Properties

Label 5.34.a.b.1.6
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 1.6
Root \(77152.3\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q+178863. q^{2} +8.55112e7 q^{3} +2.34019e10 q^{4} +1.52588e11 q^{5} +1.52948e13 q^{6} -8.09549e13 q^{7} +2.64931e15 q^{8} +1.75311e15 q^{9} +O(q^{10})\) \(q+178863. q^{2} +8.55112e7 q^{3} +2.34019e10 q^{4} +1.52588e11 q^{5} +1.52948e13 q^{6} -8.09549e13 q^{7} +2.64931e15 q^{8} +1.75311e15 q^{9} +2.72923e16 q^{10} +1.95800e17 q^{11} +2.00113e18 q^{12} -2.59207e18 q^{13} -1.44798e19 q^{14} +1.30480e19 q^{15} +2.72841e20 q^{16} -1.52177e20 q^{17} +3.13565e20 q^{18} +1.39526e21 q^{19} +3.57085e21 q^{20} -6.92255e21 q^{21} +3.50214e22 q^{22} -3.40316e22 q^{23} +2.26546e23 q^{24} +2.32831e22 q^{25} -4.63625e23 q^{26} -3.25452e23 q^{27} -1.89450e24 q^{28} -1.49246e24 q^{29} +2.33380e24 q^{30} -1.38398e24 q^{31} +2.60438e25 q^{32} +1.67431e25 q^{33} -2.72188e25 q^{34} -1.23527e25 q^{35} +4.10261e25 q^{36} +1.15380e26 q^{37} +2.49559e26 q^{38} -2.21651e26 q^{39} +4.04252e26 q^{40} -6.35087e25 q^{41} -1.23819e27 q^{42} -2.64294e26 q^{43} +4.58211e27 q^{44} +2.67503e26 q^{45} -6.08698e27 q^{46} +1.03700e27 q^{47} +2.33310e28 q^{48} -1.17730e27 q^{49} +4.16447e27 q^{50} -1.30128e28 q^{51} -6.06594e28 q^{52} +5.20280e28 q^{53} -5.82111e28 q^{54} +2.98768e28 q^{55} -2.14475e29 q^{56} +1.19310e29 q^{57} -2.66946e29 q^{58} -6.17754e28 q^{59} +3.05348e29 q^{60} -1.21654e29 q^{61} -2.47543e29 q^{62} -1.41923e29 q^{63} +2.31456e30 q^{64} -3.95519e29 q^{65} +2.99472e30 q^{66} -2.87484e29 q^{67} -3.56123e30 q^{68} -2.91008e30 q^{69} -2.20944e30 q^{70} -2.84409e30 q^{71} +4.64452e30 q^{72} -2.67045e30 q^{73} +2.06372e31 q^{74} +1.99096e30 q^{75} +3.26517e31 q^{76} -1.58510e31 q^{77} -3.96451e31 q^{78} -7.84640e30 q^{79} +4.16323e31 q^{80} -3.75754e31 q^{81} -1.13593e31 q^{82} +1.28723e31 q^{83} -1.62001e32 q^{84} -2.32203e31 q^{85} -4.72724e31 q^{86} -1.27622e32 q^{87} +5.18736e32 q^{88} -1.56902e32 q^{89} +4.78463e31 q^{90} +2.09841e32 q^{91} -7.96404e32 q^{92} -1.18346e32 q^{93} +1.85481e32 q^{94} +2.12899e32 q^{95} +2.22703e33 q^{96} +4.84738e32 q^{97} -2.10574e32 q^{98} +3.43259e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + O(q^{10}) \) \( 6q + 147350q^{2} + 26513900q^{3} + 29520645652q^{4} + 915527343750q^{5} + 6615759249352q^{6} + 19113832847500q^{7} + 3069820115785800q^{8} + 13602102583345438q^{9} + 22483825683593750q^{10} + 150760896555890192q^{11} + 466351581756413200q^{12} - 1403095636752804700q^{13} - 7086110008989891456q^{14} + 4045700073242187500q^{15} + 64511520005858668816q^{16} + \)\(13\!\cdots\!00\)\(q^{17} + \)\(67\!\cdots\!50\)\(q^{18} + \)\(17\!\cdots\!00\)\(q^{19} + \)\(45\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(24\!\cdots\!00\)\(q^{22} + \)\(68\!\cdots\!00\)\(q^{23} + \)\(21\!\cdots\!00\)\(q^{24} + \)\(13\!\cdots\!50\)\(q^{25} - \)\(36\!\cdots\!88\)\(q^{26} - \)\(34\!\cdots\!00\)\(q^{27} - \)\(17\!\cdots\!00\)\(q^{28} + \)\(13\!\cdots\!00\)\(q^{29} + \)\(10\!\cdots\!00\)\(q^{30} + \)\(10\!\cdots\!52\)\(q^{31} + \)\(26\!\cdots\!00\)\(q^{32} + \)\(34\!\cdots\!00\)\(q^{33} + \)\(88\!\cdots\!24\)\(q^{34} + \)\(29\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!96\)\(q^{36} + \)\(27\!\cdots\!00\)\(q^{37} + \)\(83\!\cdots\!00\)\(q^{38} + \)\(57\!\cdots\!56\)\(q^{39} + \)\(46\!\cdots\!00\)\(q^{40} + \)\(44\!\cdots\!32\)\(q^{41} + \)\(14\!\cdots\!00\)\(q^{42} + \)\(22\!\cdots\!00\)\(q^{43} + \)\(71\!\cdots\!64\)\(q^{44} + \)\(20\!\cdots\!50\)\(q^{45} + \)\(34\!\cdots\!72\)\(q^{46} + \)\(38\!\cdots\!00\)\(q^{47} + \)\(24\!\cdots\!00\)\(q^{48} - \)\(71\!\cdots\!58\)\(q^{49} + \)\(34\!\cdots\!50\)\(q^{50} - \)\(54\!\cdots\!88\)\(q^{51} - \)\(90\!\cdots\!00\)\(q^{52} + \)\(47\!\cdots\!00\)\(q^{53} - \)\(18\!\cdots\!00\)\(q^{54} + \)\(23\!\cdots\!00\)\(q^{55} - \)\(39\!\cdots\!00\)\(q^{56} - \)\(24\!\cdots\!00\)\(q^{57} - \)\(44\!\cdots\!00\)\(q^{58} - \)\(17\!\cdots\!00\)\(q^{59} + \)\(71\!\cdots\!00\)\(q^{60} - \)\(28\!\cdots\!08\)\(q^{61} + \)\(34\!\cdots\!00\)\(q^{62} - \)\(55\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!72\)\(q^{64} - \)\(21\!\cdots\!00\)\(q^{65} + \)\(50\!\cdots\!64\)\(q^{66} + \)\(33\!\cdots\!00\)\(q^{67} + \)\(38\!\cdots\!00\)\(q^{68} + \)\(31\!\cdots\!36\)\(q^{69} - \)\(10\!\cdots\!00\)\(q^{70} + \)\(84\!\cdots\!72\)\(q^{71} + \)\(87\!\cdots\!00\)\(q^{72} - \)\(17\!\cdots\!00\)\(q^{73} + \)\(20\!\cdots\!84\)\(q^{74} + \)\(61\!\cdots\!00\)\(q^{75} + \)\(29\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!00\)\(q^{77} - \)\(57\!\cdots\!00\)\(q^{78} - \)\(22\!\cdots\!00\)\(q^{79} + \)\(98\!\cdots\!00\)\(q^{80} - \)\(13\!\cdots\!74\)\(q^{81} - \)\(15\!\cdots\!00\)\(q^{82} - \)\(47\!\cdots\!00\)\(q^{83} - \)\(23\!\cdots\!76\)\(q^{84} + \)\(20\!\cdots\!00\)\(q^{85} - \)\(12\!\cdots\!08\)\(q^{86} - \)\(17\!\cdots\!00\)\(q^{87} + \)\(49\!\cdots\!00\)\(q^{88} - \)\(33\!\cdots\!00\)\(q^{89} + \)\(10\!\cdots\!50\)\(q^{90} + \)\(19\!\cdots\!32\)\(q^{91} - \)\(41\!\cdots\!00\)\(q^{92} + \)\(21\!\cdots\!00\)\(q^{93} + \)\(14\!\cdots\!64\)\(q^{94} + \)\(26\!\cdots\!00\)\(q^{95} + \)\(31\!\cdots\!72\)\(q^{96} + \)\(25\!\cdots\!00\)\(q^{97} + \)\(69\!\cdots\!50\)\(q^{98} + \)\(16\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 178863. 1.92986 0.964928 0.262516i \(-0.0845524\pi\)
0.964928 + 0.262516i \(0.0845524\pi\)
\(3\) 8.55112e7 1.14689 0.573446 0.819243i \(-0.305606\pi\)
0.573446 + 0.819243i \(0.305606\pi\)
\(4\) 2.34019e10 2.72434
\(5\) 1.52588e11 0.447214
\(6\) 1.52948e13 2.21333
\(7\) −8.09549e13 −0.920716 −0.460358 0.887733i \(-0.652279\pi\)
−0.460358 + 0.887733i \(0.652279\pi\)
\(8\) 2.64931e15 3.32773
\(9\) 1.75311e15 0.315360
\(10\) 2.72923e16 0.863057
\(11\) 1.95800e17 1.28480 0.642398 0.766371i \(-0.277939\pi\)
0.642398 + 0.766371i \(0.277939\pi\)
\(12\) 2.00113e18 3.12452
\(13\) −2.59207e18 −1.08039 −0.540197 0.841539i \(-0.681650\pi\)
−0.540197 + 0.841539i \(0.681650\pi\)
\(14\) −1.44798e19 −1.77685
\(15\) 1.30480e19 0.512906
\(16\) 2.72841e20 3.69769
\(17\) −1.52177e20 −0.758475 −0.379238 0.925299i \(-0.623814\pi\)
−0.379238 + 0.925299i \(0.623814\pi\)
\(18\) 3.13565e20 0.608600
\(19\) 1.39526e21 1.10974 0.554868 0.831938i \(-0.312769\pi\)
0.554868 + 0.831938i \(0.312769\pi\)
\(20\) 3.57085e21 1.21836
\(21\) −6.92255e21 −1.05596
\(22\) 3.50214e22 2.47947
\(23\) −3.40316e22 −1.15711 −0.578553 0.815645i \(-0.696382\pi\)
−0.578553 + 0.815645i \(0.696382\pi\)
\(24\) 2.26546e23 3.81654
\(25\) 2.32831e22 0.200000
\(26\) −4.63625e23 −2.08500
\(27\) −3.25452e23 −0.785207
\(28\) −1.89450e24 −2.50834
\(29\) −1.49246e24 −1.10748 −0.553741 0.832689i \(-0.686800\pi\)
−0.553741 + 0.832689i \(0.686800\pi\)
\(30\) 2.33380e24 0.989833
\(31\) −1.38398e24 −0.341714 −0.170857 0.985296i \(-0.554654\pi\)
−0.170857 + 0.985296i \(0.554654\pi\)
\(32\) 2.60438e25 3.80828
\(33\) 1.67431e25 1.47352
\(34\) −2.72188e25 −1.46375
\(35\) −1.23527e25 −0.411757
\(36\) 4.10261e25 0.859149
\(37\) 1.15380e26 1.53745 0.768727 0.639577i \(-0.220891\pi\)
0.768727 + 0.639577i \(0.220891\pi\)
\(38\) 2.49559e26 2.14163
\(39\) −2.21651e26 −1.23909
\(40\) 4.04252e26 1.48821
\(41\) −6.35087e25 −0.155561 −0.0777804 0.996971i \(-0.524783\pi\)
−0.0777804 + 0.996971i \(0.524783\pi\)
\(42\) −1.23819e27 −2.03785
\(43\) −2.64294e26 −0.295025 −0.147512 0.989060i \(-0.547127\pi\)
−0.147512 + 0.989060i \(0.547127\pi\)
\(44\) 4.58211e27 3.50022
\(45\) 2.67503e26 0.141033
\(46\) −6.08698e27 −2.23305
\(47\) 1.03700e27 0.266788 0.133394 0.991063i \(-0.457412\pi\)
0.133394 + 0.991063i \(0.457412\pi\)
\(48\) 2.33310e28 4.24085
\(49\) −1.17730e27 −0.152283
\(50\) 4.16447e27 0.385971
\(51\) −1.30128e28 −0.869889
\(52\) −6.06594e28 −2.94336
\(53\) 5.20280e28 1.84368 0.921839 0.387574i \(-0.126687\pi\)
0.921839 + 0.387574i \(0.126687\pi\)
\(54\) −5.82111e28 −1.51534
\(55\) 2.98768e28 0.574579
\(56\) −2.14475e29 −3.06389
\(57\) 1.19310e29 1.27275
\(58\) −2.66946e29 −2.13728
\(59\) −6.17754e28 −0.373042 −0.186521 0.982451i \(-0.559721\pi\)
−0.186521 + 0.982451i \(0.559721\pi\)
\(60\) 3.05348e29 1.39733
\(61\) −1.21654e29 −0.423822 −0.211911 0.977289i \(-0.567969\pi\)
−0.211911 + 0.977289i \(0.567969\pi\)
\(62\) −2.47543e29 −0.659458
\(63\) −1.41923e29 −0.290357
\(64\) 2.31456e30 3.65174
\(65\) −3.95519e29 −0.483167
\(66\) 2.99472e30 2.84369
\(67\) −2.87484e29 −0.213000 −0.106500 0.994313i \(-0.533964\pi\)
−0.106500 + 0.994313i \(0.533964\pi\)
\(68\) −3.56123e30 −2.06634
\(69\) −2.91008e30 −1.32707
\(70\) −2.20944e30 −0.794631
\(71\) −2.84409e30 −0.809432 −0.404716 0.914442i \(-0.632630\pi\)
−0.404716 + 0.914442i \(0.632630\pi\)
\(72\) 4.64452e30 1.04943
\(73\) −2.67045e30 −0.480570 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(74\) 2.06372e31 2.96706
\(75\) 1.99096e30 0.229378
\(76\) 3.26517e31 3.02330
\(77\) −1.58510e31 −1.18293
\(78\) −3.96451e31 −2.39127
\(79\) −7.84640e30 −0.383551 −0.191776 0.981439i \(-0.561425\pi\)
−0.191776 + 0.981439i \(0.561425\pi\)
\(80\) 4.16323e31 1.65366
\(81\) −3.75754e31 −1.21591
\(82\) −1.13593e31 −0.300210
\(83\) 1.28723e31 0.278527 0.139263 0.990255i \(-0.455527\pi\)
0.139263 + 0.990255i \(0.455527\pi\)
\(84\) −1.62001e32 −2.87680
\(85\) −2.32203e31 −0.339200
\(86\) −4.72724e31 −0.569355
\(87\) −1.27622e32 −1.27016
\(88\) 5.18736e32 4.27545
\(89\) −1.56902e32 −1.07323 −0.536616 0.843826i \(-0.680298\pi\)
−0.536616 + 0.843826i \(0.680298\pi\)
\(90\) 4.78463e31 0.272174
\(91\) 2.09841e32 0.994735
\(92\) −7.96404e32 −3.15235
\(93\) −1.18346e32 −0.391909
\(94\) 1.85481e32 0.514862
\(95\) 2.12899e32 0.496289
\(96\) 2.22703e33 4.36769
\(97\) 4.84738e32 0.801259 0.400630 0.916240i \(-0.368791\pi\)
0.400630 + 0.916240i \(0.368791\pi\)
\(98\) −2.10574e32 −0.293883
\(99\) 3.43259e32 0.405174
\(100\) 5.44868e32 0.544868
\(101\) 2.51128e32 0.213105 0.106552 0.994307i \(-0.466019\pi\)
0.106552 + 0.994307i \(0.466019\pi\)
\(102\) −2.32751e33 −1.67876
\(103\) −2.60164e33 −1.59747 −0.798737 0.601681i \(-0.794498\pi\)
−0.798737 + 0.601681i \(0.794498\pi\)
\(104\) −6.86720e33 −3.59525
\(105\) −1.05630e33 −0.472240
\(106\) 9.30586e33 3.55803
\(107\) 3.74478e33 1.22629 0.613146 0.789970i \(-0.289904\pi\)
0.613146 + 0.789970i \(0.289904\pi\)
\(108\) −7.61619e33 −2.13917
\(109\) −2.76732e33 −0.667609 −0.333805 0.942642i \(-0.608333\pi\)
−0.333805 + 0.942642i \(0.608333\pi\)
\(110\) 5.34384e33 1.10885
\(111\) 9.86628e33 1.76329
\(112\) −2.20879e34 −3.40452
\(113\) 1.26307e34 1.68125 0.840626 0.541617i \(-0.182188\pi\)
0.840626 + 0.541617i \(0.182188\pi\)
\(114\) 2.13401e34 2.45622
\(115\) −5.19281e33 −0.517473
\(116\) −3.49265e34 −3.01716
\(117\) −4.54418e33 −0.340713
\(118\) −1.10493e34 −0.719917
\(119\) 1.23195e34 0.698340
\(120\) 3.45681e34 1.70681
\(121\) 1.51127e34 0.650703
\(122\) −2.17593e34 −0.817915
\(123\) −5.43071e33 −0.178411
\(124\) −3.23878e34 −0.930945
\(125\) 3.55271e33 0.0894427
\(126\) −2.53847e34 −0.560348
\(127\) −2.24824e33 −0.0435594 −0.0217797 0.999763i \(-0.506933\pi\)
−0.0217797 + 0.999763i \(0.506933\pi\)
\(128\) 1.90275e35 3.23905
\(129\) −2.26001e34 −0.338361
\(130\) −7.07435e34 −0.932441
\(131\) 7.19207e34 0.835368 0.417684 0.908592i \(-0.362842\pi\)
0.417684 + 0.908592i \(0.362842\pi\)
\(132\) 3.91821e35 4.01438
\(133\) −1.12953e35 −1.02175
\(134\) −5.14202e34 −0.411059
\(135\) −4.96600e34 −0.351155
\(136\) −4.03163e35 −2.52400
\(137\) 2.56636e35 1.42373 0.711867 0.702314i \(-0.247850\pi\)
0.711867 + 0.702314i \(0.247850\pi\)
\(138\) −5.20505e35 −2.56106
\(139\) 7.81097e34 0.341162 0.170581 0.985344i \(-0.445436\pi\)
0.170581 + 0.985344i \(0.445436\pi\)
\(140\) −2.89078e35 −1.12177
\(141\) 8.86755e34 0.305977
\(142\) −5.08701e35 −1.56209
\(143\) −5.07529e35 −1.38809
\(144\) 4.78320e35 1.16611
\(145\) −2.27732e35 −0.495281
\(146\) −4.77643e35 −0.927431
\(147\) −1.00672e35 −0.174652
\(148\) 2.70011e36 4.18855
\(149\) −1.40823e35 −0.195479 −0.0977397 0.995212i \(-0.531161\pi\)
−0.0977397 + 0.995212i \(0.531161\pi\)
\(150\) 3.56109e35 0.442667
\(151\) 4.46232e35 0.497097 0.248548 0.968619i \(-0.420046\pi\)
0.248548 + 0.968619i \(0.420046\pi\)
\(152\) 3.69647e36 3.69290
\(153\) −2.66782e35 −0.239193
\(154\) −2.83515e36 −2.28289
\(155\) −2.11179e35 −0.152819
\(156\) −5.18706e36 −3.37571
\(157\) 7.61070e35 0.445739 0.222869 0.974848i \(-0.428458\pi\)
0.222869 + 0.974848i \(0.428458\pi\)
\(158\) −1.40343e36 −0.740199
\(159\) 4.44897e36 2.11450
\(160\) 3.97396e36 1.70311
\(161\) 2.75502e36 1.06537
\(162\) −6.72084e36 −2.34653
\(163\) 1.95336e36 0.616152 0.308076 0.951362i \(-0.400315\pi\)
0.308076 + 0.951362i \(0.400315\pi\)
\(164\) −1.48623e36 −0.423800
\(165\) 2.55480e36 0.658979
\(166\) 2.30237e36 0.537516
\(167\) 2.87170e36 0.607180 0.303590 0.952803i \(-0.401815\pi\)
0.303590 + 0.952803i \(0.401815\pi\)
\(168\) −1.83400e37 −3.51395
\(169\) 9.62710e35 0.167249
\(170\) −4.15325e36 −0.654608
\(171\) 2.44604e36 0.349967
\(172\) −6.18499e36 −0.803748
\(173\) 1.61105e37 1.90261 0.951303 0.308258i \(-0.0997461\pi\)
0.951303 + 0.308258i \(0.0997461\pi\)
\(174\) −2.28269e37 −2.45123
\(175\) −1.88488e36 −0.184143
\(176\) 5.34225e37 4.75078
\(177\) −5.28249e36 −0.427839
\(178\) −2.80639e37 −2.07118
\(179\) 9.06671e33 0.000610063 0 0.000305031 1.00000i \(-0.499903\pi\)
0.000305031 1.00000i \(0.499903\pi\)
\(180\) 6.26008e36 0.384223
\(181\) 1.89723e36 0.106273 0.0531364 0.998587i \(-0.483078\pi\)
0.0531364 + 0.998587i \(0.483078\pi\)
\(182\) 3.75327e37 1.91969
\(183\) −1.04028e37 −0.486078
\(184\) −9.01602e37 −3.85053
\(185\) 1.76056e37 0.687570
\(186\) −2.11677e37 −0.756327
\(187\) −2.97963e37 −0.974487
\(188\) 2.42679e37 0.726821
\(189\) 2.63469e37 0.722953
\(190\) 3.80798e37 0.957767
\(191\) −6.88314e37 −1.58758 −0.793790 0.608192i \(-0.791895\pi\)
−0.793790 + 0.608192i \(0.791895\pi\)
\(192\) 1.97921e38 4.18815
\(193\) 5.10528e37 0.991571 0.495786 0.868445i \(-0.334880\pi\)
0.495786 + 0.868445i \(0.334880\pi\)
\(194\) 8.67015e37 1.54631
\(195\) −3.38213e37 −0.554140
\(196\) −2.75510e37 −0.414869
\(197\) −6.02889e37 −0.834727 −0.417364 0.908740i \(-0.637046\pi\)
−0.417364 + 0.908740i \(0.637046\pi\)
\(198\) 6.13963e37 0.781927
\(199\) −1.42678e38 −1.67218 −0.836089 0.548594i \(-0.815163\pi\)
−0.836089 + 0.548594i \(0.815163\pi\)
\(200\) 6.16840e37 0.665546
\(201\) −2.45831e37 −0.244288
\(202\) 4.49175e37 0.411261
\(203\) 1.20822e38 1.01968
\(204\) −3.04525e38 −2.36987
\(205\) −9.69067e36 −0.0695689
\(206\) −4.65337e38 −3.08289
\(207\) −5.96610e37 −0.364905
\(208\) −7.07225e38 −3.99496
\(209\) 2.73192e38 1.42579
\(210\) −1.88932e38 −0.911355
\(211\) 3.27612e38 1.46116 0.730582 0.682825i \(-0.239249\pi\)
0.730582 + 0.682825i \(0.239249\pi\)
\(212\) 1.21755e39 5.02280
\(213\) −2.43201e38 −0.928331
\(214\) 6.69801e38 2.36656
\(215\) −4.03281e37 −0.131939
\(216\) −8.62222e38 −2.61296
\(217\) 1.12040e38 0.314621
\(218\) −4.94971e38 −1.28839
\(219\) −2.28353e38 −0.551162
\(220\) 6.99174e38 1.56535
\(221\) 3.94453e38 0.819451
\(222\) 1.76471e39 3.40290
\(223\) −3.22330e38 −0.577126 −0.288563 0.957461i \(-0.593177\pi\)
−0.288563 + 0.957461i \(0.593177\pi\)
\(224\) −2.10837e39 −3.50634
\(225\) 4.08177e37 0.0630721
\(226\) 2.25916e39 3.24457
\(227\) −6.02003e38 −0.803845 −0.401922 0.915674i \(-0.631658\pi\)
−0.401922 + 0.915674i \(0.631658\pi\)
\(228\) 2.79209e39 3.46740
\(229\) −3.71091e38 −0.428741 −0.214370 0.976752i \(-0.568770\pi\)
−0.214370 + 0.976752i \(0.568770\pi\)
\(230\) −9.28799e38 −0.998649
\(231\) −1.35544e39 −1.35670
\(232\) −3.95400e39 −3.68540
\(233\) −3.81211e38 −0.330973 −0.165486 0.986212i \(-0.552919\pi\)
−0.165486 + 0.986212i \(0.552919\pi\)
\(234\) −8.12784e38 −0.657527
\(235\) 1.58234e38 0.119311
\(236\) −1.44566e39 −1.01629
\(237\) −6.70955e38 −0.439892
\(238\) 2.20349e39 1.34770
\(239\) 8.52350e38 0.486466 0.243233 0.969968i \(-0.421792\pi\)
0.243233 + 0.969968i \(0.421792\pi\)
\(240\) 3.56003e39 1.89657
\(241\) 3.41820e39 1.70027 0.850133 0.526568i \(-0.176522\pi\)
0.850133 + 0.526568i \(0.176522\pi\)
\(242\) 2.70309e39 1.25576
\(243\) −1.40391e39 −0.609308
\(244\) −2.84693e39 −1.15464
\(245\) −1.79641e38 −0.0681028
\(246\) −9.71351e38 −0.344308
\(247\) −3.61661e39 −1.19895
\(248\) −3.66660e39 −1.13713
\(249\) 1.10072e39 0.319440
\(250\) 6.35448e38 0.172611
\(251\) 2.52321e39 0.641706 0.320853 0.947129i \(-0.396030\pi\)
0.320853 + 0.947129i \(0.396030\pi\)
\(252\) −3.32126e39 −0.791032
\(253\) −6.66340e39 −1.48665
\(254\) −4.02127e38 −0.0840633
\(255\) −1.98560e39 −0.389026
\(256\) 1.41511e40 2.59915
\(257\) 4.18511e39 0.720793 0.360396 0.932799i \(-0.382641\pi\)
0.360396 + 0.932799i \(0.382641\pi\)
\(258\) −4.04232e39 −0.652988
\(259\) −9.34058e39 −1.41556
\(260\) −9.25590e39 −1.31631
\(261\) −2.61645e39 −0.349256
\(262\) 1.28639e40 1.61214
\(263\) 1.15657e40 1.36114 0.680570 0.732683i \(-0.261732\pi\)
0.680570 + 0.732683i \(0.261732\pi\)
\(264\) 4.43577e40 4.90348
\(265\) 7.93884e39 0.824518
\(266\) −2.02031e40 −1.97183
\(267\) −1.34169e40 −1.23088
\(268\) −6.72768e39 −0.580284
\(269\) −7.21991e39 −0.585624 −0.292812 0.956170i \(-0.594591\pi\)
−0.292812 + 0.956170i \(0.594591\pi\)
\(270\) −8.88232e39 −0.677679
\(271\) 2.28804e40 1.64237 0.821183 0.570665i \(-0.193315\pi\)
0.821183 + 0.570665i \(0.193315\pi\)
\(272\) −4.15202e40 −2.80461
\(273\) 1.79438e40 1.14085
\(274\) 4.59026e40 2.74760
\(275\) 4.55884e39 0.256959
\(276\) −6.81015e40 −3.61540
\(277\) 2.67522e40 1.33796 0.668981 0.743279i \(-0.266731\pi\)
0.668981 + 0.743279i \(0.266731\pi\)
\(278\) 1.39709e40 0.658394
\(279\) −2.42627e39 −0.107763
\(280\) −3.27262e40 −1.37021
\(281\) −2.51780e40 −0.993955 −0.496977 0.867763i \(-0.665557\pi\)
−0.496977 + 0.867763i \(0.665557\pi\)
\(282\) 1.58607e40 0.590490
\(283\) 4.17854e40 1.46740 0.733699 0.679475i \(-0.237792\pi\)
0.733699 + 0.679475i \(0.237792\pi\)
\(284\) −6.65571e40 −2.20517
\(285\) 1.82053e40 0.569190
\(286\) −9.07780e40 −2.67880
\(287\) 5.14135e39 0.143227
\(288\) 4.56575e40 1.20098
\(289\) −1.70967e40 −0.424715
\(290\) −4.07327e40 −0.955821
\(291\) 4.14505e40 0.918958
\(292\) −6.24936e40 −1.30924
\(293\) −1.81801e40 −0.359981 −0.179991 0.983668i \(-0.557607\pi\)
−0.179991 + 0.983668i \(0.557607\pi\)
\(294\) −1.80064e40 −0.337052
\(295\) −9.42619e39 −0.166829
\(296\) 3.05677e41 5.11623
\(297\) −6.37236e40 −1.00883
\(298\) −2.51880e40 −0.377247
\(299\) 8.82124e40 1.25013
\(300\) 4.65923e40 0.624905
\(301\) 2.13959e40 0.271634
\(302\) 7.98142e40 0.959325
\(303\) 2.14743e40 0.244408
\(304\) 3.80684e41 4.10346
\(305\) −1.85629e40 −0.189539
\(306\) −4.77174e40 −0.461608
\(307\) −1.04678e40 −0.0959564 −0.0479782 0.998848i \(-0.515278\pi\)
−0.0479782 + 0.998848i \(0.515278\pi\)
\(308\) −3.70944e41 −3.22271
\(309\) −2.22470e41 −1.83213
\(310\) −3.77720e40 −0.294919
\(311\) 1.01794e41 0.753660 0.376830 0.926282i \(-0.377014\pi\)
0.376830 + 0.926282i \(0.377014\pi\)
\(312\) −5.87223e41 −4.12337
\(313\) −2.12567e41 −1.41584 −0.707921 0.706292i \(-0.750367\pi\)
−0.707921 + 0.706292i \(0.750367\pi\)
\(314\) 1.36127e41 0.860212
\(315\) −2.16557e40 −0.129852
\(316\) −1.83621e41 −1.04492
\(317\) 5.12986e40 0.277094 0.138547 0.990356i \(-0.455757\pi\)
0.138547 + 0.990356i \(0.455757\pi\)
\(318\) 7.95755e41 4.08067
\(319\) −2.92225e41 −1.42289
\(320\) 3.53174e41 1.63311
\(321\) 3.20220e41 1.40642
\(322\) 4.92771e41 2.05600
\(323\) −2.12326e41 −0.841708
\(324\) −8.79336e41 −3.31255
\(325\) −6.03514e40 −0.216079
\(326\) 3.49384e41 1.18908
\(327\) −2.36637e41 −0.765676
\(328\) −1.68254e41 −0.517664
\(329\) −8.39506e40 −0.245636
\(330\) 4.56958e41 1.27173
\(331\) −4.71143e41 −1.24736 −0.623679 0.781681i \(-0.714363\pi\)
−0.623679 + 0.781681i \(0.714363\pi\)
\(332\) 3.01236e41 0.758802
\(333\) 2.02274e41 0.484852
\(334\) 5.13640e41 1.17177
\(335\) −4.38666e40 −0.0952565
\(336\) −1.88876e42 −3.90462
\(337\) 8.62495e40 0.169771 0.0848854 0.996391i \(-0.472948\pi\)
0.0848854 + 0.996391i \(0.472948\pi\)
\(338\) 1.72193e41 0.322767
\(339\) 1.08007e42 1.92821
\(340\) −5.43400e41 −0.924097
\(341\) −2.70984e41 −0.439033
\(342\) 4.37505e41 0.675386
\(343\) 7.21170e41 1.06092
\(344\) −7.00197e41 −0.981762
\(345\) −4.44043e41 −0.593486
\(346\) 2.88157e42 3.67175
\(347\) 2.78000e41 0.337760 0.168880 0.985637i \(-0.445985\pi\)
0.168880 + 0.985637i \(0.445985\pi\)
\(348\) −2.98661e42 −3.46036
\(349\) −1.12911e42 −1.24772 −0.623860 0.781536i \(-0.714437\pi\)
−0.623860 + 0.781536i \(0.714437\pi\)
\(350\) −3.37134e41 −0.355370
\(351\) 8.43594e41 0.848333
\(352\) 5.09938e42 4.89287
\(353\) 1.75490e42 1.60683 0.803413 0.595422i \(-0.203015\pi\)
0.803413 + 0.595422i \(0.203015\pi\)
\(354\) −9.44841e41 −0.825667
\(355\) −4.33973e41 −0.361989
\(356\) −3.67181e42 −2.92385
\(357\) 1.05345e42 0.800920
\(358\) 1.62170e39 0.00117733
\(359\) −2.42990e42 −1.68473 −0.842365 0.538907i \(-0.818837\pi\)
−0.842365 + 0.538907i \(0.818837\pi\)
\(360\) 7.08698e41 0.469321
\(361\) 3.65974e41 0.231516
\(362\) 3.39343e41 0.205091
\(363\) 1.29230e42 0.746286
\(364\) 4.91068e42 2.71000
\(365\) −4.07478e41 −0.214918
\(366\) −1.86067e42 −0.938060
\(367\) −2.37509e42 −1.14470 −0.572349 0.820010i \(-0.693968\pi\)
−0.572349 + 0.820010i \(0.693968\pi\)
\(368\) −9.28523e42 −4.27862
\(369\) −1.11338e41 −0.0490577
\(370\) 3.14898e42 1.32691
\(371\) −4.21192e42 −1.69750
\(372\) −2.76952e42 −1.06769
\(373\) 1.58778e42 0.585592 0.292796 0.956175i \(-0.405414\pi\)
0.292796 + 0.956175i \(0.405414\pi\)
\(374\) −5.32944e42 −1.88062
\(375\) 3.03797e41 0.102581
\(376\) 2.74734e42 0.887797
\(377\) 3.86858e42 1.19652
\(378\) 4.71248e42 1.39519
\(379\) −2.74032e42 −0.776703 −0.388351 0.921511i \(-0.626955\pi\)
−0.388351 + 0.921511i \(0.626955\pi\)
\(380\) 4.98225e42 1.35206
\(381\) −1.92250e41 −0.0499579
\(382\) −1.23114e43 −3.06380
\(383\) 3.57273e42 0.851570 0.425785 0.904824i \(-0.359998\pi\)
0.425785 + 0.904824i \(0.359998\pi\)
\(384\) 1.62706e43 3.71483
\(385\) −2.41867e42 −0.529024
\(386\) 9.13144e42 1.91359
\(387\) −4.63336e41 −0.0930391
\(388\) 1.13438e43 2.18290
\(389\) −2.24258e42 −0.413599 −0.206799 0.978383i \(-0.566305\pi\)
−0.206799 + 0.978383i \(0.566305\pi\)
\(390\) −6.04937e42 −1.06941
\(391\) 5.17882e42 0.877636
\(392\) −3.11902e42 −0.506755
\(393\) 6.15003e42 0.958077
\(394\) −1.07834e43 −1.61090
\(395\) −1.19727e42 −0.171529
\(396\) 8.03292e42 1.10383
\(397\) −8.69665e41 −0.114633 −0.0573164 0.998356i \(-0.518254\pi\)
−0.0573164 + 0.998356i \(0.518254\pi\)
\(398\) −2.55198e43 −3.22706
\(399\) −9.65875e42 −1.17184
\(400\) 6.35259e42 0.739538
\(401\) 1.79590e41 0.0200632 0.0100316 0.999950i \(-0.496807\pi\)
0.0100316 + 0.999950i \(0.496807\pi\)
\(402\) −4.39700e42 −0.471440
\(403\) 3.58738e42 0.369185
\(404\) 5.87688e42 0.580569
\(405\) −5.73355e42 −0.543771
\(406\) 2.16106e43 1.96783
\(407\) 2.25915e43 1.97532
\(408\) −3.44750e43 −2.89475
\(409\) 1.72895e43 1.39427 0.697136 0.716939i \(-0.254457\pi\)
0.697136 + 0.716939i \(0.254457\pi\)
\(410\) −1.73330e42 −0.134258
\(411\) 2.19453e43 1.63287
\(412\) −6.08834e43 −4.35206
\(413\) 5.00103e42 0.343466
\(414\) −1.06711e43 −0.704214
\(415\) 1.96415e42 0.124561
\(416\) −6.75073e43 −4.11444
\(417\) 6.67926e42 0.391276
\(418\) 4.88639e43 2.75156
\(419\) −3.07423e43 −1.66420 −0.832099 0.554628i \(-0.812861\pi\)
−0.832099 + 0.554628i \(0.812861\pi\)
\(420\) −2.47194e43 −1.28654
\(421\) −1.46291e43 −0.732090 −0.366045 0.930597i \(-0.619288\pi\)
−0.366045 + 0.930597i \(0.619288\pi\)
\(422\) 5.85975e43 2.81983
\(423\) 1.81798e42 0.0841343
\(424\) 1.37838e44 6.13526
\(425\) −3.54314e42 −0.151695
\(426\) −4.34997e43 −1.79154
\(427\) 9.84848e42 0.390220
\(428\) 8.76349e43 3.34083
\(429\) −4.33994e43 −1.59198
\(430\) −7.21319e42 −0.254623
\(431\) 3.24328e43 1.10182 0.550909 0.834565i \(-0.314281\pi\)
0.550909 + 0.834565i \(0.314281\pi\)
\(432\) −8.87967e43 −2.90345
\(433\) −2.61817e42 −0.0824040 −0.0412020 0.999151i \(-0.513119\pi\)
−0.0412020 + 0.999151i \(0.513119\pi\)
\(434\) 2.00398e43 0.607174
\(435\) −1.94736e43 −0.568034
\(436\) −6.47606e43 −1.81880
\(437\) −4.74828e43 −1.28408
\(438\) −4.08439e43 −1.06366
\(439\) −6.39695e43 −1.60438 −0.802192 0.597066i \(-0.796333\pi\)
−0.802192 + 0.597066i \(0.796333\pi\)
\(440\) 7.91528e43 1.91204
\(441\) −2.06393e42 −0.0480239
\(442\) 7.05530e43 1.58142
\(443\) 1.30321e43 0.281418 0.140709 0.990051i \(-0.455062\pi\)
0.140709 + 0.990051i \(0.455062\pi\)
\(444\) 2.30890e44 4.80381
\(445\) −2.39414e43 −0.479964
\(446\) −5.76528e43 −1.11377
\(447\) −1.20420e43 −0.224194
\(448\) −1.87375e44 −3.36221
\(449\) −9.56472e43 −1.65428 −0.827138 0.561999i \(-0.810032\pi\)
−0.827138 + 0.561999i \(0.810032\pi\)
\(450\) 7.30076e42 0.121720
\(451\) −1.24350e43 −0.199864
\(452\) 2.95582e44 4.58030
\(453\) 3.81578e43 0.570116
\(454\) −1.07676e44 −1.55130
\(455\) 3.20192e43 0.444859
\(456\) 3.16090e44 4.23536
\(457\) −3.78578e42 −0.0489258 −0.0244629 0.999701i \(-0.507788\pi\)
−0.0244629 + 0.999701i \(0.507788\pi\)
\(458\) −6.63743e43 −0.827408
\(459\) 4.95262e43 0.595560
\(460\) −1.21522e44 −1.40977
\(461\) 7.04190e43 0.788179 0.394089 0.919072i \(-0.371060\pi\)
0.394089 + 0.919072i \(0.371060\pi\)
\(462\) −2.42437e44 −2.61823
\(463\) 1.41714e44 1.47682 0.738409 0.674353i \(-0.235577\pi\)
0.738409 + 0.674353i \(0.235577\pi\)
\(464\) −4.07206e44 −4.09513
\(465\) −1.80582e43 −0.175267
\(466\) −6.81843e43 −0.638729
\(467\) −1.83277e44 −1.65721 −0.828606 0.559831i \(-0.810866\pi\)
−0.828606 + 0.559831i \(0.810866\pi\)
\(468\) −1.06343e44 −0.928219
\(469\) 2.32732e43 0.196112
\(470\) 2.83022e43 0.230253
\(471\) 6.50801e43 0.511214
\(472\) −1.63662e44 −1.24138
\(473\) −5.17490e43 −0.379047
\(474\) −1.20009e44 −0.848928
\(475\) 3.24859e43 0.221947
\(476\) 2.88299e44 1.90252
\(477\) 9.12106e43 0.581423
\(478\) 1.52454e44 0.938809
\(479\) −6.67837e43 −0.397314 −0.198657 0.980069i \(-0.563658\pi\)
−0.198657 + 0.980069i \(0.563658\pi\)
\(480\) 3.39818e44 1.95329
\(481\) −2.99073e44 −1.66105
\(482\) 6.11389e44 3.28127
\(483\) 2.35586e44 1.22186
\(484\) 3.53666e44 1.77274
\(485\) 7.39651e43 0.358334
\(486\) −2.51108e44 −1.17588
\(487\) −1.75263e44 −0.793345 −0.396673 0.917960i \(-0.629835\pi\)
−0.396673 + 0.917960i \(0.629835\pi\)
\(488\) −3.22299e44 −1.41036
\(489\) 1.67035e44 0.706659
\(490\) −3.21311e43 −0.131429
\(491\) 3.92240e44 1.55134 0.775670 0.631139i \(-0.217412\pi\)
0.775670 + 0.631139i \(0.217412\pi\)
\(492\) −1.27089e44 −0.486053
\(493\) 2.27118e44 0.839998
\(494\) −6.46876e44 −2.31380
\(495\) 5.23772e43 0.181199
\(496\) −3.77608e44 −1.26355
\(497\) 2.30243e44 0.745257
\(498\) 1.96878e44 0.616473
\(499\) 7.64433e43 0.231569 0.115785 0.993274i \(-0.463062\pi\)
0.115785 + 0.993274i \(0.463062\pi\)
\(500\) 8.31403e43 0.243672
\(501\) 2.45563e44 0.696370
\(502\) 4.51307e44 1.23840
\(503\) −4.88916e44 −1.29826 −0.649132 0.760676i \(-0.724868\pi\)
−0.649132 + 0.760676i \(0.724868\pi\)
\(504\) −3.75997e44 −0.966230
\(505\) 3.83191e43 0.0953033
\(506\) −1.19183e45 −2.86901
\(507\) 8.23225e43 0.191817
\(508\) −5.26132e43 −0.118671
\(509\) −3.35020e44 −0.731522 −0.365761 0.930709i \(-0.619191\pi\)
−0.365761 + 0.930709i \(0.619191\pi\)
\(510\) −3.55150e44 −0.750764
\(511\) 2.16186e44 0.442469
\(512\) 8.96657e44 1.77694
\(513\) −4.54089e44 −0.871374
\(514\) 7.48560e44 1.39103
\(515\) −3.96979e44 −0.714412
\(516\) −5.28886e44 −0.921812
\(517\) 2.03046e44 0.342768
\(518\) −1.67068e45 −2.73182
\(519\) 1.37763e45 2.18208
\(520\) −1.04785e45 −1.60785
\(521\) −5.22367e44 −0.776521 −0.388261 0.921550i \(-0.626924\pi\)
−0.388261 + 0.921550i \(0.626924\pi\)
\(522\) −4.67985e44 −0.674014
\(523\) −1.10438e45 −1.54113 −0.770566 0.637360i \(-0.780026\pi\)
−0.770566 + 0.637360i \(0.780026\pi\)
\(524\) 1.68308e45 2.27583
\(525\) −1.61178e44 −0.211192
\(526\) 2.06868e45 2.62680
\(527\) 2.10610e44 0.259182
\(528\) 4.56822e45 5.44863
\(529\) 2.93144e44 0.338893
\(530\) 1.41996e45 1.59120
\(531\) −1.08299e44 −0.117643
\(532\) −2.64332e45 −2.78360
\(533\) 1.64619e44 0.168067
\(534\) −2.39978e45 −2.37542
\(535\) 5.71408e44 0.548414
\(536\) −7.61634e44 −0.708806
\(537\) 7.75305e41 0.000699676 0
\(538\) −1.29137e45 −1.13017
\(539\) −2.30515e44 −0.195652
\(540\) −1.16214e45 −0.956667
\(541\) −1.40716e45 −1.12354 −0.561772 0.827292i \(-0.689880\pi\)
−0.561772 + 0.827292i \(0.689880\pi\)
\(542\) 4.09244e45 3.16953
\(543\) 1.62234e44 0.121883
\(544\) −3.96326e45 −2.88849
\(545\) −4.22260e44 −0.298564
\(546\) 3.20947e45 2.20168
\(547\) −1.00599e45 −0.669579 −0.334789 0.942293i \(-0.608665\pi\)
−0.334789 + 0.942293i \(0.608665\pi\)
\(548\) 6.00578e45 3.87874
\(549\) −2.13272e44 −0.133657
\(550\) 8.15405e44 0.495894
\(551\) −2.08237e45 −1.22901
\(552\) −7.70971e45 −4.41614
\(553\) 6.35205e44 0.353142
\(554\) 4.78498e45 2.58207
\(555\) 1.50548e45 0.788568
\(556\) 1.82792e45 0.929442
\(557\) 6.35386e44 0.313637 0.156818 0.987627i \(-0.449876\pi\)
0.156818 + 0.987627i \(0.449876\pi\)
\(558\) −4.33969e44 −0.207967
\(559\) 6.85070e44 0.318743
\(560\) −3.37034e45 −1.52255
\(561\) −2.54792e45 −1.11763
\(562\) −4.50340e45 −1.91819
\(563\) −1.73714e45 −0.718534 −0.359267 0.933235i \(-0.616973\pi\)
−0.359267 + 0.933235i \(0.616973\pi\)
\(564\) 2.07518e45 0.833584
\(565\) 1.92729e45 0.751878
\(566\) 7.47384e45 2.83187
\(567\) 3.04191e45 1.11951
\(568\) −7.53487e45 −2.69357
\(569\) 3.27076e45 1.13579 0.567894 0.823102i \(-0.307759\pi\)
0.567894 + 0.823102i \(0.307759\pi\)
\(570\) 3.25625e45 1.09845
\(571\) 2.07979e45 0.681591 0.340795 0.940137i \(-0.389304\pi\)
0.340795 + 0.940137i \(0.389304\pi\)
\(572\) −1.18771e46 −3.78162
\(573\) −5.88585e45 −1.82078
\(574\) 9.19595e44 0.276408
\(575\) −7.92360e44 −0.231421
\(576\) 4.05768e45 1.15161
\(577\) −2.30164e45 −0.634800 −0.317400 0.948292i \(-0.602810\pi\)
−0.317400 + 0.948292i \(0.602810\pi\)
\(578\) −3.05796e45 −0.819639
\(579\) 4.36559e45 1.13722
\(580\) −5.32936e45 −1.34931
\(581\) −1.04207e45 −0.256444
\(582\) 7.41395e45 1.77346
\(583\) 1.01871e46 2.36875
\(584\) −7.07484e45 −1.59921
\(585\) −6.93387e44 −0.152372
\(586\) −3.25174e45 −0.694712
\(587\) 1.99372e45 0.414128 0.207064 0.978327i \(-0.433609\pi\)
0.207064 + 0.978327i \(0.433609\pi\)
\(588\) −2.35592e45 −0.475810
\(589\) −1.93101e45 −0.379213
\(590\) −1.68599e45 −0.321957
\(591\) −5.15538e45 −0.957341
\(592\) 3.14804e46 5.68503
\(593\) −6.54556e45 −1.14959 −0.574797 0.818296i \(-0.694919\pi\)
−0.574797 + 0.818296i \(0.694919\pi\)
\(594\) −1.13978e46 −1.94690
\(595\) 1.87980e45 0.312307
\(596\) −3.29553e45 −0.532553
\(597\) −1.22006e46 −1.91781
\(598\) 1.57779e46 2.41257
\(599\) 1.89735e45 0.282231 0.141115 0.989993i \(-0.454931\pi\)
0.141115 + 0.989993i \(0.454931\pi\)
\(600\) 5.27468e45 0.763309
\(601\) −8.66013e45 −1.21926 −0.609629 0.792687i \(-0.708681\pi\)
−0.609629 + 0.792687i \(0.708681\pi\)
\(602\) 3.82693e45 0.524214
\(603\) −5.03991e44 −0.0671718
\(604\) 1.04427e46 1.35426
\(605\) 2.30601e45 0.291003
\(606\) 3.84095e45 0.471672
\(607\) 8.81789e45 1.05378 0.526892 0.849932i \(-0.323357\pi\)
0.526892 + 0.849932i \(0.323357\pi\)
\(608\) 3.63378e46 4.22619
\(609\) 1.03317e46 1.16946
\(610\) −3.32021e45 −0.365783
\(611\) −2.68799e45 −0.288236
\(612\) −6.24322e45 −0.651643
\(613\) −1.91712e46 −1.94783 −0.973915 0.226912i \(-0.927137\pi\)
−0.973915 + 0.226912i \(0.927137\pi\)
\(614\) −1.87231e45 −0.185182
\(615\) −8.28661e44 −0.0797879
\(616\) −4.19942e46 −3.93648
\(617\) −1.53369e46 −1.39969 −0.699844 0.714295i \(-0.746747\pi\)
−0.699844 + 0.714295i \(0.746747\pi\)
\(618\) −3.97915e46 −3.53574
\(619\) 8.04204e45 0.695778 0.347889 0.937536i \(-0.386899\pi\)
0.347889 + 0.937536i \(0.386899\pi\)
\(620\) −4.94199e45 −0.416331
\(621\) 1.10756e46 0.908568
\(622\) 1.82071e46 1.45446
\(623\) 1.27020e46 0.988142
\(624\) −6.04757e46 −4.58179
\(625\) 5.42101e44 0.0400000
\(626\) −3.80203e46 −2.73237
\(627\) 2.33610e46 1.63522
\(628\) 1.78105e46 1.21434
\(629\) −1.75582e46 −1.16612
\(630\) −3.87339e45 −0.250595
\(631\) 2.52921e46 1.59405 0.797023 0.603949i \(-0.206407\pi\)
0.797023 + 0.603949i \(0.206407\pi\)
\(632\) −2.07875e46 −1.27635
\(633\) 2.80145e46 1.67580
\(634\) 9.17540e45 0.534752
\(635\) −3.43055e44 −0.0194804
\(636\) 1.04114e47 5.76061
\(637\) 3.05163e45 0.164525
\(638\) −5.22682e46 −2.74597
\(639\) −4.98599e45 −0.255263
\(640\) 2.90337e46 1.44855
\(641\) 2.51177e46 1.22130 0.610651 0.791900i \(-0.290908\pi\)
0.610651 + 0.791900i \(0.290908\pi\)
\(642\) 5.72755e46 2.71419
\(643\) −1.47547e46 −0.681473 −0.340736 0.940159i \(-0.610676\pi\)
−0.340736 + 0.940159i \(0.610676\pi\)
\(644\) 6.44728e46 2.90242
\(645\) −3.44851e45 −0.151320
\(646\) −3.79772e46 −1.62437
\(647\) −4.64548e46 −1.93691 −0.968457 0.249182i \(-0.919838\pi\)
−0.968457 + 0.249182i \(0.919838\pi\)
\(648\) −9.95488e46 −4.04621
\(649\) −1.20957e46 −0.479283
\(650\) −1.07946e46 −0.417000
\(651\) 9.58069e45 0.360837
\(652\) 4.57124e46 1.67861
\(653\) 3.12135e46 1.11757 0.558786 0.829312i \(-0.311267\pi\)
0.558786 + 0.829312i \(0.311267\pi\)
\(654\) −4.23255e46 −1.47764
\(655\) 1.09742e46 0.373588
\(656\) −1.73278e46 −0.575215
\(657\) −4.68158e45 −0.151553
\(658\) −1.50156e46 −0.474041
\(659\) 1.16512e46 0.358724 0.179362 0.983783i \(-0.442597\pi\)
0.179362 + 0.983783i \(0.442597\pi\)
\(660\) 5.97872e46 1.79528
\(661\) −1.14126e46 −0.334241 −0.167121 0.985936i \(-0.553447\pi\)
−0.167121 + 0.985936i \(0.553447\pi\)
\(662\) −8.42699e46 −2.40722
\(663\) 3.37302e46 0.939822
\(664\) 3.41026e46 0.926861
\(665\) −1.72353e46 −0.456942
\(666\) 3.61792e46 0.935694
\(667\) 5.07909e46 1.28147
\(668\) 6.72033e46 1.65417
\(669\) −2.75628e46 −0.661901
\(670\) −7.84609e45 −0.183831
\(671\) −2.38199e46 −0.544525
\(672\) −1.80289e47 −4.02140
\(673\) 4.26138e45 0.0927475 0.0463737 0.998924i \(-0.485233\pi\)
0.0463737 + 0.998924i \(0.485233\pi\)
\(674\) 1.54268e46 0.327633
\(675\) −7.57751e45 −0.157041
\(676\) 2.25292e46 0.455644
\(677\) −6.45770e46 −1.27457 −0.637287 0.770627i \(-0.719943\pi\)
−0.637287 + 0.770627i \(0.719943\pi\)
\(678\) 1.93183e47 3.72117
\(679\) −3.92419e46 −0.737732
\(680\) −6.15179e46 −1.12877
\(681\) −5.14780e46 −0.921923
\(682\) −4.84690e46 −0.847270
\(683\) 3.35691e46 0.572794 0.286397 0.958111i \(-0.407542\pi\)
0.286397 + 0.958111i \(0.407542\pi\)
\(684\) 5.72419e46 0.953430
\(685\) 3.91596e46 0.636713
\(686\) 1.28990e47 2.04743
\(687\) −3.17324e46 −0.491719
\(688\) −7.21105e46 −1.09091
\(689\) −1.34860e47 −1.99190
\(690\) −7.94228e46 −1.14534
\(691\) −4.55000e46 −0.640654 −0.320327 0.947307i \(-0.603793\pi\)
−0.320327 + 0.947307i \(0.603793\pi\)
\(692\) 3.77017e47 5.18334
\(693\) −2.77885e46 −0.373050
\(694\) 4.97238e46 0.651828
\(695\) 1.19186e46 0.152572
\(696\) −3.38111e47 −4.22676
\(697\) 9.66456e45 0.117989
\(698\) −2.01956e47 −2.40792
\(699\) −3.25978e46 −0.379590
\(700\) −4.41098e46 −0.501669
\(701\) −1.37611e47 −1.52864 −0.764320 0.644837i \(-0.776925\pi\)
−0.764320 + 0.644837i \(0.776925\pi\)
\(702\) 1.50888e47 1.63716
\(703\) 1.60985e47 1.70617
\(704\) 4.53193e47 4.69174
\(705\) 1.35308e46 0.136837
\(706\) 3.13885e47 3.10094
\(707\) −2.03301e46 −0.196209
\(708\) −1.23620e47 −1.16558
\(709\) −1.72099e47 −1.58531 −0.792656 0.609670i \(-0.791302\pi\)
−0.792656 + 0.609670i \(0.791302\pi\)
\(710\) −7.76216e46 −0.698586
\(711\) −1.37556e46 −0.120957
\(712\) −4.15682e47 −3.57143
\(713\) 4.70991e46 0.395399
\(714\) 1.88423e47 1.54566
\(715\) −7.74428e46 −0.620771
\(716\) 2.12178e44 0.00166202
\(717\) 7.28855e46 0.557924
\(718\) −4.34619e47 −3.25128
\(719\) 1.00489e47 0.734667 0.367334 0.930089i \(-0.380271\pi\)
0.367334 + 0.930089i \(0.380271\pi\)
\(720\) 7.29859e46 0.521498
\(721\) 2.10616e47 1.47082
\(722\) 6.54591e46 0.446793
\(723\) 2.92295e47 1.95002
\(724\) 4.43987e46 0.289524
\(725\) −3.47491e46 −0.221497
\(726\) 2.31145e47 1.44022
\(727\) 1.79204e47 1.09151 0.545757 0.837944i \(-0.316242\pi\)
0.545757 + 0.837944i \(0.316242\pi\)
\(728\) 5.55934e47 3.31021
\(729\) 8.88336e46 0.517098
\(730\) −7.28826e46 −0.414760
\(731\) 4.02195e46 0.223769
\(732\) −2.43445e47 −1.32424
\(733\) 1.91032e46 0.101599 0.0507996 0.998709i \(-0.483823\pi\)
0.0507996 + 0.998709i \(0.483823\pi\)
\(734\) −4.24816e47 −2.20910
\(735\) −1.53613e46 −0.0781065
\(736\) −8.86310e47 −4.40658
\(737\) −5.62895e46 −0.273662
\(738\) −1.99141e46 −0.0946742
\(739\) 2.81727e47 1.30977 0.654886 0.755728i \(-0.272717\pi\)
0.654886 + 0.755728i \(0.272717\pi\)
\(740\) 4.12004e47 1.87318
\(741\) −3.09261e47 −1.37507
\(742\) −7.53355e47 −3.27593
\(743\) −5.77441e46 −0.245580 −0.122790 0.992433i \(-0.539184\pi\)
−0.122790 + 0.992433i \(0.539184\pi\)
\(744\) −3.13535e47 −1.30417
\(745\) −2.14879e46 −0.0874211
\(746\) 2.83995e47 1.13011
\(747\) 2.25665e46 0.0878363
\(748\) −6.97290e47 −2.65483
\(749\) −3.03158e47 −1.12907
\(750\) 5.43379e46 0.197967
\(751\) 2.71539e47 0.967772 0.483886 0.875131i \(-0.339225\pi\)
0.483886 + 0.875131i \(0.339225\pi\)
\(752\) 2.82938e47 0.986498
\(753\) 2.15762e47 0.735968
\(754\) 6.91944e47 2.30910
\(755\) 6.80896e46 0.222308
\(756\) 6.16568e47 1.96957
\(757\) 2.34370e47 0.732521 0.366260 0.930512i \(-0.380638\pi\)
0.366260 + 0.930512i \(0.380638\pi\)
\(758\) −4.90141e47 −1.49892
\(759\) −5.69796e47 −1.70502
\(760\) 5.64036e47 1.65152
\(761\) −3.85769e47 −1.10530 −0.552651 0.833413i \(-0.686384\pi\)
−0.552651 + 0.833413i \(0.686384\pi\)
\(762\) −3.43863e46 −0.0964115
\(763\) 2.24028e47 0.614679
\(764\) −1.61079e48 −4.32511
\(765\) −4.07078e46 −0.106970
\(766\) 6.39028e47 1.64341
\(767\) 1.60126e47 0.403032
\(768\) 1.21008e48 2.98094
\(769\) 5.88677e47 1.41936 0.709679 0.704525i \(-0.248840\pi\)
0.709679 + 0.704525i \(0.248840\pi\)
\(770\) −4.32610e47 −1.02094
\(771\) 3.57874e47 0.826671
\(772\) 1.19473e48 2.70138
\(773\) −4.68346e47 −1.03659 −0.518293 0.855203i \(-0.673432\pi\)
−0.518293 + 0.855203i \(0.673432\pi\)
\(774\) −8.28736e46 −0.179552
\(775\) −3.22234e46 −0.0683428
\(776\) 1.28422e48 2.66637
\(777\) −7.98724e47 −1.62349
\(778\) −4.01113e47 −0.798185
\(779\) −8.86111e46 −0.172631
\(780\) −7.91483e47 −1.50967
\(781\) −5.56874e47 −1.03996
\(782\) 9.26297e47 1.69371
\(783\) 4.85725e47 0.869604
\(784\) −3.21215e47 −0.563094
\(785\) 1.16130e47 0.199341
\(786\) 1.10001e48 1.84895
\(787\) −3.57150e47 −0.587851 −0.293926 0.955828i \(-0.594962\pi\)
−0.293926 + 0.955828i \(0.594962\pi\)
\(788\) −1.41087e48 −2.27408
\(789\) 9.88999e47 1.56108
\(790\) −2.14146e47 −0.331027
\(791\) −1.02252e48 −1.54795
\(792\) 9.09400e47 1.34831
\(793\) 3.15336e47 0.457895
\(794\) −1.55551e47 −0.221225
\(795\) 6.78859e47 0.945632
\(796\) −3.33895e48 −4.55558
\(797\) −3.36343e47 −0.449490 −0.224745 0.974418i \(-0.572155\pi\)
−0.224745 + 0.974418i \(0.572155\pi\)
\(798\) −1.72759e48 −2.26148
\(799\) −1.57808e47 −0.202352
\(800\) 6.06378e47 0.761656
\(801\) −2.75066e47 −0.338455
\(802\) 3.21219e46 0.0387190
\(803\) −5.22875e47 −0.617435
\(804\) −5.75292e47 −0.665523
\(805\) 4.20383e47 0.476446
\(806\) 6.41649e47 0.712474
\(807\) −6.17383e47 −0.671647
\(808\) 6.65316e47 0.709154
\(809\) 8.08353e47 0.844210 0.422105 0.906547i \(-0.361291\pi\)
0.422105 + 0.906547i \(0.361291\pi\)
\(810\) −1.02552e48 −1.04940
\(811\) −1.18729e48 −1.19045 −0.595225 0.803559i \(-0.702937\pi\)
−0.595225 + 0.803559i \(0.702937\pi\)
\(812\) 2.82747e48 2.77795
\(813\) 1.95653e48 1.88362
\(814\) 4.04077e48 3.81207
\(815\) 2.98060e47 0.275551
\(816\) −3.55044e48 −3.21658
\(817\) −3.68759e47 −0.327400
\(818\) 3.09244e48 2.69074
\(819\) 3.67874e47 0.313700
\(820\) −2.26780e47 −0.189529
\(821\) −1.55006e48 −1.26966 −0.634829 0.772653i \(-0.718929\pi\)
−0.634829 + 0.772653i \(0.718929\pi\)
\(822\) 3.92519e48 3.15120
\(823\) 2.91534e47 0.229399 0.114700 0.993400i \(-0.463409\pi\)
0.114700 + 0.993400i \(0.463409\pi\)
\(824\) −6.89256e48 −5.31596
\(825\) 3.89832e47 0.294705
\(826\) 8.94497e47 0.662839
\(827\) −1.33839e48 −0.972166 −0.486083 0.873913i \(-0.661575\pi\)
−0.486083 + 0.873913i \(0.661575\pi\)
\(828\) −1.39618e48 −0.994126
\(829\) −2.06685e47 −0.144264 −0.0721321 0.997395i \(-0.522980\pi\)
−0.0721321 + 0.997395i \(0.522980\pi\)
\(830\) 3.51314e47 0.240385
\(831\) 2.28762e48 1.53450
\(832\) −5.99952e48 −3.94531
\(833\) 1.79157e47 0.115502
\(834\) 1.19467e48 0.755106
\(835\) 4.38187e47 0.271539
\(836\) 6.39322e48 3.88433
\(837\) 4.50419e47 0.268316
\(838\) −5.49865e48 −3.21166
\(839\) −1.80225e48 −1.03215 −0.516075 0.856544i \(-0.672607\pi\)
−0.516075 + 0.856544i \(0.672607\pi\)
\(840\) −2.79846e48 −1.57149
\(841\) 4.11374e47 0.226518
\(842\) −2.61661e48 −1.41283
\(843\) −2.15300e48 −1.13996
\(844\) 7.66674e48 3.98071
\(845\) 1.46898e47 0.0747962
\(846\) 3.25169e47 0.162367
\(847\) −1.22345e48 −0.599113
\(848\) 1.41954e49 6.81735
\(849\) 3.57312e48 1.68295
\(850\) −6.33736e47 −0.292749
\(851\) −3.92656e48 −1.77900
\(852\) −5.69138e48 −2.52909
\(853\) −3.50343e48 −1.52699 −0.763493 0.645816i \(-0.776517\pi\)
−0.763493 + 0.645816i \(0.776517\pi\)
\(854\) 1.76153e48 0.753068
\(855\) 3.73236e47 0.156510
\(856\) 9.92107e48 4.08076
\(857\) 4.03540e48 1.62818 0.814091 0.580737i \(-0.197236\pi\)
0.814091 + 0.580737i \(0.197236\pi\)
\(858\) −7.76254e48 −3.07230
\(859\) −4.93399e46 −0.0191563 −0.00957813 0.999954i \(-0.503049\pi\)
−0.00957813 + 0.999954i \(0.503049\pi\)
\(860\) −9.43755e47 −0.359447
\(861\) 4.39643e47 0.164266
\(862\) 5.80102e48 2.12635
\(863\) −5.86818e47 −0.211021 −0.105510 0.994418i \(-0.533648\pi\)
−0.105510 + 0.994418i \(0.533648\pi\)
\(864\) −8.47598e48 −2.99029
\(865\) 2.45827e48 0.850871
\(866\) −4.68294e47 −0.159028
\(867\) −1.46196e48 −0.487103
\(868\) 2.62195e48 0.857136
\(869\) −1.53633e48 −0.492786
\(870\) −3.48311e48 −1.09622
\(871\) 7.45180e47 0.230124
\(872\) −7.33149e48 −2.22162
\(873\) 8.49797e47 0.252686
\(874\) −8.49291e48 −2.47809
\(875\) −2.87610e47 −0.0823513
\(876\) −5.34390e48 −1.50155
\(877\) −5.15342e48 −1.42103 −0.710514 0.703683i \(-0.751537\pi\)
−0.710514 + 0.703683i \(0.751537\pi\)
\(878\) −1.14418e49 −3.09623
\(879\) −1.55460e48 −0.412860
\(880\) 8.15163e48 2.12461
\(881\) 7.21570e48 1.84576 0.922882 0.385084i \(-0.125827\pi\)
0.922882 + 0.385084i \(0.125827\pi\)
\(882\) −3.69159e47 −0.0926791
\(883\) 7.21502e48 1.77781 0.888906 0.458089i \(-0.151466\pi\)
0.888906 + 0.458089i \(0.151466\pi\)
\(884\) 9.23096e48 2.23246
\(885\) −8.06045e47 −0.191335
\(886\) 2.33095e48 0.543097
\(887\) −2.04483e48 −0.467647 −0.233824 0.972279i \(-0.575124\pi\)
−0.233824 + 0.972279i \(0.575124\pi\)
\(888\) 2.61388e49 5.86776
\(889\) 1.82006e47 0.0401058
\(890\) −4.28222e48 −0.926261
\(891\) −7.35728e48 −1.56220
\(892\) −7.54314e48 −1.57229
\(893\) 1.44689e48 0.296064
\(894\) −2.15386e48 −0.432661
\(895\) 1.38347e45 0.000272828 0
\(896\) −1.54037e49 −2.98224
\(897\) 7.54315e48 1.43376
\(898\) −1.71077e49 −3.19251
\(899\) 2.06554e48 0.378442
\(900\) 9.55213e47 0.171830
\(901\) −7.91745e48 −1.39838
\(902\) −2.22416e48 −0.385708
\(903\) 1.82959e48 0.311535
\(904\) 3.34626e49 5.59475
\(905\) 2.89494e47 0.0475267
\(906\) 6.82501e48 1.10024
\(907\) 4.33823e48 0.686739 0.343370 0.939200i \(-0.388432\pi\)
0.343370 + 0.939200i \(0.388432\pi\)
\(908\) −1.40880e49 −2.18995
\(909\) 4.40255e47 0.0672048
\(910\) 5.72704e48 0.858513
\(911\) −1.54797e48 −0.227882 −0.113941 0.993488i \(-0.536348\pi\)
−0.113941 + 0.993488i \(0.536348\pi\)
\(912\) 3.25528e49 4.70623
\(913\) 2.52040e48 0.357850
\(914\) −6.77134e47 −0.0944196
\(915\) −1.58734e48 −0.217381
\(916\) −8.68424e48 −1.16804
\(917\) −5.82234e48 −0.769136
\(918\) 8.85839e48 1.14935
\(919\) 4.44681e48 0.566686 0.283343 0.959019i \(-0.408557\pi\)
0.283343 + 0.959019i \(0.408557\pi\)
\(920\) −1.37574e49 −1.72201
\(921\) −8.95118e47 −0.110052
\(922\) 1.25953e49 1.52107
\(923\) 7.37208e48 0.874505
\(924\) −3.17199e49 −3.69610
\(925\) 2.68640e48 0.307491
\(926\) 2.53474e49 2.85005
\(927\) −4.56096e48 −0.503780
\(928\) −3.88694e49 −4.21760
\(929\) 7.81292e48 0.832826 0.416413 0.909176i \(-0.363287\pi\)
0.416413 + 0.909176i \(0.363287\pi\)
\(930\) −3.22993e48 −0.338240
\(931\) −1.64263e48 −0.168994
\(932\) −8.92105e48 −0.901682
\(933\) 8.70453e48 0.864367
\(934\) −3.27813e49 −3.19818
\(935\) −4.54655e48 −0.435804
\(936\) −1.20389e49 −1.13380
\(937\) 1.29441e49 1.19776 0.598880 0.800839i \(-0.295613\pi\)
0.598880 + 0.800839i \(0.295613\pi\)
\(938\) 4.16271e48 0.378469
\(939\) −1.81769e49 −1.62382
\(940\) 3.70298e48 0.325044
\(941\) −5.82381e47 −0.0502318 −0.0251159 0.999685i \(-0.507995\pi\)
−0.0251159 + 0.999685i \(0.507995\pi\)
\(942\) 1.16404e49 0.986569
\(943\) 2.16130e48 0.180000
\(944\) −1.68549e49 −1.37939
\(945\) 4.02022e48 0.323314
\(946\) −9.25596e48 −0.731505
\(947\) 1.87865e49 1.45905 0.729526 0.683953i \(-0.239741\pi\)
0.729526 + 0.683953i \(0.239741\pi\)
\(948\) −1.57016e49 −1.19842
\(949\) 6.92200e48 0.519205
\(950\) 5.81051e48 0.428326
\(951\) 4.38661e48 0.317797
\(952\) 3.26381e49 2.32389
\(953\) 1.71040e49 1.19692 0.598459 0.801154i \(-0.295780\pi\)
0.598459 + 0.801154i \(0.295780\pi\)
\(954\) 1.63142e49 1.12206
\(955\) −1.05028e49 −0.709988
\(956\) 1.99466e49 1.32530
\(957\) −2.49885e49 −1.63190
\(958\) −1.19451e49 −0.766759
\(959\) −2.07760e49 −1.31085
\(960\) 3.02004e49 1.87300
\(961\) −1.44881e49 −0.883232
\(962\) −5.34930e49 −3.20559
\(963\) 6.56500e48 0.386724
\(964\) 7.99925e49 4.63210
\(965\) 7.79004e48 0.443444
\(966\) 4.21374e49 2.35801
\(967\) −3.31445e49 −1.82337 −0.911683 0.410893i \(-0.865217\pi\)
−0.911683 + 0.410893i \(0.865217\pi\)
\(968\) 4.00382e49 2.16536
\(969\) −1.81562e49 −0.965348
\(970\) 1.32296e49 0.691533
\(971\) −1.48405e49 −0.762662 −0.381331 0.924439i \(-0.624534\pi\)
−0.381331 + 0.924439i \(0.624534\pi\)
\(972\) −3.28542e49 −1.65996
\(973\) −6.32337e48 −0.314113
\(974\) −3.13480e49 −1.53104
\(975\) −5.16072e48 −0.247819
\(976\) −3.31922e49 −1.56716
\(977\) −7.11883e47 −0.0330482 −0.0165241 0.999863i \(-0.505260\pi\)
−0.0165241 + 0.999863i \(0.505260\pi\)
\(978\) 2.98762e49 1.36375
\(979\) −3.07215e49 −1.37889
\(980\) −4.20394e48 −0.185535
\(981\) −4.85141e48 −0.210538
\(982\) 7.01570e49 2.99386
\(983\) 3.13902e49 1.31723 0.658614 0.752481i \(-0.271143\pi\)
0.658614 + 0.752481i \(0.271143\pi\)
\(984\) −1.43876e49 −0.593704
\(985\) −9.19935e48 −0.373301
\(986\) 4.06230e49 1.62107
\(987\) −7.17872e48 −0.281717
\(988\) −8.46356e49 −3.26635
\(989\) 8.99436e48 0.341375
\(990\) 9.36833e48 0.349689
\(991\) 2.53674e49 0.931239 0.465619 0.884985i \(-0.345832\pi\)
0.465619 + 0.884985i \(0.345832\pi\)
\(992\) −3.60441e49 −1.30134
\(993\) −4.02880e49 −1.43058
\(994\) 4.11819e49 1.43824
\(995\) −2.17710e49 −0.747821
\(996\) 2.57590e49 0.870263
\(997\) 4.24313e48 0.140999 0.0704995 0.997512i \(-0.477541\pi\)
0.0704995 + 0.997512i \(0.477541\pi\)
\(998\) 1.36729e49 0.446895
\(999\) −3.75506e49 −1.20722
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.1.6 6
5.2 odd 4 25.34.b.c.24.12 12
5.3 odd 4 25.34.b.c.24.1 12
5.4 even 2 25.34.a.c.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.34.a.b.1.6 6 1.1 even 1 trivial
25.34.a.c.1.1 6 5.4 even 2
25.34.b.c.24.1 12 5.3 odd 4
25.34.b.c.24.12 12 5.2 odd 4