Properties

Label 1.44.a.a.1.2
Level $1$
Weight $44$
Character 1.1
Self dual yes
Analytic conductor $11.711$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 44 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.7110395346\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 11258260111 x - 264759545317170\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4}\cdot 5\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(116336.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.18359e6 q^{2} -1.79507e10 q^{3} -7.39521e12 q^{4} -6.39116e14 q^{5} +2.12463e16 q^{6} -1.72730e18 q^{7} +1.91639e19 q^{8} -6.02939e18 q^{9} +O(q^{10})\) \(q-1.18359e6 q^{2} -1.79507e10 q^{3} -7.39521e12 q^{4} -6.39116e14 q^{5} +2.12463e16 q^{6} -1.72730e18 q^{7} +1.91639e19 q^{8} -6.02939e18 q^{9} +7.56451e20 q^{10} +1.05408e22 q^{11} +1.32749e23 q^{12} +1.50541e24 q^{13} +2.04442e24 q^{14} +1.14726e25 q^{15} +4.23668e25 q^{16} -5.54217e26 q^{17} +7.13632e24 q^{18} -1.99446e27 q^{19} +4.72640e27 q^{20} +3.10063e28 q^{21} -1.24760e28 q^{22} +7.48572e28 q^{23} -3.44005e29 q^{24} -7.28399e29 q^{25} -1.78179e30 q^{26} +6.00067e30 q^{27} +1.27738e31 q^{28} -7.64381e30 q^{29} -1.35788e31 q^{30} +1.08077e31 q^{31} -2.18712e32 q^{32} -1.89215e32 q^{33} +6.55966e32 q^{34} +1.10395e33 q^{35} +4.45886e31 q^{36} +2.93069e32 q^{37} +2.36062e33 q^{38} -2.70232e34 q^{39} -1.22479e34 q^{40} +7.49273e34 q^{41} -3.66987e34 q^{42} +1.23211e35 q^{43} -7.79515e34 q^{44} +3.85348e33 q^{45} -8.86002e34 q^{46} -5.61634e35 q^{47} -7.60514e35 q^{48} +7.99756e35 q^{49} +8.62125e35 q^{50} +9.94859e36 q^{51} -1.11328e37 q^{52} +2.77981e36 q^{53} -7.10233e36 q^{54} -6.73680e36 q^{55} -3.31018e37 q^{56} +3.58019e37 q^{57} +9.04713e36 q^{58} +1.73860e38 q^{59} -8.48422e37 q^{60} -1.16569e38 q^{61} -1.27918e37 q^{62} +1.04146e37 q^{63} -1.13797e38 q^{64} -9.62132e38 q^{65} +2.23953e38 q^{66} +9.18410e38 q^{67} +4.09855e39 q^{68} -1.34374e39 q^{69} -1.30662e39 q^{70} -3.76161e39 q^{71} -1.15546e38 q^{72} -9.44690e39 q^{73} -3.46873e38 q^{74} +1.30753e40 q^{75} +1.47494e40 q^{76} -1.82072e40 q^{77} +3.19843e40 q^{78} +3.86685e40 q^{79} -2.70773e40 q^{80} -1.05737e41 q^{81} -8.86831e40 q^{82} +1.39471e41 q^{83} -2.29298e41 q^{84} +3.54209e41 q^{85} -1.45831e41 q^{86} +1.37212e41 q^{87} +2.02002e41 q^{88} +9.05928e41 q^{89} -4.56094e39 q^{90} -2.60030e42 q^{91} -5.53585e41 q^{92} -1.94005e41 q^{93} +6.64744e41 q^{94} +1.27469e42 q^{95} +3.92603e42 q^{96} -1.23492e42 q^{97} -9.46583e41 q^{98} -6.35546e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2209944q^{2} + 24401437812q^{3} + 9822618421824q^{4} + 535205380774170q^{5} - 91793974758443424q^{6} + 301971425665478856q^{7} - 15830863913787348480q^{8} + 477482125171066743231q^{9} + O(q^{10}) \) \( 3q - 2209944q^{2} + 24401437812q^{3} + 9822618421824q^{4} + 535205380774170q^{5} - 91793974758443424q^{6} + 301971425665478856q^{7} - 15830863913787348480q^{8} + \)\(47\!\cdots\!31\)\(q^{9} + \)\(42\!\cdots\!20\)\(q^{10} + \)\(26\!\cdots\!96\)\(q^{11} + \)\(59\!\cdots\!36\)\(q^{12} + \)\(26\!\cdots\!82\)\(q^{13} + \)\(14\!\cdots\!28\)\(q^{14} + \)\(35\!\cdots\!40\)\(q^{15} - \)\(79\!\cdots\!92\)\(q^{16} - \)\(40\!\cdots\!94\)\(q^{17} - \)\(41\!\cdots\!48\)\(q^{18} + \)\(15\!\cdots\!00\)\(q^{19} + \)\(14\!\cdots\!60\)\(q^{20} + \)\(39\!\cdots\!36\)\(q^{21} + \)\(13\!\cdots\!92\)\(q^{22} - \)\(12\!\cdots\!48\)\(q^{23} - \)\(11\!\cdots\!00\)\(q^{24} - \)\(23\!\cdots\!75\)\(q^{25} - \)\(17\!\cdots\!44\)\(q^{26} + \)\(12\!\cdots\!80\)\(q^{27} + \)\(16\!\cdots\!68\)\(q^{28} + \)\(57\!\cdots\!50\)\(q^{29} - \)\(73\!\cdots\!60\)\(q^{30} - \)\(25\!\cdots\!24\)\(q^{31} - \)\(14\!\cdots\!84\)\(q^{32} - \)\(27\!\cdots\!16\)\(q^{33} + \)\(46\!\cdots\!88\)\(q^{34} + \)\(23\!\cdots\!20\)\(q^{35} + \)\(81\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!94\)\(q^{37} - \)\(30\!\cdots\!20\)\(q^{38} - \)\(39\!\cdots\!28\)\(q^{39} - \)\(32\!\cdots\!00\)\(q^{40} + \)\(25\!\cdots\!66\)\(q^{41} + \)\(14\!\cdots\!32\)\(q^{42} + \)\(24\!\cdots\!92\)\(q^{43} - \)\(10\!\cdots\!32\)\(q^{44} + \)\(25\!\cdots\!90\)\(q^{45} - \)\(18\!\cdots\!64\)\(q^{46} + \)\(30\!\cdots\!56\)\(q^{47} - \)\(25\!\cdots\!48\)\(q^{48} + \)\(34\!\cdots\!79\)\(q^{49} + \)\(19\!\cdots\!00\)\(q^{50} + \)\(13\!\cdots\!56\)\(q^{51} - \)\(17\!\cdots\!04\)\(q^{52} + \)\(15\!\cdots\!62\)\(q^{53} - \)\(84\!\cdots\!00\)\(q^{54} + \)\(39\!\cdots\!40\)\(q^{55} - \)\(64\!\cdots\!00\)\(q^{56} + \)\(19\!\cdots\!60\)\(q^{57} - \)\(10\!\cdots\!80\)\(q^{58} + \)\(22\!\cdots\!00\)\(q^{59} + \)\(17\!\cdots\!20\)\(q^{60} - \)\(93\!\cdots\!54\)\(q^{61} - \)\(20\!\cdots\!48\)\(q^{62} - \)\(96\!\cdots\!48\)\(q^{63} - \)\(11\!\cdots\!36\)\(q^{64} - \)\(27\!\cdots\!60\)\(q^{65} + \)\(29\!\cdots\!32\)\(q^{66} - \)\(73\!\cdots\!44\)\(q^{67} + \)\(54\!\cdots\!68\)\(q^{68} + \)\(19\!\cdots\!32\)\(q^{69} + \)\(59\!\cdots\!20\)\(q^{70} - \)\(18\!\cdots\!64\)\(q^{71} - \)\(98\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!98\)\(q^{73} + \)\(16\!\cdots\!08\)\(q^{74} - \)\(21\!\cdots\!00\)\(q^{75} + \)\(77\!\cdots\!00\)\(q^{76} + \)\(59\!\cdots\!92\)\(q^{77} - \)\(19\!\cdots\!96\)\(q^{78} + \)\(15\!\cdots\!00\)\(q^{79} - \)\(10\!\cdots\!80\)\(q^{80} + \)\(73\!\cdots\!63\)\(q^{81} - \)\(32\!\cdots\!68\)\(q^{82} - \)\(89\!\cdots\!28\)\(q^{83} - \)\(34\!\cdots\!12\)\(q^{84} + \)\(43\!\cdots\!20\)\(q^{85} + \)\(25\!\cdots\!96\)\(q^{86} + \)\(17\!\cdots\!40\)\(q^{87} - \)\(25\!\cdots\!60\)\(q^{88} + \)\(20\!\cdots\!50\)\(q^{89} - \)\(23\!\cdots\!60\)\(q^{90} - \)\(11\!\cdots\!84\)\(q^{91} + \)\(68\!\cdots\!56\)\(q^{92} - \)\(49\!\cdots\!96\)\(q^{93} - \)\(13\!\cdots\!32\)\(q^{94} + \)\(31\!\cdots\!00\)\(q^{95} + \)\(10\!\cdots\!36\)\(q^{96} - \)\(38\!\cdots\!94\)\(q^{97} + \)\(24\!\cdots\!08\)\(q^{98} - \)\(14\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18359e6 −0.399077 −0.199538 0.979890i \(-0.563944\pi\)
−0.199538 + 0.979890i \(0.563944\pi\)
\(3\) −1.79507e10 −0.990773 −0.495387 0.868673i \(-0.664974\pi\)
−0.495387 + 0.868673i \(0.664974\pi\)
\(4\) −7.39521e12 −0.840738
\(5\) −6.39116e14 −0.599411 −0.299706 0.954032i \(-0.596888\pi\)
−0.299706 + 0.954032i \(0.596888\pi\)
\(6\) 2.12463e16 0.395394
\(7\) −1.72730e18 −1.16885 −0.584427 0.811446i \(-0.698681\pi\)
−0.584427 + 0.811446i \(0.698681\pi\)
\(8\) 1.91639e19 0.734595
\(9\) −6.02939e18 −0.0183679
\(10\) 7.56451e20 0.239211
\(11\) 1.05408e22 0.429468 0.214734 0.976673i \(-0.431111\pi\)
0.214734 + 0.976673i \(0.431111\pi\)
\(12\) 1.32749e23 0.832981
\(13\) 1.50541e24 1.68995 0.844973 0.534809i \(-0.179617\pi\)
0.844973 + 0.534809i \(0.179617\pi\)
\(14\) 2.04442e24 0.466462
\(15\) 1.14726e25 0.593881
\(16\) 4.23668e25 0.547578
\(17\) −5.54217e26 −1.94549 −0.972743 0.231884i \(-0.925511\pi\)
−0.972743 + 0.231884i \(0.925511\pi\)
\(18\) 7.13632e24 0.00733019
\(19\) −1.99446e27 −0.640652 −0.320326 0.947307i \(-0.603792\pi\)
−0.320326 + 0.947307i \(0.603792\pi\)
\(20\) 4.72640e27 0.503948
\(21\) 3.10063e28 1.15807
\(22\) −1.24760e28 −0.171391
\(23\) 7.48572e28 0.395444 0.197722 0.980258i \(-0.436646\pi\)
0.197722 + 0.980258i \(0.436646\pi\)
\(24\) −3.44005e29 −0.727818
\(25\) −7.28399e29 −0.640706
\(26\) −1.78179e30 −0.674418
\(27\) 6.00067e30 1.00897
\(28\) 1.27738e31 0.982700
\(29\) −7.64381e30 −0.276537 −0.138268 0.990395i \(-0.544154\pi\)
−0.138268 + 0.990395i \(0.544154\pi\)
\(30\) −1.35788e31 −0.237004
\(31\) 1.08077e31 0.0932085 0.0466043 0.998913i \(-0.485160\pi\)
0.0466043 + 0.998913i \(0.485160\pi\)
\(32\) −2.18712e32 −0.953121
\(33\) −1.89215e32 −0.425506
\(34\) 6.55966e32 0.776398
\(35\) 1.10395e33 0.700624
\(36\) 4.45886e31 0.0154426
\(37\) 2.93069e32 0.0563161 0.0281580 0.999603i \(-0.491036\pi\)
0.0281580 + 0.999603i \(0.491036\pi\)
\(38\) 2.36062e33 0.255669
\(39\) −2.70232e34 −1.67435
\(40\) −1.22479e34 −0.440325
\(41\) 7.49273e34 1.58412 0.792058 0.610446i \(-0.209010\pi\)
0.792058 + 0.610446i \(0.209010\pi\)
\(42\) −3.66987e34 −0.462158
\(43\) 1.23211e35 0.935572 0.467786 0.883842i \(-0.345052\pi\)
0.467786 + 0.883842i \(0.345052\pi\)
\(44\) −7.79515e34 −0.361070
\(45\) 3.85348e33 0.0110099
\(46\) −8.86002e34 −0.157812
\(47\) −5.61634e35 −0.630013 −0.315006 0.949090i \(-0.602007\pi\)
−0.315006 + 0.949090i \(0.602007\pi\)
\(48\) −7.60514e35 −0.542526
\(49\) 7.99756e35 0.366220
\(50\) 8.62125e35 0.255691
\(51\) 9.94859e36 1.92754
\(52\) −1.11328e37 −1.42080
\(53\) 2.77981e36 0.235551 0.117775 0.993040i \(-0.462424\pi\)
0.117775 + 0.993040i \(0.462424\pi\)
\(54\) −7.10233e36 −0.402657
\(55\) −6.73680e36 −0.257428
\(56\) −3.31018e37 −0.858635
\(57\) 3.58019e37 0.634741
\(58\) 9.04713e36 0.110359
\(59\) 1.73860e38 1.46852 0.734262 0.678866i \(-0.237528\pi\)
0.734262 + 0.678866i \(0.237528\pi\)
\(60\) −8.48422e37 −0.499298
\(61\) −1.16569e38 −0.480829 −0.240414 0.970670i \(-0.577283\pi\)
−0.240414 + 0.970670i \(0.577283\pi\)
\(62\) −1.27918e37 −0.0371973
\(63\) 1.04146e37 0.0214694
\(64\) −1.13797e38 −0.167210
\(65\) −9.62132e38 −1.01297
\(66\) 2.23953e38 0.169809
\(67\) 9.18410e38 0.503998 0.251999 0.967728i \(-0.418912\pi\)
0.251999 + 0.967728i \(0.418912\pi\)
\(68\) 4.09855e39 1.63564
\(69\) −1.34374e39 −0.391796
\(70\) −1.30662e39 −0.279603
\(71\) −3.76161e39 −0.593361 −0.296681 0.954977i \(-0.595880\pi\)
−0.296681 + 0.954977i \(0.595880\pi\)
\(72\) −1.15546e38 −0.0134930
\(73\) −9.44690e39 −0.820065 −0.410032 0.912071i \(-0.634483\pi\)
−0.410032 + 0.912071i \(0.634483\pi\)
\(74\) −3.46873e38 −0.0224744
\(75\) 1.30753e40 0.634795
\(76\) 1.47494e40 0.538620
\(77\) −1.82072e40 −0.501986
\(78\) 3.19843e40 0.668195
\(79\) 3.86685e40 0.614293 0.307146 0.951662i \(-0.400626\pi\)
0.307146 + 0.951662i \(0.400626\pi\)
\(80\) −2.70773e40 −0.328224
\(81\) −1.05737e41 −0.981295
\(82\) −8.86831e40 −0.632183
\(83\) 1.39471e41 0.766137 0.383068 0.923720i \(-0.374867\pi\)
0.383068 + 0.923720i \(0.374867\pi\)
\(84\) −2.29298e41 −0.973633
\(85\) 3.54209e41 1.16615
\(86\) −1.45831e41 −0.373365
\(87\) 1.37212e41 0.273985
\(88\) 2.02002e41 0.315485
\(89\) 9.05928e41 1.10971 0.554854 0.831948i \(-0.312774\pi\)
0.554854 + 0.831948i \(0.312774\pi\)
\(90\) −4.56094e39 −0.00439380
\(91\) −2.60030e42 −1.97530
\(92\) −5.53585e41 −0.332465
\(93\) −1.94005e41 −0.0923486
\(94\) 6.64744e41 0.251423
\(95\) 1.27469e42 0.384014
\(96\) 3.92603e42 0.944327
\(97\) −1.23492e42 −0.237709 −0.118855 0.992912i \(-0.537922\pi\)
−0.118855 + 0.992912i \(0.537922\pi\)
\(98\) −9.46583e41 −0.146150
\(99\) −6.35546e40 −0.00788842
\(100\) 5.38666e42 0.538666
\(101\) 9.34212e41 0.0754286 0.0377143 0.999289i \(-0.487992\pi\)
0.0377143 + 0.999289i \(0.487992\pi\)
\(102\) −1.17750e43 −0.769235
\(103\) −2.71649e43 −1.43882 −0.719412 0.694584i \(-0.755589\pi\)
−0.719412 + 0.694584i \(0.755589\pi\)
\(104\) 2.88495e43 1.24143
\(105\) −1.98166e43 −0.694160
\(106\) −3.29016e42 −0.0940027
\(107\) 7.12131e43 1.66268 0.831340 0.555764i \(-0.187574\pi\)
0.831340 + 0.555764i \(0.187574\pi\)
\(108\) −4.43762e43 −0.848281
\(109\) 5.74242e43 0.900379 0.450190 0.892933i \(-0.351356\pi\)
0.450190 + 0.892933i \(0.351356\pi\)
\(110\) 7.97361e42 0.102733
\(111\) −5.26079e42 −0.0557965
\(112\) −7.31803e43 −0.640039
\(113\) −6.84403e43 −0.494454 −0.247227 0.968958i \(-0.579519\pi\)
−0.247227 + 0.968958i \(0.579519\pi\)
\(114\) −4.23747e43 −0.253310
\(115\) −4.78425e43 −0.237034
\(116\) 5.65275e43 0.232495
\(117\) −9.07670e42 −0.0310407
\(118\) −2.05779e44 −0.586053
\(119\) 9.57300e44 2.27399
\(120\) 2.19859e44 0.436262
\(121\) −4.91292e44 −0.815557
\(122\) 1.37969e44 0.191888
\(123\) −1.34500e45 −1.56950
\(124\) −7.99250e43 −0.0783640
\(125\) 1.19212e45 0.983458
\(126\) −1.23266e43 −0.00856792
\(127\) −2.23889e45 −1.31297 −0.656483 0.754341i \(-0.727957\pi\)
−0.656483 + 0.754341i \(0.727957\pi\)
\(128\) 2.05850e45 1.01985
\(129\) −2.21172e45 −0.926940
\(130\) 1.13877e45 0.404253
\(131\) 2.93570e45 0.883850 0.441925 0.897052i \(-0.354296\pi\)
0.441925 + 0.897052i \(0.354296\pi\)
\(132\) 1.39928e45 0.357739
\(133\) 3.44503e45 0.748829
\(134\) −1.08702e45 −0.201134
\(135\) −3.83513e45 −0.604789
\(136\) −1.06209e46 −1.42915
\(137\) 1.51920e45 0.174631 0.0873157 0.996181i \(-0.472171\pi\)
0.0873157 + 0.996181i \(0.472171\pi\)
\(138\) 1.59044e45 0.156356
\(139\) 6.55245e44 0.0551551 0.0275775 0.999620i \(-0.491221\pi\)
0.0275775 + 0.999620i \(0.491221\pi\)
\(140\) −8.16392e45 −0.589041
\(141\) 1.00817e46 0.624200
\(142\) 4.45220e45 0.236797
\(143\) 1.58682e46 0.725778
\(144\) −2.55446e44 −0.0100579
\(145\) 4.88528e45 0.165759
\(146\) 1.11813e46 0.327269
\(147\) −1.43562e46 −0.362841
\(148\) −2.16730e45 −0.0473470
\(149\) −8.85478e46 −1.67368 −0.836841 0.547446i \(-0.815600\pi\)
−0.836841 + 0.547446i \(0.815600\pi\)
\(150\) −1.54757e46 −0.253332
\(151\) 8.54056e46 1.21194 0.605971 0.795486i \(-0.292785\pi\)
0.605971 + 0.795486i \(0.292785\pi\)
\(152\) −3.82215e46 −0.470620
\(153\) 3.34159e45 0.0357345
\(154\) 2.15498e46 0.200331
\(155\) −6.90736e45 −0.0558702
\(156\) 1.99842e47 1.40769
\(157\) −6.33166e46 −0.388754 −0.194377 0.980927i \(-0.562269\pi\)
−0.194377 + 0.980927i \(0.562269\pi\)
\(158\) −4.57677e46 −0.245150
\(159\) −4.98996e46 −0.233377
\(160\) 1.39782e47 0.571311
\(161\) −1.29301e47 −0.462217
\(162\) 1.25149e47 0.391612
\(163\) −2.42368e47 −0.664419 −0.332210 0.943206i \(-0.607794\pi\)
−0.332210 + 0.943206i \(0.607794\pi\)
\(164\) −5.54103e47 −1.33183
\(165\) 1.20930e47 0.255053
\(166\) −1.65077e47 −0.305747
\(167\) 2.12976e47 0.346677 0.173339 0.984862i \(-0.444544\pi\)
0.173339 + 0.984862i \(0.444544\pi\)
\(168\) 5.94200e47 0.850713
\(169\) 1.47273e48 1.85592
\(170\) −4.19238e47 −0.465382
\(171\) 1.20253e46 0.0117674
\(172\) −9.11170e47 −0.786571
\(173\) −9.17738e47 −0.699403 −0.349702 0.936861i \(-0.613717\pi\)
−0.349702 + 0.936861i \(0.613717\pi\)
\(174\) −1.62402e47 −0.109341
\(175\) 1.25816e48 0.748892
\(176\) 4.46580e47 0.235167
\(177\) −3.12091e48 −1.45497
\(178\) −1.07225e48 −0.442858
\(179\) 1.88488e48 0.690150 0.345075 0.938575i \(-0.387853\pi\)
0.345075 + 0.938575i \(0.387853\pi\)
\(180\) −2.84973e46 −0.00925645
\(181\) −1.01885e47 −0.0293779 −0.0146889 0.999892i \(-0.504676\pi\)
−0.0146889 + 0.999892i \(0.504676\pi\)
\(182\) 3.07768e48 0.788296
\(183\) 2.09249e48 0.476392
\(184\) 1.43455e48 0.290491
\(185\) −1.87305e47 −0.0337565
\(186\) 2.29623e47 0.0368541
\(187\) −5.84190e48 −0.835525
\(188\) 4.15340e48 0.529676
\(189\) −1.03650e49 −1.17934
\(190\) −1.50871e48 −0.153251
\(191\) 8.44008e48 0.765824 0.382912 0.923785i \(-0.374921\pi\)
0.382912 + 0.923785i \(0.374921\pi\)
\(192\) 2.04274e48 0.165667
\(193\) −2.13716e49 −1.55008 −0.775042 0.631909i \(-0.782272\pi\)
−0.775042 + 0.631909i \(0.782272\pi\)
\(194\) 1.46164e48 0.0948641
\(195\) 1.72709e49 1.00363
\(196\) −5.91436e48 −0.307895
\(197\) 1.92220e49 0.896963 0.448482 0.893792i \(-0.351965\pi\)
0.448482 + 0.893792i \(0.351965\pi\)
\(198\) 7.52225e46 0.00314808
\(199\) 3.32032e49 1.24692 0.623460 0.781855i \(-0.285726\pi\)
0.623460 + 0.781855i \(0.285726\pi\)
\(200\) −1.39589e49 −0.470660
\(201\) −1.64861e49 −0.499347
\(202\) −1.10572e48 −0.0301018
\(203\) 1.32032e49 0.323231
\(204\) −7.35719e49 −1.62055
\(205\) −4.78872e49 −0.949537
\(206\) 3.21521e49 0.574201
\(207\) −4.51343e47 −0.00726347
\(208\) 6.37794e49 0.925377
\(209\) −2.10232e49 −0.275140
\(210\) 2.34547e49 0.277023
\(211\) 7.61623e49 0.812208 0.406104 0.913827i \(-0.366887\pi\)
0.406104 + 0.913827i \(0.366887\pi\)
\(212\) −2.05573e49 −0.198036
\(213\) 6.75235e49 0.587887
\(214\) −8.42871e49 −0.663537
\(215\) −7.87460e49 −0.560792
\(216\) 1.14996e50 0.741186
\(217\) −1.86681e49 −0.108947
\(218\) −6.79667e49 −0.359320
\(219\) 1.69579e50 0.812498
\(220\) 4.98200e49 0.216430
\(221\) −8.34324e50 −3.28777
\(222\) 6.22661e48 0.0222671
\(223\) 2.81313e50 0.913344 0.456672 0.889635i \(-0.349041\pi\)
0.456672 + 0.889635i \(0.349041\pi\)
\(224\) 3.77782e50 1.11406
\(225\) 4.39180e48 0.0117684
\(226\) 8.10052e49 0.197325
\(227\) 4.74569e50 1.05134 0.525670 0.850689i \(-0.323815\pi\)
0.525670 + 0.850689i \(0.323815\pi\)
\(228\) −2.64762e50 −0.533651
\(229\) −1.73705e50 −0.318676 −0.159338 0.987224i \(-0.550936\pi\)
−0.159338 + 0.987224i \(0.550936\pi\)
\(230\) 5.66258e49 0.0945946
\(231\) 3.26831e50 0.497354
\(232\) −1.46485e50 −0.203143
\(233\) −3.86377e50 −0.488494 −0.244247 0.969713i \(-0.578541\pi\)
−0.244247 + 0.969713i \(0.578541\pi\)
\(234\) 1.07431e49 0.0123876
\(235\) 3.58949e50 0.377637
\(236\) −1.28573e51 −1.23464
\(237\) −6.94127e50 −0.608625
\(238\) −1.13305e51 −0.907496
\(239\) 1.53965e51 1.12685 0.563427 0.826166i \(-0.309483\pi\)
0.563427 + 0.826166i \(0.309483\pi\)
\(240\) 4.86057e50 0.325196
\(241\) 1.69305e51 1.03586 0.517932 0.855422i \(-0.326702\pi\)
0.517932 + 0.855422i \(0.326702\pi\)
\(242\) 5.81488e50 0.325470
\(243\) −7.17082e49 −0.0367311
\(244\) 8.62050e50 0.404251
\(245\) −5.11137e50 −0.219516
\(246\) 1.59192e51 0.626351
\(247\) −3.00247e51 −1.08267
\(248\) 2.07117e50 0.0684706
\(249\) −2.50361e51 −0.759068
\(250\) −1.41098e51 −0.392475
\(251\) 1.12233e51 0.286506 0.143253 0.989686i \(-0.454244\pi\)
0.143253 + 0.989686i \(0.454244\pi\)
\(252\) −7.70179e49 −0.0180501
\(253\) 7.89055e50 0.169831
\(254\) 2.64993e51 0.523974
\(255\) −6.35830e51 −1.15539
\(256\) −1.43545e51 −0.239788
\(257\) 5.15162e51 0.791374 0.395687 0.918385i \(-0.370506\pi\)
0.395687 + 0.918385i \(0.370506\pi\)
\(258\) 2.61777e51 0.369920
\(259\) −5.06218e50 −0.0658252
\(260\) 7.11517e51 0.851644
\(261\) 4.60875e49 0.00507939
\(262\) −3.47466e51 −0.352724
\(263\) 9.78033e51 0.914755 0.457377 0.889273i \(-0.348789\pi\)
0.457377 + 0.889273i \(0.348789\pi\)
\(264\) −3.62609e51 −0.312575
\(265\) −1.77662e51 −0.141192
\(266\) −4.07750e51 −0.298840
\(267\) −1.62620e52 −1.09947
\(268\) −6.79184e51 −0.423730
\(269\) −1.17046e52 −0.674037 −0.337019 0.941498i \(-0.609419\pi\)
−0.337019 + 0.941498i \(0.609419\pi\)
\(270\) 4.53922e51 0.241357
\(271\) 1.90564e52 0.935839 0.467919 0.883771i \(-0.345004\pi\)
0.467919 + 0.883771i \(0.345004\pi\)
\(272\) −2.34804e52 −1.06531
\(273\) 4.66771e52 1.95707
\(274\) −1.79811e51 −0.0696913
\(275\) −7.67791e51 −0.275163
\(276\) 9.93723e51 0.329397
\(277\) 3.73097e51 0.114421 0.0572106 0.998362i \(-0.481779\pi\)
0.0572106 + 0.998362i \(0.481779\pi\)
\(278\) −7.75541e50 −0.0220111
\(279\) −6.51636e49 −0.00171204
\(280\) 2.11559e52 0.514675
\(281\) 3.03658e51 0.0684225 0.0342112 0.999415i \(-0.489108\pi\)
0.0342112 + 0.999415i \(0.489108\pi\)
\(282\) −1.19326e52 −0.249104
\(283\) −6.91493e52 −1.33776 −0.668882 0.743369i \(-0.733227\pi\)
−0.668882 + 0.743369i \(0.733227\pi\)
\(284\) 2.78179e52 0.498861
\(285\) −2.28816e52 −0.380471
\(286\) −1.87815e52 −0.289641
\(287\) −1.29422e53 −1.85160
\(288\) 1.31870e51 0.0175068
\(289\) 2.26004e53 2.78492
\(290\) −5.78217e51 −0.0661506
\(291\) 2.21676e52 0.235516
\(292\) 6.98618e52 0.689459
\(293\) −7.58660e52 −0.695654 −0.347827 0.937559i \(-0.613080\pi\)
−0.347827 + 0.937559i \(0.613080\pi\)
\(294\) 1.69918e52 0.144801
\(295\) −1.11117e53 −0.880250
\(296\) 5.61632e51 0.0413695
\(297\) 6.32519e52 0.433321
\(298\) 1.04804e53 0.667927
\(299\) 1.12691e53 0.668279
\(300\) −9.66943e52 −0.533696
\(301\) −2.12822e53 −1.09355
\(302\) −1.01085e53 −0.483658
\(303\) −1.67698e52 −0.0747326
\(304\) −8.44988e52 −0.350807
\(305\) 7.45010e52 0.288214
\(306\) −3.95507e51 −0.0142608
\(307\) −3.17728e53 −1.06802 −0.534011 0.845478i \(-0.679316\pi\)
−0.534011 + 0.845478i \(0.679316\pi\)
\(308\) 1.34646e53 0.422038
\(309\) 4.87629e53 1.42555
\(310\) 8.17548e51 0.0222965
\(311\) 6.14862e53 1.56469 0.782347 0.622843i \(-0.214022\pi\)
0.782347 + 0.622843i \(0.214022\pi\)
\(312\) −5.17868e53 −1.22997
\(313\) 3.42329e53 0.758997 0.379498 0.925192i \(-0.376097\pi\)
0.379498 + 0.925192i \(0.376097\pi\)
\(314\) 7.49409e52 0.155143
\(315\) −6.65612e51 −0.0128690
\(316\) −2.85962e53 −0.516459
\(317\) −5.98968e53 −1.01072 −0.505358 0.862909i \(-0.668640\pi\)
−0.505358 + 0.862909i \(0.668640\pi\)
\(318\) 5.90606e52 0.0931354
\(319\) −8.05719e52 −0.118764
\(320\) 7.27296e52 0.100228
\(321\) −1.27833e54 −1.64734
\(322\) 1.53039e53 0.184460
\(323\) 1.10536e54 1.24638
\(324\) 7.81948e53 0.825012
\(325\) −1.09654e54 −1.08276
\(326\) 2.86864e53 0.265154
\(327\) −1.03081e54 −0.892072
\(328\) 1.43590e54 1.16368
\(329\) 9.70111e53 0.736393
\(330\) −1.43132e53 −0.101786
\(331\) 1.33462e54 0.889317 0.444659 0.895700i \(-0.353325\pi\)
0.444659 + 0.895700i \(0.353325\pi\)
\(332\) −1.03142e54 −0.644120
\(333\) −1.76702e51 −0.00103441
\(334\) −2.52076e53 −0.138351
\(335\) −5.86971e53 −0.302102
\(336\) 1.31364e54 0.634134
\(337\) −2.37074e54 −1.07359 −0.536797 0.843711i \(-0.680366\pi\)
−0.536797 + 0.843711i \(0.680366\pi\)
\(338\) −1.74310e54 −0.740652
\(339\) 1.22855e54 0.489891
\(340\) −2.61945e54 −0.980423
\(341\) 1.13922e53 0.0400301
\(342\) −1.42331e52 −0.00469610
\(343\) 2.39069e54 0.740796
\(344\) 2.36119e54 0.687266
\(345\) 8.58806e53 0.234847
\(346\) 1.08623e54 0.279115
\(347\) −5.56591e54 −1.34417 −0.672083 0.740476i \(-0.734600\pi\)
−0.672083 + 0.740476i \(0.734600\pi\)
\(348\) −1.01471e54 −0.230350
\(349\) 5.55165e54 1.18488 0.592441 0.805614i \(-0.298164\pi\)
0.592441 + 0.805614i \(0.298164\pi\)
\(350\) −1.48915e54 −0.298865
\(351\) 9.03347e54 1.70511
\(352\) −2.30540e54 −0.409335
\(353\) −2.79315e54 −0.466592 −0.233296 0.972406i \(-0.574951\pi\)
−0.233296 + 0.972406i \(0.574951\pi\)
\(354\) 3.69387e54 0.580646
\(355\) 2.40411e54 0.355667
\(356\) −6.69952e54 −0.932973
\(357\) −1.71842e55 −2.25301
\(358\) −2.23092e54 −0.275423
\(359\) 4.56336e54 0.530584 0.265292 0.964168i \(-0.414532\pi\)
0.265292 + 0.964168i \(0.414532\pi\)
\(360\) 7.38475e52 0.00808783
\(361\) −5.71395e54 −0.589565
\(362\) 1.20590e53 0.0117240
\(363\) 8.81904e54 0.808032
\(364\) 1.92297e55 1.66071
\(365\) 6.03767e54 0.491556
\(366\) −2.47665e54 −0.190117
\(367\) −9.24553e54 −0.669286 −0.334643 0.942345i \(-0.608616\pi\)
−0.334643 + 0.942345i \(0.608616\pi\)
\(368\) 3.17146e54 0.216537
\(369\) −4.51765e53 −0.0290969
\(370\) 2.21692e53 0.0134714
\(371\) −4.80157e54 −0.275324
\(372\) 1.43471e54 0.0776409
\(373\) 9.10042e54 0.464859 0.232430 0.972613i \(-0.425332\pi\)
0.232430 + 0.972613i \(0.425332\pi\)
\(374\) 6.91441e54 0.333438
\(375\) −2.13994e55 −0.974384
\(376\) −1.07631e55 −0.462804
\(377\) −1.15071e55 −0.467332
\(378\) 1.22679e55 0.470647
\(379\) −2.67644e55 −0.970096 −0.485048 0.874488i \(-0.661198\pi\)
−0.485048 + 0.874488i \(0.661198\pi\)
\(380\) −9.42660e54 −0.322855
\(381\) 4.01897e55 1.30085
\(382\) −9.98959e54 −0.305622
\(383\) 2.36692e55 0.684556 0.342278 0.939599i \(-0.388801\pi\)
0.342278 + 0.939599i \(0.388801\pi\)
\(384\) −3.69515e55 −1.01044
\(385\) 1.16365e55 0.300896
\(386\) 2.52952e55 0.618603
\(387\) −7.42886e53 −0.0171845
\(388\) 9.13247e54 0.199851
\(389\) 9.04290e55 1.87237 0.936184 0.351509i \(-0.114331\pi\)
0.936184 + 0.351509i \(0.114331\pi\)
\(390\) −2.04417e55 −0.400524
\(391\) −4.14872e55 −0.769331
\(392\) 1.53264e55 0.269023
\(393\) −5.26978e55 −0.875695
\(394\) −2.27510e55 −0.357957
\(395\) −2.47137e55 −0.368214
\(396\) 4.69999e53 0.00663210
\(397\) 5.22770e55 0.698738 0.349369 0.936985i \(-0.386396\pi\)
0.349369 + 0.936985i \(0.386396\pi\)
\(398\) −3.92990e55 −0.497617
\(399\) −6.18407e55 −0.741920
\(400\) −3.08599e55 −0.350837
\(401\) 2.74708e55 0.295983 0.147992 0.988989i \(-0.452719\pi\)
0.147992 + 0.988989i \(0.452719\pi\)
\(402\) 1.95128e55 0.199278
\(403\) 1.62700e55 0.157517
\(404\) −6.90869e54 −0.0634156
\(405\) 6.75783e55 0.588199
\(406\) −1.56271e55 −0.128994
\(407\) 3.08918e54 0.0241860
\(408\) 1.90653e56 1.41596
\(409\) −2.29499e55 −0.161708 −0.0808538 0.996726i \(-0.525765\pi\)
−0.0808538 + 0.996726i \(0.525765\pi\)
\(410\) 5.66788e55 0.378938
\(411\) −2.72707e55 −0.173020
\(412\) 2.00890e56 1.20967
\(413\) −3.00308e56 −1.71649
\(414\) 5.34205e53 0.00289868
\(415\) −8.91385e55 −0.459231
\(416\) −3.29251e56 −1.61072
\(417\) −1.17621e55 −0.0546462
\(418\) 2.48828e55 0.109802
\(419\) −3.63801e54 −0.0152497 −0.00762487 0.999971i \(-0.502427\pi\)
−0.00762487 + 0.999971i \(0.502427\pi\)
\(420\) 1.46548e56 0.583606
\(421\) 1.16447e56 0.440620 0.220310 0.975430i \(-0.429293\pi\)
0.220310 + 0.975430i \(0.429293\pi\)
\(422\) −9.01449e55 −0.324133
\(423\) 3.38631e54 0.0115720
\(424\) 5.32719e55 0.173034
\(425\) 4.03691e56 1.24649
\(426\) −7.99201e55 −0.234612
\(427\) 2.01349e56 0.562019
\(428\) −5.26636e56 −1.39788
\(429\) −2.84846e56 −0.719082
\(430\) 9.32030e55 0.223799
\(431\) 5.90924e56 1.34980 0.674901 0.737908i \(-0.264186\pi\)
0.674901 + 0.737908i \(0.264186\pi\)
\(432\) 2.54229e56 0.552491
\(433\) 1.91269e56 0.395507 0.197754 0.980252i \(-0.436635\pi\)
0.197754 + 0.980252i \(0.436635\pi\)
\(434\) 2.20954e55 0.0434783
\(435\) −8.76942e55 −0.164230
\(436\) −4.24664e56 −0.756983
\(437\) −1.49299e56 −0.253342
\(438\) −2.00711e56 −0.324249
\(439\) −1.21770e57 −1.87307 −0.936537 0.350569i \(-0.885988\pi\)
−0.936537 + 0.350569i \(0.885988\pi\)
\(440\) −1.29103e56 −0.189105
\(441\) −4.82204e54 −0.00672669
\(442\) 9.87497e56 1.31207
\(443\) 2.89543e56 0.366465 0.183233 0.983070i \(-0.441344\pi\)
0.183233 + 0.983070i \(0.441344\pi\)
\(444\) 3.89046e55 0.0469102
\(445\) −5.78993e56 −0.665171
\(446\) −3.32959e56 −0.364494
\(447\) 1.58949e57 1.65824
\(448\) 1.96562e56 0.195444
\(449\) −7.37718e55 −0.0699188 −0.0349594 0.999389i \(-0.511130\pi\)
−0.0349594 + 0.999389i \(0.511130\pi\)
\(450\) −5.19809e54 −0.00469650
\(451\) 7.89794e56 0.680327
\(452\) 5.06130e56 0.415706
\(453\) −1.53309e57 −1.20076
\(454\) −5.61694e56 −0.419565
\(455\) 1.66189e57 1.18402
\(456\) 6.86102e56 0.466278
\(457\) −1.57216e57 −1.01929 −0.509646 0.860384i \(-0.670224\pi\)
−0.509646 + 0.860384i \(0.670224\pi\)
\(458\) 2.05596e56 0.127176
\(459\) −3.32568e57 −1.96294
\(460\) 3.53805e56 0.199283
\(461\) 4.69628e56 0.252455 0.126228 0.992001i \(-0.459713\pi\)
0.126228 + 0.992001i \(0.459713\pi\)
\(462\) −3.86834e56 −0.198482
\(463\) −3.45809e56 −0.169373 −0.0846866 0.996408i \(-0.526989\pi\)
−0.0846866 + 0.996408i \(0.526989\pi\)
\(464\) −3.23844e56 −0.151425
\(465\) 1.23992e56 0.0553547
\(466\) 4.57312e56 0.194946
\(467\) 3.48051e57 1.41687 0.708436 0.705775i \(-0.249401\pi\)
0.708436 + 0.705775i \(0.249401\pi\)
\(468\) 6.71241e55 0.0260971
\(469\) −1.58637e57 −0.589100
\(470\) −4.24849e56 −0.150706
\(471\) 1.13658e57 0.385167
\(472\) 3.33182e57 1.07877
\(473\) 1.29874e57 0.401798
\(474\) 8.21562e56 0.242888
\(475\) 1.45276e57 0.410470
\(476\) −7.07944e57 −1.91183
\(477\) −1.67606e55 −0.00432657
\(478\) −1.82232e57 −0.449701
\(479\) 3.13467e56 0.0739567 0.0369784 0.999316i \(-0.488227\pi\)
0.0369784 + 0.999316i \(0.488227\pi\)
\(480\) −2.50919e57 −0.566040
\(481\) 4.41188e56 0.0951711
\(482\) −2.00387e57 −0.413389
\(483\) 2.32104e57 0.457952
\(484\) 3.63321e57 0.685670
\(485\) 7.89256e56 0.142485
\(486\) 8.48731e55 0.0146585
\(487\) −8.38372e57 −1.38536 −0.692682 0.721243i \(-0.743571\pi\)
−0.692682 + 0.721243i \(0.743571\pi\)
\(488\) −2.23391e57 −0.353215
\(489\) 4.35068e57 0.658289
\(490\) 6.04977e56 0.0876038
\(491\) −5.79408e57 −0.803031 −0.401516 0.915852i \(-0.631516\pi\)
−0.401516 + 0.915852i \(0.631516\pi\)
\(492\) 9.94653e57 1.31954
\(493\) 4.23633e57 0.537998
\(494\) 3.55370e57 0.432067
\(495\) 4.06188e55 0.00472841
\(496\) 4.57887e56 0.0510390
\(497\) 6.49743e57 0.693553
\(498\) 2.96325e57 0.302926
\(499\) 6.67553e56 0.0653618 0.0326809 0.999466i \(-0.489595\pi\)
0.0326809 + 0.999466i \(0.489595\pi\)
\(500\) −8.81600e57 −0.826830
\(501\) −3.82306e57 −0.343479
\(502\) −1.32837e57 −0.114338
\(503\) −2.00370e58 −1.65242 −0.826212 0.563359i \(-0.809509\pi\)
−0.826212 + 0.563359i \(0.809509\pi\)
\(504\) 1.99583e56 0.0157713
\(505\) −5.97070e56 −0.0452127
\(506\) −9.33918e56 −0.0677755
\(507\) −2.64365e58 −1.83879
\(508\) 1.65571e58 1.10386
\(509\) 2.35405e58 1.50447 0.752233 0.658897i \(-0.228977\pi\)
0.752233 + 0.658897i \(0.228977\pi\)
\(510\) 7.52562e57 0.461088
\(511\) 1.63177e58 0.958536
\(512\) −1.64078e58 −0.924157
\(513\) −1.19681e58 −0.646400
\(514\) −6.09741e57 −0.315819
\(515\) 1.73615e58 0.862447
\(516\) 1.63561e58 0.779313
\(517\) −5.92007e57 −0.270571
\(518\) 5.99154e56 0.0262693
\(519\) 1.64740e58 0.692950
\(520\) −1.84382e58 −0.744125
\(521\) 1.49380e58 0.578471 0.289236 0.957258i \(-0.406599\pi\)
0.289236 + 0.957258i \(0.406599\pi\)
\(522\) −5.45486e55 −0.00202707
\(523\) 1.11209e58 0.396602 0.198301 0.980141i \(-0.436458\pi\)
0.198301 + 0.980141i \(0.436458\pi\)
\(524\) −2.17101e58 −0.743086
\(525\) −2.25849e58 −0.741983
\(526\) −1.15759e58 −0.365057
\(527\) −5.98980e57 −0.181336
\(528\) −8.01643e57 −0.232998
\(529\) −3.02305e58 −0.843624
\(530\) 2.10279e57 0.0563463
\(531\) −1.04827e57 −0.0269737
\(532\) −2.54767e58 −0.629569
\(533\) 1.12796e59 2.67707
\(534\) 1.92476e58 0.438772
\(535\) −4.55135e58 −0.996629
\(536\) 1.76003e58 0.370234
\(537\) −3.38349e58 −0.683782
\(538\) 1.38535e58 0.268992
\(539\) 8.43008e57 0.157280
\(540\) 2.83616e58 0.508469
\(541\) 8.34052e57 0.143698 0.0718492 0.997416i \(-0.477110\pi\)
0.0718492 + 0.997416i \(0.477110\pi\)
\(542\) −2.25550e58 −0.373471
\(543\) 1.82891e57 0.0291068
\(544\) 1.21214e59 1.85428
\(545\) −3.67008e58 −0.539697
\(546\) −5.52466e58 −0.781023
\(547\) −6.38951e58 −0.868440 −0.434220 0.900807i \(-0.642976\pi\)
−0.434220 + 0.900807i \(0.642976\pi\)
\(548\) −1.12348e58 −0.146819
\(549\) 7.02838e56 0.00883181
\(550\) 9.08749e57 0.109811
\(551\) 1.52452e58 0.177164
\(552\) −2.57512e58 −0.287811
\(553\) −6.67922e58 −0.718019
\(554\) −4.41593e57 −0.0456628
\(555\) 3.36225e57 0.0334450
\(556\) −4.84567e57 −0.0463710
\(557\) −1.47103e59 −1.35436 −0.677181 0.735816i \(-0.736799\pi\)
−0.677181 + 0.735816i \(0.736799\pi\)
\(558\) 7.71270e55 0.000683237 0
\(559\) 1.85483e59 1.58107
\(560\) 4.67707e58 0.383646
\(561\) 1.04866e59 0.827816
\(562\) −3.59406e57 −0.0273058
\(563\) 9.38359e58 0.686181 0.343090 0.939302i \(-0.388526\pi\)
0.343090 + 0.939302i \(0.388526\pi\)
\(564\) −7.45564e58 −0.524789
\(565\) 4.37413e58 0.296381
\(566\) 8.18444e58 0.533870
\(567\) 1.82640e59 1.14699
\(568\) −7.20869e58 −0.435880
\(569\) −2.42417e59 −1.41140 −0.705698 0.708513i \(-0.749366\pi\)
−0.705698 + 0.708513i \(0.749366\pi\)
\(570\) 2.70824e58 0.151837
\(571\) −2.26275e59 −1.22169 −0.610844 0.791751i \(-0.709170\pi\)
−0.610844 + 0.791751i \(0.709170\pi\)
\(572\) −1.17349e59 −0.610189
\(573\) −1.51505e59 −0.758758
\(574\) 1.53182e59 0.738930
\(575\) −5.45259e58 −0.253364
\(576\) 6.86127e56 0.00307129
\(577\) 2.80486e59 1.20957 0.604786 0.796388i \(-0.293259\pi\)
0.604786 + 0.796388i \(0.293259\pi\)
\(578\) −2.67496e59 −1.11140
\(579\) 3.83636e59 1.53578
\(580\) −3.61277e58 −0.139360
\(581\) −2.40909e59 −0.895502
\(582\) −2.62374e58 −0.0939888
\(583\) 2.93015e58 0.101162
\(584\) −1.81039e59 −0.602416
\(585\) 5.80107e57 0.0186062
\(586\) 8.97942e58 0.277619
\(587\) 6.13483e59 1.82845 0.914226 0.405204i \(-0.132800\pi\)
0.914226 + 0.405204i \(0.132800\pi\)
\(588\) 1.06167e59 0.305054
\(589\) −2.15554e58 −0.0597142
\(590\) 1.31517e59 0.351287
\(591\) −3.45048e59 −0.888687
\(592\) 1.24164e58 0.0308374
\(593\) 3.38684e59 0.811183 0.405591 0.914055i \(-0.367066\pi\)
0.405591 + 0.914055i \(0.367066\pi\)
\(594\) −7.48643e58 −0.172928
\(595\) −6.11826e59 −1.36305
\(596\) 6.54829e59 1.40713
\(597\) −5.96021e59 −1.23542
\(598\) −1.33380e59 −0.266694
\(599\) −8.69352e59 −1.67695 −0.838473 0.544944i \(-0.816551\pi\)
−0.838473 + 0.544944i \(0.816551\pi\)
\(600\) 2.50573e59 0.466317
\(601\) 2.05552e59 0.369080 0.184540 0.982825i \(-0.440920\pi\)
0.184540 + 0.982825i \(0.440920\pi\)
\(602\) 2.51894e59 0.436409
\(603\) −5.53745e57 −0.00925737
\(604\) −6.31592e59 −1.01893
\(605\) 3.13993e59 0.488854
\(606\) 1.98485e58 0.0298240
\(607\) 7.51891e59 1.09043 0.545215 0.838296i \(-0.316448\pi\)
0.545215 + 0.838296i \(0.316448\pi\)
\(608\) 4.36211e59 0.610619
\(609\) −2.37006e59 −0.320249
\(610\) −8.81785e58 −0.115020
\(611\) −8.45489e59 −1.06469
\(612\) −2.47118e58 −0.0300433
\(613\) 6.96117e59 0.817112 0.408556 0.912733i \(-0.366032\pi\)
0.408556 + 0.912733i \(0.366032\pi\)
\(614\) 3.76059e59 0.426222
\(615\) 8.59609e59 0.940776
\(616\) −3.48919e59 −0.368756
\(617\) 1.68634e60 1.72113 0.860567 0.509337i \(-0.170109\pi\)
0.860567 + 0.509337i \(0.170109\pi\)
\(618\) −5.77152e59 −0.568903
\(619\) −1.32244e60 −1.25901 −0.629503 0.776998i \(-0.716742\pi\)
−0.629503 + 0.776998i \(0.716742\pi\)
\(620\) 5.10814e58 0.0469722
\(621\) 4.49194e59 0.398992
\(622\) −7.27744e59 −0.624433
\(623\) −1.56481e60 −1.29709
\(624\) −1.14489e60 −0.916839
\(625\) 6.61886e58 0.0512110
\(626\) −4.05176e59 −0.302898
\(627\) 3.77381e59 0.272601
\(628\) 4.68240e59 0.326840
\(629\) −1.62424e59 −0.109562
\(630\) 7.87811e57 0.00513571
\(631\) 1.50474e60 0.948048 0.474024 0.880512i \(-0.342801\pi\)
0.474024 + 0.880512i \(0.342801\pi\)
\(632\) 7.41038e59 0.451257
\(633\) −1.36717e60 −0.804714
\(634\) 7.08932e59 0.403353
\(635\) 1.43091e60 0.787007
\(636\) 3.69018e59 0.196209
\(637\) 1.20396e60 0.618892
\(638\) 9.53640e58 0.0473958
\(639\) 2.26802e58 0.0108988
\(640\) −1.31562e60 −0.611310
\(641\) −1.27833e60 −0.574373 −0.287187 0.957875i \(-0.592720\pi\)
−0.287187 + 0.957875i \(0.592720\pi\)
\(642\) 1.51301e60 0.657415
\(643\) −1.28540e60 −0.540134 −0.270067 0.962842i \(-0.587046\pi\)
−0.270067 + 0.962842i \(0.587046\pi\)
\(644\) 9.56208e59 0.388603
\(645\) 1.41355e60 0.555618
\(646\) −1.30830e60 −0.497401
\(647\) −3.49078e60 −1.28375 −0.641875 0.766809i \(-0.721843\pi\)
−0.641875 + 0.766809i \(0.721843\pi\)
\(648\) −2.02633e60 −0.720855
\(649\) 1.83262e60 0.630684
\(650\) 1.29785e60 0.432104
\(651\) 3.35106e59 0.107942
\(652\) 1.79236e60 0.558602
\(653\) −4.91548e60 −1.48229 −0.741143 0.671347i \(-0.765716\pi\)
−0.741143 + 0.671347i \(0.765716\pi\)
\(654\) 1.22005e60 0.356005
\(655\) −1.87625e60 −0.529790
\(656\) 3.17443e60 0.867427
\(657\) 5.69590e58 0.0150629
\(658\) −1.14821e60 −0.293877
\(659\) −4.43095e60 −1.09764 −0.548821 0.835940i \(-0.684923\pi\)
−0.548821 + 0.835940i \(0.684923\pi\)
\(660\) −8.94305e59 −0.214433
\(661\) 3.53419e60 0.820274 0.410137 0.912024i \(-0.365481\pi\)
0.410137 + 0.912024i \(0.365481\pi\)
\(662\) −1.57965e60 −0.354906
\(663\) 1.49767e61 3.25743
\(664\) 2.67281e60 0.562800
\(665\) −2.20177e60 −0.448856
\(666\) 2.09143e57 0.000412807 0
\(667\) −5.72194e59 −0.109355
\(668\) −1.57500e60 −0.291465
\(669\) −5.04976e60 −0.904917
\(670\) 6.94733e59 0.120562
\(671\) −1.22873e60 −0.206501
\(672\) −6.78144e60 −1.10378
\(673\) 3.42060e60 0.539236 0.269618 0.962967i \(-0.413103\pi\)
0.269618 + 0.962967i \(0.413103\pi\)
\(674\) 2.80598e60 0.428446
\(675\) −4.37088e60 −0.646455
\(676\) −1.08911e61 −1.56034
\(677\) 6.63114e60 0.920305 0.460152 0.887840i \(-0.347795\pi\)
0.460152 + 0.887840i \(0.347795\pi\)
\(678\) −1.45410e60 −0.195504
\(679\) 2.13307e60 0.277847
\(680\) 6.78802e60 0.856646
\(681\) −8.51884e60 −1.04164
\(682\) −1.34836e59 −0.0159751
\(683\) 4.07501e60 0.467825 0.233913 0.972258i \(-0.424847\pi\)
0.233913 + 0.972258i \(0.424847\pi\)
\(684\) −8.89300e58 −0.00989332
\(685\) −9.70945e59 −0.104676
\(686\) −2.82959e60 −0.295634
\(687\) 3.11813e60 0.315736
\(688\) 5.22005e60 0.512299
\(689\) 4.18476e60 0.398068
\(690\) −1.01647e60 −0.0937218
\(691\) 1.23638e61 1.10503 0.552514 0.833504i \(-0.313669\pi\)
0.552514 + 0.833504i \(0.313669\pi\)
\(692\) 6.78687e60 0.588015
\(693\) 1.09778e59 0.00922042
\(694\) 6.58776e60 0.536425
\(695\) −4.18778e59 −0.0330606
\(696\) 2.62950e60 0.201268
\(697\) −4.15260e61 −3.08188
\(698\) −6.57087e60 −0.472859
\(699\) 6.93574e60 0.483987
\(700\) −9.30439e60 −0.629622
\(701\) 1.41956e61 0.931574 0.465787 0.884897i \(-0.345771\pi\)
0.465787 + 0.884897i \(0.345771\pi\)
\(702\) −1.06919e61 −0.680468
\(703\) −5.84513e59 −0.0360790
\(704\) −1.19951e60 −0.0718114
\(705\) −6.44339e60 −0.374152
\(706\) 3.30594e60 0.186206
\(707\) −1.61367e60 −0.0881650
\(708\) 2.30797e61 1.22325
\(709\) −6.77303e60 −0.348248 −0.174124 0.984724i \(-0.555709\pi\)
−0.174124 + 0.984724i \(0.555709\pi\)
\(710\) −2.84547e60 −0.141938
\(711\) −2.33148e59 −0.0112833
\(712\) 1.73611e61 0.815186
\(713\) 8.09032e59 0.0368588
\(714\) 2.03391e61 0.899123
\(715\) −1.01416e61 −0.435039
\(716\) −1.39391e61 −0.580235
\(717\) −2.76378e61 −1.11646
\(718\) −5.40114e60 −0.211744
\(719\) 3.64283e61 1.38601 0.693006 0.720931i \(-0.256286\pi\)
0.693006 + 0.720931i \(0.256286\pi\)
\(720\) 1.63260e59 0.00602879
\(721\) 4.69219e61 1.68177
\(722\) 6.76297e60 0.235282
\(723\) −3.03914e61 −1.02631
\(724\) 7.53460e59 0.0246991
\(725\) 5.56774e60 0.177179
\(726\) −1.04381e61 −0.322467
\(727\) −1.87172e61 −0.561372 −0.280686 0.959800i \(-0.590562\pi\)
−0.280686 + 0.959800i \(0.590562\pi\)
\(728\) −4.98317e61 −1.45105
\(729\) 3.59962e61 1.01769
\(730\) −7.14612e60 −0.196168
\(731\) −6.82856e61 −1.82014
\(732\) −1.54744e61 −0.400521
\(733\) 4.58324e61 1.15196 0.575980 0.817464i \(-0.304621\pi\)
0.575980 + 0.817464i \(0.304621\pi\)
\(734\) 1.09429e61 0.267096
\(735\) 9.17527e60 0.217491
\(736\) −1.63722e61 −0.376906
\(737\) 9.68078e60 0.216451
\(738\) 5.34705e59 0.0116119
\(739\) −6.45765e59 −0.0136213 −0.00681066 0.999977i \(-0.502168\pi\)
−0.00681066 + 0.999977i \(0.502168\pi\)
\(740\) 1.38516e60 0.0283803
\(741\) 5.38965e61 1.07268
\(742\) 5.68309e60 0.109875
\(743\) 3.46765e61 0.651291 0.325646 0.945492i \(-0.394418\pi\)
0.325646 + 0.945492i \(0.394418\pi\)
\(744\) −3.71789e60 −0.0678388
\(745\) 5.65923e61 1.00322
\(746\) −1.07712e61 −0.185514
\(747\) −8.40927e59 −0.0140723
\(748\) 4.32020e61 0.702457
\(749\) −1.23007e62 −1.94343
\(750\) 2.53281e61 0.388854
\(751\) −3.57168e61 −0.532861 −0.266430 0.963854i \(-0.585844\pi\)
−0.266430 + 0.963854i \(0.585844\pi\)
\(752\) −2.37946e61 −0.344981
\(753\) −2.01465e61 −0.283863
\(754\) 1.36196e61 0.186501
\(755\) −5.45841e61 −0.726452
\(756\) 7.66511e61 0.991517
\(757\) −1.06737e62 −1.34200 −0.671002 0.741456i \(-0.734136\pi\)
−0.671002 + 0.741456i \(0.734136\pi\)
\(758\) 3.16781e61 0.387142
\(759\) −1.41641e61 −0.168264
\(760\) 2.44280e61 0.282095
\(761\) 9.90270e61 1.11169 0.555845 0.831286i \(-0.312395\pi\)
0.555845 + 0.831286i \(0.312395\pi\)
\(762\) −4.75681e61 −0.519140
\(763\) −9.91890e61 −1.05241
\(764\) −6.24161e61 −0.643857
\(765\) −2.13566e60 −0.0214196
\(766\) −2.80146e61 −0.273190
\(767\) 2.61730e62 2.48173
\(768\) 2.57673e61 0.237576
\(769\) −2.55003e61 −0.228628 −0.114314 0.993445i \(-0.536467\pi\)
−0.114314 + 0.993445i \(0.536467\pi\)
\(770\) −1.37728e61 −0.120080
\(771\) −9.24752e61 −0.784073
\(772\) 1.58048e62 1.30322
\(773\) 1.50600e62 1.20772 0.603861 0.797090i \(-0.293628\pi\)
0.603861 + 0.797090i \(0.293628\pi\)
\(774\) 8.79272e59 0.00685792
\(775\) −7.87229e60 −0.0597193
\(776\) −2.36658e61 −0.174620
\(777\) 9.08696e60 0.0652179
\(778\) −1.07031e62 −0.747219
\(779\) −1.49439e62 −1.01487
\(780\) −1.27722e62 −0.843786
\(781\) −3.96504e61 −0.254830
\(782\) 4.91038e61 0.307022
\(783\) −4.58680e61 −0.279018
\(784\) 3.38831e61 0.200534
\(785\) 4.04667e61 0.233024
\(786\) 6.23726e61 0.349469
\(787\) 1.74985e62 0.953989 0.476994 0.878906i \(-0.341726\pi\)
0.476994 + 0.878906i \(0.341726\pi\)
\(788\) −1.42151e62 −0.754111
\(789\) −1.75564e62 −0.906315
\(790\) 2.92509e61 0.146946
\(791\) 1.18217e62 0.577944
\(792\) −1.21795e60 −0.00579480
\(793\) −1.75484e62 −0.812575
\(794\) −6.18745e61 −0.278850
\(795\) 3.18916e61 0.139889
\(796\) −2.45545e62 −1.04833
\(797\) 3.53459e62 1.46888 0.734438 0.678676i \(-0.237446\pi\)
0.734438 + 0.678676i \(0.237446\pi\)
\(798\) 7.31939e61 0.296083
\(799\) 3.11267e62 1.22568
\(800\) 1.59310e62 0.610671
\(801\) −5.46219e60 −0.0203830
\(802\) −3.25142e61 −0.118120
\(803\) −9.95780e61 −0.352192
\(804\) 1.21918e62 0.419820
\(805\) 8.26384e61 0.277058
\(806\) −1.92570e61 −0.0628615
\(807\) 2.10106e62 0.667818
\(808\) 1.79031e61 0.0554095
\(809\) −4.31937e62 −1.30175 −0.650875 0.759185i \(-0.725598\pi\)
−0.650875 + 0.759185i \(0.725598\pi\)
\(810\) −7.99850e61 −0.234736
\(811\) −5.78809e62 −1.65419 −0.827097 0.562059i \(-0.810010\pi\)
−0.827097 + 0.562059i \(0.810010\pi\)
\(812\) −9.76401e61 −0.271753
\(813\) −3.42076e62 −0.927204
\(814\) −3.65632e60 −0.00965205
\(815\) 1.54901e62 0.398260
\(816\) 4.21490e62 1.05548
\(817\) −2.45739e62 −0.599376
\(818\) 2.71633e61 0.0645337
\(819\) 1.56782e61 0.0362821
\(820\) 3.54136e62 0.798311
\(821\) −1.86128e62 −0.408727 −0.204364 0.978895i \(-0.565512\pi\)
−0.204364 + 0.978895i \(0.565512\pi\)
\(822\) 3.22773e61 0.0690483
\(823\) 6.65210e62 1.38632 0.693158 0.720785i \(-0.256219\pi\)
0.693158 + 0.720785i \(0.256219\pi\)
\(824\) −5.20584e62 −1.05695
\(825\) 1.37824e62 0.272624
\(826\) 3.55442e62 0.685011
\(827\) −6.49406e61 −0.121940 −0.0609702 0.998140i \(-0.519419\pi\)
−0.0609702 + 0.998140i \(0.519419\pi\)
\(828\) 3.33778e60 0.00610668
\(829\) 4.83956e62 0.862746 0.431373 0.902174i \(-0.358029\pi\)
0.431373 + 0.902174i \(0.358029\pi\)
\(830\) 1.05503e62 0.183268
\(831\) −6.69735e61 −0.113365
\(832\) −1.71311e62 −0.282576
\(833\) −4.43239e62 −0.712476
\(834\) 1.39215e61 0.0218080
\(835\) −1.36116e62 −0.207802
\(836\) 1.55471e62 0.231320
\(837\) 6.48533e61 0.0940448
\(838\) 4.30591e60 0.00608582
\(839\) 5.22756e62 0.720140 0.360070 0.932925i \(-0.382753\pi\)
0.360070 + 0.932925i \(0.382753\pi\)
\(840\) −3.79763e62 −0.509927
\(841\) −7.05608e62 −0.923527
\(842\) −1.37826e62 −0.175841
\(843\) −5.45087e61 −0.0677912
\(844\) −5.63236e62 −0.682854
\(845\) −9.41244e62 −1.11246
\(846\) −4.00800e60 −0.00461812
\(847\) 8.48610e62 0.953267
\(848\) 1.17772e62 0.128982
\(849\) 1.24128e63 1.32542
\(850\) −4.77805e62 −0.497443
\(851\) 2.19383e61 0.0222699
\(852\) −4.99351e62 −0.494259
\(853\) 3.48905e62 0.336747 0.168373 0.985723i \(-0.446149\pi\)
0.168373 + 0.985723i \(0.446149\pi\)
\(854\) −2.38315e62 −0.224289
\(855\) −7.68560e60 −0.00705352
\(856\) 1.36472e63 1.22140
\(857\) 5.09487e62 0.444678 0.222339 0.974969i \(-0.428631\pi\)
0.222339 + 0.974969i \(0.428631\pi\)
\(858\) 3.37141e62 0.286969
\(859\) −1.66852e63 −1.38509 −0.692546 0.721374i \(-0.743511\pi\)
−0.692546 + 0.721374i \(0.743511\pi\)
\(860\) 5.82343e62 0.471479
\(861\) 2.32321e63 1.83452
\(862\) −6.99411e62 −0.538674
\(863\) 6.32017e62 0.474785 0.237392 0.971414i \(-0.423707\pi\)
0.237392 + 0.971414i \(0.423707\pi\)
\(864\) −1.31242e63 −0.961672
\(865\) 5.86541e62 0.419230
\(866\) −2.26384e62 −0.157838
\(867\) −4.05693e63 −2.75922
\(868\) 1.38055e62 0.0915960
\(869\) 4.07598e62 0.263819
\(870\) 1.03794e62 0.0655403
\(871\) 1.38258e63 0.851728
\(872\) 1.10047e63 0.661414
\(873\) 7.44579e60 0.00436621
\(874\) 1.76709e62 0.101103
\(875\) −2.05916e63 −1.14952
\(876\) −1.25407e63 −0.683098
\(877\) −2.16093e63 −1.14855 −0.574274 0.818664i \(-0.694715\pi\)
−0.574274 + 0.818664i \(0.694715\pi\)
\(878\) 1.44126e63 0.747500
\(879\) 1.36185e63 0.689236
\(880\) −2.85417e62 −0.140962
\(881\) −1.77705e63 −0.856481 −0.428241 0.903665i \(-0.640866\pi\)
−0.428241 + 0.903665i \(0.640866\pi\)
\(882\) 5.70732e60 0.00268446
\(883\) −2.16218e63 −0.992515 −0.496258 0.868175i \(-0.665293\pi\)
−0.496258 + 0.868175i \(0.665293\pi\)
\(884\) 6.17000e63 2.76415
\(885\) 1.99462e63 0.872128
\(886\) −3.42700e62 −0.146248
\(887\) 9.41993e62 0.392365 0.196182 0.980567i \(-0.437146\pi\)
0.196182 + 0.980567i \(0.437146\pi\)
\(888\) −1.00817e62 −0.0409878
\(889\) 3.86725e63 1.53467
\(890\) 6.85290e62 0.265454
\(891\) −1.11455e63 −0.421435
\(892\) −2.08037e63 −0.767883
\(893\) 1.12015e63 0.403619
\(894\) −1.88131e63 −0.661765
\(895\) −1.20466e63 −0.413684
\(896\) −3.55565e63 −1.19206
\(897\) −2.02288e63 −0.662113
\(898\) 8.73155e61 0.0279030
\(899\) −8.26118e61 −0.0257756
\(900\) −3.24783e61 −0.00989416
\(901\) −1.54062e63 −0.458261
\(902\) −9.34791e62 −0.271503
\(903\) 3.82031e63 1.08346
\(904\) −1.31158e63 −0.363223
\(905\) 6.51163e61 0.0176094
\(906\) 1.81455e63 0.479195
\(907\) 4.24432e63 1.09459 0.547295 0.836940i \(-0.315658\pi\)
0.547295 + 0.836940i \(0.315658\pi\)
\(908\) −3.50953e63 −0.883901
\(909\) −5.63272e60 −0.00138546
\(910\) −1.96700e63 −0.472513
\(911\) −1.73895e63 −0.407983 −0.203991 0.978973i \(-0.565391\pi\)
−0.203991 + 0.978973i \(0.565391\pi\)
\(912\) 1.51681e63 0.347570
\(913\) 1.47014e63 0.329031
\(914\) 1.86079e63 0.406776
\(915\) −1.33734e63 −0.285555
\(916\) 1.28459e63 0.267923
\(917\) −5.07084e63 −1.03309
\(918\) 3.93624e63 0.783364
\(919\) 8.49800e63 1.65209 0.826044 0.563606i \(-0.190586\pi\)
0.826044 + 0.563606i \(0.190586\pi\)
\(920\) −9.16846e62 −0.174124
\(921\) 5.70343e63 1.05817
\(922\) −5.55847e62 −0.100749
\(923\) −5.66276e63 −1.00275
\(924\) −2.41698e63 −0.418145
\(925\) −2.13471e62 −0.0360821
\(926\) 4.09296e62 0.0675929
\(927\) 1.63788e62 0.0264281
\(928\) 1.67179e63 0.263573
\(929\) −6.41656e63 −0.988472 −0.494236 0.869328i \(-0.664552\pi\)
−0.494236 + 0.869328i \(0.664552\pi\)
\(930\) −1.46756e62 −0.0220908
\(931\) −1.59508e63 −0.234619
\(932\) 2.85734e63 0.410695
\(933\) −1.10372e64 −1.55026
\(934\) −4.11950e63 −0.565440
\(935\) 3.73365e63 0.500823
\(936\) −1.73945e62 −0.0228024
\(937\) 4.22960e63 0.541874 0.270937 0.962597i \(-0.412666\pi\)
0.270937 + 0.962597i \(0.412666\pi\)
\(938\) 1.87761e63 0.235096
\(939\) −6.14504e63 −0.751994
\(940\) −2.65451e63 −0.317493
\(941\) 5.97856e63 0.698907 0.349454 0.936954i \(-0.386367\pi\)
0.349454 + 0.936954i \(0.386367\pi\)
\(942\) −1.34524e63 −0.153711
\(943\) 5.60885e63 0.626429
\(944\) 7.36589e63 0.804132
\(945\) 6.62442e63 0.706910
\(946\) −1.53718e63 −0.160348
\(947\) −3.09116e63 −0.315208 −0.157604 0.987502i \(-0.550377\pi\)
−0.157604 + 0.987502i \(0.550377\pi\)
\(948\) 5.13322e63 0.511694
\(949\) −1.42215e64 −1.38586
\(950\) −1.71947e63 −0.163809
\(951\) 1.07519e64 1.00139
\(952\) 1.83456e64 1.67046
\(953\) −8.78118e62 −0.0781727 −0.0390864 0.999236i \(-0.512445\pi\)
−0.0390864 + 0.999236i \(0.512445\pi\)
\(954\) 1.98376e61 0.00172663
\(955\) −5.39419e63 −0.459044
\(956\) −1.13860e64 −0.947389
\(957\) 1.44632e63 0.117668
\(958\) −3.71016e62 −0.0295144
\(959\) −2.62411e63 −0.204119
\(960\) −1.30555e63 −0.0993028
\(961\) −1.33279e64 −0.991312
\(962\) −5.22186e62 −0.0379805
\(963\) −4.29371e62 −0.0305399
\(964\) −1.25204e64 −0.870891
\(965\) 1.36590e64 0.929138
\(966\) −2.74716e63 −0.182758
\(967\) 1.67955e63 0.109275 0.0546377 0.998506i \(-0.482600\pi\)
0.0546377 + 0.998506i \(0.482600\pi\)
\(968\) −9.41505e63 −0.599104
\(969\) −1.98420e64 −1.23488
\(970\) −9.34155e62 −0.0568626
\(971\) 2.39350e64 1.42502 0.712508 0.701664i \(-0.247559\pi\)
0.712508 + 0.701664i \(0.247559\pi\)
\(972\) 5.30297e62 0.0308812
\(973\) −1.13181e63 −0.0644682
\(974\) 9.92288e63 0.552866
\(975\) 1.96836e64 1.07277
\(976\) −4.93864e63 −0.263291
\(977\) 1.55784e64 0.812438 0.406219 0.913776i \(-0.366847\pi\)
0.406219 + 0.913776i \(0.366847\pi\)
\(978\) −5.14942e63 −0.262708
\(979\) 9.54921e63 0.476584
\(980\) 3.77997e63 0.184556
\(981\) −3.46233e62 −0.0165381
\(982\) 6.85781e63 0.320471
\(983\) 8.28128e63 0.378614 0.189307 0.981918i \(-0.439376\pi\)
0.189307 + 0.981918i \(0.439376\pi\)
\(984\) −2.57753e64 −1.15295
\(985\) −1.22851e64 −0.537650
\(986\) −5.01408e63 −0.214703
\(987\) −1.74142e64 −0.729599
\(988\) 2.22039e64 0.910239
\(989\) 9.22322e63 0.369966
\(990\) −4.80760e61 −0.00188700
\(991\) −1.98538e64 −0.762537 −0.381269 0.924464i \(-0.624513\pi\)
−0.381269 + 0.924464i \(0.624513\pi\)
\(992\) −2.36377e63 −0.0888390
\(993\) −2.39574e64 −0.881112
\(994\) −7.69029e63 −0.276781
\(995\) −2.12207e64 −0.747418
\(996\) 1.85147e64 0.638177
\(997\) 5.32681e64 1.79689 0.898444 0.439088i \(-0.144698\pi\)
0.898444 + 0.439088i \(0.144698\pi\)
\(998\) −7.90108e62 −0.0260844
\(999\) 1.75861e63 0.0568213
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 1.44.a.a.1.2 3
3.2 odd 2 9.44.a.b.1.2 3
4.3 odd 2 16.44.a.c.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.44.a.a.1.2 3 1.1 even 1 trivial
9.44.a.b.1.2 3 3.2 odd 2
16.44.a.c.1.3 3 4.3 odd 2