Properties

Label 3.36.a.a.1.1
Level $3$
Weight $36$
Character 3.1
Self dual yes
Analytic conductor $23.279$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.2785391901\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{2196841}) \)
Defining polynomial: \(x^{2} - x - 549210\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{4}\cdot 3\cdot 7 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(741.587\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-279461. q^{2} +1.29140e8 q^{3} +4.37389e10 q^{4} -3.65354e11 q^{5} -3.60897e13 q^{6} -6.36148e14 q^{7} -2.62111e15 q^{8} +1.66772e16 q^{9} +O(q^{10})\) \(q-279461. q^{2} +1.29140e8 q^{3} +4.37389e10 q^{4} -3.65354e11 q^{5} -3.60897e13 q^{6} -6.36148e14 q^{7} -2.62111e15 q^{8} +1.66772e16 q^{9} +1.02102e17 q^{10} +1.49276e17 q^{11} +5.64845e18 q^{12} +5.52590e19 q^{13} +1.77779e20 q^{14} -4.71819e19 q^{15} -7.70358e20 q^{16} +1.81211e21 q^{17} -4.66063e21 q^{18} -3.32454e22 q^{19} -1.59802e22 q^{20} -8.21522e22 q^{21} -4.17169e22 q^{22} +1.00717e24 q^{23} -3.38490e23 q^{24} -2.77690e24 q^{25} -1.54428e25 q^{26} +2.15369e24 q^{27} -2.78244e25 q^{28} -4.49573e25 q^{29} +1.31855e25 q^{30} -2.23850e25 q^{31} +3.05346e26 q^{32} +1.92775e25 q^{33} -5.06414e26 q^{34} +2.32419e26 q^{35} +7.29441e26 q^{36} -2.91588e27 q^{37} +9.29079e27 q^{38} +7.13616e27 q^{39} +9.57633e26 q^{40} -4.18186e27 q^{41} +2.29584e28 q^{42} -5.84123e28 q^{43} +6.52916e27 q^{44} -6.09308e27 q^{45} -2.81465e29 q^{46} -5.23894e28 q^{47} -9.94842e28 q^{48} +2.58653e28 q^{49} +7.76036e29 q^{50} +2.34016e29 q^{51} +2.41697e30 q^{52} -2.64063e30 q^{53} -6.01874e29 q^{54} -5.45386e28 q^{55} +1.66741e30 q^{56} -4.29331e30 q^{57} +1.25638e31 q^{58} +2.44829e30 q^{59} -2.06368e30 q^{60} -1.37521e31 q^{61} +6.25575e30 q^{62} -1.06092e31 q^{63} -5.88631e31 q^{64} -2.01891e31 q^{65} -5.38732e30 q^{66} -6.70306e31 q^{67} +7.92595e31 q^{68} +1.30066e32 q^{69} -6.49522e31 q^{70} +4.91498e32 q^{71} -4.37127e31 q^{72} +1.37337e32 q^{73} +8.14875e32 q^{74} -3.58609e32 q^{75} -1.45411e33 q^{76} -9.49616e31 q^{77} -1.99428e33 q^{78} +1.07453e33 q^{79} +2.81454e32 q^{80} +2.78128e32 q^{81} +1.16867e33 q^{82} -3.27927e33 q^{83} -3.59325e33 q^{84} -6.62061e32 q^{85} +1.63240e34 q^{86} -5.80579e33 q^{87} -3.91268e32 q^{88} +3.27218e33 q^{89} +1.70278e33 q^{90} -3.51529e34 q^{91} +4.40526e34 q^{92} -2.89081e33 q^{93} +1.46408e34 q^{94} +1.21463e34 q^{95} +3.94324e34 q^{96} -1.46799e34 q^{97} -7.22835e33 q^{98} +2.48950e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 60912q^{2} + 258280326q^{3} + 57142939904q^{4} - 1333779496740q^{5} - 7866185608656q^{6} - 1201512782952944q^{7} - 7200956480385024q^{8} + 33354363399333138q^{9} + O(q^{10}) \) \( 2q - 60912q^{2} + 258280326q^{3} + 57142939904q^{4} - 1333779496740q^{5} - 7866185608656q^{6} - 1201512782952944q^{7} - 7200956480385024q^{8} + 33354363399333138q^{9} - 109546268366103840q^{10} - 1474443852221320632q^{11} + 7379448573501764352q^{12} + 30005213658205678828q^{13} + 54218555116626208896q^{14} - \)\(17\!\cdots\!20\)\(q^{15} - \)\(22\!\cdots\!20\)\(q^{16} + \)\(61\!\cdots\!32\)\(q^{17} - \)\(10\!\cdots\!28\)\(q^{18} - \)\(16\!\cdots\!64\)\(q^{19} - \)\(28\!\cdots\!20\)\(q^{20} - \)\(15\!\cdots\!72\)\(q^{21} - \)\(39\!\cdots\!16\)\(q^{22} + \)\(49\!\cdots\!72\)\(q^{23} - \)\(92\!\cdots\!12\)\(q^{24} - \)\(47\!\cdots\!50\)\(q^{25} - \)\(20\!\cdots\!56\)\(q^{26} + \)\(43\!\cdots\!94\)\(q^{27} - \)\(35\!\cdots\!72\)\(q^{28} - \)\(78\!\cdots\!48\)\(q^{29} - \)\(14\!\cdots\!20\)\(q^{30} - \)\(12\!\cdots\!48\)\(q^{31} + \)\(14\!\cdots\!76\)\(q^{32} - \)\(19\!\cdots\!16\)\(q^{33} + \)\(44\!\cdots\!88\)\(q^{34} + \)\(77\!\cdots\!60\)\(q^{35} + \)\(95\!\cdots\!76\)\(q^{36} + \)\(16\!\cdots\!16\)\(q^{37} + \)\(13\!\cdots\!12\)\(q^{38} + \)\(38\!\cdots\!64\)\(q^{39} + \)\(53\!\cdots\!00\)\(q^{40} - \)\(32\!\cdots\!88\)\(q^{41} + \)\(70\!\cdots\!48\)\(q^{42} + \)\(10\!\cdots\!20\)\(q^{43} - \)\(15\!\cdots\!68\)\(q^{44} - \)\(22\!\cdots\!60\)\(q^{45} - \)\(39\!\cdots\!48\)\(q^{46} - \)\(52\!\cdots\!20\)\(q^{47} - \)\(28\!\cdots\!60\)\(q^{48} - \)\(33\!\cdots\!50\)\(q^{49} + \)\(34\!\cdots\!00\)\(q^{50} + \)\(79\!\cdots\!16\)\(q^{51} + \)\(20\!\cdots\!12\)\(q^{52} - \)\(31\!\cdots\!68\)\(q^{53} - \)\(13\!\cdots\!64\)\(q^{54} + \)\(15\!\cdots\!20\)\(q^{55} + \)\(42\!\cdots\!20\)\(q^{56} - \)\(20\!\cdots\!32\)\(q^{57} + \)\(51\!\cdots\!24\)\(q^{58} + \)\(82\!\cdots\!64\)\(q^{59} - \)\(37\!\cdots\!60\)\(q^{60} - \)\(40\!\cdots\!40\)\(q^{61} - \)\(15\!\cdots\!68\)\(q^{62} - \)\(20\!\cdots\!36\)\(q^{63} - \)\(44\!\cdots\!64\)\(q^{64} + \)\(42\!\cdots\!20\)\(q^{65} - \)\(51\!\cdots\!08\)\(q^{66} + \)\(96\!\cdots\!12\)\(q^{67} + \)\(13\!\cdots\!04\)\(q^{68} + \)\(63\!\cdots\!36\)\(q^{69} + \)\(54\!\cdots\!60\)\(q^{70} + \)\(44\!\cdots\!24\)\(q^{71} - \)\(12\!\cdots\!56\)\(q^{72} - \)\(13\!\cdots\!08\)\(q^{73} + \)\(18\!\cdots\!76\)\(q^{74} - \)\(61\!\cdots\!50\)\(q^{75} - \)\(12\!\cdots\!64\)\(q^{76} + \)\(82\!\cdots\!12\)\(q^{77} - \)\(27\!\cdots\!28\)\(q^{78} - \)\(10\!\cdots\!80\)\(q^{79} + \)\(16\!\cdots\!60\)\(q^{80} + \)\(55\!\cdots\!22\)\(q^{81} - \)\(51\!\cdots\!48\)\(q^{82} - \)\(55\!\cdots\!44\)\(q^{83} - \)\(45\!\cdots\!36\)\(q^{84} - \)\(48\!\cdots\!40\)\(q^{85} + \)\(31\!\cdots\!88\)\(q^{86} - \)\(10\!\cdots\!24\)\(q^{87} + \)\(70\!\cdots\!36\)\(q^{88} + \)\(24\!\cdots\!36\)\(q^{89} - \)\(18\!\cdots\!60\)\(q^{90} - \)\(20\!\cdots\!28\)\(q^{91} + \)\(37\!\cdots\!36\)\(q^{92} - \)\(15\!\cdots\!24\)\(q^{93} + \)\(14\!\cdots\!04\)\(q^{94} - \)\(45\!\cdots\!00\)\(q^{95} + \)\(18\!\cdots\!88\)\(q^{96} + \)\(83\!\cdots\!52\)\(q^{97} - \)\(20\!\cdots\!08\)\(q^{98} - \)\(24\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −279461. −1.50764 −0.753818 0.657083i \(-0.771790\pi\)
−0.753818 + 0.657083i \(0.771790\pi\)
\(3\) 1.29140e8 0.577350
\(4\) 4.37389e10 1.27297
\(5\) −3.65354e11 −0.214160 −0.107080 0.994250i \(-0.534150\pi\)
−0.107080 + 0.994250i \(0.534150\pi\)
\(6\) −3.60897e13 −0.870435
\(7\) −6.36148e14 −1.03358 −0.516788 0.856113i \(-0.672872\pi\)
−0.516788 + 0.856113i \(0.672872\pi\)
\(8\) −2.62111e15 −0.411538
\(9\) 1.66772e16 0.333333
\(10\) 1.02102e17 0.322876
\(11\) 1.49276e17 0.0890467 0.0445234 0.999008i \(-0.485823\pi\)
0.0445234 + 0.999008i \(0.485823\pi\)
\(12\) 5.64845e18 0.734949
\(13\) 5.52590e19 1.77172 0.885858 0.463956i \(-0.153570\pi\)
0.885858 + 0.463956i \(0.153570\pi\)
\(14\) 1.77779e20 1.55826
\(15\) −4.71819e19 −0.123646
\(16\) −7.70358e20 −0.652519
\(17\) 1.81211e21 0.531285 0.265643 0.964072i \(-0.414416\pi\)
0.265643 + 0.964072i \(0.414416\pi\)
\(18\) −4.66063e21 −0.502546
\(19\) −3.32454e22 −1.39169 −0.695846 0.718191i \(-0.744970\pi\)
−0.695846 + 0.718191i \(0.744970\pi\)
\(20\) −1.59802e22 −0.272620
\(21\) −8.21522e22 −0.596735
\(22\) −4.17169e22 −0.134250
\(23\) 1.00717e24 1.48890 0.744451 0.667677i \(-0.232711\pi\)
0.744451 + 0.667677i \(0.232711\pi\)
\(24\) −3.38490e23 −0.237602
\(25\) −2.77690e24 −0.954135
\(26\) −1.54428e25 −2.67111
\(27\) 2.15369e24 0.192450
\(28\) −2.78244e25 −1.31571
\(29\) −4.49573e25 −1.15036 −0.575182 0.818026i \(-0.695069\pi\)
−0.575182 + 0.818026i \(0.695069\pi\)
\(30\) 1.31855e25 0.186413
\(31\) −2.23850e25 −0.178291 −0.0891453 0.996019i \(-0.528414\pi\)
−0.0891453 + 0.996019i \(0.528414\pi\)
\(32\) 3.05346e26 1.39530
\(33\) 1.92775e25 0.0514112
\(34\) −5.06414e26 −0.800985
\(35\) 2.32419e26 0.221351
\(36\) 7.29441e26 0.424323
\(37\) −2.91588e27 −1.05012 −0.525060 0.851065i \(-0.675957\pi\)
−0.525060 + 0.851065i \(0.675957\pi\)
\(38\) 9.29079e27 2.09817
\(39\) 7.13616e27 1.02290
\(40\) 9.57633e26 0.0881352
\(41\) −4.18186e27 −0.249834 −0.124917 0.992167i \(-0.539866\pi\)
−0.124917 + 0.992167i \(0.539866\pi\)
\(42\) 2.29584e28 0.899660
\(43\) −5.84123e28 −1.51638 −0.758188 0.652037i \(-0.773915\pi\)
−0.758188 + 0.652037i \(0.773915\pi\)
\(44\) 6.52916e27 0.113354
\(45\) −6.09308e27 −0.0713868
\(46\) −2.81465e29 −2.24472
\(47\) −5.23894e28 −0.286768 −0.143384 0.989667i \(-0.545798\pi\)
−0.143384 + 0.989667i \(0.545798\pi\)
\(48\) −9.94842e28 −0.376732
\(49\) 2.58653e28 0.0682788
\(50\) 7.76036e29 1.43849
\(51\) 2.34016e29 0.306738
\(52\) 2.41697e30 2.25534
\(53\) −2.64063e30 −1.76555 −0.882775 0.469796i \(-0.844327\pi\)
−0.882775 + 0.469796i \(0.844327\pi\)
\(54\) −6.01874e29 −0.290145
\(55\) −5.45386e28 −0.0190703
\(56\) 1.66741e30 0.425356
\(57\) −4.29331e30 −0.803493
\(58\) 1.25638e31 1.73433
\(59\) 2.44829e30 0.250584 0.125292 0.992120i \(-0.460013\pi\)
0.125292 + 0.992120i \(0.460013\pi\)
\(60\) −2.06368e30 −0.157397
\(61\) −1.37521e31 −0.785412 −0.392706 0.919664i \(-0.628461\pi\)
−0.392706 + 0.919664i \(0.628461\pi\)
\(62\) 6.25575e30 0.268797
\(63\) −1.06092e31 −0.344525
\(64\) −5.88631e31 −1.45109
\(65\) −2.01891e31 −0.379432
\(66\) −5.38732e30 −0.0775093
\(67\) −6.70306e31 −0.741249 −0.370625 0.928783i \(-0.620856\pi\)
−0.370625 + 0.928783i \(0.620856\pi\)
\(68\) 7.92595e31 0.676310
\(69\) 1.30066e32 0.859618
\(70\) −6.49522e31 −0.333717
\(71\) 4.91498e32 1.97015 0.985077 0.172113i \(-0.0550595\pi\)
0.985077 + 0.172113i \(0.0550595\pi\)
\(72\) −4.37127e31 −0.137179
\(73\) 1.37337e32 0.338561 0.169280 0.985568i \(-0.445856\pi\)
0.169280 + 0.985568i \(0.445856\pi\)
\(74\) 8.14875e32 1.58320
\(75\) −3.58609e32 −0.550870
\(76\) −1.45411e33 −1.77158
\(77\) −9.49616e31 −0.0920365
\(78\) −1.99428e33 −1.54216
\(79\) 1.07453e33 0.664879 0.332440 0.943125i \(-0.392128\pi\)
0.332440 + 0.943125i \(0.392128\pi\)
\(80\) 2.81454e32 0.139744
\(81\) 2.78128e32 0.111111
\(82\) 1.16867e33 0.376659
\(83\) −3.27927e33 −0.854890 −0.427445 0.904041i \(-0.640586\pi\)
−0.427445 + 0.904041i \(0.640586\pi\)
\(84\) −3.59325e33 −0.759625
\(85\) −6.62061e32 −0.113780
\(86\) 1.63240e34 2.28614
\(87\) −5.80579e33 −0.664163
\(88\) −3.91268e32 −0.0366461
\(89\) 3.27218e33 0.251485 0.125743 0.992063i \(-0.459869\pi\)
0.125743 + 0.992063i \(0.459869\pi\)
\(90\) 1.70278e33 0.107625
\(91\) −3.51529e34 −1.83120
\(92\) 4.40526e34 1.89533
\(93\) −2.89081e33 −0.102936
\(94\) 1.46408e34 0.432343
\(95\) 1.21463e34 0.298045
\(96\) 3.94324e34 0.805577
\(97\) −1.46799e34 −0.250160 −0.125080 0.992147i \(-0.539919\pi\)
−0.125080 + 0.992147i \(0.539919\pi\)
\(98\) −7.22835e33 −0.102940
\(99\) 2.48950e33 0.0296822
\(100\) −1.21458e35 −1.21458
\(101\) −2.12591e35 −1.78617 −0.893083 0.449893i \(-0.851462\pi\)
−0.893083 + 0.449893i \(0.851462\pi\)
\(102\) −6.53984e34 −0.462449
\(103\) −5.17494e34 −0.308499 −0.154250 0.988032i \(-0.549296\pi\)
−0.154250 + 0.988032i \(0.549296\pi\)
\(104\) −1.44840e35 −0.729129
\(105\) 3.00147e34 0.127797
\(106\) 7.37954e35 2.66181
\(107\) 1.53325e35 0.469242 0.234621 0.972087i \(-0.424615\pi\)
0.234621 + 0.972087i \(0.424615\pi\)
\(108\) 9.42002e34 0.244983
\(109\) 4.10693e35 0.908979 0.454489 0.890752i \(-0.349822\pi\)
0.454489 + 0.890752i \(0.349822\pi\)
\(110\) 1.52414e34 0.0287511
\(111\) −3.76557e35 −0.606288
\(112\) 4.90062e35 0.674428
\(113\) −1.00388e36 −1.18253 −0.591263 0.806479i \(-0.701371\pi\)
−0.591263 + 0.806479i \(0.701371\pi\)
\(114\) 1.19981e36 1.21138
\(115\) −3.67974e35 −0.318864
\(116\) −1.96638e36 −1.46438
\(117\) 9.21564e35 0.590572
\(118\) −6.84203e35 −0.377790
\(119\) −1.15277e36 −0.549124
\(120\) 1.23669e35 0.0508849
\(121\) −2.78796e36 −0.992071
\(122\) 3.84318e36 1.18412
\(123\) −5.40046e35 −0.144242
\(124\) −9.79097e35 −0.226958
\(125\) 2.07787e36 0.418498
\(126\) 2.96485e36 0.519419
\(127\) −4.93177e36 −0.752381 −0.376191 0.926542i \(-0.622766\pi\)
−0.376191 + 0.926542i \(0.622766\pi\)
\(128\) 5.95834e36 0.792412
\(129\) −7.54338e36 −0.875480
\(130\) 5.64208e36 0.572045
\(131\) −1.37663e37 −1.22059 −0.610294 0.792175i \(-0.708949\pi\)
−0.610294 + 0.792175i \(0.708949\pi\)
\(132\) 8.43177e35 0.0654448
\(133\) 2.11490e37 1.43842
\(134\) 1.87325e37 1.11753
\(135\) −7.86861e35 −0.0412152
\(136\) −4.74973e36 −0.218644
\(137\) 1.40102e37 0.567328 0.283664 0.958924i \(-0.408450\pi\)
0.283664 + 0.958924i \(0.408450\pi\)
\(138\) −3.63485e37 −1.29599
\(139\) 4.03059e37 1.26651 0.633256 0.773942i \(-0.281718\pi\)
0.633256 + 0.773942i \(0.281718\pi\)
\(140\) 1.01658e37 0.281773
\(141\) −6.76558e36 −0.165566
\(142\) −1.37355e38 −2.97028
\(143\) 8.24884e36 0.157766
\(144\) −1.28474e37 −0.217506
\(145\) 1.64253e37 0.246362
\(146\) −3.83803e37 −0.510427
\(147\) 3.34025e36 0.0394208
\(148\) −1.27537e38 −1.33677
\(149\) 1.09713e38 1.02211 0.511054 0.859548i \(-0.329255\pi\)
0.511054 + 0.859548i \(0.329255\pi\)
\(150\) 1.00217e38 0.830512
\(151\) 1.08195e38 0.798199 0.399099 0.916908i \(-0.369323\pi\)
0.399099 + 0.916908i \(0.369323\pi\)
\(152\) 8.71396e37 0.572734
\(153\) 3.02208e37 0.177095
\(154\) 2.65381e37 0.138758
\(155\) 8.17847e36 0.0381828
\(156\) 3.12127e38 1.30212
\(157\) 3.80493e38 1.41939 0.709697 0.704507i \(-0.248832\pi\)
0.709697 + 0.704507i \(0.248832\pi\)
\(158\) −3.00288e38 −1.00240
\(159\) −3.41012e38 −1.01934
\(160\) −1.11559e38 −0.298818
\(161\) −6.40710e38 −1.53889
\(162\) −7.77261e37 −0.167515
\(163\) −5.15630e38 −0.997826 −0.498913 0.866652i \(-0.666267\pi\)
−0.498913 + 0.866652i \(0.666267\pi\)
\(164\) −1.82910e38 −0.318031
\(165\) −7.04313e36 −0.0110102
\(166\) 9.16428e38 1.28886
\(167\) −2.92786e38 −0.370691 −0.185346 0.982673i \(-0.559340\pi\)
−0.185346 + 0.982673i \(0.559340\pi\)
\(168\) 2.15330e38 0.245579
\(169\) 2.08077e39 2.13898
\(170\) 1.85020e38 0.171539
\(171\) −5.54439e38 −0.463897
\(172\) −2.55489e39 −1.93030
\(173\) −2.25696e39 −1.54070 −0.770349 0.637623i \(-0.779918\pi\)
−0.770349 + 0.637623i \(0.779918\pi\)
\(174\) 1.62249e39 1.00132
\(175\) 1.76652e39 0.986171
\(176\) −1.14996e38 −0.0581047
\(177\) 3.16173e38 0.144675
\(178\) −9.14448e38 −0.379148
\(179\) 3.55925e39 1.33792 0.668961 0.743298i \(-0.266739\pi\)
0.668961 + 0.743298i \(0.266739\pi\)
\(180\) −2.66504e38 −0.0908732
\(181\) −4.44114e39 −1.37442 −0.687211 0.726458i \(-0.741165\pi\)
−0.687211 + 0.726458i \(0.741165\pi\)
\(182\) 9.82387e39 2.76079
\(183\) −1.77595e39 −0.453458
\(184\) −2.63990e39 −0.612740
\(185\) 1.06533e39 0.224894
\(186\) 8.07869e38 0.155190
\(187\) 2.70504e38 0.0473092
\(188\) −2.29146e39 −0.365047
\(189\) −1.37007e39 −0.198912
\(190\) −3.39443e39 −0.449344
\(191\) −8.19302e39 −0.989373 −0.494686 0.869072i \(-0.664717\pi\)
−0.494686 + 0.869072i \(0.664717\pi\)
\(192\) −7.60158e39 −0.837785
\(193\) 3.38085e39 0.340230 0.170115 0.985424i \(-0.445586\pi\)
0.170115 + 0.985424i \(0.445586\pi\)
\(194\) 4.10246e39 0.377150
\(195\) −2.60722e39 −0.219065
\(196\) 1.13132e39 0.0869168
\(197\) −1.27322e40 −0.894836 −0.447418 0.894325i \(-0.647656\pi\)
−0.447418 + 0.894325i \(0.647656\pi\)
\(198\) −6.95720e38 −0.0447500
\(199\) −7.27758e39 −0.428606 −0.214303 0.976767i \(-0.568748\pi\)
−0.214303 + 0.976767i \(0.568748\pi\)
\(200\) 7.27855e39 0.392663
\(201\) −8.65635e39 −0.427960
\(202\) 5.94111e40 2.69289
\(203\) 2.85995e40 1.18899
\(204\) 1.02356e40 0.390468
\(205\) 1.52786e39 0.0535046
\(206\) 1.44620e40 0.465105
\(207\) 1.67968e40 0.496301
\(208\) −4.25692e40 −1.15608
\(209\) −4.96273e39 −0.123926
\(210\) −8.38794e39 −0.192672
\(211\) −2.76616e40 −0.584701 −0.292351 0.956311i \(-0.594437\pi\)
−0.292351 + 0.956311i \(0.594437\pi\)
\(212\) −1.15498e41 −2.24749
\(213\) 6.34721e40 1.13747
\(214\) −4.28484e40 −0.707446
\(215\) 2.13412e40 0.324747
\(216\) −5.64506e39 −0.0792005
\(217\) 1.42402e40 0.184277
\(218\) −1.14773e41 −1.37041
\(219\) 1.77357e40 0.195468
\(220\) −2.38546e39 −0.0242759
\(221\) 1.00135e41 0.941287
\(222\) 1.05233e41 0.914062
\(223\) 3.35919e40 0.269712 0.134856 0.990865i \(-0.456943\pi\)
0.134856 + 0.990865i \(0.456943\pi\)
\(224\) −1.94245e41 −1.44215
\(225\) −4.63109e40 −0.318045
\(226\) 2.80547e41 1.78282
\(227\) 1.89749e41 1.11616 0.558081 0.829787i \(-0.311538\pi\)
0.558081 + 0.829787i \(0.311538\pi\)
\(228\) −1.87785e41 −1.02282
\(229\) −1.77014e41 −0.893071 −0.446536 0.894766i \(-0.647342\pi\)
−0.446536 + 0.894766i \(0.647342\pi\)
\(230\) 1.02835e41 0.480731
\(231\) −1.22634e40 −0.0531373
\(232\) 1.17838e41 0.473419
\(233\) −1.57002e40 −0.0585026 −0.0292513 0.999572i \(-0.509312\pi\)
−0.0292513 + 0.999572i \(0.509312\pi\)
\(234\) −2.57542e41 −0.890369
\(235\) 1.91407e40 0.0614144
\(236\) 1.07086e41 0.318986
\(237\) 1.38764e41 0.383868
\(238\) 3.22154e41 0.827879
\(239\) −2.98699e41 −0.713297 −0.356648 0.934239i \(-0.616081\pi\)
−0.356648 + 0.934239i \(0.616081\pi\)
\(240\) 3.63470e40 0.0806811
\(241\) −6.82984e40 −0.140965 −0.0704827 0.997513i \(-0.522454\pi\)
−0.0704827 + 0.997513i \(0.522454\pi\)
\(242\) 7.79127e41 1.49568
\(243\) 3.59175e40 0.0641500
\(244\) −6.01502e41 −0.999805
\(245\) −9.45000e39 −0.0146226
\(246\) 1.50922e41 0.217464
\(247\) −1.83710e42 −2.46568
\(248\) 5.86736e40 0.0733734
\(249\) −4.23485e41 −0.493571
\(250\) −5.80685e41 −0.630944
\(251\) −8.56382e40 −0.0867715 −0.0433858 0.999058i \(-0.513814\pi\)
−0.0433858 + 0.999058i \(0.513814\pi\)
\(252\) −4.64032e41 −0.438570
\(253\) 1.50347e41 0.132582
\(254\) 1.37824e42 1.13432
\(255\) −8.54987e40 −0.0656911
\(256\) 3.57394e41 0.256417
\(257\) 1.59187e42 1.06679 0.533393 0.845868i \(-0.320917\pi\)
0.533393 + 0.845868i \(0.320917\pi\)
\(258\) 2.10808e42 1.31991
\(259\) 1.85493e42 1.08538
\(260\) −8.83049e41 −0.483005
\(261\) −7.49761e41 −0.383455
\(262\) 3.84715e42 1.84020
\(263\) −1.67624e42 −0.750085 −0.375043 0.927008i \(-0.622372\pi\)
−0.375043 + 0.927008i \(0.622372\pi\)
\(264\) −5.05285e40 −0.0211576
\(265\) 9.64766e41 0.378111
\(266\) −5.91032e42 −2.16861
\(267\) 4.22570e41 0.145195
\(268\) −2.93184e42 −0.943587
\(269\) −8.26329e41 −0.249166 −0.124583 0.992209i \(-0.539759\pi\)
−0.124583 + 0.992209i \(0.539759\pi\)
\(270\) 2.19897e41 0.0621375
\(271\) 5.20129e42 1.37768 0.688840 0.724914i \(-0.258120\pi\)
0.688840 + 0.724914i \(0.258120\pi\)
\(272\) −1.39597e42 −0.346674
\(273\) −4.53965e42 −1.05725
\(274\) −3.91531e42 −0.855325
\(275\) −4.14524e41 −0.0849626
\(276\) 5.68895e42 1.09427
\(277\) −8.57159e41 −0.154762 −0.0773812 0.997002i \(-0.524656\pi\)
−0.0773812 + 0.997002i \(0.524656\pi\)
\(278\) −1.12639e43 −1.90944
\(279\) −3.73319e41 −0.0594302
\(280\) −6.09196e41 −0.0910944
\(281\) 7.78049e42 1.09307 0.546533 0.837438i \(-0.315947\pi\)
0.546533 + 0.837438i \(0.315947\pi\)
\(282\) 1.89072e42 0.249613
\(283\) −5.95094e41 −0.0738454 −0.0369227 0.999318i \(-0.511756\pi\)
−0.0369227 + 0.999318i \(0.511756\pi\)
\(284\) 2.14976e43 2.50795
\(285\) 1.56858e42 0.172076
\(286\) −2.30523e42 −0.237853
\(287\) 2.66028e42 0.258222
\(288\) 5.09231e42 0.465100
\(289\) −8.34982e42 −0.717736
\(290\) −4.59025e42 −0.371425
\(291\) −1.89576e42 −0.144430
\(292\) 6.00696e42 0.430977
\(293\) −1.97041e43 −1.33160 −0.665800 0.746130i \(-0.731910\pi\)
−0.665800 + 0.746130i \(0.731910\pi\)
\(294\) −9.33470e41 −0.0594322
\(295\) −8.94495e41 −0.0536652
\(296\) 7.64283e42 0.432165
\(297\) 3.21495e41 0.0171371
\(298\) −3.06605e43 −1.54097
\(299\) 5.56553e43 2.63791
\(300\) −1.56852e43 −0.701241
\(301\) 3.71589e43 1.56729
\(302\) −3.02363e43 −1.20339
\(303\) −2.74541e43 −1.03124
\(304\) 2.56108e43 0.908105
\(305\) 5.02439e42 0.168204
\(306\) −8.44556e42 −0.266995
\(307\) −3.56177e43 −1.06352 −0.531759 0.846896i \(-0.678469\pi\)
−0.531759 + 0.846896i \(0.678469\pi\)
\(308\) −4.15351e42 −0.117160
\(309\) −6.68293e42 −0.178112
\(310\) −2.28557e42 −0.0575658
\(311\) 3.70185e43 0.881276 0.440638 0.897685i \(-0.354752\pi\)
0.440638 + 0.897685i \(0.354752\pi\)
\(312\) −1.87046e43 −0.420963
\(313\) −4.19837e43 −0.893419 −0.446709 0.894679i \(-0.647404\pi\)
−0.446709 + 0.894679i \(0.647404\pi\)
\(314\) −1.06333e44 −2.13993
\(315\) 3.87610e42 0.0737837
\(316\) 4.69986e43 0.846371
\(317\) 3.62720e43 0.618066 0.309033 0.951051i \(-0.399995\pi\)
0.309033 + 0.951051i \(0.399995\pi\)
\(318\) 9.52995e43 1.53680
\(319\) −6.71104e42 −0.102436
\(320\) 2.15059e43 0.310765
\(321\) 1.98004e43 0.270917
\(322\) 1.79054e44 2.32009
\(323\) −6.02441e43 −0.739385
\(324\) 1.21650e43 0.141441
\(325\) −1.53449e44 −1.69046
\(326\) 1.44099e44 1.50436
\(327\) 5.30370e43 0.524799
\(328\) 1.09611e43 0.102816
\(329\) 3.33274e43 0.296397
\(330\) 1.96828e42 0.0165994
\(331\) −1.52756e44 −1.22182 −0.610911 0.791700i \(-0.709197\pi\)
−0.610911 + 0.791700i \(0.709197\pi\)
\(332\) −1.43432e44 −1.08825
\(333\) −4.86286e43 −0.350040
\(334\) 8.18224e43 0.558868
\(335\) 2.44899e43 0.158746
\(336\) 6.32867e43 0.389381
\(337\) −1.48437e44 −0.867002 −0.433501 0.901153i \(-0.642722\pi\)
−0.433501 + 0.901153i \(0.642722\pi\)
\(338\) −5.81495e44 −3.22481
\(339\) −1.29642e44 −0.682732
\(340\) −2.89578e43 −0.144839
\(341\) −3.34155e42 −0.0158762
\(342\) 1.54944e44 0.699388
\(343\) 2.24531e44 0.963004
\(344\) 1.53105e44 0.624046
\(345\) −4.75203e43 −0.184096
\(346\) 6.30734e44 2.32281
\(347\) 4.00770e44 1.40323 0.701616 0.712555i \(-0.252462\pi\)
0.701616 + 0.712555i \(0.252462\pi\)
\(348\) −2.53939e44 −0.845459
\(349\) 9.71517e43 0.307614 0.153807 0.988101i \(-0.450847\pi\)
0.153807 + 0.988101i \(0.450847\pi\)
\(350\) −4.93674e44 −1.48679
\(351\) 1.19011e44 0.340967
\(352\) 4.55808e43 0.124247
\(353\) 5.81527e44 1.50839 0.754193 0.656653i \(-0.228028\pi\)
0.754193 + 0.656653i \(0.228028\pi\)
\(354\) −8.83581e43 −0.218117
\(355\) −1.79571e44 −0.421929
\(356\) 1.43122e44 0.320133
\(357\) −1.48869e44 −0.317037
\(358\) −9.94673e44 −2.01710
\(359\) −3.64874e43 −0.0704676 −0.0352338 0.999379i \(-0.511218\pi\)
−0.0352338 + 0.999379i \(0.511218\pi\)
\(360\) 1.59706e43 0.0293784
\(361\) 5.34595e44 0.936805
\(362\) 1.24113e45 2.07213
\(363\) −3.60038e44 −0.572772
\(364\) −1.53755e45 −2.33107
\(365\) −5.01766e43 −0.0725063
\(366\) 4.96309e44 0.683650
\(367\) 6.94503e44 0.912049 0.456025 0.889967i \(-0.349273\pi\)
0.456025 + 0.889967i \(0.349273\pi\)
\(368\) −7.75883e44 −0.971537
\(369\) −6.97416e43 −0.0832780
\(370\) −2.97718e44 −0.339059
\(371\) 1.67983e45 1.82483
\(372\) −1.26441e44 −0.131034
\(373\) −1.97985e45 −1.95762 −0.978808 0.204781i \(-0.934352\pi\)
−0.978808 + 0.204781i \(0.934352\pi\)
\(374\) −7.55954e43 −0.0713251
\(375\) 2.68337e44 0.241620
\(376\) 1.37318e44 0.118016
\(377\) −2.48429e45 −2.03812
\(378\) 3.82881e44 0.299887
\(379\) 1.79049e45 1.33902 0.669508 0.742805i \(-0.266505\pi\)
0.669508 + 0.742805i \(0.266505\pi\)
\(380\) 5.31267e44 0.379402
\(381\) −6.36890e44 −0.434387
\(382\) 2.28963e45 1.49162
\(383\) −1.49796e45 −0.932225 −0.466113 0.884725i \(-0.654346\pi\)
−0.466113 + 0.884725i \(0.654346\pi\)
\(384\) 7.69461e44 0.457499
\(385\) 3.46946e43 0.0197106
\(386\) −9.44816e44 −0.512943
\(387\) −9.74153e44 −0.505458
\(388\) −6.42082e44 −0.318446
\(389\) 1.77359e45 0.840882 0.420441 0.907320i \(-0.361875\pi\)
0.420441 + 0.907320i \(0.361875\pi\)
\(390\) 7.28618e44 0.330270
\(391\) 1.82510e45 0.791032
\(392\) −6.77957e43 −0.0280993
\(393\) −1.77778e45 −0.704707
\(394\) 3.55815e45 1.34909
\(395\) −3.92583e44 −0.142391
\(396\) 1.08888e44 0.0377846
\(397\) −2.45730e44 −0.0815876 −0.0407938 0.999168i \(-0.512989\pi\)
−0.0407938 + 0.999168i \(0.512989\pi\)
\(398\) 2.03380e45 0.646182
\(399\) 2.73118e45 0.830471
\(400\) 2.13921e45 0.622591
\(401\) −3.47243e45 −0.967401 −0.483701 0.875234i \(-0.660708\pi\)
−0.483701 + 0.875234i \(0.660708\pi\)
\(402\) 2.41911e45 0.645209
\(403\) −1.23698e45 −0.315880
\(404\) −9.29851e45 −2.27373
\(405\) −1.01615e44 −0.0237956
\(406\) −7.99245e45 −1.79256
\(407\) −4.35271e44 −0.0935098
\(408\) −6.13381e44 −0.126234
\(409\) −5.60182e45 −1.10451 −0.552257 0.833674i \(-0.686233\pi\)
−0.552257 + 0.833674i \(0.686233\pi\)
\(410\) −4.26978e44 −0.0806655
\(411\) 1.80928e45 0.327547
\(412\) −2.26346e45 −0.392710
\(413\) −1.55748e45 −0.258998
\(414\) −4.69405e45 −0.748242
\(415\) 1.19809e45 0.183084
\(416\) 1.68731e46 2.47208
\(417\) 5.20511e45 0.731221
\(418\) 1.38689e45 0.186835
\(419\) 1.30103e46 1.68090 0.840449 0.541891i \(-0.182291\pi\)
0.840449 + 0.541891i \(0.182291\pi\)
\(420\) 1.31281e45 0.162682
\(421\) −3.23759e45 −0.384844 −0.192422 0.981312i \(-0.561634\pi\)
−0.192422 + 0.981312i \(0.561634\pi\)
\(422\) 7.73034e45 0.881517
\(423\) −8.73708e44 −0.0955894
\(424\) 6.92138e45 0.726591
\(425\) −5.03204e45 −0.506918
\(426\) −1.77380e46 −1.71489
\(427\) 8.74838e45 0.811783
\(428\) 6.70626e45 0.597330
\(429\) 1.06526e45 0.0910860
\(430\) −5.96404e45 −0.489601
\(431\) −7.33523e45 −0.578178 −0.289089 0.957302i \(-0.593352\pi\)
−0.289089 + 0.957302i \(0.593352\pi\)
\(432\) −1.65912e45 −0.125577
\(433\) −3.13432e44 −0.0227827 −0.0113913 0.999935i \(-0.503626\pi\)
−0.0113913 + 0.999935i \(0.503626\pi\)
\(434\) −3.97958e45 −0.277823
\(435\) 2.12117e45 0.142237
\(436\) 1.79633e46 1.15710
\(437\) −3.34838e46 −2.07209
\(438\) −4.95644e45 −0.294695
\(439\) −4.96227e45 −0.283499 −0.141749 0.989903i \(-0.545273\pi\)
−0.141749 + 0.989903i \(0.545273\pi\)
\(440\) 1.42952e44 0.00784815
\(441\) 4.31360e44 0.0227596
\(442\) −2.79839e46 −1.41912
\(443\) 3.90477e46 1.90340 0.951701 0.307026i \(-0.0993340\pi\)
0.951701 + 0.307026i \(0.0993340\pi\)
\(444\) −1.64702e46 −0.771785
\(445\) −1.19551e45 −0.0538581
\(446\) −9.38765e45 −0.406627
\(447\) 1.41683e46 0.590115
\(448\) 3.74456e46 1.49981
\(449\) 9.78942e45 0.377091 0.188545 0.982064i \(-0.439623\pi\)
0.188545 + 0.982064i \(0.439623\pi\)
\(450\) 1.29421e46 0.479497
\(451\) −6.24251e44 −0.0222469
\(452\) −4.39088e46 −1.50532
\(453\) 1.39723e46 0.460840
\(454\) −5.30275e46 −1.68277
\(455\) 1.28433e46 0.392171
\(456\) 1.12532e46 0.330668
\(457\) −7.87990e45 −0.222837 −0.111419 0.993774i \(-0.535539\pi\)
−0.111419 + 0.993774i \(0.535539\pi\)
\(458\) 4.94685e46 1.34643
\(459\) 3.90272e45 0.102246
\(460\) −1.60948e46 −0.405904
\(461\) −6.50894e46 −1.58032 −0.790158 0.612903i \(-0.790002\pi\)
−0.790158 + 0.612903i \(0.790002\pi\)
\(462\) 3.42713e45 0.0801118
\(463\) 4.77272e46 1.07423 0.537117 0.843508i \(-0.319513\pi\)
0.537117 + 0.843508i \(0.319513\pi\)
\(464\) 3.46332e46 0.750634
\(465\) 1.05617e45 0.0220448
\(466\) 4.38759e45 0.0882008
\(467\) −3.34554e46 −0.647769 −0.323885 0.946097i \(-0.604989\pi\)
−0.323885 + 0.946097i \(0.604989\pi\)
\(468\) 4.03082e46 0.751780
\(469\) 4.26414e46 0.766137
\(470\) −5.34909e45 −0.0925906
\(471\) 4.91369e46 0.819487
\(472\) −6.41724e45 −0.103125
\(473\) −8.71956e45 −0.135028
\(474\) −3.87793e46 −0.578734
\(475\) 9.23190e46 1.32786
\(476\) −5.04208e46 −0.699017
\(477\) −4.40383e46 −0.588517
\(478\) 8.34748e46 1.07539
\(479\) −9.78794e46 −1.21568 −0.607841 0.794059i \(-0.707964\pi\)
−0.607841 + 0.794059i \(0.707964\pi\)
\(480\) −1.44068e46 −0.172523
\(481\) −1.61129e47 −1.86052
\(482\) 1.90868e46 0.212525
\(483\) −8.27414e46 −0.888481
\(484\) −1.21942e47 −1.26288
\(485\) 5.36336e45 0.0535743
\(486\) −1.00376e46 −0.0967150
\(487\) 1.03689e47 0.963777 0.481889 0.876232i \(-0.339951\pi\)
0.481889 + 0.876232i \(0.339951\pi\)
\(488\) 3.60458e46 0.323227
\(489\) −6.65885e46 −0.576095
\(490\) 2.64091e45 0.0220456
\(491\) 1.30638e46 0.105231 0.0526155 0.998615i \(-0.483244\pi\)
0.0526155 + 0.998615i \(0.483244\pi\)
\(492\) −2.36210e46 −0.183615
\(493\) −8.14674e46 −0.611171
\(494\) 5.13400e47 3.71735
\(495\) −9.09551e44 −0.00635676
\(496\) 1.72445e46 0.116338
\(497\) −3.12665e47 −2.03630
\(498\) 1.18348e47 0.744126
\(499\) 1.66085e46 0.100826 0.0504129 0.998728i \(-0.483946\pi\)
0.0504129 + 0.998728i \(0.483946\pi\)
\(500\) 9.08838e46 0.532735
\(501\) −3.78105e46 −0.214019
\(502\) 2.39326e46 0.130820
\(503\) 2.15922e47 1.13987 0.569937 0.821689i \(-0.306968\pi\)
0.569937 + 0.821689i \(0.306968\pi\)
\(504\) 2.78077e46 0.141785
\(505\) 7.76712e46 0.382526
\(506\) −4.20160e46 −0.199885
\(507\) 2.68711e47 1.23494
\(508\) −2.15710e47 −0.957758
\(509\) 3.50805e47 1.50489 0.752444 0.658656i \(-0.228875\pi\)
0.752444 + 0.658656i \(0.228875\pi\)
\(510\) 2.38936e46 0.0990383
\(511\) −8.73665e46 −0.349928
\(512\) −3.04605e47 −1.17900
\(513\) −7.16003e46 −0.267831
\(514\) −4.44865e47 −1.60832
\(515\) 1.89069e46 0.0660683
\(516\) −3.29939e47 −1.11446
\(517\) −7.82048e45 −0.0255358
\(518\) −5.18381e47 −1.63636
\(519\) −2.91464e47 −0.889522
\(520\) 5.29178e46 0.156151
\(521\) 4.99886e47 1.42630 0.713149 0.701012i \(-0.247268\pi\)
0.713149 + 0.701012i \(0.247268\pi\)
\(522\) 2.09529e47 0.578110
\(523\) −2.90357e46 −0.0774733 −0.0387367 0.999249i \(-0.512333\pi\)
−0.0387367 + 0.999249i \(0.512333\pi\)
\(524\) −6.02122e47 −1.55377
\(525\) 2.28128e47 0.569366
\(526\) 4.68444e47 1.13086
\(527\) −4.05641e46 −0.0947231
\(528\) −1.48506e46 −0.0335468
\(529\) 5.56807e47 1.21683
\(530\) −2.69615e47 −0.570054
\(531\) 4.08306e46 0.0835280
\(532\) 9.25032e47 1.83106
\(533\) −2.31085e47 −0.442635
\(534\) −1.18092e47 −0.218901
\(535\) −5.60179e46 −0.100493
\(536\) 1.75694e47 0.305052
\(537\) 4.59642e47 0.772449
\(538\) 2.30927e47 0.375651
\(539\) 3.86107e45 0.00608001
\(540\) −3.44164e46 −0.0524657
\(541\) −7.56060e47 −1.11585 −0.557923 0.829893i \(-0.688402\pi\)
−0.557923 + 0.829893i \(0.688402\pi\)
\(542\) −1.45356e48 −2.07704
\(543\) −5.73530e47 −0.793522
\(544\) 5.53320e47 0.741302
\(545\) −1.50048e47 −0.194667
\(546\) 1.26866e48 1.59394
\(547\) −5.49459e47 −0.668586 −0.334293 0.942469i \(-0.608497\pi\)
−0.334293 + 0.942469i \(0.608497\pi\)
\(548\) 6.12790e47 0.722191
\(549\) −2.29347e47 −0.261804
\(550\) 1.15844e47 0.128093
\(551\) 1.49462e48 1.60095
\(552\) −3.40918e47 −0.353766
\(553\) −6.83557e47 −0.687203
\(554\) 2.39543e47 0.233325
\(555\) 1.37577e47 0.129843
\(556\) 1.76293e48 1.61223
\(557\) 1.06798e48 0.946449 0.473225 0.880942i \(-0.343090\pi\)
0.473225 + 0.880942i \(0.343090\pi\)
\(558\) 1.04328e47 0.0895991
\(559\) −3.22781e48 −2.68659
\(560\) −1.79046e47 −0.144436
\(561\) 3.49329e46 0.0273140
\(562\) −2.17435e48 −1.64795
\(563\) −2.95577e47 −0.217157 −0.108578 0.994088i \(-0.534630\pi\)
−0.108578 + 0.994088i \(0.534630\pi\)
\(564\) −2.95919e47 −0.210760
\(565\) 3.66773e47 0.253250
\(566\) 1.66306e47 0.111332
\(567\) −1.76931e47 −0.114842
\(568\) −1.28827e48 −0.810794
\(569\) 1.55924e47 0.0951587 0.0475794 0.998867i \(-0.484849\pi\)
0.0475794 + 0.998867i \(0.484849\pi\)
\(570\) −4.38357e47 −0.259429
\(571\) 2.44889e48 1.40552 0.702761 0.711426i \(-0.251950\pi\)
0.702761 + 0.711426i \(0.251950\pi\)
\(572\) 3.60795e47 0.200831
\(573\) −1.05805e48 −0.571215
\(574\) −7.43445e47 −0.389306
\(575\) −2.79681e48 −1.42061
\(576\) −9.81670e47 −0.483695
\(577\) 2.16685e48 1.03575 0.517873 0.855458i \(-0.326724\pi\)
0.517873 + 0.855458i \(0.326724\pi\)
\(578\) 2.33345e48 1.08209
\(579\) 4.36603e47 0.196432
\(580\) 7.18426e47 0.313612
\(581\) 2.08610e48 0.883594
\(582\) 5.29792e47 0.217748
\(583\) −3.94183e47 −0.157216
\(584\) −3.59974e47 −0.139331
\(585\) −3.36697e47 −0.126477
\(586\) 5.50654e48 2.00757
\(587\) 3.51258e47 0.124296 0.0621482 0.998067i \(-0.480205\pi\)
0.0621482 + 0.998067i \(0.480205\pi\)
\(588\) 1.46099e47 0.0501814
\(589\) 7.44199e47 0.248125
\(590\) 2.49977e47 0.0809076
\(591\) −1.64423e48 −0.516634
\(592\) 2.24627e48 0.685224
\(593\) 3.58906e47 0.106298 0.0531489 0.998587i \(-0.483074\pi\)
0.0531489 + 0.998587i \(0.483074\pi\)
\(594\) −8.98454e46 −0.0258364
\(595\) 4.21169e47 0.117601
\(596\) 4.79871e48 1.30111
\(597\) −9.39828e47 −0.247456
\(598\) −1.55535e49 −3.97702
\(599\) −2.08154e48 −0.516911 −0.258456 0.966023i \(-0.583214\pi\)
−0.258456 + 0.966023i \(0.583214\pi\)
\(600\) 9.39953e47 0.226704
\(601\) −1.00213e48 −0.234758 −0.117379 0.993087i \(-0.537449\pi\)
−0.117379 + 0.993087i \(0.537449\pi\)
\(602\) −1.03845e49 −2.36290
\(603\) −1.11788e48 −0.247083
\(604\) 4.73233e48 1.01608
\(605\) 1.01859e48 0.212462
\(606\) 7.67235e48 1.55474
\(607\) −4.36540e48 −0.859453 −0.429726 0.902959i \(-0.641390\pi\)
−0.429726 + 0.902959i \(0.641390\pi\)
\(608\) −1.01513e49 −1.94183
\(609\) 3.69334e48 0.686463
\(610\) −1.40412e48 −0.253591
\(611\) −2.89499e48 −0.508072
\(612\) 1.32183e48 0.225437
\(613\) 9.45680e48 1.56742 0.783711 0.621126i \(-0.213324\pi\)
0.783711 + 0.621126i \(0.213324\pi\)
\(614\) 9.95378e48 1.60340
\(615\) 1.97308e47 0.0308909
\(616\) 2.48905e47 0.0378765
\(617\) −6.32292e47 −0.0935249 −0.0467625 0.998906i \(-0.514890\pi\)
−0.0467625 + 0.998906i \(0.514890\pi\)
\(618\) 1.86762e48 0.268528
\(619\) 2.65684e48 0.371346 0.185673 0.982612i \(-0.440553\pi\)
0.185673 + 0.982612i \(0.440553\pi\)
\(620\) 3.57717e47 0.0486055
\(621\) 2.16914e48 0.286539
\(622\) −1.03452e49 −1.32864
\(623\) −2.08159e48 −0.259929
\(624\) −5.49740e48 −0.667462
\(625\) 7.32268e48 0.864510
\(626\) 1.17328e49 1.34695
\(627\) −6.40888e47 −0.0715485
\(628\) 1.66423e49 1.80684
\(629\) −5.28389e48 −0.557914
\(630\) −1.08322e48 −0.111239
\(631\) 2.52797e47 0.0252498 0.0126249 0.999920i \(-0.495981\pi\)
0.0126249 + 0.999920i \(0.495981\pi\)
\(632\) −2.81645e48 −0.273623
\(633\) −3.57222e48 −0.337577
\(634\) −1.01366e49 −0.931819
\(635\) 1.80184e48 0.161130
\(636\) −1.49155e49 −1.29759
\(637\) 1.42929e48 0.120971
\(638\) 1.87548e48 0.154436
\(639\) 8.19679e48 0.656718
\(640\) −2.17691e48 −0.169703
\(641\) 1.43723e49 1.09021 0.545105 0.838368i \(-0.316490\pi\)
0.545105 + 0.838368i \(0.316490\pi\)
\(642\) −5.53345e48 −0.408444
\(643\) −3.98874e48 −0.286513 −0.143256 0.989686i \(-0.545757\pi\)
−0.143256 + 0.989686i \(0.545757\pi\)
\(644\) −2.80239e49 −1.95896
\(645\) 2.75601e48 0.187493
\(646\) 1.68359e49 1.11472
\(647\) −2.33006e49 −1.50156 −0.750781 0.660552i \(-0.770322\pi\)
−0.750781 + 0.660552i \(0.770322\pi\)
\(648\) −7.29004e47 −0.0457265
\(649\) 3.65471e47 0.0223137
\(650\) 4.28830e49 2.54860
\(651\) 1.83898e48 0.106392
\(652\) −2.25531e49 −1.27020
\(653\) 1.17028e49 0.641666 0.320833 0.947136i \(-0.396037\pi\)
0.320833 + 0.947136i \(0.396037\pi\)
\(654\) −1.48218e49 −0.791207
\(655\) 5.02957e48 0.261402
\(656\) 3.22153e48 0.163021
\(657\) 2.29039e48 0.112854
\(658\) −9.31372e48 −0.446859
\(659\) −1.32090e49 −0.617128 −0.308564 0.951204i \(-0.599848\pi\)
−0.308564 + 0.951204i \(0.599848\pi\)
\(660\) −3.08058e47 −0.0140157
\(661\) −3.80316e49 −1.68508 −0.842538 0.538637i \(-0.818940\pi\)
−0.842538 + 0.538637i \(0.818940\pi\)
\(662\) 4.26893e49 1.84206
\(663\) 1.29315e49 0.543452
\(664\) 8.59531e48 0.351820
\(665\) −7.72686e48 −0.308052
\(666\) 1.35898e49 0.527734
\(667\) −4.52797e49 −1.71278
\(668\) −1.28061e49 −0.471879
\(669\) 4.33807e48 0.155718
\(670\) −6.84399e48 −0.239332
\(671\) −2.05286e48 −0.0699383
\(672\) −2.50848e49 −0.832625
\(673\) 1.15552e49 0.373692 0.186846 0.982389i \(-0.440173\pi\)
0.186846 + 0.982389i \(0.440173\pi\)
\(674\) 4.14825e49 1.30712
\(675\) −5.98059e48 −0.183623
\(676\) 9.10106e49 2.72286
\(677\) 5.18340e48 0.151117 0.0755585 0.997141i \(-0.475926\pi\)
0.0755585 + 0.997141i \(0.475926\pi\)
\(678\) 3.62298e49 1.02931
\(679\) 9.33858e48 0.258559
\(680\) 1.73533e48 0.0468249
\(681\) 2.45042e49 0.644416
\(682\) 9.33834e47 0.0239355
\(683\) 4.66690e49 1.16591 0.582957 0.812503i \(-0.301896\pi\)
0.582957 + 0.812503i \(0.301896\pi\)
\(684\) −2.42505e49 −0.590527
\(685\) −5.11868e48 −0.121499
\(686\) −6.27476e49 −1.45186
\(687\) −2.28596e49 −0.515615
\(688\) 4.49984e49 0.989463
\(689\) −1.45919e50 −3.12805
\(690\) 1.32801e49 0.277550
\(691\) 5.17806e49 1.05512 0.527559 0.849519i \(-0.323107\pi\)
0.527559 + 0.849519i \(0.323107\pi\)
\(692\) −9.87170e49 −1.96126
\(693\) −1.58369e48 −0.0306788
\(694\) −1.12000e50 −2.11557
\(695\) −1.47259e49 −0.271237
\(696\) 1.52176e49 0.273328
\(697\) −7.57797e48 −0.132733
\(698\) −2.71501e49 −0.463770
\(699\) −2.02752e48 −0.0337765
\(700\) 7.72655e49 1.25537
\(701\) 1.34782e49 0.213582 0.106791 0.994281i \(-0.465942\pi\)
0.106791 + 0.994281i \(0.465942\pi\)
\(702\) −3.32590e49 −0.514055
\(703\) 9.69394e49 1.46144
\(704\) −8.78684e48 −0.129214
\(705\) 2.47183e48 0.0354576
\(706\) −1.62514e50 −2.27410
\(707\) 1.35240e50 1.84614
\(708\) 1.38291e49 0.184166
\(709\) 5.95415e49 0.773589 0.386795 0.922166i \(-0.373582\pi\)
0.386795 + 0.922166i \(0.373582\pi\)
\(710\) 5.01831e49 0.636116
\(711\) 1.79201e49 0.221626
\(712\) −8.57674e48 −0.103496
\(713\) −2.25456e49 −0.265457
\(714\) 4.16030e49 0.477976
\(715\) −3.01375e48 −0.0337871
\(716\) 1.55678e50 1.70313
\(717\) −3.85740e49 −0.411822
\(718\) 1.01968e49 0.106240
\(719\) 9.50970e49 0.966966 0.483483 0.875354i \(-0.339371\pi\)
0.483483 + 0.875354i \(0.339371\pi\)
\(720\) 4.69386e48 0.0465812
\(721\) 3.29203e49 0.318857
\(722\) −1.49399e50 −1.41236
\(723\) −8.82007e48 −0.0813864
\(724\) −1.94251e50 −1.74960
\(725\) 1.24842e50 1.09760
\(726\) 1.00617e50 0.863533
\(727\) −7.28338e49 −0.610212 −0.305106 0.952318i \(-0.598692\pi\)
−0.305106 + 0.952318i \(0.598692\pi\)
\(728\) 9.21395e49 0.753610
\(729\) 4.63840e48 0.0370370
\(730\) 1.40224e49 0.109313
\(731\) −1.05849e50 −0.805628
\(732\) −7.76781e49 −0.577238
\(733\) −2.38824e50 −1.73284 −0.866421 0.499314i \(-0.833585\pi\)
−0.866421 + 0.499314i \(0.833585\pi\)
\(734\) −1.94087e50 −1.37504
\(735\) −1.22037e48 −0.00844237
\(736\) 3.07536e50 2.07747
\(737\) −1.00061e49 −0.0660058
\(738\) 1.94901e49 0.125553
\(739\) 2.40229e50 1.51129 0.755646 0.654980i \(-0.227323\pi\)
0.755646 + 0.654980i \(0.227323\pi\)
\(740\) 4.65963e49 0.286283
\(741\) −2.37244e50 −1.42356
\(742\) −4.69448e50 −2.75118
\(743\) −3.09674e49 −0.177256 −0.0886279 0.996065i \(-0.528248\pi\)
−0.0886279 + 0.996065i \(0.528248\pi\)
\(744\) 7.57712e48 0.0423621
\(745\) −4.00840e49 −0.218895
\(746\) 5.53291e50 2.95137
\(747\) −5.46889e49 −0.284963
\(748\) 1.18315e49 0.0602232
\(749\) −9.75373e49 −0.484997
\(750\) −7.49898e49 −0.364275
\(751\) 4.66674e49 0.221470 0.110735 0.993850i \(-0.464680\pi\)
0.110735 + 0.993850i \(0.464680\pi\)
\(752\) 4.03586e49 0.187122
\(753\) −1.10593e49 −0.0500976
\(754\) 6.94264e50 3.07274
\(755\) −3.95296e49 −0.170943
\(756\) −5.99252e49 −0.253208
\(757\) −1.36549e50 −0.563780 −0.281890 0.959447i \(-0.590961\pi\)
−0.281890 + 0.959447i \(0.590961\pi\)
\(758\) −5.00373e50 −2.01875
\(759\) 1.94158e49 0.0765462
\(760\) −3.18368e49 −0.122657
\(761\) 2.28332e48 0.00859677 0.00429839 0.999991i \(-0.498632\pi\)
0.00429839 + 0.999991i \(0.498632\pi\)
\(762\) 1.77986e50 0.654899
\(763\) −2.61262e50 −0.939498
\(764\) −3.58353e50 −1.25944
\(765\) −1.10413e49 −0.0379267
\(766\) 4.18621e50 1.40546
\(767\) 1.35290e50 0.443964
\(768\) 4.61539e49 0.148043
\(769\) −5.95370e49 −0.186671 −0.0933354 0.995635i \(-0.529753\pi\)
−0.0933354 + 0.995635i \(0.529753\pi\)
\(770\) −9.69580e48 −0.0297164
\(771\) 2.05574e50 0.615909
\(772\) 1.47874e50 0.433102
\(773\) 3.53372e50 1.01179 0.505895 0.862595i \(-0.331162\pi\)
0.505895 + 0.862595i \(0.331162\pi\)
\(774\) 2.72238e50 0.762048
\(775\) 6.21610e49 0.170113
\(776\) 3.84776e49 0.102950
\(777\) 2.39546e50 0.626644
\(778\) −4.95650e50 −1.26774
\(779\) 1.39027e50 0.347692
\(780\) −1.14037e50 −0.278863
\(781\) 7.33688e49 0.175436
\(782\) −5.10046e50 −1.19259
\(783\) −9.68243e49 −0.221388
\(784\) −1.99255e49 −0.0445532
\(785\) −1.39015e50 −0.303978
\(786\) 4.96821e50 1.06244
\(787\) −2.59047e50 −0.541777 −0.270888 0.962611i \(-0.587317\pi\)
−0.270888 + 0.962611i \(0.587317\pi\)
\(788\) −5.56891e50 −1.13910
\(789\) −2.16470e50 −0.433062
\(790\) 1.09712e50 0.214674
\(791\) 6.38619e50 1.22223
\(792\) −6.52525e48 −0.0122154
\(793\) −7.59928e50 −1.39153
\(794\) 6.86720e49 0.123004
\(795\) 1.24590e50 0.218302
\(796\) −3.18313e50 −0.545602
\(797\) −2.98933e49 −0.0501249 −0.0250624 0.999686i \(-0.507978\pi\)
−0.0250624 + 0.999686i \(0.507978\pi\)
\(798\) −7.63259e50 −1.25205
\(799\) −9.49353e49 −0.152356
\(800\) −8.47915e50 −1.33130
\(801\) 5.45708e49 0.0838284
\(802\) 9.70409e50 1.45849
\(803\) 2.05011e49 0.0301477
\(804\) −3.78619e50 −0.544780
\(805\) 2.34086e50 0.329570
\(806\) 3.45687e50 0.476233
\(807\) −1.06712e50 −0.143856
\(808\) 5.57225e50 0.735075
\(809\) −5.81772e50 −0.751023 −0.375512 0.926818i \(-0.622533\pi\)
−0.375512 + 0.926818i \(0.622533\pi\)
\(810\) 2.83976e49 0.0358751
\(811\) −2.08851e50 −0.258209 −0.129104 0.991631i \(-0.541210\pi\)
−0.129104 + 0.991631i \(0.541210\pi\)
\(812\) 1.25091e51 1.51355
\(813\) 6.71695e50 0.795404
\(814\) 1.21641e50 0.140979
\(815\) 1.88388e50 0.213695
\(816\) −1.80276e50 −0.200152
\(817\) 1.94194e51 2.11033
\(818\) 1.56549e51 1.66521
\(819\) −5.86251e50 −0.610401
\(820\) 6.68269e49 0.0681097
\(821\) 4.12142e50 0.411189 0.205595 0.978637i \(-0.434087\pi\)
0.205595 + 0.978637i \(0.434087\pi\)
\(822\) −5.05623e50 −0.493822
\(823\) −1.26215e50 −0.120674 −0.0603371 0.998178i \(-0.519218\pi\)
−0.0603371 + 0.998178i \(0.519218\pi\)
\(824\) 1.35641e50 0.126959
\(825\) −5.35317e49 −0.0490532
\(826\) 4.35254e50 0.390474
\(827\) −1.65632e51 −1.45478 −0.727390 0.686224i \(-0.759267\pi\)
−0.727390 + 0.686224i \(0.759267\pi\)
\(828\) 7.34672e50 0.631776
\(829\) −1.04352e51 −0.878607 −0.439303 0.898339i \(-0.644775\pi\)
−0.439303 + 0.898339i \(0.644775\pi\)
\(830\) −3.34821e50 −0.276024
\(831\) −1.10694e50 −0.0893521
\(832\) −3.25271e51 −2.57091
\(833\) 4.68707e49 0.0362755
\(834\) −1.45463e51 −1.10242
\(835\) 1.06971e50 0.0793874
\(836\) −2.17064e50 −0.157753
\(837\) −4.82105e49 −0.0343120
\(838\) −3.63587e51 −2.53418
\(839\) 2.81406e51 1.92088 0.960438 0.278493i \(-0.0898348\pi\)
0.960438 + 0.278493i \(0.0898348\pi\)
\(840\) −7.86717e49 −0.0525934
\(841\) 4.93839e50 0.323337
\(842\) 9.04780e50 0.580205
\(843\) 1.00477e51 0.631082
\(844\) −1.20989e51 −0.744307
\(845\) −7.60218e50 −0.458085
\(846\) 2.44168e50 0.144114
\(847\) 1.77355e51 1.02538
\(848\) 2.03423e51 1.15205
\(849\) −7.68506e49 −0.0426346
\(850\) 1.40626e51 0.764248
\(851\) −2.93679e51 −1.56353
\(852\) 2.77620e51 1.44796
\(853\) 2.01221e51 1.02817 0.514085 0.857739i \(-0.328131\pi\)
0.514085 + 0.857739i \(0.328131\pi\)
\(854\) −2.44483e51 −1.22387
\(855\) 2.02567e50 0.0993484
\(856\) −4.01881e50 −0.193111
\(857\) −2.58977e50 −0.121926 −0.0609630 0.998140i \(-0.519417\pi\)
−0.0609630 + 0.998140i \(0.519417\pi\)
\(858\) −2.97698e50 −0.137325
\(859\) −3.01104e50 −0.136093 −0.0680465 0.997682i \(-0.521677\pi\)
−0.0680465 + 0.997682i \(0.521677\pi\)
\(860\) 9.33440e50 0.413393
\(861\) 3.43549e50 0.149085
\(862\) 2.04991e51 0.871682
\(863\) −3.72938e51 −1.55399 −0.776995 0.629507i \(-0.783257\pi\)
−0.776995 + 0.629507i \(0.783257\pi\)
\(864\) 6.57622e50 0.268526
\(865\) 8.24591e50 0.329956
\(866\) 8.75921e49 0.0343480
\(867\) −1.07830e51 −0.414385
\(868\) 6.22850e50 0.234579
\(869\) 1.60401e50 0.0592053
\(870\) −5.92785e50 −0.214442
\(871\) −3.70404e51 −1.31328
\(872\) −1.07647e51 −0.374079
\(873\) −2.44819e50 −0.0833866
\(874\) 9.35742e51 3.12396
\(875\) −1.32183e51 −0.432550
\(876\) 7.75739e50 0.248825
\(877\) 1.47614e51 0.464124 0.232062 0.972701i \(-0.425453\pi\)
0.232062 + 0.972701i \(0.425453\pi\)
\(878\) 1.38676e51 0.427413
\(879\) −2.54460e51 −0.768800
\(880\) 4.20143e49 0.0124437
\(881\) 5.35936e50 0.155609 0.0778045 0.996969i \(-0.475209\pi\)
0.0778045 + 0.996969i \(0.475209\pi\)
\(882\) −1.20548e50 −0.0343132
\(883\) 2.24200e51 0.625638 0.312819 0.949813i \(-0.398727\pi\)
0.312819 + 0.949813i \(0.398727\pi\)
\(884\) 4.37980e51 1.19823
\(885\) −1.15515e50 −0.0309836
\(886\) −1.09123e52 −2.86964
\(887\) −7.00150e51 −1.80521 −0.902605 0.430470i \(-0.858348\pi\)
−0.902605 + 0.430470i \(0.858348\pi\)
\(888\) 9.86997e50 0.249510
\(889\) 3.13734e51 0.777643
\(890\) 3.34097e50 0.0811985
\(891\) 4.15179e49 0.00989408
\(892\) 1.46927e51 0.343335
\(893\) 1.74171e51 0.399093
\(894\) −3.95950e51 −0.889679
\(895\) −1.30039e51 −0.286530
\(896\) −3.79038e51 −0.819017
\(897\) 7.18733e51 1.52300
\(898\) −2.73576e51 −0.568516
\(899\) 1.00637e51 0.205099
\(900\) −2.02558e51 −0.404862
\(901\) −4.78511e51 −0.938011
\(902\) 1.74454e50 0.0335403
\(903\) 4.79870e51 0.904874
\(904\) 2.63129e51 0.486655
\(905\) 1.62259e51 0.294347
\(906\) −3.90473e51 −0.694780
\(907\) −1.01982e52 −1.77990 −0.889951 0.456057i \(-0.849261\pi\)
−0.889951 + 0.456057i \(0.849261\pi\)
\(908\) 8.29941e51 1.42084
\(909\) −3.54542e51 −0.595388
\(910\) −3.58919e51 −0.591252
\(911\) −1.62989e51 −0.263382 −0.131691 0.991291i \(-0.542041\pi\)
−0.131691 + 0.991291i \(0.542041\pi\)
\(912\) 3.30739e51 0.524295
\(913\) −4.89516e50 −0.0761252
\(914\) 2.20213e51 0.335957
\(915\) 6.48851e50 0.0971127
\(916\) −7.74238e51 −1.13685
\(917\) 8.75740e51 1.26157
\(918\) −1.09066e51 −0.154150
\(919\) 7.87901e51 1.09257 0.546286 0.837599i \(-0.316041\pi\)
0.546286 + 0.837599i \(0.316041\pi\)
\(920\) 9.64500e50 0.131225
\(921\) −4.59968e51 −0.614022
\(922\) 1.81900e52 2.38254
\(923\) 2.71597e52 3.49056
\(924\) −5.36385e50 −0.0676422
\(925\) 8.09710e51 1.00196
\(926\) −1.33379e52 −1.61955
\(927\) −8.63034e50 −0.102833
\(928\) −1.37275e52 −1.60510
\(929\) −4.74316e51 −0.544243 −0.272122 0.962263i \(-0.587725\pi\)
−0.272122 + 0.962263i \(0.587725\pi\)
\(930\) −2.95158e50 −0.0332356
\(931\) −8.59901e50 −0.0950230
\(932\) −6.86708e50 −0.0744721
\(933\) 4.78057e51 0.508805
\(934\) 9.34948e51 0.976601
\(935\) −9.88298e49 −0.0101318
\(936\) −2.41552e51 −0.243043
\(937\) −1.00541e52 −0.992888 −0.496444 0.868069i \(-0.665361\pi\)
−0.496444 + 0.868069i \(0.665361\pi\)
\(938\) −1.19166e52 −1.15506
\(939\) −5.42179e51 −0.515816
\(940\) 8.37193e50 0.0781786
\(941\) −6.43294e51 −0.589646 −0.294823 0.955552i \(-0.595261\pi\)
−0.294823 + 0.955552i \(0.595261\pi\)
\(942\) −1.37319e52 −1.23549
\(943\) −4.21185e51 −0.371979
\(944\) −1.88606e51 −0.163511
\(945\) 5.00560e50 0.0425990
\(946\) 2.43678e51 0.203574
\(947\) −8.46249e51 −0.694023 −0.347011 0.937861i \(-0.612803\pi\)
−0.347011 + 0.937861i \(0.612803\pi\)
\(948\) 6.06940e51 0.488652
\(949\) 7.58909e51 0.599834
\(950\) −2.57996e52 −2.00193
\(951\) 4.68418e51 0.356841
\(952\) 3.02153e51 0.225985
\(953\) −2.50917e51 −0.184248 −0.0921242 0.995748i \(-0.529366\pi\)
−0.0921242 + 0.995748i \(0.529366\pi\)
\(954\) 1.23070e52 0.887269
\(955\) 2.99335e51 0.211884
\(956\) −1.30648e52 −0.908005
\(957\) −8.66665e50 −0.0591415
\(958\) 2.73535e52 1.83281
\(959\) −8.91255e51 −0.586376
\(960\) 2.77727e51 0.179420
\(961\) −1.52627e52 −0.968212
\(962\) 4.50292e52 2.80498
\(963\) 2.55703e51 0.156414
\(964\) −2.98730e51 −0.179445
\(965\) −1.23521e51 −0.0728638
\(966\) 2.31230e52 1.33951
\(967\) 3.67568e50 0.0209110 0.0104555 0.999945i \(-0.496672\pi\)
0.0104555 + 0.999945i \(0.496672\pi\)
\(968\) 7.30754e51 0.408275
\(969\) −7.77994e51 −0.426884
\(970\) −1.49885e51 −0.0807706
\(971\) 2.67841e52 1.41756 0.708778 0.705431i \(-0.249247\pi\)
0.708778 + 0.705431i \(0.249247\pi\)
\(972\) 1.57099e51 0.0816610
\(973\) −2.56405e52 −1.30904
\(974\) −2.89771e52 −1.45303
\(975\) −1.98164e52 −0.975986
\(976\) 1.05941e52 0.512496
\(977\) 1.70901e52 0.812062 0.406031 0.913859i \(-0.366912\pi\)
0.406031 + 0.913859i \(0.366912\pi\)
\(978\) 1.86089e52 0.868542
\(979\) 4.88458e50 0.0223939
\(980\) −4.13332e50 −0.0186141
\(981\) 6.84920e51 0.302993
\(982\) −3.65083e51 −0.158650
\(983\) 2.12016e50 0.00905069 0.00452535 0.999990i \(-0.498560\pi\)
0.00452535 + 0.999990i \(0.498560\pi\)
\(984\) 1.41552e51 0.0593610
\(985\) 4.65175e51 0.191638
\(986\) 2.27670e52 0.921424
\(987\) 4.30391e51 0.171125
\(988\) −8.03529e52 −3.13874
\(989\) −5.88312e52 −2.25773
\(990\) 2.54184e50 0.00958369
\(991\) 6.93693e50 0.0256968 0.0128484 0.999917i \(-0.495910\pi\)
0.0128484 + 0.999917i \(0.495910\pi\)
\(992\) −6.83518e51 −0.248769
\(993\) −1.97269e52 −0.705419
\(994\) 8.73778e52 3.07001
\(995\) 2.65889e51 0.0917904
\(996\) −1.85228e52 −0.628301
\(997\) 2.96189e52 0.987196 0.493598 0.869690i \(-0.335681\pi\)
0.493598 + 0.869690i \(0.335681\pi\)
\(998\) −4.64144e51 −0.152009
\(999\) −6.27991e51 −0.202096
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 3.36.a.a.1.1 2
3.2 odd 2 9.36.a.a.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.36.a.a.1.1 2 1.1 even 1 trivial
9.36.a.a.1.2 2 3.2 odd 2