Properties

Label 3.42.a.b.1.2
Level 3
Weight 42
Character 3.1
Self dual yes
Analytic conductor 31.942
Analytic rank 0
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 42 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9415011369\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 196497525461 x^{2} + 10360343667016365 x + 6095744045744274504000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{10}\cdot 5^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(263663.\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.59943e6 q^{2} +3.48678e9 q^{3} +3.59152e11 q^{4} +3.20915e14 q^{5} -5.57687e15 q^{6} +2.35480e17 q^{7} +2.94274e18 q^{8} +1.21577e19 q^{9} +O(q^{10})\) \(q-1.59943e6 q^{2} +3.48678e9 q^{3} +3.59152e11 q^{4} +3.20915e14 q^{5} -5.57687e15 q^{6} +2.35480e17 q^{7} +2.94274e18 q^{8} +1.21577e19 q^{9} -5.13282e20 q^{10} +4.09335e21 q^{11} +1.25229e21 q^{12} +2.26252e22 q^{13} -3.76634e23 q^{14} +1.11896e24 q^{15} -5.49650e24 q^{16} -2.18147e25 q^{17} -1.94453e25 q^{18} -1.65269e26 q^{19} +1.15257e26 q^{20} +8.21069e26 q^{21} -6.54702e27 q^{22} +1.04809e28 q^{23} +1.02607e28 q^{24} +5.75119e28 q^{25} -3.61875e28 q^{26} +4.23912e28 q^{27} +8.45732e28 q^{28} -1.48336e29 q^{29} -1.78970e30 q^{30} +2.32552e30 q^{31} +2.32010e30 q^{32} +1.42726e31 q^{33} +3.48911e31 q^{34} +7.55692e31 q^{35} +4.36645e30 q^{36} -5.37090e31 q^{37} +2.64337e32 q^{38} +7.88894e31 q^{39} +9.44372e32 q^{40} -9.27726e32 q^{41} -1.31324e33 q^{42} +4.47072e33 q^{43} +1.47013e33 q^{44} +3.90158e33 q^{45} -1.67634e34 q^{46} -1.02491e34 q^{47} -1.91651e34 q^{48} +1.08833e34 q^{49} -9.19863e34 q^{50} -7.60632e34 q^{51} +8.12590e33 q^{52} -2.32449e35 q^{53} -6.78017e34 q^{54} +1.31362e36 q^{55} +6.92958e35 q^{56} -5.76258e35 q^{57} +2.37253e35 q^{58} -1.00765e35 q^{59} +4.01878e35 q^{60} +1.56573e36 q^{61} -3.71950e36 q^{62} +2.86289e36 q^{63} +8.37609e36 q^{64} +7.26079e36 q^{65} -2.28280e37 q^{66} -5.00920e36 q^{67} -7.83480e36 q^{68} +3.65446e37 q^{69} -1.20868e38 q^{70} -7.95732e37 q^{71} +3.57769e37 q^{72} -1.56377e38 q^{73} +8.59038e37 q^{74} +2.00532e38 q^{75} -5.93568e37 q^{76} +9.63902e38 q^{77} -1.26178e38 q^{78} +1.20235e39 q^{79} -1.76391e39 q^{80} +1.47809e38 q^{81} +1.48383e39 q^{82} +2.45813e39 q^{83} +2.94889e38 q^{84} -7.00068e39 q^{85} -7.15060e39 q^{86} -5.17216e38 q^{87} +1.20457e40 q^{88} -1.06301e40 q^{89} -6.24030e39 q^{90} +5.32780e39 q^{91} +3.76423e39 q^{92} +8.10858e39 q^{93} +1.63927e40 q^{94} -5.30374e40 q^{95} +8.08967e39 q^{96} +2.08674e40 q^{97} -1.74071e40 q^{98} +4.97655e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + O(q^{10}) \) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + \)\(72\!\cdots\!40\)\(q^{10} + \)\(72\!\cdots\!56\)\(q^{11} + \)\(18\!\cdots\!32\)\(q^{12} - \)\(88\!\cdots\!08\)\(q^{13} + \)\(49\!\cdots\!68\)\(q^{14} + \)\(41\!\cdots\!80\)\(q^{15} - \)\(59\!\cdots\!00\)\(q^{16} - \)\(38\!\cdots\!88\)\(q^{17} - \)\(84\!\cdots\!22\)\(q^{18} + \)\(26\!\cdots\!48\)\(q^{19} + \)\(78\!\cdots\!60\)\(q^{20} + \)\(52\!\cdots\!36\)\(q^{21} - \)\(63\!\cdots\!76\)\(q^{22} - \)\(15\!\cdots\!32\)\(q^{23} + \)\(21\!\cdots\!84\)\(q^{24} + \)\(11\!\cdots\!00\)\(q^{25} - \)\(62\!\cdots\!52\)\(q^{26} + \)\(16\!\cdots\!04\)\(q^{27} + \)\(68\!\cdots\!12\)\(q^{28} - \)\(10\!\cdots\!64\)\(q^{29} + \)\(25\!\cdots\!40\)\(q^{30} + \)\(92\!\cdots\!04\)\(q^{31} + \)\(19\!\cdots\!56\)\(q^{32} + \)\(25\!\cdots\!56\)\(q^{33} + \)\(92\!\cdots\!04\)\(q^{34} + \)\(20\!\cdots\!40\)\(q^{35} + \)\(65\!\cdots\!32\)\(q^{36} + \)\(20\!\cdots\!56\)\(q^{37} + \)\(11\!\cdots\!28\)\(q^{38} - \)\(30\!\cdots\!08\)\(q^{39} + \)\(25\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!04\)\(q^{41} + \)\(17\!\cdots\!68\)\(q^{42} + \)\(39\!\cdots\!60\)\(q^{43} - \)\(18\!\cdots\!04\)\(q^{44} + \)\(14\!\cdots\!80\)\(q^{45} - \)\(44\!\cdots\!16\)\(q^{46} - \)\(88\!\cdots\!20\)\(q^{47} - \)\(20\!\cdots\!00\)\(q^{48} - \)\(33\!\cdots\!80\)\(q^{49} - \)\(21\!\cdots\!50\)\(q^{50} - \)\(13\!\cdots\!88\)\(q^{51} - \)\(59\!\cdots\!08\)\(q^{52} + \)\(95\!\cdots\!28\)\(q^{53} - \)\(29\!\cdots\!22\)\(q^{54} + \)\(12\!\cdots\!60\)\(q^{55} + \)\(19\!\cdots\!20\)\(q^{56} + \)\(91\!\cdots\!48\)\(q^{57} + \)\(38\!\cdots\!16\)\(q^{58} - \)\(18\!\cdots\!08\)\(q^{59} + \)\(27\!\cdots\!60\)\(q^{60} + \)\(53\!\cdots\!40\)\(q^{61} + \)\(14\!\cdots\!52\)\(q^{62} + \)\(18\!\cdots\!36\)\(q^{63} - \)\(38\!\cdots\!92\)\(q^{64} - \)\(97\!\cdots\!80\)\(q^{65} - \)\(22\!\cdots\!76\)\(q^{66} - \)\(73\!\cdots\!28\)\(q^{67} - \)\(89\!\cdots\!24\)\(q^{68} - \)\(53\!\cdots\!32\)\(q^{69} - \)\(12\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!52\)\(q^{71} + \)\(76\!\cdots\!84\)\(q^{72} - \)\(44\!\cdots\!32\)\(q^{73} - \)\(29\!\cdots\!12\)\(q^{74} + \)\(40\!\cdots\!00\)\(q^{75} + \)\(11\!\cdots\!72\)\(q^{76} + \)\(83\!\cdots\!52\)\(q^{77} - \)\(21\!\cdots\!52\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(15\!\cdots\!80\)\(q^{80} + \)\(59\!\cdots\!04\)\(q^{81} + \)\(61\!\cdots\!12\)\(q^{82} + \)\(15\!\cdots\!04\)\(q^{83} + \)\(23\!\cdots\!12\)\(q^{84} - \)\(28\!\cdots\!60\)\(q^{85} - \)\(12\!\cdots\!24\)\(q^{86} - \)\(36\!\cdots\!64\)\(q^{87} - \)\(13\!\cdots\!96\)\(q^{88} - \)\(39\!\cdots\!72\)\(q^{89} + \)\(88\!\cdots\!40\)\(q^{90} - \)\(88\!\cdots\!16\)\(q^{91} - \)\(65\!\cdots\!44\)\(q^{92} + \)\(32\!\cdots\!04\)\(q^{93} + \)\(98\!\cdots\!32\)\(q^{94} + \)\(78\!\cdots\!00\)\(q^{95} + \)\(68\!\cdots\!56\)\(q^{96} + \)\(36\!\cdots\!52\)\(q^{97} - \)\(68\!\cdots\!22\)\(q^{98} + \)\(88\!\cdots\!56\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59943e6 −1.07857 −0.539287 0.842122i \(-0.681306\pi\)
−0.539287 + 0.842122i \(0.681306\pi\)
\(3\) 3.48678e9 0.577350
\(4\) 3.59152e11 0.163323
\(5\) 3.20915e14 1.50489 0.752446 0.658654i \(-0.228874\pi\)
0.752446 + 0.658654i \(0.228874\pi\)
\(6\) −5.57687e15 −0.622715
\(7\) 2.35480e17 1.11544 0.557718 0.830030i \(-0.311677\pi\)
0.557718 + 0.830030i \(0.311677\pi\)
\(8\) 2.94274e18 0.902418
\(9\) 1.21577e19 0.333333
\(10\) −5.13282e20 −1.62314
\(11\) 4.09335e21 1.83455 0.917273 0.398260i \(-0.130386\pi\)
0.917273 + 0.398260i \(0.130386\pi\)
\(12\) 1.25229e21 0.0942948
\(13\) 2.26252e22 0.330183 0.165091 0.986278i \(-0.447208\pi\)
0.165091 + 0.986278i \(0.447208\pi\)
\(14\) −3.76634e23 −1.20308
\(15\) 1.11896e24 0.868850
\(16\) −5.49650e24 −1.13665
\(17\) −2.18147e25 −1.30181 −0.650904 0.759160i \(-0.725610\pi\)
−0.650904 + 0.759160i \(0.725610\pi\)
\(18\) −1.94453e25 −0.359525
\(19\) −1.65269e26 −1.00866 −0.504328 0.863512i \(-0.668260\pi\)
−0.504328 + 0.863512i \(0.668260\pi\)
\(20\) 1.15257e26 0.245784
\(21\) 8.21069e26 0.643997
\(22\) −6.54702e27 −1.97869
\(23\) 1.04809e28 1.27344 0.636718 0.771097i \(-0.280292\pi\)
0.636718 + 0.771097i \(0.280292\pi\)
\(24\) 1.02607e28 0.521011
\(25\) 5.75119e28 1.26470
\(26\) −3.61875e28 −0.356127
\(27\) 4.23912e28 0.192450
\(28\) 8.45732e28 0.182177
\(29\) −1.48336e29 −0.155628 −0.0778140 0.996968i \(-0.524794\pi\)
−0.0778140 + 0.996968i \(0.524794\pi\)
\(30\) −1.78970e30 −0.937120
\(31\) 2.32552e30 0.621734 0.310867 0.950453i \(-0.399381\pi\)
0.310867 + 0.950453i \(0.399381\pi\)
\(32\) 2.32010e30 0.323542
\(33\) 1.42726e31 1.05918
\(34\) 3.48911e31 1.40410
\(35\) 7.55692e31 1.67861
\(36\) 4.36645e30 0.0544411
\(37\) −5.37090e31 −0.381867 −0.190933 0.981603i \(-0.561151\pi\)
−0.190933 + 0.981603i \(0.561151\pi\)
\(38\) 2.64337e32 1.08791
\(39\) 7.88894e31 0.190631
\(40\) 9.44372e32 1.35804
\(41\) −9.27726e32 −0.804176 −0.402088 0.915601i \(-0.631715\pi\)
−0.402088 + 0.915601i \(0.631715\pi\)
\(42\) −1.31324e33 −0.694599
\(43\) 4.47072e33 1.45973 0.729867 0.683589i \(-0.239582\pi\)
0.729867 + 0.683589i \(0.239582\pi\)
\(44\) 1.47013e33 0.299624
\(45\) 3.90158e33 0.501631
\(46\) −1.67634e34 −1.37350
\(47\) −1.02491e34 −0.540355 −0.270177 0.962811i \(-0.587082\pi\)
−0.270177 + 0.962811i \(0.587082\pi\)
\(48\) −1.91651e34 −0.656245
\(49\) 1.08833e34 0.244198
\(50\) −9.19863e34 −1.36407
\(51\) −7.60632e34 −0.751599
\(52\) 8.12590e33 0.0539266
\(53\) −2.32449e35 −1.04393 −0.521966 0.852966i \(-0.674801\pi\)
−0.521966 + 0.852966i \(0.674801\pi\)
\(54\) −6.78017e34 −0.207572
\(55\) 1.31362e36 2.76079
\(56\) 6.92958e35 1.00659
\(57\) −5.76258e35 −0.582348
\(58\) 2.37253e35 0.167856
\(59\) −1.00765e35 −0.0502159 −0.0251080 0.999685i \(-0.507993\pi\)
−0.0251080 + 0.999685i \(0.507993\pi\)
\(60\) 4.01878e35 0.141904
\(61\) 1.56573e36 0.393964 0.196982 0.980407i \(-0.436886\pi\)
0.196982 + 0.980407i \(0.436886\pi\)
\(62\) −3.71950e36 −0.670587
\(63\) 2.86289e36 0.371812
\(64\) 8.37609e36 0.787684
\(65\) 7.26079e36 0.496890
\(66\) −2.28280e37 −1.14240
\(67\) −5.00920e36 −0.184177 −0.0920883 0.995751i \(-0.529354\pi\)
−0.0920883 + 0.995751i \(0.529354\pi\)
\(68\) −7.83480e36 −0.212616
\(69\) 3.65446e37 0.735218
\(70\) −1.20868e38 −1.81051
\(71\) −7.95732e37 −0.891191 −0.445596 0.895234i \(-0.647008\pi\)
−0.445596 + 0.895234i \(0.647008\pi\)
\(72\) 3.57769e37 0.300806
\(73\) −1.56377e38 −0.990955 −0.495477 0.868621i \(-0.665007\pi\)
−0.495477 + 0.868621i \(0.665007\pi\)
\(74\) 8.59038e37 0.411872
\(75\) 2.00532e38 0.730175
\(76\) −5.93568e37 −0.164737
\(77\) 9.63902e38 2.04632
\(78\) −1.26178e38 −0.205610
\(79\) 1.20235e39 1.50895 0.754475 0.656329i \(-0.227892\pi\)
0.754475 + 0.656329i \(0.227892\pi\)
\(80\) −1.76391e39 −1.71053
\(81\) 1.47809e38 0.111111
\(82\) 1.48383e39 0.867363
\(83\) 2.45813e39 1.12074 0.560369 0.828243i \(-0.310659\pi\)
0.560369 + 0.828243i \(0.310659\pi\)
\(84\) 2.94889e38 0.105180
\(85\) −7.00068e39 −1.95908
\(86\) −7.15060e39 −1.57443
\(87\) −5.17216e38 −0.0898519
\(88\) 1.20457e40 1.65553
\(89\) −1.06301e40 −1.15889 −0.579443 0.815012i \(-0.696730\pi\)
−0.579443 + 0.815012i \(0.696730\pi\)
\(90\) −6.24030e39 −0.541046
\(91\) 5.32780e39 0.368298
\(92\) 3.76423e39 0.207982
\(93\) 8.10858e39 0.358958
\(94\) 1.63927e40 0.582813
\(95\) −5.30374e40 −1.51792
\(96\) 8.08967e39 0.186797
\(97\) 2.08674e40 0.389626 0.194813 0.980840i \(-0.437590\pi\)
0.194813 + 0.980840i \(0.437590\pi\)
\(98\) −1.74071e40 −0.263386
\(99\) 4.97655e40 0.611515
\(100\) 2.06555e40 0.206555
\(101\) 1.04865e41 0.855146 0.427573 0.903981i \(-0.359369\pi\)
0.427573 + 0.903981i \(0.359369\pi\)
\(102\) 1.21658e41 0.810656
\(103\) −2.03937e41 −1.11258 −0.556292 0.830987i \(-0.687777\pi\)
−0.556292 + 0.830987i \(0.687777\pi\)
\(104\) 6.65803e40 0.297963
\(105\) 2.63494e41 0.969147
\(106\) 3.71786e41 1.12596
\(107\) −7.60455e41 −1.89979 −0.949896 0.312567i \(-0.898811\pi\)
−0.949896 + 0.312567i \(0.898811\pi\)
\(108\) 1.52249e40 0.0314316
\(109\) 1.97252e41 0.337115 0.168557 0.985692i \(-0.446089\pi\)
0.168557 + 0.985692i \(0.446089\pi\)
\(110\) −2.10104e42 −2.97772
\(111\) −1.87272e41 −0.220471
\(112\) −1.29432e42 −1.26786
\(113\) 7.19758e41 0.587595 0.293798 0.955868i \(-0.405081\pi\)
0.293798 + 0.955868i \(0.405081\pi\)
\(114\) 9.21685e41 0.628106
\(115\) 3.36347e42 1.91638
\(116\) −5.32752e40 −0.0254177
\(117\) 2.75070e41 0.110061
\(118\) 1.61166e41 0.0541617
\(119\) −5.13694e42 −1.45208
\(120\) 3.29282e42 0.784066
\(121\) 1.17770e43 2.36556
\(122\) −2.50428e42 −0.424919
\(123\) −3.23478e42 −0.464291
\(124\) 8.35214e41 0.101544
\(125\) 3.86292e42 0.398346
\(126\) −4.57899e42 −0.401027
\(127\) −7.84129e42 −0.583998 −0.291999 0.956419i \(-0.594320\pi\)
−0.291999 + 0.956419i \(0.594320\pi\)
\(128\) −1.84989e43 −1.17312
\(129\) 1.55884e43 0.842778
\(130\) −1.16131e43 −0.535933
\(131\) 1.88589e43 0.743799 0.371899 0.928273i \(-0.378707\pi\)
0.371899 + 0.928273i \(0.378707\pi\)
\(132\) 5.12604e42 0.172988
\(133\) −3.89177e43 −1.12509
\(134\) 8.01186e42 0.198648
\(135\) 1.36040e43 0.289617
\(136\) −6.41952e43 −1.17477
\(137\) 4.38524e43 0.690592 0.345296 0.938494i \(-0.387779\pi\)
0.345296 + 0.938494i \(0.387779\pi\)
\(138\) −5.84504e43 −0.792988
\(139\) 2.01750e43 0.236054 0.118027 0.993010i \(-0.462343\pi\)
0.118027 + 0.993010i \(0.462343\pi\)
\(140\) 2.71408e43 0.274157
\(141\) −3.57363e43 −0.311974
\(142\) 1.27272e44 0.961216
\(143\) 9.26130e43 0.605736
\(144\) −6.68246e43 −0.378883
\(145\) −4.76033e43 −0.234203
\(146\) 2.50114e44 1.06882
\(147\) 3.79479e43 0.140988
\(148\) −1.92897e43 −0.0623677
\(149\) 3.54704e44 0.998958 0.499479 0.866326i \(-0.333525\pi\)
0.499479 + 0.866326i \(0.333525\pi\)
\(150\) −3.20736e44 −0.787549
\(151\) 7.36078e44 1.57724 0.788618 0.614884i \(-0.210797\pi\)
0.788618 + 0.614884i \(0.210797\pi\)
\(152\) −4.86345e44 −0.910230
\(153\) −2.65216e44 −0.433936
\(154\) −1.54169e45 −2.20711
\(155\) 7.46294e44 0.935643
\(156\) 2.83333e43 0.0311345
\(157\) −1.20760e45 −1.16407 −0.582036 0.813163i \(-0.697744\pi\)
−0.582036 + 0.813163i \(0.697744\pi\)
\(158\) −1.92307e45 −1.62752
\(159\) −8.10499e44 −0.602714
\(160\) 7.44554e44 0.486897
\(161\) 2.46804e45 1.42044
\(162\) −2.36410e44 −0.119842
\(163\) 3.84692e45 1.71897 0.859484 0.511163i \(-0.170785\pi\)
0.859484 + 0.511163i \(0.170785\pi\)
\(164\) −3.33195e44 −0.131341
\(165\) 4.58030e45 1.59394
\(166\) −3.93160e45 −1.20880
\(167\) −1.57930e45 −0.429316 −0.214658 0.976689i \(-0.568864\pi\)
−0.214658 + 0.976689i \(0.568864\pi\)
\(168\) 2.41620e45 0.581155
\(169\) −4.18355e45 −0.890979
\(170\) 1.11971e46 2.11301
\(171\) −2.00929e45 −0.336219
\(172\) 1.60567e45 0.238409
\(173\) −1.39579e46 −1.84024 −0.920122 0.391631i \(-0.871911\pi\)
−0.920122 + 0.391631i \(0.871911\pi\)
\(174\) 8.27250e44 0.0969120
\(175\) 1.35429e46 1.41069
\(176\) −2.24991e46 −2.08523
\(177\) −3.51344e44 −0.0289922
\(178\) 1.70021e46 1.24995
\(179\) −4.81309e45 −0.315454 −0.157727 0.987483i \(-0.550417\pi\)
−0.157727 + 0.987483i \(0.550417\pi\)
\(180\) 1.40126e45 0.0819280
\(181\) −1.02164e46 −0.533199 −0.266599 0.963807i \(-0.585900\pi\)
−0.266599 + 0.963807i \(0.585900\pi\)
\(182\) −8.52144e45 −0.397237
\(183\) 5.45938e45 0.227455
\(184\) 3.08425e46 1.14917
\(185\) −1.72360e46 −0.574668
\(186\) −1.29691e46 −0.387164
\(187\) −8.92952e46 −2.38822
\(188\) −3.68098e45 −0.0882525
\(189\) 9.98228e45 0.214666
\(190\) 8.48297e46 1.63719
\(191\) 3.42603e46 0.593755 0.296878 0.954916i \(-0.404055\pi\)
0.296878 + 0.954916i \(0.404055\pi\)
\(192\) 2.92056e46 0.454770
\(193\) 1.60284e46 0.224370 0.112185 0.993687i \(-0.464215\pi\)
0.112185 + 0.993687i \(0.464215\pi\)
\(194\) −3.33759e46 −0.420241
\(195\) 2.53168e46 0.286879
\(196\) 3.90877e45 0.0398833
\(197\) 1.67914e47 1.54358 0.771792 0.635875i \(-0.219361\pi\)
0.771792 + 0.635875i \(0.219361\pi\)
\(198\) −7.95965e46 −0.659565
\(199\) −5.27435e46 −0.394168 −0.197084 0.980387i \(-0.563147\pi\)
−0.197084 + 0.980387i \(0.563147\pi\)
\(200\) 1.69243e47 1.14129
\(201\) −1.74660e46 −0.106334
\(202\) −1.67723e47 −0.922339
\(203\) −3.49302e46 −0.173593
\(204\) −2.73183e46 −0.122754
\(205\) −2.97722e47 −1.21020
\(206\) 3.26183e47 1.20001
\(207\) 1.27423e47 0.424478
\(208\) −1.24360e47 −0.375302
\(209\) −6.76504e47 −1.85043
\(210\) −4.21440e47 −1.04530
\(211\) −4.70265e47 −1.05816 −0.529081 0.848571i \(-0.677463\pi\)
−0.529081 + 0.848571i \(0.677463\pi\)
\(212\) −8.34844e46 −0.170498
\(213\) −2.77455e47 −0.514530
\(214\) 1.21629e48 2.04907
\(215\) 1.43472e48 2.19674
\(216\) 1.24746e47 0.173670
\(217\) 5.47614e47 0.693505
\(218\) −3.15490e47 −0.363603
\(219\) −5.45252e47 −0.572128
\(220\) 4.71788e47 0.450902
\(221\) −4.93564e47 −0.429835
\(222\) 2.99528e47 0.237794
\(223\) 6.26777e47 0.453799 0.226899 0.973918i \(-0.427141\pi\)
0.226899 + 0.973918i \(0.427141\pi\)
\(224\) 5.46337e47 0.360891
\(225\) 6.99211e47 0.421567
\(226\) −1.15120e48 −0.633766
\(227\) 1.14299e48 0.574794 0.287397 0.957812i \(-0.407210\pi\)
0.287397 + 0.957812i \(0.407210\pi\)
\(228\) −2.06964e47 −0.0951110
\(229\) −2.06328e48 −0.866825 −0.433413 0.901196i \(-0.642691\pi\)
−0.433413 + 0.901196i \(0.642691\pi\)
\(230\) −5.37964e48 −2.06696
\(231\) 3.36092e48 1.18144
\(232\) −4.36515e47 −0.140442
\(233\) −7.30911e47 −0.215312 −0.107656 0.994188i \(-0.534335\pi\)
−0.107656 + 0.994188i \(0.534335\pi\)
\(234\) −4.39955e47 −0.118709
\(235\) −3.28909e48 −0.813175
\(236\) −3.61898e46 −0.00820144
\(237\) 4.19233e48 0.871193
\(238\) 8.21617e48 1.56618
\(239\) 3.57354e48 0.625089 0.312545 0.949903i \(-0.398819\pi\)
0.312545 + 0.949903i \(0.398819\pi\)
\(240\) −6.15037e48 −0.987577
\(241\) 2.64837e47 0.0390507 0.0195254 0.999809i \(-0.493784\pi\)
0.0195254 + 0.999809i \(0.493784\pi\)
\(242\) −1.88364e49 −2.55143
\(243\) 5.15378e47 0.0641500
\(244\) 5.62336e47 0.0643435
\(245\) 3.49263e48 0.367492
\(246\) 5.17381e48 0.500773
\(247\) −3.73926e48 −0.333041
\(248\) 6.84340e48 0.561064
\(249\) 8.57097e48 0.647058
\(250\) −6.17847e48 −0.429646
\(251\) 1.94890e48 0.124876 0.0624380 0.998049i \(-0.480112\pi\)
0.0624380 + 0.998049i \(0.480112\pi\)
\(252\) 1.02821e48 0.0607256
\(253\) 4.29018e49 2.33617
\(254\) 1.25416e49 0.629886
\(255\) −2.44099e49 −1.13108
\(256\) 1.11685e49 0.477612
\(257\) 9.44017e48 0.372692 0.186346 0.982484i \(-0.440335\pi\)
0.186346 + 0.982484i \(0.440335\pi\)
\(258\) −2.49326e49 −0.908999
\(259\) −1.26474e49 −0.425948
\(260\) 2.60773e48 0.0811537
\(261\) −1.80342e48 −0.0518760
\(262\) −3.01635e49 −0.802243
\(263\) −5.72032e49 −1.40711 −0.703554 0.710641i \(-0.748405\pi\)
−0.703554 + 0.710641i \(0.748405\pi\)
\(264\) 4.20007e49 0.955819
\(265\) −7.45964e49 −1.57100
\(266\) 6.22461e49 1.21350
\(267\) −3.70648e49 −0.669084
\(268\) −1.79906e48 −0.0300804
\(269\) −2.68077e49 −0.415278 −0.207639 0.978206i \(-0.566578\pi\)
−0.207639 + 0.978206i \(0.566578\pi\)
\(270\) −2.17586e49 −0.312373
\(271\) −8.22411e49 −1.09451 −0.547253 0.836967i \(-0.684327\pi\)
−0.547253 + 0.836967i \(0.684327\pi\)
\(272\) 1.19905e50 1.47970
\(273\) 1.85769e49 0.212637
\(274\) −7.01388e49 −0.744855
\(275\) 2.35416e50 2.32015
\(276\) 1.31250e49 0.120078
\(277\) 2.17515e49 0.184780 0.0923898 0.995723i \(-0.470549\pi\)
0.0923898 + 0.995723i \(0.470549\pi\)
\(278\) −3.22685e49 −0.254601
\(279\) 2.82729e49 0.207245
\(280\) 2.22381e50 1.51481
\(281\) −1.76875e50 −1.11992 −0.559961 0.828519i \(-0.689184\pi\)
−0.559961 + 0.828519i \(0.689184\pi\)
\(282\) 5.71578e49 0.336487
\(283\) 1.98156e50 1.08489 0.542444 0.840092i \(-0.317499\pi\)
0.542444 + 0.840092i \(0.317499\pi\)
\(284\) −2.85789e49 −0.145552
\(285\) −1.84930e50 −0.876371
\(286\) −1.48128e50 −0.653331
\(287\) −2.18461e50 −0.897007
\(288\) 2.82069e49 0.107847
\(289\) 1.95077e50 0.694703
\(290\) 7.61382e49 0.252606
\(291\) 7.27601e49 0.224951
\(292\) −5.61630e49 −0.161846
\(293\) −5.47637e50 −1.47132 −0.735659 0.677352i \(-0.763128\pi\)
−0.735659 + 0.677352i \(0.763128\pi\)
\(294\) −6.06949e49 −0.152066
\(295\) −3.23369e49 −0.0755696
\(296\) −1.58052e50 −0.344603
\(297\) 1.73522e50 0.353058
\(298\) −5.67323e50 −1.07745
\(299\) 2.37132e50 0.420467
\(300\) 7.20213e49 0.119255
\(301\) 1.05277e51 1.62824
\(302\) −1.17731e51 −1.70117
\(303\) 3.65640e50 0.493719
\(304\) 9.08402e50 1.14649
\(305\) 5.02468e50 0.592873
\(306\) 4.24194e50 0.468032
\(307\) −1.15018e51 −1.18694 −0.593468 0.804857i \(-0.702242\pi\)
−0.593468 + 0.804857i \(0.702242\pi\)
\(308\) 3.46187e50 0.334212
\(309\) −7.11085e50 −0.642351
\(310\) −1.19365e51 −1.00916
\(311\) −9.25059e50 −0.732119 −0.366059 0.930592i \(-0.619293\pi\)
−0.366059 + 0.930592i \(0.619293\pi\)
\(312\) 2.32151e50 0.172029
\(313\) 1.36691e51 0.948597 0.474299 0.880364i \(-0.342702\pi\)
0.474299 + 0.880364i \(0.342702\pi\)
\(314\) 1.93147e51 1.25554
\(315\) 9.18746e50 0.559537
\(316\) 4.31826e50 0.246447
\(317\) 9.60481e49 0.0513776 0.0256888 0.999670i \(-0.491822\pi\)
0.0256888 + 0.999670i \(0.491822\pi\)
\(318\) 1.29634e51 0.650072
\(319\) −6.07191e50 −0.285507
\(320\) 2.68802e51 1.18538
\(321\) −2.65154e51 −1.09685
\(322\) −3.94746e51 −1.53205
\(323\) 3.60530e51 1.31308
\(324\) 5.30858e49 0.0181470
\(325\) 1.30122e51 0.417583
\(326\) −6.15288e51 −1.85404
\(327\) 6.87774e50 0.194633
\(328\) −2.73006e51 −0.725703
\(329\) −2.41346e51 −0.602731
\(330\) −7.32587e51 −1.71919
\(331\) 4.43023e51 0.977130 0.488565 0.872527i \(-0.337520\pi\)
0.488565 + 0.872527i \(0.337520\pi\)
\(332\) 8.82842e50 0.183043
\(333\) −6.52976e50 −0.127289
\(334\) 2.52598e51 0.463050
\(335\) −1.60753e51 −0.277166
\(336\) −4.51300e51 −0.731999
\(337\) −3.71004e50 −0.0566194 −0.0283097 0.999599i \(-0.509012\pi\)
−0.0283097 + 0.999599i \(0.509012\pi\)
\(338\) 6.69129e51 0.960988
\(339\) 2.50964e51 0.339248
\(340\) −2.51431e51 −0.319964
\(341\) 9.51915e51 1.14060
\(342\) 3.21372e51 0.362637
\(343\) −7.93199e51 −0.843049
\(344\) 1.31562e52 1.31729
\(345\) 1.17277e52 1.10642
\(346\) 2.23247e52 1.98484
\(347\) −2.30793e51 −0.193405 −0.0967025 0.995313i \(-0.530830\pi\)
−0.0967025 + 0.995313i \(0.530830\pi\)
\(348\) −1.85759e50 −0.0146749
\(349\) −1.85442e52 −1.38129 −0.690647 0.723192i \(-0.742674\pi\)
−0.690647 + 0.723192i \(0.742674\pi\)
\(350\) −2.16610e52 −1.52154
\(351\) 9.59110e50 0.0635437
\(352\) 9.49695e51 0.593553
\(353\) −5.30734e51 −0.312965 −0.156482 0.987681i \(-0.550015\pi\)
−0.156482 + 0.987681i \(0.550015\pi\)
\(354\) 5.61951e50 0.0312702
\(355\) −2.55363e52 −1.34115
\(356\) −3.81781e51 −0.189273
\(357\) −1.79114e52 −0.838361
\(358\) 7.69820e51 0.340241
\(359\) −6.85308e51 −0.286055 −0.143028 0.989719i \(-0.545684\pi\)
−0.143028 + 0.989719i \(0.545684\pi\)
\(360\) 1.14814e52 0.452681
\(361\) 4.66809e50 0.0173877
\(362\) 1.63405e52 0.575095
\(363\) 4.10637e52 1.36575
\(364\) 1.91349e51 0.0601517
\(365\) −5.01837e52 −1.49128
\(366\) −8.73189e51 −0.245327
\(367\) 3.14343e51 0.0835120 0.0417560 0.999128i \(-0.486705\pi\)
0.0417560 + 0.999128i \(0.486705\pi\)
\(368\) −5.76081e52 −1.44745
\(369\) −1.12790e52 −0.268059
\(370\) 2.75678e52 0.619822
\(371\) −5.47371e52 −1.16444
\(372\) 2.91221e51 0.0586263
\(373\) 9.77187e52 1.86186 0.930929 0.365199i \(-0.118999\pi\)
0.930929 + 0.365199i \(0.118999\pi\)
\(374\) 1.42821e53 2.57588
\(375\) 1.34692e52 0.229985
\(376\) −3.01604e52 −0.487626
\(377\) −3.35614e51 −0.0513857
\(378\) −1.59660e52 −0.231533
\(379\) −6.70476e52 −0.921042 −0.460521 0.887649i \(-0.652337\pi\)
−0.460521 + 0.887649i \(0.652337\pi\)
\(380\) −1.90485e52 −0.247912
\(381\) −2.73409e52 −0.337171
\(382\) −5.47970e52 −0.640410
\(383\) 2.82438e52 0.312859 0.156429 0.987689i \(-0.450002\pi\)
0.156429 + 0.987689i \(0.450002\pi\)
\(384\) −6.45017e52 −0.677300
\(385\) 3.09331e53 3.07949
\(386\) −2.56363e52 −0.242000
\(387\) 5.43535e52 0.486578
\(388\) 7.49457e51 0.0636350
\(389\) −1.90072e52 −0.153091 −0.0765457 0.997066i \(-0.524389\pi\)
−0.0765457 + 0.997066i \(0.524389\pi\)
\(390\) −4.04925e52 −0.309421
\(391\) −2.28637e53 −1.65777
\(392\) 3.20269e52 0.220369
\(393\) 6.57570e52 0.429433
\(394\) −2.68567e53 −1.66487
\(395\) 3.85852e53 2.27081
\(396\) 1.78734e52 0.0998747
\(397\) −1.59987e53 −0.848947 −0.424474 0.905440i \(-0.639541\pi\)
−0.424474 + 0.905440i \(0.639541\pi\)
\(398\) 8.43596e52 0.425139
\(399\) −1.35697e53 −0.649572
\(400\) −3.16114e53 −1.43752
\(401\) −2.13645e53 −0.923067 −0.461534 0.887123i \(-0.652701\pi\)
−0.461534 + 0.887123i \(0.652701\pi\)
\(402\) 2.79356e52 0.114690
\(403\) 5.26154e52 0.205286
\(404\) 3.76623e52 0.139665
\(405\) 4.74341e52 0.167210
\(406\) 5.58684e52 0.187233
\(407\) −2.19849e53 −0.700551
\(408\) −2.23835e53 −0.678257
\(409\) 2.66798e53 0.768872 0.384436 0.923152i \(-0.374396\pi\)
0.384436 + 0.923152i \(0.374396\pi\)
\(410\) 4.76185e53 1.30529
\(411\) 1.52904e53 0.398713
\(412\) −7.32444e52 −0.181711
\(413\) −2.37281e52 −0.0560127
\(414\) −2.03804e53 −0.457832
\(415\) 7.88851e53 1.68659
\(416\) 5.24927e52 0.106828
\(417\) 7.03459e52 0.136286
\(418\) 1.08202e54 1.99582
\(419\) −4.29684e53 −0.754678 −0.377339 0.926075i \(-0.623161\pi\)
−0.377339 + 0.926075i \(0.623161\pi\)
\(420\) 9.46343e52 0.158284
\(421\) −2.09315e53 −0.333439 −0.166720 0.986004i \(-0.553317\pi\)
−0.166720 + 0.986004i \(0.553317\pi\)
\(422\) 7.52156e53 1.14131
\(423\) −1.24605e53 −0.180118
\(424\) −6.84038e53 −0.942063
\(425\) −1.25461e54 −1.64640
\(426\) 4.43769e53 0.554959
\(427\) 3.68700e53 0.439442
\(428\) −2.73119e53 −0.310280
\(429\) 3.22921e53 0.349722
\(430\) −2.29474e54 −2.36935
\(431\) −1.17896e54 −1.16069 −0.580343 0.814372i \(-0.697081\pi\)
−0.580343 + 0.814372i \(0.697081\pi\)
\(432\) −2.33003e53 −0.218748
\(433\) 9.09513e53 0.814342 0.407171 0.913352i \(-0.366515\pi\)
0.407171 + 0.913352i \(0.366515\pi\)
\(434\) −8.75869e53 −0.747997
\(435\) −1.65983e53 −0.135217
\(436\) 7.08433e52 0.0550587
\(437\) −1.73217e54 −1.28446
\(438\) 8.72093e53 0.617083
\(439\) 2.37938e54 1.60673 0.803363 0.595490i \(-0.203042\pi\)
0.803363 + 0.595490i \(0.203042\pi\)
\(440\) 3.86564e54 2.49139
\(441\) 1.32316e53 0.0813994
\(442\) 7.89420e53 0.463609
\(443\) −2.17243e54 −1.21806 −0.609030 0.793147i \(-0.708441\pi\)
−0.609030 + 0.793147i \(0.708441\pi\)
\(444\) −6.72590e52 −0.0360080
\(445\) −3.41135e54 −1.74400
\(446\) −1.00249e54 −0.489456
\(447\) 1.23677e54 0.576748
\(448\) 1.97241e54 0.878612
\(449\) 4.64070e54 1.97485 0.987423 0.158100i \(-0.0505370\pi\)
0.987423 + 0.158100i \(0.0505370\pi\)
\(450\) −1.11834e54 −0.454691
\(451\) −3.79751e54 −1.47530
\(452\) 2.58502e53 0.0959681
\(453\) 2.56655e54 0.910617
\(454\) −1.82813e54 −0.619959
\(455\) 1.70977e54 0.554249
\(456\) −1.69578e54 −0.525521
\(457\) 2.01271e54 0.596346 0.298173 0.954512i \(-0.403623\pi\)
0.298173 + 0.954512i \(0.403623\pi\)
\(458\) 3.30008e54 0.934936
\(459\) −9.24751e53 −0.250533
\(460\) 1.20800e54 0.312990
\(461\) −4.15737e54 −1.03027 −0.515133 0.857110i \(-0.672258\pi\)
−0.515133 + 0.857110i \(0.672258\pi\)
\(462\) −5.37555e54 −1.27427
\(463\) 5.22768e54 1.18549 0.592746 0.805390i \(-0.298044\pi\)
0.592746 + 0.805390i \(0.298044\pi\)
\(464\) 8.15329e53 0.176894
\(465\) 2.60217e54 0.540194
\(466\) 1.16904e54 0.232230
\(467\) −9.76914e54 −1.85721 −0.928604 0.371073i \(-0.878990\pi\)
−0.928604 + 0.371073i \(0.878990\pi\)
\(468\) 9.87920e52 0.0179755
\(469\) −1.17957e54 −0.205437
\(470\) 5.26066e54 0.877070
\(471\) −4.21064e54 −0.672077
\(472\) −2.96524e53 −0.0453158
\(473\) 1.83002e55 2.67795
\(474\) −6.70533e54 −0.939646
\(475\) −9.50495e54 −1.27565
\(476\) −1.84494e54 −0.237159
\(477\) −2.82603e54 −0.347977
\(478\) −5.71563e54 −0.674205
\(479\) −1.65944e55 −1.87536 −0.937678 0.347505i \(-0.887029\pi\)
−0.937678 + 0.347505i \(0.887029\pi\)
\(480\) 2.59610e54 0.281110
\(481\) −1.21518e54 −0.126086
\(482\) −4.23588e53 −0.0421191
\(483\) 8.60552e54 0.820089
\(484\) 4.22972e54 0.386351
\(485\) 6.69667e54 0.586345
\(486\) −8.24310e53 −0.0691906
\(487\) 4.75101e54 0.382333 0.191167 0.981558i \(-0.438773\pi\)
0.191167 + 0.981558i \(0.438773\pi\)
\(488\) 4.60756e54 0.355520
\(489\) 1.34134e55 0.992447
\(490\) −5.58622e54 −0.396368
\(491\) 1.29983e55 0.884538 0.442269 0.896883i \(-0.354174\pi\)
0.442269 + 0.896883i \(0.354174\pi\)
\(492\) −1.16178e54 −0.0758296
\(493\) 3.23591e54 0.202598
\(494\) 5.98068e54 0.359210
\(495\) 1.59705e55 0.920264
\(496\) −1.27822e55 −0.706694
\(497\) −1.87379e55 −0.994067
\(498\) −1.37087e55 −0.697900
\(499\) 3.12552e55 1.52708 0.763539 0.645762i \(-0.223460\pi\)
0.763539 + 0.645762i \(0.223460\pi\)
\(500\) 1.38737e54 0.0650592
\(501\) −5.50669e54 −0.247866
\(502\) −3.11713e54 −0.134688
\(503\) 1.38978e55 0.576504 0.288252 0.957555i \(-0.406926\pi\)
0.288252 + 0.957555i \(0.406926\pi\)
\(504\) 8.42476e54 0.335530
\(505\) 3.36526e55 1.28690
\(506\) −6.86185e55 −2.51974
\(507\) −1.45871e55 −0.514407
\(508\) −2.81622e54 −0.0953806
\(509\) −4.24927e55 −1.38229 −0.691146 0.722715i \(-0.742894\pi\)
−0.691146 + 0.722715i \(0.742894\pi\)
\(510\) 3.90419e55 1.21995
\(511\) −3.68237e55 −1.10535
\(512\) 2.28163e55 0.657978
\(513\) −7.00595e54 −0.194116
\(514\) −1.50989e55 −0.401977
\(515\) −6.54465e55 −1.67432
\(516\) 5.59861e54 0.137645
\(517\) −4.19530e55 −0.991305
\(518\) 2.02286e55 0.459417
\(519\) −4.86683e55 −1.06247
\(520\) 2.13666e55 0.448402
\(521\) 7.63345e55 1.54009 0.770047 0.637987i \(-0.220233\pi\)
0.770047 + 0.637987i \(0.220233\pi\)
\(522\) 2.88444e54 0.0559521
\(523\) 8.49813e55 1.58504 0.792518 0.609849i \(-0.208770\pi\)
0.792518 + 0.609849i \(0.208770\pi\)
\(524\) 6.77322e54 0.121480
\(525\) 4.72213e55 0.814464
\(526\) 9.14925e55 1.51767
\(527\) −5.07305e55 −0.809379
\(528\) −7.84494e55 −1.20391
\(529\) 4.21094e55 0.621638
\(530\) 1.19312e56 1.69445
\(531\) −1.22506e54 −0.0167386
\(532\) −1.39774e55 −0.183754
\(533\) −2.09900e55 −0.265525
\(534\) 5.92825e55 0.721657
\(535\) −2.44042e56 −2.85898
\(536\) −1.47408e55 −0.166204
\(537\) −1.67822e55 −0.182128
\(538\) 4.28771e55 0.447908
\(539\) 4.45493e55 0.447993
\(540\) 4.88589e54 0.0473012
\(541\) 8.87529e54 0.0827254 0.0413627 0.999144i \(-0.486830\pi\)
0.0413627 + 0.999144i \(0.486830\pi\)
\(542\) 1.31539e56 1.18051
\(543\) −3.56226e55 −0.307842
\(544\) −5.06122e55 −0.421190
\(545\) 6.33011e55 0.507321
\(546\) −2.97124e55 −0.229345
\(547\) −1.64997e56 −1.22669 −0.613345 0.789815i \(-0.710177\pi\)
−0.613345 + 0.789815i \(0.710177\pi\)
\(548\) 1.57497e55 0.112790
\(549\) 1.90357e55 0.131321
\(550\) −3.76532e56 −2.50246
\(551\) 2.45154e55 0.156975
\(552\) 1.07541e56 0.663474
\(553\) 2.83129e56 1.68314
\(554\) −3.47900e55 −0.199299
\(555\) −6.00984e55 −0.331785
\(556\) 7.24590e54 0.0385531
\(557\) 2.56239e56 1.31405 0.657027 0.753867i \(-0.271814\pi\)
0.657027 + 0.753867i \(0.271814\pi\)
\(558\) −4.52205e55 −0.223529
\(559\) 1.01151e56 0.481979
\(560\) −4.15366e56 −1.90799
\(561\) −3.11353e56 −1.37884
\(562\) 2.82900e56 1.20792
\(563\) −1.39228e55 −0.0573196 −0.0286598 0.999589i \(-0.509124\pi\)
−0.0286598 + 0.999589i \(0.509124\pi\)
\(564\) −1.28348e55 −0.0509526
\(565\) 2.30981e56 0.884268
\(566\) −3.16936e56 −1.17013
\(567\) 3.48061e55 0.123937
\(568\) −2.34164e56 −0.804227
\(569\) −2.49708e56 −0.827239 −0.413620 0.910450i \(-0.635736\pi\)
−0.413620 + 0.910450i \(0.635736\pi\)
\(570\) 2.95783e56 0.945232
\(571\) −1.43957e56 −0.443805 −0.221902 0.975069i \(-0.571227\pi\)
−0.221902 + 0.975069i \(0.571227\pi\)
\(572\) 3.32621e55 0.0989308
\(573\) 1.19458e56 0.342805
\(574\) 3.49414e56 0.967489
\(575\) 6.02775e56 1.61051
\(576\) 1.01834e56 0.262561
\(577\) 7.48240e56 1.86181 0.930907 0.365255i \(-0.119018\pi\)
0.930907 + 0.365255i \(0.119018\pi\)
\(578\) −3.12011e56 −0.749289
\(579\) 5.58876e55 0.129540
\(580\) −1.70968e55 −0.0382509
\(581\) 5.78841e56 1.25011
\(582\) −1.16375e56 −0.242626
\(583\) −9.51493e56 −1.91514
\(584\) −4.60177e56 −0.894255
\(585\) 8.82742e55 0.165630
\(586\) 8.75907e56 1.58693
\(587\) −5.43255e56 −0.950435 −0.475217 0.879868i \(-0.657631\pi\)
−0.475217 + 0.879868i \(0.657631\pi\)
\(588\) 1.36290e55 0.0230266
\(589\) −3.84337e56 −0.627116
\(590\) 5.17206e55 0.0815074
\(591\) 5.85481e56 0.891188
\(592\) 2.95211e56 0.434048
\(593\) −9.45252e56 −1.34254 −0.671269 0.741214i \(-0.734250\pi\)
−0.671269 + 0.741214i \(0.734250\pi\)
\(594\) −2.77536e56 −0.380800
\(595\) −1.64852e57 −2.18523
\(596\) 1.27392e56 0.163153
\(597\) −1.83905e56 −0.227573
\(598\) −3.79277e56 −0.453505
\(599\) −3.47722e56 −0.401775 −0.200887 0.979614i \(-0.564383\pi\)
−0.200887 + 0.979614i \(0.564383\pi\)
\(600\) 5.90114e56 0.658923
\(601\) 6.30772e56 0.680684 0.340342 0.940302i \(-0.389457\pi\)
0.340342 + 0.940302i \(0.389457\pi\)
\(602\) −1.68382e57 −1.75618
\(603\) −6.09001e55 −0.0613922
\(604\) 2.64364e56 0.257599
\(605\) 3.77941e57 3.55991
\(606\) −5.84815e56 −0.532513
\(607\) −3.56157e56 −0.313526 −0.156763 0.987636i \(-0.550106\pi\)
−0.156763 + 0.987636i \(0.550106\pi\)
\(608\) −3.83440e56 −0.326343
\(609\) −1.21794e56 −0.100224
\(610\) −8.03662e56 −0.639458
\(611\) −2.31888e56 −0.178416
\(612\) −9.52529e55 −0.0708719
\(613\) −4.16993e56 −0.300047 −0.150023 0.988682i \(-0.547935\pi\)
−0.150023 + 0.988682i \(0.547935\pi\)
\(614\) 1.83963e57 1.28020
\(615\) −1.03809e57 −0.698708
\(616\) 2.83652e57 1.84663
\(617\) 2.42342e57 1.52610 0.763051 0.646338i \(-0.223701\pi\)
0.763051 + 0.646338i \(0.223701\pi\)
\(618\) 1.13733e57 0.692824
\(619\) −1.32231e56 −0.0779246 −0.0389623 0.999241i \(-0.512405\pi\)
−0.0389623 + 0.999241i \(0.512405\pi\)
\(620\) 2.68033e56 0.152812
\(621\) 4.44296e56 0.245073
\(622\) 1.47957e57 0.789645
\(623\) −2.50317e57 −1.29266
\(624\) −4.33615e56 −0.216681
\(625\) −1.37567e57 −0.665233
\(626\) −2.18628e57 −1.02313
\(627\) −2.35882e57 −1.06834
\(628\) −4.33711e56 −0.190120
\(629\) 1.17165e57 0.497117
\(630\) −1.46947e57 −0.603503
\(631\) 1.32515e57 0.526822 0.263411 0.964684i \(-0.415153\pi\)
0.263411 + 0.964684i \(0.415153\pi\)
\(632\) 3.53820e57 1.36170
\(633\) −1.63971e57 −0.610930
\(634\) −1.53622e56 −0.0554146
\(635\) −2.51639e57 −0.878854
\(636\) −2.91092e56 −0.0984373
\(637\) 2.46238e56 0.0806301
\(638\) 9.71159e56 0.307940
\(639\) −9.67425e56 −0.297064
\(640\) −5.93659e57 −1.76542
\(641\) −5.79020e56 −0.166765 −0.0833824 0.996518i \(-0.526572\pi\)
−0.0833824 + 0.996518i \(0.526572\pi\)
\(642\) 4.24095e57 1.18303
\(643\) 9.70178e56 0.262136 0.131068 0.991373i \(-0.458159\pi\)
0.131068 + 0.991373i \(0.458159\pi\)
\(644\) 8.86401e56 0.231990
\(645\) 5.00256e57 1.26829
\(646\) −5.76643e57 −1.41625
\(647\) −2.04507e57 −0.486598 −0.243299 0.969951i \(-0.578230\pi\)
−0.243299 + 0.969951i \(0.578230\pi\)
\(648\) 4.34964e56 0.100269
\(649\) −4.12464e56 −0.0921234
\(650\) −2.08121e57 −0.450394
\(651\) 1.90941e57 0.400395
\(652\) 1.38163e57 0.280748
\(653\) −6.17960e56 −0.121686 −0.0608430 0.998147i \(-0.519379\pi\)
−0.0608430 + 0.998147i \(0.519379\pi\)
\(654\) −1.10005e57 −0.209926
\(655\) 6.05212e57 1.11934
\(656\) 5.09925e57 0.914065
\(657\) −1.90118e57 −0.330318
\(658\) 3.86015e57 0.650091
\(659\) 2.52320e57 0.411909 0.205955 0.978562i \(-0.433970\pi\)
0.205955 + 0.978562i \(0.433970\pi\)
\(660\) 1.64502e57 0.260328
\(661\) −4.49723e57 −0.689946 −0.344973 0.938613i \(-0.612112\pi\)
−0.344973 + 0.938613i \(0.612112\pi\)
\(662\) −7.08584e57 −1.05391
\(663\) −1.72095e57 −0.248165
\(664\) 7.23365e57 1.01137
\(665\) −1.24893e58 −1.69314
\(666\) 1.04439e57 0.137291
\(667\) −1.55469e57 −0.198182
\(668\) −5.67209e56 −0.0701174
\(669\) 2.18544e57 0.262001
\(670\) 2.57113e57 0.298944
\(671\) 6.40909e57 0.722745
\(672\) 1.90496e57 0.208361
\(673\) 1.53837e58 1.63212 0.816061 0.577966i \(-0.196153\pi\)
0.816061 + 0.577966i \(0.196153\pi\)
\(674\) 5.93395e56 0.0610683
\(675\) 2.43800e57 0.243392
\(676\) −1.50253e57 −0.145518
\(677\) 1.37721e58 1.29399 0.646997 0.762492i \(-0.276024\pi\)
0.646997 + 0.762492i \(0.276024\pi\)
\(678\) −4.01399e57 −0.365905
\(679\) 4.91386e57 0.434603
\(680\) −2.06012e58 −1.76791
\(681\) 3.98536e57 0.331858
\(682\) −1.52252e58 −1.23022
\(683\) −1.94435e58 −1.52458 −0.762290 0.647236i \(-0.775925\pi\)
−0.762290 + 0.647236i \(0.775925\pi\)
\(684\) −7.21640e56 −0.0549124
\(685\) 1.40729e58 1.03927
\(686\) 1.26867e58 0.909291
\(687\) −7.19423e57 −0.500462
\(688\) −2.45733e58 −1.65921
\(689\) −5.25921e57 −0.344688
\(690\) −1.87576e58 −1.19336
\(691\) −2.44962e58 −1.51286 −0.756430 0.654074i \(-0.773058\pi\)
−0.756430 + 0.654074i \(0.773058\pi\)
\(692\) −5.01301e57 −0.300555
\(693\) 1.17188e58 0.682106
\(694\) 3.69137e57 0.208602
\(695\) 6.47447e57 0.355235
\(696\) −1.52203e57 −0.0810840
\(697\) 2.02381e58 1.04688
\(698\) 2.96601e58 1.48983
\(699\) −2.54853e57 −0.124310
\(700\) 4.86397e57 0.230399
\(701\) −1.67730e58 −0.771599 −0.385799 0.922583i \(-0.626074\pi\)
−0.385799 + 0.922583i \(0.626074\pi\)
\(702\) −1.53403e57 −0.0685367
\(703\) 8.87644e57 0.385172
\(704\) 3.42863e58 1.44504
\(705\) −1.14683e58 −0.469487
\(706\) 8.48872e57 0.337556
\(707\) 2.46935e58 0.953861
\(708\) −1.26186e56 −0.00473510
\(709\) −4.58084e58 −1.66993 −0.834963 0.550306i \(-0.814511\pi\)
−0.834963 + 0.550306i \(0.814511\pi\)
\(710\) 4.08435e58 1.44653
\(711\) 1.46177e58 0.502983
\(712\) −3.12816e58 −1.04580
\(713\) 2.43735e58 0.791739
\(714\) 2.86480e58 0.904235
\(715\) 2.97209e58 0.911567
\(716\) −1.72863e57 −0.0515211
\(717\) 1.24602e58 0.360895
\(718\) 1.09610e58 0.308532
\(719\) −4.86766e58 −1.33161 −0.665807 0.746124i \(-0.731912\pi\)
−0.665807 + 0.746124i \(0.731912\pi\)
\(720\) −2.14450e58 −0.570178
\(721\) −4.80232e58 −1.24102
\(722\) −7.46628e56 −0.0187539
\(723\) 9.23429e56 0.0225460
\(724\) −3.66926e57 −0.0870838
\(725\) −8.53109e57 −0.196823
\(726\) −6.56785e58 −1.47307
\(727\) −1.73618e58 −0.378563 −0.189282 0.981923i \(-0.560616\pi\)
−0.189282 + 0.981923i \(0.560616\pi\)
\(728\) 1.56784e58 0.332359
\(729\) 1.79701e57 0.0370370
\(730\) 8.02653e58 1.60846
\(731\) −9.75274e58 −1.90029
\(732\) 1.96075e57 0.0371487
\(733\) −2.87695e58 −0.530031 −0.265015 0.964244i \(-0.585377\pi\)
−0.265015 + 0.964244i \(0.585377\pi\)
\(734\) −5.02769e57 −0.0900739
\(735\) 1.21781e58 0.212172
\(736\) 2.43166e58 0.412010
\(737\) −2.05044e58 −0.337880
\(738\) 1.80399e58 0.289121
\(739\) −9.32596e57 −0.145373 −0.0726863 0.997355i \(-0.523157\pi\)
−0.0726863 + 0.997355i \(0.523157\pi\)
\(740\) −6.19036e57 −0.0938567
\(741\) −1.30380e58 −0.192281
\(742\) 8.75482e58 1.25593
\(743\) 6.98846e58 0.975239 0.487619 0.873056i \(-0.337865\pi\)
0.487619 + 0.873056i \(0.337865\pi\)
\(744\) 2.38615e58 0.323931
\(745\) 1.13830e59 1.50332
\(746\) −1.56294e59 −2.00815
\(747\) 2.98851e58 0.373579
\(748\) −3.20705e58 −0.390053
\(749\) −1.79072e59 −2.11910
\(750\) −2.15430e58 −0.248056
\(751\) 1.15523e58 0.129434 0.0647172 0.997904i \(-0.479385\pi\)
0.0647172 + 0.997904i \(0.479385\pi\)
\(752\) 5.63340e58 0.614193
\(753\) 6.79541e57 0.0720972
\(754\) 5.36791e57 0.0554233
\(755\) 2.36219e59 2.37357
\(756\) 3.58516e57 0.0350599
\(757\) −8.37064e58 −0.796697 −0.398348 0.917234i \(-0.630417\pi\)
−0.398348 + 0.917234i \(0.630417\pi\)
\(758\) 1.07238e59 0.993412
\(759\) 1.49589e59 1.34879
\(760\) −1.56076e59 −1.36980
\(761\) −2.09392e58 −0.178885 −0.0894425 0.995992i \(-0.528509\pi\)
−0.0894425 + 0.995992i \(0.528509\pi\)
\(762\) 4.37298e58 0.363665
\(763\) 4.64489e58 0.376030
\(764\) 1.23047e58 0.0969741
\(765\) −8.51119e58 −0.653027
\(766\) −4.51740e58 −0.337441
\(767\) −2.27982e57 −0.0165805
\(768\) 3.89421e58 0.275749
\(769\) 1.28539e59 0.886229 0.443114 0.896465i \(-0.353874\pi\)
0.443114 + 0.896465i \(0.353874\pi\)
\(770\) −4.94753e59 −3.32146
\(771\) 3.29158e58 0.215174
\(772\) 5.75663e57 0.0366449
\(773\) 1.59781e59 0.990478 0.495239 0.868757i \(-0.335080\pi\)
0.495239 + 0.868757i \(0.335080\pi\)
\(774\) −8.69346e58 −0.524811
\(775\) 1.33745e59 0.786308
\(776\) 6.14074e58 0.351605
\(777\) −4.40988e58 −0.245921
\(778\) 3.04006e58 0.165120
\(779\) 1.53325e59 0.811137
\(780\) 9.09258e57 0.0468541
\(781\) −3.25721e59 −1.63493
\(782\) 3.65689e59 1.78803
\(783\) −6.28814e57 −0.0299506
\(784\) −5.98203e58 −0.277568
\(785\) −3.87537e59 −1.75180
\(786\) −1.05174e59 −0.463175
\(787\) 7.76783e58 0.333286 0.166643 0.986017i \(-0.446707\pi\)
0.166643 + 0.986017i \(0.446707\pi\)
\(788\) 6.03068e58 0.252103
\(789\) −1.99455e59 −0.812395
\(790\) −6.17143e59 −2.44923
\(791\) 1.69489e59 0.655425
\(792\) 1.46447e59 0.551842
\(793\) 3.54251e58 0.130080
\(794\) 2.55889e59 0.915653
\(795\) −2.60102e59 −0.907020
\(796\) −1.89429e58 −0.0643768
\(797\) 1.52749e58 0.0505920 0.0252960 0.999680i \(-0.491947\pi\)
0.0252960 + 0.999680i \(0.491947\pi\)
\(798\) 2.17039e59 0.700612
\(799\) 2.23581e59 0.703438
\(800\) 1.33433e59 0.409184
\(801\) −1.29237e59 −0.386296
\(802\) 3.41710e59 0.995597
\(803\) −6.40104e59 −1.81795
\(804\) −6.27294e57 −0.0173669
\(805\) 7.92032e59 2.13760
\(806\) −8.41546e58 −0.221416
\(807\) −9.34728e58 −0.239761
\(808\) 3.08589e59 0.771699
\(809\) 5.87620e59 1.43269 0.716345 0.697747i \(-0.245814\pi\)
0.716345 + 0.697747i \(0.245814\pi\)
\(810\) −7.58675e58 −0.180349
\(811\) −2.60886e59 −0.604676 −0.302338 0.953201i \(-0.597767\pi\)
−0.302338 + 0.953201i \(0.597767\pi\)
\(812\) −1.25453e58 −0.0283518
\(813\) −2.86757e59 −0.631914
\(814\) 3.51634e59 0.755597
\(815\) 1.23454e60 2.58686
\(816\) 4.18081e59 0.854304
\(817\) −7.38872e59 −1.47237
\(818\) −4.26724e59 −0.829286
\(819\) 6.47736e58 0.122766
\(820\) −1.06927e59 −0.197654
\(821\) −2.68738e59 −0.484502 −0.242251 0.970214i \(-0.577886\pi\)
−0.242251 + 0.970214i \(0.577886\pi\)
\(822\) −2.44559e59 −0.430042
\(823\) −6.91646e59 −1.18628 −0.593140 0.805099i \(-0.702112\pi\)
−0.593140 + 0.805099i \(0.702112\pi\)
\(824\) −6.00135e59 −1.00402
\(825\) 8.20846e59 1.33954
\(826\) 3.79514e58 0.0604139
\(827\) −1.66543e58 −0.0258621 −0.0129310 0.999916i \(-0.504116\pi\)
−0.0129310 + 0.999916i \(0.504116\pi\)
\(828\) 4.57642e58 0.0693273
\(829\) −8.91805e59 −1.31796 −0.658980 0.752161i \(-0.729012\pi\)
−0.658980 + 0.752161i \(0.729012\pi\)
\(830\) −1.26171e60 −1.81911
\(831\) 7.58428e58 0.106683
\(832\) 1.89511e59 0.260080
\(833\) −2.37417e59 −0.317899
\(834\) −1.12513e59 −0.146994
\(835\) −5.06822e59 −0.646075
\(836\) −2.42968e59 −0.302218
\(837\) 9.85814e58 0.119653
\(838\) 6.87250e59 0.813977
\(839\) 6.04271e59 0.698411 0.349206 0.937046i \(-0.386451\pi\)
0.349206 + 0.937046i \(0.386451\pi\)
\(840\) 7.75395e59 0.874576
\(841\) −8.86482e59 −0.975780
\(842\) 3.34784e59 0.359639
\(843\) −6.16727e59 −0.646588
\(844\) −1.68897e59 −0.172823
\(845\) −1.34257e60 −1.34083
\(846\) 1.99297e59 0.194271
\(847\) 2.77324e60 2.63863
\(848\) 1.27765e60 1.18658
\(849\) 6.90927e59 0.626361
\(850\) 2.00666e60 1.77576
\(851\) −5.62917e59 −0.486282
\(852\) −9.96484e58 −0.0840347
\(853\) 1.07100e60 0.881727 0.440863 0.897574i \(-0.354672\pi\)
0.440863 + 0.897574i \(0.354672\pi\)
\(854\) −5.89709e59 −0.473971
\(855\) −6.44811e59 −0.505973
\(856\) −2.23782e60 −1.71441
\(857\) −1.09608e59 −0.0819855 −0.0409927 0.999159i \(-0.513052\pi\)
−0.0409927 + 0.999159i \(0.513052\pi\)
\(858\) −5.16490e59 −0.377201
\(859\) 1.21084e60 0.863430 0.431715 0.902010i \(-0.357909\pi\)
0.431715 + 0.902010i \(0.357909\pi\)
\(860\) 5.15283e59 0.358779
\(861\) −7.61728e59 −0.517887
\(862\) 1.88566e60 1.25189
\(863\) −1.35388e60 −0.877728 −0.438864 0.898554i \(-0.644619\pi\)
−0.438864 + 0.898554i \(0.644619\pi\)
\(864\) 9.83515e58 0.0622658
\(865\) −4.47931e60 −2.76937
\(866\) −1.45470e60 −0.878329
\(867\) 6.80190e59 0.401087
\(868\) 1.96676e59 0.113266
\(869\) 4.92163e60 2.76824
\(870\) 2.65477e59 0.145842
\(871\) −1.13334e59 −0.0608120
\(872\) 5.80462e59 0.304218
\(873\) 2.53699e59 0.129875
\(874\) 2.77048e60 1.38538
\(875\) 9.09641e59 0.444329
\(876\) −1.95828e59 −0.0934419
\(877\) 1.82892e60 0.852517 0.426259 0.904601i \(-0.359831\pi\)
0.426259 + 0.904601i \(0.359831\pi\)
\(878\) −3.80566e60 −1.73297
\(879\) −1.90949e60 −0.849466
\(880\) −7.22029e60 −3.13805
\(881\) 9.73145e59 0.413210 0.206605 0.978424i \(-0.433758\pi\)
0.206605 + 0.978424i \(0.433758\pi\)
\(882\) −2.11630e59 −0.0877954
\(883\) −2.26914e60 −0.919742 −0.459871 0.887986i \(-0.652104\pi\)
−0.459871 + 0.887986i \(0.652104\pi\)
\(884\) −1.77264e59 −0.0702021
\(885\) −1.12752e59 −0.0436301
\(886\) 3.47464e60 1.31377
\(887\) 9.48427e59 0.350404 0.175202 0.984532i \(-0.443942\pi\)
0.175202 + 0.984532i \(0.443942\pi\)
\(888\) −5.51093e59 −0.198957
\(889\) −1.84647e60 −0.651413
\(890\) 5.45622e60 1.88103
\(891\) 6.05033e59 0.203838
\(892\) 2.25108e59 0.0741160
\(893\) 1.69386e60 0.545032
\(894\) −1.97813e60 −0.622066
\(895\) −1.54459e60 −0.474725
\(896\) −4.35613e60 −1.30854
\(897\) 8.26830e59 0.242757
\(898\) −7.42247e60 −2.13002
\(899\) −3.44958e59 −0.0967593
\(900\) 2.51123e59 0.0688517
\(901\) 5.07081e60 1.35900
\(902\) 6.07384e60 1.59122
\(903\) 3.67077e60 0.940065
\(904\) 2.11806e60 0.530257
\(905\) −3.27862e60 −0.802407
\(906\) −4.10501e60 −0.982169
\(907\) −6.87953e59 −0.160920 −0.0804599 0.996758i \(-0.525639\pi\)
−0.0804599 + 0.996758i \(0.525639\pi\)
\(908\) 4.10507e59 0.0938774
\(909\) 1.27491e60 0.285049
\(910\) −2.73466e60 −0.597799
\(911\) −1.32323e60 −0.282819 −0.141409 0.989951i \(-0.545163\pi\)
−0.141409 + 0.989951i \(0.545163\pi\)
\(912\) 3.16740e60 0.661925
\(913\) 1.00620e61 2.05604
\(914\) −3.21918e60 −0.643204
\(915\) 1.75200e60 0.342295
\(916\) −7.41032e59 −0.141573
\(917\) 4.44091e60 0.829660
\(918\) 1.47907e60 0.270219
\(919\) −2.10890e60 −0.376780 −0.188390 0.982094i \(-0.560327\pi\)
−0.188390 + 0.982094i \(0.560327\pi\)
\(920\) 9.89784e60 1.72938
\(921\) −4.01042e60 −0.685278
\(922\) 6.64942e60 1.11122
\(923\) −1.80036e60 −0.294256
\(924\) 1.20708e60 0.192957
\(925\) −3.08891e60 −0.482947
\(926\) −8.36130e60 −1.27864
\(927\) −2.47940e60 −0.370862
\(928\) −3.44154e59 −0.0503523
\(929\) −8.23760e60 −1.17890 −0.589452 0.807803i \(-0.700656\pi\)
−0.589452 + 0.807803i \(0.700656\pi\)
\(930\) −4.16198e60 −0.582639
\(931\) −1.79868e60 −0.246312
\(932\) −2.62508e59 −0.0351655
\(933\) −3.22548e60 −0.422689
\(934\) 1.56251e61 2.00314
\(935\) −2.86562e61 −3.59402
\(936\) 8.09461e59 0.0993210
\(937\) 1.44081e61 1.72960 0.864801 0.502115i \(-0.167445\pi\)
0.864801 + 0.502115i \(0.167445\pi\)
\(938\) 1.88663e60 0.221580
\(939\) 4.76613e60 0.547673
\(940\) −1.18128e60 −0.132811
\(941\) −1.04517e61 −1.14974 −0.574870 0.818245i \(-0.694947\pi\)
−0.574870 + 0.818245i \(0.694947\pi\)
\(942\) 6.73462e60 0.724885
\(943\) −9.72339e60 −1.02407
\(944\) 5.53852e59 0.0570779
\(945\) 3.20347e60 0.323049
\(946\) −2.92699e61 −2.88837
\(947\) 9.09242e60 0.878021 0.439011 0.898482i \(-0.355329\pi\)
0.439011 + 0.898482i \(0.355329\pi\)
\(948\) 1.50568e60 0.142286
\(949\) −3.53806e60 −0.327196
\(950\) 1.52025e61 1.37588
\(951\) 3.34899e59 0.0296629
\(952\) −1.51167e61 −1.31039
\(953\) 8.38627e60 0.711483 0.355742 0.934584i \(-0.384228\pi\)
0.355742 + 0.934584i \(0.384228\pi\)
\(954\) 4.52004e60 0.375319
\(955\) 1.09947e61 0.893538
\(956\) 1.28344e60 0.102092
\(957\) −2.11714e60 −0.164837
\(958\) 2.65416e61 2.02271
\(959\) 1.03264e61 0.770311
\(960\) 9.37254e60 0.684379
\(961\) −8.58235e60 −0.613446
\(962\) 1.94359e60 0.135993
\(963\) −9.24535e60 −0.633264
\(964\) 9.51167e58 0.00637790
\(965\) 5.14376e60 0.337653
\(966\) −1.37639e61 −0.884527
\(967\) 2.28385e61 1.43689 0.718447 0.695581i \(-0.244853\pi\)
0.718447 + 0.695581i \(0.244853\pi\)
\(968\) 3.46566e61 2.13472
\(969\) 1.25709e61 0.758105
\(970\) −1.07109e61 −0.632417
\(971\) −2.76347e61 −1.59757 −0.798786 0.601616i \(-0.794524\pi\)
−0.798786 + 0.601616i \(0.794524\pi\)
\(972\) 1.85099e59 0.0104772
\(973\) 4.75082e60 0.263303
\(974\) −7.59891e60 −0.412375
\(975\) 4.53708e60 0.241091
\(976\) −8.60605e60 −0.447799
\(977\) −2.22641e61 −1.13440 −0.567199 0.823581i \(-0.691973\pi\)
−0.567199 + 0.823581i \(0.691973\pi\)
\(978\) −2.14538e61 −1.07043
\(979\) −4.35126e61 −2.12603
\(980\) 1.25439e60 0.0600201
\(981\) 2.39812e60 0.112372
\(982\) −2.07899e61 −0.954040
\(983\) 2.36280e61 1.06189 0.530945 0.847407i \(-0.321837\pi\)
0.530945 + 0.847407i \(0.321837\pi\)
\(984\) −9.51914e60 −0.418985
\(985\) 5.38863e61 2.32293
\(986\) −5.17561e60 −0.218517
\(987\) −8.41520e60 −0.347987
\(988\) −1.34296e60 −0.0543934
\(989\) 4.68570e61 1.85888
\(990\) −2.55437e61 −0.992574
\(991\) −4.84850e61 −1.84543 −0.922716 0.385481i \(-0.874035\pi\)
−0.922716 + 0.385481i \(0.874035\pi\)
\(992\) 5.39542e60 0.201157
\(993\) 1.54473e61 0.564146
\(994\) 2.99700e61 1.07218
\(995\) −1.69262e61 −0.593180
\(996\) 3.07828e60 0.105680
\(997\) 3.96621e60 0.133391 0.0666953 0.997773i \(-0.478754\pi\)
0.0666953 + 0.997773i \(0.478754\pi\)
\(998\) −4.99905e61 −1.64707
\(999\) −2.27679e60 −0.0734903
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 3.42.a.b.1.2 4
3.2 odd 2 9.42.a.c.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.42.a.b.1.2 4 1.1 even 1 trivial
9.42.a.c.1.3 4 3.2 odd 2