Properties

Label 1.54.a.a.1.1
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 1.1
Root \(-1.26509e6\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.38568e8 q^{2} -5.95414e12 q^{3} +1.01938e16 q^{4} -5.35900e18 q^{5} +8.25051e20 q^{6} +2.55363e22 q^{7} -1.64427e23 q^{8} +1.60685e25 q^{9} +O(q^{10})\) \(q-1.38568e8 q^{2} -5.95414e12 q^{3} +1.01938e16 q^{4} -5.35900e18 q^{5} +8.25051e20 q^{6} +2.55363e22 q^{7} -1.64427e23 q^{8} +1.60685e25 q^{9} +7.42585e26 q^{10} +2.25708e27 q^{11} -6.06954e28 q^{12} +1.44397e29 q^{13} -3.53851e30 q^{14} +3.19082e31 q^{15} -6.90335e31 q^{16} -6.08256e32 q^{17} -2.22657e33 q^{18} +5.84282e33 q^{19} -5.46287e34 q^{20} -1.52047e35 q^{21} -3.12758e35 q^{22} +9.54096e35 q^{23} +9.79021e35 q^{24} +1.76167e37 q^{25} -2.00088e37 q^{26} +1.97365e37 q^{27} +2.60313e38 q^{28} -4.38838e37 q^{29} -4.42145e39 q^{30} +8.43957e38 q^{31} +1.10468e40 q^{32} -1.34390e40 q^{33} +8.42846e40 q^{34} -1.36849e41 q^{35} +1.63799e41 q^{36} +1.19964e41 q^{37} -8.09626e41 q^{38} -8.59760e41 q^{39} +8.81165e41 q^{40} -8.08650e42 q^{41} +2.10688e43 q^{42} +1.66354e43 q^{43} +2.30083e43 q^{44} -8.61111e43 q^{45} -1.32207e44 q^{46} -7.16487e42 q^{47} +4.11035e44 q^{48} +3.52310e43 q^{49} -2.44110e45 q^{50} +3.62164e45 q^{51} +1.47196e45 q^{52} +3.19144e45 q^{53} -2.73484e45 q^{54} -1.20957e46 q^{55} -4.19887e45 q^{56} -3.47889e46 q^{57} +6.08088e45 q^{58} +3.07882e46 q^{59} +3.25267e47 q^{60} -2.46965e47 q^{61} -1.16945e47 q^{62} +4.10330e47 q^{63} -9.08937e47 q^{64} -7.73825e47 q^{65} +1.86221e48 q^{66} +1.37146e48 q^{67} -6.20045e48 q^{68} -5.68081e48 q^{69} +1.89629e49 q^{70} +1.40028e49 q^{71} -2.64209e48 q^{72} -1.59560e49 q^{73} -1.66231e49 q^{74} -1.04892e50 q^{75} +5.95606e49 q^{76} +5.76375e49 q^{77} +1.19135e50 q^{78} -1.73480e50 q^{79} +3.69950e50 q^{80} -4.28973e50 q^{81} +1.12053e51 q^{82} -1.32890e51 q^{83} -1.54994e51 q^{84} +3.25964e51 q^{85} -2.30513e51 q^{86} +2.61290e50 q^{87} -3.71125e50 q^{88} -6.74530e51 q^{89} +1.19322e52 q^{90} +3.68737e51 q^{91} +9.72588e51 q^{92} -5.02503e51 q^{93} +9.92819e50 q^{94} -3.13117e52 q^{95} -6.57744e52 q^{96} +4.44346e52 q^{97} -4.88188e51 q^{98} +3.62679e52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + O(q^{10}) \) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + \)\(23\!\cdots\!00\)\(q^{10} + \)\(24\!\cdots\!28\)\(q^{11} - \)\(36\!\cdots\!40\)\(q^{12} + \)\(38\!\cdots\!40\)\(q^{13} - \)\(23\!\cdots\!24\)\(q^{14} + \)\(10\!\cdots\!00\)\(q^{15} - \)\(15\!\cdots\!36\)\(q^{16} - \)\(86\!\cdots\!60\)\(q^{17} - \)\(67\!\cdots\!80\)\(q^{18} - \)\(25\!\cdots\!60\)\(q^{19} - \)\(13\!\cdots\!00\)\(q^{20} - \)\(45\!\cdots\!32\)\(q^{21} - \)\(93\!\cdots\!40\)\(q^{22} + \)\(69\!\cdots\!60\)\(q^{23} + \)\(80\!\cdots\!20\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} + \)\(88\!\cdots\!88\)\(q^{26} + \)\(85\!\cdots\!40\)\(q^{27} - \)\(56\!\cdots\!60\)\(q^{28} - \)\(14\!\cdots\!40\)\(q^{29} - \)\(57\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!32\)\(q^{31} + \)\(34\!\cdots\!80\)\(q^{32} + \)\(26\!\cdots\!40\)\(q^{33} + \)\(14\!\cdots\!36\)\(q^{34} + \)\(61\!\cdots\!00\)\(q^{35} + \)\(74\!\cdots\!84\)\(q^{36} - \)\(28\!\cdots\!80\)\(q^{37} - \)\(21\!\cdots\!40\)\(q^{38} - \)\(36\!\cdots\!16\)\(q^{39} - \)\(53\!\cdots\!00\)\(q^{40} + \)\(81\!\cdots\!88\)\(q^{41} + \)\(34\!\cdots\!40\)\(q^{42} + \)\(45\!\cdots\!00\)\(q^{43} + \)\(36\!\cdots\!96\)\(q^{44} - \)\(52\!\cdots\!00\)\(q^{45} - \)\(28\!\cdots\!52\)\(q^{46} - \)\(45\!\cdots\!40\)\(q^{47} - \)\(30\!\cdots\!40\)\(q^{48} + \)\(61\!\cdots\!28\)\(q^{49} + \)\(52\!\cdots\!00\)\(q^{50} + \)\(48\!\cdots\!48\)\(q^{51} + \)\(64\!\cdots\!00\)\(q^{52} + \)\(38\!\cdots\!20\)\(q^{53} - \)\(90\!\cdots\!60\)\(q^{54} - \)\(25\!\cdots\!00\)\(q^{55} - \)\(41\!\cdots\!60\)\(q^{56} - \)\(78\!\cdots\!20\)\(q^{57} + \)\(23\!\cdots\!40\)\(q^{58} + \)\(16\!\cdots\!20\)\(q^{59} + \)\(40\!\cdots\!00\)\(q^{60} + \)\(65\!\cdots\!28\)\(q^{61} + \)\(39\!\cdots\!60\)\(q^{62} - \)\(30\!\cdots\!20\)\(q^{63} - \)\(10\!\cdots\!32\)\(q^{64} - \)\(34\!\cdots\!00\)\(q^{65} - \)\(65\!\cdots\!04\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} + \)\(28\!\cdots\!20\)\(q^{68} + \)\(77\!\cdots\!64\)\(q^{69} + \)\(33\!\cdots\!00\)\(q^{70} + \)\(35\!\cdots\!48\)\(q^{71} + \)\(26\!\cdots\!20\)\(q^{72} - \)\(70\!\cdots\!40\)\(q^{73} - \)\(24\!\cdots\!44\)\(q^{74} - \)\(21\!\cdots\!00\)\(q^{75} + \)\(45\!\cdots\!80\)\(q^{76} - \)\(16\!\cdots\!00\)\(q^{77} + \)\(51\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!40\)\(q^{79} + \)\(11\!\cdots\!00\)\(q^{80} - \)\(49\!\cdots\!56\)\(q^{81} + \)\(15\!\cdots\!60\)\(q^{82} - \)\(26\!\cdots\!20\)\(q^{83} - \)\(76\!\cdots\!24\)\(q^{84} - \)\(23\!\cdots\!00\)\(q^{85} - \)\(77\!\cdots\!32\)\(q^{86} - \)\(45\!\cdots\!80\)\(q^{87} + \)\(56\!\cdots\!80\)\(q^{88} - \)\(37\!\cdots\!20\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(12\!\cdots\!28\)\(q^{91} + \)\(89\!\cdots\!40\)\(q^{92} - \)\(99\!\cdots\!60\)\(q^{93} - \)\(37\!\cdots\!84\)\(q^{94} - \)\(17\!\cdots\!00\)\(q^{95} - \)\(11\!\cdots\!92\)\(q^{96} + \)\(10\!\cdots\!60\)\(q^{97} - \)\(88\!\cdots\!40\)\(q^{98} + \)\(20\!\cdots\!84\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38568e8 −1.46005 −0.730024 0.683421i \(-0.760491\pi\)
−0.730024 + 0.683421i \(0.760491\pi\)
\(3\) −5.95414e12 −1.35240 −0.676201 0.736718i \(-0.736375\pi\)
−0.676201 + 0.736718i \(0.736375\pi\)
\(4\) 1.01938e16 1.13174
\(5\) −5.35900e18 −1.60834 −0.804172 0.594397i \(-0.797391\pi\)
−0.804172 + 0.594397i \(0.797391\pi\)
\(6\) 8.25051e20 1.97457
\(7\) 2.55363e22 1.02816 0.514080 0.857742i \(-0.328134\pi\)
0.514080 + 0.857742i \(0.328134\pi\)
\(8\) −1.64427e23 −0.192348
\(9\) 1.60685e25 0.828989
\(10\) 7.42585e26 2.34826
\(11\) 2.25708e27 0.571006 0.285503 0.958378i \(-0.407839\pi\)
0.285503 + 0.958378i \(0.407839\pi\)
\(12\) −6.06954e28 −1.53057
\(13\) 1.44397e29 0.436576 0.218288 0.975884i \(-0.429953\pi\)
0.218288 + 0.975884i \(0.429953\pi\)
\(14\) −3.53851e30 −1.50116
\(15\) 3.19082e31 2.17513
\(16\) −6.90335e31 −0.850903
\(17\) −6.08256e32 −1.50380 −0.751899 0.659278i \(-0.770862\pi\)
−0.751899 + 0.659278i \(0.770862\pi\)
\(18\) −2.22657e33 −1.21036
\(19\) 5.84282e33 0.757970 0.378985 0.925403i \(-0.376273\pi\)
0.378985 + 0.925403i \(0.376273\pi\)
\(20\) −5.46287e34 −1.82023
\(21\) −1.52047e35 −1.39048
\(22\) −3.12758e35 −0.833696
\(23\) 9.54096e35 0.783077 0.391538 0.920162i \(-0.371943\pi\)
0.391538 + 0.920162i \(0.371943\pi\)
\(24\) 9.79021e35 0.260132
\(25\) 1.76167e37 1.58677
\(26\) −2.00088e37 −0.637422
\(27\) 1.97365e37 0.231276
\(28\) 2.60313e38 1.16361
\(29\) −4.38838e37 −0.0774029 −0.0387015 0.999251i \(-0.512322\pi\)
−0.0387015 + 0.999251i \(0.512322\pi\)
\(30\) −4.42145e39 −3.17579
\(31\) 8.43957e38 0.254235 0.127118 0.991888i \(-0.459427\pi\)
0.127118 + 0.991888i \(0.459427\pi\)
\(32\) 1.10468e40 1.43471
\(33\) −1.34390e40 −0.772229
\(34\) 8.42846e40 2.19562
\(35\) −1.36849e41 −1.65363
\(36\) 1.63799e41 0.938200
\(37\) 1.19964e41 0.332433 0.166216 0.986089i \(-0.446845\pi\)
0.166216 + 0.986089i \(0.446845\pi\)
\(38\) −8.09626e41 −1.10667
\(39\) −8.59760e41 −0.590426
\(40\) 8.81165e41 0.309362
\(41\) −8.08650e42 −1.47567 −0.737834 0.674983i \(-0.764151\pi\)
−0.737834 + 0.674983i \(0.764151\pi\)
\(42\) 2.10688e43 2.03017
\(43\) 1.66354e43 0.859249 0.429624 0.903008i \(-0.358646\pi\)
0.429624 + 0.903008i \(0.358646\pi\)
\(44\) 2.30083e43 0.646231
\(45\) −8.61111e43 −1.33330
\(46\) −1.32207e44 −1.14333
\(47\) −7.16487e42 −0.0350441 −0.0175220 0.999846i \(-0.505578\pi\)
−0.0175220 + 0.999846i \(0.505578\pi\)
\(48\) 4.11035e44 1.15076
\(49\) 3.52310e43 0.0571122
\(50\) −2.44110e45 −2.31676
\(51\) 3.62164e45 2.03374
\(52\) 1.47196e45 0.494091
\(53\) 3.19144e45 0.646660 0.323330 0.946286i \(-0.395198\pi\)
0.323330 + 0.946286i \(0.395198\pi\)
\(54\) −2.73484e45 −0.337674
\(55\) −1.20957e46 −0.918374
\(56\) −4.19887e45 −0.197765
\(57\) −3.47889e46 −1.02508
\(58\) 6.08088e45 0.113012
\(59\) 3.07882e46 0.363752 0.181876 0.983321i \(-0.441783\pi\)
0.181876 + 0.983321i \(0.441783\pi\)
\(60\) 3.25267e47 2.46168
\(61\) −2.46965e47 −1.20613 −0.603066 0.797691i \(-0.706054\pi\)
−0.603066 + 0.797691i \(0.706054\pi\)
\(62\) −1.16945e47 −0.371195
\(63\) 4.10330e47 0.852333
\(64\) −9.08937e47 −1.24384
\(65\) −7.73825e47 −0.702164
\(66\) 1.86221e48 1.12749
\(67\) 1.37146e48 0.557445 0.278723 0.960372i \(-0.410089\pi\)
0.278723 + 0.960372i \(0.410089\pi\)
\(68\) −6.20045e48 −1.70191
\(69\) −5.68081e48 −1.05903
\(70\) 1.89629e49 2.41439
\(71\) 1.40028e49 1.22424 0.612122 0.790763i \(-0.290316\pi\)
0.612122 + 0.790763i \(0.290316\pi\)
\(72\) −2.64209e48 −0.159455
\(73\) −1.59560e49 −0.668140 −0.334070 0.942548i \(-0.608422\pi\)
−0.334070 + 0.942548i \(0.608422\pi\)
\(74\) −1.66231e49 −0.485368
\(75\) −1.04892e50 −2.14595
\(76\) 5.95606e49 0.857825
\(77\) 5.76375e49 0.587085
\(78\) 1.19135e50 0.862050
\(79\) −1.73480e50 −0.895635 −0.447818 0.894125i \(-0.647799\pi\)
−0.447818 + 0.894125i \(0.647799\pi\)
\(80\) 3.69950e50 1.36854
\(81\) −4.28973e50 −1.14177
\(82\) 1.12053e51 2.15455
\(83\) −1.32890e51 −1.85320 −0.926600 0.376048i \(-0.877283\pi\)
−0.926600 + 0.376048i \(0.877283\pi\)
\(84\) −1.54994e51 −1.57367
\(85\) 3.25964e51 2.41862
\(86\) −2.30513e51 −1.25454
\(87\) 2.61290e50 0.104680
\(88\) −3.71125e50 −0.109832
\(89\) −6.74530e51 −1.47967 −0.739837 0.672786i \(-0.765098\pi\)
−0.739837 + 0.672786i \(0.765098\pi\)
\(90\) 1.19322e52 1.94668
\(91\) 3.68737e51 0.448870
\(92\) 9.72588e51 0.886240
\(93\) −5.02503e51 −0.343828
\(94\) 9.92819e50 0.0511661
\(95\) −3.13117e52 −1.21908
\(96\) −6.57744e52 −1.94030
\(97\) 4.44346e52 0.996025 0.498012 0.867170i \(-0.334063\pi\)
0.498012 + 0.867170i \(0.334063\pi\)
\(98\) −4.88188e51 −0.0833866
\(99\) 3.62679e52 0.473357
\(100\) 1.79581e53 1.79581
\(101\) 1.33654e53 1.02675 0.513377 0.858163i \(-0.328394\pi\)
0.513377 + 0.858163i \(0.328394\pi\)
\(102\) −5.01842e53 −2.96936
\(103\) 7.98514e52 0.364835 0.182417 0.983221i \(-0.441608\pi\)
0.182417 + 0.983221i \(0.441608\pi\)
\(104\) −2.37428e52 −0.0839747
\(105\) 8.14819e53 2.23638
\(106\) −4.42230e53 −0.944155
\(107\) −1.04658e54 −1.74222 −0.871108 0.491092i \(-0.836598\pi\)
−0.871108 + 0.491092i \(0.836598\pi\)
\(108\) 2.01190e53 0.261745
\(109\) −5.02767e53 −0.512348 −0.256174 0.966631i \(-0.582462\pi\)
−0.256174 + 0.966631i \(0.582462\pi\)
\(110\) 1.67607e54 1.34087
\(111\) −7.14279e53 −0.449582
\(112\) −1.76286e54 −0.874864
\(113\) 3.92048e54 1.53731 0.768654 0.639665i \(-0.220927\pi\)
0.768654 + 0.639665i \(0.220927\pi\)
\(114\) 4.82062e54 1.49666
\(115\) −5.11300e54 −1.25946
\(116\) −4.47344e53 −0.0876001
\(117\) 2.32024e54 0.361916
\(118\) −4.26625e54 −0.531096
\(119\) −1.55326e55 −1.54615
\(120\) −5.24658e54 −0.418382
\(121\) −1.05303e55 −0.673952
\(122\) 3.42214e55 1.76101
\(123\) 4.81481e55 1.99569
\(124\) 8.60314e54 0.287728
\(125\) −3.49109e55 −0.943726
\(126\) −5.68585e55 −1.24445
\(127\) 2.95271e55 0.524110 0.262055 0.965053i \(-0.415600\pi\)
0.262055 + 0.965053i \(0.415600\pi\)
\(128\) 2.64483e55 0.381359
\(129\) −9.90494e55 −1.16205
\(130\) 1.07227e56 1.02519
\(131\) −1.59227e55 −0.124259 −0.0621296 0.998068i \(-0.519789\pi\)
−0.0621296 + 0.998068i \(0.519789\pi\)
\(132\) −1.36994e56 −0.873963
\(133\) 1.49204e56 0.779314
\(134\) −1.90041e56 −0.813897
\(135\) −1.05768e56 −0.371971
\(136\) 1.00014e56 0.289253
\(137\) 1.20350e56 0.286650 0.143325 0.989676i \(-0.454221\pi\)
0.143325 + 0.989676i \(0.454221\pi\)
\(138\) 7.87178e56 1.54624
\(139\) 1.03961e57 1.68647 0.843235 0.537546i \(-0.180648\pi\)
0.843235 + 0.537546i \(0.180648\pi\)
\(140\) −1.39502e57 −1.87149
\(141\) 4.26606e55 0.0473937
\(142\) −1.94033e57 −1.78745
\(143\) 3.25916e56 0.249287
\(144\) −1.10926e57 −0.705389
\(145\) 2.35173e56 0.124490
\(146\) 2.21098e57 0.975516
\(147\) −2.09770e56 −0.0772386
\(148\) 1.22289e57 0.376228
\(149\) −5.27498e57 −1.35764 −0.678820 0.734305i \(-0.737508\pi\)
−0.678820 + 0.734305i \(0.737508\pi\)
\(150\) 1.45347e58 3.13319
\(151\) −1.14345e57 −0.206695 −0.103347 0.994645i \(-0.532955\pi\)
−0.103347 + 0.994645i \(0.532955\pi\)
\(152\) −9.60717e56 −0.145794
\(153\) −9.77375e57 −1.24663
\(154\) −7.98670e57 −0.857173
\(155\) −4.52277e57 −0.408897
\(156\) −8.76424e57 −0.668209
\(157\) 2.71579e58 1.74806 0.874030 0.485873i \(-0.161498\pi\)
0.874030 + 0.485873i \(0.161498\pi\)
\(158\) 2.40387e58 1.30767
\(159\) −1.90023e58 −0.874544
\(160\) −5.92000e58 −2.30750
\(161\) 2.43641e58 0.805128
\(162\) 5.94419e58 1.66703
\(163\) −1.18765e58 −0.282955 −0.141478 0.989941i \(-0.545185\pi\)
−0.141478 + 0.989941i \(0.545185\pi\)
\(164\) −8.24323e58 −1.67007
\(165\) 7.20194e58 1.24201
\(166\) 1.84142e59 2.70576
\(167\) −1.03522e59 −1.29732 −0.648661 0.761078i \(-0.724671\pi\)
−0.648661 + 0.761078i \(0.724671\pi\)
\(168\) 2.50006e58 0.267457
\(169\) −8.85445e58 −0.809402
\(170\) −4.51681e59 −3.53131
\(171\) 9.38852e58 0.628348
\(172\) 1.69578e59 0.972447
\(173\) 1.05509e59 0.518881 0.259441 0.965759i \(-0.416462\pi\)
0.259441 + 0.965759i \(0.416462\pi\)
\(174\) −3.62064e58 −0.152838
\(175\) 4.49865e59 1.63145
\(176\) −1.55814e59 −0.485871
\(177\) −1.83317e59 −0.491939
\(178\) 9.34681e59 2.16040
\(179\) −8.35545e58 −0.166481 −0.0832405 0.996529i \(-0.526527\pi\)
−0.0832405 + 0.996529i \(0.526527\pi\)
\(180\) −8.77801e59 −1.50895
\(181\) −7.95749e59 −1.18112 −0.590559 0.806994i \(-0.701093\pi\)
−0.590559 + 0.806994i \(0.701093\pi\)
\(182\) −5.10951e59 −0.655371
\(183\) 1.47046e60 1.63117
\(184\) −1.56879e59 −0.150624
\(185\) −6.42885e59 −0.534666
\(186\) 6.96308e59 0.502005
\(187\) −1.37288e60 −0.858678
\(188\) −7.30373e58 −0.0396608
\(189\) 5.03998e59 0.237789
\(190\) 4.33879e60 1.77991
\(191\) −3.99509e60 −1.42607 −0.713037 0.701126i \(-0.752681\pi\)
−0.713037 + 0.701126i \(0.752681\pi\)
\(192\) 5.41194e60 1.68217
\(193\) −2.31728e60 −0.627638 −0.313819 0.949483i \(-0.601609\pi\)
−0.313819 + 0.949483i \(0.601609\pi\)
\(194\) −6.15720e60 −1.45424
\(195\) 4.60746e60 0.949607
\(196\) 3.59139e59 0.0646362
\(197\) 6.97303e60 1.09665 0.548323 0.836267i \(-0.315267\pi\)
0.548323 + 0.836267i \(0.315267\pi\)
\(198\) −5.02555e60 −0.691125
\(199\) −7.01618e60 −0.844295 −0.422148 0.906527i \(-0.638724\pi\)
−0.422148 + 0.906527i \(0.638724\pi\)
\(200\) −2.89666e60 −0.305213
\(201\) −8.16589e60 −0.753890
\(202\) −1.85202e61 −1.49911
\(203\) −1.12063e60 −0.0795826
\(204\) 3.69183e61 2.30167
\(205\) 4.33356e61 2.37338
\(206\) −1.10648e61 −0.532676
\(207\) 1.53309e61 0.649161
\(208\) −9.96823e60 −0.371484
\(209\) 1.31877e61 0.432805
\(210\) −1.12908e62 −3.26522
\(211\) 7.11365e60 0.181388 0.0906938 0.995879i \(-0.471092\pi\)
0.0906938 + 0.995879i \(0.471092\pi\)
\(212\) 3.25329e61 0.731852
\(213\) −8.33744e61 −1.65567
\(214\) 1.45022e62 2.54372
\(215\) −8.91491e61 −1.38197
\(216\) −3.24522e60 −0.0444856
\(217\) 2.15516e61 0.261394
\(218\) 6.96673e61 0.748052
\(219\) 9.50040e61 0.903593
\(220\) −1.23301e62 −1.03936
\(221\) −8.78304e61 −0.656522
\(222\) 9.89761e61 0.656412
\(223\) −1.07039e62 −0.630176 −0.315088 0.949062i \(-0.602034\pi\)
−0.315088 + 0.949062i \(0.602034\pi\)
\(224\) 2.82096e62 1.47511
\(225\) 2.83073e62 1.31541
\(226\) −5.43252e62 −2.24454
\(227\) 2.87663e62 1.05730 0.528651 0.848840i \(-0.322698\pi\)
0.528651 + 0.848840i \(0.322698\pi\)
\(228\) −3.54632e62 −1.16012
\(229\) −5.16513e62 −1.50467 −0.752334 0.658782i \(-0.771072\pi\)
−0.752334 + 0.658782i \(0.771072\pi\)
\(230\) 7.08497e62 1.83887
\(231\) −3.43182e62 −0.793975
\(232\) 7.21569e60 0.0148883
\(233\) −1.10244e62 −0.202965 −0.101483 0.994837i \(-0.532359\pi\)
−0.101483 + 0.994837i \(0.532359\pi\)
\(234\) −3.21511e62 −0.528415
\(235\) 3.83965e61 0.0563629
\(236\) 3.13849e62 0.411673
\(237\) 1.03292e63 1.21126
\(238\) 2.15232e63 2.25745
\(239\) 4.32058e61 0.0405507 0.0202753 0.999794i \(-0.493546\pi\)
0.0202753 + 0.999794i \(0.493546\pi\)
\(240\) −2.20274e63 −1.85082
\(241\) −2.12916e63 −1.60235 −0.801175 0.598431i \(-0.795791\pi\)
−0.801175 + 0.598431i \(0.795791\pi\)
\(242\) 1.45916e63 0.984003
\(243\) 2.17161e63 1.31285
\(244\) −2.51752e63 −1.36503
\(245\) −1.88803e62 −0.0918561
\(246\) −6.67178e63 −2.91381
\(247\) 8.43686e62 0.330911
\(248\) −1.38769e62 −0.0489017
\(249\) 7.91244e63 2.50627
\(250\) 4.83753e63 1.37789
\(251\) −2.49739e63 −0.639930 −0.319965 0.947429i \(-0.603671\pi\)
−0.319965 + 0.947429i \(0.603671\pi\)
\(252\) 4.18283e63 0.964620
\(253\) 2.15347e63 0.447141
\(254\) −4.09150e63 −0.765226
\(255\) −1.94084e64 −3.27095
\(256\) 4.52210e63 0.687038
\(257\) 3.80580e63 0.521457 0.260728 0.965412i \(-0.416037\pi\)
0.260728 + 0.965412i \(0.416037\pi\)
\(258\) 1.37250e64 1.69665
\(259\) 3.06343e63 0.341794
\(260\) −7.88823e63 −0.794668
\(261\) −7.05146e62 −0.0641661
\(262\) 2.20638e63 0.181425
\(263\) −1.69696e64 −1.26137 −0.630687 0.776037i \(-0.717227\pi\)
−0.630687 + 0.776037i \(0.717227\pi\)
\(264\) 2.20973e63 0.148537
\(265\) −1.71029e64 −1.04005
\(266\) −2.06749e64 −1.13784
\(267\) 4.01625e64 2.00111
\(268\) 1.39805e64 0.630884
\(269\) 6.10982e63 0.249800 0.124900 0.992169i \(-0.460139\pi\)
0.124900 + 0.992169i \(0.460139\pi\)
\(270\) 1.46560e64 0.543096
\(271\) −9.96186e63 −0.334699 −0.167350 0.985898i \(-0.553521\pi\)
−0.167350 + 0.985898i \(0.553521\pi\)
\(272\) 4.19900e64 1.27959
\(273\) −2.19551e64 −0.607052
\(274\) −1.66767e64 −0.418523
\(275\) 3.97622e64 0.906055
\(276\) −5.79092e64 −1.19855
\(277\) 2.47062e64 0.464615 0.232307 0.972642i \(-0.425372\pi\)
0.232307 + 0.972642i \(0.425372\pi\)
\(278\) −1.44056e65 −2.46233
\(279\) 1.35611e64 0.210758
\(280\) 2.25017e64 0.318074
\(281\) −1.25270e64 −0.161113 −0.0805564 0.996750i \(-0.525670\pi\)
−0.0805564 + 0.996750i \(0.525670\pi\)
\(282\) −5.91138e63 −0.0691971
\(283\) −2.70393e64 −0.288174 −0.144087 0.989565i \(-0.546025\pi\)
−0.144087 + 0.989565i \(0.546025\pi\)
\(284\) 1.42742e65 1.38553
\(285\) 1.86434e65 1.64868
\(286\) −4.51614e64 −0.363972
\(287\) −2.06500e65 −1.51722
\(288\) 1.77506e65 1.18936
\(289\) 2.06371e65 1.26141
\(290\) −3.25874e64 −0.181762
\(291\) −2.64569e65 −1.34702
\(292\) −1.62652e65 −0.756161
\(293\) −6.85669e64 −0.291154 −0.145577 0.989347i \(-0.546504\pi\)
−0.145577 + 0.989347i \(0.546504\pi\)
\(294\) 2.90674e64 0.112772
\(295\) −1.64994e65 −0.585039
\(296\) −1.97253e64 −0.0639429
\(297\) 4.45469e64 0.132060
\(298\) 7.30942e65 1.98222
\(299\) 1.37769e65 0.341872
\(300\) −1.06925e66 −2.42866
\(301\) 4.24807e65 0.883445
\(302\) 1.58446e65 0.301784
\(303\) −7.95796e65 −1.38858
\(304\) −4.03350e65 −0.644959
\(305\) 1.32349e66 1.93987
\(306\) 1.35433e66 1.82014
\(307\) −1.46437e66 −1.80502 −0.902512 0.430664i \(-0.858279\pi\)
−0.902512 + 0.430664i \(0.858279\pi\)
\(308\) 5.87547e65 0.664429
\(309\) −4.75446e65 −0.493403
\(310\) 6.26710e65 0.597010
\(311\) 2.08500e66 1.82371 0.911856 0.410511i \(-0.134650\pi\)
0.911856 + 0.410511i \(0.134650\pi\)
\(312\) 1.41368e65 0.113567
\(313\) −1.88530e66 −1.39141 −0.695706 0.718327i \(-0.744908\pi\)
−0.695706 + 0.718327i \(0.744908\pi\)
\(314\) −3.76322e66 −2.55225
\(315\) −2.19896e66 −1.37084
\(316\) −1.76842e66 −1.01363
\(317\) 1.84865e66 0.974503 0.487252 0.873262i \(-0.337999\pi\)
0.487252 + 0.873262i \(0.337999\pi\)
\(318\) 2.63310e66 1.27688
\(319\) −9.90492e64 −0.0441975
\(320\) 4.87100e66 2.00052
\(321\) 6.23147e66 2.35617
\(322\) −3.37608e66 −1.17553
\(323\) −3.55393e66 −1.13983
\(324\) −4.37288e66 −1.29218
\(325\) 2.54380e66 0.692745
\(326\) 1.64570e66 0.413129
\(327\) 2.99354e66 0.692899
\(328\) 1.32964e66 0.283842
\(329\) −1.82964e65 −0.0360309
\(330\) −9.97957e66 −1.81339
\(331\) 1.90131e66 0.318867 0.159434 0.987209i \(-0.449033\pi\)
0.159434 + 0.987209i \(0.449033\pi\)
\(332\) −1.35466e67 −2.09734
\(333\) 1.92763e66 0.275583
\(334\) 1.43449e67 1.89415
\(335\) −7.34968e66 −0.896564
\(336\) 1.04963e67 1.18317
\(337\) −9.17803e66 −0.956218 −0.478109 0.878300i \(-0.658678\pi\)
−0.478109 + 0.878300i \(0.658678\pi\)
\(338\) 1.22694e67 1.18177
\(339\) −2.33431e67 −2.07906
\(340\) 3.32282e67 2.73726
\(341\) 1.90488e66 0.145170
\(342\) −1.30095e67 −0.917419
\(343\) −1.48530e67 −0.969439
\(344\) −2.73531e66 −0.165275
\(345\) 3.04435e67 1.70329
\(346\) −1.46202e67 −0.757592
\(347\) 1.14278e67 0.548569 0.274285 0.961649i \(-0.411559\pi\)
0.274285 + 0.961649i \(0.411559\pi\)
\(348\) 2.66354e66 0.118470
\(349\) 2.72467e67 1.12316 0.561578 0.827424i \(-0.310195\pi\)
0.561578 + 0.827424i \(0.310195\pi\)
\(350\) −6.23368e67 −2.38200
\(351\) 2.84990e66 0.100970
\(352\) 2.49336e67 0.819227
\(353\) −3.17343e67 −0.967163 −0.483582 0.875299i \(-0.660664\pi\)
−0.483582 + 0.875299i \(0.660664\pi\)
\(354\) 2.54018e67 0.718255
\(355\) −7.50409e67 −1.96900
\(356\) −6.87604e67 −1.67461
\(357\) 9.24833e67 2.09101
\(358\) 1.15780e67 0.243070
\(359\) 3.93676e67 0.767601 0.383801 0.923416i \(-0.374615\pi\)
0.383801 + 0.923416i \(0.374615\pi\)
\(360\) 1.41590e67 0.256458
\(361\) −2.52826e67 −0.425482
\(362\) 1.10265e68 1.72449
\(363\) 6.26989e67 0.911454
\(364\) 3.75884e67 0.508004
\(365\) 8.55081e67 1.07460
\(366\) −2.03759e68 −2.38159
\(367\) −1.53609e68 −1.67020 −0.835098 0.550101i \(-0.814589\pi\)
−0.835098 + 0.550101i \(0.814589\pi\)
\(368\) −6.58645e67 −0.666322
\(369\) −1.29938e68 −1.22331
\(370\) 8.90831e67 0.780638
\(371\) 8.14977e67 0.664870
\(372\) −5.12243e67 −0.389124
\(373\) −1.29701e68 −0.917611 −0.458805 0.888537i \(-0.651722\pi\)
−0.458805 + 0.888537i \(0.651722\pi\)
\(374\) 1.90237e68 1.25371
\(375\) 2.07864e68 1.27630
\(376\) 1.17810e66 0.00674068
\(377\) −6.33670e66 −0.0337922
\(378\) −6.98379e67 −0.347183
\(379\) 1.95972e68 0.908354 0.454177 0.890911i \(-0.349933\pi\)
0.454177 + 0.890911i \(0.349933\pi\)
\(380\) −3.19185e68 −1.37968
\(381\) −1.75808e68 −0.708807
\(382\) 5.53590e68 2.08214
\(383\) −7.90039e67 −0.277256 −0.138628 0.990345i \(-0.544269\pi\)
−0.138628 + 0.990345i \(0.544269\pi\)
\(384\) −1.57477e68 −0.515750
\(385\) −3.08880e68 −0.944235
\(386\) 3.21100e68 0.916382
\(387\) 2.67306e68 0.712308
\(388\) 4.52958e68 1.12724
\(389\) −2.30262e68 −0.535252 −0.267626 0.963523i \(-0.586239\pi\)
−0.267626 + 0.963523i \(0.586239\pi\)
\(390\) −6.38445e68 −1.38647
\(391\) −5.80334e68 −1.17759
\(392\) −5.79293e66 −0.0109854
\(393\) 9.48062e67 0.168048
\(394\) −9.66236e68 −1.60116
\(395\) 9.29679e68 1.44049
\(396\) 3.69708e68 0.535718
\(397\) 4.76387e68 0.645671 0.322835 0.946455i \(-0.395364\pi\)
0.322835 + 0.946455i \(0.395364\pi\)
\(398\) 9.72217e68 1.23271
\(399\) −8.88382e68 −1.05394
\(400\) −1.21614e69 −1.35019
\(401\) −5.31851e68 −0.552668 −0.276334 0.961062i \(-0.589120\pi\)
−0.276334 + 0.961062i \(0.589120\pi\)
\(402\) 1.13153e69 1.10072
\(403\) 1.21865e68 0.110993
\(404\) 1.36245e69 1.16202
\(405\) 2.29887e69 1.83635
\(406\) 1.55283e68 0.116194
\(407\) 2.70767e68 0.189821
\(408\) −5.95495e68 −0.391187
\(409\) −2.07340e69 −1.27649 −0.638243 0.769835i \(-0.720338\pi\)
−0.638243 + 0.769835i \(0.720338\pi\)
\(410\) −6.00491e69 −3.46525
\(411\) −7.16581e68 −0.387666
\(412\) 8.13991e68 0.412898
\(413\) 7.86217e68 0.373995
\(414\) −2.12436e69 −0.947807
\(415\) 7.12157e69 2.98058
\(416\) 1.59513e69 0.626359
\(417\) −6.18998e69 −2.28078
\(418\) −1.82739e69 −0.631916
\(419\) 4.81874e69 1.56409 0.782045 0.623221i \(-0.214176\pi\)
0.782045 + 0.623221i \(0.214176\pi\)
\(420\) 8.30612e69 2.53100
\(421\) −4.17794e68 −0.119533 −0.0597664 0.998212i \(-0.519036\pi\)
−0.0597664 + 0.998212i \(0.519036\pi\)
\(422\) −9.85723e68 −0.264835
\(423\) −1.15129e68 −0.0290512
\(424\) −5.24759e68 −0.124384
\(425\) −1.07154e70 −2.38618
\(426\) 1.15530e70 2.41736
\(427\) −6.30658e69 −1.24010
\(428\) −1.06686e70 −1.97174
\(429\) −1.94055e69 −0.337137
\(430\) 1.23532e70 2.01774
\(431\) 2.97872e69 0.457490 0.228745 0.973486i \(-0.426538\pi\)
0.228745 + 0.973486i \(0.426538\pi\)
\(432\) −1.36248e69 −0.196794
\(433\) 2.69910e69 0.366682 0.183341 0.983049i \(-0.441309\pi\)
0.183341 + 0.983049i \(0.441309\pi\)
\(434\) −2.98635e69 −0.381648
\(435\) −1.40025e69 −0.168361
\(436\) −5.12512e69 −0.579845
\(437\) 5.57460e69 0.593548
\(438\) −1.31645e70 −1.31929
\(439\) −3.57805e68 −0.0337549 −0.0168774 0.999858i \(-0.505373\pi\)
−0.0168774 + 0.999858i \(0.505373\pi\)
\(440\) 1.98886e69 0.176648
\(441\) 5.66109e68 0.0473454
\(442\) 1.21705e70 0.958554
\(443\) −9.79799e69 −0.726839 −0.363419 0.931626i \(-0.618391\pi\)
−0.363419 + 0.931626i \(0.618391\pi\)
\(444\) −7.28123e69 −0.508811
\(445\) 3.61481e70 2.37983
\(446\) 1.48321e70 0.920088
\(447\) 3.14079e70 1.83607
\(448\) −2.32109e70 −1.27887
\(449\) −2.01028e70 −1.04407 −0.522033 0.852925i \(-0.674826\pi\)
−0.522033 + 0.852925i \(0.674826\pi\)
\(450\) −3.92248e70 −1.92057
\(451\) −1.82519e70 −0.842615
\(452\) 3.99647e70 1.73983
\(453\) 6.80827e69 0.279534
\(454\) −3.98608e70 −1.54371
\(455\) −1.97606e70 −0.721937
\(456\) 5.72024e69 0.197172
\(457\) −3.35756e70 −1.09205 −0.546027 0.837768i \(-0.683860\pi\)
−0.546027 + 0.837768i \(0.683860\pi\)
\(458\) 7.15720e70 2.19689
\(459\) −1.20048e70 −0.347793
\(460\) −5.21210e70 −1.42538
\(461\) 4.09546e70 1.05737 0.528686 0.848817i \(-0.322685\pi\)
0.528686 + 0.848817i \(0.322685\pi\)
\(462\) 4.75539e70 1.15924
\(463\) 1.86380e69 0.0429045 0.0214523 0.999770i \(-0.493171\pi\)
0.0214523 + 0.999770i \(0.493171\pi\)
\(464\) 3.02945e69 0.0658624
\(465\) 2.69292e70 0.552993
\(466\) 1.52762e70 0.296339
\(467\) 4.04901e69 0.0742081 0.0371040 0.999311i \(-0.488187\pi\)
0.0371040 + 0.999311i \(0.488187\pi\)
\(468\) 2.36521e70 0.409596
\(469\) 3.50222e70 0.573143
\(470\) −5.32052e69 −0.0822926
\(471\) −1.61702e71 −2.36408
\(472\) −5.06241e69 −0.0699672
\(473\) 3.75474e70 0.490636
\(474\) −1.43130e71 −1.76850
\(475\) 1.02931e71 1.20272
\(476\) −1.58337e71 −1.74984
\(477\) 5.12816e70 0.536074
\(478\) −5.98694e69 −0.0592059
\(479\) −1.14957e71 −1.07558 −0.537790 0.843079i \(-0.680741\pi\)
−0.537790 + 0.843079i \(0.680741\pi\)
\(480\) 3.52485e71 3.12067
\(481\) 1.73224e70 0.145132
\(482\) 2.95033e71 2.33951
\(483\) −1.45067e71 −1.08886
\(484\) −1.07344e71 −0.762739
\(485\) −2.38125e71 −1.60195
\(486\) −3.00915e71 −1.91682
\(487\) 2.40380e71 1.45004 0.725022 0.688726i \(-0.241830\pi\)
0.725022 + 0.688726i \(0.241830\pi\)
\(488\) 4.06077e70 0.231998
\(489\) 7.07145e70 0.382669
\(490\) 2.61620e70 0.134114
\(491\) 4.81194e70 0.233701 0.116850 0.993150i \(-0.462720\pi\)
0.116850 + 0.993150i \(0.462720\pi\)
\(492\) 4.90813e71 2.25861
\(493\) 2.66926e70 0.116398
\(494\) −1.16908e71 −0.483146
\(495\) −1.94360e71 −0.761321
\(496\) −5.82613e70 −0.216329
\(497\) 3.57580e71 1.25872
\(498\) −1.09641e72 −3.65928
\(499\) 4.07670e69 0.0129016 0.00645082 0.999979i \(-0.497947\pi\)
0.00645082 + 0.999979i \(0.497947\pi\)
\(500\) −3.55875e71 −1.06805
\(501\) 6.16386e71 1.75450
\(502\) 3.46057e71 0.934329
\(503\) −2.27736e71 −0.583284 −0.291642 0.956527i \(-0.594202\pi\)
−0.291642 + 0.956527i \(0.594202\pi\)
\(504\) −6.74694e70 −0.163945
\(505\) −7.16254e71 −1.65137
\(506\) −2.98401e71 −0.652848
\(507\) 5.27206e71 1.09464
\(508\) 3.00994e71 0.593157
\(509\) 3.77057e71 0.705319 0.352659 0.935752i \(-0.385277\pi\)
0.352659 + 0.935752i \(0.385277\pi\)
\(510\) 2.68937e72 4.77575
\(511\) −4.07457e71 −0.686954
\(512\) −8.64842e71 −1.38447
\(513\) 1.15317e71 0.175300
\(514\) −5.27361e71 −0.761352
\(515\) −4.27924e71 −0.586779
\(516\) −1.00969e72 −1.31514
\(517\) −1.61717e70 −0.0200104
\(518\) −4.24492e71 −0.499035
\(519\) −6.28215e71 −0.701736
\(520\) 1.27238e71 0.135060
\(521\) 1.53660e72 1.55011 0.775055 0.631894i \(-0.217722\pi\)
0.775055 + 0.631894i \(0.217722\pi\)
\(522\) 9.77106e70 0.0936857
\(523\) −5.24951e71 −0.478436 −0.239218 0.970966i \(-0.576891\pi\)
−0.239218 + 0.970966i \(0.576891\pi\)
\(524\) −1.62314e71 −0.140629
\(525\) −2.67856e72 −2.20638
\(526\) 2.35144e72 1.84167
\(527\) −5.13342e71 −0.382318
\(528\) 9.27738e71 0.657092
\(529\) −5.74185e71 −0.386791
\(530\) 2.36991e72 1.51853
\(531\) 4.94719e71 0.301546
\(532\) 1.52096e72 0.881981
\(533\) −1.16767e72 −0.644241
\(534\) −5.56522e72 −2.92172
\(535\) 5.60862e72 2.80208
\(536\) −2.25506e71 −0.107224
\(537\) 4.97495e71 0.225149
\(538\) −8.46624e71 −0.364721
\(539\) 7.95192e70 0.0326114
\(540\) −1.07818e72 −0.420975
\(541\) −4.62761e72 −1.72040 −0.860200 0.509956i \(-0.829662\pi\)
−0.860200 + 0.509956i \(0.829662\pi\)
\(542\) 1.38039e72 0.488677
\(543\) 4.73799e72 1.59735
\(544\) −6.71930e72 −2.15751
\(545\) 2.69433e72 0.824031
\(546\) 3.04227e72 0.886325
\(547\) 1.78991e72 0.496782 0.248391 0.968660i \(-0.420098\pi\)
0.248391 + 0.968660i \(0.420098\pi\)
\(548\) 1.22683e72 0.324413
\(549\) −3.96835e72 −0.999869
\(550\) −5.50976e72 −1.32288
\(551\) −2.56405e71 −0.0586691
\(552\) 9.34080e71 0.203703
\(553\) −4.43004e72 −0.920856
\(554\) −3.42349e72 −0.678360
\(555\) 3.82782e72 0.723083
\(556\) 1.05976e73 1.90865
\(557\) 2.84794e72 0.489067 0.244533 0.969641i \(-0.421365\pi\)
0.244533 + 0.969641i \(0.421365\pi\)
\(558\) −1.87913e72 −0.307717
\(559\) 2.40210e72 0.375127
\(560\) 9.44718e72 1.40708
\(561\) 8.17432e72 1.16128
\(562\) 1.73584e72 0.235232
\(563\) −8.39092e72 −1.08477 −0.542385 0.840130i \(-0.682478\pi\)
−0.542385 + 0.840130i \(0.682478\pi\)
\(564\) 4.34874e71 0.0536374
\(565\) −2.10099e73 −2.47252
\(566\) 3.74678e72 0.420748
\(567\) −1.09544e73 −1.17392
\(568\) −2.30244e72 −0.235481
\(569\) 6.11471e72 0.596899 0.298450 0.954425i \(-0.403531\pi\)
0.298450 + 0.954425i \(0.403531\pi\)
\(570\) −2.58337e73 −2.40715
\(571\) −1.26705e73 −1.12703 −0.563515 0.826106i \(-0.690551\pi\)
−0.563515 + 0.826106i \(0.690551\pi\)
\(572\) 3.32233e72 0.282129
\(573\) 2.37873e73 1.92862
\(574\) 2.86142e73 2.21522
\(575\) 1.68080e73 1.24256
\(576\) −1.46052e73 −1.03113
\(577\) 1.54639e73 1.04270 0.521350 0.853343i \(-0.325429\pi\)
0.521350 + 0.853343i \(0.325429\pi\)
\(578\) −2.85964e73 −1.84172
\(579\) 1.37974e73 0.848819
\(580\) 2.39732e72 0.140891
\(581\) −3.39352e73 −1.90539
\(582\) 3.66608e73 1.96672
\(583\) 7.20333e72 0.369247
\(584\) 2.62359e72 0.128516
\(585\) −1.24342e73 −0.582086
\(586\) 9.50116e72 0.425099
\(587\) −2.89131e73 −1.23647 −0.618237 0.785992i \(-0.712153\pi\)
−0.618237 + 0.785992i \(0.712153\pi\)
\(588\) −2.13836e72 −0.0874141
\(589\) 4.93109e72 0.192702
\(590\) 2.28628e73 0.854185
\(591\) −4.15183e73 −1.48310
\(592\) −8.28150e72 −0.282868
\(593\) −1.35508e73 −0.442606 −0.221303 0.975205i \(-0.571031\pi\)
−0.221303 + 0.975205i \(0.571031\pi\)
\(594\) −6.17276e72 −0.192814
\(595\) 8.32393e73 2.48673
\(596\) −5.37722e73 −1.53650
\(597\) 4.17753e73 1.14183
\(598\) −1.90903e73 −0.499150
\(599\) −1.38679e73 −0.346897 −0.173448 0.984843i \(-0.555491\pi\)
−0.173448 + 0.984843i \(0.555491\pi\)
\(600\) 1.72471e73 0.412770
\(601\) −4.98700e73 −1.14200 −0.571000 0.820950i \(-0.693444\pi\)
−0.571000 + 0.820950i \(0.693444\pi\)
\(602\) −5.88645e73 −1.28987
\(603\) 2.20374e73 0.462116
\(604\) −1.16561e73 −0.233925
\(605\) 5.64320e73 1.08395
\(606\) 1.10272e74 2.02740
\(607\) 4.33744e73 0.763367 0.381683 0.924293i \(-0.375344\pi\)
0.381683 + 0.924293i \(0.375344\pi\)
\(608\) 6.45446e73 1.08747
\(609\) 6.67239e72 0.107628
\(610\) −1.83392e74 −2.83231
\(611\) −1.03459e72 −0.0152994
\(612\) −9.96318e73 −1.41086
\(613\) 1.11056e74 1.50605 0.753027 0.657990i \(-0.228593\pi\)
0.753027 + 0.657990i \(0.228593\pi\)
\(614\) 2.02914e74 2.63542
\(615\) −2.58026e74 −3.20976
\(616\) −9.47717e72 −0.112925
\(617\) 6.32555e73 0.722007 0.361004 0.932564i \(-0.382434\pi\)
0.361004 + 0.932564i \(0.382434\pi\)
\(618\) 6.58815e73 0.720392
\(619\) −2.98152e73 −0.312345 −0.156173 0.987730i \(-0.549916\pi\)
−0.156173 + 0.987730i \(0.549916\pi\)
\(620\) −4.61043e73 −0.462766
\(621\) 1.88305e73 0.181107
\(622\) −2.88914e74 −2.66271
\(623\) −1.72250e74 −1.52134
\(624\) 5.93522e73 0.502395
\(625\) −8.49672e72 −0.0689336
\(626\) 2.61242e74 2.03153
\(627\) −7.85214e73 −0.585326
\(628\) 2.76843e74 1.97835
\(629\) −7.29685e73 −0.499912
\(630\) 3.04705e74 2.00150
\(631\) 2.66754e74 1.68009 0.840046 0.542515i \(-0.182528\pi\)
0.840046 + 0.542515i \(0.182528\pi\)
\(632\) 2.85248e73 0.172274
\(633\) −4.23557e73 −0.245309
\(634\) −2.56163e74 −1.42282
\(635\) −1.58236e74 −0.842949
\(636\) −1.93706e74 −0.989757
\(637\) 5.08726e72 0.0249338
\(638\) 1.37250e73 0.0645305
\(639\) 2.25003e74 1.01488
\(640\) −1.41736e74 −0.613356
\(641\) −7.34082e72 −0.0304794 −0.0152397 0.999884i \(-0.504851\pi\)
−0.0152397 + 0.999884i \(0.504851\pi\)
\(642\) −8.63481e74 −3.44013
\(643\) −2.35192e74 −0.899150 −0.449575 0.893243i \(-0.648425\pi\)
−0.449575 + 0.893243i \(0.648425\pi\)
\(644\) 2.48363e74 0.911196
\(645\) 5.30806e74 1.86897
\(646\) 4.92459e74 1.66421
\(647\) 1.32555e74 0.429963 0.214981 0.976618i \(-0.431031\pi\)
0.214981 + 0.976618i \(0.431031\pi\)
\(648\) 7.05348e73 0.219617
\(649\) 6.94914e73 0.207705
\(650\) −3.52488e74 −1.01144
\(651\) −1.28321e74 −0.353510
\(652\) −1.21067e74 −0.320232
\(653\) −8.70965e73 −0.221208 −0.110604 0.993865i \(-0.535279\pi\)
−0.110604 + 0.993865i \(0.535279\pi\)
\(654\) −4.14809e74 −1.01167
\(655\) 8.53300e73 0.199852
\(656\) 5.58239e74 1.25565
\(657\) −2.56388e74 −0.553880
\(658\) 2.53530e73 0.0526069
\(659\) 2.94646e74 0.587270 0.293635 0.955918i \(-0.405135\pi\)
0.293635 + 0.955918i \(0.405135\pi\)
\(660\) 7.34153e74 1.40563
\(661\) −1.59089e73 −0.0292618 −0.0146309 0.999893i \(-0.504657\pi\)
−0.0146309 + 0.999893i \(0.504657\pi\)
\(662\) −2.63460e74 −0.465562
\(663\) 5.22954e74 0.887881
\(664\) 2.18507e74 0.356460
\(665\) −7.99585e74 −1.25340
\(666\) −2.67108e74 −0.402364
\(667\) −4.18693e73 −0.0606124
\(668\) −1.05529e75 −1.46823
\(669\) 6.37323e74 0.852251
\(670\) 1.01843e75 1.30903
\(671\) −5.57420e74 −0.688708
\(672\) −1.67964e75 −1.99494
\(673\) −1.05609e75 −1.20587 −0.602935 0.797790i \(-0.706002\pi\)
−0.602935 + 0.797790i \(0.706002\pi\)
\(674\) 1.27178e75 1.39612
\(675\) 3.47692e74 0.366982
\(676\) −9.02607e74 −0.916033
\(677\) −1.20175e75 −1.17277 −0.586386 0.810032i \(-0.699450\pi\)
−0.586386 + 0.810032i \(0.699450\pi\)
\(678\) 3.23460e75 3.03552
\(679\) 1.13470e75 1.02407
\(680\) −5.35974e74 −0.465219
\(681\) −1.71278e75 −1.42990
\(682\) −2.63955e74 −0.211955
\(683\) 1.42292e75 1.09909 0.549543 0.835466i \(-0.314802\pi\)
0.549543 + 0.835466i \(0.314802\pi\)
\(684\) 9.57049e74 0.711127
\(685\) −6.44957e74 −0.461031
\(686\) 2.05815e75 1.41543
\(687\) 3.07539e75 2.03491
\(688\) −1.14840e75 −0.731138
\(689\) 4.60835e74 0.282316
\(690\) −4.21849e75 −2.48689
\(691\) −1.83314e75 −1.03998 −0.519992 0.854171i \(-0.674065\pi\)
−0.519992 + 0.854171i \(0.674065\pi\)
\(692\) 1.07554e75 0.587239
\(693\) 9.26148e74 0.486687
\(694\) −1.58352e75 −0.800938
\(695\) −5.57127e75 −2.71242
\(696\) −4.29632e73 −0.0201350
\(697\) 4.91866e75 2.21911
\(698\) −3.77551e75 −1.63986
\(699\) 6.56406e74 0.274490
\(700\) 4.58584e75 1.84638
\(701\) −1.33614e75 −0.517992 −0.258996 0.965878i \(-0.583392\pi\)
−0.258996 + 0.965878i \(0.583392\pi\)
\(702\) −3.94904e74 −0.147420
\(703\) 7.00925e74 0.251974
\(704\) −2.05154e75 −0.710240
\(705\) −2.28618e74 −0.0762253
\(706\) 4.39736e75 1.41211
\(707\) 3.41304e75 1.05567
\(708\) −1.86870e75 −0.556747
\(709\) −2.59964e75 −0.746084 −0.373042 0.927815i \(-0.621685\pi\)
−0.373042 + 0.927815i \(0.621685\pi\)
\(710\) 1.03982e76 2.87484
\(711\) −2.78756e75 −0.742471
\(712\) 1.10911e75 0.284613
\(713\) 8.05216e74 0.199086
\(714\) −1.28152e76 −3.05297
\(715\) −1.74658e75 −0.400940
\(716\) −8.51739e74 −0.188413
\(717\) −2.57253e74 −0.0548408
\(718\) −5.45508e75 −1.12074
\(719\) 5.36453e75 1.06222 0.531112 0.847302i \(-0.321774\pi\)
0.531112 + 0.847302i \(0.321774\pi\)
\(720\) 5.94454e75 1.13451
\(721\) 2.03911e75 0.375108
\(722\) 3.50336e75 0.621225
\(723\) 1.26773e76 2.16702
\(724\) −8.11172e75 −1.33672
\(725\) −7.73087e74 −0.122821
\(726\) −8.68805e75 −1.33077
\(727\) −4.93191e75 −0.728373 −0.364186 0.931326i \(-0.618653\pi\)
−0.364186 + 0.931326i \(0.618653\pi\)
\(728\) −6.06304e74 −0.0863394
\(729\) −4.61515e75 −0.633733
\(730\) −1.18487e76 −1.56897
\(731\) −1.01186e76 −1.29214
\(732\) 1.49896e76 1.84607
\(733\) −9.00902e75 −1.07010 −0.535048 0.844822i \(-0.679706\pi\)
−0.535048 + 0.844822i \(0.679706\pi\)
\(734\) 2.12853e76 2.43857
\(735\) 1.12416e75 0.124226
\(736\) 1.05397e76 1.12349
\(737\) 3.09550e75 0.318305
\(738\) 1.80052e76 1.78609
\(739\) 4.93120e75 0.471927 0.235964 0.971762i \(-0.424175\pi\)
0.235964 + 0.971762i \(0.424175\pi\)
\(740\) −6.55345e75 −0.605103
\(741\) −5.02342e75 −0.447525
\(742\) −1.12929e76 −0.970742
\(743\) −1.49779e76 −1.24236 −0.621181 0.783667i \(-0.713347\pi\)
−0.621181 + 0.783667i \(0.713347\pi\)
\(744\) 8.26252e74 0.0661347
\(745\) 2.82686e76 2.18355
\(746\) 1.79723e76 1.33976
\(747\) −2.13534e76 −1.53628
\(748\) −1.39949e76 −0.971801
\(749\) −2.67258e76 −1.79128
\(750\) −2.88033e76 −1.86345
\(751\) 4.11227e75 0.256817 0.128408 0.991721i \(-0.459013\pi\)
0.128408 + 0.991721i \(0.459013\pi\)
\(752\) 4.94616e74 0.0298191
\(753\) 1.48698e76 0.865442
\(754\) 8.78062e74 0.0493383
\(755\) 6.12777e75 0.332436
\(756\) 5.13767e75 0.269115
\(757\) 3.57142e76 1.80634 0.903172 0.429278i \(-0.141232\pi\)
0.903172 + 0.429278i \(0.141232\pi\)
\(758\) −2.71554e76 −1.32624
\(759\) −1.28220e76 −0.604715
\(760\) 5.14848e75 0.234487
\(761\) 2.38006e76 1.04687 0.523437 0.852064i \(-0.324649\pi\)
0.523437 + 0.852064i \(0.324649\pi\)
\(762\) 2.43614e76 1.03489
\(763\) −1.28388e76 −0.526775
\(764\) −4.07252e76 −1.61395
\(765\) 5.23775e76 2.00501
\(766\) 1.09474e76 0.404807
\(767\) 4.44572e75 0.158805
\(768\) −2.69252e76 −0.929151
\(769\) 2.37124e76 0.790546 0.395273 0.918564i \(-0.370650\pi\)
0.395273 + 0.918564i \(0.370650\pi\)
\(770\) 4.28008e76 1.37863
\(771\) −2.26603e76 −0.705219
\(772\) −2.36219e76 −0.710324
\(773\) −6.25079e76 −1.81626 −0.908131 0.418686i \(-0.862491\pi\)
−0.908131 + 0.418686i \(0.862491\pi\)
\(774\) −3.70399e76 −1.04000
\(775\) 1.48677e76 0.403412
\(776\) −7.30625e75 −0.191584
\(777\) −1.82401e76 −0.462242
\(778\) 3.19069e76 0.781494
\(779\) −4.72479e76 −1.11851
\(780\) 4.69676e76 1.07471
\(781\) 3.16054e76 0.699051
\(782\) 8.04156e76 1.71934
\(783\) −8.66113e74 −0.0179014
\(784\) −2.43212e75 −0.0485970
\(785\) −1.45540e77 −2.81148
\(786\) −1.31371e76 −0.245359
\(787\) −1.33252e76 −0.240627 −0.120314 0.992736i \(-0.538390\pi\)
−0.120314 + 0.992736i \(0.538390\pi\)
\(788\) 7.10818e76 1.24112
\(789\) 1.01039e77 1.70588
\(790\) −1.28824e77 −2.10318
\(791\) 1.00115e77 1.58060
\(792\) −5.96342e75 −0.0910496
\(793\) −3.56610e76 −0.526568
\(794\) −6.60118e76 −0.942710
\(795\) 1.01833e77 1.40657
\(796\) −7.15217e76 −0.955524
\(797\) −2.10248e76 −0.271698 −0.135849 0.990730i \(-0.543376\pi\)
−0.135849 + 0.990730i \(0.543376\pi\)
\(798\) 1.23101e77 1.53881
\(799\) 4.35807e75 0.0526993
\(800\) 1.94609e77 2.27655
\(801\) −1.08387e77 −1.22663
\(802\) 7.36975e76 0.806922
\(803\) −3.60139e76 −0.381512
\(804\) −8.32416e76 −0.853208
\(805\) −1.30567e77 −1.29492
\(806\) −1.68866e76 −0.162055
\(807\) −3.63787e76 −0.337830
\(808\) −2.19764e76 −0.197495
\(809\) 1.17401e77 1.02103 0.510514 0.859870i \(-0.329455\pi\)
0.510514 + 0.859870i \(0.329455\pi\)
\(810\) −3.18549e77 −2.68116
\(811\) 9.03233e75 0.0735779 0.0367889 0.999323i \(-0.488287\pi\)
0.0367889 + 0.999323i \(0.488287\pi\)
\(812\) −1.14235e76 −0.0900669
\(813\) 5.93143e76 0.452647
\(814\) −3.75196e76 −0.277148
\(815\) 6.36464e76 0.455090
\(816\) −2.50014e77 −1.73051
\(817\) 9.71975e76 0.651285
\(818\) 2.87307e77 1.86373
\(819\) 5.92505e76 0.372108
\(820\) 4.41755e77 2.68605
\(821\) 8.19852e76 0.482660 0.241330 0.970443i \(-0.422416\pi\)
0.241330 + 0.970443i \(0.422416\pi\)
\(822\) 9.92951e76 0.566010
\(823\) 1.15061e76 0.0635088 0.0317544 0.999496i \(-0.489891\pi\)
0.0317544 + 0.999496i \(0.489891\pi\)
\(824\) −1.31297e76 −0.0701754
\(825\) −2.36750e77 −1.22535
\(826\) −1.08944e77 −0.546051
\(827\) 4.29383e76 0.208425 0.104212 0.994555i \(-0.466768\pi\)
0.104212 + 0.994555i \(0.466768\pi\)
\(828\) 1.56280e77 0.734683
\(829\) −1.25368e77 −0.570808 −0.285404 0.958407i \(-0.592128\pi\)
−0.285404 + 0.958407i \(0.592128\pi\)
\(830\) −9.86820e77 −4.35180
\(831\) −1.47104e77 −0.628345
\(832\) −1.31248e77 −0.543031
\(833\) −2.14295e76 −0.0858853
\(834\) 8.57732e77 3.33005
\(835\) 5.54776e77 2.08654
\(836\) 1.34433e77 0.489823
\(837\) 1.66568e76 0.0587985
\(838\) −6.67722e77 −2.28365
\(839\) −1.07457e77 −0.356075 −0.178038 0.984024i \(-0.556975\pi\)
−0.178038 + 0.984024i \(0.556975\pi\)
\(840\) −1.33978e77 −0.430163
\(841\) −3.19510e77 −0.994009
\(842\) 5.78928e76 0.174524
\(843\) 7.45875e76 0.217889
\(844\) 7.25153e76 0.205284
\(845\) 4.74510e77 1.30180
\(846\) 1.59531e76 0.0424161
\(847\) −2.68906e77 −0.692930
\(848\) −2.20316e77 −0.550245
\(849\) 1.60996e77 0.389727
\(850\) 1.48481e78 3.48394
\(851\) 1.14457e77 0.260320
\(852\) −8.49904e77 −1.87379
\(853\) −7.22678e77 −1.54453 −0.772263 0.635303i \(-0.780875\pi\)
−0.772263 + 0.635303i \(0.780875\pi\)
\(854\) 8.73889e77 1.81060
\(855\) −5.03131e77 −1.01060
\(856\) 1.72086e77 0.335113
\(857\) −6.80686e77 −1.28515 −0.642577 0.766221i \(-0.722135\pi\)
−0.642577 + 0.766221i \(0.722135\pi\)
\(858\) 2.68897e77 0.492236
\(859\) 4.28760e77 0.761019 0.380510 0.924777i \(-0.375749\pi\)
0.380510 + 0.924777i \(0.375749\pi\)
\(860\) −9.08770e77 −1.56403
\(861\) 1.22953e78 2.05189
\(862\) −4.12755e77 −0.667958
\(863\) 6.31202e77 0.990564 0.495282 0.868732i \(-0.335065\pi\)
0.495282 + 0.868732i \(0.335065\pi\)
\(864\) 2.18026e77 0.331814
\(865\) −5.65423e77 −0.834539
\(866\) −3.74009e77 −0.535374
\(867\) −1.22876e78 −1.70593
\(868\) 2.19693e77 0.295831
\(869\) −3.91558e77 −0.511413
\(870\) 1.94030e77 0.245815
\(871\) 1.98036e77 0.243367
\(872\) 8.26685e76 0.0985493
\(873\) 7.13996e77 0.825693
\(874\) −7.72460e77 −0.866609
\(875\) −8.91497e77 −0.970301
\(876\) 9.68454e77 1.02263
\(877\) −8.46824e77 −0.867569 −0.433785 0.901017i \(-0.642822\pi\)
−0.433785 + 0.901017i \(0.642822\pi\)
\(878\) 4.95802e76 0.0492837
\(879\) 4.08257e77 0.393757
\(880\) 8.35008e77 0.781447
\(881\) 1.78575e78 1.62166 0.810830 0.585281i \(-0.199016\pi\)
0.810830 + 0.585281i \(0.199016\pi\)
\(882\) −7.84445e76 −0.0691265
\(883\) 8.63389e77 0.738325 0.369163 0.929365i \(-0.379645\pi\)
0.369163 + 0.929365i \(0.379645\pi\)
\(884\) −8.95327e77 −0.743013
\(885\) 9.82396e77 0.791207
\(886\) 1.35768e78 1.06122
\(887\) 1.09908e78 0.833785 0.416893 0.908956i \(-0.363119\pi\)
0.416893 + 0.908956i \(0.363119\pi\)
\(888\) 1.17447e77 0.0864764
\(889\) 7.54014e77 0.538869
\(890\) −5.00896e78 −3.47466
\(891\) −9.68227e77 −0.651956
\(892\) −1.09113e78 −0.713197
\(893\) −4.18630e76 −0.0265624
\(894\) −4.35213e78 −2.68076
\(895\) 4.47769e77 0.267759
\(896\) 6.75393e77 0.392097
\(897\) −8.20293e77 −0.462348
\(898\) 2.78560e78 1.52439
\(899\) −3.70360e76 −0.0196785
\(900\) 2.88560e78 1.48871
\(901\) −1.94121e78 −0.972446
\(902\) 2.52912e78 1.23026
\(903\) −2.52936e78 −1.19477
\(904\) −6.44633e77 −0.295699
\(905\) 4.26442e78 1.89964
\(906\) −9.43407e77 −0.408133
\(907\) −1.67275e78 −0.702812 −0.351406 0.936223i \(-0.614296\pi\)
−0.351406 + 0.936223i \(0.614296\pi\)
\(908\) 2.93238e78 1.19659
\(909\) 2.14762e78 0.851168
\(910\) 2.73819e78 1.05406
\(911\) −3.79500e78 −1.41898 −0.709488 0.704718i \(-0.751074\pi\)
−0.709488 + 0.704718i \(0.751074\pi\)
\(912\) 2.40160e78 0.872243
\(913\) −2.99943e78 −1.05819
\(914\) 4.65249e78 1.59445
\(915\) −7.88021e78 −2.62349
\(916\) −5.26524e78 −1.70289
\(917\) −4.06609e77 −0.127758
\(918\) 1.66348e78 0.507794
\(919\) 2.27887e78 0.675863 0.337932 0.941171i \(-0.390273\pi\)
0.337932 + 0.941171i \(0.390273\pi\)
\(920\) 8.40716e77 0.242254
\(921\) 8.71904e78 2.44112
\(922\) −5.67499e78 −1.54382
\(923\) 2.02196e78 0.534475
\(924\) −3.49833e78 −0.898574
\(925\) 2.11336e78 0.527494
\(926\) −2.58263e77 −0.0626427
\(927\) 1.28309e78 0.302444
\(928\) −4.84777e77 −0.111051
\(929\) −1.94979e78 −0.434082 −0.217041 0.976162i \(-0.569641\pi\)
−0.217041 + 0.976162i \(0.569641\pi\)
\(930\) −3.73151e78 −0.807397
\(931\) 2.05848e77 0.0432893
\(932\) −1.12380e78 −0.229704
\(933\) −1.24144e79 −2.46639
\(934\) −5.61062e77 −0.108347
\(935\) 7.35727e78 1.38105
\(936\) −3.81511e77 −0.0696141
\(937\) 7.29807e78 1.29452 0.647260 0.762269i \(-0.275915\pi\)
0.647260 + 0.762269i \(0.275915\pi\)
\(938\) −4.85295e78 −0.836816
\(939\) 1.12253e79 1.88175
\(940\) 3.91407e77 0.0637883
\(941\) −8.24697e78 −1.30668 −0.653341 0.757064i \(-0.726633\pi\)
−0.653341 + 0.757064i \(0.726633\pi\)
\(942\) 2.24067e79 3.45167
\(943\) −7.71529e78 −1.15556
\(944\) −2.12541e78 −0.309518
\(945\) −2.70093e78 −0.382446
\(946\) −5.20286e78 −0.716353
\(947\) 1.41218e79 1.89067 0.945335 0.326100i \(-0.105734\pi\)
0.945335 + 0.326100i \(0.105734\pi\)
\(948\) 1.05294e79 1.37083
\(949\) −2.30400e78 −0.291694
\(950\) −1.42629e79 −1.75603
\(951\) −1.10071e79 −1.31792
\(952\) 2.55398e78 0.297399
\(953\) −1.39912e79 −1.58451 −0.792253 0.610192i \(-0.791092\pi\)
−0.792253 + 0.610192i \(0.791092\pi\)
\(954\) −7.10598e78 −0.782694
\(955\) 2.14097e79 2.29362
\(956\) 4.40432e77 0.0458929
\(957\) 5.89753e77 0.0597728
\(958\) 1.59293e79 1.57040
\(959\) 3.07330e78 0.294722
\(960\) −2.90026e79 −2.70551
\(961\) −1.03074e79 −0.935365
\(962\) −2.40032e78 −0.211900
\(963\) −1.68169e79 −1.44428
\(964\) −2.17043e79 −1.81344
\(965\) 1.24183e79 1.00946
\(966\) 2.01016e79 1.58978
\(967\) 4.89301e78 0.376508 0.188254 0.982120i \(-0.439717\pi\)
0.188254 + 0.982120i \(0.439717\pi\)
\(968\) 1.73147e78 0.129634
\(969\) 2.11606e79 1.54151
\(970\) 3.29964e79 2.33892
\(971\) −5.58018e78 −0.384892 −0.192446 0.981308i \(-0.561642\pi\)
−0.192446 + 0.981308i \(0.561642\pi\)
\(972\) 2.21370e79 1.48581
\(973\) 2.65478e79 1.73396
\(974\) −3.33089e79 −2.11713
\(975\) −1.51461e79 −0.936869
\(976\) 1.70488e79 1.02630
\(977\) −2.57199e79 −1.50683 −0.753414 0.657546i \(-0.771594\pi\)
−0.753414 + 0.657546i \(0.771594\pi\)
\(978\) −9.79875e78 −0.558716
\(979\) −1.52247e79 −0.844903
\(980\) −1.92462e78 −0.103957
\(981\) −8.07871e78 −0.424730
\(982\) −6.66779e78 −0.341215
\(983\) 3.41218e79 1.69967 0.849833 0.527051i \(-0.176702\pi\)
0.849833 + 0.527051i \(0.176702\pi\)
\(984\) −7.91685e78 −0.383869
\(985\) −3.73685e79 −1.76378
\(986\) −3.69873e78 −0.169947
\(987\) 1.08940e78 0.0487283
\(988\) 8.60038e78 0.374506
\(989\) 1.58718e79 0.672858
\(990\) 2.69320e79 1.11157
\(991\) −2.88433e79 −1.15902 −0.579512 0.814964i \(-0.696757\pi\)
−0.579512 + 0.814964i \(0.696757\pi\)
\(992\) 9.32306e78 0.364753
\(993\) −1.13206e79 −0.431237
\(994\) −4.95490e79 −1.83779
\(995\) 3.75997e79 1.35792
\(996\) 8.06580e79 2.83645
\(997\) −3.11454e79 −1.06653 −0.533264 0.845949i \(-0.679035\pi\)
−0.533264 + 0.845949i \(0.679035\pi\)
\(998\) −5.64900e77 −0.0188370
\(999\) 2.36766e78 0.0768837
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.1.1 4
3.2 odd 2 9.54.a.b.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.54.a.a.1.1 4 1.1 even 1 trivial
9.54.a.b.1.4 4 3.2 odd 2