Properties

Label 1.50.a.a.1.1
Level $1$
Weight $50$
Character 1.1
Self dual yes
Analytic conductor $15.207$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 50 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.2066205099\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - x^{2} - 27962089502 x + 71708842875120\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-168486.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.54182e7 q^{2} -8.64745e11 q^{3} +8.31363e13 q^{4} +1.67413e17 q^{5} +2.19803e19 q^{6} -3.42668e20 q^{7} +1.21960e22 q^{8} +5.08484e23 q^{9} +O(q^{10})\) \(q-2.54182e7 q^{2} -8.64745e11 q^{3} +8.31363e13 q^{4} +1.67413e17 q^{5} +2.19803e19 q^{6} -3.42668e20 q^{7} +1.21960e22 q^{8} +5.08484e23 q^{9} -4.25535e24 q^{10} -2.47212e24 q^{11} -7.18917e25 q^{12} -1.86505e26 q^{13} +8.71003e27 q^{14} -1.44770e29 q^{15} -3.56803e29 q^{16} +8.08684e29 q^{17} -1.29248e31 q^{18} -1.31622e31 q^{19} +1.39181e31 q^{20} +2.96321e32 q^{21} +6.28370e31 q^{22} +3.96809e33 q^{23} -1.05464e34 q^{24} +1.02637e34 q^{25} +4.74062e33 q^{26} -2.32776e35 q^{27} -2.84882e34 q^{28} +4.73835e35 q^{29} +3.67979e36 q^{30} -5.52226e36 q^{31} +2.20354e36 q^{32} +2.13775e36 q^{33} -2.05553e37 q^{34} -5.73673e37 q^{35} +4.22735e37 q^{36} +6.02154e37 q^{37} +3.34559e38 q^{38} +1.61279e38 q^{39} +2.04178e39 q^{40} -4.00631e39 q^{41} -7.53195e39 q^{42} -1.57103e39 q^{43} -2.05523e38 q^{44} +8.51271e40 q^{45} -1.00862e41 q^{46} -3.77976e40 q^{47} +3.08543e41 q^{48} -1.39502e41 q^{49} -2.60885e41 q^{50} -6.99305e41 q^{51} -1.55053e40 q^{52} -7.38411e41 q^{53} +5.91675e42 q^{54} -4.13866e41 q^{55} -4.17919e42 q^{56} +1.13819e43 q^{57} -1.20441e43 q^{58} -3.19771e43 q^{59} -1.20356e43 q^{60} +2.48724e43 q^{61} +1.40366e44 q^{62} -1.74241e44 q^{63} +1.44852e44 q^{64} -3.12234e43 q^{65} -5.43379e43 q^{66} +5.76819e44 q^{67} +6.72310e43 q^{68} -3.43138e45 q^{69} +1.45818e45 q^{70} -1.66436e45 q^{71} +6.20148e45 q^{72} +4.80904e45 q^{73} -1.53057e45 q^{74} -8.87547e45 q^{75} -1.09425e45 q^{76} +8.47118e44 q^{77} -4.09943e45 q^{78} -4.21047e45 q^{79} -5.97335e46 q^{80} +7.96119e46 q^{81} +1.01833e47 q^{82} -1.20169e47 q^{83} +2.46350e46 q^{84} +1.35385e47 q^{85} +3.99327e46 q^{86} -4.09747e47 q^{87} -3.01500e46 q^{88} +8.70490e47 q^{89} -2.16378e48 q^{90} +6.39094e46 q^{91} +3.29892e47 q^{92} +4.77534e48 q^{93} +9.60748e47 q^{94} -2.20352e48 q^{95} -1.90550e48 q^{96} -7.30863e48 q^{97} +3.54589e48 q^{98} -1.25703e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 24225168q^{2} - 326954692404q^{3} + 31502767984896q^{4} + 63884035717079250q^{5} + 8906136249246768576q^{6} + 509391477498711192q^{7} + 12774393005516465664000q^{8} + 341625690512280455369319q^{9} + O(q^{10}) \) \( 3q - 24225168q^{2} - 326954692404q^{3} + 31502767984896q^{4} + 63884035717079250q^{5} + 8906136249246768576q^{6} + 509391477498711192q^{7} + \)\(12\!\cdots\!00\)\(q^{8} + \)\(34\!\cdots\!19\)\(q^{9} - \)\(17\!\cdots\!00\)\(q^{10} - \)\(20\!\cdots\!24\)\(q^{11} - \)\(10\!\cdots\!48\)\(q^{12} - \)\(18\!\cdots\!14\)\(q^{13} - \)\(94\!\cdots\!88\)\(q^{14} - \)\(20\!\cdots\!00\)\(q^{15} - \)\(95\!\cdots\!12\)\(q^{16} - \)\(33\!\cdots\!38\)\(q^{17} - \)\(20\!\cdots\!44\)\(q^{18} - \)\(45\!\cdots\!60\)\(q^{19} + \)\(19\!\cdots\!00\)\(q^{20} + \)\(61\!\cdots\!16\)\(q^{21} + \)\(17\!\cdots\!44\)\(q^{22} + \)\(45\!\cdots\!76\)\(q^{23} - \)\(25\!\cdots\!80\)\(q^{24} - \)\(13\!\cdots\!75\)\(q^{25} - \)\(85\!\cdots\!64\)\(q^{26} - \)\(31\!\cdots\!00\)\(q^{27} - \)\(59\!\cdots\!96\)\(q^{28} + \)\(11\!\cdots\!10\)\(q^{29} + \)\(50\!\cdots\!00\)\(q^{30} + \)\(93\!\cdots\!16\)\(q^{31} + \)\(73\!\cdots\!92\)\(q^{32} - \)\(24\!\cdots\!68\)\(q^{33} - \)\(44\!\cdots\!28\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(37\!\cdots\!08\)\(q^{36} + \)\(24\!\cdots\!02\)\(q^{37} + \)\(11\!\cdots\!00\)\(q^{38} + \)\(12\!\cdots\!48\)\(q^{39} + \)\(52\!\cdots\!00\)\(q^{40} - \)\(62\!\cdots\!14\)\(q^{41} - \)\(14\!\cdots\!76\)\(q^{42} - \)\(77\!\cdots\!44\)\(q^{43} + \)\(23\!\cdots\!32\)\(q^{44} + \)\(76\!\cdots\!50\)\(q^{45} + \)\(26\!\cdots\!96\)\(q^{46} + \)\(72\!\cdots\!72\)\(q^{47} + \)\(15\!\cdots\!76\)\(q^{48} - \)\(28\!\cdots\!29\)\(q^{49} - \)\(53\!\cdots\!00\)\(q^{50} - \)\(15\!\cdots\!04\)\(q^{51} - \)\(12\!\cdots\!68\)\(q^{52} - \)\(15\!\cdots\!54\)\(q^{53} + \)\(82\!\cdots\!40\)\(q^{54} + \)\(46\!\cdots\!00\)\(q^{55} + \)\(67\!\cdots\!40\)\(q^{56} - \)\(79\!\cdots\!00\)\(q^{57} - \)\(16\!\cdots\!00\)\(q^{58} - \)\(62\!\cdots\!80\)\(q^{59} - \)\(88\!\cdots\!00\)\(q^{60} - \)\(24\!\cdots\!74\)\(q^{61} + \)\(18\!\cdots\!04\)\(q^{62} - \)\(79\!\cdots\!64\)\(q^{63} + \)\(51\!\cdots\!36\)\(q^{64} - \)\(24\!\cdots\!00\)\(q^{65} + \)\(52\!\cdots\!92\)\(q^{66} - \)\(10\!\cdots\!88\)\(q^{67} + \)\(14\!\cdots\!44\)\(q^{68} - \)\(48\!\cdots\!72\)\(q^{69} + \)\(28\!\cdots\!00\)\(q^{70} - \)\(32\!\cdots\!04\)\(q^{71} + \)\(10\!\cdots\!00\)\(q^{72} + \)\(56\!\cdots\!26\)\(q^{73} + \)\(10\!\cdots\!92\)\(q^{74} - \)\(12\!\cdots\!00\)\(q^{75} + \)\(75\!\cdots\!80\)\(q^{76} - \)\(32\!\cdots\!36\)\(q^{77} - \)\(27\!\cdots\!08\)\(q^{78} - \)\(78\!\cdots\!40\)\(q^{79} - \)\(30\!\cdots\!00\)\(q^{80} + \)\(67\!\cdots\!43\)\(q^{81} + \)\(11\!\cdots\!84\)\(q^{82} + \)\(94\!\cdots\!16\)\(q^{83} + \)\(77\!\cdots\!12\)\(q^{84} + \)\(29\!\cdots\!00\)\(q^{85} - \)\(34\!\cdots\!84\)\(q^{86} - \)\(17\!\cdots\!00\)\(q^{87} - \)\(10\!\cdots\!00\)\(q^{88} + \)\(36\!\cdots\!30\)\(q^{89} - \)\(20\!\cdots\!00\)\(q^{90} + \)\(16\!\cdots\!76\)\(q^{91} + \)\(46\!\cdots\!12\)\(q^{92} + \)\(59\!\cdots\!12\)\(q^{93} + \)\(90\!\cdots\!52\)\(q^{94} + \)\(14\!\cdots\!00\)\(q^{95} - \)\(26\!\cdots\!44\)\(q^{96} - \)\(10\!\cdots\!78\)\(q^{97} - \)\(28\!\cdots\!76\)\(q^{98} - \)\(11\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54182e7 −1.07130 −0.535649 0.844441i \(-0.679933\pi\)
−0.535649 + 0.844441i \(0.679933\pi\)
\(3\) −8.64745e11 −1.76773 −0.883867 0.467737i \(-0.845069\pi\)
−0.883867 + 0.467737i \(0.845069\pi\)
\(4\) 8.31363e13 0.147680
\(5\) 1.67413e17 1.25610 0.628051 0.778172i \(-0.283853\pi\)
0.628051 + 0.778172i \(0.283853\pi\)
\(6\) 2.19803e19 1.89377
\(7\) −3.42668e20 −0.676040 −0.338020 0.941139i \(-0.609757\pi\)
−0.338020 + 0.941139i \(0.609757\pi\)
\(8\) 1.21960e22 0.913089
\(9\) 5.08484e23 2.12489
\(10\) −4.25535e24 −1.34566
\(11\) −2.47212e24 −0.0756744 −0.0378372 0.999284i \(-0.512047\pi\)
−0.0378372 + 0.999284i \(0.512047\pi\)
\(12\) −7.18917e25 −0.261059
\(13\) −1.86505e26 −0.0952968 −0.0476484 0.998864i \(-0.515173\pi\)
−0.0476484 + 0.998864i \(0.515173\pi\)
\(14\) 8.71003e27 0.724240
\(15\) −1.44770e29 −2.22046
\(16\) −3.56803e29 −1.12587
\(17\) 8.08684e29 0.577803 0.288902 0.957359i \(-0.406710\pi\)
0.288902 + 0.957359i \(0.406710\pi\)
\(18\) −1.29248e31 −2.27639
\(19\) −1.31622e31 −0.616402 −0.308201 0.951321i \(-0.599727\pi\)
−0.308201 + 0.951321i \(0.599727\pi\)
\(20\) 1.39181e31 0.185501
\(21\) 2.96321e32 1.19506
\(22\) 6.28370e31 0.0810699
\(23\) 3.96809e33 1.72286 0.861428 0.507879i \(-0.169570\pi\)
0.861428 + 0.507879i \(0.169570\pi\)
\(24\) −1.05464e34 −1.61410
\(25\) 1.02637e34 0.577794
\(26\) 4.74062e33 0.102091
\(27\) −2.32776e35 −1.98850
\(28\) −2.84882e34 −0.0998373
\(29\) 4.73835e35 0.702872 0.351436 0.936212i \(-0.385693\pi\)
0.351436 + 0.936212i \(0.385693\pi\)
\(30\) 3.67979e36 2.37877
\(31\) −5.52226e36 −1.59866 −0.799328 0.600895i \(-0.794811\pi\)
−0.799328 + 0.600895i \(0.794811\pi\)
\(32\) 2.20354e36 0.293054
\(33\) 2.13775e36 0.133772
\(34\) −2.05553e37 −0.619000
\(35\) −5.73673e37 −0.849175
\(36\) 4.22735e37 0.313803
\(37\) 6.02154e37 0.228436 0.114218 0.993456i \(-0.463564\pi\)
0.114218 + 0.993456i \(0.463564\pi\)
\(38\) 3.34559e38 0.660350
\(39\) 1.61279e38 0.168459
\(40\) 2.04178e39 1.14693
\(41\) −4.00631e39 −1.22897 −0.614483 0.788930i \(-0.710635\pi\)
−0.614483 + 0.788930i \(0.710635\pi\)
\(42\) −7.53195e39 −1.28026
\(43\) −1.57103e39 −0.150040 −0.0750198 0.997182i \(-0.523902\pi\)
−0.0750198 + 0.997182i \(0.523902\pi\)
\(44\) −2.05523e38 −0.0111756
\(45\) 8.51271e40 2.66908
\(46\) −1.00862e41 −1.84569
\(47\) −3.77976e40 −0.408382 −0.204191 0.978931i \(-0.565456\pi\)
−0.204191 + 0.978931i \(0.565456\pi\)
\(48\) 3.08543e41 1.99024
\(49\) −1.39502e41 −0.542970
\(50\) −2.60885e41 −0.618990
\(51\) −6.99305e41 −1.02140
\(52\) −1.55053e40 −0.0140734
\(53\) −7.38411e41 −0.420281 −0.210140 0.977671i \(-0.567392\pi\)
−0.210140 + 0.977671i \(0.567392\pi\)
\(54\) 5.91675e42 2.13028
\(55\) −4.13866e41 −0.0950549
\(56\) −4.17919e42 −0.617284
\(57\) 1.13819e43 1.08963
\(58\) −1.20441e43 −0.752986
\(59\) −3.19771e43 −1.31512 −0.657560 0.753403i \(-0.728411\pi\)
−0.657560 + 0.753403i \(0.728411\pi\)
\(60\) −1.20356e43 −0.327916
\(61\) 2.48724e43 0.451998 0.225999 0.974127i \(-0.427435\pi\)
0.225999 + 0.974127i \(0.427435\pi\)
\(62\) 1.40366e44 1.71264
\(63\) −1.74241e44 −1.43651
\(64\) 1.44852e44 0.811923
\(65\) −3.12234e43 −0.119703
\(66\) −5.43379e43 −0.143310
\(67\) 5.76819e44 1.05246 0.526232 0.850341i \(-0.323604\pi\)
0.526232 + 0.850341i \(0.323604\pi\)
\(68\) 6.72310e43 0.0853298
\(69\) −3.43138e45 −3.04555
\(70\) 1.45818e45 0.909720
\(71\) −1.66436e45 −0.733530 −0.366765 0.930314i \(-0.619535\pi\)
−0.366765 + 0.930314i \(0.619535\pi\)
\(72\) 6.20148e45 1.94021
\(73\) 4.80904e45 1.07312 0.536561 0.843862i \(-0.319723\pi\)
0.536561 + 0.843862i \(0.319723\pi\)
\(74\) −1.53057e45 −0.244723
\(75\) −8.87547e45 −1.02139
\(76\) −1.09425e45 −0.0910300
\(77\) 8.47118e44 0.0511589
\(78\) −4.09943e45 −0.180470
\(79\) −4.21047e45 −0.135665 −0.0678323 0.997697i \(-0.521608\pi\)
−0.0678323 + 0.997697i \(0.521608\pi\)
\(80\) −5.97335e46 −1.41421
\(81\) 7.96119e46 1.39026
\(82\) 1.01833e47 1.31659
\(83\) −1.20169e47 −1.15446 −0.577232 0.816581i \(-0.695867\pi\)
−0.577232 + 0.816581i \(0.695867\pi\)
\(84\) 2.46350e46 0.176486
\(85\) 1.35385e47 0.725781
\(86\) 3.99327e46 0.160737
\(87\) −4.09747e47 −1.24249
\(88\) −3.01500e46 −0.0690975
\(89\) 8.70490e47 1.51255 0.756273 0.654256i \(-0.227018\pi\)
0.756273 + 0.654256i \(0.227018\pi\)
\(90\) −2.16378e48 −2.85938
\(91\) 6.39094e46 0.0644244
\(92\) 3.29892e47 0.254431
\(93\) 4.77534e48 2.82600
\(94\) 9.60748e47 0.437499
\(95\) −2.20352e48 −0.774264
\(96\) −1.90550e48 −0.518041
\(97\) −7.30863e48 −1.54145 −0.770723 0.637171i \(-0.780105\pi\)
−0.770723 + 0.637171i \(0.780105\pi\)
\(98\) 3.54589e48 0.581683
\(99\) −1.25703e48 −0.160800
\(100\) 8.53285e47 0.0853285
\(101\) 1.06900e48 0.0837733 0.0418867 0.999122i \(-0.486663\pi\)
0.0418867 + 0.999122i \(0.486663\pi\)
\(102\) 1.77751e49 1.09423
\(103\) −3.01827e49 −1.46301 −0.731503 0.681839i \(-0.761181\pi\)
−0.731503 + 0.681839i \(0.761181\pi\)
\(104\) −2.27462e48 −0.0870145
\(105\) 4.96081e49 1.50112
\(106\) 1.87691e49 0.450246
\(107\) −4.53746e48 −0.0864790 −0.0432395 0.999065i \(-0.513768\pi\)
−0.0432395 + 0.999065i \(0.513768\pi\)
\(108\) −1.93521e49 −0.293661
\(109\) −1.12199e50 −1.35844 −0.679221 0.733933i \(-0.737682\pi\)
−0.679221 + 0.733933i \(0.737682\pi\)
\(110\) 1.05198e49 0.101832
\(111\) −5.20709e49 −0.403815
\(112\) 1.22265e50 0.761133
\(113\) −4.95437e49 −0.248066 −0.124033 0.992278i \(-0.539583\pi\)
−0.124033 + 0.992278i \(0.539583\pi\)
\(114\) −2.89308e50 −1.16732
\(115\) 6.64311e50 2.16409
\(116\) 3.93929e49 0.103800
\(117\) −9.48348e49 −0.202495
\(118\) 8.12802e50 1.40888
\(119\) −2.77110e50 −0.390618
\(120\) −1.76562e51 −2.02748
\(121\) −1.06108e51 −0.994273
\(122\) −6.32212e50 −0.484225
\(123\) 3.46444e51 2.17249
\(124\) −4.59100e50 −0.236089
\(125\) −1.25558e51 −0.530334
\(126\) 4.42891e51 1.53893
\(127\) −5.79879e50 −0.166015 −0.0830073 0.996549i \(-0.526452\pi\)
−0.0830073 + 0.996549i \(0.526452\pi\)
\(128\) −4.92236e51 −1.16286
\(129\) 1.35854e51 0.265230
\(130\) 7.93644e50 0.128237
\(131\) 5.77681e51 0.773645 0.386822 0.922154i \(-0.373573\pi\)
0.386822 + 0.922154i \(0.373573\pi\)
\(132\) 1.77725e50 0.0197555
\(133\) 4.51026e51 0.416712
\(134\) −1.46617e52 −1.12750
\(135\) −3.89698e52 −2.49776
\(136\) 9.86272e51 0.527586
\(137\) 9.99643e51 0.446880 0.223440 0.974718i \(-0.428271\pi\)
0.223440 + 0.974718i \(0.428271\pi\)
\(138\) 8.72197e52 3.26270
\(139\) −5.47789e52 −1.71692 −0.858461 0.512878i \(-0.828579\pi\)
−0.858461 + 0.512878i \(0.828579\pi\)
\(140\) −4.76930e51 −0.125406
\(141\) 3.26853e52 0.721911
\(142\) 4.23051e52 0.785829
\(143\) 4.61063e50 0.00721153
\(144\) −1.81428e53 −2.39235
\(145\) 7.93264e52 0.882880
\(146\) −1.22237e53 −1.14963
\(147\) 1.20634e53 0.959828
\(148\) 5.00608e51 0.0337354
\(149\) −3.17720e53 −1.81543 −0.907717 0.419584i \(-0.862176\pi\)
−0.907717 + 0.419584i \(0.862176\pi\)
\(150\) 2.25599e53 1.09421
\(151\) 4.36140e53 1.79759 0.898796 0.438367i \(-0.144443\pi\)
0.898796 + 0.438367i \(0.144443\pi\)
\(152\) −1.60526e53 −0.562830
\(153\) 4.11203e53 1.22777
\(154\) −2.15322e52 −0.0548064
\(155\) −9.24500e53 −2.00808
\(156\) 1.34081e52 0.0248780
\(157\) 6.03339e52 0.0957238 0.0478619 0.998854i \(-0.484759\pi\)
0.0478619 + 0.998854i \(0.484759\pi\)
\(158\) 1.07023e53 0.145337
\(159\) 6.38537e53 0.742945
\(160\) 3.68903e53 0.368106
\(161\) −1.35974e54 −1.16472
\(162\) −2.02359e54 −1.48938
\(163\) 1.51529e54 0.959179 0.479590 0.877493i \(-0.340786\pi\)
0.479590 + 0.877493i \(0.340786\pi\)
\(164\) −3.33070e53 −0.181493
\(165\) 3.57889e53 0.168032
\(166\) 3.05449e54 1.23677
\(167\) 2.55570e54 0.893217 0.446608 0.894730i \(-0.352632\pi\)
0.446608 + 0.894730i \(0.352632\pi\)
\(168\) 3.61393e54 1.09120
\(169\) −3.79544e54 −0.990919
\(170\) −3.44123e54 −0.777527
\(171\) −6.69275e54 −1.30978
\(172\) −1.30609e53 −0.0221578
\(173\) −8.31345e54 −1.22363 −0.611817 0.790999i \(-0.709561\pi\)
−0.611817 + 0.790999i \(0.709561\pi\)
\(174\) 1.04150e55 1.33108
\(175\) −3.51704e54 −0.390612
\(176\) 8.82060e53 0.0851996
\(177\) 2.76520e55 2.32478
\(178\) −2.21263e55 −1.62039
\(179\) 5.23266e54 0.334059 0.167030 0.985952i \(-0.446582\pi\)
0.167030 + 0.985952i \(0.446582\pi\)
\(180\) 7.07715e54 0.394168
\(181\) 1.38390e54 0.0672946 0.0336473 0.999434i \(-0.489288\pi\)
0.0336473 + 0.999434i \(0.489288\pi\)
\(182\) −1.62446e54 −0.0690177
\(183\) −2.15083e55 −0.799013
\(184\) 4.83948e55 1.57312
\(185\) 1.00809e55 0.286940
\(186\) −1.21381e56 −3.02749
\(187\) −1.99916e54 −0.0437249
\(188\) −3.14235e54 −0.0603097
\(189\) 7.97650e55 1.34431
\(190\) 5.60096e55 0.829467
\(191\) −4.46194e54 −0.0581040 −0.0290520 0.999578i \(-0.509249\pi\)
−0.0290520 + 0.999578i \(0.509249\pi\)
\(192\) −1.25260e56 −1.43526
\(193\) −3.91405e55 −0.394886 −0.197443 0.980314i \(-0.563264\pi\)
−0.197443 + 0.980314i \(0.563264\pi\)
\(194\) 1.85772e56 1.65135
\(195\) 2.70003e55 0.211602
\(196\) −1.15977e55 −0.0801857
\(197\) 8.64318e55 0.527535 0.263767 0.964586i \(-0.415035\pi\)
0.263767 + 0.964586i \(0.415035\pi\)
\(198\) 3.19516e55 0.172264
\(199\) −1.38403e56 −0.659545 −0.329773 0.944060i \(-0.606972\pi\)
−0.329773 + 0.944060i \(0.606972\pi\)
\(200\) 1.25176e56 0.527578
\(201\) −4.98802e56 −1.86048
\(202\) −2.71722e55 −0.0897462
\(203\) −1.62368e56 −0.475170
\(204\) −5.81376e55 −0.150841
\(205\) −6.70710e56 −1.54371
\(206\) 7.67190e56 1.56731
\(207\) 2.01771e57 3.66088
\(208\) 6.65454e55 0.107292
\(209\) 3.25385e55 0.0466458
\(210\) −1.26095e57 −1.60814
\(211\) −1.39140e57 −1.57954 −0.789770 0.613404i \(-0.789800\pi\)
−0.789770 + 0.613404i \(0.789800\pi\)
\(212\) −6.13888e55 −0.0620669
\(213\) 1.43925e57 1.29669
\(214\) 1.15334e56 0.0926448
\(215\) −2.63011e56 −0.188465
\(216\) −2.83894e57 −1.81568
\(217\) 1.89230e57 1.08076
\(218\) 2.85191e57 1.45530
\(219\) −4.15860e57 −1.89699
\(220\) −3.44073e55 −0.0140377
\(221\) −1.50824e56 −0.0550628
\(222\) 1.32355e57 0.432606
\(223\) 2.03036e57 0.594434 0.297217 0.954810i \(-0.403941\pi\)
0.297217 + 0.954810i \(0.403941\pi\)
\(224\) −7.55085e56 −0.198116
\(225\) 5.21892e57 1.22775
\(226\) 1.25931e57 0.265752
\(227\) −4.69172e57 −0.888585 −0.444292 0.895882i \(-0.646545\pi\)
−0.444292 + 0.895882i \(0.646545\pi\)
\(228\) 9.46249e56 0.160917
\(229\) 5.97819e57 0.913273 0.456636 0.889653i \(-0.349054\pi\)
0.456636 + 0.889653i \(0.349054\pi\)
\(230\) −1.68856e58 −2.31838
\(231\) −7.32541e56 −0.0904354
\(232\) 5.77890e57 0.641785
\(233\) −4.46843e57 −0.446617 −0.223308 0.974748i \(-0.571686\pi\)
−0.223308 + 0.974748i \(0.571686\pi\)
\(234\) 2.41053e57 0.216932
\(235\) −6.32782e57 −0.512970
\(236\) −2.65846e57 −0.194216
\(237\) 3.64098e57 0.239819
\(238\) 7.04366e57 0.418468
\(239\) −4.13711e57 −0.221793 −0.110897 0.993832i \(-0.535372\pi\)
−0.110897 + 0.993832i \(0.535372\pi\)
\(240\) 5.16543e58 2.49995
\(241\) −2.18261e58 −0.954022 −0.477011 0.878897i \(-0.658280\pi\)
−0.477011 + 0.878897i \(0.658280\pi\)
\(242\) 2.69707e58 1.06516
\(243\) −1.31409e58 −0.469105
\(244\) 2.06780e57 0.0667510
\(245\) −2.33545e58 −0.682027
\(246\) −8.80598e58 −2.32738
\(247\) 2.45481e57 0.0587411
\(248\) −6.73495e58 −1.45972
\(249\) 1.03916e59 2.04078
\(250\) 3.19146e58 0.568146
\(251\) 5.93439e58 0.958009 0.479005 0.877812i \(-0.340998\pi\)
0.479005 + 0.877812i \(0.340998\pi\)
\(252\) −1.44858e58 −0.212143
\(253\) −9.80960e57 −0.130376
\(254\) 1.47395e58 0.177851
\(255\) −1.17073e59 −1.28299
\(256\) 4.35734e58 0.433852
\(257\) 9.93030e58 0.898671 0.449336 0.893363i \(-0.351661\pi\)
0.449336 + 0.893363i \(0.351661\pi\)
\(258\) −3.45316e58 −0.284141
\(259\) −2.06339e58 −0.154432
\(260\) −2.59580e57 −0.0176776
\(261\) 2.40938e59 1.49352
\(262\) −1.46836e59 −0.828804
\(263\) −6.39723e58 −0.328909 −0.164455 0.986385i \(-0.552586\pi\)
−0.164455 + 0.986385i \(0.552586\pi\)
\(264\) 2.60721e58 0.122146
\(265\) −1.23620e59 −0.527916
\(266\) −1.14643e59 −0.446423
\(267\) −7.52752e59 −2.67378
\(268\) 4.79546e58 0.155428
\(269\) 3.93934e59 1.16545 0.582723 0.812671i \(-0.301987\pi\)
0.582723 + 0.812671i \(0.301987\pi\)
\(270\) 9.90544e59 2.67585
\(271\) 2.92581e59 0.721935 0.360968 0.932578i \(-0.382446\pi\)
0.360968 + 0.932578i \(0.382446\pi\)
\(272\) −2.88540e59 −0.650532
\(273\) −5.52653e58 −0.113885
\(274\) −2.54092e59 −0.478742
\(275\) −2.53731e58 −0.0437243
\(276\) −2.85272e59 −0.449767
\(277\) 8.20576e59 1.18403 0.592017 0.805925i \(-0.298332\pi\)
0.592017 + 0.805925i \(0.298332\pi\)
\(278\) 1.39238e60 1.83934
\(279\) −2.80798e60 −3.39696
\(280\) −6.99652e59 −0.775373
\(281\) 1.23805e60 1.25729 0.628643 0.777694i \(-0.283611\pi\)
0.628643 + 0.777694i \(0.283611\pi\)
\(282\) −8.30801e59 −0.773382
\(283\) −1.21811e60 −1.03972 −0.519862 0.854250i \(-0.674017\pi\)
−0.519862 + 0.854250i \(0.674017\pi\)
\(284\) −1.38369e59 −0.108327
\(285\) 1.90548e60 1.36869
\(286\) −1.17194e58 −0.00772570
\(287\) 1.37284e60 0.830830
\(288\) 1.12047e60 0.622706
\(289\) −1.30486e60 −0.666143
\(290\) −2.01634e60 −0.945828
\(291\) 6.32009e60 2.72487
\(292\) 3.99806e59 0.158478
\(293\) −2.58132e60 −0.940992 −0.470496 0.882402i \(-0.655925\pi\)
−0.470496 + 0.882402i \(0.655925\pi\)
\(294\) −3.06629e60 −1.02826
\(295\) −5.35340e60 −1.65192
\(296\) 7.34388e59 0.208583
\(297\) 5.75451e59 0.150479
\(298\) 8.07587e60 1.94487
\(299\) −7.40068e59 −0.164183
\(300\) −7.37874e59 −0.150838
\(301\) 5.38341e59 0.101433
\(302\) −1.10859e61 −1.92576
\(303\) −9.24416e59 −0.148089
\(304\) 4.69629e60 0.693988
\(305\) 4.16398e60 0.567756
\(306\) −1.04520e61 −1.31530
\(307\) 2.63375e60 0.305974 0.152987 0.988228i \(-0.451111\pi\)
0.152987 + 0.988228i \(0.451111\pi\)
\(308\) 7.04263e58 0.00755513
\(309\) 2.61003e61 2.58621
\(310\) 2.34992e61 2.15125
\(311\) −1.91232e61 −1.61783 −0.808913 0.587928i \(-0.799944\pi\)
−0.808913 + 0.587928i \(0.799944\pi\)
\(312\) 1.96696e60 0.153818
\(313\) −1.92491e61 −1.39179 −0.695896 0.718143i \(-0.744992\pi\)
−0.695896 + 0.718143i \(0.744992\pi\)
\(314\) −1.53358e60 −0.102549
\(315\) −2.91704e61 −1.80440
\(316\) −3.50043e59 −0.0200349
\(317\) 4.85204e60 0.257023 0.128512 0.991708i \(-0.458980\pi\)
0.128512 + 0.991708i \(0.458980\pi\)
\(318\) −1.62305e61 −0.795916
\(319\) −1.17138e60 −0.0531895
\(320\) 2.42501e61 1.01986
\(321\) 3.92375e60 0.152872
\(322\) 3.45621e61 1.24776
\(323\) −1.06440e61 −0.356159
\(324\) 6.61864e60 0.205313
\(325\) −1.91423e60 −0.0550619
\(326\) −3.85160e61 −1.02757
\(327\) 9.70238e61 2.40137
\(328\) −4.88610e61 −1.12216
\(329\) 1.29520e61 0.276082
\(330\) −9.09690e60 −0.180012
\(331\) −3.46456e61 −0.636594 −0.318297 0.947991i \(-0.603111\pi\)
−0.318297 + 0.947991i \(0.603111\pi\)
\(332\) −9.99042e60 −0.170491
\(333\) 3.06186e61 0.485401
\(334\) −6.49614e61 −0.956901
\(335\) 9.65673e61 1.32200
\(336\) −1.05728e62 −1.34548
\(337\) −1.47496e62 −1.74521 −0.872605 0.488427i \(-0.837571\pi\)
−0.872605 + 0.488427i \(0.837571\pi\)
\(338\) 9.64734e61 1.06157
\(339\) 4.28427e61 0.438515
\(340\) 1.12554e61 0.107183
\(341\) 1.36517e61 0.120977
\(342\) 1.70118e62 1.40317
\(343\) 1.35843e62 1.04311
\(344\) −1.91602e61 −0.137000
\(345\) −5.74459e62 −3.82553
\(346\) 2.11313e62 1.31088
\(347\) 1.49446e62 0.863799 0.431900 0.901922i \(-0.357843\pi\)
0.431900 + 0.901922i \(0.357843\pi\)
\(348\) −3.40648e61 −0.183491
\(349\) 2.27300e62 1.14124 0.570620 0.821214i \(-0.306703\pi\)
0.570620 + 0.821214i \(0.306703\pi\)
\(350\) 8.93970e61 0.418462
\(351\) 4.34139e61 0.189498
\(352\) −5.44743e60 −0.0221767
\(353\) −2.58609e61 −0.0982119 −0.0491059 0.998794i \(-0.515637\pi\)
−0.0491059 + 0.998794i \(0.515637\pi\)
\(354\) −7.02866e62 −2.49053
\(355\) −2.78636e62 −0.921389
\(356\) 7.23693e61 0.223372
\(357\) 2.39630e62 0.690509
\(358\) −1.33005e62 −0.357877
\(359\) −5.12401e62 −1.28765 −0.643823 0.765175i \(-0.722653\pi\)
−0.643823 + 0.765175i \(0.722653\pi\)
\(360\) 1.03821e63 2.43710
\(361\) −2.82717e62 −0.620049
\(362\) −3.51763e61 −0.0720926
\(363\) 9.17562e62 1.75761
\(364\) 5.31319e60 0.00951418
\(365\) 8.05099e62 1.34795
\(366\) 5.46702e62 0.855981
\(367\) 1.03293e61 0.0151270 0.00756348 0.999971i \(-0.497592\pi\)
0.00756348 + 0.999971i \(0.497592\pi\)
\(368\) −1.41582e63 −1.93971
\(369\) −2.03714e63 −2.61141
\(370\) −2.56238e62 −0.307398
\(371\) 2.53030e62 0.284127
\(372\) 3.97004e62 0.417343
\(373\) 6.36683e62 0.626696 0.313348 0.949638i \(-0.398549\pi\)
0.313348 + 0.949638i \(0.398549\pi\)
\(374\) 5.08152e61 0.0468425
\(375\) 1.08576e63 0.937490
\(376\) −4.60980e62 −0.372889
\(377\) −8.83726e61 −0.0669815
\(378\) −2.02748e63 −1.44015
\(379\) 1.19758e63 0.797340 0.398670 0.917094i \(-0.369472\pi\)
0.398670 + 0.917094i \(0.369472\pi\)
\(380\) −1.83193e62 −0.114343
\(381\) 5.01447e62 0.293470
\(382\) 1.13415e62 0.0622467
\(383\) −1.72054e63 −0.885717 −0.442859 0.896591i \(-0.646036\pi\)
−0.442859 + 0.896591i \(0.646036\pi\)
\(384\) 4.25659e63 2.05564
\(385\) 1.41819e62 0.0642609
\(386\) 9.94881e62 0.423041
\(387\) −7.98841e62 −0.318817
\(388\) −6.07612e62 −0.227640
\(389\) −1.24290e63 −0.437189 −0.218595 0.975816i \(-0.570147\pi\)
−0.218595 + 0.975816i \(0.570147\pi\)
\(390\) −6.86300e62 −0.226689
\(391\) 3.20893e63 0.995473
\(392\) −1.70137e63 −0.495780
\(393\) −4.99547e63 −1.36760
\(394\) −2.19694e63 −0.565147
\(395\) −7.04889e62 −0.170409
\(396\) −1.04505e62 −0.0237468
\(397\) 5.98417e63 1.27831 0.639155 0.769078i \(-0.279284\pi\)
0.639155 + 0.769078i \(0.279284\pi\)
\(398\) 3.51795e63 0.706570
\(399\) −3.90022e63 −0.736636
\(400\) −3.66211e63 −0.650522
\(401\) −9.27508e63 −1.54982 −0.774909 0.632073i \(-0.782204\pi\)
−0.774909 + 0.632073i \(0.782204\pi\)
\(402\) 1.26786e64 1.99313
\(403\) 1.02993e63 0.152347
\(404\) 8.88730e61 0.0123716
\(405\) 1.33281e64 1.74631
\(406\) 4.12712e63 0.509048
\(407\) −1.48860e62 −0.0172868
\(408\) −8.52873e63 −0.932632
\(409\) −9.43587e63 −0.971764 −0.485882 0.874024i \(-0.661502\pi\)
−0.485882 + 0.874024i \(0.661502\pi\)
\(410\) 1.70483e64 1.65377
\(411\) −8.64436e63 −0.789966
\(412\) −2.50928e63 −0.216056
\(413\) 1.09576e64 0.889073
\(414\) −5.12866e64 −3.92189
\(415\) −2.01179e64 −1.45012
\(416\) −4.10972e62 −0.0279271
\(417\) 4.73698e64 3.03506
\(418\) −8.27070e62 −0.0499716
\(419\) 7.04245e63 0.401310 0.200655 0.979662i \(-0.435693\pi\)
0.200655 + 0.979662i \(0.435693\pi\)
\(420\) 4.12423e63 0.221684
\(421\) 1.20251e64 0.609788 0.304894 0.952386i \(-0.401379\pi\)
0.304894 + 0.952386i \(0.401379\pi\)
\(422\) 3.53668e64 1.69216
\(423\) −1.92195e64 −0.867765
\(424\) −9.00567e63 −0.383754
\(425\) 8.30008e63 0.333852
\(426\) −3.65831e64 −1.38914
\(427\) −8.52299e63 −0.305569
\(428\) −3.77228e62 −0.0127712
\(429\) −3.98702e62 −0.0127481
\(430\) 6.68527e63 0.201902
\(431\) 4.44020e63 0.126680 0.0633402 0.997992i \(-0.479825\pi\)
0.0633402 + 0.997992i \(0.479825\pi\)
\(432\) 8.30551e64 2.23880
\(433\) −1.83425e63 −0.0467201 −0.0233601 0.999727i \(-0.507436\pi\)
−0.0233601 + 0.999727i \(0.507436\pi\)
\(434\) −4.80990e64 −1.15781
\(435\) −6.85971e64 −1.56070
\(436\) −9.32784e63 −0.200614
\(437\) −5.22286e64 −1.06197
\(438\) 1.05704e65 2.03225
\(439\) −1.95740e64 −0.355876 −0.177938 0.984042i \(-0.556943\pi\)
−0.177938 + 0.984042i \(0.556943\pi\)
\(440\) −5.04752e63 −0.0867936
\(441\) −7.09345e64 −1.15375
\(442\) 3.83367e63 0.0589887
\(443\) −3.98745e63 −0.0580502 −0.0290251 0.999579i \(-0.509240\pi\)
−0.0290251 + 0.999579i \(0.509240\pi\)
\(444\) −4.32898e63 −0.0596353
\(445\) 1.45732e65 1.89991
\(446\) −5.16081e64 −0.636816
\(447\) 2.74746e65 3.20921
\(448\) −4.96362e64 −0.548892
\(449\) 1.31465e64 0.137649 0.0688246 0.997629i \(-0.478075\pi\)
0.0688246 + 0.997629i \(0.478075\pi\)
\(450\) −1.32656e65 −1.31528
\(451\) 9.90409e63 0.0930013
\(452\) −4.11888e63 −0.0366343
\(453\) −3.77150e65 −3.17767
\(454\) 1.19255e65 0.951939
\(455\) 1.06993e64 0.0809237
\(456\) 1.38814e65 0.994934
\(457\) 1.24818e65 0.847873 0.423937 0.905692i \(-0.360648\pi\)
0.423937 + 0.905692i \(0.360648\pi\)
\(458\) −1.51955e65 −0.978388
\(459\) −1.88242e65 −1.14896
\(460\) 5.52284e64 0.319591
\(461\) −6.76961e64 −0.371442 −0.185721 0.982603i \(-0.559462\pi\)
−0.185721 + 0.982603i \(0.559462\pi\)
\(462\) 1.86199e64 0.0968833
\(463\) −2.06723e65 −1.02013 −0.510063 0.860137i \(-0.670378\pi\)
−0.510063 + 0.860137i \(0.670378\pi\)
\(464\) −1.69066e65 −0.791343
\(465\) 7.99456e65 3.54975
\(466\) 1.13580e65 0.478460
\(467\) 2.20986e65 0.883284 0.441642 0.897191i \(-0.354396\pi\)
0.441642 + 0.897191i \(0.354396\pi\)
\(468\) −7.88421e63 −0.0299044
\(469\) −1.97658e65 −0.711507
\(470\) 1.60842e65 0.549544
\(471\) −5.21734e64 −0.169214
\(472\) −3.89993e65 −1.20082
\(473\) 3.88377e63 0.0113542
\(474\) −9.25472e64 −0.256918
\(475\) −1.35092e65 −0.356153
\(476\) −2.30379e64 −0.0576864
\(477\) −3.75470e65 −0.893049
\(478\) 1.05158e65 0.237607
\(479\) 7.25016e64 0.155642 0.0778211 0.996967i \(-0.475204\pi\)
0.0778211 + 0.996967i \(0.475204\pi\)
\(480\) −3.19007e65 −0.650713
\(481\) −1.12305e64 −0.0217693
\(482\) 5.54781e65 1.02204
\(483\) 1.17583e66 2.05892
\(484\) −8.82141e64 −0.146834
\(485\) −1.22356e66 −1.93621
\(486\) 3.34017e65 0.502551
\(487\) −5.28007e65 −0.755405 −0.377702 0.925927i \(-0.623286\pi\)
−0.377702 + 0.925927i \(0.623286\pi\)
\(488\) 3.03344e65 0.412715
\(489\) −1.31034e66 −1.69557
\(490\) 5.93630e65 0.730654
\(491\) 1.31061e66 1.53454 0.767271 0.641324i \(-0.221614\pi\)
0.767271 + 0.641324i \(0.221614\pi\)
\(492\) 2.88020e65 0.320832
\(493\) 3.83183e65 0.406122
\(494\) −6.23968e64 −0.0629292
\(495\) −2.10444e65 −0.201981
\(496\) 1.97036e66 1.79988
\(497\) 5.70324e65 0.495895
\(498\) −2.64135e66 −2.18629
\(499\) −2.40608e65 −0.189603 −0.0948016 0.995496i \(-0.530222\pi\)
−0.0948016 + 0.995496i \(0.530222\pi\)
\(500\) −1.04384e65 −0.0783195
\(501\) −2.21003e66 −1.57897
\(502\) −1.50842e66 −1.02631
\(503\) 1.13819e66 0.737560 0.368780 0.929517i \(-0.379776\pi\)
0.368780 + 0.929517i \(0.379776\pi\)
\(504\) −2.12505e66 −1.31166
\(505\) 1.78966e65 0.105228
\(506\) 2.49343e65 0.139672
\(507\) 3.28209e66 1.75168
\(508\) −4.82090e64 −0.0245170
\(509\) 1.25631e66 0.608849 0.304425 0.952536i \(-0.401536\pi\)
0.304425 + 0.952536i \(0.401536\pi\)
\(510\) 2.97579e66 1.37446
\(511\) −1.64791e66 −0.725472
\(512\) 1.66349e66 0.698080
\(513\) 3.06383e66 1.22572
\(514\) −2.52411e66 −0.962745
\(515\) −5.05299e66 −1.83769
\(516\) 1.12944e65 0.0391691
\(517\) 9.34402e64 0.0309041
\(518\) 5.24478e65 0.165443
\(519\) 7.18901e66 2.16306
\(520\) −3.80801e65 −0.109299
\(521\) −5.06272e66 −1.38631 −0.693154 0.720789i \(-0.743780\pi\)
−0.693154 + 0.720789i \(0.743780\pi\)
\(522\) −6.12421e66 −1.60001
\(523\) −2.50752e66 −0.625105 −0.312552 0.949901i \(-0.601184\pi\)
−0.312552 + 0.949901i \(0.601184\pi\)
\(524\) 4.80263e65 0.114252
\(525\) 3.04134e66 0.690498
\(526\) 1.62606e66 0.352360
\(527\) −4.46576e66 −0.923709
\(528\) −7.62756e65 −0.150610
\(529\) 1.04410e67 1.96824
\(530\) 3.14220e66 0.565555
\(531\) −1.62599e67 −2.79448
\(532\) 3.74966e65 0.0615399
\(533\) 7.47197e65 0.117117
\(534\) 1.91336e67 2.86442
\(535\) −7.59632e65 −0.108627
\(536\) 7.03490e66 0.960993
\(537\) −4.52492e66 −0.590528
\(538\) −1.00131e67 −1.24854
\(539\) 3.44866e65 0.0410890
\(540\) −3.23981e66 −0.368869
\(541\) 9.85403e66 1.07221 0.536106 0.844151i \(-0.319895\pi\)
0.536106 + 0.844151i \(0.319895\pi\)
\(542\) −7.43689e66 −0.773408
\(543\) −1.19672e66 −0.118959
\(544\) 1.78197e66 0.169327
\(545\) −1.87837e67 −1.70634
\(546\) 1.40475e66 0.122005
\(547\) 2.04995e67 1.70237 0.851185 0.524866i \(-0.175885\pi\)
0.851185 + 0.524866i \(0.175885\pi\)
\(548\) 8.31066e65 0.0659951
\(549\) 1.26472e67 0.960445
\(550\) 6.44939e65 0.0468417
\(551\) −6.23669e66 −0.433252
\(552\) −4.18492e67 −2.78086
\(553\) 1.44279e66 0.0917147
\(554\) −2.08576e67 −1.26845
\(555\) −8.71737e66 −0.507233
\(556\) −4.55411e66 −0.253555
\(557\) 2.90683e67 1.54870 0.774351 0.632757i \(-0.218077\pi\)
0.774351 + 0.632757i \(0.218077\pi\)
\(558\) 7.13739e67 3.63916
\(559\) 2.93004e65 0.0142983
\(560\) 2.04688e67 0.956061
\(561\) 1.72877e66 0.0772941
\(562\) −3.14691e67 −1.34693
\(563\) 6.00209e65 0.0245950 0.0122975 0.999924i \(-0.496085\pi\)
0.0122975 + 0.999924i \(0.496085\pi\)
\(564\) 2.71733e66 0.106612
\(565\) −8.29429e66 −0.311596
\(566\) 3.09621e67 1.11385
\(567\) −2.72805e67 −0.939869
\(568\) −2.02986e67 −0.669778
\(569\) −2.48462e67 −0.785252 −0.392626 0.919698i \(-0.628433\pi\)
−0.392626 + 0.919698i \(0.628433\pi\)
\(570\) −4.84340e67 −1.46628
\(571\) −8.26527e66 −0.239702 −0.119851 0.992792i \(-0.538242\pi\)
−0.119851 + 0.992792i \(0.538242\pi\)
\(572\) 3.83311e64 0.00106500
\(573\) 3.85844e66 0.102712
\(574\) −3.48951e67 −0.890067
\(575\) 4.07272e67 0.995457
\(576\) 7.36548e67 1.72524
\(577\) −1.45109e67 −0.325751 −0.162875 0.986647i \(-0.552077\pi\)
−0.162875 + 0.986647i \(0.552077\pi\)
\(578\) 3.31673e67 0.713638
\(579\) 3.38465e67 0.698054
\(580\) 6.59490e66 0.130383
\(581\) 4.11782e67 0.780463
\(582\) −1.60646e68 −2.91915
\(583\) 1.82544e66 0.0318045
\(584\) 5.86512e67 0.979855
\(585\) −1.58766e67 −0.254354
\(586\) 6.56127e67 1.00808
\(587\) −8.02541e67 −1.18259 −0.591295 0.806456i \(-0.701383\pi\)
−0.591295 + 0.806456i \(0.701383\pi\)
\(588\) 1.00290e67 0.141747
\(589\) 7.26848e67 0.985414
\(590\) 1.36074e68 1.76970
\(591\) −7.47415e67 −0.932542
\(592\) −2.14850e67 −0.257190
\(593\) −1.46805e68 −1.68617 −0.843086 0.537779i \(-0.819263\pi\)
−0.843086 + 0.537779i \(0.819263\pi\)
\(594\) −1.46269e67 −0.161208
\(595\) −4.63920e67 −0.490656
\(596\) −2.64140e67 −0.268103
\(597\) 1.19683e68 1.16590
\(598\) 1.88112e67 0.175889
\(599\) −9.17136e67 −0.823145 −0.411573 0.911377i \(-0.635020\pi\)
−0.411573 + 0.911377i \(0.635020\pi\)
\(600\) −1.08245e68 −0.932618
\(601\) −2.27601e67 −0.188257 −0.0941283 0.995560i \(-0.530006\pi\)
−0.0941283 + 0.995560i \(0.530006\pi\)
\(602\) −1.36837e67 −0.108665
\(603\) 2.93303e68 2.23637
\(604\) 3.62591e67 0.265468
\(605\) −1.77639e68 −1.24891
\(606\) 2.34970e67 0.158648
\(607\) 1.39704e68 0.905914 0.452957 0.891532i \(-0.350369\pi\)
0.452957 + 0.891532i \(0.350369\pi\)
\(608\) −2.90034e67 −0.180639
\(609\) 1.40407e68 0.839974
\(610\) −1.05841e68 −0.608236
\(611\) 7.04944e66 0.0389175
\(612\) 3.41859e67 0.181316
\(613\) −1.66422e68 −0.848066 −0.424033 0.905647i \(-0.639386\pi\)
−0.424033 + 0.905647i \(0.639386\pi\)
\(614\) −6.69452e67 −0.327789
\(615\) 5.79993e68 2.72887
\(616\) 1.03315e67 0.0467126
\(617\) 7.60071e67 0.330269 0.165134 0.986271i \(-0.447194\pi\)
0.165134 + 0.986271i \(0.447194\pi\)
\(618\) −6.63424e68 −2.77060
\(619\) 3.95260e68 1.58658 0.793291 0.608843i \(-0.208366\pi\)
0.793291 + 0.608843i \(0.208366\pi\)
\(620\) −7.68595e67 −0.296552
\(621\) −9.23676e68 −3.42590
\(622\) 4.86079e68 1.73317
\(623\) −2.98290e68 −1.02254
\(624\) −5.75448e67 −0.189664
\(625\) −3.92521e68 −1.24395
\(626\) 4.89278e68 1.49102
\(627\) −2.81375e67 −0.0824575
\(628\) 5.01593e66 0.0141365
\(629\) 4.86952e67 0.131991
\(630\) 7.41459e68 1.93305
\(631\) −2.28574e68 −0.573201 −0.286600 0.958050i \(-0.592525\pi\)
−0.286600 + 0.958050i \(0.592525\pi\)
\(632\) −5.13509e67 −0.123874
\(633\) 1.20320e69 2.79221
\(634\) −1.23330e68 −0.275348
\(635\) −9.70796e67 −0.208531
\(636\) 5.30856e67 0.109718
\(637\) 2.60178e67 0.0517433
\(638\) 2.97744e67 0.0569818
\(639\) −8.46300e68 −1.55867
\(640\) −8.24069e68 −1.46068
\(641\) −1.91449e68 −0.326611 −0.163305 0.986576i \(-0.552216\pi\)
−0.163305 + 0.986576i \(0.552216\pi\)
\(642\) −9.97347e67 −0.163771
\(643\) −2.09210e68 −0.330684 −0.165342 0.986236i \(-0.552873\pi\)
−0.165342 + 0.986236i \(0.552873\pi\)
\(644\) −1.13044e68 −0.172005
\(645\) 2.27437e68 0.333157
\(646\) 2.70552e68 0.381552
\(647\) 9.01802e68 1.22449 0.612247 0.790667i \(-0.290266\pi\)
0.612247 + 0.790667i \(0.290266\pi\)
\(648\) 9.70948e68 1.26943
\(649\) 7.90514e67 0.0995209
\(650\) 4.86563e67 0.0589878
\(651\) −1.63636e69 −1.91049
\(652\) 1.25976e68 0.141651
\(653\) −8.06774e68 −0.873734 −0.436867 0.899526i \(-0.643912\pi\)
−0.436867 + 0.899526i \(0.643912\pi\)
\(654\) −2.46617e69 −2.57258
\(655\) 9.67116e68 0.971777
\(656\) 1.42946e69 1.38366
\(657\) 2.44532e69 2.28026
\(658\) −3.29218e68 −0.295767
\(659\) −1.45122e69 −1.25615 −0.628075 0.778153i \(-0.716157\pi\)
−0.628075 + 0.778153i \(0.716157\pi\)
\(660\) 2.97535e67 0.0248149
\(661\) 1.72306e69 1.38473 0.692365 0.721548i \(-0.256569\pi\)
0.692365 + 0.721548i \(0.256569\pi\)
\(662\) 8.80631e68 0.681982
\(663\) 1.30424e68 0.0973364
\(664\) −1.46559e69 −1.05413
\(665\) 7.55077e68 0.523433
\(666\) −7.78270e68 −0.520010
\(667\) 1.88022e69 1.21095
\(668\) 2.12472e68 0.131910
\(669\) −1.75574e69 −1.05080
\(670\) −2.45457e69 −1.41626
\(671\) −6.14876e67 −0.0342047
\(672\) 6.52956e68 0.350216
\(673\) −3.25113e69 −1.68138 −0.840690 0.541517i \(-0.817850\pi\)
−0.840690 + 0.541517i \(0.817850\pi\)
\(674\) 3.74909e69 1.86964
\(675\) −2.38914e69 −1.14895
\(676\) −3.15539e68 −0.146339
\(677\) −2.07144e69 −0.926512 −0.463256 0.886225i \(-0.653319\pi\)
−0.463256 + 0.886225i \(0.653319\pi\)
\(678\) −1.08899e69 −0.469780
\(679\) 2.50444e69 1.04208
\(680\) 1.65115e69 0.662702
\(681\) 4.05714e69 1.57078
\(682\) −3.47002e68 −0.129603
\(683\) 1.47023e69 0.529760 0.264880 0.964281i \(-0.414668\pi\)
0.264880 + 0.964281i \(0.414668\pi\)
\(684\) −5.56410e68 −0.193428
\(685\) 1.67354e69 0.561327
\(686\) −3.45288e69 −1.11748
\(687\) −5.16961e69 −1.61442
\(688\) 5.60546e68 0.168925
\(689\) 1.37717e68 0.0400514
\(690\) 1.46017e70 4.09828
\(691\) 1.33225e69 0.360890 0.180445 0.983585i \(-0.442246\pi\)
0.180445 + 0.983585i \(0.442246\pi\)
\(692\) −6.91149e68 −0.180706
\(693\) 4.30746e68 0.108707
\(694\) −3.79866e69 −0.925386
\(695\) −9.17073e69 −2.15663
\(696\) −4.99727e69 −1.13451
\(697\) −3.23984e69 −0.710101
\(698\) −5.77757e69 −1.22261
\(699\) 3.86405e69 0.789500
\(700\) −2.92394e68 −0.0576854
\(701\) 7.12825e69 1.35797 0.678987 0.734150i \(-0.262419\pi\)
0.678987 + 0.734150i \(0.262419\pi\)
\(702\) −1.10350e69 −0.203009
\(703\) −7.92564e68 −0.140809
\(704\) −3.58091e68 −0.0614418
\(705\) 5.47195e69 0.906795
\(706\) 6.57339e68 0.105214
\(707\) −3.66314e68 −0.0566341
\(708\) 2.29889e69 0.343323
\(709\) 4.28430e69 0.618083 0.309042 0.951049i \(-0.399992\pi\)
0.309042 + 0.951049i \(0.399992\pi\)
\(710\) 7.08244e69 0.987082
\(711\) −2.14096e69 −0.288272
\(712\) 1.06165e70 1.38109
\(713\) −2.19128e70 −2.75426
\(714\) −6.09096e69 −0.739741
\(715\) 7.71881e67 0.00905842
\(716\) 4.35024e68 0.0493338
\(717\) 3.57754e69 0.392072
\(718\) 1.30243e70 1.37945
\(719\) 3.53639e69 0.361995 0.180997 0.983484i \(-0.442067\pi\)
0.180997 + 0.983484i \(0.442067\pi\)
\(720\) −3.03736e70 −3.00503
\(721\) 1.03427e70 0.989050
\(722\) 7.18617e69 0.664257
\(723\) 1.88740e70 1.68646
\(724\) 1.15052e68 0.00993804
\(725\) 4.86330e69 0.406116
\(726\) −2.33228e70 −1.88293
\(727\) −3.98958e69 −0.311411 −0.155706 0.987804i \(-0.549765\pi\)
−0.155706 + 0.987804i \(0.549765\pi\)
\(728\) 7.79439e68 0.0588252
\(729\) −7.68760e69 −0.561004
\(730\) −2.04642e70 −1.44406
\(731\) −1.27046e69 −0.0866934
\(732\) −1.78812e69 −0.117998
\(733\) −8.35656e69 −0.533310 −0.266655 0.963792i \(-0.585918\pi\)
−0.266655 + 0.963792i \(0.585918\pi\)
\(734\) −2.62552e68 −0.0162055
\(735\) 2.01957e70 1.20564
\(736\) 8.74385e69 0.504890
\(737\) −1.42597e69 −0.0796446
\(738\) 5.17806e70 2.79760
\(739\) −1.56314e70 −0.816974 −0.408487 0.912764i \(-0.633944\pi\)
−0.408487 + 0.912764i \(0.633944\pi\)
\(740\) 8.38086e68 0.0423751
\(741\) −2.12278e69 −0.103839
\(742\) −6.43158e69 −0.304384
\(743\) 3.92359e70 1.79662 0.898312 0.439357i \(-0.144794\pi\)
0.898312 + 0.439357i \(0.144794\pi\)
\(744\) 5.82401e70 2.58039
\(745\) −5.31905e70 −2.28037
\(746\) −1.61833e70 −0.671378
\(747\) −6.11041e70 −2.45310
\(748\) −1.66203e68 −0.00645729
\(749\) 1.55485e69 0.0584632
\(750\) −2.75980e70 −1.00433
\(751\) 1.76438e70 0.621462 0.310731 0.950498i \(-0.399426\pi\)
0.310731 + 0.950498i \(0.399426\pi\)
\(752\) 1.34863e70 0.459785
\(753\) −5.13173e70 −1.69351
\(754\) 2.24628e69 0.0717571
\(755\) 7.30158e70 2.25796
\(756\) 6.63137e69 0.198527
\(757\) −1.73845e70 −0.503864 −0.251932 0.967745i \(-0.581066\pi\)
−0.251932 + 0.967745i \(0.581066\pi\)
\(758\) −3.04403e70 −0.854189
\(759\) 8.48280e69 0.230471
\(760\) −2.68742e70 −0.706972
\(761\) −1.36361e70 −0.347349 −0.173675 0.984803i \(-0.555564\pi\)
−0.173675 + 0.984803i \(0.555564\pi\)
\(762\) −1.27459e70 −0.314394
\(763\) 3.84472e70 0.918361
\(764\) −3.70949e68 −0.00858078
\(765\) 6.88409e70 1.54220
\(766\) 4.37331e70 0.948867
\(767\) 5.96389e69 0.125327
\(768\) −3.76798e70 −0.766936
\(769\) 8.59382e70 1.69430 0.847152 0.531351i \(-0.178316\pi\)
0.847152 + 0.531351i \(0.178316\pi\)
\(770\) −3.60479e69 −0.0688425
\(771\) −8.58718e70 −1.58861
\(772\) −3.25399e69 −0.0583167
\(773\) 4.66524e69 0.0809983 0.0404992 0.999180i \(-0.487105\pi\)
0.0404992 + 0.999180i \(0.487105\pi\)
\(774\) 2.03051e70 0.341548
\(775\) −5.66787e70 −0.923695
\(776\) −8.91361e70 −1.40748
\(777\) 1.78431e70 0.272995
\(778\) 3.15922e70 0.468360
\(779\) 5.27317e70 0.757537
\(780\) 2.24470e69 0.0312494
\(781\) 4.11450e69 0.0555094
\(782\) −8.15652e70 −1.06645
\(783\) −1.10297e71 −1.39766
\(784\) 4.97746e70 0.611314
\(785\) 1.01007e70 0.120239
\(786\) 1.26976e71 1.46511
\(787\) −6.73785e70 −0.753599 −0.376799 0.926295i \(-0.622975\pi\)
−0.376799 + 0.926295i \(0.622975\pi\)
\(788\) 7.18562e69 0.0779062
\(789\) 5.53197e70 0.581425
\(790\) 1.79170e70 0.182559
\(791\) 1.69771e70 0.167702
\(792\) −1.53308e70 −0.146824
\(793\) −4.63883e69 −0.0430740
\(794\) −1.52107e71 −1.36945
\(795\) 1.06900e71 0.933215
\(796\) −1.15063e70 −0.0974014
\(797\) −1.67868e71 −1.37797 −0.688985 0.724775i \(-0.741944\pi\)
−0.688985 + 0.724775i \(0.741944\pi\)
\(798\) 9.91367e70 0.789157
\(799\) −3.05663e70 −0.235964
\(800\) 2.26165e70 0.169325
\(801\) 4.42630e71 3.21399
\(802\) 2.35756e71 1.66032
\(803\) −1.18885e70 −0.0812078
\(804\) −4.14685e70 −0.274755
\(805\) −2.27638e71 −1.46301
\(806\) −2.61790e70 −0.163209
\(807\) −3.40652e71 −2.06020
\(808\) 1.30376e70 0.0764925
\(809\) 7.08887e70 0.403495 0.201748 0.979438i \(-0.435338\pi\)
0.201748 + 0.979438i \(0.435338\pi\)
\(810\) −3.38777e71 −1.87081
\(811\) −1.30313e71 −0.698193 −0.349097 0.937087i \(-0.613512\pi\)
−0.349097 + 0.937087i \(0.613512\pi\)
\(812\) −1.34987e70 −0.0701729
\(813\) −2.53008e71 −1.27619
\(814\) 3.78375e69 0.0185193
\(815\) 2.53680e71 1.20483
\(816\) 2.49514e71 1.14997
\(817\) 2.06781e70 0.0924847
\(818\) 2.39843e71 1.04105
\(819\) 3.24969e70 0.136895
\(820\) −5.57603e70 −0.227974
\(821\) 6.12434e70 0.243026 0.121513 0.992590i \(-0.461225\pi\)
0.121513 + 0.992590i \(0.461225\pi\)
\(822\) 2.19724e71 0.846289
\(823\) 4.66189e71 1.74288 0.871438 0.490506i \(-0.163188\pi\)
0.871438 + 0.490506i \(0.163188\pi\)
\(824\) −3.68108e71 −1.33585
\(825\) 2.19412e70 0.0772929
\(826\) −2.78522e71 −0.952462
\(827\) 1.89180e71 0.628043 0.314022 0.949416i \(-0.398324\pi\)
0.314022 + 0.949416i \(0.398324\pi\)
\(828\) 1.67745e71 0.540637
\(829\) −1.94307e71 −0.607998 −0.303999 0.952672i \(-0.598322\pi\)
−0.303999 + 0.952672i \(0.598322\pi\)
\(830\) 5.11362e71 1.55352
\(831\) −7.09589e71 −2.09306
\(832\) −2.70156e70 −0.0773736
\(833\) −1.12813e71 −0.313730
\(834\) −1.20406e72 −3.25146
\(835\) 4.27859e71 1.12197
\(836\) 2.70513e69 0.00688864
\(837\) 1.28545e72 3.17893
\(838\) −1.79007e71 −0.429923
\(839\) −1.81889e71 −0.424266 −0.212133 0.977241i \(-0.568041\pi\)
−0.212133 + 0.977241i \(0.568041\pi\)
\(840\) 6.05021e71 1.37065
\(841\) −2.29947e71 −0.505970
\(842\) −3.05658e71 −0.653265
\(843\) −1.07060e72 −2.22255
\(844\) −1.15675e71 −0.233266
\(845\) −6.35408e71 −1.24470
\(846\) 4.88525e71 0.929636
\(847\) 3.63598e71 0.672168
\(848\) 2.63467e71 0.473182
\(849\) 1.05335e72 1.83796
\(850\) −2.10973e71 −0.357655
\(851\) 2.38940e71 0.393563
\(852\) 1.19654e71 0.191494
\(853\) −8.16161e70 −0.126918 −0.0634592 0.997984i \(-0.520213\pi\)
−0.0634592 + 0.997984i \(0.520213\pi\)
\(854\) 2.16639e71 0.327355
\(855\) −1.12046e72 −1.64522
\(856\) −5.53390e70 −0.0789630
\(857\) 1.39103e72 1.92889 0.964445 0.264285i \(-0.0851358\pi\)
0.964445 + 0.264285i \(0.0851358\pi\)
\(858\) 1.01343e70 0.0136570
\(859\) 3.97272e71 0.520301 0.260151 0.965568i \(-0.416228\pi\)
0.260151 + 0.965568i \(0.416228\pi\)
\(860\) −2.18657e70 −0.0278325
\(861\) −1.18715e72 −1.46869
\(862\) −1.12862e71 −0.135712
\(863\) 4.45935e71 0.521203 0.260601 0.965446i \(-0.416079\pi\)
0.260601 + 0.965446i \(0.416079\pi\)
\(864\) −5.12932e71 −0.582738
\(865\) −1.39178e72 −1.53701
\(866\) 4.66233e70 0.0500512
\(867\) 1.12837e72 1.17756
\(868\) 1.57319e71 0.159606
\(869\) 1.04088e70 0.0102663
\(870\) 1.74362e72 1.67197
\(871\) −1.07580e71 −0.100296
\(872\) −1.36839e72 −1.24038
\(873\) −3.71632e72 −3.27540
\(874\) 1.32756e72 1.13769
\(875\) 4.30248e71 0.358527
\(876\) −3.45730e71 −0.280147
\(877\) −1.15171e72 −0.907512 −0.453756 0.891126i \(-0.649916\pi\)
−0.453756 + 0.891126i \(0.649916\pi\)
\(878\) 4.97536e71 0.381249
\(879\) 2.23219e72 1.66342
\(880\) 1.47669e71 0.107019
\(881\) −2.42451e72 −1.70889 −0.854447 0.519539i \(-0.826104\pi\)
−0.854447 + 0.519539i \(0.826104\pi\)
\(882\) 1.80303e72 1.23601
\(883\) 1.55419e72 1.03626 0.518128 0.855303i \(-0.326629\pi\)
0.518128 + 0.855303i \(0.326629\pi\)
\(884\) −1.25389e70 −0.00813166
\(885\) 4.62932e72 2.92017
\(886\) 1.01354e71 0.0621891
\(887\) 5.49889e71 0.328206 0.164103 0.986443i \(-0.447527\pi\)
0.164103 + 0.986443i \(0.447527\pi\)
\(888\) −6.35058e71 −0.368719
\(889\) 1.98706e71 0.112232
\(890\) −3.70424e72 −2.03537
\(891\) −1.96810e71 −0.105207
\(892\) 1.68797e71 0.0877859
\(893\) 4.97498e71 0.251727
\(894\) −6.98356e72 −3.43802
\(895\) 8.76018e71 0.419613
\(896\) 1.68674e72 0.786143
\(897\) 6.39970e71 0.290232
\(898\) −3.34160e71 −0.147463
\(899\) −2.61664e72 −1.12365
\(900\) 4.33882e71 0.181313
\(901\) −5.97141e71 −0.242840
\(902\) −2.51744e71 −0.0996322
\(903\) −4.65527e71 −0.179306
\(904\) −6.04236e71 −0.226506
\(905\) 2.31684e71 0.0845289
\(906\) 9.58649e72 3.40423
\(907\) 2.00638e72 0.693482 0.346741 0.937961i \(-0.387288\pi\)
0.346741 + 0.937961i \(0.387288\pi\)
\(908\) −3.90052e71 −0.131226
\(909\) 5.43572e71 0.178009
\(910\) −2.71957e71 −0.0866934
\(911\) −6.79753e70 −0.0210936 −0.0105468 0.999944i \(-0.503357\pi\)
−0.0105468 + 0.999944i \(0.503357\pi\)
\(912\) −4.06109e72 −1.22679
\(913\) 2.97073e71 0.0873633
\(914\) −3.17266e72 −0.908325
\(915\) −3.60078e72 −1.00364
\(916\) 4.97005e71 0.134872
\(917\) −1.97953e72 −0.523014
\(918\) 4.78478e72 1.23088
\(919\) 7.92073e71 0.198397 0.0991985 0.995068i \(-0.468372\pi\)
0.0991985 + 0.995068i \(0.468372\pi\)
\(920\) 8.10195e72 1.97600
\(921\) −2.27752e72 −0.540881
\(922\) 1.72071e72 0.397925
\(923\) 3.10411e71 0.0699030
\(924\) −6.09007e70 −0.0133555
\(925\) 6.18032e71 0.131989
\(926\) 5.25453e72 1.09286
\(927\) −1.53474e73 −3.10872
\(928\) 1.04412e72 0.205979
\(929\) 4.36095e72 0.837908 0.418954 0.908008i \(-0.362397\pi\)
0.418954 + 0.908008i \(0.362397\pi\)
\(930\) −2.03208e73 −3.80284
\(931\) 1.83615e72 0.334688
\(932\) −3.71489e71 −0.0659562
\(933\) 1.65367e73 2.85989
\(934\) −5.61706e72 −0.946260
\(935\) −3.34687e71 −0.0549230
\(936\) −1.15661e72 −0.184896
\(937\) −8.38565e72 −1.30592 −0.652960 0.757392i \(-0.726473\pi\)
−0.652960 + 0.757392i \(0.726473\pi\)
\(938\) 5.02411e72 0.762236
\(939\) 1.66456e73 2.46032
\(940\) −5.26072e71 −0.0757552
\(941\) −5.95096e72 −0.834913 −0.417456 0.908697i \(-0.637078\pi\)
−0.417456 + 0.908697i \(0.637078\pi\)
\(942\) 1.32616e72 0.181279
\(943\) −1.58974e73 −2.11733
\(944\) 1.14095e73 1.48065
\(945\) 1.33537e73 1.68859
\(946\) −9.87184e70 −0.0121637
\(947\) 5.80008e72 0.696402 0.348201 0.937420i \(-0.386793\pi\)
0.348201 + 0.937420i \(0.386793\pi\)
\(948\) 3.02697e71 0.0354164
\(949\) −8.96911e71 −0.102265
\(950\) 3.43381e72 0.381546
\(951\) −4.19577e72 −0.454349
\(952\) −3.37964e72 −0.356669
\(953\) −1.78856e73 −1.83962 −0.919810 0.392365i \(-0.871657\pi\)
−0.919810 + 0.392365i \(0.871657\pi\)
\(954\) 9.54379e72 0.956722
\(955\) −7.46988e71 −0.0729846
\(956\) −3.43944e71 −0.0327544
\(957\) 1.01294e72 0.0940249
\(958\) −1.84286e72 −0.166739
\(959\) −3.42546e72 −0.302109
\(960\) −2.09702e73 −1.80284
\(961\) 1.85631e73 1.55570
\(962\) 2.85459e71 0.0233214
\(963\) −2.30723e72 −0.183758
\(964\) −1.81454e72 −0.140890
\(965\) −6.55264e72 −0.496018
\(966\) −2.98874e73 −2.20571
\(967\) 8.21075e72 0.590792 0.295396 0.955375i \(-0.404548\pi\)
0.295396 + 0.955375i \(0.404548\pi\)
\(968\) −1.29409e73 −0.907860
\(969\) 9.20436e72 0.629595
\(970\) 3.11008e73 2.07426
\(971\) 1.52584e73 0.992288 0.496144 0.868240i \(-0.334749\pi\)
0.496144 + 0.868240i \(0.334749\pi\)
\(972\) −1.09248e72 −0.0692773
\(973\) 1.87710e73 1.16071
\(974\) 1.34210e73 0.809264
\(975\) 1.65532e72 0.0973349
\(976\) −8.87454e72 −0.508892
\(977\) 5.10455e72 0.285457 0.142728 0.989762i \(-0.454412\pi\)
0.142728 + 0.989762i \(0.454412\pi\)
\(978\) 3.33065e73 1.81647
\(979\) −2.15196e72 −0.114461
\(980\) −1.94161e72 −0.100721
\(981\) −5.70516e73 −2.88654
\(982\) −3.33135e73 −1.64395
\(983\) −3.35654e73 −1.61559 −0.807793 0.589466i \(-0.799338\pi\)
−0.807793 + 0.589466i \(0.799338\pi\)
\(984\) 4.22523e73 1.98367
\(985\) 1.44699e73 0.662638
\(986\) −9.73983e72 −0.435078
\(987\) −1.12002e73 −0.488041
\(988\) 2.04084e71 0.00867487
\(989\) −6.23396e72 −0.258497
\(990\) 5.34913e72 0.216382
\(991\) 3.04908e73 1.20327 0.601637 0.798770i \(-0.294516\pi\)
0.601637 + 0.798770i \(0.294516\pi\)
\(992\) −1.21685e73 −0.468492
\(993\) 2.99596e73 1.12533
\(994\) −1.44966e73 −0.531251
\(995\) −2.31705e73 −0.828457
\(996\) 8.63916e72 0.301382
\(997\) −5.00437e70 −0.00170341 −0.000851703 1.00000i \(-0.500271\pi\)
−0.000851703 1.00000i \(0.500271\pi\)
\(998\) 6.11582e72 0.203122
\(999\) −1.40167e73 −0.454246
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 1.50.a.a.1.1 3
3.2 odd 2 9.50.a.a.1.3 3
4.3 odd 2 16.50.a.c.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.50.a.a.1.1 3 1.1 even 1 trivial
9.50.a.a.1.3 3 3.2 odd 2
16.50.a.c.1.3 3 4.3 odd 2