Properties

Label 3.38.a.b.1.1
Level 3
Weight 38
Character 3.1
Self dual yes
Analytic conductor 26.014
Analytic rank 0
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 38 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.0142114374\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{10}\cdot 5\cdot 7 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(105009.\) of \(x^{4} - x^{3} - 11777633936 x^{2} - 35120319927360 x + 11967042111800832000\)
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-520663. q^{2} +3.87420e8 q^{3} +1.33651e11 q^{4} -2.63441e12 q^{5} -2.01716e14 q^{6} +8.34393e15 q^{7} +1.97212e15 q^{8} +1.50095e17 q^{9} +O(q^{10})\) \(q-520663. q^{2} +3.87420e8 q^{3} +1.33651e11 q^{4} -2.63441e12 q^{5} -2.01716e14 q^{6} +8.34393e15 q^{7} +1.97212e15 q^{8} +1.50095e17 q^{9} +1.37164e18 q^{10} -2.00696e19 q^{11} +5.17792e19 q^{12} -1.05373e20 q^{13} -4.34438e21 q^{14} -1.02062e21 q^{15} -1.93957e22 q^{16} +1.77033e22 q^{17} -7.81488e22 q^{18} +4.00776e23 q^{19} -3.52092e23 q^{20} +3.23261e24 q^{21} +1.04495e25 q^{22} -1.07722e25 q^{23} +7.64040e23 q^{24} -6.58195e25 q^{25} +5.48640e25 q^{26} +5.81497e25 q^{27} +1.11518e27 q^{28} +1.59166e27 q^{29} +5.31401e26 q^{30} +4.20936e27 q^{31} +9.82758e27 q^{32} -7.77537e27 q^{33} -9.21743e27 q^{34} -2.19813e28 q^{35} +2.00603e28 q^{36} +1.71917e29 q^{37} -2.08669e29 q^{38} -4.08238e28 q^{39} -5.19537e27 q^{40} -3.95960e29 q^{41} -1.68310e30 q^{42} +3.48956e29 q^{43} -2.68233e30 q^{44} -3.95410e29 q^{45} +5.60870e30 q^{46} -2.42346e30 q^{47} -7.51429e30 q^{48} +5.10591e31 q^{49} +3.42698e31 q^{50} +6.85860e30 q^{51} -1.40833e31 q^{52} -1.34925e32 q^{53} -3.02764e31 q^{54} +5.28715e31 q^{55} +1.64552e31 q^{56} +1.55269e32 q^{57} -8.28718e32 q^{58} +1.06678e33 q^{59} -1.36408e32 q^{60} -7.04574e32 q^{61} -2.19166e33 q^{62} +1.25238e33 q^{63} -2.45114e33 q^{64} +2.77596e32 q^{65} +4.04835e33 q^{66} +7.19450e33 q^{67} +2.36606e33 q^{68} -4.17338e33 q^{69} +1.14449e34 q^{70} +2.35209e34 q^{71} +2.96005e32 q^{72} +2.69218e33 q^{73} -8.95108e34 q^{74} -2.54998e34 q^{75} +5.35642e34 q^{76} -1.67459e35 q^{77} +2.12554e34 q^{78} +2.20044e34 q^{79} +5.10962e34 q^{80} +2.25284e34 q^{81} +2.06162e35 q^{82} -2.35934e35 q^{83} +4.32042e35 q^{84} -4.66376e34 q^{85} -1.81689e35 q^{86} +6.16641e35 q^{87} -3.95797e34 q^{88} +1.13980e35 q^{89} +2.05876e35 q^{90} -8.79227e35 q^{91} -1.43972e36 q^{92} +1.63079e36 q^{93} +1.26181e36 q^{94} -1.05581e36 q^{95} +3.80741e36 q^{96} +8.44145e36 q^{97} -2.65846e37 q^{98} -3.01234e36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 437562q^{2} + 1549681956q^{3} + 346098955492q^{4} - 4099829756904q^{5} + 169520484007818q^{6} + 6605809948153184q^{7} + 140484113342159976q^{8} + 600378541187996484q^{9} + O(q^{10}) \) \( 4q + 437562q^{2} + 1549681956q^{3} + 346098955492q^{4} - 4099829756904q^{5} + 169520484007818q^{6} + 6605809948153184q^{7} + 140484113342159976q^{8} + 600378541187996484q^{9} - 21511023001649316q^{10} + 20953708852195292976q^{11} + \)\(13\!\cdots\!88\)\(q^{12} + 51830892788989874168q^{13} - \)\(18\!\cdots\!12\)\(q^{14} - \)\(15\!\cdots\!56\)\(q^{15} + \)\(55\!\cdots\!40\)\(q^{16} + \)\(81\!\cdots\!28\)\(q^{17} + \)\(65\!\cdots\!02\)\(q^{18} - \)\(54\!\cdots\!32\)\(q^{19} - \)\(35\!\cdots\!76\)\(q^{20} + \)\(25\!\cdots\!76\)\(q^{21} + \)\(23\!\cdots\!76\)\(q^{22} - \)\(61\!\cdots\!88\)\(q^{23} + \)\(54\!\cdots\!64\)\(q^{24} + \)\(95\!\cdots\!16\)\(q^{25} + \)\(42\!\cdots\!88\)\(q^{26} + \)\(23\!\cdots\!76\)\(q^{27} + \)\(24\!\cdots\!48\)\(q^{28} + \)\(41\!\cdots\!36\)\(q^{29} - \)\(83\!\cdots\!24\)\(q^{30} + \)\(89\!\cdots\!64\)\(q^{31} + \)\(36\!\cdots\!84\)\(q^{32} + \)\(81\!\cdots\!64\)\(q^{33} + \)\(31\!\cdots\!24\)\(q^{34} + \)\(42\!\cdots\!40\)\(q^{35} + \)\(51\!\cdots\!32\)\(q^{36} + \)\(55\!\cdots\!24\)\(q^{37} - \)\(73\!\cdots\!68\)\(q^{38} + \)\(20\!\cdots\!52\)\(q^{39} - \)\(26\!\cdots\!52\)\(q^{40} - \)\(86\!\cdots\!76\)\(q^{41} - \)\(70\!\cdots\!68\)\(q^{42} - \)\(50\!\cdots\!80\)\(q^{43} + \)\(28\!\cdots\!36\)\(q^{44} - \)\(61\!\cdots\!84\)\(q^{45} - \)\(14\!\cdots\!96\)\(q^{46} + \)\(42\!\cdots\!20\)\(q^{47} + \)\(21\!\cdots\!60\)\(q^{48} + \)\(40\!\cdots\!20\)\(q^{49} + \)\(10\!\cdots\!14\)\(q^{50} + \)\(31\!\cdots\!92\)\(q^{51} + \)\(18\!\cdots\!68\)\(q^{52} - \)\(12\!\cdots\!88\)\(q^{53} + \)\(25\!\cdots\!78\)\(q^{54} - \)\(32\!\cdots\!24\)\(q^{55} + \)\(49\!\cdots\!80\)\(q^{56} - \)\(21\!\cdots\!48\)\(q^{57} - \)\(75\!\cdots\!56\)\(q^{58} - \)\(13\!\cdots\!88\)\(q^{59} - \)\(13\!\cdots\!64\)\(q^{60} - \)\(12\!\cdots\!60\)\(q^{61} - \)\(37\!\cdots\!92\)\(q^{62} + \)\(99\!\cdots\!64\)\(q^{63} + \)\(85\!\cdots\!28\)\(q^{64} + \)\(15\!\cdots\!68\)\(q^{65} + \)\(92\!\cdots\!64\)\(q^{66} + \)\(16\!\cdots\!48\)\(q^{67} + \)\(63\!\cdots\!84\)\(q^{68} - \)\(23\!\cdots\!32\)\(q^{69} + \)\(82\!\cdots\!60\)\(q^{70} + \)\(10\!\cdots\!88\)\(q^{71} + \)\(21\!\cdots\!96\)\(q^{72} - \)\(19\!\cdots\!48\)\(q^{73} - \)\(89\!\cdots\!12\)\(q^{74} + \)\(36\!\cdots\!24\)\(q^{75} - \)\(95\!\cdots\!68\)\(q^{76} - \)\(25\!\cdots\!92\)\(q^{77} + \)\(16\!\cdots\!32\)\(q^{78} + \)\(42\!\cdots\!20\)\(q^{79} - \)\(95\!\cdots\!36\)\(q^{80} + \)\(90\!\cdots\!64\)\(q^{81} + \)\(33\!\cdots\!48\)\(q^{82} - \)\(46\!\cdots\!24\)\(q^{83} + \)\(95\!\cdots\!72\)\(q^{84} + \)\(18\!\cdots\!12\)\(q^{85} - \)\(36\!\cdots\!04\)\(q^{86} + \)\(16\!\cdots\!04\)\(q^{87} + \)\(42\!\cdots\!56\)\(q^{88} - \)\(31\!\cdots\!52\)\(q^{89} - \)\(32\!\cdots\!36\)\(q^{90} + \)\(26\!\cdots\!24\)\(q^{91} - \)\(16\!\cdots\!16\)\(q^{92} + \)\(34\!\cdots\!96\)\(q^{93} - \)\(57\!\cdots\!48\)\(q^{94} - \)\(89\!\cdots\!56\)\(q^{95} + \)\(14\!\cdots\!76\)\(q^{96} + \)\(44\!\cdots\!48\)\(q^{97} - \)\(43\!\cdots\!78\)\(q^{98} + \)\(31\!\cdots\!96\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −520663. −1.40444 −0.702218 0.711962i \(-0.747807\pi\)
−0.702218 + 0.711962i \(0.747807\pi\)
\(3\) 3.87420e8 0.577350
\(4\) 1.33651e11 0.972441
\(5\) −2.63441e12 −0.308843 −0.154422 0.988005i \(-0.549351\pi\)
−0.154422 + 0.988005i \(0.549351\pi\)
\(6\) −2.01716e14 −0.810852
\(7\) 8.34393e15 1.93668 0.968338 0.249642i \(-0.0803128\pi\)
0.968338 + 0.249642i \(0.0803128\pi\)
\(8\) 1.97212e15 0.0387051
\(9\) 1.50095e17 0.333333
\(10\) 1.37164e18 0.433750
\(11\) −2.00696e19 −1.08836 −0.544182 0.838967i \(-0.683160\pi\)
−0.544182 + 0.838967i \(0.683160\pi\)
\(12\) 5.17792e19 0.561439
\(13\) −1.05373e20 −0.259883 −0.129942 0.991522i \(-0.541479\pi\)
−0.129942 + 0.991522i \(0.541479\pi\)
\(14\) −4.34438e21 −2.71994
\(15\) −1.02062e21 −0.178311
\(16\) −1.93957e22 −1.02680
\(17\) 1.77033e22 0.305315 0.152657 0.988279i \(-0.451217\pi\)
0.152657 + 0.988279i \(0.451217\pi\)
\(18\) −7.81488e22 −0.468145
\(19\) 4.00776e23 0.882999 0.441499 0.897262i \(-0.354447\pi\)
0.441499 + 0.897262i \(0.354447\pi\)
\(20\) −3.52092e23 −0.300332
\(21\) 3.23261e24 1.11814
\(22\) 1.04495e25 1.52854
\(23\) −1.07722e25 −0.692374 −0.346187 0.938166i \(-0.612524\pi\)
−0.346187 + 0.938166i \(0.612524\pi\)
\(24\) 7.64040e23 0.0223464
\(25\) −6.58195e25 −0.904616
\(26\) 5.48640e25 0.364989
\(27\) 5.81497e25 0.192450
\(28\) 1.11518e27 1.88330
\(29\) 1.59166e27 1.40439 0.702193 0.711986i \(-0.252204\pi\)
0.702193 + 0.711986i \(0.252204\pi\)
\(30\) 5.31401e26 0.250426
\(31\) 4.20936e27 1.08149 0.540747 0.841185i \(-0.318142\pi\)
0.540747 + 0.841185i \(0.318142\pi\)
\(32\) 9.82758e27 1.40337
\(33\) −7.77537e27 −0.628367
\(34\) −9.21743e27 −0.428795
\(35\) −2.19813e28 −0.598129
\(36\) 2.00603e28 0.324147
\(37\) 1.71917e29 1.67335 0.836675 0.547700i \(-0.184496\pi\)
0.836675 + 0.547700i \(0.184496\pi\)
\(38\) −2.08669e29 −1.24012
\(39\) −4.08238e28 −0.150044
\(40\) −5.19537e27 −0.0119538
\(41\) −3.95960e29 −0.576965 −0.288483 0.957485i \(-0.593151\pi\)
−0.288483 + 0.957485i \(0.593151\pi\)
\(42\) −1.68310e30 −1.57036
\(43\) 3.48956e29 0.210671 0.105335 0.994437i \(-0.466408\pi\)
0.105335 + 0.994437i \(0.466408\pi\)
\(44\) −2.68233e30 −1.05837
\(45\) −3.95410e29 −0.102948
\(46\) 5.60870e30 0.972395
\(47\) −2.42346e30 −0.282244 −0.141122 0.989992i \(-0.545071\pi\)
−0.141122 + 0.989992i \(0.545071\pi\)
\(48\) −7.51429e30 −0.592823
\(49\) 5.10591e31 2.75072
\(50\) 3.42698e31 1.27048
\(51\) 6.85860e30 0.176274
\(52\) −1.40833e31 −0.252721
\(53\) −1.34925e32 −1.70212 −0.851060 0.525068i \(-0.824040\pi\)
−0.851060 + 0.525068i \(0.824040\pi\)
\(54\) −3.02764e31 −0.270284
\(55\) 5.28715e31 0.336134
\(56\) 1.64552e31 0.0749593
\(57\) 1.55269e32 0.509800
\(58\) −8.28718e32 −1.97237
\(59\) 1.06678e33 1.85061 0.925304 0.379226i \(-0.123810\pi\)
0.925304 + 0.379226i \(0.123810\pi\)
\(60\) −1.36408e32 −0.173397
\(61\) −7.04574e32 −0.659667 −0.329833 0.944039i \(-0.606993\pi\)
−0.329833 + 0.944039i \(0.606993\pi\)
\(62\) −2.19166e33 −1.51889
\(63\) 1.25238e33 0.645559
\(64\) −2.45114e33 −0.944143
\(65\) 2.77596e32 0.0802632
\(66\) 4.04835e33 0.882501
\(67\) 7.19450e33 1.18745 0.593727 0.804667i \(-0.297656\pi\)
0.593727 + 0.804667i \(0.297656\pi\)
\(68\) 2.36606e33 0.296901
\(69\) −4.17338e33 −0.399742
\(70\) 1.14449e34 0.840034
\(71\) 2.35209e34 1.32793 0.663964 0.747765i \(-0.268873\pi\)
0.663964 + 0.747765i \(0.268873\pi\)
\(72\) 2.96005e32 0.0129017
\(73\) 2.69218e33 0.0909140 0.0454570 0.998966i \(-0.485526\pi\)
0.0454570 + 0.998966i \(0.485526\pi\)
\(74\) −8.95108e34 −2.35011
\(75\) −2.54998e34 −0.522280
\(76\) 5.35642e34 0.858664
\(77\) −1.67459e35 −2.10781
\(78\) 2.12554e34 0.210727
\(79\) 2.20044e34 0.172349 0.0861746 0.996280i \(-0.472536\pi\)
0.0861746 + 0.996280i \(0.472536\pi\)
\(80\) 5.10962e34 0.317120
\(81\) 2.25284e34 0.111111
\(82\) 2.06162e35 0.810311
\(83\) −2.35934e35 −0.741046 −0.370523 0.928823i \(-0.620822\pi\)
−0.370523 + 0.928823i \(0.620822\pi\)
\(84\) 4.32042e35 1.08733
\(85\) −4.66376e34 −0.0942944
\(86\) −1.81689e35 −0.295874
\(87\) 6.16641e35 0.810823
\(88\) −3.95797e34 −0.0421253
\(89\) 1.13980e35 0.0984271 0.0492135 0.998788i \(-0.484329\pi\)
0.0492135 + 0.998788i \(0.484329\pi\)
\(90\) 2.05876e35 0.144583
\(91\) −8.79227e35 −0.503310
\(92\) −1.43972e36 −0.673293
\(93\) 1.63079e36 0.624401
\(94\) 1.26181e36 0.396394
\(95\) −1.05581e36 −0.272708
\(96\) 3.80741e36 0.810236
\(97\) 8.44145e36 1.48300 0.741498 0.670955i \(-0.234116\pi\)
0.741498 + 0.670955i \(0.234116\pi\)
\(98\) −2.65846e37 −3.86321
\(99\) −3.01234e36 −0.362788
\(100\) −8.79685e36 −0.879685
\(101\) 6.86236e36 0.570858 0.285429 0.958400i \(-0.407864\pi\)
0.285429 + 0.958400i \(0.407864\pi\)
\(102\) −3.57102e36 −0.247565
\(103\) 1.30579e37 0.755760 0.377880 0.925855i \(-0.376653\pi\)
0.377880 + 0.925855i \(0.376653\pi\)
\(104\) −2.07809e35 −0.0100588
\(105\) −8.51601e36 −0.345330
\(106\) 7.02507e37 2.39052
\(107\) 4.38206e37 1.25337 0.626683 0.779274i \(-0.284412\pi\)
0.626683 + 0.779274i \(0.284412\pi\)
\(108\) 7.77178e36 0.187146
\(109\) −1.05626e37 −0.214476 −0.107238 0.994233i \(-0.534201\pi\)
−0.107238 + 0.994233i \(0.534201\pi\)
\(110\) −2.75282e37 −0.472078
\(111\) 6.66041e37 0.966109
\(112\) −1.61836e38 −1.98858
\(113\) −6.38435e37 −0.665527 −0.332763 0.943010i \(-0.607981\pi\)
−0.332763 + 0.943010i \(0.607981\pi\)
\(114\) −8.08428e37 −0.715981
\(115\) 2.83784e37 0.213835
\(116\) 2.12727e38 1.36568
\(117\) −1.58160e37 −0.0866278
\(118\) −5.55435e38 −2.59906
\(119\) 1.47715e38 0.591296
\(120\) −2.01279e36 −0.00690154
\(121\) 6.27494e37 0.184536
\(122\) 3.66846e38 0.926460
\(123\) −1.53403e38 −0.333111
\(124\) 5.62586e38 1.05169
\(125\) 3.65074e38 0.588227
\(126\) −6.52068e38 −0.906646
\(127\) −2.81304e38 −0.337915 −0.168957 0.985623i \(-0.554040\pi\)
−0.168957 + 0.985623i \(0.554040\pi\)
\(128\) −7.44763e37 −0.0773809
\(129\) 1.35193e38 0.121631
\(130\) −1.44534e38 −0.112724
\(131\) 1.95973e39 1.32641 0.663206 0.748437i \(-0.269195\pi\)
0.663206 + 0.748437i \(0.269195\pi\)
\(132\) −1.03919e39 −0.611050
\(133\) 3.34405e39 1.71008
\(134\) −3.74591e39 −1.66770
\(135\) −1.53190e38 −0.0594369
\(136\) 3.49129e37 0.0118173
\(137\) 1.41955e39 0.419586 0.209793 0.977746i \(-0.432721\pi\)
0.209793 + 0.977746i \(0.432721\pi\)
\(138\) 2.17293e39 0.561412
\(139\) −2.88414e39 −0.651992 −0.325996 0.945371i \(-0.605700\pi\)
−0.325996 + 0.945371i \(0.605700\pi\)
\(140\) −2.93783e39 −0.581645
\(141\) −9.38897e38 −0.162954
\(142\) −1.22465e40 −1.86499
\(143\) 2.11480e39 0.282848
\(144\) −2.91119e39 −0.342267
\(145\) −4.19308e39 −0.433735
\(146\) −1.40172e39 −0.127683
\(147\) 1.97813e40 1.58813
\(148\) 2.29769e40 1.62723
\(149\) −1.54836e40 −0.968111 −0.484055 0.875037i \(-0.660837\pi\)
−0.484055 + 0.875037i \(0.660837\pi\)
\(150\) 1.32768e40 0.733509
\(151\) −5.65320e39 −0.276198 −0.138099 0.990418i \(-0.544099\pi\)
−0.138099 + 0.990418i \(0.544099\pi\)
\(152\) 7.90378e38 0.0341766
\(153\) 2.65716e39 0.101772
\(154\) 8.71900e40 2.96028
\(155\) −1.10892e40 −0.334012
\(156\) −5.45615e39 −0.145909
\(157\) −6.59332e40 −1.56661 −0.783304 0.621638i \(-0.786467\pi\)
−0.783304 + 0.621638i \(0.786467\pi\)
\(158\) −1.14569e40 −0.242053
\(159\) −5.22729e40 −0.982720
\(160\) −2.58899e40 −0.433421
\(161\) −8.98828e40 −1.34090
\(162\) −1.17297e40 −0.156048
\(163\) 3.78789e40 0.449704 0.224852 0.974393i \(-0.427810\pi\)
0.224852 + 0.974393i \(0.427810\pi\)
\(164\) −5.29205e40 −0.561065
\(165\) 2.04835e40 0.194067
\(166\) 1.22842e41 1.04075
\(167\) 1.83545e41 1.39151 0.695757 0.718277i \(-0.255069\pi\)
0.695757 + 0.718277i \(0.255069\pi\)
\(168\) 6.37510e39 0.0432778
\(169\) −1.53297e41 −0.932461
\(170\) 2.42825e40 0.132430
\(171\) 6.01543e40 0.294333
\(172\) 4.66384e40 0.204865
\(173\) 1.65118e41 0.651540 0.325770 0.945449i \(-0.394376\pi\)
0.325770 + 0.945449i \(0.394376\pi\)
\(174\) −3.21062e41 −1.13875
\(175\) −5.49193e41 −1.75195
\(176\) 3.89264e41 1.11753
\(177\) 4.13294e41 1.06845
\(178\) −5.93454e40 −0.138235
\(179\) 4.97609e41 1.04498 0.522489 0.852646i \(-0.325004\pi\)
0.522489 + 0.852646i \(0.325004\pi\)
\(180\) −5.28471e40 −0.100111
\(181\) −7.52929e40 −0.128736 −0.0643680 0.997926i \(-0.520503\pi\)
−0.0643680 + 0.997926i \(0.520503\pi\)
\(182\) 4.57781e41 0.706867
\(183\) −2.72966e41 −0.380859
\(184\) −2.12441e40 −0.0267984
\(185\) −4.52899e41 −0.516803
\(186\) −8.49093e41 −0.876931
\(187\) −3.55297e41 −0.332294
\(188\) −3.23898e41 −0.274466
\(189\) 4.85198e41 0.372714
\(190\) 5.49720e41 0.383001
\(191\) −3.49406e41 −0.220909 −0.110454 0.993881i \(-0.535231\pi\)
−0.110454 + 0.993881i \(0.535231\pi\)
\(192\) −9.49620e41 −0.545101
\(193\) −8.39189e41 −0.437572 −0.218786 0.975773i \(-0.570210\pi\)
−0.218786 + 0.975773i \(0.570210\pi\)
\(194\) −4.39515e42 −2.08277
\(195\) 1.07546e41 0.0463400
\(196\) 6.82411e42 2.67491
\(197\) −7.30118e41 −0.260476 −0.130238 0.991483i \(-0.541574\pi\)
−0.130238 + 0.991483i \(0.541574\pi\)
\(198\) 1.56841e42 0.509512
\(199\) 5.82003e41 0.172244 0.0861218 0.996285i \(-0.472553\pi\)
0.0861218 + 0.996285i \(0.472553\pi\)
\(200\) −1.29804e41 −0.0350133
\(201\) 2.78730e42 0.685577
\(202\) −3.57298e42 −0.801733
\(203\) 1.32807e43 2.71984
\(204\) 9.16661e41 0.171416
\(205\) 1.04312e42 0.178192
\(206\) −6.79875e42 −1.06142
\(207\) −1.61685e42 −0.230791
\(208\) 2.04379e42 0.266848
\(209\) −8.04341e42 −0.961024
\(210\) 4.43398e42 0.484994
\(211\) −1.25054e43 −1.25277 −0.626384 0.779515i \(-0.715466\pi\)
−0.626384 + 0.779515i \(0.715466\pi\)
\(212\) −1.80330e43 −1.65521
\(213\) 9.11248e42 0.766680
\(214\) −2.28158e43 −1.76027
\(215\) −9.19292e41 −0.0650642
\(216\) 1.14678e41 0.00744881
\(217\) 3.51226e43 2.09450
\(218\) 5.49955e42 0.301219
\(219\) 1.04300e42 0.0524892
\(220\) 7.06634e42 0.326870
\(221\) −1.86545e42 −0.0793462
\(222\) −3.46783e43 −1.35684
\(223\) −1.91165e43 −0.688287 −0.344143 0.938917i \(-0.611831\pi\)
−0.344143 + 0.938917i \(0.611831\pi\)
\(224\) 8.20007e43 2.71787
\(225\) −9.87915e42 −0.301539
\(226\) 3.32410e43 0.934690
\(227\) −2.06794e43 −0.535871 −0.267936 0.963437i \(-0.586341\pi\)
−0.267936 + 0.963437i \(0.586341\pi\)
\(228\) 2.07519e43 0.495750
\(229\) 6.73090e42 0.148292 0.0741458 0.997247i \(-0.476377\pi\)
0.0741458 + 0.997247i \(0.476377\pi\)
\(230\) −1.47756e43 −0.300317
\(231\) −6.48772e43 −1.21694
\(232\) 3.13894e42 0.0543570
\(233\) −5.29076e43 −0.846123 −0.423062 0.906101i \(-0.639045\pi\)
−0.423062 + 0.906101i \(0.639045\pi\)
\(234\) 8.23479e42 0.121663
\(235\) 6.38437e42 0.0871692
\(236\) 1.42577e44 1.79961
\(237\) 8.52497e42 0.0995058
\(238\) −7.69096e43 −0.830438
\(239\) 8.90649e43 0.889908 0.444954 0.895553i \(-0.353220\pi\)
0.444954 + 0.895553i \(0.353220\pi\)
\(240\) 1.97957e43 0.183089
\(241\) −1.14469e44 −0.980331 −0.490166 0.871629i \(-0.663064\pi\)
−0.490166 + 0.871629i \(0.663064\pi\)
\(242\) −3.26713e43 −0.259168
\(243\) 8.72796e42 0.0641500
\(244\) −9.41672e43 −0.641487
\(245\) −1.34510e44 −0.849540
\(246\) 7.98713e43 0.467833
\(247\) −4.22311e43 −0.229477
\(248\) 8.30135e42 0.0418594
\(249\) −9.14055e43 −0.427843
\(250\) −1.90080e44 −0.826128
\(251\) −1.57202e44 −0.634590 −0.317295 0.948327i \(-0.602774\pi\)
−0.317295 + 0.948327i \(0.602774\pi\)
\(252\) 1.67382e44 0.627768
\(253\) 2.16194e44 0.753555
\(254\) 1.46465e44 0.474579
\(255\) −1.80684e43 −0.0544409
\(256\) 3.75659e44 1.05282
\(257\) 2.35997e44 0.615380 0.307690 0.951487i \(-0.400444\pi\)
0.307690 + 0.951487i \(0.400444\pi\)
\(258\) −7.03899e43 −0.170823
\(259\) 1.43446e45 3.24074
\(260\) 3.71011e43 0.0780512
\(261\) 2.38899e44 0.468129
\(262\) −1.02036e45 −1.86286
\(263\) −1.02621e45 −1.74604 −0.873022 0.487680i \(-0.837843\pi\)
−0.873022 + 0.487680i \(0.837843\pi\)
\(264\) −1.53340e43 −0.0243210
\(265\) 3.55449e44 0.525688
\(266\) −1.74112e45 −2.40170
\(267\) 4.41583e43 0.0568269
\(268\) 9.61554e44 1.15473
\(269\) 2.39378e44 0.268328 0.134164 0.990959i \(-0.457165\pi\)
0.134164 + 0.990959i \(0.457165\pi\)
\(270\) 7.97605e43 0.0834753
\(271\) −1.10518e45 −1.08019 −0.540094 0.841605i \(-0.681611\pi\)
−0.540094 + 0.841605i \(0.681611\pi\)
\(272\) −3.43367e44 −0.313497
\(273\) −3.40631e44 −0.290586
\(274\) −7.39109e44 −0.589282
\(275\) 1.32097e45 0.984551
\(276\) −5.57778e44 −0.388726
\(277\) −2.08812e45 −1.36107 −0.680534 0.732717i \(-0.738252\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(278\) 1.50166e45 0.915681
\(279\) 6.31802e44 0.360498
\(280\) −4.33498e43 −0.0231507
\(281\) 2.01962e45 1.00973 0.504863 0.863200i \(-0.331543\pi\)
0.504863 + 0.863200i \(0.331543\pi\)
\(282\) 4.88849e44 0.228858
\(283\) 2.43661e45 1.06841 0.534204 0.845356i \(-0.320612\pi\)
0.534204 + 0.845356i \(0.320612\pi\)
\(284\) 3.14360e45 1.29133
\(285\) −4.09041e44 −0.157448
\(286\) −1.10110e45 −0.397241
\(287\) −3.30386e45 −1.11740
\(288\) 1.47507e45 0.467790
\(289\) −3.04869e45 −0.906783
\(290\) 2.18318e45 0.609153
\(291\) 3.27039e45 0.856208
\(292\) 3.59813e44 0.0884084
\(293\) 5.41508e44 0.124898 0.0624488 0.998048i \(-0.480109\pi\)
0.0624488 + 0.998048i \(0.480109\pi\)
\(294\) −1.02994e46 −2.23042
\(295\) −2.81034e45 −0.571547
\(296\) 3.39041e44 0.0647672
\(297\) −1.16704e45 −0.209456
\(298\) 8.06172e45 1.35965
\(299\) 1.13511e45 0.179936
\(300\) −3.40808e45 −0.507887
\(301\) 2.91167e45 0.408001
\(302\) 2.94341e45 0.387903
\(303\) 2.65862e45 0.329585
\(304\) −7.77333e45 −0.906663
\(305\) 1.85614e45 0.203734
\(306\) −1.38349e45 −0.142932
\(307\) 3.09102e45 0.300637 0.150318 0.988638i \(-0.451970\pi\)
0.150318 + 0.988638i \(0.451970\pi\)
\(308\) −2.23812e46 −2.04972
\(309\) 5.05889e45 0.436338
\(310\) 5.77372e45 0.469099
\(311\) −2.15029e46 −1.64600 −0.823001 0.568040i \(-0.807702\pi\)
−0.823001 + 0.568040i \(0.807702\pi\)
\(312\) −8.05093e43 −0.00580746
\(313\) −1.50052e42 −0.000102017 0 −5.10083e−5 1.00000i \(-0.500016\pi\)
−5.10083e−5 1.00000i \(0.500016\pi\)
\(314\) 3.43290e46 2.20020
\(315\) −3.29928e45 −0.199376
\(316\) 2.94092e45 0.167599
\(317\) −7.41293e45 −0.398468 −0.199234 0.979952i \(-0.563845\pi\)
−0.199234 + 0.979952i \(0.563845\pi\)
\(318\) 2.72166e46 1.38017
\(319\) −3.19439e46 −1.52848
\(320\) 6.45729e45 0.291592
\(321\) 1.69770e46 0.723632
\(322\) 4.67987e46 1.88321
\(323\) 7.09504e45 0.269593
\(324\) 3.01095e45 0.108049
\(325\) 6.93561e45 0.235095
\(326\) −1.97221e46 −0.631580
\(327\) −4.09216e45 −0.123828
\(328\) −7.80880e44 −0.0223315
\(329\) −2.02212e46 −0.546616
\(330\) −1.06650e46 −0.272554
\(331\) −2.02313e46 −0.488883 −0.244441 0.969664i \(-0.578605\pi\)
−0.244441 + 0.969664i \(0.578605\pi\)
\(332\) −3.15328e46 −0.720623
\(333\) 2.58038e46 0.557783
\(334\) −9.55651e46 −1.95429
\(335\) −1.89532e46 −0.366737
\(336\) −6.26987e46 −1.14811
\(337\) 1.40951e46 0.244295 0.122148 0.992512i \(-0.461022\pi\)
0.122148 + 0.992512i \(0.461022\pi\)
\(338\) 7.98163e46 1.30958
\(339\) −2.47343e46 −0.384242
\(340\) −6.23317e45 −0.0916957
\(341\) −8.44801e46 −1.17706
\(342\) −3.13201e46 −0.413372
\(343\) 2.71153e47 3.39057
\(344\) 6.88183e44 0.00815404
\(345\) 1.09944e46 0.123458
\(346\) −8.59708e46 −0.915046
\(347\) 1.91978e46 0.193711 0.0968557 0.995298i \(-0.469121\pi\)
0.0968557 + 0.995298i \(0.469121\pi\)
\(348\) 8.24148e46 0.788477
\(349\) 1.61862e47 1.46851 0.734253 0.678876i \(-0.237533\pi\)
0.734253 + 0.678876i \(0.237533\pi\)
\(350\) 2.85945e47 2.46050
\(351\) −6.12743e45 −0.0500146
\(352\) −1.97236e47 −1.52738
\(353\) −9.35860e46 −0.687668 −0.343834 0.939030i \(-0.611726\pi\)
−0.343834 + 0.939030i \(0.611726\pi\)
\(354\) −2.15187e47 −1.50057
\(355\) −6.19636e46 −0.410121
\(356\) 1.52336e46 0.0957145
\(357\) 5.72277e46 0.341385
\(358\) −2.59086e47 −1.46760
\(359\) 3.05449e47 1.64321 0.821603 0.570060i \(-0.193080\pi\)
0.821603 + 0.570060i \(0.193080\pi\)
\(360\) −7.79797e44 −0.00398460
\(361\) −4.53862e46 −0.220313
\(362\) 3.92022e46 0.180802
\(363\) 2.43104e46 0.106542
\(364\) −1.17510e47 −0.489439
\(365\) −7.09229e45 −0.0280781
\(366\) 1.42124e47 0.534892
\(367\) −3.45206e47 −1.23526 −0.617628 0.786471i \(-0.711906\pi\)
−0.617628 + 0.786471i \(0.711906\pi\)
\(368\) 2.08935e47 0.710929
\(369\) −5.94314e46 −0.192322
\(370\) 2.35808e47 0.725816
\(371\) −1.12581e48 −3.29646
\(372\) 2.17957e47 0.607193
\(373\) 5.25222e47 1.39229 0.696145 0.717901i \(-0.254897\pi\)
0.696145 + 0.717901i \(0.254897\pi\)
\(374\) 1.84990e47 0.466685
\(375\) 1.41437e47 0.339613
\(376\) −4.77935e45 −0.0109243
\(377\) −1.67718e47 −0.364977
\(378\) −2.52625e47 −0.523452
\(379\) 1.07624e47 0.212365 0.106183 0.994347i \(-0.466137\pi\)
0.106183 + 0.994347i \(0.466137\pi\)
\(380\) −1.41110e47 −0.265192
\(381\) −1.08983e47 −0.195095
\(382\) 1.81923e47 0.310252
\(383\) 3.92097e44 0.000637112 0 0.000318556 1.00000i \(-0.499899\pi\)
0.000318556 1.00000i \(0.499899\pi\)
\(384\) −2.88536e46 −0.0446759
\(385\) 4.41156e47 0.650982
\(386\) 4.36935e47 0.614542
\(387\) 5.23764e46 0.0702236
\(388\) 1.12821e48 1.44213
\(389\) −1.07652e48 −1.31206 −0.656029 0.754736i \(-0.727765\pi\)
−0.656029 + 0.754736i \(0.727765\pi\)
\(390\) −5.59955e46 −0.0650815
\(391\) −1.90704e47 −0.211392
\(392\) 1.00695e47 0.106467
\(393\) 7.59241e47 0.765804
\(394\) 3.80145e47 0.365822
\(395\) −5.79687e46 −0.0532288
\(396\) −4.02603e47 −0.352790
\(397\) −9.91329e47 −0.829074 −0.414537 0.910032i \(-0.636056\pi\)
−0.414537 + 0.910032i \(0.636056\pi\)
\(398\) −3.03027e47 −0.241905
\(399\) 1.29555e48 0.987317
\(400\) 1.27661e48 0.928859
\(401\) 5.74839e47 0.399370 0.199685 0.979860i \(-0.436008\pi\)
0.199685 + 0.979860i \(0.436008\pi\)
\(402\) −1.45124e48 −0.962849
\(403\) −4.43553e47 −0.281062
\(404\) 9.17163e47 0.555125
\(405\) −5.93490e46 −0.0343159
\(406\) −6.91477e48 −3.81985
\(407\) −3.45030e48 −1.82121
\(408\) 1.35260e46 0.00682269
\(409\) −1.42222e48 −0.685623 −0.342812 0.939404i \(-0.611379\pi\)
−0.342812 + 0.939404i \(0.611379\pi\)
\(410\) −5.43114e47 −0.250259
\(411\) 5.49964e47 0.242248
\(412\) 1.74520e48 0.734932
\(413\) 8.90118e48 3.58403
\(414\) 8.41836e47 0.324132
\(415\) 6.21545e47 0.228867
\(416\) −1.03556e48 −0.364712
\(417\) −1.11737e48 −0.376428
\(418\) 4.18791e48 1.34970
\(419\) −2.58159e47 −0.0796026 −0.0398013 0.999208i \(-0.512672\pi\)
−0.0398013 + 0.999208i \(0.512672\pi\)
\(420\) −1.13818e48 −0.335813
\(421\) 2.31697e48 0.654186 0.327093 0.944992i \(-0.393931\pi\)
0.327093 + 0.944992i \(0.393931\pi\)
\(422\) 6.51108e48 1.75943
\(423\) −3.63748e47 −0.0940814
\(424\) −2.66089e47 −0.0658808
\(425\) −1.16522e48 −0.276193
\(426\) −4.74453e48 −1.07675
\(427\) −5.87892e48 −1.27756
\(428\) 5.85668e48 1.21883
\(429\) 8.19317e47 0.163302
\(430\) 4.78642e47 0.0913785
\(431\) −3.89804e48 −0.712881 −0.356441 0.934318i \(-0.616010\pi\)
−0.356441 + 0.934318i \(0.616010\pi\)
\(432\) −1.12785e48 −0.197608
\(433\) 9.77220e48 1.64046 0.820231 0.572032i \(-0.193845\pi\)
0.820231 + 0.572032i \(0.193845\pi\)
\(434\) −1.82870e49 −2.94160
\(435\) −1.62448e48 −0.250417
\(436\) −1.41170e48 −0.208566
\(437\) −4.31725e48 −0.611365
\(438\) −5.43054e47 −0.0737177
\(439\) −1.19379e48 −0.155359 −0.0776793 0.996978i \(-0.524751\pi\)
−0.0776793 + 0.996978i \(0.524751\pi\)
\(440\) 1.04269e47 0.0130101
\(441\) 7.66370e48 0.916905
\(442\) 9.71271e47 0.111437
\(443\) −1.49848e48 −0.164886 −0.0824429 0.996596i \(-0.526272\pi\)
−0.0824429 + 0.996596i \(0.526272\pi\)
\(444\) 8.90173e48 0.939484
\(445\) −3.00271e47 −0.0303985
\(446\) 9.95328e48 0.966655
\(447\) −5.99865e48 −0.558939
\(448\) −2.04521e49 −1.82850
\(449\) 9.14003e48 0.784134 0.392067 0.919937i \(-0.371760\pi\)
0.392067 + 0.919937i \(0.371760\pi\)
\(450\) 5.14371e48 0.423492
\(451\) 7.94675e48 0.627948
\(452\) −8.53277e48 −0.647185
\(453\) −2.19016e48 −0.159463
\(454\) 1.07670e49 0.752597
\(455\) 2.31624e48 0.155444
\(456\) 3.06209e47 0.0197319
\(457\) −7.21363e48 −0.446379 −0.223190 0.974775i \(-0.571647\pi\)
−0.223190 + 0.974775i \(0.571647\pi\)
\(458\) −3.50453e48 −0.208266
\(459\) 1.02944e48 0.0587579
\(460\) 3.79281e48 0.207942
\(461\) −3.62582e48 −0.190959 −0.0954793 0.995431i \(-0.530438\pi\)
−0.0954793 + 0.995431i \(0.530438\pi\)
\(462\) 3.37792e49 1.70912
\(463\) −2.42342e49 −1.17810 −0.589048 0.808098i \(-0.700497\pi\)
−0.589048 + 0.808098i \(0.700497\pi\)
\(464\) −3.08713e49 −1.44202
\(465\) −4.29617e48 −0.192842
\(466\) 2.75471e49 1.18833
\(467\) 2.11890e49 0.878514 0.439257 0.898362i \(-0.355242\pi\)
0.439257 + 0.898362i \(0.355242\pi\)
\(468\) −2.11382e48 −0.0842404
\(469\) 6.00304e49 2.29971
\(470\) −3.32411e48 −0.122424
\(471\) −2.55439e49 −0.904482
\(472\) 2.10383e48 0.0716280
\(473\) −7.00341e48 −0.229286
\(474\) −4.43864e48 −0.139750
\(475\) −2.63789e49 −0.798775
\(476\) 1.97423e49 0.575001
\(477\) −2.02516e49 −0.567374
\(478\) −4.63728e49 −1.24982
\(479\) −3.96549e49 −1.02823 −0.514115 0.857721i \(-0.671879\pi\)
−0.514115 + 0.857721i \(0.671879\pi\)
\(480\) −1.00303e49 −0.250236
\(481\) −1.81154e49 −0.434876
\(482\) 5.95998e49 1.37681
\(483\) −3.48224e49 −0.774171
\(484\) 8.38653e48 0.179450
\(485\) −2.22382e49 −0.458013
\(486\) −4.54433e48 −0.0900946
\(487\) −3.49809e49 −0.667644 −0.333822 0.942636i \(-0.608338\pi\)
−0.333822 + 0.942636i \(0.608338\pi\)
\(488\) −1.38950e48 −0.0255325
\(489\) 1.46751e49 0.259636
\(490\) 7.00347e49 1.19312
\(491\) 1.54468e49 0.253414 0.126707 0.991940i \(-0.459559\pi\)
0.126707 + 0.991940i \(0.459559\pi\)
\(492\) −2.05025e49 −0.323931
\(493\) 2.81775e49 0.428780
\(494\) 2.19882e49 0.322285
\(495\) 7.93573e48 0.112045
\(496\) −8.16434e49 −1.11048
\(497\) 1.96257e50 2.57177
\(498\) 4.75915e49 0.600878
\(499\) −8.88148e49 −1.08050 −0.540250 0.841504i \(-0.681670\pi\)
−0.540250 + 0.841504i \(0.681670\pi\)
\(500\) 4.87926e49 0.572016
\(501\) 7.11090e49 0.803391
\(502\) 8.18491e49 0.891240
\(503\) −4.16645e49 −0.437279 −0.218639 0.975806i \(-0.570162\pi\)
−0.218639 + 0.975806i \(0.570162\pi\)
\(504\) 2.46984e48 0.0249864
\(505\) −1.80782e49 −0.176305
\(506\) −1.12564e50 −1.05832
\(507\) −5.93905e49 −0.538356
\(508\) −3.75966e49 −0.328602
\(509\) 1.88211e50 1.58623 0.793114 0.609074i \(-0.208459\pi\)
0.793114 + 0.609074i \(0.208459\pi\)
\(510\) 9.40753e48 0.0764588
\(511\) 2.24633e49 0.176071
\(512\) −1.85356e50 −1.40124
\(513\) 2.33050e49 0.169933
\(514\) −1.22875e50 −0.864262
\(515\) −3.43998e49 −0.233411
\(516\) 1.80687e49 0.118279
\(517\) 4.86378e49 0.307184
\(518\) −7.46872e50 −4.55141
\(519\) 6.39700e49 0.376167
\(520\) 5.47453e47 0.00310660
\(521\) 2.50866e50 1.37386 0.686931 0.726723i \(-0.258957\pi\)
0.686931 + 0.726723i \(0.258957\pi\)
\(522\) −1.24386e50 −0.657457
\(523\) 1.68115e49 0.0857682 0.0428841 0.999080i \(-0.486345\pi\)
0.0428841 + 0.999080i \(0.486345\pi\)
\(524\) 2.61921e50 1.28986
\(525\) −2.12769e50 −1.01149
\(526\) 5.34310e50 2.45221
\(527\) 7.45193e49 0.330196
\(528\) 1.50809e50 0.645207
\(529\) −1.26023e50 −0.520618
\(530\) −1.85069e50 −0.738295
\(531\) 1.60119e50 0.616869
\(532\) 4.46936e50 1.66295
\(533\) 4.17236e49 0.149944
\(534\) −2.29916e49 −0.0798098
\(535\) −1.15441e50 −0.387094
\(536\) 1.41884e49 0.0459606
\(537\) 1.92784e50 0.603318
\(538\) −1.24635e50 −0.376850
\(539\) −1.02474e51 −2.99378
\(540\) −2.04740e49 −0.0577988
\(541\) 9.81522e49 0.267763 0.133882 0.990997i \(-0.457256\pi\)
0.133882 + 0.990997i \(0.457256\pi\)
\(542\) 5.75425e50 1.51706
\(543\) −2.91700e49 −0.0743258
\(544\) 1.73980e50 0.428470
\(545\) 2.78261e49 0.0662396
\(546\) 1.77354e50 0.408110
\(547\) −6.05828e50 −1.34767 −0.673836 0.738881i \(-0.735354\pi\)
−0.673836 + 0.738881i \(0.735354\pi\)
\(548\) 1.89725e50 0.408023
\(549\) −1.05753e50 −0.219889
\(550\) −6.87781e50 −1.38274
\(551\) 6.37898e50 1.24007
\(552\) −8.23041e48 −0.0154721
\(553\) 1.83604e50 0.333785
\(554\) 1.08721e51 1.91153
\(555\) −1.75462e50 −0.298376
\(556\) −3.85469e50 −0.634023
\(557\) 1.04564e50 0.166365 0.0831826 0.996534i \(-0.473492\pi\)
0.0831826 + 0.996534i \(0.473492\pi\)
\(558\) −3.28956e50 −0.506297
\(559\) −3.67706e49 −0.0547498
\(560\) 4.26343e50 0.614159
\(561\) −1.37649e50 −0.191850
\(562\) −1.05154e51 −1.41809
\(563\) −6.57533e50 −0.858050 −0.429025 0.903293i \(-0.641143\pi\)
−0.429025 + 0.903293i \(0.641143\pi\)
\(564\) −1.25485e50 −0.158463
\(565\) 1.68190e50 0.205543
\(566\) −1.26865e51 −1.50051
\(567\) 1.87975e50 0.215186
\(568\) 4.63860e49 0.0513976
\(569\) −2.74695e50 −0.294628 −0.147314 0.989090i \(-0.547063\pi\)
−0.147314 + 0.989090i \(0.547063\pi\)
\(570\) 2.12973e50 0.221126
\(571\) −2.57528e50 −0.258855 −0.129428 0.991589i \(-0.541314\pi\)
−0.129428 + 0.991589i \(0.541314\pi\)
\(572\) 2.82646e50 0.275053
\(573\) −1.35367e50 −0.127542
\(574\) 1.72020e51 1.56931
\(575\) 7.09023e50 0.626332
\(576\) −3.67902e50 −0.314714
\(577\) 1.01888e51 0.844058 0.422029 0.906582i \(-0.361318\pi\)
0.422029 + 0.906582i \(0.361318\pi\)
\(578\) 1.58734e51 1.27352
\(579\) −3.25119e50 −0.252632
\(580\) −5.60410e50 −0.421782
\(581\) −1.96861e51 −1.43517
\(582\) −1.70277e51 −1.20249
\(583\) 2.70790e51 1.85253
\(584\) 5.30929e48 0.00351884
\(585\) 4.16657e49 0.0267544
\(586\) −2.81943e50 −0.175411
\(587\) 2.83210e51 1.70728 0.853638 0.520867i \(-0.174391\pi\)
0.853638 + 0.520867i \(0.174391\pi\)
\(588\) 2.64380e51 1.54436
\(589\) 1.68701e51 0.954958
\(590\) 1.46324e51 0.802702
\(591\) −2.82863e50 −0.150386
\(592\) −3.33445e51 −1.71820
\(593\) −3.45126e51 −1.72372 −0.861858 0.507150i \(-0.830699\pi\)
−0.861858 + 0.507150i \(0.830699\pi\)
\(594\) 6.07636e50 0.294167
\(595\) −3.89141e50 −0.182618
\(596\) −2.06940e51 −0.941430
\(597\) 2.25480e50 0.0994449
\(598\) −5.91007e50 −0.252709
\(599\) −4.18318e51 −1.73425 −0.867123 0.498094i \(-0.834034\pi\)
−0.867123 + 0.498094i \(0.834034\pi\)
\(600\) −5.02887e49 −0.0202149
\(601\) −2.49077e51 −0.970860 −0.485430 0.874276i \(-0.661337\pi\)
−0.485430 + 0.874276i \(0.661337\pi\)
\(602\) −1.51600e51 −0.573011
\(603\) 1.07986e51 0.395818
\(604\) −7.55557e50 −0.268586
\(605\) −1.65307e50 −0.0569925
\(606\) −1.38424e51 −0.462881
\(607\) 1.98679e50 0.0644409 0.0322204 0.999481i \(-0.489742\pi\)
0.0322204 + 0.999481i \(0.489742\pi\)
\(608\) 3.93866e51 1.23917
\(609\) 5.14521e51 1.57030
\(610\) −9.66421e50 −0.286131
\(611\) 2.55368e50 0.0733505
\(612\) 3.55133e50 0.0989669
\(613\) 3.22821e50 0.0872856 0.0436428 0.999047i \(-0.486104\pi\)
0.0436428 + 0.999047i \(0.486104\pi\)
\(614\) −1.60938e51 −0.422225
\(615\) 4.04126e50 0.102879
\(616\) −3.30250e50 −0.0815830
\(617\) 2.17195e51 0.520683 0.260342 0.965517i \(-0.416165\pi\)
0.260342 + 0.965517i \(0.416165\pi\)
\(618\) −2.63398e51 −0.612809
\(619\) 3.90977e51 0.882824 0.441412 0.897305i \(-0.354478\pi\)
0.441412 + 0.897305i \(0.354478\pi\)
\(620\) −1.48208e51 −0.324807
\(621\) −6.26402e50 −0.133247
\(622\) 1.11958e52 2.31171
\(623\) 9.51044e50 0.190621
\(624\) 7.91805e50 0.154065
\(625\) 3.82724e51 0.722946
\(626\) 7.81264e47 0.000143276 0
\(627\) −3.11618e51 −0.554847
\(628\) −8.81205e51 −1.52343
\(629\) 3.04349e51 0.510899
\(630\) 1.71781e51 0.280011
\(631\) −7.04074e51 −1.11449 −0.557244 0.830349i \(-0.688141\pi\)
−0.557244 + 0.830349i \(0.688141\pi\)
\(632\) 4.33954e49 0.00667080
\(633\) −4.84483e51 −0.723286
\(634\) 3.85964e51 0.559623
\(635\) 7.41069e50 0.104363
\(636\) −6.98634e51 −0.955637
\(637\) −5.38026e51 −0.714865
\(638\) 1.66320e52 2.14666
\(639\) 3.53036e51 0.442643
\(640\) 1.96201e50 0.0238985
\(641\) −1.31488e52 −1.55601 −0.778003 0.628260i \(-0.783767\pi\)
−0.778003 + 0.628260i \(0.783767\pi\)
\(642\) −8.83929e51 −1.01629
\(643\) 1.39124e52 1.55417 0.777084 0.629397i \(-0.216698\pi\)
0.777084 + 0.629397i \(0.216698\pi\)
\(644\) −1.20129e52 −1.30395
\(645\) −3.56153e50 −0.0375648
\(646\) −3.69413e51 −0.378626
\(647\) 1.43133e52 1.42564 0.712821 0.701346i \(-0.247417\pi\)
0.712821 + 0.701346i \(0.247417\pi\)
\(648\) 4.44287e49 0.00430057
\(649\) −2.14099e52 −2.01413
\(650\) −3.61112e51 −0.330175
\(651\) 1.36072e52 1.20926
\(652\) 5.06256e51 0.437310
\(653\) 5.93896e51 0.498674 0.249337 0.968417i \(-0.419787\pi\)
0.249337 + 0.968417i \(0.419787\pi\)
\(654\) 2.13064e51 0.173909
\(655\) −5.16274e51 −0.409653
\(656\) 7.67992e51 0.592428
\(657\) 4.04081e50 0.0303047
\(658\) 1.05284e52 0.767687
\(659\) −1.23688e52 −0.876898 −0.438449 0.898756i \(-0.644472\pi\)
−0.438449 + 0.898756i \(0.644472\pi\)
\(660\) 2.73765e51 0.188718
\(661\) −2.33294e52 −1.56378 −0.781891 0.623415i \(-0.785745\pi\)
−0.781891 + 0.623415i \(0.785745\pi\)
\(662\) 1.05337e52 0.686605
\(663\) −7.22713e50 −0.0458106
\(664\) −4.65289e50 −0.0286823
\(665\) −8.80959e51 −0.528147
\(666\) −1.34351e52 −0.783371
\(667\) −1.71457e52 −0.972361
\(668\) 2.45310e52 1.35316
\(669\) −7.40614e51 −0.397382
\(670\) 9.86826e51 0.515058
\(671\) 1.41405e52 0.717958
\(672\) 3.17687e52 1.56916
\(673\) 1.92388e52 0.924484 0.462242 0.886754i \(-0.347045\pi\)
0.462242 + 0.886754i \(0.347045\pi\)
\(674\) −7.33880e51 −0.343097
\(675\) −3.82739e51 −0.174093
\(676\) −2.04884e52 −0.906763
\(677\) −6.78443e51 −0.292162 −0.146081 0.989273i \(-0.546666\pi\)
−0.146081 + 0.989273i \(0.546666\pi\)
\(678\) 1.28782e52 0.539644
\(679\) 7.04349e52 2.87208
\(680\) −9.19749e49 −0.00364968
\(681\) −8.01164e51 −0.309385
\(682\) 4.39857e52 1.65310
\(683\) −1.97532e52 −0.722528 −0.361264 0.932464i \(-0.617655\pi\)
−0.361264 + 0.932464i \(0.617655\pi\)
\(684\) 8.03970e51 0.286221
\(685\) −3.73968e51 −0.129586
\(686\) −1.41179e53 −4.76184
\(687\) 2.60769e51 0.0856162
\(688\) −6.76824e51 −0.216317
\(689\) 1.42175e52 0.442353
\(690\) −5.72438e51 −0.173388
\(691\) −2.82676e52 −0.833575 −0.416788 0.909004i \(-0.636844\pi\)
−0.416788 + 0.909004i \(0.636844\pi\)
\(692\) 2.20682e52 0.633584
\(693\) −2.51348e52 −0.702603
\(694\) −9.99557e51 −0.272055
\(695\) 7.59799e51 0.201363
\(696\) 1.21609e51 0.0313830
\(697\) −7.00977e51 −0.176156
\(698\) −8.42758e52 −2.06242
\(699\) −2.04975e52 −0.488510
\(700\) −7.34004e52 −1.70367
\(701\) 6.97961e52 1.57778 0.788892 0.614532i \(-0.210655\pi\)
0.788892 + 0.614532i \(0.210655\pi\)
\(702\) 3.19033e51 0.0702423
\(703\) 6.89002e52 1.47757
\(704\) 4.91933e52 1.02757
\(705\) 2.47344e51 0.0503271
\(706\) 4.87268e52 0.965785
\(707\) 5.72591e52 1.10557
\(708\) 5.52373e52 1.03900
\(709\) −2.71632e52 −0.497766 −0.248883 0.968534i \(-0.580063\pi\)
−0.248883 + 0.968534i \(0.580063\pi\)
\(710\) 3.22622e52 0.575989
\(711\) 3.30275e51 0.0574497
\(712\) 2.24783e50 0.00380963
\(713\) −4.53441e52 −0.748798
\(714\) −2.97964e52 −0.479453
\(715\) −5.57124e51 −0.0873555
\(716\) 6.65060e52 1.01618
\(717\) 3.45056e52 0.513789
\(718\) −1.59036e53 −2.30778
\(719\) 1.18694e53 1.67860 0.839298 0.543672i \(-0.182967\pi\)
0.839298 + 0.543672i \(0.182967\pi\)
\(720\) 7.66926e51 0.105707
\(721\) 1.08954e53 1.46366
\(722\) 2.36309e52 0.309416
\(723\) −4.43477e52 −0.565995
\(724\) −1.00630e52 −0.125188
\(725\) −1.04762e53 −1.27043
\(726\) −1.26575e52 −0.149631
\(727\) −5.48820e52 −0.632475 −0.316237 0.948680i \(-0.602420\pi\)
−0.316237 + 0.948680i \(0.602420\pi\)
\(728\) −1.73394e51 −0.0194807
\(729\) 3.38139e51 0.0370370
\(730\) 3.69269e51 0.0394340
\(731\) 6.17765e51 0.0643209
\(732\) −3.64823e52 −0.370363
\(733\) −1.43675e53 −1.42219 −0.711097 0.703094i \(-0.751801\pi\)
−0.711097 + 0.703094i \(0.751801\pi\)
\(734\) 1.79736e53 1.73484
\(735\) −5.21121e52 −0.490482
\(736\) −1.05865e53 −0.971656
\(737\) −1.44391e53 −1.29238
\(738\) 3.09438e52 0.270104
\(739\) −1.14941e53 −0.978484 −0.489242 0.872148i \(-0.662727\pi\)
−0.489242 + 0.872148i \(0.662727\pi\)
\(740\) −6.05306e52 −0.502560
\(741\) −1.63612e52 −0.132488
\(742\) 5.86167e53 4.62966
\(743\) −7.23269e52 −0.557195 −0.278597 0.960408i \(-0.589870\pi\)
−0.278597 + 0.960408i \(0.589870\pi\)
\(744\) 3.21611e51 0.0241675
\(745\) 4.07900e52 0.298994
\(746\) −2.73464e53 −1.95538
\(747\) −3.54124e52 −0.247015
\(748\) −4.74859e52 −0.323136
\(749\) 3.65636e53 2.42737
\(750\) −7.36411e52 −0.476965
\(751\) −1.89145e53 −1.19524 −0.597621 0.801779i \(-0.703887\pi\)
−0.597621 + 0.801779i \(0.703887\pi\)
\(752\) 4.70046e52 0.289808
\(753\) −6.09031e52 −0.366380
\(754\) 8.73247e52 0.512586
\(755\) 1.48928e52 0.0853018
\(756\) 6.48473e52 0.362442
\(757\) 1.52507e53 0.831796 0.415898 0.909411i \(-0.363467\pi\)
0.415898 + 0.909411i \(0.363467\pi\)
\(758\) −5.60358e52 −0.298253
\(759\) 8.37581e52 0.435065
\(760\) −2.08218e51 −0.0105552
\(761\) −1.93715e53 −0.958399 −0.479199 0.877706i \(-0.659073\pi\)
−0.479199 + 0.877706i \(0.659073\pi\)
\(762\) 5.67434e52 0.273999
\(763\) −8.81334e52 −0.415372
\(764\) −4.66986e52 −0.214821
\(765\) −7.00005e51 −0.0314315
\(766\) −2.04150e50 −0.000894783 0
\(767\) −1.12411e53 −0.480942
\(768\) 1.45538e53 0.607846
\(769\) 3.76633e53 1.53561 0.767805 0.640683i \(-0.221349\pi\)
0.767805 + 0.640683i \(0.221349\pi\)
\(770\) −2.29694e53 −0.914263
\(771\) 9.14300e52 0.355290
\(772\) −1.12159e53 −0.425513
\(773\) 2.46250e53 0.912127 0.456064 0.889947i \(-0.349259\pi\)
0.456064 + 0.889947i \(0.349259\pi\)
\(774\) −2.72705e52 −0.0986245
\(775\) −2.77058e53 −0.978337
\(776\) 1.66475e52 0.0573995
\(777\) 5.55741e53 1.87104
\(778\) 5.60503e53 1.84270
\(779\) −1.58691e53 −0.509460
\(780\) 1.43737e52 0.0450629
\(781\) −4.72055e53 −1.44527
\(782\) 9.92923e52 0.296887
\(783\) 9.25545e52 0.270274
\(784\) −9.90327e53 −2.82443
\(785\) 1.73695e53 0.483836
\(786\) −3.95309e53 −1.07552
\(787\) 3.69252e53 0.981275 0.490638 0.871364i \(-0.336764\pi\)
0.490638 + 0.871364i \(0.336764\pi\)
\(788\) −9.75812e52 −0.253298
\(789\) −3.97575e53 −1.00808
\(790\) 3.01822e52 0.0747565
\(791\) −5.32706e53 −1.28891
\(792\) −5.94069e51 −0.0140418
\(793\) 7.42433e52 0.171436
\(794\) 5.16148e53 1.16438
\(795\) 1.37708e53 0.303506
\(796\) 7.77854e52 0.167497
\(797\) 5.45878e53 1.14846 0.574231 0.818694i \(-0.305301\pi\)
0.574231 + 0.818694i \(0.305301\pi\)
\(798\) −6.74547e53 −1.38662
\(799\) −4.29031e52 −0.0861733
\(800\) −6.46846e53 −1.26951
\(801\) 1.71078e52 0.0328090
\(802\) −2.99297e53 −0.560889
\(803\) −5.40309e52 −0.0989475
\(804\) 3.72526e53 0.666683
\(805\) 2.36788e53 0.414129
\(806\) 2.30942e53 0.394734
\(807\) 9.27399e52 0.154920
\(808\) 1.35334e52 0.0220951
\(809\) −1.10283e54 −1.75979 −0.879893 0.475171i \(-0.842386\pi\)
−0.879893 + 0.475171i \(0.842386\pi\)
\(810\) 3.09008e52 0.0481945
\(811\) 7.85452e53 1.19739 0.598693 0.800979i \(-0.295687\pi\)
0.598693 + 0.800979i \(0.295687\pi\)
\(812\) 1.77498e54 2.64489
\(813\) −4.28168e53 −0.623647
\(814\) 1.79645e54 2.55778
\(815\) −9.97884e52 −0.138888
\(816\) −1.33027e53 −0.180998
\(817\) 1.39853e53 0.186022
\(818\) 7.40497e53 0.962914
\(819\) −1.31967e53 −0.167770
\(820\) 1.39414e53 0.173281
\(821\) 1.01998e54 1.23949 0.619744 0.784804i \(-0.287236\pi\)
0.619744 + 0.784804i \(0.287236\pi\)
\(822\) −2.86346e53 −0.340222
\(823\) −1.92578e52 −0.0223722 −0.0111861 0.999937i \(-0.503561\pi\)
−0.0111861 + 0.999937i \(0.503561\pi\)
\(824\) 2.57517e52 0.0292518
\(825\) 5.11771e53 0.568431
\(826\) −4.63452e54 −5.03354
\(827\) −5.47526e53 −0.581504 −0.290752 0.956798i \(-0.593905\pi\)
−0.290752 + 0.956798i \(0.593905\pi\)
\(828\) −2.16095e53 −0.224431
\(829\) −1.39168e53 −0.141346 −0.0706728 0.997500i \(-0.522515\pi\)
−0.0706728 + 0.997500i \(0.522515\pi\)
\(830\) −3.23616e53 −0.321429
\(831\) −8.08980e53 −0.785813
\(832\) 2.58284e53 0.245367
\(833\) 9.03912e53 0.839835
\(834\) 5.81776e53 0.528669
\(835\) −4.83532e53 −0.429759
\(836\) −1.07501e54 −0.934539
\(837\) 2.44773e53 0.208134
\(838\) 1.34414e53 0.111797
\(839\) −1.43760e54 −1.16961 −0.584804 0.811174i \(-0.698829\pi\)
−0.584804 + 0.811174i \(0.698829\pi\)
\(840\) −1.67946e52 −0.0133660
\(841\) 1.24890e54 0.972302
\(842\) −1.20636e54 −0.918762
\(843\) 7.82443e53 0.582965
\(844\) −1.67136e54 −1.21824
\(845\) 4.03848e53 0.287984
\(846\) 1.89390e53 0.132131
\(847\) 5.23577e53 0.357386
\(848\) 2.61697e54 1.74774
\(849\) 9.43992e53 0.616845
\(850\) 6.06687e53 0.387895
\(851\) −1.85193e54 −1.15858
\(852\) 1.21789e54 0.745550
\(853\) 1.36560e54 0.818024 0.409012 0.912529i \(-0.365873\pi\)
0.409012 + 0.912529i \(0.365873\pi\)
\(854\) 3.06094e54 1.79425
\(855\) −1.58471e53 −0.0909027
\(856\) 8.64194e52 0.0485117
\(857\) −3.06618e54 −1.68443 −0.842213 0.539145i \(-0.818747\pi\)
−0.842213 + 0.539145i \(0.818747\pi\)
\(858\) −4.26588e53 −0.229347
\(859\) −2.99741e53 −0.157715 −0.0788575 0.996886i \(-0.525127\pi\)
−0.0788575 + 0.996886i \(0.525127\pi\)
\(860\) −1.22865e53 −0.0632711
\(861\) −1.27998e54 −0.645128
\(862\) 2.02957e54 1.00120
\(863\) −4.97031e53 −0.239985 −0.119992 0.992775i \(-0.538287\pi\)
−0.119992 + 0.992775i \(0.538287\pi\)
\(864\) 5.71471e53 0.270079
\(865\) −4.34988e53 −0.201224
\(866\) −5.08802e54 −2.30392
\(867\) −1.18113e54 −0.523531
\(868\) 4.69418e54 2.03678
\(869\) −4.41620e53 −0.187579
\(870\) 8.45809e53 0.351695
\(871\) −7.58108e53 −0.308599
\(872\) −2.08307e52 −0.00830134
\(873\) 1.26702e54 0.494332
\(874\) 2.24783e54 0.858624
\(875\) 3.04615e54 1.13921
\(876\) 1.39399e53 0.0510426
\(877\) 5.81431e53 0.208452 0.104226 0.994554i \(-0.466764\pi\)
0.104226 + 0.994554i \(0.466764\pi\)
\(878\) 6.21564e53 0.218191
\(879\) 2.09791e53 0.0721096
\(880\) −1.02548e54 −0.345142
\(881\) −2.08913e54 −0.688510 −0.344255 0.938876i \(-0.611869\pi\)
−0.344255 + 0.938876i \(0.611869\pi\)
\(882\) −3.99021e54 −1.28774
\(883\) −3.47147e54 −1.09709 −0.548543 0.836122i \(-0.684817\pi\)
−0.548543 + 0.836122i \(0.684817\pi\)
\(884\) −2.49320e53 −0.0771595
\(885\) −1.08879e54 −0.329983
\(886\) 7.80205e53 0.231572
\(887\) 5.12164e54 1.48875 0.744376 0.667761i \(-0.232747\pi\)
0.744376 + 0.667761i \(0.232747\pi\)
\(888\) 1.31351e53 0.0373934
\(889\) −2.34718e54 −0.654431
\(890\) 1.56340e53 0.0426928
\(891\) −4.52136e53 −0.120929
\(892\) −2.55495e54 −0.669318
\(893\) −9.71264e53 −0.249221
\(894\) 3.12328e54 0.784994
\(895\) −1.31090e54 −0.322734
\(896\) −6.21425e53 −0.149862
\(897\) 4.39763e53 0.103886
\(898\) −4.75888e54 −1.10127
\(899\) 6.69985e54 1.51884
\(900\) −1.32036e54 −0.293228
\(901\) −2.38862e54 −0.519683
\(902\) −4.13758e54 −0.881913
\(903\) 1.12804e54 0.235560
\(904\) −1.25907e53 −0.0257593
\(905\) 1.98352e53 0.0397592
\(906\) 1.14034e54 0.223956
\(907\) −6.23293e53 −0.119938 −0.0599691 0.998200i \(-0.519100\pi\)
−0.0599691 + 0.998200i \(0.519100\pi\)
\(908\) −2.76383e54 −0.521103
\(909\) 1.03000e54 0.190286
\(910\) −1.20598e54 −0.218311
\(911\) 2.11014e54 0.374302 0.187151 0.982331i \(-0.440075\pi\)
0.187151 + 0.982331i \(0.440075\pi\)
\(912\) −3.01155e54 −0.523462
\(913\) 4.73509e54 0.806527
\(914\) 3.75587e54 0.626911
\(915\) 7.19105e53 0.117626
\(916\) 8.99593e53 0.144205
\(917\) 1.63519e55 2.56883
\(918\) −5.35991e53 −0.0825217
\(919\) 1.59651e52 0.00240899 0.00120450 0.999999i \(-0.499617\pi\)
0.00120450 + 0.999999i \(0.499617\pi\)
\(920\) 5.59657e52 0.00827651
\(921\) 1.19752e54 0.173573
\(922\) 1.88783e54 0.268189
\(923\) −2.47847e54 −0.345106
\(924\) −8.67092e54 −1.18341
\(925\) −1.13155e55 −1.51374
\(926\) 1.26179e55 1.65456
\(927\) 1.95992e54 0.251920
\(928\) 1.56421e55 1.97087
\(929\) −4.23691e54 −0.523309 −0.261654 0.965162i \(-0.584268\pi\)
−0.261654 + 0.965162i \(0.584268\pi\)
\(930\) 2.23686e54 0.270834
\(931\) 2.04633e55 2.42888
\(932\) −7.07117e54 −0.822805
\(933\) −8.33068e54 −0.950320
\(934\) −1.10323e55 −1.23382
\(935\) 9.35998e53 0.102627
\(936\) −3.11910e52 −0.00335294
\(937\) −1.28910e55 −1.35863 −0.679317 0.733845i \(-0.737724\pi\)
−0.679317 + 0.733845i \(0.737724\pi\)
\(938\) −3.12556e55 −3.22980
\(939\) −5.81331e50 −5.88993e−5 0
\(940\) 8.53279e53 0.0847668
\(941\) −4.90525e54 −0.477807 −0.238904 0.971043i \(-0.576788\pi\)
−0.238904 + 0.971043i \(0.576788\pi\)
\(942\) 1.32998e55 1.27029
\(943\) 4.26537e54 0.399476
\(944\) −2.06910e55 −1.90020
\(945\) −1.27821e54 −0.115110
\(946\) 3.64642e54 0.322018
\(947\) −7.97016e54 −0.690228 −0.345114 0.938561i \(-0.612160\pi\)
−0.345114 + 0.938561i \(0.612160\pi\)
\(948\) 1.13937e54 0.0967635
\(949\) −2.83683e53 −0.0236270
\(950\) 1.37345e55 1.12183
\(951\) −2.87192e54 −0.230056
\(952\) 2.91311e53 0.0228862
\(953\) −1.23666e55 −0.952864 −0.476432 0.879211i \(-0.658070\pi\)
−0.476432 + 0.879211i \(0.658070\pi\)
\(954\) 1.05443e55 0.796840
\(955\) 9.20478e53 0.0682262
\(956\) 1.19036e55 0.865383
\(957\) −1.23757e55 −0.882470
\(958\) 2.06469e55 1.44408
\(959\) 1.18447e55 0.812603
\(960\) 2.50169e54 0.168351
\(961\) 2.56972e54 0.169630
\(962\) 9.43205e54 0.610755
\(963\) 6.57723e54 0.417789
\(964\) −1.52989e55 −0.953314
\(965\) 2.21077e54 0.135141
\(966\) 1.81308e55 1.08727
\(967\) −1.79944e55 −1.05864 −0.529318 0.848424i \(-0.677552\pi\)
−0.529318 + 0.848424i \(0.677552\pi\)
\(968\) 1.23749e53 0.00714247
\(969\) 2.74876e54 0.155649
\(970\) 1.15786e55 0.643250
\(971\) 1.81554e55 0.989577 0.494789 0.869013i \(-0.335245\pi\)
0.494789 + 0.869013i \(0.335245\pi\)
\(972\) 1.16650e54 0.0623821
\(973\) −2.40651e55 −1.26270
\(974\) 1.82133e55 0.937664
\(975\) 2.68700e54 0.135732
\(976\) 1.36657e55 0.677346
\(977\) −1.52699e54 −0.0742656 −0.0371328 0.999310i \(-0.511822\pi\)
−0.0371328 + 0.999310i \(0.511822\pi\)
\(978\) −7.64076e54 −0.364643
\(979\) −2.28754e54 −0.107124
\(980\) −1.79775e55 −0.826127
\(981\) −1.58539e54 −0.0714922
\(982\) −8.04259e54 −0.355904
\(983\) −3.38697e55 −1.47086 −0.735431 0.677600i \(-0.763020\pi\)
−0.735431 + 0.677600i \(0.763020\pi\)
\(984\) −3.02529e53 −0.0128931
\(985\) 1.92343e54 0.0804462
\(986\) −1.46710e55 −0.602194
\(987\) −7.83409e54 −0.315589
\(988\) −5.64424e54 −0.223152
\(989\) −3.75903e54 −0.145863
\(990\) −4.13184e54 −0.157359
\(991\) 4.67890e55 1.74897 0.874483 0.485057i \(-0.161201\pi\)
0.874483 + 0.485057i \(0.161201\pi\)
\(992\) 4.13678e55 1.51774
\(993\) −7.83800e54 −0.282257
\(994\) −1.02184e56 −3.61188
\(995\) −1.53323e54 −0.0531962
\(996\) −1.22165e55 −0.416052
\(997\) 4.89388e55 1.63603 0.818017 0.575193i \(-0.195073\pi\)
0.818017 + 0.575193i \(0.195073\pi\)
\(998\) 4.62426e55 1.51749
\(999\) 9.99693e54 0.322036
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 3.38.a.b.1.1 4
3.2 odd 2 9.38.a.c.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.38.a.b.1.1 4 1.1 even 1 trivial
9.38.a.c.1.4 4 3.2 odd 2