Properties

Label 1.50.a.a.1.2
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 1.2
Root \(165922.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.25719e7 q^{2} +5.57972e11 q^{3} -5.34581e13 q^{4} -1.06460e17 q^{5} -1.25945e19 q^{6} +5.68014e20 q^{7} +1.39135e22 q^{8} +7.20337e22 q^{9} +O(q^{10})\) \(q-2.25719e7 q^{2} +5.57972e11 q^{3} -5.34581e13 q^{4} -1.06460e17 q^{5} -1.25945e19 q^{6} +5.68014e20 q^{7} +1.39135e22 q^{8} +7.20337e22 q^{9} +2.40300e24 q^{10} -4.66926e25 q^{11} -2.98281e25 q^{12} +1.95401e27 q^{13} -1.28212e28 q^{14} -5.94017e28 q^{15} -2.83961e29 q^{16} -1.59552e30 q^{17} -1.62594e30 q^{18} -3.45099e31 q^{19} +5.69114e30 q^{20} +3.16936e32 q^{21} +1.05394e33 q^{22} -2.46487e33 q^{23} +7.76336e33 q^{24} -6.42986e33 q^{25} -4.41057e34 q^{26} -9.33296e34 q^{27} -3.03649e34 q^{28} +4.27652e35 q^{29} +1.34081e36 q^{30} +2.26555e36 q^{31} -1.42307e36 q^{32} -2.60532e37 q^{33} +3.60138e37 q^{34} -6.04707e37 q^{35} -3.85078e36 q^{36} -1.55810e38 q^{37} +7.78954e38 q^{38} +1.09028e39 q^{39} -1.48123e39 q^{40} -1.49379e39 q^{41} -7.15386e39 q^{42} +5.17800e39 q^{43} +2.49610e39 q^{44} -7.66870e39 q^{45} +5.56368e40 q^{46} +5.79235e40 q^{47} -1.58442e41 q^{48} +6.57162e40 q^{49} +1.45134e41 q^{50} -8.90253e41 q^{51} -1.04457e41 q^{52} -5.51356e41 q^{53} +2.10663e42 q^{54} +4.97089e42 q^{55} +7.90307e42 q^{56} -1.92555e43 q^{57} -9.65293e42 q^{58} -1.93125e42 q^{59} +3.17550e42 q^{60} +2.41153e43 q^{61} -5.11377e43 q^{62} +4.09161e43 q^{63} +1.91977e44 q^{64} -2.08023e44 q^{65} +5.88070e44 q^{66} -8.25642e44 q^{67} +8.52932e43 q^{68} -1.37533e45 q^{69} +1.36494e45 q^{70} -1.77228e45 q^{71} +1.00224e45 q^{72} +6.25517e45 q^{73} +3.51693e45 q^{74} -3.58768e45 q^{75} +1.84483e45 q^{76} -2.65220e46 q^{77} -2.46097e46 q^{78} +4.72997e46 q^{79} +3.02304e46 q^{80} -6.93129e46 q^{81} +3.37178e46 q^{82} +4.29785e46 q^{83} -1.69428e46 q^{84} +1.69858e47 q^{85} -1.16877e47 q^{86} +2.38618e47 q^{87} -6.49658e47 q^{88} -7.42748e47 q^{89} +1.73097e47 q^{90} +1.10990e48 q^{91} +1.31767e47 q^{92} +1.26411e48 q^{93} -1.30744e48 q^{94} +3.67392e48 q^{95} -7.94036e47 q^{96} -5.90631e48 q^{97} -1.48334e48 q^{98} -3.36344e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 24225168q^{2} - 326954692404q^{3} + 31502767984896q^{4} + 63884035717079250q^{5} + 8906136249246768576q^{6} + 509391477498711192q^{7} + 12774393005516465664000q^{8} + 341625690512280455369319q^{9} + O(q^{10}) \) \( 3q - 24225168q^{2} - 326954692404q^{3} + 31502767984896q^{4} + 63884035717079250q^{5} + 8906136249246768576q^{6} + 509391477498711192q^{7} + \)\(12\!\cdots\!00\)\(q^{8} + \)\(34\!\cdots\!19\)\(q^{9} - \)\(17\!\cdots\!00\)\(q^{10} - \)\(20\!\cdots\!24\)\(q^{11} - \)\(10\!\cdots\!48\)\(q^{12} - \)\(18\!\cdots\!14\)\(q^{13} - \)\(94\!\cdots\!88\)\(q^{14} - \)\(20\!\cdots\!00\)\(q^{15} - \)\(95\!\cdots\!12\)\(q^{16} - \)\(33\!\cdots\!38\)\(q^{17} - \)\(20\!\cdots\!44\)\(q^{18} - \)\(45\!\cdots\!60\)\(q^{19} + \)\(19\!\cdots\!00\)\(q^{20} + \)\(61\!\cdots\!16\)\(q^{21} + \)\(17\!\cdots\!44\)\(q^{22} + \)\(45\!\cdots\!76\)\(q^{23} - \)\(25\!\cdots\!80\)\(q^{24} - \)\(13\!\cdots\!75\)\(q^{25} - \)\(85\!\cdots\!64\)\(q^{26} - \)\(31\!\cdots\!00\)\(q^{27} - \)\(59\!\cdots\!96\)\(q^{28} + \)\(11\!\cdots\!10\)\(q^{29} + \)\(50\!\cdots\!00\)\(q^{30} + \)\(93\!\cdots\!16\)\(q^{31} + \)\(73\!\cdots\!92\)\(q^{32} - \)\(24\!\cdots\!68\)\(q^{33} - \)\(44\!\cdots\!28\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(37\!\cdots\!08\)\(q^{36} + \)\(24\!\cdots\!02\)\(q^{37} + \)\(11\!\cdots\!00\)\(q^{38} + \)\(12\!\cdots\!48\)\(q^{39} + \)\(52\!\cdots\!00\)\(q^{40} - \)\(62\!\cdots\!14\)\(q^{41} - \)\(14\!\cdots\!76\)\(q^{42} - \)\(77\!\cdots\!44\)\(q^{43} + \)\(23\!\cdots\!32\)\(q^{44} + \)\(76\!\cdots\!50\)\(q^{45} + \)\(26\!\cdots\!96\)\(q^{46} + \)\(72\!\cdots\!72\)\(q^{47} + \)\(15\!\cdots\!76\)\(q^{48} - \)\(28\!\cdots\!29\)\(q^{49} - \)\(53\!\cdots\!00\)\(q^{50} - \)\(15\!\cdots\!04\)\(q^{51} - \)\(12\!\cdots\!68\)\(q^{52} - \)\(15\!\cdots\!54\)\(q^{53} + \)\(82\!\cdots\!40\)\(q^{54} + \)\(46\!\cdots\!00\)\(q^{55} + \)\(67\!\cdots\!40\)\(q^{56} - \)\(79\!\cdots\!00\)\(q^{57} - \)\(16\!\cdots\!00\)\(q^{58} - \)\(62\!\cdots\!80\)\(q^{59} - \)\(88\!\cdots\!00\)\(q^{60} - \)\(24\!\cdots\!74\)\(q^{61} + \)\(18\!\cdots\!04\)\(q^{62} - \)\(79\!\cdots\!64\)\(q^{63} + \)\(51\!\cdots\!36\)\(q^{64} - \)\(24\!\cdots\!00\)\(q^{65} + \)\(52\!\cdots\!92\)\(q^{66} - \)\(10\!\cdots\!88\)\(q^{67} + \)\(14\!\cdots\!44\)\(q^{68} - \)\(48\!\cdots\!72\)\(q^{69} + \)\(28\!\cdots\!00\)\(q^{70} - \)\(32\!\cdots\!04\)\(q^{71} + \)\(10\!\cdots\!00\)\(q^{72} + \)\(56\!\cdots\!26\)\(q^{73} + \)\(10\!\cdots\!92\)\(q^{74} - \)\(12\!\cdots\!00\)\(q^{75} + \)\(75\!\cdots\!80\)\(q^{76} - \)\(32\!\cdots\!36\)\(q^{77} - \)\(27\!\cdots\!08\)\(q^{78} - \)\(78\!\cdots\!40\)\(q^{79} - \)\(30\!\cdots\!00\)\(q^{80} + \)\(67\!\cdots\!43\)\(q^{81} + \)\(11\!\cdots\!84\)\(q^{82} + \)\(94\!\cdots\!16\)\(q^{83} + \)\(77\!\cdots\!12\)\(q^{84} + \)\(29\!\cdots\!00\)\(q^{85} - \)\(34\!\cdots\!84\)\(q^{86} - \)\(17\!\cdots\!00\)\(q^{87} - \)\(10\!\cdots\!00\)\(q^{88} + \)\(36\!\cdots\!30\)\(q^{89} - \)\(20\!\cdots\!00\)\(q^{90} + \)\(16\!\cdots\!76\)\(q^{91} + \)\(46\!\cdots\!12\)\(q^{92} + \)\(59\!\cdots\!12\)\(q^{93} + \)\(90\!\cdots\!52\)\(q^{94} + \)\(14\!\cdots\!00\)\(q^{95} - \)\(26\!\cdots\!44\)\(q^{96} - \)\(10\!\cdots\!78\)\(q^{97} - \)\(28\!\cdots\!76\)\(q^{98} - \)\(11\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25719e7 −0.951336 −0.475668 0.879625i \(-0.657794\pi\)
−0.475668 + 0.879625i \(0.657794\pi\)
\(3\) 5.57972e11 1.14062 0.570311 0.821429i \(-0.306823\pi\)
0.570311 + 0.821429i \(0.306823\pi\)
\(4\) −5.34581e13 −0.0949606
\(5\) −1.06460e17 −0.798768 −0.399384 0.916784i \(-0.630776\pi\)
−0.399384 + 0.916784i \(0.630776\pi\)
\(6\) −1.25945e19 −1.08511
\(7\) 5.68014e20 1.12062 0.560308 0.828284i \(-0.310683\pi\)
0.560308 + 0.828284i \(0.310683\pi\)
\(8\) 1.39135e22 1.04167
\(9\) 7.20337e22 0.301019
\(10\) 2.40300e24 0.759897
\(11\) −4.66926e25 −1.42931 −0.714656 0.699476i \(-0.753417\pi\)
−0.714656 + 0.699476i \(0.753417\pi\)
\(12\) −2.98281e25 −0.108314
\(13\) 1.95401e27 0.998421 0.499211 0.866481i \(-0.333623\pi\)
0.499211 + 0.866481i \(0.333623\pi\)
\(14\) −1.28212e28 −1.06608
\(15\) −5.94017e28 −0.911093
\(16\) −2.83961e29 −0.896022
\(17\) −1.59552e30 −1.13999 −0.569997 0.821647i \(-0.693056\pi\)
−0.569997 + 0.821647i \(0.693056\pi\)
\(18\) −1.62594e30 −0.286370
\(19\) −3.45099e31 −1.61614 −0.808072 0.589084i \(-0.799489\pi\)
−0.808072 + 0.589084i \(0.799489\pi\)
\(20\) 5.69114e30 0.0758515
\(21\) 3.16936e32 1.27820
\(22\) 1.05394e33 1.35976
\(23\) −2.46487e33 −1.07019 −0.535096 0.844791i \(-0.679725\pi\)
−0.535096 + 0.844791i \(0.679725\pi\)
\(24\) 7.76336e33 1.18816
\(25\) −6.42986e33 −0.361969
\(26\) −4.41057e34 −0.949834
\(27\) −9.33296e34 −0.797273
\(28\) −3.03649e34 −0.106414
\(29\) 4.27652e35 0.634365 0.317183 0.948364i \(-0.397263\pi\)
0.317183 + 0.948364i \(0.397263\pi\)
\(30\) 1.34081e36 0.866755
\(31\) 2.26555e36 0.655861 0.327930 0.944702i \(-0.393649\pi\)
0.327930 + 0.944702i \(0.393649\pi\)
\(32\) −1.42307e36 −0.189258
\(33\) −2.60532e37 −1.63031
\(34\) 3.60138e37 1.08452
\(35\) −6.04707e37 −0.895113
\(36\) −3.85078e36 −0.0285850
\(37\) −1.55810e38 −0.591088 −0.295544 0.955329i \(-0.595501\pi\)
−0.295544 + 0.955329i \(0.595501\pi\)
\(38\) 7.78954e38 1.53749
\(39\) 1.09028e39 1.13882
\(40\) −1.48123e39 −0.832057
\(41\) −1.49379e39 −0.458233 −0.229117 0.973399i \(-0.573584\pi\)
−0.229117 + 0.973399i \(0.573584\pi\)
\(42\) −7.15386e39 −1.21600
\(43\) 5.17800e39 0.494521 0.247260 0.968949i \(-0.420470\pi\)
0.247260 + 0.968949i \(0.420470\pi\)
\(44\) 2.49610e39 0.135728
\(45\) −7.66870e39 −0.240445
\(46\) 5.56368e40 1.01811
\(47\) 5.79235e40 0.625831 0.312916 0.949781i \(-0.398694\pi\)
0.312916 + 0.949781i \(0.398694\pi\)
\(48\) −1.58442e41 −1.02202
\(49\) 6.57162e40 0.255781
\(50\) 1.45134e41 0.344354
\(51\) −8.90253e41 −1.30030
\(52\) −1.04457e41 −0.0948107
\(53\) −5.51356e41 −0.313815 −0.156907 0.987613i \(-0.550152\pi\)
−0.156907 + 0.987613i \(0.550152\pi\)
\(54\) 2.10663e42 0.758474
\(55\) 4.97089e42 1.14169
\(56\) 7.90307e42 1.16732
\(57\) −1.92555e43 −1.84341
\(58\) −9.65293e42 −0.603494
\(59\) −1.93125e42 −0.0794262 −0.0397131 0.999211i \(-0.512644\pi\)
−0.0397131 + 0.999211i \(0.512644\pi\)
\(60\) 3.17550e42 0.0865180
\(61\) 2.41153e43 0.438239 0.219120 0.975698i \(-0.429681\pi\)
0.219120 + 0.975698i \(0.429681\pi\)
\(62\) −5.11377e43 −0.623943
\(63\) 4.09161e43 0.337327
\(64\) 1.91977e44 1.07607
\(65\) −2.08023e44 −0.797507
\(66\) 5.88070e44 1.55097
\(67\) −8.25642e44 −1.50646 −0.753232 0.657755i \(-0.771506\pi\)
−0.753232 + 0.657755i \(0.771506\pi\)
\(68\) 8.52932e43 0.108254
\(69\) −1.37533e45 −1.22069
\(70\) 1.36494e45 0.851553
\(71\) −1.77228e45 −0.781094 −0.390547 0.920583i \(-0.627714\pi\)
−0.390547 + 0.920583i \(0.627714\pi\)
\(72\) 1.00224e45 0.313564
\(73\) 6.25517e45 1.39582 0.697910 0.716186i \(-0.254114\pi\)
0.697910 + 0.716186i \(0.254114\pi\)
\(74\) 3.51693e45 0.562323
\(75\) −3.58768e45 −0.412870
\(76\) 1.84483e45 0.153470
\(77\) −2.65220e46 −1.60171
\(78\) −2.46097e46 −1.08340
\(79\) 4.72997e46 1.52404 0.762018 0.647556i \(-0.224209\pi\)
0.762018 + 0.647556i \(0.224209\pi\)
\(80\) 3.02304e46 0.715714
\(81\) −6.93129e46 −1.21041
\(82\) 3.37178e46 0.435933
\(83\) 4.29785e46 0.412893 0.206447 0.978458i \(-0.433810\pi\)
0.206447 + 0.978458i \(0.433810\pi\)
\(84\) −1.69428e46 −0.121379
\(85\) 1.69858e47 0.910591
\(86\) −1.16877e47 −0.470455
\(87\) 2.38618e47 0.723571
\(88\) −6.49658e47 −1.48888
\(89\) −7.42748e47 −1.29058 −0.645292 0.763936i \(-0.723264\pi\)
−0.645292 + 0.763936i \(0.723264\pi\)
\(90\) 1.73097e47 0.228744
\(91\) 1.10990e48 1.11885
\(92\) 1.31767e47 0.101626
\(93\) 1.26411e48 0.748089
\(94\) −1.30744e48 −0.595375
\(95\) 3.67392e48 1.29092
\(96\) −7.94036e47 −0.215871
\(97\) −5.90631e48 −1.24569 −0.622843 0.782347i \(-0.714023\pi\)
−0.622843 + 0.782347i \(0.714023\pi\)
\(98\) −1.48334e48 −0.243334
\(99\) −3.36344e48 −0.430250
\(100\) 3.43728e47 0.0343728
\(101\) −1.67953e48 −0.131618 −0.0658090 0.997832i \(-0.520963\pi\)
−0.0658090 + 0.997832i \(0.520963\pi\)
\(102\) 2.00947e49 1.23702
\(103\) −9.66426e48 −0.468443 −0.234221 0.972183i \(-0.575254\pi\)
−0.234221 + 0.972183i \(0.575254\pi\)
\(104\) 2.71871e49 1.04003
\(105\) −3.37410e49 −1.02099
\(106\) 1.24452e49 0.298543
\(107\) 1.13270e49 0.215879 0.107940 0.994157i \(-0.465575\pi\)
0.107940 + 0.994157i \(0.465575\pi\)
\(108\) 4.98922e48 0.0757095
\(109\) 4.53029e49 0.548500 0.274250 0.961658i \(-0.411570\pi\)
0.274250 + 0.961658i \(0.411570\pi\)
\(110\) −1.12203e50 −1.08613
\(111\) −8.69375e49 −0.674208
\(112\) −1.61294e50 −1.00410
\(113\) 9.56756e48 0.0479048 0.0239524 0.999713i \(-0.492375\pi\)
0.0239524 + 0.999713i \(0.492375\pi\)
\(114\) 4.34635e50 1.75370
\(115\) 2.62410e50 0.854836
\(116\) −2.28614e49 −0.0602397
\(117\) 1.40754e50 0.300544
\(118\) 4.35920e49 0.0755609
\(119\) −9.06275e50 −1.27750
\(120\) −8.26486e50 −0.949063
\(121\) 1.11301e51 1.04293
\(122\) −5.44328e50 −0.416913
\(123\) −8.33496e50 −0.522671
\(124\) −1.21112e50 −0.0622809
\(125\) 2.57563e51 1.08790
\(126\) −9.23556e50 −0.320911
\(127\) 3.33633e51 0.955164 0.477582 0.878587i \(-0.341513\pi\)
0.477582 + 0.878587i \(0.341513\pi\)
\(128\) −3.53218e51 −0.834445
\(129\) 2.88918e51 0.564061
\(130\) 4.69549e51 0.758697
\(131\) −7.56140e51 −1.01264 −0.506320 0.862346i \(-0.668995\pi\)
−0.506320 + 0.862346i \(0.668995\pi\)
\(132\) 1.39275e51 0.154815
\(133\) −1.96021e52 −1.81108
\(134\) 1.86363e52 1.43315
\(135\) 9.93586e51 0.636837
\(136\) −2.21992e52 −1.18750
\(137\) −3.63264e52 −1.62393 −0.811967 0.583704i \(-0.801603\pi\)
−0.811967 + 0.583704i \(0.801603\pi\)
\(138\) 3.10438e52 1.16128
\(139\) 4.58875e52 1.43824 0.719121 0.694885i \(-0.244545\pi\)
0.719121 + 0.694885i \(0.244545\pi\)
\(140\) 3.23265e51 0.0850005
\(141\) 3.23197e52 0.713837
\(142\) 4.00038e52 0.743082
\(143\) −9.12376e52 −1.42706
\(144\) −2.04547e52 −0.269720
\(145\) −4.55278e52 −0.506711
\(146\) −1.41191e53 −1.32789
\(147\) 3.66678e52 0.291750
\(148\) 8.32929e51 0.0561301
\(149\) 1.90143e53 1.08647 0.543233 0.839582i \(-0.317200\pi\)
0.543233 + 0.839582i \(0.317200\pi\)
\(150\) 8.09809e52 0.392778
\(151\) 2.73658e53 1.12791 0.563953 0.825807i \(-0.309280\pi\)
0.563953 + 0.825807i \(0.309280\pi\)
\(152\) −4.80153e53 −1.68350
\(153\) −1.14931e53 −0.343160
\(154\) 5.98654e53 1.52376
\(155\) −2.41190e53 −0.523881
\(156\) −5.82843e52 −0.108143
\(157\) 6.65092e53 1.05521 0.527607 0.849489i \(-0.323090\pi\)
0.527607 + 0.849489i \(0.323090\pi\)
\(158\) −1.06765e54 −1.44987
\(159\) −3.07642e53 −0.357944
\(160\) 1.51500e53 0.151173
\(161\) −1.40008e54 −1.19928
\(162\) 1.56453e54 1.15150
\(163\) −4.80475e53 −0.304141 −0.152070 0.988370i \(-0.548594\pi\)
−0.152070 + 0.988370i \(0.548594\pi\)
\(164\) 7.98554e52 0.0435141
\(165\) 2.77362e54 1.30224
\(166\) −9.70107e53 −0.392800
\(167\) −5.81006e53 −0.203061 −0.101531 0.994832i \(-0.532374\pi\)
−0.101531 + 0.994832i \(0.532374\pi\)
\(168\) 4.40969e54 1.33147
\(169\) −1.20849e52 −0.00315515
\(170\) −3.83403e54 −0.866277
\(171\) −2.48587e54 −0.486490
\(172\) −2.76806e53 −0.0469600
\(173\) −5.03434e54 −0.740991 −0.370496 0.928834i \(-0.620812\pi\)
−0.370496 + 0.928834i \(0.620812\pi\)
\(174\) −5.38606e54 −0.688359
\(175\) −3.65225e54 −0.405628
\(176\) 1.32589e55 1.28070
\(177\) −1.07758e54 −0.0905953
\(178\) 1.67653e55 1.22778
\(179\) 1.02146e55 0.652114 0.326057 0.945350i \(-0.394280\pi\)
0.326057 + 0.945350i \(0.394280\pi\)
\(180\) 4.09954e53 0.0228328
\(181\) −4.89697e54 −0.238124 −0.119062 0.992887i \(-0.537989\pi\)
−0.119062 + 0.992887i \(0.537989\pi\)
\(182\) −2.50526e55 −1.06440
\(183\) 1.34557e55 0.499866
\(184\) −3.42950e55 −1.11479
\(185\) 1.65875e55 0.472143
\(186\) −2.85334e55 −0.711684
\(187\) 7.44987e55 1.62941
\(188\) −3.09648e54 −0.0594293
\(189\) −5.30125e55 −0.893437
\(190\) −8.29273e55 −1.22810
\(191\) −2.57335e55 −0.335105 −0.167553 0.985863i \(-0.553586\pi\)
−0.167553 + 0.985863i \(0.553586\pi\)
\(192\) 1.07118e56 1.22739
\(193\) 6.57181e55 0.663026 0.331513 0.943451i \(-0.392441\pi\)
0.331513 + 0.943451i \(0.392441\pi\)
\(194\) 1.33317e56 1.18507
\(195\) −1.16071e56 −0.909655
\(196\) −3.51306e54 −0.0242891
\(197\) 1.67063e56 1.01967 0.509833 0.860273i \(-0.329707\pi\)
0.509833 + 0.860273i \(0.329707\pi\)
\(198\) 7.59193e55 0.409313
\(199\) −2.81794e56 −1.34286 −0.671431 0.741067i \(-0.734320\pi\)
−0.671431 + 0.741067i \(0.734320\pi\)
\(200\) −8.94620e55 −0.377054
\(201\) −4.60685e56 −1.71831
\(202\) 3.79103e55 0.125213
\(203\) 2.42912e56 0.710880
\(204\) 4.75912e55 0.123477
\(205\) 1.59029e56 0.366022
\(206\) 2.18141e56 0.445646
\(207\) −1.77554e56 −0.322148
\(208\) −5.54861e56 −0.894607
\(209\) 1.61135e57 2.30997
\(210\) 7.61599e56 0.971300
\(211\) −1.09882e57 −1.24741 −0.623703 0.781662i \(-0.714372\pi\)
−0.623703 + 0.781662i \(0.714372\pi\)
\(212\) 2.94745e55 0.0298001
\(213\) −9.88884e56 −0.890933
\(214\) −2.55671e56 −0.205373
\(215\) −5.51249e56 −0.395008
\(216\) −1.29854e57 −0.830499
\(217\) 1.28686e57 0.734968
\(218\) −1.02257e57 −0.521808
\(219\) 3.49021e57 1.59210
\(220\) −2.65734e56 −0.108416
\(221\) −3.11765e57 −1.13819
\(222\) 1.96235e57 0.641398
\(223\) 1.62911e57 0.476958 0.238479 0.971148i \(-0.423351\pi\)
0.238479 + 0.971148i \(0.423351\pi\)
\(224\) −8.08326e56 −0.212085
\(225\) −4.63167e56 −0.108960
\(226\) −2.15958e56 −0.0455736
\(227\) 3.87678e57 0.734239 0.367120 0.930174i \(-0.380344\pi\)
0.367120 + 0.930174i \(0.380344\pi\)
\(228\) 1.02936e57 0.175051
\(229\) 6.74432e57 1.03031 0.515156 0.857097i \(-0.327734\pi\)
0.515156 + 0.857097i \(0.327734\pi\)
\(230\) −5.92309e57 −0.813236
\(231\) −1.47986e58 −1.82695
\(232\) 5.95014e57 0.660802
\(233\) −1.07268e58 −1.07214 −0.536069 0.844174i \(-0.680091\pi\)
−0.536069 + 0.844174i \(0.680091\pi\)
\(234\) −3.17709e57 −0.285918
\(235\) −6.16653e57 −0.499894
\(236\) 1.03241e56 0.00754236
\(237\) 2.63919e58 1.73835
\(238\) 2.04564e58 1.21533
\(239\) −6.84695e57 −0.367070 −0.183535 0.983013i \(-0.558754\pi\)
−0.183535 + 0.983013i \(0.558754\pi\)
\(240\) 1.68677e58 0.816359
\(241\) 6.43851e57 0.281429 0.140714 0.990050i \(-0.455060\pi\)
0.140714 + 0.990050i \(0.455060\pi\)
\(242\) −2.51227e58 −0.992180
\(243\) −1.63410e58 −0.583344
\(244\) −1.28916e57 −0.0416155
\(245\) −6.99614e57 −0.204310
\(246\) 1.88136e58 0.497235
\(247\) −6.74325e58 −1.61359
\(248\) 3.15217e58 0.683193
\(249\) 2.39808e58 0.470955
\(250\) −5.81369e58 −1.03496
\(251\) 4.88114e57 0.0787980 0.0393990 0.999224i \(-0.487456\pi\)
0.0393990 + 0.999224i \(0.487456\pi\)
\(252\) −2.18730e57 −0.0320328
\(253\) 1.15091e59 1.52964
\(254\) −7.53074e58 −0.908682
\(255\) 9.47762e58 1.03864
\(256\) −2.83455e58 −0.282232
\(257\) 9.71196e58 0.878912 0.439456 0.898264i \(-0.355171\pi\)
0.439456 + 0.898264i \(0.355171\pi\)
\(258\) −6.52143e58 −0.536612
\(259\) −8.85021e58 −0.662383
\(260\) 1.11205e58 0.0757318
\(261\) 3.08053e58 0.190956
\(262\) 1.70675e59 0.963361
\(263\) −1.69871e59 −0.873381 −0.436690 0.899612i \(-0.643849\pi\)
−0.436690 + 0.899612i \(0.643849\pi\)
\(264\) −3.62491e59 −1.69825
\(265\) 5.86973e58 0.250666
\(266\) 4.42457e59 1.72294
\(267\) −4.14433e59 −1.47207
\(268\) 4.41372e58 0.143055
\(269\) 3.89211e58 0.115148 0.0575738 0.998341i \(-0.481664\pi\)
0.0575738 + 0.998341i \(0.481664\pi\)
\(270\) −2.24271e59 −0.605845
\(271\) −2.42138e59 −0.597468 −0.298734 0.954336i \(-0.596564\pi\)
−0.298734 + 0.954336i \(0.596564\pi\)
\(272\) 4.53064e59 1.02146
\(273\) 6.19295e59 1.27618
\(274\) 8.19956e59 1.54491
\(275\) 3.00227e59 0.517367
\(276\) 7.35224e58 0.115917
\(277\) −1.36745e60 −1.97313 −0.986566 0.163363i \(-0.947766\pi\)
−0.986566 + 0.163363i \(0.947766\pi\)
\(278\) −1.03577e60 −1.36825
\(279\) 1.63196e59 0.197427
\(280\) −8.41360e59 −0.932417
\(281\) 1.32527e60 1.34585 0.672927 0.739709i \(-0.265037\pi\)
0.672927 + 0.739709i \(0.265037\pi\)
\(282\) −7.29518e59 −0.679098
\(283\) −1.55414e60 −1.32655 −0.663273 0.748378i \(-0.730833\pi\)
−0.663273 + 0.748378i \(0.730833\pi\)
\(284\) 9.47427e58 0.0741731
\(285\) 2.04994e60 1.47246
\(286\) 2.05941e60 1.35761
\(287\) −8.48496e59 −0.513504
\(288\) −1.02509e59 −0.0569701
\(289\) 5.86836e59 0.299585
\(290\) 1.02765e60 0.482052
\(291\) −3.29556e60 −1.42086
\(292\) −3.34389e59 −0.132548
\(293\) 3.60920e60 1.31569 0.657846 0.753152i \(-0.271468\pi\)
0.657846 + 0.753152i \(0.271468\pi\)
\(294\) −8.27664e59 −0.277552
\(295\) 2.05600e59 0.0634431
\(296\) −2.16786e60 −0.615722
\(297\) 4.35780e60 1.13955
\(298\) −4.29189e60 −1.03359
\(299\) −4.81637e60 −1.06850
\(300\) 1.91791e59 0.0392064
\(301\) 2.94117e60 0.554168
\(302\) −6.17699e60 −1.07302
\(303\) −9.37133e59 −0.150126
\(304\) 9.79944e60 1.44810
\(305\) −2.56731e60 −0.350052
\(306\) 2.59421e60 0.326460
\(307\) 6.56165e60 0.762295 0.381147 0.924514i \(-0.375529\pi\)
0.381147 + 0.924514i \(0.375529\pi\)
\(308\) 1.41782e60 0.152099
\(309\) −5.39239e60 −0.534316
\(310\) 5.44412e60 0.498386
\(311\) −4.77277e60 −0.403776 −0.201888 0.979409i \(-0.564708\pi\)
−0.201888 + 0.979409i \(0.564708\pi\)
\(312\) 1.51696e61 1.18628
\(313\) −9.64049e59 −0.0697048 −0.0348524 0.999392i \(-0.511096\pi\)
−0.0348524 + 0.999392i \(0.511096\pi\)
\(314\) −1.50124e61 −1.00386
\(315\) −4.35593e60 −0.269446
\(316\) −2.52855e60 −0.144723
\(317\) −1.84778e61 −0.978809 −0.489405 0.872057i \(-0.662786\pi\)
−0.489405 + 0.872057i \(0.662786\pi\)
\(318\) 6.94406e60 0.340525
\(319\) −1.99682e61 −0.906706
\(320\) −2.04379e61 −0.859530
\(321\) 6.32013e60 0.246237
\(322\) 3.16025e61 1.14091
\(323\) 5.50610e61 1.84239
\(324\) 3.70534e60 0.114941
\(325\) −1.25640e61 −0.361397
\(326\) 1.08452e61 0.289340
\(327\) 2.52778e61 0.625631
\(328\) −2.07839e61 −0.477330
\(329\) 3.29013e61 0.701317
\(330\) −6.26059e61 −1.23886
\(331\) −6.60491e61 −1.21361 −0.606807 0.794849i \(-0.707550\pi\)
−0.606807 + 0.794849i \(0.707550\pi\)
\(332\) −2.29755e60 −0.0392086
\(333\) −1.12235e61 −0.177929
\(334\) 1.31144e61 0.193179
\(335\) 8.78977e61 1.20332
\(336\) −8.99974e61 −1.14530
\(337\) 5.02594e61 0.594682 0.297341 0.954771i \(-0.403900\pi\)
0.297341 + 0.954771i \(0.403900\pi\)
\(338\) 2.72780e59 0.00300160
\(339\) 5.33843e60 0.0546413
\(340\) −9.08030e60 −0.0864703
\(341\) −1.05784e62 −0.937430
\(342\) 5.61109e61 0.462815
\(343\) −1.08608e62 −0.833984
\(344\) 7.20441e61 0.515130
\(345\) 1.46417e62 0.975045
\(346\) 1.13635e62 0.704931
\(347\) 2.35153e62 1.35919 0.679594 0.733589i \(-0.262156\pi\)
0.679594 + 0.733589i \(0.262156\pi\)
\(348\) −1.27561e61 −0.0687108
\(349\) −2.73741e62 −1.37441 −0.687206 0.726463i \(-0.741163\pi\)
−0.687206 + 0.726463i \(0.741163\pi\)
\(350\) 8.24383e61 0.385889
\(351\) −1.82367e62 −0.796014
\(352\) 6.64470e61 0.270508
\(353\) −3.98901e62 −1.51490 −0.757452 0.652891i \(-0.773556\pi\)
−0.757452 + 0.652891i \(0.773556\pi\)
\(354\) 2.43231e61 0.0861865
\(355\) 1.88677e62 0.623913
\(356\) 3.97059e61 0.122555
\(357\) −5.05676e62 −1.45714
\(358\) −2.30564e62 −0.620379
\(359\) 3.99475e62 1.00387 0.501933 0.864906i \(-0.332622\pi\)
0.501933 + 0.864906i \(0.332622\pi\)
\(360\) −1.06699e62 −0.250465
\(361\) 7.34970e62 1.61192
\(362\) 1.10534e62 0.226536
\(363\) 6.21028e62 1.18959
\(364\) −5.93333e61 −0.106246
\(365\) −6.65925e62 −1.11494
\(366\) −3.03720e62 −0.475540
\(367\) 4.47176e62 0.654878 0.327439 0.944872i \(-0.393814\pi\)
0.327439 + 0.944872i \(0.393814\pi\)
\(368\) 6.99926e62 0.958916
\(369\) −1.07604e62 −0.137937
\(370\) −3.74412e62 −0.449166
\(371\) −3.13178e62 −0.351666
\(372\) −6.75770e61 −0.0710390
\(373\) −1.90519e63 −1.87531 −0.937654 0.347569i \(-0.887007\pi\)
−0.937654 + 0.347569i \(0.887007\pi\)
\(374\) −1.68158e63 −1.55011
\(375\) 1.43713e63 1.24088
\(376\) 8.05919e62 0.651913
\(377\) 8.35634e62 0.633364
\(378\) 1.19659e63 0.849959
\(379\) −1.10306e63 −0.734408 −0.367204 0.930140i \(-0.619685\pi\)
−0.367204 + 0.930140i \(0.619685\pi\)
\(380\) −1.96400e62 −0.122587
\(381\) 1.86158e63 1.08948
\(382\) 5.80855e62 0.318798
\(383\) −1.13569e63 −0.584643 −0.292321 0.956320i \(-0.594428\pi\)
−0.292321 + 0.956320i \(0.594428\pi\)
\(384\) −1.97086e63 −0.951787
\(385\) 2.82353e63 1.27940
\(386\) −1.48338e63 −0.630760
\(387\) 3.72990e62 0.148860
\(388\) 3.15740e62 0.118291
\(389\) −2.42232e63 −0.852053 −0.426026 0.904711i \(-0.640087\pi\)
−0.426026 + 0.904711i \(0.640087\pi\)
\(390\) 2.61995e63 0.865387
\(391\) 3.93273e63 1.22001
\(392\) 9.14344e62 0.266441
\(393\) −4.21905e63 −1.15504
\(394\) −3.77094e63 −0.970045
\(395\) −5.03552e63 −1.21735
\(396\) 1.79803e62 0.0408568
\(397\) −2.38482e62 −0.0509434 −0.0254717 0.999676i \(-0.508109\pi\)
−0.0254717 + 0.999676i \(0.508109\pi\)
\(398\) 6.36064e63 1.27751
\(399\) −1.09374e64 −2.06575
\(400\) 1.82583e63 0.324332
\(401\) 3.76821e63 0.629649 0.314824 0.949150i \(-0.398054\pi\)
0.314824 + 0.949150i \(0.398054\pi\)
\(402\) 1.03986e64 1.63469
\(403\) 4.42689e63 0.654825
\(404\) 8.97846e61 0.0124985
\(405\) 7.37905e63 0.966835
\(406\) −5.48300e63 −0.676286
\(407\) 7.27516e63 0.844850
\(408\) −1.23866e64 −1.35449
\(409\) 4.86604e63 0.501135 0.250567 0.968099i \(-0.419383\pi\)
0.250567 + 0.968099i \(0.419383\pi\)
\(410\) −3.58960e63 −0.348210
\(411\) −2.02691e64 −1.85229
\(412\) 5.16633e62 0.0444836
\(413\) −1.09698e63 −0.0890063
\(414\) 4.00773e63 0.306471
\(415\) −4.57548e63 −0.329806
\(416\) −2.78070e63 −0.188959
\(417\) 2.56040e64 1.64049
\(418\) −3.63714e64 −2.19756
\(419\) 2.47515e64 1.41045 0.705225 0.708983i \(-0.250846\pi\)
0.705225 + 0.708983i \(0.250846\pi\)
\(420\) 1.80373e63 0.0969535
\(421\) −1.56805e64 −0.795149 −0.397575 0.917570i \(-0.630148\pi\)
−0.397575 + 0.917570i \(0.630148\pi\)
\(422\) 2.48026e64 1.18670
\(423\) 4.17244e63 0.188387
\(424\) −7.67131e63 −0.326893
\(425\) 1.02589e64 0.412642
\(426\) 2.23210e64 0.847576
\(427\) 1.36978e64 0.491098
\(428\) −6.05517e62 −0.0205000
\(429\) −5.09080e64 −1.62773
\(430\) 1.24427e64 0.375785
\(431\) −5.26924e64 −1.50333 −0.751666 0.659544i \(-0.770749\pi\)
−0.751666 + 0.659544i \(0.770749\pi\)
\(432\) 2.65019e64 0.714374
\(433\) 3.37012e64 0.858405 0.429202 0.903208i \(-0.358795\pi\)
0.429202 + 0.903208i \(0.358795\pi\)
\(434\) −2.90470e64 −0.699201
\(435\) −2.54032e64 −0.577966
\(436\) −2.42181e63 −0.0520859
\(437\) 8.50623e64 1.72958
\(438\) −7.87808e64 −1.51462
\(439\) −7.18240e64 −1.30584 −0.652918 0.757428i \(-0.726456\pi\)
−0.652918 + 0.757428i \(0.726456\pi\)
\(440\) 6.91625e64 1.18927
\(441\) 4.73378e63 0.0769951
\(442\) 7.03713e64 1.08280
\(443\) −1.13418e65 −1.65116 −0.825582 0.564282i \(-0.809153\pi\)
−0.825582 + 0.564282i \(0.809153\pi\)
\(444\) 4.64751e63 0.0640232
\(445\) 7.90729e64 1.03088
\(446\) −3.67720e64 −0.453747
\(447\) 1.06094e65 1.23925
\(448\) 1.09046e65 1.20586
\(449\) −1.35648e65 −1.42030 −0.710148 0.704053i \(-0.751372\pi\)
−0.710148 + 0.704053i \(0.751372\pi\)
\(450\) 1.04546e64 0.103657
\(451\) 6.97491e64 0.654958
\(452\) −5.11463e62 −0.00454907
\(453\) 1.52694e65 1.28652
\(454\) −8.75064e64 −0.698508
\(455\) −1.18160e65 −0.893700
\(456\) −2.67912e65 −1.92023
\(457\) −2.05883e65 −1.39854 −0.699268 0.714859i \(-0.746491\pi\)
−0.699268 + 0.714859i \(0.746491\pi\)
\(458\) −1.52232e65 −0.980172
\(459\) 1.48909e65 0.908886
\(460\) −1.40279e64 −0.0811757
\(461\) 2.18282e65 1.19769 0.598847 0.800863i \(-0.295626\pi\)
0.598847 + 0.800863i \(0.295626\pi\)
\(462\) 3.34032e65 1.73804
\(463\) 9.59055e64 0.473270 0.236635 0.971599i \(-0.423955\pi\)
0.236635 + 0.971599i \(0.423955\pi\)
\(464\) −1.21436e65 −0.568405
\(465\) −1.34577e65 −0.597550
\(466\) 2.42125e65 1.01996
\(467\) 1.86197e65 0.744234 0.372117 0.928186i \(-0.378632\pi\)
0.372117 + 0.928186i \(0.378632\pi\)
\(468\) −7.52445e63 −0.0285398
\(469\) −4.68976e65 −1.68817
\(470\) 1.39190e65 0.475567
\(471\) 3.71103e65 1.20360
\(472\) −2.68704e64 −0.0827363
\(473\) −2.41774e65 −0.706825
\(474\) −5.95717e65 −1.65375
\(475\) 2.21894e65 0.584994
\(476\) 4.84477e64 0.121312
\(477\) −3.97162e64 −0.0944643
\(478\) 1.54549e65 0.349207
\(479\) 9.86762e64 0.211832 0.105916 0.994375i \(-0.466222\pi\)
0.105916 + 0.994375i \(0.466222\pi\)
\(480\) 8.45330e64 0.172431
\(481\) −3.04453e65 −0.590155
\(482\) −1.45330e65 −0.267733
\(483\) −7.81206e65 −1.36792
\(484\) −5.94993e64 −0.0990376
\(485\) 6.28785e65 0.995015
\(486\) 3.68847e65 0.554956
\(487\) 3.74023e65 0.535104 0.267552 0.963543i \(-0.413785\pi\)
0.267552 + 0.963543i \(0.413785\pi\)
\(488\) 3.35528e65 0.456503
\(489\) −2.68092e65 −0.346910
\(490\) 1.57916e65 0.194367
\(491\) 1.40013e65 0.163935 0.0819676 0.996635i \(-0.473880\pi\)
0.0819676 + 0.996635i \(0.473880\pi\)
\(492\) 4.45571e64 0.0496331
\(493\) −6.82325e65 −0.723172
\(494\) 1.52208e66 1.53507
\(495\) 3.58071e65 0.343670
\(496\) −6.43326e65 −0.587665
\(497\) −1.00668e66 −0.875306
\(498\) −5.41293e65 −0.448036
\(499\) 2.84241e65 0.223987 0.111994 0.993709i \(-0.464276\pi\)
0.111994 + 0.993709i \(0.464276\pi\)
\(500\) −1.37688e65 −0.103307
\(501\) −3.24185e65 −0.231616
\(502\) −1.10177e65 −0.0749634
\(503\) −9.62685e65 −0.623833 −0.311917 0.950109i \(-0.600971\pi\)
−0.311917 + 0.950109i \(0.600971\pi\)
\(504\) 5.69287e65 0.351385
\(505\) 1.78803e65 0.105132
\(506\) −2.59783e66 −1.45520
\(507\) −6.74305e63 −0.00359883
\(508\) −1.78354e65 −0.0907030
\(509\) 3.05352e66 1.47984 0.739921 0.672694i \(-0.234863\pi\)
0.739921 + 0.672694i \(0.234863\pi\)
\(510\) −2.13928e66 −0.988095
\(511\) 3.55303e66 1.56418
\(512\) 2.62825e66 1.10294
\(513\) 3.22079e66 1.28851
\(514\) −2.19218e66 −0.836140
\(515\) 1.02886e66 0.374177
\(516\) −1.54450e65 −0.0535636
\(517\) −2.70460e66 −0.894508
\(518\) 1.99766e66 0.630149
\(519\) −2.80902e66 −0.845191
\(520\) −2.89434e66 −0.830743
\(521\) −4.02652e66 −1.10257 −0.551284 0.834318i \(-0.685862\pi\)
−0.551284 + 0.834318i \(0.685862\pi\)
\(522\) −6.95336e65 −0.181663
\(523\) 6.70243e65 0.167086 0.0835431 0.996504i \(-0.473376\pi\)
0.0835431 + 0.996504i \(0.473376\pi\)
\(524\) 4.04218e65 0.0961609
\(525\) −2.03785e66 −0.462669
\(526\) 3.83432e66 0.830878
\(527\) −3.61471e66 −0.747677
\(528\) 7.39807e66 1.46079
\(529\) 7.70839e65 0.145311
\(530\) −1.32491e66 −0.238467
\(531\) −1.39115e65 −0.0239088
\(532\) 1.04789e66 0.171981
\(533\) −2.91888e66 −0.457510
\(534\) 9.35455e66 1.40043
\(535\) −1.20587e66 −0.172437
\(536\) −1.14876e67 −1.56925
\(537\) 5.69948e66 0.743816
\(538\) −8.78525e65 −0.109544
\(539\) −3.06846e66 −0.365591
\(540\) −5.31152e65 −0.0604744
\(541\) 1.63687e67 1.78107 0.890536 0.454913i \(-0.150330\pi\)
0.890536 + 0.454913i \(0.150330\pi\)
\(542\) 5.46552e66 0.568393
\(543\) −2.73238e66 −0.271609
\(544\) 2.27054e66 0.215752
\(545\) −4.82294e66 −0.438125
\(546\) −1.39787e67 −1.21408
\(547\) −1.21163e67 −1.00619 −0.503095 0.864231i \(-0.667805\pi\)
−0.503095 + 0.864231i \(0.667805\pi\)
\(548\) 1.94194e66 0.154210
\(549\) 1.73711e66 0.131918
\(550\) −6.77670e66 −0.492189
\(551\) −1.47582e67 −1.02523
\(552\) −1.91357e67 −1.27156
\(553\) 2.68669e67 1.70786
\(554\) 3.08659e67 1.87711
\(555\) 9.25536e66 0.538536
\(556\) −2.45306e66 −0.136576
\(557\) −2.42193e67 −1.29035 −0.645177 0.764033i \(-0.723217\pi\)
−0.645177 + 0.764033i \(0.723217\pi\)
\(558\) −3.68364e66 −0.187819
\(559\) 1.01178e67 0.493740
\(560\) 1.71713e67 0.802041
\(561\) 4.15682e67 1.85854
\(562\) −2.99138e67 −1.28036
\(563\) 3.00539e66 0.123153 0.0615764 0.998102i \(-0.480387\pi\)
0.0615764 + 0.998102i \(0.480387\pi\)
\(564\) −1.72775e66 −0.0677864
\(565\) −1.01856e66 −0.0382649
\(566\) 3.50799e67 1.26199
\(567\) −3.93707e67 −1.35640
\(568\) −2.46587e67 −0.813646
\(569\) 1.27892e67 0.404197 0.202099 0.979365i \(-0.435224\pi\)
0.202099 + 0.979365i \(0.435224\pi\)
\(570\) −4.62712e67 −1.40080
\(571\) −1.78328e67 −0.517172 −0.258586 0.965988i \(-0.583257\pi\)
−0.258586 + 0.965988i \(0.583257\pi\)
\(572\) 4.87739e66 0.135514
\(573\) −1.43586e67 −0.382229
\(574\) 1.91522e67 0.488514
\(575\) 1.58488e67 0.387376
\(576\) 1.38288e67 0.323917
\(577\) −4.00078e67 −0.898127 −0.449064 0.893500i \(-0.648242\pi\)
−0.449064 + 0.893500i \(0.648242\pi\)
\(578\) −1.32460e67 −0.285006
\(579\) 3.66688e67 0.756262
\(580\) 2.43383e66 0.0481176
\(581\) 2.44124e67 0.462695
\(582\) 7.43871e67 1.35171
\(583\) 2.57443e67 0.448540
\(584\) 8.70315e67 1.45399
\(585\) −1.49847e67 −0.240065
\(586\) −8.14666e67 −1.25167
\(587\) −9.20452e67 −1.35634 −0.678168 0.734907i \(-0.737226\pi\)
−0.678168 + 0.734907i \(0.737226\pi\)
\(588\) −1.96019e66 −0.0277047
\(589\) −7.81837e67 −1.05996
\(590\) −4.64080e66 −0.0603557
\(591\) 9.32166e67 1.16305
\(592\) 4.42438e67 0.529628
\(593\) −3.70854e66 −0.0425954 −0.0212977 0.999773i \(-0.506780\pi\)
−0.0212977 + 0.999773i \(0.506780\pi\)
\(594\) −9.83639e67 −1.08410
\(595\) 9.64819e67 1.02042
\(596\) −1.01647e67 −0.103171
\(597\) −1.57233e68 −1.53170
\(598\) 1.08715e68 1.01650
\(599\) 1.91162e67 0.171571 0.0857857 0.996314i \(-0.472660\pi\)
0.0857857 + 0.996314i \(0.472660\pi\)
\(600\) −4.99173e67 −0.430076
\(601\) 3.78925e67 0.313421 0.156711 0.987645i \(-0.449911\pi\)
0.156711 + 0.987645i \(0.449911\pi\)
\(602\) −6.63879e67 −0.527200
\(603\) −5.94740e67 −0.453475
\(604\) −1.46292e67 −0.107107
\(605\) −1.18491e68 −0.833063
\(606\) 2.11529e67 0.142821
\(607\) 2.02918e68 1.31582 0.657910 0.753096i \(-0.271441\pi\)
0.657910 + 0.753096i \(0.271441\pi\)
\(608\) 4.91101e67 0.305867
\(609\) 1.35538e68 0.810846
\(610\) 5.79491e67 0.333017
\(611\) 1.13183e68 0.624843
\(612\) 6.14398e66 0.0325867
\(613\) 2.45514e68 1.25111 0.625553 0.780182i \(-0.284874\pi\)
0.625553 + 0.780182i \(0.284874\pi\)
\(614\) −1.48109e68 −0.725198
\(615\) 8.87339e67 0.417493
\(616\) −3.69015e68 −1.66846
\(617\) −2.87337e68 −1.24855 −0.624274 0.781205i \(-0.714605\pi\)
−0.624274 + 0.781205i \(0.714605\pi\)
\(618\) 1.21717e68 0.508314
\(619\) −3.11706e68 −1.25119 −0.625596 0.780147i \(-0.715144\pi\)
−0.625596 + 0.780147i \(0.715144\pi\)
\(620\) 1.28935e67 0.0497480
\(621\) 2.30045e68 0.853236
\(622\) 1.07731e68 0.384127
\(623\) −4.21891e68 −1.44625
\(624\) −3.09597e68 −1.02041
\(625\) −1.59984e68 −0.507010
\(626\) 2.17604e67 0.0663127
\(627\) 8.99091e68 2.63481
\(628\) −3.55545e67 −0.100204
\(629\) 2.48597e68 0.673837
\(630\) 9.83217e67 0.256334
\(631\) −2.97792e68 −0.746781 −0.373391 0.927674i \(-0.621805\pi\)
−0.373391 + 0.927674i \(0.621805\pi\)
\(632\) 6.58106e68 1.58755
\(633\) −6.13113e68 −1.42282
\(634\) 4.17079e68 0.931176
\(635\) −3.55185e68 −0.762955
\(636\) 1.64459e67 0.0339906
\(637\) 1.28410e68 0.255377
\(638\) 4.50720e68 0.862582
\(639\) −1.27664e68 −0.235124
\(640\) 3.76035e68 0.666529
\(641\) −9.83451e68 −1.67776 −0.838882 0.544314i \(-0.816790\pi\)
−0.838882 + 0.544314i \(0.816790\pi\)
\(642\) −1.42657e68 −0.234254
\(643\) 2.53725e68 0.401046 0.200523 0.979689i \(-0.435736\pi\)
0.200523 + 0.979689i \(0.435736\pi\)
\(644\) 7.48456e67 0.113884
\(645\) −3.07582e68 −0.450554
\(646\) −1.24283e69 −1.75273
\(647\) 8.46297e68 1.14913 0.574563 0.818460i \(-0.305172\pi\)
0.574563 + 0.818460i \(0.305172\pi\)
\(648\) −9.64387e68 −1.26085
\(649\) 9.01749e67 0.113525
\(650\) 2.83593e68 0.343810
\(651\) 7.18033e68 0.838321
\(652\) 2.56853e67 0.0288814
\(653\) 5.94791e68 0.644157 0.322079 0.946713i \(-0.395618\pi\)
0.322079 + 0.946713i \(0.395618\pi\)
\(654\) −5.70568e68 −0.595185
\(655\) 8.04985e68 0.808865
\(656\) 4.24179e68 0.410587
\(657\) 4.50583e68 0.420168
\(658\) −7.42647e68 −0.667187
\(659\) −1.75187e69 −1.51638 −0.758190 0.652034i \(-0.773916\pi\)
−0.758190 + 0.652034i \(0.773916\pi\)
\(660\) −1.48272e68 −0.123661
\(661\) 1.24865e69 1.00347 0.501736 0.865021i \(-0.332695\pi\)
0.501736 + 0.865021i \(0.332695\pi\)
\(662\) 1.49085e69 1.15455
\(663\) −1.73956e69 −1.29825
\(664\) 5.97982e68 0.430101
\(665\) 2.08683e69 1.44663
\(666\) 2.53337e68 0.169270
\(667\) −1.05411e69 −0.678893
\(668\) 3.10595e67 0.0192828
\(669\) 9.08996e68 0.544029
\(670\) −1.98402e69 −1.14476
\(671\) −1.12600e69 −0.626381
\(672\) −4.51023e68 −0.241909
\(673\) 2.09516e68 0.108355 0.0541773 0.998531i \(-0.482746\pi\)
0.0541773 + 0.998531i \(0.482746\pi\)
\(674\) −1.13445e69 −0.565742
\(675\) 6.00096e68 0.288588
\(676\) 6.46037e65 0.000299615 0
\(677\) −2.83899e69 −1.26982 −0.634910 0.772586i \(-0.718963\pi\)
−0.634910 + 0.772586i \(0.718963\pi\)
\(678\) −1.20499e68 −0.0519822
\(679\) −3.35487e69 −1.39594
\(680\) 2.36333e69 0.948540
\(681\) 2.16314e69 0.837490
\(682\) 2.38775e69 0.891810
\(683\) 1.06976e69 0.385460 0.192730 0.981252i \(-0.438266\pi\)
0.192730 + 0.981252i \(0.438266\pi\)
\(684\) 1.32890e68 0.0461974
\(685\) 3.86730e69 1.29715
\(686\) 2.45150e69 0.793398
\(687\) 3.76314e69 1.17520
\(688\) −1.47035e69 −0.443101
\(689\) −1.07735e69 −0.313320
\(690\) −3.30492e69 −0.927595
\(691\) −2.08108e69 −0.563738 −0.281869 0.959453i \(-0.590954\pi\)
−0.281869 + 0.959453i \(0.590954\pi\)
\(692\) 2.69126e68 0.0703650
\(693\) −1.91048e69 −0.482146
\(694\) −5.30787e69 −1.29304
\(695\) −4.88518e69 −1.14882
\(696\) 3.32001e69 0.753726
\(697\) 2.38337e69 0.522383
\(698\) 6.17886e69 1.30753
\(699\) −5.98527e69 −1.22290
\(700\) 1.95242e68 0.0385187
\(701\) −4.28863e69 −0.817010 −0.408505 0.912756i \(-0.633950\pi\)
−0.408505 + 0.912756i \(0.633950\pi\)
\(702\) 4.11637e69 0.757277
\(703\) 5.37697e69 0.955283
\(704\) −8.96391e69 −1.53804
\(705\) −3.44075e69 −0.570190
\(706\) 9.00397e69 1.44118
\(707\) −9.53998e68 −0.147493
\(708\) 5.76055e67 0.00860298
\(709\) 1.06701e70 1.53935 0.769673 0.638438i \(-0.220419\pi\)
0.769673 + 0.638438i \(0.220419\pi\)
\(710\) −4.25880e69 −0.593551
\(711\) 3.40717e69 0.458764
\(712\) −1.03342e70 −1.34437
\(713\) −5.58427e69 −0.701897
\(714\) 1.14141e70 1.38623
\(715\) 9.71314e69 1.13989
\(716\) −5.46055e68 −0.0619251
\(717\) −3.82041e69 −0.418688
\(718\) −9.01693e69 −0.955014
\(719\) 1.57271e70 1.60987 0.804936 0.593362i \(-0.202200\pi\)
0.804936 + 0.593362i \(0.202200\pi\)
\(720\) 2.17761e69 0.215444
\(721\) −5.48943e69 −0.524945
\(722\) −1.65897e70 −1.53348
\(723\) 3.59251e69 0.321004
\(724\) 2.61783e68 0.0226124
\(725\) −2.74974e69 −0.229621
\(726\) −1.40178e70 −1.13170
\(727\) −1.05830e70 −0.826067 −0.413033 0.910716i \(-0.635531\pi\)
−0.413033 + 0.910716i \(0.635531\pi\)
\(728\) 1.54426e70 1.16548
\(729\) 7.46872e69 0.545032
\(730\) 1.50312e70 1.06068
\(731\) −8.26157e69 −0.563750
\(732\) −7.19313e68 −0.0474675
\(733\) −2.28917e70 −1.46093 −0.730466 0.682949i \(-0.760697\pi\)
−0.730466 + 0.682949i \(0.760697\pi\)
\(734\) −1.00936e70 −0.623008
\(735\) −3.90365e69 −0.233041
\(736\) 3.50769e69 0.202542
\(737\) 3.85513e70 2.15321
\(738\) 2.42882e69 0.131224
\(739\) 2.74741e70 1.43594 0.717968 0.696076i \(-0.245072\pi\)
0.717968 + 0.696076i \(0.245072\pi\)
\(740\) −8.86735e68 −0.0448350
\(741\) −3.76254e70 −1.84050
\(742\) 7.06903e69 0.334553
\(743\) 1.03737e70 0.475017 0.237508 0.971386i \(-0.423669\pi\)
0.237508 + 0.971386i \(0.423669\pi\)
\(744\) 1.75882e70 0.779266
\(745\) −2.02426e70 −0.867834
\(746\) 4.30039e70 1.78405
\(747\) 3.09590e69 0.124289
\(748\) −3.98256e69 −0.154729
\(749\) 6.43387e69 0.241918
\(750\) −3.24388e70 −1.18049
\(751\) −5.36589e70 −1.89001 −0.945003 0.327062i \(-0.893941\pi\)
−0.945003 + 0.327062i \(0.893941\pi\)
\(752\) −1.64480e70 −0.560758
\(753\) 2.72354e69 0.0898788
\(754\) −1.88619e70 −0.602541
\(755\) −2.91336e70 −0.900936
\(756\) 2.83395e69 0.0848414
\(757\) −3.78086e70 −1.09583 −0.547913 0.836535i \(-0.684578\pi\)
−0.547913 + 0.836535i \(0.684578\pi\)
\(758\) 2.48981e70 0.698668
\(759\) 6.42176e70 1.74474
\(760\) 5.11171e70 1.34472
\(761\) 3.04475e70 0.775581 0.387791 0.921748i \(-0.373238\pi\)
0.387791 + 0.921748i \(0.373238\pi\)
\(762\) −4.20195e70 −1.03646
\(763\) 2.57327e70 0.614658
\(764\) 1.37566e69 0.0318218
\(765\) 1.22355e70 0.274105
\(766\) 2.56348e70 0.556192
\(767\) −3.77367e69 −0.0793008
\(768\) −1.58160e70 −0.321920
\(769\) −1.49566e70 −0.294874 −0.147437 0.989071i \(-0.547102\pi\)
−0.147437 + 0.989071i \(0.547102\pi\)
\(770\) −6.37326e70 −1.21714
\(771\) 5.41900e70 1.00251
\(772\) −3.51316e69 −0.0629614
\(773\) 3.62206e70 0.628866 0.314433 0.949280i \(-0.398186\pi\)
0.314433 + 0.949280i \(0.398186\pi\)
\(774\) −8.41910e69 −0.141616
\(775\) −1.45671e70 −0.237401
\(776\) −8.21776e70 −1.29760
\(777\) −4.93817e70 −0.755529
\(778\) 5.46765e70 0.810588
\(779\) 5.15506e70 0.740570
\(780\) 6.20494e69 0.0863814
\(781\) 8.27524e70 1.11643
\(782\) −8.87694e70 −1.16064
\(783\) −3.99126e70 −0.505762
\(784\) −1.86608e70 −0.229186
\(785\) −7.08056e70 −0.842871
\(786\) 9.52321e70 1.09883
\(787\) −5.90448e70 −0.660391 −0.330195 0.943913i \(-0.607115\pi\)
−0.330195 + 0.943913i \(0.607115\pi\)
\(788\) −8.93087e69 −0.0968282
\(789\) −9.47834e70 −0.996198
\(790\) 1.13662e71 1.15811
\(791\) 5.43451e69 0.0536829
\(792\) −4.67973e70 −0.448181
\(793\) 4.71214e70 0.437547
\(794\) 5.38299e69 0.0484642
\(795\) 3.27515e70 0.285915
\(796\) 1.50642e70 0.127519
\(797\) 1.73928e71 1.42771 0.713856 0.700292i \(-0.246947\pi\)
0.713856 + 0.700292i \(0.246947\pi\)
\(798\) 2.46879e71 1.96523
\(799\) −9.24178e70 −0.713443
\(800\) 9.15017e69 0.0685053
\(801\) −5.35029e70 −0.388491
\(802\) −8.50558e70 −0.599007
\(803\) −2.92070e71 −1.99506
\(804\) 2.46273e70 0.163171
\(805\) 1.49052e71 0.957943
\(806\) −9.99235e70 −0.622958
\(807\) 2.17169e70 0.131340
\(808\) −2.33682e70 −0.137103
\(809\) 1.56081e71 0.888403 0.444202 0.895927i \(-0.353487\pi\)
0.444202 + 0.895927i \(0.353487\pi\)
\(810\) −1.66559e71 −0.919784
\(811\) −9.44857e70 −0.506238 −0.253119 0.967435i \(-0.581456\pi\)
−0.253119 + 0.967435i \(0.581456\pi\)
\(812\) −1.29856e70 −0.0675056
\(813\) −1.35106e71 −0.681486
\(814\) −1.64214e71 −0.803736
\(815\) 5.11513e70 0.242938
\(816\) 2.52797e71 1.16510
\(817\) −1.78692e71 −0.799216
\(818\) −1.09836e71 −0.476747
\(819\) 7.99504e70 0.336794
\(820\) −8.50140e69 −0.0347577
\(821\) 4.10899e71 1.63053 0.815263 0.579091i \(-0.196592\pi\)
0.815263 + 0.579091i \(0.196592\pi\)
\(822\) 4.57513e71 1.76215
\(823\) −7.73454e70 −0.289160 −0.144580 0.989493i \(-0.546183\pi\)
−0.144580 + 0.989493i \(0.546183\pi\)
\(824\) −1.34464e71 −0.487965
\(825\) 1.67518e71 0.590120
\(826\) 2.47608e70 0.0846748
\(827\) −2.26640e71 −0.752404 −0.376202 0.926538i \(-0.622770\pi\)
−0.376202 + 0.926538i \(0.622770\pi\)
\(828\) 9.49167e69 0.0305914
\(829\) 4.51215e71 1.41188 0.705939 0.708273i \(-0.250525\pi\)
0.705939 + 0.708273i \(0.250525\pi\)
\(830\) 1.03277e71 0.313756
\(831\) −7.62997e71 −2.25060
\(832\) 3.75125e71 1.07437
\(833\) −1.04851e71 −0.291589
\(834\) −5.77931e71 −1.56066
\(835\) 6.18538e70 0.162199
\(836\) −8.61399e70 −0.219357
\(837\) −2.11443e71 −0.522900
\(838\) −5.58689e71 −1.34181
\(839\) 7.26480e71 1.69456 0.847278 0.531150i \(-0.178240\pi\)
0.847278 + 0.531150i \(0.178240\pi\)
\(840\) −4.69456e71 −1.06354
\(841\) −2.71580e71 −0.597581
\(842\) 3.53939e71 0.756454
\(843\) 7.39461e71 1.53511
\(844\) 5.87410e70 0.118454
\(845\) 1.28656e69 0.00252023
\(846\) −9.41800e70 −0.179219
\(847\) 6.32204e71 1.16873
\(848\) 1.56564e71 0.281185
\(849\) −8.67166e71 −1.51309
\(850\) −2.31564e71 −0.392561
\(851\) 3.84050e71 0.632578
\(852\) 5.28638e70 0.0846035
\(853\) −5.90172e71 −0.917757 −0.458878 0.888499i \(-0.651749\pi\)
−0.458878 + 0.888499i \(0.651749\pi\)
\(854\) −3.09186e71 −0.467199
\(855\) 2.64646e71 0.388593
\(856\) 1.57598e71 0.224876
\(857\) 7.99787e71 1.10903 0.554516 0.832173i \(-0.312903\pi\)
0.554516 + 0.832173i \(0.312903\pi\)
\(858\) 1.14909e72 1.54852
\(859\) −6.56838e71 −0.860252 −0.430126 0.902769i \(-0.641531\pi\)
−0.430126 + 0.902769i \(0.641531\pi\)
\(860\) 2.94687e70 0.0375102
\(861\) −4.73437e71 −0.585714
\(862\) 1.18937e72 1.43017
\(863\) −1.10305e72 −1.28924 −0.644618 0.764505i \(-0.722984\pi\)
−0.644618 + 0.764505i \(0.722984\pi\)
\(864\) 1.32815e71 0.150890
\(865\) 5.35955e71 0.591880
\(866\) −7.60701e71 −0.816631
\(867\) 3.27438e71 0.341713
\(868\) −6.87932e70 −0.0697930
\(869\) −2.20855e72 −2.17832
\(870\) 5.73400e71 0.549839
\(871\) −1.61331e72 −1.50409
\(872\) 6.30323e71 0.571359
\(873\) −4.25453e71 −0.374976
\(874\) −1.92002e72 −1.64541
\(875\) 1.46299e72 1.21912
\(876\) −1.86580e71 −0.151187
\(877\) 1.55281e72 1.22357 0.611783 0.791026i \(-0.290453\pi\)
0.611783 + 0.791026i \(0.290453\pi\)
\(878\) 1.62121e72 1.24229
\(879\) 2.01383e72 1.50071
\(880\) −1.41154e72 −1.02298
\(881\) 6.02597e71 0.424734 0.212367 0.977190i \(-0.431883\pi\)
0.212367 + 0.977190i \(0.431883\pi\)
\(882\) −1.06851e71 −0.0732482
\(883\) −3.02172e71 −0.201473 −0.100737 0.994913i \(-0.532120\pi\)
−0.100737 + 0.994913i \(0.532120\pi\)
\(884\) 1.66663e71 0.108084
\(885\) 1.14719e71 0.0723646
\(886\) 2.56006e72 1.57081
\(887\) −1.92132e72 −1.14675 −0.573377 0.819291i \(-0.694367\pi\)
−0.573377 + 0.819291i \(0.694367\pi\)
\(888\) −1.20961e72 −0.702306
\(889\) 1.89508e72 1.07037
\(890\) −1.78483e72 −0.980711
\(891\) 3.23640e72 1.73005
\(892\) −8.70888e70 −0.0452922
\(893\) −1.99893e72 −1.01143
\(894\) −2.39475e72 −1.17894
\(895\) −1.08745e72 −0.520888
\(896\) −2.00632e72 −0.935093
\(897\) −2.68740e72 −1.21876
\(898\) 3.06184e72 1.35118
\(899\) 9.68865e71 0.416055
\(900\) 2.47600e70 0.0103469
\(901\) 8.79698e71 0.357747
\(902\) −1.57437e72 −0.623085
\(903\) 1.64109e72 0.632096
\(904\) 1.33118e71 0.0499013
\(905\) 5.21331e71 0.190206
\(906\) −3.44659e72 −1.22391
\(907\) 5.55555e71 0.192021 0.0960105 0.995380i \(-0.469392\pi\)
0.0960105 + 0.995380i \(0.469392\pi\)
\(908\) −2.07245e71 −0.0697238
\(909\) −1.20983e71 −0.0396195
\(910\) 2.66710e72 0.850208
\(911\) 2.02494e72 0.628365 0.314182 0.949363i \(-0.398270\pi\)
0.314182 + 0.949363i \(0.398270\pi\)
\(912\) 5.46782e72 1.65173
\(913\) −2.00678e72 −0.590153
\(914\) 4.64718e72 1.33048
\(915\) −1.43249e72 −0.399277
\(916\) −3.60538e71 −0.0978390
\(917\) −4.29498e72 −1.13478
\(918\) −3.36116e72 −0.864656
\(919\) −1.46950e72 −0.368077 −0.184038 0.982919i \(-0.558917\pi\)
−0.184038 + 0.982919i \(0.558917\pi\)
\(920\) 3.65104e72 0.890461
\(921\) 3.66122e72 0.869490
\(922\) −4.92706e72 −1.13941
\(923\) −3.46305e72 −0.779861
\(924\) 7.91103e71 0.173488
\(925\) 1.00183e72 0.213956
\(926\) −2.16477e72 −0.450239
\(927\) −6.96152e71 −0.141010
\(928\) −6.08580e71 −0.120058
\(929\) 7.04427e72 1.35348 0.676739 0.736223i \(-0.263393\pi\)
0.676739 + 0.736223i \(0.263393\pi\)
\(930\) 3.03767e72 0.568471
\(931\) −2.26786e72 −0.413379
\(932\) 5.73435e71 0.101811
\(933\) −2.66307e72 −0.460556
\(934\) −4.20283e72 −0.708016
\(935\) −7.93113e72 −1.30152
\(936\) 1.95839e72 0.313069
\(937\) −9.24309e72 −1.43945 −0.719726 0.694258i \(-0.755733\pi\)
−0.719726 + 0.694258i \(0.755733\pi\)
\(938\) 1.05857e73 1.60602
\(939\) −5.37912e71 −0.0795068
\(940\) 3.29651e71 0.0474702
\(941\) 8.82463e72 1.23809 0.619043 0.785357i \(-0.287521\pi\)
0.619043 + 0.785357i \(0.287521\pi\)
\(942\) −8.37651e72 −1.14503
\(943\) 3.68201e72 0.490397
\(944\) 5.48398e71 0.0711676
\(945\) 5.64371e72 0.713650
\(946\) 5.45730e72 0.672427
\(947\) 1.12021e73 1.34501 0.672504 0.740093i \(-0.265219\pi\)
0.672504 + 0.740093i \(0.265219\pi\)
\(948\) −1.41086e72 −0.165075
\(949\) 1.22226e73 1.39362
\(950\) −5.00856e72 −0.556525
\(951\) −1.03101e73 −1.11645
\(952\) −1.26095e73 −1.33073
\(953\) 8.31437e72 0.855172 0.427586 0.903975i \(-0.359364\pi\)
0.427586 + 0.903975i \(0.359364\pi\)
\(954\) 8.96472e71 0.0898673
\(955\) 2.73959e72 0.267672
\(956\) 3.66025e71 0.0348572
\(957\) −1.11417e73 −1.03421
\(958\) −2.22731e72 −0.201524
\(959\) −2.06339e73 −1.81981
\(960\) −1.14038e73 −0.980399
\(961\) −6.79957e72 −0.569847
\(962\) 6.87209e72 0.561435
\(963\) 8.15922e71 0.0649837
\(964\) −3.44191e71 −0.0267246
\(965\) −6.99634e72 −0.529604
\(966\) 1.76333e73 1.30135
\(967\) 1.19977e73 0.863277 0.431639 0.902047i \(-0.357936\pi\)
0.431639 + 0.902047i \(0.357936\pi\)
\(968\) 1.54859e73 1.08640
\(969\) 3.07225e73 2.10147
\(970\) −1.41929e73 −0.946593
\(971\) −2.62188e73 −1.70507 −0.852535 0.522671i \(-0.824936\pi\)
−0.852535 + 0.522671i \(0.824936\pi\)
\(972\) 8.73557e71 0.0553947
\(973\) 2.60648e73 1.61172
\(974\) −8.44242e72 −0.509064
\(975\) −7.01036e72 −0.412218
\(976\) −6.84779e72 −0.392672
\(977\) −1.17201e73 −0.655413 −0.327706 0.944780i \(-0.606276\pi\)
−0.327706 + 0.944780i \(0.606276\pi\)
\(978\) 6.05135e72 0.330027
\(979\) 3.46808e73 1.84465
\(980\) 3.74000e71 0.0194014
\(981\) 3.26333e72 0.165109
\(982\) −3.16037e72 −0.155957
\(983\) −2.13585e73 −1.02804 −0.514019 0.857779i \(-0.671844\pi\)
−0.514019 + 0.857779i \(0.671844\pi\)
\(984\) −1.15969e73 −0.544453
\(985\) −1.77855e73 −0.814477
\(986\) 1.54014e73 0.687979
\(987\) 1.83580e73 0.799937
\(988\) 3.60481e72 0.153228
\(989\) −1.27631e73 −0.529232
\(990\) −8.08236e72 −0.326946
\(991\) −2.03182e73 −0.801827 −0.400913 0.916116i \(-0.631307\pi\)
−0.400913 + 0.916116i \(0.631307\pi\)
\(992\) −3.22404e72 −0.124127
\(993\) −3.68535e73 −1.38428
\(994\) 2.27227e73 0.832710
\(995\) 2.99998e73 1.07264
\(996\) −1.28197e72 −0.0447222
\(997\) −1.66206e73 −0.565739 −0.282869 0.959158i \(-0.591286\pi\)
−0.282869 + 0.959158i \(0.591286\pi\)
\(998\) −6.41587e72 −0.213087
\(999\) 1.45417e73 0.471259
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.1.2 3
3.2 odd 2 9.50.a.a.1.2 3
4.3 odd 2 16.50.a.c.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.50.a.a.1.2 3 1.1 even 1 trivial
9.50.a.a.1.2 3 3.2 odd 2
16.50.a.c.1.1 3 4.3 odd 2