Properties

Label 1.62.a.a.1.3
Level $1$
Weight $62$
Character 1.1
Self dual yes
Analytic conductor $23.566$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 62 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.5656183265\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 180363795469121 x^{2} + 166129321978984507920 x + 2785609847439483545242446300\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{28}\cdot 3^{8}\cdot 5^{2}\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-3.61406e6\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.80478e8 q^{2} +2.49037e14 q^{3} -1.34451e18 q^{4} +1.59503e20 q^{5} +2.44176e23 q^{6} +1.63507e25 q^{7} -3.57909e27 q^{8} -6.51539e28 q^{9} +O(q^{10})\) \(q+9.80478e8 q^{2} +2.49037e14 q^{3} -1.34451e18 q^{4} +1.59503e20 q^{5} +2.44176e23 q^{6} +1.63507e25 q^{7} -3.57909e27 q^{8} -6.51539e28 q^{9} +1.56389e29 q^{10} +1.92532e30 q^{11} -3.34832e32 q^{12} -1.30898e34 q^{13} +1.60315e34 q^{14} +3.97221e34 q^{15} -4.08993e35 q^{16} +2.98908e37 q^{17} -6.38819e37 q^{18} -7.88343e38 q^{19} -2.14452e38 q^{20} +4.07194e39 q^{21} +1.88773e39 q^{22} -4.50060e41 q^{23} -8.91326e41 q^{24} -4.31137e42 q^{25} -1.28343e43 q^{26} -4.78967e43 q^{27} -2.19837e43 q^{28} -5.51506e44 q^{29} +3.89466e43 q^{30} +4.17012e45 q^{31} +7.85180e45 q^{32} +4.79477e44 q^{33} +2.93073e46 q^{34} +2.60798e45 q^{35} +8.75998e46 q^{36} -6.95142e47 q^{37} -7.72953e47 q^{38} -3.25985e48 q^{39} -5.70874e47 q^{40} +1.25327e49 q^{41} +3.99245e48 q^{42} +8.92745e49 q^{43} -2.58861e48 q^{44} -1.03922e49 q^{45} -4.41273e50 q^{46} +1.21258e50 q^{47} -1.01854e50 q^{48} -3.28881e51 q^{49} -4.22720e51 q^{50} +7.44393e51 q^{51} +1.75994e52 q^{52} +5.55328e52 q^{53} -4.69616e52 q^{54} +3.07094e50 q^{55} -5.85207e52 q^{56} -1.96327e53 q^{57} -5.40740e53 q^{58} +4.29424e53 q^{59} -5.34066e52 q^{60} +1.17661e53 q^{61} +4.08871e54 q^{62} -1.06531e54 q^{63} +8.64159e54 q^{64} -2.08786e54 q^{65} +4.70116e53 q^{66} -3.47829e55 q^{67} -4.01884e55 q^{68} -1.12082e56 q^{69} +2.55707e54 q^{70} +3.07606e56 q^{71} +2.33191e56 q^{72} +7.42117e56 q^{73} -6.81572e56 q^{74} -1.07369e57 q^{75} +1.05993e57 q^{76} +3.14804e55 q^{77} -3.19621e57 q^{78} -4.19454e57 q^{79} -6.52354e55 q^{80} -3.64222e57 q^{81} +1.22880e58 q^{82} +3.40233e58 q^{83} -5.47475e57 q^{84} +4.76766e57 q^{85} +8.75316e58 q^{86} -1.37346e59 q^{87} -6.89089e57 q^{88} -3.77146e59 q^{89} -1.01893e58 q^{90} -2.14028e59 q^{91} +6.05108e59 q^{92} +1.03852e60 q^{93} +1.18890e59 q^{94} -1.25743e59 q^{95} +1.95539e60 q^{96} -2.29644e60 q^{97} -3.22460e60 q^{98} -1.25442e59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} + O(q^{10}) \) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} - \)\(14\!\cdots\!00\)\(q^{10} - \)\(41\!\cdots\!52\)\(q^{11} - \)\(99\!\cdots\!00\)\(q^{12} + \)\(10\!\cdots\!00\)\(q^{13} - \)\(21\!\cdots\!04\)\(q^{14} + \)\(11\!\cdots\!00\)\(q^{15} + \)\(10\!\cdots\!24\)\(q^{16} - \)\(40\!\cdots\!00\)\(q^{17} + \)\(15\!\cdots\!00\)\(q^{18} - \)\(35\!\cdots\!20\)\(q^{19} - \)\(50\!\cdots\!00\)\(q^{20} - \)\(55\!\cdots\!72\)\(q^{21} - \)\(17\!\cdots\!00\)\(q^{22} - \)\(41\!\cdots\!00\)\(q^{23} - \)\(61\!\cdots\!60\)\(q^{24} - \)\(16\!\cdots\!00\)\(q^{25} - \)\(49\!\cdots\!32\)\(q^{26} - \)\(12\!\cdots\!00\)\(q^{27} - \)\(79\!\cdots\!00\)\(q^{28} + \)\(66\!\cdots\!20\)\(q^{29} + \)\(95\!\cdots\!00\)\(q^{30} + \)\(32\!\cdots\!28\)\(q^{31} + \)\(29\!\cdots\!00\)\(q^{32} + \)\(80\!\cdots\!00\)\(q^{33} + \)\(39\!\cdots\!16\)\(q^{34} + \)\(94\!\cdots\!00\)\(q^{35} - \)\(49\!\cdots\!36\)\(q^{36} - \)\(71\!\cdots\!00\)\(q^{37} - \)\(65\!\cdots\!00\)\(q^{38} - \)\(53\!\cdots\!76\)\(q^{39} - \)\(69\!\cdots\!00\)\(q^{40} + \)\(16\!\cdots\!68\)\(q^{41} + \)\(15\!\cdots\!00\)\(q^{42} + \)\(75\!\cdots\!00\)\(q^{43} + \)\(15\!\cdots\!36\)\(q^{44} + \)\(60\!\cdots\!00\)\(q^{45} - \)\(15\!\cdots\!12\)\(q^{46} - \)\(21\!\cdots\!00\)\(q^{47} - \)\(84\!\cdots\!00\)\(q^{48} + \)\(15\!\cdots\!28\)\(q^{49} - \)\(37\!\cdots\!00\)\(q^{50} + \)\(20\!\cdots\!88\)\(q^{51} + \)\(34\!\cdots\!00\)\(q^{52} + \)\(84\!\cdots\!00\)\(q^{53} + \)\(20\!\cdots\!80\)\(q^{54} - \)\(18\!\cdots\!00\)\(q^{55} - \)\(89\!\cdots\!20\)\(q^{56} - \)\(48\!\cdots\!00\)\(q^{57} - \)\(42\!\cdots\!00\)\(q^{58} - \)\(21\!\cdots\!60\)\(q^{59} + \)\(16\!\cdots\!00\)\(q^{60} + \)\(42\!\cdots\!48\)\(q^{61} + \)\(51\!\cdots\!00\)\(q^{62} + \)\(17\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!08\)\(q^{64} - \)\(40\!\cdots\!00\)\(q^{65} - \)\(32\!\cdots\!24\)\(q^{66} - \)\(15\!\cdots\!00\)\(q^{67} - \)\(19\!\cdots\!00\)\(q^{68} - \)\(65\!\cdots\!16\)\(q^{69} + \)\(16\!\cdots\!00\)\(q^{70} + \)\(26\!\cdots\!88\)\(q^{71} + \)\(10\!\cdots\!00\)\(q^{72} + \)\(43\!\cdots\!00\)\(q^{73} + \)\(27\!\cdots\!56\)\(q^{74} + \)\(22\!\cdots\!00\)\(q^{75} - \)\(91\!\cdots\!40\)\(q^{76} - \)\(62\!\cdots\!00\)\(q^{77} - \)\(62\!\cdots\!00\)\(q^{78} - \)\(21\!\cdots\!80\)\(q^{79} - \)\(81\!\cdots\!00\)\(q^{80} + \)\(16\!\cdots\!84\)\(q^{81} + \)\(41\!\cdots\!00\)\(q^{82} - \)\(19\!\cdots\!00\)\(q^{83} + \)\(26\!\cdots\!96\)\(q^{84} + \)\(23\!\cdots\!00\)\(q^{85} - \)\(71\!\cdots\!72\)\(q^{86} - \)\(25\!\cdots\!00\)\(q^{87} - \)\(45\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!40\)\(q^{89} - \)\(12\!\cdots\!00\)\(q^{90} - \)\(45\!\cdots\!52\)\(q^{91} + \)\(16\!\cdots\!00\)\(q^{92} - \)\(43\!\cdots\!00\)\(q^{93} + \)\(64\!\cdots\!76\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} + \)\(15\!\cdots\!08\)\(q^{96} - \)\(80\!\cdots\!00\)\(q^{97} + \)\(17\!\cdots\!00\)\(q^{98} - \)\(31\!\cdots\!76\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.80478e8 0.645688 0.322844 0.946452i \(-0.395361\pi\)
0.322844 + 0.946452i \(0.395361\pi\)
\(3\) 2.49037e14 0.698339 0.349169 0.937060i \(-0.386464\pi\)
0.349169 + 0.937060i \(0.386464\pi\)
\(4\) −1.34451e18 −0.583087
\(5\) 1.59503e20 0.0765919 0.0382959 0.999266i \(-0.487807\pi\)
0.0382959 + 0.999266i \(0.487807\pi\)
\(6\) 2.44176e23 0.450909
\(7\) 1.63507e25 0.274187 0.137094 0.990558i \(-0.456224\pi\)
0.137094 + 0.990558i \(0.456224\pi\)
\(8\) −3.57909e27 −1.02218
\(9\) −6.51539e28 −0.512323
\(10\) 1.56389e29 0.0494545
\(11\) 1.92532e30 0.0332680 0.0166340 0.999862i \(-0.494705\pi\)
0.0166340 + 0.999862i \(0.494705\pi\)
\(12\) −3.34832e32 −0.407192
\(13\) −1.30898e34 −1.38568 −0.692838 0.721094i \(-0.743640\pi\)
−0.692838 + 0.721094i \(0.743640\pi\)
\(14\) 1.60315e34 0.177039
\(15\) 3.97221e34 0.0534871
\(16\) −4.08993e35 −0.0769230
\(17\) 2.98908e37 0.884801 0.442401 0.896818i \(-0.354127\pi\)
0.442401 + 0.896818i \(0.354127\pi\)
\(18\) −6.38819e37 −0.330801
\(19\) −7.88343e38 −0.784748 −0.392374 0.919806i \(-0.628346\pi\)
−0.392374 + 0.919806i \(0.628346\pi\)
\(20\) −2.14452e38 −0.0446597
\(21\) 4.07194e39 0.191476
\(22\) 1.88773e39 0.0214807
\(23\) −4.50060e41 −1.31999 −0.659995 0.751270i \(-0.729442\pi\)
−0.659995 + 0.751270i \(0.729442\pi\)
\(24\) −8.91326e41 −0.713828
\(25\) −4.31137e42 −0.994134
\(26\) −1.28343e43 −0.894714
\(27\) −4.78967e43 −1.05611
\(28\) −2.19837e43 −0.159875
\(29\) −5.51506e44 −1.37534 −0.687672 0.726021i \(-0.741367\pi\)
−0.687672 + 0.726021i \(0.741367\pi\)
\(30\) 3.89466e43 0.0345360
\(31\) 4.17012e45 1.36025 0.680123 0.733098i \(-0.261926\pi\)
0.680123 + 0.733098i \(0.261926\pi\)
\(32\) 7.85180e45 0.972512
\(33\) 4.79477e44 0.0232323
\(34\) 2.93073e46 0.571306
\(35\) 2.60798e45 0.0210005
\(36\) 8.75998e46 0.298729
\(37\) −6.95142e47 −1.02783 −0.513915 0.857841i \(-0.671805\pi\)
−0.513915 + 0.857841i \(0.671805\pi\)
\(38\) −7.72953e47 −0.506703
\(39\) −3.25985e48 −0.967671
\(40\) −5.70874e47 −0.0782907
\(41\) 1.25327e49 0.809351 0.404676 0.914460i \(-0.367384\pi\)
0.404676 + 0.914460i \(0.367384\pi\)
\(42\) 3.99245e48 0.123633
\(43\) 8.92745e49 1.34877 0.674387 0.738378i \(-0.264408\pi\)
0.674387 + 0.738378i \(0.264408\pi\)
\(44\) −2.58861e48 −0.0193981
\(45\) −1.03922e49 −0.0392398
\(46\) −4.41273e50 −0.852303
\(47\) 1.21258e50 0.121541 0.0607707 0.998152i \(-0.480644\pi\)
0.0607707 + 0.998152i \(0.480644\pi\)
\(48\) −1.01854e50 −0.0537183
\(49\) −3.28881e51 −0.924821
\(50\) −4.22720e51 −0.641900
\(51\) 7.44393e51 0.617891
\(52\) 1.75994e52 0.807969
\(53\) 5.55328e52 1.42605 0.713026 0.701138i \(-0.247324\pi\)
0.713026 + 0.701138i \(0.247324\pi\)
\(54\) −4.69616e52 −0.681920
\(55\) 3.07094e50 0.00254806
\(56\) −5.85207e52 −0.280269
\(57\) −1.96327e53 −0.548020
\(58\) −5.40740e53 −0.888044
\(59\) 4.29424e53 0.418697 0.209348 0.977841i \(-0.432866\pi\)
0.209348 + 0.977841i \(0.432866\pi\)
\(60\) −5.34066e52 −0.0311876
\(61\) 1.17661e53 0.0415024 0.0207512 0.999785i \(-0.493394\pi\)
0.0207512 + 0.999785i \(0.493394\pi\)
\(62\) 4.08871e54 0.878294
\(63\) −1.06531e54 −0.140472
\(64\) 8.64159e54 0.704863
\(65\) −2.08786e54 −0.106131
\(66\) 4.70116e53 0.0150008
\(67\) −3.47829e55 −0.701592 −0.350796 0.936452i \(-0.614089\pi\)
−0.350796 + 0.936452i \(0.614089\pi\)
\(68\) −4.01884e55 −0.515916
\(69\) −1.12082e56 −0.921801
\(70\) 2.55707e54 0.0135598
\(71\) 3.07606e56 1.05831 0.529157 0.848524i \(-0.322508\pi\)
0.529157 + 0.848524i \(0.322508\pi\)
\(72\) 2.33191e56 0.523687
\(73\) 7.42117e56 1.09427 0.547136 0.837044i \(-0.315718\pi\)
0.547136 + 0.837044i \(0.315718\pi\)
\(74\) −6.81572e56 −0.663657
\(75\) −1.07369e57 −0.694242
\(76\) 1.05993e57 0.457576
\(77\) 3.14804e55 0.00912165
\(78\) −3.19621e57 −0.624814
\(79\) −4.19454e57 −0.555978 −0.277989 0.960584i \(-0.589668\pi\)
−0.277989 + 0.960584i \(0.589668\pi\)
\(80\) −6.52354e55 −0.00589168
\(81\) −3.64222e57 −0.225202
\(82\) 1.22880e58 0.522588
\(83\) 3.40233e58 0.999758 0.499879 0.866095i \(-0.333378\pi\)
0.499879 + 0.866095i \(0.333378\pi\)
\(84\) −5.47475e57 −0.111647
\(85\) 4.76766e57 0.0677686
\(86\) 8.75316e58 0.870888
\(87\) −1.37346e59 −0.960457
\(88\) −6.89089e57 −0.0340059
\(89\) −3.77146e59 −1.31860 −0.659302 0.751878i \(-0.729148\pi\)
−0.659302 + 0.751878i \(0.729148\pi\)
\(90\) −1.01893e58 −0.0253367
\(91\) −2.14028e59 −0.379934
\(92\) 6.05108e59 0.769669
\(93\) 1.03852e60 0.949912
\(94\) 1.18890e59 0.0784779
\(95\) −1.25743e59 −0.0601053
\(96\) 1.95539e60 0.679143
\(97\) −2.29644e60 −0.581457 −0.290728 0.956806i \(-0.593898\pi\)
−0.290728 + 0.956806i \(0.593898\pi\)
\(98\) −3.22460e60 −0.597146
\(99\) −1.25442e59 −0.0170439
\(100\) 5.79666e60 0.579666
\(101\) −1.42955e61 −1.05535 −0.527675 0.849446i \(-0.676936\pi\)
−0.527675 + 0.849446i \(0.676936\pi\)
\(102\) 7.29860e60 0.398965
\(103\) −4.01328e61 −1.62916 −0.814581 0.580051i \(-0.803033\pi\)
−0.814581 + 0.580051i \(0.803033\pi\)
\(104\) 4.68496e61 1.41641
\(105\) 6.49486e59 0.0146655
\(106\) 5.44486e61 0.920785
\(107\) 4.31345e61 0.547796 0.273898 0.961759i \(-0.411687\pi\)
0.273898 + 0.961759i \(0.411687\pi\)
\(108\) 6.43974e61 0.615806
\(109\) −1.94980e62 −1.40761 −0.703805 0.710393i \(-0.748517\pi\)
−0.703805 + 0.710393i \(0.748517\pi\)
\(110\) 3.01099e59 0.00164525
\(111\) −1.73116e62 −0.717773
\(112\) −6.68733e60 −0.0210913
\(113\) −6.70205e61 −0.161182 −0.0805908 0.996747i \(-0.525681\pi\)
−0.0805908 + 0.996747i \(0.525681\pi\)
\(114\) −1.92494e62 −0.353850
\(115\) −7.17857e61 −0.101101
\(116\) 7.41504e62 0.801945
\(117\) 8.52853e62 0.709913
\(118\) 4.21040e62 0.270347
\(119\) 4.88737e62 0.242601
\(120\) −1.42169e62 −0.0546734
\(121\) −3.34559e63 −0.998893
\(122\) 1.15364e62 0.0267976
\(123\) 3.12111e63 0.565201
\(124\) −5.60676e63 −0.793141
\(125\) −1.37941e63 −0.152734
\(126\) −1.04452e63 −0.0907014
\(127\) −2.06063e63 −0.140600 −0.0703002 0.997526i \(-0.522396\pi\)
−0.0703002 + 0.997526i \(0.522396\pi\)
\(128\) −9.63214e63 −0.517391
\(129\) 2.22327e64 0.941902
\(130\) −2.04710e63 −0.0685278
\(131\) 6.07543e64 1.60991 0.804957 0.593333i \(-0.202188\pi\)
0.804957 + 0.593333i \(0.202188\pi\)
\(132\) −6.44660e62 −0.0135465
\(133\) −1.28900e64 −0.215168
\(134\) −3.41039e64 −0.453010
\(135\) −7.63965e63 −0.0808897
\(136\) −1.06982e65 −0.904426
\(137\) −1.12737e65 −0.762238 −0.381119 0.924526i \(-0.624461\pi\)
−0.381119 + 0.924526i \(0.624461\pi\)
\(138\) −1.09894e65 −0.595196
\(139\) 3.26131e65 1.41723 0.708616 0.705594i \(-0.249320\pi\)
0.708616 + 0.705594i \(0.249320\pi\)
\(140\) −3.50645e63 −0.0122451
\(141\) 3.01977e64 0.0848771
\(142\) 3.01600e65 0.683341
\(143\) −2.52021e64 −0.0460986
\(144\) 2.66475e64 0.0394094
\(145\) −8.79667e64 −0.105340
\(146\) 7.27630e65 0.706559
\(147\) −8.19036e65 −0.645839
\(148\) 9.34623e65 0.599314
\(149\) −2.77156e66 −1.44725 −0.723625 0.690194i \(-0.757525\pi\)
−0.723625 + 0.690194i \(0.757525\pi\)
\(150\) −1.05273e66 −0.448264
\(151\) −1.14707e65 −0.0398836 −0.0199418 0.999801i \(-0.506348\pi\)
−0.0199418 + 0.999801i \(0.506348\pi\)
\(152\) 2.82155e66 0.802154
\(153\) −1.94750e66 −0.453304
\(154\) 3.08659e64 0.00588974
\(155\) 6.65146e65 0.104184
\(156\) 4.38290e66 0.564236
\(157\) 4.92931e66 0.522212 0.261106 0.965310i \(-0.415913\pi\)
0.261106 + 0.965310i \(0.415913\pi\)
\(158\) −4.11265e66 −0.358988
\(159\) 1.38297e67 0.995867
\(160\) 1.25238e66 0.0744865
\(161\) −7.35880e66 −0.361925
\(162\) −3.57111e66 −0.145410
\(163\) −5.45632e67 −1.84153 −0.920764 0.390121i \(-0.872433\pi\)
−0.920764 + 0.390121i \(0.872433\pi\)
\(164\) −1.68503e67 −0.471922
\(165\) 7.64778e64 0.00177941
\(166\) 3.33591e67 0.645532
\(167\) 4.21801e67 0.679603 0.339801 0.940497i \(-0.389640\pi\)
0.339801 + 0.940497i \(0.389640\pi\)
\(168\) −1.45738e67 −0.195723
\(169\) 8.21065e67 0.920096
\(170\) 4.67459e66 0.0437574
\(171\) 5.13636e67 0.402045
\(172\) −1.20030e68 −0.786453
\(173\) 1.33954e68 0.735443 0.367721 0.929936i \(-0.380138\pi\)
0.367721 + 0.929936i \(0.380138\pi\)
\(174\) −1.34664e68 −0.620155
\(175\) −7.04940e67 −0.272579
\(176\) −7.87443e65 −0.00255907
\(177\) 1.06942e68 0.292392
\(178\) −3.69784e68 −0.851408
\(179\) −1.01313e68 −0.196630 −0.0983150 0.995155i \(-0.531345\pi\)
−0.0983150 + 0.995155i \(0.531345\pi\)
\(180\) 1.39724e67 0.0228802
\(181\) 4.25098e67 0.0587885 0.0293943 0.999568i \(-0.490642\pi\)
0.0293943 + 0.999568i \(0.490642\pi\)
\(182\) −2.09850e68 −0.245319
\(183\) 2.93020e67 0.0289827
\(184\) 1.61080e69 1.34927
\(185\) −1.10877e68 −0.0787234
\(186\) 1.01824e69 0.613347
\(187\) 5.75494e67 0.0294355
\(188\) −1.63032e68 −0.0708692
\(189\) −7.83146e68 −0.289573
\(190\) −1.23288e68 −0.0388093
\(191\) −5.32231e69 −1.42752 −0.713761 0.700389i \(-0.753010\pi\)
−0.713761 + 0.700389i \(0.753010\pi\)
\(192\) 2.15208e69 0.492233
\(193\) −2.00291e69 −0.390988 −0.195494 0.980705i \(-0.562631\pi\)
−0.195494 + 0.980705i \(0.562631\pi\)
\(194\) −2.25161e69 −0.375440
\(195\) −5.19955e68 −0.0741157
\(196\) 4.42182e69 0.539251
\(197\) −2.47637e69 −0.258580 −0.129290 0.991607i \(-0.541270\pi\)
−0.129290 + 0.991607i \(0.541270\pi\)
\(198\) −1.22993e68 −0.0110051
\(199\) 2.26238e70 1.73599 0.867994 0.496575i \(-0.165409\pi\)
0.867994 + 0.496575i \(0.165409\pi\)
\(200\) 1.54308e70 1.01618
\(201\) −8.66225e69 −0.489949
\(202\) −1.40164e70 −0.681427
\(203\) −9.01754e69 −0.377102
\(204\) −1.00084e70 −0.360284
\(205\) 1.99900e69 0.0619897
\(206\) −3.93493e70 −1.05193
\(207\) 2.93231e70 0.676262
\(208\) 5.35364e69 0.106590
\(209\) −1.51781e69 −0.0261070
\(210\) 6.36806e68 0.00946932
\(211\) −1.43805e70 −0.184995 −0.0924975 0.995713i \(-0.529485\pi\)
−0.0924975 + 0.995713i \(0.529485\pi\)
\(212\) −7.46642e70 −0.831512
\(213\) 7.66053e70 0.739062
\(214\) 4.22924e70 0.353706
\(215\) 1.42395e70 0.103305
\(216\) 1.71426e71 1.07954
\(217\) 6.81846e70 0.372962
\(218\) −1.91174e71 −0.908877
\(219\) 1.84815e71 0.764173
\(220\) −4.12890e68 −0.00148574
\(221\) −3.91265e71 −1.22605
\(222\) −1.69737e71 −0.463458
\(223\) −3.83507e71 −0.913009 −0.456504 0.889721i \(-0.650899\pi\)
−0.456504 + 0.889721i \(0.650899\pi\)
\(224\) 1.28383e71 0.266650
\(225\) 2.80902e71 0.509318
\(226\) −6.57121e70 −0.104073
\(227\) −4.91476e71 −0.680320 −0.340160 0.940368i \(-0.610481\pi\)
−0.340160 + 0.940368i \(0.610481\pi\)
\(228\) 2.63963e71 0.319543
\(229\) 1.61052e72 1.70602 0.853012 0.521891i \(-0.174773\pi\)
0.853012 + 0.521891i \(0.174773\pi\)
\(230\) −7.03842e70 −0.0652794
\(231\) 7.83980e69 0.00637000
\(232\) 1.97389e72 1.40585
\(233\) −2.97343e72 −1.85739 −0.928693 0.370850i \(-0.879066\pi\)
−0.928693 + 0.370850i \(0.879066\pi\)
\(234\) 8.36203e71 0.458383
\(235\) 1.93409e70 0.00930908
\(236\) −5.77363e71 −0.244136
\(237\) −1.04460e72 −0.388261
\(238\) 4.79196e71 0.156645
\(239\) −5.09144e72 −1.46455 −0.732275 0.681009i \(-0.761542\pi\)
−0.732275 + 0.681009i \(0.761542\pi\)
\(240\) −1.62461e70 −0.00411439
\(241\) 4.14476e72 0.924655 0.462327 0.886709i \(-0.347015\pi\)
0.462327 + 0.886709i \(0.347015\pi\)
\(242\) −3.28028e72 −0.644974
\(243\) 5.18414e72 0.898846
\(244\) −1.58196e71 −0.0241995
\(245\) −5.24573e71 −0.0708338
\(246\) 3.06018e72 0.364944
\(247\) 1.03193e73 1.08741
\(248\) −1.49252e73 −1.39042
\(249\) 8.47307e72 0.698170
\(250\) −1.35248e72 −0.0986188
\(251\) 3.22599e72 0.208264 0.104132 0.994563i \(-0.466794\pi\)
0.104132 + 0.994563i \(0.466794\pi\)
\(252\) 1.43232e72 0.0819076
\(253\) −8.66509e71 −0.0439134
\(254\) −2.02040e72 −0.0907840
\(255\) 1.18733e72 0.0473254
\(256\) −2.93702e73 −1.03894
\(257\) −4.70005e73 −1.47619 −0.738095 0.674697i \(-0.764274\pi\)
−0.738095 + 0.674697i \(0.764274\pi\)
\(258\) 2.17986e73 0.608175
\(259\) −1.13661e73 −0.281818
\(260\) 2.80714e72 0.0618838
\(261\) 3.59328e73 0.704621
\(262\) 5.95683e73 1.03950
\(263\) 6.53435e73 1.01520 0.507601 0.861592i \(-0.330532\pi\)
0.507601 + 0.861592i \(0.330532\pi\)
\(264\) −1.71609e72 −0.0237476
\(265\) 8.85762e72 0.109224
\(266\) −1.26383e73 −0.138931
\(267\) −9.39235e73 −0.920833
\(268\) 4.67659e73 0.409089
\(269\) −7.56525e73 −0.590716 −0.295358 0.955387i \(-0.595439\pi\)
−0.295358 + 0.955387i \(0.595439\pi\)
\(270\) −7.49050e72 −0.0522295
\(271\) −5.25878e73 −0.327583 −0.163792 0.986495i \(-0.552372\pi\)
−0.163792 + 0.986495i \(0.552372\pi\)
\(272\) −1.22251e73 −0.0680615
\(273\) −5.33010e73 −0.265323
\(274\) −1.10537e74 −0.492168
\(275\) −8.30077e72 −0.0330728
\(276\) 1.50694e74 0.537490
\(277\) 1.19304e72 0.00381085 0.00190543 0.999998i \(-0.499393\pi\)
0.00190543 + 0.999998i \(0.499393\pi\)
\(278\) 3.19764e74 0.915090
\(279\) −2.71700e74 −0.696885
\(280\) −9.33420e72 −0.0214663
\(281\) 5.85184e74 1.20712 0.603559 0.797319i \(-0.293749\pi\)
0.603559 + 0.797319i \(0.293749\pi\)
\(282\) 2.96081e73 0.0548041
\(283\) 1.48848e74 0.247318 0.123659 0.992325i \(-0.460537\pi\)
0.123659 + 0.992325i \(0.460537\pi\)
\(284\) −4.13578e74 −0.617089
\(285\) −3.13146e73 −0.0419739
\(286\) −2.47101e73 −0.0297653
\(287\) 2.04919e74 0.221914
\(288\) −5.11576e74 −0.498240
\(289\) −2.47798e74 −0.217127
\(290\) −8.62494e73 −0.0680169
\(291\) −5.71899e74 −0.406054
\(292\) −9.97782e74 −0.638056
\(293\) 7.53743e74 0.434271 0.217136 0.976141i \(-0.430329\pi\)
0.217136 + 0.976141i \(0.430329\pi\)
\(294\) −8.03046e74 −0.417010
\(295\) 6.84942e73 0.0320688
\(296\) 2.48797e75 1.05063
\(297\) −9.22165e73 −0.0351348
\(298\) −2.71745e75 −0.934472
\(299\) 5.89120e75 1.82908
\(300\) 1.44359e75 0.404803
\(301\) 1.45970e75 0.369817
\(302\) −1.12468e74 −0.0257523
\(303\) −3.56010e75 −0.736992
\(304\) 3.22427e74 0.0603652
\(305\) 1.87673e73 0.00317875
\(306\) −1.90948e75 −0.292693
\(307\) −1.13968e76 −1.58147 −0.790735 0.612159i \(-0.790301\pi\)
−0.790735 + 0.612159i \(0.790301\pi\)
\(308\) −4.23256e73 −0.00531871
\(309\) −9.99456e75 −1.13771
\(310\) 6.52160e74 0.0672702
\(311\) 1.39236e76 1.30185 0.650923 0.759144i \(-0.274382\pi\)
0.650923 + 0.759144i \(0.274382\pi\)
\(312\) 1.16673e76 0.989134
\(313\) −2.81704e75 −0.216616 −0.108308 0.994117i \(-0.534543\pi\)
−0.108308 + 0.994117i \(0.534543\pi\)
\(314\) 4.83308e75 0.337186
\(315\) −1.69920e74 −0.0107590
\(316\) 5.63958e75 0.324183
\(317\) −1.48589e76 −0.775674 −0.387837 0.921728i \(-0.626778\pi\)
−0.387837 + 0.921728i \(0.626778\pi\)
\(318\) 1.35597e76 0.643020
\(319\) −1.06183e75 −0.0457549
\(320\) 1.37836e75 0.0539867
\(321\) 1.07421e76 0.382547
\(322\) −7.21514e75 −0.233690
\(323\) −2.35642e76 −0.694346
\(324\) 4.89698e75 0.131312
\(325\) 5.64350e76 1.37755
\(326\) −5.34980e76 −1.18905
\(327\) −4.85574e76 −0.982989
\(328\) −4.48556e76 −0.827303
\(329\) 1.98265e75 0.0333251
\(330\) 7.49848e73 0.00114894
\(331\) 9.37638e76 1.31003 0.655015 0.755616i \(-0.272662\pi\)
0.655015 + 0.755616i \(0.272662\pi\)
\(332\) −4.57446e76 −0.582946
\(333\) 4.52912e76 0.526581
\(334\) 4.13566e76 0.438811
\(335\) −5.54797e75 −0.0537363
\(336\) −1.66540e75 −0.0147289
\(337\) 4.95449e76 0.400209 0.200105 0.979775i \(-0.435872\pi\)
0.200105 + 0.979775i \(0.435872\pi\)
\(338\) 8.05036e76 0.594095
\(339\) −1.66906e76 −0.112559
\(340\) −6.41015e75 −0.0395150
\(341\) 8.02883e75 0.0452526
\(342\) 5.03609e76 0.259595
\(343\) −1.11920e77 −0.527761
\(344\) −3.19521e77 −1.37869
\(345\) −1.78773e76 −0.0706024
\(346\) 1.31339e77 0.474867
\(347\) −4.94026e77 −1.63569 −0.817844 0.575440i \(-0.804831\pi\)
−0.817844 + 0.575440i \(0.804831\pi\)
\(348\) 1.84662e77 0.560030
\(349\) −3.62283e76 −0.100664 −0.0503318 0.998733i \(-0.516028\pi\)
−0.0503318 + 0.998733i \(0.516028\pi\)
\(350\) −6.91178e76 −0.176001
\(351\) 6.26959e77 1.46343
\(352\) 1.51172e76 0.0323535
\(353\) 1.78348e77 0.350057 0.175028 0.984563i \(-0.443998\pi\)
0.175028 + 0.984563i \(0.443998\pi\)
\(354\) 1.04855e77 0.188794
\(355\) 4.90639e76 0.0810583
\(356\) 5.07076e77 0.768861
\(357\) 1.21714e77 0.169418
\(358\) −9.93356e76 −0.126962
\(359\) −8.52288e77 −1.00047 −0.500237 0.865889i \(-0.666754\pi\)
−0.500237 + 0.865889i \(0.666754\pi\)
\(360\) 3.71946e76 0.0401101
\(361\) −3.87698e77 −0.384170
\(362\) 4.16799e76 0.0379591
\(363\) −8.33177e77 −0.697566
\(364\) 2.87762e77 0.221535
\(365\) 1.18370e77 0.0838124
\(366\) 2.87300e76 0.0187138
\(367\) −1.13900e77 −0.0682664 −0.0341332 0.999417i \(-0.510867\pi\)
−0.0341332 + 0.999417i \(0.510867\pi\)
\(368\) 1.84071e77 0.101538
\(369\) −8.16554e77 −0.414649
\(370\) −1.08712e77 −0.0508308
\(371\) 9.08002e77 0.391005
\(372\) −1.39629e78 −0.553881
\(373\) 2.11898e78 0.774476 0.387238 0.921980i \(-0.373429\pi\)
0.387238 + 0.921980i \(0.373429\pi\)
\(374\) 5.64259e76 0.0190062
\(375\) −3.43524e77 −0.106660
\(376\) −4.33991e77 −0.124237
\(377\) 7.21912e78 1.90578
\(378\) −7.67857e77 −0.186974
\(379\) 1.08570e78 0.243902 0.121951 0.992536i \(-0.461085\pi\)
0.121951 + 0.992536i \(0.461085\pi\)
\(380\) 1.69062e77 0.0350466
\(381\) −5.13174e77 −0.0981867
\(382\) −5.21841e78 −0.921734
\(383\) −6.68528e78 −1.09033 −0.545164 0.838329i \(-0.683533\pi\)
−0.545164 + 0.838329i \(0.683533\pi\)
\(384\) −2.39876e78 −0.361314
\(385\) 5.02121e75 0.000698644 0
\(386\) −1.96381e78 −0.252456
\(387\) −5.81658e78 −0.691008
\(388\) 3.08758e78 0.339040
\(389\) 1.21345e79 1.23185 0.615926 0.787804i \(-0.288782\pi\)
0.615926 + 0.787804i \(0.288782\pi\)
\(390\) −5.09804e77 −0.0478556
\(391\) −1.34526e79 −1.16793
\(392\) 1.17709e79 0.945334
\(393\) 1.51301e79 1.12427
\(394\) −2.42802e78 −0.166962
\(395\) −6.69039e77 −0.0425834
\(396\) 1.68658e77 0.00993810
\(397\) 1.96626e77 0.0107283 0.00536414 0.999986i \(-0.498293\pi\)
0.00536414 + 0.999986i \(0.498293\pi\)
\(398\) 2.21821e79 1.12091
\(399\) −3.21009e78 −0.150260
\(400\) 1.76332e78 0.0764717
\(401\) −1.33975e79 −0.538417 −0.269209 0.963082i \(-0.586762\pi\)
−0.269209 + 0.963082i \(0.586762\pi\)
\(402\) −8.49314e78 −0.316354
\(403\) −5.45862e79 −1.88486
\(404\) 1.92204e79 0.615361
\(405\) −5.80943e77 −0.0172487
\(406\) −8.84149e78 −0.243490
\(407\) −1.33837e78 −0.0341938
\(408\) −2.66425e79 −0.631596
\(409\) 5.24362e79 1.15364 0.576820 0.816871i \(-0.304293\pi\)
0.576820 + 0.816871i \(0.304293\pi\)
\(410\) 1.95997e78 0.0400260
\(411\) −2.80758e79 −0.532301
\(412\) 5.39588e79 0.949942
\(413\) 7.02139e78 0.114801
\(414\) 2.87507e79 0.436654
\(415\) 5.42681e78 0.0765733
\(416\) −1.02779e80 −1.34759
\(417\) 8.12188e79 0.989708
\(418\) −1.48818e78 −0.0168570
\(419\) −1.15357e79 −0.121483 −0.0607417 0.998154i \(-0.519347\pi\)
−0.0607417 + 0.998154i \(0.519347\pi\)
\(420\) −8.73238e77 −0.00855124
\(421\) 1.70015e80 1.54840 0.774201 0.632939i \(-0.218152\pi\)
0.774201 + 0.632939i \(0.218152\pi\)
\(422\) −1.40998e79 −0.119449
\(423\) −7.90041e78 −0.0622685
\(424\) −1.98757e80 −1.45768
\(425\) −1.28870e80 −0.879611
\(426\) 7.51098e79 0.477203
\(427\) 1.92385e78 0.0113794
\(428\) −5.79946e79 −0.319413
\(429\) −6.27627e78 −0.0321924
\(430\) 1.39615e79 0.0667029
\(431\) −3.88868e80 −1.73080 −0.865398 0.501085i \(-0.832934\pi\)
−0.865398 + 0.501085i \(0.832934\pi\)
\(432\) 1.95894e79 0.0812394
\(433\) 3.92018e80 1.51505 0.757523 0.652809i \(-0.226410\pi\)
0.757523 + 0.652809i \(0.226410\pi\)
\(434\) 6.68535e79 0.240817
\(435\) −2.19070e79 −0.0735632
\(436\) 2.62152e80 0.820759
\(437\) 3.54801e80 1.03586
\(438\) 1.81207e80 0.493417
\(439\) −1.77739e80 −0.451455 −0.225727 0.974191i \(-0.572476\pi\)
−0.225727 + 0.974191i \(0.572476\pi\)
\(440\) −1.09912e78 −0.00260457
\(441\) 2.14279e80 0.473807
\(442\) −3.83627e80 −0.791644
\(443\) −5.81258e80 −1.11958 −0.559790 0.828635i \(-0.689118\pi\)
−0.559790 + 0.828635i \(0.689118\pi\)
\(444\) 2.32756e80 0.418524
\(445\) −6.01558e79 −0.100994
\(446\) −3.76020e80 −0.589519
\(447\) −6.90222e80 −1.01067
\(448\) 1.41296e80 0.193264
\(449\) 2.43094e80 0.310642 0.155321 0.987864i \(-0.450359\pi\)
0.155321 + 0.987864i \(0.450359\pi\)
\(450\) 2.75419e80 0.328860
\(451\) 2.41295e79 0.0269255
\(452\) 9.01096e79 0.0939828
\(453\) −2.85664e79 −0.0278522
\(454\) −4.81881e80 −0.439275
\(455\) −3.41381e79 −0.0290999
\(456\) 7.02670e80 0.560175
\(457\) 4.97936e80 0.371304 0.185652 0.982616i \(-0.440560\pi\)
0.185652 + 0.982616i \(0.440560\pi\)
\(458\) 1.57908e81 1.10156
\(459\) −1.43167e81 −0.934451
\(460\) 9.65163e79 0.0589504
\(461\) 1.47837e81 0.845091 0.422546 0.906342i \(-0.361137\pi\)
0.422546 + 0.906342i \(0.361137\pi\)
\(462\) 7.68675e78 0.00411304
\(463\) −1.44774e80 −0.0725219 −0.0362610 0.999342i \(-0.511545\pi\)
−0.0362610 + 0.999342i \(0.511545\pi\)
\(464\) 2.25562e80 0.105796
\(465\) 1.65646e80 0.0727555
\(466\) −2.91538e81 −1.19929
\(467\) −7.76500e78 −0.00299210 −0.00149605 0.999999i \(-0.500476\pi\)
−0.00149605 + 0.999999i \(0.500476\pi\)
\(468\) −1.14667e81 −0.413941
\(469\) −5.68727e80 −0.192368
\(470\) 1.89633e79 0.00601077
\(471\) 1.22758e81 0.364681
\(472\) −1.53694e81 −0.427983
\(473\) 1.71882e80 0.0448710
\(474\) −1.02420e81 −0.250695
\(475\) 3.39884e81 0.780145
\(476\) −6.57110e80 −0.141457
\(477\) −3.61818e81 −0.730599
\(478\) −4.99204e81 −0.945643
\(479\) 5.86941e81 1.04318 0.521592 0.853195i \(-0.325338\pi\)
0.521592 + 0.853195i \(0.325338\pi\)
\(480\) 3.11890e80 0.0520168
\(481\) 9.09929e81 1.42424
\(482\) 4.06384e81 0.597039
\(483\) −1.83262e81 −0.252746
\(484\) 4.49817e81 0.582441
\(485\) −3.66288e80 −0.0445348
\(486\) 5.08293e81 0.580374
\(487\) −6.11323e81 −0.655597 −0.327799 0.944748i \(-0.606307\pi\)
−0.327799 + 0.944748i \(0.606307\pi\)
\(488\) −4.21120e80 −0.0424230
\(489\) −1.35883e82 −1.28601
\(490\) −5.14332e80 −0.0457365
\(491\) −6.46236e81 −0.540015 −0.270008 0.962858i \(-0.587026\pi\)
−0.270008 + 0.962858i \(0.587026\pi\)
\(492\) −4.19635e81 −0.329561
\(493\) −1.64850e82 −1.21691
\(494\) 1.01178e82 0.702125
\(495\) −2.00084e79 −0.00130543
\(496\) −1.70555e81 −0.104634
\(497\) 5.02958e81 0.290176
\(498\) 8.30766e81 0.450800
\(499\) 1.13795e82 0.580838 0.290419 0.956900i \(-0.406205\pi\)
0.290419 + 0.956900i \(0.406205\pi\)
\(500\) 1.85462e81 0.0890574
\(501\) 1.05044e82 0.474593
\(502\) 3.16301e81 0.134474
\(503\) 5.18866e80 0.0207602 0.0103801 0.999946i \(-0.496696\pi\)
0.0103801 + 0.999946i \(0.496696\pi\)
\(504\) 3.81285e81 0.143588
\(505\) −2.28016e81 −0.0808312
\(506\) −8.49593e80 −0.0283544
\(507\) 2.04476e82 0.642539
\(508\) 2.77053e81 0.0819822
\(509\) −5.17719e82 −1.44279 −0.721393 0.692526i \(-0.756498\pi\)
−0.721393 + 0.692526i \(0.756498\pi\)
\(510\) 1.16415e81 0.0305575
\(511\) 1.21342e82 0.300035
\(512\) −6.58667e81 −0.153438
\(513\) 3.77590e82 0.828783
\(514\) −4.60830e82 −0.953159
\(515\) −6.40128e81 −0.124780
\(516\) −2.98920e82 −0.549210
\(517\) 2.33460e80 0.00404344
\(518\) −1.11442e82 −0.181966
\(519\) 3.33595e82 0.513588
\(520\) 7.47263e81 0.108485
\(521\) −1.12930e83 −1.54617 −0.773087 0.634300i \(-0.781288\pi\)
−0.773087 + 0.634300i \(0.781288\pi\)
\(522\) 3.52313e82 0.454965
\(523\) 1.20266e83 1.46501 0.732506 0.680761i \(-0.238351\pi\)
0.732506 + 0.680761i \(0.238351\pi\)
\(524\) −8.16846e82 −0.938720
\(525\) −1.75556e82 −0.190352
\(526\) 6.40679e82 0.655504
\(527\) 1.24648e83 1.20355
\(528\) −1.96103e80 −0.00178710
\(529\) 8.63022e82 0.742376
\(530\) 8.68470e81 0.0705246
\(531\) −2.79786e82 −0.214508
\(532\) 1.73307e82 0.125462
\(533\) −1.64051e83 −1.12150
\(534\) −9.20899e82 −0.594571
\(535\) 6.88006e81 0.0419567
\(536\) 1.24491e83 0.717154
\(537\) −2.52308e82 −0.137314
\(538\) −7.41756e82 −0.381418
\(539\) −6.33201e81 −0.0307669
\(540\) 1.02716e82 0.0471657
\(541\) −4.18244e83 −1.81515 −0.907576 0.419889i \(-0.862069\pi\)
−0.907576 + 0.419889i \(0.862069\pi\)
\(542\) −5.15612e82 −0.211517
\(543\) 1.05865e82 0.0410543
\(544\) 2.34697e83 0.860480
\(545\) −3.10999e82 −0.107811
\(546\) −5.22604e82 −0.171316
\(547\) 2.73670e83 0.848426 0.424213 0.905563i \(-0.360551\pi\)
0.424213 + 0.905563i \(0.360551\pi\)
\(548\) 1.51576e83 0.444451
\(549\) −7.66609e81 −0.0212626
\(550\) −8.13872e81 −0.0213547
\(551\) 4.34776e83 1.07930
\(552\) 4.01150e83 0.942247
\(553\) −6.85837e82 −0.152442
\(554\) 1.16975e81 0.00246062
\(555\) −2.76125e82 −0.0549756
\(556\) −4.38486e83 −0.826369
\(557\) 6.78023e82 0.120965 0.0604826 0.998169i \(-0.480736\pi\)
0.0604826 + 0.998169i \(0.480736\pi\)
\(558\) −2.66396e83 −0.449970
\(559\) −1.16859e84 −1.86896
\(560\) −1.06665e81 −0.00161542
\(561\) 1.43320e82 0.0205560
\(562\) 5.73760e83 0.779421
\(563\) 6.36301e82 0.0818760 0.0409380 0.999162i \(-0.486965\pi\)
0.0409380 + 0.999162i \(0.486965\pi\)
\(564\) −4.06010e82 −0.0494907
\(565\) −1.06899e82 −0.0123452
\(566\) 1.45942e83 0.159691
\(567\) −5.95529e82 −0.0617475
\(568\) −1.10095e84 −1.08179
\(569\) 1.58075e84 1.47211 0.736054 0.676923i \(-0.236687\pi\)
0.736054 + 0.676923i \(0.236687\pi\)
\(570\) −3.07033e82 −0.0271020
\(571\) −2.70603e83 −0.226429 −0.113214 0.993571i \(-0.536115\pi\)
−0.113214 + 0.993571i \(0.536115\pi\)
\(572\) 3.38844e82 0.0268795
\(573\) −1.32545e84 −0.996894
\(574\) 2.00918e83 0.143287
\(575\) 1.94037e84 1.31225
\(576\) −5.63033e83 −0.361117
\(577\) 2.52668e84 1.53705 0.768525 0.639820i \(-0.220991\pi\)
0.768525 + 0.639820i \(0.220991\pi\)
\(578\) −2.42961e83 −0.140196
\(579\) −4.98799e83 −0.273042
\(580\) 1.18272e83 0.0614225
\(581\) 5.56306e83 0.274121
\(582\) −5.60735e83 −0.262184
\(583\) 1.06918e83 0.0474419
\(584\) −2.65610e84 −1.11854
\(585\) 1.36032e83 0.0543736
\(586\) 7.39028e83 0.280404
\(587\) −2.58255e84 −0.930223 −0.465112 0.885252i \(-0.653986\pi\)
−0.465112 + 0.885252i \(0.653986\pi\)
\(588\) 1.10120e84 0.376580
\(589\) −3.28749e84 −1.06745
\(590\) 6.71570e82 0.0207064
\(591\) −6.16708e83 −0.180577
\(592\) 2.84308e83 0.0790637
\(593\) −7.02737e83 −0.185620 −0.0928100 0.995684i \(-0.529585\pi\)
−0.0928100 + 0.995684i \(0.529585\pi\)
\(594\) −9.04162e82 −0.0226861
\(595\) 7.79548e82 0.0185813
\(596\) 3.72638e84 0.843872
\(597\) 5.63417e84 1.21231
\(598\) 5.77619e84 1.18101
\(599\) −9.83291e84 −1.91057 −0.955287 0.295679i \(-0.904454\pi\)
−0.955287 + 0.295679i \(0.904454\pi\)
\(600\) 3.84283e84 0.709641
\(601\) 2.15831e84 0.378828 0.189414 0.981897i \(-0.439341\pi\)
0.189414 + 0.981897i \(0.439341\pi\)
\(602\) 1.43121e84 0.238786
\(603\) 2.26624e84 0.359442
\(604\) 1.54225e83 0.0232556
\(605\) −5.33630e83 −0.0765071
\(606\) −3.49060e84 −0.475867
\(607\) −9.71024e83 −0.125885 −0.0629426 0.998017i \(-0.520049\pi\)
−0.0629426 + 0.998017i \(0.520049\pi\)
\(608\) −6.18991e84 −0.763177
\(609\) −2.24570e84 −0.263345
\(610\) 1.84009e82 0.00205248
\(611\) −1.58724e84 −0.168417
\(612\) 2.61843e84 0.264316
\(613\) −6.21883e84 −0.597261 −0.298630 0.954369i \(-0.596530\pi\)
−0.298630 + 0.954369i \(0.596530\pi\)
\(614\) −1.11743e85 −1.02114
\(615\) 4.97825e83 0.0432898
\(616\) −1.12671e83 −0.00932397
\(617\) 2.26334e85 1.78259 0.891297 0.453421i \(-0.149796\pi\)
0.891297 + 0.453421i \(0.149796\pi\)
\(618\) −9.79944e84 −0.734603
\(619\) −1.15292e85 −0.822689 −0.411344 0.911480i \(-0.634941\pi\)
−0.411344 + 0.911480i \(0.634941\pi\)
\(620\) −8.94293e83 −0.0607482
\(621\) 2.15564e85 1.39406
\(622\) 1.36518e85 0.840587
\(623\) −6.16662e84 −0.361545
\(624\) 1.33326e84 0.0744361
\(625\) 1.84776e85 0.982435
\(626\) −2.76204e84 −0.139866
\(627\) −3.77992e83 −0.0182315
\(628\) −6.62749e84 −0.304495
\(629\) −2.07784e85 −0.909425
\(630\) −1.66603e83 −0.00694699
\(631\) 1.45194e84 0.0576838 0.0288419 0.999584i \(-0.490818\pi\)
0.0288419 + 0.999584i \(0.490818\pi\)
\(632\) 1.50126e85 0.568310
\(633\) −3.58129e84 −0.129189
\(634\) −1.45688e85 −0.500844
\(635\) −3.28676e83 −0.0107688
\(636\) −1.85942e85 −0.580677
\(637\) 4.30499e85 1.28150
\(638\) −1.04110e84 −0.0295434
\(639\) −2.00417e85 −0.542199
\(640\) −1.53635e84 −0.0396279
\(641\) −3.93288e85 −0.967254 −0.483627 0.875274i \(-0.660681\pi\)
−0.483627 + 0.875274i \(0.660681\pi\)
\(642\) 1.05324e85 0.247006
\(643\) −6.28047e85 −1.40461 −0.702307 0.711874i \(-0.747847\pi\)
−0.702307 + 0.711874i \(0.747847\pi\)
\(644\) 9.89396e84 0.211033
\(645\) 3.54617e84 0.0721420
\(646\) −2.31042e85 −0.448331
\(647\) 8.04540e85 1.48925 0.744624 0.667484i \(-0.232629\pi\)
0.744624 + 0.667484i \(0.232629\pi\)
\(648\) 1.30358e85 0.230197
\(649\) 8.26778e83 0.0139292
\(650\) 5.53333e85 0.889465
\(651\) 1.69805e85 0.260454
\(652\) 7.33606e85 1.07377
\(653\) 2.27157e85 0.317303 0.158651 0.987335i \(-0.449285\pi\)
0.158651 + 0.987335i \(0.449285\pi\)
\(654\) −4.76094e85 −0.634704
\(655\) 9.69047e84 0.123306
\(656\) −5.12578e84 −0.0622577
\(657\) −4.83518e85 −0.560621
\(658\) 1.94395e84 0.0215176
\(659\) −1.63534e84 −0.0172823 −0.00864117 0.999963i \(-0.502751\pi\)
−0.00864117 + 0.999963i \(0.502751\pi\)
\(660\) −1.02825e83 −0.00103755
\(661\) −1.97954e86 −1.90730 −0.953649 0.300920i \(-0.902706\pi\)
−0.953649 + 0.300920i \(0.902706\pi\)
\(662\) 9.19333e85 0.845871
\(663\) −9.74397e85 −0.856196
\(664\) −1.21772e86 −1.02193
\(665\) −2.05599e84 −0.0164801
\(666\) 4.44070e85 0.340007
\(667\) 2.48211e86 1.81544
\(668\) −5.67114e85 −0.396267
\(669\) −9.55075e85 −0.637589
\(670\) −5.43966e84 −0.0346969
\(671\) 2.26536e83 0.00138070
\(672\) 3.19721e85 0.186212
\(673\) −2.07904e85 −0.115719 −0.0578594 0.998325i \(-0.518428\pi\)
−0.0578594 + 0.998325i \(0.518428\pi\)
\(674\) 4.85777e85 0.258410
\(675\) 2.06500e86 1.04992
\(676\) −1.10393e86 −0.536496
\(677\) 3.55563e86 1.65182 0.825909 0.563803i \(-0.190662\pi\)
0.825909 + 0.563803i \(0.190662\pi\)
\(678\) −1.63648e85 −0.0726782
\(679\) −3.75485e85 −0.159428
\(680\) −1.70639e85 −0.0692717
\(681\) −1.22396e86 −0.475094
\(682\) 7.87209e84 0.0292191
\(683\) −1.05935e86 −0.376018 −0.188009 0.982167i \(-0.560203\pi\)
−0.188009 + 0.982167i \(0.560203\pi\)
\(684\) −6.90587e85 −0.234427
\(685\) −1.79819e85 −0.0583813
\(686\) −1.09735e86 −0.340769
\(687\) 4.01081e86 1.19138
\(688\) −3.65126e85 −0.103752
\(689\) −7.26914e86 −1.97604
\(690\) −1.75283e85 −0.0455872
\(691\) 3.75049e86 0.933271 0.466635 0.884450i \(-0.345466\pi\)
0.466635 + 0.884450i \(0.345466\pi\)
\(692\) −1.80102e86 −0.428827
\(693\) −2.05107e84 −0.00467323
\(694\) −4.84381e86 −1.05614
\(695\) 5.20188e85 0.108548
\(696\) 4.91572e86 0.981760
\(697\) 3.74613e86 0.716115
\(698\) −3.55211e85 −0.0649974
\(699\) −7.40495e86 −1.29708
\(700\) 9.47797e85 0.158937
\(701\) 1.21524e85 0.0195103 0.00975516 0.999952i \(-0.496895\pi\)
0.00975516 + 0.999952i \(0.496895\pi\)
\(702\) 6.14719e86 0.944920
\(703\) 5.48011e86 0.806587
\(704\) 1.66378e85 0.0234494
\(705\) 4.81661e84 0.00650089
\(706\) 1.74866e86 0.226028
\(707\) −2.33741e86 −0.289363
\(708\) −1.43785e86 −0.170490
\(709\) 1.78732e86 0.202998 0.101499 0.994836i \(-0.467636\pi\)
0.101499 + 0.994836i \(0.467636\pi\)
\(710\) 4.81060e85 0.0523384
\(711\) 2.73290e86 0.284840
\(712\) 1.34984e87 1.34785
\(713\) −1.87680e87 −1.79551
\(714\) 1.19338e86 0.109391
\(715\) −4.01980e84 −0.00353078
\(716\) 1.36217e86 0.114652
\(717\) −1.26796e87 −1.02275
\(718\) −8.35649e86 −0.645994
\(719\) −1.18320e87 −0.876651 −0.438325 0.898816i \(-0.644428\pi\)
−0.438325 + 0.898816i \(0.644428\pi\)
\(720\) 4.25034e84 0.00301844
\(721\) −6.56201e86 −0.446695
\(722\) −3.80129e86 −0.248054
\(723\) 1.03220e87 0.645722
\(724\) −5.71547e85 −0.0342788
\(725\) 2.37775e87 1.36728
\(726\) −8.16911e86 −0.450410
\(727\) 7.32315e86 0.387167 0.193584 0.981084i \(-0.437989\pi\)
0.193584 + 0.981084i \(0.437989\pi\)
\(728\) 7.66025e86 0.388361
\(729\) 1.75424e87 0.852901
\(730\) 1.16059e86 0.0541166
\(731\) 2.66849e87 1.19340
\(732\) −3.93968e85 −0.0168995
\(733\) −5.10204e86 −0.209929 −0.104965 0.994476i \(-0.533473\pi\)
−0.104965 + 0.994476i \(0.533473\pi\)
\(734\) −1.11676e86 −0.0440788
\(735\) −1.30638e86 −0.0494660
\(736\) −3.53378e87 −1.28371
\(737\) −6.69683e85 −0.0233406
\(738\) −8.00613e86 −0.267734
\(739\) −2.70980e87 −0.869524 −0.434762 0.900545i \(-0.643168\pi\)
−0.434762 + 0.900545i \(0.643168\pi\)
\(740\) 1.49075e86 0.0459026
\(741\) 2.56988e87 0.759378
\(742\) 8.90275e86 0.252467
\(743\) 6.18077e86 0.168222 0.0841112 0.996456i \(-0.473195\pi\)
0.0841112 + 0.996456i \(0.473195\pi\)
\(744\) −3.71694e87 −0.970982
\(745\) −4.42071e86 −0.110848
\(746\) 2.07762e87 0.500070
\(747\) −2.21675e87 −0.512199
\(748\) −7.73756e85 −0.0171635
\(749\) 7.05280e86 0.150199
\(750\) −3.36817e86 −0.0688693
\(751\) −5.20963e87 −1.02279 −0.511397 0.859344i \(-0.670872\pi\)
−0.511397 + 0.859344i \(0.670872\pi\)
\(752\) −4.95935e85 −0.00934933
\(753\) 8.03392e86 0.145439
\(754\) 7.07819e87 1.23054
\(755\) −1.82961e85 −0.00305476
\(756\) 1.05295e87 0.168846
\(757\) 2.22778e87 0.343121 0.171561 0.985174i \(-0.445119\pi\)
0.171561 + 0.985174i \(0.445119\pi\)
\(758\) 1.06451e87 0.157485
\(759\) −2.15793e86 −0.0306664
\(760\) 4.50044e86 0.0614385
\(761\) 5.32204e87 0.697985 0.348992 0.937126i \(-0.386524\pi\)
0.348992 + 0.937126i \(0.386524\pi\)
\(762\) −5.03155e86 −0.0633980
\(763\) −3.18807e87 −0.385949
\(764\) 7.15589e87 0.832369
\(765\) −3.10632e86 −0.0347194
\(766\) −6.55477e87 −0.704012
\(767\) −5.62108e87 −0.580178
\(768\) −7.31429e87 −0.725529
\(769\) 1.48822e88 1.41878 0.709389 0.704818i \(-0.248971\pi\)
0.709389 + 0.704818i \(0.248971\pi\)
\(770\) 4.92318e84 0.000451106 0
\(771\) −1.17049e88 −1.03088
\(772\) 2.69293e87 0.227980
\(773\) −1.68328e87 −0.136988 −0.0684938 0.997652i \(-0.521819\pi\)
−0.0684938 + 0.997652i \(0.521819\pi\)
\(774\) −5.70303e87 −0.446176
\(775\) −1.79789e88 −1.35227
\(776\) 8.21916e87 0.594354
\(777\) −2.83058e87 −0.196804
\(778\) 1.18976e88 0.795392
\(779\) −9.88006e87 −0.635137
\(780\) 6.99083e86 0.0432159
\(781\) 5.92240e86 0.0352080
\(782\) −1.31900e88 −0.754118
\(783\) 2.64153e88 1.45252
\(784\) 1.34510e87 0.0711400
\(785\) 7.86238e86 0.0399972
\(786\) 1.48347e88 0.725925
\(787\) 1.03317e88 0.486342 0.243171 0.969983i \(-0.421812\pi\)
0.243171 + 0.969983i \(0.421812\pi\)
\(788\) 3.32949e87 0.150775
\(789\) 1.62730e88 0.708955
\(790\) −6.55978e86 −0.0274956
\(791\) −1.09584e87 −0.0441939
\(792\) 4.48968e86 0.0174220
\(793\) −1.54016e87 −0.0575089
\(794\) 1.92787e86 0.00692712
\(795\) 2.20588e87 0.0762753
\(796\) −3.04178e88 −1.01223
\(797\) −3.51204e88 −1.12481 −0.562407 0.826861i \(-0.690124\pi\)
−0.562407 + 0.826861i \(0.690124\pi\)
\(798\) −3.14742e87 −0.0970211
\(799\) 3.62449e87 0.107540
\(800\) −3.38520e88 −0.966807
\(801\) 2.45726e88 0.675552
\(802\) −1.31359e88 −0.347650
\(803\) 1.42881e87 0.0364042
\(804\) 1.16465e88 0.285683
\(805\) −1.17375e87 −0.0277205
\(806\) −5.35205e88 −1.21703
\(807\) −1.88403e88 −0.412520
\(808\) 5.11647e88 1.07876
\(809\) 4.70026e88 0.954316 0.477158 0.878818i \(-0.341667\pi\)
0.477158 + 0.878818i \(0.341667\pi\)
\(810\) −5.69601e86 −0.0111373
\(811\) 7.07672e88 1.33259 0.666294 0.745689i \(-0.267880\pi\)
0.666294 + 0.745689i \(0.267880\pi\)
\(812\) 1.21241e88 0.219883
\(813\) −1.30963e88 −0.228764
\(814\) −1.31224e87 −0.0220785
\(815\) −8.70298e87 −0.141046
\(816\) −3.04451e87 −0.0475300
\(817\) −7.03789e88 −1.05845
\(818\) 5.14125e88 0.744892
\(819\) 1.39448e88 0.194649
\(820\) −2.68767e87 −0.0361454
\(821\) −5.20477e88 −0.674428 −0.337214 0.941428i \(-0.609485\pi\)
−0.337214 + 0.941428i \(0.609485\pi\)
\(822\) −2.75277e88 −0.343700
\(823\) 4.31597e88 0.519258 0.259629 0.965708i \(-0.416400\pi\)
0.259629 + 0.965708i \(0.416400\pi\)
\(824\) 1.43639e89 1.66530
\(825\) −2.06720e87 −0.0230960
\(826\) 6.88432e87 0.0741258
\(827\) −1.50785e89 −1.56473 −0.782365 0.622821i \(-0.785987\pi\)
−0.782365 + 0.622821i \(0.785987\pi\)
\(828\) −3.94251e88 −0.394319
\(829\) 3.48420e88 0.335885 0.167942 0.985797i \(-0.446288\pi\)
0.167942 + 0.985797i \(0.446288\pi\)
\(830\) 5.32086e87 0.0494425
\(831\) 2.97112e86 0.00266127
\(832\) −1.13117e89 −0.976711
\(833\) −9.83051e88 −0.818283
\(834\) 7.96332e88 0.639043
\(835\) 6.72783e87 0.0520520
\(836\) 2.04071e87 0.0152226
\(837\) −1.99735e89 −1.43657
\(838\) −1.13105e88 −0.0784404
\(839\) 1.17215e89 0.783872 0.391936 0.919992i \(-0.371805\pi\)
0.391936 + 0.919992i \(0.371805\pi\)
\(840\) −2.32456e87 −0.0149908
\(841\) 1.43362e89 0.891574
\(842\) 1.66696e89 0.999785
\(843\) 1.45733e89 0.842977
\(844\) 1.93347e88 0.107868
\(845\) 1.30962e88 0.0704719
\(846\) −7.74617e87 −0.0402060
\(847\) −5.47029e88 −0.273884
\(848\) −2.27125e88 −0.109696
\(849\) 3.70687e88 0.172712
\(850\) −1.26354e89 −0.567954
\(851\) 3.12855e89 1.35673
\(852\) −1.02996e89 −0.430937
\(853\) −1.25601e89 −0.507045 −0.253523 0.967329i \(-0.581589\pi\)
−0.253523 + 0.967329i \(0.581589\pi\)
\(854\) 1.88629e87 0.00734756
\(855\) 8.19263e87 0.0307933
\(856\) −1.54382e89 −0.559947
\(857\) −1.93234e89 −0.676347 −0.338173 0.941084i \(-0.609809\pi\)
−0.338173 + 0.941084i \(0.609809\pi\)
\(858\) −6.15374e87 −0.0207863
\(859\) −4.33998e88 −0.141481 −0.0707403 0.997495i \(-0.522536\pi\)
−0.0707403 + 0.997495i \(0.522536\pi\)
\(860\) −1.91451e88 −0.0602359
\(861\) 5.10324e88 0.154971
\(862\) −3.81277e89 −1.11755
\(863\) 1.76145e89 0.498359 0.249179 0.968457i \(-0.419839\pi\)
0.249179 + 0.968457i \(0.419839\pi\)
\(864\) −3.76075e89 −1.02708
\(865\) 2.13660e88 0.0563289
\(866\) 3.84365e89 0.978247
\(867\) −6.17110e88 −0.151628
\(868\) −9.16746e88 −0.217469
\(869\) −8.07583e87 −0.0184963
\(870\) −2.14793e88 −0.0474989
\(871\) 4.55302e89 0.972179
\(872\) 6.97851e89 1.43883
\(873\) 1.49622e89 0.297894
\(874\) 3.47875e89 0.668843
\(875\) −2.25543e88 −0.0418778
\(876\) −2.48485e89 −0.445579
\(877\) −1.31068e89 −0.226991 −0.113495 0.993539i \(-0.536205\pi\)
−0.113495 + 0.993539i \(0.536205\pi\)
\(878\) −1.74269e89 −0.291499
\(879\) 1.87710e89 0.303268
\(880\) −1.25599e86 −0.000196004 0
\(881\) −1.11397e90 −1.67923 −0.839614 0.543184i \(-0.817219\pi\)
−0.839614 + 0.543184i \(0.817219\pi\)
\(882\) 2.10095e89 0.305932
\(883\) 2.93644e89 0.413067 0.206533 0.978440i \(-0.433782\pi\)
0.206533 + 0.978440i \(0.433782\pi\)
\(884\) 5.26059e89 0.714892
\(885\) 1.70576e88 0.0223949
\(886\) −5.69910e89 −0.722900
\(887\) −1.32601e90 −1.62509 −0.812544 0.582900i \(-0.801918\pi\)
−0.812544 + 0.582900i \(0.801918\pi\)
\(888\) 6.19598e89 0.733694
\(889\) −3.36928e88 −0.0385508
\(890\) −5.89814e88 −0.0652109
\(891\) −7.01244e87 −0.00749202
\(892\) 5.15628e89 0.532363
\(893\) −9.55926e88 −0.0953794
\(894\) −6.76748e89 −0.652578
\(895\) −1.61598e88 −0.0150603
\(896\) −1.57493e89 −0.141862
\(897\) 1.46713e90 1.27732
\(898\) 2.38348e89 0.200578
\(899\) −2.29985e90 −1.87081
\(900\) −3.77675e89 −0.296976
\(901\) 1.65992e90 1.26177
\(902\) 2.36584e88 0.0173855
\(903\) 3.63521e89 0.258257
\(904\) 2.39872e89 0.164757
\(905\) 6.78043e87 0.00450272
\(906\) −2.80087e88 −0.0179839
\(907\) 1.13903e90 0.707150 0.353575 0.935406i \(-0.384966\pi\)
0.353575 + 0.935406i \(0.384966\pi\)
\(908\) 6.60792e89 0.396686
\(909\) 9.31405e89 0.540680
\(910\) −3.34716e88 −0.0187894
\(911\) −4.40257e89 −0.238999 −0.119499 0.992834i \(-0.538129\pi\)
−0.119499 + 0.992834i \(0.538129\pi\)
\(912\) 8.02962e88 0.0421553
\(913\) 6.55058e88 0.0332599
\(914\) 4.88215e89 0.239746
\(915\) 4.67375e87 0.00221984
\(916\) −2.16536e90 −0.994760
\(917\) 9.93378e89 0.441418
\(918\) −1.40372e90 −0.603364
\(919\) −2.54886e90 −1.05980 −0.529898 0.848061i \(-0.677770\pi\)
−0.529898 + 0.848061i \(0.677770\pi\)
\(920\) 2.56927e89 0.103343
\(921\) −2.83822e90 −1.10440
\(922\) 1.44950e90 0.545665
\(923\) −4.02650e90 −1.46648
\(924\) −1.05407e88 −0.00371426
\(925\) 2.99701e90 1.02180
\(926\) −1.41947e89 −0.0468266
\(927\) 2.61481e90 0.834657
\(928\) −4.33032e90 −1.33754
\(929\) 2.58810e90 0.773575 0.386788 0.922169i \(-0.373585\pi\)
0.386788 + 0.922169i \(0.373585\pi\)
\(930\) 1.62412e89 0.0469774
\(931\) 2.59271e90 0.725752
\(932\) 3.99780e90 1.08302
\(933\) 3.46750e90 0.909130
\(934\) −7.61340e87 −0.00193196
\(935\) 9.17928e87 0.00225452
\(936\) −3.05243e90 −0.725659
\(937\) 1.46131e90 0.336266 0.168133 0.985764i \(-0.446226\pi\)
0.168133 + 0.985764i \(0.446226\pi\)
\(938\) −5.57624e89 −0.124209
\(939\) −7.01547e89 −0.151271
\(940\) −2.60040e88 −0.00542800
\(941\) 1.30889e90 0.264496 0.132248 0.991217i \(-0.457780\pi\)
0.132248 + 0.991217i \(0.457780\pi\)
\(942\) 1.20362e90 0.235470
\(943\) −5.64046e90 −1.06834
\(944\) −1.75631e89 −0.0322074
\(945\) −1.24914e89 −0.0221789
\(946\) 1.68527e89 0.0289727
\(947\) 4.48696e90 0.746927 0.373464 0.927645i \(-0.378170\pi\)
0.373464 + 0.927645i \(0.378170\pi\)
\(948\) 1.40447e90 0.226390
\(949\) −9.71419e90 −1.51631
\(950\) 3.33248e90 0.503730
\(951\) −3.70042e90 −0.541683
\(952\) −1.74923e90 −0.247982
\(953\) −7.56718e90 −1.03896 −0.519482 0.854481i \(-0.673875\pi\)
−0.519482 + 0.854481i \(0.673875\pi\)
\(954\) −3.54754e90 −0.471739
\(955\) −8.48923e89 −0.109337
\(956\) 6.84547e90 0.853960
\(957\) −2.64435e89 −0.0319524
\(958\) 5.75482e90 0.673572
\(959\) −1.84334e90 −0.208996
\(960\) 3.43262e89 0.0377010
\(961\) 7.99133e90 0.850268
\(962\) 8.92165e90 0.919614
\(963\) −2.81038e90 −0.280649
\(964\) −5.57266e90 −0.539154
\(965\) −3.19469e89 −0.0299465
\(966\) −1.79684e90 −0.163195
\(967\) 6.35826e90 0.559539 0.279770 0.960067i \(-0.409742\pi\)
0.279770 + 0.960067i \(0.409742\pi\)
\(968\) 1.19742e91 1.02105
\(969\) −5.86837e90 −0.484889
\(970\) −3.59137e89 −0.0287556
\(971\) −3.23669e90 −0.251139 −0.125570 0.992085i \(-0.540076\pi\)
−0.125570 + 0.992085i \(0.540076\pi\)
\(972\) −6.97011e90 −0.524105
\(973\) 5.33248e90 0.388587
\(974\) −5.99388e90 −0.423311
\(975\) 1.40544e91 0.961994
\(976\) −4.81226e88 −0.00319249
\(977\) −1.41204e90 −0.0907953 −0.0453977 0.998969i \(-0.514455\pi\)
−0.0453977 + 0.998969i \(0.514455\pi\)
\(978\) −1.33230e91 −0.830361
\(979\) −7.26128e89 −0.0438673
\(980\) 7.05292e89 0.0413022
\(981\) 1.27037e91 0.721151
\(982\) −6.33620e90 −0.348681
\(983\) −8.68181e89 −0.0463157 −0.0231578 0.999732i \(-0.507372\pi\)
−0.0231578 + 0.999732i \(0.507372\pi\)
\(984\) −1.11707e91 −0.577738
\(985\) −3.94987e89 −0.0198051
\(986\) −1.61631e91 −0.785742
\(987\) 4.93754e89 0.0232722
\(988\) −1.38743e91 −0.634052
\(989\) −4.01788e91 −1.78037
\(990\) −1.96177e88 −0.000842899 0
\(991\) 1.85513e91 0.772907 0.386454 0.922309i \(-0.373700\pi\)
0.386454 + 0.922309i \(0.373700\pi\)
\(992\) 3.27430e91 1.32286
\(993\) 2.33507e91 0.914845
\(994\) 4.93139e90 0.187363
\(995\) 3.60855e90 0.132963
\(996\) −1.13921e91 −0.407093
\(997\) 6.39525e90 0.221643 0.110822 0.993840i \(-0.464652\pi\)
0.110822 + 0.993840i \(0.464652\pi\)
\(998\) 1.11573e91 0.375040
\(999\) 3.32950e91 1.08551
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 1.62.a.a.1.3 4
3.2 odd 2 9.62.a.a.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.62.a.a.1.3 4 1.1 even 1 trivial
9.62.a.a.1.2 4 3.2 odd 2