Properties

Label 1.76.a.a.1.3
Level $1$
Weight $76$
Character 1.1
Self dual yes
Analytic conductor $35.623$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 76 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.6228392822\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 3 x^{5} - 38457853073924058692 x^{4} - 10276556354621685339901678086 x^{3} + 371187556674475060057870954681799784505 x^{2} + 52686123927652036687598761277591247931691204025 x - 675344021115865838575279495800656435684060652010336995750\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.60397e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.25000e11 q^{2} +1.35148e17 q^{3} -2.21540e22 q^{4} +1.80927e26 q^{5} -1.68935e28 q^{6} +2.76229e31 q^{7} +7.49160e33 q^{8} -5.90002e35 q^{9} +O(q^{10})\) \(q-1.25000e11 q^{2} +1.35148e17 q^{3} -2.21540e22 q^{4} +1.80927e26 q^{5} -1.68935e28 q^{6} +2.76229e31 q^{7} +7.49160e33 q^{8} -5.90002e35 q^{9} -2.26158e37 q^{10} +7.60456e38 q^{11} -2.99408e39 q^{12} +2.57727e41 q^{13} -3.45284e42 q^{14} +2.44520e43 q^{15} -9.94899e43 q^{16} -1.39330e46 q^{17} +7.37500e46 q^{18} -1.16447e48 q^{19} -4.00827e48 q^{20} +3.73318e48 q^{21} -9.50567e49 q^{22} +9.81970e50 q^{23} +1.01248e51 q^{24} +6.26484e51 q^{25} -3.22158e52 q^{26} -1.61944e53 q^{27} -6.11958e53 q^{28} +3.47815e54 q^{29} -3.05649e54 q^{30} +1.19579e56 q^{31} -2.70588e56 q^{32} +1.02774e56 q^{33} +1.74162e57 q^{34} +4.99772e57 q^{35} +1.30709e58 q^{36} +1.03750e59 q^{37} +1.45558e59 q^{38} +3.48314e58 q^{39} +1.35543e60 q^{40} +4.07748e60 q^{41} -4.66646e59 q^{42} +2.20097e61 q^{43} -1.68472e61 q^{44} -1.06747e62 q^{45} -1.22746e62 q^{46} -4.37785e62 q^{47} -1.34459e61 q^{48} -1.64884e63 q^{49} -7.83102e62 q^{50} -1.88302e63 q^{51} -5.70970e63 q^{52} +7.68796e64 q^{53} +2.02429e64 q^{54} +1.37587e65 q^{55} +2.06939e65 q^{56} -1.57376e65 q^{57} -4.34767e65 q^{58} -3.79588e66 q^{59} -5.41711e65 q^{60} +5.02447e66 q^{61} -1.49473e67 q^{62} -1.62975e67 q^{63} +3.75820e67 q^{64} +4.66298e67 q^{65} -1.28468e67 q^{66} +3.39062e68 q^{67} +3.08672e68 q^{68} +1.32712e68 q^{69} -6.24713e68 q^{70} -3.17915e69 q^{71} -4.42005e69 q^{72} +7.11742e69 q^{73} -1.29687e70 q^{74} +8.46682e68 q^{75} +2.57978e70 q^{76} +2.10060e70 q^{77} -4.35391e69 q^{78} +9.47303e70 q^{79} -1.80004e70 q^{80} +3.36992e71 q^{81} -5.09684e71 q^{82} -1.43323e71 q^{83} -8.27051e70 q^{84} -2.52086e72 q^{85} -2.75120e72 q^{86} +4.70066e71 q^{87} +5.69703e72 q^{88} +9.94475e72 q^{89} +1.33434e73 q^{90} +7.11916e72 q^{91} -2.17546e73 q^{92} +1.61609e73 q^{93} +5.47229e73 q^{94} -2.10685e74 q^{95} -3.65695e73 q^{96} -7.42743e73 q^{97} +2.06105e74 q^{98} -4.48671e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + O(q^{10}) \) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + \)\(13\!\cdots\!60\)\(q^{10} - \)\(94\!\cdots\!88\)\(q^{11} - \)\(11\!\cdots\!80\)\(q^{12} + \)\(53\!\cdots\!20\)\(q^{13} + \)\(82\!\cdots\!76\)\(q^{14} - \)\(30\!\cdots\!80\)\(q^{15} + \)\(26\!\cdots\!16\)\(q^{16} + \)\(18\!\cdots\!80\)\(q^{17} - \)\(43\!\cdots\!40\)\(q^{18} + \)\(10\!\cdots\!80\)\(q^{19} + \)\(92\!\cdots\!80\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(15\!\cdots\!20\)\(q^{22} + \)\(15\!\cdots\!80\)\(q^{23} - \)\(76\!\cdots\!60\)\(q^{24} + \)\(19\!\cdots\!50\)\(q^{25} + \)\(11\!\cdots\!52\)\(q^{26} - \)\(10\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!20\)\(q^{28} + \)\(14\!\cdots\!20\)\(q^{29} - \)\(25\!\cdots\!80\)\(q^{30} - \)\(41\!\cdots\!88\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(59\!\cdots\!20\)\(q^{33} + \)\(30\!\cdots\!56\)\(q^{34} + \)\(27\!\cdots\!60\)\(q^{35} + \)\(17\!\cdots\!16\)\(q^{36} + \)\(98\!\cdots\!40\)\(q^{37} + \)\(12\!\cdots\!80\)\(q^{38} + \)\(24\!\cdots\!44\)\(q^{39} + \)\(88\!\cdots\!00\)\(q^{40} + \)\(50\!\cdots\!12\)\(q^{41} + \)\(43\!\cdots\!80\)\(q^{42} + \)\(27\!\cdots\!00\)\(q^{43} - \)\(86\!\cdots\!44\)\(q^{44} - \)\(23\!\cdots\!80\)\(q^{45} - \)\(82\!\cdots\!88\)\(q^{46} - \)\(13\!\cdots\!80\)\(q^{47} - \)\(82\!\cdots\!20\)\(q^{48} - \)\(57\!\cdots\!42\)\(q^{49} + \)\(31\!\cdots\!00\)\(q^{50} + \)\(28\!\cdots\!32\)\(q^{51} + \)\(41\!\cdots\!00\)\(q^{52} + \)\(64\!\cdots\!60\)\(q^{53} + \)\(78\!\cdots\!80\)\(q^{54} + \)\(43\!\cdots\!20\)\(q^{55} + \)\(28\!\cdots\!20\)\(q^{56} - \)\(67\!\cdots\!40\)\(q^{57} - \)\(17\!\cdots\!80\)\(q^{58} - \)\(24\!\cdots\!60\)\(q^{59} - \)\(31\!\cdots\!40\)\(q^{60} - \)\(25\!\cdots\!88\)\(q^{61} - \)\(29\!\cdots\!80\)\(q^{62} + \)\(42\!\cdots\!40\)\(q^{63} + \)\(47\!\cdots\!48\)\(q^{64} + \)\(12\!\cdots\!20\)\(q^{65} + \)\(93\!\cdots\!84\)\(q^{66} + \)\(95\!\cdots\!80\)\(q^{67} + \)\(12\!\cdots\!60\)\(q^{68} - \)\(14\!\cdots\!36\)\(q^{69} - \)\(34\!\cdots\!40\)\(q^{70} - \)\(25\!\cdots\!88\)\(q^{71} - \)\(21\!\cdots\!60\)\(q^{72} - \)\(30\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!84\)\(q^{74} + \)\(19\!\cdots\!00\)\(q^{75} + \)\(10\!\cdots\!40\)\(q^{76} + \)\(15\!\cdots\!00\)\(q^{77} + \)\(13\!\cdots\!00\)\(q^{78} + \)\(11\!\cdots\!20\)\(q^{79} + \)\(12\!\cdots\!60\)\(q^{80} + \)\(29\!\cdots\!86\)\(q^{81} - \)\(25\!\cdots\!80\)\(q^{82} - \)\(79\!\cdots\!60\)\(q^{83} - \)\(91\!\cdots\!64\)\(q^{84} - \)\(36\!\cdots\!40\)\(q^{85} + \)\(72\!\cdots\!32\)\(q^{86} - \)\(14\!\cdots\!60\)\(q^{87} - \)\(48\!\cdots\!60\)\(q^{88} + \)\(53\!\cdots\!60\)\(q^{89} + \)\(85\!\cdots\!20\)\(q^{90} + \)\(34\!\cdots\!32\)\(q^{91} + \)\(18\!\cdots\!80\)\(q^{92} - \)\(16\!\cdots\!80\)\(q^{93} - \)\(29\!\cdots\!04\)\(q^{94} + \)\(19\!\cdots\!00\)\(q^{95} - \)\(89\!\cdots\!08\)\(q^{96} - \)\(74\!\cdots\!80\)\(q^{97} - \)\(16\!\cdots\!20\)\(q^{98} - \)\(18\!\cdots\!36\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25000e11 −0.643108 −0.321554 0.946891i \(-0.604205\pi\)
−0.321554 + 0.946891i \(0.604205\pi\)
\(3\) 1.35148e17 0.173286 0.0866430 0.996239i \(-0.472386\pi\)
0.0866430 + 0.996239i \(0.472386\pi\)
\(4\) −2.21540e22 −0.586413
\(5\) 1.80927e26 1.11206 0.556030 0.831162i \(-0.312324\pi\)
0.556030 + 0.831162i \(0.312324\pi\)
\(6\) −1.68935e28 −0.111442
\(7\) 2.76229e31 0.562461 0.281230 0.959640i \(-0.409258\pi\)
0.281230 + 0.959640i \(0.409258\pi\)
\(8\) 7.49160e33 1.02023
\(9\) −5.90002e35 −0.969972
\(10\) −2.26158e37 −0.715175
\(11\) 7.60456e38 0.674293 0.337146 0.941452i \(-0.390538\pi\)
0.337146 + 0.941452i \(0.390538\pi\)
\(12\) −2.99408e39 −0.101617
\(13\) 2.57727e41 0.434795 0.217397 0.976083i \(-0.430243\pi\)
0.217397 + 0.976083i \(0.430243\pi\)
\(14\) −3.45284e42 −0.361723
\(15\) 2.44520e43 0.192705
\(16\) −9.94899e43 −0.0697076
\(17\) −1.39330e46 −1.00510 −0.502551 0.864548i \(-0.667605\pi\)
−0.502551 + 0.864548i \(0.667605\pi\)
\(18\) 7.37500e46 0.623796
\(19\) −1.16447e48 −1.29679 −0.648394 0.761305i \(-0.724559\pi\)
−0.648394 + 0.761305i \(0.724559\pi\)
\(20\) −4.00827e48 −0.652126
\(21\) 3.73318e48 0.0974666
\(22\) −9.50567e49 −0.433643
\(23\) 9.81970e50 0.845872 0.422936 0.906160i \(-0.361000\pi\)
0.422936 + 0.906160i \(0.361000\pi\)
\(24\) 1.01248e51 0.176792
\(25\) 6.26484e51 0.236679
\(26\) −3.22158e52 −0.279620
\(27\) −1.61944e53 −0.341369
\(28\) −6.11958e53 −0.329834
\(29\) 3.47815e54 0.502832 0.251416 0.967879i \(-0.419104\pi\)
0.251416 + 0.967879i \(0.419104\pi\)
\(30\) −3.05649e54 −0.123930
\(31\) 1.19579e56 1.41773 0.708863 0.705346i \(-0.249209\pi\)
0.708863 + 0.705346i \(0.249209\pi\)
\(32\) −2.70588e56 −0.975405
\(33\) 1.02774e56 0.116846
\(34\) 1.74162e57 0.646388
\(35\) 4.99772e57 0.625490
\(36\) 1.30709e58 0.568804
\(37\) 1.03750e59 1.61593 0.807963 0.589233i \(-0.200570\pi\)
0.807963 + 0.589233i \(0.200570\pi\)
\(38\) 1.45558e59 0.833974
\(39\) 3.48314e58 0.0753439
\(40\) 1.35543e60 1.13456
\(41\) 4.07748e60 1.35207 0.676033 0.736872i \(-0.263698\pi\)
0.676033 + 0.736872i \(0.263698\pi\)
\(42\) −4.66646e59 −0.0626815
\(43\) 2.20097e61 1.22334 0.611670 0.791113i \(-0.290498\pi\)
0.611670 + 0.791113i \(0.290498\pi\)
\(44\) −1.68472e61 −0.395414
\(45\) −1.06747e62 −1.07867
\(46\) −1.22746e62 −0.543987
\(47\) −4.37785e62 −0.866146 −0.433073 0.901359i \(-0.642571\pi\)
−0.433073 + 0.901359i \(0.642571\pi\)
\(48\) −1.34459e61 −0.0120793
\(49\) −1.64884e63 −0.683638
\(50\) −7.83102e62 −0.152210
\(51\) −1.88302e63 −0.174170
\(52\) −5.70970e63 −0.254969
\(53\) 7.68796e64 1.68061 0.840303 0.542117i \(-0.182377\pi\)
0.840303 + 0.542117i \(0.182377\pi\)
\(54\) 2.02429e64 0.219537
\(55\) 1.37587e65 0.749855
\(56\) 2.06939e65 0.573841
\(57\) −1.57376e65 −0.224715
\(58\) −4.34767e65 −0.323375
\(59\) −3.79588e66 −1.48717 −0.743587 0.668639i \(-0.766877\pi\)
−0.743587 + 0.668639i \(0.766877\pi\)
\(60\) −5.41711e65 −0.113004
\(61\) 5.02447e66 0.563925 0.281962 0.959425i \(-0.409015\pi\)
0.281962 + 0.959425i \(0.409015\pi\)
\(62\) −1.49473e67 −0.911750
\(63\) −1.62975e67 −0.545571
\(64\) 3.75820e67 0.696998
\(65\) 4.66298e67 0.483518
\(66\) −1.28468e67 −0.0751443
\(67\) 3.39062e68 1.12843 0.564214 0.825629i \(-0.309179\pi\)
0.564214 + 0.825629i \(0.309179\pi\)
\(68\) 3.08672e68 0.589404
\(69\) 1.32712e68 0.146578
\(70\) −6.24713e68 −0.402258
\(71\) −3.17915e69 −1.20261 −0.601303 0.799021i \(-0.705352\pi\)
−0.601303 + 0.799021i \(0.705352\pi\)
\(72\) −4.42005e69 −0.989598
\(73\) 7.11742e69 0.949982 0.474991 0.879991i \(-0.342451\pi\)
0.474991 + 0.879991i \(0.342451\pi\)
\(74\) −1.29687e70 −1.03921
\(75\) 8.46682e68 0.0410131
\(76\) 2.57978e70 0.760453
\(77\) 2.10060e70 0.379263
\(78\) −4.35391e69 −0.0484542
\(79\) 9.47303e70 0.653842 0.326921 0.945052i \(-0.393989\pi\)
0.326921 + 0.945052i \(0.393989\pi\)
\(80\) −1.80004e70 −0.0775190
\(81\) 3.36992e71 0.910818
\(82\) −5.09684e71 −0.869523
\(83\) −1.43323e71 −0.155198 −0.0775992 0.996985i \(-0.524725\pi\)
−0.0775992 + 0.996985i \(0.524725\pi\)
\(84\) −8.27051e70 −0.0571556
\(85\) −2.52086e72 −1.11773
\(86\) −2.75120e72 −0.786739
\(87\) 4.70066e71 0.0871338
\(88\) 5.69703e72 0.687937
\(89\) 9.94475e72 0.786083 0.393042 0.919521i \(-0.371423\pi\)
0.393042 + 0.919521i \(0.371423\pi\)
\(90\) 1.33434e73 0.693699
\(91\) 7.11916e72 0.244555
\(92\) −2.17546e73 −0.496030
\(93\) 1.61609e73 0.245672
\(94\) 5.47229e73 0.557025
\(95\) −2.10685e74 −1.44211
\(96\) −3.65695e73 −0.169024
\(97\) −7.42743e73 −0.232755 −0.116377 0.993205i \(-0.537128\pi\)
−0.116377 + 0.993205i \(0.537128\pi\)
\(98\) 2.06105e74 0.439653
\(99\) −4.48671e74 −0.654045
\(100\) −1.38791e74 −0.138791
\(101\) 1.42243e74 0.0979445 0.0489722 0.998800i \(-0.484405\pi\)
0.0489722 + 0.998800i \(0.484405\pi\)
\(102\) 2.35377e74 0.112010
\(103\) 4.64143e75 1.53199 0.765996 0.642846i \(-0.222246\pi\)
0.765996 + 0.642846i \(0.222246\pi\)
\(104\) 1.93079e75 0.443592
\(105\) 6.75434e74 0.108389
\(106\) −9.60991e75 −1.08081
\(107\) 5.79865e75 0.458601 0.229301 0.973356i \(-0.426356\pi\)
0.229301 + 0.973356i \(0.426356\pi\)
\(108\) 3.58771e75 0.200183
\(109\) −4.52515e76 −1.78706 −0.893531 0.449001i \(-0.851780\pi\)
−0.893531 + 0.449001i \(0.851780\pi\)
\(110\) −1.71983e76 −0.482237
\(111\) 1.40216e76 0.280018
\(112\) −2.74820e75 −0.0392078
\(113\) 7.93579e76 0.811239 0.405619 0.914042i \(-0.367056\pi\)
0.405619 + 0.914042i \(0.367056\pi\)
\(114\) 1.96720e76 0.144516
\(115\) 1.77665e77 0.940661
\(116\) −7.70550e76 −0.294867
\(117\) −1.52059e77 −0.421739
\(118\) 4.74483e77 0.956413
\(119\) −3.84869e77 −0.565330
\(120\) 1.83184e77 0.196604
\(121\) −6.93601e77 −0.545329
\(122\) −6.28056e77 −0.362664
\(123\) 5.51065e77 0.234294
\(124\) −2.64916e78 −0.831372
\(125\) −3.65562e78 −0.848859
\(126\) 2.03718e78 0.350861
\(127\) 9.37430e78 1.20033 0.600163 0.799878i \(-0.295102\pi\)
0.600163 + 0.799878i \(0.295102\pi\)
\(128\) 5.52480e78 0.527160
\(129\) 2.97457e78 0.211988
\(130\) −5.82871e78 −0.310954
\(131\) 2.91749e79 1.16771 0.583857 0.811857i \(-0.301543\pi\)
0.583857 + 0.811857i \(0.301543\pi\)
\(132\) −2.27687e78 −0.0685197
\(133\) −3.21660e79 −0.729392
\(134\) −4.23826e79 −0.725700
\(135\) −2.93001e79 −0.379623
\(136\) −1.04380e80 −1.02544
\(137\) 9.29317e79 0.693653 0.346827 0.937929i \(-0.387259\pi\)
0.346827 + 0.937929i \(0.387259\pi\)
\(138\) −1.65889e79 −0.0942653
\(139\) 2.02447e80 0.877518 0.438759 0.898605i \(-0.355418\pi\)
0.438759 + 0.898605i \(0.355418\pi\)
\(140\) −1.10720e80 −0.366795
\(141\) −5.91659e79 −0.150091
\(142\) 3.97393e80 0.773405
\(143\) 1.95990e80 0.293179
\(144\) 5.86992e79 0.0676144
\(145\) 6.29291e80 0.559180
\(146\) −8.89674e80 −0.610940
\(147\) −2.22838e80 −0.118465
\(148\) −2.29847e81 −0.947600
\(149\) 2.75595e81 0.882646 0.441323 0.897348i \(-0.354509\pi\)
0.441323 + 0.897348i \(0.354509\pi\)
\(150\) −1.05835e80 −0.0263759
\(151\) −5.55612e81 −1.07928 −0.539642 0.841894i \(-0.681441\pi\)
−0.539642 + 0.841894i \(0.681441\pi\)
\(152\) −8.72375e81 −1.32303
\(153\) 8.22049e81 0.974920
\(154\) −2.62574e81 −0.243907
\(155\) 2.16351e82 1.57660
\(156\) −7.71656e80 −0.0441826
\(157\) 2.68318e82 1.20896 0.604481 0.796619i \(-0.293380\pi\)
0.604481 + 0.796619i \(0.293380\pi\)
\(158\) −1.18412e82 −0.420491
\(159\) 1.03901e82 0.291226
\(160\) −4.89568e82 −1.08471
\(161\) 2.71248e82 0.475770
\(162\) −4.21238e82 −0.585754
\(163\) −4.12916e82 −0.455855 −0.227927 0.973678i \(-0.573195\pi\)
−0.227927 + 0.973678i \(0.573195\pi\)
\(164\) −9.03328e82 −0.792868
\(165\) 1.85947e82 0.129939
\(166\) 1.79153e82 0.0998093
\(167\) 1.65503e83 0.736103 0.368052 0.929805i \(-0.380025\pi\)
0.368052 + 0.929805i \(0.380025\pi\)
\(168\) 2.79675e82 0.0994387
\(169\) −2.84936e83 −0.810954
\(170\) 3.15106e83 0.718823
\(171\) 6.87040e83 1.25785
\(172\) −4.87604e83 −0.717382
\(173\) 2.24737e83 0.266039 0.133019 0.991113i \(-0.457533\pi\)
0.133019 + 0.991113i \(0.457533\pi\)
\(174\) −5.87580e82 −0.0560364
\(175\) 1.73053e83 0.133123
\(176\) −7.56578e82 −0.0470033
\(177\) −5.13007e83 −0.257707
\(178\) −1.24309e84 −0.505536
\(179\) −2.15324e84 −0.709748 −0.354874 0.934914i \(-0.615476\pi\)
−0.354874 + 0.934914i \(0.615476\pi\)
\(180\) 2.36488e84 0.632544
\(181\) −5.53508e84 −1.20275 −0.601377 0.798965i \(-0.705381\pi\)
−0.601377 + 0.798965i \(0.705381\pi\)
\(182\) −8.89892e83 −0.157275
\(183\) 6.79048e83 0.0977203
\(184\) 7.35652e84 0.862987
\(185\) 1.87711e85 1.79701
\(186\) −2.02011e84 −0.157994
\(187\) −1.05954e85 −0.677733
\(188\) 9.69871e84 0.507919
\(189\) −4.47336e84 −0.192006
\(190\) 2.63355e85 0.927430
\(191\) −4.53880e85 −1.31277 −0.656387 0.754424i \(-0.727916\pi\)
−0.656387 + 0.754424i \(0.727916\pi\)
\(192\) 5.07915e84 0.120780
\(193\) −9.26819e85 −1.81383 −0.906914 0.421316i \(-0.861568\pi\)
−0.906914 + 0.421316i \(0.861568\pi\)
\(194\) 9.28425e84 0.149686
\(195\) 6.30194e84 0.0837870
\(196\) 3.65285e85 0.400894
\(197\) 4.97463e85 0.451105 0.225552 0.974231i \(-0.427581\pi\)
0.225552 + 0.974231i \(0.427581\pi\)
\(198\) 5.60836e85 0.420621
\(199\) −7.14033e85 −0.443331 −0.221666 0.975123i \(-0.571149\pi\)
−0.221666 + 0.975123i \(0.571149\pi\)
\(200\) 4.69336e85 0.241468
\(201\) 4.58236e85 0.195541
\(202\) −1.77803e85 −0.0629888
\(203\) 9.60764e85 0.282823
\(204\) 4.17165e85 0.102135
\(205\) 7.37727e86 1.50358
\(206\) −5.80177e86 −0.985235
\(207\) −5.79364e86 −0.820472
\(208\) −2.56413e85 −0.0303085
\(209\) −8.85530e86 −0.874415
\(210\) −8.44289e85 −0.0697056
\(211\) 1.15343e87 0.796892 0.398446 0.917192i \(-0.369550\pi\)
0.398446 + 0.917192i \(0.369550\pi\)
\(212\) −1.70319e87 −0.985529
\(213\) −4.29657e86 −0.208395
\(214\) −7.24828e86 −0.294930
\(215\) 3.98215e87 1.36043
\(216\) −1.21322e87 −0.348276
\(217\) 3.30312e87 0.797415
\(218\) 5.65642e87 1.14927
\(219\) 9.61907e86 0.164619
\(220\) −3.04811e87 −0.439724
\(221\) −3.59091e87 −0.437013
\(222\) −1.75269e87 −0.180081
\(223\) −2.95594e87 −0.256604 −0.128302 0.991735i \(-0.540953\pi\)
−0.128302 + 0.991735i \(0.540953\pi\)
\(224\) −7.47442e87 −0.548627
\(225\) −3.69626e87 −0.229572
\(226\) −9.91971e87 −0.521714
\(227\) −9.67879e87 −0.431371 −0.215686 0.976463i \(-0.569199\pi\)
−0.215686 + 0.976463i \(0.569199\pi\)
\(228\) 3.48652e87 0.131776
\(229\) 4.56764e88 1.46508 0.732540 0.680723i \(-0.238334\pi\)
0.732540 + 0.680723i \(0.238334\pi\)
\(230\) −2.22081e88 −0.604946
\(231\) 2.83892e87 0.0657210
\(232\) 2.60569e88 0.513007
\(233\) 1.95700e88 0.327902 0.163951 0.986468i \(-0.447576\pi\)
0.163951 + 0.986468i \(0.447576\pi\)
\(234\) 1.90074e88 0.271223
\(235\) −7.92072e88 −0.963207
\(236\) 8.40941e88 0.872098
\(237\) 1.28026e88 0.113302
\(238\) 4.81084e88 0.363568
\(239\) −5.75419e88 −0.371589 −0.185795 0.982589i \(-0.559486\pi\)
−0.185795 + 0.982589i \(0.559486\pi\)
\(240\) −2.43273e87 −0.0134330
\(241\) −3.37052e89 −1.59242 −0.796210 0.605020i \(-0.793165\pi\)
−0.796210 + 0.605020i \(0.793165\pi\)
\(242\) 8.66999e88 0.350705
\(243\) 1.44049e89 0.499201
\(244\) −1.11312e89 −0.330693
\(245\) −2.98320e89 −0.760247
\(246\) −6.88829e88 −0.150676
\(247\) −3.00116e89 −0.563837
\(248\) 8.95839e89 1.44641
\(249\) −1.93699e88 −0.0268937
\(250\) 4.56951e89 0.545908
\(251\) 8.76805e89 0.901858 0.450929 0.892560i \(-0.351093\pi\)
0.450929 + 0.892560i \(0.351093\pi\)
\(252\) 3.61056e89 0.319930
\(253\) 7.46746e89 0.570365
\(254\) −1.17178e90 −0.771939
\(255\) −3.40689e89 −0.193688
\(256\) −2.11041e90 −1.03602
\(257\) −1.45805e90 −0.618416 −0.309208 0.950995i \(-0.600064\pi\)
−0.309208 + 0.950995i \(0.600064\pi\)
\(258\) −3.71820e89 −0.136331
\(259\) 2.86586e90 0.908895
\(260\) −1.03304e90 −0.283541
\(261\) −2.05211e90 −0.487733
\(262\) −3.64685e90 −0.750965
\(263\) −1.04913e90 −0.187280 −0.0936398 0.995606i \(-0.529850\pi\)
−0.0936398 + 0.995606i \(0.529850\pi\)
\(264\) 7.69944e89 0.119210
\(265\) 1.39096e91 1.86894
\(266\) 4.02074e90 0.469078
\(267\) 1.34402e90 0.136217
\(268\) −7.51159e90 −0.661724
\(269\) 1.36688e90 0.104717 0.0523587 0.998628i \(-0.483326\pi\)
0.0523587 + 0.998628i \(0.483326\pi\)
\(270\) 3.66249e90 0.244138
\(271\) −3.50139e90 −0.203185 −0.101593 0.994826i \(-0.532394\pi\)
−0.101593 + 0.994826i \(0.532394\pi\)
\(272\) 1.38619e90 0.0700631
\(273\) 9.62142e89 0.0423780
\(274\) −1.16164e91 −0.446094
\(275\) 4.76414e90 0.159591
\(276\) −2.94010e90 −0.0859551
\(277\) 3.00814e90 0.0767903 0.0383951 0.999263i \(-0.487775\pi\)
0.0383951 + 0.999263i \(0.487775\pi\)
\(278\) −2.53058e91 −0.564338
\(279\) −7.05519e91 −1.37515
\(280\) 3.74409e91 0.638146
\(281\) −1.95826e91 −0.292000 −0.146000 0.989285i \(-0.546640\pi\)
−0.146000 + 0.989285i \(0.546640\pi\)
\(282\) 7.39571e90 0.0965247
\(283\) 7.34668e91 0.839653 0.419826 0.907604i \(-0.362091\pi\)
0.419826 + 0.907604i \(0.362091\pi\)
\(284\) 7.04311e91 0.705224
\(285\) −2.84737e91 −0.249897
\(286\) −2.44987e91 −0.188546
\(287\) 1.12632e92 0.760483
\(288\) 1.59648e92 0.946115
\(289\) 1.96546e90 0.0102281
\(290\) −7.86611e91 −0.359613
\(291\) −1.00380e91 −0.0403331
\(292\) −1.57680e92 −0.557081
\(293\) −3.78620e92 −1.17670 −0.588352 0.808605i \(-0.700223\pi\)
−0.588352 + 0.808605i \(0.700223\pi\)
\(294\) 2.78547e91 0.0761857
\(295\) −6.86777e92 −1.65383
\(296\) 7.77250e92 1.64862
\(297\) −1.23151e92 −0.230182
\(298\) −3.44493e92 −0.567637
\(299\) 2.53080e92 0.367781
\(300\) −1.87574e91 −0.0240506
\(301\) 6.07971e92 0.688080
\(302\) 6.94513e92 0.694096
\(303\) 1.92239e91 0.0169724
\(304\) 1.15853e92 0.0903959
\(305\) 9.09062e92 0.627119
\(306\) −1.02756e93 −0.626978
\(307\) 1.04256e92 0.0562878 0.0281439 0.999604i \(-0.491040\pi\)
0.0281439 + 0.999604i \(0.491040\pi\)
\(308\) −4.65367e92 −0.222405
\(309\) 6.27282e92 0.265473
\(310\) −2.70438e93 −1.01392
\(311\) 2.13035e93 0.707843 0.353921 0.935275i \(-0.384848\pi\)
0.353921 + 0.935275i \(0.384848\pi\)
\(312\) 2.60943e92 0.0768684
\(313\) −2.58095e91 −0.00674322 −0.00337161 0.999994i \(-0.501073\pi\)
−0.00337161 + 0.999994i \(0.501073\pi\)
\(314\) −3.35396e93 −0.777493
\(315\) −2.94867e93 −0.606708
\(316\) −2.09866e93 −0.383421
\(317\) 1.87491e93 0.304269 0.152135 0.988360i \(-0.451385\pi\)
0.152135 + 0.988360i \(0.451385\pi\)
\(318\) −1.29876e93 −0.187289
\(319\) 2.64498e93 0.339056
\(320\) 6.79961e93 0.775104
\(321\) 7.83678e92 0.0794692
\(322\) −3.39059e93 −0.305971
\(323\) 1.62246e94 1.30340
\(324\) −7.46574e93 −0.534115
\(325\) 1.61462e93 0.102907
\(326\) 5.16143e93 0.293164
\(327\) −6.11567e93 −0.309673
\(328\) 3.05469e94 1.37942
\(329\) −1.20929e94 −0.487173
\(330\) −2.32433e93 −0.0835650
\(331\) −5.42826e94 −1.74225 −0.871125 0.491061i \(-0.836609\pi\)
−0.871125 + 0.491061i \(0.836609\pi\)
\(332\) 3.17518e93 0.0910103
\(333\) −6.12124e94 −1.56740
\(334\) −2.06878e94 −0.473394
\(335\) 6.13454e94 1.25488
\(336\) −3.71414e92 −0.00679416
\(337\) 1.16963e94 0.191393 0.0956965 0.995411i \(-0.469492\pi\)
0.0956965 + 0.995411i \(0.469492\pi\)
\(338\) 3.56169e94 0.521530
\(339\) 1.07251e94 0.140576
\(340\) 5.58471e94 0.655453
\(341\) 9.09348e94 0.955962
\(342\) −8.58797e94 −0.808931
\(343\) −1.12168e95 −0.946980
\(344\) 1.64888e95 1.24809
\(345\) 2.40111e94 0.163003
\(346\) −2.80920e94 −0.171092
\(347\) 7.78575e94 0.425545 0.212772 0.977102i \(-0.431751\pi\)
0.212772 + 0.977102i \(0.431751\pi\)
\(348\) −1.04139e94 −0.0510964
\(349\) −3.88388e95 −1.71125 −0.855623 0.517600i \(-0.826826\pi\)
−0.855623 + 0.517600i \(0.826826\pi\)
\(350\) −2.16315e94 −0.0856121
\(351\) −4.17373e94 −0.148425
\(352\) −2.05771e95 −0.657708
\(353\) 6.23918e95 1.79298 0.896492 0.443060i \(-0.146107\pi\)
0.896492 + 0.443060i \(0.146107\pi\)
\(354\) 6.41256e94 0.165733
\(355\) −5.75195e95 −1.33737
\(356\) −2.20316e95 −0.460969
\(357\) −5.20144e94 −0.0979638
\(358\) 2.69154e95 0.456444
\(359\) 7.02370e95 1.07281 0.536407 0.843960i \(-0.319781\pi\)
0.536407 + 0.843960i \(0.319781\pi\)
\(360\) −7.99708e95 −1.10049
\(361\) 5.49651e95 0.681659
\(362\) 6.91882e95 0.773500
\(363\) −9.37391e94 −0.0944979
\(364\) −1.57718e95 −0.143410
\(365\) 1.28773e96 1.05644
\(366\) −8.48807e94 −0.0628447
\(367\) 4.84188e95 0.323621 0.161810 0.986822i \(-0.448267\pi\)
0.161810 + 0.986822i \(0.448267\pi\)
\(368\) −9.76962e94 −0.0589637
\(369\) −2.40572e96 −1.31147
\(370\) −2.34638e96 −1.15567
\(371\) 2.12363e96 0.945275
\(372\) −3.58030e95 −0.144065
\(373\) −3.19767e96 −1.16346 −0.581732 0.813380i \(-0.697625\pi\)
−0.581732 + 0.813380i \(0.697625\pi\)
\(374\) 1.32442e96 0.435855
\(375\) −4.94051e95 −0.147095
\(376\) −3.27971e96 −0.883672
\(377\) 8.96413e95 0.218629
\(378\) 5.59167e95 0.123481
\(379\) 6.31380e96 1.26276 0.631380 0.775474i \(-0.282489\pi\)
0.631380 + 0.775474i \(0.282489\pi\)
\(380\) 4.66751e96 0.845670
\(381\) 1.26692e96 0.208000
\(382\) 5.67348e96 0.844255
\(383\) −1.05836e97 −1.42785 −0.713923 0.700225i \(-0.753083\pi\)
−0.713923 + 0.700225i \(0.753083\pi\)
\(384\) 7.46667e95 0.0913495
\(385\) 3.80055e96 0.421764
\(386\) 1.15852e97 1.16649
\(387\) −1.29858e97 −1.18661
\(388\) 1.64548e96 0.136490
\(389\) −6.81840e96 −0.513538 −0.256769 0.966473i \(-0.582658\pi\)
−0.256769 + 0.966473i \(0.582658\pi\)
\(390\) −7.87740e95 −0.0538840
\(391\) −1.36818e97 −0.850187
\(392\) −1.23525e97 −0.697471
\(393\) 3.94294e96 0.202348
\(394\) −6.21826e96 −0.290109
\(395\) 1.71393e97 0.727112
\(396\) 9.93987e96 0.383540
\(397\) −3.56797e96 −0.125250 −0.0626250 0.998037i \(-0.519947\pi\)
−0.0626250 + 0.998037i \(0.519947\pi\)
\(398\) 8.92539e96 0.285110
\(399\) −4.34719e96 −0.126393
\(400\) −6.23288e95 −0.0164983
\(401\) −1.50986e97 −0.363934 −0.181967 0.983305i \(-0.558246\pi\)
−0.181967 + 0.983305i \(0.558246\pi\)
\(402\) −5.72793e96 −0.125754
\(403\) 3.08188e97 0.616420
\(404\) −3.15126e96 −0.0574359
\(405\) 6.09710e97 1.01288
\(406\) −1.20095e97 −0.181886
\(407\) 7.88970e97 1.08961
\(408\) −1.41068e97 −0.177694
\(409\) −9.27122e96 −0.106540 −0.0532700 0.998580i \(-0.516964\pi\)
−0.0532700 + 0.998580i \(0.516964\pi\)
\(410\) −9.22156e97 −0.966963
\(411\) 1.25596e97 0.120200
\(412\) −1.02827e98 −0.898379
\(413\) −1.04853e98 −0.836477
\(414\) 7.24203e97 0.527652
\(415\) −2.59310e97 −0.172590
\(416\) −6.97379e97 −0.424101
\(417\) 2.73604e97 0.152062
\(418\) 1.10691e98 0.562343
\(419\) −2.22993e98 −1.03577 −0.517887 0.855449i \(-0.673281\pi\)
−0.517887 + 0.855449i \(0.673281\pi\)
\(420\) −1.49636e97 −0.0635605
\(421\) 2.56359e98 0.996023 0.498012 0.867170i \(-0.334064\pi\)
0.498012 + 0.867170i \(0.334064\pi\)
\(422\) −1.44178e98 −0.512487
\(423\) 2.58294e98 0.840137
\(424\) 5.75951e98 1.71461
\(425\) −8.72879e97 −0.237886
\(426\) 5.37070e97 0.134020
\(427\) 1.38790e98 0.317185
\(428\) −1.28464e98 −0.268929
\(429\) 2.64877e97 0.0508038
\(430\) −4.97767e98 −0.874902
\(431\) −5.84060e98 −0.940935 −0.470468 0.882417i \(-0.655915\pi\)
−0.470468 + 0.882417i \(0.655915\pi\)
\(432\) 1.61118e97 0.0237960
\(433\) −2.66887e97 −0.0361436 −0.0180718 0.999837i \(-0.505753\pi\)
−0.0180718 + 0.999837i \(0.505753\pi\)
\(434\) −4.12888e98 −0.512823
\(435\) 8.50477e97 0.0968981
\(436\) 1.00250e99 1.04796
\(437\) −1.14348e99 −1.09692
\(438\) −1.20238e98 −0.105867
\(439\) −1.07199e99 −0.866509 −0.433255 0.901272i \(-0.642635\pi\)
−0.433255 + 0.901272i \(0.642635\pi\)
\(440\) 1.03075e99 0.765027
\(441\) 9.72820e98 0.663110
\(442\) 4.48862e98 0.281046
\(443\) −2.88329e98 −0.165863 −0.0829315 0.996555i \(-0.526428\pi\)
−0.0829315 + 0.996555i \(0.526428\pi\)
\(444\) −3.10635e98 −0.164206
\(445\) 1.79927e99 0.874172
\(446\) 3.69491e98 0.165024
\(447\) 3.72462e98 0.152950
\(448\) 1.03812e99 0.392034
\(449\) −3.37230e99 −1.17135 −0.585676 0.810545i \(-0.699171\pi\)
−0.585676 + 0.810545i \(0.699171\pi\)
\(450\) 4.62031e98 0.147639
\(451\) 3.10075e99 0.911688
\(452\) −1.75810e99 −0.475721
\(453\) −7.50900e98 −0.187025
\(454\) 1.20984e99 0.277418
\(455\) 1.28805e99 0.271960
\(456\) −1.17900e99 −0.229262
\(457\) −6.02179e99 −1.07862 −0.539310 0.842107i \(-0.681315\pi\)
−0.539310 + 0.842107i \(0.681315\pi\)
\(458\) −5.70953e99 −0.942205
\(459\) 2.25636e99 0.343110
\(460\) −3.93600e99 −0.551615
\(461\) 8.06561e99 1.04196 0.520982 0.853568i \(-0.325566\pi\)
0.520982 + 0.853568i \(0.325566\pi\)
\(462\) −3.54864e98 −0.0422657
\(463\) −8.25998e99 −0.907176 −0.453588 0.891211i \(-0.649856\pi\)
−0.453588 + 0.891211i \(0.649856\pi\)
\(464\) −3.46041e98 −0.0350512
\(465\) 2.92395e99 0.273202
\(466\) −2.44624e99 −0.210876
\(467\) 2.12206e100 1.68801 0.844005 0.536335i \(-0.180192\pi\)
0.844005 + 0.536335i \(0.180192\pi\)
\(468\) 3.36873e99 0.247313
\(469\) 9.36585e99 0.634696
\(470\) 9.90086e99 0.619446
\(471\) 3.62627e99 0.209496
\(472\) −2.84372e100 −1.51727
\(473\) 1.67374e100 0.824889
\(474\) −1.60032e99 −0.0728652
\(475\) −7.29523e99 −0.306922
\(476\) 8.52640e99 0.331516
\(477\) −4.53591e100 −1.63014
\(478\) 7.19271e99 0.238972
\(479\) −6.07031e100 −1.86479 −0.932394 0.361445i \(-0.882284\pi\)
−0.932394 + 0.361445i \(0.882284\pi\)
\(480\) −6.61642e99 −0.187965
\(481\) 2.67391e100 0.702597
\(482\) 4.21314e100 1.02410
\(483\) 3.66587e99 0.0824442
\(484\) 1.53661e100 0.319788
\(485\) −1.34382e100 −0.258837
\(486\) −1.80061e100 −0.321040
\(487\) −3.82403e100 −0.631226 −0.315613 0.948888i \(-0.602210\pi\)
−0.315613 + 0.948888i \(0.602210\pi\)
\(488\) 3.76413e100 0.575335
\(489\) −5.58049e99 −0.0789933
\(490\) 3.72899e100 0.488921
\(491\) 1.61347e101 1.95977 0.979884 0.199566i \(-0.0639532\pi\)
0.979884 + 0.199566i \(0.0639532\pi\)
\(492\) −1.22083e100 −0.137393
\(493\) −4.84610e100 −0.505397
\(494\) 3.75144e100 0.362608
\(495\) −8.11767e100 −0.727338
\(496\) −1.18969e100 −0.0988262
\(497\) −8.78173e100 −0.676419
\(498\) 2.42122e99 0.0172956
\(499\) −7.09381e99 −0.0470012 −0.0235006 0.999724i \(-0.507481\pi\)
−0.0235006 + 0.999724i \(0.507481\pi\)
\(500\) 8.09868e100 0.497782
\(501\) 2.23675e100 0.127556
\(502\) −1.09600e101 −0.579992
\(503\) 2.88098e100 0.141495 0.0707475 0.997494i \(-0.477462\pi\)
0.0707475 + 0.997494i \(0.477462\pi\)
\(504\) −1.22095e101 −0.556610
\(505\) 2.57356e100 0.108920
\(506\) −9.33429e100 −0.366806
\(507\) −3.85086e100 −0.140527
\(508\) −2.07679e101 −0.703886
\(509\) 3.40536e100 0.107213 0.0536063 0.998562i \(-0.482928\pi\)
0.0536063 + 0.998562i \(0.482928\pi\)
\(510\) 4.25860e100 0.124562
\(511\) 1.96603e101 0.534327
\(512\) 5.50789e100 0.139111
\(513\) 1.88579e101 0.442683
\(514\) 1.82256e101 0.397708
\(515\) 8.39761e101 1.70367
\(516\) −6.58988e100 −0.124312
\(517\) −3.32916e101 −0.584036
\(518\) −3.58231e101 −0.584517
\(519\) 3.03728e100 0.0461008
\(520\) 3.49332e101 0.493302
\(521\) −2.83196e100 −0.0372111 −0.0186055 0.999827i \(-0.505923\pi\)
−0.0186055 + 0.999827i \(0.505923\pi\)
\(522\) 2.56513e101 0.313665
\(523\) −6.78214e101 −0.771887 −0.385943 0.922522i \(-0.626124\pi\)
−0.385943 + 0.922522i \(0.626124\pi\)
\(524\) −6.46343e101 −0.684762
\(525\) 2.33878e100 0.0230683
\(526\) 1.31141e101 0.120441
\(527\) −1.66610e102 −1.42496
\(528\) −1.02250e100 −0.00814502
\(529\) −3.83417e101 −0.284501
\(530\) −1.73869e102 −1.20193
\(531\) 2.23957e102 1.44252
\(532\) 7.12608e101 0.427725
\(533\) 1.05088e102 0.587871
\(534\) −1.68001e101 −0.0876024
\(535\) 1.04913e102 0.509992
\(536\) 2.54011e102 1.15126
\(537\) −2.91007e101 −0.122989
\(538\) −1.70859e101 −0.0673445
\(539\) −1.25387e102 −0.460972
\(540\) 6.49115e101 0.222616
\(541\) −1.95501e101 −0.0625536 −0.0312768 0.999511i \(-0.509957\pi\)
−0.0312768 + 0.999511i \(0.509957\pi\)
\(542\) 4.37673e101 0.130670
\(543\) −7.48056e101 −0.208421
\(544\) 3.77010e102 0.980380
\(545\) −8.18723e102 −1.98732
\(546\) −1.20267e101 −0.0272536
\(547\) 5.36210e102 1.13451 0.567257 0.823541i \(-0.308004\pi\)
0.567257 + 0.823541i \(0.308004\pi\)
\(548\) −2.05881e102 −0.406767
\(549\) −2.96444e102 −0.546991
\(550\) −5.95515e101 −0.102634
\(551\) −4.05021e102 −0.652067
\(552\) 9.94222e101 0.149544
\(553\) 2.61672e102 0.367760
\(554\) −3.76016e101 −0.0493844
\(555\) 2.53688e102 0.311397
\(556\) −4.48502e102 −0.514588
\(557\) −1.00958e103 −1.08286 −0.541430 0.840746i \(-0.682117\pi\)
−0.541430 + 0.840746i \(0.682117\pi\)
\(558\) 8.81896e102 0.884372
\(559\) 5.67250e102 0.531902
\(560\) −4.97223e101 −0.0436014
\(561\) −1.43195e102 −0.117442
\(562\) 2.44781e102 0.187787
\(563\) 1.59566e103 1.14518 0.572591 0.819841i \(-0.305938\pi\)
0.572591 + 0.819841i \(0.305938\pi\)
\(564\) 1.31076e102 0.0880153
\(565\) 1.43580e103 0.902147
\(566\) −9.18332e102 −0.539987
\(567\) 9.30868e102 0.512299
\(568\) −2.38169e103 −1.22694
\(569\) 6.65325e102 0.320866 0.160433 0.987047i \(-0.448711\pi\)
0.160433 + 0.987047i \(0.448711\pi\)
\(570\) 3.55919e102 0.160711
\(571\) −1.13478e103 −0.479798 −0.239899 0.970798i \(-0.577114\pi\)
−0.239899 + 0.970798i \(0.577114\pi\)
\(572\) −4.34198e102 −0.171924
\(573\) −6.13412e102 −0.227485
\(574\) −1.40789e103 −0.489073
\(575\) 6.15188e102 0.200200
\(576\) −2.21735e103 −0.676068
\(577\) −1.02337e103 −0.292374 −0.146187 0.989257i \(-0.546700\pi\)
−0.146187 + 0.989257i \(0.546700\pi\)
\(578\) −2.45682e101 −0.00657778
\(579\) −1.25258e103 −0.314311
\(580\) −1.39413e103 −0.327910
\(581\) −3.95899e102 −0.0872930
\(582\) 1.25475e102 0.0259385
\(583\) 5.84636e103 1.13322
\(584\) 5.33208e103 0.969204
\(585\) −2.75117e103 −0.468999
\(586\) 4.73273e103 0.756748
\(587\) 1.04432e104 1.56641 0.783206 0.621763i \(-0.213583\pi\)
0.783206 + 0.621763i \(0.213583\pi\)
\(588\) 4.93677e102 0.0694693
\(589\) −1.39247e104 −1.83849
\(590\) 8.58469e103 1.06359
\(591\) 6.72313e102 0.0781701
\(592\) −1.03220e103 −0.112642
\(593\) −9.71824e103 −0.995489 −0.497745 0.867324i \(-0.665838\pi\)
−0.497745 + 0.867324i \(0.665838\pi\)
\(594\) 1.53939e103 0.148032
\(595\) −6.96332e103 −0.628681
\(596\) −6.10555e103 −0.517595
\(597\) −9.65004e102 −0.0768231
\(598\) −3.16349e103 −0.236523
\(599\) 2.58692e104 1.81667 0.908337 0.418240i \(-0.137353\pi\)
0.908337 + 0.418240i \(0.137353\pi\)
\(600\) 6.34300e102 0.0418430
\(601\) −2.18067e104 −1.35144 −0.675720 0.737158i \(-0.736167\pi\)
−0.675720 + 0.737158i \(0.736167\pi\)
\(602\) −7.59961e103 −0.442510
\(603\) −2.00047e104 −1.09454
\(604\) 1.23091e104 0.632906
\(605\) −1.25491e104 −0.606439
\(606\) −2.40298e102 −0.0109151
\(607\) 3.95671e104 1.68950 0.844750 0.535161i \(-0.179749\pi\)
0.844750 + 0.535161i \(0.179749\pi\)
\(608\) 3.15092e104 1.26489
\(609\) 1.29846e103 0.0490093
\(610\) −1.13632e104 −0.403305
\(611\) −1.12829e104 −0.376596
\(612\) −1.82117e104 −0.571705
\(613\) 5.60714e102 0.0165567 0.00827834 0.999966i \(-0.497365\pi\)
0.00827834 + 0.999966i \(0.497365\pi\)
\(614\) −1.30320e103 −0.0361991
\(615\) 9.97026e103 0.260549
\(616\) 1.57368e104 0.386937
\(617\) 4.75635e104 1.10047 0.550237 0.835009i \(-0.314537\pi\)
0.550237 + 0.835009i \(0.314537\pi\)
\(618\) −7.84100e103 −0.170728
\(619\) 3.45849e104 0.708740 0.354370 0.935105i \(-0.384695\pi\)
0.354370 + 0.935105i \(0.384695\pi\)
\(620\) −4.79305e104 −0.924536
\(621\) −1.59024e104 −0.288754
\(622\) −2.66293e104 −0.455219
\(623\) 2.74702e104 0.442141
\(624\) −3.46537e102 −0.00525204
\(625\) −8.27230e104 −1.18066
\(626\) 3.22618e102 0.00433662
\(627\) −1.19678e104 −0.151524
\(628\) −5.94433e104 −0.708951
\(629\) −1.44554e105 −1.62417
\(630\) 3.68582e104 0.390179
\(631\) 1.13799e105 1.13510 0.567552 0.823337i \(-0.307890\pi\)
0.567552 + 0.823337i \(0.307890\pi\)
\(632\) 7.09681e104 0.667072
\(633\) 1.55884e104 0.138090
\(634\) −2.34363e104 −0.195678
\(635\) 1.69606e105 1.33484
\(636\) −2.30184e104 −0.170778
\(637\) −4.24951e104 −0.297242
\(638\) −3.30621e104 −0.218050
\(639\) 1.87571e105 1.16649
\(640\) 9.99586e104 0.586234
\(641\) −1.25933e105 −0.696569 −0.348285 0.937389i \(-0.613236\pi\)
−0.348285 + 0.937389i \(0.613236\pi\)
\(642\) −9.79593e103 −0.0511072
\(643\) 2.15243e105 1.05930 0.529648 0.848218i \(-0.322324\pi\)
0.529648 + 0.848218i \(0.322324\pi\)
\(644\) −6.00925e104 −0.278997
\(645\) 5.38181e104 0.235743
\(646\) −2.02806e105 −0.838228
\(647\) −4.52853e105 −1.76623 −0.883115 0.469157i \(-0.844558\pi\)
−0.883115 + 0.469157i \(0.844558\pi\)
\(648\) 2.52461e105 0.929247
\(649\) −2.88660e105 −1.00279
\(650\) −2.01827e104 −0.0661801
\(651\) 4.46411e104 0.138181
\(652\) 9.14776e104 0.267319
\(653\) −4.91238e105 −1.35534 −0.677669 0.735367i \(-0.737010\pi\)
−0.677669 + 0.735367i \(0.737010\pi\)
\(654\) 7.64456e104 0.199153
\(655\) 5.27854e105 1.29857
\(656\) −4.05669e104 −0.0942492
\(657\) −4.19929e105 −0.921456
\(658\) 1.51160e105 0.313305
\(659\) 1.98171e105 0.388005 0.194003 0.981001i \(-0.437853\pi\)
0.194003 + 0.981001i \(0.437853\pi\)
\(660\) −4.11947e104 −0.0761981
\(661\) 2.87807e105 0.502975 0.251487 0.967861i \(-0.419080\pi\)
0.251487 + 0.967861i \(0.419080\pi\)
\(662\) 6.78530e105 1.12045
\(663\) −4.85305e104 −0.0757282
\(664\) −1.07372e105 −0.158339
\(665\) −5.81971e105 −0.811128
\(666\) 7.65153e105 1.00801
\(667\) 3.41544e105 0.425332
\(668\) −3.66656e105 −0.431660
\(669\) −3.99490e104 −0.0444658
\(670\) −7.66815e105 −0.807023
\(671\) 3.82089e105 0.380250
\(672\) −1.01016e105 −0.0950693
\(673\) 2.37451e105 0.211353 0.105676 0.994401i \(-0.466299\pi\)
0.105676 + 0.994401i \(0.466299\pi\)
\(674\) −1.46203e105 −0.123086
\(675\) −1.01455e105 −0.0807947
\(676\) 6.31249e105 0.475553
\(677\) −5.88403e105 −0.419372 −0.209686 0.977769i \(-0.567244\pi\)
−0.209686 + 0.977769i \(0.567244\pi\)
\(678\) −1.34063e105 −0.0904057
\(679\) −2.05167e105 −0.130915
\(680\) −1.88852e106 −1.14035
\(681\) −1.30807e105 −0.0747506
\(682\) −1.13668e106 −0.614787
\(683\) 3.15565e105 0.161552 0.0807760 0.996732i \(-0.474260\pi\)
0.0807760 + 0.996732i \(0.474260\pi\)
\(684\) −1.52207e106 −0.737618
\(685\) 1.68139e106 0.771385
\(686\) 1.40210e106 0.609010
\(687\) 6.17309e105 0.253878
\(688\) −2.18974e105 −0.0852760
\(689\) 1.98140e106 0.730719
\(690\) −3.00138e105 −0.104829
\(691\) 4.44799e106 1.47142 0.735710 0.677296i \(-0.236849\pi\)
0.735710 + 0.677296i \(0.236849\pi\)
\(692\) −4.97883e105 −0.156009
\(693\) −1.23936e106 −0.367875
\(694\) −9.73215e105 −0.273671
\(695\) 3.66281e106 0.975853
\(696\) 3.52154e105 0.0888969
\(697\) −5.68115e106 −1.35896
\(698\) 4.85483e106 1.10052
\(699\) 2.64485e105 0.0568208
\(700\) −3.83382e105 −0.0780647
\(701\) −2.53368e106 −0.489020 −0.244510 0.969647i \(-0.578627\pi\)
−0.244510 + 0.969647i \(0.578627\pi\)
\(702\) 5.21715e105 0.0954534
\(703\) −1.20813e107 −2.09551
\(704\) 2.85795e106 0.469981
\(705\) −1.07047e106 −0.166910
\(706\) −7.79895e106 −1.15308
\(707\) 3.92916e105 0.0550899
\(708\) 1.13652e106 0.151122
\(709\) −1.30039e106 −0.163998 −0.0819990 0.996632i \(-0.526130\pi\)
−0.0819990 + 0.996632i \(0.526130\pi\)
\(710\) 7.18991e106 0.860074
\(711\) −5.58910e106 −0.634208
\(712\) 7.45020e106 0.801989
\(713\) 1.17423e107 1.19921
\(714\) 6.50178e105 0.0630012
\(715\) 3.54599e106 0.326033
\(716\) 4.77030e106 0.416205
\(717\) −7.77669e105 −0.0643912
\(718\) −8.77960e106 −0.689935
\(719\) −4.99955e106 −0.372905 −0.186452 0.982464i \(-0.559699\pi\)
−0.186452 + 0.982464i \(0.559699\pi\)
\(720\) 1.06203e106 0.0751913
\(721\) 1.28210e107 0.861685
\(722\) −6.87061e106 −0.438380
\(723\) −4.55520e106 −0.275944
\(724\) 1.22624e107 0.705310
\(725\) 2.17900e106 0.119010
\(726\) 1.17173e106 0.0607723
\(727\) 1.34392e106 0.0661963 0.0330981 0.999452i \(-0.489463\pi\)
0.0330981 + 0.999452i \(0.489463\pi\)
\(728\) 5.33338e106 0.249503
\(729\) −1.85513e107 −0.824313
\(730\) −1.60966e107 −0.679403
\(731\) −3.06661e107 −1.22958
\(732\) −1.50437e106 −0.0573044
\(733\) 2.35888e107 0.853703 0.426851 0.904322i \(-0.359623\pi\)
0.426851 + 0.904322i \(0.359623\pi\)
\(734\) −6.05233e106 −0.208123
\(735\) −4.03175e106 −0.131740
\(736\) −2.65710e107 −0.825067
\(737\) 2.57842e107 0.760890
\(738\) 3.00714e107 0.843413
\(739\) 2.54158e107 0.677543 0.338771 0.940869i \(-0.389989\pi\)
0.338771 + 0.940869i \(0.389989\pi\)
\(740\) −4.15856e107 −1.05379
\(741\) −4.05602e106 −0.0977050
\(742\) −2.65453e107 −0.607913
\(743\) −1.66703e107 −0.362964 −0.181482 0.983394i \(-0.558089\pi\)
−0.181482 + 0.983394i \(0.558089\pi\)
\(744\) 1.21071e107 0.250643
\(745\) 4.98627e107 0.981556
\(746\) 3.99708e107 0.748233
\(747\) 8.45608e106 0.150538
\(748\) 2.34732e107 0.397431
\(749\) 1.60175e107 0.257945
\(750\) 6.17562e106 0.0945982
\(751\) −4.43790e105 −0.00646666 −0.00323333 0.999995i \(-0.501029\pi\)
−0.00323333 + 0.999995i \(0.501029\pi\)
\(752\) 4.35552e106 0.0603769
\(753\) 1.18499e107 0.156279
\(754\) −1.12051e107 −0.140602
\(755\) −1.00525e108 −1.20023
\(756\) 9.91029e106 0.112595
\(757\) 1.15903e108 1.25314 0.626571 0.779364i \(-0.284458\pi\)
0.626571 + 0.779364i \(0.284458\pi\)
\(758\) −7.89223e107 −0.812090
\(759\) 1.00921e107 0.0988364
\(760\) −1.57836e108 −1.47129
\(761\) −1.37920e108 −1.22377 −0.611887 0.790945i \(-0.709589\pi\)
−0.611887 + 0.790945i \(0.709589\pi\)
\(762\) −1.58365e107 −0.133766
\(763\) −1.24998e108 −1.00515
\(764\) 1.00553e108 0.769827
\(765\) 1.48731e108 1.08417
\(766\) 1.32295e108 0.918258
\(767\) −9.78301e107 −0.646616
\(768\) −2.85218e107 −0.179528
\(769\) 4.00119e107 0.239856 0.119928 0.992783i \(-0.461734\pi\)
0.119928 + 0.992783i \(0.461734\pi\)
\(770\) −4.75067e107 −0.271239
\(771\) −1.97053e107 −0.107163
\(772\) 2.05328e108 1.06365
\(773\) 1.87052e108 0.923064 0.461532 0.887124i \(-0.347300\pi\)
0.461532 + 0.887124i \(0.347300\pi\)
\(774\) 1.62321e108 0.763115
\(775\) 7.49144e107 0.335546
\(776\) −5.56433e107 −0.237464
\(777\) 3.87316e107 0.157499
\(778\) 8.52296e107 0.330260
\(779\) −4.74812e108 −1.75334
\(780\) −1.39613e107 −0.0491337
\(781\) −2.41761e108 −0.810909
\(782\) 1.71022e108 0.546761
\(783\) −5.63265e107 −0.171651
\(784\) 1.64043e107 0.0476547
\(785\) 4.85460e108 1.34444
\(786\) −4.92866e107 −0.130132
\(787\) −6.55380e108 −1.64983 −0.824917 0.565253i \(-0.808778\pi\)
−0.824917 + 0.565253i \(0.808778\pi\)
\(788\) −1.10208e108 −0.264533
\(789\) −1.41789e107 −0.0324530
\(790\) −2.14240e108 −0.467611
\(791\) 2.19209e108 0.456290
\(792\) −3.36126e108 −0.667279
\(793\) 1.29494e108 0.245192
\(794\) 4.45995e107 0.0805492
\(795\) 1.87986e108 0.323861
\(796\) 1.58187e108 0.259975
\(797\) −9.83900e106 −0.0154264 −0.00771319 0.999970i \(-0.502455\pi\)
−0.00771319 + 0.999970i \(0.502455\pi\)
\(798\) 5.43396e107 0.0812846
\(799\) 6.09965e108 0.870564
\(800\) −1.69519e108 −0.230858
\(801\) −5.86742e108 −0.762479
\(802\) 1.88732e108 0.234049
\(803\) 5.41249e108 0.640566
\(804\) −1.01518e108 −0.114668
\(805\) 4.90762e108 0.529085
\(806\) −3.85234e108 −0.396424
\(807\) 1.84731e107 0.0181460
\(808\) 1.06563e108 0.0999263
\(809\) 1.09522e109 0.980463 0.490231 0.871592i \(-0.336912\pi\)
0.490231 + 0.871592i \(0.336912\pi\)
\(810\) −7.62135e108 −0.651394
\(811\) 1.44228e109 1.17698 0.588488 0.808506i \(-0.299724\pi\)
0.588488 + 0.808506i \(0.299724\pi\)
\(812\) −2.12848e108 −0.165851
\(813\) −4.73208e107 −0.0352092
\(814\) −9.86209e108 −0.700735
\(815\) −7.47077e108 −0.506938
\(816\) 1.87342e107 0.0121410
\(817\) −2.56297e109 −1.58641
\(818\) 1.15890e108 0.0685167
\(819\) −4.20032e108 −0.237211
\(820\) −1.63436e109 −0.881717
\(821\) 1.67032e109 0.860858 0.430429 0.902624i \(-0.358362\pi\)
0.430429 + 0.902624i \(0.358362\pi\)
\(822\) −1.56994e108 −0.0773018
\(823\) −2.67065e109 −1.25639 −0.628193 0.778057i \(-0.716205\pi\)
−0.628193 + 0.778057i \(0.716205\pi\)
\(824\) 3.47717e109 1.56299
\(825\) 6.43865e107 0.0276549
\(826\) 1.31066e109 0.537945
\(827\) −3.63648e108 −0.142634 −0.0713172 0.997454i \(-0.522720\pi\)
−0.0713172 + 0.997454i \(0.522720\pi\)
\(828\) 1.28353e109 0.481135
\(829\) −8.52744e108 −0.305509 −0.152754 0.988264i \(-0.548814\pi\)
−0.152754 + 0.988264i \(0.548814\pi\)
\(830\) 3.24136e108 0.110994
\(831\) 4.06545e107 0.0133067
\(832\) 9.68591e108 0.303051
\(833\) 2.29733e109 0.687125
\(834\) −3.42003e108 −0.0977920
\(835\) 2.99440e109 0.818591
\(836\) 1.96181e109 0.512768
\(837\) −1.93651e109 −0.483967
\(838\) 2.78740e109 0.666115
\(839\) −1.65765e109 −0.378809 −0.189404 0.981899i \(-0.560656\pi\)
−0.189404 + 0.981899i \(0.560656\pi\)
\(840\) 5.06008e108 0.110582
\(841\) −3.57490e109 −0.747160
\(842\) −3.20447e109 −0.640550
\(843\) −2.64655e108 −0.0505995
\(844\) −2.55532e109 −0.467308
\(845\) −5.15527e109 −0.901829
\(846\) −3.22866e109 −0.540299
\(847\) −1.91593e109 −0.306726
\(848\) −7.64875e108 −0.117151
\(849\) 9.92891e108 0.145500
\(850\) 1.09109e109 0.152986
\(851\) 1.01879e110 1.36687
\(852\) 9.51865e108 0.122205
\(853\) −5.77263e109 −0.709227 −0.354613 0.935013i \(-0.615387\pi\)
−0.354613 + 0.935013i \(0.615387\pi\)
\(854\) −1.73487e109 −0.203984
\(855\) 1.24304e110 1.39880
\(856\) 4.34411e109 0.467880
\(857\) −1.55041e110 −1.59833 −0.799164 0.601113i \(-0.794724\pi\)
−0.799164 + 0.601113i \(0.794724\pi\)
\(858\) −3.31096e108 −0.0326723
\(859\) 1.13730e110 1.07431 0.537156 0.843483i \(-0.319499\pi\)
0.537156 + 0.843483i \(0.319499\pi\)
\(860\) −8.82208e109 −0.797772
\(861\) 1.52220e109 0.131781
\(862\) 7.30072e109 0.605122
\(863\) 2.94758e109 0.233917 0.116958 0.993137i \(-0.462686\pi\)
0.116958 + 0.993137i \(0.462686\pi\)
\(864\) 4.38201e109 0.332973
\(865\) 4.06610e109 0.295851
\(866\) 3.33608e108 0.0232442
\(867\) 2.65629e107 0.00177239
\(868\) −7.31774e109 −0.467614
\(869\) 7.20382e109 0.440881
\(870\) −1.06309e109 −0.0623159
\(871\) 8.73854e109 0.490634
\(872\) −3.39006e110 −1.82322
\(873\) 4.38219e109 0.225765
\(874\) 1.42934e110 0.705435
\(875\) −1.00979e110 −0.477450
\(876\) −2.13101e109 −0.0965344
\(877\) −5.57654e109 −0.242036 −0.121018 0.992650i \(-0.538616\pi\)
−0.121018 + 0.992650i \(0.538616\pi\)
\(878\) 1.33999e110 0.557259
\(879\) −5.11698e109 −0.203906
\(880\) −1.36885e109 −0.0522705
\(881\) −5.10259e110 −1.86721 −0.933607 0.358299i \(-0.883357\pi\)
−0.933607 + 0.358299i \(0.883357\pi\)
\(882\) −1.21602e110 −0.426451
\(883\) 1.13575e110 0.381730 0.190865 0.981616i \(-0.438871\pi\)
0.190865 + 0.981616i \(0.438871\pi\)
\(884\) 7.95531e109 0.256270
\(885\) −9.28168e109 −0.286585
\(886\) 3.60411e109 0.106668
\(887\) 3.22462e110 0.914835 0.457417 0.889252i \(-0.348775\pi\)
0.457417 + 0.889252i \(0.348775\pi\)
\(888\) 1.05044e110 0.285683
\(889\) 2.58945e110 0.675136
\(890\) −2.24909e110 −0.562187
\(891\) 2.56268e110 0.614158
\(892\) 6.54860e109 0.150476
\(893\) 5.09788e110 1.12321
\(894\) −4.65576e109 −0.0983635
\(895\) −3.89580e110 −0.789283
\(896\) 1.52611e110 0.296507
\(897\) 3.42034e109 0.0637313
\(898\) 4.21535e110 0.753306
\(899\) 4.15914e110 0.712878
\(900\) 8.18872e109 0.134624
\(901\) −1.07116e111 −1.68918
\(902\) −3.87592e110 −0.586313
\(903\) 8.21662e109 0.119235
\(904\) 5.94518e110 0.827654
\(905\) −1.00145e111 −1.33754
\(906\) 9.38622e109 0.120277
\(907\) −1.38032e111 −1.69709 −0.848547 0.529120i \(-0.822522\pi\)
−0.848547 + 0.529120i \(0.822522\pi\)
\(908\) 2.14424e110 0.252962
\(909\) −8.39237e109 −0.0950034
\(910\) −1.61005e110 −0.174899
\(911\) 2.99939e110 0.312676 0.156338 0.987704i \(-0.450031\pi\)
0.156338 + 0.987704i \(0.450031\pi\)
\(912\) 1.56574e109 0.0156644
\(913\) −1.08991e110 −0.104649
\(914\) 7.52721e110 0.693668
\(915\) 1.22858e110 0.108671
\(916\) −1.01192e111 −0.859142
\(917\) 8.05895e110 0.656793
\(918\) −2.82044e110 −0.220657
\(919\) 2.25950e111 1.69700 0.848498 0.529199i \(-0.177508\pi\)
0.848498 + 0.529199i \(0.177508\pi\)
\(920\) 1.33099e111 0.959694
\(921\) 1.40901e109 0.00975388
\(922\) −1.00820e111 −0.670095
\(923\) −8.19354e110 −0.522887
\(924\) −6.28936e109 −0.0385396
\(925\) 6.49974e110 0.382456
\(926\) 1.03249e111 0.583412
\(927\) −2.73845e111 −1.48599
\(928\) −9.41146e110 −0.490465
\(929\) 3.73615e111 1.86997 0.934985 0.354688i \(-0.115413\pi\)
0.934985 + 0.354688i \(0.115413\pi\)
\(930\) −3.65492e110 −0.175698
\(931\) 1.92003e111 0.886534
\(932\) −4.33555e110 −0.192286
\(933\) 2.87914e110 0.122659
\(934\) −2.65257e111 −1.08557
\(935\) −1.91700e111 −0.753680
\(936\) −1.13917e111 −0.430272
\(937\) −2.04035e111 −0.740405 −0.370203 0.928951i \(-0.620712\pi\)
−0.370203 + 0.928951i \(0.620712\pi\)
\(938\) −1.17073e111 −0.408178
\(939\) −3.48812e108 −0.00116851
\(940\) 1.75476e111 0.564837
\(941\) 1.19436e111 0.369425 0.184712 0.982793i \(-0.440865\pi\)
0.184712 + 0.982793i \(0.440865\pi\)
\(942\) −4.53282e110 −0.134729
\(943\) 4.00397e111 1.14367
\(944\) 3.77652e110 0.103667
\(945\) −8.09351e110 −0.213523
\(946\) −2.09217e111 −0.530493
\(947\) −5.14584e111 −1.25410 −0.627050 0.778979i \(-0.715738\pi\)
−0.627050 + 0.778979i \(0.715738\pi\)
\(948\) −2.83630e110 −0.0664416
\(949\) 1.83435e111 0.413047
\(950\) 9.11900e110 0.197384
\(951\) 2.53391e110 0.0527256
\(952\) −2.88328e111 −0.576769
\(953\) 8.87914e111 1.70760 0.853802 0.520597i \(-0.174291\pi\)
0.853802 + 0.520597i \(0.174291\pi\)
\(954\) 5.66987e111 1.04836
\(955\) −8.21192e111 −1.45988
\(956\) 1.27479e111 0.217905
\(957\) 3.57465e110 0.0587537
\(958\) 7.58786e111 1.19926
\(959\) 2.56704e111 0.390153
\(960\) 9.18956e110 0.134315
\(961\) 7.18497e111 1.00995
\(962\) −3.34237e111 −0.451845
\(963\) −3.42121e111 −0.444830
\(964\) 7.46707e111 0.933816
\(965\) −1.67687e112 −2.01709
\(966\) −4.58233e110 −0.0530205
\(967\) −1.49205e112 −1.66070 −0.830351 0.557241i \(-0.811860\pi\)
−0.830351 + 0.557241i \(0.811860\pi\)
\(968\) −5.19618e111 −0.556363
\(969\) 2.19272e111 0.225862
\(970\) 1.67977e111 0.166460
\(971\) −2.06690e111 −0.197060 −0.0985299 0.995134i \(-0.531414\pi\)
−0.0985299 + 0.995134i \(0.531414\pi\)
\(972\) −3.19127e111 −0.292738
\(973\) 5.59216e111 0.493569
\(974\) 4.78002e111 0.405946
\(975\) 2.18213e110 0.0178323
\(976\) −4.99884e110 −0.0393098
\(977\) −1.87496e112 −1.41888 −0.709439 0.704767i \(-0.751051\pi\)
−0.709439 + 0.704767i \(0.751051\pi\)
\(978\) 6.97559e110 0.0508012
\(979\) 7.56255e111 0.530050
\(980\) 6.60900e111 0.445818
\(981\) 2.66985e112 1.73340
\(982\) −2.01683e112 −1.26034
\(983\) 7.83556e111 0.471317 0.235659 0.971836i \(-0.424275\pi\)
0.235659 + 0.971836i \(0.424275\pi\)
\(984\) 4.12836e111 0.239035
\(985\) 9.00045e111 0.501656
\(986\) 6.05760e111 0.325025
\(987\) −1.63433e111 −0.0844203
\(988\) 6.64878e111 0.330641
\(989\) 2.16129e112 1.03479
\(990\) 1.01470e112 0.467757
\(991\) −1.41350e112 −0.627383 −0.313692 0.949525i \(-0.601566\pi\)
−0.313692 + 0.949525i \(0.601566\pi\)
\(992\) −3.23567e112 −1.38286
\(993\) −7.33620e111 −0.301908
\(994\) 1.09771e112 0.435010
\(995\) −1.29188e112 −0.493011
\(996\) 4.29121e110 0.0157708
\(997\) −4.15637e111 −0.147111 −0.0735556 0.997291i \(-0.523435\pi\)
−0.0735556 + 0.997291i \(0.523435\pi\)
\(998\) 8.86724e110 0.0302269
\(999\) −1.68016e112 −0.551627
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 1.76.a.a.1.3 6
3.2 odd 2 9.76.a.c.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.76.a.a.1.3 6 1.1 even 1 trivial
9.76.a.c.1.4 6 3.2 odd 2