Properties

Label 1.62.a.a.1.1
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 1.1
Root \(1.21599e7\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.04812e9 q^{2} +1.78996e14 q^{3} +1.88894e18 q^{4} -2.27994e20 q^{5} -3.66606e23 q^{6} -4.42559e25 q^{7} +8.53860e26 q^{8} -9.51338e28 q^{9} +O(q^{10})\) \(q-2.04812e9 q^{2} +1.78996e14 q^{3} +1.88894e18 q^{4} -2.27994e20 q^{5} -3.66606e23 q^{6} -4.42559e25 q^{7} +8.53860e26 q^{8} -9.51338e28 q^{9} +4.66958e29 q^{10} +7.45476e31 q^{11} +3.38114e32 q^{12} +1.57894e34 q^{13} +9.06412e34 q^{14} -4.08100e34 q^{15} -6.10441e36 q^{16} -3.16443e37 q^{17} +1.94845e38 q^{18} +4.06426e38 q^{19} -4.30667e38 q^{20} -7.92164e39 q^{21} -1.52682e41 q^{22} +5.44945e40 q^{23} +1.52838e41 q^{24} -4.28483e42 q^{25} -3.23385e43 q^{26} -3.97922e43 q^{27} -8.35968e43 q^{28} +2.13683e44 q^{29} +8.35837e43 q^{30} -2.29937e45 q^{31} +1.05337e46 q^{32} +1.33437e46 q^{33} +6.48113e46 q^{34} +1.00901e46 q^{35} -1.79702e47 q^{36} -1.07009e48 q^{37} -8.32407e47 q^{38} +2.82624e48 q^{39} -1.94675e47 q^{40} -1.40249e49 q^{41} +1.62244e49 q^{42} +5.79966e49 q^{43} +1.40816e50 q^{44} +2.16899e49 q^{45} -1.11611e50 q^{46} -1.51708e51 q^{47} -1.09267e51 q^{48} -1.59757e51 q^{49} +8.77583e51 q^{50} -5.66421e51 q^{51} +2.98252e52 q^{52} -4.58000e52 q^{53} +8.14991e52 q^{54} -1.69964e52 q^{55} -3.77883e52 q^{56} +7.27487e52 q^{57} -4.37649e53 q^{58} -1.78535e54 q^{59} -7.70878e52 q^{60} +4.41900e54 q^{61} +4.70938e54 q^{62} +4.21023e54 q^{63} -7.49842e54 q^{64} -3.59987e54 q^{65} -2.73296e55 q^{66} +2.75737e55 q^{67} -5.97743e55 q^{68} +9.75431e54 q^{69} -2.06656e55 q^{70} +1.08638e56 q^{71} -8.12310e55 q^{72} -1.85098e56 q^{73} +2.19168e57 q^{74} -7.66968e56 q^{75} +7.67715e56 q^{76} -3.29917e57 q^{77} -5.78847e57 q^{78} -4.07387e57 q^{79} +1.39177e57 q^{80} +4.97584e57 q^{81} +2.87246e58 q^{82} +2.46467e58 q^{83} -1.49635e58 q^{84} +7.21470e57 q^{85} -1.18784e59 q^{86} +3.82485e58 q^{87} +6.36532e58 q^{88} -6.63380e57 q^{89} -4.44234e58 q^{90} -6.98772e59 q^{91} +1.02937e59 q^{92} -4.11578e59 q^{93} +3.10715e60 q^{94} -9.26624e58 q^{95} +1.88549e60 q^{96} -2.67905e60 q^{97} +3.27201e60 q^{98} -7.09200e60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} + O(q^{10}) \) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} - \)\(14\!\cdots\!00\)\(q^{10} - \)\(41\!\cdots\!52\)\(q^{11} - \)\(99\!\cdots\!00\)\(q^{12} + \)\(10\!\cdots\!00\)\(q^{13} - \)\(21\!\cdots\!04\)\(q^{14} + \)\(11\!\cdots\!00\)\(q^{15} + \)\(10\!\cdots\!24\)\(q^{16} - \)\(40\!\cdots\!00\)\(q^{17} + \)\(15\!\cdots\!00\)\(q^{18} - \)\(35\!\cdots\!20\)\(q^{19} - \)\(50\!\cdots\!00\)\(q^{20} - \)\(55\!\cdots\!72\)\(q^{21} - \)\(17\!\cdots\!00\)\(q^{22} - \)\(41\!\cdots\!00\)\(q^{23} - \)\(61\!\cdots\!60\)\(q^{24} - \)\(16\!\cdots\!00\)\(q^{25} - \)\(49\!\cdots\!32\)\(q^{26} - \)\(12\!\cdots\!00\)\(q^{27} - \)\(79\!\cdots\!00\)\(q^{28} + \)\(66\!\cdots\!20\)\(q^{29} + \)\(95\!\cdots\!00\)\(q^{30} + \)\(32\!\cdots\!28\)\(q^{31} + \)\(29\!\cdots\!00\)\(q^{32} + \)\(80\!\cdots\!00\)\(q^{33} + \)\(39\!\cdots\!16\)\(q^{34} + \)\(94\!\cdots\!00\)\(q^{35} - \)\(49\!\cdots\!36\)\(q^{36} - \)\(71\!\cdots\!00\)\(q^{37} - \)\(65\!\cdots\!00\)\(q^{38} - \)\(53\!\cdots\!76\)\(q^{39} - \)\(69\!\cdots\!00\)\(q^{40} + \)\(16\!\cdots\!68\)\(q^{41} + \)\(15\!\cdots\!00\)\(q^{42} + \)\(75\!\cdots\!00\)\(q^{43} + \)\(15\!\cdots\!36\)\(q^{44} + \)\(60\!\cdots\!00\)\(q^{45} - \)\(15\!\cdots\!12\)\(q^{46} - \)\(21\!\cdots\!00\)\(q^{47} - \)\(84\!\cdots\!00\)\(q^{48} + \)\(15\!\cdots\!28\)\(q^{49} - \)\(37\!\cdots\!00\)\(q^{50} + \)\(20\!\cdots\!88\)\(q^{51} + \)\(34\!\cdots\!00\)\(q^{52} + \)\(84\!\cdots\!00\)\(q^{53} + \)\(20\!\cdots\!80\)\(q^{54} - \)\(18\!\cdots\!00\)\(q^{55} - \)\(89\!\cdots\!20\)\(q^{56} - \)\(48\!\cdots\!00\)\(q^{57} - \)\(42\!\cdots\!00\)\(q^{58} - \)\(21\!\cdots\!60\)\(q^{59} + \)\(16\!\cdots\!00\)\(q^{60} + \)\(42\!\cdots\!48\)\(q^{61} + \)\(51\!\cdots\!00\)\(q^{62} + \)\(17\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!08\)\(q^{64} - \)\(40\!\cdots\!00\)\(q^{65} - \)\(32\!\cdots\!24\)\(q^{66} - \)\(15\!\cdots\!00\)\(q^{67} - \)\(19\!\cdots\!00\)\(q^{68} - \)\(65\!\cdots\!16\)\(q^{69} + \)\(16\!\cdots\!00\)\(q^{70} + \)\(26\!\cdots\!88\)\(q^{71} + \)\(10\!\cdots\!00\)\(q^{72} + \)\(43\!\cdots\!00\)\(q^{73} + \)\(27\!\cdots\!56\)\(q^{74} + \)\(22\!\cdots\!00\)\(q^{75} - \)\(91\!\cdots\!40\)\(q^{76} - \)\(62\!\cdots\!00\)\(q^{77} - \)\(62\!\cdots\!00\)\(q^{78} - \)\(21\!\cdots\!80\)\(q^{79} - \)\(81\!\cdots\!00\)\(q^{80} + \)\(16\!\cdots\!84\)\(q^{81} + \)\(41\!\cdots\!00\)\(q^{82} - \)\(19\!\cdots\!00\)\(q^{83} + \)\(26\!\cdots\!96\)\(q^{84} + \)\(23\!\cdots\!00\)\(q^{85} - \)\(71\!\cdots\!72\)\(q^{86} - \)\(25\!\cdots\!00\)\(q^{87} - \)\(45\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!40\)\(q^{89} - \)\(12\!\cdots\!00\)\(q^{90} - \)\(45\!\cdots\!52\)\(q^{91} + \)\(16\!\cdots\!00\)\(q^{92} - \)\(43\!\cdots\!00\)\(q^{93} + \)\(64\!\cdots\!76\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} + \)\(15\!\cdots\!08\)\(q^{96} - \)\(80\!\cdots\!00\)\(q^{97} + \)\(17\!\cdots\!00\)\(q^{98} - \)\(31\!\cdots\!76\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.04812e9 −1.34878 −0.674388 0.738377i \(-0.735593\pi\)
−0.674388 + 0.738377i \(0.735593\pi\)
\(3\) 1.78996e14 0.501933 0.250967 0.967996i \(-0.419252\pi\)
0.250967 + 0.967996i \(0.419252\pi\)
\(4\) 1.88894e18 0.819198
\(5\) −2.27994e20 −0.109481 −0.0547403 0.998501i \(-0.517433\pi\)
−0.0547403 + 0.998501i \(0.517433\pi\)
\(6\) −3.66606e23 −0.676996
\(7\) −4.42559e25 −0.742131 −0.371066 0.928607i \(-0.621007\pi\)
−0.371066 + 0.928607i \(0.621007\pi\)
\(8\) 8.53860e26 0.243861
\(9\) −9.51338e28 −0.748063
\(10\) 4.66958e29 0.147665
\(11\) 7.45476e31 1.28812 0.644061 0.764974i \(-0.277248\pi\)
0.644061 + 0.764974i \(0.277248\pi\)
\(12\) 3.38114e32 0.411183
\(13\) 1.57894e34 1.67145 0.835723 0.549151i \(-0.185049\pi\)
0.835723 + 0.549151i \(0.185049\pi\)
\(14\) 9.06412e34 1.00097
\(15\) −4.08100e34 −0.0549520
\(16\) −6.10441e36 −1.14811
\(17\) −3.16443e37 −0.936706 −0.468353 0.883541i \(-0.655152\pi\)
−0.468353 + 0.883541i \(0.655152\pi\)
\(18\) 1.94845e38 1.00897
\(19\) 4.06426e38 0.404572 0.202286 0.979326i \(-0.435163\pi\)
0.202286 + 0.979326i \(0.435163\pi\)
\(20\) −4.30667e38 −0.0896864
\(21\) −7.92164e39 −0.372500
\(22\) −1.52682e41 −1.73739
\(23\) 5.44945e40 0.159828 0.0799141 0.996802i \(-0.474535\pi\)
0.0799141 + 0.996802i \(0.474535\pi\)
\(24\) 1.52838e41 0.122402
\(25\) −4.28483e42 −0.988014
\(26\) −3.23385e43 −2.25441
\(27\) −3.97922e43 −0.877411
\(28\) −8.35968e43 −0.607953
\(29\) 2.13683e44 0.532883 0.266442 0.963851i \(-0.414152\pi\)
0.266442 + 0.963851i \(0.414152\pi\)
\(30\) 8.35837e43 0.0741179
\(31\) −2.29937e45 −0.750027 −0.375013 0.927019i \(-0.622362\pi\)
−0.375013 + 0.927019i \(0.622362\pi\)
\(32\) 1.05337e46 1.30469
\(33\) 1.33437e46 0.646551
\(34\) 6.48113e46 1.26341
\(35\) 1.00901e46 0.0812490
\(36\) −1.79702e47 −0.612812
\(37\) −1.07009e48 −1.58223 −0.791114 0.611668i \(-0.790499\pi\)
−0.791114 + 0.611668i \(0.790499\pi\)
\(38\) −8.32407e47 −0.545678
\(39\) 2.82624e48 0.838954
\(40\) −1.94675e47 −0.0266980
\(41\) −1.40249e49 −0.905714 −0.452857 0.891583i \(-0.649595\pi\)
−0.452857 + 0.891583i \(0.649595\pi\)
\(42\) 1.62244e49 0.502419
\(43\) 5.79966e49 0.876223 0.438111 0.898921i \(-0.355648\pi\)
0.438111 + 0.898921i \(0.355648\pi\)
\(44\) 1.40816e50 1.05523
\(45\) 2.16899e49 0.0818984
\(46\) −1.11611e50 −0.215573
\(47\) −1.51708e51 −1.52063 −0.760314 0.649555i \(-0.774955\pi\)
−0.760314 + 0.649555i \(0.774955\pi\)
\(48\) −1.09267e51 −0.576276
\(49\) −1.59757e51 −0.449242
\(50\) 8.77583e51 1.33261
\(51\) −5.66421e51 −0.470164
\(52\) 2.98252e52 1.36925
\(53\) −4.58000e52 −1.17612 −0.588060 0.808817i \(-0.700108\pi\)
−0.588060 + 0.808817i \(0.700108\pi\)
\(54\) 8.14991e52 1.18343
\(55\) −1.69964e52 −0.141024
\(56\) −3.77883e52 −0.180977
\(57\) 7.27487e52 0.203068
\(58\) −4.37649e53 −0.718740
\(59\) −1.78535e54 −1.74075 −0.870374 0.492391i \(-0.836123\pi\)
−0.870374 + 0.492391i \(0.836123\pi\)
\(60\) −7.70878e52 −0.0450166
\(61\) 4.41900e54 1.55871 0.779353 0.626585i \(-0.215548\pi\)
0.779353 + 0.626585i \(0.215548\pi\)
\(62\) 4.70938e54 1.01162
\(63\) 4.21023e54 0.555161
\(64\) −7.49842e54 −0.611618
\(65\) −3.59987e54 −0.182991
\(66\) −2.73296e55 −0.872053
\(67\) 2.75737e55 0.556178 0.278089 0.960555i \(-0.410299\pi\)
0.278089 + 0.960555i \(0.410299\pi\)
\(68\) −5.97743e55 −0.767348
\(69\) 9.75431e54 0.0802231
\(70\) −2.06656e55 −0.109587
\(71\) 1.08638e56 0.373768 0.186884 0.982382i \(-0.440161\pi\)
0.186884 + 0.982382i \(0.440161\pi\)
\(72\) −8.12310e55 −0.182423
\(73\) −1.85098e56 −0.272932 −0.136466 0.990645i \(-0.543574\pi\)
−0.136466 + 0.990645i \(0.543574\pi\)
\(74\) 2.19168e57 2.13407
\(75\) −7.66968e56 −0.495917
\(76\) 7.67715e56 0.331425
\(77\) −3.29917e57 −0.955955
\(78\) −5.78847e57 −1.13156
\(79\) −4.07387e57 −0.539984 −0.269992 0.962863i \(-0.587021\pi\)
−0.269992 + 0.962863i \(0.587021\pi\)
\(80\) 1.39177e57 0.125696
\(81\) 4.97584e57 0.307662
\(82\) 2.87246e58 1.22161
\(83\) 2.46467e58 0.724231 0.362115 0.932133i \(-0.382055\pi\)
0.362115 + 0.932133i \(0.382055\pi\)
\(84\) −1.49635e58 −0.305152
\(85\) 7.21470e57 0.102551
\(86\) −1.18784e59 −1.18183
\(87\) 3.82485e58 0.267472
\(88\) 6.36532e58 0.314122
\(89\) −6.63380e57 −0.0231936 −0.0115968 0.999933i \(-0.503691\pi\)
−0.0115968 + 0.999933i \(0.503691\pi\)
\(90\) −4.44234e58 −0.110463
\(91\) −6.98772e59 −1.24043
\(92\) 1.02937e59 0.130931
\(93\) −4.11578e59 −0.376463
\(94\) 3.10715e60 2.05099
\(95\) −9.26624e58 −0.0442928
\(96\) 1.88549e60 0.654865
\(97\) −2.67905e60 −0.678333 −0.339166 0.940726i \(-0.610145\pi\)
−0.339166 + 0.940726i \(0.610145\pi\)
\(98\) 3.27201e60 0.605926
\(99\) −7.09200e60 −0.963596
\(100\) −8.09380e60 −0.809380
\(101\) −1.78180e61 −1.31540 −0.657699 0.753281i \(-0.728470\pi\)
−0.657699 + 0.753281i \(0.728470\pi\)
\(102\) 1.16010e61 0.634146
\(103\) 2.23869e61 0.908778 0.454389 0.890803i \(-0.349858\pi\)
0.454389 + 0.890803i \(0.349858\pi\)
\(104\) 1.34819e61 0.407600
\(105\) 1.80608e60 0.0407816
\(106\) 9.38038e61 1.58632
\(107\) −1.07119e62 −1.36038 −0.680192 0.733034i \(-0.738104\pi\)
−0.680192 + 0.733034i \(0.738104\pi\)
\(108\) −7.51652e61 −0.718774
\(109\) 1.00368e62 0.724585 0.362292 0.932064i \(-0.381994\pi\)
0.362292 + 0.932064i \(0.381994\pi\)
\(110\) 3.48106e61 0.190210
\(111\) −1.91543e62 −0.794173
\(112\) 2.70156e62 0.852050
\(113\) −4.77242e62 −1.14775 −0.573874 0.818944i \(-0.694560\pi\)
−0.573874 + 0.818944i \(0.694560\pi\)
\(114\) −1.48998e62 −0.273894
\(115\) −1.24244e61 −0.0174981
\(116\) 4.03636e62 0.436537
\(117\) −1.50210e63 −1.25035
\(118\) 3.65660e63 2.34788
\(119\) 1.40045e63 0.695159
\(120\) −3.48460e61 −0.0134006
\(121\) 2.20805e63 0.659257
\(122\) −9.05064e63 −2.10235
\(123\) −2.51040e63 −0.454608
\(124\) −4.34338e63 −0.614421
\(125\) 1.96568e63 0.217649
\(126\) −8.62304e63 −0.748788
\(127\) 2.87823e64 1.96386 0.981932 0.189235i \(-0.0606007\pi\)
0.981932 + 0.189235i \(0.0606007\pi\)
\(128\) −8.93139e63 −0.479750
\(129\) 1.03812e64 0.439805
\(130\) 7.37297e63 0.246814
\(131\) −3.69910e63 −0.0980217 −0.0490108 0.998798i \(-0.515607\pi\)
−0.0490108 + 0.998798i \(0.515607\pi\)
\(132\) 2.52056e64 0.529653
\(133\) −1.79867e64 −0.300246
\(134\) −5.64742e64 −0.750160
\(135\) 9.07236e63 0.0960595
\(136\) −2.70198e64 −0.228426
\(137\) 4.88169e64 0.330060 0.165030 0.986289i \(-0.447228\pi\)
0.165030 + 0.986289i \(0.447228\pi\)
\(138\) −1.99780e64 −0.108203
\(139\) −1.13820e65 −0.494614 −0.247307 0.968937i \(-0.579546\pi\)
−0.247307 + 0.968937i \(0.579546\pi\)
\(140\) 1.90595e64 0.0665591
\(141\) −2.71551e65 −0.763254
\(142\) −2.22504e65 −0.504130
\(143\) 1.17706e66 2.15303
\(144\) 5.80736e65 0.858861
\(145\) −4.87184e64 −0.0583404
\(146\) 3.79102e65 0.368124
\(147\) −2.85959e65 −0.225489
\(148\) −2.02135e66 −1.29616
\(149\) −2.13216e66 −1.11337 −0.556684 0.830724i \(-0.687927\pi\)
−0.556684 + 0.830724i \(0.687927\pi\)
\(150\) 1.57084e66 0.668881
\(151\) −3.70988e66 −1.28992 −0.644961 0.764216i \(-0.723126\pi\)
−0.644961 + 0.764216i \(0.723126\pi\)
\(152\) 3.47031e65 0.0986594
\(153\) 3.01044e66 0.700715
\(154\) 6.75709e66 1.28937
\(155\) 5.24241e65 0.0821134
\(156\) 5.33860e66 0.687270
\(157\) −1.01374e67 −1.07396 −0.536979 0.843596i \(-0.680435\pi\)
−0.536979 + 0.843596i \(0.680435\pi\)
\(158\) 8.34376e66 0.728317
\(159\) −8.19803e66 −0.590333
\(160\) −2.40161e66 −0.142838
\(161\) −2.41170e66 −0.118613
\(162\) −1.01911e67 −0.414967
\(163\) 3.38270e67 1.14167 0.570836 0.821064i \(-0.306619\pi\)
0.570836 + 0.821064i \(0.306619\pi\)
\(164\) −2.64922e67 −0.741959
\(165\) −3.04229e66 −0.0707848
\(166\) −5.04793e67 −0.976825
\(167\) −1.22693e67 −0.197682 −0.0988411 0.995103i \(-0.531514\pi\)
−0.0988411 + 0.995103i \(0.531514\pi\)
\(168\) −6.76397e66 −0.0908382
\(169\) 1.60067e68 1.79373
\(170\) −1.47765e67 −0.138319
\(171\) −3.86648e67 −0.302646
\(172\) 1.09552e68 0.717800
\(173\) 1.07923e68 0.592528 0.296264 0.955106i \(-0.404259\pi\)
0.296264 + 0.955106i \(0.404259\pi\)
\(174\) −7.83375e67 −0.360760
\(175\) 1.89629e68 0.733236
\(176\) −4.55069e68 −1.47891
\(177\) −3.19570e68 −0.873739
\(178\) 1.35868e67 0.0312829
\(179\) −6.21601e68 −1.20641 −0.603204 0.797587i \(-0.706110\pi\)
−0.603204 + 0.797587i \(0.706110\pi\)
\(180\) 4.09710e67 0.0670911
\(181\) 1.52963e68 0.211539 0.105770 0.994391i \(-0.466269\pi\)
0.105770 + 0.994391i \(0.466269\pi\)
\(182\) 1.43117e69 1.67307
\(183\) 7.90985e68 0.782367
\(184\) 4.65307e67 0.0389759
\(185\) 2.43974e68 0.173223
\(186\) 8.42961e68 0.507765
\(187\) −2.35901e69 −1.20659
\(188\) −2.86567e69 −1.24570
\(189\) 1.76104e69 0.651154
\(190\) 1.89783e68 0.0597411
\(191\) 2.62596e69 0.704322 0.352161 0.935939i \(-0.385447\pi\)
0.352161 + 0.935939i \(0.385447\pi\)
\(192\) −1.34219e69 −0.306991
\(193\) −6.76456e69 −1.32051 −0.660255 0.751042i \(-0.729552\pi\)
−0.660255 + 0.751042i \(0.729552\pi\)
\(194\) 5.48701e69 0.914919
\(195\) −6.44364e68 −0.0918493
\(196\) −3.01772e69 −0.368018
\(197\) −7.24378e69 −0.756389 −0.378195 0.925726i \(-0.623455\pi\)
−0.378195 + 0.925726i \(0.623455\pi\)
\(198\) 1.45252e70 1.29968
\(199\) 9.15268e68 0.0702311 0.0351155 0.999383i \(-0.488820\pi\)
0.0351155 + 0.999383i \(0.488820\pi\)
\(200\) −3.65864e69 −0.240938
\(201\) 4.93559e69 0.279164
\(202\) 3.64934e70 1.77418
\(203\) −9.45674e69 −0.395469
\(204\) −1.06994e70 −0.385158
\(205\) 3.19758e69 0.0991581
\(206\) −4.58509e70 −1.22574
\(207\) −5.18427e69 −0.119562
\(208\) −9.63848e70 −1.91901
\(209\) 3.02981e70 0.521138
\(210\) −3.69907e69 −0.0550052
\(211\) 1.42797e71 1.83698 0.918491 0.395443i \(-0.129409\pi\)
0.918491 + 0.395443i \(0.129409\pi\)
\(212\) −8.65136e70 −0.963475
\(213\) 1.94458e70 0.187607
\(214\) 2.19392e71 1.83485
\(215\) −1.32228e70 −0.0959294
\(216\) −3.39770e70 −0.213966
\(217\) 1.01761e71 0.556618
\(218\) −2.05566e71 −0.977303
\(219\) −3.31318e70 −0.136993
\(220\) −3.21052e70 −0.115527
\(221\) −4.99644e71 −1.56565
\(222\) 3.92302e71 1.07116
\(223\) −7.24022e70 −0.172367 −0.0861834 0.996279i \(-0.527467\pi\)
−0.0861834 + 0.996279i \(0.527467\pi\)
\(224\) −4.66177e71 −0.968248
\(225\) 4.07632e71 0.739097
\(226\) 9.77448e71 1.54805
\(227\) −7.90928e71 −1.09483 −0.547417 0.836860i \(-0.684389\pi\)
−0.547417 + 0.836860i \(0.684389\pi\)
\(228\) 1.37418e71 0.166353
\(229\) −2.69486e71 −0.285466 −0.142733 0.989761i \(-0.545589\pi\)
−0.142733 + 0.989761i \(0.545589\pi\)
\(230\) 2.54466e70 0.0236010
\(231\) −5.90539e71 −0.479825
\(232\) 1.82456e71 0.129949
\(233\) 1.65753e72 1.03539 0.517696 0.855565i \(-0.326790\pi\)
0.517696 + 0.855565i \(0.326790\pi\)
\(234\) 3.07648e72 1.68644
\(235\) 3.45884e71 0.166479
\(236\) −3.37242e72 −1.42602
\(237\) −7.29207e71 −0.271036
\(238\) −2.86828e72 −0.937614
\(239\) −1.37118e72 −0.394421 −0.197210 0.980361i \(-0.563188\pi\)
−0.197210 + 0.980361i \(0.563188\pi\)
\(240\) 2.49121e71 0.0630910
\(241\) −3.48714e72 −0.777946 −0.388973 0.921249i \(-0.627170\pi\)
−0.388973 + 0.921249i \(0.627170\pi\)
\(242\) −4.52234e72 −0.889191
\(243\) 5.95117e72 1.03184
\(244\) 8.34725e72 1.27689
\(245\) 3.64236e71 0.0491833
\(246\) 5.14159e72 0.613164
\(247\) 6.41720e72 0.676221
\(248\) −1.96334e72 −0.182902
\(249\) 4.41167e72 0.363515
\(250\) −4.02594e72 −0.293560
\(251\) −1.53704e73 −0.992283 −0.496142 0.868242i \(-0.665250\pi\)
−0.496142 + 0.868242i \(0.665250\pi\)
\(252\) 7.95288e72 0.454787
\(253\) 4.06243e72 0.205878
\(254\) −5.89495e73 −2.64881
\(255\) 1.29140e72 0.0514739
\(256\) 3.55827e73 1.25869
\(257\) 7.08695e72 0.222587 0.111293 0.993788i \(-0.464501\pi\)
0.111293 + 0.993788i \(0.464501\pi\)
\(258\) −2.12619e73 −0.593199
\(259\) 4.73579e73 1.17422
\(260\) −6.79996e72 −0.149906
\(261\) −2.03285e73 −0.398630
\(262\) 7.57620e72 0.132209
\(263\) 2.21707e72 0.0344453 0.0172227 0.999852i \(-0.494518\pi\)
0.0172227 + 0.999852i \(0.494518\pi\)
\(264\) 1.13937e73 0.157668
\(265\) 1.04421e73 0.128762
\(266\) 3.68389e73 0.404964
\(267\) −1.18743e72 −0.0116416
\(268\) 5.20852e73 0.455620
\(269\) −5.72433e73 −0.446972 −0.223486 0.974707i \(-0.571744\pi\)
−0.223486 + 0.974707i \(0.571744\pi\)
\(270\) −1.85813e73 −0.129563
\(271\) −1.25491e74 −0.781715 −0.390858 0.920451i \(-0.627821\pi\)
−0.390858 + 0.920451i \(0.627821\pi\)
\(272\) 1.93170e74 1.07544
\(273\) −1.25078e74 −0.622614
\(274\) −9.99828e73 −0.445177
\(275\) −3.19424e74 −1.27268
\(276\) 1.84253e73 0.0657186
\(277\) −9.29554e73 −0.296922 −0.148461 0.988918i \(-0.547432\pi\)
−0.148461 + 0.988918i \(0.547432\pi\)
\(278\) 2.33116e74 0.667124
\(279\) 2.18748e74 0.561068
\(280\) 8.61549e72 0.0198134
\(281\) 6.92706e74 1.42891 0.714457 0.699680i \(-0.246674\pi\)
0.714457 + 0.699680i \(0.246674\pi\)
\(282\) 5.56169e74 1.02946
\(283\) 2.76298e73 0.0459083 0.0229542 0.999737i \(-0.492693\pi\)
0.0229542 + 0.999737i \(0.492693\pi\)
\(284\) 2.05211e74 0.306190
\(285\) −1.65862e73 −0.0222320
\(286\) −2.41076e75 −2.90395
\(287\) 6.20682e74 0.672158
\(288\) −1.00211e75 −0.975988
\(289\) −1.39897e74 −0.122581
\(290\) 9.97811e73 0.0786882
\(291\) −4.79540e74 −0.340478
\(292\) −3.49639e74 −0.223585
\(293\) 2.78327e75 1.60359 0.801794 0.597601i \(-0.203879\pi\)
0.801794 + 0.597601i \(0.203879\pi\)
\(294\) 5.85679e74 0.304135
\(295\) 4.07047e74 0.190578
\(296\) −9.13710e74 −0.385844
\(297\) −2.96641e75 −1.13021
\(298\) 4.36692e75 1.50169
\(299\) 8.60433e74 0.267144
\(300\) −1.44876e75 −0.406254
\(301\) −2.56669e75 −0.650272
\(302\) 7.59828e75 1.73982
\(303\) −3.18936e75 −0.660242
\(304\) −2.48099e75 −0.464494
\(305\) −1.00750e75 −0.170648
\(306\) −6.16574e75 −0.945109
\(307\) 1.07115e76 1.48637 0.743187 0.669084i \(-0.233313\pi\)
0.743187 + 0.669084i \(0.233313\pi\)
\(308\) −6.23194e75 −0.783117
\(309\) 4.00716e75 0.456146
\(310\) −1.07371e75 −0.110753
\(311\) −1.92669e76 −1.80144 −0.900719 0.434402i \(-0.856960\pi\)
−0.900719 + 0.434402i \(0.856960\pi\)
\(312\) 2.41321e75 0.204588
\(313\) −7.23121e75 −0.556043 −0.278022 0.960575i \(-0.589679\pi\)
−0.278022 + 0.960575i \(0.589679\pi\)
\(314\) 2.07626e76 1.44853
\(315\) −9.59905e74 −0.0607794
\(316\) −7.69530e75 −0.442354
\(317\) 2.35562e76 1.22969 0.614847 0.788646i \(-0.289218\pi\)
0.614847 + 0.788646i \(0.289218\pi\)
\(318\) 1.67905e76 0.796228
\(319\) 1.59296e76 0.686418
\(320\) 1.70959e75 0.0669603
\(321\) −1.91739e76 −0.682822
\(322\) 4.93945e75 0.159983
\(323\) −1.28611e76 −0.378965
\(324\) 9.39908e75 0.252036
\(325\) −6.76547e76 −1.65141
\(326\) −6.92816e76 −1.53986
\(327\) 1.79656e76 0.363693
\(328\) −1.19753e76 −0.220868
\(329\) 6.71396e76 1.12851
\(330\) 6.23096e75 0.0954729
\(331\) −4.64715e76 −0.649282 −0.324641 0.945837i \(-0.605243\pi\)
−0.324641 + 0.945837i \(0.605243\pi\)
\(332\) 4.65562e76 0.593289
\(333\) 1.01802e77 1.18361
\(334\) 2.51290e76 0.266629
\(335\) −6.28663e75 −0.0608907
\(336\) 4.83569e76 0.427672
\(337\) 2.10365e77 1.69927 0.849634 0.527372i \(-0.176823\pi\)
0.849634 + 0.527372i \(0.176823\pi\)
\(338\) −3.27837e77 −2.41935
\(339\) −8.54246e76 −0.576092
\(340\) 1.36282e76 0.0840098
\(341\) −1.71412e77 −0.966126
\(342\) 7.91901e76 0.408201
\(343\) 2.28083e77 1.07553
\(344\) 4.95210e76 0.213676
\(345\) −2.22392e75 −0.00878288
\(346\) −2.21040e77 −0.799188
\(347\) −2.00534e76 −0.0663956 −0.0331978 0.999449i \(-0.510569\pi\)
−0.0331978 + 0.999449i \(0.510569\pi\)
\(348\) 7.22493e76 0.219112
\(349\) −2.60527e76 −0.0723897 −0.0361948 0.999345i \(-0.511524\pi\)
−0.0361948 + 0.999345i \(0.511524\pi\)
\(350\) −3.88382e77 −0.988971
\(351\) −6.28293e77 −1.46655
\(352\) 7.85261e77 1.68059
\(353\) 1.11807e76 0.0219452 0.0109726 0.999940i \(-0.496507\pi\)
0.0109726 + 0.999940i \(0.496507\pi\)
\(354\) 6.54517e77 1.17848
\(355\) −2.47688e76 −0.0409204
\(356\) −1.25309e76 −0.0190001
\(357\) 2.50675e77 0.348923
\(358\) 1.27311e78 1.62718
\(359\) −6.93433e77 −0.813999 −0.407000 0.913428i \(-0.633425\pi\)
−0.407000 + 0.913428i \(0.633425\pi\)
\(360\) 1.85201e76 0.0199718
\(361\) −8.44001e77 −0.836321
\(362\) −3.13287e77 −0.285319
\(363\) 3.95233e77 0.330903
\(364\) −1.31994e78 −1.01616
\(365\) 4.22011e76 0.0298807
\(366\) −1.62003e78 −1.05524
\(367\) −4.69690e77 −0.281511 −0.140756 0.990044i \(-0.544953\pi\)
−0.140756 + 0.990044i \(0.544953\pi\)
\(368\) −3.32657e77 −0.183501
\(369\) 1.33424e78 0.677531
\(370\) −4.99688e77 −0.233640
\(371\) 2.02692e78 0.872835
\(372\) −7.77448e77 −0.308398
\(373\) 2.32868e78 0.851118 0.425559 0.904931i \(-0.360078\pi\)
0.425559 + 0.904931i \(0.360078\pi\)
\(374\) 4.83152e78 1.62742
\(375\) 3.51849e77 0.109245
\(376\) −1.29537e78 −0.370822
\(377\) 3.37393e78 0.890686
\(378\) −3.60681e78 −0.878261
\(379\) −7.98852e78 −1.79461 −0.897306 0.441409i \(-0.854479\pi\)
−0.897306 + 0.441409i \(0.854479\pi\)
\(380\) −1.75034e77 −0.0362846
\(381\) 5.15192e78 0.985728
\(382\) −5.37828e78 −0.949973
\(383\) −3.22231e78 −0.525539 −0.262770 0.964859i \(-0.584636\pi\)
−0.262770 + 0.964859i \(0.584636\pi\)
\(384\) −1.59869e78 −0.240802
\(385\) 7.52189e77 0.104659
\(386\) 1.38546e79 1.78107
\(387\) −5.51743e78 −0.655470
\(388\) −5.06057e78 −0.555689
\(389\) 4.01485e77 0.0407574 0.0203787 0.999792i \(-0.493513\pi\)
0.0203787 + 0.999792i \(0.493513\pi\)
\(390\) 1.31973e78 0.123884
\(391\) −1.72444e78 −0.149712
\(392\) −1.36410e78 −0.109552
\(393\) −6.62126e77 −0.0492003
\(394\) 1.48361e79 1.02020
\(395\) 9.28815e77 0.0591178
\(396\) −1.33964e79 −0.789377
\(397\) 1.01434e79 0.553444 0.276722 0.960950i \(-0.410752\pi\)
0.276722 + 0.960950i \(0.410752\pi\)
\(398\) −1.87458e78 −0.0947260
\(399\) −3.21956e78 −0.150703
\(400\) 2.61564e79 1.13435
\(401\) 3.51734e79 1.41355 0.706775 0.707438i \(-0.250149\pi\)
0.706775 + 0.707438i \(0.250149\pi\)
\(402\) −1.01087e79 −0.376530
\(403\) −3.63056e79 −1.25363
\(404\) −3.36572e79 −1.07757
\(405\) −1.13446e78 −0.0336830
\(406\) 1.93685e79 0.533399
\(407\) −7.97729e79 −2.03810
\(408\) −4.83645e78 −0.114655
\(409\) −1.93067e78 −0.0424763 −0.0212381 0.999774i \(-0.506761\pi\)
−0.0212381 + 0.999774i \(0.506761\pi\)
\(410\) −6.54901e78 −0.133742
\(411\) 8.73805e78 0.165668
\(412\) 4.22875e79 0.744469
\(413\) 7.90120e79 1.29186
\(414\) 1.06180e79 0.161262
\(415\) −5.61929e78 −0.0792892
\(416\) 1.66320e80 2.18071
\(417\) −2.03733e79 −0.248263
\(418\) −6.20540e79 −0.702899
\(419\) −4.55786e79 −0.479991 −0.239995 0.970774i \(-0.577146\pi\)
−0.239995 + 0.970774i \(0.577146\pi\)
\(420\) 3.41159e78 0.0334082
\(421\) 1.05786e79 0.0963442 0.0481721 0.998839i \(-0.484660\pi\)
0.0481721 + 0.998839i \(0.484660\pi\)
\(422\) −2.92465e80 −2.47768
\(423\) 1.44325e80 1.13753
\(424\) −3.91068e79 −0.286810
\(425\) 1.35590e80 0.925479
\(426\) −3.98273e79 −0.253040
\(427\) −1.95567e80 −1.15676
\(428\) −2.02342e80 −1.11442
\(429\) 2.10689e80 1.08068
\(430\) 2.70819e79 0.129387
\(431\) −9.69521e79 −0.431520 −0.215760 0.976446i \(-0.569223\pi\)
−0.215760 + 0.976446i \(0.569223\pi\)
\(432\) 2.42908e80 1.00737
\(433\) 3.23814e80 1.25146 0.625728 0.780042i \(-0.284802\pi\)
0.625728 + 0.780042i \(0.284802\pi\)
\(434\) −2.08418e80 −0.750754
\(435\) −8.72042e78 −0.0292830
\(436\) 1.89590e80 0.593579
\(437\) 2.21479e79 0.0646621
\(438\) 6.78578e79 0.184773
\(439\) −6.77960e80 −1.72201 −0.861007 0.508594i \(-0.830165\pi\)
−0.861007 + 0.508594i \(0.830165\pi\)
\(440\) −1.45125e79 −0.0343903
\(441\) 1.51983e80 0.336061
\(442\) 1.02333e81 2.11172
\(443\) −3.49885e80 −0.673925 −0.336963 0.941518i \(-0.609400\pi\)
−0.336963 + 0.941518i \(0.609400\pi\)
\(444\) −3.61813e80 −0.650585
\(445\) 1.51246e78 0.00253925
\(446\) 1.48288e80 0.232484
\(447\) −3.81649e80 −0.558836
\(448\) 3.31849e80 0.453901
\(449\) 3.39509e80 0.433848 0.216924 0.976188i \(-0.430398\pi\)
0.216924 + 0.976188i \(0.430398\pi\)
\(450\) −8.34878e80 −0.996877
\(451\) −1.04552e81 −1.16667
\(452\) −9.01483e80 −0.940233
\(453\) −6.64055e80 −0.647454
\(454\) 1.61991e81 1.47669
\(455\) 1.59316e80 0.135803
\(456\) 6.21172e79 0.0495204
\(457\) 1.36423e81 1.01729 0.508643 0.860978i \(-0.330147\pi\)
0.508643 + 0.860978i \(0.330147\pi\)
\(458\) 5.51939e80 0.385030
\(459\) 1.25920e81 0.821876
\(460\) −2.34690e79 −0.0143344
\(461\) 1.28858e81 0.736600 0.368300 0.929707i \(-0.379940\pi\)
0.368300 + 0.929707i \(0.379940\pi\)
\(462\) 1.20949e81 0.647177
\(463\) −1.15302e81 −0.577588 −0.288794 0.957391i \(-0.593254\pi\)
−0.288794 + 0.957391i \(0.593254\pi\)
\(464\) −1.30441e81 −0.611810
\(465\) 9.38372e79 0.0412155
\(466\) −3.39481e81 −1.39651
\(467\) 1.31873e81 0.508148 0.254074 0.967185i \(-0.418229\pi\)
0.254074 + 0.967185i \(0.418229\pi\)
\(468\) −2.83739e81 −1.02428
\(469\) −1.22030e81 −0.412757
\(470\) −7.08411e80 −0.224544
\(471\) −1.81456e81 −0.539055
\(472\) −1.52443e81 −0.424500
\(473\) 4.32351e81 1.12868
\(474\) 1.49350e81 0.365567
\(475\) −1.74146e81 −0.399723
\(476\) 2.64536e81 0.569473
\(477\) 4.35713e81 0.879812
\(478\) 2.80835e81 0.531986
\(479\) 5.79250e81 1.02952 0.514758 0.857336i \(-0.327882\pi\)
0.514758 + 0.857336i \(0.327882\pi\)
\(480\) −4.29880e80 −0.0716951
\(481\) −1.68961e82 −2.64461
\(482\) 7.14207e81 1.04928
\(483\) −4.31685e80 −0.0595360
\(484\) 4.17088e81 0.540063
\(485\) 6.10806e80 0.0742643
\(486\) −1.21887e82 −1.39172
\(487\) 5.48178e81 0.587880 0.293940 0.955824i \(-0.405033\pi\)
0.293940 + 0.955824i \(0.405033\pi\)
\(488\) 3.77321e81 0.380108
\(489\) 6.05490e81 0.573043
\(490\) −7.45998e80 −0.0663372
\(491\) −3.71140e81 −0.310136 −0.155068 0.987904i \(-0.549560\pi\)
−0.155068 + 0.987904i \(0.549560\pi\)
\(492\) −4.74200e81 −0.372414
\(493\) −6.76186e81 −0.499155
\(494\) −1.31432e82 −0.912071
\(495\) 1.61693e81 0.105495
\(496\) 1.40363e82 0.861115
\(497\) −4.80787e81 −0.277385
\(498\) −9.03561e81 −0.490301
\(499\) −2.04541e81 −0.104403 −0.0522016 0.998637i \(-0.516624\pi\)
−0.0522016 + 0.998637i \(0.516624\pi\)
\(500\) 3.71305e81 0.178298
\(501\) −2.19616e81 −0.0992232
\(502\) 3.14803e82 1.33837
\(503\) −7.58593e81 −0.303518 −0.151759 0.988417i \(-0.548494\pi\)
−0.151759 + 0.988417i \(0.548494\pi\)
\(504\) 3.59495e81 0.135382
\(505\) 4.06239e81 0.144011
\(506\) −8.32034e81 −0.277684
\(507\) 2.86515e82 0.900334
\(508\) 5.43680e82 1.60879
\(509\) −2.88197e82 −0.803152 −0.401576 0.915826i \(-0.631537\pi\)
−0.401576 + 0.915826i \(0.631537\pi\)
\(510\) −2.64495e81 −0.0694267
\(511\) 8.19166e81 0.202551
\(512\) −5.22832e82 −1.21795
\(513\) −1.61726e82 −0.354976
\(514\) −1.45149e82 −0.300220
\(515\) −5.10406e81 −0.0994936
\(516\) 1.96094e82 0.360288
\(517\) −1.13095e83 −1.95875
\(518\) −9.69946e82 −1.58376
\(519\) 1.93179e82 0.297410
\(520\) −3.07379e81 −0.0446244
\(521\) 1.39898e83 1.91541 0.957704 0.287755i \(-0.0929087\pi\)
0.957704 + 0.287755i \(0.0929087\pi\)
\(522\) 4.16352e82 0.537663
\(523\) 1.36677e83 1.66493 0.832463 0.554081i \(-0.186930\pi\)
0.832463 + 0.554081i \(0.186930\pi\)
\(524\) −6.98740e81 −0.0802992
\(525\) 3.39428e82 0.368035
\(526\) −4.54083e81 −0.0464590
\(527\) 7.27619e82 0.702555
\(528\) −8.14557e82 −0.742313
\(529\) −1.13282e83 −0.974455
\(530\) −2.13867e82 −0.173672
\(531\) 1.69847e83 1.30219
\(532\) −3.39759e82 −0.245961
\(533\) −2.21444e83 −1.51385
\(534\) 2.43199e81 0.0157019
\(535\) 2.44224e82 0.148936
\(536\) 2.35441e82 0.135630
\(537\) −1.11264e83 −0.605536
\(538\) 1.17241e83 0.602865
\(539\) −1.19095e83 −0.578678
\(540\) 1.71372e82 0.0786918
\(541\) −3.34816e82 −0.145308 −0.0726539 0.997357i \(-0.523147\pi\)
−0.0726539 + 0.997357i \(0.523147\pi\)
\(542\) 2.57020e83 1.05436
\(543\) 2.73799e82 0.106178
\(544\) −3.33331e83 −1.22211
\(545\) −2.28834e82 −0.0793280
\(546\) 2.56174e83 0.839767
\(547\) −2.56243e83 −0.794398 −0.397199 0.917733i \(-0.630018\pi\)
−0.397199 + 0.917733i \(0.630018\pi\)
\(548\) 9.22124e82 0.270385
\(549\) −4.20397e83 −1.16601
\(550\) 6.54217e83 1.71656
\(551\) 8.68464e82 0.215590
\(552\) 8.32882e81 0.0195633
\(553\) 1.80293e83 0.400739
\(554\) 1.90384e83 0.400481
\(555\) 4.36705e82 0.0869466
\(556\) −2.14999e83 −0.405187
\(557\) 3.57336e83 0.637519 0.318759 0.947836i \(-0.396734\pi\)
0.318759 + 0.947836i \(0.396734\pi\)
\(558\) −4.48021e83 −0.756755
\(559\) 9.15729e83 1.46456
\(560\) −6.15938e82 −0.0932830
\(561\) −4.22254e83 −0.605628
\(562\) −1.41874e84 −1.92729
\(563\) −4.27507e83 −0.550094 −0.275047 0.961431i \(-0.588693\pi\)
−0.275047 + 0.961431i \(0.588693\pi\)
\(564\) −5.12945e83 −0.625256
\(565\) 1.08808e83 0.125656
\(566\) −5.65891e82 −0.0619200
\(567\) −2.20210e83 −0.228325
\(568\) 9.27617e82 0.0911475
\(569\) 3.86056e83 0.359522 0.179761 0.983710i \(-0.442468\pi\)
0.179761 + 0.983710i \(0.442468\pi\)
\(570\) 3.39705e82 0.0299861
\(571\) 6.19137e83 0.518066 0.259033 0.965868i \(-0.416596\pi\)
0.259033 + 0.965868i \(0.416596\pi\)
\(572\) 2.22340e84 1.76376
\(573\) 4.70038e83 0.353522
\(574\) −1.27123e84 −0.906591
\(575\) −2.33499e83 −0.157913
\(576\) 7.13353e83 0.457529
\(577\) 2.27749e84 1.38546 0.692731 0.721196i \(-0.256408\pi\)
0.692731 + 0.721196i \(0.256408\pi\)
\(578\) 2.86526e83 0.165335
\(579\) −1.21083e84 −0.662807
\(580\) −9.20264e82 −0.0477924
\(581\) −1.09076e84 −0.537474
\(582\) 9.82154e83 0.459228
\(583\) −3.41428e84 −1.51499
\(584\) −1.58047e83 −0.0665573
\(585\) 3.42470e83 0.136889
\(586\) −5.70046e84 −2.16288
\(587\) 3.60186e84 1.29737 0.648687 0.761055i \(-0.275318\pi\)
0.648687 + 0.761055i \(0.275318\pi\)
\(588\) −5.40161e83 −0.184720
\(589\) −9.34522e83 −0.303440
\(590\) −8.33680e83 −0.257047
\(591\) −1.29661e84 −0.379657
\(592\) 6.53229e84 1.81658
\(593\) 5.90369e83 0.155939 0.0779696 0.996956i \(-0.475156\pi\)
0.0779696 + 0.996956i \(0.475156\pi\)
\(594\) 6.07556e84 1.52440
\(595\) −3.19293e83 −0.0761064
\(596\) −4.02753e84 −0.912070
\(597\) 1.63830e83 0.0352513
\(598\) −1.76227e84 −0.360318
\(599\) −5.66096e84 −1.09995 −0.549973 0.835182i \(-0.685362\pi\)
−0.549973 + 0.835182i \(0.685362\pi\)
\(600\) −6.54884e83 −0.120935
\(601\) 7.05697e84 1.23864 0.619322 0.785137i \(-0.287407\pi\)
0.619322 + 0.785137i \(0.287407\pi\)
\(602\) 5.25688e84 0.877072
\(603\) −2.62319e84 −0.416056
\(604\) −7.00776e84 −1.05670
\(605\) −5.03421e83 −0.0721759
\(606\) 6.53218e84 0.890519
\(607\) 8.24801e84 1.06929 0.534643 0.845078i \(-0.320446\pi\)
0.534643 + 0.845078i \(0.320446\pi\)
\(608\) 4.28116e84 0.527840
\(609\) −1.69272e84 −0.198499
\(610\) 2.06349e84 0.230166
\(611\) −2.39537e85 −2.54165
\(612\) 5.68655e84 0.574025
\(613\) 6.79006e84 0.652122 0.326061 0.945349i \(-0.394278\pi\)
0.326061 + 0.945349i \(0.394278\pi\)
\(614\) −2.19383e85 −2.00479
\(615\) 5.72355e83 0.0497707
\(616\) −2.81703e84 −0.233120
\(617\) −1.10340e84 −0.0869033 −0.0434516 0.999056i \(-0.513835\pi\)
−0.0434516 + 0.999056i \(0.513835\pi\)
\(618\) −8.20714e84 −0.615239
\(619\) 6.79023e84 0.484529 0.242264 0.970210i \(-0.422110\pi\)
0.242264 + 0.970210i \(0.422110\pi\)
\(620\) 9.90262e83 0.0672672
\(621\) −2.16845e84 −0.140235
\(622\) 3.94608e85 2.42974
\(623\) 2.93585e83 0.0172127
\(624\) −1.72525e85 −0.963214
\(625\) 1.81343e85 0.964186
\(626\) 1.48104e85 0.749978
\(627\) 5.42324e84 0.261577
\(628\) −1.91490e85 −0.879785
\(629\) 3.38624e85 1.48208
\(630\) 1.96600e84 0.0819778
\(631\) −3.17635e85 −1.26192 −0.630962 0.775814i \(-0.717339\pi\)
−0.630962 + 0.775814i \(0.717339\pi\)
\(632\) −3.47851e84 −0.131681
\(633\) 2.55602e85 0.922042
\(634\) −4.82458e85 −1.65858
\(635\) −6.56217e84 −0.215005
\(636\) −1.54856e85 −0.483600
\(637\) −2.52246e85 −0.750883
\(638\) −3.26257e85 −0.925825
\(639\) −1.03352e85 −0.279602
\(640\) 2.03630e84 0.0525234
\(641\) 3.73749e85 0.919201 0.459600 0.888126i \(-0.347993\pi\)
0.459600 + 0.888126i \(0.347993\pi\)
\(642\) 3.92704e85 0.920974
\(643\) 1.63121e85 0.364817 0.182408 0.983223i \(-0.441611\pi\)
0.182408 + 0.983223i \(0.441611\pi\)
\(644\) −4.55556e84 −0.0971680
\(645\) −2.36684e84 −0.0481501
\(646\) 2.63409e85 0.511140
\(647\) 3.23904e85 0.599564 0.299782 0.954008i \(-0.403086\pi\)
0.299782 + 0.954008i \(0.403086\pi\)
\(648\) 4.24867e84 0.0750266
\(649\) −1.33093e86 −2.24229
\(650\) 1.38565e86 2.22739
\(651\) 1.82148e85 0.279385
\(652\) 6.38972e85 0.935256
\(653\) −1.07815e86 −1.50601 −0.753003 0.658018i \(-0.771395\pi\)
−0.753003 + 0.658018i \(0.771395\pi\)
\(654\) −3.67956e85 −0.490541
\(655\) 8.43372e83 0.0107315
\(656\) 8.56135e85 1.03986
\(657\) 1.76090e85 0.204170
\(658\) −1.37510e86 −1.52210
\(659\) −6.27013e85 −0.662631 −0.331315 0.943520i \(-0.607492\pi\)
−0.331315 + 0.943520i \(0.607492\pi\)
\(660\) −5.74671e84 −0.0579868
\(661\) 1.19678e86 1.15311 0.576556 0.817058i \(-0.304396\pi\)
0.576556 + 0.817058i \(0.304396\pi\)
\(662\) 9.51792e85 0.875736
\(663\) −8.94344e85 −0.785854
\(664\) 2.10448e85 0.176612
\(665\) 4.10085e84 0.0328711
\(666\) −2.08503e86 −1.59642
\(667\) 1.16446e85 0.0851698
\(668\) −2.31760e85 −0.161941
\(669\) −1.29597e85 −0.0865166
\(670\) 1.28758e85 0.0821280
\(671\) 3.29426e86 2.00780
\(672\) −8.34440e85 −0.485996
\(673\) −1.68005e86 −0.935111 −0.467555 0.883964i \(-0.654865\pi\)
−0.467555 + 0.883964i \(0.654865\pi\)
\(674\) −4.30853e86 −2.29193
\(675\) 1.70503e86 0.866894
\(676\) 3.02358e86 1.46942
\(677\) 6.44384e85 0.299358 0.149679 0.988735i \(-0.452176\pi\)
0.149679 + 0.988735i \(0.452176\pi\)
\(678\) 1.74960e86 0.777020
\(679\) 1.18564e86 0.503412
\(680\) 6.16034e84 0.0250082
\(681\) −1.41573e86 −0.549533
\(682\) 3.51073e86 1.30309
\(683\) 3.53739e86 1.25560 0.627800 0.778375i \(-0.283956\pi\)
0.627800 + 0.778375i \(0.283956\pi\)
\(684\) −7.30356e85 −0.247927
\(685\) −1.11299e85 −0.0361352
\(686\) −4.67140e86 −1.45065
\(687\) −4.82370e85 −0.143285
\(688\) −3.54035e86 −1.00600
\(689\) −7.23153e86 −1.96582
\(690\) 4.55485e84 0.0118461
\(691\) −4.67576e86 −1.16352 −0.581758 0.813362i \(-0.697635\pi\)
−0.581758 + 0.813362i \(0.697635\pi\)
\(692\) 2.03861e86 0.485398
\(693\) 3.13862e86 0.715115
\(694\) 4.10717e85 0.0895528
\(695\) 2.59502e85 0.0541507
\(696\) 3.26589e85 0.0652259
\(697\) 4.43807e86 0.848388
\(698\) 5.33589e85 0.0976375
\(699\) 2.96691e86 0.519697
\(700\) 3.58198e86 0.600666
\(701\) −2.70001e86 −0.433476 −0.216738 0.976230i \(-0.569542\pi\)
−0.216738 + 0.976230i \(0.569542\pi\)
\(702\) 1.28682e87 1.97804
\(703\) −4.34913e86 −0.640126
\(704\) −5.58989e86 −0.787838
\(705\) 6.19120e85 0.0835615
\(706\) −2.28993e85 −0.0295992
\(707\) 7.88551e86 0.976198
\(708\) −6.03650e86 −0.715766
\(709\) −8.12454e86 −0.922759 −0.461380 0.887203i \(-0.652645\pi\)
−0.461380 + 0.887203i \(0.652645\pi\)
\(710\) 5.07294e85 0.0551925
\(711\) 3.87562e86 0.403942
\(712\) −5.66434e84 −0.00565600
\(713\) −1.25303e86 −0.119875
\(714\) −5.13411e86 −0.470619
\(715\) −2.68362e86 −0.235715
\(716\) −1.17417e87 −0.988288
\(717\) −2.45437e86 −0.197973
\(718\) 1.42023e87 1.09790
\(719\) 2.24300e86 0.166188 0.0830938 0.996542i \(-0.473520\pi\)
0.0830938 + 0.996542i \(0.473520\pi\)
\(720\) −1.32404e86 −0.0940286
\(721\) −9.90750e86 −0.674432
\(722\) 1.72861e87 1.12801
\(723\) −6.24185e86 −0.390477
\(724\) 2.88939e86 0.173292
\(725\) −9.15597e86 −0.526496
\(726\) −8.09483e86 −0.446314
\(727\) 1.90000e87 1.00451 0.502255 0.864720i \(-0.332504\pi\)
0.502255 + 0.864720i \(0.332504\pi\)
\(728\) −5.96654e86 −0.302493
\(729\) 4.32442e86 0.210251
\(730\) −8.64327e85 −0.0403024
\(731\) −1.83526e87 −0.820763
\(732\) 1.49413e87 0.640913
\(733\) 1.78617e87 0.734941 0.367471 0.930035i \(-0.380224\pi\)
0.367471 + 0.930035i \(0.380224\pi\)
\(734\) 9.61980e86 0.379696
\(735\) 6.51969e85 0.0246867
\(736\) 5.74028e86 0.208526
\(737\) 2.05555e87 0.716425
\(738\) −2.73268e87 −0.913838
\(739\) 2.67566e87 0.858569 0.429284 0.903169i \(-0.358766\pi\)
0.429284 + 0.903169i \(0.358766\pi\)
\(740\) 4.60854e86 0.141904
\(741\) 1.14866e87 0.339418
\(742\) −4.15137e87 −1.17726
\(743\) −3.68577e87 −1.00316 −0.501579 0.865112i \(-0.667247\pi\)
−0.501579 + 0.865112i \(0.667247\pi\)
\(744\) −3.51430e86 −0.0918047
\(745\) 4.86119e86 0.121892
\(746\) −4.76940e87 −1.14797
\(747\) −2.34473e87 −0.541770
\(748\) −4.45603e87 −0.988438
\(749\) 4.74064e87 1.00958
\(750\) −7.20628e86 −0.147347
\(751\) −6.47968e85 −0.0127214 −0.00636071 0.999980i \(-0.502025\pi\)
−0.00636071 + 0.999980i \(0.502025\pi\)
\(752\) 9.26087e87 1.74585
\(753\) −2.75124e87 −0.498060
\(754\) −6.91020e87 −1.20134
\(755\) 8.45829e86 0.141221
\(756\) 3.32650e87 0.533424
\(757\) 3.85344e87 0.593506 0.296753 0.954954i \(-0.404096\pi\)
0.296753 + 0.954954i \(0.404096\pi\)
\(758\) 1.63614e88 2.42053
\(759\) 7.27161e86 0.103337
\(760\) −7.91207e85 −0.0108013
\(761\) 8.59743e87 1.12755 0.563776 0.825928i \(-0.309348\pi\)
0.563776 + 0.825928i \(0.309348\pi\)
\(762\) −1.05517e88 −1.32953
\(763\) −4.44189e87 −0.537737
\(764\) 4.96030e87 0.576979
\(765\) −6.86361e86 −0.0767148
\(766\) 6.59967e87 0.708835
\(767\) −2.81895e88 −2.90957
\(768\) 6.36917e87 0.631780
\(769\) −1.59932e88 −1.52469 −0.762344 0.647172i \(-0.775952\pi\)
−0.762344 + 0.647172i \(0.775952\pi\)
\(770\) −1.54057e87 −0.141161
\(771\) 1.26854e87 0.111724
\(772\) −1.27779e88 −1.08176
\(773\) 6.47128e87 0.526642 0.263321 0.964708i \(-0.415182\pi\)
0.263321 + 0.964708i \(0.415182\pi\)
\(774\) 1.13004e88 0.884082
\(775\) 9.85240e87 0.741037
\(776\) −2.28753e87 −0.165419
\(777\) 8.47689e87 0.589380
\(778\) −8.22288e86 −0.0549726
\(779\) −5.70006e87 −0.366427
\(780\) −1.21717e87 −0.0752428
\(781\) 8.09871e87 0.481459
\(782\) 3.53186e87 0.201928
\(783\) −8.50293e87 −0.467557
\(784\) 9.75224e87 0.515780
\(785\) 2.31126e87 0.117578
\(786\) 1.35611e87 0.0663602
\(787\) −1.25948e88 −0.592871 −0.296436 0.955053i \(-0.595798\pi\)
−0.296436 + 0.955053i \(0.595798\pi\)
\(788\) −1.36831e88 −0.619633
\(789\) 3.96848e86 0.0172892
\(790\) −1.90232e87 −0.0797367
\(791\) 2.11208e88 0.851779
\(792\) −6.05557e87 −0.234983
\(793\) 6.97733e88 2.60530
\(794\) −2.07749e88 −0.746472
\(795\) 1.86910e87 0.0646301
\(796\) 1.72889e87 0.0575332
\(797\) −5.76161e88 −1.84529 −0.922645 0.385649i \(-0.873977\pi\)
−0.922645 + 0.385649i \(0.873977\pi\)
\(798\) 6.59403e87 0.203265
\(799\) 4.80069e88 1.42438
\(800\) −4.51350e88 −1.28905
\(801\) 6.31099e86 0.0173502
\(802\) −7.20393e88 −1.90656
\(803\) −1.37986e88 −0.351569
\(804\) 9.32305e87 0.228691
\(805\) 5.49852e86 0.0129859
\(806\) 7.43581e88 1.69087
\(807\) −1.02463e88 −0.224350
\(808\) −1.52141e88 −0.320774
\(809\) −4.29220e88 −0.871465 −0.435732 0.900076i \(-0.643511\pi\)
−0.435732 + 0.900076i \(0.643511\pi\)
\(810\) 2.32351e87 0.0454308
\(811\) −1.37221e88 −0.258395 −0.129198 0.991619i \(-0.541240\pi\)
−0.129198 + 0.991619i \(0.541240\pi\)
\(812\) −1.78633e88 −0.323968
\(813\) −2.24624e88 −0.392369
\(814\) 1.63384e89 2.74895
\(815\) −7.71233e87 −0.124991
\(816\) 3.45767e88 0.539801
\(817\) 2.35713e88 0.354495
\(818\) 3.95423e87 0.0572910
\(819\) 6.64768e88 0.927922
\(820\) 6.04004e87 0.0812302
\(821\) 5.04540e87 0.0653777 0.0326888 0.999466i \(-0.489593\pi\)
0.0326888 + 0.999466i \(0.489593\pi\)
\(822\) −1.78965e88 −0.223449
\(823\) −3.45387e88 −0.415538 −0.207769 0.978178i \(-0.566620\pi\)
−0.207769 + 0.978178i \(0.566620\pi\)
\(824\) 1.91152e88 0.221615
\(825\) −5.71757e88 −0.638801
\(826\) −1.61826e89 −1.74243
\(827\) 2.64181e88 0.274147 0.137074 0.990561i \(-0.456230\pi\)
0.137074 + 0.990561i \(0.456230\pi\)
\(828\) −9.79278e87 −0.0979447
\(829\) −1.24760e89 −1.20271 −0.601356 0.798981i \(-0.705373\pi\)
−0.601356 + 0.798981i \(0.705373\pi\)
\(830\) 1.15090e88 0.106943
\(831\) −1.66387e88 −0.149035
\(832\) −1.18395e89 −1.02229
\(833\) 5.05540e88 0.420807
\(834\) 4.17270e88 0.334851
\(835\) 2.79732e87 0.0216424
\(836\) 5.72313e88 0.426916
\(837\) 9.14969e88 0.658082
\(838\) 9.33503e88 0.647400
\(839\) 1.14813e89 0.767804 0.383902 0.923374i \(-0.374580\pi\)
0.383902 + 0.923374i \(0.374580\pi\)
\(840\) 1.54214e87 0.00994503
\(841\) −1.15136e89 −0.716036
\(842\) −2.16663e88 −0.129947
\(843\) 1.23992e89 0.717219
\(844\) 2.69736e89 1.50485
\(845\) −3.64943e88 −0.196379
\(846\) −2.95595e89 −1.53427
\(847\) −9.77191e88 −0.489255
\(848\) 2.79582e89 1.35032
\(849\) 4.94563e87 0.0230429
\(850\) −2.77705e89 −1.24826
\(851\) −5.83142e88 −0.252885
\(852\) 3.67320e88 0.153687
\(853\) −1.40717e89 −0.568070 −0.284035 0.958814i \(-0.591673\pi\)
−0.284035 + 0.958814i \(0.591673\pi\)
\(854\) 4.00544e89 1.56022
\(855\) 8.81532e87 0.0331338
\(856\) −9.14647e88 −0.331744
\(857\) −2.64572e89 −0.926038 −0.463019 0.886348i \(-0.653234\pi\)
−0.463019 + 0.886348i \(0.653234\pi\)
\(858\) −4.31517e89 −1.45759
\(859\) 4.88791e89 1.59342 0.796712 0.604359i \(-0.206571\pi\)
0.796712 + 0.604359i \(0.206571\pi\)
\(860\) −2.49772e88 −0.0785852
\(861\) 1.11100e89 0.337378
\(862\) 1.98569e89 0.582024
\(863\) 2.17102e89 0.614235 0.307117 0.951672i \(-0.400636\pi\)
0.307117 + 0.951672i \(0.400636\pi\)
\(864\) −4.19158e89 −1.14475
\(865\) −2.46058e88 −0.0648704
\(866\) −6.63210e89 −1.68793
\(867\) −2.50410e88 −0.0615276
\(868\) 1.92220e89 0.455981
\(869\) −3.03697e89 −0.695565
\(870\) 1.78604e88 0.0394962
\(871\) 4.35371e89 0.929621
\(872\) 8.57007e88 0.176698
\(873\) 2.54868e89 0.507436
\(874\) −4.53616e88 −0.0872147
\(875\) −8.69927e88 −0.161524
\(876\) −6.25841e88 −0.112225
\(877\) 2.09369e89 0.362598 0.181299 0.983428i \(-0.441970\pi\)
0.181299 + 0.983428i \(0.441970\pi\)
\(878\) 1.38854e90 2.32261
\(879\) 4.98195e89 0.804894
\(880\) 1.03753e89 0.161912
\(881\) 3.71437e89 0.559912 0.279956 0.960013i \(-0.409680\pi\)
0.279956 + 0.960013i \(0.409680\pi\)
\(882\) −3.11279e89 −0.453271
\(883\) −1.22390e90 −1.72165 −0.860823 0.508905i \(-0.830050\pi\)
−0.860823 + 0.508905i \(0.830050\pi\)
\(884\) −9.43798e89 −1.28258
\(885\) 7.28599e88 0.0956575
\(886\) 7.16606e89 0.908974
\(887\) −1.05036e90 −1.28727 −0.643633 0.765334i \(-0.722574\pi\)
−0.643633 + 0.765334i \(0.722574\pi\)
\(888\) −1.63551e89 −0.193668
\(889\) −1.27378e90 −1.45744
\(890\) −3.09770e87 −0.00342488
\(891\) 3.70937e89 0.396306
\(892\) −1.36764e89 −0.141203
\(893\) −6.16579e89 −0.615204
\(894\) 7.81662e89 0.753745
\(895\) 1.41721e89 0.132078
\(896\) 3.95266e89 0.356037
\(897\) 1.54014e89 0.134089
\(898\) −6.95355e89 −0.585165
\(899\) −4.91337e89 −0.399677
\(900\) 7.69993e89 0.605467
\(901\) 1.44931e90 1.10168
\(902\) 2.14135e90 1.57358
\(903\) −4.59428e89 −0.326393
\(904\) −4.07498e89 −0.279891
\(905\) −3.48746e88 −0.0231594
\(906\) 1.36006e90 0.873271
\(907\) 2.03009e89 0.126035 0.0630177 0.998012i \(-0.479928\pi\)
0.0630177 + 0.998012i \(0.479928\pi\)
\(908\) −1.49402e90 −0.896886
\(909\) 1.69509e90 0.984001
\(910\) −3.26297e89 −0.183168
\(911\) −2.13327e90 −1.15807 −0.579036 0.815302i \(-0.696571\pi\)
−0.579036 + 0.815302i \(0.696571\pi\)
\(912\) −4.44088e89 −0.233145
\(913\) 1.83735e90 0.932897
\(914\) −2.79410e90 −1.37209
\(915\) −1.80340e89 −0.0856540
\(916\) −5.09044e89 −0.233853
\(917\) 1.63707e89 0.0727449
\(918\) −2.57898e90 −1.10853
\(919\) 2.52842e89 0.105130 0.0525649 0.998618i \(-0.483260\pi\)
0.0525649 + 0.998618i \(0.483260\pi\)
\(920\) −1.06087e88 −0.00426710
\(921\) 1.91731e90 0.746060
\(922\) −2.63916e90 −0.993509
\(923\) 1.71533e90 0.624734
\(924\) −1.11549e90 −0.393072
\(925\) 4.58517e90 1.56326
\(926\) 2.36153e90 0.779037
\(927\) −2.12975e90 −0.679823
\(928\) 2.25087e90 0.695245
\(929\) −4.65955e90 −1.39272 −0.696362 0.717691i \(-0.745199\pi\)
−0.696362 + 0.717691i \(0.745199\pi\)
\(930\) −1.92190e89 −0.0555904
\(931\) −6.49294e89 −0.181751
\(932\) 3.13097e90 0.848191
\(933\) −3.44870e90 −0.904201
\(934\) −2.70091e90 −0.685378
\(935\) 5.37838e89 0.132098
\(936\) −1.28259e90 −0.304911
\(937\) 7.49140e90 1.72387 0.861937 0.507015i \(-0.169251\pi\)
0.861937 + 0.507015i \(0.169251\pi\)
\(938\) 2.49931e90 0.556717
\(939\) −1.29436e90 −0.279097
\(940\) 6.53355e89 0.136380
\(941\) 1.93054e89 0.0390117 0.0195058 0.999810i \(-0.493791\pi\)
0.0195058 + 0.999810i \(0.493791\pi\)
\(942\) 3.71643e90 0.727065
\(943\) −7.64277e89 −0.144759
\(944\) 1.08985e91 1.99857
\(945\) −4.01505e89 −0.0712887
\(946\) −8.85505e90 −1.52234
\(947\) −1.00121e91 −1.66668 −0.833339 0.552762i \(-0.813574\pi\)
−0.833339 + 0.552762i \(0.813574\pi\)
\(948\) −1.37743e90 −0.222032
\(949\) −2.92258e90 −0.456190
\(950\) 3.56672e90 0.539137
\(951\) 4.21647e90 0.617224
\(952\) 1.19578e90 0.169522
\(953\) −6.15324e90 −0.844832 −0.422416 0.906402i \(-0.638818\pi\)
−0.422416 + 0.906402i \(0.638818\pi\)
\(954\) −8.92391e90 −1.18667
\(955\) −5.98703e89 −0.0771096
\(956\) −2.59009e90 −0.323109
\(957\) 2.85134e90 0.344536
\(958\) −1.18637e91 −1.38859
\(959\) −2.16043e90 −0.244948
\(960\) 3.06010e89 0.0336096
\(961\) −4.11151e90 −0.437460
\(962\) 3.46052e91 3.56699
\(963\) 1.01906e91 1.01765
\(964\) −6.58701e90 −0.637292
\(965\) 1.54228e90 0.144570
\(966\) 8.84143e89 0.0803008
\(967\) 1.38599e91 1.21970 0.609848 0.792518i \(-0.291230\pi\)
0.609848 + 0.792518i \(0.291230\pi\)
\(968\) 1.88537e90 0.160767
\(969\) −2.30208e90 −0.190215
\(970\) −1.25100e90 −0.100166
\(971\) −2.49235e90 −0.193385 −0.0966924 0.995314i \(-0.530826\pi\)
−0.0966924 + 0.995314i \(0.530826\pi\)
\(972\) 1.12414e91 0.845279
\(973\) 5.03719e90 0.367068
\(974\) −1.12273e91 −0.792918
\(975\) −1.21099e91 −0.828899
\(976\) −2.69754e91 −1.78957
\(977\) 7.93411e90 0.510169 0.255084 0.966919i \(-0.417897\pi\)
0.255084 + 0.966919i \(0.417897\pi\)
\(978\) −1.24012e91 −0.772907
\(979\) −4.94534e89 −0.0298761
\(980\) 6.88021e89 0.0402908
\(981\) −9.54844e90 −0.542035
\(982\) 7.60138e90 0.418304
\(983\) −1.27832e91 −0.681960 −0.340980 0.940071i \(-0.610759\pi\)
−0.340980 + 0.940071i \(0.610759\pi\)
\(984\) −2.14353e90 −0.110861
\(985\) 1.65153e90 0.0828100
\(986\) 1.38491e91 0.673248
\(987\) 1.20177e91 0.566434
\(988\) 1.21217e91 0.553959
\(989\) 3.16049e90 0.140045
\(990\) −3.31166e90 −0.142289
\(991\) 1.10655e91 0.461023 0.230512 0.973070i \(-0.425960\pi\)
0.230512 + 0.973070i \(0.425960\pi\)
\(992\) −2.42208e91 −0.978550
\(993\) −8.31824e90 −0.325896
\(994\) 9.84709e90 0.374131
\(995\) −2.08675e89 −0.00768894
\(996\) 8.33339e90 0.297791
\(997\) −2.30608e90 −0.0799232 −0.0399616 0.999201i \(-0.512724\pi\)
−0.0399616 + 0.999201i \(0.512724\pi\)
\(998\) 4.18924e90 0.140817
\(999\) 4.25814e91 1.38826
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.1.1 4
3.2 odd 2 9.62.a.a.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.62.a.a.1.1 4 1.1 even 1 trivial
9.62.a.a.1.4 4 3.2 odd 2