Properties

Label 1.48.a.a.1.2
Level $1$
Weight $48$
Character 1.1
Self dual yes
Analytic conductor $13.991$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 48 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.9907662655\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 832803191366 x^{2} + 3710135215485780 x + 13175318942671469337000\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{20}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-124721.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.54692e6 q^{2} +1.52034e11 q^{3} -1.38345e14 q^{4} +4.23962e16 q^{5} -2.35185e17 q^{6} -3.90714e19 q^{7} +4.31719e20 q^{8} -3.47448e21 q^{9} +O(q^{10})\) \(q-1.54692e6 q^{2} +1.52034e11 q^{3} -1.38345e14 q^{4} +4.23962e16 q^{5} -2.35185e17 q^{6} -3.90714e19 q^{7} +4.31719e20 q^{8} -3.47448e21 q^{9} -6.55837e22 q^{10} +2.66558e24 q^{11} -2.10331e25 q^{12} +2.26259e26 q^{13} +6.04405e25 q^{14} +6.44566e27 q^{15} +1.88024e28 q^{16} +8.41583e28 q^{17} +5.37476e27 q^{18} +3.16735e29 q^{19} -5.86528e30 q^{20} -5.94018e30 q^{21} -4.12345e30 q^{22} +2.26985e31 q^{23} +6.56359e31 q^{24} +1.08689e33 q^{25} -3.50006e32 q^{26} -4.57064e33 q^{27} +5.40532e33 q^{28} -3.39685e34 q^{29} -9.97095e33 q^{30} +1.81646e35 q^{31} -8.98449e34 q^{32} +4.05259e35 q^{33} -1.30186e35 q^{34} -1.65648e36 q^{35} +4.80676e35 q^{36} -7.13789e36 q^{37} -4.89965e35 q^{38} +3.43991e37 q^{39} +1.83032e37 q^{40} -2.78383e37 q^{41} +9.18901e36 q^{42} -4.92777e37 q^{43} -3.68769e38 q^{44} -1.47305e38 q^{45} -3.51128e37 q^{46} +1.86825e39 q^{47} +2.85861e39 q^{48} -3.71676e39 q^{49} -1.68134e39 q^{50} +1.27949e40 q^{51} -3.13017e40 q^{52} -2.48904e40 q^{53} +7.07044e39 q^{54} +1.13011e41 q^{55} -1.68679e40 q^{56} +4.81545e40 q^{57} +5.25467e40 q^{58} +3.69239e40 q^{59} -8.91722e41 q^{60} +3.52589e41 q^{61} -2.80993e41 q^{62} +1.35753e41 q^{63} -2.50722e42 q^{64} +9.59253e42 q^{65} -6.26905e41 q^{66} -1.26183e42 q^{67} -1.16428e43 q^{68} +3.45094e42 q^{69} +2.56245e42 q^{70} -3.26023e43 q^{71} -1.50000e42 q^{72} +3.59179e43 q^{73} +1.10418e43 q^{74} +1.65245e44 q^{75} -4.38186e43 q^{76} -1.04148e44 q^{77} -5.32128e43 q^{78} -5.82596e44 q^{79} +7.97151e44 q^{80} -6.02511e44 q^{81} +4.30637e43 q^{82} -3.51619e44 q^{83} +8.21792e44 q^{84} +3.56799e45 q^{85} +7.62288e43 q^{86} -5.16437e45 q^{87} +1.15078e45 q^{88} -2.92401e45 q^{89} +2.27869e44 q^{90} -8.84027e45 q^{91} -3.14021e45 q^{92} +2.76164e46 q^{93} -2.89005e45 q^{94} +1.34284e46 q^{95} -1.36595e46 q^{96} +2.17182e46 q^{97} +5.74955e45 q^{98} -9.26152e45 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + 2392716988073784337920q^{8} - 17071972417358142200172q^{9} + O(q^{10}) \) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + \)\(23\!\cdots\!20\)\(q^{8} - \)\(17\!\cdots\!72\)\(q^{9} + \)\(16\!\cdots\!00\)\(q^{10} - \)\(19\!\cdots\!12\)\(q^{11} + \)\(50\!\cdots\!20\)\(q^{12} + \)\(12\!\cdots\!20\)\(q^{13} + \)\(34\!\cdots\!04\)\(q^{14} + \)\(12\!\cdots\!00\)\(q^{15} + \)\(12\!\cdots\!84\)\(q^{16} + \)\(21\!\cdots\!80\)\(q^{17} + \)\(40\!\cdots\!60\)\(q^{18} - \)\(10\!\cdots\!40\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(26\!\cdots\!12\)\(q^{21} - \)\(79\!\cdots\!80\)\(q^{22} + \)\(13\!\cdots\!80\)\(q^{23} + \)\(11\!\cdots\!80\)\(q^{24} + \)\(10\!\cdots\!00\)\(q^{25} + \)\(22\!\cdots\!88\)\(q^{26} - \)\(73\!\cdots\!20\)\(q^{27} - \)\(36\!\cdots\!80\)\(q^{28} - \)\(22\!\cdots\!60\)\(q^{29} - \)\(25\!\cdots\!00\)\(q^{30} + \)\(75\!\cdots\!48\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(26\!\cdots\!20\)\(q^{33} - \)\(12\!\cdots\!16\)\(q^{34} - \)\(13\!\cdots\!00\)\(q^{35} - \)\(13\!\cdots\!36\)\(q^{36} - \)\(11\!\cdots\!60\)\(q^{37} + \)\(29\!\cdots\!80\)\(q^{38} + \)\(39\!\cdots\!36\)\(q^{39} + \)\(70\!\cdots\!00\)\(q^{40} + \)\(13\!\cdots\!28\)\(q^{41} - \)\(10\!\cdots\!20\)\(q^{42} - \)\(44\!\cdots\!00\)\(q^{43} - \)\(15\!\cdots\!56\)\(q^{44} + \)\(86\!\cdots\!00\)\(q^{45} + \)\(12\!\cdots\!68\)\(q^{46} + \)\(20\!\cdots\!20\)\(q^{47} + \)\(10\!\cdots\!80\)\(q^{48} + \)\(91\!\cdots\!72\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(18\!\cdots\!52\)\(q^{51} - \)\(55\!\cdots\!00\)\(q^{52} + \)\(29\!\cdots\!60\)\(q^{53} - \)\(11\!\cdots\!40\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} + \)\(27\!\cdots\!40\)\(q^{56} + \)\(55\!\cdots\!60\)\(q^{57} - \)\(73\!\cdots\!80\)\(q^{58} + \)\(47\!\cdots\!80\)\(q^{59} - \)\(21\!\cdots\!00\)\(q^{60} + \)\(62\!\cdots\!88\)\(q^{61} - \)\(68\!\cdots\!80\)\(q^{62} + \)\(58\!\cdots\!40\)\(q^{63} + \)\(55\!\cdots\!72\)\(q^{64} + \)\(12\!\cdots\!00\)\(q^{65} - \)\(89\!\cdots\!24\)\(q^{66} + \)\(18\!\cdots\!80\)\(q^{67} - \)\(27\!\cdots\!40\)\(q^{68} - \)\(20\!\cdots\!04\)\(q^{69} - \)\(97\!\cdots\!00\)\(q^{70} + \)\(22\!\cdots\!68\)\(q^{71} - \)\(17\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!80\)\(q^{73} + \)\(18\!\cdots\!44\)\(q^{74} + \)\(32\!\cdots\!00\)\(q^{75} + \)\(35\!\cdots\!80\)\(q^{76} - \)\(26\!\cdots\!00\)\(q^{77} - \)\(49\!\cdots\!00\)\(q^{78} - \)\(13\!\cdots\!60\)\(q^{79} - \)\(94\!\cdots\!00\)\(q^{80} - \)\(10\!\cdots\!16\)\(q^{81} + \)\(38\!\cdots\!20\)\(q^{82} - \)\(14\!\cdots\!60\)\(q^{83} + \)\(52\!\cdots\!44\)\(q^{84} - \)\(10\!\cdots\!00\)\(q^{85} + \)\(95\!\cdots\!28\)\(q^{86} - \)\(43\!\cdots\!60\)\(q^{87} - \)\(15\!\cdots\!60\)\(q^{88} - \)\(79\!\cdots\!80\)\(q^{89} - \)\(16\!\cdots\!00\)\(q^{90} + \)\(53\!\cdots\!68\)\(q^{91} + \)\(13\!\cdots\!80\)\(q^{92} + \)\(10\!\cdots\!20\)\(q^{93} + \)\(34\!\cdots\!24\)\(q^{94} + \)\(75\!\cdots\!00\)\(q^{95} + \)\(64\!\cdots\!28\)\(q^{96} + \)\(95\!\cdots\!20\)\(q^{97} - \)\(29\!\cdots\!20\)\(q^{98} + \)\(53\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.54692e6 −0.130396 −0.0651980 0.997872i \(-0.520768\pi\)
−0.0651980 + 0.997872i \(0.520768\pi\)
\(3\) 1.52034e11 0.932376 0.466188 0.884686i \(-0.345627\pi\)
0.466188 + 0.884686i \(0.345627\pi\)
\(4\) −1.38345e14 −0.982997
\(5\) 4.23962e16 1.59049 0.795246 0.606286i \(-0.207341\pi\)
0.795246 + 0.606286i \(0.207341\pi\)
\(6\) −2.35185e17 −0.121578
\(7\) −3.90714e19 −0.539579 −0.269790 0.962919i \(-0.586954\pi\)
−0.269790 + 0.962919i \(0.586954\pi\)
\(8\) 4.31719e20 0.258575
\(9\) −3.47448e21 −0.130675
\(10\) −6.55837e22 −0.207394
\(11\) 2.66558e24 0.897561 0.448781 0.893642i \(-0.351858\pi\)
0.448781 + 0.893642i \(0.351858\pi\)
\(12\) −2.10331e25 −0.916523
\(13\) 2.26259e26 1.50293 0.751463 0.659776i \(-0.229349\pi\)
0.751463 + 0.659776i \(0.229349\pi\)
\(14\) 6.04405e25 0.0703589
\(15\) 6.44566e27 1.48294
\(16\) 1.88024e28 0.949280
\(17\) 8.41583e28 1.02223 0.511114 0.859513i \(-0.329233\pi\)
0.511114 + 0.859513i \(0.329233\pi\)
\(18\) 5.37476e27 0.0170394
\(19\) 3.16735e29 0.281830 0.140915 0.990022i \(-0.454996\pi\)
0.140915 + 0.990022i \(0.454996\pi\)
\(20\) −5.86528e30 −1.56345
\(21\) −5.94018e30 −0.503091
\(22\) −4.12345e30 −0.117038
\(23\) 2.26985e31 0.226669 0.113335 0.993557i \(-0.463847\pi\)
0.113335 + 0.993557i \(0.463847\pi\)
\(24\) 6.56359e31 0.241089
\(25\) 1.08689e33 1.52967
\(26\) −3.50006e32 −0.195975
\(27\) −4.57064e33 −1.05421
\(28\) 5.40532e33 0.530405
\(29\) −3.39685e34 −1.46125 −0.730624 0.682780i \(-0.760771\pi\)
−0.730624 + 0.682780i \(0.760771\pi\)
\(30\) −9.97095e33 −0.193369
\(31\) 1.81646e35 1.63015 0.815074 0.579357i \(-0.196696\pi\)
0.815074 + 0.579357i \(0.196696\pi\)
\(32\) −8.98449e34 −0.382357
\(33\) 4.05259e35 0.836865
\(34\) −1.30186e35 −0.133294
\(35\) −1.65648e36 −0.858197
\(36\) 4.80676e35 0.128453
\(37\) −7.13789e36 −1.00191 −0.500956 0.865473i \(-0.667018\pi\)
−0.500956 + 0.865473i \(0.667018\pi\)
\(38\) −4.89965e35 −0.0367494
\(39\) 3.43991e37 1.40129
\(40\) 1.83032e37 0.411261
\(41\) −2.78383e37 −0.350124 −0.175062 0.984557i \(-0.556013\pi\)
−0.175062 + 0.984557i \(0.556013\pi\)
\(42\) 9.18901e36 0.0656010
\(43\) −4.92777e37 −0.202368 −0.101184 0.994868i \(-0.532263\pi\)
−0.101184 + 0.994868i \(0.532263\pi\)
\(44\) −3.68769e38 −0.882300
\(45\) −1.47305e38 −0.207837
\(46\) −3.51128e37 −0.0295567
\(47\) 1.86825e39 0.948716 0.474358 0.880332i \(-0.342680\pi\)
0.474358 + 0.880332i \(0.342680\pi\)
\(48\) 2.85861e39 0.885086
\(49\) −3.71676e39 −0.708854
\(50\) −1.68134e39 −0.199462
\(51\) 1.27949e40 0.953100
\(52\) −3.13017e40 −1.47737
\(53\) −2.48904e40 −0.750843 −0.375421 0.926854i \(-0.622502\pi\)
−0.375421 + 0.926854i \(0.622502\pi\)
\(54\) 7.07044e39 0.137465
\(55\) 1.13011e41 1.42756
\(56\) −1.68679e40 −0.139522
\(57\) 4.81545e40 0.262771
\(58\) 5.25467e40 0.190541
\(59\) 3.69239e40 0.0895953 0.0447976 0.998996i \(-0.485736\pi\)
0.0447976 + 0.998996i \(0.485736\pi\)
\(60\) −8.91722e41 −1.45772
\(61\) 3.52589e41 0.390857 0.195429 0.980718i \(-0.437390\pi\)
0.195429 + 0.980718i \(0.437390\pi\)
\(62\) −2.80993e41 −0.212565
\(63\) 1.35753e41 0.0705093
\(64\) −2.50722e42 −0.899422
\(65\) 9.59253e42 2.39039
\(66\) −6.26905e41 −0.109124
\(67\) −1.26183e42 −0.154257 −0.0771283 0.997021i \(-0.524575\pi\)
−0.0771283 + 0.997021i \(0.524575\pi\)
\(68\) −1.16428e43 −1.00485
\(69\) 3.45094e42 0.211341
\(70\) 2.56245e42 0.111905
\(71\) −3.26023e43 −1.02018 −0.510090 0.860121i \(-0.670388\pi\)
−0.510090 + 0.860121i \(0.670388\pi\)
\(72\) −1.50000e42 −0.0337891
\(73\) 3.59179e43 0.585092 0.292546 0.956251i \(-0.405498\pi\)
0.292546 + 0.956251i \(0.405498\pi\)
\(74\) 1.10418e43 0.130645
\(75\) 1.65245e44 1.42623
\(76\) −4.38186e43 −0.277038
\(77\) −1.04148e44 −0.484305
\(78\) −5.32128e43 −0.182723
\(79\) −5.82596e44 −1.48297 −0.741483 0.670972i \(-0.765877\pi\)
−0.741483 + 0.670972i \(0.765877\pi\)
\(80\) 7.97151e44 1.50982
\(81\) −6.02511e44 −0.852250
\(82\) 4.30637e43 0.0456547
\(83\) −3.51619e44 −0.280373 −0.140187 0.990125i \(-0.544770\pi\)
−0.140187 + 0.990125i \(0.544770\pi\)
\(84\) 8.21792e44 0.494537
\(85\) 3.56799e45 1.62584
\(86\) 7.62288e43 0.0263879
\(87\) −5.16437e45 −1.36243
\(88\) 1.15078e45 0.232087
\(89\) −2.92401e45 −0.452182 −0.226091 0.974106i \(-0.572595\pi\)
−0.226091 + 0.974106i \(0.572595\pi\)
\(90\) 2.27869e44 0.0271011
\(91\) −8.84027e45 −0.810947
\(92\) −3.14021e45 −0.222815
\(93\) 2.76164e46 1.51991
\(94\) −2.89005e45 −0.123709
\(95\) 1.34284e46 0.448248
\(96\) −1.36595e46 −0.356500
\(97\) 2.17182e46 0.444311 0.222156 0.975011i \(-0.428691\pi\)
0.222156 + 0.975011i \(0.428691\pi\)
\(98\) 5.74955e45 0.0924317
\(99\) −9.26152e45 −0.117288
\(100\) −1.50366e47 −1.50366
\(101\) −5.11557e46 −0.404894 −0.202447 0.979293i \(-0.564889\pi\)
−0.202447 + 0.979293i \(0.564889\pi\)
\(102\) −1.97928e46 −0.124280
\(103\) 3.19569e47 1.59547 0.797736 0.603006i \(-0.206031\pi\)
0.797736 + 0.603006i \(0.206031\pi\)
\(104\) 9.76803e46 0.388618
\(105\) −2.51841e47 −0.800162
\(106\) 3.85036e46 0.0979068
\(107\) 2.00584e47 0.409051 0.204526 0.978861i \(-0.434435\pi\)
0.204526 + 0.978861i \(0.434435\pi\)
\(108\) 6.32323e47 1.03629
\(109\) −5.86410e47 −0.773888 −0.386944 0.922103i \(-0.626469\pi\)
−0.386944 + 0.922103i \(0.626469\pi\)
\(110\) −1.74819e47 −0.186149
\(111\) −1.08520e48 −0.934158
\(112\) −7.34637e47 −0.512212
\(113\) 3.11593e47 0.176297 0.0881484 0.996107i \(-0.471905\pi\)
0.0881484 + 0.996107i \(0.471905\pi\)
\(114\) −7.44914e46 −0.0342643
\(115\) 9.62329e47 0.360516
\(116\) 4.69936e48 1.43640
\(117\) −7.86134e47 −0.196394
\(118\) −5.71184e46 −0.0116829
\(119\) −3.28818e48 −0.551572
\(120\) 2.78271e48 0.383450
\(121\) −1.71442e48 −0.194384
\(122\) −5.45429e47 −0.0509662
\(123\) −4.23236e48 −0.326447
\(124\) −2.51298e49 −1.60243
\(125\) 1.59559e49 0.842432
\(126\) −2.09999e47 −0.00919412
\(127\) 2.66165e49 0.967749 0.483875 0.875137i \(-0.339229\pi\)
0.483875 + 0.875137i \(0.339229\pi\)
\(128\) 1.65230e49 0.499638
\(129\) −7.49188e48 −0.188683
\(130\) −1.48389e49 −0.311697
\(131\) 6.34924e49 1.11390 0.556950 0.830546i \(-0.311972\pi\)
0.556950 + 0.830546i \(0.311972\pi\)
\(132\) −5.60654e49 −0.822636
\(133\) −1.23753e49 −0.152069
\(134\) 1.95196e48 0.0201144
\(135\) −1.93778e50 −1.67672
\(136\) 3.63327e49 0.264322
\(137\) 1.99734e50 1.22326 0.611631 0.791143i \(-0.290514\pi\)
0.611631 + 0.791143i \(0.290514\pi\)
\(138\) −5.33834e48 −0.0275580
\(139\) −3.16608e50 −1.37935 −0.689674 0.724120i \(-0.742246\pi\)
−0.689674 + 0.724120i \(0.742246\pi\)
\(140\) 2.29165e50 0.843605
\(141\) 2.84038e50 0.884560
\(142\) 5.04332e49 0.133027
\(143\) 6.03113e50 1.34897
\(144\) −6.53287e49 −0.124047
\(145\) −1.44014e51 −2.32410
\(146\) −5.55623e49 −0.0762936
\(147\) −5.65074e50 −0.660919
\(148\) 9.87488e50 0.984876
\(149\) 1.00267e50 0.0853651 0.0426826 0.999089i \(-0.486410\pi\)
0.0426826 + 0.999089i \(0.486410\pi\)
\(150\) −2.55621e50 −0.185974
\(151\) −2.40479e49 −0.0149664 −0.00748321 0.999972i \(-0.502382\pi\)
−0.00748321 + 0.999972i \(0.502382\pi\)
\(152\) 1.36740e50 0.0728740
\(153\) −2.92407e50 −0.133579
\(154\) 1.61109e50 0.0631514
\(155\) 7.70111e51 2.59274
\(156\) −4.75892e51 −1.37747
\(157\) −1.42274e51 −0.354391 −0.177196 0.984176i \(-0.556702\pi\)
−0.177196 + 0.984176i \(0.556702\pi\)
\(158\) 9.01232e50 0.193373
\(159\) −3.78419e51 −0.700068
\(160\) −3.80908e51 −0.608136
\(161\) −8.86862e50 −0.122306
\(162\) 9.32038e50 0.111130
\(163\) −4.79256e51 −0.494492 −0.247246 0.968953i \(-0.579525\pi\)
−0.247246 + 0.968953i \(0.579525\pi\)
\(164\) 3.85127e51 0.344170
\(165\) 1.71814e52 1.33103
\(166\) 5.43927e50 0.0365596
\(167\) −9.89736e51 −0.577673 −0.288837 0.957378i \(-0.593268\pi\)
−0.288837 + 0.957378i \(0.593268\pi\)
\(168\) −2.56449e51 −0.130087
\(169\) 2.85292e52 1.25878
\(170\) −5.51941e51 −0.212004
\(171\) −1.10049e51 −0.0368280
\(172\) 6.81729e51 0.198927
\(173\) −7.43991e52 −1.89446 −0.947228 0.320562i \(-0.896128\pi\)
−0.947228 + 0.320562i \(0.896128\pi\)
\(174\) 7.98889e51 0.177656
\(175\) −4.24665e52 −0.825377
\(176\) 5.01194e52 0.852037
\(177\) 5.61369e51 0.0835365
\(178\) 4.52321e51 0.0589627
\(179\) 3.60632e52 0.412115 0.206057 0.978540i \(-0.433937\pi\)
0.206057 + 0.978540i \(0.433937\pi\)
\(180\) 2.03788e52 0.204303
\(181\) 6.19557e52 0.545299 0.272650 0.962113i \(-0.412100\pi\)
0.272650 + 0.962113i \(0.412100\pi\)
\(182\) 1.36752e52 0.105744
\(183\) 5.36056e52 0.364426
\(184\) 9.79935e51 0.0586109
\(185\) −3.02619e53 −1.59353
\(186\) −4.27205e52 −0.198190
\(187\) 2.24331e53 0.917511
\(188\) −2.58463e53 −0.932585
\(189\) 1.78581e53 0.568832
\(190\) −2.07727e52 −0.0584497
\(191\) −3.09862e53 −0.770699 −0.385349 0.922771i \(-0.625919\pi\)
−0.385349 + 0.922771i \(0.625919\pi\)
\(192\) −3.81183e53 −0.838600
\(193\) 4.75475e53 0.925829 0.462914 0.886403i \(-0.346804\pi\)
0.462914 + 0.886403i \(0.346804\pi\)
\(194\) −3.35963e52 −0.0579364
\(195\) 1.45839e54 2.22874
\(196\) 5.14194e53 0.696802
\(197\) −7.61644e53 −0.915790 −0.457895 0.889006i \(-0.651396\pi\)
−0.457895 + 0.889006i \(0.651396\pi\)
\(198\) 1.43269e52 0.0152939
\(199\) −1.90631e54 −1.80778 −0.903890 0.427765i \(-0.859301\pi\)
−0.903890 + 0.427765i \(0.859301\pi\)
\(200\) 4.69232e53 0.395533
\(201\) −1.91841e53 −0.143825
\(202\) 7.91339e52 0.0527965
\(203\) 1.32720e54 0.788459
\(204\) −1.77011e54 −0.936895
\(205\) −1.18024e54 −0.556869
\(206\) −4.94348e53 −0.208043
\(207\) −7.88655e52 −0.0296199
\(208\) 4.25422e54 1.42670
\(209\) 8.44284e53 0.252959
\(210\) 3.89579e53 0.104338
\(211\) 1.25520e54 0.300660 0.150330 0.988636i \(-0.451966\pi\)
0.150330 + 0.988636i \(0.451966\pi\)
\(212\) 3.44345e54 0.738076
\(213\) −4.95665e54 −0.951191
\(214\) −3.10288e53 −0.0533386
\(215\) −2.08918e54 −0.321864
\(216\) −1.97323e54 −0.272593
\(217\) −7.09718e54 −0.879594
\(218\) 9.07131e53 0.100912
\(219\) 5.46075e54 0.545526
\(220\) −1.56344e55 −1.40329
\(221\) 1.90416e55 1.53633
\(222\) 1.67872e54 0.121810
\(223\) −1.43141e54 −0.0934545 −0.0467272 0.998908i \(-0.514879\pi\)
−0.0467272 + 0.998908i \(0.514879\pi\)
\(224\) 3.51037e54 0.206312
\(225\) −3.77639e54 −0.199889
\(226\) −4.82011e53 −0.0229884
\(227\) 3.38487e55 1.45524 0.727619 0.685982i \(-0.240627\pi\)
0.727619 + 0.685982i \(0.240627\pi\)
\(228\) −6.66191e54 −0.258303
\(229\) −4.65218e54 −0.162750 −0.0813752 0.996684i \(-0.525931\pi\)
−0.0813752 + 0.996684i \(0.525931\pi\)
\(230\) −1.48865e54 −0.0470098
\(231\) −1.58341e55 −0.451555
\(232\) −1.46649e55 −0.377842
\(233\) −6.87236e55 −1.60045 −0.800225 0.599700i \(-0.795287\pi\)
−0.800225 + 0.599700i \(0.795287\pi\)
\(234\) 1.21609e54 0.0256090
\(235\) 7.92068e55 1.50893
\(236\) −5.10822e54 −0.0880719
\(237\) −8.85744e55 −1.38268
\(238\) 5.08657e54 0.0719228
\(239\) 1.09219e56 1.39942 0.699710 0.714427i \(-0.253313\pi\)
0.699710 + 0.714427i \(0.253313\pi\)
\(240\) 1.21194e56 1.40772
\(241\) −4.82622e55 −0.508401 −0.254201 0.967152i \(-0.581812\pi\)
−0.254201 + 0.967152i \(0.581812\pi\)
\(242\) 2.65207e54 0.0253468
\(243\) 2.99259e55 0.259597
\(244\) −4.87788e55 −0.384211
\(245\) −1.57577e56 −1.12743
\(246\) 6.54714e54 0.0425674
\(247\) 7.16642e55 0.423569
\(248\) 7.84201e55 0.421515
\(249\) −5.34580e55 −0.261414
\(250\) −2.46825e55 −0.109850
\(251\) −4.06217e56 −1.64599 −0.822993 0.568052i \(-0.807697\pi\)
−0.822993 + 0.568052i \(0.807697\pi\)
\(252\) −1.87807e55 −0.0693104
\(253\) 6.05047e55 0.203450
\(254\) −4.11736e55 −0.126191
\(255\) 5.42456e56 1.51590
\(256\) 3.27300e56 0.834271
\(257\) 1.93698e56 0.450501 0.225251 0.974301i \(-0.427680\pi\)
0.225251 + 0.974301i \(0.427680\pi\)
\(258\) 1.15894e55 0.0246035
\(259\) 2.78887e56 0.540611
\(260\) −1.32707e57 −2.34975
\(261\) 1.18023e56 0.190948
\(262\) −9.82178e55 −0.145248
\(263\) 8.33659e56 1.12727 0.563636 0.826023i \(-0.309402\pi\)
0.563636 + 0.826023i \(0.309402\pi\)
\(264\) 1.74958e56 0.216392
\(265\) −1.05526e57 −1.19421
\(266\) 1.91436e55 0.0198292
\(267\) −4.44548e56 −0.421604
\(268\) 1.74568e56 0.151634
\(269\) −1.88490e57 −1.50006 −0.750032 0.661402i \(-0.769962\pi\)
−0.750032 + 0.661402i \(0.769962\pi\)
\(270\) 2.99759e56 0.218637
\(271\) 2.56612e57 1.71593 0.857963 0.513712i \(-0.171730\pi\)
0.857963 + 0.513712i \(0.171730\pi\)
\(272\) 1.58238e57 0.970380
\(273\) −1.34402e57 −0.756108
\(274\) −3.08974e56 −0.159508
\(275\) 2.89721e57 1.37297
\(276\) −4.77419e56 −0.207748
\(277\) −8.36679e56 −0.334414 −0.167207 0.985922i \(-0.553475\pi\)
−0.167207 + 0.985922i \(0.553475\pi\)
\(278\) 4.89768e56 0.179861
\(279\) −6.31127e56 −0.213019
\(280\) −7.15133e56 −0.221908
\(281\) −3.96974e57 −1.13283 −0.566414 0.824121i \(-0.691670\pi\)
−0.566414 + 0.824121i \(0.691670\pi\)
\(282\) −4.39385e56 −0.115343
\(283\) −4.45361e57 −1.07580 −0.537900 0.843009i \(-0.680782\pi\)
−0.537900 + 0.843009i \(0.680782\pi\)
\(284\) 4.51034e57 1.00283
\(285\) 2.04157e57 0.417936
\(286\) −9.32969e56 −0.175900
\(287\) 1.08768e57 0.188919
\(288\) 3.12165e56 0.0499643
\(289\) 3.04657e56 0.0449481
\(290\) 2.22778e57 0.303054
\(291\) 3.30190e57 0.414265
\(292\) −4.96905e57 −0.575144
\(293\) 1.05167e58 1.12328 0.561641 0.827381i \(-0.310170\pi\)
0.561641 + 0.827381i \(0.310170\pi\)
\(294\) 8.74127e56 0.0861811
\(295\) 1.56543e57 0.142501
\(296\) −3.08156e57 −0.259069
\(297\) −1.21834e58 −0.946222
\(298\) −1.55105e56 −0.0111313
\(299\) 5.13574e57 0.340667
\(300\) −2.28607e58 −1.40198
\(301\) 1.92535e57 0.109193
\(302\) 3.72002e55 0.00195156
\(303\) −7.77740e57 −0.377514
\(304\) 5.95539e57 0.267535
\(305\) 1.49484e58 0.621656
\(306\) 4.52331e56 0.0174182
\(307\) 5.43218e57 0.193741 0.0968707 0.995297i \(-0.469117\pi\)
0.0968707 + 0.995297i \(0.469117\pi\)
\(308\) 1.44083e58 0.476071
\(309\) 4.85853e58 1.48758
\(310\) −1.19130e58 −0.338082
\(311\) −4.80030e58 −1.26299 −0.631493 0.775381i \(-0.717558\pi\)
−0.631493 + 0.775381i \(0.717558\pi\)
\(312\) 1.48507e58 0.362339
\(313\) −2.50321e58 −0.566507 −0.283253 0.959045i \(-0.591414\pi\)
−0.283253 + 0.959045i \(0.591414\pi\)
\(314\) 2.20087e57 0.0462111
\(315\) 5.75541e57 0.112145
\(316\) 8.05990e58 1.45775
\(317\) −6.65301e58 −1.11719 −0.558593 0.829442i \(-0.688659\pi\)
−0.558593 + 0.829442i \(0.688659\pi\)
\(318\) 5.85385e57 0.0912860
\(319\) −9.05460e58 −1.31156
\(320\) −1.06297e59 −1.43052
\(321\) 3.04956e58 0.381390
\(322\) 1.37191e57 0.0159482
\(323\) 2.66559e58 0.288094
\(324\) 8.33540e58 0.837759
\(325\) 2.45920e59 2.29898
\(326\) 7.41372e57 0.0644797
\(327\) −8.91542e58 −0.721555
\(328\) −1.20183e58 −0.0905331
\(329\) −7.29953e58 −0.511907
\(330\) −2.65784e58 −0.173561
\(331\) −1.52984e58 −0.0930438 −0.0465219 0.998917i \(-0.514814\pi\)
−0.0465219 + 0.998917i \(0.514814\pi\)
\(332\) 4.86445e58 0.275606
\(333\) 2.48005e58 0.130924
\(334\) 1.53105e58 0.0753262
\(335\) −5.34969e58 −0.245344
\(336\) −1.11690e59 −0.477574
\(337\) −1.19696e59 −0.477284 −0.238642 0.971108i \(-0.576702\pi\)
−0.238642 + 0.971108i \(0.576702\pi\)
\(338\) −4.41324e58 −0.164140
\(339\) 4.73727e58 0.164375
\(340\) −4.93612e59 −1.59820
\(341\) 4.84194e59 1.46316
\(342\) 1.70238e57 0.00480222
\(343\) 3.50084e59 0.922062
\(344\) −2.12741e58 −0.0523272
\(345\) 1.46307e59 0.336136
\(346\) 1.15090e59 0.247029
\(347\) −6.60768e59 −1.32528 −0.662638 0.748940i \(-0.730563\pi\)
−0.662638 + 0.748940i \(0.730563\pi\)
\(348\) 7.14463e59 1.33927
\(349\) 7.13810e59 1.25079 0.625396 0.780308i \(-0.284937\pi\)
0.625396 + 0.780308i \(0.284937\pi\)
\(350\) 6.56924e58 0.107626
\(351\) −1.03415e60 −1.58441
\(352\) −2.39489e59 −0.343189
\(353\) 4.98386e58 0.0668129 0.0334064 0.999442i \(-0.489364\pi\)
0.0334064 + 0.999442i \(0.489364\pi\)
\(354\) −8.68394e57 −0.0108928
\(355\) −1.38221e60 −1.62259
\(356\) 4.04520e59 0.444493
\(357\) −4.99916e59 −0.514273
\(358\) −5.57870e58 −0.0537381
\(359\) 2.08989e60 1.88540 0.942700 0.333641i \(-0.108277\pi\)
0.942700 + 0.333641i \(0.108277\pi\)
\(360\) −6.35942e58 −0.0537414
\(361\) −1.16273e60 −0.920572
\(362\) −9.58408e58 −0.0711048
\(363\) −2.60649e59 −0.181239
\(364\) 1.22300e60 0.797159
\(365\) 1.52278e60 0.930585
\(366\) −8.29237e58 −0.0475197
\(367\) −1.22059e59 −0.0656021 −0.0328011 0.999462i \(-0.510443\pi\)
−0.0328011 + 0.999462i \(0.510443\pi\)
\(368\) 4.26786e59 0.215173
\(369\) 9.67236e58 0.0457523
\(370\) 4.68129e59 0.207790
\(371\) 9.72503e59 0.405139
\(372\) −3.82058e60 −1.49407
\(373\) −2.41910e60 −0.888172 −0.444086 0.895984i \(-0.646472\pi\)
−0.444086 + 0.895984i \(0.646472\pi\)
\(374\) −3.47023e59 −0.119640
\(375\) 2.42583e60 0.785463
\(376\) 8.06560e59 0.245314
\(377\) −7.68569e60 −2.19615
\(378\) −2.76252e59 −0.0741734
\(379\) 6.29795e60 1.58920 0.794598 0.607135i \(-0.207681\pi\)
0.794598 + 0.607135i \(0.207681\pi\)
\(380\) −1.85774e60 −0.440626
\(381\) 4.04661e60 0.902306
\(382\) 4.79333e59 0.100496
\(383\) 3.88964e60 0.766898 0.383449 0.923562i \(-0.374736\pi\)
0.383449 + 0.923562i \(0.374736\pi\)
\(384\) 2.51206e60 0.465850
\(385\) −4.41548e60 −0.770284
\(386\) −7.35523e59 −0.120724
\(387\) 1.71214e59 0.0264443
\(388\) −3.00459e60 −0.436757
\(389\) 5.15774e60 0.705739 0.352869 0.935673i \(-0.385206\pi\)
0.352869 + 0.935673i \(0.385206\pi\)
\(390\) −2.25602e60 −0.290619
\(391\) 1.91027e60 0.231707
\(392\) −1.60460e60 −0.183292
\(393\) 9.65300e60 1.03857
\(394\) 1.17821e60 0.119415
\(395\) −2.46999e61 −2.35865
\(396\) 1.28128e60 0.115294
\(397\) −1.92619e61 −1.63351 −0.816754 0.576986i \(-0.804229\pi\)
−0.816754 + 0.576986i \(0.804229\pi\)
\(398\) 2.94891e60 0.235727
\(399\) −1.88146e60 −0.141786
\(400\) 2.04362e61 1.45208
\(401\) 5.06490e58 0.00339374 0.00169687 0.999999i \(-0.499460\pi\)
0.00169687 + 0.999999i \(0.499460\pi\)
\(402\) 2.96764e59 0.0187542
\(403\) 4.10992e61 2.44999
\(404\) 7.07710e60 0.398010
\(405\) −2.55442e61 −1.35550
\(406\) −2.05308e60 −0.102812
\(407\) −1.90266e61 −0.899277
\(408\) 5.52381e60 0.246448
\(409\) 1.50217e61 0.632733 0.316367 0.948637i \(-0.397537\pi\)
0.316367 + 0.948637i \(0.397537\pi\)
\(410\) 1.82574e60 0.0726135
\(411\) 3.03664e61 1.14054
\(412\) −4.42106e61 −1.56834
\(413\) −1.44267e60 −0.0483437
\(414\) 1.21999e59 0.00386232
\(415\) −1.49073e61 −0.445932
\(416\) −2.03282e61 −0.574654
\(417\) −4.81352e61 −1.28607
\(418\) −1.30604e60 −0.0329849
\(419\) 6.95944e61 1.66167 0.830835 0.556518i \(-0.187863\pi\)
0.830835 + 0.556518i \(0.187863\pi\)
\(420\) 3.48408e61 0.786557
\(421\) −3.78966e61 −0.809042 −0.404521 0.914529i \(-0.632562\pi\)
−0.404521 + 0.914529i \(0.632562\pi\)
\(422\) −1.94170e60 −0.0392049
\(423\) −6.49121e60 −0.123973
\(424\) −1.07457e61 −0.194149
\(425\) 9.14712e61 1.56367
\(426\) 7.66756e60 0.124031
\(427\) −1.37762e61 −0.210898
\(428\) −2.77497e61 −0.402096
\(429\) 9.16936e61 1.25775
\(430\) 3.23181e60 0.0419698
\(431\) 4.06747e60 0.0500160 0.0250080 0.999687i \(-0.492039\pi\)
0.0250080 + 0.999687i \(0.492039\pi\)
\(432\) −8.59392e61 −1.00074
\(433\) −2.59125e61 −0.285788 −0.142894 0.989738i \(-0.545641\pi\)
−0.142894 + 0.989738i \(0.545641\pi\)
\(434\) 1.09788e61 0.114695
\(435\) −2.18950e62 −2.16694
\(436\) 8.11265e61 0.760730
\(437\) 7.18941e60 0.0638821
\(438\) −8.44736e60 −0.0711344
\(439\) 3.51058e61 0.280196 0.140098 0.990138i \(-0.455258\pi\)
0.140098 + 0.990138i \(0.455258\pi\)
\(440\) 4.87888e61 0.369132
\(441\) 1.29138e61 0.0926293
\(442\) −2.94559e61 −0.200331
\(443\) −4.43894e61 −0.286281 −0.143140 0.989702i \(-0.545720\pi\)
−0.143140 + 0.989702i \(0.545720\pi\)
\(444\) 1.50132e62 0.918275
\(445\) −1.23967e62 −0.719192
\(446\) 2.21428e60 0.0121861
\(447\) 1.52440e61 0.0795924
\(448\) 9.79607e61 0.485309
\(449\) 3.43198e62 1.61345 0.806725 0.590927i \(-0.201238\pi\)
0.806725 + 0.590927i \(0.201238\pi\)
\(450\) 5.84179e60 0.0260647
\(451\) −7.42052e61 −0.314257
\(452\) −4.31072e61 −0.173299
\(453\) −3.65609e60 −0.0139543
\(454\) −5.23613e61 −0.189757
\(455\) −3.74794e62 −1.28981
\(456\) 2.07892e61 0.0679460
\(457\) −9.64466e60 −0.0299403 −0.0149701 0.999888i \(-0.504765\pi\)
−0.0149701 + 0.999888i \(0.504765\pi\)
\(458\) 7.19656e60 0.0212220
\(459\) −3.84658e62 −1.07765
\(460\) −1.33133e62 −0.354386
\(461\) −6.32143e61 −0.159898 −0.0799491 0.996799i \(-0.525476\pi\)
−0.0799491 + 0.996799i \(0.525476\pi\)
\(462\) 2.44941e61 0.0588809
\(463\) 6.86213e62 1.56785 0.783927 0.620853i \(-0.213214\pi\)
0.783927 + 0.620853i \(0.213214\pi\)
\(464\) −6.38691e62 −1.38713
\(465\) 1.17083e63 2.41741
\(466\) 1.06310e62 0.208692
\(467\) −2.91371e62 −0.543876 −0.271938 0.962315i \(-0.587665\pi\)
−0.271938 + 0.962315i \(0.587665\pi\)
\(468\) 1.08757e62 0.193055
\(469\) 4.93016e61 0.0832337
\(470\) −1.22527e62 −0.196758
\(471\) −2.16304e62 −0.330426
\(472\) 1.59407e61 0.0231671
\(473\) −1.31354e62 −0.181637
\(474\) 1.37018e62 0.180296
\(475\) 3.44258e62 0.431106
\(476\) 4.54902e62 0.542194
\(477\) 8.64813e61 0.0981161
\(478\) −1.68954e62 −0.182479
\(479\) −9.39830e62 −0.966417 −0.483209 0.875505i \(-0.660529\pi\)
−0.483209 + 0.875505i \(0.660529\pi\)
\(480\) −5.79110e62 −0.567011
\(481\) −1.61501e63 −1.50580
\(482\) 7.46579e61 0.0662934
\(483\) −1.34833e62 −0.114035
\(484\) 2.37180e62 0.191079
\(485\) 9.20767e62 0.706674
\(486\) −4.62931e61 −0.0338504
\(487\) 2.39350e63 1.66764 0.833820 0.552037i \(-0.186149\pi\)
0.833820 + 0.552037i \(0.186149\pi\)
\(488\) 1.52219e62 0.101066
\(489\) −7.28632e62 −0.461052
\(490\) 2.43759e62 0.147012
\(491\) 1.23586e63 0.710481 0.355241 0.934775i \(-0.384399\pi\)
0.355241 + 0.934775i \(0.384399\pi\)
\(492\) 5.85524e62 0.320896
\(493\) −2.85874e63 −1.49373
\(494\) −1.10859e62 −0.0552317
\(495\) −3.92653e62 −0.186546
\(496\) 3.41539e63 1.54747
\(497\) 1.27382e63 0.550468
\(498\) 8.26955e61 0.0340873
\(499\) −2.94657e63 −1.15865 −0.579327 0.815095i \(-0.696684\pi\)
−0.579327 + 0.815095i \(0.696684\pi\)
\(500\) −2.20741e63 −0.828108
\(501\) −1.50473e63 −0.538609
\(502\) 6.28387e62 0.214630
\(503\) −1.27808e63 −0.416591 −0.208296 0.978066i \(-0.566792\pi\)
−0.208296 + 0.978066i \(0.566792\pi\)
\(504\) 5.86071e61 0.0182319
\(505\) −2.16880e63 −0.643981
\(506\) −9.35961e61 −0.0265290
\(507\) 4.33740e63 1.17366
\(508\) −3.68224e63 −0.951294
\(509\) 7.25177e63 1.78886 0.894429 0.447209i \(-0.147582\pi\)
0.894429 + 0.447209i \(0.147582\pi\)
\(510\) −8.39138e62 −0.197667
\(511\) −1.40336e63 −0.315704
\(512\) −2.83172e63 −0.608423
\(513\) −1.44768e63 −0.297109
\(514\) −2.99635e62 −0.0587435
\(515\) 1.35485e64 2.53759
\(516\) 1.03646e63 0.185475
\(517\) 4.97998e63 0.851531
\(518\) −4.31418e62 −0.0704934
\(519\) −1.13112e64 −1.76634
\(520\) 4.14127e63 0.618095
\(521\) −9.84138e63 −1.40401 −0.702004 0.712173i \(-0.747711\pi\)
−0.702004 + 0.712173i \(0.747711\pi\)
\(522\) −1.82573e62 −0.0248988
\(523\) 4.91409e62 0.0640698 0.0320349 0.999487i \(-0.489801\pi\)
0.0320349 + 0.999487i \(0.489801\pi\)
\(524\) −8.78382e63 −1.09496
\(525\) −6.45635e63 −0.769561
\(526\) −1.28961e63 −0.146992
\(527\) 1.52871e64 1.66638
\(528\) 7.61986e63 0.794419
\(529\) −9.51264e63 −0.948621
\(530\) 1.63240e63 0.155720
\(531\) −1.28291e62 −0.0117078
\(532\) 1.71205e63 0.149484
\(533\) −6.29866e63 −0.526210
\(534\) 6.87682e62 0.0549754
\(535\) 8.50400e63 0.650593
\(536\) −5.44756e62 −0.0398869
\(537\) 5.48283e63 0.384246
\(538\) 2.91580e63 0.195602
\(539\) −9.90734e63 −0.636240
\(540\) 2.68081e64 1.64821
\(541\) 6.71742e61 0.00395428 0.00197714 0.999998i \(-0.499371\pi\)
0.00197714 + 0.999998i \(0.499371\pi\)
\(542\) −3.96959e63 −0.223750
\(543\) 9.41938e63 0.508424
\(544\) −7.56119e63 −0.390856
\(545\) −2.48615e64 −1.23086
\(546\) 2.07910e63 0.0985934
\(547\) 4.01645e62 0.0182449 0.00912243 0.999958i \(-0.497096\pi\)
0.00912243 + 0.999958i \(0.497096\pi\)
\(548\) −2.76322e64 −1.20246
\(549\) −1.22507e63 −0.0510751
\(550\) −4.48176e63 −0.179030
\(551\) −1.07590e64 −0.411823
\(552\) 1.48983e63 0.0546474
\(553\) 2.27629e64 0.800177
\(554\) 1.29428e63 0.0436062
\(555\) −4.60084e64 −1.48577
\(556\) 4.38010e64 1.35589
\(557\) 6.03614e64 1.79127 0.895637 0.444785i \(-0.146720\pi\)
0.895637 + 0.444785i \(0.146720\pi\)
\(558\) 9.76306e62 0.0277768
\(559\) −1.11495e64 −0.304144
\(560\) −3.11458e64 −0.814669
\(561\) 3.41059e64 0.855466
\(562\) 6.14089e63 0.147716
\(563\) −3.47404e63 −0.0801470 −0.0400735 0.999197i \(-0.512759\pi\)
−0.0400735 + 0.999197i \(0.512759\pi\)
\(564\) −3.92951e64 −0.869520
\(565\) 1.32104e64 0.280399
\(566\) 6.88940e63 0.140280
\(567\) 2.35409e64 0.459856
\(568\) −1.40750e64 −0.263793
\(569\) 9.25178e64 1.66375 0.831873 0.554966i \(-0.187269\pi\)
0.831873 + 0.554966i \(0.187269\pi\)
\(570\) −3.15815e63 −0.0544971
\(571\) −1.04188e65 −1.72532 −0.862658 0.505787i \(-0.831202\pi\)
−0.862658 + 0.505787i \(0.831202\pi\)
\(572\) −8.34373e64 −1.32603
\(573\) −4.71096e64 −0.718581
\(574\) −1.68256e63 −0.0246343
\(575\) 2.46708e64 0.346728
\(576\) 8.71130e63 0.117532
\(577\) −8.68105e64 −1.12445 −0.562225 0.826984i \(-0.690055\pi\)
−0.562225 + 0.826984i \(0.690055\pi\)
\(578\) −4.71281e62 −0.00586105
\(579\) 7.22883e64 0.863221
\(580\) 1.99235e65 2.28459
\(581\) 1.37382e64 0.151284
\(582\) −5.10778e63 −0.0540185
\(583\) −6.63474e64 −0.673928
\(584\) 1.55064e64 0.151290
\(585\) −3.33291e64 −0.312364
\(586\) −1.62685e64 −0.146471
\(587\) 5.04453e64 0.436340 0.218170 0.975911i \(-0.429991\pi\)
0.218170 + 0.975911i \(0.429991\pi\)
\(588\) 7.81749e64 0.649681
\(589\) 5.75338e64 0.459424
\(590\) −2.42160e63 −0.0185815
\(591\) −1.15796e65 −0.853861
\(592\) −1.34210e65 −0.951094
\(593\) 1.82757e65 1.24477 0.622385 0.782712i \(-0.286164\pi\)
0.622385 + 0.782712i \(0.286164\pi\)
\(594\) 1.88468e64 0.123383
\(595\) −1.39406e65 −0.877272
\(596\) −1.38714e64 −0.0839137
\(597\) −2.89823e65 −1.68553
\(598\) −7.94459e63 −0.0444216
\(599\) 6.30818e64 0.339136 0.169568 0.985519i \(-0.445763\pi\)
0.169568 + 0.985519i \(0.445763\pi\)
\(600\) 7.13392e64 0.368786
\(601\) 1.16613e65 0.579693 0.289847 0.957073i \(-0.406396\pi\)
0.289847 + 0.957073i \(0.406396\pi\)
\(602\) −2.97837e63 −0.0142384
\(603\) 4.38422e63 0.0201574
\(604\) 3.32689e63 0.0147119
\(605\) −7.26847e64 −0.309166
\(606\) 1.20310e64 0.0492262
\(607\) −8.69736e64 −0.342337 −0.171168 0.985242i \(-0.554754\pi\)
−0.171168 + 0.985242i \(0.554754\pi\)
\(608\) −2.84570e64 −0.107760
\(609\) 2.01779e65 0.735141
\(610\) −2.31241e64 −0.0810614
\(611\) 4.22709e65 1.42585
\(612\) 4.04529e64 0.131308
\(613\) 3.95467e65 1.23535 0.617674 0.786435i \(-0.288075\pi\)
0.617674 + 0.786435i \(0.288075\pi\)
\(614\) −8.40317e63 −0.0252631
\(615\) −1.79436e65 −0.519212
\(616\) −4.49627e64 −0.125229
\(617\) −4.10300e65 −1.10002 −0.550009 0.835159i \(-0.685376\pi\)
−0.550009 + 0.835159i \(0.685376\pi\)
\(618\) −7.51577e64 −0.193974
\(619\) 1.39273e65 0.346047 0.173024 0.984918i \(-0.444646\pi\)
0.173024 + 0.984918i \(0.444646\pi\)
\(620\) −1.06541e66 −2.54865
\(621\) −1.03747e65 −0.238958
\(622\) 7.42569e64 0.164688
\(623\) 1.14245e65 0.243988
\(624\) 6.46786e65 1.33022
\(625\) −9.58171e64 −0.189785
\(626\) 3.87227e64 0.0738702
\(627\) 1.28360e65 0.235853
\(628\) 1.96828e65 0.348365
\(629\) −6.00713e65 −1.02418
\(630\) −8.90318e63 −0.0146232
\(631\) 1.54026e65 0.243728 0.121864 0.992547i \(-0.461113\pi\)
0.121864 + 0.992547i \(0.461113\pi\)
\(632\) −2.51518e65 −0.383457
\(633\) 1.90833e65 0.280328
\(634\) 1.02917e65 0.145677
\(635\) 1.12844e66 1.53920
\(636\) 5.23522e65 0.688165
\(637\) −8.40952e65 −1.06536
\(638\) 1.40068e65 0.171022
\(639\) 1.13276e65 0.133312
\(640\) 7.00513e65 0.794670
\(641\) −1.65837e65 −0.181350 −0.0906752 0.995881i \(-0.528903\pi\)
−0.0906752 + 0.995881i \(0.528903\pi\)
\(642\) −4.71743e64 −0.0497316
\(643\) −1.22213e66 −1.24211 −0.621053 0.783768i \(-0.713295\pi\)
−0.621053 + 0.783768i \(0.713295\pi\)
\(644\) 1.22692e65 0.120226
\(645\) −3.17627e65 −0.300099
\(646\) −4.12346e64 −0.0375663
\(647\) −9.62351e65 −0.845440 −0.422720 0.906260i \(-0.638925\pi\)
−0.422720 + 0.906260i \(0.638925\pi\)
\(648\) −2.60115e65 −0.220370
\(649\) 9.84237e64 0.0804173
\(650\) −3.80419e65 −0.299777
\(651\) −1.07901e66 −0.820112
\(652\) 6.63024e65 0.486084
\(653\) 3.91841e65 0.277109 0.138554 0.990355i \(-0.455754\pi\)
0.138554 + 0.990355i \(0.455754\pi\)
\(654\) 1.37915e65 0.0940878
\(655\) 2.69183e66 1.77165
\(656\) −5.23427e65 −0.332365
\(657\) −1.24796e65 −0.0764567
\(658\) 1.12918e65 0.0667506
\(659\) 2.16961e66 1.23758 0.618792 0.785555i \(-0.287622\pi\)
0.618792 + 0.785555i \(0.287622\pi\)
\(660\) −2.37696e66 −1.30840
\(661\) −9.87453e65 −0.524544 −0.262272 0.964994i \(-0.584472\pi\)
−0.262272 + 0.964994i \(0.584472\pi\)
\(662\) 2.36654e64 0.0121325
\(663\) 2.89497e66 1.43244
\(664\) −1.51800e65 −0.0724975
\(665\) −5.24665e65 −0.241865
\(666\) −3.83644e64 −0.0170720
\(667\) −7.71034e65 −0.331220
\(668\) 1.36925e66 0.567851
\(669\) −2.17623e65 −0.0871347
\(670\) 8.27556e64 0.0319919
\(671\) 9.39857e65 0.350818
\(672\) 5.33695e65 0.192360
\(673\) −5.18176e66 −1.80353 −0.901765 0.432227i \(-0.857728\pi\)
−0.901765 + 0.432227i \(0.857728\pi\)
\(674\) 1.85161e65 0.0622359
\(675\) −4.96780e66 −1.61260
\(676\) −3.94685e66 −1.23738
\(677\) 5.62905e66 1.70452 0.852259 0.523120i \(-0.175232\pi\)
0.852259 + 0.523120i \(0.175232\pi\)
\(678\) −7.32820e64 −0.0214338
\(679\) −8.48559e65 −0.239741
\(680\) 1.54037e66 0.420402
\(681\) 5.14615e66 1.35683
\(682\) −7.49010e65 −0.190790
\(683\) −2.17309e66 −0.534800 −0.267400 0.963586i \(-0.586165\pi\)
−0.267400 + 0.963586i \(0.586165\pi\)
\(684\) 1.52247e65 0.0362018
\(685\) 8.46798e66 1.94559
\(686\) −5.41553e65 −0.120233
\(687\) −7.07289e65 −0.151745
\(688\) −9.26539e65 −0.192104
\(689\) −5.63168e66 −1.12846
\(690\) −2.26325e65 −0.0438308
\(691\) 3.80507e66 0.712244 0.356122 0.934439i \(-0.384099\pi\)
0.356122 + 0.934439i \(0.384099\pi\)
\(692\) 1.02927e67 1.86224
\(693\) 3.61861e65 0.0632864
\(694\) 1.02216e66 0.172811
\(695\) −1.34230e67 −2.19384
\(696\) −2.22956e66 −0.352291
\(697\) −2.34282e66 −0.357906
\(698\) −1.10421e66 −0.163098
\(699\) −1.04483e67 −1.49222
\(700\) 5.87500e66 0.811343
\(701\) 4.48575e66 0.599048 0.299524 0.954089i \(-0.403172\pi\)
0.299524 + 0.954089i \(0.403172\pi\)
\(702\) 1.59975e66 0.206600
\(703\) −2.26082e66 −0.282368
\(704\) −6.68321e66 −0.807286
\(705\) 1.20421e67 1.40689
\(706\) −7.70965e64 −0.00871212
\(707\) 1.99872e66 0.218472
\(708\) −7.76623e65 −0.0821161
\(709\) −1.23589e67 −1.26414 −0.632068 0.774913i \(-0.717794\pi\)
−0.632068 + 0.774913i \(0.717794\pi\)
\(710\) 2.13818e66 0.211579
\(711\) 2.02422e66 0.193786
\(712\) −1.26235e66 −0.116923
\(713\) 4.12310e66 0.369504
\(714\) 7.73331e65 0.0670591
\(715\) 2.55697e67 2.14552
\(716\) −4.98915e66 −0.405108
\(717\) 1.66050e67 1.30479
\(718\) −3.23290e66 −0.245848
\(719\) −5.05205e66 −0.371825 −0.185913 0.982566i \(-0.559524\pi\)
−0.185913 + 0.982566i \(0.559524\pi\)
\(720\) −2.76969e66 −0.197295
\(721\) −1.24860e67 −0.860884
\(722\) 1.79865e66 0.120039
\(723\) −7.33749e66 −0.474021
\(724\) −8.57124e66 −0.536028
\(725\) −3.69202e67 −2.23522
\(726\) 4.03205e65 0.0236328
\(727\) 2.10795e67 1.19619 0.598097 0.801424i \(-0.295924\pi\)
0.598097 + 0.801424i \(0.295924\pi\)
\(728\) −3.81651e66 −0.209690
\(729\) 2.05698e67 1.09429
\(730\) −2.35563e66 −0.121344
\(731\) −4.14712e66 −0.206866
\(732\) −7.41604e66 −0.358230
\(733\) 2.34941e67 1.09905 0.549523 0.835478i \(-0.314809\pi\)
0.549523 + 0.835478i \(0.314809\pi\)
\(734\) 1.88816e65 0.00855425
\(735\) −2.39570e67 −1.05119
\(736\) −2.03934e66 −0.0866685
\(737\) −3.36352e66 −0.138455
\(738\) −1.49624e65 −0.00596591
\(739\) −8.69448e66 −0.335814 −0.167907 0.985803i \(-0.553701\pi\)
−0.167907 + 0.985803i \(0.553701\pi\)
\(740\) 4.18657e67 1.56644
\(741\) 1.08954e67 0.394926
\(742\) −1.50439e66 −0.0528285
\(743\) 1.83903e67 0.625679 0.312840 0.949806i \(-0.398720\pi\)
0.312840 + 0.949806i \(0.398720\pi\)
\(744\) 1.19225e67 0.393011
\(745\) 4.25094e66 0.135773
\(746\) 3.74217e66 0.115814
\(747\) 1.22169e66 0.0366377
\(748\) −3.10350e67 −0.901911
\(749\) −7.83710e66 −0.220715
\(750\) −3.75258e66 −0.102421
\(751\) −2.92872e67 −0.774709 −0.387355 0.921931i \(-0.626611\pi\)
−0.387355 + 0.921931i \(0.626611\pi\)
\(752\) 3.51277e67 0.900597
\(753\) −6.17588e67 −1.53468
\(754\) 1.18892e67 0.286369
\(755\) −1.01954e66 −0.0238040
\(756\) −2.47058e67 −0.559160
\(757\) −3.60671e67 −0.791330 −0.395665 0.918395i \(-0.629486\pi\)
−0.395665 + 0.918395i \(0.629486\pi\)
\(758\) −9.74245e66 −0.207225
\(759\) 9.19877e66 0.189691
\(760\) 5.79727e66 0.115906
\(761\) 6.36047e67 1.23296 0.616481 0.787370i \(-0.288558\pi\)
0.616481 + 0.787370i \(0.288558\pi\)
\(762\) −6.25979e66 −0.117657
\(763\) 2.29118e67 0.417574
\(764\) 4.28678e67 0.757595
\(765\) −1.23969e67 −0.212457
\(766\) −6.01697e66 −0.100000
\(767\) 8.35437e66 0.134655
\(768\) 4.97608e67 0.777855
\(769\) −1.58030e67 −0.239591 −0.119795 0.992799i \(-0.538224\pi\)
−0.119795 + 0.992799i \(0.538224\pi\)
\(770\) 6.83041e66 0.100442
\(771\) 2.94486e67 0.420037
\(772\) −6.57793e67 −0.910087
\(773\) −1.20430e68 −1.61628 −0.808142 0.588988i \(-0.799526\pi\)
−0.808142 + 0.588988i \(0.799526\pi\)
\(774\) −2.64856e65 −0.00344823
\(775\) 1.97430e68 2.49358
\(776\) 9.37613e66 0.114888
\(777\) 4.24004e67 0.504052
\(778\) −7.97864e66 −0.0920255
\(779\) −8.81736e66 −0.0986752
\(780\) −2.01760e68 −2.19085
\(781\) −8.69040e67 −0.915674
\(782\) −2.95503e66 −0.0302137
\(783\) 1.55258e68 1.54047
\(784\) −6.98842e67 −0.672901
\(785\) −6.03186e67 −0.563656
\(786\) −1.49324e67 −0.135426
\(787\) −1.72836e68 −1.52134 −0.760671 0.649137i \(-0.775130\pi\)
−0.760671 + 0.649137i \(0.775130\pi\)
\(788\) 1.05369e68 0.900219
\(789\) 1.26745e68 1.05104
\(790\) 3.82088e67 0.307558
\(791\) −1.21744e67 −0.0951261
\(792\) −3.99837e66 −0.0303278
\(793\) 7.97766e67 0.587429
\(794\) 2.97966e67 0.213003
\(795\) −1.60435e68 −1.11345
\(796\) 2.63727e68 1.77704
\(797\) −5.17743e67 −0.338722 −0.169361 0.985554i \(-0.554170\pi\)
−0.169361 + 0.985554i \(0.554170\pi\)
\(798\) 2.91048e66 0.0184883
\(799\) 1.57229e68 0.969803
\(800\) −9.76519e67 −0.584879
\(801\) 1.01594e67 0.0590887
\(802\) −7.83502e64 −0.000442530 0
\(803\) 9.57423e67 0.525156
\(804\) 2.65402e67 0.141380
\(805\) −3.75995e67 −0.194527
\(806\) −6.35773e67 −0.319469
\(807\) −2.86569e68 −1.39862
\(808\) −2.20848e67 −0.104695
\(809\) −1.34819e68 −0.620812 −0.310406 0.950604i \(-0.600465\pi\)
−0.310406 + 0.950604i \(0.600465\pi\)
\(810\) 3.95149e67 0.176751
\(811\) −1.29768e68 −0.563869 −0.281934 0.959434i \(-0.590976\pi\)
−0.281934 + 0.959434i \(0.590976\pi\)
\(812\) −1.83611e68 −0.775053
\(813\) 3.90137e68 1.59989
\(814\) 2.94328e67 0.117262
\(815\) −2.03186e68 −0.786485
\(816\) 2.40576e68 0.904759
\(817\) −1.56080e67 −0.0570332
\(818\) −2.32374e67 −0.0825059
\(819\) 3.07154e67 0.105970
\(820\) 1.63279e68 0.547401
\(821\) −3.05518e68 −0.995342 −0.497671 0.867366i \(-0.665811\pi\)
−0.497671 + 0.867366i \(0.665811\pi\)
\(822\) −4.69745e67 −0.148722
\(823\) −3.54128e68 −1.08959 −0.544796 0.838568i \(-0.683393\pi\)
−0.544796 + 0.838568i \(0.683393\pi\)
\(824\) 1.37964e68 0.412549
\(825\) 4.40474e68 1.28012
\(826\) 2.23170e66 0.00630383
\(827\) 5.88899e68 1.61682 0.808410 0.588620i \(-0.200328\pi\)
0.808410 + 0.588620i \(0.200328\pi\)
\(828\) 1.09106e67 0.0291163
\(829\) 7.14204e68 1.85264 0.926319 0.376740i \(-0.122955\pi\)
0.926319 + 0.376740i \(0.122955\pi\)
\(830\) 2.30604e67 0.0581477
\(831\) −1.27204e68 −0.311799
\(832\) −5.67282e68 −1.35176
\(833\) −3.12797e68 −0.724610
\(834\) 7.44614e67 0.167698
\(835\) −4.19610e68 −0.918785
\(836\) −1.16802e68 −0.248658
\(837\) −8.30241e68 −1.71852
\(838\) −1.07657e68 −0.216675
\(839\) 4.08251e68 0.798953 0.399477 0.916743i \(-0.369192\pi\)
0.399477 + 0.916743i \(0.369192\pi\)
\(840\) −1.08724e68 −0.206902
\(841\) 6.13474e68 1.13525
\(842\) 5.86231e67 0.105496
\(843\) −6.03536e68 −1.05622
\(844\) −1.73650e68 −0.295548
\(845\) 1.20953e69 2.00209
\(846\) 1.00414e67 0.0161656
\(847\) 6.69846e67 0.104885
\(848\) −4.68000e68 −0.712760
\(849\) −6.77100e68 −1.00305
\(850\) −1.41499e68 −0.203896
\(851\) −1.62019e68 −0.227102
\(852\) 6.85726e68 0.935018
\(853\) 6.69695e68 0.888331 0.444166 0.895945i \(-0.353500\pi\)
0.444166 + 0.895945i \(0.353500\pi\)
\(854\) 2.13107e67 0.0275003
\(855\) −4.66566e67 −0.0585746
\(856\) 8.65958e67 0.105770
\(857\) 1.01115e69 1.20162 0.600809 0.799393i \(-0.294845\pi\)
0.600809 + 0.799393i \(0.294845\pi\)
\(858\) −1.41843e68 −0.164005
\(859\) −4.13647e68 −0.465361 −0.232681 0.972553i \(-0.574750\pi\)
−0.232681 + 0.972553i \(0.574750\pi\)
\(860\) 2.89027e68 0.316392
\(861\) 1.65364e68 0.176144
\(862\) −6.29207e66 −0.00652188
\(863\) 6.85332e68 0.691270 0.345635 0.938369i \(-0.387664\pi\)
0.345635 + 0.938369i \(0.387664\pi\)
\(864\) 4.10649e68 0.403086
\(865\) −3.15424e69 −3.01312
\(866\) 4.00847e67 0.0372656
\(867\) 4.63182e67 0.0419086
\(868\) 9.81856e68 0.864638
\(869\) −1.55296e69 −1.33105
\(870\) 3.38699e68 0.282560
\(871\) −2.85501e68 −0.231836
\(872\) −2.53164e68 −0.200108
\(873\) −7.54594e67 −0.0580602
\(874\) −1.11215e67 −0.00832997
\(875\) −6.23418e68 −0.454559
\(876\) −7.55464e68 −0.536250
\(877\) 6.43840e68 0.444925 0.222463 0.974941i \(-0.428590\pi\)
0.222463 + 0.974941i \(0.428590\pi\)
\(878\) −5.43059e67 −0.0365364
\(879\) 1.59889e69 1.04732
\(880\) 2.12487e69 1.35516
\(881\) 8.86127e68 0.550253 0.275126 0.961408i \(-0.411280\pi\)
0.275126 + 0.961408i \(0.411280\pi\)
\(882\) −1.99767e67 −0.0120785
\(883\) 4.16643e68 0.245294 0.122647 0.992450i \(-0.460862\pi\)
0.122647 + 0.992450i \(0.460862\pi\)
\(884\) −2.63430e69 −1.51021
\(885\) 2.37999e68 0.132864
\(886\) 6.86670e67 0.0373298
\(887\) 2.94393e69 1.55856 0.779278 0.626679i \(-0.215586\pi\)
0.779278 + 0.626679i \(0.215586\pi\)
\(888\) −4.68502e68 −0.241550
\(889\) −1.03994e69 −0.522177
\(890\) 1.91767e68 0.0937797
\(891\) −1.60604e69 −0.764946
\(892\) 1.98028e68 0.0918654
\(893\) 5.91742e68 0.267376
\(894\) −2.35813e67 −0.0103785
\(895\) 1.52894e69 0.655466
\(896\) −6.45578e68 −0.269594
\(897\) 7.80807e68 0.317630
\(898\) −5.30901e68 −0.210387
\(899\) −6.17026e69 −2.38205
\(900\) 5.22443e68 0.196490
\(901\) −2.09473e69 −0.767532
\(902\) 1.14790e68 0.0409779
\(903\) 2.92718e68 0.101809
\(904\) 1.34521e68 0.0455859
\(905\) 2.62669e69 0.867295
\(906\) 5.65569e66 0.00181959
\(907\) 3.36233e69 1.05407 0.527034 0.849844i \(-0.323304\pi\)
0.527034 + 0.849844i \(0.323304\pi\)
\(908\) −4.68278e69 −1.43049
\(909\) 1.77739e68 0.0529094
\(910\) 5.79777e68 0.168185
\(911\) 4.29823e69 1.21509 0.607544 0.794286i \(-0.292155\pi\)
0.607544 + 0.794286i \(0.292155\pi\)
\(912\) 9.05422e68 0.249443
\(913\) −9.37269e68 −0.251652
\(914\) 1.49195e67 0.00390409
\(915\) 2.27267e69 0.579617
\(916\) 6.43603e68 0.159983
\(917\) −2.48074e69 −0.601037
\(918\) 5.95036e68 0.140521
\(919\) 5.89124e69 1.35610 0.678050 0.735015i \(-0.262825\pi\)
0.678050 + 0.735015i \(0.262825\pi\)
\(920\) 4.15455e68 0.0932202
\(921\) 8.25876e68 0.180640
\(922\) 9.77877e67 0.0208501
\(923\) −7.37656e69 −1.53325
\(924\) 2.19055e69 0.443877
\(925\) −7.75813e69 −1.53259
\(926\) −1.06152e69 −0.204442
\(927\) −1.11034e69 −0.208488
\(928\) 3.05190e69 0.558718
\(929\) −3.81127e69 −0.680301 −0.340150 0.940371i \(-0.610478\pi\)
−0.340150 + 0.940371i \(0.610478\pi\)
\(930\) −1.81119e69 −0.315220
\(931\) −1.17723e69 −0.199776
\(932\) 9.50754e69 1.57324
\(933\) −7.29808e69 −1.17758
\(934\) 4.50729e68 0.0709192
\(935\) 9.51078e69 1.45930
\(936\) −3.39388e68 −0.0507826
\(937\) −3.18868e69 −0.465298 −0.232649 0.972561i \(-0.574739\pi\)
−0.232649 + 0.972561i \(0.574739\pi\)
\(938\) −7.62658e67 −0.0108533
\(939\) −3.80573e69 −0.528197
\(940\) −1.09578e70 −1.48327
\(941\) 7.20176e69 0.950785 0.475393 0.879774i \(-0.342306\pi\)
0.475393 + 0.879774i \(0.342306\pi\)
\(942\) 3.34606e68 0.0430862
\(943\) −6.31886e68 −0.0793623
\(944\) 6.94259e68 0.0850510
\(945\) 7.57117e69 0.904723
\(946\) 2.03194e68 0.0236848
\(947\) 7.19607e69 0.818222 0.409111 0.912485i \(-0.365839\pi\)
0.409111 + 0.912485i \(0.365839\pi\)
\(948\) 1.22538e70 1.35917
\(949\) 8.12676e69 0.879350
\(950\) −5.32540e68 −0.0562144
\(951\) −1.01148e70 −1.04164
\(952\) −1.41957e69 −0.142623
\(953\) 1.03533e70 1.01483 0.507417 0.861700i \(-0.330600\pi\)
0.507417 + 0.861700i \(0.330600\pi\)
\(954\) −1.33780e68 −0.0127939
\(955\) −1.31370e70 −1.22579
\(956\) −1.51099e70 −1.37563
\(957\) −1.37661e70 −1.22287
\(958\) 1.45384e69 0.126017
\(959\) −7.80391e69 −0.660047
\(960\) −1.61607e70 −1.33379
\(961\) 2.05789e70 1.65738
\(962\) 2.49830e69 0.196350
\(963\) −6.96926e68 −0.0534526
\(964\) 6.67681e69 0.499757
\(965\) 2.01583e70 1.47252
\(966\) 2.08576e68 0.0148697
\(967\) −1.88655e70 −1.31264 −0.656321 0.754482i \(-0.727888\pi\)
−0.656321 + 0.754482i \(0.727888\pi\)
\(968\) −7.40145e68 −0.0502627
\(969\) 4.05260e69 0.268612
\(970\) −1.42436e69 −0.0921474
\(971\) −1.54065e70 −0.972862 −0.486431 0.873719i \(-0.661701\pi\)
−0.486431 + 0.873719i \(0.661701\pi\)
\(972\) −4.14008e69 −0.255183
\(973\) 1.23703e70 0.744268
\(974\) −3.70256e69 −0.217453
\(975\) 3.73882e70 2.14351
\(976\) 6.62954e69 0.371033
\(977\) −1.28077e70 −0.699760 −0.349880 0.936795i \(-0.613778\pi\)
−0.349880 + 0.936795i \(0.613778\pi\)
\(978\) 1.12714e69 0.0601193
\(979\) −7.79418e69 −0.405861
\(980\) 2.17999e70 1.10826
\(981\) 2.03747e69 0.101128
\(982\) −1.91177e69 −0.0926438
\(983\) 1.22658e70 0.580349 0.290174 0.956974i \(-0.406287\pi\)
0.290174 + 0.956974i \(0.406287\pi\)
\(984\) −1.82719e69 −0.0844109
\(985\) −3.22908e70 −1.45656
\(986\) 4.42225e69 0.194776
\(987\) −1.10978e70 −0.477290
\(988\) −9.91435e69 −0.416367
\(989\) −1.11853e69 −0.0458705
\(990\) 6.07405e68 0.0243249
\(991\) 2.78865e70 1.09059 0.545296 0.838244i \(-0.316417\pi\)
0.545296 + 0.838244i \(0.316417\pi\)
\(992\) −1.63200e70 −0.623298
\(993\) −2.32587e69 −0.0867519
\(994\) −1.97050e69 −0.0717787
\(995\) −8.08202e70 −2.87526
\(996\) 7.39562e69 0.256969
\(997\) 2.05189e70 0.696336 0.348168 0.937432i \(-0.386804\pi\)
0.348168 + 0.937432i \(0.386804\pi\)
\(998\) 4.55812e69 0.151084
\(999\) 3.26247e70 1.05623
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 1.48.a.a.1.2 4
3.2 odd 2 9.48.a.c.1.3 4
4.3 odd 2 16.48.a.d.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.48.a.a.1.2 4 1.1 even 1 trivial
9.48.a.c.1.3 4 3.2 odd 2
16.48.a.d.1.1 4 4.3 odd 2