Properties

Label 1.94.a.a.1.3
Level $1$
Weight $94$
Character 1.1
Self dual yes
Analytic conductor $54.773$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 94 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.7725430605\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 160477500301516091326739 x^{5} + 877016488484326647371325741724874 x^{4} + 7260529465737129707868752892581169765229378456 x^{3} - 20781038399188480098606854392326662967337072615105929280 x^{2} - 71309214652872234197294752847774640455181142633761719353245451878000 x - 1353216958878139720025204995487184336935523797943751976847532373756765247900000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{88}\cdot 3^{34}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-9.86534e10\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.05764e13 q^{2} +2.16277e22 q^{3} -7.34554e27 q^{4} +1.20105e32 q^{5} -1.09385e36 q^{6} -1.85159e39 q^{7} +8.72396e41 q^{8} +2.32102e44 q^{9} +O(q^{10})\) \(q-5.05764e13 q^{2} +2.16277e22 q^{3} -7.34554e27 q^{4} +1.20105e32 q^{5} -1.09385e36 q^{6} -1.85159e39 q^{7} +8.72396e41 q^{8} +2.32102e44 q^{9} -6.07451e45 q^{10} +6.89038e47 q^{11} -1.58867e50 q^{12} +5.57716e51 q^{13} +9.36469e52 q^{14} +2.59760e54 q^{15} +2.86240e55 q^{16} -1.91697e57 q^{17} -1.17389e58 q^{18} -4.84589e59 q^{19} -8.82240e59 q^{20} -4.00457e61 q^{21} -3.48491e61 q^{22} +2.71891e63 q^{23} +1.88679e64 q^{24} -8.65489e64 q^{25} -2.82073e65 q^{26} -7.68416e64 q^{27} +1.36009e67 q^{28} +1.52941e68 q^{29} -1.31378e68 q^{30} +1.67865e69 q^{31} -1.00875e70 q^{32} +1.49023e70 q^{33} +9.69535e70 q^{34} -2.22386e71 q^{35} -1.70492e72 q^{36} -8.48939e72 q^{37} +2.45088e73 q^{38} +1.20621e74 q^{39} +1.04780e74 q^{40} -1.65968e75 q^{41} +2.02537e75 q^{42} -1.12790e75 q^{43} -5.06136e75 q^{44} +2.78767e76 q^{45} -1.37513e77 q^{46} +5.85334e76 q^{47} +6.19072e77 q^{48} -4.99122e77 q^{49} +4.37733e78 q^{50} -4.14596e79 q^{51} -4.09673e79 q^{52} -1.38747e79 q^{53} +3.88637e78 q^{54} +8.27573e79 q^{55} -1.61532e81 q^{56} -1.04806e82 q^{57} -7.73524e81 q^{58} -4.69043e81 q^{59} -1.90808e82 q^{60} -1.85512e83 q^{61} -8.49001e82 q^{62} -4.29758e83 q^{63} +2.26711e83 q^{64} +6.69848e83 q^{65} -7.53706e83 q^{66} -7.55695e84 q^{67} +1.40812e85 q^{68} +5.88037e85 q^{69} +1.12475e85 q^{70} +1.37506e86 q^{71} +2.02485e86 q^{72} -4.41142e86 q^{73} +4.29363e86 q^{74} -1.87185e87 q^{75} +3.55957e87 q^{76} -1.27582e87 q^{77} -6.10059e87 q^{78} -3.34870e88 q^{79} +3.43790e87 q^{80} -5.63579e88 q^{81} +8.39409e88 q^{82} -4.06731e88 q^{83} +2.94157e89 q^{84} -2.30239e89 q^{85} +5.70450e88 q^{86} +3.30777e90 q^{87} +6.01114e89 q^{88} +2.67415e89 q^{89} -1.40991e90 q^{90} -1.03266e91 q^{91} -1.99718e91 q^{92} +3.63053e91 q^{93} -2.96041e90 q^{94} -5.82018e91 q^{95} -2.18169e92 q^{96} -5.40723e91 q^{97} +2.52438e91 q^{98} +1.59927e92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + O(q^{10}) \) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + \)\(56\!\cdots\!00\)\(q^{10} + \)\(10\!\cdots\!24\)\(q^{11} - \)\(16\!\cdots\!48\)\(q^{12} + \)\(19\!\cdots\!26\)\(q^{13} - \)\(82\!\cdots\!32\)\(q^{14} - \)\(16\!\cdots\!00\)\(q^{15} - \)\(18\!\cdots\!48\)\(q^{16} + \)\(80\!\cdots\!42\)\(q^{17} + \)\(79\!\cdots\!36\)\(q^{18} - \)\(49\!\cdots\!00\)\(q^{19} - \)\(58\!\cdots\!00\)\(q^{20} + \)\(54\!\cdots\!84\)\(q^{21} + \)\(34\!\cdots\!44\)\(q^{22} - \)\(25\!\cdots\!64\)\(q^{23} - \)\(29\!\cdots\!00\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(79\!\cdots\!64\)\(q^{26} - \)\(10\!\cdots\!40\)\(q^{27} + \)\(19\!\cdots\!24\)\(q^{28} + \)\(11\!\cdots\!50\)\(q^{29} - \)\(64\!\cdots\!00\)\(q^{30} - \)\(11\!\cdots\!56\)\(q^{31} - \)\(70\!\cdots\!88\)\(q^{32} + \)\(66\!\cdots\!12\)\(q^{33} + \)\(80\!\cdots\!28\)\(q^{34} - \)\(16\!\cdots\!00\)\(q^{35} + \)\(52\!\cdots\!12\)\(q^{36} + \)\(11\!\cdots\!42\)\(q^{37} - \)\(42\!\cdots\!60\)\(q^{38} - \)\(20\!\cdots\!68\)\(q^{39} + \)\(76\!\cdots\!00\)\(q^{40} - \)\(50\!\cdots\!46\)\(q^{41} - \)\(54\!\cdots\!76\)\(q^{42} - \)\(72\!\cdots\!44\)\(q^{43} + \)\(94\!\cdots\!08\)\(q^{44} + \)\(16\!\cdots\!50\)\(q^{45} - \)\(63\!\cdots\!16\)\(q^{46} - \)\(37\!\cdots\!08\)\(q^{47} - \)\(41\!\cdots\!64\)\(q^{48} + \)\(25\!\cdots\!99\)\(q^{49} - \)\(31\!\cdots\!00\)\(q^{50} - \)\(55\!\cdots\!36\)\(q^{51} - \)\(55\!\cdots\!28\)\(q^{52} - \)\(36\!\cdots\!34\)\(q^{53} - \)\(19\!\cdots\!00\)\(q^{54} - \)\(35\!\cdots\!00\)\(q^{55} - \)\(12\!\cdots\!00\)\(q^{56} - \)\(13\!\cdots\!80\)\(q^{57} - \)\(73\!\cdots\!40\)\(q^{58} - \)\(11\!\cdots\!00\)\(q^{59} - \)\(46\!\cdots\!00\)\(q^{60} - \)\(32\!\cdots\!26\)\(q^{61} - \)\(99\!\cdots\!36\)\(q^{62} - \)\(22\!\cdots\!64\)\(q^{63} - \)\(47\!\cdots\!16\)\(q^{64} + \)\(24\!\cdots\!00\)\(q^{65} + \)\(12\!\cdots\!08\)\(q^{66} + \)\(97\!\cdots\!92\)\(q^{67} + \)\(51\!\cdots\!24\)\(q^{68} + \)\(12\!\cdots\!92\)\(q^{69} + \)\(43\!\cdots\!00\)\(q^{70} + \)\(42\!\cdots\!84\)\(q^{71} + \)\(11\!\cdots\!80\)\(q^{72} + \)\(24\!\cdots\!86\)\(q^{73} + \)\(98\!\cdots\!48\)\(q^{74} + \)\(94\!\cdots\!00\)\(q^{75} - \)\(98\!\cdots\!00\)\(q^{76} - \)\(16\!\cdots\!56\)\(q^{77} - \)\(73\!\cdots\!28\)\(q^{78} - \)\(43\!\cdots\!00\)\(q^{79} - \)\(88\!\cdots\!00\)\(q^{80} - \)\(70\!\cdots\!53\)\(q^{81} - \)\(23\!\cdots\!76\)\(q^{82} - \)\(20\!\cdots\!04\)\(q^{83} + \)\(16\!\cdots\!28\)\(q^{84} + \)\(16\!\cdots\!00\)\(q^{85} + \)\(32\!\cdots\!24\)\(q^{86} + \)\(65\!\cdots\!80\)\(q^{87} + \)\(63\!\cdots\!20\)\(q^{88} + \)\(55\!\cdots\!50\)\(q^{89} + \)\(19\!\cdots\!00\)\(q^{90} - \)\(18\!\cdots\!96\)\(q^{91} - \)\(81\!\cdots\!08\)\(q^{92} - \)\(12\!\cdots\!28\)\(q^{93} - \)\(30\!\cdots\!92\)\(q^{94} - \)\(21\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!16\)\(q^{96} + \)\(43\!\cdots\!42\)\(q^{97} - \)\(69\!\cdots\!56\)\(q^{98} + \)\(30\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.05764e13 −0.508222 −0.254111 0.967175i \(-0.581783\pi\)
−0.254111 + 0.967175i \(0.581783\pi\)
\(3\) 2.16277e22 1.40887 0.704437 0.709767i \(-0.251200\pi\)
0.704437 + 0.709767i \(0.251200\pi\)
\(4\) −7.34554e27 −0.741710
\(5\) 1.20105e32 0.377970 0.188985 0.981980i \(-0.439480\pi\)
0.188985 + 0.981980i \(0.439480\pi\)
\(6\) −1.09385e36 −0.716020
\(7\) −1.85159e39 −0.934300 −0.467150 0.884178i \(-0.654719\pi\)
−0.467150 + 0.884178i \(0.654719\pi\)
\(8\) 8.72396e41 0.885176
\(9\) 2.32102e44 0.984923
\(10\) −6.07451e45 −0.192093
\(11\) 6.89038e47 0.259110 0.129555 0.991572i \(-0.458645\pi\)
0.129555 + 0.991572i \(0.458645\pi\)
\(12\) −1.58867e50 −1.04498
\(13\) 5.57716e51 0.887253 0.443626 0.896212i \(-0.353692\pi\)
0.443626 + 0.896212i \(0.353692\pi\)
\(14\) 9.36469e52 0.474832
\(15\) 2.59760e54 0.532512
\(16\) 2.86240e55 0.291845
\(17\) −1.91697e57 −1.16611 −0.583056 0.812432i \(-0.698143\pi\)
−0.583056 + 0.812432i \(0.698143\pi\)
\(18\) −1.17389e58 −0.500560
\(19\) −4.84589e59 −1.67237 −0.836183 0.548450i \(-0.815218\pi\)
−0.836183 + 0.548450i \(0.815218\pi\)
\(20\) −8.82240e59 −0.280344
\(21\) −4.00457e61 −1.31631
\(22\) −3.48491e61 −0.131685
\(23\) 2.71891e63 1.30032 0.650159 0.759798i \(-0.274702\pi\)
0.650159 + 0.759798i \(0.274702\pi\)
\(24\) 1.88679e64 1.24710
\(25\) −8.65489e64 −0.857139
\(26\) −2.82073e65 −0.450921
\(27\) −7.68416e64 −0.0212413
\(28\) 1.36009e67 0.692980
\(29\) 1.52941e68 1.52412 0.762059 0.647508i \(-0.224189\pi\)
0.762059 + 0.647508i \(0.224189\pi\)
\(30\) −1.31378e68 −0.270634
\(31\) 1.67865e69 0.752733 0.376367 0.926471i \(-0.377173\pi\)
0.376367 + 0.926471i \(0.377173\pi\)
\(32\) −1.00875e70 −1.03350
\(33\) 1.49023e70 0.365052
\(34\) 9.69535e70 0.592644
\(35\) −2.22386e71 −0.353138
\(36\) −1.70492e72 −0.730528
\(37\) −8.48939e72 −1.01741 −0.508705 0.860941i \(-0.669876\pi\)
−0.508705 + 0.860941i \(0.669876\pi\)
\(38\) 2.45088e73 0.849934
\(39\) 1.20621e74 1.25003
\(40\) 1.04780e74 0.334570
\(41\) −1.65968e75 −1.68103 −0.840516 0.541787i \(-0.817748\pi\)
−0.840516 + 0.541787i \(0.817748\pi\)
\(42\) 2.02537e75 0.668978
\(43\) −1.12790e75 −0.124734 −0.0623672 0.998053i \(-0.519865\pi\)
−0.0623672 + 0.998053i \(0.519865\pi\)
\(44\) −5.06136e75 −0.192184
\(45\) 2.78767e76 0.372272
\(46\) −1.37513e77 −0.660851
\(47\) 5.85334e76 0.103479 0.0517396 0.998661i \(-0.483523\pi\)
0.0517396 + 0.998661i \(0.483523\pi\)
\(48\) 6.19072e77 0.411172
\(49\) −4.99122e77 −0.127083
\(50\) 4.37733e78 0.435617
\(51\) −4.14596e79 −1.64290
\(52\) −4.09673e79 −0.658085
\(53\) −1.38747e79 −0.0919173 −0.0459586 0.998943i \(-0.514634\pi\)
−0.0459586 + 0.998943i \(0.514634\pi\)
\(54\) 3.88637e78 0.0107953
\(55\) 8.27573e79 0.0979357
\(56\) −1.61532e81 −0.827020
\(57\) −1.04806e82 −2.35615
\(58\) −7.73524e81 −0.774590
\(59\) −4.69043e81 −0.212126 −0.106063 0.994359i \(-0.533825\pi\)
−0.106063 + 0.994359i \(0.533825\pi\)
\(60\) −1.90808e82 −0.394970
\(61\) −1.85512e83 −1.78047 −0.890234 0.455504i \(-0.849459\pi\)
−0.890234 + 0.455504i \(0.849459\pi\)
\(62\) −8.49001e82 −0.382556
\(63\) −4.29758e83 −0.920214
\(64\) 2.26711e83 0.233402
\(65\) 6.69848e83 0.335355
\(66\) −7.53706e83 −0.185528
\(67\) −7.55695e84 −0.924417 −0.462209 0.886771i \(-0.652943\pi\)
−0.462209 + 0.886771i \(0.652943\pi\)
\(68\) 1.40812e85 0.864918
\(69\) 5.88037e85 1.83198
\(70\) 1.12475e85 0.179472
\(71\) 1.37506e86 1.13451 0.567257 0.823541i \(-0.308005\pi\)
0.567257 + 0.823541i \(0.308005\pi\)
\(72\) 2.02485e86 0.871830
\(73\) −4.41142e86 −1.00015 −0.500076 0.865982i \(-0.666694\pi\)
−0.500076 + 0.865982i \(0.666694\pi\)
\(74\) 4.29363e86 0.517071
\(75\) −1.87185e87 −1.20760
\(76\) 3.55957e87 1.24041
\(77\) −1.27582e87 −0.242086
\(78\) −6.10059e87 −0.635291
\(79\) −3.34870e88 −1.92849 −0.964244 0.265015i \(-0.914623\pi\)
−0.964244 + 0.265015i \(0.914623\pi\)
\(80\) 3.43790e87 0.110309
\(81\) −5.63579e88 −1.01485
\(82\) 8.39409e88 0.854337
\(83\) −4.06731e88 −0.235600 −0.117800 0.993037i \(-0.537584\pi\)
−0.117800 + 0.993037i \(0.537584\pi\)
\(84\) 2.94157e89 0.976321
\(85\) −2.30239e89 −0.440756
\(86\) 5.70450e88 0.0633927
\(87\) 3.30777e90 2.14729
\(88\) 6.01114e89 0.229357
\(89\) 2.67415e89 0.0603324 0.0301662 0.999545i \(-0.490396\pi\)
0.0301662 + 0.999545i \(0.490396\pi\)
\(90\) −1.40991e90 −0.189197
\(91\) −1.03266e91 −0.828960
\(92\) −1.99718e91 −0.964460
\(93\) 3.63053e91 1.06051
\(94\) −2.96041e90 −0.0525904
\(95\) −5.82018e91 −0.632105
\(96\) −2.18169e92 −1.45607
\(97\) −5.40723e91 −0.222889 −0.111445 0.993771i \(-0.535548\pi\)
−0.111445 + 0.993771i \(0.535548\pi\)
\(98\) 2.52438e91 0.0645866
\(99\) 1.59927e92 0.255203
\(100\) 6.35749e92 0.635749
\(101\) 2.20531e93 1.38844 0.694218 0.719764i \(-0.255750\pi\)
0.694218 + 0.719764i \(0.255750\pi\)
\(102\) 2.09688e93 0.834960
\(103\) −3.68693e93 −0.932684 −0.466342 0.884605i \(-0.654428\pi\)
−0.466342 + 0.884605i \(0.654428\pi\)
\(104\) 4.86549e93 0.785374
\(105\) −4.80970e93 −0.497526
\(106\) 7.01735e92 0.0467144
\(107\) −1.33971e94 −0.576321 −0.288161 0.957582i \(-0.593044\pi\)
−0.288161 + 0.957582i \(0.593044\pi\)
\(108\) 5.64443e92 0.0157549
\(109\) −2.23851e94 −0.407031 −0.203515 0.979072i \(-0.565237\pi\)
−0.203515 + 0.979072i \(0.565237\pi\)
\(110\) −4.18557e93 −0.0497731
\(111\) −1.83606e95 −1.43340
\(112\) −5.30000e94 −0.272670
\(113\) 1.75390e95 0.596840 0.298420 0.954435i \(-0.403540\pi\)
0.298420 + 0.954435i \(0.403540\pi\)
\(114\) 5.30069e95 1.19745
\(115\) 3.26556e95 0.491482
\(116\) −1.12344e96 −1.13045
\(117\) 1.29447e96 0.873876
\(118\) 2.37225e95 0.107807
\(119\) 3.54945e96 1.08950
\(120\) 2.26614e96 0.471367
\(121\) −6.59686e96 −0.932862
\(122\) 9.38252e96 0.904873
\(123\) −3.58951e97 −2.36836
\(124\) −1.23306e97 −0.558310
\(125\) −2.25225e97 −0.701943
\(126\) 2.17356e97 0.467673
\(127\) 3.30674e97 0.492637 0.246319 0.969189i \(-0.420779\pi\)
0.246319 + 0.969189i \(0.420779\pi\)
\(128\) 8.84355e97 0.914878
\(129\) −2.43938e97 −0.175735
\(130\) −3.38785e97 −0.170435
\(131\) −7.10571e96 −0.0250318 −0.0125159 0.999922i \(-0.503984\pi\)
−0.0125159 + 0.999922i \(0.503984\pi\)
\(132\) −1.09466e98 −0.270763
\(133\) 8.97262e98 1.56249
\(134\) 3.82204e98 0.469809
\(135\) −9.22909e96 −0.00802858
\(136\) −1.67236e99 −1.03221
\(137\) 1.91186e99 0.839362 0.419681 0.907672i \(-0.362142\pi\)
0.419681 + 0.907672i \(0.362142\pi\)
\(138\) −2.97408e99 −0.931055
\(139\) −6.59713e99 −1.47627 −0.738136 0.674652i \(-0.764294\pi\)
−0.738136 + 0.674652i \(0.764294\pi\)
\(140\) 1.63355e99 0.261926
\(141\) 1.26594e99 0.145789
\(142\) −6.95459e99 −0.576585
\(143\) 3.84288e99 0.229896
\(144\) 6.64370e99 0.287445
\(145\) 1.83691e100 0.576071
\(146\) 2.23114e100 0.508299
\(147\) −1.07949e100 −0.179044
\(148\) 6.23592e100 0.754624
\(149\) 1.72761e100 0.152857 0.0764284 0.997075i \(-0.475648\pi\)
0.0764284 + 0.997075i \(0.475648\pi\)
\(150\) 9.46716e100 0.613729
\(151\) 2.99143e100 0.142381 0.0711904 0.997463i \(-0.477320\pi\)
0.0711904 + 0.997463i \(0.477320\pi\)
\(152\) −4.22754e101 −1.48034
\(153\) −4.44933e101 −1.14853
\(154\) 6.45263e100 0.123033
\(155\) 2.01615e101 0.284511
\(156\) −8.86028e101 −0.927158
\(157\) 7.17255e101 0.557622 0.278811 0.960346i \(-0.410060\pi\)
0.278811 + 0.960346i \(0.410060\pi\)
\(158\) 1.69366e102 0.980100
\(159\) −3.00079e101 −0.129500
\(160\) −1.21156e102 −0.390631
\(161\) −5.03430e102 −1.21489
\(162\) 2.85038e102 0.515769
\(163\) 1.07628e103 1.46285 0.731426 0.681921i \(-0.238855\pi\)
0.731426 + 0.681921i \(0.238855\pi\)
\(164\) 1.21913e103 1.24684
\(165\) 1.78985e102 0.137979
\(166\) 2.05710e102 0.119737
\(167\) −1.94781e103 −0.857492 −0.428746 0.903425i \(-0.641044\pi\)
−0.428746 + 0.903425i \(0.641044\pi\)
\(168\) −3.49357e103 −1.16517
\(169\) −8.40752e102 −0.212783
\(170\) 1.16446e103 0.224002
\(171\) −1.12474e104 −1.64715
\(172\) 8.28501e102 0.0925168
\(173\) 1.97197e104 1.68173 0.840864 0.541247i \(-0.182047\pi\)
0.840864 + 0.541247i \(0.182047\pi\)
\(174\) −1.67295e104 −1.09130
\(175\) 1.60253e104 0.800825
\(176\) 1.97231e103 0.0756197
\(177\) −1.01443e104 −0.298859
\(178\) −1.35249e103 −0.0306623
\(179\) 1.05683e105 1.84645 0.923224 0.384262i \(-0.125544\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(180\) −2.04770e104 −0.276118
\(181\) 3.41629e104 0.356042 0.178021 0.984027i \(-0.443031\pi\)
0.178021 + 0.984027i \(0.443031\pi\)
\(182\) 5.22284e104 0.421296
\(183\) −4.01219e105 −2.50845
\(184\) 2.37196e105 1.15101
\(185\) −1.01962e105 −0.384551
\(186\) −1.83619e105 −0.538972
\(187\) −1.32087e105 −0.302151
\(188\) −4.29959e104 −0.0767516
\(189\) 1.42279e104 0.0198458
\(190\) 2.94364e105 0.321250
\(191\) −4.66141e105 −0.398534 −0.199267 0.979945i \(-0.563856\pi\)
−0.199267 + 0.979945i \(0.563856\pi\)
\(192\) 4.90323e105 0.328833
\(193\) 3.64694e105 0.192094 0.0960471 0.995377i \(-0.469380\pi\)
0.0960471 + 0.995377i \(0.469380\pi\)
\(194\) 2.73478e105 0.113277
\(195\) 1.44873e106 0.472473
\(196\) 3.66632e105 0.0942591
\(197\) 6.37141e106 1.29287 0.646437 0.762967i \(-0.276258\pi\)
0.646437 + 0.762967i \(0.276258\pi\)
\(198\) −8.08855e105 −0.129700
\(199\) 4.40148e106 0.558381 0.279190 0.960236i \(-0.409934\pi\)
0.279190 + 0.960236i \(0.409934\pi\)
\(200\) −7.55049e106 −0.758718
\(201\) −1.63439e107 −1.30239
\(202\) −1.11537e107 −0.705634
\(203\) −2.83185e107 −1.42398
\(204\) 3.04544e107 1.21856
\(205\) −1.99337e107 −0.635380
\(206\) 1.86472e107 0.474011
\(207\) 6.31064e107 1.28071
\(208\) 1.59641e107 0.258940
\(209\) −3.33901e107 −0.433326
\(210\) 2.43258e107 0.252854
\(211\) −1.08995e108 −0.908392 −0.454196 0.890902i \(-0.650073\pi\)
−0.454196 + 0.890902i \(0.650073\pi\)
\(212\) 1.01918e107 0.0681760
\(213\) 2.97395e108 1.59839
\(214\) 6.77577e107 0.292899
\(215\) −1.35467e107 −0.0471459
\(216\) −6.70363e106 −0.0188023
\(217\) −3.10817e108 −0.703279
\(218\) 1.13216e108 0.206862
\(219\) −9.54089e108 −1.40909
\(220\) −6.07897e107 −0.0726399
\(221\) −1.06912e109 −1.03464
\(222\) 9.28613e108 0.728487
\(223\) 4.86481e108 0.309663 0.154832 0.987941i \(-0.450517\pi\)
0.154832 + 0.987941i \(0.450517\pi\)
\(224\) 1.86779e109 0.965597
\(225\) −2.00882e109 −0.844216
\(226\) −8.87062e108 −0.303327
\(227\) −9.58249e108 −0.266855 −0.133428 0.991059i \(-0.542598\pi\)
−0.133428 + 0.991059i \(0.542598\pi\)
\(228\) 7.69854e109 1.74758
\(229\) 2.66341e109 0.493274 0.246637 0.969108i \(-0.420674\pi\)
0.246637 + 0.969108i \(0.420674\pi\)
\(230\) −1.65160e109 −0.249782
\(231\) −2.75930e109 −0.341069
\(232\) 1.33426e110 1.34911
\(233\) −7.83842e109 −0.648900 −0.324450 0.945903i \(-0.605179\pi\)
−0.324450 + 0.945903i \(0.605179\pi\)
\(234\) −6.54697e109 −0.444123
\(235\) 7.03018e108 0.0391121
\(236\) 3.44538e109 0.157336
\(237\) −7.24247e110 −2.71700
\(238\) −1.79518e110 −0.553707
\(239\) 3.53328e110 0.896760 0.448380 0.893843i \(-0.352001\pi\)
0.448380 + 0.893843i \(0.352001\pi\)
\(240\) 7.43539e109 0.155411
\(241\) 6.85756e110 1.18135 0.590673 0.806911i \(-0.298862\pi\)
0.590673 + 0.806911i \(0.298862\pi\)
\(242\) 3.33646e110 0.474101
\(243\) −1.20078e111 −1.40855
\(244\) 1.36268e111 1.32059
\(245\) −5.99473e109 −0.0480338
\(246\) 1.81545e111 1.20365
\(247\) −2.70263e111 −1.48381
\(248\) 1.46445e111 0.666301
\(249\) −8.79664e110 −0.331931
\(250\) 1.13911e111 0.356743
\(251\) −2.00152e111 −0.520633 −0.260317 0.965523i \(-0.583827\pi\)
−0.260317 + 0.965523i \(0.583827\pi\)
\(252\) 3.15681e111 0.682532
\(253\) 1.87343e111 0.336925
\(254\) −1.67243e111 −0.250369
\(255\) −4.97953e111 −0.620969
\(256\) −6.71799e111 −0.698362
\(257\) −2.15173e112 −1.86594 −0.932972 0.359949i \(-0.882794\pi\)
−0.932972 + 0.359949i \(0.882794\pi\)
\(258\) 1.23375e111 0.0893123
\(259\) 1.57189e112 0.950567
\(260\) −4.92039e111 −0.248736
\(261\) 3.54980e112 1.50114
\(262\) 3.59381e110 0.0127217
\(263\) 2.80215e112 0.830899 0.415450 0.909616i \(-0.363624\pi\)
0.415450 + 0.909616i \(0.363624\pi\)
\(264\) 1.30007e112 0.323136
\(265\) −1.66643e111 −0.0347420
\(266\) −4.53803e112 −0.794093
\(267\) 5.78358e111 0.0850008
\(268\) 5.55099e112 0.685650
\(269\) −6.54356e112 −0.679725 −0.339862 0.940475i \(-0.610380\pi\)
−0.339862 + 0.940475i \(0.610380\pi\)
\(270\) 4.66775e110 0.00408030
\(271\) 8.26366e112 0.608276 0.304138 0.952628i \(-0.401632\pi\)
0.304138 + 0.952628i \(0.401632\pi\)
\(272\) −5.48714e112 −0.340324
\(273\) −2.23341e113 −1.16790
\(274\) −9.66950e112 −0.426582
\(275\) −5.96355e112 −0.222093
\(276\) −4.31945e113 −1.35880
\(277\) 3.61986e113 0.962460 0.481230 0.876595i \(-0.340190\pi\)
0.481230 + 0.876595i \(0.340190\pi\)
\(278\) 3.33659e113 0.750274
\(279\) 3.89618e113 0.741385
\(280\) −1.94009e113 −0.312589
\(281\) 8.73104e113 1.19185 0.595926 0.803040i \(-0.296785\pi\)
0.595926 + 0.803040i \(0.296785\pi\)
\(282\) −6.40268e112 −0.0740932
\(283\) 8.05802e113 0.790968 0.395484 0.918473i \(-0.370577\pi\)
0.395484 + 0.918473i \(0.370577\pi\)
\(284\) −1.01006e114 −0.841481
\(285\) −1.25877e114 −0.890555
\(286\) −1.94359e113 −0.116838
\(287\) 3.07306e114 1.57059
\(288\) −2.34133e114 −1.01792
\(289\) 9.72373e113 0.359818
\(290\) −9.29044e113 −0.292772
\(291\) −1.16946e114 −0.314023
\(292\) 3.24043e114 0.741822
\(293\) −7.90158e114 −1.54301 −0.771507 0.636221i \(-0.780497\pi\)
−0.771507 + 0.636221i \(0.780497\pi\)
\(294\) 5.45965e113 0.0909943
\(295\) −5.63346e113 −0.0801773
\(296\) −7.40611e114 −0.900587
\(297\) −5.29468e112 −0.00550383
\(298\) −8.73764e113 −0.0776852
\(299\) 1.51638e115 1.15371
\(300\) 1.37498e115 0.895689
\(301\) 2.08840e114 0.116539
\(302\) −1.51296e114 −0.0723610
\(303\) 4.76958e115 1.95613
\(304\) −1.38709e115 −0.488071
\(305\) −2.22810e115 −0.672964
\(306\) 2.25031e115 0.583709
\(307\) −7.39463e115 −1.64809 −0.824047 0.566521i \(-0.808289\pi\)
−0.824047 + 0.566521i \(0.808289\pi\)
\(308\) 9.37157e114 0.179558
\(309\) −7.97399e115 −1.31403
\(310\) −1.01970e115 −0.144595
\(311\) 6.85748e115 0.837156 0.418578 0.908181i \(-0.362529\pi\)
0.418578 + 0.908181i \(0.362529\pi\)
\(312\) 1.05229e116 1.10649
\(313\) −1.86223e116 −1.68741 −0.843706 0.536805i \(-0.819631\pi\)
−0.843706 + 0.536805i \(0.819631\pi\)
\(314\) −3.62762e115 −0.283396
\(315\) −5.16163e115 −0.347813
\(316\) 2.45981e116 1.43038
\(317\) −6.89517e115 −0.346170 −0.173085 0.984907i \(-0.555374\pi\)
−0.173085 + 0.984907i \(0.555374\pi\)
\(318\) 1.51769e115 0.0658146
\(319\) 1.05383e116 0.394913
\(320\) 2.72292e115 0.0882188
\(321\) −2.89748e116 −0.811964
\(322\) 2.54617e116 0.617433
\(323\) 9.28943e116 1.95017
\(324\) 4.13980e116 0.752724
\(325\) −4.82697e116 −0.760498
\(326\) −5.44342e116 −0.743453
\(327\) −4.84139e116 −0.573455
\(328\) −1.44790e117 −1.48801
\(329\) −1.08380e116 −0.0966806
\(330\) −9.05242e115 −0.0701240
\(331\) 2.05417e117 1.38240 0.691201 0.722663i \(-0.257082\pi\)
0.691201 + 0.722663i \(0.257082\pi\)
\(332\) 2.98766e116 0.174747
\(333\) −1.97041e117 −1.00207
\(334\) 9.85131e116 0.435796
\(335\) −9.07631e116 −0.349402
\(336\) −1.14627e117 −0.384158
\(337\) −2.14639e117 −0.626496 −0.313248 0.949671i \(-0.601417\pi\)
−0.313248 + 0.949671i \(0.601417\pi\)
\(338\) 4.25223e116 0.108141
\(339\) 3.79329e117 0.840872
\(340\) 1.69123e117 0.326913
\(341\) 1.15665e117 0.195040
\(342\) 5.68855e117 0.837119
\(343\) 8.19632e117 1.05303
\(344\) −9.83973e116 −0.110412
\(345\) 7.06264e117 0.692435
\(346\) −9.97350e117 −0.854691
\(347\) −2.55511e117 −0.191465 −0.0957323 0.995407i \(-0.530519\pi\)
−0.0957323 + 0.995407i \(0.530519\pi\)
\(348\) −2.42974e118 −1.59267
\(349\) −7.79802e117 −0.447303 −0.223652 0.974669i \(-0.571798\pi\)
−0.223652 + 0.974669i \(0.571798\pi\)
\(350\) −8.10504e117 −0.406997
\(351\) −4.28558e116 −0.0188464
\(352\) −6.95067e117 −0.267789
\(353\) 4.16579e117 0.140661 0.0703305 0.997524i \(-0.477595\pi\)
0.0703305 + 0.997524i \(0.477595\pi\)
\(354\) 5.13063e117 0.151887
\(355\) 1.65153e118 0.428812
\(356\) −1.96431e117 −0.0447492
\(357\) 7.67663e118 1.53497
\(358\) −5.34505e118 −0.938406
\(359\) −4.71590e118 −0.727232 −0.363616 0.931549i \(-0.618458\pi\)
−0.363616 + 0.931549i \(0.618458\pi\)
\(360\) 2.43196e118 0.329526
\(361\) 1.50865e119 1.79681
\(362\) −1.72784e118 −0.180948
\(363\) −1.42675e119 −1.31428
\(364\) 7.58547e118 0.614848
\(365\) −5.29836e118 −0.378027
\(366\) 2.02922e119 1.27485
\(367\) −1.13188e118 −0.0626368 −0.0313184 0.999509i \(-0.509971\pi\)
−0.0313184 + 0.999509i \(0.509971\pi\)
\(368\) 7.78261e118 0.379491
\(369\) −3.85216e119 −1.65569
\(370\) 5.15689e118 0.195437
\(371\) 2.56904e118 0.0858783
\(372\) −2.66682e119 −0.786588
\(373\) −2.27689e119 −0.592765 −0.296382 0.955069i \(-0.595780\pi\)
−0.296382 + 0.955069i \(0.595780\pi\)
\(374\) 6.68047e118 0.153560
\(375\) −4.87111e119 −0.988949
\(376\) 5.10643e118 0.0915973
\(377\) 8.52979e119 1.35228
\(378\) −7.19598e117 −0.0100860
\(379\) 9.67039e118 0.119873 0.0599364 0.998202i \(-0.480910\pi\)
0.0599364 + 0.998202i \(0.480910\pi\)
\(380\) 4.27524e119 0.468839
\(381\) 7.15172e119 0.694063
\(382\) 2.35757e119 0.202544
\(383\) −1.71702e120 −1.30627 −0.653135 0.757241i \(-0.726547\pi\)
−0.653135 + 0.757241i \(0.726547\pi\)
\(384\) 1.91266e120 1.28895
\(385\) −1.53233e119 −0.0915013
\(386\) −1.84449e119 −0.0976265
\(387\) −2.61787e119 −0.122854
\(388\) 3.97190e119 0.165319
\(389\) 2.27940e120 0.841715 0.420857 0.907127i \(-0.361729\pi\)
0.420857 + 0.907127i \(0.361729\pi\)
\(390\) −7.32714e119 −0.240121
\(391\) −5.21206e120 −1.51632
\(392\) −4.35432e119 −0.112491
\(393\) −1.53680e119 −0.0352666
\(394\) −3.22243e120 −0.657067
\(395\) −4.02198e120 −0.728911
\(396\) −1.17475e120 −0.189287
\(397\) −2.02832e120 −0.290655 −0.145327 0.989384i \(-0.546424\pi\)
−0.145327 + 0.989384i \(0.546424\pi\)
\(398\) −2.22611e120 −0.283781
\(399\) 1.94057e121 2.20135
\(400\) −2.47738e120 −0.250151
\(401\) 1.22235e121 1.09896 0.549480 0.835507i \(-0.314826\pi\)
0.549480 + 0.835507i \(0.314826\pi\)
\(402\) 8.26618e120 0.661902
\(403\) 9.36210e120 0.667865
\(404\) −1.61992e121 −1.02982
\(405\) −6.76890e120 −0.383583
\(406\) 1.43225e121 0.723699
\(407\) −5.84951e120 −0.263621
\(408\) −3.61692e121 −1.45426
\(409\) −1.63408e121 −0.586326 −0.293163 0.956063i \(-0.594708\pi\)
−0.293163 + 0.956063i \(0.594708\pi\)
\(410\) 1.00818e121 0.322914
\(411\) 4.13491e121 1.18255
\(412\) 2.70825e121 0.691781
\(413\) 8.68476e120 0.198189
\(414\) −3.19170e121 −0.650887
\(415\) −4.88506e120 −0.0890498
\(416\) −5.62596e121 −0.916973
\(417\) −1.42681e122 −2.07988
\(418\) 1.68875e121 0.220226
\(419\) 6.80062e121 0.793590 0.396795 0.917907i \(-0.370122\pi\)
0.396795 + 0.917907i \(0.370122\pi\)
\(420\) 3.53299e121 0.369020
\(421\) 9.07457e120 0.0848611 0.0424306 0.999099i \(-0.486490\pi\)
0.0424306 + 0.999099i \(0.486490\pi\)
\(422\) 5.51259e121 0.461665
\(423\) 1.35857e121 0.101919
\(424\) −1.21043e121 −0.0813629
\(425\) 1.65912e122 0.999520
\(426\) −1.50412e122 −0.812335
\(427\) 3.43492e122 1.66349
\(428\) 9.84089e121 0.427464
\(429\) 8.31126e121 0.323894
\(430\) 6.85142e120 0.0239606
\(431\) −6.00864e122 −1.88618 −0.943090 0.332537i \(-0.892096\pi\)
−0.943090 + 0.332537i \(0.892096\pi\)
\(432\) −2.19952e120 −0.00619916
\(433\) −4.16397e122 −1.05395 −0.526976 0.849880i \(-0.676674\pi\)
−0.526976 + 0.849880i \(0.676674\pi\)
\(434\) 1.57200e122 0.357422
\(435\) 3.97281e122 0.811611
\(436\) 1.64431e122 0.301899
\(437\) −1.31755e123 −2.17461
\(438\) 4.82544e122 0.716128
\(439\) −3.92818e122 −0.524314 −0.262157 0.965025i \(-0.584434\pi\)
−0.262157 + 0.965025i \(0.584434\pi\)
\(440\) 7.21971e121 0.0866903
\(441\) −1.15847e122 −0.125167
\(442\) 5.40725e122 0.525825
\(443\) −4.72253e122 −0.413429 −0.206715 0.978401i \(-0.566277\pi\)
−0.206715 + 0.978401i \(0.566277\pi\)
\(444\) 1.34869e123 1.06317
\(445\) 3.21180e121 0.0228039
\(446\) −2.46045e122 −0.157378
\(447\) 3.73643e122 0.215356
\(448\) −4.19776e122 −0.218067
\(449\) 3.72064e123 1.74246 0.871230 0.490875i \(-0.163323\pi\)
0.871230 + 0.490875i \(0.163323\pi\)
\(450\) 1.01599e123 0.429049
\(451\) −1.14359e123 −0.435571
\(452\) −1.28834e123 −0.442682
\(453\) 6.46978e122 0.200596
\(454\) 4.84648e122 0.135622
\(455\) −1.24028e123 −0.313322
\(456\) −9.14319e123 −2.08561
\(457\) 1.39159e123 0.286687 0.143344 0.989673i \(-0.454215\pi\)
0.143344 + 0.989673i \(0.454215\pi\)
\(458\) −1.34706e123 −0.250693
\(459\) 1.47303e122 0.0247698
\(460\) −2.39873e123 −0.364537
\(461\) 6.88216e123 0.945435 0.472718 0.881214i \(-0.343273\pi\)
0.472718 + 0.881214i \(0.343273\pi\)
\(462\) 1.39556e123 0.173339
\(463\) −4.77146e123 −0.535964 −0.267982 0.963424i \(-0.586357\pi\)
−0.267982 + 0.963424i \(0.586357\pi\)
\(464\) 4.37780e123 0.444805
\(465\) 4.36047e123 0.400840
\(466\) 3.96439e123 0.329785
\(467\) −1.67559e124 −1.26163 −0.630815 0.775934i \(-0.717279\pi\)
−0.630815 + 0.775934i \(0.717279\pi\)
\(468\) −9.50859e123 −0.648163
\(469\) 1.39924e124 0.863683
\(470\) −3.55561e122 −0.0198776
\(471\) 1.55126e124 0.785618
\(472\) −4.09191e123 −0.187769
\(473\) −7.77164e122 −0.0323199
\(474\) 3.66299e124 1.38084
\(475\) 4.19407e124 1.43345
\(476\) −2.60726e124 −0.808093
\(477\) −3.22036e123 −0.0905315
\(478\) −1.78701e124 −0.455753
\(479\) −1.44179e124 −0.333656 −0.166828 0.985986i \(-0.553352\pi\)
−0.166828 + 0.985986i \(0.553352\pi\)
\(480\) −2.62033e124 −0.550350
\(481\) −4.73467e124 −0.902700
\(482\) −3.46831e124 −0.600386
\(483\) −1.08880e125 −1.71162
\(484\) 4.84575e124 0.691914
\(485\) −6.49438e123 −0.0842455
\(486\) 6.07314e124 0.715858
\(487\) 1.20536e125 1.29128 0.645641 0.763641i \(-0.276590\pi\)
0.645641 + 0.763641i \(0.276590\pi\)
\(488\) −1.61840e125 −1.57603
\(489\) 2.32774e125 2.06097
\(490\) 3.03192e123 0.0244118
\(491\) −9.38769e124 −0.687495 −0.343747 0.939062i \(-0.611696\pi\)
−0.343747 + 0.939062i \(0.611696\pi\)
\(492\) 2.63669e125 1.75664
\(493\) −2.93184e125 −1.77729
\(494\) 1.36690e125 0.754106
\(495\) 1.92081e124 0.0964591
\(496\) 4.80497e124 0.219681
\(497\) −2.54606e125 −1.05998
\(498\) 4.44903e124 0.168694
\(499\) 5.48346e125 1.89400 0.946999 0.321237i \(-0.104099\pi\)
0.946999 + 0.321237i \(0.104099\pi\)
\(500\) 1.65440e125 0.520638
\(501\) −4.21266e125 −1.20810
\(502\) 1.01230e125 0.264597
\(503\) −6.31756e125 −1.50535 −0.752676 0.658391i \(-0.771237\pi\)
−0.752676 + 0.658391i \(0.771237\pi\)
\(504\) −3.74920e125 −0.814551
\(505\) 2.64870e125 0.524788
\(506\) −9.47514e124 −0.171233
\(507\) −1.81835e125 −0.299784
\(508\) −2.42898e125 −0.365394
\(509\) −1.89152e125 −0.259677 −0.129838 0.991535i \(-0.541446\pi\)
−0.129838 + 0.991535i \(0.541446\pi\)
\(510\) 2.51847e125 0.315590
\(511\) 8.16815e125 0.934441
\(512\) −5.36051e125 −0.559954
\(513\) 3.72366e124 0.0355233
\(514\) 1.08827e126 0.948314
\(515\) −4.42821e125 −0.352527
\(516\) 1.79186e125 0.130344
\(517\) 4.03317e124 0.0268125
\(518\) −7.95005e125 −0.483099
\(519\) 4.26491e126 2.36934
\(520\) 5.84373e125 0.296848
\(521\) −2.43131e126 −1.12950 −0.564750 0.825262i \(-0.691027\pi\)
−0.564750 + 0.825262i \(0.691027\pi\)
\(522\) −1.79536e126 −0.762912
\(523\) −3.48691e125 −0.135554 −0.0677770 0.997700i \(-0.521591\pi\)
−0.0677770 + 0.997700i \(0.521591\pi\)
\(524\) 5.21953e124 0.0185663
\(525\) 3.46591e126 1.12826
\(526\) −1.41723e126 −0.422281
\(527\) −3.21792e126 −0.877772
\(528\) 4.26564e125 0.106539
\(529\) 3.02036e126 0.690829
\(530\) 8.42822e124 0.0176566
\(531\) −1.08866e126 −0.208928
\(532\) −6.59088e126 −1.15892
\(533\) −9.25632e126 −1.49150
\(534\) −2.92513e125 −0.0431993
\(535\) −1.60906e126 −0.217832
\(536\) −6.59265e126 −0.818272
\(537\) 2.28567e127 2.60141
\(538\) 3.30950e126 0.345451
\(539\) −3.43914e125 −0.0329285
\(540\) 6.77927e124 0.00595488
\(541\) 1.30995e127 1.05580 0.527902 0.849305i \(-0.322979\pi\)
0.527902 + 0.849305i \(0.322979\pi\)
\(542\) −4.17947e126 −0.309139
\(543\) 7.38865e126 0.501618
\(544\) 1.93374e127 1.20517
\(545\) −2.68858e126 −0.153846
\(546\) 1.12958e127 0.593552
\(547\) −1.55998e127 −0.752848 −0.376424 0.926447i \(-0.622846\pi\)
−0.376424 + 0.926447i \(0.622846\pi\)
\(548\) −1.40436e127 −0.622563
\(549\) −4.30577e127 −1.75362
\(550\) 3.01615e126 0.112872
\(551\) −7.41138e127 −2.54888
\(552\) 5.13001e127 1.62163
\(553\) 6.20043e127 1.80179
\(554\) −1.83080e127 −0.489143
\(555\) −2.20521e127 −0.541783
\(556\) 4.84595e127 1.09497
\(557\) −3.34419e127 −0.695063 −0.347531 0.937668i \(-0.612980\pi\)
−0.347531 + 0.937668i \(0.612980\pi\)
\(558\) −1.97055e127 −0.376788
\(559\) −6.29046e126 −0.110671
\(560\) −6.36559e126 −0.103061
\(561\) −2.85673e127 −0.425692
\(562\) −4.41585e127 −0.605725
\(563\) 1.02212e128 1.29080 0.645402 0.763843i \(-0.276690\pi\)
0.645402 + 0.763843i \(0.276690\pi\)
\(564\) −9.29903e126 −0.108133
\(565\) 2.10653e127 0.225588
\(566\) −4.07546e127 −0.401987
\(567\) 1.04352e128 0.948174
\(568\) 1.19960e128 1.00424
\(569\) −7.09301e127 −0.547155 −0.273577 0.961850i \(-0.588207\pi\)
−0.273577 + 0.961850i \(0.588207\pi\)
\(570\) 6.36642e127 0.452600
\(571\) 1.97537e128 1.29440 0.647201 0.762319i \(-0.275939\pi\)
0.647201 + 0.762319i \(0.275939\pi\)
\(572\) −2.82280e127 −0.170516
\(573\) −1.00815e128 −0.561484
\(574\) −1.55424e128 −0.798208
\(575\) −2.35318e128 −1.11455
\(576\) 5.26201e127 0.229883
\(577\) −1.23481e128 −0.497652 −0.248826 0.968548i \(-0.580045\pi\)
−0.248826 + 0.968548i \(0.580045\pi\)
\(578\) −4.91792e127 −0.182868
\(579\) 7.88750e127 0.270636
\(580\) −1.34931e128 −0.427278
\(581\) 7.53099e127 0.220121
\(582\) 5.91470e127 0.159593
\(583\) −9.56023e126 −0.0238166
\(584\) −3.84851e128 −0.885309
\(585\) 1.55473e128 0.330299
\(586\) 3.99634e128 0.784194
\(587\) −1.66918e128 −0.302574 −0.151287 0.988490i \(-0.548342\pi\)
−0.151287 + 0.988490i \(0.548342\pi\)
\(588\) 7.92941e127 0.132799
\(589\) −8.13456e128 −1.25885
\(590\) 2.84920e127 0.0407479
\(591\) 1.37799e129 1.82150
\(592\) −2.43001e128 −0.296926
\(593\) 1.16393e129 1.31487 0.657434 0.753512i \(-0.271642\pi\)
0.657434 + 0.753512i \(0.271642\pi\)
\(594\) 2.67786e126 0.00279717
\(595\) 4.26308e128 0.411798
\(596\) −1.26902e128 −0.113375
\(597\) 9.51938e128 0.786687
\(598\) −7.66930e128 −0.586342
\(599\) 1.69191e127 0.0119682 0.00598412 0.999982i \(-0.498095\pi\)
0.00598412 + 0.999982i \(0.498095\pi\)
\(600\) −1.63300e129 −1.06894
\(601\) −5.01379e128 −0.303741 −0.151870 0.988400i \(-0.548530\pi\)
−0.151870 + 0.988400i \(0.548530\pi\)
\(602\) −1.05624e128 −0.0592278
\(603\) −1.75398e129 −0.910480
\(604\) −2.19737e128 −0.105605
\(605\) −7.92319e128 −0.352594
\(606\) −2.41228e129 −0.994149
\(607\) 1.33417e129 0.509258 0.254629 0.967039i \(-0.418047\pi\)
0.254629 + 0.967039i \(0.418047\pi\)
\(608\) 4.88829e129 1.72839
\(609\) −6.12464e129 −2.00621
\(610\) 1.12689e129 0.342015
\(611\) 3.26450e128 0.0918122
\(612\) 3.26827e129 0.851878
\(613\) 2.92658e129 0.707046 0.353523 0.935426i \(-0.384984\pi\)
0.353523 + 0.935426i \(0.384984\pi\)
\(614\) 3.73994e129 0.837598
\(615\) −4.31120e129 −0.895170
\(616\) −1.11302e129 −0.214289
\(617\) 6.96398e129 1.24336 0.621681 0.783270i \(-0.286450\pi\)
0.621681 + 0.783270i \(0.286450\pi\)
\(618\) 4.03296e129 0.667821
\(619\) −8.69061e129 −1.33486 −0.667429 0.744673i \(-0.732605\pi\)
−0.667429 + 0.744673i \(0.732605\pi\)
\(620\) −1.48097e129 −0.211025
\(621\) −2.08925e128 −0.0276205
\(622\) −3.46827e129 −0.425461
\(623\) −4.95144e128 −0.0563686
\(624\) 3.45266e129 0.364814
\(625\) 6.03412e129 0.591825
\(626\) 9.41849e129 0.857580
\(627\) −7.22150e129 −0.610502
\(628\) −5.26863e129 −0.413594
\(629\) 1.62739e130 1.18642
\(630\) 2.61057e129 0.176766
\(631\) −1.68043e130 −1.05695 −0.528475 0.848949i \(-0.677236\pi\)
−0.528475 + 0.848949i \(0.677236\pi\)
\(632\) −2.92140e130 −1.70705
\(633\) −2.35732e130 −1.27981
\(634\) 3.48733e129 0.175931
\(635\) 3.97158e129 0.186202
\(636\) 2.20424e129 0.0960513
\(637\) −2.78368e129 −0.112755
\(638\) −5.32987e129 −0.200704
\(639\) 3.19155e130 1.11741
\(640\) 1.06216e130 0.345797
\(641\) 1.12855e130 0.341683 0.170841 0.985299i \(-0.445351\pi\)
0.170841 + 0.985299i \(0.445351\pi\)
\(642\) 1.46544e130 0.412658
\(643\) 1.78740e130 0.468178 0.234089 0.972215i \(-0.424789\pi\)
0.234089 + 0.972215i \(0.424789\pi\)
\(644\) 3.69797e130 0.901095
\(645\) −2.92983e129 −0.0664225
\(646\) −4.69827e130 −0.991118
\(647\) 7.40078e130 1.45288 0.726438 0.687232i \(-0.241175\pi\)
0.726438 + 0.687232i \(0.241175\pi\)
\(648\) −4.91664e130 −0.898320
\(649\) −3.23189e129 −0.0549639
\(650\) 2.44131e130 0.386502
\(651\) −6.72226e130 −0.990830
\(652\) −7.90584e130 −1.08501
\(653\) 8.19216e130 1.04697 0.523487 0.852034i \(-0.324631\pi\)
0.523487 + 0.852034i \(0.324631\pi\)
\(654\) 2.44860e130 0.291442
\(655\) −8.53434e128 −0.00946127
\(656\) −4.75069e130 −0.490600
\(657\) −1.02390e131 −0.985072
\(658\) 5.48147e129 0.0491352
\(659\) 1.38301e131 1.15519 0.577597 0.816322i \(-0.303991\pi\)
0.577597 + 0.816322i \(0.303991\pi\)
\(660\) −1.31474e130 −0.102340
\(661\) −1.17338e131 −0.851279 −0.425640 0.904893i \(-0.639951\pi\)
−0.425640 + 0.904893i \(0.639951\pi\)
\(662\) −1.03892e131 −0.702567
\(663\) −2.31227e131 −1.45767
\(664\) −3.54830e130 −0.208547
\(665\) 1.07766e131 0.590576
\(666\) 9.96561e130 0.509275
\(667\) 4.15834e131 1.98184
\(668\) 1.43077e131 0.636010
\(669\) 1.05215e131 0.436276
\(670\) 4.59047e130 0.177574
\(671\) −1.27825e131 −0.461336
\(672\) 4.03960e131 1.36040
\(673\) −5.22348e131 −1.64157 −0.820786 0.571236i \(-0.806464\pi\)
−0.820786 + 0.571236i \(0.806464\pi\)
\(674\) 1.08557e131 0.318399
\(675\) 6.65055e129 0.0182067
\(676\) 6.17578e130 0.157823
\(677\) −1.57989e131 −0.376925 −0.188462 0.982080i \(-0.560350\pi\)
−0.188462 + 0.982080i \(0.560350\pi\)
\(678\) −1.91851e131 −0.427350
\(679\) 1.00120e131 0.208245
\(680\) −2.00859e131 −0.390146
\(681\) −2.07247e131 −0.375965
\(682\) −5.84994e130 −0.0991238
\(683\) −7.37705e131 −1.16767 −0.583834 0.811873i \(-0.698448\pi\)
−0.583834 + 0.811873i \(0.698448\pi\)
\(684\) 8.26184e131 1.22171
\(685\) 2.29625e131 0.317254
\(686\) −4.14541e131 −0.535175
\(687\) 5.76034e131 0.694961
\(688\) −3.22850e130 −0.0364031
\(689\) −7.73817e130 −0.0815538
\(690\) −3.57203e131 −0.351911
\(691\) −3.20174e131 −0.294888 −0.147444 0.989070i \(-0.547105\pi\)
−0.147444 + 0.989070i \(0.547105\pi\)
\(692\) −1.44852e132 −1.24735
\(693\) −2.96120e131 −0.238436
\(694\) 1.29228e131 0.0973065
\(695\) −7.92351e131 −0.557987
\(696\) 2.88569e132 1.90073
\(697\) 3.18156e132 1.96027
\(698\) 3.94396e131 0.227329
\(699\) −1.69527e132 −0.914218
\(700\) −1.17715e132 −0.593980
\(701\) 7.57694e131 0.357772 0.178886 0.983870i \(-0.442751\pi\)
0.178886 + 0.983870i \(0.442751\pi\)
\(702\) 2.16749e130 0.00957816
\(703\) 4.11387e132 1.70148
\(704\) 1.56212e131 0.0604766
\(705\) 1.52047e131 0.0551039
\(706\) −2.10691e131 −0.0714870
\(707\) −4.08334e132 −1.29722
\(708\) 7.45155e131 0.221667
\(709\) −2.69771e132 −0.751529 −0.375764 0.926715i \(-0.622620\pi\)
−0.375764 + 0.926715i \(0.622620\pi\)
\(710\) −8.35284e131 −0.217932
\(711\) −7.77241e132 −1.89941
\(712\) 2.33292e131 0.0534048
\(713\) 4.56409e132 0.978793
\(714\) −3.88257e132 −0.780103
\(715\) 4.61551e131 0.0868937
\(716\) −7.76296e132 −1.36953
\(717\) 7.64168e132 1.26342
\(718\) 2.38514e132 0.369595
\(719\) 4.75148e132 0.690137 0.345069 0.938577i \(-0.387856\pi\)
0.345069 + 0.938577i \(0.387856\pi\)
\(720\) 7.97945e131 0.108645
\(721\) 6.82670e132 0.871407
\(722\) −7.63019e132 −0.913179
\(723\) 1.48313e133 1.66437
\(724\) −2.50945e132 −0.264080
\(725\) −1.32369e133 −1.30638
\(726\) 7.21599e132 0.667948
\(727\) 1.00321e133 0.871051 0.435526 0.900176i \(-0.356563\pi\)
0.435526 + 0.900176i \(0.356563\pi\)
\(728\) −9.00891e132 −0.733775
\(729\) −1.26892e133 −0.969623
\(730\) 2.67972e132 0.192122
\(731\) 2.16214e132 0.145454
\(732\) 2.94717e133 1.86055
\(733\) 2.91877e132 0.172928 0.0864640 0.996255i \(-0.472443\pi\)
0.0864640 + 0.996255i \(0.472443\pi\)
\(734\) 5.72467e131 0.0318334
\(735\) −1.29652e132 −0.0676735
\(736\) −2.74270e133 −1.34388
\(737\) −5.20703e132 −0.239525
\(738\) 1.94829e133 0.841457
\(739\) −3.91770e133 −1.58878 −0.794391 0.607406i \(-0.792210\pi\)
−0.794391 + 0.607406i \(0.792210\pi\)
\(740\) 7.48968e132 0.285225
\(741\) −5.84517e133 −2.09050
\(742\) −1.29933e132 −0.0436452
\(743\) 6.95679e132 0.219497 0.109749 0.993959i \(-0.464995\pi\)
0.109749 + 0.993959i \(0.464995\pi\)
\(744\) 3.16726e133 0.938734
\(745\) 2.07496e132 0.0577753
\(746\) 1.15157e133 0.301256
\(747\) −9.44030e132 −0.232048
\(748\) 9.70248e132 0.224108
\(749\) 2.48059e133 0.538457
\(750\) 2.46363e133 0.502605
\(751\) 4.33173e133 0.830624 0.415312 0.909679i \(-0.363672\pi\)
0.415312 + 0.909679i \(0.363672\pi\)
\(752\) 1.67546e132 0.0301999
\(753\) −4.32883e133 −0.733506
\(754\) −4.31407e133 −0.687257
\(755\) 3.59287e132 0.0538157
\(756\) −1.04512e132 −0.0147198
\(757\) 7.50220e133 0.993643 0.496821 0.867853i \(-0.334500\pi\)
0.496821 + 0.867853i \(0.334500\pi\)
\(758\) −4.89094e132 −0.0609220
\(759\) 4.05180e133 0.474685
\(760\) −5.07751e133 −0.559524
\(761\) 3.42648e133 0.355191 0.177595 0.984104i \(-0.443168\pi\)
0.177595 + 0.984104i \(0.443168\pi\)
\(762\) −3.61708e133 −0.352738
\(763\) 4.14481e133 0.380289
\(764\) 3.42406e133 0.295597
\(765\) −5.34389e133 −0.434111
\(766\) 8.68409e133 0.663875
\(767\) −2.61593e133 −0.188209
\(768\) −1.45295e134 −0.983904
\(769\) 4.49538e132 0.0286544 0.0143272 0.999897i \(-0.495439\pi\)
0.0143272 + 0.999897i \(0.495439\pi\)
\(770\) 7.74996e132 0.0465030
\(771\) −4.65371e134 −2.62888
\(772\) −2.67888e133 −0.142478
\(773\) 6.94124e133 0.347609 0.173804 0.984780i \(-0.444394\pi\)
0.173804 + 0.984780i \(0.444394\pi\)
\(774\) 1.32403e133 0.0624370
\(775\) −1.45285e134 −0.645197
\(776\) −4.71724e133 −0.197296
\(777\) 3.39963e134 1.33923
\(778\) −1.15284e134 −0.427778
\(779\) 8.04265e134 2.81130
\(780\) −1.06417e134 −0.350438
\(781\) 9.47472e133 0.293963
\(782\) 2.63608e134 0.770626
\(783\) −1.17523e133 −0.0323742
\(784\) −1.42869e133 −0.0370886
\(785\) 8.61462e133 0.210764
\(786\) 7.77259e132 0.0179233
\(787\) −4.53355e134 −0.985401 −0.492700 0.870199i \(-0.663990\pi\)
−0.492700 + 0.870199i \(0.663990\pi\)
\(788\) −4.68015e134 −0.958938
\(789\) 6.06040e134 1.17063
\(790\) 2.03417e134 0.370449
\(791\) −3.24751e134 −0.557628
\(792\) 1.39520e134 0.225899
\(793\) −1.03463e135 −1.57972
\(794\) 1.02585e134 0.147717
\(795\) −3.60411e133 −0.0489471
\(796\) −3.23312e134 −0.414157
\(797\) 8.18029e134 0.988455 0.494228 0.869333i \(-0.335451\pi\)
0.494228 + 0.869333i \(0.335451\pi\)
\(798\) −9.81471e134 −1.11878
\(799\) −1.12207e134 −0.120668
\(800\) 8.73061e134 0.885850
\(801\) 6.20676e133 0.0594228
\(802\) −6.18220e134 −0.558516
\(803\) −3.03964e134 −0.259149
\(804\) 1.20055e135 0.965994
\(805\) −6.04647e134 −0.459191
\(806\) −4.73502e134 −0.339424
\(807\) −1.41522e135 −0.957646
\(808\) 1.92391e135 1.22901
\(809\) −7.01065e134 −0.422816 −0.211408 0.977398i \(-0.567805\pi\)
−0.211408 + 0.977398i \(0.567805\pi\)
\(810\) 3.42347e134 0.194945
\(811\) −2.27619e134 −0.122388 −0.0611940 0.998126i \(-0.519491\pi\)
−0.0611940 + 0.998126i \(0.519491\pi\)
\(812\) 2.08015e135 1.05618
\(813\) 1.78724e135 0.856983
\(814\) 2.95848e134 0.133978
\(815\) 1.29267e135 0.552914
\(816\) −1.18674e135 −0.479473
\(817\) 5.46567e134 0.208602
\(818\) 8.26458e134 0.297984
\(819\) −2.39683e135 −0.816462
\(820\) 1.46424e135 0.471268
\(821\) −2.38392e135 −0.724996 −0.362498 0.931985i \(-0.618076\pi\)
−0.362498 + 0.931985i \(0.618076\pi\)
\(822\) −2.09129e135 −0.601000
\(823\) 4.89963e135 1.33067 0.665335 0.746545i \(-0.268289\pi\)
0.665335 + 0.746545i \(0.268289\pi\)
\(824\) −3.21647e135 −0.825589
\(825\) −1.28978e135 −0.312901
\(826\) −4.39244e134 −0.100724
\(827\) −2.84246e135 −0.616152 −0.308076 0.951362i \(-0.599685\pi\)
−0.308076 + 0.951362i \(0.599685\pi\)
\(828\) −4.63551e135 −0.949919
\(829\) −5.72864e135 −1.10985 −0.554927 0.831899i \(-0.687254\pi\)
−0.554927 + 0.831899i \(0.687254\pi\)
\(830\) 2.47069e134 0.0452571
\(831\) 7.82892e135 1.35598
\(832\) 1.26440e135 0.207086
\(833\) 9.56802e134 0.148194
\(834\) 7.21628e135 1.05704
\(835\) −2.33942e135 −0.324106
\(836\) 2.45268e135 0.321403
\(837\) −1.28990e134 −0.0159890
\(838\) −3.43951e135 −0.403320
\(839\) −1.53346e136 −1.70114 −0.850571 0.525860i \(-0.823743\pi\)
−0.850571 + 0.525860i \(0.823743\pi\)
\(840\) −4.19597e135 −0.440398
\(841\) 1.33215e136 1.32293
\(842\) −4.58960e134 −0.0431283
\(843\) 1.88832e136 1.67917
\(844\) 8.00629e135 0.673764
\(845\) −1.00979e135 −0.0804255
\(846\) −6.87117e134 −0.0517975
\(847\) 1.22147e136 0.871573
\(848\) −3.97151e134 −0.0268256
\(849\) 1.74276e136 1.11437
\(850\) −8.39122e135 −0.507978
\(851\) −2.30819e136 −1.32296
\(852\) −2.18453e136 −1.18554
\(853\) 1.78771e136 0.918684 0.459342 0.888260i \(-0.348085\pi\)
0.459342 + 0.888260i \(0.348085\pi\)
\(854\) −1.73726e136 −0.845423
\(855\) −1.35088e136 −0.622575
\(856\) −1.16876e136 −0.510146
\(857\) −1.68084e136 −0.694894 −0.347447 0.937700i \(-0.612951\pi\)
−0.347447 + 0.937700i \(0.612951\pi\)
\(858\) −4.20354e135 −0.164610
\(859\) −4.56777e136 −1.69442 −0.847212 0.531255i \(-0.821721\pi\)
−0.847212 + 0.531255i \(0.821721\pi\)
\(860\) 9.95075e134 0.0349686
\(861\) 6.64631e136 2.21276
\(862\) 3.03896e136 0.958599
\(863\) −2.14397e136 −0.640791 −0.320395 0.947284i \(-0.603816\pi\)
−0.320395 + 0.947284i \(0.603816\pi\)
\(864\) 7.75139e134 0.0219528
\(865\) 2.36844e136 0.635643
\(866\) 2.10599e136 0.535641
\(867\) 2.10302e136 0.506938
\(868\) 2.28312e136 0.521629
\(869\) −2.30739e136 −0.499690
\(870\) −2.00931e136 −0.412478
\(871\) −4.21463e136 −0.820192
\(872\) −1.95287e136 −0.360294
\(873\) −1.25503e136 −0.219529
\(874\) 6.66372e136 1.10518
\(875\) 4.17026e136 0.655825
\(876\) 7.00830e136 1.04513
\(877\) −4.90563e136 −0.693767 −0.346883 0.937908i \(-0.612760\pi\)
−0.346883 + 0.937908i \(0.612760\pi\)
\(878\) 1.98673e136 0.266468
\(879\) −1.70893e137 −2.17391
\(880\) 2.36885e135 0.0285820
\(881\) 1.65361e137 1.89257 0.946287 0.323328i \(-0.104802\pi\)
0.946287 + 0.323328i \(0.104802\pi\)
\(882\) 5.85914e135 0.0636128
\(883\) −3.55857e136 −0.366524 −0.183262 0.983064i \(-0.558666\pi\)
−0.183262 + 0.983064i \(0.558666\pi\)
\(884\) 7.85330e136 0.767401
\(885\) −1.21839e136 −0.112960
\(886\) 2.38849e136 0.210114
\(887\) −1.45980e137 −1.21856 −0.609278 0.792956i \(-0.708541\pi\)
−0.609278 + 0.792956i \(0.708541\pi\)
\(888\) −1.60177e137 −1.26881
\(889\) −6.12273e136 −0.460271
\(890\) −1.62442e135 −0.0115894
\(891\) −3.88328e136 −0.262957
\(892\) −3.57346e136 −0.229680
\(893\) −2.83646e136 −0.173055
\(894\) −1.88975e136 −0.109449
\(895\) 1.26930e137 0.697903
\(896\) −1.63746e137 −0.854770
\(897\) 3.27958e137 1.62543
\(898\) −1.88177e137 −0.885556
\(899\) 2.56735e137 1.14725
\(900\) 1.47559e137 0.626163
\(901\) 2.65975e136 0.107186
\(902\) 5.78385e136 0.221367
\(903\) 4.51674e136 0.164189
\(904\) 1.53010e137 0.528308
\(905\) 4.10315e136 0.134573
\(906\) −3.27218e136 −0.101947
\(907\) −4.43491e137 −1.31264 −0.656321 0.754482i \(-0.727888\pi\)
−0.656321 + 0.754482i \(0.727888\pi\)
\(908\) 7.03886e136 0.197929
\(909\) 5.11857e137 1.36750
\(910\) 6.27292e136 0.159237
\(911\) −5.56999e136 −0.134354 −0.0671769 0.997741i \(-0.521399\pi\)
−0.0671769 + 0.997741i \(0.521399\pi\)
\(912\) −2.99996e137 −0.687630
\(913\) −2.80253e136 −0.0610463
\(914\) −7.03818e136 −0.145701
\(915\) −4.81886e137 −0.948120
\(916\) −1.95642e137 −0.365867
\(917\) 1.31569e136 0.0233872
\(918\) −7.45006e135 −0.0125885
\(919\) 3.23898e137 0.520280 0.260140 0.965571i \(-0.416231\pi\)
0.260140 + 0.965571i \(0.416231\pi\)
\(920\) 2.84886e137 0.435048
\(921\) −1.59929e138 −2.32196
\(922\) −3.48075e137 −0.480491
\(923\) 7.66896e137 1.00660
\(924\) 2.02686e137 0.252974
\(925\) 7.34747e137 0.872062
\(926\) 2.41324e137 0.272389
\(927\) −8.55745e137 −0.918622
\(928\) −1.54280e138 −1.57517
\(929\) 1.34434e138 1.30551 0.652753 0.757571i \(-0.273614\pi\)
0.652753 + 0.757571i \(0.273614\pi\)
\(930\) −2.20537e137 −0.203715
\(931\) 2.41869e137 0.212530
\(932\) 5.75774e137 0.481296
\(933\) 1.48311e138 1.17945
\(934\) 8.47452e137 0.641188
\(935\) −1.58643e137 −0.114204
\(936\) 1.12929e138 0.773533
\(937\) 2.26993e138 1.47952 0.739761 0.672870i \(-0.234938\pi\)
0.739761 + 0.672870i \(0.234938\pi\)
\(938\) −7.07685e137 −0.438943
\(939\) −4.02757e138 −2.37735
\(940\) −5.16405e136 −0.0290098
\(941\) 3.49457e138 1.86843 0.934213 0.356716i \(-0.116104\pi\)
0.934213 + 0.356716i \(0.116104\pi\)
\(942\) −7.84571e137 −0.399269
\(943\) −4.51252e138 −2.18588
\(944\) −1.34259e137 −0.0619079
\(945\) 1.70885e136 0.00750110
\(946\) 3.93062e136 0.0164257
\(947\) −3.15534e138 −1.25537 −0.627685 0.778467i \(-0.715997\pi\)
−0.627685 + 0.778467i \(0.715997\pi\)
\(948\) 5.31999e138 2.01522
\(949\) −2.46032e138 −0.887387
\(950\) −2.12121e138 −0.728511
\(951\) −1.49127e138 −0.487710
\(952\) 3.09652e138 0.964398
\(953\) 2.76357e138 0.819692 0.409846 0.912155i \(-0.365582\pi\)
0.409846 + 0.912155i \(0.365582\pi\)
\(954\) 1.62874e137 0.0460101
\(955\) −5.59860e137 −0.150634
\(956\) −2.59539e138 −0.665136
\(957\) 2.27918e138 0.556383
\(958\) 7.29204e137 0.169571
\(959\) −3.53998e138 −0.784216
\(960\) 5.88905e137 0.124289
\(961\) −2.15536e138 −0.433393
\(962\) 2.39463e138 0.458772
\(963\) −3.10949e138 −0.567632
\(964\) −5.03725e138 −0.876217
\(965\) 4.38018e137 0.0726059
\(966\) 5.50678e138 0.869884
\(967\) 6.63903e138 0.999479 0.499740 0.866176i \(-0.333429\pi\)
0.499740 + 0.866176i \(0.333429\pi\)
\(968\) −5.75508e138 −0.825747
\(969\) 2.00909e139 2.74754
\(970\) 3.28462e137 0.0428154
\(971\) −1.84814e138 −0.229636 −0.114818 0.993387i \(-0.536628\pi\)
−0.114818 + 0.993387i \(0.536628\pi\)
\(972\) 8.82041e138 1.04474
\(973\) 1.22152e139 1.37928
\(974\) −6.09629e138 −0.656258
\(975\) −1.04396e139 −1.07145
\(976\) −5.31009e138 −0.519620
\(977\) −1.80423e139 −1.68342 −0.841712 0.539926i \(-0.818452\pi\)
−0.841712 + 0.539926i \(0.818452\pi\)
\(978\) −1.17729e139 −1.04743
\(979\) 1.84259e137 0.0156327
\(980\) 4.40345e137 0.0356271
\(981\) −5.19563e138 −0.400894
\(982\) 4.74796e138 0.349400
\(983\) 5.12719e138 0.359866 0.179933 0.983679i \(-0.442412\pi\)
0.179933 + 0.983679i \(0.442412\pi\)
\(984\) −3.13148e139 −2.09641
\(985\) 7.65242e138 0.488668
\(986\) 1.48282e139 0.903259
\(987\) −2.34401e138 −0.136211
\(988\) 1.98523e139 1.10056
\(989\) −3.06664e138 −0.162194
\(990\) −9.71479e137 −0.0490227
\(991\) −2.29485e139 −1.10491 −0.552457 0.833541i \(-0.686310\pi\)
−0.552457 + 0.833541i \(0.686310\pi\)
\(992\) −1.69334e139 −0.777948
\(993\) 4.44269e139 1.94763
\(994\) 1.28771e139 0.538703
\(995\) 5.28641e138 0.211051
\(996\) 6.46161e138 0.246196
\(997\) 3.11371e139 1.13228 0.566139 0.824310i \(-0.308436\pi\)
0.566139 + 0.824310i \(0.308436\pi\)
\(998\) −2.77334e139 −0.962571
\(999\) 6.52338e137 0.0216111
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 1.94.a.a.1.3 7
3.2 odd 2 9.94.a.b.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.94.a.a.1.3 7 1.1 even 1 trivial
9.94.a.b.1.5 7 3.2 odd 2