Properties

Label 1.52.a.a.1.1
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 1.1
Root \(-457245.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.71140e7 q^{2} +6.49653e11 q^{3} +5.33705e15 q^{4} +8.70295e17 q^{5} -5.65939e19 q^{6} +3.14283e21 q^{7} -2.68769e23 q^{8} -1.73165e24 q^{9} +O(q^{10})\) \(q-8.71140e7 q^{2} +6.49653e11 q^{3} +5.33705e15 q^{4} +8.70295e17 q^{5} -5.65939e19 q^{6} +3.14283e21 q^{7} -2.68769e23 q^{8} -1.73165e24 q^{9} -7.58149e25 q^{10} +4.69985e26 q^{11} +3.46723e27 q^{12} +9.04757e27 q^{13} -2.73785e29 q^{14} +5.65389e29 q^{15} +1.13956e31 q^{16} -1.94276e30 q^{17} +1.50851e32 q^{18} -2.88440e32 q^{19} +4.64481e33 q^{20} +2.04175e33 q^{21} -4.09423e34 q^{22} +1.73996e34 q^{23} -1.74606e35 q^{24} +3.13324e35 q^{25} -7.88170e35 q^{26} -2.52412e36 q^{27} +1.67734e37 q^{28} +2.51798e37 q^{29} -4.92533e37 q^{30} -3.39978e37 q^{31} -3.87499e38 q^{32} +3.05327e38 q^{33} +1.69241e38 q^{34} +2.73519e39 q^{35} -9.24188e39 q^{36} +1.41519e40 q^{37} +2.51271e40 q^{38} +5.87778e39 q^{39} -2.33908e41 q^{40} +1.62359e41 q^{41} -1.77865e41 q^{42} -1.06168e41 q^{43} +2.50834e42 q^{44} -1.50704e42 q^{45} -1.51575e42 q^{46} -2.33100e42 q^{47} +7.40315e42 q^{48} -2.71188e42 q^{49} -2.72949e43 q^{50} -1.26212e42 q^{51} +4.82874e43 q^{52} -5.52737e43 q^{53} +2.19886e44 q^{54} +4.09026e44 q^{55} -8.44695e44 q^{56} -1.87386e44 q^{57} -2.19351e45 q^{58} +2.66580e45 q^{59} +3.01751e45 q^{60} -3.00082e45 q^{61} +2.96168e45 q^{62} -5.44227e45 q^{63} +8.09610e45 q^{64} +7.87405e45 q^{65} -2.65983e46 q^{66} +1.24565e45 q^{67} -1.03686e46 q^{68} +1.13037e46 q^{69} -2.38273e47 q^{70} +2.67507e47 q^{71} +4.65412e47 q^{72} +4.01968e47 q^{73} -1.23283e48 q^{74} +2.03552e47 q^{75} -1.53942e48 q^{76} +1.47708e48 q^{77} -5.12037e47 q^{78} -3.09063e48 q^{79} +9.91749e48 q^{80} +2.08963e48 q^{81} -1.41437e49 q^{82} +1.48588e48 q^{83} +1.08969e49 q^{84} -1.69077e48 q^{85} +9.24873e48 q^{86} +1.63581e49 q^{87} -1.26317e50 q^{88} -1.49141e49 q^{89} +1.31284e50 q^{90} +2.84350e49 q^{91} +9.28627e49 q^{92} -2.20867e49 q^{93} +2.03063e50 q^{94} -2.51028e50 q^{95} -2.51740e50 q^{96} -5.46477e50 q^{97} +2.36242e50 q^{98} -8.13847e50 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} + O(q^{10}) \) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} - \)\(26\!\cdots\!20\)\(q^{10} + \)\(35\!\cdots\!48\)\(q^{11} - \)\(49\!\cdots\!20\)\(q^{12} + \)\(30\!\cdots\!80\)\(q^{13} + \)\(11\!\cdots\!24\)\(q^{14} + \)\(14\!\cdots\!60\)\(q^{15} + \)\(13\!\cdots\!44\)\(q^{16} + \)\(48\!\cdots\!20\)\(q^{17} + \)\(73\!\cdots\!40\)\(q^{18} + \)\(81\!\cdots\!80\)\(q^{19} + \)\(66\!\cdots\!40\)\(q^{20} + \)\(31\!\cdots\!48\)\(q^{21} - \)\(34\!\cdots\!20\)\(q^{22} - \)\(54\!\cdots\!80\)\(q^{23} - \)\(87\!\cdots\!60\)\(q^{24} - \)\(57\!\cdots\!00\)\(q^{25} + \)\(15\!\cdots\!48\)\(q^{26} + \)\(36\!\cdots\!20\)\(q^{27} + \)\(34\!\cdots\!80\)\(q^{28} + \)\(24\!\cdots\!20\)\(q^{29} - \)\(32\!\cdots\!40\)\(q^{30} - \)\(74\!\cdots\!72\)\(q^{31} - \)\(69\!\cdots\!60\)\(q^{32} - \)\(17\!\cdots\!20\)\(q^{33} + \)\(59\!\cdots\!64\)\(q^{34} + \)\(54\!\cdots\!80\)\(q^{35} + \)\(12\!\cdots\!84\)\(q^{36} + \)\(92\!\cdots\!60\)\(q^{37} + \)\(42\!\cdots\!20\)\(q^{38} - \)\(11\!\cdots\!04\)\(q^{39} - \)\(26\!\cdots\!00\)\(q^{40} + \)\(14\!\cdots\!68\)\(q^{41} - \)\(39\!\cdots\!80\)\(q^{42} - \)\(38\!\cdots\!00\)\(q^{43} + \)\(39\!\cdots\!44\)\(q^{44} + \)\(25\!\cdots\!60\)\(q^{45} - \)\(68\!\cdots\!12\)\(q^{46} + \)\(70\!\cdots\!80\)\(q^{47} - \)\(19\!\cdots\!80\)\(q^{48} - \)\(21\!\cdots\!28\)\(q^{49} - \)\(65\!\cdots\!00\)\(q^{50} + \)\(69\!\cdots\!28\)\(q^{51} + \)\(20\!\cdots\!00\)\(q^{52} - \)\(46\!\cdots\!60\)\(q^{53} + \)\(29\!\cdots\!80\)\(q^{54} + \)\(28\!\cdots\!60\)\(q^{55} - \)\(71\!\cdots\!80\)\(q^{56} - \)\(88\!\cdots\!60\)\(q^{57} - \)\(32\!\cdots\!20\)\(q^{58} + \)\(11\!\cdots\!40\)\(q^{59} + \)\(55\!\cdots\!80\)\(q^{60} + \)\(34\!\cdots\!48\)\(q^{61} + \)\(96\!\cdots\!80\)\(q^{62} + \)\(21\!\cdots\!60\)\(q^{63} - \)\(34\!\cdots\!28\)\(q^{64} + \)\(10\!\cdots\!60\)\(q^{65} - \)\(15\!\cdots\!04\)\(q^{66} + \)\(30\!\cdots\!20\)\(q^{67} - \)\(92\!\cdots\!60\)\(q^{68} + \)\(15\!\cdots\!76\)\(q^{69} - \)\(12\!\cdots\!20\)\(q^{70} + \)\(39\!\cdots\!88\)\(q^{71} + \)\(50\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!56\)\(q^{74} + \)\(72\!\cdots\!00\)\(q^{75} - \)\(19\!\cdots\!60\)\(q^{76} + \)\(13\!\cdots\!00\)\(q^{77} - \)\(96\!\cdots\!00\)\(q^{78} + \)\(40\!\cdots\!20\)\(q^{79} + \)\(65\!\cdots\!80\)\(q^{80} + \)\(15\!\cdots\!44\)\(q^{81} + \)\(26\!\cdots\!80\)\(q^{82} + \)\(10\!\cdots\!60\)\(q^{83} - \)\(18\!\cdots\!56\)\(q^{84} - \)\(22\!\cdots\!20\)\(q^{85} - \)\(43\!\cdots\!32\)\(q^{86} - \)\(62\!\cdots\!40\)\(q^{87} - \)\(25\!\cdots\!40\)\(q^{88} - \)\(90\!\cdots\!40\)\(q^{89} + \)\(31\!\cdots\!60\)\(q^{90} + \)\(10\!\cdots\!88\)\(q^{91} + \)\(19\!\cdots\!20\)\(q^{92} - \)\(31\!\cdots\!20\)\(q^{93} + \)\(63\!\cdots\!84\)\(q^{94} - \)\(41\!\cdots\!00\)\(q^{95} - \)\(24\!\cdots\!32\)\(q^{96} - \)\(13\!\cdots\!20\)\(q^{97} - \)\(31\!\cdots\!80\)\(q^{98} - \)\(17\!\cdots\!64\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.71140e7 −1.83579 −0.917895 0.396823i \(-0.870113\pi\)
−0.917895 + 0.396823i \(0.870113\pi\)
\(3\) 6.49653e11 0.442679 0.221340 0.975197i \(-0.428957\pi\)
0.221340 + 0.975197i \(0.428957\pi\)
\(4\) 5.33705e15 2.37013
\(5\) 8.70295e17 1.30596 0.652982 0.757373i \(-0.273518\pi\)
0.652982 + 0.757373i \(0.273518\pi\)
\(6\) −5.65939e19 −0.812667
\(7\) 3.14283e21 0.885770 0.442885 0.896578i \(-0.353955\pi\)
0.442885 + 0.896578i \(0.353955\pi\)
\(8\) −2.68769e23 −2.51527
\(9\) −1.73165e24 −0.804035
\(10\) −7.58149e25 −2.39748
\(11\) 4.69985e26 1.30789 0.653944 0.756543i \(-0.273113\pi\)
0.653944 + 0.756543i \(0.273113\pi\)
\(12\) 3.46723e27 1.04921
\(13\) 9.04757e27 0.355612 0.177806 0.984066i \(-0.443100\pi\)
0.177806 + 0.984066i \(0.443100\pi\)
\(14\) −2.73785e29 −1.62609
\(15\) 5.65389e29 0.578123
\(16\) 1.13956e31 2.24738
\(17\) −1.94276e30 −0.0816527 −0.0408264 0.999166i \(-0.512999\pi\)
−0.0408264 + 0.999166i \(0.512999\pi\)
\(18\) 1.50851e32 1.47604
\(19\) −2.88440e32 −0.710949 −0.355474 0.934686i \(-0.615681\pi\)
−0.355474 + 0.934686i \(0.615681\pi\)
\(20\) 4.64481e33 3.09530
\(21\) 2.04175e33 0.392112
\(22\) −4.09423e34 −2.40101
\(23\) 1.73996e34 0.328458 0.164229 0.986422i \(-0.447486\pi\)
0.164229 + 0.986422i \(0.447486\pi\)
\(24\) −1.74606e35 −1.11346
\(25\) 3.13324e35 0.705542
\(26\) −7.88170e35 −0.652829
\(27\) −2.52412e36 −0.798609
\(28\) 1.67734e37 2.09939
\(29\) 2.51798e37 1.28796 0.643980 0.765042i \(-0.277282\pi\)
0.643980 + 0.765042i \(0.277282\pi\)
\(30\) −4.92533e37 −1.06131
\(31\) −3.39978e37 −0.317488 −0.158744 0.987320i \(-0.550744\pi\)
−0.158744 + 0.987320i \(0.550744\pi\)
\(32\) −3.87499e38 −1.61045
\(33\) 3.05327e38 0.578975
\(34\) 1.69241e38 0.149897
\(35\) 2.73519e39 1.15678
\(36\) −9.24188e39 −1.90567
\(37\) 1.41519e40 1.45101 0.725506 0.688216i \(-0.241606\pi\)
0.725506 + 0.688216i \(0.241606\pi\)
\(38\) 2.51271e40 1.30515
\(39\) 5.87778e39 0.157422
\(40\) −2.33908e41 −3.28485
\(41\) 1.62359e41 1.21475 0.607375 0.794415i \(-0.292222\pi\)
0.607375 + 0.794415i \(0.292222\pi\)
\(42\) −1.77865e41 −0.719835
\(43\) −1.06168e41 −0.235802 −0.117901 0.993025i \(-0.537617\pi\)
−0.117901 + 0.993025i \(0.537617\pi\)
\(44\) 2.50834e42 3.09986
\(45\) −1.50704e42 −1.05004
\(46\) −1.51575e42 −0.602980
\(47\) −2.33100e42 −0.535854 −0.267927 0.963439i \(-0.586339\pi\)
−0.267927 + 0.963439i \(0.586339\pi\)
\(48\) 7.40315e42 0.994867
\(49\) −2.71188e42 −0.215412
\(50\) −2.72949e43 −1.29523
\(51\) −1.26212e42 −0.0361460
\(52\) 4.82874e43 0.842846
\(53\) −5.52737e43 −0.593587 −0.296793 0.954942i \(-0.595917\pi\)
−0.296793 + 0.954942i \(0.595917\pi\)
\(54\) 2.19886e44 1.46608
\(55\) 4.09026e44 1.70805
\(56\) −8.44695e44 −2.22795
\(57\) −1.87386e44 −0.314722
\(58\) −2.19351e45 −2.36443
\(59\) 2.66580e45 1.85824 0.929119 0.369782i \(-0.120567\pi\)
0.929119 + 0.369782i \(0.120567\pi\)
\(60\) 3.01751e45 1.37023
\(61\) −3.00082e45 −0.893983 −0.446992 0.894538i \(-0.647505\pi\)
−0.446992 + 0.894538i \(0.647505\pi\)
\(62\) 2.96168e45 0.582842
\(63\) −5.44227e45 −0.712190
\(64\) 8.09610e45 0.709066
\(65\) 7.87405e45 0.464417
\(66\) −2.65983e46 −1.06288
\(67\) 1.24565e45 0.0339224 0.0169612 0.999856i \(-0.494601\pi\)
0.0169612 + 0.999856i \(0.494601\pi\)
\(68\) −1.03686e46 −0.193527
\(69\) 1.13037e46 0.145402
\(70\) −2.38273e47 −2.12361
\(71\) 2.67507e47 1.66053 0.830266 0.557368i \(-0.188189\pi\)
0.830266 + 0.557368i \(0.188189\pi\)
\(72\) 4.65412e47 2.02236
\(73\) 4.01968e47 1.22874 0.614368 0.789020i \(-0.289411\pi\)
0.614368 + 0.789020i \(0.289411\pi\)
\(74\) −1.23283e48 −2.66376
\(75\) 2.03552e47 0.312329
\(76\) −1.53942e48 −1.68504
\(77\) 1.47708e48 1.15849
\(78\) −5.12037e47 −0.288994
\(79\) −3.09063e48 −1.26054 −0.630269 0.776377i \(-0.717056\pi\)
−0.630269 + 0.776377i \(0.717056\pi\)
\(80\) 9.91749e48 2.93499
\(81\) 2.08963e48 0.450507
\(82\) −1.41437e49 −2.23003
\(83\) 1.48588e48 0.171986 0.0859929 0.996296i \(-0.472594\pi\)
0.0859929 + 0.996296i \(0.472594\pi\)
\(84\) 1.08969e49 0.929355
\(85\) −1.69077e48 −0.106636
\(86\) 9.24873e48 0.432884
\(87\) 1.63581e49 0.570153
\(88\) −1.26317e50 −3.28969
\(89\) −1.49141e49 −0.291173 −0.145587 0.989346i \(-0.546507\pi\)
−0.145587 + 0.989346i \(0.546507\pi\)
\(90\) 1.31284e50 1.92766
\(91\) 2.84350e49 0.314990
\(92\) 9.28627e49 0.778487
\(93\) −2.20867e49 −0.140545
\(94\) 2.03063e50 0.983716
\(95\) −2.51028e50 −0.928473
\(96\) −2.51740e50 −0.712911
\(97\) −5.46477e50 −1.18821 −0.594105 0.804388i \(-0.702494\pi\)
−0.594105 + 0.804388i \(0.702494\pi\)
\(98\) 2.36242e50 0.395451
\(99\) −8.13847e50 −1.05159
\(100\) 1.67223e51 1.67223
\(101\) 1.57367e51 1.22101 0.610503 0.792014i \(-0.290968\pi\)
0.610503 + 0.792014i \(0.290968\pi\)
\(102\) 1.09948e50 0.0663564
\(103\) −2.10363e51 −0.989966 −0.494983 0.868903i \(-0.664826\pi\)
−0.494983 + 0.868903i \(0.664826\pi\)
\(104\) −2.43170e51 −0.894459
\(105\) 1.77692e51 0.512084
\(106\) 4.81512e51 1.08970
\(107\) 2.77520e51 0.494319 0.247160 0.968975i \(-0.420503\pi\)
0.247160 + 0.968975i \(0.420503\pi\)
\(108\) −1.34714e52 −1.89281
\(109\) 1.47283e52 1.63597 0.817986 0.575238i \(-0.195091\pi\)
0.817986 + 0.575238i \(0.195091\pi\)
\(110\) −3.56319e52 −3.13563
\(111\) 9.19383e51 0.642333
\(112\) 3.58143e52 1.99066
\(113\) −3.63164e52 −1.60917 −0.804586 0.593836i \(-0.797613\pi\)
−0.804586 + 0.593836i \(0.797613\pi\)
\(114\) 1.63239e52 0.577764
\(115\) 1.51428e52 0.428954
\(116\) 1.34386e53 3.05263
\(117\) −1.56672e52 −0.285925
\(118\) −2.32229e53 −3.41134
\(119\) −6.10575e51 −0.0723255
\(120\) −1.51959e53 −1.45413
\(121\) 9.17560e52 0.710571
\(122\) 2.61414e53 1.64117
\(123\) 1.05477e53 0.537745
\(124\) −1.81448e53 −0.752487
\(125\) −1.13805e53 −0.384551
\(126\) 4.74098e53 1.30743
\(127\) −2.33329e53 −0.525986 −0.262993 0.964798i \(-0.584710\pi\)
−0.262993 + 0.964798i \(0.584710\pi\)
\(128\) 1.67287e53 0.308750
\(129\) −6.89724e52 −0.104385
\(130\) −6.85940e53 −0.852572
\(131\) −3.64141e53 −0.372264 −0.186132 0.982525i \(-0.559595\pi\)
−0.186132 + 0.982525i \(0.559595\pi\)
\(132\) 1.62955e54 1.37224
\(133\) −9.06517e53 −0.629737
\(134\) −1.08513e53 −0.0622745
\(135\) −2.19673e54 −1.04295
\(136\) 5.22152e53 0.205378
\(137\) −4.42139e53 −0.144273 −0.0721364 0.997395i \(-0.522982\pi\)
−0.0721364 + 0.997395i \(0.522982\pi\)
\(138\) −9.84711e53 −0.266927
\(139\) 6.82260e54 1.53841 0.769205 0.639002i \(-0.220652\pi\)
0.769205 + 0.639002i \(0.220652\pi\)
\(140\) 1.45978e55 2.74172
\(141\) −1.51434e54 −0.237212
\(142\) −2.33036e55 −3.04839
\(143\) 4.25222e54 0.465101
\(144\) −1.97331e55 −1.80697
\(145\) 2.19138e55 1.68203
\(146\) −3.50170e55 −2.25570
\(147\) −1.76178e54 −0.0953584
\(148\) 7.55295e55 3.43908
\(149\) −1.19546e55 −0.458441 −0.229221 0.973374i \(-0.573618\pi\)
−0.229221 + 0.973374i \(0.573618\pi\)
\(150\) −1.77322e55 −0.573371
\(151\) −1.21853e55 −0.332602 −0.166301 0.986075i \(-0.553182\pi\)
−0.166301 + 0.986075i \(0.553182\pi\)
\(152\) 7.75236e55 1.78823
\(153\) 3.36416e54 0.0656516
\(154\) −1.28675e56 −2.12674
\(155\) −2.95881e55 −0.414628
\(156\) 3.13700e55 0.373110
\(157\) −3.87399e55 −0.391487 −0.195743 0.980655i \(-0.562712\pi\)
−0.195743 + 0.980655i \(0.562712\pi\)
\(158\) 2.69237e56 2.31409
\(159\) −3.59087e55 −0.262768
\(160\) −3.37238e56 −2.10319
\(161\) 5.46840e55 0.290938
\(162\) −1.82036e56 −0.827037
\(163\) −1.93511e56 −0.751487 −0.375743 0.926724i \(-0.622613\pi\)
−0.375743 + 0.926724i \(0.622613\pi\)
\(164\) 8.66517e56 2.87911
\(165\) 2.65724e56 0.756120
\(166\) −1.29441e56 −0.315730
\(167\) 2.83095e56 0.592463 0.296232 0.955116i \(-0.404270\pi\)
0.296232 + 0.955116i \(0.404270\pi\)
\(168\) −5.48758e56 −0.986266
\(169\) −5.65449e56 −0.873540
\(170\) 1.47290e56 0.195760
\(171\) 4.99475e56 0.571628
\(172\) −5.66625e56 −0.558882
\(173\) −2.17979e57 −1.85455 −0.927275 0.374380i \(-0.877856\pi\)
−0.927275 + 0.374380i \(0.877856\pi\)
\(174\) −1.42502e57 −1.04668
\(175\) 9.84723e56 0.624948
\(176\) 5.35574e57 2.93932
\(177\) 1.73184e57 0.822603
\(178\) 1.29923e57 0.534533
\(179\) 4.26922e56 0.152264 0.0761319 0.997098i \(-0.475743\pi\)
0.0761319 + 0.997098i \(0.475743\pi\)
\(180\) −8.04316e57 −2.48873
\(181\) 2.18558e57 0.587168 0.293584 0.955933i \(-0.405152\pi\)
0.293584 + 0.955933i \(0.405152\pi\)
\(182\) −2.47708e57 −0.578256
\(183\) −1.94949e57 −0.395748
\(184\) −4.67647e57 −0.826160
\(185\) 1.23163e58 1.89497
\(186\) 1.92407e57 0.258012
\(187\) −9.13066e56 −0.106793
\(188\) −1.24407e58 −1.27004
\(189\) −7.93288e57 −0.707384
\(190\) 2.18680e58 1.70448
\(191\) −1.12224e58 −0.765130 −0.382565 0.923929i \(-0.624959\pi\)
−0.382565 + 0.923929i \(0.624959\pi\)
\(192\) 5.25965e57 0.313889
\(193\) −1.46948e58 −0.768159 −0.384080 0.923300i \(-0.625481\pi\)
−0.384080 + 0.923300i \(0.625481\pi\)
\(194\) 4.76058e58 2.18130
\(195\) 5.11540e57 0.205588
\(196\) −1.44734e58 −0.510554
\(197\) −3.80845e58 −1.17994 −0.589969 0.807426i \(-0.700860\pi\)
−0.589969 + 0.807426i \(0.700860\pi\)
\(198\) 7.08975e58 1.93050
\(199\) −2.34549e58 −0.561669 −0.280834 0.959756i \(-0.590611\pi\)
−0.280834 + 0.959756i \(0.590611\pi\)
\(200\) −8.42116e58 −1.77463
\(201\) 8.09237e56 0.0150168
\(202\) −1.37088e59 −2.24151
\(203\) 7.91357e58 1.14084
\(204\) −6.73598e57 −0.0856705
\(205\) 1.41300e59 1.58642
\(206\) 1.83256e59 1.81737
\(207\) −3.01300e58 −0.264092
\(208\) 1.03102e59 0.799194
\(209\) −1.35562e59 −0.929841
\(210\) −1.54795e59 −0.940079
\(211\) 6.94465e58 0.373635 0.186818 0.982395i \(-0.440183\pi\)
0.186818 + 0.982395i \(0.440183\pi\)
\(212\) −2.94999e59 −1.40688
\(213\) 1.73787e59 0.735083
\(214\) −2.41759e59 −0.907466
\(215\) −9.23975e58 −0.307950
\(216\) 6.78405e59 2.00872
\(217\) −1.06849e59 −0.281221
\(218\) −1.28304e60 −3.00330
\(219\) 2.61140e59 0.543936
\(220\) 2.18299e60 4.04831
\(221\) −1.75772e58 −0.0290367
\(222\) −8.00911e59 −1.17919
\(223\) −7.27716e59 −0.955406 −0.477703 0.878521i \(-0.658530\pi\)
−0.477703 + 0.878521i \(0.658530\pi\)
\(224\) −1.21784e60 −1.42648
\(225\) −5.42566e59 −0.567281
\(226\) 3.16367e60 2.95410
\(227\) 1.77581e60 1.48162 0.740809 0.671716i \(-0.234442\pi\)
0.740809 + 0.671716i \(0.234442\pi\)
\(228\) −1.00009e60 −0.745932
\(229\) −5.95206e59 −0.397066 −0.198533 0.980094i \(-0.563618\pi\)
−0.198533 + 0.980094i \(0.563618\pi\)
\(230\) −1.31915e60 −0.787470
\(231\) 9.59591e59 0.512838
\(232\) −6.76753e60 −3.23957
\(233\) −5.94034e59 −0.254821 −0.127410 0.991850i \(-0.540667\pi\)
−0.127410 + 0.991850i \(0.540667\pi\)
\(234\) 1.36483e60 0.524898
\(235\) −2.02866e60 −0.699806
\(236\) 1.42275e61 4.40426
\(237\) −2.00784e60 −0.558014
\(238\) 5.31896e59 0.132774
\(239\) −6.11275e60 −1.37117 −0.685583 0.727995i \(-0.740453\pi\)
−0.685583 + 0.727995i \(0.740453\pi\)
\(240\) 6.44292e60 1.29926
\(241\) 5.01746e60 0.910016 0.455008 0.890487i \(-0.349636\pi\)
0.455008 + 0.890487i \(0.349636\pi\)
\(242\) −7.99324e60 −1.30446
\(243\) 6.79372e60 0.998039
\(244\) −1.60155e61 −2.11885
\(245\) −2.36013e60 −0.281320
\(246\) −9.18850e60 −0.987187
\(247\) −2.60968e60 −0.252822
\(248\) 9.13754e60 0.798567
\(249\) 9.65307e59 0.0761346
\(250\) 9.91397e60 0.705956
\(251\) 2.83094e61 1.82075 0.910376 0.413783i \(-0.135793\pi\)
0.910376 + 0.413783i \(0.135793\pi\)
\(252\) −2.90457e61 −1.68798
\(253\) 8.17756e60 0.429586
\(254\) 2.03263e61 0.965601
\(255\) −1.09841e60 −0.0472053
\(256\) −3.28038e61 −1.27587
\(257\) −2.64892e61 −0.932769 −0.466384 0.884582i \(-0.654444\pi\)
−0.466384 + 0.884582i \(0.654444\pi\)
\(258\) 6.00846e60 0.191629
\(259\) 4.44771e61 1.28526
\(260\) 4.20242e61 1.10073
\(261\) −4.36024e61 −1.03557
\(262\) 3.17217e61 0.683399
\(263\) −3.49990e61 −0.684201 −0.342101 0.939663i \(-0.611138\pi\)
−0.342101 + 0.939663i \(0.611138\pi\)
\(264\) −8.20624e61 −1.45628
\(265\) −4.81044e61 −0.775203
\(266\) 7.89703e61 1.15606
\(267\) −9.68897e60 −0.128896
\(268\) 6.64808e60 0.0804005
\(269\) −1.25062e62 −1.37544 −0.687718 0.725978i \(-0.741388\pi\)
−0.687718 + 0.725978i \(0.741388\pi\)
\(270\) 1.91366e62 1.91465
\(271\) 8.34364e61 0.759694 0.379847 0.925049i \(-0.375977\pi\)
0.379847 + 0.925049i \(0.375977\pi\)
\(272\) −2.21388e61 −0.183504
\(273\) 1.84729e61 0.139440
\(274\) 3.85165e61 0.264855
\(275\) 1.47257e62 0.922770
\(276\) 6.03285e61 0.344620
\(277\) 7.61658e61 0.396758 0.198379 0.980125i \(-0.436432\pi\)
0.198379 + 0.980125i \(0.436432\pi\)
\(278\) −5.94344e62 −2.82420
\(279\) 5.88721e61 0.255272
\(280\) −7.35133e62 −2.90962
\(281\) 1.57065e61 0.0567634 0.0283817 0.999597i \(-0.490965\pi\)
0.0283817 + 0.999597i \(0.490965\pi\)
\(282\) 1.31920e62 0.435471
\(283\) −2.43727e61 −0.0735104 −0.0367552 0.999324i \(-0.511702\pi\)
−0.0367552 + 0.999324i \(0.511702\pi\)
\(284\) 1.42770e63 3.93567
\(285\) −1.63081e62 −0.411016
\(286\) −3.70428e62 −0.853828
\(287\) 5.10266e62 1.07599
\(288\) 6.71011e62 1.29486
\(289\) −5.62328e62 −0.993333
\(290\) −1.90900e63 −3.08786
\(291\) −3.55020e62 −0.525996
\(292\) 2.14532e63 2.91226
\(293\) −3.92051e62 −0.487773 −0.243887 0.969804i \(-0.578422\pi\)
−0.243887 + 0.969804i \(0.578422\pi\)
\(294\) 1.53475e62 0.175058
\(295\) 2.32003e63 2.42679
\(296\) −3.80359e63 −3.64968
\(297\) −1.18630e63 −1.04449
\(298\) 1.04141e63 0.841602
\(299\) 1.57424e62 0.116804
\(300\) 1.08637e63 0.740259
\(301\) −3.33668e62 −0.208867
\(302\) 1.06151e63 0.610588
\(303\) 1.02234e63 0.540514
\(304\) −3.28693e63 −1.59777
\(305\) −2.61160e63 −1.16751
\(306\) −2.93066e62 −0.120523
\(307\) 3.00029e63 1.13536 0.567682 0.823248i \(-0.307840\pi\)
0.567682 + 0.823248i \(0.307840\pi\)
\(308\) 7.88327e63 2.74576
\(309\) −1.36663e63 −0.438237
\(310\) 2.57754e63 0.761170
\(311\) −2.05385e63 −0.558700 −0.279350 0.960189i \(-0.590119\pi\)
−0.279350 + 0.960189i \(0.590119\pi\)
\(312\) −1.57976e63 −0.395959
\(313\) −3.26529e63 −0.754295 −0.377147 0.926153i \(-0.623095\pi\)
−0.377147 + 0.926153i \(0.623095\pi\)
\(314\) 3.37479e63 0.718688
\(315\) −4.73638e63 −0.930094
\(316\) −1.64949e64 −2.98764
\(317\) −2.33370e63 −0.389972 −0.194986 0.980806i \(-0.562466\pi\)
−0.194986 + 0.980806i \(0.562466\pi\)
\(318\) 3.12815e63 0.482388
\(319\) 1.18341e64 1.68451
\(320\) 7.04599e63 0.926014
\(321\) 1.80291e63 0.218825
\(322\) −4.76375e63 −0.534101
\(323\) 5.60368e62 0.0580509
\(324\) 1.11525e64 1.06776
\(325\) 2.83482e63 0.250899
\(326\) 1.68575e64 1.37957
\(327\) 9.56825e63 0.724211
\(328\) −4.36369e64 −3.05542
\(329\) −7.32593e63 −0.474644
\(330\) −2.31483e64 −1.38808
\(331\) 3.40604e64 1.89076 0.945378 0.325977i \(-0.105693\pi\)
0.945378 + 0.325977i \(0.105693\pi\)
\(332\) 7.93023e63 0.407628
\(333\) −2.45061e64 −1.16666
\(334\) −2.46615e64 −1.08764
\(335\) 1.08408e63 0.0443015
\(336\) 2.32668e64 0.881223
\(337\) 2.02190e64 0.709899 0.354949 0.934885i \(-0.384498\pi\)
0.354949 + 0.934885i \(0.384498\pi\)
\(338\) 4.92586e64 1.60364
\(339\) −2.35930e64 −0.712347
\(340\) −9.02373e63 −0.252740
\(341\) −1.59784e64 −0.415239
\(342\) −4.35113e64 −1.04939
\(343\) −4.80889e64 −1.07658
\(344\) 2.85347e64 0.593106
\(345\) 9.83755e63 0.189889
\(346\) 1.89890e65 3.40457
\(347\) −9.66734e64 −1.61029 −0.805147 0.593075i \(-0.797914\pi\)
−0.805147 + 0.593075i \(0.797914\pi\)
\(348\) 8.73040e64 1.35134
\(349\) 5.19371e64 0.747187 0.373594 0.927593i \(-0.378126\pi\)
0.373594 + 0.927593i \(0.378126\pi\)
\(350\) −8.57832e64 −1.14727
\(351\) −2.28372e64 −0.283995
\(352\) −1.82119e65 −2.10628
\(353\) −3.23561e64 −0.348097 −0.174049 0.984737i \(-0.555685\pi\)
−0.174049 + 0.984737i \(0.555685\pi\)
\(354\) −1.50868e65 −1.51013
\(355\) 2.32810e65 2.16859
\(356\) −7.95972e64 −0.690117
\(357\) −3.96662e63 −0.0320170
\(358\) −3.71909e64 −0.279524
\(359\) 2.12862e63 0.0149001 0.00745005 0.999972i \(-0.497629\pi\)
0.00745005 + 0.999972i \(0.497629\pi\)
\(360\) 4.05046e65 2.64113
\(361\) −8.14040e64 −0.494552
\(362\) −1.90394e65 −1.07792
\(363\) 5.96095e64 0.314555
\(364\) 1.51759e65 0.746567
\(365\) 3.49831e65 1.60468
\(366\) 1.69828e65 0.726510
\(367\) −3.44041e65 −1.37286 −0.686429 0.727196i \(-0.740823\pi\)
−0.686429 + 0.727196i \(0.740823\pi\)
\(368\) 1.98278e65 0.738169
\(369\) −2.81148e65 −0.976702
\(370\) −1.07293e66 −3.47877
\(371\) −1.73716e65 −0.525781
\(372\) −1.17878e65 −0.333110
\(373\) 6.74887e65 1.78097 0.890484 0.455015i \(-0.150366\pi\)
0.890484 + 0.455015i \(0.150366\pi\)
\(374\) 7.95408e64 0.196049
\(375\) −7.39334e64 −0.170233
\(376\) 6.26500e65 1.34782
\(377\) 2.27816e65 0.458014
\(378\) 6.91065e65 1.29861
\(379\) −2.27327e65 −0.399348 −0.199674 0.979862i \(-0.563988\pi\)
−0.199674 + 0.979862i \(0.563988\pi\)
\(380\) −1.33975e66 −2.20060
\(381\) −1.51583e65 −0.232843
\(382\) 9.77629e65 1.40462
\(383\) −1.15048e66 −1.54637 −0.773183 0.634183i \(-0.781336\pi\)
−0.773183 + 0.634183i \(0.781336\pi\)
\(384\) 1.08678e65 0.136677
\(385\) 1.28550e66 1.51294
\(386\) 1.28012e66 1.41018
\(387\) 1.83845e65 0.189593
\(388\) −2.91658e66 −2.81621
\(389\) 7.64966e65 0.691715 0.345857 0.938287i \(-0.387588\pi\)
0.345857 + 0.938287i \(0.387588\pi\)
\(390\) −4.45623e65 −0.377416
\(391\) −3.38032e64 −0.0268195
\(392\) 7.28868e65 0.541819
\(393\) −2.36565e65 −0.164794
\(394\) 3.31769e66 2.16612
\(395\) −2.68976e66 −1.64622
\(396\) −4.34355e66 −2.49240
\(397\) −1.60215e66 −0.862074 −0.431037 0.902334i \(-0.641852\pi\)
−0.431037 + 0.902334i \(0.641852\pi\)
\(398\) 2.04325e66 1.03111
\(399\) −5.88921e65 −0.278771
\(400\) 3.57050e66 1.58562
\(401\) 1.99632e65 0.0831857 0.0415929 0.999135i \(-0.486757\pi\)
0.0415929 + 0.999135i \(0.486757\pi\)
\(402\) −7.04959e64 −0.0275676
\(403\) −3.07597e65 −0.112903
\(404\) 8.39874e66 2.89394
\(405\) 1.81860e66 0.588347
\(406\) −6.89383e66 −2.09434
\(407\) 6.65119e66 1.89776
\(408\) 3.39217e65 0.0909168
\(409\) −3.81426e66 −0.960430 −0.480215 0.877151i \(-0.659441\pi\)
−0.480215 + 0.877151i \(0.659441\pi\)
\(410\) −1.23092e67 −2.91234
\(411\) −2.87237e65 −0.0638666
\(412\) −1.12272e67 −2.34635
\(413\) 8.37815e66 1.64597
\(414\) 2.62474e66 0.484817
\(415\) 1.29315e66 0.224607
\(416\) −3.50593e66 −0.572694
\(417\) 4.43232e66 0.681022
\(418\) 1.18094e67 1.70699
\(419\) −4.78644e66 −0.650961 −0.325480 0.945549i \(-0.605526\pi\)
−0.325480 + 0.945549i \(0.605526\pi\)
\(420\) 9.48353e66 1.21370
\(421\) −8.14181e66 −0.980681 −0.490340 0.871531i \(-0.663128\pi\)
−0.490340 + 0.871531i \(0.663128\pi\)
\(422\) −6.04977e66 −0.685916
\(423\) 4.03646e66 0.430846
\(424\) 1.48559e67 1.49303
\(425\) −6.08711e65 −0.0576094
\(426\) −1.51392e67 −1.34946
\(427\) −9.43107e66 −0.791863
\(428\) 1.48114e67 1.17160
\(429\) 2.76247e66 0.205890
\(430\) 8.04912e66 0.565331
\(431\) −5.75151e66 −0.380725 −0.190362 0.981714i \(-0.560966\pi\)
−0.190362 + 0.981714i \(0.560966\pi\)
\(432\) −2.87638e67 −1.79478
\(433\) −3.28347e67 −1.93148 −0.965742 0.259505i \(-0.916441\pi\)
−0.965742 + 0.259505i \(0.916441\pi\)
\(434\) 9.30807e66 0.516263
\(435\) 1.42364e67 0.744600
\(436\) 7.86055e67 3.87746
\(437\) −5.01874e66 −0.233517
\(438\) −2.27489e67 −0.998552
\(439\) 1.32507e67 0.548775 0.274388 0.961619i \(-0.411525\pi\)
0.274388 + 0.961619i \(0.411525\pi\)
\(440\) −1.09933e68 −4.29621
\(441\) 4.69601e66 0.173199
\(442\) 1.53122e66 0.0533053
\(443\) 2.21195e67 0.726909 0.363454 0.931612i \(-0.381597\pi\)
0.363454 + 0.931612i \(0.381597\pi\)
\(444\) 4.90679e67 1.52241
\(445\) −1.29796e67 −0.380262
\(446\) 6.33943e67 1.75393
\(447\) −7.76631e66 −0.202943
\(448\) 2.54447e67 0.628069
\(449\) 2.50690e66 0.0584596 0.0292298 0.999573i \(-0.490695\pi\)
0.0292298 + 0.999573i \(0.490695\pi\)
\(450\) 4.72651e67 1.04141
\(451\) 7.63061e67 1.58876
\(452\) −1.93822e68 −3.81394
\(453\) −7.91623e66 −0.147236
\(454\) −1.54698e68 −2.71994
\(455\) 2.47468e67 0.411366
\(456\) 5.03634e67 0.791610
\(457\) −6.35904e67 −0.945211 −0.472605 0.881274i \(-0.656686\pi\)
−0.472605 + 0.881274i \(0.656686\pi\)
\(458\) 5.18508e67 0.728930
\(459\) 4.90375e66 0.0652086
\(460\) 8.08179e67 1.01668
\(461\) −2.39534e67 −0.285097 −0.142549 0.989788i \(-0.545530\pi\)
−0.142549 + 0.989788i \(0.545530\pi\)
\(462\) −8.35938e67 −0.941464
\(463\) −4.29264e67 −0.457519 −0.228759 0.973483i \(-0.573467\pi\)
−0.228759 + 0.973483i \(0.573467\pi\)
\(464\) 2.86937e68 2.89453
\(465\) −1.92220e67 −0.183547
\(466\) 5.17487e67 0.467798
\(467\) 1.29125e68 1.10518 0.552588 0.833455i \(-0.313640\pi\)
0.552588 + 0.833455i \(0.313640\pi\)
\(468\) −8.36166e67 −0.677678
\(469\) 3.91485e66 0.0300475
\(470\) 1.76724e68 1.28470
\(471\) −2.51675e67 −0.173303
\(472\) −7.16484e68 −4.67396
\(473\) −4.98974e67 −0.308403
\(474\) 1.74911e68 1.02440
\(475\) −9.03750e67 −0.501604
\(476\) −3.25867e67 −0.171421
\(477\) 9.57145e67 0.477264
\(478\) 5.32506e68 2.51717
\(479\) 1.65481e67 0.0741637 0.0370819 0.999312i \(-0.488194\pi\)
0.0370819 + 0.999312i \(0.488194\pi\)
\(480\) −2.19088e68 −0.931037
\(481\) 1.28040e68 0.515997
\(482\) −4.37091e68 −1.67060
\(483\) 3.55256e67 0.128792
\(484\) 4.89707e68 1.68414
\(485\) −4.75596e68 −1.55176
\(486\) −5.91828e68 −1.83219
\(487\) 2.64354e68 0.776599 0.388300 0.921533i \(-0.373063\pi\)
0.388300 + 0.921533i \(0.373063\pi\)
\(488\) 8.06527e68 2.24861
\(489\) −1.25715e68 −0.332668
\(490\) 2.05601e68 0.516445
\(491\) −2.78351e68 −0.663766 −0.331883 0.943320i \(-0.607684\pi\)
−0.331883 + 0.943320i \(0.607684\pi\)
\(492\) 5.62935e68 1.27452
\(493\) −4.89181e67 −0.105165
\(494\) 2.27340e68 0.464128
\(495\) −7.08287e68 −1.37334
\(496\) −3.87424e68 −0.713515
\(497\) 8.40729e68 1.47085
\(498\) −8.40917e67 −0.139767
\(499\) 6.14422e67 0.0970293 0.0485147 0.998822i \(-0.484551\pi\)
0.0485147 + 0.998822i \(0.484551\pi\)
\(500\) −6.07381e68 −0.911436
\(501\) 1.83913e68 0.262271
\(502\) −2.46614e69 −3.34252
\(503\) −2.46940e68 −0.318133 −0.159066 0.987268i \(-0.550848\pi\)
−0.159066 + 0.987268i \(0.550848\pi\)
\(504\) 1.46271e69 1.79135
\(505\) 1.36955e69 1.59459
\(506\) −7.12380e68 −0.788630
\(507\) −3.67346e68 −0.386698
\(508\) −1.24529e69 −1.24665
\(509\) 1.09348e69 1.04114 0.520570 0.853819i \(-0.325719\pi\)
0.520570 + 0.853819i \(0.325719\pi\)
\(510\) 9.56872e67 0.0866591
\(511\) 1.26332e69 1.08838
\(512\) 2.48098e69 2.03347
\(513\) 7.28057e68 0.567770
\(514\) 2.30758e69 1.71237
\(515\) −1.83078e69 −1.29286
\(516\) −3.68109e68 −0.247405
\(517\) −1.09553e69 −0.700837
\(518\) −3.87457e69 −2.35947
\(519\) −1.41611e69 −0.820971
\(520\) −2.11630e69 −1.16813
\(521\) −1.75420e69 −0.921972 −0.460986 0.887407i \(-0.652504\pi\)
−0.460986 + 0.887407i \(0.652504\pi\)
\(522\) 3.79838e69 1.90108
\(523\) 1.24675e69 0.594272 0.297136 0.954835i \(-0.403969\pi\)
0.297136 + 0.954835i \(0.403969\pi\)
\(524\) −1.94344e69 −0.882313
\(525\) 6.39728e68 0.276652
\(526\) 3.04890e69 1.25605
\(527\) 6.60494e67 0.0259238
\(528\) 3.47937e69 1.30118
\(529\) −2.50346e69 −0.892115
\(530\) 4.19057e69 1.42311
\(531\) −4.61622e69 −1.49409
\(532\) −4.83813e69 −1.49256
\(533\) 1.46895e69 0.431980
\(534\) 8.44045e68 0.236627
\(535\) 2.41524e69 0.645563
\(536\) −3.34791e68 −0.0853240
\(537\) 2.77351e68 0.0674040
\(538\) 1.08946e70 2.52501
\(539\) −1.27454e69 −0.281735
\(540\) −1.17241e70 −2.47194
\(541\) 1.90153e69 0.382449 0.191225 0.981546i \(-0.438754\pi\)
0.191225 + 0.981546i \(0.438754\pi\)
\(542\) −7.26848e69 −1.39464
\(543\) 1.41986e69 0.259927
\(544\) 7.52816e68 0.131497
\(545\) 1.28179e70 2.13652
\(546\) −1.60924e69 −0.255982
\(547\) −1.93403e69 −0.293621 −0.146810 0.989165i \(-0.546901\pi\)
−0.146810 + 0.989165i \(0.546901\pi\)
\(548\) −2.35972e69 −0.341945
\(549\) 5.19636e69 0.718794
\(550\) −1.28282e70 −1.69401
\(551\) −7.26284e69 −0.915674
\(552\) −3.03808e69 −0.365724
\(553\) −9.71332e69 −1.11655
\(554\) −6.63511e69 −0.728365
\(555\) 8.00134e69 0.838864
\(556\) 3.64126e70 3.64623
\(557\) −3.13526e69 −0.299893 −0.149946 0.988694i \(-0.547910\pi\)
−0.149946 + 0.988694i \(0.547910\pi\)
\(558\) −5.12859e69 −0.468625
\(559\) −9.60563e68 −0.0838542
\(560\) 3.11690e70 2.59973
\(561\) −5.93176e68 −0.0472749
\(562\) −1.36826e69 −0.104206
\(563\) 9.08297e69 0.661095 0.330547 0.943789i \(-0.392767\pi\)
0.330547 + 0.943789i \(0.392767\pi\)
\(564\) −8.08211e69 −0.562222
\(565\) −3.16060e70 −2.10152
\(566\) 2.12320e69 0.134950
\(567\) 6.56736e69 0.399046
\(568\) −7.18975e70 −4.17668
\(569\) 7.13609e69 0.396367 0.198184 0.980165i \(-0.436496\pi\)
0.198184 + 0.980165i \(0.436496\pi\)
\(570\) 1.42066e70 0.754539
\(571\) 3.32172e70 1.68710 0.843552 0.537048i \(-0.180460\pi\)
0.843552 + 0.537048i \(0.180460\pi\)
\(572\) 2.26943e70 1.10235
\(573\) −7.29067e69 −0.338707
\(574\) −4.44513e70 −1.97529
\(575\) 5.45171e69 0.231741
\(576\) −1.40196e70 −0.570114
\(577\) −2.70924e70 −1.05406 −0.527028 0.849848i \(-0.676694\pi\)
−0.527028 + 0.849848i \(0.676694\pi\)
\(578\) 4.89867e70 1.82355
\(579\) −9.54649e69 −0.340048
\(580\) 1.16955e71 3.98663
\(581\) 4.66987e69 0.152340
\(582\) 3.09273e70 0.965618
\(583\) −2.59778e70 −0.776345
\(584\) −1.08036e71 −3.09060
\(585\) −1.36351e70 −0.373407
\(586\) 3.41531e70 0.895450
\(587\) 4.21203e70 1.05735 0.528676 0.848824i \(-0.322689\pi\)
0.528676 + 0.848824i \(0.322689\pi\)
\(588\) −9.40270e69 −0.226012
\(589\) 9.80631e69 0.225718
\(590\) −2.02107e71 −4.45508
\(591\) −2.47417e70 −0.522334
\(592\) 1.61269e71 3.26097
\(593\) −6.81213e68 −0.0131944 −0.00659718 0.999978i \(-0.502100\pi\)
−0.00659718 + 0.999978i \(0.502100\pi\)
\(594\) 1.03343e71 1.91747
\(595\) −5.31380e69 −0.0944545
\(596\) −6.38021e70 −1.08656
\(597\) −1.52375e70 −0.248639
\(598\) −1.37139e70 −0.214427
\(599\) 6.95350e70 1.04188 0.520942 0.853592i \(-0.325581\pi\)
0.520942 + 0.853592i \(0.325581\pi\)
\(600\) −5.47083e70 −0.785591
\(601\) −1.18115e71 −1.62557 −0.812786 0.582563i \(-0.802050\pi\)
−0.812786 + 0.582563i \(0.802050\pi\)
\(602\) 2.90672e70 0.383436
\(603\) −2.15702e69 −0.0272748
\(604\) −6.50338e70 −0.788310
\(605\) 7.98548e70 0.927980
\(606\) −8.90598e70 −0.992270
\(607\) 6.67421e70 0.712998 0.356499 0.934296i \(-0.383970\pi\)
0.356499 + 0.934296i \(0.383970\pi\)
\(608\) 1.11770e71 1.14494
\(609\) 5.14107e70 0.505025
\(610\) 2.27507e71 2.14330
\(611\) −2.10899e70 −0.190556
\(612\) 1.79547e70 0.155603
\(613\) 1.23137e71 1.02364 0.511821 0.859092i \(-0.328971\pi\)
0.511821 + 0.859092i \(0.328971\pi\)
\(614\) −2.61367e71 −2.08429
\(615\) 9.17958e70 0.702275
\(616\) −3.96994e71 −2.91391
\(617\) 5.54308e70 0.390372 0.195186 0.980766i \(-0.437469\pi\)
0.195186 + 0.980766i \(0.437469\pi\)
\(618\) 1.19053e71 0.804512
\(619\) −1.74222e71 −1.12978 −0.564888 0.825168i \(-0.691081\pi\)
−0.564888 + 0.825168i \(0.691081\pi\)
\(620\) −1.57913e71 −0.982721
\(621\) −4.39187e70 −0.262309
\(622\) 1.78919e71 1.02566
\(623\) −4.68724e70 −0.257912
\(624\) 6.69805e70 0.353787
\(625\) −2.38187e71 −1.20775
\(626\) 2.84453e71 1.38473
\(627\) −8.80684e70 −0.411621
\(628\) −2.06757e71 −0.927874
\(629\) −2.74937e70 −0.118479
\(630\) 4.12605e71 1.70746
\(631\) 3.02907e70 0.120382 0.0601909 0.998187i \(-0.480829\pi\)
0.0601909 + 0.998187i \(0.480829\pi\)
\(632\) 8.30665e71 3.17059
\(633\) 4.51161e70 0.165401
\(634\) 2.03298e71 0.715906
\(635\) −2.03065e71 −0.686919
\(636\) −1.91647e71 −0.622795
\(637\) −2.45359e70 −0.0766031
\(638\) −1.03092e72 −3.09240
\(639\) −4.63227e71 −1.33513
\(640\) 1.45589e71 0.403217
\(641\) 4.16260e71 1.10786 0.553929 0.832564i \(-0.313128\pi\)
0.553929 + 0.832564i \(0.313128\pi\)
\(642\) −1.57059e71 −0.401717
\(643\) −1.46280e71 −0.359587 −0.179794 0.983704i \(-0.557543\pi\)
−0.179794 + 0.983704i \(0.557543\pi\)
\(644\) 2.91852e71 0.689560
\(645\) −6.00263e70 −0.136323
\(646\) −4.88159e70 −0.106569
\(647\) 4.77442e71 1.00199 0.500993 0.865451i \(-0.332968\pi\)
0.500993 + 0.865451i \(0.332968\pi\)
\(648\) −5.61628e71 −1.13315
\(649\) 1.25289e72 2.43037
\(650\) −2.46952e71 −0.460599
\(651\) −6.94149e70 −0.124491
\(652\) −1.03278e72 −1.78112
\(653\) 2.35120e71 0.389946 0.194973 0.980809i \(-0.437538\pi\)
0.194973 + 0.980809i \(0.437538\pi\)
\(654\) −8.33529e71 −1.32950
\(655\) −3.16910e71 −0.486163
\(656\) 1.85017e72 2.73000
\(657\) −6.96066e71 −0.987947
\(658\) 6.38192e71 0.871346
\(659\) 3.04611e71 0.400099 0.200050 0.979786i \(-0.435890\pi\)
0.200050 + 0.979786i \(0.435890\pi\)
\(660\) 1.41819e72 1.79210
\(661\) 5.21186e71 0.633659 0.316830 0.948482i \(-0.397382\pi\)
0.316830 + 0.948482i \(0.397382\pi\)
\(662\) −2.96713e72 −3.47103
\(663\) −1.14191e70 −0.0128539
\(664\) −3.99358e71 −0.432590
\(665\) −7.88937e71 −0.822414
\(666\) 2.13482e72 2.14175
\(667\) 4.38118e71 0.423041
\(668\) 1.51089e72 1.40421
\(669\) −4.72763e71 −0.422938
\(670\) −9.44385e70 −0.0813283
\(671\) −1.41034e72 −1.16923
\(672\) −7.91175e71 −0.631475
\(673\) 6.60671e71 0.507693 0.253846 0.967245i \(-0.418304\pi\)
0.253846 + 0.967245i \(0.418304\pi\)
\(674\) −1.76136e72 −1.30323
\(675\) −7.90867e71 −0.563452
\(676\) −3.01783e72 −2.07040
\(677\) 6.23542e71 0.411959 0.205980 0.978556i \(-0.433962\pi\)
0.205980 + 0.978556i \(0.433962\pi\)
\(678\) 2.05528e72 1.30772
\(679\) −1.71749e72 −1.05248
\(680\) 4.54426e71 0.268217
\(681\) 1.15366e72 0.655882
\(682\) 1.39195e72 0.762292
\(683\) 3.27198e72 1.72617 0.863083 0.505062i \(-0.168530\pi\)
0.863083 + 0.505062i \(0.168530\pi\)
\(684\) 2.66573e72 1.35483
\(685\) −3.84792e71 −0.188415
\(686\) 4.18921e72 1.97637
\(687\) −3.86677e71 −0.175773
\(688\) −1.20984e72 −0.529937
\(689\) −5.00093e71 −0.211087
\(690\) −8.56989e71 −0.348597
\(691\) −2.74210e72 −1.07496 −0.537481 0.843276i \(-0.680624\pi\)
−0.537481 + 0.843276i \(0.680624\pi\)
\(692\) −1.16336e73 −4.39552
\(693\) −2.55778e72 −0.931465
\(694\) 8.42161e72 2.95616
\(695\) 5.93767e72 2.00911
\(696\) −4.39655e72 −1.43409
\(697\) −3.15423e71 −0.0991877
\(698\) −4.52445e72 −1.37168
\(699\) −3.85915e71 −0.112804
\(700\) 5.25552e72 1.48121
\(701\) −2.11073e72 −0.573619 −0.286810 0.957988i \(-0.592595\pi\)
−0.286810 + 0.957988i \(0.592595\pi\)
\(702\) 1.98944e72 0.521355
\(703\) −4.08197e72 −1.03160
\(704\) 3.80505e72 0.927379
\(705\) −1.31792e72 −0.309790
\(706\) 2.81867e72 0.639034
\(707\) 4.94576e72 1.08153
\(708\) 9.24294e72 1.94967
\(709\) −1.26460e72 −0.257321 −0.128661 0.991689i \(-0.541068\pi\)
−0.128661 + 0.991689i \(0.541068\pi\)
\(710\) −2.02810e73 −3.98108
\(711\) 5.35188e72 1.01352
\(712\) 4.00844e72 0.732378
\(713\) −5.91548e71 −0.104281
\(714\) 3.45548e71 0.0587765
\(715\) 3.70069e72 0.607405
\(716\) 2.27851e72 0.360884
\(717\) −3.97116e72 −0.606987
\(718\) −1.85432e71 −0.0273535
\(719\) 5.81095e72 0.827296 0.413648 0.910437i \(-0.364254\pi\)
0.413648 + 0.910437i \(0.364254\pi\)
\(720\) −1.71736e73 −2.35984
\(721\) −6.61135e72 −0.876882
\(722\) 7.09143e72 0.907894
\(723\) 3.25960e72 0.402845
\(724\) 1.16645e73 1.39166
\(725\) 7.88941e72 0.908711
\(726\) −5.19283e72 −0.577457
\(727\) 3.02801e72 0.325110 0.162555 0.986700i \(-0.448027\pi\)
0.162555 + 0.986700i \(0.448027\pi\)
\(728\) −7.64243e72 −0.792285
\(729\) −8.68717e70 −0.00869614
\(730\) −3.04751e73 −2.94587
\(731\) 2.06259e71 0.0192539
\(732\) −1.04045e73 −0.937973
\(733\) −1.84067e72 −0.160259 −0.0801297 0.996784i \(-0.525533\pi\)
−0.0801297 + 0.996784i \(0.525533\pi\)
\(734\) 2.99708e73 2.52028
\(735\) −1.53327e72 −0.124535
\(736\) −6.74234e72 −0.528964
\(737\) 5.85435e71 0.0443668
\(738\) 2.44919e73 1.79302
\(739\) −2.72537e73 −1.92749 −0.963746 0.266820i \(-0.914027\pi\)
−0.963746 + 0.266820i \(0.914027\pi\)
\(740\) 6.57329e73 4.49132
\(741\) −1.69538e72 −0.111919
\(742\) 1.51331e73 0.965224
\(743\) −1.44844e73 −0.892662 −0.446331 0.894868i \(-0.647270\pi\)
−0.446331 + 0.894868i \(0.647270\pi\)
\(744\) 5.93623e72 0.353509
\(745\) −1.04040e73 −0.598708
\(746\) −5.87922e73 −3.26948
\(747\) −2.57302e72 −0.138283
\(748\) −4.87308e72 −0.253112
\(749\) 8.72197e72 0.437853
\(750\) 6.44064e72 0.312512
\(751\) 1.83054e73 0.858539 0.429270 0.903176i \(-0.358771\pi\)
0.429270 + 0.903176i \(0.358771\pi\)
\(752\) −2.65630e73 −1.20427
\(753\) 1.83913e73 0.806009
\(754\) −1.98459e73 −0.840818
\(755\) −1.06048e73 −0.434367
\(756\) −4.23382e73 −1.67659
\(757\) −3.21435e73 −1.23069 −0.615344 0.788259i \(-0.710983\pi\)
−0.615344 + 0.788259i \(0.710983\pi\)
\(758\) 1.98034e73 0.733120
\(759\) 5.31257e72 0.190169
\(760\) 6.74684e73 2.33536
\(761\) 2.98468e73 0.999055 0.499527 0.866298i \(-0.333507\pi\)
0.499527 + 0.866298i \(0.333507\pi\)
\(762\) 1.32050e73 0.427452
\(763\) 4.62884e73 1.44909
\(764\) −5.98946e73 −1.81346
\(765\) 2.92781e72 0.0857387
\(766\) 1.00223e74 2.83880
\(767\) 2.41190e73 0.660812
\(768\) −2.13111e73 −0.564800
\(769\) −2.25014e73 −0.576883 −0.288442 0.957498i \(-0.593137\pi\)
−0.288442 + 0.957498i \(0.593137\pi\)
\(770\) −1.11985e74 −2.77745
\(771\) −1.72088e73 −0.412917
\(772\) −7.84267e73 −1.82064
\(773\) 1.94895e73 0.437746 0.218873 0.975753i \(-0.429762\pi\)
0.218873 + 0.975753i \(0.429762\pi\)
\(774\) −1.60155e73 −0.348054
\(775\) −1.06523e73 −0.224001
\(776\) 1.46876e74 2.98866
\(777\) 2.88946e73 0.568959
\(778\) −6.66392e73 −1.26984
\(779\) −4.68307e73 −0.863625
\(780\) 2.73012e73 0.487269
\(781\) 1.25724e74 2.17179
\(782\) 2.94473e72 0.0492350
\(783\) −6.35567e73 −1.02858
\(784\) −3.09033e73 −0.484112
\(785\) −3.37151e73 −0.511268
\(786\) 2.06081e73 0.302526
\(787\) −5.33534e73 −0.758240 −0.379120 0.925348i \(-0.623773\pi\)
−0.379120 + 0.925348i \(0.623773\pi\)
\(788\) −2.03259e74 −2.79660
\(789\) −2.27372e73 −0.302882
\(790\) 2.34316e74 3.02211
\(791\) −1.14136e74 −1.42536
\(792\) 2.18737e74 2.64502
\(793\) −2.71501e73 −0.317911
\(794\) 1.39569e74 1.58259
\(795\) −3.12512e73 −0.343166
\(796\) −1.25180e74 −1.33123
\(797\) 6.56993e73 0.676664 0.338332 0.941027i \(-0.390137\pi\)
0.338332 + 0.941027i \(0.390137\pi\)
\(798\) 5.13033e73 0.511766
\(799\) 4.52856e72 0.0437540
\(800\) −1.21413e74 −1.13624
\(801\) 2.58259e73 0.234113
\(802\) −1.73908e73 −0.152712
\(803\) 1.88919e74 1.60705
\(804\) 4.31894e72 0.0355916
\(805\) 4.75912e73 0.379955
\(806\) 2.67960e73 0.207265
\(807\) −8.12466e73 −0.608877
\(808\) −4.22952e74 −3.07115
\(809\) −1.11962e74 −0.787738 −0.393869 0.919167i \(-0.628864\pi\)
−0.393869 + 0.919167i \(0.628864\pi\)
\(810\) −1.58425e74 −1.08008
\(811\) 1.56076e74 1.03111 0.515553 0.856858i \(-0.327587\pi\)
0.515553 + 0.856858i \(0.327587\pi\)
\(812\) 4.22351e74 2.70393
\(813\) 5.42047e73 0.336301
\(814\) −5.79412e74 −3.48389
\(815\) −1.68411e74 −0.981414
\(816\) −1.43825e73 −0.0812336
\(817\) 3.06231e73 0.167643
\(818\) 3.32275e74 1.76315
\(819\) −4.92393e73 −0.253263
\(820\) 7.54125e74 3.76002
\(821\) −2.63166e74 −1.27198 −0.635989 0.771698i \(-0.719408\pi\)
−0.635989 + 0.771698i \(0.719408\pi\)
\(822\) 2.50224e73 0.117246
\(823\) 3.49608e74 1.58813 0.794063 0.607835i \(-0.207962\pi\)
0.794063 + 0.607835i \(0.207962\pi\)
\(824\) 5.65390e74 2.49003
\(825\) 9.56662e73 0.408491
\(826\) −7.29855e74 −3.02166
\(827\) −3.08226e74 −1.23731 −0.618656 0.785662i \(-0.712322\pi\)
−0.618656 + 0.785662i \(0.712322\pi\)
\(828\) −1.60805e74 −0.625931
\(829\) −3.63825e73 −0.137326 −0.0686629 0.997640i \(-0.521873\pi\)
−0.0686629 + 0.997640i \(0.521873\pi\)
\(830\) −1.12652e74 −0.412332
\(831\) 4.94813e73 0.175637
\(832\) 7.32500e73 0.252152
\(833\) 5.26851e72 0.0175890
\(834\) −3.86117e74 −1.25021
\(835\) 2.46376e74 0.773736
\(836\) −7.23503e74 −2.20384
\(837\) 8.58145e73 0.253549
\(838\) 4.16966e74 1.19503
\(839\) 1.84060e74 0.511717 0.255859 0.966714i \(-0.417642\pi\)
0.255859 + 0.966714i \(0.417642\pi\)
\(840\) −4.77581e74 −1.28803
\(841\) 2.51814e74 0.658842
\(842\) 7.09266e74 1.80032
\(843\) 1.02038e73 0.0251280
\(844\) 3.70640e74 0.885564
\(845\) −4.92108e74 −1.14081
\(846\) −3.51633e74 −0.790942
\(847\) 2.88374e74 0.629402
\(848\) −6.29875e74 −1.33401
\(849\) −1.58338e73 −0.0325415
\(850\) 5.30273e73 0.105759
\(851\) 2.46238e74 0.476597
\(852\) 9.27508e74 1.74224
\(853\) −8.40007e74 −1.53138 −0.765689 0.643211i \(-0.777602\pi\)
−0.765689 + 0.643211i \(0.777602\pi\)
\(854\) 8.21578e74 1.45370
\(855\) 4.34691e74 0.746525
\(856\) −7.45886e74 −1.24334
\(857\) 2.87444e74 0.465095 0.232548 0.972585i \(-0.425294\pi\)
0.232548 + 0.972585i \(0.425294\pi\)
\(858\) −2.40650e74 −0.377972
\(859\) −9.96707e74 −1.51964 −0.759822 0.650131i \(-0.774714\pi\)
−0.759822 + 0.650131i \(0.774714\pi\)
\(860\) −4.93130e74 −0.729880
\(861\) 3.31495e74 0.476318
\(862\) 5.01037e74 0.698931
\(863\) 9.87545e74 1.33746 0.668732 0.743504i \(-0.266838\pi\)
0.668732 + 0.743504i \(0.266838\pi\)
\(864\) 9.78095e74 1.28612
\(865\) −1.89706e75 −2.42198
\(866\) 2.86036e75 3.54580
\(867\) −3.65318e74 −0.439728
\(868\) −5.70260e74 −0.666530
\(869\) −1.45255e75 −1.64864
\(870\) −1.24019e75 −1.36693
\(871\) 1.12701e73 0.0120632
\(872\) −3.95850e75 −4.11491
\(873\) 9.46305e74 0.955362
\(874\) 4.37202e74 0.428688
\(875\) −3.57668e74 −0.340624
\(876\) 1.39372e75 1.28920
\(877\) 1.76322e75 1.58422 0.792112 0.610375i \(-0.208981\pi\)
0.792112 + 0.610375i \(0.208981\pi\)
\(878\) −1.15432e75 −1.00744
\(879\) −2.54697e74 −0.215927
\(880\) 4.66107e75 3.83864
\(881\) 3.09062e74 0.247263 0.123632 0.992328i \(-0.460546\pi\)
0.123632 + 0.992328i \(0.460546\pi\)
\(882\) −4.09088e74 −0.317957
\(883\) 1.81758e75 1.37245 0.686223 0.727392i \(-0.259268\pi\)
0.686223 + 0.727392i \(0.259268\pi\)
\(884\) −9.38105e73 −0.0688206
\(885\) 1.50721e75 1.07429
\(886\) −1.92692e75 −1.33445
\(887\) −1.25497e75 −0.844461 −0.422230 0.906489i \(-0.638753\pi\)
−0.422230 + 0.906489i \(0.638753\pi\)
\(888\) −2.47101e75 −1.61564
\(889\) −7.33315e74 −0.465903
\(890\) 1.13071e75 0.698081
\(891\) 9.82096e74 0.589213
\(892\) −3.88386e75 −2.26443
\(893\) 6.72353e74 0.380965
\(894\) 6.76555e74 0.372560
\(895\) 3.71548e74 0.198851
\(896\) 5.25754e74 0.273482
\(897\) 1.02271e74 0.0517065
\(898\) −2.18386e74 −0.107320
\(899\) −8.56056e74 −0.408912
\(900\) −2.89570e75 −1.34453
\(901\) 1.07383e74 0.0484680
\(902\) −6.64733e75 −2.91663
\(903\) −2.16768e74 −0.0924610
\(904\) 9.76071e75 4.04750
\(905\) 1.90209e75 0.766820
\(906\) 6.89615e74 0.270295
\(907\) −1.93095e75 −0.735845 −0.367922 0.929857i \(-0.619931\pi\)
−0.367922 + 0.929857i \(0.619931\pi\)
\(908\) 9.47757e75 3.51162
\(909\) −2.72503e75 −0.981731
\(910\) −2.15579e75 −0.755182
\(911\) −9.00047e74 −0.306582 −0.153291 0.988181i \(-0.548987\pi\)
−0.153291 + 0.988181i \(0.548987\pi\)
\(912\) −2.13536e75 −0.707299
\(913\) 6.98342e74 0.224938
\(914\) 5.53962e75 1.73521
\(915\) −1.69663e75 −0.516832
\(916\) −3.17665e75 −0.941097
\(917\) −1.14443e75 −0.329740
\(918\) −4.27185e74 −0.119709
\(919\) −6.41329e75 −1.74798 −0.873988 0.485948i \(-0.838475\pi\)
−0.873988 + 0.485948i \(0.838475\pi\)
\(920\) −4.06991e75 −1.07893
\(921\) 1.94915e75 0.502602
\(922\) 2.08667e75 0.523379
\(923\) 2.42029e75 0.590505
\(924\) 5.12139e75 1.21549
\(925\) 4.43413e75 1.02375
\(926\) 3.73949e75 0.839909
\(927\) 3.64274e75 0.795967
\(928\) −9.75713e75 −2.07419
\(929\) −6.16892e75 −1.27588 −0.637938 0.770088i \(-0.720212\pi\)
−0.637938 + 0.770088i \(0.720212\pi\)
\(930\) 1.67450e75 0.336954
\(931\) 7.82212e74 0.153147
\(932\) −3.17039e75 −0.603958
\(933\) −1.33429e75 −0.247325
\(934\) −1.12486e76 −2.02887
\(935\) −7.94636e74 −0.139467
\(936\) 4.21085e75 0.719177
\(937\) 1.06049e76 1.76258 0.881290 0.472575i \(-0.156675\pi\)
0.881290 + 0.472575i \(0.156675\pi\)
\(938\) −3.41039e74 −0.0551609
\(939\) −2.12130e75 −0.333911
\(940\) −1.08270e76 −1.65863
\(941\) 3.41799e75 0.509608 0.254804 0.966993i \(-0.417989\pi\)
0.254804 + 0.966993i \(0.417989\pi\)
\(942\) 2.19244e75 0.318148
\(943\) 2.82498e75 0.398994
\(944\) 3.03783e76 4.17616
\(945\) −6.90395e75 −0.923818
\(946\) 4.34676e75 0.566164
\(947\) −6.63593e75 −0.841351 −0.420675 0.907211i \(-0.638207\pi\)
−0.420675 + 0.907211i \(0.638207\pi\)
\(948\) −1.07159e76 −1.32257
\(949\) 3.63683e75 0.436953
\(950\) 7.87293e75 0.920840
\(951\) −1.51609e75 −0.172632
\(952\) 1.64103e75 0.181918
\(953\) 1.31580e76 1.42010 0.710052 0.704149i \(-0.248671\pi\)
0.710052 + 0.704149i \(0.248671\pi\)
\(954\) −8.33808e75 −0.876158
\(955\) −9.76680e75 −0.999232
\(956\) −3.26241e76 −3.24984
\(957\) 7.68806e75 0.745697
\(958\) −1.44157e75 −0.136149
\(959\) −1.38957e75 −0.127793
\(960\) 4.57745e75 0.409927
\(961\) −1.03111e76 −0.899201
\(962\) −1.11541e76 −0.947263
\(963\) −4.80566e75 −0.397450
\(964\) 2.67784e76 2.15685
\(965\) −1.27888e76 −1.00319
\(966\) −3.09478e75 −0.236436
\(967\) 1.67049e76 1.24299 0.621496 0.783417i \(-0.286525\pi\)
0.621496 + 0.783417i \(0.286525\pi\)
\(968\) −2.46612e76 −1.78728
\(969\) 3.64044e74 0.0256979
\(970\) 4.14311e76 2.84870
\(971\) 1.63388e76 1.09428 0.547142 0.837040i \(-0.315716\pi\)
0.547142 + 0.837040i \(0.315716\pi\)
\(972\) 3.62584e76 2.36548
\(973\) 2.14423e76 1.36268
\(974\) −2.30289e76 −1.42567
\(975\) 1.84165e75 0.111068
\(976\) −3.41960e76 −2.00912
\(977\) −2.38186e76 −1.36334 −0.681672 0.731658i \(-0.738747\pi\)
−0.681672 + 0.731658i \(0.738747\pi\)
\(978\) 1.09515e76 0.610708
\(979\) −7.00939e75 −0.380822
\(980\) −1.25961e76 −0.666765
\(981\) −2.55041e76 −1.31538
\(982\) 2.42483e76 1.21854
\(983\) 3.78819e76 1.85488 0.927442 0.373966i \(-0.122002\pi\)
0.927442 + 0.373966i \(0.122002\pi\)
\(984\) −2.83488e76 −1.35257
\(985\) −3.31447e76 −1.54096
\(986\) 4.26145e75 0.193062
\(987\) −4.75931e75 −0.210115
\(988\) −1.39280e76 −0.599220
\(989\) −1.84728e75 −0.0774512
\(990\) 6.17017e76 2.52116
\(991\) 2.49197e76 0.992349 0.496175 0.868223i \(-0.334738\pi\)
0.496175 + 0.868223i \(0.334738\pi\)
\(992\) 1.31741e76 0.511298
\(993\) 2.21274e76 0.836998
\(994\) −7.32392e76 −2.70017
\(995\) −2.04127e76 −0.733519
\(996\) 5.15189e75 0.180449
\(997\) −2.96256e76 −1.01144 −0.505721 0.862697i \(-0.668773\pi\)
−0.505721 + 0.862697i \(0.668773\pi\)
\(998\) −5.35248e75 −0.178126
\(999\) −3.57211e76 −1.15879
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.1.1 4
3.2 odd 2 9.52.a.b.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.52.a.a.1.1 4 1.1 even 1 trivial
9.52.a.b.1.4 4 3.2 odd 2