Properties

Label 1.76.a.a.1.4
Level $1$
Weight $76$
Character 1.1
Self dual yes
Analytic conductor $35.623$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 76 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.6228392822\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 3 x^{5} - 38457853073924058692 x^{4} - 10276556354621685339901678086 x^{3} + 371187556674475060057870954681799784505 x^{2} + 52686123927652036687598761277591247931691204025 x - 675344021115865838575279495800656435684060652010336995750\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.46671e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.60898e10 q^{2} -6.47242e17 q^{3} -2.85457e22 q^{4} -1.49650e26 q^{5} -6.21934e28 q^{6} -3.16100e31 q^{7} -6.37312e33 q^{8} -1.89344e35 q^{9} +O(q^{10})\) \(q+9.60898e10 q^{2} -6.47242e17 q^{3} -2.85457e22 q^{4} -1.49650e26 q^{5} -6.21934e28 q^{6} -3.16100e31 q^{7} -6.37312e33 q^{8} -1.89344e35 q^{9} -1.43799e37 q^{10} -9.04175e38 q^{11} +1.84760e40 q^{12} -1.02333e42 q^{13} -3.03740e42 q^{14} +9.68599e43 q^{15} +4.66033e44 q^{16} +2.82749e45 q^{17} -1.81941e46 q^{18} +5.13524e47 q^{19} +4.27187e48 q^{20} +2.04593e49 q^{21} -8.68820e49 q^{22} -1.06901e51 q^{23} +4.12495e51 q^{24} -4.07461e51 q^{25} -9.83316e52 q^{26} +5.16248e53 q^{27} +9.02328e53 q^{28} -5.54224e54 q^{29} +9.30725e54 q^{30} -6.85555e55 q^{31} +2.85551e56 q^{32} +5.85220e56 q^{33} +2.71693e56 q^{34} +4.73044e57 q^{35} +5.40496e57 q^{36} +1.00154e59 q^{37} +4.93445e58 q^{38} +6.62342e59 q^{39} +9.53739e59 q^{40} +4.31368e60 q^{41} +1.96593e60 q^{42} -1.74752e61 q^{43} +2.58103e61 q^{44} +2.83354e61 q^{45} -1.02721e62 q^{46} -9.73598e62 q^{47} -3.01636e62 q^{48} -1.41267e63 q^{49} -3.91528e62 q^{50} -1.83007e63 q^{51} +2.92116e64 q^{52} -2.55811e63 q^{53} +4.96061e64 q^{54} +1.35310e65 q^{55} +2.01454e65 q^{56} -3.32375e65 q^{57} -5.32553e65 q^{58} +5.98212e65 q^{59} -2.76493e66 q^{60} -1.23057e67 q^{61} -6.58749e66 q^{62} +5.98517e66 q^{63} +9.83229e66 q^{64} +1.53141e68 q^{65} +5.62337e67 q^{66} -9.36690e67 q^{67} -8.07127e67 q^{68} +6.91907e68 q^{69} +4.54547e68 q^{70} -3.34843e69 q^{71} +1.20671e69 q^{72} -1.44439e70 q^{73} +9.62381e69 q^{74} +2.63726e69 q^{75} -1.46589e70 q^{76} +2.85810e70 q^{77} +6.36444e70 q^{78} +1.89027e71 q^{79} -6.97419e70 q^{80} -2.18965e71 q^{81} +4.14501e71 q^{82} -1.25156e72 q^{83} -5.84025e71 q^{84} -4.23135e71 q^{85} -1.67919e72 q^{86} +3.58717e72 q^{87} +5.76242e72 q^{88} -1.25211e73 q^{89} +2.72275e72 q^{90} +3.23474e73 q^{91} +3.05156e73 q^{92} +4.43720e73 q^{93} -9.35529e73 q^{94} -7.68490e73 q^{95} -1.84820e74 q^{96} -8.39965e73 q^{97} -1.35744e74 q^{98} +1.71200e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + O(q^{10}) \) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + \)\(13\!\cdots\!60\)\(q^{10} - \)\(94\!\cdots\!88\)\(q^{11} - \)\(11\!\cdots\!80\)\(q^{12} + \)\(53\!\cdots\!20\)\(q^{13} + \)\(82\!\cdots\!76\)\(q^{14} - \)\(30\!\cdots\!80\)\(q^{15} + \)\(26\!\cdots\!16\)\(q^{16} + \)\(18\!\cdots\!80\)\(q^{17} - \)\(43\!\cdots\!40\)\(q^{18} + \)\(10\!\cdots\!80\)\(q^{19} + \)\(92\!\cdots\!80\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(15\!\cdots\!20\)\(q^{22} + \)\(15\!\cdots\!80\)\(q^{23} - \)\(76\!\cdots\!60\)\(q^{24} + \)\(19\!\cdots\!50\)\(q^{25} + \)\(11\!\cdots\!52\)\(q^{26} - \)\(10\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!20\)\(q^{28} + \)\(14\!\cdots\!20\)\(q^{29} - \)\(25\!\cdots\!80\)\(q^{30} - \)\(41\!\cdots\!88\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(59\!\cdots\!20\)\(q^{33} + \)\(30\!\cdots\!56\)\(q^{34} + \)\(27\!\cdots\!60\)\(q^{35} + \)\(17\!\cdots\!16\)\(q^{36} + \)\(98\!\cdots\!40\)\(q^{37} + \)\(12\!\cdots\!80\)\(q^{38} + \)\(24\!\cdots\!44\)\(q^{39} + \)\(88\!\cdots\!00\)\(q^{40} + \)\(50\!\cdots\!12\)\(q^{41} + \)\(43\!\cdots\!80\)\(q^{42} + \)\(27\!\cdots\!00\)\(q^{43} - \)\(86\!\cdots\!44\)\(q^{44} - \)\(23\!\cdots\!80\)\(q^{45} - \)\(82\!\cdots\!88\)\(q^{46} - \)\(13\!\cdots\!80\)\(q^{47} - \)\(82\!\cdots\!20\)\(q^{48} - \)\(57\!\cdots\!42\)\(q^{49} + \)\(31\!\cdots\!00\)\(q^{50} + \)\(28\!\cdots\!32\)\(q^{51} + \)\(41\!\cdots\!00\)\(q^{52} + \)\(64\!\cdots\!60\)\(q^{53} + \)\(78\!\cdots\!80\)\(q^{54} + \)\(43\!\cdots\!20\)\(q^{55} + \)\(28\!\cdots\!20\)\(q^{56} - \)\(67\!\cdots\!40\)\(q^{57} - \)\(17\!\cdots\!80\)\(q^{58} - \)\(24\!\cdots\!60\)\(q^{59} - \)\(31\!\cdots\!40\)\(q^{60} - \)\(25\!\cdots\!88\)\(q^{61} - \)\(29\!\cdots\!80\)\(q^{62} + \)\(42\!\cdots\!40\)\(q^{63} + \)\(47\!\cdots\!48\)\(q^{64} + \)\(12\!\cdots\!20\)\(q^{65} + \)\(93\!\cdots\!84\)\(q^{66} + \)\(95\!\cdots\!80\)\(q^{67} + \)\(12\!\cdots\!60\)\(q^{68} - \)\(14\!\cdots\!36\)\(q^{69} - \)\(34\!\cdots\!40\)\(q^{70} - \)\(25\!\cdots\!88\)\(q^{71} - \)\(21\!\cdots\!60\)\(q^{72} - \)\(30\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!84\)\(q^{74} + \)\(19\!\cdots\!00\)\(q^{75} + \)\(10\!\cdots\!40\)\(q^{76} + \)\(15\!\cdots\!00\)\(q^{77} + \)\(13\!\cdots\!00\)\(q^{78} + \)\(11\!\cdots\!20\)\(q^{79} + \)\(12\!\cdots\!60\)\(q^{80} + \)\(29\!\cdots\!86\)\(q^{81} - \)\(25\!\cdots\!80\)\(q^{82} - \)\(79\!\cdots\!60\)\(q^{83} - \)\(91\!\cdots\!64\)\(q^{84} - \)\(36\!\cdots\!40\)\(q^{85} + \)\(72\!\cdots\!32\)\(q^{86} - \)\(14\!\cdots\!60\)\(q^{87} - \)\(48\!\cdots\!60\)\(q^{88} + \)\(53\!\cdots\!60\)\(q^{89} + \)\(85\!\cdots\!20\)\(q^{90} + \)\(34\!\cdots\!32\)\(q^{91} + \)\(18\!\cdots\!80\)\(q^{92} - \)\(16\!\cdots\!80\)\(q^{93} - \)\(29\!\cdots\!04\)\(q^{94} + \)\(19\!\cdots\!00\)\(q^{95} - \)\(89\!\cdots\!08\)\(q^{96} - \)\(74\!\cdots\!80\)\(q^{97} - \)\(16\!\cdots\!20\)\(q^{98} - \)\(18\!\cdots\!36\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.60898e10 0.494371 0.247185 0.968968i \(-0.420494\pi\)
0.247185 + 0.968968i \(0.420494\pi\)
\(3\) −6.47242e17 −0.829888 −0.414944 0.909847i \(-0.636199\pi\)
−0.414944 + 0.909847i \(0.636199\pi\)
\(4\) −2.85457e22 −0.755598
\(5\) −1.49650e26 −0.919818 −0.459909 0.887966i \(-0.652118\pi\)
−0.459909 + 0.887966i \(0.652118\pi\)
\(6\) −6.21934e28 −0.410272
\(7\) −3.16100e31 −0.643647 −0.321824 0.946800i \(-0.604296\pi\)
−0.321824 + 0.946800i \(0.604296\pi\)
\(8\) −6.37312e33 −0.867916
\(9\) −1.89344e35 −0.311285
\(10\) −1.43799e37 −0.454731
\(11\) −9.04175e38 −0.801727 −0.400864 0.916138i \(-0.631290\pi\)
−0.400864 + 0.916138i \(0.631290\pi\)
\(12\) 1.84760e40 0.627062
\(13\) −1.02333e42 −1.72639 −0.863197 0.504867i \(-0.831541\pi\)
−0.863197 + 0.504867i \(0.831541\pi\)
\(14\) −3.03740e42 −0.318200
\(15\) 9.68599e43 0.763347
\(16\) 4.66033e44 0.326526
\(17\) 2.82749e45 0.203970 0.101985 0.994786i \(-0.467481\pi\)
0.101985 + 0.994786i \(0.467481\pi\)
\(18\) −1.81941e46 −0.153890
\(19\) 5.13524e47 0.571875 0.285937 0.958248i \(-0.407695\pi\)
0.285937 + 0.958248i \(0.407695\pi\)
\(20\) 4.27187e48 0.695013
\(21\) 2.04593e49 0.534155
\(22\) −8.68820e49 −0.396350
\(23\) −1.06901e51 −0.920846 −0.460423 0.887700i \(-0.652302\pi\)
−0.460423 + 0.887700i \(0.652302\pi\)
\(24\) 4.12495e51 0.720273
\(25\) −4.07461e51 −0.153934
\(26\) −9.83316e52 −0.853478
\(27\) 5.16248e53 1.08822
\(28\) 9.02328e53 0.486338
\(29\) −5.54224e54 −0.801236 −0.400618 0.916245i \(-0.631204\pi\)
−0.400618 + 0.916245i \(0.631204\pi\)
\(30\) 9.30725e54 0.377376
\(31\) −6.85555e55 −0.812791 −0.406396 0.913697i \(-0.633215\pi\)
−0.406396 + 0.913697i \(0.633215\pi\)
\(32\) 2.85551e56 1.02934
\(33\) 5.85220e56 0.665344
\(34\) 2.71693e56 0.100837
\(35\) 4.73044e57 0.592038
\(36\) 5.40496e57 0.235206
\(37\) 1.00154e59 1.55993 0.779965 0.625823i \(-0.215237\pi\)
0.779965 + 0.625823i \(0.215237\pi\)
\(38\) 4.93445e58 0.282718
\(39\) 6.62342e59 1.43271
\(40\) 9.53739e59 0.798325
\(41\) 4.31368e60 1.43039 0.715193 0.698927i \(-0.246339\pi\)
0.715193 + 0.698927i \(0.246339\pi\)
\(42\) 1.96593e60 0.264071
\(43\) −1.74752e61 −0.971303 −0.485651 0.874153i \(-0.661418\pi\)
−0.485651 + 0.874153i \(0.661418\pi\)
\(44\) 2.58103e61 0.605783
\(45\) 2.83354e61 0.286326
\(46\) −1.02721e62 −0.455239
\(47\) −9.73598e62 −1.92624 −0.963119 0.269076i \(-0.913282\pi\)
−0.963119 + 0.269076i \(0.913282\pi\)
\(48\) −3.01636e62 −0.270980
\(49\) −1.41267e63 −0.585718
\(50\) −3.91528e62 −0.0761006
\(51\) −1.83007e63 −0.169273
\(52\) 2.92116e64 1.30446
\(53\) −2.55811e63 −0.0559209 −0.0279604 0.999609i \(-0.508901\pi\)
−0.0279604 + 0.999609i \(0.508901\pi\)
\(54\) 4.96061e64 0.537984
\(55\) 1.35310e65 0.737444
\(56\) 2.01454e65 0.558631
\(57\) −3.32375e65 −0.474592
\(58\) −5.32553e65 −0.396107
\(59\) 5.98212e65 0.234372 0.117186 0.993110i \(-0.462613\pi\)
0.117186 + 0.993110i \(0.462613\pi\)
\(60\) −2.76493e66 −0.576783
\(61\) −1.23057e67 −1.38114 −0.690571 0.723265i \(-0.742641\pi\)
−0.690571 + 0.723265i \(0.742641\pi\)
\(62\) −6.58749e66 −0.401820
\(63\) 5.98517e66 0.200358
\(64\) 9.83229e66 0.182350
\(65\) 1.53141e68 1.58797
\(66\) 5.62337e67 0.328927
\(67\) −9.36690e67 −0.311739 −0.155869 0.987778i \(-0.549818\pi\)
−0.155869 + 0.987778i \(0.549818\pi\)
\(68\) −8.07127e67 −0.154120
\(69\) 6.91907e68 0.764200
\(70\) 4.54547e68 0.292686
\(71\) −3.34843e69 −1.26664 −0.633320 0.773890i \(-0.718308\pi\)
−0.633320 + 0.773890i \(0.718308\pi\)
\(72\) 1.20671e69 0.270169
\(73\) −1.44439e70 −1.92787 −0.963934 0.266141i \(-0.914251\pi\)
−0.963934 + 0.266141i \(0.914251\pi\)
\(74\) 9.62381e69 0.771183
\(75\) 2.63726e69 0.127748
\(76\) −1.46589e70 −0.432107
\(77\) 2.85810e70 0.516029
\(78\) 6.36444e70 0.708292
\(79\) 1.89027e71 1.30469 0.652347 0.757920i \(-0.273784\pi\)
0.652347 + 0.757920i \(0.273784\pi\)
\(80\) −6.97419e70 −0.300344
\(81\) −2.18965e71 −0.591816
\(82\) 4.14501e71 0.707140
\(83\) −1.25156e72 −1.35526 −0.677630 0.735403i \(-0.736993\pi\)
−0.677630 + 0.735403i \(0.736993\pi\)
\(84\) −5.84025e71 −0.403607
\(85\) −4.23135e71 −0.187616
\(86\) −1.67919e72 −0.480184
\(87\) 3.58717e72 0.664936
\(88\) 5.76242e72 0.695832
\(89\) −1.25211e73 −0.989728 −0.494864 0.868971i \(-0.664782\pi\)
−0.494864 + 0.868971i \(0.664782\pi\)
\(90\) 2.72275e72 0.141551
\(91\) 3.23474e73 1.11119
\(92\) 3.05156e73 0.695789
\(93\) 4.43720e73 0.674526
\(94\) −9.35529e73 −0.952275
\(95\) −7.68490e73 −0.526021
\(96\) −1.84820e74 −0.854238
\(97\) −8.39965e73 −0.263221 −0.131611 0.991301i \(-0.542015\pi\)
−0.131611 + 0.991301i \(0.542015\pi\)
\(98\) −1.35744e74 −0.289562
\(99\) 1.71200e74 0.249566
\(100\) 1.16312e74 0.116312
\(101\) 8.71215e74 0.599893 0.299947 0.953956i \(-0.403031\pi\)
0.299947 + 0.953956i \(0.403031\pi\)
\(102\) −1.75851e74 −0.0836834
\(103\) 5.77353e74 0.190566 0.0952831 0.995450i \(-0.469624\pi\)
0.0952831 + 0.995450i \(0.469624\pi\)
\(104\) 6.52180e75 1.49836
\(105\) −3.06174e75 −0.491326
\(106\) −2.45808e74 −0.0276456
\(107\) −1.00257e76 −0.792909 −0.396455 0.918054i \(-0.629760\pi\)
−0.396455 + 0.918054i \(0.629760\pi\)
\(108\) −1.47366e76 −0.822257
\(109\) 1.41952e76 0.560593 0.280296 0.959914i \(-0.409567\pi\)
0.280296 + 0.959914i \(0.409567\pi\)
\(110\) 1.30019e76 0.364570
\(111\) −6.48241e76 −1.29457
\(112\) −1.47313e76 −0.210167
\(113\) 5.89790e76 0.602914 0.301457 0.953480i \(-0.402527\pi\)
0.301457 + 0.953480i \(0.402527\pi\)
\(114\) −3.19378e76 −0.234625
\(115\) 1.59977e77 0.847011
\(116\) 1.58207e77 0.605412
\(117\) 1.93762e77 0.537401
\(118\) 5.74821e76 0.115866
\(119\) −8.93770e76 −0.131285
\(120\) −6.17300e77 −0.662521
\(121\) −4.54363e77 −0.357233
\(122\) −1.18245e78 −0.682796
\(123\) −2.79199e78 −1.18706
\(124\) 1.95696e78 0.614143
\(125\) 4.57097e78 1.06141
\(126\) 5.75114e77 0.0990510
\(127\) 8.79169e77 0.112573 0.0562863 0.998415i \(-0.482074\pi\)
0.0562863 + 0.998415i \(0.482074\pi\)
\(128\) −9.84302e78 −0.939192
\(129\) 1.13107e79 0.806073
\(130\) 1.47153e79 0.785045
\(131\) 1.67353e79 0.669823 0.334911 0.942250i \(-0.391294\pi\)
0.334911 + 0.942250i \(0.391294\pi\)
\(132\) −1.67055e79 −0.502733
\(133\) −1.62325e79 −0.368086
\(134\) −9.00064e78 −0.154114
\(135\) −7.72565e79 −1.00097
\(136\) −1.80200e79 −0.177029
\(137\) 6.01048e78 0.0448629 0.0224315 0.999748i \(-0.492859\pi\)
0.0224315 + 0.999748i \(0.492859\pi\)
\(138\) 6.64852e79 0.377798
\(139\) −1.32009e80 −0.572201 −0.286101 0.958200i \(-0.592359\pi\)
−0.286101 + 0.958200i \(0.592359\pi\)
\(140\) −1.35034e80 −0.447343
\(141\) 6.30154e80 1.59856
\(142\) −3.21750e80 −0.626190
\(143\) 9.25269e80 1.38410
\(144\) −8.82408e79 −0.101643
\(145\) 8.29397e80 0.736991
\(146\) −1.38791e81 −0.953081
\(147\) 9.14342e80 0.486081
\(148\) −2.85897e81 −1.17868
\(149\) −4.92682e81 −1.57791 −0.788955 0.614451i \(-0.789377\pi\)
−0.788955 + 0.614451i \(0.789377\pi\)
\(150\) 2.53414e80 0.0631550
\(151\) 7.65678e81 1.48734 0.743670 0.668546i \(-0.233083\pi\)
0.743670 + 0.668546i \(0.233083\pi\)
\(152\) −3.27275e81 −0.496339
\(153\) −5.35370e80 −0.0634929
\(154\) 2.74634e81 0.255110
\(155\) 1.02593e82 0.747620
\(156\) −1.89070e82 −1.08256
\(157\) 2.43970e82 1.09926 0.549629 0.835409i \(-0.314769\pi\)
0.549629 + 0.835409i \(0.314769\pi\)
\(158\) 1.81636e82 0.645003
\(159\) 1.65572e81 0.0464081
\(160\) −4.27327e82 −0.946806
\(161\) 3.37913e82 0.592700
\(162\) −2.10403e82 −0.292577
\(163\) 1.18316e82 0.130620 0.0653099 0.997865i \(-0.479196\pi\)
0.0653099 + 0.997865i \(0.479196\pi\)
\(164\) −1.23137e83 −1.08080
\(165\) −8.75783e82 −0.611996
\(166\) −1.20262e83 −0.670001
\(167\) 1.90144e83 0.845698 0.422849 0.906200i \(-0.361030\pi\)
0.422849 + 0.906200i \(0.361030\pi\)
\(168\) −1.30390e83 −0.463602
\(169\) 6.95845e83 1.98044
\(170\) −4.06590e82 −0.0927517
\(171\) −9.72330e82 −0.178016
\(172\) 4.98841e83 0.733914
\(173\) −5.07453e83 −0.600713 −0.300356 0.953827i \(-0.597106\pi\)
−0.300356 + 0.953827i \(0.597106\pi\)
\(174\) 3.44691e83 0.328725
\(175\) 1.28798e83 0.0990794
\(176\) −4.21375e83 −0.261785
\(177\) −3.87188e83 −0.194502
\(178\) −1.20315e84 −0.489292
\(179\) −3.95061e84 −1.30219 −0.651097 0.758994i \(-0.725691\pi\)
−0.651097 + 0.758994i \(0.725691\pi\)
\(180\) −8.08854e83 −0.216347
\(181\) 9.70552e83 0.210898 0.105449 0.994425i \(-0.466372\pi\)
0.105449 + 0.994425i \(0.466372\pi\)
\(182\) 3.10826e84 0.549339
\(183\) 7.96478e84 1.14619
\(184\) 6.81292e84 0.799217
\(185\) −1.49881e85 −1.43485
\(186\) 4.26370e84 0.333466
\(187\) −2.55655e84 −0.163529
\(188\) 2.77920e85 1.45546
\(189\) −1.63186e85 −0.700430
\(190\) −7.38441e84 −0.260049
\(191\) 1.65608e85 0.478995 0.239498 0.970897i \(-0.423017\pi\)
0.239498 + 0.970897i \(0.423017\pi\)
\(192\) −6.36387e84 −0.151330
\(193\) −3.10563e85 −0.607787 −0.303893 0.952706i \(-0.598287\pi\)
−0.303893 + 0.952706i \(0.598287\pi\)
\(194\) −8.07121e84 −0.130129
\(195\) −9.91196e85 −1.31784
\(196\) 4.03257e85 0.442568
\(197\) −8.70072e85 −0.788990 −0.394495 0.918898i \(-0.629081\pi\)
−0.394495 + 0.918898i \(0.629081\pi\)
\(198\) 1.64506e85 0.123378
\(199\) 2.78509e86 1.72921 0.864606 0.502450i \(-0.167568\pi\)
0.864606 + 0.502450i \(0.167568\pi\)
\(200\) 2.59680e85 0.133602
\(201\) 6.06265e85 0.258708
\(202\) 8.37149e85 0.296570
\(203\) 1.75190e86 0.515713
\(204\) 5.22407e85 0.127902
\(205\) −6.45542e86 −1.31569
\(206\) 5.54778e85 0.0942103
\(207\) 2.02411e86 0.286646
\(208\) −4.76906e86 −0.563712
\(209\) −4.64316e86 −0.458488
\(210\) −2.94202e86 −0.242897
\(211\) −7.50575e86 −0.518564 −0.259282 0.965802i \(-0.583486\pi\)
−0.259282 + 0.965802i \(0.583486\pi\)
\(212\) 7.30230e85 0.0422537
\(213\) 2.16725e87 1.05117
\(214\) −9.63369e86 −0.391991
\(215\) 2.61516e87 0.893422
\(216\) −3.29011e87 −0.944484
\(217\) 2.16704e87 0.523151
\(218\) 1.36401e87 0.277140
\(219\) 9.34870e87 1.59992
\(220\) −3.86251e87 −0.557211
\(221\) −2.89346e87 −0.352133
\(222\) −6.22894e87 −0.639996
\(223\) −7.58008e86 −0.0658023 −0.0329012 0.999459i \(-0.510475\pi\)
−0.0329012 + 0.999459i \(0.510475\pi\)
\(224\) −9.02625e87 −0.662532
\(225\) 7.71504e86 0.0479175
\(226\) 5.66728e87 0.298063
\(227\) −3.93121e87 −0.175209 −0.0876046 0.996155i \(-0.527921\pi\)
−0.0876046 + 0.996155i \(0.527921\pi\)
\(228\) 9.48786e87 0.358601
\(229\) −4.79839e88 −1.53909 −0.769546 0.638591i \(-0.779518\pi\)
−0.769546 + 0.638591i \(0.779518\pi\)
\(230\) 1.53722e88 0.418737
\(231\) −1.84988e88 −0.428247
\(232\) 3.53213e88 0.695405
\(233\) 6.03818e88 1.01172 0.505859 0.862616i \(-0.331176\pi\)
0.505859 + 0.862616i \(0.331176\pi\)
\(234\) 1.86185e88 0.265675
\(235\) 1.45699e89 1.77179
\(236\) −1.70764e88 −0.177091
\(237\) −1.22347e89 −1.08275
\(238\) −8.58822e87 −0.0649034
\(239\) −1.88840e89 −1.21947 −0.609737 0.792604i \(-0.708725\pi\)
−0.609737 + 0.792604i \(0.708725\pi\)
\(240\) 4.51399e88 0.249252
\(241\) −1.29168e89 −0.610261 −0.305131 0.952311i \(-0.598700\pi\)
−0.305131 + 0.952311i \(0.598700\pi\)
\(242\) −4.36597e88 −0.176606
\(243\) −1.72293e89 −0.597079
\(244\) 3.51275e89 1.04359
\(245\) 2.11407e89 0.538755
\(246\) −2.68282e89 −0.586848
\(247\) −5.25505e89 −0.987282
\(248\) 4.36913e89 0.705434
\(249\) 8.10061e89 1.12471
\(250\) 4.39224e89 0.524730
\(251\) −6.21006e89 −0.638751 −0.319375 0.947628i \(-0.603473\pi\)
−0.319375 + 0.947628i \(0.603473\pi\)
\(252\) −1.70851e89 −0.151390
\(253\) 9.66570e89 0.738268
\(254\) 8.44792e88 0.0556526
\(255\) 2.73871e89 0.155700
\(256\) −1.31727e90 −0.646659
\(257\) −4.17118e89 −0.176916 −0.0884580 0.996080i \(-0.528194\pi\)
−0.0884580 + 0.996080i \(0.528194\pi\)
\(258\) 1.08684e90 0.398499
\(259\) −3.16588e90 −1.00404
\(260\) −4.37153e90 −1.19987
\(261\) 1.04939e90 0.249413
\(262\) 1.60809e90 0.331141
\(263\) 4.77873e90 0.853045 0.426523 0.904477i \(-0.359738\pi\)
0.426523 + 0.904477i \(0.359738\pi\)
\(264\) −3.72968e90 −0.577463
\(265\) 3.82821e89 0.0514370
\(266\) −1.55978e90 −0.181971
\(267\) 8.10416e90 0.821364
\(268\) 2.67385e90 0.235549
\(269\) 1.60979e91 1.23327 0.616636 0.787249i \(-0.288495\pi\)
0.616636 + 0.787249i \(0.288495\pi\)
\(270\) −7.42357e90 −0.494848
\(271\) 4.15988e90 0.241397 0.120699 0.992689i \(-0.461486\pi\)
0.120699 + 0.992689i \(0.461486\pi\)
\(272\) 1.31771e90 0.0666016
\(273\) −2.09366e91 −0.922163
\(274\) 5.77546e89 0.0221789
\(275\) 3.68416e90 0.123413
\(276\) −1.97510e91 −0.577428
\(277\) −4.01519e91 −1.02498 −0.512489 0.858694i \(-0.671277\pi\)
−0.512489 + 0.858694i \(0.671277\pi\)
\(278\) −1.26847e91 −0.282879
\(279\) 1.29806e91 0.253010
\(280\) −3.01477e91 −0.513839
\(281\) 4.24980e91 0.633697 0.316848 0.948476i \(-0.397375\pi\)
0.316848 + 0.948476i \(0.397375\pi\)
\(282\) 6.05513e91 0.790282
\(283\) −1.80371e91 −0.206146 −0.103073 0.994674i \(-0.532868\pi\)
−0.103073 + 0.994674i \(0.532868\pi\)
\(284\) 9.55833e91 0.957071
\(285\) 4.97399e91 0.436539
\(286\) 8.89090e91 0.684257
\(287\) −1.36355e92 −0.920663
\(288\) −5.40674e91 −0.320418
\(289\) −1.84168e92 −0.958396
\(290\) 7.96966e91 0.364347
\(291\) 5.43660e91 0.218444
\(292\) 4.12311e92 1.45669
\(293\) −3.12319e92 −0.970650 −0.485325 0.874334i \(-0.661299\pi\)
−0.485325 + 0.874334i \(0.661299\pi\)
\(294\) 8.78590e91 0.240304
\(295\) −8.95226e91 −0.215579
\(296\) −6.38296e92 −1.35389
\(297\) −4.66778e92 −0.872456
\(298\) −4.73418e92 −0.780072
\(299\) 1.09395e93 1.58974
\(300\) −7.52823e91 −0.0965263
\(301\) 5.52390e92 0.625176
\(302\) 7.35738e92 0.735298
\(303\) −5.63887e92 −0.497844
\(304\) 2.39319e92 0.186732
\(305\) 1.84155e93 1.27040
\(306\) −5.14436e91 −0.0313890
\(307\) −6.03921e92 −0.326055 −0.163028 0.986622i \(-0.552126\pi\)
−0.163028 + 0.986622i \(0.552126\pi\)
\(308\) −8.15863e92 −0.389911
\(309\) −3.73688e92 −0.158149
\(310\) 9.85819e92 0.369601
\(311\) 8.09285e92 0.268897 0.134449 0.990921i \(-0.457074\pi\)
0.134449 + 0.990921i \(0.457074\pi\)
\(312\) −4.22119e93 −1.24348
\(313\) −3.76956e93 −0.984869 −0.492434 0.870350i \(-0.663893\pi\)
−0.492434 + 0.870350i \(0.663893\pi\)
\(314\) 2.34431e93 0.543441
\(315\) −8.95682e92 −0.184293
\(316\) −5.39592e93 −0.985824
\(317\) 4.64348e93 0.753565 0.376783 0.926302i \(-0.377030\pi\)
0.376783 + 0.926302i \(0.377030\pi\)
\(318\) 1.59097e92 0.0229428
\(319\) 5.01115e93 0.642373
\(320\) −1.47140e93 −0.167729
\(321\) 6.48906e93 0.658026
\(322\) 3.24700e93 0.293013
\(323\) 1.45199e93 0.116646
\(324\) 6.25051e93 0.447175
\(325\) 4.16967e93 0.265751
\(326\) 1.13690e93 0.0645746
\(327\) −9.18772e93 −0.465229
\(328\) −2.74916e94 −1.24145
\(329\) 3.07754e94 1.23982
\(330\) −8.41538e93 −0.302553
\(331\) −6.01033e94 −1.92907 −0.964536 0.263952i \(-0.914974\pi\)
−0.964536 + 0.263952i \(0.914974\pi\)
\(332\) 3.57266e94 1.02403
\(333\) −1.89637e94 −0.485583
\(334\) 1.82709e94 0.418088
\(335\) 1.40176e94 0.286743
\(336\) 9.53472e93 0.174415
\(337\) −9.17041e94 −1.50061 −0.750304 0.661093i \(-0.770093\pi\)
−0.750304 + 0.661093i \(0.770093\pi\)
\(338\) 6.68636e94 0.979070
\(339\) −3.81737e94 −0.500352
\(340\) 1.20787e94 0.141762
\(341\) 6.19862e94 0.651637
\(342\) −9.34310e93 −0.0880060
\(343\) 1.20894e95 1.02064
\(344\) 1.11371e95 0.843009
\(345\) −1.03544e95 −0.702925
\(346\) −4.87611e94 −0.296975
\(347\) 1.82468e95 0.997311 0.498655 0.866800i \(-0.333827\pi\)
0.498655 + 0.866800i \(0.333827\pi\)
\(348\) −1.02398e95 −0.502424
\(349\) 2.90622e94 0.128049 0.0640244 0.997948i \(-0.479606\pi\)
0.0640244 + 0.997948i \(0.479606\pi\)
\(350\) 1.23762e94 0.0489819
\(351\) −5.28292e95 −1.87870
\(352\) −2.58188e95 −0.825251
\(353\) −2.60592e95 −0.748876 −0.374438 0.927252i \(-0.622164\pi\)
−0.374438 + 0.927252i \(0.622164\pi\)
\(354\) −3.72049e94 −0.0961562
\(355\) 5.01094e95 1.16508
\(356\) 3.57422e95 0.747836
\(357\) 5.78486e94 0.108952
\(358\) −3.79614e95 −0.643767
\(359\) 1.18369e96 1.80798 0.903992 0.427549i \(-0.140623\pi\)
0.903992 + 0.427549i \(0.140623\pi\)
\(360\) −1.80585e95 −0.248507
\(361\) −5.42636e95 −0.672959
\(362\) 9.32602e94 0.104262
\(363\) 2.94083e95 0.296464
\(364\) −9.23380e95 −0.839612
\(365\) 2.16153e96 1.77329
\(366\) 7.65334e95 0.566644
\(367\) −1.04271e96 −0.696923 −0.348462 0.937323i \(-0.613296\pi\)
−0.348462 + 0.937323i \(0.613296\pi\)
\(368\) −4.98193e95 −0.300680
\(369\) −8.16771e95 −0.445258
\(370\) −1.44020e96 −0.709349
\(371\) 8.08618e94 0.0359933
\(372\) −1.26663e96 −0.509670
\(373\) −1.28066e96 −0.465966 −0.232983 0.972481i \(-0.574849\pi\)
−0.232983 + 0.972481i \(0.574849\pi\)
\(374\) −2.45658e95 −0.0808437
\(375\) −2.95853e96 −0.880852
\(376\) 6.20486e96 1.67181
\(377\) 5.67154e96 1.38325
\(378\) −1.56805e96 −0.346272
\(379\) −7.43491e96 −1.48698 −0.743490 0.668747i \(-0.766831\pi\)
−0.743490 + 0.668747i \(0.766831\pi\)
\(380\) 2.19371e96 0.397460
\(381\) −5.69035e95 −0.0934227
\(382\) 1.59133e96 0.236801
\(383\) 7.91229e96 1.06745 0.533726 0.845658i \(-0.320791\pi\)
0.533726 + 0.845658i \(0.320791\pi\)
\(384\) 6.37082e96 0.779425
\(385\) −4.27714e96 −0.474653
\(386\) −2.98420e96 −0.300472
\(387\) 3.30883e96 0.302352
\(388\) 2.39774e96 0.198889
\(389\) −5.40930e96 −0.407409 −0.203705 0.979032i \(-0.565298\pi\)
−0.203705 + 0.979032i \(0.565298\pi\)
\(390\) −9.52439e96 −0.651500
\(391\) −3.02261e96 −0.187825
\(392\) 9.00314e96 0.508354
\(393\) −1.08318e97 −0.555878
\(394\) −8.36051e96 −0.390054
\(395\) −2.82880e97 −1.20008
\(396\) −4.88703e96 −0.188571
\(397\) 1.66947e96 0.0586051 0.0293025 0.999571i \(-0.490671\pi\)
0.0293025 + 0.999571i \(0.490671\pi\)
\(398\) 2.67619e97 0.854872
\(399\) 1.05064e97 0.305470
\(400\) −1.89890e96 −0.0502635
\(401\) 3.18207e97 0.767001 0.383501 0.923541i \(-0.374718\pi\)
0.383501 + 0.923541i \(0.374718\pi\)
\(402\) 5.82559e96 0.127898
\(403\) 7.01549e97 1.40320
\(404\) −2.48694e97 −0.453278
\(405\) 3.27682e97 0.544364
\(406\) 1.68340e97 0.254953
\(407\) −9.05570e97 −1.25064
\(408\) 1.16633e97 0.146914
\(409\) −4.59307e97 −0.527812 −0.263906 0.964548i \(-0.585011\pi\)
−0.263906 + 0.964548i \(0.585011\pi\)
\(410\) −6.20301e97 −0.650441
\(411\) −3.89023e96 −0.0372312
\(412\) −1.64809e97 −0.143991
\(413\) −1.89095e97 −0.150853
\(414\) 1.94496e97 0.141709
\(415\) 1.87296e98 1.24659
\(416\) −2.92213e98 −1.77705
\(417\) 8.54418e97 0.474863
\(418\) −4.46160e97 −0.226663
\(419\) −4.37040e97 −0.203000 −0.101500 0.994836i \(-0.532364\pi\)
−0.101500 + 0.994836i \(0.532364\pi\)
\(420\) 8.73994e97 0.371245
\(421\) 9.39287e97 0.364939 0.182469 0.983212i \(-0.441591\pi\)
0.182469 + 0.983212i \(0.441591\pi\)
\(422\) −7.21226e97 −0.256363
\(423\) 1.84345e98 0.599609
\(424\) 1.63031e97 0.0485346
\(425\) −1.15209e97 −0.0313980
\(426\) 2.08250e98 0.519668
\(427\) 3.88984e98 0.888968
\(428\) 2.86191e98 0.599120
\(429\) −5.98873e98 −1.14865
\(430\) 2.51291e98 0.441682
\(431\) −7.00214e98 −1.12806 −0.564032 0.825753i \(-0.690750\pi\)
−0.564032 + 0.825753i \(0.690750\pi\)
\(432\) 2.40588e98 0.355332
\(433\) −6.63616e98 −0.898712 −0.449356 0.893353i \(-0.648346\pi\)
−0.449356 + 0.893353i \(0.648346\pi\)
\(434\) 2.08230e98 0.258630
\(435\) −5.36821e98 −0.611620
\(436\) −4.05211e98 −0.423582
\(437\) −5.48962e98 −0.526609
\(438\) 8.98315e98 0.790951
\(439\) 1.20506e99 0.974067 0.487033 0.873383i \(-0.338079\pi\)
0.487033 + 0.873383i \(0.338079\pi\)
\(440\) −8.62346e98 −0.640039
\(441\) 2.67482e98 0.182325
\(442\) −2.78032e98 −0.174084
\(443\) −2.73293e99 −1.57213 −0.786067 0.618141i \(-0.787886\pi\)
−0.786067 + 0.618141i \(0.787886\pi\)
\(444\) 1.85045e99 0.978172
\(445\) 1.87378e99 0.910370
\(446\) −7.28368e97 −0.0325307
\(447\) 3.18885e99 1.30949
\(448\) −3.10799e98 −0.117369
\(449\) 4.89234e99 1.69933 0.849667 0.527319i \(-0.176803\pi\)
0.849667 + 0.527319i \(0.176803\pi\)
\(450\) 7.41337e97 0.0236890
\(451\) −3.90032e99 −1.14678
\(452\) −1.68359e99 −0.455561
\(453\) −4.95579e99 −1.23433
\(454\) −3.77750e98 −0.0866183
\(455\) −4.84080e99 −1.02209
\(456\) 2.11826e99 0.411906
\(457\) 3.25924e99 0.583792 0.291896 0.956450i \(-0.405714\pi\)
0.291896 + 0.956450i \(0.405714\pi\)
\(458\) −4.61076e99 −0.760882
\(459\) 1.45969e99 0.221965
\(460\) −4.56666e99 −0.640000
\(461\) 3.65189e99 0.471773 0.235887 0.971781i \(-0.424201\pi\)
0.235887 + 0.971781i \(0.424201\pi\)
\(462\) −1.77755e99 −0.211713
\(463\) 1.23373e100 1.35498 0.677492 0.735530i \(-0.263067\pi\)
0.677492 + 0.735530i \(0.263067\pi\)
\(464\) −2.58287e99 −0.261624
\(465\) −6.64028e99 −0.620441
\(466\) 5.80208e99 0.500163
\(467\) 1.09207e100 0.868698 0.434349 0.900745i \(-0.356978\pi\)
0.434349 + 0.900745i \(0.356978\pi\)
\(468\) −5.53106e99 −0.406059
\(469\) 2.96088e99 0.200650
\(470\) 1.40002e100 0.875920
\(471\) −1.57908e100 −0.912262
\(472\) −3.81248e99 −0.203415
\(473\) 1.58006e100 0.778720
\(474\) −1.17563e100 −0.535280
\(475\) −2.09241e99 −0.0880312
\(476\) 2.55133e99 0.0991986
\(477\) 4.84364e98 0.0174073
\(478\) −1.81456e100 −0.602872
\(479\) 2.78687e100 0.856119 0.428060 0.903751i \(-0.359197\pi\)
0.428060 + 0.903751i \(0.359197\pi\)
\(480\) 2.76584e100 0.785744
\(481\) −1.02491e101 −2.69305
\(482\) −1.24117e100 −0.301695
\(483\) −2.18712e100 −0.491875
\(484\) 1.29701e100 0.269925
\(485\) 1.25701e100 0.242116
\(486\) −1.65556e100 −0.295178
\(487\) 4.50886e100 0.744271 0.372135 0.928178i \(-0.378626\pi\)
0.372135 + 0.928178i \(0.378626\pi\)
\(488\) 7.84258e100 1.19871
\(489\) −7.65793e99 −0.108400
\(490\) 2.03141e100 0.266344
\(491\) 2.15050e100 0.261206 0.130603 0.991435i \(-0.458309\pi\)
0.130603 + 0.991435i \(0.458309\pi\)
\(492\) 7.96993e100 0.896940
\(493\) −1.56706e100 −0.163428
\(494\) −5.04957e100 −0.488083
\(495\) −2.56202e100 −0.229555
\(496\) −3.19491e100 −0.265397
\(497\) 1.05844e101 0.815270
\(498\) 7.78386e100 0.556026
\(499\) −1.72948e101 −1.14590 −0.572948 0.819592i \(-0.694200\pi\)
−0.572948 + 0.819592i \(0.694200\pi\)
\(500\) −1.30482e101 −0.801999
\(501\) −1.23069e101 −0.701835
\(502\) −5.96724e100 −0.315780
\(503\) 2.47749e101 1.21678 0.608391 0.793637i \(-0.291815\pi\)
0.608391 + 0.793637i \(0.291815\pi\)
\(504\) −3.81442e100 −0.173894
\(505\) −1.30377e101 −0.551793
\(506\) 9.28776e100 0.364978
\(507\) −4.50380e101 −1.64354
\(508\) −2.50965e100 −0.0850596
\(509\) 2.05274e101 0.646276 0.323138 0.946352i \(-0.395262\pi\)
0.323138 + 0.946352i \(0.395262\pi\)
\(510\) 2.63162e100 0.0769735
\(511\) 4.56572e101 1.24087
\(512\) 2.45283e101 0.619503
\(513\) 2.65106e101 0.622326
\(514\) −4.00808e100 −0.0874620
\(515\) −8.64010e100 −0.175286
\(516\) −3.22871e101 −0.609067
\(517\) 8.80303e101 1.54432
\(518\) −3.04209e101 −0.496370
\(519\) 3.28445e101 0.498525
\(520\) −9.75989e101 −1.37822
\(521\) −6.95456e101 −0.913808 −0.456904 0.889516i \(-0.651042\pi\)
−0.456904 + 0.889516i \(0.651042\pi\)
\(522\) 1.00836e101 0.123302
\(523\) 3.62848e101 0.412963 0.206481 0.978451i \(-0.433799\pi\)
0.206481 + 0.978451i \(0.433799\pi\)
\(524\) −4.77721e101 −0.506117
\(525\) −8.33637e100 −0.0822248
\(526\) 4.59187e101 0.421720
\(527\) −1.93840e101 −0.165785
\(528\) 2.72732e101 0.217252
\(529\) −2.04904e101 −0.152042
\(530\) 3.67853e100 0.0254290
\(531\) −1.13268e101 −0.0729564
\(532\) 4.63368e101 0.278125
\(533\) −4.41431e102 −2.46941
\(534\) 7.78727e101 0.406058
\(535\) 1.50035e102 0.729332
\(536\) 5.96964e101 0.270563
\(537\) 2.55700e102 1.08068
\(538\) 1.54684e102 0.609693
\(539\) 1.27730e102 0.469587
\(540\) 2.20534e102 0.756327
\(541\) −1.59160e102 −0.509257 −0.254628 0.967039i \(-0.581953\pi\)
−0.254628 + 0.967039i \(0.581953\pi\)
\(542\) 3.99723e101 0.119340
\(543\) −6.28182e101 −0.175022
\(544\) 8.07393e101 0.209955
\(545\) −2.12431e102 −0.515643
\(546\) −2.01180e102 −0.455890
\(547\) −4.34376e102 −0.919053 −0.459527 0.888164i \(-0.651981\pi\)
−0.459527 + 0.888164i \(0.651981\pi\)
\(548\) −1.71573e101 −0.0338983
\(549\) 2.33002e102 0.429929
\(550\) 3.54010e101 0.0610119
\(551\) −2.84607e102 −0.458207
\(552\) −4.40961e102 −0.663261
\(553\) −5.97515e102 −0.839763
\(554\) −3.85819e102 −0.506719
\(555\) 9.70094e102 1.19077
\(556\) 3.76829e102 0.432354
\(557\) −4.83045e102 −0.518105 −0.259053 0.965863i \(-0.583410\pi\)
−0.259053 + 0.965863i \(0.583410\pi\)
\(558\) 1.24730e102 0.125081
\(559\) 1.78829e103 1.67685
\(560\) 2.20454e102 0.193316
\(561\) 1.65471e102 0.135711
\(562\) 4.08362e102 0.313281
\(563\) 8.05465e102 0.578072 0.289036 0.957318i \(-0.406665\pi\)
0.289036 + 0.957318i \(0.406665\pi\)
\(564\) −1.79882e103 −1.20787
\(565\) −8.82621e102 −0.554571
\(566\) −1.73318e102 −0.101912
\(567\) 6.92149e102 0.380921
\(568\) 2.13400e103 1.09934
\(569\) −5.36992e102 −0.258975 −0.129488 0.991581i \(-0.541333\pi\)
−0.129488 + 0.991581i \(0.541333\pi\)
\(570\) 4.77950e102 0.215812
\(571\) −3.90521e102 −0.165116 −0.0825582 0.996586i \(-0.526309\pi\)
−0.0825582 + 0.996586i \(0.526309\pi\)
\(572\) −2.64124e103 −1.04582
\(573\) −1.07189e103 −0.397513
\(574\) −1.31024e103 −0.455149
\(575\) 4.35579e102 0.141750
\(576\) −1.86169e102 −0.0567628
\(577\) −1.53569e103 −0.438743 −0.219372 0.975641i \(-0.570401\pi\)
−0.219372 + 0.975641i \(0.570401\pi\)
\(578\) −1.76967e103 −0.473803
\(579\) 2.01010e103 0.504395
\(580\) −2.36757e103 −0.556869
\(581\) 3.95617e103 0.872309
\(582\) 5.22402e102 0.107992
\(583\) 2.31298e102 0.0448333
\(584\) 9.20527e103 1.67323
\(585\) −2.89965e103 −0.494311
\(586\) −3.00107e103 −0.479861
\(587\) 4.98256e103 0.747349 0.373674 0.927560i \(-0.378098\pi\)
0.373674 + 0.927560i \(0.378098\pi\)
\(588\) −2.61005e103 −0.367282
\(589\) −3.52049e103 −0.464815
\(590\) −8.60221e102 −0.106576
\(591\) 5.63147e103 0.654774
\(592\) 4.66752e103 0.509357
\(593\) −8.67897e101 −0.00889031 −0.00444516 0.999990i \(-0.501415\pi\)
−0.00444516 + 0.999990i \(0.501415\pi\)
\(594\) −4.48526e103 −0.431317
\(595\) 1.33753e103 0.120758
\(596\) 1.40640e104 1.19226
\(597\) −1.80263e104 −1.43505
\(598\) 1.05117e104 0.785922
\(599\) −2.53386e104 −1.77942 −0.889708 0.456531i \(-0.849092\pi\)
−0.889708 + 0.456531i \(0.849092\pi\)
\(600\) −1.68076e103 −0.110875
\(601\) −9.89909e103 −0.613483 −0.306742 0.951793i \(-0.599239\pi\)
−0.306742 + 0.951793i \(0.599239\pi\)
\(602\) 5.30791e103 0.309069
\(603\) 1.77357e103 0.0970397
\(604\) −2.18568e104 −1.12383
\(605\) 6.79955e103 0.328590
\(606\) −5.41838e103 −0.246120
\(607\) 3.73213e103 0.159361 0.0796803 0.996820i \(-0.474610\pi\)
0.0796803 + 0.996820i \(0.474610\pi\)
\(608\) 1.46637e104 0.588654
\(609\) −1.13390e104 −0.427984
\(610\) 1.76955e104 0.628048
\(611\) 9.96312e104 3.32545
\(612\) 1.52825e103 0.0479751
\(613\) −4.35614e104 −1.28627 −0.643137 0.765751i \(-0.722368\pi\)
−0.643137 + 0.765751i \(0.722368\pi\)
\(614\) −5.80306e103 −0.161192
\(615\) 4.17822e104 1.09188
\(616\) −1.82150e104 −0.447870
\(617\) −5.43863e104 −1.25833 −0.629167 0.777270i \(-0.716604\pi\)
−0.629167 + 0.777270i \(0.716604\pi\)
\(618\) −3.59076e103 −0.0781841
\(619\) 2.50377e104 0.513093 0.256546 0.966532i \(-0.417415\pi\)
0.256546 + 0.966532i \(0.417415\pi\)
\(620\) −2.92860e104 −0.564900
\(621\) −5.51873e104 −1.00208
\(622\) 7.77640e103 0.132935
\(623\) 3.95790e104 0.637035
\(624\) 3.08673e104 0.467818
\(625\) −5.76193e104 −0.822370
\(626\) −3.62217e104 −0.486890
\(627\) 3.00525e104 0.380494
\(628\) −6.96430e104 −0.830597
\(629\) 2.83186e104 0.318179
\(630\) −8.60660e103 −0.0911089
\(631\) 8.30271e104 0.828169 0.414085 0.910238i \(-0.364102\pi\)
0.414085 + 0.910238i \(0.364102\pi\)
\(632\) −1.20469e105 −1.13237
\(633\) 4.85804e104 0.430350
\(634\) 4.46191e104 0.372540
\(635\) −1.31568e104 −0.103546
\(636\) −4.72635e103 −0.0350658
\(637\) 1.44563e105 1.01118
\(638\) 4.81521e104 0.317570
\(639\) 6.34007e104 0.394287
\(640\) 1.47301e105 0.863886
\(641\) −2.75789e105 −1.52546 −0.762729 0.646718i \(-0.776141\pi\)
−0.762729 + 0.646718i \(0.776141\pi\)
\(642\) 6.23533e104 0.325309
\(643\) 1.32726e105 0.653198 0.326599 0.945163i \(-0.394097\pi\)
0.326599 + 0.945163i \(0.394097\pi\)
\(644\) −9.64596e104 −0.447843
\(645\) −1.69264e105 −0.741441
\(646\) 1.39521e104 0.0576661
\(647\) 2.44039e103 0.00951806 0.00475903 0.999989i \(-0.498485\pi\)
0.00475903 + 0.999989i \(0.498485\pi\)
\(648\) 1.39549e105 0.513647
\(649\) −5.40889e104 −0.187902
\(650\) 4.00663e104 0.131380
\(651\) −1.40260e105 −0.434157
\(652\) −3.37742e104 −0.0986961
\(653\) −6.41133e105 −1.76890 −0.884451 0.466632i \(-0.845467\pi\)
−0.884451 + 0.466632i \(0.845467\pi\)
\(654\) −8.82847e104 −0.229996
\(655\) −2.50444e105 −0.616115
\(656\) 2.01032e105 0.467058
\(657\) 2.73487e105 0.600117
\(658\) 2.95720e105 0.612929
\(659\) 4.80095e105 0.939992 0.469996 0.882669i \(-0.344255\pi\)
0.469996 + 0.882669i \(0.344255\pi\)
\(660\) 2.49998e105 0.462423
\(661\) −4.07366e105 −0.711919 −0.355959 0.934501i \(-0.615846\pi\)
−0.355959 + 0.934501i \(0.615846\pi\)
\(662\) −5.77531e105 −0.953676
\(663\) 1.87277e105 0.292231
\(664\) 7.97633e105 1.17625
\(665\) 2.42920e105 0.338572
\(666\) −1.82221e105 −0.240058
\(667\) 5.92470e105 0.737815
\(668\) −5.42779e105 −0.639008
\(669\) 4.90614e104 0.0546086
\(670\) 1.34695e105 0.141757
\(671\) 1.11265e106 1.10730
\(672\) 5.84217e105 0.549828
\(673\) −7.62407e105 −0.678613 −0.339306 0.940676i \(-0.610192\pi\)
−0.339306 + 0.940676i \(0.610192\pi\)
\(674\) −8.81183e105 −0.741856
\(675\) −2.10351e105 −0.167514
\(676\) −1.98634e106 −1.49641
\(677\) −1.87091e106 −1.33345 −0.666727 0.745302i \(-0.732305\pi\)
−0.666727 + 0.745302i \(0.732305\pi\)
\(678\) −3.66810e105 −0.247359
\(679\) 2.65513e105 0.169422
\(680\) 2.69669e105 0.162835
\(681\) 2.54445e105 0.145404
\(682\) 5.95624e105 0.322150
\(683\) 1.12098e106 0.573881 0.286941 0.957948i \(-0.407362\pi\)
0.286941 + 0.957948i \(0.407362\pi\)
\(684\) 2.77558e105 0.134509
\(685\) −8.99469e104 −0.0412657
\(686\) 1.16166e106 0.504576
\(687\) 3.10572e106 1.27728
\(688\) −8.14401e105 −0.317155
\(689\) 2.61779e105 0.0965415
\(690\) −9.94953e105 −0.347505
\(691\) −2.18789e106 −0.723768 −0.361884 0.932223i \(-0.617866\pi\)
−0.361884 + 0.932223i \(0.617866\pi\)
\(692\) 1.44856e106 0.453897
\(693\) −5.41164e105 −0.160632
\(694\) 1.75333e106 0.493041
\(695\) 1.97552e106 0.526321
\(696\) −2.28615e106 −0.577109
\(697\) 1.21969e106 0.291756
\(698\) 2.79258e105 0.0633035
\(699\) −3.90817e106 −0.839613
\(700\) −3.67663e105 −0.0748641
\(701\) 6.49232e106 1.25307 0.626533 0.779395i \(-0.284473\pi\)
0.626533 + 0.779395i \(0.284473\pi\)
\(702\) −5.07634e106 −0.928773
\(703\) 5.14317e106 0.892085
\(704\) −8.89011e105 −0.146195
\(705\) −9.43026e106 −1.47039
\(706\) −2.50402e106 −0.370222
\(707\) −2.75391e106 −0.386119
\(708\) 1.10526e106 0.146965
\(709\) −8.42609e106 −1.06266 −0.531328 0.847166i \(-0.678307\pi\)
−0.531328 + 0.847166i \(0.678307\pi\)
\(710\) 4.81500e106 0.575981
\(711\) −3.57913e106 −0.406132
\(712\) 7.97982e106 0.859000
\(713\) 7.32864e106 0.748456
\(714\) 5.55866e105 0.0538626
\(715\) −1.38467e107 −1.27312
\(716\) 1.12773e107 0.983936
\(717\) 1.22225e107 1.01203
\(718\) 1.13740e107 0.893814
\(719\) −2.53914e106 −0.189388 −0.0946942 0.995506i \(-0.530187\pi\)
−0.0946942 + 0.995506i \(0.530187\pi\)
\(720\) 1.32052e106 0.0934927
\(721\) −1.82501e106 −0.122657
\(722\) −5.21418e106 −0.332691
\(723\) 8.36030e106 0.506449
\(724\) −2.77051e106 −0.159354
\(725\) 2.25824e106 0.123338
\(726\) 2.82584e106 0.146563
\(727\) −2.75247e107 −1.35576 −0.677880 0.735172i \(-0.737101\pi\)
−0.677880 + 0.735172i \(0.737101\pi\)
\(728\) −2.06154e107 −0.964418
\(729\) 2.44704e107 1.08733
\(730\) 2.07701e107 0.876662
\(731\) −4.94110e106 −0.198117
\(732\) −2.27360e107 −0.866061
\(733\) −1.63836e107 −0.592938 −0.296469 0.955042i \(-0.595809\pi\)
−0.296469 + 0.955042i \(0.595809\pi\)
\(734\) −1.00194e107 −0.344538
\(735\) −1.36831e107 −0.447106
\(736\) −3.05256e107 −0.947864
\(737\) 8.46932e106 0.249930
\(738\) −7.84834e106 −0.220122
\(739\) 2.59618e107 0.692100 0.346050 0.938216i \(-0.387523\pi\)
0.346050 + 0.938216i \(0.387523\pi\)
\(740\) 4.27846e107 1.08417
\(741\) 3.40129e107 0.819334
\(742\) 7.77000e105 0.0177940
\(743\) −1.39254e107 −0.303199 −0.151600 0.988442i \(-0.548442\pi\)
−0.151600 + 0.988442i \(0.548442\pi\)
\(744\) −2.82788e107 −0.585432
\(745\) 7.37300e107 1.45139
\(746\) −1.23059e107 −0.230360
\(747\) 2.36976e107 0.421872
\(748\) 7.29784e106 0.123562
\(749\) 3.16912e107 0.510354
\(750\) −2.84284e107 −0.435467
\(751\) −1.89224e107 −0.275726 −0.137863 0.990451i \(-0.544023\pi\)
−0.137863 + 0.990451i \(0.544023\pi\)
\(752\) −4.53729e107 −0.628966
\(753\) 4.01941e107 0.530092
\(754\) 5.44977e107 0.683837
\(755\) −1.14584e108 −1.36808
\(756\) 4.65825e107 0.529243
\(757\) −6.82237e107 −0.737632 −0.368816 0.929502i \(-0.620237\pi\)
−0.368816 + 0.929502i \(0.620237\pi\)
\(758\) −7.14419e107 −0.735120
\(759\) −6.25605e107 −0.612680
\(760\) 4.89768e107 0.456542
\(761\) 5.62396e107 0.499020 0.249510 0.968372i \(-0.419731\pi\)
0.249510 + 0.968372i \(0.419731\pi\)
\(762\) −5.46785e106 −0.0461855
\(763\) −4.48710e107 −0.360824
\(764\) −4.72741e107 −0.361928
\(765\) 8.01182e106 0.0584020
\(766\) 7.60291e107 0.527717
\(767\) −6.12169e107 −0.404618
\(768\) 8.52591e107 0.536655
\(769\) 1.14718e108 0.687694 0.343847 0.939026i \(-0.388270\pi\)
0.343847 + 0.939026i \(0.388270\pi\)
\(770\) −4.10990e107 −0.234655
\(771\) 2.69976e107 0.146821
\(772\) 8.86524e107 0.459242
\(773\) −3.23382e108 −1.59582 −0.797912 0.602774i \(-0.794062\pi\)
−0.797912 + 0.602774i \(0.794062\pi\)
\(774\) 3.17945e107 0.149474
\(775\) 2.79337e107 0.125116
\(776\) 5.35320e107 0.228454
\(777\) 2.04909e108 0.833245
\(778\) −5.19779e107 −0.201411
\(779\) 2.21518e108 0.818001
\(780\) 2.82944e108 0.995755
\(781\) 3.02757e108 1.01550
\(782\) −2.90442e107 −0.0928553
\(783\) −2.86117e108 −0.871921
\(784\) −6.58353e107 −0.191252
\(785\) −3.65102e108 −1.01112
\(786\) −1.04083e108 −0.274810
\(787\) −7.72858e108 −1.94557 −0.972786 0.231704i \(-0.925570\pi\)
−0.972786 + 0.231704i \(0.925570\pi\)
\(788\) 2.48368e108 0.596159
\(789\) −3.09300e108 −0.707932
\(790\) −2.71819e108 −0.593285
\(791\) −1.86432e108 −0.388064
\(792\) −1.09108e108 −0.216602
\(793\) 1.25928e109 2.38439
\(794\) 1.60419e107 0.0289726
\(795\) −2.47778e107 −0.0426870
\(796\) −7.95022e108 −1.30659
\(797\) 9.15620e108 1.43558 0.717791 0.696259i \(-0.245153\pi\)
0.717791 + 0.696259i \(0.245153\pi\)
\(798\) 1.00955e108 0.151015
\(799\) −2.75284e108 −0.392895
\(800\) −1.16351e108 −0.158451
\(801\) 2.37079e108 0.308088
\(802\) 3.05765e108 0.379183
\(803\) 1.30598e109 1.54562
\(804\) −1.73063e108 −0.195480
\(805\) −5.05688e108 −0.545176
\(806\) 6.74118e108 0.693700
\(807\) −1.04192e109 −1.02348
\(808\) −5.55236e108 −0.520657
\(809\) 1.40487e109 1.25767 0.628837 0.777538i \(-0.283531\pi\)
0.628837 + 0.777538i \(0.283531\pi\)
\(810\) 3.14869e108 0.269117
\(811\) −3.14760e108 −0.256860 −0.128430 0.991719i \(-0.540994\pi\)
−0.128430 + 0.991719i \(0.540994\pi\)
\(812\) −5.00092e108 −0.389672
\(813\) −2.69245e108 −0.200333
\(814\) −8.70161e108 −0.618279
\(815\) −1.77060e108 −0.120147
\(816\) −8.52874e107 −0.0552719
\(817\) −8.97393e108 −0.555464
\(818\) −4.41348e108 −0.260935
\(819\) −6.12481e108 −0.345896
\(820\) 1.84274e109 0.994136
\(821\) −2.88576e109 −1.48727 −0.743637 0.668583i \(-0.766901\pi\)
−0.743637 + 0.668583i \(0.766901\pi\)
\(822\) −3.73812e107 −0.0184060
\(823\) 1.73999e109 0.818567 0.409283 0.912407i \(-0.365779\pi\)
0.409283 + 0.912407i \(0.365779\pi\)
\(824\) −3.67954e108 −0.165395
\(825\) −2.38454e108 −0.102419
\(826\) −1.81701e108 −0.0745771
\(827\) 3.34216e109 1.31090 0.655451 0.755238i \(-0.272479\pi\)
0.655451 + 0.755238i \(0.272479\pi\)
\(828\) −5.77795e108 −0.216589
\(829\) −2.05561e107 −0.00736455 −0.00368228 0.999993i \(-0.501172\pi\)
−0.00368228 + 0.999993i \(0.501172\pi\)
\(830\) 1.79972e109 0.616279
\(831\) 2.59880e109 0.850618
\(832\) −1.00617e109 −0.314808
\(833\) −3.99433e108 −0.119469
\(834\) 8.21009e108 0.234758
\(835\) −2.84551e109 −0.777889
\(836\) 1.32542e109 0.346432
\(837\) −3.53916e109 −0.884496
\(838\) −4.19951e108 −0.100357
\(839\) 6.16118e109 1.40796 0.703981 0.710219i \(-0.251404\pi\)
0.703981 + 0.710219i \(0.251404\pi\)
\(840\) 1.95128e109 0.426429
\(841\) −1.71301e109 −0.358022
\(842\) 9.02559e108 0.180415
\(843\) −2.75065e109 −0.525897
\(844\) 2.14257e109 0.391826
\(845\) −1.04133e110 −1.82164
\(846\) 1.77137e109 0.296429
\(847\) 1.43624e109 0.229932
\(848\) −1.19216e108 −0.0182596
\(849\) 1.16744e109 0.171078
\(850\) −1.10704e108 −0.0155223
\(851\) −1.07066e110 −1.43646
\(852\) −6.18655e109 −0.794262
\(853\) 3.10108e107 0.00380999 0.00190499 0.999998i \(-0.499394\pi\)
0.00190499 + 0.999998i \(0.499394\pi\)
\(854\) 3.73774e109 0.439480
\(855\) 1.45509e109 0.163743
\(856\) 6.38950e109 0.688178
\(857\) 2.75939e109 0.284467 0.142234 0.989833i \(-0.454572\pi\)
0.142234 + 0.989833i \(0.454572\pi\)
\(858\) −5.75456e109 −0.567857
\(859\) 1.64858e110 1.55728 0.778638 0.627474i \(-0.215911\pi\)
0.778638 + 0.627474i \(0.215911\pi\)
\(860\) −7.46516e109 −0.675068
\(861\) 8.82549e109 0.764048
\(862\) −6.72835e109 −0.557681
\(863\) 6.66654e109 0.529049 0.264525 0.964379i \(-0.414785\pi\)
0.264525 + 0.964379i \(0.414785\pi\)
\(864\) 1.47415e110 1.12015
\(865\) 7.59404e109 0.552547
\(866\) −6.37667e109 −0.444297
\(867\) 1.19201e110 0.795362
\(868\) −6.18596e109 −0.395292
\(869\) −1.70914e110 −1.04601
\(870\) −5.15830e109 −0.302367
\(871\) 9.58543e109 0.538184
\(872\) −9.04676e109 −0.486547
\(873\) 1.59043e109 0.0819369
\(874\) −5.27497e109 −0.260340
\(875\) −1.44488e110 −0.683173
\(876\) −2.66865e110 −1.20889
\(877\) −4.10529e110 −1.78180 −0.890901 0.454197i \(-0.849926\pi\)
−0.890901 + 0.454197i \(0.849926\pi\)
\(878\) 1.15794e110 0.481550
\(879\) 2.02146e110 0.805531
\(880\) 6.30589e109 0.240794
\(881\) 2.60424e110 0.952980 0.476490 0.879180i \(-0.341909\pi\)
0.476490 + 0.879180i \(0.341909\pi\)
\(882\) 2.57023e109 0.0901363
\(883\) 2.39725e110 0.805725 0.402863 0.915260i \(-0.368015\pi\)
0.402863 + 0.915260i \(0.368015\pi\)
\(884\) 8.25957e109 0.266071
\(885\) 5.79428e109 0.178907
\(886\) −2.62607e110 −0.777217
\(887\) −5.65377e110 −1.60399 −0.801996 0.597330i \(-0.796228\pi\)
−0.801996 + 0.597330i \(0.796228\pi\)
\(888\) 4.13132e110 1.12358
\(889\) −2.77905e109 −0.0724571
\(890\) 1.80051e110 0.450060
\(891\) 1.97983e110 0.474475
\(892\) 2.16378e109 0.0497201
\(893\) −4.99966e110 −1.10157
\(894\) 3.06416e110 0.647373
\(895\) 5.91210e110 1.19778
\(896\) 3.11138e110 0.604508
\(897\) −7.08049e110 −1.31931
\(898\) 4.70104e110 0.840101
\(899\) 3.79951e110 0.651237
\(900\) −2.20231e109 −0.0362063
\(901\) −7.23304e108 −0.0114062
\(902\) −3.74781e110 −0.566934
\(903\) −3.57530e110 −0.518827
\(904\) −3.75880e110 −0.523279
\(905\) −1.45243e110 −0.193988
\(906\) −4.76201e110 −0.610215
\(907\) −6.45915e110 −0.794150 −0.397075 0.917786i \(-0.629975\pi\)
−0.397075 + 0.917786i \(0.629975\pi\)
\(908\) 1.12219e110 0.132388
\(909\) −1.64960e110 −0.186738
\(910\) −4.65152e110 −0.505292
\(911\) 8.29756e110 0.864991 0.432495 0.901636i \(-0.357633\pi\)
0.432495 + 0.901636i \(0.357633\pi\)
\(912\) −1.54898e110 −0.154967
\(913\) 1.13163e111 1.08655
\(914\) 3.13180e110 0.288610
\(915\) −1.19193e111 −1.05429
\(916\) 1.36973e111 1.16294
\(917\) −5.29003e110 −0.431130
\(918\) 1.40261e110 0.109733
\(919\) −1.37516e111 −1.03282 −0.516408 0.856343i \(-0.672731\pi\)
−0.516408 + 0.856343i \(0.672731\pi\)
\(920\) −1.01955e111 −0.735135
\(921\) 3.90883e110 0.270589
\(922\) 3.50910e110 0.233231
\(923\) 3.42655e111 2.18672
\(924\) 5.28061e110 0.323582
\(925\) −4.08089e110 −0.240127
\(926\) 1.18549e111 0.669864
\(927\) −1.09319e110 −0.0593204
\(928\) −1.58259e111 −0.824744
\(929\) 2.86857e111 1.43574 0.717870 0.696177i \(-0.245117\pi\)
0.717870 + 0.696177i \(0.245117\pi\)
\(930\) −6.38064e110 −0.306728
\(931\) −7.25443e110 −0.334958
\(932\) −1.72364e111 −0.764451
\(933\) −5.23803e110 −0.223155
\(934\) 1.04937e111 0.429459
\(935\) 3.82588e110 0.150417
\(936\) −1.23487e111 −0.466419
\(937\) −4.28248e111 −1.55403 −0.777017 0.629480i \(-0.783268\pi\)
−0.777017 + 0.629480i \(0.783268\pi\)
\(938\) 2.84510e110 0.0991953
\(939\) 2.43982e111 0.817331
\(940\) −4.15908e111 −1.33876
\(941\) 1.54957e111 0.479294 0.239647 0.970860i \(-0.422968\pi\)
0.239647 + 0.970860i \(0.422968\pi\)
\(942\) −1.51733e111 −0.450996
\(943\) −4.61136e111 −1.31716
\(944\) 2.78787e110 0.0765284
\(945\) 2.44208e111 0.644268
\(946\) 1.51828e111 0.384976
\(947\) −4.69614e111 −1.14450 −0.572251 0.820079i \(-0.693930\pi\)
−0.572251 + 0.820079i \(0.693930\pi\)
\(948\) 3.49246e111 0.818124
\(949\) 1.47809e112 3.32826
\(950\) −2.01059e110 −0.0435200
\(951\) −3.00545e111 −0.625375
\(952\) 5.69611e110 0.113944
\(953\) −5.56877e110 −0.107097 −0.0535483 0.998565i \(-0.517053\pi\)
−0.0535483 + 0.998565i \(0.517053\pi\)
\(954\) 4.65424e109 0.00860568
\(955\) −2.47833e111 −0.440589
\(956\) 5.39056e111 0.921432
\(957\) −3.24343e111 −0.533098
\(958\) 2.67789e111 0.423240
\(959\) −1.89991e110 −0.0288759
\(960\) 9.52355e110 0.139196
\(961\) −2.41435e111 −0.339370
\(962\) −9.84833e111 −1.33137
\(963\) 1.89831e111 0.246821
\(964\) 3.68719e111 0.461112
\(965\) 4.64759e111 0.559053
\(966\) −2.10160e111 −0.243168
\(967\) −8.93151e111 −0.994104 −0.497052 0.867721i \(-0.665584\pi\)
−0.497052 + 0.867721i \(0.665584\pi\)
\(968\) 2.89571e111 0.310048
\(969\) −9.39787e110 −0.0968028
\(970\) 1.20786e111 0.119695
\(971\) −1.46304e112 −1.39487 −0.697436 0.716647i \(-0.745676\pi\)
−0.697436 + 0.716647i \(0.745676\pi\)
\(972\) 4.91821e111 0.451151
\(973\) 4.17280e111 0.368296
\(974\) 4.33256e111 0.367946
\(975\) −2.69878e111 −0.220544
\(976\) −5.73487e111 −0.450978
\(977\) −5.34284e111 −0.404321 −0.202161 0.979352i \(-0.564796\pi\)
−0.202161 + 0.979352i \(0.564796\pi\)
\(978\) −7.35849e110 −0.0535897
\(979\) 1.13212e112 0.793492
\(980\) −6.03475e111 −0.407082
\(981\) −2.68778e111 −0.174504
\(982\) 2.06641e111 0.129133
\(983\) −2.30266e111 −0.138508 −0.0692538 0.997599i \(-0.522062\pi\)
−0.0692538 + 0.997599i \(0.522062\pi\)
\(984\) 1.77937e112 1.03027
\(985\) 1.30206e112 0.725728
\(986\) −1.50579e111 −0.0807941
\(987\) −1.99191e112 −1.02891
\(988\) 1.50009e112 0.745988
\(989\) 1.86811e112 0.894421
\(990\) −2.46184e111 −0.113485
\(991\) 2.38412e112 1.05820 0.529098 0.848560i \(-0.322530\pi\)
0.529098 + 0.848560i \(0.322530\pi\)
\(992\) −1.95761e112 −0.836639
\(993\) 3.89014e112 1.60091
\(994\) 1.01705e112 0.403045
\(995\) −4.16789e112 −1.59056
\(996\) −2.31237e112 −0.849832
\(997\) −3.57199e112 −1.26427 −0.632137 0.774856i \(-0.717822\pi\)
−0.632137 + 0.774856i \(0.717822\pi\)
\(998\) −1.66185e112 −0.566497
\(999\) 5.17044e112 1.69755
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 1.76.a.a.1.4 6
3.2 odd 2 9.76.a.c.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.76.a.a.1.4 6 1.1 even 1 trivial
9.76.a.c.1.3 6 3.2 odd 2