Properties

Label 1.54.a.a.1.4
Level $1$
Weight $54$
Character 1.1
Self dual yes
Analytic conductor $17.790$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 54 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.7903107608\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 2315873743412 x^{2} - 421178019174503472 x + 612167648493870378955584\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{27}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.52611e6\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.29387e8 q^{2} +1.34470e12 q^{3} +7.73392e15 q^{4} -4.81259e18 q^{5} +1.73988e20 q^{6} -1.66125e22 q^{7} -1.64746e23 q^{8} -1.75750e25 q^{9} +O(q^{10})\) \(q+1.29387e8 q^{2} +1.34470e12 q^{3} +7.73392e15 q^{4} -4.81259e18 q^{5} +1.73988e20 q^{6} -1.66125e22 q^{7} -1.64746e23 q^{8} -1.75750e25 q^{9} -6.22689e26 q^{10} -9.74180e26 q^{11} +1.03998e28 q^{12} +4.82001e29 q^{13} -2.14945e30 q^{14} -6.47150e30 q^{15} -9.09771e31 q^{16} +5.02736e32 q^{17} -2.27399e33 q^{18} -1.38519e34 q^{19} -3.72202e34 q^{20} -2.23389e34 q^{21} -1.26047e35 q^{22} -5.29051e35 q^{23} -2.21535e35 q^{24} +1.20588e37 q^{25} +6.23649e37 q^{26} -4.96979e37 q^{27} -1.28480e38 q^{28} -3.32225e38 q^{29} -8.37331e38 q^{30} +2.69343e39 q^{31} -1.02874e40 q^{32} -1.30998e39 q^{33} +6.50477e40 q^{34} +7.99492e40 q^{35} -1.35924e41 q^{36} +2.08872e41 q^{37} -1.79226e42 q^{38} +6.48148e41 q^{39} +7.92857e41 q^{40} +2.96475e42 q^{41} -2.89037e42 q^{42} +1.06838e43 q^{43} -7.53423e42 q^{44} +8.45814e43 q^{45} -6.84525e43 q^{46} -2.94705e44 q^{47} -1.22337e44 q^{48} -3.40898e44 q^{49} +1.56026e45 q^{50} +6.76030e44 q^{51} +3.72776e45 q^{52} -5.52073e45 q^{53} -6.43028e45 q^{54} +4.68833e45 q^{55} +2.73685e45 q^{56} -1.86266e46 q^{57} -4.29858e46 q^{58} +1.07917e47 q^{59} -5.00501e46 q^{60} +3.62994e46 q^{61} +3.48496e47 q^{62} +2.91965e47 q^{63} -5.11611e47 q^{64} -2.31967e48 q^{65} -1.69495e47 q^{66} +7.15705e47 q^{67} +3.88812e48 q^{68} -7.11416e47 q^{69} +1.03444e49 q^{70} -9.79077e48 q^{71} +2.89542e48 q^{72} -2.48596e49 q^{73} +2.70254e49 q^{74} +1.62155e49 q^{75} -1.07129e50 q^{76} +1.61836e49 q^{77} +8.38622e49 q^{78} -2.29029e50 q^{79} +4.37835e50 q^{80} +2.73832e50 q^{81} +3.83601e50 q^{82} -8.70995e50 q^{83} -1.72767e50 q^{84} -2.41946e51 q^{85} +1.38235e51 q^{86} -4.46744e50 q^{87} +1.60493e50 q^{88} +2.82739e51 q^{89} +1.09438e52 q^{90} -8.00725e51 q^{91} -4.09163e51 q^{92} +3.62186e51 q^{93} -3.81311e52 q^{94} +6.66634e52 q^{95} -1.38335e52 q^{96} -5.70641e52 q^{97} -4.41079e52 q^{98} +1.71212e52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + O(q^{10}) \) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + \)\(23\!\cdots\!00\)\(q^{10} + \)\(24\!\cdots\!28\)\(q^{11} - \)\(36\!\cdots\!40\)\(q^{12} + \)\(38\!\cdots\!40\)\(q^{13} - \)\(23\!\cdots\!24\)\(q^{14} + \)\(10\!\cdots\!00\)\(q^{15} - \)\(15\!\cdots\!36\)\(q^{16} - \)\(86\!\cdots\!60\)\(q^{17} - \)\(67\!\cdots\!80\)\(q^{18} - \)\(25\!\cdots\!60\)\(q^{19} - \)\(13\!\cdots\!00\)\(q^{20} - \)\(45\!\cdots\!32\)\(q^{21} - \)\(93\!\cdots\!40\)\(q^{22} + \)\(69\!\cdots\!60\)\(q^{23} + \)\(80\!\cdots\!20\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} + \)\(88\!\cdots\!88\)\(q^{26} + \)\(85\!\cdots\!40\)\(q^{27} - \)\(56\!\cdots\!60\)\(q^{28} - \)\(14\!\cdots\!40\)\(q^{29} - \)\(57\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!32\)\(q^{31} + \)\(34\!\cdots\!80\)\(q^{32} + \)\(26\!\cdots\!40\)\(q^{33} + \)\(14\!\cdots\!36\)\(q^{34} + \)\(61\!\cdots\!00\)\(q^{35} + \)\(74\!\cdots\!84\)\(q^{36} - \)\(28\!\cdots\!80\)\(q^{37} - \)\(21\!\cdots\!40\)\(q^{38} - \)\(36\!\cdots\!16\)\(q^{39} - \)\(53\!\cdots\!00\)\(q^{40} + \)\(81\!\cdots\!88\)\(q^{41} + \)\(34\!\cdots\!40\)\(q^{42} + \)\(45\!\cdots\!00\)\(q^{43} + \)\(36\!\cdots\!96\)\(q^{44} - \)\(52\!\cdots\!00\)\(q^{45} - \)\(28\!\cdots\!52\)\(q^{46} - \)\(45\!\cdots\!40\)\(q^{47} - \)\(30\!\cdots\!40\)\(q^{48} + \)\(61\!\cdots\!28\)\(q^{49} + \)\(52\!\cdots\!00\)\(q^{50} + \)\(48\!\cdots\!48\)\(q^{51} + \)\(64\!\cdots\!00\)\(q^{52} + \)\(38\!\cdots\!20\)\(q^{53} - \)\(90\!\cdots\!60\)\(q^{54} - \)\(25\!\cdots\!00\)\(q^{55} - \)\(41\!\cdots\!60\)\(q^{56} - \)\(78\!\cdots\!20\)\(q^{57} + \)\(23\!\cdots\!40\)\(q^{58} + \)\(16\!\cdots\!20\)\(q^{59} + \)\(40\!\cdots\!00\)\(q^{60} + \)\(65\!\cdots\!28\)\(q^{61} + \)\(39\!\cdots\!60\)\(q^{62} - \)\(30\!\cdots\!20\)\(q^{63} - \)\(10\!\cdots\!32\)\(q^{64} - \)\(34\!\cdots\!00\)\(q^{65} - \)\(65\!\cdots\!04\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} + \)\(28\!\cdots\!20\)\(q^{68} + \)\(77\!\cdots\!64\)\(q^{69} + \)\(33\!\cdots\!00\)\(q^{70} + \)\(35\!\cdots\!48\)\(q^{71} + \)\(26\!\cdots\!20\)\(q^{72} - \)\(70\!\cdots\!40\)\(q^{73} - \)\(24\!\cdots\!44\)\(q^{74} - \)\(21\!\cdots\!00\)\(q^{75} + \)\(45\!\cdots\!80\)\(q^{76} - \)\(16\!\cdots\!00\)\(q^{77} + \)\(51\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!40\)\(q^{79} + \)\(11\!\cdots\!00\)\(q^{80} - \)\(49\!\cdots\!56\)\(q^{81} + \)\(15\!\cdots\!60\)\(q^{82} - \)\(26\!\cdots\!20\)\(q^{83} - \)\(76\!\cdots\!24\)\(q^{84} - \)\(23\!\cdots\!00\)\(q^{85} - \)\(77\!\cdots\!32\)\(q^{86} - \)\(45\!\cdots\!80\)\(q^{87} + \)\(56\!\cdots\!80\)\(q^{88} - \)\(37\!\cdots\!20\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(12\!\cdots\!28\)\(q^{91} + \)\(89\!\cdots\!40\)\(q^{92} - \)\(99\!\cdots\!60\)\(q^{93} - \)\(37\!\cdots\!84\)\(q^{94} - \)\(17\!\cdots\!00\)\(q^{95} - \)\(11\!\cdots\!92\)\(q^{96} + \)\(10\!\cdots\!60\)\(q^{97} - \)\(88\!\cdots\!40\)\(q^{98} + \)\(20\!\cdots\!84\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29387e8 1.36332 0.681659 0.731670i \(-0.261259\pi\)
0.681659 + 0.731670i \(0.261259\pi\)
\(3\) 1.34470e12 0.305431 0.152715 0.988270i \(-0.451198\pi\)
0.152715 + 0.988270i \(0.451198\pi\)
\(4\) 7.73392e15 0.858638
\(5\) −4.81259e18 −1.44435 −0.722177 0.691708i \(-0.756858\pi\)
−0.722177 + 0.691708i \(0.756858\pi\)
\(6\) 1.73988e20 0.416400
\(7\) −1.66125e22 −0.668863 −0.334432 0.942420i \(-0.608544\pi\)
−0.334432 + 0.942420i \(0.608544\pi\)
\(8\) −1.64746e23 −0.192722
\(9\) −1.75750e25 −0.906712
\(10\) −6.22689e26 −1.96912
\(11\) −9.74180e26 −0.246452 −0.123226 0.992379i \(-0.539324\pi\)
−0.123226 + 0.992379i \(0.539324\pi\)
\(12\) 1.03998e28 0.262254
\(13\) 4.82001e29 1.45730 0.728650 0.684886i \(-0.240148\pi\)
0.728650 + 0.684886i \(0.240148\pi\)
\(14\) −2.14945e30 −0.911873
\(15\) −6.47150e30 −0.441150
\(16\) −9.09771e31 −1.12138
\(17\) 5.02736e32 1.24292 0.621460 0.783446i \(-0.286540\pi\)
0.621460 + 0.783446i \(0.286540\pi\)
\(18\) −2.27399e33 −1.23614
\(19\) −1.38519e34 −1.79696 −0.898479 0.439017i \(-0.855327\pi\)
−0.898479 + 0.439017i \(0.855327\pi\)
\(20\) −3.72202e34 −1.24018
\(21\) −2.23389e34 −0.204291
\(22\) −1.26047e35 −0.335993
\(23\) −5.29051e35 −0.434220 −0.217110 0.976147i \(-0.569663\pi\)
−0.217110 + 0.976147i \(0.569663\pi\)
\(24\) −2.21535e35 −0.0588633
\(25\) 1.20588e37 1.08616
\(26\) 6.23649e37 1.98676
\(27\) −4.96979e37 −0.582369
\(28\) −1.28480e38 −0.574311
\(29\) −3.32225e38 −0.585984 −0.292992 0.956115i \(-0.594651\pi\)
−0.292992 + 0.956115i \(0.594651\pi\)
\(30\) −8.37331e38 −0.601429
\(31\) 2.69343e39 0.811374 0.405687 0.914012i \(-0.367032\pi\)
0.405687 + 0.914012i \(0.367032\pi\)
\(32\) −1.02874e40 −1.33607
\(33\) −1.30998e39 −0.0752742
\(34\) 6.50477e40 1.69450
\(35\) 7.99492e40 0.966075
\(36\) −1.35924e41 −0.778537
\(37\) 2.08872e41 0.578808 0.289404 0.957207i \(-0.406543\pi\)
0.289404 + 0.957207i \(0.406543\pi\)
\(38\) −1.79226e42 −2.44983
\(39\) 6.48148e41 0.445105
\(40\) 7.92857e41 0.278359
\(41\) 2.96475e42 0.541022 0.270511 0.962717i \(-0.412807\pi\)
0.270511 + 0.962717i \(0.412807\pi\)
\(42\) −2.89037e42 −0.278514
\(43\) 1.06838e43 0.551837 0.275919 0.961181i \(-0.411018\pi\)
0.275919 + 0.961181i \(0.411018\pi\)
\(44\) −7.53423e42 −0.211613
\(45\) 8.45814e43 1.30961
\(46\) −6.84525e43 −0.591980
\(47\) −2.94705e44 −1.44143 −0.720716 0.693230i \(-0.756187\pi\)
−0.720716 + 0.693230i \(0.756187\pi\)
\(48\) −1.22337e44 −0.342504
\(49\) −3.40898e44 −0.552622
\(50\) 1.56026e45 1.48078
\(51\) 6.76030e44 0.379626
\(52\) 3.72776e45 1.25129
\(53\) −5.52073e45 −1.11863 −0.559314 0.828956i \(-0.688936\pi\)
−0.559314 + 0.828956i \(0.688936\pi\)
\(54\) −6.43028e45 −0.793954
\(55\) 4.68833e45 0.355965
\(56\) 2.73685e45 0.128905
\(57\) −1.86266e46 −0.548846
\(58\) −4.29858e46 −0.798883
\(59\) 1.07917e47 1.27501 0.637503 0.770448i \(-0.279967\pi\)
0.637503 + 0.770448i \(0.279967\pi\)
\(60\) −5.00501e46 −0.378788
\(61\) 3.62994e46 0.177280 0.0886398 0.996064i \(-0.471748\pi\)
0.0886398 + 0.996064i \(0.471748\pi\)
\(62\) 3.48496e47 1.10616
\(63\) 2.91965e47 0.606466
\(64\) −5.11611e47 −0.700117
\(65\) −2.31967e48 −2.10486
\(66\) −1.69495e47 −0.102623
\(67\) 7.15705e47 0.290905 0.145453 0.989365i \(-0.453536\pi\)
0.145453 + 0.989365i \(0.453536\pi\)
\(68\) 3.88812e48 1.06722
\(69\) −7.11416e47 −0.132624
\(70\) 1.03444e49 1.31707
\(71\) −9.79077e48 −0.855994 −0.427997 0.903780i \(-0.640781\pi\)
−0.427997 + 0.903780i \(0.640781\pi\)
\(72\) 2.89542e48 0.174743
\(73\) −2.48596e49 −1.04097 −0.520485 0.853871i \(-0.674249\pi\)
−0.520485 + 0.853871i \(0.674249\pi\)
\(74\) 2.70254e49 0.789100
\(75\) 1.62155e49 0.331747
\(76\) −1.07129e50 −1.54294
\(77\) 1.61836e49 0.164843
\(78\) 8.38622e49 0.606819
\(79\) −2.29029e50 −1.18242 −0.591210 0.806517i \(-0.701350\pi\)
−0.591210 + 0.806517i \(0.701350\pi\)
\(80\) 4.37835e50 1.61967
\(81\) 2.73832e50 0.728839
\(82\) 3.83601e50 0.737586
\(83\) −8.70995e50 −1.21464 −0.607318 0.794459i \(-0.707755\pi\)
−0.607318 + 0.794459i \(0.707755\pi\)
\(84\) −1.72767e50 −0.175412
\(85\) −2.41946e51 −1.79522
\(86\) 1.38235e51 0.752330
\(87\) −4.46744e50 −0.178978
\(88\) 1.60493e50 0.0474968
\(89\) 2.82739e51 0.620227 0.310114 0.950700i \(-0.399633\pi\)
0.310114 + 0.950700i \(0.399633\pi\)
\(90\) 1.09438e52 1.78542
\(91\) −8.00725e51 −0.974734
\(92\) −4.09163e51 −0.372837
\(93\) 3.62186e51 0.247819
\(94\) −3.81311e52 −1.96513
\(95\) 6.66634e52 2.59544
\(96\) −1.38335e52 −0.408079
\(97\) −5.70641e52 −1.27912 −0.639561 0.768740i \(-0.720884\pi\)
−0.639561 + 0.768740i \(0.720884\pi\)
\(98\) −4.41079e52 −0.753400
\(99\) 1.71212e52 0.223461
\(100\) 9.32617e52 0.932617
\(101\) 2.16630e52 0.166418 0.0832092 0.996532i \(-0.473483\pi\)
0.0832092 + 0.996532i \(0.473483\pi\)
\(102\) 8.74698e52 0.517552
\(103\) 1.64434e53 0.751284 0.375642 0.926765i \(-0.377422\pi\)
0.375642 + 0.926765i \(0.377422\pi\)
\(104\) −7.94079e52 −0.280854
\(105\) 1.07508e53 0.295069
\(106\) −7.14313e53 −1.52505
\(107\) −6.28499e53 −1.04625 −0.523124 0.852257i \(-0.675234\pi\)
−0.523124 + 0.852257i \(0.675234\pi\)
\(108\) −3.84359e53 −0.500044
\(109\) 1.11123e54 1.13240 0.566201 0.824267i \(-0.308412\pi\)
0.566201 + 0.824267i \(0.308412\pi\)
\(110\) 6.06611e53 0.485293
\(111\) 2.80871e53 0.176786
\(112\) 1.51136e54 0.750049
\(113\) 3.22273e53 0.126371 0.0631853 0.998002i \(-0.479874\pi\)
0.0631853 + 0.998002i \(0.479874\pi\)
\(114\) −2.41005e54 −0.748253
\(115\) 2.54610e54 0.627167
\(116\) −2.56940e54 −0.503148
\(117\) −8.47118e54 −1.32135
\(118\) 1.39631e55 1.73824
\(119\) −8.35170e54 −0.831344
\(120\) 1.06616e54 0.0850194
\(121\) −1.46757e55 −0.939261
\(122\) 4.69669e54 0.241689
\(123\) 3.98670e54 0.165245
\(124\) 2.08308e55 0.696676
\(125\) −4.60355e54 −0.124445
\(126\) 3.77766e55 0.826807
\(127\) 1.88562e55 0.334700 0.167350 0.985898i \(-0.446479\pi\)
0.167350 + 0.985898i \(0.446479\pi\)
\(128\) 2.64645e55 0.381593
\(129\) 1.43665e55 0.168548
\(130\) −3.00137e56 −2.86959
\(131\) −7.70511e55 −0.601298 −0.300649 0.953735i \(-0.597203\pi\)
−0.300649 + 0.953735i \(0.597203\pi\)
\(132\) −1.01313e55 −0.0646332
\(133\) 2.30114e56 1.20192
\(134\) 9.26033e55 0.396597
\(135\) 2.39176e56 0.841147
\(136\) −8.28239e55 −0.239538
\(137\) 2.23996e56 0.533513 0.266757 0.963764i \(-0.414048\pi\)
0.266757 + 0.963764i \(0.414048\pi\)
\(138\) −9.20483e55 −0.180809
\(139\) −4.13628e56 −0.670993 −0.335496 0.942042i \(-0.608904\pi\)
−0.335496 + 0.942042i \(0.608904\pi\)
\(140\) 6.18321e56 0.829509
\(141\) −3.96291e56 −0.440258
\(142\) −1.26680e57 −1.16699
\(143\) −4.69556e56 −0.359155
\(144\) 1.59892e57 1.01677
\(145\) 1.59886e57 0.846369
\(146\) −3.21652e57 −1.41917
\(147\) −4.58406e56 −0.168788
\(148\) 1.61540e57 0.496986
\(149\) −2.00904e57 −0.517073 −0.258536 0.966001i \(-0.583240\pi\)
−0.258536 + 0.966001i \(0.583240\pi\)
\(150\) 2.09808e57 0.452276
\(151\) 1.00882e58 1.82358 0.911790 0.410656i \(-0.134700\pi\)
0.911790 + 0.410656i \(0.134700\pi\)
\(152\) 2.28205e57 0.346313
\(153\) −8.83559e57 −1.12697
\(154\) 2.09395e57 0.224733
\(155\) −1.29624e58 −1.17191
\(156\) 5.01272e57 0.382183
\(157\) −6.27576e57 −0.403948 −0.201974 0.979391i \(-0.564736\pi\)
−0.201974 + 0.979391i \(0.564736\pi\)
\(158\) −2.96334e58 −1.61202
\(159\) −7.42374e57 −0.341664
\(160\) 4.95090e58 1.92977
\(161\) 8.78886e57 0.290433
\(162\) 3.54304e58 0.993639
\(163\) 9.18357e55 0.00218796 0.00109398 0.999999i \(-0.499652\pi\)
0.00109398 + 0.999999i \(0.499652\pi\)
\(164\) 2.29291e58 0.464542
\(165\) 6.30441e57 0.108723
\(166\) −1.12696e59 −1.65594
\(167\) −3.13517e58 −0.392893 −0.196447 0.980515i \(-0.562940\pi\)
−0.196447 + 0.980515i \(0.562940\pi\)
\(168\) 3.68025e57 0.0393715
\(169\) 1.22930e59 1.12372
\(170\) −3.13048e59 −2.44745
\(171\) 2.43447e59 1.62932
\(172\) 8.26275e58 0.473828
\(173\) −4.28978e58 −0.210966 −0.105483 0.994421i \(-0.533639\pi\)
−0.105483 + 0.994421i \(0.533639\pi\)
\(174\) −5.78031e58 −0.244004
\(175\) −2.00327e59 −0.726492
\(176\) 8.86280e58 0.276367
\(177\) 1.45117e59 0.389426
\(178\) 3.65829e59 0.845567
\(179\) 1.12342e59 0.223840 0.111920 0.993717i \(-0.464300\pi\)
0.111920 + 0.993717i \(0.464300\pi\)
\(180\) 6.54146e59 1.12448
\(181\) −6.03513e59 −0.895786 −0.447893 0.894087i \(-0.647825\pi\)
−0.447893 + 0.894087i \(0.647825\pi\)
\(182\) −1.03604e60 −1.32887
\(183\) 4.88119e58 0.0541467
\(184\) 8.71592e58 0.0836837
\(185\) −1.00522e60 −0.836004
\(186\) 4.68624e59 0.337856
\(187\) −4.89755e59 −0.306321
\(188\) −2.27922e60 −1.23767
\(189\) 8.25606e59 0.389525
\(190\) 8.62540e60 3.53842
\(191\) −1.23426e60 −0.440577 −0.220289 0.975435i \(-0.570700\pi\)
−0.220289 + 0.975435i \(0.570700\pi\)
\(192\) −6.87964e59 −0.213837
\(193\) 4.53607e60 1.22860 0.614301 0.789072i \(-0.289438\pi\)
0.614301 + 0.789072i \(0.289438\pi\)
\(194\) −7.38338e60 −1.74385
\(195\) −3.11927e60 −0.642889
\(196\) −2.63648e60 −0.474502
\(197\) −2.14130e60 −0.336761 −0.168381 0.985722i \(-0.553854\pi\)
−0.168381 + 0.985722i \(0.553854\pi\)
\(198\) 2.21527e60 0.304649
\(199\) 9.14306e59 0.110023 0.0550117 0.998486i \(-0.482480\pi\)
0.0550117 + 0.998486i \(0.482480\pi\)
\(200\) −1.98664e60 −0.209327
\(201\) 9.62411e59 0.0888515
\(202\) 2.80292e60 0.226881
\(203\) 5.51910e60 0.391943
\(204\) 5.22836e60 0.325961
\(205\) −1.42681e61 −0.781428
\(206\) 2.12756e61 1.02424
\(207\) 9.29807e60 0.393712
\(208\) −4.38510e61 −1.63419
\(209\) 1.34942e61 0.442864
\(210\) 1.39102e61 0.402273
\(211\) 6.72523e61 1.71483 0.857417 0.514623i \(-0.172068\pi\)
0.857417 + 0.514623i \(0.172068\pi\)
\(212\) −4.26969e61 −0.960497
\(213\) −1.31657e61 −0.261447
\(214\) −8.13199e61 −1.42637
\(215\) −5.14167e61 −0.797049
\(216\) 8.18755e60 0.112235
\(217\) −4.47447e61 −0.542698
\(218\) 1.43779e62 1.54383
\(219\) −3.34288e61 −0.317944
\(220\) 3.62592e61 0.305645
\(221\) 2.42319e62 1.81131
\(222\) 3.63412e61 0.241015
\(223\) −1.36676e62 −0.804660 −0.402330 0.915495i \(-0.631799\pi\)
−0.402330 + 0.915495i \(0.631799\pi\)
\(224\) 1.70899e62 0.893651
\(225\) −2.11934e62 −0.984834
\(226\) 4.16981e61 0.172283
\(227\) −4.41921e62 −1.62427 −0.812137 0.583467i \(-0.801696\pi\)
−0.812137 + 0.583467i \(0.801696\pi\)
\(228\) −1.44057e62 −0.471260
\(229\) −1.20175e62 −0.350087 −0.175043 0.984561i \(-0.556007\pi\)
−0.175043 + 0.984561i \(0.556007\pi\)
\(230\) 3.29434e62 0.855029
\(231\) 2.17621e61 0.0503481
\(232\) 5.47329e61 0.112932
\(233\) 3.74033e62 0.688618 0.344309 0.938856i \(-0.388113\pi\)
0.344309 + 0.938856i \(0.388113\pi\)
\(234\) −1.09606e63 −1.80142
\(235\) 1.41829e63 2.08194
\(236\) 8.34623e62 1.09477
\(237\) −3.07975e62 −0.361148
\(238\) −1.08061e63 −1.13339
\(239\) −2.03152e62 −0.190668 −0.0953339 0.995445i \(-0.530392\pi\)
−0.0953339 + 0.995445i \(0.530392\pi\)
\(240\) 5.88758e62 0.494697
\(241\) 2.85110e62 0.214566 0.107283 0.994229i \(-0.465785\pi\)
0.107283 + 0.994229i \(0.465785\pi\)
\(242\) −1.89885e63 −1.28051
\(243\) 1.33153e63 0.804979
\(244\) 2.80737e62 0.152219
\(245\) 1.64060e63 0.798182
\(246\) 5.15829e62 0.225282
\(247\) −6.67661e63 −2.61871
\(248\) −4.43733e62 −0.156370
\(249\) −1.17123e63 −0.370987
\(250\) −5.95642e62 −0.169658
\(251\) 7.65328e63 1.96107 0.980537 0.196336i \(-0.0629045\pi\)
0.980537 + 0.196336i \(0.0629045\pi\)
\(252\) 2.25804e63 0.520735
\(253\) 5.15390e62 0.107014
\(254\) 2.43976e63 0.456302
\(255\) −3.25346e63 −0.548315
\(256\) 8.03236e63 1.22035
\(257\) −3.77322e63 −0.516993 −0.258496 0.966012i \(-0.583227\pi\)
−0.258496 + 0.966012i \(0.583227\pi\)
\(258\) 1.85885e63 0.229785
\(259\) −3.46989e63 −0.387143
\(260\) −1.79402e64 −1.80731
\(261\) 5.83887e63 0.531319
\(262\) −9.96945e63 −0.819761
\(263\) −2.00429e64 −1.48982 −0.744911 0.667164i \(-0.767508\pi\)
−0.744911 + 0.667164i \(0.767508\pi\)
\(264\) 2.15815e62 0.0145070
\(265\) 2.65690e64 1.61570
\(266\) 2.97739e64 1.63860
\(267\) 3.80200e63 0.189437
\(268\) 5.53521e63 0.249782
\(269\) −3.27370e64 −1.33846 −0.669228 0.743058i \(-0.733375\pi\)
−0.669228 + 0.743058i \(0.733375\pi\)
\(270\) 3.09463e64 1.14675
\(271\) 1.33847e64 0.449699 0.224849 0.974394i \(-0.427811\pi\)
0.224849 + 0.974394i \(0.427811\pi\)
\(272\) −4.57374e64 −1.39379
\(273\) −1.07674e64 −0.297714
\(274\) 2.89823e64 0.727348
\(275\) −1.17474e64 −0.267687
\(276\) −5.50203e63 −0.113876
\(277\) 4.06188e64 0.763858 0.381929 0.924192i \(-0.375260\pi\)
0.381929 + 0.924192i \(0.375260\pi\)
\(278\) −5.35183e64 −0.914777
\(279\) −4.73371e64 −0.735682
\(280\) −1.31713e64 −0.186184
\(281\) 7.96754e64 1.02472 0.512362 0.858770i \(-0.328771\pi\)
0.512362 + 0.858770i \(0.328771\pi\)
\(282\) −5.12750e64 −0.600212
\(283\) 4.10609e64 0.437611 0.218806 0.975768i \(-0.429784\pi\)
0.218806 + 0.975768i \(0.429784\pi\)
\(284\) −7.57210e64 −0.734988
\(285\) 8.96424e64 0.792729
\(286\) −6.07546e64 −0.489643
\(287\) −4.92519e64 −0.361870
\(288\) 1.80801e65 1.21144
\(289\) 8.91397e64 0.544852
\(290\) 2.06873e65 1.15387
\(291\) −7.67342e64 −0.390683
\(292\) −1.92262e65 −0.893816
\(293\) 1.54719e65 0.656980 0.328490 0.944507i \(-0.393460\pi\)
0.328490 + 0.944507i \(0.393460\pi\)
\(294\) −5.93120e64 −0.230112
\(295\) −5.19361e65 −1.84156
\(296\) −3.44109e64 −0.111549
\(297\) 4.84147e64 0.143526
\(298\) −2.59944e65 −0.704935
\(299\) −2.55003e65 −0.632788
\(300\) 1.25409e65 0.284850
\(301\) −1.77484e65 −0.369104
\(302\) 1.30529e66 2.48612
\(303\) 2.91302e64 0.0508293
\(304\) 1.26020e66 2.01507
\(305\) −1.74694e65 −0.256055
\(306\) −1.14321e66 −1.53642
\(307\) −5.91230e64 −0.0728769 −0.0364384 0.999336i \(-0.511601\pi\)
−0.0364384 + 0.999336i \(0.511601\pi\)
\(308\) 1.25162e65 0.141540
\(309\) 2.21114e65 0.229465
\(310\) −1.67717e66 −1.59769
\(311\) 6.42175e63 0.00561699 0.00280849 0.999996i \(-0.499106\pi\)
0.00280849 + 0.999996i \(0.499106\pi\)
\(312\) −1.06780e65 −0.0857815
\(313\) 1.94924e66 1.43860 0.719302 0.694698i \(-0.244462\pi\)
0.719302 + 0.694698i \(0.244462\pi\)
\(314\) −8.12005e65 −0.550710
\(315\) −1.40511e66 −0.875952
\(316\) −1.77129e66 −1.01527
\(317\) 3.17927e66 1.67593 0.837967 0.545721i \(-0.183744\pi\)
0.837967 + 0.545721i \(0.183744\pi\)
\(318\) −9.60539e65 −0.465797
\(319\) 3.23647e65 0.144417
\(320\) 2.46217e66 1.01122
\(321\) −8.45145e65 −0.319557
\(322\) 1.13717e66 0.395953
\(323\) −6.96383e66 −2.23348
\(324\) 2.11780e66 0.625808
\(325\) 5.81235e66 1.58286
\(326\) 1.18824e64 0.00298289
\(327\) 1.49427e66 0.345871
\(328\) −4.88431e65 −0.104267
\(329\) 4.89579e66 0.964121
\(330\) 8.15711e65 0.148224
\(331\) −9.10692e66 −1.52732 −0.763659 0.645620i \(-0.776599\pi\)
−0.763659 + 0.645620i \(0.776599\pi\)
\(332\) −6.73621e66 −1.04293
\(333\) −3.67093e66 −0.524812
\(334\) −4.05651e66 −0.535638
\(335\) −3.44440e66 −0.420171
\(336\) 2.03233e66 0.229088
\(337\) 6.75654e66 0.703934 0.351967 0.936012i \(-0.385513\pi\)
0.351967 + 0.936012i \(0.385513\pi\)
\(338\) 1.59056e67 1.53199
\(339\) 4.33362e65 0.0385975
\(340\) −1.87119e67 −1.54144
\(341\) −2.62389e66 −0.199965
\(342\) 3.14990e67 2.22129
\(343\) 1.59110e67 1.03849
\(344\) −1.76012e66 −0.106351
\(345\) 3.42375e66 0.191556
\(346\) −5.55043e66 −0.287614
\(347\) −3.44317e67 −1.65283 −0.826413 0.563064i \(-0.809622\pi\)
−0.826413 + 0.563064i \(0.809622\pi\)
\(348\) −3.45508e66 −0.153677
\(349\) 3.11481e66 0.128398 0.0641989 0.997937i \(-0.479551\pi\)
0.0641989 + 0.997937i \(0.479551\pi\)
\(350\) −2.59198e67 −0.990440
\(351\) −2.39544e67 −0.848686
\(352\) 1.00218e67 0.329279
\(353\) −8.64866e66 −0.263584 −0.131792 0.991277i \(-0.542073\pi\)
−0.131792 + 0.991277i \(0.542073\pi\)
\(354\) 1.87763e67 0.530912
\(355\) 4.71190e67 1.23636
\(356\) 2.18668e67 0.532550
\(357\) −1.12306e67 −0.253918
\(358\) 1.45357e67 0.305166
\(359\) −5.93891e67 −1.15799 −0.578993 0.815332i \(-0.696554\pi\)
−0.578993 + 0.815332i \(0.696554\pi\)
\(360\) −1.39345e67 −0.252391
\(361\) 1.32453e68 2.22906
\(362\) −7.80870e67 −1.22124
\(363\) −1.97344e67 −0.286879
\(364\) −6.19274e67 −0.836944
\(365\) 1.19639e68 1.50353
\(366\) 6.31565e66 0.0738192
\(367\) 1.25080e66 0.0136000 0.00679999 0.999977i \(-0.497835\pi\)
0.00679999 + 0.999977i \(0.497835\pi\)
\(368\) 4.81315e67 0.486925
\(369\) −5.21055e67 −0.490551
\(370\) −1.30062e68 −1.13974
\(371\) 9.17132e67 0.748209
\(372\) 2.80112e67 0.212786
\(373\) −2.22554e68 −1.57453 −0.787267 0.616613i \(-0.788504\pi\)
−0.787267 + 0.616613i \(0.788504\pi\)
\(374\) −6.33682e67 −0.417613
\(375\) −6.19041e66 −0.0380094
\(376\) 4.85516e67 0.277796
\(377\) −1.60133e68 −0.853955
\(378\) 1.06823e68 0.531047
\(379\) 1.79817e68 0.833474 0.416737 0.909027i \(-0.363174\pi\)
0.416737 + 0.909027i \(0.363174\pi\)
\(380\) 5.15569e68 2.22855
\(381\) 2.53560e67 0.102228
\(382\) −1.59698e68 −0.600647
\(383\) −7.96579e67 −0.279551 −0.139776 0.990183i \(-0.544638\pi\)
−0.139776 + 0.990183i \(0.544638\pi\)
\(384\) 3.55869e67 0.116550
\(385\) −7.78849e67 −0.238092
\(386\) 5.86911e68 1.67498
\(387\) −1.87768e68 −0.500357
\(388\) −4.41329e68 −1.09830
\(389\) −4.61806e68 −1.07348 −0.536741 0.843747i \(-0.680345\pi\)
−0.536741 + 0.843747i \(0.680345\pi\)
\(390\) −4.03595e68 −0.876462
\(391\) −2.65973e68 −0.539701
\(392\) 5.61617e67 0.106502
\(393\) −1.03611e68 −0.183655
\(394\) −2.77057e68 −0.459113
\(395\) 1.10222e69 1.70783
\(396\) 1.32414e68 0.191872
\(397\) 9.49592e68 1.28703 0.643515 0.765434i \(-0.277475\pi\)
0.643515 + 0.765434i \(0.277475\pi\)
\(398\) 1.18300e68 0.149997
\(399\) 3.09435e68 0.367103
\(400\) −1.09707e69 −1.21800
\(401\) −4.54047e68 −0.471818 −0.235909 0.971775i \(-0.575807\pi\)
−0.235909 + 0.971775i \(0.575807\pi\)
\(402\) 1.24524e68 0.121133
\(403\) 1.29824e69 1.18242
\(404\) 1.67540e68 0.142893
\(405\) −1.31784e69 −1.05270
\(406\) 7.14102e68 0.534343
\(407\) −2.03479e68 −0.142649
\(408\) −1.11374e68 −0.0731624
\(409\) −4.09199e68 −0.251923 −0.125961 0.992035i \(-0.540202\pi\)
−0.125961 + 0.992035i \(0.540202\pi\)
\(410\) −1.84611e69 −1.06534
\(411\) 3.01208e68 0.162951
\(412\) 1.27172e69 0.645080
\(413\) −1.79278e69 −0.852805
\(414\) 1.20305e69 0.536755
\(415\) 4.19174e69 1.75437
\(416\) −4.95853e69 −1.94706
\(417\) −5.56207e68 −0.204942
\(418\) 1.74598e69 0.603765
\(419\) −3.39626e69 −1.10238 −0.551188 0.834381i \(-0.685825\pi\)
−0.551188 + 0.834381i \(0.685825\pi\)
\(420\) 8.31457e68 0.253358
\(421\) −5.62917e69 −1.61053 −0.805264 0.592916i \(-0.797977\pi\)
−0.805264 + 0.592916i \(0.797977\pi\)
\(422\) 8.70160e69 2.33786
\(423\) 5.17945e69 1.30696
\(424\) 9.09521e68 0.215584
\(425\) 6.06239e69 1.35001
\(426\) −1.70347e69 −0.356435
\(427\) −6.03024e68 −0.118576
\(428\) −4.86076e69 −0.898348
\(429\) −6.31413e68 −0.109697
\(430\) −6.65267e69 −1.08663
\(431\) −4.87848e69 −0.749267 −0.374633 0.927173i \(-0.622231\pi\)
−0.374633 + 0.927173i \(0.622231\pi\)
\(432\) 4.52137e69 0.653056
\(433\) −1.12249e70 −1.52494 −0.762469 0.647025i \(-0.776013\pi\)
−0.762469 + 0.647025i \(0.776013\pi\)
\(434\) −5.78940e69 −0.739870
\(435\) 2.15000e69 0.258507
\(436\) 8.59415e69 0.972323
\(437\) 7.32834e69 0.780274
\(438\) −4.32526e69 −0.433460
\(439\) −1.69286e68 −0.0159702 −0.00798509 0.999968i \(-0.502542\pi\)
−0.00798509 + 0.999968i \(0.502542\pi\)
\(440\) −7.72385e68 −0.0686022
\(441\) 5.99129e69 0.501069
\(442\) 3.13531e70 2.46939
\(443\) −1.39750e69 −0.103670 −0.0518351 0.998656i \(-0.516507\pi\)
−0.0518351 + 0.998656i \(0.516507\pi\)
\(444\) 2.17223e69 0.151795
\(445\) −1.36071e70 −0.895828
\(446\) −1.76841e70 −1.09701
\(447\) −2.70156e69 −0.157930
\(448\) 8.49914e69 0.468282
\(449\) 1.04380e70 0.542110 0.271055 0.962564i \(-0.412627\pi\)
0.271055 + 0.962564i \(0.412627\pi\)
\(450\) −2.74215e70 −1.34264
\(451\) −2.88820e69 −0.133336
\(452\) 2.49244e69 0.108506
\(453\) 1.35656e70 0.556978
\(454\) −5.71790e70 −2.21440
\(455\) 3.85356e70 1.40786
\(456\) 3.06867e69 0.105775
\(457\) 3.06454e70 0.996751 0.498376 0.866961i \(-0.333930\pi\)
0.498376 + 0.866961i \(0.333930\pi\)
\(458\) −1.55492e70 −0.477280
\(459\) −2.49849e70 −0.723838
\(460\) 1.96914e70 0.538509
\(461\) −1.38267e70 −0.356979 −0.178489 0.983942i \(-0.557121\pi\)
−0.178489 + 0.983942i \(0.557121\pi\)
\(462\) 2.81574e69 0.0686405
\(463\) −2.87526e69 −0.0661882 −0.0330941 0.999452i \(-0.510536\pi\)
−0.0330941 + 0.999452i \(0.510536\pi\)
\(464\) 3.02249e70 0.657110
\(465\) −1.74305e70 −0.357938
\(466\) 4.83952e70 0.938805
\(467\) −3.27527e69 −0.0600275 −0.0300137 0.999549i \(-0.509555\pi\)
−0.0300137 + 0.999549i \(0.509555\pi\)
\(468\) −6.55154e70 −1.13456
\(469\) −1.18897e70 −0.194576
\(470\) 1.83510e71 2.83835
\(471\) −8.43903e69 −0.123378
\(472\) −1.77790e70 −0.245722
\(473\) −1.04079e70 −0.136002
\(474\) −3.98482e70 −0.492359
\(475\) −1.67037e71 −1.95178
\(476\) −6.45914e70 −0.713823
\(477\) 9.70269e70 1.01427
\(478\) −2.62854e70 −0.259941
\(479\) −1.92415e71 −1.80032 −0.900158 0.435564i \(-0.856549\pi\)
−0.900158 + 0.435564i \(0.856549\pi\)
\(480\) 6.65749e70 0.589410
\(481\) 1.00677e71 0.843497
\(482\) 3.68897e70 0.292522
\(483\) 1.18184e70 0.0887074
\(484\) −1.13501e71 −0.806485
\(485\) 2.74626e71 1.84751
\(486\) 1.72283e71 1.09744
\(487\) −1.33015e71 −0.802388 −0.401194 0.915993i \(-0.631405\pi\)
−0.401194 + 0.915993i \(0.631405\pi\)
\(488\) −5.98020e69 −0.0341657
\(489\) 1.23492e68 0.000668272 0
\(490\) 2.12273e71 1.08818
\(491\) 3.09725e71 1.50424 0.752120 0.659027i \(-0.229032\pi\)
0.752120 + 0.659027i \(0.229032\pi\)
\(492\) 3.08328e70 0.141886
\(493\) −1.67022e71 −0.728332
\(494\) −8.63870e71 −3.57013
\(495\) −8.23975e70 −0.322757
\(496\) −2.45041e71 −0.909858
\(497\) 1.62649e71 0.572543
\(498\) −1.51542e71 −0.505774
\(499\) 4.41016e71 1.39569 0.697847 0.716247i \(-0.254142\pi\)
0.697847 + 0.716247i \(0.254142\pi\)
\(500\) −3.56035e70 −0.106853
\(501\) −4.21587e70 −0.120002
\(502\) 9.90238e71 2.67357
\(503\) −6.61525e71 −1.69432 −0.847158 0.531341i \(-0.821688\pi\)
−0.847158 + 0.531341i \(0.821688\pi\)
\(504\) −4.81002e70 −0.116879
\(505\) −1.04255e71 −0.240367
\(506\) 6.66851e70 0.145895
\(507\) 1.65304e71 0.343220
\(508\) 1.45832e71 0.287386
\(509\) −3.73962e71 −0.699530 −0.349765 0.936837i \(-0.613739\pi\)
−0.349765 + 0.936837i \(0.613739\pi\)
\(510\) −4.20956e71 −0.747528
\(511\) 4.12980e71 0.696267
\(512\) 8.00916e71 1.28213
\(513\) 6.88408e71 1.04649
\(514\) −4.88208e71 −0.704826
\(515\) −7.91351e71 −1.08512
\(516\) 1.11109e71 0.144722
\(517\) 2.87096e71 0.355244
\(518\) −4.48960e71 −0.527800
\(519\) −5.76847e70 −0.0644356
\(520\) 3.82158e71 0.405653
\(521\) −8.23378e71 −0.830614 −0.415307 0.909681i \(-0.636326\pi\)
−0.415307 + 0.909681i \(0.636326\pi\)
\(522\) 7.55476e71 0.724357
\(523\) −1.56757e71 −0.142867 −0.0714336 0.997445i \(-0.522757\pi\)
−0.0714336 + 0.997445i \(0.522757\pi\)
\(524\) −5.95907e71 −0.516297
\(525\) −2.69380e71 −0.221893
\(526\) −2.59331e72 −2.03110
\(527\) 1.35408e72 1.00847
\(528\) 1.19178e71 0.0844109
\(529\) −1.20459e72 −0.811453
\(530\) 3.43770e72 2.20271
\(531\) −1.89665e72 −1.15606
\(532\) 1.77969e72 1.03201
\(533\) 1.42901e72 0.788432
\(534\) 4.91931e71 0.258262
\(535\) 3.02471e72 1.51115
\(536\) −1.17910e71 −0.0560639
\(537\) 1.51067e71 0.0683678
\(538\) −4.23576e72 −1.82474
\(539\) 3.32096e71 0.136195
\(540\) 1.84976e72 0.722240
\(541\) −3.10699e72 −1.15508 −0.577541 0.816362i \(-0.695987\pi\)
−0.577541 + 0.816362i \(0.695987\pi\)
\(542\) 1.73181e72 0.613082
\(543\) −8.11545e71 −0.273601
\(544\) −5.17184e72 −1.66063
\(545\) −5.34788e72 −1.63559
\(546\) −1.39316e72 −0.405879
\(547\) 6.13544e72 1.70287 0.851435 0.524460i \(-0.175733\pi\)
0.851435 + 0.524460i \(0.175733\pi\)
\(548\) 1.73237e72 0.458094
\(549\) −6.37963e71 −0.160742
\(550\) −1.51997e72 −0.364942
\(551\) 4.60194e72 1.05299
\(552\) 1.17203e71 0.0255596
\(553\) 3.80474e72 0.790877
\(554\) 5.25556e72 1.04138
\(555\) −1.35172e72 −0.255341
\(556\) −3.19897e72 −0.576140
\(557\) 3.45443e72 0.593217 0.296608 0.954999i \(-0.404144\pi\)
0.296608 + 0.954999i \(0.404144\pi\)
\(558\) −6.12483e72 −1.00297
\(559\) 5.14959e72 0.804193
\(560\) −7.27355e72 −1.08334
\(561\) −6.58575e71 −0.0935598
\(562\) 1.03090e73 1.39702
\(563\) −7.65255e72 −0.989313 −0.494656 0.869089i \(-0.664706\pi\)
−0.494656 + 0.869089i \(0.664706\pi\)
\(564\) −3.06488e72 −0.378022
\(565\) −1.55097e72 −0.182524
\(566\) 5.31277e72 0.596603
\(567\) −4.54904e72 −0.487493
\(568\) 1.61299e72 0.164969
\(569\) −1.06701e73 −1.04158 −0.520789 0.853686i \(-0.674362\pi\)
−0.520789 + 0.853686i \(0.674362\pi\)
\(570\) 1.15986e73 1.08074
\(571\) 4.28488e72 0.381137 0.190569 0.981674i \(-0.438967\pi\)
0.190569 + 0.981674i \(0.438967\pi\)
\(572\) −3.63151e72 −0.308384
\(573\) −1.65971e72 −0.134566
\(574\) −6.37257e72 −0.493344
\(575\) −6.37971e72 −0.471632
\(576\) 8.99157e72 0.634804
\(577\) −2.73962e73 −1.84727 −0.923636 0.383271i \(-0.874798\pi\)
−0.923636 + 0.383271i \(0.874798\pi\)
\(578\) 1.15336e73 0.742806
\(579\) 6.09966e72 0.375253
\(580\) 1.23655e73 0.726724
\(581\) 1.44694e73 0.812425
\(582\) −9.92845e72 −0.532626
\(583\) 5.37818e72 0.275689
\(584\) 4.09553e72 0.200618
\(585\) 4.07683e73 1.90850
\(586\) 2.00187e73 0.895673
\(587\) −1.81383e72 −0.0775689 −0.0387844 0.999248i \(-0.512349\pi\)
−0.0387844 + 0.999248i \(0.512349\pi\)
\(588\) −3.54528e72 −0.144928
\(589\) −3.73091e73 −1.45800
\(590\) −6.71988e73 −2.51063
\(591\) −2.87941e72 −0.102857
\(592\) −1.90026e73 −0.649063
\(593\) 4.87506e72 0.159232 0.0796161 0.996826i \(-0.474631\pi\)
0.0796161 + 0.996826i \(0.474631\pi\)
\(594\) 6.26425e72 0.195672
\(595\) 4.01933e73 1.20075
\(596\) −1.55377e73 −0.443978
\(597\) 1.22947e72 0.0336045
\(598\) −3.29942e73 −0.862692
\(599\) −1.49187e73 −0.373181 −0.186590 0.982438i \(-0.559744\pi\)
−0.186590 + 0.982438i \(0.559744\pi\)
\(600\) −2.67144e72 −0.0639349
\(601\) 7.02936e73 1.60969 0.804845 0.593485i \(-0.202248\pi\)
0.804845 + 0.593485i \(0.202248\pi\)
\(602\) −2.29643e73 −0.503206
\(603\) −1.25785e73 −0.263767
\(604\) 7.80214e73 1.56579
\(605\) 7.06281e73 1.35663
\(606\) 3.76909e72 0.0692966
\(607\) −9.09644e73 −1.60093 −0.800463 0.599382i \(-0.795413\pi\)
−0.800463 + 0.599382i \(0.795413\pi\)
\(608\) 1.42500e74 2.40087
\(609\) 7.42154e72 0.119712
\(610\) −2.26032e73 −0.349084
\(611\) −1.42048e74 −2.10060
\(612\) −6.83338e73 −0.967660
\(613\) −1.39239e73 −0.188825 −0.0944125 0.995533i \(-0.530097\pi\)
−0.0944125 + 0.995533i \(0.530097\pi\)
\(614\) −7.64978e72 −0.0993544
\(615\) −1.91864e73 −0.238672
\(616\) −2.66619e72 −0.0317689
\(617\) 1.12495e73 0.128403 0.0642015 0.997937i \(-0.479550\pi\)
0.0642015 + 0.997937i \(0.479550\pi\)
\(618\) 2.86094e73 0.312834
\(619\) 1.38480e74 1.45072 0.725360 0.688369i \(-0.241673\pi\)
0.725360 + 0.688369i \(0.241673\pi\)
\(620\) −1.00250e74 −1.00625
\(621\) 2.62927e73 0.252876
\(622\) 8.30895e71 0.00765774
\(623\) −4.69701e73 −0.414847
\(624\) −5.89666e73 −0.499131
\(625\) −1.11725e74 −0.906417
\(626\) 2.52208e74 1.96127
\(627\) 1.81457e73 0.135264
\(628\) −4.85362e73 −0.346845
\(629\) 1.05007e74 0.719412
\(630\) −1.81803e74 −1.19420
\(631\) −8.85014e73 −0.557406 −0.278703 0.960377i \(-0.589905\pi\)
−0.278703 + 0.960377i \(0.589905\pi\)
\(632\) 3.77317e73 0.227878
\(633\) 9.04343e73 0.523763
\(634\) 4.11358e74 2.28483
\(635\) −9.07471e73 −0.483425
\(636\) −5.74146e73 −0.293365
\(637\) −1.64313e74 −0.805337
\(638\) 4.18759e73 0.196887
\(639\) 1.72073e74 0.776140
\(640\) −1.27363e74 −0.551155
\(641\) 1.61877e74 0.672122 0.336061 0.941840i \(-0.390905\pi\)
0.336061 + 0.941840i \(0.390905\pi\)
\(642\) −1.09351e74 −0.435657
\(643\) −1.44296e74 −0.551648 −0.275824 0.961208i \(-0.588951\pi\)
−0.275824 + 0.961208i \(0.588951\pi\)
\(644\) 6.79723e73 0.249377
\(645\) −6.91401e73 −0.243443
\(646\) −9.01032e74 −3.04494
\(647\) 3.96918e72 0.0128747 0.00643735 0.999979i \(-0.497951\pi\)
0.00643735 + 0.999979i \(0.497951\pi\)
\(648\) −4.51129e73 −0.140463
\(649\) −1.05131e74 −0.314228
\(650\) 7.52045e74 2.15794
\(651\) −6.01683e73 −0.165757
\(652\) 7.10250e71 0.00187867
\(653\) 1.24882e74 0.317175 0.158588 0.987345i \(-0.449306\pi\)
0.158588 + 0.987345i \(0.449306\pi\)
\(654\) 1.93340e74 0.471532
\(655\) 3.70815e74 0.868487
\(656\) −2.69724e74 −0.606691
\(657\) 4.36908e74 0.943860
\(658\) 6.33454e74 1.31440
\(659\) −1.41749e74 −0.282524 −0.141262 0.989972i \(-0.545116\pi\)
−0.141262 + 0.989972i \(0.545116\pi\)
\(660\) 4.87578e73 0.0933533
\(661\) 3.68248e74 0.677333 0.338666 0.940906i \(-0.390024\pi\)
0.338666 + 0.940906i \(0.390024\pi\)
\(662\) −1.17832e75 −2.08222
\(663\) 3.25847e74 0.553230
\(664\) 1.43493e74 0.234087
\(665\) −1.10745e75 −1.73600
\(666\) −4.74972e74 −0.715486
\(667\) 1.75764e74 0.254446
\(668\) −2.42471e74 −0.337353
\(669\) −1.83788e74 −0.245768
\(670\) −4.45662e74 −0.572826
\(671\) −3.53622e73 −0.0436910
\(672\) 2.29809e74 0.272949
\(673\) 1.04283e75 1.19073 0.595366 0.803455i \(-0.297007\pi\)
0.595366 + 0.803455i \(0.297007\pi\)
\(674\) 8.74211e74 0.959686
\(675\) −5.99296e74 −0.632545
\(676\) 9.50730e74 0.964872
\(677\) −1.67343e75 −1.63309 −0.816543 0.577285i \(-0.804112\pi\)
−0.816543 + 0.577285i \(0.804112\pi\)
\(678\) 5.60716e73 0.0526206
\(679\) 9.47978e74 0.855558
\(680\) 3.98598e74 0.345978
\(681\) −5.94252e74 −0.496103
\(682\) −3.39498e74 −0.272616
\(683\) −1.24036e74 −0.0958078 −0.0479039 0.998852i \(-0.515254\pi\)
−0.0479039 + 0.998852i \(0.515254\pi\)
\(684\) 1.88280e75 1.39900
\(685\) −1.07800e75 −0.770582
\(686\) 2.05868e75 1.41579
\(687\) −1.61600e74 −0.106927
\(688\) −9.71979e74 −0.618819
\(689\) −2.66100e75 −1.63018
\(690\) 4.42991e74 0.261152
\(691\) 2.95439e75 1.67610 0.838049 0.545595i \(-0.183696\pi\)
0.838049 + 0.545595i \(0.183696\pi\)
\(692\) −3.31768e74 −0.181144
\(693\) −2.84427e74 −0.149465
\(694\) −4.45503e75 −2.25333
\(695\) 1.99062e75 0.969151
\(696\) 7.35995e73 0.0344929
\(697\) 1.49048e75 0.672448
\(698\) 4.03017e74 0.175047
\(699\) 5.02963e74 0.210325
\(700\) −1.54931e75 −0.623793
\(701\) −6.43274e74 −0.249384 −0.124692 0.992196i \(-0.539794\pi\)
−0.124692 + 0.992196i \(0.539794\pi\)
\(702\) −3.09940e75 −1.15703
\(703\) −2.89327e75 −1.04009
\(704\) 4.98401e74 0.172545
\(705\) 1.90718e75 0.635889
\(706\) −1.11903e75 −0.359349
\(707\) −3.59876e74 −0.111311
\(708\) 1.12232e75 0.334376
\(709\) 5.30581e75 1.52274 0.761372 0.648315i \(-0.224526\pi\)
0.761372 + 0.648315i \(0.224526\pi\)
\(710\) 6.09660e75 1.68555
\(711\) 4.02518e75 1.07211
\(712\) −4.65803e74 −0.119531
\(713\) −1.42496e75 −0.352315
\(714\) −1.45309e75 −0.346171
\(715\) 2.25978e75 0.518747
\(716\) 8.68847e74 0.192198
\(717\) −2.73179e74 −0.0582358
\(718\) −7.68420e75 −1.57870
\(719\) −7.52021e75 −1.48907 −0.744534 0.667585i \(-0.767328\pi\)
−0.744534 + 0.667585i \(0.767328\pi\)
\(720\) −7.69497e75 −1.46857
\(721\) −2.73165e75 −0.502506
\(722\) 1.71378e76 3.03891
\(723\) 3.83388e74 0.0655351
\(724\) −4.66752e75 −0.769156
\(725\) −4.00624e75 −0.636472
\(726\) −2.55339e75 −0.391108
\(727\) −9.24803e75 −1.36580 −0.682900 0.730512i \(-0.739282\pi\)
−0.682900 + 0.730512i \(0.739282\pi\)
\(728\) 1.31917e75 0.187853
\(729\) −3.51724e75 −0.482973
\(730\) 1.54798e76 2.04979
\(731\) 5.37112e75 0.685890
\(732\) 3.77507e74 0.0464924
\(733\) 1.08537e76 1.28921 0.644603 0.764517i \(-0.277023\pi\)
0.644603 + 0.764517i \(0.277023\pi\)
\(734\) 1.61838e74 0.0185411
\(735\) 2.20612e75 0.243790
\(736\) 5.44255e75 0.580150
\(737\) −6.97226e74 −0.0716943
\(738\) −6.74179e75 −0.668778
\(739\) −3.55012e75 −0.339755 −0.169877 0.985465i \(-0.554337\pi\)
−0.169877 + 0.985465i \(0.554337\pi\)
\(740\) −7.77425e75 −0.717824
\(741\) −8.97806e75 −0.799834
\(742\) 1.18665e76 1.02005
\(743\) −1.21666e75 −0.100917 −0.0504586 0.998726i \(-0.516068\pi\)
−0.0504586 + 0.998726i \(0.516068\pi\)
\(744\) −5.96689e74 −0.0477601
\(745\) 9.66867e75 0.746837
\(746\) −2.87957e76 −2.14659
\(747\) 1.53078e76 1.10133
\(748\) −3.78773e75 −0.263018
\(749\) 1.04410e76 0.699797
\(750\) −8.00961e74 −0.0518189
\(751\) −1.83232e76 −1.14431 −0.572153 0.820147i \(-0.693892\pi\)
−0.572153 + 0.820147i \(0.693892\pi\)
\(752\) 2.68114e76 1.61639
\(753\) 1.02914e76 0.598972
\(754\) −2.07192e76 −1.16421
\(755\) −4.85504e76 −2.63390
\(756\) 6.38517e75 0.334461
\(757\) 1.67987e76 0.849639 0.424819 0.905278i \(-0.360338\pi\)
0.424819 + 0.905278i \(0.360338\pi\)
\(758\) 2.32661e76 1.13629
\(759\) 6.93047e74 0.0326855
\(760\) −1.09826e76 −0.500199
\(761\) −6.65143e74 −0.0292565 −0.0146282 0.999893i \(-0.504656\pi\)
−0.0146282 + 0.999893i \(0.504656\pi\)
\(762\) 3.28075e75 0.139369
\(763\) −1.84603e76 −0.757422
\(764\) −9.54566e75 −0.378296
\(765\) 4.25221e76 1.62775
\(766\) −1.03067e76 −0.381117
\(767\) 5.20162e76 1.85807
\(768\) 1.08011e76 0.372732
\(769\) 1.78455e75 0.0594952 0.0297476 0.999557i \(-0.490530\pi\)
0.0297476 + 0.999557i \(0.490530\pi\)
\(770\) −1.00773e76 −0.324595
\(771\) −5.07386e75 −0.157906
\(772\) 3.50816e76 1.05492
\(773\) −6.01277e76 −1.74710 −0.873550 0.486735i \(-0.838188\pi\)
−0.873550 + 0.486735i \(0.838188\pi\)
\(774\) −2.42948e76 −0.682147
\(775\) 3.24795e76 0.881282
\(776\) 9.40111e75 0.246515
\(777\) −4.66597e75 −0.118246
\(778\) −5.97519e76 −1.46350
\(779\) −4.10673e76 −0.972194
\(780\) −2.41242e76 −0.552008
\(781\) 9.53797e75 0.210962
\(782\) −3.44135e76 −0.735784
\(783\) 1.65109e76 0.341259
\(784\) 3.10139e76 0.619699
\(785\) 3.02027e76 0.583444
\(786\) −1.34059e76 −0.250380
\(787\) 7.06315e75 0.127546 0.0637732 0.997964i \(-0.479687\pi\)
0.0637732 + 0.997964i \(0.479687\pi\)
\(788\) −1.65606e76 −0.289156
\(789\) −2.69518e76 −0.455037
\(790\) 1.42614e77 2.32832
\(791\) −5.35377e75 −0.0845246
\(792\) −2.82066e75 −0.0430659
\(793\) 1.74963e76 0.258350
\(794\) 1.22865e77 1.75463
\(795\) 3.57274e76 0.493484
\(796\) 7.07117e75 0.0944702
\(797\) −5.54535e76 −0.716612 −0.358306 0.933604i \(-0.616645\pi\)
−0.358306 + 0.933604i \(0.616645\pi\)
\(798\) 4.00370e76 0.500478
\(799\) −1.48159e77 −1.79159
\(800\) −1.24054e77 −1.45119
\(801\) −4.96915e76 −0.562367
\(802\) −5.87479e76 −0.643238
\(803\) 2.42177e76 0.256550
\(804\) 7.44321e75 0.0762912
\(805\) −4.22972e76 −0.419489
\(806\) 1.67976e77 1.61201
\(807\) −4.40216e76 −0.408806
\(808\) −3.56890e75 −0.0320725
\(809\) 7.38311e76 0.642101 0.321050 0.947062i \(-0.395964\pi\)
0.321050 + 0.947062i \(0.395964\pi\)
\(810\) −1.70512e77 −1.43517
\(811\) 1.49559e77 1.21832 0.609159 0.793048i \(-0.291507\pi\)
0.609159 + 0.793048i \(0.291507\pi\)
\(812\) 4.26842e76 0.336537
\(813\) 1.79984e76 0.137352
\(814\) −2.63276e76 −0.194475
\(815\) −4.41968e74 −0.00316019
\(816\) −6.15032e76 −0.425705
\(817\) −1.47990e77 −0.991628
\(818\) −5.29453e76 −0.343451
\(819\) 1.40728e77 0.883803
\(820\) −1.10348e77 −0.670963
\(821\) 2.15004e77 1.26576 0.632881 0.774249i \(-0.281872\pi\)
0.632881 + 0.774249i \(0.281872\pi\)
\(822\) 3.89725e76 0.222155
\(823\) 2.98860e77 1.64958 0.824788 0.565442i \(-0.191294\pi\)
0.824788 + 0.565442i \(0.191294\pi\)
\(824\) −2.70898e76 −0.144789
\(825\) −1.57968e76 −0.0817598
\(826\) −2.31963e77 −1.16264
\(827\) −1.03100e77 −0.500451 −0.250226 0.968188i \(-0.580505\pi\)
−0.250226 + 0.968188i \(0.580505\pi\)
\(828\) 7.19106e76 0.338056
\(829\) −1.73661e77 −0.790692 −0.395346 0.918532i \(-0.629375\pi\)
−0.395346 + 0.918532i \(0.629375\pi\)
\(830\) 5.42359e77 2.39176
\(831\) 5.46202e76 0.233306
\(832\) −2.46597e77 −1.02028
\(833\) −1.71382e77 −0.686866
\(834\) −7.19662e76 −0.279401
\(835\) 1.50883e77 0.567477
\(836\) 1.04363e77 0.380260
\(837\) −1.33858e77 −0.472519
\(838\) −4.39434e77 −1.50289
\(839\) 1.10592e77 0.366464 0.183232 0.983070i \(-0.441344\pi\)
0.183232 + 0.983070i \(0.441344\pi\)
\(840\) −1.77115e76 −0.0568664
\(841\) −2.11062e77 −0.656623
\(842\) −7.28344e77 −2.19566
\(843\) 1.07140e77 0.312982
\(844\) 5.20124e77 1.47242
\(845\) −5.91611e77 −1.62306
\(846\) 6.70155e77 1.78181
\(847\) 2.43800e77 0.628237
\(848\) 5.02260e77 1.25441
\(849\) 5.52147e76 0.133660
\(850\) 7.84397e77 1.84049
\(851\) −1.10504e77 −0.251330
\(852\) −1.01822e77 −0.224488
\(853\) 4.30141e77 0.919309 0.459655 0.888098i \(-0.347973\pi\)
0.459655 + 0.888098i \(0.347973\pi\)
\(854\) −7.80238e76 −0.161657
\(855\) −1.17161e78 −2.35332
\(856\) 1.03543e77 0.201635
\(857\) 4.39078e77 0.828992 0.414496 0.910051i \(-0.363958\pi\)
0.414496 + 0.910051i \(0.363958\pi\)
\(858\) −8.16969e76 −0.149552
\(859\) 2.05806e77 0.365291 0.182646 0.983179i \(-0.441534\pi\)
0.182646 + 0.983179i \(0.441534\pi\)
\(860\) −3.97652e77 −0.684376
\(861\) −6.62291e76 −0.110526
\(862\) −6.31214e77 −1.02149
\(863\) −4.32424e77 −0.678615 −0.339307 0.940676i \(-0.610193\pi\)
−0.339307 + 0.940676i \(0.610193\pi\)
\(864\) 5.11261e77 0.778088
\(865\) 2.06449e77 0.304710
\(866\) −1.45236e78 −2.07898
\(867\) 1.19866e77 0.166414
\(868\) −3.46052e77 −0.465981
\(869\) 2.23115e77 0.291410
\(870\) 2.78183e77 0.352428
\(871\) 3.44971e77 0.423937
\(872\) −1.83071e77 −0.218239
\(873\) 1.00290e78 1.15980
\(874\) 9.48195e77 1.06376
\(875\) 7.64765e76 0.0832367
\(876\) −2.58535e77 −0.272999
\(877\) 3.01916e77 0.309313 0.154656 0.987968i \(-0.450573\pi\)
0.154656 + 0.987968i \(0.450573\pi\)
\(878\) −2.19034e76 −0.0217725
\(879\) 2.08051e77 0.200662
\(880\) −4.26530e77 −0.399171
\(881\) −9.08145e77 −0.824696 −0.412348 0.911026i \(-0.635291\pi\)
−0.412348 + 0.911026i \(0.635291\pi\)
\(882\) 7.75198e77 0.683117
\(883\) −1.16332e78 −0.994812 −0.497406 0.867518i \(-0.665714\pi\)
−0.497406 + 0.867518i \(0.665714\pi\)
\(884\) 1.87408e78 1.55526
\(885\) −6.98386e77 −0.562470
\(886\) −1.80819e77 −0.141336
\(887\) 7.38531e77 0.560264 0.280132 0.959962i \(-0.409622\pi\)
0.280132 + 0.959962i \(0.409622\pi\)
\(888\) −4.62725e76 −0.0340705
\(889\) −3.13249e77 −0.223868
\(890\) −1.76059e78 −1.22130
\(891\) −2.66762e77 −0.179624
\(892\) −1.05704e78 −0.690911
\(893\) 4.08221e78 2.59019
\(894\) −3.49548e77 −0.215309
\(895\) −5.40658e77 −0.323305
\(896\) −4.39643e77 −0.255233
\(897\) −3.42903e77 −0.193273
\(898\) 1.35054e78 0.739069
\(899\) −8.94826e77 −0.475452
\(900\) −1.63908e78 −0.845615
\(901\) −2.77547e78 −1.39037
\(902\) −3.73696e77 −0.181780
\(903\) −2.38664e77 −0.112736
\(904\) −5.30934e76 −0.0243544
\(905\) 2.90446e78 1.29383
\(906\) 1.75522e78 0.759338
\(907\) −2.54346e78 −1.06864 −0.534321 0.845281i \(-0.679433\pi\)
−0.534321 + 0.845281i \(0.679433\pi\)
\(908\) −3.41778e78 −1.39466
\(909\) −3.80727e77 −0.150894
\(910\) 4.98602e78 1.91936
\(911\) 4.02246e78 1.50403 0.752013 0.659149i \(-0.229083\pi\)
0.752013 + 0.659149i \(0.229083\pi\)
\(912\) 1.69460e78 0.615465
\(913\) 8.48506e77 0.299350
\(914\) 3.96514e78 1.35889
\(915\) −2.34912e77 −0.0782070
\(916\) −9.29427e77 −0.300598
\(917\) 1.28001e78 0.402186
\(918\) −3.23273e78 −0.986822
\(919\) −4.43829e78 −1.31630 −0.658150 0.752887i \(-0.728661\pi\)
−0.658150 + 0.752887i \(0.728661\pi\)
\(920\) −4.19461e77 −0.120869
\(921\) −7.95029e76 −0.0222588
\(922\) −1.78900e78 −0.486676
\(923\) −4.71916e78 −1.24744
\(924\) 1.68306e77 0.0432308
\(925\) 2.51874e78 0.628678
\(926\) −3.72023e77 −0.0902357
\(927\) −2.88992e78 −0.681198
\(928\) 3.41773e78 0.782919
\(929\) −8.06660e78 −1.79587 −0.897934 0.440131i \(-0.854932\pi\)
−0.897934 + 0.440131i \(0.854932\pi\)
\(930\) −2.25529e78 −0.487984
\(931\) 4.72207e78 0.993039
\(932\) 2.89274e78 0.591273
\(933\) 8.63535e75 0.00171560
\(934\) −4.23779e77 −0.0818366
\(935\) 2.35699e78 0.442436
\(936\) 1.39560e78 0.254654
\(937\) 8.82372e76 0.0156514 0.00782569 0.999969i \(-0.497509\pi\)
0.00782569 + 0.999969i \(0.497509\pi\)
\(938\) −1.53837e78 −0.265269
\(939\) 2.62115e78 0.439394
\(940\) 1.09690e79 1.78763
\(941\) 1.02741e79 1.62787 0.813937 0.580954i \(-0.197320\pi\)
0.813937 + 0.580954i \(0.197320\pi\)
\(942\) −1.09190e78 −0.168204
\(943\) −1.56850e78 −0.234923
\(944\) −9.81799e78 −1.42977
\(945\) −3.97331e78 −0.562612
\(946\) −1.34666e78 −0.185413
\(947\) 1.04239e79 1.39558 0.697792 0.716301i \(-0.254166\pi\)
0.697792 + 0.716301i \(0.254166\pi\)
\(948\) −2.38186e78 −0.310095
\(949\) −1.19824e79 −1.51701
\(950\) −2.16125e79 −2.66090
\(951\) 4.27517e78 0.511882
\(952\) 1.37591e78 0.160218
\(953\) 1.23008e79 1.39306 0.696532 0.717526i \(-0.254725\pi\)
0.696532 + 0.717526i \(0.254725\pi\)
\(954\) 1.25541e79 1.38278
\(955\) 5.93998e78 0.636349
\(956\) −1.57116e78 −0.163714
\(957\) 4.35209e77 0.0441095
\(958\) −2.48961e79 −2.45440
\(959\) −3.72113e78 −0.356847
\(960\) 3.31089e78 0.308857
\(961\) −3.76513e78 −0.341672
\(962\) 1.30263e79 1.14996
\(963\) 1.10459e79 0.948646
\(964\) 2.20502e78 0.184235
\(965\) −2.18302e79 −1.77454
\(966\) 1.52915e78 0.120936
\(967\) −1.31832e79 −1.01442 −0.507211 0.861822i \(-0.669324\pi\)
−0.507211 + 0.861822i \(0.669324\pi\)
\(968\) 2.41777e78 0.181016
\(969\) −9.36428e78 −0.682173
\(970\) 3.55332e79 2.51874
\(971\) 5.52826e77 0.0381311 0.0190655 0.999818i \(-0.493931\pi\)
0.0190655 + 0.999818i \(0.493931\pi\)
\(972\) 1.02979e79 0.691185
\(973\) 6.87140e78 0.448802
\(974\) −1.72105e79 −1.09391
\(975\) 7.81588e78 0.483455
\(976\) −3.30241e78 −0.198798
\(977\) −1.64164e78 −0.0961772 −0.0480886 0.998843i \(-0.515313\pi\)
−0.0480886 + 0.998843i \(0.515313\pi\)
\(978\) 1.59783e76 0.000911067 0
\(979\) −2.75439e78 −0.152856
\(980\) 1.26883e79 0.685349
\(981\) −1.95299e79 −1.02676
\(982\) 4.00746e79 2.05076
\(983\) 9.35921e77 0.0466198 0.0233099 0.999728i \(-0.492580\pi\)
0.0233099 + 0.999728i \(0.492580\pi\)
\(984\) −6.56795e77 −0.0318463
\(985\) 1.03052e79 0.486402
\(986\) −2.16105e79 −0.992948
\(987\) 6.58338e78 0.294472
\(988\) −5.16364e79 −2.24852
\(989\) −5.65226e78 −0.239619
\(990\) −1.06612e79 −0.440021
\(991\) −1.55923e79 −0.626553 −0.313277 0.949662i \(-0.601427\pi\)
−0.313277 + 0.949662i \(0.601427\pi\)
\(992\) −2.77084e79 −1.08406
\(993\) −1.22461e79 −0.466490
\(994\) 2.10448e79 0.780558
\(995\) −4.40018e78 −0.158913
\(996\) −9.05819e78 −0.318544
\(997\) 3.05684e79 1.04677 0.523385 0.852097i \(-0.324669\pi\)
0.523385 + 0.852097i \(0.324669\pi\)
\(998\) 5.70620e79 1.90278
\(999\) −1.03805e79 −0.337080
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 1.54.a.a.1.4 4
3.2 odd 2 9.54.a.b.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.54.a.a.1.4 4 1.1 even 1 trivial
9.54.a.b.1.1 4 3.2 odd 2