Properties

Label 6019.2.a.b.1.4
Level $6019$
Weight $2$
Character 6019.1
Self dual yes
Analytic conductor $48.062$
Analytic rank $1$
Dimension $101$
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] = [6019,2,Mod(1,6019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6019 = 13 \cdot 463 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6019.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: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(101\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.61088 q^{2} -2.81902 q^{3} +4.81671 q^{4} -3.25148 q^{5} +7.36014 q^{6} +3.68170 q^{7} -7.35411 q^{8} +4.94689 q^{9} +O(q^{10})\) \(q-2.61088 q^{2} -2.81902 q^{3} +4.81671 q^{4} -3.25148 q^{5} +7.36014 q^{6} +3.68170 q^{7} -7.35411 q^{8} +4.94689 q^{9} +8.48923 q^{10} +0.379576 q^{11} -13.5784 q^{12} +1.00000 q^{13} -9.61249 q^{14} +9.16600 q^{15} +9.56729 q^{16} +0.171129 q^{17} -12.9158 q^{18} +2.47353 q^{19} -15.6614 q^{20} -10.3788 q^{21} -0.991029 q^{22} +5.01910 q^{23} +20.7314 q^{24} +5.57212 q^{25} -2.61088 q^{26} -5.48833 q^{27} +17.7337 q^{28} -0.620211 q^{29} -23.9313 q^{30} +0.609189 q^{31} -10.2709 q^{32} -1.07003 q^{33} -0.446799 q^{34} -11.9710 q^{35} +23.8277 q^{36} +5.70011 q^{37} -6.45809 q^{38} -2.81902 q^{39} +23.9117 q^{40} -3.49063 q^{41} +27.0978 q^{42} -4.03815 q^{43} +1.82831 q^{44} -16.0847 q^{45} -13.1043 q^{46} +2.69340 q^{47} -26.9704 q^{48} +6.55491 q^{49} -14.5482 q^{50} -0.482418 q^{51} +4.81671 q^{52} -0.117488 q^{53} +14.3294 q^{54} -1.23418 q^{55} -27.0756 q^{56} -6.97293 q^{57} +1.61930 q^{58} +1.60477 q^{59} +44.1500 q^{60} -10.3768 q^{61} -1.59052 q^{62} +18.2130 q^{63} +7.68144 q^{64} -3.25148 q^{65} +2.79373 q^{66} -8.42378 q^{67} +0.824281 q^{68} -14.1490 q^{69} +31.2548 q^{70} -15.5506 q^{71} -36.3800 q^{72} +6.10722 q^{73} -14.8823 q^{74} -15.7079 q^{75} +11.9143 q^{76} +1.39749 q^{77} +7.36014 q^{78} -2.55754 q^{79} -31.1078 q^{80} +0.631060 q^{81} +9.11363 q^{82} -12.1349 q^{83} -49.9917 q^{84} -0.556424 q^{85} +10.5431 q^{86} +1.74839 q^{87} -2.79144 q^{88} +1.81108 q^{89} +41.9953 q^{90} +3.68170 q^{91} +24.1756 q^{92} -1.71732 q^{93} -7.03215 q^{94} -8.04262 q^{95} +28.9538 q^{96} +13.1598 q^{97} -17.1141 q^{98} +1.87772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61088 −1.84617 −0.923087 0.384592i \(-0.874342\pi\)
−0.923087 + 0.384592i \(0.874342\pi\)
\(3\) −2.81902 −1.62756 −0.813782 0.581170i \(-0.802595\pi\)
−0.813782 + 0.581170i \(0.802595\pi\)
\(4\) 4.81671 2.40836
\(5\) −3.25148 −1.45411 −0.727053 0.686581i \(-0.759111\pi\)
−0.727053 + 0.686581i \(0.759111\pi\)
\(6\) 7.36014 3.00476
\(7\) 3.68170 1.39155 0.695776 0.718259i \(-0.255061\pi\)
0.695776 + 0.718259i \(0.255061\pi\)
\(8\) −7.35411 −2.60007
\(9\) 4.94689 1.64896
\(10\) 8.48923 2.68453
\(11\) 0.379576 0.114447 0.0572233 0.998361i \(-0.481775\pi\)
0.0572233 + 0.998361i \(0.481775\pi\)
\(12\) −13.5784 −3.91975
\(13\) 1.00000 0.277350
\(14\) −9.61249 −2.56905
\(15\) 9.16600 2.36665
\(16\) 9.56729 2.39182
\(17\) 0.171129 0.0415050 0.0207525 0.999785i \(-0.493394\pi\)
0.0207525 + 0.999785i \(0.493394\pi\)
\(18\) −12.9158 −3.04427
\(19\) 2.47353 0.567466 0.283733 0.958903i \(-0.408427\pi\)
0.283733 + 0.958903i \(0.408427\pi\)
\(20\) −15.6614 −3.50200
\(21\) −10.3788 −2.26484
\(22\) −0.991029 −0.211288
\(23\) 5.01910 1.04656 0.523278 0.852162i \(-0.324709\pi\)
0.523278 + 0.852162i \(0.324709\pi\)
\(24\) 20.7314 4.23178
\(25\) 5.57212 1.11442
\(26\) −2.61088 −0.512036
\(27\) −5.48833 −1.05623
\(28\) 17.7337 3.35135
\(29\) −0.620211 −0.115170 −0.0575852 0.998341i \(-0.518340\pi\)
−0.0575852 + 0.998341i \(0.518340\pi\)
\(30\) −23.9313 −4.36925
\(31\) 0.609189 0.109414 0.0547068 0.998502i \(-0.482578\pi\)
0.0547068 + 0.998502i \(0.482578\pi\)
\(32\) −10.2709 −1.81565
\(33\) −1.07003 −0.186269
\(34\) −0.446799 −0.0766254
\(35\) −11.9710 −2.02346
\(36\) 23.8277 3.97129
\(37\) 5.70011 0.937093 0.468546 0.883439i \(-0.344778\pi\)
0.468546 + 0.883439i \(0.344778\pi\)
\(38\) −6.45809 −1.04764
\(39\) −2.81902 −0.451405
\(40\) 23.9117 3.78078
\(41\) −3.49063 −0.545145 −0.272573 0.962135i \(-0.587874\pi\)
−0.272573 + 0.962135i \(0.587874\pi\)
\(42\) 27.0978 4.18128
\(43\) −4.03815 −0.615812 −0.307906 0.951417i \(-0.599628\pi\)
−0.307906 + 0.951417i \(0.599628\pi\)
\(44\) 1.82831 0.275628
\(45\) −16.0847 −2.39777
\(46\) −13.1043 −1.93212
\(47\) 2.69340 0.392873 0.196436 0.980517i \(-0.437063\pi\)
0.196436 + 0.980517i \(0.437063\pi\)
\(48\) −26.9704 −3.89284
\(49\) 6.55491 0.936416
\(50\) −14.5482 −2.05742
\(51\) −0.482418 −0.0675520
\(52\) 4.81671 0.667958
\(53\) −0.117488 −0.0161382 −0.00806909 0.999967i \(-0.502569\pi\)
−0.00806909 + 0.999967i \(0.502569\pi\)
\(54\) 14.3294 1.94998
\(55\) −1.23418 −0.166417
\(56\) −27.0756 −3.61813
\(57\) −6.97293 −0.923587
\(58\) 1.61930 0.212624
\(59\) 1.60477 0.208923 0.104462 0.994529i \(-0.466688\pi\)
0.104462 + 0.994529i \(0.466688\pi\)
\(60\) 44.1500 5.69974
\(61\) −10.3768 −1.32862 −0.664309 0.747458i \(-0.731274\pi\)
−0.664309 + 0.747458i \(0.731274\pi\)
\(62\) −1.59052 −0.201996
\(63\) 18.2130 2.29462
\(64\) 7.68144 0.960180
\(65\) −3.25148 −0.403296
\(66\) 2.79373 0.343885
\(67\) −8.42378 −1.02913 −0.514564 0.857452i \(-0.672046\pi\)
−0.514564 + 0.857452i \(0.672046\pi\)
\(68\) 0.824281 0.0999588
\(69\) −14.1490 −1.70334
\(70\) 31.2548 3.73566
\(71\) −15.5506 −1.84552 −0.922758 0.385381i \(-0.874070\pi\)
−0.922758 + 0.385381i \(0.874070\pi\)
\(72\) −36.3800 −4.28742
\(73\) 6.10722 0.714796 0.357398 0.933952i \(-0.383664\pi\)
0.357398 + 0.933952i \(0.383664\pi\)
\(74\) −14.8823 −1.73004
\(75\) −15.7079 −1.81380
\(76\) 11.9143 1.36666
\(77\) 1.39749 0.159258
\(78\) 7.36014 0.833372
\(79\) −2.55754 −0.287746 −0.143873 0.989596i \(-0.545956\pi\)
−0.143873 + 0.989596i \(0.545956\pi\)
\(80\) −31.1078 −3.47796
\(81\) 0.631060 0.0701178
\(82\) 9.11363 1.00643
\(83\) −12.1349 −1.33198 −0.665991 0.745960i \(-0.731991\pi\)
−0.665991 + 0.745960i \(0.731991\pi\)
\(84\) −49.9917 −5.45454
\(85\) −0.556424 −0.0603527
\(86\) 10.5431 1.13690
\(87\) 1.74839 0.187447
\(88\) −2.79144 −0.297569
\(89\) 1.81108 0.191974 0.0959869 0.995383i \(-0.469399\pi\)
0.0959869 + 0.995383i \(0.469399\pi\)
\(90\) 41.9953 4.42669
\(91\) 3.68170 0.385947
\(92\) 24.1756 2.52048
\(93\) −1.71732 −0.178077
\(94\) −7.03215 −0.725311
\(95\) −8.04262 −0.825156
\(96\) 28.9538 2.95508
\(97\) 13.1598 1.33618 0.668090 0.744080i \(-0.267112\pi\)
0.668090 + 0.744080i \(0.267112\pi\)
\(98\) −17.1141 −1.72879
\(99\) 1.87772 0.188718
\(100\) 26.8393 2.68393
\(101\) −9.47629 −0.942926 −0.471463 0.881886i \(-0.656274\pi\)
−0.471463 + 0.881886i \(0.656274\pi\)
\(102\) 1.25954 0.124713
\(103\) −0.836489 −0.0824218 −0.0412109 0.999150i \(-0.513122\pi\)
−0.0412109 + 0.999150i \(0.513122\pi\)
\(104\) −7.35411 −0.721129
\(105\) 33.7464 3.29332
\(106\) 0.306747 0.0297939
\(107\) −1.28587 −0.124310 −0.0621548 0.998067i \(-0.519797\pi\)
−0.0621548 + 0.998067i \(0.519797\pi\)
\(108\) −26.4357 −2.54378
\(109\) −12.2550 −1.17381 −0.586906 0.809655i \(-0.699654\pi\)
−0.586906 + 0.809655i \(0.699654\pi\)
\(110\) 3.22231 0.307235
\(111\) −16.0687 −1.52518
\(112\) 35.2239 3.32834
\(113\) −3.39434 −0.319312 −0.159656 0.987173i \(-0.551039\pi\)
−0.159656 + 0.987173i \(0.551039\pi\)
\(114\) 18.2055 1.70510
\(115\) −16.3195 −1.52180
\(116\) −2.98738 −0.277371
\(117\) 4.94689 0.457340
\(118\) −4.18986 −0.385708
\(119\) 0.630047 0.0577563
\(120\) −67.4077 −6.15345
\(121\) −10.8559 −0.986902
\(122\) 27.0927 2.45286
\(123\) 9.84017 0.887259
\(124\) 2.93429 0.263507
\(125\) −1.86023 −0.166384
\(126\) −47.5519 −4.23626
\(127\) 16.2661 1.44338 0.721690 0.692216i \(-0.243366\pi\)
0.721690 + 0.692216i \(0.243366\pi\)
\(128\) 0.486372 0.0429896
\(129\) 11.3836 1.00227
\(130\) 8.48923 0.744555
\(131\) −8.32041 −0.726957 −0.363479 0.931603i \(-0.618411\pi\)
−0.363479 + 0.931603i \(0.618411\pi\)
\(132\) −5.15404 −0.448602
\(133\) 9.10678 0.789658
\(134\) 21.9935 1.89995
\(135\) 17.8452 1.53587
\(136\) −1.25850 −0.107916
\(137\) 7.50857 0.641500 0.320750 0.947164i \(-0.396065\pi\)
0.320750 + 0.947164i \(0.396065\pi\)
\(138\) 36.9413 3.14465
\(139\) 1.71100 0.145125 0.0725626 0.997364i \(-0.476882\pi\)
0.0725626 + 0.997364i \(0.476882\pi\)
\(140\) −57.6607 −4.87322
\(141\) −7.59276 −0.639425
\(142\) 40.6008 3.40714
\(143\) 0.379576 0.0317417
\(144\) 47.3283 3.94403
\(145\) 2.01660 0.167470
\(146\) −15.9452 −1.31964
\(147\) −18.4784 −1.52408
\(148\) 27.4558 2.25685
\(149\) 12.9223 1.05863 0.529317 0.848424i \(-0.322448\pi\)
0.529317 + 0.848424i \(0.322448\pi\)
\(150\) 41.0116 3.34858
\(151\) 0.993156 0.0808219 0.0404109 0.999183i \(-0.487133\pi\)
0.0404109 + 0.999183i \(0.487133\pi\)
\(152\) −18.1906 −1.47545
\(153\) 0.846559 0.0684402
\(154\) −3.64867 −0.294018
\(155\) −1.98076 −0.159099
\(156\) −13.5784 −1.08714
\(157\) −4.64854 −0.370994 −0.185497 0.982645i \(-0.559389\pi\)
−0.185497 + 0.982645i \(0.559389\pi\)
\(158\) 6.67745 0.531229
\(159\) 0.331201 0.0262659
\(160\) 33.3955 2.64015
\(161\) 18.4788 1.45634
\(162\) −1.64762 −0.129450
\(163\) −22.3868 −1.75347 −0.876735 0.480973i \(-0.840284\pi\)
−0.876735 + 0.480973i \(0.840284\pi\)
\(164\) −16.8134 −1.31290
\(165\) 3.47919 0.270855
\(166\) 31.6829 2.45907
\(167\) −1.74851 −0.135304 −0.0676519 0.997709i \(-0.521551\pi\)
−0.0676519 + 0.997709i \(0.521551\pi\)
\(168\) 76.3268 5.88874
\(169\) 1.00000 0.0769231
\(170\) 1.45276 0.111421
\(171\) 12.2363 0.935731
\(172\) −19.4506 −1.48309
\(173\) 6.45492 0.490759 0.245379 0.969427i \(-0.421087\pi\)
0.245379 + 0.969427i \(0.421087\pi\)
\(174\) −4.56484 −0.346060
\(175\) 20.5149 1.55078
\(176\) 3.63151 0.273736
\(177\) −4.52388 −0.340036
\(178\) −4.72851 −0.354417
\(179\) 0.00252205 0.000188507 0 9.42535e−5 1.00000i \(-0.499970\pi\)
9.42535e−5 1.00000i \(0.499970\pi\)
\(180\) −77.4754 −5.77468
\(181\) 4.91839 0.365581 0.182791 0.983152i \(-0.441487\pi\)
0.182791 + 0.983152i \(0.441487\pi\)
\(182\) −9.61249 −0.712525
\(183\) 29.2526 2.16241
\(184\) −36.9110 −2.72112
\(185\) −18.5338 −1.36263
\(186\) 4.48371 0.328762
\(187\) 0.0649567 0.00475010
\(188\) 12.9733 0.946177
\(189\) −20.2064 −1.46980
\(190\) 20.9984 1.52338
\(191\) −8.64851 −0.625784 −0.312892 0.949789i \(-0.601298\pi\)
−0.312892 + 0.949789i \(0.601298\pi\)
\(192\) −21.6542 −1.56275
\(193\) −5.33669 −0.384143 −0.192072 0.981381i \(-0.561521\pi\)
−0.192072 + 0.981381i \(0.561521\pi\)
\(194\) −34.3588 −2.46682
\(195\) 9.16600 0.656391
\(196\) 31.5731 2.25522
\(197\) −8.75961 −0.624097 −0.312048 0.950066i \(-0.601015\pi\)
−0.312048 + 0.950066i \(0.601015\pi\)
\(198\) −4.90251 −0.348406
\(199\) 1.22515 0.0868485 0.0434242 0.999057i \(-0.486173\pi\)
0.0434242 + 0.999057i \(0.486173\pi\)
\(200\) −40.9779 −2.89758
\(201\) 23.7468 1.67497
\(202\) 24.7415 1.74080
\(203\) −2.28343 −0.160265
\(204\) −2.32367 −0.162689
\(205\) 11.3497 0.792699
\(206\) 2.18398 0.152165
\(207\) 24.8290 1.72573
\(208\) 9.56729 0.663372
\(209\) 0.938892 0.0649445
\(210\) −88.1080 −6.08003
\(211\) 8.78344 0.604677 0.302339 0.953201i \(-0.402233\pi\)
0.302339 + 0.953201i \(0.402233\pi\)
\(212\) −0.565905 −0.0388665
\(213\) 43.8375 3.00369
\(214\) 3.35725 0.229497
\(215\) 13.1300 0.895455
\(216\) 40.3618 2.74627
\(217\) 2.24285 0.152255
\(218\) 31.9963 2.16706
\(219\) −17.2164 −1.16338
\(220\) −5.94471 −0.400792
\(221\) 0.171129 0.0115114
\(222\) 41.9536 2.81574
\(223\) 5.90090 0.395153 0.197577 0.980287i \(-0.436693\pi\)
0.197577 + 0.980287i \(0.436693\pi\)
\(224\) −37.8142 −2.52657
\(225\) 27.5647 1.83764
\(226\) 8.86222 0.589506
\(227\) 28.7527 1.90838 0.954191 0.299197i \(-0.0967189\pi\)
0.954191 + 0.299197i \(0.0967189\pi\)
\(228\) −33.5866 −2.22433
\(229\) 19.3289 1.27729 0.638644 0.769502i \(-0.279496\pi\)
0.638644 + 0.769502i \(0.279496\pi\)
\(230\) 42.6083 2.80951
\(231\) −3.93954 −0.259203
\(232\) 4.56110 0.299451
\(233\) −9.17650 −0.601172 −0.300586 0.953755i \(-0.597182\pi\)
−0.300586 + 0.953755i \(0.597182\pi\)
\(234\) −12.9158 −0.844329
\(235\) −8.75753 −0.571279
\(236\) 7.72971 0.503161
\(237\) 7.20977 0.468325
\(238\) −1.64498 −0.106628
\(239\) −7.38972 −0.478001 −0.239001 0.971019i \(-0.576820\pi\)
−0.239001 + 0.971019i \(0.576820\pi\)
\(240\) 87.6937 5.66060
\(241\) 28.6478 1.84537 0.922683 0.385560i \(-0.125992\pi\)
0.922683 + 0.385560i \(0.125992\pi\)
\(242\) 28.3435 1.82199
\(243\) 14.6860 0.942109
\(244\) −49.9823 −3.19979
\(245\) −21.3132 −1.36165
\(246\) −25.6915 −1.63803
\(247\) 2.47353 0.157387
\(248\) −4.48004 −0.284483
\(249\) 34.2086 2.16788
\(250\) 4.85685 0.307174
\(251\) −20.6925 −1.30610 −0.653050 0.757314i \(-0.726511\pi\)
−0.653050 + 0.757314i \(0.726511\pi\)
\(252\) 87.7266 5.52626
\(253\) 1.90513 0.119775
\(254\) −42.4688 −2.66473
\(255\) 1.56857 0.0982278
\(256\) −16.6327 −1.03955
\(257\) 26.0995 1.62804 0.814022 0.580835i \(-0.197274\pi\)
0.814022 + 0.580835i \(0.197274\pi\)
\(258\) −29.7213 −1.85037
\(259\) 20.9861 1.30401
\(260\) −15.6614 −0.971281
\(261\) −3.06812 −0.189912
\(262\) 21.7236 1.34209
\(263\) −1.59496 −0.0983496 −0.0491748 0.998790i \(-0.515659\pi\)
−0.0491748 + 0.998790i \(0.515659\pi\)
\(264\) 7.86914 0.484312
\(265\) 0.382009 0.0234666
\(266\) −23.7767 −1.45785
\(267\) −5.10547 −0.312450
\(268\) −40.5749 −2.47851
\(269\) −7.63145 −0.465298 −0.232649 0.972561i \(-0.574739\pi\)
−0.232649 + 0.972561i \(0.574739\pi\)
\(270\) −46.5917 −2.83548
\(271\) −11.3837 −0.691511 −0.345756 0.938325i \(-0.612377\pi\)
−0.345756 + 0.938325i \(0.612377\pi\)
\(272\) 1.63724 0.0992725
\(273\) −10.3788 −0.628153
\(274\) −19.6040 −1.18432
\(275\) 2.11504 0.127542
\(276\) −68.1515 −4.10224
\(277\) −14.6567 −0.880633 −0.440317 0.897843i \(-0.645134\pi\)
−0.440317 + 0.897843i \(0.645134\pi\)
\(278\) −4.46722 −0.267926
\(279\) 3.01359 0.180419
\(280\) 88.0358 5.26114
\(281\) 19.3454 1.15405 0.577026 0.816726i \(-0.304213\pi\)
0.577026 + 0.816726i \(0.304213\pi\)
\(282\) 19.8238 1.18049
\(283\) −12.4503 −0.740092 −0.370046 0.929014i \(-0.620658\pi\)
−0.370046 + 0.929014i \(0.620658\pi\)
\(284\) −74.9027 −4.44466
\(285\) 22.6723 1.34299
\(286\) −0.991029 −0.0586008
\(287\) −12.8515 −0.758598
\(288\) −50.8088 −2.99394
\(289\) −16.9707 −0.998277
\(290\) −5.26512 −0.309178
\(291\) −37.0979 −2.17472
\(292\) 29.4167 1.72148
\(293\) −19.3113 −1.12818 −0.564090 0.825713i \(-0.690773\pi\)
−0.564090 + 0.825713i \(0.690773\pi\)
\(294\) 48.2451 2.81371
\(295\) −5.21787 −0.303796
\(296\) −41.9192 −2.43651
\(297\) −2.08324 −0.120882
\(298\) −33.7386 −1.95442
\(299\) 5.01910 0.290262
\(300\) −75.6606 −4.36827
\(301\) −14.8672 −0.856934
\(302\) −2.59301 −0.149211
\(303\) 26.7139 1.53467
\(304\) 23.6649 1.35728
\(305\) 33.7401 1.93195
\(306\) −2.21027 −0.126353
\(307\) 30.6038 1.74665 0.873324 0.487140i \(-0.161960\pi\)
0.873324 + 0.487140i \(0.161960\pi\)
\(308\) 6.73128 0.383550
\(309\) 2.35808 0.134147
\(310\) 5.17154 0.293724
\(311\) 16.2031 0.918794 0.459397 0.888231i \(-0.348066\pi\)
0.459397 + 0.888231i \(0.348066\pi\)
\(312\) 20.7314 1.17368
\(313\) −30.0032 −1.69588 −0.847939 0.530093i \(-0.822157\pi\)
−0.847939 + 0.530093i \(0.822157\pi\)
\(314\) 12.1368 0.684919
\(315\) −59.2191 −3.33662
\(316\) −12.3189 −0.692995
\(317\) 15.2765 0.858012 0.429006 0.903302i \(-0.358864\pi\)
0.429006 + 0.903302i \(0.358864\pi\)
\(318\) −0.864727 −0.0484915
\(319\) −0.235417 −0.0131808
\(320\) −24.9760 −1.39620
\(321\) 3.62489 0.202322
\(322\) −48.2461 −2.68865
\(323\) 0.423293 0.0235527
\(324\) 3.03963 0.168869
\(325\) 5.57212 0.309086
\(326\) 58.4494 3.23721
\(327\) 34.5470 1.91045
\(328\) 25.6705 1.41742
\(329\) 9.91629 0.546703
\(330\) −9.08377 −0.500045
\(331\) −26.7196 −1.46864 −0.734321 0.678802i \(-0.762499\pi\)
−0.734321 + 0.678802i \(0.762499\pi\)
\(332\) −58.4504 −3.20788
\(333\) 28.1978 1.54523
\(334\) 4.56516 0.249794
\(335\) 27.3897 1.49646
\(336\) −99.2969 −5.41709
\(337\) 14.7494 0.803453 0.401727 0.915760i \(-0.368410\pi\)
0.401727 + 0.915760i \(0.368410\pi\)
\(338\) −2.61088 −0.142013
\(339\) 9.56872 0.519701
\(340\) −2.68013 −0.145351
\(341\) 0.231233 0.0125220
\(342\) −31.9475 −1.72752
\(343\) −1.63869 −0.0884809
\(344\) 29.6970 1.60115
\(345\) 46.0051 2.47683
\(346\) −16.8530 −0.906025
\(347\) −24.4068 −1.31022 −0.655112 0.755532i \(-0.727379\pi\)
−0.655112 + 0.755532i \(0.727379\pi\)
\(348\) 8.42149 0.451439
\(349\) 10.0823 0.539694 0.269847 0.962903i \(-0.413027\pi\)
0.269847 + 0.962903i \(0.413027\pi\)
\(350\) −53.5619 −2.86301
\(351\) −5.48833 −0.292945
\(352\) −3.89857 −0.207795
\(353\) −17.2236 −0.916718 −0.458359 0.888767i \(-0.651563\pi\)
−0.458359 + 0.888767i \(0.651563\pi\)
\(354\) 11.8113 0.627765
\(355\) 50.5624 2.68357
\(356\) 8.72344 0.462341
\(357\) −1.77612 −0.0940021
\(358\) −0.00658478 −0.000348017 0
\(359\) −30.0890 −1.58803 −0.794017 0.607895i \(-0.792014\pi\)
−0.794017 + 0.607895i \(0.792014\pi\)
\(360\) 118.289 6.23436
\(361\) −12.8817 −0.677982
\(362\) −12.8413 −0.674926
\(363\) 30.6031 1.60625
\(364\) 17.7337 0.929498
\(365\) −19.8575 −1.03939
\(366\) −76.3750 −3.99219
\(367\) −2.39286 −0.124906 −0.0624532 0.998048i \(-0.519892\pi\)
−0.0624532 + 0.998048i \(0.519892\pi\)
\(368\) 48.0192 2.50317
\(369\) −17.2678 −0.898925
\(370\) 48.3896 2.51565
\(371\) −0.432555 −0.0224571
\(372\) −8.27182 −0.428874
\(373\) −1.83549 −0.0950379 −0.0475190 0.998870i \(-0.515131\pi\)
−0.0475190 + 0.998870i \(0.515131\pi\)
\(374\) −0.169594 −0.00876951
\(375\) 5.24404 0.270801
\(376\) −19.8075 −1.02150
\(377\) −0.620211 −0.0319425
\(378\) 52.7565 2.71350
\(379\) 15.3036 0.786091 0.393046 0.919519i \(-0.371421\pi\)
0.393046 + 0.919519i \(0.371421\pi\)
\(380\) −38.7390 −1.98727
\(381\) −45.8544 −2.34919
\(382\) 22.5802 1.15531
\(383\) 26.3457 1.34620 0.673102 0.739550i \(-0.264961\pi\)
0.673102 + 0.739550i \(0.264961\pi\)
\(384\) −1.37109 −0.0699683
\(385\) −4.54389 −0.231578
\(386\) 13.9335 0.709195
\(387\) −19.9763 −1.01545
\(388\) 63.3872 3.21800
\(389\) 11.7425 0.595369 0.297685 0.954664i \(-0.403786\pi\)
0.297685 + 0.954664i \(0.403786\pi\)
\(390\) −23.9313 −1.21181
\(391\) 0.858917 0.0434373
\(392\) −48.2055 −2.43475
\(393\) 23.4554 1.18317
\(394\) 22.8703 1.15219
\(395\) 8.31580 0.418413
\(396\) 9.04444 0.454500
\(397\) −16.9380 −0.850092 −0.425046 0.905172i \(-0.639742\pi\)
−0.425046 + 0.905172i \(0.639742\pi\)
\(398\) −3.19872 −0.160337
\(399\) −25.6722 −1.28522
\(400\) 53.3101 2.66550
\(401\) −4.92942 −0.246163 −0.123082 0.992397i \(-0.539278\pi\)
−0.123082 + 0.992397i \(0.539278\pi\)
\(402\) −62.0002 −3.09229
\(403\) 0.609189 0.0303458
\(404\) −45.6445 −2.27090
\(405\) −2.05188 −0.101959
\(406\) 5.96177 0.295878
\(407\) 2.16363 0.107247
\(408\) 3.54775 0.175640
\(409\) 14.6684 0.725304 0.362652 0.931925i \(-0.381871\pi\)
0.362652 + 0.931925i \(0.381871\pi\)
\(410\) −29.6328 −1.46346
\(411\) −21.1668 −1.04408
\(412\) −4.02913 −0.198501
\(413\) 5.90828 0.290727
\(414\) −64.8255 −3.18600
\(415\) 39.4565 1.93684
\(416\) −10.2709 −0.503570
\(417\) −4.82335 −0.236201
\(418\) −2.45134 −0.119899
\(419\) 8.81562 0.430671 0.215336 0.976540i \(-0.430915\pi\)
0.215336 + 0.976540i \(0.430915\pi\)
\(420\) 162.547 7.93148
\(421\) −21.7311 −1.05911 −0.529554 0.848276i \(-0.677641\pi\)
−0.529554 + 0.848276i \(0.677641\pi\)
\(422\) −22.9325 −1.11634
\(423\) 13.3240 0.647833
\(424\) 0.864017 0.0419604
\(425\) 0.953554 0.0462542
\(426\) −114.455 −5.54534
\(427\) −38.2044 −1.84884
\(428\) −6.19365 −0.299382
\(429\) −1.07003 −0.0516617
\(430\) −34.2808 −1.65317
\(431\) 14.9790 0.721513 0.360757 0.932660i \(-0.382518\pi\)
0.360757 + 0.932660i \(0.382518\pi\)
\(432\) −52.5084 −2.52631
\(433\) 34.5418 1.65997 0.829986 0.557784i \(-0.188348\pi\)
0.829986 + 0.557784i \(0.188348\pi\)
\(434\) −5.85582 −0.281088
\(435\) −5.68485 −0.272568
\(436\) −59.0286 −2.82696
\(437\) 12.4149 0.593885
\(438\) 44.9500 2.14779
\(439\) −2.61292 −0.124708 −0.0623539 0.998054i \(-0.519861\pi\)
−0.0623539 + 0.998054i \(0.519861\pi\)
\(440\) 9.07632 0.432696
\(441\) 32.4264 1.54412
\(442\) −0.446799 −0.0212521
\(443\) −26.3263 −1.25080 −0.625401 0.780304i \(-0.715064\pi\)
−0.625401 + 0.780304i \(0.715064\pi\)
\(444\) −77.3985 −3.67317
\(445\) −5.88868 −0.279150
\(446\) −15.4066 −0.729522
\(447\) −36.4282 −1.72299
\(448\) 28.2808 1.33614
\(449\) −19.9592 −0.941934 −0.470967 0.882151i \(-0.656095\pi\)
−0.470967 + 0.882151i \(0.656095\pi\)
\(450\) −71.9681 −3.39261
\(451\) −1.32496 −0.0623900
\(452\) −16.3495 −0.769018
\(453\) −2.79973 −0.131543
\(454\) −75.0699 −3.52320
\(455\) −11.9710 −0.561208
\(456\) 51.2797 2.40139
\(457\) −23.0819 −1.07972 −0.539862 0.841753i \(-0.681524\pi\)
−0.539862 + 0.841753i \(0.681524\pi\)
\(458\) −50.4655 −2.35810
\(459\) −0.939215 −0.0438388
\(460\) −78.6064 −3.66504
\(461\) −10.8863 −0.507027 −0.253514 0.967332i \(-0.581586\pi\)
−0.253514 + 0.967332i \(0.581586\pi\)
\(462\) 10.2857 0.478533
\(463\) 1.00000 0.0464739
\(464\) −5.93374 −0.275467
\(465\) 5.58382 0.258943
\(466\) 23.9588 1.10987
\(467\) 39.3814 1.82235 0.911177 0.412015i \(-0.135175\pi\)
0.911177 + 0.412015i \(0.135175\pi\)
\(468\) 23.8277 1.10144
\(469\) −31.0138 −1.43208
\(470\) 22.8649 1.05468
\(471\) 13.1043 0.603816
\(472\) −11.8016 −0.543215
\(473\) −1.53278 −0.0704775
\(474\) −18.8239 −0.864609
\(475\) 13.7828 0.632398
\(476\) 3.03476 0.139098
\(477\) −0.581199 −0.0266113
\(478\) 19.2937 0.882473
\(479\) 20.1566 0.920980 0.460490 0.887665i \(-0.347674\pi\)
0.460490 + 0.887665i \(0.347674\pi\)
\(480\) −94.1427 −4.29700
\(481\) 5.70011 0.259903
\(482\) −74.7960 −3.40686
\(483\) −52.0923 −2.37028
\(484\) −52.2898 −2.37681
\(485\) −42.7890 −1.94295
\(486\) −38.3435 −1.73930
\(487\) −24.3701 −1.10432 −0.552158 0.833739i \(-0.686196\pi\)
−0.552158 + 0.833739i \(0.686196\pi\)
\(488\) 76.3124 3.45450
\(489\) 63.1090 2.85389
\(490\) 55.6462 2.51384
\(491\) 18.2187 0.822199 0.411099 0.911591i \(-0.365145\pi\)
0.411099 + 0.911591i \(0.365145\pi\)
\(492\) 47.3973 2.13683
\(493\) −0.106136 −0.00478014
\(494\) −6.45809 −0.290563
\(495\) −6.10537 −0.274416
\(496\) 5.82828 0.261698
\(497\) −57.2526 −2.56813
\(498\) −89.3148 −4.00229
\(499\) 9.39938 0.420774 0.210387 0.977618i \(-0.432528\pi\)
0.210387 + 0.977618i \(0.432528\pi\)
\(500\) −8.96021 −0.400713
\(501\) 4.92909 0.220216
\(502\) 54.0258 2.41129
\(503\) 26.5267 1.18277 0.591384 0.806390i \(-0.298582\pi\)
0.591384 + 0.806390i \(0.298582\pi\)
\(504\) −133.940 −5.96616
\(505\) 30.8119 1.37111
\(506\) −4.97408 −0.221125
\(507\) −2.81902 −0.125197
\(508\) 78.3490 3.47617
\(509\) −17.1045 −0.758146 −0.379073 0.925367i \(-0.623757\pi\)
−0.379073 + 0.925367i \(0.623757\pi\)
\(510\) −4.09536 −0.181346
\(511\) 22.4850 0.994676
\(512\) 42.4534 1.87619
\(513\) −13.5755 −0.599375
\(514\) −68.1428 −3.00565
\(515\) 2.71983 0.119850
\(516\) 54.8317 2.41383
\(517\) 1.02235 0.0449629
\(518\) −54.7922 −2.40743
\(519\) −18.1966 −0.798741
\(520\) 23.9117 1.04860
\(521\) −35.6188 −1.56049 −0.780245 0.625474i \(-0.784906\pi\)
−0.780245 + 0.625474i \(0.784906\pi\)
\(522\) 8.01050 0.350610
\(523\) 9.15540 0.400338 0.200169 0.979761i \(-0.435851\pi\)
0.200169 + 0.979761i \(0.435851\pi\)
\(524\) −40.0770 −1.75077
\(525\) −57.8319 −2.52399
\(526\) 4.16426 0.181570
\(527\) 0.104250 0.00454121
\(528\) −10.2373 −0.445522
\(529\) 2.19141 0.0952785
\(530\) −0.997381 −0.0433235
\(531\) 7.93862 0.344507
\(532\) 43.8647 1.90178
\(533\) −3.49063 −0.151196
\(534\) 13.3298 0.576836
\(535\) 4.18097 0.180759
\(536\) 61.9493 2.67580
\(537\) −0.00710972 −0.000306807 0
\(538\) 19.9248 0.859020
\(539\) 2.48809 0.107169
\(540\) 85.9552 3.69892
\(541\) −14.9081 −0.640949 −0.320475 0.947257i \(-0.603842\pi\)
−0.320475 + 0.947257i \(0.603842\pi\)
\(542\) 29.7215 1.27665
\(543\) −13.8651 −0.595006
\(544\) −1.75765 −0.0753585
\(545\) 39.8467 1.70685
\(546\) 27.0978 1.15968
\(547\) −2.51931 −0.107718 −0.0538590 0.998549i \(-0.517152\pi\)
−0.0538590 + 0.998549i \(0.517152\pi\)
\(548\) 36.1666 1.54496
\(549\) −51.3331 −2.19084
\(550\) −5.52213 −0.235464
\(551\) −1.53411 −0.0653553
\(552\) 104.053 4.42879
\(553\) −9.41611 −0.400414
\(554\) 38.2668 1.62580
\(555\) 52.2472 2.21777
\(556\) 8.24140 0.349513
\(557\) 19.8919 0.842845 0.421422 0.906864i \(-0.361531\pi\)
0.421422 + 0.906864i \(0.361531\pi\)
\(558\) −7.86813 −0.333085
\(559\) −4.03815 −0.170795
\(560\) −114.530 −4.83976
\(561\) −0.183114 −0.00773109
\(562\) −50.5087 −2.13058
\(563\) −43.0671 −1.81506 −0.907531 0.419985i \(-0.862035\pi\)
−0.907531 + 0.419985i \(0.862035\pi\)
\(564\) −36.5721 −1.53996
\(565\) 11.0366 0.464314
\(566\) 32.5062 1.36634
\(567\) 2.32337 0.0975725
\(568\) 114.361 4.79847
\(569\) −30.1139 −1.26244 −0.631221 0.775603i \(-0.717446\pi\)
−0.631221 + 0.775603i \(0.717446\pi\)
\(570\) −59.1948 −2.47940
\(571\) −24.7281 −1.03484 −0.517419 0.855732i \(-0.673107\pi\)
−0.517419 + 0.855732i \(0.673107\pi\)
\(572\) 1.82831 0.0764454
\(573\) 24.3803 1.01850
\(574\) 33.5537 1.40050
\(575\) 27.9670 1.16631
\(576\) 37.9993 1.58330
\(577\) −4.78224 −0.199087 −0.0995437 0.995033i \(-0.531738\pi\)
−0.0995437 + 0.995033i \(0.531738\pi\)
\(578\) 44.3086 1.84299
\(579\) 15.0442 0.625217
\(580\) 9.71340 0.403327
\(581\) −44.6771 −1.85352
\(582\) 96.8583 4.01491
\(583\) −0.0445956 −0.00184696
\(584\) −44.9132 −1.85852
\(585\) −16.0847 −0.665021
\(586\) 50.4196 2.08281
\(587\) 23.1341 0.954845 0.477422 0.878674i \(-0.341571\pi\)
0.477422 + 0.878674i \(0.341571\pi\)
\(588\) −89.0053 −3.67052
\(589\) 1.50684 0.0620884
\(590\) 13.6233 0.560861
\(591\) 24.6936 1.01576
\(592\) 54.5346 2.24136
\(593\) 16.1018 0.661222 0.330611 0.943767i \(-0.392745\pi\)
0.330611 + 0.943767i \(0.392745\pi\)
\(594\) 5.43910 0.223169
\(595\) −2.04859 −0.0839838
\(596\) 62.2429 2.54957
\(597\) −3.45372 −0.141351
\(598\) −13.1043 −0.535874
\(599\) 3.15559 0.128934 0.0644669 0.997920i \(-0.479465\pi\)
0.0644669 + 0.997920i \(0.479465\pi\)
\(600\) 115.518 4.71599
\(601\) 22.8514 0.932130 0.466065 0.884751i \(-0.345671\pi\)
0.466065 + 0.884751i \(0.345671\pi\)
\(602\) 38.8166 1.58205
\(603\) −41.6715 −1.69700
\(604\) 4.78374 0.194648
\(605\) 35.2978 1.43506
\(606\) −69.7468 −2.83327
\(607\) −36.3461 −1.47524 −0.737621 0.675214i \(-0.764051\pi\)
−0.737621 + 0.675214i \(0.764051\pi\)
\(608\) −25.4053 −1.03032
\(609\) 6.43705 0.260842
\(610\) −88.0914 −3.56672
\(611\) 2.69340 0.108963
\(612\) 4.07763 0.164828
\(613\) 46.2547 1.86821 0.934104 0.357001i \(-0.116201\pi\)
0.934104 + 0.357001i \(0.116201\pi\)
\(614\) −79.9028 −3.22462
\(615\) −31.9951 −1.29017
\(616\) −10.2773 −0.414082
\(617\) 10.2995 0.414643 0.207322 0.978273i \(-0.433525\pi\)
0.207322 + 0.978273i \(0.433525\pi\)
\(618\) −6.15668 −0.247658
\(619\) −7.35776 −0.295733 −0.147867 0.989007i \(-0.547241\pi\)
−0.147867 + 0.989007i \(0.547241\pi\)
\(620\) −9.54077 −0.383167
\(621\) −27.5465 −1.10540
\(622\) −42.3044 −1.69625
\(623\) 6.66784 0.267141
\(624\) −26.9704 −1.07968
\(625\) −21.8121 −0.872483
\(626\) 78.3347 3.13089
\(627\) −2.64676 −0.105701
\(628\) −22.3907 −0.893485
\(629\) 0.975457 0.0388940
\(630\) 154.614 6.15997
\(631\) −0.774104 −0.0308166 −0.0154083 0.999881i \(-0.504905\pi\)
−0.0154083 + 0.999881i \(0.504905\pi\)
\(632\) 18.8084 0.748160
\(633\) −24.7607 −0.984151
\(634\) −39.8851 −1.58404
\(635\) −52.8888 −2.09883
\(636\) 1.59530 0.0632577
\(637\) 6.55491 0.259715
\(638\) 0.614647 0.0243341
\(639\) −76.9271 −3.04319
\(640\) −1.58143 −0.0625114
\(641\) −21.5952 −0.852959 −0.426480 0.904497i \(-0.640246\pi\)
−0.426480 + 0.904497i \(0.640246\pi\)
\(642\) −9.46417 −0.373521
\(643\) −29.1196 −1.14836 −0.574182 0.818728i \(-0.694680\pi\)
−0.574182 + 0.818728i \(0.694680\pi\)
\(644\) 89.0072 3.50738
\(645\) −37.0136 −1.45741
\(646\) −1.10517 −0.0434823
\(647\) 2.40262 0.0944569 0.0472284 0.998884i \(-0.484961\pi\)
0.0472284 + 0.998884i \(0.484961\pi\)
\(648\) −4.64088 −0.182311
\(649\) 0.609132 0.0239105
\(650\) −14.5482 −0.570625
\(651\) −6.32264 −0.247804
\(652\) −107.831 −4.22298
\(653\) −23.4039 −0.915866 −0.457933 0.888987i \(-0.651410\pi\)
−0.457933 + 0.888987i \(0.651410\pi\)
\(654\) −90.1982 −3.52703
\(655\) 27.0536 1.05707
\(656\) −33.3959 −1.30389
\(657\) 30.2118 1.17867
\(658\) −25.8903 −1.00931
\(659\) −31.0942 −1.21126 −0.605629 0.795747i \(-0.707078\pi\)
−0.605629 + 0.795747i \(0.707078\pi\)
\(660\) 16.7583 0.652315
\(661\) −39.7818 −1.54733 −0.773666 0.633594i \(-0.781579\pi\)
−0.773666 + 0.633594i \(0.781579\pi\)
\(662\) 69.7618 2.71137
\(663\) −0.482418 −0.0187356
\(664\) 89.2415 3.46324
\(665\) −29.6105 −1.14825
\(666\) −73.6213 −2.85277
\(667\) −3.11291 −0.120532
\(668\) −8.42207 −0.325860
\(669\) −16.6348 −0.643137
\(670\) −71.5114 −2.76273
\(671\) −3.93880 −0.152056
\(672\) 106.599 4.11215
\(673\) −23.4838 −0.905234 −0.452617 0.891705i \(-0.649509\pi\)
−0.452617 + 0.891705i \(0.649509\pi\)
\(674\) −38.5091 −1.48331
\(675\) −30.5816 −1.17709
\(676\) 4.81671 0.185258
\(677\) 16.0482 0.616782 0.308391 0.951260i \(-0.400209\pi\)
0.308391 + 0.951260i \(0.400209\pi\)
\(678\) −24.9828 −0.959459
\(679\) 48.4506 1.85936
\(680\) 4.09200 0.156921
\(681\) −81.0545 −3.10601
\(682\) −0.603723 −0.0231178
\(683\) 28.9030 1.10594 0.552972 0.833200i \(-0.313494\pi\)
0.552972 + 0.833200i \(0.313494\pi\)
\(684\) 58.9386 2.25357
\(685\) −24.4140 −0.932809
\(686\) 4.27842 0.163351
\(687\) −54.4886 −2.07887
\(688\) −38.6341 −1.47291
\(689\) −0.117488 −0.00447593
\(690\) −120.114 −4.57266
\(691\) 15.1346 0.575749 0.287875 0.957668i \(-0.407051\pi\)
0.287875 + 0.957668i \(0.407051\pi\)
\(692\) 31.0915 1.18192
\(693\) 6.91321 0.262611
\(694\) 63.7232 2.41890
\(695\) −5.56329 −0.211027
\(696\) −12.8578 −0.487375
\(697\) −0.597350 −0.0226262
\(698\) −26.3238 −0.996369
\(699\) 25.8688 0.978447
\(700\) 98.8142 3.73483
\(701\) 8.82552 0.333335 0.166668 0.986013i \(-0.446699\pi\)
0.166668 + 0.986013i \(0.446699\pi\)
\(702\) 14.3294 0.540828
\(703\) 14.0994 0.531768
\(704\) 2.91569 0.109889
\(705\) 24.6877 0.929792
\(706\) 44.9687 1.69242
\(707\) −34.8888 −1.31213
\(708\) −21.7902 −0.818927
\(709\) −21.2446 −0.797857 −0.398929 0.916982i \(-0.630618\pi\)
−0.398929 + 0.916982i \(0.630618\pi\)
\(710\) −132.013 −4.95434
\(711\) −12.6519 −0.474483
\(712\) −13.3189 −0.499145
\(713\) 3.05758 0.114507
\(714\) 4.63724 0.173544
\(715\) −1.23418 −0.0461559
\(716\) 0.0121480 0.000453992 0
\(717\) 20.8318 0.777978
\(718\) 78.5588 2.93179
\(719\) −8.06348 −0.300717 −0.150359 0.988632i \(-0.548043\pi\)
−0.150359 + 0.988632i \(0.548043\pi\)
\(720\) −153.887 −5.73503
\(721\) −3.07970 −0.114694
\(722\) 33.6325 1.25167
\(723\) −80.7588 −3.00345
\(724\) 23.6905 0.880449
\(725\) −3.45589 −0.128349
\(726\) −79.9011 −2.96541
\(727\) −34.2844 −1.27154 −0.635768 0.771880i \(-0.719317\pi\)
−0.635768 + 0.771880i \(0.719317\pi\)
\(728\) −27.0756 −1.00349
\(729\) −43.2934 −1.60346
\(730\) 51.8456 1.91889
\(731\) −0.691046 −0.0255593
\(732\) 140.901 5.20786
\(733\) −2.80435 −0.103581 −0.0517905 0.998658i \(-0.516493\pi\)
−0.0517905 + 0.998658i \(0.516493\pi\)
\(734\) 6.24749 0.230599
\(735\) 60.0823 2.21617
\(736\) −51.5505 −1.90018
\(737\) −3.19746 −0.117780
\(738\) 45.0842 1.65957
\(739\) −30.5337 −1.12320 −0.561600 0.827409i \(-0.689814\pi\)
−0.561600 + 0.827409i \(0.689814\pi\)
\(740\) −89.2720 −3.28170
\(741\) −6.97293 −0.256157
\(742\) 1.12935 0.0414597
\(743\) 24.0083 0.880778 0.440389 0.897807i \(-0.354841\pi\)
0.440389 + 0.897807i \(0.354841\pi\)
\(744\) 12.6293 0.463014
\(745\) −42.0165 −1.53937
\(746\) 4.79224 0.175457
\(747\) −60.0302 −2.19639
\(748\) 0.312877 0.0114399
\(749\) −4.73418 −0.172983
\(750\) −13.6916 −0.499946
\(751\) 10.1566 0.370620 0.185310 0.982680i \(-0.440671\pi\)
0.185310 + 0.982680i \(0.440671\pi\)
\(752\) 25.7685 0.939682
\(753\) 58.3327 2.12576
\(754\) 1.61930 0.0589714
\(755\) −3.22923 −0.117524
\(756\) −97.3283 −3.53980
\(757\) −43.9592 −1.59773 −0.798863 0.601513i \(-0.794565\pi\)
−0.798863 + 0.601513i \(0.794565\pi\)
\(758\) −39.9558 −1.45126
\(759\) −5.37061 −0.194941
\(760\) 59.1463 2.14546
\(761\) −18.6461 −0.675922 −0.337961 0.941160i \(-0.609737\pi\)
−0.337961 + 0.941160i \(0.609737\pi\)
\(762\) 119.721 4.33702
\(763\) −45.1191 −1.63342
\(764\) −41.6574 −1.50711
\(765\) −2.75257 −0.0995193
\(766\) −68.7856 −2.48533
\(767\) 1.60477 0.0579449
\(768\) 46.8881 1.69193
\(769\) −12.3991 −0.447123 −0.223562 0.974690i \(-0.571768\pi\)
−0.223562 + 0.974690i \(0.571768\pi\)
\(770\) 11.8636 0.427534
\(771\) −73.5751 −2.64974
\(772\) −25.7053 −0.925153
\(773\) 23.1628 0.833110 0.416555 0.909111i \(-0.363237\pi\)
0.416555 + 0.909111i \(0.363237\pi\)
\(774\) 52.1557 1.87470
\(775\) 3.39447 0.121933
\(776\) −96.7789 −3.47416
\(777\) −59.1603 −2.12236
\(778\) −30.6583 −1.09915
\(779\) −8.63417 −0.309351
\(780\) 44.1500 1.58082
\(781\) −5.90263 −0.211213
\(782\) −2.24253 −0.0801927
\(783\) 3.40393 0.121646
\(784\) 62.7127 2.23974
\(785\) 15.1146 0.539464
\(786\) −61.2394 −2.18434
\(787\) 13.0822 0.466329 0.233165 0.972437i \(-0.425092\pi\)
0.233165 + 0.972437i \(0.425092\pi\)
\(788\) −42.1925 −1.50305
\(789\) 4.49624 0.160070
\(790\) −21.7116 −0.772463
\(791\) −12.4969 −0.444340
\(792\) −13.8090 −0.490680
\(793\) −10.3768 −0.368492
\(794\) 44.2231 1.56942
\(795\) −1.07689 −0.0381934
\(796\) 5.90119 0.209162
\(797\) −30.1599 −1.06832 −0.534160 0.845384i \(-0.679372\pi\)
−0.534160 + 0.845384i \(0.679372\pi\)
\(798\) 67.0272 2.37274
\(799\) 0.460920 0.0163062
\(800\) −57.2305 −2.02340
\(801\) 8.95920 0.316558
\(802\) 12.8701 0.454460
\(803\) 2.31816 0.0818059
\(804\) 114.382 4.03393
\(805\) −60.0835 −2.11767
\(806\) −1.59052 −0.0560237
\(807\) 21.5132 0.757302
\(808\) 69.6896 2.45167
\(809\) 48.3152 1.69867 0.849337 0.527851i \(-0.177002\pi\)
0.849337 + 0.527851i \(0.177002\pi\)
\(810\) 5.35721 0.188233
\(811\) −42.7157 −1.49995 −0.749976 0.661465i \(-0.769935\pi\)
−0.749976 + 0.661465i \(0.769935\pi\)
\(812\) −10.9986 −0.385976
\(813\) 32.0910 1.12548
\(814\) −5.64898 −0.197996
\(815\) 72.7903 2.54973
\(816\) −4.61543 −0.161572
\(817\) −9.98847 −0.349452
\(818\) −38.2974 −1.33904
\(819\) 18.2130 0.636413
\(820\) 54.6683 1.90910
\(821\) 38.7440 1.35218 0.676088 0.736821i \(-0.263674\pi\)
0.676088 + 0.736821i \(0.263674\pi\)
\(822\) 55.2641 1.92756
\(823\) −27.2814 −0.950970 −0.475485 0.879724i \(-0.657727\pi\)
−0.475485 + 0.879724i \(0.657727\pi\)
\(824\) 6.15163 0.214302
\(825\) −5.96236 −0.207583
\(826\) −15.4258 −0.536733
\(827\) 19.6805 0.684357 0.342179 0.939635i \(-0.388835\pi\)
0.342179 + 0.939635i \(0.388835\pi\)
\(828\) 119.594 4.15618
\(829\) 39.9718 1.38828 0.694140 0.719840i \(-0.255785\pi\)
0.694140 + 0.719840i \(0.255785\pi\)
\(830\) −103.016 −3.57575
\(831\) 41.3175 1.43329
\(832\) 7.68144 0.266306
\(833\) 1.12174 0.0388659
\(834\) 12.5932 0.436067
\(835\) 5.68525 0.196746
\(836\) 4.52237 0.156409
\(837\) −3.34343 −0.115566
\(838\) −23.0166 −0.795094
\(839\) −10.5143 −0.362995 −0.181497 0.983391i \(-0.558094\pi\)
−0.181497 + 0.983391i \(0.558094\pi\)
\(840\) −248.175 −8.56285
\(841\) −28.6153 −0.986736
\(842\) 56.7373 1.95530
\(843\) −54.5352 −1.87829
\(844\) 42.3073 1.45628
\(845\) −3.25148 −0.111854
\(846\) −34.7873 −1.19601
\(847\) −39.9682 −1.37332
\(848\) −1.12404 −0.0385997
\(849\) 35.0976 1.20455
\(850\) −2.48962 −0.0853932
\(851\) 28.6095 0.980719
\(852\) 211.152 7.23396
\(853\) 20.3293 0.696061 0.348030 0.937483i \(-0.386851\pi\)
0.348030 + 0.937483i \(0.386851\pi\)
\(854\) 99.7473 3.41328
\(855\) −39.7860 −1.36065
\(856\) 9.45641 0.323213
\(857\) 9.44347 0.322583 0.161291 0.986907i \(-0.448434\pi\)
0.161291 + 0.986907i \(0.448434\pi\)
\(858\) 2.79373 0.0953765
\(859\) 1.29149 0.0440651 0.0220325 0.999757i \(-0.492986\pi\)
0.0220325 + 0.999757i \(0.492986\pi\)
\(860\) 63.2432 2.15658
\(861\) 36.2286 1.23467
\(862\) −39.1084 −1.33204
\(863\) 0.297237 0.0101181 0.00505904 0.999987i \(-0.498390\pi\)
0.00505904 + 0.999987i \(0.498390\pi\)
\(864\) 56.3699 1.91774
\(865\) −20.9880 −0.713615
\(866\) −90.1846 −3.06460
\(867\) 47.8408 1.62476
\(868\) 10.8032 0.366683
\(869\) −0.970782 −0.0329315
\(870\) 14.8425 0.503208
\(871\) −8.42378 −0.285429
\(872\) 90.1242 3.05199
\(873\) 65.1003 2.20331
\(874\) −32.4138 −1.09641
\(875\) −6.84882 −0.231532
\(876\) −82.9264 −2.80183
\(877\) 7.74947 0.261681 0.130841 0.991403i \(-0.458232\pi\)
0.130841 + 0.991403i \(0.458232\pi\)
\(878\) 6.82202 0.230232
\(879\) 54.4391 1.83618
\(880\) −11.8078 −0.398041
\(881\) 20.2727 0.683004 0.341502 0.939881i \(-0.389064\pi\)
0.341502 + 0.939881i \(0.389064\pi\)
\(882\) −84.6616 −2.85070
\(883\) 12.5895 0.423671 0.211836 0.977305i \(-0.432056\pi\)
0.211836 + 0.977305i \(0.432056\pi\)
\(884\) 0.824281 0.0277236
\(885\) 14.7093 0.494448
\(886\) 68.7350 2.30920
\(887\) −57.7191 −1.93802 −0.969009 0.247027i \(-0.920546\pi\)
−0.969009 + 0.247027i \(0.920546\pi\)
\(888\) 118.171 3.96557
\(889\) 59.8868 2.00854
\(890\) 15.3747 0.515360
\(891\) 0.239535 0.00802473
\(892\) 28.4229 0.951670
\(893\) 6.66220 0.222942
\(894\) 95.1098 3.18095
\(895\) −0.00820040 −0.000274109 0
\(896\) 1.79068 0.0598223
\(897\) −14.1490 −0.472420
\(898\) 52.1112 1.73897
\(899\) −0.377826 −0.0126012
\(900\) 132.771 4.42570
\(901\) −0.0201056 −0.000669815 0
\(902\) 3.45932 0.115183
\(903\) 41.9111 1.39471
\(904\) 24.9623 0.830234
\(905\) −15.9920 −0.531594
\(906\) 7.30976 0.242851
\(907\) 21.5448 0.715382 0.357691 0.933840i \(-0.383564\pi\)
0.357691 + 0.933840i \(0.383564\pi\)
\(908\) 138.493 4.59606
\(909\) −46.8782 −1.55485
\(910\) 31.2548 1.03609
\(911\) 50.6324 1.67753 0.838764 0.544495i \(-0.183279\pi\)
0.838764 + 0.544495i \(0.183279\pi\)
\(912\) −66.7120 −2.20906
\(913\) −4.60613 −0.152441
\(914\) 60.2641 1.99336
\(915\) −95.1141 −3.14437
\(916\) 93.1016 3.07616
\(917\) −30.6332 −1.01160
\(918\) 2.45218 0.0809340
\(919\) −46.1772 −1.52325 −0.761623 0.648020i \(-0.775597\pi\)
−0.761623 + 0.648020i \(0.775597\pi\)
\(920\) 120.015 3.95679
\(921\) −86.2727 −2.84278
\(922\) 28.4230 0.936060
\(923\) −15.5506 −0.511854
\(924\) −18.9756 −0.624253
\(925\) 31.7617 1.04432
\(926\) −2.61088 −0.0857989
\(927\) −4.13802 −0.135910
\(928\) 6.37010 0.209109
\(929\) 53.3269 1.74960 0.874800 0.484484i \(-0.160993\pi\)
0.874800 + 0.484484i \(0.160993\pi\)
\(930\) −14.5787 −0.478054
\(931\) 16.2137 0.531384
\(932\) −44.2006 −1.44784
\(933\) −45.6769 −1.49540
\(934\) −102.820 −3.36438
\(935\) −0.211205 −0.00690715
\(936\) −36.3800 −1.18912
\(937\) −5.73763 −0.187440 −0.0937201 0.995599i \(-0.529876\pi\)
−0.0937201 + 0.995599i \(0.529876\pi\)
\(938\) 80.9735 2.64388
\(939\) 84.5796 2.76015
\(940\) −42.1825 −1.37584
\(941\) −16.2390 −0.529376 −0.264688 0.964334i \(-0.585269\pi\)
−0.264688 + 0.964334i \(0.585269\pi\)
\(942\) −34.2139 −1.11475
\(943\) −17.5198 −0.570525
\(944\) 15.3533 0.499707
\(945\) 65.7007 2.13724
\(946\) 4.00192 0.130114
\(947\) −46.2988 −1.50451 −0.752254 0.658873i \(-0.771034\pi\)
−0.752254 + 0.658873i \(0.771034\pi\)
\(948\) 34.7274 1.12789
\(949\) 6.10722 0.198249
\(950\) −35.9853 −1.16752
\(951\) −43.0647 −1.39647
\(952\) −4.63343 −0.150170
\(953\) −45.1077 −1.46118 −0.730590 0.682816i \(-0.760755\pi\)
−0.730590 + 0.682816i \(0.760755\pi\)
\(954\) 1.51744 0.0491290
\(955\) 28.1204 0.909956
\(956\) −35.5942 −1.15120
\(957\) 0.663647 0.0214527
\(958\) −52.6266 −1.70029
\(959\) 27.6443 0.892681
\(960\) 70.4081 2.27241
\(961\) −30.6289 −0.988029
\(962\) −14.8823 −0.479825
\(963\) −6.36105 −0.204982
\(964\) 137.988 4.44430
\(965\) 17.3521 0.558585
\(966\) 136.007 4.37595
\(967\) 20.8649 0.670970 0.335485 0.942045i \(-0.391100\pi\)
0.335485 + 0.942045i \(0.391100\pi\)
\(968\) 79.8356 2.56601
\(969\) −1.19327 −0.0383335
\(970\) 111.717 3.58702
\(971\) −42.5483 −1.36544 −0.682720 0.730680i \(-0.739203\pi\)
−0.682720 + 0.730680i \(0.739203\pi\)
\(972\) 70.7383 2.26893
\(973\) 6.29939 0.201949
\(974\) 63.6276 2.03876
\(975\) −15.7079 −0.503056
\(976\) −99.2782 −3.17782
\(977\) −60.4983 −1.93551 −0.967755 0.251892i \(-0.918947\pi\)
−0.967755 + 0.251892i \(0.918947\pi\)
\(978\) −164.770 −5.26877
\(979\) 0.687442 0.0219707
\(980\) −102.659 −3.27933
\(981\) −60.6239 −1.93557
\(982\) −47.5669 −1.51792
\(983\) 21.9233 0.699244 0.349622 0.936891i \(-0.386310\pi\)
0.349622 + 0.936891i \(0.386310\pi\)
\(984\) −72.3657 −2.30693
\(985\) 28.4817 0.907503
\(986\) 0.277110 0.00882498
\(987\) −27.9542 −0.889794
\(988\) 11.9143 0.379043
\(989\) −20.2679 −0.644481
\(990\) 15.9404 0.506620
\(991\) 56.0460 1.78036 0.890180 0.455608i \(-0.150578\pi\)
0.890180 + 0.455608i \(0.150578\pi\)
\(992\) −6.25689 −0.198656
\(993\) 75.3232 2.39031
\(994\) 149.480 4.74121
\(995\) −3.98354 −0.126287
\(996\) 164.773 5.22104
\(997\) 33.4915 1.06069 0.530344 0.847783i \(-0.322063\pi\)
0.530344 + 0.847783i \(0.322063\pi\)
\(998\) −24.5407 −0.776822
\(999\) −31.2841 −0.989785
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 6019.2.a.b.1.4 101
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6019.2.a.b.1.4 101 1.1 even 1 trivial