Properties

Label 1.74.a.a.1.2
Level 1
Weight 74
Character 1.1
Self dual yes
Analytic conductor 33.748
Analytic rank 1
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 74 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.7483973737\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 10073499617947743056 x^{3} + 1429272143092482488433869600 x^{2} + 7661214288514935343595600445215756800 x + 1722510836040319301450745177697157900206688000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.10442e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-7.14302e10 q^{2} -1.08968e17 q^{3} -4.34246e21 q^{4} -5.37334e25 q^{5} +7.78363e27 q^{6} +1.02465e31 q^{7} +9.84822e32 q^{8} -5.57111e34 q^{9} +O(q^{10})\) \(q-7.14302e10 q^{2} -1.08968e17 q^{3} -4.34246e21 q^{4} -5.37334e25 q^{5} +7.78363e27 q^{6} +1.02465e31 q^{7} +9.84822e32 q^{8} -5.57111e34 q^{9} +3.83819e36 q^{10} -4.39076e37 q^{11} +4.73190e38 q^{12} +5.53509e40 q^{13} -7.31912e41 q^{14} +5.85525e42 q^{15} -2.93327e43 q^{16} +9.40723e44 q^{17} +3.97946e45 q^{18} +1.72590e46 q^{19} +2.33335e47 q^{20} -1.11655e48 q^{21} +3.13633e48 q^{22} -5.77480e49 q^{23} -1.07314e50 q^{24} +1.82849e51 q^{25} -3.95373e51 q^{26} +1.34354e52 q^{27} -4.44951e52 q^{28} -8.69385e52 q^{29} -4.18242e53 q^{30} +1.48414e54 q^{31} -7.20614e54 q^{32} +4.78454e54 q^{33} -6.71960e55 q^{34} -5.50582e56 q^{35} +2.41923e56 q^{36} -2.64558e57 q^{37} -1.23282e57 q^{38} -6.03150e57 q^{39} -5.29179e58 q^{40} +3.07305e57 q^{41} +7.97553e58 q^{42} +3.24223e59 q^{43} +1.90667e59 q^{44} +2.99355e60 q^{45} +4.12496e60 q^{46} -8.51145e60 q^{47} +3.19634e60 q^{48} +5.57697e61 q^{49} -1.30610e62 q^{50} -1.02509e62 q^{51} -2.40359e62 q^{52} -8.36780e62 q^{53} -9.59693e62 q^{54} +2.35931e63 q^{55} +1.00910e64 q^{56} -1.88069e63 q^{57} +6.21004e63 q^{58} +2.35468e64 q^{59} -2.54261e64 q^{60} +5.89372e64 q^{61} -1.06012e65 q^{62} -5.70846e65 q^{63} +7.91776e65 q^{64} -2.97420e66 q^{65} -3.41761e65 q^{66} +6.87121e66 q^{67} -4.08505e66 q^{68} +6.29271e66 q^{69} +3.93282e67 q^{70} +8.24197e66 q^{71} -5.48655e67 q^{72} -1.53931e68 q^{73} +1.88974e68 q^{74} -1.99248e68 q^{75} -7.49465e67 q^{76} -4.49901e68 q^{77} +4.30831e68 q^{78} -3.64169e68 q^{79} +1.57615e69 q^{80} +2.30121e69 q^{81} -2.19509e68 q^{82} +1.69878e70 q^{83} +4.84856e69 q^{84} -5.05483e70 q^{85} -2.31594e70 q^{86} +9.47355e69 q^{87} -4.32412e70 q^{88} +7.76576e69 q^{89} -2.13830e71 q^{90} +5.67155e71 q^{91} +2.50768e71 q^{92} -1.61724e71 q^{93} +6.07975e71 q^{94} -9.27387e71 q^{95} +7.85241e71 q^{96} +4.51236e71 q^{97} -3.98365e72 q^{98} +2.44614e72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} + O(q^{10}) \) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} - \)\(10\!\cdots\!00\)\(q^{10} + \)\(50\!\cdots\!60\)\(q^{11} + \)\(13\!\cdots\!92\)\(q^{12} + \)\(47\!\cdots\!86\)\(q^{13} + \)\(26\!\cdots\!20\)\(q^{14} - \)\(50\!\cdots\!00\)\(q^{15} + \)\(57\!\cdots\!80\)\(q^{16} + \)\(66\!\cdots\!02\)\(q^{17} + \)\(69\!\cdots\!16\)\(q^{18} + \)\(31\!\cdots\!00\)\(q^{19} + \)\(68\!\cdots\!00\)\(q^{20} + \)\(87\!\cdots\!60\)\(q^{21} - \)\(94\!\cdots\!16\)\(q^{22} - \)\(41\!\cdots\!24\)\(q^{23} + \)\(16\!\cdots\!00\)\(q^{24} + \)\(32\!\cdots\!75\)\(q^{25} + \)\(44\!\cdots\!60\)\(q^{26} - \)\(12\!\cdots\!80\)\(q^{27} - \)\(37\!\cdots\!16\)\(q^{28} - \)\(21\!\cdots\!50\)\(q^{29} - \)\(80\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!40\)\(q^{31} - \)\(94\!\cdots\!68\)\(q^{32} - \)\(73\!\cdots\!28\)\(q^{33} - \)\(32\!\cdots\!80\)\(q^{34} - \)\(10\!\cdots\!00\)\(q^{35} - \)\(34\!\cdots\!20\)\(q^{36} - \)\(67\!\cdots\!78\)\(q^{37} - \)\(20\!\cdots\!20\)\(q^{38} - \)\(53\!\cdots\!20\)\(q^{39} - \)\(87\!\cdots\!00\)\(q^{40} - \)\(89\!\cdots\!90\)\(q^{41} + \)\(15\!\cdots\!84\)\(q^{42} + \)\(11\!\cdots\!56\)\(q^{43} + \)\(36\!\cdots\!20\)\(q^{44} + \)\(86\!\cdots\!50\)\(q^{45} + \)\(13\!\cdots\!60\)\(q^{46} + \)\(26\!\cdots\!32\)\(q^{47} - \)\(30\!\cdots\!24\)\(q^{48} - \)\(47\!\cdots\!15\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(66\!\cdots\!40\)\(q^{51} - \)\(18\!\cdots\!28\)\(q^{52} - \)\(22\!\cdots\!54\)\(q^{53} - \)\(98\!\cdots\!00\)\(q^{54} + \)\(52\!\cdots\!00\)\(q^{55} + \)\(17\!\cdots\!00\)\(q^{56} + \)\(39\!\cdots\!40\)\(q^{57} + \)\(63\!\cdots\!20\)\(q^{58} + \)\(49\!\cdots\!00\)\(q^{59} + \)\(91\!\cdots\!00\)\(q^{60} - \)\(20\!\cdots\!90\)\(q^{61} - \)\(45\!\cdots\!96\)\(q^{62} - \)\(14\!\cdots\!44\)\(q^{63} - \)\(26\!\cdots\!40\)\(q^{64} - \)\(22\!\cdots\!00\)\(q^{65} - \)\(79\!\cdots\!80\)\(q^{66} + \)\(17\!\cdots\!52\)\(q^{67} + \)\(25\!\cdots\!04\)\(q^{68} + \)\(43\!\cdots\!80\)\(q^{69} + \)\(60\!\cdots\!00\)\(q^{70} + \)\(29\!\cdots\!60\)\(q^{71} + \)\(59\!\cdots\!60\)\(q^{72} - \)\(23\!\cdots\!74\)\(q^{73} - \)\(38\!\cdots\!80\)\(q^{74} - \)\(78\!\cdots\!00\)\(q^{75} - \)\(40\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!56\)\(q^{77} + \)\(33\!\cdots\!72\)\(q^{78} + \)\(12\!\cdots\!00\)\(q^{79} + \)\(76\!\cdots\!00\)\(q^{80} + \)\(12\!\cdots\!05\)\(q^{81} + \)\(19\!\cdots\!64\)\(q^{82} + \)\(10\!\cdots\!16\)\(q^{83} - \)\(17\!\cdots\!80\)\(q^{84} - \)\(28\!\cdots\!00\)\(q^{85} - \)\(13\!\cdots\!40\)\(q^{86} - \)\(15\!\cdots\!40\)\(q^{87} - \)\(22\!\cdots\!60\)\(q^{88} - \)\(44\!\cdots\!50\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(50\!\cdots\!60\)\(q^{91} + \)\(10\!\cdots\!52\)\(q^{92} + \)\(20\!\cdots\!32\)\(q^{93} + \)\(12\!\cdots\!20\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} - \)\(12\!\cdots\!40\)\(q^{96} - \)\(47\!\cdots\!18\)\(q^{97} - \)\(76\!\cdots\!16\)\(q^{98} - \)\(15\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.14302e10 −0.735000 −0.367500 0.930024i \(-0.619786\pi\)
−0.367500 + 0.930024i \(0.619786\pi\)
\(3\) −1.08968e17 −0.419155 −0.209577 0.977792i \(-0.567209\pi\)
−0.209577 + 0.977792i \(0.567209\pi\)
\(4\) −4.34246e21 −0.459775
\(5\) −5.37334e25 −1.65135 −0.825676 0.564145i \(-0.809206\pi\)
−0.825676 + 0.564145i \(0.809206\pi\)
\(6\) 7.78363e27 0.308079
\(7\) 1.02465e31 1.46049 0.730245 0.683185i \(-0.239406\pi\)
0.730245 + 0.683185i \(0.239406\pi\)
\(8\) 9.84822e32 1.07293
\(9\) −5.57111e34 −0.824309
\(10\) 3.83819e36 1.21374
\(11\) −4.39076e37 −0.428260 −0.214130 0.976805i \(-0.568692\pi\)
−0.214130 + 0.976805i \(0.568692\pi\)
\(12\) 4.73190e38 0.192717
\(13\) 5.53509e40 1.21393 0.606963 0.794730i \(-0.292388\pi\)
0.606963 + 0.794730i \(0.292388\pi\)
\(14\) −7.31912e41 −1.07346
\(15\) 5.85525e42 0.692172
\(16\) −2.93327e43 −0.328831
\(17\) 9.40723e44 1.15365 0.576827 0.816866i \(-0.304290\pi\)
0.576827 + 0.816866i \(0.304290\pi\)
\(18\) 3.97946e45 0.605867
\(19\) 1.72590e46 0.365182 0.182591 0.983189i \(-0.441552\pi\)
0.182591 + 0.983189i \(0.441552\pi\)
\(20\) 2.33335e47 0.759251
\(21\) −1.11655e48 −0.612172
\(22\) 3.13633e48 0.314771
\(23\) −5.77480e49 −1.14412 −0.572059 0.820212i \(-0.693855\pi\)
−0.572059 + 0.820212i \(0.693855\pi\)
\(24\) −1.07314e50 −0.449726
\(25\) 1.82849e51 1.72696
\(26\) −3.95373e51 −0.892236
\(27\) 1.34354e52 0.764668
\(28\) −4.44951e52 −0.671497
\(29\) −8.69385e52 −0.364490 −0.182245 0.983253i \(-0.558336\pi\)
−0.182245 + 0.983253i \(0.558336\pi\)
\(30\) −4.18242e53 −0.508746
\(31\) 1.48414e54 0.545472 0.272736 0.962089i \(-0.412071\pi\)
0.272736 + 0.962089i \(0.412071\pi\)
\(32\) −7.20614e54 −0.831244
\(33\) 4.78454e54 0.179507
\(34\) −6.71960e55 −0.847936
\(35\) −5.50582e56 −2.41178
\(36\) 2.41923e56 0.378997
\(37\) −2.64558e57 −1.52461 −0.762304 0.647219i \(-0.775932\pi\)
−0.762304 + 0.647219i \(0.775932\pi\)
\(38\) −1.23282e57 −0.268409
\(39\) −6.03150e57 −0.508823
\(40\) −5.29179e58 −1.77179
\(41\) 3.07305e57 0.0417791 0.0208896 0.999782i \(-0.493350\pi\)
0.0208896 + 0.999782i \(0.493350\pi\)
\(42\) 7.97553e58 0.449946
\(43\) 3.24223e59 0.774900 0.387450 0.921891i \(-0.373356\pi\)
0.387450 + 0.921891i \(0.373356\pi\)
\(44\) 1.90667e59 0.196903
\(45\) 2.99355e60 1.36122
\(46\) 4.12496e60 0.840927
\(47\) −8.51145e60 −0.791465 −0.395732 0.918366i \(-0.629509\pi\)
−0.395732 + 0.918366i \(0.629509\pi\)
\(48\) 3.19634e60 0.137831
\(49\) 5.57697e61 1.13303
\(50\) −1.30610e62 −1.26932
\(51\) −1.02509e62 −0.483560
\(52\) −2.40359e62 −0.558133
\(53\) −8.36780e62 −0.969488 −0.484744 0.874656i \(-0.661087\pi\)
−0.484744 + 0.874656i \(0.661087\pi\)
\(54\) −9.59693e62 −0.562031
\(55\) 2.35931e63 0.707207
\(56\) 1.00910e64 1.56701
\(57\) −1.88069e63 −0.153068
\(58\) 6.21004e63 0.267900
\(59\) 2.35468e64 0.544293 0.272147 0.962256i \(-0.412266\pi\)
0.272147 + 0.962256i \(0.412266\pi\)
\(60\) −2.54261e64 −0.318244
\(61\) 5.89372e64 0.403507 0.201753 0.979436i \(-0.435336\pi\)
0.201753 + 0.979436i \(0.435336\pi\)
\(62\) −1.06012e65 −0.400922
\(63\) −5.70846e65 −1.20390
\(64\) 7.91776e65 0.939795
\(65\) −2.97420e66 −2.00462
\(66\) −3.41761e65 −0.131938
\(67\) 6.87121e66 1.53216 0.766078 0.642747i \(-0.222206\pi\)
0.766078 + 0.642747i \(0.222206\pi\)
\(68\) −4.08505e66 −0.530422
\(69\) 6.29271e66 0.479563
\(70\) 3.93282e67 1.77266
\(71\) 8.24197e66 0.221361 0.110681 0.993856i \(-0.464697\pi\)
0.110681 + 0.993856i \(0.464697\pi\)
\(72\) −5.48655e67 −0.884430
\(73\) −1.53931e68 −1.49983 −0.749913 0.661537i \(-0.769905\pi\)
−0.749913 + 0.661537i \(0.769905\pi\)
\(74\) 1.88974e68 1.12059
\(75\) −1.99248e68 −0.723865
\(76\) −7.49465e67 −0.167902
\(77\) −4.49901e68 −0.625469
\(78\) 4.30831e68 0.373985
\(79\) −3.64169e68 −0.198570 −0.0992850 0.995059i \(-0.531656\pi\)
−0.0992850 + 0.995059i \(0.531656\pi\)
\(80\) 1.57615e69 0.543016
\(81\) 2.30121e69 0.503795
\(82\) −2.19509e68 −0.0307076
\(83\) 1.69878e70 1.52682 0.763409 0.645915i \(-0.223524\pi\)
0.763409 + 0.645915i \(0.223524\pi\)
\(84\) 4.84856e69 0.281461
\(85\) −5.05483e70 −1.90509
\(86\) −2.31594e70 −0.569552
\(87\) 9.47355e69 0.152778
\(88\) −4.32412e70 −0.459495
\(89\) 7.76576e69 0.0546322 0.0273161 0.999627i \(-0.491304\pi\)
0.0273161 + 0.999627i \(0.491304\pi\)
\(90\) −2.13830e71 −1.00050
\(91\) 5.67155e71 1.77293
\(92\) 2.50768e71 0.526038
\(93\) −1.61724e71 −0.228637
\(94\) 6.07975e71 0.581726
\(95\) −9.27387e71 −0.603044
\(96\) 7.85241e71 0.348420
\(97\) 4.51236e71 0.137162 0.0685812 0.997646i \(-0.478153\pi\)
0.0685812 + 0.997646i \(0.478153\pi\)
\(98\) −3.98365e72 −0.832777
\(99\) 2.44614e72 0.353018
\(100\) −7.94014e72 −0.794014
\(101\) −9.01684e72 −0.627082 −0.313541 0.949575i \(-0.601515\pi\)
−0.313541 + 0.949575i \(0.601515\pi\)
\(102\) 7.32224e72 0.355417
\(103\) −2.78483e73 −0.946762 −0.473381 0.880858i \(-0.656967\pi\)
−0.473381 + 0.880858i \(0.656967\pi\)
\(104\) 5.45108e73 1.30246
\(105\) 5.99960e73 1.01091
\(106\) 5.97714e73 0.712573
\(107\) 7.06643e72 0.0597988 0.0298994 0.999553i \(-0.490481\pi\)
0.0298994 + 0.999553i \(0.490481\pi\)
\(108\) −5.83426e73 −0.351576
\(109\) −1.98041e74 −0.852486 −0.426243 0.904609i \(-0.640163\pi\)
−0.426243 + 0.904609i \(0.640163\pi\)
\(110\) −1.68526e74 −0.519797
\(111\) 2.88285e74 0.639047
\(112\) −3.00559e74 −0.480255
\(113\) −1.25005e75 −1.44400 −0.721998 0.691896i \(-0.756776\pi\)
−0.721998 + 0.691896i \(0.756776\pi\)
\(114\) 1.34338e74 0.112505
\(115\) 3.10300e75 1.88934
\(116\) 3.77527e74 0.167583
\(117\) −3.08366e75 −1.00065
\(118\) −1.68195e75 −0.400055
\(119\) 9.63915e75 1.68490
\(120\) 5.76637e75 0.742655
\(121\) −8.58365e75 −0.816594
\(122\) −4.20990e75 −0.296577
\(123\) −3.34866e74 −0.0175119
\(124\) −6.44481e75 −0.250795
\(125\) −4.13587e76 −1.20047
\(126\) 4.07756e76 0.884863
\(127\) −7.12034e76 −1.15788 −0.578942 0.815369i \(-0.696534\pi\)
−0.578942 + 0.815369i \(0.696534\pi\)
\(128\) 1.15033e76 0.140494
\(129\) −3.53301e76 −0.324803
\(130\) 2.12447e77 1.47339
\(131\) 2.45112e77 1.28517 0.642587 0.766213i \(-0.277861\pi\)
0.642587 + 0.766213i \(0.277861\pi\)
\(132\) −2.07767e76 −0.0825330
\(133\) 1.76845e77 0.533345
\(134\) −4.90812e77 −1.12613
\(135\) −7.21930e77 −1.26274
\(136\) 9.26444e77 1.23780
\(137\) −6.33470e77 −0.647776 −0.323888 0.946095i \(-0.604990\pi\)
−0.323888 + 0.946095i \(0.604990\pi\)
\(138\) −4.49490e77 −0.352479
\(139\) −1.79078e78 −1.07895 −0.539475 0.842002i \(-0.681377\pi\)
−0.539475 + 0.842002i \(0.681377\pi\)
\(140\) 2.39088e78 1.10888
\(141\) 9.27478e77 0.331746
\(142\) −5.88726e77 −0.162700
\(143\) −2.43033e78 −0.519876
\(144\) 1.63416e78 0.271059
\(145\) 4.67151e78 0.601901
\(146\) 1.09953e79 1.10237
\(147\) −6.07714e78 −0.474915
\(148\) 1.14883e79 0.700977
\(149\) −2.55369e79 −1.21862 −0.609310 0.792932i \(-0.708554\pi\)
−0.609310 + 0.792932i \(0.708554\pi\)
\(150\) 1.42323e79 0.532040
\(151\) −4.58400e79 −1.34458 −0.672289 0.740289i \(-0.734689\pi\)
−0.672289 + 0.740289i \(0.734689\pi\)
\(152\) 1.69971e79 0.391817
\(153\) −5.24087e79 −0.950968
\(154\) 3.21365e79 0.459719
\(155\) −7.97479e79 −0.900767
\(156\) 2.61915e79 0.233944
\(157\) 2.23717e80 1.58257 0.791283 0.611450i \(-0.209414\pi\)
0.791283 + 0.611450i \(0.209414\pi\)
\(158\) 2.60126e79 0.145949
\(159\) 9.11826e79 0.406366
\(160\) 3.87211e80 1.37268
\(161\) −5.91717e80 −1.67097
\(162\) −1.64376e80 −0.370289
\(163\) 1.41890e80 0.255331 0.127665 0.991817i \(-0.459252\pi\)
0.127665 + 0.991817i \(0.459252\pi\)
\(164\) −1.33446e79 −0.0192090
\(165\) −2.57090e80 −0.296429
\(166\) −1.21344e81 −1.12221
\(167\) 5.60731e80 0.416489 0.208244 0.978077i \(-0.433225\pi\)
0.208244 + 0.978077i \(0.433225\pi\)
\(168\) −1.09960e81 −0.656820
\(169\) 9.84674e80 0.473618
\(170\) 3.61067e81 1.40024
\(171\) −9.61519e80 −0.301023
\(172\) −1.40793e81 −0.356280
\(173\) −3.93500e81 −0.805864 −0.402932 0.915230i \(-0.632009\pi\)
−0.402932 + 0.915230i \(0.632009\pi\)
\(174\) −6.76698e80 −0.112292
\(175\) 1.87357e82 2.52221
\(176\) 1.28793e81 0.140825
\(177\) −2.56585e81 −0.228143
\(178\) −5.54710e80 −0.0401547
\(179\) −3.22411e82 −1.90228 −0.951140 0.308759i \(-0.900086\pi\)
−0.951140 + 0.308759i \(0.900086\pi\)
\(180\) −1.29994e82 −0.625857
\(181\) 3.64648e82 1.43419 0.717095 0.696976i \(-0.245472\pi\)
0.717095 + 0.696976i \(0.245472\pi\)
\(182\) −4.05120e82 −1.30310
\(183\) −6.42229e81 −0.169132
\(184\) −5.68715e82 −1.22756
\(185\) 1.42156e83 2.51766
\(186\) 1.15520e82 0.168048
\(187\) −4.13049e82 −0.494064
\(188\) 3.69606e82 0.363896
\(189\) 1.37666e83 1.11679
\(190\) 6.62435e82 0.443238
\(191\) −1.38052e83 −0.762649 −0.381325 0.924441i \(-0.624532\pi\)
−0.381325 + 0.924441i \(0.624532\pi\)
\(192\) −8.62785e82 −0.393920
\(193\) −2.46248e83 −0.930101 −0.465051 0.885284i \(-0.653964\pi\)
−0.465051 + 0.885284i \(0.653964\pi\)
\(194\) −3.22319e82 −0.100814
\(195\) 3.24093e83 0.840246
\(196\) −2.42178e83 −0.520940
\(197\) −4.95791e83 −0.885689 −0.442844 0.896598i \(-0.646031\pi\)
−0.442844 + 0.896598i \(0.646031\pi\)
\(198\) −1.74729e83 −0.259468
\(199\) −4.06154e82 −0.0501826 −0.0250913 0.999685i \(-0.507988\pi\)
−0.0250913 + 0.999685i \(0.507988\pi\)
\(200\) 1.80074e84 1.85292
\(201\) −7.48745e83 −0.642211
\(202\) 6.44075e83 0.460905
\(203\) −8.90819e83 −0.532334
\(204\) 4.45141e83 0.222329
\(205\) −1.65126e83 −0.0689920
\(206\) 1.98921e84 0.695870
\(207\) 3.21721e84 0.943108
\(208\) −1.62359e84 −0.399177
\(209\) −7.57803e83 −0.156393
\(210\) −4.28553e84 −0.743019
\(211\) −9.12088e84 −1.32962 −0.664810 0.747013i \(-0.731487\pi\)
−0.664810 + 0.747013i \(0.731487\pi\)
\(212\) 3.63368e84 0.445747
\(213\) −8.98114e83 −0.0927846
\(214\) −5.04757e83 −0.0439521
\(215\) −1.74216e85 −1.27963
\(216\) 1.32315e85 0.820439
\(217\) 1.52073e85 0.796657
\(218\) 1.41461e85 0.626577
\(219\) 1.67736e85 0.628659
\(220\) −1.02452e85 −0.325156
\(221\) 5.20699e85 1.40045
\(222\) −2.05922e85 −0.469699
\(223\) −1.10503e85 −0.213918 −0.106959 0.994263i \(-0.534111\pi\)
−0.106959 + 0.994263i \(0.534111\pi\)
\(224\) −7.38379e85 −1.21402
\(225\) −1.01867e86 −1.42355
\(226\) 8.92917e85 1.06134
\(227\) 9.88450e84 0.100003 0.0500013 0.998749i \(-0.484077\pi\)
0.0500013 + 0.998749i \(0.484077\pi\)
\(228\) 8.16680e84 0.0703769
\(229\) 6.28394e85 0.461569 0.230785 0.973005i \(-0.425871\pi\)
0.230785 + 0.973005i \(0.425871\pi\)
\(230\) −2.21648e86 −1.38867
\(231\) 4.90250e85 0.262168
\(232\) −8.56190e85 −0.391074
\(233\) 7.37366e85 0.287867 0.143934 0.989587i \(-0.454025\pi\)
0.143934 + 0.989587i \(0.454025\pi\)
\(234\) 2.20267e86 0.735478
\(235\) 4.57349e86 1.30699
\(236\) −1.02251e86 −0.250253
\(237\) 3.96828e85 0.0832316
\(238\) −6.88526e86 −1.23840
\(239\) 5.40038e86 0.833491 0.416746 0.909023i \(-0.363171\pi\)
0.416746 + 0.909023i \(0.363171\pi\)
\(240\) −1.71750e86 −0.227608
\(241\) 4.43408e86 0.504873 0.252436 0.967614i \(-0.418768\pi\)
0.252436 + 0.967614i \(0.418768\pi\)
\(242\) 6.13132e86 0.600196
\(243\) −1.15879e87 −0.975836
\(244\) −2.55932e86 −0.185522
\(245\) −2.99670e87 −1.87103
\(246\) 2.39195e85 0.0128713
\(247\) 9.55303e86 0.443305
\(248\) 1.46161e87 0.585256
\(249\) −1.85113e87 −0.639973
\(250\) 2.95426e87 0.882345
\(251\) −4.58295e86 −0.118319 −0.0591595 0.998249i \(-0.518842\pi\)
−0.0591595 + 0.998249i \(0.518842\pi\)
\(252\) 2.47887e87 0.553521
\(253\) 2.53558e87 0.489980
\(254\) 5.08608e87 0.851044
\(255\) 5.50816e87 0.798528
\(256\) −8.29980e87 −1.04306
\(257\) −5.46778e87 −0.596008 −0.298004 0.954565i \(-0.596321\pi\)
−0.298004 + 0.954565i \(0.596321\pi\)
\(258\) 2.52364e87 0.238730
\(259\) −2.71080e88 −2.22667
\(260\) 1.29153e88 0.921675
\(261\) 4.84344e87 0.300452
\(262\) −1.75084e88 −0.944603
\(263\) −5.24740e87 −0.246354 −0.123177 0.992385i \(-0.539308\pi\)
−0.123177 + 0.992385i \(0.539308\pi\)
\(264\) 4.71192e87 0.192599
\(265\) 4.49631e88 1.60096
\(266\) −1.26321e88 −0.392009
\(267\) −8.46222e86 −0.0228994
\(268\) −2.98379e88 −0.704448
\(269\) −6.27826e87 −0.129384 −0.0646920 0.997905i \(-0.520607\pi\)
−0.0646920 + 0.997905i \(0.520607\pi\)
\(270\) 5.15676e88 0.928111
\(271\) 8.67497e88 1.36423 0.682117 0.731243i \(-0.261059\pi\)
0.682117 + 0.731243i \(0.261059\pi\)
\(272\) −2.75940e88 −0.379358
\(273\) −6.18019e88 −0.743131
\(274\) 4.52489e88 0.476116
\(275\) −8.02848e88 −0.739588
\(276\) −2.73258e88 −0.220491
\(277\) 1.05020e89 0.742610 0.371305 0.928511i \(-0.378910\pi\)
0.371305 + 0.928511i \(0.378910\pi\)
\(278\) 1.27916e89 0.793027
\(279\) −8.26830e88 −0.449638
\(280\) −5.42225e89 −2.58768
\(281\) −1.29679e89 −0.543362 −0.271681 0.962387i \(-0.587580\pi\)
−0.271681 + 0.962387i \(0.587580\pi\)
\(282\) −6.62500e88 −0.243833
\(283\) 5.99633e89 1.93946 0.969729 0.244182i \(-0.0785194\pi\)
0.969729 + 0.244182i \(0.0785194\pi\)
\(284\) −3.57904e88 −0.101776
\(285\) 1.01056e89 0.252769
\(286\) 1.73599e89 0.382109
\(287\) 3.14881e88 0.0610180
\(288\) 4.01462e89 0.685202
\(289\) 2.20036e89 0.330920
\(290\) −3.33687e89 −0.442397
\(291\) −4.91704e88 −0.0574923
\(292\) 6.68437e89 0.689583
\(293\) −3.90288e89 −0.355400 −0.177700 0.984085i \(-0.556866\pi\)
−0.177700 + 0.984085i \(0.556866\pi\)
\(294\) 4.34091e89 0.349063
\(295\) −1.26525e90 −0.898819
\(296\) −2.60543e90 −1.63580
\(297\) −5.89917e89 −0.327477
\(298\) 1.82410e90 0.895686
\(299\) −3.19641e90 −1.38888
\(300\) 8.65225e89 0.332815
\(301\) 3.32217e90 1.13173
\(302\) 3.27436e90 0.988265
\(303\) 9.82550e89 0.262844
\(304\) −5.06254e89 −0.120083
\(305\) −3.16690e90 −0.666331
\(306\) 3.74356e90 0.698962
\(307\) −5.03208e90 −0.834059 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(308\) 1.95368e90 0.287575
\(309\) 3.03459e90 0.396840
\(310\) 5.69641e90 0.662063
\(311\) 5.56953e90 0.575525 0.287763 0.957702i \(-0.407089\pi\)
0.287763 + 0.957702i \(0.407089\pi\)
\(312\) −5.93995e90 −0.545934
\(313\) −1.93772e91 −1.58461 −0.792305 0.610125i \(-0.791119\pi\)
−0.792305 + 0.610125i \(0.791119\pi\)
\(314\) −1.59802e91 −1.16319
\(315\) 3.06735e91 1.98805
\(316\) 1.58139e90 0.0912976
\(317\) −1.45832e91 −0.750221 −0.375110 0.926980i \(-0.622395\pi\)
−0.375110 + 0.926980i \(0.622395\pi\)
\(318\) −6.51319e90 −0.298679
\(319\) 3.81727e90 0.156096
\(320\) −4.25448e91 −1.55193
\(321\) −7.70018e89 −0.0250650
\(322\) 4.22665e91 1.22817
\(323\) 1.62360e91 0.421294
\(324\) −9.99291e90 −0.231632
\(325\) 1.01209e92 2.09640
\(326\) −1.01352e91 −0.187668
\(327\) 2.15802e91 0.357324
\(328\) 3.02641e90 0.0448263
\(329\) −8.72128e91 −1.15593
\(330\) 1.83640e91 0.217876
\(331\) −5.05919e91 −0.537476 −0.268738 0.963213i \(-0.586607\pi\)
−0.268738 + 0.963213i \(0.586607\pi\)
\(332\) −7.37688e91 −0.701993
\(333\) 1.47388e92 1.25675
\(334\) −4.00531e91 −0.306119
\(335\) −3.69214e92 −2.53013
\(336\) 3.27514e91 0.201301
\(337\) 1.39888e92 0.771419 0.385710 0.922620i \(-0.373957\pi\)
0.385710 + 0.922620i \(0.373957\pi\)
\(338\) −7.03355e91 −0.348109
\(339\) 1.36216e92 0.605258
\(340\) 2.19504e92 0.875913
\(341\) −6.51650e91 −0.233604
\(342\) 6.86815e91 0.221252
\(343\) 6.70944e91 0.194290
\(344\) 3.19302e92 0.831417
\(345\) −3.38129e92 −0.791927
\(346\) 2.81078e92 0.592310
\(347\) −9.06972e91 −0.172016 −0.0860078 0.996294i \(-0.527411\pi\)
−0.0860078 + 0.996294i \(0.527411\pi\)
\(348\) −4.11385e91 −0.0702434
\(349\) 4.50813e92 0.693216 0.346608 0.938010i \(-0.387333\pi\)
0.346608 + 0.938010i \(0.387333\pi\)
\(350\) −1.33830e93 −1.85382
\(351\) 7.43661e92 0.928251
\(352\) 3.16405e92 0.355988
\(353\) −1.31440e93 −1.33337 −0.666685 0.745339i \(-0.732288\pi\)
−0.666685 + 0.745339i \(0.732288\pi\)
\(354\) 1.83279e92 0.167685
\(355\) −4.42869e92 −0.365545
\(356\) −3.37225e91 −0.0251185
\(357\) −1.05036e93 −0.706235
\(358\) 2.30299e93 1.39818
\(359\) −1.25513e93 −0.688245 −0.344122 0.938925i \(-0.611824\pi\)
−0.344122 + 0.938925i \(0.611824\pi\)
\(360\) 2.94811e93 1.46050
\(361\) −1.93576e93 −0.866642
\(362\) −2.60469e93 −1.05413
\(363\) 9.35346e92 0.342279
\(364\) −2.46285e93 −0.815148
\(365\) 8.27122e93 2.47674
\(366\) 4.58746e92 0.124312
\(367\) 5.71510e93 1.40189 0.700943 0.713217i \(-0.252763\pi\)
0.700943 + 0.713217i \(0.252763\pi\)
\(368\) 1.69391e93 0.376222
\(369\) −1.71203e92 −0.0344389
\(370\) −1.01542e94 −1.85048
\(371\) −8.57410e93 −1.41593
\(372\) 7.02280e92 0.105122
\(373\) −3.74173e93 −0.507809 −0.253905 0.967229i \(-0.581715\pi\)
−0.253905 + 0.967229i \(0.581715\pi\)
\(374\) 2.95042e93 0.363137
\(375\) 4.50679e93 0.503183
\(376\) −8.38226e93 −0.849190
\(377\) −4.81213e93 −0.442464
\(378\) −9.83353e93 −0.820841
\(379\) 2.02793e94 1.53717 0.768586 0.639747i \(-0.220961\pi\)
0.768586 + 0.639747i \(0.220961\pi\)
\(380\) 4.02714e93 0.277265
\(381\) 7.75892e93 0.485333
\(382\) 9.86109e93 0.560547
\(383\) −8.75423e93 −0.452337 −0.226169 0.974088i \(-0.572620\pi\)
−0.226169 + 0.974088i \(0.572620\pi\)
\(384\) −1.25350e93 −0.0588889
\(385\) 2.41747e94 1.03287
\(386\) 1.75895e94 0.683624
\(387\) −1.80628e94 −0.638757
\(388\) −1.95947e93 −0.0630639
\(389\) −1.08943e94 −0.319182 −0.159591 0.987183i \(-0.551018\pi\)
−0.159591 + 0.987183i \(0.551018\pi\)
\(390\) −2.31500e94 −0.617581
\(391\) −5.43249e94 −1.31992
\(392\) 5.49233e94 1.21567
\(393\) −2.67094e94 −0.538687
\(394\) 3.54144e94 0.650981
\(395\) 1.95680e94 0.327909
\(396\) −1.06223e94 −0.162309
\(397\) −1.01644e95 −1.41654 −0.708268 0.705944i \(-0.750523\pi\)
−0.708268 + 0.705944i \(0.750523\pi\)
\(398\) 2.90116e93 0.0368842
\(399\) −1.92705e94 −0.223554
\(400\) −5.36347e94 −0.567879
\(401\) 1.22596e95 1.18497 0.592483 0.805583i \(-0.298148\pi\)
0.592483 + 0.805583i \(0.298148\pi\)
\(402\) 5.34830e94 0.472025
\(403\) 8.21484e94 0.662163
\(404\) 3.91552e94 0.288317
\(405\) −1.23652e95 −0.831942
\(406\) 6.36314e94 0.391265
\(407\) 1.16161e95 0.652928
\(408\) −1.00953e95 −0.518828
\(409\) 2.38071e94 0.111894 0.0559469 0.998434i \(-0.482182\pi\)
0.0559469 + 0.998434i \(0.482182\pi\)
\(410\) 1.17950e94 0.0507091
\(411\) 6.90281e94 0.271519
\(412\) 1.20930e95 0.435298
\(413\) 2.41273e95 0.794935
\(414\) −2.29806e95 −0.693184
\(415\) −9.12814e95 −2.52131
\(416\) −3.98866e95 −1.00907
\(417\) 1.95138e95 0.452247
\(418\) 5.41300e94 0.114949
\(419\) 6.44324e95 1.25399 0.626993 0.779025i \(-0.284286\pi\)
0.626993 + 0.779025i \(0.284286\pi\)
\(420\) −2.60530e95 −0.464792
\(421\) −6.80537e95 −1.11315 −0.556577 0.830796i \(-0.687886\pi\)
−0.556577 + 0.830796i \(0.687886\pi\)
\(422\) 6.51507e95 0.977270
\(423\) 4.74182e95 0.652412
\(424\) −8.24080e95 −1.04020
\(425\) 1.72010e96 1.99232
\(426\) 6.41525e94 0.0681966
\(427\) 6.03902e95 0.589318
\(428\) −3.06857e94 −0.0274940
\(429\) 2.64829e95 0.217908
\(430\) 1.24443e96 0.940530
\(431\) −2.50780e96 −1.74130 −0.870649 0.491904i \(-0.836301\pi\)
−0.870649 + 0.491904i \(0.836301\pi\)
\(432\) −3.94097e95 −0.251447
\(433\) −1.03865e96 −0.609063 −0.304531 0.952502i \(-0.598500\pi\)
−0.304531 + 0.952502i \(0.598500\pi\)
\(434\) −1.08626e96 −0.585543
\(435\) −5.09046e95 −0.252290
\(436\) 8.59983e95 0.391952
\(437\) −9.96675e95 −0.417812
\(438\) −1.19814e96 −0.462064
\(439\) 4.08395e96 1.44919 0.724596 0.689174i \(-0.242027\pi\)
0.724596 + 0.689174i \(0.242027\pi\)
\(440\) 2.32350e96 0.758787
\(441\) −3.10699e96 −0.933968
\(442\) −3.71936e96 −1.02933
\(443\) 2.68993e96 0.685496 0.342748 0.939427i \(-0.388642\pi\)
0.342748 + 0.939427i \(0.388642\pi\)
\(444\) −1.25186e96 −0.293818
\(445\) −4.17281e95 −0.0902170
\(446\) 7.89325e95 0.157229
\(447\) 2.78271e96 0.510791
\(448\) 8.11296e96 1.37256
\(449\) −8.90575e96 −1.38893 −0.694463 0.719528i \(-0.744358\pi\)
−0.694463 + 0.719528i \(0.744358\pi\)
\(450\) 7.27640e96 1.04631
\(451\) −1.34931e95 −0.0178923
\(452\) 5.42831e96 0.663913
\(453\) 4.99511e96 0.563587
\(454\) −7.06052e95 −0.0735019
\(455\) −3.04752e97 −2.92773
\(456\) −1.85214e96 −0.164232
\(457\) 1.95894e97 1.60354 0.801769 0.597634i \(-0.203892\pi\)
0.801769 + 0.597634i \(0.203892\pi\)
\(458\) −4.48863e96 −0.339253
\(459\) 1.26390e97 0.882163
\(460\) −1.34746e97 −0.868673
\(461\) −1.16420e97 −0.693335 −0.346667 0.937988i \(-0.612687\pi\)
−0.346667 + 0.937988i \(0.612687\pi\)
\(462\) −3.50187e96 −0.192694
\(463\) −2.97083e97 −1.51068 −0.755338 0.655336i \(-0.772527\pi\)
−0.755338 + 0.655336i \(0.772527\pi\)
\(464\) 2.55014e96 0.119856
\(465\) 8.69000e96 0.377561
\(466\) −5.26702e96 −0.211582
\(467\) 3.83937e97 1.42624 0.713122 0.701040i \(-0.247281\pi\)
0.713122 + 0.701040i \(0.247281\pi\)
\(468\) 1.33907e97 0.460075
\(469\) 7.04061e97 2.23770
\(470\) −3.26686e97 −0.960635
\(471\) −2.43781e97 −0.663340
\(472\) 2.31894e97 0.583991
\(473\) −1.42359e97 −0.331859
\(474\) −2.83455e96 −0.0611752
\(475\) 3.15580e97 0.630656
\(476\) −4.18576e97 −0.774676
\(477\) 4.66180e97 0.799158
\(478\) −3.85751e97 −0.612616
\(479\) 7.62727e93 0.000112234 0 5.61168e−5 1.00000i \(-0.499982\pi\)
5.61168e−5 1.00000i \(0.499982\pi\)
\(480\) −4.21937e97 −0.575364
\(481\) −1.46435e98 −1.85076
\(482\) −3.16728e97 −0.371081
\(483\) 6.44785e97 0.700397
\(484\) 3.72741e97 0.375450
\(485\) −2.42464e97 −0.226503
\(486\) 8.27729e97 0.717239
\(487\) −7.46183e97 −0.599844 −0.299922 0.953964i \(-0.596961\pi\)
−0.299922 + 0.953964i \(0.596961\pi\)
\(488\) 5.80427e97 0.432936
\(489\) −1.54615e97 −0.107023
\(490\) 2.14055e98 1.37521
\(491\) 8.28295e97 0.493982 0.246991 0.969018i \(-0.420558\pi\)
0.246991 + 0.969018i \(0.420558\pi\)
\(492\) 1.45414e96 0.00805155
\(493\) −8.17850e97 −0.420495
\(494\) −6.82375e97 −0.325829
\(495\) −1.31440e98 −0.582957
\(496\) −4.35338e97 −0.179368
\(497\) 8.44516e97 0.323296
\(498\) 1.32227e98 0.470380
\(499\) 1.76754e98 0.584387 0.292193 0.956359i \(-0.405615\pi\)
0.292193 + 0.956359i \(0.405615\pi\)
\(500\) 1.79598e98 0.551946
\(501\) −6.11019e97 −0.174573
\(502\) 3.27361e97 0.0869644
\(503\) −6.60146e98 −1.63083 −0.815414 0.578878i \(-0.803491\pi\)
−0.815414 + 0.578878i \(0.803491\pi\)
\(504\) −5.62181e98 −1.29170
\(505\) 4.84506e98 1.03553
\(506\) −1.81117e98 −0.360135
\(507\) −1.07298e98 −0.198519
\(508\) 3.09198e98 0.532366
\(509\) 4.28277e98 0.686319 0.343159 0.939277i \(-0.388503\pi\)
0.343159 + 0.939277i \(0.388503\pi\)
\(510\) −3.93449e98 −0.586918
\(511\) −1.57726e99 −2.19048
\(512\) 4.84211e98 0.626153
\(513\) 2.31882e98 0.279243
\(514\) 3.90565e98 0.438066
\(515\) 1.49639e99 1.56344
\(516\) 1.53419e98 0.149337
\(517\) 3.73718e98 0.338952
\(518\) 1.93633e99 1.63661
\(519\) 4.28790e98 0.337782
\(520\) −2.92905e99 −2.15083
\(521\) 9.97828e98 0.683091 0.341546 0.939865i \(-0.389050\pi\)
0.341546 + 0.939865i \(0.389050\pi\)
\(522\) −3.45968e98 −0.220832
\(523\) −5.97094e98 −0.355411 −0.177706 0.984084i \(-0.556867\pi\)
−0.177706 + 0.984084i \(0.556867\pi\)
\(524\) −1.06439e99 −0.590891
\(525\) −2.04160e99 −1.05720
\(526\) 3.74823e98 0.181070
\(527\) 1.39616e99 0.629287
\(528\) −1.40344e98 −0.0590276
\(529\) 7.87231e98 0.309008
\(530\) −3.21172e99 −1.17671
\(531\) −1.31182e99 −0.448666
\(532\) −7.67942e98 −0.245219
\(533\) 1.70096e98 0.0507168
\(534\) 6.04458e97 0.0168310
\(535\) −3.79704e98 −0.0987488
\(536\) 6.76692e99 1.64390
\(537\) 3.51326e99 0.797350
\(538\) 4.48457e98 0.0950973
\(539\) −2.44872e99 −0.485231
\(540\) 3.13495e99 0.580575
\(541\) 6.65195e99 1.15146 0.575730 0.817640i \(-0.304718\pi\)
0.575730 + 0.817640i \(0.304718\pi\)
\(542\) −6.19655e99 −1.00271
\(543\) −3.97351e99 −0.601147
\(544\) −6.77898e99 −0.958968
\(545\) 1.06414e100 1.40775
\(546\) 4.41453e99 0.546201
\(547\) −1.55974e100 −1.80515 −0.902576 0.430531i \(-0.858326\pi\)
−0.902576 + 0.430531i \(0.858326\pi\)
\(548\) 2.75081e99 0.297832
\(549\) −3.28346e99 −0.332614
\(550\) 5.73476e99 0.543597
\(551\) −1.50047e99 −0.133105
\(552\) 6.19720e99 0.514540
\(553\) −3.73147e99 −0.290009
\(554\) −7.50161e99 −0.545818
\(555\) −1.54905e100 −1.05529
\(556\) 7.77636e99 0.496074
\(557\) −2.03966e100 −1.21855 −0.609275 0.792959i \(-0.708540\pi\)
−0.609275 + 0.792959i \(0.708540\pi\)
\(558\) 5.90607e99 0.330484
\(559\) 1.79461e100 0.940672
\(560\) 1.61501e100 0.793070
\(561\) 4.50093e99 0.207089
\(562\) 9.26301e99 0.399371
\(563\) −3.81014e100 −1.53952 −0.769758 0.638336i \(-0.779623\pi\)
−0.769758 + 0.638336i \(0.779623\pi\)
\(564\) −4.02753e99 −0.152529
\(565\) 6.71697e100 2.38454
\(566\) −4.28319e100 −1.42550
\(567\) 2.35795e100 0.735787
\(568\) 8.11687e99 0.237506
\(569\) 2.20282e100 0.604480 0.302240 0.953232i \(-0.402266\pi\)
0.302240 + 0.953232i \(0.402266\pi\)
\(570\) −7.21844e99 −0.185785
\(571\) 7.36336e99 0.177770 0.0888850 0.996042i \(-0.471670\pi\)
0.0888850 + 0.996042i \(0.471670\pi\)
\(572\) 1.05536e100 0.239026
\(573\) 1.50433e100 0.319668
\(574\) −2.24921e99 −0.0448482
\(575\) −1.05592e101 −1.97585
\(576\) −4.41107e100 −0.774682
\(577\) −1.01125e101 −1.66702 −0.833512 0.552501i \(-0.813674\pi\)
−0.833512 + 0.552501i \(0.813674\pi\)
\(578\) −1.57172e100 −0.243226
\(579\) 2.68332e100 0.389857
\(580\) −2.02858e100 −0.276739
\(581\) 1.74066e101 2.22990
\(582\) 3.51225e99 0.0422568
\(583\) 3.67411e100 0.415192
\(584\) −1.51594e101 −1.60921
\(585\) 1.65696e101 1.65243
\(586\) 2.78784e100 0.261219
\(587\) −5.72321e100 −0.503906 −0.251953 0.967740i \(-0.581073\pi\)
−0.251953 + 0.967740i \(0.581073\pi\)
\(588\) 2.63897e100 0.218354
\(589\) 2.56148e100 0.199197
\(590\) 9.03770e100 0.660632
\(591\) 5.40255e100 0.371241
\(592\) 7.76021e100 0.501339
\(593\) −3.32917e100 −0.202227 −0.101114 0.994875i \(-0.532241\pi\)
−0.101114 + 0.994875i \(0.532241\pi\)
\(594\) 4.21379e100 0.240695
\(595\) −5.17945e101 −2.78236
\(596\) 1.10893e101 0.560292
\(597\) 4.42579e99 0.0210343
\(598\) 2.28320e101 1.02082
\(599\) −2.64261e100 −0.111162 −0.0555808 0.998454i \(-0.517701\pi\)
−0.0555808 + 0.998454i \(0.517701\pi\)
\(600\) −1.96224e101 −0.776659
\(601\) 8.61412e100 0.320843 0.160422 0.987049i \(-0.448715\pi\)
0.160422 + 0.987049i \(0.448715\pi\)
\(602\) −2.37303e101 −0.831824
\(603\) −3.82803e101 −1.26297
\(604\) 1.99058e101 0.618204
\(605\) 4.61229e101 1.34848
\(606\) −7.01838e100 −0.193191
\(607\) −1.93297e101 −0.501001 −0.250501 0.968116i \(-0.580595\pi\)
−0.250501 + 0.968116i \(0.580595\pi\)
\(608\) −1.24371e101 −0.303556
\(609\) 9.70710e100 0.223130
\(610\) 2.26212e101 0.489753
\(611\) −4.71116e101 −0.960780
\(612\) 2.27582e101 0.437232
\(613\) 4.68691e101 0.848358 0.424179 0.905578i \(-0.360563\pi\)
0.424179 + 0.905578i \(0.360563\pi\)
\(614\) 3.59443e101 0.613033
\(615\) 1.79935e100 0.0289183
\(616\) −4.43073e101 −0.671087
\(617\) 1.24724e102 1.78049 0.890246 0.455479i \(-0.150532\pi\)
0.890246 + 0.455479i \(0.150532\pi\)
\(618\) −2.16761e101 −0.291677
\(619\) −5.63173e101 −0.714386 −0.357193 0.934031i \(-0.616266\pi\)
−0.357193 + 0.934031i \(0.616266\pi\)
\(620\) 3.46302e101 0.414150
\(621\) −7.75868e101 −0.874871
\(622\) −3.97833e101 −0.423011
\(623\) 7.95721e100 0.0797898
\(624\) 1.76920e101 0.167317
\(625\) 2.86353e101 0.255436
\(626\) 1.38412e102 1.16469
\(627\) 8.25766e100 0.0655528
\(628\) −9.71481e101 −0.727625
\(629\) −2.48876e102 −1.75887
\(630\) −2.19102e102 −1.46122
\(631\) −1.04720e102 −0.659111 −0.329555 0.944136i \(-0.606899\pi\)
−0.329555 + 0.944136i \(0.606899\pi\)
\(632\) −3.58641e101 −0.213053
\(633\) 9.93888e101 0.557316
\(634\) 1.04168e102 0.551412
\(635\) 3.82600e102 1.91207
\(636\) −3.95956e101 −0.186837
\(637\) 3.08691e102 1.37542
\(638\) −2.72668e101 −0.114731
\(639\) −4.59169e101 −0.182470
\(640\) −6.18112e101 −0.232006
\(641\) 1.40637e102 0.498635 0.249317 0.968422i \(-0.419794\pi\)
0.249317 + 0.968422i \(0.419794\pi\)
\(642\) 5.50025e100 0.0184227
\(643\) −1.43530e102 −0.454195 −0.227098 0.973872i \(-0.572924\pi\)
−0.227098 + 0.973872i \(0.572924\pi\)
\(644\) 2.56951e102 0.768273
\(645\) 1.89841e102 0.536364
\(646\) −1.15974e102 −0.309651
\(647\) −4.09180e102 −1.03254 −0.516271 0.856425i \(-0.672680\pi\)
−0.516271 + 0.856425i \(0.672680\pi\)
\(648\) 2.26629e102 0.540539
\(649\) −1.03388e102 −0.233099
\(650\) −7.22936e102 −1.54086
\(651\) −1.65711e102 −0.333923
\(652\) −6.16150e101 −0.117395
\(653\) 6.20506e102 1.11793 0.558965 0.829191i \(-0.311198\pi\)
0.558965 + 0.829191i \(0.311198\pi\)
\(654\) −1.54148e102 −0.262633
\(655\) −1.31707e103 −2.12227
\(656\) −9.01411e100 −0.0137383
\(657\) 8.57564e102 1.23632
\(658\) 6.22963e102 0.849605
\(659\) 4.77744e102 0.616422 0.308211 0.951318i \(-0.400270\pi\)
0.308211 + 0.951318i \(0.400270\pi\)
\(660\) 1.11640e102 0.136291
\(661\) −6.60511e102 −0.763004 −0.381502 0.924368i \(-0.624593\pi\)
−0.381502 + 0.924368i \(0.624593\pi\)
\(662\) 3.61379e102 0.395045
\(663\) −5.67397e102 −0.587007
\(664\) 1.67300e103 1.63818
\(665\) −9.50250e102 −0.880740
\(666\) −1.05280e103 −0.923710
\(667\) 5.02053e102 0.417020
\(668\) −2.43495e102 −0.191491
\(669\) 1.20413e102 0.0896646
\(670\) 2.63730e103 1.85964
\(671\) −2.58780e102 −0.172806
\(672\) 8.04600e102 0.508864
\(673\) −1.40758e103 −0.843186 −0.421593 0.906785i \(-0.638529\pi\)
−0.421593 + 0.906785i \(0.638529\pi\)
\(674\) −9.99226e102 −0.566993
\(675\) 2.45665e103 1.32055
\(676\) −4.27590e102 −0.217758
\(677\) −1.99664e103 −0.963417 −0.481708 0.876332i \(-0.659984\pi\)
−0.481708 + 0.876332i \(0.659984\pi\)
\(678\) −9.72997e102 −0.444864
\(679\) 4.62360e102 0.200324
\(680\) −4.97810e103 −2.04404
\(681\) −1.07710e102 −0.0419166
\(682\) 4.65475e102 0.171699
\(683\) 9.40230e102 0.328760 0.164380 0.986397i \(-0.447438\pi\)
0.164380 + 0.986397i \(0.447438\pi\)
\(684\) 4.17535e102 0.138403
\(685\) 3.40385e103 1.06971
\(686\) −4.79257e102 −0.142803
\(687\) −6.84751e102 −0.193469
\(688\) −9.51036e102 −0.254811
\(689\) −4.63166e103 −1.17689
\(690\) 2.41526e103 0.582066
\(691\) 2.43467e103 0.556534 0.278267 0.960504i \(-0.410240\pi\)
0.278267 + 0.960504i \(0.410240\pi\)
\(692\) 1.70875e103 0.370516
\(693\) 2.50645e103 0.515580
\(694\) 6.47852e102 0.126431
\(695\) 9.62245e103 1.78172
\(696\) 9.32976e102 0.163920
\(697\) 2.89089e102 0.0481987
\(698\) −3.22017e103 −0.509514
\(699\) −8.03495e102 −0.120661
\(700\) −8.13590e103 −1.15965
\(701\) 5.37926e103 0.727805 0.363902 0.931437i \(-0.381444\pi\)
0.363902 + 0.931437i \(0.381444\pi\)
\(702\) −5.31199e103 −0.682264
\(703\) −4.56602e103 −0.556760
\(704\) −3.47650e103 −0.402476
\(705\) −4.98366e103 −0.547830
\(706\) 9.38879e103 0.980027
\(707\) −9.23913e103 −0.915846
\(708\) 1.11421e103 0.104895
\(709\) −1.07535e104 −0.961530 −0.480765 0.876849i \(-0.659641\pi\)
−0.480765 + 0.876849i \(0.659641\pi\)
\(710\) 3.16343e103 0.268675
\(711\) 2.02882e103 0.163683
\(712\) 7.64789e102 0.0586168
\(713\) −8.57061e103 −0.624085
\(714\) 7.50276e103 0.519082
\(715\) 1.30590e104 0.858498
\(716\) 1.40006e104 0.874622
\(717\) −5.88471e103 −0.349362
\(718\) 8.96545e103 0.505860
\(719\) 3.21953e104 1.72659 0.863293 0.504703i \(-0.168398\pi\)
0.863293 + 0.504703i \(0.168398\pi\)
\(720\) −8.78090e103 −0.447613
\(721\) −2.85349e104 −1.38274
\(722\) 1.38272e104 0.636982
\(723\) −4.83175e103 −0.211620
\(724\) −1.58347e104 −0.659405
\(725\) −1.58966e104 −0.629460
\(726\) −6.68120e103 −0.251575
\(727\) 1.43449e104 0.513678 0.256839 0.966454i \(-0.417319\pi\)
0.256839 + 0.966454i \(0.417319\pi\)
\(728\) 5.58547e104 1.90224
\(729\) −2.92561e103 −0.0947681
\(730\) −5.90815e104 −1.82040
\(731\) 3.05004e104 0.893968
\(732\) 2.78885e103 0.0777627
\(733\) −3.44849e104 −0.914817 −0.457408 0.889257i \(-0.651222\pi\)
−0.457408 + 0.889257i \(0.651222\pi\)
\(734\) −4.08231e104 −1.03039
\(735\) 3.26546e104 0.784252
\(736\) 4.16140e104 0.951042
\(737\) −3.01699e104 −0.656161
\(738\) 1.22291e103 0.0253126
\(739\) −6.34155e104 −1.24932 −0.624660 0.780897i \(-0.714762\pi\)
−0.624660 + 0.780897i \(0.714762\pi\)
\(740\) −6.17307e104 −1.15756
\(741\) −1.04098e104 −0.185813
\(742\) 6.12450e104 1.04071
\(743\) 4.62751e104 0.748611 0.374305 0.927305i \(-0.377881\pi\)
0.374305 + 0.927305i \(0.377881\pi\)
\(744\) −1.59270e104 −0.245313
\(745\) 1.37218e105 2.01237
\(746\) 2.67273e104 0.373240
\(747\) −9.46410e104 −1.25857
\(748\) 1.79365e104 0.227158
\(749\) 7.24065e103 0.0873355
\(750\) −3.21921e104 −0.369839
\(751\) 4.35926e104 0.477040 0.238520 0.971138i \(-0.423338\pi\)
0.238520 + 0.971138i \(0.423338\pi\)
\(752\) 2.49664e104 0.260258
\(753\) 4.99397e103 0.0495940
\(754\) 3.43731e104 0.325211
\(755\) 2.46314e105 2.22037
\(756\) −5.97809e104 −0.513473
\(757\) −7.98775e104 −0.653770 −0.326885 0.945064i \(-0.605999\pi\)
−0.326885 + 0.945064i \(0.605999\pi\)
\(758\) −1.44856e105 −1.12982
\(759\) −2.76298e104 −0.205378
\(760\) −9.13311e104 −0.647027
\(761\) −2.56065e105 −1.72906 −0.864529 0.502583i \(-0.832383\pi\)
−0.864529 + 0.502583i \(0.832383\pi\)
\(762\) −5.54221e104 −0.356719
\(763\) −2.02923e105 −1.24505
\(764\) 5.99485e104 0.350647
\(765\) 2.81610e105 1.57038
\(766\) 6.25316e104 0.332468
\(767\) 1.30333e105 0.660732
\(768\) 9.04415e104 0.437203
\(769\) −6.72521e104 −0.310023 −0.155012 0.987913i \(-0.549542\pi\)
−0.155012 + 0.987913i \(0.549542\pi\)
\(770\) −1.72681e105 −0.759158
\(771\) 5.95815e104 0.249820
\(772\) 1.06932e105 0.427638
\(773\) −2.46049e105 −0.938578 −0.469289 0.883045i \(-0.655490\pi\)
−0.469289 + 0.883045i \(0.655490\pi\)
\(774\) 1.29023e105 0.469487
\(775\) 2.71374e105 0.942010
\(776\) 4.44387e104 0.147166
\(777\) 2.95392e105 0.933322
\(778\) 7.78182e104 0.234599
\(779\) 5.30379e103 0.0152570
\(780\) −1.40736e105 −0.386324
\(781\) −3.61885e104 −0.0948000
\(782\) 3.88044e105 0.970140
\(783\) −1.16805e105 −0.278714
\(784\) −1.63588e105 −0.372576
\(785\) −1.20211e106 −2.61337
\(786\) 1.90786e105 0.395935
\(787\) 2.71217e105 0.537328 0.268664 0.963234i \(-0.413418\pi\)
0.268664 + 0.963234i \(0.413418\pi\)
\(788\) 2.15295e105 0.407218
\(789\) 5.71800e104 0.103260
\(790\) −1.39775e105 −0.241013
\(791\) −1.28087e106 −2.10894
\(792\) 2.40902e105 0.378766
\(793\) 3.26223e105 0.489828
\(794\) 7.26044e105 1.04115
\(795\) −4.89955e105 −0.671052
\(796\) 1.76370e104 0.0230727
\(797\) 1.45163e106 1.81395 0.906977 0.421179i \(-0.138384\pi\)
0.906977 + 0.421179i \(0.138384\pi\)
\(798\) 1.37650e105 0.164312
\(799\) −8.00691e105 −0.913077
\(800\) −1.31764e106 −1.43553
\(801\) −4.32639e104 −0.0450338
\(802\) −8.75705e105 −0.870950
\(803\) 6.75873e105 0.642315
\(804\) 3.25139e105 0.295273
\(805\) 3.17950e106 2.75937
\(806\) −5.86788e105 −0.486690
\(807\) 6.84131e104 0.0542320
\(808\) −8.87998e105 −0.672818
\(809\) 3.21507e104 0.0232847 0.0116423 0.999932i \(-0.496294\pi\)
0.0116423 + 0.999932i \(0.496294\pi\)
\(810\) 8.83250e105 0.611477
\(811\) 8.87148e105 0.587131 0.293566 0.955939i \(-0.405158\pi\)
0.293566 + 0.955939i \(0.405158\pi\)
\(812\) 3.86834e105 0.244754
\(813\) −9.45297e105 −0.571826
\(814\) −8.29742e105 −0.479902
\(815\) −7.62423e105 −0.421641
\(816\) 3.00687e105 0.159010
\(817\) 5.59578e105 0.282980
\(818\) −1.70055e105 −0.0822419
\(819\) −3.15968e106 −1.46144
\(820\) 7.17051e104 0.0317208
\(821\) 1.04180e105 0.0440817 0.0220409 0.999757i \(-0.492984\pi\)
0.0220409 + 0.999757i \(0.492984\pi\)
\(822\) −4.93070e105 −0.199566
\(823\) −1.21303e106 −0.469653 −0.234827 0.972037i \(-0.575452\pi\)
−0.234827 + 0.972037i \(0.575452\pi\)
\(824\) −2.74257e106 −1.01581
\(825\) 8.74850e105 0.310002
\(826\) −1.72342e106 −0.584277
\(827\) 2.35778e106 0.764808 0.382404 0.923995i \(-0.375096\pi\)
0.382404 + 0.923995i \(0.375096\pi\)
\(828\) −1.39706e106 −0.433618
\(829\) 1.61461e106 0.479543 0.239771 0.970829i \(-0.422928\pi\)
0.239771 + 0.970829i \(0.422928\pi\)
\(830\) 6.52025e106 1.85316
\(831\) −1.14439e106 −0.311269
\(832\) 4.38255e106 1.14084
\(833\) 5.24639e106 1.30713
\(834\) −1.39387e106 −0.332401
\(835\) −3.01300e106 −0.687769
\(836\) 3.29073e105 0.0719056
\(837\) 1.99400e106 0.417105
\(838\) −4.60242e106 −0.921679
\(839\) −5.26994e106 −1.01040 −0.505201 0.863002i \(-0.668582\pi\)
−0.505201 + 0.863002i \(0.668582\pi\)
\(840\) 5.90854e106 1.08464
\(841\) −4.93340e106 −0.867147
\(842\) 4.86109e106 0.818168
\(843\) 1.41309e106 0.227753
\(844\) 3.96070e106 0.611326
\(845\) −5.29099e106 −0.782109
\(846\) −3.38709e106 −0.479522
\(847\) −8.79527e106 −1.19263
\(848\) 2.45451e106 0.318798
\(849\) −6.53410e106 −0.812934
\(850\) −1.22867e107 −1.46435
\(851\) 1.52777e107 1.74433
\(852\) 3.90002e105 0.0426601
\(853\) 3.38806e105 0.0355068 0.0177534 0.999842i \(-0.494349\pi\)
0.0177534 + 0.999842i \(0.494349\pi\)
\(854\) −4.31369e106 −0.433148
\(855\) 5.16657e106 0.497095
\(856\) 6.95918e105 0.0641602
\(857\) 1.33280e107 1.17751 0.588754 0.808313i \(-0.299619\pi\)
0.588754 + 0.808313i \(0.299619\pi\)
\(858\) −1.89168e106 −0.160163
\(859\) −1.17251e107 −0.951405 −0.475702 0.879606i \(-0.657806\pi\)
−0.475702 + 0.879606i \(0.657806\pi\)
\(860\) 7.56527e106 0.588344
\(861\) −3.43121e105 −0.0255760
\(862\) 1.79133e107 1.27985
\(863\) −2.09858e107 −1.43725 −0.718623 0.695400i \(-0.755227\pi\)
−0.718623 + 0.695400i \(0.755227\pi\)
\(864\) −9.68173e106 −0.635626
\(865\) 2.11441e107 1.33076
\(866\) 7.41912e106 0.447661
\(867\) −2.39770e106 −0.138707
\(868\) −6.60369e106 −0.366283
\(869\) 1.59898e106 0.0850395
\(870\) 3.63613e106 0.185433
\(871\) 3.80328e107 1.85993
\(872\) −1.95035e107 −0.914661
\(873\) −2.51388e106 −0.113064
\(874\) 7.11927e106 0.307092
\(875\) −4.23783e107 −1.75327
\(876\) −7.28385e106 −0.289042
\(877\) 1.41996e107 0.540493 0.270246 0.962791i \(-0.412895\pi\)
0.270246 + 0.962791i \(0.412895\pi\)
\(878\) −2.91718e107 −1.06516
\(879\) 4.25291e106 0.148968
\(880\) −6.92050e106 −0.232552
\(881\) 7.66883e106 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(882\) 2.21933e107 0.686466
\(883\) −3.35873e107 −0.996802 −0.498401 0.866947i \(-0.666079\pi\)
−0.498401 + 0.866947i \(0.666079\pi\)
\(884\) −2.26111e107 −0.643893
\(885\) 1.37872e107 0.376744
\(886\) −1.92142e107 −0.503839
\(887\) 6.18714e107 1.55696 0.778481 0.627669i \(-0.215991\pi\)
0.778481 + 0.627669i \(0.215991\pi\)
\(888\) 2.83909e107 0.685656
\(889\) −7.29588e107 −1.69108
\(890\) 2.98065e106 0.0663094
\(891\) −1.01041e107 −0.215755
\(892\) 4.79854e106 0.0983540
\(893\) −1.46899e107 −0.289029
\(894\) −1.98770e107 −0.375431
\(895\) 1.73243e108 3.14133
\(896\) 1.17869e107 0.205191
\(897\) 3.48307e107 0.582154
\(898\) 6.36140e107 1.02086
\(899\) −1.29029e107 −0.198819
\(900\) 4.42354e107 0.654513
\(901\) −7.87178e107 −1.11845
\(902\) 9.63812e105 0.0131508
\(903\) −3.62011e107 −0.474372
\(904\) −1.23108e108 −1.54931
\(905\) −1.95938e108 −2.36835
\(906\) −3.56802e107 −0.414236
\(907\) 7.84800e107 0.875171 0.437586 0.899177i \(-0.355834\pi\)
0.437586 + 0.899177i \(0.355834\pi\)
\(908\) −4.29230e106 −0.0459787
\(909\) 5.02338e107 0.516909
\(910\) 2.17685e108 2.15188
\(911\) −1.50467e108 −1.42896 −0.714482 0.699653i \(-0.753338\pi\)
−0.714482 + 0.699653i \(0.753338\pi\)
\(912\) 5.51657e106 0.0503335
\(913\) −7.45895e107 −0.653874
\(914\) −1.39927e108 −1.17860
\(915\) 3.45092e107 0.279296
\(916\) −2.72877e107 −0.212218
\(917\) 2.51155e108 1.87698
\(918\) −9.02805e107 −0.648390
\(919\) −1.19946e108 −0.827887 −0.413944 0.910303i \(-0.635849\pi\)
−0.413944 + 0.910303i \(0.635849\pi\)
\(920\) 3.05590e108 2.02714
\(921\) 5.48337e107 0.349600
\(922\) 8.31589e107 0.509601
\(923\) 4.56200e107 0.268716
\(924\) −2.12889e107 −0.120539
\(925\) −4.83742e108 −2.63294
\(926\) 2.12207e108 1.11035
\(927\) 1.55146e108 0.780424
\(928\) 6.26491e107 0.302980
\(929\) 3.42076e107 0.159056 0.0795278 0.996833i \(-0.474659\pi\)
0.0795278 + 0.996833i \(0.474659\pi\)
\(930\) −6.20728e107 −0.277507
\(931\) 9.62531e107 0.413763
\(932\) −3.20198e107 −0.132354
\(933\) −6.06903e107 −0.241234
\(934\) −2.74247e108 −1.04829
\(935\) 2.21946e108 0.815873
\(936\) −3.03686e108 −1.07363
\(937\) 5.24351e108 1.78290 0.891450 0.453119i \(-0.149689\pi\)
0.891450 + 0.453119i \(0.149689\pi\)
\(938\) −5.02913e108 −1.64471
\(939\) 2.11150e108 0.664197
\(940\) −1.98602e108 −0.600920
\(941\) −5.99656e107 −0.174534 −0.0872672 0.996185i \(-0.527813\pi\)
−0.0872672 + 0.996185i \(0.527813\pi\)
\(942\) 1.74133e108 0.487555
\(943\) −1.77463e107 −0.0478003
\(944\) −6.90691e107 −0.178981
\(945\) −7.39728e108 −1.84421
\(946\) 1.01687e108 0.243916
\(947\) 6.02710e108 1.39102 0.695511 0.718515i \(-0.255178\pi\)
0.695511 + 0.718515i \(0.255178\pi\)
\(948\) −1.72321e107 −0.0382678
\(949\) −8.52020e108 −1.82068
\(950\) −2.25419e108 −0.463532
\(951\) 1.58910e108 0.314459
\(952\) 9.49284e108 1.80779
\(953\) 7.10042e108 1.30135 0.650674 0.759357i \(-0.274487\pi\)
0.650674 + 0.759357i \(0.274487\pi\)
\(954\) −3.32993e108 −0.587381
\(955\) 7.41801e108 1.25940
\(956\) −2.34509e108 −0.383219
\(957\) −4.15961e107 −0.0654285
\(958\) −5.44818e104 −8.24916e−5 0
\(959\) −6.49087e108 −0.946071
\(960\) 4.63604e108 0.650500
\(961\) −5.20026e108 −0.702460
\(962\) 1.04599e109 1.36031
\(963\) −3.93679e107 −0.0492927
\(964\) −1.92548e108 −0.232128
\(965\) 1.32317e109 1.53592
\(966\) −4.60571e108 −0.514792
\(967\) −3.03350e108 −0.326495 −0.163248 0.986585i \(-0.552197\pi\)
−0.163248 + 0.986585i \(0.552197\pi\)
\(968\) −8.45337e108 −0.876152
\(969\) −1.76921e108 −0.176588
\(970\) 1.73193e108 0.166480
\(971\) −2.07397e109 −1.91999 −0.959997 0.280012i \(-0.909662\pi\)
−0.959997 + 0.280012i \(0.909662\pi\)
\(972\) 5.03201e108 0.448665
\(973\) −1.83492e109 −1.57579
\(974\) 5.33000e108 0.440885
\(975\) −1.10285e109 −0.878718
\(976\) −1.72879e108 −0.132686
\(977\) 1.80962e109 1.33794 0.668969 0.743290i \(-0.266736\pi\)
0.668969 + 0.743290i \(0.266736\pi\)
\(978\) 1.10442e108 0.0786620
\(979\) −3.40976e107 −0.0233968
\(980\) 1.30130e109 0.860254
\(981\) 1.10331e109 0.702712
\(982\) −5.91653e108 −0.363076
\(983\) −1.37476e109 −0.812875 −0.406438 0.913679i \(-0.633229\pi\)
−0.406438 + 0.913679i \(0.633229\pi\)
\(984\) −3.29783e107 −0.0187892
\(985\) 2.66405e109 1.46258
\(986\) 5.84192e108 0.309064
\(987\) 9.50344e108 0.484512
\(988\) −4.14836e108 −0.203820
\(989\) −1.87233e109 −0.886578
\(990\) 9.38877e108 0.428474
\(991\) 2.85911e109 1.25760 0.628800 0.777567i \(-0.283546\pi\)
0.628800 + 0.777567i \(0.283546\pi\)
\(992\) −1.06949e109 −0.453420
\(993\) 5.51292e108 0.225286
\(994\) −6.03240e108 −0.237622
\(995\) 2.18240e108 0.0828691
\(996\) 8.03847e108 0.294244
\(997\) −8.40964e108 −0.296759 −0.148380 0.988930i \(-0.547406\pi\)
−0.148380 + 0.988930i \(0.547406\pi\)
\(998\) −1.26256e109 −0.429524
\(999\) −3.55444e109 −1.16582
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 1.74.a.a.1.2 5
3.2 odd 2 9.74.a.a.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.74.a.a.1.2 5 1.1 even 1 trivial
9.74.a.a.1.4 5 3.2 odd 2