Properties

Label 1.36.a.a.1.1
Level $1$
Weight $36$
Character 1.1
Self dual yes
Analytic conductor $7.760$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.75951306336\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 12422194 x - 2645665785\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{12}\cdot 3^{3}\cdot 5\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-213.765\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-165109. q^{2} -3.45913e8 q^{3} -7.09870e9 q^{4} -2.05014e12 q^{5} +5.71135e13 q^{6} -1.25160e14 q^{7} +6.84517e15 q^{8} +6.96245e16 q^{9} +O(q^{10})\) \(q-165109. q^{2} -3.45913e8 q^{3} -7.09870e9 q^{4} -2.05014e12 q^{5} +5.71135e13 q^{6} -1.25160e14 q^{7} +6.84517e15 q^{8} +6.96245e16 q^{9} +3.38496e17 q^{10} -1.70842e18 q^{11} +2.45554e18 q^{12} -4.94986e19 q^{13} +2.06651e19 q^{14} +7.09169e20 q^{15} -8.86291e20 q^{16} +1.32045e21 q^{17} -1.14956e22 q^{18} +3.94388e21 q^{19} +1.45533e22 q^{20} +4.32945e22 q^{21} +2.82076e23 q^{22} -3.48881e23 q^{23} -2.36784e24 q^{24} +1.29267e24 q^{25} +8.17268e24 q^{26} -6.77748e24 q^{27} +8.88473e23 q^{28} +3.21628e25 q^{29} -1.17090e26 q^{30} +3.41044e25 q^{31} -8.88635e25 q^{32} +5.90965e26 q^{33} -2.18018e26 q^{34} +2.56595e26 q^{35} -4.94244e26 q^{36} -4.03624e27 q^{37} -6.51171e26 q^{38} +1.71222e28 q^{39} -1.40335e28 q^{40} +8.65857e27 q^{41} -7.14832e27 q^{42} +9.89389e26 q^{43} +1.21276e28 q^{44} -1.42740e29 q^{45} +5.76034e28 q^{46} +1.95852e29 q^{47} +3.06580e29 q^{48} -3.63154e29 q^{49} -2.13432e29 q^{50} -4.56760e29 q^{51} +3.51376e29 q^{52} -9.96909e29 q^{53} +1.11902e30 q^{54} +3.50249e30 q^{55} -8.56741e29 q^{56} -1.36424e30 q^{57} -5.31037e30 q^{58} +3.91953e30 q^{59} -5.03418e30 q^{60} +7.64909e29 q^{61} -5.63096e30 q^{62} -8.71420e30 q^{63} +4.51249e31 q^{64} +1.01479e32 q^{65} -9.75738e31 q^{66} -1.64301e32 q^{67} -9.37346e30 q^{68} +1.20682e32 q^{69} -4.23662e31 q^{70} +7.65930e31 q^{71} +4.76592e32 q^{72} -7.08063e32 q^{73} +6.66421e32 q^{74} -4.47152e32 q^{75} -2.79964e31 q^{76} +2.13826e32 q^{77} -2.82704e33 q^{78} +2.34599e33 q^{79} +1.81702e33 q^{80} -1.13900e33 q^{81} -1.42961e33 q^{82} +5.18971e33 q^{83} -3.07335e32 q^{84} -2.70710e33 q^{85} -1.63357e32 q^{86} -1.11255e34 q^{87} -1.16944e34 q^{88} +1.44578e34 q^{89} +2.35676e34 q^{90} +6.19525e33 q^{91} +2.47660e33 q^{92} -1.17972e34 q^{93} -3.23369e34 q^{94} -8.08549e33 q^{95} +3.07391e34 q^{96} -2.87399e34 q^{97} +5.99600e34 q^{98} -1.18948e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 139656q^{2} - 104875308q^{3} + 34841262144q^{4} + 892652054010q^{5} - 4786530564384q^{6} + 878422149346056q^{7} + 22336009925337600q^{8} + 150091978876243551q^{9} + O(q^{10}) \) \( 3q + 139656q^{2} - 104875308q^{3} + 34841262144q^{4} + 892652054010q^{5} - 4786530564384q^{6} + 878422149346056q^{7} + 22336009925337600q^{8} + 150091978876243551q^{9} + 1019870812729298160q^{10} - 1157945428549987044q^{11} - 22548891526776486144q^{12} - 62139610550998650558q^{13} + \)\(13\!\cdots\!28\)\(q^{14} + \)\(70\!\cdots\!20\)\(q^{15} + \)\(21\!\cdots\!48\)\(q^{16} - \)\(39\!\cdots\!94\)\(q^{17} - \)\(23\!\cdots\!08\)\(q^{18} - \)\(32\!\cdots\!40\)\(q^{19} + \)\(14\!\cdots\!80\)\(q^{20} + \)\(22\!\cdots\!76\)\(q^{21} + \)\(22\!\cdots\!12\)\(q^{22} - \)\(51\!\cdots\!08\)\(q^{23} - \)\(37\!\cdots\!20\)\(q^{24} + \)\(64\!\cdots\!25\)\(q^{25} + \)\(42\!\cdots\!36\)\(q^{26} + \)\(27\!\cdots\!00\)\(q^{27} + \)\(10\!\cdots\!08\)\(q^{28} - \)\(38\!\cdots\!10\)\(q^{29} - \)\(23\!\cdots\!80\)\(q^{30} + \)\(10\!\cdots\!56\)\(q^{31} - \)\(92\!\cdots\!44\)\(q^{32} + \)\(11\!\cdots\!84\)\(q^{33} - \)\(55\!\cdots\!12\)\(q^{34} + \)\(15\!\cdots\!60\)\(q^{35} - \)\(60\!\cdots\!52\)\(q^{36} + \)\(24\!\cdots\!06\)\(q^{37} - \)\(12\!\cdots\!00\)\(q^{38} + \)\(18\!\cdots\!12\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!06\)\(q^{41} - \)\(33\!\cdots\!88\)\(q^{42} - \)\(47\!\cdots\!08\)\(q^{43} - \)\(80\!\cdots\!12\)\(q^{44} - \)\(11\!\cdots\!30\)\(q^{45} + \)\(31\!\cdots\!56\)\(q^{46} + \)\(16\!\cdots\!56\)\(q^{47} + \)\(44\!\cdots\!92\)\(q^{48} - \)\(59\!\cdots\!21\)\(q^{49} + \)\(37\!\cdots\!00\)\(q^{50} - \)\(18\!\cdots\!04\)\(q^{51} - \)\(51\!\cdots\!44\)\(q^{52} - \)\(16\!\cdots\!58\)\(q^{53} + \)\(44\!\cdots\!60\)\(q^{54} + \)\(30\!\cdots\!20\)\(q^{55} + \)\(56\!\cdots\!40\)\(q^{56} + \)\(40\!\cdots\!00\)\(q^{57} - \)\(23\!\cdots\!00\)\(q^{58} + \)\(43\!\cdots\!80\)\(q^{59} - \)\(40\!\cdots\!40\)\(q^{60} + \)\(23\!\cdots\!06\)\(q^{61} + \)\(29\!\cdots\!12\)\(q^{62} + \)\(45\!\cdots\!92\)\(q^{63} + \)\(93\!\cdots\!84\)\(q^{64} + \)\(75\!\cdots\!20\)\(q^{65} - \)\(75\!\cdots\!68\)\(q^{66} - \)\(18\!\cdots\!44\)\(q^{67} + \)\(21\!\cdots\!08\)\(q^{68} - \)\(32\!\cdots\!48\)\(q^{69} + \)\(22\!\cdots\!60\)\(q^{70} + \)\(34\!\cdots\!56\)\(q^{71} + \)\(31\!\cdots\!00\)\(q^{72} - \)\(28\!\cdots\!58\)\(q^{73} + \)\(21\!\cdots\!08\)\(q^{74} - \)\(15\!\cdots\!00\)\(q^{75} - \)\(27\!\cdots\!20\)\(q^{76} + \)\(69\!\cdots\!12\)\(q^{77} - \)\(22\!\cdots\!16\)\(q^{78} - \)\(42\!\cdots\!60\)\(q^{79} + \)\(68\!\cdots\!60\)\(q^{80} + \)\(18\!\cdots\!63\)\(q^{81} - \)\(40\!\cdots\!88\)\(q^{82} + \)\(14\!\cdots\!92\)\(q^{83} - \)\(13\!\cdots\!52\)\(q^{84} - \)\(87\!\cdots\!40\)\(q^{85} + \)\(14\!\cdots\!96\)\(q^{86} - \)\(78\!\cdots\!00\)\(q^{87} - \)\(18\!\cdots\!00\)\(q^{88} + \)\(30\!\cdots\!70\)\(q^{89} + \)\(28\!\cdots\!20\)\(q^{90} + \)\(10\!\cdots\!96\)\(q^{91} + \)\(83\!\cdots\!56\)\(q^{92} - \)\(40\!\cdots\!16\)\(q^{93} + \)\(19\!\cdots\!68\)\(q^{94} - \)\(84\!\cdots\!00\)\(q^{95} - \)\(32\!\cdots\!84\)\(q^{96} - \)\(10\!\cdots\!94\)\(q^{97} - \)\(13\!\cdots\!92\)\(q^{98} + \)\(30\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −165109. −0.890730 −0.445365 0.895349i \(-0.646926\pi\)
−0.445365 + 0.895349i \(0.646926\pi\)
\(3\) −3.45913e8 −1.54648 −0.773242 0.634111i \(-0.781366\pi\)
−0.773242 + 0.634111i \(0.781366\pi\)
\(4\) −7.09870e9 −0.206599
\(5\) −2.05014e12 −1.20173 −0.600866 0.799350i \(-0.705177\pi\)
−0.600866 + 0.799350i \(0.705177\pi\)
\(6\) 5.71135e13 1.37750
\(7\) −1.25160e14 −0.203353 −0.101676 0.994818i \(-0.532421\pi\)
−0.101676 + 0.994818i \(0.532421\pi\)
\(8\) 6.84517e15 1.07475
\(9\) 6.96245e16 1.39161
\(10\) 3.38496e17 1.07042
\(11\) −1.70842e18 −1.01911 −0.509557 0.860437i \(-0.670191\pi\)
−0.509557 + 0.860437i \(0.670191\pi\)
\(12\) 2.45554e18 0.319503
\(13\) −4.94986e19 −1.58703 −0.793514 0.608552i \(-0.791751\pi\)
−0.793514 + 0.608552i \(0.791751\pi\)
\(14\) 2.06651e19 0.181132
\(15\) 7.09169e20 1.85846
\(16\) −8.86291e20 −0.750717
\(17\) 1.32045e21 0.387137 0.193569 0.981087i \(-0.437994\pi\)
0.193569 + 0.981087i \(0.437994\pi\)
\(18\) −1.14956e22 −1.23955
\(19\) 3.94388e21 0.165096 0.0825479 0.996587i \(-0.473694\pi\)
0.0825479 + 0.996587i \(0.473694\pi\)
\(20\) 1.45533e22 0.248277
\(21\) 4.32945e22 0.314482
\(22\) 2.82076e23 0.907756
\(23\) −3.48881e23 −0.515750 −0.257875 0.966178i \(-0.583022\pi\)
−0.257875 + 0.966178i \(0.583022\pi\)
\(24\) −2.36784e24 −1.66209
\(25\) 1.29267e24 0.444159
\(26\) 8.17268e24 1.41361
\(27\) −6.77748e24 −0.605623
\(28\) 8.88473e23 0.0420125
\(29\) 3.21628e25 0.822979 0.411489 0.911415i \(-0.365009\pi\)
0.411489 + 0.911415i \(0.365009\pi\)
\(30\) −1.17090e26 −1.65539
\(31\) 3.41044e25 0.271632 0.135816 0.990734i \(-0.456634\pi\)
0.135816 + 0.990734i \(0.456634\pi\)
\(32\) −8.88635e25 −0.406068
\(33\) 5.90965e26 1.57604
\(34\) −2.18018e26 −0.344835
\(35\) 2.56595e26 0.244375
\(36\) −4.94244e26 −0.287506
\(37\) −4.03624e27 −1.45361 −0.726804 0.686845i \(-0.758995\pi\)
−0.726804 + 0.686845i \(0.758995\pi\)
\(38\) −6.51171e26 −0.147056
\(39\) 1.71222e28 2.45431
\(40\) −1.40335e28 −1.29157
\(41\) 8.65857e27 0.517283 0.258642 0.965973i \(-0.416725\pi\)
0.258642 + 0.965973i \(0.416725\pi\)
\(42\) −7.14832e27 −0.280118
\(43\) 9.89389e26 0.0256844 0.0128422 0.999918i \(-0.495912\pi\)
0.0128422 + 0.999918i \(0.495912\pi\)
\(44\) 1.21276e28 0.210548
\(45\) −1.42740e29 −1.67234
\(46\) 5.76034e28 0.459395
\(47\) 1.95852e29 1.07205 0.536025 0.844202i \(-0.319925\pi\)
0.536025 + 0.844202i \(0.319925\pi\)
\(48\) 3.06580e29 1.16097
\(49\) −3.63154e29 −0.958648
\(50\) −2.13432e29 −0.395626
\(51\) −4.56760e29 −0.598702
\(52\) 3.51376e29 0.327879
\(53\) −9.96909e29 −0.666543 −0.333271 0.942831i \(-0.608153\pi\)
−0.333271 + 0.942831i \(0.608153\pi\)
\(54\) 1.11902e30 0.539447
\(55\) 3.50249e30 1.22470
\(56\) −8.56741e29 −0.218554
\(57\) −1.36424e30 −0.255318
\(58\) −5.31037e30 −0.733052
\(59\) 3.91953e30 0.401166 0.200583 0.979677i \(-0.435716\pi\)
0.200583 + 0.979677i \(0.435716\pi\)
\(60\) −5.03418e30 −0.383956
\(61\) 7.64909e29 0.0436855 0.0218428 0.999761i \(-0.493047\pi\)
0.0218428 + 0.999761i \(0.493047\pi\)
\(62\) −5.63096e30 −0.241951
\(63\) −8.71420e30 −0.282988
\(64\) 4.51249e31 1.11241
\(65\) 1.01479e32 1.90718
\(66\) −9.75738e31 −1.40383
\(67\) −1.64301e32 −1.81690 −0.908451 0.417992i \(-0.862734\pi\)
−0.908451 + 0.417992i \(0.862734\pi\)
\(68\) −9.37346e30 −0.0799823
\(69\) 1.20682e32 0.797600
\(70\) −4.23662e31 −0.217672
\(71\) 7.65930e31 0.307021 0.153510 0.988147i \(-0.450942\pi\)
0.153510 + 0.988147i \(0.450942\pi\)
\(72\) 4.76592e32 1.49564
\(73\) −7.08063e32 −1.74551 −0.872754 0.488160i \(-0.837668\pi\)
−0.872754 + 0.488160i \(0.837668\pi\)
\(74\) 6.66421e32 1.29477
\(75\) −4.47152e32 −0.686884
\(76\) −2.79964e31 −0.0341087
\(77\) 2.13826e32 0.207239
\(78\) −2.82704e33 −2.18613
\(79\) 2.34599e33 1.45162 0.725809 0.687896i \(-0.241466\pi\)
0.725809 + 0.687896i \(0.241466\pi\)
\(80\) 1.81702e33 0.902161
\(81\) −1.13900e33 −0.455027
\(82\) −1.42961e33 −0.460760
\(83\) 5.18971e33 1.35293 0.676467 0.736473i \(-0.263510\pi\)
0.676467 + 0.736473i \(0.263510\pi\)
\(84\) −3.07335e32 −0.0649717
\(85\) −2.70710e33 −0.465235
\(86\) −1.63357e32 −0.0228779
\(87\) −1.11255e34 −1.27272
\(88\) −1.16944e34 −1.09530
\(89\) 1.44578e34 1.11116 0.555582 0.831461i \(-0.312495\pi\)
0.555582 + 0.831461i \(0.312495\pi\)
\(90\) 2.35676e34 1.48961
\(91\) 6.19525e33 0.322726
\(92\) 2.47660e33 0.106554
\(93\) −1.17972e34 −0.420075
\(94\) −3.23369e34 −0.954907
\(95\) −8.08549e33 −0.198401
\(96\) 3.07391e34 0.627978
\(97\) −2.87399e34 −0.489756 −0.244878 0.969554i \(-0.578748\pi\)
−0.244878 + 0.969554i \(0.578748\pi\)
\(98\) 5.99600e34 0.853897
\(99\) −1.18948e35 −1.41821
\(100\) −9.17629e33 −0.0917629
\(101\) 1.13198e35 0.951079 0.475539 0.879694i \(-0.342253\pi\)
0.475539 + 0.879694i \(0.342253\pi\)
\(102\) 7.54153e34 0.533282
\(103\) 2.53635e35 1.51202 0.756011 0.654559i \(-0.227145\pi\)
0.756011 + 0.654559i \(0.227145\pi\)
\(104\) −3.38826e35 −1.70567
\(105\) −8.87596e34 −0.377922
\(106\) 1.64599e35 0.593710
\(107\) −3.63939e35 −1.11381 −0.556907 0.830575i \(-0.688012\pi\)
−0.556907 + 0.830575i \(0.688012\pi\)
\(108\) 4.81113e34 0.125121
\(109\) −4.65371e34 −0.103000 −0.0514998 0.998673i \(-0.516400\pi\)
−0.0514998 + 0.998673i \(0.516400\pi\)
\(110\) −5.78294e35 −1.09088
\(111\) 1.39619e36 2.24798
\(112\) 1.10928e35 0.152660
\(113\) −2.18346e35 −0.257201 −0.128601 0.991696i \(-0.541049\pi\)
−0.128601 + 0.991696i \(0.541049\pi\)
\(114\) 2.25249e35 0.227419
\(115\) 7.15252e35 0.619794
\(116\) −2.28314e35 −0.170027
\(117\) −3.44632e36 −2.20853
\(118\) −6.47150e35 −0.357330
\(119\) −1.65267e35 −0.0787254
\(120\) 4.85438e36 1.99739
\(121\) 1.08456e35 0.0385932
\(122\) −1.26293e35 −0.0389120
\(123\) −2.99511e36 −0.799970
\(124\) −2.42097e35 −0.0561191
\(125\) 3.31653e36 0.667972
\(126\) 1.43880e36 0.252066
\(127\) 4.19558e36 0.640070 0.320035 0.947406i \(-0.396305\pi\)
0.320035 + 0.947406i \(0.396305\pi\)
\(128\) −4.39721e36 −0.584793
\(129\) −3.42243e35 −0.0397205
\(130\) −1.67551e37 −1.69878
\(131\) 2.40631e36 0.213355 0.106678 0.994294i \(-0.465979\pi\)
0.106678 + 0.994294i \(0.465979\pi\)
\(132\) −4.19509e36 −0.325610
\(133\) −4.93616e35 −0.0335727
\(134\) 2.71276e37 1.61837
\(135\) 1.38947e37 0.727796
\(136\) 9.03869e36 0.416078
\(137\) −2.14718e37 −0.869477 −0.434739 0.900557i \(-0.643159\pi\)
−0.434739 + 0.900557i \(0.643159\pi\)
\(138\) −1.99258e37 −0.710446
\(139\) 2.63209e37 0.827068 0.413534 0.910489i \(-0.364294\pi\)
0.413534 + 0.910489i \(0.364294\pi\)
\(140\) −1.82149e36 −0.0504878
\(141\) −6.77477e37 −1.65791
\(142\) −1.26462e37 −0.273473
\(143\) 8.45645e37 1.61736
\(144\) −6.17076e37 −1.04471
\(145\) −6.59381e37 −0.989000
\(146\) 1.16908e38 1.55478
\(147\) 1.25620e38 1.48253
\(148\) 2.86521e37 0.300314
\(149\) −1.74389e38 −1.62465 −0.812324 0.583206i \(-0.801798\pi\)
−0.812324 + 0.583206i \(0.801798\pi\)
\(150\) 7.38290e37 0.611829
\(151\) −1.40947e38 −1.03982 −0.519912 0.854220i \(-0.674035\pi\)
−0.519912 + 0.854220i \(0.674035\pi\)
\(152\) 2.69965e37 0.177437
\(153\) 9.19355e37 0.538745
\(154\) −3.53046e37 −0.184595
\(155\) −6.99187e37 −0.326429
\(156\) −1.21546e38 −0.507059
\(157\) 1.49924e38 0.559277 0.279639 0.960105i \(-0.409785\pi\)
0.279639 + 0.960105i \(0.409785\pi\)
\(158\) −3.87345e38 −1.29300
\(159\) 3.44844e38 1.03080
\(160\) 1.82182e38 0.487985
\(161\) 4.36659e37 0.104879
\(162\) 1.88060e38 0.405306
\(163\) 8.60787e38 1.66576 0.832880 0.553453i \(-0.186690\pi\)
0.832880 + 0.553453i \(0.186690\pi\)
\(164\) −6.14646e37 −0.106870
\(165\) −1.21156e39 −1.89398
\(166\) −8.56869e38 −1.20510
\(167\) −9.23344e38 −1.16903 −0.584515 0.811383i \(-0.698715\pi\)
−0.584515 + 0.811383i \(0.698715\pi\)
\(168\) 2.96358e38 0.337991
\(169\) 1.47733e39 1.51866
\(170\) 4.46966e38 0.414399
\(171\) 2.74591e38 0.229749
\(172\) −7.02337e36 −0.00530638
\(173\) −1.33161e39 −0.909012 −0.454506 0.890744i \(-0.650184\pi\)
−0.454506 + 0.890744i \(0.650184\pi\)
\(174\) 1.83693e39 1.13365
\(175\) −1.61791e38 −0.0903208
\(176\) 1.51416e39 0.765066
\(177\) −1.35582e39 −0.620396
\(178\) −2.38712e39 −0.989748
\(179\) 6.27202e38 0.235765 0.117883 0.993028i \(-0.462389\pi\)
0.117883 + 0.993028i \(0.462389\pi\)
\(180\) 1.01327e39 0.345505
\(181\) −2.39965e39 −0.742629 −0.371315 0.928507i \(-0.621093\pi\)
−0.371315 + 0.928507i \(0.621093\pi\)
\(182\) −1.02289e39 −0.287462
\(183\) −2.64592e38 −0.0675590
\(184\) −2.38815e39 −0.554305
\(185\) 8.27484e39 1.74685
\(186\) 1.94782e39 0.374174
\(187\) −2.25588e39 −0.394537
\(188\) −1.39029e39 −0.221485
\(189\) 8.48269e38 0.123155
\(190\) 1.33499e39 0.176722
\(191\) 8.14518e39 0.983596 0.491798 0.870709i \(-0.336340\pi\)
0.491798 + 0.870709i \(0.336340\pi\)
\(192\) −1.56093e40 −1.72033
\(193\) 1.38549e40 1.39428 0.697139 0.716936i \(-0.254456\pi\)
0.697139 + 0.716936i \(0.254456\pi\)
\(194\) 4.74522e39 0.436240
\(195\) −3.51029e40 −2.94942
\(196\) 2.57792e39 0.198056
\(197\) −1.15539e40 −0.812026 −0.406013 0.913867i \(-0.633081\pi\)
−0.406013 + 0.913867i \(0.633081\pi\)
\(198\) 1.96394e40 1.26324
\(199\) −4.76691e39 −0.280742 −0.140371 0.990099i \(-0.544830\pi\)
−0.140371 + 0.990099i \(0.544830\pi\)
\(200\) 8.84856e39 0.477362
\(201\) 5.68340e40 2.80981
\(202\) −1.86901e40 −0.847155
\(203\) −4.02549e39 −0.167355
\(204\) 3.24241e39 0.123691
\(205\) −1.77512e40 −0.621636
\(206\) −4.18775e40 −1.34680
\(207\) −2.42906e40 −0.717725
\(208\) 4.38702e40 1.19141
\(209\) −6.73781e39 −0.168251
\(210\) 1.46550e40 0.336627
\(211\) −1.87354e40 −0.396022 −0.198011 0.980200i \(-0.563448\pi\)
−0.198011 + 0.980200i \(0.563448\pi\)
\(212\) 7.07676e39 0.137707
\(213\) −2.64945e40 −0.474803
\(214\) 6.00896e40 0.992107
\(215\) −2.02838e39 −0.0308657
\(216\) −4.63930e40 −0.650896
\(217\) −4.26851e39 −0.0552371
\(218\) 7.68370e39 0.0917448
\(219\) 2.44929e41 2.69940
\(220\) −2.48631e40 −0.253023
\(221\) −6.53603e40 −0.614398
\(222\) −2.30524e41 −2.00234
\(223\) −7.12100e40 −0.571750 −0.285875 0.958267i \(-0.592284\pi\)
−0.285875 + 0.958267i \(0.592284\pi\)
\(224\) 1.11222e40 0.0825750
\(225\) 9.00017e40 0.618097
\(226\) 3.60510e40 0.229097
\(227\) −1.04005e41 −0.611787 −0.305893 0.952066i \(-0.598955\pi\)
−0.305893 + 0.952066i \(0.598955\pi\)
\(228\) 9.68434e39 0.0527485
\(229\) 1.82859e41 0.922564 0.461282 0.887254i \(-0.347390\pi\)
0.461282 + 0.887254i \(0.347390\pi\)
\(230\) −1.18095e41 −0.552069
\(231\) −7.39652e40 −0.320493
\(232\) 2.20160e41 0.884501
\(233\) 1.57847e41 0.588177 0.294088 0.955778i \(-0.404984\pi\)
0.294088 + 0.955778i \(0.404984\pi\)
\(234\) 5.69019e41 1.96720
\(235\) −4.01523e41 −1.28832
\(236\) −2.78236e40 −0.0828806
\(237\) −8.11510e41 −2.24490
\(238\) 2.72871e40 0.0701231
\(239\) 5.00984e41 1.19636 0.598178 0.801363i \(-0.295892\pi\)
0.598178 + 0.801363i \(0.295892\pi\)
\(240\) −6.28530e41 −1.39518
\(241\) −3.33164e41 −0.687638 −0.343819 0.939036i \(-0.611721\pi\)
−0.343819 + 0.939036i \(0.611721\pi\)
\(242\) −1.79072e40 −0.0343762
\(243\) 7.33084e41 1.30931
\(244\) −5.42986e39 −0.00902540
\(245\) 7.44514e41 1.15204
\(246\) 4.94521e41 0.712558
\(247\) −1.95217e41 −0.262011
\(248\) 2.33451e41 0.291938
\(249\) −1.79519e42 −2.09229
\(250\) −5.47589e41 −0.594983
\(251\) 1.52760e42 1.54782 0.773909 0.633297i \(-0.218299\pi\)
0.773909 + 0.633297i \(0.218299\pi\)
\(252\) 6.18595e40 0.0584652
\(253\) 5.96035e41 0.525608
\(254\) −6.92730e41 −0.570130
\(255\) 9.36421e41 0.719479
\(256\) −8.24460e41 −0.591521
\(257\) −2.72482e42 −1.82603 −0.913016 0.407925i \(-0.866253\pi\)
−0.913016 + 0.407925i \(0.866253\pi\)
\(258\) 5.65074e40 0.0353802
\(259\) 5.05176e41 0.295595
\(260\) −7.20368e41 −0.394022
\(261\) 2.23932e42 1.14527
\(262\) −3.97303e41 −0.190042
\(263\) 4.22055e40 0.0188861 0.00944307 0.999955i \(-0.496994\pi\)
0.00944307 + 0.999955i \(0.496994\pi\)
\(264\) 4.04526e42 1.69386
\(265\) 2.04380e42 0.801005
\(266\) 8.15005e40 0.0299042
\(267\) −5.00116e42 −1.71840
\(268\) 1.16632e42 0.375371
\(269\) −1.30618e42 −0.393858 −0.196929 0.980418i \(-0.563097\pi\)
−0.196929 + 0.980418i \(0.563097\pi\)
\(270\) −2.29415e42 −0.648270
\(271\) −4.11918e41 −0.109106 −0.0545529 0.998511i \(-0.517373\pi\)
−0.0545529 + 0.998511i \(0.517373\pi\)
\(272\) −1.17030e42 −0.290631
\(273\) −2.14302e42 −0.499091
\(274\) 3.54519e42 0.774470
\(275\) −2.20843e42 −0.452648
\(276\) −8.56689e41 −0.164784
\(277\) 7.38232e42 1.33290 0.666449 0.745551i \(-0.267813\pi\)
0.666449 + 0.745551i \(0.267813\pi\)
\(278\) −4.34582e42 −0.736694
\(279\) 2.37451e42 0.378007
\(280\) 1.75644e42 0.262643
\(281\) 4.08223e42 0.573505 0.286752 0.958005i \(-0.407424\pi\)
0.286752 + 0.958005i \(0.407424\pi\)
\(282\) 1.11858e43 1.47675
\(283\) −1.06503e43 −1.32159 −0.660796 0.750565i \(-0.729781\pi\)
−0.660796 + 0.750565i \(0.729781\pi\)
\(284\) −5.43711e41 −0.0634303
\(285\) 2.79688e42 0.306824
\(286\) −1.39624e43 −1.44063
\(287\) −1.08371e42 −0.105191
\(288\) −6.18708e42 −0.565089
\(289\) −9.88997e42 −0.850125
\(290\) 1.08870e43 0.880932
\(291\) 9.94151e42 0.757399
\(292\) 5.02633e42 0.360621
\(293\) 1.90474e43 1.28722 0.643610 0.765353i \(-0.277436\pi\)
0.643610 + 0.765353i \(0.277436\pi\)
\(294\) −2.07410e43 −1.32054
\(295\) −8.03556e42 −0.482093
\(296\) −2.76288e43 −1.56227
\(297\) 1.15788e43 0.617199
\(298\) 2.87932e43 1.44712
\(299\) 1.72691e43 0.818510
\(300\) 3.17420e42 0.141910
\(301\) −1.23832e41 −0.00522298
\(302\) 2.32717e43 0.926203
\(303\) −3.91569e43 −1.47083
\(304\) −3.49543e42 −0.123940
\(305\) −1.56817e42 −0.0524983
\(306\) −1.51794e43 −0.479877
\(307\) −1.39752e43 −0.417288 −0.208644 0.977992i \(-0.566905\pi\)
−0.208644 + 0.977992i \(0.566905\pi\)
\(308\) −1.51789e42 −0.0428156
\(309\) −8.77359e43 −2.33832
\(310\) 1.15442e43 0.290760
\(311\) 2.22377e43 0.529399 0.264700 0.964331i \(-0.414727\pi\)
0.264700 + 0.964331i \(0.414727\pi\)
\(312\) 1.17205e44 2.63778
\(313\) 3.63171e43 0.772833 0.386417 0.922324i \(-0.373713\pi\)
0.386417 + 0.922324i \(0.373713\pi\)
\(314\) −2.47538e43 −0.498165
\(315\) 1.78653e43 0.340076
\(316\) −1.66535e43 −0.299903
\(317\) 5.29385e43 0.902058 0.451029 0.892509i \(-0.351057\pi\)
0.451029 + 0.892509i \(0.351057\pi\)
\(318\) −5.69370e43 −0.918163
\(319\) −5.49476e43 −0.838709
\(320\) −9.25121e43 −1.33682
\(321\) 1.25891e44 1.72249
\(322\) −7.20964e42 −0.0934191
\(323\) 5.20769e42 0.0639147
\(324\) 8.08544e42 0.0940083
\(325\) −6.39855e43 −0.704892
\(326\) −1.42124e44 −1.48374
\(327\) 1.60978e43 0.159287
\(328\) 5.92693e43 0.555953
\(329\) −2.45128e43 −0.218004
\(330\) 2.00040e44 1.68703
\(331\) 6.25551e43 0.500349 0.250174 0.968201i \(-0.419512\pi\)
0.250174 + 0.968201i \(0.419512\pi\)
\(332\) −3.68402e43 −0.279515
\(333\) −2.81022e44 −2.02286
\(334\) 1.52453e44 1.04129
\(335\) 3.36840e44 2.18343
\(336\) −3.83715e43 −0.236087
\(337\) −1.04185e44 −0.608529 −0.304264 0.952588i \(-0.598411\pi\)
−0.304264 + 0.952588i \(0.598411\pi\)
\(338\) −2.43920e44 −1.35271
\(339\) 7.55289e43 0.397757
\(340\) 1.92169e43 0.0961173
\(341\) −5.82647e43 −0.276824
\(342\) −4.53375e43 −0.204645
\(343\) 9.28652e43 0.398296
\(344\) 6.77253e42 0.0276044
\(345\) −2.47415e44 −0.958501
\(346\) 2.19861e44 0.809685
\(347\) −3.07657e44 −1.07721 −0.538606 0.842557i \(-0.681049\pi\)
−0.538606 + 0.842557i \(0.681049\pi\)
\(348\) 7.89769e43 0.262944
\(349\) −2.62767e44 −0.832005 −0.416003 0.909363i \(-0.636569\pi\)
−0.416003 + 0.909363i \(0.636569\pi\)
\(350\) 2.67131e43 0.0804515
\(351\) 3.35476e44 0.961140
\(352\) 1.51816e44 0.413830
\(353\) 7.06671e44 1.83299 0.916494 0.400048i \(-0.131006\pi\)
0.916494 + 0.400048i \(0.131006\pi\)
\(354\) 2.23858e44 0.552606
\(355\) −1.57026e44 −0.368957
\(356\) −1.02632e44 −0.229566
\(357\) 5.71681e43 0.121748
\(358\) −1.03557e44 −0.210003
\(359\) −5.35788e44 −1.03476 −0.517380 0.855756i \(-0.673093\pi\)
−0.517380 + 0.855756i \(0.673093\pi\)
\(360\) −9.77077e44 −1.79736
\(361\) −5.55104e44 −0.972743
\(362\) 3.96204e44 0.661483
\(363\) −3.75165e43 −0.0596838
\(364\) −4.39782e43 −0.0666750
\(365\) 1.45163e45 2.09763
\(366\) 4.36866e43 0.0601768
\(367\) −3.00056e44 −0.394045 −0.197022 0.980399i \(-0.563127\pi\)
−0.197022 + 0.980399i \(0.563127\pi\)
\(368\) 3.09210e44 0.387183
\(369\) 6.02849e44 0.719858
\(370\) −1.36625e45 −1.55597
\(371\) 1.24773e44 0.135543
\(372\) 8.37447e43 0.0867872
\(373\) 1.08201e45 1.06986 0.534932 0.844895i \(-0.320337\pi\)
0.534932 + 0.844895i \(0.320337\pi\)
\(374\) 3.72466e44 0.351426
\(375\) −1.14723e45 −1.03301
\(376\) 1.34064e45 1.15219
\(377\) −1.59201e45 −1.30609
\(378\) −1.40057e44 −0.109698
\(379\) 1.21847e45 0.911229 0.455614 0.890177i \(-0.349420\pi\)
0.455614 + 0.890177i \(0.349420\pi\)
\(380\) 5.73965e43 0.0409895
\(381\) −1.45131e45 −0.989858
\(382\) −1.34484e45 −0.876119
\(383\) −9.53201e43 −0.0593207 −0.0296603 0.999560i \(-0.509443\pi\)
−0.0296603 + 0.999560i \(0.509443\pi\)
\(384\) 1.52105e45 0.904373
\(385\) −4.38372e44 −0.249046
\(386\) −2.28757e45 −1.24193
\(387\) 6.88857e43 0.0357427
\(388\) 2.04016e44 0.101183
\(389\) 1.90493e45 0.903152 0.451576 0.892233i \(-0.350862\pi\)
0.451576 + 0.892233i \(0.350862\pi\)
\(390\) 5.79581e45 2.62714
\(391\) −4.60678e44 −0.199666
\(392\) −2.48585e45 −1.03031
\(393\) −8.32373e44 −0.329950
\(394\) 1.90766e45 0.723296
\(395\) −4.80960e45 −1.74446
\(396\) 8.44376e44 0.293002
\(397\) 3.96399e45 1.31613 0.658065 0.752961i \(-0.271375\pi\)
0.658065 + 0.752961i \(0.271375\pi\)
\(398\) 7.87060e44 0.250066
\(399\) 1.70748e44 0.0519196
\(400\) −1.14568e45 −0.333438
\(401\) −5.53039e44 −0.154074 −0.0770369 0.997028i \(-0.524546\pi\)
−0.0770369 + 0.997028i \(0.524546\pi\)
\(402\) −9.38381e45 −2.50278
\(403\) −1.68812e45 −0.431088
\(404\) −8.03562e44 −0.196492
\(405\) 2.33511e45 0.546820
\(406\) 6.64646e44 0.149068
\(407\) 6.89560e45 1.48139
\(408\) −3.12660e45 −0.643457
\(409\) 3.35495e45 0.661498 0.330749 0.943719i \(-0.392699\pi\)
0.330749 + 0.943719i \(0.392699\pi\)
\(410\) 2.93089e45 0.553710
\(411\) 7.42738e45 1.34463
\(412\) −1.80048e45 −0.312383
\(413\) −4.90568e44 −0.0815781
\(414\) 4.01061e45 0.639299
\(415\) −1.06396e46 −1.62586
\(416\) 4.39862e45 0.644441
\(417\) −9.10474e45 −1.27905
\(418\) 1.11247e45 0.149867
\(419\) −7.69138e45 −0.993708 −0.496854 0.867834i \(-0.665512\pi\)
−0.496854 + 0.867834i \(0.665512\pi\)
\(420\) 6.30078e44 0.0780785
\(421\) −2.77229e45 −0.329535 −0.164767 0.986332i \(-0.552687\pi\)
−0.164767 + 0.986332i \(0.552687\pi\)
\(422\) 3.09338e45 0.352749
\(423\) 1.36361e46 1.49188
\(424\) −6.82401e45 −0.716370
\(425\) 1.70691e45 0.171950
\(426\) 4.37449e45 0.422921
\(427\) −9.57360e43 −0.00888357
\(428\) 2.58349e45 0.230113
\(429\) −2.92520e46 −2.50122
\(430\) 3.34904e44 0.0274930
\(431\) 6.18484e45 0.487502 0.243751 0.969838i \(-0.421622\pi\)
0.243751 + 0.969838i \(0.421622\pi\)
\(432\) 6.00681e45 0.454651
\(433\) 2.21783e46 1.61209 0.806047 0.591852i \(-0.201603\pi\)
0.806047 + 0.591852i \(0.201603\pi\)
\(434\) 7.04770e44 0.0492014
\(435\) 2.28089e46 1.52947
\(436\) 3.30353e44 0.0212796
\(437\) −1.37594e45 −0.0851482
\(438\) −4.04399e46 −2.40444
\(439\) 1.91766e45 0.109557 0.0547787 0.998499i \(-0.482555\pi\)
0.0547787 + 0.998499i \(0.482555\pi\)
\(440\) 2.39752e46 1.31625
\(441\) −2.52844e46 −1.33407
\(442\) 1.07916e46 0.547263
\(443\) −3.00864e46 −1.46658 −0.733290 0.679916i \(-0.762016\pi\)
−0.733290 + 0.679916i \(0.762016\pi\)
\(444\) −9.91114e45 −0.464431
\(445\) −2.96405e46 −1.33532
\(446\) 1.17574e46 0.509275
\(447\) 6.03235e46 2.51249
\(448\) −5.64783e45 −0.226212
\(449\) 5.68788e45 0.219099 0.109549 0.993981i \(-0.465059\pi\)
0.109549 + 0.993981i \(0.465059\pi\)
\(450\) −1.48601e46 −0.550558
\(451\) −1.47925e46 −0.527171
\(452\) 1.54997e45 0.0531376
\(453\) 4.87555e46 1.60807
\(454\) 1.71721e46 0.544937
\(455\) −1.27011e46 −0.387830
\(456\) −9.33846e45 −0.274404
\(457\) 4.67626e46 1.32241 0.661204 0.750206i \(-0.270046\pi\)
0.661204 + 0.750206i \(0.270046\pi\)
\(458\) −3.01918e46 −0.821755
\(459\) −8.94930e45 −0.234459
\(460\) −5.07736e45 −0.128049
\(461\) −3.72978e46 −0.905560 −0.452780 0.891622i \(-0.649568\pi\)
−0.452780 + 0.891622i \(0.649568\pi\)
\(462\) 1.22123e46 0.285472
\(463\) −3.67649e46 −0.827497 −0.413748 0.910391i \(-0.635781\pi\)
−0.413748 + 0.910391i \(0.635781\pi\)
\(464\) −2.85056e46 −0.617825
\(465\) 2.41858e46 0.504817
\(466\) −2.60620e46 −0.523907
\(467\) −2.37743e46 −0.460323 −0.230161 0.973152i \(-0.573925\pi\)
−0.230161 + 0.973152i \(0.573925\pi\)
\(468\) 2.44644e46 0.456280
\(469\) 2.05639e46 0.369472
\(470\) 6.62951e46 1.14754
\(471\) −5.18607e46 −0.864914
\(472\) 2.68298e46 0.431155
\(473\) −1.69029e45 −0.0261753
\(474\) 1.33988e47 1.99960
\(475\) 5.09814e45 0.0733287
\(476\) 1.17318e45 0.0162646
\(477\) −6.94094e46 −0.927569
\(478\) −8.27170e46 −1.06563
\(479\) −8.80315e46 −1.09337 −0.546684 0.837339i \(-0.684110\pi\)
−0.546684 + 0.837339i \(0.684110\pi\)
\(480\) −6.30193e46 −0.754661
\(481\) 1.99788e47 2.30691
\(482\) 5.50084e46 0.612500
\(483\) −1.51046e46 −0.162194
\(484\) −7.69900e44 −0.00797334
\(485\) 5.89206e46 0.588555
\(486\) −1.21039e47 −1.16625
\(487\) 7.13443e46 0.663136 0.331568 0.943431i \(-0.392422\pi\)
0.331568 + 0.943431i \(0.392422\pi\)
\(488\) 5.23593e45 0.0469512
\(489\) −2.97758e47 −2.57607
\(490\) −1.22926e47 −1.02615
\(491\) 8.49115e46 0.683975 0.341988 0.939704i \(-0.388900\pi\)
0.341988 + 0.939704i \(0.388900\pi\)
\(492\) 2.12614e46 0.165273
\(493\) 4.24693e46 0.318606
\(494\) 3.22321e46 0.233382
\(495\) 2.43859e47 1.70431
\(496\) −3.02265e46 −0.203919
\(497\) −9.58638e45 −0.0624335
\(498\) 2.96402e47 1.86367
\(499\) −1.75876e47 −1.06770 −0.533848 0.845581i \(-0.679255\pi\)
−0.533848 + 0.845581i \(0.679255\pi\)
\(500\) −2.35430e46 −0.138003
\(501\) 3.19397e47 1.80789
\(502\) −2.52221e47 −1.37869
\(503\) 1.24051e47 0.654880 0.327440 0.944872i \(-0.393814\pi\)
0.327440 + 0.944872i \(0.393814\pi\)
\(504\) −5.96502e46 −0.304143
\(505\) −2.32072e47 −1.14294
\(506\) −9.84108e46 −0.468175
\(507\) −5.11027e47 −2.34858
\(508\) −2.97832e46 −0.132238
\(509\) 3.71512e47 1.59372 0.796859 0.604166i \(-0.206493\pi\)
0.796859 + 0.604166i \(0.206493\pi\)
\(510\) −1.54612e47 −0.640861
\(511\) 8.86212e46 0.354954
\(512\) 2.87213e47 1.11168
\(513\) −2.67296e46 −0.0999857
\(514\) 4.49893e47 1.62650
\(515\) −5.19987e47 −1.81705
\(516\) 2.42948e45 0.00820623
\(517\) −3.34597e47 −1.09254
\(518\) −8.34092e46 −0.263295
\(519\) 4.60621e47 1.40577
\(520\) 6.94640e47 2.04975
\(521\) 7.89659e45 0.0225309 0.0112655 0.999937i \(-0.496414\pi\)
0.0112655 + 0.999937i \(0.496414\pi\)
\(522\) −3.69732e47 −1.02012
\(523\) 1.18122e47 0.315175 0.157588 0.987505i \(-0.449628\pi\)
0.157588 + 0.987505i \(0.449628\pi\)
\(524\) −1.70816e46 −0.0440790
\(525\) 5.59656e46 0.139680
\(526\) −6.96851e45 −0.0168225
\(527\) 4.50331e46 0.105159
\(528\) −5.23767e47 −1.18316
\(529\) −3.35870e47 −0.734001
\(530\) −3.37450e47 −0.713480
\(531\) 2.72895e47 0.558267
\(532\) 3.50403e45 0.00693609
\(533\) −4.28587e47 −0.820943
\(534\) 8.25738e47 1.53063
\(535\) 7.46124e47 1.33850
\(536\) −1.12467e48 −1.95272
\(537\) −2.16958e47 −0.364607
\(538\) 2.15663e47 0.350821
\(539\) 6.20419e47 0.976971
\(540\) −9.86346e46 −0.150362
\(541\) −6.62658e47 −0.977997 −0.488998 0.872285i \(-0.662638\pi\)
−0.488998 + 0.872285i \(0.662638\pi\)
\(542\) 6.80114e46 0.0971839
\(543\) 8.30070e47 1.14846
\(544\) −1.17340e47 −0.157204
\(545\) 9.54073e46 0.123778
\(546\) 3.53832e47 0.444555
\(547\) −1.12424e47 −0.136798 −0.0683990 0.997658i \(-0.521789\pi\)
−0.0683990 + 0.997658i \(0.521789\pi\)
\(548\) 1.52422e47 0.179633
\(549\) 5.32564e46 0.0607933
\(550\) 3.64631e47 0.403188
\(551\) 1.26846e47 0.135870
\(552\) 8.26092e47 0.857224
\(553\) −2.93624e47 −0.295190
\(554\) −1.21889e48 −1.18725
\(555\) −2.86238e48 −2.70147
\(556\) −1.86844e47 −0.170872
\(557\) 6.68090e47 0.592064 0.296032 0.955178i \(-0.404336\pi\)
0.296032 + 0.955178i \(0.404336\pi\)
\(558\) −3.92053e47 −0.336702
\(559\) −4.89734e46 −0.0407618
\(560\) −2.27418e47 −0.183457
\(561\) 7.80339e47 0.610145
\(562\) −6.74014e47 −0.510838
\(563\) 2.47733e48 1.82007 0.910033 0.414536i \(-0.136056\pi\)
0.910033 + 0.414536i \(0.136056\pi\)
\(564\) 4.80921e47 0.342523
\(565\) 4.47639e47 0.309087
\(566\) 1.75846e48 1.17718
\(567\) 1.42558e47 0.0925309
\(568\) 5.24292e47 0.329972
\(569\) 8.59661e47 0.524641 0.262321 0.964981i \(-0.415512\pi\)
0.262321 + 0.964981i \(0.415512\pi\)
\(570\) −4.61790e47 −0.273297
\(571\) −3.39185e48 −1.94673 −0.973364 0.229266i \(-0.926367\pi\)
−0.973364 + 0.229266i \(0.926367\pi\)
\(572\) −6.00298e47 −0.334146
\(573\) −2.81753e48 −1.52112
\(574\) 1.78930e47 0.0936968
\(575\) −4.50988e47 −0.229075
\(576\) 3.14180e48 1.54805
\(577\) 2.12534e48 1.01590 0.507951 0.861386i \(-0.330403\pi\)
0.507951 + 0.861386i \(0.330403\pi\)
\(578\) 1.63292e48 0.757232
\(579\) −4.79258e48 −2.15623
\(580\) 4.68075e47 0.204327
\(581\) −6.49544e47 −0.275123
\(582\) −1.64143e48 −0.674639
\(583\) 1.70314e48 0.679283
\(584\) −4.84681e48 −1.87599
\(585\) 7.06542e48 2.65406
\(586\) −3.14491e48 −1.14657
\(587\) 1.06269e48 0.376044 0.188022 0.982165i \(-0.439792\pi\)
0.188022 + 0.982165i \(0.439792\pi\)
\(588\) −8.91737e47 −0.306290
\(589\) 1.34504e47 0.0448453
\(590\) 1.32675e48 0.429415
\(591\) 3.99665e48 1.25578
\(592\) 3.57728e48 1.09125
\(593\) −3.98260e48 −1.17953 −0.589766 0.807574i \(-0.700780\pi\)
−0.589766 + 0.807574i \(0.700780\pi\)
\(594\) −1.91176e48 −0.549758
\(595\) 3.38820e47 0.0946068
\(596\) 1.23794e48 0.335651
\(597\) 1.64894e48 0.434163
\(598\) −2.85129e48 −0.729072
\(599\) 5.14535e48 1.27775 0.638874 0.769311i \(-0.279401\pi\)
0.638874 + 0.769311i \(0.279401\pi\)
\(600\) −3.06083e48 −0.738232
\(601\) −1.83878e48 −0.430751 −0.215375 0.976531i \(-0.569098\pi\)
−0.215375 + 0.976531i \(0.569098\pi\)
\(602\) 2.04458e46 0.00465227
\(603\) −1.14394e49 −2.52842
\(604\) 1.00054e48 0.214827
\(605\) −2.22350e47 −0.0463787
\(606\) 6.46516e48 1.31011
\(607\) 2.06846e48 0.407236 0.203618 0.979050i \(-0.434730\pi\)
0.203618 + 0.979050i \(0.434730\pi\)
\(608\) −3.50467e47 −0.0670401
\(609\) 1.39247e48 0.258812
\(610\) 2.58919e47 0.0467618
\(611\) −9.69439e48 −1.70137
\(612\) −6.52623e47 −0.111304
\(613\) 1.02050e48 0.169143 0.0845717 0.996417i \(-0.473048\pi\)
0.0845717 + 0.996417i \(0.473048\pi\)
\(614\) 2.30743e48 0.371691
\(615\) 6.14039e48 0.961350
\(616\) 1.46367e48 0.222732
\(617\) −3.46313e48 −0.512246 −0.256123 0.966644i \(-0.582445\pi\)
−0.256123 + 0.966644i \(0.582445\pi\)
\(618\) 1.44860e49 2.08281
\(619\) 6.56428e48 0.917488 0.458744 0.888568i \(-0.348299\pi\)
0.458744 + 0.888568i \(0.348299\pi\)
\(620\) 4.96332e47 0.0674400
\(621\) 2.36453e48 0.312350
\(622\) −3.67165e48 −0.471552
\(623\) −1.80954e48 −0.225958
\(624\) −1.51753e49 −1.84249
\(625\) −1.05615e49 −1.24688
\(626\) −5.99629e48 −0.688386
\(627\) 2.33070e48 0.260198
\(628\) −1.06427e48 −0.115546
\(629\) −5.32965e48 −0.562746
\(630\) −2.94972e48 −0.302916
\(631\) 5.18692e48 0.518079 0.259039 0.965867i \(-0.416594\pi\)
0.259039 + 0.965867i \(0.416594\pi\)
\(632\) 1.60587e49 1.56013
\(633\) 6.48082e48 0.612442
\(634\) −8.74063e48 −0.803490
\(635\) −8.60152e48 −0.769192
\(636\) −2.44795e48 −0.212962
\(637\) 1.79756e49 1.52140
\(638\) 9.07235e48 0.747064
\(639\) 5.33275e48 0.427254
\(640\) 9.01487e48 0.702765
\(641\) −6.15569e48 −0.466940 −0.233470 0.972364i \(-0.575008\pi\)
−0.233470 + 0.972364i \(0.575008\pi\)
\(642\) −2.07858e49 −1.53428
\(643\) −6.50853e48 −0.467510 −0.233755 0.972296i \(-0.575101\pi\)
−0.233755 + 0.972296i \(0.575101\pi\)
\(644\) −3.09971e47 −0.0216680
\(645\) 7.01644e47 0.0477333
\(646\) −8.59837e47 −0.0569308
\(647\) 2.43533e49 1.56940 0.784698 0.619878i \(-0.212818\pi\)
0.784698 + 0.619878i \(0.212818\pi\)
\(648\) −7.79667e48 −0.489042
\(649\) −6.69620e48 −0.408833
\(650\) 1.05646e49 0.627869
\(651\) 1.47654e48 0.0854233
\(652\) −6.11047e48 −0.344145
\(653\) 4.33343e48 0.237602 0.118801 0.992918i \(-0.462095\pi\)
0.118801 + 0.992918i \(0.462095\pi\)
\(654\) −2.65789e48 −0.141882
\(655\) −4.93325e48 −0.256396
\(656\) −7.67401e48 −0.388334
\(657\) −4.92986e49 −2.42907
\(658\) 4.04729e48 0.194183
\(659\) 2.26798e49 1.05960 0.529802 0.848121i \(-0.322266\pi\)
0.529802 + 0.848121i \(0.322266\pi\)
\(660\) 8.60050e48 0.391295
\(661\) −2.84364e49 −1.25994 −0.629969 0.776620i \(-0.716932\pi\)
−0.629969 + 0.776620i \(0.716932\pi\)
\(662\) −1.03284e49 −0.445676
\(663\) 2.26090e49 0.950156
\(664\) 3.55245e49 1.45407
\(665\) 1.01198e48 0.0403453
\(666\) 4.63992e49 1.80182
\(667\) −1.12210e49 −0.424452
\(668\) 6.55455e48 0.241521
\(669\) 2.46325e49 0.884202
\(670\) −5.56153e49 −1.94485
\(671\) −1.30679e48 −0.0445205
\(672\) −3.84730e48 −0.127701
\(673\) 1.14434e49 0.370077 0.185039 0.982731i \(-0.440759\pi\)
0.185039 + 0.982731i \(0.440759\pi\)
\(674\) 1.72019e49 0.542035
\(675\) −8.76105e48 −0.268993
\(676\) −1.04871e49 −0.313753
\(677\) −3.00594e49 −0.876351 −0.438175 0.898890i \(-0.644375\pi\)
−0.438175 + 0.898890i \(0.644375\pi\)
\(678\) −1.24705e49 −0.354295
\(679\) 3.59708e48 0.0995931
\(680\) −1.85305e49 −0.500014
\(681\) 3.59766e49 0.946119
\(682\) 9.62004e48 0.246576
\(683\) −7.78736e49 −1.94549 −0.972743 0.231885i \(-0.925511\pi\)
−0.972743 + 0.231885i \(0.925511\pi\)
\(684\) −1.94924e48 −0.0474661
\(685\) 4.40201e49 1.04488
\(686\) −1.53329e49 −0.354774
\(687\) −6.32535e49 −1.42673
\(688\) −8.76886e47 −0.0192817
\(689\) 4.93456e49 1.05782
\(690\) 4.08505e49 0.853766
\(691\) 9.61614e49 1.95945 0.979726 0.200340i \(-0.0642046\pi\)
0.979726 + 0.200340i \(0.0642046\pi\)
\(692\) 9.45269e48 0.187801
\(693\) 1.48875e49 0.288397
\(694\) 5.07971e49 0.959506
\(695\) −5.39613e49 −0.993913
\(696\) −7.61562e49 −1.36787
\(697\) 1.14332e49 0.200260
\(698\) 4.33853e49 0.741093
\(699\) −5.46014e49 −0.909606
\(700\) 1.14850e48 0.0186602
\(701\) 1.19741e49 0.189748 0.0948742 0.995489i \(-0.469755\pi\)
0.0948742 + 0.995489i \(0.469755\pi\)
\(702\) −5.53901e49 −0.856116
\(703\) −1.59185e49 −0.239984
\(704\) −7.70923e49 −1.13368
\(705\) 1.38892e50 1.99236
\(706\) −1.16678e50 −1.63270
\(707\) −1.41679e49 −0.193404
\(708\) 9.62454e48 0.128173
\(709\) −4.80032e49 −0.623680 −0.311840 0.950135i \(-0.600945\pi\)
−0.311840 + 0.950135i \(0.600945\pi\)
\(710\) 2.59264e49 0.328641
\(711\) 1.63339e50 2.02009
\(712\) 9.89664e49 1.19423
\(713\) −1.18984e49 −0.140094
\(714\) −9.43898e48 −0.108444
\(715\) −1.73369e50 −1.94363
\(716\) −4.45232e48 −0.0487089
\(717\) −1.73297e50 −1.85015
\(718\) 8.84635e49 0.921693
\(719\) −1.45387e49 −0.147832 −0.0739162 0.997264i \(-0.523550\pi\)
−0.0739162 + 0.997264i \(0.523550\pi\)
\(720\) 1.26509e50 1.25546
\(721\) −3.17450e49 −0.307474
\(722\) 9.16528e49 0.866452
\(723\) 1.15246e50 1.06342
\(724\) 1.70344e49 0.153427
\(725\) 4.15759e49 0.365533
\(726\) 6.19432e48 0.0531622
\(727\) 1.25503e50 1.05148 0.525742 0.850644i \(-0.323788\pi\)
0.525742 + 0.850644i \(0.323788\pi\)
\(728\) 4.24075e49 0.346851
\(729\) −1.96598e50 −1.56981
\(730\) −2.39677e50 −1.86843
\(731\) 1.30644e48 0.00994338
\(732\) 1.87826e48 0.0139576
\(733\) −1.40440e50 −1.01899 −0.509495 0.860473i \(-0.670168\pi\)
−0.509495 + 0.860473i \(0.670168\pi\)
\(734\) 4.95419e49 0.350988
\(735\) −2.57537e50 −1.78161
\(736\) 3.10027e49 0.209430
\(737\) 2.80695e50 1.85163
\(738\) −9.95358e49 −0.641199
\(739\) 2.93572e49 0.184687 0.0923435 0.995727i \(-0.470564\pi\)
0.0923435 + 0.995727i \(0.470564\pi\)
\(740\) −5.87406e49 −0.360897
\(741\) 6.75281e49 0.405197
\(742\) −2.06012e49 −0.120732
\(743\) 1.10795e50 0.634185 0.317093 0.948395i \(-0.397293\pi\)
0.317093 + 0.948395i \(0.397293\pi\)
\(744\) −8.07537e49 −0.451478
\(745\) 3.57521e50 1.95239
\(746\) −1.78650e50 −0.952960
\(747\) 3.61331e50 1.88276
\(748\) 1.60138e49 0.0815111
\(749\) 4.55506e49 0.226497
\(750\) 1.89418e50 0.920132
\(751\) −4.13601e50 −1.96283 −0.981416 0.191892i \(-0.938538\pi\)
−0.981416 + 0.191892i \(0.938538\pi\)
\(752\) −1.73582e50 −0.804806
\(753\) −5.28418e50 −2.39368
\(754\) 2.62856e50 1.16337
\(755\) 2.88961e50 1.24959
\(756\) −6.02161e48 −0.0254437
\(757\) 3.15399e50 1.30221 0.651106 0.758987i \(-0.274305\pi\)
0.651106 + 0.758987i \(0.274305\pi\)
\(758\) −2.01180e50 −0.811659
\(759\) −2.06176e50 −0.812845
\(760\) −5.53465e49 −0.213232
\(761\) −3.65841e50 −1.37740 −0.688702 0.725045i \(-0.741819\pi\)
−0.688702 + 0.725045i \(0.741819\pi\)
\(762\) 2.39624e50 0.881696
\(763\) 5.82458e48 0.0209452
\(764\) −5.78202e49 −0.203210
\(765\) −1.88480e50 −0.647427
\(766\) 1.57382e49 0.0528387
\(767\) −1.94011e50 −0.636661
\(768\) 2.85192e50 0.914778
\(769\) −2.07264e50 −0.649849 −0.324925 0.945740i \(-0.605339\pi\)
−0.324925 + 0.945740i \(0.605339\pi\)
\(770\) 7.23792e49 0.221833
\(771\) 9.42552e50 2.82393
\(772\) −9.83516e49 −0.288057
\(773\) 2.04692e50 0.586084 0.293042 0.956100i \(-0.405332\pi\)
0.293042 + 0.956100i \(0.405332\pi\)
\(774\) −1.13737e49 −0.0318371
\(775\) 4.40859e49 0.120648
\(776\) −1.96729e50 −0.526367
\(777\) −1.74747e50 −0.457133
\(778\) −3.14521e50 −0.804465
\(779\) 3.41484e49 0.0854013
\(780\) 2.49185e50 0.609349
\(781\) −1.30853e50 −0.312889
\(782\) 7.60622e49 0.177849
\(783\) −2.17983e50 −0.498415
\(784\) 3.21860e50 0.719673
\(785\) −3.07365e50 −0.672101
\(786\) 1.37432e50 0.293897
\(787\) −2.74398e50 −0.573882 −0.286941 0.957948i \(-0.592638\pi\)
−0.286941 + 0.957948i \(0.592638\pi\)
\(788\) 8.20177e49 0.167764
\(789\) −1.45994e49 −0.0292071
\(790\) 7.94109e50 1.55384
\(791\) 2.73282e49 0.0523025
\(792\) −8.14219e50 −1.52423
\(793\) −3.78619e49 −0.0693301
\(794\) −6.54491e50 −1.17232
\(795\) −7.06978e50 −1.23874
\(796\) 3.38388e49 0.0580012
\(797\) 3.73868e50 0.626899 0.313450 0.949605i \(-0.398515\pi\)
0.313450 + 0.949605i \(0.398515\pi\)
\(798\) −2.81921e49 −0.0462463
\(799\) 2.58612e50 0.415030
\(800\) −1.14871e50 −0.180359
\(801\) 1.00662e51 1.54631
\(802\) 9.13117e49 0.137238
\(803\) 1.20967e51 1.77887
\(804\) −4.03447e50 −0.580505
\(805\) −8.95210e49 −0.126037
\(806\) 2.78725e50 0.383983
\(807\) 4.51827e50 0.609095
\(808\) 7.74862e50 1.02218
\(809\) −3.87407e50 −0.500114 −0.250057 0.968231i \(-0.580449\pi\)
−0.250057 + 0.968231i \(0.580449\pi\)
\(810\) −3.85548e50 −0.487069
\(811\) −9.21816e50 −1.13967 −0.569835 0.821759i \(-0.692993\pi\)
−0.569835 + 0.821759i \(0.692993\pi\)
\(812\) 2.85758e49 0.0345754
\(813\) 1.42488e50 0.168730
\(814\) −1.13853e51 −1.31952
\(815\) −1.76473e51 −2.00180
\(816\) 4.04823e50 0.449456
\(817\) 3.90203e48 0.00424038
\(818\) −5.53933e50 −0.589216
\(819\) 4.31341e50 0.449110
\(820\) 1.26011e50 0.128430
\(821\) 1.64737e51 1.64357 0.821783 0.569801i \(-0.192980\pi\)
0.821783 + 0.569801i \(0.192980\pi\)
\(822\) −1.22633e51 −1.19771
\(823\) −6.02163e50 −0.575727 −0.287864 0.957671i \(-0.592945\pi\)
−0.287864 + 0.957671i \(0.592945\pi\)
\(824\) 1.73618e51 1.62505
\(825\) 7.63924e50 0.700013
\(826\) 8.09973e49 0.0726641
\(827\) −4.30476e50 −0.378097 −0.189048 0.981968i \(-0.560540\pi\)
−0.189048 + 0.981968i \(0.560540\pi\)
\(828\) 1.72432e50 0.148282
\(829\) 8.88751e50 0.748300 0.374150 0.927368i \(-0.377935\pi\)
0.374150 + 0.927368i \(0.377935\pi\)
\(830\) 1.75670e51 1.44821
\(831\) −2.55364e51 −2.06131
\(832\) −2.23362e51 −1.76543
\(833\) −4.79525e50 −0.371128
\(834\) 1.50328e51 1.13929
\(835\) 1.89298e51 1.40486
\(836\) 4.78297e49 0.0347606
\(837\) −2.31142e50 −0.164507
\(838\) 1.26992e51 0.885126
\(839\) 3.76912e50 0.257280 0.128640 0.991691i \(-0.458939\pi\)
0.128640 + 0.991691i \(0.458939\pi\)
\(840\) −6.07574e50 −0.406174
\(841\) −4.92875e50 −0.322706
\(842\) 4.57730e50 0.293527
\(843\) −1.41210e51 −0.886916
\(844\) 1.32997e50 0.0818179
\(845\) −3.02872e51 −1.82502
\(846\) −2.25144e51 −1.32886
\(847\) −1.35744e49 −0.00784804
\(848\) 8.83551e50 0.500385
\(849\) 3.68407e51 2.04382
\(850\) −2.81826e50 −0.153161
\(851\) 1.40817e51 0.749699
\(852\) 1.88077e50 0.0980940
\(853\) −3.00248e51 −1.53417 −0.767083 0.641547i \(-0.778293\pi\)
−0.767083 + 0.641547i \(0.778293\pi\)
\(854\) 1.58069e49 0.00791286
\(855\) −5.62949e50 −0.276097
\(856\) −2.49122e51 −1.19708
\(857\) −2.46088e50 −0.115858 −0.0579291 0.998321i \(-0.518450\pi\)
−0.0579291 + 0.998321i \(0.518450\pi\)
\(858\) 4.82977e51 2.22792
\(859\) 2.64506e51 1.19551 0.597757 0.801677i \(-0.296059\pi\)
0.597757 + 0.801677i \(0.296059\pi\)
\(860\) 1.43989e49 0.00637684
\(861\) 3.74868e50 0.162676
\(862\) −1.02117e51 −0.434233
\(863\) −9.93861e50 −0.414130 −0.207065 0.978327i \(-0.566391\pi\)
−0.207065 + 0.978327i \(0.566391\pi\)
\(864\) 6.02270e50 0.245924
\(865\) 2.72998e51 1.09239
\(866\) −3.66184e51 −1.43594
\(867\) 3.42107e51 1.31470
\(868\) 3.03009e49 0.0114120
\(869\) −4.00794e51 −1.47936
\(870\) −3.76595e51 −1.36235
\(871\) 8.13268e51 2.88347
\(872\) −3.18554e50 −0.110699
\(873\) −2.00100e51 −0.681550
\(874\) 2.27181e50 0.0758441
\(875\) −4.15096e50 −0.135834
\(876\) −1.73867e51 −0.557695
\(877\) −2.79832e50 −0.0879842 −0.0439921 0.999032i \(-0.514008\pi\)
−0.0439921 + 0.999032i \(0.514008\pi\)
\(878\) −3.16623e50 −0.0975861
\(879\) −6.58876e51 −1.99067
\(880\) −3.10423e51 −0.919404
\(881\) −5.95050e50 −0.172773 −0.0863863 0.996262i \(-0.527532\pi\)
−0.0863863 + 0.996262i \(0.527532\pi\)
\(882\) 4.17469e51 1.18829
\(883\) −3.85350e51 −1.07533 −0.537667 0.843157i \(-0.680694\pi\)
−0.537667 + 0.843157i \(0.680694\pi\)
\(884\) 4.63973e50 0.126934
\(885\) 2.77961e51 0.745550
\(886\) 4.96755e51 1.30633
\(887\) −4.56338e50 −0.117658 −0.0588292 0.998268i \(-0.518737\pi\)
−0.0588292 + 0.998268i \(0.518737\pi\)
\(888\) 9.55716e51 2.41603
\(889\) −5.25119e50 −0.130160
\(890\) 4.89393e51 1.18941
\(891\) 1.94590e51 0.463724
\(892\) 5.05498e50 0.118123
\(893\) 7.72416e50 0.176991
\(894\) −9.95996e51 −2.23795
\(895\) −1.28585e51 −0.283326
\(896\) 5.50354e50 0.118919
\(897\) −5.97362e51 −1.26581
\(898\) −9.39122e50 −0.195158
\(899\) 1.09689e51 0.223548
\(900\) −6.38895e50 −0.127698
\(901\) −1.31637e51 −0.258044
\(902\) 2.44237e51 0.469567
\(903\) 4.28351e49 0.00807726
\(904\) −1.49462e51 −0.276428
\(905\) 4.91960e51 0.892441
\(906\) −8.04998e51 −1.43236
\(907\) −4.12286e51 −0.719566 −0.359783 0.933036i \(-0.617149\pi\)
−0.359783 + 0.933036i \(0.617149\pi\)
\(908\) 7.38298e50 0.126395
\(909\) 7.88139e51 1.32353
\(910\) 2.09707e51 0.345452
\(911\) 6.95561e51 1.12399 0.561996 0.827140i \(-0.310034\pi\)
0.561996 + 0.827140i \(0.310034\pi\)
\(912\) 1.20911e51 0.191672
\(913\) −8.86621e51 −1.37879
\(914\) −7.72094e51 −1.17791
\(915\) 5.42450e50 0.0811877
\(916\) −1.29806e51 −0.190601
\(917\) −3.01173e50 −0.0433863
\(918\) 1.47761e51 0.208840
\(919\) 1.23335e51 0.171027 0.0855136 0.996337i \(-0.472747\pi\)
0.0855136 + 0.996337i \(0.472747\pi\)
\(920\) 4.89602e51 0.666126
\(921\) 4.83420e51 0.645329
\(922\) 6.15821e51 0.806610
\(923\) −3.79125e51 −0.487251
\(924\) 5.25057e50 0.0662136
\(925\) −5.21754e51 −0.645632
\(926\) 6.07023e51 0.737076
\(927\) 1.76592e52 2.10415
\(928\) −2.85810e51 −0.334185
\(929\) −9.97208e51 −1.14422 −0.572112 0.820176i \(-0.693876\pi\)
−0.572112 + 0.820176i \(0.693876\pi\)
\(930\) −3.99330e51 −0.449656
\(931\) −1.43224e51 −0.158269
\(932\) −1.12051e51 −0.121517
\(933\) −7.69232e51 −0.818707
\(934\) 3.92536e51 0.410024
\(935\) 4.62486e51 0.474128
\(936\) −2.35906e52 −2.37363
\(937\) 6.01334e51 0.593844 0.296922 0.954902i \(-0.404040\pi\)
0.296922 + 0.954902i \(0.404040\pi\)
\(938\) −3.39529e51 −0.329100
\(939\) −1.25626e52 −1.19517
\(940\) 2.85029e51 0.266165
\(941\) 1.38035e52 1.26523 0.632617 0.774465i \(-0.281981\pi\)
0.632617 + 0.774465i \(0.281981\pi\)
\(942\) 8.56268e51 0.770405
\(943\) −3.02081e51 −0.266789
\(944\) −3.47384e51 −0.301162
\(945\) −1.73907e51 −0.147999
\(946\) 2.79083e50 0.0233151
\(947\) −9.01648e51 −0.739456 −0.369728 0.929140i \(-0.620549\pi\)
−0.369728 + 0.929140i \(0.620549\pi\)
\(948\) 5.76067e51 0.463796
\(949\) 3.50482e52 2.77017
\(950\) −8.41750e50 −0.0653161
\(951\) −1.83121e52 −1.39502
\(952\) −1.13128e51 −0.0846105
\(953\) 4.32450e51 0.317549 0.158774 0.987315i \(-0.449246\pi\)
0.158774 + 0.987315i \(0.449246\pi\)
\(954\) 1.14601e52 0.826214
\(955\) −1.66987e52 −1.18202
\(956\) −3.55633e51 −0.247166
\(957\) 1.90071e52 1.29705
\(958\) 1.45348e52 0.973897
\(959\) 2.68741e51 0.176810
\(960\) 3.20012e52 2.06738
\(961\) −1.46006e52 −0.926216
\(962\) −3.29869e52 −2.05484
\(963\) −2.53391e52 −1.55000
\(964\) 2.36503e51 0.142066
\(965\) −2.84044e52 −1.67555
\(966\) 2.49391e51 0.144471
\(967\) −1.91085e51 −0.108709 −0.0543543 0.998522i \(-0.517310\pi\)
−0.0543543 + 0.998522i \(0.517310\pi\)
\(968\) 7.42403e50 0.0414783
\(969\) −1.80141e51 −0.0988431
\(970\) −9.72834e51 −0.524244
\(971\) 2.54698e52 1.34800 0.674000 0.738732i \(-0.264575\pi\)
0.674000 + 0.738732i \(0.264575\pi\)
\(972\) −5.20394e51 −0.270504
\(973\) −3.29432e51 −0.168186
\(974\) −1.17796e52 −0.590675
\(975\) 2.21334e52 1.09010
\(976\) −6.77932e50 −0.0327955
\(977\) 2.34465e52 1.11410 0.557048 0.830480i \(-0.311934\pi\)
0.557048 + 0.830480i \(0.311934\pi\)
\(978\) 4.91625e52 2.29459
\(979\) −2.47001e52 −1.13240
\(980\) −5.28508e51 −0.238010
\(981\) −3.24012e51 −0.143335
\(982\) −1.40197e52 −0.609238
\(983\) 1.06892e52 0.456308 0.228154 0.973625i \(-0.426731\pi\)
0.228154 + 0.973625i \(0.426731\pi\)
\(984\) −2.05021e52 −0.859772
\(985\) 2.36871e52 0.975837
\(986\) −7.01207e51 −0.283792
\(987\) 8.47931e51 0.337140
\(988\) 1.38579e51 0.0541314
\(989\) −3.45178e50 −0.0132467
\(990\) −4.02634e52 −1.51808
\(991\) 1.97227e52 0.730597 0.365298 0.930891i \(-0.380967\pi\)
0.365298 + 0.930891i \(0.380967\pi\)
\(992\) −3.03064e51 −0.110301
\(993\) −2.16387e52 −0.773782
\(994\) 1.58280e51 0.0556114
\(995\) 9.77280e51 0.337377
\(996\) 1.27435e52 0.432266
\(997\) −1.44359e52 −0.481149 −0.240575 0.970631i \(-0.577336\pi\)
−0.240575 + 0.970631i \(0.577336\pi\)
\(998\) 2.90388e52 0.951029
\(999\) 2.73555e52 0.880338
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.36.a.a.1.1 3
3.2 odd 2 9.36.a.b.1.3 3
4.3 odd 2 16.36.a.d.1.3 3
5.2 odd 4 25.36.b.a.24.2 6
5.3 odd 4 25.36.b.a.24.5 6
5.4 even 2 25.36.a.a.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.36.a.a.1.1 3 1.1 even 1 trivial
9.36.a.b.1.3 3 3.2 odd 2
16.36.a.d.1.3 3 4.3 odd 2
25.36.a.a.1.3 3 5.4 even 2
25.36.b.a.24.2 6 5.2 odd 4
25.36.b.a.24.5 6 5.3 odd 4