Properties

Label 1.48.a.a.1.1
Level $1$
Weight $48$
Character 1.1
Self dual yes
Analytic conductor $13.991$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 48 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.9907662655\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 832803191366 x^{2} + 3710135215485780 x + 13175318942671469337000\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{20}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-906006.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.02978e7 q^{2} -2.01642e10 q^{3} +2.71261e14 q^{4} -3.11682e16 q^{5} +4.09288e17 q^{6} -1.26592e20 q^{7} -2.64934e21 q^{8} -2.61822e22 q^{9} +O(q^{10})\) \(q-2.02978e7 q^{2} -2.01642e10 q^{3} +2.71261e14 q^{4} -3.11682e16 q^{5} +4.09288e17 q^{6} -1.26592e20 q^{7} -2.64934e21 q^{8} -2.61822e22 q^{9} +6.32644e23 q^{10} -1.78518e23 q^{11} -5.46976e24 q^{12} -1.12359e26 q^{13} +2.56953e27 q^{14} +6.28481e26 q^{15} +1.55990e28 q^{16} +4.31126e28 q^{17} +5.31440e29 q^{18} -7.19841e29 q^{19} -8.45472e30 q^{20} +2.55262e30 q^{21} +3.62352e30 q^{22} +8.88061e30 q^{23} +5.34218e31 q^{24} +2.60913e32 q^{25} +2.28064e33 q^{26} +1.06408e33 q^{27} -3.43395e34 q^{28} +2.84937e34 q^{29} -1.27568e34 q^{30} +1.11855e35 q^{31} +5.62362e34 q^{32} +3.59967e33 q^{33} -8.75090e35 q^{34} +3.94564e36 q^{35} -7.10222e36 q^{36} -9.87647e36 q^{37} +1.46112e37 q^{38} +2.26563e36 q^{39} +8.25752e37 q^{40} -3.56038e37 q^{41} -5.18125e37 q^{42} -3.37056e38 q^{43} -4.84250e37 q^{44} +8.16052e38 q^{45} -1.80256e38 q^{46} -1.22952e39 q^{47} -3.14542e38 q^{48} +1.07822e40 q^{49} -5.29595e39 q^{50} -8.69331e38 q^{51} -3.04787e40 q^{52} -1.08443e39 q^{53} -2.15985e40 q^{54} +5.56408e39 q^{55} +3.35385e41 q^{56} +1.45150e40 q^{57} -5.78358e41 q^{58} -1.45567e40 q^{59} +1.70483e41 q^{60} +4.79341e41 q^{61} -2.27041e42 q^{62} +3.31446e42 q^{63} -3.33684e42 q^{64} +3.50203e42 q^{65} -7.30652e40 q^{66} +3.35317e42 q^{67} +1.16948e43 q^{68} -1.79070e41 q^{69} -8.00876e43 q^{70} +9.20990e42 q^{71} +6.93656e43 q^{72} -5.22911e43 q^{73} +2.00470e44 q^{74} -5.26110e42 q^{75} -1.95265e44 q^{76} +2.25989e43 q^{77} -4.59873e43 q^{78} -7.68215e43 q^{79} -4.86194e44 q^{80} +6.74698e44 q^{81} +7.22677e44 q^{82} -1.71031e45 q^{83} +6.92428e44 q^{84} -1.34374e45 q^{85} +6.84147e45 q^{86} -5.74552e44 q^{87} +4.72955e44 q^{88} -9.70124e45 q^{89} -1.65640e46 q^{90} +1.42238e46 q^{91} +2.40897e45 q^{92} -2.25547e45 q^{93} +2.49565e46 q^{94} +2.24361e46 q^{95} -1.13396e45 q^{96} +5.35657e46 q^{97} -2.18854e47 q^{98} +4.67400e45 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + 2392716988073784337920q^{8} - 17071972417358142200172q^{9} + O(q^{10}) \) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + \)\(23\!\cdots\!20\)\(q^{8} - \)\(17\!\cdots\!72\)\(q^{9} + \)\(16\!\cdots\!00\)\(q^{10} - \)\(19\!\cdots\!12\)\(q^{11} + \)\(50\!\cdots\!20\)\(q^{12} + \)\(12\!\cdots\!20\)\(q^{13} + \)\(34\!\cdots\!04\)\(q^{14} + \)\(12\!\cdots\!00\)\(q^{15} + \)\(12\!\cdots\!84\)\(q^{16} + \)\(21\!\cdots\!80\)\(q^{17} + \)\(40\!\cdots\!60\)\(q^{18} - \)\(10\!\cdots\!40\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(26\!\cdots\!12\)\(q^{21} - \)\(79\!\cdots\!80\)\(q^{22} + \)\(13\!\cdots\!80\)\(q^{23} + \)\(11\!\cdots\!80\)\(q^{24} + \)\(10\!\cdots\!00\)\(q^{25} + \)\(22\!\cdots\!88\)\(q^{26} - \)\(73\!\cdots\!20\)\(q^{27} - \)\(36\!\cdots\!80\)\(q^{28} - \)\(22\!\cdots\!60\)\(q^{29} - \)\(25\!\cdots\!00\)\(q^{30} + \)\(75\!\cdots\!48\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(26\!\cdots\!20\)\(q^{33} - \)\(12\!\cdots\!16\)\(q^{34} - \)\(13\!\cdots\!00\)\(q^{35} - \)\(13\!\cdots\!36\)\(q^{36} - \)\(11\!\cdots\!60\)\(q^{37} + \)\(29\!\cdots\!80\)\(q^{38} + \)\(39\!\cdots\!36\)\(q^{39} + \)\(70\!\cdots\!00\)\(q^{40} + \)\(13\!\cdots\!28\)\(q^{41} - \)\(10\!\cdots\!20\)\(q^{42} - \)\(44\!\cdots\!00\)\(q^{43} - \)\(15\!\cdots\!56\)\(q^{44} + \)\(86\!\cdots\!00\)\(q^{45} + \)\(12\!\cdots\!68\)\(q^{46} + \)\(20\!\cdots\!20\)\(q^{47} + \)\(10\!\cdots\!80\)\(q^{48} + \)\(91\!\cdots\!72\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(18\!\cdots\!52\)\(q^{51} - \)\(55\!\cdots\!00\)\(q^{52} + \)\(29\!\cdots\!60\)\(q^{53} - \)\(11\!\cdots\!40\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} + \)\(27\!\cdots\!40\)\(q^{56} + \)\(55\!\cdots\!60\)\(q^{57} - \)\(73\!\cdots\!80\)\(q^{58} + \)\(47\!\cdots\!80\)\(q^{59} - \)\(21\!\cdots\!00\)\(q^{60} + \)\(62\!\cdots\!88\)\(q^{61} - \)\(68\!\cdots\!80\)\(q^{62} + \)\(58\!\cdots\!40\)\(q^{63} + \)\(55\!\cdots\!72\)\(q^{64} + \)\(12\!\cdots\!00\)\(q^{65} - \)\(89\!\cdots\!24\)\(q^{66} + \)\(18\!\cdots\!80\)\(q^{67} - \)\(27\!\cdots\!40\)\(q^{68} - \)\(20\!\cdots\!04\)\(q^{69} - \)\(97\!\cdots\!00\)\(q^{70} + \)\(22\!\cdots\!68\)\(q^{71} - \)\(17\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!80\)\(q^{73} + \)\(18\!\cdots\!44\)\(q^{74} + \)\(32\!\cdots\!00\)\(q^{75} + \)\(35\!\cdots\!80\)\(q^{76} - \)\(26\!\cdots\!00\)\(q^{77} - \)\(49\!\cdots\!00\)\(q^{78} - \)\(13\!\cdots\!60\)\(q^{79} - \)\(94\!\cdots\!00\)\(q^{80} - \)\(10\!\cdots\!16\)\(q^{81} + \)\(38\!\cdots\!20\)\(q^{82} - \)\(14\!\cdots\!60\)\(q^{83} + \)\(52\!\cdots\!44\)\(q^{84} - \)\(10\!\cdots\!00\)\(q^{85} + \)\(95\!\cdots\!28\)\(q^{86} - \)\(43\!\cdots\!60\)\(q^{87} - \)\(15\!\cdots\!60\)\(q^{88} - \)\(79\!\cdots\!80\)\(q^{89} - \)\(16\!\cdots\!00\)\(q^{90} + \)\(53\!\cdots\!68\)\(q^{91} + \)\(13\!\cdots\!80\)\(q^{92} + \)\(10\!\cdots\!20\)\(q^{93} + \)\(34\!\cdots\!24\)\(q^{94} + \)\(75\!\cdots\!00\)\(q^{95} + \)\(64\!\cdots\!28\)\(q^{96} + \)\(95\!\cdots\!20\)\(q^{97} - \)\(29\!\cdots\!20\)\(q^{98} + \)\(53\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.02978e7 −1.71097 −0.855486 0.517825i \(-0.826742\pi\)
−0.855486 + 0.517825i \(0.826742\pi\)
\(3\) −2.01642e10 −0.123661 −0.0618303 0.998087i \(-0.519694\pi\)
−0.0618303 + 0.998087i \(0.519694\pi\)
\(4\) 2.71261e14 1.92743
\(5\) −3.11682e16 −1.16927 −0.584637 0.811295i \(-0.698763\pi\)
−0.584637 + 0.811295i \(0.698763\pi\)
\(6\) 4.09288e17 0.211580
\(7\) −1.26592e20 −1.74824 −0.874122 0.485707i \(-0.838562\pi\)
−0.874122 + 0.485707i \(0.838562\pi\)
\(8\) −2.64934e21 −1.58680
\(9\) −2.61822e22 −0.984708
\(10\) 6.32644e23 2.00060
\(11\) −1.78518e23 −0.0601110 −0.0300555 0.999548i \(-0.509568\pi\)
−0.0300555 + 0.999548i \(0.509568\pi\)
\(12\) −5.46976e24 −0.238347
\(13\) −1.12359e26 −0.746346 −0.373173 0.927762i \(-0.621730\pi\)
−0.373173 + 0.927762i \(0.621730\pi\)
\(14\) 2.56953e27 2.99120
\(15\) 6.28481e26 0.144593
\(16\) 1.55990e28 0.787550
\(17\) 4.31126e28 0.523667 0.261833 0.965113i \(-0.415673\pi\)
0.261833 + 0.965113i \(0.415673\pi\)
\(18\) 5.31440e29 1.68481
\(19\) −7.19841e29 −0.640511 −0.320256 0.947331i \(-0.603769\pi\)
−0.320256 + 0.947331i \(0.603769\pi\)
\(20\) −8.45472e30 −2.25369
\(21\) 2.55262e30 0.216189
\(22\) 3.62352e30 0.102848
\(23\) 8.88061e30 0.0886826 0.0443413 0.999016i \(-0.485881\pi\)
0.0443413 + 0.999016i \(0.485881\pi\)
\(24\) 5.34218e31 0.196225
\(25\) 2.60913e32 0.367202
\(26\) 2.28064e33 1.27698
\(27\) 1.06408e33 0.245430
\(28\) −3.43395e34 −3.36961
\(29\) 2.84937e34 1.22573 0.612866 0.790187i \(-0.290017\pi\)
0.612866 + 0.790187i \(0.290017\pi\)
\(30\) −1.27568e34 −0.247395
\(31\) 1.11855e35 1.00382 0.501911 0.864919i \(-0.332630\pi\)
0.501911 + 0.864919i \(0.332630\pi\)
\(32\) 5.62362e34 0.239327
\(33\) 3.59967e33 0.00743336
\(34\) −8.75090e35 −0.895980
\(35\) 3.94564e36 2.04418
\(36\) −7.10222e36 −1.89795
\(37\) −9.87647e36 −1.38631 −0.693156 0.720787i \(-0.743780\pi\)
−0.693156 + 0.720787i \(0.743780\pi\)
\(38\) 1.46112e37 1.09590
\(39\) 2.26563e36 0.0922935
\(40\) 8.25752e37 1.85541
\(41\) −3.56038e37 −0.447791 −0.223896 0.974613i \(-0.571877\pi\)
−0.223896 + 0.974613i \(0.571877\pi\)
\(42\) −5.18125e37 −0.369893
\(43\) −3.37056e38 −1.38418 −0.692091 0.721811i \(-0.743310\pi\)
−0.692091 + 0.721811i \(0.743310\pi\)
\(44\) −4.84250e37 −0.115860
\(45\) 8.16052e38 1.15139
\(46\) −1.80256e38 −0.151734
\(47\) −1.22952e39 −0.624361 −0.312181 0.950023i \(-0.601059\pi\)
−0.312181 + 0.950023i \(0.601059\pi\)
\(48\) −3.14542e38 −0.0973889
\(49\) 1.07822e40 2.05635
\(50\) −5.29595e39 −0.628273
\(51\) −8.69331e38 −0.0647569
\(52\) −3.04787e40 −1.43853
\(53\) −1.08443e39 −0.0327129 −0.0163565 0.999866i \(-0.505207\pi\)
−0.0163565 + 0.999866i \(0.505207\pi\)
\(54\) −2.15985e40 −0.419924
\(55\) 5.56408e39 0.0702863
\(56\) 3.35385e41 2.77412
\(57\) 1.45150e40 0.0792060
\(58\) −5.78358e41 −2.09719
\(59\) −1.45567e40 −0.0353216 −0.0176608 0.999844i \(-0.505622\pi\)
−0.0176608 + 0.999844i \(0.505622\pi\)
\(60\) 1.70483e41 0.278693
\(61\) 4.79341e41 0.531366 0.265683 0.964060i \(-0.414403\pi\)
0.265683 + 0.964060i \(0.414403\pi\)
\(62\) −2.27041e42 −1.71751
\(63\) 3.31446e42 1.72151
\(64\) −3.33684e42 −1.19703
\(65\) 3.50203e42 0.872683
\(66\) −7.30652e40 −0.0127183
\(67\) 3.35317e42 0.409919 0.204959 0.978770i \(-0.434294\pi\)
0.204959 + 0.978770i \(0.434294\pi\)
\(68\) 1.16948e43 1.00933
\(69\) −1.79070e41 −0.0109665
\(70\) −8.00876e43 −3.49753
\(71\) 9.20990e42 0.288193 0.144097 0.989564i \(-0.453972\pi\)
0.144097 + 0.989564i \(0.453972\pi\)
\(72\) 6.93656e43 1.56254
\(73\) −5.22911e43 −0.851805 −0.425903 0.904769i \(-0.640043\pi\)
−0.425903 + 0.904769i \(0.640043\pi\)
\(74\) 2.00470e44 2.37194
\(75\) −5.26110e42 −0.0454085
\(76\) −1.95265e44 −1.23454
\(77\) 2.25989e43 0.105089
\(78\) −4.59873e43 −0.157912
\(79\) −7.68215e43 −0.195545 −0.0977724 0.995209i \(-0.531172\pi\)
−0.0977724 + 0.995209i \(0.531172\pi\)
\(80\) −4.86194e44 −0.920862
\(81\) 6.74698e44 0.954358
\(82\) 7.22677e44 0.766158
\(83\) −1.71031e45 −1.36377 −0.681884 0.731460i \(-0.738839\pi\)
−0.681884 + 0.731460i \(0.738839\pi\)
\(84\) 6.92428e44 0.416688
\(85\) −1.34374e45 −0.612310
\(86\) 6.84147e45 2.36830
\(87\) −5.74552e44 −0.151575
\(88\) 4.72955e44 0.0953844
\(89\) −9.70124e45 −1.50024 −0.750122 0.661299i \(-0.770005\pi\)
−0.750122 + 0.661299i \(0.770005\pi\)
\(90\) −1.65640e46 −1.97000
\(91\) 1.42238e46 1.30479
\(92\) 2.40897e45 0.170929
\(93\) −2.25547e45 −0.124133
\(94\) 2.49565e46 1.06827
\(95\) 2.24361e46 0.748933
\(96\) −1.13396e45 −0.0295953
\(97\) 5.35657e46 1.09585 0.547925 0.836528i \(-0.315418\pi\)
0.547925 + 0.836528i \(0.315418\pi\)
\(98\) −2.18854e47 −3.51837
\(99\) 4.67400e45 0.0591918
\(100\) 7.07756e46 0.707756
\(101\) 1.46056e47 1.15602 0.578011 0.816029i \(-0.303829\pi\)
0.578011 + 0.816029i \(0.303829\pi\)
\(102\) 1.76455e46 0.110797
\(103\) −3.94670e47 −1.97042 −0.985212 0.171342i \(-0.945190\pi\)
−0.985212 + 0.171342i \(0.945190\pi\)
\(104\) 2.97678e47 1.18430
\(105\) −7.95606e46 −0.252784
\(106\) 2.20115e46 0.0559709
\(107\) 5.84600e47 1.19218 0.596088 0.802919i \(-0.296721\pi\)
0.596088 + 0.802919i \(0.296721\pi\)
\(108\) 2.88645e47 0.473049
\(109\) −7.05835e47 −0.931494 −0.465747 0.884918i \(-0.654214\pi\)
−0.465747 + 0.884918i \(0.654214\pi\)
\(110\) −1.12938e47 −0.120258
\(111\) 1.99151e47 0.171432
\(112\) −1.97471e48 −1.37683
\(113\) −6.63621e47 −0.375471 −0.187736 0.982220i \(-0.560115\pi\)
−0.187736 + 0.982220i \(0.560115\pi\)
\(114\) −2.94622e47 −0.135519
\(115\) −2.76792e47 −0.103694
\(116\) 7.72923e48 2.36251
\(117\) 2.94181e48 0.734933
\(118\) 2.95468e47 0.0604342
\(119\) −5.45771e48 −0.915497
\(120\) −1.66506e48 −0.229441
\(121\) −8.78788e48 −0.996387
\(122\) −9.72955e48 −0.909152
\(123\) 7.17921e47 0.0553741
\(124\) 3.03420e49 1.93479
\(125\) 1.40141e49 0.739914
\(126\) −6.72760e49 −2.94546
\(127\) 1.84983e49 0.672580 0.336290 0.941758i \(-0.390828\pi\)
0.336290 + 0.941758i \(0.390828\pi\)
\(128\) 5.98158e49 1.80876
\(129\) 6.79645e48 0.171169
\(130\) −7.10834e49 −1.49314
\(131\) 3.62008e49 0.635100 0.317550 0.948242i \(-0.397140\pi\)
0.317550 + 0.948242i \(0.397140\pi\)
\(132\) 9.76452e47 0.0143273
\(133\) 9.11260e49 1.11977
\(134\) −6.80618e49 −0.701360
\(135\) −3.31656e49 −0.286975
\(136\) −1.14220e50 −0.830956
\(137\) −2.09650e50 −1.28399 −0.641994 0.766709i \(-0.721893\pi\)
−0.641994 + 0.766709i \(0.721893\pi\)
\(138\) 3.63472e48 0.0187635
\(139\) −1.18819e50 −0.517653 −0.258826 0.965924i \(-0.583336\pi\)
−0.258826 + 0.965924i \(0.583336\pi\)
\(140\) 1.07030e51 3.94000
\(141\) 2.47923e49 0.0772089
\(142\) −1.86940e50 −0.493091
\(143\) 2.00582e49 0.0448636
\(144\) −4.08417e50 −0.775507
\(145\) −8.88096e50 −1.43322
\(146\) 1.06139e51 1.45742
\(147\) −2.17414e50 −0.254290
\(148\) −2.67910e51 −2.67202
\(149\) 1.81480e51 1.54508 0.772540 0.634966i \(-0.218986\pi\)
0.772540 + 0.634966i \(0.218986\pi\)
\(150\) 1.06788e50 0.0776926
\(151\) 1.57042e51 0.977366 0.488683 0.872461i \(-0.337477\pi\)
0.488683 + 0.872461i \(0.337477\pi\)
\(152\) 1.90710e51 1.01637
\(153\) −1.12878e51 −0.515659
\(154\) −4.58708e50 −0.179804
\(155\) −3.48633e51 −1.17374
\(156\) 6.14579e50 0.177889
\(157\) 3.70380e51 0.922584 0.461292 0.887248i \(-0.347386\pi\)
0.461292 + 0.887248i \(0.347386\pi\)
\(158\) 1.55930e51 0.334572
\(159\) 2.18667e49 0.00404530
\(160\) −1.75278e51 −0.279839
\(161\) −1.12421e51 −0.155039
\(162\) −1.36948e52 −1.63288
\(163\) 4.02579e51 0.415377 0.207688 0.978195i \(-0.433406\pi\)
0.207688 + 0.978195i \(0.433406\pi\)
\(164\) −9.65793e51 −0.863085
\(165\) −1.12195e50 −0.00869164
\(166\) 3.47155e52 2.33337
\(167\) 1.17072e52 0.683308 0.341654 0.939826i \(-0.389013\pi\)
0.341654 + 0.939826i \(0.389013\pi\)
\(168\) −6.76277e51 −0.343049
\(169\) −1.00394e52 −0.442968
\(170\) 2.72750e52 1.04765
\(171\) 1.88470e52 0.630717
\(172\) −9.14302e52 −2.66791
\(173\) −2.17798e52 −0.554587 −0.277293 0.960785i \(-0.589437\pi\)
−0.277293 + 0.960785i \(0.589437\pi\)
\(174\) 1.16621e52 0.259340
\(175\) −3.30295e52 −0.641959
\(176\) −2.78471e51 −0.0473404
\(177\) 2.93523e50 0.00436788
\(178\) 1.96913e53 2.56688
\(179\) −9.95625e52 −1.13776 −0.568879 0.822421i \(-0.692623\pi\)
−0.568879 + 0.822421i \(0.692623\pi\)
\(180\) 2.21363e53 2.21923
\(181\) −6.46484e52 −0.568998 −0.284499 0.958676i \(-0.591827\pi\)
−0.284499 + 0.958676i \(0.591827\pi\)
\(182\) −2.88711e53 −2.23247
\(183\) −9.66552e51 −0.0657090
\(184\) −2.35278e52 −0.140722
\(185\) 3.07832e53 1.62098
\(186\) 4.57810e52 0.212388
\(187\) −7.69638e51 −0.0314781
\(188\) −3.33521e53 −1.20341
\(189\) −1.34704e53 −0.429072
\(190\) −4.55403e53 −1.28140
\(191\) 7.79937e53 1.93988 0.969942 0.243337i \(-0.0782421\pi\)
0.969942 + 0.243337i \(0.0782421\pi\)
\(192\) 6.72846e52 0.148026
\(193\) 6.70136e52 0.130487 0.0652433 0.997869i \(-0.479218\pi\)
0.0652433 + 0.997869i \(0.479218\pi\)
\(194\) −1.08726e54 −1.87497
\(195\) −7.06157e52 −0.107916
\(196\) 2.92478e54 3.96348
\(197\) −1.22925e54 −1.47804 −0.739019 0.673685i \(-0.764711\pi\)
−0.739019 + 0.673685i \(0.764711\pi\)
\(198\) −9.48717e52 −0.101276
\(199\) 1.40028e54 1.32790 0.663952 0.747775i \(-0.268878\pi\)
0.663952 + 0.747775i \(0.268878\pi\)
\(200\) −6.91248e53 −0.582678
\(201\) −6.76139e52 −0.0506908
\(202\) −2.96460e54 −1.97792
\(203\) −3.60707e54 −2.14288
\(204\) −2.35816e53 −0.124814
\(205\) 1.10971e54 0.523591
\(206\) 8.01092e54 3.37134
\(207\) −2.32514e53 −0.0873265
\(208\) −1.75270e54 −0.587785
\(209\) 1.28505e53 0.0385018
\(210\) 1.61490e54 0.432506
\(211\) 7.49292e53 0.179479 0.0897394 0.995965i \(-0.471397\pi\)
0.0897394 + 0.995965i \(0.471397\pi\)
\(212\) −2.94164e53 −0.0630518
\(213\) −1.85710e53 −0.0356381
\(214\) −1.18661e55 −2.03978
\(215\) 1.05054e55 1.61849
\(216\) −2.81912e54 −0.389449
\(217\) −1.41600e55 −1.75493
\(218\) 1.43269e55 1.59376
\(219\) 1.05441e54 0.105335
\(220\) 1.50932e54 0.135472
\(221\) −4.84410e54 −0.390836
\(222\) −4.04232e54 −0.293316
\(223\) 7.65012e54 0.499464 0.249732 0.968315i \(-0.419658\pi\)
0.249732 + 0.968315i \(0.419658\pi\)
\(224\) −7.11905e54 −0.418402
\(225\) −6.83128e54 −0.361587
\(226\) 1.34700e55 0.642421
\(227\) 1.58232e55 0.680277 0.340138 0.940375i \(-0.389526\pi\)
0.340138 + 0.940375i \(0.389526\pi\)
\(228\) 3.93736e54 0.152664
\(229\) 2.86045e55 1.00069 0.500347 0.865825i \(-0.333206\pi\)
0.500347 + 0.865825i \(0.333206\pi\)
\(230\) 5.61827e54 0.177418
\(231\) −4.55689e53 −0.0129953
\(232\) −7.54894e55 −1.94500
\(233\) −3.61119e55 −0.840980 −0.420490 0.907297i \(-0.638142\pi\)
−0.420490 + 0.907297i \(0.638142\pi\)
\(234\) −5.97122e55 −1.25745
\(235\) 3.83219e55 0.730050
\(236\) −3.94866e54 −0.0680798
\(237\) 1.54904e54 0.0241812
\(238\) 1.10779e56 1.56639
\(239\) 5.47124e55 0.701027 0.350514 0.936558i \(-0.386007\pi\)
0.350514 + 0.936558i \(0.386007\pi\)
\(240\) 9.80370e54 0.113874
\(241\) −8.92529e55 −0.940204 −0.470102 0.882612i \(-0.655783\pi\)
−0.470102 + 0.882612i \(0.655783\pi\)
\(242\) 1.78374e56 1.70479
\(243\) −4.18975e55 −0.363447
\(244\) 1.30027e56 1.02417
\(245\) −3.36060e56 −2.40444
\(246\) −1.45722e55 −0.0947436
\(247\) 8.08808e55 0.478043
\(248\) −2.96343e56 −1.59287
\(249\) 3.44871e55 0.168644
\(250\) −2.84456e56 −1.26597
\(251\) 1.98048e56 0.802487 0.401244 0.915971i \(-0.368578\pi\)
0.401244 + 0.915971i \(0.368578\pi\)
\(252\) 8.99084e56 3.31808
\(253\) −1.58535e54 −0.00533080
\(254\) −3.75474e56 −1.15077
\(255\) 2.70955e55 0.0757186
\(256\) −7.44508e56 −1.89771
\(257\) −1.71029e55 −0.0397778 −0.0198889 0.999802i \(-0.506331\pi\)
−0.0198889 + 0.999802i \(0.506331\pi\)
\(258\) −1.37953e56 −0.292865
\(259\) 1.25028e57 2.42361
\(260\) 9.49967e56 1.68203
\(261\) −7.46028e56 −1.20699
\(262\) −7.34794e56 −1.08664
\(263\) 3.32579e56 0.449712 0.224856 0.974392i \(-0.427809\pi\)
0.224856 + 0.974392i \(0.427809\pi\)
\(264\) −9.53676e54 −0.0117953
\(265\) 3.37998e55 0.0382504
\(266\) −1.84965e57 −1.91590
\(267\) 1.95618e56 0.185521
\(268\) 9.09585e56 0.790088
\(269\) −1.74613e57 −1.38963 −0.694815 0.719189i \(-0.744514\pi\)
−0.694815 + 0.719189i \(0.744514\pi\)
\(270\) 6.73187e56 0.491007
\(271\) 1.96258e56 0.131235 0.0656174 0.997845i \(-0.479098\pi\)
0.0656174 + 0.997845i \(0.479098\pi\)
\(272\) 6.72516e56 0.412414
\(273\) −2.86811e56 −0.161352
\(274\) 4.25542e57 2.19687
\(275\) −4.65777e55 −0.0220729
\(276\) −4.85748e55 −0.0211372
\(277\) 1.40234e57 0.560503 0.280252 0.959927i \(-0.409582\pi\)
0.280252 + 0.959927i \(0.409582\pi\)
\(278\) 2.41176e57 0.885690
\(279\) −2.92862e57 −0.988472
\(280\) −1.04533e58 −3.24371
\(281\) −3.15409e57 −0.900068 −0.450034 0.893011i \(-0.648588\pi\)
−0.450034 + 0.893011i \(0.648588\pi\)
\(282\) −5.03228e56 −0.132102
\(283\) 6.43417e57 1.55422 0.777108 0.629368i \(-0.216686\pi\)
0.777108 + 0.629368i \(0.216686\pi\)
\(284\) 2.49829e57 0.555472
\(285\) −4.52406e56 −0.0926135
\(286\) −4.07136e56 −0.0767604
\(287\) 4.50715e57 0.782848
\(288\) −1.47239e57 −0.235667
\(289\) −4.91926e57 −0.725773
\(290\) 1.80264e58 2.45219
\(291\) −1.08011e57 −0.135513
\(292\) −1.41845e58 −1.64179
\(293\) −7.47274e57 −0.798162 −0.399081 0.916916i \(-0.630671\pi\)
−0.399081 + 0.916916i \(0.630671\pi\)
\(294\) 4.41301e57 0.435083
\(295\) 4.53705e56 0.0413006
\(296\) 2.61661e58 2.19981
\(297\) −1.89958e56 −0.0147531
\(298\) −3.68363e58 −2.64359
\(299\) −9.97819e56 −0.0661879
\(300\) −1.42713e57 −0.0875215
\(301\) 4.26685e58 2.41989
\(302\) −3.18760e58 −1.67225
\(303\) −2.94510e57 −0.142954
\(304\) −1.12288e58 −0.504435
\(305\) −1.49402e58 −0.621312
\(306\) 2.29118e58 0.882278
\(307\) −2.04451e58 −0.729183 −0.364592 0.931168i \(-0.618791\pi\)
−0.364592 + 0.931168i \(0.618791\pi\)
\(308\) 6.13022e57 0.202551
\(309\) 7.95820e57 0.243664
\(310\) 7.07646e58 2.00824
\(311\) 3.46247e58 0.910997 0.455499 0.890236i \(-0.349461\pi\)
0.455499 + 0.890236i \(0.349461\pi\)
\(312\) −6.00243e57 −0.146452
\(313\) 7.50527e58 1.69853 0.849267 0.527963i \(-0.177044\pi\)
0.849267 + 0.527963i \(0.177044\pi\)
\(314\) −7.51789e58 −1.57852
\(315\) −1.03306e59 −2.01292
\(316\) −2.08387e58 −0.376898
\(317\) −9.59709e58 −1.61156 −0.805781 0.592213i \(-0.798254\pi\)
−0.805781 + 0.592213i \(0.798254\pi\)
\(318\) −4.43844e56 −0.00692139
\(319\) −5.08663e57 −0.0736800
\(320\) 1.04003e59 1.39966
\(321\) −1.17880e58 −0.147425
\(322\) 2.28190e58 0.265267
\(323\) −3.10342e58 −0.335414
\(324\) 1.83019e59 1.83946
\(325\) −2.93160e58 −0.274060
\(326\) −8.17144e58 −0.710698
\(327\) 1.42326e58 0.115189
\(328\) 9.43265e58 0.710556
\(329\) 1.55647e59 1.09154
\(330\) 2.27731e57 0.0148712
\(331\) −9.45783e58 −0.575219 −0.287610 0.957748i \(-0.592861\pi\)
−0.287610 + 0.957748i \(0.592861\pi\)
\(332\) −4.63942e59 −2.62856
\(333\) 2.58588e59 1.36511
\(334\) −2.37630e59 −1.16912
\(335\) −1.04512e59 −0.479307
\(336\) 3.98184e58 0.170259
\(337\) 4.62637e59 1.84475 0.922375 0.386295i \(-0.126245\pi\)
0.922375 + 0.386295i \(0.126245\pi\)
\(338\) 2.03778e59 0.757906
\(339\) 1.33814e58 0.0464310
\(340\) −3.64505e59 −1.18018
\(341\) −1.99682e58 −0.0603408
\(342\) −3.82552e59 −1.07914
\(343\) −7.01170e59 −1.84677
\(344\) 8.92975e59 2.19642
\(345\) 5.58129e57 0.0128229
\(346\) 4.42080e59 0.948883
\(347\) 4.68114e59 0.938878 0.469439 0.882965i \(-0.344456\pi\)
0.469439 + 0.882965i \(0.344456\pi\)
\(348\) −1.55854e59 −0.292149
\(349\) −1.32904e59 −0.232884 −0.116442 0.993197i \(-0.537149\pi\)
−0.116442 + 0.993197i \(0.537149\pi\)
\(350\) 6.70424e59 1.09837
\(351\) −1.19560e59 −0.183176
\(352\) −1.00392e58 −0.0143862
\(353\) −7.06798e59 −0.947523 −0.473762 0.880653i \(-0.657104\pi\)
−0.473762 + 0.880653i \(0.657104\pi\)
\(354\) −5.95787e57 −0.00747333
\(355\) −2.87056e59 −0.336977
\(356\) −2.63157e60 −2.89161
\(357\) 1.10050e59 0.113211
\(358\) 2.02090e60 1.94667
\(359\) 8.86439e59 0.799704 0.399852 0.916580i \(-0.369061\pi\)
0.399852 + 0.916580i \(0.369061\pi\)
\(360\) −2.16200e60 −1.82704
\(361\) −7.44875e59 −0.589745
\(362\) 1.31222e60 0.973541
\(363\) 1.77200e59 0.123214
\(364\) 3.85836e60 2.51490
\(365\) 1.62982e60 0.995994
\(366\) 1.96188e59 0.112426
\(367\) −1.87716e60 −1.00890 −0.504451 0.863440i \(-0.668305\pi\)
−0.504451 + 0.863440i \(0.668305\pi\)
\(368\) 1.38529e59 0.0698420
\(369\) 9.32186e59 0.440943
\(370\) −6.24829e60 −2.77345
\(371\) 1.37280e59 0.0571901
\(372\) −6.11822e59 −0.239258
\(373\) −2.92907e59 −0.107541 −0.0537703 0.998553i \(-0.517124\pi\)
−0.0537703 + 0.998553i \(0.517124\pi\)
\(374\) 1.56219e59 0.0538582
\(375\) −2.82584e59 −0.0914982
\(376\) 3.25742e60 0.990739
\(377\) −3.20153e60 −0.914820
\(378\) 2.73420e60 0.734130
\(379\) 1.26439e60 0.319051 0.159525 0.987194i \(-0.449004\pi\)
0.159525 + 0.987194i \(0.449004\pi\)
\(380\) 6.08605e60 1.44352
\(381\) −3.73003e59 −0.0831716
\(382\) −1.58310e61 −3.31909
\(383\) 7.65652e60 1.50959 0.754797 0.655958i \(-0.227735\pi\)
0.754797 + 0.655958i \(0.227735\pi\)
\(384\) −1.20614e60 −0.223673
\(385\) −7.04368e59 −0.122877
\(386\) −1.36023e60 −0.223259
\(387\) 8.82487e60 1.36301
\(388\) 1.45303e61 2.11217
\(389\) −7.85479e60 −1.07478 −0.537389 0.843335i \(-0.680589\pi\)
−0.537389 + 0.843335i \(0.680589\pi\)
\(390\) 1.43334e60 0.184642
\(391\) 3.82867e59 0.0464401
\(392\) −2.85656e61 −3.26303
\(393\) −7.29959e59 −0.0785368
\(394\) 2.49511e61 2.52888
\(395\) 2.39439e60 0.228645
\(396\) 1.26788e60 0.114088
\(397\) −1.21556e61 −1.03086 −0.515430 0.856932i \(-0.672368\pi\)
−0.515430 + 0.856932i \(0.672368\pi\)
\(398\) −2.84225e61 −2.27201
\(399\) −1.83748e60 −0.138471
\(400\) 4.06999e60 0.289190
\(401\) 1.13229e61 0.758692 0.379346 0.925255i \(-0.376149\pi\)
0.379346 + 0.925255i \(0.376149\pi\)
\(402\) 1.37241e60 0.0867305
\(403\) −1.25680e61 −0.749198
\(404\) 3.96193e61 2.22815
\(405\) −2.10291e61 −1.11591
\(406\) 7.32154e61 3.66640
\(407\) 1.76313e60 0.0833327
\(408\) 2.30316e60 0.102757
\(409\) −1.93004e61 −0.812958 −0.406479 0.913660i \(-0.633244\pi\)
−0.406479 + 0.913660i \(0.633244\pi\)
\(410\) −2.25245e61 −0.895849
\(411\) 4.22742e60 0.158779
\(412\) −1.07059e62 −3.79785
\(413\) 1.84276e60 0.0617507
\(414\) 4.71951e60 0.149413
\(415\) 5.33073e61 1.59462
\(416\) −6.31866e60 −0.178621
\(417\) 2.39589e60 0.0640132
\(418\) −2.60835e60 −0.0658755
\(419\) −3.12082e60 −0.0745141 −0.0372571 0.999306i \(-0.511862\pi\)
−0.0372571 + 0.999306i \(0.511862\pi\)
\(420\) −2.15817e61 −0.487223
\(421\) 6.12499e61 1.30760 0.653802 0.756666i \(-0.273173\pi\)
0.653802 + 0.756666i \(0.273173\pi\)
\(422\) −1.52089e61 −0.307084
\(423\) 3.21916e61 0.614814
\(424\) 2.87303e60 0.0519090
\(425\) 1.12487e61 0.192292
\(426\) 3.76950e60 0.0609759
\(427\) −6.06807e61 −0.928957
\(428\) 1.58579e62 2.29783
\(429\) −4.04456e59 −0.00554786
\(430\) −2.13236e62 −2.76919
\(431\) −7.83169e61 −0.963030 −0.481515 0.876438i \(-0.659913\pi\)
−0.481515 + 0.876438i \(0.659913\pi\)
\(432\) 1.65987e61 0.193288
\(433\) 2.94510e61 0.324814 0.162407 0.986724i \(-0.448074\pi\)
0.162407 + 0.986724i \(0.448074\pi\)
\(434\) 2.87416e62 3.00263
\(435\) 1.79077e61 0.177232
\(436\) −1.91466e62 −1.79539
\(437\) −6.39262e60 −0.0568022
\(438\) −2.14021e61 −0.180225
\(439\) −8.39024e60 −0.0669666 −0.0334833 0.999439i \(-0.510660\pi\)
−0.0334833 + 0.999439i \(0.510660\pi\)
\(440\) −1.47412e61 −0.111530
\(441\) −2.82301e62 −2.02491
\(442\) 9.83245e61 0.668711
\(443\) −7.70512e61 −0.496926 −0.248463 0.968641i \(-0.579925\pi\)
−0.248463 + 0.968641i \(0.579925\pi\)
\(444\) 5.40220e61 0.330423
\(445\) 3.02370e62 1.75420
\(446\) −1.55280e62 −0.854569
\(447\) −3.65939e61 −0.191065
\(448\) 4.22417e62 2.09270
\(449\) 1.71627e62 0.806857 0.403429 0.915011i \(-0.367818\pi\)
0.403429 + 0.915011i \(0.367818\pi\)
\(450\) 1.38660e62 0.618666
\(451\) 6.35592e60 0.0269172
\(452\) −1.80015e62 −0.723693
\(453\) −3.16662e61 −0.120862
\(454\) −3.21175e62 −1.16394
\(455\) −4.43329e62 −1.52566
\(456\) −3.84552e61 −0.125684
\(457\) 4.06573e62 1.26214 0.631070 0.775726i \(-0.282616\pi\)
0.631070 + 0.775726i \(0.282616\pi\)
\(458\) −5.80608e62 −1.71216
\(459\) 4.58755e61 0.128524
\(460\) −7.50831e61 −0.199863
\(461\) 2.67924e62 0.677704 0.338852 0.940840i \(-0.389961\pi\)
0.338852 + 0.940840i \(0.389961\pi\)
\(462\) 9.24946e60 0.0222346
\(463\) −5.44459e62 −1.24397 −0.621987 0.783027i \(-0.713675\pi\)
−0.621987 + 0.783027i \(0.713675\pi\)
\(464\) 4.44474e62 0.965325
\(465\) 7.02989e61 0.145146
\(466\) 7.32990e62 1.43889
\(467\) 4.82071e62 0.899839 0.449919 0.893069i \(-0.351453\pi\)
0.449919 + 0.893069i \(0.351453\pi\)
\(468\) 7.98001e62 1.41653
\(469\) −4.24484e62 −0.716637
\(470\) −7.77849e62 −1.24910
\(471\) −7.46841e61 −0.114087
\(472\) 3.85656e61 0.0560484
\(473\) 6.01705e61 0.0832045
\(474\) −3.14421e61 −0.0413733
\(475\) −1.87816e62 −0.235197
\(476\) −1.48047e63 −1.76455
\(477\) 2.83928e61 0.0322127
\(478\) −1.11054e63 −1.19944
\(479\) 1.74319e63 1.79251 0.896253 0.443543i \(-0.146279\pi\)
0.896253 + 0.443543i \(0.146279\pi\)
\(480\) 3.53434e61 0.0346050
\(481\) 1.10971e63 1.03467
\(482\) 1.81163e63 1.60866
\(483\) 2.26688e61 0.0191722
\(484\) −2.38381e63 −1.92046
\(485\) −1.66955e63 −1.28135
\(486\) 8.50425e62 0.621847
\(487\) −2.19497e63 −1.52932 −0.764661 0.644433i \(-0.777093\pi\)
−0.764661 + 0.644433i \(0.777093\pi\)
\(488\) −1.26994e63 −0.843173
\(489\) −8.11767e61 −0.0513657
\(490\) 6.82127e63 4.11394
\(491\) −4.81659e62 −0.276901 −0.138451 0.990369i \(-0.544212\pi\)
−0.138451 + 0.990369i \(0.544212\pi\)
\(492\) 1.94744e62 0.106730
\(493\) 1.22844e63 0.641875
\(494\) −1.64170e63 −0.817918
\(495\) −1.45680e62 −0.0692114
\(496\) 1.74483e63 0.790560
\(497\) −1.16590e63 −0.503832
\(498\) −7.00010e62 −0.288546
\(499\) −2.59805e63 −1.02161 −0.510805 0.859696i \(-0.670653\pi\)
−0.510805 + 0.859696i \(0.670653\pi\)
\(500\) 3.80149e63 1.42613
\(501\) −2.36066e62 −0.0844983
\(502\) −4.01993e63 −1.37303
\(503\) 5.26346e63 1.71563 0.857816 0.513958i \(-0.171821\pi\)
0.857816 + 0.513958i \(0.171821\pi\)
\(504\) −8.78112e63 −2.73170
\(505\) −4.55229e63 −1.35171
\(506\) 3.21790e61 0.00912086
\(507\) 2.02437e62 0.0547777
\(508\) 5.01787e63 1.29635
\(509\) −1.22138e63 −0.301289 −0.150644 0.988588i \(-0.548135\pi\)
−0.150644 + 0.988588i \(0.548135\pi\)
\(510\) −5.49977e62 −0.129552
\(511\) 6.61963e63 1.48916
\(512\) 6.69351e63 1.43817
\(513\) −7.65972e62 −0.157201
\(514\) 3.47150e62 0.0680587
\(515\) 1.23012e64 2.30397
\(516\) 1.84361e63 0.329915
\(517\) 2.19492e62 0.0375310
\(518\) −2.53779e64 −4.14673
\(519\) 4.39171e62 0.0685805
\(520\) −9.27808e63 −1.38478
\(521\) −9.22332e62 −0.131583 −0.0657916 0.997833i \(-0.520957\pi\)
−0.0657916 + 0.997833i \(0.520957\pi\)
\(522\) 1.51427e64 2.06512
\(523\) −1.18236e64 −1.54155 −0.770777 0.637105i \(-0.780132\pi\)
−0.770777 + 0.637105i \(0.780132\pi\)
\(524\) 9.81987e63 1.22411
\(525\) 6.66012e62 0.0793850
\(526\) −6.75060e63 −0.769444
\(527\) 4.82238e63 0.525668
\(528\) 5.61514e61 0.00585414
\(529\) −9.94900e63 −0.992135
\(530\) −6.86059e62 −0.0654453
\(531\) 3.81126e62 0.0347814
\(532\) 2.47190e64 2.15828
\(533\) 4.00041e63 0.334207
\(534\) −3.97060e63 −0.317422
\(535\) −1.82209e64 −1.39398
\(536\) −8.88369e63 −0.650460
\(537\) 2.00760e63 0.140696
\(538\) 3.54426e64 2.37762
\(539\) −1.92481e63 −0.123610
\(540\) −8.99654e63 −0.553124
\(541\) −1.28271e64 −0.755077 −0.377539 0.925994i \(-0.623229\pi\)
−0.377539 + 0.925994i \(0.623229\pi\)
\(542\) −3.98360e63 −0.224539
\(543\) 1.30358e63 0.0703627
\(544\) 2.42449e63 0.125328
\(545\) 2.19996e64 1.08917
\(546\) 5.82161e63 0.276068
\(547\) 3.21410e64 1.46001 0.730007 0.683440i \(-0.239517\pi\)
0.730007 + 0.683440i \(0.239517\pi\)
\(548\) −5.68699e64 −2.47479
\(549\) −1.25502e64 −0.523240
\(550\) 9.45422e62 0.0377661
\(551\) −2.05109e64 −0.785095
\(552\) 4.74418e62 0.0174018
\(553\) 9.72498e63 0.341860
\(554\) −2.84643e64 −0.959006
\(555\) −6.20717e63 −0.200451
\(556\) −3.22310e64 −0.997738
\(557\) −1.16869e64 −0.346819 −0.173409 0.984850i \(-0.555478\pi\)
−0.173409 + 0.984850i \(0.555478\pi\)
\(558\) 5.94444e64 1.69125
\(559\) 3.78713e64 1.03308
\(560\) 6.15482e64 1.60989
\(561\) 1.55191e62 0.00389260
\(562\) 6.40209e64 1.53999
\(563\) 9.31800e63 0.214969 0.107484 0.994207i \(-0.465720\pi\)
0.107484 + 0.994207i \(0.465720\pi\)
\(564\) 6.72519e63 0.148815
\(565\) 2.06839e64 0.439029
\(566\) −1.30599e65 −2.65922
\(567\) −8.54113e64 −1.66845
\(568\) −2.44002e64 −0.457306
\(569\) 7.98965e64 1.43678 0.718388 0.695642i \(-0.244880\pi\)
0.718388 + 0.695642i \(0.244880\pi\)
\(570\) 9.18283e63 0.158459
\(571\) −7.20740e64 −1.19352 −0.596761 0.802419i \(-0.703546\pi\)
−0.596761 + 0.802419i \(0.703546\pi\)
\(572\) 5.44100e63 0.0864713
\(573\) −1.57268e64 −0.239887
\(574\) −9.14850e64 −1.33943
\(575\) 2.31707e63 0.0325645
\(576\) 8.73658e64 1.17873
\(577\) 3.11163e64 0.403047 0.201523 0.979484i \(-0.435411\pi\)
0.201523 + 0.979484i \(0.435411\pi\)
\(578\) 9.98500e64 1.24178
\(579\) −1.35127e63 −0.0161360
\(580\) −2.40906e65 −2.76242
\(581\) 2.16512e65 2.38420
\(582\) 2.19238e64 0.231860
\(583\) 1.93591e62 0.00196641
\(584\) 1.38537e65 1.35165
\(585\) −9.16910e64 −0.859338
\(586\) 1.51680e65 1.36563
\(587\) −1.26293e65 −1.09241 −0.546205 0.837652i \(-0.683928\pi\)
−0.546205 + 0.837652i \(0.683928\pi\)
\(588\) −5.89759e64 −0.490126
\(589\) −8.05180e64 −0.642959
\(590\) −9.20919e63 −0.0706642
\(591\) 2.47869e64 0.182775
\(592\) −1.54063e65 −1.09179
\(593\) −1.16829e65 −0.795726 −0.397863 0.917445i \(-0.630248\pi\)
−0.397863 + 0.917445i \(0.630248\pi\)
\(594\) 3.85573e63 0.0252421
\(595\) 1.70107e65 1.07047
\(596\) 4.92284e65 2.97803
\(597\) −2.82354e64 −0.164209
\(598\) 2.02535e64 0.113246
\(599\) −2.64716e65 −1.42315 −0.711573 0.702612i \(-0.752017\pi\)
−0.711573 + 0.702612i \(0.752017\pi\)
\(600\) 1.39384e64 0.0720543
\(601\) −1.04245e65 −0.518208 −0.259104 0.965849i \(-0.583427\pi\)
−0.259104 + 0.965849i \(0.583427\pi\)
\(602\) −8.66075e65 −4.14036
\(603\) −8.77934e64 −0.403650
\(604\) 4.25994e65 1.88380
\(605\) 2.73902e65 1.16505
\(606\) 5.97788e64 0.244591
\(607\) 2.13825e65 0.841635 0.420818 0.907145i \(-0.361743\pi\)
0.420818 + 0.907145i \(0.361743\pi\)
\(608\) −4.04811e64 −0.153292
\(609\) 7.27336e64 0.264989
\(610\) 3.03252e65 1.06305
\(611\) 1.38148e65 0.465990
\(612\) −3.06196e65 −0.993895
\(613\) −9.41515e64 −0.294108 −0.147054 0.989129i \(-0.546979\pi\)
−0.147054 + 0.989129i \(0.546979\pi\)
\(614\) 4.14989e65 1.24761
\(615\) −2.23763e64 −0.0647475
\(616\) −5.98723e64 −0.166755
\(617\) 3.62608e65 0.972156 0.486078 0.873916i \(-0.338427\pi\)
0.486078 + 0.873916i \(0.338427\pi\)
\(618\) −1.61534e65 −0.416902
\(619\) −1.97673e65 −0.491154 −0.245577 0.969377i \(-0.578977\pi\)
−0.245577 + 0.969377i \(0.578977\pi\)
\(620\) −9.45706e65 −2.26231
\(621\) 9.44972e63 0.0217654
\(622\) −7.02804e65 −1.55869
\(623\) 1.22810e66 2.62279
\(624\) 3.53417e64 0.0726858
\(625\) −6.22185e65 −1.23236
\(626\) −1.52340e66 −2.90615
\(627\) −2.59119e63 −0.00476115
\(628\) 1.00470e66 1.77821
\(629\) −4.25801e65 −0.725966
\(630\) 2.09687e66 3.44405
\(631\) −1.83594e65 −0.290515 −0.145257 0.989394i \(-0.546401\pi\)
−0.145257 + 0.989394i \(0.546401\pi\)
\(632\) 2.03526e65 0.310291
\(633\) −1.51089e64 −0.0221945
\(634\) 1.94799e66 2.75734
\(635\) −5.76558e65 −0.786431
\(636\) 5.93158e63 0.00779701
\(637\) −1.21148e66 −1.53475
\(638\) 1.03247e65 0.126064
\(639\) −2.41136e65 −0.283786
\(640\) −1.86435e66 −2.11494
\(641\) 9.34817e64 0.102226 0.0511132 0.998693i \(-0.483723\pi\)
0.0511132 + 0.998693i \(0.483723\pi\)
\(642\) 2.39270e65 0.252240
\(643\) 6.98717e65 0.710139 0.355070 0.934840i \(-0.384457\pi\)
0.355070 + 0.934840i \(0.384457\pi\)
\(644\) −3.04955e65 −0.298826
\(645\) −2.11833e65 −0.200143
\(646\) 6.29925e65 0.573885
\(647\) 8.30387e65 0.729508 0.364754 0.931104i \(-0.381153\pi\)
0.364754 + 0.931104i \(0.381153\pi\)
\(648\) −1.78750e66 −1.51438
\(649\) 2.59863e63 0.00212321
\(650\) 5.95049e65 0.468909
\(651\) 2.85524e65 0.217015
\(652\) 1.09204e66 0.800609
\(653\) −7.01610e65 −0.496176 −0.248088 0.968737i \(-0.579802\pi\)
−0.248088 + 0.968737i \(0.579802\pi\)
\(654\) −2.88889e65 −0.197085
\(655\) −1.12831e66 −0.742606
\(656\) −5.55385e65 −0.352658
\(657\) 1.36910e66 0.838780
\(658\) −3.15929e66 −1.86759
\(659\) 2.56897e66 1.46539 0.732693 0.680559i \(-0.238263\pi\)
0.732693 + 0.680559i \(0.238263\pi\)
\(660\) −3.04342e64 −0.0167525
\(661\) 1.01472e66 0.539028 0.269514 0.962996i \(-0.413137\pi\)
0.269514 + 0.962996i \(0.413137\pi\)
\(662\) 1.91973e66 0.984185
\(663\) 9.76774e64 0.0483311
\(664\) 4.53120e66 2.16403
\(665\) −2.84023e66 −1.30932
\(666\) −5.24875e66 −2.33567
\(667\) 2.53041e65 0.108701
\(668\) 3.17572e66 1.31703
\(669\) −1.54258e65 −0.0617640
\(670\) 2.12136e66 0.820082
\(671\) −8.55710e64 −0.0319409
\(672\) 1.43550e65 0.0517398
\(673\) 1.27088e66 0.442334 0.221167 0.975236i \(-0.429013\pi\)
0.221167 + 0.975236i \(0.429013\pi\)
\(674\) −9.39049e66 −3.15632
\(675\) 2.77634e65 0.0901225
\(676\) −2.72331e66 −0.853789
\(677\) 2.17082e66 0.657341 0.328671 0.944445i \(-0.393399\pi\)
0.328671 + 0.944445i \(0.393399\pi\)
\(678\) −2.71612e65 −0.0794421
\(679\) −6.78098e66 −1.91581
\(680\) 3.56003e66 0.971616
\(681\) −3.19061e65 −0.0841234
\(682\) 4.05309e65 0.103241
\(683\) 7.17341e64 0.0176538 0.00882692 0.999961i \(-0.497190\pi\)
0.00882692 + 0.999961i \(0.497190\pi\)
\(684\) 5.11247e66 1.21566
\(685\) 6.53440e66 1.50133
\(686\) 1.42322e67 3.15976
\(687\) −5.76787e65 −0.123746
\(688\) −5.25774e66 −1.09011
\(689\) 1.21846e65 0.0244151
\(690\) −1.13288e65 −0.0219396
\(691\) −4.47891e66 −0.838374 −0.419187 0.907900i \(-0.637685\pi\)
−0.419187 + 0.907900i \(0.637685\pi\)
\(692\) −5.90801e66 −1.06893
\(693\) −5.91690e65 −0.103482
\(694\) −9.50166e66 −1.60639
\(695\) 3.70338e66 0.605278
\(696\) 1.52218e66 0.240519
\(697\) −1.53497e66 −0.234493
\(698\) 2.69765e66 0.398459
\(699\) 7.28166e65 0.103996
\(700\) −8.95962e66 −1.23733
\(701\) −3.84070e66 −0.512905 −0.256452 0.966557i \(-0.582554\pi\)
−0.256452 + 0.966557i \(0.582554\pi\)
\(702\) 2.42680e66 0.313409
\(703\) 7.10949e66 0.887949
\(704\) 5.95686e65 0.0719548
\(705\) −7.72730e65 −0.0902784
\(706\) 1.43464e67 1.62119
\(707\) −1.84895e67 −2.02101
\(708\) 7.96216e64 0.00841878
\(709\) 6.56172e64 0.00671168 0.00335584 0.999994i \(-0.498932\pi\)
0.00335584 + 0.999994i \(0.498932\pi\)
\(710\) 5.82659e66 0.576558
\(711\) 2.01136e66 0.192555
\(712\) 2.57019e67 2.38059
\(713\) 9.93343e65 0.0890216
\(714\) −2.23377e66 −0.193701
\(715\) −6.25176e65 −0.0524579
\(716\) −2.70075e67 −2.19294
\(717\) −1.10323e66 −0.0866894
\(718\) −1.79927e67 −1.36827
\(719\) −2.12438e67 −1.56352 −0.781760 0.623580i \(-0.785678\pi\)
−0.781760 + 0.623580i \(0.785678\pi\)
\(720\) 1.27296e67 0.906780
\(721\) 4.99620e67 3.44478
\(722\) 1.51193e67 1.00904
\(723\) 1.79971e66 0.116266
\(724\) −1.75366e67 −1.09670
\(725\) 7.43437e66 0.450092
\(726\) −3.59677e66 −0.210815
\(727\) 2.27873e67 1.29311 0.646554 0.762868i \(-0.276209\pi\)
0.646554 + 0.762868i \(0.276209\pi\)
\(728\) −3.76836e67 −2.07045
\(729\) −1.70946e67 −0.909414
\(730\) −3.30816e67 −1.70412
\(731\) −1.45314e67 −0.724850
\(732\) −2.62188e66 −0.126649
\(733\) −2.32774e66 −0.108891 −0.0544454 0.998517i \(-0.517339\pi\)
−0.0544454 + 0.998517i \(0.517339\pi\)
\(734\) 3.81022e67 1.72620
\(735\) 6.77639e66 0.297335
\(736\) 4.99412e65 0.0212242
\(737\) −5.98601e65 −0.0246406
\(738\) −1.89213e67 −0.754442
\(739\) −1.90706e65 −0.00736579 −0.00368290 0.999993i \(-0.501172\pi\)
−0.00368290 + 0.999993i \(0.501172\pi\)
\(740\) 8.35028e67 3.12432
\(741\) −1.63090e66 −0.0591151
\(742\) −2.78648e66 −0.0978507
\(743\) 3.96691e67 1.34963 0.674816 0.737986i \(-0.264223\pi\)
0.674816 + 0.737986i \(0.264223\pi\)
\(744\) 5.97551e66 0.196975
\(745\) −5.65639e67 −1.80662
\(746\) 5.94536e66 0.183999
\(747\) 4.47798e67 1.34291
\(748\) −2.08773e66 −0.0606718
\(749\) −7.40056e67 −2.08421
\(750\) 5.73582e66 0.156551
\(751\) −4.47498e67 −1.18373 −0.591865 0.806037i \(-0.701608\pi\)
−0.591865 + 0.806037i \(0.701608\pi\)
\(752\) −1.91793e67 −0.491716
\(753\) −3.99348e66 −0.0992360
\(754\) 6.49838e67 1.56523
\(755\) −4.89471e67 −1.14281
\(756\) −3.65401e67 −0.827004
\(757\) 1.35751e67 0.297845 0.148922 0.988849i \(-0.452420\pi\)
0.148922 + 0.988849i \(0.452420\pi\)
\(758\) −2.56643e67 −0.545887
\(759\) 3.19673e64 0.000659210 0
\(760\) −5.94410e67 −1.18841
\(761\) 3.22776e67 0.625693 0.312846 0.949804i \(-0.398717\pi\)
0.312846 + 0.949804i \(0.398717\pi\)
\(762\) 7.57112e66 0.142304
\(763\) 8.93529e67 1.62848
\(764\) 2.11567e68 3.73899
\(765\) 3.51822e67 0.602947
\(766\) −1.55410e68 −2.58288
\(767\) 1.63558e66 0.0263621
\(768\) 1.50124e67 0.234672
\(769\) −6.92939e67 −1.05057 −0.525287 0.850925i \(-0.676042\pi\)
−0.525287 + 0.850925i \(0.676042\pi\)
\(770\) 1.42971e67 0.210240
\(771\) 3.44865e65 0.00491894
\(772\) 1.81782e67 0.251504
\(773\) 1.00550e68 1.34947 0.674733 0.738062i \(-0.264259\pi\)
0.674733 + 0.738062i \(0.264259\pi\)
\(774\) −1.79125e68 −2.33208
\(775\) 2.91845e67 0.368606
\(776\) −1.41914e68 −1.73890
\(777\) −2.52109e67 −0.299705
\(778\) 1.59435e68 1.83892
\(779\) 2.56291e67 0.286815
\(780\) −1.91553e67 −0.208001
\(781\) −1.64413e66 −0.0173236
\(782\) −7.77133e66 −0.0794578
\(783\) 3.03197e67 0.300831
\(784\) 1.68191e68 1.61948
\(785\) −1.15441e68 −1.07875
\(786\) 1.48165e67 0.134374
\(787\) −2.41454e66 −0.0212534 −0.0106267 0.999944i \(-0.503383\pi\)
−0.0106267 + 0.999944i \(0.503383\pi\)
\(788\) −3.33449e68 −2.84881
\(789\) −6.70618e66 −0.0556116
\(790\) −4.86007e67 −0.391206
\(791\) 8.40090e67 0.656415
\(792\) −1.23830e67 −0.0939258
\(793\) −5.38584e67 −0.396583
\(794\) 2.46732e68 1.76377
\(795\) −6.81544e65 −0.00473006
\(796\) 3.79841e68 2.55944
\(797\) −2.29036e68 −1.49842 −0.749210 0.662332i \(-0.769567\pi\)
−0.749210 + 0.662332i \(0.769567\pi\)
\(798\) 3.72967e67 0.236921
\(799\) −5.30079e67 −0.326957
\(800\) 1.46728e67 0.0878815
\(801\) 2.54000e68 1.47730
\(802\) −2.29830e68 −1.29810
\(803\) 9.33490e66 0.0512029
\(804\) −1.83410e67 −0.0977028
\(805\) 3.50397e67 0.181283
\(806\) 2.55102e68 1.28186
\(807\) 3.52094e67 0.171842
\(808\) −3.86952e68 −1.83438
\(809\) 7.74628e66 0.0356700 0.0178350 0.999841i \(-0.494323\pi\)
0.0178350 + 0.999841i \(0.494323\pi\)
\(810\) 4.26844e68 1.90929
\(811\) −2.32748e68 −1.01134 −0.505669 0.862727i \(-0.668754\pi\)
−0.505669 + 0.862727i \(0.668754\pi\)
\(812\) −9.78458e68 −4.13024
\(813\) −3.95739e66 −0.0162286
\(814\) −3.57875e67 −0.142580
\(815\) −1.25476e68 −0.485689
\(816\) −1.35607e67 −0.0509993
\(817\) 2.42626e68 0.886584
\(818\) 3.91754e68 1.39095
\(819\) −3.72410e68 −1.28484
\(820\) 3.01020e68 1.00918
\(821\) 4.26945e68 1.39094 0.695470 0.718556i \(-0.255196\pi\)
0.695470 + 0.718556i \(0.255196\pi\)
\(822\) −8.58071e67 −0.271666
\(823\) 1.89793e68 0.583961 0.291981 0.956424i \(-0.405686\pi\)
0.291981 + 0.956424i \(0.405686\pi\)
\(824\) 1.04562e69 3.12667
\(825\) 9.39201e65 0.00272955
\(826\) −3.74038e67 −0.105654
\(827\) −8.12864e67 −0.223171 −0.111586 0.993755i \(-0.535593\pi\)
−0.111586 + 0.993755i \(0.535593\pi\)
\(828\) −6.30721e67 −0.168316
\(829\) −6.84615e68 −1.77589 −0.887943 0.459953i \(-0.847866\pi\)
−0.887943 + 0.459953i \(0.847866\pi\)
\(830\) −1.08202e69 −2.72835
\(831\) −2.82770e67 −0.0693122
\(832\) 3.74925e68 0.893400
\(833\) 4.64848e68 1.07684
\(834\) −4.86312e67 −0.109525
\(835\) −3.64893e68 −0.798975
\(836\) 3.48583e67 0.0742094
\(837\) 1.19024e68 0.246368
\(838\) 6.33456e67 0.127492
\(839\) −4.43097e67 −0.0867147 −0.0433574 0.999060i \(-0.513805\pi\)
−0.0433574 + 0.999060i \(0.513805\pi\)
\(840\) 2.10783e68 0.401118
\(841\) 2.71501e68 0.502418
\(842\) −1.24324e69 −2.23727
\(843\) 6.35996e67 0.111303
\(844\) 2.03254e68 0.345933
\(845\) 3.12911e68 0.517951
\(846\) −6.53417e68 −1.05193
\(847\) 1.11247e69 1.74193
\(848\) −1.69161e67 −0.0257630
\(849\) −1.29740e68 −0.192195
\(850\) −2.28322e68 −0.329006
\(851\) −8.77091e67 −0.122942
\(852\) −5.03760e67 −0.0686899
\(853\) 1.15923e69 1.53768 0.768842 0.639439i \(-0.220833\pi\)
0.768842 + 0.639439i \(0.220833\pi\)
\(854\) 1.23168e69 1.58942
\(855\) −5.87428e68 −0.737481
\(856\) −1.54881e69 −1.89175
\(857\) −1.19885e69 −1.42467 −0.712334 0.701840i \(-0.752362\pi\)
−0.712334 + 0.701840i \(0.752362\pi\)
\(858\) 8.20956e66 0.00949223
\(859\) −1.22015e69 −1.37269 −0.686345 0.727276i \(-0.740786\pi\)
−0.686345 + 0.727276i \(0.740786\pi\)
\(860\) 2.84971e69 3.11952
\(861\) −9.08830e67 −0.0968074
\(862\) 1.58966e69 1.64772
\(863\) 5.27188e68 0.531755 0.265878 0.964007i \(-0.414338\pi\)
0.265878 + 0.964007i \(0.414338\pi\)
\(864\) 5.98401e67 0.0587381
\(865\) 6.78835e68 0.648464
\(866\) −5.97789e68 −0.555748
\(867\) 9.91930e67 0.0897495
\(868\) −3.84105e69 −3.38249
\(869\) 1.37140e67 0.0117544
\(870\) −3.63487e68 −0.303240
\(871\) −3.76760e68 −0.305941
\(872\) 1.87000e69 1.47810
\(873\) −1.40247e69 −1.07909
\(874\) 1.29756e68 0.0971871
\(875\) −1.77408e69 −1.29355
\(876\) 2.86020e68 0.203025
\(877\) −1.25938e69 −0.870296 −0.435148 0.900359i \(-0.643304\pi\)
−0.435148 + 0.900359i \(0.643304\pi\)
\(878\) 1.70303e68 0.114578
\(879\) 1.50682e68 0.0987011
\(880\) 8.67943e67 0.0553539
\(881\) 1.05379e69 0.654365 0.327182 0.944961i \(-0.393901\pi\)
0.327182 + 0.944961i \(0.393901\pi\)
\(882\) 5.73008e69 3.46456
\(883\) 1.51174e69 0.890021 0.445010 0.895525i \(-0.353200\pi\)
0.445010 + 0.895525i \(0.353200\pi\)
\(884\) −1.31402e69 −0.753309
\(885\) −9.14859e66 −0.00510725
\(886\) 1.56397e69 0.850227
\(887\) 2.55796e69 1.35422 0.677108 0.735883i \(-0.263233\pi\)
0.677108 + 0.735883i \(0.263233\pi\)
\(888\) −5.27619e68 −0.272029
\(889\) −2.34173e69 −1.17583
\(890\) −6.13743e69 −3.00138
\(891\) −1.20446e68 −0.0573674
\(892\) 2.07518e69 0.962680
\(893\) 8.85059e68 0.399911
\(894\) 7.42774e68 0.326908
\(895\) 3.10318e69 1.33035
\(896\) −7.57219e69 −3.16216
\(897\) 2.01202e67 0.00818483
\(898\) −3.48364e69 −1.38051
\(899\) 3.18717e69 1.23042
\(900\) −1.85306e69 −0.696933
\(901\) −4.67527e67 −0.0171307
\(902\) −1.29011e68 −0.0460546
\(903\) −8.60376e68 −0.299244
\(904\) 1.75816e69 0.595799
\(905\) 2.01497e69 0.665315
\(906\) 6.42753e68 0.206791
\(907\) −1.67267e69 −0.524373 −0.262186 0.965017i \(-0.584443\pi\)
−0.262186 + 0.965017i \(0.584443\pi\)
\(908\) 4.29221e69 1.31118
\(909\) −3.82406e69 −1.13835
\(910\) 8.99858e69 2.61037
\(911\) −2.16759e68 −0.0612767 −0.0306383 0.999531i \(-0.509754\pi\)
−0.0306383 + 0.999531i \(0.509754\pi\)
\(912\) 2.26420e68 0.0623787
\(913\) 3.05322e68 0.0819775
\(914\) −8.25251e69 −2.15949
\(915\) 3.01257e68 0.0768318
\(916\) 7.75931e69 1.92876
\(917\) −4.58272e69 −1.11031
\(918\) −9.31170e68 −0.219900
\(919\) −1.42756e69 −0.328610 −0.164305 0.986410i \(-0.552538\pi\)
−0.164305 + 0.986410i \(0.552538\pi\)
\(920\) 7.33318e68 0.164543
\(921\) 4.12258e68 0.0901712
\(922\) −5.43826e69 −1.15953
\(923\) −1.03482e69 −0.215092
\(924\) −1.23611e68 −0.0250475
\(925\) −2.57690e69 −0.509057
\(926\) 1.10513e70 2.12841
\(927\) 1.03333e70 1.94029
\(928\) 1.60238e69 0.293351
\(929\) 8.84307e68 0.157846 0.0789231 0.996881i \(-0.474852\pi\)
0.0789231 + 0.996881i \(0.474852\pi\)
\(930\) −1.42691e69 −0.248340
\(931\) −7.76144e69 −1.31712
\(932\) −9.79575e69 −1.62093
\(933\) −6.98179e68 −0.112654
\(934\) −9.78496e69 −1.53960
\(935\) 2.39882e68 0.0368066
\(936\) −7.79387e69 −1.16619
\(937\) −4.16313e69 −0.607491 −0.303746 0.952753i \(-0.598237\pi\)
−0.303746 + 0.952753i \(0.598237\pi\)
\(938\) 8.61607e69 1.22615
\(939\) −1.51338e69 −0.210042
\(940\) 1.03953e70 1.40712
\(941\) 1.24869e70 1.64853 0.824266 0.566203i \(-0.191588\pi\)
0.824266 + 0.566203i \(0.191588\pi\)
\(942\) 1.51592e69 0.195200
\(943\) −3.16183e68 −0.0397113
\(944\) −2.27070e68 −0.0278175
\(945\) 4.19849e69 0.501702
\(946\) −1.22133e69 −0.142361
\(947\) −6.06340e69 −0.689433 −0.344716 0.938707i \(-0.612025\pi\)
−0.344716 + 0.938707i \(0.612025\pi\)
\(948\) 4.20196e68 0.0466075
\(949\) 5.87539e69 0.635741
\(950\) 3.81224e69 0.402416
\(951\) 1.93518e69 0.199287
\(952\) 1.44593e70 1.45271
\(953\) −3.62312e69 −0.355140 −0.177570 0.984108i \(-0.556824\pi\)
−0.177570 + 0.984108i \(0.556824\pi\)
\(954\) −5.76310e68 −0.0551150
\(955\) −2.43092e70 −2.26826
\(956\) 1.48414e70 1.35118
\(957\) 1.02568e68 0.00911131
\(958\) −3.53829e70 −3.06693
\(959\) 2.65400e70 2.24472
\(960\) −2.09714e69 −0.173083
\(961\) 9.50929e67 0.00765858
\(962\) −2.25247e70 −1.77029
\(963\) −1.53061e70 −1.17394
\(964\) −2.42109e70 −1.81217
\(965\) −2.08869e69 −0.152575
\(966\) −4.60126e68 −0.0328031
\(967\) 2.47757e70 1.72387 0.861933 0.507023i \(-0.169254\pi\)
0.861933 + 0.507023i \(0.169254\pi\)
\(968\) 2.32821e70 1.58107
\(969\) 6.25780e68 0.0414775
\(970\) 3.38880e70 2.19235
\(971\) −1.69313e70 −1.06915 −0.534574 0.845122i \(-0.679528\pi\)
−0.534574 + 0.845122i \(0.679528\pi\)
\(972\) −1.13652e70 −0.700517
\(973\) 1.50415e70 0.904983
\(974\) 4.45530e70 2.61663
\(975\) 5.91133e68 0.0338904
\(976\) 7.47726e69 0.418477
\(977\) −1.88519e70 −1.02999 −0.514994 0.857193i \(-0.672206\pi\)
−0.514994 + 0.857193i \(0.672206\pi\)
\(978\) 1.64771e69 0.0878853
\(979\) 1.73185e69 0.0901812
\(980\) −9.11602e70 −4.63439
\(981\) 1.84803e70 0.917250
\(982\) 9.77660e69 0.473770
\(983\) 1.50691e69 0.0712982 0.0356491 0.999364i \(-0.488650\pi\)
0.0356491 + 0.999364i \(0.488650\pi\)
\(984\) −1.90202e69 −0.0878678
\(985\) 3.83136e70 1.72823
\(986\) −2.49345e70 −1.09823
\(987\) −3.13850e69 −0.134980
\(988\) 2.19398e70 0.921393
\(989\) −2.99326e69 −0.122753
\(990\) 2.95698e69 0.118419
\(991\) −3.55474e70 −1.39020 −0.695099 0.718914i \(-0.744639\pi\)
−0.695099 + 0.718914i \(0.744639\pi\)
\(992\) 6.29032e69 0.240242
\(993\) 1.90709e69 0.0711319
\(994\) 2.36651e70 0.862043
\(995\) −4.36441e70 −1.55268
\(996\) 9.35501e69 0.325050
\(997\) −1.08915e70 −0.369618 −0.184809 0.982774i \(-0.559167\pi\)
−0.184809 + 0.982774i \(0.559167\pi\)
\(998\) 5.27347e70 1.74795
\(999\) −1.05094e70 −0.340243
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 1.48.a.a.1.1 4
3.2 odd 2 9.48.a.c.1.4 4
4.3 odd 2 16.48.a.d.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.48.a.a.1.1 4 1.1 even 1 trivial
9.48.a.c.1.4 4 3.2 odd 2
16.48.a.d.1.3 4 4.3 odd 2