Properties

Label 3.40.a.b.1.2
Level $3$
Weight $40$
Character 3.1
Self dual yes
Analytic conductor $28.902$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 40 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.9018654169\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 3876249523 x - 18467420411022\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-4792.65\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+264126. q^{2} -1.16226e9 q^{3} -4.79993e11 q^{4} -6.30487e13 q^{5} -3.06983e14 q^{6} -4.59086e16 q^{7} -2.71983e17 q^{8} +1.35085e18 q^{9} +O(q^{10})\) \(q+264126. q^{2} -1.16226e9 q^{3} -4.79993e11 q^{4} -6.30487e13 q^{5} -3.06983e14 q^{6} -4.59086e16 q^{7} -2.71983e17 q^{8} +1.35085e18 q^{9} -1.66528e19 q^{10} -1.42816e20 q^{11} +5.57878e20 q^{12} +2.23742e20 q^{13} -1.21256e22 q^{14} +7.32790e22 q^{15} +1.92041e23 q^{16} +3.05051e23 q^{17} +3.56795e23 q^{18} -1.47192e25 q^{19} +3.02629e25 q^{20} +5.33578e25 q^{21} -3.77213e25 q^{22} -5.75448e26 q^{23} +3.16116e26 q^{24} +2.15614e27 q^{25} +5.90959e25 q^{26} -1.57004e27 q^{27} +2.20358e28 q^{28} +1.59256e28 q^{29} +1.93549e28 q^{30} +2.90720e28 q^{31} +2.00247e29 q^{32} +1.65989e29 q^{33} +8.05717e28 q^{34} +2.89448e30 q^{35} -6.48400e29 q^{36} +4.49195e30 q^{37} -3.88772e30 q^{38} -2.60046e29 q^{39} +1.71482e31 q^{40} -3.98145e31 q^{41} +1.40932e31 q^{42} -1.13795e32 q^{43} +6.85506e31 q^{44} -8.51694e31 q^{45} -1.51990e32 q^{46} -4.87913e32 q^{47} -2.23202e32 q^{48} +1.19806e33 q^{49} +5.69493e32 q^{50} -3.54549e32 q^{51} -1.07395e32 q^{52} -5.94518e32 q^{53} -4.14689e32 q^{54} +9.00434e33 q^{55} +1.24864e34 q^{56} +1.71076e34 q^{57} +4.20636e33 q^{58} -2.61158e34 q^{59} -3.51734e34 q^{60} -4.20907e34 q^{61} +7.67866e33 q^{62} -6.20157e34 q^{63} -5.26854e34 q^{64} -1.41066e34 q^{65} +4.38420e34 q^{66} -4.97358e35 q^{67} -1.46422e35 q^{68} +6.68820e35 q^{69} +7.64506e35 q^{70} +8.30261e35 q^{71} -3.67409e35 q^{72} -5.71462e35 q^{73} +1.18644e36 q^{74} -2.50600e36 q^{75} +7.06513e36 q^{76} +6.55647e36 q^{77} -6.86849e34 q^{78} -1.34537e37 q^{79} -1.21080e37 q^{80} +1.82480e36 q^{81} -1.05160e37 q^{82} +2.31025e37 q^{83} -2.56114e37 q^{84} -1.92330e37 q^{85} -3.00563e37 q^{86} -1.85097e37 q^{87} +3.88435e37 q^{88} +5.53932e37 q^{89} -2.24954e37 q^{90} -1.02717e37 q^{91} +2.76211e38 q^{92} -3.37893e37 q^{93} -1.28870e38 q^{94} +9.28027e38 q^{95} -2.32740e38 q^{96} -5.58017e38 q^{97} +3.16438e38 q^{98} -1.92923e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} + O(q^{10}) \) \( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} - 39868781226579858780q^{10} - \)\(53\!\cdots\!40\)\(q^{11} - \)\(11\!\cdots\!44\)\(q^{12} + \)\(54\!\cdots\!90\)\(q^{13} + \)\(31\!\cdots\!52\)\(q^{14} + \)\(62\!\cdots\!10\)\(q^{15} + \)\(12\!\cdots\!36\)\(q^{16} + \)\(72\!\cdots\!58\)\(q^{17} + \)\(72\!\cdots\!86\)\(q^{18} - \)\(10\!\cdots\!24\)\(q^{19} + \)\(30\!\cdots\!60\)\(q^{20} + \)\(18\!\cdots\!76\)\(q^{21} - \)\(10\!\cdots\!24\)\(q^{22} + \)\(41\!\cdots\!64\)\(q^{23} - \)\(51\!\cdots\!32\)\(q^{24} - \)\(11\!\cdots\!75\)\(q^{25} + \)\(92\!\cdots\!76\)\(q^{26} - \)\(47\!\cdots\!89\)\(q^{27} + \)\(64\!\cdots\!56\)\(q^{28} + \)\(72\!\cdots\!62\)\(q^{29} + \)\(46\!\cdots\!60\)\(q^{30} - \)\(38\!\cdots\!56\)\(q^{31} + \)\(37\!\cdots\!12\)\(q^{32} + \)\(61\!\cdots\!80\)\(q^{33} + \)\(37\!\cdots\!44\)\(q^{34} + \)\(27\!\cdots\!20\)\(q^{35} + \)\(12\!\cdots\!48\)\(q^{36} + \)\(29\!\cdots\!22\)\(q^{37} + \)\(74\!\cdots\!92\)\(q^{38} - \)\(63\!\cdots\!30\)\(q^{39} + \)\(15\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!26\)\(q^{41} - \)\(36\!\cdots\!84\)\(q^{42} - \)\(24\!\cdots\!28\)\(q^{43} - \)\(21\!\cdots\!12\)\(q^{44} - \)\(72\!\cdots\!70\)\(q^{45} - \)\(10\!\cdots\!56\)\(q^{46} - \)\(10\!\cdots\!04\)\(q^{47} - \)\(13\!\cdots\!12\)\(q^{48} + \)\(92\!\cdots\!43\)\(q^{49} - \)\(11\!\cdots\!50\)\(q^{50} - \)\(84\!\cdots\!86\)\(q^{51} + \)\(59\!\cdots\!88\)\(q^{52} + \)\(62\!\cdots\!34\)\(q^{53} - \)\(83\!\cdots\!62\)\(q^{54} + \)\(72\!\cdots\!40\)\(q^{55} + \)\(36\!\cdots\!00\)\(q^{56} + \)\(12\!\cdots\!08\)\(q^{57} + \)\(28\!\cdots\!84\)\(q^{58} - \)\(75\!\cdots\!56\)\(q^{59} - \)\(35\!\cdots\!20\)\(q^{60} - \)\(71\!\cdots\!98\)\(q^{61} - \)\(33\!\cdots\!16\)\(q^{62} - \)\(21\!\cdots\!92\)\(q^{63} - \)\(35\!\cdots\!56\)\(q^{64} - \)\(71\!\cdots\!60\)\(q^{65} + \)\(11\!\cdots\!08\)\(q^{66} - \)\(51\!\cdots\!72\)\(q^{67} + \)\(11\!\cdots\!92\)\(q^{68} - \)\(48\!\cdots\!88\)\(q^{69} + \)\(38\!\cdots\!20\)\(q^{70} + \)\(84\!\cdots\!76\)\(q^{71} + \)\(60\!\cdots\!44\)\(q^{72} + \)\(63\!\cdots\!14\)\(q^{73} + \)\(89\!\cdots\!12\)\(q^{74} + \)\(13\!\cdots\!25\)\(q^{75} + \)\(12\!\cdots\!36\)\(q^{76} - \)\(22\!\cdots\!36\)\(q^{77} - \)\(10\!\cdots\!92\)\(q^{78} - \)\(16\!\cdots\!00\)\(q^{79} - \)\(18\!\cdots\!80\)\(q^{80} + \)\(54\!\cdots\!63\)\(q^{81} - \)\(48\!\cdots\!36\)\(q^{82} + \)\(59\!\cdots\!48\)\(q^{83} - \)\(74\!\cdots\!52\)\(q^{84} - \)\(52\!\cdots\!80\)\(q^{85} + \)\(85\!\cdots\!00\)\(q^{86} - \)\(84\!\cdots\!54\)\(q^{87} - \)\(10\!\cdots\!64\)\(q^{88} + \)\(18\!\cdots\!86\)\(q^{89} - \)\(53\!\cdots\!20\)\(q^{90} + \)\(23\!\cdots\!24\)\(q^{91} + \)\(96\!\cdots\!32\)\(q^{92} + \)\(44\!\cdots\!52\)\(q^{93} - \)\(12\!\cdots\!20\)\(q^{94} + \)\(84\!\cdots\!00\)\(q^{95} - \)\(44\!\cdots\!04\)\(q^{96} - \)\(99\!\cdots\!42\)\(q^{97} + \)\(19\!\cdots\!10\)\(q^{98} - \)\(71\!\cdots\!60\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 264126. 0.356226 0.178113 0.984010i \(-0.443001\pi\)
0.178113 + 0.984010i \(0.443001\pi\)
\(3\) −1.16226e9 −0.577350
\(4\) −4.79993e11 −0.873103
\(5\) −6.30487e13 −1.47829 −0.739147 0.673544i \(-0.764771\pi\)
−0.739147 + 0.673544i \(0.764771\pi\)
\(6\) −3.06983e14 −0.205667
\(7\) −4.59086e16 −1.52224 −0.761119 0.648613i \(-0.775350\pi\)
−0.761119 + 0.648613i \(0.775350\pi\)
\(8\) −2.71983e17 −0.667248
\(9\) 1.35085e18 0.333333
\(10\) −1.66528e19 −0.526607
\(11\) −1.42816e20 −0.704075 −0.352037 0.935986i \(-0.614511\pi\)
−0.352037 + 0.935986i \(0.614511\pi\)
\(12\) 5.57878e20 0.504086
\(13\) 2.23742e20 0.0424474 0.0212237 0.999775i \(-0.493244\pi\)
0.0212237 + 0.999775i \(0.493244\pi\)
\(14\) −1.21256e22 −0.542261
\(15\) 7.32790e22 0.853493
\(16\) 1.92041e23 0.635412
\(17\) 3.05051e23 0.309470 0.154735 0.987956i \(-0.450548\pi\)
0.154735 + 0.987956i \(0.450548\pi\)
\(18\) 3.56795e23 0.118742
\(19\) −1.47192e25 −1.70683 −0.853413 0.521235i \(-0.825472\pi\)
−0.853413 + 0.521235i \(0.825472\pi\)
\(20\) 3.02629e25 1.29070
\(21\) 5.33578e25 0.878864
\(22\) −3.77213e25 −0.250810
\(23\) −5.75448e26 −1.60810 −0.804050 0.594562i \(-0.797325\pi\)
−0.804050 + 0.594562i \(0.797325\pi\)
\(24\) 3.16116e26 0.385236
\(25\) 2.15614e27 1.18535
\(26\) 5.90959e25 0.0151209
\(27\) −1.57004e27 −0.192450
\(28\) 2.20358e28 1.32907
\(29\) 1.59256e28 0.484546 0.242273 0.970208i \(-0.422107\pi\)
0.242273 + 0.970208i \(0.422107\pi\)
\(30\) 1.93549e28 0.304037
\(31\) 2.90720e28 0.240947 0.120474 0.992717i \(-0.461559\pi\)
0.120474 + 0.992717i \(0.461559\pi\)
\(32\) 2.00247e29 0.893598
\(33\) 1.65989e29 0.406498
\(34\) 8.05717e28 0.110241
\(35\) 2.89448e30 2.25031
\(36\) −6.48400e29 −0.291034
\(37\) 4.49195e30 1.18168 0.590842 0.806787i \(-0.298796\pi\)
0.590842 + 0.806787i \(0.298796\pi\)
\(38\) −3.88772e30 −0.608016
\(39\) −2.60046e29 −0.0245070
\(40\) 1.71482e31 0.986389
\(41\) −3.98145e31 −1.41500 −0.707499 0.706715i \(-0.750176\pi\)
−0.707499 + 0.706715i \(0.750176\pi\)
\(42\) 1.40932e31 0.313074
\(43\) −1.13795e32 −1.59768 −0.798840 0.601544i \(-0.794552\pi\)
−0.798840 + 0.601544i \(0.794552\pi\)
\(44\) 6.85506e31 0.614730
\(45\) −8.51694e31 −0.492765
\(46\) −1.51990e32 −0.572847
\(47\) −4.87913e32 −1.20902 −0.604511 0.796597i \(-0.706631\pi\)
−0.604511 + 0.796597i \(0.706631\pi\)
\(48\) −2.23202e32 −0.366855
\(49\) 1.19806e33 1.31721
\(50\) 5.69493e32 0.422253
\(51\) −3.54549e32 −0.178672
\(52\) −1.07395e32 −0.0370610
\(53\) −5.94518e32 −0.141509 −0.0707547 0.997494i \(-0.522541\pi\)
−0.0707547 + 0.997494i \(0.522541\pi\)
\(54\) −4.14689e32 −0.0685557
\(55\) 9.00434e33 1.04083
\(56\) 1.24864e34 1.01571
\(57\) 1.71076e34 0.985437
\(58\) 4.20636e33 0.172608
\(59\) −2.61158e34 −0.767872 −0.383936 0.923360i \(-0.625432\pi\)
−0.383936 + 0.923360i \(0.625432\pi\)
\(60\) −3.51734e34 −0.745188
\(61\) −4.20907e34 −0.646032 −0.323016 0.946393i \(-0.604697\pi\)
−0.323016 + 0.946393i \(0.604697\pi\)
\(62\) 7.67866e33 0.0858317
\(63\) −6.20157e34 −0.507413
\(64\) −5.26854e34 −0.317089
\(65\) −1.41066e34 −0.0627498
\(66\) 4.38420e34 0.144805
\(67\) −4.97358e35 −1.22521 −0.612605 0.790389i \(-0.709878\pi\)
−0.612605 + 0.790389i \(0.709878\pi\)
\(68\) −1.46422e35 −0.270199
\(69\) 6.68820e35 0.928437
\(70\) 7.64506e35 0.801621
\(71\) 8.30261e35 0.660202 0.330101 0.943946i \(-0.392917\pi\)
0.330101 + 0.943946i \(0.392917\pi\)
\(72\) −3.67409e35 −0.222416
\(73\) −5.71462e35 −0.264358 −0.132179 0.991226i \(-0.542197\pi\)
−0.132179 + 0.991226i \(0.542197\pi\)
\(74\) 1.18644e36 0.420947
\(75\) −2.50600e36 −0.684364
\(76\) 7.06513e36 1.49024
\(77\) 6.55647e36 1.07177
\(78\) −6.86849e34 −0.00873005
\(79\) −1.34537e37 −1.33387 −0.666935 0.745116i \(-0.732394\pi\)
−0.666935 + 0.745116i \(0.732394\pi\)
\(80\) −1.21080e37 −0.939325
\(81\) 1.82480e36 0.111111
\(82\) −1.05160e37 −0.504059
\(83\) 2.31025e37 0.874252 0.437126 0.899400i \(-0.355996\pi\)
0.437126 + 0.899400i \(0.355996\pi\)
\(84\) −2.56114e37 −0.767339
\(85\) −1.92330e37 −0.457487
\(86\) −3.00563e37 −0.569135
\(87\) −1.85097e37 −0.279753
\(88\) 3.88435e37 0.469793
\(89\) 5.53932e37 0.537466 0.268733 0.963215i \(-0.413395\pi\)
0.268733 + 0.963215i \(0.413395\pi\)
\(90\) −2.24954e37 −0.175536
\(91\) −1.02717e37 −0.0646151
\(92\) 2.76211e38 1.40404
\(93\) −3.37893e37 −0.139111
\(94\) −1.28870e38 −0.430685
\(95\) 9.28027e38 2.52319
\(96\) −2.32740e38 −0.515919
\(97\) −5.58017e38 −1.01065 −0.505323 0.862930i \(-0.668627\pi\)
−0.505323 + 0.862930i \(0.668627\pi\)
\(98\) 3.16438e38 0.469224
\(99\) −1.92923e38 −0.234692
\(100\) −1.03493e39 −1.03493
\(101\) −8.58640e38 −0.707203 −0.353602 0.935396i \(-0.615043\pi\)
−0.353602 + 0.935396i \(0.615043\pi\)
\(102\) −9.36454e37 −0.0636478
\(103\) 7.23179e38 0.406368 0.203184 0.979141i \(-0.434871\pi\)
0.203184 + 0.979141i \(0.434871\pi\)
\(104\) −6.08540e37 −0.0283230
\(105\) −3.36414e39 −1.29922
\(106\) −1.57027e38 −0.0504094
\(107\) 6.55460e39 1.75211 0.876057 0.482208i \(-0.160165\pi\)
0.876057 + 0.482208i \(0.160165\pi\)
\(108\) 7.53610e38 0.168029
\(109\) −5.87754e39 −1.09491 −0.547456 0.836835i \(-0.684403\pi\)
−0.547456 + 0.836835i \(0.684403\pi\)
\(110\) 2.37828e39 0.370771
\(111\) −5.22082e39 −0.682246
\(112\) −8.81636e39 −0.967248
\(113\) 1.66536e40 1.53631 0.768154 0.640265i \(-0.221175\pi\)
0.768154 + 0.640265i \(0.221175\pi\)
\(114\) 4.51855e39 0.351038
\(115\) 3.62812e40 2.37724
\(116\) −7.64418e39 −0.423058
\(117\) 3.02242e38 0.0141491
\(118\) −6.89785e39 −0.273536
\(119\) −1.40045e40 −0.471086
\(120\) −1.99307e40 −0.569492
\(121\) −2.07484e40 −0.504279
\(122\) −1.11172e40 −0.230133
\(123\) 4.62748e40 0.816949
\(124\) −1.39544e40 −0.210372
\(125\) −2.12571e40 −0.274005
\(126\) −1.63799e40 −0.180754
\(127\) −1.17179e41 −1.10835 −0.554177 0.832399i \(-0.686967\pi\)
−0.554177 + 0.832399i \(0.686967\pi\)
\(128\) −1.24003e41 −1.00655
\(129\) 1.32260e41 0.922420
\(130\) −3.72592e39 −0.0223531
\(131\) −2.69471e40 −0.139227 −0.0696133 0.997574i \(-0.522177\pi\)
−0.0696133 + 0.997574i \(0.522177\pi\)
\(132\) −7.96737e40 −0.354914
\(133\) 6.75739e41 2.59820
\(134\) −1.31365e41 −0.436452
\(135\) 9.89891e40 0.284498
\(136\) −8.29687e40 −0.206493
\(137\) 1.62934e41 0.351528 0.175764 0.984432i \(-0.443760\pi\)
0.175764 + 0.984432i \(0.443760\pi\)
\(138\) 1.76653e41 0.330733
\(139\) 5.71049e41 0.928720 0.464360 0.885647i \(-0.346284\pi\)
0.464360 + 0.885647i \(0.346284\pi\)
\(140\) −1.38933e42 −1.96476
\(141\) 5.67083e41 0.698029
\(142\) 2.19293e41 0.235181
\(143\) −3.19538e40 −0.0298862
\(144\) 2.59419e41 0.211804
\(145\) −1.00409e42 −0.716301
\(146\) −1.50938e41 −0.0941711
\(147\) −1.39246e42 −0.760490
\(148\) −2.15611e42 −1.03173
\(149\) −4.00637e41 −0.168120 −0.0840598 0.996461i \(-0.526789\pi\)
−0.0840598 + 0.996461i \(0.526789\pi\)
\(150\) −6.61900e41 −0.243788
\(151\) 8.19755e41 0.265237 0.132618 0.991167i \(-0.457662\pi\)
0.132618 + 0.991167i \(0.457662\pi\)
\(152\) 4.00338e42 1.13888
\(153\) 4.12078e41 0.103157
\(154\) 1.73173e42 0.381792
\(155\) −1.83295e42 −0.356191
\(156\) 1.24820e41 0.0213972
\(157\) 2.75060e42 0.416279 0.208139 0.978099i \(-0.433259\pi\)
0.208139 + 0.978099i \(0.433259\pi\)
\(158\) −3.55347e42 −0.475159
\(159\) 6.90985e41 0.0817005
\(160\) −1.26253e43 −1.32100
\(161\) 2.64180e43 2.44791
\(162\) 4.81977e41 0.0395807
\(163\) −3.05226e41 −0.0222313 −0.0111156 0.999938i \(-0.503538\pi\)
−0.0111156 + 0.999938i \(0.503538\pi\)
\(164\) 1.91107e43 1.23544
\(165\) −1.04654e43 −0.600923
\(166\) 6.10197e42 0.311431
\(167\) −8.60063e42 −0.390444 −0.195222 0.980759i \(-0.562543\pi\)
−0.195222 + 0.980759i \(0.562543\pi\)
\(168\) −1.45124e43 −0.586421
\(169\) −2.77337e43 −0.998198
\(170\) −5.07994e42 −0.162969
\(171\) −1.98835e43 −0.568942
\(172\) 5.46210e43 1.39494
\(173\) −3.58571e43 −0.817856 −0.408928 0.912567i \(-0.634097\pi\)
−0.408928 + 0.912567i \(0.634097\pi\)
\(174\) −4.88889e42 −0.0996551
\(175\) −9.89856e43 −1.80439
\(176\) −2.74265e43 −0.447377
\(177\) 3.03534e43 0.443331
\(178\) 1.46308e43 0.191459
\(179\) 1.32734e44 1.55721 0.778606 0.627514i \(-0.215927\pi\)
0.778606 + 0.627514i \(0.215927\pi\)
\(180\) 4.08807e43 0.430234
\(181\) 4.48145e43 0.423337 0.211668 0.977342i \(-0.432110\pi\)
0.211668 + 0.977342i \(0.432110\pi\)
\(182\) −2.71301e42 −0.0230176
\(183\) 4.89204e43 0.372987
\(184\) 1.56512e44 1.07300
\(185\) −2.83211e44 −1.74688
\(186\) −8.92462e42 −0.0495550
\(187\) −4.35661e43 −0.217890
\(188\) 2.34195e44 1.05560
\(189\) 7.20785e43 0.292955
\(190\) 2.45116e44 0.898826
\(191\) −3.37653e44 −1.11769 −0.558843 0.829274i \(-0.688755\pi\)
−0.558843 + 0.829274i \(0.688755\pi\)
\(192\) 6.12342e43 0.183071
\(193\) −3.65762e43 −0.0988168 −0.0494084 0.998779i \(-0.515734\pi\)
−0.0494084 + 0.998779i \(0.515734\pi\)
\(194\) −1.47387e44 −0.360018
\(195\) 1.63956e43 0.0362286
\(196\) −5.75060e44 −1.15006
\(197\) −2.25016e44 −0.407494 −0.203747 0.979024i \(-0.565312\pi\)
−0.203747 + 0.979024i \(0.565312\pi\)
\(198\) −5.09559e43 −0.0836033
\(199\) 4.01172e43 0.0596617 0.0298308 0.999555i \(-0.490503\pi\)
0.0298308 + 0.999555i \(0.490503\pi\)
\(200\) −5.86435e44 −0.790924
\(201\) 5.78060e44 0.707375
\(202\) −2.26789e44 −0.251924
\(203\) −7.31122e44 −0.737593
\(204\) 1.70181e44 0.155999
\(205\) 2.51025e45 2.09178
\(206\) 1.91010e44 0.144759
\(207\) −7.77344e44 −0.536033
\(208\) 4.29677e43 0.0269716
\(209\) 2.10214e45 1.20173
\(210\) −8.88555e44 −0.462816
\(211\) −2.64355e45 −1.25510 −0.627552 0.778575i \(-0.715943\pi\)
−0.627552 + 0.778575i \(0.715943\pi\)
\(212\) 2.85365e44 0.123552
\(213\) −9.64981e44 −0.381168
\(214\) 1.73124e45 0.624149
\(215\) 7.17464e45 2.36184
\(216\) 4.27025e44 0.128412
\(217\) −1.33466e45 −0.366779
\(218\) −1.55241e45 −0.390036
\(219\) 6.64189e44 0.152627
\(220\) −4.32202e45 −0.908751
\(221\) 6.82526e43 0.0131362
\(222\) −1.37895e45 −0.243034
\(223\) −6.61885e45 −1.06866 −0.534328 0.845277i \(-0.679435\pi\)
−0.534328 + 0.845277i \(0.679435\pi\)
\(224\) −9.19308e45 −1.36027
\(225\) 2.91263e45 0.395117
\(226\) 4.39864e45 0.547273
\(227\) 1.14636e46 1.30863 0.654317 0.756220i \(-0.272956\pi\)
0.654317 + 0.756220i \(0.272956\pi\)
\(228\) −8.21152e45 −0.860388
\(229\) −5.43505e45 −0.522892 −0.261446 0.965218i \(-0.584199\pi\)
−0.261446 + 0.965218i \(0.584199\pi\)
\(230\) 9.58279e45 0.846836
\(231\) −7.62034e45 −0.618786
\(232\) −4.33149e45 −0.323312
\(233\) −2.44861e46 −1.68066 −0.840328 0.542079i \(-0.817638\pi\)
−0.840328 + 0.542079i \(0.817638\pi\)
\(234\) 7.98298e43 0.00504029
\(235\) 3.07623e46 1.78729
\(236\) 1.25354e46 0.670432
\(237\) 1.56367e46 0.770110
\(238\) −3.69894e45 −0.167813
\(239\) 3.20935e46 1.34171 0.670855 0.741589i \(-0.265927\pi\)
0.670855 + 0.741589i \(0.265927\pi\)
\(240\) 1.40726e46 0.542320
\(241\) −4.03396e45 −0.143351 −0.0716753 0.997428i \(-0.522835\pi\)
−0.0716753 + 0.997428i \(0.522835\pi\)
\(242\) −5.48020e45 −0.179637
\(243\) −2.12090e45 −0.0641500
\(244\) 2.02032e46 0.564053
\(245\) −7.55359e46 −1.94722
\(246\) 1.22224e46 0.291019
\(247\) −3.29330e45 −0.0724504
\(248\) −7.90710e45 −0.160772
\(249\) −2.68512e46 −0.504750
\(250\) −5.61455e45 −0.0976079
\(251\) −9.02920e46 −1.45215 −0.726076 0.687615i \(-0.758658\pi\)
−0.726076 + 0.687615i \(0.758658\pi\)
\(252\) 2.97671e46 0.443023
\(253\) 8.21830e46 1.13222
\(254\) −3.09501e46 −0.394824
\(255\) 2.23538e46 0.264130
\(256\) −3.78821e45 −0.0414720
\(257\) 4.29725e45 0.0436008 0.0218004 0.999762i \(-0.493060\pi\)
0.0218004 + 0.999762i \(0.493060\pi\)
\(258\) 3.49332e46 0.328590
\(259\) −2.06219e47 −1.79880
\(260\) 6.77108e45 0.0547870
\(261\) 2.15131e46 0.161515
\(262\) −7.11742e45 −0.0495961
\(263\) 1.26887e47 0.820879 0.410439 0.911888i \(-0.365375\pi\)
0.410439 + 0.911888i \(0.365375\pi\)
\(264\) −4.51463e46 −0.271235
\(265\) 3.74835e46 0.209193
\(266\) 1.78480e47 0.925545
\(267\) −6.43813e46 −0.310306
\(268\) 2.38729e47 1.06973
\(269\) 5.74667e46 0.239468 0.119734 0.992806i \(-0.461796\pi\)
0.119734 + 0.992806i \(0.461796\pi\)
\(270\) 2.61456e46 0.101346
\(271\) −3.95688e46 −0.142709 −0.0713546 0.997451i \(-0.522732\pi\)
−0.0713546 + 0.997451i \(0.522732\pi\)
\(272\) 5.85824e46 0.196641
\(273\) 1.19384e46 0.0373055
\(274\) 4.30349e46 0.125223
\(275\) −3.07931e47 −0.834577
\(276\) −3.21029e47 −0.810621
\(277\) 4.47297e47 1.05254 0.526272 0.850316i \(-0.323589\pi\)
0.526272 + 0.850316i \(0.323589\pi\)
\(278\) 1.50829e47 0.330834
\(279\) 3.92720e46 0.0803158
\(280\) −7.87249e47 −1.50152
\(281\) 3.99175e47 0.710215 0.355108 0.934825i \(-0.384444\pi\)
0.355108 + 0.934825i \(0.384444\pi\)
\(282\) 1.49781e47 0.248656
\(283\) −8.24030e47 −1.27675 −0.638377 0.769724i \(-0.720394\pi\)
−0.638377 + 0.769724i \(0.720394\pi\)
\(284\) −3.98520e47 −0.576424
\(285\) −1.07861e48 −1.45676
\(286\) −8.43983e45 −0.0106462
\(287\) 1.82783e48 2.15396
\(288\) 2.70505e47 0.297866
\(289\) −8.78590e47 −0.904228
\(290\) −2.65205e47 −0.255165
\(291\) 6.48562e47 0.583497
\(292\) 2.74298e47 0.230811
\(293\) −6.28416e47 −0.494685 −0.247343 0.968928i \(-0.579557\pi\)
−0.247343 + 0.968928i \(0.579557\pi\)
\(294\) −3.67783e47 −0.270906
\(295\) 1.64657e48 1.13514
\(296\) −1.22174e48 −0.788476
\(297\) 2.24227e47 0.135499
\(298\) −1.05818e47 −0.0598886
\(299\) −1.28752e47 −0.0682597
\(300\) 1.20286e48 0.597520
\(301\) 5.22419e48 2.43205
\(302\) 2.16518e47 0.0944842
\(303\) 9.97964e47 0.408304
\(304\) −2.82670e48 −1.08454
\(305\) 2.65376e48 0.955025
\(306\) 1.08840e47 0.0367471
\(307\) −2.43683e48 −0.772018 −0.386009 0.922495i \(-0.626147\pi\)
−0.386009 + 0.922495i \(0.626147\pi\)
\(308\) −3.14706e48 −0.935765
\(309\) −8.40523e47 −0.234617
\(310\) −4.84129e47 −0.126884
\(311\) −6.81462e48 −1.67731 −0.838657 0.544660i \(-0.816659\pi\)
−0.838657 + 0.544660i \(0.816659\pi\)
\(312\) 7.07282e46 0.0163523
\(313\) −2.62388e48 −0.569941 −0.284970 0.958536i \(-0.591984\pi\)
−0.284970 + 0.958536i \(0.591984\pi\)
\(314\) 7.26504e47 0.148289
\(315\) 3.91001e48 0.750105
\(316\) 6.45769e48 1.16461
\(317\) −6.51955e48 −1.10551 −0.552754 0.833344i \(-0.686423\pi\)
−0.552754 + 0.833344i \(0.686423\pi\)
\(318\) 1.82507e47 0.0291039
\(319\) −2.27443e48 −0.341156
\(320\) 3.32174e48 0.468750
\(321\) −7.61816e48 −1.01158
\(322\) 6.97767e48 0.872009
\(323\) −4.49011e48 −0.528211
\(324\) −8.75892e47 −0.0970114
\(325\) 4.82419e47 0.0503152
\(326\) −8.06181e46 −0.00791935
\(327\) 6.83124e48 0.632147
\(328\) 1.08289e49 0.944154
\(329\) 2.23994e49 1.84042
\(330\) −2.76418e48 −0.214064
\(331\) −2.04347e49 −1.49184 −0.745919 0.666036i \(-0.767990\pi\)
−0.745919 + 0.666036i \(0.767990\pi\)
\(332\) −1.10891e49 −0.763312
\(333\) 6.06796e48 0.393895
\(334\) −2.27165e48 −0.139087
\(335\) 3.13577e49 1.81122
\(336\) 1.02469e49 0.558441
\(337\) −1.34582e49 −0.692154 −0.346077 0.938206i \(-0.612486\pi\)
−0.346077 + 0.938206i \(0.612486\pi\)
\(338\) −7.32518e48 −0.355584
\(339\) −1.93558e49 −0.886988
\(340\) 9.23173e48 0.399433
\(341\) −4.15194e48 −0.169645
\(342\) −5.25174e48 −0.202672
\(343\) −1.32453e49 −0.482865
\(344\) 3.09504e49 1.06605
\(345\) −4.21682e49 −1.37250
\(346\) −9.47079e48 −0.291342
\(347\) 3.60982e49 1.04969 0.524844 0.851198i \(-0.324124\pi\)
0.524844 + 0.851198i \(0.324124\pi\)
\(348\) 8.88454e48 0.244253
\(349\) 1.29981e49 0.337896 0.168948 0.985625i \(-0.445963\pi\)
0.168948 + 0.985625i \(0.445963\pi\)
\(350\) −2.61446e49 −0.642770
\(351\) −3.51284e47 −0.00816901
\(352\) −2.85985e49 −0.629160
\(353\) −7.99353e49 −1.66392 −0.831959 0.554837i \(-0.812781\pi\)
−0.831959 + 0.554837i \(0.812781\pi\)
\(354\) 8.01711e48 0.157926
\(355\) −5.23469e49 −0.975973
\(356\) −2.65884e49 −0.469263
\(357\) 1.62768e49 0.271982
\(358\) 3.50584e49 0.554719
\(359\) 7.75277e49 1.16176 0.580878 0.813990i \(-0.302709\pi\)
0.580878 + 0.813990i \(0.302709\pi\)
\(360\) 2.31646e49 0.328796
\(361\) 1.42286e50 1.91326
\(362\) 1.18367e49 0.150804
\(363\) 2.41151e49 0.291146
\(364\) 4.93033e48 0.0564156
\(365\) 3.60299e49 0.390798
\(366\) 1.29211e49 0.132868
\(367\) 1.56697e49 0.152782 0.0763909 0.997078i \(-0.475660\pi\)
0.0763909 + 0.997078i \(0.475660\pi\)
\(368\) −1.10510e50 −1.02181
\(369\) −5.37834e49 −0.471666
\(370\) −7.48034e49 −0.622283
\(371\) 2.72935e49 0.215411
\(372\) 1.62186e49 0.121458
\(373\) 5.67952e49 0.403636 0.201818 0.979423i \(-0.435315\pi\)
0.201818 + 0.979423i \(0.435315\pi\)
\(374\) −1.15069e49 −0.0776180
\(375\) 2.47063e49 0.158197
\(376\) 1.32704e50 0.806718
\(377\) 3.56322e48 0.0205677
\(378\) 1.90378e49 0.104358
\(379\) −3.40282e49 −0.177163 −0.0885817 0.996069i \(-0.528233\pi\)
−0.0885817 + 0.996069i \(0.528233\pi\)
\(380\) −4.45447e50 −2.20301
\(381\) 1.36193e50 0.639908
\(382\) −8.91828e49 −0.398149
\(383\) −1.51395e50 −0.642295 −0.321147 0.947029i \(-0.604068\pi\)
−0.321147 + 0.947029i \(0.604068\pi\)
\(384\) 1.44124e50 0.581134
\(385\) −4.13377e50 −1.58439
\(386\) −9.66071e48 −0.0352011
\(387\) −1.53721e50 −0.532560
\(388\) 2.67845e50 0.882398
\(389\) 3.64065e50 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(390\) 4.33049e48 0.0129056
\(391\) −1.75541e50 −0.497658
\(392\) −3.25852e50 −0.878904
\(393\) 3.13196e49 0.0803825
\(394\) −5.94324e49 −0.145160
\(395\) 8.48238e50 1.97185
\(396\) 9.26017e49 0.204910
\(397\) 6.19440e50 1.30492 0.652461 0.757823i \(-0.273737\pi\)
0.652461 + 0.757823i \(0.273737\pi\)
\(398\) 1.05960e49 0.0212530
\(399\) −7.85385e50 −1.50007
\(400\) 4.14069e50 0.753187
\(401\) 1.98149e50 0.343302 0.171651 0.985158i \(-0.445090\pi\)
0.171651 + 0.985158i \(0.445090\pi\)
\(402\) 1.52680e50 0.251985
\(403\) 6.50462e48 0.0102276
\(404\) 4.12141e50 0.617461
\(405\) −1.15051e50 −0.164255
\(406\) −1.93108e50 −0.262750
\(407\) −6.41521e50 −0.831994
\(408\) 9.64313e49 0.119219
\(409\) −8.18635e50 −0.964908 −0.482454 0.875921i \(-0.660254\pi\)
−0.482454 + 0.875921i \(0.660254\pi\)
\(410\) 6.63021e50 0.745147
\(411\) −1.89371e50 −0.202955
\(412\) −3.47121e50 −0.354802
\(413\) 1.19894e51 1.16888
\(414\) −2.05317e50 −0.190949
\(415\) −1.45658e51 −1.29240
\(416\) 4.48037e49 0.0379310
\(417\) −6.63708e50 −0.536197
\(418\) 5.55228e50 0.428089
\(419\) −9.92910e50 −0.730696 −0.365348 0.930871i \(-0.619050\pi\)
−0.365348 + 0.930871i \(0.619050\pi\)
\(420\) 1.61476e51 1.13435
\(421\) −6.39132e50 −0.428637 −0.214319 0.976764i \(-0.568753\pi\)
−0.214319 + 0.976764i \(0.568753\pi\)
\(422\) −6.98230e50 −0.447101
\(423\) −6.59098e50 −0.403007
\(424\) 1.61699e50 0.0944219
\(425\) 6.57733e50 0.366831
\(426\) −2.54876e50 −0.135782
\(427\) 1.93232e51 0.983414
\(428\) −3.14616e51 −1.52978
\(429\) 3.71387e49 0.0172548
\(430\) 1.89501e51 0.841349
\(431\) 3.21896e50 0.136587 0.0682935 0.997665i \(-0.478245\pi\)
0.0682935 + 0.997665i \(0.478245\pi\)
\(432\) −3.01513e50 −0.122285
\(433\) −4.43633e51 −1.71993 −0.859963 0.510356i \(-0.829514\pi\)
−0.859963 + 0.510356i \(0.829514\pi\)
\(434\) −3.52517e50 −0.130656
\(435\) 1.16701e51 0.413556
\(436\) 2.82118e51 0.955970
\(437\) 8.47013e51 2.74475
\(438\) 1.75429e50 0.0543697
\(439\) 3.25569e51 0.965128 0.482564 0.875861i \(-0.339706\pi\)
0.482564 + 0.875861i \(0.339706\pi\)
\(440\) −2.44903e51 −0.694491
\(441\) 1.61840e51 0.439069
\(442\) 1.80273e49 0.00467946
\(443\) −4.09722e51 −1.01769 −0.508846 0.860858i \(-0.669928\pi\)
−0.508846 + 0.860858i \(0.669928\pi\)
\(444\) 2.50596e51 0.595671
\(445\) −3.49246e51 −0.794533
\(446\) −1.74821e51 −0.380683
\(447\) 4.65644e50 0.0970639
\(448\) 2.41871e51 0.482684
\(449\) −8.07315e51 −1.54255 −0.771275 0.636502i \(-0.780381\pi\)
−0.771275 + 0.636502i \(0.780381\pi\)
\(450\) 7.69300e50 0.140751
\(451\) 5.68613e51 0.996264
\(452\) −7.99362e51 −1.34136
\(453\) −9.52770e50 −0.153134
\(454\) 3.02784e51 0.466170
\(455\) 6.47615e50 0.0955201
\(456\) −4.65297e51 −0.657531
\(457\) 3.57503e51 0.484076 0.242038 0.970267i \(-0.422184\pi\)
0.242038 + 0.970267i \(0.422184\pi\)
\(458\) −1.43554e51 −0.186268
\(459\) −4.78943e50 −0.0595575
\(460\) −1.74147e52 −2.07558
\(461\) 8.00610e51 0.914645 0.457323 0.889301i \(-0.348808\pi\)
0.457323 + 0.889301i \(0.348808\pi\)
\(462\) −2.01273e51 −0.220428
\(463\) −8.57929e51 −0.900787 −0.450393 0.892830i \(-0.648716\pi\)
−0.450393 + 0.892830i \(0.648716\pi\)
\(464\) 3.05837e51 0.307886
\(465\) 2.13037e51 0.205647
\(466\) −6.46740e51 −0.598693
\(467\) 1.12846e52 1.00186 0.500932 0.865487i \(-0.332991\pi\)
0.500932 + 0.865487i \(0.332991\pi\)
\(468\) −1.45074e50 −0.0123537
\(469\) 2.28330e52 1.86506
\(470\) 8.12510e51 0.636679
\(471\) −3.19692e51 −0.240339
\(472\) 7.10306e51 0.512361
\(473\) 1.62518e52 1.12489
\(474\) 4.13006e51 0.274333
\(475\) −3.17367e52 −2.02319
\(476\) 6.72205e51 0.411307
\(477\) −8.03105e50 −0.0471698
\(478\) 8.47673e51 0.477952
\(479\) −2.24291e52 −1.21414 −0.607071 0.794648i \(-0.707656\pi\)
−0.607071 + 0.794648i \(0.707656\pi\)
\(480\) 1.46739e52 0.762680
\(481\) 1.00504e51 0.0501594
\(482\) −1.06547e51 −0.0510652
\(483\) −3.07046e52 −1.41330
\(484\) 9.95912e51 0.440287
\(485\) 3.51822e52 1.49403
\(486\) −5.60183e50 −0.0228519
\(487\) 6.05465e51 0.237287 0.118644 0.992937i \(-0.462145\pi\)
0.118644 + 0.992937i \(0.462145\pi\)
\(488\) 1.14480e52 0.431064
\(489\) 3.54753e50 0.0128352
\(490\) −1.99510e52 −0.693650
\(491\) −3.63912e52 −1.21593 −0.607963 0.793965i \(-0.708013\pi\)
−0.607963 + 0.793965i \(0.708013\pi\)
\(492\) −2.22116e52 −0.713281
\(493\) 4.85811e51 0.149952
\(494\) −8.69845e50 −0.0258087
\(495\) 1.21635e52 0.346943
\(496\) 5.58303e51 0.153101
\(497\) −3.81161e52 −1.00498
\(498\) −7.09209e51 −0.179805
\(499\) −5.72391e52 −1.39551 −0.697754 0.716337i \(-0.745817\pi\)
−0.697754 + 0.716337i \(0.745817\pi\)
\(500\) 1.02033e52 0.239235
\(501\) 9.99619e51 0.225423
\(502\) −2.38484e52 −0.517294
\(503\) 1.75324e52 0.365818 0.182909 0.983130i \(-0.441449\pi\)
0.182909 + 0.983130i \(0.441449\pi\)
\(504\) 1.68672e52 0.338570
\(505\) 5.41361e52 1.04545
\(506\) 2.17066e52 0.403327
\(507\) 3.22338e52 0.576310
\(508\) 5.62453e52 0.967707
\(509\) −9.36160e52 −1.55008 −0.775039 0.631913i \(-0.782270\pi\)
−0.775039 + 0.631913i \(0.782270\pi\)
\(510\) 5.90422e51 0.0940901
\(511\) 2.62351e52 0.402415
\(512\) 6.71707e52 0.991780
\(513\) 2.31098e52 0.328479
\(514\) 1.13501e51 0.0155317
\(515\) −4.55955e52 −0.600732
\(516\) −6.34839e52 −0.805368
\(517\) 6.96817e52 0.851242
\(518\) −5.44678e52 −0.640781
\(519\) 4.16754e52 0.472189
\(520\) 3.83676e51 0.0418697
\(521\) −6.14605e52 −0.646042 −0.323021 0.946392i \(-0.604698\pi\)
−0.323021 + 0.946392i \(0.604698\pi\)
\(522\) 5.68217e51 0.0575359
\(523\) −2.50871e52 −0.244719 −0.122359 0.992486i \(-0.539046\pi\)
−0.122359 + 0.992486i \(0.539046\pi\)
\(524\) 1.29344e52 0.121559
\(525\) 1.15047e53 1.04176
\(526\) 3.35140e52 0.292418
\(527\) 8.86844e51 0.0745659
\(528\) 3.18768e52 0.258293
\(529\) 2.03088e53 1.58598
\(530\) 9.90037e51 0.0745198
\(531\) −3.52786e52 −0.255957
\(532\) −3.24350e53 −2.26849
\(533\) −8.90815e51 −0.0600630
\(534\) −1.70048e52 −0.110539
\(535\) −4.13259e53 −2.59014
\(536\) 1.35273e53 0.817519
\(537\) −1.54271e53 −0.899056
\(538\) 1.51784e52 0.0853046
\(539\) −1.71101e53 −0.927412
\(540\) −4.75141e52 −0.248396
\(541\) 2.37622e53 1.19823 0.599114 0.800664i \(-0.295520\pi\)
0.599114 + 0.800664i \(0.295520\pi\)
\(542\) −1.04511e52 −0.0508368
\(543\) −5.20861e52 −0.244414
\(544\) 6.10856e52 0.276542
\(545\) 3.70571e53 1.61860
\(546\) 3.15323e51 0.0132892
\(547\) 1.01438e53 0.412524 0.206262 0.978497i \(-0.433870\pi\)
0.206262 + 0.978497i \(0.433870\pi\)
\(548\) −7.82071e52 −0.306920
\(549\) −5.68583e52 −0.215344
\(550\) −8.13325e52 −0.297298
\(551\) −2.34412e53 −0.827035
\(552\) −1.81908e53 −0.619498
\(553\) 6.17641e53 2.03047
\(554\) 1.18143e53 0.374944
\(555\) 3.29166e53 1.00856
\(556\) −2.74100e53 −0.810868
\(557\) 3.06102e53 0.874358 0.437179 0.899374i \(-0.355978\pi\)
0.437179 + 0.899374i \(0.355978\pi\)
\(558\) 1.03727e52 0.0286106
\(559\) −2.54608e52 −0.0678174
\(560\) 5.55859e53 1.42988
\(561\) 5.06351e52 0.125799
\(562\) 1.05432e53 0.252997
\(563\) 1.09661e53 0.254179 0.127090 0.991891i \(-0.459436\pi\)
0.127090 + 0.991891i \(0.459436\pi\)
\(564\) −2.72196e53 −0.609451
\(565\) −1.04999e54 −2.27111
\(566\) −2.17647e53 −0.454813
\(567\) −8.37741e52 −0.169138
\(568\) −2.25817e53 −0.440519
\(569\) 6.98263e53 1.31622 0.658112 0.752920i \(-0.271355\pi\)
0.658112 + 0.752920i \(0.271355\pi\)
\(570\) −2.84888e53 −0.518938
\(571\) −2.15970e53 −0.380180 −0.190090 0.981767i \(-0.560878\pi\)
−0.190090 + 0.981767i \(0.560878\pi\)
\(572\) 1.53376e52 0.0260937
\(573\) 3.92441e53 0.645296
\(574\) 4.82776e53 0.767298
\(575\) −1.24075e54 −1.90616
\(576\) −7.11702e52 −0.105696
\(577\) 2.02592e53 0.290867 0.145433 0.989368i \(-0.453542\pi\)
0.145433 + 0.989368i \(0.453542\pi\)
\(578\) −2.32058e53 −0.322110
\(579\) 4.25111e52 0.0570519
\(580\) 4.81955e53 0.625404
\(581\) −1.06061e54 −1.33082
\(582\) 1.71302e53 0.207857
\(583\) 8.49065e52 0.0996332
\(584\) 1.55428e53 0.176392
\(585\) −1.90559e52 −0.0209166
\(586\) −1.65981e53 −0.176220
\(587\) −7.06852e53 −0.725914 −0.362957 0.931806i \(-0.618233\pi\)
−0.362957 + 0.931806i \(0.618233\pi\)
\(588\) 6.68370e53 0.663986
\(589\) −4.27917e53 −0.411255
\(590\) 4.34900e53 0.404367
\(591\) 2.61527e53 0.235267
\(592\) 8.62641e53 0.750856
\(593\) −1.68827e53 −0.142192 −0.0710959 0.997469i \(-0.522650\pi\)
−0.0710959 + 0.997469i \(0.522650\pi\)
\(594\) 5.92241e52 0.0482684
\(595\) 8.82962e53 0.696404
\(596\) 1.92303e53 0.146786
\(597\) −4.66267e52 −0.0344457
\(598\) −3.40066e52 −0.0243159
\(599\) −8.66168e53 −0.599486 −0.299743 0.954020i \(-0.596901\pi\)
−0.299743 + 0.954020i \(0.596901\pi\)
\(600\) 6.81591e53 0.456640
\(601\) 1.01881e54 0.660758 0.330379 0.943848i \(-0.392823\pi\)
0.330379 + 0.943848i \(0.392823\pi\)
\(602\) 1.37984e54 0.866359
\(603\) −6.71857e53 −0.408403
\(604\) −3.93477e53 −0.231579
\(605\) 1.30816e54 0.745472
\(606\) 2.63588e53 0.145449
\(607\) −3.59220e53 −0.191947 −0.0959734 0.995384i \(-0.530596\pi\)
−0.0959734 + 0.995384i \(0.530596\pi\)
\(608\) −2.94748e54 −1.52522
\(609\) 8.49755e53 0.425850
\(610\) 7.00926e53 0.340205
\(611\) −1.09166e53 −0.0513199
\(612\) −1.97795e53 −0.0900663
\(613\) 9.11862e53 0.402207 0.201104 0.979570i \(-0.435547\pi\)
0.201104 + 0.979570i \(0.435547\pi\)
\(614\) −6.43631e53 −0.275013
\(615\) −2.91757e54 −1.20769
\(616\) −1.78325e54 −0.715136
\(617\) 2.52497e54 0.981061 0.490530 0.871424i \(-0.336803\pi\)
0.490530 + 0.871424i \(0.336803\pi\)
\(618\) −2.22004e53 −0.0835767
\(619\) 3.13318e53 0.114292 0.0571462 0.998366i \(-0.481800\pi\)
0.0571462 + 0.998366i \(0.481800\pi\)
\(620\) 8.79804e53 0.310991
\(621\) 9.03477e53 0.309479
\(622\) −1.79992e54 −0.597503
\(623\) −2.54302e54 −0.818151
\(624\) −4.99397e52 −0.0155721
\(625\) −2.58177e54 −0.780292
\(626\) −6.93035e53 −0.203028
\(627\) −2.44323e54 −0.693821
\(628\) −1.32027e54 −0.363454
\(629\) 1.37027e54 0.365695
\(630\) 1.03273e54 0.267207
\(631\) −3.45716e54 −0.867256 −0.433628 0.901092i \(-0.642767\pi\)
−0.433628 + 0.901092i \(0.642767\pi\)
\(632\) 3.65918e54 0.890022
\(633\) 3.07250e54 0.724635
\(634\) −1.72198e54 −0.393811
\(635\) 7.38800e54 1.63847
\(636\) −3.31668e53 −0.0713330
\(637\) 2.68055e53 0.0559121
\(638\) −6.00734e53 −0.121529
\(639\) 1.12156e54 0.220067
\(640\) 7.81821e54 1.48798
\(641\) 3.85151e54 0.711050 0.355525 0.934667i \(-0.384302\pi\)
0.355525 + 0.934667i \(0.384302\pi\)
\(642\) −2.01215e54 −0.360352
\(643\) 1.53024e54 0.265855 0.132928 0.991126i \(-0.457562\pi\)
0.132928 + 0.991126i \(0.457562\pi\)
\(644\) −1.26805e55 −2.13728
\(645\) −8.33881e54 −1.36361
\(646\) −1.18595e54 −0.188163
\(647\) 1.27086e55 1.95644 0.978219 0.207577i \(-0.0665578\pi\)
0.978219 + 0.207577i \(0.0665578\pi\)
\(648\) −4.96315e53 −0.0741387
\(649\) 3.72975e54 0.540639
\(650\) 1.27419e53 0.0179236
\(651\) 1.55122e54 0.211760
\(652\) 1.46507e53 0.0194102
\(653\) 9.19237e54 1.18201 0.591004 0.806669i \(-0.298732\pi\)
0.591004 + 0.806669i \(0.298732\pi\)
\(654\) 1.80431e54 0.225187
\(655\) 1.69898e54 0.205818
\(656\) −7.64603e54 −0.899106
\(657\) −7.71961e53 −0.0881192
\(658\) 5.91626e54 0.655605
\(659\) −2.57996e54 −0.277554 −0.138777 0.990324i \(-0.544317\pi\)
−0.138777 + 0.990324i \(0.544317\pi\)
\(660\) 5.02332e54 0.524668
\(661\) −1.12332e55 −1.13914 −0.569568 0.821944i \(-0.692890\pi\)
−0.569568 + 0.821944i \(0.692890\pi\)
\(662\) −5.39732e54 −0.531432
\(663\) −7.93273e52 −0.00758419
\(664\) −6.28350e54 −0.583343
\(665\) −4.26044e55 −3.84090
\(666\) 1.60270e54 0.140316
\(667\) −9.16434e54 −0.779197
\(668\) 4.12825e54 0.340898
\(669\) 7.69283e54 0.616989
\(670\) 8.28239e54 0.645204
\(671\) 6.01121e54 0.454855
\(672\) 1.06848e55 0.785352
\(673\) −1.50888e54 −0.107736 −0.0538681 0.998548i \(-0.517155\pi\)
−0.0538681 + 0.998548i \(0.517155\pi\)
\(674\) −3.55464e54 −0.246563
\(675\) −3.38524e54 −0.228121
\(676\) 1.33120e55 0.871530
\(677\) 5.88105e54 0.374090 0.187045 0.982351i \(-0.440109\pi\)
0.187045 + 0.982351i \(0.440109\pi\)
\(678\) −5.11237e54 −0.315968
\(679\) 2.56178e55 1.53844
\(680\) 5.23106e54 0.305257
\(681\) −1.33237e55 −0.755540
\(682\) −1.09663e54 −0.0604319
\(683\) 1.21018e55 0.648109 0.324054 0.946038i \(-0.394954\pi\)
0.324054 + 0.946038i \(0.394954\pi\)
\(684\) 9.54394e54 0.496745
\(685\) −1.02727e55 −0.519661
\(686\) −3.49842e54 −0.172009
\(687\) 6.31695e54 0.301892
\(688\) −2.18534e55 −1.01518
\(689\) −1.33018e53 −0.00600671
\(690\) −1.11377e55 −0.488921
\(691\) 1.62764e55 0.694601 0.347300 0.937754i \(-0.387098\pi\)
0.347300 + 0.937754i \(0.387098\pi\)
\(692\) 1.72112e55 0.714072
\(693\) 8.85682e54 0.357256
\(694\) 9.53445e54 0.373926
\(695\) −3.60039e55 −1.37292
\(696\) 5.03433e54 0.186664
\(697\) −1.21454e55 −0.437899
\(698\) 3.43312e54 0.120367
\(699\) 2.84592e55 0.970327
\(700\) 4.75124e55 1.57542
\(701\) 1.79427e55 0.578610 0.289305 0.957237i \(-0.406576\pi\)
0.289305 + 0.957237i \(0.406576\pi\)
\(702\) −9.27831e52 −0.00291002
\(703\) −6.61180e55 −2.01693
\(704\) 7.52430e54 0.223254
\(705\) −3.57538e55 −1.03189
\(706\) −2.11130e55 −0.592731
\(707\) 3.94190e55 1.07653
\(708\) −1.45694e55 −0.387074
\(709\) 1.14395e55 0.295669 0.147834 0.989012i \(-0.452770\pi\)
0.147834 + 0.989012i \(0.452770\pi\)
\(710\) −1.38261e55 −0.347667
\(711\) −1.81740e55 −0.444623
\(712\) −1.50660e55 −0.358623
\(713\) −1.67294e55 −0.387467
\(714\) 4.29913e54 0.0968870
\(715\) 2.01465e54 0.0441805
\(716\) −6.37114e55 −1.35961
\(717\) −3.73011e55 −0.774636
\(718\) 2.04771e55 0.413848
\(719\) 6.82369e55 1.34216 0.671082 0.741383i \(-0.265830\pi\)
0.671082 + 0.741383i \(0.265830\pi\)
\(720\) −1.63560e55 −0.313108
\(721\) −3.32002e55 −0.618589
\(722\) 3.75815e55 0.681552
\(723\) 4.68852e54 0.0827635
\(724\) −2.15107e55 −0.369617
\(725\) 3.43379e55 0.574357
\(726\) 6.36942e54 0.103714
\(727\) 4.73186e55 0.750085 0.375043 0.927008i \(-0.377628\pi\)
0.375043 + 0.927008i \(0.377628\pi\)
\(728\) 2.79372e54 0.0431143
\(729\) 2.46503e54 0.0370370
\(730\) 9.51643e54 0.139213
\(731\) −3.47134e55 −0.494433
\(732\) −2.34815e55 −0.325656
\(733\) 7.44240e54 0.100505 0.0502523 0.998737i \(-0.483997\pi\)
0.0502523 + 0.998737i \(0.483997\pi\)
\(734\) 4.13876e54 0.0544248
\(735\) 8.77925e55 1.12423
\(736\) −1.15232e56 −1.43700
\(737\) 7.10305e55 0.862639
\(738\) −1.42056e55 −0.168020
\(739\) 9.48337e55 1.09244 0.546218 0.837643i \(-0.316067\pi\)
0.546218 + 0.837643i \(0.316067\pi\)
\(740\) 1.35940e56 1.52520
\(741\) 3.82768e54 0.0418293
\(742\) 7.20891e54 0.0767350
\(743\) −2.79365e55 −0.289661 −0.144830 0.989456i \(-0.546264\pi\)
−0.144830 + 0.989456i \(0.546264\pi\)
\(744\) 9.19012e54 0.0928215
\(745\) 2.52596e55 0.248530
\(746\) 1.50011e55 0.143786
\(747\) 3.12081e55 0.291417
\(748\) 2.09114e55 0.190240
\(749\) −3.00912e56 −2.66713
\(750\) 6.52557e54 0.0563539
\(751\) −8.12653e55 −0.683796 −0.341898 0.939737i \(-0.611070\pi\)
−0.341898 + 0.939737i \(0.611070\pi\)
\(752\) −9.36995e55 −0.768227
\(753\) 1.04943e56 0.838400
\(754\) 9.41137e53 0.00732676
\(755\) −5.16845e55 −0.392098
\(756\) −3.45972e55 −0.255780
\(757\) 2.71381e56 1.95528 0.977642 0.210277i \(-0.0674367\pi\)
0.977642 + 0.210277i \(0.0674367\pi\)
\(758\) −8.98771e54 −0.0631102
\(759\) −9.55181e55 −0.653689
\(760\) −2.52408e56 −1.68359
\(761\) −2.53928e56 −1.65086 −0.825428 0.564507i \(-0.809066\pi\)
−0.825428 + 0.564507i \(0.809066\pi\)
\(762\) 3.59721e55 0.227952
\(763\) 2.69830e56 1.66671
\(764\) 1.62071e56 0.975855
\(765\) −2.59810e55 −0.152496
\(766\) −3.99872e55 −0.228802
\(767\) −5.84319e54 −0.0325942
\(768\) 4.40289e54 0.0239439
\(769\) −3.16540e56 −1.67828 −0.839140 0.543915i \(-0.816941\pi\)
−0.839140 + 0.543915i \(0.816941\pi\)
\(770\) −1.09183e56 −0.564401
\(771\) −4.99452e54 −0.0251729
\(772\) 1.75563e55 0.0862773
\(773\) −8.83478e55 −0.423346 −0.211673 0.977341i \(-0.567891\pi\)
−0.211673 + 0.977341i \(0.567891\pi\)
\(774\) −4.06016e55 −0.189712
\(775\) 6.26834e55 0.285607
\(776\) 1.51771e56 0.674352
\(777\) 2.39681e56 1.03854
\(778\) 9.61590e55 0.406338
\(779\) 5.86038e56 2.41516
\(780\) −7.86976e54 −0.0316313
\(781\) −1.18574e56 −0.464832
\(782\) −4.63648e55 −0.177279
\(783\) −2.50039e55 −0.0932508
\(784\) 2.30077e56 0.836969
\(785\) −1.73422e56 −0.615382
\(786\) 8.27231e54 0.0286343
\(787\) 2.01468e56 0.680299 0.340149 0.940371i \(-0.389522\pi\)
0.340149 + 0.940371i \(0.389522\pi\)
\(788\) 1.08006e56 0.355784
\(789\) −1.47475e56 −0.473934
\(790\) 2.24041e56 0.702425
\(791\) −7.64544e56 −2.33863
\(792\) 5.24718e55 0.156598
\(793\) −9.41744e54 −0.0274224
\(794\) 1.63610e56 0.464847
\(795\) −4.35657e55 −0.120777
\(796\) −1.92560e55 −0.0520908
\(797\) 4.87383e56 1.28657 0.643285 0.765627i \(-0.277571\pi\)
0.643285 + 0.765627i \(0.277571\pi\)
\(798\) −2.07440e56 −0.534364
\(799\) −1.48838e56 −0.374156
\(800\) 4.31762e56 1.05923
\(801\) 7.48279e55 0.179155
\(802\) 5.23362e55 0.122293
\(803\) 8.16138e55 0.186128
\(804\) −2.77465e56 −0.617611
\(805\) −1.66562e57 −3.61873
\(806\) 1.71804e54 0.00364333
\(807\) −6.67913e55 −0.138257
\(808\) 2.33536e56 0.471880
\(809\) 2.97630e56 0.587057 0.293529 0.955950i \(-0.405170\pi\)
0.293529 + 0.955950i \(0.405170\pi\)
\(810\) −3.03880e55 −0.0585119
\(811\) −7.70370e56 −1.44808 −0.724041 0.689757i \(-0.757717\pi\)
−0.724041 + 0.689757i \(0.757717\pi\)
\(812\) 3.50934e56 0.643995
\(813\) 4.59893e55 0.0823932
\(814\) −1.69442e56 −0.296378
\(815\) 1.92441e55 0.0328643
\(816\) −6.80880e55 −0.113531
\(817\) 1.67498e57 2.72696
\(818\) −2.16223e56 −0.343725
\(819\) −1.38755e55 −0.0215384
\(820\) −1.20490e57 −1.82634
\(821\) 4.31761e55 0.0639075 0.0319537 0.999489i \(-0.489827\pi\)
0.0319537 + 0.999489i \(0.489827\pi\)
\(822\) −5.00179e55 −0.0722977
\(823\) 4.12553e56 0.582348 0.291174 0.956670i \(-0.405954\pi\)
0.291174 + 0.956670i \(0.405954\pi\)
\(824\) −1.96693e56 −0.271149
\(825\) 3.57897e56 0.481843
\(826\) 3.16671e56 0.416387
\(827\) −6.96480e56 −0.894440 −0.447220 0.894424i \(-0.647586\pi\)
−0.447220 + 0.894424i \(0.647586\pi\)
\(828\) 3.73120e56 0.468012
\(829\) 1.42775e57 1.74920 0.874600 0.484845i \(-0.161124\pi\)
0.874600 + 0.484845i \(0.161124\pi\)
\(830\) −3.84721e56 −0.460387
\(831\) −5.19876e56 −0.607686
\(832\) −1.17879e55 −0.0134596
\(833\) 3.65468e56 0.407636
\(834\) −1.75302e56 −0.191007
\(835\) 5.42258e56 0.577192
\(836\) −1.00901e57 −1.04924
\(837\) −4.56443e55 −0.0463703
\(838\) −2.62253e56 −0.260293
\(839\) 6.94535e56 0.673497 0.336749 0.941595i \(-0.390673\pi\)
0.336749 + 0.941595i \(0.390673\pi\)
\(840\) 9.14989e56 0.866902
\(841\) −8.26620e56 −0.765216
\(842\) −1.68811e56 −0.152692
\(843\) −4.63946e56 −0.410043
\(844\) 1.26889e57 1.09584
\(845\) 1.74857e57 1.47563
\(846\) −1.74085e56 −0.143562
\(847\) 9.52532e56 0.767632
\(848\) −1.14172e56 −0.0899168
\(849\) 9.57738e56 0.737135
\(850\) 1.73724e56 0.130675
\(851\) −2.58488e57 −1.90027
\(852\) 4.63184e56 0.332799
\(853\) −4.76945e56 −0.334936 −0.167468 0.985878i \(-0.553559\pi\)
−0.167468 + 0.985878i \(0.553559\pi\)
\(854\) 5.10377e56 0.350318
\(855\) 1.25363e57 0.841064
\(856\) −1.78274e57 −1.16909
\(857\) −7.15190e56 −0.458454 −0.229227 0.973373i \(-0.573620\pi\)
−0.229227 + 0.973373i \(0.573620\pi\)
\(858\) 9.80928e54 0.00614660
\(859\) −3.14874e57 −1.92872 −0.964362 0.264586i \(-0.914765\pi\)
−0.964362 + 0.264586i \(0.914765\pi\)
\(860\) −3.44378e57 −2.06213
\(861\) −2.12441e57 −1.24359
\(862\) 8.50211e55 0.0486558
\(863\) 6.33719e56 0.354557 0.177279 0.984161i \(-0.443271\pi\)
0.177279 + 0.984161i \(0.443271\pi\)
\(864\) −3.14397e56 −0.171973
\(865\) 2.26074e57 1.20903
\(866\) −1.17175e57 −0.612683
\(867\) 1.02115e57 0.522057
\(868\) 6.40626e56 0.320236
\(869\) 1.92140e57 0.939144
\(870\) 3.08238e56 0.147320
\(871\) −1.11280e56 −0.0520070
\(872\) 1.59859e57 0.730577
\(873\) −7.53799e56 −0.336882
\(874\) 2.23718e57 0.977750
\(875\) 9.75885e56 0.417101
\(876\) −3.18806e56 −0.133259
\(877\) −2.07724e57 −0.849171 −0.424585 0.905388i \(-0.639580\pi\)
−0.424585 + 0.905388i \(0.639580\pi\)
\(878\) 8.59911e56 0.343804
\(879\) 7.30384e56 0.285607
\(880\) 1.72921e57 0.661355
\(881\) −1.44068e57 −0.538937 −0.269468 0.963009i \(-0.586848\pi\)
−0.269468 + 0.963009i \(0.586848\pi\)
\(882\) 4.27460e56 0.156408
\(883\) −2.21527e57 −0.792852 −0.396426 0.918067i \(-0.629750\pi\)
−0.396426 + 0.918067i \(0.629750\pi\)
\(884\) −3.27608e55 −0.0114693
\(885\) −1.91374e57 −0.655374
\(886\) −1.08218e57 −0.362528
\(887\) 4.62524e56 0.151574 0.0757868 0.997124i \(-0.475853\pi\)
0.0757868 + 0.997124i \(0.475853\pi\)
\(888\) 1.41998e57 0.455227
\(889\) 5.37954e57 1.68718
\(890\) −9.22450e56 −0.283033
\(891\) −2.60610e56 −0.0782305
\(892\) 3.17700e57 0.933046
\(893\) 7.18170e57 2.06359
\(894\) 1.22989e56 0.0345767
\(895\) −8.36869e57 −2.30202
\(896\) 5.69280e57 1.53221
\(897\) 1.49643e56 0.0394097
\(898\) −2.13233e57 −0.549497
\(899\) 4.62989e56 0.116750
\(900\) −1.39804e57 −0.344978
\(901\) −1.81358e56 −0.0437929
\(902\) 1.50185e57 0.354895
\(903\) −6.07187e57 −1.40414
\(904\) −4.52950e57 −1.02510
\(905\) −2.82549e57 −0.625816
\(906\) −2.51651e56 −0.0545505
\(907\) 5.47083e57 1.16068 0.580339 0.814375i \(-0.302920\pi\)
0.580339 + 0.814375i \(0.302920\pi\)
\(908\) −5.50247e57 −1.14257
\(909\) −1.15989e57 −0.235734
\(910\) 1.71052e56 0.0340267
\(911\) −5.88844e56 −0.114655 −0.0573274 0.998355i \(-0.518258\pi\)
−0.0573274 + 0.998355i \(0.518258\pi\)
\(912\) 3.28536e57 0.626158
\(913\) −3.29940e57 −0.615539
\(914\) 9.44258e56 0.172441
\(915\) −3.08436e57 −0.551384
\(916\) 2.60879e57 0.456538
\(917\) 1.23710e57 0.211936
\(918\) −1.26501e56 −0.0212159
\(919\) −3.41668e57 −0.560986 −0.280493 0.959856i \(-0.590498\pi\)
−0.280493 + 0.959856i \(0.590498\pi\)
\(920\) −9.86788e57 −1.58621
\(921\) 2.83224e57 0.445725
\(922\) 2.11462e57 0.325821
\(923\) 1.85764e56 0.0280239
\(924\) 3.65771e57 0.540264
\(925\) 9.68529e57 1.40071
\(926\) −2.26601e57 −0.320884
\(927\) 9.76908e56 0.135456
\(928\) 3.18906e57 0.432989
\(929\) −5.60274e57 −0.744893 −0.372447 0.928054i \(-0.621481\pi\)
−0.372447 + 0.928054i \(0.621481\pi\)
\(930\) 5.62685e56 0.0732568
\(931\) −1.76345e58 −2.24824
\(932\) 1.17532e58 1.46739
\(933\) 7.92037e57 0.968397
\(934\) 2.98056e57 0.356890
\(935\) 2.74678e57 0.322105
\(936\) −8.22047e55 −0.00944099
\(937\) 2.84316e57 0.319800 0.159900 0.987133i \(-0.448883\pi\)
0.159900 + 0.987133i \(0.448883\pi\)
\(938\) 6.03079e57 0.664383
\(939\) 3.04964e57 0.329055
\(940\) −1.47657e58 −1.56049
\(941\) −3.10342e57 −0.321250 −0.160625 0.987016i \(-0.551351\pi\)
−0.160625 + 0.987016i \(0.551351\pi\)
\(942\) −8.44388e56 −0.0856149
\(943\) 2.29111e58 2.27546
\(944\) −5.01531e57 −0.487915
\(945\) −4.54445e57 −0.433073
\(946\) 4.29251e57 0.400714
\(947\) 1.09739e58 1.00354 0.501771 0.865000i \(-0.332682\pi\)
0.501771 + 0.865000i \(0.332682\pi\)
\(948\) −7.50552e57 −0.672386
\(949\) −1.27860e56 −0.0112213
\(950\) −8.38249e57 −0.720713
\(951\) 7.57742e57 0.638265
\(952\) 3.80898e57 0.314332
\(953\) −1.56833e58 −1.26802 −0.634009 0.773326i \(-0.718592\pi\)
−0.634009 + 0.773326i \(0.718592\pi\)
\(954\) −2.12121e56 −0.0168031
\(955\) 2.12886e58 1.65227
\(956\) −1.54047e58 −1.17145
\(957\) 2.64348e57 0.196967
\(958\) −5.92410e57 −0.432509
\(959\) −7.48006e57 −0.535109
\(960\) −3.86073e57 −0.270633
\(961\) −1.37130e58 −0.941944
\(962\) 2.65456e56 0.0178681
\(963\) 8.85429e57 0.584038
\(964\) 1.93627e57 0.125160
\(965\) 2.30608e57 0.146080
\(966\) −8.10988e57 −0.503455
\(967\) −6.70320e57 −0.407817 −0.203909 0.978990i \(-0.565365\pi\)
−0.203909 + 0.978990i \(0.565365\pi\)
\(968\) 5.64323e57 0.336479
\(969\) 5.21868e57 0.304963
\(970\) 9.29254e57 0.532213
\(971\) −1.00902e57 −0.0566405 −0.0283202 0.999599i \(-0.509016\pi\)
−0.0283202 + 0.999599i \(0.509016\pi\)
\(972\) 1.01802e57 0.0560096
\(973\) −2.62161e58 −1.41373
\(974\) 1.59919e57 0.0845279
\(975\) −5.60697e56 −0.0290495
\(976\) −8.08315e57 −0.410496
\(977\) −1.41653e58 −0.705150 −0.352575 0.935784i \(-0.614694\pi\)
−0.352575 + 0.935784i \(0.614694\pi\)
\(978\) 9.36994e55 0.00457224
\(979\) −7.91101e57 −0.378416
\(980\) 3.62567e58 1.70012
\(981\) −7.93968e57 −0.364970
\(982\) −9.61185e57 −0.433145
\(983\) −8.83216e57 −0.390187 −0.195094 0.980785i \(-0.562501\pi\)
−0.195094 + 0.980785i \(0.562501\pi\)
\(984\) −1.25860e58 −0.545108
\(985\) 1.41869e58 0.602396
\(986\) 1.28315e57 0.0534169
\(987\) −2.60340e58 −1.06257
\(988\) 1.58076e57 0.0632567
\(989\) 6.54832e58 2.56923
\(990\) 3.21270e57 0.123590
\(991\) 2.39176e58 0.902156 0.451078 0.892484i \(-0.351040\pi\)
0.451078 + 0.892484i \(0.351040\pi\)
\(992\) 5.82159e57 0.215310
\(993\) 2.37504e58 0.861313
\(994\) −1.00675e58 −0.358002
\(995\) −2.52933e57 −0.0881975
\(996\) 1.28884e58 0.440698
\(997\) 1.65650e58 0.555439 0.277719 0.960662i \(-0.410421\pi\)
0.277719 + 0.960662i \(0.410421\pi\)
\(998\) −1.51183e58 −0.497116
\(999\) −7.05255e57 −0.227415
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 3.40.a.b.1.2 3
3.2 odd 2 9.40.a.c.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.40.a.b.1.2 3 1.1 even 1 trivial
9.40.a.c.1.2 3 3.2 odd 2