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Properties

Label 1.118.a.a.1.9
Level $1$
Weight $118$
Character 1.1
Self dual yes
Analytic conductor $86.689$
Analytic rank $1$
Dimension $9$
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] = [1,118,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, 118, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1.1");
 
S:= CuspForms(chi, 118);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 118 \)
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: \(86.6887159558\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 4 x^{8} + \cdots - 93\!\cdots\!48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{151}\cdot 3^{56}\cdot 5^{18}\cdot 7^{7}\cdot 11^{4}\cdot 13^{4}\cdot 17^{2}\cdot 19\cdot 23\cdot 29^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-2.64602e15\) 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)
 
\(f(q)\) \(=\) \(q+7.66546e17 q^{2} -7.42736e27 q^{3} +4.21439e35 q^{4} -1.57195e40 q^{5} -5.69341e45 q^{6} +1.22056e49 q^{7} +1.95688e53 q^{8} -1.13902e55 q^{9} +O(q^{10})\) \(q+7.66546e17 q^{2} -7.42736e27 q^{3} +4.21439e35 q^{4} -1.57195e40 q^{5} -5.69341e45 q^{6} +1.22056e49 q^{7} +1.95688e53 q^{8} -1.13902e55 q^{9} -1.20497e58 q^{10} -1.59352e61 q^{11} -3.13018e63 q^{12} +1.81884e65 q^{13} +9.35613e66 q^{14} +1.16755e68 q^{15} +7.99800e70 q^{16} -1.54465e72 q^{17} -8.73114e72 q^{18} +3.70030e74 q^{19} -6.62482e75 q^{20} -9.06552e76 q^{21} -1.22151e79 q^{22} -3.22877e78 q^{23} -1.45344e81 q^{24} -5.77143e81 q^{25} +1.39422e83 q^{26} +5.78934e83 q^{27} +5.14390e84 q^{28} -3.97175e85 q^{29} +8.94978e85 q^{30} -1.94444e86 q^{31} +2.87941e88 q^{32} +1.18357e89 q^{33} -1.18404e90 q^{34} -1.91866e89 q^{35} -4.80029e90 q^{36} +5.99642e90 q^{37} +2.83645e92 q^{38} -1.35092e93 q^{39} -3.07612e93 q^{40} +1.15289e94 q^{41} -6.94913e94 q^{42} -3.66555e94 q^{43} -6.71572e96 q^{44} +1.79050e95 q^{45} -2.47500e96 q^{46} -7.36452e97 q^{47} -5.94040e98 q^{48} -6.03462e98 q^{49} -4.42406e99 q^{50} +1.14727e100 q^{51} +7.66529e100 q^{52} -1.15221e101 q^{53} +4.43780e101 q^{54} +2.50495e101 q^{55} +2.38848e102 q^{56} -2.74835e102 q^{57} -3.04453e103 q^{58} -2.87765e103 q^{59} +4.92050e103 q^{60} -2.83787e104 q^{61} -1.49050e104 q^{62} -1.39025e104 q^{63} +8.78304e105 q^{64} -2.85913e105 q^{65} +9.07258e106 q^{66} -3.02391e106 q^{67} -6.50974e107 q^{68} +2.39812e106 q^{69} -1.47074e107 q^{70} +2.09964e108 q^{71} -2.22893e108 q^{72} +2.34519e108 q^{73} +4.59653e108 q^{74} +4.28665e109 q^{75} +1.55945e110 q^{76} -1.94499e110 q^{77} -1.03554e111 q^{78} -2.20505e110 q^{79} -1.25725e111 q^{80} -3.54187e111 q^{81} +8.83744e111 q^{82} +1.58111e112 q^{83} -3.82056e112 q^{84} +2.42812e112 q^{85} -2.80981e112 q^{86} +2.94997e113 q^{87} -3.11833e114 q^{88} -1.16764e114 q^{89} +1.37250e113 q^{90} +2.22000e114 q^{91} -1.36073e114 q^{92} +1.44421e114 q^{93} -5.64524e115 q^{94} -5.81671e114 q^{95} -2.13864e116 q^{96} +1.07918e116 q^{97} -4.62581e116 q^{98} +1.81506e116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 40\!\cdots\!52 q^{2}+ \cdots + 22\!\cdots\!97 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q + 40\!\cdots\!52 q^{2}+ \cdots - 15\!\cdots\!16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.66546e17 1.88054 0.940271 − 0.340426i \(-0.110571\pi\)
0.940271 + 0.340426i \(0.110571\pi\)
\(3\) −7.42736e27 −0.910419 −0.455209 − 0.890384i \(-0.650436\pi\)
−0.455209 + 0.890384i \(0.650436\pi\)
\(4\) 4.21439e35 2.53644
\(5\) −1.57195e40 −0.202626 −0.101313 − 0.994855i \(-0.532304\pi\)
−0.101313 + 0.994855i \(0.532304\pi\)
\(6\) −5.69341e45 −1.71208
\(7\) 1.22056e49 0.444962 0.222481 − 0.974937i \(-0.428584\pi\)
0.222481 + 0.974937i \(0.428584\pi\)
\(8\) 1.95688e53 2.88934
\(9\) −1.13902e55 −0.171138
\(10\) −1.20497e58 −0.381047
\(11\) −1.59352e61 −1.90935 −0.954677 − 0.297645i \(-0.903799\pi\)
−0.954677 + 0.297645i \(0.903799\pi\)
\(12\) −3.13018e63 −2.30922
\(13\) 1.81884e65 1.24196 0.620981 − 0.783826i \(-0.286734\pi\)
0.620981 + 0.783826i \(0.286734\pi\)
\(14\) 9.35613e66 0.836770
\(15\) 1.16755e68 0.184474
\(16\) 7.99800e70 2.89709
\(17\) −1.54465e72 −1.61275 −0.806376 − 0.591403i \(-0.798574\pi\)
−0.806376 + 0.591403i \(0.798574\pi\)
\(18\) −8.73114e72 −0.321832
\(19\) 3.70030e74 0.576968 0.288484 − 0.957485i \(-0.406849\pi\)
0.288484 + 0.957485i \(0.406849\pi\)
\(20\) −6.62482e75 −0.513948
\(21\) −9.06552e76 −0.405102
\(22\) −1.22151e79 −3.59062
\(23\) −3.22877e78 −0.0704626 −0.0352313 − 0.999379i \(-0.511217\pi\)
−0.0352313 + 0.999379i \(0.511217\pi\)
\(24\) −1.45344e81 −2.63051
\(25\) −5.77143e81 −0.958943
\(26\) 1.39422e83 2.33556
\(27\) 5.78934e83 1.06623
\(28\) 5.14390e84 1.12862
\(29\) −3.97175e85 −1.11866 −0.559332 − 0.828944i \(-0.688942\pi\)
−0.559332 + 0.828944i \(0.688942\pi\)
\(30\) 8.94978e85 0.346912
\(31\) −1.94444e86 −0.110697 −0.0553485 − 0.998467i \(-0.517627\pi\)
−0.0553485 + 0.998467i \(0.517627\pi\)
\(32\) 2.87941e88 2.55876
\(33\) 1.18357e89 1.73831
\(34\) −1.18404e90 −3.03285
\(35\) −1.91866e89 −0.0901608
\(36\) −4.80029e90 −0.434081
\(37\) 5.99642e90 0.109167 0.0545834 − 0.998509i \(-0.482617\pi\)
0.0545834 + 0.998509i \(0.482617\pi\)
\(38\) 2.83645e92 1.08501
\(39\) −1.35092e93 −1.13071
\(40\) −3.07612e93 −0.585455
\(41\) 1.15289e94 0.517527 0.258763 − 0.965941i \(-0.416685\pi\)
0.258763 + 0.965941i \(0.416685\pi\)
\(42\) −6.94913e94 −0.761811
\(43\) −3.66555e94 −0.101446 −0.0507229 − 0.998713i \(-0.516153\pi\)
−0.0507229 + 0.998713i \(0.516153\pi\)
\(44\) −6.71572e96 −4.84296
\(45\) 1.79050e95 0.0346770
\(46\) −2.47500e96 −0.132508
\(47\) −7.36452e97 −1.12052 −0.560260 − 0.828317i \(-0.689299\pi\)
−0.560260 + 0.828317i \(0.689299\pi\)
\(48\) −5.94040e98 −2.63757
\(49\) −6.03462e98 −0.802009
\(50\) −4.42406e99 −1.80333
\(51\) 1.14727e100 1.46828
\(52\) 7.66529e100 3.15016
\(53\) −1.15221e101 −1.55380 −0.776898 − 0.629626i \(-0.783208\pi\)
−0.776898 + 0.629626i \(0.783208\pi\)
\(54\) 4.43780e101 2.00508
\(55\) 2.50495e101 0.386884
\(56\) 2.38848e102 1.28565
\(57\) −2.74835e102 −0.525282
\(58\) −3.04453e103 −2.10369
\(59\) −2.87765e103 −0.731469 −0.365734 − 0.930719i \(-0.619182\pi\)
−0.365734 + 0.930719i \(0.619182\pi\)
\(60\) 4.92050e103 0.467908
\(61\) −2.83787e104 −1.02612 −0.513059 − 0.858353i \(-0.671488\pi\)
−0.513059 + 0.858353i \(0.671488\pi\)
\(62\) −1.49050e104 −0.208170
\(63\) −1.39025e104 −0.0761499
\(64\) 8.78304e105 1.91477
\(65\) −2.85913e105 −0.251654
\(66\) 9.07258e106 3.26897
\(67\) −3.02391e106 −0.452057 −0.226029 − 0.974121i \(-0.572574\pi\)
−0.226029 + 0.974121i \(0.572574\pi\)
\(68\) −6.50974e107 −4.09065
\(69\) 2.39812e106 0.0641504
\(70\) −1.47074e107 −0.169551
\(71\) 2.09964e108 1.05568 0.527840 − 0.849344i \(-0.323002\pi\)
0.527840 + 0.849344i \(0.323002\pi\)
\(72\) −2.22893e108 −0.494476
\(73\) 2.34519e108 0.232162 0.116081 − 0.993240i \(-0.462967\pi\)
0.116081 + 0.993240i \(0.462967\pi\)
\(74\) 4.59653e108 0.205293
\(75\) 4.28665e109 0.873039
\(76\) 1.55945e110 1.46344
\(77\) −1.94499e110 −0.849590
\(78\) −1.03554e111 −2.12634
\(79\) −2.20505e110 −0.214898 −0.107449 − 0.994211i \(-0.534268\pi\)
−0.107449 + 0.994211i \(0.534268\pi\)
\(80\) −1.25725e111 −0.587026
\(81\) −3.54187e111 −0.799574
\(82\) 8.83744e111 0.973231
\(83\) 1.58111e112 0.856830 0.428415 − 0.903582i \(-0.359072\pi\)
0.428415 + 0.903582i \(0.359072\pi\)
\(84\) −3.82056e112 −1.02752
\(85\) 2.42812e112 0.326785
\(86\) −2.80981e112 −0.190773
\(87\) 2.94997e113 1.01845
\(88\) −3.11833e114 −5.51678
\(89\) −1.16764e114 −1.06658 −0.533292 − 0.845931i \(-0.679045\pi\)
−0.533292 + 0.845931i \(0.679045\pi\)
\(90\) 1.37250e113 0.0652115
\(91\) 2.22000e114 0.552626
\(92\) −1.36073e114 −0.178724
\(93\) 1.44421e114 0.100781
\(94\) −5.64524e115 −2.10719
\(95\) −5.81671e114 −0.116909
\(96\) −2.13864e116 −2.32954
\(97\) 1.07918e116 0.641130 0.320565 − 0.947227i \(-0.396127\pi\)
0.320565 + 0.947227i \(0.396127\pi\)
\(98\) −4.62581e116 −1.50821
\(99\) 1.81506e116 0.326763
\(100\) −2.43230e117 −2.43230
\(101\) 9.73913e116 0.544151 0.272076 − 0.962276i \(-0.412290\pi\)
0.272076 + 0.962276i \(0.412290\pi\)
\(102\) 8.79431e117 2.76116
\(103\) −5.98855e117 −1.06254 −0.531268 − 0.847204i \(-0.678284\pi\)
−0.531268 + 0.847204i \(0.678284\pi\)
\(104\) 3.55924e118 3.58845
\(105\) 1.42506e117 0.0820841
\(106\) −8.83223e118 −2.92198
\(107\) −1.87534e118 −0.358202 −0.179101 − 0.983831i \(-0.557319\pi\)
−0.179101 + 0.983831i \(0.557319\pi\)
\(108\) 2.43985e119 2.70442
\(109\) 2.91021e118 0.188137 0.0940686 − 0.995566i \(-0.470013\pi\)
0.0940686 + 0.995566i \(0.470013\pi\)
\(110\) 1.92016e119 0.727552
\(111\) −4.45375e118 −0.0993875
\(112\) 9.76202e119 1.28910
\(113\) 1.70082e120 1.33527 0.667637 − 0.744487i \(-0.267306\pi\)
0.667637 + 0.744487i \(0.267306\pi\)
\(114\) −2.10673e120 −0.987816
\(115\) 5.07548e118 0.0142775
\(116\) −1.67385e121 −2.83742
\(117\) −2.07170e120 −0.212547
\(118\) −2.20585e121 −1.37556
\(119\) −1.88533e121 −0.717613
\(120\) 2.28475e121 0.533010
\(121\) 1.84278e122 2.64563
\(122\) −2.17536e122 −1.92966
\(123\) −8.56294e121 −0.471166
\(124\) −8.19463e121 −0.280776
\(125\) 1.85333e122 0.396932
\(126\) −1.06569e122 −0.143203
\(127\) 6.04774e122 0.511771 0.255886 − 0.966707i \(-0.417633\pi\)
0.255886 + 0.966707i \(0.417633\pi\)
\(128\) 1.94836e123 1.04204
\(129\) 2.72253e122 0.0923581
\(130\) −2.19166e123 −0.473245
\(131\) −3.31626e123 −0.457381 −0.228690 − 0.973499i \(-0.573444\pi\)
−0.228690 + 0.973499i \(0.573444\pi\)
\(132\) 4.98801e124 4.40912
\(133\) 4.51643e123 0.256729
\(134\) −2.31797e124 −0.850113
\(135\) −9.10059e123 −0.216045
\(136\) −3.02268e125 −4.65979
\(137\) 8.87924e124 0.891708 0.445854 − 0.895106i \(-0.352900\pi\)
0.445854 + 0.895106i \(0.352900\pi\)
\(138\) 1.83827e124 0.120638
\(139\) −1.55424e125 −0.668577 −0.334289 − 0.942471i \(-0.608496\pi\)
−0.334289 + 0.942471i \(0.608496\pi\)
\(140\) −8.08598e124 −0.228688
\(141\) 5.46989e125 1.02014
\(142\) 1.60947e126 1.98525
\(143\) −2.89836e126 −2.37134
\(144\) −9.10992e125 −0.495802
\(145\) 6.24342e125 0.226670
\(146\) 1.79769e126 0.436590
\(147\) 4.48213e126 0.730164
\(148\) 2.52712e126 0.276895
\(149\) −1.72799e127 −1.27686 −0.638432 − 0.769679i \(-0.720416\pi\)
−0.638432 + 0.769679i \(0.720416\pi\)
\(150\) 3.28591e127 1.64179
\(151\) 2.69671e127 0.913446 0.456723 − 0.889609i \(-0.349023\pi\)
0.456723 + 0.889609i \(0.349023\pi\)
\(152\) 7.24103e127 1.66706
\(153\) 1.75939e127 0.276003
\(154\) −1.49092e128 −1.59769
\(155\) 3.05657e126 0.0224301
\(156\) −5.69329e128 −2.86797
\(157\) −1.13801e128 −0.394474 −0.197237 − 0.980356i \(-0.563197\pi\)
−0.197237 + 0.980356i \(0.563197\pi\)
\(158\) −1.69027e128 −0.404126
\(159\) 8.55790e128 1.41461
\(160\) −4.52630e128 −0.518471
\(161\) −3.94090e127 −0.0313532
\(162\) −2.71500e129 −1.50363
\(163\) 4.39139e129 1.69679 0.848393 − 0.529367i \(-0.177571\pi\)
0.848393 + 0.529367i \(0.177571\pi\)
\(164\) 4.85873e129 1.31268
\(165\) −1.86051e129 −0.352227
\(166\) 1.21200e130 1.61130
\(167\) −1.31996e130 −1.23494 −0.617472 − 0.786593i \(-0.711843\pi\)
−0.617472 + 0.786593i \(0.711843\pi\)
\(168\) −1.77401e130 −1.17048
\(169\) 1.16345e130 0.542470
\(170\) 1.86126e130 0.614533
\(171\) −4.21474e129 −0.0987411
\(172\) −1.54480e130 −0.257311
\(173\) 1.62385e131 1.92686 0.963430 − 0.267962i \(-0.0863500\pi\)
0.963430 + 0.267962i \(0.0863500\pi\)
\(174\) 2.26128e131 1.91524
\(175\) −7.04436e130 −0.426693
\(176\) −1.27450e132 −5.53157
\(177\) 2.13734e131 0.665943
\(178\) −8.95052e131 −2.00576
\(179\) 8.57149e131 1.38406 0.692028 − 0.721870i \(-0.256717\pi\)
0.692028 + 0.721870i \(0.256717\pi\)
\(180\) 7.54584e130 0.0879561
\(181\) 3.17372e131 0.267530 0.133765 − 0.991013i \(-0.457293\pi\)
0.133765 + 0.991013i \(0.457293\pi\)
\(182\) 1.70173e132 1.03924
\(183\) 2.10779e132 0.934198
\(184\) −6.31830e131 −0.203590
\(185\) −9.42609e130 −0.0221200
\(186\) 1.10705e132 0.189522
\(187\) 2.46143e133 3.07931
\(188\) −3.10369e133 −2.84213
\(189\) 7.06623e132 0.474430
\(190\) −4.45877e132 −0.219852
\(191\) −1.90776e133 −0.691946 −0.345973 − 0.938244i \(-0.612451\pi\)
−0.345973 + 0.938244i \(0.612451\pi\)
\(192\) −6.52348e133 −1.74324
\(193\) 8.50029e133 1.67622 0.838110 − 0.545501i \(-0.183661\pi\)
0.838110 + 0.545501i \(0.183661\pi\)
\(194\) 8.27238e133 1.20567
\(195\) 2.12358e133 0.229110
\(196\) −2.54322e134 −2.03425
\(197\) −7.85059e133 −0.466260 −0.233130 − 0.972446i \(-0.574897\pi\)
−0.233130 + 0.972446i \(0.574897\pi\)
\(198\) 1.39133e134 0.614492
\(199\) 1.28071e134 0.421255 0.210627 − 0.977566i \(-0.432449\pi\)
0.210627 + 0.977566i \(0.432449\pi\)
\(200\) −1.12940e135 −2.77071
\(201\) 2.24597e134 0.411561
\(202\) 7.46548e134 1.02330
\(203\) −4.84775e134 −0.497763
\(204\) 4.83502e135 3.72420
\(205\) −1.81229e134 −0.104864
\(206\) −4.59050e135 −1.99815
\(207\) 3.67765e133 0.0120588
\(208\) 1.45471e136 3.59808
\(209\) −5.89652e135 −1.10164
\(210\) 1.09237e135 0.154363
\(211\) 9.80623e134 0.104949 0.0524745 − 0.998622i \(-0.483289\pi\)
0.0524745 + 0.998622i \(0.483289\pi\)
\(212\) −4.85587e136 −3.94111
\(213\) −1.55948e136 −0.961110
\(214\) −1.43753e136 −0.673615
\(215\) 5.76207e134 0.0205555
\(216\) 1.13290e137 3.08069
\(217\) −2.37330e135 −0.0492559
\(218\) 2.23081e136 0.353800
\(219\) −1.74186e136 −0.211364
\(220\) 1.05568e137 0.981309
\(221\) −2.80947e137 −2.00298
\(222\) −3.41401e136 −0.186903
\(223\) −1.29841e137 −0.546483 −0.273242 − 0.961945i \(-0.588096\pi\)
−0.273242 + 0.961945i \(0.588096\pi\)
\(224\) 3.51449e137 1.13855
\(225\) 6.57380e136 0.164112
\(226\) 1.30376e138 2.51104
\(227\) −3.45785e137 −0.514391 −0.257195 − 0.966359i \(-0.582798\pi\)
−0.257195 + 0.966359i \(0.582798\pi\)
\(228\) −1.15826e138 −1.33235
\(229\) 1.00939e138 0.898839 0.449419 − 0.893321i \(-0.351631\pi\)
0.449419 + 0.893321i \(0.351631\pi\)
\(230\) 3.89058e136 0.0268495
\(231\) 1.44461e138 0.773482
\(232\) −7.77223e138 −3.23220
\(233\) 3.65689e138 1.18247 0.591236 − 0.806499i \(-0.298640\pi\)
0.591236 + 0.806499i \(0.298640\pi\)
\(234\) −1.58806e138 −0.399704
\(235\) 1.15767e138 0.227046
\(236\) −1.21275e139 −1.85533
\(237\) 1.63777e138 0.195648
\(238\) −1.44519e139 −1.34950
\(239\) 1.47687e139 1.07911 0.539556 − 0.841950i \(-0.318592\pi\)
0.539556 + 0.841950i \(0.318592\pi\)
\(240\) 9.33804e138 0.534439
\(241\) 7.84639e138 0.352105 0.176053 − 0.984381i \(-0.443667\pi\)
0.176053 + 0.984381i \(0.443667\pi\)
\(242\) 1.41257e140 4.97522
\(243\) −1.22248e139 −0.338279
\(244\) −1.19599e140 −2.60269
\(245\) 9.48615e138 0.162508
\(246\) −6.56388e139 −0.886048
\(247\) 6.73026e139 0.716572
\(248\) −3.80503e139 −0.319842
\(249\) −1.17435e140 −0.780074
\(250\) 1.42066e140 0.746448
\(251\) −3.02402e140 −1.25797 −0.628987 − 0.777416i \(-0.716530\pi\)
−0.628987 + 0.777416i \(0.716530\pi\)
\(252\) −5.85903e139 −0.193150
\(253\) 5.14512e139 0.134538
\(254\) 4.63587e140 0.962407
\(255\) −1.80345e140 −0.297511
\(256\) 3.41736e139 0.0448386
\(257\) −4.39830e140 −0.459407 −0.229703 − 0.973261i \(-0.573776\pi\)
−0.229703 + 0.973261i \(0.573776\pi\)
\(258\) 2.08695e140 0.173683
\(259\) 7.31897e139 0.0485751
\(260\) −1.20495e141 −0.638304
\(261\) 4.52393e140 0.191446
\(262\) −2.54206e141 −0.860124
\(263\) −6.26108e141 −1.69527 −0.847633 − 0.530583i \(-0.821973\pi\)
−0.847633 + 0.530583i \(0.821973\pi\)
\(264\) 2.31609e142 5.02258
\(265\) 1.81123e141 0.314839
\(266\) 3.46205e141 0.482789
\(267\) 8.67251e141 0.971037
\(268\) −1.27439e142 −1.14662
\(269\) −1.47530e142 −1.06751 −0.533754 − 0.845640i \(-0.679219\pi\)
−0.533754 + 0.845640i \(0.679219\pi\)
\(270\) −6.97601e141 −0.406282
\(271\) 1.03483e142 0.485472 0.242736 − 0.970092i \(-0.421955\pi\)
0.242736 + 0.970092i \(0.421955\pi\)
\(272\) −1.23541e143 −4.67229
\(273\) −1.64887e142 −0.503121
\(274\) 6.80634e142 1.67689
\(275\) 9.19690e142 1.83096
\(276\) 1.01066e142 0.162714
\(277\) 4.13500e142 0.538777 0.269389 − 0.963032i \(-0.413178\pi\)
0.269389 + 0.963032i \(0.413178\pi\)
\(278\) −1.19139e143 −1.25729
\(279\) 2.21477e141 0.0189445
\(280\) −3.75458e142 −0.260505
\(281\) 1.04782e143 0.590155 0.295078 − 0.955473i \(-0.404654\pi\)
0.295078 + 0.955473i \(0.404654\pi\)
\(282\) 4.19292e143 1.91842
\(283\) −2.11078e143 −0.785120 −0.392560 − 0.919726i \(-0.628410\pi\)
−0.392560 + 0.919726i \(0.628410\pi\)
\(284\) 8.84871e143 2.67767
\(285\) 4.32028e142 0.106436
\(286\) −2.22173e144 −4.45941
\(287\) 1.40717e143 0.230280
\(288\) −3.27972e143 −0.437901
\(289\) 1.46861e144 1.60097
\(290\) 4.78586e143 0.426263
\(291\) −8.01544e143 −0.583697
\(292\) 9.88353e143 0.588864
\(293\) −3.07506e144 −1.50002 −0.750010 − 0.661426i \(-0.769952\pi\)
−0.750010 + 0.661426i \(0.769952\pi\)
\(294\) 3.43576e144 1.37310
\(295\) 4.52354e143 0.148214
\(296\) 1.17342e144 0.315420
\(297\) −9.22545e144 −2.03580
\(298\) −1.32458e145 −2.40120
\(299\) −5.87261e143 −0.0875118
\(300\) 1.80656e145 2.21441
\(301\) −4.47401e143 −0.0451395
\(302\) 2.06715e145 1.71777
\(303\) −7.23360e144 −0.495405
\(304\) 2.95950e145 1.67153
\(305\) 4.46101e144 0.207918
\(306\) 1.34865e145 0.519036
\(307\) 8.66906e144 0.275662 0.137831 − 0.990456i \(-0.455987\pi\)
0.137831 + 0.990456i \(0.455987\pi\)
\(308\) −8.19692e145 −2.15493
\(309\) 4.44791e145 0.967353
\(310\) 2.34300e144 0.0421807
\(311\) −6.47602e144 −0.0965662 −0.0482831 − 0.998834i \(-0.515375\pi\)
−0.0482831 + 0.998834i \(0.515375\pi\)
\(312\) −2.64358e146 −3.26700
\(313\) 7.37997e145 0.756329 0.378165 − 0.925738i \(-0.376555\pi\)
0.378165 + 0.925738i \(0.376555\pi\)
\(314\) −8.72340e145 −0.741825
\(315\) 2.18540e144 0.0154299
\(316\) −9.29293e145 −0.545077
\(317\) −1.53720e146 −0.749486 −0.374743 − 0.927129i \(-0.622269\pi\)
−0.374743 + 0.927129i \(0.622269\pi\)
\(318\) 6.56002e146 2.66023
\(319\) 6.32908e146 2.13592
\(320\) −1.38065e146 −0.387982
\(321\) 1.39288e146 0.326114
\(322\) −3.02088e145 −0.0589610
\(323\) −5.71566e146 −0.930506
\(324\) −1.49268e147 −2.02807
\(325\) −1.04973e147 −1.19097
\(326\) 3.36620e147 3.19088
\(327\) −2.16152e146 −0.171284
\(328\) 2.25607e147 1.49531
\(329\) −8.98882e146 −0.498589
\(330\) −1.42617e147 −0.662377
\(331\) −2.71011e147 −1.05450 −0.527252 − 0.849709i \(-0.676778\pi\)
−0.527252 + 0.849709i \(0.676778\pi\)
\(332\) 6.66342e147 2.17330
\(333\) −6.83007e145 −0.0186826
\(334\) −1.01181e148 −2.32236
\(335\) 4.75346e146 0.0915985
\(336\) −7.25060e147 −1.17362
\(337\) 1.39629e147 0.189945 0.0949723 − 0.995480i \(-0.469724\pi\)
0.0949723 + 0.995480i \(0.469724\pi\)
\(338\) 8.91838e147 1.02014
\(339\) −1.26326e148 −1.21566
\(340\) 1.02330e148 0.828871
\(341\) 3.09851e147 0.211360
\(342\) −3.23079e147 −0.185687
\(343\) −1.65495e148 −0.801825
\(344\) −7.17302e147 −0.293112
\(345\) −3.76974e146 −0.0129985
\(346\) 1.24476e149 3.62354
\(347\) −1.90389e148 −0.468130 −0.234065 − 0.972221i \(-0.575203\pi\)
−0.234065 + 0.972221i \(0.575203\pi\)
\(348\) 1.24323e149 2.58324
\(349\) −2.94631e148 −0.517596 −0.258798 − 0.965931i \(-0.583326\pi\)
−0.258798 + 0.965931i \(0.583326\pi\)
\(350\) −5.39982e148 −0.802415
\(351\) 1.05299e149 1.32421
\(352\) −4.58841e149 −4.88558
\(353\) −1.13521e149 −1.02390 −0.511950 − 0.859015i \(-0.671077\pi\)
−0.511950 + 0.859015i \(0.671077\pi\)
\(354\) 1.63837e149 1.25233
\(355\) −3.30054e148 −0.213908
\(356\) −4.92090e149 −2.70533
\(357\) 1.40030e149 0.653328
\(358\) 6.57043e149 2.60278
\(359\) 3.39665e149 1.14294 0.571472 − 0.820621i \(-0.306372\pi\)
0.571472 + 0.820621i \(0.306372\pi\)
\(360\) 3.50378e148 0.100194
\(361\) −2.74390e149 −0.667108
\(362\) 2.43280e149 0.503101
\(363\) −1.36870e150 −2.40863
\(364\) 9.35593e149 1.40170
\(365\) −3.68653e148 −0.0470420
\(366\) 1.61572e150 1.75680
\(367\) −8.53386e149 −0.791008 −0.395504 − 0.918464i \(-0.629430\pi\)
−0.395504 + 0.918464i \(0.629430\pi\)
\(368\) −2.58237e149 −0.204136
\(369\) −1.31317e149 −0.0885685
\(370\) −7.22553e148 −0.0415977
\(371\) −1.40634e150 −0.691381
\(372\) 6.08644e149 0.255624
\(373\) −4.38587e150 −1.57431 −0.787154 − 0.616757i \(-0.788446\pi\)
−0.787154 + 0.616757i \(0.788446\pi\)
\(374\) 1.88680e151 5.79078
\(375\) −1.37653e150 −0.361375
\(376\) −1.44115e151 −3.23757
\(377\) −7.22398e150 −1.38934
\(378\) 5.41659e150 0.892186
\(379\) 2.24593e150 0.316958 0.158479 − 0.987362i \(-0.449341\pi\)
0.158479 + 0.987362i \(0.449341\pi\)
\(380\) −2.45138e150 −0.296532
\(381\) −4.49188e150 −0.465926
\(382\) −1.46239e151 −1.30123
\(383\) −1.10758e151 −0.845760 −0.422880 − 0.906186i \(-0.638981\pi\)
−0.422880 + 0.906186i \(0.638981\pi\)
\(384\) −1.44712e151 −0.948696
\(385\) 3.05743e150 0.172149
\(386\) 6.51586e151 3.15220
\(387\) 4.17515e149 0.0173612
\(388\) 4.54807e151 1.62619
\(389\) 3.25458e151 1.00102 0.500510 − 0.865731i \(-0.333146\pi\)
0.500510 + 0.865731i \(0.333146\pi\)
\(390\) 1.62782e151 0.430851
\(391\) 4.98731e150 0.113639
\(392\) −1.18090e152 −2.31728
\(393\) 2.46311e151 0.416408
\(394\) −6.01783e151 −0.876822
\(395\) 3.46624e150 0.0435440
\(396\) 7.64937e151 0.828815
\(397\) −7.17826e151 −0.671080 −0.335540 − 0.942026i \(-0.608919\pi\)
−0.335540 + 0.942026i \(0.608919\pi\)
\(398\) 9.81720e151 0.792188
\(399\) −3.35452e151 −0.233731
\(400\) −4.61599e152 −2.77815
\(401\) −1.40881e152 −0.732667 −0.366334 − 0.930484i \(-0.619387\pi\)
−0.366334 + 0.930484i \(0.619387\pi\)
\(402\) 1.72164e152 0.773959
\(403\) −3.53663e151 −0.137481
\(404\) 4.10444e152 1.38021
\(405\) 5.56765e151 0.162014
\(406\) −3.71602e152 −0.936064
\(407\) −9.55543e151 −0.208438
\(408\) 2.24506e153 4.24236
\(409\) −1.78914e152 −0.292976 −0.146488 − 0.989212i \(-0.546797\pi\)
−0.146488 + 0.989212i \(0.546797\pi\)
\(410\) −1.38921e152 −0.197202
\(411\) −6.59493e152 −0.811828
\(412\) −2.52381e153 −2.69506
\(413\) −3.51234e152 −0.325476
\(414\) 2.81908e151 0.0226771
\(415\) −2.48544e152 −0.173616
\(416\) 5.23719e153 3.17789
\(417\) 1.15439e153 0.608685
\(418\) −4.51995e153 −2.07167
\(419\) 4.46951e153 1.78131 0.890655 − 0.454679i \(-0.150246\pi\)
0.890655 + 0.454679i \(0.150246\pi\)
\(420\) 6.00575e152 0.208201
\(421\) 1.94654e152 0.0587165 0.0293583 − 0.999569i \(-0.490654\pi\)
0.0293583 + 0.999569i \(0.490654\pi\)
\(422\) 7.51692e152 0.197361
\(423\) 8.38837e152 0.191764
\(424\) −2.25474e154 −4.48945
\(425\) 8.91482e153 1.54654
\(426\) −1.19541e154 −1.80741
\(427\) −3.46379e153 −0.456584
\(428\) −7.90340e153 −0.908559
\(429\) 2.15272e154 2.15892
\(430\) 4.41689e152 0.0386556
\(431\) 2.52588e153 0.192971 0.0964856 − 0.995334i \(-0.469240\pi\)
0.0964856 + 0.995334i \(0.469240\pi\)
\(432\) 4.63032e154 3.08895
\(433\) −1.50925e154 −0.879469 −0.439735 − 0.898128i \(-0.644927\pi\)
−0.439735 + 0.898128i \(0.644927\pi\)
\(434\) −1.81924e153 −0.0926279
\(435\) −4.63721e153 −0.206365
\(436\) 1.22648e154 0.477199
\(437\) −1.19474e153 −0.0406546
\(438\) −1.33521e154 −0.397480
\(439\) 7.61819e154 1.98462 0.992310 − 0.123776i \(-0.0395004\pi\)
0.992310 + 0.123776i \(0.0395004\pi\)
\(440\) 4.90187e154 1.11784
\(441\) 6.87358e153 0.137254
\(442\) −2.15358e155 −3.76668
\(443\) −1.00250e155 −1.53626 −0.768132 − 0.640292i \(-0.778813\pi\)
−0.768132 + 0.640292i \(0.778813\pi\)
\(444\) −1.87698e154 −0.252091
\(445\) 1.83548e154 0.216117
\(446\) −9.95289e154 −1.02769
\(447\) 1.28344e155 1.16248
\(448\) 1.07202e155 0.852000
\(449\) −3.64359e154 −0.254166 −0.127083 − 0.991892i \(-0.540562\pi\)
−0.127083 + 0.991892i \(0.540562\pi\)
\(450\) 5.03912e154 0.308619
\(451\) −1.83716e155 −0.988141
\(452\) 7.16793e155 3.38685
\(453\) −2.00294e155 −0.831618
\(454\) −2.65060e155 −0.967333
\(455\) −3.48974e154 −0.111976
\(456\) −5.37818e155 −1.51772
\(457\) 3.45472e155 0.857659 0.428830 − 0.903385i \(-0.358926\pi\)
0.428830 + 0.903385i \(0.358926\pi\)
\(458\) 7.73741e155 1.69030
\(459\) −8.94250e155 −1.71956
\(460\) 2.13900e154 0.0362141
\(461\) 8.88912e155 1.32542 0.662712 − 0.748874i \(-0.269405\pi\)
0.662712 + 0.748874i \(0.269405\pi\)
\(462\) 1.10736e156 1.45457
\(463\) 3.73859e155 0.432733 0.216367 − 0.976312i \(-0.430579\pi\)
0.216367 + 0.976312i \(0.430579\pi\)
\(464\) −3.17661e156 −3.24087
\(465\) −2.27023e154 −0.0204207
\(466\) 2.80318e156 2.22369
\(467\) −6.63528e155 −0.464324 −0.232162 − 0.972677i \(-0.574580\pi\)
−0.232162 + 0.972677i \(0.574580\pi\)
\(468\) −8.73096e155 −0.539113
\(469\) −3.69086e155 −0.201148
\(470\) 8.87406e155 0.426970
\(471\) 8.45244e155 0.359136
\(472\) −5.63121e156 −2.11346
\(473\) 5.84113e155 0.193696
\(474\) 1.25542e156 0.367924
\(475\) −2.13560e156 −0.553279
\(476\) −7.94551e156 −1.82018
\(477\) 1.31240e156 0.265914
\(478\) 1.13209e157 2.02931
\(479\) −1.03562e157 −1.64276 −0.821379 − 0.570383i \(-0.806795\pi\)
−0.821379 + 0.570383i \(0.806795\pi\)
\(480\) 3.36185e156 0.472026
\(481\) 1.09065e156 0.135581
\(482\) 6.01461e156 0.662149
\(483\) 2.92705e155 0.0285445
\(484\) 7.76618e157 6.71048
\(485\) −1.69642e156 −0.129910
\(486\) −9.37087e156 −0.636148
\(487\) −2.66333e157 −1.60318 −0.801588 − 0.597877i \(-0.796011\pi\)
−0.801588 + 0.597877i \(0.796011\pi\)
\(488\) −5.55337e157 −2.96481
\(489\) −3.26164e157 −1.54479
\(490\) 7.27156e156 0.305603
\(491\) −3.49113e157 −1.30226 −0.651131 − 0.758965i \(-0.725705\pi\)
−0.651131 + 0.758965i \(0.725705\pi\)
\(492\) −3.60875e157 −1.19508
\(493\) 6.13496e157 1.80413
\(494\) 5.15905e157 1.34754
\(495\) −2.85320e156 −0.0662106
\(496\) −1.55516e157 −0.320699
\(497\) 2.56274e157 0.469737
\(498\) −9.00192e157 −1.46696
\(499\) 4.09712e157 0.593741 0.296870 − 0.954918i \(-0.404057\pi\)
0.296870 + 0.954918i \(0.404057\pi\)
\(500\) 7.81064e157 1.00680
\(501\) 9.80382e157 1.12432
\(502\) −2.31805e158 −2.36567
\(503\) 1.28087e158 1.16353 0.581765 − 0.813357i \(-0.302362\pi\)
0.581765 + 0.813357i \(0.302362\pi\)
\(504\) −2.72054e157 −0.220023
\(505\) −1.53095e157 −0.110259
\(506\) 3.94397e157 0.253004
\(507\) −8.64136e157 −0.493875
\(508\) 2.54875e158 1.29808
\(509\) 1.30517e158 0.592485 0.296243 − 0.955113i \(-0.404266\pi\)
0.296243 + 0.955113i \(0.404266\pi\)
\(510\) −1.38243e158 −0.559483
\(511\) 2.86244e157 0.103303
\(512\) −2.97531e158 −0.957723
\(513\) 2.14223e158 0.615178
\(514\) −3.37150e158 −0.863934
\(515\) 9.41373e157 0.215297
\(516\) 1.14738e158 0.234261
\(517\) 1.17355e159 2.13947
\(518\) 5.61032e157 0.0913476
\(519\) −1.20610e159 −1.75425
\(520\) −5.59497e158 −0.727114
\(521\) −4.93284e158 −0.572915 −0.286457 − 0.958093i \(-0.592478\pi\)
−0.286457 + 0.958093i \(0.592478\pi\)
\(522\) 3.46780e158 0.360022
\(523\) −3.90530e158 −0.362498 −0.181249 − 0.983437i \(-0.558014\pi\)
−0.181249 + 0.983437i \(0.558014\pi\)
\(524\) −1.39760e159 −1.16012
\(525\) 5.23210e158 0.388469
\(526\) −4.79940e159 −3.18802
\(527\) 3.00348e158 0.178527
\(528\) 9.46617e159 5.03605
\(529\) −2.08927e159 −0.995035
\(530\) 1.38839e159 0.592069
\(531\) 3.27772e158 0.125182
\(532\) 1.90340e159 0.651177
\(533\) 2.09692e159 0.642748
\(534\) 6.64787e159 1.82608
\(535\) 2.94795e158 0.0725811
\(536\) −5.91743e159 −1.30615
\(537\) −6.36635e159 −1.26007
\(538\) −1.13088e160 −2.00749
\(539\) 9.61630e159 1.53132
\(540\) −3.83534e159 −0.547985
\(541\) 1.00616e160 1.29011 0.645056 − 0.764136i \(-0.276834\pi\)
0.645056 + 0.764136i \(0.276834\pi\)
\(542\) 7.93241e159 0.912950
\(543\) −2.35724e159 −0.243564
\(544\) −4.44767e160 −4.12665
\(545\) −4.57473e158 −0.0381215
\(546\) −1.26394e160 −0.946140
\(547\) −1.85146e160 −1.24525 −0.622623 − 0.782522i \(-0.713933\pi\)
−0.622623 + 0.782522i \(0.713933\pi\)
\(548\) 3.74205e160 2.26176
\(549\) 3.23241e159 0.175608
\(550\) 7.04984e160 3.44320
\(551\) −1.46967e160 −0.645433
\(552\) 4.69283e159 0.185353
\(553\) −2.69139e159 −0.0956217
\(554\) 3.16967e160 1.01319
\(555\) 7.00110e158 0.0201385
\(556\) −6.55016e160 −1.69581
\(557\) 4.14247e159 0.0965452 0.0482726 − 0.998834i \(-0.484628\pi\)
0.0482726 + 0.998834i \(0.484628\pi\)
\(558\) 1.69772e159 0.0356259
\(559\) −6.66704e159 −0.125992
\(560\) −1.53454e160 −0.261204
\(561\) −1.82819e161 −2.80346
\(562\) 8.03200e160 1.10981
\(563\) 1.22215e161 1.52189 0.760947 − 0.648814i \(-0.224735\pi\)
0.760947 + 0.648814i \(0.224735\pi\)
\(564\) 2.30522e161 2.58753
\(565\) −2.67362e160 −0.270561
\(566\) −1.61801e161 −1.47645
\(567\) −4.32305e160 −0.355780
\(568\) 4.10874e161 3.05022
\(569\) −2.06685e161 −1.38434 −0.692169 − 0.721736i \(-0.743345\pi\)
−0.692169 + 0.721736i \(0.743345\pi\)
\(570\) 3.31169e160 0.200157
\(571\) 8.07364e160 0.440410 0.220205 − 0.975454i \(-0.429327\pi\)
0.220205 + 0.975454i \(0.429327\pi\)
\(572\) −1.22148e162 −6.01477
\(573\) 1.41696e161 0.629960
\(574\) 1.07866e161 0.433051
\(575\) 1.86346e160 0.0675696
\(576\) −1.00041e161 −0.327690
\(577\) 4.65764e160 0.137842 0.0689209 − 0.997622i \(-0.478044\pi\)
0.0689209 + 0.997622i \(0.478044\pi\)
\(578\) 1.12576e162 3.01069
\(579\) −6.31347e161 −1.52606
\(580\) 2.63122e161 0.574935
\(581\) 1.92984e161 0.381257
\(582\) −6.14420e161 −1.09767
\(583\) 1.83608e162 2.96675
\(584\) 4.58924e161 0.670795
\(585\) 3.25662e160 0.0430675
\(586\) −2.35717e162 −2.82085
\(587\) 9.44418e160 0.102291 0.0511453 − 0.998691i \(-0.483713\pi\)
0.0511453 + 0.998691i \(0.483713\pi\)
\(588\) 1.88894e162 1.85202
\(589\) −7.19502e160 −0.0638686
\(590\) 3.46750e161 0.278724
\(591\) 5.83092e161 0.424492
\(592\) 4.79593e161 0.316266
\(593\) 1.25663e162 0.750773 0.375387 − 0.926868i \(-0.377510\pi\)
0.375387 + 0.926868i \(0.377510\pi\)
\(594\) −7.07173e162 −3.82841
\(595\) 2.96366e161 0.145407
\(596\) −7.28241e162 −3.23869
\(597\) −9.51227e161 −0.383518
\(598\) −4.50162e161 −0.164570
\(599\) 3.41335e162 1.13165 0.565825 − 0.824525i \(-0.308558\pi\)
0.565825 + 0.824525i \(0.308558\pi\)
\(600\) 8.38844e162 2.52251
\(601\) 6.02389e161 0.164331 0.0821657 − 0.996619i \(-0.473816\pi\)
0.0821657 + 0.996619i \(0.473816\pi\)
\(602\) −3.42953e161 −0.0848868
\(603\) 3.44431e161 0.0773642
\(604\) 1.13650e163 2.31690
\(605\) −2.89676e162 −0.536073
\(606\) −5.54488e162 −0.931631
\(607\) −9.61191e162 −1.46646 −0.733232 − 0.679979i \(-0.761989\pi\)
−0.733232 + 0.679979i \(0.761989\pi\)
\(608\) 1.06547e163 1.47632
\(609\) 3.60060e162 0.453172
\(610\) 3.41957e162 0.390999
\(611\) −1.33949e163 −1.39164
\(612\) 7.41476e162 0.700066
\(613\) −6.69652e162 −0.574661 −0.287330 − 0.957832i \(-0.592768\pi\)
−0.287330 + 0.957832i \(0.592768\pi\)
\(614\) 6.64523e162 0.518394
\(615\) 1.34606e162 0.0954704
\(616\) −3.80610e163 −2.45476
\(617\) 1.26619e163 0.742709 0.371354 − 0.928491i \(-0.378894\pi\)
0.371354 + 0.928491i \(0.378894\pi\)
\(618\) 3.40953e163 1.81915
\(619\) 1.28549e163 0.623971 0.311986 − 0.950087i \(-0.399006\pi\)
0.311986 + 0.950087i \(0.399006\pi\)
\(620\) 1.28816e162 0.0568925
\(621\) −1.86924e162 −0.0751290
\(622\) −4.96416e162 −0.181597
\(623\) −1.42518e163 −0.474589
\(624\) −1.08046e164 −3.27576
\(625\) 3.18222e163 0.878514
\(626\) 5.65708e163 1.42231
\(627\) 4.37956e163 1.00295
\(628\) −4.79603e163 −1.00056
\(629\) −9.26235e162 −0.176059
\(630\) 1.67521e162 0.0290167
\(631\) −6.30949e163 −0.996040 −0.498020 − 0.867166i \(-0.665939\pi\)
−0.498020 + 0.867166i \(0.665939\pi\)
\(632\) −4.31501e163 −0.620915
\(633\) −7.28344e162 −0.0955476
\(634\) −1.17833e164 −1.40944
\(635\) −9.50678e162 −0.103698
\(636\) 3.60663e164 3.58806
\(637\) −1.09760e164 −0.996065
\(638\) 4.85153e164 4.01670
\(639\) −2.39155e163 −0.180667
\(640\) −3.06273e163 −0.211145
\(641\) 8.56580e163 0.538980 0.269490 − 0.963003i \(-0.413145\pi\)
0.269490 + 0.963003i \(0.413145\pi\)
\(642\) 1.06771e164 0.613272
\(643\) −2.04635e164 −1.07309 −0.536546 − 0.843871i \(-0.680271\pi\)
−0.536546 + 0.843871i \(0.680271\pi\)
\(644\) −1.66085e163 −0.0795254
\(645\) −4.27970e162 −0.0187141
\(646\) −4.38132e164 −1.74986
\(647\) −5.08118e164 −1.85381 −0.926903 − 0.375301i \(-0.877540\pi\)
−0.926903 + 0.375301i \(0.877540\pi\)
\(648\) −6.93099e164 −2.31024
\(649\) 4.58561e164 1.39663
\(650\) −8.04666e164 −2.23967
\(651\) 1.76274e163 0.0448435
\(652\) 1.85070e165 4.30380
\(653\) −3.73815e164 −0.794759 −0.397379 − 0.917654i \(-0.630080\pi\)
−0.397379 + 0.917654i \(0.630080\pi\)
\(654\) −1.65690e164 −0.322106
\(655\) 5.21301e163 0.0926771
\(656\) 9.22082e164 1.49932
\(657\) −2.67123e163 −0.0397317
\(658\) −6.89034e164 −0.937618
\(659\) 2.22639e164 0.277207 0.138604 − 0.990348i \(-0.455739\pi\)
0.138604 + 0.990348i \(0.455739\pi\)
\(660\) −7.84092e164 −0.893402
\(661\) 8.68363e164 0.905557 0.452779 − 0.891623i \(-0.350433\pi\)
0.452779 + 0.891623i \(0.350433\pi\)
\(662\) −2.07742e165 −1.98304
\(663\) 2.08669e165 1.82355
\(664\) 3.09404e165 2.47567
\(665\) −7.09963e163 −0.0520199
\(666\) −5.23556e163 −0.0351334
\(667\) 1.28239e164 0.0788239
\(668\) −5.56282e165 −3.13236
\(669\) 9.64375e164 0.497528
\(670\) 3.64374e164 0.172255
\(671\) 4.52222e165 1.95922
\(672\) −2.61034e165 −1.03656
\(673\) −3.90393e165 −1.42109 −0.710544 − 0.703652i \(-0.751551\pi\)
−0.710544 + 0.703652i \(0.751551\pi\)
\(674\) 1.07032e165 0.357199
\(675\) −3.34128e165 −1.02245
\(676\) 4.90323e165 1.37594
\(677\) 3.77391e165 0.971302 0.485651 − 0.874153i \(-0.338583\pi\)
0.485651 + 0.874153i \(0.338583\pi\)
\(678\) −9.68349e165 −2.28610
\(679\) 1.31720e165 0.285279
\(680\) 4.75152e165 0.944194
\(681\) 2.56827e165 0.468311
\(682\) 2.37515e165 0.397471
\(683\) −1.96070e164 −0.0301163 −0.0150581 − 0.999887i \(-0.504793\pi\)
−0.0150581 + 0.999887i \(0.504793\pi\)
\(684\) −1.77625e165 −0.250451
\(685\) −1.39578e165 −0.180683
\(686\) −1.26860e166 −1.50787
\(687\) −7.49708e165 −0.818320
\(688\) −2.93170e165 −0.293898
\(689\) −2.09569e166 −1.92976
\(690\) −2.88968e164 −0.0244443
\(691\) 1.74760e166 1.35824 0.679119 − 0.734028i \(-0.262362\pi\)
0.679119 + 0.734028i \(0.262362\pi\)
\(692\) 6.84355e166 4.88736
\(693\) 2.21539e165 0.145397
\(694\) −1.45942e166 −0.880339
\(695\) 2.44319e165 0.135471
\(696\) 5.77272e166 2.94266
\(697\) −1.78081e166 −0.834642
\(698\) −2.25848e166 −0.973362
\(699\) −2.71611e166 −1.07654
\(700\) −2.96876e166 −1.08228
\(701\) −1.41238e166 −0.473640 −0.236820 − 0.971554i \(-0.576105\pi\)
−0.236820 + 0.971554i \(0.576105\pi\)
\(702\) 8.07164e166 2.49024
\(703\) 2.21885e165 0.0629858
\(704\) −1.39960e167 −3.65597
\(705\) −8.59843e165 −0.206707
\(706\) −8.70193e166 −1.92549
\(707\) 1.18872e166 0.242127
\(708\) 9.00756e166 1.68912
\(709\) 7.02592e166 1.21310 0.606552 − 0.795044i \(-0.292552\pi\)
0.606552 + 0.795044i \(0.292552\pi\)
\(710\) −2.53002e166 −0.402263
\(711\) 2.51161e165 0.0367773
\(712\) −2.28493e167 −3.08173
\(713\) 6.27815e164 0.00779999
\(714\) 1.07340e167 1.22861
\(715\) 4.55610e166 0.480496
\(716\) 3.61235e167 3.51058
\(717\) −1.09693e167 −0.982443
\(718\) 2.60369e167 2.14936
\(719\) −1.02318e166 −0.0778599 −0.0389300 − 0.999242i \(-0.512395\pi\)
−0.0389300 + 0.999242i \(0.512395\pi\)
\(720\) 1.43204e166 0.100462
\(721\) −7.30937e166 −0.472788
\(722\) −2.10332e167 −1.25453
\(723\) −5.82780e166 −0.320563
\(724\) 1.33753e167 0.678574
\(725\) 2.29227e167 1.07273
\(726\) −1.04917e168 −4.52953
\(727\) −2.82353e167 −1.12468 −0.562340 − 0.826906i \(-0.690099\pi\)
−0.562340 + 0.826906i \(0.690099\pi\)
\(728\) 4.34426e167 1.59673
\(729\) 3.26530e167 1.10755
\(730\) −2.82589e166 −0.0884644
\(731\) 5.66198e166 0.163607
\(732\) 8.88304e167 2.36954
\(733\) −2.21725e167 −0.546050 −0.273025 − 0.962007i \(-0.588024\pi\)
−0.273025 + 0.962007i \(0.588024\pi\)
\(734\) −6.54159e167 −1.48752
\(735\) −7.04570e166 −0.147950
\(736\) −9.29695e166 −0.180297
\(737\) 4.81868e167 0.863137
\(738\) −1.00661e167 −0.166557
\(739\) −5.36783e166 −0.0820539 −0.0410269 − 0.999158i \(-0.513063\pi\)
−0.0410269 + 0.999158i \(0.513063\pi\)
\(740\) −3.97252e166 −0.0561061
\(741\) −4.99880e167 −0.652381
\(742\) −1.07802e168 −1.30017
\(743\) −3.58009e167 −0.399069 −0.199535 − 0.979891i \(-0.563943\pi\)
−0.199535 + 0.979891i \(0.563943\pi\)
\(744\) 2.82613e167 0.291190
\(745\) 2.71632e167 0.258725
\(746\) −3.36197e168 −2.96055
\(747\) −1.80093e167 −0.146636
\(748\) 1.03734e169 7.81049
\(749\) −2.28896e167 −0.159386
\(750\) −1.05518e168 −0.679580
\(751\) 2.54657e168 1.51712 0.758559 − 0.651605i \(-0.225904\pi\)
0.758559 + 0.651605i \(0.225904\pi\)
\(752\) −5.89014e168 −3.24625
\(753\) 2.24605e168 1.14528
\(754\) −5.53751e168 −2.61271
\(755\) −4.23910e167 −0.185088
\(756\) 2.97798e168 1.20336
\(757\) 3.06877e168 1.14777 0.573886 − 0.818935i \(-0.305435\pi\)
0.573886 + 0.818935i \(0.305435\pi\)
\(758\) 1.72160e168 0.596053
\(759\) −3.82146e167 −0.122486
\(760\) −1.13826e168 −0.337789
\(761\) 3.32095e168 0.912558 0.456279 − 0.889837i \(-0.349182\pi\)
0.456279 + 0.889837i \(0.349182\pi\)
\(762\) −3.44323e168 −0.876194
\(763\) 3.55208e167 0.0837139
\(764\) −8.04004e168 −1.75508
\(765\) −2.76568e167 −0.0559254
\(766\) −8.49011e168 −1.59049
\(767\) −5.23399e168 −0.908456
\(768\) −2.53819e167 −0.0408219
\(769\) −1.20333e169 −1.79346 −0.896732 − 0.442574i \(-0.854065\pi\)
−0.896732 + 0.442574i \(0.854065\pi\)
\(770\) 2.34366e168 0.323733
\(771\) 3.26678e168 0.418252
\(772\) 3.58235e169 4.25163
\(773\) −8.53618e168 −0.939211 −0.469605 − 0.882876i \(-0.655604\pi\)
−0.469605 + 0.882876i \(0.655604\pi\)
\(774\) 3.20044e167 0.0326485
\(775\) 1.12222e168 0.106152
\(776\) 2.11182e169 1.85244
\(777\) −5.43606e167 −0.0442237
\(778\) 2.49478e169 1.88246
\(779\) 4.26605e168 0.298596
\(780\) 8.94959e168 0.581124
\(781\) −3.34583e169 −2.01567
\(782\) 3.82300e168 0.213702
\(783\) −2.29939e169 −1.19275
\(784\) −4.82649e169 −2.32349
\(785\) 1.78891e168 0.0799306
\(786\) 1.88808e169 0.783073
\(787\) −1.26089e169 −0.485463 −0.242731 − 0.970094i \(-0.578043\pi\)
−0.242731 + 0.970094i \(0.578043\pi\)
\(788\) −3.30854e169 −1.18264
\(789\) 4.65033e169 1.54340
\(790\) 2.65703e168 0.0818863
\(791\) 2.07595e169 0.594146
\(792\) 3.55185e169 0.944130
\(793\) −5.16164e169 −1.27440
\(794\) −5.50246e169 −1.26200
\(795\) −1.34526e169 −0.286636
\(796\) 5.39739e169 1.06849
\(797\) 6.92863e169 1.27449 0.637244 − 0.770662i \(-0.280074\pi\)
0.637244 + 0.770662i \(0.280074\pi\)
\(798\) −2.57139e169 −0.439540
\(799\) 1.13756e170 1.80712
\(800\) −1.66183e170 −2.45371
\(801\) 1.32997e169 0.182533
\(802\) −1.07992e170 −1.37781
\(803\) −3.73711e169 −0.443279
\(804\) 9.46539e169 1.04390
\(805\) 6.19491e167 0.00635296
\(806\) −2.71099e169 −0.258540
\(807\) 1.09576e170 0.971878
\(808\) 1.90583e170 1.57224
\(809\) −1.63882e170 −1.25760 −0.628800 − 0.777567i \(-0.716454\pi\)
−0.628800 + 0.777567i \(0.716454\pi\)
\(810\) 4.26786e169 0.304675
\(811\) 1.36341e170 0.905541 0.452770 − 0.891627i \(-0.350436\pi\)
0.452770 + 0.891627i \(0.350436\pi\)
\(812\) −2.04303e170 −1.26255
\(813\) −7.68603e169 −0.441982
\(814\) −7.32467e169 −0.391977
\(815\) −6.90306e169 −0.343813
\(816\) 9.17583e170 4.25374
\(817\) −1.35636e169 −0.0585310
\(818\) −1.37146e170 −0.550954
\(819\) −2.52863e169 −0.0945753
\(820\) −7.63770e169 −0.265982
\(821\) 5.60425e170 1.81737 0.908684 − 0.417484i \(-0.137088\pi\)
0.908684 + 0.417484i \(0.137088\pi\)
\(822\) −5.05532e170 −1.52668
\(823\) −4.66099e170 −1.31096 −0.655478 − 0.755215i \(-0.727533\pi\)
−0.655478 + 0.755215i \(0.727533\pi\)
\(824\) −1.17188e171 −3.07003
\(825\) −6.83087e170 −1.66694
\(826\) −2.69237e170 −0.612071
\(827\) 3.75095e170 0.794455 0.397228 − 0.917720i \(-0.369972\pi\)
0.397228 + 0.917720i \(0.369972\pi\)
\(828\) 1.54990e169 0.0305865
\(829\) 6.54959e170 1.20441 0.602205 − 0.798342i \(-0.294289\pi\)
0.602205 + 0.798342i \(0.294289\pi\)
\(830\) −1.90520e170 −0.326492
\(831\) −3.07122e170 −0.490513
\(832\) 1.59749e171 2.37807
\(833\) 9.32136e170 1.29344
\(834\) 8.84891e170 1.14466
\(835\) 2.07492e170 0.250231
\(836\) −2.48502e171 −2.79423
\(837\) −1.12570e170 −0.118028
\(838\) 3.42608e171 3.34983
\(839\) −1.55091e171 −1.41420 −0.707101 − 0.707113i \(-0.749997\pi\)
−0.707101 + 0.707113i \(0.749997\pi\)
\(840\) 2.78866e170 0.237169
\(841\) 3.16917e170 0.251408
\(842\) 1.49211e170 0.110419
\(843\) −7.78253e170 −0.537288
\(844\) 4.13272e170 0.266197
\(845\) −1.82889e170 −0.109918
\(846\) 6.43007e170 0.360620
\(847\) 2.24922e171 1.17720
\(848\) −9.21539e171 −4.50149
\(849\) 1.56775e171 0.714788
\(850\) 6.83362e171 2.90833
\(851\) −1.93610e169 −0.00769218
\(852\) −6.57225e171 −2.43780
\(853\) −3.40773e171 −1.18018 −0.590088 − 0.807339i \(-0.700907\pi\)
−0.590088 + 0.807339i \(0.700907\pi\)
\(854\) −2.65515e171 −0.858626
\(855\) 6.62538e169 0.0200075
\(856\) −3.66980e171 −1.03497
\(857\) 2.76478e170 0.0728254 0.0364127 − 0.999337i \(-0.488407\pi\)
0.0364127 + 0.999337i \(0.488407\pi\)
\(858\) 1.65016e172 4.05993
\(859\) −3.02976e171 −0.696319 −0.348160 − 0.937435i \(-0.613193\pi\)
−0.348160 + 0.937435i \(0.613193\pi\)
\(860\) 2.42836e170 0.0521379
\(861\) −1.04516e171 −0.209651
\(862\) 1.93620e171 0.362891
\(863\) 1.12573e171 0.197152 0.0985762 − 0.995130i \(-0.468571\pi\)
0.0985762 + 0.995130i \(0.468571\pi\)
\(864\) 1.66699e172 2.72822
\(865\) −2.55263e171 −0.390431
\(866\) −1.15691e172 −1.65388
\(867\) −1.09079e172 −1.45755
\(868\) −1.00020e171 −0.124935
\(869\) 3.51380e171 0.410317
\(870\) −3.55463e171 −0.388078
\(871\) −5.50002e171 −0.561438
\(872\) 5.69493e171 0.543593
\(873\) −1.22921e171 −0.109722
\(874\) −9.15824e170 −0.0764528
\(875\) 2.26209e171 0.176620
\(876\) −7.34086e171 −0.536113
\(877\) −7.81347e171 −0.533787 −0.266893 − 0.963726i \(-0.585997\pi\)
−0.266893 + 0.963726i \(0.585997\pi\)
\(878\) 5.83969e172 3.73216
\(879\) 2.28396e172 1.36565
\(880\) 2.00346e172 1.12084
\(881\) −6.21708e171 −0.325458 −0.162729 − 0.986671i \(-0.552030\pi\)
−0.162729 + 0.986671i \(0.552030\pi\)
\(882\) 5.26891e171 0.258112
\(883\) 1.56032e171 0.0715339 0.0357670 − 0.999360i \(-0.488613\pi\)
0.0357670 + 0.999360i \(0.488613\pi\)
\(884\) −1.18402e173 −5.08043
\(885\) −3.35980e171 −0.134937
\(886\) −7.68461e172 −2.88901
\(887\) 2.72249e172 0.958154 0.479077 − 0.877773i \(-0.340972\pi\)
0.479077 + 0.877773i \(0.340972\pi\)
\(888\) −8.71544e171 −0.287165
\(889\) 7.38162e171 0.227719
\(890\) 1.40698e172 0.406418
\(891\) 5.64405e172 1.52667
\(892\) −5.47199e172 −1.38612
\(893\) −2.72509e172 −0.646504
\(894\) 9.83815e172 2.18609
\(895\) −1.34740e172 −0.280446
\(896\) 2.37809e172 0.463670
\(897\) 4.36180e171 0.0796724
\(898\) −2.79298e172 −0.477971
\(899\) 7.72284e171 0.123833
\(900\) 2.77045e172 0.416259
\(901\) 1.77976e173 2.50589
\(902\) −1.40827e173 −1.85824
\(903\) 3.32301e171 0.0410959
\(904\) 3.32830e173 3.85807
\(905\) −4.98895e171 −0.0542085
\(906\) −1.53535e173 −1.56389
\(907\) 1.55157e172 0.148165 0.0740825 − 0.997252i \(-0.476397\pi\)
0.0740825 + 0.997252i \(0.476397\pi\)
\(908\) −1.45727e173 −1.30472
\(909\) −1.10931e172 −0.0931250
\(910\) −2.67504e172 −0.210576
\(911\) −1.04525e173 −0.771607 −0.385804 − 0.922581i \(-0.626076\pi\)
−0.385804 + 0.922581i \(0.626076\pi\)
\(912\) −2.19813e173 −1.52179
\(913\) −2.51954e173 −1.63599
\(914\) 2.64820e173 1.61287
\(915\) −3.31335e172 −0.189293
\(916\) 4.25394e173 2.27985
\(917\) −4.04769e172 −0.203517
\(918\) −6.85483e173 −3.23370
\(919\) −2.51866e173 −1.11484 −0.557419 − 0.830232i \(-0.688208\pi\)
−0.557419 + 0.830232i \(0.688208\pi\)
\(920\) 9.93208e171 0.0412527
\(921\) −6.43882e172 −0.250968
\(922\) 6.81392e173 2.49252
\(923\) 3.81892e173 1.31111
\(924\) 6.08815e173 1.96189
\(925\) −3.46079e172 −0.104685
\(926\) 2.86580e173 0.813773
\(927\) 6.82111e172 0.181840
\(928\) −1.14363e174 −2.86239
\(929\) −5.89909e173 −1.38633 −0.693164 − 0.720780i \(-0.743784\pi\)
−0.693164 + 0.720780i \(0.743784\pi\)
\(930\) −1.74023e172 −0.0384021
\(931\) −2.23299e173 −0.462733
\(932\) 1.54116e174 2.99927
\(933\) 4.80997e172 0.0879157
\(934\) −5.08624e173 −0.873182
\(935\) −3.86926e173 −0.623948
\(936\) −4.05407e173 −0.614121
\(937\) 1.26096e174 1.79447 0.897235 − 0.441553i \(-0.145572\pi\)
0.897235 + 0.441553i \(0.145572\pi\)
\(938\) −2.82921e173 −0.378268
\(939\) −5.48137e173 −0.688576
\(940\) 4.87886e173 0.575890
\(941\) 1.22625e174 1.36015 0.680076 − 0.733141i \(-0.261947\pi\)
0.680076 + 0.733141i \(0.261947\pi\)
\(942\) 6.47918e173 0.675371
\(943\) −3.72242e172 −0.0364662
\(944\) −2.30155e174 −2.11913
\(945\) −1.11078e173 −0.0961318
\(946\) 4.47749e173 0.364253
\(947\) −1.38206e174 −1.05695 −0.528473 − 0.848950i \(-0.677235\pi\)
−0.528473 + 0.848950i \(0.677235\pi\)
\(948\) 6.90219e173 0.496249
\(949\) 4.26552e173 0.288336
\(950\) −1.63704e174 −1.04046
\(951\) 1.14173e174 0.682346
\(952\) −3.68936e174 −2.07343
\(953\) 2.38454e174 1.26029 0.630144 − 0.776478i \(-0.282996\pi\)
0.630144 + 0.776478i \(0.282996\pi\)
\(954\) 1.00601e174 0.500062
\(955\) 2.99892e173 0.140206
\(956\) 6.22412e174 2.73710
\(957\) −4.70084e174 −1.94458
\(958\) −7.93851e174 −3.08928
\(959\) 1.08376e174 0.396776
\(960\) 1.02546e174 0.353226
\(961\) −3.04764e174 −0.987746
\(962\) 8.36034e173 0.254966
\(963\) 2.13606e173 0.0613021
\(964\) 3.30677e174 0.893095
\(965\) −1.33621e174 −0.339645
\(966\) 2.24371e173 0.0536792
\(967\) 1.34517e173 0.0302920 0.0151460 − 0.999885i \(-0.495179\pi\)
0.0151460 + 0.999885i \(0.495179\pi\)
\(968\) 3.60609e175 7.64413
\(969\) 4.24523e174 0.847150
\(970\) −1.30038e174 −0.244300
\(971\) −9.62971e174 −1.70329 −0.851644 − 0.524121i \(-0.824394\pi\)
−0.851644 + 0.524121i \(0.824394\pi\)
\(972\) −5.15200e174 −0.858025
\(973\) −1.89704e174 −0.297491
\(974\) −2.04156e175 −3.01484
\(975\) 7.79672e174 1.08428
\(976\) −2.26973e175 −2.97276
\(977\) 9.80608e174 1.20966 0.604830 − 0.796354i \(-0.293241\pi\)
0.604830 + 0.796354i \(0.293241\pi\)
\(978\) −2.50020e175 −2.90503
\(979\) 1.86067e175 2.03648
\(980\) 3.99783e174 0.412191
\(981\) −3.31481e173 −0.0321974
\(982\) −2.67611e175 −2.44896
\(983\) −5.26545e173 −0.0453999 −0.0226999 − 0.999742i \(-0.507226\pi\)
−0.0226999 + 0.999742i \(0.507226\pi\)
\(984\) −1.67566e175 −1.36136
\(985\) 1.23408e174 0.0944763
\(986\) 4.70273e175 3.39274
\(987\) 6.67632e174 0.453925
\(988\) 2.83639e175 1.81754
\(989\) 1.18352e173 0.00714813
\(990\) −2.18710e174 −0.124512
\(991\) −1.46839e175 −0.788013 −0.394006 − 0.919108i \(-0.628911\pi\)
−0.394006 + 0.919108i \(0.628911\pi\)
\(992\) −5.59885e174 −0.283247
\(993\) 2.01289e175 0.960041
\(994\) 1.96445e175 0.883361
\(995\) −2.01321e174 −0.0853571
\(996\) −4.94916e175 −1.97861
\(997\) −3.96363e175 −1.49426 −0.747131 − 0.664677i \(-0.768569\pi\)
−0.747131 + 0.664677i \(0.768569\pi\)
\(998\) 3.14063e175 1.11655
\(999\) 3.47153e174 0.116397
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 1.118.a.a.1.9 ✓ 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.118.a.a.1.9 ✓ 9 1.1 even 1 trivial