Properties

Label 1.68.a.a.1.3
Level 1
Weight 68
Character 1.1
Self dual yes
Analytic conductor 28.429
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 68 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.4290351930\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 939384011925257456 x^{3} + 31046449413968483513911200 x^{2} + 156793504704482691874379743265203200 x + 20916736226052669578405116700517591609696000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.64845e8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.06726e9 q^{2} -7.82458e15 q^{3} -1.21897e20 q^{4} -8.33551e22 q^{5} -3.96491e25 q^{6} -1.15070e28 q^{7} -1.36548e30 q^{8} -3.14854e31 q^{9} +O(q^{10})\) \(q+5.06726e9 q^{2} -7.82458e15 q^{3} -1.21897e20 q^{4} -8.33551e22 q^{5} -3.96491e25 q^{6} -1.15070e28 q^{7} -1.36548e30 q^{8} -3.14854e31 q^{9} -4.22381e32 q^{10} -1.09259e35 q^{11} +9.53792e35 q^{12} +1.54273e37 q^{13} -5.83087e37 q^{14} +6.52218e38 q^{15} +1.10696e40 q^{16} +8.24456e40 q^{17} -1.59545e41 q^{18} -5.93328e42 q^{19} +1.01607e43 q^{20} +9.00371e43 q^{21} -5.53645e44 q^{22} +2.28489e45 q^{23} +1.06843e46 q^{24} -6.08146e46 q^{25} +7.81738e46 q^{26} +9.71773e47 q^{27} +1.40266e48 q^{28} +1.07438e49 q^{29} +3.30496e48 q^{30} +1.32534e50 q^{31} +2.57601e50 q^{32} +8.54908e50 q^{33} +4.17773e50 q^{34} +9.59164e50 q^{35} +3.83798e51 q^{36} -5.20056e52 q^{37} -3.00655e52 q^{38} -1.20712e53 q^{39} +1.13819e53 q^{40} -1.63973e54 q^{41} +4.56241e53 q^{42} +5.64177e54 q^{43} +1.33184e55 q^{44} +2.62447e54 q^{45} +1.15781e55 q^{46} +2.41027e55 q^{47} -8.66148e55 q^{48} -2.85968e56 q^{49} -3.08163e56 q^{50} -6.45102e56 q^{51} -1.88053e57 q^{52} +2.84898e57 q^{53} +4.92422e57 q^{54} +9.10731e57 q^{55} +1.57125e58 q^{56} +4.64254e58 q^{57} +5.44415e58 q^{58} -3.30680e59 q^{59} -7.95034e58 q^{60} -6.89383e59 q^{61} +6.71583e59 q^{62} +3.62302e59 q^{63} -3.28249e59 q^{64} -1.28594e60 q^{65} +4.33204e60 q^{66} +2.58683e61 q^{67} -1.00499e61 q^{68} -1.78783e61 q^{69} +4.86033e60 q^{70} -1.34953e62 q^{71} +4.29927e61 q^{72} -1.11285e62 q^{73} -2.63526e62 q^{74} +4.75848e62 q^{75} +7.23248e62 q^{76} +1.25724e63 q^{77} -6.11677e62 q^{78} +1.23916e63 q^{79} -9.22705e62 q^{80} -4.68471e63 q^{81} -8.30894e63 q^{82} +3.41100e63 q^{83} -1.09752e64 q^{84} -6.87226e63 q^{85} +2.85883e64 q^{86} -8.40656e64 q^{87} +1.49191e65 q^{88} +3.04246e65 q^{89} +1.32989e64 q^{90} -1.77521e65 q^{91} -2.78521e65 q^{92} -1.03702e66 q^{93} +1.22134e65 q^{94} +4.94569e65 q^{95} -2.01562e66 q^{96} +2.29986e66 q^{97} -1.44907e66 q^{98} +3.44008e66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} + O(q^{10}) \) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} - \)\(52\!\cdots\!00\)\(q^{10} + \)\(20\!\cdots\!60\)\(q^{11} - \)\(20\!\cdots\!24\)\(q^{12} + \)\(17\!\cdots\!02\)\(q^{13} + \)\(29\!\cdots\!80\)\(q^{14} - \)\(93\!\cdots\!00\)\(q^{15} + \)\(18\!\cdots\!80\)\(q^{16} + \)\(75\!\cdots\!06\)\(q^{17} - \)\(10\!\cdots\!68\)\(q^{18} + \)\(39\!\cdots\!00\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(17\!\cdots\!40\)\(q^{21} + \)\(18\!\cdots\!32\)\(q^{22} - \)\(41\!\cdots\!68\)\(q^{23} - \)\(13\!\cdots\!00\)\(q^{24} + \)\(17\!\cdots\!75\)\(q^{25} + \)\(21\!\cdots\!60\)\(q^{26} + \)\(18\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!48\)\(q^{28} + \)\(18\!\cdots\!50\)\(q^{29} + \)\(18\!\cdots\!00\)\(q^{30} + \)\(36\!\cdots\!60\)\(q^{31} + \)\(15\!\cdots\!96\)\(q^{32} + \)\(24\!\cdots\!84\)\(q^{33} + \)\(78\!\cdots\!80\)\(q^{34} + \)\(45\!\cdots\!00\)\(q^{35} - \)\(38\!\cdots\!20\)\(q^{36} - \)\(56\!\cdots\!94\)\(q^{37} - \)\(31\!\cdots\!80\)\(q^{38} - \)\(71\!\cdots\!80\)\(q^{39} - \)\(18\!\cdots\!00\)\(q^{40} + \)\(11\!\cdots\!10\)\(q^{41} + \)\(28\!\cdots\!92\)\(q^{42} + \)\(65\!\cdots\!92\)\(q^{43} + \)\(49\!\cdots\!80\)\(q^{44} + \)\(99\!\cdots\!50\)\(q^{45} + \)\(79\!\cdots\!60\)\(q^{46} - \)\(12\!\cdots\!44\)\(q^{47} - \)\(19\!\cdots\!68\)\(q^{48} - \)\(77\!\cdots\!35\)\(q^{49} - \)\(39\!\cdots\!00\)\(q^{50} - \)\(33\!\cdots\!40\)\(q^{51} + \)\(67\!\cdots\!16\)\(q^{52} + \)\(10\!\cdots\!22\)\(q^{53} + \)\(19\!\cdots\!00\)\(q^{54} + \)\(66\!\cdots\!00\)\(q^{55} + \)\(16\!\cdots\!00\)\(q^{56} - \)\(92\!\cdots\!60\)\(q^{57} - \)\(61\!\cdots\!20\)\(q^{58} - \)\(30\!\cdots\!00\)\(q^{59} - \)\(13\!\cdots\!00\)\(q^{60} - \)\(11\!\cdots\!90\)\(q^{61} - \)\(21\!\cdots\!28\)\(q^{62} - \)\(20\!\cdots\!68\)\(q^{63} + \)\(63\!\cdots\!40\)\(q^{64} + \)\(17\!\cdots\!00\)\(q^{65} + \)\(27\!\cdots\!20\)\(q^{66} - \)\(11\!\cdots\!44\)\(q^{67} + \)\(81\!\cdots\!48\)\(q^{68} + \)\(35\!\cdots\!20\)\(q^{69} - \)\(26\!\cdots\!00\)\(q^{70} - \)\(11\!\cdots\!40\)\(q^{71} - \)\(74\!\cdots\!40\)\(q^{72} - \)\(30\!\cdots\!18\)\(q^{73} + \)\(92\!\cdots\!80\)\(q^{74} + \)\(21\!\cdots\!00\)\(q^{75} + \)\(20\!\cdots\!00\)\(q^{76} + \)\(50\!\cdots\!32\)\(q^{77} + \)\(61\!\cdots\!64\)\(q^{78} + \)\(29\!\cdots\!00\)\(q^{79} - \)\(15\!\cdots\!00\)\(q^{80} - \)\(11\!\cdots\!95\)\(q^{81} - \)\(17\!\cdots\!08\)\(q^{82} - \)\(47\!\cdots\!88\)\(q^{83} - \)\(52\!\cdots\!20\)\(q^{84} - \)\(39\!\cdots\!00\)\(q^{85} + \)\(49\!\cdots\!60\)\(q^{86} + \)\(35\!\cdots\!60\)\(q^{87} + \)\(43\!\cdots\!60\)\(q^{88} - \)\(11\!\cdots\!50\)\(q^{89} + \)\(47\!\cdots\!00\)\(q^{90} + \)\(23\!\cdots\!60\)\(q^{91} - \)\(98\!\cdots\!44\)\(q^{92} - \)\(18\!\cdots\!36\)\(q^{93} - \)\(49\!\cdots\!20\)\(q^{94} - \)\(20\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!40\)\(q^{96} + \)\(28\!\cdots\!06\)\(q^{97} + \)\(12\!\cdots\!08\)\(q^{98} + \)\(16\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.06726e9 0.417127 0.208563 0.978009i \(-0.433121\pi\)
0.208563 + 0.978009i \(0.433121\pi\)
\(3\) −7.82458e15 −0.812641 −0.406321 0.913731i \(-0.633188\pi\)
−0.406321 + 0.913731i \(0.633188\pi\)
\(4\) −1.21897e20 −0.826005
\(5\) −8.33551e22 −0.320211 −0.160106 0.987100i \(-0.551184\pi\)
−0.160106 + 0.987100i \(0.551184\pi\)
\(6\) −3.96491e25 −0.338974
\(7\) −1.15070e28 −0.562570 −0.281285 0.959624i \(-0.590761\pi\)
−0.281285 + 0.959624i \(0.590761\pi\)
\(8\) −1.36548e30 −0.761676
\(9\) −3.14854e31 −0.339614
\(10\) −4.22381e32 −0.133569
\(11\) −1.09259e35 −1.41842 −0.709208 0.705000i \(-0.750947\pi\)
−0.709208 + 0.705000i \(0.750947\pi\)
\(12\) 9.53792e35 0.671246
\(13\) 1.54273e37 0.743338 0.371669 0.928365i \(-0.378786\pi\)
0.371669 + 0.928365i \(0.378786\pi\)
\(14\) −5.83087e37 −0.234663
\(15\) 6.52218e38 0.260217
\(16\) 1.10696e40 0.508290
\(17\) 8.24456e40 0.496739 0.248370 0.968665i \(-0.420105\pi\)
0.248370 + 0.968665i \(0.420105\pi\)
\(18\) −1.59545e41 −0.141662
\(19\) −5.93328e42 −0.861091 −0.430546 0.902569i \(-0.641679\pi\)
−0.430546 + 0.902569i \(0.641679\pi\)
\(20\) 1.01607e43 0.264496
\(21\) 9.00371e43 0.457167
\(22\) −5.53645e44 −0.591659
\(23\) 2.28489e45 0.550785 0.275393 0.961332i \(-0.411192\pi\)
0.275393 + 0.961332i \(0.411192\pi\)
\(24\) 1.06843e46 0.618969
\(25\) −6.08146e46 −0.897465
\(26\) 7.81738e46 0.310066
\(27\) 9.71773e47 1.08863
\(28\) 1.40266e48 0.464686
\(29\) 1.07438e49 1.09856 0.549281 0.835638i \(-0.314902\pi\)
0.549281 + 0.835638i \(0.314902\pi\)
\(30\) 3.30496e48 0.108543
\(31\) 1.32534e50 1.45114 0.725572 0.688147i \(-0.241575\pi\)
0.725572 + 0.688147i \(0.241575\pi\)
\(32\) 2.57601e50 0.973697
\(33\) 8.54908e50 1.15266
\(34\) 4.17773e50 0.207203
\(35\) 9.59164e50 0.180141
\(36\) 3.83798e51 0.280523
\(37\) −5.20056e52 −1.51807 −0.759037 0.651048i \(-0.774330\pi\)
−0.759037 + 0.651048i \(0.774330\pi\)
\(38\) −3.00655e52 −0.359184
\(39\) −1.20712e53 −0.604067
\(40\) 1.13819e53 0.243897
\(41\) −1.63973e54 −1.53643 −0.768217 0.640190i \(-0.778856\pi\)
−0.768217 + 0.640190i \(0.778856\pi\)
\(42\) 4.56241e53 0.190697
\(43\) 5.64177e54 1.07207 0.536034 0.844197i \(-0.319922\pi\)
0.536034 + 0.844197i \(0.319922\pi\)
\(44\) 1.33184e55 1.17162
\(45\) 2.62447e54 0.108748
\(46\) 1.15781e55 0.229747
\(47\) 2.41027e55 0.232695 0.116347 0.993209i \(-0.462881\pi\)
0.116347 + 0.993209i \(0.462881\pi\)
\(48\) −8.66148e55 −0.413057
\(49\) −2.85968e56 −0.683515
\(50\) −3.08163e56 −0.374356
\(51\) −6.45102e56 −0.403671
\(52\) −1.88053e57 −0.614001
\(53\) 2.84898e57 0.491414 0.245707 0.969344i \(-0.420980\pi\)
0.245707 + 0.969344i \(0.420980\pi\)
\(54\) 4.92422e57 0.454095
\(55\) 9.10731e57 0.454193
\(56\) 1.57125e58 0.428496
\(57\) 4.64254e58 0.699759
\(58\) 5.44415e58 0.458239
\(59\) −3.30680e59 −1.56987 −0.784937 0.619575i \(-0.787305\pi\)
−0.784937 + 0.619575i \(0.787305\pi\)
\(60\) −7.95034e58 −0.214941
\(61\) −6.89383e59 −1.07130 −0.535650 0.844440i \(-0.679933\pi\)
−0.535650 + 0.844440i \(0.679933\pi\)
\(62\) 6.71583e59 0.605311
\(63\) 3.62302e59 0.191057
\(64\) −3.28249e59 −0.102135
\(65\) −1.28594e60 −0.238025
\(66\) 4.33204e60 0.480806
\(67\) 2.58683e61 1.73485 0.867424 0.497569i \(-0.165774\pi\)
0.867424 + 0.497569i \(0.165774\pi\)
\(68\) −1.00499e61 −0.410309
\(69\) −1.78783e61 −0.447591
\(70\) 4.86033e60 0.0751418
\(71\) −1.34953e62 −1.29726 −0.648630 0.761104i \(-0.724658\pi\)
−0.648630 + 0.761104i \(0.724658\pi\)
\(72\) 4.29927e61 0.258676
\(73\) −1.11285e62 −0.421814 −0.210907 0.977506i \(-0.567642\pi\)
−0.210907 + 0.977506i \(0.567642\pi\)
\(74\) −2.63526e62 −0.633229
\(75\) 4.75848e62 0.729317
\(76\) 7.23248e62 0.711266
\(77\) 1.25724e63 0.797958
\(78\) −6.11677e62 −0.251973
\(79\) 1.23916e63 0.333135 0.166568 0.986030i \(-0.446732\pi\)
0.166568 + 0.986030i \(0.446732\pi\)
\(80\) −9.22705e62 −0.162760
\(81\) −4.68471e63 −0.545048
\(82\) −8.30894e63 −0.640887
\(83\) 3.41100e63 0.175294 0.0876468 0.996152i \(-0.472065\pi\)
0.0876468 + 0.996152i \(0.472065\pi\)
\(84\) −1.09752e64 −0.377623
\(85\) −6.87226e63 −0.159062
\(86\) 2.85883e64 0.447188
\(87\) −8.40656e64 −0.892736
\(88\) 1.49191e65 1.08037
\(89\) 3.04246e65 1.50890 0.754448 0.656360i \(-0.227905\pi\)
0.754448 + 0.656360i \(0.227905\pi\)
\(90\) 1.32989e64 0.0453618
\(91\) −1.77521e65 −0.418180
\(92\) −2.78521e65 −0.454951
\(93\) −1.03702e66 −1.17926
\(94\) 1.22134e65 0.0970633
\(95\) 4.94569e65 0.275731
\(96\) −2.01562e66 −0.791266
\(97\) 2.29986e66 0.638041 0.319021 0.947748i \(-0.396646\pi\)
0.319021 + 0.947748i \(0.396646\pi\)
\(98\) −1.44907e66 −0.285112
\(99\) 3.44008e66 0.481714
\(100\) 7.41311e66 0.741311
\(101\) 8.83103e66 0.632769 0.316385 0.948631i \(-0.397531\pi\)
0.316385 + 0.948631i \(0.397531\pi\)
\(102\) −3.26890e66 −0.168382
\(103\) −1.08466e67 −0.402947 −0.201473 0.979494i \(-0.564573\pi\)
−0.201473 + 0.979494i \(0.564573\pi\)
\(104\) −2.10656e67 −0.566182
\(105\) −7.50505e66 −0.146390
\(106\) 1.44365e67 0.204982
\(107\) −2.87086e67 −0.297616 −0.148808 0.988866i \(-0.547544\pi\)
−0.148808 + 0.988866i \(0.547544\pi\)
\(108\) −1.18456e68 −0.899211
\(109\) 5.52911e66 0.0308225 0.0154112 0.999881i \(-0.495094\pi\)
0.0154112 + 0.999881i \(0.495094\pi\)
\(110\) 4.61491e67 0.189456
\(111\) 4.06922e68 1.23365
\(112\) −1.27377e68 −0.285949
\(113\) 5.97000e68 0.995054 0.497527 0.867449i \(-0.334242\pi\)
0.497527 + 0.867449i \(0.334242\pi\)
\(114\) 2.35250e68 0.291888
\(115\) −1.90457e68 −0.176368
\(116\) −1.30963e69 −0.907418
\(117\) −4.85734e68 −0.252448
\(118\) −1.67564e69 −0.654837
\(119\) −9.48698e68 −0.279451
\(120\) −8.90589e68 −0.198201
\(121\) 6.00410e69 1.01190
\(122\) −3.49328e69 −0.446868
\(123\) 1.28302e70 1.24857
\(124\) −1.61555e70 −1.19865
\(125\) 1.07176e70 0.607590
\(126\) 1.83588e69 0.0796948
\(127\) 5.53532e70 1.84382 0.921909 0.387406i \(-0.126629\pi\)
0.921909 + 0.387406i \(0.126629\pi\)
\(128\) −3.96786e70 −1.01630
\(129\) −4.41445e70 −0.871206
\(130\) −6.51619e69 −0.0992867
\(131\) −3.42212e70 −0.403373 −0.201687 0.979450i \(-0.564642\pi\)
−0.201687 + 0.979450i \(0.564642\pi\)
\(132\) −1.04211e71 −0.952106
\(133\) 6.82741e70 0.484424
\(134\) 1.31081e71 0.723652
\(135\) −8.10022e70 −0.348590
\(136\) −1.12578e71 −0.378354
\(137\) 4.32164e71 1.13634 0.568171 0.822910i \(-0.307651\pi\)
0.568171 + 0.822910i \(0.307651\pi\)
\(138\) −9.05938e70 −0.186702
\(139\) 8.25204e71 1.33526 0.667629 0.744494i \(-0.267309\pi\)
0.667629 + 0.744494i \(0.267309\pi\)
\(140\) −1.16919e71 −0.148798
\(141\) −1.88593e71 −0.189098
\(142\) −6.83840e71 −0.541122
\(143\) −1.68557e72 −1.05436
\(144\) −3.48530e71 −0.172622
\(145\) −8.95549e71 −0.351772
\(146\) −5.63910e71 −0.175950
\(147\) 2.23758e72 0.555453
\(148\) 6.33932e72 1.25394
\(149\) −6.68758e72 −1.05567 −0.527836 0.849346i \(-0.676997\pi\)
−0.527836 + 0.849346i \(0.676997\pi\)
\(150\) 2.41125e72 0.304218
\(151\) 2.60779e72 0.263357 0.131679 0.991292i \(-0.457963\pi\)
0.131679 + 0.991292i \(0.457963\pi\)
\(152\) 8.10176e72 0.655872
\(153\) −2.59584e72 −0.168700
\(154\) 6.37077e72 0.332849
\(155\) −1.10474e73 −0.464673
\(156\) 1.47144e73 0.498963
\(157\) −4.90233e73 −1.34204 −0.671018 0.741441i \(-0.734143\pi\)
−0.671018 + 0.741441i \(0.734143\pi\)
\(158\) 6.27915e72 0.138960
\(159\) −2.22921e73 −0.399344
\(160\) −2.14724e73 −0.311789
\(161\) −2.62921e73 −0.309855
\(162\) −2.37386e73 −0.227354
\(163\) 1.63101e74 1.27108 0.635538 0.772069i \(-0.280778\pi\)
0.635538 + 0.772069i \(0.280778\pi\)
\(164\) 1.99878e74 1.26910
\(165\) −7.12609e73 −0.369096
\(166\) 1.72844e73 0.0731196
\(167\) 8.02398e73 0.277580 0.138790 0.990322i \(-0.455679\pi\)
0.138790 + 0.990322i \(0.455679\pi\)
\(168\) −1.22944e74 −0.348213
\(169\) −1.92729e74 −0.447449
\(170\) −3.48235e73 −0.0663489
\(171\) 1.86812e74 0.292439
\(172\) −6.87714e74 −0.885533
\(173\) −4.19257e74 −0.444566 −0.222283 0.974982i \(-0.571351\pi\)
−0.222283 + 0.974982i \(0.571351\pi\)
\(174\) −4.25982e74 −0.372384
\(175\) 6.99791e74 0.504887
\(176\) −1.20945e75 −0.720966
\(177\) 2.58743e75 1.27574
\(178\) 1.54169e75 0.629401
\(179\) 2.46277e75 0.833389 0.416695 0.909046i \(-0.363188\pi\)
0.416695 + 0.909046i \(0.363188\pi\)
\(180\) −3.19915e74 −0.0898267
\(181\) −5.01874e75 −1.17048 −0.585238 0.810862i \(-0.698999\pi\)
−0.585238 + 0.810862i \(0.698999\pi\)
\(182\) −8.99544e74 −0.174434
\(183\) 5.39413e75 0.870583
\(184\) −3.11996e75 −0.419520
\(185\) 4.33493e75 0.486104
\(186\) −5.25486e75 −0.491900
\(187\) −9.00795e75 −0.704583
\(188\) −2.93804e75 −0.192207
\(189\) −1.11822e76 −0.612428
\(190\) 2.50611e75 0.115015
\(191\) −1.28809e75 −0.0495825 −0.0247912 0.999693i \(-0.507892\pi\)
−0.0247912 + 0.999693i \(0.507892\pi\)
\(192\) 2.56841e75 0.0829991
\(193\) 5.85943e76 1.59106 0.795528 0.605916i \(-0.207193\pi\)
0.795528 + 0.605916i \(0.207193\pi\)
\(194\) 1.16540e76 0.266144
\(195\) 1.00619e76 0.193429
\(196\) 3.48586e76 0.564587
\(197\) −6.37062e76 −0.870087 −0.435044 0.900409i \(-0.643267\pi\)
−0.435044 + 0.900409i \(0.643267\pi\)
\(198\) 1.74317e76 0.200936
\(199\) −9.92421e76 −0.966313 −0.483157 0.875534i \(-0.660510\pi\)
−0.483157 + 0.875534i \(0.660510\pi\)
\(200\) 8.30409e76 0.683577
\(201\) −2.02408e77 −1.40981
\(202\) 4.47491e76 0.263945
\(203\) −1.23628e77 −0.618018
\(204\) 7.86359e76 0.333434
\(205\) 1.36680e77 0.491984
\(206\) −5.49626e76 −0.168080
\(207\) −7.19407e76 −0.187054
\(208\) 1.70773e77 0.377831
\(209\) 6.48266e77 1.22139
\(210\) −3.80300e76 −0.0610633
\(211\) −2.29628e77 −0.314459 −0.157229 0.987562i \(-0.550256\pi\)
−0.157229 + 0.987562i \(0.550256\pi\)
\(212\) −3.47282e77 −0.405911
\(213\) 1.05595e78 1.05421
\(214\) −1.45474e77 −0.124144
\(215\) −4.70270e77 −0.343288
\(216\) −1.32693e78 −0.829180
\(217\) −1.52506e78 −0.816369
\(218\) 2.80174e76 0.0128569
\(219\) 8.70759e77 0.342784
\(220\) −1.11015e78 −0.375166
\(221\) 1.27191e78 0.369245
\(222\) 2.06198e78 0.514588
\(223\) −3.32066e77 −0.0712871 −0.0356436 0.999365i \(-0.511348\pi\)
−0.0356436 + 0.999365i \(0.511348\pi\)
\(224\) −2.96421e78 −0.547773
\(225\) 1.91477e78 0.304792
\(226\) 3.02515e78 0.415064
\(227\) 1.36540e79 1.61582 0.807909 0.589307i \(-0.200599\pi\)
0.807909 + 0.589307i \(0.200599\pi\)
\(228\) −5.65911e78 −0.578004
\(229\) 4.64291e78 0.409545 0.204773 0.978810i \(-0.434354\pi\)
0.204773 + 0.978810i \(0.434354\pi\)
\(230\) −9.65094e77 −0.0735677
\(231\) −9.83739e78 −0.648453
\(232\) −1.46704e79 −0.836747
\(233\) −2.73417e79 −1.35021 −0.675105 0.737721i \(-0.735902\pi\)
−0.675105 + 0.737721i \(0.735902\pi\)
\(234\) −2.46134e78 −0.105303
\(235\) −2.00908e78 −0.0745116
\(236\) 4.03088e79 1.29672
\(237\) −9.69591e78 −0.270719
\(238\) −4.80730e78 −0.116566
\(239\) 5.49826e79 1.15850 0.579249 0.815150i \(-0.303346\pi\)
0.579249 + 0.815150i \(0.303346\pi\)
\(240\) 7.21978e78 0.132266
\(241\) −3.38224e79 −0.539056 −0.269528 0.962993i \(-0.586868\pi\)
−0.269528 + 0.962993i \(0.586868\pi\)
\(242\) 3.04243e79 0.422091
\(243\) −5.34366e79 −0.645697
\(244\) 8.40336e79 0.884900
\(245\) 2.38368e79 0.218869
\(246\) 6.50140e79 0.520812
\(247\) −9.15342e79 −0.640082
\(248\) −1.80972e80 −1.10530
\(249\) −2.66897e79 −0.142451
\(250\) 5.43086e79 0.253442
\(251\) −8.54919e79 −0.349024 −0.174512 0.984655i \(-0.555835\pi\)
−0.174512 + 0.984655i \(0.555835\pi\)
\(252\) −4.41635e79 −0.157814
\(253\) −2.49645e80 −0.781242
\(254\) 2.80489e80 0.769106
\(255\) 5.37725e79 0.129260
\(256\) −1.52620e80 −0.321791
\(257\) 7.14436e80 1.32191 0.660957 0.750423i \(-0.270150\pi\)
0.660957 + 0.750423i \(0.270150\pi\)
\(258\) −2.23691e80 −0.363403
\(259\) 5.98427e80 0.854022
\(260\) 1.56752e80 0.196610
\(261\) −3.38273e80 −0.373087
\(262\) −1.73408e80 −0.168258
\(263\) 8.76506e80 0.748578 0.374289 0.927312i \(-0.377887\pi\)
0.374289 + 0.927312i \(0.377887\pi\)
\(264\) −1.16736e81 −0.877955
\(265\) −2.37477e80 −0.157357
\(266\) 3.45962e80 0.202066
\(267\) −2.38059e81 −1.22619
\(268\) −3.15326e81 −1.43299
\(269\) 4.76354e81 1.91086 0.955428 0.295223i \(-0.0953940\pi\)
0.955428 + 0.295223i \(0.0953940\pi\)
\(270\) −4.10459e80 −0.145406
\(271\) −3.02040e81 −0.945352 −0.472676 0.881236i \(-0.656712\pi\)
−0.472676 + 0.881236i \(0.656712\pi\)
\(272\) 9.12638e80 0.252488
\(273\) 1.38903e81 0.339830
\(274\) 2.18988e81 0.473999
\(275\) 6.64456e81 1.27298
\(276\) 2.17931e81 0.369712
\(277\) −3.30476e81 −0.496670 −0.248335 0.968674i \(-0.579883\pi\)
−0.248335 + 0.968674i \(0.579883\pi\)
\(278\) 4.18152e81 0.556972
\(279\) −4.17289e81 −0.492829
\(280\) −1.30972e81 −0.137209
\(281\) −9.67683e81 −0.899645 −0.449823 0.893118i \(-0.648513\pi\)
−0.449823 + 0.893118i \(0.648513\pi\)
\(282\) −9.55650e80 −0.0788776
\(283\) −1.18626e82 −0.869630 −0.434815 0.900520i \(-0.643186\pi\)
−0.434815 + 0.900520i \(0.643186\pi\)
\(284\) 1.64503e82 1.07154
\(285\) −3.86979e81 −0.224071
\(286\) −8.54122e81 −0.439802
\(287\) 1.88683e82 0.864351
\(288\) −8.11069e81 −0.330681
\(289\) −2.07499e82 −0.753250
\(290\) −4.53798e81 −0.146733
\(291\) −1.79954e82 −0.518499
\(292\) 1.35653e82 0.348421
\(293\) 7.50510e82 1.71906 0.859530 0.511085i \(-0.170756\pi\)
0.859530 + 0.511085i \(0.170756\pi\)
\(294\) 1.13384e82 0.231694
\(295\) 2.75638e82 0.502692
\(296\) 7.10125e82 1.15628
\(297\) −1.06175e83 −1.54412
\(298\) −3.38877e82 −0.440349
\(299\) 3.52495e82 0.409419
\(300\) −5.80044e82 −0.602420
\(301\) −6.49196e82 −0.603113
\(302\) 1.32144e82 0.109853
\(303\) −6.90991e82 −0.514214
\(304\) −6.56789e82 −0.437684
\(305\) 5.74636e82 0.343043
\(306\) −1.31538e82 −0.0703691
\(307\) 1.38135e83 0.662475 0.331237 0.943547i \(-0.392534\pi\)
0.331237 + 0.943547i \(0.392534\pi\)
\(308\) −1.53254e83 −0.659117
\(309\) 8.48703e82 0.327451
\(310\) −5.59799e82 −0.193827
\(311\) 3.94064e83 1.22488 0.612441 0.790516i \(-0.290188\pi\)
0.612441 + 0.790516i \(0.290188\pi\)
\(312\) 1.64829e83 0.460103
\(313\) 2.68725e83 0.673864 0.336932 0.941529i \(-0.390611\pi\)
0.336932 + 0.941529i \(0.390611\pi\)
\(314\) −2.48414e83 −0.559799
\(315\) −3.01997e82 −0.0611785
\(316\) −1.51050e83 −0.275171
\(317\) 2.06813e83 0.338917 0.169458 0.985537i \(-0.445798\pi\)
0.169458 + 0.985537i \(0.445798\pi\)
\(318\) −1.12960e83 −0.166577
\(319\) −1.17386e84 −1.55822
\(320\) 2.73612e82 0.0327048
\(321\) 2.24633e83 0.241855
\(322\) −1.33229e83 −0.129249
\(323\) −4.89173e83 −0.427738
\(324\) 5.71052e83 0.450213
\(325\) −9.38202e83 −0.667120
\(326\) 8.26474e83 0.530200
\(327\) −4.32629e82 −0.0250476
\(328\) 2.23902e84 1.17026
\(329\) −2.77349e83 −0.130907
\(330\) −3.61097e83 −0.153960
\(331\) 5.77944e83 0.222663 0.111332 0.993783i \(-0.464488\pi\)
0.111332 + 0.993783i \(0.464488\pi\)
\(332\) −4.15791e83 −0.144793
\(333\) 1.63742e84 0.515559
\(334\) 4.06596e83 0.115786
\(335\) −2.15625e84 −0.555518
\(336\) 9.96673e83 0.232374
\(337\) 3.23409e84 0.682576 0.341288 0.939959i \(-0.389137\pi\)
0.341288 + 0.939959i \(0.389137\pi\)
\(338\) −9.76609e83 −0.186643
\(339\) −4.67127e84 −0.808622
\(340\) 8.37707e83 0.131386
\(341\) −1.44806e85 −2.05832
\(342\) 9.46624e83 0.121984
\(343\) 8.10488e84 0.947095
\(344\) −7.70371e84 −0.816568
\(345\) 1.49024e84 0.143324
\(346\) −2.12448e84 −0.185440
\(347\) 7.38268e84 0.585028 0.292514 0.956261i \(-0.405508\pi\)
0.292514 + 0.956261i \(0.405508\pi\)
\(348\) 1.02473e85 0.737405
\(349\) 2.25397e85 1.47331 0.736657 0.676266i \(-0.236403\pi\)
0.736657 + 0.676266i \(0.236403\pi\)
\(350\) 3.54602e84 0.210602
\(351\) 1.49918e85 0.809217
\(352\) −2.81453e85 −1.38111
\(353\) −2.28605e85 −1.02008 −0.510038 0.860152i \(-0.670369\pi\)
−0.510038 + 0.860152i \(0.670369\pi\)
\(354\) 1.31112e85 0.532147
\(355\) 1.12490e85 0.415397
\(356\) −3.70866e85 −1.24636
\(357\) 7.42317e84 0.227093
\(358\) 1.24795e85 0.347629
\(359\) −7.82216e84 −0.198455 −0.0992276 0.995065i \(-0.531637\pi\)
−0.0992276 + 0.995065i \(0.531637\pi\)
\(360\) −3.58366e84 −0.0828309
\(361\) −1.22740e85 −0.258521
\(362\) −2.54312e85 −0.488237
\(363\) −4.69796e85 −0.822313
\(364\) 2.16392e85 0.345418
\(365\) 9.27618e84 0.135070
\(366\) 2.73335e85 0.363143
\(367\) 6.12079e85 0.742155 0.371077 0.928602i \(-0.378988\pi\)
0.371077 + 0.928602i \(0.378988\pi\)
\(368\) 2.52927e85 0.279959
\(369\) 5.16277e85 0.521794
\(370\) 2.19662e85 0.202767
\(371\) −3.27831e85 −0.276455
\(372\) 1.26410e86 0.974074
\(373\) −1.28610e86 −0.905791 −0.452895 0.891564i \(-0.649609\pi\)
−0.452895 + 0.891564i \(0.649609\pi\)
\(374\) −4.56456e85 −0.293900
\(375\) −8.38604e85 −0.493753
\(376\) −3.29117e85 −0.177238
\(377\) 1.65747e86 0.816602
\(378\) −5.66628e85 −0.255460
\(379\) 5.21083e85 0.215027 0.107514 0.994204i \(-0.465711\pi\)
0.107514 + 0.994204i \(0.465711\pi\)
\(380\) −6.02864e85 −0.227756
\(381\) −4.33115e86 −1.49836
\(382\) −6.52708e84 −0.0206822
\(383\) −1.33278e86 −0.386901 −0.193451 0.981110i \(-0.561968\pi\)
−0.193451 + 0.981110i \(0.561968\pi\)
\(384\) 3.10468e86 0.825888
\(385\) −1.04798e86 −0.255515
\(386\) 2.96912e86 0.663672
\(387\) −1.77634e86 −0.364089
\(388\) −2.80346e86 −0.527025
\(389\) 9.94670e86 1.71541 0.857704 0.514144i \(-0.171890\pi\)
0.857704 + 0.514144i \(0.171890\pi\)
\(390\) 5.09864e85 0.0806845
\(391\) 1.88379e86 0.273597
\(392\) 3.90482e86 0.520617
\(393\) 2.67766e86 0.327798
\(394\) −3.22815e86 −0.362937
\(395\) −1.03290e86 −0.106674
\(396\) −4.19335e86 −0.397898
\(397\) −5.37440e86 −0.468649 −0.234325 0.972158i \(-0.575288\pi\)
−0.234325 + 0.972158i \(0.575288\pi\)
\(398\) −5.02885e86 −0.403075
\(399\) −5.34216e86 −0.393663
\(400\) −6.73192e86 −0.456172
\(401\) −4.13165e86 −0.257506 −0.128753 0.991677i \(-0.541097\pi\)
−0.128753 + 0.991677i \(0.541097\pi\)
\(402\) −1.02565e87 −0.588069
\(403\) 2.04463e87 1.07869
\(404\) −1.07647e87 −0.522671
\(405\) 3.90495e86 0.174531
\(406\) −6.26456e86 −0.257792
\(407\) 5.68210e87 2.15326
\(408\) 8.80872e86 0.307466
\(409\) −2.75139e87 −0.884753 −0.442376 0.896830i \(-0.645864\pi\)
−0.442376 + 0.896830i \(0.645864\pi\)
\(410\) 6.92592e86 0.205219
\(411\) −3.38150e87 −0.923439
\(412\) 1.32217e87 0.332836
\(413\) 3.80512e87 0.883164
\(414\) −3.64542e86 −0.0780254
\(415\) −2.84324e86 −0.0561310
\(416\) 3.97408e87 0.723786
\(417\) −6.45687e87 −1.08509
\(418\) 3.28493e87 0.509472
\(419\) −1.09982e87 −0.157454 −0.0787268 0.996896i \(-0.525085\pi\)
−0.0787268 + 0.996896i \(0.525085\pi\)
\(420\) 9.14842e86 0.120919
\(421\) −1.24851e88 −1.52385 −0.761923 0.647668i \(-0.775744\pi\)
−0.761923 + 0.647668i \(0.775744\pi\)
\(422\) −1.16359e87 −0.131169
\(423\) −7.58883e86 −0.0790265
\(424\) −3.89022e87 −0.374298
\(425\) −5.01389e87 −0.445806
\(426\) 5.35076e87 0.439738
\(427\) 7.93271e87 0.602681
\(428\) 3.49949e87 0.245832
\(429\) 1.31889e88 0.856818
\(430\) −2.38298e87 −0.143195
\(431\) −2.68649e87 −0.149347 −0.0746736 0.997208i \(-0.523791\pi\)
−0.0746736 + 0.997208i \(0.523791\pi\)
\(432\) 1.07571e88 0.553338
\(433\) 6.74157e87 0.320934 0.160467 0.987041i \(-0.448700\pi\)
0.160467 + 0.987041i \(0.448700\pi\)
\(434\) −7.72789e87 −0.340530
\(435\) 7.00729e87 0.285864
\(436\) −6.73981e86 −0.0254595
\(437\) −1.35569e88 −0.474276
\(438\) 4.41236e87 0.142984
\(439\) 1.55673e88 0.467360 0.233680 0.972314i \(-0.424923\pi\)
0.233680 + 0.972314i \(0.424923\pi\)
\(440\) −1.24358e88 −0.345948
\(441\) 9.00382e87 0.232131
\(442\) 6.44509e87 0.154022
\(443\) −7.64486e88 −1.69373 −0.846866 0.531806i \(-0.821513\pi\)
−0.846866 + 0.531806i \(0.821513\pi\)
\(444\) −4.96025e88 −1.01900
\(445\) −2.53604e88 −0.483166
\(446\) −1.68266e87 −0.0297358
\(447\) 5.23275e88 0.857883
\(448\) 3.77715e87 0.0574581
\(449\) 3.05563e88 0.431368 0.215684 0.976463i \(-0.430802\pi\)
0.215684 + 0.976463i \(0.430802\pi\)
\(450\) 9.70265e87 0.127137
\(451\) 1.79156e89 2.17930
\(452\) −7.27724e88 −0.821920
\(453\) −2.04049e88 −0.214015
\(454\) 6.91882e88 0.674001
\(455\) 1.47973e88 0.133906
\(456\) −6.33929e88 −0.532989
\(457\) −4.84706e88 −0.378692 −0.189346 0.981910i \(-0.560637\pi\)
−0.189346 + 0.981910i \(0.560637\pi\)
\(458\) 2.35268e88 0.170832
\(459\) 8.01184e88 0.540763
\(460\) 2.32161e88 0.145681
\(461\) −2.17512e89 −1.26912 −0.634560 0.772874i \(-0.718818\pi\)
−0.634560 + 0.772874i \(0.718818\pi\)
\(462\) −4.98486e88 −0.270487
\(463\) −7.57996e88 −0.382564 −0.191282 0.981535i \(-0.561264\pi\)
−0.191282 + 0.981535i \(0.561264\pi\)
\(464\) 1.18929e89 0.558388
\(465\) 8.64410e88 0.377612
\(466\) −1.38547e89 −0.563209
\(467\) −1.00599e89 −0.380607 −0.190304 0.981725i \(-0.560947\pi\)
−0.190304 + 0.981725i \(0.560947\pi\)
\(468\) 5.92094e88 0.208523
\(469\) −2.97665e89 −0.975973
\(470\) −1.01805e88 −0.0310808
\(471\) 3.83587e89 1.09059
\(472\) 4.51536e89 1.19574
\(473\) −6.16416e89 −1.52064
\(474\) −4.91317e88 −0.112924
\(475\) 3.60830e89 0.772799
\(476\) 1.15643e89 0.230828
\(477\) −8.97014e88 −0.166891
\(478\) 2.78611e89 0.483241
\(479\) 9.96571e89 1.61164 0.805821 0.592159i \(-0.201724\pi\)
0.805821 + 0.592159i \(0.201724\pi\)
\(480\) 1.68012e89 0.253373
\(481\) −8.02304e89 −1.12844
\(482\) −1.71387e89 −0.224855
\(483\) 2.05725e89 0.251801
\(484\) −7.31881e89 −0.835836
\(485\) −1.91705e89 −0.204308
\(486\) −2.70777e89 −0.269337
\(487\) −1.58587e90 −1.47247 −0.736236 0.676725i \(-0.763399\pi\)
−0.736236 + 0.676725i \(0.763399\pi\)
\(488\) 9.41337e89 0.815983
\(489\) −1.27620e90 −1.03293
\(490\) 1.20787e89 0.0912963
\(491\) 2.42050e90 1.70874 0.854369 0.519668i \(-0.173944\pi\)
0.854369 + 0.519668i \(0.173944\pi\)
\(492\) −1.56396e90 −1.03132
\(493\) 8.85778e89 0.545699
\(494\) −4.63827e89 −0.266995
\(495\) −2.86748e89 −0.154250
\(496\) 1.46709e90 0.737602
\(497\) 1.55290e90 0.729799
\(498\) −1.35243e89 −0.0594200
\(499\) 1.18042e90 0.484918 0.242459 0.970162i \(-0.422046\pi\)
0.242459 + 0.970162i \(0.422046\pi\)
\(500\) −1.30644e90 −0.501872
\(501\) −6.27843e89 −0.225573
\(502\) −4.33210e89 −0.145587
\(503\) 5.26757e90 1.65609 0.828043 0.560665i \(-0.189455\pi\)
0.828043 + 0.560665i \(0.189455\pi\)
\(504\) −4.94715e89 −0.145523
\(505\) −7.36111e89 −0.202620
\(506\) −1.26502e90 −0.325877
\(507\) 1.50803e90 0.363615
\(508\) −6.74738e90 −1.52300
\(509\) −7.88037e90 −1.66533 −0.832666 0.553776i \(-0.813186\pi\)
−0.832666 + 0.553776i \(0.813186\pi\)
\(510\) 2.72479e89 0.0539178
\(511\) 1.28055e90 0.237300
\(512\) 5.08216e90 0.882073
\(513\) −5.76580e90 −0.937406
\(514\) 3.62023e90 0.551406
\(515\) 9.04121e89 0.129028
\(516\) 5.38107e90 0.719621
\(517\) −2.63344e90 −0.330058
\(518\) 3.03238e90 0.356235
\(519\) 3.28051e90 0.361273
\(520\) 1.75592e90 0.181298
\(521\) −1.48169e90 −0.143448 −0.0717239 0.997425i \(-0.522850\pi\)
−0.0717239 + 0.997425i \(0.522850\pi\)
\(522\) −1.71411e90 −0.155625
\(523\) −1.36105e90 −0.115896 −0.0579481 0.998320i \(-0.518456\pi\)
−0.0579481 + 0.998320i \(0.518456\pi\)
\(524\) 4.17146e90 0.333188
\(525\) −5.47557e90 −0.410292
\(526\) 4.44148e90 0.312252
\(527\) 1.09268e91 0.720840
\(528\) 9.46347e90 0.585887
\(529\) −1.19887e91 −0.696636
\(530\) −1.20336e90 −0.0656376
\(531\) 1.04116e91 0.533151
\(532\) −8.32239e90 −0.400137
\(533\) −2.52966e91 −1.14209
\(534\) −1.20631e91 −0.511477
\(535\) 2.39301e90 0.0953000
\(536\) −3.53226e91 −1.32139
\(537\) −1.92702e91 −0.677247
\(538\) 2.41381e91 0.797069
\(539\) 3.12446e91 0.969508
\(540\) 9.87391e90 0.287938
\(541\) −2.07523e90 −0.0568797 −0.0284399 0.999596i \(-0.509054\pi\)
−0.0284399 + 0.999596i \(0.509054\pi\)
\(542\) −1.53052e91 −0.394332
\(543\) 3.92695e91 0.951177
\(544\) 2.12381e91 0.483674
\(545\) −4.60879e89 −0.00986971
\(546\) 7.03855e90 0.141752
\(547\) 5.89842e91 1.11728 0.558638 0.829412i \(-0.311324\pi\)
0.558638 + 0.829412i \(0.311324\pi\)
\(548\) −5.26794e91 −0.938625
\(549\) 2.17055e91 0.363829
\(550\) 3.36697e91 0.530993
\(551\) −6.37459e91 −0.945962
\(552\) 2.44124e91 0.340919
\(553\) −1.42590e91 −0.187412
\(554\) −1.67461e91 −0.207174
\(555\) −3.39190e91 −0.395029
\(556\) −1.00590e92 −1.10293
\(557\) −5.36319e91 −0.553700 −0.276850 0.960913i \(-0.589290\pi\)
−0.276850 + 0.960913i \(0.589290\pi\)
\(558\) −2.11451e91 −0.205572
\(559\) 8.70370e91 0.796908
\(560\) 1.06175e91 0.0915640
\(561\) 7.04834e91 0.572573
\(562\) −4.90350e91 −0.375266
\(563\) −2.64660e91 −0.190835 −0.0954174 0.995437i \(-0.530419\pi\)
−0.0954174 + 0.995437i \(0.530419\pi\)
\(564\) 2.29889e91 0.156196
\(565\) −4.97630e91 −0.318628
\(566\) −6.01108e91 −0.362746
\(567\) 5.39068e91 0.306628
\(568\) 1.84275e92 0.988091
\(569\) 1.56640e92 0.791848 0.395924 0.918283i \(-0.370424\pi\)
0.395924 + 0.918283i \(0.370424\pi\)
\(570\) −1.96092e91 −0.0934659
\(571\) −1.15568e92 −0.519433 −0.259717 0.965685i \(-0.583629\pi\)
−0.259717 + 0.965685i \(0.583629\pi\)
\(572\) 2.05466e92 0.870908
\(573\) 1.00788e91 0.0402928
\(574\) 9.56107e91 0.360544
\(575\) −1.38954e92 −0.494310
\(576\) 1.03351e91 0.0346865
\(577\) −2.87114e90 −0.00909210 −0.00454605 0.999990i \(-0.501447\pi\)
−0.00454605 + 0.999990i \(0.501447\pi\)
\(578\) −1.05145e92 −0.314201
\(579\) −4.58476e92 −1.29296
\(580\) 1.09165e92 0.290565
\(581\) −3.92503e91 −0.0986149
\(582\) −9.11875e91 −0.216280
\(583\) −3.11278e92 −0.697030
\(584\) 1.51957e92 0.321286
\(585\) 4.04884e91 0.0808367
\(586\) 3.80303e92 0.717066
\(587\) 2.33816e92 0.416387 0.208194 0.978088i \(-0.433242\pi\)
0.208194 + 0.978088i \(0.433242\pi\)
\(588\) −2.72753e92 −0.458807
\(589\) −7.86361e92 −1.24957
\(590\) 1.39673e92 0.209686
\(591\) 4.98474e92 0.707069
\(592\) −5.75680e92 −0.771621
\(593\) 1.19409e93 1.51253 0.756267 0.654263i \(-0.227021\pi\)
0.756267 + 0.654263i \(0.227021\pi\)
\(594\) −5.38017e92 −0.644095
\(595\) 7.90788e91 0.0894833
\(596\) 8.15196e92 0.871991
\(597\) 7.76528e92 0.785266
\(598\) 1.78618e92 0.170780
\(599\) 1.02253e93 0.924434 0.462217 0.886767i \(-0.347054\pi\)
0.462217 + 0.886767i \(0.347054\pi\)
\(600\) −6.49760e92 −0.555503
\(601\) −3.89386e92 −0.314837 −0.157418 0.987532i \(-0.550317\pi\)
−0.157418 + 0.987532i \(0.550317\pi\)
\(602\) −3.28964e92 −0.251574
\(603\) −8.14474e92 −0.589179
\(604\) −3.17882e92 −0.217535
\(605\) −5.00472e92 −0.324022
\(606\) −3.50143e92 −0.214493
\(607\) −2.57597e93 −1.49321 −0.746603 0.665270i \(-0.768317\pi\)
−0.746603 + 0.665270i \(0.768317\pi\)
\(608\) −1.52842e93 −0.838442
\(609\) 9.67340e92 0.502227
\(610\) 2.91183e92 0.143092
\(611\) 3.71838e92 0.172971
\(612\) 3.16424e92 0.139347
\(613\) 4.23652e93 1.76638 0.883189 0.469017i \(-0.155392\pi\)
0.883189 + 0.469017i \(0.155392\pi\)
\(614\) 6.99967e92 0.276336
\(615\) −1.06946e93 −0.399806
\(616\) −1.71674e93 −0.607785
\(617\) 8.17102e92 0.273983 0.136991 0.990572i \(-0.456257\pi\)
0.136991 + 0.990572i \(0.456257\pi\)
\(618\) 4.30060e92 0.136589
\(619\) −2.52814e92 −0.0760613 −0.0380306 0.999277i \(-0.512108\pi\)
−0.0380306 + 0.999277i \(0.512108\pi\)
\(620\) 1.34664e93 0.383822
\(621\) 2.22039e93 0.599599
\(622\) 1.99683e93 0.510931
\(623\) −3.50095e93 −0.848859
\(624\) −1.33623e93 −0.307041
\(625\) 3.22759e93 0.702907
\(626\) 1.36170e93 0.281087
\(627\) −5.07241e93 −0.992548
\(628\) 5.97579e93 1.10853
\(629\) −4.28764e93 −0.754087
\(630\) −1.53030e92 −0.0255192
\(631\) −7.14064e93 −1.12915 −0.564577 0.825380i \(-0.690961\pi\)
−0.564577 + 0.825380i \(0.690961\pi\)
\(632\) −1.69205e93 −0.253741
\(633\) 1.79675e93 0.255542
\(634\) 1.04798e93 0.141371
\(635\) −4.61397e93 −0.590412
\(636\) 2.71733e93 0.329860
\(637\) −4.41169e93 −0.508083
\(638\) −5.94824e93 −0.649974
\(639\) 4.24905e93 0.440568
\(640\) 3.30741e93 0.325431
\(641\) 1.19515e94 1.11603 0.558017 0.829830i \(-0.311563\pi\)
0.558017 + 0.829830i \(0.311563\pi\)
\(642\) 1.13827e93 0.100884
\(643\) −3.95521e93 −0.332738 −0.166369 0.986064i \(-0.553204\pi\)
−0.166369 + 0.986064i \(0.553204\pi\)
\(644\) 3.20493e93 0.255942
\(645\) 3.67966e93 0.278970
\(646\) −2.47876e93 −0.178421
\(647\) −9.68870e93 −0.662174 −0.331087 0.943600i \(-0.607415\pi\)
−0.331087 + 0.943600i \(0.607415\pi\)
\(648\) 6.39687e93 0.415150
\(649\) 3.61298e94 2.22673
\(650\) −4.75411e93 −0.278273
\(651\) 1.19330e94 0.663416
\(652\) −1.98815e94 −1.04992
\(653\) −2.58186e94 −1.29522 −0.647608 0.761974i \(-0.724230\pi\)
−0.647608 + 0.761974i \(0.724230\pi\)
\(654\) −2.19224e92 −0.0104480
\(655\) 2.85251e93 0.129165
\(656\) −1.81511e94 −0.780954
\(657\) 3.50386e93 0.143254
\(658\) −1.40540e93 −0.0546049
\(659\) −5.02240e92 −0.0185460 −0.00927300 0.999957i \(-0.502952\pi\)
−0.00927300 + 0.999957i \(0.502952\pi\)
\(660\) 8.68648e93 0.304875
\(661\) −2.75448e94 −0.918948 −0.459474 0.888191i \(-0.651962\pi\)
−0.459474 + 0.888191i \(0.651962\pi\)
\(662\) 2.92859e93 0.0928787
\(663\) −9.95215e93 −0.300064
\(664\) −4.65765e93 −0.133517
\(665\) −5.69099e93 −0.155118
\(666\) 8.29723e93 0.215053
\(667\) 2.45483e94 0.605071
\(668\) −9.78098e93 −0.229282
\(669\) 2.59827e93 0.0579309
\(670\) −1.09263e94 −0.231722
\(671\) 7.53215e94 1.51955
\(672\) 2.31937e94 0.445143
\(673\) 7.54513e94 1.37772 0.688862 0.724893i \(-0.258111\pi\)
0.688862 + 0.724893i \(0.258111\pi\)
\(674\) 1.63880e94 0.284721
\(675\) −5.90979e94 −0.977003
\(676\) 2.34931e94 0.369595
\(677\) −4.57696e94 −0.685262 −0.342631 0.939470i \(-0.611318\pi\)
−0.342631 + 0.939470i \(0.611318\pi\)
\(678\) −2.36705e94 −0.337298
\(679\) −2.64644e94 −0.358943
\(680\) 9.38391e93 0.121153
\(681\) −1.06837e95 −1.31308
\(682\) −7.33767e94 −0.858582
\(683\) 9.77094e94 1.08854 0.544268 0.838911i \(-0.316807\pi\)
0.544268 + 0.838911i \(0.316807\pi\)
\(684\) −2.27718e94 −0.241556
\(685\) −3.60230e94 −0.363870
\(686\) 4.10695e94 0.395059
\(687\) −3.63288e94 −0.332813
\(688\) 6.24520e94 0.544921
\(689\) 4.39519e94 0.365287
\(690\) 7.55145e93 0.0597841
\(691\) −1.14117e95 −0.860669 −0.430334 0.902670i \(-0.641604\pi\)
−0.430334 + 0.902670i \(0.641604\pi\)
\(692\) 5.11061e94 0.367214
\(693\) −3.95848e94 −0.270998
\(694\) 3.74099e94 0.244031
\(695\) −6.87849e94 −0.427565
\(696\) 1.14790e95 0.679976
\(697\) −1.35189e95 −0.763207
\(698\) 1.14214e95 0.614559
\(699\) 2.13937e95 1.09724
\(700\) −8.53023e94 −0.417039
\(701\) −7.36200e92 −0.00343117 −0.00171558 0.999999i \(-0.500546\pi\)
−0.00171558 + 0.999999i \(0.500546\pi\)
\(702\) 7.59672e94 0.337546
\(703\) 3.08564e95 1.30720
\(704\) 3.58643e94 0.144870
\(705\) 1.57202e94 0.0605512
\(706\) −1.15840e95 −0.425501
\(707\) −1.01618e95 −0.355977
\(708\) −3.15399e95 −1.05377
\(709\) −2.42896e95 −0.774053 −0.387027 0.922069i \(-0.626498\pi\)
−0.387027 + 0.922069i \(0.626498\pi\)
\(710\) 5.70015e94 0.173273
\(711\) −3.90155e94 −0.113137
\(712\) −4.15441e95 −1.14929
\(713\) 3.02825e95 0.799268
\(714\) 3.76151e94 0.0947266
\(715\) 1.40501e95 0.337619
\(716\) −3.00204e95 −0.688384
\(717\) −4.30216e95 −0.941444
\(718\) −3.96369e94 −0.0827810
\(719\) 6.97731e95 1.39082 0.695409 0.718614i \(-0.255223\pi\)
0.695409 + 0.718614i \(0.255223\pi\)
\(720\) 2.90518e94 0.0552757
\(721\) 1.24812e95 0.226686
\(722\) −6.21957e94 −0.107836
\(723\) 2.64646e95 0.438059
\(724\) 6.11769e95 0.966819
\(725\) −6.53379e95 −0.985920
\(726\) −2.38058e95 −0.343009
\(727\) 5.00262e95 0.688327 0.344164 0.938910i \(-0.388162\pi\)
0.344164 + 0.938910i \(0.388162\pi\)
\(728\) 2.42401e95 0.318517
\(729\) 8.52436e95 1.06977
\(730\) 4.70048e94 0.0563412
\(731\) 4.65139e95 0.532538
\(732\) −6.57528e95 −0.719106
\(733\) −8.92678e95 −0.932634 −0.466317 0.884618i \(-0.654419\pi\)
−0.466317 + 0.884618i \(0.654419\pi\)
\(734\) 3.10156e95 0.309573
\(735\) −1.86513e95 −0.177862
\(736\) 5.88590e95 0.536298
\(737\) −2.82635e96 −2.46074
\(738\) 2.61611e95 0.217654
\(739\) 3.28768e95 0.261397 0.130699 0.991422i \(-0.458278\pi\)
0.130699 + 0.991422i \(0.458278\pi\)
\(740\) −5.28415e95 −0.401525
\(741\) 7.16217e95 0.520157
\(742\) −1.66120e95 −0.115317
\(743\) −1.93595e96 −1.28460 −0.642301 0.766453i \(-0.722020\pi\)
−0.642301 + 0.766453i \(0.722020\pi\)
\(744\) 1.41603e96 0.898213
\(745\) 5.57444e95 0.338038
\(746\) −6.51698e95 −0.377830
\(747\) −1.07397e95 −0.0595322
\(748\) 1.09804e96 0.581989
\(749\) 3.30349e95 0.167430
\(750\) −4.24942e95 −0.205957
\(751\) 2.33056e96 1.08025 0.540123 0.841586i \(-0.318378\pi\)
0.540123 + 0.841586i \(0.318378\pi\)
\(752\) 2.66806e95 0.118277
\(753\) 6.68938e95 0.283631
\(754\) 8.39883e95 0.340627
\(755\) −2.17373e95 −0.0843301
\(756\) 1.36307e96 0.505869
\(757\) −3.90449e96 −1.38628 −0.693141 0.720802i \(-0.743774\pi\)
−0.693141 + 0.720802i \(0.743774\pi\)
\(758\) 2.64046e95 0.0896936
\(759\) 1.95337e96 0.634869
\(760\) −6.75323e95 −0.210018
\(761\) 4.58353e95 0.136400 0.0681999 0.997672i \(-0.478274\pi\)
0.0681999 + 0.997672i \(0.478274\pi\)
\(762\) −2.19471e96 −0.625007
\(763\) −6.36232e94 −0.0173398
\(764\) 1.57014e95 0.0409554
\(765\) 2.16376e95 0.0540196
\(766\) −6.75355e95 −0.161387
\(767\) −5.10148e96 −1.16695
\(768\) 1.19419e96 0.261501
\(769\) 6.37251e96 1.33591 0.667956 0.744201i \(-0.267169\pi\)
0.667956 + 0.744201i \(0.267169\pi\)
\(770\) −5.31036e95 −0.106582
\(771\) −5.59016e96 −1.07424
\(772\) −7.14246e96 −1.31422
\(773\) 1.01535e97 1.78897 0.894486 0.447096i \(-0.147542\pi\)
0.894486 + 0.447096i \(0.147542\pi\)
\(774\) −9.00115e95 −0.151871
\(775\) −8.05999e96 −1.30235
\(776\) −3.14041e96 −0.485980
\(777\) −4.68244e96 −0.694014
\(778\) 5.04025e96 0.715542
\(779\) 9.72899e96 1.32301
\(780\) −1.22652e96 −0.159774
\(781\) 1.47448e97 1.84005
\(782\) 9.54564e95 0.114124
\(783\) 1.04405e97 1.19592
\(784\) −3.16554e96 −0.347424
\(785\) 4.08634e96 0.429735
\(786\) 1.35684e96 0.136733
\(787\) −1.79495e97 −1.73340 −0.866699 0.498832i \(-0.833762\pi\)
−0.866699 + 0.498832i \(0.833762\pi\)
\(788\) 7.76558e96 0.718697
\(789\) −6.85829e96 −0.608326
\(790\) −5.23399e95 −0.0444964
\(791\) −6.86966e96 −0.559787
\(792\) −4.69735e96 −0.366910
\(793\) −1.06353e97 −0.796338
\(794\) −2.72334e96 −0.195486
\(795\) 1.85816e96 0.127874
\(796\) 1.20973e97 0.798180
\(797\) −2.24378e96 −0.141947 −0.0709737 0.997478i \(-0.522611\pi\)
−0.0709737 + 0.997478i \(0.522611\pi\)
\(798\) −2.70701e96 −0.164207
\(799\) 1.98716e96 0.115589
\(800\) −1.56659e97 −0.873859
\(801\) −9.57931e96 −0.512442
\(802\) −2.09361e96 −0.107413
\(803\) 1.21589e97 0.598308
\(804\) 2.46729e97 1.16451
\(805\) 2.19158e96 0.0992191
\(806\) 1.03607e97 0.449950
\(807\) −3.72727e97 −1.55284
\(808\) −1.20586e97 −0.481965
\(809\) 4.98406e97 1.91121 0.955603 0.294658i \(-0.0952057\pi\)
0.955603 + 0.294658i \(0.0952057\pi\)
\(810\) 1.97874e96 0.0728014
\(811\) −6.56249e96 −0.231670 −0.115835 0.993268i \(-0.536954\pi\)
−0.115835 + 0.993268i \(0.536954\pi\)
\(812\) 1.50699e97 0.510486
\(813\) 2.36334e97 0.768232
\(814\) 2.87926e97 0.898181
\(815\) −1.35953e97 −0.407013
\(816\) −7.14101e96 −0.205182
\(817\) −3.34742e97 −0.923148
\(818\) −1.39420e97 −0.369054
\(819\) 5.58932e96 0.142020
\(820\) −1.66609e97 −0.406381
\(821\) −1.14583e96 −0.0268302 −0.0134151 0.999910i \(-0.504270\pi\)
−0.0134151 + 0.999910i \(0.504270\pi\)
\(822\) −1.71349e97 −0.385191
\(823\) −4.59764e95 −0.00992295 −0.00496147 0.999988i \(-0.501579\pi\)
−0.00496147 + 0.999988i \(0.501579\pi\)
\(824\) 1.48108e97 0.306915
\(825\) −5.19908e97 −1.03447
\(826\) 1.92815e97 0.368391
\(827\) −7.95450e97 −1.45941 −0.729707 0.683760i \(-0.760343\pi\)
−0.729707 + 0.683760i \(0.760343\pi\)
\(828\) 8.76934e96 0.154508
\(829\) 9.08914e97 1.53796 0.768982 0.639271i \(-0.220764\pi\)
0.768982 + 0.639271i \(0.220764\pi\)
\(830\) −1.44074e96 −0.0234137
\(831\) 2.58584e97 0.403614
\(832\) −5.06398e96 −0.0759208
\(833\) −2.35768e97 −0.339529
\(834\) −3.27186e97 −0.452619
\(835\) −6.68839e96 −0.0888843
\(836\) −7.90216e97 −1.00887
\(837\) 1.28793e98 1.57975
\(838\) −5.57308e96 −0.0656781
\(839\) 8.73266e97 0.988828 0.494414 0.869227i \(-0.335383\pi\)
0.494414 + 0.869227i \(0.335383\pi\)
\(840\) 1.02480e97 0.111502
\(841\) 1.97831e97 0.206837
\(842\) −6.32651e97 −0.635636
\(843\) 7.57171e97 0.731089
\(844\) 2.79910e97 0.259744
\(845\) 1.60650e97 0.143278
\(846\) −3.84546e96 −0.0329641
\(847\) −6.90890e97 −0.569265
\(848\) 3.15370e97 0.249781
\(849\) 9.28198e97 0.706697
\(850\) −2.54067e97 −0.185958
\(851\) −1.18827e98 −0.836132
\(852\) −1.28717e98 −0.870780
\(853\) −5.65226e97 −0.367646 −0.183823 0.982959i \(-0.558847\pi\)
−0.183823 + 0.982959i \(0.558847\pi\)
\(854\) 4.01971e97 0.251394
\(855\) −1.55717e97 −0.0936422
\(856\) 3.92010e97 0.226687
\(857\) −3.44343e98 −1.91484 −0.957422 0.288692i \(-0.906780\pi\)
−0.957422 + 0.288692i \(0.906780\pi\)
\(858\) 6.68314e97 0.357402
\(859\) 1.63520e97 0.0841008 0.0420504 0.999115i \(-0.486611\pi\)
0.0420504 + 0.999115i \(0.486611\pi\)
\(860\) 5.73244e97 0.283558
\(861\) −1.47637e98 −0.702407
\(862\) −1.36131e97 −0.0622967
\(863\) 1.28936e98 0.567559 0.283779 0.958890i \(-0.408412\pi\)
0.283779 + 0.958890i \(0.408412\pi\)
\(864\) 2.50330e98 1.05999
\(865\) 3.49472e97 0.142355
\(866\) 3.41612e97 0.133870
\(867\) 1.62360e98 0.612122
\(868\) 1.85900e98 0.674326
\(869\) −1.35390e98 −0.472524
\(870\) 3.55077e97 0.119242
\(871\) 3.99076e98 1.28958
\(872\) −7.54987e96 −0.0234767
\(873\) −7.24122e97 −0.216688
\(874\) −6.86962e97 −0.197833
\(875\) −1.23327e98 −0.341812
\(876\) −1.06143e98 −0.283141
\(877\) −3.61956e98 −0.929329 −0.464665 0.885487i \(-0.653825\pi\)
−0.464665 + 0.885487i \(0.653825\pi\)
\(878\) 7.88834e97 0.194948
\(879\) −5.87242e98 −1.39698
\(880\) 1.00814e98 0.230862
\(881\) 2.86429e98 0.631428 0.315714 0.948854i \(-0.397756\pi\)
0.315714 + 0.948854i \(0.397756\pi\)
\(882\) 4.56246e97 0.0968282
\(883\) 4.85729e98 0.992454 0.496227 0.868193i \(-0.334718\pi\)
0.496227 + 0.868193i \(0.334718\pi\)
\(884\) −1.55042e98 −0.304998
\(885\) −2.15675e98 −0.408508
\(886\) −3.87385e98 −0.706501
\(887\) 5.57320e98 0.978730 0.489365 0.872079i \(-0.337229\pi\)
0.489365 + 0.872079i \(0.337229\pi\)
\(888\) −5.55643e98 −0.939640
\(889\) −6.36947e98 −1.03728
\(890\) −1.28508e98 −0.201541
\(891\) 5.11848e98 0.773105
\(892\) 4.04778e97 0.0588835
\(893\) −1.43008e98 −0.200372
\(894\) 2.65157e98 0.357846
\(895\) −2.05285e98 −0.266861
\(896\) 4.56580e98 0.571740
\(897\) −2.75813e98 −0.332711
\(898\) 1.54836e98 0.179935
\(899\) 1.42392e99 1.59417
\(900\) −2.33405e98 −0.251759
\(901\) 2.34886e98 0.244105
\(902\) 9.07829e98 0.909044
\(903\) 5.07969e98 0.490114
\(904\) −8.15190e98 −0.757908
\(905\) 4.18337e98 0.374800
\(906\) −1.03397e98 −0.0892714
\(907\) −1.07550e99 −0.894882 −0.447441 0.894313i \(-0.647665\pi\)
−0.447441 + 0.894313i \(0.647665\pi\)
\(908\) −1.66438e99 −1.33467
\(909\) −2.78049e98 −0.214897
\(910\) 7.49815e97 0.0558557
\(911\) 9.91254e98 0.711737 0.355868 0.934536i \(-0.384185\pi\)
0.355868 + 0.934536i \(0.384185\pi\)
\(912\) 5.13910e98 0.355680
\(913\) −3.72684e98 −0.248639
\(914\) −2.45613e98 −0.157962
\(915\) −4.49628e98 −0.278771
\(916\) −5.65957e98 −0.338287
\(917\) 3.93782e98 0.226926
\(918\) 4.05980e98 0.225567
\(919\) −1.32361e99 −0.709073 −0.354537 0.935042i \(-0.615361\pi\)
−0.354537 + 0.935042i \(0.615361\pi\)
\(920\) 2.60065e98 0.134335
\(921\) −1.08085e99 −0.538354
\(922\) −1.10219e99 −0.529383
\(923\) −2.08195e99 −0.964302
\(924\) 1.19915e99 0.535626
\(925\) 3.16270e99 1.36242
\(926\) −3.84096e98 −0.159578
\(927\) 3.41511e98 0.136846
\(928\) 2.76761e99 1.06967
\(929\) −1.24297e98 −0.0463377 −0.0231688 0.999732i \(-0.507376\pi\)
−0.0231688 + 0.999732i \(0.507376\pi\)
\(930\) 4.38019e98 0.157512
\(931\) 1.69673e99 0.588569
\(932\) 3.33286e99 1.11528
\(933\) −3.08339e99 −0.995389
\(934\) −5.09760e98 −0.158761
\(935\) 7.50858e98 0.225615
\(936\) 6.63259e98 0.192284
\(937\) 4.03865e99 1.12969 0.564846 0.825197i \(-0.308936\pi\)
0.564846 + 0.825197i \(0.308936\pi\)
\(938\) −1.50835e99 −0.407105
\(939\) −2.10266e99 −0.547610
\(940\) 2.44901e98 0.0615470
\(941\) −7.13430e99 −1.73021 −0.865105 0.501591i \(-0.832748\pi\)
−0.865105 + 0.501591i \(0.832748\pi\)
\(942\) 1.94373e99 0.454916
\(943\) −3.74660e99 −0.846244
\(944\) −3.66048e99 −0.797952
\(945\) 9.32089e98 0.196106
\(946\) −3.12354e99 −0.634298
\(947\) 3.01348e99 0.590668 0.295334 0.955394i \(-0.404569\pi\)
0.295334 + 0.955394i \(0.404569\pi\)
\(948\) 1.18190e99 0.223616
\(949\) −1.71682e99 −0.313551
\(950\) 1.82842e99 0.322355
\(951\) −1.61823e99 −0.275418
\(952\) 1.29543e99 0.212851
\(953\) 4.15491e99 0.659097 0.329549 0.944139i \(-0.393103\pi\)
0.329549 + 0.944139i \(0.393103\pi\)
\(954\) −4.54540e98 −0.0696148
\(955\) 1.07369e98 0.0158769
\(956\) −6.70220e99 −0.956926
\(957\) 9.18494e99 1.26627
\(958\) 5.04988e99 0.672259
\(959\) −4.97289e99 −0.639272
\(960\) −2.14090e98 −0.0265773
\(961\) 9.22395e99 1.10582
\(962\) −4.06548e99 −0.470703
\(963\) 9.03904e98 0.101075
\(964\) 4.12285e99 0.445263
\(965\) −4.88413e99 −0.509475
\(966\) 1.04246e99 0.105033
\(967\) 4.64253e99 0.451823 0.225911 0.974148i \(-0.427464\pi\)
0.225911 + 0.974148i \(0.427464\pi\)
\(968\) −8.19847e99 −0.770741
\(969\) 3.82757e99 0.347598
\(970\) −9.71419e98 −0.0852224
\(971\) 1.49343e99 0.126573 0.0632863 0.997995i \(-0.479842\pi\)
0.0632863 + 0.997995i \(0.479842\pi\)
\(972\) 6.51376e99 0.533349
\(973\) −9.49559e99 −0.751176
\(974\) −8.03600e99 −0.614207
\(975\) 7.34103e99 0.542129
\(976\) −7.63118e99 −0.544531
\(977\) 1.94135e100 1.33855 0.669275 0.743014i \(-0.266605\pi\)
0.669275 + 0.743014i \(0.266605\pi\)
\(978\) −6.46681e99 −0.430862
\(979\) −3.32417e100 −2.14024
\(980\) −2.90564e99 −0.180787
\(981\) −1.74086e98 −0.0104677
\(982\) 1.22653e100 0.712760
\(983\) −7.70721e99 −0.432867 −0.216433 0.976297i \(-0.569442\pi\)
−0.216433 + 0.976297i \(0.569442\pi\)
\(984\) −1.75194e100 −0.951005
\(985\) 5.31023e99 0.278612
\(986\) 4.48846e99 0.227625
\(987\) 2.17014e99 0.106381
\(988\) 1.11577e100 0.528711
\(989\) 1.28908e100 0.590479
\(990\) −1.45302e99 −0.0643419
\(991\) 4.23472e99 0.181283 0.0906415 0.995884i \(-0.471108\pi\)
0.0906415 + 0.995884i \(0.471108\pi\)
\(992\) 3.41409e100 1.41297
\(993\) −4.52217e99 −0.180945
\(994\) 7.86892e99 0.304419
\(995\) 8.27233e99 0.309425
\(996\) 3.25339e99 0.117665
\(997\) 1.09542e100 0.383082 0.191541 0.981485i \(-0.438652\pi\)
0.191541 + 0.981485i \(0.438652\pi\)
\(998\) 5.98149e99 0.202272
\(999\) −5.05377e100 −1.65261
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 1.68.a.a.1.3 5
3.2 odd 2 9.68.a.a.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.68.a.a.1.3 5 1.1 even 1 trivial
9.68.a.a.1.3 5 3.2 odd 2