Properties

Label 3.40.a.b.1.1
Level $3$
Weight $40$
Character 3.1
Self dual yes
Analytic conductor $28.902$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 40 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.9018654169\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 3876249523 x - 18467420411022\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(64517.4\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-983454. q^{2} -1.16226e9 q^{3} +4.17427e11 q^{4} +1.57969e13 q^{5} +1.14303e15 q^{6} +5.39162e15 q^{7} +1.30140e17 q^{8} +1.35085e18 q^{9} +O(q^{10})\) \(q-983454. q^{2} -1.16226e9 q^{3} +4.17427e11 q^{4} +1.57969e13 q^{5} +1.14303e15 q^{6} +5.39162e15 q^{7} +1.30140e17 q^{8} +1.35085e18 q^{9} -1.55355e19 q^{10} -1.89252e20 q^{11} -4.85159e20 q^{12} -1.17129e21 q^{13} -5.30242e21 q^{14} -1.83601e22 q^{15} -3.57469e23 q^{16} -1.39600e24 q^{17} -1.32850e24 q^{18} -2.79398e24 q^{19} +6.59403e24 q^{20} -6.26648e24 q^{21} +1.86120e26 q^{22} +5.34440e26 q^{23} -1.51256e26 q^{24} -1.56945e27 q^{25} +1.15191e27 q^{26} -1.57004e27 q^{27} +2.25061e27 q^{28} +2.12460e28 q^{29} +1.80563e28 q^{30} +1.34079e29 q^{31} +2.80010e29 q^{32} +2.19960e29 q^{33} +1.37291e30 q^{34} +8.51707e28 q^{35} +5.63882e29 q^{36} -4.34673e30 q^{37} +2.74775e30 q^{38} +1.36135e30 q^{39} +2.05580e30 q^{40} +3.17213e31 q^{41} +6.16279e30 q^{42} -8.86307e31 q^{43} -7.89987e31 q^{44} +2.13392e31 q^{45} -5.25597e32 q^{46} -3.38028e32 q^{47} +4.15473e32 q^{48} -8.80474e32 q^{49} +1.54348e33 q^{50} +1.62252e33 q^{51} -4.88930e32 q^{52} +7.04033e33 q^{53} +1.54407e33 q^{54} -2.98958e33 q^{55} +7.01664e32 q^{56} +3.24734e33 q^{57} -2.08945e34 q^{58} +1.96619e34 q^{59} -7.66399e33 q^{60} +6.79380e34 q^{61} -1.31860e35 q^{62} +7.28328e33 q^{63} -7.88559e34 q^{64} -1.85028e34 q^{65} -2.16320e35 q^{66} +4.10558e35 q^{67} -5.82729e35 q^{68} -6.21159e35 q^{69} -8.37615e34 q^{70} +8.69914e35 q^{71} +1.75799e35 q^{72} +3.39418e36 q^{73} +4.27481e36 q^{74} +1.82411e36 q^{75} -1.16628e36 q^{76} -1.02037e36 q^{77} -1.33883e36 q^{78} -1.47904e37 q^{79} -5.64689e36 q^{80} +1.82480e36 q^{81} -3.11965e37 q^{82} +1.98587e37 q^{83} -2.61579e36 q^{84} -2.20525e37 q^{85} +8.71642e37 q^{86} -2.46934e37 q^{87} -2.46291e37 q^{88} -1.95350e37 q^{89} -2.09861e37 q^{90} -6.31518e36 q^{91} +2.23089e38 q^{92} -1.55834e38 q^{93} +3.32435e38 q^{94} -4.41362e37 q^{95} -3.25444e38 q^{96} +3.46965e38 q^{97} +8.65906e38 q^{98} -2.55651e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} + O(q^{10}) \) \( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} - 39868781226579858780q^{10} - \)\(53\!\cdots\!40\)\(q^{11} - \)\(11\!\cdots\!44\)\(q^{12} + \)\(54\!\cdots\!90\)\(q^{13} + \)\(31\!\cdots\!52\)\(q^{14} + \)\(62\!\cdots\!10\)\(q^{15} + \)\(12\!\cdots\!36\)\(q^{16} + \)\(72\!\cdots\!58\)\(q^{17} + \)\(72\!\cdots\!86\)\(q^{18} - \)\(10\!\cdots\!24\)\(q^{19} + \)\(30\!\cdots\!60\)\(q^{20} + \)\(18\!\cdots\!76\)\(q^{21} - \)\(10\!\cdots\!24\)\(q^{22} + \)\(41\!\cdots\!64\)\(q^{23} - \)\(51\!\cdots\!32\)\(q^{24} - \)\(11\!\cdots\!75\)\(q^{25} + \)\(92\!\cdots\!76\)\(q^{26} - \)\(47\!\cdots\!89\)\(q^{27} + \)\(64\!\cdots\!56\)\(q^{28} + \)\(72\!\cdots\!62\)\(q^{29} + \)\(46\!\cdots\!60\)\(q^{30} - \)\(38\!\cdots\!56\)\(q^{31} + \)\(37\!\cdots\!12\)\(q^{32} + \)\(61\!\cdots\!80\)\(q^{33} + \)\(37\!\cdots\!44\)\(q^{34} + \)\(27\!\cdots\!20\)\(q^{35} + \)\(12\!\cdots\!48\)\(q^{36} + \)\(29\!\cdots\!22\)\(q^{37} + \)\(74\!\cdots\!92\)\(q^{38} - \)\(63\!\cdots\!30\)\(q^{39} + \)\(15\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!26\)\(q^{41} - \)\(36\!\cdots\!84\)\(q^{42} - \)\(24\!\cdots\!28\)\(q^{43} - \)\(21\!\cdots\!12\)\(q^{44} - \)\(72\!\cdots\!70\)\(q^{45} - \)\(10\!\cdots\!56\)\(q^{46} - \)\(10\!\cdots\!04\)\(q^{47} - \)\(13\!\cdots\!12\)\(q^{48} + \)\(92\!\cdots\!43\)\(q^{49} - \)\(11\!\cdots\!50\)\(q^{50} - \)\(84\!\cdots\!86\)\(q^{51} + \)\(59\!\cdots\!88\)\(q^{52} + \)\(62\!\cdots\!34\)\(q^{53} - \)\(83\!\cdots\!62\)\(q^{54} + \)\(72\!\cdots\!40\)\(q^{55} + \)\(36\!\cdots\!00\)\(q^{56} + \)\(12\!\cdots\!08\)\(q^{57} + \)\(28\!\cdots\!84\)\(q^{58} - \)\(75\!\cdots\!56\)\(q^{59} - \)\(35\!\cdots\!20\)\(q^{60} - \)\(71\!\cdots\!98\)\(q^{61} - \)\(33\!\cdots\!16\)\(q^{62} - \)\(21\!\cdots\!92\)\(q^{63} - \)\(35\!\cdots\!56\)\(q^{64} - \)\(71\!\cdots\!60\)\(q^{65} + \)\(11\!\cdots\!08\)\(q^{66} - \)\(51\!\cdots\!72\)\(q^{67} + \)\(11\!\cdots\!92\)\(q^{68} - \)\(48\!\cdots\!88\)\(q^{69} + \)\(38\!\cdots\!20\)\(q^{70} + \)\(84\!\cdots\!76\)\(q^{71} + \)\(60\!\cdots\!44\)\(q^{72} + \)\(63\!\cdots\!14\)\(q^{73} + \)\(89\!\cdots\!12\)\(q^{74} + \)\(13\!\cdots\!25\)\(q^{75} + \)\(12\!\cdots\!36\)\(q^{76} - \)\(22\!\cdots\!36\)\(q^{77} - \)\(10\!\cdots\!92\)\(q^{78} - \)\(16\!\cdots\!00\)\(q^{79} - \)\(18\!\cdots\!80\)\(q^{80} + \)\(54\!\cdots\!63\)\(q^{81} - \)\(48\!\cdots\!36\)\(q^{82} + \)\(59\!\cdots\!48\)\(q^{83} - \)\(74\!\cdots\!52\)\(q^{84} - \)\(52\!\cdots\!80\)\(q^{85} + \)\(85\!\cdots\!00\)\(q^{86} - \)\(84\!\cdots\!54\)\(q^{87} - \)\(10\!\cdots\!64\)\(q^{88} + \)\(18\!\cdots\!86\)\(q^{89} - \)\(53\!\cdots\!20\)\(q^{90} + \)\(23\!\cdots\!24\)\(q^{91} + \)\(96\!\cdots\!32\)\(q^{92} + \)\(44\!\cdots\!52\)\(q^{93} - \)\(12\!\cdots\!20\)\(q^{94} + \)\(84\!\cdots\!00\)\(q^{95} - \)\(44\!\cdots\!04\)\(q^{96} - \)\(99\!\cdots\!42\)\(q^{97} + \)\(19\!\cdots\!10\)\(q^{98} - \)\(71\!\cdots\!60\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −983454. −1.32638 −0.663192 0.748449i \(-0.730799\pi\)
−0.663192 + 0.748449i \(0.730799\pi\)
\(3\) −1.16226e9 −0.577350
\(4\) 4.17427e11 0.759295
\(5\) 1.57969e13 0.370387 0.185193 0.982702i \(-0.440709\pi\)
0.185193 + 0.982702i \(0.440709\pi\)
\(6\) 1.14303e15 0.765788
\(7\) 5.39162e15 0.178775 0.0893877 0.995997i \(-0.471509\pi\)
0.0893877 + 0.995997i \(0.471509\pi\)
\(8\) 1.30140e17 0.319268
\(9\) 1.35085e18 0.333333
\(10\) −1.55355e19 −0.491275
\(11\) −1.89252e20 −0.933001 −0.466501 0.884521i \(-0.654485\pi\)
−0.466501 + 0.884521i \(0.654485\pi\)
\(12\) −4.85159e20 −0.438379
\(13\) −1.17129e21 −0.222214 −0.111107 0.993808i \(-0.535440\pi\)
−0.111107 + 0.993808i \(0.535440\pi\)
\(14\) −5.30242e21 −0.237125
\(15\) −1.83601e22 −0.213843
\(16\) −3.57469e23 −1.18277
\(17\) −1.39600e24 −1.41623 −0.708113 0.706099i \(-0.750453\pi\)
−0.708113 + 0.706099i \(0.750453\pi\)
\(18\) −1.32850e24 −0.442128
\(19\) −2.79398e24 −0.323988 −0.161994 0.986792i \(-0.551792\pi\)
−0.161994 + 0.986792i \(0.551792\pi\)
\(20\) 6.59403e24 0.281233
\(21\) −6.26648e24 −0.103216
\(22\) 1.86120e26 1.23752
\(23\) 5.34440e26 1.49350 0.746751 0.665103i \(-0.231613\pi\)
0.746751 + 0.665103i \(0.231613\pi\)
\(24\) −1.51256e26 −0.184329
\(25\) −1.56945e27 −0.862813
\(26\) 1.15191e27 0.294741
\(27\) −1.57004e27 −0.192450
\(28\) 2.25061e27 0.135743
\(29\) 2.12460e28 0.646422 0.323211 0.946327i \(-0.395238\pi\)
0.323211 + 0.946327i \(0.395238\pi\)
\(30\) 1.80563e28 0.283638
\(31\) 1.34079e29 1.11124 0.555618 0.831438i \(-0.312482\pi\)
0.555618 + 0.831438i \(0.312482\pi\)
\(32\) 2.80010e29 1.24953
\(33\) 2.19960e29 0.538669
\(34\) 1.37291e30 1.87846
\(35\) 8.51707e28 0.0662161
\(36\) 5.63882e29 0.253098
\(37\) −4.34673e30 −1.14348 −0.571741 0.820434i \(-0.693732\pi\)
−0.571741 + 0.820434i \(0.693732\pi\)
\(38\) 2.74775e30 0.429732
\(39\) 1.36135e30 0.128295
\(40\) 2.05580e30 0.118253
\(41\) 3.17213e31 1.12737 0.563684 0.825990i \(-0.309384\pi\)
0.563684 + 0.825990i \(0.309384\pi\)
\(42\) 6.16279e30 0.136904
\(43\) −8.86307e31 −1.24437 −0.622184 0.782871i \(-0.713755\pi\)
−0.622184 + 0.782871i \(0.713755\pi\)
\(44\) −7.89987e31 −0.708423
\(45\) 2.13392e31 0.123462
\(46\) −5.25597e32 −1.98096
\(47\) −3.38028e32 −0.837616 −0.418808 0.908075i \(-0.637552\pi\)
−0.418808 + 0.908075i \(0.637552\pi\)
\(48\) 4.15473e32 0.682870
\(49\) −8.80474e32 −0.968039
\(50\) 1.54348e33 1.14442
\(51\) 1.62252e33 0.817659
\(52\) −4.88930e32 −0.168726
\(53\) 7.04033e33 1.67577 0.837883 0.545849i \(-0.183793\pi\)
0.837883 + 0.545849i \(0.183793\pi\)
\(54\) 1.54407e33 0.255263
\(55\) −2.98958e33 −0.345572
\(56\) 7.01664e32 0.0570772
\(57\) 3.24734e33 0.187054
\(58\) −2.08945e34 −0.857404
\(59\) 1.96619e34 0.578110 0.289055 0.957313i \(-0.406659\pi\)
0.289055 + 0.957313i \(0.406659\pi\)
\(60\) −7.66399e33 −0.162370
\(61\) 6.79380e34 1.04275 0.521376 0.853327i \(-0.325419\pi\)
0.521376 + 0.853327i \(0.325419\pi\)
\(62\) −1.31860e35 −1.47393
\(63\) 7.28328e33 0.0595918
\(64\) −7.88559e34 −0.474597
\(65\) −1.85028e34 −0.0823050
\(66\) −2.16320e35 −0.714481
\(67\) 4.10558e35 1.01138 0.505691 0.862714i \(-0.331237\pi\)
0.505691 + 0.862714i \(0.331237\pi\)
\(68\) −5.82729e35 −1.07533
\(69\) −6.21159e35 −0.862274
\(70\) −8.37615e34 −0.0878280
\(71\) 8.69914e35 0.691733 0.345867 0.938284i \(-0.387585\pi\)
0.345867 + 0.938284i \(0.387585\pi\)
\(72\) 1.75799e35 0.106423
\(73\) 3.39418e36 1.57014 0.785071 0.619405i \(-0.212626\pi\)
0.785071 + 0.619405i \(0.212626\pi\)
\(74\) 4.27481e36 1.51670
\(75\) 1.82411e36 0.498146
\(76\) −1.16628e36 −0.246002
\(77\) −1.02037e36 −0.166798
\(78\) −1.33883e36 −0.170169
\(79\) −1.47904e37 −1.46639 −0.733197 0.680016i \(-0.761973\pi\)
−0.733197 + 0.680016i \(0.761973\pi\)
\(80\) −5.64689e36 −0.438081
\(81\) 1.82480e36 0.111111
\(82\) −3.11965e37 −1.49532
\(83\) 1.98587e37 0.751500 0.375750 0.926721i \(-0.377385\pi\)
0.375750 + 0.926721i \(0.377385\pi\)
\(84\) −2.61579e36 −0.0783714
\(85\) −2.20525e37 −0.524552
\(86\) 8.71642e37 1.65051
\(87\) −2.46934e37 −0.373212
\(88\) −2.46291e37 −0.297877
\(89\) −1.95350e37 −0.189543 −0.0947717 0.995499i \(-0.530212\pi\)
−0.0947717 + 0.995499i \(0.530212\pi\)
\(90\) −2.09861e37 −0.163758
\(91\) −6.31518e36 −0.0397263
\(92\) 2.23089e38 1.13401
\(93\) −1.55834e38 −0.641572
\(94\) 3.32435e38 1.11100
\(95\) −4.41362e37 −0.120001
\(96\) −3.25444e38 −0.721419
\(97\) 3.46965e38 0.628400 0.314200 0.949357i \(-0.398264\pi\)
0.314200 + 0.949357i \(0.398264\pi\)
\(98\) 8.65906e38 1.28399
\(99\) −2.55651e38 −0.311000
\(100\) −6.55130e38 −0.655130
\(101\) 9.43292e38 0.776925 0.388463 0.921464i \(-0.373006\pi\)
0.388463 + 0.921464i \(0.373006\pi\)
\(102\) −1.59568e39 −1.08453
\(103\) −1.80882e39 −1.01641 −0.508205 0.861236i \(-0.669691\pi\)
−0.508205 + 0.861236i \(0.669691\pi\)
\(104\) −1.52432e38 −0.0709456
\(105\) −9.89907e37 −0.0382299
\(106\) −6.92384e39 −2.22271
\(107\) 4.01033e39 1.07201 0.536003 0.844216i \(-0.319934\pi\)
0.536003 + 0.844216i \(0.319934\pi\)
\(108\) −6.55378e38 −0.146126
\(109\) 2.19571e39 0.409033 0.204517 0.978863i \(-0.434438\pi\)
0.204517 + 0.978863i \(0.434438\pi\)
\(110\) 2.94012e39 0.458361
\(111\) 5.05204e39 0.660190
\(112\) −1.92734e39 −0.211450
\(113\) 1.80870e40 1.66854 0.834272 0.551353i \(-0.185888\pi\)
0.834272 + 0.551353i \(0.185888\pi\)
\(114\) −3.19361e39 −0.248106
\(115\) 8.44247e39 0.553174
\(116\) 8.86865e39 0.490825
\(117\) −1.58225e39 −0.0740712
\(118\) −1.93365e40 −0.766796
\(119\) −7.52673e39 −0.253186
\(120\) −2.38937e39 −0.0682731
\(121\) −5.32861e39 −0.129509
\(122\) −6.68140e40 −1.38309
\(123\) −3.68685e40 −0.650886
\(124\) 5.59680e40 0.843756
\(125\) −5.35267e40 −0.689962
\(126\) −7.16278e39 −0.0790416
\(127\) 1.44477e41 1.36655 0.683277 0.730159i \(-0.260554\pi\)
0.683277 + 0.730159i \(0.260554\pi\)
\(128\) −7.63857e40 −0.620037
\(129\) 1.03012e41 0.718437
\(130\) 1.81966e40 0.109168
\(131\) −1.14560e41 −0.591892 −0.295946 0.955205i \(-0.595635\pi\)
−0.295946 + 0.955205i \(0.595635\pi\)
\(132\) 9.18171e40 0.409008
\(133\) −1.50641e40 −0.0579210
\(134\) −4.03765e41 −1.34148
\(135\) −2.48017e40 −0.0712810
\(136\) −1.81675e41 −0.452155
\(137\) 6.64327e41 1.43328 0.716640 0.697443i \(-0.245679\pi\)
0.716640 + 0.697443i \(0.245679\pi\)
\(138\) 6.10881e41 1.14371
\(139\) 6.31930e41 1.02773 0.513867 0.857870i \(-0.328213\pi\)
0.513867 + 0.857870i \(0.328213\pi\)
\(140\) 3.55525e40 0.0502775
\(141\) 3.92877e41 0.483598
\(142\) −8.55521e41 −0.917504
\(143\) 2.21669e41 0.207326
\(144\) −4.82888e41 −0.394255
\(145\) 3.35620e41 0.239426
\(146\) −3.33802e42 −2.08261
\(147\) 1.02334e42 0.558898
\(148\) −1.81444e42 −0.868240
\(149\) −3.63083e41 −0.152361 −0.0761805 0.997094i \(-0.524273\pi\)
−0.0761805 + 0.997094i \(0.524273\pi\)
\(150\) −1.79393e42 −0.660732
\(151\) 1.34108e42 0.433913 0.216957 0.976181i \(-0.430387\pi\)
0.216957 + 0.976181i \(0.430387\pi\)
\(152\) −3.63608e41 −0.103439
\(153\) −1.88579e42 −0.472076
\(154\) 1.00349e42 0.221238
\(155\) 2.11802e42 0.411587
\(156\) 5.68264e41 0.0974138
\(157\) 7.18671e42 1.08764 0.543822 0.839200i \(-0.316977\pi\)
0.543822 + 0.839200i \(0.316977\pi\)
\(158\) 1.45457e43 1.94500
\(159\) −8.18270e42 −0.967504
\(160\) 4.42327e42 0.462811
\(161\) 2.88150e42 0.267002
\(162\) −1.79461e42 −0.147376
\(163\) −1.01241e43 −0.737395 −0.368697 0.929549i \(-0.620196\pi\)
−0.368697 + 0.929549i \(0.620196\pi\)
\(164\) 1.32413e43 0.856005
\(165\) 3.47468e42 0.199516
\(166\) −1.95302e43 −0.996777
\(167\) −1.84485e43 −0.837511 −0.418756 0.908099i \(-0.637534\pi\)
−0.418756 + 0.908099i \(0.637534\pi\)
\(168\) −8.15517e41 −0.0329535
\(169\) −2.64118e43 −0.950621
\(170\) 2.16876e43 0.695757
\(171\) −3.77426e42 −0.107996
\(172\) −3.69968e43 −0.944843
\(173\) 1.26682e43 0.288944 0.144472 0.989509i \(-0.453852\pi\)
0.144472 + 0.989509i \(0.453852\pi\)
\(174\) 2.42848e43 0.495022
\(175\) −8.46188e42 −0.154250
\(176\) 6.76516e43 1.10352
\(177\) −2.28522e43 −0.333772
\(178\) 1.92118e43 0.251407
\(179\) −1.09111e44 −1.28008 −0.640038 0.768343i \(-0.721081\pi\)
−0.640038 + 0.768343i \(0.721081\pi\)
\(180\) 8.90756e42 0.0937443
\(181\) 7.55663e43 0.713832 0.356916 0.934136i \(-0.383828\pi\)
0.356916 + 0.934136i \(0.383828\pi\)
\(182\) 6.21069e42 0.0526924
\(183\) −7.89618e43 −0.602033
\(184\) 6.95518e43 0.476827
\(185\) −6.86647e43 −0.423531
\(186\) 1.53256e44 0.850971
\(187\) 2.64196e44 1.32134
\(188\) −1.41102e44 −0.635997
\(189\) −8.46508e42 −0.0344053
\(190\) 4.34059e43 0.159167
\(191\) −1.39897e44 −0.463081 −0.231540 0.972825i \(-0.574377\pi\)
−0.231540 + 0.972825i \(0.574377\pi\)
\(192\) 9.16512e43 0.274009
\(193\) 6.10898e44 1.65044 0.825222 0.564808i \(-0.191050\pi\)
0.825222 + 0.564808i \(0.191050\pi\)
\(194\) −3.41224e44 −0.833500
\(195\) 2.15051e43 0.0475188
\(196\) −3.67533e44 −0.735027
\(197\) −4.59710e44 −0.832517 −0.416258 0.909246i \(-0.636659\pi\)
−0.416258 + 0.909246i \(0.636659\pi\)
\(198\) 2.51421e44 0.412506
\(199\) −1.14245e45 −1.69903 −0.849514 0.527566i \(-0.823105\pi\)
−0.849514 + 0.527566i \(0.823105\pi\)
\(200\) −2.04247e44 −0.275468
\(201\) −4.77175e44 −0.583922
\(202\) −9.27685e44 −1.03050
\(203\) 1.14550e44 0.115564
\(204\) 6.77284e44 0.620844
\(205\) 5.01097e44 0.417563
\(206\) 1.77889e45 1.34815
\(207\) 7.21949e44 0.497834
\(208\) 4.18702e44 0.262827
\(209\) 5.28766e44 0.302281
\(210\) 9.73528e43 0.0507075
\(211\) 2.97530e45 1.41261 0.706307 0.707906i \(-0.250360\pi\)
0.706307 + 0.707906i \(0.250360\pi\)
\(212\) 2.93882e45 1.27240
\(213\) −1.01107e45 −0.399372
\(214\) −3.94398e45 −1.42189
\(215\) −1.40009e45 −0.460898
\(216\) −2.04325e44 −0.0614431
\(217\) 7.22901e44 0.198662
\(218\) −2.15938e45 −0.542535
\(219\) −3.94493e45 −0.906522
\(220\) −1.24793e45 −0.262391
\(221\) 1.63513e45 0.314705
\(222\) −4.96845e45 −0.875665
\(223\) 9.60122e45 1.55018 0.775089 0.631852i \(-0.217705\pi\)
0.775089 + 0.631852i \(0.217705\pi\)
\(224\) 1.50971e45 0.223386
\(225\) −2.12009e45 −0.287604
\(226\) −1.77878e46 −2.21313
\(227\) 8.83193e45 1.00821 0.504105 0.863642i \(-0.331822\pi\)
0.504105 + 0.863642i \(0.331822\pi\)
\(228\) 1.35553e45 0.142029
\(229\) 5.23661e45 0.503800 0.251900 0.967753i \(-0.418945\pi\)
0.251900 + 0.967753i \(0.418945\pi\)
\(230\) −8.30279e45 −0.733721
\(231\) 1.18594e45 0.0963007
\(232\) 2.76495e45 0.206382
\(233\) 4.92640e45 0.338134 0.169067 0.985605i \(-0.445925\pi\)
0.169067 + 0.985605i \(0.445925\pi\)
\(234\) 1.55607e45 0.0982469
\(235\) −5.33979e45 −0.310242
\(236\) 8.20739e45 0.438956
\(237\) 1.71903e46 0.846623
\(238\) 7.40219e45 0.335823
\(239\) −1.38643e46 −0.579613 −0.289806 0.957085i \(-0.593591\pi\)
−0.289806 + 0.957085i \(0.593591\pi\)
\(240\) 6.56316e45 0.252926
\(241\) −2.68139e46 −0.952857 −0.476429 0.879213i \(-0.658069\pi\)
−0.476429 + 0.879213i \(0.658069\pi\)
\(242\) 5.24044e45 0.171778
\(243\) −2.12090e45 −0.0641500
\(244\) 2.83591e46 0.791756
\(245\) −1.39087e46 −0.358549
\(246\) 3.62584e46 0.863325
\(247\) 3.27258e45 0.0719945
\(248\) 1.74489e46 0.354782
\(249\) −2.30810e46 −0.433879
\(250\) 5.26411e46 0.915154
\(251\) −3.67189e46 −0.590544 −0.295272 0.955413i \(-0.595410\pi\)
−0.295272 + 0.955413i \(0.595410\pi\)
\(252\) 3.04024e45 0.0452477
\(253\) −1.01144e47 −1.39344
\(254\) −1.42087e47 −1.81258
\(255\) 2.56308e46 0.302850
\(256\) 1.18473e47 1.29700
\(257\) −1.07481e47 −1.09052 −0.545262 0.838266i \(-0.683570\pi\)
−0.545262 + 0.838266i \(0.683570\pi\)
\(258\) −1.01308e47 −0.952923
\(259\) −2.34359e46 −0.204426
\(260\) −7.72355e45 −0.0624938
\(261\) 2.87002e46 0.215474
\(262\) 1.12665e47 0.785077
\(263\) 4.28852e46 0.277441 0.138720 0.990332i \(-0.455701\pi\)
0.138720 + 0.990332i \(0.455701\pi\)
\(264\) 2.86255e46 0.171979
\(265\) 1.11215e47 0.620682
\(266\) 1.48149e46 0.0768255
\(267\) 2.27048e46 0.109433
\(268\) 1.71378e47 0.767938
\(269\) 3.54634e47 1.47779 0.738893 0.673823i \(-0.235349\pi\)
0.738893 + 0.673823i \(0.235349\pi\)
\(270\) 2.43914e46 0.0945460
\(271\) −1.75773e47 −0.633944 −0.316972 0.948435i \(-0.602666\pi\)
−0.316972 + 0.948435i \(0.602666\pi\)
\(272\) 4.99028e47 1.67506
\(273\) 7.33989e45 0.0229360
\(274\) −6.53336e47 −1.90108
\(275\) 2.97021e47 0.805006
\(276\) −2.59288e47 −0.654720
\(277\) −4.57384e47 −1.07628 −0.538140 0.842856i \(-0.680873\pi\)
−0.538140 + 0.842856i \(0.680873\pi\)
\(278\) −6.21475e47 −1.36317
\(279\) 1.81120e47 0.370412
\(280\) 1.10841e46 0.0211406
\(281\) 8.97102e46 0.159613 0.0798065 0.996810i \(-0.474570\pi\)
0.0798065 + 0.996810i \(0.474570\pi\)
\(282\) −3.86377e47 −0.641436
\(283\) −6.02752e47 −0.933906 −0.466953 0.884282i \(-0.654648\pi\)
−0.466953 + 0.884282i \(0.654648\pi\)
\(284\) 3.63126e47 0.525230
\(285\) 5.12978e46 0.0692825
\(286\) −2.18002e47 −0.274993
\(287\) 1.71029e47 0.201546
\(288\) 3.78251e47 0.416512
\(289\) 9.77182e47 1.00570
\(290\) −3.30067e47 −0.317571
\(291\) −4.03264e47 −0.362807
\(292\) 1.41682e48 1.19220
\(293\) 5.28590e47 0.416102 0.208051 0.978118i \(-0.433288\pi\)
0.208051 + 0.978118i \(0.433288\pi\)
\(294\) −1.00641e48 −0.741313
\(295\) 3.10596e47 0.214124
\(296\) −5.65682e47 −0.365077
\(297\) 2.97133e47 0.179556
\(298\) 3.57076e47 0.202089
\(299\) −6.25986e47 −0.331877
\(300\) 7.61432e47 0.378239
\(301\) −4.77863e47 −0.222463
\(302\) −1.31889e48 −0.575535
\(303\) −1.09635e48 −0.448558
\(304\) 9.98763e47 0.383202
\(305\) 1.07321e48 0.386222
\(306\) 1.85459e48 0.626153
\(307\) 4.29049e48 1.35928 0.679639 0.733547i \(-0.262136\pi\)
0.679639 + 0.733547i \(0.262136\pi\)
\(308\) −4.25931e47 −0.126649
\(309\) 2.10232e48 0.586824
\(310\) −2.08298e48 −0.545923
\(311\) −2.42927e48 −0.597928 −0.298964 0.954264i \(-0.596641\pi\)
−0.298964 + 0.954264i \(0.596641\pi\)
\(312\) 1.77166e47 0.0409605
\(313\) −1.42549e48 −0.309635 −0.154818 0.987943i \(-0.549479\pi\)
−0.154818 + 0.987943i \(0.549479\pi\)
\(314\) −7.06780e48 −1.44263
\(315\) 1.15053e47 0.0220720
\(316\) −6.17390e48 −1.11343
\(317\) −7.18697e47 −0.121868 −0.0609341 0.998142i \(-0.519408\pi\)
−0.0609341 + 0.998142i \(0.519408\pi\)
\(318\) 8.04732e48 1.28328
\(319\) −4.02084e48 −0.603113
\(320\) −1.24568e48 −0.175784
\(321\) −4.66106e48 −0.618922
\(322\) −2.83382e48 −0.354147
\(323\) 3.90041e48 0.458840
\(324\) 7.61720e47 0.0843661
\(325\) 1.83829e48 0.191729
\(326\) 9.95663e48 0.978069
\(327\) −2.55199e48 −0.236155
\(328\) 4.12820e48 0.359932
\(329\) −1.82252e48 −0.149745
\(330\) −3.41718e48 −0.264635
\(331\) 1.29273e49 0.943759 0.471880 0.881663i \(-0.343576\pi\)
0.471880 + 0.881663i \(0.343576\pi\)
\(332\) 8.28957e48 0.570610
\(333\) −5.87179e48 −0.381161
\(334\) 1.81433e49 1.11086
\(335\) 6.48552e48 0.374603
\(336\) 2.24007e48 0.122080
\(337\) 1.11373e48 0.0572792 0.0286396 0.999590i \(-0.490882\pi\)
0.0286396 + 0.999590i \(0.490882\pi\)
\(338\) 2.59748e49 1.26089
\(339\) −2.10219e49 −0.963334
\(340\) −9.20530e48 −0.398290
\(341\) −2.53746e49 −1.03678
\(342\) 3.71181e48 0.143244
\(343\) −9.65110e48 −0.351837
\(344\) −1.15344e49 −0.397287
\(345\) −9.81236e48 −0.319375
\(346\) −1.24586e49 −0.383251
\(347\) −2.89424e49 −0.841608 −0.420804 0.907152i \(-0.638252\pi\)
−0.420804 + 0.907152i \(0.638252\pi\)
\(348\) −1.03077e49 −0.283378
\(349\) −4.65598e49 −1.21036 −0.605181 0.796088i \(-0.706899\pi\)
−0.605181 + 0.796088i \(0.706899\pi\)
\(350\) 8.32187e48 0.204595
\(351\) 1.83898e48 0.0427650
\(352\) −5.29923e49 −1.16582
\(353\) 9.33522e49 1.94320 0.971600 0.236628i \(-0.0760422\pi\)
0.971600 + 0.236628i \(0.0760422\pi\)
\(354\) 2.24741e49 0.442710
\(355\) 1.37419e49 0.256209
\(356\) −8.15444e48 −0.143919
\(357\) 8.74803e48 0.146177
\(358\) 1.07306e50 1.69787
\(359\) 8.40096e49 1.25889 0.629444 0.777046i \(-0.283283\pi\)
0.629444 + 0.777046i \(0.283283\pi\)
\(360\) 2.77708e48 0.0394175
\(361\) −6.65624e49 −0.895032
\(362\) −7.43161e49 −0.946816
\(363\) 6.19323e48 0.0747719
\(364\) −2.63612e48 −0.0301640
\(365\) 5.36174e49 0.581560
\(366\) 7.76553e49 0.798527
\(367\) −5.51580e49 −0.537799 −0.268900 0.963168i \(-0.586660\pi\)
−0.268900 + 0.963168i \(0.586660\pi\)
\(368\) −1.91046e50 −1.76646
\(369\) 4.28508e49 0.375789
\(370\) 6.75286e49 0.561765
\(371\) 3.79588e49 0.299586
\(372\) −6.50494e49 −0.487143
\(373\) 2.65526e50 1.88706 0.943529 0.331291i \(-0.107484\pi\)
0.943529 + 0.331291i \(0.107484\pi\)
\(374\) −2.59825e50 −1.75261
\(375\) 6.22120e49 0.398350
\(376\) −4.39909e49 −0.267423
\(377\) −2.48853e49 −0.143644
\(378\) 8.32502e48 0.0456347
\(379\) 2.97919e49 0.155108 0.0775539 0.996988i \(-0.475289\pi\)
0.0775539 + 0.996988i \(0.475289\pi\)
\(380\) −1.84236e49 −0.0911160
\(381\) −1.67920e50 −0.788980
\(382\) 1.37582e50 0.614223
\(383\) 1.50203e50 0.637240 0.318620 0.947883i \(-0.396781\pi\)
0.318620 + 0.947883i \(0.396781\pi\)
\(384\) 8.87802e49 0.357979
\(385\) −1.61187e49 −0.0617797
\(386\) −6.00790e50 −2.18912
\(387\) −1.19727e50 −0.414790
\(388\) 1.44832e50 0.477141
\(389\) 3.70754e50 1.16163 0.580816 0.814035i \(-0.302734\pi\)
0.580816 + 0.814035i \(0.302734\pi\)
\(390\) −2.11492e49 −0.0630282
\(391\) −7.46080e50 −2.11514
\(392\) −1.14585e50 −0.309064
\(393\) 1.33149e50 0.341729
\(394\) 4.52104e50 1.10424
\(395\) −2.33641e50 −0.543133
\(396\) −1.06716e50 −0.236141
\(397\) −6.45741e50 −1.36033 −0.680164 0.733060i \(-0.738091\pi\)
−0.680164 + 0.733060i \(0.738091\pi\)
\(398\) 1.12354e51 2.25356
\(399\) 1.75084e49 0.0334407
\(400\) 5.61029e50 1.02051
\(401\) 4.44619e50 0.770322 0.385161 0.922849i \(-0.374146\pi\)
0.385161 + 0.922849i \(0.374146\pi\)
\(402\) 4.69280e50 0.774505
\(403\) −1.57045e50 −0.246932
\(404\) 3.93755e50 0.589915
\(405\) 2.88261e49 0.0411541
\(406\) −1.12655e50 −0.153283
\(407\) 8.22626e50 1.06687
\(408\) 2.11154e50 0.261052
\(409\) −6.28638e50 −0.740963 −0.370481 0.928840i \(-0.620807\pi\)
−0.370481 + 0.928840i \(0.620807\pi\)
\(410\) −4.92806e50 −0.553848
\(411\) −7.72122e50 −0.827505
\(412\) −7.55049e50 −0.771755
\(413\) 1.06009e50 0.103352
\(414\) −7.10004e50 −0.660319
\(415\) 3.13706e50 0.278346
\(416\) −3.27974e50 −0.277664
\(417\) −7.34468e50 −0.593362
\(418\) −5.20017e50 −0.400941
\(419\) −3.74717e49 −0.0275759 −0.0137879 0.999905i \(-0.504389\pi\)
−0.0137879 + 0.999905i \(0.504389\pi\)
\(420\) −4.13213e49 −0.0290277
\(421\) −1.68026e50 −0.112687 −0.0563437 0.998411i \(-0.517944\pi\)
−0.0563437 + 0.998411i \(0.517944\pi\)
\(422\) −2.92607e51 −1.87367
\(423\) −4.56626e50 −0.279205
\(424\) 9.16226e50 0.535018
\(425\) 2.19096e51 1.22194
\(426\) 9.94339e50 0.529721
\(427\) 3.66296e50 0.186418
\(428\) 1.67402e51 0.813968
\(429\) −2.57638e50 −0.119699
\(430\) 1.37692e51 0.611328
\(431\) −3.10054e51 −1.31562 −0.657809 0.753184i \(-0.728517\pi\)
−0.657809 + 0.753184i \(0.728517\pi\)
\(432\) 5.61242e50 0.227623
\(433\) 5.11038e51 1.98125 0.990624 0.136616i \(-0.0436225\pi\)
0.990624 + 0.136616i \(0.0436225\pi\)
\(434\) −7.10940e50 −0.263502
\(435\) −3.90078e50 −0.138233
\(436\) 9.16548e50 0.310577
\(437\) −1.49322e51 −0.483876
\(438\) 3.87965e51 1.20240
\(439\) −2.58440e51 −0.766129 −0.383065 0.923722i \(-0.625131\pi\)
−0.383065 + 0.923722i \(0.625131\pi\)
\(440\) −3.89063e50 −0.110330
\(441\) −1.18939e51 −0.322680
\(442\) −1.60808e51 −0.417420
\(443\) 7.44976e51 1.85042 0.925209 0.379459i \(-0.123890\pi\)
0.925209 + 0.379459i \(0.123890\pi\)
\(444\) 2.10886e51 0.501278
\(445\) −3.08592e50 −0.0702044
\(446\) −9.44236e51 −2.05613
\(447\) 4.21997e50 0.0879657
\(448\) −4.25161e50 −0.0848462
\(449\) −5.14327e51 −0.982733 −0.491366 0.870953i \(-0.663502\pi\)
−0.491366 + 0.870953i \(0.663502\pi\)
\(450\) 2.08501e51 0.381474
\(451\) −6.00331e51 −1.05184
\(452\) 7.55001e51 1.26692
\(453\) −1.55868e51 −0.250520
\(454\) −8.68580e51 −1.33727
\(455\) −9.97600e49 −0.0147141
\(456\) 4.22607e50 0.0597204
\(457\) 7.10120e51 0.961536 0.480768 0.876848i \(-0.340358\pi\)
0.480768 + 0.876848i \(0.340358\pi\)
\(458\) −5.14996e51 −0.668232
\(459\) 2.19179e51 0.272553
\(460\) 3.52411e51 0.420022
\(461\) 1.14310e52 1.30592 0.652961 0.757392i \(-0.273527\pi\)
0.652961 + 0.757392i \(0.273527\pi\)
\(462\) −1.16632e51 −0.127732
\(463\) 6.36169e51 0.667948 0.333974 0.942582i \(-0.391610\pi\)
0.333974 + 0.942582i \(0.391610\pi\)
\(464\) −7.59479e51 −0.764566
\(465\) −2.46169e51 −0.237630
\(466\) −4.84489e51 −0.448496
\(467\) −1.61556e52 −1.43431 −0.717155 0.696913i \(-0.754556\pi\)
−0.717155 + 0.696913i \(0.754556\pi\)
\(468\) −6.60471e50 −0.0562419
\(469\) 2.21357e51 0.180810
\(470\) 5.25144e51 0.411500
\(471\) −8.35284e51 −0.627952
\(472\) 2.55879e51 0.184572
\(473\) 1.67735e52 1.16100
\(474\) −1.69059e52 −1.12295
\(475\) 4.38501e51 0.279541
\(476\) −3.14186e51 −0.192243
\(477\) 9.51044e51 0.558589
\(478\) 1.36349e52 0.768789
\(479\) 2.76529e52 1.49692 0.748459 0.663181i \(-0.230794\pi\)
0.748459 + 0.663181i \(0.230794\pi\)
\(480\) −5.14100e51 −0.267204
\(481\) 5.09130e51 0.254097
\(482\) 2.63703e52 1.26385
\(483\) −3.34905e51 −0.154153
\(484\) −2.22430e51 −0.0983353
\(485\) 5.48095e51 0.232751
\(486\) 2.08580e51 0.0850876
\(487\) −4.32447e52 −1.69480 −0.847398 0.530957i \(-0.821832\pi\)
−0.847398 + 0.530957i \(0.821832\pi\)
\(488\) 8.84143e51 0.332917
\(489\) 1.17669e52 0.425735
\(490\) 1.36786e52 0.475574
\(491\) −4.34756e52 −1.45264 −0.726318 0.687359i \(-0.758770\pi\)
−0.726318 + 0.687359i \(0.758770\pi\)
\(492\) −1.53899e52 −0.494215
\(493\) −2.96595e52 −0.915480
\(494\) −3.21843e51 −0.0954923
\(495\) −4.03848e51 −0.115191
\(496\) −4.79289e52 −1.31433
\(497\) 4.69025e51 0.123665
\(498\) 2.26992e52 0.575490
\(499\) −3.90961e52 −0.953176 −0.476588 0.879127i \(-0.658127\pi\)
−0.476588 + 0.879127i \(0.658127\pi\)
\(500\) −2.23435e52 −0.523884
\(501\) 2.14420e52 0.483537
\(502\) 3.61114e52 0.783288
\(503\) −9.26181e52 −1.93250 −0.966252 0.257599i \(-0.917069\pi\)
−0.966252 + 0.257599i \(0.917069\pi\)
\(504\) 9.47844e50 0.0190257
\(505\) 1.49011e52 0.287763
\(506\) 9.94701e52 1.84824
\(507\) 3.06974e52 0.548841
\(508\) 6.03087e52 1.03762
\(509\) 4.50967e52 0.746703 0.373351 0.927690i \(-0.378209\pi\)
0.373351 + 0.927690i \(0.378209\pi\)
\(510\) −2.52067e52 −0.401696
\(511\) 1.83001e52 0.280703
\(512\) −7.45197e52 −1.10029
\(513\) 4.38667e51 0.0623515
\(514\) 1.05702e53 1.44645
\(515\) −2.85736e52 −0.376465
\(516\) 4.30000e52 0.545505
\(517\) 6.39724e52 0.781496
\(518\) 2.30482e52 0.271148
\(519\) −1.47237e52 −0.166822
\(520\) −2.40794e51 −0.0262773
\(521\) 1.49958e52 0.157629 0.0788143 0.996889i \(-0.474887\pi\)
0.0788143 + 0.996889i \(0.474887\pi\)
\(522\) −2.82253e52 −0.285801
\(523\) −7.38472e52 −0.720363 −0.360181 0.932882i \(-0.617285\pi\)
−0.360181 + 0.932882i \(0.617285\pi\)
\(524\) −4.78204e52 −0.449421
\(525\) 9.83491e51 0.0890562
\(526\) −4.21757e52 −0.367993
\(527\) −1.87174e53 −1.57376
\(528\) −7.86289e52 −0.637119
\(529\) 1.57574e53 1.23055
\(530\) −1.09375e53 −0.823263
\(531\) 2.65603e52 0.192703
\(532\) −6.28816e51 −0.0439791
\(533\) −3.71550e52 −0.250517
\(534\) −2.23291e52 −0.145150
\(535\) 6.33507e52 0.397057
\(536\) 5.34298e52 0.322902
\(537\) 1.26816e53 0.739052
\(538\) −3.48767e53 −1.96011
\(539\) 1.66631e53 0.903182
\(540\) −1.03529e52 −0.0541233
\(541\) 2.27671e53 1.14805 0.574026 0.818837i \(-0.305381\pi\)
0.574026 + 0.818837i \(0.305381\pi\)
\(542\) 1.72865e53 0.840854
\(543\) −8.78279e52 −0.412131
\(544\) −3.90895e53 −1.76962
\(545\) 3.46853e52 0.151501
\(546\) −7.21845e51 −0.0304220
\(547\) −5.88442e52 −0.239305 −0.119652 0.992816i \(-0.538178\pi\)
−0.119652 + 0.992816i \(0.538178\pi\)
\(548\) 2.77308e53 1.08828
\(549\) 9.17742e52 0.347584
\(550\) −2.92106e53 −1.06775
\(551\) −5.93610e52 −0.209433
\(552\) −8.08374e52 −0.275296
\(553\) −7.97441e52 −0.262155
\(554\) 4.49816e53 1.42756
\(555\) 7.98064e52 0.244526
\(556\) 2.63785e53 0.780353
\(557\) 2.92686e53 0.836036 0.418018 0.908439i \(-0.362725\pi\)
0.418018 + 0.908439i \(0.362725\pi\)
\(558\) −1.78123e53 −0.491309
\(559\) 1.03813e53 0.276516
\(560\) −3.04459e52 −0.0783181
\(561\) −3.07065e53 −0.762877
\(562\) −8.82259e52 −0.211708
\(563\) −4.41627e53 −1.02363 −0.511813 0.859097i \(-0.671026\pi\)
−0.511813 + 0.859097i \(0.671026\pi\)
\(564\) 1.63997e53 0.367193
\(565\) 2.85718e53 0.618007
\(566\) 5.92779e53 1.23872
\(567\) 9.83864e51 0.0198639
\(568\) 1.13210e53 0.220848
\(569\) −5.05383e53 −0.952646 −0.476323 0.879270i \(-0.658031\pi\)
−0.476323 + 0.879270i \(0.658031\pi\)
\(570\) −5.04490e52 −0.0918952
\(571\) 2.64819e53 0.466170 0.233085 0.972456i \(-0.425118\pi\)
0.233085 + 0.972456i \(0.425118\pi\)
\(572\) 9.25307e52 0.157421
\(573\) 1.62597e53 0.267360
\(574\) −1.68200e53 −0.267327
\(575\) −8.38776e53 −1.28861
\(576\) −1.06523e53 −0.158199
\(577\) 9.15202e53 1.31398 0.656989 0.753900i \(-0.271830\pi\)
0.656989 + 0.753900i \(0.271830\pi\)
\(578\) −9.61014e53 −1.33394
\(579\) −7.10023e53 −0.952884
\(580\) 1.40097e53 0.181795
\(581\) 1.07071e53 0.134350
\(582\) 3.96591e53 0.481222
\(583\) −1.33239e54 −1.56349
\(584\) 4.41717e53 0.501296
\(585\) −2.49945e52 −0.0274350
\(586\) −5.19844e53 −0.551911
\(587\) −1.24680e54 −1.28042 −0.640212 0.768199i \(-0.721153\pi\)
−0.640212 + 0.768199i \(0.721153\pi\)
\(588\) 4.27170e53 0.424368
\(589\) −3.74613e53 −0.360027
\(590\) −3.05457e53 −0.284011
\(591\) 5.34304e53 0.480654
\(592\) 1.55382e54 1.35247
\(593\) 1.19143e54 1.00346 0.501730 0.865024i \(-0.332697\pi\)
0.501730 + 0.865024i \(0.332697\pi\)
\(594\) −2.92217e53 −0.238160
\(595\) −1.18899e53 −0.0937770
\(596\) −1.51561e53 −0.115687
\(597\) 1.32782e54 0.980935
\(598\) 6.15629e53 0.440196
\(599\) 1.12943e54 0.781694 0.390847 0.920456i \(-0.372182\pi\)
0.390847 + 0.920456i \(0.372182\pi\)
\(600\) 2.37389e53 0.159042
\(601\) 1.31522e54 0.852997 0.426498 0.904488i \(-0.359747\pi\)
0.426498 + 0.904488i \(0.359747\pi\)
\(602\) 4.69957e53 0.295071
\(603\) 5.54603e53 0.337128
\(604\) 5.59801e53 0.329468
\(605\) −8.41753e52 −0.0479683
\(606\) 1.07821e54 0.594960
\(607\) −1.47634e54 −0.788872 −0.394436 0.918924i \(-0.629060\pi\)
−0.394436 + 0.918924i \(0.629060\pi\)
\(608\) −7.82342e53 −0.404834
\(609\) −1.33138e53 −0.0667211
\(610\) −1.05545e54 −0.512279
\(611\) 3.95931e53 0.186130
\(612\) −7.87181e53 −0.358444
\(613\) −2.90350e54 −1.28069 −0.640343 0.768089i \(-0.721208\pi\)
−0.640343 + 0.768089i \(0.721208\pi\)
\(614\) −4.21950e54 −1.80292
\(615\) −5.82406e53 −0.241080
\(616\) −1.32791e53 −0.0532531
\(617\) 4.37494e53 0.169985 0.0849926 0.996382i \(-0.472913\pi\)
0.0849926 + 0.996382i \(0.472913\pi\)
\(618\) −2.06753e54 −0.778355
\(619\) −1.36826e54 −0.499114 −0.249557 0.968360i \(-0.580285\pi\)
−0.249557 + 0.968360i \(0.580285\pi\)
\(620\) 8.84118e53 0.312516
\(621\) −8.39093e53 −0.287425
\(622\) 2.38908e54 0.793082
\(623\) −1.05325e53 −0.0338857
\(624\) −4.86641e53 −0.151743
\(625\) 2.00926e54 0.607261
\(626\) 1.40191e54 0.410695
\(627\) −6.14564e53 −0.174522
\(628\) 2.99993e54 0.825843
\(629\) 6.06806e54 1.61943
\(630\) −1.13149e53 −0.0292760
\(631\) −2.93523e54 −0.736325 −0.368162 0.929762i \(-0.620013\pi\)
−0.368162 + 0.929762i \(0.620013\pi\)
\(632\) −1.92481e54 −0.468172
\(633\) −3.45808e54 −0.815573
\(634\) 7.06806e53 0.161644
\(635\) 2.28229e54 0.506154
\(636\) −3.41568e54 −0.734621
\(637\) 1.03129e54 0.215112
\(638\) 3.95431e54 0.799959
\(639\) 1.17513e54 0.230578
\(640\) −1.20665e54 −0.229654
\(641\) −4.74778e54 −0.876514 −0.438257 0.898850i \(-0.644404\pi\)
−0.438257 + 0.898850i \(0.644404\pi\)
\(642\) 4.58394e54 0.820929
\(643\) 3.92907e54 0.682616 0.341308 0.939952i \(-0.389130\pi\)
0.341308 + 0.939952i \(0.389130\pi\)
\(644\) 1.20281e54 0.202733
\(645\) 1.62727e54 0.266100
\(646\) −3.83588e54 −0.608598
\(647\) 3.76973e54 0.580332 0.290166 0.956976i \(-0.406289\pi\)
0.290166 + 0.956976i \(0.406289\pi\)
\(648\) 2.37479e53 0.0354742
\(649\) −3.72104e54 −0.539377
\(650\) −1.80787e54 −0.254306
\(651\) −8.40200e53 −0.114697
\(652\) −4.22609e54 −0.559900
\(653\) 7.52716e54 0.967886 0.483943 0.875100i \(-0.339204\pi\)
0.483943 + 0.875100i \(0.339204\pi\)
\(654\) 2.50977e54 0.313233
\(655\) −1.80969e54 −0.219229
\(656\) −1.13394e55 −1.33341
\(657\) 4.58503e54 0.523381
\(658\) 1.79237e54 0.198619
\(659\) 1.58833e55 1.70874 0.854369 0.519666i \(-0.173944\pi\)
0.854369 + 0.519666i \(0.173944\pi\)
\(660\) 1.45042e54 0.151491
\(661\) −8.67678e54 −0.879893 −0.439947 0.898024i \(-0.645003\pi\)
−0.439947 + 0.898024i \(0.645003\pi\)
\(662\) −1.27134e55 −1.25179
\(663\) −1.90045e54 −0.181695
\(664\) 2.58441e54 0.239929
\(665\) −2.37966e53 −0.0214532
\(666\) 5.77464e54 0.505565
\(667\) 1.13547e55 0.965433
\(668\) −7.70091e54 −0.635918
\(669\) −1.11591e55 −0.894996
\(670\) −6.37822e54 −0.496867
\(671\) −1.28574e55 −0.972889
\(672\) −1.75467e54 −0.128972
\(673\) 6.85577e54 0.489511 0.244756 0.969585i \(-0.421292\pi\)
0.244756 + 0.969585i \(0.421292\pi\)
\(674\) −1.09530e54 −0.0759742
\(675\) 2.46410e54 0.166049
\(676\) −1.10250e55 −0.721802
\(677\) −2.36538e55 −1.50460 −0.752301 0.658819i \(-0.771056\pi\)
−0.752301 + 0.658819i \(0.771056\pi\)
\(678\) 2.06740e55 1.27775
\(679\) 1.87070e54 0.112343
\(680\) −2.86990e54 −0.167472
\(681\) −1.02650e55 −0.582091
\(682\) 2.49547e55 1.37517
\(683\) 6.41764e53 0.0343694 0.0171847 0.999852i \(-0.494530\pi\)
0.0171847 + 0.999852i \(0.494530\pi\)
\(684\) −1.57548e54 −0.0820007
\(685\) 1.04943e55 0.530868
\(686\) 9.49142e54 0.466671
\(687\) −6.08630e54 −0.290869
\(688\) 3.16827e55 1.47180
\(689\) −8.24630e54 −0.372378
\(690\) 9.65001e54 0.423614
\(691\) 8.58416e54 0.366333 0.183166 0.983082i \(-0.441365\pi\)
0.183166 + 0.983082i \(0.441365\pi\)
\(692\) 5.28803e54 0.219394
\(693\) −1.37837e54 −0.0555992
\(694\) 2.84635e55 1.11630
\(695\) 9.98251e54 0.380659
\(696\) −3.21359e54 −0.119154
\(697\) −4.42831e55 −1.59661
\(698\) 4.57894e55 1.60540
\(699\) −5.72576e54 −0.195222
\(700\) −3.53221e54 −0.117121
\(701\) −2.73445e55 −0.881797 −0.440899 0.897557i \(-0.645340\pi\)
−0.440899 + 0.897557i \(0.645340\pi\)
\(702\) −1.80856e54 −0.0567229
\(703\) 1.21447e55 0.370474
\(704\) 1.49236e55 0.442799
\(705\) 6.20623e54 0.179118
\(706\) −9.18076e55 −2.57743
\(707\) 5.08587e54 0.138895
\(708\) −9.53913e54 −0.253431
\(709\) −4.45024e55 −1.15022 −0.575112 0.818075i \(-0.695041\pi\)
−0.575112 + 0.818075i \(0.695041\pi\)
\(710\) −1.35146e55 −0.339832
\(711\) −1.99796e55 −0.488798
\(712\) −2.54228e54 −0.0605151
\(713\) 7.16569e55 1.65963
\(714\) −8.60329e54 −0.193887
\(715\) 3.50168e54 0.0767907
\(716\) −4.55460e55 −0.971955
\(717\) 1.61139e55 0.334639
\(718\) −8.26196e55 −1.66977
\(719\) −7.96989e54 −0.156761 −0.0783807 0.996924i \(-0.524975\pi\)
−0.0783807 + 0.996924i \(0.524975\pi\)
\(720\) −7.62811e54 −0.146027
\(721\) −9.75246e54 −0.181709
\(722\) 6.54611e55 1.18716
\(723\) 3.11648e55 0.550132
\(724\) 3.15434e55 0.542009
\(725\) −3.33445e55 −0.557742
\(726\) −6.09076e54 −0.0991762
\(727\) 1.16079e56 1.84006 0.920031 0.391845i \(-0.128163\pi\)
0.920031 + 0.391845i \(0.128163\pi\)
\(728\) −8.21855e53 −0.0126833
\(729\) 2.46503e54 0.0370370
\(730\) −5.27303e55 −0.771373
\(731\) 1.23729e56 1.76231
\(732\) −3.29607e55 −0.457121
\(733\) 3.74430e55 0.505642 0.252821 0.967513i \(-0.418642\pi\)
0.252821 + 0.967513i \(0.418642\pi\)
\(734\) 5.42454e55 0.713328
\(735\) 1.61656e55 0.207008
\(736\) 1.49648e56 1.86618
\(737\) −7.76987e55 −0.943621
\(738\) −4.21418e55 −0.498441
\(739\) −8.25189e54 −0.0950576 −0.0475288 0.998870i \(-0.515135\pi\)
−0.0475288 + 0.998870i \(0.515135\pi\)
\(740\) −2.86625e55 −0.321585
\(741\) −3.80359e54 −0.0415660
\(742\) −3.73308e55 −0.397366
\(743\) −4.93877e55 −0.512079 −0.256040 0.966666i \(-0.582418\pi\)
−0.256040 + 0.966666i \(0.582418\pi\)
\(744\) −2.02802e55 −0.204833
\(745\) −5.73557e54 −0.0564325
\(746\) −2.61133e56 −2.50296
\(747\) 2.68262e55 0.250500
\(748\) 1.10282e56 1.00329
\(749\) 2.16222e55 0.191648
\(750\) −6.11827e55 −0.528365
\(751\) −1.08242e56 −0.910790 −0.455395 0.890290i \(-0.650502\pi\)
−0.455395 + 0.890290i \(0.650502\pi\)
\(752\) 1.20835e56 0.990703
\(753\) 4.26770e55 0.340951
\(754\) 2.44736e55 0.190527
\(755\) 2.11848e55 0.160716
\(756\) −3.53355e54 −0.0261238
\(757\) 4.75165e55 0.342353 0.171177 0.985240i \(-0.445243\pi\)
0.171177 + 0.985240i \(0.445243\pi\)
\(758\) −2.92990e55 −0.205733
\(759\) 1.17555e56 0.804503
\(760\) −5.74386e54 −0.0383124
\(761\) −1.65472e56 −1.07578 −0.537890 0.843015i \(-0.680778\pi\)
−0.537890 + 0.843015i \(0.680778\pi\)
\(762\) 1.65142e56 1.04649
\(763\) 1.18384e55 0.0731251
\(764\) −5.83966e55 −0.351615
\(765\) −2.97896e55 −0.174851
\(766\) −1.47718e56 −0.845225
\(767\) −2.30298e55 −0.128464
\(768\) −1.37697e56 −0.748826
\(769\) −5.44232e55 −0.288550 −0.144275 0.989538i \(-0.546085\pi\)
−0.144275 + 0.989538i \(0.546085\pi\)
\(770\) 1.58520e55 0.0819436
\(771\) 1.24921e56 0.629614
\(772\) 2.55005e56 1.25317
\(773\) −2.68720e56 −1.28766 −0.643829 0.765169i \(-0.722655\pi\)
−0.643829 + 0.765169i \(0.722655\pi\)
\(774\) 1.17746e56 0.550170
\(775\) −2.10429e56 −0.958789
\(776\) 4.51538e55 0.200628
\(777\) 2.72387e55 0.118026
\(778\) −3.64620e56 −1.54077
\(779\) −8.86288e55 −0.365253
\(780\) 8.97679e54 0.0360808
\(781\) −1.64633e56 −0.645388
\(782\) 7.33736e56 2.80549
\(783\) −3.33571e55 −0.124404
\(784\) 3.14742e56 1.14496
\(785\) 1.13527e56 0.402849
\(786\) −1.30946e56 −0.453264
\(787\) 4.30176e56 1.45257 0.726287 0.687391i \(-0.241244\pi\)
0.726287 + 0.687391i \(0.241244\pi\)
\(788\) −1.91895e56 −0.632126
\(789\) −4.98438e55 −0.160181
\(790\) 2.29776e56 0.720404
\(791\) 9.75185e55 0.298295
\(792\) −3.32703e55 −0.0992923
\(793\) −7.95754e55 −0.231714
\(794\) 6.35057e56 1.80432
\(795\) −1.29261e56 −0.358351
\(796\) −4.76887e56 −1.29006
\(797\) 3.00522e56 0.793303 0.396652 0.917969i \(-0.370172\pi\)
0.396652 + 0.917969i \(0.370172\pi\)
\(798\) −1.72187e55 −0.0443552
\(799\) 4.71889e56 1.18625
\(800\) −4.39461e56 −1.07812
\(801\) −2.63889e55 −0.0631811
\(802\) −4.37262e56 −1.02174
\(803\) −6.42354e56 −1.46495
\(804\) −1.99186e56 −0.443369
\(805\) 4.55186e55 0.0988939
\(806\) 1.54447e56 0.327526
\(807\) −4.12178e56 −0.853200
\(808\) 1.22760e56 0.248047
\(809\) −4.70856e56 −0.928736 −0.464368 0.885642i \(-0.653718\pi\)
−0.464368 + 0.885642i \(0.653718\pi\)
\(810\) −2.83492e55 −0.0545862
\(811\) 3.36981e56 0.633430 0.316715 0.948521i \(-0.397420\pi\)
0.316715 + 0.948521i \(0.397420\pi\)
\(812\) 4.78164e55 0.0877474
\(813\) 2.04294e56 0.366008
\(814\) −8.09015e56 −1.41508
\(815\) −1.59930e56 −0.273121
\(816\) −5.80002e56 −0.967099
\(817\) 2.47633e56 0.403160
\(818\) 6.18237e56 0.982801
\(819\) −8.53087e54 −0.0132421
\(820\) 2.09171e56 0.317053
\(821\) −1.61083e56 −0.238428 −0.119214 0.992869i \(-0.538037\pi\)
−0.119214 + 0.992869i \(0.538037\pi\)
\(822\) 7.59347e56 1.09759
\(823\) −1.33570e57 −1.88543 −0.942716 0.333597i \(-0.891738\pi\)
−0.942716 + 0.333597i \(0.891738\pi\)
\(824\) −2.35399e56 −0.324507
\(825\) −3.45216e56 −0.464770
\(826\) −1.04255e56 −0.137084
\(827\) 1.43015e57 1.83664 0.918320 0.395840i \(-0.129546\pi\)
0.918320 + 0.395840i \(0.129546\pi\)
\(828\) 3.01361e56 0.378003
\(829\) 1.29097e57 1.58162 0.790809 0.612062i \(-0.209660\pi\)
0.790809 + 0.612062i \(0.209660\pi\)
\(830\) −3.08515e56 −0.369193
\(831\) 5.31599e56 0.621390
\(832\) 9.23635e55 0.105462
\(833\) 1.22915e57 1.37096
\(834\) 7.22316e56 0.787026
\(835\) −2.91429e56 −0.310203
\(836\) 2.20721e56 0.229520
\(837\) −2.10509e56 −0.213857
\(838\) 3.68517e55 0.0365762
\(839\) −6.05135e56 −0.586805 −0.293402 0.955989i \(-0.594788\pi\)
−0.293402 + 0.955989i \(0.594788\pi\)
\(840\) −1.28826e55 −0.0122056
\(841\) −6.28852e56 −0.582138
\(842\) 1.65246e56 0.149467
\(843\) −1.04267e56 −0.0921527
\(844\) 1.24197e57 1.07259
\(845\) −4.17224e56 −0.352098
\(846\) 4.49071e56 0.370333
\(847\) −2.87298e55 −0.0231530
\(848\) −2.51670e57 −1.98204
\(849\) 7.00556e56 0.539191
\(850\) −2.15471e57 −1.62076
\(851\) −2.32307e57 −1.70779
\(852\) −4.22047e56 −0.303241
\(853\) 2.15150e57 1.51090 0.755450 0.655206i \(-0.227418\pi\)
0.755450 + 0.655206i \(0.227418\pi\)
\(854\) −3.60236e56 −0.247262
\(855\) −5.96214e55 −0.0400003
\(856\) 5.21903e56 0.342256
\(857\) 8.05117e56 0.516099 0.258050 0.966132i \(-0.416920\pi\)
0.258050 + 0.966132i \(0.416920\pi\)
\(858\) 2.53375e56 0.158768
\(859\) −1.57853e57 −0.966909 −0.483455 0.875369i \(-0.660618\pi\)
−0.483455 + 0.875369i \(0.660618\pi\)
\(860\) −5.84433e56 −0.349957
\(861\) −1.98781e56 −0.116362
\(862\) 3.04924e57 1.74502
\(863\) 1.37204e57 0.767640 0.383820 0.923408i \(-0.374608\pi\)
0.383820 + 0.923408i \(0.374608\pi\)
\(864\) −4.39627e56 −0.240473
\(865\) 2.00117e56 0.107021
\(866\) −5.02582e57 −2.62790
\(867\) −1.13574e57 −0.580640
\(868\) 3.01758e56 0.150843
\(869\) 2.79910e57 1.36815
\(870\) 3.83624e56 0.183350
\(871\) −4.80884e56 −0.224743
\(872\) 2.85749e56 0.130591
\(873\) 4.68698e56 0.209467
\(874\) 1.46851e57 0.641806
\(875\) −2.88596e56 −0.123348
\(876\) −1.64672e57 −0.688318
\(877\) −5.43028e56 −0.221988 −0.110994 0.993821i \(-0.535403\pi\)
−0.110994 + 0.993821i \(0.535403\pi\)
\(878\) 2.54164e57 1.01618
\(879\) −6.14359e56 −0.240237
\(880\) 1.06868e57 0.408730
\(881\) 2.33735e57 0.874365 0.437183 0.899373i \(-0.355976\pi\)
0.437183 + 0.899373i \(0.355976\pi\)
\(882\) 1.16971e57 0.427997
\(883\) −1.13126e57 −0.404884 −0.202442 0.979294i \(-0.564888\pi\)
−0.202442 + 0.979294i \(0.564888\pi\)
\(884\) 6.82548e56 0.238954
\(885\) −3.60993e56 −0.123625
\(886\) −7.32650e57 −2.45436
\(887\) 6.73827e56 0.220820 0.110410 0.993886i \(-0.464784\pi\)
0.110410 + 0.993886i \(0.464784\pi\)
\(888\) 6.57471e56 0.210777
\(889\) 7.78967e56 0.244306
\(890\) 3.03486e56 0.0931180
\(891\) −3.45346e56 −0.103667
\(892\) 4.00781e57 1.17704
\(893\) 9.44445e56 0.271377
\(894\) −4.15015e56 −0.116676
\(895\) −1.72362e57 −0.474123
\(896\) −4.11843e56 −0.110847
\(897\) 7.27560e56 0.191609
\(898\) 5.05817e57 1.30348
\(899\) 2.84863e57 0.718328
\(900\) −8.84983e56 −0.218377
\(901\) −9.82833e57 −2.37327
\(902\) 5.90398e57 1.39514
\(903\) 5.55402e56 0.128439
\(904\) 2.35384e57 0.532712
\(905\) 1.19371e57 0.264394
\(906\) 1.53289e57 0.332285
\(907\) −4.11384e57 −0.872782 −0.436391 0.899757i \(-0.643744\pi\)
−0.436391 + 0.899757i \(0.643744\pi\)
\(908\) 3.68668e57 0.765529
\(909\) 1.27425e57 0.258975
\(910\) 9.81094e55 0.0195166
\(911\) −6.39052e57 −1.24431 −0.622154 0.782895i \(-0.713742\pi\)
−0.622154 + 0.782895i \(0.713742\pi\)
\(912\) −1.16082e57 −0.221242
\(913\) −3.75830e57 −0.701150
\(914\) −6.98370e57 −1.27537
\(915\) −1.24735e57 −0.222985
\(916\) 2.18590e57 0.382533
\(917\) −6.17664e56 −0.105816
\(918\) −2.15552e57 −0.361510
\(919\) 5.76262e55 0.00946166 0.00473083 0.999989i \(-0.498494\pi\)
0.00473083 + 0.999989i \(0.498494\pi\)
\(920\) 1.09870e57 0.176610
\(921\) −4.98667e57 −0.784779
\(922\) −1.12419e58 −1.73215
\(923\) −1.01893e57 −0.153713
\(924\) 4.95043e56 0.0731206
\(925\) 6.82197e57 0.986612
\(926\) −6.25643e57 −0.885956
\(927\) −2.44344e57 −0.338803
\(928\) 5.94908e57 0.807727
\(929\) −1.93034e57 −0.256642 −0.128321 0.991733i \(-0.540959\pi\)
−0.128321 + 0.991733i \(0.540959\pi\)
\(930\) 2.42096e57 0.315189
\(931\) 2.46003e57 0.313633
\(932\) 2.05641e57 0.256744
\(933\) 2.82345e57 0.345214
\(934\) 1.58883e58 1.90245
\(935\) 4.17347e57 0.489408
\(936\) −2.05913e56 −0.0236485
\(937\) 1.77370e58 1.99507 0.997537 0.0701384i \(-0.0223441\pi\)
0.997537 + 0.0701384i \(0.0223441\pi\)
\(938\) −2.17695e57 −0.239824
\(939\) 1.65680e57 0.178768
\(940\) −2.22897e57 −0.235565
\(941\) −1.24048e57 −0.128408 −0.0642038 0.997937i \(-0.520451\pi\)
−0.0642038 + 0.997937i \(0.520451\pi\)
\(942\) 8.21464e57 0.832905
\(943\) 1.69531e58 1.68373
\(944\) −7.02851e57 −0.683769
\(945\) −1.33722e56 −0.0127433
\(946\) −1.64960e58 −1.53993
\(947\) −1.13841e57 −0.104106 −0.0520530 0.998644i \(-0.516576\pi\)
−0.0520530 + 0.998644i \(0.516576\pi\)
\(948\) 7.17568e57 0.642837
\(949\) −3.97558e57 −0.348907
\(950\) −4.31246e57 −0.370779
\(951\) 8.35314e56 0.0703606
\(952\) −9.79526e56 −0.0808342
\(953\) −3.13047e57 −0.253103 −0.126552 0.991960i \(-0.540391\pi\)
−0.126552 + 0.991960i \(0.540391\pi\)
\(954\) −9.35309e57 −0.740903
\(955\) −2.20993e57 −0.171519
\(956\) −5.78731e57 −0.440097
\(957\) 4.67327e57 0.348207
\(958\) −2.71954e58 −1.98549
\(959\) 3.58180e57 0.256235
\(960\) 1.44780e57 0.101489
\(961\) 3.41891e57 0.234845
\(962\) −5.00706e57 −0.337031
\(963\) 5.41737e57 0.357335
\(964\) −1.11928e58 −0.723499
\(965\) 9.65026e57 0.611303
\(966\) 3.29364e57 0.204467
\(967\) −3.53898e57 −0.215309 −0.107655 0.994188i \(-0.534334\pi\)
−0.107655 + 0.994188i \(0.534334\pi\)
\(968\) −6.93463e56 −0.0413479
\(969\) −4.53330e57 −0.264911
\(970\) −5.39027e57 −0.308718
\(971\) −1.69979e58 −0.954155 −0.477078 0.878861i \(-0.658304\pi\)
−0.477078 + 0.878861i \(0.658304\pi\)
\(972\) −8.85318e56 −0.0487088
\(973\) 3.40713e57 0.183733
\(974\) 4.25291e58 2.24795
\(975\) −2.13657e57 −0.110695
\(976\) −2.42857e58 −1.23333
\(977\) −9.44722e57 −0.470284 −0.235142 0.971961i \(-0.575555\pi\)
−0.235142 + 0.971961i \(0.575555\pi\)
\(978\) −1.15722e58 −0.564688
\(979\) 3.69703e57 0.176844
\(980\) −5.80587e57 −0.272245
\(981\) 2.96608e57 0.136344
\(982\) 4.27563e58 1.92675
\(983\) 2.21582e58 0.978904 0.489452 0.872030i \(-0.337197\pi\)
0.489452 + 0.872030i \(0.337197\pi\)
\(984\) −4.79805e57 −0.207807
\(985\) −7.26198e57 −0.308353
\(986\) 2.91688e58 1.21428
\(987\) 2.11825e57 0.0864554
\(988\) 1.36606e57 0.0546650
\(989\) −4.73678e58 −1.85847
\(990\) 3.97166e57 0.152787
\(991\) 1.83857e58 0.693496 0.346748 0.937958i \(-0.387286\pi\)
0.346748 + 0.937958i \(0.387286\pi\)
\(992\) 3.75433e58 1.38853
\(993\) −1.50249e58 −0.544880
\(994\) −4.61265e57 −0.164027
\(995\) −1.80471e58 −0.629298
\(996\) −9.63464e57 −0.329442
\(997\) −1.92411e57 −0.0645172 −0.0322586 0.999480i \(-0.510270\pi\)
−0.0322586 + 0.999480i \(0.510270\pi\)
\(998\) 3.84492e58 1.26428
\(999\) 6.82456e57 0.220063
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3.40.a.b.1.1 3
3.2 odd 2 9.40.a.c.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.40.a.b.1.1 3 1.1 even 1 trivial
9.40.a.c.1.3 3 3.2 odd 2