Properties

Label 1.52.a.a.1.3
Level $1$
Weight $52$
Character 1.1
Self dual yes
Analytic conductor $16.473$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 52 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.4731353414\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 2 x^{3} - 495735060514 x^{2} - 23954614981416598 x + 48979992255622025570313\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-511801.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.13381e7 q^{2} +2.68083e12 q^{3} +3.83803e14 q^{4} +4.84667e17 q^{5} +1.37629e20 q^{6} +2.59004e21 q^{7} -9.58994e22 q^{8} +5.03313e24 q^{9} +O(q^{10})\) \(q+5.13381e7 q^{2} +2.68083e12 q^{3} +3.83803e14 q^{4} +4.84667e17 q^{5} +1.37629e20 q^{6} +2.59004e21 q^{7} -9.58994e22 q^{8} +5.03313e24 q^{9} +2.48819e25 q^{10} -4.45050e26 q^{11} +1.02891e27 q^{12} -1.37117e28 q^{13} +1.32968e29 q^{14} +1.29931e30 q^{15} -5.78755e30 q^{16} +2.62484e31 q^{17} +2.58392e32 q^{18} +1.11022e32 q^{19} +1.86017e32 q^{20} +6.94345e33 q^{21} -2.28480e34 q^{22} +2.36137e34 q^{23} -2.57090e35 q^{24} -2.09187e35 q^{25} -7.03932e35 q^{26} +7.71928e36 q^{27} +9.94066e35 q^{28} -2.25752e37 q^{29} +6.67040e37 q^{30} -4.11662e37 q^{31} -8.11754e37 q^{32} -1.19310e39 q^{33} +1.34754e39 q^{34} +1.25531e39 q^{35} +1.93173e39 q^{36} +5.65183e39 q^{37} +5.69965e39 q^{38} -3.67587e40 q^{39} -4.64793e40 q^{40} -5.54318e40 q^{41} +3.56464e41 q^{42} -5.70927e41 q^{43} -1.70812e41 q^{44} +2.43939e42 q^{45} +1.21229e42 q^{46} +1.49403e42 q^{47} -1.55154e43 q^{48} -5.88095e42 q^{49} -1.07393e43 q^{50} +7.03673e43 q^{51} -5.26259e42 q^{52} -1.42123e44 q^{53} +3.96293e44 q^{54} -2.15701e44 q^{55} -2.48383e44 q^{56} +2.97630e44 q^{57} -1.15897e45 q^{58} +2.24820e44 q^{59} +4.98678e44 q^{60} +2.34137e44 q^{61} -2.11340e45 q^{62} +1.30360e46 q^{63} +8.86500e45 q^{64} -6.64560e45 q^{65} -6.12516e46 q^{66} -2.65209e45 q^{67} +1.00742e46 q^{68} +6.33043e46 q^{69} +6.44450e46 q^{70} +7.64854e46 q^{71} -4.82675e47 q^{72} +5.90560e47 q^{73} +2.90154e47 q^{74} -5.60795e47 q^{75} +4.26105e46 q^{76} -1.15270e48 q^{77} -1.88712e48 q^{78} +3.15804e48 q^{79} -2.80503e48 q^{80} +9.85421e48 q^{81} -2.84576e48 q^{82} -1.40261e48 q^{83} +2.66492e48 q^{84} +1.27217e49 q^{85} -2.93103e49 q^{86} -6.05202e49 q^{87} +4.26801e49 q^{88} -1.71424e48 q^{89} +1.25234e50 q^{90} -3.55138e49 q^{91} +9.06303e48 q^{92} -1.10360e50 q^{93} +7.67005e49 q^{94} +5.38085e49 q^{95} -2.17617e50 q^{96} +6.68956e50 q^{97} -3.01917e50 q^{98} -2.24000e51 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} + O(q^{10}) \) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} - \)\(26\!\cdots\!20\)\(q^{10} + \)\(35\!\cdots\!48\)\(q^{11} - \)\(49\!\cdots\!20\)\(q^{12} + \)\(30\!\cdots\!80\)\(q^{13} + \)\(11\!\cdots\!24\)\(q^{14} + \)\(14\!\cdots\!60\)\(q^{15} + \)\(13\!\cdots\!44\)\(q^{16} + \)\(48\!\cdots\!20\)\(q^{17} + \)\(73\!\cdots\!40\)\(q^{18} + \)\(81\!\cdots\!80\)\(q^{19} + \)\(66\!\cdots\!40\)\(q^{20} + \)\(31\!\cdots\!48\)\(q^{21} - \)\(34\!\cdots\!20\)\(q^{22} - \)\(54\!\cdots\!80\)\(q^{23} - \)\(87\!\cdots\!60\)\(q^{24} - \)\(57\!\cdots\!00\)\(q^{25} + \)\(15\!\cdots\!48\)\(q^{26} + \)\(36\!\cdots\!20\)\(q^{27} + \)\(34\!\cdots\!80\)\(q^{28} + \)\(24\!\cdots\!20\)\(q^{29} - \)\(32\!\cdots\!40\)\(q^{30} - \)\(74\!\cdots\!72\)\(q^{31} - \)\(69\!\cdots\!60\)\(q^{32} - \)\(17\!\cdots\!20\)\(q^{33} + \)\(59\!\cdots\!64\)\(q^{34} + \)\(54\!\cdots\!80\)\(q^{35} + \)\(12\!\cdots\!84\)\(q^{36} + \)\(92\!\cdots\!60\)\(q^{37} + \)\(42\!\cdots\!20\)\(q^{38} - \)\(11\!\cdots\!04\)\(q^{39} - \)\(26\!\cdots\!00\)\(q^{40} + \)\(14\!\cdots\!68\)\(q^{41} - \)\(39\!\cdots\!80\)\(q^{42} - \)\(38\!\cdots\!00\)\(q^{43} + \)\(39\!\cdots\!44\)\(q^{44} + \)\(25\!\cdots\!60\)\(q^{45} - \)\(68\!\cdots\!12\)\(q^{46} + \)\(70\!\cdots\!80\)\(q^{47} - \)\(19\!\cdots\!80\)\(q^{48} - \)\(21\!\cdots\!28\)\(q^{49} - \)\(65\!\cdots\!00\)\(q^{50} + \)\(69\!\cdots\!28\)\(q^{51} + \)\(20\!\cdots\!00\)\(q^{52} - \)\(46\!\cdots\!60\)\(q^{53} + \)\(29\!\cdots\!80\)\(q^{54} + \)\(28\!\cdots\!60\)\(q^{55} - \)\(71\!\cdots\!80\)\(q^{56} - \)\(88\!\cdots\!60\)\(q^{57} - \)\(32\!\cdots\!20\)\(q^{58} + \)\(11\!\cdots\!40\)\(q^{59} + \)\(55\!\cdots\!80\)\(q^{60} + \)\(34\!\cdots\!48\)\(q^{61} + \)\(96\!\cdots\!80\)\(q^{62} + \)\(21\!\cdots\!60\)\(q^{63} - \)\(34\!\cdots\!28\)\(q^{64} + \)\(10\!\cdots\!60\)\(q^{65} - \)\(15\!\cdots\!04\)\(q^{66} + \)\(30\!\cdots\!20\)\(q^{67} - \)\(92\!\cdots\!60\)\(q^{68} + \)\(15\!\cdots\!76\)\(q^{69} - \)\(12\!\cdots\!20\)\(q^{70} + \)\(39\!\cdots\!88\)\(q^{71} + \)\(50\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!56\)\(q^{74} + \)\(72\!\cdots\!00\)\(q^{75} - \)\(19\!\cdots\!60\)\(q^{76} + \)\(13\!\cdots\!00\)\(q^{77} - \)\(96\!\cdots\!00\)\(q^{78} + \)\(40\!\cdots\!20\)\(q^{79} + \)\(65\!\cdots\!80\)\(q^{80} + \)\(15\!\cdots\!44\)\(q^{81} + \)\(26\!\cdots\!80\)\(q^{82} + \)\(10\!\cdots\!60\)\(q^{83} - \)\(18\!\cdots\!56\)\(q^{84} - \)\(22\!\cdots\!20\)\(q^{85} - \)\(43\!\cdots\!32\)\(q^{86} - \)\(62\!\cdots\!40\)\(q^{87} - \)\(25\!\cdots\!40\)\(q^{88} - \)\(90\!\cdots\!40\)\(q^{89} + \)\(31\!\cdots\!60\)\(q^{90} + \)\(10\!\cdots\!88\)\(q^{91} + \)\(19\!\cdots\!20\)\(q^{92} - \)\(31\!\cdots\!20\)\(q^{93} + \)\(63\!\cdots\!84\)\(q^{94} - \)\(41\!\cdots\!00\)\(q^{95} - \)\(24\!\cdots\!32\)\(q^{96} - \)\(13\!\cdots\!20\)\(q^{97} - \)\(31\!\cdots\!80\)\(q^{98} - \)\(17\!\cdots\!64\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.13381e7 1.08187 0.540935 0.841064i \(-0.318070\pi\)
0.540935 + 0.841064i \(0.318070\pi\)
\(3\) 2.68083e12 1.82674 0.913370 0.407131i \(-0.133471\pi\)
0.913370 + 0.407131i \(0.133471\pi\)
\(4\) 3.83803e14 0.170443
\(5\) 4.84667e17 0.727291 0.363645 0.931537i \(-0.381532\pi\)
0.363645 + 0.931537i \(0.381532\pi\)
\(6\) 1.37629e20 1.97629
\(7\) 2.59004e21 0.729972 0.364986 0.931013i \(-0.381074\pi\)
0.364986 + 0.931013i \(0.381074\pi\)
\(8\) −9.58994e22 −0.897473
\(9\) 5.03313e24 2.33698
\(10\) 2.48819e25 0.786834
\(11\) −4.45050e26 −1.23850 −0.619249 0.785194i \(-0.712563\pi\)
−0.619249 + 0.785194i \(0.712563\pi\)
\(12\) 1.02891e27 0.311355
\(13\) −1.37117e28 −0.538934 −0.269467 0.963010i \(-0.586847\pi\)
−0.269467 + 0.963010i \(0.586847\pi\)
\(14\) 1.32968e29 0.789735
\(15\) 1.29931e30 1.32857
\(16\) −5.78755e30 −1.14139
\(17\) 2.62484e31 1.10320 0.551601 0.834108i \(-0.314017\pi\)
0.551601 + 0.834108i \(0.314017\pi\)
\(18\) 2.58392e32 2.52831
\(19\) 1.11022e32 0.273647 0.136824 0.990595i \(-0.456311\pi\)
0.136824 + 0.990595i \(0.456311\pi\)
\(20\) 1.86017e32 0.123962
\(21\) 6.94345e33 1.33347
\(22\) −2.28480e34 −1.33989
\(23\) 2.36137e34 0.445764 0.222882 0.974845i \(-0.428454\pi\)
0.222882 + 0.974845i \(0.428454\pi\)
\(24\) −2.57090e35 −1.63945
\(25\) −2.09187e35 −0.471048
\(26\) −7.03932e35 −0.583056
\(27\) 7.71928e36 2.44231
\(28\) 9.94066e35 0.124419
\(29\) −2.25752e37 −1.15474 −0.577368 0.816484i \(-0.695920\pi\)
−0.577368 + 0.816484i \(0.695920\pi\)
\(30\) 6.67040e37 1.43734
\(31\) −4.11662e37 −0.384431 −0.192215 0.981353i \(-0.561567\pi\)
−0.192215 + 0.981353i \(0.561567\pi\)
\(32\) −8.11754e37 −0.337365
\(33\) −1.19310e39 −2.26241
\(34\) 1.34754e39 1.19352
\(35\) 1.25531e39 0.530902
\(36\) 1.93173e39 0.398321
\(37\) 5.65183e39 0.579488 0.289744 0.957104i \(-0.406430\pi\)
0.289744 + 0.957104i \(0.406430\pi\)
\(38\) 5.69965e39 0.296051
\(39\) −3.67587e40 −0.984492
\(40\) −4.64793e40 −0.652724
\(41\) −5.54318e40 −0.414735 −0.207367 0.978263i \(-0.566490\pi\)
−0.207367 + 0.978263i \(0.566490\pi\)
\(42\) 3.56464e41 1.44264
\(43\) −5.70927e41 −1.26805 −0.634023 0.773314i \(-0.718598\pi\)
−0.634023 + 0.773314i \(0.718598\pi\)
\(44\) −1.70812e41 −0.211093
\(45\) 2.43939e42 1.69966
\(46\) 1.21229e42 0.482259
\(47\) 1.49403e42 0.343449 0.171725 0.985145i \(-0.445066\pi\)
0.171725 + 0.985145i \(0.445066\pi\)
\(48\) −1.55154e43 −2.08503
\(49\) −5.88095e42 −0.467140
\(50\) −1.07393e43 −0.509613
\(51\) 7.03673e43 2.01526
\(52\) −5.26259e42 −0.0918574
\(53\) −1.42123e44 −1.52626 −0.763131 0.646244i \(-0.776339\pi\)
−0.763131 + 0.646244i \(0.776339\pi\)
\(54\) 3.96293e44 2.64226
\(55\) −2.15701e44 −0.900749
\(56\) −2.48383e44 −0.655131
\(57\) 2.97630e44 0.499882
\(58\) −1.15897e45 −1.24927
\(59\) 2.24820e44 0.156714 0.0783572 0.996925i \(-0.475033\pi\)
0.0783572 + 0.996925i \(0.475033\pi\)
\(60\) 4.98678e44 0.226445
\(61\) 2.34137e44 0.0697524 0.0348762 0.999392i \(-0.488896\pi\)
0.0348762 + 0.999392i \(0.488896\pi\)
\(62\) −2.11340e45 −0.415904
\(63\) 1.30360e46 1.70593
\(64\) 8.86500e45 0.776407
\(65\) −6.64560e45 −0.391962
\(66\) −6.12516e46 −2.44764
\(67\) −2.65209e45 −0.0722240 −0.0361120 0.999348i \(-0.511497\pi\)
−0.0361120 + 0.999348i \(0.511497\pi\)
\(68\) 1.00742e46 0.188033
\(69\) 6.33043e46 0.814295
\(70\) 6.44450e46 0.574367
\(71\) 7.64854e46 0.474778 0.237389 0.971415i \(-0.423708\pi\)
0.237389 + 0.971415i \(0.423708\pi\)
\(72\) −4.82675e47 −2.09737
\(73\) 5.90560e47 1.80522 0.902611 0.430456i \(-0.141647\pi\)
0.902611 + 0.430456i \(0.141647\pi\)
\(74\) 2.90154e47 0.626931
\(75\) −5.60795e47 −0.860483
\(76\) 4.26105e46 0.0466412
\(77\) −1.15270e48 −0.904070
\(78\) −1.88712e48 −1.06509
\(79\) 3.15804e48 1.28803 0.644017 0.765011i \(-0.277267\pi\)
0.644017 + 0.765011i \(0.277267\pi\)
\(80\) −2.80503e48 −0.830124
\(81\) 9.85421e48 2.12449
\(82\) −2.84576e48 −0.448689
\(83\) −1.40261e48 −0.162348 −0.0811739 0.996700i \(-0.525867\pi\)
−0.0811739 + 0.996700i \(0.525867\pi\)
\(84\) 2.66492e48 0.227280
\(85\) 1.27217e49 0.802348
\(86\) −2.93103e49 −1.37186
\(87\) −6.05202e49 −2.10940
\(88\) 4.26801e49 1.11152
\(89\) −1.71424e48 −0.0334677 −0.0167338 0.999860i \(-0.505327\pi\)
−0.0167338 + 0.999860i \(0.505327\pi\)
\(90\) 1.25234e50 1.83881
\(91\) −3.55138e49 −0.393407
\(92\) 9.06303e48 0.0759773
\(93\) −1.10360e50 −0.702255
\(94\) 7.67005e49 0.371568
\(95\) 5.38085e49 0.199021
\(96\) −2.17617e50 −0.616278
\(97\) 6.68956e50 1.45451 0.727257 0.686365i \(-0.240795\pi\)
0.727257 + 0.686365i \(0.240795\pi\)
\(98\) −3.01917e50 −0.505385
\(99\) −2.24000e51 −2.89434
\(100\) −8.02868e49 −0.0802868
\(101\) 2.03385e51 1.57806 0.789031 0.614354i \(-0.210583\pi\)
0.789031 + 0.614354i \(0.210583\pi\)
\(102\) 3.61253e51 2.18025
\(103\) −2.62630e51 −1.23593 −0.617967 0.786204i \(-0.712043\pi\)
−0.617967 + 0.786204i \(0.712043\pi\)
\(104\) 1.31494e51 0.483679
\(105\) 3.36526e51 0.969820
\(106\) −7.29632e51 −1.65122
\(107\) −4.29375e51 −0.764804 −0.382402 0.923996i \(-0.624903\pi\)
−0.382402 + 0.923996i \(0.624903\pi\)
\(108\) 2.96268e51 0.416274
\(109\) −4.62834e49 −0.00514103 −0.00257051 0.999997i \(-0.500818\pi\)
−0.00257051 + 0.999997i \(0.500818\pi\)
\(110\) −1.10737e52 −0.974493
\(111\) 1.51516e52 1.05857
\(112\) −1.49900e52 −0.833185
\(113\) 2.75611e52 1.22123 0.610613 0.791929i \(-0.290923\pi\)
0.610613 + 0.791929i \(0.290923\pi\)
\(114\) 1.52798e52 0.540808
\(115\) 1.14448e52 0.324200
\(116\) −8.66444e51 −0.196817
\(117\) −6.90128e52 −1.25948
\(118\) 1.15418e52 0.169545
\(119\) 6.79843e52 0.805307
\(120\) −1.24603e53 −1.19236
\(121\) 6.89398e52 0.533880
\(122\) 1.20202e52 0.0754630
\(123\) −1.48603e53 −0.757613
\(124\) −1.57997e52 −0.0655235
\(125\) −3.16621e53 −1.06988
\(126\) 6.69245e53 1.84559
\(127\) 8.01732e53 1.80732 0.903659 0.428254i \(-0.140871\pi\)
0.903659 + 0.428254i \(0.140871\pi\)
\(128\) 6.37903e53 1.17734
\(129\) −1.53056e54 −2.31639
\(130\) −3.41173e53 −0.424051
\(131\) −1.06837e54 −1.09220 −0.546102 0.837719i \(-0.683889\pi\)
−0.546102 + 0.837719i \(0.683889\pi\)
\(132\) −4.57917e53 −0.385613
\(133\) 2.87551e53 0.199755
\(134\) −1.36153e53 −0.0781369
\(135\) 3.74128e54 1.77627
\(136\) −2.51720e54 −0.990094
\(137\) 1.78751e54 0.583274 0.291637 0.956529i \(-0.405800\pi\)
0.291637 + 0.956529i \(0.405800\pi\)
\(138\) 3.24993e54 0.880961
\(139\) −5.89879e54 −1.33010 −0.665052 0.746797i \(-0.731591\pi\)
−0.665052 + 0.746797i \(0.731591\pi\)
\(140\) 4.81790e53 0.0904885
\(141\) 4.00522e54 0.627392
\(142\) 3.92662e54 0.513648
\(143\) 6.10239e54 0.667469
\(144\) −2.91295e55 −2.66741
\(145\) −1.09414e55 −0.839829
\(146\) 3.03182e55 1.95302
\(147\) −1.57658e55 −0.853344
\(148\) 2.16919e54 0.0987697
\(149\) 2.84854e55 1.09238 0.546188 0.837663i \(-0.316078\pi\)
0.546188 + 0.837663i \(0.316078\pi\)
\(150\) −2.87902e55 −0.930930
\(151\) 7.60980e54 0.207712 0.103856 0.994592i \(-0.466882\pi\)
0.103856 + 0.994592i \(0.466882\pi\)
\(152\) −1.06469e55 −0.245591
\(153\) 1.32112e56 2.57816
\(154\) −5.91774e55 −0.978086
\(155\) −1.99519e55 −0.279593
\(156\) −1.41081e55 −0.167800
\(157\) −1.29871e56 −1.31242 −0.656209 0.754579i \(-0.727841\pi\)
−0.656209 + 0.754579i \(0.727841\pi\)
\(158\) 1.62128e56 1.39349
\(159\) −3.81006e56 −2.78808
\(160\) −3.93430e55 −0.245362
\(161\) 6.11605e55 0.325395
\(162\) 5.05897e56 2.29842
\(163\) 4.13179e56 1.60455 0.802277 0.596952i \(-0.203622\pi\)
0.802277 + 0.596952i \(0.203622\pi\)
\(164\) −2.12749e55 −0.0706886
\(165\) −5.78257e56 −1.64543
\(166\) −7.20075e55 −0.175639
\(167\) 4.33151e56 0.906504 0.453252 0.891383i \(-0.350264\pi\)
0.453252 + 0.891383i \(0.350264\pi\)
\(168\) −6.65873e56 −1.19675
\(169\) −4.59298e56 −0.709550
\(170\) 6.53109e56 0.868037
\(171\) 5.58787e56 0.639508
\(172\) −2.19124e56 −0.216130
\(173\) 4.65407e56 0.395966 0.197983 0.980205i \(-0.436561\pi\)
0.197983 + 0.980205i \(0.436561\pi\)
\(174\) −3.10699e57 −2.28210
\(175\) −5.41804e56 −0.343852
\(176\) 2.57575e57 1.41361
\(177\) 6.02704e56 0.286276
\(178\) −8.80057e55 −0.0362077
\(179\) 5.11036e57 1.82263 0.911316 0.411708i \(-0.135068\pi\)
0.911316 + 0.411708i \(0.135068\pi\)
\(180\) 9.36247e56 0.289695
\(181\) −4.70440e57 −1.26387 −0.631933 0.775023i \(-0.717738\pi\)
−0.631933 + 0.775023i \(0.717738\pi\)
\(182\) −1.82321e57 −0.425615
\(183\) 6.27680e56 0.127419
\(184\) −2.26454e57 −0.400061
\(185\) 2.73925e57 0.421457
\(186\) −5.66565e57 −0.759748
\(187\) −1.16818e58 −1.36631
\(188\) 5.73412e56 0.0585385
\(189\) 1.99932e58 1.78282
\(190\) 2.76243e57 0.215315
\(191\) −2.06433e58 −1.40743 −0.703717 0.710481i \(-0.748478\pi\)
−0.703717 + 0.710481i \(0.748478\pi\)
\(192\) 2.37655e58 1.41829
\(193\) 6.31461e57 0.330092 0.165046 0.986286i \(-0.447223\pi\)
0.165046 + 0.986286i \(0.447223\pi\)
\(194\) 3.43429e58 1.57360
\(195\) −1.78157e58 −0.716012
\(196\) −2.25713e57 −0.0796207
\(197\) −2.12414e58 −0.658104 −0.329052 0.944312i \(-0.606729\pi\)
−0.329052 + 0.944312i \(0.606729\pi\)
\(198\) −1.14997e59 −3.13130
\(199\) 5.17721e58 1.23977 0.619887 0.784691i \(-0.287178\pi\)
0.619887 + 0.784691i \(0.287178\pi\)
\(200\) 2.00610e58 0.422753
\(201\) −7.10980e57 −0.131934
\(202\) 1.04414e59 1.70726
\(203\) −5.84707e58 −0.842925
\(204\) 2.70072e58 0.343487
\(205\) −2.68659e58 −0.301633
\(206\) −1.34829e59 −1.33712
\(207\) 1.18851e59 1.04174
\(208\) 7.93570e58 0.615135
\(209\) −4.94103e58 −0.338912
\(210\) 1.72766e59 1.04922
\(211\) −4.46281e57 −0.0240107 −0.0120054 0.999928i \(-0.503822\pi\)
−0.0120054 + 0.999928i \(0.503822\pi\)
\(212\) −5.45472e58 −0.260140
\(213\) 2.05044e59 0.867296
\(214\) −2.20433e59 −0.827419
\(215\) −2.76709e59 −0.922238
\(216\) −7.40274e59 −2.19191
\(217\) −1.06622e59 −0.280624
\(218\) −2.37610e57 −0.00556192
\(219\) 1.58319e60 3.29767
\(220\) −8.27868e58 −0.153526
\(221\) −3.59910e59 −0.594553
\(222\) 7.77853e59 1.14524
\(223\) 5.20757e57 0.00683694 0.00341847 0.999994i \(-0.498912\pi\)
0.00341847 + 0.999994i \(0.498912\pi\)
\(224\) −2.10248e59 −0.246267
\(225\) −1.05287e60 −1.10083
\(226\) 1.41493e60 1.32121
\(227\) −5.70910e59 −0.476330 −0.238165 0.971225i \(-0.576546\pi\)
−0.238165 + 0.971225i \(0.576546\pi\)
\(228\) 1.14231e59 0.0852014
\(229\) −1.79988e60 −1.20071 −0.600354 0.799734i \(-0.704974\pi\)
−0.600354 + 0.799734i \(0.704974\pi\)
\(230\) 5.87554e59 0.350742
\(231\) −3.09018e60 −1.65150
\(232\) 2.16495e60 1.03634
\(233\) 2.07611e60 0.890581 0.445290 0.895386i \(-0.353100\pi\)
0.445290 + 0.895386i \(0.353100\pi\)
\(234\) −3.54299e60 −1.36259
\(235\) 7.24104e59 0.249787
\(236\) 8.62867e58 0.0267109
\(237\) 8.46617e60 2.35290
\(238\) 3.49019e60 0.871237
\(239\) −4.43052e60 −0.993822 −0.496911 0.867802i \(-0.665532\pi\)
−0.496911 + 0.867802i \(0.665532\pi\)
\(240\) −7.51980e60 −1.51642
\(241\) −4.39407e60 −0.796952 −0.398476 0.917179i \(-0.630461\pi\)
−0.398476 + 0.917179i \(0.630461\pi\)
\(242\) 3.53924e60 0.577588
\(243\) 9.79245e60 1.43857
\(244\) 8.98625e58 0.0118888
\(245\) −2.85030e60 −0.339747
\(246\) −7.62900e60 −0.819638
\(247\) −1.52230e60 −0.147478
\(248\) 3.94782e60 0.345016
\(249\) −3.76016e60 −0.296567
\(250\) −1.62547e61 −1.15747
\(251\) −2.03323e60 −0.130770 −0.0653849 0.997860i \(-0.520828\pi\)
−0.0653849 + 0.997860i \(0.520828\pi\)
\(252\) 5.00327e60 0.290763
\(253\) −1.05093e61 −0.552078
\(254\) 4.11594e61 1.95528
\(255\) 3.41047e61 1.46568
\(256\) 1.27866e61 0.497318
\(257\) 3.10631e61 1.09383 0.546915 0.837188i \(-0.315802\pi\)
0.546915 + 0.837188i \(0.315802\pi\)
\(258\) −7.85759e61 −2.50603
\(259\) 1.46385e61 0.423011
\(260\) −2.55060e60 −0.0668071
\(261\) −1.13624e62 −2.69859
\(262\) −5.48481e61 −1.18162
\(263\) 7.24647e61 1.41663 0.708313 0.705899i \(-0.249457\pi\)
0.708313 + 0.705899i \(0.249457\pi\)
\(264\) 1.14418e62 2.03046
\(265\) −6.88822e61 −1.11004
\(266\) 1.47623e61 0.216109
\(267\) −4.59557e60 −0.0611368
\(268\) −1.01788e60 −0.0123101
\(269\) −5.04207e61 −0.554531 −0.277265 0.960793i \(-0.589428\pi\)
−0.277265 + 0.960793i \(0.589428\pi\)
\(270\) 1.92070e62 1.92169
\(271\) 5.33395e61 0.485660 0.242830 0.970069i \(-0.421924\pi\)
0.242830 + 0.970069i \(0.421924\pi\)
\(272\) −1.51914e62 −1.25919
\(273\) −9.52064e61 −0.718652
\(274\) 9.17672e61 0.631027
\(275\) 9.30990e61 0.583393
\(276\) 2.42964e61 0.138791
\(277\) 1.79274e62 0.933861 0.466931 0.884294i \(-0.345360\pi\)
0.466931 + 0.884294i \(0.345360\pi\)
\(278\) −3.02833e62 −1.43900
\(279\) −2.07195e62 −0.898406
\(280\) −1.20383e62 −0.476470
\(281\) −1.23411e62 −0.446006 −0.223003 0.974818i \(-0.571586\pi\)
−0.223003 + 0.974818i \(0.571586\pi\)
\(282\) 2.05621e62 0.678757
\(283\) 5.28631e61 0.159440 0.0797202 0.996817i \(-0.474597\pi\)
0.0797202 + 0.996817i \(0.474597\pi\)
\(284\) 2.93553e61 0.0809225
\(285\) 1.44251e62 0.363560
\(286\) 3.13285e62 0.722115
\(287\) −1.43571e62 −0.302745
\(288\) −4.08567e62 −0.788414
\(289\) 1.22875e62 0.217054
\(290\) −5.61713e62 −0.908586
\(291\) 1.79335e63 2.65702
\(292\) 2.26659e62 0.307687
\(293\) 3.24054e62 0.403174 0.201587 0.979471i \(-0.435390\pi\)
0.201587 + 0.979471i \(0.435390\pi\)
\(294\) −8.09387e62 −0.923207
\(295\) 1.08963e62 0.113977
\(296\) −5.42007e62 −0.520075
\(297\) −3.43547e63 −3.02480
\(298\) 1.46239e63 1.18181
\(299\) −3.23784e62 −0.240237
\(300\) −2.15235e62 −0.146663
\(301\) −1.47872e63 −0.925639
\(302\) 3.90673e62 0.224717
\(303\) 5.45240e63 2.88271
\(304\) −6.42543e62 −0.312339
\(305\) 1.13478e62 0.0507303
\(306\) 6.78236e63 2.78923
\(307\) −4.26649e63 −1.61451 −0.807257 0.590200i \(-0.799049\pi\)
−0.807257 + 0.590200i \(0.799049\pi\)
\(308\) −4.42409e62 −0.154092
\(309\) −7.04065e63 −2.25773
\(310\) −1.02429e63 −0.302483
\(311\) 2.40513e63 0.654258 0.327129 0.944980i \(-0.393919\pi\)
0.327129 + 0.944980i \(0.393919\pi\)
\(312\) 3.52513e63 0.883555
\(313\) −4.21400e62 −0.0973451 −0.0486726 0.998815i \(-0.515499\pi\)
−0.0486726 + 0.998815i \(0.515499\pi\)
\(314\) −6.66736e63 −1.41987
\(315\) 6.31812e63 1.24071
\(316\) 1.21207e63 0.219536
\(317\) 3.76818e63 0.629681 0.314840 0.949145i \(-0.398049\pi\)
0.314840 + 0.949145i \(0.398049\pi\)
\(318\) −1.95602e64 −3.01634
\(319\) 1.00471e64 1.43014
\(320\) 4.29657e63 0.564674
\(321\) −1.15108e64 −1.39710
\(322\) 3.13987e63 0.352036
\(323\) 2.91414e63 0.301888
\(324\) 3.78208e63 0.362103
\(325\) 2.86831e63 0.253864
\(326\) 2.12118e64 1.73592
\(327\) −1.24078e62 −0.00939132
\(328\) 5.31588e63 0.372213
\(329\) 3.86959e63 0.250709
\(330\) −2.96866e64 −1.78014
\(331\) −3.48200e64 −1.93293 −0.966463 0.256807i \(-0.917330\pi\)
−0.966463 + 0.256807i \(0.917330\pi\)
\(332\) −5.38328e62 −0.0276710
\(333\) 2.84464e64 1.35425
\(334\) 2.22372e64 0.980719
\(335\) −1.28538e63 −0.0525278
\(336\) −4.01855e64 −1.52201
\(337\) −3.75434e64 −1.31817 −0.659085 0.752068i \(-0.729056\pi\)
−0.659085 + 0.752068i \(0.729056\pi\)
\(338\) −2.35795e64 −0.767641
\(339\) 7.38864e64 2.23086
\(340\) 4.88263e63 0.136755
\(341\) 1.83210e64 0.476117
\(342\) 2.86871e64 0.691864
\(343\) −4.78386e64 −1.07097
\(344\) 5.47516e64 1.13804
\(345\) 3.06815e64 0.592229
\(346\) 2.38931e64 0.428383
\(347\) 1.26312e63 0.0210399 0.0105200 0.999945i \(-0.496651\pi\)
0.0105200 + 0.999945i \(0.496651\pi\)
\(348\) −2.32278e64 −0.359533
\(349\) −6.61603e64 −0.951808 −0.475904 0.879497i \(-0.657879\pi\)
−0.475904 + 0.879497i \(0.657879\pi\)
\(350\) −2.78152e64 −0.372004
\(351\) −1.05844e65 −1.31624
\(352\) 3.61271e64 0.417826
\(353\) −1.20269e65 −1.29390 −0.646949 0.762533i \(-0.723955\pi\)
−0.646949 + 0.762533i \(0.723955\pi\)
\(354\) 3.09417e64 0.309714
\(355\) 3.70699e64 0.345302
\(356\) −6.57930e62 −0.00570433
\(357\) 1.82254e65 1.47109
\(358\) 2.62356e65 1.97185
\(359\) 1.83244e63 0.0128269 0.00641344 0.999979i \(-0.497959\pi\)
0.00641344 + 0.999979i \(0.497959\pi\)
\(360\) −2.33936e65 −1.52540
\(361\) −1.52276e65 −0.925117
\(362\) −2.41515e65 −1.36734
\(363\) 1.84816e65 0.975259
\(364\) −1.36303e64 −0.0670534
\(365\) 2.86225e65 1.31292
\(366\) 3.22239e64 0.137851
\(367\) 3.73824e65 1.49170 0.745851 0.666112i \(-0.232043\pi\)
0.745851 + 0.666112i \(0.232043\pi\)
\(368\) −1.36666e65 −0.508791
\(369\) −2.78996e65 −0.969226
\(370\) 1.40628e65 0.455961
\(371\) −3.68104e65 −1.11413
\(372\) −4.23563e64 −0.119694
\(373\) 4.09981e65 1.08190 0.540952 0.841054i \(-0.318064\pi\)
0.540952 + 0.841054i \(0.318064\pi\)
\(374\) −5.99724e65 −1.47817
\(375\) −8.48807e65 −1.95439
\(376\) −1.43276e65 −0.308236
\(377\) 3.09544e65 0.622326
\(378\) 1.02642e66 1.92878
\(379\) −3.52556e65 −0.619338 −0.309669 0.950844i \(-0.600218\pi\)
−0.309669 + 0.950844i \(0.600218\pi\)
\(380\) 2.06519e64 0.0339217
\(381\) 2.14930e66 3.30150
\(382\) −1.05979e66 −1.52266
\(383\) −5.89561e65 −0.792429 −0.396214 0.918158i \(-0.629676\pi\)
−0.396214 + 0.918158i \(0.629676\pi\)
\(384\) 1.71011e66 2.15069
\(385\) −5.58674e65 −0.657522
\(386\) 3.24180e65 0.357117
\(387\) −2.87355e66 −2.96340
\(388\) 2.56747e65 0.247912
\(389\) 1.54980e66 1.40140 0.700698 0.713458i \(-0.252872\pi\)
0.700698 + 0.713458i \(0.252872\pi\)
\(390\) −9.14624e65 −0.774632
\(391\) 6.19822e65 0.491768
\(392\) 5.63980e65 0.419246
\(393\) −2.86412e66 −1.99517
\(394\) −1.09049e66 −0.711983
\(395\) 1.53060e66 0.936775
\(396\) −8.59718e65 −0.493320
\(397\) −3.73577e65 −0.201012 −0.100506 0.994936i \(-0.532046\pi\)
−0.100506 + 0.994936i \(0.532046\pi\)
\(398\) 2.65788e66 1.34127
\(399\) 7.70874e65 0.364900
\(400\) 1.21068e66 0.537651
\(401\) −2.11569e65 −0.0881600 −0.0440800 0.999028i \(-0.514036\pi\)
−0.0440800 + 0.999028i \(0.514036\pi\)
\(402\) −3.65004e65 −0.142736
\(403\) 5.64459e65 0.207183
\(404\) 7.80598e65 0.268969
\(405\) 4.77601e66 1.54512
\(406\) −3.00177e66 −0.911936
\(407\) −2.51535e66 −0.717696
\(408\) −6.74819e66 −1.80864
\(409\) 1.06566e66 0.268332 0.134166 0.990959i \(-0.457164\pi\)
0.134166 + 0.990959i \(0.457164\pi\)
\(410\) −1.37925e66 −0.326328
\(411\) 4.79199e66 1.06549
\(412\) −1.00798e66 −0.210656
\(413\) 5.82293e65 0.114397
\(414\) 6.10159e66 1.12703
\(415\) −6.79800e65 −0.118074
\(416\) 1.11305e66 0.181817
\(417\) −1.58136e67 −2.42975
\(418\) −2.53663e66 −0.366659
\(419\) 5.15077e65 0.0700511 0.0350255 0.999386i \(-0.488849\pi\)
0.0350255 + 0.999386i \(0.488849\pi\)
\(420\) 1.29160e66 0.165299
\(421\) 5.05760e66 0.609187 0.304594 0.952482i \(-0.401479\pi\)
0.304594 + 0.952482i \(0.401479\pi\)
\(422\) −2.29112e65 −0.0259765
\(423\) 7.51963e66 0.802633
\(424\) 1.36295e67 1.36978
\(425\) −5.49083e66 −0.519661
\(426\) 1.05266e67 0.938301
\(427\) 6.06424e65 0.0509173
\(428\) −1.64795e66 −0.130355
\(429\) 1.63594e67 1.21929
\(430\) −1.42057e67 −0.997742
\(431\) −6.54142e66 −0.433014 −0.216507 0.976281i \(-0.569466\pi\)
−0.216507 + 0.976281i \(0.569466\pi\)
\(432\) −4.46757e67 −2.78763
\(433\) 3.67034e66 0.215906 0.107953 0.994156i \(-0.465570\pi\)
0.107953 + 0.994156i \(0.465570\pi\)
\(434\) −5.47378e66 −0.303598
\(435\) −2.93321e67 −1.53415
\(436\) −1.77637e64 −0.000876252 0
\(437\) 2.62164e66 0.121982
\(438\) 8.12779e67 3.56765
\(439\) 7.98143e66 0.330549 0.165274 0.986248i \(-0.447149\pi\)
0.165274 + 0.986248i \(0.447149\pi\)
\(440\) 2.06856e67 0.808398
\(441\) −2.95996e67 −1.09170
\(442\) −1.84771e67 −0.643229
\(443\) −1.14974e67 −0.377836 −0.188918 0.981993i \(-0.560498\pi\)
−0.188918 + 0.981993i \(0.560498\pi\)
\(444\) 5.81522e66 0.180426
\(445\) −8.30834e65 −0.0243407
\(446\) 2.67347e65 0.00739668
\(447\) 7.63643e67 1.99549
\(448\) 2.29607e67 0.566756
\(449\) −7.25393e67 −1.69158 −0.845789 0.533518i \(-0.820870\pi\)
−0.845789 + 0.533518i \(0.820870\pi\)
\(450\) −5.40523e67 −1.19095
\(451\) 2.46699e67 0.513649
\(452\) 1.05780e67 0.208149
\(453\) 2.04005e67 0.379435
\(454\) −2.93094e67 −0.515327
\(455\) −1.72124e67 −0.286121
\(456\) −2.85425e67 −0.448631
\(457\) −3.92391e67 −0.583251 −0.291626 0.956533i \(-0.594196\pi\)
−0.291626 + 0.956533i \(0.594196\pi\)
\(458\) −9.24022e67 −1.29901
\(459\) 2.02618e68 2.69436
\(460\) 4.39255e66 0.0552576
\(461\) −2.24623e67 −0.267350 −0.133675 0.991025i \(-0.542678\pi\)
−0.133675 + 0.991025i \(0.542678\pi\)
\(462\) −1.58644e68 −1.78671
\(463\) 8.68251e67 0.925401 0.462701 0.886515i \(-0.346880\pi\)
0.462701 + 0.886515i \(0.346880\pi\)
\(464\) 1.30655e68 1.31801
\(465\) −5.34876e67 −0.510743
\(466\) 1.06583e68 0.963493
\(467\) 3.24322e67 0.277585 0.138792 0.990322i \(-0.455678\pi\)
0.138792 + 0.990322i \(0.455678\pi\)
\(468\) −2.64873e67 −0.214669
\(469\) −6.86903e66 −0.0527215
\(470\) 3.71742e67 0.270238
\(471\) −3.48163e68 −2.39745
\(472\) −2.15601e67 −0.140647
\(473\) 2.54091e68 1.57047
\(474\) 4.34637e68 2.54553
\(475\) −2.32244e67 −0.128901
\(476\) 2.60926e67 0.137259
\(477\) −7.15323e68 −3.56684
\(478\) −2.27455e68 −1.07519
\(479\) 2.10847e68 0.944959 0.472479 0.881342i \(-0.343359\pi\)
0.472479 + 0.881342i \(0.343359\pi\)
\(480\) −1.05472e68 −0.448213
\(481\) −7.74961e67 −0.312306
\(482\) −2.25583e68 −0.862199
\(483\) 1.63961e68 0.594413
\(484\) 2.64593e67 0.0909960
\(485\) 3.24220e68 1.05785
\(486\) 5.02726e68 1.55635
\(487\) −1.64479e68 −0.483195 −0.241597 0.970377i \(-0.577671\pi\)
−0.241597 + 0.970377i \(0.577671\pi\)
\(488\) −2.24536e67 −0.0626009
\(489\) 1.10766e69 2.93110
\(490\) −1.46329e68 −0.367562
\(491\) −2.01454e68 −0.480395 −0.240197 0.970724i \(-0.577212\pi\)
−0.240197 + 0.970724i \(0.577212\pi\)
\(492\) −5.70343e67 −0.129130
\(493\) −5.92562e68 −1.27391
\(494\) −7.81518e67 −0.159552
\(495\) −1.08565e69 −2.10503
\(496\) 2.38251e68 0.438786
\(497\) 1.98100e68 0.346575
\(498\) −1.93040e68 −0.320847
\(499\) −3.52023e68 −0.555914 −0.277957 0.960594i \(-0.589657\pi\)
−0.277957 + 0.960594i \(0.589657\pi\)
\(500\) −1.21520e68 −0.182353
\(501\) 1.16120e69 1.65595
\(502\) −1.04382e68 −0.141476
\(503\) 1.03779e69 1.33698 0.668492 0.743719i \(-0.266940\pi\)
0.668492 + 0.743719i \(0.266940\pi\)
\(504\) −1.25015e69 −1.53103
\(505\) 9.85739e68 1.14771
\(506\) −5.39528e68 −0.597277
\(507\) −1.23130e69 −1.29616
\(508\) 3.07707e68 0.308044
\(509\) −1.43270e69 −1.36411 −0.682057 0.731299i \(-0.738914\pi\)
−0.682057 + 0.731299i \(0.738914\pi\)
\(510\) 1.75087e69 1.58568
\(511\) 1.52957e69 1.31776
\(512\) −7.79993e68 −0.639303
\(513\) 8.57008e68 0.668331
\(514\) 1.59472e69 1.18338
\(515\) −1.27288e69 −0.898883
\(516\) −5.87433e68 −0.394812
\(517\) −6.64917e68 −0.425362
\(518\) 7.51511e68 0.457642
\(519\) 1.24768e69 0.723326
\(520\) 6.37309e68 0.351775
\(521\) 7.41512e67 0.0389723 0.0194862 0.999810i \(-0.493797\pi\)
0.0194862 + 0.999810i \(0.493797\pi\)
\(522\) −5.83324e69 −2.91953
\(523\) −1.30708e69 −0.623030 −0.311515 0.950241i \(-0.600836\pi\)
−0.311515 + 0.950241i \(0.600836\pi\)
\(524\) −4.10044e68 −0.186158
\(525\) −1.45248e69 −0.628129
\(526\) 3.72020e69 1.53260
\(527\) −1.08055e69 −0.424104
\(528\) 6.90513e69 2.58230
\(529\) −2.24860e69 −0.801294
\(530\) −3.53628e69 −1.20091
\(531\) 1.13155e69 0.366238
\(532\) 1.10363e68 0.0340468
\(533\) 7.60064e68 0.223515
\(534\) −2.35928e68 −0.0661420
\(535\) −2.08104e69 −0.556235
\(536\) 2.54334e68 0.0648191
\(537\) 1.37000e70 3.32947
\(538\) −2.58850e69 −0.599930
\(539\) 2.61732e69 0.578553
\(540\) 1.43591e69 0.302752
\(541\) −7.56485e69 −1.52149 −0.760746 0.649049i \(-0.775167\pi\)
−0.760746 + 0.649049i \(0.775167\pi\)
\(542\) 2.73835e69 0.525421
\(543\) −1.26117e70 −2.30875
\(544\) −2.13072e69 −0.372182
\(545\) −2.24320e67 −0.00373902
\(546\) −4.88772e69 −0.777488
\(547\) −3.07662e68 −0.0467087 −0.0233543 0.999727i \(-0.507435\pi\)
−0.0233543 + 0.999727i \(0.507435\pi\)
\(548\) 6.86050e68 0.0994150
\(549\) 1.17844e69 0.163010
\(550\) 4.77953e69 0.631155
\(551\) −2.50634e69 −0.315990
\(552\) −6.07085e69 −0.730807
\(553\) 8.17946e69 0.940229
\(554\) 9.20357e69 1.01032
\(555\) 7.34346e69 0.769891
\(556\) −2.26398e69 −0.226707
\(557\) 2.02206e70 1.93414 0.967068 0.254519i \(-0.0819171\pi\)
0.967068 + 0.254519i \(0.0819171\pi\)
\(558\) −1.06370e70 −0.971958
\(559\) 7.82838e69 0.683393
\(560\) −7.26514e69 −0.605967
\(561\) −3.13170e70 −2.49590
\(562\) −6.33567e69 −0.482521
\(563\) 1.22868e69 0.0894285 0.0447142 0.999000i \(-0.485762\pi\)
0.0447142 + 0.999000i \(0.485762\pi\)
\(564\) 1.53722e69 0.106935
\(565\) 1.33579e70 0.888186
\(566\) 2.71389e69 0.172494
\(567\) 2.55228e70 1.55082
\(568\) −7.33491e69 −0.426100
\(569\) −5.32852e69 −0.295967 −0.147984 0.988990i \(-0.547278\pi\)
−0.147984 + 0.988990i \(0.547278\pi\)
\(570\) 7.40559e69 0.393324
\(571\) −6.57707e69 −0.334050 −0.167025 0.985953i \(-0.553416\pi\)
−0.167025 + 0.985953i \(0.553416\pi\)
\(572\) 2.34212e69 0.113765
\(573\) −5.53410e70 −2.57101
\(574\) −7.37064e69 −0.327531
\(575\) −4.93970e69 −0.209976
\(576\) 4.46187e70 1.81445
\(577\) −4.36043e70 −1.69647 −0.848235 0.529620i \(-0.822335\pi\)
−0.848235 + 0.529620i \(0.822335\pi\)
\(578\) 6.30816e69 0.234824
\(579\) 1.69284e70 0.602993
\(580\) −4.19936e69 −0.143143
\(581\) −3.63282e69 −0.118509
\(582\) 9.20674e70 2.87455
\(583\) 6.32518e70 1.89027
\(584\) −5.66343e70 −1.62014
\(585\) −3.34482e70 −0.916005
\(586\) 1.66363e70 0.436182
\(587\) 1.47836e70 0.371115 0.185557 0.982633i \(-0.440591\pi\)
0.185557 + 0.982633i \(0.440591\pi\)
\(588\) −6.05097e69 −0.145446
\(589\) −4.57035e69 −0.105198
\(590\) 5.59395e69 0.123308
\(591\) −5.69445e70 −1.20218
\(592\) −3.27102e70 −0.661424
\(593\) 4.45541e70 0.862964 0.431482 0.902122i \(-0.357991\pi\)
0.431482 + 0.902122i \(0.357991\pi\)
\(594\) −1.76370e71 −3.27244
\(595\) 3.29497e70 0.585692
\(596\) 1.09328e70 0.186188
\(597\) 1.38792e71 2.26474
\(598\) −1.66225e70 −0.259906
\(599\) −2.36232e70 −0.353961 −0.176980 0.984214i \(-0.556633\pi\)
−0.176980 + 0.984214i \(0.556633\pi\)
\(600\) 5.37800e70 0.772260
\(601\) −7.60000e70 −1.04596 −0.522979 0.852345i \(-0.675180\pi\)
−0.522979 + 0.852345i \(0.675180\pi\)
\(602\) −7.59149e70 −1.00142
\(603\) −1.33483e70 −0.168786
\(604\) 2.92067e69 0.0354030
\(605\) 3.34128e70 0.388286
\(606\) 2.79916e71 3.11871
\(607\) 7.81615e70 0.834990 0.417495 0.908679i \(-0.362908\pi\)
0.417495 + 0.908679i \(0.362908\pi\)
\(608\) −9.01223e69 −0.0923190
\(609\) −1.56750e71 −1.53981
\(610\) 5.82577e69 0.0548836
\(611\) −2.04856e70 −0.185096
\(612\) 5.07049e70 0.439429
\(613\) 9.82908e70 0.817091 0.408546 0.912738i \(-0.366036\pi\)
0.408546 + 0.912738i \(0.366036\pi\)
\(614\) −2.19033e71 −1.74669
\(615\) −7.20229e70 −0.551005
\(616\) 1.10543e71 0.811378
\(617\) 6.23909e68 0.00439389 0.00219695 0.999998i \(-0.499301\pi\)
0.00219695 + 0.999998i \(0.499301\pi\)
\(618\) −3.61454e71 −2.44257
\(619\) −3.87928e70 −0.251559 −0.125779 0.992058i \(-0.540143\pi\)
−0.125779 + 0.992058i \(0.540143\pi\)
\(620\) −7.65760e69 −0.0476546
\(621\) 1.82281e71 1.08869
\(622\) 1.23475e71 0.707822
\(623\) −4.43994e69 −0.0244305
\(624\) 2.12742e71 1.12369
\(625\) −6.05579e70 −0.307065
\(626\) −2.16339e70 −0.105315
\(627\) −1.32460e71 −0.619104
\(628\) −4.98451e70 −0.223692
\(629\) 1.48351e71 0.639293
\(630\) 3.24361e71 1.34228
\(631\) −4.57404e71 −1.81782 −0.908911 0.416989i \(-0.863085\pi\)
−0.908911 + 0.416989i \(0.863085\pi\)
\(632\) −3.02855e71 −1.15598
\(633\) −1.19640e70 −0.0438614
\(634\) 1.93451e71 0.681233
\(635\) 3.88573e71 1.31444
\(636\) −1.46232e71 −0.475209
\(637\) 8.06377e70 0.251758
\(638\) 5.15799e71 1.54723
\(639\) 3.84961e71 1.10955
\(640\) 3.09170e71 0.856266
\(641\) −3.22553e71 −0.858463 −0.429231 0.903195i \(-0.641216\pi\)
−0.429231 + 0.903195i \(0.641216\pi\)
\(642\) −5.90942e71 −1.51148
\(643\) −7.02269e71 −1.72633 −0.863165 0.504922i \(-0.831521\pi\)
−0.863165 + 0.504922i \(0.831521\pi\)
\(644\) 2.34736e70 0.0554613
\(645\) −7.41810e71 −1.68469
\(646\) 1.49606e71 0.326604
\(647\) 8.46993e71 1.77755 0.888773 0.458347i \(-0.151558\pi\)
0.888773 + 0.458347i \(0.151558\pi\)
\(648\) −9.45013e71 −1.90667
\(649\) −1.00056e71 −0.194091
\(650\) 1.47254e71 0.274648
\(651\) −2.85836e71 −0.512626
\(652\) 1.58580e71 0.273485
\(653\) 7.34453e71 1.21809 0.609043 0.793137i \(-0.291554\pi\)
0.609043 + 0.793137i \(0.291554\pi\)
\(654\) −6.36992e69 −0.0101602
\(655\) −5.17803e71 −0.794350
\(656\) 3.20814e71 0.473375
\(657\) 2.97237e72 4.21876
\(658\) 1.98657e71 0.271234
\(659\) 5.48627e70 0.0720608 0.0360304 0.999351i \(-0.488529\pi\)
0.0360304 + 0.999351i \(0.488529\pi\)
\(660\) −2.21937e71 −0.280452
\(661\) −9.86251e71 −1.19909 −0.599543 0.800343i \(-0.704651\pi\)
−0.599543 + 0.800343i \(0.704651\pi\)
\(662\) −1.78759e72 −2.09117
\(663\) −9.64855e71 −1.08609
\(664\) 1.34510e71 0.145703
\(665\) 1.39366e71 0.145280
\(666\) 1.46038e72 1.46512
\(667\) −5.33085e71 −0.514740
\(668\) 1.66245e71 0.154507
\(669\) 1.39606e70 0.0124893
\(670\) −6.59890e70 −0.0568283
\(671\) −1.04203e71 −0.0863883
\(672\) −5.63637e71 −0.449866
\(673\) 1.21639e72 0.934739 0.467369 0.884062i \(-0.345202\pi\)
0.467369 + 0.884062i \(0.345202\pi\)
\(674\) −1.92741e72 −1.42609
\(675\) −1.61478e72 −1.15045
\(676\) −1.76280e71 −0.120938
\(677\) −9.64935e71 −0.637510 −0.318755 0.947837i \(-0.603265\pi\)
−0.318755 + 0.947837i \(0.603265\pi\)
\(678\) 3.79319e72 2.41350
\(679\) 1.73262e72 1.06176
\(680\) −1.22000e72 −0.720086
\(681\) −1.53051e72 −0.870131
\(682\) 9.40568e71 0.515097
\(683\) 3.44340e72 1.81660 0.908299 0.418321i \(-0.137381\pi\)
0.908299 + 0.418321i \(0.137381\pi\)
\(684\) 2.14464e71 0.109000
\(685\) 8.66344e71 0.424210
\(686\) −2.45594e72 −1.15865
\(687\) −4.82515e72 −2.19338
\(688\) 3.30427e72 1.44734
\(689\) 1.94874e72 0.822554
\(690\) 1.57513e72 0.640715
\(691\) −1.61159e70 −0.00631779 −0.00315889 0.999995i \(-0.501006\pi\)
−0.00315889 + 0.999995i \(0.501006\pi\)
\(692\) 1.78625e71 0.0674895
\(693\) −5.80168e72 −2.11279
\(694\) 6.48463e70 0.0227624
\(695\) −2.85895e72 −0.967373
\(696\) 5.80385e72 1.89313
\(697\) −1.45499e72 −0.457536
\(698\) −3.39655e72 −1.02973
\(699\) 5.56568e72 1.62686
\(700\) −2.07946e71 −0.0586072
\(701\) 7.31953e71 0.198918 0.0994589 0.995042i \(-0.468289\pi\)
0.0994589 + 0.995042i \(0.468289\pi\)
\(702\) −5.43385e72 −1.42400
\(703\) 6.27476e71 0.158575
\(704\) −3.94537e72 −0.961579
\(705\) 1.94120e72 0.456297
\(706\) −6.17440e72 −1.39983
\(707\) 5.26775e72 1.15194
\(708\) 2.31320e71 0.0487938
\(709\) −4.60802e72 −0.937637 −0.468819 0.883294i \(-0.655320\pi\)
−0.468819 + 0.883294i \(0.655320\pi\)
\(710\) 1.90310e72 0.373571
\(711\) 1.58949e73 3.01011
\(712\) 1.64394e71 0.0300364
\(713\) −9.72089e71 −0.171365
\(714\) 9.35659e72 1.59152
\(715\) 2.95763e72 0.485444
\(716\) 1.96137e72 0.310655
\(717\) −1.18775e73 −1.81545
\(718\) 9.40739e70 0.0138770
\(719\) 8.14014e72 1.15890 0.579449 0.815009i \(-0.303268\pi\)
0.579449 + 0.815009i \(0.303268\pi\)
\(720\) −1.41181e73 −1.93998
\(721\) −6.80222e72 −0.902197
\(722\) −7.81754e72 −1.00086
\(723\) −1.17797e73 −1.45582
\(724\) −1.80557e72 −0.215417
\(725\) 4.72245e72 0.543937
\(726\) 9.48809e72 1.05510
\(727\) −8.09226e72 −0.868845 −0.434423 0.900709i \(-0.643048\pi\)
−0.434423 + 0.900709i \(0.643048\pi\)
\(728\) 3.40576e72 0.353072
\(729\) 5.02892e72 0.503411
\(730\) 1.46942e73 1.42041
\(731\) −1.49859e73 −1.39891
\(732\) 2.40906e71 0.0217177
\(733\) 1.72167e73 1.49899 0.749495 0.662010i \(-0.230297\pi\)
0.749495 + 0.662010i \(0.230297\pi\)
\(734\) 1.91914e73 1.61383
\(735\) −7.64116e72 −0.620629
\(736\) −1.91685e72 −0.150385
\(737\) 1.18031e72 0.0894493
\(738\) −1.43231e73 −1.04858
\(739\) −4.89392e72 −0.346118 −0.173059 0.984911i \(-0.555365\pi\)
−0.173059 + 0.984911i \(0.555365\pi\)
\(740\) 1.05133e72 0.0718343
\(741\) −4.08101e72 −0.269404
\(742\) −1.88978e73 −1.20534
\(743\) 1.78935e73 1.10276 0.551379 0.834255i \(-0.314102\pi\)
0.551379 + 0.834255i \(0.314102\pi\)
\(744\) 1.05834e73 0.630254
\(745\) 1.38059e73 0.794475
\(746\) 2.10477e73 1.17048
\(747\) −7.05954e72 −0.379403
\(748\) −4.48353e72 −0.232879
\(749\) −1.11210e73 −0.558286
\(750\) −4.35762e73 −2.11440
\(751\) 1.11871e73 0.524685 0.262343 0.964975i \(-0.415505\pi\)
0.262343 + 0.964975i \(0.415505\pi\)
\(752\) −8.64674e72 −0.392010
\(753\) −5.45075e72 −0.238882
\(754\) 1.58914e73 0.673276
\(755\) 3.68822e72 0.151067
\(756\) 7.67347e72 0.303869
\(757\) −7.85188e72 −0.300628 −0.150314 0.988638i \(-0.548028\pi\)
−0.150314 + 0.988638i \(0.548028\pi\)
\(758\) −1.80995e73 −0.670043
\(759\) −2.81736e73 −1.00850
\(760\) −5.16021e72 −0.178616
\(761\) −3.37728e73 −1.13047 −0.565234 0.824931i \(-0.691214\pi\)
−0.565234 + 0.824931i \(0.691214\pi\)
\(762\) 1.10341e74 3.57179
\(763\) −1.19876e71 −0.00375281
\(764\) −7.92296e72 −0.239887
\(765\) 6.40301e73 1.87507
\(766\) −3.02670e73 −0.857305
\(767\) −3.08266e72 −0.0844587
\(768\) 3.42785e73 0.908471
\(769\) −7.30333e73 −1.87240 −0.936202 0.351464i \(-0.885684\pi\)
−0.936202 + 0.351464i \(0.885684\pi\)
\(770\) −2.86813e73 −0.711353
\(771\) 8.32747e73 1.99814
\(772\) 2.42357e72 0.0562619
\(773\) 8.48856e73 1.90659 0.953294 0.302043i \(-0.0976687\pi\)
0.953294 + 0.302043i \(0.0976687\pi\)
\(774\) −1.47523e74 −3.20601
\(775\) 8.61146e72 0.181085
\(776\) −6.41525e73 −1.30539
\(777\) 3.92431e73 0.772730
\(778\) 7.95638e73 1.51613
\(779\) −6.15414e72 −0.113491
\(780\) −6.83772e72 −0.122039
\(781\) −3.40398e73 −0.588012
\(782\) 3.18205e73 0.532029
\(783\) −1.74264e74 −2.82022
\(784\) 3.40363e73 0.533190
\(785\) −6.29443e73 −0.954510
\(786\) −1.47038e74 −2.15852
\(787\) 5.38760e73 0.765667 0.382833 0.923817i \(-0.374948\pi\)
0.382833 + 0.923817i \(0.374948\pi\)
\(788\) −8.15252e72 −0.112169
\(789\) 1.94265e74 2.58781
\(790\) 7.85780e73 1.01347
\(791\) 7.13843e73 0.891461
\(792\) 2.14815e74 2.59760
\(793\) −3.21041e72 −0.0375919
\(794\) −1.91788e73 −0.217469
\(795\) −1.84661e74 −2.02775
\(796\) 1.98703e73 0.211311
\(797\) −6.28418e73 −0.647234 −0.323617 0.946188i \(-0.604899\pi\)
−0.323617 + 0.946188i \(0.604899\pi\)
\(798\) 3.95752e73 0.394775
\(799\) 3.92157e73 0.378894
\(800\) 1.69809e73 0.158915
\(801\) −8.62799e72 −0.0782132
\(802\) −1.08616e73 −0.0953776
\(803\) −2.62829e74 −2.23577
\(804\) −2.72876e72 −0.0224873
\(805\) 2.96425e73 0.236657
\(806\) 2.89782e73 0.224145
\(807\) −1.35169e74 −1.01298
\(808\) −1.95045e74 −1.41627
\(809\) 9.71872e73 0.683788 0.341894 0.939738i \(-0.388932\pi\)
0.341894 + 0.939738i \(0.388932\pi\)
\(810\) 2.45191e74 1.67162
\(811\) 1.93558e74 1.27873 0.639366 0.768903i \(-0.279197\pi\)
0.639366 + 0.768903i \(0.279197\pi\)
\(812\) −2.24412e73 −0.143671
\(813\) 1.42994e74 0.887174
\(814\) −1.29133e74 −0.776454
\(815\) 2.00254e74 1.16698
\(816\) −4.07254e74 −2.30020
\(817\) −6.33853e73 −0.346998
\(818\) 5.47088e73 0.290300
\(819\) −1.78746e74 −0.919383
\(820\) −1.03112e73 −0.0514112
\(821\) −8.81688e73 −0.426152 −0.213076 0.977036i \(-0.568348\pi\)
−0.213076 + 0.977036i \(0.568348\pi\)
\(822\) 2.46012e74 1.15272
\(823\) −1.57751e74 −0.716600 −0.358300 0.933606i \(-0.616644\pi\)
−0.358300 + 0.933606i \(0.616644\pi\)
\(824\) 2.51861e74 1.10922
\(825\) 2.49582e74 1.06571
\(826\) 2.98938e73 0.123763
\(827\) 4.29357e74 1.72357 0.861784 0.507276i \(-0.169347\pi\)
0.861784 + 0.507276i \(0.169347\pi\)
\(828\) 4.56154e73 0.177557
\(829\) −4.05215e74 −1.52949 −0.764743 0.644336i \(-0.777134\pi\)
−0.764743 + 0.644336i \(0.777134\pi\)
\(830\) −3.48996e73 −0.127741
\(831\) 4.80601e74 1.70592
\(832\) −1.21554e74 −0.418432
\(833\) −1.54365e74 −0.515350
\(834\) −8.11843e74 −2.62868
\(835\) 2.09934e74 0.659292
\(836\) −1.89638e73 −0.0577651
\(837\) −3.17774e74 −0.938898
\(838\) 2.64431e73 0.0757862
\(839\) 3.20891e73 0.0892128 0.0446064 0.999005i \(-0.485797\pi\)
0.0446064 + 0.999005i \(0.485797\pi\)
\(840\) −3.22726e74 −0.870387
\(841\) 1.27433e74 0.333415
\(842\) 2.59647e74 0.659061
\(843\) −3.30842e74 −0.814738
\(844\) −1.71284e72 −0.00409246
\(845\) −2.22606e74 −0.516049
\(846\) 3.86044e74 0.868345
\(847\) 1.78557e74 0.389717
\(848\) 8.22542e74 1.74206
\(849\) 1.41717e74 0.291256
\(850\) −2.81889e74 −0.562206
\(851\) 1.33461e74 0.258315
\(852\) 7.86966e73 0.147824
\(853\) −3.28210e74 −0.598345 −0.299172 0.954199i \(-0.596711\pi\)
−0.299172 + 0.954199i \(0.596711\pi\)
\(854\) 3.11327e73 0.0550859
\(855\) 2.70826e74 0.465108
\(856\) 4.11768e74 0.686391
\(857\) −1.05278e75 −1.70344 −0.851719 0.523999i \(-0.824440\pi\)
−0.851719 + 0.523999i \(0.824440\pi\)
\(858\) 8.39863e74 1.31912
\(859\) 7.91408e74 1.20663 0.603316 0.797502i \(-0.293846\pi\)
0.603316 + 0.797502i \(0.293846\pi\)
\(860\) −1.06202e74 −0.157189
\(861\) −3.84888e74 −0.553036
\(862\) −3.35824e74 −0.468465
\(863\) −9.98167e74 −1.35185 −0.675924 0.736971i \(-0.736255\pi\)
−0.675924 + 0.736971i \(0.736255\pi\)
\(864\) −6.26615e74 −0.823950
\(865\) 2.25567e74 0.287982
\(866\) 1.88428e74 0.233582
\(867\) 3.29406e74 0.396501
\(868\) −4.09219e73 −0.0478303
\(869\) −1.40549e75 −1.59523
\(870\) −1.50586e75 −1.65975
\(871\) 3.63647e73 0.0389239
\(872\) 4.43856e72 0.00461393
\(873\) 3.36694e75 3.39917
\(874\) 1.34590e74 0.131969
\(875\) −8.20062e74 −0.780983
\(876\) 6.07633e74 0.562065
\(877\) 8.86567e73 0.0796567 0.0398283 0.999207i \(-0.487319\pi\)
0.0398283 + 0.999207i \(0.487319\pi\)
\(878\) 4.09752e74 0.357611
\(879\) 8.68732e74 0.736494
\(880\) 1.24838e75 1.02811
\(881\) −4.12425e74 −0.329958 −0.164979 0.986297i \(-0.552756\pi\)
−0.164979 + 0.986297i \(0.552756\pi\)
\(882\) −1.51959e75 −1.18107
\(883\) −3.74600e74 −0.282859 −0.141429 0.989948i \(-0.545170\pi\)
−0.141429 + 0.989948i \(0.545170\pi\)
\(884\) −1.38134e74 −0.101337
\(885\) 2.92110e74 0.208206
\(886\) −5.90253e74 −0.408770
\(887\) 7.25014e74 0.487859 0.243929 0.969793i \(-0.421563\pi\)
0.243929 + 0.969793i \(0.421563\pi\)
\(888\) −1.45303e75 −0.950042
\(889\) 2.07652e75 1.31929
\(890\) −4.26534e73 −0.0263335
\(891\) −4.38562e75 −2.63117
\(892\) 1.99868e72 0.00116531
\(893\) 1.65869e74 0.0939840
\(894\) 3.92040e75 2.15886
\(895\) 2.47682e75 1.32558
\(896\) 1.65219e75 0.859423
\(897\) −8.68009e74 −0.438851
\(898\) −3.72403e75 −1.83007
\(899\) 9.29336e74 0.443916
\(900\) −4.04094e74 −0.187629
\(901\) −3.73049e75 −1.68377
\(902\) 1.26651e75 0.555701
\(903\) −3.96420e75 −1.69090
\(904\) −2.64309e75 −1.09602
\(905\) −2.28007e75 −0.919198
\(906\) 1.04733e75 0.410500
\(907\) 2.49801e75 0.951936 0.475968 0.879463i \(-0.342098\pi\)
0.475968 + 0.879463i \(0.342098\pi\)
\(908\) −2.19117e74 −0.0811871
\(909\) 1.02366e76 3.68789
\(910\) −8.83650e74 −0.309546
\(911\) 4.96282e75 1.69048 0.845240 0.534387i \(-0.179457\pi\)
0.845240 + 0.534387i \(0.179457\pi\)
\(912\) −1.72255e75 −0.570562
\(913\) 6.24233e74 0.201068
\(914\) −2.01446e75 −0.631002
\(915\) 3.04216e74 0.0926710
\(916\) −6.90798e74 −0.204652
\(917\) −2.76712e75 −0.797279
\(918\) 1.04021e76 2.91495
\(919\) 8.27126e74 0.225437 0.112719 0.993627i \(-0.464044\pi\)
0.112719 + 0.993627i \(0.464044\pi\)
\(920\) −1.09755e75 −0.290961
\(921\) −1.14377e76 −2.94930
\(922\) −1.15317e75 −0.289238
\(923\) −1.04874e75 −0.255874
\(924\) −1.18602e75 −0.281487
\(925\) −1.18229e75 −0.272967
\(926\) 4.45744e75 1.00116
\(927\) −1.32185e76 −2.88835
\(928\) 1.83255e75 0.389567
\(929\) 6.26908e75 1.29659 0.648296 0.761389i \(-0.275482\pi\)
0.648296 + 0.761389i \(0.275482\pi\)
\(930\) −2.74595e75 −0.552558
\(931\) −6.52913e74 −0.127832
\(932\) 7.96816e74 0.151793
\(933\) 6.44774e75 1.19516
\(934\) 1.66501e75 0.300311
\(935\) −5.66180e75 −0.993707
\(936\) 6.61829e75 1.13035
\(937\) 4.04271e75 0.671913 0.335956 0.941878i \(-0.390941\pi\)
0.335956 + 0.941878i \(0.390941\pi\)
\(938\) −3.52643e74 −0.0570378
\(939\) −1.12970e75 −0.177824
\(940\) 2.77914e74 0.0425745
\(941\) 5.70557e75 0.850675 0.425337 0.905035i \(-0.360155\pi\)
0.425337 + 0.905035i \(0.360155\pi\)
\(942\) −1.78740e76 −2.59373
\(943\) −1.30895e75 −0.184874
\(944\) −1.30116e75 −0.178873
\(945\) 9.69005e75 1.29663
\(946\) 1.30446e76 1.69905
\(947\) 9.10957e75 1.15498 0.577489 0.816399i \(-0.304033\pi\)
0.577489 + 0.816399i \(0.304033\pi\)
\(948\) 3.24934e75 0.401035
\(949\) −8.09757e75 −0.972896
\(950\) −1.19230e75 −0.139454
\(951\) 1.01018e76 1.15026
\(952\) −6.51966e75 −0.722741
\(953\) −8.74403e75 −0.943719 −0.471859 0.881674i \(-0.656417\pi\)
−0.471859 + 0.881674i \(0.656417\pi\)
\(954\) −3.67233e76 −3.85886
\(955\) −1.00051e76 −1.02361
\(956\) −1.70045e75 −0.169390
\(957\) 2.69345e76 2.61249
\(958\) 1.08245e76 1.02232
\(959\) 4.62971e75 0.425774
\(960\) 1.15184e76 1.03151
\(961\) −9.77225e75 −0.852213
\(962\) −3.97850e75 −0.337874
\(963\) −2.16110e76 −1.78733
\(964\) −1.68646e75 −0.135835
\(965\) 3.06048e75 0.240073
\(966\) 8.41744e75 0.643077
\(967\) 8.14685e75 0.606198 0.303099 0.952959i \(-0.401979\pi\)
0.303099 + 0.952959i \(0.401979\pi\)
\(968\) −6.61129e75 −0.479143
\(969\) 7.81230e75 0.551471
\(970\) 1.66449e76 1.14446
\(971\) −7.24090e75 −0.484956 −0.242478 0.970157i \(-0.577960\pi\)
−0.242478 + 0.970157i \(0.577960\pi\)
\(972\) 3.75838e75 0.245194
\(973\) −1.52781e76 −0.970940
\(974\) −8.44405e75 −0.522754
\(975\) 7.68945e75 0.463743
\(976\) −1.35508e75 −0.0796148
\(977\) −2.93870e76 −1.68207 −0.841034 0.540982i \(-0.818053\pi\)
−0.841034 + 0.540982i \(0.818053\pi\)
\(978\) 5.68653e76 3.17107
\(979\) 7.62922e74 0.0414497
\(980\) −1.09395e75 −0.0579074
\(981\) −2.32951e74 −0.0120145
\(982\) −1.03423e76 −0.519725
\(983\) 3.52481e76 1.72592 0.862961 0.505271i \(-0.168607\pi\)
0.862961 + 0.505271i \(0.168607\pi\)
\(984\) 1.42509e76 0.679937
\(985\) −1.02950e76 −0.478633
\(986\) −3.04210e76 −1.37820
\(987\) 1.03737e76 0.457979
\(988\) −5.84262e74 −0.0251365
\(989\) −1.34817e76 −0.565249
\(990\) −5.57353e76 −2.27737
\(991\) 1.68555e76 0.671218 0.335609 0.942001i \(-0.391058\pi\)
0.335609 + 0.942001i \(0.391058\pi\)
\(992\) 3.34169e75 0.129693
\(993\) −9.33464e76 −3.53095
\(994\) 1.01701e76 0.374949
\(995\) 2.50922e76 0.901676
\(996\) −1.44316e75 −0.0505478
\(997\) 8.12879e75 0.277523 0.138762 0.990326i \(-0.455688\pi\)
0.138762 + 0.990326i \(0.455688\pi\)
\(998\) −1.80722e76 −0.601426
\(999\) 4.36280e76 1.41529
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 1.52.a.a.1.3 4
3.2 odd 2 9.52.a.b.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.52.a.a.1.3 4 1.1 even 1 trivial
9.52.a.b.1.2 4 3.2 odd 2