Properties

Label 3.42.a.b.1.3
Level $3$
Weight $42$
Character 3.1
Self dual yes
Analytic conductor $31.942$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 42 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9415011369\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 196497525461 x^{2} + 10360343667016365 x + 6095744045744274504000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{10}\cdot 5^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-161109.\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+949201. q^{2} +3.48678e9 q^{3} -1.29804e12 q^{4} -1.14706e14 q^{5} +3.30966e15 q^{6} -7.22302e16 q^{7} -3.31942e18 q^{8} +1.21577e19 q^{9} +O(q^{10})\) \(q+949201. q^{2} +3.48678e9 q^{3} -1.29804e12 q^{4} -1.14706e14 q^{5} +3.30966e15 q^{6} -7.22302e16 q^{7} -3.31942e18 q^{8} +1.21577e19 q^{9} -1.08879e20 q^{10} +2.08542e21 q^{11} -4.52599e21 q^{12} +1.02587e23 q^{13} -6.85610e22 q^{14} -3.99954e23 q^{15} -2.96374e23 q^{16} +1.36112e25 q^{17} +1.15401e25 q^{18} +1.23562e26 q^{19} +1.48892e26 q^{20} -2.51851e26 q^{21} +1.97949e27 q^{22} -4.97896e27 q^{23} -1.15741e28 q^{24} -3.23174e28 q^{25} +9.73760e28 q^{26} +4.23912e28 q^{27} +9.37577e28 q^{28} +7.01030e29 q^{29} -3.79637e29 q^{30} +1.80793e30 q^{31} +7.01816e30 q^{32} +7.27142e30 q^{33} +1.29198e31 q^{34} +8.28521e30 q^{35} -1.57811e31 q^{36} +2.23556e32 q^{37} +1.17286e32 q^{38} +3.57700e32 q^{39} +3.80756e32 q^{40} +1.70393e33 q^{41} -2.39057e32 q^{42} -2.72718e33 q^{43} -2.70696e33 q^{44} -1.39455e33 q^{45} -4.72604e33 q^{46} -4.84907e33 q^{47} -1.03339e33 q^{48} -3.93504e34 q^{49} -3.06757e34 q^{50} +4.74594e34 q^{51} -1.33162e35 q^{52} -5.39056e33 q^{53} +4.02377e34 q^{54} -2.39210e35 q^{55} +2.39762e35 q^{56} +4.30836e35 q^{57} +6.65419e35 q^{58} +3.17087e36 q^{59} +5.19156e35 q^{60} -1.06464e36 q^{61} +1.71609e36 q^{62} -8.78151e35 q^{63} +7.31338e36 q^{64} -1.17673e37 q^{65} +6.90204e36 q^{66} -3.93766e37 q^{67} -1.76679e37 q^{68} -1.73606e37 q^{69} +7.86433e36 q^{70} -1.01810e38 q^{71} -4.03564e37 q^{72} +2.40996e38 q^{73} +2.12200e38 q^{74} -1.12684e38 q^{75} -1.60389e38 q^{76} -1.50630e38 q^{77} +3.39529e38 q^{78} +3.87752e38 q^{79} +3.39958e37 q^{80} +1.47809e38 q^{81} +1.61738e39 q^{82} +7.28847e38 q^{83} +3.26913e38 q^{84} -1.56128e39 q^{85} -2.58864e39 q^{86} +2.44434e39 q^{87} -6.92238e39 q^{88} -1.16027e40 q^{89} -1.32371e39 q^{90} -7.40991e39 q^{91} +6.46289e39 q^{92} +6.30385e39 q^{93} -4.60274e39 q^{94} -1.41733e40 q^{95} +2.44708e40 q^{96} +9.69468e40 q^{97} -3.73515e40 q^{98} +2.53539e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + O(q^{10}) \) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + \)\(72\!\cdots\!40\)\(q^{10} + \)\(72\!\cdots\!56\)\(q^{11} + \)\(18\!\cdots\!32\)\(q^{12} - \)\(88\!\cdots\!08\)\(q^{13} + \)\(49\!\cdots\!68\)\(q^{14} + \)\(41\!\cdots\!80\)\(q^{15} - \)\(59\!\cdots\!00\)\(q^{16} - \)\(38\!\cdots\!88\)\(q^{17} - \)\(84\!\cdots\!22\)\(q^{18} + \)\(26\!\cdots\!48\)\(q^{19} + \)\(78\!\cdots\!60\)\(q^{20} + \)\(52\!\cdots\!36\)\(q^{21} - \)\(63\!\cdots\!76\)\(q^{22} - \)\(15\!\cdots\!32\)\(q^{23} + \)\(21\!\cdots\!84\)\(q^{24} + \)\(11\!\cdots\!00\)\(q^{25} - \)\(62\!\cdots\!52\)\(q^{26} + \)\(16\!\cdots\!04\)\(q^{27} + \)\(68\!\cdots\!12\)\(q^{28} - \)\(10\!\cdots\!64\)\(q^{29} + \)\(25\!\cdots\!40\)\(q^{30} + \)\(92\!\cdots\!04\)\(q^{31} + \)\(19\!\cdots\!56\)\(q^{32} + \)\(25\!\cdots\!56\)\(q^{33} + \)\(92\!\cdots\!04\)\(q^{34} + \)\(20\!\cdots\!40\)\(q^{35} + \)\(65\!\cdots\!32\)\(q^{36} + \)\(20\!\cdots\!56\)\(q^{37} + \)\(11\!\cdots\!28\)\(q^{38} - \)\(30\!\cdots\!08\)\(q^{39} + \)\(25\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!04\)\(q^{41} + \)\(17\!\cdots\!68\)\(q^{42} + \)\(39\!\cdots\!60\)\(q^{43} - \)\(18\!\cdots\!04\)\(q^{44} + \)\(14\!\cdots\!80\)\(q^{45} - \)\(44\!\cdots\!16\)\(q^{46} - \)\(88\!\cdots\!20\)\(q^{47} - \)\(20\!\cdots\!00\)\(q^{48} - \)\(33\!\cdots\!80\)\(q^{49} - \)\(21\!\cdots\!50\)\(q^{50} - \)\(13\!\cdots\!88\)\(q^{51} - \)\(59\!\cdots\!08\)\(q^{52} + \)\(95\!\cdots\!28\)\(q^{53} - \)\(29\!\cdots\!22\)\(q^{54} + \)\(12\!\cdots\!60\)\(q^{55} + \)\(19\!\cdots\!20\)\(q^{56} + \)\(91\!\cdots\!48\)\(q^{57} + \)\(38\!\cdots\!16\)\(q^{58} - \)\(18\!\cdots\!08\)\(q^{59} + \)\(27\!\cdots\!60\)\(q^{60} + \)\(53\!\cdots\!40\)\(q^{61} + \)\(14\!\cdots\!52\)\(q^{62} + \)\(18\!\cdots\!36\)\(q^{63} - \)\(38\!\cdots\!92\)\(q^{64} - \)\(97\!\cdots\!80\)\(q^{65} - \)\(22\!\cdots\!76\)\(q^{66} - \)\(73\!\cdots\!28\)\(q^{67} - \)\(89\!\cdots\!24\)\(q^{68} - \)\(53\!\cdots\!32\)\(q^{69} - \)\(12\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!52\)\(q^{71} + \)\(76\!\cdots\!84\)\(q^{72} - \)\(44\!\cdots\!32\)\(q^{73} - \)\(29\!\cdots\!12\)\(q^{74} + \)\(40\!\cdots\!00\)\(q^{75} + \)\(11\!\cdots\!72\)\(q^{76} + \)\(83\!\cdots\!52\)\(q^{77} - \)\(21\!\cdots\!52\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(15\!\cdots\!80\)\(q^{80} + \)\(59\!\cdots\!04\)\(q^{81} + \)\(61\!\cdots\!12\)\(q^{82} + \)\(15\!\cdots\!04\)\(q^{83} + \)\(23\!\cdots\!12\)\(q^{84} - \)\(28\!\cdots\!60\)\(q^{85} - \)\(12\!\cdots\!24\)\(q^{86} - \)\(36\!\cdots\!64\)\(q^{87} - \)\(13\!\cdots\!96\)\(q^{88} - \)\(39\!\cdots\!72\)\(q^{89} + \)\(88\!\cdots\!40\)\(q^{90} - \)\(88\!\cdots\!16\)\(q^{91} - \)\(65\!\cdots\!44\)\(q^{92} + \)\(32\!\cdots\!04\)\(q^{93} + \)\(98\!\cdots\!32\)\(q^{94} + \)\(78\!\cdots\!00\)\(q^{95} + \)\(68\!\cdots\!56\)\(q^{96} + \)\(36\!\cdots\!52\)\(q^{97} - \)\(68\!\cdots\!22\)\(q^{98} + \)\(88\!\cdots\!56\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 949201. 0.640093 0.320047 0.947402i \(-0.396301\pi\)
0.320047 + 0.947402i \(0.396301\pi\)
\(3\) 3.48678e9 0.577350
\(4\) −1.29804e12 −0.590280
\(5\) −1.14706e14 −0.537897 −0.268949 0.963154i \(-0.586676\pi\)
−0.268949 + 0.963154i \(0.586676\pi\)
\(6\) 3.30966e15 0.369558
\(7\) −7.22302e16 −0.342144 −0.171072 0.985259i \(-0.554723\pi\)
−0.171072 + 0.985259i \(0.554723\pi\)
\(8\) −3.31942e18 −1.01793
\(9\) 1.21577e19 0.333333
\(10\) −1.08879e20 −0.344305
\(11\) 2.08542e21 0.934639 0.467319 0.884089i \(-0.345220\pi\)
0.467319 + 0.884089i \(0.345220\pi\)
\(12\) −4.52599e21 −0.340799
\(13\) 1.02587e23 1.49711 0.748557 0.663070i \(-0.230747\pi\)
0.748557 + 0.663070i \(0.230747\pi\)
\(14\) −6.85610e22 −0.219004
\(15\) −3.99954e23 −0.310555
\(16\) −2.96374e23 −0.0612887
\(17\) 1.36112e25 0.812259 0.406130 0.913815i \(-0.366878\pi\)
0.406130 + 0.913815i \(0.366878\pi\)
\(18\) 1.15401e25 0.213364
\(19\) 1.23562e26 0.754115 0.377058 0.926190i \(-0.376936\pi\)
0.377058 + 0.926190i \(0.376936\pi\)
\(20\) 1.48892e26 0.317510
\(21\) −2.51851e26 −0.197537
\(22\) 1.97949e27 0.598256
\(23\) −4.97896e27 −0.604948 −0.302474 0.953158i \(-0.597813\pi\)
−0.302474 + 0.953158i \(0.597813\pi\)
\(24\) −1.15741e28 −0.587701
\(25\) −3.23174e28 −0.710666
\(26\) 9.73760e28 0.958293
\(27\) 4.23912e28 0.192450
\(28\) 9.37577e28 0.201961
\(29\) 7.01030e29 0.735492 0.367746 0.929926i \(-0.380130\pi\)
0.367746 + 0.929926i \(0.380130\pi\)
\(30\) −3.79637e29 −0.198784
\(31\) 1.80793e30 0.483355 0.241677 0.970357i \(-0.422302\pi\)
0.241677 + 0.970357i \(0.422302\pi\)
\(32\) 7.01816e30 0.978698
\(33\) 7.27142e30 0.539614
\(34\) 1.29198e31 0.519922
\(35\) 8.28521e30 0.184038
\(36\) −1.57811e31 −0.196760
\(37\) 2.23556e32 1.58947 0.794733 0.606959i \(-0.207611\pi\)
0.794733 + 0.606959i \(0.207611\pi\)
\(38\) 1.17286e32 0.482704
\(39\) 3.57700e32 0.864359
\(40\) 3.80756e32 0.547541
\(41\) 1.70393e33 1.47701 0.738505 0.674248i \(-0.235532\pi\)
0.738505 + 0.674248i \(0.235532\pi\)
\(42\) −2.39057e32 −0.126442
\(43\) −2.72718e33 −0.890451 −0.445226 0.895418i \(-0.646877\pi\)
−0.445226 + 0.895418i \(0.646877\pi\)
\(44\) −2.70696e33 −0.551699
\(45\) −1.39455e33 −0.179299
\(46\) −4.72604e33 −0.387223
\(47\) −4.84907e33 −0.255654 −0.127827 0.991796i \(-0.540800\pi\)
−0.127827 + 0.991796i \(0.540800\pi\)
\(48\) −1.03339e33 −0.0353851
\(49\) −3.93504e34 −0.882937
\(50\) −3.06757e34 −0.454893
\(51\) 4.74594e34 0.468958
\(52\) −1.33162e35 −0.883717
\(53\) −5.39056e33 −0.0242091 −0.0121045 0.999927i \(-0.503853\pi\)
−0.0121045 + 0.999927i \(0.503853\pi\)
\(54\) 4.02377e34 0.123186
\(55\) −2.39210e35 −0.502740
\(56\) 2.39762e35 0.348278
\(57\) 4.30836e35 0.435389
\(58\) 6.65419e35 0.470783
\(59\) 3.17087e36 1.58020 0.790099 0.612979i \(-0.210029\pi\)
0.790099 + 0.612979i \(0.210029\pi\)
\(60\) 5.19156e35 0.183315
\(61\) −1.06464e36 −0.267882 −0.133941 0.990989i \(-0.542763\pi\)
−0.133941 + 0.990989i \(0.542763\pi\)
\(62\) 1.71609e36 0.309392
\(63\) −8.78151e35 −0.114048
\(64\) 7.31338e36 0.687747
\(65\) −1.17673e37 −0.805294
\(66\) 6.90204e36 0.345403
\(67\) −3.93766e37 −1.44779 −0.723893 0.689912i \(-0.757649\pi\)
−0.723893 + 0.689912i \(0.757649\pi\)
\(68\) −1.76679e37 −0.479461
\(69\) −1.73606e37 −0.349267
\(70\) 7.86433e36 0.117802
\(71\) −1.01810e38 −1.14023 −0.570115 0.821565i \(-0.693102\pi\)
−0.570115 + 0.821565i \(0.693102\pi\)
\(72\) −4.03564e37 −0.339309
\(73\) 2.40996e38 1.52718 0.763591 0.645701i \(-0.223435\pi\)
0.763591 + 0.645701i \(0.223435\pi\)
\(74\) 2.12200e38 1.01741
\(75\) −1.12684e38 −0.410303
\(76\) −1.60389e38 −0.445140
\(77\) −1.50630e38 −0.319781
\(78\) 3.39529e38 0.553271
\(79\) 3.87752e38 0.486630 0.243315 0.969947i \(-0.421765\pi\)
0.243315 + 0.969947i \(0.421765\pi\)
\(80\) 3.39958e37 0.0329671
\(81\) 1.47809e38 0.111111
\(82\) 1.61738e39 0.945425
\(83\) 7.28847e38 0.332304 0.166152 0.986100i \(-0.446866\pi\)
0.166152 + 0.986100i \(0.446866\pi\)
\(84\) 3.26913e38 0.116602
\(85\) −1.56128e39 −0.436912
\(86\) −2.58864e39 −0.569972
\(87\) 2.44434e39 0.424636
\(88\) −6.92238e39 −0.951395
\(89\) −1.16027e40 −1.26492 −0.632459 0.774594i \(-0.717954\pi\)
−0.632459 + 0.774594i \(0.717954\pi\)
\(90\) −1.32371e39 −0.114768
\(91\) −7.40991e39 −0.512229
\(92\) 6.46289e39 0.357089
\(93\) 6.30385e39 0.279065
\(94\) −4.60274e39 −0.163642
\(95\) −1.41733e40 −0.405637
\(96\) 2.44708e40 0.565051
\(97\) 9.69468e40 1.81014 0.905071 0.425260i \(-0.139817\pi\)
0.905071 + 0.425260i \(0.139817\pi\)
\(98\) −3.73515e40 −0.565162
\(99\) 2.53539e40 0.311546
\(100\) 4.19492e40 0.419492
\(101\) −3.64422e40 −0.297178 −0.148589 0.988899i \(-0.547473\pi\)
−0.148589 + 0.988899i \(0.547473\pi\)
\(102\) 4.50486e40 0.300177
\(103\) 2.48116e41 1.35360 0.676802 0.736165i \(-0.263365\pi\)
0.676802 + 0.736165i \(0.263365\pi\)
\(104\) −3.40530e41 −1.52395
\(105\) 2.88887e40 0.106255
\(106\) −5.11672e39 −0.0154961
\(107\) −3.56168e41 −0.889791 −0.444895 0.895583i \(-0.646759\pi\)
−0.444895 + 0.895583i \(0.646759\pi\)
\(108\) −5.50254e40 −0.113600
\(109\) −1.67738e41 −0.286674 −0.143337 0.989674i \(-0.545783\pi\)
−0.143337 + 0.989674i \(0.545783\pi\)
\(110\) −2.27058e41 −0.321801
\(111\) 7.79493e41 0.917679
\(112\) 2.14072e40 0.0209696
\(113\) −2.13093e42 −1.73965 −0.869825 0.493360i \(-0.835768\pi\)
−0.869825 + 0.493360i \(0.835768\pi\)
\(114\) 4.08950e41 0.278689
\(115\) 5.71115e41 0.325400
\(116\) −9.09965e41 −0.434146
\(117\) 1.24722e42 0.499038
\(118\) 3.00979e42 1.01147
\(119\) −9.83143e41 −0.277910
\(120\) 1.32761e42 0.316123
\(121\) −6.29534e41 −0.126450
\(122\) −1.01056e42 −0.171469
\(123\) 5.94125e42 0.852752
\(124\) −2.34676e42 −0.285315
\(125\) 8.92319e42 0.920163
\(126\) −8.33542e41 −0.0730014
\(127\) 1.48181e43 1.10361 0.551805 0.833973i \(-0.313939\pi\)
0.551805 + 0.833973i \(0.313939\pi\)
\(128\) −8.49122e42 −0.538475
\(129\) −9.50908e42 −0.514102
\(130\) −1.11696e43 −0.515463
\(131\) −2.99812e43 −1.18246 −0.591232 0.806501i \(-0.701358\pi\)
−0.591232 + 0.806501i \(0.701358\pi\)
\(132\) −9.43859e42 −0.318524
\(133\) −8.92495e42 −0.258016
\(134\) −3.73763e43 −0.926718
\(135\) −4.86250e42 −0.103518
\(136\) −4.51814e43 −0.826822
\(137\) 1.16632e44 1.83674 0.918369 0.395726i \(-0.129507\pi\)
0.918369 + 0.395726i \(0.129507\pi\)
\(138\) −1.64787e43 −0.223564
\(139\) 1.35351e44 1.58364 0.791822 0.610752i \(-0.209133\pi\)
0.791822 + 0.610752i \(0.209133\pi\)
\(140\) −1.07545e43 −0.108634
\(141\) −1.69077e43 −0.147602
\(142\) −9.66379e43 −0.729854
\(143\) 2.13938e44 1.39926
\(144\) −3.60322e42 −0.0204296
\(145\) −8.04121e43 −0.395619
\(146\) 2.28753e44 0.977539
\(147\) −1.37206e44 −0.509764
\(148\) −2.90185e44 −0.938231
\(149\) 5.31972e44 1.49820 0.749100 0.662457i \(-0.230486\pi\)
0.749100 + 0.662457i \(0.230486\pi\)
\(150\) −1.06959e44 −0.262633
\(151\) −7.04551e43 −0.150968 −0.0754840 0.997147i \(-0.524050\pi\)
−0.0754840 + 0.997147i \(0.524050\pi\)
\(152\) −4.10155e44 −0.767635
\(153\) 1.65481e44 0.270753
\(154\) −1.42979e44 −0.204690
\(155\) −2.07379e44 −0.259995
\(156\) −4.64309e44 −0.510214
\(157\) −5.91730e44 −0.570401 −0.285201 0.958468i \(-0.592060\pi\)
−0.285201 + 0.958468i \(0.592060\pi\)
\(158\) 3.68055e44 0.311489
\(159\) −1.87957e43 −0.0139771
\(160\) −8.05022e44 −0.526439
\(161\) 3.59632e44 0.206980
\(162\) 1.40300e44 0.0711215
\(163\) 2.16790e45 0.968707 0.484354 0.874872i \(-0.339055\pi\)
0.484354 + 0.874872i \(0.339055\pi\)
\(164\) −2.21177e45 −0.871850
\(165\) −8.34072e44 −0.290257
\(166\) 6.91823e44 0.212706
\(167\) 2.71432e45 0.737858 0.368929 0.929458i \(-0.379725\pi\)
0.368929 + 0.929458i \(0.379725\pi\)
\(168\) 8.35999e44 0.201078
\(169\) 5.82871e45 1.24135
\(170\) −1.48197e45 −0.279665
\(171\) 1.50223e45 0.251372
\(172\) 3.53999e45 0.525616
\(173\) −7.77679e45 −1.02531 −0.512655 0.858595i \(-0.671338\pi\)
−0.512655 + 0.858595i \(0.671338\pi\)
\(174\) 2.32017e45 0.271807
\(175\) 2.33429e45 0.243150
\(176\) −6.18065e44 −0.0572828
\(177\) 1.10561e46 0.912328
\(178\) −1.10133e46 −0.809666
\(179\) −1.94084e46 −1.27205 −0.636023 0.771670i \(-0.719422\pi\)
−0.636023 + 0.771670i \(0.719422\pi\)
\(180\) 1.81018e45 0.105837
\(181\) −2.43655e46 −1.27164 −0.635822 0.771836i \(-0.719339\pi\)
−0.635822 + 0.771836i \(0.719339\pi\)
\(182\) −7.03349e45 −0.327874
\(183\) −3.71219e45 −0.154662
\(184\) 1.65273e46 0.615794
\(185\) −2.56432e46 −0.854970
\(186\) 5.98362e45 0.178628
\(187\) 2.83852e46 0.759169
\(188\) 6.29428e45 0.150907
\(189\) −3.06192e45 −0.0658457
\(190\) −1.34533e46 −0.259645
\(191\) 6.56910e46 1.13847 0.569236 0.822174i \(-0.307239\pi\)
0.569236 + 0.822174i \(0.307239\pi\)
\(192\) 2.55002e46 0.397071
\(193\) 2.17137e46 0.303954 0.151977 0.988384i \(-0.451436\pi\)
0.151977 + 0.988384i \(0.451436\pi\)
\(194\) 9.20220e46 1.15866
\(195\) −4.10302e46 −0.464937
\(196\) 5.10784e46 0.521181
\(197\) −1.54064e47 −1.41626 −0.708132 0.706080i \(-0.750462\pi\)
−0.708132 + 0.706080i \(0.750462\pi\)
\(198\) 2.40659e46 0.199419
\(199\) 2.19642e45 0.0164145 0.00820726 0.999966i \(-0.497388\pi\)
0.00820726 + 0.999966i \(0.497388\pi\)
\(200\) 1.07275e47 0.723407
\(201\) −1.37298e47 −0.835880
\(202\) −3.45910e46 −0.190222
\(203\) −5.06356e46 −0.251644
\(204\) −6.16043e46 −0.276817
\(205\) −1.95451e47 −0.794480
\(206\) 2.35512e47 0.866433
\(207\) −6.05326e46 −0.201649
\(208\) −3.04042e46 −0.0917563
\(209\) 2.57680e47 0.704826
\(210\) 2.74212e46 0.0680129
\(211\) −3.89810e47 −0.877127 −0.438564 0.898700i \(-0.644513\pi\)
−0.438564 + 0.898700i \(0.644513\pi\)
\(212\) 6.99716e45 0.0142901
\(213\) −3.54988e47 −0.658313
\(214\) −3.38075e47 −0.569549
\(215\) 3.12823e47 0.478971
\(216\) −1.40714e47 −0.195900
\(217\) −1.30587e47 −0.165377
\(218\) −1.59217e47 −0.183498
\(219\) 8.40300e47 0.881719
\(220\) 3.10504e47 0.296757
\(221\) 1.39634e48 1.21605
\(222\) 7.39895e47 0.587400
\(223\) 1.89724e48 1.37364 0.686821 0.726827i \(-0.259006\pi\)
0.686821 + 0.726827i \(0.259006\pi\)
\(224\) −5.06923e47 −0.334856
\(225\) −3.92904e47 −0.236889
\(226\) −2.02269e48 −1.11354
\(227\) −1.93755e48 −0.974370 −0.487185 0.873299i \(-0.661976\pi\)
−0.487185 + 0.873299i \(0.661976\pi\)
\(228\) −5.59242e47 −0.257001
\(229\) 4.36087e48 1.83209 0.916043 0.401080i \(-0.131365\pi\)
0.916043 + 0.401080i \(0.131365\pi\)
\(230\) 5.42103e47 0.208287
\(231\) −5.25216e47 −0.184626
\(232\) −2.32701e48 −0.748678
\(233\) −4.66734e48 −1.37491 −0.687453 0.726229i \(-0.741271\pi\)
−0.687453 + 0.726229i \(0.741271\pi\)
\(234\) 1.18387e48 0.319431
\(235\) 5.56215e47 0.137515
\(236\) −4.11591e48 −0.932760
\(237\) 1.35201e48 0.280956
\(238\) −9.33200e47 −0.177888
\(239\) −3.69664e48 −0.646622 −0.323311 0.946293i \(-0.604796\pi\)
−0.323311 + 0.946293i \(0.604796\pi\)
\(240\) 1.18536e47 0.0190335
\(241\) 3.93114e46 0.00579654 0.00289827 0.999996i \(-0.499077\pi\)
0.00289827 + 0.999996i \(0.499077\pi\)
\(242\) −5.97554e47 −0.0809399
\(243\) 5.15378e47 0.0641500
\(244\) 1.38195e48 0.158125
\(245\) 4.51371e48 0.474930
\(246\) 5.63944e48 0.545841
\(247\) 1.26759e49 1.12900
\(248\) −6.00126e48 −0.492020
\(249\) 2.54133e48 0.191856
\(250\) 8.46990e48 0.588990
\(251\) 1.04813e49 0.671592 0.335796 0.941935i \(-0.390995\pi\)
0.335796 + 0.941935i \(0.390995\pi\)
\(252\) 1.13988e48 0.0673203
\(253\) −1.03832e49 −0.565408
\(254\) 1.40653e49 0.706414
\(255\) −5.44386e48 −0.252251
\(256\) −2.41422e49 −1.03242
\(257\) 3.09114e48 0.122036 0.0610182 0.998137i \(-0.480565\pi\)
0.0610182 + 0.998137i \(0.480565\pi\)
\(258\) −9.02603e48 −0.329073
\(259\) −1.61475e49 −0.543827
\(260\) 1.52745e49 0.475349
\(261\) 8.52289e48 0.245164
\(262\) −2.84582e49 −0.756888
\(263\) −3.75357e47 −0.00923318 −0.00461659 0.999989i \(-0.501470\pi\)
−0.00461659 + 0.999989i \(0.501470\pi\)
\(264\) −2.41369e49 −0.549288
\(265\) 6.18327e47 0.0130220
\(266\) −8.47157e48 −0.165154
\(267\) −4.04560e49 −0.730301
\(268\) 5.11124e49 0.854600
\(269\) 4.83757e49 0.749386 0.374693 0.927149i \(-0.377748\pi\)
0.374693 + 0.927149i \(0.377748\pi\)
\(270\) −4.61549e48 −0.0662615
\(271\) −6.10803e49 −0.812888 −0.406444 0.913676i \(-0.633231\pi\)
−0.406444 + 0.913676i \(0.633231\pi\)
\(272\) −4.03402e48 −0.0497823
\(273\) −2.58367e49 −0.295736
\(274\) 1.10707e50 1.17568
\(275\) −6.73953e49 −0.664216
\(276\) 2.25347e49 0.206166
\(277\) −7.20270e49 −0.611871 −0.305936 0.952052i \(-0.598969\pi\)
−0.305936 + 0.952052i \(0.598969\pi\)
\(278\) 1.28475e50 1.01368
\(279\) 2.19802e49 0.161118
\(280\) −2.75021e49 −0.187338
\(281\) 7.49278e49 0.474421 0.237210 0.971458i \(-0.423767\pi\)
0.237210 + 0.971458i \(0.423767\pi\)
\(282\) −1.60488e49 −0.0944789
\(283\) 6.15623e49 0.337049 0.168524 0.985697i \(-0.446100\pi\)
0.168524 + 0.985697i \(0.446100\pi\)
\(284\) 1.32153e50 0.673056
\(285\) −4.94193e49 −0.234194
\(286\) 2.03070e50 0.895658
\(287\) −1.23075e50 −0.505350
\(288\) 8.53244e49 0.326233
\(289\) −9.55399e49 −0.340235
\(290\) −7.63272e49 −0.253233
\(291\) 3.38032e50 1.04509
\(292\) −3.12822e50 −0.901465
\(293\) −2.36755e50 −0.636082 −0.318041 0.948077i \(-0.603025\pi\)
−0.318041 + 0.948077i \(0.603025\pi\)
\(294\) −1.30237e50 −0.326297
\(295\) −3.63716e50 −0.849985
\(296\) −7.42076e50 −1.61796
\(297\) 8.84034e49 0.179871
\(298\) 5.04948e50 0.958988
\(299\) −5.10779e50 −0.905677
\(300\) 1.46268e50 0.242194
\(301\) 1.96985e50 0.304663
\(302\) −6.68760e49 −0.0966336
\(303\) −1.27066e50 −0.171576
\(304\) −3.66207e49 −0.0462188
\(305\) 1.22121e50 0.144093
\(306\) 1.57075e50 0.173307
\(307\) 1.27033e51 1.31094 0.655468 0.755223i \(-0.272472\pi\)
0.655468 + 0.755223i \(0.272472\pi\)
\(308\) 1.95524e50 0.188761
\(309\) 8.65127e50 0.781504
\(310\) −1.96845e50 −0.166421
\(311\) 1.73922e51 1.37647 0.688236 0.725487i \(-0.258385\pi\)
0.688236 + 0.725487i \(0.258385\pi\)
\(312\) −1.18736e51 −0.879856
\(313\) 3.53188e50 0.245102 0.122551 0.992462i \(-0.460893\pi\)
0.122551 + 0.992462i \(0.460893\pi\)
\(314\) −5.61670e50 −0.365110
\(315\) 1.00729e50 0.0613462
\(316\) −5.03318e50 −0.287248
\(317\) −7.02233e50 −0.375635 −0.187818 0.982204i \(-0.560141\pi\)
−0.187818 + 0.982204i \(0.560141\pi\)
\(318\) −1.78409e49 −0.00894666
\(319\) 1.46194e51 0.687419
\(320\) −8.38885e50 −0.369937
\(321\) −1.24188e51 −0.513721
\(322\) 3.41363e50 0.132486
\(323\) 1.68184e51 0.612537
\(324\) −1.91862e50 −0.0655867
\(325\) −3.31535e51 −1.06395
\(326\) 2.05777e51 0.620063
\(327\) −5.84866e50 −0.165511
\(328\) −5.65606e51 −1.50349
\(329\) 3.50249e50 0.0874704
\(330\) −7.91702e50 −0.185792
\(331\) −3.92842e51 −0.866452 −0.433226 0.901285i \(-0.642625\pi\)
−0.433226 + 0.901285i \(0.642625\pi\)
\(332\) −9.46073e50 −0.196153
\(333\) 2.71792e51 0.529822
\(334\) 2.57643e51 0.472298
\(335\) 4.51671e51 0.778760
\(336\) 7.46422e49 0.0121068
\(337\) −1.03514e51 −0.157975 −0.0789873 0.996876i \(-0.525169\pi\)
−0.0789873 + 0.996876i \(0.525169\pi\)
\(338\) 5.53262e51 0.794581
\(339\) −7.43011e51 −1.00439
\(340\) 2.02661e51 0.257901
\(341\) 3.77029e51 0.451762
\(342\) 1.42592e51 0.160901
\(343\) 6.06142e51 0.644236
\(344\) 9.05264e51 0.906415
\(345\) 1.99135e51 0.187870
\(346\) −7.38174e51 −0.656295
\(347\) −1.97747e52 −1.65713 −0.828565 0.559894i \(-0.810842\pi\)
−0.828565 + 0.559894i \(0.810842\pi\)
\(348\) −3.17285e51 −0.250654
\(349\) 1.12256e52 0.836158 0.418079 0.908411i \(-0.362704\pi\)
0.418079 + 0.908411i \(0.362704\pi\)
\(350\) 2.21571e51 0.155639
\(351\) 4.34880e51 0.288120
\(352\) 1.46358e52 0.914729
\(353\) −1.33863e52 −0.789368 −0.394684 0.918817i \(-0.629146\pi\)
−0.394684 + 0.918817i \(0.629146\pi\)
\(354\) 1.04945e52 0.583975
\(355\) 1.16781e52 0.613327
\(356\) 1.50607e52 0.746657
\(357\) −3.42801e51 −0.160451
\(358\) −1.84225e52 −0.814229
\(359\) −3.81033e52 −1.59047 −0.795237 0.606298i \(-0.792654\pi\)
−0.795237 + 0.606298i \(0.792654\pi\)
\(360\) 4.62910e51 0.182514
\(361\) −1.15794e52 −0.431310
\(362\) −2.31278e52 −0.813970
\(363\) −2.19505e51 −0.0730060
\(364\) 9.61836e51 0.302359
\(365\) −2.76435e52 −0.821467
\(366\) −3.52361e51 −0.0989979
\(367\) 8.16575e51 0.216941 0.108470 0.994100i \(-0.465405\pi\)
0.108470 + 0.994100i \(0.465405\pi\)
\(368\) 1.47564e51 0.0370765
\(369\) 2.07158e52 0.492337
\(370\) −2.43405e52 −0.547261
\(371\) 3.89361e50 0.00828300
\(372\) −8.18265e51 −0.164727
\(373\) −2.50717e51 −0.0477696 −0.0238848 0.999715i \(-0.507603\pi\)
−0.0238848 + 0.999715i \(0.507603\pi\)
\(374\) 2.69432e52 0.485939
\(375\) 3.11132e52 0.531256
\(376\) 1.60961e52 0.260237
\(377\) 7.19168e52 1.10112
\(378\) −2.90638e51 −0.0421474
\(379\) 3.00144e52 0.412312 0.206156 0.978519i \(-0.433905\pi\)
0.206156 + 0.978519i \(0.433905\pi\)
\(380\) 1.83975e52 0.239439
\(381\) 5.16674e52 0.637170
\(382\) 6.23540e52 0.728728
\(383\) −4.77869e52 −0.529340 −0.264670 0.964339i \(-0.585263\pi\)
−0.264670 + 0.964339i \(0.585263\pi\)
\(384\) −2.96071e52 −0.310889
\(385\) 1.72782e52 0.172010
\(386\) 2.06106e52 0.194559
\(387\) −3.31561e52 −0.296817
\(388\) −1.25841e53 −1.06849
\(389\) −9.56063e51 −0.0770052 −0.0385026 0.999259i \(-0.512259\pi\)
−0.0385026 + 0.999259i \(0.512259\pi\)
\(390\) −3.89459e52 −0.297603
\(391\) −6.77698e52 −0.491375
\(392\) 1.30621e53 0.898767
\(393\) −1.04538e53 −0.682696
\(394\) −1.46238e53 −0.906542
\(395\) −4.44774e52 −0.261757
\(396\) −3.29103e52 −0.183900
\(397\) 5.70592e52 0.302775 0.151388 0.988474i \(-0.451626\pi\)
0.151388 + 0.988474i \(0.451626\pi\)
\(398\) 2.08485e51 0.0105068
\(399\) −3.11194e52 −0.148966
\(400\) 9.57803e51 0.0435558
\(401\) −2.10266e52 −0.0908469 −0.0454234 0.998968i \(-0.514464\pi\)
−0.0454234 + 0.998968i \(0.514464\pi\)
\(402\) −1.30323e53 −0.535041
\(403\) 1.85470e53 0.723637
\(404\) 4.73035e52 0.175418
\(405\) −1.69545e52 −0.0597664
\(406\) −4.80633e52 −0.161076
\(407\) 4.66209e53 1.48558
\(408\) −1.57538e53 −0.477366
\(409\) −4.22684e51 −0.0121811 −0.00609056 0.999981i \(-0.501939\pi\)
−0.00609056 + 0.999981i \(0.501939\pi\)
\(410\) −1.85522e53 −0.508541
\(411\) 4.06672e53 1.06044
\(412\) −3.22065e53 −0.799006
\(413\) −2.29032e53 −0.540656
\(414\) −5.74576e52 −0.129074
\(415\) −8.36029e52 −0.178746
\(416\) 7.19974e53 1.46522
\(417\) 4.71939e53 0.914317
\(418\) 2.44590e53 0.451154
\(419\) −3.36354e53 −0.590757 −0.295379 0.955380i \(-0.595446\pi\)
−0.295379 + 0.955380i \(0.595446\pi\)
\(420\) −3.74988e52 −0.0627200
\(421\) 5.17107e53 0.823755 0.411877 0.911239i \(-0.364873\pi\)
0.411877 + 0.911239i \(0.364873\pi\)
\(422\) −3.70008e53 −0.561443
\(423\) −5.89533e52 −0.0852179
\(424\) 1.78935e52 0.0246431
\(425\) −4.39879e53 −0.577245
\(426\) −3.36955e53 −0.421382
\(427\) 7.68995e52 0.0916542
\(428\) 4.62321e53 0.525226
\(429\) 7.45955e53 0.807864
\(430\) 2.96932e53 0.306586
\(431\) −1.75749e54 −1.73025 −0.865124 0.501559i \(-0.832760\pi\)
−0.865124 + 0.501559i \(0.832760\pi\)
\(432\) −1.25636e52 −0.0117950
\(433\) −1.46349e54 −1.31035 −0.655176 0.755476i \(-0.727406\pi\)
−0.655176 + 0.755476i \(0.727406\pi\)
\(434\) −1.23953e53 −0.105857
\(435\) −2.80380e53 −0.228411
\(436\) 2.17731e53 0.169218
\(437\) −6.15213e53 −0.456201
\(438\) 7.97614e53 0.564382
\(439\) −1.27414e53 −0.0860387 −0.0430194 0.999074i \(-0.513698\pi\)
−0.0430194 + 0.999074i \(0.513698\pi\)
\(440\) 7.94036e53 0.511753
\(441\) −4.78409e53 −0.294312
\(442\) 1.32541e54 0.778383
\(443\) −2.79495e54 −1.56710 −0.783551 0.621328i \(-0.786594\pi\)
−0.783551 + 0.621328i \(0.786594\pi\)
\(444\) −1.01181e54 −0.541688
\(445\) 1.33089e54 0.680396
\(446\) 1.80087e54 0.879259
\(447\) 1.85487e54 0.864987
\(448\) −5.28247e53 −0.235309
\(449\) −2.51902e54 −1.07197 −0.535985 0.844228i \(-0.680060\pi\)
−0.535985 + 0.844228i \(0.680060\pi\)
\(450\) −3.72945e53 −0.151631
\(451\) 3.55342e54 1.38047
\(452\) 2.76604e54 1.02688
\(453\) −2.45662e53 −0.0871614
\(454\) −1.83913e54 −0.623688
\(455\) 8.49958e53 0.275527
\(456\) −1.43012e54 −0.443194
\(457\) 1.55517e54 0.460782 0.230391 0.973098i \(-0.426000\pi\)
0.230391 + 0.973098i \(0.426000\pi\)
\(458\) 4.13934e54 1.17271
\(459\) 5.76996e53 0.156319
\(460\) −7.41330e53 −0.192077
\(461\) 6.49280e54 1.60903 0.804513 0.593935i \(-0.202426\pi\)
0.804513 + 0.593935i \(0.202426\pi\)
\(462\) −4.98536e53 −0.118178
\(463\) −6.66332e54 −1.51106 −0.755528 0.655116i \(-0.772620\pi\)
−0.755528 + 0.655116i \(0.772620\pi\)
\(464\) −2.07767e53 −0.0450774
\(465\) −7.23086e53 −0.150108
\(466\) −4.43024e54 −0.880068
\(467\) −3.67556e54 −0.698759 −0.349379 0.936981i \(-0.613608\pi\)
−0.349379 + 0.936981i \(0.613608\pi\)
\(468\) −1.61895e54 −0.294572
\(469\) 2.84418e54 0.495351
\(470\) 5.27960e53 0.0880228
\(471\) −2.06323e54 −0.329321
\(472\) −1.05254e55 −1.60853
\(473\) −5.68732e54 −0.832250
\(474\) 1.28333e54 0.179838
\(475\) −3.99321e54 −0.535924
\(476\) 1.27616e54 0.164045
\(477\) −6.55366e52 −0.00806969
\(478\) −3.50886e54 −0.413899
\(479\) 1.46454e55 1.65510 0.827550 0.561393i \(-0.189734\pi\)
0.827550 + 0.561393i \(0.189734\pi\)
\(480\) −2.80694e54 −0.303940
\(481\) 2.29340e55 2.37961
\(482\) 3.73144e52 0.00371033
\(483\) 1.25396e54 0.119500
\(484\) 8.17160e53 0.0746410
\(485\) −1.11203e55 −0.973671
\(486\) 4.89197e53 0.0410620
\(487\) −5.71157e53 −0.0459633 −0.0229817 0.999736i \(-0.507316\pi\)
−0.0229817 + 0.999736i \(0.507316\pi\)
\(488\) 3.53400e54 0.272684
\(489\) 7.55899e54 0.559283
\(490\) 4.28442e54 0.303999
\(491\) −1.22705e55 −0.835013 −0.417507 0.908674i \(-0.637096\pi\)
−0.417507 + 0.908674i \(0.637096\pi\)
\(492\) −7.71198e54 −0.503363
\(493\) 9.54189e54 0.597410
\(494\) 1.20320e55 0.722664
\(495\) −2.90823e54 −0.167580
\(496\) −5.35822e53 −0.0296242
\(497\) 7.35373e54 0.390123
\(498\) 2.41224e54 0.122806
\(499\) 2.84787e54 0.139142 0.0695711 0.997577i \(-0.477837\pi\)
0.0695711 + 0.997577i \(0.477837\pi\)
\(500\) −1.15827e55 −0.543154
\(501\) 9.46424e54 0.426003
\(502\) 9.94890e54 0.429882
\(503\) −3.82363e55 −1.58610 −0.793052 0.609154i \(-0.791509\pi\)
−0.793052 + 0.609154i \(0.791509\pi\)
\(504\) 2.91495e54 0.116093
\(505\) 4.18013e54 0.159851
\(506\) −9.85578e54 −0.361914
\(507\) 2.03235e55 0.716695
\(508\) −1.92345e55 −0.651439
\(509\) 8.07505e54 0.262682 0.131341 0.991337i \(-0.458072\pi\)
0.131341 + 0.991337i \(0.458072\pi\)
\(510\) −5.16732e54 −0.161464
\(511\) −1.74072e55 −0.522516
\(512\) −4.24338e54 −0.122371
\(513\) 5.23796e54 0.145130
\(514\) 2.93411e54 0.0781146
\(515\) −2.84603e55 −0.728100
\(516\) 1.23432e55 0.303464
\(517\) −1.01124e55 −0.238944
\(518\) −1.53272e55 −0.348100
\(519\) −2.71160e55 −0.591963
\(520\) 3.90607e55 0.819731
\(521\) −2.48709e55 −0.501785 −0.250892 0.968015i \(-0.580724\pi\)
−0.250892 + 0.968015i \(0.580724\pi\)
\(522\) 8.08994e54 0.156928
\(523\) −2.78580e55 −0.519595 −0.259798 0.965663i \(-0.583656\pi\)
−0.259798 + 0.965663i \(0.583656\pi\)
\(524\) 3.89169e55 0.697985
\(525\) 8.13917e54 0.140383
\(526\) −3.56289e53 −0.00591010
\(527\) 2.46081e55 0.392609
\(528\) −2.15506e54 −0.0330723
\(529\) −4.29493e55 −0.634037
\(530\) 5.86917e53 0.00833530
\(531\) 3.85503e55 0.526733
\(532\) 1.15849e55 0.152302
\(533\) 1.74802e56 2.21125
\(534\) −3.84009e55 −0.467461
\(535\) 4.08545e55 0.478616
\(536\) 1.30707e56 1.47374
\(537\) −6.76730e55 −0.734416
\(538\) 4.59183e55 0.479677
\(539\) −8.20623e55 −0.825228
\(540\) 6.31172e54 0.0611049
\(541\) −4.88133e55 −0.454982 −0.227491 0.973780i \(-0.573052\pi\)
−0.227491 + 0.973780i \(0.573052\pi\)
\(542\) −5.79775e55 −0.520324
\(543\) −8.49574e55 −0.734184
\(544\) 9.55258e55 0.794956
\(545\) 1.92405e55 0.154201
\(546\) −2.45243e55 −0.189298
\(547\) −4.27578e55 −0.317889 −0.158945 0.987288i \(-0.550809\pi\)
−0.158945 + 0.987288i \(0.550809\pi\)
\(548\) −1.51393e56 −1.08419
\(549\) −1.29436e55 −0.0892939
\(550\) −6.39717e55 −0.425161
\(551\) 8.66210e55 0.554646
\(552\) 5.76270e55 0.355529
\(553\) −2.80074e55 −0.166498
\(554\) −6.83681e55 −0.391655
\(555\) −8.94121e55 −0.493617
\(556\) −1.75691e56 −0.934794
\(557\) 1.34558e56 0.690047 0.345024 0.938594i \(-0.387871\pi\)
0.345024 + 0.938594i \(0.387871\pi\)
\(558\) 2.08636e55 0.103131
\(559\) −2.79774e56 −1.33311
\(560\) −2.45552e54 −0.0112795
\(561\) 9.89730e55 0.438307
\(562\) 7.11216e55 0.303674
\(563\) −1.26109e56 −0.519189 −0.259594 0.965718i \(-0.583589\pi\)
−0.259594 + 0.965718i \(0.583589\pi\)
\(564\) 2.19468e55 0.0871264
\(565\) 2.44430e56 0.935753
\(566\) 5.84350e55 0.215743
\(567\) −1.06763e55 −0.0380160
\(568\) 3.37949e56 1.16067
\(569\) 3.82146e56 1.26598 0.632992 0.774159i \(-0.281827\pi\)
0.632992 + 0.774159i \(0.281827\pi\)
\(570\) −4.69088e55 −0.149906
\(571\) −2.98561e56 −0.920434 −0.460217 0.887806i \(-0.652228\pi\)
−0.460217 + 0.887806i \(0.652228\pi\)
\(572\) −2.77700e56 −0.825957
\(573\) 2.29050e56 0.657297
\(574\) −1.16823e56 −0.323472
\(575\) 1.60907e56 0.429916
\(576\) 8.89136e55 0.229249
\(577\) 6.45520e56 1.60622 0.803111 0.595829i \(-0.203177\pi\)
0.803111 + 0.595829i \(0.203177\pi\)
\(578\) −9.06865e55 −0.217782
\(579\) 7.57109e55 0.175488
\(580\) 1.04378e56 0.233526
\(581\) −5.26448e55 −0.113696
\(582\) 3.20861e56 0.668953
\(583\) −1.12416e55 −0.0226267
\(584\) −7.99965e56 −1.55456
\(585\) −1.43063e56 −0.268431
\(586\) −2.24728e56 −0.407152
\(587\) −7.69679e56 −1.34657 −0.673285 0.739383i \(-0.735117\pi\)
−0.673285 + 0.739383i \(0.735117\pi\)
\(588\) 1.78100e56 0.300904
\(589\) 2.23392e56 0.364505
\(590\) −3.45240e56 −0.544070
\(591\) −5.37189e56 −0.817681
\(592\) −6.62563e55 −0.0974164
\(593\) 9.29163e56 1.31969 0.659843 0.751404i \(-0.270623\pi\)
0.659843 + 0.751404i \(0.270623\pi\)
\(594\) 8.39127e55 0.115134
\(595\) 1.12772e56 0.149487
\(596\) −6.90521e56 −0.884358
\(597\) 7.65846e54 0.00947693
\(598\) −4.84832e56 −0.579718
\(599\) −2.79378e55 −0.0322807 −0.0161403 0.999870i \(-0.505138\pi\)
−0.0161403 + 0.999870i \(0.505138\pi\)
\(600\) 3.74044e56 0.417659
\(601\) 6.98610e56 0.753891 0.376945 0.926236i \(-0.376974\pi\)
0.376945 + 0.926236i \(0.376974\pi\)
\(602\) 1.86978e56 0.195013
\(603\) −4.78727e56 −0.482595
\(604\) 9.14535e55 0.0891134
\(605\) 7.22111e55 0.0680172
\(606\) −1.20611e56 −0.109825
\(607\) −7.02909e56 −0.618772 −0.309386 0.950936i \(-0.600124\pi\)
−0.309386 + 0.950936i \(0.600124\pi\)
\(608\) 8.67181e56 0.738051
\(609\) −1.76555e56 −0.145287
\(610\) 1.15917e56 0.0922329
\(611\) −4.97453e56 −0.382743
\(612\) −2.14801e56 −0.159820
\(613\) −9.34826e56 −0.672653 −0.336327 0.941745i \(-0.609185\pi\)
−0.336327 + 0.941745i \(0.609185\pi\)
\(614\) 1.20580e57 0.839121
\(615\) −6.81494e56 −0.458693
\(616\) 5.00005e56 0.325514
\(617\) 1.77746e57 1.11932 0.559661 0.828722i \(-0.310931\pi\)
0.559661 + 0.828722i \(0.310931\pi\)
\(618\) 8.21180e56 0.500235
\(619\) −1.27117e57 −0.749111 −0.374555 0.927205i \(-0.622205\pi\)
−0.374555 + 0.927205i \(0.622205\pi\)
\(620\) 2.69186e56 0.153470
\(621\) −2.11064e56 −0.116422
\(622\) 1.65087e57 0.881071
\(623\) 8.38063e56 0.432784
\(624\) −1.06013e56 −0.0529755
\(625\) 4.46084e56 0.215713
\(626\) 3.35246e56 0.156888
\(627\) 8.98474e56 0.406931
\(628\) 7.68089e56 0.336697
\(629\) 3.04288e57 1.29106
\(630\) 9.56119e55 0.0392673
\(631\) −3.85953e57 −1.53438 −0.767189 0.641421i \(-0.778345\pi\)
−0.767189 + 0.641421i \(0.778345\pi\)
\(632\) −1.28711e57 −0.495355
\(633\) −1.35918e57 −0.506410
\(634\) −6.66560e56 −0.240442
\(635\) −1.69972e57 −0.593629
\(636\) 2.43976e55 0.00825042
\(637\) −4.03686e57 −1.32186
\(638\) 1.38768e57 0.440013
\(639\) −1.23777e57 −0.380077
\(640\) 9.73991e56 0.289645
\(641\) −3.96246e57 −1.14124 −0.570618 0.821215i \(-0.693296\pi\)
−0.570618 + 0.821215i \(0.693296\pi\)
\(642\) −1.17880e57 −0.328829
\(643\) 6.28846e56 0.169910 0.0849551 0.996385i \(-0.472925\pi\)
0.0849551 + 0.996385i \(0.472925\pi\)
\(644\) −4.66816e56 −0.122176
\(645\) 1.09074e57 0.276534
\(646\) 1.59640e57 0.392081
\(647\) −1.90563e57 −0.453420 −0.226710 0.973962i \(-0.572797\pi\)
−0.226710 + 0.973962i \(0.572797\pi\)
\(648\) −4.90639e56 −0.113103
\(649\) 6.61259e57 1.47692
\(650\) −3.14694e57 −0.681027
\(651\) −4.55328e56 −0.0954804
\(652\) −2.81402e57 −0.571809
\(653\) 2.23393e57 0.439896 0.219948 0.975512i \(-0.429411\pi\)
0.219948 + 0.975512i \(0.429411\pi\)
\(654\) −5.55156e56 −0.105943
\(655\) 3.43902e57 0.636045
\(656\) −5.05002e56 −0.0905241
\(657\) 2.92994e57 0.509060
\(658\) 3.32457e56 0.0559893
\(659\) 1.63351e57 0.266668 0.133334 0.991071i \(-0.457432\pi\)
0.133334 + 0.991071i \(0.457432\pi\)
\(660\) 1.08266e57 0.171333
\(661\) 9.61694e57 1.47539 0.737695 0.675134i \(-0.235914\pi\)
0.737695 + 0.675134i \(0.235914\pi\)
\(662\) −3.72886e57 −0.554610
\(663\) 4.86874e57 0.702084
\(664\) −2.41935e57 −0.338262
\(665\) 1.02374e57 0.138786
\(666\) 2.57986e57 0.339136
\(667\) −3.49040e57 −0.444934
\(668\) −3.52329e57 −0.435543
\(669\) 6.61528e57 0.793072
\(670\) 4.28727e57 0.498479
\(671\) −2.22023e57 −0.250373
\(672\) −1.76753e57 −0.193329
\(673\) 3.39459e57 0.360146 0.180073 0.983653i \(-0.442367\pi\)
0.180073 + 0.983653i \(0.442367\pi\)
\(674\) −9.82558e56 −0.101118
\(675\) −1.36997e57 −0.136768
\(676\) −7.56590e57 −0.732746
\(677\) −7.93301e57 −0.745368 −0.372684 0.927958i \(-0.621562\pi\)
−0.372684 + 0.927958i \(0.621562\pi\)
\(678\) −7.05267e57 −0.642902
\(679\) −7.00249e57 −0.619330
\(680\) 5.18256e57 0.444745
\(681\) −6.75583e57 −0.562552
\(682\) 3.57876e57 0.289170
\(683\) −1.09757e57 −0.0860612 −0.0430306 0.999074i \(-0.513701\pi\)
−0.0430306 + 0.999074i \(0.513701\pi\)
\(684\) −1.94996e57 −0.148380
\(685\) −1.33784e58 −0.987976
\(686\) 5.75351e57 0.412371
\(687\) 1.52054e58 1.05776
\(688\) 8.08265e56 0.0545746
\(689\) −5.53003e56 −0.0362438
\(690\) 1.89020e57 0.120254
\(691\) −7.67027e57 −0.473708 −0.236854 0.971545i \(-0.576116\pi\)
−0.236854 + 0.971545i \(0.576116\pi\)
\(692\) 1.00946e58 0.605221
\(693\) −1.83132e57 −0.106594
\(694\) −1.87702e58 −1.06072
\(695\) −1.55255e58 −0.851838
\(696\) −8.11379e57 −0.432249
\(697\) 2.31926e58 1.19972
\(698\) 1.06554e58 0.535219
\(699\) −1.62740e58 −0.793802
\(700\) −3.03000e57 −0.143527
\(701\) 1.47954e58 0.680623 0.340312 0.940313i \(-0.389467\pi\)
0.340312 + 0.940313i \(0.389467\pi\)
\(702\) 4.12788e57 0.184424
\(703\) 2.76232e58 1.19864
\(704\) 1.52515e58 0.642795
\(705\) 1.93940e57 0.0793946
\(706\) −1.27063e58 −0.505269
\(707\) 2.63223e57 0.101678
\(708\) −1.43513e58 −0.538529
\(709\) 4.06301e57 0.148115 0.0740576 0.997254i \(-0.476405\pi\)
0.0740576 + 0.997254i \(0.476405\pi\)
\(710\) 1.10849e58 0.392587
\(711\) 4.71416e57 0.162210
\(712\) 3.85141e58 1.28760
\(713\) −9.00160e57 −0.292405
\(714\) −3.25387e57 −0.102704
\(715\) −2.45399e58 −0.752659
\(716\) 2.51929e58 0.750864
\(717\) −1.28894e58 −0.373328
\(718\) −3.61677e58 −1.01805
\(719\) 2.21575e58 0.606148 0.303074 0.952967i \(-0.401987\pi\)
0.303074 + 0.952967i \(0.401987\pi\)
\(720\) 4.13309e56 0.0109890
\(721\) −1.79215e58 −0.463128
\(722\) −1.09912e58 −0.276079
\(723\) 1.37070e56 0.00334663
\(724\) 3.16275e58 0.750626
\(725\) −2.26554e58 −0.522689
\(726\) −2.08354e57 −0.0467306
\(727\) 3.71059e58 0.809072 0.404536 0.914522i \(-0.367433\pi\)
0.404536 + 0.914522i \(0.367433\pi\)
\(728\) 2.45966e58 0.521412
\(729\) 1.79701e57 0.0370370
\(730\) −2.62393e58 −0.525816
\(731\) −3.71203e58 −0.723277
\(732\) 4.81857e57 0.0912937
\(733\) −5.86816e58 −1.08111 −0.540556 0.841308i \(-0.681786\pi\)
−0.540556 + 0.841308i \(0.681786\pi\)
\(734\) 7.75094e57 0.138862
\(735\) 1.57384e58 0.274201
\(736\) −3.49431e58 −0.592061
\(737\) −8.21167e58 −1.35316
\(738\) 1.96635e58 0.315142
\(739\) 3.10061e58 0.483322 0.241661 0.970361i \(-0.422308\pi\)
0.241661 + 0.970361i \(0.422308\pi\)
\(740\) 3.32858e58 0.504672
\(741\) 4.41983e58 0.651827
\(742\) 3.69582e56 0.00530189
\(743\) −1.14471e59 −1.59744 −0.798722 0.601701i \(-0.794490\pi\)
−0.798722 + 0.601701i \(0.794490\pi\)
\(744\) −2.09251e58 −0.284068
\(745\) −6.10201e58 −0.805878
\(746\) −2.37980e57 −0.0305770
\(747\) 8.86108e57 0.110768
\(748\) −3.68451e58 −0.448123
\(749\) 2.57261e58 0.304437
\(750\) 2.95327e58 0.340054
\(751\) 1.66331e59 1.86360 0.931802 0.362966i \(-0.118236\pi\)
0.931802 + 0.362966i \(0.118236\pi\)
\(752\) 1.43714e57 0.0156687
\(753\) 3.65462e58 0.387744
\(754\) 6.82635e58 0.704817
\(755\) 8.08159e57 0.0812053
\(756\) 3.97450e57 0.0388674
\(757\) 1.61727e59 1.53927 0.769637 0.638482i \(-0.220437\pi\)
0.769637 + 0.638482i \(0.220437\pi\)
\(758\) 2.84897e58 0.263918
\(759\) −3.62041e58 −0.326439
\(760\) 4.70471e58 0.412909
\(761\) −8.01236e58 −0.684503 −0.342251 0.939608i \(-0.611189\pi\)
−0.342251 + 0.939608i \(0.611189\pi\)
\(762\) 4.90428e58 0.407848
\(763\) 1.21158e58 0.0980838
\(764\) −8.52696e58 −0.672017
\(765\) −1.89816e58 −0.145637
\(766\) −4.53594e58 −0.338827
\(767\) 3.25291e59 2.36574
\(768\) −8.41785e58 −0.596069
\(769\) −1.30604e59 −0.900465 −0.450233 0.892911i \(-0.648659\pi\)
−0.450233 + 0.892911i \(0.648659\pi\)
\(770\) 1.64004e58 0.110102
\(771\) 1.07781e58 0.0704577
\(772\) −2.81852e58 −0.179418
\(773\) −2.04229e59 −1.26601 −0.633006 0.774147i \(-0.718179\pi\)
−0.633006 + 0.774147i \(0.718179\pi\)
\(774\) −3.14718e58 −0.189991
\(775\) −5.84274e58 −0.343504
\(776\) −3.21807e59 −1.84259
\(777\) −5.63029e58 −0.313979
\(778\) −9.07497e57 −0.0492905
\(779\) 2.10542e59 1.11384
\(780\) 5.32588e58 0.274443
\(781\) −2.12316e59 −1.06570
\(782\) −6.43272e58 −0.314526
\(783\) 2.97175e58 0.141545
\(784\) 1.16625e58 0.0541141
\(785\) 6.78747e58 0.306817
\(786\) −9.92277e58 −0.436989
\(787\) 1.36195e59 0.584356 0.292178 0.956364i \(-0.405620\pi\)
0.292178 + 0.956364i \(0.405620\pi\)
\(788\) 1.99982e59 0.835993
\(789\) −1.30879e57 −0.00533078
\(790\) −4.22180e58 −0.167549
\(791\) 1.53918e59 0.595211
\(792\) −8.41600e58 −0.317132
\(793\) −1.09219e59 −0.401050
\(794\) 5.41607e58 0.193805
\(795\) 2.15597e57 0.00751826
\(796\) −2.85105e57 −0.00968917
\(797\) 1.40416e59 0.465073 0.232537 0.972588i \(-0.425297\pi\)
0.232537 + 0.972588i \(0.425297\pi\)
\(798\) −2.95385e58 −0.0953520
\(799\) −6.60018e58 −0.207657
\(800\) −2.26808e59 −0.695527
\(801\) −1.41061e59 −0.421639
\(802\) −1.99585e58 −0.0581505
\(803\) 5.02578e59 1.42736
\(804\) 1.78218e59 0.493403
\(805\) −4.12518e58 −0.111334
\(806\) 1.76049e59 0.463195
\(807\) 1.68676e59 0.432658
\(808\) 1.20967e59 0.302506
\(809\) 5.07691e59 1.23781 0.618907 0.785465i \(-0.287576\pi\)
0.618907 + 0.785465i \(0.287576\pi\)
\(810\) −1.60932e58 −0.0382561
\(811\) −6.03203e59 −1.39809 −0.699047 0.715076i \(-0.746392\pi\)
−0.699047 + 0.715076i \(0.746392\pi\)
\(812\) 6.57270e58 0.148541
\(813\) −2.12974e59 −0.469321
\(814\) 4.42526e59 0.950909
\(815\) −2.48670e59 −0.521065
\(816\) −1.40658e58 −0.0287419
\(817\) −3.36977e59 −0.671503
\(818\) −4.01212e57 −0.00779706
\(819\) −9.00872e58 −0.170743
\(820\) 2.53703e59 0.468966
\(821\) −3.15683e59 −0.569136 −0.284568 0.958656i \(-0.591850\pi\)
−0.284568 + 0.958656i \(0.591850\pi\)
\(822\) 3.86013e59 0.678781
\(823\) 1.14484e60 1.96357 0.981785 0.189995i \(-0.0608471\pi\)
0.981785 + 0.189995i \(0.0608471\pi\)
\(824\) −8.23601e59 −1.37787
\(825\) −2.34993e59 −0.383486
\(826\) −2.17398e59 −0.346070
\(827\) −8.01118e59 −1.24404 −0.622019 0.783002i \(-0.713687\pi\)
−0.622019 + 0.783002i \(0.713687\pi\)
\(828\) 7.85737e58 0.119030
\(829\) −3.02291e59 −0.446743 −0.223371 0.974733i \(-0.571706\pi\)
−0.223371 + 0.974733i \(0.571706\pi\)
\(830\) −7.93559e58 −0.114414
\(831\) −2.51143e59 −0.353264
\(832\) 7.50260e59 1.02964
\(833\) −5.35608e59 −0.717174
\(834\) 4.47965e59 0.585249
\(835\) −3.11347e59 −0.396892
\(836\) −3.34479e59 −0.416045
\(837\) 7.66401e58 0.0930216
\(838\) −3.19268e59 −0.378140
\(839\) 3.04705e59 0.352175 0.176088 0.984374i \(-0.443656\pi\)
0.176088 + 0.984374i \(0.443656\pi\)
\(840\) −9.58938e58 −0.108160
\(841\) −4.17042e59 −0.459052
\(842\) 4.90839e59 0.527280
\(843\) 2.61257e59 0.273907
\(844\) 5.05989e59 0.517751
\(845\) −6.68586e59 −0.667720
\(846\) −5.59586e58 −0.0545474
\(847\) 4.54714e58 0.0432642
\(848\) 1.59762e57 0.00148374
\(849\) 2.14654e59 0.194595
\(850\) −4.17534e59 −0.369491
\(851\) −1.11308e60 −0.961545
\(852\) 4.60789e59 0.388589
\(853\) 2.51869e59 0.207358 0.103679 0.994611i \(-0.466939\pi\)
0.103679 + 0.994611i \(0.466939\pi\)
\(854\) 7.29931e58 0.0586672
\(855\) −1.72314e59 −0.135212
\(856\) 1.18227e60 0.905743
\(857\) 2.02217e60 1.51256 0.756278 0.654250i \(-0.227016\pi\)
0.756278 + 0.654250i \(0.227016\pi\)
\(858\) 7.08062e59 0.517108
\(859\) 1.10285e60 0.786423 0.393211 0.919448i \(-0.371364\pi\)
0.393211 + 0.919448i \(0.371364\pi\)
\(860\) −4.06056e59 −0.282727
\(861\) −4.29138e59 −0.291764
\(862\) −1.66821e60 −1.10752
\(863\) 2.89368e60 1.87599 0.937993 0.346653i \(-0.112682\pi\)
0.937993 + 0.346653i \(0.112682\pi\)
\(864\) 2.97508e59 0.188350
\(865\) 8.92042e59 0.551512
\(866\) −1.38915e60 −0.838748
\(867\) −3.33127e59 −0.196435
\(868\) 1.69507e59 0.0976188
\(869\) 8.08627e59 0.454824
\(870\) −2.66137e59 −0.146204
\(871\) −4.03954e60 −2.16750
\(872\) 5.56792e59 0.291814
\(873\) 1.17865e60 0.603381
\(874\) −5.83961e59 −0.292011
\(875\) −6.44524e59 −0.314828
\(876\) −1.09074e60 −0.520461
\(877\) 3.19678e60 1.49012 0.745060 0.666997i \(-0.232421\pi\)
0.745060 + 0.666997i \(0.232421\pi\)
\(878\) −1.20941e59 −0.0550728
\(879\) −8.25514e59 −0.367242
\(880\) 7.08955e58 0.0308123
\(881\) −2.79351e60 −1.18616 −0.593081 0.805143i \(-0.702089\pi\)
−0.593081 + 0.805143i \(0.702089\pi\)
\(882\) −4.54107e59 −0.188387
\(883\) −4.93461e59 −0.200013 −0.100007 0.994987i \(-0.531886\pi\)
−0.100007 + 0.994987i \(0.531886\pi\)
\(884\) −1.81251e60 −0.717808
\(885\) −1.26820e60 −0.490739
\(886\) −2.65297e60 −1.00309
\(887\) 4.55196e60 1.68176 0.840881 0.541220i \(-0.182037\pi\)
0.840881 + 0.541220i \(0.182037\pi\)
\(888\) −2.58746e60 −0.934131
\(889\) −1.07031e60 −0.377594
\(890\) 1.26328e60 0.435517
\(891\) 3.08244e59 0.103849
\(892\) −2.46270e60 −0.810834
\(893\) −5.99163e59 −0.192792
\(894\) 1.76065e60 0.553672
\(895\) 2.22625e60 0.684231
\(896\) 6.13323e59 0.184236
\(897\) −1.78097e60 −0.522893
\(898\) −2.39106e60 −0.686161
\(899\) 1.26741e60 0.355503
\(900\) 5.10005e59 0.139831
\(901\) −7.33721e58 −0.0196641
\(902\) 3.37291e60 0.883631
\(903\) 6.86843e59 0.175897
\(904\) 7.07346e60 1.77084
\(905\) 2.79486e60 0.684014
\(906\) −2.33182e59 −0.0557914
\(907\) 4.67172e60 1.09277 0.546383 0.837535i \(-0.316004\pi\)
0.546383 + 0.837535i \(0.316004\pi\)
\(908\) 2.51502e60 0.575151
\(909\) −4.43052e59 −0.0990594
\(910\) 8.06781e59 0.176363
\(911\) −8.38645e60 −1.79247 −0.896235 0.443580i \(-0.853708\pi\)
−0.896235 + 0.443580i \(0.853708\pi\)
\(912\) −1.27689e59 −0.0266844
\(913\) 1.51995e60 0.310584
\(914\) 1.47617e60 0.294943
\(915\) 4.25809e59 0.0831921
\(916\) −5.66059e60 −1.08144
\(917\) 2.16555e60 0.404573
\(918\) 5.47685e59 0.100059
\(919\) −3.88394e60 −0.693912 −0.346956 0.937881i \(-0.612785\pi\)
−0.346956 + 0.937881i \(0.612785\pi\)
\(920\) −1.89577e60 −0.331234
\(921\) 4.42938e60 0.756869
\(922\) 6.16297e60 1.02993
\(923\) −1.04444e61 −1.70706
\(924\) 6.81752e59 0.108981
\(925\) −7.22475e60 −1.12958
\(926\) −6.32484e60 −0.967217
\(927\) 3.01651e60 0.451201
\(928\) 4.91994e60 0.719824
\(929\) 2.93154e60 0.419540 0.209770 0.977751i \(-0.432728\pi\)
0.209770 + 0.977751i \(0.432728\pi\)
\(930\) −6.86355e59 −0.0960833
\(931\) −4.86224e60 −0.665837
\(932\) 6.05839e60 0.811580
\(933\) 6.06430e60 0.794707
\(934\) −3.48884e60 −0.447271
\(935\) −3.25594e60 −0.408355
\(936\) −4.14005e60 −0.507985
\(937\) 5.93664e60 0.712655 0.356328 0.934361i \(-0.384029\pi\)
0.356328 + 0.934361i \(0.384029\pi\)
\(938\) 2.69970e60 0.317071
\(939\) 1.23149e60 0.141510
\(940\) −7.21990e59 −0.0811727
\(941\) −7.34737e60 −0.808248 −0.404124 0.914704i \(-0.632424\pi\)
−0.404124 + 0.914704i \(0.632424\pi\)
\(942\) −1.95842e60 −0.210796
\(943\) −8.48382e60 −0.893515
\(944\) −9.39763e59 −0.0968484
\(945\) 3.51220e59 0.0354182
\(946\) −5.39841e60 −0.532718
\(947\) −1.09463e61 −1.05704 −0.528522 0.848920i \(-0.677253\pi\)
−0.528522 + 0.848920i \(0.677253\pi\)
\(948\) −1.75496e60 −0.165843
\(949\) 2.47231e61 2.28637
\(950\) −3.79036e60 −0.343042
\(951\) −2.44853e60 −0.216873
\(952\) 3.26346e60 0.282892
\(953\) 1.58150e60 0.134173 0.0670864 0.997747i \(-0.478630\pi\)
0.0670864 + 0.997747i \(0.478630\pi\)
\(954\) −6.22074e58 −0.00516536
\(955\) −7.53513e60 −0.612381
\(956\) 4.79839e60 0.381688
\(957\) 5.09748e60 0.396882
\(958\) 1.39015e61 1.05942
\(959\) −8.42438e60 −0.628429
\(960\) −2.92501e60 −0.213583
\(961\) −1.07218e61 −0.766368
\(962\) 2.17690e61 1.52318
\(963\) −4.33017e60 −0.296597
\(964\) −5.10278e58 −0.00342158
\(965\) −2.49068e60 −0.163496
\(966\) 1.19026e60 0.0764910
\(967\) 3.03716e61 1.91084 0.955421 0.295248i \(-0.0954023\pi\)
0.955421 + 0.295248i \(0.0954023\pi\)
\(968\) 2.08969e60 0.128717
\(969\) 5.86421e60 0.353649
\(970\) −1.05554e61 −0.623240
\(971\) 1.71562e61 0.991809 0.495904 0.868377i \(-0.334837\pi\)
0.495904 + 0.868377i \(0.334837\pi\)
\(972\) −6.68981e59 −0.0378665
\(973\) −9.77642e60 −0.541835
\(974\) −5.42143e59 −0.0294208
\(975\) −1.15599e61 −0.614271
\(976\) 3.15533e59 0.0164181
\(977\) 2.61636e61 1.33309 0.666545 0.745465i \(-0.267772\pi\)
0.666545 + 0.745465i \(0.267772\pi\)
\(978\) 7.17500e60 0.357994
\(979\) −2.41964e61 −1.18224
\(980\) −5.85898e60 −0.280342
\(981\) −2.03930e60 −0.0955580
\(982\) −1.16472e61 −0.534486
\(983\) −2.15613e61 −0.969007 −0.484504 0.874789i \(-0.661000\pi\)
−0.484504 + 0.874789i \(0.661000\pi\)
\(984\) −1.97215e61 −0.868040
\(985\) 1.76720e61 0.761805
\(986\) 9.05717e60 0.382398
\(987\) 1.22124e60 0.0505011
\(988\) −1.64539e61 −0.666425
\(989\) 1.35785e61 0.538677
\(990\) −2.76050e60 −0.107267
\(991\) −2.71176e61 −1.03215 −0.516073 0.856545i \(-0.672607\pi\)
−0.516073 + 0.856545i \(0.672607\pi\)
\(992\) 1.26883e61 0.473058
\(993\) −1.36976e61 −0.500246
\(994\) 6.98017e60 0.249715
\(995\) −2.51942e59 −0.00882933
\(996\) −3.29875e60 −0.113249
\(997\) −2.74351e61 −0.922690 −0.461345 0.887221i \(-0.652633\pi\)
−0.461345 + 0.887221i \(0.652633\pi\)
\(998\) 2.70320e60 0.0890640
\(999\) 9.47681e60 0.305893
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 3.42.a.b.1.3 4
3.2 odd 2 9.42.a.c.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.42.a.b.1.3 4 1.1 even 1 trivial
9.42.a.c.1.2 4 3.2 odd 2