Properties

Label 1.64.a.a.1.2
Level $1$
Weight $64$
Character 1.1
Self dual yes
Analytic conductor $25.136$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 64 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.1360966918\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 2 x^{4} - 5096287552528786 x^{3} + 574038763744383494840 x^{2} + 3502610791787684740809332695881 x - 35880030333954415007358004861309901934\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{37}\cdot 3^{17}\cdot 5^{3}\cdot 7^{2}\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.73795e7\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.14986e9 q^{2} +2.06926e15 q^{3} -7.90120e18 q^{4} -9.56939e21 q^{5} -2.37936e24 q^{6} -1.15073e26 q^{7} +1.96908e28 q^{8} +3.13728e30 q^{9} +O(q^{10})\) \(q-1.14986e9 q^{2} +2.06926e15 q^{3} -7.90120e18 q^{4} -9.56939e21 q^{5} -2.37936e24 q^{6} -1.15073e26 q^{7} +1.96908e28 q^{8} +3.13728e30 q^{9} +1.10034e31 q^{10} -2.43908e32 q^{11} -1.63496e34 q^{12} +1.25036e35 q^{13} +1.32317e35 q^{14} -1.98016e37 q^{15} +5.02341e37 q^{16} +7.86280e38 q^{17} -3.60742e39 q^{18} -2.70961e39 q^{19} +7.56097e40 q^{20} -2.38116e41 q^{21} +2.80460e41 q^{22} +3.63454e42 q^{23} +4.07454e43 q^{24} -1.68470e43 q^{25} -1.43774e44 q^{26} +4.12346e45 q^{27} +9.09213e44 q^{28} +3.93841e45 q^{29} +2.27690e46 q^{30} +1.18807e47 q^{31} -2.39378e47 q^{32} -5.04710e47 q^{33} -9.04110e47 q^{34} +1.10118e48 q^{35} -2.47883e49 q^{36} +1.80510e49 q^{37} +3.11567e48 q^{38} +2.58732e50 q^{39} -1.88429e50 q^{40} +3.23583e50 q^{41} +2.73799e50 q^{42} +8.59653e50 q^{43} +1.92717e51 q^{44} -3.00219e52 q^{45} -4.17920e51 q^{46} +1.26451e52 q^{47} +1.03947e53 q^{48} -1.61010e53 q^{49} +1.93716e52 q^{50} +1.62702e54 q^{51} -9.87934e53 q^{52} -5.19617e53 q^{53} -4.74139e54 q^{54} +2.33405e54 q^{55} -2.26588e54 q^{56} -5.60690e54 q^{57} -4.52860e54 q^{58} -4.37498e55 q^{59} +1.56456e56 q^{60} +2.79669e56 q^{61} -1.36611e56 q^{62} -3.61016e56 q^{63} -1.88077e56 q^{64} -1.19652e57 q^{65} +5.80344e56 q^{66} +1.12890e57 q^{67} -6.21256e57 q^{68} +7.52080e57 q^{69} -1.26620e57 q^{70} +1.56870e58 q^{71} +6.17756e58 q^{72} -9.21857e58 q^{73} -2.07560e58 q^{74} -3.48607e58 q^{75} +2.14092e58 q^{76} +2.80672e58 q^{77} -2.97505e59 q^{78} -4.18902e59 q^{79} -4.80710e59 q^{80} +4.94170e60 q^{81} -3.72075e59 q^{82} -3.28273e60 q^{83} +1.88140e60 q^{84} -7.52422e60 q^{85} -9.88478e59 q^{86} +8.14959e60 q^{87} -4.80275e60 q^{88} -3.02241e61 q^{89} +3.45209e61 q^{90} -1.43882e61 q^{91} -2.87172e61 q^{92} +2.45843e62 q^{93} -1.45400e61 q^{94} +2.59294e61 q^{95} -4.95335e62 q^{96} +5.45642e61 q^{97} +1.85138e62 q^{98} -7.65208e62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 507315096q^{2} + 953245351116252q^{3} + 6772922881670488640q^{4} - \)\(50\!\cdots\!30\)\(q^{5} + \)\(10\!\cdots\!60\)\(q^{6} + \)\(37\!\cdots\!56\)\(q^{7} + \)\(73\!\cdots\!00\)\(q^{8} + \)\(63\!\cdots\!85\)\(q^{9} + O(q^{10}) \) \( 5q + 507315096q^{2} + 953245351116252q^{3} + 6772922881670488640q^{4} - \)\(50\!\cdots\!30\)\(q^{5} + \)\(10\!\cdots\!60\)\(q^{6} + \)\(37\!\cdots\!56\)\(q^{7} + \)\(73\!\cdots\!00\)\(q^{8} + \)\(63\!\cdots\!85\)\(q^{9} + \)\(34\!\cdots\!20\)\(q^{10} - \)\(54\!\cdots\!40\)\(q^{11} - \)\(26\!\cdots\!84\)\(q^{12} + \)\(10\!\cdots\!62\)\(q^{13} - \)\(54\!\cdots\!20\)\(q^{14} - \)\(34\!\cdots\!60\)\(q^{15} - \)\(15\!\cdots\!20\)\(q^{16} + \)\(23\!\cdots\!26\)\(q^{17} - \)\(87\!\cdots\!08\)\(q^{18} - \)\(78\!\cdots\!00\)\(q^{19} + \)\(11\!\cdots\!60\)\(q^{20} + \)\(12\!\cdots\!60\)\(q^{21} + \)\(52\!\cdots\!72\)\(q^{22} + \)\(15\!\cdots\!72\)\(q^{23} + \)\(81\!\cdots\!00\)\(q^{24} + \)\(29\!\cdots\!75\)\(q^{25} + \)\(18\!\cdots\!60\)\(q^{26} + \)\(59\!\cdots\!00\)\(q^{27} + \)\(20\!\cdots\!48\)\(q^{28} + \)\(50\!\cdots\!50\)\(q^{29} + \)\(11\!\cdots\!40\)\(q^{30} + \)\(15\!\cdots\!60\)\(q^{31} - \)\(28\!\cdots\!44\)\(q^{32} - \)\(19\!\cdots\!36\)\(q^{33} - \)\(77\!\cdots\!20\)\(q^{34} - \)\(10\!\cdots\!80\)\(q^{35} - \)\(37\!\cdots\!20\)\(q^{36} - \)\(17\!\cdots\!34\)\(q^{37} + \)\(96\!\cdots\!00\)\(q^{38} + \)\(49\!\cdots\!20\)\(q^{39} + \)\(89\!\cdots\!00\)\(q^{40} + \)\(15\!\cdots\!10\)\(q^{41} + \)\(20\!\cdots\!52\)\(q^{42} - \)\(29\!\cdots\!08\)\(q^{43} - \)\(18\!\cdots\!20\)\(q^{44} - \)\(42\!\cdots\!10\)\(q^{45} - \)\(51\!\cdots\!40\)\(q^{46} - \)\(48\!\cdots\!64\)\(q^{47} + \)\(10\!\cdots\!72\)\(q^{48} + \)\(33\!\cdots\!65\)\(q^{49} + \)\(11\!\cdots\!00\)\(q^{50} + \)\(15\!\cdots\!60\)\(q^{51} + \)\(11\!\cdots\!96\)\(q^{52} - \)\(69\!\cdots\!98\)\(q^{53} - \)\(12\!\cdots\!00\)\(q^{54} - \)\(20\!\cdots\!60\)\(q^{55} - \)\(23\!\cdots\!00\)\(q^{56} - \)\(17\!\cdots\!00\)\(q^{57} + \)\(24\!\cdots\!00\)\(q^{58} + \)\(10\!\cdots\!00\)\(q^{59} + \)\(34\!\cdots\!20\)\(q^{60} + \)\(39\!\cdots\!10\)\(q^{61} + \)\(51\!\cdots\!32\)\(q^{62} - \)\(68\!\cdots\!88\)\(q^{63} - \)\(21\!\cdots\!60\)\(q^{64} - \)\(17\!\cdots\!60\)\(q^{65} - \)\(55\!\cdots\!80\)\(q^{66} - \)\(47\!\cdots\!24\)\(q^{67} - \)\(12\!\cdots\!92\)\(q^{68} + \)\(17\!\cdots\!20\)\(q^{69} + \)\(40\!\cdots\!20\)\(q^{70} + \)\(50\!\cdots\!60\)\(q^{71} + \)\(61\!\cdots\!00\)\(q^{72} - \)\(29\!\cdots\!78\)\(q^{73} - \)\(14\!\cdots\!20\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(45\!\cdots\!00\)\(q^{76} - \)\(58\!\cdots\!08\)\(q^{77} - \)\(22\!\cdots\!96\)\(q^{78} + \)\(58\!\cdots\!00\)\(q^{79} + \)\(10\!\cdots\!20\)\(q^{80} + \)\(45\!\cdots\!05\)\(q^{81} + \)\(39\!\cdots\!12\)\(q^{82} + \)\(27\!\cdots\!32\)\(q^{83} - \)\(12\!\cdots\!20\)\(q^{84} - \)\(12\!\cdots\!80\)\(q^{85} - \)\(25\!\cdots\!40\)\(q^{86} - \)\(16\!\cdots\!00\)\(q^{87} - \)\(37\!\cdots\!00\)\(q^{88} + \)\(32\!\cdots\!50\)\(q^{89} + \)\(39\!\cdots\!40\)\(q^{90} + \)\(10\!\cdots\!60\)\(q^{91} + \)\(16\!\cdots\!76\)\(q^{92} + \)\(37\!\cdots\!84\)\(q^{93} - \)\(20\!\cdots\!20\)\(q^{94} + \)\(13\!\cdots\!00\)\(q^{95} - \)\(90\!\cdots\!40\)\(q^{96} - \)\(17\!\cdots\!14\)\(q^{97} - \)\(19\!\cdots\!72\)\(q^{98} - \)\(12\!\cdots\!80\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.14986e9 −0.378616 −0.189308 0.981918i \(-0.560624\pi\)
−0.189308 + 0.981918i \(0.560624\pi\)
\(3\) 2.06926e15 1.93418 0.967088 0.254444i \(-0.0818925\pi\)
0.967088 + 0.254444i \(0.0818925\pi\)
\(4\) −7.90120e18 −0.856650
\(5\) −9.56939e21 −0.919029 −0.459514 0.888170i \(-0.651977\pi\)
−0.459514 + 0.888170i \(0.651977\pi\)
\(6\) −2.37936e24 −0.732310
\(7\) −1.15073e26 −0.275667 −0.137833 0.990455i \(-0.544014\pi\)
−0.137833 + 0.990455i \(0.544014\pi\)
\(8\) 1.96908e28 0.702958
\(9\) 3.13728e30 2.74103
\(10\) 1.10034e31 0.347959
\(11\) −2.43908e32 −0.383139 −0.191570 0.981479i \(-0.561358\pi\)
−0.191570 + 0.981479i \(0.561358\pi\)
\(12\) −1.63496e34 −1.65691
\(13\) 1.25036e35 1.01817 0.509084 0.860717i \(-0.329984\pi\)
0.509084 + 0.860717i \(0.329984\pi\)
\(14\) 1.32317e35 0.104372
\(15\) −1.98016e37 −1.77756
\(16\) 5.02341e37 0.590499
\(17\) 7.86280e38 1.36910 0.684552 0.728964i \(-0.259998\pi\)
0.684552 + 0.728964i \(0.259998\pi\)
\(18\) −3.60742e39 −1.03780
\(19\) −2.70961e39 −0.141961 −0.0709805 0.997478i \(-0.522613\pi\)
−0.0709805 + 0.997478i \(0.522613\pi\)
\(20\) 7.56097e40 0.787286
\(21\) −2.38116e41 −0.533188
\(22\) 2.80460e41 0.145063
\(23\) 3.63454e42 0.463471 0.231735 0.972779i \(-0.425560\pi\)
0.231735 + 0.972779i \(0.425560\pi\)
\(24\) 4.07454e43 1.35964
\(25\) −1.68470e43 −0.155386
\(26\) −1.43774e44 −0.385495
\(27\) 4.12346e45 3.36746
\(28\) 9.09213e44 0.236150
\(29\) 3.93841e45 0.338675 0.169338 0.985558i \(-0.445837\pi\)
0.169338 + 0.985558i \(0.445837\pi\)
\(30\) 2.27690e46 0.673014
\(31\) 1.18807e47 1.25011 0.625055 0.780581i \(-0.285076\pi\)
0.625055 + 0.780581i \(0.285076\pi\)
\(32\) −2.39378e47 −0.926530
\(33\) −5.04710e47 −0.741058
\(34\) −9.04110e47 −0.518365
\(35\) 1.10118e48 0.253346
\(36\) −2.47883e49 −2.34811
\(37\) 1.80510e49 0.721350 0.360675 0.932692i \(-0.382546\pi\)
0.360675 + 0.932692i \(0.382546\pi\)
\(38\) 3.11567e48 0.0537487
\(39\) 2.58732e50 1.96932
\(40\) −1.88429e50 −0.646038
\(41\) 3.23583e50 0.509677 0.254838 0.966984i \(-0.417978\pi\)
0.254838 + 0.966984i \(0.417978\pi\)
\(42\) 2.73799e50 0.201873
\(43\) 8.59653e50 0.302042 0.151021 0.988531i \(-0.451744\pi\)
0.151021 + 0.988531i \(0.451744\pi\)
\(44\) 1.92717e51 0.328216
\(45\) −3.00219e52 −2.51909
\(46\) −4.17920e51 −0.175477
\(47\) 1.26451e52 0.269674 0.134837 0.990868i \(-0.456949\pi\)
0.134837 + 0.990868i \(0.456949\pi\)
\(48\) 1.03947e53 1.14213
\(49\) −1.61010e53 −0.924008
\(50\) 1.93716e52 0.0588315
\(51\) 1.62702e54 2.64809
\(52\) −9.87934e53 −0.872213
\(53\) −5.19617e53 −0.251764 −0.125882 0.992045i \(-0.540176\pi\)
−0.125882 + 0.992045i \(0.540176\pi\)
\(54\) −4.74139e54 −1.27498
\(55\) 2.33405e54 0.352116
\(56\) −2.26588e54 −0.193782
\(57\) −5.60690e54 −0.274577
\(58\) −4.52860e54 −0.128228
\(59\) −4.37498e55 −0.722999 −0.361500 0.932372i \(-0.617735\pi\)
−0.361500 + 0.932372i \(0.617735\pi\)
\(60\) 1.56456e56 1.52275
\(61\) 2.79669e56 1.61716 0.808582 0.588383i \(-0.200235\pi\)
0.808582 + 0.588383i \(0.200235\pi\)
\(62\) −1.36611e56 −0.473312
\(63\) −3.61016e56 −0.755612
\(64\) −1.88077e56 −0.239700
\(65\) −1.19652e57 −0.935726
\(66\) 5.80344e56 0.280577
\(67\) 1.12890e57 0.339860 0.169930 0.985456i \(-0.445646\pi\)
0.169930 + 0.985456i \(0.445646\pi\)
\(68\) −6.21256e57 −1.17284
\(69\) 7.52080e57 0.896433
\(70\) −1.26620e57 −0.0959208
\(71\) 1.56870e58 0.760154 0.380077 0.924955i \(-0.375897\pi\)
0.380077 + 0.924955i \(0.375897\pi\)
\(72\) 6.17756e58 1.92683
\(73\) −9.21857e58 −1.86206 −0.931030 0.364943i \(-0.881088\pi\)
−0.931030 + 0.364943i \(0.881088\pi\)
\(74\) −2.07560e58 −0.273115
\(75\) −3.48607e58 −0.300543
\(76\) 2.14092e58 0.121611
\(77\) 2.80672e58 0.105619
\(78\) −2.97505e59 −0.745615
\(79\) −4.18902e59 −0.702844 −0.351422 0.936217i \(-0.614302\pi\)
−0.351422 + 0.936217i \(0.614302\pi\)
\(80\) −4.80710e59 −0.542685
\(81\) 4.94170e60 3.77223
\(82\) −3.72075e59 −0.192972
\(83\) −3.28273e60 −1.16218 −0.581092 0.813838i \(-0.697374\pi\)
−0.581092 + 0.813838i \(0.697374\pi\)
\(84\) 1.88140e60 0.456755
\(85\) −7.52422e60 −1.25825
\(86\) −9.88478e59 −0.114358
\(87\) 8.14959e60 0.655057
\(88\) −4.80275e60 −0.269331
\(89\) −3.02241e61 −1.18732 −0.593660 0.804716i \(-0.702317\pi\)
−0.593660 + 0.804716i \(0.702317\pi\)
\(90\) 3.45209e61 0.953768
\(91\) −1.43882e61 −0.280675
\(92\) −2.87172e61 −0.397032
\(93\) 2.45843e62 2.41793
\(94\) −1.45400e61 −0.102103
\(95\) 2.59294e61 0.130466
\(96\) −4.95335e62 −1.79207
\(97\) 5.45642e61 0.142429 0.0712145 0.997461i \(-0.477313\pi\)
0.0712145 + 0.997461i \(0.477313\pi\)
\(98\) 1.85138e62 0.349844
\(99\) −7.65208e62 −1.05020
\(100\) 1.33111e62 0.133111
\(101\) 7.79995e62 0.570123 0.285061 0.958509i \(-0.407986\pi\)
0.285061 + 0.958509i \(0.407986\pi\)
\(102\) −1.87084e63 −1.00261
\(103\) 2.40638e63 0.948401 0.474200 0.880417i \(-0.342737\pi\)
0.474200 + 0.880417i \(0.342737\pi\)
\(104\) 2.46206e63 0.715729
\(105\) 2.27862e63 0.490015
\(106\) 5.97486e62 0.0953219
\(107\) 9.53357e63 1.13153 0.565766 0.824566i \(-0.308581\pi\)
0.565766 + 0.824566i \(0.308581\pi\)
\(108\) −3.25802e64 −2.88474
\(109\) −4.35388e63 −0.288365 −0.144182 0.989551i \(-0.546055\pi\)
−0.144182 + 0.989551i \(0.546055\pi\)
\(110\) −2.68383e63 −0.133317
\(111\) 3.73521e64 1.39522
\(112\) −5.78057e63 −0.162781
\(113\) −3.09629e64 −0.658978 −0.329489 0.944159i \(-0.606877\pi\)
−0.329489 + 0.944159i \(0.606877\pi\)
\(114\) 6.44713e63 0.103959
\(115\) −3.47803e64 −0.425943
\(116\) −3.11181e64 −0.290126
\(117\) 3.92273e65 2.79083
\(118\) 5.03060e64 0.273739
\(119\) −9.04794e64 −0.377416
\(120\) −3.89909e65 −1.24955
\(121\) −3.45774e65 −0.853204
\(122\) −3.21579e65 −0.612285
\(123\) 6.69579e65 0.985804
\(124\) −9.38717e65 −1.07091
\(125\) 1.19873e66 1.06183
\(126\) 4.15116e65 0.286087
\(127\) −1.71483e66 −0.921308 −0.460654 0.887580i \(-0.652385\pi\)
−0.460654 + 0.887580i \(0.652385\pi\)
\(128\) 2.42413e66 1.01728
\(129\) 1.77885e66 0.584201
\(130\) 1.37583e66 0.354281
\(131\) −4.29490e66 −0.868774 −0.434387 0.900726i \(-0.643035\pi\)
−0.434387 + 0.900726i \(0.643035\pi\)
\(132\) 3.98781e66 0.634828
\(133\) 3.11803e65 0.0391339
\(134\) −1.29808e66 −0.128676
\(135\) −3.94590e67 −3.09480
\(136\) 1.54825e67 0.962422
\(137\) 2.53921e67 1.25315 0.626573 0.779363i \(-0.284457\pi\)
0.626573 + 0.779363i \(0.284457\pi\)
\(138\) −8.64785e66 −0.339404
\(139\) 1.60697e67 0.502390 0.251195 0.967937i \(-0.419176\pi\)
0.251195 + 0.967937i \(0.419176\pi\)
\(140\) −8.70062e66 −0.217029
\(141\) 2.61660e67 0.521597
\(142\) −1.80378e67 −0.287807
\(143\) −3.04973e67 −0.390100
\(144\) 1.57598e68 1.61858
\(145\) −3.76881e67 −0.311252
\(146\) 1.06000e68 0.705006
\(147\) −3.33171e68 −1.78719
\(148\) −1.42624e68 −0.617944
\(149\) −1.60985e68 −0.564181 −0.282091 0.959388i \(-0.591028\pi\)
−0.282091 + 0.959388i \(0.591028\pi\)
\(150\) 4.00849e67 0.113791
\(151\) −2.49704e68 −0.574979 −0.287490 0.957784i \(-0.592821\pi\)
−0.287490 + 0.957784i \(0.592821\pi\)
\(152\) −5.33545e67 −0.0997925
\(153\) 2.46678e69 3.75276
\(154\) −3.22733e67 −0.0399890
\(155\) −1.13691e69 −1.14889
\(156\) −2.04429e69 −1.68701
\(157\) 1.93952e69 1.30875 0.654373 0.756172i \(-0.272933\pi\)
0.654373 + 0.756172i \(0.272933\pi\)
\(158\) 4.81678e68 0.266108
\(159\) −1.07522e69 −0.486956
\(160\) 2.29070e69 0.851508
\(161\) −4.18236e68 −0.127763
\(162\) −5.68225e69 −1.42823
\(163\) −3.46413e69 −0.717274 −0.358637 0.933477i \(-0.616758\pi\)
−0.358637 + 0.933477i \(0.616758\pi\)
\(164\) −2.55670e69 −0.436614
\(165\) 4.82976e69 0.681054
\(166\) 3.77467e69 0.440021
\(167\) 1.46319e70 1.41166 0.705831 0.708380i \(-0.250574\pi\)
0.705831 + 0.708380i \(0.250574\pi\)
\(168\) −4.68869e69 −0.374808
\(169\) 5.52965e68 0.0366662
\(170\) 8.65178e69 0.476392
\(171\) −8.50082e69 −0.389120
\(172\) −6.79229e69 −0.258744
\(173\) 6.95687e69 0.220781 0.110390 0.993888i \(-0.464790\pi\)
0.110390 + 0.993888i \(0.464790\pi\)
\(174\) −9.37087e69 −0.248015
\(175\) 1.93863e69 0.0428347
\(176\) −1.22525e70 −0.226243
\(177\) −9.05298e70 −1.39841
\(178\) 3.47534e70 0.449538
\(179\) −7.72748e70 −0.837852 −0.418926 0.908020i \(-0.637593\pi\)
−0.418926 + 0.908020i \(0.637593\pi\)
\(180\) 2.37209e71 2.15798
\(181\) −2.40823e71 −1.84002 −0.920011 0.391892i \(-0.871821\pi\)
−0.920011 + 0.391892i \(0.871821\pi\)
\(182\) 1.65444e70 0.106268
\(183\) 5.78708e71 3.12788
\(184\) 7.15670e70 0.325800
\(185\) −1.72737e71 −0.662941
\(186\) −2.82684e71 −0.915468
\(187\) −1.91780e71 −0.524557
\(188\) −9.99113e70 −0.231016
\(189\) −4.74497e71 −0.928297
\(190\) −2.98151e70 −0.0493966
\(191\) 1.08495e72 1.52356 0.761780 0.647836i \(-0.224326\pi\)
0.761780 + 0.647836i \(0.224326\pi\)
\(192\) −3.89181e71 −0.463621
\(193\) 1.08691e71 0.109936 0.0549679 0.998488i \(-0.482494\pi\)
0.0549679 + 0.998488i \(0.482494\pi\)
\(194\) −6.27410e70 −0.0539259
\(195\) −2.47591e72 −1.80986
\(196\) 1.27217e72 0.791551
\(197\) 1.84925e72 0.980186 0.490093 0.871670i \(-0.336963\pi\)
0.490093 + 0.871670i \(0.336963\pi\)
\(198\) 8.79880e71 0.397622
\(199\) 1.80760e72 0.696997 0.348498 0.937309i \(-0.386692\pi\)
0.348498 + 0.937309i \(0.386692\pi\)
\(200\) −3.31730e71 −0.109230
\(201\) 2.33599e72 0.657349
\(202\) −8.96883e71 −0.215858
\(203\) −4.53203e71 −0.0933615
\(204\) −1.28554e73 −2.26848
\(205\) −3.09650e72 −0.468408
\(206\) −2.76700e72 −0.359080
\(207\) 1.14026e73 1.27039
\(208\) 6.28107e72 0.601227
\(209\) 6.60897e71 0.0543908
\(210\) −2.62009e72 −0.185528
\(211\) −1.54379e73 −0.941221 −0.470611 0.882341i \(-0.655966\pi\)
−0.470611 + 0.882341i \(0.655966\pi\)
\(212\) 4.10560e72 0.215674
\(213\) 3.24605e73 1.47027
\(214\) −1.09622e73 −0.428416
\(215\) −8.22636e72 −0.277585
\(216\) 8.11942e73 2.36718
\(217\) −1.36714e73 −0.344614
\(218\) 5.00635e72 0.109180
\(219\) −1.90756e74 −3.60155
\(220\) −1.84418e73 −0.301640
\(221\) 9.83133e73 1.39398
\(222\) −4.29496e73 −0.528252
\(223\) 2.35527e73 0.251442 0.125721 0.992066i \(-0.459876\pi\)
0.125721 + 0.992066i \(0.459876\pi\)
\(224\) 2.75459e73 0.255413
\(225\) −5.28536e73 −0.425917
\(226\) 3.56030e73 0.249500
\(227\) 2.46957e74 1.50594 0.752968 0.658057i \(-0.228622\pi\)
0.752968 + 0.658057i \(0.228622\pi\)
\(228\) 4.43012e73 0.235217
\(229\) −2.99938e74 −1.38744 −0.693719 0.720245i \(-0.744029\pi\)
−0.693719 + 0.720245i \(0.744029\pi\)
\(230\) 3.99924e73 0.161269
\(231\) 5.80783e73 0.204285
\(232\) 7.75504e73 0.238074
\(233\) 4.83092e74 1.29514 0.647572 0.762004i \(-0.275784\pi\)
0.647572 + 0.762004i \(0.275784\pi\)
\(234\) −4.51058e74 −1.05665
\(235\) −1.21006e74 −0.247838
\(236\) 3.45676e74 0.619357
\(237\) −8.66818e74 −1.35942
\(238\) 1.04038e74 0.142896
\(239\) −6.21166e74 −0.747608 −0.373804 0.927508i \(-0.621947\pi\)
−0.373804 + 0.927508i \(0.621947\pi\)
\(240\) −9.94714e74 −1.04965
\(241\) −3.17493e74 −0.293898 −0.146949 0.989144i \(-0.546945\pi\)
−0.146949 + 0.989144i \(0.546945\pi\)
\(242\) 3.97591e74 0.323037
\(243\) 5.50611e75 3.92869
\(244\) −2.20972e75 −1.38534
\(245\) 1.54077e75 0.849190
\(246\) −7.69920e74 −0.373241
\(247\) −3.38799e74 −0.144540
\(248\) 2.33941e75 0.878775
\(249\) −6.79282e75 −2.24787
\(250\) −1.37837e75 −0.402027
\(251\) 3.82426e75 0.983615 0.491807 0.870704i \(-0.336336\pi\)
0.491807 + 0.870704i \(0.336336\pi\)
\(252\) 2.85246e75 0.647294
\(253\) −8.86493e74 −0.177574
\(254\) 1.97182e75 0.348822
\(255\) −1.55696e76 −2.43367
\(256\) −1.05270e75 −0.145461
\(257\) 7.62665e75 0.932052 0.466026 0.884771i \(-0.345685\pi\)
0.466026 + 0.884771i \(0.345685\pi\)
\(258\) −2.04542e75 −0.221188
\(259\) −2.07717e75 −0.198852
\(260\) 9.45393e75 0.801589
\(261\) 1.23559e76 0.928320
\(262\) 4.93852e75 0.328932
\(263\) 1.28572e76 0.759521 0.379760 0.925085i \(-0.376006\pi\)
0.379760 + 0.925085i \(0.376006\pi\)
\(264\) −9.93814e75 −0.520933
\(265\) 4.97242e75 0.231378
\(266\) −3.58529e74 −0.0148167
\(267\) −6.25415e76 −2.29648
\(268\) −8.91968e75 −0.291141
\(269\) 3.17052e76 0.920310 0.460155 0.887838i \(-0.347794\pi\)
0.460155 + 0.887838i \(0.347794\pi\)
\(270\) 4.53722e76 1.17174
\(271\) −5.69145e76 −1.30825 −0.654125 0.756387i \(-0.726963\pi\)
−0.654125 + 0.756387i \(0.726963\pi\)
\(272\) 3.94980e76 0.808454
\(273\) −2.97730e76 −0.542875
\(274\) −2.91973e76 −0.474461
\(275\) 4.10911e75 0.0595344
\(276\) −5.94234e76 −0.767929
\(277\) −3.83488e76 −0.442221 −0.221110 0.975249i \(-0.570968\pi\)
−0.221110 + 0.975249i \(0.570968\pi\)
\(278\) −1.84778e76 −0.190213
\(279\) 3.72731e77 3.42659
\(280\) 2.16831e76 0.178091
\(281\) 9.26162e76 0.679888 0.339944 0.940446i \(-0.389592\pi\)
0.339944 + 0.940446i \(0.389592\pi\)
\(282\) −3.00871e76 −0.197485
\(283\) −2.27051e77 −1.33306 −0.666532 0.745477i \(-0.732222\pi\)
−0.666532 + 0.745477i \(0.732222\pi\)
\(284\) −1.23946e77 −0.651186
\(285\) 5.36546e76 0.252345
\(286\) 3.50675e76 0.147698
\(287\) −3.72356e76 −0.140501
\(288\) −7.50995e77 −2.53965
\(289\) 2.88412e77 0.874444
\(290\) 4.33360e76 0.117845
\(291\) 1.12908e77 0.275482
\(292\) 7.28378e77 1.59513
\(293\) −7.85286e77 −1.54418 −0.772090 0.635513i \(-0.780788\pi\)
−0.772090 + 0.635513i \(0.780788\pi\)
\(294\) 3.83099e77 0.676660
\(295\) 4.18659e77 0.664457
\(296\) 3.55438e77 0.507078
\(297\) −1.00574e78 −1.29021
\(298\) 1.85110e77 0.213608
\(299\) 4.54448e77 0.471891
\(300\) 2.75442e77 0.257460
\(301\) −9.89227e76 −0.0832628
\(302\) 2.87124e77 0.217697
\(303\) 1.61401e78 1.10272
\(304\) −1.36115e77 −0.0838278
\(305\) −2.67626e78 −1.48622
\(306\) −2.83645e78 −1.42085
\(307\) −2.46188e78 −1.11278 −0.556388 0.830923i \(-0.687813\pi\)
−0.556388 + 0.830923i \(0.687813\pi\)
\(308\) −2.21764e77 −0.0904783
\(309\) 4.97943e78 1.83437
\(310\) 1.30728e78 0.434987
\(311\) −4.46651e78 −1.34281 −0.671407 0.741089i \(-0.734310\pi\)
−0.671407 + 0.741089i \(0.734310\pi\)
\(312\) 5.09465e78 1.38435
\(313\) 2.75654e78 0.677201 0.338601 0.940930i \(-0.390046\pi\)
0.338601 + 0.940930i \(0.390046\pi\)
\(314\) −2.23017e78 −0.495512
\(315\) 3.45470e78 0.694429
\(316\) 3.30983e78 0.602092
\(317\) −1.07470e79 −1.76978 −0.884888 0.465803i \(-0.845766\pi\)
−0.884888 + 0.465803i \(0.845766\pi\)
\(318\) 1.23635e78 0.184369
\(319\) −9.60609e77 −0.129760
\(320\) 1.79979e78 0.220291
\(321\) 1.97274e79 2.18858
\(322\) 4.80912e77 0.0483733
\(323\) −2.13051e78 −0.194359
\(324\) −3.90453e79 −3.23148
\(325\) −2.10648e78 −0.158209
\(326\) 3.98326e78 0.271571
\(327\) −9.00932e78 −0.557748
\(328\) 6.37162e78 0.358281
\(329\) −1.45510e78 −0.0743402
\(330\) −5.55354e78 −0.257858
\(331\) 2.07542e79 0.876041 0.438021 0.898965i \(-0.355680\pi\)
0.438021 + 0.898965i \(0.355680\pi\)
\(332\) 2.59375e79 0.995584
\(333\) 5.66309e79 1.97724
\(334\) −1.68246e79 −0.534478
\(335\) −1.08029e79 −0.312341
\(336\) −1.19615e79 −0.314847
\(337\) −2.57458e79 −0.617114 −0.308557 0.951206i \(-0.599846\pi\)
−0.308557 + 0.951206i \(0.599846\pi\)
\(338\) −6.35831e77 −0.0138824
\(339\) −6.40704e79 −1.27458
\(340\) 5.94504e79 1.07788
\(341\) −2.89780e79 −0.478966
\(342\) 9.77473e78 0.147327
\(343\) 3.85794e79 0.530385
\(344\) 1.69273e79 0.212322
\(345\) −7.19695e79 −0.823848
\(346\) −7.99941e78 −0.0835912
\(347\) −4.77104e78 −0.0455234 −0.0227617 0.999741i \(-0.507246\pi\)
−0.0227617 + 0.999741i \(0.507246\pi\)
\(348\) −6.43915e79 −0.561155
\(349\) −2.34138e80 −1.86411 −0.932053 0.362323i \(-0.881984\pi\)
−0.932053 + 0.362323i \(0.881984\pi\)
\(350\) −2.22914e78 −0.0162179
\(351\) 5.15580e80 3.42864
\(352\) 5.83862e79 0.354990
\(353\) −7.30803e79 −0.406347 −0.203173 0.979143i \(-0.565126\pi\)
−0.203173 + 0.979143i \(0.565126\pi\)
\(354\) 1.04096e80 0.529459
\(355\) −1.50115e80 −0.698604
\(356\) 2.38806e80 1.01712
\(357\) −1.87226e80 −0.729989
\(358\) 8.88549e79 0.317224
\(359\) 3.10624e80 1.01569 0.507844 0.861449i \(-0.330443\pi\)
0.507844 + 0.861449i \(0.330443\pi\)
\(360\) −5.91155e80 −1.77081
\(361\) −3.56973e80 −0.979847
\(362\) 2.76912e80 0.696662
\(363\) −7.15496e80 −1.65025
\(364\) 1.13684e80 0.240440
\(365\) 8.82161e80 1.71129
\(366\) −6.65432e80 −1.18427
\(367\) −2.95687e80 −0.482893 −0.241447 0.970414i \(-0.577622\pi\)
−0.241447 + 0.970414i \(0.577622\pi\)
\(368\) 1.82578e80 0.273679
\(369\) 1.01517e81 1.39704
\(370\) 1.98623e80 0.251000
\(371\) 5.97938e79 0.0694029
\(372\) −1.94245e81 −2.07132
\(373\) 6.53601e80 0.640449 0.320224 0.947342i \(-0.396242\pi\)
0.320224 + 0.947342i \(0.396242\pi\)
\(374\) 2.20520e80 0.198606
\(375\) 2.48049e81 2.05377
\(376\) 2.48992e80 0.189569
\(377\) 4.92442e80 0.344828
\(378\) 5.45604e80 0.351468
\(379\) −1.70057e81 −1.00800 −0.503998 0.863705i \(-0.668138\pi\)
−0.503998 + 0.863705i \(0.668138\pi\)
\(380\) −2.04873e80 −0.111764
\(381\) −3.54844e81 −1.78197
\(382\) −1.24754e81 −0.576844
\(383\) −4.22264e81 −1.79814 −0.899068 0.437808i \(-0.855755\pi\)
−0.899068 + 0.437808i \(0.855755\pi\)
\(384\) 5.01616e81 1.96761
\(385\) −2.68586e80 −0.0970667
\(386\) −1.24979e80 −0.0416235
\(387\) 2.69697e81 0.827906
\(388\) −4.31123e80 −0.122012
\(389\) 1.74537e81 0.455487 0.227744 0.973721i \(-0.426865\pi\)
0.227744 + 0.973721i \(0.426865\pi\)
\(390\) 2.84694e81 0.685241
\(391\) 2.85776e81 0.634539
\(392\) −3.17041e81 −0.649538
\(393\) −8.88726e81 −1.68036
\(394\) −2.12637e81 −0.371114
\(395\) 4.00864e81 0.645934
\(396\) 6.04606e81 0.899651
\(397\) 1.07185e82 1.47310 0.736551 0.676382i \(-0.236453\pi\)
0.736551 + 0.676382i \(0.236453\pi\)
\(398\) −2.07848e81 −0.263894
\(399\) 6.45201e80 0.0756918
\(400\) −8.46291e80 −0.0917551
\(401\) −1.05350e82 −1.05582 −0.527908 0.849301i \(-0.677024\pi\)
−0.527908 + 0.849301i \(0.677024\pi\)
\(402\) −2.68606e81 −0.248883
\(403\) 1.48551e82 1.27282
\(404\) −6.16290e81 −0.488396
\(405\) −4.72890e82 −3.46679
\(406\) 5.21119e80 0.0353482
\(407\) −4.40278e81 −0.276377
\(408\) 3.20373e82 1.86149
\(409\) −4.74020e81 −0.254984 −0.127492 0.991840i \(-0.540693\pi\)
−0.127492 + 0.991840i \(0.540693\pi\)
\(410\) 3.56053e81 0.177347
\(411\) 5.25430e82 2.42380
\(412\) −1.90133e82 −0.812447
\(413\) 5.03441e81 0.199307
\(414\) −1.31113e82 −0.480989
\(415\) 3.14137e82 1.06808
\(416\) −2.99308e82 −0.943363
\(417\) 3.32524e82 0.971710
\(418\) −7.59937e80 −0.0205932
\(419\) −4.38377e82 −1.10181 −0.550904 0.834569i \(-0.685717\pi\)
−0.550904 + 0.834569i \(0.685717\pi\)
\(420\) −1.80038e82 −0.419771
\(421\) −1.14158e82 −0.246956 −0.123478 0.992347i \(-0.539405\pi\)
−0.123478 + 0.992347i \(0.539405\pi\)
\(422\) 1.77514e82 0.356362
\(423\) 3.96712e82 0.739185
\(424\) −1.02317e82 −0.176979
\(425\) −1.32464e82 −0.212739
\(426\) −3.73249e82 −0.556669
\(427\) −3.21823e82 −0.445798
\(428\) −7.53266e82 −0.969326
\(429\) −6.31069e82 −0.754522
\(430\) 9.45914e81 0.105098
\(431\) 1.31107e83 1.35391 0.676956 0.736023i \(-0.263299\pi\)
0.676956 + 0.736023i \(0.263299\pi\)
\(432\) 2.07138e83 1.98848
\(433\) −5.01725e82 −0.447813 −0.223907 0.974611i \(-0.571881\pi\)
−0.223907 + 0.974611i \(0.571881\pi\)
\(434\) 1.57202e82 0.130476
\(435\) −7.79866e82 −0.602017
\(436\) 3.44009e82 0.247028
\(437\) −9.84819e81 −0.0657947
\(438\) 2.19343e83 1.36360
\(439\) 6.75059e82 0.390579 0.195290 0.980746i \(-0.437435\pi\)
0.195290 + 0.980746i \(0.437435\pi\)
\(440\) 4.59594e82 0.247523
\(441\) −5.05133e83 −2.53274
\(442\) −1.13046e83 −0.527782
\(443\) 2.29536e83 0.998005 0.499002 0.866601i \(-0.333700\pi\)
0.499002 + 0.866601i \(0.333700\pi\)
\(444\) −2.95127e83 −1.19521
\(445\) 2.89226e83 1.09118
\(446\) −2.70822e82 −0.0951999
\(447\) −3.33120e83 −1.09122
\(448\) 2.16426e82 0.0660772
\(449\) 2.84021e83 0.808333 0.404167 0.914685i \(-0.367562\pi\)
0.404167 + 0.914685i \(0.367562\pi\)
\(450\) 6.07741e82 0.161259
\(451\) −7.89246e82 −0.195277
\(452\) 2.44644e83 0.564514
\(453\) −5.16704e83 −1.11211
\(454\) −2.83965e83 −0.570172
\(455\) 1.37687e83 0.257948
\(456\) −1.10404e83 −0.193016
\(457\) −3.53890e83 −0.577442 −0.288721 0.957413i \(-0.593230\pi\)
−0.288721 + 0.957413i \(0.593230\pi\)
\(458\) 3.44886e83 0.525307
\(459\) 3.24219e84 4.61040
\(460\) 2.74806e83 0.364884
\(461\) −9.02523e83 −1.11913 −0.559563 0.828788i \(-0.689031\pi\)
−0.559563 + 0.828788i \(0.689031\pi\)
\(462\) −6.67818e82 −0.0773456
\(463\) −1.17555e84 −1.27187 −0.635933 0.771744i \(-0.719385\pi\)
−0.635933 + 0.771744i \(0.719385\pi\)
\(464\) 1.97842e83 0.199987
\(465\) −2.35256e84 −2.22215
\(466\) −5.55487e83 −0.490363
\(467\) 1.78581e84 1.47351 0.736757 0.676157i \(-0.236356\pi\)
0.736757 + 0.676157i \(0.236356\pi\)
\(468\) −3.09943e84 −2.39077
\(469\) −1.29906e83 −0.0936881
\(470\) 1.39139e83 0.0938356
\(471\) 4.01337e84 2.53134
\(472\) −8.61469e83 −0.508238
\(473\) −2.09676e83 −0.115724
\(474\) 9.96717e83 0.514700
\(475\) 4.56487e82 0.0220587
\(476\) 7.14896e83 0.323313
\(477\) −1.63018e84 −0.690093
\(478\) 7.14253e83 0.283056
\(479\) −4.37337e84 −1.62274 −0.811368 0.584536i \(-0.801277\pi\)
−0.811368 + 0.584536i \(0.801277\pi\)
\(480\) 4.74006e84 1.64697
\(481\) 2.25702e84 0.734455
\(482\) 3.65071e83 0.111275
\(483\) −8.65440e83 −0.247117
\(484\) 2.73203e84 0.730897
\(485\) −5.22146e83 −0.130896
\(486\) −6.33125e84 −1.48746
\(487\) 4.62469e84 1.01841 0.509203 0.860647i \(-0.329940\pi\)
0.509203 + 0.860647i \(0.329940\pi\)
\(488\) 5.50691e84 1.13680
\(489\) −7.16819e84 −1.38733
\(490\) −1.77166e84 −0.321517
\(491\) −1.06620e85 −1.81455 −0.907277 0.420533i \(-0.861843\pi\)
−0.907277 + 0.420533i \(0.861843\pi\)
\(492\) −5.29047e84 −0.844489
\(493\) 3.09669e84 0.463681
\(494\) 3.89571e83 0.0547252
\(495\) 7.32258e84 0.965162
\(496\) 5.96816e84 0.738189
\(497\) −1.80515e84 −0.209549
\(498\) 7.81077e84 0.851078
\(499\) −8.87919e84 −0.908252 −0.454126 0.890938i \(-0.650048\pi\)
−0.454126 + 0.890938i \(0.650048\pi\)
\(500\) −9.47141e84 −0.909619
\(501\) 3.02772e85 2.73040
\(502\) −4.39735e84 −0.372412
\(503\) 1.82243e84 0.144964 0.0724818 0.997370i \(-0.476908\pi\)
0.0724818 + 0.997370i \(0.476908\pi\)
\(504\) −7.10869e84 −0.531163
\(505\) −7.46408e84 −0.523959
\(506\) 1.01934e84 0.0672323
\(507\) 1.14423e84 0.0709189
\(508\) 1.35493e85 0.789239
\(509\) −1.57331e85 −0.861401 −0.430700 0.902495i \(-0.641733\pi\)
−0.430700 + 0.902495i \(0.641733\pi\)
\(510\) 1.79028e85 0.921426
\(511\) 1.06081e85 0.513308
\(512\) −2.11482e85 −0.962210
\(513\) −1.11730e85 −0.478048
\(514\) −8.76956e84 −0.352890
\(515\) −2.30276e85 −0.871608
\(516\) −1.40550e85 −0.500456
\(517\) −3.08424e84 −0.103323
\(518\) 2.38845e84 0.0752886
\(519\) 1.43956e85 0.427029
\(520\) −2.35604e85 −0.657776
\(521\) 2.23640e85 0.587707 0.293853 0.955850i \(-0.405062\pi\)
0.293853 + 0.955850i \(0.405062\pi\)
\(522\) −1.42075e85 −0.351477
\(523\) 8.37853e85 1.95148 0.975741 0.218927i \(-0.0702555\pi\)
0.975741 + 0.218927i \(0.0702555\pi\)
\(524\) 3.39348e85 0.744235
\(525\) 4.01152e84 0.0828497
\(526\) −1.47839e85 −0.287567
\(527\) 9.34155e85 1.71153
\(528\) −2.53536e85 −0.437594
\(529\) −4.82871e85 −0.785195
\(530\) −5.71757e84 −0.0876036
\(531\) −1.37255e86 −1.98176
\(532\) −2.46362e84 −0.0335241
\(533\) 4.04596e85 0.518937
\(534\) 7.19138e85 0.869486
\(535\) −9.12305e85 −1.03991
\(536\) 2.22290e85 0.238907
\(537\) −1.59902e86 −1.62055
\(538\) −3.64565e85 −0.348444
\(539\) 3.92716e85 0.354024
\(540\) 3.11773e86 2.65116
\(541\) 1.46553e86 1.17565 0.587827 0.808986i \(-0.299983\pi\)
0.587827 + 0.808986i \(0.299983\pi\)
\(542\) 6.54436e85 0.495324
\(543\) −4.98326e86 −3.55893
\(544\) −1.88218e86 −1.26852
\(545\) 4.16640e85 0.265016
\(546\) 3.42347e85 0.205541
\(547\) 1.03373e83 0.000585878 0 0.000292939 1.00000i \(-0.499907\pi\)
0.000292939 1.00000i \(0.499907\pi\)
\(548\) −2.00628e86 −1.07351
\(549\) 8.77400e86 4.43270
\(550\) −4.72489e84 −0.0225407
\(551\) −1.06716e85 −0.0480787
\(552\) 1.48091e86 0.630155
\(553\) 4.82042e85 0.193751
\(554\) 4.40956e85 0.167432
\(555\) −3.57437e86 −1.28224
\(556\) −1.26970e86 −0.430372
\(557\) −1.52548e86 −0.488616 −0.244308 0.969698i \(-0.578561\pi\)
−0.244308 + 0.969698i \(0.578561\pi\)
\(558\) −4.28587e86 −1.29736
\(559\) 1.07488e86 0.307529
\(560\) 5.53166e85 0.149600
\(561\) −3.96843e86 −1.01459
\(562\) −1.06495e86 −0.257417
\(563\) 6.23004e86 1.42389 0.711945 0.702235i \(-0.247814\pi\)
0.711945 + 0.702235i \(0.247814\pi\)
\(564\) −2.06743e86 −0.446826
\(565\) 2.96296e86 0.605620
\(566\) 2.61076e86 0.504719
\(567\) −5.68655e86 −1.03988
\(568\) 3.08890e86 0.534356
\(569\) −2.01891e86 −0.330431 −0.165216 0.986257i \(-0.552832\pi\)
−0.165216 + 0.986257i \(0.552832\pi\)
\(570\) −6.16951e85 −0.0955417
\(571\) −8.80331e86 −1.29006 −0.645028 0.764159i \(-0.723154\pi\)
−0.645028 + 0.764159i \(0.723154\pi\)
\(572\) 2.40965e86 0.334179
\(573\) 2.24505e87 2.94683
\(574\) 4.28157e85 0.0531959
\(575\) −6.12309e85 −0.0720167
\(576\) −5.90051e86 −0.657024
\(577\) 4.21339e86 0.444215 0.222107 0.975022i \(-0.428706\pi\)
0.222107 + 0.975022i \(0.428706\pi\)
\(578\) −3.31633e86 −0.331079
\(579\) 2.24910e86 0.212635
\(580\) 2.97782e86 0.266634
\(581\) 3.77752e86 0.320375
\(582\) −1.29828e86 −0.104302
\(583\) 1.26739e86 0.0964607
\(584\) −1.81521e87 −1.30895
\(585\) −3.75381e87 −2.56486
\(586\) 9.02967e86 0.584651
\(587\) −1.93457e87 −1.18709 −0.593545 0.804801i \(-0.702272\pi\)
−0.593545 + 0.804801i \(0.702272\pi\)
\(588\) 2.63245e87 1.53100
\(589\) −3.21921e86 −0.177467
\(590\) −4.81398e86 −0.251574
\(591\) 3.82657e87 1.89585
\(592\) 9.06773e86 0.425956
\(593\) −3.07531e87 −1.36983 −0.684914 0.728624i \(-0.740160\pi\)
−0.684914 + 0.728624i \(0.740160\pi\)
\(594\) 1.15646e87 0.488493
\(595\) 8.65833e86 0.346856
\(596\) 1.27198e87 0.483306
\(597\) 3.74040e87 1.34811
\(598\) −5.22550e86 −0.178666
\(599\) −3.29040e87 −1.06734 −0.533672 0.845692i \(-0.679188\pi\)
−0.533672 + 0.845692i \(0.679188\pi\)
\(600\) −6.86437e86 −0.211269
\(601\) −3.89130e87 −1.13645 −0.568224 0.822874i \(-0.692369\pi\)
−0.568224 + 0.822874i \(0.692369\pi\)
\(602\) 1.13747e86 0.0315247
\(603\) 3.54168e87 0.931568
\(604\) 1.97296e87 0.492556
\(605\) 3.30885e87 0.784119
\(606\) −1.85589e87 −0.417507
\(607\) −3.00692e87 −0.642212 −0.321106 0.947043i \(-0.604055\pi\)
−0.321106 + 0.947043i \(0.604055\pi\)
\(608\) 6.48621e86 0.131531
\(609\) −9.37796e86 −0.180577
\(610\) 3.07732e87 0.562707
\(611\) 1.58109e87 0.274574
\(612\) −1.94905e88 −3.21480
\(613\) 7.23158e87 1.13300 0.566498 0.824063i \(-0.308298\pi\)
0.566498 + 0.824063i \(0.308298\pi\)
\(614\) 2.83081e87 0.421315
\(615\) −6.40746e87 −0.905982
\(616\) 5.52666e86 0.0742455
\(617\) −6.75048e87 −0.861691 −0.430846 0.902426i \(-0.641785\pi\)
−0.430846 + 0.902426i \(0.641785\pi\)
\(618\) −5.72564e87 −0.694523
\(619\) 7.11084e87 0.819720 0.409860 0.912149i \(-0.365578\pi\)
0.409860 + 0.912149i \(0.365578\pi\)
\(620\) 8.98295e87 0.984194
\(621\) 1.49869e88 1.56072
\(622\) 5.13585e87 0.508411
\(623\) 3.47797e87 0.327304
\(624\) 1.29972e88 1.16288
\(625\) −9.64457e87 −0.820470
\(626\) −3.16963e87 −0.256399
\(627\) 1.36757e87 0.105201
\(628\) −1.53245e88 −1.12114
\(629\) 1.41931e88 0.987603
\(630\) −3.97241e87 −0.262922
\(631\) −1.17327e88 −0.738708 −0.369354 0.929289i \(-0.620421\pi\)
−0.369354 + 0.929289i \(0.620421\pi\)
\(632\) −8.24853e87 −0.494070
\(633\) −3.19451e88 −1.82049
\(634\) 1.23575e88 0.670066
\(635\) 1.64099e88 0.846709
\(636\) 8.49556e87 0.417150
\(637\) −2.01320e88 −0.940795
\(638\) 1.10456e87 0.0491291
\(639\) 4.92145e88 2.08361
\(640\) −2.31975e88 −0.934914
\(641\) −5.85075e87 −0.224483 −0.112241 0.993681i \(-0.535803\pi\)
−0.112241 + 0.993681i \(0.535803\pi\)
\(642\) −2.26837e88 −0.828631
\(643\) −3.09879e88 −1.07782 −0.538910 0.842363i \(-0.681164\pi\)
−0.538910 + 0.842363i \(0.681164\pi\)
\(644\) 3.30457e87 0.109448
\(645\) −1.70225e88 −0.536898
\(646\) 2.44979e87 0.0735875
\(647\) 3.14549e88 0.899919 0.449959 0.893049i \(-0.351438\pi\)
0.449959 + 0.893049i \(0.351438\pi\)
\(648\) 9.73061e88 2.65172
\(649\) 1.06709e88 0.277009
\(650\) 2.42215e87 0.0599004
\(651\) −2.82898e88 −0.666543
\(652\) 2.73708e88 0.614452
\(653\) 1.00332e88 0.214622 0.107311 0.994226i \(-0.465776\pi\)
0.107311 + 0.994226i \(0.465776\pi\)
\(654\) 1.03594e88 0.211172
\(655\) 4.10995e88 0.798428
\(656\) 1.62549e88 0.300963
\(657\) −2.89212e89 −5.10397
\(658\) 1.67316e87 0.0281464
\(659\) 3.87613e88 0.621595 0.310798 0.950476i \(-0.399404\pi\)
0.310798 + 0.950476i \(0.399404\pi\)
\(660\) −3.81609e88 −0.583425
\(661\) 5.13511e88 0.748521 0.374261 0.927324i \(-0.377897\pi\)
0.374261 + 0.927324i \(0.377897\pi\)
\(662\) −2.38644e88 −0.331683
\(663\) 2.03436e89 2.69620
\(664\) −6.46395e88 −0.816966
\(665\) −2.98376e87 −0.0359652
\(666\) −6.51175e88 −0.748616
\(667\) 1.43143e88 0.156966
\(668\) −1.15609e89 −1.20930
\(669\) 4.87367e88 0.486332
\(670\) 1.24218e88 0.118257
\(671\) −6.82135e88 −0.619599
\(672\) 5.69996e88 0.494014
\(673\) 1.51230e89 1.25073 0.625366 0.780332i \(-0.284950\pi\)
0.625366 + 0.780332i \(0.284950\pi\)
\(674\) 2.96040e88 0.233649
\(675\) −6.94677e88 −0.523256
\(676\) −4.36909e87 −0.0314101
\(677\) 9.60349e87 0.0659001 0.0329500 0.999457i \(-0.489510\pi\)
0.0329500 + 0.999457i \(0.489510\pi\)
\(678\) 7.36718e88 0.482576
\(679\) −6.27885e87 −0.0392629
\(680\) −1.48158e89 −0.884493
\(681\) 5.11018e89 2.91274
\(682\) 3.33205e88 0.181344
\(683\) −1.20923e89 −0.628431 −0.314215 0.949352i \(-0.601741\pi\)
−0.314215 + 0.949352i \(0.601741\pi\)
\(684\) 6.71666e88 0.333339
\(685\) −2.42987e89 −1.15168
\(686\) −4.43609e88 −0.200812
\(687\) −6.20650e89 −2.68355
\(688\) 4.31839e88 0.178355
\(689\) −6.49708e88 −0.256338
\(690\) 8.27547e88 0.311922
\(691\) −5.63672e88 −0.202987 −0.101494 0.994836i \(-0.532362\pi\)
−0.101494 + 0.994836i \(0.532362\pi\)
\(692\) −5.49676e88 −0.189132
\(693\) 8.80546e88 0.289504
\(694\) 5.48602e87 0.0172359
\(695\) −1.53777e89 −0.461711
\(696\) 1.60472e89 0.460477
\(697\) 2.54427e89 0.697800
\(698\) 2.69225e89 0.705780
\(699\) 9.99643e89 2.50504
\(700\) −1.53175e88 −0.0366943
\(701\) −3.32347e89 −0.761158 −0.380579 0.924748i \(-0.624275\pi\)
−0.380579 + 0.924748i \(0.624275\pi\)
\(702\) −5.92844e89 −1.29814
\(703\) −4.89111e88 −0.102404
\(704\) 4.58736e88 0.0918383
\(705\) −2.50393e89 −0.479363
\(706\) 8.40319e88 0.153849
\(707\) −8.97562e88 −0.157164
\(708\) 7.15294e89 1.19794
\(709\) 3.99117e89 0.639357 0.319678 0.947526i \(-0.396425\pi\)
0.319678 + 0.947526i \(0.396425\pi\)
\(710\) 1.72611e89 0.264503
\(711\) −1.31421e90 −1.92652
\(712\) −5.95136e89 −0.834635
\(713\) 4.31808e89 0.579389
\(714\) 2.15283e89 0.276386
\(715\) 2.91841e89 0.358513
\(716\) 6.10563e89 0.717745
\(717\) −1.28536e90 −1.44600
\(718\) −3.57174e89 −0.384556
\(719\) 2.39039e89 0.246325 0.123162 0.992387i \(-0.460696\pi\)
0.123162 + 0.992387i \(0.460696\pi\)
\(720\) −1.50812e90 −1.48752
\(721\) −2.76909e89 −0.261442
\(722\) 4.10468e89 0.370986
\(723\) −6.56975e89 −0.568451
\(724\) 1.90279e90 1.57626
\(725\) −6.63501e88 −0.0526253
\(726\) 8.22719e89 0.624810
\(727\) −6.96567e88 −0.0506558 −0.0253279 0.999679i \(-0.508063\pi\)
−0.0253279 + 0.999679i \(0.508063\pi\)
\(728\) −2.83316e89 −0.197303
\(729\) 5.73751e90 3.82654
\(730\) −1.01436e90 −0.647921
\(731\) 6.75928e89 0.413526
\(732\) −4.57249e90 −2.67950
\(733\) −1.46414e90 −0.821880 −0.410940 0.911662i \(-0.634799\pi\)
−0.410940 + 0.911662i \(0.634799\pi\)
\(734\) 3.39998e89 0.182831
\(735\) 3.18825e90 1.64248
\(736\) −8.70027e89 −0.429419
\(737\) −2.75348e89 −0.130214
\(738\) −1.16730e90 −0.528942
\(739\) −3.24476e90 −1.40891 −0.704454 0.709749i \(-0.748808\pi\)
−0.704454 + 0.709749i \(0.748808\pi\)
\(740\) 1.36483e90 0.567909
\(741\) −7.01064e89 −0.279566
\(742\) −6.87543e88 −0.0262771
\(743\) 1.23913e90 0.453909 0.226955 0.973905i \(-0.427123\pi\)
0.226955 + 0.973905i \(0.427123\pi\)
\(744\) 4.84084e90 1.69970
\(745\) 1.54053e90 0.518499
\(746\) −7.51548e89 −0.242484
\(747\) −1.02988e91 −3.18558
\(748\) 1.51529e90 0.449362
\(749\) −1.09705e90 −0.311925
\(750\) −2.85221e90 −0.777591
\(751\) −2.90019e90 −0.758172 −0.379086 0.925361i \(-0.623762\pi\)
−0.379086 + 0.925361i \(0.623762\pi\)
\(752\) 6.35214e89 0.159242
\(753\) 7.91339e90 1.90248
\(754\) −5.66239e89 −0.130558
\(755\) 2.38952e90 0.528423
\(756\) 3.74910e90 0.795226
\(757\) 5.88673e90 1.19772 0.598858 0.800855i \(-0.295621\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(758\) 1.95541e90 0.381643
\(759\) −1.83439e90 −0.343459
\(760\) 5.10570e89 0.0917122
\(761\) 6.18701e90 1.06626 0.533131 0.846033i \(-0.321015\pi\)
0.533131 + 0.846033i \(0.321015\pi\)
\(762\) 4.08020e90 0.674683
\(763\) 5.01013e89 0.0794926
\(764\) −8.57242e90 −1.30516
\(765\) −2.36056e91 −3.44889
\(766\) 4.85543e90 0.680804
\(767\) −5.47030e90 −0.736135
\(768\) −2.17831e90 −0.281346
\(769\) −7.95075e88 −0.00985663 −0.00492832 0.999988i \(-0.501569\pi\)
−0.00492832 + 0.999988i \(0.501569\pi\)
\(770\) 3.08835e89 0.0367510
\(771\) 1.57815e91 1.80275
\(772\) −8.58791e89 −0.0941765
\(773\) −2.44555e90 −0.257468 −0.128734 0.991679i \(-0.541091\pi\)
−0.128734 + 0.991679i \(0.541091\pi\)
\(774\) −3.10113e90 −0.313459
\(775\) −2.00153e90 −0.194249
\(776\) 1.07441e90 0.100121
\(777\) −4.29822e90 −0.384615
\(778\) −2.00693e90 −0.172455
\(779\) −8.76786e89 −0.0723542
\(780\) 1.95627e91 1.55041
\(781\) −3.82619e90 −0.291245
\(782\) −3.28602e90 −0.240247
\(783\) 1.62398e91 1.14048
\(784\) −8.08818e90 −0.545625
\(785\) −1.85600e91 −1.20278
\(786\) 1.02191e91 0.636212
\(787\) 1.22272e91 0.731345 0.365673 0.930744i \(-0.380839\pi\)
0.365673 + 0.930744i \(0.380839\pi\)
\(788\) −1.46113e91 −0.839676
\(789\) 2.66049e91 1.46905
\(790\) −4.60936e90 −0.244561
\(791\) 3.56299e90 0.181658
\(792\) −1.50676e91 −0.738244
\(793\) 3.49687e91 1.64655
\(794\) −1.23247e91 −0.557740
\(795\) 1.02892e91 0.447526
\(796\) −1.42822e91 −0.597082
\(797\) −3.33569e91 −1.34044 −0.670222 0.742161i \(-0.733801\pi\)
−0.670222 + 0.742161i \(0.733801\pi\)
\(798\) −7.41889e89 −0.0286581
\(799\) 9.94258e90 0.369212
\(800\) 4.03279e90 0.143970
\(801\) −9.48213e91 −3.25448
\(802\) 1.21138e91 0.399749
\(803\) 2.24848e91 0.713428
\(804\) −1.84572e91 −0.563118
\(805\) 4.00227e90 0.117418
\(806\) −1.70813e91 −0.481911
\(807\) 6.56064e91 1.78004
\(808\) 1.53587e91 0.400772
\(809\) 5.41859e91 1.35990 0.679952 0.733257i \(-0.262001\pi\)
0.679952 + 0.733257i \(0.262001\pi\)
\(810\) 5.43757e91 1.31258
\(811\) −4.10679e91 −0.953556 −0.476778 0.879024i \(-0.658195\pi\)
−0.476778 + 0.879024i \(0.658195\pi\)
\(812\) 3.58085e90 0.0799781
\(813\) −1.17771e92 −2.53038
\(814\) 5.06256e90 0.104641
\(815\) 3.31496e91 0.659195
\(816\) 8.17318e91 1.56369
\(817\) −2.32933e90 −0.0428781
\(818\) 5.45056e90 0.0965410
\(819\) −4.51399e91 −0.769340
\(820\) 2.44660e91 0.401261
\(821\) 7.47546e91 1.17986 0.589928 0.807456i \(-0.299156\pi\)
0.589928 + 0.807456i \(0.299156\pi\)
\(822\) −6.04169e91 −0.917690
\(823\) −1.00127e92 −1.46372 −0.731859 0.681456i \(-0.761347\pi\)
−0.731859 + 0.681456i \(0.761347\pi\)
\(824\) 4.73836e91 0.666685
\(825\) 8.50282e90 0.115150
\(826\) −5.78886e90 −0.0754608
\(827\) 7.70914e91 0.967348 0.483674 0.875248i \(-0.339302\pi\)
0.483674 + 0.875248i \(0.339302\pi\)
\(828\) −9.00939e91 −1.08828
\(829\) 8.89462e90 0.103433 0.0517166 0.998662i \(-0.483531\pi\)
0.0517166 + 0.998662i \(0.483531\pi\)
\(830\) −3.61213e91 −0.404392
\(831\) −7.93537e91 −0.855332
\(832\) −2.35164e91 −0.244054
\(833\) −1.26599e92 −1.26506
\(834\) −3.82355e91 −0.367905
\(835\) −1.40018e92 −1.29736
\(836\) −5.22188e90 −0.0465939
\(837\) 4.89895e92 4.20970
\(838\) 5.04071e91 0.417162
\(839\) 1.70386e91 0.135810 0.0679049 0.997692i \(-0.478369\pi\)
0.0679049 + 0.997692i \(0.478369\pi\)
\(840\) 4.48679e91 0.344460
\(841\) −1.19719e92 −0.885299
\(842\) 1.31265e91 0.0935015
\(843\) 1.91647e92 1.31502
\(844\) 1.21978e92 0.806297
\(845\) −5.29154e90 −0.0336973
\(846\) −4.56162e91 −0.279868
\(847\) 3.97892e91 0.235200
\(848\) −2.61025e91 −0.148666
\(849\) −4.69828e92 −2.57838
\(850\) 1.52315e91 0.0805465
\(851\) 6.56069e91 0.334324
\(852\) −2.56477e92 −1.25951
\(853\) 2.48680e91 0.117692 0.0588460 0.998267i \(-0.481258\pi\)
0.0588460 + 0.998267i \(0.481258\pi\)
\(854\) 3.70050e91 0.168786
\(855\) 8.13476e91 0.357612
\(856\) 1.87724e92 0.795418
\(857\) 1.41839e92 0.579296 0.289648 0.957133i \(-0.406462\pi\)
0.289648 + 0.957133i \(0.406462\pi\)
\(858\) 7.25639e91 0.285674
\(859\) −3.07690e91 −0.116769 −0.0583847 0.998294i \(-0.518595\pi\)
−0.0583847 + 0.998294i \(0.518595\pi\)
\(860\) 6.49981e91 0.237793
\(861\) −7.70503e91 −0.271753
\(862\) −1.50754e92 −0.512613
\(863\) −2.87438e91 −0.0942334 −0.0471167 0.998889i \(-0.515003\pi\)
−0.0471167 + 0.998889i \(0.515003\pi\)
\(864\) −9.87064e92 −3.12005
\(865\) −6.65730e91 −0.202904
\(866\) 5.76912e91 0.169549
\(867\) 5.96801e92 1.69133
\(868\) 1.08021e92 0.295213
\(869\) 1.02174e92 0.269287
\(870\) 8.96735e91 0.227933
\(871\) 1.41153e92 0.346035
\(872\) −8.57315e91 −0.202708
\(873\) 1.71183e92 0.390402
\(874\) 1.13240e91 0.0249109
\(875\) −1.37941e92 −0.292712
\(876\) 1.50720e93 3.08527
\(877\) 7.89285e92 1.55864 0.779322 0.626624i \(-0.215564\pi\)
0.779322 + 0.626624i \(0.215564\pi\)
\(878\) −7.76222e91 −0.147880
\(879\) −1.62496e93 −2.98671
\(880\) 1.17249e92 0.207924
\(881\) −1.02239e93 −1.74934 −0.874671 0.484717i \(-0.838923\pi\)
−0.874671 + 0.484717i \(0.838923\pi\)
\(882\) 5.80831e92 0.958935
\(883\) −6.60718e92 −1.05258 −0.526289 0.850306i \(-0.676417\pi\)
−0.526289 + 0.850306i \(0.676417\pi\)
\(884\) −7.76793e92 −1.19415
\(885\) 8.66315e92 1.28518
\(886\) −2.63933e92 −0.377861
\(887\) −2.71527e92 −0.375162 −0.187581 0.982249i \(-0.560065\pi\)
−0.187581 + 0.982249i \(0.560065\pi\)
\(888\) 7.35494e92 0.980778
\(889\) 1.97331e92 0.253974
\(890\) −3.32568e92 −0.413139
\(891\) −1.20532e93 −1.44529
\(892\) −1.86095e92 −0.215398
\(893\) −3.42633e91 −0.0382832
\(894\) 3.83041e92 0.413155
\(895\) 7.39472e92 0.770010
\(896\) −2.78952e92 −0.280431
\(897\) 9.40371e92 0.912720
\(898\) −3.26583e92 −0.306048
\(899\) 4.67910e92 0.423381
\(900\) 4.17607e92 0.364862
\(901\) −4.08565e92 −0.344691
\(902\) 9.07521e91 0.0739351
\(903\) −2.04697e92 −0.161045
\(904\) −6.09685e92 −0.463234
\(905\) 2.30453e93 1.69103
\(906\) 5.94135e92 0.421063
\(907\) −9.32414e92 −0.638233 −0.319116 0.947716i \(-0.603386\pi\)
−0.319116 + 0.947716i \(0.603386\pi\)
\(908\) −1.95125e93 −1.29006
\(909\) 2.44706e93 1.56273
\(910\) −1.58320e92 −0.0976635
\(911\) 6.82273e92 0.406564 0.203282 0.979120i \(-0.434839\pi\)
0.203282 + 0.979120i \(0.434839\pi\)
\(912\) −2.81657e92 −0.162138
\(913\) 8.00683e92 0.445278
\(914\) 4.06923e92 0.218629
\(915\) −5.53788e93 −2.87461
\(916\) 2.36987e93 1.18855
\(917\) 4.94226e92 0.239492
\(918\) −3.72806e93 −1.74557
\(919\) 8.29916e92 0.375487 0.187744 0.982218i \(-0.439883\pi\)
0.187744 + 0.982218i \(0.439883\pi\)
\(920\) −6.84853e92 −0.299420
\(921\) −5.09427e93 −2.15230
\(922\) 1.03777e93 0.423719
\(923\) 1.96144e93 0.773965
\(924\) −4.58888e92 −0.175001
\(925\) −3.04104e92 −0.112087
\(926\) 1.35172e93 0.481549
\(927\) 7.54949e93 2.59960
\(928\) −9.42767e92 −0.313793
\(929\) 3.38716e93 1.08978 0.544892 0.838506i \(-0.316571\pi\)
0.544892 + 0.838506i \(0.316571\pi\)
\(930\) 2.70511e93 0.841342
\(931\) 4.36274e92 0.131173
\(932\) −3.81701e93 −1.10949
\(933\) −9.24238e93 −2.59724
\(934\) −2.05343e93 −0.557896
\(935\) 1.83522e93 0.482083
\(936\) 7.72418e93 1.96184
\(937\) −3.03836e93 −0.746179 −0.373089 0.927795i \(-0.621702\pi\)
−0.373089 + 0.927795i \(0.621702\pi\)
\(938\) 1.49373e92 0.0354718
\(939\) 5.70400e93 1.30983
\(940\) 9.56091e92 0.212311
\(941\) −2.32725e93 −0.499769 −0.249884 0.968276i \(-0.580393\pi\)
−0.249884 + 0.968276i \(0.580393\pi\)
\(942\) −4.61481e93 −0.958408
\(943\) 1.17608e93 0.236220
\(944\) −2.19773e93 −0.426930
\(945\) 4.54065e93 0.853132
\(946\) 2.41098e92 0.0438150
\(947\) 6.25689e93 1.09985 0.549926 0.835213i \(-0.314656\pi\)
0.549926 + 0.835213i \(0.314656\pi\)
\(948\) 6.84890e93 1.16455
\(949\) −1.15265e94 −1.89589
\(950\) −5.24895e91 −0.00835178
\(951\) −2.22382e94 −3.42306
\(952\) −1.78161e93 −0.265308
\(953\) 6.65569e93 0.958885 0.479443 0.877573i \(-0.340839\pi\)
0.479443 + 0.877573i \(0.340839\pi\)
\(954\) 1.87448e93 0.261280
\(955\) −1.03823e94 −1.40020
\(956\) 4.90796e93 0.640438
\(957\) −1.98775e93 −0.250978
\(958\) 5.02876e93 0.614394
\(959\) −2.92194e93 −0.345450
\(960\) 3.72423e93 0.426081
\(961\) 5.08303e93 0.562776
\(962\) −2.59525e93 −0.278077
\(963\) 2.99095e94 3.10156
\(964\) 2.50857e93 0.251768
\(965\) −1.04011e93 −0.101034
\(966\) 9.95132e92 0.0935624
\(967\) 1.16513e94 1.06033 0.530165 0.847895i \(-0.322130\pi\)
0.530165 + 0.847895i \(0.322130\pi\)
\(968\) −6.80857e93 −0.599766
\(969\) −4.40859e93 −0.375925
\(970\) 6.00394e92 0.0495594
\(971\) 3.52112e93 0.281368 0.140684 0.990055i \(-0.455070\pi\)
0.140684 + 0.990055i \(0.455070\pi\)
\(972\) −4.35049e94 −3.36551
\(973\) −1.84918e93 −0.138492
\(974\) −5.31774e93 −0.385585
\(975\) −4.35885e93 −0.306003
\(976\) 1.40489e94 0.954934
\(977\) 1.56288e94 1.02860 0.514301 0.857610i \(-0.328052\pi\)
0.514301 + 0.857610i \(0.328052\pi\)
\(978\) 8.24240e93 0.525267
\(979\) 7.37189e93 0.454909
\(980\) −1.21739e94 −0.727458
\(981\) −1.36594e94 −0.790417
\(982\) 1.22597e94 0.687020
\(983\) −2.15640e94 −1.17029 −0.585146 0.810928i \(-0.698963\pi\)
−0.585146 + 0.810928i \(0.698963\pi\)
\(984\) 1.31846e94 0.692978
\(985\) −1.76962e94 −0.900819
\(986\) −3.56075e93 −0.175557
\(987\) −3.01099e93 −0.143787
\(988\) 2.67692e93 0.123820
\(989\) 3.12444e93 0.139987
\(990\) −8.41992e93 −0.365426
\(991\) 1.31180e94 0.551501 0.275750 0.961229i \(-0.411074\pi\)
0.275750 + 0.961229i \(0.411074\pi\)
\(992\) −2.84397e94 −1.15826
\(993\) 4.29459e94 1.69442
\(994\) 2.07566e93 0.0793387
\(995\) −1.72976e94 −0.640560
\(996\) 5.36714e94 1.92563
\(997\) −3.78877e94 −1.31705 −0.658523 0.752560i \(-0.728819\pi\)
−0.658523 + 0.752560i \(0.728819\pi\)
\(998\) 1.02098e94 0.343879
\(999\) 7.44323e94 2.42912
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 1.64.a.a.1.2 5
3.2 odd 2 9.64.a.c.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.64.a.a.1.2 5 1.1 even 1 trivial
9.64.a.c.1.4 5 3.2 odd 2