Properties

Label 1.68.a.a.1.5
Level 1
Weight 68
Character 1.1
Self dual yes
Analytic conductor 28.429
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 68 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.4290351930\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 939384011925257456 x^{3} + 31046449413968483513911200 x^{2} + 156793504704482691874379743265203200 x + 20916736226052669578405116700517591609696000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-8.99335e8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.26950e10 q^{2} -1.28429e15 q^{3} +3.67490e20 q^{4} -1.61198e23 q^{5} -2.91471e25 q^{6} +2.93806e28 q^{7} +4.99099e30 q^{8} -9.10601e31 q^{9} +O(q^{10})\) \(q+2.26950e10 q^{2} -1.28429e15 q^{3} +3.67490e20 q^{4} -1.61198e23 q^{5} -2.91471e25 q^{6} +2.93806e28 q^{7} +4.99099e30 q^{8} -9.10601e31 q^{9} -3.65838e33 q^{10} +1.03989e35 q^{11} -4.71965e35 q^{12} -9.30624e35 q^{13} +6.66794e38 q^{14} +2.07025e38 q^{15} +5.90387e40 q^{16} +2.52116e41 q^{17} -2.06661e42 q^{18} -4.10720e41 q^{19} -5.92385e43 q^{20} -3.77334e43 q^{21} +2.36002e45 q^{22} -7.28152e44 q^{23} -6.40990e45 q^{24} -4.17779e46 q^{25} -2.11205e46 q^{26} +2.36014e47 q^{27} +1.07971e49 q^{28} -8.66841e48 q^{29} +4.69844e48 q^{30} +5.42697e49 q^{31} +6.03344e50 q^{32} -1.33552e50 q^{33} +5.72177e51 q^{34} -4.73609e51 q^{35} -3.34636e52 q^{36} +2.44090e52 q^{37} -9.32129e51 q^{38} +1.19520e51 q^{39} -8.04536e53 q^{40} +8.84851e52 q^{41} -8.56360e53 q^{42} -3.35174e54 q^{43} +3.82147e55 q^{44} +1.46787e55 q^{45} -1.65254e55 q^{46} -1.34362e56 q^{47} -7.58230e55 q^{48} +4.44845e56 q^{49} -9.48151e56 q^{50} -3.23791e56 q^{51} -3.41995e56 q^{52} -3.87432e57 q^{53} +5.35634e57 q^{54} -1.67627e58 q^{55} +1.46639e59 q^{56} +5.27485e56 q^{57} -1.96730e59 q^{58} -2.62052e59 q^{59} +7.60797e58 q^{60} -4.77635e59 q^{61} +1.23165e60 q^{62} -2.67540e60 q^{63} +4.98032e60 q^{64} +1.50015e59 q^{65} -3.03096e60 q^{66} -2.36430e61 q^{67} +9.26500e61 q^{68} +9.35162e59 q^{69} -1.07486e62 q^{70} +2.36087e61 q^{71} -4.54480e62 q^{72} +7.86035e61 q^{73} +5.53962e62 q^{74} +5.36551e61 q^{75} -1.50935e62 q^{76} +3.05525e63 q^{77} +2.71250e61 q^{78} -2.74602e63 q^{79} -9.51690e63 q^{80} +8.13902e63 q^{81} +2.00817e63 q^{82} +9.16622e63 q^{83} -1.38666e64 q^{84} -4.06405e64 q^{85} -7.60679e64 q^{86} +1.11328e64 q^{87} +5.19006e65 q^{88} -3.36134e65 q^{89} +3.33133e65 q^{90} -2.73423e64 q^{91} -2.67588e65 q^{92} -6.96983e64 q^{93} -3.04935e66 q^{94} +6.62071e64 q^{95} -7.74871e65 q^{96} +6.50306e66 q^{97} +1.00958e67 q^{98} -9.46921e66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} + O(q^{10}) \) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} - \)\(52\!\cdots\!00\)\(q^{10} + \)\(20\!\cdots\!60\)\(q^{11} - \)\(20\!\cdots\!24\)\(q^{12} + \)\(17\!\cdots\!02\)\(q^{13} + \)\(29\!\cdots\!80\)\(q^{14} - \)\(93\!\cdots\!00\)\(q^{15} + \)\(18\!\cdots\!80\)\(q^{16} + \)\(75\!\cdots\!06\)\(q^{17} - \)\(10\!\cdots\!68\)\(q^{18} + \)\(39\!\cdots\!00\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(17\!\cdots\!40\)\(q^{21} + \)\(18\!\cdots\!32\)\(q^{22} - \)\(41\!\cdots\!68\)\(q^{23} - \)\(13\!\cdots\!00\)\(q^{24} + \)\(17\!\cdots\!75\)\(q^{25} + \)\(21\!\cdots\!60\)\(q^{26} + \)\(18\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!48\)\(q^{28} + \)\(18\!\cdots\!50\)\(q^{29} + \)\(18\!\cdots\!00\)\(q^{30} + \)\(36\!\cdots\!60\)\(q^{31} + \)\(15\!\cdots\!96\)\(q^{32} + \)\(24\!\cdots\!84\)\(q^{33} + \)\(78\!\cdots\!80\)\(q^{34} + \)\(45\!\cdots\!00\)\(q^{35} - \)\(38\!\cdots\!20\)\(q^{36} - \)\(56\!\cdots\!94\)\(q^{37} - \)\(31\!\cdots\!80\)\(q^{38} - \)\(71\!\cdots\!80\)\(q^{39} - \)\(18\!\cdots\!00\)\(q^{40} + \)\(11\!\cdots\!10\)\(q^{41} + \)\(28\!\cdots\!92\)\(q^{42} + \)\(65\!\cdots\!92\)\(q^{43} + \)\(49\!\cdots\!80\)\(q^{44} + \)\(99\!\cdots\!50\)\(q^{45} + \)\(79\!\cdots\!60\)\(q^{46} - \)\(12\!\cdots\!44\)\(q^{47} - \)\(19\!\cdots\!68\)\(q^{48} - \)\(77\!\cdots\!35\)\(q^{49} - \)\(39\!\cdots\!00\)\(q^{50} - \)\(33\!\cdots\!40\)\(q^{51} + \)\(67\!\cdots\!16\)\(q^{52} + \)\(10\!\cdots\!22\)\(q^{53} + \)\(19\!\cdots\!00\)\(q^{54} + \)\(66\!\cdots\!00\)\(q^{55} + \)\(16\!\cdots\!00\)\(q^{56} - \)\(92\!\cdots\!60\)\(q^{57} - \)\(61\!\cdots\!20\)\(q^{58} - \)\(30\!\cdots\!00\)\(q^{59} - \)\(13\!\cdots\!00\)\(q^{60} - \)\(11\!\cdots\!90\)\(q^{61} - \)\(21\!\cdots\!28\)\(q^{62} - \)\(20\!\cdots\!68\)\(q^{63} + \)\(63\!\cdots\!40\)\(q^{64} + \)\(17\!\cdots\!00\)\(q^{65} + \)\(27\!\cdots\!20\)\(q^{66} - \)\(11\!\cdots\!44\)\(q^{67} + \)\(81\!\cdots\!48\)\(q^{68} + \)\(35\!\cdots\!20\)\(q^{69} - \)\(26\!\cdots\!00\)\(q^{70} - \)\(11\!\cdots\!40\)\(q^{71} - \)\(74\!\cdots\!40\)\(q^{72} - \)\(30\!\cdots\!18\)\(q^{73} + \)\(92\!\cdots\!80\)\(q^{74} + \)\(21\!\cdots\!00\)\(q^{75} + \)\(20\!\cdots\!00\)\(q^{76} + \)\(50\!\cdots\!32\)\(q^{77} + \)\(61\!\cdots\!64\)\(q^{78} + \)\(29\!\cdots\!00\)\(q^{79} - \)\(15\!\cdots\!00\)\(q^{80} - \)\(11\!\cdots\!95\)\(q^{81} - \)\(17\!\cdots\!08\)\(q^{82} - \)\(47\!\cdots\!88\)\(q^{83} - \)\(52\!\cdots\!20\)\(q^{84} - \)\(39\!\cdots\!00\)\(q^{85} + \)\(49\!\cdots\!60\)\(q^{86} + \)\(35\!\cdots\!60\)\(q^{87} + \)\(43\!\cdots\!60\)\(q^{88} - \)\(11\!\cdots\!50\)\(q^{89} + \)\(47\!\cdots\!00\)\(q^{90} + \)\(23\!\cdots\!60\)\(q^{91} - \)\(98\!\cdots\!44\)\(q^{92} - \)\(18\!\cdots\!36\)\(q^{93} - \)\(49\!\cdots\!20\)\(q^{94} - \)\(20\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!40\)\(q^{96} + \)\(28\!\cdots\!06\)\(q^{97} + \)\(12\!\cdots\!08\)\(q^{98} + \)\(16\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.26950e10 1.86821 0.934105 0.356999i \(-0.116200\pi\)
0.934105 + 0.356999i \(0.116200\pi\)
\(3\) −1.28429e15 −0.133384 −0.0666918 0.997774i \(-0.521244\pi\)
−0.0666918 + 0.997774i \(0.521244\pi\)
\(4\) 3.67490e20 2.49021
\(5\) −1.61198e23 −0.619247 −0.309623 0.950859i \(-0.600203\pi\)
−0.309623 + 0.950859i \(0.600203\pi\)
\(6\) −2.91471e25 −0.249189
\(7\) 2.93806e28 1.43641 0.718203 0.695834i \(-0.244965\pi\)
0.718203 + 0.695834i \(0.244965\pi\)
\(8\) 4.99099e30 2.78402
\(9\) −9.10601e31 −0.982209
\(10\) −3.65838e33 −1.15688
\(11\) 1.03989e35 1.34999 0.674995 0.737822i \(-0.264146\pi\)
0.674995 + 0.737822i \(0.264146\pi\)
\(12\) −4.71965e35 −0.332153
\(13\) −9.30624e35 −0.0448407 −0.0224203 0.999749i \(-0.507137\pi\)
−0.0224203 + 0.999749i \(0.507137\pi\)
\(14\) 6.66794e38 2.68351
\(15\) 2.07025e38 0.0825974
\(16\) 5.90387e40 2.71092
\(17\) 2.52116e41 1.51901 0.759506 0.650500i \(-0.225441\pi\)
0.759506 + 0.650500i \(0.225441\pi\)
\(18\) −2.06661e42 −1.83497
\(19\) −4.10720e41 −0.0596074 −0.0298037 0.999556i \(-0.509488\pi\)
−0.0298037 + 0.999556i \(0.509488\pi\)
\(20\) −5.92385e43 −1.54205
\(21\) −3.77334e43 −0.191593
\(22\) 2.36002e45 2.52207
\(23\) −7.28152e44 −0.175525 −0.0877626 0.996141i \(-0.527972\pi\)
−0.0877626 + 0.996141i \(0.527972\pi\)
\(24\) −6.40990e45 −0.371342
\(25\) −4.17779e46 −0.616533
\(26\) −2.11205e46 −0.0837718
\(27\) 2.36014e47 0.264394
\(28\) 1.07971e49 3.57695
\(29\) −8.66841e48 −0.886353 −0.443176 0.896434i \(-0.646148\pi\)
−0.443176 + 0.896434i \(0.646148\pi\)
\(30\) 4.69844e48 0.154309
\(31\) 5.42697e49 0.594211 0.297106 0.954845i \(-0.403979\pi\)
0.297106 + 0.954845i \(0.403979\pi\)
\(32\) 6.03344e50 2.28056
\(33\) −1.33552e50 −0.180067
\(34\) 5.72177e51 2.83783
\(35\) −4.73609e51 −0.889490
\(36\) −3.34636e52 −2.44590
\(37\) 2.44090e52 0.712511 0.356255 0.934389i \(-0.384053\pi\)
0.356255 + 0.934389i \(0.384053\pi\)
\(38\) −9.32129e51 −0.111359
\(39\) 1.19520e51 0.00598101
\(40\) −8.04536e53 −1.72399
\(41\) 8.84851e52 0.0829108 0.0414554 0.999140i \(-0.486801\pi\)
0.0414554 + 0.999140i \(0.486801\pi\)
\(42\) −8.56360e53 −0.357936
\(43\) −3.35174e54 −0.636909 −0.318455 0.947938i \(-0.603164\pi\)
−0.318455 + 0.947938i \(0.603164\pi\)
\(44\) 3.82147e55 3.36176
\(45\) 1.46787e55 0.608230
\(46\) −1.65254e55 −0.327918
\(47\) −1.34362e56 −1.29718 −0.648588 0.761140i \(-0.724640\pi\)
−0.648588 + 0.761140i \(0.724640\pi\)
\(48\) −7.58230e55 −0.361593
\(49\) 4.44845e56 1.06326
\(50\) −9.48151e56 −1.15181
\(51\) −3.23791e56 −0.202611
\(52\) −3.41995e56 −0.111663
\(53\) −3.87432e57 −0.668273 −0.334136 0.942525i \(-0.608445\pi\)
−0.334136 + 0.942525i \(0.608445\pi\)
\(54\) 5.35634e57 0.493944
\(55\) −1.67627e58 −0.835977
\(56\) 1.46639e59 3.99898
\(57\) 5.27485e56 0.00795064
\(58\) −1.96730e59 −1.65589
\(59\) −2.62052e59 −1.24407 −0.622035 0.782989i \(-0.713694\pi\)
−0.622035 + 0.782989i \(0.713694\pi\)
\(60\) 7.60797e58 0.205685
\(61\) −4.77635e59 −0.742244 −0.371122 0.928584i \(-0.621027\pi\)
−0.371122 + 0.928584i \(0.621027\pi\)
\(62\) 1.23165e60 1.11011
\(63\) −2.67540e60 −1.41085
\(64\) 4.98032e60 1.54963
\(65\) 1.50015e59 0.0277674
\(66\) −3.03096e60 −0.336402
\(67\) −2.36430e61 −1.58561 −0.792805 0.609476i \(-0.791380\pi\)
−0.792805 + 0.609476i \(0.791380\pi\)
\(68\) 9.26500e61 3.78265
\(69\) 9.35162e59 0.0234122
\(70\) −1.07486e62 −1.66175
\(71\) 2.36087e61 0.226943 0.113471 0.993541i \(-0.463803\pi\)
0.113471 + 0.993541i \(0.463803\pi\)
\(72\) −4.54480e62 −2.73449
\(73\) 7.86035e61 0.297938 0.148969 0.988842i \(-0.452404\pi\)
0.148969 + 0.988842i \(0.452404\pi\)
\(74\) 5.53962e62 1.33112
\(75\) 5.36551e61 0.0822354
\(76\) −1.50935e62 −0.148435
\(77\) 3.05525e63 1.93913
\(78\) 2.71250e61 0.0111738
\(79\) −2.74602e63 −0.738237 −0.369118 0.929382i \(-0.620340\pi\)
−0.369118 + 0.929382i \(0.620340\pi\)
\(80\) −9.51690e63 −1.67873
\(81\) 8.13902e63 0.946943
\(82\) 2.00817e63 0.154895
\(83\) 9.16622e63 0.471058 0.235529 0.971867i \(-0.424318\pi\)
0.235529 + 0.971867i \(0.424318\pi\)
\(84\) −1.38666e64 −0.477106
\(85\) −4.06405e64 −0.940643
\(86\) −7.60679e64 −1.18988
\(87\) 1.11328e64 0.118225
\(88\) 5.19006e65 3.75840
\(89\) −3.36134e65 −1.66704 −0.833521 0.552488i \(-0.813679\pi\)
−0.833521 + 0.552488i \(0.813679\pi\)
\(90\) 3.33133e65 1.13630
\(91\) −2.73423e64 −0.0644094
\(92\) −2.67588e65 −0.437094
\(93\) −6.96983e64 −0.0792580
\(94\) −3.04935e66 −2.42340
\(95\) 6.62071e64 0.0369117
\(96\) −7.74871e65 −0.304189
\(97\) 6.50306e66 1.80412 0.902059 0.431614i \(-0.142056\pi\)
0.902059 + 0.431614i \(0.142056\pi\)
\(98\) 1.00958e67 1.98639
\(99\) −9.46921e66 −1.32597
\(100\) −1.53530e67 −1.53530
\(101\) 1.99950e67 1.43270 0.716352 0.697739i \(-0.245811\pi\)
0.716352 + 0.697739i \(0.245811\pi\)
\(102\) −7.34844e66 −0.378520
\(103\) 2.01461e67 0.748417 0.374209 0.927345i \(-0.377914\pi\)
0.374209 + 0.927345i \(0.377914\pi\)
\(104\) −4.64474e66 −0.124837
\(105\) 6.08254e66 0.118643
\(106\) −8.79277e67 −1.24847
\(107\) −3.65427e67 −0.378830 −0.189415 0.981897i \(-0.560659\pi\)
−0.189415 + 0.981897i \(0.560659\pi\)
\(108\) 8.67327e67 0.658396
\(109\) −5.60552e67 −0.312484 −0.156242 0.987719i \(-0.549938\pi\)
−0.156242 + 0.987719i \(0.549938\pi\)
\(110\) −3.80430e68 −1.56178
\(111\) −3.13483e67 −0.0950373
\(112\) 1.73460e69 3.89399
\(113\) −9.31318e66 −0.0155228 −0.00776140 0.999970i \(-0.502471\pi\)
−0.00776140 + 0.999970i \(0.502471\pi\)
\(114\) 1.19713e67 0.0148535
\(115\) 1.17376e68 0.108693
\(116\) −3.18555e69 −2.20720
\(117\) 8.47427e67 0.0440429
\(118\) −5.94727e69 −2.32418
\(119\) 7.40733e69 2.18192
\(120\) 1.03326e69 0.229953
\(121\) 4.88014e69 0.822474
\(122\) −1.08399e70 −1.38667
\(123\) −1.13641e68 −0.0110589
\(124\) 1.99436e70 1.47971
\(125\) 1.76577e70 1.00103
\(126\) −6.07183e70 −2.63576
\(127\) 2.79868e70 0.932243 0.466121 0.884721i \(-0.345651\pi\)
0.466121 + 0.884721i \(0.345651\pi\)
\(128\) 2.39907e70 0.614480
\(129\) 4.30463e69 0.0849533
\(130\) 3.40458e69 0.0518754
\(131\) −2.72280e70 −0.320943 −0.160471 0.987040i \(-0.551301\pi\)
−0.160471 + 0.987040i \(0.551301\pi\)
\(132\) −4.90790e70 −0.448403
\(133\) −1.20672e70 −0.0856204
\(134\) −5.36578e71 −2.96225
\(135\) −3.80449e70 −0.163725
\(136\) 1.25831e72 4.22896
\(137\) 3.57817e70 0.0940853 0.0470427 0.998893i \(-0.485020\pi\)
0.0470427 + 0.998893i \(0.485020\pi\)
\(138\) 2.12235e70 0.0437389
\(139\) 7.45641e71 1.20652 0.603259 0.797545i \(-0.293869\pi\)
0.603259 + 0.797545i \(0.293869\pi\)
\(140\) −1.74047e72 −2.21501
\(141\) 1.72561e71 0.173022
\(142\) 5.35799e71 0.423977
\(143\) −9.67743e70 −0.0605345
\(144\) −5.37607e72 −2.66269
\(145\) 1.39733e72 0.548871
\(146\) 1.78391e72 0.556611
\(147\) −5.71311e71 −0.141822
\(148\) 8.97004e72 1.77430
\(149\) 1.30102e72 0.205373 0.102686 0.994714i \(-0.467256\pi\)
0.102686 + 0.994714i \(0.467256\pi\)
\(150\) 1.21770e72 0.153633
\(151\) −1.36349e73 −1.37697 −0.688486 0.725250i \(-0.741724\pi\)
−0.688486 + 0.725250i \(0.741724\pi\)
\(152\) −2.04990e72 −0.165948
\(153\) −2.29577e73 −1.49199
\(154\) 6.93390e73 3.62271
\(155\) −8.74816e72 −0.367963
\(156\) 4.39222e71 0.0148940
\(157\) −1.66635e73 −0.456171 −0.228085 0.973641i \(-0.573247\pi\)
−0.228085 + 0.973641i \(0.573247\pi\)
\(158\) −6.23209e73 −1.37918
\(159\) 4.97576e72 0.0891366
\(160\) −9.72577e73 −1.41223
\(161\) −2.13936e73 −0.252125
\(162\) 1.84715e74 1.76909
\(163\) −9.35739e70 −0.000729239 0 −0.000364620 1.00000i \(-0.500116\pi\)
−0.000364620 1.00000i \(0.500116\pi\)
\(164\) 3.25174e73 0.206465
\(165\) 2.15283e73 0.111506
\(166\) 2.08027e74 0.880035
\(167\) 4.79288e74 1.65804 0.829019 0.559220i \(-0.188899\pi\)
0.829019 + 0.559220i \(0.188899\pi\)
\(168\) −1.88327e74 −0.533398
\(169\) −4.29863e74 −0.997989
\(170\) −9.22337e74 −1.75732
\(171\) 3.74002e73 0.0585469
\(172\) −1.23173e75 −1.58604
\(173\) 1.22221e75 1.29599 0.647995 0.761645i \(-0.275608\pi\)
0.647995 + 0.761645i \(0.275608\pi\)
\(174\) 2.52659e74 0.220869
\(175\) −1.22746e75 −0.885592
\(176\) 6.13935e75 3.65972
\(177\) 3.36552e74 0.165939
\(178\) −7.62856e75 −3.11438
\(179\) −1.85195e75 −0.626689 −0.313344 0.949640i \(-0.601449\pi\)
−0.313344 + 0.949640i \(0.601449\pi\)
\(180\) 5.39426e75 1.51462
\(181\) 4.04550e75 0.943497 0.471748 0.881733i \(-0.343623\pi\)
0.471748 + 0.881733i \(0.343623\pi\)
\(182\) −6.20535e74 −0.120330
\(183\) 6.13424e74 0.0990032
\(184\) −3.63420e75 −0.488666
\(185\) −3.93467e75 −0.441220
\(186\) −1.58180e75 −0.148071
\(187\) 2.62172e76 2.05065
\(188\) −4.93767e76 −3.23024
\(189\) 6.93425e75 0.379777
\(190\) 1.50257e75 0.0689587
\(191\) 8.00578e74 0.0308167 0.0154083 0.999881i \(-0.495095\pi\)
0.0154083 + 0.999881i \(0.495095\pi\)
\(192\) −6.39620e75 −0.206695
\(193\) −5.34503e76 −1.45138 −0.725688 0.688024i \(-0.758478\pi\)
−0.725688 + 0.688024i \(0.758478\pi\)
\(194\) 1.47587e77 3.37047
\(195\) −1.92663e74 −0.00370372
\(196\) 1.63476e77 2.64774
\(197\) 2.95191e75 0.0403166 0.0201583 0.999797i \(-0.493583\pi\)
0.0201583 + 0.999797i \(0.493583\pi\)
\(198\) −2.14904e77 −2.47719
\(199\) −1.57308e77 −1.53170 −0.765850 0.643019i \(-0.777682\pi\)
−0.765850 + 0.643019i \(0.777682\pi\)
\(200\) −2.08513e77 −1.71644
\(201\) 3.03645e76 0.211494
\(202\) 4.53788e77 2.67659
\(203\) −2.54684e77 −1.27316
\(204\) −1.18990e77 −0.504544
\(205\) −1.42636e76 −0.0513422
\(206\) 4.57216e77 1.39820
\(207\) 6.63056e76 0.172402
\(208\) −5.49428e76 −0.121560
\(209\) −4.27102e76 −0.0804694
\(210\) 1.38043e77 0.221651
\(211\) 9.28985e77 1.27217 0.636087 0.771618i \(-0.280552\pi\)
0.636087 + 0.771618i \(0.280552\pi\)
\(212\) −1.42377e78 −1.66414
\(213\) −3.03205e76 −0.0302705
\(214\) −8.29337e77 −0.707734
\(215\) 5.40294e77 0.394404
\(216\) 1.17794e78 0.736078
\(217\) 1.59448e78 0.853528
\(218\) −1.27217e78 −0.583786
\(219\) −1.00950e77 −0.0397401
\(220\) −6.16013e78 −2.08176
\(221\) −2.34625e77 −0.0681135
\(222\) −7.11450e77 −0.177550
\(223\) −6.42241e78 −1.37875 −0.689374 0.724406i \(-0.742114\pi\)
−0.689374 + 0.724406i \(0.742114\pi\)
\(224\) 1.77266e79 3.27580
\(225\) 3.80430e78 0.605565
\(226\) −2.11363e77 −0.0289999
\(227\) 1.17887e79 1.39509 0.697543 0.716543i \(-0.254277\pi\)
0.697543 + 0.716543i \(0.254277\pi\)
\(228\) 1.93845e77 0.0197988
\(229\) −1.55534e79 −1.37194 −0.685972 0.727628i \(-0.740623\pi\)
−0.685972 + 0.727628i \(0.740623\pi\)
\(230\) 2.66386e78 0.203062
\(231\) −3.92384e78 −0.258649
\(232\) −4.32640e79 −2.46762
\(233\) 1.81926e79 0.898403 0.449201 0.893431i \(-0.351709\pi\)
0.449201 + 0.893431i \(0.351709\pi\)
\(234\) 1.92324e78 0.0822814
\(235\) 2.16589e79 0.803272
\(236\) −9.63014e79 −3.09799
\(237\) 3.52669e78 0.0984687
\(238\) 1.68109e80 4.07628
\(239\) −2.13612e79 −0.450087 −0.225043 0.974349i \(-0.572252\pi\)
−0.225043 + 0.974349i \(0.572252\pi\)
\(240\) 1.22225e79 0.223915
\(241\) −3.27834e79 −0.522497 −0.261248 0.965272i \(-0.584134\pi\)
−0.261248 + 0.965272i \(0.584134\pi\)
\(242\) 1.10755e80 1.53655
\(243\) −3.23336e79 −0.390701
\(244\) −1.75526e80 −1.84834
\(245\) −7.17080e79 −0.658421
\(246\) −2.57908e78 −0.0206604
\(247\) 3.82226e77 0.00267283
\(248\) 2.70860e80 1.65430
\(249\) −1.17721e79 −0.0628314
\(250\) 4.00742e80 1.87014
\(251\) −2.97257e80 −1.21356 −0.606782 0.794868i \(-0.707540\pi\)
−0.606782 + 0.794868i \(0.707540\pi\)
\(252\) −9.83183e80 −3.51331
\(253\) −7.57195e79 −0.236957
\(254\) 6.35161e80 1.74162
\(255\) 5.21943e79 0.125466
\(256\) −1.90498e80 −0.401653
\(257\) 2.91395e80 0.539166 0.269583 0.962977i \(-0.413114\pi\)
0.269583 + 0.962977i \(0.413114\pi\)
\(258\) 9.76935e79 0.158710
\(259\) 7.17151e80 1.02345
\(260\) 5.51288e79 0.0691467
\(261\) 7.89346e80 0.870583
\(262\) −6.17940e80 −0.599588
\(263\) 8.50029e79 0.0725966 0.0362983 0.999341i \(-0.488443\pi\)
0.0362983 + 0.999341i \(0.488443\pi\)
\(264\) −6.66556e80 −0.501309
\(265\) 6.24531e80 0.413826
\(266\) −2.73866e80 −0.159957
\(267\) 4.31694e80 0.222356
\(268\) −8.68855e81 −3.94850
\(269\) −1.19177e81 −0.478070 −0.239035 0.971011i \(-0.576831\pi\)
−0.239035 + 0.971011i \(0.576831\pi\)
\(270\) −8.63430e80 −0.305873
\(271\) 3.56294e81 1.11516 0.557580 0.830123i \(-0.311730\pi\)
0.557580 + 0.830123i \(0.311730\pi\)
\(272\) 1.48846e82 4.11793
\(273\) 3.51156e79 0.00859115
\(274\) 8.12066e80 0.175771
\(275\) −4.34443e81 −0.832314
\(276\) 3.43662e80 0.0583012
\(277\) −1.14305e82 −1.71787 −0.858937 0.512081i \(-0.828875\pi\)
−0.858937 + 0.512081i \(0.828875\pi\)
\(278\) 1.69223e82 2.25403
\(279\) −4.94180e81 −0.583640
\(280\) −2.36378e82 −2.47636
\(281\) 1.56122e82 1.45145 0.725727 0.687983i \(-0.241504\pi\)
0.725727 + 0.687983i \(0.241504\pi\)
\(282\) 3.91626e81 0.323241
\(283\) −9.49072e81 −0.695751 −0.347875 0.937541i \(-0.613097\pi\)
−0.347875 + 0.937541i \(0.613097\pi\)
\(284\) 8.67594e81 0.565135
\(285\) −8.50294e79 −0.00492341
\(286\) −2.19629e81 −0.113091
\(287\) 2.59975e81 0.119094
\(288\) −5.49405e82 −2.23998
\(289\) 3.60152e82 1.30740
\(290\) 3.17124e82 1.02541
\(291\) −8.35184e81 −0.240640
\(292\) 2.88860e82 0.741928
\(293\) −8.72184e82 −1.99776 −0.998879 0.0473268i \(-0.984930\pi\)
−0.998879 + 0.0473268i \(0.984930\pi\)
\(294\) −1.29659e82 −0.264952
\(295\) 4.22422e82 0.770387
\(296\) 1.21825e83 1.98364
\(297\) 2.45428e82 0.356930
\(298\) 2.95266e82 0.383679
\(299\) 6.77636e80 0.00787067
\(300\) 1.97177e82 0.204783
\(301\) −9.84764e82 −0.914860
\(302\) −3.09445e83 −2.57247
\(303\) −2.56795e82 −0.191099
\(304\) −2.42484e82 −0.161591
\(305\) 7.69937e82 0.459632
\(306\) −5.21025e83 −2.78734
\(307\) 1.53054e83 0.734021 0.367010 0.930217i \(-0.380381\pi\)
0.367010 + 0.930217i \(0.380381\pi\)
\(308\) 1.12277e84 4.82884
\(309\) −2.58735e82 −0.0998266
\(310\) −1.98540e83 −0.687433
\(311\) −5.46579e82 −0.169895 −0.0849473 0.996385i \(-0.527072\pi\)
−0.0849473 + 0.996385i \(0.527072\pi\)
\(312\) 5.96521e81 0.0166512
\(313\) 3.36258e83 0.843214 0.421607 0.906779i \(-0.361466\pi\)
0.421607 + 0.906779i \(0.361466\pi\)
\(314\) −3.78178e83 −0.852222
\(315\) 4.31269e83 0.873664
\(316\) −1.00913e84 −1.83836
\(317\) 6.50933e83 1.06672 0.533360 0.845888i \(-0.320929\pi\)
0.533360 + 0.845888i \(0.320929\pi\)
\(318\) 1.12925e83 0.166526
\(319\) −9.01416e83 −1.19657
\(320\) −8.02817e83 −0.959604
\(321\) 4.69316e82 0.0505297
\(322\) −4.85528e83 −0.471023
\(323\) −1.03549e83 −0.0905443
\(324\) 2.99100e84 2.35808
\(325\) 3.88796e82 0.0276458
\(326\) −2.12366e81 −0.00136237
\(327\) 7.19914e82 0.0416803
\(328\) 4.41628e83 0.230825
\(329\) −3.94765e84 −1.86327
\(330\) 4.88584e83 0.208316
\(331\) −2.75141e84 −1.06003 −0.530014 0.847989i \(-0.677813\pi\)
−0.530014 + 0.847989i \(0.677813\pi\)
\(332\) 3.36849e84 1.17303
\(333\) −2.22268e84 −0.699835
\(334\) 1.08774e85 3.09756
\(335\) 3.81119e84 0.981883
\(336\) −2.22773e84 −0.519394
\(337\) 8.52892e83 0.180008 0.0900041 0.995941i \(-0.471312\pi\)
0.0900041 + 0.995941i \(0.471312\pi\)
\(338\) −9.75576e84 −1.86445
\(339\) 1.19609e82 0.00207049
\(340\) −1.49350e85 −2.34240
\(341\) 5.64343e84 0.802180
\(342\) 8.48797e83 0.109378
\(343\) 7.77614e83 0.0908681
\(344\) −1.67285e85 −1.77317
\(345\) −1.50746e83 −0.0144979
\(346\) 2.77381e85 2.42118
\(347\) 1.21189e84 0.0960340 0.0480170 0.998847i \(-0.484710\pi\)
0.0480170 + 0.998847i \(0.484710\pi\)
\(348\) 4.09118e84 0.294404
\(349\) 1.49172e85 0.975067 0.487534 0.873104i \(-0.337897\pi\)
0.487534 + 0.873104i \(0.337897\pi\)
\(350\) −2.78573e85 −1.65447
\(351\) −2.19640e83 −0.0118556
\(352\) 6.27409e85 3.07873
\(353\) 3.26597e84 0.145734 0.0728668 0.997342i \(-0.476785\pi\)
0.0728668 + 0.997342i \(0.476785\pi\)
\(354\) 7.63804e84 0.310008
\(355\) −3.80566e84 −0.140534
\(356\) −1.23526e86 −4.15128
\(357\) −9.51318e84 −0.291032
\(358\) −4.20300e85 −1.17079
\(359\) 2.09151e85 0.530636 0.265318 0.964161i \(-0.414523\pi\)
0.265318 + 0.964161i \(0.414523\pi\)
\(360\) 7.32611e85 1.69332
\(361\) −4.73092e85 −0.996447
\(362\) 9.18128e85 1.76265
\(363\) −6.26754e84 −0.109705
\(364\) −1.00480e85 −0.160393
\(365\) −1.26707e85 −0.184497
\(366\) 1.39217e85 0.184959
\(367\) 7.55910e85 0.916552 0.458276 0.888810i \(-0.348467\pi\)
0.458276 + 0.888810i \(0.348467\pi\)
\(368\) −4.29892e85 −0.475836
\(369\) −8.05746e84 −0.0814357
\(370\) −8.92974e85 −0.824292
\(371\) −1.13830e86 −0.959911
\(372\) −2.56134e85 −0.197369
\(373\) 1.75561e86 1.23647 0.618233 0.785995i \(-0.287849\pi\)
0.618233 + 0.785995i \(0.287849\pi\)
\(374\) 5.94999e86 3.83105
\(375\) −2.26777e85 −0.133521
\(376\) −6.70600e86 −3.61136
\(377\) 8.06703e84 0.0397446
\(378\) 1.57373e86 0.709503
\(379\) −2.06583e86 −0.852475 −0.426237 0.904611i \(-0.640161\pi\)
−0.426237 + 0.904611i \(0.640161\pi\)
\(380\) 2.43304e85 0.0919177
\(381\) −3.59433e85 −0.124346
\(382\) 1.81691e85 0.0575720
\(383\) 1.50230e86 0.436111 0.218055 0.975936i \(-0.430029\pi\)
0.218055 + 0.975936i \(0.430029\pi\)
\(384\) −3.08110e85 −0.0819616
\(385\) −4.92500e86 −1.20080
\(386\) −1.21305e87 −2.71147
\(387\) 3.05210e86 0.625578
\(388\) 2.38981e87 4.49263
\(389\) −6.44644e86 −1.11175 −0.555876 0.831265i \(-0.687617\pi\)
−0.555876 + 0.831265i \(0.687617\pi\)
\(390\) −4.37248e84 −0.00691933
\(391\) −1.83579e86 −0.266625
\(392\) 2.22022e87 2.96014
\(393\) 3.49688e85 0.0428085
\(394\) 6.69936e85 0.0753199
\(395\) 4.42652e86 0.457151
\(396\) −3.47984e87 −3.30195
\(397\) 1.17131e87 1.02139 0.510694 0.859762i \(-0.329388\pi\)
0.510694 + 0.859762i \(0.329388\pi\)
\(398\) −3.57012e87 −2.86154
\(399\) 1.54978e85 0.0114203
\(400\) −2.46651e87 −1.67138
\(401\) 2.38898e87 1.48894 0.744469 0.667657i \(-0.232703\pi\)
0.744469 + 0.667657i \(0.232703\pi\)
\(402\) 6.89123e86 0.395116
\(403\) −5.05047e85 −0.0266448
\(404\) 7.34797e87 3.56773
\(405\) −1.31199e87 −0.586391
\(406\) −5.78005e87 −2.37853
\(407\) 2.53825e87 0.961883
\(408\) −1.61604e87 −0.564074
\(409\) 2.85528e87 0.918159 0.459079 0.888395i \(-0.348179\pi\)
0.459079 + 0.888395i \(0.348179\pi\)
\(410\) −3.23713e86 −0.0959181
\(411\) −4.59542e85 −0.0125494
\(412\) 7.40348e87 1.86371
\(413\) −7.69926e87 −1.78699
\(414\) 1.50481e87 0.322084
\(415\) −1.47757e87 −0.291701
\(416\) −5.61486e86 −0.102262
\(417\) −9.57622e86 −0.160930
\(418\) −9.69308e86 −0.150334
\(419\) −3.71561e87 −0.531937 −0.265969 0.963982i \(-0.585692\pi\)
−0.265969 + 0.963982i \(0.585692\pi\)
\(420\) 2.23527e87 0.295446
\(421\) −8.25851e87 −1.00798 −0.503990 0.863710i \(-0.668135\pi\)
−0.503990 + 0.863710i \(0.668135\pi\)
\(422\) 2.10833e88 2.37669
\(423\) 1.22350e88 1.27410
\(424\) −1.93367e88 −1.86048
\(425\) −1.05329e88 −0.936522
\(426\) −6.88123e86 −0.0565516
\(427\) −1.40332e88 −1.06616
\(428\) −1.34291e88 −0.943365
\(429\) 1.24287e86 0.00807431
\(430\) 1.22620e88 0.736830
\(431\) 2.02458e88 1.12550 0.562750 0.826627i \(-0.309743\pi\)
0.562750 + 0.826627i \(0.309743\pi\)
\(432\) 1.39340e88 0.716752
\(433\) 2.20914e88 1.05167 0.525835 0.850587i \(-0.323753\pi\)
0.525835 + 0.850587i \(0.323753\pi\)
\(434\) 3.61867e88 1.59457
\(435\) −1.79458e87 −0.0732104
\(436\) −2.05997e88 −0.778151
\(437\) 2.99067e86 0.0104626
\(438\) −2.29106e87 −0.0742428
\(439\) 4.98644e86 0.0149703 0.00748513 0.999972i \(-0.497617\pi\)
0.00748513 + 0.999972i \(0.497617\pi\)
\(440\) −8.36626e88 −2.32738
\(441\) −4.05076e88 −1.04434
\(442\) −5.32482e87 −0.127250
\(443\) 4.20816e88 0.932324 0.466162 0.884699i \(-0.345636\pi\)
0.466162 + 0.884699i \(0.345636\pi\)
\(444\) −1.15202e88 −0.236662
\(445\) 5.41840e88 1.03231
\(446\) −1.45757e89 −2.57579
\(447\) −1.67089e87 −0.0273933
\(448\) 1.46325e89 2.22590
\(449\) −5.36803e88 −0.757814 −0.378907 0.925435i \(-0.623700\pi\)
−0.378907 + 0.925435i \(0.623700\pi\)
\(450\) 8.63386e88 1.13132
\(451\) 9.20144e87 0.111929
\(452\) −3.42250e87 −0.0386550
\(453\) 1.75112e88 0.183665
\(454\) 2.67546e89 2.60631
\(455\) 4.40752e87 0.0398853
\(456\) 2.63267e87 0.0221347
\(457\) −2.47901e89 −1.93680 −0.968401 0.249399i \(-0.919767\pi\)
−0.968401 + 0.249399i \(0.919767\pi\)
\(458\) −3.52984e89 −2.56308
\(459\) 5.95029e88 0.401618
\(460\) 4.31347e88 0.270669
\(461\) 1.39269e89 0.812593 0.406297 0.913741i \(-0.366820\pi\)
0.406297 + 0.913741i \(0.366820\pi\)
\(462\) −8.90517e88 −0.483210
\(463\) 2.69968e89 1.36254 0.681271 0.732032i \(-0.261428\pi\)
0.681271 + 0.732032i \(0.261428\pi\)
\(464\) −5.11772e89 −2.40283
\(465\) 1.12352e88 0.0490803
\(466\) 4.12881e89 1.67840
\(467\) 3.76688e89 1.42517 0.712584 0.701586i \(-0.247525\pi\)
0.712584 + 0.701586i \(0.247525\pi\)
\(468\) 3.11421e88 0.109676
\(469\) −6.94646e89 −2.27758
\(470\) 4.91549e89 1.50068
\(471\) 2.14008e88 0.0608457
\(472\) −1.30790e90 −3.46352
\(473\) −3.48543e89 −0.859822
\(474\) 8.00383e88 0.183960
\(475\) 1.71590e88 0.0367499
\(476\) 2.72212e90 5.43343
\(477\) 3.52796e89 0.656383
\(478\) −4.84793e89 −0.840857
\(479\) −6.97444e89 −1.12790 −0.563949 0.825810i \(-0.690718\pi\)
−0.563949 + 0.825810i \(0.690718\pi\)
\(480\) 1.24907e89 0.188368
\(481\) −2.27156e88 −0.0319495
\(482\) −7.44020e89 −0.976133
\(483\) 2.74757e88 0.0336294
\(484\) 1.79340e90 2.04813
\(485\) −1.04828e90 −1.11719
\(486\) −7.33812e89 −0.729911
\(487\) 2.50021e89 0.232143 0.116072 0.993241i \(-0.462970\pi\)
0.116072 + 0.993241i \(0.462970\pi\)
\(488\) −2.38387e90 −2.06642
\(489\) 1.20176e86 9.72686e−5 0
\(490\) −1.62741e90 −1.23007
\(491\) 2.37132e90 1.67402 0.837009 0.547189i \(-0.184302\pi\)
0.837009 + 0.547189i \(0.184302\pi\)
\(492\) −4.17619e88 −0.0275390
\(493\) −2.18544e90 −1.34638
\(494\) 8.67462e87 0.00499341
\(495\) 1.52641e90 0.821104
\(496\) 3.20401e90 1.61086
\(497\) 6.93638e89 0.325982
\(498\) −2.67168e89 −0.117382
\(499\) 3.70263e90 1.52104 0.760522 0.649312i \(-0.224943\pi\)
0.760522 + 0.649312i \(0.224943\pi\)
\(500\) 6.48902e90 2.49278
\(501\) −6.15546e89 −0.221155
\(502\) −6.74626e90 −2.26719
\(503\) 3.39121e90 1.06617 0.533086 0.846061i \(-0.321032\pi\)
0.533086 + 0.846061i \(0.321032\pi\)
\(504\) −1.33529e91 −3.92783
\(505\) −3.22316e90 −0.887197
\(506\) −1.71846e90 −0.442686
\(507\) 5.52071e89 0.133115
\(508\) 1.02849e91 2.32148
\(509\) −6.34938e89 −0.134179 −0.0670897 0.997747i \(-0.521371\pi\)
−0.0670897 + 0.997747i \(0.521371\pi\)
\(510\) 1.18455e90 0.234398
\(511\) 2.30942e90 0.427960
\(512\) −7.86374e90 −1.36485
\(513\) −9.69356e88 −0.0157598
\(514\) 6.61321e90 1.00727
\(515\) −3.24750e90 −0.463455
\(516\) 1.58191e90 0.211551
\(517\) −1.39721e91 −1.75117
\(518\) 1.62758e91 1.91203
\(519\) −1.56968e90 −0.172864
\(520\) 7.48721e89 0.0773051
\(521\) −6.72297e90 −0.650874 −0.325437 0.945564i \(-0.605511\pi\)
−0.325437 + 0.945564i \(0.605511\pi\)
\(522\) 1.79142e91 1.62643
\(523\) −3.61652e90 −0.307953 −0.153977 0.988075i \(-0.549208\pi\)
−0.153977 + 0.988075i \(0.549208\pi\)
\(524\) −1.00060e91 −0.799214
\(525\) 1.57642e90 0.118123
\(526\) 1.92914e90 0.135626
\(527\) 1.36823e91 0.902614
\(528\) −7.88473e90 −0.488147
\(529\) −1.66792e91 −0.969191
\(530\) 1.41738e91 0.773113
\(531\) 2.38625e91 1.22194
\(532\) −4.43458e90 −0.213212
\(533\) −8.23464e88 −0.00371777
\(534\) 9.79731e90 0.415408
\(535\) 5.89060e90 0.234589
\(536\) −1.18002e92 −4.41437
\(537\) 2.37844e90 0.0835900
\(538\) −2.70473e91 −0.893135
\(539\) 4.62588e91 1.43539
\(540\) −1.39811e91 −0.407710
\(541\) −5.31972e91 −1.45808 −0.729039 0.684472i \(-0.760033\pi\)
−0.729039 + 0.684472i \(0.760033\pi\)
\(542\) 8.08610e91 2.08335
\(543\) −5.19562e90 −0.125847
\(544\) 1.52113e92 3.46419
\(545\) 9.03597e90 0.193505
\(546\) 7.96949e89 0.0160501
\(547\) −1.75688e90 −0.0332788 −0.0166394 0.999862i \(-0.505297\pi\)
−0.0166394 + 0.999862i \(0.505297\pi\)
\(548\) 1.31494e91 0.234292
\(549\) 4.34935e91 0.729039
\(550\) −9.85968e91 −1.55494
\(551\) 3.56029e90 0.0528331
\(552\) 4.66738e90 0.0651800
\(553\) −8.06798e91 −1.06041
\(554\) −2.59414e92 −3.20935
\(555\) 5.05327e90 0.0588515
\(556\) 2.74015e92 3.00448
\(557\) 4.64449e91 0.479500 0.239750 0.970835i \(-0.422935\pi\)
0.239750 + 0.970835i \(0.422935\pi\)
\(558\) −1.12154e92 −1.09036
\(559\) 3.11921e90 0.0285594
\(560\) −2.79613e92 −2.41134
\(561\) −3.36705e91 −0.273523
\(562\) 3.54320e92 2.71162
\(563\) 8.66238e90 0.0624606 0.0312303 0.999512i \(-0.490057\pi\)
0.0312303 + 0.999512i \(0.490057\pi\)
\(564\) 6.34142e91 0.430860
\(565\) 1.50126e90 0.00961245
\(566\) −2.15392e92 −1.29981
\(567\) 2.39130e92 1.36019
\(568\) 1.17831e92 0.631813
\(569\) 1.65010e92 0.834162 0.417081 0.908869i \(-0.363053\pi\)
0.417081 + 0.908869i \(0.363053\pi\)
\(570\) −1.92974e90 −0.00919796
\(571\) −3.09486e92 −1.39101 −0.695507 0.718519i \(-0.744820\pi\)
−0.695507 + 0.718519i \(0.744820\pi\)
\(572\) −3.55636e91 −0.150743
\(573\) −1.02818e90 −0.00411044
\(574\) 5.90014e91 0.222492
\(575\) 3.04207e91 0.108217
\(576\) −4.53508e92 −1.52206
\(577\) −4.88740e92 −1.54771 −0.773853 0.633366i \(-0.781673\pi\)
−0.773853 + 0.633366i \(0.781673\pi\)
\(578\) 8.17365e92 2.44249
\(579\) 6.86459e91 0.193590
\(580\) 5.13504e92 1.36680
\(581\) 2.69309e92 0.676630
\(582\) −1.89545e92 −0.449565
\(583\) −4.02885e92 −0.902162
\(584\) 3.92310e92 0.829466
\(585\) −1.36603e91 −0.0272734
\(586\) −1.97942e93 −3.73223
\(587\) −4.93586e92 −0.878995 −0.439498 0.898244i \(-0.644843\pi\)
−0.439498 + 0.898244i \(0.644843\pi\)
\(588\) −2.09951e92 −0.353165
\(589\) −2.22896e91 −0.0354194
\(590\) 9.58687e92 1.43924
\(591\) −3.79112e90 −0.00537758
\(592\) 1.44107e93 1.93156
\(593\) 8.91235e92 1.12891 0.564456 0.825463i \(-0.309086\pi\)
0.564456 + 0.825463i \(0.309086\pi\)
\(594\) 5.56999e92 0.666819
\(595\) −1.19404e93 −1.35115
\(596\) 4.78110e92 0.511420
\(597\) 2.02030e92 0.204304
\(598\) 1.53790e91 0.0147041
\(599\) 1.27437e92 0.115212 0.0576059 0.998339i \(-0.481653\pi\)
0.0576059 + 0.998339i \(0.481653\pi\)
\(600\) 2.67792e92 0.228945
\(601\) 1.93861e93 1.56746 0.783728 0.621104i \(-0.213316\pi\)
0.783728 + 0.621104i \(0.213316\pi\)
\(602\) −2.23492e93 −1.70915
\(603\) 2.15293e93 1.55740
\(604\) −5.01069e93 −3.42894
\(605\) −7.86668e92 −0.509315
\(606\) −5.82797e92 −0.357013
\(607\) 4.21833e92 0.244523 0.122261 0.992498i \(-0.460985\pi\)
0.122261 + 0.992498i \(0.460985\pi\)
\(608\) −2.47805e92 −0.135938
\(609\) 3.27089e92 0.169819
\(610\) 1.74737e93 0.858690
\(611\) 1.25041e92 0.0581662
\(612\) −8.43671e93 −3.71536
\(613\) −8.48939e92 −0.353957 −0.176979 0.984215i \(-0.556632\pi\)
−0.176979 + 0.984215i \(0.556632\pi\)
\(614\) 3.47356e93 1.37130
\(615\) 1.83187e91 0.00684821
\(616\) 1.52487e94 5.39859
\(617\) 5.31064e93 1.78071 0.890357 0.455263i \(-0.150455\pi\)
0.890357 + 0.455263i \(0.150455\pi\)
\(618\) −5.87200e92 −0.186497
\(619\) −5.93673e93 −1.78612 −0.893060 0.449937i \(-0.851446\pi\)
−0.893060 + 0.449937i \(0.851446\pi\)
\(620\) −3.21486e93 −0.916305
\(621\) −1.71854e92 −0.0464079
\(622\) −1.24046e93 −0.317399
\(623\) −9.87582e93 −2.39455
\(624\) 7.05628e91 0.0162141
\(625\) −1.53972e91 −0.00335322
\(626\) 7.63139e93 1.57530
\(627\) 5.48524e91 0.0107333
\(628\) −6.12366e93 −1.13596
\(629\) 6.15389e93 1.08231
\(630\) 9.78766e93 1.63219
\(631\) −4.19002e93 −0.662572 −0.331286 0.943530i \(-0.607482\pi\)
−0.331286 + 0.943530i \(0.607482\pi\)
\(632\) −1.37053e94 −2.05527
\(633\) −1.19309e93 −0.169687
\(634\) 1.47729e94 1.99286
\(635\) −4.51141e93 −0.577288
\(636\) 1.82854e93 0.221969
\(637\) −4.13983e92 −0.0476773
\(638\) −2.04576e94 −2.23544
\(639\) −2.14981e93 −0.222905
\(640\) −3.86724e93 −0.380515
\(641\) 1.17710e94 1.09919 0.549593 0.835433i \(-0.314783\pi\)
0.549593 + 0.835433i \(0.314783\pi\)
\(642\) 1.06511e93 0.0944000
\(643\) 2.15010e94 1.80880 0.904400 0.426686i \(-0.140319\pi\)
0.904400 + 0.426686i \(0.140319\pi\)
\(644\) −7.86192e93 −0.627845
\(645\) −6.93896e92 −0.0526070
\(646\) −2.35004e93 −0.169156
\(647\) −5.59785e93 −0.382585 −0.191292 0.981533i \(-0.561268\pi\)
−0.191292 + 0.981533i \(0.561268\pi\)
\(648\) 4.06218e94 2.63631
\(649\) −2.72504e94 −1.67948
\(650\) 8.82372e92 0.0516481
\(651\) −2.04778e93 −0.113847
\(652\) −3.43875e91 −0.00181596
\(653\) 3.65193e94 1.83202 0.916012 0.401150i \(-0.131389\pi\)
0.916012 + 0.401150i \(0.131389\pi\)
\(654\) 1.63384e93 0.0778675
\(655\) 4.38909e93 0.198743
\(656\) 5.22405e93 0.224765
\(657\) −7.15764e93 −0.292638
\(658\) −8.95919e94 −3.48098
\(659\) −2.31946e94 −0.856497 −0.428249 0.903661i \(-0.640869\pi\)
−0.428249 + 0.903661i \(0.640869\pi\)
\(660\) 7.91142e93 0.277672
\(661\) 1.29957e94 0.433563 0.216782 0.976220i \(-0.430444\pi\)
0.216782 + 0.976220i \(0.430444\pi\)
\(662\) −6.24433e94 −1.98035
\(663\) 3.01328e92 0.00908522
\(664\) 4.57485e94 1.31143
\(665\) 1.94521e93 0.0530201
\(666\) −5.04438e94 −1.30744
\(667\) 6.31192e93 0.155577
\(668\) 1.76133e95 4.12886
\(669\) 8.24826e93 0.183902
\(670\) 8.64951e94 1.83436
\(671\) −4.96686e94 −1.00202
\(672\) −2.27662e94 −0.436938
\(673\) 3.32902e94 0.607872 0.303936 0.952693i \(-0.401699\pi\)
0.303936 + 0.952693i \(0.401699\pi\)
\(674\) 1.93564e94 0.336293
\(675\) −9.86018e93 −0.163008
\(676\) −1.57970e95 −2.48520
\(677\) −7.15153e94 −1.07073 −0.535364 0.844622i \(-0.679825\pi\)
−0.535364 + 0.844622i \(0.679825\pi\)
\(678\) 2.71452e92 0.00386811
\(679\) 1.91064e95 2.59144
\(680\) −2.02836e95 −2.61877
\(681\) −1.51402e94 −0.186082
\(682\) 1.28078e95 1.49864
\(683\) −4.63147e94 −0.515971 −0.257985 0.966149i \(-0.583059\pi\)
−0.257985 + 0.966149i \(0.583059\pi\)
\(684\) 1.37442e94 0.145794
\(685\) −5.76793e93 −0.0582620
\(686\) 1.76480e94 0.169761
\(687\) 1.99751e94 0.182995
\(688\) −1.97883e95 −1.72661
\(689\) 3.60554e93 0.0299658
\(690\) −3.42118e93 −0.0270852
\(691\) 3.93163e94 0.296523 0.148261 0.988948i \(-0.452632\pi\)
0.148261 + 0.988948i \(0.452632\pi\)
\(692\) 4.49150e95 3.22728
\(693\) −2.78211e95 −1.90463
\(694\) 2.75038e94 0.179412
\(695\) −1.20196e95 −0.747132
\(696\) 5.55636e94 0.329140
\(697\) 2.23085e94 0.125942
\(698\) 3.38545e95 1.82163
\(699\) −2.33646e94 −0.119832
\(700\) −4.51080e95 −2.20531
\(701\) −2.12972e95 −0.992588 −0.496294 0.868154i \(-0.665306\pi\)
−0.496294 + 0.868154i \(0.665306\pi\)
\(702\) −4.98474e93 −0.0221488
\(703\) −1.00252e94 −0.0424709
\(704\) 5.17897e95 2.09199
\(705\) −2.78164e94 −0.107143
\(706\) 7.41213e94 0.272261
\(707\) 5.87467e95 2.05794
\(708\) 1.23679e95 0.413221
\(709\) −4.82912e94 −0.153893 −0.0769466 0.997035i \(-0.524517\pi\)
−0.0769466 + 0.997035i \(0.524517\pi\)
\(710\) −8.63695e94 −0.262546
\(711\) 2.50052e95 0.725103
\(712\) −1.67764e96 −4.64108
\(713\) −3.95166e94 −0.104299
\(714\) −2.15902e95 −0.543709
\(715\) 1.55998e94 0.0374858
\(716\) −6.80571e95 −1.56059
\(717\) 2.74341e94 0.0600342
\(718\) 4.74669e95 0.991339
\(719\) −3.57892e93 −0.00713401 −0.00356700 0.999994i \(-0.501135\pi\)
−0.00356700 + 0.999994i \(0.501135\pi\)
\(720\) 8.66610e95 1.64886
\(721\) 5.91905e95 1.07503
\(722\) −1.07368e96 −1.86157
\(723\) 4.21036e94 0.0696925
\(724\) 1.48668e96 2.34950
\(725\) 3.62148e95 0.546466
\(726\) −1.42242e95 −0.204951
\(727\) 1.13472e96 1.56129 0.780646 0.624973i \(-0.214890\pi\)
0.780646 + 0.624973i \(0.214890\pi\)
\(728\) −1.36465e95 −0.179317
\(729\) −7.13038e95 −0.894830
\(730\) −2.87562e95 −0.344680
\(731\) −8.45028e95 −0.967473
\(732\) 2.25427e95 0.246538
\(733\) −7.88530e95 −0.823826 −0.411913 0.911223i \(-0.635139\pi\)
−0.411913 + 0.911223i \(0.635139\pi\)
\(734\) 1.71554e96 1.71231
\(735\) 9.20941e94 0.0878225
\(736\) −4.39326e95 −0.400295
\(737\) −2.45860e96 −2.14056
\(738\) −1.82864e95 −0.152139
\(739\) 8.22688e95 0.654104 0.327052 0.945006i \(-0.393945\pi\)
0.327052 + 0.945006i \(0.393945\pi\)
\(740\) −1.44595e96 −1.09873
\(741\) −4.90890e92 −0.000356512 0
\(742\) −2.58337e96 −1.79331
\(743\) 1.18799e96 0.788293 0.394147 0.919048i \(-0.371040\pi\)
0.394147 + 0.919048i \(0.371040\pi\)
\(744\) −3.47863e95 −0.220656
\(745\) −2.09721e95 −0.127176
\(746\) 3.98436e96 2.30998
\(747\) −8.34676e95 −0.462677
\(748\) 9.63454e96 5.10655
\(749\) −1.07365e96 −0.544153
\(750\) −5.14670e95 −0.249446
\(751\) −2.90797e96 −1.34788 −0.673941 0.738785i \(-0.735400\pi\)
−0.673941 + 0.738785i \(0.735400\pi\)
\(752\) −7.93257e96 −3.51654
\(753\) 3.81766e95 0.161870
\(754\) 1.83081e95 0.0742513
\(755\) 2.19792e96 0.852685
\(756\) 2.54826e96 0.945724
\(757\) 1.73071e96 0.614487 0.307244 0.951631i \(-0.400593\pi\)
0.307244 + 0.951631i \(0.400593\pi\)
\(758\) −4.68841e96 −1.59260
\(759\) 9.72461e94 0.0316062
\(760\) 3.30439e95 0.102763
\(761\) 3.70707e96 1.10318 0.551588 0.834117i \(-0.314022\pi\)
0.551588 + 0.834117i \(0.314022\pi\)
\(762\) −8.15734e95 −0.232304
\(763\) −1.64694e96 −0.448854
\(764\) 2.94204e95 0.0767399
\(765\) 3.70073e96 0.923908
\(766\) 3.40947e96 0.814746
\(767\) 2.43872e95 0.0557849
\(768\) 2.44655e95 0.0535739
\(769\) −9.72162e95 −0.203801 −0.101900 0.994795i \(-0.532492\pi\)
−0.101900 + 0.994795i \(0.532492\pi\)
\(770\) −1.11773e97 −2.24335
\(771\) −3.74237e95 −0.0719158
\(772\) −1.96424e97 −3.61423
\(773\) −7.27011e95 −0.128094 −0.0640469 0.997947i \(-0.520401\pi\)
−0.0640469 + 0.997947i \(0.520401\pi\)
\(774\) 6.92675e96 1.16871
\(775\) −2.26728e96 −0.366351
\(776\) 3.24567e97 5.02270
\(777\) −9.21033e95 −0.136512
\(778\) −1.46302e97 −2.07699
\(779\) −3.63426e94 −0.00494209
\(780\) −7.08016e94 −0.00922303
\(781\) 2.45503e96 0.306371
\(782\) −4.16632e96 −0.498111
\(783\) −2.04587e96 −0.234346
\(784\) 2.62631e97 2.88242
\(785\) 2.68611e96 0.282482
\(786\) 7.93617e95 0.0799752
\(787\) −1.49904e96 −0.144764 −0.0723820 0.997377i \(-0.523060\pi\)
−0.0723820 + 0.997377i \(0.523060\pi\)
\(788\) 1.08480e96 0.100397
\(789\) −1.09169e95 −0.00968320
\(790\) 1.00460e97 0.854053
\(791\) −2.73627e95 −0.0222970
\(792\) −4.72607e97 −3.69153
\(793\) 4.44499e95 0.0332827
\(794\) 2.65830e97 1.90817
\(795\) −8.02082e95 −0.0551976
\(796\) −5.78092e97 −3.81425
\(797\) 1.40542e97 0.889107 0.444553 0.895752i \(-0.353362\pi\)
0.444553 + 0.895752i \(0.353362\pi\)
\(798\) 3.51724e95 0.0213356
\(799\) −3.38748e97 −1.97043
\(800\) −2.52065e97 −1.40604
\(801\) 3.06083e97 1.63738
\(802\) 5.42180e97 2.78165
\(803\) 8.17387e96 0.402214
\(804\) 1.11587e97 0.526664
\(805\) 3.44860e96 0.156128
\(806\) −1.14621e96 −0.0497781
\(807\) 1.53058e96 0.0637667
\(808\) 9.97951e97 3.98867
\(809\) −1.72375e97 −0.660996 −0.330498 0.943807i \(-0.607217\pi\)
−0.330498 + 0.943807i \(0.607217\pi\)
\(810\) −2.97757e97 −1.09550
\(811\) −3.10291e97 −1.09540 −0.547698 0.836676i \(-0.684496\pi\)
−0.547698 + 0.836676i \(0.684496\pi\)
\(812\) −9.35936e97 −3.17044
\(813\) −4.57586e96 −0.148744
\(814\) 5.76057e97 1.79700
\(815\) 1.50839e94 0.000451579 0
\(816\) −1.91162e97 −0.549264
\(817\) 1.37663e96 0.0379645
\(818\) 6.48006e97 1.71531
\(819\) 2.48980e96 0.0632635
\(820\) −5.24173e96 −0.127853
\(821\) −4.71160e97 −1.10325 −0.551623 0.834094i \(-0.685991\pi\)
−0.551623 + 0.834094i \(0.685991\pi\)
\(822\) −1.04293e96 −0.0234450
\(823\) −3.28396e97 −0.708766 −0.354383 0.935100i \(-0.615309\pi\)
−0.354383 + 0.935100i \(0.615309\pi\)
\(824\) 1.00549e98 2.08361
\(825\) 5.57952e96 0.111017
\(826\) −1.74735e98 −3.33847
\(827\) 1.14554e97 0.210172 0.105086 0.994463i \(-0.466488\pi\)
0.105086 + 0.994463i \(0.466488\pi\)
\(828\) 2.43666e97 0.429318
\(829\) 5.31404e97 0.899183 0.449591 0.893234i \(-0.351570\pi\)
0.449591 + 0.893234i \(0.351570\pi\)
\(830\) −3.35336e97 −0.544959
\(831\) 1.46801e97 0.229136
\(832\) −4.63481e96 −0.0694865
\(833\) 1.12152e98 1.61511
\(834\) −2.17332e97 −0.300650
\(835\) −7.72601e97 −1.02673
\(836\) −1.56955e97 −0.200385
\(837\) 1.28084e97 0.157106
\(838\) −8.43258e97 −0.993770
\(839\) 8.20510e97 0.929091 0.464545 0.885549i \(-0.346218\pi\)
0.464545 + 0.885549i \(0.346218\pi\)
\(840\) 3.03579e97 0.330305
\(841\) −2.05045e97 −0.214379
\(842\) −1.87427e98 −1.88312
\(843\) −2.00507e97 −0.193600
\(844\) 3.41392e98 3.16797
\(845\) 6.92930e97 0.618002
\(846\) 2.77674e98 2.38028
\(847\) 1.43382e98 1.18141
\(848\) −2.28735e98 −1.81164
\(849\) 1.21889e97 0.0928017
\(850\) −2.39044e98 −1.74962
\(851\) −1.77734e97 −0.125064
\(852\) −1.11425e97 −0.0753797
\(853\) −2.75788e97 −0.179384 −0.0896918 0.995970i \(-0.528588\pi\)
−0.0896918 + 0.995970i \(0.528588\pi\)
\(854\) −3.18484e98 −1.99182
\(855\) −6.02882e96 −0.0362550
\(856\) −1.82384e98 −1.05467
\(857\) −2.49466e98 −1.38725 −0.693624 0.720337i \(-0.743987\pi\)
−0.693624 + 0.720337i \(0.743987\pi\)
\(858\) 2.82069e96 0.0150845
\(859\) −5.28515e97 −0.271823 −0.135912 0.990721i \(-0.543396\pi\)
−0.135912 + 0.990721i \(0.543396\pi\)
\(860\) 1.98552e98 0.982148
\(861\) −3.33884e96 −0.0158851
\(862\) 4.59478e98 2.10267
\(863\) −1.41322e96 −0.00622084 −0.00311042 0.999995i \(-0.500990\pi\)
−0.00311042 + 0.999995i \(0.500990\pi\)
\(864\) 1.42398e98 0.602965
\(865\) −1.97018e98 −0.802537
\(866\) 5.01365e98 1.96474
\(867\) −4.62541e97 −0.174385
\(868\) 5.85955e98 2.12546
\(869\) −2.85554e98 −0.996613
\(870\) −4.07280e97 −0.136772
\(871\) 2.20027e97 0.0710998
\(872\) −2.79771e98 −0.869962
\(873\) −5.92169e98 −1.77202
\(874\) 6.78732e96 0.0195463
\(875\) 5.18794e98 1.43789
\(876\) −3.70981e97 −0.0989610
\(877\) 4.90704e98 1.25989 0.629946 0.776639i \(-0.283077\pi\)
0.629946 + 0.776639i \(0.283077\pi\)
\(878\) 1.13167e97 0.0279676
\(879\) 1.12014e98 0.266468
\(880\) −9.89649e98 −2.26627
\(881\) −1.83004e98 −0.403430 −0.201715 0.979444i \(-0.564651\pi\)
−0.201715 + 0.979444i \(0.564651\pi\)
\(882\) −9.19320e98 −1.95105
\(883\) 1.47514e98 0.301404 0.150702 0.988579i \(-0.451847\pi\)
0.150702 + 0.988579i \(0.451847\pi\)
\(884\) −8.62223e97 −0.169617
\(885\) −5.42514e97 −0.102757
\(886\) 9.55042e98 1.74178
\(887\) −4.64176e98 −0.815157 −0.407579 0.913170i \(-0.633627\pi\)
−0.407579 + 0.913170i \(0.633627\pi\)
\(888\) −1.56459e98 −0.264586
\(889\) 8.22271e98 1.33908
\(890\) 1.22971e99 1.92857
\(891\) 8.46365e98 1.27836
\(892\) −2.36017e99 −3.43337
\(893\) 5.51852e97 0.0773212
\(894\) −3.79208e97 −0.0511765
\(895\) 2.98530e98 0.388075
\(896\) 7.04861e98 0.882643
\(897\) −8.70284e95 −0.00104982
\(898\) −1.21828e99 −1.41576
\(899\) −4.70432e98 −0.526681
\(900\) 1.39804e99 1.50798
\(901\) −9.76777e98 −1.01511
\(902\) 2.08827e98 0.209106
\(903\) 1.26473e98 0.122027
\(904\) −4.64820e97 −0.0432158
\(905\) −6.52126e98 −0.584257
\(906\) 3.97418e98 0.343125
\(907\) 8.33172e98 0.693251 0.346626 0.938004i \(-0.387327\pi\)
0.346626 + 0.938004i \(0.387327\pi\)
\(908\) 4.33224e99 3.47405
\(909\) −1.82075e99 −1.40721
\(910\) 1.00029e98 0.0745141
\(911\) 1.45347e99 1.04362 0.521809 0.853062i \(-0.325257\pi\)
0.521809 + 0.853062i \(0.325257\pi\)
\(912\) 3.11420e97 0.0215536
\(913\) 9.53182e98 0.635924
\(914\) −5.62611e99 −3.61835
\(915\) −9.88826e97 −0.0613074
\(916\) −5.71571e99 −3.41643
\(917\) −7.99977e98 −0.461004
\(918\) 1.35042e99 0.750306
\(919\) 1.11251e99 0.595984 0.297992 0.954568i \(-0.403683\pi\)
0.297992 + 0.954568i \(0.403683\pi\)
\(920\) 5.85825e98 0.302605
\(921\) −1.96566e98 −0.0979063
\(922\) 3.16071e99 1.51809
\(923\) −2.19708e97 −0.0101763
\(924\) −1.44197e99 −0.644089
\(925\) −1.01976e99 −0.439287
\(926\) 6.12694e99 2.54551
\(927\) −1.83450e99 −0.735102
\(928\) −5.23003e99 −2.02138
\(929\) 3.66789e99 1.36738 0.683692 0.729771i \(-0.260373\pi\)
0.683692 + 0.729771i \(0.260373\pi\)
\(930\) 2.54983e98 0.0916923
\(931\) −1.82707e98 −0.0633782
\(932\) 6.68559e99 2.23721
\(933\) 7.01968e97 0.0226612
\(934\) 8.54894e99 2.66251
\(935\) −4.22615e99 −1.26986
\(936\) 4.22950e98 0.122616
\(937\) 1.86027e98 0.0520354 0.0260177 0.999661i \(-0.491717\pi\)
0.0260177 + 0.999661i \(0.491717\pi\)
\(938\) −1.57650e100 −4.25499
\(939\) −4.31854e98 −0.112471
\(940\) 7.95941e99 2.00031
\(941\) 4.09124e99 0.992208 0.496104 0.868263i \(-0.334763\pi\)
0.496104 + 0.868263i \(0.334763\pi\)
\(942\) 4.85692e98 0.113672
\(943\) −6.44306e97 −0.0145529
\(944\) −1.54712e100 −3.37258
\(945\) −1.11778e99 −0.235176
\(946\) −7.91019e99 −1.60633
\(947\) −4.63796e99 −0.909082 −0.454541 0.890726i \(-0.650197\pi\)
−0.454541 + 0.890726i \(0.650197\pi\)
\(948\) 1.29602e99 0.245207
\(949\) −7.31504e97 −0.0133598
\(950\) 3.89424e98 0.0686566
\(951\) −8.35989e98 −0.142283
\(952\) 3.69699e100 6.07450
\(953\) −2.75137e99 −0.436452 −0.218226 0.975898i \(-0.570027\pi\)
−0.218226 + 0.975898i \(0.570027\pi\)
\(954\) 8.00670e99 1.22626
\(955\) −1.29051e98 −0.0190831
\(956\) −7.85003e99 −1.12081
\(957\) 1.15768e99 0.159602
\(958\) −1.58285e100 −2.10715
\(959\) 1.05129e99 0.135145
\(960\) 1.03105e99 0.127995
\(961\) −5.39609e99 −0.646913
\(962\) −5.15530e98 −0.0596883
\(963\) 3.32758e99 0.372090
\(964\) −1.20476e100 −1.30112
\(965\) 8.61606e99 0.898760
\(966\) 6.23560e98 0.0628268
\(967\) 4.36496e99 0.424809 0.212404 0.977182i \(-0.431871\pi\)
0.212404 + 0.977182i \(0.431871\pi\)
\(968\) 2.43567e100 2.28978
\(969\) 1.32987e98 0.0120771
\(970\) −2.37907e100 −2.08715
\(971\) 6.33150e99 0.536614 0.268307 0.963333i \(-0.413536\pi\)
0.268307 + 0.963333i \(0.413536\pi\)
\(972\) −1.18823e100 −0.972926
\(973\) 2.19074e100 1.73305
\(974\) 5.67423e99 0.433692
\(975\) −4.99328e97 −0.00368749
\(976\) −2.81990e100 −2.01217
\(977\) 1.58929e100 1.09581 0.547905 0.836540i \(-0.315425\pi\)
0.547905 + 0.836540i \(0.315425\pi\)
\(978\) 2.72741e96 0.000181718 0
\(979\) −3.49541e100 −2.25049
\(980\) −2.63519e100 −1.63960
\(981\) 5.10439e99 0.306925
\(982\) 5.38171e100 3.12742
\(983\) 4.62180e97 0.00259578 0.00129789 0.999999i \(-0.499587\pi\)
0.00129789 + 0.999999i \(0.499587\pi\)
\(984\) −5.67181e98 −0.0307883
\(985\) −4.75841e98 −0.0249659
\(986\) −4.95987e100 −2.51532
\(987\) 5.06994e99 0.248530
\(988\) 1.40464e98 0.00665591
\(989\) 2.44058e99 0.111794
\(990\) 3.46420e100 1.53399
\(991\) −4.58345e100 −1.96212 −0.981059 0.193708i \(-0.937948\pi\)
−0.981059 + 0.193708i \(0.937948\pi\)
\(992\) 3.27433e100 1.35513
\(993\) 3.53362e99 0.141390
\(994\) 1.57421e100 0.609003
\(995\) 2.53578e100 0.948501
\(996\) −4.32613e99 −0.156463
\(997\) −4.49091e100 −1.57053 −0.785266 0.619159i \(-0.787474\pi\)
−0.785266 + 0.619159i \(0.787474\pi\)
\(998\) 8.40312e100 2.84163
\(999\) 5.76086e99 0.188384
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 1.68.a.a.1.5 5
3.2 odd 2 9.68.a.a.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.68.a.a.1.5 5 1.1 even 1 trivial
9.68.a.a.1.1 5 3.2 odd 2