Properties

Label 1.44.a.a.1.3
Level $1$
Weight $44$
Character 1.1
Self dual yes
Analytic conductor $11.711$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 44 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.7110395346\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 11258260111 x - 264759545317170\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4}\cdot 5\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-91450.2\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.62707e6 q^{2} +1.01494e10 q^{3} +4.35955e12 q^{4} +6.19839e14 q^{5} +3.68127e16 q^{6} +2.58688e18 q^{7} -1.60917e19 q^{8} -2.25246e20 q^{9} +O(q^{10})\) \(q+3.62707e6 q^{2} +1.01494e10 q^{3} +4.35955e12 q^{4} +6.19839e14 q^{5} +3.68127e16 q^{6} +2.58688e18 q^{7} -1.60917e19 q^{8} -2.25246e20 q^{9} +2.24820e21 q^{10} +2.74302e22 q^{11} +4.42469e22 q^{12} +6.62621e23 q^{13} +9.38279e24 q^{14} +6.29101e24 q^{15} -9.67126e25 q^{16} +5.82021e25 q^{17} -8.16984e26 q^{18} -1.98043e27 q^{19} +2.70222e27 q^{20} +2.62553e28 q^{21} +9.94913e28 q^{22} -2.61209e29 q^{23} -1.63321e29 q^{24} -7.52667e29 q^{25} +2.40337e30 q^{26} -5.61774e30 q^{27} +1.12776e31 q^{28} +2.27846e31 q^{29} +2.28180e31 q^{30} -1.73342e32 q^{31} -2.09240e32 q^{32} +2.78401e32 q^{33} +2.11103e32 q^{34} +1.60345e33 q^{35} -9.81972e32 q^{36} +5.95565e32 q^{37} -7.18317e33 q^{38} +6.72522e33 q^{39} -9.97424e33 q^{40} -5.56734e34 q^{41} +9.52299e34 q^{42} +1.13992e35 q^{43} +1.19583e35 q^{44} -1.39616e35 q^{45} -9.47425e35 q^{46} +2.48937e35 q^{47} -9.81577e35 q^{48} +4.50812e36 q^{49} -2.72998e36 q^{50} +5.90718e35 q^{51} +2.88873e36 q^{52} +3.93516e36 q^{53} -2.03759e37 q^{54} +1.70023e37 q^{55} -4.16271e37 q^{56} -2.01003e37 q^{57} +8.26415e37 q^{58} +6.06171e37 q^{59} +2.74260e37 q^{60} +3.31999e38 q^{61} -6.28725e38 q^{62} -5.82684e38 q^{63} +9.17655e37 q^{64} +4.10719e38 q^{65} +1.00978e39 q^{66} +2.46431e38 q^{67} +2.53735e38 q^{68} -2.65112e39 q^{69} +5.81582e39 q^{70} -5.22282e39 q^{71} +3.62458e39 q^{72} -1.32868e40 q^{73} +2.16016e39 q^{74} -7.63914e39 q^{75} -8.63380e39 q^{76} +7.09585e40 q^{77} +2.43929e40 q^{78} -1.99325e40 q^{79} -5.99463e40 q^{80} +1.69218e40 q^{81} -2.01932e41 q^{82} -5.56384e39 q^{83} +1.14461e41 q^{84} +3.60760e40 q^{85} +4.13456e41 q^{86} +2.31251e41 q^{87} -4.41397e41 q^{88} -2.64137e41 q^{89} -5.06399e41 q^{90} +1.71412e42 q^{91} -1.13876e42 q^{92} -1.75933e42 q^{93} +9.02914e41 q^{94} -1.22755e42 q^{95} -2.12366e42 q^{96} +3.46950e42 q^{97} +1.63513e43 q^{98} -6.17855e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2209944q^{2} + 24401437812q^{3} + 9822618421824q^{4} + 535205380774170q^{5} - 91793974758443424q^{6} + 301971425665478856q^{7} - 15830863913787348480q^{8} + 477482125171066743231q^{9} + O(q^{10}) \) \( 3q - 2209944q^{2} + 24401437812q^{3} + 9822618421824q^{4} + 535205380774170q^{5} - 91793974758443424q^{6} + 301971425665478856q^{7} - 15830863913787348480q^{8} + \)\(47\!\cdots\!31\)\(q^{9} + \)\(42\!\cdots\!20\)\(q^{10} + \)\(26\!\cdots\!96\)\(q^{11} + \)\(59\!\cdots\!36\)\(q^{12} + \)\(26\!\cdots\!82\)\(q^{13} + \)\(14\!\cdots\!28\)\(q^{14} + \)\(35\!\cdots\!40\)\(q^{15} - \)\(79\!\cdots\!92\)\(q^{16} - \)\(40\!\cdots\!94\)\(q^{17} - \)\(41\!\cdots\!48\)\(q^{18} + \)\(15\!\cdots\!00\)\(q^{19} + \)\(14\!\cdots\!60\)\(q^{20} + \)\(39\!\cdots\!36\)\(q^{21} + \)\(13\!\cdots\!92\)\(q^{22} - \)\(12\!\cdots\!48\)\(q^{23} - \)\(11\!\cdots\!00\)\(q^{24} - \)\(23\!\cdots\!75\)\(q^{25} - \)\(17\!\cdots\!44\)\(q^{26} + \)\(12\!\cdots\!80\)\(q^{27} + \)\(16\!\cdots\!68\)\(q^{28} + \)\(57\!\cdots\!50\)\(q^{29} - \)\(73\!\cdots\!60\)\(q^{30} - \)\(25\!\cdots\!24\)\(q^{31} - \)\(14\!\cdots\!84\)\(q^{32} - \)\(27\!\cdots\!16\)\(q^{33} + \)\(46\!\cdots\!88\)\(q^{34} + \)\(23\!\cdots\!20\)\(q^{35} + \)\(81\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!94\)\(q^{37} - \)\(30\!\cdots\!20\)\(q^{38} - \)\(39\!\cdots\!28\)\(q^{39} - \)\(32\!\cdots\!00\)\(q^{40} + \)\(25\!\cdots\!66\)\(q^{41} + \)\(14\!\cdots\!32\)\(q^{42} + \)\(24\!\cdots\!92\)\(q^{43} - \)\(10\!\cdots\!32\)\(q^{44} + \)\(25\!\cdots\!90\)\(q^{45} - \)\(18\!\cdots\!64\)\(q^{46} + \)\(30\!\cdots\!56\)\(q^{47} - \)\(25\!\cdots\!48\)\(q^{48} + \)\(34\!\cdots\!79\)\(q^{49} + \)\(19\!\cdots\!00\)\(q^{50} + \)\(13\!\cdots\!56\)\(q^{51} - \)\(17\!\cdots\!04\)\(q^{52} + \)\(15\!\cdots\!62\)\(q^{53} - \)\(84\!\cdots\!00\)\(q^{54} + \)\(39\!\cdots\!40\)\(q^{55} - \)\(64\!\cdots\!00\)\(q^{56} + \)\(19\!\cdots\!60\)\(q^{57} - \)\(10\!\cdots\!80\)\(q^{58} + \)\(22\!\cdots\!00\)\(q^{59} + \)\(17\!\cdots\!20\)\(q^{60} - \)\(93\!\cdots\!54\)\(q^{61} - \)\(20\!\cdots\!48\)\(q^{62} - \)\(96\!\cdots\!48\)\(q^{63} - \)\(11\!\cdots\!36\)\(q^{64} - \)\(27\!\cdots\!60\)\(q^{65} + \)\(29\!\cdots\!32\)\(q^{66} - \)\(73\!\cdots\!44\)\(q^{67} + \)\(54\!\cdots\!68\)\(q^{68} + \)\(19\!\cdots\!32\)\(q^{69} + \)\(59\!\cdots\!20\)\(q^{70} - \)\(18\!\cdots\!64\)\(q^{71} - \)\(98\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!98\)\(q^{73} + \)\(16\!\cdots\!08\)\(q^{74} - \)\(21\!\cdots\!00\)\(q^{75} + \)\(77\!\cdots\!00\)\(q^{76} + \)\(59\!\cdots\!92\)\(q^{77} - \)\(19\!\cdots\!96\)\(q^{78} + \)\(15\!\cdots\!00\)\(q^{79} - \)\(10\!\cdots\!80\)\(q^{80} + \)\(73\!\cdots\!63\)\(q^{81} - \)\(32\!\cdots\!68\)\(q^{82} - \)\(89\!\cdots\!28\)\(q^{83} - \)\(34\!\cdots\!12\)\(q^{84} + \)\(43\!\cdots\!20\)\(q^{85} + \)\(25\!\cdots\!96\)\(q^{86} + \)\(17\!\cdots\!40\)\(q^{87} - \)\(25\!\cdots\!60\)\(q^{88} + \)\(20\!\cdots\!50\)\(q^{89} - \)\(23\!\cdots\!60\)\(q^{90} - \)\(11\!\cdots\!84\)\(q^{91} + \)\(68\!\cdots\!56\)\(q^{92} - \)\(49\!\cdots\!96\)\(q^{93} - \)\(13\!\cdots\!32\)\(q^{94} + \)\(31\!\cdots\!00\)\(q^{95} + \)\(10\!\cdots\!36\)\(q^{96} - \)\(38\!\cdots\!94\)\(q^{97} + \)\(24\!\cdots\!08\)\(q^{98} - \)\(14\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.62707e6 1.22296 0.611478 0.791261i \(-0.290575\pi\)
0.611478 + 0.791261i \(0.290575\pi\)
\(3\) 1.01494e10 0.560189 0.280094 0.959972i \(-0.409634\pi\)
0.280094 + 0.959972i \(0.409634\pi\)
\(4\) 4.35955e12 0.495624
\(5\) 6.19839e14 0.581332 0.290666 0.956825i \(-0.406123\pi\)
0.290666 + 0.956825i \(0.406123\pi\)
\(6\) 3.68127e16 0.685087
\(7\) 2.58688e18 1.75052 0.875262 0.483650i \(-0.160689\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(8\) −1.60917e19 −0.616831
\(9\) −2.25246e20 −0.686188
\(10\) 2.24820e21 0.710944
\(11\) 2.74302e22 1.11760 0.558800 0.829303i \(-0.311262\pi\)
0.558800 + 0.829303i \(0.311262\pi\)
\(12\) 4.42469e22 0.277643
\(13\) 6.62621e23 0.743846 0.371923 0.928264i \(-0.378698\pi\)
0.371923 + 0.928264i \(0.378698\pi\)
\(14\) 9.38279e24 2.14081
\(15\) 6.29101e24 0.325656
\(16\) −9.67126e25 −1.24998
\(17\) 5.82021e25 0.204309 0.102154 0.994769i \(-0.467426\pi\)
0.102154 + 0.994769i \(0.467426\pi\)
\(18\) −8.16984e26 −0.839179
\(19\) −1.98043e27 −0.636147 −0.318074 0.948066i \(-0.603036\pi\)
−0.318074 + 0.948066i \(0.603036\pi\)
\(20\) 2.70222e27 0.288122
\(21\) 2.62553e28 0.980624
\(22\) 9.94913e28 1.36678
\(23\) −2.61209e29 −1.37988 −0.689938 0.723868i \(-0.742362\pi\)
−0.689938 + 0.723868i \(0.742362\pi\)
\(24\) −1.63321e29 −0.345542
\(25\) −7.52667e29 −0.662053
\(26\) 2.40337e30 0.909692
\(27\) −5.61774e30 −0.944584
\(28\) 1.12776e31 0.867601
\(29\) 2.27846e31 0.824300 0.412150 0.911116i \(-0.364778\pi\)
0.412150 + 0.911116i \(0.364778\pi\)
\(30\) 2.28180e31 0.398263
\(31\) −1.73342e32 −1.49496 −0.747478 0.664287i \(-0.768735\pi\)
−0.747478 + 0.664287i \(0.768735\pi\)
\(32\) −2.09240e32 −0.911842
\(33\) 2.78401e32 0.626067
\(34\) 2.11103e32 0.249861
\(35\) 1.60345e33 1.01763
\(36\) −9.81972e32 −0.340091
\(37\) 5.95565e32 0.114444 0.0572218 0.998361i \(-0.481776\pi\)
0.0572218 + 0.998361i \(0.481776\pi\)
\(38\) −7.18317e33 −0.777981
\(39\) 6.72522e33 0.416694
\(40\) −9.97424e33 −0.358583
\(41\) −5.56734e34 −1.17705 −0.588525 0.808479i \(-0.700291\pi\)
−0.588525 + 0.808479i \(0.700291\pi\)
\(42\) 9.52299e34 1.19926
\(43\) 1.13992e35 0.865568 0.432784 0.901498i \(-0.357531\pi\)
0.432784 + 0.901498i \(0.357531\pi\)
\(44\) 1.19583e35 0.553909
\(45\) −1.39616e35 −0.398903
\(46\) −9.47425e35 −1.68753
\(47\) 2.48937e35 0.279246 0.139623 0.990205i \(-0.455411\pi\)
0.139623 + 0.990205i \(0.455411\pi\)
\(48\) −9.81577e35 −0.700225
\(49\) 4.50812e36 2.06433
\(50\) −2.72998e36 −0.809663
\(51\) 5.90718e35 0.114451
\(52\) 2.88873e36 0.368668
\(53\) 3.93516e36 0.333451 0.166725 0.986003i \(-0.446681\pi\)
0.166725 + 0.986003i \(0.446681\pi\)
\(54\) −2.03759e37 −1.15519
\(55\) 1.70023e37 0.649696
\(56\) −4.16271e37 −1.07978
\(57\) −2.01003e37 −0.356363
\(58\) 8.26415e37 1.00808
\(59\) 6.06171e37 0.512009 0.256004 0.966676i \(-0.417594\pi\)
0.256004 + 0.966676i \(0.417594\pi\)
\(60\) 2.74260e37 0.161403
\(61\) 3.31999e38 1.36945 0.684724 0.728802i \(-0.259923\pi\)
0.684724 + 0.728802i \(0.259923\pi\)
\(62\) −6.28725e38 −1.82827
\(63\) −5.82684e38 −1.20119
\(64\) 9.17655e37 0.134837
\(65\) 4.10719e38 0.432422
\(66\) 1.00978e39 0.765653
\(67\) 2.46431e38 0.135234 0.0676172 0.997711i \(-0.478460\pi\)
0.0676172 + 0.997711i \(0.478460\pi\)
\(68\) 2.53735e38 0.101260
\(69\) −2.65112e39 −0.772991
\(70\) 5.81582e39 1.24452
\(71\) −5.22282e39 −0.823855 −0.411927 0.911217i \(-0.635144\pi\)
−0.411927 + 0.911217i \(0.635144\pi\)
\(72\) 3.62458e39 0.423262
\(73\) −1.32868e40 −1.15340 −0.576699 0.816957i \(-0.695659\pi\)
−0.576699 + 0.816957i \(0.695659\pi\)
\(74\) 2.16016e39 0.139960
\(75\) −7.63914e39 −0.370875
\(76\) −8.63380e39 −0.315290
\(77\) 7.09585e40 1.95638
\(78\) 2.43929e40 0.509599
\(79\) −1.99325e40 −0.316650 −0.158325 0.987387i \(-0.550609\pi\)
−0.158325 + 0.987387i \(0.550609\pi\)
\(80\) −5.99463e40 −0.726654
\(81\) 1.69218e40 0.157043
\(82\) −2.01932e41 −1.43948
\(83\) −5.56384e39 −0.0305630 −0.0152815 0.999883i \(-0.504864\pi\)
−0.0152815 + 0.999883i \(0.504864\pi\)
\(84\) 1.14461e41 0.486020
\(85\) 3.60760e40 0.118771
\(86\) 4.13456e41 1.05855
\(87\) 2.31251e41 0.461764
\(88\) −4.41397e41 −0.689369
\(89\) −2.64137e41 −0.323552 −0.161776 0.986827i \(-0.551722\pi\)
−0.161776 + 0.986827i \(0.551722\pi\)
\(90\) −5.06399e41 −0.487841
\(91\) 1.71412e42 1.30212
\(92\) −1.13876e42 −0.683899
\(93\) −1.75933e42 −0.837458
\(94\) 9.02914e41 0.341505
\(95\) −1.22755e42 −0.369813
\(96\) −2.12366e42 −0.510804
\(97\) 3.46950e42 0.667844 0.333922 0.942601i \(-0.391628\pi\)
0.333922 + 0.942601i \(0.391628\pi\)
\(98\) 1.63513e43 2.52459
\(99\) −6.17855e42 −0.766884
\(100\) −3.28129e42 −0.328129
\(101\) −1.33544e43 −1.07824 −0.539118 0.842230i \(-0.681242\pi\)
−0.539118 + 0.842230i \(0.681242\pi\)
\(102\) 2.14258e42 0.139969
\(103\) −1.58698e43 −0.840567 −0.420283 0.907393i \(-0.638069\pi\)
−0.420283 + 0.907393i \(0.638069\pi\)
\(104\) −1.06627e43 −0.458827
\(105\) 1.62741e43 0.570068
\(106\) 1.42731e43 0.407796
\(107\) 6.39702e43 1.49357 0.746786 0.665064i \(-0.231596\pi\)
0.746786 + 0.665064i \(0.231596\pi\)
\(108\) −2.44908e43 −0.468158
\(109\) −4.11078e43 −0.644547 −0.322274 0.946647i \(-0.604447\pi\)
−0.322274 + 0.946647i \(0.604447\pi\)
\(110\) 6.16686e43 0.794550
\(111\) 6.04464e42 0.0641101
\(112\) −2.50184e44 −2.18812
\(113\) 2.52895e44 1.82706 0.913532 0.406766i \(-0.133343\pi\)
0.913532 + 0.406766i \(0.133343\pi\)
\(114\) −7.29051e43 −0.435816
\(115\) −1.61908e44 −0.802166
\(116\) 9.93308e43 0.408542
\(117\) −1.49253e44 −0.510419
\(118\) 2.19863e44 0.626164
\(119\) 1.50562e44 0.357647
\(120\) −1.01233e44 −0.200874
\(121\) 1.50015e44 0.249028
\(122\) 1.20418e45 1.67478
\(123\) −5.65053e44 −0.659371
\(124\) −7.55695e44 −0.740935
\(125\) −1.17121e45 −0.966205
\(126\) −2.11344e45 −1.46900
\(127\) 6.08493e44 0.356841 0.178421 0.983954i \(-0.442901\pi\)
0.178421 + 0.983954i \(0.442901\pi\)
\(128\) 2.17333e45 1.07674
\(129\) 1.15695e45 0.484882
\(130\) 1.48971e45 0.528833
\(131\) 1.63203e45 0.491356 0.245678 0.969351i \(-0.420989\pi\)
0.245678 + 0.969351i \(0.420989\pi\)
\(132\) 1.21370e45 0.310293
\(133\) −5.12314e45 −1.11359
\(134\) 8.93823e44 0.165386
\(135\) −3.48210e45 −0.549117
\(136\) −9.36568e44 −0.126024
\(137\) 4.99784e45 0.574500 0.287250 0.957856i \(-0.407259\pi\)
0.287250 + 0.957856i \(0.407259\pi\)
\(138\) −9.61582e45 −0.945335
\(139\) 7.86097e44 0.0661695 0.0330847 0.999453i \(-0.489467\pi\)
0.0330847 + 0.999453i \(0.489467\pi\)
\(140\) 6.99032e45 0.504364
\(141\) 2.52657e45 0.156430
\(142\) −1.89435e46 −1.00754
\(143\) 1.81758e46 0.831322
\(144\) 2.17841e46 0.857722
\(145\) 1.41228e46 0.479192
\(146\) −4.81922e46 −1.41056
\(147\) 4.57548e46 1.15642
\(148\) 2.59639e45 0.0567210
\(149\) −2.89598e46 −0.547382 −0.273691 0.961818i \(-0.588244\pi\)
−0.273691 + 0.961818i \(0.588244\pi\)
\(150\) −2.77077e46 −0.453564
\(151\) −1.31169e47 −1.86135 −0.930675 0.365847i \(-0.880779\pi\)
−0.930675 + 0.365847i \(0.880779\pi\)
\(152\) 3.18684e46 0.392395
\(153\) −1.31098e46 −0.140194
\(154\) 2.57372e47 2.39257
\(155\) −1.07444e47 −0.869066
\(156\) 2.93190e46 0.206524
\(157\) 2.40050e47 1.47387 0.736935 0.675964i \(-0.236272\pi\)
0.736935 + 0.675964i \(0.236272\pi\)
\(158\) −7.22967e46 −0.387250
\(159\) 3.99396e46 0.186795
\(160\) −1.29695e47 −0.530083
\(161\) −6.75716e47 −2.41551
\(162\) 6.13766e46 0.192057
\(163\) 4.76715e47 1.30685 0.653425 0.756991i \(-0.273332\pi\)
0.653425 + 0.756991i \(0.273332\pi\)
\(164\) −2.42711e47 −0.583374
\(165\) 1.72564e47 0.363953
\(166\) −2.01805e46 −0.0373772
\(167\) 6.00740e47 0.977873 0.488936 0.872320i \(-0.337385\pi\)
0.488936 + 0.872320i \(0.337385\pi\)
\(168\) −4.22491e47 −0.604879
\(169\) −3.54465e47 −0.446693
\(170\) 1.30850e47 0.145252
\(171\) 4.46085e47 0.436517
\(172\) 4.96952e47 0.428996
\(173\) 5.43885e47 0.414491 0.207246 0.978289i \(-0.433550\pi\)
0.207246 + 0.978289i \(0.433550\pi\)
\(174\) 8.38764e47 0.564717
\(175\) −1.94706e48 −1.15894
\(176\) −2.65284e48 −1.39698
\(177\) 6.15229e47 0.286822
\(178\) −9.58045e47 −0.395691
\(179\) 1.67643e48 0.613828 0.306914 0.951737i \(-0.400704\pi\)
0.306914 + 0.951737i \(0.400704\pi\)
\(180\) −6.08665e47 −0.197706
\(181\) −3.59480e48 −1.03654 −0.518269 0.855218i \(-0.673423\pi\)
−0.518269 + 0.855218i \(0.673423\pi\)
\(182\) 6.21723e48 1.59244
\(183\) 3.36960e48 0.767150
\(184\) 4.20329e48 0.851150
\(185\) 3.69154e47 0.0665298
\(186\) −6.38120e48 −1.02417
\(187\) 1.59650e48 0.228335
\(188\) 1.08526e48 0.138401
\(189\) −1.45324e49 −1.65352
\(190\) −4.45241e48 −0.452265
\(191\) 5.26498e47 0.0477727 0.0238863 0.999715i \(-0.492396\pi\)
0.0238863 + 0.999715i \(0.492396\pi\)
\(192\) 9.31367e47 0.0755343
\(193\) 1.27068e48 0.0921625 0.0460813 0.998938i \(-0.485327\pi\)
0.0460813 + 0.998938i \(0.485327\pi\)
\(194\) 1.25841e49 0.816745
\(195\) 4.16856e48 0.242238
\(196\) 1.96534e49 1.02313
\(197\) −5.67999e48 −0.265048 −0.132524 0.991180i \(-0.542308\pi\)
−0.132524 + 0.991180i \(0.542308\pi\)
\(198\) −2.24100e49 −0.937866
\(199\) 4.85226e48 0.182223 0.0911115 0.995841i \(-0.470958\pi\)
0.0911115 + 0.995841i \(0.470958\pi\)
\(200\) 1.21117e49 0.408375
\(201\) 2.50113e48 0.0757568
\(202\) −4.84372e49 −1.31864
\(203\) 5.89410e49 1.44296
\(204\) 2.57527e48 0.0567248
\(205\) −3.45086e49 −0.684257
\(206\) −5.75610e49 −1.02798
\(207\) 5.88364e49 0.946855
\(208\) −6.40838e49 −0.929794
\(209\) −5.43237e49 −0.710958
\(210\) 5.90272e49 0.697168
\(211\) 9.39783e49 1.00220 0.501101 0.865389i \(-0.332929\pi\)
0.501101 + 0.865389i \(0.332929\pi\)
\(212\) 1.71555e49 0.165266
\(213\) −5.30086e49 −0.461514
\(214\) 2.32024e50 1.82657
\(215\) 7.06565e49 0.503182
\(216\) 9.03987e49 0.582648
\(217\) −4.48415e50 −2.61695
\(218\) −1.49101e50 −0.788254
\(219\) −1.34853e50 −0.646120
\(220\) 7.41225e49 0.322005
\(221\) 3.85659e49 0.151974
\(222\) 2.19243e49 0.0784039
\(223\) 3.04735e50 0.989391 0.494695 0.869066i \(-0.335280\pi\)
0.494695 + 0.869066i \(0.335280\pi\)
\(224\) −5.41277e50 −1.59620
\(225\) 1.69535e50 0.454293
\(226\) 9.17269e50 2.23442
\(227\) −5.39198e49 −0.119452 −0.0597259 0.998215i \(-0.519023\pi\)
−0.0597259 + 0.998215i \(0.519023\pi\)
\(228\) −8.76281e49 −0.176622
\(229\) −7.10477e49 −0.130343 −0.0651714 0.997874i \(-0.520759\pi\)
−0.0651714 + 0.997874i \(0.520759\pi\)
\(230\) −5.87251e50 −0.981015
\(231\) 7.20188e50 1.09594
\(232\) −3.66642e50 −0.508453
\(233\) −4.35161e50 −0.550171 −0.275086 0.961420i \(-0.588706\pi\)
−0.275086 + 0.961420i \(0.588706\pi\)
\(234\) −5.41351e50 −0.624220
\(235\) 1.54301e50 0.162334
\(236\) 2.64264e50 0.253764
\(237\) −2.02304e50 −0.177384
\(238\) 5.46098e50 0.437387
\(239\) 5.98898e50 0.438327 0.219164 0.975688i \(-0.429667\pi\)
0.219164 + 0.975688i \(0.429667\pi\)
\(240\) −6.08420e50 −0.407063
\(241\) −2.41674e51 −1.47864 −0.739320 0.673354i \(-0.764853\pi\)
−0.739320 + 0.673354i \(0.764853\pi\)
\(242\) 5.44114e50 0.304551
\(243\) 2.01581e51 1.03256
\(244\) 1.44737e51 0.678731
\(245\) 2.79431e51 1.20006
\(246\) −2.04949e51 −0.806382
\(247\) −1.31228e51 −0.473196
\(248\) 2.78937e51 0.922135
\(249\) −5.64698e49 −0.0171210
\(250\) −4.24806e51 −1.18163
\(251\) −1.10770e51 −0.282774 −0.141387 0.989954i \(-0.545156\pi\)
−0.141387 + 0.989954i \(0.545156\pi\)
\(252\) −2.54024e51 −0.595337
\(253\) −7.16502e51 −1.54215
\(254\) 2.20705e51 0.436402
\(255\) 3.66150e50 0.0665343
\(256\) 7.07565e51 1.18197
\(257\) 5.71497e51 0.877914 0.438957 0.898508i \(-0.355348\pi\)
0.438957 + 0.898508i \(0.355348\pi\)
\(258\) 4.19634e51 0.592989
\(259\) 1.54065e51 0.200336
\(260\) 1.79055e51 0.214318
\(261\) −5.13215e51 −0.565625
\(262\) 5.91951e51 0.600908
\(263\) −8.60748e51 −0.805058 −0.402529 0.915407i \(-0.631869\pi\)
−0.402529 + 0.915407i \(0.631869\pi\)
\(264\) −4.47993e51 −0.386177
\(265\) 2.43917e51 0.193845
\(266\) −1.85820e52 −1.36187
\(267\) −2.68084e51 −0.181250
\(268\) 1.07433e51 0.0670254
\(269\) 3.31536e52 1.90922 0.954612 0.297853i \(-0.0962705\pi\)
0.954612 + 0.297853i \(0.0962705\pi\)
\(270\) −1.26298e52 −0.671546
\(271\) −1.65260e52 −0.811575 −0.405787 0.913968i \(-0.633003\pi\)
−0.405787 + 0.913968i \(0.633003\pi\)
\(272\) −5.62888e51 −0.255382
\(273\) 1.73973e52 0.729433
\(274\) 1.81275e52 0.702589
\(275\) −2.06458e52 −0.739910
\(276\) −1.15577e52 −0.383113
\(277\) 3.44644e52 1.05695 0.528476 0.848948i \(-0.322763\pi\)
0.528476 + 0.848948i \(0.322763\pi\)
\(278\) 2.85123e51 0.0809224
\(279\) 3.90447e52 1.02582
\(280\) −2.58021e52 −0.627708
\(281\) −1.84357e52 −0.415406 −0.207703 0.978192i \(-0.566599\pi\)
−0.207703 + 0.978192i \(0.566599\pi\)
\(282\) 9.16406e51 0.191307
\(283\) −2.27219e52 −0.439579 −0.219790 0.975547i \(-0.570537\pi\)
−0.219790 + 0.975547i \(0.570537\pi\)
\(284\) −2.27692e52 −0.408322
\(285\) −1.24589e52 −0.207165
\(286\) 6.59250e52 1.01667
\(287\) −1.44020e53 −2.06045
\(288\) 4.71304e52 0.625696
\(289\) −7.77653e52 −0.958258
\(290\) 5.12245e52 0.586031
\(291\) 3.52135e52 0.374119
\(292\) −5.79245e52 −0.571651
\(293\) 2.15060e53 1.97200 0.985999 0.166752i \(-0.0533278\pi\)
0.985999 + 0.166752i \(0.0533278\pi\)
\(294\) 1.65956e53 1.41425
\(295\) 3.75729e52 0.297647
\(296\) −9.58362e51 −0.0705924
\(297\) −1.54096e53 −1.05567
\(298\) −1.05039e53 −0.669424
\(299\) −1.73083e53 −1.02642
\(300\) −3.33032e52 −0.183814
\(301\) 2.94882e53 1.51520
\(302\) −4.75761e53 −2.27635
\(303\) −1.35539e53 −0.604015
\(304\) 1.91533e53 0.795172
\(305\) 2.05786e53 0.796104
\(306\) −4.75502e52 −0.171452
\(307\) 2.45017e53 0.823609 0.411804 0.911272i \(-0.364899\pi\)
0.411804 + 0.911272i \(0.364899\pi\)
\(308\) 3.09347e53 0.969630
\(309\) −1.61070e53 −0.470876
\(310\) −3.89709e53 −1.06283
\(311\) 2.63881e53 0.671522 0.335761 0.941947i \(-0.391007\pi\)
0.335761 + 0.941947i \(0.391007\pi\)
\(312\) −1.08220e53 −0.257030
\(313\) −1.59181e53 −0.352930 −0.176465 0.984307i \(-0.556466\pi\)
−0.176465 + 0.984307i \(0.556466\pi\)
\(314\) 8.70678e53 1.80248
\(315\) −3.61171e53 −0.698289
\(316\) −8.68969e52 −0.156939
\(317\) −6.66397e53 −1.12450 −0.562249 0.826968i \(-0.690064\pi\)
−0.562249 + 0.826968i \(0.690064\pi\)
\(318\) 1.44864e53 0.228443
\(319\) 6.24987e53 0.921237
\(320\) 5.68799e52 0.0783852
\(321\) 6.49260e53 0.836683
\(322\) −2.45087e54 −2.95406
\(323\) −1.15265e53 −0.129970
\(324\) 7.37715e52 0.0778342
\(325\) −4.98733e53 −0.492466
\(326\) 1.72908e54 1.59822
\(327\) −4.17221e53 −0.361068
\(328\) 8.95878e53 0.726041
\(329\) 6.43971e53 0.488826
\(330\) 6.25901e53 0.445098
\(331\) −1.10752e53 −0.0737991 −0.0368996 0.999319i \(-0.511748\pi\)
−0.0368996 + 0.999319i \(0.511748\pi\)
\(332\) −2.42559e52 −0.0151477
\(333\) −1.34149e53 −0.0785299
\(334\) 2.17893e54 1.19590
\(335\) 1.52748e53 0.0786161
\(336\) −2.53922e54 −1.22576
\(337\) −4.25604e54 −1.92736 −0.963680 0.267061i \(-0.913948\pi\)
−0.963680 + 0.267061i \(0.913948\pi\)
\(338\) −1.28567e54 −0.546286
\(339\) 2.56674e54 1.02350
\(340\) 1.57275e53 0.0588658
\(341\) −4.75482e54 −1.67076
\(342\) 1.61798e54 0.533841
\(343\) 6.01268e54 1.86314
\(344\) −1.83431e54 −0.533909
\(345\) −1.64327e54 −0.449365
\(346\) 1.97271e54 0.506905
\(347\) 4.53734e54 1.09577 0.547883 0.836555i \(-0.315434\pi\)
0.547883 + 0.836555i \(0.315434\pi\)
\(348\) 1.00815e54 0.228861
\(349\) 8.33491e54 1.77891 0.889455 0.457022i \(-0.151084\pi\)
0.889455 + 0.457022i \(0.151084\pi\)
\(350\) −7.06212e54 −1.41733
\(351\) −3.72243e54 −0.702625
\(352\) −5.73949e54 −1.01907
\(353\) −2.09801e53 −0.0350471 −0.0175235 0.999846i \(-0.505578\pi\)
−0.0175235 + 0.999846i \(0.505578\pi\)
\(354\) 2.23148e54 0.350770
\(355\) −3.23731e54 −0.478933
\(356\) −1.15152e54 −0.160360
\(357\) 1.52811e54 0.200350
\(358\) 6.08055e54 0.750685
\(359\) 4.45690e53 0.0518206 0.0259103 0.999664i \(-0.491752\pi\)
0.0259103 + 0.999664i \(0.491752\pi\)
\(360\) 2.24666e54 0.246056
\(361\) −5.76969e54 −0.595317
\(362\) −1.30386e55 −1.26764
\(363\) 1.52256e54 0.139503
\(364\) 7.47279e54 0.645362
\(365\) −8.23569e54 −0.670507
\(366\) 1.22218e55 0.938191
\(367\) −1.43102e55 −1.03591 −0.517957 0.855406i \(-0.673307\pi\)
−0.517957 + 0.855406i \(0.673307\pi\)
\(368\) 2.52622e55 1.72482
\(369\) 1.25402e55 0.807679
\(370\) 1.33895e54 0.0813630
\(371\) 1.01798e55 0.583713
\(372\) −7.66987e54 −0.415064
\(373\) −1.98870e55 −1.01585 −0.507925 0.861401i \(-0.669587\pi\)
−0.507925 + 0.861401i \(0.669587\pi\)
\(374\) 5.79060e54 0.279244
\(375\) −1.18871e55 −0.541257
\(376\) −4.00582e54 −0.172247
\(377\) 1.50976e55 0.613152
\(378\) −5.27100e55 −2.02218
\(379\) −1.23931e55 −0.449197 −0.224599 0.974451i \(-0.572107\pi\)
−0.224599 + 0.974451i \(0.572107\pi\)
\(380\) −5.35157e54 −0.183288
\(381\) 6.17585e54 0.199899
\(382\) 1.90965e54 0.0584239
\(383\) 3.56358e55 1.03066 0.515328 0.856993i \(-0.327670\pi\)
0.515328 + 0.856993i \(0.327670\pi\)
\(384\) 2.20581e55 0.603179
\(385\) 4.39829e55 1.13731
\(386\) 4.60885e54 0.112711
\(387\) −2.56762e55 −0.593943
\(388\) 1.51255e55 0.330999
\(389\) 1.74666e55 0.361653 0.180827 0.983515i \(-0.442123\pi\)
0.180827 + 0.983515i \(0.442123\pi\)
\(390\) 1.51197e55 0.296246
\(391\) −1.52029e55 −0.281921
\(392\) −7.25430e55 −1.27334
\(393\) 1.65642e55 0.275252
\(394\) −2.06017e55 −0.324142
\(395\) −1.23550e55 −0.184079
\(396\) −2.69357e55 −0.380086
\(397\) −3.61165e55 −0.482736 −0.241368 0.970434i \(-0.577596\pi\)
−0.241368 + 0.970434i \(0.577596\pi\)
\(398\) 1.75995e55 0.222851
\(399\) −5.19969e55 −0.623821
\(400\) 7.27924e55 0.827554
\(401\) 1.08123e56 1.16497 0.582483 0.812843i \(-0.302081\pi\)
0.582483 + 0.812843i \(0.302081\pi\)
\(402\) 9.07179e54 0.0926473
\(403\) −1.14860e56 −1.11202
\(404\) −5.82190e55 −0.534399
\(405\) 1.04888e55 0.0912941
\(406\) 2.13783e56 1.76467
\(407\) 1.63365e55 0.127902
\(408\) −9.50563e54 −0.0705972
\(409\) −4.80971e55 −0.338897 −0.169448 0.985539i \(-0.554199\pi\)
−0.169448 + 0.985539i \(0.554199\pi\)
\(410\) −1.25165e56 −0.836817
\(411\) 5.07252e55 0.321829
\(412\) −6.91854e55 −0.416605
\(413\) 1.56809e56 0.896283
\(414\) 2.13404e56 1.15796
\(415\) −3.44869e54 −0.0177672
\(416\) −1.38647e56 −0.678270
\(417\) 7.97843e54 0.0370674
\(418\) −1.97036e56 −0.869471
\(419\) −4.52052e56 −1.89490 −0.947451 0.319900i \(-0.896351\pi\)
−0.947451 + 0.319900i \(0.896351\pi\)
\(420\) 7.09477e55 0.282539
\(421\) −1.37281e56 −0.519453 −0.259727 0.965682i \(-0.583632\pi\)
−0.259727 + 0.965682i \(0.583632\pi\)
\(422\) 3.40866e56 1.22565
\(423\) −5.60722e55 −0.191615
\(424\) −6.33233e55 −0.205682
\(425\) −4.38068e55 −0.135263
\(426\) −1.92266e56 −0.564412
\(427\) 8.58841e56 2.39725
\(428\) 2.78881e56 0.740250
\(429\) 1.84474e56 0.465697
\(430\) 2.56276e56 0.615370
\(431\) −1.97671e56 −0.451524 −0.225762 0.974182i \(-0.572487\pi\)
−0.225762 + 0.974182i \(0.572487\pi\)
\(432\) 5.43306e56 1.18071
\(433\) −5.20903e56 −1.07713 −0.538563 0.842585i \(-0.681033\pi\)
−0.538563 + 0.842585i \(0.681033\pi\)
\(434\) −1.62643e57 −3.20042
\(435\) 1.43338e56 0.268438
\(436\) −1.79212e56 −0.319453
\(437\) 5.17307e56 0.877805
\(438\) −4.89123e56 −0.790177
\(439\) 8.78281e56 1.35097 0.675486 0.737373i \(-0.263934\pi\)
0.675486 + 0.737373i \(0.263934\pi\)
\(440\) −2.73595e56 −0.400752
\(441\) −1.01544e57 −1.41652
\(442\) 1.39881e56 0.185858
\(443\) 7.62338e56 0.964867 0.482433 0.875933i \(-0.339753\pi\)
0.482433 + 0.875933i \(0.339753\pi\)
\(444\) 2.63519e55 0.0317745
\(445\) −1.63723e56 −0.188091
\(446\) 1.10530e57 1.20998
\(447\) −2.93925e56 −0.306637
\(448\) 2.37386e56 0.236036
\(449\) 3.22300e56 0.305467 0.152734 0.988267i \(-0.451192\pi\)
0.152734 + 0.988267i \(0.451192\pi\)
\(450\) 6.14917e56 0.555581
\(451\) −1.52713e57 −1.31547
\(452\) 1.10251e57 0.905537
\(453\) −1.33129e57 −1.04271
\(454\) −1.95571e56 −0.146084
\(455\) 1.06248e57 0.756964
\(456\) 3.23446e56 0.219815
\(457\) −3.49540e56 −0.226620 −0.113310 0.993560i \(-0.536145\pi\)
−0.113310 + 0.993560i \(0.536145\pi\)
\(458\) −2.57695e56 −0.159404
\(459\) −3.26964e56 −0.192987
\(460\) −7.05846e56 −0.397572
\(461\) −1.01829e57 −0.547397 −0.273699 0.961816i \(-0.588247\pi\)
−0.273699 + 0.961816i \(0.588247\pi\)
\(462\) 2.61217e57 1.34029
\(463\) −1.12662e57 −0.551807 −0.275903 0.961185i \(-0.588977\pi\)
−0.275903 + 0.961185i \(0.588977\pi\)
\(464\) −2.20356e57 −1.03036
\(465\) −1.09050e57 −0.486841
\(466\) −1.57836e57 −0.672835
\(467\) 4.32781e57 1.76180 0.880898 0.473307i \(-0.156940\pi\)
0.880898 + 0.473307i \(0.156940\pi\)
\(468\) −6.50675e56 −0.252976
\(469\) 6.37487e56 0.236731
\(470\) 5.59662e56 0.198528
\(471\) 2.43637e57 0.825645
\(472\) −9.75430e56 −0.315823
\(473\) 3.12681e57 0.967358
\(474\) −7.33770e56 −0.216933
\(475\) 1.49061e57 0.421163
\(476\) 6.56381e56 0.177258
\(477\) −8.86380e56 −0.228810
\(478\) 2.17225e57 0.536055
\(479\) −5.08788e57 −1.20039 −0.600196 0.799853i \(-0.704911\pi\)
−0.600196 + 0.799853i \(0.704911\pi\)
\(480\) −1.31633e57 −0.296947
\(481\) 3.94634e56 0.0851285
\(482\) −8.76567e57 −1.80831
\(483\) −6.85813e57 −1.35314
\(484\) 6.53997e56 0.123424
\(485\) 2.15054e57 0.388239
\(486\) 7.31148e57 1.26277
\(487\) 1.44042e57 0.238022 0.119011 0.992893i \(-0.462028\pi\)
0.119011 + 0.992893i \(0.462028\pi\)
\(488\) −5.34242e57 −0.844718
\(489\) 4.83839e57 0.732083
\(490\) 1.01352e58 1.46762
\(491\) 5.96607e57 0.826868 0.413434 0.910534i \(-0.364329\pi\)
0.413434 + 0.910534i \(0.364329\pi\)
\(492\) −2.46338e57 −0.326800
\(493\) 1.32611e57 0.168412
\(494\) −4.75972e57 −0.578698
\(495\) −3.82971e57 −0.445814
\(496\) 1.67644e58 1.86867
\(497\) −1.35108e58 −1.44218
\(498\) −2.04820e56 −0.0209383
\(499\) −1.54904e58 −1.51670 −0.758350 0.651848i \(-0.773994\pi\)
−0.758350 + 0.651848i \(0.773994\pi\)
\(500\) −5.10595e57 −0.478874
\(501\) 6.09716e57 0.547793
\(502\) −4.01772e57 −0.345820
\(503\) 2.17882e58 1.79684 0.898420 0.439137i \(-0.144716\pi\)
0.898420 + 0.439137i \(0.144716\pi\)
\(504\) 9.37635e57 0.740930
\(505\) −8.27756e57 −0.626813
\(506\) −2.59880e58 −1.88598
\(507\) −3.59761e57 −0.250232
\(508\) 2.65275e57 0.176859
\(509\) 2.00199e58 1.27947 0.639734 0.768596i \(-0.279044\pi\)
0.639734 + 0.768596i \(0.279044\pi\)
\(510\) 1.32805e57 0.0813686
\(511\) −3.43713e58 −2.01905
\(512\) 6.54706e57 0.368759
\(513\) 1.11256e58 0.600895
\(514\) 2.07286e58 1.07365
\(515\) −9.83675e57 −0.488648
\(516\) 5.04378e57 0.240319
\(517\) 6.82840e57 0.312085
\(518\) 5.58806e57 0.245003
\(519\) 5.52012e57 0.232193
\(520\) −6.60914e57 −0.266731
\(521\) 4.15960e58 1.61080 0.805398 0.592735i \(-0.201952\pi\)
0.805398 + 0.592735i \(0.201952\pi\)
\(522\) −1.86147e58 −0.691735
\(523\) −1.32108e58 −0.471131 −0.235565 0.971858i \(-0.575694\pi\)
−0.235565 + 0.971858i \(0.575694\pi\)
\(524\) 7.11494e57 0.243528
\(525\) −1.97615e58 −0.649225
\(526\) −3.12199e58 −0.984552
\(527\) −1.00889e58 −0.305433
\(528\) −2.69249e58 −0.782571
\(529\) 3.23962e58 0.904059
\(530\) 8.84704e57 0.237065
\(531\) −1.36538e58 −0.351334
\(532\) −2.23346e58 −0.551922
\(533\) −3.68904e58 −0.875545
\(534\) −9.72360e57 −0.221661
\(535\) 3.96512e58 0.868261
\(536\) −3.96548e57 −0.0834167
\(537\) 1.70149e58 0.343859
\(538\) 1.20250e59 2.33490
\(539\) 1.23659e59 2.30710
\(540\) −1.51804e58 −0.272155
\(541\) −6.56868e58 −1.13171 −0.565857 0.824503i \(-0.691455\pi\)
−0.565857 + 0.824503i \(0.691455\pi\)
\(542\) −5.99410e58 −0.992521
\(543\) −3.64851e58 −0.580657
\(544\) −1.21782e58 −0.186297
\(545\) −2.54803e58 −0.374696
\(546\) 6.31013e58 0.892065
\(547\) −3.35920e58 −0.456571 −0.228286 0.973594i \(-0.573312\pi\)
−0.228286 + 0.973594i \(0.573312\pi\)
\(548\) 2.17883e58 0.284736
\(549\) −7.47815e58 −0.939699
\(550\) −7.48838e58 −0.904878
\(551\) −4.51234e58 −0.524376
\(552\) 4.26610e58 0.476805
\(553\) −5.15630e58 −0.554304
\(554\) 1.25005e59 1.29261
\(555\) 3.74671e57 0.0372692
\(556\) 3.42703e57 0.0327952
\(557\) −7.51741e57 −0.0692120 −0.0346060 0.999401i \(-0.511018\pi\)
−0.0346060 + 0.999401i \(0.511018\pi\)
\(558\) 1.41618e59 1.25454
\(559\) 7.55333e58 0.643850
\(560\) −1.55074e59 −1.27202
\(561\) 1.62035e58 0.127911
\(562\) −6.68675e58 −0.508024
\(563\) −3.08360e58 −0.225490 −0.112745 0.993624i \(-0.535964\pi\)
−0.112745 + 0.993624i \(0.535964\pi\)
\(564\) 1.10147e58 0.0775305
\(565\) 1.56754e59 1.06213
\(566\) −8.24141e58 −0.537586
\(567\) 4.37746e58 0.274907
\(568\) 8.40438e58 0.508179
\(569\) −1.05318e59 −0.613179 −0.306590 0.951842i \(-0.599188\pi\)
−0.306590 + 0.951842i \(0.599188\pi\)
\(570\) −4.51894e58 −0.253354
\(571\) 2.73679e59 1.47763 0.738814 0.673910i \(-0.235386\pi\)
0.738814 + 0.673910i \(0.235386\pi\)
\(572\) 7.92384e58 0.412023
\(573\) 5.34365e57 0.0267617
\(574\) −5.22372e59 −2.51985
\(575\) 1.96604e59 0.913552
\(576\) −2.06698e58 −0.0925238
\(577\) −2.69178e59 −1.16081 −0.580403 0.814330i \(-0.697105\pi\)
−0.580403 + 0.814330i \(0.697105\pi\)
\(578\) −2.82060e59 −1.17191
\(579\) 1.28967e58 0.0516284
\(580\) 6.15691e58 0.237499
\(581\) −1.43930e58 −0.0535012
\(582\) 1.27722e59 0.457531
\(583\) 1.07942e59 0.372664
\(584\) 2.13807e59 0.711451
\(585\) −9.25128e58 −0.296723
\(586\) 7.80039e59 2.41167
\(587\) −5.77693e59 −1.72178 −0.860890 0.508790i \(-0.830093\pi\)
−0.860890 + 0.508790i \(0.830093\pi\)
\(588\) 1.99470e59 0.573147
\(589\) 3.43293e59 0.951012
\(590\) 1.36280e59 0.364009
\(591\) −5.76487e58 −0.148477
\(592\) −5.75986e58 −0.143052
\(593\) −2.43327e58 −0.0582793 −0.0291396 0.999575i \(-0.509277\pi\)
−0.0291396 + 0.999575i \(0.509277\pi\)
\(594\) −5.58916e59 −1.29103
\(595\) 9.33241e58 0.207912
\(596\) −1.26252e59 −0.271295
\(597\) 4.92477e58 0.102079
\(598\) −6.27784e59 −1.25526
\(599\) −3.96268e59 −0.764386 −0.382193 0.924083i \(-0.624831\pi\)
−0.382193 + 0.924083i \(0.624831\pi\)
\(600\) 1.22926e59 0.228767
\(601\) −3.77157e59 −0.677207 −0.338603 0.940929i \(-0.609954\pi\)
−0.338603 + 0.940929i \(0.609954\pi\)
\(602\) 1.06956e60 1.85302
\(603\) −5.55077e58 −0.0927963
\(604\) −5.71839e59 −0.922529
\(605\) 9.29851e58 0.144768
\(606\) −4.91610e59 −0.738685
\(607\) 7.51902e59 1.09045 0.545223 0.838291i \(-0.316445\pi\)
0.545223 + 0.838291i \(0.316445\pi\)
\(608\) 4.14385e59 0.580066
\(609\) 5.98218e59 0.808328
\(610\) 7.46401e59 0.973601
\(611\) 1.64951e59 0.207716
\(612\) −5.71528e58 −0.0694836
\(613\) −1.39353e60 −1.63575 −0.817876 0.575395i \(-0.804848\pi\)
−0.817876 + 0.575395i \(0.804848\pi\)
\(614\) 8.88693e59 1.00724
\(615\) −3.50242e59 −0.383313
\(616\) −1.14184e60 −1.20676
\(617\) 1.43273e60 1.46229 0.731146 0.682221i \(-0.238986\pi\)
0.731146 + 0.682221i \(0.238986\pi\)
\(618\) −5.84212e59 −0.575861
\(619\) −1.09264e60 −1.04022 −0.520112 0.854098i \(-0.674110\pi\)
−0.520112 + 0.854098i \(0.674110\pi\)
\(620\) −4.68410e59 −0.430729
\(621\) 1.46741e60 1.30341
\(622\) 9.57116e59 0.821242
\(623\) −6.83291e59 −0.566386
\(624\) −6.50414e59 −0.520860
\(625\) 1.29722e59 0.100368
\(626\) −5.77361e59 −0.431618
\(627\) −5.51354e59 −0.398271
\(628\) 1.04651e60 0.730485
\(629\) 3.46631e58 0.0233818
\(630\) −1.30999e60 −0.853978
\(631\) −5.43638e59 −0.342514 −0.171257 0.985226i \(-0.554783\pi\)
−0.171257 + 0.985226i \(0.554783\pi\)
\(632\) 3.20747e59 0.195320
\(633\) 9.53826e59 0.561422
\(634\) −2.41707e60 −1.37521
\(635\) 3.77168e59 0.207443
\(636\) 1.74119e59 0.0925801
\(637\) 2.98717e60 1.53555
\(638\) 2.26687e60 1.12663
\(639\) 1.17642e60 0.565320
\(640\) 1.34712e60 0.625945
\(641\) −3.34810e60 −1.50436 −0.752179 0.658959i \(-0.770997\pi\)
−0.752179 + 0.658959i \(0.770997\pi\)
\(642\) 2.35491e60 1.02323
\(643\) 7.77539e59 0.326728 0.163364 0.986566i \(-0.447766\pi\)
0.163364 + 0.986566i \(0.447766\pi\)
\(644\) −2.94582e60 −1.19718
\(645\) 7.17123e59 0.281877
\(646\) −4.18076e59 −0.158948
\(647\) −3.09018e60 −1.13643 −0.568214 0.822881i \(-0.692365\pi\)
−0.568214 + 0.822881i \(0.692365\pi\)
\(648\) −2.72300e59 −0.0968689
\(649\) 1.66274e60 0.572220
\(650\) −1.80894e60 −0.602265
\(651\) −4.55116e60 −1.46599
\(652\) 2.07826e60 0.647706
\(653\) −6.18136e60 −1.86402 −0.932010 0.362433i \(-0.881946\pi\)
−0.932010 + 0.362433i \(0.881946\pi\)
\(654\) −1.51329e60 −0.441571
\(655\) 1.01160e60 0.285641
\(656\) 5.38432e60 1.47129
\(657\) 2.99280e60 0.791448
\(658\) 2.33573e60 0.597813
\(659\) 6.32794e60 1.56757 0.783784 0.621034i \(-0.213287\pi\)
0.783784 + 0.621034i \(0.213287\pi\)
\(660\) 7.52300e59 0.180383
\(661\) −1.18734e60 −0.275577 −0.137789 0.990462i \(-0.543999\pi\)
−0.137789 + 0.990462i \(0.543999\pi\)
\(662\) −4.01707e59 −0.0902531
\(663\) 3.91422e59 0.0851343
\(664\) 8.95314e58 0.0188522
\(665\) −3.17552e60 −0.647366
\(666\) −4.86567e59 −0.0960387
\(667\) −5.95156e60 −1.13743
\(668\) 2.61896e60 0.484657
\(669\) 3.09289e60 0.554246
\(670\) 5.54027e59 0.0961441
\(671\) 9.10680e60 1.53049
\(672\) −5.49365e60 −0.894174
\(673\) −5.49460e60 −0.866188 −0.433094 0.901349i \(-0.642578\pi\)
−0.433094 + 0.901349i \(0.642578\pi\)
\(674\) −1.54370e61 −2.35708
\(675\) 4.22829e60 0.625365
\(676\) −1.54531e60 −0.221391
\(677\) −5.42453e59 −0.0752845 −0.0376423 0.999291i \(-0.511985\pi\)
−0.0376423 + 0.999291i \(0.511985\pi\)
\(678\) 9.30975e60 1.25170
\(679\) 8.97518e60 1.16908
\(680\) −5.80522e59 −0.0732617
\(681\) −5.47255e59 −0.0669156
\(682\) −1.72461e61 −2.04327
\(683\) −2.55176e60 −0.292951 −0.146475 0.989214i \(-0.546793\pi\)
−0.146475 + 0.989214i \(0.546793\pi\)
\(684\) 1.94473e60 0.216348
\(685\) 3.09786e60 0.333975
\(686\) 2.18084e61 2.27854
\(687\) −7.21094e59 −0.0730166
\(688\) −1.10244e61 −1.08194
\(689\) 2.60752e60 0.248036
\(690\) −5.96026e60 −0.549553
\(691\) 1.08476e61 0.969518 0.484759 0.874648i \(-0.338907\pi\)
0.484759 + 0.874648i \(0.338907\pi\)
\(692\) 2.37109e60 0.205432
\(693\) −1.59831e61 −1.34245
\(694\) 1.64573e61 1.34007
\(695\) 4.87254e59 0.0384664
\(696\) −3.72121e60 −0.284830
\(697\) −3.24031e60 −0.240482
\(698\) 3.02313e61 2.17553
\(699\) −4.41663e60 −0.308200
\(700\) −8.48830e60 −0.574398
\(701\) −2.44763e61 −1.60623 −0.803116 0.595822i \(-0.796826\pi\)
−0.803116 + 0.595822i \(0.796826\pi\)
\(702\) −1.35015e61 −0.859281
\(703\) −1.17948e60 −0.0728030
\(704\) 2.51714e60 0.150694
\(705\) 1.56607e60 0.0909379
\(706\) −7.60964e59 −0.0428610
\(707\) −3.45461e61 −1.88748
\(708\) 2.68212e60 0.142156
\(709\) 1.87862e61 0.965929 0.482965 0.875640i \(-0.339560\pi\)
0.482965 + 0.875640i \(0.339560\pi\)
\(710\) −1.17420e61 −0.585715
\(711\) 4.48973e60 0.217282
\(712\) 4.25041e60 0.199577
\(713\) 4.52786e61 2.06285
\(714\) 5.54258e60 0.245019
\(715\) 1.12661e61 0.483274
\(716\) 7.30850e60 0.304228
\(717\) 6.07847e60 0.245546
\(718\) 1.61655e60 0.0633744
\(719\) 2.37257e61 0.902710 0.451355 0.892345i \(-0.350941\pi\)
0.451355 + 0.892345i \(0.350941\pi\)
\(720\) 1.35027e61 0.498621
\(721\) −4.10533e61 −1.47143
\(722\) −2.09271e61 −0.728047
\(723\) −2.45285e61 −0.828318
\(724\) −1.56717e61 −0.513732
\(725\) −1.71493e61 −0.545730
\(726\) 5.52245e60 0.170606
\(727\) 1.81553e61 0.544518 0.272259 0.962224i \(-0.412229\pi\)
0.272259 + 0.962224i \(0.412229\pi\)
\(728\) −2.75830e61 −0.803188
\(729\) 1.49046e61 0.421384
\(730\) −2.98714e61 −0.820001
\(731\) 6.63455e60 0.176843
\(732\) 1.46899e61 0.380217
\(733\) 1.31563e61 0.330672 0.165336 0.986237i \(-0.447129\pi\)
0.165336 + 0.986237i \(0.447129\pi\)
\(734\) −5.19040e61 −1.26688
\(735\) 2.83606e61 0.672261
\(736\) 5.46554e61 1.25823
\(737\) 6.75965e60 0.151138
\(738\) 4.54843e61 0.987756
\(739\) −5.98405e61 −1.26223 −0.631117 0.775688i \(-0.717403\pi\)
−0.631117 + 0.775688i \(0.717403\pi\)
\(740\) 1.60935e60 0.0329737
\(741\) −1.33189e61 −0.265079
\(742\) 3.69228e61 0.713856
\(743\) −5.00463e60 −0.0939967 −0.0469983 0.998895i \(-0.514966\pi\)
−0.0469983 + 0.998895i \(0.514966\pi\)
\(744\) 2.83105e61 0.516570
\(745\) −1.79504e61 −0.318210
\(746\) −7.21316e61 −1.24234
\(747\) 1.25323e60 0.0209720
\(748\) 6.96000e60 0.113168
\(749\) 1.65483e62 2.61453
\(750\) −4.31153e61 −0.661934
\(751\) −3.12943e61 −0.466881 −0.233441 0.972371i \(-0.574998\pi\)
−0.233441 + 0.972371i \(0.574998\pi\)
\(752\) −2.40754e61 −0.349052
\(753\) −1.12426e61 −0.158407
\(754\) 5.47600e61 0.749859
\(755\) −8.13039e61 −1.08206
\(756\) −6.33547e61 −0.819522
\(757\) 1.08176e62 1.36010 0.680048 0.733167i \(-0.261959\pi\)
0.680048 + 0.733167i \(0.261959\pi\)
\(758\) −4.49507e61 −0.549349
\(759\) −7.27209e61 −0.863895
\(760\) 1.97533e61 0.228112
\(761\) −6.63216e61 −0.744535 −0.372268 0.928125i \(-0.621420\pi\)
−0.372268 + 0.928125i \(0.621420\pi\)
\(762\) 2.24002e61 0.244467
\(763\) −1.06341e62 −1.12830
\(764\) 2.29530e60 0.0236773
\(765\) −8.12597e60 −0.0814994
\(766\) 1.29254e62 1.26045
\(767\) 4.01662e61 0.380856
\(768\) 7.18138e61 0.662128
\(769\) −6.68870e61 −0.599688 −0.299844 0.953988i \(-0.596935\pi\)
−0.299844 + 0.953988i \(0.596935\pi\)
\(770\) 1.59529e62 1.39088
\(771\) 5.80037e61 0.491797
\(772\) 5.53960e60 0.0456779
\(773\) −4.99608e61 −0.400655 −0.200327 0.979729i \(-0.564201\pi\)
−0.200327 + 0.979729i \(0.564201\pi\)
\(774\) −9.31293e61 −0.726366
\(775\) 1.30469e62 0.989740
\(776\) −5.58301e61 −0.411947
\(777\) 1.56367e61 0.112226
\(778\) 6.33526e61 0.442286
\(779\) 1.10258e62 0.748778
\(780\) 1.81730e61 0.120059
\(781\) −1.43263e62 −0.920740
\(782\) −5.51421e61 −0.344777
\(783\) −1.27998e62 −0.778620
\(784\) −4.35992e62 −2.58037
\(785\) 1.48792e62 0.856807
\(786\) 6.00796e61 0.336622
\(787\) −2.83453e62 −1.54534 −0.772671 0.634806i \(-0.781080\pi\)
−0.772671 + 0.634806i \(0.781080\pi\)
\(788\) −2.47622e61 −0.131364
\(789\) −8.73610e61 −0.450985
\(790\) −4.48124e61 −0.225121
\(791\) 6.54209e62 3.19832
\(792\) 9.94230e61 0.473037
\(793\) 2.19990e62 1.01866
\(794\) −1.30997e62 −0.590365
\(795\) 2.47562e61 0.108590
\(796\) 2.11537e61 0.0903140
\(797\) 4.08442e61 0.169737 0.0848685 0.996392i \(-0.472953\pi\)
0.0848685 + 0.996392i \(0.472953\pi\)
\(798\) −1.88596e62 −0.762906
\(799\) 1.44887e61 0.0570523
\(800\) 1.57488e62 0.603688
\(801\) 5.94959e61 0.222018
\(802\) 3.92169e62 1.42470
\(803\) −3.64460e62 −1.28904
\(804\) 1.09038e61 0.0375469
\(805\) −4.18836e62 −1.40421
\(806\) −4.16607e62 −1.35995
\(807\) 3.36490e62 1.06953
\(808\) 2.14894e62 0.665089
\(809\) −2.70018e62 −0.813765 −0.406882 0.913481i \(-0.633384\pi\)
−0.406882 + 0.913481i \(0.633384\pi\)
\(810\) 3.80436e61 0.111649
\(811\) 4.07164e61 0.116365 0.0581823 0.998306i \(-0.481470\pi\)
0.0581823 + 0.998306i \(0.481470\pi\)
\(812\) 2.56957e62 0.715163
\(813\) −1.67730e62 −0.454635
\(814\) 5.92535e61 0.156419
\(815\) 2.95487e62 0.759713
\(816\) −5.71299e61 −0.143062
\(817\) −2.25753e62 −0.550629
\(818\) −1.74451e62 −0.414456
\(819\) −3.86099e62 −0.893500
\(820\) −1.50442e62 −0.339134
\(821\) −4.97093e62 −1.09159 −0.545795 0.837919i \(-0.683772\pi\)
−0.545795 + 0.837919i \(0.683772\pi\)
\(822\) 1.83984e62 0.393582
\(823\) 7.87730e62 1.64165 0.820826 0.571179i \(-0.193514\pi\)
0.820826 + 0.571179i \(0.193514\pi\)
\(824\) 2.55372e62 0.518487
\(825\) −2.09543e62 −0.414489
\(826\) 5.68758e62 1.09612
\(827\) −7.36002e62 −1.38201 −0.691004 0.722851i \(-0.742831\pi\)
−0.691004 + 0.722851i \(0.742831\pi\)
\(828\) 2.56500e62 0.469284
\(829\) 3.97702e62 0.708983 0.354491 0.935059i \(-0.384654\pi\)
0.354491 + 0.935059i \(0.384654\pi\)
\(830\) −1.25086e61 −0.0217286
\(831\) 3.49794e62 0.592093
\(832\) 6.08058e61 0.100298
\(833\) 2.62382e62 0.421761
\(834\) 2.89383e61 0.0453318
\(835\) 3.72362e62 0.568468
\(836\) −2.36827e62 −0.352367
\(837\) 9.73792e62 1.41211
\(838\) −1.63962e63 −2.31738
\(839\) −6.29957e62 −0.867818 −0.433909 0.900957i \(-0.642866\pi\)
−0.433909 + 0.900957i \(0.642866\pi\)
\(840\) −2.61877e62 −0.351635
\(841\) −2.44896e62 −0.320530
\(842\) −4.97929e62 −0.635269
\(843\) −1.87111e62 −0.232706
\(844\) 4.09703e62 0.496715
\(845\) −2.19711e62 −0.259677
\(846\) −2.03378e62 −0.234337
\(847\) 3.88070e62 0.435930
\(848\) −3.80580e62 −0.416807
\(849\) −2.30615e62 −0.246247
\(850\) −1.58890e62 −0.165421
\(851\) −1.55567e62 −0.157918
\(852\) −2.31094e62 −0.228737
\(853\) 1.37710e63 1.32911 0.664557 0.747238i \(-0.268620\pi\)
0.664557 + 0.747238i \(0.268620\pi\)
\(854\) 3.11508e63 2.93173
\(855\) 2.76501e62 0.253761
\(856\) −1.02939e63 −0.921281
\(857\) 6.27513e62 0.547690 0.273845 0.961774i \(-0.411704\pi\)
0.273845 + 0.961774i \(0.411704\pi\)
\(858\) 6.69101e62 0.569528
\(859\) −1.57268e63 −1.30553 −0.652767 0.757559i \(-0.726392\pi\)
−0.652767 + 0.757559i \(0.726392\pi\)
\(860\) 3.08031e62 0.249389
\(861\) −1.46172e63 −1.15424
\(862\) −7.16966e62 −0.552195
\(863\) 1.77472e63 1.33321 0.666603 0.745413i \(-0.267748\pi\)
0.666603 + 0.745413i \(0.267748\pi\)
\(864\) 1.17545e63 0.861311
\(865\) 3.37121e62 0.240957
\(866\) −1.88935e63 −1.31728
\(867\) −7.89273e62 −0.536805
\(868\) −1.95489e63 −1.29702
\(869\) −5.46753e62 −0.353888
\(870\) 5.19899e62 0.328288
\(871\) 1.63290e62 0.100594
\(872\) 6.61493e62 0.397577
\(873\) −7.81492e62 −0.458267
\(874\) 1.87631e63 1.07352
\(875\) −3.02977e63 −1.69136
\(876\) −5.87900e62 −0.320233
\(877\) 1.15736e62 0.0615147 0.0307573 0.999527i \(-0.490208\pi\)
0.0307573 + 0.999527i \(0.490208\pi\)
\(878\) 3.18559e63 1.65218
\(879\) 2.18274e63 1.10469
\(880\) −1.64434e63 −0.812108
\(881\) 3.96934e63 1.91310 0.956548 0.291576i \(-0.0941798\pi\)
0.956548 + 0.291576i \(0.0941798\pi\)
\(882\) −3.68306e63 −1.73234
\(883\) −1.37793e63 −0.632515 −0.316258 0.948673i \(-0.602426\pi\)
−0.316258 + 0.948673i \(0.602426\pi\)
\(884\) 1.68130e62 0.0753220
\(885\) 3.81343e62 0.166738
\(886\) 2.76505e63 1.17999
\(887\) −3.36758e63 −1.40268 −0.701341 0.712826i \(-0.747415\pi\)
−0.701341 + 0.712826i \(0.747415\pi\)
\(888\) −9.72682e61 −0.0395451
\(889\) 1.57410e63 0.624659
\(890\) −5.93834e62 −0.230028
\(891\) 4.64168e62 0.175511
\(892\) 1.32851e63 0.490365
\(893\) −4.93004e62 −0.177641
\(894\) −1.06609e63 −0.375004
\(895\) 1.03912e63 0.356838
\(896\) 5.62214e63 1.88486
\(897\) −1.75669e63 −0.574987
\(898\) 1.16901e63 0.373573
\(899\) −3.94954e63 −1.23229
\(900\) 7.39098e62 0.225158
\(901\) 2.29035e62 0.0681268
\(902\) −5.53902e63 −1.60876
\(903\) 2.99289e63 0.848796
\(904\) −4.06950e63 −1.12699
\(905\) −2.22820e63 −0.602572
\(906\) −4.82870e63 −1.27519
\(907\) −3.22814e63 −0.832522 −0.416261 0.909245i \(-0.636660\pi\)
−0.416261 + 0.909245i \(0.636660\pi\)
\(908\) −2.35066e62 −0.0592031
\(909\) 3.00802e63 0.739873
\(910\) 3.85369e63 0.925734
\(911\) 6.66803e63 1.56442 0.782208 0.623017i \(-0.214093\pi\)
0.782208 + 0.623017i \(0.214093\pi\)
\(912\) 1.94395e63 0.445446
\(913\) −1.52617e62 −0.0341572
\(914\) −1.26781e63 −0.277147
\(915\) 2.08861e63 0.445969
\(916\) −3.09736e62 −0.0646010
\(917\) 4.22187e63 0.860131
\(918\) −1.18592e63 −0.236014
\(919\) 3.12159e63 0.606866 0.303433 0.952853i \(-0.401867\pi\)
0.303433 + 0.952853i \(0.401867\pi\)
\(920\) 2.60536e63 0.494801
\(921\) 2.48678e63 0.461376
\(922\) −3.69342e63 −0.669443
\(923\) −3.46075e63 −0.612822
\(924\) 3.13970e63 0.543176
\(925\) −4.48262e62 −0.0757678
\(926\) −4.08634e63 −0.674836
\(927\) 3.57462e63 0.576787
\(928\) −4.76745e63 −0.751631
\(929\) −1.01789e64 −1.56806 −0.784028 0.620725i \(-0.786838\pi\)
−0.784028 + 0.620725i \(0.786838\pi\)
\(930\) −3.95532e63 −0.595385
\(931\) −8.92802e63 −1.31322
\(932\) −1.89711e63 −0.272678
\(933\) 2.67824e63 0.376179
\(934\) 1.56973e64 2.15460
\(935\) 9.89571e62 0.132739
\(936\) 2.40173e63 0.314842
\(937\) −5.70526e63 −0.730928 −0.365464 0.930826i \(-0.619090\pi\)
−0.365464 + 0.930826i \(0.619090\pi\)
\(938\) 2.31221e63 0.289512
\(939\) −1.61560e63 −0.197707
\(940\) 6.72684e62 0.0804567
\(941\) −1.04360e64 −1.22000 −0.609999 0.792402i \(-0.708830\pi\)
−0.609999 + 0.792402i \(0.708830\pi\)
\(942\) 8.83688e63 1.00973
\(943\) 1.45424e64 1.62418
\(944\) −5.86244e63 −0.640001
\(945\) −9.00775e63 −0.961242
\(946\) 1.13412e64 1.18304
\(947\) 1.40457e64 1.43225 0.716124 0.697973i \(-0.245914\pi\)
0.716124 + 0.697973i \(0.245914\pi\)
\(948\) −8.81954e62 −0.0879157
\(949\) −8.80412e63 −0.857951
\(950\) 5.40654e63 0.515065
\(951\) −6.76354e63 −0.629931
\(952\) −2.42279e63 −0.220608
\(953\) −5.00331e63 −0.445410 −0.222705 0.974886i \(-0.571489\pi\)
−0.222705 + 0.974886i \(0.571489\pi\)
\(954\) −3.21496e63 −0.279825
\(955\) 3.26344e62 0.0277718
\(956\) 2.61093e63 0.217245
\(957\) 6.34326e63 0.516067
\(958\) −1.84541e64 −1.46803
\(959\) 1.29288e64 1.00568
\(960\) 5.77298e62 0.0439105
\(961\) 1.66028e64 1.23489
\(962\) 1.43136e63 0.104109
\(963\) −1.44090e64 −1.02487
\(964\) −1.05359e64 −0.732849
\(965\) 7.87618e62 0.0535770
\(966\) −2.48749e64 −1.65483
\(967\) 1.23774e64 0.805307 0.402654 0.915352i \(-0.368088\pi\)
0.402654 + 0.915352i \(0.368088\pi\)
\(968\) −2.41399e63 −0.153608
\(969\) −1.16988e63 −0.0728080
\(970\) 7.80015e63 0.474800
\(971\) −6.90009e63 −0.410810 −0.205405 0.978677i \(-0.565851\pi\)
−0.205405 + 0.978677i \(0.565851\pi\)
\(972\) 8.78802e63 0.511760
\(973\) 2.03353e63 0.115831
\(974\) 5.22452e63 0.291091
\(975\) −5.06186e63 −0.275874
\(976\) −3.21085e64 −1.71178
\(977\) 2.22048e64 1.15801 0.579006 0.815323i \(-0.303441\pi\)
0.579006 + 0.815323i \(0.303441\pi\)
\(978\) 1.75492e64 0.895306
\(979\) −7.24534e63 −0.361602
\(980\) 1.21819e64 0.594779
\(981\) 9.25938e63 0.442281
\(982\) 2.16394e64 1.01122
\(983\) 8.17397e63 0.373708 0.186854 0.982388i \(-0.440171\pi\)
0.186854 + 0.982388i \(0.440171\pi\)
\(984\) 9.09264e63 0.406720
\(985\) −3.52068e63 −0.154081
\(986\) 4.80991e63 0.205960
\(987\) 6.53593e63 0.273835
\(988\) −5.72094e63 −0.234527
\(989\) −2.97757e64 −1.19438
\(990\) −1.38906e64 −0.545211
\(991\) −3.43882e64 −1.32077 −0.660383 0.750929i \(-0.729606\pi\)
−0.660383 + 0.750929i \(0.729606\pi\)
\(992\) 3.62701e64 1.36316
\(993\) −1.12407e63 −0.0413414
\(994\) −4.90046e64 −1.76372
\(995\) 3.00762e63 0.105932
\(996\) −2.46183e62 −0.00848560
\(997\) −2.06533e64 −0.696697 −0.348349 0.937365i \(-0.613257\pi\)
−0.348349 + 0.937365i \(0.613257\pi\)
\(998\) −5.61846e64 −1.85486
\(999\) −3.34573e63 −0.108102
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 1.44.a.a.1.3 3
3.2 odd 2 9.44.a.b.1.1 3
4.3 odd 2 16.44.a.c.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.44.a.a.1.3 3 1.1 even 1 trivial
9.44.a.b.1.1 3 3.2 odd 2
16.44.a.c.1.2 3 4.3 odd 2