Properties

Label 1.124.a.a.1.6
Level $1$
Weight $124$
Character 1.1
Self dual yes
Analytic conductor $95.808$
Analytic rank $0$
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] = [1,124,Mod(1,1)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1, base_ring=CyclotomicField(1))
 
chi = DirichletCharacter(H, H._module([]))
 
N = Newforms(chi, 124, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1.1");
 
S:= CuspForms(chi, 124);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 124 \)
Character orbit: \([\chi]\) \(=\) 1.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: \(95.8076224914\)
Analytic rank: \(0\)
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: \( x^{10} - 5 x^{9} + \cdots - 30\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{178}\cdot 3^{70}\cdot 5^{22}\cdot 7^{9}\cdot 11^{6}\cdot 13^{2}\cdot 17\cdot 31^{2}\cdot 41^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-2.24732e16\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.83831e18 q^{2} +1.91755e29 q^{3} -7.25444e36 q^{4} -8.31906e42 q^{5} +3.52506e47 q^{6} -1.53178e52 q^{7} -3.28842e55 q^{8} -1.17492e58 q^{9} +O(q^{10})\) \(q+1.83831e18 q^{2} +1.91755e29 q^{3} -7.25444e36 q^{4} -8.31906e42 q^{5} +3.52506e47 q^{6} -1.53178e52 q^{7} -3.28842e55 q^{8} -1.17492e58 q^{9} -1.52930e61 q^{10} -3.64877e63 q^{11} -1.39108e66 q^{12} -3.93413e68 q^{13} -2.81589e70 q^{14} -1.59522e72 q^{15} +1.66911e73 q^{16} +6.26916e75 q^{17} -2.15987e76 q^{18} -7.77701e78 q^{19} +6.03501e79 q^{20} -2.93727e81 q^{21} -6.70757e81 q^{22} +4.70089e83 q^{23} -6.30571e84 q^{24} -2.48327e85 q^{25} -7.23216e86 q^{26} -1.15568e88 q^{27} +1.11122e89 q^{28} +6.71958e89 q^{29} -2.93252e90 q^{30} +2.07270e91 q^{31} +3.80368e92 q^{32} -6.99671e92 q^{33} +1.15247e94 q^{34} +1.27430e95 q^{35} +8.52340e94 q^{36} +8.83217e95 q^{37} -1.42966e97 q^{38} -7.54391e97 q^{39} +2.73566e98 q^{40} -6.43781e97 q^{41} -5.39961e99 q^{42} +3.49211e100 q^{43} +2.64698e100 q^{44} +9.77424e100 q^{45} +8.64169e101 q^{46} -8.32956e102 q^{47} +3.20061e102 q^{48} +1.46111e104 q^{49} -4.56503e103 q^{50} +1.20214e105 q^{51} +2.85399e105 q^{52} -4.35998e105 q^{53} -2.12450e106 q^{54} +3.03543e106 q^{55} +5.03713e107 q^{56} -1.49128e108 q^{57} +1.23527e108 q^{58} -8.62805e108 q^{59} +1.15725e109 q^{60} -7.55451e109 q^{61} +3.81026e109 q^{62} +1.79972e110 q^{63} +5.21744e110 q^{64} +3.27283e111 q^{65} -1.28621e111 q^{66} -1.06990e112 q^{67} -4.54793e112 q^{68} +9.01420e112 q^{69} +2.34255e113 q^{70} -9.58273e113 q^{71} +3.86363e113 q^{72} -1.40162e114 q^{73} +1.62363e114 q^{74} -4.76181e114 q^{75} +5.64179e115 q^{76} +5.58911e115 q^{77} -1.38680e116 q^{78} -1.66329e116 q^{79} -1.38854e116 q^{80} -1.64601e117 q^{81} -1.18347e116 q^{82} +6.67836e117 q^{83} +2.13082e118 q^{84} -5.21536e118 q^{85} +6.41959e118 q^{86} +1.28852e119 q^{87} +1.19987e119 q^{88} -1.04169e120 q^{89} +1.79681e119 q^{90} +6.02623e120 q^{91} -3.41023e120 q^{92} +3.97450e120 q^{93} -1.53123e121 q^{94} +6.46975e121 q^{95} +7.29376e121 q^{96} +1.90065e122 q^{97} +2.68598e122 q^{98} +4.28702e121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 11\!\cdots\!70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 22\!\cdots\!00 q^{2}+ \cdots + 42\!\cdots\!40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.83831e18 0.563734 0.281867 0.959454i \(-0.409046\pi\)
0.281867 + 0.959454i \(0.409046\pi\)
\(3\) 1.91755e29 0.870543 0.435271 0.900299i \(-0.356652\pi\)
0.435271 + 0.900299i \(0.356652\pi\)
\(4\) −7.25444e36 −0.682204
\(5\) −8.31906e42 −0.857865 −0.428933 0.903336i \(-0.641110\pi\)
−0.428933 + 0.903336i \(0.641110\pi\)
\(6\) 3.52506e47 0.490754
\(7\) −1.53178e52 −1.62805 −0.814023 0.580832i \(-0.802727\pi\)
−0.814023 + 0.580832i \(0.802727\pi\)
\(8\) −3.28842e55 −0.948315
\(9\) −1.17492e58 −0.242156
\(10\) −1.52930e61 −0.483608
\(11\) −3.64877e63 −0.328470 −0.164235 0.986421i \(-0.552516\pi\)
−0.164235 + 0.986421i \(0.552516\pi\)
\(12\) −1.39108e66 −0.593888
\(13\) −3.93413e68 −1.22274 −0.611368 0.791346i \(-0.709381\pi\)
−0.611368 + 0.791346i \(0.709381\pi\)
\(14\) −2.81589e70 −0.917785
\(15\) −1.59522e72 −0.746808
\(16\) 1.66911e73 0.147607
\(17\) 6.26916e75 1.33230 0.666148 0.745819i \(-0.267942\pi\)
0.666148 + 0.745819i \(0.267942\pi\)
\(18\) −2.15987e76 −0.136511
\(19\) −7.77701e78 −1.76794 −0.883968 0.467548i \(-0.845138\pi\)
−0.883968 + 0.467548i \(0.845138\pi\)
\(20\) 6.03501e79 0.585239
\(21\) −2.93727e81 −1.41728
\(22\) −6.70757e81 −0.185170
\(23\) 4.70089e83 0.843176 0.421588 0.906788i \(-0.361473\pi\)
0.421588 + 0.906788i \(0.361473\pi\)
\(24\) −6.30571e84 −0.825549
\(25\) −2.48327e85 −0.264067
\(26\) −7.23216e86 −0.689298
\(27\) −1.15568e88 −1.08135
\(28\) 1.11122e89 1.11066
\(29\) 6.71958e89 0.776007 0.388003 0.921658i \(-0.373165\pi\)
0.388003 + 0.921658i \(0.373165\pi\)
\(30\) −2.93252e90 −0.421001
\(31\) 2.07270e91 0.396088 0.198044 0.980193i \(-0.436541\pi\)
0.198044 + 0.980193i \(0.436541\pi\)
\(32\) 3.80368e92 1.03153
\(33\) −6.99671e92 −0.285948
\(34\) 1.15247e94 0.751061
\(35\) 1.27430e95 1.39664
\(36\) 8.52340e94 0.165200
\(37\) 8.83217e95 0.317440 0.158720 0.987324i \(-0.449263\pi\)
0.158720 + 0.987324i \(0.449263\pi\)
\(38\) −1.42966e97 −0.996645
\(39\) −7.54391e97 −1.06444
\(40\) 2.73566e98 0.813527
\(41\) −6.43781e97 −0.0419306 −0.0209653 0.999780i \(-0.506674\pi\)
−0.0209653 + 0.999780i \(0.506674\pi\)
\(42\) −5.39961e99 −0.798971
\(43\) 3.49211e100 1.21557 0.607783 0.794103i \(-0.292059\pi\)
0.607783 + 0.794103i \(0.292059\pi\)
\(44\) 2.64698e100 0.224084
\(45\) 9.77424e100 0.207737
\(46\) 8.64169e101 0.475327
\(47\) −8.32956e102 −1.22068 −0.610342 0.792138i \(-0.708968\pi\)
−0.610342 + 0.792138i \(0.708968\pi\)
\(48\) 3.20061e102 0.128498
\(49\) 1.46111e104 1.65054
\(50\) −4.56503e103 −0.148863
\(51\) 1.20214e105 1.15982
\(52\) 2.85399e105 0.834156
\(53\) −4.35998e105 −0.394928 −0.197464 0.980310i \(-0.563271\pi\)
−0.197464 + 0.980310i \(0.563271\pi\)
\(54\) −2.12450e106 −0.609593
\(55\) 3.03543e106 0.281783
\(56\) 5.03713e107 1.54390
\(57\) −1.49128e108 −1.53906
\(58\) 1.23527e108 0.437461
\(59\) −8.62805e108 −1.06786 −0.533930 0.845529i \(-0.679285\pi\)
−0.533930 + 0.845529i \(0.679285\pi\)
\(60\) 1.15725e109 0.509476
\(61\) −7.55451e109 −1.20343 −0.601716 0.798710i \(-0.705516\pi\)
−0.601716 + 0.798710i \(0.705516\pi\)
\(62\) 3.81026e109 0.223288
\(63\) 1.79972e110 0.394241
\(64\) 5.21744e110 0.433899
\(65\) 3.27283e111 1.04894
\(66\) −1.28621e111 −0.161198
\(67\) −1.06990e112 −0.531793 −0.265896 0.964002i \(-0.585668\pi\)
−0.265896 + 0.964002i \(0.585668\pi\)
\(68\) −4.54793e112 −0.908898
\(69\) 9.01420e112 0.734021
\(70\) 2.34255e113 0.787336
\(71\) −9.58273e113 −1.34617 −0.673087 0.739564i \(-0.735032\pi\)
−0.673087 + 0.739564i \(0.735032\pi\)
\(72\) 3.86363e113 0.229640
\(73\) −1.40162e114 −0.356675 −0.178338 0.983969i \(-0.557072\pi\)
−0.178338 + 0.983969i \(0.557072\pi\)
\(74\) 1.62363e114 0.178952
\(75\) −4.76181e114 −0.229881
\(76\) 5.64179e115 1.20609
\(77\) 5.58911e115 0.534765
\(78\) −1.38680e116 −0.600063
\(79\) −1.66329e116 −0.328777 −0.164389 0.986396i \(-0.552565\pi\)
−0.164389 + 0.986396i \(0.552565\pi\)
\(80\) −1.38854e116 −0.126627
\(81\) −1.64601e117 −0.699205
\(82\) −1.18347e116 −0.0236377
\(83\) 6.67836e117 0.632946 0.316473 0.948601i \(-0.397501\pi\)
0.316473 + 0.948601i \(0.397501\pi\)
\(84\) 2.13082e118 0.966877
\(85\) −5.21536e118 −1.14293
\(86\) 6.41959e118 0.685255
\(87\) 1.28852e119 0.675547
\(88\) 1.19987e119 0.311494
\(89\) −1.04169e120 −1.34974 −0.674872 0.737934i \(-0.735801\pi\)
−0.674872 + 0.737934i \(0.735801\pi\)
\(90\) 1.79681e119 0.117108
\(91\) 6.02623e120 1.99067
\(92\) −3.41023e120 −0.575218
\(93\) 3.97450e120 0.344811
\(94\) −1.53123e121 −0.688141
\(95\) 6.46975e121 1.51665
\(96\) 7.29376e121 0.897988
\(97\) 1.90065e122 1.23720 0.618602 0.785704i \(-0.287699\pi\)
0.618602 + 0.785704i \(0.287699\pi\)
\(98\) 2.68598e122 0.930463
\(99\) 4.28702e121 0.0795410
\(100\) 1.80148e122 0.180148
\(101\) 7.23189e122 0.392182 0.196091 0.980586i \(-0.437175\pi\)
0.196091 + 0.980586i \(0.437175\pi\)
\(102\) 2.20992e123 0.653830
\(103\) 1.07903e124 1.75204 0.876021 0.482274i \(-0.160189\pi\)
0.876021 + 0.482274i \(0.160189\pi\)
\(104\) 1.29371e124 1.15954
\(105\) 2.44353e124 1.21584
\(106\) −8.01499e123 −0.222634
\(107\) 6.45004e124 1.00568 0.502840 0.864379i \(-0.332288\pi\)
0.502840 + 0.864379i \(0.332288\pi\)
\(108\) 8.38381e124 0.737701
\(109\) −1.22678e125 −0.612400 −0.306200 0.951967i \(-0.599058\pi\)
−0.306200 + 0.951967i \(0.599058\pi\)
\(110\) 5.58007e124 0.158851
\(111\) 1.69361e125 0.276345
\(112\) −2.55671e125 −0.240311
\(113\) 4.82188e125 0.262357 0.131178 0.991359i \(-0.458124\pi\)
0.131178 + 0.991359i \(0.458124\pi\)
\(114\) −2.74144e126 −0.867622
\(115\) −3.91070e126 −0.723332
\(116\) −4.87468e126 −0.529395
\(117\) 4.62230e126 0.296093
\(118\) −1.58610e127 −0.601988
\(119\) −9.60298e127 −2.16904
\(120\) 5.24576e127 0.708210
\(121\) −1.10082e128 −0.892107
\(122\) −1.38875e128 −0.678415
\(123\) −1.23448e127 −0.0365024
\(124\) −1.50362e128 −0.270213
\(125\) 9.88906e128 1.08440
\(126\) 3.30844e128 0.222247
\(127\) 4.11989e129 1.70199 0.850995 0.525173i \(-0.175999\pi\)
0.850995 + 0.525173i \(0.175999\pi\)
\(128\) −3.08564e129 −0.786923
\(129\) 6.69631e129 1.05820
\(130\) 6.01648e129 0.591325
\(131\) −2.42268e130 −1.48631 −0.743157 0.669117i \(-0.766672\pi\)
−0.743157 + 0.669117i \(0.766672\pi\)
\(132\) 5.07572e129 0.195075
\(133\) 1.19127e131 2.87828
\(134\) −1.96681e130 −0.299790
\(135\) 9.61417e130 0.927652
\(136\) −2.06156e131 −1.26344
\(137\) −3.96219e131 −1.54746 −0.773732 0.633514i \(-0.781612\pi\)
−0.773732 + 0.633514i \(0.781612\pi\)
\(138\) 1.65709e131 0.413792
\(139\) 1.50811e131 0.241558 0.120779 0.992679i \(-0.461461\pi\)
0.120779 + 0.992679i \(0.461461\pi\)
\(140\) −9.24431e131 −0.952797
\(141\) −1.59724e132 −1.06266
\(142\) −1.76160e132 −0.758883
\(143\) 1.43548e132 0.401633
\(144\) −1.96107e131 −0.0357438
\(145\) −5.59006e132 −0.665709
\(146\) −2.57661e132 −0.201070
\(147\) 2.80176e133 1.43686
\(148\) −6.40724e132 −0.216559
\(149\) 5.69247e133 1.27158 0.635792 0.771860i \(-0.280673\pi\)
0.635792 + 0.771860i \(0.280673\pi\)
\(150\) −8.75368e132 −0.129592
\(151\) −5.66160e133 −0.557002 −0.278501 0.960436i \(-0.589838\pi\)
−0.278501 + 0.960436i \(0.589838\pi\)
\(152\) 2.55741e134 1.67656
\(153\) −7.36577e133 −0.322623
\(154\) 1.02745e134 0.301465
\(155\) −1.72429e134 −0.339790
\(156\) 5.47268e134 0.726169
\(157\) 2.23778e134 0.200442 0.100221 0.994965i \(-0.468045\pi\)
0.100221 + 0.994965i \(0.468045\pi\)
\(158\) −3.05764e134 −0.185343
\(159\) −8.36048e134 −0.343802
\(160\) −3.16431e135 −0.884911
\(161\) −7.20073e135 −1.37273
\(162\) −3.02588e135 −0.394166
\(163\) −5.59907e135 −0.499549 −0.249775 0.968304i \(-0.580357\pi\)
−0.249775 + 0.968304i \(0.580357\pi\)
\(164\) 4.67027e134 0.0286052
\(165\) 5.82060e135 0.245305
\(166\) 1.22769e136 0.356813
\(167\) −7.56334e135 −0.151933 −0.0759663 0.997110i \(-0.524204\pi\)
−0.0759663 + 0.997110i \(0.524204\pi\)
\(168\) 9.65896e136 1.34403
\(169\) 5.12522e136 0.495086
\(170\) −9.58744e136 −0.644309
\(171\) 9.13738e136 0.428115
\(172\) −2.53333e137 −0.829264
\(173\) 7.60124e137 1.74200 0.871002 0.491279i \(-0.163470\pi\)
0.871002 + 0.491279i \(0.163470\pi\)
\(174\) 2.36869e137 0.380829
\(175\) 3.80383e137 0.429913
\(176\) −6.09020e136 −0.0484845
\(177\) −1.65447e138 −0.929617
\(178\) −1.91494e138 −0.760897
\(179\) 2.84392e137 0.0800674 0.0400337 0.999198i \(-0.487253\pi\)
0.0400337 + 0.999198i \(0.487253\pi\)
\(180\) −7.09067e137 −0.141719
\(181\) −7.36733e138 −1.04732 −0.523658 0.851929i \(-0.675433\pi\)
−0.523658 + 0.851929i \(0.675433\pi\)
\(182\) 1.10781e139 1.12221
\(183\) −1.44862e139 −1.04764
\(184\) −1.54585e139 −0.799597
\(185\) −7.34754e138 −0.272321
\(186\) 7.30637e138 0.194382
\(187\) −2.28747e139 −0.437620
\(188\) 6.04263e139 0.832756
\(189\) 1.77025e140 1.76049
\(190\) 1.18934e140 0.854987
\(191\) −1.02618e140 −0.534160 −0.267080 0.963674i \(-0.586059\pi\)
−0.267080 + 0.963674i \(0.586059\pi\)
\(192\) 1.00047e140 0.377728
\(193\) −1.92038e140 −0.526761 −0.263381 0.964692i \(-0.584837\pi\)
−0.263381 + 0.964692i \(0.584837\pi\)
\(194\) 3.49399e140 0.697454
\(195\) 6.27583e140 0.913150
\(196\) −1.05996e141 −1.12600
\(197\) −1.93333e141 −1.50188 −0.750938 0.660373i \(-0.770398\pi\)
−0.750938 + 0.660373i \(0.770398\pi\)
\(198\) 7.88087e139 0.0448399
\(199\) 1.15580e141 0.482411 0.241205 0.970474i \(-0.422457\pi\)
0.241205 + 0.970474i \(0.422457\pi\)
\(200\) 8.16604e140 0.250419
\(201\) −2.05159e141 −0.462948
\(202\) 1.32945e141 0.221086
\(203\) −1.02929e142 −1.26338
\(204\) −8.72089e141 −0.791235
\(205\) 5.35565e140 0.0359708
\(206\) 1.98359e142 0.987685
\(207\) −5.52318e141 −0.204180
\(208\) −6.56651e141 −0.180484
\(209\) 2.83765e142 0.580715
\(210\) 4.49197e142 0.685410
\(211\) 1.57848e143 1.79832 0.899160 0.437620i \(-0.144179\pi\)
0.899160 + 0.437620i \(0.144179\pi\)
\(212\) 3.16292e142 0.269422
\(213\) −1.83754e143 −1.17190
\(214\) 1.18572e143 0.566936
\(215\) −2.90511e143 −1.04279
\(216\) 3.80036e143 1.02546
\(217\) −3.17491e143 −0.644849
\(218\) −2.25519e143 −0.345231
\(219\) −2.68767e143 −0.310501
\(220\) −2.20204e143 −0.192234
\(221\) −2.46637e144 −1.62905
\(222\) 3.11339e143 0.155785
\(223\) 3.64941e144 1.38507 0.692537 0.721382i \(-0.256493\pi\)
0.692537 + 0.721382i \(0.256493\pi\)
\(224\) −5.82640e144 −1.67937
\(225\) 2.91765e143 0.0639453
\(226\) 8.86412e143 0.147899
\(227\) 1.15604e145 1.47022 0.735110 0.677948i \(-0.237131\pi\)
0.735110 + 0.677948i \(0.237131\pi\)
\(228\) 1.08184e145 1.04996
\(229\) −4.59197e144 −0.340500 −0.170250 0.985401i \(-0.554457\pi\)
−0.170250 + 0.985401i \(0.554457\pi\)
\(230\) −7.18908e144 −0.407766
\(231\) 1.07174e145 0.465536
\(232\) −2.20968e145 −0.735899
\(233\) 1.33984e145 0.342502 0.171251 0.985227i \(-0.445219\pi\)
0.171251 + 0.985227i \(0.445219\pi\)
\(234\) 8.49722e144 0.166917
\(235\) 6.92941e145 1.04718
\(236\) 6.25917e145 0.728498
\(237\) −3.18944e145 −0.286214
\(238\) −1.76533e146 −1.22276
\(239\) −1.38760e146 −0.742668 −0.371334 0.928499i \(-0.621100\pi\)
−0.371334 + 0.928499i \(0.621100\pi\)
\(240\) −2.66261e145 −0.110234
\(241\) −3.78427e146 −1.21320 −0.606602 0.795006i \(-0.707468\pi\)
−0.606602 + 0.795006i \(0.707468\pi\)
\(242\) −2.02365e146 −0.502911
\(243\) 2.45096e146 0.472661
\(244\) 5.48037e146 0.820986
\(245\) −1.21551e147 −1.41594
\(246\) −2.26936e145 −0.0205776
\(247\) 3.05958e147 2.16172
\(248\) −6.81589e146 −0.375616
\(249\) 1.28061e147 0.551007
\(250\) 1.81792e147 0.611313
\(251\) 1.31467e147 0.345847 0.172923 0.984935i \(-0.444679\pi\)
0.172923 + 0.984935i \(0.444679\pi\)
\(252\) −1.30560e147 −0.268953
\(253\) −1.71525e147 −0.276958
\(254\) 7.57364e147 0.959470
\(255\) −1.00007e148 −0.994970
\(256\) −1.12205e148 −0.877514
\(257\) 1.10486e148 0.679859 0.339929 0.940451i \(-0.389597\pi\)
0.339929 + 0.940451i \(0.389597\pi\)
\(258\) 1.23099e148 0.596544
\(259\) −1.35289e148 −0.516807
\(260\) −2.37426e148 −0.715594
\(261\) −7.89498e147 −0.187914
\(262\) −4.45363e148 −0.837885
\(263\) −4.79340e148 −0.713452 −0.356726 0.934209i \(-0.616107\pi\)
−0.356726 + 0.934209i \(0.616107\pi\)
\(264\) 2.30081e148 0.271168
\(265\) 3.62709e148 0.338795
\(266\) 2.18992e149 1.62258
\(267\) −1.99749e149 −1.17501
\(268\) 7.76152e148 0.362791
\(269\) −2.68638e148 −0.0998625 −0.0499313 0.998753i \(-0.515900\pi\)
−0.0499313 + 0.998753i \(0.515900\pi\)
\(270\) 1.76738e149 0.522949
\(271\) 6.66346e148 0.157068 0.0785341 0.996911i \(-0.474976\pi\)
0.0785341 + 0.996911i \(0.474976\pi\)
\(272\) 1.04639e149 0.196656
\(273\) 1.15556e150 1.73297
\(274\) −7.28373e149 −0.872357
\(275\) 9.06089e148 0.0867382
\(276\) −6.53930e149 −0.500752
\(277\) 9.02775e149 0.553444 0.276722 0.960950i \(-0.410752\pi\)
0.276722 + 0.960950i \(0.410752\pi\)
\(278\) 2.77237e149 0.136175
\(279\) −2.43525e149 −0.0959149
\(280\) −4.19042e150 −1.32446
\(281\) −5.60846e150 −1.42366 −0.711828 0.702354i \(-0.752132\pi\)
−0.711828 + 0.702354i \(0.752132\pi\)
\(282\) −2.93621e150 −0.599056
\(283\) −4.73677e150 −0.777349 −0.388675 0.921375i \(-0.627067\pi\)
−0.388675 + 0.921375i \(0.627067\pi\)
\(284\) 6.95174e150 0.918365
\(285\) 1.24061e151 1.32031
\(286\) 2.63885e150 0.226414
\(287\) 9.86130e149 0.0682649
\(288\) −4.46902e150 −0.249790
\(289\) 1.71604e151 0.775015
\(290\) −1.02763e151 −0.375283
\(291\) 3.64460e151 1.07704
\(292\) 1.01679e151 0.243325
\(293\) −9.51924e151 −1.84605 −0.923026 0.384738i \(-0.874292\pi\)
−0.923026 + 0.384738i \(0.874292\pi\)
\(294\) 5.15051e151 0.810008
\(295\) 7.17773e151 0.916079
\(296\) −2.90439e151 −0.301033
\(297\) 4.21681e151 0.355191
\(298\) 1.04645e152 0.716835
\(299\) −1.84939e152 −1.03098
\(300\) 3.45442e151 0.156826
\(301\) −5.34915e152 −1.97900
\(302\) −1.04078e152 −0.314001
\(303\) 1.38675e152 0.341411
\(304\) −1.29807e152 −0.260959
\(305\) 6.28465e152 1.03238
\(306\) −1.35406e152 −0.181874
\(307\) −1.37302e153 −1.50892 −0.754459 0.656347i \(-0.772101\pi\)
−0.754459 + 0.656347i \(0.772101\pi\)
\(308\) −4.05459e152 −0.364819
\(309\) 2.06910e153 1.52523
\(310\) −3.16978e152 −0.191551
\(311\) 1.97533e153 0.979210 0.489605 0.871944i \(-0.337141\pi\)
0.489605 + 0.871944i \(0.337141\pi\)
\(312\) 2.48075e153 1.00943
\(313\) 2.29332e152 0.0766456 0.0383228 0.999265i \(-0.487798\pi\)
0.0383228 + 0.999265i \(0.487798\pi\)
\(314\) 4.11373e152 0.112996
\(315\) −1.49720e153 −0.338205
\(316\) 1.20662e153 0.224293
\(317\) 1.61583e152 0.0247315 0.0123658 0.999924i \(-0.496064\pi\)
0.0123658 + 0.999924i \(0.496064\pi\)
\(318\) −1.53692e153 −0.193813
\(319\) −2.45182e153 −0.254895
\(320\) −4.34042e153 −0.372227
\(321\) 1.23683e154 0.875488
\(322\) −1.32372e154 −0.773854
\(323\) −4.87554e154 −2.35541
\(324\) 1.19409e154 0.477001
\(325\) 9.76953e153 0.322884
\(326\) −1.02928e154 −0.281613
\(327\) −2.35241e154 −0.533121
\(328\) 2.11702e153 0.0397634
\(329\) 1.27590e155 1.98733
\(330\) 1.07001e154 0.138286
\(331\) 3.52184e154 0.377875 0.188937 0.981989i \(-0.439496\pi\)
0.188937 + 0.981989i \(0.439496\pi\)
\(332\) −4.84477e154 −0.431799
\(333\) −1.03771e154 −0.0768698
\(334\) −1.39038e154 −0.0856495
\(335\) 8.90056e154 0.456207
\(336\) −4.90263e154 −0.209201
\(337\) −1.28842e153 −0.00457952 −0.00228976 0.999997i \(-0.500729\pi\)
−0.00228976 + 0.999997i \(0.500729\pi\)
\(338\) 9.42175e154 0.279097
\(339\) 9.24622e154 0.228393
\(340\) 3.78345e155 0.779713
\(341\) −7.56279e154 −0.130103
\(342\) 1.67973e155 0.241343
\(343\) −8.82118e155 −1.05910
\(344\) −1.14835e156 −1.15274
\(345\) −7.49897e155 −0.629691
\(346\) 1.39734e156 0.982027
\(347\) −1.68942e156 −0.994205 −0.497102 0.867692i \(-0.665603\pi\)
−0.497102 + 0.867692i \(0.665603\pi\)
\(348\) −9.34746e155 −0.460861
\(349\) −1.85162e156 −0.765221 −0.382611 0.923910i \(-0.624975\pi\)
−0.382611 + 0.923910i \(0.624975\pi\)
\(350\) 6.99262e155 0.242357
\(351\) 4.54660e156 1.32221
\(352\) −1.38788e156 −0.338826
\(353\) 8.44770e156 1.73218 0.866092 0.499884i \(-0.166624\pi\)
0.866092 + 0.499884i \(0.166624\pi\)
\(354\) −3.04144e156 −0.524056
\(355\) 7.97194e156 1.15484
\(356\) 7.55685e156 0.920802
\(357\) −1.84142e157 −1.88824
\(358\) 5.22800e155 0.0451367
\(359\) 2.59815e156 0.188954 0.0944770 0.995527i \(-0.469882\pi\)
0.0944770 + 0.995527i \(0.469882\pi\)
\(360\) −3.21418e156 −0.197000
\(361\) 4.11314e157 2.12560
\(362\) −1.35434e157 −0.590407
\(363\) −2.11088e157 −0.776617
\(364\) −4.37169e157 −1.35805
\(365\) 1.16601e157 0.305979
\(366\) −2.66301e157 −0.590589
\(367\) −3.01128e157 −0.564661 −0.282331 0.959317i \(-0.591107\pi\)
−0.282331 + 0.959317i \(0.591107\pi\)
\(368\) 7.84631e156 0.124459
\(369\) 7.56392e155 0.0101537
\(370\) −1.35071e157 −0.153516
\(371\) 6.67852e157 0.642962
\(372\) −2.88328e157 −0.235232
\(373\) −2.77145e157 −0.191696 −0.0958481 0.995396i \(-0.530556\pi\)
−0.0958481 + 0.995396i \(0.530556\pi\)
\(374\) −4.20509e157 −0.246701
\(375\) 1.89628e158 0.944016
\(376\) 2.73911e158 1.15759
\(377\) −2.64357e158 −0.948852
\(378\) 3.25426e158 0.992446
\(379\) −1.70323e158 −0.441532 −0.220766 0.975327i \(-0.570856\pi\)
−0.220766 + 0.975327i \(0.570856\pi\)
\(380\) −4.69344e158 −1.03467
\(381\) 7.90011e158 1.48166
\(382\) −1.88644e158 −0.301124
\(383\) 1.09260e159 1.48504 0.742519 0.669825i \(-0.233631\pi\)
0.742519 + 0.669825i \(0.233631\pi\)
\(384\) −5.91687e158 −0.685050
\(385\) −4.64962e158 −0.458757
\(386\) −3.53026e158 −0.296953
\(387\) −4.10296e158 −0.294356
\(388\) −1.37882e159 −0.844026
\(389\) −3.77080e158 −0.197030 −0.0985150 0.995136i \(-0.531409\pi\)
−0.0985150 + 0.995136i \(0.531409\pi\)
\(390\) 1.15369e159 0.514774
\(391\) 2.94707e159 1.12336
\(392\) −4.80475e159 −1.56523
\(393\) −4.64561e159 −1.29390
\(394\) −3.55407e159 −0.846658
\(395\) 1.38370e159 0.282046
\(396\) −3.10999e158 −0.0542632
\(397\) 1.04375e160 1.55949 0.779744 0.626098i \(-0.215349\pi\)
0.779744 + 0.626098i \(0.215349\pi\)
\(398\) 2.12471e159 0.271951
\(399\) 2.28432e160 2.50567
\(400\) −4.14486e158 −0.0389781
\(401\) −1.66506e159 −0.134293 −0.0671463 0.997743i \(-0.521389\pi\)
−0.0671463 + 0.997743i \(0.521389\pi\)
\(402\) −3.77146e159 −0.260980
\(403\) −8.15427e159 −0.484311
\(404\) −5.24633e159 −0.267548
\(405\) 1.36933e160 0.599824
\(406\) −1.89216e160 −0.712207
\(407\) −3.22266e159 −0.104270
\(408\) −3.95315e160 −1.09988
\(409\) 6.84012e160 1.63712 0.818560 0.574421i \(-0.194773\pi\)
0.818560 + 0.574421i \(0.194773\pi\)
\(410\) 9.84535e158 0.0202780
\(411\) −7.59770e160 −1.34713
\(412\) −7.82776e160 −1.19525
\(413\) 1.32163e161 1.73852
\(414\) −1.01533e160 −0.115103
\(415\) −5.55577e160 −0.542983
\(416\) −1.49642e161 −1.26129
\(417\) 2.89188e160 0.210287
\(418\) 5.21649e160 0.327368
\(419\) 1.24603e161 0.675097 0.337549 0.941308i \(-0.390402\pi\)
0.337549 + 0.941308i \(0.390402\pi\)
\(420\) −1.77265e161 −0.829450
\(421\) 1.44201e161 0.582932 0.291466 0.956581i \(-0.405857\pi\)
0.291466 + 0.956581i \(0.405857\pi\)
\(422\) 2.90173e161 1.01377
\(423\) 9.78657e160 0.295596
\(424\) 1.43374e161 0.374516
\(425\) −1.55680e161 −0.351815
\(426\) −3.37797e161 −0.660640
\(427\) 1.15718e162 1.95924
\(428\) −4.67914e161 −0.686080
\(429\) 2.75260e161 0.349639
\(430\) −5.34049e161 −0.587857
\(431\) −7.35947e161 −0.702254 −0.351127 0.936328i \(-0.614201\pi\)
−0.351127 + 0.936328i \(0.614201\pi\)
\(432\) −1.92896e161 −0.159615
\(433\) 1.20458e162 0.864632 0.432316 0.901722i \(-0.357697\pi\)
0.432316 + 0.901722i \(0.357697\pi\)
\(434\) −5.83648e161 −0.363523
\(435\) −1.07192e162 −0.579528
\(436\) 8.89957e161 0.417782
\(437\) −3.65589e162 −1.49068
\(438\) −4.94077e161 −0.175040
\(439\) 4.62284e161 0.142345 0.0711723 0.997464i \(-0.477326\pi\)
0.0711723 + 0.997464i \(0.477326\pi\)
\(440\) −9.98178e161 −0.267220
\(441\) −1.71669e162 −0.399686
\(442\) −4.53396e162 −0.918350
\(443\) 9.37803e162 1.65304 0.826518 0.562910i \(-0.190318\pi\)
0.826518 + 0.562910i \(0.190318\pi\)
\(444\) −1.22862e162 −0.188524
\(445\) 8.66586e162 1.15790
\(446\) 6.70874e162 0.780813
\(447\) 1.09156e163 1.10697
\(448\) −7.99197e162 −0.706409
\(449\) 1.36044e162 0.104841 0.0524203 0.998625i \(-0.483306\pi\)
0.0524203 + 0.998625i \(0.483306\pi\)
\(450\) 5.36355e161 0.0360481
\(451\) 2.34901e161 0.0137730
\(452\) −3.49801e162 −0.178981
\(453\) −1.08564e163 −0.484894
\(454\) 2.12516e163 0.828812
\(455\) −5.01326e163 −1.70773
\(456\) 4.90396e163 1.45952
\(457\) −4.60761e163 −1.19848 −0.599238 0.800571i \(-0.704530\pi\)
−0.599238 + 0.800571i \(0.704530\pi\)
\(458\) −8.44146e162 −0.191951
\(459\) −7.24515e163 −1.44068
\(460\) 2.83699e163 0.493460
\(461\) −6.94769e161 −0.0105739 −0.00528693 0.999986i \(-0.501683\pi\)
−0.00528693 + 0.999986i \(0.501683\pi\)
\(462\) 1.97019e163 0.262438
\(463\) 8.10358e163 0.945031 0.472515 0.881322i \(-0.343346\pi\)
0.472515 + 0.881322i \(0.343346\pi\)
\(464\) 1.12157e163 0.114544
\(465\) −3.30641e163 −0.295802
\(466\) 2.46304e163 0.193080
\(467\) −2.43027e164 −1.66981 −0.834905 0.550394i \(-0.814478\pi\)
−0.834905 + 0.550394i \(0.814478\pi\)
\(468\) −3.35322e163 −0.201996
\(469\) 1.63885e164 0.865784
\(470\) 1.27384e164 0.590333
\(471\) 4.29106e163 0.174493
\(472\) 2.83726e164 1.01267
\(473\) −1.27419e164 −0.399277
\(474\) −5.86319e163 −0.161349
\(475\) 1.93125e164 0.466853
\(476\) 6.96642e164 1.47973
\(477\) 5.12263e163 0.0956341
\(478\) −2.55085e164 −0.418667
\(479\) −2.17864e164 −0.314450 −0.157225 0.987563i \(-0.550255\pi\)
−0.157225 + 0.987563i \(0.550255\pi\)
\(480\) −6.06772e164 −0.770353
\(481\) −3.47469e164 −0.388145
\(482\) −6.95666e164 −0.683924
\(483\) −1.38078e165 −1.19502
\(484\) 7.98585e164 0.608599
\(485\) −1.58117e165 −1.06136
\(486\) 4.50562e164 0.266455
\(487\) 1.99967e165 1.04214 0.521072 0.853513i \(-0.325532\pi\)
0.521072 + 0.853513i \(0.325532\pi\)
\(488\) 2.48424e165 1.14123
\(489\) −1.07365e165 −0.434879
\(490\) −2.23448e165 −0.798212
\(491\) −5.00204e165 −1.57629 −0.788143 0.615492i \(-0.788957\pi\)
−0.788143 + 0.615492i \(0.788957\pi\)
\(492\) 8.95549e163 0.0249021
\(493\) 4.21262e165 1.03387
\(494\) 5.62446e165 1.21863
\(495\) −3.56640e164 −0.0682354
\(496\) 3.45956e164 0.0584653
\(497\) 1.46786e166 2.19163
\(498\) 2.35416e165 0.310621
\(499\) −6.80979e165 −0.794237 −0.397119 0.917767i \(-0.629990\pi\)
−0.397119 + 0.917767i \(0.629990\pi\)
\(500\) −7.17396e165 −0.739782
\(501\) −1.45031e165 −0.132264
\(502\) 2.41678e165 0.194965
\(503\) −7.94197e164 −0.0566888 −0.0283444 0.999598i \(-0.509024\pi\)
−0.0283444 + 0.999598i \(0.509024\pi\)
\(504\) −5.91823e165 −0.373864
\(505\) −6.01626e165 −0.336439
\(506\) −3.15316e165 −0.156131
\(507\) 9.82788e165 0.430993
\(508\) −2.98875e166 −1.16111
\(509\) −2.81399e166 −0.968675 −0.484338 0.874881i \(-0.660939\pi\)
−0.484338 + 0.874881i \(0.660939\pi\)
\(510\) −1.83844e166 −0.560898
\(511\) 2.14697e166 0.580684
\(512\) 1.21854e166 0.292238
\(513\) 8.98774e166 1.91176
\(514\) 2.03107e166 0.383259
\(515\) −8.97652e166 −1.50302
\(516\) −4.85780e166 −0.721909
\(517\) 3.03926e166 0.400959
\(518\) −2.48704e166 −0.291341
\(519\) 1.45758e167 1.51649
\(520\) −1.07624e167 −0.994730
\(521\) 5.82912e166 0.478722 0.239361 0.970931i \(-0.423062\pi\)
0.239361 + 0.970931i \(0.423062\pi\)
\(522\) −1.45134e166 −0.105934
\(523\) 4.42302e166 0.286989 0.143494 0.989651i \(-0.454166\pi\)
0.143494 + 0.989651i \(0.454166\pi\)
\(524\) 1.75752e167 1.01397
\(525\) 7.29404e166 0.374258
\(526\) −8.81175e166 −0.402197
\(527\) 1.29941e167 0.527706
\(528\) −1.16783e166 −0.0422078
\(529\) −8.98469e166 −0.289054
\(530\) 6.66772e166 0.190990
\(531\) 1.01373e167 0.258588
\(532\) −8.64198e167 −1.96358
\(533\) 2.53272e166 0.0512701
\(534\) −3.67200e167 −0.662393
\(535\) −5.36583e167 −0.862739
\(536\) 3.51828e167 0.504307
\(537\) 5.45336e166 0.0697021
\(538\) −4.93840e166 −0.0562959
\(539\) −5.33127e167 −0.542152
\(540\) −6.97454e167 −0.632848
\(541\) 2.24152e168 1.81514 0.907570 0.419901i \(-0.137935\pi\)
0.907570 + 0.419901i \(0.137935\pi\)
\(542\) 1.22495e167 0.0885446
\(543\) −1.41272e168 −0.911733
\(544\) 2.38459e168 1.37430
\(545\) 1.02056e168 0.525357
\(546\) 2.12428e168 0.976931
\(547\) −2.42945e168 −0.998360 −0.499180 0.866498i \(-0.666365\pi\)
−0.499180 + 0.866498i \(0.666365\pi\)
\(548\) 2.87435e168 1.05569
\(549\) 8.87596e167 0.291418
\(550\) 1.66567e167 0.0488972
\(551\) −5.22583e168 −1.37193
\(552\) −2.96425e168 −0.696083
\(553\) 2.54779e168 0.535264
\(554\) 1.65958e168 0.311995
\(555\) −1.40893e168 −0.237067
\(556\) −1.09405e168 −0.164792
\(557\) 6.38649e168 0.861326 0.430663 0.902513i \(-0.358280\pi\)
0.430663 + 0.902513i \(0.358280\pi\)
\(558\) −4.47675e167 −0.0540704
\(559\) −1.37384e169 −1.48632
\(560\) 2.12694e168 0.206154
\(561\) −4.38635e168 −0.380967
\(562\) −1.03101e169 −0.802563
\(563\) −9.62259e168 −0.671469 −0.335734 0.941957i \(-0.608984\pi\)
−0.335734 + 0.941957i \(0.608984\pi\)
\(564\) 1.15870e169 0.724950
\(565\) −4.01136e168 −0.225067
\(566\) −8.70765e168 −0.438218
\(567\) 2.52133e169 1.13834
\(568\) 3.15120e169 1.27660
\(569\) −1.66824e169 −0.606531 −0.303266 0.952906i \(-0.598077\pi\)
−0.303266 + 0.952906i \(0.598077\pi\)
\(570\) 2.28062e169 0.744303
\(571\) 1.32112e169 0.387098 0.193549 0.981091i \(-0.438000\pi\)
0.193549 + 0.981091i \(0.438000\pi\)
\(572\) −1.04136e169 −0.273996
\(573\) −1.96775e169 −0.465009
\(574\) 1.81281e168 0.0384833
\(575\) −1.16736e169 −0.222655
\(576\) −6.13008e168 −0.105071
\(577\) 6.60626e169 1.01775 0.508877 0.860839i \(-0.330061\pi\)
0.508877 + 0.860839i \(0.330061\pi\)
\(578\) 3.15461e169 0.436902
\(579\) −3.68244e169 −0.458568
\(580\) 4.05528e169 0.454150
\(581\) −1.02298e170 −1.03047
\(582\) 6.69991e169 0.607163
\(583\) 1.59085e169 0.129722
\(584\) 4.60910e169 0.338241
\(585\) −3.84532e169 −0.254008
\(586\) −1.74993e170 −1.04068
\(587\) −1.10122e170 −0.589700 −0.294850 0.955544i \(-0.595270\pi\)
−0.294850 + 0.955544i \(0.595270\pi\)
\(588\) −2.03252e170 −0.980233
\(589\) −1.61194e170 −0.700258
\(590\) 1.31949e170 0.516425
\(591\) −3.70727e170 −1.30745
\(592\) 1.47419e169 0.0468563
\(593\) 5.95213e170 1.70533 0.852665 0.522458i \(-0.174985\pi\)
0.852665 + 0.522458i \(0.174985\pi\)
\(594\) 7.75180e169 0.200233
\(595\) 7.98878e170 1.86075
\(596\) −4.12957e170 −0.867481
\(597\) 2.21630e170 0.419959
\(598\) −3.39976e170 −0.581200
\(599\) 5.03707e170 0.777013 0.388507 0.921446i \(-0.372991\pi\)
0.388507 + 0.921446i \(0.372991\pi\)
\(600\) 1.56588e170 0.218000
\(601\) 9.98664e170 1.25499 0.627494 0.778622i \(-0.284081\pi\)
0.627494 + 0.778622i \(0.284081\pi\)
\(602\) −9.83339e170 −1.11563
\(603\) 1.25705e170 0.128777
\(604\) 4.10717e170 0.379989
\(605\) 9.15781e170 0.765308
\(606\) 2.54928e170 0.192465
\(607\) −2.29593e171 −1.56622 −0.783112 0.621881i \(-0.786369\pi\)
−0.783112 + 0.621881i \(0.786369\pi\)
\(608\) −2.95813e171 −1.82367
\(609\) −1.97372e171 −1.09982
\(610\) 1.15531e171 0.581989
\(611\) 3.27696e171 1.49258
\(612\) 5.34346e170 0.220095
\(613\) 1.19254e171 0.444278 0.222139 0.975015i \(-0.428696\pi\)
0.222139 + 0.975015i \(0.428696\pi\)
\(614\) −2.52403e171 −0.850628
\(615\) 1.02697e170 0.0313141
\(616\) −1.83793e171 −0.507126
\(617\) −4.58978e171 −1.14618 −0.573091 0.819491i \(-0.694256\pi\)
−0.573091 + 0.819491i \(0.694256\pi\)
\(618\) 3.80364e171 0.859822
\(619\) −1.36892e171 −0.280157 −0.140079 0.990140i \(-0.544736\pi\)
−0.140079 + 0.990140i \(0.544736\pi\)
\(620\) 1.25088e171 0.231806
\(621\) −5.43272e171 −0.911768
\(622\) 3.63127e171 0.552014
\(623\) 1.59563e172 2.19745
\(624\) −1.25916e171 −0.157119
\(625\) −5.89151e171 −0.666202
\(626\) 4.21583e170 0.0432077
\(627\) 5.44135e171 0.505537
\(628\) −1.62338e171 −0.136742
\(629\) 5.53703e171 0.422924
\(630\) −2.75232e171 −0.190658
\(631\) −1.66513e171 −0.104627 −0.0523133 0.998631i \(-0.516659\pi\)
−0.0523133 + 0.998631i \(0.516659\pi\)
\(632\) 5.46959e171 0.311784
\(633\) 3.02681e172 1.56551
\(634\) 2.97039e170 0.0139420
\(635\) −3.42737e172 −1.46008
\(636\) 6.06506e171 0.234543
\(637\) −5.74822e172 −2.01817
\(638\) −4.50721e171 −0.143693
\(639\) 1.12590e172 0.325983
\(640\) 2.56696e172 0.675074
\(641\) −5.07748e172 −1.21305 −0.606526 0.795064i \(-0.707437\pi\)
−0.606526 + 0.795064i \(0.707437\pi\)
\(642\) 2.27368e172 0.493542
\(643\) −2.14595e172 −0.423297 −0.211648 0.977346i \(-0.567883\pi\)
−0.211648 + 0.977346i \(0.567883\pi\)
\(644\) 5.22373e172 0.936482
\(645\) −5.57070e172 −0.907794
\(646\) −8.96275e172 −1.32783
\(647\) 6.10334e172 0.822156 0.411078 0.911600i \(-0.365152\pi\)
0.411078 + 0.911600i \(0.365152\pi\)
\(648\) 5.41278e172 0.663067
\(649\) 3.14818e172 0.350760
\(650\) 1.79594e172 0.182021
\(651\) −6.08806e172 −0.561369
\(652\) 4.06181e172 0.340795
\(653\) 1.03044e173 0.786797 0.393399 0.919368i \(-0.371299\pi\)
0.393399 + 0.919368i \(0.371299\pi\)
\(654\) −4.32445e172 −0.300538
\(655\) 2.01544e173 1.27506
\(656\) −1.07454e171 −0.00618924
\(657\) 1.64679e172 0.0863709
\(658\) 2.34551e173 1.12033
\(659\) −3.11673e171 −0.0135596 −0.00677979 0.999977i \(-0.502158\pi\)
−0.00677979 + 0.999977i \(0.502158\pi\)
\(660\) −4.22252e172 −0.167348
\(661\) −9.08000e172 −0.327866 −0.163933 0.986471i \(-0.552418\pi\)
−0.163933 + 0.986471i \(0.552418\pi\)
\(662\) 6.47424e172 0.213021
\(663\) −4.72940e173 −1.41816
\(664\) −2.19612e173 −0.600233
\(665\) −9.91023e173 −2.46918
\(666\) −1.90763e172 −0.0433341
\(667\) 3.15880e173 0.654310
\(668\) 5.48678e172 0.103649
\(669\) 6.99793e173 1.20577
\(670\) 1.63620e173 0.257179
\(671\) 2.75647e173 0.395292
\(672\) −1.11724e174 −1.46197
\(673\) 7.84062e173 0.936320 0.468160 0.883644i \(-0.344917\pi\)
0.468160 + 0.883644i \(0.344917\pi\)
\(674\) −2.36852e171 −0.00258163
\(675\) 2.86987e173 0.285549
\(676\) −3.71806e173 −0.337750
\(677\) 3.25468e173 0.269964 0.134982 0.990848i \(-0.456902\pi\)
0.134982 + 0.990848i \(0.456902\pi\)
\(678\) 1.69974e173 0.128753
\(679\) −2.91138e174 −2.01423
\(680\) 1.71503e174 1.08386
\(681\) 2.21676e174 1.27989
\(682\) −1.39028e173 −0.0733435
\(683\) 8.08437e173 0.389738 0.194869 0.980829i \(-0.437572\pi\)
0.194869 + 0.980829i \(0.437572\pi\)
\(684\) −6.62866e173 −0.292062
\(685\) 3.29617e174 1.32752
\(686\) −1.62161e174 −0.597052
\(687\) −8.80534e173 −0.296419
\(688\) 5.82873e173 0.179426
\(689\) 1.71527e174 0.482893
\(690\) −1.37854e174 −0.354978
\(691\) 3.33428e174 0.785421 0.392710 0.919662i \(-0.371537\pi\)
0.392710 + 0.919662i \(0.371537\pi\)
\(692\) −5.51428e174 −1.18840
\(693\) −6.56677e173 −0.129496
\(694\) −3.10568e174 −0.560467
\(695\) −1.25460e174 −0.207225
\(696\) −4.23718e174 −0.640632
\(697\) −4.03597e173 −0.0558640
\(698\) −3.40384e174 −0.431381
\(699\) 2.56921e174 0.298163
\(700\) −2.75946e174 −0.293289
\(701\) −5.23508e174 −0.509642 −0.254821 0.966988i \(-0.582017\pi\)
−0.254821 + 0.966988i \(0.582017\pi\)
\(702\) 8.35806e174 0.745372
\(703\) −6.86879e174 −0.561213
\(704\) −1.90372e174 −0.142523
\(705\) 1.32875e175 0.911618
\(706\) 1.55295e175 0.976491
\(707\) −1.10777e175 −0.638491
\(708\) 1.20023e175 0.634188
\(709\) −2.46995e174 −0.119659 −0.0598294 0.998209i \(-0.519056\pi\)
−0.0598294 + 0.998209i \(0.519056\pi\)
\(710\) 1.46549e175 0.651020
\(711\) 1.95423e174 0.0796152
\(712\) 3.42550e175 1.27998
\(713\) 9.74352e174 0.333972
\(714\) −3.38510e175 −1.06447
\(715\) −1.19418e175 −0.344547
\(716\) −2.06310e174 −0.0546223
\(717\) −2.66080e175 −0.646524
\(718\) 4.77621e174 0.106520
\(719\) 8.28565e175 1.69629 0.848145 0.529765i \(-0.177720\pi\)
0.848145 + 0.529765i \(0.177720\pi\)
\(720\) 1.63143e174 0.0306634
\(721\) −1.65284e176 −2.85240
\(722\) 7.56123e175 1.19827
\(723\) −7.25653e175 −1.05615
\(724\) 5.34458e175 0.714483
\(725\) −1.66866e175 −0.204918
\(726\) −3.88046e175 −0.437805
\(727\) −1.03615e176 −1.07413 −0.537065 0.843541i \(-0.680467\pi\)
−0.537065 + 0.843541i \(0.680467\pi\)
\(728\) −1.98168e176 −1.88779
\(729\) 1.26862e176 1.11068
\(730\) 2.14349e175 0.172491
\(731\) 2.18926e176 1.61949
\(732\) 1.05089e176 0.714704
\(733\) 1.23434e176 0.771863 0.385931 0.922528i \(-0.373880\pi\)
0.385931 + 0.922528i \(0.373880\pi\)
\(734\) −5.53566e175 −0.318319
\(735\) −2.33080e176 −1.23263
\(736\) 1.78807e176 0.869758
\(737\) 3.90382e175 0.174678
\(738\) 1.39048e174 0.00572400
\(739\) −2.31018e176 −0.875010 −0.437505 0.899216i \(-0.644138\pi\)
−0.437505 + 0.899216i \(0.644138\pi\)
\(740\) 5.33023e175 0.185778
\(741\) 5.86691e176 1.88187
\(742\) 1.22772e176 0.362459
\(743\) −2.17632e175 −0.0591441 −0.0295720 0.999563i \(-0.509414\pi\)
−0.0295720 + 0.999563i \(0.509414\pi\)
\(744\) −1.30698e176 −0.326990
\(745\) −4.73560e176 −1.09085
\(746\) −5.09478e175 −0.108066
\(747\) −7.84654e175 −0.153271
\(748\) 1.65943e176 0.298546
\(749\) −9.88004e176 −1.63730
\(750\) 3.48595e176 0.532174
\(751\) 1.27682e177 1.79587 0.897933 0.440133i \(-0.145069\pi\)
0.897933 + 0.440133i \(0.145069\pi\)
\(752\) −1.39030e176 −0.180181
\(753\) 2.52095e176 0.301074
\(754\) −4.85971e176 −0.534900
\(755\) 4.70992e176 0.477833
\(756\) −1.28421e177 −1.20101
\(757\) −1.48488e177 −1.28025 −0.640123 0.768272i \(-0.721117\pi\)
−0.640123 + 0.768272i \(0.721117\pi\)
\(758\) −3.13106e176 −0.248906
\(759\) −3.28908e176 −0.241104
\(760\) −2.12752e177 −1.43826
\(761\) 1.35393e176 0.0844189 0.0422095 0.999109i \(-0.486560\pi\)
0.0422095 + 0.999109i \(0.486560\pi\)
\(762\) 1.45229e177 0.835259
\(763\) 1.87915e177 0.997017
\(764\) 7.44435e176 0.364406
\(765\) 6.12763e176 0.276767
\(766\) 2.00854e177 0.837167
\(767\) 3.39439e177 1.30571
\(768\) −2.15159e177 −0.763914
\(769\) 1.92276e177 0.630168 0.315084 0.949064i \(-0.397967\pi\)
0.315084 + 0.949064i \(0.397967\pi\)
\(770\) −8.54744e176 −0.258617
\(771\) 2.11862e177 0.591846
\(772\) 1.39313e177 0.359359
\(773\) −5.45552e176 −0.129956 −0.0649782 0.997887i \(-0.520698\pi\)
−0.0649782 + 0.997887i \(0.520698\pi\)
\(774\) −7.54251e176 −0.165938
\(775\) −5.14707e176 −0.104594
\(776\) −6.25015e177 −1.17326
\(777\) −2.59424e177 −0.449902
\(778\) −6.93189e176 −0.111072
\(779\) 5.00669e176 0.0741306
\(780\) −4.55276e177 −0.622955
\(781\) 3.49652e177 0.442178
\(782\) 5.41762e177 0.633276
\(783\) −7.76569e177 −0.839134
\(784\) 2.43876e177 0.243630
\(785\) −1.86162e177 −0.171952
\(786\) −8.54007e177 −0.729415
\(787\) −1.22207e178 −0.965275 −0.482637 0.875820i \(-0.660321\pi\)
−0.482637 + 0.875820i \(0.660321\pi\)
\(788\) 1.40253e178 1.02459
\(789\) −9.19159e177 −0.621091
\(790\) 2.54367e177 0.158999
\(791\) −7.38606e177 −0.427129
\(792\) −1.40975e177 −0.0754299
\(793\) 2.97205e178 1.47148
\(794\) 1.91874e178 0.879136
\(795\) 6.95514e177 0.294936
\(796\) −8.38465e177 −0.329102
\(797\) 7.22875e177 0.262649 0.131325 0.991339i \(-0.458077\pi\)
0.131325 + 0.991339i \(0.458077\pi\)
\(798\) 4.19928e178 1.41253
\(799\) −5.22193e178 −1.62631
\(800\) −9.44558e177 −0.272392
\(801\) 1.22390e178 0.326848
\(802\) −3.06090e177 −0.0757053
\(803\) 5.11417e177 0.117157
\(804\) 1.48831e178 0.315825
\(805\) 5.99033e178 1.17762
\(806\) −1.49901e178 −0.273023
\(807\) −5.15128e177 −0.0869346
\(808\) −2.37815e178 −0.371912
\(809\) −1.16706e179 −1.69145 −0.845723 0.533622i \(-0.820830\pi\)
−0.845723 + 0.533622i \(0.820830\pi\)
\(810\) 2.51725e178 0.338141
\(811\) −9.72451e178 −1.21084 −0.605418 0.795908i \(-0.706994\pi\)
−0.605418 + 0.795908i \(0.706994\pi\)
\(812\) 7.46694e178 0.861880
\(813\) 1.27775e178 0.136735
\(814\) −5.92424e177 −0.0587803
\(815\) 4.65790e178 0.428546
\(816\) 2.00651e178 0.171197
\(817\) −2.71582e179 −2.14904
\(818\) 1.25743e179 0.922900
\(819\) −7.08034e178 −0.482053
\(820\) −3.88523e177 −0.0245394
\(821\) 2.77613e179 1.62680 0.813402 0.581702i \(-0.197613\pi\)
0.813402 + 0.581702i \(0.197613\pi\)
\(822\) −1.39669e179 −0.759424
\(823\) 6.66809e178 0.336443 0.168222 0.985749i \(-0.446198\pi\)
0.168222 + 0.985749i \(0.446198\pi\)
\(824\) −3.54830e179 −1.66149
\(825\) 1.73747e178 0.0755093
\(826\) 2.42956e179 0.980065
\(827\) 3.43479e179 1.28621 0.643104 0.765779i \(-0.277646\pi\)
0.643104 + 0.765779i \(0.277646\pi\)
\(828\) 4.00675e178 0.139292
\(829\) −5.56651e178 −0.179672 −0.0898359 0.995957i \(-0.528634\pi\)
−0.0898359 + 0.995957i \(0.528634\pi\)
\(830\) −1.02132e179 −0.306098
\(831\) 1.73112e179 0.481796
\(832\) −2.05261e179 −0.530545
\(833\) 9.15996e179 2.19900
\(834\) 5.31617e178 0.118546
\(835\) 6.29199e178 0.130338
\(836\) −2.05856e179 −0.396166
\(837\) −2.39537e179 −0.428309
\(838\) 2.29059e179 0.380575
\(839\) −3.00269e179 −0.463608 −0.231804 0.972763i \(-0.574463\pi\)
−0.231804 + 0.972763i \(0.574463\pi\)
\(840\) −8.03535e179 −1.15300
\(841\) −2.98286e179 −0.397813
\(842\) 2.65085e179 0.328619
\(843\) −1.07545e180 −1.23935
\(844\) −1.14510e180 −1.22682
\(845\) −4.26371e179 −0.424717
\(846\) 1.79908e179 0.166637
\(847\) 1.68622e180 1.45239
\(848\) −7.27729e178 −0.0582941
\(849\) −9.08300e179 −0.676716
\(850\) −2.86189e179 −0.198330
\(851\) 4.15191e179 0.267658
\(852\) 1.33303e180 0.799476
\(853\) 1.48180e180 0.826848 0.413424 0.910539i \(-0.364333\pi\)
0.413424 + 0.910539i \(0.364333\pi\)
\(854\) 2.12726e180 1.10449
\(855\) −7.60144e179 −0.367265
\(856\) −2.12104e180 −0.953703
\(857\) −3.01163e179 −0.126032 −0.0630160 0.998013i \(-0.520072\pi\)
−0.0630160 + 0.998013i \(0.520072\pi\)
\(858\) 5.06013e179 0.197103
\(859\) 1.79804e180 0.651957 0.325978 0.945377i \(-0.394306\pi\)
0.325978 + 0.945377i \(0.394306\pi\)
\(860\) 2.10750e180 0.711397
\(861\) 1.89096e179 0.0594275
\(862\) −1.35290e180 −0.395884
\(863\) 3.52886e180 0.961548 0.480774 0.876845i \(-0.340356\pi\)
0.480774 + 0.876845i \(0.340356\pi\)
\(864\) −4.39584e180 −1.11544
\(865\) −6.32352e180 −1.49441
\(866\) 2.21440e180 0.487422
\(867\) 3.29060e180 0.674683
\(868\) 2.30322e180 0.439919
\(869\) 6.06896e179 0.107994
\(870\) −1.97053e180 −0.326700
\(871\) 4.20913e180 0.650243
\(872\) 4.03415e180 0.580749
\(873\) −2.23312e180 −0.299596
\(874\) −6.72066e180 −0.840347
\(875\) −1.51479e181 −1.76545
\(876\) 1.94976e180 0.211825
\(877\) −2.94272e180 −0.298039 −0.149020 0.988834i \(-0.547612\pi\)
−0.149020 + 0.988834i \(0.547612\pi\)
\(878\) 8.49822e179 0.0802445
\(879\) −1.82536e181 −1.60707
\(880\) 5.06648e179 0.0415932
\(881\) 1.22554e181 0.938228 0.469114 0.883138i \(-0.344573\pi\)
0.469114 + 0.883138i \(0.344573\pi\)
\(882\) −3.15581e180 −0.225317
\(883\) 4.21674e180 0.280798 0.140399 0.990095i \(-0.455162\pi\)
0.140399 + 0.990095i \(0.455162\pi\)
\(884\) 1.78922e181 1.11134
\(885\) 1.37637e181 0.797486
\(886\) 1.72397e181 0.931872
\(887\) 6.09390e180 0.307321 0.153661 0.988124i \(-0.450894\pi\)
0.153661 + 0.988124i \(0.450894\pi\)
\(888\) −5.56931e180 −0.262062
\(889\) −6.31077e181 −2.77092
\(890\) 1.59305e181 0.652747
\(891\) 6.00592e180 0.229668
\(892\) −2.64744e181 −0.944904
\(893\) 6.47791e181 2.15809
\(894\) 2.00663e181 0.624036
\(895\) −2.36587e180 −0.0686870
\(896\) 4.72652e181 1.28115
\(897\) −3.54631e181 −0.897514
\(898\) 2.50091e180 0.0591022
\(899\) 1.39277e181 0.307367
\(900\) −2.11659e180 −0.0436237
\(901\) −2.73334e181 −0.526162
\(902\) 4.31821e179 0.00776428
\(903\) −1.02573e182 −1.72280
\(904\) −1.58564e181 −0.248797
\(905\) 6.12893e181 0.898456
\(906\) −1.99575e181 −0.273351
\(907\) 6.03501e180 0.0772378 0.0386189 0.999254i \(-0.487704\pi\)
0.0386189 + 0.999254i \(0.487704\pi\)
\(908\) −8.38641e181 −1.00299
\(909\) −8.49691e180 −0.0949690
\(910\) −9.21592e181 −0.962705
\(911\) 3.46381e181 0.338200 0.169100 0.985599i \(-0.445914\pi\)
0.169100 + 0.985599i \(0.445914\pi\)
\(912\) −2.48912e181 −0.227176
\(913\) −2.43678e181 −0.207904
\(914\) −8.47021e181 −0.675621
\(915\) 1.20511e182 0.898733
\(916\) 3.33122e181 0.232290
\(917\) 3.71100e182 2.41979
\(918\) −1.33188e182 −0.812159
\(919\) 8.27431e181 0.471876 0.235938 0.971768i \(-0.424184\pi\)
0.235938 + 0.971768i \(0.424184\pi\)
\(920\) 1.28600e182 0.685946
\(921\) −2.63283e182 −1.31358
\(922\) −1.27720e180 −0.00596084
\(923\) 3.76998e182 1.64602
\(924\) −7.77488e181 −0.317591
\(925\) −2.19327e181 −0.0838253
\(926\) 1.48969e182 0.532746
\(927\) −1.26778e182 −0.424267
\(928\) 2.55591e182 0.800471
\(929\) 2.49107e182 0.730163 0.365082 0.930976i \(-0.381041\pi\)
0.365082 + 0.930976i \(0.381041\pi\)
\(930\) −6.07821e181 −0.166753
\(931\) −1.13631e183 −2.91804
\(932\) −9.71977e181 −0.233656
\(933\) 3.78780e182 0.852444
\(934\) −4.46760e182 −0.941329
\(935\) 1.90296e182 0.375419
\(936\) −1.52000e182 −0.280789
\(937\) −2.72308e182 −0.471059 −0.235529 0.971867i \(-0.575682\pi\)
−0.235529 + 0.971867i \(0.575682\pi\)
\(938\) 3.01272e182 0.488072
\(939\) 4.39755e181 0.0667233
\(940\) −5.02690e182 −0.714393
\(941\) 1.39301e183 1.85436 0.927179 0.374620i \(-0.122227\pi\)
0.927179 + 0.374620i \(0.122227\pi\)
\(942\) 7.88829e181 0.0983677
\(943\) −3.02634e181 −0.0353549
\(944\) −1.44012e182 −0.157623
\(945\) −1.47268e183 −1.51026
\(946\) −2.34236e182 −0.225086
\(947\) −1.09472e183 −0.985782 −0.492891 0.870091i \(-0.664060\pi\)
−0.492891 + 0.870091i \(0.664060\pi\)
\(948\) 2.31376e182 0.195257
\(949\) 5.51415e182 0.436120
\(950\) 3.55023e182 0.263181
\(951\) 3.09843e181 0.0215298
\(952\) 3.15786e183 2.05694
\(953\) −1.95172e183 −1.19180 −0.595900 0.803058i \(-0.703205\pi\)
−0.595900 + 0.803058i \(0.703205\pi\)
\(954\) 9.41698e181 0.0539121
\(955\) 8.53685e182 0.458237
\(956\) 1.00663e183 0.506651
\(957\) −4.70150e182 −0.221897
\(958\) −4.00502e182 −0.177266
\(959\) 6.06920e183 2.51934
\(960\) −8.32298e182 −0.324040
\(961\) −2.30874e183 −0.843114
\(962\) −6.38757e182 −0.218811
\(963\) −7.57829e182 −0.243531
\(964\) 2.74527e183 0.827653
\(965\) 1.59758e183 0.451890
\(966\) −2.53830e183 −0.673673
\(967\) −6.70395e183 −1.66956 −0.834782 0.550581i \(-0.814406\pi\)
−0.834782 + 0.550581i \(0.814406\pi\)
\(968\) 3.61996e183 0.845999
\(969\) −9.34910e183 −2.05049
\(970\) −2.90667e183 −0.598322
\(971\) 5.25177e183 1.01467 0.507333 0.861750i \(-0.330631\pi\)
0.507333 + 0.861750i \(0.330631\pi\)
\(972\) −1.77803e183 −0.322452
\(973\) −2.31009e183 −0.393268
\(974\) 3.67602e183 0.587492
\(975\) 1.87336e183 0.281085
\(976\) −1.26093e183 −0.177635
\(977\) −5.07777e183 −0.671673 −0.335836 0.941920i \(-0.609019\pi\)
−0.335836 + 0.941920i \(0.609019\pi\)
\(978\) −1.97370e183 −0.245156
\(979\) 3.80088e183 0.443351
\(980\) 8.81784e183 0.965959
\(981\) 1.44136e183 0.148296
\(982\) −9.19530e183 −0.888606
\(983\) −7.90467e183 −0.717534 −0.358767 0.933427i \(-0.616803\pi\)
−0.358767 + 0.933427i \(0.616803\pi\)
\(984\) 4.05950e182 0.0346157
\(985\) 1.60835e184 1.28841
\(986\) 7.74410e183 0.582828
\(987\) 2.44661e184 1.73006
\(988\) −2.21956e184 −1.47473
\(989\) 1.64160e184 1.02494
\(990\) −6.55614e182 −0.0384666
\(991\) −1.75082e184 −0.965411 −0.482706 0.875783i \(-0.660346\pi\)
−0.482706 + 0.875783i \(0.660346\pi\)
\(992\) 7.88387e183 0.408575
\(993\) 6.75331e183 0.328956
\(994\) 2.69839e184 1.23550
\(995\) −9.61514e183 −0.413843
\(996\) −9.29011e183 −0.375899
\(997\) 1.12976e184 0.429767 0.214883 0.976640i \(-0.431063\pi\)
0.214883 + 0.976640i \(0.431063\pi\)
\(998\) −1.25185e184 −0.447738
\(999\) −1.02072e184 −0.343263
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 1.124.a.a.1.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.124.a.a.1.6 10 1.1 even 1 trivial