Properties

Label 3.38.a.b.1.2
Level 3
Weight 38
Character 3.1
Self dual yes
Analytic conductor 26.014
Analytic rank 0
Dimension 4
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.2
Root \(31743.2\)
Character \(\chi\) = 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-81067.1 q^{2} +3.87420e8 q^{3} -1.30867e11 q^{4} -7.16603e12 q^{5} -3.14071e13 q^{6} -5.96869e15 q^{7} +2.17508e16 q^{8} +1.50095e17 q^{9} +O(q^{10})\) \(q-81067.1 q^{2} +3.87420e8 q^{3} -1.30867e11 q^{4} -7.16603e12 q^{5} -3.14071e13 q^{6} -5.96869e15 q^{7} +2.17508e16 q^{8} +1.50095e17 q^{9} +5.80929e17 q^{10} +2.06526e19 q^{11} -5.07006e19 q^{12} -4.02756e20 q^{13} +4.83865e20 q^{14} -2.77627e21 q^{15} +1.62230e22 q^{16} -4.55890e22 q^{17} -1.21677e22 q^{18} +1.54990e23 q^{19} +9.37797e23 q^{20} -2.31239e24 q^{21} -1.67424e24 q^{22} +2.42540e25 q^{23} +8.42671e24 q^{24} -2.14076e25 q^{25} +3.26502e25 q^{26} +5.81497e25 q^{27} +7.81105e26 q^{28} +1.52016e27 q^{29} +2.25064e26 q^{30} +6.09023e27 q^{31} -4.30456e27 q^{32} +8.00122e27 q^{33} +3.69577e27 q^{34} +4.27718e28 q^{35} -1.96424e28 q^{36} -6.28281e28 q^{37} -1.25646e28 q^{38} -1.56036e29 q^{39} -1.55867e29 q^{40} -8.11303e29 q^{41} +1.87459e29 q^{42} +4.69121e29 q^{43} -2.70274e30 q^{44} -1.07558e30 q^{45} -1.96620e30 q^{46} +1.02212e31 q^{47} +6.28511e30 q^{48} +1.70631e31 q^{49} +1.73545e30 q^{50} -1.76621e31 q^{51} +5.27075e31 q^{52} +5.42457e31 q^{53} -4.71403e30 q^{54} -1.47997e32 q^{55} -1.29824e32 q^{56} +6.00462e31 q^{57} -1.23235e32 q^{58} -5.27739e32 q^{59} +3.63322e32 q^{60} -6.19951e31 q^{61} -4.93717e32 q^{62} -8.95868e32 q^{63} -1.88071e33 q^{64} +2.88616e33 q^{65} -6.48636e32 q^{66} +9.30348e33 q^{67} +5.96611e33 q^{68} +9.39649e33 q^{69} -3.46739e33 q^{70} -2.75965e34 q^{71} +3.26468e33 q^{72} +2.09192e34 q^{73} +5.09329e33 q^{74} -8.29375e33 q^{75} -2.02831e34 q^{76} -1.23269e35 q^{77} +1.26494e34 q^{78} +1.20341e34 q^{79} -1.16254e35 q^{80} +2.25284e34 q^{81} +6.57700e34 q^{82} -3.25180e34 q^{83} +3.02616e35 q^{84} +3.26692e35 q^{85} -3.80303e34 q^{86} +5.88942e35 q^{87} +4.49210e35 q^{88} -1.39444e36 q^{89} +8.71944e34 q^{90} +2.40392e36 q^{91} -3.17405e36 q^{92} +2.35948e36 q^{93} -8.28600e35 q^{94} -1.11066e36 q^{95} -1.66767e36 q^{96} -6.18707e36 q^{97} -1.38326e36 q^{98} +3.09984e36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 437562q^{2} + 1549681956q^{3} + 346098955492q^{4} - 4099829756904q^{5} + 169520484007818q^{6} + 6605809948153184q^{7} + 140484113342159976q^{8} + 600378541187996484q^{9} + O(q^{10}) \) \( 4q + 437562q^{2} + 1549681956q^{3} + 346098955492q^{4} - 4099829756904q^{5} + 169520484007818q^{6} + 6605809948153184q^{7} + 140484113342159976q^{8} + 600378541187996484q^{9} - 21511023001649316q^{10} + 20953708852195292976q^{11} + \)\(13\!\cdots\!88\)\(q^{12} + 51830892788989874168q^{13} - \)\(18\!\cdots\!12\)\(q^{14} - \)\(15\!\cdots\!56\)\(q^{15} + \)\(55\!\cdots\!40\)\(q^{16} + \)\(81\!\cdots\!28\)\(q^{17} + \)\(65\!\cdots\!02\)\(q^{18} - \)\(54\!\cdots\!32\)\(q^{19} - \)\(35\!\cdots\!76\)\(q^{20} + \)\(25\!\cdots\!76\)\(q^{21} + \)\(23\!\cdots\!76\)\(q^{22} - \)\(61\!\cdots\!88\)\(q^{23} + \)\(54\!\cdots\!64\)\(q^{24} + \)\(95\!\cdots\!16\)\(q^{25} + \)\(42\!\cdots\!88\)\(q^{26} + \)\(23\!\cdots\!76\)\(q^{27} + \)\(24\!\cdots\!48\)\(q^{28} + \)\(41\!\cdots\!36\)\(q^{29} - \)\(83\!\cdots\!24\)\(q^{30} + \)\(89\!\cdots\!64\)\(q^{31} + \)\(36\!\cdots\!84\)\(q^{32} + \)\(81\!\cdots\!64\)\(q^{33} + \)\(31\!\cdots\!24\)\(q^{34} + \)\(42\!\cdots\!40\)\(q^{35} + \)\(51\!\cdots\!32\)\(q^{36} + \)\(55\!\cdots\!24\)\(q^{37} - \)\(73\!\cdots\!68\)\(q^{38} + \)\(20\!\cdots\!52\)\(q^{39} - \)\(26\!\cdots\!52\)\(q^{40} - \)\(86\!\cdots\!76\)\(q^{41} - \)\(70\!\cdots\!68\)\(q^{42} - \)\(50\!\cdots\!80\)\(q^{43} + \)\(28\!\cdots\!36\)\(q^{44} - \)\(61\!\cdots\!84\)\(q^{45} - \)\(14\!\cdots\!96\)\(q^{46} + \)\(42\!\cdots\!20\)\(q^{47} + \)\(21\!\cdots\!60\)\(q^{48} + \)\(40\!\cdots\!20\)\(q^{49} + \)\(10\!\cdots\!14\)\(q^{50} + \)\(31\!\cdots\!92\)\(q^{51} + \)\(18\!\cdots\!68\)\(q^{52} - \)\(12\!\cdots\!88\)\(q^{53} + \)\(25\!\cdots\!78\)\(q^{54} - \)\(32\!\cdots\!24\)\(q^{55} + \)\(49\!\cdots\!80\)\(q^{56} - \)\(21\!\cdots\!48\)\(q^{57} - \)\(75\!\cdots\!56\)\(q^{58} - \)\(13\!\cdots\!88\)\(q^{59} - \)\(13\!\cdots\!64\)\(q^{60} - \)\(12\!\cdots\!60\)\(q^{61} - \)\(37\!\cdots\!92\)\(q^{62} + \)\(99\!\cdots\!64\)\(q^{63} + \)\(85\!\cdots\!28\)\(q^{64} + \)\(15\!\cdots\!68\)\(q^{65} + \)\(92\!\cdots\!64\)\(q^{66} + \)\(16\!\cdots\!48\)\(q^{67} + \)\(63\!\cdots\!84\)\(q^{68} - \)\(23\!\cdots\!32\)\(q^{69} + \)\(82\!\cdots\!60\)\(q^{70} + \)\(10\!\cdots\!88\)\(q^{71} + \)\(21\!\cdots\!96\)\(q^{72} - \)\(19\!\cdots\!48\)\(q^{73} - \)\(89\!\cdots\!12\)\(q^{74} + \)\(36\!\cdots\!24\)\(q^{75} - \)\(95\!\cdots\!68\)\(q^{76} - \)\(25\!\cdots\!92\)\(q^{77} + \)\(16\!\cdots\!32\)\(q^{78} + \)\(42\!\cdots\!20\)\(q^{79} - \)\(95\!\cdots\!36\)\(q^{80} + \)\(90\!\cdots\!64\)\(q^{81} + \)\(33\!\cdots\!48\)\(q^{82} - \)\(46\!\cdots\!24\)\(q^{83} + \)\(95\!\cdots\!72\)\(q^{84} + \)\(18\!\cdots\!12\)\(q^{85} - \)\(36\!\cdots\!04\)\(q^{86} + \)\(16\!\cdots\!04\)\(q^{87} + \)\(42\!\cdots\!56\)\(q^{88} - \)\(31\!\cdots\!52\)\(q^{89} - \)\(32\!\cdots\!36\)\(q^{90} + \)\(26\!\cdots\!24\)\(q^{91} - \)\(16\!\cdots\!16\)\(q^{92} + \)\(34\!\cdots\!96\)\(q^{93} - \)\(57\!\cdots\!48\)\(q^{94} - \)\(89\!\cdots\!56\)\(q^{95} + \)\(14\!\cdots\!76\)\(q^{96} + \)\(44\!\cdots\!48\)\(q^{97} - \)\(43\!\cdots\!78\)\(q^{98} + \)\(31\!\cdots\!96\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −81067.1 −0.218670 −0.109335 0.994005i \(-0.534872\pi\)
−0.109335 + 0.994005i \(0.534872\pi\)
\(3\) 3.87420e8 0.577350
\(4\) −1.30867e11 −0.952183
\(5\) −7.16603e12 −0.840105 −0.420052 0.907500i \(-0.637988\pi\)
−0.420052 + 0.907500i \(0.637988\pi\)
\(6\) −3.14071e13 −0.126249
\(7\) −5.96869e15 −1.38537 −0.692684 0.721241i \(-0.743572\pi\)
−0.692684 + 0.721241i \(0.743572\pi\)
\(8\) 2.17508e16 0.426885
\(9\) 1.50095e17 0.333333
\(10\) 5.80929e17 0.183706
\(11\) 2.06526e19 1.11998 0.559989 0.828500i \(-0.310806\pi\)
0.559989 + 0.828500i \(0.310806\pi\)
\(12\) −5.07006e19 −0.549743
\(13\) −4.02756e20 −0.993321 −0.496661 0.867945i \(-0.665441\pi\)
−0.496661 + 0.867945i \(0.665441\pi\)
\(14\) 4.83865e20 0.302939
\(15\) −2.77627e21 −0.485035
\(16\) 1.62230e22 0.858836
\(17\) −4.55890e22 −0.786241 −0.393120 0.919487i \(-0.628604\pi\)
−0.393120 + 0.919487i \(0.628604\pi\)
\(18\) −1.21677e22 −0.0728901
\(19\) 1.54990e23 0.341477 0.170738 0.985316i \(-0.445385\pi\)
0.170738 + 0.985316i \(0.445385\pi\)
\(20\) 9.37797e23 0.799934
\(21\) −2.31239e24 −0.799843
\(22\) −1.67424e24 −0.244906
\(23\) 2.42540e25 1.55890 0.779450 0.626464i \(-0.215499\pi\)
0.779450 + 0.626464i \(0.215499\pi\)
\(24\) 8.42671e24 0.246462
\(25\) −2.14076e25 −0.294224
\(26\) 3.26502e25 0.217210
\(27\) 5.81497e25 0.192450
\(28\) 7.81105e26 1.31912
\(29\) 1.52016e27 1.34130 0.670652 0.741772i \(-0.266015\pi\)
0.670652 + 0.741772i \(0.266015\pi\)
\(30\) 2.25064e26 0.106063
\(31\) 6.09023e27 1.56474 0.782370 0.622814i \(-0.214011\pi\)
0.782370 + 0.622814i \(0.214011\pi\)
\(32\) −4.30456e27 −0.614687
\(33\) 8.00122e27 0.646619
\(34\) 3.69577e27 0.171928
\(35\) 4.27718e28 1.16385
\(36\) −1.96424e28 −0.317394
\(37\) −6.28281e28 −0.611536 −0.305768 0.952106i \(-0.598913\pi\)
−0.305768 + 0.952106i \(0.598913\pi\)
\(38\) −1.25646e28 −0.0746709
\(39\) −1.56036e29 −0.573494
\(40\) −1.55867e29 −0.358628
\(41\) −8.11303e29 −1.18217 −0.591087 0.806608i \(-0.701301\pi\)
−0.591087 + 0.806608i \(0.701301\pi\)
\(42\) 1.87459e29 0.174902
\(43\) 4.69121e29 0.283216 0.141608 0.989923i \(-0.454773\pi\)
0.141608 + 0.989923i \(0.454773\pi\)
\(44\) −2.70274e30 −1.06642
\(45\) −1.07558e30 −0.280035
\(46\) −1.96620e30 −0.340885
\(47\) 1.02212e31 1.19039 0.595196 0.803581i \(-0.297074\pi\)
0.595196 + 0.803581i \(0.297074\pi\)
\(48\) 6.28511e30 0.495849
\(49\) 1.70631e31 0.919245
\(50\) 1.73545e30 0.0643380
\(51\) −1.76621e31 −0.453936
\(52\) 5.27075e31 0.945824
\(53\) 5.42457e31 0.684323 0.342162 0.939641i \(-0.388841\pi\)
0.342162 + 0.939641i \(0.388841\pi\)
\(54\) −4.71403e30 −0.0420831
\(55\) −1.47997e32 −0.940898
\(56\) −1.29824e32 −0.591392
\(57\) 6.00462e31 0.197152
\(58\) −1.23235e32 −0.293303
\(59\) −5.27739e32 −0.915496 −0.457748 0.889082i \(-0.651344\pi\)
−0.457748 + 0.889082i \(0.651344\pi\)
\(60\) 3.63322e32 0.461842
\(61\) −6.19951e31 −0.0580437 −0.0290219 0.999579i \(-0.509239\pi\)
−0.0290219 + 0.999579i \(0.509239\pi\)
\(62\) −4.93717e32 −0.342162
\(63\) −8.95868e32 −0.461789
\(64\) −1.88071e33 −0.724423
\(65\) 2.88616e33 0.834494
\(66\) −6.48636e32 −0.141396
\(67\) 9.30348e33 1.53554 0.767771 0.640725i \(-0.221366\pi\)
0.767771 + 0.640725i \(0.221366\pi\)
\(68\) 5.96611e33 0.748645
\(69\) 9.39649e33 0.900031
\(70\) −3.46739e33 −0.254500
\(71\) −2.75965e34 −1.55802 −0.779012 0.627010i \(-0.784279\pi\)
−0.779012 + 0.627010i \(0.784279\pi\)
\(72\) 3.26468e33 0.142295
\(73\) 2.09192e34 0.706436 0.353218 0.935541i \(-0.385087\pi\)
0.353218 + 0.935541i \(0.385087\pi\)
\(74\) 5.09329e33 0.133725
\(75\) −8.29375e33 −0.169870
\(76\) −2.02831e34 −0.325149
\(77\) −1.23269e35 −1.55158
\(78\) 1.26494e34 0.125406
\(79\) 1.20341e34 0.0942567 0.0471283 0.998889i \(-0.484993\pi\)
0.0471283 + 0.998889i \(0.484993\pi\)
\(80\) −1.16254e35 −0.721512
\(81\) 2.25284e34 0.111111
\(82\) 6.57700e34 0.258506
\(83\) −3.25180e34 −0.102136 −0.0510681 0.998695i \(-0.516263\pi\)
−0.0510681 + 0.998695i \(0.516263\pi\)
\(84\) 3.02616e35 0.761597
\(85\) 3.26692e35 0.660525
\(86\) −3.80303e34 −0.0619310
\(87\) 5.88942e35 0.774402
\(88\) 4.49210e35 0.478101
\(89\) −1.39444e36 −1.20416 −0.602081 0.798435i \(-0.705662\pi\)
−0.602081 + 0.798435i \(0.705662\pi\)
\(90\) 8.71944e34 0.0612353
\(91\) 2.40392e36 1.37612
\(92\) −3.17405e36 −1.48436
\(93\) 2.35948e36 0.903403
\(94\) −8.28600e35 −0.260303
\(95\) −1.11066e36 −0.286876
\(96\) −1.66767e36 −0.354889
\(97\) −6.18707e36 −1.08695 −0.543473 0.839427i \(-0.682891\pi\)
−0.543473 + 0.839427i \(0.682891\pi\)
\(98\) −1.38326e36 −0.201012
\(99\) 3.09984e36 0.373326
\(100\) 2.80155e36 0.280155
\(101\) −1.95203e37 −1.62384 −0.811918 0.583772i \(-0.801576\pi\)
−0.811918 + 0.583772i \(0.801576\pi\)
\(102\) 1.43182e36 0.0992624
\(103\) 3.11250e37 1.80144 0.900722 0.434397i \(-0.143038\pi\)
0.900722 + 0.434397i \(0.143038\pi\)
\(104\) −8.76026e36 −0.424033
\(105\) 1.65707e37 0.671952
\(106\) −4.39754e36 −0.149641
\(107\) 2.91526e37 0.833831 0.416915 0.908945i \(-0.363111\pi\)
0.416915 + 0.908945i \(0.363111\pi\)
\(108\) −7.60989e36 −0.183248
\(109\) 4.34807e37 0.882890 0.441445 0.897288i \(-0.354466\pi\)
0.441445 + 0.897288i \(0.354466\pi\)
\(110\) 1.19977e37 0.205747
\(111\) −2.43409e37 −0.353070
\(112\) −9.68298e37 −1.18980
\(113\) 1.30612e38 1.36155 0.680774 0.732493i \(-0.261644\pi\)
0.680774 + 0.732493i \(0.261644\pi\)
\(114\) −4.86777e36 −0.0431112
\(115\) −1.73805e38 −1.30964
\(116\) −1.98939e38 −1.27717
\(117\) −6.04515e37 −0.331107
\(118\) 4.27822e37 0.200192
\(119\) 2.72107e38 1.08923
\(120\) −6.03860e37 −0.207054
\(121\) 8.64886e37 0.254349
\(122\) 5.02576e36 0.0126924
\(123\) −3.14315e38 −0.682529
\(124\) −7.97010e38 −1.48992
\(125\) 6.74805e38 1.08728
\(126\) 7.26255e37 0.100980
\(127\) 1.12113e39 1.34675 0.673373 0.739303i \(-0.264845\pi\)
0.673373 + 0.739303i \(0.264845\pi\)
\(128\) 7.44077e38 0.773096
\(129\) 1.81747e38 0.163515
\(130\) −2.33973e38 −0.182479
\(131\) 1.51287e39 1.02396 0.511980 0.858997i \(-0.328912\pi\)
0.511980 + 0.858997i \(0.328912\pi\)
\(132\) −1.04710e39 −0.615700
\(133\) −9.25086e38 −0.473071
\(134\) −7.54206e38 −0.335777
\(135\) −4.16703e38 −0.161678
\(136\) −9.91598e38 −0.335634
\(137\) −5.50009e38 −0.162570 −0.0812848 0.996691i \(-0.525902\pi\)
−0.0812848 + 0.996691i \(0.525902\pi\)
\(138\) −7.61747e38 −0.196810
\(139\) 2.01159e39 0.454743 0.227372 0.973808i \(-0.426987\pi\)
0.227372 + 0.973808i \(0.426987\pi\)
\(140\) −5.59742e39 −1.10820
\(141\) 3.95989e39 0.687273
\(142\) 2.23717e39 0.340693
\(143\) −8.31793e39 −1.11250
\(144\) 2.43498e39 0.286279
\(145\) −1.08935e40 −1.12684
\(146\) −1.69586e39 −0.154477
\(147\) 6.61061e39 0.530726
\(148\) 8.22213e39 0.582294
\(149\) 1.36577e40 0.853949 0.426975 0.904264i \(-0.359579\pi\)
0.426975 + 0.904264i \(0.359579\pi\)
\(150\) 6.72350e38 0.0371456
\(151\) 3.14967e40 1.53883 0.769415 0.638749i \(-0.220548\pi\)
0.769415 + 0.638749i \(0.220548\pi\)
\(152\) 3.37115e39 0.145771
\(153\) −6.84267e39 −0.262080
\(154\) 9.99304e39 0.339285
\(155\) −4.36428e40 −1.31455
\(156\) 2.04199e40 0.546072
\(157\) −1.57563e40 −0.374378 −0.187189 0.982324i \(-0.559938\pi\)
−0.187189 + 0.982324i \(0.559938\pi\)
\(158\) −9.75569e38 −0.0206111
\(159\) 2.10159e40 0.395094
\(160\) 3.08466e40 0.516401
\(161\) −1.44765e41 −2.15965
\(162\) −1.82631e39 −0.0242967
\(163\) −9.57266e40 −1.13648 −0.568240 0.822863i \(-0.692376\pi\)
−0.568240 + 0.822863i \(0.692376\pi\)
\(164\) 1.06173e41 1.12565
\(165\) −5.73370e40 −0.543228
\(166\) 2.63614e39 0.0223342
\(167\) 1.21079e41 0.917942 0.458971 0.888451i \(-0.348218\pi\)
0.458971 + 0.888451i \(0.348218\pi\)
\(168\) −5.02964e40 −0.341441
\(169\) −2.18871e39 −0.0133132
\(170\) −2.64840e40 −0.144437
\(171\) 2.32631e40 0.113826
\(172\) −6.13925e40 −0.269674
\(173\) 2.37365e41 0.936621 0.468310 0.883564i \(-0.344863\pi\)
0.468310 + 0.883564i \(0.344863\pi\)
\(174\) −4.77438e40 −0.169339
\(175\) 1.27775e41 0.407608
\(176\) 3.35046e41 0.961877
\(177\) −2.04457e41 −0.528562
\(178\) 1.13043e41 0.263315
\(179\) 3.87672e41 0.814110 0.407055 0.913404i \(-0.366556\pi\)
0.407055 + 0.913404i \(0.366556\pi\)
\(180\) 1.40758e41 0.266645
\(181\) −9.37245e41 −1.60250 −0.801252 0.598326i \(-0.795833\pi\)
−0.801252 + 0.598326i \(0.795833\pi\)
\(182\) −1.94879e41 −0.300916
\(183\) −2.40182e40 −0.0335115
\(184\) 5.27544e41 0.665470
\(185\) 4.50228e41 0.513754
\(186\) −1.91276e41 −0.197547
\(187\) −9.41530e41 −0.880572
\(188\) −1.33761e42 −1.13347
\(189\) −3.47078e41 −0.266614
\(190\) 9.00381e40 0.0627314
\(191\) −7.76327e41 −0.490826 −0.245413 0.969419i \(-0.578924\pi\)
−0.245413 + 0.969419i \(0.578924\pi\)
\(192\) −7.28625e41 −0.418246
\(193\) 1.83873e42 0.958758 0.479379 0.877608i \(-0.340862\pi\)
0.479379 + 0.877608i \(0.340862\pi\)
\(194\) 5.01568e41 0.237683
\(195\) 1.11816e42 0.481795
\(196\) −2.23300e42 −0.875290
\(197\) 2.38170e42 0.849693 0.424847 0.905265i \(-0.360328\pi\)
0.424847 + 0.905265i \(0.360328\pi\)
\(198\) −2.51295e41 −0.0816353
\(199\) 3.72548e42 1.10256 0.551278 0.834322i \(-0.314141\pi\)
0.551278 + 0.834322i \(0.314141\pi\)
\(200\) −4.65633e41 −0.125600
\(201\) 3.60436e42 0.886545
\(202\) 1.58246e42 0.355085
\(203\) −9.07338e42 −1.85820
\(204\) 2.31139e42 0.432230
\(205\) 5.81382e42 0.993150
\(206\) −2.52321e42 −0.393922
\(207\) 3.64039e42 0.519633
\(208\) −6.53389e42 −0.853100
\(209\) 3.20093e42 0.382446
\(210\) −1.34334e42 −0.146936
\(211\) 5.66343e42 0.567354 0.283677 0.958920i \(-0.408446\pi\)
0.283677 + 0.958920i \(0.408446\pi\)
\(212\) −7.09897e42 −0.651601
\(213\) −1.06914e43 −0.899525
\(214\) −2.36332e42 −0.182334
\(215\) −3.36173e42 −0.237932
\(216\) 1.26480e42 0.0821540
\(217\) −3.63507e43 −2.16774
\(218\) −3.52486e42 −0.193062
\(219\) 8.10454e42 0.407861
\(220\) 1.93679e43 0.895907
\(221\) 1.83612e43 0.780989
\(222\) 1.97325e42 0.0772060
\(223\) 3.12041e43 1.12350 0.561749 0.827308i \(-0.310129\pi\)
0.561749 + 0.827308i \(0.310129\pi\)
\(224\) 2.56926e43 0.851567
\(225\) −3.21317e42 −0.0980746
\(226\) −1.05884e43 −0.297730
\(227\) −1.69570e43 −0.439411 −0.219705 0.975566i \(-0.570510\pi\)
−0.219705 + 0.975566i \(0.570510\pi\)
\(228\) −7.85807e42 −0.187725
\(229\) −4.70639e42 −0.103689 −0.0518444 0.998655i \(-0.516510\pi\)
−0.0518444 + 0.998655i \(0.516510\pi\)
\(230\) 1.40899e43 0.286379
\(231\) −4.77568e43 −0.895806
\(232\) 3.30648e43 0.572582
\(233\) 8.91929e43 1.42641 0.713207 0.700953i \(-0.247242\pi\)
0.713207 + 0.700953i \(0.247242\pi\)
\(234\) 4.90063e42 0.0724033
\(235\) −7.32451e43 −1.00005
\(236\) 6.90636e43 0.871720
\(237\) 4.66225e42 0.0544191
\(238\) −2.20589e43 −0.238183
\(239\) −7.05888e43 −0.705301 −0.352651 0.935755i \(-0.614720\pi\)
−0.352651 + 0.935755i \(0.614720\pi\)
\(240\) −4.50393e43 −0.416565
\(241\) −1.03720e44 −0.888271 −0.444136 0.895960i \(-0.646489\pi\)
−0.444136 + 0.895960i \(0.646489\pi\)
\(242\) −7.01138e42 −0.0556185
\(243\) 8.72796e42 0.0641500
\(244\) 8.11311e42 0.0552682
\(245\) −1.22275e44 −0.772262
\(246\) 2.54806e43 0.149249
\(247\) −6.24230e43 −0.339196
\(248\) 1.32467e44 0.667963
\(249\) −1.25982e43 −0.0589684
\(250\) −5.47045e43 −0.237757
\(251\) −1.06389e44 −0.429470 −0.214735 0.976672i \(-0.568889\pi\)
−0.214735 + 0.976672i \(0.568889\pi\)
\(252\) 1.17240e44 0.439708
\(253\) 5.00907e44 1.74593
\(254\) −9.08865e43 −0.294494
\(255\) 1.26567e44 0.381354
\(256\) 1.98162e44 0.555369
\(257\) −2.17429e44 −0.566962 −0.283481 0.958978i \(-0.591489\pi\)
−0.283481 + 0.958978i \(0.591489\pi\)
\(258\) −1.47337e43 −0.0357559
\(259\) 3.75001e44 0.847202
\(260\) −3.77703e44 −0.794591
\(261\) 2.28168e44 0.447101
\(262\) −1.22644e44 −0.223910
\(263\) 5.98155e44 1.01773 0.508865 0.860847i \(-0.330065\pi\)
0.508865 + 0.860847i \(0.330065\pi\)
\(264\) 1.74033e44 0.276032
\(265\) −3.88726e44 −0.574903
\(266\) 7.49940e43 0.103447
\(267\) −5.40235e44 −0.695224
\(268\) −1.21752e45 −1.46212
\(269\) −1.15434e45 −1.29394 −0.646972 0.762514i \(-0.723965\pi\)
−0.646972 + 0.762514i \(0.723965\pi\)
\(270\) 3.37809e43 0.0353542
\(271\) 1.52915e45 1.49457 0.747287 0.664501i \(-0.231356\pi\)
0.747287 + 0.664501i \(0.231356\pi\)
\(272\) −7.39589e44 −0.675252
\(273\) 9.31329e44 0.794501
\(274\) 4.45877e43 0.0355492
\(275\) −4.42122e44 −0.329524
\(276\) −1.22969e45 −0.856995
\(277\) −5.76088e44 −0.375503 −0.187751 0.982217i \(-0.560120\pi\)
−0.187751 + 0.982217i \(0.560120\pi\)
\(278\) −1.63074e44 −0.0994388
\(279\) 9.14111e44 0.521580
\(280\) 9.30321e44 0.496832
\(281\) 9.77482e44 0.488699 0.244350 0.969687i \(-0.421426\pi\)
0.244350 + 0.969687i \(0.421426\pi\)
\(282\) −3.21017e44 −0.150286
\(283\) −2.00519e45 −0.879237 −0.439619 0.898185i \(-0.644886\pi\)
−0.439619 + 0.898185i \(0.644886\pi\)
\(284\) 3.61147e45 1.48352
\(285\) −4.30293e44 −0.165628
\(286\) 6.74311e44 0.243270
\(287\) 4.84241e45 1.63775
\(288\) −6.46091e44 −0.204896
\(289\) −1.28373e45 −0.381826
\(290\) 8.83107e44 0.246406
\(291\) −2.39700e45 −0.627548
\(292\) −2.73764e45 −0.672656
\(293\) 2.43417e45 0.561435 0.280717 0.959790i \(-0.409428\pi\)
0.280717 + 0.959790i \(0.409428\pi\)
\(294\) −5.35903e44 −0.116054
\(295\) 3.78179e45 0.769113
\(296\) −1.36656e45 −0.261055
\(297\) 1.20094e45 0.215540
\(298\) −1.10719e45 −0.186733
\(299\) −9.76843e45 −1.54849
\(300\) 1.08538e45 0.161748
\(301\) −2.80004e45 −0.392359
\(302\) −2.55334e45 −0.336497
\(303\) −7.56258e45 −0.937522
\(304\) 2.51439e45 0.293273
\(305\) 4.44258e44 0.0487628
\(306\) 5.54716e44 0.0573092
\(307\) −5.23869e45 −0.509522 −0.254761 0.967004i \(-0.581997\pi\)
−0.254761 + 0.967004i \(0.581997\pi\)
\(308\) 1.61318e46 1.47739
\(309\) 1.20585e46 1.04006
\(310\) 3.53799e45 0.287452
\(311\) −1.81624e46 −1.39029 −0.695146 0.718869i \(-0.744660\pi\)
−0.695146 + 0.718869i \(0.744660\pi\)
\(312\) −3.39390e45 −0.244816
\(313\) −1.26517e45 −0.0860161 −0.0430081 0.999075i \(-0.513694\pi\)
−0.0430081 + 0.999075i \(0.513694\pi\)
\(314\) 1.27732e45 0.0818655
\(315\) 6.41982e45 0.387952
\(316\) −1.57487e45 −0.0897496
\(317\) −1.12945e46 −0.607117 −0.303558 0.952813i \(-0.598175\pi\)
−0.303558 + 0.952813i \(0.598175\pi\)
\(318\) −1.70370e45 −0.0863954
\(319\) 3.13952e46 1.50223
\(320\) 1.34772e46 0.608591
\(321\) 1.12943e46 0.481412
\(322\) 1.17356e46 0.472252
\(323\) −7.06583e45 −0.268483
\(324\) −2.94823e45 −0.105798
\(325\) 8.62204e45 0.292259
\(326\) 7.76028e45 0.248515
\(327\) 1.68453e46 0.509737
\(328\) −1.76465e46 −0.504652
\(329\) −6.10069e46 −1.64913
\(330\) 4.64815e45 0.118788
\(331\) −3.60502e46 −0.871145 −0.435572 0.900154i \(-0.643454\pi\)
−0.435572 + 0.900154i \(0.643454\pi\)
\(332\) 4.25554e45 0.0972524
\(333\) −9.43016e45 −0.203845
\(334\) −9.81555e45 −0.200727
\(335\) −6.66690e46 −1.29002
\(336\) −3.75138e46 −0.686934
\(337\) 3.50453e46 0.607403 0.303701 0.952767i \(-0.401777\pi\)
0.303701 + 0.952767i \(0.401777\pi\)
\(338\) 1.77432e44 0.00291121
\(339\) 5.06019e46 0.786090
\(340\) −4.27533e46 −0.628940
\(341\) 1.25779e47 1.75247
\(342\) −1.88588e45 −0.0248903
\(343\) 8.94695e45 0.111875
\(344\) 1.02038e46 0.120901
\(345\) −6.73355e46 −0.756121
\(346\) −1.92425e46 −0.204811
\(347\) 1.32955e47 1.34156 0.670781 0.741655i \(-0.265959\pi\)
0.670781 + 0.741655i \(0.265959\pi\)
\(348\) −7.70731e46 −0.737373
\(349\) 5.30968e46 0.481724 0.240862 0.970559i \(-0.422570\pi\)
0.240862 + 0.970559i \(0.422570\pi\)
\(350\) −1.03584e46 −0.0891319
\(351\) −2.34201e46 −0.191165
\(352\) −8.89001e46 −0.688435
\(353\) 9.80590e46 0.720535 0.360268 0.932849i \(-0.382685\pi\)
0.360268 + 0.932849i \(0.382685\pi\)
\(354\) 1.65747e46 0.115581
\(355\) 1.97757e47 1.30890
\(356\) 1.82487e47 1.14658
\(357\) 1.05420e47 0.628869
\(358\) −3.14274e46 −0.178022
\(359\) −3.23469e47 −1.74015 −0.870073 0.492924i \(-0.835928\pi\)
−0.870073 + 0.492924i \(0.835928\pi\)
\(360\) −2.33948e46 −0.119543
\(361\) −1.81986e47 −0.883394
\(362\) 7.59797e46 0.350420
\(363\) 3.35075e46 0.146848
\(364\) −3.14594e47 −1.31031
\(365\) −1.49908e47 −0.593480
\(366\) 1.94708e45 0.00732798
\(367\) 5.30423e46 0.189802 0.0949009 0.995487i \(-0.469747\pi\)
0.0949009 + 0.995487i \(0.469747\pi\)
\(368\) 3.93472e47 1.33884
\(369\) −1.21772e47 −0.394058
\(370\) −3.64987e46 −0.112343
\(371\) −3.23775e47 −0.948040
\(372\) −3.08778e47 −0.860205
\(373\) 1.73609e47 0.460212 0.230106 0.973166i \(-0.426093\pi\)
0.230106 + 0.973166i \(0.426093\pi\)
\(374\) 7.63272e46 0.192555
\(375\) 2.61433e47 0.627744
\(376\) 2.22318e47 0.508160
\(377\) −6.12254e47 −1.33235
\(378\) 2.81366e46 0.0583006
\(379\) −7.77135e45 −0.0153345 −0.00766727 0.999971i \(-0.502441\pi\)
−0.00766727 + 0.999971i \(0.502441\pi\)
\(380\) 1.45349e47 0.273159
\(381\) 4.34348e47 0.777545
\(382\) 6.29346e46 0.107329
\(383\) −1.37051e47 −0.222692 −0.111346 0.993782i \(-0.535516\pi\)
−0.111346 + 0.993782i \(0.535516\pi\)
\(384\) 2.88271e47 0.446347
\(385\) 8.83347e47 1.30349
\(386\) −1.49061e47 −0.209652
\(387\) 7.04126e46 0.0944055
\(388\) 8.09683e47 1.03497
\(389\) −5.22275e47 −0.636549 −0.318274 0.947999i \(-0.603103\pi\)
−0.318274 + 0.947999i \(0.603103\pi\)
\(390\) −9.06458e46 −0.105354
\(391\) −1.10572e48 −1.22567
\(392\) 3.71137e47 0.392412
\(393\) 5.86118e47 0.591184
\(394\) −1.93078e47 −0.185803
\(395\) −8.62367e46 −0.0791855
\(396\) −4.05667e47 −0.355474
\(397\) 1.08193e48 0.904844 0.452422 0.891804i \(-0.350560\pi\)
0.452422 + 0.891804i \(0.350560\pi\)
\(398\) −3.02014e47 −0.241096
\(399\) −3.58397e47 −0.273128
\(400\) −3.47295e47 −0.252690
\(401\) −1.57080e48 −1.09132 −0.545659 0.838007i \(-0.683721\pi\)
−0.545659 + 0.838007i \(0.683721\pi\)
\(402\) −2.92195e47 −0.193861
\(403\) −2.45287e48 −1.55429
\(404\) 2.55457e48 1.54619
\(405\) −1.61439e47 −0.0933450
\(406\) 7.35553e47 0.406333
\(407\) −1.29756e48 −0.684906
\(408\) −3.84165e47 −0.193778
\(409\) 7.85596e47 0.378720 0.189360 0.981908i \(-0.439359\pi\)
0.189360 + 0.981908i \(0.439359\pi\)
\(410\) −4.71309e47 −0.217172
\(411\) −2.13085e47 −0.0938596
\(412\) −4.07324e48 −1.71530
\(413\) 3.14991e48 1.26830
\(414\) −2.95116e47 −0.113628
\(415\) 2.33025e47 0.0858051
\(416\) 1.73368e48 0.610581
\(417\) 7.79332e47 0.262546
\(418\) −2.59491e47 −0.0836297
\(419\) 4.22926e48 1.30408 0.652040 0.758184i \(-0.273913\pi\)
0.652040 + 0.758184i \(0.273913\pi\)
\(420\) −2.16856e48 −0.639821
\(421\) 4.83549e48 1.36528 0.682640 0.730755i \(-0.260832\pi\)
0.682640 + 0.730755i \(0.260832\pi\)
\(422\) −4.59118e47 −0.124063
\(423\) 1.53414e48 0.396797
\(424\) 1.17989e48 0.292127
\(425\) 9.75953e47 0.231331
\(426\) 8.66724e47 0.196699
\(427\) 3.70029e47 0.0804119
\(428\) −3.81512e48 −0.793960
\(429\) −3.22254e48 −0.642300
\(430\) 2.72526e47 0.0520286
\(431\) −1.35672e48 −0.248119 −0.124060 0.992275i \(-0.539591\pi\)
−0.124060 + 0.992275i \(0.539591\pi\)
\(432\) 9.43361e47 0.165283
\(433\) −3.36809e48 −0.565403 −0.282701 0.959208i \(-0.591231\pi\)
−0.282701 + 0.959208i \(0.591231\pi\)
\(434\) 2.94685e48 0.474021
\(435\) −4.22038e48 −0.650579
\(436\) −5.69019e48 −0.840673
\(437\) 3.75912e48 0.532328
\(438\) −6.57012e47 −0.0891871
\(439\) −3.07628e48 −0.400343 −0.200172 0.979761i \(-0.564150\pi\)
−0.200172 + 0.979761i \(0.564150\pi\)
\(440\) −3.21905e48 −0.401655
\(441\) 2.56109e48 0.306415
\(442\) −1.48849e48 −0.170779
\(443\) −1.21772e49 −1.33992 −0.669961 0.742396i \(-0.733689\pi\)
−0.669961 + 0.742396i \(0.733689\pi\)
\(444\) 3.18542e48 0.336188
\(445\) 9.99261e48 1.01162
\(446\) −2.52963e48 −0.245675
\(447\) 5.29128e48 0.493028
\(448\) 1.12254e49 1.00359
\(449\) 6.54698e48 0.561674 0.280837 0.959756i \(-0.409388\pi\)
0.280837 + 0.959756i \(0.409388\pi\)
\(450\) 2.60482e47 0.0214460
\(451\) −1.67555e49 −1.32401
\(452\) −1.70929e49 −1.29644
\(453\) 1.22024e49 0.888444
\(454\) 1.37466e48 0.0960861
\(455\) −1.72266e49 −1.15608
\(456\) 1.30605e48 0.0841611
\(457\) 1.51332e49 0.936444 0.468222 0.883611i \(-0.344895\pi\)
0.468222 + 0.883611i \(0.344895\pi\)
\(458\) 3.81534e47 0.0226737
\(459\) −2.65099e48 −0.151312
\(460\) 2.27453e49 1.24702
\(461\) 2.09024e49 1.10085 0.550426 0.834884i \(-0.314465\pi\)
0.550426 + 0.834884i \(0.314465\pi\)
\(462\) 3.87151e48 0.195886
\(463\) 1.99414e49 0.969412 0.484706 0.874677i \(-0.338927\pi\)
0.484706 + 0.874677i \(0.338927\pi\)
\(464\) 2.46615e49 1.15196
\(465\) −1.69081e49 −0.758953
\(466\) −7.23061e48 −0.311915
\(467\) −1.49903e49 −0.621508 −0.310754 0.950490i \(-0.600582\pi\)
−0.310754 + 0.950490i \(0.600582\pi\)
\(468\) 7.91111e48 0.315275
\(469\) −5.55296e49 −2.12729
\(470\) 5.93777e48 0.218682
\(471\) −6.10432e48 −0.216147
\(472\) −1.14787e49 −0.390811
\(473\) 9.68855e48 0.317196
\(474\) −3.77956e47 −0.0118998
\(475\) −3.31796e48 −0.100471
\(476\) −3.56098e49 −1.03715
\(477\) 8.14198e48 0.228108
\(478\) 5.72243e48 0.154229
\(479\) −1.97535e49 −0.512198 −0.256099 0.966651i \(-0.582437\pi\)
−0.256099 + 0.966651i \(0.582437\pi\)
\(480\) 1.19506e49 0.298144
\(481\) 2.53044e49 0.607451
\(482\) 8.40825e48 0.194239
\(483\) −5.60847e49 −1.24687
\(484\) −1.13185e49 −0.242187
\(485\) 4.43367e49 0.913148
\(486\) −7.07551e47 −0.0140277
\(487\) −2.15937e49 −0.412136 −0.206068 0.978538i \(-0.566067\pi\)
−0.206068 + 0.978538i \(0.566067\pi\)
\(488\) −1.34844e48 −0.0247780
\(489\) −3.70864e49 −0.656147
\(490\) 9.91248e48 0.168871
\(491\) 4.27399e49 0.701174 0.350587 0.936530i \(-0.385982\pi\)
0.350587 + 0.936530i \(0.385982\pi\)
\(492\) 4.11335e49 0.649892
\(493\) −6.93028e49 −1.05459
\(494\) 5.06045e48 0.0741722
\(495\) −2.22135e49 −0.313633
\(496\) 9.88015e49 1.34386
\(497\) 1.64715e50 2.15844
\(498\) 1.02130e48 0.0128946
\(499\) −6.52314e49 −0.793591 −0.396796 0.917907i \(-0.629878\pi\)
−0.396796 + 0.917907i \(0.629878\pi\)
\(500\) −8.83097e49 −1.03529
\(501\) 4.69086e49 0.529974
\(502\) 8.62466e48 0.0939124
\(503\) 8.97219e49 0.941653 0.470826 0.882226i \(-0.343956\pi\)
0.470826 + 0.882226i \(0.343956\pi\)
\(504\) −1.94859e49 −0.197131
\(505\) 1.39883e50 1.36419
\(506\) −4.06071e49 −0.381784
\(507\) −8.47950e47 −0.00768640
\(508\) −1.46719e50 −1.28235
\(509\) 4.50563e49 0.379731 0.189866 0.981810i \(-0.439195\pi\)
0.189866 + 0.981810i \(0.439195\pi\)
\(510\) −1.02605e49 −0.0833908
\(511\) −1.24860e50 −0.978674
\(512\) −1.18330e50 −0.894539
\(513\) 9.01261e48 0.0657173
\(514\) 1.76263e49 0.123978
\(515\) −2.23043e50 −1.51340
\(516\) −2.37847e49 −0.155696
\(517\) 2.11093e50 1.33321
\(518\) −3.04003e49 −0.185258
\(519\) 9.19601e49 0.540758
\(520\) 6.27763e49 0.356233
\(521\) −5.45339e49 −0.298654 −0.149327 0.988788i \(-0.547711\pi\)
−0.149327 + 0.988788i \(0.547711\pi\)
\(522\) −1.84969e49 −0.0977678
\(523\) −1.36223e50 −0.694975 −0.347488 0.937685i \(-0.612965\pi\)
−0.347488 + 0.937685i \(0.612965\pi\)
\(524\) −1.97985e50 −0.974998
\(525\) 4.95028e49 0.235333
\(526\) −4.84907e49 −0.222547
\(527\) −2.77648e50 −1.23026
\(528\) 1.29804e50 0.555340
\(529\) 3.46192e50 1.43017
\(530\) 3.15129e49 0.125714
\(531\) −7.92107e49 −0.305165
\(532\) 1.21063e50 0.450451
\(533\) 3.26757e50 1.17428
\(534\) 4.37953e49 0.152025
\(535\) −2.08909e50 −0.700505
\(536\) 2.02358e50 0.655499
\(537\) 1.50192e50 0.470026
\(538\) 9.35787e49 0.282947
\(539\) 3.52397e50 1.02953
\(540\) 5.45327e49 0.153947
\(541\) −1.89994e50 −0.518310 −0.259155 0.965836i \(-0.583444\pi\)
−0.259155 + 0.965836i \(0.583444\pi\)
\(542\) −1.23964e50 −0.326819
\(543\) −3.63108e50 −0.925207
\(544\) 1.96241e50 0.483292
\(545\) −3.11584e50 −0.741720
\(546\) −7.55002e49 −0.173734
\(547\) −1.73538e49 −0.0386037 −0.0193019 0.999814i \(-0.506144\pi\)
−0.0193019 + 0.999814i \(0.506144\pi\)
\(548\) 7.19781e49 0.154796
\(549\) −9.30513e48 −0.0193479
\(550\) 3.58416e49 0.0720571
\(551\) 2.35610e50 0.458024
\(552\) 2.04381e50 0.384209
\(553\) −7.18278e49 −0.130580
\(554\) 4.67018e49 0.0821114
\(555\) 1.74427e50 0.296616
\(556\) −2.63251e50 −0.432999
\(557\) −9.83753e50 −1.56518 −0.782591 0.622536i \(-0.786102\pi\)
−0.782591 + 0.622536i \(0.786102\pi\)
\(558\) −7.41043e49 −0.114054
\(559\) −1.88941e50 −0.281325
\(560\) 6.93885e50 0.999560
\(561\) −3.64768e50 −0.508398
\(562\) −7.92416e49 −0.106864
\(563\) 2.99781e50 0.391200 0.195600 0.980684i \(-0.437335\pi\)
0.195600 + 0.980684i \(0.437335\pi\)
\(564\) −5.18219e50 −0.654410
\(565\) −9.35972e50 −1.14384
\(566\) 1.62555e50 0.192263
\(567\) −1.34465e50 −0.153930
\(568\) −6.00245e50 −0.665096
\(569\) 1.02631e51 1.10078 0.550392 0.834906i \(-0.314478\pi\)
0.550392 + 0.834906i \(0.314478\pi\)
\(570\) 3.48826e49 0.0362180
\(571\) −8.60079e47 −0.000864511 0 −0.000432255 1.00000i \(-0.500138\pi\)
−0.000432255 1.00000i \(0.500138\pi\)
\(572\) 1.08854e51 1.05930
\(573\) −3.00765e50 −0.283379
\(574\) −3.92560e50 −0.358127
\(575\) −5.19220e50 −0.458666
\(576\) −2.82284e50 −0.241474
\(577\) 1.49637e51 1.23961 0.619806 0.784755i \(-0.287211\pi\)
0.619806 + 0.784755i \(0.287211\pi\)
\(578\) 1.04069e50 0.0834940
\(579\) 7.12364e50 0.553539
\(580\) 1.42560e51 1.07295
\(581\) 1.94090e50 0.141496
\(582\) 1.94318e50 0.137226
\(583\) 1.12031e51 0.766427
\(584\) 4.55010e50 0.301567
\(585\) 4.33197e50 0.278165
\(586\) −1.97331e50 −0.122769
\(587\) −2.21173e51 −1.33330 −0.666650 0.745371i \(-0.732272\pi\)
−0.666650 + 0.745371i \(0.732272\pi\)
\(588\) −8.65111e50 −0.505349
\(589\) 9.43923e50 0.534323
\(590\) −3.06579e50 −0.168182
\(591\) 9.22720e50 0.490571
\(592\) −1.01926e51 −0.525209
\(593\) −9.58294e50 −0.478616 −0.239308 0.970944i \(-0.576921\pi\)
−0.239308 + 0.970944i \(0.576921\pi\)
\(594\) −9.73568e49 −0.0471321
\(595\) −1.94993e51 −0.915070
\(596\) −1.78734e51 −0.813116
\(597\) 1.44333e51 0.636560
\(598\) 7.91899e50 0.338608
\(599\) 1.22432e49 0.00507572 0.00253786 0.999997i \(-0.499192\pi\)
0.00253786 + 0.999997i \(0.499192\pi\)
\(600\) −1.80396e50 −0.0725150
\(601\) −1.08866e51 −0.424339 −0.212169 0.977233i \(-0.568053\pi\)
−0.212169 + 0.977233i \(0.568053\pi\)
\(602\) 2.26991e50 0.0857973
\(603\) 1.39640e51 0.511847
\(604\) −4.12188e51 −1.46525
\(605\) −6.19780e50 −0.213680
\(606\) 6.13077e50 0.205008
\(607\) 4.94921e51 1.60526 0.802629 0.596479i \(-0.203434\pi\)
0.802629 + 0.596479i \(0.203434\pi\)
\(608\) −6.67162e50 −0.209901
\(609\) −3.51521e51 −1.07283
\(610\) −3.60148e49 −0.0106630
\(611\) −4.11663e51 −1.18244
\(612\) 8.95480e50 0.249548
\(613\) 3.53515e51 0.955848 0.477924 0.878401i \(-0.341390\pi\)
0.477924 + 0.878401i \(0.341390\pi\)
\(614\) 4.24685e50 0.111417
\(615\) 2.25239e51 0.573396
\(616\) −2.68119e51 −0.662346
\(617\) −3.24058e51 −0.776868 −0.388434 0.921477i \(-0.626984\pi\)
−0.388434 + 0.921477i \(0.626984\pi\)
\(618\) −9.77545e50 −0.227431
\(619\) 2.49425e51 0.563201 0.281600 0.959532i \(-0.409135\pi\)
0.281600 + 0.959532i \(0.409135\pi\)
\(620\) 5.71140e51 1.25169
\(621\) 1.41036e51 0.300010
\(622\) 1.47237e51 0.304016
\(623\) 8.32299e51 1.66821
\(624\) −2.53136e51 −0.492538
\(625\) −3.27806e51 −0.619208
\(626\) 1.02564e50 0.0188092
\(627\) 1.24011e51 0.220805
\(628\) 2.06198e51 0.356477
\(629\) 2.86427e51 0.480814
\(630\) −5.20436e50 −0.0848335
\(631\) 3.22282e51 0.510145 0.255072 0.966922i \(-0.417901\pi\)
0.255072 + 0.966922i \(0.417901\pi\)
\(632\) 2.61751e50 0.0402367
\(633\) 2.19413e51 0.327562
\(634\) 9.15616e50 0.132758
\(635\) −8.03403e51 −1.13141
\(636\) −2.75029e51 −0.376202
\(637\) −6.87227e51 −0.913106
\(638\) −2.54512e51 −0.328493
\(639\) −4.14208e51 −0.519341
\(640\) −5.33208e51 −0.649482
\(641\) −8.20930e51 −0.971477 −0.485739 0.874104i \(-0.661449\pi\)
−0.485739 + 0.874104i \(0.661449\pi\)
\(642\) −9.15599e50 −0.105271
\(643\) −4.47682e51 −0.500112 −0.250056 0.968231i \(-0.580449\pi\)
−0.250056 + 0.968231i \(0.580449\pi\)
\(644\) 1.89449e52 2.05638
\(645\) −1.30241e51 −0.137370
\(646\) 5.72807e50 0.0587093
\(647\) 1.90676e52 1.89919 0.949594 0.313483i \(-0.101496\pi\)
0.949594 + 0.313483i \(0.101496\pi\)
\(648\) 4.90011e50 0.0474316
\(649\) −1.08991e52 −1.02533
\(650\) −6.98964e50 −0.0639083
\(651\) −1.40830e52 −1.25155
\(652\) 1.25275e52 1.08214
\(653\) −9.48302e51 −0.796256 −0.398128 0.917330i \(-0.630340\pi\)
−0.398128 + 0.917330i \(0.630340\pi\)
\(654\) −1.36560e51 −0.111464
\(655\) −1.08413e52 −0.860234
\(656\) −1.31617e52 −1.01529
\(657\) 3.13986e51 0.235479
\(658\) 4.94566e51 0.360616
\(659\) 1.04759e52 0.742693 0.371347 0.928494i \(-0.378896\pi\)
0.371347 + 0.928494i \(0.378896\pi\)
\(660\) 7.50353e51 0.517252
\(661\) −8.65976e51 −0.580469 −0.290234 0.956956i \(-0.593733\pi\)
−0.290234 + 0.956956i \(0.593733\pi\)
\(662\) 2.92249e51 0.190494
\(663\) 7.11352e51 0.450904
\(664\) −7.07293e50 −0.0436004
\(665\) 6.62919e51 0.397429
\(666\) 7.64476e50 0.0445749
\(667\) 3.68700e52 2.09096
\(668\) −1.58453e52 −0.874049
\(669\) 1.20891e52 0.648651
\(670\) 5.40467e51 0.282088
\(671\) −1.28036e51 −0.0650076
\(672\) 9.95382e51 0.491653
\(673\) −2.18723e52 −1.05103 −0.525515 0.850784i \(-0.676127\pi\)
−0.525515 + 0.850784i \(0.676127\pi\)
\(674\) −2.84102e51 −0.132821
\(675\) −1.24485e51 −0.0566234
\(676\) 2.86430e50 0.0126766
\(677\) −1.59031e52 −0.684845 −0.342422 0.939546i \(-0.611247\pi\)
−0.342422 + 0.939546i \(0.611247\pi\)
\(678\) −4.10215e51 −0.171895
\(679\) 3.69287e52 1.50582
\(680\) 7.10582e51 0.281968
\(681\) −6.56949e51 −0.253694
\(682\) −1.01965e52 −0.383214
\(683\) −3.09230e51 −0.113109 −0.0565547 0.998400i \(-0.518012\pi\)
−0.0565547 + 0.998400i \(0.518012\pi\)
\(684\) −3.04438e51 −0.108383
\(685\) 3.94138e51 0.136576
\(686\) −7.25303e50 −0.0244638
\(687\) −1.82335e51 −0.0598647
\(688\) 7.61053e51 0.243237
\(689\) −2.18477e52 −0.679753
\(690\) 5.45870e51 0.165341
\(691\) −4.14754e52 −1.22306 −0.611528 0.791222i \(-0.709445\pi\)
−0.611528 + 0.791222i \(0.709445\pi\)
\(692\) −3.10633e52 −0.891835
\(693\) −1.85020e52 −0.517194
\(694\) −1.07783e52 −0.293360
\(695\) −1.44151e52 −0.382032
\(696\) 1.28100e52 0.330580
\(697\) 3.69865e52 0.929473
\(698\) −4.30440e51 −0.105339
\(699\) 3.45552e52 0.823541
\(700\) −1.67216e52 −0.388118
\(701\) −2.82631e52 −0.638904 −0.319452 0.947602i \(-0.603499\pi\)
−0.319452 + 0.947602i \(0.603499\pi\)
\(702\) 1.89860e51 0.0418021
\(703\) −9.73771e51 −0.208825
\(704\) −3.88414e52 −0.811337
\(705\) −2.83767e52 −0.577381
\(706\) −7.94936e51 −0.157560
\(707\) 1.16511e53 2.24961
\(708\) 2.67567e52 0.503288
\(709\) 4.89940e52 0.897817 0.448909 0.893578i \(-0.351813\pi\)
0.448909 + 0.893578i \(0.351813\pi\)
\(710\) −1.60316e52 −0.286218
\(711\) 1.80625e51 0.0314189
\(712\) −3.03302e52 −0.514039
\(713\) 1.47712e53 2.43927
\(714\) −8.54608e51 −0.137515
\(715\) 5.96066e52 0.934614
\(716\) −5.07334e52 −0.775182
\(717\) −2.73476e52 −0.407206
\(718\) 2.62227e52 0.380518
\(719\) 4.55246e52 0.643816 0.321908 0.946771i \(-0.395676\pi\)
0.321908 + 0.946771i \(0.395676\pi\)
\(720\) −1.74491e52 −0.240504
\(721\) −1.85775e53 −2.49566
\(722\) 1.47531e52 0.193172
\(723\) −4.01831e52 −0.512844
\(724\) 1.22654e53 1.52588
\(725\) −3.25430e52 −0.394644
\(726\) −2.71635e51 −0.0321114
\(727\) −6.55544e52 −0.755467 −0.377733 0.925914i \(-0.623296\pi\)
−0.377733 + 0.925914i \(0.623296\pi\)
\(728\) 5.22873e52 0.587442
\(729\) 3.38139e51 0.0370370
\(730\) 1.21526e52 0.129777
\(731\) −2.13868e52 −0.222676
\(732\) 3.14319e51 0.0319091
\(733\) 5.46489e52 0.540951 0.270476 0.962727i \(-0.412819\pi\)
0.270476 + 0.962727i \(0.412819\pi\)
\(734\) −4.29999e51 −0.0415040
\(735\) −4.73718e52 −0.445866
\(736\) −1.04403e53 −0.958235
\(737\) 1.92141e53 1.71977
\(738\) 9.87172e51 0.0861688
\(739\) −1.98761e53 −1.69203 −0.846017 0.533156i \(-0.821006\pi\)
−0.846017 + 0.533156i \(0.821006\pi\)
\(740\) −5.89200e52 −0.489188
\(741\) −2.41839e52 −0.195835
\(742\) 2.62476e52 0.207308
\(743\) −1.44490e53 −1.11313 −0.556564 0.830805i \(-0.687880\pi\)
−0.556564 + 0.830805i \(0.687880\pi\)
\(744\) 5.13206e52 0.385649
\(745\) −9.78716e52 −0.717407
\(746\) −1.40740e52 −0.100635
\(747\) −4.88078e51 −0.0340454
\(748\) 1.23215e53 0.838465
\(749\) −1.74003e53 −1.15516
\(750\) −2.11936e52 −0.137269
\(751\) 1.98670e53 1.25544 0.627718 0.778441i \(-0.283989\pi\)
0.627718 + 0.778441i \(0.283989\pi\)
\(752\) 1.65817e53 1.02235
\(753\) −4.12173e52 −0.247955
\(754\) 4.96337e52 0.291344
\(755\) −2.25706e53 −1.29278
\(756\) 4.54210e52 0.253866
\(757\) 3.23306e53 1.76336 0.881679 0.471850i \(-0.156414\pi\)
0.881679 + 0.471850i \(0.156414\pi\)
\(758\) 6.30001e50 0.00335321
\(759\) 1.94062e53 1.00801
\(760\) −2.41578e52 −0.122463
\(761\) −4.26585e52 −0.211052 −0.105526 0.994417i \(-0.533653\pi\)
−0.105526 + 0.994417i \(0.533653\pi\)
\(762\) −3.52113e52 −0.170026
\(763\) −2.59523e53 −1.22313
\(764\) 1.01596e53 0.467356
\(765\) 4.90348e52 0.220175
\(766\) 1.11103e52 0.0486962
\(767\) 2.12550e53 0.909382
\(768\) 7.67722e52 0.320643
\(769\) 4.26123e53 1.73739 0.868695 0.495347i \(-0.164959\pi\)
0.868695 + 0.495347i \(0.164959\pi\)
\(770\) −7.16104e52 −0.285035
\(771\) −8.42364e52 −0.327336
\(772\) −2.40630e53 −0.912913
\(773\) −9.95037e52 −0.368569 −0.184284 0.982873i \(-0.558997\pi\)
−0.184284 + 0.982873i \(0.558997\pi\)
\(774\) −5.70814e51 −0.0206437
\(775\) −1.30377e53 −0.460384
\(776\) −1.34574e53 −0.464000
\(777\) 1.45283e53 0.489132
\(778\) 4.23394e52 0.139194
\(779\) −1.25744e53 −0.403685
\(780\) −1.46330e53 −0.458757
\(781\) −5.69937e53 −1.74495
\(782\) 8.96373e52 0.268018
\(783\) 8.83971e52 0.258134
\(784\) 2.76815e53 0.789481
\(785\) 1.12910e53 0.314517
\(786\) −4.75149e52 −0.129274
\(787\) 4.51390e53 1.19955 0.599777 0.800167i \(-0.295256\pi\)
0.599777 + 0.800167i \(0.295256\pi\)
\(788\) −3.11686e53 −0.809064
\(789\) 2.31737e53 0.587586
\(790\) 6.99096e51 0.0173155
\(791\) −7.79585e53 −1.88625
\(792\) 6.74240e52 0.159367
\(793\) 2.49689e52 0.0576560
\(794\) −8.77088e52 −0.197863
\(795\) −1.50600e53 −0.331921
\(796\) −4.87543e53 −1.04983
\(797\) 3.86364e53 0.812864 0.406432 0.913681i \(-0.366773\pi\)
0.406432 + 0.913681i \(0.366773\pi\)
\(798\) 2.90542e52 0.0597250
\(799\) −4.65973e53 −0.935934
\(800\) 9.21502e52 0.180856
\(801\) −2.09298e53 −0.401388
\(802\) 1.27341e53 0.238639
\(803\) 4.32036e53 0.791192
\(804\) −4.71692e53 −0.844154
\(805\) 1.03739e54 1.81433
\(806\) 1.98847e53 0.339877
\(807\) −4.47214e53 −0.747059
\(808\) −4.24583e53 −0.693190
\(809\) 8.90010e53 1.42019 0.710097 0.704104i \(-0.248651\pi\)
0.710097 + 0.704104i \(0.248651\pi\)
\(810\) 1.30874e52 0.0204118
\(811\) −3.07699e53 −0.469072 −0.234536 0.972107i \(-0.575357\pi\)
−0.234536 + 0.972107i \(0.575357\pi\)
\(812\) 1.18741e54 1.76935
\(813\) 5.92423e53 0.862893
\(814\) 1.05189e53 0.149769
\(815\) 6.85980e53 0.954763
\(816\) −2.86532e53 −0.389857
\(817\) 7.27090e52 0.0967119
\(818\) −6.36860e52 −0.0828148
\(819\) 3.60816e53 0.458705
\(820\) −7.60837e53 −0.945661
\(821\) −1.44038e54 −1.75037 −0.875185 0.483789i \(-0.839260\pi\)
−0.875185 + 0.483789i \(0.839260\pi\)
\(822\) 1.72742e52 0.0205243
\(823\) 7.25265e53 0.842558 0.421279 0.906931i \(-0.361581\pi\)
0.421279 + 0.906931i \(0.361581\pi\)
\(824\) 6.76993e53 0.769008
\(825\) −1.71287e53 −0.190251
\(826\) −2.55354e53 −0.277339
\(827\) −4.48759e53 −0.476608 −0.238304 0.971191i \(-0.576592\pi\)
−0.238304 + 0.971191i \(0.576592\pi\)
\(828\) −4.76408e53 −0.494786
\(829\) −4.38009e53 −0.444861 −0.222430 0.974949i \(-0.571399\pi\)
−0.222430 + 0.974949i \(0.571399\pi\)
\(830\) −1.88907e52 −0.0187630
\(831\) −2.23188e53 −0.216797
\(832\) 7.57466e53 0.719584
\(833\) −7.77892e53 −0.722748
\(834\) −6.31782e52 −0.0574110
\(835\) −8.67658e53 −0.771167
\(836\) −4.18897e53 −0.364159
\(837\) 3.54145e53 0.301134
\(838\) −3.42854e53 −0.285164
\(839\) −3.60758e53 −0.293508 −0.146754 0.989173i \(-0.546883\pi\)
−0.146754 + 0.989173i \(0.546883\pi\)
\(840\) 3.60425e53 0.286846
\(841\) 1.02642e54 0.799095
\(842\) −3.91999e53 −0.298546
\(843\) 3.78696e53 0.282151
\(844\) −7.41156e53 −0.540225
\(845\) 1.56843e52 0.0111845
\(846\) −1.24368e53 −0.0867678
\(847\) −5.16224e53 −0.352367
\(848\) 8.80025e53 0.587722
\(849\) −7.76851e53 −0.507628
\(850\) −7.91177e52 −0.0505852
\(851\) −1.52383e54 −0.953323
\(852\) 1.39916e54 0.856513
\(853\) −3.15083e53 −0.188742 −0.0943708 0.995537i \(-0.530084\pi\)
−0.0943708 + 0.995537i \(0.530084\pi\)
\(854\) −2.99972e52 −0.0175837
\(855\) −1.66704e53 −0.0956255
\(856\) 6.34093e53 0.355949
\(857\) 9.67011e53 0.531234 0.265617 0.964079i \(-0.414424\pi\)
0.265617 + 0.964079i \(0.414424\pi\)
\(858\) 2.61242e53 0.140452
\(859\) 3.56564e54 1.87614 0.938068 0.346452i \(-0.112614\pi\)
0.938068 + 0.346452i \(0.112614\pi\)
\(860\) 4.39940e53 0.226554
\(861\) 1.87605e54 0.945553
\(862\) 1.09985e53 0.0542564
\(863\) −2.25029e54 −1.08652 −0.543262 0.839564i \(-0.682811\pi\)
−0.543262 + 0.839564i \(0.682811\pi\)
\(864\) −2.50309e53 −0.118296
\(865\) −1.70096e54 −0.786860
\(866\) 2.73042e53 0.123637
\(867\) −4.97345e53 −0.220447
\(868\) 4.75711e54 2.06409
\(869\) 2.48535e53 0.105565
\(870\) 3.42134e53 0.142262
\(871\) −3.74703e54 −1.52529
\(872\) 9.45740e53 0.376892
\(873\) −9.28645e53 −0.362315
\(874\) −3.04741e53 −0.116404
\(875\) −4.02770e54 −1.50629
\(876\) −1.06062e54 −0.388358
\(877\) 4.14049e54 1.48443 0.742214 0.670163i \(-0.233776\pi\)
0.742214 + 0.670163i \(0.233776\pi\)
\(878\) 2.49385e53 0.0875432
\(879\) 9.43046e53 0.324145
\(880\) −2.40095e54 −0.808077
\(881\) 3.03676e54 1.00082 0.500410 0.865789i \(-0.333183\pi\)
0.500410 + 0.865789i \(0.333183\pi\)
\(882\) −2.07620e53 −0.0670039
\(883\) 2.77430e54 0.876760 0.438380 0.898790i \(-0.355552\pi\)
0.438380 + 0.898790i \(0.355552\pi\)
\(884\) −2.40288e54 −0.743645
\(885\) 1.46514e54 0.444047
\(886\) 9.87173e53 0.293001
\(887\) −9.39883e53 −0.273204 −0.136602 0.990626i \(-0.543618\pi\)
−0.136602 + 0.990626i \(0.543618\pi\)
\(888\) −5.29434e53 −0.150720
\(889\) −6.69166e54 −1.86574
\(890\) −8.10072e53 −0.221212
\(891\) 4.65269e53 0.124442
\(892\) −4.08359e54 −1.06978
\(893\) 1.58418e54 0.406491
\(894\) −4.28949e53 −0.107811
\(895\) −2.77807e54 −0.683937
\(896\) −4.44117e54 −1.07102
\(897\) −3.78449e54 −0.894020
\(898\) −5.30745e53 −0.122821
\(899\) 9.25814e54 2.09879
\(900\) 4.20498e53 0.0933850
\(901\) −2.47301e54 −0.538043
\(902\) 1.35832e54 0.289521
\(903\) −1.08479e54 −0.226529
\(904\) 2.84092e54 0.581224
\(905\) 6.71632e54 1.34627
\(906\) −9.89218e53 −0.194276
\(907\) 2.17105e54 0.417767 0.208884 0.977941i \(-0.433017\pi\)
0.208884 + 0.977941i \(0.433017\pi\)
\(908\) 2.21911e54 0.418400
\(909\) −2.92990e54 −0.541278
\(910\) 1.39651e54 0.252801
\(911\) 7.42098e54 1.31635 0.658175 0.752865i \(-0.271329\pi\)
0.658175 + 0.752865i \(0.271329\pi\)
\(912\) 9.74127e53 0.169321
\(913\) −6.71581e53 −0.114390
\(914\) −1.22681e54 −0.204772
\(915\) 1.72115e53 0.0281532
\(916\) 6.15912e53 0.0987307
\(917\) −9.02986e54 −1.41856
\(918\) 2.14908e53 0.0330875
\(919\) 6.80622e54 1.02700 0.513498 0.858091i \(-0.328349\pi\)
0.513498 + 0.858091i \(0.328349\pi\)
\(920\) −3.78039e54 −0.559065
\(921\) −2.02958e54 −0.294172
\(922\) −1.69450e54 −0.240724
\(923\) 1.11146e55 1.54762
\(924\) 6.24979e54 0.852971
\(925\) 1.34500e54 0.179928
\(926\) −1.61660e54 −0.211982
\(927\) 4.67169e54 0.600481
\(928\) −6.54362e54 −0.824481
\(929\) −6.45233e54 −0.796940 −0.398470 0.917181i \(-0.630459\pi\)
−0.398470 + 0.917181i \(0.630459\pi\)
\(930\) 1.37069e54 0.165961
\(931\) 2.64461e54 0.313901
\(932\) −1.16724e55 −1.35821
\(933\) −7.03648e54 −0.802685
\(934\) 1.21522e54 0.135905
\(935\) 6.74703e54 0.739772
\(936\) −1.31487e54 −0.141344
\(937\) 7.02165e53 0.0740042 0.0370021 0.999315i \(-0.488219\pi\)
0.0370021 + 0.999315i \(0.488219\pi\)
\(938\) 4.50162e54 0.465175
\(939\) −4.90154e53 −0.0496614
\(940\) 9.58538e54 0.952234
\(941\) −8.40171e53 −0.0818388 −0.0409194 0.999162i \(-0.513029\pi\)
−0.0409194 + 0.999162i \(0.513029\pi\)
\(942\) 4.94859e53 0.0472650
\(943\) −1.96773e55 −1.84289
\(944\) −8.56148e54 −0.786261
\(945\) 2.48717e54 0.223984
\(946\) −7.85423e53 −0.0693613
\(947\) −7.39324e54 −0.640266 −0.320133 0.947373i \(-0.603728\pi\)
−0.320133 + 0.947373i \(0.603728\pi\)
\(948\) −6.10136e53 −0.0518170
\(949\) −8.42534e54 −0.701718
\(950\) 2.68977e53 0.0219700
\(951\) −4.37573e54 −0.350519
\(952\) 5.91854e54 0.464977
\(953\) −2.15051e55 −1.65700 −0.828499 0.559990i \(-0.810805\pi\)
−0.828499 + 0.559990i \(0.810805\pi\)
\(954\) −6.60047e53 −0.0498804
\(955\) 5.56319e54 0.412345
\(956\) 9.23775e54 0.671576
\(957\) 1.21632e55 0.867312
\(958\) 1.60136e54 0.112002
\(959\) 3.28283e54 0.225219
\(960\) 5.22135e54 0.351370
\(961\) 2.19419e55 1.44841
\(962\) −2.05135e54 −0.132832
\(963\) 4.37565e54 0.277944
\(964\) 1.35735e55 0.845797
\(965\) −1.31764e55 −0.805457
\(966\) 4.54663e54 0.272655
\(967\) 1.31747e55 0.775085 0.387543 0.921852i \(-0.373324\pi\)
0.387543 + 0.921852i \(0.373324\pi\)
\(968\) 1.88120e54 0.108578
\(969\) −2.73745e54 −0.155009
\(970\) −3.59425e54 −0.199678
\(971\) 8.47915e54 0.462164 0.231082 0.972934i \(-0.425773\pi\)
0.231082 + 0.972934i \(0.425773\pi\)
\(972\) −1.14220e54 −0.0610826
\(973\) −1.20066e55 −0.629987
\(974\) 1.75054e54 0.0901220
\(975\) 3.34035e54 0.168736
\(976\) −1.00574e54 −0.0498500
\(977\) 1.06113e55 0.516080 0.258040 0.966134i \(-0.416923\pi\)
0.258040 + 0.966134i \(0.416923\pi\)
\(978\) 3.00649e54 0.143480
\(979\) −2.87988e55 −1.34863
\(980\) 1.60018e55 0.735335
\(981\) 6.52622e54 0.294297
\(982\) −3.46480e54 −0.153326
\(983\) 1.52477e54 0.0662161 0.0331081 0.999452i \(-0.489459\pi\)
0.0331081 + 0.999452i \(0.489459\pi\)
\(984\) −6.83661e54 −0.291361
\(985\) −1.70673e55 −0.713831
\(986\) 5.61818e54 0.230607
\(987\) −2.36353e55 −0.952126
\(988\) 8.16912e54 0.322977
\(989\) 1.13781e55 0.441506
\(990\) 1.80079e54 0.0685822
\(991\) 2.88078e55 1.07683 0.538416 0.842679i \(-0.319023\pi\)
0.538416 + 0.842679i \(0.319023\pi\)
\(992\) −2.62157e55 −0.961825
\(993\) −1.39666e55 −0.502956
\(994\) −1.33529e55 −0.471986
\(995\) −2.66969e55 −0.926262
\(996\) 1.64868e54 0.0561487
\(997\) −2.89753e55 −0.968651 −0.484326 0.874888i \(-0.660935\pi\)
−0.484326 + 0.874888i \(0.660935\pi\)
\(998\) 5.28813e54 0.173535
\(999\) −3.65344e54 −0.117690
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.1.2 4
3.2 odd 2 9.38.a.c.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.38.a.b.1.2 4 1.1 even 1 trivial
9.38.a.c.1.3 4 3.2 odd 2