Properties

Label 1.46.a.a.1.3
Level $1$
Weight $46$
Character 1.1
Self dual yes
Analytic conductor $12.826$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 46 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.8255726074\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - x^{2} - 148878150 x + 389915850150\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{14}\cdot 3^{6}\cdot 5 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(10585.6\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+7.36851e6 q^{2} -5.75337e10 q^{3} +1.91106e13 q^{4} +5.97253e15 q^{5} -4.23938e17 q^{6} -1.35754e19 q^{7} -1.18440e20 q^{8} +3.55813e20 q^{9} +O(q^{10})\) \(q+7.36851e6 q^{2} -5.75337e10 q^{3} +1.91106e13 q^{4} +5.97253e15 q^{5} -4.23938e17 q^{6} -1.35754e19 q^{7} -1.18440e20 q^{8} +3.55813e20 q^{9} +4.40087e22 q^{10} -4.62684e23 q^{11} -1.09950e24 q^{12} +1.84657e24 q^{13} -1.00031e26 q^{14} -3.43622e26 q^{15} -1.54512e27 q^{16} +5.39007e27 q^{17} +2.62181e27 q^{18} +2.04232e28 q^{19} +1.14139e29 q^{20} +7.81043e29 q^{21} -3.40930e30 q^{22} -4.06607e30 q^{23} +6.81427e30 q^{24} +7.24945e30 q^{25} +1.36065e31 q^{26} +1.49501e32 q^{27} -2.59434e32 q^{28} +6.91615e32 q^{29} -2.53198e33 q^{30} -4.29419e32 q^{31} -7.21801e33 q^{32} +2.66199e34 q^{33} +3.97168e34 q^{34} -8.10796e34 q^{35} +6.79980e33 q^{36} -1.38069e35 q^{37} +1.50489e35 q^{38} -1.06240e35 q^{39} -7.07385e35 q^{40} +9.02413e35 q^{41} +5.75513e36 q^{42} -2.22460e36 q^{43} -8.84218e36 q^{44} +2.12510e36 q^{45} -2.99609e37 q^{46} -1.00563e37 q^{47} +8.88964e37 q^{48} +7.72848e37 q^{49} +5.34177e37 q^{50} -3.10111e38 q^{51} +3.52891e37 q^{52} -2.47477e38 q^{53} +1.10160e39 q^{54} -2.76340e39 q^{55} +1.60787e39 q^{56} -1.17502e39 q^{57} +5.09618e39 q^{58} +1.01841e40 q^{59} -6.56683e39 q^{60} -2.35593e40 q^{61} -3.16418e39 q^{62} -4.83030e39 q^{63} +1.17807e39 q^{64} +1.10287e40 q^{65} +1.96149e41 q^{66} -2.39925e41 q^{67} +1.03008e41 q^{68} +2.33936e41 q^{69} -5.97436e41 q^{70} +4.61674e40 q^{71} -4.21424e40 q^{72} +6.89694e41 q^{73} -1.01736e42 q^{74} -4.17088e41 q^{75} +3.90301e41 q^{76} +6.28113e42 q^{77} -7.82832e41 q^{78} -1.80775e42 q^{79} -9.22828e42 q^{80} -9.65254e42 q^{81} +6.64944e42 q^{82} +1.09933e42 q^{83} +1.49262e43 q^{84} +3.21924e43 q^{85} -1.63920e43 q^{86} -3.97912e43 q^{87} +5.48002e43 q^{88} -5.72005e43 q^{89} +1.56589e43 q^{90} -2.50680e43 q^{91} -7.77051e43 q^{92} +2.47061e43 q^{93} -7.41002e43 q^{94} +1.21978e44 q^{95} +4.15279e44 q^{96} -2.85037e44 q^{97} +5.69474e44 q^{98} -1.64629e44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3814272q^{2} + 5359866876q^{3} - 1915164893184q^{4} - 912448458460350q^{5} - 84402581069044224q^{6} - 7619710926638056008q^{7} - 108947667758662287360q^{8} + 1158701600689591796919q^{9} + O(q^{10}) \) \( 3q + 3814272q^{2} + 5359866876q^{3} - 1915164893184q^{4} - 912448458460350q^{5} - 84402581069044224q^{6} - 7619710926638056008q^{7} - \)\(10\!\cdots\!60\)\(q^{8} + \)\(11\!\cdots\!19\)\(q^{9} + \)\(14\!\cdots\!00\)\(q^{10} - \)\(29\!\cdots\!44\)\(q^{11} - \)\(33\!\cdots\!48\)\(q^{12} - \)\(24\!\cdots\!54\)\(q^{13} - \)\(20\!\cdots\!48\)\(q^{14} - \)\(11\!\cdots\!00\)\(q^{15} - \)\(25\!\cdots\!32\)\(q^{16} + \)\(11\!\cdots\!82\)\(q^{17} + \)\(29\!\cdots\!76\)\(q^{18} + \)\(13\!\cdots\!80\)\(q^{19} + \)\(38\!\cdots\!00\)\(q^{20} + \)\(22\!\cdots\!96\)\(q^{21} - \)\(36\!\cdots\!56\)\(q^{22} - \)\(10\!\cdots\!84\)\(q^{23} - \)\(10\!\cdots\!60\)\(q^{24} + \)\(43\!\cdots\!25\)\(q^{25} + \)\(10\!\cdots\!16\)\(q^{26} + \)\(28\!\cdots\!40\)\(q^{27} + \)\(53\!\cdots\!84\)\(q^{28} - \)\(67\!\cdots\!30\)\(q^{29} - \)\(44\!\cdots\!00\)\(q^{30} - \)\(43\!\cdots\!44\)\(q^{31} + \)\(27\!\cdots\!72\)\(q^{32} + \)\(32\!\cdots\!52\)\(q^{33} + \)\(53\!\cdots\!32\)\(q^{34} + \)\(15\!\cdots\!00\)\(q^{35} - \)\(10\!\cdots\!32\)\(q^{36} - \)\(38\!\cdots\!38\)\(q^{37} - \)\(29\!\cdots\!40\)\(q^{38} - \)\(40\!\cdots\!32\)\(q^{39} + \)\(14\!\cdots\!00\)\(q^{40} + \)\(27\!\cdots\!06\)\(q^{41} + \)\(55\!\cdots\!24\)\(q^{42} + \)\(12\!\cdots\!56\)\(q^{43} - \)\(10\!\cdots\!68\)\(q^{44} - \)\(36\!\cdots\!50\)\(q^{45} - \)\(29\!\cdots\!44\)\(q^{46} - \)\(53\!\cdots\!48\)\(q^{47} + \)\(14\!\cdots\!16\)\(q^{48} + \)\(78\!\cdots\!71\)\(q^{49} + \)\(36\!\cdots\!00\)\(q^{50} - \)\(37\!\cdots\!64\)\(q^{51} + \)\(13\!\cdots\!92\)\(q^{52} - \)\(18\!\cdots\!74\)\(q^{53} + \)\(59\!\cdots\!80\)\(q^{54} - \)\(34\!\cdots\!00\)\(q^{55} + \)\(52\!\cdots\!80\)\(q^{56} + \)\(10\!\cdots\!80\)\(q^{57} + \)\(13\!\cdots\!40\)\(q^{58} - \)\(35\!\cdots\!60\)\(q^{59} + \)\(13\!\cdots\!00\)\(q^{60} - \)\(51\!\cdots\!94\)\(q^{61} - \)\(56\!\cdots\!56\)\(q^{62} - \)\(63\!\cdots\!64\)\(q^{63} + \)\(41\!\cdots\!36\)\(q^{64} + \)\(37\!\cdots\!00\)\(q^{65} + \)\(22\!\cdots\!52\)\(q^{66} + \)\(14\!\cdots\!32\)\(q^{67} + \)\(12\!\cdots\!64\)\(q^{68} - \)\(91\!\cdots\!12\)\(q^{69} - \)\(61\!\cdots\!00\)\(q^{70} - \)\(12\!\cdots\!44\)\(q^{71} - \)\(11\!\cdots\!80\)\(q^{72} + \)\(54\!\cdots\!66\)\(q^{73} - \)\(92\!\cdots\!08\)\(q^{74} + \)\(46\!\cdots\!00\)\(q^{75} - \)\(25\!\cdots\!40\)\(q^{76} + \)\(66\!\cdots\!84\)\(q^{77} - \)\(45\!\cdots\!88\)\(q^{78} + \)\(90\!\cdots\!20\)\(q^{79} - \)\(16\!\cdots\!00\)\(q^{80} - \)\(10\!\cdots\!77\)\(q^{81} - \)\(70\!\cdots\!56\)\(q^{82} + \)\(14\!\cdots\!36\)\(q^{83} + \)\(28\!\cdots\!12\)\(q^{84} + \)\(38\!\cdots\!00\)\(q^{85} + \)\(49\!\cdots\!36\)\(q^{86} - \)\(19\!\cdots\!80\)\(q^{87} + \)\(52\!\cdots\!80\)\(q^{88} - \)\(15\!\cdots\!90\)\(q^{89} - \)\(34\!\cdots\!00\)\(q^{90} - \)\(20\!\cdots\!64\)\(q^{91} + \)\(31\!\cdots\!32\)\(q^{92} - \)\(19\!\cdots\!48\)\(q^{93} + \)\(38\!\cdots\!72\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} + \)\(97\!\cdots\!76\)\(q^{96} + \)\(37\!\cdots\!02\)\(q^{97} + \)\(19\!\cdots\!04\)\(q^{98} - \)\(52\!\cdots\!12\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.36851e6 1.24224 0.621119 0.783716i \(-0.286678\pi\)
0.621119 + 0.783716i \(0.286678\pi\)
\(3\) −5.75337e10 −1.05851 −0.529254 0.848464i \(-0.677528\pi\)
−0.529254 + 0.848464i \(0.677528\pi\)
\(4\) 1.91106e13 0.543156
\(5\) 5.97253e15 1.12030 0.560149 0.828392i \(-0.310744\pi\)
0.560149 + 0.828392i \(0.310744\pi\)
\(6\) −4.23938e17 −1.31492
\(7\) −1.35754e19 −1.31234 −0.656171 0.754612i \(-0.727825\pi\)
−0.656171 + 0.754612i \(0.727825\pi\)
\(8\) −1.18440e20 −0.567509
\(9\) 3.55813e20 0.120438
\(10\) 4.40087e22 1.39168
\(11\) −4.62684e23 −1.71376 −0.856879 0.515518i \(-0.827600\pi\)
−0.856879 + 0.515518i \(0.827600\pi\)
\(12\) −1.09950e24 −0.574935
\(13\) 1.84657e24 0.159456 0.0797280 0.996817i \(-0.474595\pi\)
0.0797280 + 0.996817i \(0.474595\pi\)
\(14\) −1.00031e26 −1.63024
\(15\) −3.43622e26 −1.18584
\(16\) −1.54512e27 −1.24814
\(17\) 5.39007e27 1.11300 0.556498 0.830849i \(-0.312145\pi\)
0.556498 + 0.830849i \(0.312145\pi\)
\(18\) 2.62181e27 0.149613
\(19\) 2.04232e28 0.345278 0.172639 0.984985i \(-0.444771\pi\)
0.172639 + 0.984985i \(0.444771\pi\)
\(20\) 1.14139e29 0.608497
\(21\) 7.81043e29 1.38912
\(22\) −3.40930e30 −2.12890
\(23\) −4.06607e30 −0.933896 −0.466948 0.884285i \(-0.654647\pi\)
−0.466948 + 0.884285i \(0.654647\pi\)
\(24\) 6.81427e30 0.600712
\(25\) 7.24945e30 0.255067
\(26\) 1.36065e31 0.198082
\(27\) 1.49501e32 0.931023
\(28\) −2.59434e32 −0.712807
\(29\) 6.91615e32 0.862799 0.431400 0.902161i \(-0.358020\pi\)
0.431400 + 0.902161i \(0.358020\pi\)
\(30\) −2.53198e33 −1.47310
\(31\) −4.29419e32 −0.119466 −0.0597329 0.998214i \(-0.519025\pi\)
−0.0597329 + 0.998214i \(0.519025\pi\)
\(32\) −7.21801e33 −0.982976
\(33\) 2.66199e34 1.81403
\(34\) 3.97168e34 1.38261
\(35\) −8.10796e34 −1.47021
\(36\) 6.79980e33 0.0654169
\(37\) −1.38069e35 −0.717062 −0.358531 0.933518i \(-0.616722\pi\)
−0.358531 + 0.933518i \(0.616722\pi\)
\(38\) 1.50489e35 0.428917
\(39\) −1.06240e35 −0.168785
\(40\) −7.07385e35 −0.635779
\(41\) 9.02413e35 0.465338 0.232669 0.972556i \(-0.425254\pi\)
0.232669 + 0.972556i \(0.425254\pi\)
\(42\) 5.75513e36 1.72562
\(43\) −2.22460e36 −0.392837 −0.196418 0.980520i \(-0.562931\pi\)
−0.196418 + 0.980520i \(0.562931\pi\)
\(44\) −8.84218e36 −0.930839
\(45\) 2.12510e36 0.134927
\(46\) −2.99609e37 −1.16012
\(47\) −1.00563e37 −0.240014 −0.120007 0.992773i \(-0.538292\pi\)
−0.120007 + 0.992773i \(0.538292\pi\)
\(48\) 8.88964e37 1.32116
\(49\) 7.72848e37 0.722241
\(50\) 5.34177e37 0.316855
\(51\) −3.10111e38 −1.17811
\(52\) 3.52891e37 0.0866095
\(53\) −2.47477e38 −0.395666 −0.197833 0.980236i \(-0.563390\pi\)
−0.197833 + 0.980236i \(0.563390\pi\)
\(54\) 1.10160e39 1.15655
\(55\) −2.76340e39 −1.91992
\(56\) 1.60787e39 0.744765
\(57\) −1.17502e39 −0.365479
\(58\) 5.09618e39 1.07180
\(59\) 1.01841e40 1.45798 0.728991 0.684524i \(-0.239990\pi\)
0.728991 + 0.684524i \(0.239990\pi\)
\(60\) −6.56683e39 −0.644099
\(61\) −2.35593e40 −1.59309 −0.796545 0.604580i \(-0.793341\pi\)
−0.796545 + 0.604580i \(0.793341\pi\)
\(62\) −3.16418e39 −0.148405
\(63\) −4.83030e39 −0.158056
\(64\) 1.17807e39 0.0270473
\(65\) 1.10287e40 0.178638
\(66\) 1.96149e41 2.25345
\(67\) −2.39925e41 −1.96513 −0.982567 0.185910i \(-0.940477\pi\)
−0.982567 + 0.185910i \(0.940477\pi\)
\(68\) 1.03008e41 0.604531
\(69\) 2.33936e41 0.988536
\(70\) −5.97436e41 −1.82636
\(71\) 4.61674e40 0.102570 0.0512852 0.998684i \(-0.483668\pi\)
0.0512852 + 0.998684i \(0.483668\pi\)
\(72\) −4.21424e40 −0.0683499
\(73\) 6.89694e41 0.820148 0.410074 0.912052i \(-0.365503\pi\)
0.410074 + 0.912052i \(0.365503\pi\)
\(74\) −1.01736e42 −0.890762
\(75\) −4.17088e41 −0.269991
\(76\) 3.90301e41 0.187540
\(77\) 6.28113e42 2.24904
\(78\) −7.82832e41 −0.209672
\(79\) −1.80775e42 −0.363520 −0.181760 0.983343i \(-0.558179\pi\)
−0.181760 + 0.983343i \(0.558179\pi\)
\(80\) −9.22828e42 −1.39829
\(81\) −9.65254e42 −1.10593
\(82\) 6.64944e42 0.578061
\(83\) 1.09933e42 0.0727566 0.0363783 0.999338i \(-0.488418\pi\)
0.0363783 + 0.999338i \(0.488418\pi\)
\(84\) 1.49262e43 0.754512
\(85\) 3.21924e43 1.24689
\(86\) −1.63920e43 −0.487997
\(87\) −3.97912e43 −0.913279
\(88\) 5.48002e43 0.972573
\(89\) −5.72005e43 −0.787272 −0.393636 0.919266i \(-0.628783\pi\)
−0.393636 + 0.919266i \(0.628783\pi\)
\(90\) 1.56589e43 0.167611
\(91\) −2.50680e43 −0.209261
\(92\) −7.77051e43 −0.507252
\(93\) 2.47061e43 0.126455
\(94\) −7.41002e43 −0.298155
\(95\) 1.21978e44 0.386814
\(96\) 4.15279e44 1.04049
\(97\) −2.85037e44 −0.565635 −0.282818 0.959174i \(-0.591269\pi\)
−0.282818 + 0.959174i \(0.591269\pi\)
\(98\) 5.69474e44 0.897196
\(99\) −1.64629e44 −0.206402
\(100\) 1.38542e44 0.138542
\(101\) −1.12852e45 −0.902146 −0.451073 0.892487i \(-0.648959\pi\)
−0.451073 + 0.892487i \(0.648959\pi\)
\(102\) −2.28505e45 −1.46350
\(103\) 4.56079e44 0.234532 0.117266 0.993101i \(-0.462587\pi\)
0.117266 + 0.993101i \(0.462587\pi\)
\(104\) −2.18707e44 −0.0904927
\(105\) 4.66481e45 1.55623
\(106\) −1.82354e45 −0.491511
\(107\) 7.56988e45 1.65179 0.825894 0.563826i \(-0.190671\pi\)
0.825894 + 0.563826i \(0.190671\pi\)
\(108\) 2.85706e45 0.505691
\(109\) −8.09431e45 −1.16435 −0.582175 0.813063i \(-0.697798\pi\)
−0.582175 + 0.813063i \(0.697798\pi\)
\(110\) −2.03621e46 −2.38500
\(111\) 7.94361e45 0.759015
\(112\) 2.09756e46 1.63798
\(113\) −6.69178e45 −0.427836 −0.213918 0.976852i \(-0.568622\pi\)
−0.213918 + 0.976852i \(0.568622\pi\)
\(114\) −8.65818e45 −0.454012
\(115\) −2.42847e46 −1.04624
\(116\) 1.32172e46 0.468635
\(117\) 6.57034e44 0.0192046
\(118\) 7.50416e46 1.81116
\(119\) −7.31724e46 −1.46063
\(120\) 4.06985e46 0.672977
\(121\) 1.41186e47 1.93697
\(122\) −1.73597e47 −1.97900
\(123\) −5.19192e46 −0.492564
\(124\) −8.20647e45 −0.0648886
\(125\) −1.26452e47 −0.834546
\(126\) −3.55922e46 −0.196344
\(127\) 4.47769e46 0.206762 0.103381 0.994642i \(-0.467034\pi\)
0.103381 + 0.994642i \(0.467034\pi\)
\(128\) 2.62642e47 1.01657
\(129\) 1.27990e47 0.415821
\(130\) 8.12652e46 0.221911
\(131\) 4.74426e46 0.109035 0.0545173 0.998513i \(-0.482638\pi\)
0.0545173 + 0.998513i \(0.482638\pi\)
\(132\) 5.08724e47 0.985300
\(133\) −2.77254e47 −0.453122
\(134\) −1.76789e48 −2.44116
\(135\) 8.92902e47 1.04302
\(136\) −6.38398e47 −0.631635
\(137\) −5.92244e47 −0.496922 −0.248461 0.968642i \(-0.579925\pi\)
−0.248461 + 0.968642i \(0.579925\pi\)
\(138\) 1.72376e48 1.22800
\(139\) 1.01012e48 0.611701 0.305851 0.952080i \(-0.401059\pi\)
0.305851 + 0.952080i \(0.401059\pi\)
\(140\) −1.54948e48 −0.798556
\(141\) 5.78577e47 0.254057
\(142\) 3.40185e47 0.127417
\(143\) −8.54380e47 −0.273269
\(144\) −5.49773e47 −0.150324
\(145\) 4.13070e48 0.966592
\(146\) 5.08202e48 1.01882
\(147\) −4.44648e48 −0.764498
\(148\) −2.63858e48 −0.389477
\(149\) −1.22411e49 −1.55285 −0.776426 0.630208i \(-0.782969\pi\)
−0.776426 + 0.630208i \(0.782969\pi\)
\(150\) −3.07332e48 −0.335393
\(151\) 1.39518e48 0.131114 0.0655572 0.997849i \(-0.479118\pi\)
0.0655572 + 0.997849i \(0.479118\pi\)
\(152\) −2.41892e48 −0.195948
\(153\) 1.91786e48 0.134047
\(154\) 4.62826e49 2.79384
\(155\) −2.56472e48 −0.133837
\(156\) −2.03031e48 −0.0916769
\(157\) −1.81397e49 −0.709393 −0.354697 0.934981i \(-0.615416\pi\)
−0.354697 + 0.934981i \(0.615416\pi\)
\(158\) −1.33204e49 −0.451578
\(159\) 1.42383e49 0.418815
\(160\) −4.31098e49 −1.10123
\(161\) 5.51986e49 1.22559
\(162\) −7.11249e49 −1.37383
\(163\) −6.75472e49 −1.13602 −0.568010 0.823022i \(-0.692287\pi\)
−0.568010 + 0.823022i \(0.692287\pi\)
\(164\) 1.72457e49 0.252751
\(165\) 1.58989e50 2.03225
\(166\) 8.10045e48 0.0903810
\(167\) 4.33548e49 0.422587 0.211294 0.977423i \(-0.432232\pi\)
0.211294 + 0.977423i \(0.432232\pi\)
\(168\) −9.25065e49 −0.788340
\(169\) −1.30697e50 −0.974574
\(170\) 2.37210e50 1.54893
\(171\) 7.26685e48 0.0415847
\(172\) −4.25135e49 −0.213372
\(173\) 1.27763e49 0.0562816 0.0281408 0.999604i \(-0.491041\pi\)
0.0281408 + 0.999604i \(0.491041\pi\)
\(174\) −2.93202e50 −1.13451
\(175\) −9.84143e49 −0.334736
\(176\) 7.14903e50 2.13901
\(177\) −5.85928e50 −1.54328
\(178\) −4.21483e50 −0.977980
\(179\) −1.84054e50 −0.376489 −0.188244 0.982122i \(-0.560280\pi\)
−0.188244 + 0.982122i \(0.560280\pi\)
\(180\) 4.06120e49 0.0732864
\(181\) 1.05925e51 1.68745 0.843725 0.536775i \(-0.180358\pi\)
0.843725 + 0.536775i \(0.180358\pi\)
\(182\) −1.84714e50 −0.259952
\(183\) 1.35545e51 1.68630
\(184\) 4.81584e50 0.529994
\(185\) −8.24620e50 −0.803323
\(186\) 1.82047e50 0.157088
\(187\) −2.49390e51 −1.90741
\(188\) −1.92183e50 −0.130365
\(189\) −2.02954e51 −1.22182
\(190\) 8.98800e50 0.480515
\(191\) 1.00828e51 0.478992 0.239496 0.970897i \(-0.423018\pi\)
0.239496 + 0.970897i \(0.423018\pi\)
\(192\) −6.77790e49 −0.0286297
\(193\) 4.75247e51 1.78600 0.892998 0.450061i \(-0.148598\pi\)
0.892998 + 0.450061i \(0.148598\pi\)
\(194\) −2.10030e51 −0.702654
\(195\) −6.34523e50 −0.189090
\(196\) 1.47696e51 0.392290
\(197\) 1.24255e51 0.294324 0.147162 0.989112i \(-0.452986\pi\)
0.147162 + 0.989112i \(0.452986\pi\)
\(198\) −1.21307e51 −0.256401
\(199\) −3.30064e51 −0.622880 −0.311440 0.950266i \(-0.600811\pi\)
−0.311440 + 0.950266i \(0.600811\pi\)
\(200\) −8.58623e50 −0.144753
\(201\) 1.38038e52 2.08011
\(202\) −8.31549e51 −1.12068
\(203\) −9.38896e51 −1.13229
\(204\) −5.92640e51 −0.639901
\(205\) 5.38969e51 0.521317
\(206\) 3.36062e51 0.291345
\(207\) −1.44676e51 −0.112477
\(208\) −2.85317e51 −0.199023
\(209\) −9.44951e51 −0.591722
\(210\) 3.43727e52 1.93321
\(211\) −1.03587e52 −0.523540 −0.261770 0.965130i \(-0.584306\pi\)
−0.261770 + 0.965130i \(0.584306\pi\)
\(212\) −4.72945e51 −0.214908
\(213\) −2.65618e51 −0.108572
\(214\) 5.57788e52 2.05191
\(215\) −1.32865e52 −0.440094
\(216\) −1.77069e52 −0.528363
\(217\) 5.82954e51 0.156780
\(218\) −5.96430e52 −1.44640
\(219\) −3.96806e52 −0.868132
\(220\) −5.28102e52 −1.04282
\(221\) 9.95315e51 0.177474
\(222\) 5.85326e52 0.942878
\(223\) 5.37304e52 0.782277 0.391139 0.920332i \(-0.372081\pi\)
0.391139 + 0.920332i \(0.372081\pi\)
\(224\) 9.79874e52 1.29000
\(225\) 2.57945e51 0.0307199
\(226\) −4.93085e52 −0.531474
\(227\) 2.78314e52 0.271615 0.135807 0.990735i \(-0.456637\pi\)
0.135807 + 0.990735i \(0.456637\pi\)
\(228\) −2.24554e52 −0.198512
\(229\) 2.18798e53 1.75285 0.876425 0.481539i \(-0.159922\pi\)
0.876425 + 0.481539i \(0.159922\pi\)
\(230\) −1.78942e53 −1.29968
\(231\) −3.61377e53 −2.38062
\(232\) −8.19147e52 −0.489646
\(233\) 3.51723e53 1.90850 0.954252 0.299004i \(-0.0966545\pi\)
0.954252 + 0.299004i \(0.0966545\pi\)
\(234\) 4.84136e51 0.0238567
\(235\) −6.00617e52 −0.268888
\(236\) 1.94624e53 0.791912
\(237\) 1.04006e53 0.384789
\(238\) −5.39172e53 −1.81445
\(239\) −4.11764e53 −1.26094 −0.630472 0.776212i \(-0.717139\pi\)
−0.630472 + 0.776212i \(0.717139\pi\)
\(240\) 5.30937e53 1.48010
\(241\) −2.61521e53 −0.663931 −0.331966 0.943291i \(-0.607712\pi\)
−0.331966 + 0.943291i \(0.607712\pi\)
\(242\) 1.04033e54 2.40617
\(243\) 1.13673e53 0.239616
\(244\) −4.50232e53 −0.865297
\(245\) 4.61586e53 0.809125
\(246\) −3.82567e53 −0.611882
\(247\) 3.77130e52 0.0550566
\(248\) 5.08603e52 0.0677979
\(249\) −6.32487e52 −0.0770134
\(250\) −9.31763e53 −1.03671
\(251\) −1.56252e54 −1.58916 −0.794581 0.607158i \(-0.792309\pi\)
−0.794581 + 0.607158i \(0.792309\pi\)
\(252\) −9.23101e52 −0.0858493
\(253\) 1.88131e54 1.60047
\(254\) 3.29939e53 0.256847
\(255\) −1.85215e54 −1.31984
\(256\) 1.89383e54 1.23578
\(257\) 1.24463e53 0.0743951 0.0371975 0.999308i \(-0.488157\pi\)
0.0371975 + 0.999308i \(0.488157\pi\)
\(258\) 9.43093e53 0.516549
\(259\) 1.87434e54 0.941030
\(260\) 2.10766e53 0.0970285
\(261\) 2.46086e53 0.103914
\(262\) 3.49582e53 0.135447
\(263\) −2.80486e54 −0.997487 −0.498743 0.866750i \(-0.666205\pi\)
−0.498743 + 0.866750i \(0.666205\pi\)
\(264\) −3.15286e54 −1.02948
\(265\) −1.47807e54 −0.443264
\(266\) −2.04295e54 −0.562886
\(267\) 3.29096e54 0.833334
\(268\) −4.58511e54 −1.06737
\(269\) 1.28461e54 0.275009 0.137504 0.990501i \(-0.456092\pi\)
0.137504 + 0.990501i \(0.456092\pi\)
\(270\) 6.57936e54 1.29568
\(271\) 9.12323e54 1.65325 0.826627 0.562750i \(-0.190257\pi\)
0.826627 + 0.562750i \(0.190257\pi\)
\(272\) −8.32830e54 −1.38917
\(273\) 1.44225e54 0.221504
\(274\) −4.36396e54 −0.617295
\(275\) −3.35421e54 −0.437124
\(276\) 4.47066e54 0.536930
\(277\) −8.28825e53 −0.0917630 −0.0458815 0.998947i \(-0.514610\pi\)
−0.0458815 + 0.998947i \(0.514610\pi\)
\(278\) 7.44307e54 0.759879
\(279\) −1.52793e53 −0.0143883
\(280\) 9.60304e54 0.834359
\(281\) −5.88447e54 −0.471862 −0.235931 0.971770i \(-0.575814\pi\)
−0.235931 + 0.971770i \(0.575814\pi\)
\(282\) 4.26326e54 0.315600
\(283\) −2.28277e55 −1.56051 −0.780257 0.625458i \(-0.784912\pi\)
−0.780257 + 0.625458i \(0.784912\pi\)
\(284\) 8.82287e53 0.0557118
\(285\) −7.01787e54 −0.409445
\(286\) −6.29551e54 −0.339465
\(287\) −1.22506e55 −0.610683
\(288\) −2.56826e54 −0.118388
\(289\) 5.59968e54 0.238760
\(290\) 3.04371e55 1.20074
\(291\) 1.63992e55 0.598729
\(292\) 1.31805e55 0.445468
\(293\) 2.32198e55 0.726671 0.363335 0.931658i \(-0.381638\pi\)
0.363335 + 0.931658i \(0.381638\pi\)
\(294\) −3.27639e55 −0.949689
\(295\) 6.08248e55 1.63337
\(296\) 1.63528e55 0.406939
\(297\) −6.91719e55 −1.59555
\(298\) −9.01988e55 −1.92901
\(299\) −7.50829e54 −0.148915
\(300\) −7.97080e54 −0.146647
\(301\) 3.01999e55 0.515536
\(302\) 1.02804e55 0.162875
\(303\) 6.49277e55 0.954929
\(304\) −3.15563e55 −0.430954
\(305\) −1.40708e56 −1.78473
\(306\) 1.41317e55 0.166519
\(307\) 1.19437e56 1.30775 0.653875 0.756603i \(-0.273142\pi\)
0.653875 + 0.756603i \(0.273142\pi\)
\(308\) 1.20036e56 1.22158
\(309\) −2.62399e55 −0.248254
\(310\) −1.88982e55 −0.166258
\(311\) 1.65762e56 1.35636 0.678181 0.734895i \(-0.262768\pi\)
0.678181 + 0.734895i \(0.262768\pi\)
\(312\) 1.25830e55 0.0957872
\(313\) −2.27179e56 −1.60924 −0.804619 0.593792i \(-0.797630\pi\)
−0.804619 + 0.593792i \(0.797630\pi\)
\(314\) −1.33662e56 −0.881236
\(315\) −2.88492e55 −0.177070
\(316\) −3.45472e55 −0.197448
\(317\) 3.49229e56 1.85899 0.929494 0.368836i \(-0.120244\pi\)
0.929494 + 0.368836i \(0.120244\pi\)
\(318\) 1.04915e56 0.520269
\(319\) −3.20000e56 −1.47863
\(320\) 7.03609e54 0.0303010
\(321\) −4.35523e56 −1.74843
\(322\) 4.06731e56 1.52248
\(323\) 1.10083e56 0.384293
\(324\) −1.84466e56 −0.600695
\(325\) 1.33866e55 0.0406720
\(326\) −4.97722e56 −1.41121
\(327\) 4.65695e56 1.23247
\(328\) −1.06882e56 −0.264083
\(329\) 1.36519e56 0.314981
\(330\) 1.17151e57 2.52454
\(331\) 1.49551e55 0.0301065 0.0150533 0.999887i \(-0.495208\pi\)
0.0150533 + 0.999887i \(0.495208\pi\)
\(332\) 2.10089e55 0.0395182
\(333\) −4.91266e55 −0.0863618
\(334\) 3.19460e56 0.524954
\(335\) −1.43296e57 −2.20154
\(336\) −1.20681e57 −1.73382
\(337\) 3.73633e56 0.502080 0.251040 0.967977i \(-0.419227\pi\)
0.251040 + 0.967977i \(0.419227\pi\)
\(338\) −9.63043e56 −1.21065
\(339\) 3.85003e56 0.452867
\(340\) 6.15216e56 0.677255
\(341\) 1.98686e56 0.204735
\(342\) 5.35459e55 0.0516581
\(343\) 4.03490e56 0.364515
\(344\) 2.63481e56 0.222938
\(345\) 1.39719e57 1.10746
\(346\) 9.41420e55 0.0699151
\(347\) 9.19083e56 0.639649 0.319824 0.947477i \(-0.396376\pi\)
0.319824 + 0.947477i \(0.396376\pi\)
\(348\) −7.60434e56 −0.496054
\(349\) −1.53571e57 −0.939158 −0.469579 0.882891i \(-0.655594\pi\)
−0.469579 + 0.882891i \(0.655594\pi\)
\(350\) −7.25167e56 −0.415822
\(351\) 2.76065e56 0.148457
\(352\) 3.33966e57 1.68458
\(353\) −1.08285e57 −0.512435 −0.256217 0.966619i \(-0.582476\pi\)
−0.256217 + 0.966619i \(0.582476\pi\)
\(354\) −4.31742e57 −1.91713
\(355\) 2.75736e56 0.114909
\(356\) −1.09314e57 −0.427612
\(357\) 4.20988e57 1.54609
\(358\) −1.35620e57 −0.467689
\(359\) −9.45652e56 −0.306271 −0.153136 0.988205i \(-0.548937\pi\)
−0.153136 + 0.988205i \(0.548937\pi\)
\(360\) −2.51697e56 −0.0765722
\(361\) −3.08163e57 −0.880783
\(362\) 7.80511e57 2.09622
\(363\) −8.12297e57 −2.05029
\(364\) −4.79064e56 −0.113661
\(365\) 4.11922e57 0.918810
\(366\) 9.98766e57 2.09478
\(367\) −8.46364e57 −1.66944 −0.834719 0.550675i \(-0.814370\pi\)
−0.834719 + 0.550675i \(0.814370\pi\)
\(368\) 6.28257e57 1.16563
\(369\) 3.21090e56 0.0560446
\(370\) −6.07623e57 −0.997919
\(371\) 3.35961e57 0.519249
\(372\) 4.72148e56 0.0686851
\(373\) 7.28034e57 0.997017 0.498509 0.866885i \(-0.333881\pi\)
0.498509 + 0.866885i \(0.333881\pi\)
\(374\) −1.83763e58 −2.36945
\(375\) 7.27525e57 0.883374
\(376\) 1.19107e57 0.136210
\(377\) 1.27712e57 0.137578
\(378\) −1.49547e58 −1.51779
\(379\) −1.15746e58 −1.10694 −0.553471 0.832868i \(-0.686697\pi\)
−0.553471 + 0.832868i \(0.686697\pi\)
\(380\) 2.33108e57 0.210100
\(381\) −2.57618e57 −0.218859
\(382\) 7.42949e57 0.595022
\(383\) 1.13149e58 0.854436 0.427218 0.904149i \(-0.359494\pi\)
0.427218 + 0.904149i \(0.359494\pi\)
\(384\) −1.51107e58 −1.07605
\(385\) 3.75143e58 2.51959
\(386\) 3.50187e58 2.21863
\(387\) −7.91542e56 −0.0473127
\(388\) −5.44723e57 −0.307229
\(389\) −3.09651e58 −1.64819 −0.824094 0.566453i \(-0.808315\pi\)
−0.824094 + 0.566453i \(0.808315\pi\)
\(390\) −4.67549e57 −0.234895
\(391\) −2.19164e58 −1.03942
\(392\) −9.15359e57 −0.409878
\(393\) −2.72955e57 −0.115414
\(394\) 9.15577e57 0.365620
\(395\) −1.07968e58 −0.407251
\(396\) −3.14616e57 −0.112109
\(397\) 2.54438e58 0.856633 0.428317 0.903629i \(-0.359107\pi\)
0.428317 + 0.903629i \(0.359107\pi\)
\(398\) −2.43208e58 −0.773766
\(399\) 1.59514e58 0.479633
\(400\) −1.12013e58 −0.318359
\(401\) −2.41926e58 −0.650031 −0.325016 0.945709i \(-0.605370\pi\)
−0.325016 + 0.945709i \(0.605370\pi\)
\(402\) 1.01713e59 2.58399
\(403\) −7.92954e56 −0.0190495
\(404\) −2.15666e58 −0.490007
\(405\) −5.76501e58 −1.23897
\(406\) −6.91827e58 −1.40657
\(407\) 6.38823e58 1.22887
\(408\) 3.67294e58 0.668590
\(409\) 4.68095e58 0.806418 0.403209 0.915108i \(-0.367895\pi\)
0.403209 + 0.915108i \(0.367895\pi\)
\(410\) 3.97140e58 0.647600
\(411\) 3.40740e58 0.525996
\(412\) 8.71595e57 0.127388
\(413\) −1.38253e59 −1.91337
\(414\) −1.06605e58 −0.139723
\(415\) 6.56581e57 0.0815091
\(416\) −1.33286e58 −0.156741
\(417\) −5.81158e58 −0.647490
\(418\) −6.96288e58 −0.735060
\(419\) 4.10143e58 0.410317 0.205158 0.978729i \(-0.434229\pi\)
0.205158 + 0.978729i \(0.434229\pi\)
\(420\) 8.91474e58 0.845278
\(421\) −5.12871e58 −0.460958 −0.230479 0.973077i \(-0.574029\pi\)
−0.230479 + 0.973077i \(0.574029\pi\)
\(422\) −7.63282e58 −0.650362
\(423\) −3.57817e57 −0.0289070
\(424\) 2.93112e58 0.224544
\(425\) 3.90751e58 0.283889
\(426\) −1.95721e58 −0.134872
\(427\) 3.19826e59 2.09068
\(428\) 1.44665e59 0.897179
\(429\) 4.91556e58 0.289257
\(430\) −9.79019e58 −0.546702
\(431\) −1.63043e59 −0.864100 −0.432050 0.901850i \(-0.642210\pi\)
−0.432050 + 0.901850i \(0.642210\pi\)
\(432\) −2.30997e59 −1.16204
\(433\) 2.91636e59 1.39272 0.696360 0.717692i \(-0.254802\pi\)
0.696360 + 0.717692i \(0.254802\pi\)
\(434\) 4.29551e58 0.194758
\(435\) −2.37654e59 −1.02315
\(436\) −1.54687e59 −0.632424
\(437\) −8.30423e58 −0.322453
\(438\) −2.92387e59 −1.07843
\(439\) −2.21702e59 −0.776816 −0.388408 0.921488i \(-0.626975\pi\)
−0.388408 + 0.921488i \(0.626975\pi\)
\(440\) 3.27296e59 1.08957
\(441\) 2.74989e58 0.0869856
\(442\) 7.33399e58 0.220465
\(443\) 3.23420e59 0.924024 0.462012 0.886874i \(-0.347128\pi\)
0.462012 + 0.886874i \(0.347128\pi\)
\(444\) 1.51807e59 0.412264
\(445\) −3.41632e59 −0.881980
\(446\) 3.95913e59 0.971775
\(447\) 7.04277e59 1.64371
\(448\) −1.59928e58 −0.0354952
\(449\) −5.32736e59 −1.12453 −0.562263 0.826959i \(-0.690069\pi\)
−0.562263 + 0.826959i \(0.690069\pi\)
\(450\) 1.90067e58 0.0381615
\(451\) −4.17532e59 −0.797477
\(452\) −1.27884e59 −0.232382
\(453\) −8.02701e58 −0.138786
\(454\) 2.05076e59 0.337410
\(455\) −1.49719e59 −0.234434
\(456\) 1.39169e59 0.207412
\(457\) −1.11648e60 −1.58393 −0.791967 0.610564i \(-0.790943\pi\)
−0.791967 + 0.610564i \(0.790943\pi\)
\(458\) 1.61221e60 2.17746
\(459\) 8.05822e59 1.03622
\(460\) −4.64096e59 −0.568273
\(461\) 8.63646e59 1.00708 0.503541 0.863971i \(-0.332030\pi\)
0.503541 + 0.863971i \(0.332030\pi\)
\(462\) −2.66281e60 −2.95730
\(463\) −7.81313e59 −0.826519 −0.413260 0.910613i \(-0.635610\pi\)
−0.413260 + 0.910613i \(0.635610\pi\)
\(464\) −1.06863e60 −1.07689
\(465\) 1.47558e59 0.141668
\(466\) 2.59168e60 2.37082
\(467\) −1.35783e60 −1.18363 −0.591816 0.806073i \(-0.701589\pi\)
−0.591816 + 0.806073i \(0.701589\pi\)
\(468\) 1.25563e58 0.0104311
\(469\) 3.25708e60 2.57893
\(470\) −4.42566e59 −0.334023
\(471\) 1.04364e60 0.750898
\(472\) −1.20620e60 −0.827417
\(473\) 1.02929e60 0.673227
\(474\) 7.66372e59 0.477999
\(475\) 1.48057e59 0.0880691
\(476\) −1.39837e60 −0.793351
\(477\) −8.80557e58 −0.0476534
\(478\) −3.03409e60 −1.56639
\(479\) −1.42047e60 −0.699653 −0.349827 0.936814i \(-0.613760\pi\)
−0.349827 + 0.936814i \(0.613760\pi\)
\(480\) 2.48027e60 1.16566
\(481\) −2.54954e59 −0.114340
\(482\) −1.92702e60 −0.824761
\(483\) −3.17578e60 −1.29730
\(484\) 2.69816e60 1.05208
\(485\) −1.70239e60 −0.633680
\(486\) 8.37600e59 0.297660
\(487\) 5.47125e59 0.185646 0.0928229 0.995683i \(-0.470411\pi\)
0.0928229 + 0.995683i \(0.470411\pi\)
\(488\) 2.79035e60 0.904092
\(489\) 3.88624e60 1.20249
\(490\) 3.40120e60 1.00513
\(491\) −5.08915e60 −1.43652 −0.718260 0.695775i \(-0.755061\pi\)
−0.718260 + 0.695775i \(0.755061\pi\)
\(492\) −9.92207e59 −0.267539
\(493\) 3.72785e60 0.960292
\(494\) 2.77888e59 0.0683934
\(495\) −9.83253e59 −0.231232
\(496\) 6.63504e59 0.149110
\(497\) −6.26741e59 −0.134607
\(498\) −4.66049e59 −0.0956690
\(499\) 2.10435e59 0.0412910 0.0206455 0.999787i \(-0.493428\pi\)
0.0206455 + 0.999787i \(0.493428\pi\)
\(500\) −2.41658e60 −0.453289
\(501\) −2.49436e60 −0.447312
\(502\) −1.15135e61 −1.97412
\(503\) 4.53975e60 0.744307 0.372153 0.928171i \(-0.378620\pi\)
0.372153 + 0.928171i \(0.378620\pi\)
\(504\) 5.72100e59 0.0896984
\(505\) −6.74010e60 −1.01067
\(506\) 1.38624e61 1.98817
\(507\) 7.51948e60 1.03159
\(508\) 8.55714e59 0.112304
\(509\) 2.61966e60 0.328923 0.164462 0.986383i \(-0.447411\pi\)
0.164462 + 0.986383i \(0.447411\pi\)
\(510\) −1.36476e61 −1.63956
\(511\) −9.36288e60 −1.07631
\(512\) 4.71382e60 0.518560
\(513\) 3.05330e60 0.321461
\(514\) 9.17106e59 0.0924165
\(515\) 2.72395e60 0.262746
\(516\) 2.44596e60 0.225856
\(517\) 4.65290e60 0.411327
\(518\) 1.38111e61 1.16898
\(519\) −7.35065e59 −0.0595745
\(520\) −1.30624e60 −0.101379
\(521\) −2.08020e61 −1.54617 −0.773083 0.634305i \(-0.781287\pi\)
−0.773083 + 0.634305i \(0.781287\pi\)
\(522\) 1.81328e60 0.129086
\(523\) 2.10397e61 1.43467 0.717336 0.696728i \(-0.245361\pi\)
0.717336 + 0.696728i \(0.245361\pi\)
\(524\) 9.06658e59 0.0592229
\(525\) 5.66214e60 0.354320
\(526\) −2.06677e61 −1.23912
\(527\) −2.31460e60 −0.132965
\(528\) −4.11310e61 −2.26415
\(529\) −2.42332e60 −0.127838
\(530\) −1.08912e61 −0.550639
\(531\) 3.62363e60 0.175597
\(532\) −5.29849e60 −0.246116
\(533\) 1.66637e60 0.0742009
\(534\) 2.42495e61 1.03520
\(535\) 4.52114e61 1.85049
\(536\) 2.84166e61 1.11523
\(537\) 1.05893e61 0.398516
\(538\) 9.46570e60 0.341627
\(539\) −3.57585e61 −1.23775
\(540\) 1.70639e61 0.566524
\(541\) −2.45649e61 −0.782306 −0.391153 0.920326i \(-0.627924\pi\)
−0.391153 + 0.920326i \(0.627924\pi\)
\(542\) 6.72246e61 2.05374
\(543\) −6.09426e61 −1.78618
\(544\) −3.89056e61 −1.09405
\(545\) −4.83435e61 −1.30442
\(546\) 1.06273e61 0.275161
\(547\) 4.92625e61 1.22406 0.612028 0.790836i \(-0.290354\pi\)
0.612028 + 0.790836i \(0.290354\pi\)
\(548\) −1.13182e61 −0.269906
\(549\) −8.38268e60 −0.191869
\(550\) −2.47155e61 −0.543012
\(551\) 1.41250e61 0.297905
\(552\) −2.77073e61 −0.561003
\(553\) 2.45409e61 0.477062
\(554\) −6.10721e60 −0.113992
\(555\) 4.74435e61 0.850323
\(556\) 1.93040e61 0.332249
\(557\) −1.15656e62 −1.91173 −0.955863 0.293813i \(-0.905076\pi\)
−0.955863 + 0.293813i \(0.905076\pi\)
\(558\) −1.12586e60 −0.0178737
\(559\) −4.10789e60 −0.0626402
\(560\) 1.25278e62 1.83503
\(561\) 1.43483e62 2.01900
\(562\) −4.33598e61 −0.586165
\(563\) −5.89709e61 −0.765947 −0.382974 0.923759i \(-0.625100\pi\)
−0.382974 + 0.923759i \(0.625100\pi\)
\(564\) 1.10570e61 0.137993
\(565\) −3.99669e61 −0.479303
\(566\) −1.68206e62 −1.93853
\(567\) 1.31037e62 1.45136
\(568\) −5.46805e60 −0.0582096
\(569\) 7.93806e61 0.812248 0.406124 0.913818i \(-0.366880\pi\)
0.406124 + 0.913818i \(0.366880\pi\)
\(570\) −5.17113e61 −0.508629
\(571\) 7.67118e61 0.725354 0.362677 0.931915i \(-0.381863\pi\)
0.362677 + 0.931915i \(0.381863\pi\)
\(572\) −1.63277e61 −0.148428
\(573\) −5.80098e61 −0.507017
\(574\) −9.02689e61 −0.758614
\(575\) −2.94768e61 −0.238207
\(576\) 4.19174e59 0.00325753
\(577\) 6.82798e60 0.0510313 0.0255156 0.999674i \(-0.491877\pi\)
0.0255156 + 0.999674i \(0.491877\pi\)
\(578\) 4.12613e61 0.296597
\(579\) −2.73427e62 −1.89049
\(580\) 7.89401e61 0.525011
\(581\) −1.49239e61 −0.0954815
\(582\) 1.20838e62 0.743765
\(583\) 1.14504e62 0.678076
\(584\) −8.16871e61 −0.465441
\(585\) 3.92416e60 0.0215149
\(586\) 1.71096e62 0.902698
\(587\) 1.68156e62 0.853800 0.426900 0.904299i \(-0.359606\pi\)
0.426900 + 0.904299i \(0.359606\pi\)
\(588\) −8.49750e61 −0.415242
\(589\) −8.77013e60 −0.0412489
\(590\) 4.48189e62 2.02904
\(591\) −7.14887e61 −0.311544
\(592\) 2.13333e62 0.894992
\(593\) −7.10812e61 −0.287094 −0.143547 0.989644i \(-0.545851\pi\)
−0.143547 + 0.989644i \(0.545851\pi\)
\(594\) −5.09694e62 −1.98205
\(595\) −4.37025e62 −1.63634
\(596\) −2.33935e62 −0.843441
\(597\) 1.89898e62 0.659323
\(598\) −5.53250e61 −0.184988
\(599\) −3.72514e62 −1.19961 −0.599804 0.800147i \(-0.704755\pi\)
−0.599804 + 0.800147i \(0.704755\pi\)
\(600\) 4.93997e61 0.153222
\(601\) 1.98326e61 0.0592520 0.0296260 0.999561i \(-0.490568\pi\)
0.0296260 + 0.999561i \(0.490568\pi\)
\(602\) 2.22528e62 0.640419
\(603\) −8.53683e61 −0.236678
\(604\) 2.66628e61 0.0712156
\(605\) 8.43241e62 2.16998
\(606\) 4.78421e62 1.18625
\(607\) −3.31764e62 −0.792653 −0.396327 0.918110i \(-0.629715\pi\)
−0.396327 + 0.918110i \(0.629715\pi\)
\(608\) −1.47415e62 −0.339400
\(609\) 5.40182e62 1.19853
\(610\) −1.03681e63 −2.21707
\(611\) −1.85697e61 −0.0382717
\(612\) 3.66514e61 0.0728088
\(613\) 4.55123e62 0.871501 0.435750 0.900068i \(-0.356483\pi\)
0.435750 + 0.900068i \(0.356483\pi\)
\(614\) 8.80072e62 1.62454
\(615\) −3.10089e62 −0.551818
\(616\) −7.43935e62 −1.27635
\(617\) −4.88458e62 −0.808000 −0.404000 0.914759i \(-0.632380\pi\)
−0.404000 + 0.914759i \(0.632380\pi\)
\(618\) −1.93349e62 −0.308391
\(619\) 3.98061e62 0.612223 0.306111 0.951996i \(-0.400972\pi\)
0.306111 + 0.951996i \(0.400972\pi\)
\(620\) −4.90134e61 −0.0726946
\(621\) −6.07883e62 −0.869479
\(622\) 1.22142e63 1.68493
\(623\) 7.76521e62 1.03317
\(624\) 1.64154e62 0.210667
\(625\) −9.61281e62 −1.19001
\(626\) −1.67397e63 −1.99906
\(627\) 5.43665e62 0.626342
\(628\) −3.46660e62 −0.385312
\(629\) −7.44200e62 −0.798087
\(630\) −2.12575e62 −0.219963
\(631\) 2.17238e62 0.216908 0.108454 0.994101i \(-0.465410\pi\)
0.108454 + 0.994101i \(0.465410\pi\)
\(632\) 2.14109e62 0.206301
\(633\) 5.95974e62 0.554171
\(634\) 2.57330e63 2.30931
\(635\) 2.67432e62 0.231635
\(636\) 2.72103e62 0.227482
\(637\) 1.42712e62 0.115166
\(638\) −2.35792e63 −1.83681
\(639\) 1.64269e61 0.0123534
\(640\) 1.56864e63 1.13887
\(641\) 1.15093e63 0.806757 0.403379 0.915033i \(-0.367836\pi\)
0.403379 + 0.915033i \(0.367836\pi\)
\(642\) −3.20916e63 −2.17197
\(643\) 1.21311e63 0.792781 0.396391 0.918082i \(-0.370263\pi\)
0.396391 + 0.918082i \(0.370263\pi\)
\(644\) 1.05488e63 0.665688
\(645\) 7.64422e62 0.465843
\(646\) 8.11145e62 0.477383
\(647\) −2.91798e63 −1.65858 −0.829290 0.558818i \(-0.811255\pi\)
−0.829290 + 0.558818i \(0.811255\pi\)
\(648\) 1.14324e63 0.627627
\(649\) −4.71202e63 −2.49863
\(650\) 9.86396e61 0.0505244
\(651\) −3.35395e62 −0.165953
\(652\) −1.29087e63 −0.617037
\(653\) −9.80474e62 −0.452782 −0.226391 0.974036i \(-0.572693\pi\)
−0.226391 + 0.974036i \(0.572693\pi\)
\(654\) 3.43148e63 1.53103
\(655\) 2.83353e62 0.122151
\(656\) −1.39434e63 −0.580806
\(657\) 2.45402e62 0.0987773
\(658\) 1.00594e63 0.391282
\(659\) 1.71493e63 0.644651 0.322325 0.946629i \(-0.395535\pi\)
0.322325 + 0.946629i \(0.395535\pi\)
\(660\) 3.03837e63 1.10383
\(661\) 4.68459e63 1.64490 0.822448 0.568840i \(-0.192608\pi\)
0.822448 + 0.568840i \(0.192608\pi\)
\(662\) 1.10197e62 0.0373995
\(663\) −5.72642e62 −0.187857
\(664\) −1.30205e62 −0.0412900
\(665\) −1.65591e63 −0.507632
\(666\) −3.61990e62 −0.107282
\(667\) −2.81216e63 −0.805765
\(668\) 8.28537e62 0.229531
\(669\) −3.09131e63 −0.828046
\(670\) −1.05588e64 −2.73483
\(671\) 1.09005e64 2.73017
\(672\) −5.63758e63 −1.36548
\(673\) 1.53030e63 0.358458 0.179229 0.983807i \(-0.442640\pi\)
0.179229 + 0.983807i \(0.442640\pi\)
\(674\) 2.75312e63 0.623703
\(675\) 1.08380e63 0.237474
\(676\) −2.49770e63 −0.529346
\(677\) −2.15211e63 −0.441184 −0.220592 0.975366i \(-0.570799\pi\)
−0.220592 + 0.975366i \(0.570799\pi\)
\(678\) 2.83690e63 0.562569
\(679\) 3.86949e63 0.742307
\(680\) −3.81285e63 −0.707619
\(681\) −1.60124e63 −0.287506
\(682\) 1.46402e63 0.254330
\(683\) 5.70299e63 0.958599 0.479299 0.877651i \(-0.340891\pi\)
0.479299 + 0.877651i \(0.340891\pi\)
\(684\) 1.38874e62 0.0225870
\(685\) −3.53720e63 −0.556700
\(686\) 2.97312e63 0.452814
\(687\) −1.25882e64 −1.85540
\(688\) 3.43728e63 0.490315
\(689\) −4.56985e62 −0.0630913
\(690\) 1.02952e64 1.37572
\(691\) −8.52122e62 −0.110216 −0.0551081 0.998480i \(-0.517550\pi\)
−0.0551081 + 0.998480i \(0.517550\pi\)
\(692\) 2.44162e62 0.0305697
\(693\) 2.23491e63 0.270870
\(694\) 6.77227e63 0.794596
\(695\) 6.03297e63 0.685288
\(696\) 4.71285e63 0.518294
\(697\) 4.86407e63 0.517919
\(698\) −1.13159e64 −1.16666
\(699\) −2.02359e64 −2.02017
\(700\) −1.88076e63 −0.181814
\(701\) −1.29219e64 −1.20968 −0.604842 0.796346i \(-0.706764\pi\)
−0.604842 + 0.796346i \(0.706764\pi\)
\(702\) 2.03419e63 0.184419
\(703\) −2.81981e63 −0.247585
\(704\) −5.45077e62 −0.0463524
\(705\) 3.45557e63 0.284620
\(706\) −7.97902e63 −0.636566
\(707\) 1.53201e64 1.18392
\(708\) −1.11975e64 −0.838245
\(709\) 8.82566e63 0.640040 0.320020 0.947411i \(-0.396310\pi\)
0.320020 + 0.947411i \(0.396310\pi\)
\(710\) 2.03176e63 0.142745
\(711\) −6.43220e62 −0.0437818
\(712\) 6.77481e63 0.446784
\(713\) 1.74605e63 0.111569
\(714\) 3.10205e64 1.92061
\(715\) −5.10281e63 −0.306143
\(716\) −3.51739e63 −0.204492
\(717\) 2.36903e64 1.33472
\(718\) −6.96805e63 −0.380462
\(719\) −1.32233e64 −0.699747 −0.349873 0.936797i \(-0.613775\pi\)
−0.349873 + 0.936797i \(0.613775\pi\)
\(720\) −3.28354e63 −0.168407
\(721\) −6.19146e63 −0.307786
\(722\) −2.27071e64 −1.09414
\(723\) 1.50463e64 0.702776
\(724\) 2.02429e64 0.916550
\(725\) 5.01383e63 0.220072
\(726\) −5.98542e64 −2.54695
\(727\) −3.36741e64 −1.38922 −0.694611 0.719386i \(-0.744423\pi\)
−0.694611 + 0.719386i \(0.744423\pi\)
\(728\) 2.96904e63 0.118757
\(729\) 2.19766e64 0.852298
\(730\) 3.03525e64 1.14138
\(731\) −1.19908e64 −0.437226
\(732\) 2.59035e64 0.915923
\(733\) −1.74069e64 −0.596873 −0.298437 0.954429i \(-0.596465\pi\)
−0.298437 + 0.954429i \(0.596465\pi\)
\(734\) −6.23644e64 −2.07384
\(735\) −2.65567e64 −0.856465
\(736\) 2.93489e64 0.917997
\(737\) 1.11009e65 3.36776
\(738\) 2.36596e63 0.0696207
\(739\) 1.59709e64 0.455858 0.227929 0.973678i \(-0.426805\pi\)
0.227929 + 0.973678i \(0.426805\pi\)
\(740\) −1.57590e64 −0.436330
\(741\) −2.16977e63 −0.0582778
\(742\) 2.47553e64 0.645031
\(743\) −1.55533e64 −0.393164 −0.196582 0.980487i \(-0.562984\pi\)
−0.196582 + 0.980487i \(0.562984\pi\)
\(744\) −2.92618e63 −0.0717646
\(745\) −7.31105e64 −1.73966
\(746\) 5.36453e64 1.23853
\(747\) 3.91157e62 0.00876269
\(748\) −4.76600e64 −1.03602
\(749\) −1.02764e65 −2.16771
\(750\) 5.36078e64 1.09736
\(751\) 5.84568e64 1.16128 0.580639 0.814161i \(-0.302803\pi\)
0.580639 + 0.814161i \(0.302803\pi\)
\(752\) 1.55382e64 0.299571
\(753\) 8.98978e64 1.68214
\(754\) 9.41046e63 0.170905
\(755\) 8.33279e63 0.146887
\(756\) −3.87858e64 −0.663639
\(757\) −1.20065e64 −0.199416 −0.0997080 0.995017i \(-0.531791\pi\)
−0.0997080 + 0.995017i \(0.531791\pi\)
\(758\) −8.52879e64 −1.37509
\(759\) −1.08239e65 −1.69411
\(760\) −1.44471e64 −0.219520
\(761\) −3.56581e64 −0.526022 −0.263011 0.964793i \(-0.584716\pi\)
−0.263011 + 0.964793i \(0.584716\pi\)
\(762\) −1.89826e64 −0.271875
\(763\) 1.09884e65 1.52803
\(764\) 1.92688e64 0.260168
\(765\) 1.14545e64 0.150173
\(766\) 8.33743e64 1.06141
\(767\) 1.88057e64 0.232484
\(768\) −1.08959e65 −1.30808
\(769\) −1.39554e65 −1.62704 −0.813521 0.581536i \(-0.802452\pi\)
−0.813521 + 0.581536i \(0.802452\pi\)
\(770\) 2.76424e65 3.12993
\(771\) −7.16080e63 −0.0787478
\(772\) 9.08227e64 0.970075
\(773\) 1.32949e65 1.37926 0.689629 0.724163i \(-0.257773\pi\)
0.689629 + 0.724163i \(0.257773\pi\)
\(774\) −5.83249e63 −0.0587736
\(775\) −3.11305e63 −0.0304718
\(776\) 3.37596e64 0.321003
\(777\) −1.07838e65 −0.996088
\(778\) −2.28167e65 −2.04744
\(779\) 1.84302e64 0.160671
\(780\) −1.21261e64 −0.102705
\(781\) −2.13609e64 −0.175781
\(782\) −1.61491e65 −1.29121
\(783\) 1.03397e65 0.803285
\(784\) −1.19414e65 −0.901456
\(785\) −1.08340e65 −0.794732
\(786\) −2.01127e64 −0.143372
\(787\) 1.01514e65 0.703227 0.351613 0.936145i \(-0.385633\pi\)
0.351613 + 0.936145i \(0.385633\pi\)
\(788\) 2.37460e64 0.159864
\(789\) 1.61374e65 1.05585
\(790\) −7.95566e64 −0.505902
\(791\) 9.08437e64 0.561466
\(792\) 1.94986e64 0.117135
\(793\) −4.35039e64 −0.254028
\(794\) 1.87483e65 1.06414
\(795\) 8.50387e64 0.469198
\(796\) −6.30773e64 −0.338321
\(797\) 6.73597e64 0.351227 0.175613 0.984459i \(-0.443809\pi\)
0.175613 + 0.984459i \(0.443809\pi\)
\(798\) 1.17538e65 0.595819
\(799\) −5.42043e64 −0.267135
\(800\) −5.23266e64 −0.250725
\(801\) −2.03527e64 −0.0948178
\(802\) −1.78264e65 −0.807494
\(803\) −3.19111e65 −1.40553
\(804\) 2.63798e65 1.12982
\(805\) 3.29675e65 1.37303
\(806\) −5.84289e63 −0.0236641
\(807\) −7.39086e64 −0.291099
\(808\) 1.33661e65 0.511976
\(809\) −2.59532e65 −0.966829 −0.483414 0.875392i \(-0.660604\pi\)
−0.483414 + 0.875392i \(0.660604\pi\)
\(810\) −4.24796e65 −1.53910
\(811\) 3.24133e65 1.14223 0.571115 0.820870i \(-0.306511\pi\)
0.571115 + 0.820870i \(0.306511\pi\)
\(812\) −1.79429e65 −0.615009
\(813\) −5.24893e65 −1.74998
\(814\) 4.70717e65 1.52655
\(815\) −4.03428e65 −1.27268
\(816\) 4.79158e65 1.47045
\(817\) −4.54336e64 −0.135638
\(818\) 3.44917e65 1.00176
\(819\) −8.91950e63 −0.0252030
\(820\) 1.03000e65 0.283157
\(821\) −6.22943e65 −1.66620 −0.833100 0.553123i \(-0.813436\pi\)
−0.833100 + 0.553123i \(0.813436\pi\)
\(822\) 2.51075e65 0.653412
\(823\) 1.49111e65 0.377585 0.188792 0.982017i \(-0.439543\pi\)
0.188792 + 0.982017i \(0.439543\pi\)
\(824\) −5.40179e64 −0.133099
\(825\) 1.92980e65 0.462699
\(826\) −1.01872e66 −2.37686
\(827\) 7.39891e65 1.67994 0.839970 0.542633i \(-0.182573\pi\)
0.839970 + 0.542633i \(0.182573\pi\)
\(828\) −2.76485e64 −0.0610926
\(829\) 6.47384e65 1.39215 0.696073 0.717971i \(-0.254929\pi\)
0.696073 + 0.717971i \(0.254929\pi\)
\(830\) 4.83802e64 0.101254
\(831\) 4.76853e64 0.0971319
\(832\) 2.17540e63 0.00431285
\(833\) 4.16570e65 0.803852
\(834\) −4.28227e65 −0.804337
\(835\) 2.58938e65 0.473424
\(836\) −1.80586e65 −0.321398
\(837\) −6.41987e64 −0.111225
\(838\) 3.02214e65 0.509711
\(839\) −4.81442e65 −0.790497 −0.395248 0.918574i \(-0.629341\pi\)
−0.395248 + 0.918574i \(0.629341\pi\)
\(840\) −5.52498e65 −0.883176
\(841\) −1.64223e65 −0.255578
\(842\) −3.77910e65 −0.572619
\(843\) 3.38555e65 0.499469
\(844\) −1.97961e65 −0.284364
\(845\) −7.80592e65 −1.09181
\(846\) −2.63658e64 −0.0359093
\(847\) −1.91666e66 −2.54196
\(848\) 3.82382e65 0.493845
\(849\) 1.31336e66 1.65182
\(850\) 2.87925e65 0.352658
\(851\) 5.61397e65 0.669661
\(852\) −5.07612e64 −0.0589713
\(853\) 1.52156e66 1.72162 0.860808 0.508929i \(-0.169959\pi\)
0.860808 + 0.508929i \(0.169959\pi\)
\(854\) 2.35665e66 2.59712
\(855\) 4.34015e64 0.0465872
\(856\) −8.96575e65 −0.937404
\(857\) −5.36235e63 −0.00546118 −0.00273059 0.999996i \(-0.500869\pi\)
−0.00273059 + 0.999996i \(0.500869\pi\)
\(858\) 3.62204e65 0.359327
\(859\) −1.03735e66 −1.00249 −0.501243 0.865306i \(-0.667124\pi\)
−0.501243 + 0.865306i \(0.667124\pi\)
\(860\) −2.53914e65 −0.239040
\(861\) 7.04824e65 0.646412
\(862\) −1.20139e66 −1.07342
\(863\) −1.99751e66 −1.73878 −0.869391 0.494124i \(-0.835489\pi\)
−0.869391 + 0.494124i \(0.835489\pi\)
\(864\) −1.07910e66 −0.915173
\(865\) 7.63066e64 0.0630521
\(866\) 2.14893e66 1.73009
\(867\) −3.22170e65 −0.252729
\(868\) 1.11406e65 0.0851560
\(869\) 8.36417e65 0.622985
\(870\) −1.75116e66 −1.27099
\(871\) −4.43038e65 −0.313352
\(872\) 9.58687e65 0.660779
\(873\) −1.01420e65 −0.0681243
\(874\) −6.11898e65 −0.400564
\(875\) 1.71664e66 1.09521
\(876\) −7.58321e65 −0.471532
\(877\) −4.71670e65 −0.285856 −0.142928 0.989733i \(-0.545652\pi\)
−0.142928 + 0.989733i \(0.545652\pi\)
\(878\) −1.63361e66 −0.964991
\(879\) −1.33592e66 −0.769187
\(880\) 4.26978e66 2.39632
\(881\) −4.33691e65 −0.237259 −0.118629 0.992939i \(-0.537850\pi\)
−0.118629 + 0.992939i \(0.537850\pi\)
\(882\) 2.02626e65 0.108057
\(883\) 2.23934e66 1.16413 0.582067 0.813141i \(-0.302244\pi\)
0.582067 + 0.813141i \(0.302244\pi\)
\(884\) 1.90211e65 0.0963961
\(885\) −3.49948e66 −1.72894
\(886\) 2.38312e66 1.14786
\(887\) −4.37952e65 −0.205658 −0.102829 0.994699i \(-0.532789\pi\)
−0.102829 + 0.994699i \(0.532789\pi\)
\(888\) −9.40838e65 −0.430748
\(889\) −6.07865e65 −0.271342
\(890\) −2.51732e66 −1.09563
\(891\) 4.46608e66 1.89530
\(892\) 1.02682e66 0.424899
\(893\) −2.05383e65 −0.0828716
\(894\) 5.18947e66 2.04187
\(895\) −1.09927e66 −0.421780
\(896\) −3.56547e66 −1.33409
\(897\) 4.31980e65 0.157628
\(898\) −3.92547e66 −1.39693
\(899\) −2.96993e65 −0.103075
\(900\) 4.92948e64 0.0166857
\(901\) −1.33392e66 −0.440375
\(902\) −3.07659e66 −0.990656
\(903\) −1.73751e66 −0.545699
\(904\) 7.92573e65 0.242800
\(905\) 6.32641e66 1.89045
\(906\) −5.91471e65 −0.172405
\(907\) −4.19442e66 −1.19264 −0.596319 0.802748i \(-0.703370\pi\)
−0.596319 + 0.802748i \(0.703370\pi\)
\(908\) 5.31875e65 0.147529
\(909\) −4.01541e65 −0.108653
\(910\) −1.10321e66 −0.291223
\(911\) 3.79357e66 0.976979 0.488489 0.872570i \(-0.337548\pi\)
0.488489 + 0.872570i \(0.337548\pi\)
\(912\) 1.81555e66 0.456168
\(913\) −5.08645e65 −0.124687
\(914\) −8.22681e66 −1.96762
\(915\) 8.09548e66 1.88916
\(916\) 4.18136e66 0.952071
\(917\) −6.44053e65 −0.143091
\(918\) 5.93771e66 1.28724
\(919\) 2.48234e66 0.525125 0.262563 0.964915i \(-0.415432\pi\)
0.262563 + 0.964915i \(0.415432\pi\)
\(920\) 2.87628e66 0.593751
\(921\) −6.87164e66 −1.38426
\(922\) 6.36379e66 1.25104
\(923\) 8.52513e64 0.0163555
\(924\) −6.90613e66 −1.29305
\(925\) −1.00092e66 −0.182899
\(926\) −5.75712e66 −1.02673
\(927\) 1.62279e65 0.0282467
\(928\) −4.99208e66 −0.848111
\(929\) −3.46738e66 −0.574974 −0.287487 0.957784i \(-0.592820\pi\)
−0.287487 + 0.957784i \(0.592820\pi\)
\(930\) 1.08728e66 0.175985
\(931\) 1.57841e66 0.249374
\(932\) 6.72165e66 1.03662
\(933\) −9.53689e66 −1.43572
\(934\) −1.00052e67 −1.47035
\(935\) −1.48949e67 −2.13686
\(936\) −7.78189e64 −0.0108988
\(937\) 1.05128e67 1.43740 0.718701 0.695319i \(-0.244737\pi\)
0.718701 + 0.695319i \(0.244737\pi\)
\(938\) 2.39998e67 3.20364
\(939\) 1.30704e67 1.70339
\(940\) −1.14782e66 −0.146048
\(941\) 2.44367e66 0.303582 0.151791 0.988413i \(-0.451496\pi\)
0.151791 + 0.988413i \(0.451496\pi\)
\(942\) 7.69009e66 0.932795
\(943\) −3.66928e66 −0.434578
\(944\) −1.57356e67 −1.81976
\(945\) −1.21215e67 −1.36880
\(946\) 7.58433e66 0.836309
\(947\) 7.28326e66 0.784244 0.392122 0.919913i \(-0.371741\pi\)
0.392122 + 0.919913i \(0.371741\pi\)
\(948\) 1.98763e66 0.209000
\(949\) 1.27357e66 0.130777
\(950\) 1.09096e66 0.109403
\(951\) −2.00924e67 −1.96775
\(952\) 8.66651e66 0.828921
\(953\) −1.42251e66 −0.132882 −0.0664410 0.997790i \(-0.521164\pi\)
−0.0664410 + 0.997790i \(0.521164\pi\)
\(954\) −6.48839e65 −0.0591969
\(955\) 6.02196e66 0.536614
\(956\) −7.86907e66 −0.684890
\(957\) 1.84108e67 1.56514
\(958\) −1.04667e67 −0.869136
\(959\) 8.03996e66 0.652131
\(960\) −4.04812e65 −0.0320738
\(961\) −1.27360e67 −0.985728
\(962\) −1.87863e66 −0.142037
\(963\) 2.69346e66 0.198939
\(964\) −4.99783e66 −0.360619
\(965\) 2.83843e67 2.00085
\(966\) −2.34008e67 −1.61155
\(967\) −8.11376e66 −0.545917 −0.272959 0.962026i \(-0.588002\pi\)
−0.272959 + 0.962026i \(0.588002\pi\)
\(968\) −1.67221e67 −1.09925
\(969\) −6.33346e66 −0.406777
\(970\) −1.25441e67 −0.787182
\(971\) 2.08461e67 1.27818 0.639090 0.769132i \(-0.279311\pi\)
0.639090 + 0.769132i \(0.279311\pi\)
\(972\) 2.17236e66 0.130149
\(973\) −1.37128e67 −0.802761
\(974\) 4.03150e66 0.230616
\(975\) −7.70183e65 −0.0430517
\(976\) 3.64019e67 1.98839
\(977\) 1.98080e66 0.105734 0.0528668 0.998602i \(-0.483164\pi\)
0.0528668 + 0.998602i \(0.483164\pi\)
\(978\) 2.86358e67 1.49377
\(979\) 2.64658e67 1.34919
\(980\) 8.82119e66 0.439482
\(981\) −2.88006e66 −0.140232
\(982\) −3.74995e67 −1.78450
\(983\) −3.93540e67 −1.83035 −0.915176 0.403055i \(-0.867948\pi\)
−0.915176 + 0.403055i \(0.867948\pi\)
\(984\) 6.14929e66 0.279534
\(985\) 7.42119e66 0.329730
\(986\) 2.74687e67 1.19291
\(987\) −7.85442e66 −0.333410
\(988\) 7.20718e65 0.0299043
\(989\) 9.04539e66 0.366869
\(990\) −7.24511e66 −0.287245
\(991\) −3.91335e67 −1.51667 −0.758336 0.651864i \(-0.773987\pi\)
−0.758336 + 0.651864i \(0.773987\pi\)
\(992\) 3.09955e66 0.117432
\(993\) −8.60424e65 −0.0318680
\(994\) −4.61815e66 −0.167215
\(995\) −1.97132e67 −0.697811
\(996\) −1.20872e66 −0.0418303
\(997\) −2.80874e67 −0.950323 −0.475161 0.879899i \(-0.657610\pi\)
−0.475161 + 0.879899i \(0.657610\pi\)
\(998\) 1.55059e66 0.0512933
\(999\) −2.06415e67 −0.667601
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 1.46.a.a.1.3 3
3.2 odd 2 9.46.a.b.1.1 3
4.3 odd 2 16.46.a.c.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.46.a.a.1.3 3 1.1 even 1 trivial
9.46.a.b.1.1 3 3.2 odd 2
16.46.a.c.1.3 3 4.3 odd 2