Properties

Label 1.62.a.a.1.2
Level 1
Weight 62
Character 1.1
Self dual yes
Analytic conductor 23.566
Analytic rank 1
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 62 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.5656183265\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 180363795469121 x^{2} + 166129321978984507920 x + 2785609847439483545242446300\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{28}\cdot 3^{8}\cdot 5^{2}\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(4.76281e6\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.27881e8 q^{2} -6.22194e14 q^{3} -1.91161e18 q^{4} +2.33985e20 q^{5} +3.90664e23 q^{6} +6.25792e25 q^{7} +2.64806e27 q^{8} +2.59952e29 q^{9} +O(q^{10})\) \(q-6.27881e8 q^{2} -6.22194e14 q^{3} -1.91161e18 q^{4} +2.33985e20 q^{5} +3.90664e23 q^{6} +6.25792e25 q^{7} +2.64806e27 q^{8} +2.59952e29 q^{9} -1.46915e29 q^{10} -9.05394e31 q^{11} +1.18939e33 q^{12} +7.79086e33 q^{13} -3.92923e34 q^{14} -1.45584e35 q^{15} +2.74521e36 q^{16} -1.64134e37 q^{17} -1.63219e38 q^{18} +1.45265e39 q^{19} -4.47288e38 q^{20} -3.89364e40 q^{21} +5.68480e40 q^{22} -1.28631e41 q^{23} -1.64761e42 q^{24} -4.28206e42 q^{25} -4.89173e42 q^{26} -8.26143e43 q^{27} -1.19627e44 q^{28} +1.23922e44 q^{29} +9.14095e43 q^{30} +2.17946e45 q^{31} -7.82966e45 q^{32} +5.63331e46 q^{33} +1.03057e46 q^{34} +1.46426e46 q^{35} -4.96927e47 q^{36} +5.13297e47 q^{37} -9.12091e47 q^{38} -4.84743e48 q^{39} +6.19606e47 q^{40} +1.44082e49 q^{41} +2.44474e49 q^{42} -4.68902e49 q^{43} +1.73076e50 q^{44} +6.08250e49 q^{45} +8.07652e49 q^{46} -1.55786e51 q^{47} -1.70805e51 q^{48} +3.60006e50 q^{49} +2.68862e51 q^{50} +1.02123e52 q^{51} -1.48931e52 q^{52} +2.61505e52 q^{53} +5.18719e52 q^{54} -2.11849e52 q^{55} +1.65713e53 q^{56} -9.03831e53 q^{57} -7.78081e52 q^{58} +5.85447e53 q^{59} +2.78300e53 q^{60} -6.99841e53 q^{61} -1.36844e54 q^{62} +1.62676e55 q^{63} -1.41392e54 q^{64} +1.82294e54 q^{65} -3.53705e55 q^{66} -5.65118e55 q^{67} +3.13760e55 q^{68} +8.00337e55 q^{69} -9.19381e54 q^{70} -4.76482e56 q^{71} +6.88368e56 q^{72} +4.87633e56 q^{73} -3.22289e56 q^{74} +2.66427e57 q^{75} -2.77690e57 q^{76} -5.66589e57 q^{77} +3.04361e57 q^{78} -6.21907e57 q^{79} +6.42337e56 q^{80} +1.83431e58 q^{81} -9.04662e57 q^{82} -1.18158e58 q^{83} +7.44312e58 q^{84} -3.84049e57 q^{85} +2.94414e58 q^{86} -7.71034e58 q^{87} -2.39753e59 q^{88} -8.44939e58 q^{89} -3.81908e58 q^{90} +4.87546e59 q^{91} +2.45893e59 q^{92} -1.35605e60 q^{93} +9.78147e59 q^{94} +3.39899e59 q^{95} +4.87157e60 q^{96} +8.57527e59 q^{97} -2.26041e59 q^{98} -2.35359e61 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} + O(q^{10}) \) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} - \)\(14\!\cdots\!00\)\(q^{10} - \)\(41\!\cdots\!52\)\(q^{11} - \)\(99\!\cdots\!00\)\(q^{12} + \)\(10\!\cdots\!00\)\(q^{13} - \)\(21\!\cdots\!04\)\(q^{14} + \)\(11\!\cdots\!00\)\(q^{15} + \)\(10\!\cdots\!24\)\(q^{16} - \)\(40\!\cdots\!00\)\(q^{17} + \)\(15\!\cdots\!00\)\(q^{18} - \)\(35\!\cdots\!20\)\(q^{19} - \)\(50\!\cdots\!00\)\(q^{20} - \)\(55\!\cdots\!72\)\(q^{21} - \)\(17\!\cdots\!00\)\(q^{22} - \)\(41\!\cdots\!00\)\(q^{23} - \)\(61\!\cdots\!60\)\(q^{24} - \)\(16\!\cdots\!00\)\(q^{25} - \)\(49\!\cdots\!32\)\(q^{26} - \)\(12\!\cdots\!00\)\(q^{27} - \)\(79\!\cdots\!00\)\(q^{28} + \)\(66\!\cdots\!20\)\(q^{29} + \)\(95\!\cdots\!00\)\(q^{30} + \)\(32\!\cdots\!28\)\(q^{31} + \)\(29\!\cdots\!00\)\(q^{32} + \)\(80\!\cdots\!00\)\(q^{33} + \)\(39\!\cdots\!16\)\(q^{34} + \)\(94\!\cdots\!00\)\(q^{35} - \)\(49\!\cdots\!36\)\(q^{36} - \)\(71\!\cdots\!00\)\(q^{37} - \)\(65\!\cdots\!00\)\(q^{38} - \)\(53\!\cdots\!76\)\(q^{39} - \)\(69\!\cdots\!00\)\(q^{40} + \)\(16\!\cdots\!68\)\(q^{41} + \)\(15\!\cdots\!00\)\(q^{42} + \)\(75\!\cdots\!00\)\(q^{43} + \)\(15\!\cdots\!36\)\(q^{44} + \)\(60\!\cdots\!00\)\(q^{45} - \)\(15\!\cdots\!12\)\(q^{46} - \)\(21\!\cdots\!00\)\(q^{47} - \)\(84\!\cdots\!00\)\(q^{48} + \)\(15\!\cdots\!28\)\(q^{49} - \)\(37\!\cdots\!00\)\(q^{50} + \)\(20\!\cdots\!88\)\(q^{51} + \)\(34\!\cdots\!00\)\(q^{52} + \)\(84\!\cdots\!00\)\(q^{53} + \)\(20\!\cdots\!80\)\(q^{54} - \)\(18\!\cdots\!00\)\(q^{55} - \)\(89\!\cdots\!20\)\(q^{56} - \)\(48\!\cdots\!00\)\(q^{57} - \)\(42\!\cdots\!00\)\(q^{58} - \)\(21\!\cdots\!60\)\(q^{59} + \)\(16\!\cdots\!00\)\(q^{60} + \)\(42\!\cdots\!48\)\(q^{61} + \)\(51\!\cdots\!00\)\(q^{62} + \)\(17\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!08\)\(q^{64} - \)\(40\!\cdots\!00\)\(q^{65} - \)\(32\!\cdots\!24\)\(q^{66} - \)\(15\!\cdots\!00\)\(q^{67} - \)\(19\!\cdots\!00\)\(q^{68} - \)\(65\!\cdots\!16\)\(q^{69} + \)\(16\!\cdots\!00\)\(q^{70} + \)\(26\!\cdots\!88\)\(q^{71} + \)\(10\!\cdots\!00\)\(q^{72} + \)\(43\!\cdots\!00\)\(q^{73} + \)\(27\!\cdots\!56\)\(q^{74} + \)\(22\!\cdots\!00\)\(q^{75} - \)\(91\!\cdots\!40\)\(q^{76} - \)\(62\!\cdots\!00\)\(q^{77} - \)\(62\!\cdots\!00\)\(q^{78} - \)\(21\!\cdots\!80\)\(q^{79} - \)\(81\!\cdots\!00\)\(q^{80} + \)\(16\!\cdots\!84\)\(q^{81} + \)\(41\!\cdots\!00\)\(q^{82} - \)\(19\!\cdots\!00\)\(q^{83} + \)\(26\!\cdots\!96\)\(q^{84} + \)\(23\!\cdots\!00\)\(q^{85} - \)\(71\!\cdots\!72\)\(q^{86} - \)\(25\!\cdots\!00\)\(q^{87} - \)\(45\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!40\)\(q^{89} - \)\(12\!\cdots\!00\)\(q^{90} - \)\(45\!\cdots\!52\)\(q^{91} + \)\(16\!\cdots\!00\)\(q^{92} - \)\(43\!\cdots\!00\)\(q^{93} + \)\(64\!\cdots\!76\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} + \)\(15\!\cdots\!08\)\(q^{96} - \)\(80\!\cdots\!00\)\(q^{97} + \)\(17\!\cdots\!00\)\(q^{98} - \)\(31\!\cdots\!76\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.27881e8 −0.413487 −0.206744 0.978395i \(-0.566287\pi\)
−0.206744 + 0.978395i \(0.566287\pi\)
\(3\) −6.22194e14 −1.74473 −0.872364 0.488857i \(-0.837414\pi\)
−0.872364 + 0.488857i \(0.837414\pi\)
\(4\) −1.91161e18 −0.829028
\(5\) 2.33985e20 0.112358 0.0561789 0.998421i \(-0.482108\pi\)
0.0561789 + 0.998421i \(0.482108\pi\)
\(6\) 3.90664e23 0.721423
\(7\) 6.25792e25 1.04940 0.524699 0.851288i \(-0.324178\pi\)
0.524699 + 0.851288i \(0.324178\pi\)
\(8\) 2.64806e27 0.756280
\(9\) 2.59952e29 2.04408
\(10\) −1.46915e29 −0.0464585
\(11\) −9.05394e31 −1.56445 −0.782223 0.622998i \(-0.785914\pi\)
−0.782223 + 0.622998i \(0.785914\pi\)
\(12\) 1.18939e33 1.44643
\(13\) 7.79086e33 0.824732 0.412366 0.911018i \(-0.364702\pi\)
0.412366 + 0.911018i \(0.364702\pi\)
\(14\) −3.92923e34 −0.433913
\(15\) −1.45584e35 −0.196034
\(16\) 2.74521e36 0.516316
\(17\) −1.64134e37 −0.485855 −0.242927 0.970044i \(-0.578108\pi\)
−0.242927 + 0.970044i \(0.578108\pi\)
\(18\) −1.63219e38 −0.845200
\(19\) 1.45265e39 1.44603 0.723014 0.690834i \(-0.242756\pi\)
0.723014 + 0.690834i \(0.242756\pi\)
\(20\) −4.47288e38 −0.0931477
\(21\) −3.89364e40 −1.83091
\(22\) 5.68480e40 0.646879
\(23\) −1.28631e41 −0.377266 −0.188633 0.982048i \(-0.560406\pi\)
−0.188633 + 0.982048i \(0.560406\pi\)
\(24\) −1.64761e42 −1.31950
\(25\) −4.28206e42 −0.987376
\(26\) −4.89173e42 −0.341016
\(27\) −8.26143e43 −1.82163
\(28\) −1.19627e44 −0.869980
\(29\) 1.23922e44 0.309036 0.154518 0.987990i \(-0.450618\pi\)
0.154518 + 0.987990i \(0.450618\pi\)
\(30\) 9.14095e43 0.0810575
\(31\) 2.17946e45 0.710915 0.355457 0.934692i \(-0.384325\pi\)
0.355457 + 0.934692i \(0.384325\pi\)
\(32\) −7.82966e45 −0.969770
\(33\) 5.63331e46 2.72953
\(34\) 1.03057e46 0.200895
\(35\) 1.46426e46 0.117908
\(36\) −4.96927e47 −1.69460
\(37\) 5.13297e47 0.758955 0.379478 0.925201i \(-0.376104\pi\)
0.379478 + 0.925201i \(0.376104\pi\)
\(38\) −9.12091e47 −0.597914
\(39\) −4.84743e48 −1.43893
\(40\) 6.19606e47 0.0849739
\(41\) 1.44082e49 0.930469 0.465234 0.885188i \(-0.345970\pi\)
0.465234 + 0.885188i \(0.345970\pi\)
\(42\) 2.44474e49 0.757059
\(43\) −4.68902e49 −0.708425 −0.354213 0.935165i \(-0.615251\pi\)
−0.354213 + 0.935165i \(0.615251\pi\)
\(44\) 1.73076e50 1.29697
\(45\) 6.08250e49 0.229668
\(46\) 8.07652e49 0.155995
\(47\) −1.55786e51 −1.56150 −0.780751 0.624842i \(-0.785163\pi\)
−0.780751 + 0.624842i \(0.785163\pi\)
\(48\) −1.70805e51 −0.900831
\(49\) 3.60006e50 0.101235
\(50\) 2.68862e51 0.408267
\(51\) 1.02123e52 0.847685
\(52\) −1.48931e52 −0.683726
\(53\) 2.61505e52 0.671531 0.335765 0.941946i \(-0.391005\pi\)
0.335765 + 0.941946i \(0.391005\pi\)
\(54\) 5.18719e52 0.753221
\(55\) −2.11849e52 −0.175778
\(56\) 1.65713e53 0.793638
\(57\) −9.03831e53 −2.52292
\(58\) −7.78081e52 −0.127782
\(59\) 5.85447e53 0.570823 0.285411 0.958405i \(-0.407870\pi\)
0.285411 + 0.958405i \(0.407870\pi\)
\(60\) 2.78300e53 0.162517
\(61\) −6.99841e53 −0.246854 −0.123427 0.992354i \(-0.539388\pi\)
−0.123427 + 0.992354i \(0.539388\pi\)
\(62\) −1.36844e54 −0.293954
\(63\) 1.62676e55 2.14505
\(64\) −1.41392e54 −0.115328
\(65\) 1.82294e54 0.0926650
\(66\) −3.53705e55 −1.12863
\(67\) −5.65118e55 −1.13988 −0.569938 0.821688i \(-0.693033\pi\)
−0.569938 + 0.821688i \(0.693033\pi\)
\(68\) 3.13760e55 0.402787
\(69\) 8.00337e55 0.658227
\(70\) −9.19381e54 −0.0487534
\(71\) −4.76482e56 −1.63933 −0.819667 0.572841i \(-0.805841\pi\)
−0.819667 + 0.572841i \(0.805841\pi\)
\(72\) 6.88368e56 1.54589
\(73\) 4.87633e56 0.719028 0.359514 0.933140i \(-0.382942\pi\)
0.359514 + 0.933140i \(0.382942\pi\)
\(74\) −3.22289e56 −0.313818
\(75\) 2.66427e57 1.72270
\(76\) −2.77690e57 −1.19880
\(77\) −5.66589e57 −1.64173
\(78\) 3.04361e57 0.594981
\(79\) −6.21907e57 −0.824326 −0.412163 0.911110i \(-0.635227\pi\)
−0.412163 + 0.911110i \(0.635227\pi\)
\(80\) 6.42337e56 0.0580121
\(81\) 1.83431e58 1.13417
\(82\) −9.04662e57 −0.384737
\(83\) −1.18158e58 −0.347202 −0.173601 0.984816i \(-0.555540\pi\)
−0.173601 + 0.984816i \(0.555540\pi\)
\(84\) 7.44312e58 1.51788
\(85\) −3.84049e57 −0.0545895
\(86\) 2.94414e58 0.292925
\(87\) −7.71034e58 −0.539183
\(88\) −2.39753e59 −1.18316
\(89\) −8.44939e58 −0.295414 −0.147707 0.989031i \(-0.547189\pi\)
−0.147707 + 0.989031i \(0.547189\pi\)
\(90\) −3.81908e58 −0.0949647
\(91\) 4.87546e59 0.865472
\(92\) 2.45893e59 0.312764
\(93\) −1.35605e60 −1.24035
\(94\) 9.78147e59 0.645661
\(95\) 3.39899e59 0.162472
\(96\) 4.87157e60 1.69199
\(97\) 8.57527e59 0.217125 0.108563 0.994090i \(-0.465375\pi\)
0.108563 + 0.994090i \(0.465375\pi\)
\(98\) −2.26041e59 −0.0418593
\(99\) −2.35359e61 −3.19785
\(100\) 8.18562e60 0.818562
\(101\) −4.46035e59 −0.0329281 −0.0164641 0.999864i \(-0.505241\pi\)
−0.0164641 + 0.999864i \(0.505241\pi\)
\(102\) −6.41212e60 −0.350507
\(103\) 1.96351e61 0.797074 0.398537 0.917152i \(-0.369518\pi\)
0.398537 + 0.917152i \(0.369518\pi\)
\(104\) 2.06306e61 0.623728
\(105\) −9.11055e60 −0.205717
\(106\) −1.64194e61 −0.277670
\(107\) 1.32237e61 0.167937 0.0839687 0.996468i \(-0.473240\pi\)
0.0839687 + 0.996468i \(0.473240\pi\)
\(108\) 1.57926e62 1.51018
\(109\) −1.12679e62 −0.813455 −0.406728 0.913549i \(-0.633330\pi\)
−0.406728 + 0.913549i \(0.633330\pi\)
\(110\) 1.33016e61 0.0726819
\(111\) −3.19371e62 −1.32417
\(112\) 1.71793e62 0.541821
\(113\) −6.52796e62 −1.56995 −0.784973 0.619530i \(-0.787323\pi\)
−0.784973 + 0.619530i \(0.787323\pi\)
\(114\) 5.67498e62 1.04320
\(115\) −3.00978e61 −0.0423888
\(116\) −2.36890e62 −0.256199
\(117\) 2.02525e63 1.68582
\(118\) −3.67591e62 −0.236028
\(119\) −1.02714e63 −0.509855
\(120\) −3.85515e62 −0.148256
\(121\) 4.84809e63 1.44749
\(122\) 4.39417e62 0.102071
\(123\) −8.96469e63 −1.62341
\(124\) −4.16628e63 −0.589369
\(125\) −2.01669e63 −0.223297
\(126\) −1.02141e64 −0.886950
\(127\) 9.36757e63 0.639166 0.319583 0.947558i \(-0.396457\pi\)
0.319583 + 0.947558i \(0.396457\pi\)
\(128\) 1.89418e64 1.01746
\(129\) 2.91748e64 1.23601
\(130\) −1.14459e63 −0.0383158
\(131\) 2.23839e63 0.0593144 0.0296572 0.999560i \(-0.490558\pi\)
0.0296572 + 0.999560i \(0.490558\pi\)
\(132\) −1.07687e65 −2.26286
\(133\) 9.09058e64 1.51746
\(134\) 3.54827e64 0.471324
\(135\) −1.93305e64 −0.204674
\(136\) −4.34636e64 −0.367442
\(137\) −3.22204e64 −0.217848 −0.108924 0.994050i \(-0.534741\pi\)
−0.108924 + 0.994050i \(0.534741\pi\)
\(138\) −5.02516e64 −0.272169
\(139\) −4.43557e65 −1.92752 −0.963758 0.266776i \(-0.914042\pi\)
−0.963758 + 0.266776i \(0.914042\pi\)
\(140\) −2.79909e64 −0.0977490
\(141\) 9.69289e65 2.72440
\(142\) 2.99174e65 0.677843
\(143\) −7.05380e65 −1.29025
\(144\) 7.13623e65 1.05539
\(145\) 2.89958e64 0.0347226
\(146\) −3.06175e65 −0.297309
\(147\) −2.23994e65 −0.176627
\(148\) −9.81223e65 −0.629195
\(149\) 1.19782e66 0.625478 0.312739 0.949839i \(-0.398754\pi\)
0.312739 + 0.949839i \(0.398754\pi\)
\(150\) −1.67285e66 −0.712316
\(151\) −3.40521e66 −1.18399 −0.591994 0.805943i \(-0.701659\pi\)
−0.591994 + 0.805943i \(0.701659\pi\)
\(152\) 3.84670e66 1.09360
\(153\) −4.26670e66 −0.993125
\(154\) 3.55750e66 0.678833
\(155\) 5.09962e65 0.0798768
\(156\) 9.26638e66 1.19292
\(157\) 6.21574e66 0.658496 0.329248 0.944243i \(-0.393205\pi\)
0.329248 + 0.944243i \(0.393205\pi\)
\(158\) 3.90483e66 0.340849
\(159\) −1.62707e67 −1.17164
\(160\) −1.83202e66 −0.108961
\(161\) −8.04965e66 −0.395902
\(162\) −1.15173e67 −0.468966
\(163\) 1.73234e67 0.584670 0.292335 0.956316i \(-0.405568\pi\)
0.292335 + 0.956316i \(0.405568\pi\)
\(164\) −2.75428e67 −0.771385
\(165\) 1.31811e67 0.306684
\(166\) 7.41893e66 0.143564
\(167\) 3.54014e67 0.570385 0.285193 0.958470i \(-0.407942\pi\)
0.285193 + 0.958470i \(0.407942\pi\)
\(168\) −1.03106e68 −1.38468
\(169\) −2.85395e67 −0.319817
\(170\) 2.41137e66 0.0225721
\(171\) 3.77620e68 2.95579
\(172\) 8.96357e67 0.587304
\(173\) −1.75625e68 −0.964231 −0.482116 0.876108i \(-0.660131\pi\)
−0.482116 + 0.876108i \(0.660131\pi\)
\(174\) 4.84118e67 0.222946
\(175\) −2.67968e68 −1.03615
\(176\) −2.48549e68 −0.807749
\(177\) −3.64262e68 −0.995931
\(178\) 5.30521e67 0.122150
\(179\) 4.59004e68 0.890839 0.445419 0.895322i \(-0.353055\pi\)
0.445419 + 0.895322i \(0.353055\pi\)
\(180\) −1.16274e68 −0.190401
\(181\) 4.08776e68 0.565312 0.282656 0.959221i \(-0.408784\pi\)
0.282656 + 0.959221i \(0.408784\pi\)
\(182\) −3.06121e68 −0.357862
\(183\) 4.35437e68 0.430692
\(184\) −3.40623e68 −0.285319
\(185\) 1.20104e68 0.0852745
\(186\) 8.51437e68 0.512870
\(187\) 1.48606e69 0.760094
\(188\) 2.97801e69 1.29453
\(189\) −5.16994e69 −1.91161
\(190\) −2.13416e68 −0.0671803
\(191\) −6.52737e69 −1.75074 −0.875368 0.483457i \(-0.839381\pi\)
−0.875368 + 0.483457i \(0.839381\pi\)
\(192\) 8.79734e68 0.201217
\(193\) 3.40957e69 0.665582 0.332791 0.943001i \(-0.392010\pi\)
0.332791 + 0.943001i \(0.392010\pi\)
\(194\) −5.38425e68 −0.0897785
\(195\) −1.13423e69 −0.161675
\(196\) −6.88191e68 −0.0839264
\(197\) 5.81412e69 0.607105 0.303552 0.952815i \(-0.401827\pi\)
0.303552 + 0.952815i \(0.401827\pi\)
\(198\) 1.47778e70 1.32227
\(199\) −1.86375e70 −1.43011 −0.715055 0.699068i \(-0.753599\pi\)
−0.715055 + 0.699068i \(0.753599\pi\)
\(200\) −1.13391e70 −0.746733
\(201\) 3.51613e70 1.98877
\(202\) 2.80057e68 0.0136154
\(203\) 7.75493e69 0.324301
\(204\) −1.95220e70 −0.702754
\(205\) 3.37130e69 0.104545
\(206\) −1.23285e70 −0.329580
\(207\) −3.34380e70 −0.771161
\(208\) 2.13875e70 0.425822
\(209\) −1.31522e71 −2.26223
\(210\) 5.72033e69 0.0850615
\(211\) 1.02222e71 1.31501 0.657506 0.753449i \(-0.271611\pi\)
0.657506 + 0.753449i \(0.271611\pi\)
\(212\) −4.99895e70 −0.556718
\(213\) 2.96465e71 2.86019
\(214\) −8.30290e69 −0.0694400
\(215\) −1.09716e70 −0.0795971
\(216\) −2.18767e71 −1.37766
\(217\) 1.36389e71 0.746032
\(218\) 7.07488e70 0.336353
\(219\) −3.03403e71 −1.25451
\(220\) 4.04972e70 0.145725
\(221\) −1.27874e71 −0.400700
\(222\) 2.00527e71 0.547528
\(223\) 4.66041e71 1.10950 0.554748 0.832019i \(-0.312815\pi\)
0.554748 + 0.832019i \(0.312815\pi\)
\(224\) −4.89974e71 −1.01767
\(225\) −1.11313e72 −2.01827
\(226\) 4.09878e71 0.649153
\(227\) −4.66130e71 −0.645236 −0.322618 0.946529i \(-0.604563\pi\)
−0.322618 + 0.946529i \(0.604563\pi\)
\(228\) 1.72777e72 2.09158
\(229\) −8.29575e71 −0.878767 −0.439383 0.898300i \(-0.644803\pi\)
−0.439383 + 0.898300i \(0.644803\pi\)
\(230\) 1.88978e70 0.0175272
\(231\) 3.52528e72 2.86437
\(232\) 3.28152e71 0.233718
\(233\) −2.87441e72 −1.79553 −0.897767 0.440471i \(-0.854812\pi\)
−0.897767 + 0.440471i \(0.854812\pi\)
\(234\) −1.27162e72 −0.697064
\(235\) −3.64515e71 −0.175447
\(236\) −1.11915e72 −0.473228
\(237\) 3.86947e72 1.43823
\(238\) 6.44920e71 0.210818
\(239\) −5.74905e72 −1.65371 −0.826857 0.562412i \(-0.809873\pi\)
−0.826857 + 0.562412i \(0.809873\pi\)
\(240\) −3.99659e71 −0.101215
\(241\) 1.60687e72 0.358476 0.179238 0.983806i \(-0.442637\pi\)
0.179238 + 0.983806i \(0.442637\pi\)
\(242\) −3.04402e72 −0.598520
\(243\) −9.06622e71 −0.157194
\(244\) 1.33782e72 0.204649
\(245\) 8.42361e70 0.0113745
\(246\) 5.62876e72 0.671261
\(247\) 1.13174e73 1.19258
\(248\) 5.77134e72 0.537651
\(249\) 7.35174e72 0.605773
\(250\) 1.26624e72 0.0923305
\(251\) −2.02500e73 −1.30730 −0.653651 0.756796i \(-0.726764\pi\)
−0.653651 + 0.756796i \(0.726764\pi\)
\(252\) −3.10973e73 −1.77831
\(253\) 1.16462e73 0.590213
\(254\) −5.88172e72 −0.264287
\(255\) 2.38953e72 0.0952439
\(256\) −8.63288e72 −0.305377
\(257\) 1.08823e73 0.341790 0.170895 0.985289i \(-0.445334\pi\)
0.170895 + 0.985289i \(0.445334\pi\)
\(258\) −1.83183e73 −0.511074
\(259\) 3.21217e73 0.796446
\(260\) −3.48476e72 −0.0768219
\(261\) 3.22138e73 0.631693
\(262\) −1.40544e72 −0.0245258
\(263\) −1.14768e74 −1.78307 −0.891536 0.452950i \(-0.850372\pi\)
−0.891536 + 0.452950i \(0.850372\pi\)
\(264\) 1.49173e74 2.06429
\(265\) 6.11883e72 0.0754517
\(266\) −5.70780e73 −0.627449
\(267\) 5.25717e73 0.515416
\(268\) 1.08028e74 0.944989
\(269\) 1.34285e72 0.0104853 0.00524267 0.999986i \(-0.498331\pi\)
0.00524267 + 0.999986i \(0.498331\pi\)
\(270\) 1.21372e73 0.0846302
\(271\) −3.00222e74 −1.87016 −0.935080 0.354437i \(-0.884673\pi\)
−0.935080 + 0.354437i \(0.884673\pi\)
\(272\) −4.50582e73 −0.250855
\(273\) −3.03348e74 −1.51001
\(274\) 2.02306e73 0.0900775
\(275\) 3.87695e74 1.54470
\(276\) −1.52993e74 −0.545689
\(277\) −8.70383e73 −0.278021 −0.139011 0.990291i \(-0.544392\pi\)
−0.139011 + 0.990291i \(0.544392\pi\)
\(278\) 2.78501e74 0.797004
\(279\) 5.66556e74 1.45316
\(280\) 3.87744e73 0.0891714
\(281\) −1.17276e74 −0.241917 −0.120959 0.992658i \(-0.538597\pi\)
−0.120959 + 0.992658i \(0.538597\pi\)
\(282\) −6.08598e74 −1.12650
\(283\) −1.34561e74 −0.223580 −0.111790 0.993732i \(-0.535658\pi\)
−0.111790 + 0.993732i \(0.535658\pi\)
\(284\) 9.10848e74 1.35905
\(285\) −2.11483e74 −0.283470
\(286\) 4.42894e74 0.533502
\(287\) 9.01653e74 0.976431
\(288\) −2.03534e75 −1.98228
\(289\) −8.71859e74 −0.763945
\(290\) −1.82059e73 −0.0143573
\(291\) −5.33549e74 −0.378824
\(292\) −9.32164e74 −0.596095
\(293\) 3.33052e74 0.191889 0.0959445 0.995387i \(-0.469413\pi\)
0.0959445 + 0.995387i \(0.469413\pi\)
\(294\) 1.40641e74 0.0730331
\(295\) 1.36986e74 0.0641364
\(296\) 1.35924e75 0.573983
\(297\) 7.47985e75 2.84984
\(298\) −7.52090e74 −0.258627
\(299\) −1.00215e75 −0.311144
\(300\) −5.09305e75 −1.42817
\(301\) −2.93435e75 −0.743419
\(302\) 2.13807e75 0.489564
\(303\) 2.77520e74 0.0574506
\(304\) 3.98783e75 0.746607
\(305\) −1.63752e74 −0.0277359
\(306\) 2.67898e75 0.410644
\(307\) −1.19531e76 −1.65868 −0.829338 0.558748i \(-0.811282\pi\)
−0.829338 + 0.558748i \(0.811282\pi\)
\(308\) 1.08310e76 1.36104
\(309\) −1.22169e76 −1.39068
\(310\) −3.20195e74 −0.0330280
\(311\) −3.79842e75 −0.355150 −0.177575 0.984107i \(-0.556825\pi\)
−0.177575 + 0.984107i \(0.556825\pi\)
\(312\) −1.28363e76 −1.08824
\(313\) 1.65384e76 1.27172 0.635861 0.771804i \(-0.280645\pi\)
0.635861 + 0.771804i \(0.280645\pi\)
\(314\) −3.90274e75 −0.272280
\(315\) 3.80638e75 0.241013
\(316\) 1.18884e76 0.683390
\(317\) 2.82467e76 1.47455 0.737275 0.675592i \(-0.236112\pi\)
0.737275 + 0.675592i \(0.236112\pi\)
\(318\) 1.02161e76 0.484458
\(319\) −1.12198e76 −0.483470
\(320\) −3.30836e74 −0.0129580
\(321\) −8.22770e75 −0.293005
\(322\) 5.05422e75 0.163701
\(323\) −2.38429e76 −0.702559
\(324\) −3.50648e76 −0.940261
\(325\) −3.33609e76 −0.814321
\(326\) −1.08770e76 −0.241754
\(327\) 7.01081e76 1.41926
\(328\) 3.81537e76 0.703695
\(329\) −9.74894e76 −1.63864
\(330\) −8.27616e75 −0.126810
\(331\) 1.56426e75 0.0218553 0.0109276 0.999940i \(-0.496522\pi\)
0.0109276 + 0.999940i \(0.496522\pi\)
\(332\) 2.25872e76 0.287840
\(333\) 1.33433e77 1.55136
\(334\) −2.22279e76 −0.235847
\(335\) −1.32229e76 −0.128074
\(336\) −1.06889e77 −0.945330
\(337\) 4.48909e76 0.362615 0.181308 0.983426i \(-0.441967\pi\)
0.181308 + 0.983426i \(0.441967\pi\)
\(338\) 1.79194e76 0.132240
\(339\) 4.06166e77 2.73913
\(340\) 7.34152e75 0.0452563
\(341\) −1.97327e77 −1.11219
\(342\) −2.37100e77 −1.22218
\(343\) −2.00012e77 −0.943162
\(344\) −1.24168e77 −0.535768
\(345\) 1.87267e76 0.0739569
\(346\) 1.10272e77 0.398697
\(347\) −2.97382e77 −0.984615 −0.492307 0.870421i \(-0.663846\pi\)
−0.492307 + 0.870421i \(0.663846\pi\)
\(348\) 1.47392e77 0.446998
\(349\) 5.36967e77 1.49201 0.746005 0.665940i \(-0.231969\pi\)
0.746005 + 0.665940i \(0.231969\pi\)
\(350\) 1.68252e77 0.428435
\(351\) −6.43636e77 −1.50236
\(352\) 7.08893e77 1.51715
\(353\) −7.22267e77 −1.41765 −0.708825 0.705384i \(-0.750774\pi\)
−0.708825 + 0.705384i \(0.750774\pi\)
\(354\) 2.28713e77 0.411805
\(355\) −1.11490e77 −0.184192
\(356\) 1.61519e77 0.244906
\(357\) 6.39079e77 0.889558
\(358\) −2.88200e77 −0.368351
\(359\) 7.97496e77 0.936155 0.468078 0.883687i \(-0.344947\pi\)
0.468078 + 0.883687i \(0.344947\pi\)
\(360\) 1.61068e77 0.173693
\(361\) 1.10101e78 1.09099
\(362\) −2.56662e77 −0.233750
\(363\) −3.01645e78 −2.52548
\(364\) −9.31997e77 −0.717500
\(365\) 1.14099e77 0.0807884
\(366\) −2.73402e77 −0.178086
\(367\) −2.30364e78 −1.38070 −0.690350 0.723476i \(-0.742543\pi\)
−0.690350 + 0.723476i \(0.742543\pi\)
\(368\) −3.53120e77 −0.194789
\(369\) 3.74544e78 1.90195
\(370\) −7.54109e76 −0.0352599
\(371\) 1.63648e78 0.704703
\(372\) 2.59224e78 1.02829
\(373\) 3.65569e77 0.133613 0.0668067 0.997766i \(-0.478719\pi\)
0.0668067 + 0.997766i \(0.478719\pi\)
\(374\) −9.33068e77 −0.314289
\(375\) 1.25477e78 0.389593
\(376\) −4.12529e78 −1.18093
\(377\) 9.65457e77 0.254872
\(378\) 3.24610e78 0.790428
\(379\) −1.75228e78 −0.393647 −0.196823 0.980439i \(-0.563063\pi\)
−0.196823 + 0.980439i \(0.563063\pi\)
\(380\) −6.49753e77 −0.134694
\(381\) −5.82845e78 −1.11517
\(382\) 4.09841e78 0.723907
\(383\) 1.06584e79 1.73832 0.869158 0.494534i \(-0.164661\pi\)
0.869158 + 0.494534i \(0.164661\pi\)
\(384\) −1.17855e79 −1.77519
\(385\) −1.32573e78 −0.184461
\(386\) −2.14080e78 −0.275210
\(387\) −1.21892e79 −1.44808
\(388\) −1.63926e78 −0.180003
\(389\) 1.40497e79 1.42628 0.713140 0.701021i \(-0.247272\pi\)
0.713140 + 0.701021i \(0.247272\pi\)
\(390\) 7.12158e77 0.0668507
\(391\) 2.11128e78 0.183297
\(392\) 9.53317e77 0.0765618
\(393\) −1.39271e78 −0.103488
\(394\) −3.65057e78 −0.251030
\(395\) −1.45517e78 −0.0926194
\(396\) 4.49915e79 2.65111
\(397\) 5.99515e78 0.327107 0.163553 0.986534i \(-0.447704\pi\)
0.163553 + 0.986534i \(0.447704\pi\)
\(398\) 1.17021e79 0.591333
\(399\) −5.65611e79 −2.64755
\(400\) −1.17551e79 −0.509798
\(401\) 1.50995e79 0.606818 0.303409 0.952860i \(-0.401875\pi\)
0.303409 + 0.952860i \(0.401875\pi\)
\(402\) −2.20771e79 −0.822333
\(403\) 1.69799e79 0.586314
\(404\) 8.52644e77 0.0272983
\(405\) 4.29201e78 0.127433
\(406\) −4.86917e78 −0.134094
\(407\) −4.64736e79 −1.18735
\(408\) 2.70428e79 0.641087
\(409\) −2.38844e79 −0.525476 −0.262738 0.964867i \(-0.584626\pi\)
−0.262738 + 0.964867i \(0.584626\pi\)
\(410\) −2.11677e78 −0.0432282
\(411\) 2.00474e79 0.380086
\(412\) −3.75347e79 −0.660796
\(413\) 3.66368e79 0.599020
\(414\) 2.09951e79 0.318865
\(415\) −2.76473e78 −0.0390108
\(416\) −6.09998e79 −0.799801
\(417\) 2.75979e80 3.36299
\(418\) 8.25802e79 0.935405
\(419\) −1.50267e80 −1.58247 −0.791233 0.611514i \(-0.790561\pi\)
−0.791233 + 0.611514i \(0.790561\pi\)
\(420\) 1.74158e79 0.170545
\(421\) 6.15744e79 0.560785 0.280392 0.959885i \(-0.409535\pi\)
0.280392 + 0.959885i \(0.409535\pi\)
\(422\) −6.41833e79 −0.543741
\(423\) −4.04968e80 −3.19183
\(424\) 6.92480e79 0.507865
\(425\) 7.02832e79 0.479721
\(426\) −1.86144e80 −1.18265
\(427\) −4.37955e79 −0.259047
\(428\) −2.52785e79 −0.139225
\(429\) 4.38883e80 2.25113
\(430\) 6.88886e78 0.0329124
\(431\) 2.96244e80 1.31854 0.659269 0.751907i \(-0.270866\pi\)
0.659269 + 0.751907i \(0.270866\pi\)
\(432\) −2.26793e80 −0.940537
\(433\) −2.82927e80 −1.09344 −0.546719 0.837316i \(-0.684123\pi\)
−0.546719 + 0.837316i \(0.684123\pi\)
\(434\) −8.56360e79 −0.308475
\(435\) −1.80411e79 −0.0605814
\(436\) 2.15398e80 0.674377
\(437\) −1.86857e80 −0.545537
\(438\) 1.90501e80 0.518723
\(439\) 6.24335e80 1.58580 0.792902 0.609349i \(-0.208569\pi\)
0.792902 + 0.609349i \(0.208569\pi\)
\(440\) −5.60987e79 −0.132937
\(441\) 9.35845e79 0.206932
\(442\) 8.02899e79 0.165684
\(443\) −7.11121e80 −1.36971 −0.684857 0.728678i \(-0.740135\pi\)
−0.684857 + 0.728678i \(0.740135\pi\)
\(444\) 6.10512e80 1.09778
\(445\) −1.97703e79 −0.0331920
\(446\) −2.92618e80 −0.458762
\(447\) −7.45279e80 −1.09129
\(448\) −8.84821e79 −0.121025
\(449\) −1.48296e81 −1.89503 −0.947514 0.319714i \(-0.896413\pi\)
−0.947514 + 0.319714i \(0.896413\pi\)
\(450\) 6.98914e80 0.834530
\(451\) −1.30451e81 −1.45567
\(452\) 1.24789e81 1.30153
\(453\) 2.11870e81 2.06574
\(454\) 2.92674e80 0.266797
\(455\) 1.14078e80 0.0972424
\(456\) −2.39340e81 −1.90804
\(457\) 8.32281e80 0.620620 0.310310 0.950635i \(-0.399567\pi\)
0.310310 + 0.950635i \(0.399567\pi\)
\(458\) 5.20874e80 0.363359
\(459\) 1.35598e81 0.885048
\(460\) 5.75353e79 0.0351415
\(461\) 1.90621e81 1.08966 0.544832 0.838545i \(-0.316594\pi\)
0.544832 + 0.838545i \(0.316594\pi\)
\(462\) −2.21346e81 −1.18438
\(463\) −7.11693e80 −0.356511 −0.178255 0.983984i \(-0.557045\pi\)
−0.178255 + 0.983984i \(0.557045\pi\)
\(464\) 3.40191e80 0.159560
\(465\) −3.17295e80 −0.139363
\(466\) 1.80479e81 0.742431
\(467\) 1.96641e81 0.757721 0.378860 0.925454i \(-0.376316\pi\)
0.378860 + 0.925454i \(0.376316\pi\)
\(468\) −3.87149e81 −1.39759
\(469\) −3.53646e81 −1.19618
\(470\) 2.28872e80 0.0725451
\(471\) −3.86740e81 −1.14890
\(472\) 1.55030e81 0.431702
\(473\) 4.24541e81 1.10829
\(474\) −2.42957e81 −0.594688
\(475\) −6.22034e81 −1.42777
\(476\) 1.96349e81 0.422684
\(477\) 6.79788e81 1.37266
\(478\) 3.60972e81 0.683790
\(479\) 2.12205e81 0.377158 0.188579 0.982058i \(-0.439612\pi\)
0.188579 + 0.982058i \(0.439612\pi\)
\(480\) 1.13988e81 0.190108
\(481\) 3.99902e81 0.625935
\(482\) −1.00892e81 −0.148225
\(483\) 5.00845e81 0.690742
\(484\) −9.26765e81 −1.20001
\(485\) 2.00649e80 0.0243957
\(486\) 5.69250e80 0.0649976
\(487\) −6.70124e81 −0.718658 −0.359329 0.933211i \(-0.616994\pi\)
−0.359329 + 0.933211i \(0.616994\pi\)
\(488\) −1.85322e81 −0.186690
\(489\) −1.07785e82 −1.02009
\(490\) −5.28902e79 −0.00470321
\(491\) 8.10525e81 0.677300 0.338650 0.940912i \(-0.390030\pi\)
0.338650 + 0.940912i \(0.390030\pi\)
\(492\) 1.71370e82 1.34586
\(493\) −2.03398e81 −0.150147
\(494\) −7.10597e81 −0.493119
\(495\) −5.50706e81 −0.359303
\(496\) 5.98307e81 0.367057
\(497\) −2.98179e82 −1.72031
\(498\) −4.61602e81 −0.250480
\(499\) 6.93437e81 0.353949 0.176974 0.984215i \(-0.443369\pi\)
0.176974 + 0.984215i \(0.443369\pi\)
\(500\) 3.85512e81 0.185120
\(501\) −2.20266e82 −0.995167
\(502\) 1.27146e82 0.540553
\(503\) 4.44563e82 1.77873 0.889364 0.457200i \(-0.151147\pi\)
0.889364 + 0.457200i \(0.151147\pi\)
\(504\) 4.30776e82 1.62226
\(505\) −1.04366e80 −0.00369973
\(506\) −7.31243e81 −0.244046
\(507\) 1.77571e82 0.557994
\(508\) −1.79071e82 −0.529886
\(509\) −1.53808e82 −0.428635 −0.214317 0.976764i \(-0.568753\pi\)
−0.214317 + 0.976764i \(0.568753\pi\)
\(510\) −1.50034e81 −0.0393822
\(511\) 3.05157e82 0.754546
\(512\) −3.82563e82 −0.891187
\(513\) −1.20010e83 −2.63413
\(514\) −6.83276e81 −0.141326
\(515\) 4.59433e81 0.0895574
\(516\) −5.57708e82 −1.02469
\(517\) 1.41047e83 2.44289
\(518\) −2.01686e82 −0.329320
\(519\) 1.09273e83 1.68232
\(520\) 4.82726e81 0.0700807
\(521\) −1.18328e83 −1.62009 −0.810044 0.586369i \(-0.800557\pi\)
−0.810044 + 0.586369i \(0.800557\pi\)
\(522\) −2.02264e82 −0.261197
\(523\) −9.45207e82 −1.15140 −0.575699 0.817662i \(-0.695270\pi\)
−0.575699 + 0.817662i \(0.695270\pi\)
\(524\) −4.27892e81 −0.0491733
\(525\) 1.66728e83 1.80780
\(526\) 7.20603e82 0.737278
\(527\) −3.57724e82 −0.345401
\(528\) 1.54646e83 1.40930
\(529\) −9.97053e82 −0.857670
\(530\) −3.84189e81 −0.0311983
\(531\) 1.52188e83 1.16681
\(532\) −1.73776e83 −1.25801
\(533\) 1.12252e83 0.767387
\(534\) −3.30087e82 −0.213118
\(535\) 3.09415e81 0.0188691
\(536\) −1.49646e83 −0.862065
\(537\) −2.85590e83 −1.55427
\(538\) −8.43148e80 −0.00433555
\(539\) −3.25948e82 −0.158376
\(540\) 3.69524e82 0.169681
\(541\) 1.48411e82 0.0644093 0.0322046 0.999481i \(-0.489747\pi\)
0.0322046 + 0.999481i \(0.489747\pi\)
\(542\) 1.88503e83 0.773287
\(543\) −2.54338e83 −0.986316
\(544\) 1.28511e83 0.471167
\(545\) −2.63651e82 −0.0913980
\(546\) 1.90466e83 0.624371
\(547\) 3.24255e83 1.00525 0.502624 0.864505i \(-0.332368\pi\)
0.502624 + 0.864505i \(0.332368\pi\)
\(548\) 6.15929e82 0.180602
\(549\) −1.81925e83 −0.504588
\(550\) −2.43426e83 −0.638713
\(551\) 1.80015e83 0.446874
\(552\) 2.11934e83 0.497804
\(553\) −3.89185e83 −0.865046
\(554\) 5.46497e82 0.114958
\(555\) −7.47279e82 −0.148781
\(556\) 8.47908e83 1.59797
\(557\) 4.33577e83 0.773540 0.386770 0.922176i \(-0.373591\pi\)
0.386770 + 0.922176i \(0.373591\pi\)
\(558\) −3.55730e83 −0.600865
\(559\) −3.65315e83 −0.584261
\(560\) 4.01970e82 0.0608777
\(561\) −9.24618e83 −1.32616
\(562\) 7.36355e82 0.100030
\(563\) 8.30382e83 1.06849 0.534247 0.845328i \(-0.320595\pi\)
0.534247 + 0.845328i \(0.320595\pi\)
\(564\) −1.85290e84 −2.25860
\(565\) −1.52744e83 −0.176396
\(566\) 8.44882e82 0.0924474
\(567\) 1.14790e84 1.19020
\(568\) −1.26175e84 −1.23979
\(569\) −1.27745e84 −1.18965 −0.594826 0.803854i \(-0.702779\pi\)
−0.594826 + 0.803854i \(0.702779\pi\)
\(570\) 1.32786e83 0.117211
\(571\) 8.91829e83 0.746243 0.373121 0.927783i \(-0.378288\pi\)
0.373121 + 0.927783i \(0.378288\pi\)
\(572\) 1.34841e84 1.06965
\(573\) 4.06129e84 3.05456
\(574\) −5.66131e83 −0.403742
\(575\) 5.50807e83 0.372504
\(576\) −3.67552e83 −0.235740
\(577\) −1.15402e84 −0.702023 −0.351012 0.936371i \(-0.614162\pi\)
−0.351012 + 0.936371i \(0.614162\pi\)
\(578\) 5.47424e83 0.315882
\(579\) −2.12142e84 −1.16126
\(580\) −5.54287e82 −0.0287860
\(581\) −7.39425e83 −0.364353
\(582\) 3.35005e83 0.156639
\(583\) −2.36765e84 −1.05057
\(584\) 1.29128e84 0.543787
\(585\) 4.73879e83 0.189414
\(586\) −2.09117e83 −0.0793437
\(587\) −1.26376e84 −0.455200 −0.227600 0.973755i \(-0.573088\pi\)
−0.227600 + 0.973755i \(0.573088\pi\)
\(588\) 4.28189e83 0.146429
\(589\) 3.16600e84 1.02800
\(590\) −8.60108e82 −0.0265196
\(591\) −3.61751e84 −1.05923
\(592\) 1.40911e84 0.391861
\(593\) −2.81980e84 −0.744818 −0.372409 0.928069i \(-0.621468\pi\)
−0.372409 + 0.928069i \(0.621468\pi\)
\(594\) −4.69645e84 −1.17837
\(595\) −2.40335e83 −0.0572861
\(596\) −2.28977e84 −0.518539
\(597\) 1.15962e85 2.49515
\(598\) 6.29230e83 0.128654
\(599\) 2.57638e84 0.500602 0.250301 0.968168i \(-0.419470\pi\)
0.250301 + 0.968168i \(0.419470\pi\)
\(600\) 7.05515e84 1.30285
\(601\) 1.93837e84 0.340224 0.170112 0.985425i \(-0.445587\pi\)
0.170112 + 0.985425i \(0.445587\pi\)
\(602\) 1.84242e84 0.307395
\(603\) −1.46904e85 −2.32999
\(604\) 6.50943e84 0.981559
\(605\) 1.13438e84 0.162637
\(606\) −1.74250e83 −0.0237551
\(607\) 9.64610e83 0.125054 0.0625269 0.998043i \(-0.480084\pi\)
0.0625269 + 0.998043i \(0.480084\pi\)
\(608\) −1.13738e85 −1.40231
\(609\) −4.82507e84 −0.565818
\(610\) 1.02817e83 0.0114684
\(611\) −1.21370e85 −1.28782
\(612\) 8.15627e84 0.823328
\(613\) 1.07878e85 1.03607 0.518034 0.855360i \(-0.326664\pi\)
0.518034 + 0.855360i \(0.326664\pi\)
\(614\) 7.50514e84 0.685841
\(615\) −2.09760e84 −0.182403
\(616\) −1.50036e85 −1.24160
\(617\) −3.73172e84 −0.293908 −0.146954 0.989143i \(-0.546947\pi\)
−0.146954 + 0.989143i \(0.546947\pi\)
\(618\) 7.67073e84 0.575027
\(619\) −8.80827e84 −0.628529 −0.314265 0.949335i \(-0.601758\pi\)
−0.314265 + 0.949335i \(0.601758\pi\)
\(620\) −9.74847e83 −0.0662201
\(621\) 1.06268e85 0.687240
\(622\) 2.38496e84 0.146850
\(623\) −5.28757e84 −0.310006
\(624\) −1.33072e85 −0.742944
\(625\) 1.80986e85 0.962287
\(626\) −1.03842e85 −0.525841
\(627\) 8.18324e85 3.94698
\(628\) −1.18821e85 −0.545912
\(629\) −8.42495e84 −0.368742
\(630\) −2.38995e84 −0.0996558
\(631\) 1.68356e85 0.668856 0.334428 0.942421i \(-0.391457\pi\)
0.334428 + 0.942421i \(0.391457\pi\)
\(632\) −1.64684e85 −0.623422
\(633\) −6.36020e85 −2.29434
\(634\) −1.77355e85 −0.609708
\(635\) 2.19187e84 0.0718152
\(636\) 3.11032e85 0.971322
\(637\) 2.80476e84 0.0834915
\(638\) 7.04470e84 0.199909
\(639\) −1.23863e86 −3.35092
\(640\) 4.43209e84 0.114319
\(641\) 6.42250e85 1.57955 0.789777 0.613394i \(-0.210196\pi\)
0.789777 + 0.613394i \(0.210196\pi\)
\(642\) 5.16602e84 0.121154
\(643\) −3.55027e84 −0.0794011 −0.0397005 0.999212i \(-0.512640\pi\)
−0.0397005 + 0.999212i \(0.512640\pi\)
\(644\) 1.53878e85 0.328214
\(645\) 6.82647e84 0.138875
\(646\) 1.49705e85 0.290499
\(647\) 8.24068e85 1.52539 0.762697 0.646755i \(-0.223875\pi\)
0.762697 + 0.646755i \(0.223875\pi\)
\(648\) 4.85735e85 0.857752
\(649\) −5.30061e85 −0.893022
\(650\) 2.09467e85 0.336711
\(651\) −8.48605e85 −1.30162
\(652\) −3.31155e85 −0.484708
\(653\) 3.96464e85 0.553799 0.276899 0.960899i \(-0.410693\pi\)
0.276899 + 0.960899i \(0.410693\pi\)
\(654\) −4.40195e85 −0.586845
\(655\) 5.23749e83 0.00666443
\(656\) 3.95534e85 0.480416
\(657\) 1.26761e86 1.46975
\(658\) 6.12117e85 0.677555
\(659\) −8.56515e85 −0.905169 −0.452585 0.891721i \(-0.649498\pi\)
−0.452585 + 0.891721i \(0.649498\pi\)
\(660\) −2.51971e85 −0.254250
\(661\) −1.49484e86 −1.44029 −0.720144 0.693825i \(-0.755924\pi\)
−0.720144 + 0.693825i \(0.755924\pi\)
\(662\) −9.82171e83 −0.00903688
\(663\) 7.95628e85 0.699113
\(664\) −3.12890e85 −0.262582
\(665\) 2.12706e85 0.170498
\(666\) −8.37799e85 −0.641469
\(667\) −1.59402e85 −0.116589
\(668\) −6.76737e85 −0.472865
\(669\) −2.89968e86 −1.93577
\(670\) 8.30241e84 0.0529569
\(671\) 6.33632e85 0.386189
\(672\) 3.04859e86 1.77556
\(673\) 9.30605e85 0.517972 0.258986 0.965881i \(-0.416612\pi\)
0.258986 + 0.965881i \(0.416612\pi\)
\(674\) −2.81861e85 −0.149937
\(675\) 3.53759e86 1.79863
\(676\) 5.45563e85 0.265137
\(677\) 1.12642e85 0.0523293 0.0261646 0.999658i \(-0.491671\pi\)
0.0261646 + 0.999658i \(0.491671\pi\)
\(678\) −2.55024e86 −1.13260
\(679\) 5.36634e85 0.227851
\(680\) −1.01698e85 −0.0412850
\(681\) 2.90023e86 1.12576
\(682\) 1.23898e86 0.459876
\(683\) −3.40704e86 −1.20933 −0.604666 0.796479i \(-0.706693\pi\)
−0.604666 + 0.796479i \(0.706693\pi\)
\(684\) −7.21862e86 −2.45043
\(685\) −7.53910e84 −0.0244769
\(686\) 1.25584e86 0.389986
\(687\) 5.16157e86 1.53321
\(688\) −1.28723e86 −0.365771
\(689\) 2.03735e86 0.553833
\(690\) −1.17581e85 −0.0305803
\(691\) −4.85715e85 −0.120865 −0.0604326 0.998172i \(-0.519248\pi\)
−0.0604326 + 0.998172i \(0.519248\pi\)
\(692\) 3.35727e86 0.799375
\(693\) −1.47286e87 −3.35581
\(694\) 1.86721e86 0.407126
\(695\) −1.03786e86 −0.216571
\(696\) −2.04174e86 −0.407774
\(697\) −2.36487e86 −0.452073
\(698\) −3.37151e86 −0.616927
\(699\) 1.78844e87 3.13272
\(700\) 5.12250e86 0.858997
\(701\) −9.30644e86 −1.49411 −0.747057 0.664759i \(-0.768534\pi\)
−0.747057 + 0.664759i \(0.768534\pi\)
\(702\) 4.04126e86 0.621206
\(703\) 7.45642e86 1.09747
\(704\) 1.28016e86 0.180425
\(705\) 2.26799e86 0.306107
\(706\) 4.53497e86 0.586180
\(707\) −2.79125e85 −0.0345547
\(708\) 6.96326e86 0.825655
\(709\) −1.39697e87 −1.58663 −0.793316 0.608810i \(-0.791647\pi\)
−0.793316 + 0.608810i \(0.791647\pi\)
\(710\) 7.00023e85 0.0761610
\(711\) −1.61666e87 −1.68499
\(712\) −2.23745e86 −0.223415
\(713\) −2.80347e86 −0.268204
\(714\) −4.01266e86 −0.367821
\(715\) −1.65048e86 −0.144970
\(716\) −8.77436e86 −0.738530
\(717\) 3.57703e87 2.88528
\(718\) −5.00732e86 −0.387088
\(719\) −1.38529e87 −1.02639 −0.513193 0.858273i \(-0.671537\pi\)
−0.513193 + 0.858273i \(0.671537\pi\)
\(720\) 1.66977e86 0.118581
\(721\) 1.22875e87 0.836447
\(722\) −6.91304e86 −0.451112
\(723\) −9.99784e86 −0.625444
\(724\) −7.81419e86 −0.468660
\(725\) −5.30641e86 −0.305134
\(726\) 1.89397e87 1.04426
\(727\) 3.07878e85 0.0162772 0.00813860 0.999967i \(-0.497409\pi\)
0.00813860 + 0.999967i \(0.497409\pi\)
\(728\) 1.29105e87 0.654539
\(729\) −1.76866e87 −0.859913
\(730\) −7.16405e85 −0.0334050
\(731\) 7.69627e86 0.344192
\(732\) −8.32385e86 −0.357056
\(733\) 2.95619e87 1.21636 0.608178 0.793801i \(-0.291901\pi\)
0.608178 + 0.793801i \(0.291901\pi\)
\(734\) 1.44641e87 0.570902
\(735\) −5.24112e85 −0.0198454
\(736\) 1.00714e87 0.365862
\(737\) 5.11654e87 1.78328
\(738\) −2.35169e87 −0.786432
\(739\) −2.83483e87 −0.909646 −0.454823 0.890582i \(-0.650297\pi\)
−0.454823 + 0.890582i \(0.650297\pi\)
\(740\) −2.29592e86 −0.0706950
\(741\) −7.04162e87 −2.08074
\(742\) −1.02751e87 −0.291386
\(743\) 4.13337e87 1.12498 0.562491 0.826804i \(-0.309843\pi\)
0.562491 + 0.826804i \(0.309843\pi\)
\(744\) −3.59089e87 −0.938054
\(745\) 2.80273e86 0.0702773
\(746\) −2.29534e86 −0.0552475
\(747\) −3.07155e87 −0.709708
\(748\) −2.84077e87 −0.630139
\(749\) 8.27528e86 0.176233
\(750\) −7.87846e86 −0.161092
\(751\) 3.63538e87 0.713727 0.356863 0.934157i \(-0.383846\pi\)
0.356863 + 0.934157i \(0.383846\pi\)
\(752\) −4.27664e87 −0.806229
\(753\) 1.25994e88 2.28089
\(754\) −6.06192e86 −0.105386
\(755\) −7.96768e86 −0.133030
\(756\) 9.88290e87 1.58478
\(757\) −1.27239e87 −0.195972 −0.0979861 0.995188i \(-0.531240\pi\)
−0.0979861 + 0.995188i \(0.531240\pi\)
\(758\) 1.10022e87 0.162768
\(759\) −7.24621e87 −1.02976
\(760\) 9.00071e86 0.122875
\(761\) −4.01227e87 −0.526209 −0.263104 0.964767i \(-0.584746\pi\)
−0.263104 + 0.964767i \(0.584746\pi\)
\(762\) 3.65957e87 0.461109
\(763\) −7.05135e87 −0.853638
\(764\) 1.24778e88 1.45141
\(765\) −9.98345e86 −0.111585
\(766\) −6.69219e87 −0.718772
\(767\) 4.56113e87 0.470776
\(768\) 5.37133e87 0.532800
\(769\) −1.06276e87 −0.101317 −0.0506584 0.998716i \(-0.516132\pi\)
−0.0506584 + 0.998716i \(0.516132\pi\)
\(770\) 8.32402e86 0.0762721
\(771\) −6.77088e87 −0.596330
\(772\) −6.51777e87 −0.551787
\(773\) −1.73425e88 −1.41136 −0.705679 0.708532i \(-0.749358\pi\)
−0.705679 + 0.708532i \(0.749358\pi\)
\(774\) 7.65337e87 0.598761
\(775\) −9.33259e87 −0.701940
\(776\) 2.27078e87 0.164207
\(777\) −1.99860e88 −1.38958
\(778\) −8.82155e87 −0.589749
\(779\) 2.09301e88 1.34548
\(780\) 2.16820e87 0.134033
\(781\) 4.31404e88 2.56465
\(782\) −1.32563e87 −0.0757909
\(783\) −1.02377e88 −0.562949
\(784\) 9.88291e86 0.0522691
\(785\) 1.45439e87 0.0739871
\(786\) 8.74456e86 0.0427908
\(787\) 7.10492e87 0.334449 0.167224 0.985919i \(-0.446520\pi\)
0.167224 + 0.985919i \(0.446520\pi\)
\(788\) −1.11143e88 −0.503307
\(789\) 7.14077e88 3.11098
\(790\) 9.13673e86 0.0382970
\(791\) −4.08514e88 −1.64750
\(792\) −6.23245e88 −2.41847
\(793\) −5.45236e87 −0.203588
\(794\) −3.76424e87 −0.135255
\(795\) −3.80710e87 −0.131643
\(796\) 3.56277e88 1.18560
\(797\) −2.01224e88 −0.644467 −0.322233 0.946660i \(-0.604434\pi\)
−0.322233 + 0.946660i \(0.604434\pi\)
\(798\) 3.55136e88 1.09473
\(799\) 2.55697e88 0.758663
\(800\) 3.35271e88 0.957528
\(801\) −2.19644e88 −0.603848
\(802\) −9.48066e87 −0.250911
\(803\) −4.41500e88 −1.12488
\(804\) −6.72147e88 −1.64875
\(805\) −1.88350e87 −0.0444827
\(806\) −1.06613e88 −0.242434
\(807\) −8.35512e86 −0.0182941
\(808\) −1.18113e87 −0.0249029
\(809\) −1.07349e88 −0.217957 −0.108978 0.994044i \(-0.534758\pi\)
−0.108978 + 0.994044i \(0.534758\pi\)
\(810\) −2.69487e87 −0.0526920
\(811\) −7.32258e87 −0.137888 −0.0689442 0.997621i \(-0.521963\pi\)
−0.0689442 + 0.997621i \(0.521963\pi\)
\(812\) −1.48244e88 −0.268855
\(813\) 1.86796e89 3.26292
\(814\) 2.91799e88 0.490952
\(815\) 4.05341e87 0.0656922
\(816\) 2.80349e88 0.437673
\(817\) −6.81151e88 −1.02440
\(818\) 1.49965e88 0.217278
\(819\) 1.26739e89 1.76909
\(820\) −6.44461e87 −0.0866710
\(821\) −8.61776e88 −1.11668 −0.558339 0.829613i \(-0.688561\pi\)
−0.558339 + 0.829613i \(0.688561\pi\)
\(822\) −1.25874e88 −0.157161
\(823\) −8.68150e87 −0.104448 −0.0522240 0.998635i \(-0.516631\pi\)
−0.0522240 + 0.998635i \(0.516631\pi\)
\(824\) 5.19949e88 0.602811
\(825\) −2.41222e89 −2.69508
\(826\) −2.30036e88 −0.247687
\(827\) −2.76062e88 −0.286476 −0.143238 0.989688i \(-0.545751\pi\)
−0.143238 + 0.989688i \(0.545751\pi\)
\(828\) 6.39205e88 0.639315
\(829\) −1.28246e88 −0.123632 −0.0618162 0.998088i \(-0.519689\pi\)
−0.0618162 + 0.998088i \(0.519689\pi\)
\(830\) 1.73592e87 0.0161305
\(831\) 5.41548e88 0.485071
\(832\) −1.10157e88 −0.0951149
\(833\) −5.90893e87 −0.0491854
\(834\) −1.73282e89 −1.39056
\(835\) 8.28340e87 0.0640872
\(836\) 2.51419e89 1.87545
\(837\) −1.80055e89 −1.29502
\(838\) 9.43495e88 0.654330
\(839\) 1.98229e89 1.32565 0.662824 0.748776i \(-0.269358\pi\)
0.662824 + 0.748776i \(0.269358\pi\)
\(840\) −2.41252e88 −0.155580
\(841\) −1.45440e89 −0.904497
\(842\) −3.86614e88 −0.231878
\(843\) 7.29686e88 0.422080
\(844\) −1.95409e89 −1.09018
\(845\) −6.67781e87 −0.0359339
\(846\) 2.54272e89 1.31978
\(847\) 3.03390e89 1.51900
\(848\) 7.17885e88 0.346722
\(849\) 8.37230e88 0.390086
\(850\) −4.41294e88 −0.198359
\(851\) −6.60261e88 −0.286328
\(852\) −5.66724e89 −2.37118
\(853\) 1.96594e89 0.793641 0.396821 0.917896i \(-0.370114\pi\)
0.396821 + 0.917896i \(0.370114\pi\)
\(854\) 2.74983e88 0.107113
\(855\) 8.83574e88 0.332106
\(856\) 3.50171e88 0.127008
\(857\) 1.54952e89 0.542353 0.271177 0.962530i \(-0.412587\pi\)
0.271177 + 0.962530i \(0.412587\pi\)
\(858\) −2.75566e89 −0.930816
\(859\) −2.29205e89 −0.747192 −0.373596 0.927592i \(-0.621875\pi\)
−0.373596 + 0.927592i \(0.621875\pi\)
\(860\) 2.09734e88 0.0659882
\(861\) −5.61003e89 −1.70361
\(862\) −1.86006e89 −0.545199
\(863\) −2.50671e89 −0.709211 −0.354606 0.935016i \(-0.615385\pi\)
−0.354606 + 0.935016i \(0.615385\pi\)
\(864\) 6.46842e89 1.76656
\(865\) −4.10937e88 −0.108339
\(866\) 1.77645e89 0.452123
\(867\) 5.42466e89 1.33288
\(868\) −2.60722e89 −0.618482
\(869\) 5.63071e89 1.28961
\(870\) 1.13276e88 0.0250497
\(871\) −4.40275e89 −0.940092
\(872\) −2.98380e89 −0.615200
\(873\) 2.22916e89 0.443820
\(874\) 1.17324e89 0.225573
\(875\) −1.26203e89 −0.234327
\(876\) 5.79987e89 1.04002
\(877\) 2.61925e89 0.453617 0.226809 0.973939i \(-0.427171\pi\)
0.226809 + 0.973939i \(0.427171\pi\)
\(878\) −3.92008e89 −0.655710
\(879\) −2.07223e89 −0.334794
\(880\) −5.81569e88 −0.0907568
\(881\) −7.15408e87 −0.0107842 −0.00539211 0.999985i \(-0.501716\pi\)
−0.00539211 + 0.999985i \(0.501716\pi\)
\(882\) −5.87599e88 −0.0855636
\(883\) 8.44585e89 1.18807 0.594035 0.804439i \(-0.297534\pi\)
0.594035 + 0.804439i \(0.297534\pi\)
\(884\) 2.44446e89 0.332192
\(885\) −8.52319e88 −0.111901
\(886\) 4.46499e89 0.566359
\(887\) −6.84839e89 −0.839302 −0.419651 0.907686i \(-0.637847\pi\)
−0.419651 + 0.907686i \(0.637847\pi\)
\(888\) −8.45711e89 −1.00144
\(889\) 5.86215e89 0.670739
\(890\) 1.24134e88 0.0137245
\(891\) −1.66077e90 −1.77435
\(892\) −8.90887e89 −0.919803
\(893\) −2.26302e90 −2.25797
\(894\) 4.67946e89 0.451234
\(895\) 1.07400e89 0.100093
\(896\) 1.18536e90 1.06772
\(897\) 6.23531e89 0.542861
\(898\) 9.31121e89 0.783570
\(899\) 2.70083e89 0.219698
\(900\) 2.12787e90 1.67320
\(901\) −4.29219e89 −0.326267
\(902\) 8.19076e89 0.601901
\(903\) 1.82574e90 1.29706
\(904\) −1.72864e90 −1.18732
\(905\) 9.56474e88 0.0635172
\(906\) −1.33029e90 −0.854156
\(907\) 1.40576e90 0.872748 0.436374 0.899765i \(-0.356262\pi\)
0.436374 + 0.899765i \(0.356262\pi\)
\(908\) 8.91058e89 0.534919
\(909\) −1.15948e89 −0.0673076
\(910\) −7.16276e88 −0.0402085
\(911\) −2.64352e90 −1.43507 −0.717534 0.696523i \(-0.754729\pi\)
−0.717534 + 0.696523i \(0.754729\pi\)
\(912\) −2.48120e90 −1.30263
\(913\) 1.06980e90 0.543179
\(914\) −5.22573e89 −0.256618
\(915\) 1.01886e89 0.0483916
\(916\) 1.58582e90 0.728522
\(917\) 1.40076e89 0.0622444
\(918\) −8.51394e89 −0.365956
\(919\) −4.96356e89 −0.206381 −0.103191 0.994662i \(-0.532905\pi\)
−0.103191 + 0.994662i \(0.532905\pi\)
\(920\) −7.97008e88 −0.0320578
\(921\) 7.43717e90 2.89394
\(922\) −1.19687e90 −0.450562
\(923\) −3.71221e90 −1.35201
\(924\) −6.73896e90 −2.37464
\(925\) −2.19797e90 −0.749374
\(926\) 4.46858e89 0.147413
\(927\) 5.10420e90 1.62928
\(928\) −9.70266e89 −0.299694
\(929\) −3.32635e90 −0.994234 −0.497117 0.867684i \(-0.665608\pi\)
−0.497117 + 0.867684i \(0.665608\pi\)
\(930\) 1.99223e89 0.0576250
\(931\) 5.22963e89 0.146388
\(932\) 5.49475e90 1.48855
\(933\) 2.36336e90 0.619640
\(934\) −1.23467e90 −0.313308
\(935\) 3.47716e89 0.0854024
\(936\) 5.36298e90 1.27495
\(937\) 5.45798e90 1.25596 0.627978 0.778231i \(-0.283883\pi\)
0.627978 + 0.778231i \(0.283883\pi\)
\(938\) 2.22048e90 0.494606
\(939\) −1.02901e91 −2.21881
\(940\) 6.96810e89 0.145450
\(941\) −2.34364e90 −0.473595 −0.236797 0.971559i \(-0.576098\pi\)
−0.236797 + 0.971559i \(0.576098\pi\)
\(942\) 2.42826e90 0.475054
\(943\) −1.85335e90 −0.351034
\(944\) 1.60717e90 0.294725
\(945\) −1.20969e90 −0.214785
\(946\) −2.66561e90 −0.458265
\(947\) 4.24224e90 0.706190 0.353095 0.935588i \(-0.385129\pi\)
0.353095 + 0.935588i \(0.385129\pi\)
\(948\) −7.39691e90 −1.19233
\(949\) 3.79908e90 0.593006
\(950\) 3.90563e90 0.590366
\(951\) −1.75749e91 −2.57269
\(952\) −2.71992e90 −0.385593
\(953\) 4.76356e90 0.654031 0.327015 0.945019i \(-0.393957\pi\)
0.327015 + 0.945019i \(0.393957\pi\)
\(954\) −4.26826e90 −0.567578
\(955\) −1.52731e90 −0.196709
\(956\) 1.09899e91 1.37098
\(957\) 6.98090e90 0.843524
\(958\) −1.33240e90 −0.155950
\(959\) −2.01633e90 −0.228609
\(960\) 2.05844e89 0.0226082
\(961\) −4.64855e90 −0.494600
\(962\) −2.51091e90 −0.258816
\(963\) 3.43753e90 0.343277
\(964\) −3.07170e90 −0.297187
\(965\) 7.97789e89 0.0747833
\(966\) −3.14471e90 −0.285613
\(967\) 1.00304e91 0.882699 0.441350 0.897335i \(-0.354500\pi\)
0.441350 + 0.897335i \(0.354500\pi\)
\(968\) 1.28380e91 1.09471
\(969\) 1.48349e91 1.22577
\(970\) −1.25983e89 −0.0100873
\(971\) 3.02928e90 0.235046 0.117523 0.993070i \(-0.462505\pi\)
0.117523 + 0.993070i \(0.462505\pi\)
\(972\) 1.73311e90 0.130318
\(973\) −2.77575e91 −2.02273
\(974\) 4.20758e90 0.297156
\(975\) 2.07570e91 1.42077
\(976\) −1.92121e90 −0.127454
\(977\) −2.66487e91 −1.71353 −0.856764 0.515709i \(-0.827529\pi\)
−0.856764 + 0.515709i \(0.827529\pi\)
\(978\) 6.76762e90 0.421794
\(979\) 7.65003e90 0.462159
\(980\) −1.61026e89 −0.00942979
\(981\) −2.92911e91 −1.66277
\(982\) −5.08913e90 −0.280055
\(983\) −2.34161e91 −1.24920 −0.624601 0.780944i \(-0.714739\pi\)
−0.624601 + 0.780944i \(0.714739\pi\)
\(984\) −2.37390e91 −1.22776
\(985\) 1.36042e90 0.0682129
\(986\) 1.27710e90 0.0620837
\(987\) 6.06574e91 2.85897
\(988\) −2.16344e91 −0.988687
\(989\) 6.03155e90 0.267265
\(990\) 3.45777e90 0.148567
\(991\) 3.94657e91 1.64427 0.822135 0.569292i \(-0.192783\pi\)
0.822135 + 0.569292i \(0.192783\pi\)
\(992\) −1.70645e91 −0.689424
\(993\) −9.73276e89 −0.0381315
\(994\) 1.87221e91 0.711327
\(995\) −4.36090e90 −0.160684
\(996\) −1.40537e91 −0.502203
\(997\) 5.53684e91 1.91893 0.959466 0.281823i \(-0.0909390\pi\)
0.959466 + 0.281823i \(0.0909390\pi\)
\(998\) −4.35396e90 −0.146353
\(999\) −4.24057e91 −1.38254
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.62.a.a.1.2 4
3.2 odd 2 9.62.a.a.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.62.a.a.1.2 4 1.1 even 1 trivial
9.62.a.a.1.3 4 3.2 odd 2