Properties

Label 4027.2.a.b.1.6
Level $4027$
Weight $2$
Character 4027.1
Self dual yes
Analytic conductor $32.156$
Analytic rank $1$
Dimension $159$
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] = [4027,2,Mod(1,4027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4027 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4027.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: \(32.1557568940\)
Analytic rank: \(1\)
Dimension: \(159\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 4027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.70494 q^{2} +2.29108 q^{3} +5.31668 q^{4} -3.64034 q^{5} -6.19723 q^{6} +2.95034 q^{7} -8.97141 q^{8} +2.24905 q^{9} +O(q^{10})\) \(q-2.70494 q^{2} +2.29108 q^{3} +5.31668 q^{4} -3.64034 q^{5} -6.19723 q^{6} +2.95034 q^{7} -8.97141 q^{8} +2.24905 q^{9} +9.84688 q^{10} +0.0557392 q^{11} +12.1809 q^{12} +0.308532 q^{13} -7.98047 q^{14} -8.34031 q^{15} +13.6337 q^{16} +0.0875711 q^{17} -6.08354 q^{18} +5.39100 q^{19} -19.3545 q^{20} +6.75946 q^{21} -0.150771 q^{22} -9.19884 q^{23} -20.5542 q^{24} +8.25206 q^{25} -0.834560 q^{26} -1.72049 q^{27} +15.6860 q^{28} +5.34661 q^{29} +22.5600 q^{30} -5.28856 q^{31} -18.9355 q^{32} +0.127703 q^{33} -0.236874 q^{34} -10.7402 q^{35} +11.9575 q^{36} -9.66142 q^{37} -14.5823 q^{38} +0.706873 q^{39} +32.6589 q^{40} +10.2560 q^{41} -18.2839 q^{42} -3.32164 q^{43} +0.296347 q^{44} -8.18730 q^{45} +24.8823 q^{46} -12.7133 q^{47} +31.2359 q^{48} +1.70448 q^{49} -22.3213 q^{50} +0.200633 q^{51} +1.64037 q^{52} -12.0783 q^{53} +4.65380 q^{54} -0.202909 q^{55} -26.4687 q^{56} +12.3512 q^{57} -14.4622 q^{58} +4.08845 q^{59} -44.3427 q^{60} -9.71062 q^{61} +14.3052 q^{62} +6.63545 q^{63} +23.9520 q^{64} -1.12316 q^{65} -0.345428 q^{66} +4.90596 q^{67} +0.465588 q^{68} -21.0753 q^{69} +29.0516 q^{70} +8.92690 q^{71} -20.1771 q^{72} +4.01351 q^{73} +26.1335 q^{74} +18.9061 q^{75} +28.6622 q^{76} +0.164449 q^{77} -1.91205 q^{78} +4.32177 q^{79} -49.6313 q^{80} -10.6889 q^{81} -27.7418 q^{82} +12.7382 q^{83} +35.9379 q^{84} -0.318789 q^{85} +8.98481 q^{86} +12.2495 q^{87} -0.500059 q^{88} +14.7033 q^{89} +22.1461 q^{90} +0.910274 q^{91} -48.9073 q^{92} -12.1165 q^{93} +34.3887 q^{94} -19.6251 q^{95} -43.3828 q^{96} -16.4466 q^{97} -4.61052 q^{98} +0.125360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70494 −1.91268 −0.956339 0.292259i \(-0.905593\pi\)
−0.956339 + 0.292259i \(0.905593\pi\)
\(3\) 2.29108 1.32276 0.661378 0.750053i \(-0.269972\pi\)
0.661378 + 0.750053i \(0.269972\pi\)
\(4\) 5.31668 2.65834
\(5\) −3.64034 −1.62801 −0.814004 0.580859i \(-0.802717\pi\)
−0.814004 + 0.580859i \(0.802717\pi\)
\(6\) −6.19723 −2.53001
\(7\) 2.95034 1.11512 0.557561 0.830136i \(-0.311737\pi\)
0.557561 + 0.830136i \(0.311737\pi\)
\(8\) −8.97141 −3.17187
\(9\) 2.24905 0.749683
\(10\) 9.84688 3.11386
\(11\) 0.0557392 0.0168060 0.00840300 0.999965i \(-0.497325\pi\)
0.00840300 + 0.999965i \(0.497325\pi\)
\(12\) 12.1809 3.51633
\(13\) 0.308532 0.0855715 0.0427857 0.999084i \(-0.486377\pi\)
0.0427857 + 0.999084i \(0.486377\pi\)
\(14\) −7.98047 −2.13287
\(15\) −8.34031 −2.15346
\(16\) 13.6337 3.40843
\(17\) 0.0875711 0.0212391 0.0106196 0.999944i \(-0.496620\pi\)
0.0106196 + 0.999944i \(0.496620\pi\)
\(18\) −6.08354 −1.43390
\(19\) 5.39100 1.23678 0.618390 0.785871i \(-0.287785\pi\)
0.618390 + 0.785871i \(0.287785\pi\)
\(20\) −19.3545 −4.32780
\(21\) 6.75946 1.47503
\(22\) −0.150771 −0.0321445
\(23\) −9.19884 −1.91809 −0.959045 0.283253i \(-0.908586\pi\)
−0.959045 + 0.283253i \(0.908586\pi\)
\(24\) −20.5542 −4.19561
\(25\) 8.25206 1.65041
\(26\) −0.834560 −0.163671
\(27\) −1.72049 −0.331108
\(28\) 15.6860 2.96437
\(29\) 5.34661 0.992840 0.496420 0.868083i \(-0.334648\pi\)
0.496420 + 0.868083i \(0.334648\pi\)
\(30\) 22.5600 4.11887
\(31\) −5.28856 −0.949853 −0.474926 0.880025i \(-0.657525\pi\)
−0.474926 + 0.880025i \(0.657525\pi\)
\(32\) −18.9355 −3.34736
\(33\) 0.127703 0.0222302
\(34\) −0.236874 −0.0406236
\(35\) −10.7402 −1.81543
\(36\) 11.9575 1.99291
\(37\) −9.66142 −1.58833 −0.794164 0.607704i \(-0.792091\pi\)
−0.794164 + 0.607704i \(0.792091\pi\)
\(38\) −14.5823 −2.36556
\(39\) 0.706873 0.113190
\(40\) 32.6589 5.16383
\(41\) 10.2560 1.60172 0.800859 0.598853i \(-0.204377\pi\)
0.800859 + 0.598853i \(0.204377\pi\)
\(42\) −18.2839 −2.82127
\(43\) −3.32164 −0.506545 −0.253272 0.967395i \(-0.581507\pi\)
−0.253272 + 0.967395i \(0.581507\pi\)
\(44\) 0.296347 0.0446760
\(45\) −8.18730 −1.22049
\(46\) 24.8823 3.66869
\(47\) −12.7133 −1.85443 −0.927214 0.374533i \(-0.877803\pi\)
−0.927214 + 0.374533i \(0.877803\pi\)
\(48\) 31.2359 4.50852
\(49\) 1.70448 0.243498
\(50\) −22.3213 −3.15671
\(51\) 0.200633 0.0280942
\(52\) 1.64037 0.227478
\(53\) −12.0783 −1.65908 −0.829542 0.558444i \(-0.811399\pi\)
−0.829542 + 0.558444i \(0.811399\pi\)
\(54\) 4.65380 0.633303
\(55\) −0.202909 −0.0273603
\(56\) −26.4687 −3.53702
\(57\) 12.3512 1.63596
\(58\) −14.4622 −1.89898
\(59\) 4.08845 0.532271 0.266135 0.963936i \(-0.414253\pi\)
0.266135 + 0.963936i \(0.414253\pi\)
\(60\) −44.3427 −5.72462
\(61\) −9.71062 −1.24332 −0.621659 0.783288i \(-0.713541\pi\)
−0.621659 + 0.783288i \(0.713541\pi\)
\(62\) 14.3052 1.81676
\(63\) 6.63545 0.835989
\(64\) 23.9520 2.99399
\(65\) −1.12316 −0.139311
\(66\) −0.345428 −0.0425193
\(67\) 4.90596 0.599358 0.299679 0.954040i \(-0.403120\pi\)
0.299679 + 0.954040i \(0.403120\pi\)
\(68\) 0.465588 0.0564608
\(69\) −21.0753 −2.53717
\(70\) 29.0516 3.47233
\(71\) 8.92690 1.05943 0.529714 0.848176i \(-0.322299\pi\)
0.529714 + 0.848176i \(0.322299\pi\)
\(72\) −20.1771 −2.37790
\(73\) 4.01351 0.469746 0.234873 0.972026i \(-0.424533\pi\)
0.234873 + 0.972026i \(0.424533\pi\)
\(74\) 26.1335 3.03796
\(75\) 18.9061 2.18309
\(76\) 28.6622 3.28778
\(77\) 0.164449 0.0187407
\(78\) −1.91205 −0.216497
\(79\) 4.32177 0.486237 0.243118 0.969997i \(-0.421830\pi\)
0.243118 + 0.969997i \(0.421830\pi\)
\(80\) −49.6313 −5.54895
\(81\) −10.6889 −1.18766
\(82\) −27.7418 −3.06357
\(83\) 12.7382 1.39820 0.699102 0.715022i \(-0.253584\pi\)
0.699102 + 0.715022i \(0.253584\pi\)
\(84\) 35.9379 3.92114
\(85\) −0.318789 −0.0345775
\(86\) 8.98481 0.968857
\(87\) 12.2495 1.31328
\(88\) −0.500059 −0.0533064
\(89\) 14.7033 1.55854 0.779272 0.626686i \(-0.215589\pi\)
0.779272 + 0.626686i \(0.215589\pi\)
\(90\) 22.1461 2.33441
\(91\) 0.910274 0.0954227
\(92\) −48.9073 −5.09894
\(93\) −12.1165 −1.25642
\(94\) 34.3887 3.54692
\(95\) −19.6251 −2.01349
\(96\) −43.3828 −4.42774
\(97\) −16.4466 −1.66990 −0.834948 0.550329i \(-0.814502\pi\)
−0.834948 + 0.550329i \(0.814502\pi\)
\(98\) −4.61052 −0.465733
\(99\) 0.125360 0.0125992
\(100\) 43.8736 4.38736
\(101\) −0.955208 −0.0950467 −0.0475234 0.998870i \(-0.515133\pi\)
−0.0475234 + 0.998870i \(0.515133\pi\)
\(102\) −0.542698 −0.0537351
\(103\) −8.26485 −0.814360 −0.407180 0.913348i \(-0.633488\pi\)
−0.407180 + 0.913348i \(0.633488\pi\)
\(104\) −2.76797 −0.271422
\(105\) −24.6067 −2.40137
\(106\) 32.6711 3.17330
\(107\) 0.444664 0.0429873 0.0214937 0.999769i \(-0.493158\pi\)
0.0214937 + 0.999769i \(0.493158\pi\)
\(108\) −9.14727 −0.880197
\(109\) −11.1928 −1.07208 −0.536038 0.844194i \(-0.680080\pi\)
−0.536038 + 0.844194i \(0.680080\pi\)
\(110\) 0.548857 0.0523315
\(111\) −22.1351 −2.10097
\(112\) 40.2241 3.80082
\(113\) 4.77855 0.449528 0.224764 0.974413i \(-0.427839\pi\)
0.224764 + 0.974413i \(0.427839\pi\)
\(114\) −33.4092 −3.12906
\(115\) 33.4869 3.12267
\(116\) 28.4262 2.63930
\(117\) 0.693905 0.0641515
\(118\) −11.0590 −1.01806
\(119\) 0.258364 0.0236842
\(120\) 74.8243 6.83049
\(121\) −10.9969 −0.999718
\(122\) 26.2666 2.37807
\(123\) 23.4973 2.11868
\(124\) −28.1176 −2.52503
\(125\) −11.8386 −1.05888
\(126\) −17.9485 −1.59898
\(127\) 9.27930 0.823405 0.411702 0.911318i \(-0.364934\pi\)
0.411702 + 0.911318i \(0.364934\pi\)
\(128\) −26.9175 −2.37919
\(129\) −7.61013 −0.670035
\(130\) 3.03808 0.266457
\(131\) −2.63832 −0.230511 −0.115256 0.993336i \(-0.536769\pi\)
−0.115256 + 0.993336i \(0.536769\pi\)
\(132\) 0.678956 0.0590955
\(133\) 15.9053 1.37916
\(134\) −13.2703 −1.14638
\(135\) 6.26315 0.539046
\(136\) −0.785636 −0.0673677
\(137\) 12.0878 1.03273 0.516365 0.856368i \(-0.327285\pi\)
0.516365 + 0.856368i \(0.327285\pi\)
\(138\) 57.0073 4.85278
\(139\) 18.6926 1.58548 0.792742 0.609558i \(-0.208653\pi\)
0.792742 + 0.609558i \(0.208653\pi\)
\(140\) −57.1023 −4.82603
\(141\) −29.1272 −2.45295
\(142\) −24.1467 −2.02635
\(143\) 0.0171973 0.00143811
\(144\) 30.6629 2.55524
\(145\) −19.4634 −1.61635
\(146\) −10.8563 −0.898472
\(147\) 3.90511 0.322088
\(148\) −51.3667 −4.22231
\(149\) −7.97920 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(150\) −51.1399 −4.17555
\(151\) −7.39471 −0.601773 −0.300886 0.953660i \(-0.597282\pi\)
−0.300886 + 0.953660i \(0.597282\pi\)
\(152\) −48.3648 −3.92291
\(153\) 0.196952 0.0159226
\(154\) −0.444825 −0.0358450
\(155\) 19.2521 1.54637
\(156\) 3.75822 0.300898
\(157\) −7.28696 −0.581563 −0.290781 0.956790i \(-0.593915\pi\)
−0.290781 + 0.956790i \(0.593915\pi\)
\(158\) −11.6901 −0.930014
\(159\) −27.6724 −2.19456
\(160\) 68.9317 5.44953
\(161\) −27.1397 −2.13891
\(162\) 28.9129 2.27161
\(163\) −21.3759 −1.67429 −0.837145 0.546981i \(-0.815777\pi\)
−0.837145 + 0.546981i \(0.815777\pi\)
\(164\) 54.5279 4.25791
\(165\) −0.464882 −0.0361910
\(166\) −34.4561 −2.67431
\(167\) −17.3736 −1.34441 −0.672205 0.740365i \(-0.734652\pi\)
−0.672205 + 0.740365i \(0.734652\pi\)
\(168\) −60.6418 −4.67862
\(169\) −12.9048 −0.992678
\(170\) 0.862303 0.0661356
\(171\) 12.1246 0.927194
\(172\) −17.6601 −1.34657
\(173\) −19.2011 −1.45983 −0.729915 0.683538i \(-0.760440\pi\)
−0.729915 + 0.683538i \(0.760440\pi\)
\(174\) −33.1341 −2.51189
\(175\) 24.3464 1.84041
\(176\) 0.759932 0.0572821
\(177\) 9.36697 0.704064
\(178\) −39.7714 −2.98099
\(179\) −14.9536 −1.11769 −0.558843 0.829274i \(-0.688754\pi\)
−0.558843 + 0.829274i \(0.688754\pi\)
\(180\) −43.5293 −3.24448
\(181\) −10.9716 −0.815515 −0.407757 0.913090i \(-0.633689\pi\)
−0.407757 + 0.913090i \(0.633689\pi\)
\(182\) −2.46223 −0.182513
\(183\) −22.2478 −1.64461
\(184\) 82.5265 6.08393
\(185\) 35.1708 2.58581
\(186\) 32.7744 2.40313
\(187\) 0.00488114 0.000356945 0
\(188\) −67.5926 −4.92970
\(189\) −5.07601 −0.369226
\(190\) 53.0845 3.85116
\(191\) −5.41905 −0.392109 −0.196054 0.980593i \(-0.562813\pi\)
−0.196054 + 0.980593i \(0.562813\pi\)
\(192\) 54.8759 3.96032
\(193\) −4.22668 −0.304243 −0.152122 0.988362i \(-0.548611\pi\)
−0.152122 + 0.988362i \(0.548611\pi\)
\(194\) 44.4869 3.19397
\(195\) −2.57326 −0.184275
\(196\) 9.06220 0.647300
\(197\) 10.1157 0.720712 0.360356 0.932815i \(-0.382655\pi\)
0.360356 + 0.932815i \(0.382655\pi\)
\(198\) −0.339091 −0.0240982
\(199\) −7.87397 −0.558171 −0.279085 0.960266i \(-0.590031\pi\)
−0.279085 + 0.960266i \(0.590031\pi\)
\(200\) −74.0326 −5.23489
\(201\) 11.2399 0.792804
\(202\) 2.58378 0.181794
\(203\) 15.7743 1.10714
\(204\) 1.06670 0.0746839
\(205\) −37.3353 −2.60761
\(206\) 22.3559 1.55761
\(207\) −20.6887 −1.43796
\(208\) 4.20644 0.291664
\(209\) 0.300490 0.0207853
\(210\) 66.5596 4.59305
\(211\) −12.2701 −0.844710 −0.422355 0.906430i \(-0.638796\pi\)
−0.422355 + 0.906430i \(0.638796\pi\)
\(212\) −64.2165 −4.41041
\(213\) 20.4523 1.40137
\(214\) −1.20279 −0.0822209
\(215\) 12.0919 0.824659
\(216\) 15.4352 1.05023
\(217\) −15.6030 −1.05920
\(218\) 30.2758 2.05054
\(219\) 9.19527 0.621359
\(220\) −1.07880 −0.0727330
\(221\) 0.0270185 0.00181746
\(222\) 59.8740 4.01848
\(223\) 12.8492 0.860448 0.430224 0.902722i \(-0.358435\pi\)
0.430224 + 0.902722i \(0.358435\pi\)
\(224\) −55.8662 −3.73272
\(225\) 18.5593 1.23729
\(226\) −12.9257 −0.859803
\(227\) 12.1830 0.808615 0.404307 0.914623i \(-0.367513\pi\)
0.404307 + 0.914623i \(0.367513\pi\)
\(228\) 65.6674 4.34893
\(229\) 25.5787 1.69029 0.845145 0.534538i \(-0.179514\pi\)
0.845145 + 0.534538i \(0.179514\pi\)
\(230\) −90.5799 −5.97266
\(231\) 0.376767 0.0247894
\(232\) −47.9666 −3.14916
\(233\) 7.24926 0.474915 0.237457 0.971398i \(-0.423686\pi\)
0.237457 + 0.971398i \(0.423686\pi\)
\(234\) −1.87697 −0.122701
\(235\) 46.2808 3.01902
\(236\) 21.7370 1.41496
\(237\) 9.90151 0.643172
\(238\) −0.698859 −0.0453003
\(239\) 12.9354 0.836725 0.418362 0.908280i \(-0.362604\pi\)
0.418362 + 0.908280i \(0.362604\pi\)
\(240\) −113.709 −7.33991
\(241\) 6.62577 0.426803 0.213402 0.976965i \(-0.431546\pi\)
0.213402 + 0.976965i \(0.431546\pi\)
\(242\) 29.7459 1.91214
\(243\) −19.3277 −1.23987
\(244\) −51.6283 −3.30516
\(245\) −6.20490 −0.396416
\(246\) −63.5588 −4.05236
\(247\) 1.66330 0.105833
\(248\) 47.4458 3.01281
\(249\) 29.1843 1.84948
\(250\) 32.0227 2.02529
\(251\) −15.6506 −0.987860 −0.493930 0.869502i \(-0.664440\pi\)
−0.493930 + 0.869502i \(0.664440\pi\)
\(252\) 35.2786 2.22234
\(253\) −0.512736 −0.0322354
\(254\) −25.0999 −1.57491
\(255\) −0.730370 −0.0457376
\(256\) 24.9061 1.55663
\(257\) −0.393204 −0.0245274 −0.0122637 0.999925i \(-0.503904\pi\)
−0.0122637 + 0.999925i \(0.503904\pi\)
\(258\) 20.5849 1.28156
\(259\) −28.5044 −1.77118
\(260\) −5.97149 −0.370336
\(261\) 12.0248 0.744315
\(262\) 7.13650 0.440894
\(263\) −14.6232 −0.901704 −0.450852 0.892599i \(-0.648880\pi\)
−0.450852 + 0.892599i \(0.648880\pi\)
\(264\) −1.14567 −0.0705114
\(265\) 43.9692 2.70100
\(266\) −43.0227 −2.63789
\(267\) 33.6864 2.06157
\(268\) 26.0834 1.59330
\(269\) −0.823071 −0.0501835 −0.0250917 0.999685i \(-0.507988\pi\)
−0.0250917 + 0.999685i \(0.507988\pi\)
\(270\) −16.9414 −1.03102
\(271\) −6.49379 −0.394470 −0.197235 0.980356i \(-0.563196\pi\)
−0.197235 + 0.980356i \(0.563196\pi\)
\(272\) 1.19392 0.0723921
\(273\) 2.08551 0.126221
\(274\) −32.6967 −1.97528
\(275\) 0.459963 0.0277368
\(276\) −112.051 −6.74465
\(277\) 16.6222 0.998730 0.499365 0.866392i \(-0.333567\pi\)
0.499365 + 0.866392i \(0.333567\pi\)
\(278\) −50.5622 −3.03252
\(279\) −11.8942 −0.712089
\(280\) 96.3549 5.75831
\(281\) −13.4768 −0.803957 −0.401979 0.915649i \(-0.631677\pi\)
−0.401979 + 0.915649i \(0.631677\pi\)
\(282\) 78.7873 4.69171
\(283\) 6.28908 0.373847 0.186923 0.982374i \(-0.440148\pi\)
0.186923 + 0.982374i \(0.440148\pi\)
\(284\) 47.4615 2.81632
\(285\) −44.9626 −2.66335
\(286\) −0.0465177 −0.00275065
\(287\) 30.2587 1.78611
\(288\) −42.5870 −2.50946
\(289\) −16.9923 −0.999549
\(290\) 52.6474 3.09156
\(291\) −37.6804 −2.20887
\(292\) 21.3385 1.24874
\(293\) 12.6587 0.739530 0.369765 0.929125i \(-0.379438\pi\)
0.369765 + 0.929125i \(0.379438\pi\)
\(294\) −10.5631 −0.616051
\(295\) −14.8833 −0.866541
\(296\) 86.6765 5.03797
\(297\) −0.0958985 −0.00556459
\(298\) 21.5832 1.25028
\(299\) −2.83814 −0.164134
\(300\) 100.518 5.80340
\(301\) −9.79994 −0.564859
\(302\) 20.0022 1.15100
\(303\) −2.18846 −0.125724
\(304\) 73.4994 4.21548
\(305\) 35.3499 2.02413
\(306\) −0.532742 −0.0304549
\(307\) −14.5728 −0.831715 −0.415857 0.909430i \(-0.636518\pi\)
−0.415857 + 0.909430i \(0.636518\pi\)
\(308\) 0.874324 0.0498193
\(309\) −18.9354 −1.07720
\(310\) −52.0758 −2.95771
\(311\) 22.2480 1.26157 0.630785 0.775958i \(-0.282733\pi\)
0.630785 + 0.775958i \(0.282733\pi\)
\(312\) −6.34164 −0.359025
\(313\) −26.0567 −1.47281 −0.736407 0.676539i \(-0.763479\pi\)
−0.736407 + 0.676539i \(0.763479\pi\)
\(314\) 19.7108 1.11234
\(315\) −24.1553 −1.36100
\(316\) 22.9774 1.29258
\(317\) 9.86820 0.554253 0.277127 0.960833i \(-0.410618\pi\)
0.277127 + 0.960833i \(0.410618\pi\)
\(318\) 74.8521 4.19750
\(319\) 0.298015 0.0166857
\(320\) −87.1932 −4.87425
\(321\) 1.01876 0.0568617
\(322\) 73.4111 4.09104
\(323\) 0.472096 0.0262681
\(324\) −56.8296 −3.15720
\(325\) 2.54603 0.141228
\(326\) 57.8204 3.20238
\(327\) −25.6436 −1.41810
\(328\) −92.0107 −5.08044
\(329\) −37.5085 −2.06791
\(330\) 1.25748 0.0692218
\(331\) −9.04341 −0.497071 −0.248535 0.968623i \(-0.579949\pi\)
−0.248535 + 0.968623i \(0.579949\pi\)
\(332\) 67.7251 3.71690
\(333\) −21.7290 −1.19074
\(334\) 46.9945 2.57142
\(335\) −17.8593 −0.975760
\(336\) 92.1566 5.02755
\(337\) 16.2383 0.884558 0.442279 0.896877i \(-0.354170\pi\)
0.442279 + 0.896877i \(0.354170\pi\)
\(338\) 34.9067 1.89867
\(339\) 10.9480 0.594616
\(340\) −1.69490 −0.0919187
\(341\) −0.294780 −0.0159632
\(342\) −32.7963 −1.77342
\(343\) −15.6236 −0.843593
\(344\) 29.7997 1.60669
\(345\) 76.7211 4.13053
\(346\) 51.9376 2.79218
\(347\) −31.3678 −1.68391 −0.841956 0.539547i \(-0.818596\pi\)
−0.841956 + 0.539547i \(0.818596\pi\)
\(348\) 65.1267 3.49116
\(349\) 16.8525 0.902096 0.451048 0.892500i \(-0.351050\pi\)
0.451048 + 0.892500i \(0.351050\pi\)
\(350\) −65.8553 −3.52012
\(351\) −0.530826 −0.0283334
\(352\) −1.05545 −0.0562557
\(353\) −10.7676 −0.573104 −0.286552 0.958065i \(-0.592509\pi\)
−0.286552 + 0.958065i \(0.592509\pi\)
\(354\) −25.3370 −1.34665
\(355\) −32.4969 −1.72476
\(356\) 78.1726 4.14314
\(357\) 0.591933 0.0313284
\(358\) 40.4486 2.13777
\(359\) −12.1766 −0.642654 −0.321327 0.946968i \(-0.604129\pi\)
−0.321327 + 0.946968i \(0.604129\pi\)
\(360\) 73.4516 3.87124
\(361\) 10.0629 0.529625
\(362\) 29.6776 1.55982
\(363\) −25.1948 −1.32238
\(364\) 4.83964 0.253666
\(365\) −14.6105 −0.764750
\(366\) 60.1789 3.14560
\(367\) 31.5158 1.64511 0.822555 0.568685i \(-0.192548\pi\)
0.822555 + 0.568685i \(0.192548\pi\)
\(368\) −125.414 −6.53768
\(369\) 23.0663 1.20078
\(370\) −95.1348 −4.94582
\(371\) −35.6351 −1.85008
\(372\) −64.4196 −3.34000
\(373\) −28.0341 −1.45155 −0.725775 0.687932i \(-0.758519\pi\)
−0.725775 + 0.687932i \(0.758519\pi\)
\(374\) −0.0132032 −0.000682720 0
\(375\) −27.1232 −1.40064
\(376\) 114.056 5.88200
\(377\) 1.64960 0.0849588
\(378\) 13.7303 0.706210
\(379\) −23.9854 −1.23205 −0.616023 0.787729i \(-0.711257\pi\)
−0.616023 + 0.787729i \(0.711257\pi\)
\(380\) −104.340 −5.35254
\(381\) 21.2596 1.08916
\(382\) 14.6582 0.749978
\(383\) 5.95479 0.304275 0.152138 0.988359i \(-0.451384\pi\)
0.152138 + 0.988359i \(0.451384\pi\)
\(384\) −61.6700 −3.14709
\(385\) −0.598651 −0.0305101
\(386\) 11.4329 0.581919
\(387\) −7.47052 −0.379748
\(388\) −87.4411 −4.43915
\(389\) 18.6180 0.943970 0.471985 0.881607i \(-0.343538\pi\)
0.471985 + 0.881607i \(0.343538\pi\)
\(390\) 6.96049 0.352458
\(391\) −0.805553 −0.0407386
\(392\) −15.2916 −0.772343
\(393\) −6.04461 −0.304910
\(394\) −27.3623 −1.37849
\(395\) −15.7327 −0.791597
\(396\) 0.666500 0.0334929
\(397\) 0.513203 0.0257569 0.0128785 0.999917i \(-0.495901\pi\)
0.0128785 + 0.999917i \(0.495901\pi\)
\(398\) 21.2986 1.06760
\(399\) 36.4402 1.82429
\(400\) 112.506 5.62531
\(401\) 23.2637 1.16173 0.580867 0.813999i \(-0.302714\pi\)
0.580867 + 0.813999i \(0.302714\pi\)
\(402\) −30.4033 −1.51638
\(403\) −1.63169 −0.0812803
\(404\) −5.07853 −0.252666
\(405\) 38.9113 1.93352
\(406\) −42.6684 −2.11760
\(407\) −0.538520 −0.0266934
\(408\) −1.79996 −0.0891111
\(409\) −16.8777 −0.834549 −0.417275 0.908780i \(-0.637015\pi\)
−0.417275 + 0.908780i \(0.637015\pi\)
\(410\) 100.990 4.98752
\(411\) 27.6941 1.36605
\(412\) −43.9416 −2.16485
\(413\) 12.0623 0.593547
\(414\) 55.9615 2.75036
\(415\) −46.3715 −2.27629
\(416\) −5.84222 −0.286439
\(417\) 42.8262 2.09721
\(418\) −0.812806 −0.0397556
\(419\) −24.2427 −1.18433 −0.592166 0.805816i \(-0.701727\pi\)
−0.592166 + 0.805816i \(0.701727\pi\)
\(420\) −130.826 −6.38366
\(421\) −38.6264 −1.88253 −0.941267 0.337663i \(-0.890364\pi\)
−0.941267 + 0.337663i \(0.890364\pi\)
\(422\) 33.1899 1.61566
\(423\) −28.5929 −1.39023
\(424\) 108.359 5.26240
\(425\) 0.722642 0.0350533
\(426\) −55.3220 −2.68036
\(427\) −28.6496 −1.38645
\(428\) 2.36414 0.114275
\(429\) 0.0394005 0.00190227
\(430\) −32.7077 −1.57731
\(431\) −27.4211 −1.32083 −0.660413 0.750903i \(-0.729619\pi\)
−0.660413 + 0.750903i \(0.729619\pi\)
\(432\) −23.4566 −1.12856
\(433\) −8.86253 −0.425906 −0.212953 0.977062i \(-0.568308\pi\)
−0.212953 + 0.977062i \(0.568308\pi\)
\(434\) 42.2052 2.02591
\(435\) −44.5923 −2.13804
\(436\) −59.5086 −2.84994
\(437\) −49.5909 −2.37226
\(438\) −24.8726 −1.18846
\(439\) 28.7215 1.37080 0.685402 0.728165i \(-0.259627\pi\)
0.685402 + 0.728165i \(0.259627\pi\)
\(440\) 1.82038 0.0867834
\(441\) 3.83347 0.182546
\(442\) −0.0730834 −0.00347622
\(443\) −11.9513 −0.567825 −0.283912 0.958850i \(-0.591633\pi\)
−0.283912 + 0.958850i \(0.591633\pi\)
\(444\) −117.685 −5.58509
\(445\) −53.5249 −2.53732
\(446\) −34.7563 −1.64576
\(447\) −18.2810 −0.864662
\(448\) 70.6663 3.33867
\(449\) −36.4429 −1.71985 −0.859924 0.510422i \(-0.829489\pi\)
−0.859924 + 0.510422i \(0.829489\pi\)
\(450\) −50.2017 −2.36653
\(451\) 0.571661 0.0269185
\(452\) 25.4060 1.19500
\(453\) −16.9419 −0.795998
\(454\) −32.9543 −1.54662
\(455\) −3.31371 −0.155349
\(456\) −110.808 −5.18905
\(457\) −5.58640 −0.261321 −0.130660 0.991427i \(-0.541710\pi\)
−0.130660 + 0.991427i \(0.541710\pi\)
\(458\) −69.1888 −3.23298
\(459\) −0.150665 −0.00703244
\(460\) 178.039 8.30111
\(461\) 10.7489 0.500628 0.250314 0.968165i \(-0.419466\pi\)
0.250314 + 0.968165i \(0.419466\pi\)
\(462\) −1.01913 −0.0474142
\(463\) 15.3458 0.713178 0.356589 0.934261i \(-0.383940\pi\)
0.356589 + 0.934261i \(0.383940\pi\)
\(464\) 72.8941 3.38402
\(465\) 44.1082 2.04547
\(466\) −19.6088 −0.908360
\(467\) −22.8959 −1.05950 −0.529748 0.848155i \(-0.677714\pi\)
−0.529748 + 0.848155i \(0.677714\pi\)
\(468\) 3.68927 0.170537
\(469\) 14.4742 0.668357
\(470\) −125.186 −5.77442
\(471\) −16.6950 −0.769266
\(472\) −36.6791 −1.68829
\(473\) −0.185145 −0.00851299
\(474\) −26.7830 −1.23018
\(475\) 44.4869 2.04120
\(476\) 1.37364 0.0629607
\(477\) −27.1647 −1.24379
\(478\) −34.9896 −1.60039
\(479\) −0.759954 −0.0347232 −0.0173616 0.999849i \(-0.505527\pi\)
−0.0173616 + 0.999849i \(0.505527\pi\)
\(480\) 157.928 7.20840
\(481\) −2.98086 −0.135916
\(482\) −17.9223 −0.816337
\(483\) −62.1792 −2.82925
\(484\) −58.4670 −2.65759
\(485\) 59.8711 2.71861
\(486\) 52.2803 2.37148
\(487\) 36.3345 1.64647 0.823236 0.567699i \(-0.192166\pi\)
0.823236 + 0.567699i \(0.192166\pi\)
\(488\) 87.1179 3.94364
\(489\) −48.9739 −2.21468
\(490\) 16.7839 0.758217
\(491\) −12.1803 −0.549691 −0.274845 0.961488i \(-0.588627\pi\)
−0.274845 + 0.961488i \(0.588627\pi\)
\(492\) 124.928 5.63218
\(493\) 0.468208 0.0210870
\(494\) −4.49911 −0.202425
\(495\) −0.456354 −0.0205116
\(496\) −72.1027 −3.23751
\(497\) 26.3374 1.18139
\(498\) −78.9417 −3.53746
\(499\) −28.1849 −1.26173 −0.630866 0.775892i \(-0.717300\pi\)
−0.630866 + 0.775892i \(0.717300\pi\)
\(500\) −62.9421 −2.81485
\(501\) −39.8043 −1.77833
\(502\) 42.3340 1.88946
\(503\) −19.7762 −0.881778 −0.440889 0.897562i \(-0.645337\pi\)
−0.440889 + 0.897562i \(0.645337\pi\)
\(504\) −59.5294 −2.65165
\(505\) 3.47728 0.154737
\(506\) 1.38692 0.0616560
\(507\) −29.5660 −1.31307
\(508\) 49.3350 2.18889
\(509\) 3.98402 0.176589 0.0882944 0.996094i \(-0.471858\pi\)
0.0882944 + 0.996094i \(0.471858\pi\)
\(510\) 1.97560 0.0874813
\(511\) 11.8412 0.523824
\(512\) −13.5344 −0.598143
\(513\) −9.27514 −0.409507
\(514\) 1.06359 0.0469130
\(515\) 30.0869 1.32579
\(516\) −40.4606 −1.78118
\(517\) −0.708630 −0.0311655
\(518\) 77.1027 3.38770
\(519\) −43.9912 −1.93100
\(520\) 10.0763 0.441877
\(521\) −29.4263 −1.28919 −0.644595 0.764524i \(-0.722974\pi\)
−0.644595 + 0.764524i \(0.722974\pi\)
\(522\) −32.5263 −1.42364
\(523\) 21.6341 0.945993 0.472996 0.881064i \(-0.343172\pi\)
0.472996 + 0.881064i \(0.343172\pi\)
\(524\) −14.0271 −0.612778
\(525\) 55.7795 2.43442
\(526\) 39.5548 1.72467
\(527\) −0.463125 −0.0201740
\(528\) 1.74107 0.0757702
\(529\) 61.6186 2.67907
\(530\) −118.934 −5.16615
\(531\) 9.19513 0.399035
\(532\) 84.5632 3.66628
\(533\) 3.16431 0.137061
\(534\) −91.1195 −3.94313
\(535\) −1.61873 −0.0699837
\(536\) −44.0133 −1.90109
\(537\) −34.2599 −1.47843
\(538\) 2.22635 0.0959849
\(539\) 0.0950066 0.00409222
\(540\) 33.2992 1.43297
\(541\) 3.33019 0.143176 0.0715880 0.997434i \(-0.477193\pi\)
0.0715880 + 0.997434i \(0.477193\pi\)
\(542\) 17.5653 0.754494
\(543\) −25.1369 −1.07873
\(544\) −1.65821 −0.0710950
\(545\) 40.7456 1.74535
\(546\) −5.64118 −0.241420
\(547\) 3.15290 0.134808 0.0674042 0.997726i \(-0.478528\pi\)
0.0674042 + 0.997726i \(0.478528\pi\)
\(548\) 64.2670 2.74535
\(549\) −21.8397 −0.932095
\(550\) −1.24417 −0.0530516
\(551\) 28.8235 1.22792
\(552\) 189.075 8.04756
\(553\) 12.7507 0.542213
\(554\) −44.9619 −1.91025
\(555\) 80.5792 3.42040
\(556\) 99.3824 4.21475
\(557\) 2.64369 0.112017 0.0560083 0.998430i \(-0.482163\pi\)
0.0560083 + 0.998430i \(0.482163\pi\)
\(558\) 32.1731 1.36200
\(559\) −1.02483 −0.0433458
\(560\) −146.429 −6.18776
\(561\) 0.0111831 0.000472151 0
\(562\) 36.4538 1.53771
\(563\) −24.3531 −1.02636 −0.513180 0.858281i \(-0.671532\pi\)
−0.513180 + 0.858281i \(0.671532\pi\)
\(564\) −154.860 −6.52079
\(565\) −17.3955 −0.731836
\(566\) −17.0116 −0.715049
\(567\) −31.5359 −1.32438
\(568\) −80.0869 −3.36037
\(569\) 26.2539 1.10062 0.550310 0.834960i \(-0.314509\pi\)
0.550310 + 0.834960i \(0.314509\pi\)
\(570\) 121.621 5.09414
\(571\) 27.0258 1.13099 0.565497 0.824751i \(-0.308684\pi\)
0.565497 + 0.824751i \(0.308684\pi\)
\(572\) 0.0914328 0.00382300
\(573\) −12.4155 −0.518664
\(574\) −81.8477 −3.41626
\(575\) −75.9094 −3.16564
\(576\) 53.8692 2.24455
\(577\) 8.35160 0.347682 0.173841 0.984774i \(-0.444382\pi\)
0.173841 + 0.984774i \(0.444382\pi\)
\(578\) 45.9632 1.91182
\(579\) −9.68367 −0.402439
\(580\) −103.481 −4.29681
\(581\) 37.5821 1.55917
\(582\) 101.923 4.22485
\(583\) −0.673236 −0.0278826
\(584\) −36.0068 −1.48997
\(585\) −2.52605 −0.104439
\(586\) −34.2410 −1.41448
\(587\) −9.09715 −0.375480 −0.187740 0.982219i \(-0.560116\pi\)
−0.187740 + 0.982219i \(0.560116\pi\)
\(588\) 20.7622 0.856220
\(589\) −28.5106 −1.17476
\(590\) 40.2585 1.65742
\(591\) 23.1758 0.953326
\(592\) −131.721 −5.41370
\(593\) −26.5313 −1.08951 −0.544754 0.838596i \(-0.683377\pi\)
−0.544754 + 0.838596i \(0.683377\pi\)
\(594\) 0.259399 0.0106433
\(595\) −0.940533 −0.0385581
\(596\) −42.4229 −1.73771
\(597\) −18.0399 −0.738324
\(598\) 7.67699 0.313935
\(599\) −44.4492 −1.81615 −0.908073 0.418812i \(-0.862446\pi\)
−0.908073 + 0.418812i \(0.862446\pi\)
\(600\) −169.615 −6.92449
\(601\) 19.1121 0.779601 0.389800 0.920899i \(-0.372544\pi\)
0.389800 + 0.920899i \(0.372544\pi\)
\(602\) 26.5082 1.08039
\(603\) 11.0337 0.449329
\(604\) −39.3153 −1.59972
\(605\) 40.0324 1.62755
\(606\) 5.91964 0.240469
\(607\) −38.6939 −1.57054 −0.785269 0.619154i \(-0.787476\pi\)
−0.785269 + 0.619154i \(0.787476\pi\)
\(608\) −102.081 −4.13995
\(609\) 36.1402 1.46447
\(610\) −95.6193 −3.87151
\(611\) −3.92247 −0.158686
\(612\) 1.04713 0.0423277
\(613\) 35.7708 1.44477 0.722384 0.691493i \(-0.243047\pi\)
0.722384 + 0.691493i \(0.243047\pi\)
\(614\) 39.4186 1.59080
\(615\) −85.5382 −3.44923
\(616\) −1.47534 −0.0594432
\(617\) −17.5074 −0.704821 −0.352411 0.935845i \(-0.614638\pi\)
−0.352411 + 0.935845i \(0.614638\pi\)
\(618\) 51.2192 2.06034
\(619\) −0.268718 −0.0108007 −0.00540035 0.999985i \(-0.501719\pi\)
−0.00540035 + 0.999985i \(0.501719\pi\)
\(620\) 102.357 4.11077
\(621\) 15.8265 0.635095
\(622\) −60.1795 −2.41298
\(623\) 43.3796 1.73797
\(624\) 9.63730 0.385801
\(625\) 1.83621 0.0734484
\(626\) 70.4818 2.81702
\(627\) 0.688447 0.0274939
\(628\) −38.7424 −1.54599
\(629\) −0.846061 −0.0337347
\(630\) 65.3385 2.60315
\(631\) 3.75402 0.149445 0.0747226 0.997204i \(-0.476193\pi\)
0.0747226 + 0.997204i \(0.476193\pi\)
\(632\) −38.7723 −1.54228
\(633\) −28.1118 −1.11735
\(634\) −26.6929 −1.06011
\(635\) −33.7798 −1.34051
\(636\) −147.125 −5.83390
\(637\) 0.525889 0.0208365
\(638\) −0.806113 −0.0319143
\(639\) 20.0771 0.794236
\(640\) 97.9886 3.87334
\(641\) −29.1855 −1.15276 −0.576380 0.817182i \(-0.695535\pi\)
−0.576380 + 0.817182i \(0.695535\pi\)
\(642\) −2.75569 −0.108758
\(643\) 38.4436 1.51607 0.758035 0.652214i \(-0.226160\pi\)
0.758035 + 0.652214i \(0.226160\pi\)
\(644\) −144.293 −5.68594
\(645\) 27.7035 1.09082
\(646\) −1.27699 −0.0502425
\(647\) −7.86962 −0.309387 −0.154693 0.987963i \(-0.549439\pi\)
−0.154693 + 0.987963i \(0.549439\pi\)
\(648\) 95.8947 3.76710
\(649\) 0.227887 0.00894534
\(650\) −6.88684 −0.270124
\(651\) −35.7478 −1.40107
\(652\) −113.649 −4.45083
\(653\) 13.5511 0.530295 0.265148 0.964208i \(-0.414579\pi\)
0.265148 + 0.964208i \(0.414579\pi\)
\(654\) 69.3644 2.71236
\(655\) 9.60439 0.375275
\(656\) 139.827 5.45934
\(657\) 9.02658 0.352160
\(658\) 101.458 3.95525
\(659\) −14.8092 −0.576883 −0.288442 0.957497i \(-0.593137\pi\)
−0.288442 + 0.957497i \(0.593137\pi\)
\(660\) −2.47163 −0.0962080
\(661\) 10.4107 0.404929 0.202464 0.979290i \(-0.435105\pi\)
0.202464 + 0.979290i \(0.435105\pi\)
\(662\) 24.4619 0.950737
\(663\) 0.0619016 0.00240406
\(664\) −114.280 −4.43492
\(665\) −57.9005 −2.24529
\(666\) 58.7756 2.27751
\(667\) −49.1826 −1.90436
\(668\) −92.3698 −3.57390
\(669\) 29.4386 1.13816
\(670\) 48.3084 1.86632
\(671\) −0.541262 −0.0208952
\(672\) −127.994 −4.93747
\(673\) 11.3851 0.438862 0.219431 0.975628i \(-0.429580\pi\)
0.219431 + 0.975628i \(0.429580\pi\)
\(674\) −43.9236 −1.69188
\(675\) −14.1976 −0.546464
\(676\) −68.6107 −2.63887
\(677\) −2.43282 −0.0935010 −0.0467505 0.998907i \(-0.514887\pi\)
−0.0467505 + 0.998907i \(0.514887\pi\)
\(678\) −29.6138 −1.13731
\(679\) −48.5229 −1.86214
\(680\) 2.85998 0.109675
\(681\) 27.9122 1.06960
\(682\) 0.797361 0.0305325
\(683\) 18.2028 0.696509 0.348255 0.937400i \(-0.386774\pi\)
0.348255 + 0.937400i \(0.386774\pi\)
\(684\) 64.4628 2.46480
\(685\) −44.0037 −1.68129
\(686\) 42.2607 1.61352
\(687\) 58.6029 2.23584
\(688\) −45.2862 −1.72652
\(689\) −3.72655 −0.141970
\(690\) −207.526 −7.90037
\(691\) 27.5374 1.04757 0.523787 0.851849i \(-0.324519\pi\)
0.523787 + 0.851849i \(0.324519\pi\)
\(692\) −102.086 −3.88072
\(693\) 0.369855 0.0140496
\(694\) 84.8479 3.22078
\(695\) −68.0473 −2.58118
\(696\) −109.895 −4.16557
\(697\) 0.898130 0.0340191
\(698\) −45.5850 −1.72542
\(699\) 16.6086 0.628197
\(700\) 129.442 4.89244
\(701\) 29.1269 1.10011 0.550055 0.835129i \(-0.314607\pi\)
0.550055 + 0.835129i \(0.314607\pi\)
\(702\) 1.43585 0.0541927
\(703\) −52.0847 −1.96441
\(704\) 1.33506 0.0503171
\(705\) 106.033 3.99343
\(706\) 29.1258 1.09616
\(707\) −2.81818 −0.105989
\(708\) 49.8012 1.87164
\(709\) 7.84561 0.294648 0.147324 0.989088i \(-0.452934\pi\)
0.147324 + 0.989088i \(0.452934\pi\)
\(710\) 87.9022 3.29891
\(711\) 9.71987 0.364524
\(712\) −131.909 −4.94350
\(713\) 48.6486 1.82190
\(714\) −1.60114 −0.0599212
\(715\) −0.0626041 −0.00234126
\(716\) −79.5036 −2.97119
\(717\) 29.6362 1.10678
\(718\) 32.9368 1.22919
\(719\) 12.4554 0.464508 0.232254 0.972655i \(-0.425390\pi\)
0.232254 + 0.972655i \(0.425390\pi\)
\(720\) −111.623 −4.15996
\(721\) −24.3841 −0.908111
\(722\) −27.2194 −1.01300
\(723\) 15.1802 0.564556
\(724\) −58.3326 −2.16791
\(725\) 44.1205 1.63859
\(726\) 68.1502 2.52929
\(727\) 28.3786 1.05250 0.526251 0.850329i \(-0.323597\pi\)
0.526251 + 0.850329i \(0.323597\pi\)
\(728\) −8.16644 −0.302668
\(729\) −12.2146 −0.452393
\(730\) 39.5205 1.46272
\(731\) −0.290879 −0.0107586
\(732\) −118.285 −4.37192
\(733\) 1.24568 0.0460101 0.0230051 0.999735i \(-0.492677\pi\)
0.0230051 + 0.999735i \(0.492677\pi\)
\(734\) −85.2482 −3.14657
\(735\) −14.2159 −0.524362
\(736\) 174.185 6.42054
\(737\) 0.273454 0.0100728
\(738\) −62.3928 −2.29671
\(739\) 30.9573 1.13878 0.569391 0.822067i \(-0.307179\pi\)
0.569391 + 0.822067i \(0.307179\pi\)
\(740\) 186.992 6.87396
\(741\) 3.81075 0.139991
\(742\) 96.3907 3.53861
\(743\) 38.4267 1.40974 0.704869 0.709337i \(-0.251006\pi\)
0.704869 + 0.709337i \(0.251006\pi\)
\(744\) 108.702 3.98521
\(745\) 29.0470 1.06420
\(746\) 75.8305 2.77635
\(747\) 28.6489 1.04821
\(748\) 0.0259515 0.000948880 0
\(749\) 1.31191 0.0479361
\(750\) 73.3665 2.67897
\(751\) 21.2600 0.775789 0.387895 0.921704i \(-0.373202\pi\)
0.387895 + 0.921704i \(0.373202\pi\)
\(752\) −173.330 −6.32068
\(753\) −35.8569 −1.30670
\(754\) −4.46207 −0.162499
\(755\) 26.9192 0.979691
\(756\) −26.9875 −0.981527
\(757\) 6.20929 0.225681 0.112840 0.993613i \(-0.464005\pi\)
0.112840 + 0.993613i \(0.464005\pi\)
\(758\) 64.8789 2.35651
\(759\) −1.17472 −0.0426396
\(760\) 176.064 6.38653
\(761\) 3.91027 0.141747 0.0708736 0.997485i \(-0.477421\pi\)
0.0708736 + 0.997485i \(0.477421\pi\)
\(762\) −57.5059 −2.08322
\(763\) −33.0225 −1.19550
\(764\) −28.8114 −1.04236
\(765\) −0.716972 −0.0259222
\(766\) −16.1073 −0.581981
\(767\) 1.26142 0.0455472
\(768\) 57.0618 2.05904
\(769\) 1.90872 0.0688302 0.0344151 0.999408i \(-0.489043\pi\)
0.0344151 + 0.999408i \(0.489043\pi\)
\(770\) 1.61931 0.0583560
\(771\) −0.900862 −0.0324437
\(772\) −22.4719 −0.808782
\(773\) −38.1640 −1.37267 −0.686333 0.727288i \(-0.740781\pi\)
−0.686333 + 0.727288i \(0.740781\pi\)
\(774\) 20.2073 0.726336
\(775\) −43.6415 −1.56765
\(776\) 147.549 5.29669
\(777\) −65.3060 −2.34284
\(778\) −50.3605 −1.80551
\(779\) 55.2901 1.98097
\(780\) −13.6812 −0.489865
\(781\) 0.497578 0.0178048
\(782\) 2.17897 0.0779198
\(783\) −9.19876 −0.328737
\(784\) 23.2385 0.829945
\(785\) 26.5270 0.946789
\(786\) 16.3503 0.583196
\(787\) −6.92428 −0.246824 −0.123412 0.992356i \(-0.539384\pi\)
−0.123412 + 0.992356i \(0.539384\pi\)
\(788\) 53.7818 1.91590
\(789\) −33.5029 −1.19273
\(790\) 42.5559 1.51407
\(791\) 14.0983 0.501279
\(792\) −1.12466 −0.0399630
\(793\) −2.99604 −0.106393
\(794\) −1.38818 −0.0492647
\(795\) 100.737 3.57277
\(796\) −41.8634 −1.48381
\(797\) −20.7141 −0.733730 −0.366865 0.930274i \(-0.619569\pi\)
−0.366865 + 0.930274i \(0.619569\pi\)
\(798\) −98.5685 −3.48929
\(799\) −1.11332 −0.0393864
\(800\) −156.257 −5.52452
\(801\) 33.0684 1.16841
\(802\) −62.9268 −2.22202
\(803\) 0.223710 0.00789454
\(804\) 59.7592 2.10754
\(805\) 98.7976 3.48216
\(806\) 4.41362 0.155463
\(807\) −1.88572 −0.0663805
\(808\) 8.56955 0.301476
\(809\) −11.3197 −0.397981 −0.198990 0.980001i \(-0.563766\pi\)
−0.198990 + 0.980001i \(0.563766\pi\)
\(810\) −105.253 −3.69820
\(811\) −28.6002 −1.00429 −0.502145 0.864783i \(-0.667456\pi\)
−0.502145 + 0.864783i \(0.667456\pi\)
\(812\) 83.8668 2.94315
\(813\) −14.8778 −0.521787
\(814\) 1.45666 0.0510559
\(815\) 77.8155 2.72576
\(816\) 2.73537 0.0957570
\(817\) −17.9069 −0.626484
\(818\) 45.6531 1.59622
\(819\) 2.04725 0.0715368
\(820\) −198.500 −6.93192
\(821\) 48.7945 1.70294 0.851469 0.524404i \(-0.175712\pi\)
0.851469 + 0.524404i \(0.175712\pi\)
\(822\) −74.9108 −2.61282
\(823\) −8.69685 −0.303153 −0.151577 0.988446i \(-0.548435\pi\)
−0.151577 + 0.988446i \(0.548435\pi\)
\(824\) 74.1474 2.58305
\(825\) 1.05381 0.0366890
\(826\) −32.6277 −1.13526
\(827\) −40.4758 −1.40748 −0.703741 0.710456i \(-0.748489\pi\)
−0.703741 + 0.710456i \(0.748489\pi\)
\(828\) −109.995 −3.82259
\(829\) −8.30921 −0.288591 −0.144295 0.989535i \(-0.546092\pi\)
−0.144295 + 0.989535i \(0.546092\pi\)
\(830\) 125.432 4.35381
\(831\) 38.0828 1.32108
\(832\) 7.38995 0.256201
\(833\) 0.149264 0.00517168
\(834\) −115.842 −4.01128
\(835\) 63.2458 2.18871
\(836\) 1.59761 0.0552544
\(837\) 9.09889 0.314504
\(838\) 65.5749 2.26525
\(839\) −39.3013 −1.35683 −0.678416 0.734678i \(-0.737333\pi\)
−0.678416 + 0.734678i \(0.737333\pi\)
\(840\) 220.757 7.61683
\(841\) −0.413815 −0.0142695
\(842\) 104.482 3.60068
\(843\) −30.8764 −1.06344
\(844\) −65.2363 −2.24553
\(845\) 46.9779 1.61609
\(846\) 77.3419 2.65907
\(847\) −32.4445 −1.11481
\(848\) −164.672 −5.65487
\(849\) 14.4088 0.494508
\(850\) −1.95470 −0.0670457
\(851\) 88.8738 3.04656
\(852\) 108.738 3.72531
\(853\) −49.3940 −1.69122 −0.845609 0.533803i \(-0.820762\pi\)
−0.845609 + 0.533803i \(0.820762\pi\)
\(854\) 77.4953 2.65184
\(855\) −44.1377 −1.50948
\(856\) −3.98926 −0.136350
\(857\) −3.62130 −0.123701 −0.0618506 0.998085i \(-0.519700\pi\)
−0.0618506 + 0.998085i \(0.519700\pi\)
\(858\) −0.106576 −0.00363844
\(859\) 43.6033 1.48773 0.743863 0.668332i \(-0.232991\pi\)
0.743863 + 0.668332i \(0.232991\pi\)
\(860\) 64.2886 2.19222
\(861\) 69.3250 2.36259
\(862\) 74.1722 2.52632
\(863\) −23.4576 −0.798507 −0.399253 0.916841i \(-0.630731\pi\)
−0.399253 + 0.916841i \(0.630731\pi\)
\(864\) 32.5783 1.10834
\(865\) 69.8983 2.37661
\(866\) 23.9726 0.814621
\(867\) −38.9308 −1.32216
\(868\) −82.9563 −2.81572
\(869\) 0.240892 0.00817169
\(870\) 120.619 4.08938
\(871\) 1.51365 0.0512880
\(872\) 100.415 3.40049
\(873\) −36.9892 −1.25189
\(874\) 134.140 4.53736
\(875\) −34.9279 −1.18078
\(876\) 48.8883 1.65178
\(877\) −3.71082 −0.125306 −0.0626528 0.998035i \(-0.519956\pi\)
−0.0626528 + 0.998035i \(0.519956\pi\)
\(878\) −77.6899 −2.62191
\(879\) 29.0021 0.978217
\(880\) −2.76641 −0.0932557
\(881\) 6.83985 0.230440 0.115220 0.993340i \(-0.463243\pi\)
0.115220 + 0.993340i \(0.463243\pi\)
\(882\) −10.3693 −0.349152
\(883\) 0.0532323 0.00179141 0.000895705 1.00000i \(-0.499715\pi\)
0.000895705 1.00000i \(0.499715\pi\)
\(884\) 0.143649 0.00483143
\(885\) −34.0989 −1.14622
\(886\) 32.3276 1.08607
\(887\) 50.7192 1.70298 0.851491 0.524369i \(-0.175699\pi\)
0.851491 + 0.524369i \(0.175699\pi\)
\(888\) 198.583 6.66400
\(889\) 27.3770 0.918197
\(890\) 144.781 4.85308
\(891\) −0.595792 −0.0199598
\(892\) 68.3152 2.28736
\(893\) −68.5374 −2.29352
\(894\) 49.4489 1.65382
\(895\) 54.4362 1.81960
\(896\) −79.4155 −2.65309
\(897\) −6.50241 −0.217109
\(898\) 98.5758 3.28952
\(899\) −28.2758 −0.943052
\(900\) 98.6739 3.28913
\(901\) −1.05771 −0.0352375
\(902\) −1.54631 −0.0514864
\(903\) −22.4525 −0.747171
\(904\) −42.8703 −1.42585
\(905\) 39.9404 1.32766
\(906\) 45.8267 1.52249
\(907\) −12.7213 −0.422403 −0.211201 0.977443i \(-0.567738\pi\)
−0.211201 + 0.977443i \(0.567738\pi\)
\(908\) 64.7731 2.14957
\(909\) −2.14831 −0.0712549
\(910\) 8.96336 0.297133
\(911\) 41.7710 1.38393 0.691967 0.721929i \(-0.256744\pi\)
0.691967 + 0.721929i \(0.256744\pi\)
\(912\) 168.393 5.57605
\(913\) 0.710019 0.0234982
\(914\) 15.1109 0.499823
\(915\) 80.9896 2.67743
\(916\) 135.994 4.49336
\(917\) −7.78394 −0.257048
\(918\) 0.407539 0.0134508
\(919\) 16.0793 0.530408 0.265204 0.964192i \(-0.414561\pi\)
0.265204 + 0.964192i \(0.414561\pi\)
\(920\) −300.424 −9.90470
\(921\) −33.3875 −1.10016
\(922\) −29.0752 −0.957540
\(923\) 2.75424 0.0906569
\(924\) 2.00315 0.0658987
\(925\) −79.7266 −2.62139
\(926\) −41.5093 −1.36408
\(927\) −18.5881 −0.610512
\(928\) −101.241 −3.32339
\(929\) −32.4133 −1.06345 −0.531724 0.846918i \(-0.678455\pi\)
−0.531724 + 0.846918i \(0.678455\pi\)
\(930\) −119.310 −3.91232
\(931\) 9.18887 0.301153
\(932\) 38.5420 1.26249
\(933\) 50.9720 1.66875
\(934\) 61.9320 2.02648
\(935\) −0.0177690 −0.000581109 0
\(936\) −6.22530 −0.203480
\(937\) −58.3735 −1.90698 −0.953490 0.301424i \(-0.902538\pi\)
−0.953490 + 0.301424i \(0.902538\pi\)
\(938\) −39.1518 −1.27835
\(939\) −59.6981 −1.94817
\(940\) 246.060 8.02559
\(941\) −53.4042 −1.74093 −0.870463 0.492234i \(-0.836180\pi\)
−0.870463 + 0.492234i \(0.836180\pi\)
\(942\) 45.1589 1.47136
\(943\) −94.3433 −3.07224
\(944\) 55.7408 1.81421
\(945\) 18.4784 0.601102
\(946\) 0.500806 0.0162826
\(947\) 21.9724 0.714008 0.357004 0.934103i \(-0.383798\pi\)
0.357004 + 0.934103i \(0.383798\pi\)
\(948\) 52.6432 1.70977
\(949\) 1.23830 0.0401968
\(950\) −120.334 −3.90415
\(951\) 22.6088 0.733142
\(952\) −2.31789 −0.0751233
\(953\) −11.9508 −0.387126 −0.193563 0.981088i \(-0.562004\pi\)
−0.193563 + 0.981088i \(0.562004\pi\)
\(954\) 73.4789 2.37897
\(955\) 19.7272 0.638356
\(956\) 68.7736 2.22430
\(957\) 0.682777 0.0220711
\(958\) 2.05563 0.0664143
\(959\) 35.6631 1.15162
\(960\) −199.767 −6.44744
\(961\) −3.03116 −0.0977794
\(962\) 8.06304 0.259963
\(963\) 1.00007 0.0322269
\(964\) 35.2271 1.13459
\(965\) 15.3865 0.495310
\(966\) 168.191 5.41145
\(967\) 8.42422 0.270905 0.135452 0.990784i \(-0.456751\pi\)
0.135452 + 0.990784i \(0.456751\pi\)
\(968\) 98.6576 3.17097
\(969\) 1.08161 0.0347463
\(970\) −161.947 −5.19982
\(971\) 8.39926 0.269545 0.134773 0.990877i \(-0.456970\pi\)
0.134773 + 0.990877i \(0.456970\pi\)
\(972\) −102.759 −3.29601
\(973\) 55.1494 1.76801
\(974\) −98.2825 −3.14917
\(975\) 5.83316 0.186811
\(976\) −132.392 −4.23776
\(977\) −34.4356 −1.10169 −0.550846 0.834607i \(-0.685695\pi\)
−0.550846 + 0.834607i \(0.685695\pi\)
\(978\) 132.471 4.23596
\(979\) 0.819549 0.0261929
\(980\) −32.9895 −1.05381
\(981\) −25.1732 −0.803718
\(982\) 32.9470 1.05138
\(983\) 0.294686 0.00939902 0.00469951 0.999989i \(-0.498504\pi\)
0.00469951 + 0.999989i \(0.498504\pi\)
\(984\) −210.804 −6.72019
\(985\) −36.8245 −1.17333
\(986\) −1.26647 −0.0403327
\(987\) −85.9351 −2.73534
\(988\) 8.84322 0.281340
\(989\) 30.5552 0.971598
\(990\) 1.23441 0.0392320
\(991\) −47.0066 −1.49321 −0.746607 0.665266i \(-0.768318\pi\)
−0.746607 + 0.665266i \(0.768318\pi\)
\(992\) 100.142 3.17950
\(993\) −20.7192 −0.657504
\(994\) −71.2409 −2.25962
\(995\) 28.6639 0.908707
\(996\) 155.164 4.91655
\(997\) 5.23646 0.165840 0.0829202 0.996556i \(-0.473575\pi\)
0.0829202 + 0.996556i \(0.473575\pi\)
\(998\) 76.2385 2.41329
\(999\) 16.6223 0.525907
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 4027.2.a.b.1.6 159
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.b.1.6 159 1.1 even 1 trivial