Properties

Label 1.44.a.a.1.1
Level $1$
Weight $44$
Character 1.1
Self dual yes
Analytic conductor $11.711$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 44 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.7110395346\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 11258260111 x - 264759545317170\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4}\cdot 5\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-24885.9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.65343e6 q^{2} +3.22027e10 q^{3} +1.28583e13 q^{4} +5.54482e14 q^{5} -1.49853e17 q^{6} -5.57604e17 q^{7} -1.89031e19 q^{8} +7.08758e20 q^{9} +O(q^{10})\) \(q-4.65343e6 q^{2} +3.22027e10 q^{3} +1.28583e13 q^{4} +5.54482e14 q^{5} -1.49853e17 q^{6} -5.57604e17 q^{7} -1.89031e19 q^{8} +7.08758e20 q^{9} -2.58024e21 q^{10} -1.13059e22 q^{11} +4.14071e23 q^{12} +5.07130e23 q^{13} +2.59477e24 q^{14} +1.78558e25 q^{15} -2.51386e25 q^{16} +8.73610e25 q^{17} -3.29815e27 q^{18} +5.55222e27 q^{19} +7.12968e27 q^{20} -1.79564e28 q^{21} +5.26114e28 q^{22} +1.85137e29 q^{23} -6.08730e29 q^{24} -8.29418e29 q^{25} -2.35989e30 q^{26} +1.22532e31 q^{27} -7.16982e30 q^{28} +4.19782e31 q^{29} -8.30908e31 q^{30} -9.30312e31 q^{31} +2.83254e32 q^{32} -3.64082e32 q^{33} -4.06528e32 q^{34} -3.09181e32 q^{35} +9.11340e33 q^{36} -3.20928e33 q^{37} -2.58368e34 q^{38} +1.63309e34 q^{39} -1.04814e34 q^{40} +6.48857e33 q^{41} +8.35585e34 q^{42} +3.51189e33 q^{43} -1.45375e35 q^{44} +3.92993e35 q^{45} -8.61520e35 q^{46} +6.21410e35 q^{47} -8.09530e35 q^{48} -1.87289e36 q^{49} +3.85963e36 q^{50} +2.81326e36 q^{51} +6.52081e36 q^{52} +8.28552e36 q^{53} -5.70191e37 q^{54} -6.26895e36 q^{55} +1.05404e37 q^{56} +1.78797e38 q^{57} -1.95342e38 q^{58} -7.48073e36 q^{59} +2.29595e38 q^{60} -2.24824e38 q^{61} +4.32914e38 q^{62} -3.95206e38 q^{63} -1.09698e39 q^{64} +2.81194e38 q^{65} +1.69423e39 q^{66} -1.89786e39 q^{67} +1.12331e39 q^{68} +5.96191e39 q^{69} +1.43875e39 q^{70} -9.53945e39 q^{71} -1.33977e40 q^{72} +2.48260e39 q^{73} +1.49341e40 q^{74} -2.67095e40 q^{75} +7.13920e40 q^{76} +6.30424e39 q^{77} -7.59948e40 q^{78} -3.50244e39 q^{79} -1.39389e40 q^{80} +1.61930e41 q^{81} -3.01941e40 q^{82} -2.23114e41 q^{83} -2.30888e41 q^{84} +4.84401e40 q^{85} -1.63423e40 q^{86} +1.35181e42 q^{87} +2.13717e41 q^{88} -4.38099e41 q^{89} -1.82877e42 q^{90} -2.82777e41 q^{91} +2.38054e42 q^{92} -2.99586e42 q^{93} -2.89169e42 q^{94} +3.07861e42 q^{95} +9.12154e42 q^{96} -6.11565e42 q^{97} +8.71537e42 q^{98} -8.01318e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2209944q^{2} + 24401437812q^{3} + 9822618421824q^{4} + 535205380774170q^{5} - 91793974758443424q^{6} + 301971425665478856q^{7} - 15830863913787348480q^{8} + 477482125171066743231q^{9} + O(q^{10}) \) \( 3q - 2209944q^{2} + 24401437812q^{3} + 9822618421824q^{4} + 535205380774170q^{5} - 91793974758443424q^{6} + 301971425665478856q^{7} - 15830863913787348480q^{8} + \)\(47\!\cdots\!31\)\(q^{9} + \)\(42\!\cdots\!20\)\(q^{10} + \)\(26\!\cdots\!96\)\(q^{11} + \)\(59\!\cdots\!36\)\(q^{12} + \)\(26\!\cdots\!82\)\(q^{13} + \)\(14\!\cdots\!28\)\(q^{14} + \)\(35\!\cdots\!40\)\(q^{15} - \)\(79\!\cdots\!92\)\(q^{16} - \)\(40\!\cdots\!94\)\(q^{17} - \)\(41\!\cdots\!48\)\(q^{18} + \)\(15\!\cdots\!00\)\(q^{19} + \)\(14\!\cdots\!60\)\(q^{20} + \)\(39\!\cdots\!36\)\(q^{21} + \)\(13\!\cdots\!92\)\(q^{22} - \)\(12\!\cdots\!48\)\(q^{23} - \)\(11\!\cdots\!00\)\(q^{24} - \)\(23\!\cdots\!75\)\(q^{25} - \)\(17\!\cdots\!44\)\(q^{26} + \)\(12\!\cdots\!80\)\(q^{27} + \)\(16\!\cdots\!68\)\(q^{28} + \)\(57\!\cdots\!50\)\(q^{29} - \)\(73\!\cdots\!60\)\(q^{30} - \)\(25\!\cdots\!24\)\(q^{31} - \)\(14\!\cdots\!84\)\(q^{32} - \)\(27\!\cdots\!16\)\(q^{33} + \)\(46\!\cdots\!88\)\(q^{34} + \)\(23\!\cdots\!20\)\(q^{35} + \)\(81\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!94\)\(q^{37} - \)\(30\!\cdots\!20\)\(q^{38} - \)\(39\!\cdots\!28\)\(q^{39} - \)\(32\!\cdots\!00\)\(q^{40} + \)\(25\!\cdots\!66\)\(q^{41} + \)\(14\!\cdots\!32\)\(q^{42} + \)\(24\!\cdots\!92\)\(q^{43} - \)\(10\!\cdots\!32\)\(q^{44} + \)\(25\!\cdots\!90\)\(q^{45} - \)\(18\!\cdots\!64\)\(q^{46} + \)\(30\!\cdots\!56\)\(q^{47} - \)\(25\!\cdots\!48\)\(q^{48} + \)\(34\!\cdots\!79\)\(q^{49} + \)\(19\!\cdots\!00\)\(q^{50} + \)\(13\!\cdots\!56\)\(q^{51} - \)\(17\!\cdots\!04\)\(q^{52} + \)\(15\!\cdots\!62\)\(q^{53} - \)\(84\!\cdots\!00\)\(q^{54} + \)\(39\!\cdots\!40\)\(q^{55} - \)\(64\!\cdots\!00\)\(q^{56} + \)\(19\!\cdots\!60\)\(q^{57} - \)\(10\!\cdots\!80\)\(q^{58} + \)\(22\!\cdots\!00\)\(q^{59} + \)\(17\!\cdots\!20\)\(q^{60} - \)\(93\!\cdots\!54\)\(q^{61} - \)\(20\!\cdots\!48\)\(q^{62} - \)\(96\!\cdots\!48\)\(q^{63} - \)\(11\!\cdots\!36\)\(q^{64} - \)\(27\!\cdots\!60\)\(q^{65} + \)\(29\!\cdots\!32\)\(q^{66} - \)\(73\!\cdots\!44\)\(q^{67} + \)\(54\!\cdots\!68\)\(q^{68} + \)\(19\!\cdots\!32\)\(q^{69} + \)\(59\!\cdots\!20\)\(q^{70} - \)\(18\!\cdots\!64\)\(q^{71} - \)\(98\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!98\)\(q^{73} + \)\(16\!\cdots\!08\)\(q^{74} - \)\(21\!\cdots\!00\)\(q^{75} + \)\(77\!\cdots\!00\)\(q^{76} + \)\(59\!\cdots\!92\)\(q^{77} - \)\(19\!\cdots\!96\)\(q^{78} + \)\(15\!\cdots\!00\)\(q^{79} - \)\(10\!\cdots\!80\)\(q^{80} + \)\(73\!\cdots\!63\)\(q^{81} - \)\(32\!\cdots\!68\)\(q^{82} - \)\(89\!\cdots\!28\)\(q^{83} - \)\(34\!\cdots\!12\)\(q^{84} + \)\(43\!\cdots\!20\)\(q^{85} + \)\(25\!\cdots\!96\)\(q^{86} + \)\(17\!\cdots\!40\)\(q^{87} - \)\(25\!\cdots\!60\)\(q^{88} + \)\(20\!\cdots\!50\)\(q^{89} - \)\(23\!\cdots\!60\)\(q^{90} - \)\(11\!\cdots\!84\)\(q^{91} + \)\(68\!\cdots\!56\)\(q^{92} - \)\(49\!\cdots\!96\)\(q^{93} - \)\(13\!\cdots\!32\)\(q^{94} + \)\(31\!\cdots\!00\)\(q^{95} + \)\(10\!\cdots\!36\)\(q^{96} - \)\(38\!\cdots\!94\)\(q^{97} + \)\(24\!\cdots\!08\)\(q^{98} - \)\(14\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.65343e6 −1.56902 −0.784509 0.620118i \(-0.787085\pi\)
−0.784509 + 0.620118i \(0.787085\pi\)
\(3\) 3.22027e10 1.77740 0.888701 0.458488i \(-0.151609\pi\)
0.888701 + 0.458488i \(0.151609\pi\)
\(4\) 1.28583e13 1.46182
\(5\) 5.54482e14 0.520035 0.260017 0.965604i \(-0.416272\pi\)
0.260017 + 0.965604i \(0.416272\pi\)
\(6\) −1.49853e17 −2.78877
\(7\) −5.57604e17 −0.377327 −0.188663 0.982042i \(-0.560416\pi\)
−0.188663 + 0.982042i \(0.560416\pi\)
\(8\) −1.89031e19 −0.724599
\(9\) 7.08758e20 2.15915
\(10\) −2.58024e21 −0.815944
\(11\) −1.13059e22 −0.460643 −0.230321 0.973115i \(-0.573978\pi\)
−0.230321 + 0.973115i \(0.573978\pi\)
\(12\) 4.14071e23 2.59823
\(13\) 5.07130e23 0.569294 0.284647 0.958632i \(-0.408124\pi\)
0.284647 + 0.958632i \(0.408124\pi\)
\(14\) 2.59477e24 0.592033
\(15\) 1.78558e25 0.924311
\(16\) −2.51386e25 −0.324909
\(17\) 8.73610e25 0.306666 0.153333 0.988175i \(-0.450999\pi\)
0.153333 + 0.988175i \(0.450999\pi\)
\(18\) −3.29815e27 −3.38775
\(19\) 5.55222e27 1.78346 0.891732 0.452564i \(-0.149491\pi\)
0.891732 + 0.452564i \(0.149491\pi\)
\(20\) 7.12968e27 0.760196
\(21\) −1.79564e28 −0.670661
\(22\) 5.26114e28 0.722757
\(23\) 1.85137e29 0.978012 0.489006 0.872280i \(-0.337360\pi\)
0.489006 + 0.872280i \(0.337360\pi\)
\(24\) −6.08730e29 −1.28790
\(25\) −8.29418e29 −0.729564
\(26\) −2.35989e30 −0.893233
\(27\) 1.22532e31 2.06028
\(28\) −7.16982e30 −0.551583
\(29\) 4.19782e31 1.51868 0.759340 0.650694i \(-0.225522\pi\)
0.759340 + 0.650694i \(0.225522\pi\)
\(30\) −8.30908e31 −1.45026
\(31\) −9.30312e31 −0.802329 −0.401164 0.916006i \(-0.631394\pi\)
−0.401164 + 0.916006i \(0.631394\pi\)
\(32\) 2.83254e32 1.23439
\(33\) −3.64082e32 −0.818747
\(34\) −4.06528e32 −0.481165
\(35\) −3.09181e32 −0.196223
\(36\) 9.11340e33 3.15629
\(37\) −3.20928e33 −0.616695 −0.308347 0.951274i \(-0.599776\pi\)
−0.308347 + 0.951274i \(0.599776\pi\)
\(38\) −2.58368e34 −2.79829
\(39\) 1.63309e34 1.01186
\(40\) −1.04814e34 −0.376817
\(41\) 6.48857e33 0.137182 0.0685908 0.997645i \(-0.478150\pi\)
0.0685908 + 0.997645i \(0.478150\pi\)
\(42\) 8.35585e34 1.05228
\(43\) 3.51189e33 0.0266667 0.0133333 0.999911i \(-0.495756\pi\)
0.0133333 + 0.999911i \(0.495756\pi\)
\(44\) −1.45375e35 −0.673375
\(45\) 3.92993e35 1.12284
\(46\) −8.61520e35 −1.53452
\(47\) 6.21410e35 0.697067 0.348533 0.937296i \(-0.386680\pi\)
0.348533 + 0.937296i \(0.386680\pi\)
\(48\) −8.09530e35 −0.577493
\(49\) −1.87289e36 −0.857624
\(50\) 3.85963e36 1.14470
\(51\) 2.81326e36 0.545069
\(52\) 6.52081e36 0.832204
\(53\) 8.28552e36 0.702083 0.351042 0.936360i \(-0.385828\pi\)
0.351042 + 0.936360i \(0.385828\pi\)
\(54\) −5.70191e37 −3.23262
\(55\) −6.26895e36 −0.239550
\(56\) 1.05404e37 0.273411
\(57\) 1.78797e38 3.16993
\(58\) −1.95342e38 −2.38284
\(59\) −7.48073e36 −0.0631867 −0.0315933 0.999501i \(-0.510058\pi\)
−0.0315933 + 0.999501i \(0.510058\pi\)
\(60\) 2.29595e38 1.35117
\(61\) −2.24824e38 −0.927366 −0.463683 0.886001i \(-0.653472\pi\)
−0.463683 + 0.886001i \(0.653472\pi\)
\(62\) 4.32914e38 1.25887
\(63\) −3.95206e38 −0.814707
\(64\) −1.09698e39 −1.61186
\(65\) 2.81194e38 0.296053
\(66\) 1.69423e39 1.28463
\(67\) −1.89786e39 −1.04149 −0.520745 0.853712i \(-0.674346\pi\)
−0.520745 + 0.853712i \(0.674346\pi\)
\(68\) 1.12331e39 0.448290
\(69\) 5.96191e39 1.73832
\(70\) 1.43875e39 0.307878
\(71\) −9.53945e39 −1.50476 −0.752382 0.658727i \(-0.771095\pi\)
−0.752382 + 0.658727i \(0.771095\pi\)
\(72\) −1.33977e40 −1.56452
\(73\) 2.48260e39 0.215509 0.107755 0.994178i \(-0.465634\pi\)
0.107755 + 0.994178i \(0.465634\pi\)
\(74\) 1.49341e40 0.967605
\(75\) −2.67095e40 −1.29673
\(76\) 7.13920e40 2.60710
\(77\) 6.30424e39 0.173813
\(78\) −7.59948e40 −1.58763
\(79\) −3.50244e39 −0.0556402 −0.0278201 0.999613i \(-0.508857\pi\)
−0.0278201 + 0.999613i \(0.508857\pi\)
\(80\) −1.39389e40 −0.168964
\(81\) 1.61930e41 1.50280
\(82\) −3.01941e40 −0.215240
\(83\) −2.23114e41 −1.22560 −0.612799 0.790239i \(-0.709957\pi\)
−0.612799 + 0.790239i \(0.709957\pi\)
\(84\) −2.30888e41 −0.980384
\(85\) 4.84401e40 0.159477
\(86\) −1.63423e40 −0.0418405
\(87\) 1.35181e42 2.69930
\(88\) 2.13717e41 0.333781
\(89\) −4.38099e41 −0.536645 −0.268323 0.963329i \(-0.586469\pi\)
−0.268323 + 0.963329i \(0.586469\pi\)
\(90\) −1.82877e42 −1.76175
\(91\) −2.82777e41 −0.214810
\(92\) 2.38054e42 1.42967
\(93\) −2.99586e42 −1.42606
\(94\) −2.89169e42 −1.09371
\(95\) 3.07861e42 0.927463
\(96\) 9.12154e42 2.19400
\(97\) −6.11565e42 −1.17720 −0.588600 0.808424i \(-0.700321\pi\)
−0.588600 + 0.808424i \(0.700321\pi\)
\(98\) 8.71537e42 1.34563
\(99\) −8.01318e42 −0.994599
\(100\) −1.06649e43 −1.06649
\(101\) 8.20815e42 0.662728 0.331364 0.943503i \(-0.392491\pi\)
0.331364 + 0.943503i \(0.392491\pi\)
\(102\) −1.30913e43 −0.855222
\(103\) 2.72199e43 1.44174 0.720868 0.693072i \(-0.243743\pi\)
0.720868 + 0.693072i \(0.243743\pi\)
\(104\) −9.58630e42 −0.412510
\(105\) −9.95648e42 −0.348767
\(106\) −3.85561e43 −1.10158
\(107\) −4.26383e43 −0.995517 −0.497758 0.867316i \(-0.665843\pi\)
−0.497758 + 0.867316i \(0.665843\pi\)
\(108\) 1.57554e44 3.01176
\(109\) 2.42680e43 0.380508 0.190254 0.981735i \(-0.439069\pi\)
0.190254 + 0.981735i \(0.439069\pi\)
\(110\) 2.91721e43 0.375859
\(111\) −1.03347e44 −1.09611
\(112\) 1.40174e43 0.122597
\(113\) 1.73831e44 1.25586 0.627931 0.778269i \(-0.283902\pi\)
0.627931 + 0.778269i \(0.283902\pi\)
\(114\) −8.32016e44 −4.97368
\(115\) 1.02655e44 0.508600
\(116\) 5.39767e44 2.22003
\(117\) 3.59432e44 1.22919
\(118\) 3.48110e43 0.0991410
\(119\) −4.87128e43 −0.115713
\(120\) −3.37530e44 −0.669754
\(121\) −4.74576e44 −0.787808
\(122\) 1.04620e45 1.45505
\(123\) 2.08949e44 0.243827
\(124\) −1.19622e45 −1.17286
\(125\) −1.09027e45 −0.899433
\(126\) 1.83906e45 1.27829
\(127\) −2.81930e45 −1.65334 −0.826669 0.562688i \(-0.809767\pi\)
−0.826669 + 0.562688i \(0.809767\pi\)
\(128\) 2.61318e45 1.29466
\(129\) 1.13092e44 0.0473974
\(130\) −1.30852e45 −0.464512
\(131\) 5.22187e45 1.57215 0.786073 0.618133i \(-0.212111\pi\)
0.786073 + 0.618133i \(0.212111\pi\)
\(132\) −4.68147e45 −1.19686
\(133\) −3.09594e45 −0.672949
\(134\) 8.83154e45 1.63412
\(135\) 6.79416e45 1.07142
\(136\) −1.65139e45 −0.222210
\(137\) −1.17929e46 −1.35559 −0.677794 0.735252i \(-0.737064\pi\)
−0.677794 + 0.735252i \(0.737064\pi\)
\(138\) −2.77433e46 −2.72745
\(139\) 7.89914e45 0.664908 0.332454 0.943119i \(-0.392123\pi\)
0.332454 + 0.943119i \(0.392123\pi\)
\(140\) −3.97554e45 −0.286842
\(141\) 2.00111e46 1.23897
\(142\) 4.43911e46 2.36100
\(143\) −5.73358e45 −0.262241
\(144\) −1.78172e46 −0.701528
\(145\) 2.32761e46 0.789767
\(146\) −1.15526e46 −0.338138
\(147\) −6.03122e46 −1.52434
\(148\) −4.12658e46 −0.901495
\(149\) 5.77438e45 0.109144 0.0545721 0.998510i \(-0.482621\pi\)
0.0545721 + 0.998510i \(0.482621\pi\)
\(150\) 1.24291e47 2.03459
\(151\) −1.97310e46 −0.279992 −0.139996 0.990152i \(-0.544709\pi\)
−0.139996 + 0.990152i \(0.544709\pi\)
\(152\) −1.04954e47 −1.29230
\(153\) 6.19178e46 0.662140
\(154\) −2.93363e46 −0.272715
\(155\) −5.15842e46 −0.417239
\(156\) 2.09988e47 1.47916
\(157\) −1.33604e47 −0.820306 −0.410153 0.912017i \(-0.634525\pi\)
−0.410153 + 0.912017i \(0.634525\pi\)
\(158\) 1.62984e46 0.0873005
\(159\) 2.66816e47 1.24788
\(160\) 1.57059e47 0.641924
\(161\) −1.03233e47 −0.369030
\(162\) −7.53530e47 −2.35791
\(163\) −1.04926e47 −0.287641 −0.143820 0.989604i \(-0.545939\pi\)
−0.143820 + 0.989604i \(0.545939\pi\)
\(164\) 8.34318e46 0.200534
\(165\) −2.01877e47 −0.425777
\(166\) 1.03825e48 1.92299
\(167\) −6.74904e47 −1.09860 −0.549298 0.835627i \(-0.685105\pi\)
−0.549298 + 0.835627i \(0.685105\pi\)
\(168\) 3.39430e47 0.485960
\(169\) −5.36351e47 −0.675904
\(170\) −2.25412e47 −0.250222
\(171\) 3.93518e48 3.85077
\(172\) 4.51569e46 0.0389818
\(173\) −4.15452e47 −0.316614 −0.158307 0.987390i \(-0.550603\pi\)
−0.158307 + 0.987390i \(0.550603\pi\)
\(174\) −6.29055e48 −4.23526
\(175\) 4.62486e47 0.275284
\(176\) 2.84215e47 0.149667
\(177\) −2.40900e47 −0.112308
\(178\) 2.03866e48 0.842006
\(179\) −6.34938e47 −0.232483 −0.116241 0.993221i \(-0.537085\pi\)
−0.116241 + 0.993221i \(0.537085\pi\)
\(180\) 5.05322e48 1.64138
\(181\) 5.38506e47 0.155275 0.0776375 0.996982i \(-0.475262\pi\)
0.0776375 + 0.996982i \(0.475262\pi\)
\(182\) 1.31588e48 0.337041
\(183\) −7.23994e48 −1.64830
\(184\) −3.49965e48 −0.708666
\(185\) −1.77949e48 −0.320703
\(186\) 1.39410e49 2.23751
\(187\) −9.87699e47 −0.141263
\(188\) 7.99026e48 1.01898
\(189\) −6.83240e48 −0.777400
\(190\) −1.43261e49 −1.45521
\(191\) 1.22017e49 1.10714 0.553572 0.832802i \(-0.313265\pi\)
0.553572 + 0.832802i \(0.313265\pi\)
\(192\) −3.53257e49 −2.86493
\(193\) 8.36996e46 0.00607073 0.00303537 0.999995i \(-0.499034\pi\)
0.00303537 + 0.999995i \(0.499034\pi\)
\(194\) 2.84587e49 1.84705
\(195\) 9.05522e48 0.526205
\(196\) −2.40822e49 −1.25369
\(197\) 1.24344e49 0.580229 0.290115 0.956992i \(-0.406307\pi\)
0.290115 + 0.956992i \(0.406307\pi\)
\(198\) 3.72887e49 1.56054
\(199\) 2.54032e49 0.953997 0.476999 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(200\) 1.56785e49 0.528641
\(201\) −6.11161e49 −1.85115
\(202\) −3.81960e49 −1.03983
\(203\) −2.34072e49 −0.573039
\(204\) 3.61737e49 0.796790
\(205\) 3.59779e48 0.0713392
\(206\) −1.26666e50 −2.26211
\(207\) 1.31217e50 2.11168
\(208\) −1.27485e49 −0.184969
\(209\) −6.27731e49 −0.821540
\(210\) 4.63317e49 0.547222
\(211\) 1.72327e50 1.83772 0.918861 0.394582i \(-0.129110\pi\)
0.918861 + 0.394582i \(0.129110\pi\)
\(212\) 1.06538e50 1.02632
\(213\) −3.07196e50 −2.67457
\(214\) 1.98414e50 1.56198
\(215\) 1.94728e48 0.0138676
\(216\) −2.31622e50 −1.49288
\(217\) 5.18746e49 0.302740
\(218\) −1.12929e50 −0.597024
\(219\) 7.99465e49 0.383046
\(220\) −8.06078e49 −0.350179
\(221\) 4.43033e49 0.174583
\(222\) 4.80920e50 1.71982
\(223\) −1.43740e50 −0.466683 −0.233342 0.972395i \(-0.574966\pi\)
−0.233342 + 0.972395i \(0.574966\pi\)
\(224\) −1.57943e50 −0.465767
\(225\) −5.87856e50 −1.57524
\(226\) −8.08911e50 −1.97047
\(227\) −7.21848e48 −0.0159915 −0.00799576 0.999968i \(-0.502545\pi\)
−0.00799576 + 0.999968i \(0.502545\pi\)
\(228\) 2.29902e51 4.63386
\(229\) 8.60814e50 1.57923 0.789617 0.613600i \(-0.210279\pi\)
0.789617 + 0.613600i \(0.210279\pi\)
\(230\) −4.77698e50 −0.798003
\(231\) 2.03014e50 0.308935
\(232\) −7.93516e50 −1.10043
\(233\) −8.15789e50 −1.03140 −0.515698 0.856770i \(-0.672467\pi\)
−0.515698 + 0.856770i \(0.672467\pi\)
\(234\) −1.67259e51 −1.92863
\(235\) 3.44561e50 0.362499
\(236\) −9.61892e49 −0.0923673
\(237\) −1.12788e50 −0.0988950
\(238\) 2.26681e50 0.181556
\(239\) 1.19865e51 0.877276 0.438638 0.898664i \(-0.355461\pi\)
0.438638 + 0.898664i \(0.355461\pi\)
\(240\) −4.48870e50 −0.300316
\(241\) 1.15117e51 0.704326 0.352163 0.935939i \(-0.385446\pi\)
0.352163 + 0.935939i \(0.385446\pi\)
\(242\) 2.20841e51 1.23609
\(243\) 1.19241e51 0.610786
\(244\) −2.89085e51 −1.35564
\(245\) −1.03849e51 −0.445995
\(246\) −9.72331e50 −0.382568
\(247\) 2.81570e51 1.01532
\(248\) 1.75858e51 0.581366
\(249\) −7.18488e51 −2.17838
\(250\) 5.07349e51 1.41123
\(251\) −3.52535e51 −0.899948 −0.449974 0.893042i \(-0.648567\pi\)
−0.449974 + 0.893042i \(0.648567\pi\)
\(252\) −5.08167e51 −1.19095
\(253\) −2.09315e51 −0.450514
\(254\) 1.31194e52 2.59412
\(255\) 1.55990e51 0.283455
\(256\) −2.51112e51 −0.419478
\(257\) −9.00901e51 −1.38393 −0.691967 0.721930i \(-0.743255\pi\)
−0.691967 + 0.721930i \(0.743255\pi\)
\(258\) −5.26267e50 −0.0743674
\(259\) 1.78951e51 0.232696
\(260\) 3.61567e51 0.432775
\(261\) 2.97523e52 3.27907
\(262\) −2.42996e52 −2.46673
\(263\) −8.70831e51 −0.814489 −0.407245 0.913319i \(-0.633510\pi\)
−0.407245 + 0.913319i \(0.633510\pi\)
\(264\) 6.88227e51 0.593263
\(265\) 4.59417e51 0.365108
\(266\) 1.44067e52 1.05587
\(267\) −1.41080e52 −0.953834
\(268\) −2.44032e52 −1.52247
\(269\) 2.29589e52 1.32214 0.661071 0.750324i \(-0.270102\pi\)
0.661071 + 0.750324i \(0.270102\pi\)
\(270\) −3.16161e52 −1.68108
\(271\) −2.04437e52 −1.00397 −0.501983 0.864877i \(-0.667396\pi\)
−0.501983 + 0.864877i \(0.667396\pi\)
\(272\) −2.19613e51 −0.0996384
\(273\) −9.10620e51 −0.381804
\(274\) 5.48773e52 2.12694
\(275\) 9.37735e51 0.336068
\(276\) 7.66598e52 2.54110
\(277\) 3.67190e52 1.12610 0.563049 0.826424i \(-0.309628\pi\)
0.563049 + 0.826424i \(0.309628\pi\)
\(278\) −3.67581e52 −1.04325
\(279\) −6.59366e52 −1.73235
\(280\) 5.84447e51 0.142183
\(281\) −3.21289e52 −0.723952 −0.361976 0.932187i \(-0.617898\pi\)
−0.361976 + 0.932187i \(0.617898\pi\)
\(282\) −9.31201e52 −1.94396
\(283\) 7.76513e52 1.50224 0.751121 0.660164i \(-0.229513\pi\)
0.751121 + 0.660164i \(0.229513\pi\)
\(284\) −1.22661e53 −2.19969
\(285\) 9.91395e52 1.64847
\(286\) 2.66808e52 0.411461
\(287\) −3.61805e51 −0.0517623
\(288\) 2.00758e53 2.66523
\(289\) −7.35209e52 −0.905956
\(290\) −1.08314e53 −1.23916
\(291\) −1.96940e53 −2.09236
\(292\) 3.19220e52 0.315035
\(293\) 7.07016e52 0.648299 0.324150 0.946006i \(-0.394922\pi\)
0.324150 + 0.946006i \(0.394922\pi\)
\(294\) 2.80658e53 2.39172
\(295\) −4.14793e51 −0.0328593
\(296\) 6.06652e52 0.446856
\(297\) −1.38533e53 −0.949054
\(298\) −2.68707e52 −0.171249
\(299\) 9.38883e52 0.556777
\(300\) −3.43438e53 −1.89558
\(301\) −1.95824e51 −0.0100621
\(302\) 9.18168e52 0.439312
\(303\) 2.64325e53 1.17793
\(304\) −1.39575e53 −0.579463
\(305\) −1.24661e53 −0.482263
\(306\) −2.88130e53 −1.03891
\(307\) −4.17987e53 −1.40504 −0.702518 0.711666i \(-0.747941\pi\)
−0.702518 + 0.711666i \(0.747941\pi\)
\(308\) 8.10616e52 0.254083
\(309\) 8.76554e53 2.56255
\(310\) 2.40043e53 0.654655
\(311\) 1.08737e53 0.276714 0.138357 0.990382i \(-0.455818\pi\)
0.138357 + 0.990382i \(0.455818\pi\)
\(312\) −3.08705e53 −0.733196
\(313\) 5.09671e52 0.113002 0.0565011 0.998403i \(-0.482006\pi\)
0.0565011 + 0.998403i \(0.482006\pi\)
\(314\) 6.21715e53 1.28707
\(315\) −2.19135e53 −0.423676
\(316\) −4.50354e52 −0.0813358
\(317\) 5.92996e53 1.00064 0.500320 0.865841i \(-0.333216\pi\)
0.500320 + 0.865841i \(0.333216\pi\)
\(318\) −1.24161e54 −1.95795
\(319\) −4.74603e53 −0.699569
\(320\) −6.08255e53 −0.838226
\(321\) −1.37307e54 −1.76943
\(322\) 4.80387e53 0.579015
\(323\) 4.85047e53 0.546928
\(324\) 2.08214e54 2.19681
\(325\) −4.20622e53 −0.415336
\(326\) 4.88266e53 0.451313
\(327\) 7.81494e53 0.676315
\(328\) −1.22654e53 −0.0994016
\(329\) −3.46501e53 −0.263022
\(330\) 9.39420e53 0.668052
\(331\) 4.62094e53 0.307913 0.153957 0.988078i \(-0.450798\pi\)
0.153957 + 0.988078i \(0.450798\pi\)
\(332\) −2.86886e54 −1.79160
\(333\) −2.27460e54 −1.33154
\(334\) 3.14061e54 1.72372
\(335\) −1.05233e54 −0.541611
\(336\) 4.51397e53 0.217904
\(337\) −2.44988e54 −1.10943 −0.554717 0.832039i \(-0.687173\pi\)
−0.554717 + 0.832039i \(0.687173\pi\)
\(338\) 2.49587e54 1.06051
\(339\) 5.59784e54 2.23217
\(340\) 6.22856e53 0.233126
\(341\) 1.05181e54 0.369587
\(342\) −1.83121e55 −6.04193
\(343\) 2.26203e54 0.700932
\(344\) −6.63855e52 −0.0193227
\(345\) 3.30577e54 0.903987
\(346\) 1.93327e54 0.496772
\(347\) 2.06865e54 0.499579 0.249789 0.968300i \(-0.419639\pi\)
0.249789 + 0.968300i \(0.419639\pi\)
\(348\) 1.73820e55 3.94589
\(349\) −9.24540e54 −1.97324 −0.986618 0.163050i \(-0.947867\pi\)
−0.986618 + 0.163050i \(0.947867\pi\)
\(350\) −2.15215e54 −0.431926
\(351\) 6.21394e54 1.17291
\(352\) −3.20245e54 −0.568611
\(353\) −3.55103e54 −0.593196 −0.296598 0.955002i \(-0.595852\pi\)
−0.296598 + 0.955002i \(0.595852\pi\)
\(354\) 1.12101e54 0.176213
\(355\) −5.28945e54 −0.782530
\(356\) −5.63320e54 −0.784477
\(357\) −1.56868e54 −0.205669
\(358\) 2.95463e54 0.364770
\(359\) −6.37557e54 −0.741291 −0.370645 0.928774i \(-0.620863\pi\)
−0.370645 + 0.928774i \(0.620863\pi\)
\(360\) −7.42878e54 −0.813605
\(361\) 2.11353e55 2.18074
\(362\) −2.50590e54 −0.243629
\(363\) −1.52826e55 −1.40025
\(364\) −3.63603e54 −0.314013
\(365\) 1.37656e54 0.112072
\(366\) 3.36905e55 2.58621
\(367\) 1.19284e55 0.863502 0.431751 0.901993i \(-0.357896\pi\)
0.431751 + 0.901993i \(0.357896\pi\)
\(368\) −4.65408e54 −0.317764
\(369\) 4.59882e54 0.296196
\(370\) 8.28071e54 0.503189
\(371\) −4.62004e54 −0.264915
\(372\) −3.85216e55 −2.08464
\(373\) −6.58590e54 −0.336415 −0.168208 0.985752i \(-0.553798\pi\)
−0.168208 + 0.985752i \(0.553798\pi\)
\(374\) 4.59618e54 0.221645
\(375\) −3.51097e55 −1.59865
\(376\) −1.17466e55 −0.505094
\(377\) 2.12884e55 0.864576
\(378\) 3.17941e55 1.21975
\(379\) 4.25975e55 1.54398 0.771989 0.635636i \(-0.219262\pi\)
0.771989 + 0.635636i \(0.219262\pi\)
\(380\) 3.95856e55 1.35578
\(381\) −9.07892e55 −2.93865
\(382\) −5.67798e55 −1.73713
\(383\) −1.85965e53 −0.00537846 −0.00268923 0.999996i \(-0.500856\pi\)
−0.00268923 + 0.999996i \(0.500856\pi\)
\(384\) 8.41515e55 2.30113
\(385\) 3.49559e54 0.0903888
\(386\) −3.89490e53 −0.00952509
\(387\) 2.48908e54 0.0575775
\(388\) −7.86367e55 −1.72085
\(389\) 7.73460e55 1.60148 0.800740 0.599012i \(-0.204440\pi\)
0.800740 + 0.599012i \(0.204440\pi\)
\(390\) −4.21378e55 −0.825625
\(391\) 1.61737e55 0.299923
\(392\) 3.54034e55 0.621434
\(393\) 1.68158e56 2.79434
\(394\) −5.78624e55 −0.910390
\(395\) −1.94204e54 −0.0289349
\(396\) −1.03036e56 −1.45392
\(397\) −5.40998e55 −0.723102 −0.361551 0.932352i \(-0.617753\pi\)
−0.361551 + 0.932352i \(0.617753\pi\)
\(398\) −1.18212e56 −1.49684
\(399\) −9.96976e55 −1.19610
\(400\) 2.08504e55 0.237041
\(401\) −1.27603e56 −1.37486 −0.687429 0.726252i \(-0.741261\pi\)
−0.687429 + 0.726252i \(0.741261\pi\)
\(402\) 2.84399e56 2.90448
\(403\) −4.71789e55 −0.456761
\(404\) 1.05543e56 0.968787
\(405\) 8.97874e55 0.781506
\(406\) 1.08924e56 0.899108
\(407\) 3.62839e55 0.284076
\(408\) −5.31793e55 −0.394956
\(409\) 1.15025e56 0.810481 0.405240 0.914210i \(-0.367188\pi\)
0.405240 + 0.914210i \(0.367188\pi\)
\(410\) −1.67421e55 −0.111932
\(411\) −3.79763e56 −2.40942
\(412\) 3.50001e56 2.10756
\(413\) 4.17128e54 0.0238420
\(414\) −6.10609e56 −3.31326
\(415\) −1.23713e56 −0.637354
\(416\) 1.43646e56 0.702729
\(417\) 2.54374e56 1.18181
\(418\) 2.92110e56 1.28901
\(419\) −3.32264e55 −0.139278 −0.0696389 0.997572i \(-0.522185\pi\)
−0.0696389 + 0.997572i \(0.522185\pi\)
\(420\) −1.28023e56 −0.509834
\(421\) −3.83623e55 −0.145158 −0.0725788 0.997363i \(-0.523123\pi\)
−0.0725788 + 0.997363i \(0.523123\pi\)
\(422\) −8.01909e56 −2.88342
\(423\) 4.40429e56 1.50507
\(424\) −1.56622e56 −0.508729
\(425\) −7.24588e55 −0.223732
\(426\) 1.42951e57 4.19645
\(427\) 1.25363e56 0.349920
\(428\) −5.48255e56 −1.45526
\(429\) −1.84637e56 −0.466108
\(430\) −9.06153e54 −0.0217585
\(431\) 2.91528e56 0.665916 0.332958 0.942942i \(-0.391953\pi\)
0.332958 + 0.942942i \(0.391953\pi\)
\(432\) −3.08027e56 −0.669404
\(433\) −8.91932e56 −1.84434 −0.922172 0.386780i \(-0.873587\pi\)
−0.922172 + 0.386780i \(0.873587\pi\)
\(434\) −2.41394e56 −0.475005
\(435\) 7.49555e56 1.40373
\(436\) 3.12044e56 0.556233
\(437\) 1.02792e57 1.74425
\(438\) −3.72025e56 −0.601006
\(439\) −4.59768e56 −0.707216 −0.353608 0.935394i \(-0.615045\pi\)
−0.353608 + 0.935394i \(0.615045\pi\)
\(440\) 1.18502e56 0.173578
\(441\) −1.32743e57 −1.85174
\(442\) −2.06162e56 −0.273924
\(443\) 7.17753e56 0.908437 0.454219 0.890890i \(-0.349918\pi\)
0.454219 + 0.890890i \(0.349918\pi\)
\(444\) −1.32887e57 −1.60232
\(445\) −2.42918e56 −0.279074
\(446\) 6.68882e56 0.732234
\(447\) 1.85951e56 0.193993
\(448\) 6.11679e56 0.608200
\(449\) −2.56945e56 −0.243526 −0.121763 0.992559i \(-0.538855\pi\)
−0.121763 + 0.992559i \(0.538855\pi\)
\(450\) 2.73555e57 2.47158
\(451\) −7.33594e55 −0.0631917
\(452\) 2.23517e57 1.83584
\(453\) −6.35392e56 −0.497657
\(454\) 3.35907e55 0.0250910
\(455\) −1.56795e56 −0.111709
\(456\) −3.37980e57 −2.29693
\(457\) −1.11475e57 −0.722733 −0.361367 0.932424i \(-0.617690\pi\)
−0.361367 + 0.932424i \(0.617690\pi\)
\(458\) −4.00574e57 −2.47785
\(459\) 1.07045e57 0.631819
\(460\) 1.31997e57 0.743481
\(461\) 2.02024e57 1.08601 0.543003 0.839731i \(-0.317287\pi\)
0.543003 + 0.839731i \(0.317287\pi\)
\(462\) −9.44708e56 −0.484725
\(463\) −2.86426e56 −0.140288 −0.0701442 0.997537i \(-0.522346\pi\)
−0.0701442 + 0.997537i \(0.522346\pi\)
\(464\) −1.05527e57 −0.493432
\(465\) −1.66115e57 −0.741601
\(466\) 3.79621e57 1.61828
\(467\) 1.63037e57 0.663701 0.331850 0.943332i \(-0.392327\pi\)
0.331850 + 0.943332i \(0.392327\pi\)
\(468\) 4.62168e57 1.79686
\(469\) 1.05825e57 0.392982
\(470\) −1.60339e57 −0.568767
\(471\) −4.30240e57 −1.45801
\(472\) 1.41409e56 0.0457850
\(473\) −3.97052e55 −0.0122838
\(474\) 5.24852e56 0.155168
\(475\) −4.60511e57 −1.30115
\(476\) −6.26363e56 −0.169152
\(477\) 5.87243e57 1.51591
\(478\) −5.57781e57 −1.37646
\(479\) 7.76358e57 1.83168 0.915838 0.401548i \(-0.131528\pi\)
0.915838 + 0.401548i \(0.131528\pi\)
\(480\) 5.05773e57 1.14096
\(481\) −1.62752e57 −0.351081
\(482\) −5.35690e57 −1.10510
\(483\) −3.32438e57 −0.655915
\(484\) −6.10223e57 −1.15163
\(485\) −3.39102e57 −0.612185
\(486\) −5.54877e57 −0.958335
\(487\) 1.02143e58 1.68786 0.843932 0.536451i \(-0.180235\pi\)
0.843932 + 0.536451i \(0.180235\pi\)
\(488\) 4.24986e57 0.671968
\(489\) −3.37891e57 −0.511253
\(490\) 4.83251e57 0.699773
\(491\) 4.75337e57 0.658794 0.329397 0.944192i \(-0.393155\pi\)
0.329397 + 0.944192i \(0.393155\pi\)
\(492\) 2.68673e57 0.356430
\(493\) 3.66725e57 0.465728
\(494\) −1.31026e58 −1.59305
\(495\) −4.44316e57 −0.517226
\(496\) 2.33867e57 0.260683
\(497\) 5.31923e57 0.567788
\(498\) 3.34343e58 3.41792
\(499\) −6.28971e57 −0.615841 −0.307921 0.951412i \(-0.599633\pi\)
−0.307921 + 0.951412i \(0.599633\pi\)
\(500\) −1.40190e58 −1.31481
\(501\) −2.17337e58 −1.95264
\(502\) 1.64050e58 1.41203
\(503\) −2.08189e58 −1.71690 −0.858451 0.512896i \(-0.828573\pi\)
−0.858451 + 0.512896i \(0.828573\pi\)
\(504\) 7.47060e57 0.590336
\(505\) 4.55127e57 0.344642
\(506\) 9.74030e57 0.706865
\(507\) −1.72720e58 −1.20135
\(508\) −3.62514e58 −2.41688
\(509\) 4.65765e57 0.297669 0.148835 0.988862i \(-0.452448\pi\)
0.148835 + 0.988862i \(0.452448\pi\)
\(510\) −7.25889e57 −0.444745
\(511\) −1.38431e57 −0.0813174
\(512\) −1.13005e58 −0.636491
\(513\) 6.80322e58 3.67444
\(514\) 4.19228e58 2.17142
\(515\) 1.50929e58 0.749754
\(516\) 1.45417e57 0.0692863
\(517\) −7.02563e57 −0.321099
\(518\) −8.32733e57 −0.365104
\(519\) −1.33787e58 −0.562749
\(520\) −5.31543e57 −0.214520
\(521\) 4.15022e57 0.160716 0.0803582 0.996766i \(-0.474394\pi\)
0.0803582 + 0.996766i \(0.474394\pi\)
\(522\) −1.38450e59 −5.14491
\(523\) −3.61441e57 −0.128899 −0.0644497 0.997921i \(-0.520529\pi\)
−0.0644497 + 0.997921i \(0.520529\pi\)
\(524\) 6.71442e58 2.29819
\(525\) 1.48933e58 0.489290
\(526\) 4.05235e58 1.27795
\(527\) −8.12730e57 −0.246047
\(528\) 9.15251e57 0.266018
\(529\) −1.55852e57 −0.0434925
\(530\) −2.13787e58 −0.572861
\(531\) −5.30202e57 −0.136430
\(532\) −3.98084e58 −0.983728
\(533\) 3.29054e57 0.0780967
\(534\) 6.56504e58 1.49658
\(535\) −2.36422e58 −0.517703
\(536\) 3.58753e58 0.754662
\(537\) −2.04467e58 −0.413215
\(538\) −1.06838e59 −2.07446
\(539\) 2.11748e58 0.395058
\(540\) 8.73611e58 1.56622
\(541\) −4.79722e58 −0.826511 −0.413256 0.910615i \(-0.635608\pi\)
−0.413256 + 0.910615i \(0.635608\pi\)
\(542\) 9.51331e58 1.57524
\(543\) 1.73414e58 0.275986
\(544\) 2.47453e58 0.378544
\(545\) 1.34562e58 0.197877
\(546\) 4.23750e58 0.599057
\(547\) 3.67046e58 0.498877 0.249439 0.968391i \(-0.419754\pi\)
0.249439 + 0.968391i \(0.419754\pi\)
\(548\) −1.51636e59 −1.98162
\(549\) −1.59346e59 −2.00233
\(550\) −4.36368e58 −0.527297
\(551\) 2.33072e59 2.70851
\(552\) −1.12698e59 −1.25958
\(553\) 1.95298e57 0.0209946
\(554\) −1.70869e59 −1.76687
\(555\) −5.73043e58 −0.570018
\(556\) 1.01569e59 0.971974
\(557\) −1.44377e59 −1.32926 −0.664632 0.747171i \(-0.731412\pi\)
−0.664632 + 0.747171i \(0.731412\pi\)
\(558\) 3.06831e59 2.71809
\(559\) 1.78098e57 0.0151812
\(560\) 7.77238e57 0.0637546
\(561\) −3.18066e58 −0.251082
\(562\) 1.49509e59 1.13589
\(563\) −1.85030e58 −0.135304 −0.0676521 0.997709i \(-0.521551\pi\)
−0.0676521 + 0.997709i \(0.521551\pi\)
\(564\) 2.57308e59 1.81114
\(565\) 9.63864e58 0.653092
\(566\) −3.61344e59 −2.35705
\(567\) −9.02928e58 −0.567045
\(568\) 1.80325e59 1.09035
\(569\) 7.55839e58 0.440064 0.220032 0.975493i \(-0.429384\pi\)
0.220032 + 0.975493i \(0.429384\pi\)
\(570\) −4.61338e59 −2.58649
\(571\) 1.65354e59 0.892767 0.446384 0.894842i \(-0.352712\pi\)
0.446384 + 0.894842i \(0.352712\pi\)
\(572\) −7.37239e58 −0.383349
\(573\) 3.92929e59 1.96784
\(574\) 1.68363e58 0.0812160
\(575\) −1.53556e59 −0.713522
\(576\) −7.77492e59 −3.48027
\(577\) −4.04625e59 −1.74491 −0.872453 0.488697i \(-0.837472\pi\)
−0.872453 + 0.488697i \(0.837472\pi\)
\(578\) 3.42124e59 1.42146
\(579\) 2.69535e57 0.0107901
\(580\) 2.99291e59 1.15449
\(581\) 1.24409e59 0.462451
\(582\) 9.16448e59 3.28294
\(583\) −9.36757e58 −0.323410
\(584\) −4.69288e58 −0.156158
\(585\) 1.99299e59 0.639224
\(586\) −3.29005e59 −1.01719
\(587\) 3.79894e59 1.13225 0.566126 0.824319i \(-0.308442\pi\)
0.566126 + 0.824319i \(0.308442\pi\)
\(588\) −7.75511e59 −2.22831
\(589\) −5.16530e59 −1.43092
\(590\) 1.93021e58 0.0515568
\(591\) 4.00420e59 1.03130
\(592\) 8.06767e58 0.200369
\(593\) −4.79450e59 −1.14833 −0.574166 0.818739i \(-0.694674\pi\)
−0.574166 + 0.818739i \(0.694674\pi\)
\(594\) 6.44655e59 1.48908
\(595\) −2.70104e58 −0.0601750
\(596\) 7.42486e58 0.159549
\(597\) 8.18052e59 1.69564
\(598\) −4.36902e59 −0.873592
\(599\) −4.48279e59 −0.864713 −0.432356 0.901703i \(-0.642318\pi\)
−0.432356 + 0.901703i \(0.642318\pi\)
\(600\) 5.04892e59 0.939607
\(601\) −1.41250e59 −0.253621 −0.126811 0.991927i \(-0.540474\pi\)
−0.126811 + 0.991927i \(0.540474\pi\)
\(602\) 9.11254e57 0.0157876
\(603\) −1.34512e60 −2.24874
\(604\) −2.53707e59 −0.409296
\(605\) −2.63144e59 −0.409688
\(606\) −1.23001e60 −1.84820
\(607\) 7.01925e59 1.01797 0.508984 0.860776i \(-0.330021\pi\)
0.508984 + 0.860776i \(0.330021\pi\)
\(608\) 1.57269e60 2.20148
\(609\) −7.53775e59 −1.01852
\(610\) 5.80100e59 0.756679
\(611\) 3.15135e59 0.396836
\(612\) 7.96156e59 0.967927
\(613\) 1.03814e60 1.21858 0.609292 0.792946i \(-0.291454\pi\)
0.609292 + 0.792946i \(0.291454\pi\)
\(614\) 1.94507e60 2.20453
\(615\) 1.15859e59 0.126798
\(616\) −1.19169e59 −0.125945
\(617\) −1.00931e60 −1.03014 −0.515069 0.857149i \(-0.672234\pi\)
−0.515069 + 0.857149i \(0.672234\pi\)
\(618\) −4.07898e60 −4.02068
\(619\) 1.22876e59 0.116981 0.0584907 0.998288i \(-0.481371\pi\)
0.0584907 + 0.998288i \(0.481371\pi\)
\(620\) −6.63283e59 −0.609927
\(621\) 2.26851e60 2.01498
\(622\) −5.06001e59 −0.434169
\(623\) 2.44286e59 0.202491
\(624\) −4.10537e59 −0.328763
\(625\) 3.38403e59 0.261827
\(626\) −2.37172e59 −0.177302
\(627\) −2.02146e60 −1.46021
\(628\) −1.71791e60 −1.19914
\(629\) −2.80366e59 −0.189119
\(630\) 1.01973e60 0.664755
\(631\) 2.36287e60 1.48870 0.744352 0.667787i \(-0.232758\pi\)
0.744352 + 0.667787i \(0.232758\pi\)
\(632\) 6.62069e58 0.0403168
\(633\) 5.54939e60 3.26637
\(634\) −2.75946e60 −1.57002
\(635\) −1.56325e60 −0.859794
\(636\) 3.43080e60 1.82418
\(637\) −9.49799e59 −0.488241
\(638\) 2.20853e60 1.09764
\(639\) −6.76116e60 −3.24902
\(640\) 1.44896e60 0.673268
\(641\) −3.06701e60 −1.37806 −0.689029 0.724734i \(-0.741963\pi\)
−0.689029 + 0.724734i \(0.741963\pi\)
\(642\) 6.38947e60 2.77627
\(643\) 8.63761e59 0.362959 0.181479 0.983395i \(-0.441911\pi\)
0.181479 + 0.983395i \(0.441911\pi\)
\(644\) −1.32740e60 −0.539455
\(645\) 6.27077e58 0.0246483
\(646\) −2.25713e60 −0.858139
\(647\) −1.57232e60 −0.578228 −0.289114 0.957295i \(-0.593361\pi\)
−0.289114 + 0.957295i \(0.593361\pi\)
\(648\) −3.06098e60 −1.08892
\(649\) 8.45767e58 0.0291065
\(650\) 1.95733e60 0.651670
\(651\) 1.67050e60 0.538091
\(652\) −1.34917e60 −0.420478
\(653\) 1.42220e60 0.428870 0.214435 0.976738i \(-0.431209\pi\)
0.214435 + 0.976738i \(0.431209\pi\)
\(654\) −3.63663e60 −1.06115
\(655\) 2.89543e60 0.817571
\(656\) −1.63113e59 −0.0445715
\(657\) 1.75956e60 0.465317
\(658\) 1.61241e60 0.412686
\(659\) 2.37773e60 0.589015 0.294507 0.955649i \(-0.404844\pi\)
0.294507 + 0.955649i \(0.404844\pi\)
\(660\) −2.59579e60 −0.622408
\(661\) −7.09142e60 −1.64589 −0.822947 0.568119i \(-0.807671\pi\)
−0.822947 + 0.568119i \(0.807671\pi\)
\(662\) −2.15032e60 −0.483121
\(663\) 1.42669e60 0.310304
\(664\) 4.21754e60 0.888067
\(665\) −1.71664e60 −0.349957
\(666\) 1.05847e61 2.08921
\(667\) 7.77170e60 1.48529
\(668\) −8.67810e60 −1.60595
\(669\) −4.62881e60 −0.829483
\(670\) 4.89693e60 0.849798
\(671\) 2.54185e60 0.427184
\(672\) −5.08620e60 −0.827855
\(673\) 7.62590e60 1.20217 0.601086 0.799184i \(-0.294735\pi\)
0.601086 + 0.799184i \(0.294735\pi\)
\(674\) 1.14003e61 1.74072
\(675\) −1.01630e61 −1.50311
\(676\) −6.89655e60 −0.988048
\(677\) −1.33549e61 −1.85347 −0.926735 0.375717i \(-0.877397\pi\)
−0.926735 + 0.375717i \(0.877397\pi\)
\(678\) −2.60491e61 −3.50231
\(679\) 3.41011e60 0.444189
\(680\) −9.15667e59 −0.115557
\(681\) −2.32455e59 −0.0284233
\(682\) −4.89450e60 −0.579888
\(683\) 7.17925e60 0.824202 0.412101 0.911138i \(-0.364795\pi\)
0.412101 + 0.911138i \(0.364795\pi\)
\(684\) 5.05996e61 5.62913
\(685\) −6.53894e60 −0.704953
\(686\) −1.05262e61 −1.09977
\(687\) 2.77206e61 2.80693
\(688\) −8.82839e58 −0.00866424
\(689\) 4.20183e60 0.399692
\(690\) −1.53832e61 −1.41837
\(691\) −1.17437e61 −1.04961 −0.524803 0.851224i \(-0.675861\pi\)
−0.524803 + 0.851224i \(0.675861\pi\)
\(692\) −5.34200e60 −0.462831
\(693\) 4.46818e60 0.375289
\(694\) −9.62632e60 −0.783848
\(695\) 4.37993e60 0.345776
\(696\) −2.55534e61 −1.95591
\(697\) 5.66848e59 0.0420689
\(698\) 4.30228e61 3.09604
\(699\) −2.62706e61 −1.83320
\(700\) 5.94678e60 0.402415
\(701\) 1.27675e61 0.837854 0.418927 0.908020i \(-0.362406\pi\)
0.418927 + 0.908020i \(0.362406\pi\)
\(702\) −2.89161e61 −1.84031
\(703\) −1.78186e61 −1.09985
\(704\) 1.24024e61 0.742494
\(705\) 1.10958e61 0.644306
\(706\) 1.65245e61 0.930735
\(707\) −4.57689e60 −0.250065
\(708\) −3.09755e60 −0.164174
\(709\) −2.73809e61 −1.40784 −0.703921 0.710278i \(-0.748569\pi\)
−0.703921 + 0.710278i \(0.748569\pi\)
\(710\) 2.46141e61 1.22780
\(711\) −2.48238e60 −0.120136
\(712\) 8.28142e60 0.388852
\(713\) −1.72235e61 −0.784687
\(714\) 7.29976e60 0.322698
\(715\) −3.17917e60 −0.136375
\(716\) −8.16420e60 −0.339847
\(717\) 3.85997e61 1.55927
\(718\) 2.96683e61 1.16310
\(719\) 2.16831e61 0.824993 0.412496 0.910959i \(-0.364657\pi\)
0.412496 + 0.910959i \(0.364657\pi\)
\(720\) −9.87930e60 −0.364819
\(721\) −1.51779e61 −0.544006
\(722\) −9.83518e61 −3.42162
\(723\) 3.70709e61 1.25187
\(724\) 6.92426e60 0.226984
\(725\) −3.48174e61 −1.10797
\(726\) 7.11166e61 2.19702
\(727\) 1.57652e61 0.472835 0.236418 0.971652i \(-0.424027\pi\)
0.236418 + 0.971652i \(0.424027\pi\)
\(728\) 5.34536e60 0.155651
\(729\) −1.47560e61 −0.417183
\(730\) −6.40571e60 −0.175843
\(731\) 3.06802e59 0.00817777
\(732\) −9.30931e61 −2.40951
\(733\) 2.88722e61 0.725679 0.362840 0.931852i \(-0.381807\pi\)
0.362840 + 0.931852i \(0.381807\pi\)
\(734\) −5.55081e61 −1.35485
\(735\) −3.34420e61 −0.792711
\(736\) 5.24407e61 1.20724
\(737\) 2.14571e61 0.479755
\(738\) −2.14003e61 −0.464737
\(739\) 7.66659e60 0.161714 0.0808568 0.996726i \(-0.474234\pi\)
0.0808568 + 0.996726i \(0.474234\pi\)
\(740\) −2.28811e61 −0.468809
\(741\) 9.06730e61 1.80462
\(742\) 2.14990e61 0.415656
\(743\) 5.63267e61 1.05792 0.528962 0.848645i \(-0.322581\pi\)
0.528962 + 0.848645i \(0.322581\pi\)
\(744\) 5.66309e61 1.03332
\(745\) 3.20179e60 0.0567588
\(746\) 3.06470e61 0.527841
\(747\) −1.58134e62 −2.64626
\(748\) −1.27001e61 −0.206501
\(749\) 2.37753e61 0.375635
\(750\) 1.63380e62 2.50832
\(751\) −5.65647e60 −0.0843892 −0.0421946 0.999109i \(-0.513435\pi\)
−0.0421946 + 0.999109i \(0.513435\pi\)
\(752\) −1.56214e61 −0.226483
\(753\) −1.13526e62 −1.59957
\(754\) −9.90638e61 −1.35654
\(755\) −1.09405e61 −0.145605
\(756\) −8.78529e61 −1.13642
\(757\) 4.86809e61 0.612065 0.306032 0.952021i \(-0.400998\pi\)
0.306032 + 0.952021i \(0.400998\pi\)
\(758\) −1.98224e62 −2.42253
\(759\) −6.74050e61 −0.800744
\(760\) −5.81951e61 −0.672039
\(761\) 5.98651e61 0.672053 0.336026 0.941853i \(-0.390917\pi\)
0.336026 + 0.941853i \(0.390917\pi\)
\(762\) 4.22481e62 4.61079
\(763\) −1.35319e61 −0.143576
\(764\) 1.56893e62 1.61844
\(765\) 3.43323e61 0.344336
\(766\) 8.65375e59 0.00843890
\(767\) −3.79370e60 −0.0359718
\(768\) −8.08650e61 −0.745580
\(769\) −2.53056e61 −0.226882 −0.113441 0.993545i \(-0.536187\pi\)
−0.113441 + 0.993545i \(0.536187\pi\)
\(770\) −1.62665e61 −0.141822
\(771\) −2.90115e62 −2.45980
\(772\) 1.07623e60 0.00887430
\(773\) 1.22577e62 0.982992 0.491496 0.870880i \(-0.336450\pi\)
0.491496 + 0.870880i \(0.336450\pi\)
\(774\) −1.15827e61 −0.0903402
\(775\) 7.71618e61 0.585350
\(776\) 1.15605e62 0.852998
\(777\) 5.76269e61 0.413593
\(778\) −3.59924e62 −2.51275
\(779\) 3.60260e61 0.244658
\(780\) 1.16434e62 0.769215
\(781\) 1.07852e62 0.693159
\(782\) −7.52633e61 −0.470585
\(783\) 5.14365e62 3.12891
\(784\) 4.70819e61 0.278649
\(785\) −7.40809e61 −0.426588
\(786\) −7.82512e62 −4.38436
\(787\) −5.88188e61 −0.320671 −0.160335 0.987063i \(-0.551258\pi\)
−0.160335 + 0.987063i \(0.551258\pi\)
\(788\) 1.59884e62 0.848189
\(789\) −2.80431e62 −1.44767
\(790\) 9.03715e60 0.0453993
\(791\) −9.69290e61 −0.473870
\(792\) 1.51474e62 0.720685
\(793\) −1.14015e62 −0.527944
\(794\) 2.51749e62 1.13456
\(795\) 1.47945e62 0.648943
\(796\) 3.26641e62 1.39457
\(797\) −1.91183e62 −0.794504 −0.397252 0.917710i \(-0.630036\pi\)
−0.397252 + 0.917710i \(0.630036\pi\)
\(798\) 4.63935e62 1.87670
\(799\) 5.42870e61 0.213767
\(800\) −2.34936e62 −0.900563
\(801\) −3.10506e62 −1.15870
\(802\) 5.93792e62 2.15718
\(803\) −2.80682e61 −0.0992727
\(804\) −7.85848e62 −2.70604
\(805\) −5.72408e61 −0.191909
\(806\) 2.19543e62 0.716667
\(807\) 7.39340e62 2.34998
\(808\) −1.55159e62 −0.480212
\(809\) 3.32609e62 1.00240 0.501200 0.865332i \(-0.332892\pi\)
0.501200 + 0.865332i \(0.332892\pi\)
\(810\) −4.17819e62 −1.22620
\(811\) 2.53671e61 0.0724974 0.0362487 0.999343i \(-0.488459\pi\)
0.0362487 + 0.999343i \(0.488459\pi\)
\(812\) −3.00976e62 −0.837678
\(813\) −6.58342e62 −1.78445
\(814\) −1.68845e62 −0.445720
\(815\) −5.81797e61 −0.149583
\(816\) −7.07214e61 −0.177097
\(817\) 1.94988e61 0.0475591
\(818\) −5.35262e62 −1.27166
\(819\) −2.00421e62 −0.463808
\(820\) 4.62614e61 0.104285
\(821\) 8.50693e62 1.86808 0.934039 0.357170i \(-0.116258\pi\)
0.934039 + 0.357170i \(0.116258\pi\)
\(822\) 1.76720e63 3.78043
\(823\) −5.42465e62 −1.13051 −0.565256 0.824915i \(-0.691223\pi\)
−0.565256 + 0.824915i \(0.691223\pi\)
\(824\) −5.14539e62 −1.04468
\(825\) 3.01976e62 0.597328
\(826\) −1.94107e61 −0.0374086
\(827\) −7.20567e62 −1.35303 −0.676513 0.736431i \(-0.736510\pi\)
−0.676513 + 0.736431i \(0.736510\pi\)
\(828\) 1.68723e63 3.08689
\(829\) −8.50026e62 −1.51534 −0.757669 0.652639i \(-0.773662\pi\)
−0.757669 + 0.652639i \(0.773662\pi\)
\(830\) 5.75689e62 1.00002
\(831\) 1.18245e63 2.00153
\(832\) −5.56310e62 −0.917626
\(833\) −1.63618e62 −0.263004
\(834\) −1.18371e63 −1.85428
\(835\) −3.74222e62 −0.571308
\(836\) −8.07154e62 −1.20094
\(837\) −1.13993e63 −1.65302
\(838\) 1.54617e62 0.218529
\(839\) 5.84952e62 0.805820 0.402910 0.915240i \(-0.367999\pi\)
0.402910 + 0.915240i \(0.367999\pi\)
\(840\) 1.88208e62 0.252716
\(841\) 9.98130e62 1.30639
\(842\) 1.78516e62 0.227755
\(843\) −1.03464e63 −1.28675
\(844\) 2.21582e63 2.68641
\(845\) −2.97397e62 −0.351494
\(846\) −2.04950e63 −2.36149
\(847\) 2.64625e62 0.297261
\(848\) −2.08286e62 −0.228113
\(849\) 2.50058e63 2.67009
\(850\) 3.37181e62 0.351040
\(851\) −5.94155e62 −0.603135
\(852\) −3.95001e63 −3.90973
\(853\) 6.11541e62 0.590230 0.295115 0.955462i \(-0.404642\pi\)
0.295115 + 0.955462i \(0.404642\pi\)
\(854\) −5.83366e62 −0.549031
\(855\) 2.18199e63 2.00254
\(856\) 8.05994e62 0.721350
\(857\) −3.04840e62 −0.266063 −0.133032 0.991112i \(-0.542471\pi\)
−0.133032 + 0.991112i \(0.542471\pi\)
\(858\) 8.59194e62 0.731332
\(859\) −4.98228e62 −0.413595 −0.206798 0.978384i \(-0.566304\pi\)
−0.206798 + 0.978384i \(0.566304\pi\)
\(860\) 2.50387e61 0.0202719
\(861\) −1.16511e62 −0.0920024
\(862\) −1.35661e63 −1.04483
\(863\) 2.55705e61 0.0192091 0.00960454 0.999954i \(-0.496943\pi\)
0.00960454 + 0.999954i \(0.496943\pi\)
\(864\) 3.47075e63 2.54318
\(865\) −2.30361e62 −0.164650
\(866\) 4.15054e63 2.89381
\(867\) −2.36757e63 −1.61025
\(868\) 6.67017e62 0.442551
\(869\) 3.95985e61 0.0256303
\(870\) −3.48800e63 −2.20248
\(871\) −9.62459e62 −0.592914
\(872\) −4.58739e62 −0.275715
\(873\) −4.33451e63 −2.54176
\(874\) −4.78335e63 −2.73676
\(875\) 6.07939e62 0.339380
\(876\) 1.02797e63 0.559943
\(877\) 2.16419e63 1.15028 0.575141 0.818054i \(-0.304947\pi\)
0.575141 + 0.818054i \(0.304947\pi\)
\(878\) 2.13950e63 1.10963
\(879\) 2.27678e63 1.15229
\(880\) 1.57592e62 0.0778319
\(881\) −8.01449e62 −0.386273 −0.193136 0.981172i \(-0.561866\pi\)
−0.193136 + 0.981172i \(0.561866\pi\)
\(882\) 6.17708e63 2.90542
\(883\) −1.13427e62 −0.0520667 −0.0260334 0.999661i \(-0.508288\pi\)
−0.0260334 + 0.999661i \(0.508288\pi\)
\(884\) 5.69665e62 0.255209
\(885\) −1.33575e62 −0.0584041
\(886\) −3.34001e63 −1.42535
\(887\) −2.15665e63 −0.898299 −0.449150 0.893457i \(-0.648273\pi\)
−0.449150 + 0.893457i \(0.648273\pi\)
\(888\) 1.95358e63 0.794243
\(889\) 1.57205e63 0.623849
\(890\) 1.13040e63 0.437872
\(891\) −1.83077e63 −0.692252
\(892\) −1.84825e63 −0.682205
\(893\) 3.45021e63 1.24319
\(894\) −8.65308e62 −0.304378
\(895\) −3.52062e62 −0.120899
\(896\) −1.45712e63 −0.488510
\(897\) 3.02346e63 0.989616
\(898\) 1.19568e63 0.382096
\(899\) −3.90528e63 −1.21848
\(900\) −7.55882e63 −2.30271
\(901\) 7.23832e62 0.215305
\(902\) 3.41372e62 0.0991489
\(903\) −6.30607e61 −0.0178843
\(904\) −3.28595e63 −0.909995
\(905\) 2.98592e62 0.0807484
\(906\) 2.95675e63 0.780833
\(907\) 7.76445e62 0.200241 0.100121 0.994975i \(-0.468077\pi\)
0.100121 + 0.994975i \(0.468077\pi\)
\(908\) −9.28172e61 −0.0233767
\(909\) 5.81759e63 1.43093
\(910\) 7.29634e62 0.175273
\(911\) −2.02334e62 −0.0474704 −0.0237352 0.999718i \(-0.507556\pi\)
−0.0237352 + 0.999718i \(0.507556\pi\)
\(912\) −4.49469e63 −1.02994
\(913\) 2.52252e63 0.564563
\(914\) 5.18739e63 1.13398
\(915\) −4.01442e63 −0.857174
\(916\) 1.10686e64 2.30855
\(917\) −2.91173e63 −0.593213
\(918\) −4.98125e63 −0.991335
\(919\) 9.59396e63 1.86515 0.932577 0.360972i \(-0.117555\pi\)
0.932577 + 0.360972i \(0.117555\pi\)
\(920\) −1.94049e63 −0.368531
\(921\) −1.34603e64 −2.49731
\(922\) −9.40102e63 −1.70396
\(923\) −4.83773e63 −0.856654
\(924\) 2.61040e63 0.451607
\(925\) 2.66183e63 0.449918
\(926\) 1.33286e63 0.220115
\(927\) 1.92923e64 3.11293
\(928\) 1.18905e64 1.87464
\(929\) −7.48220e63 −1.15263 −0.576317 0.817226i \(-0.695511\pi\)
−0.576317 + 0.817226i \(0.695511\pi\)
\(930\) 7.73004e63 1.16359
\(931\) −1.03987e64 −1.52954
\(932\) −1.04896e64 −1.50771
\(933\) 3.50164e63 0.491831
\(934\) −7.58679e63 −1.04136
\(935\) −5.47661e62 −0.0734619
\(936\) −6.79437e63 −0.890673
\(937\) −5.90450e63 −0.756453 −0.378227 0.925713i \(-0.623466\pi\)
−0.378227 + 0.925713i \(0.623466\pi\)
\(938\) −4.92450e63 −0.616596
\(939\) 1.64128e63 0.200850
\(940\) 4.43046e63 0.529907
\(941\) −1.10650e64 −1.29352 −0.646759 0.762694i \(-0.723876\pi\)
−0.646759 + 0.762694i \(0.723876\pi\)
\(942\) 2.00209e64 2.28765
\(943\) 1.20127e63 0.134165
\(944\) 1.88055e62 0.0205299
\(945\) −3.78845e63 −0.404275
\(946\) 1.84765e62 0.0192735
\(947\) 7.68969e63 0.784123 0.392062 0.919939i \(-0.371762\pi\)
0.392062 + 0.919939i \(0.371762\pi\)
\(948\) −1.45026e63 −0.144566
\(949\) 1.25900e63 0.122688
\(950\) 2.14295e64 2.04153
\(951\) 1.90961e64 1.77854
\(952\) 9.20821e62 0.0838457
\(953\) 5.87345e63 0.522873 0.261436 0.965221i \(-0.415804\pi\)
0.261436 + 0.965221i \(0.415804\pi\)
\(954\) −2.73269e64 −2.37849
\(955\) 6.76564e63 0.575753
\(956\) 1.54125e64 1.28242
\(957\) −1.52835e64 −1.24341
\(958\) −3.61273e64 −2.87393
\(959\) 6.57576e63 0.511500
\(960\) −1.95875e64 −1.48986
\(961\) −4.78994e63 −0.356268
\(962\) 7.57354e63 0.550852
\(963\) −3.02202e64 −2.14947
\(964\) 1.48021e64 1.02960
\(965\) 4.64099e61 0.00315699
\(966\) 1.54698e64 1.02914
\(967\) −1.95511e64 −1.27205 −0.636023 0.771670i \(-0.719422\pi\)
−0.636023 + 0.771670i \(0.719422\pi\)
\(968\) 8.97095e63 0.570845
\(969\) 1.56198e64 0.972110
\(970\) 1.57799e64 0.960529
\(971\) 2.50785e64 1.49310 0.746549 0.665330i \(-0.231709\pi\)
0.746549 + 0.665330i \(0.231709\pi\)
\(972\) 1.53323e64 0.892858
\(973\) −4.40459e63 −0.250888
\(974\) −4.75316e64 −2.64829
\(975\) −1.35452e64 −0.738220
\(976\) 5.65175e63 0.301309
\(977\) 3.39735e64 1.77177 0.885884 0.463906i \(-0.153553\pi\)
0.885884 + 0.463906i \(0.153553\pi\)
\(978\) 1.57235e64 0.802165
\(979\) 4.95312e63 0.247202
\(980\) −1.33531e64 −0.651962
\(981\) 1.72001e64 0.821575
\(982\) −2.21195e64 −1.03366
\(983\) −2.21328e64 −1.01189 −0.505947 0.862565i \(-0.668857\pi\)
−0.505947 + 0.862565i \(0.668857\pi\)
\(984\) −3.94979e63 −0.176677
\(985\) 6.89463e63 0.301739
\(986\) −1.70653e64 −0.730735
\(987\) −1.11583e64 −0.467496
\(988\) 3.62050e64 1.48421
\(989\) 6.50180e62 0.0260803
\(990\) 2.06759e64 0.811537
\(991\) 2.88177e64 1.10682 0.553408 0.832910i \(-0.313327\pi\)
0.553408 + 0.832910i \(0.313327\pi\)
\(992\) −2.63514e64 −0.990383
\(993\) 1.48807e64 0.547285
\(994\) −2.47526e64 −0.890870
\(995\) 1.40856e64 0.496112
\(996\) −9.23852e64 −3.18439
\(997\) −2.97127e64 −1.00230 −0.501148 0.865361i \(-0.667089\pi\)
−0.501148 + 0.865361i \(0.667089\pi\)
\(998\) 2.92687e64 0.966266
\(999\) −3.93238e64 −1.27057
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 1.44.a.a.1.1 3
3.2 odd 2 9.44.a.b.1.3 3
4.3 odd 2 16.44.a.c.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.44.a.a.1.1 3 1.1 even 1 trivial
9.44.a.b.1.3 3 3.2 odd 2
16.44.a.c.1.1 3 4.3 odd 2