Properties

Label 1.76.a.a.1.6
Level $1$
Weight $76$
Character 1.1
Self dual yes
Analytic conductor $35.623$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.6
Root \(5.23553e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.67444e11 q^{2} -8.83049e17 q^{3} +9.72365e22 q^{4} +2.43619e26 q^{5} -3.24471e29 q^{6} +1.21530e31 q^{7} +2.18473e34 q^{8} +1.71508e35 q^{9} +O(q^{10})\) \(q+3.67444e11 q^{2} -8.83049e17 q^{3} +9.72365e22 q^{4} +2.43619e26 q^{5} -3.24471e29 q^{6} +1.21530e31 q^{7} +2.18473e34 q^{8} +1.71508e35 q^{9} +8.95165e37 q^{10} -5.65037e38 q^{11} -8.58645e40 q^{12} +5.30382e40 q^{13} +4.46553e42 q^{14} -2.15128e44 q^{15} +4.35419e45 q^{16} +1.14821e45 q^{17} +6.30198e46 q^{18} +1.24645e48 q^{19} +2.36887e49 q^{20} -1.07316e49 q^{21} -2.07620e50 q^{22} +8.02205e50 q^{23} -1.92923e52 q^{24} +3.28805e52 q^{25} +1.94886e52 q^{26} +3.85679e53 q^{27} +1.18171e54 q^{28} +8.53673e54 q^{29} -7.90474e55 q^{30} -6.18737e55 q^{31} +7.74555e56 q^{32} +4.98956e56 q^{33} +4.21904e56 q^{34} +2.96069e57 q^{35} +1.66769e58 q^{36} -5.98766e58 q^{37} +4.58002e59 q^{38} -4.68354e58 q^{39} +5.32243e60 q^{40} -5.32628e60 q^{41} -3.94328e60 q^{42} +2.59254e61 q^{43} -5.49422e61 q^{44} +4.17827e61 q^{45} +2.94766e62 q^{46} -5.76440e62 q^{47} -3.84496e63 q^{48} -2.26417e63 q^{49} +1.20818e64 q^{50} -1.01393e63 q^{51} +5.15725e63 q^{52} +5.92558e63 q^{53} +1.41716e65 q^{54} -1.37654e65 q^{55} +2.65510e65 q^{56} -1.10068e66 q^{57} +3.13677e66 q^{58} +2.82712e66 q^{59} -2.09183e67 q^{60} +5.43239e66 q^{61} -2.27352e67 q^{62} +2.08433e66 q^{63} +1.20109e68 q^{64} +1.29211e67 q^{65} +1.83338e68 q^{66} -2.61376e68 q^{67} +1.11648e68 q^{68} -7.08386e68 q^{69} +1.08789e69 q^{70} +1.78760e67 q^{71} +3.74700e69 q^{72} -1.09051e70 q^{73} -2.20013e70 q^{74} -2.90351e70 q^{75} +1.21201e71 q^{76} -6.86687e69 q^{77} -1.72094e70 q^{78} -1.49375e71 q^{79} +1.06076e72 q^{80} -4.44896e71 q^{81} -1.95711e72 q^{82} +3.39100e71 q^{83} -1.04351e72 q^{84} +2.79727e71 q^{85} +9.52613e72 q^{86} -7.53835e72 q^{87} -1.23446e73 q^{88} +2.45405e72 q^{89} +1.53528e73 q^{90} +6.44571e71 q^{91} +7.80036e73 q^{92} +5.46375e73 q^{93} -2.11810e74 q^{94} +3.03660e74 q^{95} -6.83970e74 q^{96} +1.36838e74 q^{97} -8.31957e74 q^{98} -9.69086e73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + O(q^{10}) \) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + \)\(13\!\cdots\!60\)\(q^{10} - \)\(94\!\cdots\!88\)\(q^{11} - \)\(11\!\cdots\!80\)\(q^{12} + \)\(53\!\cdots\!20\)\(q^{13} + \)\(82\!\cdots\!76\)\(q^{14} - \)\(30\!\cdots\!80\)\(q^{15} + \)\(26\!\cdots\!16\)\(q^{16} + \)\(18\!\cdots\!80\)\(q^{17} - \)\(43\!\cdots\!40\)\(q^{18} + \)\(10\!\cdots\!80\)\(q^{19} + \)\(92\!\cdots\!80\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(15\!\cdots\!20\)\(q^{22} + \)\(15\!\cdots\!80\)\(q^{23} - \)\(76\!\cdots\!60\)\(q^{24} + \)\(19\!\cdots\!50\)\(q^{25} + \)\(11\!\cdots\!52\)\(q^{26} - \)\(10\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!20\)\(q^{28} + \)\(14\!\cdots\!20\)\(q^{29} - \)\(25\!\cdots\!80\)\(q^{30} - \)\(41\!\cdots\!88\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(59\!\cdots\!20\)\(q^{33} + \)\(30\!\cdots\!56\)\(q^{34} + \)\(27\!\cdots\!60\)\(q^{35} + \)\(17\!\cdots\!16\)\(q^{36} + \)\(98\!\cdots\!40\)\(q^{37} + \)\(12\!\cdots\!80\)\(q^{38} + \)\(24\!\cdots\!44\)\(q^{39} + \)\(88\!\cdots\!00\)\(q^{40} + \)\(50\!\cdots\!12\)\(q^{41} + \)\(43\!\cdots\!80\)\(q^{42} + \)\(27\!\cdots\!00\)\(q^{43} - \)\(86\!\cdots\!44\)\(q^{44} - \)\(23\!\cdots\!80\)\(q^{45} - \)\(82\!\cdots\!88\)\(q^{46} - \)\(13\!\cdots\!80\)\(q^{47} - \)\(82\!\cdots\!20\)\(q^{48} - \)\(57\!\cdots\!42\)\(q^{49} + \)\(31\!\cdots\!00\)\(q^{50} + \)\(28\!\cdots\!32\)\(q^{51} + \)\(41\!\cdots\!00\)\(q^{52} + \)\(64\!\cdots\!60\)\(q^{53} + \)\(78\!\cdots\!80\)\(q^{54} + \)\(43\!\cdots\!20\)\(q^{55} + \)\(28\!\cdots\!20\)\(q^{56} - \)\(67\!\cdots\!40\)\(q^{57} - \)\(17\!\cdots\!80\)\(q^{58} - \)\(24\!\cdots\!60\)\(q^{59} - \)\(31\!\cdots\!40\)\(q^{60} - \)\(25\!\cdots\!88\)\(q^{61} - \)\(29\!\cdots\!80\)\(q^{62} + \)\(42\!\cdots\!40\)\(q^{63} + \)\(47\!\cdots\!48\)\(q^{64} + \)\(12\!\cdots\!20\)\(q^{65} + \)\(93\!\cdots\!84\)\(q^{66} + \)\(95\!\cdots\!80\)\(q^{67} + \)\(12\!\cdots\!60\)\(q^{68} - \)\(14\!\cdots\!36\)\(q^{69} - \)\(34\!\cdots\!40\)\(q^{70} - \)\(25\!\cdots\!88\)\(q^{71} - \)\(21\!\cdots\!60\)\(q^{72} - \)\(30\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!84\)\(q^{74} + \)\(19\!\cdots\!00\)\(q^{75} + \)\(10\!\cdots\!40\)\(q^{76} + \)\(15\!\cdots\!00\)\(q^{77} + \)\(13\!\cdots\!00\)\(q^{78} + \)\(11\!\cdots\!20\)\(q^{79} + \)\(12\!\cdots\!60\)\(q^{80} + \)\(29\!\cdots\!86\)\(q^{81} - \)\(25\!\cdots\!80\)\(q^{82} - \)\(79\!\cdots\!60\)\(q^{83} - \)\(91\!\cdots\!64\)\(q^{84} - \)\(36\!\cdots\!40\)\(q^{85} + \)\(72\!\cdots\!32\)\(q^{86} - \)\(14\!\cdots\!60\)\(q^{87} - \)\(48\!\cdots\!60\)\(q^{88} + \)\(53\!\cdots\!60\)\(q^{89} + \)\(85\!\cdots\!20\)\(q^{90} + \)\(34\!\cdots\!32\)\(q^{91} + \)\(18\!\cdots\!80\)\(q^{92} - \)\(16\!\cdots\!80\)\(q^{93} - \)\(29\!\cdots\!04\)\(q^{94} + \)\(19\!\cdots\!00\)\(q^{95} - \)\(89\!\cdots\!08\)\(q^{96} - \)\(74\!\cdots\!80\)\(q^{97} - \)\(16\!\cdots\!20\)\(q^{98} - \)\(18\!\cdots\!36\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.67444e11 1.89046 0.945229 0.326409i \(-0.105839\pi\)
0.945229 + 0.326409i \(0.105839\pi\)
\(3\) −8.83049e17 −1.13224 −0.566119 0.824324i \(-0.691556\pi\)
−0.566119 + 0.824324i \(0.691556\pi\)
\(4\) 9.72365e22 2.57383
\(5\) 2.43619e26 1.49739 0.748697 0.662912i \(-0.230680\pi\)
0.748697 + 0.662912i \(0.230680\pi\)
\(6\) −3.24471e29 −2.14045
\(7\) 1.21530e31 0.247460 0.123730 0.992316i \(-0.460514\pi\)
0.123730 + 0.992316i \(0.460514\pi\)
\(8\) 2.18473e34 2.97525
\(9\) 1.71508e35 0.281962
\(10\) 8.95165e37 2.83076
\(11\) −5.65037e38 −0.501016 −0.250508 0.968115i \(-0.580598\pi\)
−0.250508 + 0.968115i \(0.580598\pi\)
\(12\) −8.58645e40 −2.91419
\(13\) 5.30382e40 0.0894774 0.0447387 0.998999i \(-0.485754\pi\)
0.0447387 + 0.998999i \(0.485754\pi\)
\(14\) 4.46553e42 0.467813
\(15\) −2.15128e44 −1.69541
\(16\) 4.35419e45 3.05076
\(17\) 1.14821e45 0.0828300 0.0414150 0.999142i \(-0.486813\pi\)
0.0414150 + 0.999142i \(0.486813\pi\)
\(18\) 6.30198e46 0.533038
\(19\) 1.24645e48 1.38808 0.694042 0.719935i \(-0.255828\pi\)
0.694042 + 0.719935i \(0.255828\pi\)
\(20\) 2.36887e49 3.85404
\(21\) −1.07316e49 −0.280184
\(22\) −2.07620e50 −0.947149
\(23\) 8.02205e50 0.691022 0.345511 0.938415i \(-0.387706\pi\)
0.345511 + 0.938415i \(0.387706\pi\)
\(24\) −1.92923e52 −3.36869
\(25\) 3.28805e52 1.24219
\(26\) 1.94886e52 0.169153
\(27\) 3.85679e53 0.812989
\(28\) 1.18171e54 0.636920
\(29\) 8.53673e54 1.23415 0.617073 0.786906i \(-0.288318\pi\)
0.617073 + 0.786906i \(0.288318\pi\)
\(30\) −7.90474e55 −3.20509
\(31\) −6.18737e55 −0.733572 −0.366786 0.930305i \(-0.619542\pi\)
−0.366786 + 0.930305i \(0.619542\pi\)
\(32\) 7.74555e56 2.79208
\(33\) 4.98956e56 0.567269
\(34\) 4.21904e56 0.156587
\(35\) 2.96069e57 0.370546
\(36\) 1.66769e58 0.725723
\(37\) −5.98766e58 −0.932594 −0.466297 0.884628i \(-0.654412\pi\)
−0.466297 + 0.884628i \(0.654412\pi\)
\(38\) 4.58002e59 2.62411
\(39\) −4.68354e58 −0.101310
\(40\) 5.32243e60 4.45513
\(41\) −5.32628e60 −1.76616 −0.883079 0.469224i \(-0.844534\pi\)
−0.883079 + 0.469224i \(0.844534\pi\)
\(42\) −3.94328e60 −0.529675
\(43\) 2.59254e61 1.44098 0.720489 0.693466i \(-0.243917\pi\)
0.720489 + 0.693466i \(0.243917\pi\)
\(44\) −5.49422e61 −1.28953
\(45\) 4.17827e61 0.422209
\(46\) 2.94766e62 1.30635
\(47\) −5.76440e62 −1.14047 −0.570236 0.821481i \(-0.693148\pi\)
−0.570236 + 0.821481i \(0.693148\pi\)
\(48\) −3.84496e63 −3.45419
\(49\) −2.26417e63 −0.938763
\(50\) 1.20818e64 2.34831
\(51\) −1.01393e63 −0.0937833
\(52\) 5.15725e63 0.230299
\(53\) 5.92558e63 0.129535 0.0647673 0.997900i \(-0.479370\pi\)
0.0647673 + 0.997900i \(0.479370\pi\)
\(54\) 1.41716e65 1.53692
\(55\) −1.37654e65 −0.750219
\(56\) 2.65510e65 0.736257
\(57\) −1.10068e66 −1.57164
\(58\) 3.13677e66 2.33310
\(59\) 2.82712e66 1.10763 0.553814 0.832640i \(-0.313172\pi\)
0.553814 + 0.832640i \(0.313172\pi\)
\(60\) −2.09183e67 −4.36369
\(61\) 5.43239e66 0.609708 0.304854 0.952399i \(-0.401392\pi\)
0.304854 + 0.952399i \(0.401392\pi\)
\(62\) −2.27352e67 −1.38679
\(63\) 2.08433e66 0.0697745
\(64\) 1.20109e68 2.22755
\(65\) 1.29211e67 0.133983
\(66\) 1.83338e68 1.07240
\(67\) −2.61376e68 −0.869883 −0.434941 0.900459i \(-0.643231\pi\)
−0.434941 + 0.900459i \(0.643231\pi\)
\(68\) 1.11648e68 0.213190
\(69\) −7.08386e68 −0.782401
\(70\) 1.08789e69 0.700501
\(71\) 1.78760e67 0.00676213 0.00338106 0.999994i \(-0.498924\pi\)
0.00338106 + 0.999994i \(0.498924\pi\)
\(72\) 3.74700e69 0.838910
\(73\) −1.09051e70 −1.45554 −0.727770 0.685821i \(-0.759443\pi\)
−0.727770 + 0.685821i \(0.759443\pi\)
\(74\) −2.20013e70 −1.76303
\(75\) −2.90351e70 −1.40646
\(76\) 1.21201e71 3.57269
\(77\) −6.86687e69 −0.123981
\(78\) −1.72094e70 −0.191522
\(79\) −1.49375e71 −1.03101 −0.515504 0.856887i \(-0.672395\pi\)
−0.515504 + 0.856887i \(0.672395\pi\)
\(80\) 1.06076e72 4.56820
\(81\) −4.44896e71 −1.20246
\(82\) −1.95711e72 −3.33885
\(83\) 3.39100e71 0.367197 0.183599 0.983001i \(-0.441225\pi\)
0.183599 + 0.983001i \(0.441225\pi\)
\(84\) −1.04351e72 −0.721145
\(85\) 2.79727e71 0.124029
\(86\) 9.52613e72 2.72411
\(87\) −7.53835e72 −1.39735
\(88\) −1.23446e73 −1.49065
\(89\) 2.45405e72 0.193981 0.0969905 0.995285i \(-0.469078\pi\)
0.0969905 + 0.995285i \(0.469078\pi\)
\(90\) 1.53528e73 0.798168
\(91\) 6.44571e71 0.0221421
\(92\) 7.80036e73 1.77857
\(93\) 5.46375e73 0.830578
\(94\) −2.11810e74 −2.15601
\(95\) 3.03660e74 2.07851
\(96\) −6.83970e74 −3.16130
\(97\) 1.36838e74 0.428811 0.214405 0.976745i \(-0.431219\pi\)
0.214405 + 0.976745i \(0.431219\pi\)
\(98\) −8.31957e74 −1.77469
\(99\) −9.69086e73 −0.141268
\(100\) 3.19719e75 3.19719
\(101\) −2.90130e74 −0.199775 −0.0998875 0.994999i \(-0.531848\pi\)
−0.0998875 + 0.994999i \(0.531848\pi\)
\(102\) −3.72562e74 −0.177293
\(103\) 4.39725e74 0.145139 0.0725696 0.997363i \(-0.476880\pi\)
0.0725696 + 0.997363i \(0.476880\pi\)
\(104\) 1.15874e75 0.266218
\(105\) −2.61444e75 −0.419546
\(106\) 2.17732e75 0.244879
\(107\) −1.61246e76 −1.27526 −0.637629 0.770344i \(-0.720085\pi\)
−0.637629 + 0.770344i \(0.720085\pi\)
\(108\) 3.75021e76 2.09249
\(109\) −3.51780e76 −1.38924 −0.694620 0.719376i \(-0.744428\pi\)
−0.694620 + 0.719376i \(0.744428\pi\)
\(110\) −5.05802e76 −1.41826
\(111\) 5.28740e76 1.05592
\(112\) 5.29163e76 0.754942
\(113\) −3.77510e76 −0.385911 −0.192955 0.981208i \(-0.561807\pi\)
−0.192955 + 0.981208i \(0.561807\pi\)
\(114\) −4.04438e77 −2.97112
\(115\) 1.95433e77 1.03473
\(116\) 8.30081e77 3.17648
\(117\) 9.09650e75 0.0252293
\(118\) 1.03881e78 2.09392
\(119\) 1.39542e76 0.0204971
\(120\) −4.69997e78 −5.04427
\(121\) −9.52628e77 −0.748983
\(122\) 1.99610e78 1.15263
\(123\) 4.70337e78 1.99971
\(124\) −6.01638e78 −1.88809
\(125\) 1.56178e78 0.362656
\(126\) 7.65876e77 0.131906
\(127\) 5.76725e78 0.738464 0.369232 0.929337i \(-0.379621\pi\)
0.369232 + 0.929337i \(0.379621\pi\)
\(128\) 1.48716e79 1.41900
\(129\) −2.28934e79 −1.63153
\(130\) 4.74780e78 0.253289
\(131\) −1.75382e79 −0.701960 −0.350980 0.936383i \(-0.614151\pi\)
−0.350980 + 0.936383i \(0.614151\pi\)
\(132\) 4.85167e79 1.46005
\(133\) 1.51481e79 0.343495
\(134\) −9.60412e79 −1.64448
\(135\) 9.39588e79 1.21737
\(136\) 2.50854e79 0.246440
\(137\) −2.46770e80 −1.84192 −0.920961 0.389654i \(-0.872595\pi\)
−0.920961 + 0.389654i \(0.872595\pi\)
\(138\) −2.60293e80 −1.47910
\(139\) 7.49076e79 0.324691 0.162346 0.986734i \(-0.448094\pi\)
0.162346 + 0.986734i \(0.448094\pi\)
\(140\) 2.87887e80 0.953721
\(141\) 5.09025e80 1.29129
\(142\) 6.56845e78 0.0127835
\(143\) −2.99686e79 −0.0448296
\(144\) 7.46780e80 0.860200
\(145\) 2.07971e81 1.84800
\(146\) −4.00704e81 −2.75164
\(147\) 1.99937e81 1.06290
\(148\) −5.82219e81 −2.40034
\(149\) 3.07560e81 0.985020 0.492510 0.870307i \(-0.336080\pi\)
0.492510 + 0.870307i \(0.336080\pi\)
\(150\) −1.06688e82 −2.65884
\(151\) −1.13847e81 −0.221151 −0.110575 0.993868i \(-0.535269\pi\)
−0.110575 + 0.993868i \(0.535269\pi\)
\(152\) 2.72317e82 4.12990
\(153\) 1.96928e80 0.0233550
\(154\) −2.52319e81 −0.234382
\(155\) −1.50736e82 −1.09845
\(156\) −4.55410e81 −0.260754
\(157\) 2.14834e82 0.967979 0.483989 0.875074i \(-0.339187\pi\)
0.483989 + 0.875074i \(0.339187\pi\)
\(158\) −5.48870e82 −1.94908
\(159\) −5.23257e81 −0.146664
\(160\) 1.88696e83 4.18085
\(161\) 9.74916e81 0.171000
\(162\) −1.63475e83 −2.27320
\(163\) 1.14457e83 1.26359 0.631795 0.775135i \(-0.282318\pi\)
0.631795 + 0.775135i \(0.282318\pi\)
\(164\) −5.17909e83 −4.54579
\(165\) 1.21555e83 0.849426
\(166\) 1.24600e83 0.694171
\(167\) 3.68869e83 1.64061 0.820304 0.571928i \(-0.193804\pi\)
0.820304 + 0.571928i \(0.193804\pi\)
\(168\) −2.34458e83 −0.833618
\(169\) −3.48546e83 −0.991994
\(170\) 1.02784e83 0.234472
\(171\) 2.13777e83 0.391387
\(172\) 2.52089e84 3.70883
\(173\) 4.14388e83 0.490544 0.245272 0.969454i \(-0.421123\pi\)
0.245272 + 0.969454i \(0.421123\pi\)
\(174\) −2.76992e84 −2.64162
\(175\) 3.99596e83 0.307393
\(176\) −2.46028e84 −1.52848
\(177\) −2.49649e84 −1.25410
\(178\) 9.01729e83 0.366713
\(179\) 1.08783e84 0.358570 0.179285 0.983797i \(-0.442622\pi\)
0.179285 + 0.983797i \(0.442622\pi\)
\(180\) 4.06280e84 1.08669
\(181\) −2.20049e84 −0.478161 −0.239080 0.971000i \(-0.576846\pi\)
−0.239080 + 0.971000i \(0.576846\pi\)
\(182\) 2.36844e83 0.0418587
\(183\) −4.79706e84 −0.690335
\(184\) 1.75260e85 2.05596
\(185\) −1.45871e85 −1.39646
\(186\) 2.00763e85 1.57017
\(187\) −6.48783e83 −0.0414992
\(188\) −5.60510e85 −2.93538
\(189\) 4.68714e84 0.201182
\(190\) 1.11578e86 3.92933
\(191\) −8.56878e84 −0.247838 −0.123919 0.992292i \(-0.539546\pi\)
−0.123919 + 0.992292i \(0.539546\pi\)
\(192\) −1.06062e86 −2.52211
\(193\) 2.83853e85 0.555513 0.277756 0.960652i \(-0.410409\pi\)
0.277756 + 0.960652i \(0.410409\pi\)
\(194\) 5.02802e85 0.810648
\(195\) −1.14100e85 −0.151701
\(196\) −2.20160e86 −2.41622
\(197\) −1.39395e86 −1.26405 −0.632024 0.774949i \(-0.717776\pi\)
−0.632024 + 0.774949i \(0.717776\pi\)
\(198\) −3.56085e85 −0.267060
\(199\) 1.12515e86 0.698587 0.349294 0.937013i \(-0.386422\pi\)
0.349294 + 0.937013i \(0.386422\pi\)
\(200\) 7.18352e86 3.69583
\(201\) 2.30808e86 0.984914
\(202\) −1.06607e86 −0.377666
\(203\) 1.03746e86 0.305402
\(204\) −9.85908e85 −0.241382
\(205\) −1.29758e87 −2.64464
\(206\) 1.61574e86 0.274379
\(207\) 1.37585e86 0.194842
\(208\) 2.30939e86 0.272974
\(209\) −7.04292e86 −0.695452
\(210\) −9.60660e86 −0.793133
\(211\) 1.53042e87 1.05735 0.528675 0.848824i \(-0.322689\pi\)
0.528675 + 0.848824i \(0.322689\pi\)
\(212\) 5.76182e86 0.333400
\(213\) −1.57854e85 −0.00765634
\(214\) −5.92490e87 −2.41082
\(215\) 6.31591e87 2.15771
\(216\) 8.42606e87 2.41885
\(217\) −7.51948e86 −0.181530
\(218\) −1.29260e88 −2.62630
\(219\) 9.62978e87 1.64802
\(220\) −1.33850e88 −1.93093
\(221\) 6.08992e85 0.00741142
\(222\) 1.94283e88 1.99617
\(223\) −5.54993e87 −0.481787 −0.240893 0.970552i \(-0.577440\pi\)
−0.240893 + 0.970552i \(0.577440\pi\)
\(224\) 9.41313e87 0.690929
\(225\) 5.63929e87 0.350251
\(226\) −1.38714e88 −0.729548
\(227\) −5.62742e87 −0.250807 −0.125403 0.992106i \(-0.540023\pi\)
−0.125403 + 0.992106i \(0.540023\pi\)
\(228\) −1.07026e89 −4.04513
\(229\) −5.39160e86 −0.0172937 −0.00864684 0.999963i \(-0.502752\pi\)
−0.00864684 + 0.999963i \(0.502752\pi\)
\(230\) 7.18106e88 1.95612
\(231\) 6.06378e87 0.140377
\(232\) 1.86505e89 3.67190
\(233\) −1.05527e89 −1.76814 −0.884072 0.467351i \(-0.845209\pi\)
−0.884072 + 0.467351i \(0.845209\pi\)
\(234\) 3.34246e87 0.0476948
\(235\) −1.40432e89 −1.70774
\(236\) 2.74899e89 2.85085
\(237\) 1.31905e89 1.16735
\(238\) 5.12738e87 0.0387490
\(239\) −1.07654e89 −0.695201 −0.347600 0.937643i \(-0.613003\pi\)
−0.347600 + 0.937643i \(0.613003\pi\)
\(240\) −9.36707e89 −5.17228
\(241\) 3.81853e89 1.80409 0.902043 0.431647i \(-0.142067\pi\)
0.902043 + 0.431647i \(0.142067\pi\)
\(242\) −3.50038e89 −1.41592
\(243\) 1.58269e89 0.548481
\(244\) 5.28226e89 1.56928
\(245\) −5.51595e89 −1.40570
\(246\) 1.72823e90 3.78037
\(247\) 6.61097e88 0.124202
\(248\) −1.35178e90 −2.18256
\(249\) −2.99442e89 −0.415755
\(250\) 5.73868e89 0.685586
\(251\) −4.93768e89 −0.507877 −0.253939 0.967220i \(-0.581726\pi\)
−0.253939 + 0.967220i \(0.581726\pi\)
\(252\) 2.02673e89 0.179587
\(253\) −4.53276e89 −0.346213
\(254\) 2.11915e90 1.39603
\(255\) −2.47012e89 −0.140431
\(256\) 9.26877e89 0.455012
\(257\) 3.14677e90 1.33467 0.667334 0.744759i \(-0.267435\pi\)
0.667334 + 0.744759i \(0.267435\pi\)
\(258\) −8.41203e90 −3.08434
\(259\) −7.27678e89 −0.230780
\(260\) 1.25641e90 0.344849
\(261\) 1.46412e90 0.347983
\(262\) −6.44433e90 −1.32702
\(263\) −4.16943e90 −0.744279 −0.372140 0.928177i \(-0.621376\pi\)
−0.372140 + 0.928177i \(0.621376\pi\)
\(264\) 1.09009e91 1.68777
\(265\) 1.44358e90 0.193964
\(266\) 5.56608e90 0.649363
\(267\) −2.16705e90 −0.219633
\(268\) −2.54153e91 −2.23893
\(269\) 1.97317e91 1.51166 0.755829 0.654769i \(-0.227234\pi\)
0.755829 + 0.654769i \(0.227234\pi\)
\(270\) 3.45246e91 2.30138
\(271\) 2.23482e91 1.29686 0.648432 0.761273i \(-0.275425\pi\)
0.648432 + 0.761273i \(0.275425\pi\)
\(272\) 4.99954e90 0.252695
\(273\) −5.69188e89 −0.0250701
\(274\) −9.06743e91 −3.48208
\(275\) −1.85787e91 −0.622358
\(276\) −6.88810e91 −2.01376
\(277\) 3.38744e91 0.864729 0.432365 0.901699i \(-0.357679\pi\)
0.432365 + 0.901699i \(0.357679\pi\)
\(278\) 2.75244e91 0.613815
\(279\) −1.06119e91 −0.206840
\(280\) 6.46833e91 1.10247
\(281\) −7.17828e91 −1.07037 −0.535184 0.844735i \(-0.679758\pi\)
−0.535184 + 0.844735i \(0.679758\pi\)
\(282\) 1.87038e92 2.44112
\(283\) 1.11121e92 1.27000 0.635000 0.772512i \(-0.281000\pi\)
0.635000 + 0.772512i \(0.281000\pi\)
\(284\) 1.73820e90 0.0174046
\(285\) −2.68146e92 −2.35337
\(286\) −1.10118e91 −0.0847484
\(287\) −6.47300e91 −0.437054
\(288\) 1.32843e92 0.787262
\(289\) −1.90844e92 −0.993139
\(290\) 7.64178e92 3.49357
\(291\) −1.20834e92 −0.485515
\(292\) −1.06038e93 −3.74631
\(293\) 4.84927e91 0.150709 0.0753547 0.997157i \(-0.475991\pi\)
0.0753547 + 0.997157i \(0.475991\pi\)
\(294\) 7.34659e92 2.00937
\(295\) 6.88741e92 1.65856
\(296\) −1.30815e93 −2.77470
\(297\) −2.17923e92 −0.407321
\(298\) 1.13011e93 1.86214
\(299\) 4.25476e91 0.0618308
\(300\) −2.82327e93 −3.61998
\(301\) 3.15070e92 0.356585
\(302\) −4.18326e92 −0.418076
\(303\) 2.56199e92 0.226193
\(304\) 5.42729e93 4.23471
\(305\) 1.32343e93 0.912974
\(306\) 7.23601e91 0.0441515
\(307\) −5.53608e92 −0.298891 −0.149446 0.988770i \(-0.547749\pi\)
−0.149446 + 0.988770i \(0.547749\pi\)
\(308\) −6.67710e92 −0.319107
\(309\) −3.88298e92 −0.164332
\(310\) −5.53872e93 −2.07657
\(311\) −3.84755e93 −1.27841 −0.639204 0.769037i \(-0.720736\pi\)
−0.639204 + 0.769037i \(0.720736\pi\)
\(312\) −1.02323e93 −0.301422
\(313\) 2.85920e93 0.747019 0.373509 0.927626i \(-0.378154\pi\)
0.373509 + 0.927626i \(0.378154\pi\)
\(314\) 7.89395e93 1.82992
\(315\) 5.07784e92 0.104480
\(316\) −1.45247e94 −2.65364
\(317\) −7.23036e92 −0.117338 −0.0586688 0.998278i \(-0.518686\pi\)
−0.0586688 + 0.998278i \(0.518686\pi\)
\(318\) −1.92268e93 −0.277262
\(319\) −4.82357e93 −0.618327
\(320\) 2.92609e94 3.33552
\(321\) 1.42388e94 1.44389
\(322\) 3.58228e93 0.323269
\(323\) 1.43119e93 0.114975
\(324\) −4.32601e94 −3.09492
\(325\) 1.74393e93 0.111148
\(326\) 4.20565e94 2.38876
\(327\) 3.10639e94 1.57295
\(328\) −1.16365e95 −5.25477
\(329\) −7.00545e93 −0.282221
\(330\) 4.46648e94 1.60580
\(331\) −1.94545e94 −0.624409 −0.312205 0.950015i \(-0.601067\pi\)
−0.312205 + 0.950015i \(0.601067\pi\)
\(332\) 3.29729e94 0.945102
\(333\) −1.02693e94 −0.262957
\(334\) 1.35539e95 3.10150
\(335\) −6.36762e94 −1.30256
\(336\) −4.67277e94 −0.854774
\(337\) −6.36785e94 −1.04201 −0.521005 0.853554i \(-0.674443\pi\)
−0.521005 + 0.853554i \(0.674443\pi\)
\(338\) −1.28071e95 −1.87532
\(339\) 3.33360e94 0.436943
\(340\) 2.71996e94 0.319230
\(341\) 3.49610e94 0.367531
\(342\) 7.85512e94 0.739901
\(343\) −5.68276e94 −0.479767
\(344\) 5.66400e95 4.28728
\(345\) −1.72577e95 −1.17156
\(346\) 1.52264e95 0.927353
\(347\) 2.45590e94 0.134232 0.0671160 0.997745i \(-0.478620\pi\)
0.0671160 + 0.997745i \(0.478620\pi\)
\(348\) −7.33002e95 −3.59653
\(349\) 2.80433e94 0.123559 0.0617796 0.998090i \(-0.480322\pi\)
0.0617796 + 0.998090i \(0.480322\pi\)
\(350\) 1.46829e95 0.581113
\(351\) 2.04557e94 0.0727442
\(352\) −4.37652e95 −1.39888
\(353\) 3.99820e95 1.14898 0.574491 0.818511i \(-0.305200\pi\)
0.574491 + 0.818511i \(0.305200\pi\)
\(354\) −9.17320e95 −2.37082
\(355\) 4.35495e93 0.0101256
\(356\) 2.38624e95 0.499274
\(357\) −1.23222e94 −0.0232076
\(358\) 3.99718e95 0.677860
\(359\) 7.73805e95 1.18192 0.590962 0.806699i \(-0.298748\pi\)
0.590962 + 0.806699i \(0.298748\pi\)
\(360\) 9.12841e95 1.25618
\(361\) 7.47301e95 0.926777
\(362\) −8.08560e95 −0.903942
\(363\) 8.41217e95 0.848027
\(364\) 6.26758e94 0.0569899
\(365\) −2.65670e96 −2.17952
\(366\) −1.76265e96 −1.30505
\(367\) 5.77357e95 0.385893 0.192946 0.981209i \(-0.438196\pi\)
0.192946 + 0.981209i \(0.438196\pi\)
\(368\) 3.49296e96 2.10814
\(369\) −9.13502e95 −0.497990
\(370\) −5.35995e96 −2.63995
\(371\) 7.20132e94 0.0320546
\(372\) 5.31276e96 2.13776
\(373\) 3.37386e96 1.22757 0.613784 0.789474i \(-0.289646\pi\)
0.613784 + 0.789474i \(0.289646\pi\)
\(374\) −2.38392e95 −0.0784524
\(375\) −1.37913e96 −0.410613
\(376\) −1.25937e97 −3.39319
\(377\) 4.52773e95 0.110428
\(378\) 1.72226e96 0.380327
\(379\) −3.66618e96 −0.733235 −0.366618 0.930372i \(-0.619484\pi\)
−0.366618 + 0.930372i \(0.619484\pi\)
\(380\) 2.95268e97 5.34973
\(381\) −5.09277e96 −0.836117
\(382\) −3.14855e96 −0.468527
\(383\) −7.65115e96 −1.03222 −0.516111 0.856522i \(-0.672621\pi\)
−0.516111 + 0.856522i \(0.672621\pi\)
\(384\) −1.31323e97 −1.60665
\(385\) −1.67290e96 −0.185649
\(386\) 1.04300e97 1.05017
\(387\) 4.44641e96 0.406302
\(388\) 1.33056e97 1.10368
\(389\) 2.43483e97 1.83383 0.916913 0.399087i \(-0.130673\pi\)
0.916913 + 0.399087i \(0.130673\pi\)
\(390\) −4.19254e96 −0.286784
\(391\) 9.21102e95 0.0572373
\(392\) −4.94661e97 −2.79306
\(393\) 1.54871e97 0.794785
\(394\) −5.12199e97 −2.38963
\(395\) −3.63906e97 −1.54383
\(396\) −9.42305e96 −0.363599
\(397\) 5.68145e96 0.199441 0.0997207 0.995015i \(-0.468205\pi\)
0.0997207 + 0.995015i \(0.468205\pi\)
\(398\) 4.13431e97 1.32065
\(399\) −1.33765e97 −0.388919
\(400\) 1.43168e98 3.78963
\(401\) −2.25071e97 −0.542507 −0.271254 0.962508i \(-0.587438\pi\)
−0.271254 + 0.962508i \(0.587438\pi\)
\(402\) 8.48090e97 1.86194
\(403\) −3.28167e96 −0.0656381
\(404\) −2.82112e97 −0.514187
\(405\) −1.08385e98 −1.80056
\(406\) 3.81211e97 0.577349
\(407\) 3.38325e97 0.467245
\(408\) −2.21516e97 −0.279029
\(409\) 4.79631e97 0.551168 0.275584 0.961277i \(-0.411129\pi\)
0.275584 + 0.961277i \(0.411129\pi\)
\(410\) −4.76790e98 −4.99957
\(411\) 2.17910e98 2.08549
\(412\) 4.27573e97 0.373563
\(413\) 3.43579e97 0.274094
\(414\) 5.05548e97 0.368341
\(415\) 8.26113e97 0.549839
\(416\) 4.10810e97 0.249828
\(417\) −6.61470e97 −0.367628
\(418\) −2.58788e98 −1.31472
\(419\) 2.11564e98 0.982688 0.491344 0.870966i \(-0.336506\pi\)
0.491344 + 0.870966i \(0.336506\pi\)
\(420\) −2.54219e98 −1.07984
\(421\) −2.18038e97 −0.0847137 −0.0423569 0.999103i \(-0.513487\pi\)
−0.0423569 + 0.999103i \(0.513487\pi\)
\(422\) 5.62345e98 1.99887
\(423\) −9.88643e97 −0.321570
\(424\) 1.29458e98 0.385398
\(425\) 3.77539e97 0.102891
\(426\) −5.80027e96 −0.0144740
\(427\) 6.60196e97 0.150878
\(428\) −1.56790e99 −3.28229
\(429\) 2.64637e97 0.0507578
\(430\) 2.32075e99 4.07907
\(431\) −3.92051e98 −0.631605 −0.315802 0.948825i \(-0.602274\pi\)
−0.315802 + 0.948825i \(0.602274\pi\)
\(432\) 1.67932e99 2.48024
\(433\) −9.09183e98 −1.23128 −0.615638 0.788029i \(-0.711102\pi\)
−0.615638 + 0.788029i \(0.711102\pi\)
\(434\) −2.76299e98 −0.343174
\(435\) −1.83649e99 −2.09238
\(436\) −3.42058e99 −3.57567
\(437\) 9.99911e98 0.959196
\(438\) 3.53841e99 3.11551
\(439\) −9.19604e98 −0.743330 −0.371665 0.928367i \(-0.621213\pi\)
−0.371665 + 0.928367i \(0.621213\pi\)
\(440\) −3.00737e99 −2.23209
\(441\) −3.88324e98 −0.264696
\(442\) 2.23771e97 0.0140110
\(443\) 3.04060e99 1.74912 0.874561 0.484915i \(-0.161150\pi\)
0.874561 + 0.484915i \(0.161150\pi\)
\(444\) 5.14128e99 2.71775
\(445\) 5.97855e98 0.290466
\(446\) −2.03929e99 −0.910798
\(447\) −2.71591e99 −1.11528
\(448\) 1.45968e99 0.551229
\(449\) 1.16326e99 0.404055 0.202027 0.979380i \(-0.435247\pi\)
0.202027 + 0.979380i \(0.435247\pi\)
\(450\) 2.07212e99 0.662135
\(451\) 3.00955e99 0.884873
\(452\) −3.67077e99 −0.993268
\(453\) 1.00533e99 0.250395
\(454\) −2.06776e99 −0.474140
\(455\) 1.57030e98 0.0331555
\(456\) −2.40469e100 −4.67603
\(457\) 2.88576e99 0.516895 0.258447 0.966025i \(-0.416789\pi\)
0.258447 + 0.966025i \(0.416789\pi\)
\(458\) −1.98111e98 −0.0326929
\(459\) 4.42842e98 0.0673399
\(460\) 1.90032e100 2.66322
\(461\) −8.99071e99 −1.16147 −0.580737 0.814092i \(-0.697235\pi\)
−0.580737 + 0.814092i \(0.697235\pi\)
\(462\) 2.22810e99 0.265376
\(463\) 4.13924e98 0.0454604 0.0227302 0.999742i \(-0.492764\pi\)
0.0227302 + 0.999742i \(0.492764\pi\)
\(464\) 3.71706e100 3.76509
\(465\) 1.33107e100 1.24370
\(466\) −3.87754e100 −3.34260
\(467\) 1.66999e99 0.132840 0.0664202 0.997792i \(-0.478842\pi\)
0.0664202 + 0.997792i \(0.478842\pi\)
\(468\) 8.84512e98 0.0649358
\(469\) −3.17649e99 −0.215261
\(470\) −5.16009e100 −3.22840
\(471\) −1.89709e100 −1.09598
\(472\) 6.17651e100 3.29548
\(473\) −1.46488e100 −0.721953
\(474\) 4.84679e100 2.20682
\(475\) 4.09840e100 1.72427
\(476\) 1.35685e99 0.0527561
\(477\) 1.01629e99 0.0365239
\(478\) −3.95570e100 −1.31425
\(479\) −3.76475e99 −0.115652 −0.0578262 0.998327i \(-0.518417\pi\)
−0.0578262 + 0.998327i \(0.518417\pi\)
\(480\) −1.66628e101 −4.73371
\(481\) −3.17575e99 −0.0834461
\(482\) 1.40310e101 3.41055
\(483\) −8.60899e99 −0.193613
\(484\) −9.26302e100 −1.92775
\(485\) 3.33363e100 0.642099
\(486\) 5.81552e100 1.03688
\(487\) −4.27929e100 −0.706376 −0.353188 0.935552i \(-0.614902\pi\)
−0.353188 + 0.935552i \(0.614902\pi\)
\(488\) 1.18683e101 1.81404
\(489\) −1.01071e101 −1.43068
\(490\) −2.02681e101 −2.65741
\(491\) 7.91421e100 0.961284 0.480642 0.876917i \(-0.340404\pi\)
0.480642 + 0.876917i \(0.340404\pi\)
\(492\) 4.57339e101 5.14691
\(493\) 9.80198e99 0.102224
\(494\) 2.42916e100 0.234799
\(495\) −2.36088e100 −0.211533
\(496\) −2.69410e101 −2.23795
\(497\) 2.17247e98 0.00167336
\(498\) −1.10028e101 −0.785966
\(499\) 1.93019e101 1.27888 0.639441 0.768840i \(-0.279166\pi\)
0.639441 + 0.768840i \(0.279166\pi\)
\(500\) 1.51862e101 0.933415
\(501\) −3.25729e101 −1.85756
\(502\) −1.81432e101 −0.960120
\(503\) −3.34549e101 −1.64308 −0.821542 0.570147i \(-0.806886\pi\)
−0.821542 + 0.570147i \(0.806886\pi\)
\(504\) 4.55371e100 0.207597
\(505\) −7.06813e100 −0.299142
\(506\) −1.66554e101 −0.654500
\(507\) 3.07783e101 1.12317
\(508\) 5.60787e101 1.90068
\(509\) 2.90608e101 0.914935 0.457467 0.889226i \(-0.348757\pi\)
0.457467 + 0.889226i \(0.348757\pi\)
\(510\) −9.07633e100 −0.265478
\(511\) −1.32530e101 −0.360188
\(512\) −2.21256e101 −0.558819
\(513\) 4.80731e101 1.12850
\(514\) 1.15626e102 2.52313
\(515\) 1.07125e101 0.217331
\(516\) −2.22607e102 −4.19928
\(517\) 3.25710e101 0.571394
\(518\) −2.67381e101 −0.436280
\(519\) −3.65925e101 −0.555413
\(520\) 2.82292e101 0.398634
\(521\) 9.37841e101 1.23230 0.616148 0.787631i \(-0.288692\pi\)
0.616148 + 0.787631i \(0.288692\pi\)
\(522\) 5.37983e101 0.657846
\(523\) 7.17575e101 0.816684 0.408342 0.912829i \(-0.366107\pi\)
0.408342 + 0.912829i \(0.366107\pi\)
\(524\) −1.70536e102 −1.80672
\(525\) −3.52862e101 −0.348042
\(526\) −1.53203e102 −1.40703
\(527\) −7.10442e100 −0.0607618
\(528\) 2.17255e102 1.73060
\(529\) −7.04150e101 −0.522489
\(530\) 5.30437e101 0.366681
\(531\) 4.84875e101 0.312310
\(532\) 1.47295e102 0.884098
\(533\) −2.82497e101 −0.158031
\(534\) −7.96271e101 −0.415206
\(535\) −3.92827e102 −1.90956
\(536\) −5.71037e102 −2.58812
\(537\) −9.60609e101 −0.405986
\(538\) 7.25030e102 2.85773
\(539\) 1.27934e102 0.470335
\(540\) 9.13622e102 3.13329
\(541\) −4.17380e102 −1.33547 −0.667734 0.744400i \(-0.732736\pi\)
−0.667734 + 0.744400i \(0.732736\pi\)
\(542\) 8.21173e102 2.45167
\(543\) 1.94314e102 0.541392
\(544\) 8.89354e101 0.231268
\(545\) −8.57004e102 −2.08024
\(546\) −2.09145e101 −0.0473940
\(547\) 5.04913e102 1.06830 0.534148 0.845391i \(-0.320633\pi\)
0.534148 + 0.845391i \(0.320633\pi\)
\(548\) −2.39951e103 −4.74079
\(549\) 9.31700e101 0.171915
\(550\) −6.82665e102 −1.17654
\(551\) 1.06406e103 1.71310
\(552\) −1.54764e103 −2.32784
\(553\) −1.81535e102 −0.255133
\(554\) 1.24470e103 1.63473
\(555\) 1.28811e103 1.58113
\(556\) 7.28375e102 0.835700
\(557\) 2.22240e102 0.238371 0.119185 0.992872i \(-0.461972\pi\)
0.119185 + 0.992872i \(0.461972\pi\)
\(558\) −3.89927e102 −0.391022
\(559\) 1.37504e102 0.128935
\(560\) 1.28914e103 1.13045
\(561\) 5.72907e101 0.0469869
\(562\) −2.63762e103 −2.02349
\(563\) −2.54936e103 −1.82964 −0.914822 0.403858i \(-0.867669\pi\)
−0.914822 + 0.403858i \(0.867669\pi\)
\(564\) 4.94958e103 3.32355
\(565\) −9.19687e102 −0.577861
\(566\) 4.08307e103 2.40088
\(567\) −5.40680e102 −0.297561
\(568\) 3.90544e101 0.0201191
\(569\) −6.38673e102 −0.308013 −0.154006 0.988070i \(-0.549218\pi\)
−0.154006 + 0.988070i \(0.549218\pi\)
\(570\) −9.85289e103 −4.44894
\(571\) 2.66278e103 1.12585 0.562925 0.826508i \(-0.309676\pi\)
0.562925 + 0.826508i \(0.309676\pi\)
\(572\) −2.91404e102 −0.115384
\(573\) 7.56665e102 0.280611
\(574\) −2.37847e103 −0.826231
\(575\) 2.63769e103 0.858381
\(576\) 2.05997e103 0.628084
\(577\) 1.56700e103 0.447689 0.223844 0.974625i \(-0.428139\pi\)
0.223844 + 0.974625i \(0.428139\pi\)
\(578\) −7.01247e103 −1.87749
\(579\) −2.50656e103 −0.628972
\(580\) 2.02224e104 4.75644
\(581\) 4.12107e102 0.0908667
\(582\) −4.43999e103 −0.917846
\(583\) −3.34817e102 −0.0648988
\(584\) −2.38248e104 −4.33060
\(585\) 2.21608e102 0.0377782
\(586\) 1.78184e103 0.284910
\(587\) 8.05760e102 0.120858 0.0604292 0.998172i \(-0.480753\pi\)
0.0604292 + 0.998172i \(0.480753\pi\)
\(588\) 1.94412e104 2.73573
\(589\) −7.71227e103 −1.01826
\(590\) 2.53074e104 3.13543
\(591\) 1.23093e104 1.43120
\(592\) −2.60714e104 −2.84512
\(593\) −6.05490e103 −0.620234 −0.310117 0.950698i \(-0.600368\pi\)
−0.310117 + 0.950698i \(0.600368\pi\)
\(594\) −8.00746e103 −0.770022
\(595\) 3.39951e102 0.0306923
\(596\) 2.99061e104 2.53527
\(597\) −9.93563e103 −0.790967
\(598\) 1.56339e103 0.116889
\(599\) 2.34648e104 1.64782 0.823912 0.566718i \(-0.191787\pi\)
0.823912 + 0.566718i \(0.191787\pi\)
\(600\) −6.34340e104 −4.18456
\(601\) −1.86432e104 −1.15539 −0.577693 0.816254i \(-0.696047\pi\)
−0.577693 + 0.816254i \(0.696047\pi\)
\(602\) 1.15771e104 0.674108
\(603\) −4.48282e103 −0.245274
\(604\) −1.10701e104 −0.569203
\(605\) −2.32078e104 −1.12152
\(606\) 9.41389e103 0.427608
\(607\) −1.83308e104 −0.782718 −0.391359 0.920238i \(-0.627995\pi\)
−0.391359 + 0.920238i \(0.627995\pi\)
\(608\) 9.65446e104 3.87564
\(609\) −9.16132e103 −0.345788
\(610\) 4.86288e104 1.72594
\(611\) −3.05734e103 −0.102046
\(612\) 1.91486e103 0.0601116
\(613\) −3.12669e104 −0.923244 −0.461622 0.887077i \(-0.652732\pi\)
−0.461622 + 0.887077i \(0.652732\pi\)
\(614\) −2.03420e104 −0.565041
\(615\) 1.14583e105 2.99436
\(616\) −1.50023e104 −0.368876
\(617\) −2.66517e103 −0.0616640 −0.0308320 0.999525i \(-0.509816\pi\)
−0.0308320 + 0.999525i \(0.509816\pi\)
\(618\) −1.42678e104 −0.310663
\(619\) 1.58700e103 0.0325220 0.0162610 0.999868i \(-0.494824\pi\)
0.0162610 + 0.999868i \(0.494824\pi\)
\(620\) −1.46571e105 −2.82721
\(621\) 3.09394e104 0.561793
\(622\) −1.41376e105 −2.41677
\(623\) 2.98240e103 0.0480026
\(624\) −2.03930e104 −0.309072
\(625\) −4.89860e104 −0.699152
\(626\) 1.05060e105 1.41221
\(627\) 6.21924e104 0.787417
\(628\) 2.08897e105 2.49141
\(629\) −6.87511e103 −0.0772468
\(630\) 1.86582e104 0.197515
\(631\) 1.59377e105 1.58974 0.794868 0.606782i \(-0.207540\pi\)
0.794868 + 0.606782i \(0.207540\pi\)
\(632\) −3.26345e105 −3.06751
\(633\) −1.35144e105 −1.19717
\(634\) −2.65675e104 −0.221822
\(635\) 1.40501e105 1.10577
\(636\) −5.08797e104 −0.377488
\(637\) −1.20088e104 −0.0839981
\(638\) −1.77239e105 −1.16892
\(639\) 3.06589e102 0.00190667
\(640\) 3.62300e105 2.12480
\(641\) 1.17862e105 0.651925 0.325962 0.945383i \(-0.394312\pi\)
0.325962 + 0.945383i \(0.394312\pi\)
\(642\) 5.23198e105 2.72962
\(643\) −2.50923e105 −1.23489 −0.617447 0.786612i \(-0.711833\pi\)
−0.617447 + 0.786612i \(0.711833\pi\)
\(644\) 9.47974e104 0.440125
\(645\) −5.57726e105 −2.44305
\(646\) 5.25884e104 0.217355
\(647\) 4.06698e105 1.58621 0.793107 0.609082i \(-0.208462\pi\)
0.793107 + 0.609082i \(0.208462\pi\)
\(648\) −9.71980e105 −3.57762
\(649\) −1.59743e105 −0.554940
\(650\) 6.40796e104 0.210121
\(651\) 6.64007e104 0.205535
\(652\) 1.11294e106 3.25226
\(653\) −3.54682e105 −0.978576 −0.489288 0.872122i \(-0.662743\pi\)
−0.489288 + 0.872122i \(0.662743\pi\)
\(654\) 1.14143e106 2.97360
\(655\) −4.27265e105 −1.05111
\(656\) −2.31917e106 −5.38813
\(657\) −1.87032e105 −0.410408
\(658\) −2.57411e105 −0.533527
\(659\) 1.86786e105 0.365714 0.182857 0.983140i \(-0.441465\pi\)
0.182857 + 0.983140i \(0.441465\pi\)
\(660\) 1.18196e106 2.18628
\(661\) 6.71414e105 1.17337 0.586686 0.809815i \(-0.300432\pi\)
0.586686 + 0.809815i \(0.300432\pi\)
\(662\) −7.14843e105 −1.18042
\(663\) −5.37770e103 −0.00839149
\(664\) 7.40843e105 1.09251
\(665\) 3.69036e105 0.514348
\(666\) −3.77341e105 −0.497108
\(667\) 6.84821e105 0.852822
\(668\) 3.58675e106 4.22264
\(669\) 4.90086e105 0.545497
\(670\) −2.33975e106 −2.46243
\(671\) −3.06950e105 −0.305473
\(672\) −8.31225e105 −0.782296
\(673\) −2.00080e106 −1.78090 −0.890448 0.455086i \(-0.849609\pi\)
−0.890448 + 0.455086i \(0.849609\pi\)
\(674\) −2.33983e106 −1.96987
\(675\) 1.26813e106 1.00989
\(676\) −3.38914e106 −2.55322
\(677\) 7.19375e105 0.512720 0.256360 0.966581i \(-0.417477\pi\)
0.256360 + 0.966581i \(0.417477\pi\)
\(678\) 1.22491e106 0.826021
\(679\) 1.66298e105 0.106114
\(680\) 6.11128e105 0.369019
\(681\) 4.96928e105 0.283973
\(682\) 1.28462e106 0.694802
\(683\) 2.35846e106 1.20740 0.603700 0.797211i \(-0.293692\pi\)
0.603700 + 0.797211i \(0.293692\pi\)
\(684\) 2.07869e106 1.00736
\(685\) −6.01180e106 −2.75809
\(686\) −2.08810e106 −0.906978
\(687\) 4.76105e104 0.0195805
\(688\) 1.12884e107 4.39608
\(689\) 3.14282e104 0.0115904
\(690\) −6.34123e106 −2.21479
\(691\) −3.49985e105 −0.115777 −0.0578885 0.998323i \(-0.518437\pi\)
−0.0578885 + 0.998323i \(0.518437\pi\)
\(692\) 4.02936e106 1.26258
\(693\) −1.17773e105 −0.0349581
\(694\) 9.02408e105 0.253760
\(695\) 1.82489e106 0.486191
\(696\) −1.64693e107 −4.15746
\(697\) −6.11571e105 −0.146291
\(698\) 1.03043e106 0.233583
\(699\) 9.31857e106 2.00196
\(700\) 3.88553e106 0.791176
\(701\) 1.66052e106 0.320493 0.160247 0.987077i \(-0.448771\pi\)
0.160247 + 0.987077i \(0.448771\pi\)
\(702\) 7.51635e105 0.137520
\(703\) −7.46334e106 −1.29452
\(704\) −6.78661e106 −1.11604
\(705\) 1.24008e107 1.93356
\(706\) 1.46912e107 2.17210
\(707\) −3.52594e105 −0.0494364
\(708\) −2.42750e107 −3.22783
\(709\) −1.35084e107 −1.70361 −0.851805 0.523858i \(-0.824492\pi\)
−0.851805 + 0.523858i \(0.824492\pi\)
\(710\) 1.60020e105 0.0191420
\(711\) −2.56191e106 −0.290705
\(712\) 5.36146e106 0.577143
\(713\) −4.96354e106 −0.506914
\(714\) −4.52773e105 −0.0438730
\(715\) −7.30092e105 −0.0671276
\(716\) 1.05777e107 0.922896
\(717\) 9.50640e106 0.787133
\(718\) 2.84330e107 2.23438
\(719\) −1.69563e107 −1.26473 −0.632364 0.774671i \(-0.717915\pi\)
−0.632364 + 0.774671i \(0.717915\pi\)
\(720\) 1.81930e107 1.28806
\(721\) 5.34395e105 0.0359162
\(722\) 2.74591e107 1.75203
\(723\) −3.37195e107 −2.04265
\(724\) −2.13968e107 −1.23070
\(725\) 2.80692e107 1.53305
\(726\) 3.09101e107 1.60316
\(727\) −3.53639e107 −1.74189 −0.870944 0.491382i \(-0.836492\pi\)
−0.870944 + 0.491382i \(0.836492\pi\)
\(728\) 1.40822e106 0.0658784
\(729\) 1.30856e107 0.581449
\(730\) −9.76191e107 −4.12029
\(731\) 2.97678e106 0.119356
\(732\) −4.66450e107 −1.77680
\(733\) 1.06459e107 0.385286 0.192643 0.981269i \(-0.438294\pi\)
0.192643 + 0.981269i \(0.438294\pi\)
\(734\) 2.12147e107 0.729514
\(735\) 4.87086e107 1.59159
\(736\) 6.21352e107 1.92939
\(737\) 1.47687e107 0.435825
\(738\) −3.35661e107 −0.941429
\(739\) −1.41863e107 −0.378184 −0.189092 0.981959i \(-0.560554\pi\)
−0.189092 + 0.981959i \(0.560554\pi\)
\(740\) −1.41840e108 −3.59425
\(741\) −5.83780e106 −0.140626
\(742\) 2.64609e106 0.0605979
\(743\) 5.02005e107 1.09302 0.546510 0.837453i \(-0.315956\pi\)
0.546510 + 0.837453i \(0.315956\pi\)
\(744\) 1.19368e108 2.47118
\(745\) 7.49276e107 1.47496
\(746\) 1.23971e108 2.32067
\(747\) 5.81585e106 0.103536
\(748\) −6.30854e106 −0.106812
\(749\) −1.95962e107 −0.315575
\(750\) −5.06754e107 −0.776246
\(751\) −7.03488e107 −1.02508 −0.512541 0.858663i \(-0.671296\pi\)
−0.512541 + 0.858663i \(0.671296\pi\)
\(752\) −2.50993e108 −3.47931
\(753\) 4.36022e107 0.575038
\(754\) 1.66369e107 0.208760
\(755\) −2.77354e107 −0.331150
\(756\) 4.55761e107 0.517809
\(757\) −1.78445e108 −1.92934 −0.964670 0.263461i \(-0.915136\pi\)
−0.964670 + 0.263461i \(0.915136\pi\)
\(758\) −1.34712e108 −1.38615
\(759\) 4.00265e107 0.391995
\(760\) 6.63416e108 6.18409
\(761\) 1.13160e108 1.00408 0.502041 0.864844i \(-0.332583\pi\)
0.502041 + 0.864844i \(0.332583\pi\)
\(762\) −1.87131e108 −1.58064
\(763\) −4.27517e107 −0.343782
\(764\) −8.33197e107 −0.637892
\(765\) 4.79755e106 0.0349716
\(766\) −2.81137e108 −1.95137
\(767\) 1.49946e107 0.0991077
\(768\) −8.18477e107 −0.515182
\(769\) 4.36032e107 0.261385 0.130692 0.991423i \(-0.458280\pi\)
0.130692 + 0.991423i \(0.458280\pi\)
\(770\) −6.14698e107 −0.350962
\(771\) −2.77875e108 −1.51116
\(772\) 2.76008e108 1.42979
\(773\) 1.42158e108 0.701518 0.350759 0.936466i \(-0.385924\pi\)
0.350759 + 0.936466i \(0.385924\pi\)
\(774\) 1.63381e108 0.768096
\(775\) −2.03444e108 −0.911237
\(776\) 2.98954e108 1.27582
\(777\) 6.42575e107 0.261298
\(778\) 8.94664e108 3.46677
\(779\) −6.63896e108 −2.45158
\(780\) −1.10947e108 −0.390451
\(781\) −1.01006e106 −0.00338793
\(782\) 3.38454e107 0.108205
\(783\) 3.29244e108 1.00335
\(784\) −9.85864e108 −2.86394
\(785\) 5.23377e108 1.44945
\(786\) 5.69065e108 1.50251
\(787\) 2.52484e108 0.635597 0.317799 0.948158i \(-0.397056\pi\)
0.317799 + 0.948158i \(0.397056\pi\)
\(788\) −1.35543e109 −3.25344
\(789\) 3.68181e108 0.842701
\(790\) −1.33715e109 −2.91854
\(791\) −4.58786e107 −0.0954975
\(792\) −2.11720e108 −0.420307
\(793\) 2.88124e107 0.0545551
\(794\) 2.08762e108 0.377035
\(795\) −1.27476e108 −0.219614
\(796\) 1.09406e109 1.79804
\(797\) −3.24886e108 −0.509383 −0.254691 0.967022i \(-0.581974\pi\)
−0.254691 + 0.967022i \(0.581974\pi\)
\(798\) −4.91512e108 −0.735234
\(799\) −6.61876e107 −0.0944653
\(800\) 2.54678e109 3.46830
\(801\) 4.20891e107 0.0546953
\(802\) −8.27011e108 −1.02559
\(803\) 6.16182e108 0.729249
\(804\) 2.24429e109 2.53500
\(805\) 2.37508e108 0.256055
\(806\) −1.20583e108 −0.124086
\(807\) −1.74240e109 −1.71156
\(808\) −6.33857e108 −0.594382
\(809\) 7.50813e108 0.672144 0.336072 0.941836i \(-0.390901\pi\)
0.336072 + 0.941836i \(0.390901\pi\)
\(810\) −3.98256e109 −3.40388
\(811\) −7.73314e108 −0.631065 −0.315533 0.948915i \(-0.602183\pi\)
−0.315533 + 0.948915i \(0.602183\pi\)
\(812\) 1.00879e109 0.786052
\(813\) −1.97346e109 −1.46836
\(814\) 1.24316e109 0.883306
\(815\) 2.78839e109 1.89209
\(816\) −4.41484e108 −0.286111
\(817\) 3.23147e109 2.00020
\(818\) 1.76238e109 1.04196
\(819\) 1.10549e107 0.00624324
\(820\) −1.26173e110 −6.80684
\(821\) −3.36586e109 −1.73471 −0.867356 0.497689i \(-0.834182\pi\)
−0.867356 + 0.497689i \(0.834182\pi\)
\(822\) 8.00699e109 3.94254
\(823\) 1.81695e109 0.854768 0.427384 0.904070i \(-0.359435\pi\)
0.427384 + 0.904070i \(0.359435\pi\)
\(824\) 9.60681e108 0.431826
\(825\) 1.64059e109 0.704657
\(826\) 1.26246e109 0.518163
\(827\) −2.22688e109 −0.873454 −0.436727 0.899594i \(-0.643862\pi\)
−0.436727 + 0.899594i \(0.643862\pi\)
\(828\) 1.33783e109 0.501490
\(829\) −1.37867e109 −0.493931 −0.246965 0.969024i \(-0.579433\pi\)
−0.246965 + 0.969024i \(0.579433\pi\)
\(830\) 3.03551e109 1.03945
\(831\) −2.99127e109 −0.979079
\(832\) 6.37037e108 0.199315
\(833\) −2.59975e108 −0.0777578
\(834\) −2.43054e109 −0.694985
\(835\) 8.98636e109 2.45664
\(836\) −6.84829e109 −1.78997
\(837\) −2.38634e109 −0.596386
\(838\) 7.77379e109 1.85773
\(839\) −4.92096e109 −1.12454 −0.562272 0.826953i \(-0.690072\pi\)
−0.562272 + 0.826953i \(0.690072\pi\)
\(840\) −5.71185e109 −1.24826
\(841\) 2.50293e109 0.523116
\(842\) −8.01169e108 −0.160148
\(843\) 6.33877e109 1.21191
\(844\) 1.48813e110 2.72144
\(845\) −8.49126e109 −1.48541
\(846\) −3.63271e109 −0.607915
\(847\) −1.15772e109 −0.185343
\(848\) 2.58011e109 0.395179
\(849\) −9.81251e109 −1.43794
\(850\) 1.38724e109 0.194511
\(851\) −4.80334e109 −0.644443
\(852\) −1.53492e108 −0.0197061
\(853\) −1.45733e110 −1.79048 −0.895239 0.445587i \(-0.852995\pi\)
−0.895239 + 0.445587i \(0.852995\pi\)
\(854\) 2.42585e109 0.285229
\(855\) 5.20802e109 0.586062
\(856\) −3.52280e110 −3.79422
\(857\) 1.15609e109 0.119182 0.0595910 0.998223i \(-0.481020\pi\)
0.0595910 + 0.998223i \(0.481020\pi\)
\(858\) 9.72395e108 0.0959554
\(859\) 1.68941e110 1.59585 0.797924 0.602758i \(-0.205932\pi\)
0.797924 + 0.602758i \(0.205932\pi\)
\(860\) 6.14137e110 5.55359
\(861\) 5.71598e109 0.494849
\(862\) −1.44057e110 −1.19402
\(863\) 6.04075e109 0.479386 0.239693 0.970849i \(-0.422953\pi\)
0.239693 + 0.970849i \(0.422953\pi\)
\(864\) 2.98730e110 2.26993
\(865\) 1.00953e110 0.734538
\(866\) −3.34074e110 −2.32767
\(867\) 1.68525e110 1.12447
\(868\) −7.31168e109 −0.467227
\(869\) 8.44025e109 0.516551
\(870\) −6.74807e110 −3.95555
\(871\) −1.38629e109 −0.0778348
\(872\) −7.68546e110 −4.13334
\(873\) 2.34688e109 0.120908
\(874\) 3.67412e110 1.81332
\(875\) 1.89803e109 0.0897430
\(876\) 9.36366e110 4.24171
\(877\) −6.52884e107 −0.00283368 −0.00141684 0.999999i \(-0.500451\pi\)
−0.00141684 + 0.999999i \(0.500451\pi\)
\(878\) −3.37904e110 −1.40523
\(879\) −4.28214e109 −0.170639
\(880\) −5.99372e110 −2.28874
\(881\) 3.50306e110 1.28189 0.640946 0.767586i \(-0.278542\pi\)
0.640946 + 0.767586i \(0.278542\pi\)
\(882\) −1.42688e110 −0.500396
\(883\) −2.71634e110 −0.912973 −0.456487 0.889730i \(-0.650892\pi\)
−0.456487 + 0.889730i \(0.650892\pi\)
\(884\) 5.92162e108 0.0190757
\(885\) −6.08192e110 −1.87788
\(886\) 1.11725e111 3.30664
\(887\) −1.19560e110 −0.339194 −0.169597 0.985513i \(-0.554247\pi\)
−0.169597 + 0.985513i \(0.554247\pi\)
\(888\) 1.15516e111 3.14163
\(889\) 7.00892e109 0.182740
\(890\) 2.19678e110 0.549114
\(891\) 2.51383e110 0.602451
\(892\) −5.39655e110 −1.24004
\(893\) −7.18505e110 −1.58307
\(894\) −9.97944e110 −2.10838
\(895\) 2.65017e110 0.536920
\(896\) 1.80733e110 0.351146
\(897\) −3.75716e109 −0.0700072
\(898\) 4.27434e110 0.763848
\(899\) −5.28199e110 −0.905335
\(900\) 5.48344e110 0.901486
\(901\) 6.80382e108 0.0107293
\(902\) 1.10584e111 1.67281
\(903\) −2.78222e110 −0.403739
\(904\) −8.24759e110 −1.14818
\(905\) −5.36083e110 −0.715995
\(906\) 3.69402e110 0.473361
\(907\) 1.20263e111 1.47863 0.739315 0.673359i \(-0.235149\pi\)
0.739315 + 0.673359i \(0.235149\pi\)
\(908\) −5.47190e110 −0.645534
\(909\) −4.97597e109 −0.0563291
\(910\) 5.76998e109 0.0626790
\(911\) 1.56417e111 1.63059 0.815297 0.579042i \(-0.196573\pi\)
0.815297 + 0.579042i \(0.196573\pi\)
\(912\) −4.79257e111 −4.79470
\(913\) −1.91604e110 −0.183972
\(914\) 1.06036e111 0.977168
\(915\) −1.16866e111 −1.03370
\(916\) −5.24260e109 −0.0445109
\(917\) −2.13141e110 −0.173707
\(918\) 1.62720e110 0.127303
\(919\) 1.97001e111 1.47957 0.739787 0.672841i \(-0.234926\pi\)
0.739787 + 0.672841i \(0.234926\pi\)
\(920\) 4.26968e111 3.07859
\(921\) 4.88863e110 0.338416
\(922\) −3.30359e111 −2.19571
\(923\) 9.48114e107 0.000605058 0
\(924\) 5.89621e110 0.361305
\(925\) −1.96878e111 −1.15846
\(926\) 1.52094e110 0.0859409
\(927\) 7.54164e109 0.0409238
\(928\) 6.61216e111 3.44583
\(929\) −5.85098e110 −0.292846 −0.146423 0.989222i \(-0.546776\pi\)
−0.146423 + 0.989222i \(0.546776\pi\)
\(930\) 4.89096e111 2.35117
\(931\) −2.82218e111 −1.30308
\(932\) −1.02611e112 −4.55090
\(933\) 3.39757e111 1.44746
\(934\) 6.13628e110 0.251129
\(935\) −1.58056e110 −0.0621406
\(936\) 1.98734e110 0.0750635
\(937\) 4.05778e111 1.47249 0.736247 0.676713i \(-0.236596\pi\)
0.736247 + 0.676713i \(0.236596\pi\)
\(938\) −1.16718e111 −0.406942
\(939\) −2.52481e111 −0.845803
\(940\) −1.36551e112 −4.39542
\(941\) 3.76642e111 1.16498 0.582489 0.812839i \(-0.302079\pi\)
0.582489 + 0.812839i \(0.302079\pi\)
\(942\) −6.97074e111 −2.07191
\(943\) −4.27277e111 −1.22045
\(944\) 1.23098e112 3.37911
\(945\) 1.14188e111 0.301250
\(946\) −5.38262e111 −1.36482
\(947\) −1.55286e111 −0.378450 −0.189225 0.981934i \(-0.560597\pi\)
−0.189225 + 0.981934i \(0.560597\pi\)
\(948\) 1.28260e112 3.00455
\(949\) −5.78390e110 −0.130238
\(950\) 1.50594e112 3.25965
\(951\) 6.38476e110 0.132854
\(952\) 3.04862e110 0.0609842
\(953\) 3.52427e111 0.677775 0.338887 0.940827i \(-0.389949\pi\)
0.338887 + 0.940827i \(0.389949\pi\)
\(954\) 3.73429e110 0.0690468
\(955\) −2.08752e111 −0.371111
\(956\) −1.04679e112 −1.78933
\(957\) 4.25945e111 0.700093
\(958\) −1.38334e111 −0.218636
\(959\) −2.99899e111 −0.455803
\(960\) −2.58388e112 −3.77660
\(961\) −3.28586e111 −0.461872
\(962\) −1.16691e111 −0.157751
\(963\) −2.76551e111 −0.359575
\(964\) 3.71300e112 4.64341
\(965\) 6.91520e111 0.831822
\(966\) −3.16332e111 −0.366017
\(967\) −5.78672e111 −0.644080 −0.322040 0.946726i \(-0.604369\pi\)
−0.322040 + 0.946726i \(0.604369\pi\)
\(968\) −2.08124e112 −2.22841
\(969\) −1.26381e111 −0.130179
\(970\) 1.22492e112 1.21386
\(971\) −1.04108e111 −0.0992577 −0.0496288 0.998768i \(-0.515804\pi\)
−0.0496288 + 0.998768i \(0.515804\pi\)
\(972\) 1.53896e112 1.41170
\(973\) 9.10348e110 0.0803482
\(974\) −1.57240e112 −1.33537
\(975\) −1.53997e111 −0.125846
\(976\) 2.36537e112 1.86007
\(977\) 1.54003e111 0.116542 0.0582711 0.998301i \(-0.481441\pi\)
0.0582711 + 0.998301i \(0.481441\pi\)
\(978\) −3.71379e112 −2.70465
\(979\) −1.38663e111 −0.0971875
\(980\) −5.36352e112 −3.61803
\(981\) −6.03332e111 −0.391714
\(982\) 2.90803e112 1.81727
\(983\) −9.94251e110 −0.0598052 −0.0299026 0.999553i \(-0.509520\pi\)
−0.0299026 + 0.999553i \(0.509520\pi\)
\(984\) 1.02756e113 5.94965
\(985\) −3.39593e112 −1.89278
\(986\) 3.60168e111 0.193251
\(987\) 6.18615e111 0.319542
\(988\) 6.42827e111 0.319675
\(989\) 2.07975e112 0.995748
\(990\) −8.67492e111 −0.399895
\(991\) −2.08266e112 −0.924392 −0.462196 0.886778i \(-0.652938\pi\)
−0.462196 + 0.886778i \(0.652938\pi\)
\(992\) −4.79246e112 −2.04819
\(993\) 1.71792e112 0.706980
\(994\) 7.98261e109 0.00316341
\(995\) 2.74108e112 1.04606
\(996\) −2.91167e112 −1.07008
\(997\) 1.02320e112 0.362152 0.181076 0.983469i \(-0.442042\pi\)
0.181076 + 0.983469i \(0.442042\pi\)
\(998\) 7.09239e112 2.41767
\(999\) −2.30932e112 −0.758189
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.76.a.a.1.6 6
3.2 odd 2 9.76.a.c.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.76.a.a.1.6 6 1.1 even 1 trivial
9.76.a.c.1.1 6 3.2 odd 2