Properties

Label 5.34.a.b.1.2
Level 5
Weight 34
Character 5.1
Self dual yes
Analytic conductor 34.491
Analytic rank 0
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(34.4914144405\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-60371.0\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q-96184.0 q^{2} +1.07272e8 q^{3} +6.61431e8 q^{4} +1.52588e11 q^{5} -1.03179e13 q^{6} -8.61302e13 q^{7} +7.62595e14 q^{8} +5.94832e15 q^{9} +O(q^{10})\) \(q-96184.0 q^{2} +1.07272e8 q^{3} +6.61431e8 q^{4} +1.52588e11 q^{5} -1.03179e13 q^{6} -8.61302e13 q^{7} +7.62595e14 q^{8} +5.94832e15 q^{9} -1.46765e16 q^{10} +9.57101e16 q^{11} +7.09533e16 q^{12} +2.44486e18 q^{13} +8.28435e18 q^{14} +1.63685e19 q^{15} -7.90311e19 q^{16} -6.06607e19 q^{17} -5.72133e20 q^{18} -1.50149e21 q^{19} +1.00926e20 q^{20} -9.23940e21 q^{21} -9.20578e21 q^{22} +1.88217e22 q^{23} +8.18055e22 q^{24} +2.32831e22 q^{25} -2.35157e23 q^{26} +4.17567e22 q^{27} -5.69692e22 q^{28} +2.67431e24 q^{29} -1.57439e24 q^{30} +2.64569e24 q^{31} +1.05089e24 q^{32} +1.02671e25 q^{33} +5.83459e24 q^{34} -1.31424e25 q^{35} +3.93440e24 q^{36} -1.12777e26 q^{37} +1.44419e26 q^{38} +2.62266e26 q^{39} +1.16363e26 q^{40} +7.31837e26 q^{41} +8.88682e26 q^{42} +3.88890e26 q^{43} +6.33056e25 q^{44} +9.07641e26 q^{45} -1.81034e27 q^{46} +3.28337e27 q^{47} -8.47786e27 q^{48} -3.12582e26 q^{49} -2.23946e27 q^{50} -6.50723e27 q^{51} +1.61711e27 q^{52} +3.35567e28 q^{53} -4.01633e27 q^{54} +1.46042e28 q^{55} -6.56825e28 q^{56} -1.61068e29 q^{57} -2.57226e29 q^{58} +2.93443e29 q^{59} +1.08266e28 q^{60} +7.07686e28 q^{61} -2.54473e29 q^{62} -5.12330e29 q^{63} +5.77794e29 q^{64} +3.73057e29 q^{65} -9.87527e29 q^{66} +1.99482e30 q^{67} -4.01229e28 q^{68} +2.01905e30 q^{69} +1.26409e30 q^{70} -1.15434e30 q^{71} +4.53616e30 q^{72} -2.83903e30 q^{73} +1.08474e31 q^{74} +2.49763e30 q^{75} -9.93131e29 q^{76} -8.24353e30 q^{77} -2.52258e31 q^{78} +6.93520e30 q^{79} -1.20592e31 q^{80} -2.85877e31 q^{81} -7.03910e31 q^{82} +4.09391e31 q^{83} -6.11122e30 q^{84} -9.25610e30 q^{85} -3.74050e31 q^{86} +2.86880e32 q^{87} +7.29881e31 q^{88} -1.49837e32 q^{89} -8.73006e31 q^{90} -2.10577e32 q^{91} +1.24492e31 q^{92} +2.83809e32 q^{93} -3.15807e32 q^{94} -2.29109e32 q^{95} +1.12731e32 q^{96} +1.00351e33 q^{97} +3.00654e31 q^{98} +5.69314e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + O(q^{10}) \) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + 22483825683593750q^{10} + 150760896555890192q^{11} + 466351581756413200q^{12} - 1403095636752804700q^{13} - 7086110008989891456q^{14} + 4045700073242187500q^{15} + 64511520005858668816q^{16} + \)\(13\!\cdots\!00\)\(q^{17} + \)\(67\!\cdots\!50\)\(q^{18} + \)\(17\!\cdots\!00\)\(q^{19} + \)\(45\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(24\!\cdots\!00\)\(q^{22} + \)\(68\!\cdots\!00\)\(q^{23} + \)\(21\!\cdots\!00\)\(q^{24} + \)\(13\!\cdots\!50\)\(q^{25} - \)\(36\!\cdots\!88\)\(q^{26} - \)\(34\!\cdots\!00\)\(q^{27} - \)\(17\!\cdots\!00\)\(q^{28} + \)\(13\!\cdots\!00\)\(q^{29} + \)\(10\!\cdots\!00\)\(q^{30} + \)\(10\!\cdots\!52\)\(q^{31} + \)\(26\!\cdots\!00\)\(q^{32} + \)\(34\!\cdots\!00\)\(q^{33} + \)\(88\!\cdots\!24\)\(q^{34} + \)\(29\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!96\)\(q^{36} + \)\(27\!\cdots\!00\)\(q^{37} + \)\(83\!\cdots\!00\)\(q^{38} + \)\(57\!\cdots\!56\)\(q^{39} + \)\(46\!\cdots\!00\)\(q^{40} + \)\(44\!\cdots\!32\)\(q^{41} + \)\(14\!\cdots\!00\)\(q^{42} + \)\(22\!\cdots\!00\)\(q^{43} + \)\(71\!\cdots\!64\)\(q^{44} + \)\(20\!\cdots\!50\)\(q^{45} + \)\(34\!\cdots\!72\)\(q^{46} + \)\(38\!\cdots\!00\)\(q^{47} + \)\(24\!\cdots\!00\)\(q^{48} - \)\(71\!\cdots\!58\)\(q^{49} + \)\(34\!\cdots\!50\)\(q^{50} - \)\(54\!\cdots\!88\)\(q^{51} - \)\(90\!\cdots\!00\)\(q^{52} + \)\(47\!\cdots\!00\)\(q^{53} - \)\(18\!\cdots\!00\)\(q^{54} + \)\(23\!\cdots\!00\)\(q^{55} - \)\(39\!\cdots\!00\)\(q^{56} - \)\(24\!\cdots\!00\)\(q^{57} - \)\(44\!\cdots\!00\)\(q^{58} - \)\(17\!\cdots\!00\)\(q^{59} + \)\(71\!\cdots\!00\)\(q^{60} - \)\(28\!\cdots\!08\)\(q^{61} + \)\(34\!\cdots\!00\)\(q^{62} - \)\(55\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!72\)\(q^{64} - \)\(21\!\cdots\!00\)\(q^{65} + \)\(50\!\cdots\!64\)\(q^{66} + \)\(33\!\cdots\!00\)\(q^{67} + \)\(38\!\cdots\!00\)\(q^{68} + \)\(31\!\cdots\!36\)\(q^{69} - \)\(10\!\cdots\!00\)\(q^{70} + \)\(84\!\cdots\!72\)\(q^{71} + \)\(87\!\cdots\!00\)\(q^{72} - \)\(17\!\cdots\!00\)\(q^{73} + \)\(20\!\cdots\!84\)\(q^{74} + \)\(61\!\cdots\!00\)\(q^{75} + \)\(29\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!00\)\(q^{77} - \)\(57\!\cdots\!00\)\(q^{78} - \)\(22\!\cdots\!00\)\(q^{79} + \)\(98\!\cdots\!00\)\(q^{80} - \)\(13\!\cdots\!74\)\(q^{81} - \)\(15\!\cdots\!00\)\(q^{82} - \)\(47\!\cdots\!00\)\(q^{83} - \)\(23\!\cdots\!76\)\(q^{84} + \)\(20\!\cdots\!00\)\(q^{85} - \)\(12\!\cdots\!08\)\(q^{86} - \)\(17\!\cdots\!00\)\(q^{87} + \)\(49\!\cdots\!00\)\(q^{88} - \)\(33\!\cdots\!00\)\(q^{89} + \)\(10\!\cdots\!50\)\(q^{90} + \)\(19\!\cdots\!32\)\(q^{91} - \)\(41\!\cdots\!00\)\(q^{92} + \)\(21\!\cdots\!00\)\(q^{93} + \)\(14\!\cdots\!64\)\(q^{94} + \)\(26\!\cdots\!00\)\(q^{95} + \)\(31\!\cdots\!72\)\(q^{96} + \)\(25\!\cdots\!00\)\(q^{97} + \)\(69\!\cdots\!50\)\(q^{98} + \)\(16\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −96184.0 −1.03779 −0.518893 0.854839i \(-0.673656\pi\)
−0.518893 + 0.854839i \(0.673656\pi\)
\(3\) 1.07272e8 1.43876 0.719379 0.694618i \(-0.244427\pi\)
0.719379 + 0.694618i \(0.244427\pi\)
\(4\) 6.61431e8 0.0770007
\(5\) 1.52588e11 0.447214
\(6\) −1.03179e13 −1.49312
\(7\) −8.61302e13 −0.979575 −0.489788 0.871842i \(-0.662926\pi\)
−0.489788 + 0.871842i \(0.662926\pi\)
\(8\) 7.62595e14 0.957876
\(9\) 5.94832e15 1.07002
\(10\) −1.46765e16 −0.464112
\(11\) 9.57101e16 0.628027 0.314014 0.949418i \(-0.398326\pi\)
0.314014 + 0.949418i \(0.398326\pi\)
\(12\) 7.09533e16 0.110785
\(13\) 2.44486e18 1.01904 0.509518 0.860460i \(-0.329824\pi\)
0.509518 + 0.860460i \(0.329824\pi\)
\(14\) 8.28435e18 1.01659
\(15\) 1.63685e19 0.643432
\(16\) −7.90311e19 −1.07107
\(17\) −6.06607e19 −0.302343 −0.151172 0.988508i \(-0.548305\pi\)
−0.151172 + 0.988508i \(0.548305\pi\)
\(18\) −5.72133e20 −1.11045
\(19\) −1.50149e21 −1.19423 −0.597115 0.802156i \(-0.703686\pi\)
−0.597115 + 0.802156i \(0.703686\pi\)
\(20\) 1.00926e20 0.0344358
\(21\) −9.23940e21 −1.40937
\(22\) −9.20578e21 −0.651758
\(23\) 1.88217e22 0.639955 0.319977 0.947425i \(-0.396325\pi\)
0.319977 + 0.947425i \(0.396325\pi\)
\(24\) 8.18055e22 1.37815
\(25\) 2.32831e22 0.200000
\(26\) −2.35157e23 −1.05754
\(27\) 4.17567e22 0.100745
\(28\) −5.69692e22 −0.0754280
\(29\) 2.67431e24 1.98447 0.992235 0.124376i \(-0.0396929\pi\)
0.992235 + 0.124376i \(0.0396929\pi\)
\(30\) −1.57439e24 −0.667745
\(31\) 2.64569e24 0.653236 0.326618 0.945156i \(-0.394091\pi\)
0.326618 + 0.945156i \(0.394091\pi\)
\(32\) 1.05089e24 0.153667
\(33\) 1.02671e25 0.903579
\(34\) 5.83459e24 0.313768
\(35\) −1.31424e25 −0.438079
\(36\) 3.93440e24 0.0823925
\(37\) −1.12777e26 −1.50277 −0.751387 0.659862i \(-0.770615\pi\)
−0.751387 + 0.659862i \(0.770615\pi\)
\(38\) 1.44419e26 1.23935
\(39\) 2.62266e26 1.46614
\(40\) 1.16363e26 0.428375
\(41\) 7.31837e26 1.79259 0.896294 0.443460i \(-0.146249\pi\)
0.896294 + 0.443460i \(0.146249\pi\)
\(42\) 8.88682e26 1.46263
\(43\) 3.88890e26 0.434107 0.217054 0.976160i \(-0.430355\pi\)
0.217054 + 0.976160i \(0.430355\pi\)
\(44\) 6.33056e25 0.0483585
\(45\) 9.07641e26 0.478529
\(46\) −1.81034e27 −0.664136
\(47\) 3.28337e27 0.844704 0.422352 0.906432i \(-0.361205\pi\)
0.422352 + 0.906432i \(0.361205\pi\)
\(48\) −8.47786e27 −1.54101
\(49\) −3.12582e26 −0.0404323
\(50\) −2.23946e27 −0.207557
\(51\) −6.50723e27 −0.434999
\(52\) 1.61711e27 0.0784664
\(53\) 3.35567e28 1.18912 0.594562 0.804050i \(-0.297325\pi\)
0.594562 + 0.804050i \(0.297325\pi\)
\(54\) −4.01633e27 −0.104552
\(55\) 1.46042e28 0.280862
\(56\) −6.56825e28 −0.938312
\(57\) −1.61068e29 −1.71821
\(58\) −2.57226e29 −2.05946
\(59\) 2.93443e29 1.77201 0.886005 0.463676i \(-0.153470\pi\)
0.886005 + 0.463676i \(0.153470\pi\)
\(60\) 1.08266e28 0.0495447
\(61\) 7.07686e28 0.246546 0.123273 0.992373i \(-0.460661\pi\)
0.123273 + 0.992373i \(0.460661\pi\)
\(62\) −2.54473e29 −0.677920
\(63\) −5.12330e29 −1.04817
\(64\) 5.77794e29 0.911598
\(65\) 3.73057e29 0.455726
\(66\) −9.87527e29 −0.937722
\(67\) 1.99482e30 1.47798 0.738991 0.673715i \(-0.235302\pi\)
0.738991 + 0.673715i \(0.235302\pi\)
\(68\) −4.01229e28 −0.0232807
\(69\) 2.01905e30 0.920739
\(70\) 1.26409e30 0.454633
\(71\) −1.15434e30 −0.328527 −0.164263 0.986417i \(-0.552525\pi\)
−0.164263 + 0.986417i \(0.552525\pi\)
\(72\) 4.53616e30 1.02495
\(73\) −2.83903e30 −0.510908 −0.255454 0.966821i \(-0.582225\pi\)
−0.255454 + 0.966821i \(0.582225\pi\)
\(74\) 1.08474e31 1.55956
\(75\) 2.49763e30 0.287751
\(76\) −9.93131e29 −0.0919565
\(77\) −8.24353e30 −0.615200
\(78\) −2.52258e31 −1.52154
\(79\) 6.93520e30 0.339010 0.169505 0.985529i \(-0.445783\pi\)
0.169505 + 0.985529i \(0.445783\pi\)
\(80\) −1.20592e31 −0.478998
\(81\) −2.85877e31 −0.925075
\(82\) −7.03910e31 −1.86032
\(83\) 4.09391e31 0.885828 0.442914 0.896564i \(-0.353945\pi\)
0.442914 + 0.896564i \(0.353945\pi\)
\(84\) −6.11122e30 −0.108523
\(85\) −9.25610e30 −0.135212
\(86\) −3.74050e31 −0.450510
\(87\) 2.86880e32 2.85517
\(88\) 7.29881e31 0.601572
\(89\) −1.49837e32 −1.02491 −0.512454 0.858715i \(-0.671264\pi\)
−0.512454 + 0.858715i \(0.671264\pi\)
\(90\) −8.73006e31 −0.496610
\(91\) −2.10577e32 −0.998222
\(92\) 1.24492e31 0.0492769
\(93\) 2.83809e32 0.939849
\(94\) −3.15807e32 −0.876623
\(95\) −2.29109e32 −0.534075
\(96\) 1.12731e32 0.221090
\(97\) 1.00351e33 1.65878 0.829388 0.558673i \(-0.188689\pi\)
0.829388 + 0.558673i \(0.188689\pi\)
\(98\) 3.00654e31 0.0419601
\(99\) 5.69314e32 0.672003
\(100\) 1.54001e31 0.0154001
\(101\) −8.22627e31 −0.0698072 −0.0349036 0.999391i \(-0.511112\pi\)
−0.0349036 + 0.999391i \(0.511112\pi\)
\(102\) 6.25891e32 0.451436
\(103\) 1.80950e33 1.11108 0.555539 0.831491i \(-0.312512\pi\)
0.555539 + 0.831491i \(0.312512\pi\)
\(104\) 1.86444e33 0.976110
\(105\) −1.40982e33 −0.630290
\(106\) −3.22762e33 −1.23406
\(107\) −2.36850e33 −0.775605 −0.387802 0.921743i \(-0.626766\pi\)
−0.387802 + 0.921743i \(0.626766\pi\)
\(108\) 2.76192e31 0.00775744
\(109\) −3.69273e33 −0.890862 −0.445431 0.895316i \(-0.646949\pi\)
−0.445431 + 0.895316i \(0.646949\pi\)
\(110\) −1.40469e33 −0.291475
\(111\) −1.20979e34 −2.16213
\(112\) 6.80697e33 1.04920
\(113\) −1.24016e34 −1.65076 −0.825382 0.564575i \(-0.809040\pi\)
−0.825382 + 0.564575i \(0.809040\pi\)
\(114\) 1.54922e34 1.78313
\(115\) 2.87196e33 0.286196
\(116\) 1.76887e33 0.152806
\(117\) 1.45428e34 1.09039
\(118\) −2.82246e34 −1.83897
\(119\) 5.22472e33 0.296168
\(120\) 1.24825e34 0.616328
\(121\) −1.40647e34 −0.605582
\(122\) −6.80681e33 −0.255862
\(123\) 7.85059e34 2.57910
\(124\) 1.74994e33 0.0502997
\(125\) 3.55271e33 0.0894427
\(126\) 4.92780e34 1.08777
\(127\) −3.85830e34 −0.747541 −0.373771 0.927521i \(-0.621935\pi\)
−0.373771 + 0.927521i \(0.621935\pi\)
\(128\) −6.46016e34 −1.09971
\(129\) 4.17171e34 0.624575
\(130\) −3.58821e34 −0.472947
\(131\) 7.28441e34 0.846093 0.423046 0.906108i \(-0.360961\pi\)
0.423046 + 0.906108i \(0.360961\pi\)
\(132\) 6.79095e33 0.0695762
\(133\) 1.29324e35 1.16984
\(134\) −1.91870e35 −1.53383
\(135\) 6.37157e33 0.0450546
\(136\) −4.62596e34 −0.289608
\(137\) −1.31044e35 −0.726990 −0.363495 0.931596i \(-0.618417\pi\)
−0.363495 + 0.931596i \(0.618417\pi\)
\(138\) −1.94200e35 −0.955531
\(139\) −2.86050e35 −1.24939 −0.624694 0.780870i \(-0.714776\pi\)
−0.624694 + 0.780870i \(0.714776\pi\)
\(140\) −8.69281e33 −0.0337324
\(141\) 3.52215e35 1.21532
\(142\) 1.11029e35 0.340941
\(143\) 2.33998e35 0.639982
\(144\) −4.70102e35 −1.14607
\(145\) 4.08067e35 0.887482
\(146\) 2.73069e35 0.530214
\(147\) −3.35314e34 −0.0581723
\(148\) −7.45944e34 −0.115715
\(149\) −4.76533e35 −0.661485 −0.330742 0.943721i \(-0.607299\pi\)
−0.330742 + 0.943721i \(0.607299\pi\)
\(150\) −2.40232e35 −0.298625
\(151\) 2.97234e35 0.331115 0.165557 0.986200i \(-0.447058\pi\)
0.165557 + 0.986200i \(0.447058\pi\)
\(152\) −1.14503e36 −1.14392
\(153\) −3.60829e35 −0.323514
\(154\) 7.92896e35 0.638446
\(155\) 4.03700e35 0.292136
\(156\) 1.73471e35 0.112894
\(157\) 2.26342e36 1.32562 0.662812 0.748786i \(-0.269363\pi\)
0.662812 + 0.748786i \(0.269363\pi\)
\(158\) −6.67056e35 −0.351820
\(159\) 3.59971e36 1.71086
\(160\) 1.60353e35 0.0687221
\(161\) −1.62112e36 −0.626884
\(162\) 2.74968e36 0.960030
\(163\) 1.48676e35 0.0468970 0.0234485 0.999725i \(-0.492535\pi\)
0.0234485 + 0.999725i \(0.492535\pi\)
\(164\) 4.84059e35 0.138031
\(165\) 1.56663e36 0.404093
\(166\) −3.93768e36 −0.919300
\(167\) 1.71469e36 0.362546 0.181273 0.983433i \(-0.441978\pi\)
0.181273 + 0.983433i \(0.441978\pi\)
\(168\) −7.04592e36 −1.35000
\(169\) 2.21226e35 0.0384331
\(170\) 8.90288e35 0.140321
\(171\) −8.93133e36 −1.27785
\(172\) 2.57224e35 0.0334265
\(173\) −6.70788e36 −0.792181 −0.396090 0.918211i \(-0.629633\pi\)
−0.396090 + 0.918211i \(0.629633\pi\)
\(174\) −2.75932e37 −2.96306
\(175\) −2.00538e36 −0.195915
\(176\) −7.56408e36 −0.672662
\(177\) 3.14784e37 2.54949
\(178\) 1.44120e37 1.06364
\(179\) −7.92192e36 −0.533035 −0.266517 0.963830i \(-0.585873\pi\)
−0.266517 + 0.963830i \(0.585873\pi\)
\(180\) 6.00342e35 0.0368470
\(181\) 2.84989e37 1.59637 0.798183 0.602416i \(-0.205795\pi\)
0.798183 + 0.602416i \(0.205795\pi\)
\(182\) 2.02541e37 1.03594
\(183\) 7.59152e36 0.354720
\(184\) 1.43533e37 0.612997
\(185\) −1.72085e37 −0.672061
\(186\) −2.72979e37 −0.975362
\(187\) −5.80585e36 −0.189880
\(188\) 2.17172e36 0.0650428
\(189\) −3.59651e36 −0.0986874
\(190\) 2.20366e37 0.554256
\(191\) −1.67422e37 −0.386155 −0.193077 0.981184i \(-0.561847\pi\)
−0.193077 + 0.981184i \(0.561847\pi\)
\(192\) 6.19813e37 1.31157
\(193\) 2.80272e37 0.544357 0.272179 0.962247i \(-0.412256\pi\)
0.272179 + 0.962247i \(0.412256\pi\)
\(194\) −9.65216e37 −1.72146
\(195\) 4.00187e37 0.655680
\(196\) −2.06751e35 −0.00311332
\(197\) 5.75950e37 0.797428 0.398714 0.917075i \(-0.369457\pi\)
0.398714 + 0.917075i \(0.369457\pi\)
\(198\) −5.47589e37 −0.697396
\(199\) −1.44611e38 −1.69483 −0.847415 0.530931i \(-0.821842\pi\)
−0.847415 + 0.530931i \(0.821842\pi\)
\(200\) 1.77556e37 0.191575
\(201\) 2.13989e38 2.12646
\(202\) 7.91236e36 0.0724450
\(203\) −2.30339e38 −1.94394
\(204\) −4.30408e36 −0.0334952
\(205\) 1.11669e38 0.801670
\(206\) −1.74045e38 −1.15306
\(207\) 1.11957e38 0.684766
\(208\) −1.93220e38 −1.09146
\(209\) −1.43708e38 −0.750008
\(210\) 1.35602e38 0.654106
\(211\) −4.42459e37 −0.197339 −0.0986695 0.995120i \(-0.531459\pi\)
−0.0986695 + 0.995120i \(0.531459\pi\)
\(212\) 2.21954e37 0.0915634
\(213\) −1.23829e38 −0.472670
\(214\) 2.27812e38 0.804912
\(215\) 5.93398e37 0.194139
\(216\) 3.18435e37 0.0965014
\(217\) −2.27873e38 −0.639894
\(218\) 3.55182e38 0.924524
\(219\) −3.04550e38 −0.735073
\(220\) 9.65967e36 0.0216266
\(221\) −1.48307e38 −0.308099
\(222\) 1.16363e39 2.24383
\(223\) −4.20819e38 −0.753469 −0.376734 0.926321i \(-0.622953\pi\)
−0.376734 + 0.926321i \(0.622953\pi\)
\(224\) −9.05132e37 −0.150529
\(225\) 1.38495e38 0.214004
\(226\) 1.19284e39 1.71314
\(227\) −2.29758e38 −0.306793 −0.153396 0.988165i \(-0.549021\pi\)
−0.153396 + 0.988165i \(0.549021\pi\)
\(228\) −1.06536e38 −0.132303
\(229\) −1.22734e39 −1.41801 −0.709007 0.705202i \(-0.750856\pi\)
−0.709007 + 0.705202i \(0.750856\pi\)
\(230\) −2.76237e38 −0.297011
\(231\) −8.84304e38 −0.885123
\(232\) 2.03942e39 1.90088
\(233\) 2.11378e39 1.83522 0.917608 0.397486i \(-0.130117\pi\)
0.917608 + 0.397486i \(0.130117\pi\)
\(234\) −1.39879e39 −1.13159
\(235\) 5.01002e38 0.377763
\(236\) 1.94093e38 0.136446
\(237\) 7.43956e38 0.487753
\(238\) −5.02535e38 −0.307359
\(239\) −9.09248e38 −0.518940 −0.259470 0.965751i \(-0.583548\pi\)
−0.259470 + 0.965751i \(0.583548\pi\)
\(240\) −1.29362e39 −0.689162
\(241\) −1.71576e39 −0.853443 −0.426722 0.904383i \(-0.640332\pi\)
−0.426722 + 0.904383i \(0.640332\pi\)
\(242\) 1.35280e39 0.628465
\(243\) −3.29880e39 −1.43170
\(244\) 4.68085e37 0.0189842
\(245\) −4.76962e37 −0.0180819
\(246\) −7.55101e39 −2.67655
\(247\) −3.67093e39 −1.21696
\(248\) 2.01759e39 0.625720
\(249\) 4.39163e39 1.27449
\(250\) −3.41714e38 −0.0928224
\(251\) 3.71395e39 0.944537 0.472269 0.881455i \(-0.343435\pi\)
0.472269 + 0.881455i \(0.343435\pi\)
\(252\) −3.38871e38 −0.0807096
\(253\) 1.80143e39 0.401909
\(254\) 3.71107e39 0.775788
\(255\) −9.92924e38 −0.194537
\(256\) 1.25043e39 0.229668
\(257\) 3.64681e39 0.628082 0.314041 0.949409i \(-0.398317\pi\)
0.314041 + 0.949409i \(0.398317\pi\)
\(258\) −4.01252e39 −0.648175
\(259\) 9.71354e39 1.47208
\(260\) 2.46751e38 0.0350913
\(261\) 1.59076e40 2.12343
\(262\) −7.00644e39 −0.878064
\(263\) 3.70275e39 0.435767 0.217884 0.975975i \(-0.430085\pi\)
0.217884 + 0.975975i \(0.430085\pi\)
\(264\) 7.82961e39 0.865517
\(265\) 5.12035e39 0.531793
\(266\) −1.24389e40 −1.21404
\(267\) −1.60734e40 −1.47459
\(268\) 1.31944e39 0.113806
\(269\) −1.93097e40 −1.56626 −0.783129 0.621859i \(-0.786378\pi\)
−0.783129 + 0.621859i \(0.786378\pi\)
\(270\) −6.12843e38 −0.0467570
\(271\) −5.56561e37 −0.00399502 −0.00199751 0.999998i \(-0.500636\pi\)
−0.00199751 + 0.999998i \(0.500636\pi\)
\(272\) 4.79409e39 0.323831
\(273\) −2.25891e40 −1.43620
\(274\) 1.26044e40 0.754460
\(275\) 2.22842e39 0.125605
\(276\) 1.33546e39 0.0708976
\(277\) −2.59199e40 −1.29634 −0.648168 0.761497i \(-0.724465\pi\)
−0.648168 + 0.761497i \(0.724465\pi\)
\(278\) 2.75134e40 1.29660
\(279\) 1.57374e40 0.698977
\(280\) −1.00224e40 −0.419626
\(281\) 4.04959e40 1.59866 0.799331 0.600891i \(-0.205187\pi\)
0.799331 + 0.600891i \(0.205187\pi\)
\(282\) −3.38774e40 −1.26125
\(283\) 4.05121e40 1.42269 0.711343 0.702846i \(-0.248087\pi\)
0.711343 + 0.702846i \(0.248087\pi\)
\(284\) −7.63516e38 −0.0252968
\(285\) −2.45771e40 −0.768405
\(286\) −2.25069e40 −0.664165
\(287\) −6.30332e40 −1.75597
\(288\) 6.25102e39 0.164428
\(289\) −3.65748e40 −0.908588
\(290\) −3.92495e40 −0.921017
\(291\) 1.07649e41 2.38658
\(292\) −1.87782e39 −0.0393403
\(293\) 7.90241e38 0.0156475 0.00782373 0.999969i \(-0.497510\pi\)
0.00782373 + 0.999969i \(0.497510\pi\)
\(294\) 3.22519e39 0.0603704
\(295\) 4.47759e40 0.792467
\(296\) −8.60035e40 −1.43947
\(297\) 3.99654e39 0.0632707
\(298\) 4.58349e40 0.686480
\(299\) 4.60164e40 0.652136
\(300\) 1.65201e39 0.0221571
\(301\) −3.34951e40 −0.425241
\(302\) −2.85891e40 −0.343627
\(303\) −8.82452e39 −0.100436
\(304\) 1.18664e41 1.27910
\(305\) 1.07984e40 0.110259
\(306\) 3.47060e40 0.335739
\(307\) 1.53513e41 1.40722 0.703612 0.710585i \(-0.251569\pi\)
0.703612 + 0.710585i \(0.251569\pi\)
\(308\) −5.45253e39 −0.0473708
\(309\) 1.94110e41 1.59857
\(310\) −3.88295e40 −0.303175
\(311\) −2.01085e41 −1.48879 −0.744395 0.667739i \(-0.767262\pi\)
−0.744395 + 0.667739i \(0.767262\pi\)
\(312\) 2.00003e41 1.40438
\(313\) −6.89540e40 −0.459280 −0.229640 0.973276i \(-0.573755\pi\)
−0.229640 + 0.973276i \(0.573755\pi\)
\(314\) −2.17705e41 −1.37571
\(315\) −7.81753e40 −0.468755
\(316\) 4.58716e39 0.0261040
\(317\) −2.25823e41 −1.21981 −0.609903 0.792476i \(-0.708792\pi\)
−0.609903 + 0.792476i \(0.708792\pi\)
\(318\) −3.46234e41 −1.77551
\(319\) 2.55958e41 1.24630
\(320\) 8.81643e40 0.407679
\(321\) −2.54075e41 −1.11591
\(322\) 1.55925e41 0.650571
\(323\) 9.10814e40 0.361067
\(324\) −1.89088e40 −0.0712314
\(325\) 5.69239e40 0.203807
\(326\) −1.43002e40 −0.0486691
\(327\) −3.96128e41 −1.28173
\(328\) 5.58095e41 1.71708
\(329\) −2.82797e41 −0.827451
\(330\) −1.50685e41 −0.419362
\(331\) −1.74008e41 −0.460688 −0.230344 0.973109i \(-0.573985\pi\)
−0.230344 + 0.973109i \(0.573985\pi\)
\(332\) 2.70784e40 0.0682094
\(333\) −6.70836e41 −1.60800
\(334\) −1.64925e41 −0.376245
\(335\) 3.04385e41 0.660974
\(336\) 7.30200e41 1.50954
\(337\) 8.05374e41 1.58527 0.792636 0.609695i \(-0.208708\pi\)
0.792636 + 0.609695i \(0.208708\pi\)
\(338\) −2.12784e40 −0.0398853
\(339\) −1.33035e42 −2.37505
\(340\) −6.12227e39 −0.0104114
\(341\) 2.53219e41 0.410250
\(342\) 8.59052e41 1.32614
\(343\) 6.92795e41 1.01918
\(344\) 2.96565e41 0.415821
\(345\) 3.08082e41 0.411767
\(346\) 6.45191e41 0.822115
\(347\) 6.26061e41 0.760642 0.380321 0.924854i \(-0.375813\pi\)
0.380321 + 0.924854i \(0.375813\pi\)
\(348\) 1.89751e41 0.219850
\(349\) −9.05089e40 −0.100017 −0.0500083 0.998749i \(-0.515925\pi\)
−0.0500083 + 0.998749i \(0.515925\pi\)
\(350\) 1.92885e41 0.203318
\(351\) 1.02089e41 0.102663
\(352\) 1.00581e41 0.0965073
\(353\) −1.08093e42 −0.989725 −0.494862 0.868971i \(-0.664782\pi\)
−0.494862 + 0.868971i \(0.664782\pi\)
\(354\) −3.02772e42 −2.64583
\(355\) −1.76138e41 −0.146922
\(356\) −9.91071e40 −0.0789186
\(357\) 5.60469e41 0.426114
\(358\) 7.61962e41 0.553176
\(359\) −2.08351e41 −0.144456 −0.0722282 0.997388i \(-0.523011\pi\)
−0.0722282 + 0.997388i \(0.523011\pi\)
\(360\) 6.92163e41 0.458371
\(361\) 6.73698e41 0.426183
\(362\) −2.74114e42 −1.65669
\(363\) −1.50876e42 −0.871285
\(364\) −1.39282e41 −0.0768638
\(365\) −4.33202e41 −0.228485
\(366\) −7.30183e41 −0.368124
\(367\) −1.16121e42 −0.559654 −0.279827 0.960050i \(-0.590277\pi\)
−0.279827 + 0.960050i \(0.590277\pi\)
\(368\) −1.48750e42 −0.685437
\(369\) 4.35320e42 1.91811
\(370\) 1.65518e42 0.697456
\(371\) −2.89024e42 −1.16484
\(372\) 1.87720e41 0.0723690
\(373\) −1.34955e42 −0.497728 −0.248864 0.968538i \(-0.580057\pi\)
−0.248864 + 0.968538i \(0.580057\pi\)
\(374\) 5.58430e41 0.197055
\(375\) 3.81108e41 0.128686
\(376\) 2.50388e42 0.809122
\(377\) 6.53832e42 2.02225
\(378\) 3.45927e41 0.102416
\(379\) 3.19198e42 0.904717 0.452358 0.891836i \(-0.350583\pi\)
0.452358 + 0.891836i \(0.350583\pi\)
\(380\) −1.51540e41 −0.0411242
\(381\) −4.13890e42 −1.07553
\(382\) 1.61033e42 0.400746
\(383\) −3.06206e42 −0.729849 −0.364925 0.931037i \(-0.618905\pi\)
−0.364925 + 0.931037i \(0.618905\pi\)
\(384\) −6.92997e42 −1.58222
\(385\) −1.25786e42 −0.275126
\(386\) −2.69577e42 −0.564926
\(387\) 2.31324e42 0.464504
\(388\) 6.63752e41 0.127727
\(389\) 5.44019e42 1.00333 0.501667 0.865061i \(-0.332720\pi\)
0.501667 + 0.865061i \(0.332720\pi\)
\(390\) −3.84916e42 −0.680456
\(391\) −1.14174e42 −0.193486
\(392\) −2.38374e41 −0.0387292
\(393\) 7.81416e42 1.21732
\(394\) −5.53971e42 −0.827560
\(395\) 1.05823e42 0.151610
\(396\) 3.76562e41 0.0517447
\(397\) 4.34919e42 0.573277 0.286639 0.958039i \(-0.407462\pi\)
0.286639 + 0.958039i \(0.407462\pi\)
\(398\) 1.39093e43 1.75887
\(399\) 1.38729e43 1.68311
\(400\) −1.84009e42 −0.214214
\(401\) −1.13262e42 −0.126532 −0.0632660 0.997997i \(-0.520152\pi\)
−0.0632660 + 0.997997i \(0.520152\pi\)
\(402\) −2.05823e43 −2.20681
\(403\) 6.46834e42 0.665671
\(404\) −5.44111e40 −0.00537520
\(405\) −4.36214e42 −0.413706
\(406\) 2.21549e43 2.01739
\(407\) −1.07939e43 −0.943783
\(408\) −4.96238e42 −0.416675
\(409\) 6.57876e42 0.530530 0.265265 0.964176i \(-0.414541\pi\)
0.265265 + 0.964176i \(0.414541\pi\)
\(410\) −1.07408e43 −0.831962
\(411\) −1.40574e43 −1.04596
\(412\) 1.19686e42 0.0855538
\(413\) −2.52743e43 −1.73582
\(414\) −1.07685e43 −0.710640
\(415\) 6.24681e42 0.396154
\(416\) 2.56928e42 0.156593
\(417\) −3.06853e43 −1.79757
\(418\) 1.38224e43 0.778349
\(419\) −2.13895e43 −1.15789 −0.578947 0.815365i \(-0.696536\pi\)
−0.578947 + 0.815365i \(0.696536\pi\)
\(420\) −9.32499e41 −0.0485328
\(421\) −5.34625e42 −0.267544 −0.133772 0.991012i \(-0.542709\pi\)
−0.133772 + 0.991012i \(0.542709\pi\)
\(422\) 4.25575e42 0.204796
\(423\) 1.95305e43 0.903852
\(424\) 2.55902e43 1.13903
\(425\) −1.41237e42 −0.0604687
\(426\) 1.19104e43 0.490531
\(427\) −6.09531e42 −0.241511
\(428\) −1.56660e42 −0.0597221
\(429\) 2.51016e43 0.920779
\(430\) −5.70754e42 −0.201474
\(431\) 2.33735e43 0.794053 0.397026 0.917807i \(-0.370042\pi\)
0.397026 + 0.917807i \(0.370042\pi\)
\(432\) −3.30008e42 −0.107905
\(433\) −1.61313e43 −0.507714 −0.253857 0.967242i \(-0.581699\pi\)
−0.253857 + 0.967242i \(0.581699\pi\)
\(434\) 2.19178e43 0.664074
\(435\) 4.37744e43 1.27687
\(436\) −2.44249e42 −0.0685970
\(437\) −2.82605e43 −0.764252
\(438\) 2.92928e43 0.762849
\(439\) 4.60088e43 1.15392 0.576961 0.816772i \(-0.304238\pi\)
0.576961 + 0.816772i \(0.304238\pi\)
\(440\) 1.11371e43 0.269031
\(441\) −1.85934e42 −0.0432635
\(442\) 1.42648e43 0.319741
\(443\) −5.92450e43 −1.27935 −0.639676 0.768644i \(-0.720932\pi\)
−0.639676 + 0.768644i \(0.720932\pi\)
\(444\) −8.00193e42 −0.166485
\(445\) −2.28634e43 −0.458353
\(446\) 4.04761e43 0.781940
\(447\) −5.11189e43 −0.951716
\(448\) −4.97655e43 −0.892978
\(449\) −1.64413e43 −0.284361 −0.142181 0.989841i \(-0.545411\pi\)
−0.142181 + 0.989841i \(0.545411\pi\)
\(450\) −1.33210e43 −0.222091
\(451\) 7.00442e43 1.12579
\(452\) −8.20283e42 −0.127110
\(453\) 3.18850e43 0.476394
\(454\) 2.20991e43 0.318385
\(455\) −3.21314e43 −0.446418
\(456\) −1.22830e44 −1.64583
\(457\) 2.69494e42 0.0348283 0.0174141 0.999848i \(-0.494457\pi\)
0.0174141 + 0.999848i \(0.494457\pi\)
\(458\) 1.18051e44 1.47160
\(459\) −2.53299e42 −0.0304596
\(460\) 1.89960e42 0.0220373
\(461\) −8.91542e43 −0.997876 −0.498938 0.866638i \(-0.666276\pi\)
−0.498938 + 0.866638i \(0.666276\pi\)
\(462\) 8.50559e43 0.918569
\(463\) −7.81223e43 −0.814121 −0.407060 0.913401i \(-0.633446\pi\)
−0.407060 + 0.913401i \(0.633446\pi\)
\(464\) −2.11354e44 −2.12551
\(465\) 4.33059e43 0.420313
\(466\) −2.03312e44 −1.90456
\(467\) 1.34336e44 1.21469 0.607344 0.794439i \(-0.292235\pi\)
0.607344 + 0.794439i \(0.292235\pi\)
\(468\) 9.61907e42 0.0839608
\(469\) −1.71814e44 −1.44780
\(470\) −4.81884e43 −0.392038
\(471\) 2.42802e44 1.90725
\(472\) 2.23779e44 1.69737
\(473\) 3.72207e43 0.272631
\(474\) −7.15567e43 −0.506183
\(475\) −3.49593e43 −0.238846
\(476\) 3.45579e42 0.0228052
\(477\) 1.99606e44 1.27239
\(478\) 8.74551e43 0.538549
\(479\) 6.08543e43 0.362039 0.181020 0.983479i \(-0.442060\pi\)
0.181020 + 0.983479i \(0.442060\pi\)
\(480\) 1.72014e43 0.0988745
\(481\) −2.75725e44 −1.53138
\(482\) 1.65028e44 0.885692
\(483\) −1.73901e44 −0.901933
\(484\) −9.30285e42 −0.0466302
\(485\) 1.53123e44 0.741827
\(486\) 3.17292e44 1.48580
\(487\) −2.29550e44 −1.03908 −0.519541 0.854446i \(-0.673897\pi\)
−0.519541 + 0.854446i \(0.673897\pi\)
\(488\) 5.39678e43 0.236161
\(489\) 1.59488e43 0.0674734
\(490\) 4.58761e42 0.0187651
\(491\) −5.01787e43 −0.198461 −0.0992305 0.995064i \(-0.531638\pi\)
−0.0992305 + 0.995064i \(0.531638\pi\)
\(492\) 5.19262e43 0.198592
\(493\) −1.62226e44 −0.599992
\(494\) 3.53085e44 1.26295
\(495\) 8.68705e43 0.300529
\(496\) −2.09092e44 −0.699663
\(497\) 9.94235e43 0.321817
\(498\) −4.22405e44 −1.32265
\(499\) −1.28404e44 −0.388974 −0.194487 0.980905i \(-0.562304\pi\)
−0.194487 + 0.980905i \(0.562304\pi\)
\(500\) 2.34987e42 0.00688715
\(501\) 1.83939e44 0.521615
\(502\) −3.57222e44 −0.980228
\(503\) 3.85407e44 1.02341 0.511703 0.859163i \(-0.329015\pi\)
0.511703 + 0.859163i \(0.329015\pi\)
\(504\) −3.90700e44 −1.00401
\(505\) −1.25523e43 −0.0312187
\(506\) −1.73268e44 −0.417096
\(507\) 2.37314e43 0.0552959
\(508\) −2.55200e43 −0.0575612
\(509\) 5.40769e44 1.18078 0.590389 0.807119i \(-0.298974\pi\)
0.590389 + 0.807119i \(0.298974\pi\)
\(510\) 9.55034e43 0.201888
\(511\) 2.44526e44 0.500473
\(512\) 4.34652e44 0.861365
\(513\) −6.26972e43 −0.120313
\(514\) −3.50765e44 −0.651815
\(515\) 2.76108e44 0.496889
\(516\) 2.75930e43 0.0480927
\(517\) 3.14251e44 0.530497
\(518\) −9.34287e44 −1.52770
\(519\) −7.19570e44 −1.13976
\(520\) 2.84491e44 0.436530
\(521\) −9.57656e42 −0.0142360 −0.00711799 0.999975i \(-0.502266\pi\)
−0.00711799 + 0.999975i \(0.502266\pi\)
\(522\) −1.53006e45 −2.20366
\(523\) −7.88861e43 −0.110084 −0.0550418 0.998484i \(-0.517529\pi\)
−0.0550418 + 0.998484i \(0.517529\pi\)
\(524\) 4.81813e43 0.0651497
\(525\) −2.15122e44 −0.281874
\(526\) −3.56145e44 −0.452233
\(527\) −1.60489e44 −0.197502
\(528\) −8.11417e44 −0.967798
\(529\) −5.10749e44 −0.590458
\(530\) −4.92495e44 −0.551887
\(531\) 1.74549e45 1.89609
\(532\) 8.55386e43 0.0900783
\(533\) 1.78924e45 1.82671
\(534\) 1.54601e45 1.53031
\(535\) −3.61404e44 −0.346861
\(536\) 1.52124e45 1.41572
\(537\) −8.49804e44 −0.766907
\(538\) 1.85729e45 1.62544
\(539\) −2.99173e43 −0.0253926
\(540\) 4.21435e42 0.00346923
\(541\) −1.96609e45 −1.56981 −0.784907 0.619613i \(-0.787289\pi\)
−0.784907 + 0.619613i \(0.787289\pi\)
\(542\) 5.35323e42 0.00414598
\(543\) 3.05715e45 2.29678
\(544\) −6.37476e43 −0.0464603
\(545\) −5.63466e44 −0.398405
\(546\) 2.17271e45 1.49047
\(547\) −4.44935e44 −0.296146 −0.148073 0.988976i \(-0.547307\pi\)
−0.148073 + 0.988976i \(0.547307\pi\)
\(548\) −8.66767e43 −0.0559787
\(549\) 4.20954e44 0.263810
\(550\) −2.14339e44 −0.130352
\(551\) −4.01544e45 −2.36991
\(552\) 1.53972e45 0.881954
\(553\) −5.97331e44 −0.332086
\(554\) 2.49308e45 1.34532
\(555\) −1.84599e45 −0.966932
\(556\) −1.89202e44 −0.0962037
\(557\) −1.02978e45 −0.508318 −0.254159 0.967162i \(-0.581799\pi\)
−0.254159 + 0.967162i \(0.581799\pi\)
\(558\) −1.51368e45 −0.725389
\(559\) 9.50782e44 0.442370
\(560\) 1.03866e45 0.469214
\(561\) −6.22807e44 −0.273191
\(562\) −3.89506e45 −1.65907
\(563\) −3.82628e45 −1.58266 −0.791331 0.611388i \(-0.790612\pi\)
−0.791331 + 0.611388i \(0.790612\pi\)
\(564\) 2.32966e44 0.0935808
\(565\) −1.89234e45 −0.738244
\(566\) −3.89662e45 −1.47644
\(567\) 2.46227e45 0.906180
\(568\) −8.80294e44 −0.314688
\(569\) −1.77526e45 −0.616468 −0.308234 0.951311i \(-0.599738\pi\)
−0.308234 + 0.951311i \(0.599738\pi\)
\(570\) 2.36392e45 0.797440
\(571\) 1.00861e45 0.330544 0.165272 0.986248i \(-0.447150\pi\)
0.165272 + 0.986248i \(0.447150\pi\)
\(572\) 1.54774e44 0.0492791
\(573\) −1.79597e45 −0.555583
\(574\) 6.06279e45 1.82233
\(575\) 4.38226e44 0.127991
\(576\) 3.43690e45 0.975430
\(577\) 3.07790e45 0.848895 0.424448 0.905452i \(-0.360468\pi\)
0.424448 + 0.905452i \(0.360468\pi\)
\(578\) 3.51791e45 0.942921
\(579\) 3.00654e45 0.783198
\(580\) 2.69908e44 0.0683367
\(581\) −3.52609e45 −0.867735
\(582\) −1.03541e46 −2.47676
\(583\) 3.21171e45 0.746803
\(584\) −2.16503e45 −0.489387
\(585\) 2.21906e45 0.487638
\(586\) −7.60085e43 −0.0162387
\(587\) 3.80587e45 0.790544 0.395272 0.918564i \(-0.370650\pi\)
0.395272 + 0.918564i \(0.370650\pi\)
\(588\) −2.21787e43 −0.00447931
\(589\) −3.97247e45 −0.780114
\(590\) −4.30673e45 −0.822411
\(591\) 6.17835e45 1.14731
\(592\) 8.91292e45 1.60958
\(593\) −1.41796e45 −0.249036 −0.124518 0.992217i \(-0.539738\pi\)
−0.124518 + 0.992217i \(0.539738\pi\)
\(594\) −3.84403e44 −0.0656615
\(595\) 7.97229e44 0.132450
\(596\) −3.15194e44 −0.0509348
\(597\) −1.55128e46 −2.43845
\(598\) −4.42605e45 −0.676778
\(599\) 7.86874e45 1.17048 0.585239 0.810861i \(-0.301001\pi\)
0.585239 + 0.810861i \(0.301001\pi\)
\(600\) 1.90468e45 0.275630
\(601\) 6.55936e45 0.923491 0.461746 0.887012i \(-0.347223\pi\)
0.461746 + 0.887012i \(0.347223\pi\)
\(602\) 3.22170e45 0.441309
\(603\) 1.18658e46 1.58147
\(604\) 1.96600e44 0.0254961
\(605\) −2.14611e45 −0.270824
\(606\) 8.48778e44 0.104231
\(607\) 1.16821e46 1.39607 0.698037 0.716062i \(-0.254057\pi\)
0.698037 + 0.716062i \(0.254057\pi\)
\(608\) −1.57790e45 −0.183514
\(609\) −2.47090e46 −2.79685
\(610\) −1.03864e45 −0.114425
\(611\) 8.02738e45 0.860783
\(612\) −2.38664e44 −0.0249108
\(613\) −2.09504e45 −0.212860 −0.106430 0.994320i \(-0.533942\pi\)
−0.106430 + 0.994320i \(0.533942\pi\)
\(614\) −1.47655e46 −1.46040
\(615\) 1.19791e46 1.15341
\(616\) −6.28648e45 −0.589285
\(617\) 1.98589e45 0.181238 0.0906192 0.995886i \(-0.471115\pi\)
0.0906192 + 0.995886i \(0.471115\pi\)
\(618\) −1.86702e46 −1.65898
\(619\) −8.02615e45 −0.694403 −0.347201 0.937791i \(-0.612868\pi\)
−0.347201 + 0.937791i \(0.612868\pi\)
\(620\) 2.67019e44 0.0224947
\(621\) 7.85931e44 0.0644723
\(622\) 1.93412e46 1.54505
\(623\) 1.29055e46 1.00397
\(624\) −2.07272e46 −1.57035
\(625\) 5.42101e44 0.0400000
\(626\) 6.63227e45 0.476635
\(627\) −1.54159e46 −1.07908
\(628\) 1.49709e45 0.102074
\(629\) 6.84116e45 0.454354
\(630\) 7.51922e45 0.486467
\(631\) −2.32504e46 −1.46536 −0.732682 0.680571i \(-0.761732\pi\)
−0.732682 + 0.680571i \(0.761732\pi\)
\(632\) 5.28875e45 0.324729
\(633\) −4.74637e45 −0.283923
\(634\) 2.17206e46 1.26590
\(635\) −5.88731e45 −0.334311
\(636\) 2.38096e45 0.131738
\(637\) −7.64220e44 −0.0412020
\(638\) −2.46191e46 −1.29339
\(639\) −6.86638e45 −0.351531
\(640\) −9.85742e45 −0.491806
\(641\) 1.10320e46 0.536412 0.268206 0.963362i \(-0.413569\pi\)
0.268206 + 0.963362i \(0.413569\pi\)
\(642\) 2.44379e46 1.15807
\(643\) 1.90982e46 0.882085 0.441042 0.897486i \(-0.354609\pi\)
0.441042 + 0.897486i \(0.354609\pi\)
\(644\) −1.07226e45 −0.0482705
\(645\) 6.36553e45 0.279318
\(646\) −8.76058e45 −0.374711
\(647\) 2.77860e46 1.15853 0.579263 0.815141i \(-0.303341\pi\)
0.579263 + 0.815141i \(0.303341\pi\)
\(648\) −2.18009e46 −0.886107
\(649\) 2.80855e46 1.11287
\(650\) −5.47517e45 −0.211508
\(651\) −2.44445e46 −0.920652
\(652\) 9.83389e43 0.00361110
\(653\) −1.10232e46 −0.394676 −0.197338 0.980335i \(-0.563230\pi\)
−0.197338 + 0.980335i \(0.563230\pi\)
\(654\) 3.81012e46 1.33017
\(655\) 1.11151e46 0.378384
\(656\) −5.78379e46 −1.91999
\(657\) −1.68875e46 −0.546683
\(658\) 2.72006e46 0.858718
\(659\) 2.82127e46 0.868632 0.434316 0.900761i \(-0.356990\pi\)
0.434316 + 0.900761i \(0.356990\pi\)
\(660\) 1.03622e45 0.0311154
\(661\) 3.86133e44 0.0113087 0.00565435 0.999984i \(-0.498200\pi\)
0.00565435 + 0.999984i \(0.498200\pi\)
\(662\) 1.67368e46 0.478096
\(663\) −1.59093e46 −0.443279
\(664\) 3.12199e46 0.848514
\(665\) 1.97332e46 0.523167
\(666\) 6.45237e46 1.66876
\(667\) 5.03350e46 1.26997
\(668\) 1.13415e45 0.0279163
\(669\) −4.51423e46 −1.08406
\(670\) −2.92770e46 −0.685950
\(671\) 6.77327e45 0.154838
\(672\) −9.70957e45 −0.216574
\(673\) −3.62752e46 −0.789517 −0.394759 0.918785i \(-0.629172\pi\)
−0.394759 + 0.918785i \(0.629172\pi\)
\(674\) −7.74641e46 −1.64517
\(675\) 9.72224e44 0.0201490
\(676\) 1.46326e44 0.00295937
\(677\) −6.71996e46 −1.32634 −0.663168 0.748471i \(-0.730788\pi\)
−0.663168 + 0.748471i \(0.730788\pi\)
\(678\) 1.27959e47 2.46479
\(679\) −8.64325e46 −1.62490
\(680\) −7.05866e45 −0.129516
\(681\) −2.46468e46 −0.441400
\(682\) −2.43556e46 −0.425752
\(683\) 5.58915e45 0.0953684 0.0476842 0.998862i \(-0.484816\pi\)
0.0476842 + 0.998862i \(0.484816\pi\)
\(684\) −5.90746e45 −0.0983955
\(685\) −1.99958e46 −0.325120
\(686\) −6.66358e46 −1.05769
\(687\) −1.31660e47 −2.04018
\(688\) −3.07344e46 −0.464960
\(689\) 8.20415e46 1.21176
\(690\) −2.96326e46 −0.427326
\(691\) 5.89510e46 0.830048 0.415024 0.909810i \(-0.363773\pi\)
0.415024 + 0.909810i \(0.363773\pi\)
\(692\) −4.43680e45 −0.0609985
\(693\) −4.90352e46 −0.658278
\(694\) −6.02171e46 −0.789384
\(695\) −4.36477e46 −0.558743
\(696\) 2.18773e47 2.73490
\(697\) −4.43938e46 −0.541977
\(698\) 8.70551e45 0.103796
\(699\) 2.26750e47 2.64043
\(700\) −1.32642e45 −0.0150856
\(701\) −9.67830e46 −1.07511 −0.537554 0.843229i \(-0.680651\pi\)
−0.537554 + 0.843229i \(0.680651\pi\)
\(702\) −9.81937e45 −0.106542
\(703\) 1.69334e47 1.79466
\(704\) 5.53007e46 0.572508
\(705\) 5.37437e46 0.543510
\(706\) 1.03968e47 1.02712
\(707\) 7.08530e45 0.0683814
\(708\) 2.08208e46 0.196313
\(709\) −1.89011e46 −0.174110 −0.0870552 0.996203i \(-0.527746\pi\)
−0.0870552 + 0.996203i \(0.527746\pi\)
\(710\) 1.69417e46 0.152473
\(711\) 4.12528e46 0.362748
\(712\) −1.14265e47 −0.981735
\(713\) 4.97963e46 0.418042
\(714\) −5.39081e46 −0.442215
\(715\) 3.57053e46 0.286209
\(716\) −5.23980e45 −0.0410440
\(717\) −9.75372e46 −0.746628
\(718\) 2.00400e46 0.149915
\(719\) 1.61675e47 1.18199 0.590997 0.806674i \(-0.298735\pi\)
0.590997 + 0.806674i \(0.298735\pi\)
\(720\) −7.17319e46 −0.512538
\(721\) −1.55853e47 −1.08838
\(722\) −6.47989e46 −0.442287
\(723\) −1.84053e47 −1.22790
\(724\) 1.88501e46 0.122921
\(725\) 6.22661e46 0.396894
\(726\) 1.45118e47 0.904208
\(727\) 6.77908e44 0.00412908 0.00206454 0.999998i \(-0.499343\pi\)
0.00206454 + 0.999998i \(0.499343\pi\)
\(728\) −1.60585e47 −0.956173
\(729\) −1.94950e47 −1.13480
\(730\) 4.16671e46 0.237119
\(731\) −2.35903e46 −0.131249
\(732\) 5.02127e45 0.0273137
\(733\) 1.03172e46 0.0548714 0.0274357 0.999624i \(-0.491266\pi\)
0.0274357 + 0.999624i \(0.491266\pi\)
\(734\) 1.11690e47 0.580802
\(735\) −5.11649e45 −0.0260154
\(736\) 1.97795e46 0.0983401
\(737\) 1.90924e47 0.928213
\(738\) −4.18708e47 −1.99059
\(739\) 3.22918e46 0.150127 0.0750636 0.997179i \(-0.476084\pi\)
0.0750636 + 0.997179i \(0.476084\pi\)
\(740\) −1.13822e46 −0.0517491
\(741\) −3.93790e47 −1.75091
\(742\) 2.77995e47 1.20885
\(743\) 3.20296e47 1.36218 0.681092 0.732198i \(-0.261506\pi\)
0.681092 + 0.732198i \(0.261506\pi\)
\(744\) 2.16432e47 0.900259
\(745\) −7.27132e46 −0.295825
\(746\) 1.29805e47 0.516535
\(747\) 2.43519e47 0.947856
\(748\) −3.84017e45 −0.0146209
\(749\) 2.03999e47 0.759763
\(750\) −3.66565e46 −0.133549
\(751\) −5.04227e47 −1.79708 −0.898540 0.438891i \(-0.855371\pi\)
−0.898540 + 0.438891i \(0.855371\pi\)
\(752\) −2.59488e47 −0.904739
\(753\) 3.98404e47 1.35896
\(754\) −6.28882e47 −2.09866
\(755\) 4.53543e46 0.148079
\(756\) −2.37884e45 −0.00759900
\(757\) −5.03192e47 −1.57272 −0.786361 0.617767i \(-0.788038\pi\)
−0.786361 + 0.617767i \(0.788038\pi\)
\(758\) −3.07017e47 −0.938903
\(759\) 1.93243e47 0.578249
\(760\) −1.74717e47 −0.511578
\(761\) −3.34360e47 −0.958004 −0.479002 0.877814i \(-0.659001\pi\)
−0.479002 + 0.877814i \(0.659001\pi\)
\(762\) 3.98096e47 1.11617
\(763\) 3.18055e47 0.872666
\(764\) −1.10738e46 −0.0297342
\(765\) −5.50582e46 −0.144680
\(766\) 2.94521e47 0.757428
\(767\) 7.17429e47 1.80574
\(768\) 1.34137e47 0.330436
\(769\) −5.27752e47 −1.27246 −0.636231 0.771498i \(-0.719508\pi\)
−0.636231 + 0.771498i \(0.719508\pi\)
\(770\) 1.20986e47 0.285522
\(771\) 3.91202e47 0.903658
\(772\) 1.85380e46 0.0419159
\(773\) 1.62889e47 0.360520 0.180260 0.983619i \(-0.442306\pi\)
0.180260 + 0.983619i \(0.442306\pi\)
\(774\) −2.22497e47 −0.482056
\(775\) 6.15997e46 0.130647
\(776\) 7.65272e47 1.58890
\(777\) 1.04200e48 2.11797
\(778\) −5.23259e47 −1.04125
\(779\) −1.09884e48 −2.14076
\(780\) 2.64696e46 0.0504878
\(781\) −1.10482e47 −0.206324
\(782\) 1.09817e47 0.200797
\(783\) 1.11670e47 0.199926
\(784\) 2.47037e46 0.0433059
\(785\) 3.45370e47 0.592837
\(786\) −7.51598e47 −1.26332
\(787\) 1.50460e46 0.0247649 0.0123825 0.999923i \(-0.496058\pi\)
0.0123825 + 0.999923i \(0.496058\pi\)
\(788\) 3.80951e46 0.0614025
\(789\) 3.97203e47 0.626963
\(790\) −1.01785e47 −0.157339
\(791\) 1.06816e48 1.61705
\(792\) 4.34156e47 0.643696
\(793\) 1.73020e47 0.251239
\(794\) −4.18322e47 −0.594939
\(795\) 5.49272e47 0.765121
\(796\) −9.56503e46 −0.130503
\(797\) −5.86479e47 −0.783773 −0.391887 0.920014i \(-0.628177\pi\)
−0.391887 + 0.920014i \(0.628177\pi\)
\(798\) −1.33435e48 −1.74671
\(799\) −1.99171e47 −0.255391
\(800\) 2.44679e46 0.0307335
\(801\) −8.91280e47 −1.09667
\(802\) 1.08940e47 0.131313
\(803\) −2.71724e47 −0.320864
\(804\) 1.41539e47 0.163739
\(805\) −2.47363e47 −0.280351
\(806\) −6.22151e47 −0.690824
\(807\) −2.07140e48 −2.25347
\(808\) −6.27331e46 −0.0668667
\(809\) 1.28166e48 1.33852 0.669258 0.743030i \(-0.266612\pi\)
0.669258 + 0.743030i \(0.266612\pi\)
\(810\) 4.19568e47 0.429338
\(811\) −2.05018e47 −0.205564 −0.102782 0.994704i \(-0.532774\pi\)
−0.102782 + 0.994704i \(0.532774\pi\)
\(812\) −1.52353e47 −0.149685
\(813\) −5.97037e45 −0.00574787
\(814\) 1.03820e48 0.979445
\(815\) 2.26861e46 0.0209730
\(816\) 5.14274e47 0.465915
\(817\) −5.83913e47 −0.518423
\(818\) −6.32772e47 −0.550576
\(819\) −1.25258e48 −1.06812
\(820\) 7.38616e46 0.0617291
\(821\) 8.74853e47 0.716594 0.358297 0.933608i \(-0.383358\pi\)
0.358297 + 0.933608i \(0.383358\pi\)
\(822\) 1.35210e48 1.08549
\(823\) −2.06347e47 −0.162368 −0.0811841 0.996699i \(-0.525870\pi\)
−0.0811841 + 0.996699i \(0.525870\pi\)
\(824\) 1.37992e48 1.06427
\(825\) 2.39049e47 0.180716
\(826\) 2.43099e48 1.80141
\(827\) −2.59525e48 −1.88512 −0.942559 0.334038i \(-0.891588\pi\)
−0.942559 + 0.334038i \(0.891588\pi\)
\(828\) 7.40521e46 0.0527274
\(829\) −2.60174e48 −1.81599 −0.907996 0.418978i \(-0.862388\pi\)
−0.907996 + 0.418978i \(0.862388\pi\)
\(830\) −6.00843e47 −0.411124
\(831\) −2.78050e48 −1.86511
\(832\) 1.41263e48 0.928950
\(833\) 1.89615e46 0.0122244
\(834\) 2.95143e48 1.86549
\(835\) 2.61640e47 0.162135
\(836\) −9.50527e46 −0.0577512
\(837\) 1.10475e47 0.0658104
\(838\) 2.05733e48 1.20165
\(839\) −2.01476e48 −1.15386 −0.576928 0.816795i \(-0.695749\pi\)
−0.576928 + 0.816795i \(0.695749\pi\)
\(840\) −1.07512e48 −0.603740
\(841\) 5.33585e48 2.93812
\(842\) 5.14224e47 0.277653
\(843\) 4.34409e48 2.30009
\(844\) −2.92656e46 −0.0151952
\(845\) 3.37564e46 0.0171878
\(846\) −1.87852e48 −0.938006
\(847\) 1.21140e48 0.593213
\(848\) −2.65202e48 −1.27364
\(849\) 4.34583e48 2.04690
\(850\) 1.35847e47 0.0627536
\(851\) −2.12266e48 −0.961707
\(852\) −8.19042e46 −0.0363959
\(853\) 1.85939e48 0.810422 0.405211 0.914223i \(-0.367198\pi\)
0.405211 + 0.914223i \(0.367198\pi\)
\(854\) 5.86272e47 0.250636
\(855\) −1.36281e48 −0.571473
\(856\) −1.80621e48 −0.742933
\(857\) 1.28606e48 0.518891 0.259446 0.965758i \(-0.416460\pi\)
0.259446 + 0.965758i \(0.416460\pi\)
\(858\) −2.41437e48 −0.955572
\(859\) −3.42147e48 −1.32839 −0.664195 0.747559i \(-0.731226\pi\)
−0.664195 + 0.747559i \(0.731226\pi\)
\(860\) 3.92492e46 0.0149488
\(861\) −6.76173e48 −2.52642
\(862\) −2.24816e48 −0.824057
\(863\) 1.37063e48 0.492882 0.246441 0.969158i \(-0.420739\pi\)
0.246441 + 0.969158i \(0.420739\pi\)
\(864\) 4.38816e46 0.0154812
\(865\) −1.02354e48 −0.354274
\(866\) 1.55157e48 0.526899
\(867\) −3.92347e48 −1.30724
\(868\) −1.50723e47 −0.0492723
\(869\) 6.63769e47 0.212907
\(870\) −4.21039e48 −1.32512
\(871\) 4.87706e48 1.50612
\(872\) −2.81606e48 −0.853335
\(873\) 5.96919e48 1.77493
\(874\) 2.71821e48 0.793131
\(875\) −3.05996e47 −0.0876159
\(876\) −2.01439e47 −0.0566011
\(877\) −1.64670e48 −0.454069 −0.227035 0.973887i \(-0.572903\pi\)
−0.227035 + 0.973887i \(0.572903\pi\)
\(878\) −4.42531e48 −1.19753
\(879\) 8.47711e46 0.0225129
\(880\) −1.15419e48 −0.300824
\(881\) −3.42124e48 −0.875148 −0.437574 0.899182i \(-0.644162\pi\)
−0.437574 + 0.899182i \(0.644162\pi\)
\(882\) 1.78839e47 0.0448983
\(883\) 7.49779e48 1.84749 0.923743 0.383012i \(-0.125113\pi\)
0.923743 + 0.383012i \(0.125113\pi\)
\(884\) −9.80950e46 −0.0237238
\(885\) 4.80322e48 1.14017
\(886\) 5.69842e48 1.32769
\(887\) 1.29073e48 0.295186 0.147593 0.989048i \(-0.452847\pi\)
0.147593 + 0.989048i \(0.452847\pi\)
\(888\) −9.22581e48 −2.07105
\(889\) 3.32317e48 0.732273
\(890\) 2.19909e48 0.475672
\(891\) −2.73613e48 −0.580972
\(892\) −2.78343e47 −0.0580176
\(893\) −4.92994e48 −1.00877
\(894\) 4.91682e48 0.987678
\(895\) −1.20879e48 −0.238380
\(896\) 5.56415e48 1.07725
\(897\) 4.93630e48 0.938266
\(898\) 1.58139e48 0.295106
\(899\) 7.07538e48 1.29633
\(900\) 9.16049e46 0.0164785
\(901\) −2.03557e48 −0.359524
\(902\) −6.73713e48 −1.16833
\(903\) −3.59311e48 −0.611818
\(904\) −9.45743e48 −1.58123
\(905\) 4.34859e48 0.713916
\(906\) −3.06683e48 −0.494395
\(907\) −4.05607e48 −0.642074 −0.321037 0.947067i \(-0.604031\pi\)
−0.321037 + 0.947067i \(0.604031\pi\)
\(908\) −1.51969e47 −0.0236232
\(909\) −4.89325e47 −0.0746953
\(910\) 3.09053e48 0.463287
\(911\) −7.15538e48 −1.05337 −0.526683 0.850062i \(-0.676564\pi\)
−0.526683 + 0.850062i \(0.676564\pi\)
\(912\) 1.27294e49 1.84032
\(913\) 3.91828e48 0.556324
\(914\) −2.59210e47 −0.0361443
\(915\) 1.15837e48 0.158636
\(916\) −8.11802e47 −0.109188
\(917\) −6.27408e48 −0.828812
\(918\) 2.43633e47 0.0316106
\(919\) −1.51037e49 −1.92476 −0.962382 0.271700i \(-0.912414\pi\)
−0.962382 + 0.271700i \(0.912414\pi\)
\(920\) 2.19014e48 0.274141
\(921\) 1.64678e49 2.02465
\(922\) 8.57521e48 1.03558
\(923\) −2.82220e48 −0.334780
\(924\) −5.84906e47 −0.0681551
\(925\) −2.62580e48 −0.300555
\(926\) 7.51412e48 0.844884
\(927\) 1.07635e49 1.18888
\(928\) 2.81040e48 0.304948
\(929\) 1.54374e49 1.64557 0.822783 0.568356i \(-0.192420\pi\)
0.822783 + 0.568356i \(0.192420\pi\)
\(930\) −4.16533e48 −0.436195
\(931\) 4.69338e47 0.0482854
\(932\) 1.39812e48 0.141313
\(933\) −2.15709e49 −2.14201
\(934\) −1.29210e49 −1.26059
\(935\) −8.85902e47 −0.0849169
\(936\) 1.10903e49 1.04446
\(937\) −8.72693e48 −0.807530 −0.403765 0.914863i \(-0.632299\pi\)
−0.403765 + 0.914863i \(0.632299\pi\)
\(938\) 1.65258e49 1.50250
\(939\) −7.39687e48 −0.660793
\(940\) 3.31378e47 0.0290880
\(941\) −6.99024e48 −0.602925 −0.301463 0.953478i \(-0.597475\pi\)
−0.301463 + 0.953478i \(0.597475\pi\)
\(942\) −2.33537e49 −1.97932
\(943\) 1.37744e49 1.14717
\(944\) −2.31912e49 −1.89795
\(945\) −5.48784e47 −0.0441344
\(946\) −3.58003e48 −0.282933
\(947\) 2.43383e48 0.189024 0.0945118 0.995524i \(-0.469871\pi\)
0.0945118 + 0.995524i \(0.469871\pi\)
\(948\) 4.92076e47 0.0375573
\(949\) −6.94104e48 −0.520634
\(950\) 3.36252e48 0.247871
\(951\) −2.42246e49 −1.75501
\(952\) 3.98435e48 0.283692
\(953\) −2.16685e48 −0.151633 −0.0758167 0.997122i \(-0.524156\pi\)
−0.0758167 + 0.997122i \(0.524156\pi\)
\(954\) −1.91989e49 −1.32047
\(955\) −2.55465e48 −0.172694
\(956\) −6.01405e47 −0.0399587
\(957\) 2.74573e49 1.79313
\(958\) −5.85321e48 −0.375719
\(959\) 1.12869e49 0.712141
\(960\) 9.45760e48 0.586551
\(961\) −9.40382e48 −0.573282
\(962\) 2.65204e49 1.58924
\(963\) −1.40886e49 −0.829915
\(964\) −1.13485e48 −0.0657157
\(965\) 4.27661e48 0.243444
\(966\) 1.67265e49 0.936014
\(967\) 3.10853e49 1.71009 0.855044 0.518556i \(-0.173530\pi\)
0.855044 + 0.518556i \(0.173530\pi\)
\(968\) −1.07257e49 −0.580072
\(969\) 9.77053e48 0.519488
\(970\) −1.47280e49 −0.769858
\(971\) −1.05532e49 −0.542334 −0.271167 0.962532i \(-0.587410\pi\)
−0.271167 + 0.962532i \(0.587410\pi\)
\(972\) −2.18193e48 −0.110242
\(973\) 2.46375e49 1.22387
\(974\) 2.20790e49 1.07834
\(975\) 6.10637e48 0.293229
\(976\) −5.59292e48 −0.264069
\(977\) 1.91994e49 0.891306 0.445653 0.895206i \(-0.352971\pi\)
0.445653 + 0.895206i \(0.352971\pi\)
\(978\) −1.53402e48 −0.0700230
\(979\) −1.43409e49 −0.643670
\(980\) −3.15478e46 −0.00139232
\(981\) −2.19655e49 −0.953242
\(982\) 4.82639e48 0.205960
\(983\) −5.26490e48 −0.220931 −0.110466 0.993880i \(-0.535234\pi\)
−0.110466 + 0.993880i \(0.535234\pi\)
\(984\) 5.98682e49 2.47046
\(985\) 8.78829e48 0.356621
\(986\) 1.56035e49 0.622663
\(987\) −3.03363e49 −1.19050
\(988\) −2.42807e48 −0.0937069
\(989\) 7.31956e48 0.277809
\(990\) −8.35555e48 −0.311885
\(991\) −1.70362e48 −0.0625398 −0.0312699 0.999511i \(-0.509955\pi\)
−0.0312699 + 0.999511i \(0.509955\pi\)
\(992\) 2.78032e48 0.100381
\(993\) −1.86663e49 −0.662819
\(994\) −9.56295e48 −0.333977
\(995\) −2.20659e49 −0.757951
\(996\) 2.90476e48 0.0981367
\(997\) −3.60379e49 −1.19754 −0.598770 0.800921i \(-0.704344\pi\)
−0.598770 + 0.800921i \(0.704344\pi\)
\(998\) 1.23504e49 0.403672
\(999\) −4.70921e48 −0.151397
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 5.34.a.b.1.2 6
5.2 odd 4 25.34.b.c.24.4 12
5.3 odd 4 25.34.b.c.24.9 12
5.4 even 2 25.34.a.c.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.34.a.b.1.2 6 1.1 even 1 trivial
25.34.a.c.1.5 6 5.4 even 2
25.34.b.c.24.4 12 5.2 odd 4
25.34.b.c.24.9 12 5.3 odd 4