Properties

Label 8034.2.a.s.1.2
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8034,2,Mod(1,8034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

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: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(4.13381\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.24210 q^{5} +1.00000 q^{6} -4.80624 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.24210 q^{5} +1.00000 q^{6} -4.80624 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.24210 q^{10} -5.91070 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.80624 q^{14} +2.24210 q^{15} +1.00000 q^{16} +0.672431 q^{17} -1.00000 q^{18} -6.07560 q^{19} -2.24210 q^{20} +4.80624 q^{21} +5.91070 q^{22} -1.49584 q^{23} +1.00000 q^{24} +0.0270290 q^{25} +1.00000 q^{26} -1.00000 q^{27} -4.80624 q^{28} +4.90360 q^{29} -2.24210 q^{30} -0.627355 q^{31} -1.00000 q^{32} +5.91070 q^{33} -0.672431 q^{34} +10.7761 q^{35} +1.00000 q^{36} +9.51867 q^{37} +6.07560 q^{38} +1.00000 q^{39} +2.24210 q^{40} +4.06918 q^{41} -4.80624 q^{42} +8.49168 q^{43} -5.91070 q^{44} -2.24210 q^{45} +1.49584 q^{46} +3.45713 q^{47} -1.00000 q^{48} +16.0999 q^{49} -0.0270290 q^{50} -0.672431 q^{51} -1.00000 q^{52} +7.99289 q^{53} +1.00000 q^{54} +13.2524 q^{55} +4.80624 q^{56} +6.07560 q^{57} -4.90360 q^{58} +4.41705 q^{59} +2.24210 q^{60} -5.58215 q^{61} +0.627355 q^{62} -4.80624 q^{63} +1.00000 q^{64} +2.24210 q^{65} -5.91070 q^{66} -0.920585 q^{67} +0.672431 q^{68} +1.49584 q^{69} -10.7761 q^{70} -1.63814 q^{71} -1.00000 q^{72} -13.4188 q^{73} -9.51867 q^{74} -0.0270290 q^{75} -6.07560 q^{76} +28.4082 q^{77} -1.00000 q^{78} -6.26995 q^{79} -2.24210 q^{80} +1.00000 q^{81} -4.06918 q^{82} -5.91252 q^{83} +4.80624 q^{84} -1.50766 q^{85} -8.49168 q^{86} -4.90360 q^{87} +5.91070 q^{88} +8.71748 q^{89} +2.24210 q^{90} +4.80624 q^{91} -1.49584 q^{92} +0.627355 q^{93} -3.45713 q^{94} +13.6221 q^{95} +1.00000 q^{96} -4.09607 q^{97} -16.0999 q^{98} -5.91070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −2.24210 −1.00270 −0.501350 0.865245i \(-0.667163\pi\)
−0.501350 + 0.865245i \(0.667163\pi\)
\(6\) 1.00000 0.408248
\(7\) −4.80624 −1.81659 −0.908294 0.418332i \(-0.862615\pi\)
−0.908294 + 0.418332i \(0.862615\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.24210 0.709015
\(11\) −5.91070 −1.78214 −0.891071 0.453864i \(-0.850045\pi\)
−0.891071 + 0.453864i \(0.850045\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) 4.80624 1.28452
\(15\) 2.24210 0.578909
\(16\) 1.00000 0.250000
\(17\) 0.672431 0.163088 0.0815442 0.996670i \(-0.474015\pi\)
0.0815442 + 0.996670i \(0.474015\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.07560 −1.39384 −0.696919 0.717150i \(-0.745446\pi\)
−0.696919 + 0.717150i \(0.745446\pi\)
\(20\) −2.24210 −0.501350
\(21\) 4.80624 1.04881
\(22\) 5.91070 1.26016
\(23\) −1.49584 −0.311903 −0.155952 0.987765i \(-0.549844\pi\)
−0.155952 + 0.987765i \(0.549844\pi\)
\(24\) 1.00000 0.204124
\(25\) 0.0270290 0.00540581
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) −4.80624 −0.908294
\(29\) 4.90360 0.910575 0.455288 0.890344i \(-0.349536\pi\)
0.455288 + 0.890344i \(0.349536\pi\)
\(30\) −2.24210 −0.409350
\(31\) −0.627355 −0.112676 −0.0563381 0.998412i \(-0.517942\pi\)
−0.0563381 + 0.998412i \(0.517942\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.91070 1.02892
\(34\) −0.672431 −0.115321
\(35\) 10.7761 1.82149
\(36\) 1.00000 0.166667
\(37\) 9.51867 1.56486 0.782430 0.622739i \(-0.213980\pi\)
0.782430 + 0.622739i \(0.213980\pi\)
\(38\) 6.07560 0.985592
\(39\) 1.00000 0.160128
\(40\) 2.24210 0.354508
\(41\) 4.06918 0.635500 0.317750 0.948175i \(-0.397073\pi\)
0.317750 + 0.948175i \(0.397073\pi\)
\(42\) −4.80624 −0.741619
\(43\) 8.49168 1.29497 0.647484 0.762079i \(-0.275821\pi\)
0.647484 + 0.762079i \(0.275821\pi\)
\(44\) −5.91070 −0.891071
\(45\) −2.24210 −0.334233
\(46\) 1.49584 0.220549
\(47\) 3.45713 0.504275 0.252137 0.967691i \(-0.418867\pi\)
0.252137 + 0.967691i \(0.418867\pi\)
\(48\) −1.00000 −0.144338
\(49\) 16.0999 2.29999
\(50\) −0.0270290 −0.00382248
\(51\) −0.672431 −0.0941591
\(52\) −1.00000 −0.138675
\(53\) 7.99289 1.09791 0.548954 0.835853i \(-0.315026\pi\)
0.548954 + 0.835853i \(0.315026\pi\)
\(54\) 1.00000 0.136083
\(55\) 13.2524 1.78695
\(56\) 4.80624 0.642261
\(57\) 6.07560 0.804733
\(58\) −4.90360 −0.643874
\(59\) 4.41705 0.575052 0.287526 0.957773i \(-0.407167\pi\)
0.287526 + 0.957773i \(0.407167\pi\)
\(60\) 2.24210 0.289454
\(61\) −5.58215 −0.714721 −0.357360 0.933967i \(-0.616323\pi\)
−0.357360 + 0.933967i \(0.616323\pi\)
\(62\) 0.627355 0.0796741
\(63\) −4.80624 −0.605529
\(64\) 1.00000 0.125000
\(65\) 2.24210 0.278099
\(66\) −5.91070 −0.727556
\(67\) −0.920585 −0.112467 −0.0562337 0.998418i \(-0.517909\pi\)
−0.0562337 + 0.998418i \(0.517909\pi\)
\(68\) 0.672431 0.0815442
\(69\) 1.49584 0.180077
\(70\) −10.7761 −1.28799
\(71\) −1.63814 −0.194411 −0.0972057 0.995264i \(-0.530990\pi\)
−0.0972057 + 0.995264i \(0.530990\pi\)
\(72\) −1.00000 −0.117851
\(73\) −13.4188 −1.57055 −0.785276 0.619146i \(-0.787479\pi\)
−0.785276 + 0.619146i \(0.787479\pi\)
\(74\) −9.51867 −1.10652
\(75\) −0.0270290 −0.00312104
\(76\) −6.07560 −0.696919
\(77\) 28.4082 3.23742
\(78\) −1.00000 −0.113228
\(79\) −6.26995 −0.705425 −0.352712 0.935732i \(-0.614741\pi\)
−0.352712 + 0.935732i \(0.614741\pi\)
\(80\) −2.24210 −0.250675
\(81\) 1.00000 0.111111
\(82\) −4.06918 −0.449366
\(83\) −5.91252 −0.648983 −0.324492 0.945889i \(-0.605193\pi\)
−0.324492 + 0.945889i \(0.605193\pi\)
\(84\) 4.80624 0.524404
\(85\) −1.50766 −0.163529
\(86\) −8.49168 −0.915681
\(87\) −4.90360 −0.525721
\(88\) 5.91070 0.630082
\(89\) 8.71748 0.924051 0.462025 0.886867i \(-0.347123\pi\)
0.462025 + 0.886867i \(0.347123\pi\)
\(90\) 2.24210 0.236338
\(91\) 4.80624 0.503831
\(92\) −1.49584 −0.155952
\(93\) 0.627355 0.0650537
\(94\) −3.45713 −0.356576
\(95\) 13.6221 1.39760
\(96\) 1.00000 0.102062
\(97\) −4.09607 −0.415893 −0.207947 0.978140i \(-0.566678\pi\)
−0.207947 + 0.978140i \(0.566678\pi\)
\(98\) −16.0999 −1.62634
\(99\) −5.91070 −0.594047
\(100\) 0.0270290 0.00270290
\(101\) −3.14660 −0.313099 −0.156549 0.987670i \(-0.550037\pi\)
−0.156549 + 0.987670i \(0.550037\pi\)
\(102\) 0.672431 0.0665805
\(103\) −1.00000 −0.0985329
\(104\) 1.00000 0.0980581
\(105\) −10.7761 −1.05164
\(106\) −7.99289 −0.776338
\(107\) −11.6094 −1.12232 −0.561161 0.827707i \(-0.689645\pi\)
−0.561161 + 0.827707i \(0.689645\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 1.42987 0.136957 0.0684785 0.997653i \(-0.478186\pi\)
0.0684785 + 0.997653i \(0.478186\pi\)
\(110\) −13.2524 −1.26357
\(111\) −9.51867 −0.903472
\(112\) −4.80624 −0.454147
\(113\) −4.63061 −0.435611 −0.217805 0.975992i \(-0.569890\pi\)
−0.217805 + 0.975992i \(0.569890\pi\)
\(114\) −6.07560 −0.569032
\(115\) 3.35382 0.312745
\(116\) 4.90360 0.455288
\(117\) −1.00000 −0.0924500
\(118\) −4.41705 −0.406623
\(119\) −3.23186 −0.296264
\(120\) −2.24210 −0.204675
\(121\) 23.9363 2.17603
\(122\) 5.58215 0.505384
\(123\) −4.06918 −0.366906
\(124\) −0.627355 −0.0563381
\(125\) 11.1499 0.997279
\(126\) 4.80624 0.428174
\(127\) 7.80292 0.692397 0.346198 0.938161i \(-0.387472\pi\)
0.346198 + 0.938161i \(0.387472\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.49168 −0.747650
\(130\) −2.24210 −0.196646
\(131\) 12.7886 1.11734 0.558671 0.829389i \(-0.311311\pi\)
0.558671 + 0.829389i \(0.311311\pi\)
\(132\) 5.91070 0.514460
\(133\) 29.2008 2.53203
\(134\) 0.920585 0.0795264
\(135\) 2.24210 0.192970
\(136\) −0.672431 −0.0576604
\(137\) 7.33630 0.626782 0.313391 0.949624i \(-0.398535\pi\)
0.313391 + 0.949624i \(0.398535\pi\)
\(138\) −1.49584 −0.127334
\(139\) 13.9536 1.18353 0.591763 0.806112i \(-0.298432\pi\)
0.591763 + 0.806112i \(0.298432\pi\)
\(140\) 10.7761 0.910746
\(141\) −3.45713 −0.291143
\(142\) 1.63814 0.137470
\(143\) 5.91070 0.494277
\(144\) 1.00000 0.0833333
\(145\) −10.9944 −0.913033
\(146\) 13.4188 1.11055
\(147\) −16.0999 −1.32790
\(148\) 9.51867 0.782430
\(149\) 7.46230 0.611335 0.305668 0.952138i \(-0.401120\pi\)
0.305668 + 0.952138i \(0.401120\pi\)
\(150\) 0.0270290 0.00220691
\(151\) −22.9189 −1.86512 −0.932558 0.361020i \(-0.882429\pi\)
−0.932558 + 0.361020i \(0.882429\pi\)
\(152\) 6.07560 0.492796
\(153\) 0.672431 0.0543628
\(154\) −28.4082 −2.28920
\(155\) 1.40659 0.112980
\(156\) 1.00000 0.0800641
\(157\) −1.63459 −0.130454 −0.0652272 0.997870i \(-0.520777\pi\)
−0.0652272 + 0.997870i \(0.520777\pi\)
\(158\) 6.26995 0.498811
\(159\) −7.99289 −0.633877
\(160\) 2.24210 0.177254
\(161\) 7.18935 0.566600
\(162\) −1.00000 −0.0785674
\(163\) −11.6719 −0.914212 −0.457106 0.889412i \(-0.651114\pi\)
−0.457106 + 0.889412i \(0.651114\pi\)
\(164\) 4.06918 0.317750
\(165\) −13.2524 −1.03170
\(166\) 5.91252 0.458901
\(167\) 16.4960 1.27650 0.638249 0.769830i \(-0.279659\pi\)
0.638249 + 0.769830i \(0.279659\pi\)
\(168\) −4.80624 −0.370810
\(169\) 1.00000 0.0769231
\(170\) 1.50766 0.115632
\(171\) −6.07560 −0.464613
\(172\) 8.49168 0.647484
\(173\) 3.96489 0.301445 0.150722 0.988576i \(-0.451840\pi\)
0.150722 + 0.988576i \(0.451840\pi\)
\(174\) 4.90360 0.371741
\(175\) −0.129908 −0.00982012
\(176\) −5.91070 −0.445535
\(177\) −4.41705 −0.332006
\(178\) −8.71748 −0.653402
\(179\) −24.2136 −1.80981 −0.904904 0.425616i \(-0.860057\pi\)
−0.904904 + 0.425616i \(0.860057\pi\)
\(180\) −2.24210 −0.167117
\(181\) −22.6425 −1.68301 −0.841503 0.540252i \(-0.818329\pi\)
−0.841503 + 0.540252i \(0.818329\pi\)
\(182\) −4.80624 −0.356262
\(183\) 5.58215 0.412644
\(184\) 1.49584 0.110274
\(185\) −21.3418 −1.56908
\(186\) −0.627355 −0.0459999
\(187\) −3.97453 −0.290647
\(188\) 3.45713 0.252137
\(189\) 4.80624 0.349603
\(190\) −13.6221 −0.988253
\(191\) −9.27186 −0.670888 −0.335444 0.942060i \(-0.608886\pi\)
−0.335444 + 0.942060i \(0.608886\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −3.75521 −0.270306 −0.135153 0.990825i \(-0.543153\pi\)
−0.135153 + 0.990825i \(0.543153\pi\)
\(194\) 4.09607 0.294081
\(195\) −2.24210 −0.160560
\(196\) 16.0999 1.15000
\(197\) −0.598107 −0.0426133 −0.0213067 0.999773i \(-0.506783\pi\)
−0.0213067 + 0.999773i \(0.506783\pi\)
\(198\) 5.91070 0.420055
\(199\) 14.1966 1.00637 0.503185 0.864179i \(-0.332161\pi\)
0.503185 + 0.864179i \(0.332161\pi\)
\(200\) −0.0270290 −0.00191124
\(201\) 0.920585 0.0649331
\(202\) 3.14660 0.221394
\(203\) −23.5679 −1.65414
\(204\) −0.672431 −0.0470796
\(205\) −9.12353 −0.637215
\(206\) 1.00000 0.0696733
\(207\) −1.49584 −0.103968
\(208\) −1.00000 −0.0693375
\(209\) 35.9110 2.48402
\(210\) 10.7761 0.743621
\(211\) −18.6089 −1.28109 −0.640544 0.767922i \(-0.721291\pi\)
−0.640544 + 0.767922i \(0.721291\pi\)
\(212\) 7.99289 0.548954
\(213\) 1.63814 0.112243
\(214\) 11.6094 0.793601
\(215\) −19.0392 −1.29846
\(216\) 1.00000 0.0680414
\(217\) 3.01522 0.204686
\(218\) −1.42987 −0.0968433
\(219\) 13.4188 0.906758
\(220\) 13.2524 0.893476
\(221\) −0.672431 −0.0452326
\(222\) 9.51867 0.638851
\(223\) 10.3883 0.695655 0.347827 0.937559i \(-0.386919\pi\)
0.347827 + 0.937559i \(0.386919\pi\)
\(224\) 4.80624 0.321130
\(225\) 0.0270290 0.00180194
\(226\) 4.63061 0.308023
\(227\) 16.8032 1.11527 0.557635 0.830087i \(-0.311709\pi\)
0.557635 + 0.830087i \(0.311709\pi\)
\(228\) 6.07560 0.402366
\(229\) 9.48249 0.626621 0.313310 0.949651i \(-0.398562\pi\)
0.313310 + 0.949651i \(0.398562\pi\)
\(230\) −3.35382 −0.221144
\(231\) −28.4082 −1.86912
\(232\) −4.90360 −0.321937
\(233\) −12.4591 −0.816221 −0.408111 0.912932i \(-0.633812\pi\)
−0.408111 + 0.912932i \(0.633812\pi\)
\(234\) 1.00000 0.0653720
\(235\) −7.75125 −0.505636
\(236\) 4.41705 0.287526
\(237\) 6.26995 0.407277
\(238\) 3.23186 0.209491
\(239\) 2.52514 0.163338 0.0816688 0.996660i \(-0.473975\pi\)
0.0816688 + 0.996660i \(0.473975\pi\)
\(240\) 2.24210 0.144727
\(241\) −1.47817 −0.0952174 −0.0476087 0.998866i \(-0.515160\pi\)
−0.0476087 + 0.998866i \(0.515160\pi\)
\(242\) −23.9363 −1.53869
\(243\) −1.00000 −0.0641500
\(244\) −5.58215 −0.357360
\(245\) −36.0978 −2.30620
\(246\) 4.06918 0.259442
\(247\) 6.07560 0.386581
\(248\) 0.627355 0.0398371
\(249\) 5.91252 0.374691
\(250\) −11.1499 −0.705183
\(251\) 26.9090 1.69848 0.849240 0.528008i \(-0.177061\pi\)
0.849240 + 0.528008i \(0.177061\pi\)
\(252\) −4.80624 −0.302765
\(253\) 8.84143 0.555856
\(254\) −7.80292 −0.489599
\(255\) 1.50766 0.0944133
\(256\) 1.00000 0.0625000
\(257\) −3.78562 −0.236141 −0.118070 0.993005i \(-0.537671\pi\)
−0.118070 + 0.993005i \(0.537671\pi\)
\(258\) 8.49168 0.528669
\(259\) −45.7490 −2.84271
\(260\) 2.24210 0.139049
\(261\) 4.90360 0.303525
\(262\) −12.7886 −0.790081
\(263\) 0.134193 0.00827467 0.00413734 0.999991i \(-0.498683\pi\)
0.00413734 + 0.999991i \(0.498683\pi\)
\(264\) −5.91070 −0.363778
\(265\) −17.9209 −1.10087
\(266\) −29.2008 −1.79042
\(267\) −8.71748 −0.533501
\(268\) −0.920585 −0.0562337
\(269\) −2.04038 −0.124404 −0.0622021 0.998064i \(-0.519812\pi\)
−0.0622021 + 0.998064i \(0.519812\pi\)
\(270\) −2.24210 −0.136450
\(271\) −12.6125 −0.766153 −0.383077 0.923717i \(-0.625136\pi\)
−0.383077 + 0.923717i \(0.625136\pi\)
\(272\) 0.672431 0.0407721
\(273\) −4.80624 −0.290887
\(274\) −7.33630 −0.443202
\(275\) −0.159760 −0.00963391
\(276\) 1.49584 0.0900387
\(277\) 6.51103 0.391210 0.195605 0.980683i \(-0.437333\pi\)
0.195605 + 0.980683i \(0.437333\pi\)
\(278\) −13.9536 −0.836879
\(279\) −0.627355 −0.0375588
\(280\) −10.7761 −0.643995
\(281\) 32.0118 1.90967 0.954833 0.297142i \(-0.0960334\pi\)
0.954833 + 0.297142i \(0.0960334\pi\)
\(282\) 3.45713 0.205869
\(283\) −23.0851 −1.37227 −0.686133 0.727476i \(-0.740693\pi\)
−0.686133 + 0.727476i \(0.740693\pi\)
\(284\) −1.63814 −0.0972057
\(285\) −13.6221 −0.806905
\(286\) −5.91070 −0.349507
\(287\) −19.5575 −1.15444
\(288\) −1.00000 −0.0589256
\(289\) −16.5478 −0.973402
\(290\) 10.9944 0.645612
\(291\) 4.09607 0.240116
\(292\) −13.4188 −0.785276
\(293\) −5.80059 −0.338874 −0.169437 0.985541i \(-0.554195\pi\)
−0.169437 + 0.985541i \(0.554195\pi\)
\(294\) 16.0999 0.938968
\(295\) −9.90350 −0.576604
\(296\) −9.51867 −0.553262
\(297\) 5.91070 0.342973
\(298\) −7.46230 −0.432279
\(299\) 1.49584 0.0865064
\(300\) −0.0270290 −0.00156052
\(301\) −40.8130 −2.35242
\(302\) 22.9189 1.31884
\(303\) 3.14660 0.180768
\(304\) −6.07560 −0.348460
\(305\) 12.5158 0.716650
\(306\) −0.672431 −0.0384403
\(307\) −23.0901 −1.31782 −0.658911 0.752221i \(-0.728983\pi\)
−0.658911 + 0.752221i \(0.728983\pi\)
\(308\) 28.4082 1.61871
\(309\) 1.00000 0.0568880
\(310\) −1.40659 −0.0798892
\(311\) 19.8514 1.12567 0.562836 0.826569i \(-0.309710\pi\)
0.562836 + 0.826569i \(0.309710\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 18.6054 1.05164 0.525820 0.850596i \(-0.323759\pi\)
0.525820 + 0.850596i \(0.323759\pi\)
\(314\) 1.63459 0.0922451
\(315\) 10.7761 0.607164
\(316\) −6.26995 −0.352712
\(317\) −16.6967 −0.937783 −0.468891 0.883256i \(-0.655346\pi\)
−0.468891 + 0.883256i \(0.655346\pi\)
\(318\) 7.99289 0.448219
\(319\) −28.9837 −1.62277
\(320\) −2.24210 −0.125337
\(321\) 11.6094 0.647973
\(322\) −7.18935 −0.400647
\(323\) −4.08542 −0.227319
\(324\) 1.00000 0.0555556
\(325\) −0.0270290 −0.00149930
\(326\) 11.6719 0.646446
\(327\) −1.42987 −0.0790722
\(328\) −4.06918 −0.224683
\(329\) −16.6158 −0.916060
\(330\) 13.2524 0.729520
\(331\) 4.68546 0.257536 0.128768 0.991675i \(-0.458898\pi\)
0.128768 + 0.991675i \(0.458898\pi\)
\(332\) −5.91252 −0.324492
\(333\) 9.51867 0.521620
\(334\) −16.4960 −0.902620
\(335\) 2.06405 0.112771
\(336\) 4.80624 0.262202
\(337\) 11.0153 0.600040 0.300020 0.953933i \(-0.403007\pi\)
0.300020 + 0.953933i \(0.403007\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 4.63061 0.251500
\(340\) −1.50766 −0.0817643
\(341\) 3.70810 0.200805
\(342\) 6.07560 0.328531
\(343\) −43.7365 −2.36155
\(344\) −8.49168 −0.457841
\(345\) −3.35382 −0.180564
\(346\) −3.96489 −0.213154
\(347\) 29.7512 1.59713 0.798563 0.601911i \(-0.205594\pi\)
0.798563 + 0.601911i \(0.205594\pi\)
\(348\) −4.90360 −0.262860
\(349\) 1.29640 0.0693945 0.0346973 0.999398i \(-0.488953\pi\)
0.0346973 + 0.999398i \(0.488953\pi\)
\(350\) 0.129908 0.00694388
\(351\) 1.00000 0.0533761
\(352\) 5.91070 0.315041
\(353\) 32.1071 1.70889 0.854443 0.519545i \(-0.173898\pi\)
0.854443 + 0.519545i \(0.173898\pi\)
\(354\) 4.41705 0.234764
\(355\) 3.67288 0.194936
\(356\) 8.71748 0.462025
\(357\) 3.23186 0.171048
\(358\) 24.2136 1.27973
\(359\) 6.85815 0.361959 0.180980 0.983487i \(-0.442073\pi\)
0.180980 + 0.983487i \(0.442073\pi\)
\(360\) 2.24210 0.118169
\(361\) 17.9129 0.942785
\(362\) 22.6425 1.19007
\(363\) −23.9363 −1.25633
\(364\) 4.80624 0.251915
\(365\) 30.0863 1.57479
\(366\) −5.58215 −0.291784
\(367\) 0.851961 0.0444720 0.0222360 0.999753i \(-0.492921\pi\)
0.0222360 + 0.999753i \(0.492921\pi\)
\(368\) −1.49584 −0.0779758
\(369\) 4.06918 0.211833
\(370\) 21.3418 1.10951
\(371\) −38.4157 −1.99445
\(372\) 0.627355 0.0325268
\(373\) 23.4478 1.21408 0.607039 0.794672i \(-0.292357\pi\)
0.607039 + 0.794672i \(0.292357\pi\)
\(374\) 3.97453 0.205518
\(375\) −11.1499 −0.575779
\(376\) −3.45713 −0.178288
\(377\) −4.90360 −0.252548
\(378\) −4.80624 −0.247206
\(379\) 14.6048 0.750198 0.375099 0.926985i \(-0.377609\pi\)
0.375099 + 0.926985i \(0.377609\pi\)
\(380\) 13.6221 0.698800
\(381\) −7.80292 −0.399756
\(382\) 9.27186 0.474390
\(383\) 24.8699 1.27079 0.635395 0.772187i \(-0.280837\pi\)
0.635395 + 0.772187i \(0.280837\pi\)
\(384\) 1.00000 0.0510310
\(385\) −63.6942 −3.24616
\(386\) 3.75521 0.191135
\(387\) 8.49168 0.431656
\(388\) −4.09607 −0.207947
\(389\) −29.8539 −1.51365 −0.756826 0.653616i \(-0.773251\pi\)
−0.756826 + 0.653616i \(0.773251\pi\)
\(390\) 2.24210 0.113533
\(391\) −1.00585 −0.0508678
\(392\) −16.0999 −0.813170
\(393\) −12.7886 −0.645098
\(394\) 0.598107 0.0301322
\(395\) 14.0579 0.707329
\(396\) −5.91070 −0.297024
\(397\) 32.7033 1.64133 0.820666 0.571408i \(-0.193603\pi\)
0.820666 + 0.571408i \(0.193603\pi\)
\(398\) −14.1966 −0.711611
\(399\) −29.2008 −1.46187
\(400\) 0.0270290 0.00135145
\(401\) −21.0049 −1.04893 −0.524467 0.851431i \(-0.675735\pi\)
−0.524467 + 0.851431i \(0.675735\pi\)
\(402\) −0.920585 −0.0459146
\(403\) 0.627355 0.0312508
\(404\) −3.14660 −0.156549
\(405\) −2.24210 −0.111411
\(406\) 23.5679 1.16965
\(407\) −56.2620 −2.78880
\(408\) 0.672431 0.0332903
\(409\) 0.600833 0.0297093 0.0148546 0.999890i \(-0.495271\pi\)
0.0148546 + 0.999890i \(0.495271\pi\)
\(410\) 9.12353 0.450579
\(411\) −7.33630 −0.361873
\(412\) −1.00000 −0.0492665
\(413\) −21.2294 −1.04463
\(414\) 1.49584 0.0735163
\(415\) 13.2565 0.650735
\(416\) 1.00000 0.0490290
\(417\) −13.9536 −0.683309
\(418\) −35.9110 −1.75647
\(419\) 17.3081 0.845556 0.422778 0.906233i \(-0.361055\pi\)
0.422778 + 0.906233i \(0.361055\pi\)
\(420\) −10.7761 −0.525819
\(421\) 25.2015 1.22825 0.614123 0.789210i \(-0.289510\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(422\) 18.6089 0.905866
\(423\) 3.45713 0.168092
\(424\) −7.99289 −0.388169
\(425\) 0.0181751 0.000881624 0
\(426\) −1.63814 −0.0793681
\(427\) 26.8291 1.29835
\(428\) −11.6094 −0.561161
\(429\) −5.91070 −0.285371
\(430\) 19.0392 0.918153
\(431\) 0.589597 0.0283999 0.0141999 0.999899i \(-0.495480\pi\)
0.0141999 + 0.999899i \(0.495480\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 24.6034 1.18236 0.591182 0.806538i \(-0.298662\pi\)
0.591182 + 0.806538i \(0.298662\pi\)
\(434\) −3.01522 −0.144735
\(435\) 10.9944 0.527140
\(436\) 1.42987 0.0684785
\(437\) 9.08810 0.434743
\(438\) −13.4188 −0.641175
\(439\) 15.3763 0.733873 0.366936 0.930246i \(-0.380407\pi\)
0.366936 + 0.930246i \(0.380407\pi\)
\(440\) −13.2524 −0.631783
\(441\) 16.0999 0.766664
\(442\) 0.672431 0.0319843
\(443\) 26.8246 1.27448 0.637238 0.770667i \(-0.280077\pi\)
0.637238 + 0.770667i \(0.280077\pi\)
\(444\) −9.51867 −0.451736
\(445\) −19.5455 −0.926545
\(446\) −10.3883 −0.491902
\(447\) −7.46230 −0.352955
\(448\) −4.80624 −0.227074
\(449\) −33.0054 −1.55762 −0.778810 0.627260i \(-0.784176\pi\)
−0.778810 + 0.627260i \(0.784176\pi\)
\(450\) −0.0270290 −0.00127416
\(451\) −24.0517 −1.13255
\(452\) −4.63061 −0.217805
\(453\) 22.9189 1.07683
\(454\) −16.8032 −0.788614
\(455\) −10.7761 −0.505191
\(456\) −6.07560 −0.284516
\(457\) −15.6619 −0.732631 −0.366315 0.930491i \(-0.619381\pi\)
−0.366315 + 0.930491i \(0.619381\pi\)
\(458\) −9.48249 −0.443088
\(459\) −0.672431 −0.0313864
\(460\) 3.35382 0.156373
\(461\) −20.5765 −0.958342 −0.479171 0.877722i \(-0.659063\pi\)
−0.479171 + 0.877722i \(0.659063\pi\)
\(462\) 28.4082 1.32167
\(463\) −24.3204 −1.13026 −0.565132 0.825000i \(-0.691175\pi\)
−0.565132 + 0.825000i \(0.691175\pi\)
\(464\) 4.90360 0.227644
\(465\) −1.40659 −0.0652293
\(466\) 12.4591 0.577156
\(467\) 28.9855 1.34129 0.670643 0.741780i \(-0.266018\pi\)
0.670643 + 0.741780i \(0.266018\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 4.42455 0.204307
\(470\) 7.75125 0.357539
\(471\) 1.63459 0.0753178
\(472\) −4.41705 −0.203311
\(473\) −50.1917 −2.30782
\(474\) −6.26995 −0.287988
\(475\) −0.164218 −0.00753482
\(476\) −3.23186 −0.148132
\(477\) 7.99289 0.365969
\(478\) −2.52514 −0.115497
\(479\) −22.8890 −1.04582 −0.522912 0.852387i \(-0.675154\pi\)
−0.522912 + 0.852387i \(0.675154\pi\)
\(480\) −2.24210 −0.102338
\(481\) −9.51867 −0.434014
\(482\) 1.47817 0.0673288
\(483\) −7.18935 −0.327127
\(484\) 23.9363 1.08801
\(485\) 9.18382 0.417016
\(486\) 1.00000 0.0453609
\(487\) −42.1614 −1.91052 −0.955258 0.295775i \(-0.904422\pi\)
−0.955258 + 0.295775i \(0.904422\pi\)
\(488\) 5.58215 0.252692
\(489\) 11.6719 0.527821
\(490\) 36.0978 1.63073
\(491\) −18.3178 −0.826671 −0.413335 0.910579i \(-0.635636\pi\)
−0.413335 + 0.910579i \(0.635636\pi\)
\(492\) −4.06918 −0.183453
\(493\) 3.29733 0.148504
\(494\) −6.07560 −0.273354
\(495\) 13.2524 0.595651
\(496\) −0.627355 −0.0281691
\(497\) 7.87329 0.353165
\(498\) −5.91252 −0.264946
\(499\) −12.0980 −0.541580 −0.270790 0.962639i \(-0.587285\pi\)
−0.270790 + 0.962639i \(0.587285\pi\)
\(500\) 11.1499 0.498639
\(501\) −16.4960 −0.736987
\(502\) −26.9090 −1.20101
\(503\) 14.4300 0.643404 0.321702 0.946841i \(-0.395745\pi\)
0.321702 + 0.946841i \(0.395745\pi\)
\(504\) 4.80624 0.214087
\(505\) 7.05501 0.313944
\(506\) −8.84143 −0.393049
\(507\) −1.00000 −0.0444116
\(508\) 7.80292 0.346198
\(509\) −25.7790 −1.14263 −0.571317 0.820730i \(-0.693567\pi\)
−0.571317 + 0.820730i \(0.693567\pi\)
\(510\) −1.50766 −0.0667603
\(511\) 64.4940 2.85305
\(512\) −1.00000 −0.0441942
\(513\) 6.07560 0.268244
\(514\) 3.78562 0.166977
\(515\) 2.24210 0.0987989
\(516\) −8.49168 −0.373825
\(517\) −20.4341 −0.898689
\(518\) 45.7490 2.01010
\(519\) −3.96489 −0.174039
\(520\) −2.24210 −0.0983228
\(521\) 20.1761 0.883930 0.441965 0.897032i \(-0.354282\pi\)
0.441965 + 0.897032i \(0.354282\pi\)
\(522\) −4.90360 −0.214625
\(523\) −21.5296 −0.941424 −0.470712 0.882287i \(-0.656003\pi\)
−0.470712 + 0.882287i \(0.656003\pi\)
\(524\) 12.7886 0.558671
\(525\) 0.129908 0.00566965
\(526\) −0.134193 −0.00585108
\(527\) −0.421853 −0.0183762
\(528\) 5.91070 0.257230
\(529\) −20.7625 −0.902716
\(530\) 17.9209 0.778434
\(531\) 4.41705 0.191684
\(532\) 29.2008 1.26601
\(533\) −4.06918 −0.176256
\(534\) 8.71748 0.377242
\(535\) 26.0294 1.12535
\(536\) 0.920585 0.0397632
\(537\) 24.2136 1.04489
\(538\) 2.04038 0.0879670
\(539\) −95.1619 −4.09891
\(540\) 2.24210 0.0964848
\(541\) 30.1218 1.29504 0.647518 0.762050i \(-0.275807\pi\)
0.647518 + 0.762050i \(0.275807\pi\)
\(542\) 12.6125 0.541752
\(543\) 22.6425 0.971684
\(544\) −0.672431 −0.0288302
\(545\) −3.20592 −0.137327
\(546\) 4.80624 0.205688
\(547\) 34.1821 1.46152 0.730760 0.682634i \(-0.239166\pi\)
0.730760 + 0.682634i \(0.239166\pi\)
\(548\) 7.33630 0.313391
\(549\) −5.58215 −0.238240
\(550\) 0.159760 0.00681220
\(551\) −29.7923 −1.26919
\(552\) −1.49584 −0.0636670
\(553\) 30.1349 1.28147
\(554\) −6.51103 −0.276627
\(555\) 21.3418 0.905911
\(556\) 13.9536 0.591763
\(557\) 15.0510 0.637731 0.318866 0.947800i \(-0.396698\pi\)
0.318866 + 0.947800i \(0.396698\pi\)
\(558\) 0.627355 0.0265580
\(559\) −8.49168 −0.359160
\(560\) 10.7761 0.455373
\(561\) 3.97453 0.167805
\(562\) −32.0118 −1.35034
\(563\) 44.8939 1.89205 0.946026 0.324092i \(-0.105059\pi\)
0.946026 + 0.324092i \(0.105059\pi\)
\(564\) −3.45713 −0.145572
\(565\) 10.3823 0.436787
\(566\) 23.0851 0.970339
\(567\) −4.80624 −0.201843
\(568\) 1.63814 0.0687348
\(569\) 11.8787 0.497981 0.248991 0.968506i \(-0.419901\pi\)
0.248991 + 0.968506i \(0.419901\pi\)
\(570\) 13.6221 0.570568
\(571\) −19.3920 −0.811529 −0.405765 0.913978i \(-0.632995\pi\)
−0.405765 + 0.913978i \(0.632995\pi\)
\(572\) 5.91070 0.247139
\(573\) 9.27186 0.387337
\(574\) 19.5575 0.816313
\(575\) −0.0404310 −0.00168609
\(576\) 1.00000 0.0416667
\(577\) 29.9292 1.24597 0.622985 0.782234i \(-0.285920\pi\)
0.622985 + 0.782234i \(0.285920\pi\)
\(578\) 16.5478 0.688299
\(579\) 3.75521 0.156061
\(580\) −10.9944 −0.456517
\(581\) 28.4170 1.17894
\(582\) −4.09607 −0.169788
\(583\) −47.2435 −1.95663
\(584\) 13.4188 0.555274
\(585\) 2.24210 0.0926996
\(586\) 5.80059 0.239620
\(587\) 13.4709 0.556001 0.278001 0.960581i \(-0.410328\pi\)
0.278001 + 0.960581i \(0.410328\pi\)
\(588\) −16.0999 −0.663951
\(589\) 3.81156 0.157052
\(590\) 9.90350 0.407720
\(591\) 0.598107 0.0246028
\(592\) 9.51867 0.391215
\(593\) −8.39829 −0.344876 −0.172438 0.985020i \(-0.555164\pi\)
−0.172438 + 0.985020i \(0.555164\pi\)
\(594\) −5.91070 −0.242519
\(595\) 7.24617 0.297064
\(596\) 7.46230 0.305668
\(597\) −14.1966 −0.581028
\(598\) −1.49584 −0.0611693
\(599\) −17.1173 −0.699395 −0.349697 0.936863i \(-0.613716\pi\)
−0.349697 + 0.936863i \(0.613716\pi\)
\(600\) 0.0270290 0.00110346
\(601\) −35.4088 −1.44436 −0.722178 0.691708i \(-0.756859\pi\)
−0.722178 + 0.691708i \(0.756859\pi\)
\(602\) 40.8130 1.66342
\(603\) −0.920585 −0.0374891
\(604\) −22.9189 −0.932558
\(605\) −53.6677 −2.18190
\(606\) −3.14660 −0.127822
\(607\) −43.5045 −1.76579 −0.882896 0.469569i \(-0.844409\pi\)
−0.882896 + 0.469569i \(0.844409\pi\)
\(608\) 6.07560 0.246398
\(609\) 23.5679 0.955018
\(610\) −12.5158 −0.506748
\(611\) −3.45713 −0.139861
\(612\) 0.672431 0.0271814
\(613\) −36.0677 −1.45676 −0.728381 0.685173i \(-0.759727\pi\)
−0.728381 + 0.685173i \(0.759727\pi\)
\(614\) 23.0901 0.931841
\(615\) 9.12353 0.367896
\(616\) −28.4082 −1.14460
\(617\) 14.7141 0.592366 0.296183 0.955131i \(-0.404286\pi\)
0.296183 + 0.955131i \(0.404286\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 21.8863 0.879683 0.439842 0.898075i \(-0.355035\pi\)
0.439842 + 0.898075i \(0.355035\pi\)
\(620\) 1.40659 0.0564902
\(621\) 1.49584 0.0600258
\(622\) −19.8514 −0.795970
\(623\) −41.8983 −1.67862
\(624\) 1.00000 0.0400320
\(625\) −25.1344 −1.00538
\(626\) −18.6054 −0.743621
\(627\) −35.9110 −1.43415
\(628\) −1.63459 −0.0652272
\(629\) 6.40065 0.255210
\(630\) −10.7761 −0.429330
\(631\) −9.28318 −0.369558 −0.184779 0.982780i \(-0.559157\pi\)
−0.184779 + 0.982780i \(0.559157\pi\)
\(632\) 6.26995 0.249405
\(633\) 18.6089 0.739636
\(634\) 16.6967 0.663113
\(635\) −17.4950 −0.694266
\(636\) −7.99289 −0.316939
\(637\) −16.0999 −0.637903
\(638\) 28.9837 1.14747
\(639\) −1.63814 −0.0648038
\(640\) 2.24210 0.0886269
\(641\) −30.2790 −1.19595 −0.597974 0.801515i \(-0.704027\pi\)
−0.597974 + 0.801515i \(0.704027\pi\)
\(642\) −11.6094 −0.458186
\(643\) −2.69109 −0.106126 −0.0530631 0.998591i \(-0.516898\pi\)
−0.0530631 + 0.998591i \(0.516898\pi\)
\(644\) 7.18935 0.283300
\(645\) 19.0392 0.749669
\(646\) 4.08542 0.160739
\(647\) 14.3648 0.564738 0.282369 0.959306i \(-0.408880\pi\)
0.282369 + 0.959306i \(0.408880\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −26.1079 −1.02482
\(650\) 0.0270290 0.00106017
\(651\) −3.01522 −0.118176
\(652\) −11.6719 −0.457106
\(653\) 19.1973 0.751250 0.375625 0.926772i \(-0.377428\pi\)
0.375625 + 0.926772i \(0.377428\pi\)
\(654\) 1.42987 0.0559125
\(655\) −28.6733 −1.12036
\(656\) 4.06918 0.158875
\(657\) −13.4188 −0.523517
\(658\) 16.6158 0.647752
\(659\) 30.7471 1.19774 0.598869 0.800847i \(-0.295617\pi\)
0.598869 + 0.800847i \(0.295617\pi\)
\(660\) −13.2524 −0.515849
\(661\) −13.2678 −0.516059 −0.258030 0.966137i \(-0.583073\pi\)
−0.258030 + 0.966137i \(0.583073\pi\)
\(662\) −4.68546 −0.182105
\(663\) 0.672431 0.0261150
\(664\) 5.91252 0.229450
\(665\) −65.4712 −2.53886
\(666\) −9.51867 −0.368841
\(667\) −7.33498 −0.284011
\(668\) 16.4960 0.638249
\(669\) −10.3883 −0.401637
\(670\) −2.06405 −0.0797411
\(671\) 32.9944 1.27373
\(672\) −4.80624 −0.185405
\(673\) −44.4192 −1.71223 −0.856116 0.516783i \(-0.827129\pi\)
−0.856116 + 0.516783i \(0.827129\pi\)
\(674\) −11.0153 −0.424293
\(675\) −0.0270290 −0.00104035
\(676\) 1.00000 0.0384615
\(677\) −35.7710 −1.37479 −0.687396 0.726282i \(-0.741247\pi\)
−0.687396 + 0.726282i \(0.741247\pi\)
\(678\) −4.63061 −0.177837
\(679\) 19.6867 0.755506
\(680\) 1.50766 0.0578161
\(681\) −16.8032 −0.643901
\(682\) −3.70810 −0.141991
\(683\) 31.2452 1.19556 0.597782 0.801658i \(-0.296049\pi\)
0.597782 + 0.801658i \(0.296049\pi\)
\(684\) −6.07560 −0.232306
\(685\) −16.4487 −0.628474
\(686\) 43.7365 1.66987
\(687\) −9.48249 −0.361780
\(688\) 8.49168 0.323742
\(689\) −7.99289 −0.304505
\(690\) 3.35382 0.127678
\(691\) 6.47846 0.246452 0.123226 0.992379i \(-0.460676\pi\)
0.123226 + 0.992379i \(0.460676\pi\)
\(692\) 3.96489 0.150722
\(693\) 28.4082 1.07914
\(694\) −29.7512 −1.12934
\(695\) −31.2853 −1.18672
\(696\) 4.90360 0.185870
\(697\) 2.73624 0.103643
\(698\) −1.29640 −0.0490693
\(699\) 12.4591 0.471246
\(700\) −0.129908 −0.00491006
\(701\) −27.2691 −1.02994 −0.514970 0.857208i \(-0.672197\pi\)
−0.514970 + 0.857208i \(0.672197\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −57.8316 −2.18116
\(704\) −5.91070 −0.222768
\(705\) 7.75125 0.291929
\(706\) −32.1071 −1.20837
\(707\) 15.1233 0.568771
\(708\) −4.41705 −0.166003
\(709\) 19.7022 0.739930 0.369965 0.929046i \(-0.379370\pi\)
0.369965 + 0.929046i \(0.379370\pi\)
\(710\) −3.67288 −0.137841
\(711\) −6.26995 −0.235142
\(712\) −8.71748 −0.326701
\(713\) 0.938420 0.0351441
\(714\) −3.23186 −0.120949
\(715\) −13.2524 −0.495611
\(716\) −24.2136 −0.904904
\(717\) −2.52514 −0.0943030
\(718\) −6.85815 −0.255944
\(719\) −28.8578 −1.07622 −0.538108 0.842876i \(-0.680861\pi\)
−0.538108 + 0.842876i \(0.680861\pi\)
\(720\) −2.24210 −0.0835583
\(721\) 4.80624 0.178994
\(722\) −17.9129 −0.666649
\(723\) 1.47817 0.0549738
\(724\) −22.6425 −0.841503
\(725\) 0.132539 0.00492239
\(726\) 23.9363 0.888360
\(727\) 22.9904 0.852667 0.426334 0.904566i \(-0.359805\pi\)
0.426334 + 0.904566i \(0.359805\pi\)
\(728\) −4.80624 −0.178131
\(729\) 1.00000 0.0370370
\(730\) −30.0863 −1.11355
\(731\) 5.71006 0.211194
\(732\) 5.58215 0.206322
\(733\) 33.3950 1.23347 0.616736 0.787170i \(-0.288455\pi\)
0.616736 + 0.787170i \(0.288455\pi\)
\(734\) −0.851961 −0.0314465
\(735\) 36.0978 1.33149
\(736\) 1.49584 0.0551372
\(737\) 5.44130 0.200433
\(738\) −4.06918 −0.149789
\(739\) −34.8698 −1.28271 −0.641354 0.767245i \(-0.721627\pi\)
−0.641354 + 0.767245i \(0.721627\pi\)
\(740\) −21.3418 −0.784542
\(741\) −6.07560 −0.223193
\(742\) 38.4157 1.41029
\(743\) 29.2172 1.07188 0.535938 0.844257i \(-0.319958\pi\)
0.535938 + 0.844257i \(0.319958\pi\)
\(744\) −0.627355 −0.0229999
\(745\) −16.7312 −0.612985
\(746\) −23.4478 −0.858483
\(747\) −5.91252 −0.216328
\(748\) −3.97453 −0.145323
\(749\) 55.7975 2.03880
\(750\) 11.1499 0.407137
\(751\) −8.14976 −0.297389 −0.148695 0.988883i \(-0.547507\pi\)
−0.148695 + 0.988883i \(0.547507\pi\)
\(752\) 3.45713 0.126069
\(753\) −26.9090 −0.980617
\(754\) 4.90360 0.178579
\(755\) 51.3866 1.87015
\(756\) 4.80624 0.174801
\(757\) 42.6983 1.55190 0.775948 0.630797i \(-0.217272\pi\)
0.775948 + 0.630797i \(0.217272\pi\)
\(758\) −14.6048 −0.530470
\(759\) −8.84143 −0.320924
\(760\) −13.6221 −0.494126
\(761\) −17.2520 −0.625384 −0.312692 0.949855i \(-0.601231\pi\)
−0.312692 + 0.949855i \(0.601231\pi\)
\(762\) 7.80292 0.282670
\(763\) −6.87232 −0.248795
\(764\) −9.27186 −0.335444
\(765\) −1.50766 −0.0545095
\(766\) −24.8699 −0.898585
\(767\) −4.41705 −0.159491
\(768\) −1.00000 −0.0360844
\(769\) −27.8000 −1.00249 −0.501246 0.865305i \(-0.667125\pi\)
−0.501246 + 0.865305i \(0.667125\pi\)
\(770\) 63.6942 2.29538
\(771\) 3.78562 0.136336
\(772\) −3.75521 −0.135153
\(773\) 10.9435 0.393609 0.196805 0.980443i \(-0.436944\pi\)
0.196805 + 0.980443i \(0.436944\pi\)
\(774\) −8.49168 −0.305227
\(775\) −0.0169568 −0.000609106 0
\(776\) 4.09607 0.147040
\(777\) 45.7490 1.64124
\(778\) 29.8539 1.07031
\(779\) −24.7227 −0.885783
\(780\) −2.24210 −0.0802802
\(781\) 9.68254 0.346469
\(782\) 1.00585 0.0359690
\(783\) −4.90360 −0.175240
\(784\) 16.0999 0.574998
\(785\) 3.66492 0.130806
\(786\) 12.7886 0.456153
\(787\) 28.9550 1.03213 0.516067 0.856548i \(-0.327396\pi\)
0.516067 + 0.856548i \(0.327396\pi\)
\(788\) −0.598107 −0.0213067
\(789\) −0.134193 −0.00477738
\(790\) −14.0579 −0.500157
\(791\) 22.2558 0.791326
\(792\) 5.91070 0.210027
\(793\) 5.58215 0.198228
\(794\) −32.7033 −1.16060
\(795\) 17.9209 0.635588
\(796\) 14.1966 0.503185
\(797\) 0.627633 0.0222319 0.0111159 0.999938i \(-0.496462\pi\)
0.0111159 + 0.999938i \(0.496462\pi\)
\(798\) 29.2008 1.03370
\(799\) 2.32468 0.0822414
\(800\) −0.0270290 −0.000955620 0
\(801\) 8.71748 0.308017
\(802\) 21.0049 0.741708
\(803\) 79.3144 2.79895
\(804\) 0.920585 0.0324665
\(805\) −16.1193 −0.568129
\(806\) −0.627355 −0.0220976
\(807\) 2.04038 0.0718248
\(808\) 3.14660 0.110697
\(809\) −27.9461 −0.982533 −0.491266 0.871009i \(-0.663466\pi\)
−0.491266 + 0.871009i \(0.663466\pi\)
\(810\) 2.24210 0.0787795
\(811\) −37.0432 −1.30076 −0.650381 0.759609i \(-0.725391\pi\)
−0.650381 + 0.759609i \(0.725391\pi\)
\(812\) −23.5679 −0.827070
\(813\) 12.6125 0.442339
\(814\) 56.2620 1.97198
\(815\) 26.1696 0.916680
\(816\) −0.672431 −0.0235398
\(817\) −51.5920 −1.80498
\(818\) −0.600833 −0.0210076
\(819\) 4.80624 0.167944
\(820\) −9.12353 −0.318607
\(821\) −31.6811 −1.10568 −0.552840 0.833288i \(-0.686456\pi\)
−0.552840 + 0.833288i \(0.686456\pi\)
\(822\) 7.33630 0.255883
\(823\) −32.1436 −1.12046 −0.560228 0.828339i \(-0.689286\pi\)
−0.560228 + 0.828339i \(0.689286\pi\)
\(824\) 1.00000 0.0348367
\(825\) 0.159760 0.00556214
\(826\) 21.2294 0.738666
\(827\) 1.67948 0.0584012 0.0292006 0.999574i \(-0.490704\pi\)
0.0292006 + 0.999574i \(0.490704\pi\)
\(828\) −1.49584 −0.0519839
\(829\) −16.0453 −0.557276 −0.278638 0.960396i \(-0.589883\pi\)
−0.278638 + 0.960396i \(0.589883\pi\)
\(830\) −13.2565 −0.460139
\(831\) −6.51103 −0.225865
\(832\) −1.00000 −0.0346688
\(833\) 10.8261 0.375102
\(834\) 13.9536 0.483172
\(835\) −36.9857 −1.27994
\(836\) 35.9110 1.24201
\(837\) 0.627355 0.0216846
\(838\) −17.3081 −0.597899
\(839\) −17.5745 −0.606740 −0.303370 0.952873i \(-0.598112\pi\)
−0.303370 + 0.952873i \(0.598112\pi\)
\(840\) 10.7761 0.371810
\(841\) −4.95473 −0.170853
\(842\) −25.2015 −0.868501
\(843\) −32.0118 −1.10255
\(844\) −18.6089 −0.640544
\(845\) −2.24210 −0.0771307
\(846\) −3.45713 −0.118859
\(847\) −115.044 −3.95295
\(848\) 7.99289 0.274477
\(849\) 23.0851 0.792278
\(850\) −0.0181751 −0.000623402 0
\(851\) −14.2384 −0.488085
\(852\) 1.63814 0.0561217
\(853\) 32.2588 1.10452 0.552260 0.833672i \(-0.313766\pi\)
0.552260 + 0.833672i \(0.313766\pi\)
\(854\) −26.8291 −0.918074
\(855\) 13.6221 0.465867
\(856\) 11.6094 0.396801
\(857\) −42.5618 −1.45388 −0.726941 0.686700i \(-0.759059\pi\)
−0.726941 + 0.686700i \(0.759059\pi\)
\(858\) 5.91070 0.201788
\(859\) 30.9532 1.05611 0.528055 0.849210i \(-0.322921\pi\)
0.528055 + 0.849210i \(0.322921\pi\)
\(860\) −19.0392 −0.649232
\(861\) 19.5575 0.666517
\(862\) −0.589597 −0.0200818
\(863\) −9.44732 −0.321591 −0.160795 0.986988i \(-0.551406\pi\)
−0.160795 + 0.986988i \(0.551406\pi\)
\(864\) 1.00000 0.0340207
\(865\) −8.88969 −0.302259
\(866\) −24.6034 −0.836057
\(867\) 16.5478 0.561994
\(868\) 3.01522 0.102343
\(869\) 37.0598 1.25717
\(870\) −10.9944 −0.372744
\(871\) 0.920585 0.0311928
\(872\) −1.42987 −0.0484216
\(873\) −4.09607 −0.138631
\(874\) −9.08810 −0.307409
\(875\) −53.5892 −1.81164
\(876\) 13.4188 0.453379
\(877\) 41.0730 1.38694 0.693468 0.720487i \(-0.256082\pi\)
0.693468 + 0.720487i \(0.256082\pi\)
\(878\) −15.3763 −0.518926
\(879\) 5.80059 0.195649
\(880\) 13.2524 0.446738
\(881\) −11.9675 −0.403196 −0.201598 0.979468i \(-0.564613\pi\)
−0.201598 + 0.979468i \(0.564613\pi\)
\(882\) −16.0999 −0.542113
\(883\) −19.3334 −0.650619 −0.325310 0.945608i \(-0.605469\pi\)
−0.325310 + 0.945608i \(0.605469\pi\)
\(884\) −0.672431 −0.0226163
\(885\) 9.90350 0.332902
\(886\) −26.8246 −0.901191
\(887\) 0.196098 0.00658433 0.00329217 0.999995i \(-0.498952\pi\)
0.00329217 + 0.999995i \(0.498952\pi\)
\(888\) 9.51867 0.319426
\(889\) −37.5027 −1.25780
\(890\) 19.5455 0.655166
\(891\) −5.91070 −0.198016
\(892\) 10.3883 0.347827
\(893\) −21.0042 −0.702877
\(894\) 7.46230 0.249577
\(895\) 54.2893 1.81469
\(896\) 4.80624 0.160565
\(897\) −1.49584 −0.0499445
\(898\) 33.0054 1.10140
\(899\) −3.07630 −0.102600
\(900\) 0.0270290 0.000900968 0
\(901\) 5.37466 0.179056
\(902\) 24.0517 0.800834
\(903\) 40.8130 1.35817
\(904\) 4.63061 0.154012
\(905\) 50.7669 1.68755
\(906\) −22.9189 −0.761430
\(907\) 32.7930 1.08888 0.544438 0.838801i \(-0.316743\pi\)
0.544438 + 0.838801i \(0.316743\pi\)
\(908\) 16.8032 0.557635
\(909\) −3.14660 −0.104366
\(910\) 10.7761 0.357224
\(911\) 50.8143 1.68355 0.841777 0.539825i \(-0.181510\pi\)
0.841777 + 0.539825i \(0.181510\pi\)
\(912\) 6.07560 0.201183
\(913\) 34.9471 1.15658
\(914\) 15.6619 0.518048
\(915\) −12.5158 −0.413758
\(916\) 9.48249 0.313310
\(917\) −61.4650 −2.02975
\(918\) 0.672431 0.0221935
\(919\) −6.78086 −0.223680 −0.111840 0.993726i \(-0.535674\pi\)
−0.111840 + 0.993726i \(0.535674\pi\)
\(920\) −3.35382 −0.110572
\(921\) 23.0901 0.760845
\(922\) 20.5765 0.677650
\(923\) 1.63814 0.0539200
\(924\) −28.4082 −0.934562
\(925\) 0.257280 0.00845933
\(926\) 24.3204 0.799218
\(927\) −1.00000 −0.0328443
\(928\) −4.90360 −0.160968
\(929\) 23.4158 0.768249 0.384125 0.923281i \(-0.374503\pi\)
0.384125 + 0.923281i \(0.374503\pi\)
\(930\) 1.40659 0.0461241
\(931\) −97.8168 −3.20582
\(932\) −12.4591 −0.408111
\(933\) −19.8514 −0.649907
\(934\) −28.9855 −0.948433
\(935\) 8.91131 0.291431
\(936\) 1.00000 0.0326860
\(937\) −39.2385 −1.28187 −0.640933 0.767597i \(-0.721452\pi\)
−0.640933 + 0.767597i \(0.721452\pi\)
\(938\) −4.42455 −0.144467
\(939\) −18.6054 −0.607164
\(940\) −7.75125 −0.252818
\(941\) 3.60297 0.117453 0.0587267 0.998274i \(-0.481296\pi\)
0.0587267 + 0.998274i \(0.481296\pi\)
\(942\) −1.63459 −0.0532578
\(943\) −6.08683 −0.198214
\(944\) 4.41705 0.143763
\(945\) −10.7761 −0.350546
\(946\) 50.1917 1.63187
\(947\) 6.55134 0.212890 0.106445 0.994319i \(-0.466053\pi\)
0.106445 + 0.994319i \(0.466053\pi\)
\(948\) 6.26995 0.203639
\(949\) 13.4188 0.435593
\(950\) 0.164218 0.00532792
\(951\) 16.6967 0.541429
\(952\) 3.23186 0.104745
\(953\) 51.6736 1.67387 0.836937 0.547300i \(-0.184344\pi\)
0.836937 + 0.547300i \(0.184344\pi\)
\(954\) −7.99289 −0.258779
\(955\) 20.7885 0.672699
\(956\) 2.52514 0.0816688
\(957\) 28.9837 0.936909
\(958\) 22.8890 0.739509
\(959\) −35.2600 −1.13861
\(960\) 2.24210 0.0723636
\(961\) −30.6064 −0.987304
\(962\) 9.51867 0.306894
\(963\) −11.6094 −0.374107
\(964\) −1.47817 −0.0476087
\(965\) 8.41956 0.271035
\(966\) 7.18935 0.231313
\(967\) 56.8604 1.82851 0.914254 0.405142i \(-0.132778\pi\)
0.914254 + 0.405142i \(0.132778\pi\)
\(968\) −23.9363 −0.769343
\(969\) 4.08542 0.131243
\(970\) −9.18382 −0.294875
\(971\) 0.120634 0.00387133 0.00193566 0.999998i \(-0.499384\pi\)
0.00193566 + 0.999998i \(0.499384\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −67.0642 −2.14998
\(974\) 42.1614 1.35094
\(975\) 0.0270290 0.000865622 0
\(976\) −5.58215 −0.178680
\(977\) 21.8504 0.699055 0.349528 0.936926i \(-0.386342\pi\)
0.349528 + 0.936926i \(0.386342\pi\)
\(978\) −11.6719 −0.373225
\(979\) −51.5263 −1.64679
\(980\) −36.0978 −1.15310
\(981\) 1.42987 0.0456524
\(982\) 18.3178 0.584544
\(983\) 0.160929 0.00513283 0.00256641 0.999997i \(-0.499183\pi\)
0.00256641 + 0.999997i \(0.499183\pi\)
\(984\) 4.06918 0.129721
\(985\) 1.34102 0.0427284
\(986\) −3.29733 −0.105008
\(987\) 16.6158 0.528887
\(988\) 6.07560 0.193291
\(989\) −12.7022 −0.403905
\(990\) −13.2524 −0.421189
\(991\) 50.8920 1.61664 0.808319 0.588744i \(-0.200377\pi\)
0.808319 + 0.588744i \(0.200377\pi\)
\(992\) 0.627355 0.0199185
\(993\) −4.68546 −0.148688
\(994\) −7.87329 −0.249726
\(995\) −31.8302 −1.00909
\(996\) 5.91252 0.187345
\(997\) −25.4849 −0.807116 −0.403558 0.914954i \(-0.632227\pi\)
−0.403558 + 0.914954i \(0.632227\pi\)
\(998\) 12.0980 0.382955
\(999\) −9.51867 −0.301157
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 8034.2.a.s.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.s.1.2 10 1.1 even 1 trivial