.53590i 0.289062i
\(873\) −11.2417 + 19.4711i −0.380473 + 0.658998i
\(874\) 2.19615 3.80385i 0.0742860 0.128667i
\(875\) 0 0
\(876\) 8.53590i 0.288401i
\(877\) 13.7321 + 23.7846i 0.463698 + 0.803149i 0.999142 0.0414220i \(-0.0131888\pi\)
−0.535443 + 0.844571i \(0.679855\pi\)
\(878\) −1.70577 2.95448i −0.0575670 0.0997090i
\(879\) 8.19615i 0.276449i
\(880\) 0 0
\(881\) −13.1603 + 22.7942i −0.443380 + 0.767957i −0.997938 0.0641883i \(-0.979554\pi\)
0.554558 + 0.832145i \(0.312888\pi\)
\(882\) −2.46410 + 4.26795i −0.0829706 + 0.143709i
\(883\) 4.58846i 0.154414i 0.997015 + 0.0772069i \(0.0246002\pi\)
−0.997015 + 0.0772069i \(0.975400\pi\)
\(884\) −8.19615 + 28.3923i −0.275666 + 0.954937i
\(885\) 0 0
\(886\) 19.3923 + 11.1962i 0.651497 + 0.376142i
\(887\) −35.3038 20.3827i −1.18539 0.684384i −0.228133 0.973630i \(-0.573262\pi\)
−0.957255 + 0.289246i \(0.906595\pi\)
\(888\) 0.509619 0.294229i 0.0171017 0.00987367i
\(889\) 32.4115i 1.08705i
\(890\) 0 0
\(891\) −11.5981 + 6.69615i −0.388550 + 0.224330i
\(892\) −6.46410 −0.216434
\(893\) 1.20577 0.696152i 0.0403496 0.0232959i
\(894\) −2.19615 + 3.80385i −0.0734503 + 0.127220i
\(895\) 0 0
\(896\) 3.00000 0.100223
\(897\) −18.0000 + 17.3205i −0.601003 + 0.578315i
\(898\) 15.5885i 0.520194i
\(899\) −10.3923 6.00000i −0.346603 0.200111i
\(900\) 0 0
\(901\) −1.90192 3.29423i −0.0633623 0.109747i
\(902\) 31.1769 1.03808
\(903\) 2.19615 + 3.80385i 0.0730834 + 0.126584i
\(904\) 6.00000 3.46410i 0.199557 0.115214i
\(905\) 0 0
\(906\) −8.66025 15.0000i −0.287718 0.498342i
\(907\) 3.97372 + 2.29423i 0.131945 + 0.0761786i 0.564520 0.825420i \(-0.309061\pi\)
−0.432574 + 0.901598i \(0.642395\pi\)
\(908\) −8.19615 + 14.1962i −0.271999 + 0.471116i
\(909\) 26.4449 0.877121
\(910\) 0 0
\(911\) −21.4641 −0.711137 −0.355569 0.934650i \(-0.615713\pi\)
−0.355569 + 0.934650i \(0.615713\pi\)
\(912\) 0.169873 0.294229i 0.00562506 0.00974288i
\(913\) 21.2942 + 12.2942i 0.704736 + 0.406880i
\(914\) 9.16987 + 15.8827i 0.303312 + 0.525353i
\(915\) 0 0
\(916\) 1.09808 0.633975i 0.0362815 0.0209471i
\(917\) −9.18653 15.9115i −0.303366 0.525445i
\(918\) 32.7846 1.08205
\(919\) 15.3923 + 26.6603i 0.507745 + 0.879441i 0.999960 + 0.00896670i \(0.00285423\pi\)
−0.492215 + 0.870474i \(0.663812\pi\)
\(920\) 0 0
\(921\) 17.4115 + 10.0526i 0.573730 + 0.331243i
\(922\) 30.5885i 1.00738i
\(923\) −15.0000 15.5885i −0.493731 0.513100i
\(924\) 6.58846 0.216744
\(925\) 0 0
\(926\) 6.46410 11.1962i 0.212424 0.367928i
\(927\) −19.6244 + 11.3301i −0.644548 + 0.372130i
\(928\) 2.53590 0.0832449
\(929\) 2.78461 1.60770i 0.0913601 0.0527468i −0.453624 0.891193i \(-0.649869\pi\)
0.544984 + 0.838446i \(0.316536\pi\)
\(930\) 0 0
\(931\) 0.928203i 0.0304206i
\(932\) 4.09808 2.36603i 0.134237 0.0775017i
\(933\) 5.78461 + 3.33975i 0.189380 + 0.109338i
\(934\) −32.7846 18.9282i −1.07275 0.619350i
\(935\) 0 0
\(936\) 6.40192 6.16025i 0.209253 0.201354i
\(937\) 9.60770i 0.313870i 0.987609 + 0.156935i \(0.0501613\pi\)
−0.987609 + 0.156935i \(0.949839\pi\)
\(938\) 0 0
\(939\) 9.66025 16.7321i 0.315250 0.546030i
\(940\) 0 0
\(941\) 3.21539i 0.104819i 0.998626 + 0.0524094i \(0.0166901\pi\)
−0.998626 + 0.0524094i \(0.983310\pi\)
\(942\) 4.75833 + 8.24167i 0.155035 + 0.268528i
\(943\) 49.1769 + 85.1769i 1.60142 + 2.77374i
\(944\) 10.3923i 0.338241i
\(945\) 0 0
\(946\) −3.00000 + 5.19615i −0.0975384 + 0.168941i
\(947\) 7.68653 13.3135i 0.249779 0.432630i −0.713686 0.700466i \(-0.752975\pi\)
0.963464 + 0.267837i \(0.0863088\pi\)
\(948\) 3.07180i 0.0997673i
\(949\) −10.0981 40.8109i −0.327797 1.32478i
\(950\) 0 0
\(951\) 14.7058 + 8.49038i 0.476867 + 0.275319i
\(952\) 21.2942 + 12.2942i 0.690150 + 0.398458i
\(953\) −5.70577 + 3.29423i −0.184828 + 0.106711i −0.589559 0.807725i \(-0.700698\pi\)
0.404731 + 0.914436i \(0.367365\pi\)
\(954\) 1.14359i 0.0370252i
\(955\) 0 0
\(956\) −1.90192 + 1.09808i −0.0615126 + 0.0355143i
\(957\) 5.56922 0.180027
\(958\) −35.4904 + 20.4904i −1.14664 + 0.662014i
\(959\) −3.29423 + 5.70577i −0.106376 + 0.184249i
\(960\) 0 0
\(961\) 8.60770 0.277668
\(962\) 2.08846 2.00962i 0.0673346 0.0647927i
\(963\) 43.5167i 1.40230i
\(964\) 7.50000 + 4.33013i 0.241559 + 0.139464i
\(965\) 0 0
\(966\) 10.3923 + 18.0000i 0.334367 + 0.579141i
\(967\) −44.5692 −1.43325 −0.716625 0.697459i \(-0.754314\pi\)
−0.716625 + 0.697459i \(0.754314\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) 2.41154 1.39230i 0.0774699 0.0447273i
\(970\) 0 0
\(971\) −23.3827 40.5000i −0.750386 1.29971i −0.947636 0.319354i \(-0.896534\pi\)
0.197250 0.980353i \(-0.436799\pi\)
\(972\) −13.2224 7.63397i −0.424110 0.244860i
\(973\) 1.79423 3.10770i 0.0575203 0.0996281i
\(974\) −15.2487 −0.488600
\(975\) 0 0
\(976\) 6.19615 0.198334
\(977\) 8.19615 14.1962i 0.262218 0.454175i −0.704613 0.709592i \(-0.748879\pi\)
0.966831 + 0.255417i \(0.0822127\pi\)
\(978\) −6.80385 3.92820i −0.217563 0.125610i
\(979\) −10.2058 17.6769i −0.326178 0.564957i
\(980\) 0 0
\(981\) 18.2154 10.5167i 0.581573 0.335771i
\(982\) −10.3301 17.8923i −0.329648 0.570966i
\(983\) −44.5692 −1.42154 −0.710769 0.703426i \(-0.751653\pi\)
−0.710769 + 0.703426i \(0.751653\pi\)
\(984\) 3.80385 + 6.58846i 0.121262 + 0.210032i
\(985\) 0 0
\(986\) 18.0000 + 10.3923i 0.573237 + 0.330958i
\(987\) 6.58846i 0.209713i
\(988\) 0.464102 1.60770i 0.0147650 0.0511476i
\(989\) −18.9282 −0.601882
\(990\) 0 0
\(991\) 5.58846 9.67949i 0.177523 0.307479i −0.763508 0.645798i \(-0.776525\pi\)
0.941032 + 0.338319i \(0.109858\pi\)
\(992\) 4.09808 2.36603i 0.130114 0.0751214i
\(993\) −9.46410 −0.300334
\(994\) −15.5885 + 9.00000i −0.494436 + 0.285463i
\(995\) 0 0
\(996\) 6.00000i 0.190117i
\(997\) −35.1340 + 20.2846i −1.11270 + 0.642420i −0.939528 0.342471i \(-0.888736\pi\)
−0.173176 + 0.984891i \(0.555403\pi\)
\(998\) 22.3923 + 12.9282i 0.708816 + 0.409235i
\(999\) −2.78461 1.60770i −0.0881012 0.0508652i
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 650.2.n.a.199.2 4
5.2 odd 4 130.2.l.a.121.1 yes 4
5.3 odd 4 650.2.m.a.251.2 4
5.4 even 2 650.2.n.b.199.1 4
13.10 even 6 650.2.n.b.49.1 4
15.2 even 4 1170.2.bs.c.901.2 4
20.7 even 4 1040.2.da.a.641.2 4
65.2 even 12 1690.2.e.l.991.1 4
65.7 even 12 1690.2.a.j.1.2 2
65.12 odd 4 1690.2.l.g.1161.2 4
65.17 odd 12 1690.2.d.f.1351.2 4
65.22 odd 12 1690.2.d.f.1351.4 4
65.23 odd 12 650.2.m.a.101.2 4
65.32 even 12 1690.2.a.m.1.2 2
65.33 even 12 8450.2.a.bm.1.1 2
65.37 even 12 1690.2.e.n.991.1 4
65.42 odd 12 1690.2.l.g.361.2 4
65.47 even 4 1690.2.e.n.191.1 4
65.49 even 6 inner 650.2.n.a.49.2 4
65.57 even 4 1690.2.e.l.191.1 4
65.58 even 12 8450.2.a.bf.1.1 2
65.62 odd 12 130.2.l.a.101.1 4
195.62 even 12 1170.2.bs.c.361.2 4
260.127 even 12 1040.2.da.a.881.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.l.a.101.1 4 65.62 odd 12
130.2.l.a.121.1 yes 4 5.2 odd 4
650.2.m.a.101.2 4 65.23 odd 12
650.2.m.a.251.2 4 5.3 odd 4
650.2.n.a.49.2 4 65.49 even 6 inner
650.2.n.a.199.2 4 1.1 even 1 trivial
650.2.n.b.49.1 4 13.10 even 6
650.2.n.b.199.1 4 5.4 even 2
1040.2.da.a.641.2 4 20.7 even 4
1040.2.da.a.881.2 4 260.127 even 12
1170.2.bs.c.361.2 4 195.62 even 12
1170.2.bs.c.901.2 4 15.2 even 4
1690.2.a.j.1.2 2 65.7 even 12
1690.2.a.m.1.2 2 65.32 even 12
1690.2.d.f.1351.2 4 65.17 odd 12
1690.2.d.f.1351.4 4 65.22 odd 12
1690.2.e.l.191.1 4 65.57 even 4
1690.2.e.l.991.1 4 65.2 even 12
1690.2.e.n.191.1 4 65.47 even 4
1690.2.e.n.991.1 4 65.37 even 12
1690.2.l.g.361.2 4 65.42 odd 12
1690.2.l.g.1161.2 4 65.12 odd 4
8450.2.a.bf.1.1 2 65.58 even 12
8450.2.a.bm.1.1 2 65.33 even 12