Properties

Label 3.42.a.b.1.4
Level $3$
Weight $42$
Character 3.1
Self dual yes
Analytic conductor $31.942$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 42 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9415011369\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 196497525461 x^{2} + 10360343667016365 x + 6095744045744274504000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{10}\cdot 5^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-433547.\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.58383e6 q^{2} +3.48678e9 q^{3} +4.47715e12 q^{4} +2.55548e14 q^{5} +9.00926e15 q^{6} +1.98945e17 q^{7} +5.88630e18 q^{8} +1.21577e19 q^{9} +O(q^{10})\) \(q+2.58383e6 q^{2} +3.48678e9 q^{3} +4.47715e12 q^{4} +2.55548e14 q^{5} +9.00926e15 q^{6} +1.98945e17 q^{7} +5.88630e18 q^{8} +1.21577e19 q^{9} +6.60294e20 q^{10} -2.76444e21 q^{11} +1.56109e22 q^{12} -8.56075e22 q^{13} +5.14041e23 q^{14} +8.91042e23 q^{15} +5.36384e24 q^{16} -3.38977e24 q^{17} +3.14133e25 q^{18} +2.99407e26 q^{19} +1.14413e27 q^{20} +6.93680e26 q^{21} -7.14285e27 q^{22} -1.40889e28 q^{23} +2.05243e28 q^{24} +1.98303e28 q^{25} -2.21195e29 q^{26} +4.23912e28 q^{27} +8.90709e29 q^{28} -4.94074e28 q^{29} +2.30230e30 q^{30} +5.76050e30 q^{31} +9.15126e29 q^{32} -9.63902e30 q^{33} -8.75860e30 q^{34} +5.08402e31 q^{35} +5.44317e31 q^{36} -1.16818e32 q^{37} +7.73616e32 q^{38} -2.98495e32 q^{39} +1.50424e33 q^{40} +1.48580e32 q^{41} +1.79235e33 q^{42} +2.64197e32 q^{43} -1.23768e34 q^{44} +3.10687e33 q^{45} -3.64032e34 q^{46} +2.16318e34 q^{47} +1.87025e34 q^{48} -4.98839e33 q^{49} +5.12381e34 q^{50} -1.18194e34 q^{51} -3.83278e35 q^{52} +5.57170e34 q^{53} +1.09532e35 q^{54} -7.06449e35 q^{55} +1.17105e36 q^{56} +1.04397e36 q^{57} -1.27660e35 q^{58} -2.05748e36 q^{59} +3.98933e36 q^{60} +1.01936e36 q^{61} +1.48842e37 q^{62} +2.41871e36 q^{63} -9.43067e36 q^{64} -2.18769e37 q^{65} -2.49056e37 q^{66} -2.42878e37 q^{67} -1.51765e37 q^{68} -4.91248e37 q^{69} +1.31362e38 q^{70} +5.77043e36 q^{71} +7.15637e37 q^{72} -1.22382e38 q^{73} -3.01839e38 q^{74} +6.91439e37 q^{75} +1.34049e39 q^{76} -5.49973e38 q^{77} -7.71260e38 q^{78} -7.70707e38 q^{79} +1.37072e39 q^{80} +1.47809e38 q^{81} +3.83906e38 q^{82} +1.70727e39 q^{83} +3.10571e39 q^{84} -8.66251e38 q^{85} +6.82641e38 q^{86} -1.72273e38 q^{87} -1.62723e40 q^{88} -4.08353e39 q^{89} +8.02763e39 q^{90} -1.70312e40 q^{91} -6.30780e40 q^{92} +2.00856e40 q^{93} +5.58928e40 q^{94} +7.65129e40 q^{95} +3.19085e39 q^{96} +1.60920e40 q^{97} -1.28891e40 q^{98} -3.36092e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + O(q^{10}) \) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + \)\(72\!\cdots\!40\)\(q^{10} + \)\(72\!\cdots\!56\)\(q^{11} + \)\(18\!\cdots\!32\)\(q^{12} - \)\(88\!\cdots\!08\)\(q^{13} + \)\(49\!\cdots\!68\)\(q^{14} + \)\(41\!\cdots\!80\)\(q^{15} - \)\(59\!\cdots\!00\)\(q^{16} - \)\(38\!\cdots\!88\)\(q^{17} - \)\(84\!\cdots\!22\)\(q^{18} + \)\(26\!\cdots\!48\)\(q^{19} + \)\(78\!\cdots\!60\)\(q^{20} + \)\(52\!\cdots\!36\)\(q^{21} - \)\(63\!\cdots\!76\)\(q^{22} - \)\(15\!\cdots\!32\)\(q^{23} + \)\(21\!\cdots\!84\)\(q^{24} + \)\(11\!\cdots\!00\)\(q^{25} - \)\(62\!\cdots\!52\)\(q^{26} + \)\(16\!\cdots\!04\)\(q^{27} + \)\(68\!\cdots\!12\)\(q^{28} - \)\(10\!\cdots\!64\)\(q^{29} + \)\(25\!\cdots\!40\)\(q^{30} + \)\(92\!\cdots\!04\)\(q^{31} + \)\(19\!\cdots\!56\)\(q^{32} + \)\(25\!\cdots\!56\)\(q^{33} + \)\(92\!\cdots\!04\)\(q^{34} + \)\(20\!\cdots\!40\)\(q^{35} + \)\(65\!\cdots\!32\)\(q^{36} + \)\(20\!\cdots\!56\)\(q^{37} + \)\(11\!\cdots\!28\)\(q^{38} - \)\(30\!\cdots\!08\)\(q^{39} + \)\(25\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!04\)\(q^{41} + \)\(17\!\cdots\!68\)\(q^{42} + \)\(39\!\cdots\!60\)\(q^{43} - \)\(18\!\cdots\!04\)\(q^{44} + \)\(14\!\cdots\!80\)\(q^{45} - \)\(44\!\cdots\!16\)\(q^{46} - \)\(88\!\cdots\!20\)\(q^{47} - \)\(20\!\cdots\!00\)\(q^{48} - \)\(33\!\cdots\!80\)\(q^{49} - \)\(21\!\cdots\!50\)\(q^{50} - \)\(13\!\cdots\!88\)\(q^{51} - \)\(59\!\cdots\!08\)\(q^{52} + \)\(95\!\cdots\!28\)\(q^{53} - \)\(29\!\cdots\!22\)\(q^{54} + \)\(12\!\cdots\!60\)\(q^{55} + \)\(19\!\cdots\!20\)\(q^{56} + \)\(91\!\cdots\!48\)\(q^{57} + \)\(38\!\cdots\!16\)\(q^{58} - \)\(18\!\cdots\!08\)\(q^{59} + \)\(27\!\cdots\!60\)\(q^{60} + \)\(53\!\cdots\!40\)\(q^{61} + \)\(14\!\cdots\!52\)\(q^{62} + \)\(18\!\cdots\!36\)\(q^{63} - \)\(38\!\cdots\!92\)\(q^{64} - \)\(97\!\cdots\!80\)\(q^{65} - \)\(22\!\cdots\!76\)\(q^{66} - \)\(73\!\cdots\!28\)\(q^{67} - \)\(89\!\cdots\!24\)\(q^{68} - \)\(53\!\cdots\!32\)\(q^{69} - \)\(12\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!52\)\(q^{71} + \)\(76\!\cdots\!84\)\(q^{72} - \)\(44\!\cdots\!32\)\(q^{73} - \)\(29\!\cdots\!12\)\(q^{74} + \)\(40\!\cdots\!00\)\(q^{75} + \)\(11\!\cdots\!72\)\(q^{76} + \)\(83\!\cdots\!52\)\(q^{77} - \)\(21\!\cdots\!52\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(15\!\cdots\!80\)\(q^{80} + \)\(59\!\cdots\!04\)\(q^{81} + \)\(61\!\cdots\!12\)\(q^{82} + \)\(15\!\cdots\!04\)\(q^{83} + \)\(23\!\cdots\!12\)\(q^{84} - \)\(28\!\cdots\!60\)\(q^{85} - \)\(12\!\cdots\!24\)\(q^{86} - \)\(36\!\cdots\!64\)\(q^{87} - \)\(13\!\cdots\!96\)\(q^{88} - \)\(39\!\cdots\!72\)\(q^{89} + \)\(88\!\cdots\!40\)\(q^{90} - \)\(88\!\cdots\!16\)\(q^{91} - \)\(65\!\cdots\!44\)\(q^{92} + \)\(32\!\cdots\!04\)\(q^{93} + \)\(98\!\cdots\!32\)\(q^{94} + \)\(78\!\cdots\!00\)\(q^{95} + \)\(68\!\cdots\!56\)\(q^{96} + \)\(36\!\cdots\!52\)\(q^{97} - \)\(68\!\cdots\!22\)\(q^{98} + \)\(88\!\cdots\!56\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58383e6 1.74240 0.871202 0.490924i \(-0.163341\pi\)
0.871202 + 0.490924i \(0.163341\pi\)
\(3\) 3.48678e9 0.577350
\(4\) 4.47715e12 2.03597
\(5\) 2.55548e14 1.19836 0.599181 0.800613i \(-0.295493\pi\)
0.599181 + 0.800613i \(0.295493\pi\)
\(6\) 9.00926e15 1.00598
\(7\) 1.98945e17 0.942375 0.471188 0.882033i \(-0.343825\pi\)
0.471188 + 0.882033i \(0.343825\pi\)
\(8\) 5.88630e18 1.80509
\(9\) 1.21577e19 0.333333
\(10\) 6.60294e20 2.08803
\(11\) −2.76444e21 −1.23896 −0.619480 0.785012i \(-0.712657\pi\)
−0.619480 + 0.785012i \(0.712657\pi\)
\(12\) 1.56109e22 1.17547
\(13\) −8.56075e22 −1.24932 −0.624659 0.780898i \(-0.714762\pi\)
−0.624659 + 0.780898i \(0.714762\pi\)
\(14\) 5.14041e23 1.64200
\(15\) 8.91042e23 0.691875
\(16\) 5.36384e24 1.10922
\(17\) −3.38977e24 −0.202287 −0.101143 0.994872i \(-0.532250\pi\)
−0.101143 + 0.994872i \(0.532250\pi\)
\(18\) 3.14133e25 0.580802
\(19\) 2.99407e26 1.82731 0.913656 0.406488i \(-0.133247\pi\)
0.913656 + 0.406488i \(0.133247\pi\)
\(20\) 1.14413e27 2.43983
\(21\) 6.93680e26 0.544081
\(22\) −7.14285e27 −2.15877
\(23\) −1.40889e28 −1.71181 −0.855904 0.517134i \(-0.826999\pi\)
−0.855904 + 0.517134i \(0.826999\pi\)
\(24\) 2.05243e28 1.04217
\(25\) 1.98303e28 0.436072
\(26\) −2.21195e29 −2.17682
\(27\) 4.23912e28 0.192450
\(28\) 8.90709e29 1.91865
\(29\) −4.94074e28 −0.0518361 −0.0259181 0.999664i \(-0.508251\pi\)
−0.0259181 + 0.999664i \(0.508251\pi\)
\(30\) 2.30230e30 1.20553
\(31\) 5.76050e30 1.54009 0.770044 0.637991i \(-0.220234\pi\)
0.770044 + 0.637991i \(0.220234\pi\)
\(32\) 9.15126e29 0.127616
\(33\) −9.63902e30 −0.715314
\(34\) −8.75860e30 −0.352466
\(35\) 5.08402e31 1.12931
\(36\) 5.44317e31 0.678658
\(37\) −1.16818e32 −0.830569 −0.415284 0.909692i \(-0.636318\pi\)
−0.415284 + 0.909692i \(0.636318\pi\)
\(38\) 7.73616e32 3.18392
\(39\) −2.98495e32 −0.721294
\(40\) 1.50424e33 2.16315
\(41\) 1.48580e32 0.128793 0.0643964 0.997924i \(-0.479488\pi\)
0.0643964 + 0.997924i \(0.479488\pi\)
\(42\) 1.79235e33 0.948009
\(43\) 2.64197e32 0.0862631 0.0431315 0.999069i \(-0.486267\pi\)
0.0431315 + 0.999069i \(0.486267\pi\)
\(44\) −1.23768e34 −2.52249
\(45\) 3.10687e33 0.399454
\(46\) −3.64032e34 −2.98266
\(47\) 2.16318e34 1.14048 0.570238 0.821480i \(-0.306851\pi\)
0.570238 + 0.821480i \(0.306851\pi\)
\(48\) 1.87025e34 0.640406
\(49\) −4.98839e33 −0.111928
\(50\) 5.12381e34 0.759814
\(51\) −1.18194e34 −0.116790
\(52\) −3.83278e35 −2.54358
\(53\) 5.57170e34 0.250226 0.125113 0.992142i \(-0.460071\pi\)
0.125113 + 0.992142i \(0.460071\pi\)
\(54\) 1.09532e35 0.335326
\(55\) −7.06449e35 −1.48472
\(56\) 1.17105e36 1.70107
\(57\) 1.04397e36 1.05500
\(58\) −1.27660e35 −0.0903195
\(59\) −2.05748e36 −1.02534 −0.512672 0.858584i \(-0.671344\pi\)
−0.512672 + 0.858584i \(0.671344\pi\)
\(60\) 3.98933e36 1.40864
\(61\) 1.01936e36 0.256489 0.128244 0.991743i \(-0.459066\pi\)
0.128244 + 0.991743i \(0.459066\pi\)
\(62\) 1.48842e37 2.68346
\(63\) 2.41871e36 0.314125
\(64\) −9.43067e36 −0.886856
\(65\) −2.18769e37 −1.49714
\(66\) −2.49056e37 −1.24637
\(67\) −2.42878e37 −0.893006 −0.446503 0.894782i \(-0.647331\pi\)
−0.446503 + 0.894782i \(0.647331\pi\)
\(68\) −1.51765e37 −0.411851
\(69\) −4.91248e37 −0.988313
\(70\) 1.31362e38 1.96771
\(71\) 5.77043e36 0.0646268 0.0323134 0.999478i \(-0.489713\pi\)
0.0323134 + 0.999478i \(0.489713\pi\)
\(72\) 7.15637e37 0.601695
\(73\) −1.22382e38 −0.775532 −0.387766 0.921758i \(-0.626753\pi\)
−0.387766 + 0.921758i \(0.626753\pi\)
\(74\) −3.01839e38 −1.44719
\(75\) 6.91439e37 0.251766
\(76\) 1.34049e39 3.72036
\(77\) −5.49973e38 −1.16757
\(78\) −7.71260e38 −1.25679
\(79\) −7.70707e38 −0.967240 −0.483620 0.875278i \(-0.660678\pi\)
−0.483620 + 0.875278i \(0.660678\pi\)
\(80\) 1.37072e39 1.32924
\(81\) 1.47809e38 0.111111
\(82\) 3.83906e38 0.224409
\(83\) 1.70727e39 0.778397 0.389198 0.921154i \(-0.372752\pi\)
0.389198 + 0.921154i \(0.372752\pi\)
\(84\) 3.10571e39 1.10773
\(85\) −8.66251e38 −0.242413
\(86\) 6.82641e38 0.150305
\(87\) −1.72273e38 −0.0299276
\(88\) −1.62723e40 −2.23643
\(89\) −4.08353e39 −0.445185 −0.222592 0.974912i \(-0.571452\pi\)
−0.222592 + 0.974912i \(0.571452\pi\)
\(90\) 8.02763e39 0.696011
\(91\) −1.70312e40 −1.17733
\(92\) −6.30780e40 −3.48520
\(93\) 2.00856e40 0.889170
\(94\) 5.58928e40 1.98717
\(95\) 7.65129e40 2.18978
\(96\) 3.19085e39 0.0736793
\(97\) 1.60920e40 0.300462 0.150231 0.988651i \(-0.451998\pi\)
0.150231 + 0.988651i \(0.451998\pi\)
\(98\) −1.28891e40 −0.195025
\(99\) −3.36092e40 −0.412987
\(100\) 8.87832e40 0.887832
\(101\) 8.47485e39 0.0691105 0.0345552 0.999403i \(-0.488999\pi\)
0.0345552 + 0.999403i \(0.488999\pi\)
\(102\) −3.05393e40 −0.203496
\(103\) 2.25909e41 1.23246 0.616228 0.787568i \(-0.288660\pi\)
0.616228 + 0.787568i \(0.288660\pi\)
\(104\) −5.03911e41 −2.25513
\(105\) 1.77269e41 0.652006
\(106\) 1.43963e41 0.435995
\(107\) −6.78077e41 −1.69399 −0.846996 0.531599i \(-0.821591\pi\)
−0.846996 + 0.531599i \(0.821591\pi\)
\(108\) 1.89792e41 0.391823
\(109\) 7.17358e41 1.22601 0.613003 0.790080i \(-0.289961\pi\)
0.613003 + 0.790080i \(0.289961\pi\)
\(110\) −1.82534e42 −2.58699
\(111\) −4.07320e41 −0.479529
\(112\) 1.06711e42 1.04530
\(113\) 1.60519e42 1.31045 0.655223 0.755435i \(-0.272575\pi\)
0.655223 + 0.755435i \(0.272575\pi\)
\(114\) 2.69743e42 1.83824
\(115\) −3.60039e42 −2.05137
\(116\) −2.21204e41 −0.105537
\(117\) −1.04079e42 −0.416439
\(118\) −5.31619e42 −1.78657
\(119\) −6.74380e41 −0.190630
\(120\) 5.24494e42 1.24889
\(121\) 2.66363e42 0.535024
\(122\) 2.63386e42 0.446907
\(123\) 5.18067e41 0.0743586
\(124\) 2.57906e43 3.13558
\(125\) −6.55340e42 −0.675790
\(126\) 6.24954e42 0.547333
\(127\) 2.84948e42 0.212222 0.106111 0.994354i \(-0.466160\pi\)
0.106111 + 0.994354i \(0.466160\pi\)
\(128\) −2.63796e43 −1.67288
\(129\) 9.21199e41 0.0498040
\(130\) −5.65261e43 −2.60862
\(131\) 2.19486e43 0.865656 0.432828 0.901477i \(-0.357516\pi\)
0.432828 + 0.901477i \(0.357516\pi\)
\(132\) −4.31554e43 −1.45636
\(133\) 5.95656e43 1.72201
\(134\) −6.27555e43 −1.55598
\(135\) 1.08330e43 0.230625
\(136\) −1.99532e43 −0.365145
\(137\) 3.35892e43 0.528966 0.264483 0.964390i \(-0.414799\pi\)
0.264483 + 0.964390i \(0.414799\pi\)
\(138\) −1.26930e44 −1.72204
\(139\) 4.50230e43 0.526782 0.263391 0.964689i \(-0.415159\pi\)
0.263391 + 0.964689i \(0.415159\pi\)
\(140\) 2.27619e44 2.29924
\(141\) 7.54253e43 0.658454
\(142\) 1.49098e43 0.112606
\(143\) 2.36657e44 1.54786
\(144\) 6.52117e43 0.369738
\(145\) −1.26260e43 −0.0621185
\(146\) −3.16215e44 −1.35129
\(147\) −1.73934e43 −0.0646219
\(148\) −5.23013e44 −1.69102
\(149\) −2.36545e44 −0.666186 −0.333093 0.942894i \(-0.608092\pi\)
−0.333093 + 0.942894i \(0.608092\pi\)
\(150\) 1.78656e44 0.438679
\(151\) −4.16293e44 −0.892015 −0.446007 0.895029i \(-0.647154\pi\)
−0.446007 + 0.895029i \(0.647154\pi\)
\(152\) 1.76240e45 3.29845
\(153\) −4.12117e43 −0.0674290
\(154\) −1.42104e45 −2.03437
\(155\) 1.47209e45 1.84558
\(156\) −1.33641e45 −1.46854
\(157\) 1.20032e45 1.15706 0.578528 0.815663i \(-0.303627\pi\)
0.578528 + 0.815663i \(0.303627\pi\)
\(158\) −1.99138e45 −1.68532
\(159\) 1.94273e44 0.144468
\(160\) 2.33859e44 0.152931
\(161\) −2.80291e45 −1.61317
\(162\) 3.81913e44 0.193601
\(163\) 2.08406e45 0.931246 0.465623 0.884983i \(-0.345830\pi\)
0.465623 + 0.884983i \(0.345830\pi\)
\(164\) 6.65216e44 0.262219
\(165\) −2.46324e45 −0.857206
\(166\) 4.41129e45 1.35628
\(167\) −3.55110e45 −0.965328 −0.482664 0.875806i \(-0.660331\pi\)
−0.482664 + 0.875806i \(0.660331\pi\)
\(168\) 4.08321e45 0.982112
\(169\) 2.63319e45 0.560795
\(170\) −2.23825e45 −0.422382
\(171\) 3.64009e45 0.609104
\(172\) 1.18285e45 0.175629
\(173\) 1.13689e46 1.49890 0.749449 0.662062i \(-0.230319\pi\)
0.749449 + 0.662062i \(0.230319\pi\)
\(174\) −4.45124e44 −0.0521460
\(175\) 3.94514e45 0.410944
\(176\) −1.48280e46 −1.37427
\(177\) −7.17400e45 −0.591983
\(178\) −1.05511e46 −0.775692
\(179\) 7.48686e45 0.490696 0.245348 0.969435i \(-0.421098\pi\)
0.245348 + 0.969435i \(0.421098\pi\)
\(180\) 1.39099e46 0.813278
\(181\) −5.11394e45 −0.266898 −0.133449 0.991056i \(-0.542605\pi\)
−0.133449 + 0.991056i \(0.542605\pi\)
\(182\) −4.40057e46 −2.05138
\(183\) 3.55430e45 0.148084
\(184\) −8.29313e46 −3.08996
\(185\) −2.98527e46 −0.995322
\(186\) 5.18978e46 1.54929
\(187\) 9.37084e45 0.250626
\(188\) 9.68487e46 2.32198
\(189\) 8.43352e45 0.181360
\(190\) 1.97696e47 3.81549
\(191\) −6.00314e46 −1.04039 −0.520193 0.854049i \(-0.674140\pi\)
−0.520193 + 0.854049i \(0.674140\pi\)
\(192\) −3.28827e46 −0.512026
\(193\) −9.10745e45 −0.127489 −0.0637444 0.997966i \(-0.520304\pi\)
−0.0637444 + 0.997966i \(0.520304\pi\)
\(194\) 4.15790e46 0.523526
\(195\) −7.62799e46 −0.864372
\(196\) −2.23338e46 −0.227883
\(197\) −3.20025e46 −0.294189 −0.147094 0.989122i \(-0.546992\pi\)
−0.147094 + 0.989122i \(0.546992\pi\)
\(198\) −8.68404e46 −0.719590
\(199\) −4.23622e46 −0.316585 −0.158293 0.987392i \(-0.550599\pi\)
−0.158293 + 0.987392i \(0.550599\pi\)
\(200\) 1.16727e47 0.787148
\(201\) −8.46863e46 −0.515577
\(202\) 2.18976e46 0.120418
\(203\) −9.82936e45 −0.0488491
\(204\) −5.29173e46 −0.237782
\(205\) 3.79694e46 0.154340
\(206\) 5.83712e47 2.14744
\(207\) −1.71288e47 −0.570603
\(208\) −4.59184e47 −1.38576
\(209\) −8.27693e47 −2.26397
\(210\) 4.58032e47 1.13606
\(211\) 5.34998e47 1.20382 0.601911 0.798563i \(-0.294406\pi\)
0.601911 + 0.798563i \(0.294406\pi\)
\(212\) 2.49454e47 0.509454
\(213\) 2.01203e46 0.0373123
\(214\) −1.75204e48 −2.95162
\(215\) 6.75152e46 0.103374
\(216\) 2.49527e47 0.347389
\(217\) 1.14602e48 1.45134
\(218\) 1.85353e48 2.13620
\(219\) −4.26721e47 −0.447754
\(220\) −3.16288e48 −3.02286
\(221\) 2.90190e47 0.252721
\(222\) −1.05245e48 −0.835533
\(223\) 2.57714e48 1.86590 0.932950 0.360006i \(-0.117225\pi\)
0.932950 + 0.360006i \(0.117225\pi\)
\(224\) 1.82060e47 0.120263
\(225\) 2.41090e47 0.145357
\(226\) 4.14755e48 2.28333
\(227\) 2.96815e48 1.49264 0.746320 0.665587i \(-0.231819\pi\)
0.746320 + 0.665587i \(0.231819\pi\)
\(228\) 4.67400e48 2.14795
\(229\) −2.39386e48 −1.00571 −0.502854 0.864371i \(-0.667717\pi\)
−0.502854 + 0.864371i \(0.667717\pi\)
\(230\) −9.30279e48 −3.57431
\(231\) −1.91764e48 −0.674095
\(232\) −2.90827e47 −0.0935686
\(233\) −2.35236e48 −0.692960 −0.346480 0.938057i \(-0.612623\pi\)
−0.346480 + 0.938057i \(0.612623\pi\)
\(234\) −2.68922e48 −0.725606
\(235\) 5.52796e48 1.36670
\(236\) −9.21167e48 −2.08758
\(237\) −2.68729e48 −0.558436
\(238\) −1.74248e48 −0.332155
\(239\) −5.65009e48 −0.988322 −0.494161 0.869370i \(-0.664525\pi\)
−0.494161 + 0.869370i \(0.664525\pi\)
\(240\) 4.77940e48 0.767438
\(241\) 1.15148e49 1.69788 0.848940 0.528490i \(-0.177241\pi\)
0.848940 + 0.528490i \(0.177241\pi\)
\(242\) 6.88236e48 0.932229
\(243\) 5.15378e47 0.0641500
\(244\) 4.56385e48 0.522204
\(245\) −1.27477e48 −0.134131
\(246\) 1.33860e48 0.129563
\(247\) −2.56315e49 −2.28289
\(248\) 3.39080e49 2.77999
\(249\) 5.95288e48 0.449407
\(250\) −1.69329e49 −1.17750
\(251\) 1.49455e48 0.0957634 0.0478817 0.998853i \(-0.484753\pi\)
0.0478817 + 0.998853i \(0.484753\pi\)
\(252\) 1.08289e49 0.639551
\(253\) 3.89479e49 2.12086
\(254\) 7.36258e48 0.369776
\(255\) −3.02043e48 −0.139957
\(256\) −4.74222e49 −2.02797
\(257\) −5.98105e48 −0.236129 −0.118064 0.993006i \(-0.537669\pi\)
−0.118064 + 0.993006i \(0.537669\pi\)
\(258\) 2.38022e48 0.0867787
\(259\) −2.32405e49 −0.782707
\(260\) −9.79460e49 −3.04813
\(261\) −6.00678e47 −0.0172787
\(262\) 5.67115e49 1.50832
\(263\) 3.57534e49 0.879476 0.439738 0.898126i \(-0.355071\pi\)
0.439738 + 0.898126i \(0.355071\pi\)
\(264\) −5.67382e49 −1.29120
\(265\) 1.42384e49 0.299861
\(266\) 1.53907e50 3.00045
\(267\) −1.42384e49 −0.257028
\(268\) −1.08740e50 −1.81814
\(269\) 2.52785e48 0.0391589 0.0195794 0.999808i \(-0.493767\pi\)
0.0195794 + 0.999808i \(0.493767\pi\)
\(270\) 2.79906e49 0.401842
\(271\) 5.81899e49 0.774421 0.387211 0.921991i \(-0.373439\pi\)
0.387211 + 0.921991i \(0.373439\pi\)
\(272\) −1.81822e49 −0.224380
\(273\) −5.93842e49 −0.679730
\(274\) 8.67887e49 0.921673
\(275\) −5.48197e49 −0.540277
\(276\) −2.19939e50 −2.01218
\(277\) −1.51629e50 −1.28810 −0.644048 0.764985i \(-0.722746\pi\)
−0.644048 + 0.764985i \(0.722746\pi\)
\(278\) 1.16332e50 0.917867
\(279\) 7.00342e49 0.513363
\(280\) 2.99261e50 2.03850
\(281\) −1.12012e50 −0.709226 −0.354613 0.935013i \(-0.615387\pi\)
−0.354613 + 0.935013i \(0.615387\pi\)
\(282\) 1.94886e50 1.14729
\(283\) −2.86308e50 −1.56752 −0.783758 0.621066i \(-0.786700\pi\)
−0.783758 + 0.621066i \(0.786700\pi\)
\(284\) 2.58351e49 0.131578
\(285\) 2.66784e50 1.26427
\(286\) 6.11481e50 2.69699
\(287\) 2.95593e49 0.121371
\(288\) 1.11258e49 0.0425388
\(289\) −2.69315e50 −0.959080
\(290\) −3.26234e49 −0.108236
\(291\) 5.61093e49 0.173472
\(292\) −5.47924e50 −1.57896
\(293\) −1.89439e50 −0.508960 −0.254480 0.967078i \(-0.581904\pi\)
−0.254480 + 0.967078i \(0.581904\pi\)
\(294\) −4.49417e49 −0.112598
\(295\) −5.25787e50 −1.22873
\(296\) −6.87628e50 −1.49925
\(297\) −1.17188e50 −0.238438
\(298\) −6.11193e50 −1.16077
\(299\) 1.20611e51 2.13859
\(300\) 3.09568e50 0.512590
\(301\) 5.25608e49 0.0812922
\(302\) −1.07563e51 −1.55425
\(303\) 2.95500e49 0.0399009
\(304\) 1.60597e51 2.02688
\(305\) 2.60497e50 0.307366
\(306\) −1.06484e50 −0.117489
\(307\) 4.49477e50 0.463843 0.231921 0.972735i \(-0.425499\pi\)
0.231921 + 0.972735i \(0.425499\pi\)
\(308\) −2.46231e51 −2.37713
\(309\) 7.87698e50 0.711559
\(310\) 3.80362e51 3.21575
\(311\) −4.89729e50 −0.387586 −0.193793 0.981042i \(-0.562079\pi\)
−0.193793 + 0.981042i \(0.562079\pi\)
\(312\) −1.75703e51 −1.30200
\(313\) 1.99055e51 1.38139 0.690693 0.723148i \(-0.257306\pi\)
0.690693 + 0.723148i \(0.257306\pi\)
\(314\) 3.10142e51 2.01606
\(315\) 6.18098e50 0.376436
\(316\) −3.45057e51 −1.96927
\(317\) 8.77183e50 0.469219 0.234609 0.972090i \(-0.424619\pi\)
0.234609 + 0.972090i \(0.424619\pi\)
\(318\) 5.01969e50 0.251722
\(319\) 1.36584e50 0.0642230
\(320\) −2.40999e51 −1.06277
\(321\) −2.36431e51 −0.978027
\(322\) −7.24225e51 −2.81079
\(323\) −1.01492e51 −0.369641
\(324\) 6.61763e50 0.226219
\(325\) −1.69762e51 −0.544793
\(326\) 5.38486e51 1.62261
\(327\) 2.50127e51 0.707835
\(328\) 8.74587e50 0.232482
\(329\) 4.30354e51 1.07476
\(330\) −6.36458e51 −1.49360
\(331\) 2.35505e51 0.519429 0.259715 0.965685i \(-0.416372\pi\)
0.259715 + 0.965685i \(0.416372\pi\)
\(332\) 7.64370e51 1.58479
\(333\) −1.42024e51 −0.276856
\(334\) −9.17543e51 −1.68199
\(335\) −6.20670e51 −1.07014
\(336\) 3.72078e51 0.603503
\(337\) 2.75468e51 0.420396 0.210198 0.977659i \(-0.432589\pi\)
0.210198 + 0.977659i \(0.432589\pi\)
\(338\) 6.80371e51 0.977132
\(339\) 5.59696e51 0.756587
\(340\) −3.87834e51 −0.493547
\(341\) −1.59246e52 −1.90811
\(342\) 9.40537e51 1.06131
\(343\) −9.85894e51 −1.04785
\(344\) 1.55514e51 0.155712
\(345\) −1.25538e52 −1.18436
\(346\) 2.93752e52 2.61169
\(347\) 8.25043e51 0.691389 0.345695 0.938347i \(-0.387643\pi\)
0.345695 + 0.938347i \(0.387643\pi\)
\(348\) −7.71292e50 −0.0609318
\(349\) 8.65779e51 0.644891 0.322445 0.946588i \(-0.395495\pi\)
0.322445 + 0.946588i \(0.395495\pi\)
\(350\) 1.01936e52 0.716031
\(351\) −3.62900e51 −0.240431
\(352\) −2.52981e51 −0.158112
\(353\) −6.01269e51 −0.354558 −0.177279 0.984161i \(-0.556730\pi\)
−0.177279 + 0.984161i \(0.556730\pi\)
\(354\) −1.85364e52 −1.03147
\(355\) 1.47463e51 0.0774463
\(356\) −1.82826e52 −0.906385
\(357\) −2.35142e51 −0.110060
\(358\) 1.93448e52 0.854991
\(359\) −1.54293e52 −0.644035 −0.322017 0.946734i \(-0.604361\pi\)
−0.322017 + 0.946734i \(0.604361\pi\)
\(360\) 1.82880e52 0.721049
\(361\) 6.27973e52 2.33907
\(362\) −1.32136e52 −0.465044
\(363\) 9.28750e51 0.308896
\(364\) −7.62513e52 −2.39701
\(365\) −3.12746e52 −0.929369
\(366\) 9.18372e51 0.258022
\(367\) −3.80556e52 −1.01103 −0.505515 0.862818i \(-0.668698\pi\)
−0.505515 + 0.862818i \(0.668698\pi\)
\(368\) −7.55703e52 −1.89876
\(369\) 1.80639e51 0.0429309
\(370\) −7.71344e52 −1.73425
\(371\) 1.10846e52 0.235807
\(372\) 8.99264e52 1.81033
\(373\) 4.94905e52 0.942955 0.471478 0.881878i \(-0.343721\pi\)
0.471478 + 0.881878i \(0.343721\pi\)
\(374\) 2.42126e52 0.436691
\(375\) −2.28503e52 −0.390167
\(376\) 1.27331e53 2.05865
\(377\) 4.22964e51 0.0647598
\(378\) 2.17908e52 0.316003
\(379\) 4.34671e52 0.597113 0.298557 0.954392i \(-0.403495\pi\)
0.298557 + 0.954392i \(0.403495\pi\)
\(380\) 3.42560e53 4.45834
\(381\) 9.93553e51 0.122526
\(382\) −1.55111e53 −1.81277
\(383\) −2.09548e52 −0.232118 −0.116059 0.993242i \(-0.537026\pi\)
−0.116059 + 0.993242i \(0.537026\pi\)
\(384\) −9.19801e52 −0.965837
\(385\) −1.40545e53 −1.39917
\(386\) −2.35321e52 −0.222137
\(387\) 3.21202e51 0.0287544
\(388\) 7.20463e52 0.611732
\(389\) −1.49021e53 −1.20028 −0.600139 0.799896i \(-0.704888\pi\)
−0.600139 + 0.799896i \(0.704888\pi\)
\(390\) −1.97094e53 −1.50608
\(391\) 4.77581e52 0.346277
\(392\) −2.93631e52 −0.202040
\(393\) 7.65300e52 0.499787
\(394\) −8.26890e52 −0.512596
\(395\) −1.96953e53 −1.15910
\(396\) −1.50473e53 −0.840831
\(397\) 3.46598e53 1.83916 0.919582 0.392898i \(-0.128528\pi\)
0.919582 + 0.392898i \(0.128528\pi\)
\(398\) −1.09457e53 −0.551620
\(399\) 2.07692e53 0.994205
\(400\) 1.06366e53 0.483698
\(401\) 3.81967e53 1.65031 0.825157 0.564904i \(-0.191087\pi\)
0.825157 + 0.564904i \(0.191087\pi\)
\(402\) −2.18815e53 −0.898344
\(403\) −4.93142e53 −1.92406
\(404\) 3.79432e52 0.140707
\(405\) 3.77723e52 0.133151
\(406\) −2.53974e52 −0.0851149
\(407\) 3.22938e53 1.02904
\(408\) −6.95726e52 −0.210817
\(409\) −1.49738e53 −0.431523 −0.215761 0.976446i \(-0.569223\pi\)
−0.215761 + 0.976446i \(0.569223\pi\)
\(410\) 9.81065e52 0.268923
\(411\) 1.17118e53 0.305399
\(412\) 1.01143e54 2.50925
\(413\) −4.09327e53 −0.966260
\(414\) −4.42578e53 −0.994221
\(415\) 4.36290e53 0.932801
\(416\) −7.83416e52 −0.159433
\(417\) 1.56985e53 0.304138
\(418\) −2.13862e54 −3.94475
\(419\) 5.57082e53 0.978434 0.489217 0.872162i \(-0.337283\pi\)
0.489217 + 0.872162i \(0.337283\pi\)
\(420\) 7.93659e53 1.32747
\(421\) −4.02757e53 −0.641593 −0.320797 0.947148i \(-0.603951\pi\)
−0.320797 + 0.947148i \(0.603951\pi\)
\(422\) 1.38234e54 2.09754
\(423\) 2.62992e53 0.380158
\(424\) 3.27967e53 0.451679
\(425\) −6.72201e52 −0.0882117
\(426\) 5.19873e52 0.0650131
\(427\) 2.02798e53 0.241708
\(428\) −3.03585e54 −3.44892
\(429\) 8.25172e53 0.893655
\(430\) 1.74448e53 0.180120
\(431\) −1.10307e54 −1.08597 −0.542986 0.839742i \(-0.682706\pi\)
−0.542986 + 0.839742i \(0.682706\pi\)
\(432\) 2.27379e53 0.213469
\(433\) 2.59468e53 0.232317 0.116159 0.993231i \(-0.462942\pi\)
0.116159 + 0.993231i \(0.462942\pi\)
\(434\) 2.96113e54 2.52882
\(435\) −4.40240e52 −0.0358641
\(436\) 3.21172e54 2.49612
\(437\) −4.21830e54 −3.12801
\(438\) −1.10257e54 −0.780168
\(439\) −6.51584e53 −0.439995 −0.219997 0.975500i \(-0.570605\pi\)
−0.219997 + 0.975500i \(0.570605\pi\)
\(440\) −4.15837e54 −2.68005
\(441\) −6.06471e52 −0.0373095
\(442\) 7.49801e53 0.440342
\(443\) −8.31973e53 −0.466480 −0.233240 0.972419i \(-0.574933\pi\)
−0.233240 + 0.972419i \(0.574933\pi\)
\(444\) −1.82363e54 −0.976308
\(445\) −1.04354e54 −0.533493
\(446\) 6.65889e54 3.25115
\(447\) −8.24782e53 −0.384623
\(448\) −1.87619e54 −0.835751
\(449\) 1.75134e54 0.745280 0.372640 0.927976i \(-0.378453\pi\)
0.372640 + 0.927976i \(0.378453\pi\)
\(450\) 6.22935e53 0.253271
\(451\) −4.10741e53 −0.159569
\(452\) 7.18670e54 2.66803
\(453\) −1.45153e54 −0.515005
\(454\) 7.66919e54 2.60078
\(455\) −4.35230e54 −1.41086
\(456\) 6.14510e54 1.90436
\(457\) 5.74991e54 1.70364 0.851822 0.523831i \(-0.175498\pi\)
0.851822 + 0.523831i \(0.175498\pi\)
\(458\) −6.18534e54 −1.75235
\(459\) −1.43696e53 −0.0389301
\(460\) −1.61195e55 −4.17653
\(461\) 7.61685e54 1.88758 0.943792 0.330540i \(-0.107231\pi\)
0.943792 + 0.330540i \(0.107231\pi\)
\(462\) −4.95485e54 −1.17455
\(463\) 4.82618e54 1.09444 0.547221 0.836988i \(-0.315686\pi\)
0.547221 + 0.836988i \(0.315686\pi\)
\(464\) −2.65013e53 −0.0574974
\(465\) 5.13285e54 1.06555
\(466\) −6.07811e54 −1.20742
\(467\) −8.48997e54 −1.61402 −0.807012 0.590535i \(-0.798917\pi\)
−0.807012 + 0.590535i \(0.798917\pi\)
\(468\) −4.65976e54 −0.847859
\(469\) −4.83194e54 −0.841547
\(470\) 1.42833e55 2.38135
\(471\) 4.18526e54 0.668026
\(472\) −1.21110e55 −1.85084
\(473\) −7.30358e53 −0.106877
\(474\) −6.94350e54 −0.973022
\(475\) 5.93732e54 0.796840
\(476\) −3.01930e54 −0.388118
\(477\) 6.77389e53 0.0834087
\(478\) −1.45989e55 −1.72206
\(479\) −7.54248e54 −0.852385 −0.426193 0.904632i \(-0.640145\pi\)
−0.426193 + 0.904632i \(0.640145\pi\)
\(480\) 8.15416e53 0.0882945
\(481\) 1.00005e55 1.03764
\(482\) 2.97523e55 2.95839
\(483\) −9.77315e54 −0.931362
\(484\) 1.19255e55 1.08930
\(485\) 4.11228e54 0.360062
\(486\) 1.33165e54 0.111775
\(487\) 2.26646e55 1.82392 0.911958 0.410283i \(-0.134570\pi\)
0.911958 + 0.410283i \(0.134570\pi\)
\(488\) 6.00029e54 0.462984
\(489\) 7.26667e54 0.537655
\(490\) −3.29380e54 −0.233710
\(491\) −9.02019e54 −0.613826 −0.306913 0.951738i \(-0.599296\pi\)
−0.306913 + 0.951738i \(0.599296\pi\)
\(492\) 2.31946e54 0.151392
\(493\) 1.67480e53 0.0104858
\(494\) −6.62273e55 −3.97772
\(495\) −8.58877e54 −0.494908
\(496\) 3.08984e55 1.70829
\(497\) 1.14800e54 0.0609027
\(498\) 1.53812e55 0.783050
\(499\) −4.11207e54 −0.200909 −0.100454 0.994942i \(-0.532030\pi\)
−0.100454 + 0.994942i \(0.532030\pi\)
\(500\) −2.93406e55 −1.37589
\(501\) −1.23819e55 −0.557332
\(502\) 3.86167e54 0.166859
\(503\) −3.08721e55 −1.28063 −0.640313 0.768114i \(-0.721195\pi\)
−0.640313 + 0.768114i \(0.721195\pi\)
\(504\) 1.42373e55 0.567023
\(505\) 2.16573e54 0.0828194
\(506\) 1.00635e56 3.69540
\(507\) 9.18135e54 0.323775
\(508\) 1.27576e55 0.432078
\(509\) 2.73650e54 0.0890185 0.0445092 0.999009i \(-0.485828\pi\)
0.0445092 + 0.999009i \(0.485828\pi\)
\(510\) −7.80428e54 −0.243862
\(511\) −2.43474e55 −0.730843
\(512\) −6.45215e55 −1.86067
\(513\) 1.26922e55 0.351666
\(514\) −1.54540e55 −0.411432
\(515\) 5.77308e55 1.47693
\(516\) 4.12435e54 0.101400
\(517\) −5.97998e55 −1.41300
\(518\) −6.00494e55 −1.36379
\(519\) 3.96408e55 0.865389
\(520\) −1.28774e56 −2.70246
\(521\) −7.68480e54 −0.155046 −0.0775228 0.996991i \(-0.524701\pi\)
−0.0775228 + 0.996991i \(0.524701\pi\)
\(522\) −1.55205e54 −0.0301065
\(523\) −5.42535e55 −1.01191 −0.505957 0.862559i \(-0.668860\pi\)
−0.505957 + 0.862559i \(0.668860\pi\)
\(524\) 9.82673e55 1.76245
\(525\) 1.37559e55 0.237259
\(526\) 9.23806e55 1.53240
\(527\) −1.95268e55 −0.311540
\(528\) −5.17021e55 −0.793438
\(529\) 1.30757e56 1.93029
\(530\) 3.67896e55 0.522480
\(531\) −2.50142e55 −0.341782
\(532\) 2.66684e56 3.50598
\(533\) −1.27196e55 −0.160903
\(534\) −3.67896e55 −0.447846
\(535\) −1.73282e56 −2.03002
\(536\) −1.42965e56 −1.61195
\(537\) 2.61051e55 0.283303
\(538\) 6.53154e54 0.0682306
\(539\) 1.37901e55 0.138675
\(540\) 4.85010e55 0.469546
\(541\) 1.06824e56 0.995687 0.497844 0.867267i \(-0.334125\pi\)
0.497844 + 0.867267i \(0.334125\pi\)
\(542\) 1.50353e56 1.34936
\(543\) −1.78312e55 −0.154094
\(544\) −3.10207e54 −0.0258151
\(545\) 1.83320e56 1.46920
\(546\) −1.53439e56 −1.18436
\(547\) −2.25958e56 −1.67991 −0.839956 0.542654i \(-0.817419\pi\)
−0.839956 + 0.542654i \(0.817419\pi\)
\(548\) 1.50384e56 1.07696
\(549\) 1.23931e55 0.0854962
\(550\) −1.41645e56 −0.941381
\(551\) −1.47929e55 −0.0947208
\(552\) −2.89163e56 −1.78399
\(553\) −1.53329e56 −0.911503
\(554\) −3.91785e56 −2.24438
\(555\) −1.04090e56 −0.574649
\(556\) 2.01575e56 1.07251
\(557\) −9.26630e55 −0.475198 −0.237599 0.971363i \(-0.576360\pi\)
−0.237599 + 0.971363i \(0.576360\pi\)
\(558\) 1.80957e56 0.894485
\(559\) −2.26173e55 −0.107770
\(560\) 2.72698e56 1.25264
\(561\) 3.26741e55 0.144699
\(562\) −2.89420e56 −1.23576
\(563\) 1.20733e56 0.497053 0.248526 0.968625i \(-0.420054\pi\)
0.248526 + 0.968625i \(0.420054\pi\)
\(564\) 3.37691e56 1.34059
\(565\) 4.10205e56 1.57039
\(566\) −7.39772e56 −2.73125
\(567\) 2.94059e55 0.104708
\(568\) 3.39665e55 0.116657
\(569\) 2.31976e56 0.768495 0.384248 0.923230i \(-0.374461\pi\)
0.384248 + 0.923230i \(0.374461\pi\)
\(570\) 6.89325e56 2.20287
\(571\) 2.57033e55 0.0792409 0.0396204 0.999215i \(-0.487385\pi\)
0.0396204 + 0.999215i \(0.487385\pi\)
\(572\) 1.05955e57 3.15139
\(573\) −2.09316e56 −0.600667
\(574\) 7.63763e55 0.211478
\(575\) −2.79386e56 −0.746472
\(576\) −1.14655e56 −0.295619
\(577\) −2.83608e56 −0.705690 −0.352845 0.935682i \(-0.614786\pi\)
−0.352845 + 0.935682i \(0.614786\pi\)
\(578\) −6.95864e56 −1.67111
\(579\) −3.17557e55 −0.0736057
\(580\) −5.65284e55 −0.126472
\(581\) 3.39653e56 0.733542
\(582\) 1.44977e56 0.302258
\(583\) −1.54027e56 −0.310020
\(584\) −7.20379e56 −1.39990
\(585\) −2.65971e56 −0.499045
\(586\) −4.89479e56 −0.886814
\(587\) 3.96279e56 0.693298 0.346649 0.937995i \(-0.387319\pi\)
0.346649 + 0.937995i \(0.387319\pi\)
\(588\) −7.78730e55 −0.131569
\(589\) 1.72473e57 2.81422
\(590\) −1.35854e57 −2.14095
\(591\) −1.11586e56 −0.169850
\(592\) −6.26594e56 −0.921279
\(593\) 1.25467e57 1.78200 0.891001 0.454001i \(-0.150004\pi\)
0.891001 + 0.454001i \(0.150004\pi\)
\(594\) −3.02794e56 −0.415456
\(595\) −1.72337e56 −0.228444
\(596\) −1.05905e57 −1.35634
\(597\) −1.47708e56 −0.182781
\(598\) 3.11639e57 3.72629
\(599\) −1.06361e57 −1.22895 −0.614475 0.788936i \(-0.710632\pi\)
−0.614475 + 0.788936i \(0.710632\pi\)
\(600\) 4.07002e56 0.454460
\(601\) −4.74011e56 −0.511519 −0.255759 0.966740i \(-0.582325\pi\)
−0.255759 + 0.966740i \(0.582325\pi\)
\(602\) 1.35808e56 0.141644
\(603\) −2.95283e56 −0.297669
\(604\) −1.86381e57 −1.81612
\(605\) 6.80686e56 0.641153
\(606\) 7.63521e55 0.0695236
\(607\) −3.75437e56 −0.330498 −0.165249 0.986252i \(-0.552843\pi\)
−0.165249 + 0.986252i \(0.552843\pi\)
\(608\) 2.73995e56 0.233195
\(609\) −3.42729e55 −0.0282030
\(610\) 6.73080e56 0.535556
\(611\) −1.85184e57 −1.42482
\(612\) −1.84511e56 −0.137284
\(613\) 1.97052e57 1.41788 0.708941 0.705267i \(-0.249173\pi\)
0.708941 + 0.705267i \(0.249173\pi\)
\(614\) 1.16137e57 0.808202
\(615\) 1.32391e56 0.0891085
\(616\) −3.23731e57 −2.10756
\(617\) 1.04592e57 0.658649 0.329325 0.944217i \(-0.393179\pi\)
0.329325 + 0.944217i \(0.393179\pi\)
\(618\) 2.03528e57 1.23982
\(619\) −3.26806e57 −1.92589 −0.962947 0.269692i \(-0.913078\pi\)
−0.962947 + 0.269692i \(0.913078\pi\)
\(620\) 6.59076e57 3.75756
\(621\) −5.97243e56 −0.329438
\(622\) −1.26538e57 −0.675332
\(623\) −8.12399e56 −0.419531
\(624\) −1.60108e57 −0.800070
\(625\) −2.57649e57 −1.24591
\(626\) 5.14325e57 2.40693
\(627\) −2.88599e57 −1.30710
\(628\) 5.37402e57 2.35574
\(629\) 3.95988e56 0.168013
\(630\) 1.59706e57 0.655903
\(631\) 7.88492e54 0.00313470 0.00156735 0.999999i \(-0.499501\pi\)
0.00156735 + 0.999999i \(0.499501\pi\)
\(632\) −4.53662e57 −1.74595
\(633\) 1.86542e57 0.695027
\(634\) 2.26649e57 0.817569
\(635\) 7.28181e56 0.254318
\(636\) 8.69791e56 0.294133
\(637\) 4.27043e56 0.139834
\(638\) 3.52909e56 0.111902
\(639\) 7.01550e55 0.0215423
\(640\) −6.74127e57 −2.00471
\(641\) −5.60781e57 −1.61511 −0.807557 0.589789i \(-0.799211\pi\)
−0.807557 + 0.589789i \(0.799211\pi\)
\(642\) −6.10897e57 −1.70412
\(643\) −2.39387e57 −0.646810 −0.323405 0.946261i \(-0.604828\pi\)
−0.323405 + 0.946261i \(0.604828\pi\)
\(644\) −1.25491e58 −3.28436
\(645\) 2.35411e56 0.0596832
\(646\) −2.62238e57 −0.644065
\(647\) 5.56725e57 1.32466 0.662328 0.749214i \(-0.269569\pi\)
0.662328 + 0.749214i \(0.269569\pi\)
\(648\) 8.70047e56 0.200565
\(649\) 5.68779e57 1.27036
\(650\) −4.38636e57 −0.949250
\(651\) 3.99594e57 0.837932
\(652\) 9.33066e57 1.89599
\(653\) 6.52017e57 1.28392 0.641961 0.766737i \(-0.278121\pi\)
0.641961 + 0.766737i \(0.278121\pi\)
\(654\) 6.46286e57 1.23334
\(655\) 5.60893e57 1.03737
\(656\) 7.96959e56 0.142859
\(657\) −1.48788e57 −0.258511
\(658\) 1.11196e58 1.87266
\(659\) −7.55343e57 −1.23309 −0.616543 0.787321i \(-0.711467\pi\)
−0.616543 + 0.787321i \(0.711467\pi\)
\(660\) −1.10283e58 −1.74525
\(661\) −7.41557e57 −1.13767 −0.568833 0.822453i \(-0.692605\pi\)
−0.568833 + 0.822453i \(0.692605\pi\)
\(662\) 6.08505e57 0.905056
\(663\) 1.01183e57 0.145908
\(664\) 1.00495e58 1.40507
\(665\) 1.52219e58 2.06360
\(666\) −3.66965e57 −0.482395
\(667\) 6.96093e56 0.0887336
\(668\) −1.58988e58 −1.96538
\(669\) 8.98593e57 1.07728
\(670\) −1.60371e58 −1.86463
\(671\) −2.81798e57 −0.317779
\(672\) 6.34804e56 0.0694336
\(673\) −1.69942e58 −1.80298 −0.901490 0.432800i \(-0.857526\pi\)
−0.901490 + 0.432800i \(0.857526\pi\)
\(674\) 7.11763e57 0.732500
\(675\) 8.40628e56 0.0839222
\(676\) 1.17892e58 1.14176
\(677\) −1.85953e57 −0.174717 −0.0873585 0.996177i \(-0.527843\pi\)
−0.0873585 + 0.996177i \(0.527843\pi\)
\(678\) 1.44616e58 1.31828
\(679\) 3.20143e57 0.283148
\(680\) −5.09902e57 −0.437576
\(681\) 1.03493e58 0.861776
\(682\) −4.11464e58 −3.32470
\(683\) −1.28888e58 −1.01062 −0.505312 0.862937i \(-0.668623\pi\)
−0.505312 + 0.862937i \(0.668623\pi\)
\(684\) 1.62972e58 1.24012
\(685\) 8.58366e57 0.633893
\(686\) −2.54738e58 −1.82579
\(687\) −8.34689e57 −0.580646
\(688\) 1.41711e57 0.0956843
\(689\) −4.76979e57 −0.312612
\(690\) −3.24368e58 −2.06363
\(691\) 5.69871e57 0.351947 0.175973 0.984395i \(-0.443693\pi\)
0.175973 + 0.984395i \(0.443693\pi\)
\(692\) 5.09001e58 3.05172
\(693\) −6.68639e57 −0.389189
\(694\) 2.13177e58 1.20468
\(695\) 1.15056e58 0.631276
\(696\) −1.01405e57 −0.0540219
\(697\) −5.03653e56 −0.0260531
\(698\) 2.23703e58 1.12366
\(699\) −8.20218e57 −0.400080
\(700\) 1.76630e58 0.836671
\(701\) −8.78499e57 −0.404131 −0.202065 0.979372i \(-0.564765\pi\)
−0.202065 + 0.979372i \(0.564765\pi\)
\(702\) −9.37672e57 −0.418929
\(703\) −3.49762e58 −1.51771
\(704\) 2.60706e58 1.09878
\(705\) 1.92748e58 0.789066
\(706\) −1.55358e58 −0.617784
\(707\) 1.68603e57 0.0651280
\(708\) −3.21191e58 −1.20526
\(709\) 4.95487e58 1.80628 0.903139 0.429347i \(-0.141256\pi\)
0.903139 + 0.429347i \(0.141256\pi\)
\(710\) 3.81018e57 0.134943
\(711\) −9.37000e57 −0.322413
\(712\) −2.40369e58 −0.803597
\(713\) −8.11589e58 −2.63634
\(714\) −6.07566e57 −0.191770
\(715\) 6.04773e58 1.85489
\(716\) 3.35198e58 0.999044
\(717\) −1.97007e58 −0.570608
\(718\) −3.98666e58 −1.12217
\(719\) −4.51451e58 −1.23500 −0.617501 0.786570i \(-0.711855\pi\)
−0.617501 + 0.786570i \(0.711855\pi\)
\(720\) 1.66648e58 0.443081
\(721\) 4.49436e58 1.16144
\(722\) 1.62258e59 4.07561
\(723\) 4.01496e58 0.980271
\(724\) −2.28959e58 −0.543397
\(725\) −9.79761e56 −0.0226043
\(726\) 2.39973e58 0.538223
\(727\) 1.85132e58 0.403669 0.201834 0.979420i \(-0.435310\pi\)
0.201834 + 0.979420i \(0.435310\pi\)
\(728\) −1.00251e59 −2.12517
\(729\) 1.79701e57 0.0370370
\(730\) −8.08083e58 −1.61934
\(731\) −8.95569e56 −0.0174499
\(732\) 1.59132e58 0.301495
\(733\) −7.75891e57 −0.142945 −0.0714725 0.997443i \(-0.522770\pi\)
−0.0714725 + 0.997443i \(0.522770\pi\)
\(734\) −9.83292e58 −1.76162
\(735\) −4.44486e57 −0.0774405
\(736\) −1.28931e58 −0.218455
\(737\) 6.71422e58 1.10640
\(738\) 4.66740e57 0.0748030
\(739\) −1.13939e59 −1.77608 −0.888041 0.459764i \(-0.847934\pi\)
−0.888041 + 0.459764i \(0.847934\pi\)
\(740\) −1.33655e59 −2.02645
\(741\) −8.93714e58 −1.31803
\(742\) 2.86408e58 0.410871
\(743\) 9.08942e58 1.26843 0.634213 0.773158i \(-0.281324\pi\)
0.634213 + 0.773158i \(0.281324\pi\)
\(744\) 1.18230e59 1.60503
\(745\) −6.04488e58 −0.798333
\(746\) 1.27875e59 1.64301
\(747\) 2.07564e58 0.259466
\(748\) 4.19547e58 0.510267
\(749\) −1.34900e59 −1.59638
\(750\) −5.90413e58 −0.679829
\(751\) 1.09322e59 1.22487 0.612433 0.790522i \(-0.290191\pi\)
0.612433 + 0.790522i \(0.290191\pi\)
\(752\) 1.16029e59 1.26503
\(753\) 5.21118e57 0.0552890
\(754\) 1.09287e58 0.112838
\(755\) −1.06383e59 −1.06896
\(756\) 3.77582e58 0.369245
\(757\) −1.50195e59 −1.42951 −0.714757 0.699372i \(-0.753463\pi\)
−0.714757 + 0.699372i \(0.753463\pi\)
\(758\) 1.12312e59 1.04041
\(759\) 1.35803e59 1.22448
\(760\) 4.50378e59 3.95274
\(761\) −1.91836e58 −0.163887 −0.0819436 0.996637i \(-0.526113\pi\)
−0.0819436 + 0.996637i \(0.526113\pi\)
\(762\) 2.56717e58 0.213490
\(763\) 1.42715e59 1.15536
\(764\) −2.68770e59 −2.11820
\(765\) −1.05316e58 −0.0808043
\(766\) −5.41438e58 −0.404444
\(767\) 1.76136e59 1.28098
\(768\) −1.65351e59 −1.17085
\(769\) 8.09865e58 0.558371 0.279185 0.960237i \(-0.409936\pi\)
0.279185 + 0.960237i \(0.409936\pi\)
\(770\) −3.63144e59 −2.43792
\(771\) −2.08546e58 −0.136329
\(772\) −4.07755e58 −0.259564
\(773\) −1.75935e59 −1.09062 −0.545310 0.838234i \(-0.683588\pi\)
−0.545310 + 0.838234i \(0.683588\pi\)
\(774\) 8.29932e57 0.0501017
\(775\) 1.14232e59 0.671590
\(776\) 9.47223e58 0.542359
\(777\) −8.10345e58 −0.451896
\(778\) −3.85046e59 −2.09137
\(779\) 4.44859e58 0.235345
\(780\) −3.41517e59 −1.75984
\(781\) −1.59520e58 −0.0800700
\(782\) 1.23399e59 0.603354
\(783\) −2.09443e57 −0.00997587
\(784\) −2.67569e58 −0.124153
\(785\) 3.06740e59 1.38657
\(786\) 1.97741e59 0.870831
\(787\) −1.42029e59 −0.609390 −0.304695 0.952450i \(-0.598555\pi\)
−0.304695 + 0.952450i \(0.598555\pi\)
\(788\) −1.43280e59 −0.598961
\(789\) 1.24664e59 0.507766
\(790\) −5.08893e59 −2.01963
\(791\) 3.19346e59 1.23493
\(792\) −1.97834e59 −0.745477
\(793\) −8.72652e58 −0.320436
\(794\) 8.95550e59 3.20457
\(795\) 4.96462e58 0.173125
\(796\) −1.89662e59 −0.644559
\(797\) 1.77809e59 0.588922 0.294461 0.955664i \(-0.404860\pi\)
0.294461 + 0.955664i \(0.404860\pi\)
\(798\) 5.36642e59 1.73231
\(799\) −7.33268e58 −0.230703
\(800\) 1.81472e58 0.0556500
\(801\) −4.96462e58 −0.148395
\(802\) 9.86938e59 2.87551
\(803\) 3.38319e59 0.960854
\(804\) −3.79153e59 −1.04970
\(805\) −7.16280e59 −1.93316
\(806\) −1.27419e60 −3.35249
\(807\) 8.81408e57 0.0226084
\(808\) 4.98855e58 0.124750
\(809\) −4.67029e59 −1.13867 −0.569336 0.822105i \(-0.692800\pi\)
−0.569336 + 0.822105i \(0.692800\pi\)
\(810\) 9.75972e58 0.232004
\(811\) −1.45390e59 −0.336983 −0.168492 0.985703i \(-0.553890\pi\)
−0.168492 + 0.985703i \(0.553890\pi\)
\(812\) −4.40076e58 −0.0994555
\(813\) 2.02896e59 0.447112
\(814\) 8.34416e59 1.79301
\(815\) 5.32578e59 1.11597
\(816\) −6.33974e58 −0.129546
\(817\) 7.91024e58 0.157630
\(818\) −3.86897e59 −0.751887
\(819\) −2.07060e59 −0.392442
\(820\) 1.69995e59 0.314233
\(821\) −1.07845e59 −0.194432 −0.0972158 0.995263i \(-0.530994\pi\)
−0.0972158 + 0.995263i \(0.530994\pi\)
\(822\) 3.02614e59 0.532128
\(823\) 2.28591e59 0.392069 0.196035 0.980597i \(-0.437193\pi\)
0.196035 + 0.980597i \(0.437193\pi\)
\(824\) 1.32977e60 2.22469
\(825\) −1.91144e59 −0.311929
\(826\) −1.05763e60 −1.68362
\(827\) −5.76088e59 −0.894594 −0.447297 0.894385i \(-0.647613\pi\)
−0.447297 + 0.894385i \(0.647613\pi\)
\(828\) −7.66881e59 −1.16173
\(829\) 2.25613e59 0.333424 0.166712 0.986006i \(-0.446685\pi\)
0.166712 + 0.986006i \(0.446685\pi\)
\(830\) 1.12730e60 1.62532
\(831\) −5.28699e59 −0.743682
\(832\) 8.07336e59 1.10796
\(833\) 1.69095e58 0.0226417
\(834\) 4.05624e59 0.529931
\(835\) −9.07477e59 −1.15681
\(836\) −3.70571e60 −4.60938
\(837\) 2.44194e59 0.296390
\(838\) 1.43940e60 1.70483
\(839\) −1.01240e60 −1.17012 −0.585060 0.810990i \(-0.698929\pi\)
−0.585060 + 0.810990i \(0.698929\pi\)
\(840\) 1.04346e60 1.17693
\(841\) −9.06044e59 −0.997313
\(842\) −1.04065e60 −1.11791
\(843\) −3.90561e59 −0.409472
\(844\) 2.39527e60 2.45095
\(845\) 6.72907e59 0.672036
\(846\) 6.79526e59 0.662390
\(847\) 5.29916e59 0.504194
\(848\) 2.98857e59 0.277555
\(849\) −9.98295e59 −0.905006
\(850\) −1.73685e59 −0.153701
\(851\) 1.64584e60 1.42177
\(852\) 9.00815e58 0.0759668
\(853\) −1.19199e60 −0.981337 −0.490669 0.871346i \(-0.663247\pi\)
−0.490669 + 0.871346i \(0.663247\pi\)
\(854\) 5.23995e59 0.421154
\(855\) 9.30219e59 0.729927
\(856\) −3.99136e60 −3.05780
\(857\) −1.98782e60 −1.48686 −0.743431 0.668813i \(-0.766803\pi\)
−0.743431 + 0.668813i \(0.766803\pi\)
\(858\) 2.13210e60 1.55711
\(859\) 1.93547e60 1.38015 0.690076 0.723737i \(-0.257577\pi\)
0.690076 + 0.723737i \(0.257577\pi\)
\(860\) 3.02276e59 0.210468
\(861\) 1.03067e59 0.0700737
\(862\) −2.85014e60 −1.89220
\(863\) 1.93131e60 1.25208 0.626038 0.779793i \(-0.284675\pi\)
0.626038 + 0.779793i \(0.284675\pi\)
\(864\) 3.87932e58 0.0245598
\(865\) 2.90530e60 1.79622
\(866\) 6.70421e59 0.404791
\(867\) −9.39043e59 −0.553725
\(868\) 5.13093e60 2.95489
\(869\) 2.13058e60 1.19837
\(870\) −1.13751e59 −0.0624898
\(871\) 2.07922e60 1.11565
\(872\) 4.22258e60 2.21305
\(873\) 1.95641e59 0.100154
\(874\) −1.08994e61 −5.45026
\(875\) −1.30377e60 −0.636848
\(876\) −1.91049e60 −0.911615
\(877\) 4.31437e59 0.201106 0.100553 0.994932i \(-0.467939\pi\)
0.100553 + 0.994932i \(0.467939\pi\)
\(878\) −1.68358e60 −0.766649
\(879\) −6.60534e59 −0.293848
\(880\) −3.78928e60 −1.64688
\(881\) −1.33549e60 −0.567066 −0.283533 0.958962i \(-0.591507\pi\)
−0.283533 + 0.958962i \(0.591507\pi\)
\(882\) −1.56702e59 −0.0650082
\(883\) −9.62321e59 −0.390055 −0.195027 0.980798i \(-0.562480\pi\)
−0.195027 + 0.980798i \(0.562480\pi\)
\(884\) 1.29922e60 0.514533
\(885\) −1.83330e60 −0.709410
\(886\) −2.14968e60 −0.812796
\(887\) −3.90527e60 −1.44283 −0.721417 0.692500i \(-0.756509\pi\)
−0.721417 + 0.692500i \(0.756509\pi\)
\(888\) −2.39761e60 −0.865591
\(889\) 5.66891e59 0.199993
\(890\) −2.69633e60 −0.929560
\(891\) −4.08609e59 −0.137662
\(892\) 1.15383e61 3.79892
\(893\) 6.47670e60 2.08400
\(894\) −2.13110e60 −0.670169
\(895\) 1.91325e60 0.588031
\(896\) −5.24810e60 −1.57648
\(897\) 4.20545e60 1.23472
\(898\) 4.52515e60 1.29858
\(899\) −2.84611e59 −0.0798322
\(900\) 1.07940e60 0.295944
\(901\) −1.88868e59 −0.0506175
\(902\) −1.06129e60 −0.278034
\(903\) 1.83268e59 0.0469341
\(904\) 9.44865e60 2.36547
\(905\) −1.30686e60 −0.319840
\(906\) −3.75049e60 −0.897347
\(907\) −2.96464e60 −0.693462 −0.346731 0.937965i \(-0.612708\pi\)
−0.346731 + 0.937965i \(0.612708\pi\)
\(908\) 1.32888e61 3.03898
\(909\) 1.03034e59 0.0230368
\(910\) −1.12456e61 −2.45830
\(911\) −7.01681e60 −1.49973 −0.749865 0.661591i \(-0.769882\pi\)
−0.749865 + 0.661591i \(0.769882\pi\)
\(912\) 5.59967e60 1.17022
\(913\) −4.71965e60 −0.964403
\(914\) 1.48568e61 2.96844
\(915\) 9.08297e59 0.177458
\(916\) −1.07177e61 −2.04760
\(917\) 4.36657e60 0.815773
\(918\) −3.71287e59 −0.0678321
\(919\) −6.52121e60 −1.16509 −0.582546 0.812798i \(-0.697943\pi\)
−0.582546 + 0.812798i \(0.697943\pi\)
\(920\) −2.11930e61 −3.70289
\(921\) 1.56723e60 0.267800
\(922\) 1.96806e61 3.28893
\(923\) −4.93992e59 −0.0807394
\(924\) −8.58556e60 −1.37244
\(925\) −2.31654e60 −0.362188
\(926\) 1.24700e61 1.90696
\(927\) 2.74653e60 0.410819
\(928\) −4.52140e58 −0.00661514
\(929\) −4.97882e60 −0.712532 −0.356266 0.934385i \(-0.615950\pi\)
−0.356266 + 0.934385i \(0.615950\pi\)
\(930\) 1.32624e61 1.85662
\(931\) −1.49356e60 −0.204528
\(932\) −1.05319e61 −1.41085
\(933\) −1.70758e60 −0.223773
\(934\) −2.19366e61 −2.81228
\(935\) 2.39470e60 0.300340
\(936\) −6.12639e60 −0.751708
\(937\) 9.62681e60 1.15564 0.577818 0.816166i \(-0.303904\pi\)
0.577818 + 0.816166i \(0.303904\pi\)
\(938\) −1.24849e61 −1.46632
\(939\) 6.94063e60 0.797544
\(940\) 2.47495e61 2.78257
\(941\) −3.82719e60 −0.421010 −0.210505 0.977593i \(-0.567511\pi\)
−0.210505 + 0.977593i \(0.567511\pi\)
\(942\) 1.08140e61 1.16397
\(943\) −2.09332e60 −0.220469
\(944\) −1.10360e61 −1.13733
\(945\) 2.15517e60 0.217335
\(946\) −1.88712e60 −0.186222
\(947\) 8.12706e59 0.0784800 0.0392400 0.999230i \(-0.487506\pi\)
0.0392400 + 0.999230i \(0.487506\pi\)
\(948\) −1.20314e61 −1.13696
\(949\) 1.04768e61 0.968886
\(950\) 1.53410e61 1.38842
\(951\) 3.05855e60 0.270904
\(952\) −3.96960e60 −0.344104
\(953\) −3.41043e60 −0.289337 −0.144669 0.989480i \(-0.546212\pi\)
−0.144669 + 0.989480i \(0.546212\pi\)
\(954\) 1.75026e60 0.145332
\(955\) −1.53409e61 −1.24676
\(956\) −2.52963e61 −2.01220
\(957\) 4.76238e59 0.0370791
\(958\) −1.94885e61 −1.48520
\(959\) 6.68241e60 0.498485
\(960\) −8.40313e60 −0.613593
\(961\) 1.91930e61 1.37187
\(962\) 2.58396e61 1.80800
\(963\) −8.24383e60 −0.564664
\(964\) 5.15535e61 3.45684
\(965\) −2.32740e60 −0.152778
\(966\) −2.52522e61 −1.62281
\(967\) −2.57180e61 −1.61806 −0.809030 0.587767i \(-0.800007\pi\)
−0.809030 + 0.587767i \(0.800007\pi\)
\(968\) 1.56789e61 0.965765
\(969\) −3.53881e60 −0.213413
\(970\) 1.06254e61 0.627374
\(971\) −1.55166e61 −0.897019 −0.448509 0.893778i \(-0.648045\pi\)
−0.448509 + 0.893778i \(0.648045\pi\)
\(972\) 2.30742e60 0.130608
\(973\) 8.95711e60 0.496426
\(974\) 5.85616e61 3.17800
\(975\) −5.91923e60 −0.314536
\(976\) 5.46770e60 0.284501
\(977\) 4.45394e60 0.226937 0.113469 0.993542i \(-0.463804\pi\)
0.113469 + 0.993542i \(0.463804\pi\)
\(978\) 1.87758e61 0.936812
\(979\) 1.12887e61 0.551567
\(980\) −5.70736e60 −0.273087
\(981\) 8.72140e60 0.408669
\(982\) −2.33066e61 −1.06953
\(983\) −3.36188e61 −1.51090 −0.755450 0.655207i \(-0.772582\pi\)
−0.755450 + 0.655207i \(0.772582\pi\)
\(984\) 3.04950e60 0.134224
\(985\) −8.17819e60 −0.352545
\(986\) 4.32739e59 0.0182705
\(987\) 1.50055e61 0.620510
\(988\) −1.14756e62 −4.64791
\(989\) −3.72224e60 −0.147666
\(990\) −2.21919e61 −0.862330
\(991\) 5.79150e60 0.220435 0.110218 0.993907i \(-0.464845\pi\)
0.110218 + 0.993907i \(0.464845\pi\)
\(992\) 5.27158e60 0.196540
\(993\) 8.21155e60 0.299893
\(994\) 2.96624e60 0.106117
\(995\) −1.08256e61 −0.379384
\(996\) 2.66519e61 0.914982
\(997\) 1.75910e61 0.591615 0.295808 0.955248i \(-0.404411\pi\)
0.295808 + 0.955248i \(0.404411\pi\)
\(998\) −1.06249e61 −0.350065
\(999\) −4.95206e60 −0.159843
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 3.42.a.b.1.4 4
3.2 odd 2 9.42.a.c.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.42.a.b.1.4 4 1.1 even 1 trivial
9.42.a.c.1.1 4 3.2 odd 2