Properties

Label 3.40.a.b.1.3
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 1.3
Root \(-59724.7\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.25290e6 q^{2} -1.16226e9 q^{3} +1.02001e12 q^{4} -6.13018e12 q^{5} -1.45620e15 q^{6} +3.89397e16 q^{7} +5.89182e17 q^{8} +1.35085e18 q^{9} +O(q^{10})\) \(q+1.25290e6 q^{2} -1.16226e9 q^{3} +1.02001e12 q^{4} -6.13018e12 q^{5} -1.45620e15 q^{6} +3.89397e16 q^{7} +5.89182e17 q^{8} +1.35085e18 q^{9} -7.68052e18 q^{10} -1.99093e20 q^{11} -1.18552e21 q^{12} +6.42008e21 q^{13} +4.87876e22 q^{14} +7.12487e21 q^{15} +1.77432e23 q^{16} +1.81467e24 q^{17} +1.69249e24 q^{18} +6.82963e24 q^{19} -6.25284e24 q^{20} -4.52581e25 q^{21} -2.49445e26 q^{22} +4.57450e26 q^{23} -6.84783e26 q^{24} -1.78141e27 q^{25} +8.04374e27 q^{26} -1.57004e27 q^{27} +3.97188e28 q^{28} +3.57753e28 q^{29} +8.92677e27 q^{30} -1.66982e29 q^{31} -1.01602e29 q^{32} +2.31399e29 q^{33} +2.27361e30 q^{34} -2.38707e29 q^{35} +1.37788e30 q^{36} +2.76171e30 q^{37} +8.55686e30 q^{38} -7.46181e30 q^{39} -3.61179e30 q^{40} -5.74055e30 q^{41} -5.67040e31 q^{42} -3.87508e31 q^{43} -2.03077e32 q^{44} -8.28096e30 q^{45} +5.73141e32 q^{46} -2.60656e32 q^{47} -2.06222e32 q^{48} +6.06755e32 q^{49} -2.23193e33 q^{50} -2.10912e33 q^{51} +6.54854e33 q^{52} -1.46778e32 q^{53} -1.96711e33 q^{54} +1.22048e33 q^{55} +2.29426e34 q^{56} -7.93781e33 q^{57} +4.48230e34 q^{58} -1.10436e33 q^{59} +7.26744e33 q^{60} -9.76740e34 q^{61} -2.09212e35 q^{62} +5.26017e34 q^{63} -2.24841e35 q^{64} -3.93563e34 q^{65} +2.89920e35 q^{66} -4.32024e35 q^{67} +1.85098e36 q^{68} -5.31677e35 q^{69} -2.99077e35 q^{70} -8.50906e35 q^{71} +7.95897e35 q^{72} -2.18530e36 q^{73} +3.46015e36 q^{74} +2.07046e36 q^{75} +6.96628e36 q^{76} -7.75263e36 q^{77} -9.34893e36 q^{78} +1.19375e37 q^{79} -1.08769e36 q^{80} +1.82480e36 q^{81} -7.19236e36 q^{82} +1.67750e37 q^{83} -4.61637e37 q^{84} -1.11243e37 q^{85} -4.85510e37 q^{86} -4.15802e37 q^{87} -1.17302e38 q^{88} +1.45669e38 q^{89} -1.03752e37 q^{90} +2.49996e38 q^{91} +4.66603e38 q^{92} +1.94077e38 q^{93} -3.26577e38 q^{94} -4.18668e37 q^{95} +1.18088e38 q^{96} -7.79480e38 q^{97} +7.60205e38 q^{98} -2.68946e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} + O(q^{10}) \) \( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} - 39868781226579858780q^{10} - \)\(53\!\cdots\!40\)\(q^{11} - \)\(11\!\cdots\!44\)\(q^{12} + \)\(54\!\cdots\!90\)\(q^{13} + \)\(31\!\cdots\!52\)\(q^{14} + \)\(62\!\cdots\!10\)\(q^{15} + \)\(12\!\cdots\!36\)\(q^{16} + \)\(72\!\cdots\!58\)\(q^{17} + \)\(72\!\cdots\!86\)\(q^{18} - \)\(10\!\cdots\!24\)\(q^{19} + \)\(30\!\cdots\!60\)\(q^{20} + \)\(18\!\cdots\!76\)\(q^{21} - \)\(10\!\cdots\!24\)\(q^{22} + \)\(41\!\cdots\!64\)\(q^{23} - \)\(51\!\cdots\!32\)\(q^{24} - \)\(11\!\cdots\!75\)\(q^{25} + \)\(92\!\cdots\!76\)\(q^{26} - \)\(47\!\cdots\!89\)\(q^{27} + \)\(64\!\cdots\!56\)\(q^{28} + \)\(72\!\cdots\!62\)\(q^{29} + \)\(46\!\cdots\!60\)\(q^{30} - \)\(38\!\cdots\!56\)\(q^{31} + \)\(37\!\cdots\!12\)\(q^{32} + \)\(61\!\cdots\!80\)\(q^{33} + \)\(37\!\cdots\!44\)\(q^{34} + \)\(27\!\cdots\!20\)\(q^{35} + \)\(12\!\cdots\!48\)\(q^{36} + \)\(29\!\cdots\!22\)\(q^{37} + \)\(74\!\cdots\!92\)\(q^{38} - \)\(63\!\cdots\!30\)\(q^{39} + \)\(15\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!26\)\(q^{41} - \)\(36\!\cdots\!84\)\(q^{42} - \)\(24\!\cdots\!28\)\(q^{43} - \)\(21\!\cdots\!12\)\(q^{44} - \)\(72\!\cdots\!70\)\(q^{45} - \)\(10\!\cdots\!56\)\(q^{46} - \)\(10\!\cdots\!04\)\(q^{47} - \)\(13\!\cdots\!12\)\(q^{48} + \)\(92\!\cdots\!43\)\(q^{49} - \)\(11\!\cdots\!50\)\(q^{50} - \)\(84\!\cdots\!86\)\(q^{51} + \)\(59\!\cdots\!88\)\(q^{52} + \)\(62\!\cdots\!34\)\(q^{53} - \)\(83\!\cdots\!62\)\(q^{54} + \)\(72\!\cdots\!40\)\(q^{55} + \)\(36\!\cdots\!00\)\(q^{56} + \)\(12\!\cdots\!08\)\(q^{57} + \)\(28\!\cdots\!84\)\(q^{58} - \)\(75\!\cdots\!56\)\(q^{59} - \)\(35\!\cdots\!20\)\(q^{60} - \)\(71\!\cdots\!98\)\(q^{61} - \)\(33\!\cdots\!16\)\(q^{62} - \)\(21\!\cdots\!92\)\(q^{63} - \)\(35\!\cdots\!56\)\(q^{64} - \)\(71\!\cdots\!60\)\(q^{65} + \)\(11\!\cdots\!08\)\(q^{66} - \)\(51\!\cdots\!72\)\(q^{67} + \)\(11\!\cdots\!92\)\(q^{68} - \)\(48\!\cdots\!88\)\(q^{69} + \)\(38\!\cdots\!20\)\(q^{70} + \)\(84\!\cdots\!76\)\(q^{71} + \)\(60\!\cdots\!44\)\(q^{72} + \)\(63\!\cdots\!14\)\(q^{73} + \)\(89\!\cdots\!12\)\(q^{74} + \)\(13\!\cdots\!25\)\(q^{75} + \)\(12\!\cdots\!36\)\(q^{76} - \)\(22\!\cdots\!36\)\(q^{77} - \)\(10\!\cdots\!92\)\(q^{78} - \)\(16\!\cdots\!00\)\(q^{79} - \)\(18\!\cdots\!80\)\(q^{80} + \)\(54\!\cdots\!63\)\(q^{81} - \)\(48\!\cdots\!36\)\(q^{82} + \)\(59\!\cdots\!48\)\(q^{83} - \)\(74\!\cdots\!52\)\(q^{84} - \)\(52\!\cdots\!80\)\(q^{85} + \)\(85\!\cdots\!00\)\(q^{86} - \)\(84\!\cdots\!54\)\(q^{87} - \)\(10\!\cdots\!64\)\(q^{88} + \)\(18\!\cdots\!86\)\(q^{89} - \)\(53\!\cdots\!20\)\(q^{90} + \)\(23\!\cdots\!24\)\(q^{91} + \)\(96\!\cdots\!32\)\(q^{92} + \)\(44\!\cdots\!52\)\(q^{93} - \)\(12\!\cdots\!20\)\(q^{94} + \)\(84\!\cdots\!00\)\(q^{95} - \)\(44\!\cdots\!04\)\(q^{96} - \)\(99\!\cdots\!42\)\(q^{97} + \)\(19\!\cdots\!10\)\(q^{98} - \)\(71\!\cdots\!60\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.25290e6 1.68979 0.844894 0.534933i \(-0.179663\pi\)
0.844894 + 0.534933i \(0.179663\pi\)
\(3\) −1.16226e9 −0.577350
\(4\) 1.02001e12 1.85539
\(5\) −6.13018e12 −0.143734 −0.0718668 0.997414i \(-0.522896\pi\)
−0.0718668 + 0.997414i \(0.522896\pi\)
\(6\) −1.45620e15 −0.975600
\(7\) 3.89397e16 1.29116 0.645581 0.763692i \(-0.276615\pi\)
0.645581 + 0.763692i \(0.276615\pi\)
\(8\) 5.89182e17 1.44542
\(9\) 1.35085e18 0.333333
\(10\) −7.68052e18 −0.242879
\(11\) −1.99093e20 −0.981521 −0.490760 0.871295i \(-0.663281\pi\)
−0.490760 + 0.871295i \(0.663281\pi\)
\(12\) −1.18552e21 −1.07121
\(13\) 6.42008e21 1.21799 0.608997 0.793173i \(-0.291572\pi\)
0.608997 + 0.793173i \(0.291572\pi\)
\(14\) 4.87876e22 2.18179
\(15\) 7.12487e21 0.0829846
\(16\) 1.77432e23 0.587072
\(17\) 1.81467e24 1.84096 0.920480 0.390789i \(-0.127798\pi\)
0.920480 + 0.390789i \(0.127798\pi\)
\(18\) 1.69249e24 0.563263
\(19\) 6.82963e24 0.791957 0.395979 0.918260i \(-0.370405\pi\)
0.395979 + 0.918260i \(0.370405\pi\)
\(20\) −6.25284e24 −0.266681
\(21\) −4.52581e25 −0.745453
\(22\) −2.49445e26 −1.65856
\(23\) 4.57450e26 1.27835 0.639177 0.769060i \(-0.279275\pi\)
0.639177 + 0.769060i \(0.279275\pi\)
\(24\) −6.84783e26 −0.834515
\(25\) −1.78141e27 −0.979341
\(26\) 8.04374e27 2.05815
\(27\) −1.57004e27 −0.192450
\(28\) 3.97188e28 2.39560
\(29\) 3.57753e28 1.08848 0.544242 0.838928i \(-0.316817\pi\)
0.544242 + 0.838928i \(0.316817\pi\)
\(30\) 8.92677e27 0.140226
\(31\) −1.66982e29 −1.38394 −0.691969 0.721927i \(-0.743257\pi\)
−0.691969 + 0.721927i \(0.743257\pi\)
\(32\) −1.01602e29 −0.453395
\(33\) 2.31399e29 0.566681
\(34\) 2.27361e30 3.11083
\(35\) −2.38707e29 −0.185583
\(36\) 1.37788e30 0.618462
\(37\) 2.76171e30 0.726515 0.363257 0.931689i \(-0.381665\pi\)
0.363257 + 0.931689i \(0.381665\pi\)
\(38\) 8.55686e30 1.33824
\(39\) −7.46181e30 −0.703209
\(40\) −3.61179e30 −0.207756
\(41\) −5.74055e30 −0.204018 −0.102009 0.994783i \(-0.532527\pi\)
−0.102009 + 0.994783i \(0.532527\pi\)
\(42\) −5.67040e31 −1.25966
\(43\) −3.87508e31 −0.544059 −0.272029 0.962289i \(-0.587695\pi\)
−0.272029 + 0.962289i \(0.587695\pi\)
\(44\) −2.03077e32 −1.82110
\(45\) −8.28096e30 −0.0479112
\(46\) 5.73141e32 2.16015
\(47\) −2.60656e32 −0.645892 −0.322946 0.946417i \(-0.604673\pi\)
−0.322946 + 0.946417i \(0.604673\pi\)
\(48\) −2.06222e32 −0.338946
\(49\) 6.06755e32 0.667098
\(50\) −2.23193e33 −1.65488
\(51\) −2.10912e33 −1.06288
\(52\) 6.54854e33 2.25985
\(53\) −1.46778e32 −0.0349367 −0.0174684 0.999847i \(-0.505561\pi\)
−0.0174684 + 0.999847i \(0.505561\pi\)
\(54\) −1.96711e33 −0.325200
\(55\) 1.22048e33 0.141077
\(56\) 2.29426e34 1.86627
\(57\) −7.93781e33 −0.457237
\(58\) 4.48230e34 1.83931
\(59\) −1.10436e33 −0.0324709 −0.0162355 0.999868i \(-0.505168\pi\)
−0.0162355 + 0.999868i \(0.505168\pi\)
\(60\) 7.26744e33 0.153968
\(61\) −9.76740e34 −1.49916 −0.749578 0.661916i \(-0.769744\pi\)
−0.749578 + 0.661916i \(0.769744\pi\)
\(62\) −2.09212e35 −2.33856
\(63\) 5.26017e34 0.430387
\(64\) −2.24841e35 −1.35321
\(65\) −3.93563e34 −0.175067
\(66\) 2.89920e35 0.957572
\(67\) −4.32024e35 −1.06426 −0.532131 0.846662i \(-0.678609\pi\)
−0.532131 + 0.846662i \(0.678609\pi\)
\(68\) 1.85098e36 3.41569
\(69\) −5.31677e35 −0.738058
\(70\) −2.99077e35 −0.313596
\(71\) −8.50906e35 −0.676618 −0.338309 0.941035i \(-0.609855\pi\)
−0.338309 + 0.941035i \(0.609855\pi\)
\(72\) 7.95897e35 0.481807
\(73\) −2.18530e36 −1.01091 −0.505457 0.862852i \(-0.668676\pi\)
−0.505457 + 0.862852i \(0.668676\pi\)
\(74\) 3.46015e36 1.22766
\(75\) 2.07046e36 0.565423
\(76\) 6.96628e36 1.46939
\(77\) −7.75263e36 −1.26730
\(78\) −9.34893e36 −1.18827
\(79\) 1.19375e37 1.18354 0.591771 0.806106i \(-0.298429\pi\)
0.591771 + 0.806106i \(0.298429\pi\)
\(80\) −1.08769e36 −0.0843819
\(81\) 1.82480e36 0.111111
\(82\) −7.19236e36 −0.344747
\(83\) 1.67750e37 0.634804 0.317402 0.948291i \(-0.397189\pi\)
0.317402 + 0.948291i \(0.397189\pi\)
\(84\) −4.61637e37 −1.38310
\(85\) −1.11243e37 −0.264608
\(86\) −4.85510e37 −0.919344
\(87\) −4.15802e37 −0.628437
\(88\) −1.17302e38 −1.41871
\(89\) 1.45669e38 1.41339 0.706696 0.707517i \(-0.250185\pi\)
0.706696 + 0.707517i \(0.250185\pi\)
\(90\) −1.03752e37 −0.0809598
\(91\) 2.49996e38 1.57263
\(92\) 4.66603e38 2.37184
\(93\) 1.94077e38 0.799017
\(94\) −3.26577e38 −1.09142
\(95\) −4.18668e37 −0.113831
\(96\) 1.18088e38 0.261768
\(97\) −7.79480e38 −1.41175 −0.705873 0.708339i \(-0.749445\pi\)
−0.705873 + 0.708339i \(0.749445\pi\)
\(98\) 7.60205e38 1.12726
\(99\) −2.68946e38 −0.327174
\(100\) −1.81706e39 −1.81706
\(101\) 1.03169e39 0.849736 0.424868 0.905255i \(-0.360320\pi\)
0.424868 + 0.905255i \(0.360320\pi\)
\(102\) −2.64253e39 −1.79604
\(103\) −3.94619e38 −0.221744 −0.110872 0.993835i \(-0.535364\pi\)
−0.110872 + 0.993835i \(0.535364\pi\)
\(104\) 3.78260e39 1.76052
\(105\) 2.77440e38 0.107147
\(106\) −1.83899e38 −0.0590357
\(107\) −2.82181e39 −0.754299 −0.377150 0.926152i \(-0.623096\pi\)
−0.377150 + 0.926152i \(0.623096\pi\)
\(108\) −1.60146e39 −0.357069
\(109\) 6.95509e39 1.29565 0.647823 0.761791i \(-0.275680\pi\)
0.647823 + 0.761791i \(0.275680\pi\)
\(110\) 1.52914e39 0.238391
\(111\) −3.20983e39 −0.419453
\(112\) 6.90913e39 0.758005
\(113\) −1.58601e40 −1.46311 −0.731553 0.681785i \(-0.761204\pi\)
−0.731553 + 0.681785i \(0.761204\pi\)
\(114\) −9.94531e39 −0.772633
\(115\) −2.80425e39 −0.183742
\(116\) 3.64911e40 2.01956
\(117\) 8.67258e39 0.405998
\(118\) −1.38365e39 −0.0548690
\(119\) 7.06628e40 2.37698
\(120\) 4.19785e39 0.119948
\(121\) −1.50661e39 −0.0366173
\(122\) −1.22376e41 −2.53326
\(123\) 6.67203e39 0.117790
\(124\) −1.70323e41 −2.56774
\(125\) 2.20711e40 0.284498
\(126\) 6.59049e40 0.727263
\(127\) 5.67292e40 0.536580 0.268290 0.963338i \(-0.413542\pi\)
0.268290 + 0.963338i \(0.413542\pi\)
\(128\) −2.25848e41 −1.83325
\(129\) 4.50386e40 0.314112
\(130\) −4.93096e40 −0.295826
\(131\) 1.58294e41 0.817853 0.408927 0.912567i \(-0.365903\pi\)
0.408927 + 0.912567i \(0.365903\pi\)
\(132\) 2.36029e41 1.05141
\(133\) 2.65943e41 1.02254
\(134\) −5.41284e41 −1.79838
\(135\) 9.62465e39 0.0276615
\(136\) 1.06917e42 2.66097
\(137\) 4.61937e41 0.996625 0.498312 0.866998i \(-0.333953\pi\)
0.498312 + 0.866998i \(0.333953\pi\)
\(138\) −6.66139e41 −1.24716
\(139\) 3.58776e41 0.583493 0.291746 0.956496i \(-0.405764\pi\)
0.291746 + 0.956496i \(0.405764\pi\)
\(140\) −2.43484e41 −0.344329
\(141\) 3.02951e41 0.372906
\(142\) −1.06610e42 −1.14334
\(143\) −1.27820e42 −1.19549
\(144\) 2.39684e41 0.195691
\(145\) −2.19309e41 −0.156452
\(146\) −2.73796e42 −1.70823
\(147\) −7.05208e41 −0.385149
\(148\) 2.81697e42 1.34797
\(149\) 6.71861e41 0.281934 0.140967 0.990014i \(-0.454979\pi\)
0.140967 + 0.990014i \(0.454979\pi\)
\(150\) 2.59409e42 0.955445
\(151\) −4.55554e41 −0.147397 −0.0736987 0.997281i \(-0.523480\pi\)
−0.0736987 + 0.997281i \(0.523480\pi\)
\(152\) 4.02389e42 1.14471
\(153\) 2.45135e42 0.613654
\(154\) −9.71329e42 −2.14147
\(155\) 1.02363e42 0.198918
\(156\) −7.61112e42 −1.30472
\(157\) −9.69606e42 −1.46741 −0.733706 0.679467i \(-0.762211\pi\)
−0.733706 + 0.679467i \(0.762211\pi\)
\(158\) 1.49565e43 1.99994
\(159\) 1.70595e41 0.0201707
\(160\) 6.22837e41 0.0651680
\(161\) 1.78130e43 1.65056
\(162\) 2.28630e42 0.187754
\(163\) 8.90560e42 0.648642 0.324321 0.945947i \(-0.394864\pi\)
0.324321 + 0.945947i \(0.394864\pi\)
\(164\) −5.85542e42 −0.378532
\(165\) −1.41851e42 −0.0814511
\(166\) 2.10174e43 1.07269
\(167\) −1.38680e43 −0.629569 −0.314785 0.949163i \(-0.601932\pi\)
−0.314785 + 0.949163i \(0.601932\pi\)
\(168\) −2.66652e43 −1.07749
\(169\) 1.34337e43 0.483509
\(170\) −1.39376e43 −0.447131
\(171\) 9.22581e42 0.263986
\(172\) −3.95262e43 −1.00944
\(173\) −3.87491e42 −0.0883817 −0.0441909 0.999023i \(-0.514071\pi\)
−0.0441909 + 0.999023i \(0.514071\pi\)
\(174\) −5.20960e43 −1.06193
\(175\) −6.93675e43 −1.26449
\(176\) −3.53254e43 −0.576223
\(177\) 1.28355e42 0.0187471
\(178\) 1.82509e44 2.38833
\(179\) −2.64747e43 −0.310597 −0.155299 0.987868i \(-0.549634\pi\)
−0.155299 + 0.987868i \(0.549634\pi\)
\(180\) −8.44666e42 −0.0888937
\(181\) −1.66841e44 −1.57605 −0.788025 0.615643i \(-0.788896\pi\)
−0.788025 + 0.615643i \(0.788896\pi\)
\(182\) 3.13221e44 2.65741
\(183\) 1.13523e44 0.865539
\(184\) 2.69521e44 1.84776
\(185\) −1.69298e43 −0.104425
\(186\) 2.43159e44 1.35017
\(187\) −3.61289e44 −1.80694
\(188\) −2.65872e44 −1.19838
\(189\) −6.11370e43 −0.248484
\(190\) −5.24551e43 −0.192350
\(191\) −3.09936e44 −1.02594 −0.512969 0.858407i \(-0.671455\pi\)
−0.512969 + 0.858407i \(0.671455\pi\)
\(192\) 2.61324e44 0.781278
\(193\) 1.50940e44 0.407789 0.203895 0.978993i \(-0.434640\pi\)
0.203895 + 0.978993i \(0.434640\pi\)
\(194\) −9.76613e44 −2.38555
\(195\) 4.57423e43 0.101075
\(196\) 6.18896e44 1.23773
\(197\) 9.79373e44 1.77360 0.886802 0.462150i \(-0.152922\pi\)
0.886802 + 0.462150i \(0.152922\pi\)
\(198\) −3.36963e44 −0.552854
\(199\) −1.07033e45 −1.59177 −0.795887 0.605445i \(-0.792995\pi\)
−0.795887 + 0.605445i \(0.792995\pi\)
\(200\) −1.04957e45 −1.41556
\(201\) 5.02124e44 0.614452
\(202\) 1.29261e45 1.43587
\(203\) 1.39308e45 1.40541
\(204\) −2.15133e45 −1.97205
\(205\) 3.51906e43 0.0293242
\(206\) −4.94419e44 −0.374700
\(207\) 6.17947e44 0.426118
\(208\) 1.13913e45 0.715050
\(209\) −1.35973e45 −0.777322
\(210\) 3.47606e44 0.181055
\(211\) 3.42808e45 1.62758 0.813791 0.581158i \(-0.197400\pi\)
0.813791 + 0.581158i \(0.197400\pi\)
\(212\) −1.49715e44 −0.0648211
\(213\) 9.88975e44 0.390646
\(214\) −3.53545e45 −1.27461
\(215\) 2.37549e44 0.0781995
\(216\) −9.25041e44 −0.278172
\(217\) −6.50223e45 −1.78689
\(218\) 8.71405e45 2.18937
\(219\) 2.53989e45 0.583652
\(220\) 1.24490e45 0.261753
\(221\) 1.16503e46 2.24228
\(222\) −4.02160e45 −0.708788
\(223\) −3.19344e45 −0.515601 −0.257800 0.966198i \(-0.582998\pi\)
−0.257800 + 0.966198i \(0.582998\pi\)
\(224\) −3.95634e45 −0.585406
\(225\) −2.40642e45 −0.326447
\(226\) −1.98711e46 −2.47234
\(227\) −7.46827e45 −0.852542 −0.426271 0.904595i \(-0.640173\pi\)
−0.426271 + 0.904595i \(0.640173\pi\)
\(228\) −8.09664e45 −0.848351
\(229\) −7.57162e45 −0.728445 −0.364223 0.931312i \(-0.618665\pi\)
−0.364223 + 0.931312i \(0.618665\pi\)
\(230\) −3.51345e45 −0.310486
\(231\) 9.01059e45 0.731677
\(232\) 2.10782e46 1.57332
\(233\) 6.11844e45 0.419952 0.209976 0.977707i \(-0.432661\pi\)
0.209976 + 0.977707i \(0.432661\pi\)
\(234\) 1.08659e46 0.686051
\(235\) 1.59787e45 0.0928364
\(236\) −1.12645e45 −0.0602461
\(237\) −1.38745e46 −0.683318
\(238\) 8.85336e46 4.01659
\(239\) −1.52722e46 −0.638474 −0.319237 0.947675i \(-0.603427\pi\)
−0.319237 + 0.947675i \(0.603427\pi\)
\(240\) 1.26418e45 0.0487179
\(241\) 2.09227e46 0.743507 0.371753 0.928332i \(-0.378757\pi\)
0.371753 + 0.928332i \(0.378757\pi\)
\(242\) −1.88764e45 −0.0618755
\(243\) −2.12090e45 −0.0641500
\(244\) −9.96284e46 −2.78151
\(245\) −3.71952e45 −0.0958844
\(246\) 8.35940e45 0.199040
\(247\) 4.38468e46 0.964599
\(248\) −9.83828e46 −2.00038
\(249\) −1.94969e46 −0.366504
\(250\) 2.76529e46 0.480741
\(251\) 1.03940e45 0.0167165 0.00835827 0.999965i \(-0.497339\pi\)
0.00835827 + 0.999965i \(0.497339\pi\)
\(252\) 5.36543e46 0.798534
\(253\) −9.10753e46 −1.25473
\(254\) 7.10762e46 0.906706
\(255\) 1.29293e46 0.152771
\(256\) −1.59358e47 −1.74459
\(257\) −8.33305e45 −0.0845489 −0.0422744 0.999106i \(-0.513460\pi\)
−0.0422744 + 0.999106i \(0.513460\pi\)
\(258\) 5.64289e46 0.530784
\(259\) 1.07540e47 0.938048
\(260\) −4.01437e46 −0.324816
\(261\) 4.83271e46 0.362828
\(262\) 1.98328e47 1.38200
\(263\) −2.12024e47 −1.37166 −0.685831 0.727760i \(-0.740561\pi\)
−0.685831 + 0.727760i \(0.740561\pi\)
\(264\) 1.36336e47 0.819093
\(265\) 8.99777e44 0.00502158
\(266\) 3.33201e47 1.72788
\(267\) −1.69306e47 −0.816022
\(268\) −4.40668e47 −1.97462
\(269\) −1.17005e47 −0.487569 −0.243784 0.969829i \(-0.578389\pi\)
−0.243784 + 0.969829i \(0.578389\pi\)
\(270\) 1.20587e46 0.0467422
\(271\) −1.82868e45 −0.00659534 −0.00329767 0.999995i \(-0.501050\pi\)
−0.00329767 + 0.999995i \(0.501050\pi\)
\(272\) 3.21980e47 1.08078
\(273\) −2.90561e47 −0.907957
\(274\) 5.78762e47 1.68409
\(275\) 3.54667e47 0.961243
\(276\) −5.42315e47 −1.36938
\(277\) 5.34689e47 1.25819 0.629094 0.777329i \(-0.283426\pi\)
0.629094 + 0.777329i \(0.283426\pi\)
\(278\) 4.49512e47 0.985979
\(279\) −2.25568e47 −0.461313
\(280\) −1.40642e47 −0.268246
\(281\) −4.55514e47 −0.810455 −0.405227 0.914216i \(-0.632808\pi\)
−0.405227 + 0.914216i \(0.632808\pi\)
\(282\) 3.79568e47 0.630133
\(283\) −7.69321e47 −1.19199 −0.595995 0.802989i \(-0.703242\pi\)
−0.595995 + 0.802989i \(0.703242\pi\)
\(284\) −8.67932e47 −1.25539
\(285\) 4.86602e46 0.0657203
\(286\) −1.60145e48 −2.02012
\(287\) −2.23535e47 −0.263420
\(288\) −1.37249e47 −0.151132
\(289\) 2.32139e48 2.38914
\(290\) −2.74773e47 −0.264370
\(291\) 9.05960e47 0.815072
\(292\) −2.22902e48 −1.87564
\(293\) 1.12648e48 0.886761 0.443380 0.896334i \(-0.353779\pi\)
0.443380 + 0.896334i \(0.353779\pi\)
\(294\) −8.83557e47 −0.650821
\(295\) 6.76990e45 0.00466716
\(296\) 1.62715e48 1.05012
\(297\) 3.12585e47 0.188894
\(298\) 8.41776e47 0.476409
\(299\) 2.93687e48 1.55703
\(300\) 2.11189e48 1.04908
\(301\) −1.50894e48 −0.702468
\(302\) −5.70765e47 −0.249070
\(303\) −1.19910e48 −0.490595
\(304\) 1.21179e48 0.464936
\(305\) 5.98759e47 0.215479
\(306\) 3.07131e48 1.03694
\(307\) 2.54926e48 0.807636 0.403818 0.914839i \(-0.367683\pi\)
0.403818 + 0.914839i \(0.367683\pi\)
\(308\) −7.90776e48 −2.35133
\(309\) 4.58650e47 0.128024
\(310\) 1.28251e48 0.336130
\(311\) −4.18456e48 −1.02996 −0.514982 0.857201i \(-0.672201\pi\)
−0.514982 + 0.857201i \(0.672201\pi\)
\(312\) −4.39637e48 −1.01643
\(313\) −4.76939e48 −1.03597 −0.517986 0.855389i \(-0.673318\pi\)
−0.517986 + 0.855389i \(0.673318\pi\)
\(314\) −1.21482e49 −2.47962
\(315\) −3.22458e47 −0.0618611
\(316\) 1.21763e49 2.19593
\(317\) −8.82882e47 −0.149709 −0.0748544 0.997194i \(-0.523849\pi\)
−0.0748544 + 0.997194i \(0.523849\pi\)
\(318\) 2.13738e47 0.0340843
\(319\) −7.12262e48 −1.06837
\(320\) 1.37832e48 0.194502
\(321\) 3.27968e48 0.435495
\(322\) 2.23179e49 2.78910
\(323\) 1.23935e49 1.45796
\(324\) 1.86131e48 0.206154
\(325\) −1.14368e49 −1.19283
\(326\) 1.11578e49 1.09607
\(327\) −8.08364e48 −0.748041
\(328\) −3.38223e48 −0.294892
\(329\) −1.01499e49 −0.833952
\(330\) −1.77726e48 −0.137635
\(331\) −1.56299e49 −1.14107 −0.570533 0.821275i \(-0.693263\pi\)
−0.570533 + 0.821275i \(0.693263\pi\)
\(332\) 1.71107e49 1.17781
\(333\) 3.73066e48 0.242172
\(334\) −1.73753e49 −1.06384
\(335\) 2.64838e48 0.152970
\(336\) −8.03021e48 −0.437634
\(337\) 6.12313e48 0.314913 0.157456 0.987526i \(-0.449671\pi\)
0.157456 + 0.987526i \(0.449671\pi\)
\(338\) 1.68311e49 0.817029
\(339\) 1.84336e49 0.844724
\(340\) −1.13469e49 −0.490950
\(341\) 3.32450e49 1.35836
\(342\) 1.15590e49 0.446080
\(343\) −1.17905e49 −0.429830
\(344\) −2.28313e49 −0.786395
\(345\) 3.25927e48 0.106084
\(346\) −4.85488e48 −0.149346
\(347\) 1.17564e49 0.341862 0.170931 0.985283i \(-0.445322\pi\)
0.170931 + 0.985283i \(0.445322\pi\)
\(348\) −4.24122e49 −1.16599
\(349\) 1.07382e48 0.0279149 0.0139575 0.999903i \(-0.495557\pi\)
0.0139575 + 0.999903i \(0.495557\pi\)
\(350\) −8.69108e49 −2.13672
\(351\) −1.00798e49 −0.234403
\(352\) 2.02282e49 0.445016
\(353\) −1.32350e49 −0.275497 −0.137748 0.990467i \(-0.543987\pi\)
−0.137748 + 0.990467i \(0.543987\pi\)
\(354\) 1.60816e48 0.0316786
\(355\) 5.21621e48 0.0972527
\(356\) 1.48584e50 2.62239
\(357\) −8.21287e49 −1.37235
\(358\) −3.31703e49 −0.524844
\(359\) 4.65898e49 0.698150 0.349075 0.937095i \(-0.386496\pi\)
0.349075 + 0.937095i \(0.386496\pi\)
\(360\) −4.87899e48 −0.0692519
\(361\) −2.77249e49 −0.372804
\(362\) −2.09035e50 −2.66319
\(363\) 1.75108e48 0.0211410
\(364\) 2.54998e50 2.91783
\(365\) 1.33963e49 0.145302
\(366\) 1.42233e50 1.46258
\(367\) 8.04653e49 0.784549 0.392275 0.919848i \(-0.371688\pi\)
0.392275 + 0.919848i \(0.371688\pi\)
\(368\) 8.11661e49 0.750485
\(369\) −7.75464e48 −0.0680060
\(370\) −2.12114e49 −0.176455
\(371\) −5.71549e48 −0.0451089
\(372\) 1.97960e50 1.48249
\(373\) 8.00164e49 0.568666 0.284333 0.958726i \(-0.408228\pi\)
0.284333 + 0.958726i \(0.408228\pi\)
\(374\) −4.52661e50 −3.05335
\(375\) −2.56524e49 −0.164255
\(376\) −1.53574e50 −0.933587
\(377\) 2.29680e50 1.32577
\(378\) −7.65987e49 −0.419886
\(379\) −2.21649e50 −1.15399 −0.576993 0.816749i \(-0.695774\pi\)
−0.576993 + 0.816749i \(0.695774\pi\)
\(380\) −4.27046e49 −0.211200
\(381\) −6.59342e49 −0.309794
\(382\) −3.88320e50 −1.73362
\(383\) −2.13842e50 −0.907231 −0.453615 0.891198i \(-0.649866\pi\)
−0.453615 + 0.891198i \(0.649866\pi\)
\(384\) 2.62494e50 1.05843
\(385\) 4.75250e49 0.182154
\(386\) 1.89113e50 0.689077
\(387\) −5.23466e49 −0.181353
\(388\) −7.95077e50 −2.61933
\(389\) 3.06653e50 0.960792 0.480396 0.877052i \(-0.340493\pi\)
0.480396 + 0.877052i \(0.340493\pi\)
\(390\) 5.73106e49 0.170795
\(391\) 8.30123e50 2.35340
\(392\) 3.57489e50 0.964239
\(393\) −1.83980e50 −0.472188
\(394\) 1.22706e51 2.99702
\(395\) −7.31788e49 −0.170115
\(396\) −2.74327e50 −0.607033
\(397\) 1.98105e50 0.417331 0.208665 0.977987i \(-0.433088\pi\)
0.208665 + 0.977987i \(0.433088\pi\)
\(398\) −1.34102e51 −2.68976
\(399\) −3.09096e50 −0.590366
\(400\) −3.16078e50 −0.574943
\(401\) 8.23828e50 1.42732 0.713660 0.700493i \(-0.247036\pi\)
0.713660 + 0.700493i \(0.247036\pi\)
\(402\) 6.29113e50 1.03829
\(403\) −1.07204e51 −1.68563
\(404\) 1.05234e51 1.57659
\(405\) −1.11864e49 −0.0159704
\(406\) 1.74539e51 2.37485
\(407\) −5.49838e50 −0.713089
\(408\) −1.24266e51 −1.53631
\(409\) −7.99567e50 −0.942432 −0.471216 0.882018i \(-0.656185\pi\)
−0.471216 + 0.882018i \(0.656185\pi\)
\(410\) 4.40904e49 0.0495518
\(411\) −5.36892e50 −0.575402
\(412\) −4.02515e50 −0.411421
\(413\) −4.30033e49 −0.0419252
\(414\) 7.74228e50 0.720049
\(415\) −1.02834e50 −0.0912427
\(416\) −6.52291e50 −0.552232
\(417\) −4.16992e50 −0.336880
\(418\) −1.70361e51 −1.31351
\(419\) 2.51157e51 1.84830 0.924148 0.382035i \(-0.124777\pi\)
0.924148 + 0.382035i \(0.124777\pi\)
\(420\) 2.82992e50 0.198798
\(421\) −1.87317e50 −0.125625 −0.0628125 0.998025i \(-0.520007\pi\)
−0.0628125 + 0.998025i \(0.520007\pi\)
\(422\) 4.29505e51 2.75027
\(423\) −3.52108e50 −0.215297
\(424\) −8.64790e49 −0.0504983
\(425\) −3.23268e51 −1.80293
\(426\) 1.23909e51 0.660109
\(427\) −3.80339e51 −1.93565
\(428\) −2.87827e51 −1.39952
\(429\) 1.48560e51 0.690214
\(430\) 2.97626e50 0.132141
\(431\) 1.82729e51 0.775356 0.387678 0.921795i \(-0.373277\pi\)
0.387678 + 0.921795i \(0.373277\pi\)
\(432\) −2.78575e50 −0.112982
\(433\) −3.64439e50 −0.141290 −0.0706449 0.997502i \(-0.522506\pi\)
−0.0706449 + 0.997502i \(0.522506\pi\)
\(434\) −8.14666e51 −3.01946
\(435\) 2.54894e50 0.0903275
\(436\) 7.09426e51 2.40392
\(437\) 3.12421e51 1.01240
\(438\) 3.18223e51 0.986249
\(439\) −1.31821e51 −0.390774 −0.195387 0.980726i \(-0.562596\pi\)
−0.195387 + 0.980726i \(0.562596\pi\)
\(440\) 7.19084e50 0.203916
\(441\) 8.19636e50 0.222366
\(442\) 1.45968e52 3.78898
\(443\) 1.78369e51 0.443045 0.221522 0.975155i \(-0.428897\pi\)
0.221522 + 0.975155i \(0.428897\pi\)
\(444\) −3.27405e51 −0.778248
\(445\) −8.92978e50 −0.203152
\(446\) −4.00107e51 −0.871256
\(447\) −7.80878e50 −0.162775
\(448\) −8.75524e51 −1.74722
\(449\) 9.49589e51 1.81439 0.907197 0.420705i \(-0.138217\pi\)
0.907197 + 0.420705i \(0.138217\pi\)
\(450\) −3.01501e51 −0.551626
\(451\) 1.14291e51 0.200248
\(452\) −1.61774e52 −2.71463
\(453\) 5.29473e50 0.0850999
\(454\) −9.35702e51 −1.44062
\(455\) −1.53252e51 −0.226039
\(456\) −4.67682e51 −0.660900
\(457\) 1.05375e52 1.42683 0.713416 0.700740i \(-0.247147\pi\)
0.713416 + 0.700740i \(0.247147\pi\)
\(458\) −9.48650e51 −1.23092
\(459\) −2.84912e51 −0.354293
\(460\) −2.86036e51 −0.340913
\(461\) 1.12098e51 0.128065 0.0640327 0.997948i \(-0.479604\pi\)
0.0640327 + 0.997948i \(0.479604\pi\)
\(462\) 1.12894e52 1.23638
\(463\) −9.96969e49 −0.0104677 −0.00523386 0.999986i \(-0.501666\pi\)
−0.00523386 + 0.999986i \(0.501666\pi\)
\(464\) 6.34767e51 0.639019
\(465\) −1.18973e51 −0.114846
\(466\) 7.66580e51 0.709631
\(467\) 5.53406e51 0.491320 0.245660 0.969356i \(-0.420995\pi\)
0.245660 + 0.969356i \(0.420995\pi\)
\(468\) 8.84611e51 0.753283
\(469\) −1.68229e52 −1.37414
\(470\) 2.00198e51 0.156874
\(471\) 1.12694e52 0.847210
\(472\) −6.50667e50 −0.0469342
\(473\) 7.71503e51 0.534005
\(474\) −1.73833e52 −1.15466
\(475\) −1.21664e52 −0.775596
\(476\) 7.20767e52 4.41021
\(477\) −1.98276e50 −0.0116456
\(478\) −1.91346e52 −1.07889
\(479\) −2.71951e52 −1.47214 −0.736069 0.676906i \(-0.763320\pi\)
−0.736069 + 0.676906i \(0.763320\pi\)
\(480\) −7.23899e50 −0.0376248
\(481\) 1.77304e52 0.884890
\(482\) 2.62141e52 1.25637
\(483\) −2.07033e52 −0.952952
\(484\) −1.53676e51 −0.0679392
\(485\) 4.77835e51 0.202915
\(486\) −2.65728e51 −0.108400
\(487\) −2.97071e52 −1.16425 −0.582125 0.813100i \(-0.697778\pi\)
−0.582125 + 0.813100i \(0.697778\pi\)
\(488\) −5.75477e52 −2.16691
\(489\) −1.03506e52 −0.374493
\(490\) −4.66019e51 −0.162024
\(491\) −4.43700e52 −1.48252 −0.741259 0.671219i \(-0.765771\pi\)
−0.741259 + 0.671219i \(0.765771\pi\)
\(492\) 6.80553e51 0.218546
\(493\) 6.49205e52 2.00386
\(494\) 5.49357e52 1.62997
\(495\) 1.64869e51 0.0470258
\(496\) −2.96279e52 −0.812471
\(497\) −3.31340e52 −0.873624
\(498\) −2.44278e52 −0.619315
\(499\) 7.68649e52 1.87399 0.936995 0.349342i \(-0.113595\pi\)
0.936995 + 0.349342i \(0.113595\pi\)
\(500\) 2.25127e52 0.527853
\(501\) 1.61183e52 0.363482
\(502\) 1.30227e51 0.0282474
\(503\) −3.79074e52 −0.790948 −0.395474 0.918477i \(-0.629420\pi\)
−0.395474 + 0.918477i \(0.629420\pi\)
\(504\) 3.09920e52 0.622091
\(505\) −6.32447e51 −0.122136
\(506\) −1.14108e53 −2.12023
\(507\) −1.56135e52 −0.279154
\(508\) 5.78643e52 0.995563
\(509\) 7.11720e52 1.17845 0.589227 0.807967i \(-0.299432\pi\)
0.589227 + 0.807967i \(0.299432\pi\)
\(510\) 1.61992e52 0.258151
\(511\) −8.50947e52 −1.30525
\(512\) −7.54985e52 −1.11474
\(513\) −1.07228e52 −0.152412
\(514\) −1.04405e52 −0.142870
\(515\) 2.41908e51 0.0318720
\(516\) 4.59398e52 0.582800
\(517\) 5.18950e52 0.633957
\(518\) 1.34737e53 1.58510
\(519\) 4.50366e51 0.0510272
\(520\) −2.31880e52 −0.253045
\(521\) 1.00561e53 1.05705 0.528526 0.848917i \(-0.322745\pi\)
0.528526 + 0.848917i \(0.322745\pi\)
\(522\) 6.05492e52 0.613103
\(523\) −1.33906e52 −0.130622 −0.0653111 0.997865i \(-0.520804\pi\)
−0.0653111 + 0.997865i \(0.520804\pi\)
\(524\) 1.61462e53 1.51743
\(525\) 8.06232e52 0.730052
\(526\) −2.65645e53 −2.31782
\(527\) −3.03018e53 −2.54778
\(528\) 4.10574e52 0.332683
\(529\) 8.12089e52 0.634188
\(530\) 1.12733e51 0.00848540
\(531\) −1.49182e51 −0.0108236
\(532\) 2.71265e53 1.89722
\(533\) −3.68548e52 −0.248493
\(534\) −2.12124e53 −1.37891
\(535\) 1.72982e52 0.108418
\(536\) −2.54541e53 −1.53831
\(537\) 3.07706e52 0.179323
\(538\) −1.46596e53 −0.823888
\(539\) −1.20801e53 −0.654771
\(540\) 9.81723e51 0.0513228
\(541\) −5.34936e52 −0.269746 −0.134873 0.990863i \(-0.543063\pi\)
−0.134873 + 0.990863i \(0.543063\pi\)
\(542\) −2.29116e51 −0.0111447
\(543\) 1.93913e53 0.909933
\(544\) −1.84374e53 −0.834682
\(545\) −4.26360e52 −0.186228
\(546\) −3.64044e53 −1.53425
\(547\) −1.38545e53 −0.563426 −0.281713 0.959499i \(-0.590903\pi\)
−0.281713 + 0.959499i \(0.590903\pi\)
\(548\) 4.71180e53 1.84912
\(549\) −1.31943e53 −0.499719
\(550\) 4.44363e53 1.62430
\(551\) 2.44332e53 0.862033
\(552\) −3.13254e53 −1.06681
\(553\) 4.64841e53 1.52814
\(554\) 6.69913e53 2.12607
\(555\) 1.96768e52 0.0602895
\(556\) 3.65955e53 1.08260
\(557\) 9.47357e52 0.270606 0.135303 0.990804i \(-0.456799\pi\)
0.135303 + 0.990804i \(0.456799\pi\)
\(558\) −2.82615e53 −0.779521
\(559\) −2.48783e53 −0.662660
\(560\) −4.23542e52 −0.108951
\(561\) 4.19913e53 1.04324
\(562\) −5.70715e53 −1.36950
\(563\) 5.73948e53 1.33033 0.665164 0.746697i \(-0.268362\pi\)
0.665164 + 0.746697i \(0.268362\pi\)
\(564\) 3.09013e53 0.691885
\(565\) 9.72251e52 0.210297
\(566\) −9.63885e53 −2.01421
\(567\) 7.10571e52 0.143462
\(568\) −5.01338e53 −0.977999
\(569\) −1.87196e53 −0.352864 −0.176432 0.984313i \(-0.556456\pi\)
−0.176432 + 0.984313i \(0.556456\pi\)
\(570\) 6.09665e52 0.111053
\(571\) −1.04919e54 −1.84693 −0.923464 0.383684i \(-0.874655\pi\)
−0.923464 + 0.383684i \(0.874655\pi\)
\(572\) −1.30377e54 −2.21809
\(573\) 3.60227e53 0.592326
\(574\) −2.80068e53 −0.445125
\(575\) −8.14906e53 −1.25194
\(576\) −3.03727e53 −0.451071
\(577\) 7.23103e53 1.03818 0.519089 0.854720i \(-0.326271\pi\)
0.519089 + 0.854720i \(0.326271\pi\)
\(578\) 2.90848e54 4.03714
\(579\) −1.75431e53 −0.235437
\(580\) −2.23697e53 −0.290278
\(581\) 6.53213e53 0.819635
\(582\) 1.13508e54 1.37730
\(583\) 2.92226e52 0.0342911
\(584\) −1.28754e54 −1.46120
\(585\) −5.31645e52 −0.0583555
\(586\) 1.41137e54 1.49844
\(587\) −1.03179e54 −1.05961 −0.529805 0.848119i \(-0.677735\pi\)
−0.529805 + 0.848119i \(0.677735\pi\)
\(588\) −7.19319e53 −0.714601
\(589\) −1.14043e54 −1.09602
\(590\) 8.48203e51 0.00788652
\(591\) −1.13829e54 −1.02399
\(592\) 4.90014e53 0.426516
\(593\) −3.55072e53 −0.299054 −0.149527 0.988758i \(-0.547775\pi\)
−0.149527 + 0.988758i \(0.547775\pi\)
\(594\) 3.91639e53 0.319191
\(595\) −4.33176e53 −0.341651
\(596\) 6.85304e53 0.523096
\(597\) 1.24400e54 0.919011
\(598\) 3.67961e54 2.63105
\(599\) −1.31877e54 −0.912741 −0.456370 0.889790i \(-0.650851\pi\)
−0.456370 + 0.889790i \(0.650851\pi\)
\(600\) 1.21988e54 0.817274
\(601\) 4.82020e53 0.312617 0.156309 0.987708i \(-0.450041\pi\)
0.156309 + 0.987708i \(0.450041\pi\)
\(602\) −1.89056e54 −1.18702
\(603\) −5.83600e53 −0.354754
\(604\) −4.64670e53 −0.273479
\(605\) 9.23579e51 0.00526313
\(606\) −1.50235e54 −0.829003
\(607\) 2.72766e54 1.45751 0.728754 0.684776i \(-0.240100\pi\)
0.728754 + 0.684776i \(0.240100\pi\)
\(608\) −6.93902e53 −0.359069
\(609\) −1.61912e54 −0.811414
\(610\) 7.50187e53 0.364114
\(611\) −1.67344e54 −0.786693
\(612\) 2.50040e54 1.13856
\(613\) 9.32585e52 0.0411348 0.0205674 0.999788i \(-0.493453\pi\)
0.0205674 + 0.999788i \(0.493453\pi\)
\(614\) 3.19397e54 1.36473
\(615\) −4.09007e52 −0.0169304
\(616\) −4.56771e54 −1.83179
\(617\) 5.49542e52 0.0213521 0.0106760 0.999943i \(-0.496602\pi\)
0.0106760 + 0.999943i \(0.496602\pi\)
\(618\) 5.74644e53 0.216333
\(619\) −2.05418e53 −0.0749325 −0.0374663 0.999298i \(-0.511929\pi\)
−0.0374663 + 0.999298i \(0.511929\pi\)
\(620\) 1.04411e54 0.369070
\(621\) −7.18216e53 −0.246019
\(622\) −5.24284e54 −1.74042
\(623\) 5.67231e54 1.82492
\(624\) −1.32396e54 −0.412834
\(625\) 3.10507e54 0.938449
\(626\) −5.97558e54 −1.75057
\(627\) 1.58037e54 0.448787
\(628\) −9.89007e54 −2.72261
\(629\) 5.01160e54 1.33748
\(630\) −4.04009e53 −0.104532
\(631\) −4.63715e54 −1.16327 −0.581633 0.813451i \(-0.697586\pi\)
−0.581633 + 0.813451i \(0.697586\pi\)
\(632\) 7.03334e54 1.71072
\(633\) −3.98432e54 −0.939685
\(634\) −1.10617e54 −0.252976
\(635\) −3.47760e53 −0.0771245
\(636\) 1.74008e53 0.0374245
\(637\) 3.89542e54 0.812522
\(638\) −8.92395e54 −1.80532
\(639\) −1.14945e54 −0.225539
\(640\) 1.38449e54 0.263499
\(641\) 8.56815e54 1.58181 0.790907 0.611937i \(-0.209609\pi\)
0.790907 + 0.611937i \(0.209609\pi\)
\(642\) 4.10912e54 0.735894
\(643\) 4.49793e54 0.781445 0.390723 0.920508i \(-0.372225\pi\)
0.390723 + 0.920508i \(0.372225\pi\)
\(644\) 1.81694e55 3.06243
\(645\) −2.76094e53 −0.0451485
\(646\) 1.55279e55 2.46365
\(647\) −1.10066e55 −1.69441 −0.847204 0.531267i \(-0.821716\pi\)
−0.847204 + 0.531267i \(0.821716\pi\)
\(648\) 1.07514e54 0.160602
\(649\) 2.19870e53 0.0318709
\(650\) −1.43292e55 −2.01563
\(651\) 7.55729e54 1.03166
\(652\) 9.08379e54 1.20348
\(653\) −5.67385e54 −0.729576 −0.364788 0.931091i \(-0.618859\pi\)
−0.364788 + 0.931091i \(0.618859\pi\)
\(654\) −1.01280e55 −1.26403
\(655\) −9.70373e53 −0.117553
\(656\) −1.01856e54 −0.119773
\(657\) −2.95201e54 −0.336972
\(658\) −1.27168e55 −1.40920
\(659\) 1.13716e55 1.22336 0.611680 0.791105i \(-0.290494\pi\)
0.611680 + 0.791105i \(0.290494\pi\)
\(660\) −1.44690e54 −0.151123
\(661\) −1.72872e55 −1.75306 −0.876530 0.481346i \(-0.840148\pi\)
−0.876530 + 0.481346i \(0.840148\pi\)
\(662\) −1.95828e55 −1.92816
\(663\) −1.35408e55 −1.29458
\(664\) 9.88353e54 0.917560
\(665\) −1.63028e54 −0.146974
\(666\) 4.67415e54 0.409219
\(667\) 1.63654e55 1.39147
\(668\) −1.41455e55 −1.16809
\(669\) 3.71161e54 0.297682
\(670\) 3.31817e54 0.258487
\(671\) 1.94462e55 1.47145
\(672\) 4.59830e54 0.337984
\(673\) −2.52767e55 −1.80479 −0.902396 0.430907i \(-0.858194\pi\)
−0.902396 + 0.430907i \(0.858194\pi\)
\(674\) 7.67169e54 0.532136
\(675\) 2.79689e54 0.188474
\(676\) 1.37025e55 0.897096
\(677\) −1.64497e55 −1.04635 −0.523177 0.852224i \(-0.675253\pi\)
−0.523177 + 0.852224i \(0.675253\pi\)
\(678\) 2.30955e55 1.42741
\(679\) −3.03527e55 −1.82279
\(680\) −6.55422e54 −0.382470
\(681\) 8.68008e54 0.492215
\(682\) 4.16528e55 2.29535
\(683\) 1.66325e55 0.890747 0.445373 0.895345i \(-0.353071\pi\)
0.445373 + 0.895345i \(0.353071\pi\)
\(684\) 9.41041e54 0.489795
\(685\) −2.83176e54 −0.143248
\(686\) −1.47723e55 −0.726322
\(687\) 8.80020e54 0.420568
\(688\) −6.87562e54 −0.319402
\(689\) −9.42328e53 −0.0425527
\(690\) 4.08355e54 0.179259
\(691\) 3.64610e54 0.155599 0.0777996 0.996969i \(-0.475211\pi\)
0.0777996 + 0.996969i \(0.475211\pi\)
\(692\) −3.95244e54 −0.163982
\(693\) −1.04727e55 −0.422434
\(694\) 1.47297e55 0.577675
\(695\) −2.19936e54 −0.0838674
\(696\) −2.44983e55 −0.908356
\(697\) −1.04172e55 −0.375589
\(698\) 1.34539e54 0.0471703
\(699\) −7.11122e54 −0.242460
\(700\) −7.07555e55 −2.34611
\(701\) 2.60981e55 0.841604 0.420802 0.907153i \(-0.361749\pi\)
0.420802 + 0.907153i \(0.361749\pi\)
\(702\) −1.26290e55 −0.396092
\(703\) 1.88614e55 0.575368
\(704\) 4.47644e55 1.32821
\(705\) −1.85714e54 −0.0535991
\(706\) −1.65821e55 −0.465532
\(707\) 4.01738e55 1.09715
\(708\) 1.30923e54 0.0347831
\(709\) 1.26820e55 0.327782 0.163891 0.986478i \(-0.447595\pi\)
0.163891 + 0.986478i \(0.447595\pi\)
\(710\) 6.53540e54 0.164337
\(711\) 1.61257e55 0.394514
\(712\) 8.58257e55 2.04295
\(713\) −7.63860e55 −1.76916
\(714\) −1.02899e56 −2.31898
\(715\) 7.83557e54 0.171831
\(716\) −2.70045e55 −0.576278
\(717\) 1.77503e55 0.368623
\(718\) 5.83725e55 1.17973
\(719\) 1.37548e55 0.270545 0.135273 0.990808i \(-0.456809\pi\)
0.135273 + 0.990808i \(0.456809\pi\)
\(720\) −1.46930e54 −0.0281273
\(721\) −1.53663e55 −0.286307
\(722\) −3.47367e55 −0.629960
\(723\) −2.43176e55 −0.429264
\(724\) −1.70179e56 −2.92418
\(725\) −6.37305e55 −1.06600
\(726\) 2.19393e54 0.0357238
\(727\) −2.38316e55 −0.377774 −0.188887 0.981999i \(-0.560488\pi\)
−0.188887 + 0.981999i \(0.560488\pi\)
\(728\) 1.47293e56 2.27311
\(729\) 2.46503e54 0.0370370
\(730\) 1.67842e55 0.245530
\(731\) −7.03200e55 −1.00159
\(732\) 1.15794e56 1.60591
\(733\) 7.77464e55 1.04991 0.524956 0.851130i \(-0.324082\pi\)
0.524956 + 0.851130i \(0.324082\pi\)
\(734\) 1.00815e56 1.32572
\(735\) 4.32305e54 0.0553589
\(736\) −4.64777e55 −0.579599
\(737\) 8.60130e55 1.04460
\(738\) −9.71581e54 −0.114916
\(739\) 1.23887e56 1.42712 0.713560 0.700595i \(-0.247082\pi\)
0.713560 + 0.700595i \(0.247082\pi\)
\(740\) −1.72685e55 −0.193748
\(741\) −5.09614e55 −0.556912
\(742\) −7.16096e54 −0.0762246
\(743\) 5.42590e55 0.562587 0.281293 0.959622i \(-0.409237\pi\)
0.281293 + 0.959622i \(0.409237\pi\)
\(744\) 1.14347e56 1.15492
\(745\) −4.11863e54 −0.0405233
\(746\) 1.00253e56 0.960925
\(747\) 2.26605e55 0.211601
\(748\) −3.68519e56 −3.35257
\(749\) −1.09880e56 −0.973922
\(750\) −3.21399e55 −0.277556
\(751\) 1.09351e55 0.0920116 0.0460058 0.998941i \(-0.485351\pi\)
0.0460058 + 0.998941i \(0.485351\pi\)
\(752\) −4.62487e55 −0.379185
\(753\) −1.20806e54 −0.00965130
\(754\) 2.87767e56 2.24027
\(755\) 2.79263e54 0.0211859
\(756\) −6.23603e55 −0.461034
\(757\) −1.25443e56 −0.903806 −0.451903 0.892067i \(-0.649255\pi\)
−0.451903 + 0.892067i \(0.649255\pi\)
\(758\) −2.77704e56 −1.94999
\(759\) 1.05853e56 0.724419
\(760\) −2.46672e55 −0.164534
\(761\) −7.07824e55 −0.460176 −0.230088 0.973170i \(-0.573901\pi\)
−0.230088 + 0.973170i \(0.573901\pi\)
\(762\) −8.26091e55 −0.523487
\(763\) 2.70829e56 1.67289
\(764\) −3.16138e56 −1.90351
\(765\) −1.50272e55 −0.0882026
\(766\) −2.67924e56 −1.53303
\(767\) −7.09005e54 −0.0395494
\(768\) 1.85215e56 1.00724
\(769\) 1.14286e56 0.605941 0.302971 0.953000i \(-0.402022\pi\)
0.302971 + 0.953000i \(0.402022\pi\)
\(770\) 5.95442e55 0.307801
\(771\) 9.68518e54 0.0488143
\(772\) 1.53960e56 0.756606
\(773\) −1.32163e56 −0.633298 −0.316649 0.948543i \(-0.602558\pi\)
−0.316649 + 0.948543i \(0.602558\pi\)
\(774\) −6.55852e55 −0.306448
\(775\) 2.97464e56 1.35535
\(776\) −4.59256e56 −2.04057
\(777\) −1.24990e56 −0.541582
\(778\) 3.84206e56 1.62354
\(779\) −3.92058e55 −0.161574
\(780\) 4.66575e55 0.187533
\(781\) 1.69410e56 0.664115
\(782\) 1.04006e57 3.97675
\(783\) −5.61687e55 −0.209479
\(784\) 1.07658e56 0.391635
\(785\) 5.94386e55 0.210916
\(786\) −2.30508e56 −0.797898
\(787\) −3.61019e56 −1.21905 −0.609527 0.792765i \(-0.708641\pi\)
−0.609527 + 0.792765i \(0.708641\pi\)
\(788\) 9.98969e56 3.29072
\(789\) 2.46427e56 0.791930
\(790\) −9.16859e55 −0.287458
\(791\) −6.17586e56 −1.88911
\(792\) −1.58458e56 −0.472904
\(793\) −6.27075e56 −1.82596
\(794\) 2.48206e56 0.705201
\(795\) −1.04578e54 −0.00289921
\(796\) −1.09174e57 −2.95336
\(797\) −4.01672e56 −1.06031 −0.530157 0.847900i \(-0.677867\pi\)
−0.530157 + 0.847900i \(0.677867\pi\)
\(798\) −3.87267e56 −0.997595
\(799\) −4.73006e56 −1.18906
\(800\) 1.80994e56 0.444028
\(801\) 1.96777e56 0.471131
\(802\) 1.03218e57 2.41187
\(803\) 4.35078e56 0.992234
\(804\) 5.12172e56 1.14005
\(805\) −1.09197e56 −0.237241
\(806\) −1.34316e57 −2.84836
\(807\) 1.35991e56 0.281498
\(808\) 6.07855e56 1.22823
\(809\) 4.55101e56 0.897659 0.448829 0.893617i \(-0.351841\pi\)
0.448829 + 0.893617i \(0.351841\pi\)
\(810\) −1.40154e55 −0.0269866
\(811\) −4.54018e56 −0.853426 −0.426713 0.904387i \(-0.640329\pi\)
−0.426713 + 0.904387i \(0.640329\pi\)
\(812\) 1.42095e57 2.60758
\(813\) 2.12541e54 0.00380782
\(814\) −6.88893e56 −1.20497
\(815\) −5.45929e55 −0.0932316
\(816\) −3.74225e56 −0.623986
\(817\) −2.64653e56 −0.430871
\(818\) −1.00178e57 −1.59251
\(819\) 3.37707e56 0.524209
\(820\) 3.58948e55 0.0544078
\(821\) 4.33877e56 0.642207 0.321103 0.947044i \(-0.395946\pi\)
0.321103 + 0.947044i \(0.395946\pi\)
\(822\) −6.72673e56 −0.972307
\(823\) 7.44435e56 1.05082 0.525412 0.850848i \(-0.323911\pi\)
0.525412 + 0.850848i \(0.323911\pi\)
\(824\) −2.32502e56 −0.320514
\(825\) −4.12216e56 −0.554974
\(826\) −5.38789e55 −0.0708448
\(827\) 2.16428e56 0.277943 0.138971 0.990296i \(-0.455620\pi\)
0.138971 + 0.990296i \(0.455620\pi\)
\(828\) 6.30312e56 0.790613
\(829\) 8.47965e56 1.03888 0.519439 0.854508i \(-0.326141\pi\)
0.519439 + 0.854508i \(0.326141\pi\)
\(830\) −1.28841e56 −0.154181
\(831\) −6.21448e56 −0.726415
\(832\) −1.44350e57 −1.64821
\(833\) 1.10106e57 1.22810
\(834\) −5.22450e56 −0.569255
\(835\) 8.50135e55 0.0904902
\(836\) −1.38694e57 −1.44223
\(837\) 2.62169e56 0.266339
\(838\) 3.14675e57 3.12323
\(839\) −8.45666e56 −0.820050 −0.410025 0.912074i \(-0.634480\pi\)
−0.410025 + 0.912074i \(0.634480\pi\)
\(840\) 1.63463e56 0.154872
\(841\) 1.99628e56 0.184799
\(842\) −2.34690e56 −0.212280
\(843\) 5.29427e56 0.467916
\(844\) 3.49667e57 3.01979
\(845\) −8.23510e55 −0.0694965
\(846\) −4.41157e56 −0.363807
\(847\) −5.86669e55 −0.0472788
\(848\) −2.60431e55 −0.0205104
\(849\) 8.94152e56 0.688195
\(850\) −4.05023e57 −3.04657
\(851\) 1.26334e57 0.928742
\(852\) 1.00876e57 0.724799
\(853\) 1.00803e57 0.707892 0.353946 0.935266i \(-0.384840\pi\)
0.353946 + 0.935266i \(0.384840\pi\)
\(854\) −4.76528e57 −3.27085
\(855\) −5.65559e55 −0.0379436
\(856\) −1.66256e57 −1.09028
\(857\) 1.60014e57 1.02573 0.512864 0.858470i \(-0.328584\pi\)
0.512864 + 0.858470i \(0.328584\pi\)
\(858\) 1.86131e57 1.16632
\(859\) −1.88550e57 −1.15494 −0.577471 0.816411i \(-0.695960\pi\)
−0.577471 + 0.816411i \(0.695960\pi\)
\(860\) 2.42303e56 0.145090
\(861\) 2.59807e56 0.152086
\(862\) 2.28942e57 1.31019
\(863\) −1.30074e57 −0.727745 −0.363873 0.931449i \(-0.618546\pi\)
−0.363873 + 0.931449i \(0.618546\pi\)
\(864\) 1.59519e56 0.0872558
\(865\) 2.37539e55 0.0127034
\(866\) −4.56606e56 −0.238750
\(867\) −2.69807e57 −1.37937
\(868\) −6.63233e57 −3.31537
\(869\) −2.37667e57 −1.16167
\(870\) 3.19358e56 0.152634
\(871\) −2.77363e57 −1.29627
\(872\) 4.09781e57 1.87275
\(873\) −1.05296e57 −0.470582
\(874\) 3.91434e57 1.71074
\(875\) 8.59442e56 0.367332
\(876\) 2.59071e57 1.08290
\(877\) 3.80973e57 1.55741 0.778704 0.627392i \(-0.215878\pi\)
0.778704 + 0.627392i \(0.215878\pi\)
\(878\) −1.65158e57 −0.660325
\(879\) −1.30927e57 −0.511972
\(880\) 2.16551e56 0.0828226
\(881\) 1.81431e57 0.678707 0.339353 0.940659i \(-0.389792\pi\)
0.339353 + 0.940659i \(0.389792\pi\)
\(882\) 1.02692e57 0.375752
\(883\) −2.70921e57 −0.969637 −0.484819 0.874615i \(-0.661114\pi\)
−0.484819 + 0.874615i \(0.661114\pi\)
\(884\) 1.18835e58 4.16029
\(885\) −7.86839e54 −0.00269459
\(886\) 2.23479e57 0.748652
\(887\) 2.63364e57 0.863070 0.431535 0.902096i \(-0.357972\pi\)
0.431535 + 0.902096i \(0.357972\pi\)
\(888\) −1.89117e57 −0.606287
\(889\) 2.20902e57 0.692811
\(890\) −1.11882e57 −0.343284
\(891\) −3.63306e56 −0.109058
\(892\) −3.25734e57 −0.956639
\(893\) −1.78019e57 −0.511519
\(894\) −9.78364e56 −0.275055
\(895\) 1.62295e56 0.0446432
\(896\) −8.79444e57 −2.36702
\(897\) −3.41341e57 −0.898950
\(898\) 1.18974e58 3.06594
\(899\) −5.97383e57 −1.50640
\(900\) −2.45457e57 −0.605685
\(901\) −2.66354e56 −0.0643171
\(902\) 1.43195e57 0.338377
\(903\) 1.75379e57 0.405570
\(904\) −9.34447e57 −2.11480
\(905\) 1.02276e57 0.226531
\(906\) 6.63379e56 0.143801
\(907\) 5.41882e57 1.14964 0.574821 0.818279i \(-0.305072\pi\)
0.574821 + 0.818279i \(0.305072\pi\)
\(908\) −7.61771e57 −1.58180
\(909\) 1.39367e57 0.283245
\(910\) −1.92010e57 −0.381959
\(911\) 2.21214e57 0.430730 0.215365 0.976534i \(-0.430906\pi\)
0.215365 + 0.976534i \(0.430906\pi\)
\(912\) −1.40842e57 −0.268431
\(913\) −3.33979e57 −0.623074
\(914\) 1.32025e58 2.41105
\(915\) −6.95915e56 −0.124407
\(916\) −7.72312e57 −1.35155
\(917\) 6.16394e57 1.05598
\(918\) −3.56966e57 −0.598680
\(919\) −5.45603e56 −0.0895828 −0.0447914 0.998996i \(-0.514262\pi\)
−0.0447914 + 0.998996i \(0.514262\pi\)
\(920\) −1.65221e57 −0.265585
\(921\) −2.96291e57 −0.466289
\(922\) 1.40448e57 0.216403
\(923\) −5.46288e57 −0.824117
\(924\) 9.19088e57 1.35754
\(925\) −4.91974e57 −0.711505
\(926\) −1.24910e56 −0.0176882
\(927\) −5.33071e56 −0.0739146
\(928\) −3.63483e57 −0.493513
\(929\) 8.42371e57 1.11995 0.559973 0.828511i \(-0.310811\pi\)
0.559973 + 0.828511i \(0.310811\pi\)
\(930\) −1.49061e57 −0.194065
\(931\) 4.14391e57 0.528313
\(932\) 6.24086e57 0.779174
\(933\) 4.86355e57 0.594650
\(934\) 6.93364e57 0.830227
\(935\) 2.21477e57 0.259718
\(936\) 5.10973e57 0.586838
\(937\) −3.34055e57 −0.375747 −0.187873 0.982193i \(-0.560159\pi\)
−0.187873 + 0.982193i \(0.560159\pi\)
\(938\) −2.10774e58 −2.32200
\(939\) 5.54328e57 0.598119
\(940\) 1.62984e57 0.172247
\(941\) −6.19137e57 −0.640898 −0.320449 0.947266i \(-0.603834\pi\)
−0.320449 + 0.947266i \(0.603834\pi\)
\(942\) 1.41194e58 1.43161
\(943\) −2.62602e57 −0.260807
\(944\) −1.95948e56 −0.0190628
\(945\) 3.74781e56 0.0357155
\(946\) 9.66618e57 0.902355
\(947\) −1.41767e58 −1.29643 −0.648217 0.761455i \(-0.724485\pi\)
−0.648217 + 0.761455i \(0.724485\pi\)
\(948\) −1.41521e58 −1.26782
\(949\) −1.40298e58 −1.23129
\(950\) −1.52433e58 −1.31059
\(951\) 1.02614e57 0.0864344
\(952\) 4.16332e58 3.43574
\(953\) 1.36443e58 1.10316 0.551581 0.834121i \(-0.314025\pi\)
0.551581 + 0.834121i \(0.314025\pi\)
\(954\) −2.48420e56 −0.0196786
\(955\) 1.89996e57 0.147462
\(956\) −1.55778e58 −1.18462
\(957\) 8.27835e57 0.616824
\(958\) −3.40728e58 −2.48760
\(959\) 1.79877e58 1.28680
\(960\) −1.60196e57 −0.112296
\(961\) 1.33249e58 0.915286
\(962\) 2.22145e58 1.49528
\(963\) −3.81184e57 −0.251433
\(964\) 2.13413e58 1.37949
\(965\) −9.25287e56 −0.0586130
\(966\) −2.59392e58 −1.61029
\(967\) −4.32736e57 −0.263273 −0.131637 0.991298i \(-0.542023\pi\)
−0.131637 + 0.991298i \(0.542023\pi\)
\(968\) −8.87668e56 −0.0529274
\(969\) −1.44045e58 −0.841755
\(970\) 5.98681e57 0.342884
\(971\) −4.45524e57 −0.250090 −0.125045 0.992151i \(-0.539908\pi\)
−0.125045 + 0.992151i \(0.539908\pi\)
\(972\) −2.16333e57 −0.119023
\(973\) 1.39706e58 0.753383
\(974\) −3.72201e58 −1.96733
\(975\) 1.32925e58 0.688681
\(976\) −1.73304e58 −0.880113
\(977\) −2.79388e58 −1.39080 −0.695399 0.718624i \(-0.744772\pi\)
−0.695399 + 0.718624i \(0.744772\pi\)
\(978\) −1.29683e58 −0.632815
\(979\) −2.90018e58 −1.38727
\(980\) −3.79394e57 −0.177903
\(981\) 9.39530e57 0.431882
\(982\) −5.55912e58 −2.50514
\(983\) 2.24671e58 0.992551 0.496276 0.868165i \(-0.334701\pi\)
0.496276 + 0.868165i \(0.334701\pi\)
\(984\) 3.93104e57 0.170256
\(985\) −6.00373e57 −0.254926
\(986\) 8.13390e58 3.38610
\(987\) 1.17968e58 0.481482
\(988\) 4.47241e58 1.78970
\(989\) −1.77266e58 −0.695499
\(990\) 2.06564e57 0.0794637
\(991\) 4.01647e58 1.51498 0.757492 0.652844i \(-0.226424\pi\)
0.757492 + 0.652844i \(0.226424\pi\)
\(992\) 1.69657e58 0.627470
\(993\) 1.81660e58 0.658794
\(994\) −4.15137e58 −1.47624
\(995\) 6.56130e57 0.228791
\(996\) −1.98871e58 −0.680007
\(997\) 3.28355e58 1.10100 0.550502 0.834834i \(-0.314436\pi\)
0.550502 + 0.834834i \(0.314436\pi\)
\(998\) 9.63042e58 3.16665
\(999\) −4.33600e57 −0.139818
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.1.3 3
3.2 odd 2 9.40.a.c.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.40.a.b.1.3 3 1.1 even 1 trivial
9.40.a.c.1.1 3 3.2 odd 2